NEED HELP NOWAngles not necessarily drawn to scale

The area of the triangular faces of the prism is 48 ft².

The entire surface area or surface area of the prism is 216 ft².

The surface area of a triangular prism is the area of its two triangular faces together with the areas of the three rectangular faces, which is the sum of the areas of the faces of the prism or its entire surface area.

Therefore, we have:

Surface area of the prism = b * h + \((S_1 + S_2 + S_3)\) * H, where:

Base of the triangular face (b) = 6 ft

Height of the triangular face (h) = 8 ft

\((S_1 + S_2 + S_3)\) = perimeter of the triangular base = 6 + 8 + 10 = 24 ft

length of the prism (H) = 7 ft

Surface area of the prism = 6 * 8 + (24) * 7

= 216 ft²

Area of the triangular faces of the prism = b * h = 6 * 8 = 48 ft².

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Answer:

See below.

Step-by-step explanation:

Slope of parallel line is -3/2.

Slope of perpendicular line is 2/3

Tn the given situation, the appro[riate null hypotheses and alternative hypotheses are: H₀: μ₁ ≥ μ₂a and H₁: μ₁ < μ₂

An assertion used in statistical inference experiments is known as the alternative hypothesis.

It is indicated by Ha or H1 and runs counter to the null hypothesis.

Another way to put it is that it is only a different option from the null.

An alternative theory in hypothesis testing is a claim that the researcher is testing.

The initial assertion that forms the null hypothesis frequently rests on research from the past or expert knowledge.

According to the alternative hypothesis, a population parameter is either less, larger, or different from the value predicted by the null hypothesis.

So, the new production method supposedly lowers the mean operating cost per hour.

The following are the hypothesis when comparing the average production costs of the new production method (μ₁) with the old production method (μ₂):

H₀: μ₁ ≥ μ₂

H₁: μ₁ < μ₂

Therefore, in the given situation, the appro[riate null hypotheses and alternative hypotheses are: H₀: μ₁ ≥ μ₂a and H₁: μ₁ < μ₂

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Answer:

0.75$

Step-by-step explanation:

12 bottles of water costs ---- $9

1 bottle of water costs ---- $9/12

Price per bottle = $9/12 = $0.75

Answer:

(7.5)/(9)

Because they are similar

Step-by-step explanation:

Answer:

17 hours

Step-by-step explanation:

I hope this helps!

Vertical angles are congruent, so Angle 2 = 75 degrees.  Supplementary angles add up to 180 degrees so Angle 1 is 105 degrees.

The new coordinates of the point (5, 2) after rotating counterclockwise about the origin through an angle of 5 degrees are approximately (4.993, 2.048).

To find the new coordinates of the point (5, 2) after rotating counterclockwise about the origin through an angle of 5 degrees, we can use the rotation formula:

x' = x * cos(theta) - y * sin(theta)

y' = x * sin(theta) + y * cos(theta)

Where (x, y) are the original coordinates, (x', y') are the new coordinates after rotation, and theta is the angle of rotation in radians.

Converting the angle of rotation from degrees to radians:

theta = 5 degrees * (pi/180) ≈ 0.08727 radians

Plugging in the values into the rotation formula:

x' = 5 * cos(0.08727) - 2 * sin(0.08727)

y' = 5 * sin(0.08727) + 2 * cos(0.08727)

Evaluating the trigonometric functions and simplifying:

x' ≈ 4.993

y' ≈ 2.048

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Answer:

the product of 2x and 7

Step-by-step explanation:

Answer:

(1 suptlimary)  ( 2. 41)     (3. alternate exterior)  (4. 149)

Step-by-step explanation:

Answer: Yes it is

Step-by-step explanation:

Answer: y=-3x+11

Step-by-step explanation:

The angle of depression, at which Tom threw the paper is 14.93°

In this question,

Tom throws a paper from a height of 4 feet, and it lands 15 feet from the car.

We need to find the angle of depression, at which he threw the paper.

Consider the following diagram.

Let the θ be the angle of depression, at which he threw the paper.

Consider the tangent of angle θ.

⇒ tan(θ) = 4/15

⇒ θ = \(tan^{-1}(\frac{4}{15} )\)

⇒ θ = 14.93°

Therefore, the angle of depression, at which Tom threw the paper is 14.93°

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Answer:

4x+3y=12

Step-by-step explanation:

y=mx+b

m=-4/3,b=4

y=mx+b

y=-4/3x+4

3(y=-4/3x+4)

3y=-4x+12

4x+3y=12

please rate it,thanks.

Answer:

The answer is the given information is the SAS case, Evelyn is approximately 104 meters from the plane, and the angle of elevation of the plane is 12°.

Step-by-step explanation:

Edge

Two triangle are congruent when the shape and size of both the triangle are same. The given information is the SAS case.

To find the form of the case we need to know about the triangle congruence theorem.

Two triangle are congruent when the shape and size of both the triangle are same.

Triangle congruence theorem are-

Given information-

Evelyn is 104 meters from the take off.

