ap calculus question, steps and explain please.

The correct description regarding each table is given as follows:

1. Rate of change of 4, linear.

2. Rate of change of -2/3, linear.

3. Rate of change of 1/4, linear.

4. Rate of change of -1, linear.

5. Not linear.

6. Rate of change of 3, linear.

A linear function has the definition presented as follows:

y = mx + b.

In which:

A data-set will only be classified as linear if the rate of change is constant.

Hence the tables in this problem are classified as follows:

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Answer:

Step-by-step explanation:

Find the volume of the metal as following:

Find the mass:

Answer:

3619.1 grams (nearest tenth)

Step-by-step explanation:

Volume of a cylinder

[tex]V=\pi r^2 h[/tex]

where:

The radius of a circle is half its diameter.

Find the volumes of the external and internal cylinders by substituting the given values into the formula for volume of a cylinder:

[tex]\implies \textsf{Volume of the external cylinder}&=\pi \cdot 5^2 \cdot 16=400 \pi \; \sf cm^3[/tex]

[tex]\implies \textsf{Volume of the internal cylinder}&=\pi \cdot 4^2 \cdot 16=256 \pi \; \sf cm^3[/tex]

Find the volume of the cylindrical hollow metal pipe by subtracting the volume of the internal cylinder from the volume of the external cylinder:

[tex]\begin{aligned}\implies \textsf{Volume of the metal pipe}&=\sf Volume_{external}-Volume_{internal}\\&=400 \pi - 256 \pi\\& = 144 \pi \sf \; cm^3\end{aligned}[/tex]

Density formula

[tex]\rho=\dfrac{m}{V}[/tex]

where:

Given:

Substitute the given values of density and the found volume into the density formula and solve for m:

[tex]\begin{aligned}\implies \rho&=\dfrac{m}{V}\\8&=\dfrac{m}{144 \pi}\\m&=8 \cdot 144\pi\\m&=1152 \pi \\m&=3619.11473...\\m&=3619.1\; \sf g \;(nearest\;tenth)\end{aligned}[/tex]

Therefore, the mass of the pipe is 3619.1 grams (nearest tenth).

Note: I have used the exact value of π (not a rounded value).

Answer:

A = 15

B = 3

Step-by-step explanation:

Since Team A has 12 more points than team B, then,

A - 12 = B

A = B + 12 ( equation 1 )

team A has 5 times as many points as team B, so,

5B = A. ( equation 2 )

Substitute equation 1 into equation 2

A = B + 12

5B = B + 12

5B - B = 12

4B = 12

B = 3

we'll substitute the answer into equation 2

5B = A

5(3) = A

A = 15

I hope this helps :D

have a nice day dear...

Answer: Around 10 sixth graders would get free lunch.

Step-by-step explanation: first, divide 500/25 to find the percentage of students receiving free lunches. You should get 0.05, or 5%. Then, multiply the number of sixth graders (203) by 5%. Your answer is 10.15, rounded down to 10. (Because it is impossible to have 0.15 of a student)

The amount of interest would be $8.4 Charis received at the end of two years.

Simple interest is defined as interest paid on the original principal and calculated with the following formula:

S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years. The rate of interest is in percentage r% and is to be written as r/100

We have been given data as:

Principal (P) = $140

Rate of Interest (R) = 3% = 3/100 = 0.03

Time (T) = 2 years

⇒ Simple interest  = P × R × T

Substitute the value of P, R, and T in the above formula,

⇒ Simple interest = 140 × 0.03 × 2

⇒ Simple interest = $8.4

Therefore, the amount of interest would be $8.4 Charis received at the end of two years.

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Answer: 3.5 batches is correct.

Step-by-step explanation: Take 28 and divide that by 8 and that equals 3.5

Hope this helps!

The number of batches of cookies that can be made using 28 ounces of chocolate chips is 3.5 batches.

The correct answer option is option a

Equation:

y = 8x

Where,

If there are 28 ounces of chocolate chips:

y = 8x

28 = 8 × x

28 = 8x

x = 28/8

x = 3.5 batches

So therefore, the

So therefore, 3.5 batches of cookies can be made using 28 ounces of chocolate chips.

