Komi and Jordan are each working during the summer to earn money in addition to their wecky

allowance and they are saving all their money Kimi earns $9 an hour at her job and her alowance

15 58 per week Jordan earns 57 50 an hour and his allowance is $16 per week. If the number of hours worked in a week is one, what are Kimi’s weekly total savings?

The expression for temperature change in City A is 9 + (-8)

The amount the temperature changes for City A = 1°F

The expression for temperature change in City B is -1 + (-3) = -4°F

The amount the temperature changes for City B = -4°F

Based on the available data:

The expression for that represents the temperature change from 8 am to 10 am is, therefore;

The temperature change from 8 am to 10 am are

Sum, change from 8 am to 10 am = 9 + (-8) = 1°F

The temperature change from 8 am to 10 am are

Sum, change from 8 am to 10 am = -1 + (-3) = -4°F

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Answer:

-32+20x

Step-by-step explanation:

Times the -16 and the two.

a) The maximum revenue is $648.

b) The x of the vertex represents the number of $0.50 price decreases.

c) Alex can maximize her revenue by charging a price of $6.

d) Alex must sell 108 snowboards to maximize her revenue.

To solve this problem, we can use the quadratic equation for revenue, which is given by R(x) = (P - 0.5x)(36 + 2x),

where x represents the number of $0.50 price decreases and P represents the original price of $12.

a) To find the maximum revenue, we need to find the vertex of the quadratic equation.

The vertex is given by the formula x = -b/2a,

where a and b are the coefficients of the quadratic equation.

In this case, a = -0.5 and b = 36.

Substituting these values into the formula, we have:

\(x = -36 / (2 \times -0.5)\)

x = -36 / -1

x = 36  

To find the maximum revenue, we substitute the value of x = 36 back into the revenue equation:

R(x) = (P - 0.5x)(36 + 2x)

\(R(x) = (12 - 0.5 \times 36)(36 + 2 \times 36)\)

R(x) = (12 - 18)(36 + 72)

R(x) = (-6)(108)

R(x) = -648

Therefore, the maximum revenue is -$648.

However, since revenue cannot be negative, we take the absolute value, so the maximum revenue is $648.

b) The x of the vertex represents the number of $0.50 price decreases.

c) To find the price at which Alex can maximize her revenue, we substitute the value of x = 36 back into the price equation:

Price = P - 0.5x

\(Price = 12 - 0.5 \times 36\)

Price = 12 - 18

Price = -6

Since price cannot be negative, we disregard the negative value. Therefore, Alex can maximize her revenue by charging a price of $6.

d) To find the number of snowboards that must be sold to maximize revenue, we substitute the value of x = 36 back into the rental equation:

Number of snowboards = 36 + 2x

Number of snowboards \(= 36 + 2 \times 36\)

Number of snowboards = 36 + 72

Number of snowboards = 108.

Alex must sell 108 snowboards to maximize her revenue.

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a) A sample size of approximately 3717 is required to estimate the population mean with a 95% confidence level and a margin of error of 2.

b) A sample size of approximately 1769 is required to estimate the population mean with a 99% confidence level and a margin of error of 2.5.

1) To determine the sample size required to estimate a population mean with a 95% confidence level and a margin of error of 2, we can use the formula:

n = (z² × σ²) / E²

where:

n is the sample size

z is the z-score corresponding to the desired confidence level (95% confidence level corresponds to z = 1.96)

σ is the population standard deviation

E is the margin of error

Substituting the given values into the formula:

n = (1.96² × 62.3²) / 2²

n = (3.8416 × 3872.29) / 4

n = 14865.57 / 4

n ≈ 3716.39

Therefore, a sample size of approximately 3717 is required to estimate the population mean with a 95% confidence level and a margin of error of 2.

2) Similarly, to determine the sample size required to estimate a population mean with a 99% confidence level and a margin of error of 2.5, we can use the same formula:

n = (z² × σ²) / E²

Substituting the given values into the formula:

n = (2.576² × 40.8²) / 2.5²

n = (6.6406 × 1664.64) / 6.25

n = 11051.93 / 6.25

n ≈ 1768.31

Therefore, a sample size of approximately 1769 is required to estimate the population mean with a 99% confidence level and a margin of error of 2.5.

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Answer:

2.5

Step-by-step explanation:

Answer:

Step-by-step explanation:

25%

The \((3,-3)\)is a solution of the inequality \(y\leq -5x + 3\).

We can test whether\((3,-3)\)is a solution of the inequality \(y \leq -5x + 3\) by substituting the values of x and y into the inequality and seeing if the inequality is true or false.

Substituting \(x=3\) and \(y=-3\) into the inequality, we get:

\(-3 \leq -5(3) + 3\)

Simplifying the right side of the inequality, we get:

\(-3 \leq -15 + 3\\-3 \leq -12\)

Since \(-3\) is indeed less than or equal to \(-12\), the inequality is true when \(x=3\) and \(y=-3\).

