In Stephanie's carpenter shop, she made three-legged stools and four-legged chairs. She looked at her day's output and counted 55 legs and 16 seats. How many stools and how many chairs did Stephanie complete that day?

Show all your work. Explain in words how you found your answer. Tell why you took the steps you did to solve the problem.

Answer:

hope this will help you..

Using the triangle proportionality theorem, the missing lengths that are indicated are:

1. 35

2. 14

3. 28

4. 18

The triangle proportionality theorem states that when a line is drawn to be parallel to any side of a triangle that it intersects two of the side of the triangle at two different points, then the two sides are divided proportionally or in the same ratio.

Apply the triangle proportionality theorem to find all the missing length that are indicated. Let the missing side be represented as x.

Problem 1:

x/28 = 15/12

x = (28)(15)/12

x = 35

Problem 2:

x/28 = 6/(18 - 6)

x/28 = 6/12

x/28 = 1/2

x = 28/2

x = 14

Problem 3:

x/35 = 12/(12 + 3)

x/35 = 12/15

x/35 = 4/5

x = (35)(4)/5

x = 28

Problem 4:

x/54 = 8/24

x/54 = 1/3

x = 54/3

x = 18

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Given that Mr. Townsend needs to make 13 pairs of butterfly wings for costumes for a play. Each pair of wings is made with 3/4 yards of fabric. The fabric costs $8 per yard. The total cost of the fabric is $78.

The total cost formula is used to get a total by combining the variable and fixed expenses of delivering commodities.

The step-by-step is given as follows:

1) Total cost  (TC) = 3/4 (P) x 13

2) 1 pair of wings = 3/4 yard fabric

Recall that the price of 1 yard of fabric = $8

3) 1 pair of wings = $8 x 3/4 = $6

4) Therefore total cost = $6 x 13 = $78

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Answer:

1

Step-by-step explanation:

1.5/2.5= 0.6

0.6 nearest tenth is 1

0.0-0.5 --0

0.6-0.9 --1

Answer:

a^2 - 5ab

Step-by-step explanation:

[3a * (a-b)] - [2a * (a+b)]

[3a(a) - 3a(b)] - [2a(a) + 2a(b)]

3a^2 - 3ab - (2a^2) - (2ab)

3a^2 - 2a^2 - 3ab - 2ab

a^2 - 5ab

Answer:

2.9 × 1025

(scientific notation)

= 2.9e25

(scientific e notation)

Step-by-step explanation:

hope this helped

Answer:

Step-by-step explanation:

Answer:

AP = 18, PL = 9

Step-by-step explanation:

assuming AL, is a median of the triangle

then AP = [tex]\frac{2}{3}[/tex] AL = [tex]\frac{2}{3}[/tex] × 27 = 18

PL = [tex]\frac{1}{3}[/tex] AL = [tex]\frac{1}{3}[/tex] × 27 = 9

For the given matrix A = [tex]\left[\begin{array}{ccc}8&-4\\-7&0\\\end{array}\right][/tex] and B = [tex]\left[\begin{array}{ccc}2&5\\2&0\\\end{array}\right][/tex] then value of matrix X which satisfy the given equation 3X = -3A + 4B is equal to [tex]X = \frac{1}{3} \left[\begin{array}{ccc}-16&32\\29&0\\\end{array}\right][/tex].

As given in the question,

Given matrix are equal to :

A = [tex]\left[\begin{array}{ccc}8&-4\\-7&0\\\end{array}\right][/tex]

B = [tex]\left[\begin{array}{ccc}2&5\\2&0\\\end{array}\right][/tex]

Simplify the equation which satisfy the equation 3X = -3A + 4B is given by :

Substitute the value of matrix A and matrix B in the given equation we get:

3X  =  [tex]-3\left[\begin{array}{ccc}8&-4\\-7&0\\\end{array}\right] + 4\left[\begin{array}{ccc}2&5\\2&0\\\end{array}\right][/tex]

⇒ 3X =  [tex]\left[\begin{array}{ccc}-24&12\\21&0\\\end{array}\right] + \left[\begin{array}{ccc}8&20\\8&0\\\end{array}\right][/tex]

