I really need help rn I got 5 mins left

The surface area and volume of a pentagonal prism is  5/2 × a² × √(5 + 2√5) + 5ab and (1/4) × (5 + 2√5) × a² × h respectively. We can find the solution in the following manner.

A pentagonal prism is a three-dimensional geometric shape that consists of two parallel pentagons as the top and bottom faces, and five rectangular faces connecting them.

To find the surface area and volume of a pentagonal prism, we need to know its height, the length of the sides of the pentagon, and the length of the rectangular faces.

Let's denote the height of the pentagonal prism as "h", the side length of the pentagon as "a", and the length of the rectangular face as "b".

Surface Area of a Pentagonal Prism:

The surface area of a pentagonal prism is the sum of the areas of its faces. There are two pentagonal faces and five rectangular faces in a pentagonal prism.

Area of each pentagonal face = 5/4 × a² × √(5 + 2√5)

Area of each rectangular face = a × b

Total surface area = 2 × Area of pentagonal face + 5 × Area of rectangular face

= 5/2 × a² × √(5 + 2√5) + 5ab

Volume of a Pentagonal Prism:

The volume of a pentagonal prism is given by the formula:

Volume = (1/4) × (5 + 2√5) × a² × h

Therefore, the surface area and volume of a pentagonal prism can be calculated using the above formulas, given the values of a, b, and h.

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The surface area and volume of a pentagonal prism is sum of the areas of its faces, and (1/4) × (5 + 2√5) × a² × h.

A pentagonal prism is a three-dimensional geometric shape that consists of two parallel pentagons as the top and bottom faces, and five rectangular faces connecting them.

Surface Area of a Pentagonal Prism:

The surface area of a pentagonal prism is the sum of the areas of its faces. There are two pentagonal faces and five rectangular faces in a pentagonal prism.

Total surface area = 2 × Area of pentagonal face + 5 × Area of rectangular face

Volume of a Pentagonal Prism:

The volume of a pentagonal prism is given by the formula:

Volume = (1/4) × (5 + 2√5) × a² × h

Therefore, the surface area and volume of a pentagonal prism can be calculated using the above formulas, given the values of a, b, and h.

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Answer:

r = -36

Step-by-step explanation:

\(\frac{r}{9}=-4\)

Multiply both sides by 9

r = -36

Answer:

The measure of angle WVX is 140°.

Step-by-step explanation:

Let x be the measure of angle WVX.

\( \frac{14}{9} \pi = 2x\)

\( x = \frac{7}{9} \pi( \frac{180}{\pi}) = 140 \: degrees\)

Answer:

angle = arc length/radius
in this case, the arc length is 14/9*\(\pi\) and the radius is 2. Upon multiplying these, you get 140.

so, the answer is 140 degrees.

The man can wear 15 different outfit combinations by mixing and matching his six different sport shirts and four different pairs of slacks.

Combination is a way of counting the number of different groups of items that can be selected from a larger set without regard to the order in which they are selected.

In this case, the man has six different sport shirts and four different pairs of slacks, and he wants to know how many different outfit combinations he can wear. We can use the formula for combinations to calculate the number of possibilities.

The formula for combinations is:

ⁿCₓ = n! / (x! * (n - x)!)

Where n is the total number of items, x is the number of items being selected, and the exclamation mark (!) represents the factorial of a number (i.e., the product of all positive integers up to that number).

Using this formula, we can calculate the number of different combinations the man can wear as follows:

Number of sport shirts (n) = 6

Number of slacks (x) = 4

Number of combinations = ⁶C₄ = 6! / (4! * (6 - 4)!)

= (6 * 5 * 4 * 3 * 2 * 1) / [(4 * 3 * 2 * 1) * (2 * 1)]

= 15

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Answer: The amount is 14

Answer: O 12%

Step-by-step explanation:

Let's assume that 100 customers visited the gas station that day. According to the given information, 80% of them purchased regular gas, which means 80 customers bought regular gas.

Of those 80 customers, 10% paid in cash, which is 8 customers.

The remaining 20 customers did not purchase regular gas, and 20% of them paid in cash, which is 4 customers.

Therefore, the total number of customers who paid in cash is 8 + 4 = 12.

The percentage of customers who paid in cash out of the 100 customers who visited the gas station that day is 12%, so the answer is O 12%.

The quantity of water in the reservoir after 9 hours be, 2835 gallons.

Given, water flows into an empty reservoir at a rate of 2800 + 15t gal/hour.

we have to find the quantity of water in the reservoir after 9 hours.

at the rate of 2800 + 15t

put t = 9

So, the quantity of water in the reservoir after 9 hours be,

2800 + 15(9)

2800 + 135

= 2835

So, the quantity of water in the reservoir after 9 hours be, 2835 gallons.

