The sales tax for an item was $11.70 and it cost $390 before tax.

Find the sales tax rate. Write your answer as a percentage.

1%

Х

?

**Answer:**

3%

**Step-by-step explanation:**

$390 x tax rate = 11.70

tax rate = 11.70/390

tax rate = .03 or 3%

Suppose a mutual fund qualifies as having moderate risk if the standard deviation of its monthly rate of return is less than 3%. A mutual-fund rating agency randomly selects 27 months and determines the rate of return for a certain fund. The standard deviation of the rate of return is computed to be 2.55 %. Is there sufficient evidence to conclude that the fund has moderate risk at the a= 0.05 level of significance? A normal probability plot indicates that the monthly rates of return are normally distributed. What are the correct hypotheses for this test?

The correct hypotheses for this test are:

Null hypothesis (H0): The standard deviation of the mutual fund's monthly rate of return is greater than or equal to 3%.

Alternative hypothesis (H1): The standard deviation of the mutual fund's monthly rate of return is less than 3%.

To determine if there is sufficient evidence to reject the null hypothesis and conclude that the fund has moderate risk, you would need to perform a hypothesis test. In this case, since you have a sample of 27 monthly rates of return and the normal probability plot indicates that the data is normally distributed, you can use a z-test for the population standard deviation.

To perform the test, you would need to calculate the test statistic and the p-value. The test statistic is calculated as follows:

test statistic = (sample standard deviation - population standard deviation) / (standard error)

where the sample standard deviation is 2.55%, the population standard deviation is 3%, and the standard error is calculated as:

standard error = sample standard deviation / sqrt(sample size)

Plugging in the values, the test statistic is:

test statistic = (2.55 - 3) / (2.55 / sqrt(27)) = -0.44

The p-value is the probability of observing a test statistic at least as extreme as the one calculated, given that the null hypothesis is true. To calculate the p-value, you can use a z-table or a statistical software package.

If the p-value is less than the chosen level of significance (a=0.05 in this case), you can reject the null hypothesis and conclude that the fund has moderate risk. If the p-value is greater than the level of significance, you cannot reject the null hypothesis and cannot conclude that the fund has moderate risk.

The product of three consecutive integers n - 1, n, and n + 1 is 210. Write and solve an equation to find the numbers.

We can write an **equation **to represent the relationship between the **three **integers n - 1, n, and n + 1 by multiplying these three numbers together:

We can then solve this equation to find the value of n.

To solve the equation, we can first factor the left-hand side to get (n - 1) * (n + 1) * n = 210. This **expression **can be further simplified to n^2 - 1 = 210. We can then solve this equation by adding 1 to both sides to get n^2 = 211, and then taking the** square root **of both sides to get n = sqrt(211).

The value of n must be an integer, so the only possible value for n is 14. This means that the three **consecutive integers **are 13, 14, and 15.

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I NEED HELP FAST

A colony of bacteria grows according to the law of inhibited growth. If there were 200 bacteria at noon, and 550 at 2 pm. Determine when the colony will reach a population of 2000.

logistic model:[tex]y(t)=\frac{c}{1+ae^-bt}[/tex]

I feel like I'm not given enough information. I'll assume that the limit is 10000

The colony will reach a population of **2000 **in time -

**t = - {log(2000 - c) - log(a) + log(c)}/b**.

Given is that a colony of bacteria grows according to the law of inhibited growth. If there were **200 bacteria** at noon, and **550** at **2 pm**.

The **logistic model** is given as -

y(t) = {c/(1 + a[tex]e^{-bt}[/tex])}

For y(t) = 2000

2000 = {c/(1 + a[tex]e^{-bt}[/tex])}

(2000/c) = 1/(1 + a[tex]e^{-bt}[/tex])

(1 + a[tex]e^{-bt}[/tex]) = (2000/c)

a[tex]e^{-bt}[/tex] = (2000/c) - 1

a[tex]e^{-bt}[/tex] = (2000 - c)/c

[tex]e^{-bt}[/tex] = (2000 - c)/(ac)

(-bt)log{e} = log {(2000 - c)/(ac)}

- bt = log(2000 - c) - log(ac)

- bt = log(2000 - c) - log(a) + log(c)

**t = - {log(2000 - c) - log(a) + log(c)}/b**

Therefore, the colony will reach a population of **2000 **in time -

**t = - {log(2000 - c) - log(a) + log(c)}/b**.

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I've been unable to figure this out. Anyone able to assist on which is the correct answer?

