Students at a school were able to choose whether they wanted to take a sports class for physical education
of a dance class. The 274 students who chose sports class represented 38 less than two times the number
of students who chose dance class. How many students chose dance class?

The total volume of the air space of spherical ball is A = 12.265625 inches³

Given data ,

Since each tennis ball has a diameter of 2.5 inches, the radius of each ball is 1.25 inches.

The air space around the balls can be thought of as a cylinder with a height equal to the diameter of one ball and a radius equal to the radius of one ball.

The height of the cylinder is 2.5 inches, and the radius is 1.25 inches.

The formula for the volume of a cylinder is:

V = πr²h

V = ( 3.14 ) ( 1.25 )² ( 7.5 )

V = 36.796875 inches³

where V is the volume, r is the radius, and h is the height.

So, the volume of the one ball is:

V₁ = ( 4/3 )π(1.25)³

V₁ = 8.177083 inches³

The total volume of three balls is = volume of 3 spherical balls

V₂ = 3V₁ = 3(8.177083) ≈ 24.53125 cubic inches

Therefore, the total volume of the air space around the three tennis balls is approximately A = 36.796875 inches³ - 24.53125 inches³

A = 12.265625 inches³

Hence , the volume of air space is A = 12.265625 inches³

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The corresponding areas under the curves for y = 2x-x² in the interval [1, 2] and y = x³-6x²+8x in the interval [0, 4] are 2/3 unit² and 0 unit²

Given:

1. y = 2x-x² in the interval [1, 2]

2. y = x³-6x²+8x in the interval [0, 4]

In order to find  the area under the curve for these functions for the given intervals, we will take the integral of the functions and use the intervals as upper and lower limits: Thus:

y = 2x-x² in the interval [1, 2]  will be:

\(\int\limits^2_1 {2x-x^{2} } \, dx = \left[\frac{ 2x^2}{2}-\frac{ x^3}{3}\right]_1^2\)

                   \(= \left[x^{2} -\frac{ x^3}{3}\right]_1^2\)

Substitute the value of the upper and lower limits into x:

               =  [2²- 2³/3] - [1²- 1³/3]

              =   [4 - 8/3] - [ 1 - 1/3]

              =   [4/3] - [2/3]

              = 2/3 unit²

y = x³-6x²+8x in the interval [0, 4] will be:

 \(\int\limits^4_0 {x^{3} -6x^{2} + 8x } \, dx = \left[\frac{ x^4}{4}-\frac{ 6x^3}{3}+\frac{ 8x^2}{2}\right]_0^4\)

                               \(= \left[\frac{ x^4}{4}- 2x^3+4x^2\right]_0^4\)

                              = [4⁴/4 - 2(4)³ + 4(4)²] - [0⁴/4 - 2(0)³ + 4(0)²]

                              =  [ 64 - 128 + 64] - [0 - 0 -0]

                              = 0 unit²

Therefore, the areas under the curves y = 2x-x² in the interval [1, 2]

and y = x³-6x²+8x in the interval [0, 4] are 2/3 unit² and 0 unit² respectively

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Answer:

do you got an answer key

Step-by-step explanation:

Your Answer is 4 Yards

Step-by-step explanation:

2/3 yards is 2 feet

2 yards is 6 feet

2 times 6 feet is 12 foot e.g. (2 x 6 =  12)

12 feet is 4 yards.

Formula (L x W = A)

L = length

W = Width

A = Area

Hope this helps! Please let me know if you need more help or think my answer is incorrect. Brainliest would be MUCH appreciated. Have a wonderful day!

Given -

s(d) = d³ + 9

To Find -

What is the maximum number of sales per day on the interval 0 < d ≤ 3 =?

Step-by-Step Explanation -

We are given that the function s(d) = d³ + 9

Lies between 0 < d ≤ 3.

So, the maximum number of sales per day is at d = 3

Putting d = 3 in s(d) = d³ + 9

s(d) = (3)³ + 9

s(d) = 27 + 9

s(d) = 36

Final Answer -

The maximum number of sales per day = 36

Answer:

the distributive property to simplify 5(2x+3)=10x+15

The x-intercepts and y-intercepts of the graph are x = 5 and y = 2

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

The graph

The x-intercepts are when y = 0

In this case, it is

x = 5

The y-intercepts are when x = 0

In this case, it is

y = 2

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Answer:

Three non-collinear points determine a plane.

Step-by-step explanation:

This statement means that if you have three points not on one line, then only one specific plane can go through those points. The plane is determined by the three points because the points show you exactly where the plane is

The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).

In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.

Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.

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The algebraic property illustrated is the commutative property of multiplication

The properties of algebra are those properties mostly used in simplifying algebraic expressions.

Algebraic properties are:

From the expression given we have

4/5 • 5/4 = 1

= 4/ 5 × 5/ 4

= 1

Thus, the algebraic property illustrated is the commutative property of multiplication

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Answer:

$400

Step-by-step explanation:

80% = 80/100 = 8/10 = 0.8

0.8(500)=400

For number one A we need to multiply 5x5 because exponents make you multiply the base number by the exponent the ammount of times the exponest value is. This would give is 25-6 which equals 19

number 1 B we need to add the 8 and the 3 to give us eleven over five. thats the simplest answer to this question

2a we need to multiply the 5 into the parenthesis

then we add. The answer would be 28

for 2b the answer would be 9 2/9

ill let you solve the rest. hope this helped. dont forget to leave a heart give it 5 stars and make it the brainliest answer!!