Therefore, \((3,-3)\) is a solution of the inequality \(y \leq -5x + 3\).

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The numbers in the eighth row of Pascal's Triangle are 1 7 21 35 35 21 7 1.

The numbers in the eighth row of Pascal's Triangle are:

1 7 21 35 35 21 7 1

In Pascal's Triangle, each number is obtained by adding the two numbers directly above it. The first and last numbers in each row are always 1. To generate subsequent rows, we add the adjacent numbers from the previous row to obtain the new numbers.

For example, to generate the eighth row:

Row 7: 1

Row 8: 1  +  7  +  21  +  35  +  35  +  21  +  7  +  1

Therefore, the numbers in the eighth row of Pascal's Triangle are 1 7 21 35 35 21 7 1.

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A list of steps, in order, that will solve the following equation include the following:

In order to create a list of steps and determine the solution to the equation, we would have to add 5 to both sides and divide both sides by 2 in order to open the parenthesis as follows;

2(x + 3) – 5 = 123

2(x + 3) – 5 + 5 = 123 + 5

2(x + 3) = 128

By dividing both sides of the equation by 2, we have the following:

2(x + 3)/2 = 128/2

x + 3 = 64

By subtracting 3 from both sides of the equation, we have the following:

x + 3 - 3 = 64 - 3

x = 61

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Answer:

are u ok tho

Step-by-step explanation:

The calculated area of the base is 5

From the question, we have the following parameters that can be used in our computation:

Volume of the prism = 100

Height of the prism = 20

Using the above as a guide, we have the following:

Base area = Volume of the prism /Height of the prism

substitute the known values in the above equation, so, we have the following representation

Base area = 100/20

Evaluate

Base area = 5

Hence, the area of the base is 5

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In order to find the time of the loan in months, we can use the formula for simple interest.

I = P * r * t

I = 1365€ (interest earned).

P = $28,000 (principal amount).

r = 6.5% = 0.065 (interest rate in decimal form).

We can rearrange the formula to solve for t.

t = I / (P * r).

Substituting the values.

t = 1365€ / (28000€ * 0.065).

t ≈ 0.75.

Since there are 12 months in a year, we can multiply the result by 12.

t (months) = 0.75 * 12 ≈ 9 months.

Therefore, the time of the loan is approximately 9 months.

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The approximate probability that the total score is at least 375 when a fair six-sided die is rolled 100 times is (d) 0.4420.

When a fair six-sided die is rolled, the random variable X represents the outcome. The mean (μX) of X is 3.5, and the standard deviation (σX) is 1.71.

To find the probability that the total score is at least 375 when the die is rolled 100 times, we can use the Central Limit Theorem. According to the theorem, the sum of a large number of independent and identically distributed random variables approximates a normal distribution.

In this case, the sum of the outcomes of 100 rolls of the die follows a normal distribution with a mean of μX multiplied by the number of rolls (100) and a standard deviation of σX multiplied by the square root of the number of rolls (10). Therefore, the approximate probability can be calculated by finding the probability that the sum is greater than or equal to 375.

Using a normal distribution table or a calculator, we can find that the approximate probability is 0.4420, which corresponds to answer (d). This means that there is a 44.20% chance that the total score will be at least 375 when the die is rolled 100 times.

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The coordinate of the circumcenter of a triangle is (1,3).

Here we have to find the coordinates of the circumcenter of a triangle.

Given data:

The vertices of the triangle are:

A = (0,1)

B = ( 2,1)

C= ( 2,5)

The formula to find the distance between the two points:

Distance = \(\sqrt{(x2 - x1)^{2} + (y2-y1)^{2} }\)

In the same manner distance between AB, BC, and AC are:

AB = \(\sqrt{(2-0)^{2} + (1-1)^{2} }\)

    = 2

BC = \(\sqrt{(2-2)^{2} + (5-1)^{2} }\)

      = 4

AC = \(\sqrt{(2-0)^{2} + (5-1)^{2} }\)

     = 2√5

So by the Pythagoras, we get to know that the triangle is a right-angle triangle.

The circumcenter of a right-angle triangle is the midpoint of the hypotenuse.

Midpoint of AC = (0+2)/2 , (1+5)/2

                         = 2/2, 6/2

                         = 1,3

Therefore the coordinate of the circumcenter is (1,3).

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Answer:

integer

Step-by-step explanation:

Unit price of the first bag: $2.08/kg and the unit price of the second bag: $2.04/kg. Therefore, the second bag is the better buy based on the lower unit price.

To find the unit price for each bag, we use the unitary method

Unitary method is a mathematical method that involves finding the value of a single unit, and then using that value to solve problems related to proportional quantities.