The **domain** and **range **of the given function are {-2, 0, 1, 2, 3} and {-3, 0, 2, 3, 4} respectively

The **domain** of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The **range** of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

The domain of a function can be said as all possible values of x and the range of a function is all possible values of y.

The given function is

f(x) = {(0, -3), (2, 0), (3, 2), (1, 4), (-2, 3)

The domain of the function can be given as;

Domain : {-2, 0, 1, 2, 3}

Range : {-3, 0, 2, 3, 4}

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[tex]\int\limits^2_076e^4 {x} \, dx[/tex]

∫76^4•∫x dx

76e^4•∫x^2/2

38e^4x^2|^2. 0

38e^4•2^2-38e^4•0^2

152e^4

76e^4•∫x^2/2

38e^4x^2|^2. 0

38e^4•2^2-38e^4•0^2

152e^4

Order the ratios from least to greatest.

5:8 11:16 18:32

The **least** to greatest of the **ratio** is 18 : 32, 5 : 8, and 11 : 16

Least to **greatest** arrangement can also be referred to as ascending order. **Ascending** order is the order such that each element is greater than or equal to the previous element.

5 : 8

= 5/8

= 0.625

11 : 16

= 11/16

= 0.6875

18 : 32

= 18/32

= 0.5625

Therefore, the ratio can be **arranged** as 18 : 32, 5 : 8, and 11 : 16 in ascending order.

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6r^2-8r =8

need helpp

**Answer:**

r = 2/ r = -2/3

**Step-by-step explanation:**

so you move the terms to the left side

6r^2 - 8r = 8

6r^2 -8r - 8 = 0

the common factor

6r^2 - 8r -8 = 0

2(3r^2 - 4r - 4) = 0

then you divideboth side by the same factor

2(3r^2 - 4r - 4) = 0

3r^2 - 4r - 4 = 0

use the quadratic formula

you would get 2.3

then you simplify

r = 4+8 over 6

seperate the equations

r = 4+8 over 6 change the plus into a minus

after that rearrange and issolate variable

r = 2

r = -2/3

therfore your answer is -2/3

Hypothesis 1 H0: Receiving a 20 percent off coupon does not increase the number of customers visiting the Lotions and Potions soap store. Ha: Receiving a 20 percent off coupon increases customers visiting the Lotions and Potions soap store. Data Customers on file who visited the store during coupon promo: 32 percent Customers on file who visit the store during a typical week: 30 percent Sample size: 4,500 Questions Did you use a z-test or t-test? Why? What is the P value? Do you accept or reject the alternative hypothesis? Should Lotions and Potions continue to offer this promotion in order to increase visits? Why or why not?

The data **Customers** on file who visited the store during coupon promo is 32% .

a) We use **Z-test** for testing hypothesis in this case because it is single proportion.

b) The **P-value** is 0.0017.

c) As P value < α = 0.05 , So we reject the null hypothesis.

d) **Yes**, Lotions and Potions continue to offer this promotion in order to increase visits because null hypothesis is rejected that alternative hypothesis is true which gives the same results.

The **Null and Alternative** hypothesis related to 20 percent off coupon does not increase the number of customers or increase the number of customers.

**Sample size** ,n = 4,500

**Significance ****level****,**** **0.05

a) We use z-test, because this is single proportion hypothesis test.

Below are the null and alternative Hypothesis,

Null Hypothesis, H₀ : p = 0.3

Alternative Hypothesis, Hₐ : p > 0.3

b) **Test statistic,**

z = (p-cap - p)/sqrt(p×(1-p)/n)

z = (0.32 - 0.3)/sqrt(0.3× (1-0.3)/4500)

z = 2.93

Using the **Z-table**, the P value at significance level 0.05 and z = 2.93 is 0.0017

As we see **P-value < α** = 0.05, so, **reject** the null hypothesis.

