27. Molander Corporation is a distributor of a sun umbrella used at resort hotels. Data concerning the next month’s budget appear below:

Selling price per unit $ 24
Variable expense per unit $ 14
Fixed expense per month $ 8,900
Unit sales per month 1,040

Required:
1. What is the company’s margin of safety in dollars? (Do not round intermediate calculations.)
2. What is the company’s margin of safety as a percentage of its sales? (Round your percentage answer to 2 decimal places (i.e. .1234 should be entered as 12.34).)

Answer:

The perimeter of this rectangle is 10 cm.

The given numerical data should be ordered from least to greatest as follows;

-11, -9, -8, -7, -2, 4, 5, 6, |-11|.

In Mathematics, a rational number can be defined a type of number which comprises fractions, integers, terminating or repeating decimals.

In Mathematics, an integer can be defined as a whole number that may either be positive, negative, or zero (0). This ultimately implies that, a positive integer simply refers to a whole number that is greater than or equal to one (1).

Next, we would order or sort the given numerical data from least to greatest as follows;

-11, -9, -8, -7, -2, 4, 5, 6, |-11|.

Note: |-11| is an absolute value that equals to 11.

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The probability of randomly selecting a Spade or a face card given that it's black is approximately 0.8077 or 80.77%.

To calculate the probability of randomly selecting a Spade or a face card given that it's black, we need to determine the number of favorable outcomes and the total number of possible outcomes.

Step 1: Determine the number of favorable outcomes.

In a standard deck of cards, there are 52 cards. Since we're looking for a Spade or a face card, let's calculate the number of favorable outcomes separately for each category.

Number of Spades:

In a deck, there are 13 spades (Ace of Spades, 2-10 of Spades, Jack of Spades, Queen of Spades, and King of Spades).

Number of Face Cards:

In each suit (Spades, Hearts, Diamonds, and Clubs), there are three face cards: Jack, Queen, and King. Since we're only interested in black cards, we need to consider the face cards of Spades and Clubs, which are black. Therefore, there are 2 black face cards in each suit, giving a total of 8 black face cards in the deck.

So the total number of favorable outcomes is 13 (spades) + 8 (black face cards) = 21.

Step 2: Determine the total number of possible outcomes.

In a standard deck of 52 cards, half are black cards (26 cards) since there are 26 black cards and 26 red cards.

Step 3: Calculate the probability.

The probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

Probability = (Number of favorable outcomes) / (Total number of possible outcomes)

Probability = 21 / 26

Simplifying the fraction, we get:

Probability = 0.8077 (rounded to four decimal places)

Therefore, the probability of randomly selecting a Spade or a face card given that it's black is approximately 0.8077 or 80.77%.

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Answer:

22148 pounds

Step-by-step explanation:

radius = half of diameter = 5.

Volume of hemisphere = (2/3) X π X r ³

= (2/3) X π X (5) ³ = (250/3)π

density = mass/volume, mass = density X volume

= 84.6 X (250/3)π

= 7050π

= 22148 pounds (to nearest full pound)

Answer:

After Grace gave 2 cupcakes to Wonwoo, he had a total of 5 cupcakes. However, after he gave 1 cupcake to Grace, he was left with 4 cupcakes again. But then, things took a turn for the better when Lois and Seeun each gave him 4 cupcakes. This means that Wonwoo now has a total of 12 cupcakes!

Step-by-step explanation:

I believe this is right; please tell me if it is not.

The number of possible combinations of 10 men chosen from 26 men in the juror pool is, 44128260

Since, A combination is a technique to determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

We have to given that;

Total person = 26

Number of choose person = 10

Hence, The number of possible combinations of 10 men chosen from 26 men in the juror pool is,

⇒ ²⁶ C ₁₀

⇒ 26! / 10! 16!

⇒ 44128260

Thus, The number of possible combinations of 10 men chosen from 26 men in the juror pool is, 44128260

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The interval notation of the number line is [-3, ∝) while that of the inequality is  called x >= 3

One can use interval notation to represent real numbers that are continuous by specifying the values that define their boundaries. Written intervals appear somewhat akin to ordered pairs.

The way to know the interval notation of the graph is:

Based on the number line in the question, one can see:

The rule that applies is that a closed line tells us that the number at that endpoint is one that is part of the solution set.

So this tells us that the interval notation of the number line is [-3, ∝). When depicted as an inequality, One can have x >= 3

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Answer:

The angles x, y, and z are 70 degrees, 110 degrees, and 110 degrees, respectively.

