Solve Ax + By = C for x.

1. x equals the quantity negative B times y plus C all over A
2. x equals the quantity B times y plus C all over A
3. x equals the quantity B times y minus C all over A
4. x equals the quantity negative B times y minus C all over A

(a) Sam needs to sell 5,000 sets of plates to break even.

(b) The break-even revenue is $125,000.

(c) The break-even revenue, considering the additional cost, is $303,025.

a) To calculate the number of sets of plates that need to be sold to break even, we need to consider the fixed cost, variable cost, and selling price per set.

Each set of plates includes 8 plates, and the cost of each plate is $2. Therefore, the variable cost per set of plates is 8 * $2 = $16.

To break even, the total revenue from selling sets of plates should cover the fixed cost and variable cost. We can calculate the break-even point by dividing the fixed cost by the contribution margin per set.

Contribution margin per set = Selling price per set - Variable cost per set

Contribution margin per set = $25 - $16 = $9

Break-even point = Fixed cost / Contribution margin per set

Break-even point = $45,000 / $9

Break-even point = 5,000 sets of plates

Therefore, Sam needs to sell 5,000 sets of plates to break even.

b) To obtain the break-even revenue, we multiply the break-even point (number of sets) by the selling price per set.

Break-even revenue = Break-even point * Selling price per set

Break-even revenue = 5,000 * $25

Break-even revenue = $125,000

The break-even revenue is $125,000.

c) With the addition of the assistant, the fixed cost increases by $35,000, resulting in a new fixed cost of $45,000 + $35,000 = $80,000.

The variable cost per plate increases by 15%, which means it becomes $2 + ($2 * 0.15) = $2.30.

The new variable cost per set of plates is 8 * $2.30 = $18.40.

Contribution margin per set = Selling price per set - Variable cost per set

Contribution margin per set = $25 - $18.40 = $6.60

Break-even point = Fixed cost / Contribution margin per set

Break-even point = $80,000 / $6.60

Break-even point ≈ 12,121.21 sets of plates

Therefore, Sam needs to sell approximately 12,121 sets of plates to break even with the additional cost.

Break-even revenue = Break-even point * Selling price per set

Break-even revenue = 12,121 * $25

Break-even revenue = $303,025

The break-even revenue, considering the additional cost, is $303,025.

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After considering the given data we conclude that the answer for the given sub question regarding combination are
a) the number of different groups of 10 employees that can be selected is 14,307,292
b) the number of possible groups of 10 employees that consist only of employees who either take public transit or drive to work is 77
c) employees who take public transit is 66
d) employees who drive to work is 11
e) employees that do not include anyone who takes public transit is 184,756
f) employees that do not include anyone who drives to work is 352,716
g) employees that consist of at least one person who drives to work is 14,054,576
h) employees that consist of at least one person who drives to work is 14,054,576
i) employees that consist of 5 people who take public transit and 5 people who drive to work is 365,904
j) employees that consist of 4 people who take public transit, 3 people who drive to work, and 3 people who do neither is 6,270,840

a) This is a combination problem, where the order of selection does not matter. The formula for the number of combinations of n objects taken r at a time is \(nCr = n! / (r! * (n-r)!)\), where n is the total number of objects and r is the number of objects being selected. In this case, there are 32 employees and we want to select 10 of them, so the number of different groups of 10 employees that can be selected is:
\(32C10 = 32! / (10! * (32-10)!) = 14,307,292\)

b) We can add the number of groups that consist only of employees who take public transit to the number of groups that consist only of employees who drive to work. To find the number of groups that consist only of employees who take public transit, we can choose 10 employees from the 12 who take public transit. Similarly, to find the number of groups that consist only of employees who drive to work, we can choose 10 employees from the 11 who drive to work. Therefore, the number of possible groups of 10 employees that consist only of employees who either take public transit or drive to work is:
\(12C10 + 11C10 = 66 + 11 = 77\)

