24 − 62

A.-6

B.-12

C.12

**Answer:**

None

**Step-by-step explanation:**

None of the choices are correct

Can someone please solve this problem for me.

The **cost** of one **chair** is [tex]x=54.75[/tex] $ and the cost of **one** table is [tex]y=49.5[/tex] $.

**What is the total cost?**

The **total** cost formula is used to combine the **variable** and fixed costs of providing goods to **determine** a total. The **formula** is:

**Total cost **= (Average fixed cost x average variable cost)

Let **cost **of one chair is [tex]x[/tex]

Let cost of one **table **is [tex]y[/tex]

So,

[tex]5x+3y=31[/tex] ...(1)

[tex]2x+6y=52[/tex] ......(2)

Solving **equation **(1) and (2) we get

[tex]a_1x+b_1y+x_1=0\\\\a_2x+b_2y+c_2=0[/tex]

[tex]\frac{x}{b_1c_2-b_2c_1}=\frac{y}{c_1a_2-c_2a_1}=\frac{1}{a_1b_2-a_2b_1}\\\\\frac{x}{3(31)-6(52)}=\frac{y}{31(2)-52(5)}=\frac{1}{5(2)-2(3)}\\\\\frac{x}{93-312}=\frac{y}{62-260}=\frac{1}{10-6}\\\\\frac{x}{-219}=\frac{y}{-198}=\frac{1}{-4}\\\\x=54.75,y=49.5[/tex]

Hence, the **cost** of one chair is [tex]54.75[/tex] $ and the cost of **one** table is [tex]49.5[/tex] $.

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What is as a fraction?

A fraction means a part of something or a number of parts of something. The number on the bottom shows how many parts something has been divided into ½ means 1 part of something that has been divided into 2 parts. We call this a half. If you add two halves together you get one.

**Answer: A fraction is a numerical quantity that is not a whole number**

**Step-by-step explanation:**

8. Solve the equation 1/4-2x-7/8=x/2 .

9. Dicson pays $610 for 3 DVDs and 2 blue-ray discs. If the price of each blue-ray disc is $10 less than 2 times that of a DVD, find the price of

(a) a DVD,

(b) 3 blue-ray discs.

The value of x in the **algebraic equation** is -1/2 and using** system of linear equation** to solve the problem, the cost of DVD and blue-ray are 84.3 and 178.6 respectively

This is a** mathematical statement** that represent an** algebraic problem**. It often two expression equating with one another.

8)

1/4 [(-2x - 7) / 8] = x / 2

Multiply through by 1/4

(-2x - 7) / 32 = x / 2

Cross multiply both sides

2(2x - 7) = 32x

4x - 14 = 32x

collect like terms

32x - 4x = - 14

28x = -14

x = -14 / 28

x = - 1/2

9)

To solve this problem, we should write a **system of linear equations**;

Let;

x = DVDy = blue - ray3x + 2y = 610 ...eq(i)

y - 10 = 2x ...eq(ii)

From equation (ii)

y = 2x + 10 ...eq(iii)

Put eq(iii) into equ(i)

3x + 2(2x + 10) = 610

3x + 4x + 20 = 610

x = 590/7 = 84.3

Put x = 84.3 into equ(ii)

y - 10 = 2(84.3)

y = 1250 / 7

y = 178.6

The cost of DVD is 84.3 and the cost of blue-ray is 178.6

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NO LINKS!!

The expoential function given by f(x) = e^x called the (a. natural logarithmic, natural exponential, c. 1 to 1 exponential, d. 1 to 1 algebraic, e. transcendental algebraic) function and the base e is called the (a. algebraic, b. 1 to 1, c. natural, d. rational, e. transcendental)

**Answer:**

natural exponential

natural

quizlet

**Answer:**

b. natural exponential

c. natural

**Step-by-step explanation:**

Given function:

[tex]f(x)=e^x[/tex]

The given **exponential function **is called the:

The **base e** is called the:

The number "e" occurs naturally in math and the physical sciences.

It is the **base rate of growth** shared by all continually growing processes, and so is called the **natural base**.

It is an** irrational number** and named after the 18th century Swiss mathematician, Leonhard Euler, and so is often referred to as "Euler's number".

What are the values of u and v?

u = ?°

v = ?°

v=58

u=94

You have to multiple 43 by 2 you would get 86 so now you would have to subtract that from 180 and would get 94

You have to subtract 64 from 180 and you would get 116 so now you would have to divide it by 2 and you would get 58

u=94

You have to multiple 43 by 2 you would get 86 so now you would have to subtract that from 180 and would get 94

You have to subtract 64 from 180 and you would get 116 so now you would have to divide it by 2 and you would get 58

find a polynomial function whose graph passes through (7,11) (11,-12) and (0,4)

The **polynomial **function whose graph **passes **through (7,11) (11,-12) and (0,4) will be y = -0.614x² + 5.295x + 4.

