A homeowner is planning to paint an 8 foot by 22 foot wall and wants to determine the cost of the project. She tests a 14 inch by 18 inch section of the wall and finds that 1 ounce of paint is needed for good coverage. If she uses paint that costs $28 per gallon, what will be the cost of the paint needed to give the entire wall a good coverage of paint?

The equation formed after the transformations is given as follows:

\(g(x) = \frac{1}{6}\sqrt{x + 3}\)

The parent function in this problem is defined as follows:

\(f(x) = \sqrt{x}\)

For the vertical shrink by a factor of 1/6, the function is multiplied by 1/6, hence it is given as follows:

\(g(x) = \frac{1}{6}\sqrt{x}\)

For the translation left 3 units, we have that x -> x + 3, hence:

\(g(x) = \frac{1}{6}\sqrt{x + 3}\)

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The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.

The correct answer choice is option B.

Malcolm's gift card = $50.

Cost Malcolm's car wash per visit = $7

Martha's gift card = $180

Cost Martha's car wash per visit = Difference between gift card balance of first and second visit

= $180 - $160

= $20

How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7

= $13

Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13

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Answer:

A

Step-by-step explanation:

It needs to do that route I guess. But I don't understand the last question well.

Step-by-step explanation:

Pythagoras's rule:  \(a^2 + b^2 = c^2\)  becomes  \(x^2 + 10^2 = y^2\)

If we say b = 10: \(b = 10 = \sqrt{c^2 - a^2} = \sqrt{y^2 - x^2}\)

You only need to look at the left triangle

Which of the options follows Pythagoras's rule?

Let's try the options until we get the right one (in no particular order)

If we try: 3) x = 4 y = \(29\sqrt{2}\)...

\(\sqrt{(29\sqrt{2})^2 - 4^4} = 7\sqrt{34} \neq 10\)

If we try: 4) x = 16 y = 116...

\(\sqrt{116^2 - 16^2} = 20\sqrt{3} \neq 10\)

If we try: 2) x = 16 y = 29...

\(\sqrt{29^2 - 16^2} = 3\sqrt{65} \neq 10\)

If we try: 1) x = 4 y = \(2\sqrt{29}\)...

\(\sqrt{(2\sqrt{29})^2 - 4^2} = 10\)

The correct answer is option B.

The observation of a giant storm on Saturn from spacecraft Cassini indicates that lightning was not detected in the giant storm.

Usually Mega storms on Saturn happen on every 20 to 30 years.

Through the Cassini spacecraft, scientists could see a massive storm in December 2010. They saw that the storm waves were spreading from the planet's centre and that it was seen as a ringed globe.

The storm waves covered the whole surface of Saturn and had a diameter of around 190,000 miles or 300,000 kilometres.

Simply said, this enormous storm is also known as the Great Northern Storm or the Great White Spot.

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Answer:20

Step-by-step explanation:this is wrong

Answer:

40

Step-by-step explanation:

subtract median of dogs and median of cats

With the help of probability we can say that, DUM={GG,BB,GB,BG).

Probability is the concept that describes the likelihood of an event occurring.

In real life, we frequently have to make predictions about how things will turn out.

We may be aware of the result of an occurrence or not.

When this occurs, we state that there is a possibility that the event will occur.

In general, probability has many excellent applications in games, commerce, and this newly growing area of artificial intelligence

The chance of an event can be calculated using the probability formula by only dividing the favourable number of possibilities by the total number of potential outcomes.

hence, DUM={GG,BB,GB,BG)

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Answer: It looks like you are trying to use the Law of Sines to find the value of x. The Law of Sines states that, in any triangle, the ratio of the sine of an angle to the length of the side opposite that angle is the same for all three angles and all three sides. In other words, if A, B, and C are the angles of a triangle and a, b, and c are the lengths of the sides opposite those angles, then:

sin A / a = sin B / b = sin C / c

To find the value of x, you need to plug in the values of the angles and the side lengths that you know, and then solve for x. Based on the information you provided, it looks like you know the values of A, B, and c. Therefore, you can use the Law of Sines to write the following equation:

sin A / x = sin B / b = sin C / c

You can then solve for x by cross-multiplying and rearranging the terms:

x = (b * sin A) / sin B

Plugging in the values you know, you get:

x = (b * sin 28°) / sin 83°

You can then use a calculator to find the value of x. When you do this, you will get a value of approximately 5.2. Rounded to the nearest tenth, the value of x is 5.2. The other options you gave are not equal to 5.2.