Divide the cost of the bag by its weight

Unit price of the first bag: $12.67 ÷ 6.08 kg ≈ $2.08/kg

Unit price of the second bag: $12.95 ÷ 6.35 kg ≈ $2.04/kg

Rounded to the nearest cent, the unit price of the first bag is $2.08/kg and the unit price of the second bag is $2.04/kg.

To determine which bag is the better buy based on the unit price, we look for the lower unit price. In this case, the second bag has the lower unit price, so it is the better buy.

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Answer:

16.3333333 is the correct answer.

(a) Using the given data, we can verify the calculations as follows: ∑x = 245, ∑x^2 = 14,755, ∑y = 224.

(b) To compute the sample mean, variance, and standard deviation for the percentage success of mallard duck nests (x), we use the formulas:

Sample Mean (x) = ∑x / n

Variance (s^2) = (∑x^2 - (n * x^2)) / (n - 1)

Standard Deviation (s) = √(s^2)

(c) Applying the formulas, we can compute the sample mean, variance, and standard deviation for x as follows:

Sample Mean (x) = 245 / 5 = 49

Variance (s^2) = (14,755 - (5 * 49^2)) / (5 - 1) = 4,285

Standard Deviation (s) = √(4,285) ≈ 65.5

Similarly, for the percentage success of Canada goose nests (y), the calculations can be done using the same formulas and the given values from part (a).

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Answer:

( x + 5 )² + ( y - 8 )² = 25

Step-by-step explanation:

Standard form for the equation of a circle - ( x - h )² + ( y - k )² = r²

Where r = radius and Center is located at ( h , k )

We are given that the center is at ( -5 , 8 )

Thus, h = -5 and k = 8

We are also given that the radius = 5

Thus, r = 5

Now we just plug all of the given values into the standard form equation

( x - (-5))² + ( y - 8 )² = 5²

*simplify*

in - ( - 5 ) the two negative sign cancel out and it turns into + 5

5² = 25

Thus, the equation is ( x + 5 )² + ( y - 8 )² = 25

The solution to the equation -2/(x - 8) = (x - 1)/(x + 2) is x = 3 after checking for extraneous solutions.

To solve the equation

-2/(x - 8) = (x - 1)/(x + 2)

We can start by cross-multiplying to eliminate the fractions

-2(x + 2) = (x - 1)(x - 8)

Simplifying both sides, we get

-2x - 4 = x² - 9x + 8

Bringing all the terms to one side, we get

x² - 7x + 12 = 0

Now we can factor the quadratic equation to get

(x - 3)(x - 4) = 0

So the solutions are x = 3 and x = 4. However, we need to check for any extraneous solutions that may have been introduced by the original equation.

Plugging in x = 3 to the original equation, we get

-2/(3 - 8) = (3 - 1)/(3 + 2)

Which simplifies to

2/5 = 2/5

Therefore, x = 3 is a valid solution.

Plugging in x = 4 to the original equation, we get

-2/(4 - 8) = (4 - 1)/(4 + 2)

Which simplifies to

1/2 = 3/6

Therefore, x = 4 is not a valid solution.

So the only solution to the equation is x = 3.

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Answer:

Option B ( 47° )

Step-by-step explanation:

Use the cosine identity

\(cos\alpha =\frac{base}{hypotenuse}\\\\cos\alpha =\frac{19}{28}\\\\\alpha =cos^{-1}(\frac{19}{28})\\\\\alpha=47\\\)

Answer:

No, it is AAS.

Step-by-step explanation:

By vertical angle theorem ∠KLJ≅∠MLN.

And the given congruent sides are not between the two congruent angles, therefore it cannot be ASA.

Triangle KLJ ≅ Triangle MLN

Answer: Area = π × 42 = 16π square feet

Step-by-step explanation:

Step 1: Find the radius of the window.

Radius = 8 feet / 2 = 4 feet

Step 2: Use the formula for the area of a circle.

Area = π × radius2

Step 3: Calculate the area.

Area = π × 42 = 16π square feet

The domain of this function p is (9,000 - x)/30, the marginal cost is 30 dollars per TV and revenue function is x(9,000 - x)/30. The marginal revenue is  (9,000 - 2x)/30 and  profit function in terms of x is R(x) -.

(A) To express the price p as a function of the demand x, we can solve the price-demand equation for p:

x = 9,000 - 30p

30p = 9,000 - x

p = (9,000 - x)/30

The domain of this function is the set of values of x for which the price is non-negative, since negative prices do not make sense in this context. Therefore, the domain is 0 ≤ x ≤ 9,000.

(B) The marginal cost is the derivative of the cost function with respect to x: C'(x) = 30

So the marginal cost is a constant value of 30 dollars per TV.

