Probability is expressed as

number of favorable outcomes/number of total outcomes

In a standard deck of cards, the total number of cards is 52.

There are 13 spades in a standard deck. Thus,

**probability of selecting a spade = 13/52 = 1/4**

There are 26 red cards in a standard deck of cards. Since the first card was replaced, the total number of cards remains 52.

**probability of selecting a red card = 26/52 = 1/2**

There are 4 queens in a standard deck of cards. Since the second card was also replaced, total number of cards is still 52. Thus,

**Probability of selecting a queen = 4/52 = 1/13**

Thus, the probability that the first card will be a spade, the second card will be a red card, and the third card will be a queen is

1/4 x 1/2 x 1/13

**= 1/104**

The quadratic function -2x ^ 2 + 4x + 6 is shown below. What are the solutions of this function? *

The solution for this **function** will be x = -1 and x = 3

**Quadratic polynomials **are those with at least one** variable** and a variable with a maximum **exponent** of two. Since the second-degree term is the highest degree term in a **quadratic function,** it is sometimes referred to as the **polynomial** of degree 2. In a quadratic function, at least one term must be of the second degree. It has qualities in **algebra.**

The given function is -2x² + 4x + 6

So, we'll employ the **middle term splitting strategy**.

-2x² + 4x + 6 = 0

- 2x² + 6x - 2x + 6 = 0

-2x ( x-3) -2 (x-3) = 0

(-2x-2) (x-3) = 0

So, the solution will be

-2x - 2 = 0

-2x = 2

x = 2/-2

x = -1

And, x-3 =0

x = 3

So, the solution of the quadratic function will be

x =-1 and x = 3

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Transit Technologies plans to produce 2-way radios that will sell for $59 per radio. They estimate fixed costs

in manufacturing the radios to be $41,500. The variable costs of producing each radio will be $14. How many

radios must the company sell to break even?

The company should must sell 923 radios to **break even**.

**Fixed cost **refer to those costs which do not vary directly with the level of output. For example salary given to staff.

**Variable cost **that cost which vary directly with the level of output..

The **selling price **of radio is $59.

Total radios sell are of value $41500. This is the fixed cost.

Let us say that they sell **x number** of radios,

As we know,

For break even point,

Total revenue = Total cost

Cost of one radio x number of radio = **fixed cost** plus **variable cost** of all radios

54x = 41500 + 14x

40x = 41500

x = 922.22~923

So, they should sell 923 radio to break even.

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can you please solve this practice problem for me I really need assistance. the original slope is blue and the parallel slope is green

**Answer:**

The original slope is 1, so the slope of the parallel line will also be 1.

Questions 12-15. Data from Ivy Tech’s advising center shows that their wait times follow a normal distribution. Use theEmpirical Rule to answer the following questions. 5 10 15 20 25 30 3512. What percent of students will wait between 15 and 25 minutes? (round to the nearest whole number)13. What percent of students will wait less than 20 minutes? (round to the nearest whole number)14. What percent of students will wait more than 35 minutes? (round to the hundredths place)15. If 5,300 students come to the advising center, how many students would wait more than 35 minutes? (round to thenearest student)

**Answer:**

12. 68%

13. 50%

14. 0.15%

15. 8 students

**Step-by-step explanation:**

Given a **normal distribution** with **mean 20** and **standard deviation 5**, you want several **probabilities** based on the **empirical rule**.

The empirical rule tells you the percentages of a normal distribution that are within 1, 2, or 3 standard deviations of the mean. They are ...

within 1: 68%within 2: 95%within 3: 99.7%12. Between 15 and 25Wait times between 15 and 25 are within 20±5, so within 1 standard deviation of the mean. **The percentage of students waiting 15–25 minutes is 68%**.

The mean of the distribution is 20, which is its line of symmetry.

**50% of students will wait less than 20 minutes**.

35 is 3 standard deviations above the mean, so the fraction in this group is half of the difference between 1 and 99.7%.

**0.15% of students will wait more than 35 minutes**.

Of 5300, the number waiting more than 35 minutes is ...