c) We can choose 10 employees from the 12 who take public transit, so the number of possible groups of 10 employees that consist entirely of employees who take public transit is:
\(12C10 = 66\)

d) We can choose 10 employees from the 11 who drive to work, so the number of possible groups of 10 employees that consist entirely of employees who drive to work is:
\(11C10 = 11\)

e) We can choose 10 employees from the 20 who either drive to work or do neither, so the number of possible groups of 10 employees that do not include anyone who takes public transit is:
\((20C10) = 184,756\)
f) We can choose 10 employees from the 21 who either take public transit or do neither, so the number of possible groups of 10 employees that do not include anyone who drives to work is:
\((21C10) = 352,716\)

g) We can subtract the number of possible groups of 10 employees that do not include anyone who takes public transit from the total number of possible groups of 10 employees. Therefore, the number of possible groups of 10 employees that consist of at least one person who takes public transit is:
\(32C10 - 20C10 = 14,122,536\)

h) We can subtract the number of possible groups of 10 employees that do not include anyone who drives to work from the total number of possible groups of 10 employees. Therefore, the number of possible groups of 10 employees that consist of at least one person who drives to work is:
\(32C10 - 21C10 = 14,054,576\)

i) We can choose 5 employees from the 12 who take public transit and 5 employees from the 11 who drive to work. Therefore, the number of possible groups of 10 employees that consist of 5 people who take public transit and 5 people who drive to work is:
\(12C5 * 11C5 = 792 * 462 = 365,904\)

j) We can choose 4 employees from the 12 who take public transit, 3 employees from the 11 who drive to work, and 3 employees from the 9 who do neither. Therefore, the number of possible groups of 10 employees that consist of 4 people who take public transit, 3 people who drive to work, and 3 people who do neither is:
\(12C4 * 11C3 * 9C3 = 495 * 165 * 84 = 6,270,840\)
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Answer:

B

Step-by-step explanation:

Answers:

18:12

3:2

Step-by-step explanation:

9:6 = 9 * 2 : 6 * 2 = 18:12

9:6 = 9/3 : 6/3 = 3:2

Hope this helps.

Answer:

The answer is c.

a. no b. no c. yes

i hope that helped

Step-by-step explanation:

Answer:

Step-by-step explanation:

To prove ΔXYZ ~ ΔMNO using the property of SSS, we need to know that All corresponding sides of these triangles are proportional.

Similarly, If we know the length of side XZ then addition information we need to know that angle O is congruent to angle Z and length of sides YZ, MO and NO to prove ΔXYZ ~ ΔMNO by SAS property.

Angle O is the contained angle between the sides MO and NO.

Answer:

1. MN = 6 and XZ = 17.5

2. angle Z

Step-by-step explanation:

Sorry if this is a late answer but I hope this helps :)

Answer:

Step-by-step explanation:

(-100*0.9)(x)==-90x

Blake should first multiply the numbers in parenthesis and then multiply by x, even the answer is right but the process is wrong Blake has to follow the rule

Parenthesis , Exponent, Multiplication/Division, Addition/ Subtraction

P E M D A S

Answer:

NO.2- SSA is not the method to show the congruency of two triangles.

Given that (xn) and (yn) are Cauchy sequences, then for any ε > 0, there exist N1 and N2 such that |xn - xm| < ε/2, for all n, m ≥ N1 and |yn - ym| < ε/2, for all n, m ≥ N2. Then, for all n, m ≥ max{N1, N2},

we have: |xnyn - xmym| = |xnym - xmym + xmym - xnym| ≤ |xn - xm||ym| + |ym - yn||xm| ≤ |xn - xm|ε/2 + |ym - yn|ε/2 < εThis shows that (xnyn) is a Cauchy sequence.