A **function **is an assertion, concept, or principle that establishes an association between **two variables**. Functions may be found throughout **mathematics **and are essential for the development of **significant links**.

Assume the polynomial function is **quadratic**. Then the **equation **is given as,

y = ax² + bx + c

At (0, 4), we have

4 = a(0)² + b(0) + c

c = 4

Then the **equation **is written as,

y = ax² + bx + 4

At (7, 11), we have

y = ax² + bx + 4

11 = 49a + 7b + 4 ...1

At (11, -12), we have

- 12 = 121a + 11b + 4 ...2

Equations 1 and 2 are **solved **by a **calculator**. Then we have

a = - 0.614 and b = 5.295

The **polynomial **capability whose **diagram goes **through (7,11) (11,- 12) and (0,4) will be y = - 0.614x² + 5.295x + 4.

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Use the Divergence Test to determine whether the following series diverges or state that the test is inconclusive. Select the correct answer below and fill in the answer box to complete your choice. O A. According to the Divergence Test, the series converges because lim ak = k- 00 (Simplify your answer.) OB. According to the Divergence Test, the series diverges because lim ax = kos (Simplify your answer.) OC. The Divergence Test is inconclusive because lim ak (Simplify your answer.) OD. The Divergence Test is inconclusive because lim ak does not exist.

The** Divergence Test** is inconclusive because **lim ak = ∞**

The Divergence Test is used to determine whether a given infinite series converges or **diverges.**

In order to use the Divergence Test, we must examine the limit of the terms of the series as **n approaches infinity. **

In the given series, the limit of the terms as n approaches infinity is not defined. Therefore, the Divergence Test is** inconclusive.**

The** Divergence Test **is inconclusive because lim ak = ∞

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Write an equation for the parabola when the x intercepts are (-2,0) and (-4,0)

**Answer:**

[tex]y = x^2 + 6x + 8[/tex]

**Step-by-step explanation:**

⭐**What is the equation of a parabola in ****standard form****?**

⭐**Whenever you factorise a quadratic (parabola), you are writing the parabola in terms of its x-intercepts.**

⭐ **Therefore, the expressions of the x-intercepts are the ****factors**** of your quadratic.**

⭐**What are factors of a number?**

We have to reverse-engineer this problem to find the quadratic by:

**1. Re-write the quadratic in terms of its factors**

If one of the x-intercepts is -2, then the expression for said x-intercept is: [tex](x+2)[/tex]

If one of the x-intercepts is -4, then the expression for said x-intercept is:

[tex](x+4)[/tex]

**2. Multiply the factors**

[tex]y = (x+2)(x+4)[/tex]

[tex]y = x^2 + 4x + 2x + 8[/tex]

**3. Simplify the products**

[tex]y = x^2 + 6x + 8[/tex]

For each of these lists of integers, find a simple formula or rule that generates the terms of an integer sequence that begins with the given list. Assuming that your formula or rule is correct, determine the next three terms of the sequence.

f ) 1, 3, 15, 105, 945, 10395, 135135, 2027025, 34459425, . . .

The simple formula or rule that generates the terms of an integer **sequence** that begins with the given list is given below.

Sequence is the order in which elements, such as numbers, letters, or symbols, follow one another in a specific order. It is a **fundamental concept **in mathematics and computer science, and is used in many other areas including music, language, and art. In mathematics, it is often used to describe patterns or to represent numerical values. In computer science, it is used to represent **data structures**, such as lists and arrays.

a. The sequence can be expressed as 3x2^n, where n is the position of the number in the sequence. The next three terms are 127, 162, and 201.

b. The sequence can be expressed as 4n+3, where n is the position of the number in the sequence. The next three terms are 47, 51, and 55.

c. The sequence can be expressed as 2^n+n-1, where n is the position of the number in the sequence. The next three terms are 1111, 10000, and 10011.

d. The sequence can be expressed as the number of times the previous value is repeated, starting with 1. The next three terms are 5, 5, and 8.

e. The sequence can be expressed as 4x3^n, where n is the position of the number in the sequence. The next three terms are 5906, 17718, and 53154.

f. The sequence can be expressed as (n+1)!+(n-1)!+2, where n is the position of the number in the sequence. The next three terms are 27027025, 94594500, and 34459425.

g. The sequence can be expressed as the number of times the previous number is repeated, starting with 1. The next three terms are 0, 0, and 1.

h. The sequence can be expressed as 4^n, where n is the position of the number in the sequence. The next three terms are 4294967296, 17179869184, and 68719476736.

