5. Brandon and Chloe ride their bikes for 4 hours along a flat, straight road. Brandon’s velocity, in miles per
hour, at time t hours is given by a differentiable function B for 0 st 54. Values of B(t) for selected times t
are given in the table above. Chloe's velocity, in miles per hour, at time t hours is given by the piecewise
function C defined by
C(t)
tep
for 0 12 – 3t – 12 for 2 <154.
(a) How many miles did Chloe travel from time t = 0 to time t = 2 ?
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Step 1

Find the area of the Square in the middle

Formula for finding square:

[tex]A = L*W[/tex]

Let's apply the formula and find our answer:

[tex]A = 2*2\\=4[/tex]

The area of the square is 4 units

Step 2

Find the area of all 4 triangles around the square

As you know, the formula for finding 1 triangle is as follows:

[tex]A = \frac{1}{2} *B*H[/tex]

But, to find the area of 2 triangles, we can use this formula:

[tex]A=B*H[/tex]

And to find 4 of them (with same dimensions;as required here), we can use this one:

[tex]A=2*B*H[/tex]

Let's apply the formula then! What are we waiting for!!!!

[tex]A=2*2*2\\=2*4\\=8[/tex]

The area of ALL of the triangles around the square is 8 units

Step 3

Add all areas to find FINAL ANSWER!

Easy!

4+8=12

Answer:

12 is the answer because 2 x 2 = 4 but since it is a triangular face we half it and end up with 2, 2 x 4 is 8, the square it 2 x 2 = 4 so we add 4 and 8 which equals 12  

Answer

North of the box plot speed over 72 is the answer because it is a very high speed of the chart and it shows that the its going over the average speed

Step-by-step explanation:

here you go best of luck on this

Answer:

31.25 k

Step-by-step explanation:

80 %   *  x = 25 k

.80  x    = 25 k

x   = 25 k / .80 = 31.25 k

Answer:

  125k

Step-by-step explanation:

You want to know Ola's daily allowance if 25k remained after 80% was spent.

The fraction remaining was 100% -80% = 20%. If that fraction of Ola's allowance (a) is 25k, we have ...

  0.20a = 25k

Dividing by 0.20, the value of 'a' is shown to be ...

  a = 25k/0.20 = 125k

Ola's total daily allowance was 125k.

Using the percentage concept, it is found that 1 serving of walnuts provides 10% of daily calories.

The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:

[tex]P = \frac{a}{b} \times 100\%[/tex]

In this problem, one serving has 21 grams, each with 10 calories, hence the number of calories is given by:

C = 21 x 10 = 210 calories.

Hence, out of a 2,100 calorie diet, the percentage is given by:

[tex]P = \frac{210}{2100} \times 100\% = 10\%[/tex]

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The model for representing the ratio of the number of orange and green rolls are [tex]\dfrac{3}{2}[/tex]

A model that shows the number of orange and green streamers needed to decorate 3 dorm rooms will be 3O=2G

The ratio is defined as the representation of the one number with respect to the other number. or one number is how many times to the other number.

A model that represents the ratio of different colored streamers.

[tex]\dfrac{3}{2}=\dfrac{O}{G}{[/tex]

A model that shows the number of orange and green streamers needed to decorate 3 dorm rooms.

3O=2G

Hence the models are     [tex]\dfrac{3}{2}=\dfrac{O}{G}{[/tex]   and    3O=2G

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Answer:

So looking at the expression that was given to us, we know that we must solve for g.  In order to solve for g we need to make sure that g is alone on one side of the expression.  In this example, we need to multiply both sides by 4 to get rid of the fraction on the left and in effect we would multiply 12 by 4 also.

[tex]\frac{g}{4} > 12[/tex]

[tex]\frac{g}{4}*4 > 12*4[/tex]

[tex]g > 48[/tex]

Therefore, our final answer is [tex]g > 48[/tex]

Hope this helps!  Let me know if you have any questions

Answer:

g > 48

Step-by-step explanation:

g/4 > 12

g > 12*4

g > 48

Answer:

-9.25

Step-by-step explanation:

Answer: Heyaa! ~

Your Exact Answer is... - 37/4 but your Decimal form is -9.25

Step-by-step explanation:

Convert the mixed numbers to improper fractions, then find the LCD and combine.

