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3 years ago

The surface area of a rectangular prism is the sum of:

Mathematics

1 answer:

Anastaziya [24]3 years ago

8 0

Answer:

Surface area of prism= $2(l+w)h+2(lw)$

Step-by-step explanation:

We are given that surface area of rectangular prism= $2(lw+lh+wh)$

We have to write an expression that represents the surface area of prism.

Base of prism is made from length and width

Perimeter of base =2(l+w)

Area of base=lw=Area of top

Surface area of prism=Perimeter of base multiply by height+2 area of base

Because area of base and area of top are equal.

Surface area of prism=Ph+2B=2(l+w)h+2(lw)

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Roger's Diner offers its clients a choice of regular and diet soda. Last night, the diner served 135 regular sodas and 45 diet s

kozerog [31]

Answer:

75% served are regular

Step-by-step explanation:

135+45 = 180 total sodas.

135/180 = 0.75

3 0

2 years ago

If $1500 is invested at an interest rate of 4.75% per year, compounded quarterly, find the value of the investment after the giv

Burka [1]

After n years the amount = 1500(1 + (0.0475/4)^4n

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3 years ago

The mean waiting time at the drive-through of a fast-food restaurant from the time the food is ordered to when it is received is

alexira [117]

Answer:

a) And if we replace we got: $\bar X= 78$

$s = 15.391$

b) $78-3.25\frac{15.391}{\sqrt{10}}=62.182$

$78-3.25\frac{15.391}{\sqrt{10}}=93.818$

So on this case the 99% confidence interval would be given by (62.182;93.818)

Step-by-step explanation:

Dataset given: 109 67 58 76 65 80 96 86 71 72

Part a

For this case we can calculate the sample mean with the following formula:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

And if we replace we got: $\bar X= 78$

And the deviation is given by:

$s =\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

And if we replace we got $s = 15.391$

Part b

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=10-1=9$

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,9)".And we see that $t_{\alpha/2}=3.25$

Now we have everything in order to replace into formula (1):

$78-3.25\frac{15.391}{\sqrt{10}}=62.182$

$78-3.25\frac{15.391}{\sqrt{10}}=93.818$

So on this case the 99% confidence interval would be given by (62.182;93.818)

8 0

2 years ago

Add gift box in the shape of a triangular prism has a volume of 140 in.³, that a base height of 10 inches, and a height of 4 inc

fenix001 [56]

140=10*4*x
140=40*x
7/2 = x

3.5 inches

5 0

3 years ago

Passes through the points (−4, 2) and (12, 6)?

svlad2 [7]

<u>I'll assume you need to find the equation of the line that passes through those points.</u>

Answer:

$\displaystyle y-2=\frac{1}{4}(x+4)$

Step-by-step explanation:

<u>Equation of a Line:</u>

The equation of a line passing through points (x1,y1) and (x2,y2) can be found as follows:

$\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

The given points are (-4,2) and (12,6), thus:

$\displaystyle y-2=\frac{6-2}{12+4}(x+4)$

Operating:

$\displaystyle y-2=\frac{4}{16}(x+4)$

Simplifying, the equation in point-slope form is:

$\mathbf{\displaystyle y-2=\frac{1}{4}(x+4)}$

3 0

2 years ago