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Complete questions as follows-

For each of these lists of integers, provide a simple formula or rule that generates the terms of an integer sequence that begins with the given list. Assuming that your formula or rule is correct, determine the next three terms of the sequence.

a. 3, 6, 11, 18, 27, 38, 51, 66, 83, 102, . . .

b. 7, 11, 15, 19, 23, 27, 31, 35, 39, 43, . . .

c. 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011, . . .

d. 1, 2, 2, 2, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, . . .

e. 0, 2, 8, 26, 80,242,728,2186,6560,19682, . . .

f. 1, 3, 15, 105, 945, 10395, 135135, 2027025, 34459425, . . .

g. 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, . . .

h. 2, 4, 16, 256, 65536, 4294967296, . . .

a persons weight varies directly with gravity if a person weights 180 pounds on earth they will weigh only 30 pounds on the moon if harsh weights 54 pounds on earth how much would he weight on the moon

The weight of **harsh** on the moon if he weighs 54 pounds on **earth** is 9 pounds

Weight varies directly with gravity

Let

Weight of a person = w

Gravity = g

So,

w = k × g

Where,

k = **constant** of proportionality

If w = 180 pounds and g = 30 pounds

w = k × g

180 = k × 30

180 = 30k

**divide** both sides by 30

k = 180/30

k = 6

If w = 54 pounds g = ?

w = k × g

54 = 6 × g

54 = 6g

divide both sides by 6

g = 54/6

g = 9 pounds

Therefore, harsh **weighs** 9 pounds on the moon.

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Staci pays $32.70 for 5 cell phone cases. Each case costs the same amount. How much does each case cost?

Part A

Which expression represents the problem?

$32.70 × 5

$32.70 ÷ 5

$32.70 + 5

$32.70 – 5

Part B

Evaluate the expression from Part A.

$ ( ??? )

**Answer:**

$32.70 ÷ 5

Each case is $6.54.

**Step-by-step explanation:**

$3270 for 5 cases, meaning you would split $32.70 into 5.

$32.70 ÷ 5 phone cases = $6.54

This also means each case is $6.54. To prove this, multiply by 5.

Determine the population mean, variance, and standard deviation for the set of data. (Round your answers to two decimal places.)

3, 6, 8, 12, 13, 15

mean variance standard deviation

Given the set of data, we can calculate that the **mean **is 9.5, the **variance **is 17.58 and the **standard deviation** is 4.19

**Mean**, **variance**, and **standard deviation**

The concepts of mean, variance and standard deviation are very basic but very important in **statistics**.

**Mean **is the average of all data in a sample group, which is obtained by adding up all the data values, then dividing by the number of samples.

[tex]mean = \frac{sum all of the data}{size of data}[/tex]

**Variance **is a value that describes the variation of data, by measuring how far each piece of data is spread from the average of a data set.

[tex]variance = \frac{sum (x_{i} - mean)^{2} }{n}[/tex]

**Standard Deviation** is a measure of the spread of observations in a data set relative to their mean. it measures how many observations in a data set differ from the mean and is the square root of the variance.

σ = [tex]\sqrt{variance}[/tex]

Now we can calculate the mean of the given data as follows:

[tex]mean = \frac{sum all of the data}{size of data}[/tex]

= (3 + 6 + 8 + 12 + 13 + 15) / 6

= 57 / 6

= 9.5

Then we can calculate the variance as follows:

[tex]variance = \frac{sum (x_{i} - mean)^{2} }{n}[/tex]

= [tex]\frac{((3-9,5)^{2} + (6-9,5)^{2} + (8-9,5)^{2} + (12-9,5)^{2} + (13-9,5)^{2} + (15-9,5)^{2} )}{6}[/tex]

= (42,25 + 12,25 + 2,25 + 6,25 + 12,25 + 30,25) / 6

= 105.5 / 6

= 17.58

Standard deviation can be calculated from the variance:

σ = [tex]\sqrt{variance}[/tex]

= [tex]\sqrt{17.58}[/tex]

= 4.19

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Here we show that function defined on an interval value property cannot have (a; b) and satisfying the intermediate removable or (a) jump discontinuity. Suppose has & jump discontinuity at Xo € (a,b) and lim f (x) lim f (x) xx0 {ix0 Choose 0 such that lim f (x) < 0 < lim f (x) and 0 + f(xo) xI*o Xx0 In Exercise & we showed there is interval [xo 0,.Xo) such that f(x) < 0 if Xe [xo 6,xo): Likewise, there an interval (xo, Xo + 6] such that f(x) > 0 if xe(xo, Xo + 6]. Conclude that does not satisly the intermediate value property on [xo 6,xXo + 6]. (6) Suppose has a removable discontinuity at Xo € (a,b) and a = lim f(x) < f(xo) Show that there is an interval [xo = 6,Xo) such that f(x)< a+[f(xo) - &] if x e[xo 6,Xo]: Conclude that f does not satisfy the intermediate value property

f cannot have a **jump discontinuity** at [tex]$x_0 \in(a, b)$[/tex] and [tex]$$ \lim _{x \uparrow x_0} f(x) < \lim _{x \mid x_0} f(x) .$$[/tex]

f cannot have a **removable discontinuity** at [tex]$$x_0 \in(a, b) $$[/tex] and [tex]\alpha=\lim _{x \rightarrow x_0} f(x) < f\left(x_0\right)[/tex]

Let f be a function defined on (a, b) satisfies **intermediate value property**.

