Two kids at a summer camp, Amelia and Jennifer, are competing in a potato sack race. Amelia is younger, so she is given a head start of 3 yards. When the race starts, Amelia hops at a rate of 3 yards per second, and Jennifer hops 4 yards per second. Eventually, Jennifer will overtake Amelia. How far will Jennifer have to hop? How long will that take?

[tex]\\ \sf\longmapsto \dfrac{5}{12}[/tex]

[tex]\\ \sf\longmapsto 0.4166[/tex]

[tex]\\ \sf\longmapsto 0.417[/tex]

[tex]\\ \sf\longmapsto 0.42[/tex]

Step-by-step explanation:

0.417 round to the nearest hundredth

Answer:

[tex]A=\pi(336)[/tex]

[tex]A=1055.575[/tex]

Step-by-step explanation:

1. Approach

One is given a prism. The base of the prism is a quarter of a circle, the prism's length is also given. The easiest method to find the volume of the prism is to find the area of the quarter of the circle, then multiply the result by the length of the prism.

2. Find the area of the quarter circle

The following formula can be used to find the area of a circle,

[tex]A_c=(\pi)(r^2)[/tex]

Since one is trying to find the area of a quarter of a circle, one must multiply this formula by ([tex]\frac{1}{4}[/tex]). Please note that the parameter (r) represents the radius of the circle or the distance from the center of the circle to the circumference or outer edge of the circle. The parameter ([tex]\pi[/tex]) represents the number ([tex]3.1415...[/tex]).

[tex]A_c=\frac{1}{4}(\pi)(r^2)[/tex]

Substitute the given values into the formula and simplify to evaluate,

[tex]A_c=\frac{1}{4}(\pi)(r^2)[/tex]

[tex]A_c=\frac{1}{4}(\pi)((8)^2)[/tex]

[tex]A_c=\frac{1}{4}(\pi)(64)[/tex]

[tex]A_c=(\pi)(16)[/tex]

[tex]A_c\approx 50.2655[/tex]

3. Find the volume of the prism

Now multiply the area of the quarter circle by the length of the prism to find the volume of the prism. Note that the parameter (l) represents the length of the prism,

[tex]A=A_c(l)[/tex]

Substitute and simplify to evaluate,

[tex]A=(\pi)(16)(21)[/tex]

[tex]A=\pi(336)[/tex]

[tex]A=1055.575[/tex]

Answer:

[tex]h=\displaystyle \frac{3V}{\pi r^2}+1[/tex]

Step-by-step explanation:

Hi there!

[tex]V=\displaystyle\frac{1}{3} \pi r^2(h-1)[/tex]

Divide both sides by [tex]\displaystyle\frac{1}{3} \pi r^2[/tex]:

[tex]\displaystyle \frac{V}{\displaystyle\frac{1}{3} \pi r^2}=(h-1)[/tex]

[tex]\displaystyle \frac{3V}{\pi r^2}=h-1[/tex]

Add 1 to both sides:

[tex]\displaystyle \frac{3V}{\pi r^2}+1=h[/tex]

I hope this helps!

Answer:

k = 12

Step-by-step explanation:

The constant of proportionality k is the ratio

k = [tex]\frac{laps}{swimmers}[/tex]

Use any ordered pair from the table to find k

Using number of laps = 240, number of swimmers = 20 , then

k = [tex]\frac{240}{20}[/tex] = 12

Answer:

19/30

Step-by-step explanation:

Total cakes made by Tyron = 60

Cakes given to Ana = 20% of 60

                                 [tex]=\dfrac{20}{100}*60\\\\= 2*6\\\\= 12 \ cakes[/tex]

Number of cakes given to Dora= [tex]\dfrac{1}{6}*60=10[/tex]

Remaining cakes = 60 - ( 12 +10)

                              = 60 - 22

                              = 38 cakes

Fraction of left cakes = [tex]\dfrac{38}{60}=\dfrac{19}{30}[/tex]

Answer:

Yes, it does. We can check by using the Pythagorean theorem (P.t.).

P.t.: a^2 + b^2 = c^2

a = 6, b = 8, c = 10

6^2 + 8^2 = 10^2

36 + 64 = 100

100 = 100

Brainliest, please!

Answer:

Step by step answer.

Yes

a^2 + b^2 = c^2

8^2 + 6^2 = 10^2

64 + 36 = 100

100 = 100

The Pythagorean Theorem works. C is always assumed to be the hypotenuse because it is the longest line It's position does not matter. If you did the problem like this

6^2 + 10^2 = 8^2

Of course this would not work, but it would also disobey the convention that c is the longest side.

Answer:

The board should be 4.7 feet long.

Step-by-step explanation:

To find the remaining piece, you just multiply 1.1 by 2.3 which is 2.53. That's the length of the remaining piece.

Then you add all the pieces together.

1.1+1.1+2.53 =

4.73

Round and add label.