Yes, Lotions and Potions should continue to offer this promotion in order to **increase visits**.

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Perform the following mathematical operation, and report the answer to the appropriate number of significant figures.

1204.2 + 4.72613 = [?]

The **value** of 1204.2 + 4.72613 is 1208.92613.

**What is meaning of significant figures of a number?**

Significant figures are the number of **digits** that add to the correctness of a value, frequently a measurement. The first non-zero digit is where we start counting significant figures. Determine how many significant digits there are given a range of numbers.

Given number is 1204.2 and 4.72613.

If add zeros after the last digit of the **decimal number**, then the number will remains same.

The rewrite form of 1204.2 is 1204.20000.

Before combining two **decimal integers**, make sure they both have the same number of digits after the decimal point. If they don't, move a number's right by a number of zeros until they do.

Then, place the decimal points **vertically **and write one number on top of the other. Bring the decimal point directly below the decimal point and add as you would with full numbers.

The sum of 1204.20000 and 4.72613

1204.20000

+4.72613

__________

1208.92613

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Let K=[tex]20^{20}[/tex].Suppose that [tex]\frac{20^{k} }{k^{20} } =20^{n}[/tex].find the largest power of 20 that divides n?

**Answer:**

20^2 = 400, the 2nd power of 20

**Step-by-step explanation:**

Given that **k=20^20 and 20^k/k^20 = 20^n**, you want the **largest power of 20** that **divides n**.

Taking the base-20 logarithm of both equations, we have ...

[tex]\log_{20}{k}=\log_{20}{20^{20}}\ \Longrightarrow\ \log_{20}{k}=20\\\\\log_{20}{\dfrac{20^k}{k^{20}}}=\log_{20}{20^n}\ \Longrightarrow\ k-20\log_{20}{k}=n[/tex]

Substituting for k and log(k), we get ...

[tex]20^{20} -20\cdot20=n\\\\20^2(20^{18}-1)=n[/tex]

This shows us **the largest power of 20 that is a factor of n is 20²**.

find the equation of the tangent to the circle 4x²+4y²=25 what are parallel to the line 3x+5y+7=0

**Answer:**

**Step-by-step explanation:**

To find the equation of the tangent to the circle 4x^2 + 4y^2 = 25 that is parallel to the line 3x + 5y + 7 = 0, we can use the following steps:

Rewrite the equation of the circle in standard form: (x - a)^2 + (y - b)^2 = r^2, where (a, b) is the center of the circle and r is the radius.

In this case, the equation of the circle is already in standard form, so we can skip this step.

Find the slope of the line 3x + 5y + 7 = 0. The slope is -3/5.

Find the slope of the tangent to the circle. The slope of the tangent will be equal to the slope of the line, which is -3/5.

Substitute the slope of the tangent and the coordinates of a point on the circle into the point-slope form of the equation of a line: y - y1 = m(x - x1), where (x1, y1) is a point on the circle and m is the slope.

In this case, we can substitute the coordinates of the center of the circle (which is (0, 0)) and the slope of the tangent (-3/5) into the point-slope form to get:

y - 0 = (-3/5)(x - 0)

Simplify to get the equation of the tangent: y = -3/5x.

Therefore, the equation of the tangent to the circle 4x^2 + 4y^2 = 25 that is parallel to the line 3x + 5y + 7 = 0 is y = -3/5x.

Hello may I please get some help with this question

the answer is a , b , and c .

Im a bit stuck can I get some help

The **relationship's **slope and **common difference **are both 70 and constant.

The **slope **of the line is a **tangent angle **made by line **with horizontal. i.e. m =tanx where x in degrees.**

here,

As the **relationship **given in the table is linear,

The **slope **of the **relationship **is given as,

M = (y₂ - y₁) / (x₂ - x₁)

Now, putting values from the table,

m = 140 - 70 / 2 - 1

m = 70 jumps per minute

Now,

The **common difference **between the consecutive minutes of jumping,

d = 140 - 70 = 210 - 140

d = 70 = 70

From the above evaluation, it can be said that the common difference and rate are constant.