0.15% × 5300 = 7.95 ≈ 8

**About 8 students will wait more than 35 minutes**.

__

*Additional comment*

These values are based on the empirical rule, as required by the problem statement. The actual number for P(Z>3) is about 0.0013499 (0.13%), and the number of students is about 7.15 ≈ 7. That is, the result using the empirical rule is slightly different than what you get using a calculator, spreadsheet, or table.

<95141404393>

What term must go in the space to complete the statement?

The** term** that should go in the space to complete the** statement** is 5.

The complete **statement **is 5c + 15 = 5(c + 3).

The given statement is 5c + 15 = __(c + 3).

Now, we will combine the like term from the left side of the expression which is 5, and place it on the right side space to make the expression equivalent.

Hence, the complete statement is 5c + 15 = 5(c + 3).

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A map is drawn using the scale 2cm: 100miles. On the map, Town B, is 3.5 cm from Town A and Town C is 2 cm past Town B. How many miles apart are Town A and Town C

SOLUTION

From the question, town B is 3.5cm from town A and town C is 2cm from town B. Therefore C is 5.5 cm from town A.

The scale is 2cm for every 100miles. This means 1cm for every 50 miles.

You get this by dividing 100 by 2.

Now 5.5 cm becomes 5.5 x 50 miles = 275miles.

So **town A and town C are 275 miles apart**

uncle grandpa once said, “400 reduced by twice my age is 262.” what is his age? Show work

**Answer:**

69

**Step-by-step explanation:**

400-262=138

138÷2=69

Solve by factoring: f(x) = 2x² + 7x+6

Write the final answers in the two blanks. Do NOT write x =, just the number. If there is a fraction in your answer, write as #/#.

The **factoring** of the expression 2x² + 7x + 6 is (2x + 3)(x + 2).

It should be noted that a **factor** of a number is a number that can be multiplied with another number to get the original **number**.

In this case, 2x² + 7x - 6 will be **factored** thus:

= 2x² + 7x + 6

= 2x² + 4x + 3x + 6

= 2x(x + 2) + 3(x + 2)

= (2x + 3)(x + 2)

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if A(-3,4) is on BC and divides it in the ratio of BA:AC = 1:2 find C if B is (-9,8)

The **coordinate **of the point C on the **line segment** is (9, -4)

On the **segment**, we have the following **endpoints**

A = (-3, 4)

B = (-9, 8)

The **ratio **of point A on the **line **is given as

Ratio, B : C = 1 : 2

Rewrite as

m : n = 1 : 2

The coordinate of point A is calculated using

A = 1/(m + n) * (mx₂ + nx₁, my₂ + ny₁)

Where x and y are the **coordinates **defined above

So, we have

(-3, 4) = 1/(1+2) * (1 * x + 2 * -9, 1 * y + 2 * 8)

Evaluate

(-3, 4) = 1/3 * (x - 18, y + 16)

So, we have

(x - 18, y + 16) = (-9, 12)

This means that

x - 18 = -9

y + 16 = 12

Solve

x = 9

y = -4

Hence, the **location **of the point C is (9, -4)

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A mixture of 20 pounds of candy sells for $1.15. The mixture consists of chocolates worth $1.45 a pound and chocolatesworth $0.90 a pound. If x represents the pounds of $0.90 chocolates used, then which of the following represents thepounds of $1.45 chocolates used?20 - x20 xOX-20

**Answer**

**The 1.45 dollar chocolates will weigh (20 - x) pounds.**

**Explanation**

We are told that the mixture weighed **20 pounds **and one of the chocolates in the mixture weighed **x pounds.**

We are then to cslculate the weight of the other type of chocolate in the mixture.

**Total mixture = 20 pounds**

**0.90 dollar chocolate weighed x pounds**

**The 1.45 dollar chocolates will weigh (20 - x) pounds.**

**Hope this Helps!!!**

6. Solve for x. **THINK! a) what type of angles do you have? b) what is theirrelationship (add up to 90, add up to 180, or congruent)? c) set up an equationand solve *

a) The types of angles present are:

- 1 right angle

- 1 angles of 50 degrees and 1 angle of 4x degrees

b) their relationship is add up to 90°

c) 50° + 4*x° = 90°

4*x° = 90 - 450

x° = 40/4 = 10

x = 10°

To indirectly measure the distance across a lake, Ethan makes use of a couple

landmarks at points B and C. He measures AE, EC, and DE as marked. Find the

distance across the lake (BC), rounding your answer to the nearest hundredth of a

meter.