4.7 feet

Finds how much is needed for 1 costume by dividing 6 3/4 by 3

6 3/4 /3 = 2 1/4 yards per costume.

Multiply yards per costume by 7:

2 1/4 x 7 = 15 3/4 yards total needed.

[tex]\\ \rm\hookrightarrow 6\dfrac{3}{4}yards=3costumes[/tex]

[tex]\\ \rm\hookrightarrow \dfrac{27}{4}\div 3[/tex]

[tex]\\ \rm\hookrightarrow \dfrac{27}{4}\times \dfrac{1}{3}[/tex]

[tex]\\ \rm\hookrightarrow \dfrac{27}{7}yards[/tex]

[tex]\\ \rm\hookrightarrow \dfrac{27}{7}\times 7[/tex]

[tex]\\ \rm\hookrightarrow 27yards[/tex]

Answer:

A. 4/23+3/√9

C. 4/23×3/√9

[tex].[/tex]

An exponent is added to a term when the term is multiplied by itself. The exponent s value is the number of times the term is multiplied by its self.

There are 2 a’s so a x a = a^2

There are 3 b’s so you have b^3

There are 2 c’s so it is c^2

The equation becomes: a^2 x b^3 x c^2

Answer:

[tex]a \times a \times b \times b \times b \times c \times c = {a}^{2} \times {b}^{3} \times {c}^{2} \\ thank \: you[/tex]

Answer:

x^2+2=0 or x^2−6=0

Step-by-step explanation:

x^4-4x^2-12=0

(x^2+2)(x^2−6)

x^2+2=0 or x^2−6=0

Answer:

x=6

Step-by-step explanation:

Hope It Help!

Thanks

Answer:

1.)

A.) phase shift is c = 6  

B.) Vertical shift is 21 units down  

C.) The amplitude is 5 from the midline at y = -21  

D.) The period is 16 and the frequency factor is pi/8  

E.) 5 cos(pi/8(x - 6)) - 21

2.)

Answer:

A.) Vertical shift is 12 units down

B.) The amplitude is 10

C.) The period is 6 and the frequency factor is pi/3

D.) Equation: y = 10sin(pi/3(x)) + 12

Answer:

1.)

A.) phase shift is c = 6  

B.) Vertical shift is 21 units down  

C.) The amplitude is 5 from the midline at y = -21  

D.) The period is 16 and the frequency factor is pi/8  

E.) 5 cos(pi/8(x - 6)) - 21

2.)

Answer:

A.) Vertical shift is 12 units down

B.) The amplitude is 10

C.) The period is 6 and the frequency factor is pi/3

D.) Equation: y = 10sin(pi/3(x)) + 12

Step-by-step explanation:

Answer:

the domains are x axis or intercepts and range is y axis or intercepts

Answer:

Company D is the correct choice. With a flat rate of $150 plus the hourly fee of $5, you add the hourly to the flat fee. So in this case, $150 + 7($5) = $185. This comes out to be the lowest price out of the 4 options provided.

Step-by-step explanation:

I derped. I'm sorry. Here is the answer as an actual answer :)

Answer:

Company C

Step-by-step explanation:

Answer:

The answer is -a

Step-by-step explanation:

from equation,

[tex]a+b=0\\=>b=0-a[/tex]

∴[tex]b=-a[/tex]

Therefore, -a is equal to b

hope you have understood this....

pls mark my answer as the brainliest

Answer: The perimeter is 16 units

Step-by-step explanation:

Answer:

A 1600

B 2400 hope it helps

Answer:

see below

Step-by-step explanation:

f(x) = -2/3 (x+1) (x-5)

First find the zeros

0 = -2/3 (x+1) (x-5)

Using the zero product property

x+1 =0   x-5=0

x= -1    x = 5

Then find the y intercept

y = -2/3 (0+1)(0-5)

  - 2/3 (1)(-5)

  +10/3

We know that this is a parabola that opens downward

Simplify

Graph attached

Answer:

89/100. Hope this helped.

Step-by-step explanation:

Answer:

165/14

Step-by-step explanation:

(7-4) + 17 / -14 + 2 x 5

3 + 17/-14 + 2 x 5

3 - 17/14 + 2 x 5

3 - 17/14 + 10

165/14

Answer:

D

Step-by-step explanation:

edge

Answer:

2X–3 =15

2X=15+3

2X=18

X=18/2

X= 9

I hope I helped you^_^

Answer:

18

Step-by-step explanation:

SEE THE IMAGE FOR SOLUTION

HOPE IT HELPS

HAVE A GREAT DAY

Lets form a inequality

[tex]\\ \sf\longmapsto x>-4.5[/tex]

[tex]\\ \sf\longmapsto x<-0.5[/tex]

Now

[tex]\\ \sf\longmapsto -4.5\lt x\lt -0.5[/tex]

Hence

[tex]\\ \sf\longmapsto x=\left\{-4.4,-4.3\dots -0.7,-0.6\right\}[/tex]