Name the line and plane shown in the diagram.

A soup can has a height of 4 inches and a radius of 2.5 inches. What's the volume of soup in cubic inches that would fill one so

Alenkasestr [34]

Answer:

C. 78.5 in^3

Step-by-step explanation:

A soup can is in the shape of a cylinder. The volume of a cylinder can be found using the following formula:

$v=\pi r^2h$

We know that the height is 4 inches and the radius is 2.5 inches.

r= 2.5 in

h= 4 in

$v=\pi (2.5in)^2*4in$

Evaluate the exponent.

$(2.5 in)^2=2.5 in*2.5in=6.25 in^2$

$v=\pi *6.25 in^2*4 in$

Multiply 6.25 in^2 and 4 in.

$6.25 in^2*4 in=25 in^3$

$v=\pi*25 in^3$

Multiply pi and 25 in^3.

$v=78.5398163 in^3$

Round to the nearest tenth. The 3 in the hundredth place tells us to leave the 5 in the tenth place.

$v=78.5 in^3$

78.5 cubic inches can fill one soup can.

7 0

4 years ago

Solve by substitution. 3x-y=5 -2x+y=0

Citrus2011 [14]

In order to use substitution, you need to isolate a variable on one of the equations:

-2x+y=0
y=2x

Then you plug that equation into the other equation. Since we isolated y, we plug in 2x for y in the other equation:

3x-(2x)=5
x=5

Then plug the value you found into any equation to solve for the other variable:

3(5)-y=5
15-y=5
-y=-10
y=10

So your answers are x=5, y=10

3 0

3 years ago

Read 2 more answers

why are antibiotics so important in our lives? A. they are miracle drugs, able to cure all infections. B. They are able to stop

Serjik [45]

My answer is C because without medics for instance if you had the flu and no medicine you would die

3 0

4 years ago

Read 2 more answers

Weights and heights of turkeys tend to be correlated. For a population of turkeys at a farm, this correlation is found to be 0.6

LenaWriter [7]

Answer:

a turkey at the farm which weighs more than 90% of all the turkeys is predicted to be taller than 79.37 % of them.

The average height for turkeys at the 90th percentile for weight is 34.554

Of the turkeys at the 90th percentile for weight, roughly the percentage that would be taller than 28 inches 79.37%

Step-by-step explanation:

Given that:

For a population of turkeys at a farm, the correlation found between the weights and heights of turkeys is r = 0.64

the average weight in pounds $\overline x$ = 17

the standard deviation of the weight in pounds $S_x$ = 5

the average height in inches $\overline y$ = 28

the standard deviation of the height in inches $S_y$ = 8

Also, given that the weight and height both roughly follow the normal curve

For this study , the slope of the regression line can be expressed as :

$\beta_1 = r \times ( \dfrac{S_y}{S_x})$

$\beta_1 = 0.64 \times ( \dfrac{8}{5})$

$\beta_1 = 0.64 \times 1.6$

$\beta_1 = 1.024$

To the intercept of the regression line, we have the following equation

$\beta_o = \overline y - \beta_1 \overline x$

replacing the values:

$\beta_o = 28 -(1.024)(17)$

$\beta_o = 28 -17.408$

$\beta_o = 10.592$

However, the regression line needed for this study can be computed as:

$\hat Y = \beta_o + \beta_1 X$

$\hat Y = 10.592 + 1.024 X$

Recall that;

both the weight and height roughly follow the normal curve

As such, the weight related to 90th percentile can be determined as shown below.

Using the Excel Function at 90th percentile, which can be computed as:

(=Normsinv (0.90) ; we have the desired value of 1.28

∴

$\dfrac{X - \overline x}{s_x } = 1.28$

$\dfrac{X - 17}{5} = 1.28$

$X - 17 = 6.4$

X = 6.4 + 17

X = 23.4

The predicted height $\hat Y = 10.592 + 1.024 X$

where; X = 23.4

$\hat Y = 10.592 + 1.024 (23.4)$

$\hat Y = 10.592 + 23.9616$

$\hat Y = 34.5536$

Now; the probability of predicted height less than 34.5536 can be computed as:

$P(Y < 34.5536) = P( \dfrac{Y - \overline y }{S_y} < \dfrac{34.5536-28}{8})$

$P(Y < 34.5536) = P(Z< \dfrac{6.5536}{8})$

$P(Y < 34.5536) = P(Z< 0.8192)$

From the Z tables;

P(Y < 34.5536) =0.7937

Hence, a turkey at the farm which weighs more than 90% of all the turkeys is predicted to be taller than 79.37 % of them.

The average height for turkeys at the 90th percentile for weight is :

$\hat Y = 10.592 + 1.024 X$

where; X = 23.4

$\hat Y = 10.592 + 1.024 (23.4)$

$\hat Y = 10.592 + 23.962$

$\mathbf{\hat Y = 34.554}$

Of the turkeys at the 90th percentile for weight, roughly what percent would you estimate to be taller than 28 inches?

i.e

P(Y >28) = 1 - P (Y< 28)

$P(Y >28) = 1 - P( Z < \dfrac{28 - 34.554}{8})$

$P(Y >28) = 1 - P( Z < \dfrac{-6.554}{8})$

$P(Y >28) = 1 - P( Z < -0.8193)$

From the Z tables,

$P(Y >28) = 1 - 0.2063$

$\mathbf{P(Y >28) = 0.7937}$

= 79.37%

7 0

4 years ago

What is sum of two fifths and one forth?

Alecsey [184]

2/5+1/4 = 8+5/20 = 13/20 ...answer !!!

3 0

4 years ago