Claim: f ca not have removable on jump discontinuity.

Suppose f has a jump discontinuity at [tex]$x_0 \in(a, b)$[/tex]

We take [tex]$\theta$[/tex] such that

[tex]$$\lim _{x \rightarrow x_0} f(x) < \theta < \lim _{x \downarrow x_0} f(x) \text { and } \theta \neq f\left(x_0\right)$$[/tex]

Now there exist [tex]$\delta > 0$[/tex] such that [tex]$f(x) < \theta$[/tex] for all [tex]$x \in\left[x_0-\delta, x_0\right)$[/tex] and [tex]$f(x) > \theta$[/tex] for all [tex]$x \in\left(x_0, x_0+\delta\right]$[/tex]

Now [tex]$f\left(x_0-\delta\right)[/tex][tex]< \theta < f\left(x_0+\delta\right)$[/tex] for all [tex]$x \in\left[x_0-\delta, x_0+\delta\right] \backslash\left\{x_2\right\}$[/tex] and [tex]$f\left(x_0\right) \neq \theta$[/tex].

Therefore the point [tex]$\theta$[/tex] has no **preimage **under f

that is, there does not exists [tex]$y \in\left[x_0-\delta, x_0+\delta\right][/tex] for which

[tex]$$f(y)=\theta[/tex] because [tex]\left\{\begin{array}{l}y=x_0 \Rightarrow f(y) \neq \theta \\y > x_0 \Rightarrow f(y) > \theta \\y < x_0 \Rightarrow f(y) < \theta\end{array}\right.$$[/tex]

Therefore f does not satisfies intermediate value property on [tex]$\left[x_0-\delta, x_0+\delta\right]$[/tex],

Hence f does not satisfies **IVP **on (a, b) which is not possible because we assume f satisfies IVP on (a, b),

Therefore f can not have a jump discontinuity.

Suppose f has a **removable** point of discontinuity at [tex]$x_0 \in(a, b)$[/tex],

Let [tex]$\alpha=\lim _{\alpha \rightarrow x_0} f(x)$[/tex],

Let [tex]\alpha < f\left(x_0\right)$[/tex] so [tex]$f\left(x_0\right)-\alpha > 0$[/tex].

Now [tex]$\lim _{x \rightarrow x_0} f(x)=\alpha$[/tex] then [tex]\exists$ \delta > 0$[/tex] such that

[tex]$$\begin{aligned}& |f(x)-\alpha| < \frac{f\left(x_0\right)-\alpha}{2} \text { for all } x \in\left\{x_0-\delta, x_0-\alpha\right]-\left\{x_0\right\} \\& \Rightarrow \quad f(x) < \alpha+\frac{f\left(x_0\right)-\alpha}{2} \text { for all } x \in\left[x_0-\delta, x_0+\delta\right]-\left\{x_0\right\}\end{aligned}$$[/tex]

So [tex]$f(x) < \frac{f\left(x_0\right)+\alpha}{2}$[/tex] for all [tex]$x \in\left[x_0-\delta, x_0\right]-\left\{x_0\right\}$[/tex]

Now [tex]$f\left(x_0\right) > \alpha$[/tex].

And [tex]$f(x) < \frac{f\left(x_0\right)+\alpha}{2} < f\left(x_0\right)$[/tex] for all [tex]$x \in\left[\left(x_0 \delta, x_0\right)\right.$[/tex]

Let [tex]$\mu=\frac{f\left(x_0\right)+\alpha}{2}$[/tex].

Then there does not exist [tex]$e \in\left[x_0-\delta, c\right]$[/tex] such that [tex]$f(c)=\mu$[/tex]

Because for [tex]$e=x_0 \quad f(e) > \mu$[/tex]

for [tex]$c < x_0 \quad f(c) < \mu$[/tex].

Therefore f does not satisfy IVP on [tex]$\left[x_0-\delta_1 x_0\right]$[/tex] which **contradict **our hypothesis,

therefore [tex]$\alpha \geqslant f\left(x_0\right)$[/tex]

Let [tex]$\alpha > f\left(x_0\right)$[/tex]. so [tex]$\alpha-f\left(x_0\right) > 0$[/tex]

[tex]$\lim _{x \rightarrow x_0} f(x)=\alpha$[/tex]

Then [tex]\exists $ \varepsilon > 0$[/tex] such that

[tex]$|f(x)-\alpha| < \frac{\alpha-f\left(x_0\right)}{2}$[/tex] for all [tex]$\left.x \in\left[x_0-\varepsilon_0 x_0+\varepsilon\right]\right\}\left\{x_i\right\}$[/tex]

[tex]$\Rightarrow f(x) > \alpha-\frac{\alpha-f\left(x_0\right)}{2}$[/tex] for all [tex]$x \in\left[x_0-\varepsilon_1, x_0+\varepsilon\right] \backslash\left\{x_0\right\}$[/tex]

[tex]$\Rightarrow f(x) > \frac{\alpha+f\left(x_0\right)}{2}$[/tex] for all [tex]$x \in\left[x_0-\varepsilon_1, x_0\right)$[/tex]

Now [tex]$f\left(x_0\right) < \alpha$[/tex]

The [tex]$f(x) > \frac{f\left(x_0\right)+\alpha}{2} > f\left(x_0\right)$[/tex].