To the **nearest tenth**, the distance across the lake is DE = 207.68 m.

The corresponding side lengths of two** triangles** that are similar are always proportional to each other.

ΔCDE and ΔCFG are **similar** to each other

FG = 142.1 m

FC = 130 m

DF = 60 m

DC = 130 + 60 = 190 m

Therefore,

DE/FG = DC/FC

Substitute

DE/142.1 = 190/130

Cross multiply **nearest hundredth**

Therefore, applying the **similarity theorem**, the distance across the lake to the nearest hundredth is DE = 207.68 m

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Find the value of x. The diagram is not to scale. Lines fand g are parallel. f g

5x

9x+26

A. 10

B. 11

C. 12

D. -11

X has a** value** of 11

**What is an angle?**

The **vertex** of an **angle** is the common point of contact where two **straight lines** or rays come together to produce an **angle**.

As far as we are aware, this question is answered **utilizing** a **quadrilateral's** unique property that the sum of its **adjacent angles** is 180 degrees.

By quadrilateral, what do you mean?

A closed **polygon** with four sides, **four vertices**, and four angles is known as a **quadrilateral.**

thus, A.T.Q:-

We possess 5x+9x+26=180

14x +26=180

14x=154

x = 11 degrees

Consequently, x = 11 degrees.

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Answer this please I really need you to do this

**Answer:**

x ≥ 2

**Step-by-step explanation:**

Given inequality:

[tex]-\dfrac{4(x+3)}{5} \leq 4x-12[/tex]

**Values of x less than 2**

Substitute two values where x < 2 into the inequality:

[tex]\begin{aligned}x=1 \implies -\dfrac{4(1+3)}{5} & \leq 4(1)-12\\\\ -\dfrac{4(4)}{5} & \leq 4-12\\\\ -\dfrac{16}{5} & \leq -8 \quad \Rightarrow \textsf{Not a solution}\end{aligned}[/tex]

[tex]\begin{aligned}x=0 \implies -\dfrac{4(0+3)}{5} & \leq 4(0)-12\\\\ -\dfrac{4(3)}{5} & \leq 0-12\\\\ -\dfrac{12}{5} & \leq -12 \quad \Rightarrow \textsf{Not a solution}\end{aligned}[/tex]

The values of x < 2 are not solutions to the inequality.

--------------------------------------------------------------------------------

Substitute the **value of x = 2 **into the inequality:

[tex]\begin{aligned}x=0 \implies -\dfrac{4(2+3)}{5} & \leq 4(2)-12\\\\ -\dfrac{4(5)}{5} & \leq 8-12\\\\ -\dfrac{20}{5} & \leq -4\\\\ -4 & \leq -4 \quad \Rightarrow \textsf{Yes, a solution}\end{aligned}[/tex]

The value of x = 2 is a solution to the inequality.

--------------------------------------------------------------------------------

**Values of x more than 2**

Substitute two values where x > 2 into the inequality:

[tex]\begin{aligned}x=3 \implies -\dfrac{4(3+3)}{5} & \leq 4(3)-12\\\\ -\dfrac{4(6)}{5} & \leq 12-12\\\\ -\dfrac{24}{5} & \leq 0 \quad \Rightarrow \textsf{Yes, a solution}\end{aligned}[/tex]

[tex]\begin{aligned}x=4 \implies -\dfrac{4(4+3)}{5} & \leq 4(4)-12\\\\ -\dfrac{4(7)}{5} & \leq 16-12\\\\ -\dfrac{28}{5} & \leq 4 \quad \Rightarrow \textsf{Yes, a solution}\end{aligned}[/tex]

The values of x > 2 are solutions to the inequality.

--------------------------------------------------------------------------------

Therefore, the **solution **to the inequality appears to be x ≥ 2.