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By multiplying 2 on both the numerator and denominator of  [tex]\frac{-3}{5}[/tex] .

The expression [tex]\frac{-3}{5}[/tex] + [tex]\frac{-7}{10}[/tex] with a common denominator can be written as

[tex]\frac{-6}{10}[/tex] + [tex]\frac{-7}{10}[/tex]

A fraction is written with a numerator and a denominator where the numerator is less than the denominator.

Example: 1/3 is a fraction

We have,

[tex]\frac{-3}{5}[/tex] + [tex]\frac{-7}{10}[/tex]

We have different denominators and we need to make the denominator the same.

We will multiply 2 on both the numerator and denominator of  [tex]\frac{-3}{5}[/tex].

= [tex]\frac{2 \times -3}{2 \times 5}[/tex]

= [tex]\frac{-6}{10}[/tex]

We see that,

The denominator in [tex]\frac{-6}{10}[/tex]  and [tex]\frac{-7}{10}[/tex]  is the same.

i.e 10.

Now,

[tex]\frac{-3}{5}[/tex] + [tex]\frac{-7}{10}[/tex] can be written as [tex]\frac{-6}{10}[/tex] + [tex]\frac{-7}{10}[/tex]

Thus,

By multiplying 2 on both the numerator and denominator of  [tex]\frac{-3}{5}[/tex] .

The expression [tex]\frac{-3}{5}[/tex] + [tex]\frac{-7}{10}[/tex] with a common denominator can be written as

[tex]\frac{-6}{10}[/tex] + [tex]\frac{-7}{10}[/tex]

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Answer:

x = 6

Step-by-step explanation:

5x - 9 = 3x + 3 ( subtract 3x from both sides )

2x - 9 = 3 ( add 9 to both sides )

2x = 12 ( divide both sides by 2 )

x = 6

The first number in the range of the function is 7

The range of a function is the set of output values of the graph.

This in other words mean the range of a function is the set of y values of the graph.

The function is given as

f(x) = -2x - 3

Also, we have the domain to be

(-5,-1,3,5)

The first value in this domain is

x = -5

So, we have

f(-5) = -2 x -5 - 3

Evaluate

f(-5) = 7

This represents the first number in the range

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The number of seats in Section A is 26000 ,The number of seats in Section B is 14800 and, The number of seats in Section C is 11200.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.

Let the number of seats in Section A is "a".

Let the number of seats in Section B is "b".

and, Let the number of seats in Section C is "c".

Now using the statement "stadium has 52,000 seats"

we can make equation: a + b + c = 52000  

Now using the statement "Seats sell for $28 in Section A, $24 in Section B, and $20 in Section C" and "stadium takes in$1,307,200 from each sold out event".

we can make equation: 28a + 24b + 20c = $1,307,200

Now using the statement "he number of seats in Section A equals the total number of seats in Sections b and C"

we can make equation: a = b + c

Solving these three equations. We get,

a = 26000 , b = 14800 and c = 11200

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Answer:

A. 3

Step-by-step explanation:

45 + 15 + 25 = 85

There are 85 flowers.

There are 25 roses, 45 tulips, an 15 roses.

What are all 3 of these divisible by?

5!

That means that there will be 5 bouquets.

Let's divide each number by 5 to find out how many of each type of flower is in each bouquet.

25/5 = 5

5 roses in each bouquet

45/5 = 9

9 tulips in each bouquet

15/5 = 3

3 snapdragons in each bouquet

5 + 9 + 3 = 17

There are a total of 17 flowers in each bouquet.

Out of those 17 flowers, 3 are snapdragons.

A. 3

i solved it

you graph it :)

Answer:

Step-by-step explanation:

Use a distributive property.

Distributive property:

A(B+C)=AB+AC

A(B-C)=AB-AC

First, expand by distributive property from multiply the numbers from left to right.

-9j=-9(j-20)

-9(j-20)

-9*j=-9j

9*20=180

=-9j+180

-9j=-9j+180

Add by 9j from both sides.