Step-by-step explanation:

If one angle is 70 degrees, then its corresponding angle will also be 70 degrees. Therefore, the two linear angle pairs with 70 degrees are:

70 degrees and its corresponding angle (also 70 degrees)

x degrees and y degrees, where x and y add up to 180 degrees (because they are linear angle pairs)

Since x is a vertical angle to 70 degrees, it is also equal to 70 degrees. Therefore:

x = 70 degrees

y = 180 - x = 180 - 70 = 110 degrees

To find the angle z, we can use the fact that the sum of the angles around a point is 360 degrees. Since the two lines intersect and create four angles, the angles around the point where they intersect must add up to 360 degrees. Therefore:

z + 70 + 70 + 110 = 360

z + 250 = 360

z = 110 degrees

Therefore, the angles x, y, and z are 70 degrees, 110 degrees, and 110 degrees, respectively.

Answer:

First find the sales tax: $160 \times 0.0785 = $12.56.

Then add the sales tax to the price of the purchase to find the total cost: $160 + $12.56 = $172.56.

Next find the daily interest rate: $0.042\% = 0.00042$.

Then multiply the daily interest rate by the total cost to find the interest per day: $0.00042 \times $172.56 = $0.0725752$.

Finally, multiply the interest per day by 30 days to find the total interest and add it to the total cost to find the final answer: $0.0725752 \times 30 = $2.177256 + $172.56 = $174.737256 \approx $174.74.

So the answer is b.

Answer:

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Taking the inverse tangent (arctan) of the given ratio 7/9.

Use a calculator or trigonometric table to find:

The approximate value of θ is 37.9°.

Answer:

Yes, x/5 is a linear equation. A linear equation is an equation of a straight line, which means that the degree of a linear equation must be 0 or 1 for each of its variables. In this case, the degree of variable x is 1, so it is a linear equation.

The graph of x/5 is a straight line with a slope of 1 and a y-intercept of 0.

The class intervals to use for the given data is 10.

The class interval is the difference between the upper class limit and the lower class limit. Class interval represents the width of each class in a frequency distribution

The frequency of a class interval is the number of observations that occur in a particular predefined interval.

From the given data the prepare a table for age and frequency

[tex]\begin{tabular}{c | l} Age & Frequency \\ \cline{1-2} 0-10 & 4 \\ 11-20 & 5 \\ 21-30 & 5 \\ 31-40 & 5 \\ 41-50 & 0 \\ 51-60 & 2 \\ 61-70 & 1 \end{tabular}[/tex]

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If Graph g(x) the transformation of f(x)=x² then the graph of function g(x) is x²+4

To graph the transformation of the function f(x) = x² translated up 4 units, we need to add 4 to the function.

The new function, g(x), can be defined as g(x) = f(x) + 4.

Start with the graph of the original function f(x) = x²

Shift the graph vertically upward by 4 units.

To do this, for each point (x, y) on the graph of f(x), plot a new point (x, y + 4) on the graph of g(x).

This means that every y-coordinate is increased by 4 units.

g(x)= x²+4

Hence, the red line in the graph represents f(x) and blue line in graph represents the g(x)

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The rewritten  statement : "It is not the case that there exists an x for which P(x) and Q(x) are true, and for all y, if R(y) is true, then P(y) is true."

The symbolic logic statement: ¬(∃x)(P(x) ∧ Q(x)) ∧ (∀y)(R(y) → P(y)).

The statement can be translated as: "There does not exist an x such that P(x) and Q(x) hold true, and for all y, if R(y) is true, then P(y) is true."

Potential ambiguities in this statement can arise from the unclear precedence of logical operators, specifically the negation operator "¬" in relation to the existential quantifier "∃".

To eliminate ambiguities while maintaining the original meaning, we can add parentheses to make the precedence explicit: (¬(∃x)(P(x) ∧ Q(x))) ∧ (∀y)(R(y) → P(y)).

This ensures that the negation applies only to the existential quantifier, not to the entire conjunction.

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Answer: The time it takes for a sum of money to amount to a certain amount at a certain interest rate can be calculated using the following formula:

Time = (100 x (Amount - Principal)) / (Principal x Rate)

In this case, the principal is Rs. 2000, the amount is Rs. 2240, and the rate is 4%. Therefore, the time is:

Time = (100 x (2240 - 2000)) / (2000 x 4) = 3 years

Therefore, it will take 3 years for Rs. 2000 to amount to Rs. 2240 at 4% simple interest.