To check, **solve **the **inequality**:

[tex]\begin{aligned} \implies -\dfrac{4(x+3)}{5} &\leq 4x-12\\-4(x+3) &\leq 5(4x-12)\\-4x-12 &\leq 20x-60\\ -24x & \leq-48\\x & \geq 2\end{aligned}[/tex]

When **graphing inequalities** on a number line:

To **graph **the **solution **to the **inequality **on number line, place a **closed circle** at x = 2 and shade to the **right**. (See attachment).

Evaluate r(x) = 3x - 10 when x= -4. r(-4)=_

**Answer:**

The answer is: r is equal to -22.

the last six days of August 2011 all time records for high temperatures in Austin Texas which of the following values that identifies the mean absolute deviation for these temperatures F. 4G. 107H. 103J. 3.3

We have to calculate the mean absolute deviation (MAD) for these temperatures.

We can express the MAD as:

[tex]\text{MAD}=\frac{1}{n}\sum ^n_{i=1}|x_i-\bar{x|}[/tex]So first we have to calculate the mean of the sample. We can do this as:

[tex]\bar{x}=\frac{1}{n}\sum ^n_{i=1}x_i=\frac{1}{6}(103+110+112+109+105+103)=\frac{1}{6}\cdot642=107[/tex]Now we can calculate the MAD as:

[tex]\begin{gathered} \text{MAD}=\frac{1}{6}(|103-107|+|110-107|+|112-107|+|109-107|+|105-107|+|103-107|) \\ MAD=\frac{1}{6}(4+3+5+2+2+4) \\ \text{MAD}=\frac{1}{6}(20) \\ \text{MAD}\approx3.3 \end{gathered}[/tex]**Answer: The MAD is approximately 3.3.**

Find the equation of the line with slope −3/5 and y-intercept (0,−3).

The **equation **of the **line **will be [tex]y = -\frac{3}{5}x -3[/tex]

In the question given, It is stated that the slope of the line is **m = -3/5**, and the **y-intercept** of the line is **(0, -3)**. We have to find out the **slope-intercept **form of the line. To find out the equation of line first the **standard **equation for slope intercept form is **y = mx + b**, where m is the slope, and b is the y-intercept.

Now, we have slope **m = -3/5** and **y-intercept** is **-3**. Putting these values in the slope intercept form we get:

=> **y = mx + b**

=> [tex]y = -\frac{3}{5}x -3[/tex]

Hence, we get **equation **of line [tex]y = -\frac{3}{5}x -3[/tex]

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Hola!, me ayudan porfa!!

En la cerrada economía Chalupa, el consumo familiar triplica el de las unidades productivas y este supera en $2,500 al del gobierno, que tiene un equilibrio presupuestario y sus ingresos fueron $6,700. Si el consumo de capital fijo es 25% del PNB pm y el monto de impuestos netos de subsidios $1750 encuentre el ingreso nacional.

**Answer:**

hola comasa due when 123 dfosb971 24

Given that bisects use the diagram above to complete the following statement.m∠AOB= m∠…

A line is said to **bisect** an angle if it divides it in two equal parts.

Since the segment OB bisects the angle AOC, then the angles AOB and BOC have the same measure.

**Therefore, the complete statement is:**

Teri ran 8 kilometers. One mile is approximately equal to 1.6 kilometers. Which measurement is closest to the number of miles Teri ran?

The **closest distance **or the** number of miles **Teri ran is equal to 5 miles.

**What is the unitary method ?**

The **unitary method** is a method in which you find the value of **one unit **and then the value of **required no. of units.**

It is given that Teri **ran 8 kilometers.**

It is also given that , 1 mile is **approximately equal** to 1.6 kilometers.

This is a question of **unitary method.** We know that value of one unit is given as 1 mile is equal to 1.6 kilometers approximately. We know have to **calculate** the** no. of miles **Teri ran , by converting 8 kilometers to miles.

So ,

1 miles = 1.6 kilometers

This implies :

8 kilometers = 8 / 1.6 miles

or

8 kilometers = 5 miles

or

8 kilometers is approximately equal to 5 miles.