Moreover, for any ε > 0, there exists N such that |xn - xm| < ε/2 and |yn - ym| < ε/(2max{|x1|, |x2|, . . . , |y1|, |y2|, . . . , |yn|}) for all n, m ≥ N. Then, for all n, m ≥ N,

we have: |xnyn - xmym| = |xnym - xmym + xmym - xnym| ≤ |xn - xm||ym| + |ym - yn||xm| + |ym - yn||yn| ≤ |xn - xm|ε/(2max{|x1|, |x2|, . . . , |yn|}) + |ym - yn|ε/(2max{|x1|, |x2|, . . . , |yn|}) + |yn|ε/(2max{|x1|, |x2|, . . . , |yn|}) < ε.

This shows that (xn)(yn) is also a Cauchy sequence.

Therefore, from the given definition, it has been shown that if (xn) and (yn) are Cauchy sequences, then (xn) (yn) and (xnyn) are Cauchy sequences.

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The annual depreciation expense would be calculated as ($4,800 - $800) / 10 = $400. The journal entry for the first year would be:

Depreciation Expense=  $400, Accumulated Depreciation = $400

The journal entry for the first year, given the production of 300 units, would be:

Depreciation Expense         $600 (300 units * $2)

  Accumulated Depreciation    $600

The journal entry for the first year, using a double-declining-balance rate of 20% (twice the straight-line rate of 10%), would be:

Depreciation Expense         $960 ($4,800 * 20%)

  Accumulated Depreciation    $960

1. Straight-Line Depreciation:

The straight-line depreciation method allocates an equal amount of depreciation expense each year over the useful life of the equipment. In this case, the annual depreciation expense would be calculated as ($4,800 - $800) / 10 = $400. The journal entry for the first year would be:

Depreciation Expense         $400

  Accumulated Depreciation    $400

2. Units-of-Production Depreciation:

The units-of-production method bases depreciation on the actual units produced. The depreciation per unit is calculated as ($4,800 - $800) / 2,000 = $2 per unit. The journal entry for the first year, given the production of 300 units, would be:

Depreciation Expense         $600 (300 units * $2)

  Accumulated Depreciation    $600

3. Double-Declining-Balance Depreciation:

The double-declining-balance method accelerates depreciation in the early years of the asset's life. The depreciation rate is twice the straight-line rate. The journal entry for the first year, using a double-declining-balance rate of 20% (twice the straight-line rate of 10%), would be:

Depreciation Expense         $960 ($4,800 * 20%)

  Accumulated Depreciation    $960

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They need to wash approximately 41 cars in order to have enough money to pay for the trip.

Proving Theorems about Lines and Angles: Tutorial

To calculate the number of cars they need to wash in order to have enough money to pay for the trip, we need to consider the total cost of the trip and the amount of money they have available.

The total cost of the trip includes the registration fee, transportation and food expenses, and hotel costs.

The registration fee is $110, transportation and food costs are $375, and the hotel cost per person is $42.

Let's calculate the total cost of the trip:

Total cost = Registration fee + Transportation and food costs + Hotel costs

Total cost = $110 + $375 + ($42 x 4) [since there are four student government officers]

Total cost = $110 + $375 + $168

Total cost = $653.

Now, we subtract the available budget from the total cost to find the remaining amount they need to earn:

Remaining amount = Total cost - Budgeted amount

Remaining amount = $653 - $450

Remaining amount = $203

Since they can earn money by having a car wash and charge $5 per car, we can calculate the number of cars they need to wash:

Number of cars = Remaining amount / Amount earned per car

Number of cars = $203 / $5

Number of cars ≈ 40.6

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Step-by-step explanation:

To get  TO   H   FROM   G    is 4 LEFT and DOWN 1  .

\(~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ (4)^{\frac{-4}{2}} \implies (4)^{-2}\implies 4^{-2}\implies \cfrac{1}{4^2}\implies \cfrac{1}{16}\)

Answer:

C=3.14*91

D=91*2

C=285.74

D=182

Hope This Helps!!!

Answer:

hope this helps

Step-by-step explanation:

192 fl oz. = 6 quarts

to get this you divide the fluid ounces by 32.