Thus, the **slope **of the **relationship **and the **common difference **is 70, as well as constant.

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There are only 2.1 x 108 metric tonnes of usable fossil fuels existing on Earth.

Assuming an estimated rate of fossil fuel use of 1 x 105 metric tonnes per year, calculate an order of magnitude estimation of the time left before the fossil fuel reserves run out.

Give your answer to one significant figure.\

The answer is 2000 but I cannot figure out how they got it.

The **time** that is left before the **fossil fuel** reserves run out would be= **2000 years.**

A **fossil fuel is** defined as the type of fuel that is gotten from dead and decayed organic matter that has been buried for years underneath the earth surface.

The quantity of usable **fossil fuel** existing on earth = 2.1 x 10⁸metric tonnes.

The **rate** of fossil fuel used per year = 1 x 10⁵

Mathematically,

If 1 year = 1 x 10⁵

X years = 2.1 x 108

make X years the subject of formula;

X years = 2.1× 10⁸/1× 10⁵

X years = 2.1 × 10³ or 2100

X year = **2000( to one significant figure)**

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Suppose the COMBINED area is known to be 0.10416, assume there is equal area on each side. Determine the corresponding Z-scores.

A) z=Â±1.62 B) z=Â±1.58 C) z=Â±1.72 D) z=Â±1.66 E) z=Â±1.69 F) z=Â±1.49 G) None of These

The solution is once more 1.28 since a **combined area **of 0.10416 to the right implies that it must also have an area of 0.90 to the left.

Since each normally distributed random variable has a slightly different distribution shape, standardizing the variable to give it a mean of 0 and a **standard deviation** of 1 is the only method to determine regions using a table. How do we go about doing that? Employ the** z-score**!

Z = ( x - μ)/σ

If a mean and standard deviation are present for the** random variable** X,

Then a random variable with a mean of 0 and a standard deviation of 1 is produced by converting X using the** z-score!**

With that in mind, all that remains is to understand how to find areas under the **standard normal curve**, which can then be applied to any random variable with a normal distribution.

Since an **area** of 0.10416 to the right means that it must have an area of 0.90 to the left, the answer is once again 1.28.

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To indirectly measure the distance across a river, Sebastian stands on one side of the river and uses sight-lines to a landmark on the opposite bank. Sebastian draws the diagram below to show the lengths and angles that he measured. Find PRPR, the distance across the river. Round your answer to the nearest foot.

Sebastian uses the method of similar triangles to find the **distance across** the river, and the distance across the **river **is 372 foot.

A **triangle **is a polygon with three sides and three vertices.

The triangle's total number of angles comes to 180°.

The **distances **between the formed the sight-lines are;

RB = 210 feet

OC = 275 feet

The distance between the **point **close to the river and the next point further from the **river **= 115 feet

In **triangles **ΔPRB and ΔPOC,

we have;

∠PRE = ∠POC = 90°

Given;

∠PER ≅ ∠PCO

By **corresponding **angle formed between two parallel lines and a common **transversal**.

Using angle-angle **similarity **theorem;

∴ ΔPRE is similar to ΔPOC Which gives;

PR / PO = RE / OC

Let x represent the distance **across **the river,

we have;

PR = x

PO = 115 + x

Which gives;

x / (115+x) = 210 / 275

275x = 210 × (115 + x)

275x = 24150 + 210x

275x - 210x = 24150

65x = 24150

x = 371. 54

Therefore, the **distance **across the river is 372 foot.

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One student surveys the number of pens which are sold in two stationary shops.The pens of both shops are sold in a week.In the first shop 60 pens are sold in the first day and 6 pens are sold more in everyday as comparison of previous day.Similarly in the second shop 5 pens are sold in the first day and the double number of pens are sold in everyday as comparison of previous day.Now in which shop how manv nens are sold more? Find it.Ans: 89 more in second shop

Answer: 224 pens more sold in 2nd shop

Step-by-step explanation:

Given,

1st shop, 6 pens are sold more than previous day,

1st day : 60

2nd day : 60+6 =66

3rd day : 66+6 =72

4th day : 72+6 =78

5th day : 78+6 =84

6th day : 84+6 =90

7th day : 90+6 =96

Then,

2nd shop, each day doubles the previous sold,

1st day: 5

2nd day:5*2 =10

3rd day:10*2 =20

4th day:20*2 =40

5th day:40*2 =80

6th day:80*2 =160

7th day:160*2 =320

Therefore, second shop sells more in a week which is calculated by 320-96=224 more sold than the 1st shop.