-9j+9j=-9j+180+9j

Solve.

0=180

No solution.

Therefore, the correct answer is A. no solution.

I hope this helps, let me know if you have any questions.

The simplest radical form of the hypotenuse of the given right-angled triangle is therefore discovered to be [tex]6\sqrt{2}[/tex] units.

The Pythagorean Theorem states that the square on the hypotenuse of a right triangle is equal to the sum of the squares on the triangle's legs.

If the number or algebraic expression under the radical has no factors that are perfect nth powers, then the radical is said to be in its simplest radical form.

The given right angled triangle has sides 6 units each.

We need to determine the hypotenuse using the Pythagorean theorem.

Hypotenuse = [tex]\sqrt{(side 1)^{2} + side 2)^{2} }[/tex]

                      [tex]=\sqrt{6^{2} + 6^{2} } \\\\= \sqrt{72}\\ \\= 6\sqrt{2}[/tex]

Therefore, the hypotenuse of the given right angled triangle is found to be [tex]6\sqrt{2}[/tex]  units which is the simplest radical form.

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price change: 125 - 200 = -75 coins

percent of change = price change/original price *100 = -75/200*100 = -37.5%

that is, a discount of 37.5%

Answer:

1. False, 2. False, 3. False

Step-by-step explanation:

The rate of change in enrollment from 2010 to 2020 is -53 students per year.

Interpretation:

A negative rate of change (-53 students per year) means that the enrollment in the school decreased over the 10-year period from 2010 to 2020. On average, the school lost 53 students per year during this time frame. This decline in enrollment may have implications for the school's resources, budget, and programs, as it indicates a reduction in the student population over the given period.

Here, we have,

To find the rate of change in enrollment from 2010 to 2020, we can use the formula for calculating the rate of change:

Rate of change = (Change in enrollment) / (Time interval)

Where:

Change in enrollment = Enrollment in 2020 - Enrollment in 2010

Time interval = Year in 2020 - Year in 2010

Let's calculate the rate of change:

Change in enrollment = 715 - 1245 = -530

Time interval = 2020 - 2010 = 10 years

Rate of change = (-530) / 10 = -53

The rate of change in enrollment from 2010 to 2020 is -53 students per year.

Interpretation:

A negative rate of change (-53 students per year) means that the enrollment in the school decreased over the 10-year period from 2010 to 2020. On average, the school lost 53 students per year during this time frame. This decline in enrollment may have implications for the school's resources, budget, and programs, as it indicates a reduction in the student population over the given period.

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Answer:

x^3

Step-by-step explanation:

Because they are the same base in a division question, you subtract the exponents.

5-2=3.

Answer = x^3

Hope this helps!

Btw, if this is right, please give me brainliest, thanks!

Answer:

x^3

Cancel the common factor of x^5 and x^2.

Hope you have a wonderful day :)

Answer:

Option F

Step-by-step explanation:

According to given information

1) You had F fruits and took 4 pieces out of a bag, it is:

2) Then you have 12 pieces of fruit remained:

This equation matches the answer choice F.

Answer:

1000-0=1/2(2000-0)

y= 1/2x

-1x + 2y = 0

The formula for the volume of a sphere is 4/3πr³. The formula for r is d/2. We know d, so we can substitute this for r.

4/3(3.14)(32/2)^3
4/3(3.14)(16)^3
4/3(3.14)4096
4.19(4096
17612.24 cm^3

[tex]\huge\boxed{\sf 17157.28} \\\\\\\displaystyle \sf Converting\ the\ diameter\ to\ radius\\\\r=\frac{d}{2} =\frac{32}{2} =16\\\\Finding\ the\ volume \\\\V=\frac{4}{3} \pi r^{3}=\frac{4}{3} \pi \times 16^{3} \approx 17157.28 \\\\[/tex]

Answer:

x = 3

Step-by-step explanation:

[tex]{ \rm{5x + 2 = 7x - 4}}[/tex]

- First, using equality order by collecting like terms of x together and constants together;