Answer: The ball is dropped from a height of 10 ft, so it first travels down 10 ft until it hits the ground. The distance traveled in this first part is 10 ft.

On the first bounce, the ball rebounds to one-fifth of its previous height, which is 2 ft (since 10/5 = 2). The ball then travels up 2 ft and back down 2 ft to the ground, for a total distance traveled of 10 + 2 + 2 = 14 ft.

On the second bounce, the ball rebounds to one-fifth of its previous height, which is 2/5 ft (since 2/5 x 2 = 4/5). The ball then travels up 4/5 ft and back down 4/5 ft to the ground, for a total distance traveled of 2/5 + 4/5 + 4/5 = 2 ft.

On the third bounce, the ball rebounds to one-fifth of its previous height, which is 4/25 ft (since 4/25 x 2/5 = 8/125). The ball then travels up 8/125 ft and back down 8/125 ft to the ground, for a total distance traveled of 4/25 + 8/125 + 8/125 = 0.32 ft (rounded to two decimal places).

The ball will continue to bounce, getting closer and closer to the ground with each bounce. We can calculate the total distance traveled by summing the distances traveled on each bounce:

10 + 14 + 2 + 0.32 + ...

To calculate the sum of this infinite series, we can use the formula for the sum of an infinite geometric series:

S = a / (1 - r)

where S is the sum, a is the first term, and r is the common ratio.

In this case, a = 10 (the distance traveled on the first drop), and r = 1/5 (the fraction by which the height decreases on each bounce). Plugging in these values, we get:

S = 10 / (1 - 1/5)

= 12.5

So the total distance traveled by the ball is 12.5 ft.

Step-by-step explanation:

Therefore, the mean of the data decreases by 15 when the number 646 changes to 639.

Median is a measure of central tendency that represents the middle value of a dataset when the data is arranged in order from least to greatest (or greatest to least). It is the value separating the higher half from the lower half of the data. If the dataset contains an odd number of values, the median is the middle value. If the dataset contains an even number of values, the median is the average of the two middle values. The median is a useful measure of central tendency because it is not affected by extreme values or outliers in the dataset.

Here,

(a) When the number 646 changes to 639, the median of the data changes as well. The new list of numbers of trading cards owned by the 7 middle-school students becomes:

360, 373, 402, 499, 548, 644, 639

The median is the middle value when the data is arranged in order from least to greatest. In the original list, the middle value was 499. But in the updated list, the middle value is now the average of the two middle values, which are 499 and 548. Therefore, the median of the updated list is:

Median = (499 + 548) / 2

= 523.5

So the median decreases by 523.5 - 499 = 24.5 when the number 646 changes to 639.

(b) To find out what happens to the mean when the number 646 changes to 639, we need to calculate the mean of the updated list of numbers. The new list of numbers of trading cards owned by the 7 middle-school students is:

360, 373, 402, 499, 548, 644, 639

The mean of the data is the sum of all the values divided by the total number of values. In the original list, the sum of all the values was:

Sum = 360 + 373 + 402 + 499 + 548 + 644 + 646

= 3472

And there were 7 values in the data. Therefore, the mean of the original list was:

Mean = Sum / Number of values

= 3472 / 7

= 496 (rounded to the nearest whole number)

To calculate the mean of the updated list, we need to subtract 646 and add 639, and then divide the new sum by 7. That is:

Mean = (Sum - 646 + 639) / 7

= (3472 - 646 + 639) / 7

= 481 (rounded to the nearest whole number)

Therefore, the mean of the data decreases by:

496 - 481 = 15

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Answer: See explanation.

Step-by-step explanation:

Any false inequality has no solution. For example |x+3|<-2 has no solutions for x. The graph would not display any answers for x as there is no solution due to the absolute value.

Step-by-step explanation:

For right triangles     tan B = opposite leg / adjacent leg

tan B = 3/4  

arctan (3/4) = B = 36.87 degrees

The product of x * 5 * 5 is 25x.