Step-by-step explanation:

Certainly! I'll be happy to solve and explain the given problem to you in a step-by-step manner.

In the given diagram, we have a triangle with two angles labeled as 4x° and (3x + 10)°. We need to solve for the value of x.

According to the properties of triangles, the sum of the interior angles of a triangle is always 180 degrees. Therefore, we can set up the following equation:

4x + (3x + 10) + 90 = 180

Let's simplify the equation:

4x + 3x + 10 + 90 = 180

7x + 100 = 180

Next, we'll isolate the variable term by subtracting 100 from both sides of the equation:

7x = 180 - 100

7x = 80

To solve for x, we'll divide both sides of the equation by 7:

x = 80 / 7

Now, let's calculate the value of x:

x ≈ 11.43

Therefore, the value of x is approximately 11.43.

Please note that this solution assumes the given diagram accurately represents the angle measurements, and the calculations provided are based on that assumption.

To find the subtracted value, we need to calculate the multiplicative inverse of (4/3 - 4/9) and then subtract it from the sum of 7/12 and 7/8.

First, let's find the multiplicative inverse of (4/3 - 4/9):

Multiplicative inverse = 1 / (4/3 - 4/9)

To simplify the expression, we need a common denominator:

Multiplicative inverse = 1 / ((12/9) - (4/9))

= 1 / (8/9)

= 9/8

Now, we need to subtract the multiplicative inverse from the sum of 7/12 and 7/8:

Subtracted value = (7/12 + 7/8) - (9/8)

To perform this calculation, we need a common denominator:

Subtracted value = (7/12 * 2/2 + 7/8 * 3/3) - (9/8)

= (14/24 + 21/24) - (9/8)

= 35/24 - 9/8

To simplify further, we need a common denominator:

Subtracted value = (35/24 * 1/1) - (9/8 * 3/3)

= 35/24 - 27/24

= 8/24

= 1/3

Therefore, subtracting 1/3 from the sum of 7/12 and 7/8 will give you the multiplicative inverse of (4/3 - 4/9).

Answer:

Step-by-step explanation:

1) The number of combinations of the letters A, B, C, D, and E taken 4 at a time is 5.

The formula for the number of combinations is n!/(r!(n-r)!), where n is the total number of items, and r is the number of items to be selected. In this case, n = 5 and r = 4. Therefore, the number of combinations is 5!/(4!(5-4)!) = 5.

Theoretical probability is the likelihood or chance of an event occurring based on the ratio of the number of favorable outcomes to the total number of possible outcomes.

2) The theoretical probability of rolling a 2 on a die is 1/6.

There are six possible outcomes when rolling a die, and only one of those outcomes is a 2. Therefore, the probability of rolling a 2 is 1/6.

3) The theoretical probability of landing on blue when spinning the spinner is 1/5.

There are five possible outcomes when spinning the spinner, and only one of those outcomes is blue. Therefore, the probability of landing on blue is 1/5.

4) The ratio of wine lists to cookbooks in simplest form is 3/2.

To simplify the ratio, divide both the numerator and denominator by their greatest common factor, which in this case is 6. 18/6 = 3, and 12/6 = 2, so the ratio of wine lists to cookbooks in simplest form is 3/2.

5) The probability of drawing a red or yellow marble from the bag is 8/14 or 4/7.

There are a total of 14 marbles in the bag, 5 of which are red and 3 of which are yellow. Therefore, the probability of drawing a red or yellow marble is (5+3)/14 = 8/14 or 4/7.

6) The probability of drawing a number greater than 10 from a ball numbered 1-100 is 9/10.

There are 90 numbers greater than 10 in the set of numbers from 1 to 100, and there are 100 total numbers. Therefore, the probability of drawing a number greater than 10 is 90/100, which simplifies to 9/10.

7) The mean of the set of data {10, 15, 25, 50} is 25.

To find the mean, add up all of the numbers in the set and divide by the total number of numbers. (10+15+25+50)/4 = 100/4 = 25.

8) The median of the set of data {6, 23, 46, 3, 17} is 17.

To find the median, first put the numbers in order from smallest to largest: 3, 6, 17, 23, 46. Since there are an odd number of numbers in the set, the median is the middle number, which is 17.

9) The mode of the set of data {3, 7, 10, 18, 4, 5} is no mode.

The mode is the value that appears most frequently in the data set. In this case, none of the values appear more than once, so there is no mode.

10) In a stem-and-leaf plot, the leaf represents the ones place of the numbers in the data set.

