Which interval has the most students?

0-4
5-9
10-14
15-19

Answer:

[tex]\displaystyle f(x)=-\frac{1}{24}\left(x-12\right)^2+6[/tex]

Where f(x) models the height, in inches, of the frog's leap after it had leapt x inches.

Step-by-step explanation:

We are given that a frog leaps two feet, with the highest point in the jump being six inches.

Assuming the frog starts at (0,0), we want to find a quadratic function in vertex form for the path of the jump.

First, we will convert the length of the jump to inches. Two feet is equivalent to 24 inches.

Next, since the frog started at (0, 0), in order to jump a length of 24 inches, it must have ended at (0, 24). These two points will also be our two roots: x = 0 and x = 24. We can use the factored form of a quadratic:

[tex]f(x)=a(x-p)(x-q)[/tex]

Where p and q are the roots.

Substitute in the roots:

[tex]f(x)=a(x-0)(x-24)=ax(x-24)[/tex]

Now, since the frog reached a maximum height of six inches, the y-coordinate of the function at its vertex point is 6.

Since a parabola is symmetrical along its axis of symmetry, the axis of symmetry is always halfway between the two roots.

Therefore, the x-coordinate of our vertex is:

[tex]\displaystyle x=\frac{24-0}{2}=12[/tex]

So, when x = 12, f(x) = 6. Substitute:

[tex]6=a(12)(12-24)[/tex]

Solve for a:

[tex]\displaystyle- 144a=6\Rightarrow a=-\frac{1}{24}[/tex]

Therefore, our function is:

[tex]\displaystyle f(x)=-\frac{1}{24}x(x-24)[/tex]

Now, we can place this into vertex form:

[tex]\displaystyle f(x)=a(x-h)^2+k[/tex]

Where a is the leading coefficient and (h, k) is the vertex.

Our leading coefficient is -1/24, and the vertex is (12, 6). Hence, our function is:

[tex]\displaystyle f(x)=-\frac{1}{24}\left(x-12\right)^2+6[/tex]

Where f(x) models the height, in inches, of the frog's leap after it had leapt x inches.

Answer:

B

Step-by-step explanation:

I put A and got it wrong. The correct answer is B.

The function has a range of f(x) ≤ 3/4 is f(x) = -x² + 3/4.

An function is an expression that shows the relationship between two or more numbers and variables.

The range of a function is the set of all output variables.

From the graph plotted;

The function has a range of f(x) ≤ 3/4 is f(x) = -x² + 3/4.

Find out more on equation at: https://brainly.com/question/2972832

Answer:

Yes this is a function.

Step-by-step explanation:

This graph is a function because it passes the vertical line test. The vertical line test ensures that no x value has more than one y value. You can take a pencil, hold it vertically, and move it horizontally across your paper to test whether or not the graph contains multiple y values for a single x value. If it passes this test, then the graph is indeed a function.

Answer: Answer: C. 3.2 × 10^4

Step-by-step explanation: for this case the multiplication of the values with exponent are summed, as the exponent are the 6 and -3

6 - 3 = 3

this will be the exponent of the common value which is the 10.

after you only need to multiply 8 and 4 by separate the

8 * 4 = 32.

then we only need to place the values one by one

32 × 10^3

3 is the result of the sum of the exponent.

10 is the common value.

32 is the result of the product.

if we add another zero to the multiplication we get 3.2 and exponent finish with one more zero, then we get this result

3.2 × 10^4

because of that the C is the correct answer, keep in mind that the other answers do not apply correctly the rule of the exponent, because the rest of answer give us wrong answer with final result of the exponent.

Answer:

[tex]\frac{7}{22}[/tex], the total sum of the money is    

Step-by-step explanation:

1- [tex]\frac{5}{11}[/tex]= [tex]\frac{6}{11}[/tex]

[tex]\frac{6}{11}[/tex]*[tex]\frac{7}{12}[/tex]= [tex]\frac{7}{22}[/tex]

x* [tex]\frac{7}{22}[/tex]= 4500

4500/[tex]\frac{7}{22}[/tex]= about 14142.85

this is what I got out.

Answer:

20in

Step-by-step explanation:

To find the rate of which they are similar all you have to do is divide 10 by 4 or 15 by 6 to get a rate of 2.5 then multiply that rate by 8 to find your answer

Answer:

1/2

Step-by-step explanation:

Answer:

rectangular prism

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Answer:

b 15.6 would be correct

Step-by-step explanation:

Answer:

They would have to multiply 2.5in and 8 ft because the ratio is 1in:8ft and the inches go up and you have to keep the ratio at the same value so you multiply 2.5 and 8

Step-by-step explanation:

Answer:

the area of the figure below is 56mm

Answer:

88 mm 2

Step-by-step explanation:

The small top recatngle has an area of 16 and the large bottom one has an area of 72. Add them together and you get 88 mm 2.

Answer:

1. 454

2. 96

Step-by-step explanation:

1. To find The surface area, find the are of each side. The bases of the triangular prism have the same surface area,

Surface area of triangle: 1/2b*h, half of the base times the height. base = 8, height = 10, 1/2(8) * 10 = 4*10 = 40, the other side has the same area, so double it to get 80.

The surface area of one of the rectangle is 11*14, another is 12*11, and the last is 11*8, multiply all to get 154, 132, and 88, and 154 + 132 + 88 + 80 = 454

2. The two triangles is 1/2b * h, b = 6, h = 2, 1/2(6) * 2 = 3*2 = 6, double it because there is another triangle to get 12

The three rectangles are 3*7 + 3*7 + 6*7 = 21 + 21 + 42 = 84, 84 + 12 = 96

m is independent variable and p is dependent variable.

Because number of pair of shoes depend on the number of miles run by her.

Answer: Bears: 1.80 Saints: 1.40

Step-by-step explanation: Hope this helps!!

Answer:

i think that every time she rolls the dice, she is further away from the gym

Step-by-step explanation:

Answer:

Hello Love!

All range is in math Is the highest number subtracted by the smallest number so our equation is 15 - 0 = 15

so 15 is our range!

Answer: 3/7

Step-by-step explanation:

im not sure but i thinks its 3/7

Answer:

12+12=24x3

Step-by-step explanation:

Answer:

16π

Step-by-step explanation:

ooohhhh, that makes so much more sense, I wasn't actually supposed to substitute 3.14 for π, whoops, sorry

Answer:

C, 8.5

Step-by-step explanation:

The area of a rectangular prism is Length times Width times Height. If the volume of the tank (which is a rectangular prism) is 1360, then the L x W x H is 1360. The area of the base of the tank is determined by multiplying the Length and the Width together, so that means that L x W = 160.

Our first equation

L x W x H = 1360

Our second equation

L x W = 160

We see that 1360 divided by 160 gets us the height of the prism.

1360 / 160 = 8.5, so the answer is C

Answer:

952 l

Step-by-step explanation:

Answer:

= 50% decrease

Step-by-step explanation:

There is a percentage decrease of 50% in the number of people from 72 people to 36 people

An equation is an expression used to show the relationship between two or more numbers and variables.

There is a change of 72 people to 36 people, hence:

Percentage change = [(36 - 72) / 72] * 100% = -50%

There is a percentage decrease of 50% in the number of people from 72 people to 36 people

Find out more on equation at: https://brainly.com/question/2972832