So [tex]$f\left(x_0\right) < \frac{f\left(x_0\right)+\alpha}{2} < f(x)$[/tex] for all [tex]$x \in\left[x_0 \varepsilon, \varepsilon_0\right)$[/tex]

Let [tex]$\eta=\frac{f\left(x_e\right)+\alpha}{2}$[/tex]

Then there does not exist [tex]$d \in\left[x_0-\varepsilon, x_0\right]$[/tex] such that [tex]$f(d)=\xi$[/tex].

Because if [tex]$d=x_0, f(d)=f\left(x_0\right) < \eta$[/tex] if [tex]$d E\left[x_0-\varepsilon, x_0\right)$[/tex]

Then [tex]$f(d) > \eta$[/tex]

Therefore f does not satisfies IVP on [tex]$\left[x_0-\varepsilon, x_0\right]$[/tex] which contradict olio hypothesis.

Therefore [tex]$\alpha \leq f\left(x_0\right)$[/tex] (b) From (a) and (b) it follows [tex]$\alpha=f\left(x_0\right)=\lim _{x \rightarrow x_0} f(x)$[/tex]. Therefore f can not have a removable discontinuous

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Consider the reaction: SO2(g) + 1/2 O2(g)SO3(g) Write the equilibrium constant for this reaction in terms of the equilibrium constants, and , for the reactions below: 2 S(s) + 3 O2(g) 2 SO3(g) S(s) + O2(g) SO2(g) For answers with both a subscript and a superscript, enter the subscript first. For example, enter K12 if the first equilibrium constant should be squared. K =

the **equilibrium constant** for this reaction in terms of the equilibrium constants is Knet = √Ka/Kb

and for the reactions below:

2 S(s) + 3 O2(g) 2 SO3(g) is √Ka

S(s) + O2(g) SO2(g) is 1/Kb

A reversible reaction mechanism progresses from initial conditions to chemical **equilibrium **at a constant temperature, with all reactants and products present in constant non-zero amounts. At this temperature, an **equilibrium constant "K"** exists. It is frequently followed by a subscript to indicate the type of equilibrium constant that it considers depending on the phases of reaction species that it considers. The expression for each type of **equilibrium constant** differs with the direction and stoichiometry of the balanced reaction equation. This enables existing **equations **with known "K" values to be exploited in order to derive new "**K**" values for related systems.

SO2(g) + 1/2 O2(g)SO3 (g) is the desired reaction **equation**

We consider the first given reaction system at the bottom. We divide its coefficients by two to get the square root of the initial **equilibrium constant**: 2 S(s) + 3 O2(g) (g) 2 SO3(g) = √Ka

Then we reverse the second given reaction system at the bottom. Its current **equilibrium constant** is the reciprocal of the predecessor: S(s) + O2(g) SO2(g) is 1/Kb

The above two **equations **total to yield our target equation. The product of the two values obtained above yields the target **equilibrium constant**: Knet = √Ka/Kb

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a) What is 10% of 40 ?

b) What number is 10% more than 40 ?

The **expression **10% of 40 is 4 and 10% **more than **40 is 44

From the question, we have the following parameters that can be used in our computation:

10% of 40

Express "of" as **products**

So, we have

10% of 40 = 10% * 40

Evaluate

10% of 40 = 4

b) What number is 10% more than 40?In this case, we have:

10% more than 40

This means that

10% more than 40 = 40 * (1 + 10%)

Evaluate

10% more than 40 = 44

Hence. 10% **more than **40 is 44

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Suppose that in a certain state, all automobile license plates have three uppercase letters followed by four digits. Use the method illustrated in Example 9.2.2 to answer the following questions. (a) How many different license plates are possible? To answer this question, think of creating a license plate as a 6-step process, where steps 1-3 are to choose the uppercase letters to put in positions 1-3 and the remaining steps are to choose the digits to put in the remaining positions. There are 17576 ways to perform steps 1-3, and there are 10000 ways to perform the remaining steps. Thus, the number of license plates is 175760000 (b) How many license plates could begin with A and end in 0? and the number of ways to place the 0 in the In this case, the number of ways to place the A in Step 1 is 1 final step is 1 . Thus, the answer is 676000 (c) How many license plates could begin with BWC? In this case, the number of ways to perform steps 1-3 is ___ Thus, the answer is ___(d) How many license plates are possible in which all the letters and digits are distinct? (e) How many license plates could begin with AB and have all letters and digits distinct? Enter an exact number

the **total number** of license plate is 17576000 and In this the number ways to place 'A' in step 1 is = '1'1, and the number of steps '0' in final steps id '1' thus the total answer is 67600

In mathematics, there are two alternative methods for dividing up a **collection **of items into subsets: combinations and permutations. Any order may be used by a combination to list the subset's elements. An ordered list of a subset's components is called a **permutation**.

