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3 years ago

A gallon of water weighs 8.354 pounds. Simon uses 11.81 gallons of water. About how many pounds did he use

1 answer:

7 0

Since a gallon of water weighs 8.354 pounds, and you use 11.81 gallons, it is very easy to find out how many he used. All you have to do is multiply 11.81 by 8.354 because you have 11.81 gallons and a gallon weighs 8.354 pounds. So when multiplied you get 98.66074 pounds. So Simon used 98.66074 pounds of water.

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A regular hexagon is circumscribed about a circle with a radius of 6. Find the area of the shaded region shown. Give the exact a

Alecsey [184]

Answer:

19.58 unit²

Step-by-step explanation:

To find the area of the shaded region, we use the formula:

$A_{shaded}=A_{circle} - A_{hexagon}\\\\$

As we know that,

$A_{circle} = \pi r^2$ = $\pi 6^2$

=36πunit²

Next is to split up the hexagon into 6 regular triangles.

$A_{hexagon} = 6. A_{triangle}$

=6 x $\frac{1}{2} bh$

the base is equal to the radius i.e 6 as the triangles are regular.The height can be represented by taking one of the triangles and drawing a line down the middle.

So, the newly formed triangle is a 30°-60°90° right triangle.

(see figure 1 in attachment)

Here, a= 6/2=> 3

h= a√3 => 3√3

Substituting the required values in the formula of area of hexagon, we get

$A_{hexagon}= 6.\frac{1}{2}.6.3\sqrt{3}$ => 54√3unit²

$A_{shaded}=A_{circle} - A_{hexagon}\\\\$

=36π-54√3

= 19.58 unit²

4 0

4 years ago

Consider the following data points.

Hoochie [10]

Answer:

the equation of the least-squares line for the data is: $\hat Y=9.3+1.3x$

Step-by-step explanation:

In a simple linear regression model, such as, $\hat Y=b_0+b_1x$ , the coefficients bo and b1 are estimated through the method of least squares by the use of the equations:

$b_1=\frac{S{xy}}{S_x^2}\\\\b_0=\bar{y}+b_1 \bar{x}$

For the data provided you have to:

$S_{xy}=\frac{\sum {(x_i-\bar x)(y_i-\bar y)}}{n-1}=3.25\\\\S_x^2=\frac{\sum {(x_i-\bar x)^2}}{n-1}=2.5\\\\\bar y=5.4$ , thus:

$b_1=\frac{3.25}{2,5}=1.3\\\\b_0=5.4+1.3(3.0)=9.3$

the equation of the least-squares line for the data is:

$Y=9.3+1.3x$

8 0

4 years ago

Read 2 more answers

Sin155° = _____ sin25° sin(-25)° -sin25°

patriot [66]

Answer:

sin 25

Step-by-step explanation:

sin(A − B) = sinA cosB − cosA sinB

sin 155

sin( 180 -25)

A = 180 B = 25

sin180 cos25 − cos180 sin25

Sin 180 = 0

cos 180 = -1

0 - (-1) sin 25

sin 25

3 0

4 years ago

Andy has 31 coins made up of quarters and half dollars, and their total value is $11.00. How many quarters does he have?

charle [14.2K]

Answer:

Step-by-step explanation:

This situation has two unknowns - the total number of half dollars and the total number of quarters. Because we have two unknowns, we will write a system of equations with two equations using the two unknowns.

h+q=31 is an equation representing the total number of coins
0.50h+0.25q=11 is an equation representing the total value in money based on the number of coin. 0.50 and 0.25 come from the value of a half dollar and quarter individually.

We write the first equation in terms of q by subtracting it across the equal sign to get h=31-q. We now substitute this for h in the second equation.

0.50(31-q)+0.25q=11

15.5-0.50q+0.25q=11

15.5-0.25q=11

After simplifying, we subtract 15.5 across and divide by the coefficient of q.

-0.25q=-4.5

q=4

We now know of the 31 coins that 4 are quarters.

3 0

4 years ago

Please find the surface area of each figure to the nearest tenth? Please show the work too...

MrRa [10]

The first one is 31.875 and the second is 12 I don't know how to explain to get it. Sorry

7 0

3 years ago