Hence, the quantity of water in the reservoir after 9 hours be, 2835 gallons.

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***NOTE*** we are going to use the rise over run formula to solve this problem

Joe climbed a mountain with a rise of 1, 200 feet and a run of 1, 500 feet.

So, the slope would be:

1, 200 over 1, 500

which can be simplified...

1,200/1,500 = 12/15 = 4/5

When we solve for slope for Bob, we do the same thing.

He climbed a mountain with a rise 900 feet and a run of 1, 000 feet.

So, it would look like this after we simplify it...

900/1,000 = 9/10

Finally, since Bob's mountain has the largest slope (or fraction), that means that he climbed the steepest mountain.

I hope this helps! :) Let me know if you need help with anything else! I'd be happy to help you!!

Work Shown:

L = arc length

L = (radius)*(central angle in radians)

L = (4.5 cm)*(pi/2 radians)

L = (4.5*pi/2) cm

L = (4.5*3.14/2) cm

L = 7.065 cm

L = 7.1 cm

Side note: the central angle must be in radians for that formula to work.

Answer:

  (d)  7.1 cm

Step-by-step explanation:

The arc length is given by ...

  s = rθ . . . . where r is the radius and θ is the arc length in radians

Put your given values in the formula and do the arithmetic.

  s = (4.5 cm)(3.14/2) = 7.065 cm ≈ 7.1 cm

_____

Additional comment

Among the given answer choices, you can choose the correct one based on your knowledge of angle values and the sides of a right triangle. Here the angle is π/2 radians = 90°, so you're concerned with the length of a quarter circle. It will be longer than the radius, but shorter than 2 times the radius (a square corner). The only answer choice greater than the radius length is the correct one.

Answer:

means and extremes

Step-by-step explanation:

The probability that a package of 5 tasks is processed in less than 8 minutes is 0.963.

Let X denote the time required to process a package of five tasks. X is an exponentially distributed random variable with mean 2 minutes.

The probability of X being less than 8 minutes is given by:

P(X ≤ 8) = 1 - P(X > 8)

= \(1 - (1 - e^{(-8/2)}^{5}\)

= 0.963

Therefore, the probability that a package of 5 tasks is processed in less than 8 minutes is 0.963.

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We can use the sine rule to find the hole angle, and then find the golfer angle:

Now we can find the golfer angle:

Answer: 25.6 degrees.

Answer:

C=4x+3y Constraints: x is greater than or equal to 0 2x + 3y is greater than or equal to 6 3x - 2y is less than or equal to 9 x + 5y is less than or equal to 20

Answer:

The equation for the relationship is \(y = \frac{7}{2}\cdot x\).

Step-by-step explanation:

Given that point \((x,y) = (6, 21)\) is part of a direct relationship. That is:

\(y \propto x\)

\(y = k\cdot x\) (1)

Where \(k\) is the proportionality constant.

If we know that \(x = 6\) and \(y = 21\), then the proportionality constant is:

\(k = \frac{y}{x}\)

\(k = \frac{21}{6}\)

\(k = \frac{7}{2}\)

Lastly, the equation for the relationship is \(y = \frac{7}{2}\cdot x\).

Answer: 17% increase

Step-by-step explanation:

Percentage increase/decrease = (final value - initial value) / initial value x 100
% change = (1,544,400 - 1,320,000) / 1,320,000 x 100
% change = 224,400 / 1,320,000 x 100
% change = 0.17 x 100
% change = 17% increase

Answer:

It should be 1. If y(x)= 4 then x should equal 1. This way we get 4=4 which is true.

Step-by-step explanation:

4x1 = 4, so if you substitute 1 for x in your equation you get 4.

Answer:

\(m=-2\)

Step-by-step explanation:

\(3=m+5\)

Switch sides:

\(m+5=3\)

Subtract 5 from both sides:

\(m+5-5=3-5\)

\(m=-2\)

Answer:

-2

Step-by-step explanation:

1. Add the same term to both sides of the equation

3=m+5

( 3-5 = m + 5 -5)

2. Simplify

-subtract the numbers

- add the numbers

3. Solution

-2 = m

Answer:

Step-by-step explanation:

\(G.M.=\sqrt{\frac{5}{6} \times \frac{1}{2} } =\sqrt{\frac{5}{12} }\)

For the given equation, we created a situation in which the equation would work and analysed it.

What is meant by equations?