⇒ 3X = [tex]\left[\begin{array}{ccc}-16&32\\29&0\\\end{array}\right][/tex]

To get the value of X divide both the side by 3 we have,

⇒ X   = [tex]\frac{1}{3} \left[\begin{array}{ccc}-16&32\\29&0\\\end{array}\right][/tex]

Therefore, for the given matrix A = [tex]\left[\begin{array}{ccc}8&-4\\-7&0\\\end{array}\right][/tex] and B = [tex]\left[\begin{array}{ccc}2&5\\2&0\\\end{array}\right][/tex] then value of matrix X which satisfy the given equation 3X = -3A + 4B is equal to [tex]X = \frac{1}{3} \left[\begin{array}{ccc}-16&32\\29&0\\\end{array}\right][/tex].

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Using a linear equation to solve this problem, the charge for a 3.5 hour job is 85.45 dollar.

To find how much was the bill, we need to write an equation or linear equation for this.

For every linear equation, it takes the form of y = mx + c.

Where m and c are the slope and intercepts of the straight line.

In this case, our linear equation can be written as

y = 18.70x + 20

where x = number of hours worked.

If the job took three and a half hour which is 3.5 hours, we can substitute this into the equation and solve.

y = 18.70(3.5) + 20

y = 85.45

The charge is 85.45 dollar.

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The equation that shows the relationship between the nights and the length knitted is y = 22x.

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

Let the nights = x

Let the length knitted = y

The appropriate equation will be:

y = (22 × x)

y = 22x

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Answer:

it is c

Step-by-step explanation:

you do 9x2 6+1 = 7 + 18 =25

The decimal place should be after only 1 digit so the answer is e

Answer:

y = 2 ; y = -7

Step-by-step explanation:

sum of two numbers = 5

product of two numbers = -14

the two numbers are 7 and -2

(y-2)(y+7) = 0

y = 2

y = -7

The standard deviation of the sum of the 4 random variables is 10.23

The question is incomplete the complete question is  

For each of the 4 stroke categories 2,4,6,8 consider a random variable representing the time of a randomly selected swimmer in that category is 0.6,0.8,0.2,0.7. What is the standard deviation of the sum of the 4 random variables?.

To calculate the Expected Value, we need to multiply each value by its probability and then sum the products up.

μ = E(x) = ∑xp(x)

That is, (0.6x2) + (0.8x4) + (0.2x6) + (0.7x8) = 1.2 + 3.2 + 1.2 + 5.6 = 11.2

Mean = 11.2

Now we take the first and second steps,

(2- 11.2)² x 0.6 = 84.64 x 0.6 = 50.78

(4 - 11.2)² x 0.8 = 51.84 x 0.8 = 41.47

(6 - 11.2)² x 0.2 = 27.04 x 0.2 = 5.4

(8 - 11.2)² x 0.7 = 10.24 x 0.7 = 7.16

Now we take the the third step and add our products together to get the variance V,

V = σ2 = ∑(x−μ)2P(x)

V = 50.78 + 41.47 + 5.4+ 7.16 = 104.81

Now we take the last step by taking the square root of the variance to get the standard deviation SD,

SD = σ = √σ2

Standard Deviation SD = √104.81 = 10.23

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1. The patterns regarding the polygons are given as follows:

2. The relationship between the number of sides of the polygon, and the number of non-overlapping triangles in the polygon is:

The number of non-overlapping triangles in the polygon is two less than the number of sides.

3. The relationship between the number of sides of the polygon and the sum of the interior angles is:

The sum of the interval angles of a triangle is given by the multiplication of 180º and the number of non-overlapping triangles in the polygon.

The patterns in the context of this problem are all obtained from the last row of the table, and they are all axioms for polynomial relations.

For item 2, the relationship is given by the third column of the last row, and for item 3, by the fourth column.

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The range of the given graph is [5, ∞).

Range.

Range refers the set of possible output values, and if we have the graph, then the set of all possible y values on the graph is defined as the range.

Given,

Here we have the graph.

Through the given graph we have to find the range of the line.