The value of x using sine rule is 8.5 (nearest tenth)

The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.

Sine rule is used to find unknown side and unknown angle when the other side and corresponding angle is given.

The corresponding angle to 18 is 83°

The corresponding angle to x is 28°

Therefore;

x/sin28 = 18/sin83

18sin28 = xsin83

8.45 = 0.992x

divide both sides by 0.992

x = 8.45/0.992

x = 8.5 (nearest tenth)

Therefore the value of x to the nearest tenth is 8.5

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The height of the parallelogram is 8 inches. By using the formula for the area of a parallelogram, we were able to find the missing value (height) by rearranging the formula and plugging in the given values.

To find the height of the parallelogram, we can use the formula for the area of a parallelogram, which is Area = Base × Height (A = b × h). In this problem, the area (A) is given as 40 square inches, and the base (b) is 5 inches. We need to find the height (h).

Using the formula, A = b × h, we can plug in the given values:

40 = 5 × h

To solve for h, we can divide both sides of the equation by 5:

40 ÷ 5 = 5 × h ÷ 5

8 = h
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Answer:

0.5 = 0.500

Step-by-step explanation:

Both numbers are five-tenths. The zeros to the right of the 5 are not place holders and do not change the value of the number.

0.5 = 0.500

Answer:

$8/pound

Step-by-step explanation:

$40 ÷ 5 lbs = 8$ per pound

Answer:

A

Step-by-step explanation:

-9/j  is the same as 9/-j

The firm should produce good  x₁ = 4 and x₂ = 8 to minimize cost of C = x₁² + x₂² .

What is Lagrange multipliers ?

Lagrange multipliers is a method used in optimization problems to find the maximum or minimum value of a function subject to one or more constraints. The method involves introducing a Lagrange multiplier, which is a scalar variable, to the objective function and the constraint(s). This forms the Lagrangian function, which is then optimized with respect to the original variables and the Lagrange multiplier.

To minimize the cost C = x₁² + x₂²

We can use the method of Lagrange multipliers to solve this problem. Let's define the Lagrangian function L as:

L(x₁, x₂, λ) = x₁²+ x₂² + λ(400 - 5x₁²- 8x₁x₂ - 15x₂²)

Taking partial derivatives of L with respect to x₁, x₂, and λ, we get:

∂L/∂x₁ = 2x₁ - 10λx₁ - 8λx₂ = 0

∂L/∂x₂ = 2x₂ - 30λx₂ - 8λx₁ = 0

∂L/∂λ = 400 - 5x₁² - 8x₁x₂ - 15x₂² = 0

Solving these equations simultaneously, we get:

x₁ = 4

x₂ = 8

λ = 1/20

Hence, the firm should produce a combination of x₁ = 4 and x₂ = 8 to minimize the cost of C = x₁² + x₂² while satisfying the production quota of 400.

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Answer:

AD = 15

Step-by-step explanation:

Based on the Pythagoras Theorem, the longest side of a right-angled triangle is: \(\sqrt{a^{2}+b^{2}}\) where a and b are the legs of the triangle.

In triangle BDC, we can put in the formula to find BD.

85 = \(\sqrt{77^{2}+BD^{2}}\)

85² = 77² + BD²

7225 = 5929 + BD²

BD² = 7225 - 5929

       = 1296

BD = \(\sqrt{1296}\)

BD = 36

In triangle ABD, we can put in the formula to find AD.

