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fredd [130]
3 years ago
9

The variables x=9 and y=15 vary directly. Write an equation that relates the variables

Mathematics
2 answers:
snow_tiger [21]3 years ago
8 0
I love your profile picture 56
erik [133]3 years ago
7 0

Answer:

x = 0.6y.

Step-by-step explanation:

x = ky  is direct variation where k is some constant;

Now we find k:-

Substituting for x and y:

9 = k*15

k = 9/15 = 0.6

So the equation is

x = 0.6y.

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Home CoworkHelper
9966 [12]

Answer:

See below.

Step-by-step explanation:

PROBLEM A

The formula for the volume of a cylinder is

V = πr²h, where πr² is the area of the base.

V = area of base x height

  1. Choose any four numbers that are less than 10 for the height.
  2. Then, substitute into the formula and isolate "r". 10 = πr²h
  3. Double "r" to find the diameter.
  4. The area of the base is found (bolded) while you solve πr².

*I will use the calculator button for pi (π)

<u>Cylinder A: </u><u>h = 1</u>

10 = πr²h

10 = πr²(1)

10 = πr²                       Area of the base is 10m².

r = √ (10/π)

r = 1.78                        Radius is 1.78m.

d = 2r = 1.78*2 = 3.56                     Diameter is 3.56m.

<u>Cylinder B: </u><u>h = 2</u>

10 = πr²h

10 = πr²(2)

5 = πr²                       Area of the base is 5m².

r = √ (5/π)

r = 1.26                      Radius is 1.26m.

d = 2r = 1.26*2 = 2.52                     Diameter is 2.52m.

<u>Cylinder C: </u><u>h = 4</u>

10 = πr²h

10 = πr²(4)

2.5 = πr²                       Area of the base is 2.5m².

r = √ (2.5/π)

r = 0.89                        Radius is 0.89m.

d = 2r = 0.89*2 = 1.78                     Diameter is 1.78m.

<u>Cylinder D: </u><u>h = 5</u>

10 = πr²h

10 = πr²(5)

2 = πr²                       Area of the base is 2m².

r = √ (2/π)

r = 0.80                     Radius is 0.8m.

d = 2r = 0.80*2 = 1.6                     Diameter is 1.6m.

The answers are reasonable if the answer is close to 10 when you substitute the rounded numbers back into the formula and solve.

There are infinite possibilities because any numbers when used in the formula equates to 10 are possible. The height/radius can be any decimal number, which would make the other dimensions change.

PROBLEM B

Follow similar steps if you know the diameter of a cylinder. Use the same formula V = πr²h.

We need the radius, which is half the diameter. r = d/2 = 10/2 = 5

  1. Choose a random number for volume that divides easily by 25.
  2. Substitute "V" and "r²" (r² = 25).
  3. Isolate "h".
  4. The area of the base is 78.54 cm² every time (A = πr²).

<u>Cylinder A: </u><u>V = 100</u>

100 = π25h

4 = πh

h = 1.27                      The height is 1.27m.

<u>Cylinder B: </u><u>V = 200</u>

200 = π25h

8 = πh

h = 2.55                      The height is 2.55m.

<u>Cylinder C: </u><u>V = 75</u>

75 = π25h

3 = πh

h = 0.95                      The height is 0.95m.

<u>Cylinder D: </u><u>V = 125</u>

125 = π25h

5 = πh

h = 1.59                      The height is 1.59m.

The answers are reasonable if I can substitute two rounded values into the formula and get a number close to the third. The height is also a decimal number which occurs because of pi.

6 0
3 years ago
Help me out pls!!!??
zheka24 [161]
The answer is B 

the steps are these 

interchange the x and y variables 

x=5y-8


solve for y so we get 
y = x+8
       ----
        5


5 0
3 years ago
Read 2 more answers
Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 4.6 parts
kirill115 [55]

Answer:

z=\frac{4.5-4.6}{\frac{1.1}{\sqrt{860}}}=-2.666    

p_v =2*P(Z  

If we compare the p value and the significance level given \alpha=0.02 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is different from 4.6 at 2% of signficance.  

Step-by-step explanation:

Data given and notation  

\bar X=4.5 represent the sample mean

\sigma=1.1 represent the population standard deviation

n=860 sample size  

\mu_o =4.6 represent the value that we want to test

\alpha=0.02 represent the significance level for the hypothesis test.  

z would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean is equal or not to 4.6, the system of hypothesis would be:  

Null hypothesis:\mu = 4.6  

Alternative hypothesis:\mu \neq 4.6  

If we analyze the size for the sample is > 30 and we know the population deviation so is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:  

z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}  (1)  

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic

We can replace in formula (1) the info given like this:  

z=\frac{4.5-4.6}{\frac{1.1}{\sqrt{860}}}=-2.666  

P-value

Since is a two sided test the p value would be:  

p_v =2*P(Z  

Conclusion  

If we compare the p value and the significance level given \alpha=0.02 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is different from 4.6 at 2% of signficance.  

5 0
3 years ago
How many cups did eddy order
IrinaK [193]

Answer:

9.

Step-by-step explanation:

334÷38=8.79, rounded up to 9.

4 0
3 years ago
Read 2 more answers
Write -37.75 as a mixed number.​
Burka [1]

Answer:

-37\frac{3}{4}

Step-by-step explanation:

0.75 is equivalent to three quarters, or (3/4).

3/4 would be the fraction. -37 would be the whole number.

-37.75 = \boxed{-37\frac{3}{4}}

Hope this helps.

3 0
2 years ago
Read 2 more answers
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