Hopefully this helps you!

-Matthew ~

The tower is 260 feet away from the fire.

The height of the tower is the opposite side while the distance from the tower to the fire is the adjacent side.

Given:

Angle of depression = 30°.

Opposite side = 150 feet.

Now,

tan [tex]\thtea\\[/tex][tex]\theta[/tex]= P/B

tan 30 [tex]\thtea\\[/tex]= 150/B

1/√3= 150/B

B=  150*√3

B= 150*1.732

B= 259.8

B= 260 feet.

Hence, the tower is 260 feet away from the fire.

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Answer:

x = 45

p = 18

Step-by-step explanation:

Answer:

  30√3 ≈ 51.96 miles

Step-by-step explanation:

The distance between the two ships can be found using the Law of Cosines, or using your knowledge of the side relationships in special triangles.

__

Each ship is traveling at 10 mph, so after 3 hours will have traveled 30 miles.

The triangle OS1S2 formed by the harbor and the two ship locations is an isosceles triangle with base angles of 30°. Each half of OS1S2 is a 30-60-90 triangle whose longer leg is √3 times half the hypotenuse. The sum of those two "longer legs" is the distance between the ships.

The distance between ships is 2×15√3 = 30√3 ≈ 51.96 miles.

_____

Additional comment

If you prefer to use the Law of Cosines, you are looking for the length of the side opposite the 120° angle in a triangle with sides of 30 miles.

  c² = 30² +30² -2·30·30·cos(120°) = 30²(2-2·(-0.5)) = 3·30²

  c = 30√3 . . . . . take the square root (miles)

Answer:

Kayla , why do you find the question tricky?  :/

Step-by-step explanation:

HP total = 3*3/4 +  5*1/4  + 6*3_1/3  + 8* 1/2

HP total = 9/4 + 5/4 + 18_6/3 + 8/2

HP total = 9/4 + 5/4 + 60/3 + 16/4

HP total = 27/12 + 15/12 + 240/12 +48/12

HP total = 330/12

HP total = 165/6

HP total = 55/2

HP total = 27_1/2

Answer:

27.5 HP

Step-by-step explanation:

Sum

Answer:

the pattern is going in the form of 1³ , 2³ , 3³ , 4³

therefore next term should be 5³ which is equal to 125. So the missing term is 125

I hope you got that.

By : Modern Einstein

Answer:

see explanation

Step-by-step explanation:

the arc length of a circle is calculated as

arc = circumference of circle × fraction of circle

(5)

circumference (C) is calculated as

C = 2πr ( r is the radius )

here diameter = 12 , then r = 12 ÷ 2 = 6

C = 2π × 6 = 12π ≈ 37.7 m ( to the nearest tenth )

(6)

JK = 2πr × [tex]\frac{75}{360}[/tex]

    = 2π × 7 × [tex]\frac{5}{24}[/tex]

    = 14π × [tex]\frac{5}{24}[/tex]

    = [tex]\frac{14\pi (5)}{24}[/tex] ≈ 9.2 in ( to the nearest tenth )

(7)

7.5 = 2πr × [tex]\frac{120}{360}[/tex]

7.5 = 2πr × [tex]\frac{1}{3}[/tex] ( multiply both sides by 3 to clear the fraction )

22.5 = 2πr ( divide both sides by 2π )

r = [tex]\frac{22.5}{2\pi }[/tex] ≈ 3.6 ft

When observing a performance or movement pattern, you should break down the complex skills into component parts.

Complex skills are skills that are composed of many parts. This makes it difficult  to engage in these sort of skills without a rigorous training.

Thus, when observing a performance or movement pattern, you should break down the complex skills into component parts.

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Answer: \sqrt[4]{xy^{2} }

Step-by-step explanation: Siplified

The cubic regression function of the points (1,-1), (2,-13), (3,-45), (-1,11) is y = -2x³ + 2x² - 4x + 3

The points are given as:

(x,y) = (1,-1), (2,-13), (3,-45), (-1,11)

A cubic regression function is represented as:

y = ax³ + bx² + cx + d

Next, we determine the cubic function using a graphing calculator.