39 = \(\sqrt{36^{2}+AD^{2}}\)

39² = 36² + AD²

1521 = 1296 + AD²

AD² = 1521 - 1296

       = 225

AD = \(\sqrt{225}\)

AD = 15

Answer:

x = 27 , ∠ EAF = 27°

Step-by-step explanation:

∠ GAF = 90° , then

∠ GAC + ∠ CAF = ∠ GAF , that is

x + 63 = 90 ( subtract 63 from both sides )

x = 27

∠ DAE = 90°

since CD is a straight angle of 180° , then

∠ CAE = 90° , so

∠ CAF + ∠ EAF = ∠ CAE , that is

63° + ∠ EAF = 90° ( subtract 63° from both sides )

∠ EAF = 27°

1. In this case, we want the reliability to be 95%, so the probability of not breaking down is 0.95.

2. Probability of no breakdowns = (reliability of a single machine)^3. Probability of at least one breakdown = 1 - Probability of no breakdowns

1. To determine how often the computer should be scheduled for maintenance, we need to consider the reliability and the desired level of operational condition. Since the duration for trouble-free operation follows a gamma distribution with a mean of 40 days, this means that, on average, the computer can operate for 40 days before a breakdown occurs.

To ensure operational condition with a 95% probability, we can calculate the maintenance interval using the concept of reliability. The reliability represents the probability that the machine will not break down within a certain time period. In this case, we want the reliability to be 95%, so the probability of not breaking down is 0.95.

Using the gamma distribution parameters, we can find the corresponding reliability for a specific time duration. By setting the reliability equation equal to 0.95 and solving for time, we can find the maintenance interval:

reliability = 0.95

time = maintenance interval

Using reliability and the gamma distribution parameters, we can calculate the maintenance interval.

2. To calculate the probability that at least one of the three machines will break down within the first scheduled maintenance time, we can use the complementary probability approach.

The probability that none of the machines will break down within the first scheduled maintenance time is given by the reliability of a single machine raised to the power of the number of machines:

Probability of no breakdowns = (reliability of a single machine)^3

Since the breakdown times between the machines are statistically independent, we can assume that the reliability of each machine is the same. Therefore, we can use the reliability calculated in the first part and substitute it into the formula:

Probability of at least one breakdown = 1 - Probability of no breakdowns

By calculating this expression, we can determine the probability that at least one of the three machines will break down within the first scheduled maintenance time.

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Answer: 7

i took the test

The probability of selecting a person at random is p(w and f) is 0.0216 or 2.16%.

The probability of an event occurring and another event occurring is found by using the multiplication rule of probability, which states that the probability of two events occurring together is equal to the product of the probabilities of each event occurring independently.

In this case, we are looking for the probability of a person being born in the winter (p(w)) and the probability of a person being born in the fall (p(f)), so we would calculate:

p(w and f) = p(w) * p(f)

Using the information provided, we know that:

p(w) = 12% = 0.12

p(f) = 18% = 0.18

So, to find p(w and f), we would multiply:

p(w and f) = 0.12 * 0.18 = 0.0216 or 2.16%

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Answer:

0

0.30

0.82

0.70

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

using the recursive rule \(a_{n}\) = 3\(a_{n-1}\) and a₁ = 10, then

a₁ = 10

a₂ = 3a₁ = 3 × 10 = 30

a₃ = 3a₂ = 3 × 30 = 90

the first 3 terms are 10 , 30 , 90

Answer: Yes

Step-by-step explanation:

Most fractions can be simplified into smaller fractions, while some are in it's simplest form. When putting a bit in its simplest form it is much easier to compare to other fractions  

What I did first tried to simplify all the factions, starting with 1 1/2.

After looking at 1 1/2, I can see that it is in its simplest form.

Then looking at 1 2/4 I can see that it can be simplified into 1 1/2.

Lastly looking at 1 3/6 I can see that it can be simplified into 1 1/2.

The total materials handling cost allocated to the modular homes is $246,372.84.

The total materials handling cost allocated to the Prefab Barns is closest to $108,000.

To allocate materials handling cost based on material moves, we must determine proportion of material moves for each product and then apply that proportion to the total materials handling cost.