As per the definition of range, we have identified that the range take the value of y axis.

While we lookin into the given graph, we have identified that the starting point of the line is

=> (0, 5)

In this point 0 refers the x coordinate and 5 refers the y coordinate. So, the starting range is 5.

And the end of the line is not pointed.

So, we can consider that this line goes infinitely.

So, the range of the graph is  [5, ∞).

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Y-intercept(b)= 10

equation wasnt written in the correct order so b is 10

Answer:

AM=M-A

-3 -1. -2

2 -. -3. = 5

-3. -2. -5

2. +. 5. =. 7

Check the picture below.

The equation of the line that passes through the point and slope (-2, -7) m = 4/5

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

The line contains the following point and slope. (-2, -7) m = 4/5

y - y1 = m(x - x1)

y + 7 = 4/5(x + 2)

y = 4x/5 + 8/5 - 7

y = 4x/5 - 27/5

Thus, the equation of the line that passes through the point and slope (-2, -7) m = 4/5

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Based on the data the correct interpretation of the interval is that we are 94% confident that the population mean height of college basketball players is between 65.6 and 67.1 inches. (Option B)

In statistics, a confidence interval indicates the probability that a population parameter will lie between a set of values around the population mean. It measures the degree of certainty or uncertainty in a sampling method. It is a range of values which are bounded above and below the statistic's mean that likely would contain an unknown population parameter. Confidence level is the percentage of certainty or probability of the confidence interval would include the true population parameter when a random sample is repeatedly drawn. Hence, in the given case based on the information we are 94% confident that the population mean height of college basketball players is between 65.6 and 67.1 inches.

Note: The question is missing options which are A. We are 94% confident that the population mean height of college basketball players is 66.35 inches. B. We are 94% confident that the population mean height of college basketball players is between 65.6 and 67.1 inches. C. A 94% of college basketball players have heights between 65.6 and 67.1 inches. D. There is a 94% chance that the population mean height of college basketball players is between 65.6 and 67.1 inches.

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Answer:

Incomplete question.

Step-by-step explanation:

4 cm = 50 km

1 cm = 50/4 = 12.5 km

Use above ratio or

50 km = 4 cm

1 km = 4/50 = 0.08 cm

The probability that the spinner lands on yellow and the coin toss is tails is 9/10.

What is probability?

Probability shows the likelihood of an event happening.  it can be calculated by dividing the number of outcomes of an event by the total number of possible outcomes or sample space. Probability is equal to '1' when the event is certain to occur. i.e P =1. It is less than '1' when it is not likely to occur. i.e P< 1

Probability P=no. outcomes/total no. of the possible outcomes

From the question;

No of blue=1

No of yellow=9

No. of total possible outcome=10

Therefore the probability that the spinner lands on yellow and the coin toss is tails P= 9/10.

           P= 9/10                            

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The angle measures are ∠1 = 66°, ∠2 = 114°.

Given that m<1 = (x+81)° and m<2=2x°.

Here ∠ 1 and ∠ 2 are adjacent angles and are supplementary ( sum to 180°), then

2x + x + 81 = 180 , that is

3x + 81 = 180 ( now subtract the number 81 from both the sides )

3x = 99 ( now divide both the sides by the number 3 )

So that, x = 33

Thus, putting the value of x in the below equations:

∠ 1 = 2x = 2 × 33 = 66°

∠ 2 = x + 81 = 33 + 81 = 114°

Hence the answer is the angle measures = ∠1 = 66°, ∠2 = 114°.

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We have elaborate below a real-world problem that involves a decimal divided by a decimal.

Since we are given a problem that says that Jake owns a bakery  amd he makes 8.5 boxes of cupcakes in 15.5 hours,  the question is how many cupcakes he makes in 1 hour .So the time taken is 15.5 and the number of cupcakes made in the  15.5 hours is 8.5. So 15 .5hours=8.5 cupcakes, now dividing both sides by 15.5, we get: 1 hour=8.5/15.5 =0.54 = 1 cupcake, therfore, it needs 1 hour  to make 1 cupcake. Here we had two quantities in form of decimals, so there division of expression of decimal dividing a decimal.