There are [tex]26^3[/tex] = 17576, ways to perform step 1-3, and there are [tex]10^3[/tex] = 1000, ways to perform remaining steps .

the total number of license plate is 17576000

In this the number ways to place 'A' in step 1 is = '1'1, and the number of steps '0' in final steps id '1'

thus the total answer is 67600

26 X 25 X 24 X 10 X 9 X 8 = 11232000

24 X 10 X 9 X 8 = 17280

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The two-way frequency table contains data about students' preferred exercise.

Enjoys swimming Enjoys cycling Row totals

Likes running 28 62 90

Does not like running 46 64 110

Column totals 74 126 200

What is the joint relative frequency of students who do not like to run but enjoy cycling?

64%

55%

32%

23%

The** joint relative frequency** for those **students **who don't like to run, but however enjoy cycling, is C. 32%.

The **joint frequency **for **students **who like cycling, but do not like running, can be found by the formula :

= Number of students who enjoy cycling but don't enjoy running / Number of students in total

Number of students who enjoy **cycling **but don't enjoy **running **= 64

Number of students in total = 200

The joint frequency is :

= 64 / 200 x 100%

= 0.32 x 100 %

= 32 %

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Mr. Muehlenweg S class used 1 3/4 cups baking soda for an experiment. If his students performed the experiment 6 1/2 times, how much baking soda did they use?

Total no. of cups of baking soda used for the experiment in **improper fraction** is [tex]\frac{91}{8}[/tex].

Initial no. of cups of baking soda used for an experiment = [tex]1\frac{3}{4}[/tex]

Converting **mixed fraction** to improper fraction,

[tex]1\frac{3}{4}=\frac{7}{4}[/tex]

No. of times the experiment performed by students = [tex]6\frac{1}{2}[/tex]

Converting mixed fraction to **improper fraction**,

[tex]6\frac{1}{2} = \frac{13}{2}[/tex]

Total no. of cups of baking soda =(Initial no. of cups)* (No. of times)

[tex]=\frac{7}{4} *\frac{13}{2} \\\\=\frac{91}{8} \\\\[/tex]

= 11.4 (decimal form)

What is a mixed fraction?A mixed fraction is one that has both its quotient and remainder represented. A mixed fraction like [tex]1\frac{3}{4}[/tex] is one where the remainder is 3 and the quotient is 1. Therefore, a mixed fraction is made up of both a full number and a correct fraction. A whole number and a legal fraction are both expressed together as a mixed number.A number between any two whole numbers is typically represented by it. Any fraction whose numerator exceeds or is equal to its denominator is considered improper. When the numerator value is less than the denominator, the fraction is said to be proper.To learn more about** improper fraction**, refer:

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a duck flew at 18 miles per hour for 3 hours than at 15 miles per hour for 2 ours how far did the duck fly in all

The **distance **the duck **fly **in all is 99 miles

From the question, we have the following parameters that can be used in our computation:

Distance 1: 18The distance **covered** in all can be calculated as

Distance = The sum of the product of **speed **and time

Substitute the known values in the above equation, so, we have the following representation

Distance = 18 * 3 + 15 * 2

Evaluate the products

This gives

Distance = 54 + 45

Evaluate the sum

Distance = 99 miles

Hence, the **distance** is 99 miles

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Based on the figure given below.

AC = 20cm

BC = 24Cm

AB = 16cm

CD = 15Cm and CE = 18cm then

a) Show that triangle ABC sim triangle DEC

b) How long is DC ?

**Answer:**

**Step-by-step explanation:**

A.) To show that triangle ABC is similar to triangle DEC, we need to prove that the ratios of the sides of the two triangles are equal.

First, we can write the ratios of the sides of triangle ABC as follows:

AC/AB = 20/16 = 5/4

BC/AB = 24/16 = 3/2

Now, we can write the ratios of the sides of triangle DEC as follows:

CE/CD = 18/15 = 6/5

AC/CD = 20/15 = 4/3

Since the ratios of the sides of the two triangles are equal, it follows that triangle ABC is similar to triangle DEC.

B.) To find the length of DC, we can use the fact that triangle ABC is similar to triangle DEC. Since the ratios of the sides of the two triangles are equal, we can set up a proportion to solve for DC.

First, we can write the ratio of the sides of triangle ABC as follows:

AC/AB = DC/CE

Then, we can substitute the known values for AC, AB, and CE:

20/16 = DC/18

Then, we can cross-multiply to solve for DC:

DC = (20/16) * 18

= (5/4) * 18

= 45/4

= 11.25 cm

Therefore, the length of DC is approximately 11.25 cm.