The angle of elevation of the plane is 12°.

The plane is 100 meters away from the takeoff point.

The distance is 100 meters and 104 meters. The other two sides , as are same and the angle of elevation is also same for this case (12 degrees).

Thus the two triangle formed which are congruent.

As above discussed the case of SAS exists for the triangle congruence theorem.

Hence the given information is the SAS case.

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Answer:

3x - x + 3

Step-by-step explanation:

The length of the page inside the margins is 8×(3/4) inches.

When we add two or more integers then we have to follow some set command of rule:

When adding two positive integers then we simply add them. Example: +2+3=+5

When we have two negative integers then also we add them but with a negative sign. Example:  -3-4=-7.

When we have two integers with opposite sign then we simply subtract the two number and put the sign of the integer with bigger magnitude/value. Example: +3-2=+1 and +2-5=-3.

When we are solving a statement based problem then we write down the given information at a place. Now we rearrange and form a mathematical equation using the given information and appropriate mathematical operations.

Now for the given Question:

Total Length of the year book page = 10"

Top margin on page= \(\frac{1}{2}\)"

Bottom margin of page=\(\frac{3}{4}\)"

Length of page inside margins= Total Length of page - top margin of page - bottom margin of page.

Let Length of page inside margins = x

x= 10 - \(\frac{1}{2}\) - \(\frac{3}{4}\)

For solving the above fraction we need common denominator.

x= \(\frac{40}{4}\)-\(\frac{2}{4}\)-\(\frac{3}{4}\)

x= \(\frac{40-2-3}{4}\)

x= \(\frac{40-5}{4}\)

x= \(\frac{35}{4}\)

x=8\(\frac{3}{4}\)

Hence, the length of page inside the margins is 8\(\frac{3}{4}\) inches

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Translation involves changing the position of a shape or line or point.

The value of k is -3

The given parameter is:

\(\mathbf{g(x) = f(x) + k}\)

From the attached graph, we can see that the line of f(x) is shifted down by 3 units to form g(x).

This means that:

\(\mathbf{g(x) = f(x) - 3}\)

By comparing: \(\mathbf{g(x) = f(x) - 3}\) and \(\mathbf{g(x) = f(x) + k}\)

We have:

\(\mathbf{k = -3}\)

Hence, the value of k is -3

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Answer:

The altitude to the hypotenuse of a right triangle forms two triangles that are similar to each other and to the original triangle

The Leg Rule (or Leg geometric mean theorem) relates the length of each leg of a right triangle with the segments projected by them on the hypotenuse.

Step-by-step explanation:

The altitude to the hypotenuse of a right triangle is the mean proportional between the segments into which it divides the hypotenuse. Notice the triangle used with this rule. The leg of a right triangle is the mean proportional between the hypotenuse and the projection of the leg on the hypotenuse.

Answer:

Use colon method

Step-by-step explanation:

So it is more easy

Answer:

8 or 9^8

Step-by-step explanation:

You have to add the exponents when they are being multiplied without parenthesis which means 3+5=8 so it's 9 to the 8th power.

Answer:

243x32=7776

546x12=6552

312x73=22776

Step-by-step explanation:

Answer:

243x32=7776

546x12=6552

312x73=22776

Step-by-step explanation:

I really hope this helped you out!

The dimensions of a rectangular box with a square base which has a volume of 12 cubic feet is a = 12^ 1/3, b = 12^ 1/3

Rectangular Box with Square base

Volume v = a²b = 12

S = Surface area = 2a² + 4ab

v = a²b = 12

b = 12/a²

S = 2a² + 4ab = 2a² + 4a(12/a²) =2a² + 48/a

S'(a) = 4a -48/a² = 0

4a³ = 48

a = 12^ 1/3

b = 12/a² = 12/12^ 2/3 = 12^ 1/3

Therefore, the dimensions of a rectangular box with a square base which has a volume of 12 cubic feet is a = 12^ 1/3, b = 12^ 1/3

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By combining like terms, the expression 3q + 9q - q simplifies to 11q.

To simplify the given expression, we combine the like terms, which means adding or subtracting the terms that have the same variable and exponent.

The expression 3q + 9q - q consists of three terms: 3q, 9q, and -q. Among these terms, 3q and 9q are like terms because they have the same variable (q) raised to the first power. By adding the coefficients of the like terms, we have:

3q + 9q = 12q

Then, subtract the third term, -q, from the result:

12q - q = 11q

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Let's suppose the amount of alcohol in the container after time t is x. The mixture in the container has two components, water and alcohol. The volume of the solution at any given time is y. We are given the following:  One solution is composed of alcohol and water. The container is initially filled with y gallons of a mixture of alcohol and water.