Therefore , the **closest** **distance **or the** number of miles **Teri ran is equal to 5 miles.

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PartA)What are the transformations are needed in in order to obtain the graph of G(x) from the graph of f(x) Select all that applyPartB) Graph g(x)

Part A)

Recall that:

1) The function represented by the graph of the function f(x) translated vertically n units up and horizontally m units left is:

[tex]f(x+m)+n\text{.}[/tex]2) The function represented by the graph of the function f(x) reflected over the x-axis is:

[tex]-f(x)\text{.}[/tex]Now, notice that g(x) is the function f(x) reflected over the x-axis and then translated vertically 6 units up and horizontally 4 units left.

**Answer Part A:**

Options B, C, and D.

Part B) To graph g(x) we will reflect the graph of f(x) over the x-axis and then we will translate it vertically 6 units up and horizontally 4 units left.

We know that the graph of f(x)=|x| is:

The above graph reflected over the x-axis is:

Finally, the above graph translated vertically 6 units up and horizontally 4 units left is:

**Answer part B:**

QuestionIn ABC, C = 64°, c = 32, and b = 33. What are the two possible values for angle B to the nearest tenth of a degree?Select both correct answers.

Two possible diagrams of the triangle are shown below

To find angle B in each triangle, we would apply the law of sines which is expressed as

a/SinA = b/SinB = c/SinC

For either of the triangles, by applying the sine law, we have

33/Sin B = 32/Sin 64

By crossmultiplying, we have

32 SinB = 33 Sin 64

Sin B = (33 Sin 64)/32 = 0.9269

We would find angle B by finding the inverse of sine 0.9269

Thus,

B = Sin^-1(0.9269) = 68

This is an acute angle. B can also be an obtuse angle. Greater than 90 but less than 180 degrees). Thus, another value for B is

is B the right answer? If not, which one is?

Given the rational function;

[tex]f(x)=\frac{3x+4}{x(x-2)}[/tex]To determine the constraint for this function, we shall set the denominator equal to zero;

[tex]\begin{gathered} x(x-2)=0 \\ \text{Hence;} \\ x=0 \\ x-2=0 \\ x=2 \end{gathered}[/tex]This means the equation does not exist when x = 0, and when x = 2.

**ANSWER**:

The correct answer is option C.

a. pi/3 b. pi/2c. 2pi/3d. 3pi/2 These are 4 options but there can be more than 2 or 3 correct answers.Find the solution of each equation the interval

[tex]\sin x\cdot\cos x-\frac{\sqrt[]{3}}{2}\cos x=0[/tex][tex]\cos x(\sin x-\frac{\sqrt[]{3}}{2})=0[/tex][tex]\begin{gathered} \cos x=0 \\ x=\frac{\pi}{2},\frac{3\pi}{2} \end{gathered}[/tex][tex]\begin{gathered} \sin x-\frac{\sqrt[]{3}}{2}=0 \\ \sin x=\frac{\sqrt[]{3}}{2} \\ x=\frac{\pi}{3} \end{gathered}[/tex]

so the answer is **pi/2, 3pi/2, and pi/3**

Triangles DEF and HJK are similar. DEF has side lengths DE=4, EF=6, FD=8. Which of the following could be the side lengths of HJK?• 2, 6, 7• 2, 5, 7• 8, 12, 16• 5, 7, 9

**Answer:**

(c) 8, 12, 16

**Step-by-step explanation:**

You want to identify the **side lengths** that are **proportional** to **lengths 4, 6, and 8**.

Reducing the ratios to lowest terms, we can compare them:

desired ratio: 4 : 6 : 8 = 2 : 3 : 42 : 6 : 7 — reduced, not equivalent2 : 5 : 7 — reduced, not equivalent8 : 12 : 16 = 2 : 3 : 4 . . . . . same as the desired ratios5 : 7 : 9 — reduced, not equivalent**Side lengths 8, 12, 16 will form a triangle similar to ∆DEF**.

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what is 3 1/2 x 4 1/2 x 5 ft * 5 1/6 x 5 1/4 x 3 1/3 x 4 1/2 in 5 ft x 5 1/3 * 2/3

**ANSWER**

**EXPLANATION**

h. We want to find the volume of the rectangular prism given.