**Answer:**

**Step-by-step explanation:**

To show that triangle ABC is analogous to triangle DEC, we need to prove that the rates of the sides of the two triangles are equal.

First, we can write the rates of the sides of triangle ABC as follows

AC/ AB = 20/16 = 5/4

BC/ AB = 24/16 = 3/2

Now, we can write the rates of the sides of triangle DEC as follows

CE/ CD = 18/15 = 6/5

AC/ CD = 20/15 = 4/3

Since the rates of the sides of the two triangles are equal, it follows that triangle ABC is analogous to triangleDEC.

B.) To find the length of DC, we can use the fact that triangle ABC is analogous to triangle DEC. Since the rates of the sides of the two triangles are equal, we can set up a proportion to break for DC.

First, we can write the rate of the sides of triangle ABC as follows

AC/ AB = DC/ CE

also, we can substitute the known values for AC, AB, and CE

20/16 = DC/ 18

also, we cancross-multiply to break for DC

DC = (20/16) * 18

= (5/4) * 18

= 45/4

= 11.25 cm

Thus, the length of DC is roughly11.25 cm.

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Find f. (Use C for the constant of the first antiderivative and D for the constant of the second antiderivative.)

f ''(x) = 2x + 4ex

After **integration**, the required **function** f is **(2x³ - sin (x) + Cx + D)**.

**What is the integration of 'xⁿ' and 'sin (x)'?**

[tex]\int {x^{n} } \, dx = \frac{x^{n+1} }{n+1} + C\\\\\\\int {sinx} \, dx = -cosx + C[/tex]

Given, f''(x) = 12x + sin x

Therefore,

[tex]\int {f''(x)} \, dx \\\\=\int {f'(x)} \, dx \\\\\\= \int{12x + sin x} \, dx + C\\\\= 6x^{2} - cosx + C\\[/tex]

Again, f'(x) = 6x - cos (x) + C

Therefore,

[tex]\int {f'(x)} \, dx\\ \\=\int {f(x)} \, dx \\\\= \int {6x^{2} - cosx + C } \, dx \\\\= 2x^{3} - sinx + Cx + D[/tex]

Therefore, the required **function** is **(2x³ - sin (x) + Cx + D)**.

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Suppose that there are two types of tickets to a show: advance and same-day. Advance tickets cost $30 and same-day tickets cost $35. For one performance, there were 55 tickets sold in all, and the total amount paid for them was $1825. How many tickets of each type were sold?

**Answer:**

sorry i messed up my first calculations, currently recalculating

**Step-by-step explanation:**

**Answer:**

**Step-by-step explanation:**

You want the **number of $30 advance tickets** and **$35 same-day tickets **sold, when a total of **55 tickets** were sold for **$1825**.

Let s represent the number of same-day tickets sold. Then 55-s is the number of advance tickets sold, and total revenue is ...

35s +30(55 -s) = 1825

Solution5s = 175 . . . . . . Simplify, subtract 1650

s = 35

55-s = 30

**35 same-day and 30 advance tickets were sold**.

Tom weighs 5kg more than Harry. Harry weighs 3kg more than Freddie who, in turn weighs

2 kg less than Alfie. What is the difference, in kilograms, between Tom and Alfie?

** **The difference between Tom and Alfie is** 1 kg**

Let's call the weight of **Tom T**, the weight of** Harry H**, the weight of** Freddie F, **and the weight of** Alfie A**. We are given that **T = H + 5, H = F + 3,** and **F = A - 2.**

Substituting the second and third equations into the first equation gives us:

T = (A - 2) + 3 + 5

T = A - 2 + 3 + 5

T = A + 1

So the** difference **between Tom and Alfie is T - A = A + 1 - A** = 1 kg.**

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At a movie theater, one group of people spent $54 on 3 large popcorns and 6 sodas.

Another group spent on $77 on 4 large popcorns and 9 sodas. Determine the cost of a

large popcorn and the cost of a soda

**Answer: 54**

**Step-by-step explanation: bc ? you just divid 54 by 3 and 6 then you divid 77 by 4 and 9 then divide them both tada**

**Answer:**

sodas cost $5 and a large popcorn costs $8

create formulas out of the situations making the variable p=popcorn and s=soda

so,

3p + 6s = 54

and

4p + 9s = 77

then choose one variable to solve for

3p = 54 - 6s

divide both sides by 3

p = 18 - 2s

then plug your answer for p into the other equation:

4(**1****8**** ****-**** ****2****s**) + 9s = 77

finally, solve for s

72 - 8s + 9s = 77

s = 5

if s=5 then

3p + 6(**5**) = 54

p = 8

on their next training run, pepe averaged a speed of 2/3 of a mile in 5 minutes, while paula averaged 1/4 of a mile in 2 minutes. if pepe and paula each ran at their individual pace for 60 minutes, how many total miles did they cumulatively run?