The rate at which the second solution is added is a gallons per minute. The rate at which the container is drained is b gallons per minute. The solution in the container is constantly stirred. To solve the problem, we will set up a differential equation and solve it. The differential equation is:

dy/dt = a - bAt  any given time, the amount of alcohol in the mixture is x. The percentage of alcohol in the mixture is given by:x/y * 100%Let's suppose that the concentration of the alcohol in the second solution is c%. The amount of alcohol in the second solution that is added in time t is :

c * a * t  The amount of water that is added to the container in time t is:

(1 - c) * a * t So, the total amount of alcohol in the container after time t is:

x + c * a * t The total amount of water in the container after time t is:

y + (1 - c) * a * t The total amount of solution in the container after time t is:

y + a * t - b * t Since the solution is constantly stirred, the percentage of alcohol in the mixture remains constant. Therefore:

x / (y + a * t - b * t) * 100% = x / y * 100%Solving for x, we get:

x = (y + a * t - b * t) * (x / y)The equation gives us the amount of alcohol in the container after time t. The amount of alcohol in the container after t minutes is (y + a * t - b * t) * (x / y).

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Answer:

m = -1

n= -8

Step-by-step explanation:

5m -3n = 19

m - 6 = -7

solve for m:

m = -7+6

m = -1

plug in m

5(-1) - 3n = 19

-5 - 3n = 19

-3n = 24

n = -8

The probability mode for the given value is created. The expected value and standard deviation of prospective winnings are -$0.28 and $18.33. The expected value and standard deviation if the game is played five times are -$1.40 and $40.99. The probability that the person running the game makes a profit is 0.561.

Probability is a way to determine how likely something is to happen. It is computed by dividing the frequency of the event by the total number of outcomes. The formula then becomes P(X) = frequency of the event÷total number of outcomes.

The product of the probabilities determines the likelihood that two or more occurrences will coincide. This is given by, P(A and B) = P(A)P(B).

a) To create a probability model follow the steps. Let X is an occurrence of an event.  The table is attached here.

b)  The expected value is calculated using the formula, E(X) = μ = ∑ x P(x).

\(\begin{aligned}E(X)=\mu&=x_1p_1+x_2p_2+x_3p_3\\&=40\left(\frac{1}{6}\right)+0\left(\frac{5}{36}\right)+(-10)\left(\frac{25}{36}\right)\\&=-\$ 0.28\end{aligned}\)

Also,

\(\begin{aligned}E(X^2)&={x_1}^{2}p_{1}+{x_2}^{2}p_{2}+{x_3}^{2}p_{3}\\&=(40)^2\frac{1}{6}+(0)\frac{5}{36}+(-10)^2\frac{25}{36}\\&=(1600)\frac{1}{6}+(0)\frac{5}{36}+(100)\frac{25}{36}\\&=266.67+69.44\\&=336.11\end{aligned}\)

And the standard deviation is calculated using the formula, σ=√Var[X].

\(\begin{aligned}\sigma=\sqrt{\text{Var}(X)}&=\sqrt{E(X^2)-E(X)^2}\\&=\sqrt{336.11-0.08}\\&=\sqrt{336.03}\\&=\$18.33\end{aligned}\)

c) The expected value and standard deviation for playing the game 5 times are calculated as follows.

The expected value is,

\(\begin{aligned}5\times E(X)&=5(-\$0.28)\\&=-\$1.40\\\end{aligned}\)

The standard deviation is,

\(\begin{aligned}\sigma&=\sqrt{5\times\tex{Var}(X)\\&=\sqrt{5\times336.03\\&=\sqrt{1680.15}\\&=\$40.99\end{aligned}\)

d) The dice rolling is random and the winning chance is independent. The probability the person running the game makes a profit (P(x<0)) is given by,

The population mean, μ(Y) = -$0.28

The standard deviation for a population of 100 is,

\(\begin{aligned}\sigma&=\sqrt{\frac{\text{Var}(X)}{n}}\\&=\frac{18.33}{\sqrt{100}}\\&=1.83\end{aligned}\)

The z-score for mean winning is,

\(\begin{aligned}z&=\frac{x-\mu}{\sigma}\\&=\frac{0-(-0.28)}{1.83}\\&=0.153\end{aligned}\)

For a person to make a profit, the mean winning of the player should be less than the z-score. Then,

The P-value from the z-table, P(z<0.153)=0.5608

The answer is 0.561.

The complete question is -

You pay $10 and roll a die. If you get a 6, you win$50. If not, you get to roll again. If you get a 6 this time, you get your $10 back. a) Create a probability model for this game. b) Find the expected value and standard deviation of your prospective winnings. c) You play this game five times. Find the expected value and standard deviation of your average winnings. d) 100 people play this game. What’s the probability the person running the game makes a profit?

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The dimensions of the rectangular pen to minimize the amount of material needed is 4L which gives 160ft.

The minimum length or breadth of the open space type, as measured along the longest two (2) straight lines meeting at a right angle to define the lot's maximum length and width.

With regard to the above problem,

let us say L is the lenght of the rectangle and W is the width

Based on the formula for the area of a rectangle,

L x W  = 1600ft

To minimize the perimeter, of the rectangle, we must assume that:

L = W

that is L² = 1600

If we applied square root to both sides of the equation, we'd have


L = 40

Thus the minimum perimeter is given as: 4L = 4 x 40 = 160ft.

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