[tex]{ \rm{(5x + 2) { \green{- 2}} + = (7x- 4){ \green{ - 2}}}} \\ { \rm{5x = 7x - 6}}[/tex]

[tex]{ \rm{5x - { \blue{7x}} = (7x - 6) - { \blue{7x}}}} \\ { \rm{ - 2x = - 6}}[/tex]

- Using division property of equality, by dividing -2 on both sides;

[tex]{ \rm{ \frac{ - 2x}{ \orange{ - 2}} } = \frac{ - 6}{ \orange{ - 2}} } \\ \\ { \rm{x = 3}}[/tex]

[tex]{ \boxed{ \red{ \delta}}}{ \underline{ \mathfrak{ \: \: creed}}}[/tex]

Answer:

Step-by-step explanation:

What’s x??

Solve for x

5x+2=7x-4

2 + 4 = 7x - 5x

6 = 2x

x = 6 : 2

x = 3

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

check

5 * 3 + 2 = 7 * 3 - 4

17 = 17

Answer:

x = 10

Step-by-step explanation:

The internal angles of a triangle sum 180°

74° + 45°+ (8x-19)° = 180°

119 + 8x - 19 = 180

119 - 19 + 8x = 180

100 + 8x = 180

8x = 180 - 100

8x = 80

x = 80/8

x = 10

Check:

74 + 45 + (8x-19) = 180

1100 + 8*10 = 180

100 + 80 = 180

The solution of the equation 4 = 13 – 3x is x = 3 which is the correct answer would be an option (B).

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

We have been given an equation as

4 = 13 – 3x

Rearrange the terms non-variables and variables,

3x = 13 - 4

Apply the subtraction operation,

3x = 9

x = 9/3

Apply the division operation, and we get

x = 3

Therefore, the correct answer would be an option (B).

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Answer: 9, 144, 225, 10,000

Step-by-step explanation:

9=3x3

144=12x12

225=15x15

10,000=100x100

Answer:

x = 1 ± √3

Step-by-step explanation:

    x² - 2x - 2

Co-efficient of x² = a = 1

Co-efficient of x = b = -2

Constant = c = -2

 D = b² - 4ac

     = (-2)² - 4 *1*(-2)

     = 4 + 8

     = 12

       [tex]\sf x = \dfrac{-b \ \± \sqrt{D}}{2a}[/tex]

           [tex]\sf = \dfrac{2 \ \± \sqrt{12}}{2*1}\\\\\\=\dfrac{2 \± \sqrt{2*2*3}}{2}\\\\\\= \dfrac{2 \±2\sqrt{3}}{2}\\\\\\= \dfrac{2}{2} \± \dfrac{2\sqrt{3}}{2}\\\\\\= 1 \± \sqrt{3}[/tex]

[tex]\sf x = 1 + \sqrt{3} ; \ ; or \ x = 1 - \sqrt{3}[/tex]

We have in total 432 students.

8.

We know that 23% of the students want to be a teacher, this means that:

99 students want to be a teacher.

9.

We know that 13% of the students want to be doctor or nurses, this means that 26% of them want to be one of those, then:

112 students want to be doctor or nurses.

10.

Since 9% of the students want to be lawyers, this means that 91% of them did not want to be lawyers, then:

393 students does not want to be lawyers.

Answer:

393 students do not want to be lawyers.

Step-by-step explanation:

The relation that represents a function is the mapping in: B.

A relation is defined as a function if each of the x-value (domain element of input) in the relation corresponds to exactly one y-value (range element of output).

The relation in option A is not a function because it has two different y-values, 7 and 5 that corresponds to an x-value, 6. The relations in option C and D do not represent a function also.

The mapping in option B shows a relation where each x-value (domain element) is related or corresponds to only one y-value (range element). Therefore, it is a function.

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Answer:

x=4

Step-by-step explanation:

first, you have to add all of the sides up:

x+2x+x+3x+7+5x-4=12x+7-4=12x+3

12x+3=51. now, we can subtract 3 from both sides, so that we can isolate x.

     -3  -3

12x=48

x=4