Answer:

15.5

Step-by-step explanation:

Pepe= 2/3 x 12 = 8

Paula= 1/4 x 30 = 7.5

8+7.5=15.5

The owner of the Good Deals Store estimates that during business hours, an average of 3 shoppers per minute enter the store and that each of them stays an average of 15

minutes. The store owner uses Little's law to estimate that there are 45 shoppers in the store at any time.

Little's law can be applied to any part of the store, such as a particular department or the checkout lines. The store owner determines that, during business hours, approximately 84

shoppers per hour make a purchase and each of these shoppers spends an average of 5 minutes in the checkout line. At any time during business hours, about how many shoppers,

on average, are waiting in the checkout line to make a purchase at the Good Deals Store

Note that at any time during business hours, about **7 shoppers**, on **average**, are waiting in the checkout line to make a purchase at the Good Deals Store. This is solved using** Little Law.**

**Little's Law** asserts that the long-term average number of individuals in a stable system, L, is equal to the long-term average effective arrival rate,λ, multiplied by the average duration a customer spends in the system, W.

To compute,

First, let's make sure that all the **variables** use the same time unit.

Thus, if there are 84 shoppers who are making a purchase per house, then there will be: 84/60 minutes

= 1.4

This means that λ (rate) = 1.4 and the average time (W) is 5 minutes

Using** Little's Law **which states that the queuing formula is:

L = λW

Note that:

λ = 1.4 (computed)

W = 5 mintues (given)

Hence, the **Average number **of people in queue per time is:

L = 1.4 x 5

L = 7 shoppers.

Thus, it is correct to state that at any time during work hours, about 7 shoppers, on average, are waiting in the checkout line to make a purchase at the Good Deals Store.

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**Full Question:**

If shoppers enter a store at an average rate of r shoppers per minute and each stays in the store for an average time of T minutes, the average number of shoppers in the store, N, at any one time is given by the formula N=rT. This relationship is known as Little's law.

The owner of the Good Deals Store estimates that during business hours, an average of 3 shoppers per minute enter the store and that each of them stays an average of 15 minutes. The store owner uses Little's law to estimate that there are 45 shoppers in the store at any time.

Little's law can be applied to any part of the store, such as a particular department or the checkout lines. The store owner determines that, during business hours, approximately 84 shoppers per hour make a purchase and each of these shoppers spend an average of 5 minutes in the checkout line. At any time during business hours, about how many shoppers, on average, are waiting in the checkout line to make a purchase at the Good Deals Store?

Use the scale to help you solve the equation and find the value of x. Enter the

value of x below.

x+ 5 = 12

X =

**Answer: 7**

**Step-by-step explanation:**

x=12-5

x=7

**Answer:**

x=7

**Step-by-step explanation:**

12-5=7 or 7+5=12

5x^2-13+6=0

i need helppp

**Answer:**

answer is 2.5

**Step-by-step explanation:**

PLS HELP

Select the correct answer.

A museum curator estimates that 85% of people who attend the museum would return a second time. She randomly surveys

50 people and finds that only 75% indicate that they would return a second time. So she decides to randomly survey an additional

100 people.

if her model is valld, what could she expect from the 150 total survey results?

The difference between the data and the model will get larger.

The difference between the data and the model will stay the same.

O it is impossible to predict how the difference between the data and the model will change

The difference between the data and the model will get smaller.

O

Submit

The **difference** between the model and the data will get smaller.

A sample is a **percentage **of the total population in statistics. You can use the data from a sample to make inferences about a **population **as a whole.

Given here, she 50 people and finds that only 75% and **additional** 100 people hence changing the **sample** size

As our sample size increases, the **confidence **in our estimate increases, our uncertainty decreases and we have** greater** precision. Thus with the increase in sample size, the data would move closer to the **estimated **probability.

Hence The difference between the** model** and the data will get smaller.

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**Answer:**

The difference between the data and the model will get smaller.

**Step-by-step explanation:**

Plato/Edmentum

Which of the following represents members of the domain of the graphed function?

See attached picture

Responses

{-4, 2, 3}

{-4, 0, 1}

{1, 2, 3, 4}

{1, 2, 3, 5}

The {-4, 0, 1} **represents** members of the **domain** of the graphed **function**.

**What is the domain of the function?**

A **function** is a mathematical object that **accepts** input, appears to apply a rule to it, and returns the result.

A **function** can be thought of as a machine that requires in a **number**, performs some operation(s), and then outputs the result.

The **domain** of a **function** is the collection of all its **inputs**. Its **codomain** is the set of **possible** **outputs**.

The range refers to the **outputs** which are actually used.

Domain: {-4, 0, 1}.

Simply list the domain as -4 < x < 2, which would imply ALL values between -4 and 2 inclusive.

Yes, this is a function. No x-values repeat, and it passes the Diagonal Line Test for functions.

Hence, the {-4, 0, 1} **represents** members of the **domain** of the graphed **function**.

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