Find k so that the line through (4, -3) and (k.1) is

a. parallel to 3x + 5y = 10,

b. perpendicular to 4x - 3y = - 1

a. k=

**Answer:**

a. k = -8/3 = -2 2/3

b. k = 32/5 = 6.4

**Step-by-step explanation:**

You want to find the **values of k** that place the **point (k, 1) **on the line **through the point (4, -3)** when that line is (a) **parallel to 3x +5y = 10**, and (b) **perpendicular to 3x +5y = 10**.

The equation of the parallel line will have the same x- and y-coefficients, but will have a constant that make the equation true at the point (4, -3).

3x +5y = 3(4) +5(-3) = 12 -15 = -3

The equation of the parallel line is

3x +5y = -3

When y=1, the value of k is ...

3k +5(1) = -3

3k = -8

** k = -8/3 = -2 2/3 . . . . . . on line parallel to 3x+5y=10**

b. Perpendicular

The equation of the perpendicular line will have swapped x- and y-coefficients, with one of them negated. The constant will be chosen to make the equation true at the point (4, -3).

5x -3y = 5(4) -3(-3) = 20 +9 = 29

The equation of the perpendicular line is

5x -3y = 29

When y=1, the value of k is ...

5k -3(1) = 29

5k = 32

** k = 32/5 = 6.4 . . . . . . on th eline perpendicular to 3x+5y=10**

Solve for x: −7 < x − 1 < 8

6 < x < 9

−6 > x > 9

6 > x > −9

−6 < x < 9

The **solution** for the given **inequality** is -6 < x < 9.

**What is linear equality?**

In mathematics a** linear inequality **is an **inequality** that involves a linear **function**. A linear inequality contains one of the symbols of **inequality**. It shows the data which is not equal in graph form.

The given inequality is:

-7 < x - 1 < 8

−7 + 1 < x − 1 + 1 < 8 + 1 -------- (Add 1 to all parts)

-6 < x < 9

Hence, the **solution** for the given **inequality** is -6 < x < 9.

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A man standing on the deck of a ship, h m above the sea level, observes that the angles of elevation and depression of the top and the bottom of a cliff are A and B respectively. Find the height of the cliff in terms of A, B and h

give me the correct ans with clear explainnation and I will give u the BRAINLIEST!

The height of the **cliff **in terms of A, B and h are 40 meters.

A triangle is said to be **right-angled** if one of its inner angles is 90 degrees, or if any one of its angles is a right angle.

A man standing on the deck of a **ship**.

Let C be the **position **of man.

And the angles of **elevation **and depression of the top and the bottom of a **cliff **are A and B respectively 60° and 30°.

That means, ∠DCH = 60° and ∠BCD = 30°.

The diagram is given in the **attached **image.

HD = x And BD = 10 meters.

In** right-triangle** ΔCDH,

we have,

tan60° = HD / CD

√3 = x / CD

CD = x/√3

In right-**triangle **ΔCDB,

we have,

tan30° = BD/CD

CD = 10√3

So, the **distance **of the ship from the cliff is 10√3 meters.

**Comparing**, the both values of CD,

10√3 = x/√3

x = 10√3 × √3

x = 10 × 3

x = 30 meters.

Now, the total **height **of cliff = BD + DH

= 10 + 30

= 40 **meters**.

Therefore, the **height **of the cliff is 40 meters.

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Task: Gym Membership

Instructions

Function c is defined by the equation c(n) = 50 + 4n. It gives the monthly cost, in dollars, of visiting a gym as a function of the number of visits, n.

Complete each of the 2 activities for this Task.

Activity 1 of 2

Find the value of c(7).