The product of 1 * 3 * 3 * 5 is 45.

The product of 1/3 * 2 * 5 is 10/3 or 3.33 (rounded to two decimal places).

To find the product of expressions, you multiply the numbers or variables together according to the given expression.

1. Product of x * 5 * 5:

To find the product of x, 5, and 5, you multiply them together:

x * 5 * 5 = 25x

2. Product of 1 * 3 * 3 * 5:

To find the product of 1, 3, 3, and 5, you multiply them together:

1 * 3 * 3 * 5 = 45

3. Product of 1/3 * 2 * 5:

To find the product of 1/3, 2, and 5, you multiply them together:

1/3 * 2 * 5 = (1 * 2 * 5) / 3 = 10/3 or 3.33 (rounded to two decimal places)

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Answer:

a.) Domain: all numbers from 0 to 170   and   d. Range: all numbers from 0 to 60

Step-by-step explanation:

The domain is all of the numbers that the graph is on, over the x-axis. Looking at the x-axis, the graph only spans across 0-170, so the answer would be   a.) Domain: all numbers from 0 to 170.

The range is all of the numbers that the graph is on, over the y-axis. Looking at the y-axis, the graph only spans across 0-60, so the answer would be   d. Range: all numbers from 0 to 60.

The volume of the prism is

The volume of the prism is solved by the formula

= area of triangle * depth

Area of the triangle

= 1/2 base * height

base = p = cos 51.34 * √41 = 4

height = q = sin 51.34 * √41 = 5

= 1/2 * 4 * 5

= 10

volume of the prism

= area of triangle * depth

= 10 * 7

= 70 cm³

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Answer:

Below

Step-by-step explanation:

The avg. weight of a cat is around 8 pounds

The avg. of a large dog is around 130 pounds.

Since they give no other numbers to go off of, I would just plug these in.

The dog would be 122 pounds heavier than the dog.

I’m sorry if this isn’t what you’re looking for, I think I need more information.

Answer: slide the triangle to the right 3 times and down 1

Step-by-step explanation:

The probability that a student chosen at random has a cat or a dog is; P(cat or dog) = 22/25.

What is probability?

Probability is that the branch of arithmetic regarding numerical descriptions of however probably an incident is to occur, or however probably it's that a proposition is true. The likelihood of an incident could be a range between 0 and 1.

Main body:

According to the question, the total number of students is; 25.

15 of them have a cat

16 of them have a dog

while, 3 of them have neither

where, x = number if students who own a cat and a dog.

Consequently, the total number of students who own a cat, a dog, both or neither is as follows;

15-x + x + 16-x + 3 = 25.

-x = 25 - 34

In essence, x = 9

the number of students who own a cat and a dog is 9.

Therefore, probability that a student chosen at random has a cat and a dog is therefore;

P(cat and dog) = 9/25.

Therefore probability that a student chosen at random has a cat or a dog is 22/25.

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Answer:

8 he would be able to give 8 kids 1 dollor and 25 cents

Answe

about 30-45 Percent.

Step-by-step explanation:

The total capacity of the tank is 272.675 cubic meters.

Given that,

A storage tank consist of a hemisphere and a cylinder which share a common base.

The base of both hemisphere and cylinder will be the same circle with the same radius.

Also, we have,

Height of the tank = 16.5 m

Base diameter of the cylinder = 4.7 m

Radius of the base of the cylinder = 4.7 / 2 = 2.35 m

Radius of the hemisphere = 2.35 m

Height of the cylinder = Total height of the tank - Height or radius of the hemisphere

Total capacity of the tank = Volume of hemisphere + Volume of cylinder

                                          = 2/3 π r³ + π r² h

                                          = 2/3 π (2.35)³ + π (2.35)² (16.5 - 2.35)

                                          = 8.652π + 78.143π

                                          = 272.675 cubic meters

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