Water coming out from a fountain is modeled by the function f(x) = −x2 + 8x + 2 where f(x) represents the height, in feet, of the water from the fountain at different times x, in seconds.What does the average rate of change of f(x) from x = 1 to x = 4 represent, options AWhat does the average rate of change of f(x) from x = 1 to x = 4 represent?
options: The water travels an average distance of 3 feet from 1 second to 4 seconds.
The water travels an average distance of 2 feet from 1 second to 4 seconds.
The water rises up with an average speed of 3 feet per second from 1 second to 4 seconds.
The water rises up with an average speed of 2 feet per second from 1 second to 4 seconds.

Answers

Answer 1

Answer: $f(x)=-x^(2) +8x+2$
Average rate of change from x = 1 to x = 4 = $(f(4)-f(1))/(4-1)= (( -4^(2)+8(4)+2)-(- 1^(2)+8(1)+2))/(3)= ((-16+32+2)-(-1+8+2))/(3)= (18-9)/(3)=$ $(9)/(3)=3$

This means that the water rises up with an average speed of 3 feet per second from 1 second to 4 seconds

Answer 2

Answer:

Answer:

C. The water rises an average of 3 feet per second from 1 to 4 seconds

Step-by-step explanation:

I got it correct on the test

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Compare the numbers 5.0 and 0.5. how many times greater is 5.0 than 0.5

Answers

5.0 is 10 times greater than .5

when a number is multiplied by ten, the decimal moves one place to the right

If total employee benefits are calculated as a percentage of their gross pay, which of the following employees receives the largest amount in total employee benefits?a.
Employee A: gross pay $32,600 , total job benefits $33,600
b.
Employee B: gross pay $32,900 , total job benefits $34,000
c.
Employee C: gross pay $33,400 , total job benefits $33,900
d.
Employee D: gross pay $33,700 , total job benefits $34,700

Answers

we know that

To determine which employee has received the most in employee benefits, it is done by comparing the net amount obtained by subtracting the gross pay from the job benefits obtained.

case a) Employee A: gross pay $ $32,600$ , total job benefits $ $33,600$

$33,600-32,600=1,000$

Find the percentage

by proportion

$(32,600)/(100) =(1,000)/(x) \n \n 32,600*x=1,000*100$

$x=3.067$ %

case b) Employee B: gross pay $ $32,900$ , total job benefits $ $34,000$

$34,000-32,900=1,100$

Find the percentage

by proportion

$(32,900)/(100) =(1,100)/(x) \n \n 32,900*x=1,100*100$

$x=3.343$ %

case c) Employee C: gross pay $ $33,400$ , total job benefits $ $33,900$

$33,900-33,400=500$

Find the percentage

by proportion

$(33,400)/(100) =(500)/(x) \n \n 33,400*x=500*100$

$x=1.947$ %

case d) Employee D: gross pay $ $33,700$ , total job benefits $ $34,700$

$34,700-33,700=1,000$

Find the percentage

by proportion

$(33,700)/(100) =(1,000)/(x) \n \n 33,700*x=1,000*100$

$x=2.967$ %

therefore

the answer is the option

Employee B: gross pay $ $32,900$ , total job benefits $ $34,000$

Answer:

The answer Is B or employee B.

Step-by-step explanation:

Cuz like... numbers and stuff... idk (Explanation here)

A ten foot long ladder leans against a wall, with the top of the ladder being eight feet above the ground. What is the approximate angle that the ladder makes with the ground?

Answers

Answer:

The angle that the ladder made with the ground = 53.13010235°

Step-by-step explanation:

The ladder has a length of 10 ft and it leaned against a wall to form a right angle triangle. The height from the top of the ladder to the ground is given as 8 ft. The triangle formed from the illustration can be represented with the picture below.

The angle A is the angle the ladder made with the ground.

Length of ladder = c

height from the top of the ladder to the ground = a

The distance of the foot of the ladder and the wall = b

c = 10 ft

a = 8 ft

Using SOHCAHTOA

sin A = a/c

sin A = 8/10

sin A = 0.8

A = sin-1 0.8

A = 53.13010235°

so we got hypotenuse and opposite side so to find the angle we use the trig function
sin = opposite/hypotenuse
¢=angle
sin¢=8/10
sin¢= 0.8

arcsin¢=arcsin(0.8)
¢= 53.13 degrees

In the formula l=p+prt, what does l equal when p=500,r=20%, t=2

Answers

Just plug in 500 for p, 0.2 for r (because 20% is equivalent to 0.20), and 2 for t:

$I=p+prt\nI=(500)+(500)(0.2)(2)\nI=500+200\nI=700$

So, if you start with $500 and charge an interest rate of 20% for 2 years, you will gain $200 to get $700 in total.

A piggy bank contains $5.60 in nickels and dimes. The number of nickels is 8 less than 3 times the dimes. How many nickels and dimes are there in the piggy bank?

Answers

the value of the coin times the number of coins all added up equals the total value of the piggy bank
so
0.05n + 0.10d = 5.60

then they have given us "number of nickels is 8 less than 3 times the dimes"
this translates to
n = 3d - 8

we plug this into our first equation and we get
0.05(3d - 8) + 0.10d = 5.60

now we solve for d
first we can distribute the 0.05
0.15d - 0.40 + 0.10d = 5.60

then we can add the 0.15d and 0.10d together
and get
0.25d - 0.40 = 5.60

then we can add 0.40 to both sides
0.25d = 6.00

then divide both sides by 0.25
d = 6.00 / 0.25 = 24
so we have 24 dimes

then to find nickels, we plug in 24 for d into
n = 3d - 8
and get
n = 3(24) - 8
n = 72 - 8
n = 64

therefore we have
64 nickels
and
24 dimes

Answer:

24 dimes

64 nickels

Step-by-step explanation:

Solve this inequality: 3p – 16 < 20. A. p < –12
B. p < 12
C. p < 1/3
D. p < 11/3

Answers

3p - 16 < 20
3p < 20 + 16
3p < 36
p < 12

The answer is B.

3p - 16 < 20

3p < 20 + 16

3p < 36

p < 36/3

p < 12

Option B.

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