A mathematical equation is a formula that uses the equals sign (=) to represent the equality of two expressions. The expressions on each side of the equals sign are referred to as the "left-hand side" and "right-hand side," respectively, of the equation. Typically, we consider an equation's right side to be zero. As we can balance this by deducting the right-side expression from both sides' expressions, this won't reduce the generality.

a ) Given the equation as:

 g + 3 / 16 = 15

Now we have to create a situation that the equations could represent. We have to create a word problem for the equation.

James had a packet of chocolates. There were a total of 16 students in his class. He bought three more chocolates so that each student received 15 chocolates. How many chocolates did James have in the beginning?

To solve this we take g as the number of chocolates in the beginning.

He bought 3 more chocolates.

So number of chocolates = g + 3

Now he divided it among 16 students equally.

So each student received = g + 3 /16 = 15 chocolates.

b) The situation would not work if the denominator of the equation is doubled. That is 16 * 2 = 32.

Because the number of students is 16.

But if the students were 16*2 = 32 then the situation would work.

Therefore for the given equation, we created a situation in which the equation would work and analysed it.

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a. The formula solved for t is t = I/Pr

b. The value of t in the table is 3 years

From the question, we are to solve for t in the given formula

The given formula is the formula for simple interest

I = Prt

To solve for t, we will divide both sides of the equation by Pr

That is,

I/Pr = Prt/Pr

I/Pr = t

∴ t = I/Pr

The formula solved for t is t = I/Pr

b. We are to find the value of t when

I = $75

P = $500

r = 5% = 0.05

From

t = I/Pr

t = 75/(500×0.05)

t = 75/25

t = 3 years

Hence, the value of t in the table is 3 years

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Answer:

3x^2+3x-6

Step-by-step explanation:

The value of a Chi-Square goodness-of-fit test at a 5% significance level is 13.45

We need to perform a Chi-Square goodness-of-fit test at a 5% significance level.

First we need to calculate the expected count

expected value = ∑(x)/n

= (40 + 33 + 35 + 32 + 60)/5

= 200/5

= 40

Now we need tocalculate the test statistic value

Observed  expected  O - E    (O - E)^t/E       %

40                40             0            0                   0

33                40             -7          1.225          9.11

35                40             -5          0.625         4.65

32                40             -8         1.6                11.90

60                40             20        10                 74.35

Chi square test is 13.45

Therefore, the value of test statistics is 13.45.

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Answer:

CHICKEN NOODLE

Step-by-step explanation:

I DID IT RIGHT

The area of the triangle by the given points i.e. P(1,1,1) , Q(-2,-7,-1) and R(-7,-1,4) is √4773/2. The area of the triangle is \(\frac{1}{2}\)  |PQ × PR|.

From the points that is  given in the question with the adjacent sides,

P(1,1,1) , Q(-2,-7,-1) and R(-7,-1,4)

Area of the triangle = \(\frac{1}{2}\)  |PQ × PR|

then, from the above points,

PQ = <-3,-8,-2>

and PR = <-8,-2,3>

now, The matrices can be written as,

PQ × PR = \(\left[\begin{array}{ccc}i&j&k\\-3&-8&-2\\-8&-2&3\end{array}\right]\)  

by calculating the above matrices we get,

= -28i + 25j - 58k

| PQ × PR | = \(\sqrt{28^{2} + 25^{2} + 58^{2}\)

=√4773

However, the Area of the triangle = √4773 / 2

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The question is-

Find the area of the triangle determined by the points P(1,1,1) , Q(-2,-7,-1) and R(-7,-1,4).

Answer:

9 is your answer. It's a simple equation.

Answer:The equations are 5t + e = 725 and 3t + e = 505

Step-by-step explanation:Subtract equation (2) from equation (1) and you arrive at;

2t = 220

Divide both sides of the equation by 2

t = 110

Having calculated the value of t, substitute for the value of t into equation (1)

5t + e = 725

5(110) + e = 725

550 + e = 725

Subtract 550 from both sides of the equation

e = 175

The above calculations shows that the calories burned on each gym equipment are;

Treadmill = 110 per hour

Elliptical = 175 per hour

Answer:

1/2 inch per hour

My other answer got deleted lol

Hope This Helps!

At the rate 1/2 inches per hour does the candle burn.

Given that, \(5\frac{1}{2}\) inch candle burns down in 11 hours.

A rate is a special ratio in which the two terms are in different units.

In general, we can write down the formula for rate as the ratio between two quantities with various units. Putting this in the ratio format, we get,

Rate = Quantity 1 / Quantity 2

Here, \(5\frac{1}{2}=11/2\) inches

The rate candle burns down = Length of the candle ÷ Number of hours

Now, the rate candle burns down = 11/2 ÷ 11

= 11/2 × 1/11

= 1/2 inches per hour

Therefore, at the rate 1/2 inches per hour does the candle burn.

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