4 in.7 in18 in.4 in.The surface area of the rectangular prism issquare inches.The volume of the rectangular prism isy cubic inches.

Answers

Answer 1

Answer:

We have been given a rectangular prism and we are required to find its surface area and volume.

We shall solve this question by first stating the formula of the parameter we want to find, then, we apply the respective formulas to find the values of these parameters.

Surface area:

The surface area is the sum total of all the areas of all the faces of the prism.

To solve this question, we need to note that there are 6 faces whose area we must calculate but out of the 6, there are two faces

each that are equal in area.

From the above figure, we have that:

FACE 1 = FACE 2

FACE 3 = FACE 4

FACE 5 = FACE 6.

Thus, once we find the area of FACE 1, we already have the area of FACE 2 and so on.

Also, since each face is a rectangle, the area of a rectangle is given by:

$\begin{gathered} A=l* b \n l=\text{length} \n b=\text{breadth or width} \end{gathered}$

Now, let us calculate the area of FACE 1, 3 and 5.

$\begin{gathered} \text{FACE 1:} \n A_1=18*4=72in^2 \n \text{FACE 3:} \n A_3=4*7=28in^2 \n \text{FACE 5:} \n A_5=18*7=126in^2 \end{gathered}$

Now we just sum up all the areas and multiply them by two to account for FACES 2, 4 and 6

$\begin{gathered} A_S=2*(72+28+126) \n \therefore A_S=452in^2\text{ } \end{gathered}$

Therefore, the Surface area of the rectangular prism is:

452 square inches

Volume:

The formula for the volume of a rectangular prism is given as:

$\begin{gathered} V=l* w* h \n l=\text{length} \n w=\text{width or breadth} \n h=\text{height or depth} \end{gathered}$

The length, width, and height are shown in the figure below:

Thus, we can easily calculate our volume as shown below:

$\begin{gathered} V=7*18*4in^3 \n \therefore V=504in^3 \end{gathered}$

Therefore, the Volume of the rectangular prism is:

V = 504 cubic inches

To recap, the final answers are:

Surface Area = 452 square inches

Volume = 504 cubic inches

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Two fair dice are tossed, and the following events are defined: A: {Sum of the numbers showing is odd} B: {Sum of the numbers showing is 9,11, or 12} Are events A and B independent? Why?

Someone help pls!!! Thanks

Answers

Answer:

The answers are A and C

Step-by-step explanation:

A is correct because -16 is on the left of the number line.

Karly is choosing between two health clubs. Yoga Studio A charges a membership fee of $22.00 and $24.50 per month. Yoga Studio B charges a membership fee of $47.00 and $18.25 per month. At how many months will they cost the same? *

Answers

Answer:

4 months

Step-by-step explanation:

Given

Studio A

$Membership = \$22.00$

$Monthly = \$24.50$

Studio B

$Membership = \$47.00$

$Monthly = \$18.25$

Required

Determine when the cost will be the same

For both, we have the total cost to be:

$Cost = Membership + Monthly\ Cost * m$

Where m represents the number of month

For Studio A:

$Cost = 22 + 24.5 * m$

For Studio B:

$Cost = 47 + 18.25 * m$

Equate both expressions to get the required month

$47 + 18.25 * m = 22 + 24.5 * m$

$47 + 18.25 m = 22 + 24.5m$

Collect Like Terms

$47 - 22 = 24.5m - 18.25 m$

$25= 6.25m$

Reorder

$6.25m = 25$

Solve for m

$m = 25/6.25$

$m = 4$

Hence, it'll take 4 months

Please help with this fast

Answers

Answer:

integers from -1 ≤x≤2

Step-by-step explanation:

The domain is the value of the input or the x values

The domain is -1,0,1,2

integers from -1 ≤x≤2

A random sample of size 100 was taken from a population. A 94% confidence interval to estimate the mean of the population was computed based on the sample data. The confidence interval for the mean is: (107.62,129.75). What is the z-value that was used in the computation. Round your z-value to 2 decimal places.

Answers

Answer: 1.88

Step-by-step explanation:

The confidence interval for population mean is given by :-

$\mu\ \pm z_(\alpha/2)(\sigma)/(√(n))$

Given : Significance level : $1-0.94=0.06$

Critical value : $z_(\alpha/2)=z_(0.06/2)=z_(0.03)$

By using the standard normal distribution table for z, we find the critical value of $z_(0.03)$ corresponds to the p-value 0.03.

$z_(0.03)=1.8807936\approx1.88$

Hence, the z-value that was used in the computation must be 1.88 .

If X=2 Y=3 then, xy^2

Answers

The value of the given expression for the given value is 18.

Given that, x=2 and y=3.

We need to find the value of xy².

How to find the value of the expression?

To evaluate an expression, we substitute the given number for the variable in the expression and then simplify the expression using the order of operations.

Now, xy²=2×3²

=18

Therefore, the value of the given expression for the given value is 18.

To learn more about of value of the expression visit:

brainly.com/question/23671908.

#SPJ2

Answer:

if it is

xy² then 2*3²= 18

if (xY)²=6²=36

Step-by-step explanation:

Write the slope-intercept form of the equation of the line
2x + 3y = 18