(C) The revenue function R(x) is the product of the demand x and the price p: R(x) = xp = x(9,000 - x)/30

The domain of this function is the same as the domain of the price function, which is 0 ≤ x ≤ 9,000.

(D) The marginal revenue is the derivative of the revenue function with respect to x: R'(x) = (9,000 - 2x)/30

(E) To find R'(3,000) and R'(6,000), we substitute x = 3,000 and x = 6,000 into the expression for R'(x):

R'(3,000) = (9,000 - 2(3,000))/30 = 100

R'(6,000) = (9,000 - 2(6,000))/30 = -100

Interpretation: R'(3,000) represents the extra money made from selling one more TV at a constant price when the demand is 3. When the demand is 6,000 TVs and the price remains the same, R'(6,000) represents the decrease in revenue from selling one fewer TV.

(F) To graph the cost function and the revenue function, we can plot the two functions on the same coordinate system, using the given domain of 0 ≤ x ≤ 9,000. The break-even points are the values of x for which the cost and revenue are equal, or C(x) = R(x).

C(x) = 150,000 + 30x

R(x) = x(9,000 - x)/30

Setting C(x) = R(x), we get:

150,000 + 30x = x(9,000 - x)/30

900,000 - 30x^2 = 30(150,000 + 30x)

900,000 - 30x^2 = 4,500,000 + 900x

30x^2 - 900x + 3,600,000 = 0

x^2 - 30x + 120,000 = 0

(x - 6,000)(x - 20) = 0

The break-even points are x = 6,000 and x = 20. These correspond to the intersections of the cost and revenue curves. The region to the left of x = 6,000 is a region of loss, since the revenue is less than the cost for x < 6,000. The region between x = 6,000 and x = 20 is a region of profit, since the revenue exceeds the cost for 6,000 < x < 20. The region to the right of x = 20 is again a region of loss, since the revenue is less than the cost for x > 20.

(G) The profit function is given by subtracting the cost function from the revenue function:

P(x) = R(x) -

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According to the empirical rule of IQ scores no higher than 125 and less than 77, the percentage is found to be 97.5%.

From the above data, we can determine the mean (U) and standard deviation (p), which are respectively 101 and 12.

And we're looking for the percentage that isn't greater than 125. We can utilise the calculation for the z score, which is as follows: z = X-U/p X is the percentage,

And by using the value provided, we obtained: z = (125-101)/12

z = 2.

According to the empirical rule, 95% of the values fall between two standard deviations, while 5% fall in the tails.

As a result the percentage is required to be less than the 2 standard deviation but above the mean which is equal to (100-2.5)=97.5%.

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The angle of elevation of the sun is \(tan^{-1}\)(106/ 135).

The angle of elevation:

The angle is formed by the line of sight and the horizontal plane for an object above the horizontal.

Here we have to find the angle of elevation of the sun.

Data given:

length of the tower = 106 feet

shadow form by the tower = 135 feet

The formula for the angle of elevation = height/base

tanФ = height/base

        = 106/ 135

Ф = \(tan^{-1}\)(106/135)

Therefore the angle of elevation is \(tan^{-1}\)( 106/ 135).

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Answer:

The answer is 7.5

Step-by-step explanation:

Put them in order of smallest to largest

2,6,7,7,8,8,9,15

Pick out the middle number

answer is 7.5

1 Order them from smallest to biggest

2 Cross them one by one from each side to find the middle number.

3 If there are two numbers like in this question you add them and divide by 2.

7+8= 15

15÷2=7.5

By studying the mean and standard deviation,

The value of test statistic z is 1.897

What is mean and standard deviation?

Suppose there is a data set. Mean is the average of all the values of the data set

Before knowing about standard deviation, it is important to know about variance first.

Variance is the sum of the square of deviation from mean.

On taking the square root of variance, standard deviation is obtained.

Population mean = 5.5

Population standard deviation = 2

Sample size = 10

Sample mean = 6.7

Test statistic z =

                        \(\frac{6.7 - 5.5}{\frac{2}{\sqrt{10}}}\\\\1.897\)

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In the men's 100-meter backstroke event at the 2012 Olympics, there were multiple rounds of competition, including the semifinal and final rounds.

The upper dot plot represents the times of the top 888 finishers in the final round, while the lower dot plot represents the times of the same 888 swimmers in the semifinal round. It is mentioned that the center of the semifinal round distribution is the center of the final round distribution. This means that the average times in the semifinal and final rounds are similar.

Additionally, it is stated that the variability in the semifinal round distribution is the same as the variability in the final round distribution. This implies that the spread or range of times in both rounds is similar. Therefore, the center and variability of the semifinal round distribution are comparable to those of the final round distribution in the men's 100-meter backstroke event at the 2012 Olympics.

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