The** volume of a rectangular prism** is given as:

where L = length

w = width

h = height

Therefore, we have that **the volume of the prism is:**

Which is true?A. 2680 > 2806B. 2860 > 2806C. 2680 < 2086D. 2806 < 2680

from the options;

**The correct is B**

**because 2860 is greater than 2806**

**Other options are false**

which graph represents the equation x - 4y = -16

the given equation is

x - 4y = -16

put x = 0

0 - 4y = -16

y = 4

so at x = 0 ,, y is 4

put x = 4

4 - 4y = -16

-4y = -16- 4

y = 20/4

y = 5

so, at x = 4 the value of y is 5

**thus, the correct graph is option B**

There are multiple choices. but they didn’t fit in the picture

**Explanation**

In the question,

The number of tomatoes is described as x

The number of lettuce is described as y

As per the question, the number of vegetables Aneil can plant in the garden is modelled by:

[tex]2x+3y=60[/tex]The graph of the above model can be seen above.

From the graph, we have the y-intercept to be 20 and the x-intercept to be 30.

**Answer:**

**Y-intercept = 20 ---- This is the number of lettuce plants Aneil can plant if he plants zero tomatoes**

**X- intercept =30 ---- This is the number of tomatoes plants Aneil can plant if he plants zero lettuce**

What is the effect on the graph of f(x)=x^2 when it is transformed to h(x)=2x^2 + 15

**Answer and Explanation**:

If f(x) = x^2 is transformed to h(x)=2x^2 + 15, the below will be the effect on the its graph;

* The graph will be shifted up 15 units

*The graph will be vertically stretched since the value o

negative 37 over 24 times j minus 17 over 12negative 37 over 24 times j plus 17 over 1243 over 24 times j plus 1 over 12negative 43 over 24 times j plus negative 1 over 12Simplify the expression.the expression negative one eighth j plus two thirds minus the expression five thirds j plus nine twelfthsnegative 37 over 24 times j minus 17 over 12negative 37 over 24 times j plus 17 over 1243 over 24 times j plus 1 over 12negative 43 over 24 times j plus negative 1 over 12Which expression is equivalent to 3(4.5b 2.1) (6b + 0.6)?19.5b + 1.519.5b 1.519.5b 6.919.5b 6.9
Calculate the cost of one pen is eight pens cost $32.
ASAP!! Justin bought a calculator and a binder that were both 15% off the original price. The original price of the binder was $6.20. Justin spent a total of $107.27. What was the original price of the calculator? Include all steps for branliest.
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you have a 10vdg source available design a voltage divider ciruit that has 2 vdc , 5vdc , and 8 vdc available the total circuit current is to be 2mA
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10 reasons why the Bill of Rights is still important today.
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If a1 = 7 and an3an-1 + 4 then find the value of a4.
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Read the paragraph from the section "Theatrical Beginnings." By 1592, there is evidence Shakespeare was working as an actor and a playwright in London. By the early 1590s, documents show that he was a managing partner in an acting company in London called the Lord Chamberlain's Men, later known as the King's Men. From all accounts, the King's Men was very popular, and records show that Shakespeare had works published and sold as popular literature. What is MOST LIKELY the purpose of this paragraph?
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a company has developed a new computer sound card, but the average lifetime is unknown. in order to estimate this average, 200 sound cards are randomly selected from a large production line and tested and the average lifetime is found to be 5 years. the 200 sound cards represent the:
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Which of the following statements about treating PTSD is true? a. By focusing on a persons specific traumatic memory, trauma-focused therapy has been shown to be too narrow in scope to be helpful in treating PTSD. b. The American Psychological Association has issued guidelines to replace psychotropic interventions with trauma-focused therapy. c. The American Psychological Association has issued guidelines to replace cognitive-behavioral therapy with trauma-focused therapy. d. Trauma-focused therapy is gaining support as a first-line treatment showing longer-lasting results than psychotropic medication.
Which of the following is NOT an example of matter?O All of these are examples of matterO airO goldO apple juiceO a rose bush