Activity 2 of 2

Explain what the value of c(7) you found means in this situation.

The **value** of c(7) = 78 and 78 represents the monthly **cost **of visiting the gym 7 times.

To find p(a) for a given polynomial p(x) we need to** substitute** x = a in the given **polynomial** i.e in place of x.

Here we have

**Function** c is defined by the **equation** c(n) = 50 + 4n.

It gives the monthly cost, in dollars, of visiting a gym as a function of the number of visits n.

Activity 1 of 2

Find the **value** of c(7).

=> c(7) = 50 + 4(7)

=> c(7) = 50 + 28

=> c(7) = 78

Activity 2 of 2

Explain what the value of c(7) you found means in this situation.

In c(n) = 50 + 4n, n represents the number of visits in a month and 50+4n will represent the **monthly cost **in dollars

If we apply the above statement to c(7) = 78

then 7 represents the number of **visits** and 78 represents the monthly **cost** of visiting the gym 7 times

Therefore,

The **value** of c(7) = 78 and 78 represents the monthly **cost **of visiting the gym 7 times.

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A deposit pf $6000 is made in a college savings fund that pays 5.0% interest, compounded continuously. The balance will be given to a student after the money has earned interest for 40 years. How much (in dollars) will the student receive? (Round your answer to the nearest cent.)

**Answer:**

$44,334.34

**Step-by-step explanation:**

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Continuous Compounding Formula}\\\\$ A=Pe^{rt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\\phantom{ww}$\bullet$ $P =$ principal amount \\\phantom{ww}$\bullet$ $e =$ Euler's number (constant) \\\phantom{ww}$\bullet$ $r =$ annual interest rate (in decimal form) \\\phantom{ww}$\bullet$ $t =$ time (in years) \\\end{minipage}}[/tex]

Given:

P = $6000r = 5.0% = 0.05t = 40 years**Substitute **the given **values** into the **continuous compounding formula** and **solve for A**:

[tex]\implies A=6000e^{0.05 \times40}[/tex]

[tex]\implies A=6000e^2[/tex]

[tex]\implies A=6000(7.3890560...)[/tex]

[tex]\implies A=44334.33659...[/tex]

Therefore, the **balance **of the **account **after 40 years will be $44,334.34 (nearest cent).

The table below gives values of a function g at selected values of x. x 0 1 3 7 g(x) 24 35 42 68

Which of the following statements, if true, would be sufficient to conclude that there exists a number c in the interval [0,7] such that g (c) = 50 ? I. g is defined for all in the interval (0,7). II. g is increasing for all in the interval (0,7]. III. g is continuous for all o in the interval 0,7). (A) II only (B) Ill only (C) I and Ill only (D) I, ll and III

g is **continuous **for all x in the interval [0,7] is correct statement that would be **sufficient **to conclude that there exists a number c in the interval [0,7] such that g (c) = 50.

Here the given function g(x) gives values for selected values of x.

Now we are to find a condition which will conclude that there exist a number 'c' in the **interval **[0,7] such that g(c)=50

If a function f : a, b [tex]\rightarrow[/tex] R be **continuous **on R with [tex]$\mathrm{f}(\mathrm{a}) \neq \mathrm{f}(\mathrm{b})$[/tex] then the function f(x) attains every value between f(a) and f(b) at least once in the interval [a, b]

I. The option is false.

Because if the **function** is defined in the interval [0,7] then it is not necessary that there exist a point in this interval, where the function will attain the value 50.

II. The given option is false.

Because if the function is **increasing** in the interval [0,7] then it is not necessary that there exist a point in this interval, where the function will attain the value 50.

III. This option is correct.

Since g(0) = 24 and g(7) = 68 and 'g' is **continuous** on the interval [0,7] , so the function g(x) attains every value between 24 and 68 at least once in the interval [0,7].

That is there must be a point 'c' in the interval [0,7] such that g(c)=50.

Therefore option (B) is correct.

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What is the slop in the equation

-2/3 (the number before x)

can u answerr for me pls

Part A:

The graph of the line intersects the x-axis at the point (4, 0).

