How do I do this problem?

An animal park has lions, tigers and zebras. 20% of the animals are lions and half of the animals are zebras. If there are 120 a

RoseWind [281]

Answer:

$36\ tigers$

Step-by-step explanation:

Let

x ----> the number of lions

y ----> the number f tigers

z ----> the number of zebras

we know that

$x+y+z=120$ ----> equation A

Remember that

$20\%=20/100=0.20$

$50\%=50/100=0.50$

To find out the number of lions, multiply the total animals by the percentage of lions

$x=0.20(120)=24\ lions$

To find out the number of zebras, multiply the total animals by the percentage of zebras

$z=0.50(120)=60\ zebras$

Substitute the value of x and the value of z in equation A and solve for y

$24+y+60=120$

$y+84=120$

$y=36\ tigers$

6 0

1 year ago

The function f(t) = 4t2 − 8t + 8 shows the height from the ground f(t), in meters, of a roller coaster car at different times t.

lidiya [134]

Answer:

f(t) = 4(t − 1)2 + 4; the minimum height of the roller coaster is 4 meters from the ground

Step-by-step explanation:

The function is a quadratic where t is time and f(t) is the height from the ground in meters. You can write the function f(t) = 4t2 − 8t + 8 in vertex form by completing the square. Complete the square by removing a GCF from 4t2 - 8t. Take the middle term and divide it in two. Add its square. Remember to subtract the square as well to maintain equality.

f(t) = 4t2 − 8t + 8

f(t) = 4(t2 - 2t) + 8 The middle term is -2t

f(t) = 4(t2 - 2t + 1) + 8 - 4 -2t/2 = -1; -1^2 = 1

f(t) = 4(t-1)^2 + 4 Add 1 and subtract 4 since 4*1 = 4.

The vertex (1,4) means at a minimum the roller coaster is 4 meters from the ground.

f(t) = 4(t − 1)2 + 2; the minimum height of the roller coaster is 2 meters from the ground
f(t) = 4(t − 1)2 + 2; the minimum height of the roller coaster is 4 meters from the ground
f(t) = 4(t − 1)2 + 4; the minimum height of the roller coaster is 1 meter from the ground
f(t) = 4(t − 1)2 + 4; the minimum height of the roller coaster is 4 meters from the ground

8 0

2 years ago

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Use what you know about translations of functions to analyze the graph of the function f(x) = (0.5)x−5 + 8. You may wish to grap

IrinaVladis [17]

Answer:

The Translation is 5 units to the right and 8 units up

Step-by-step explanation:

* Lets talk about some transformation

- If the function f(x) translated horizontally to the right

by h units, then the new function g(x) = f(x - h)

- If the function f(x) translated horizontally to the left

by h units, then the new function g(x) = f(x + h)

- If the function f(x) translated vertically up

by k units, then the new function g(x) = f(x) + k

- If the function f(x) translated vertically down

by k units, then the new function g(x) = f(x) – k

* Now lets solve the problem

∵ The parent function is y = (0.5)^x

∵ f(x) = (0.5)^x - 5 + 8 after translation

- The x in the first function is (x - 5) in the second function

∴ There is a horizontal translation to the right 5 units

- the first function is (0.5)^x in the second function y = (0.5)^x - 5 + 8

∴ There is a vertical translation up 8 units

* The Translation is 5 units to the right and 8 units up

- Look to the attached graph to more understand

- The purple graph is y = (0.5)^x

- The black graph is f(x) = (0.5)^x-5 + 8

- To check the answer take a point from the y = (0.5)^x as (0 , 1), the

image of this point on f(x) is (5 , 9)

-The point (0 , 1) is shifted 5 units to the right and 8 units up

∴ Its x- coordinate move from 0 to 5, y- coordinate move from 1 to 9

5 0

2 years ago

Read 2 more answers

A waterbed filled with water has the dimensions 8ft by 7 ft by .75 ft taking the density of water to be 1.00/gm cubed how many k

monitta

By definition, the density is given by:

$D = \frac{m}{V}$

Where,

m: mass

V: volume

Clearing the mass we have:

$m = DV$

The volume is given by:

$V = (8) * (7) * (0.75)$

$V = 42ft ^ 3$

Then, we have the following conversion:

$1foot = 0.3048m$

Applying the conversion we have:

$V = 42 * (0.3048) ^ 3$

$V = 1.19m ^ 3$

On the other hand we have the following conversions:

$1m = 100cm$

$1Kg = 1000g$

Applying the conversions for the density we have:

$D = (1\frac{g}{cm^3})((\frac{100}{1})^3\frac{cm^3}{1m^3})(\frac{1}{1000}\frac{Kg}{g})=1000\frac{Kg}{m^3}$

Then, the mass of the water is:

$m = (1000) * (1.19)$

$m = 1190$

Answer:

1190 kilgrams of water are required to fill the waterbed

7 0

2 years ago

Lupe can ride her bike at a rate of 20 mph when there is no wind. On one particular day, she rode 2 miles against the wind and n

lana [24]

Let wind speed = x mph

when she rode 2 miles against the wind we have:-
speed = distance / time so
20 - x = 2 / t -------(1) where t is the time she took.

when riding with the wind we have

20 + x = 3 / t--------(2) adding equations (1) and (2):-

40 = 2/t + 3/t
40 = 5/t
t = 5/40 = 1/8 hr

x = 20 - 2 / 1/8 = 20 - 16 = 4

Wind speed was 4 mph Answer

4 0

2 years ago

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