The stem-and-leaf plot is a way to organize numerical data by placing the tens digit in the stem and the ones digit in the leaf.

11) Finding quartiles is like finding medians.

Quartiles divide a data set into

To find the z-score for a population value of 21, we can use the formula:

z = (x - μ) / σ

where:

x = population value

μ = mean of the population

σ = standard deviation of the population

In this case, x = 21, μ = 12, and σ = 4.

Substituting the values into the formula:

z = (21 - 12) / 4

z = 9 / 4

z = 2.25

Therefore, the z-score for a population value of 21 is 2.25.

Note:
I hoped this helped in any kind of way.

Given statement solution :-  Party A received the most votes with a total of 47, compared to Party B's total of 38 votes.

Let's calculate the number of votes each party received based on the given information.

Assuming there is a population of 100 people (this is an arbitrary number chosen for ease of calculation), we can determine the number of votes for each party.

Percentage of people who said they would vote for Party A = 33%

Number of people who said they would vote for Party A = 33/100 * 100 = 33

Percentage of people who said they would vote for Party B = 10%

Number of people who said they would vote for Party B = 10/100 * 100 = 10

Percentage of people who said they would not vote = 15%

Number of people who said they would not vote = 15/100 * 100 = 15

Now, let's calculate the votes from the rest of the population (those who didn't state their voting preference).

Percentage of people who voted for Party A from the rest of the population = 1/3

Number of people who voted for Party A from the rest of the population = (1/3) * (100 - (33 + 10 + 15)) = (1/3) * 42 = 14

Percentage of people who voted for Party B from the rest of the population = 2/3

Number of people who voted for Party B from the rest of the population = (2/3) * (100 - (33 + 10 + 15)) = (2/3) * 42 = 28

Now, let's calculate the total votes for each party:

Total votes for Party A = votes from those who stated their preference + votes from the rest of the population

= 33 + 14 = 47

Total votes for Party B = votes from those who stated their preference + votes from the rest of the population

= 10 + 28 = 38

Therefore, Party A received the most votes with a total of 47, compared to Party B's total of 38 votes.

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Answer: C

Step-by-step explanation:

For box and whiskers plot the box is where the majority of the data is.  the whiskers(the lines on both sides will tell you where the range of numbers lie)

The middle line in the box is the median number.

The question is worded oddly where they want least likely to be more than 30 which means which one will have less than 30. (Double negative question)

You want the majority of the data to be less than 30, which is subway.  C

Answer:

Since 1 fluid ounce is equal to 0.03125 quarts, we can convert the volume of water poured into the jar from ounces to quarts:

114 ounces x 0.03125 quarts/ounce = 3.5625 quarts

Therefore, Kenna pours 3 x 3.5625 = 10.6875 quarts of water to fill the jar three times. Rounding to the nearest whole number, we get 11 quarts.

So it takes 11 quarts of water to fill the jar.

Answer:

0.0772 OR 0.95 OR 7.72

Step-by-step explanation:

A player makes 622 shots on goal and in that time scores 48 goals.

48 goals ÷ 622 shots = 0.0772.

This player’s shooting percentage is 0.0772, or 7.72%.

The correct answer is $28,100.

To calculate the difference between the costs of the accident and the premiums paid by the car owner, let's break down the expenses step by step:

(1) Annual Premium: The car owner pays an annual premium of $780 for automobile insurance. Over five years, the total premium paid is $780 * 5 = $3,900.

(2) Liability Coverage: The liability coverage provided by the insurance is up to $100,000. However, the other driver is claiming $32,000 in damages. Therefore, the insurance will cover the full amount of $32,000.

(3) Difference in Costs: To find the difference between the costs of the accident and the premiums paid, we subtract the insurance coverage from the total premium paid. In this case, the difference is $32,000 - $3,900 = $28,100.

Therefore, the costs of the accident were $28,100 more expensive than what the car owner paid in premiums.

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Answer:

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If the middle number is x, the other numbers are x - 1 and x + 1.

They sum to 3x and it is equal to 51:

The numbers are 16, 17 and 18.

Hello !

1. A quadratic equation results in the form: ax² + bx + c

2. Calculate the discriminant: Δ = b² - 4ac

3. Calculate x with the dicriminant: (-b ± √Δ) / 2a

Example:

3x² + 7x - 2 = 0 is a quadratic equation.

x = (-b ± √(b² - 4ac)) / 2a

= (-7 ± √(7² - 4*3*(-2))) / (2*3)

= (-7 ± √73)/6