Answer:

Step-by-step explanation:

50:100 and 1:2

15:20 and 3:4

15:16 and 5:2

10:5 and 2:1

Hope this helps!

The answer is false.

Answer:

false

Step-by-step explanation:

There was outbreak of illness caused by the bacteria called E. coli

In June 2015, 2631 people fell sick and while 70

The percentage of those who got sick and also died will be

Hence, the percentage of those who got sick and also died is 2.7% (nearest tenth)

Answer:

6.)66 degrees

7.)20 degrees

Step-by-step explanation:

Angle 114 and angle 3 are supplementary, meaning that they can be added to get 180 degrees

If you subtract 114 from 180 you get 66 degrees

Angle D and Angle C are both complimentary, meaning that if you add them together you get 90 degrees

If you subtract 70 from 90 you get 20

Answer:

3rd option: 32/24

Step-by-step explanation:

8/6 = 4/3

1st option: Now let's change the denominator to 24:

4/3 ==> ?/24

4/3 =

4*8 / 3*8 = 32/24, not 3/24.

2nd option: Now let's change the numerator to 24:

4/3 ==> 24/?

4/3 =

4*6 / 3*6 = 24/18, not 24/32

24/32 = 3/4, not 4/3 ==> don't get confused by this

3rd option: 32/24 is correct [Look at the explanation for 1st option]

4/3 ==> ?/24

4/3 =

4*8 / 3*8 = 32/24, not 3/24.

Hence, the 3rd option is correct.

Answer:

Step-by-step explanation:

Answer:

For month 1, the current balance is $2750.00, the interest is $45.38, and the payment is $75.00. The amount applied to principal is $29.62.

For the remaining months, the interest and payment amount will stay the same, but the current balance and amount applied to principal will change based on the previous month's numbers.

Point of view:

Here's your answer but I prefer you to focus and study hard because school isn't that easy. But i'm glad I could help you!

:)

The solution to the linear inequality written in set-builder notation is {m | m ∈ R and m ≥ 12 or m ≤ 9}

From the question, we are to solve the given linear inequality.

The given linear inequality is

-3 + m ≥ 9 OR 1 + 2m ≤ 19

Solving -3 + m ≥ 9

-3 + m ≥ 9

Add 3 to both sides of the equation

-3 + 3 + m ≥ 9 + 3

m ≥ 12

Solving 1 + 2m ≤ 19

1 + 2m ≤ 19

Subtract 1 from both sides of the equation

1 - 1 + 2m ≤ 19 - 1

2m ≤ 18

Divide both sides by 2

2m/2 ≤ 18/2

m ≤ 9

Thus,

m ≥ 12 OR m ≤ 9

In set-builder notation

{m | m ∈ R and m ≥ 12 or m ≤ 9}

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Question 1:

Sandy had an exam and answered 216 questions correctly. There were 300 questions. What is her score?

Answer:

\(\frac{216}{300}\) x 100% = 72%

Question 2:

Tommy's phone can only last 5 hours when it's fully charged. One day, he used his phone for 1 hour 24 minutes. Assuming that his phone's battery drains linearly against usage time, what is the percentage of the phone's battery left?

Answer:

Phone usage time = 1 hour + 24minutes

By converting 24 minutes to hour, we have 0.4 hours

Therefore total phone usage time is 1 + 0.4 hours = 1.4 hours

Percentage of hours used = \(\frac{1.4}{5}\) x 100% = 28%

Since he used 28%, his phone's battery should have 72%.

We can calculate it by 100% - 20% = 72%

Part a

Remember that

The equation of a circle in center radius form is equal to

Let

A, B , and C the three towers

A(0,0)

B(0,5)

C(6,3)

For each tower, we have to draw a circle with ra adius r= 3km

the equations of each circle is

A ----> x^2+y^2=9

B ---> x^2+(y-5)^2=9

C ---> (x-6)^2+(y-3)^2=9

using a graphing tool

see the figure below

please give me a minute to draw the figure

Answer:

Area of rectangle= l*b= 180

Area of triangle= 1/2 *b*h=30

Area of the complete figure= 210

Step-by-step explanation:

The value of the fraction 24(1/2 + 2/7) divided by 1 4/8 will be 16 3 / 7.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

The value of the fraction 24(1/2 + 2/7) divided by 1 4/8 will be:

= 24(1/2 + 2/7) ÷ 1 4/8:

= 24 9/14 ÷ 1 1/2

= 345 / 14 × 2/3

= 690 / 42

= 16 3 / 7

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Complete question

24(1/2 + 2/7) divided by 1 4/8 will be:

Answer:

0.53 x 10^ -8

Step-by-step explanation:

Just move the decimal over to the right and add 1 to the exponent.

Answer:

(1.5, 0.5)

Step-by-step explanation:

(5, 3) and (-2, -2)

5 - 2 / 2 = 1.5

-2 + 3 / 2 = 0.5