Part B:

The point represents the **distance** of Shari from the home.

After 4 minutes, Shari rushed past her house.

What is a graph?A function graph is a visual representation of a relation. A **function** is actually equal to its graph in set theory and current mathematical foundations. For instance, when deciding whether or not a function is onto (surjective), a codomain should be taken into account. The graph of a function alone does not reveal the **codomain**. Although they relate to the same thing, the terms "function" and "graph of a function" communicate different perspectives on it, which is why they are commonly employed.

The line's x-intercept is 4 minutes.

The time Shari will arrive at her house is indicated by the 4 minutes.

Shari's distance from home on her run across town is represented by the line 6x - 3y = 24......... (1), where y stands for blocks, and x for minutes.

Therefore, when y = 0, we obtain 6x - 0 = 24, which equals x = 4, from equation (1) above.

As a result, 4 minutes is the x-intercept of the line (1).

It is stated that Shari will get at her house in 4 minutes, and there are no blocks between them.

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a rectangle in the first and second quadrants of the coordinate plane has its base along the x-axis and two vertices on the parabola defined by y

The area of rectangle with has its **vertices **defined on parabola is 32 square units.

An example of a **quadrilateral **with equal and parallel opposite sides is a rectangle. It is a polygon with four sides and four angles that are each 90 degrees. A rectangle is a shape with only two dimensions.

Square, figure, oblong, parallelogram, plane a.re terms to describe rectangle

Equation of Parabola is y = 12 - x^2 is an even function.

Therefore, its rectangle form also is even at the origin.

We know area of rectangle = length × width

Here,

length = 2x, width = y

Area, A = 2x(12 - x2)

⇒ A = 24x - 2x^3

Take derivative of A with respect to x

⇒ A' = 24 - 6x^2

The area is largest when A' = 0

⇒ 24 - 6x^2 = 0

⇒ x^2 = 4

⇒ x = 2

Put the value of x in y = 12 - x^2

⇒ y = 12 - 4

⇒ y = 8

Area = 2(2)(8) = 32

Therefore, the largest area of a rectangle is 32 square units.

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write an integral that expresses the increase in the perimeter p(s) of a square when its side length s increases from 2 units to 5 units

The **integral** to express the increase in the **perimeter** p(s) of a square when its side length s increases from 2 units to 5 units is:

p(s) = 4s

Integral = ∫2s5s ds

= ∫2s5s dx

= [s2/2]2s5s

= (25/2) - (4/2)

= 20/2

= 10

Therefore, the **increase** in the perimeter of the square when its side **length** s increases from 2 units to 5 units is 10 units.

To calculate this increase, we used the formula for the perimeter of a **square**, which is 4s, and the integral from 2s to 5s, which gives us the area under the graph and the difference between the two **side lengths**. We then solved for the integral and **multiplied** it by 4 to get the increase in the perimeter.

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How to find the missing side Using Pythagoras Theorem?

The legs are the two sides of the triangle that are labeled a and b . The hypotenuse is the longest side of a right triangle and is labeled c . There is a special relationship between the legs of a right triangle and its hypotenuse.

he equations of two lines are given. determine whether the lines are parallel, perpendicular, or neither. y

By definition, **perpendicular** strains are strains intersecting at a proper attitude. The letters T and L are examples of perpendicular strains. By definition, parallel strains are strains at the equal aircraft that in no way **intersect**.

The letters N and Z include pairs of parallel linetwo non-vertical strains which are withinside the equal **aircraft** has the equal slope, then they may be stated to be parallel. Two parallel strains might not ever intersect. If non-vertical strains withinside the equal **aircraft** intersect at a proper attitude then they may be stated to be **perpendicular**.

We can decide from their **equations** whether or not strains are parallel with the aid of using evaluating their slopes. If the slopes are the equal and the **y-intercepts** are different, the strains are parallel. If the slopes are different, the strains aren't parallel. Unlike parallel strains, perpendicular strains do **intersect**.

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Which of the following shows 12 more than a number, written as an algebraic expression?

A. 12-n

B.12+n

C.n-12

D.12n

the answer is d i think, not totally sure

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