From the graphing calculator, we have the following coefficients:

Recall that:

y = ax³ + bx² + cx + d

So, we have:

y = -2x³ + 2x² - 4x + 3

Hence, the cubic regression function of the points is y = -2x³ + 2x² - 4x + 3

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Answer:

0.26 because the question states it. 0.262 can't be rounded up to 27 because 2 isn't high enough so it stays as 0.26

Answer: -5

Step-by-step explanation:

2(0)-5

0-5 = -5

Answer:

44 inches

Step-by-step explanation:

perimeter of triangle = length of side 1 + length of side 2 + length of side 3

length of side 1 = 26

length of side 2 = 55

125 = 26 + 55 + length of side 3 = 81 + length of side 3

subtract 81 from both sides to get the length of side 3

length of side 3 = 44 inches

New price = 90 dollars

25% of 120 = 30

Price is reduced 25% from 120 so,

120 - 30 = 90

Amount of discount = 30

The person must leave the money in the bank for about 10.1 years at interest 4.25% to reach $11200 when compounded annually.

Compound interest is when interest is added to the principal of an investment, allowing the interest to compound over time. In other words, the beginning principal as well as the total interest from prior periods are both used to compute interest. In contrast to simple interest, which only affects the initial capital, this causes the investment to expand exponentially over time. Often utilised in banking and investment, compound interest is sometimes defined in terms of a yearly interest rate and the frequency with which it is compounded.

Given that, bank pays 4.25% interest compounded annually on the invested amount.

The compound interest is given as:

[tex]A = P(1 + r/n)^{(n*t)}[/tex]

Substituting the values of P = $5500, r = 4.25% = 0.0425, A = $11200, and n = 1.

[tex]11200 = $5500(1 + 0.0425/1)^{(1*t)}\\t = log(11200/5500)/log(1.0425) = 10.1 years[/tex]

Hence, the person must leave the money in the bank for about 10.1 years to reach $11200.

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Answer:

+ 5, - 5

Step-by-step explanation:

p^2 - 8 = 17

p^2 = 17 + 8

p^2 = 25

      = 5 x 5

p^2 = 5^2

p = ± 5

Answer:

Hamburgers and Tacos.

Step-by-step explanation:

If you divide 6 by 3 you get 2, and if you divide 9 by 3 you get 3.

2:3

The amount of the profit at x = -2 can not be determined because the number of the shirt can not be negative. Then the amount of the profit at x = 12 is $ 2 and at x = 17.5 is $ 35.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

A company manufactures and sells shirts.

The daily profit the company makes depends on how many shirts they sell.

The profit, in dollars, when the company sells x shirts can be found using the function f(x) = 6x − 70.

Find and interpret the given function values and determine an appropriate domain for the function.

Then at x = −2, then the profit will be

For this condition, the amount of the profit can not be determined because the number of the shirt can not be negative.

Then at x = 12, then the profit will be

f(12) = 6 × 12 − 70

f(12) = 72 − 70

f(12) = $ 2

Then at x = 17.5, then the profit will be

f(17.5) = 6 × 17.5 − 70

f(17.5) = 105− 70

f(17.5) = $ 35

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The required area of the sculpture that is shaped like a circle is [tex]78.5m^2[/tex].

Given that,

Jessie designed a sculpture that is shaped like a circle,

The circumference of the sculpture is 10π meters.

We have to determine,

Which measurement is closest to the area of the sculpture in square meters.

According to the question,

Circumference of the circle = [tex]2\pi r[/tex]

Where, circumference = [tex]10\pi[/tex]

Then,

[tex]10\pi =2\pi r[/tex]

[tex]r=\frac{10\pi }{2\pi }[/tex]

[tex]r=5m[/tex]

Therefore,

Jessie designed a sculpture that is shaped like a circle.

Area of the circle = [tex]\pi r^2[/tex]

Where, r = 5m

Then,

Area of the circle is given by,

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

[tex]=78.5m^2[/tex]

Hence, The required area of the sculpture that is shaped like a circle is [tex]78.5m^2[/tex].

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