Proportion of material moves for Modular Homes:

= (Total expected material moves for Modular Homes) / (Total expected material moves for both products)

= 590 / (590 + 190)

= 0.756

Total materials handling cost allocated to Modular Homes:

= Proportion of material moves for Modular Homes * Total materials handling cost

= 0.756 * $325,890

= 246 372.84

= $246,372.84.

To allocate the materials handling cost based on direct labor-hours, we need to determine proportion of direct labor-hours for each product.

For Modular Homes:

Total direct labor-hours for Modular Homes:

= 6,000 units * 800 hours/unit

= 4,800,000 hours

For Prefab Barns:

Total direct labor-hours for Prefab Barns:

= 9,000 units * 300 hours/unit

= 2,700,000 hours

Total direct labor-hours for both products:

= 4,800,000 hours + 2,700,000 hours

= 7,500,000 hours

Proportion of direct labor-hours for Prefab Barns:

= 2,700,000 hours / 7,500,000 hours

= 0.36

Allocated materials handling cost for Prefab Barns:

= Proportion of direct labor-hours for Prefab Barns * Total materials handling cost

= 0.36 * $300,000

= $108,000.

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Answer:

z = 3/31

Step-by-step explanation:

5z + 3 = 36z

subtract 5z on both sides

3 = 31z

divide by 31 on both sides

z = 3/31

By definition, the Slope-Intercept form of the equation of a line is:

Where "m" is the slope of the line and "b" is the y-intercept.

In this case, you have the following equation of the line given in the exercise:

You can rewrite it as following:

Therefore, knowing the explained before, you can identify that:

The answer is:

• Slope:

• y-intercept:

At least 75% of the data might very well fall between $3.25 and $3.81. According to Chebyshev's theorem, at least 75% of the value systems in a distribution are well within 2 the mean standard deviation.

A delivery has at least 89% of its values inside of three of the mean's standard deviation.

We have the following in this problem:

Mean = $3.53

$0.14 is the standard deviation.

Using Chebyshev's Theorem, determine the range that contains least 75% of the information will live.

2 standard deviations from the mean.

So 3.53 - 2*0.14 = $3.25 becomes 3.53 + 2*0.14 = $3.81.

At least 75% of the data might very well fall between $3.25 and $3.81.

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Answer:

p = 5

Step-by-step explanation:

-3(-3-4p) = 69

-3×(-3) + -3× (-4p) = 69

9 + 12p = 69

12p + 9 - 9 = 69 - 9

12p = 60

p = 5

Hope this helps!!!

slope = -170. y-intercept = 1020

Step-by-step explanation:

Let \(P_1(0, 1020)\) and \(P_2(6, 0).\) The slope can be calculated as

\(m = \dfrac{0 - 1020}{6 - 0} = -170\:\text{m/hr}\)

So the equation can be written as

\(y = -170x + b\)

To solve for b, let's use the values for P2:

\(0 = -170(6) + b \Rightarrow b = 1020\)

Therefore,

\(y = -170x + 1020\)

To find the y-intercept, let x = 0. then the y-intercept is

\(y = -170(0) + 1020\)

or

\((0, 1020).\)

Answer:

13 hours

Step-by-step explanation:

Set up a proportion.

464 miles / 8 hours = 754 miles / x hours

Cross multiply

464x = 6032

Divide by 464 on both sides

x = 13

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Answer:

The percentage of adult female reaction times that lie between 140.5 and 648.1 milliseconds is 99.7%.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 394.3 ms

Standard deviation = 84.6 ms

Use the Empirical Rule to determine the approximate percentage of adult female reaction times that lie between 140.5 and 648.1 milliseconds.

140.5 = 394.3 - 3*84.6

So 140.5 is 3 standard deviations below the mean.

648.1 = 394.3 + 3*84.6

So 648.1 is 3 standard deviations above the mean.

By the Empirical Rule,

The percentage of adult female reaction times that lie between 140.5 and 648.1 milliseconds is 99.7%.