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A bicycle rider rides 24 km riding at a rate greater than 8 km/ h.

Given that, a bicycle rider is riding at a rate of 15 km/h for 4/9 of his ride.

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.

Let total number of km be x.

Distance1 =4/9 x

Distance2 =2/9 x

Remaining distance = x-(4x/9 + 2x/9)

= x-6x/9

=(9x-6x)/9

= 3x/9

Now, time =1 hour

8 = 3x/9 ÷ 1

⇒ 8×9=3x

⇒ x=24 km

Hence, a bicycle rider rides 24 km riding at a rate greater than 8 km/ h.

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Answer:

x= 0.41

Step-by-step explanation:

tan 9° =[tex]\frac{x}{2.6}[/tex]

x= 2.6 tan9°  (cross multiply)

x= 0.41          (solve trignomatic function)

The smaller tap take 25 hours to fill the tank and the larger tap take 10 hours to fill the tank.

How to calculate time taken to fill the tank for each tap?

Given,

Time taken for two tap together to fill the tank = [tex]9\frac{3}{8}[/tex] hours = [tex]\frac{75}{8}[/tex] hours

Time taken for smaller tap to fill the tank = x hours

Time taken for larger tap to fill the tank = x - 10 hours

So,

Tank filled by two tap together in 1 hour = [tex]\frac{8}{75}[/tex]

Tank filled by smaller tap in 1 hour = [tex]\frac{1}{x}[/tex]

Tank filled by larger tap in 1 hour = [tex]\frac{1}{x-10}[/tex]

Then, tank filled by two tap together is equal to tank filled by smaller tap and larger tap. So,

[tex]\frac{8}{75} = \frac{1}{x} + \frac{1}{x-10}[/tex]

[tex]\frac{8}{75} = \frac{x-10+x}{x(x-10)}[/tex]

[tex]\frac{8}{75} = \frac{2x-10}{x^{2}-10x}[/tex]

[tex]8x^{2}-80x = 150x - 750[/tex]

= [tex]8x^{2} - 230x + 750[/tex]

= [tex]2(4x^2 - 115x + 375)[/tex]

= [tex]4x^2 - 100x - 15x + 375[/tex]

= [tex](4x - 15) (x - 25)[/tex]

If, x = [tex]\frac{15}{4}[/tex] then x - 10 for larger tap equal to [tex]\frac{15}{4}[/tex] - 10 = [tex]- \frac{25}{4}[/tex] < 0 hours, so it is impossible.

Then, x must be 25. So, for larger thank is 25 - 10 = 15.

Smaller tap take 25 hours to fill the tank

Larger tap take 15 hours to fill the tank.

Thus, the smaller tap take 25 hours to fill the tank and the larger tap take 10 hours to fill the tank.

Your question is not complete, but most probably your full questions is (image attached)

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[tex]b = \frac{96-3m}{4}[/tex] and [tex]m = \frac{96-4b}{3}[/tex]  for the equation that models.

Jada sells b books and m magazine subscriptions to raise money for a choir trip. She earns $4 for each book and $3 for each magazine subscription she sells, and she earns a total of $96 toward the cost of her choir trip.

Given that

1. Jada sells b books and m magazines

2. She earns $4 for each book and $3 for each magazine

3. Total amount she earned is $96

Given equation is

4b + 3m = 96

Solve 4b + 3m = 96 for b

Subtract 3m from both sides

4b + 3m - 3m = 96 - 3m

4b = 96 - 3m

Now divide both sides by 4

= [tex]b = \frac{96-3m}{4}[/tex]

So, the answer for b is [tex]\frac{96-3m}{4}[/tex]

Now, solve 4b + 3m = 96 for m

Subtract 4b from both sides

4b + 3m - 4b = 96 - 4b

= 3m = 96 - 4b

Now divide both sides by 3

= [tex]m = \frac{96-4b}{3}[/tex]

So, the answer for m is [tex]\frac{96-4b}{3}[/tex]

Hence the answer is [tex]b = \frac{96-3m}{4}[/tex] and [tex]m = \frac{96-4b}{3}[/tex] for the equation that models.

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