Two homebuilders are working to get the windows installed on their homes. Tom uses the formula 42 = 7x + 2 to model the number of windows he is installing on his home and Suzanne uses the formula 37 = 6x + 5 to model the number of windows she is installing on her home. In each formula, x represents the number of days that Tom and Suzanne work on installing windows.

The word problem is given thus: Given this gridlock, which child between Matt and Riley still had more proportionate remaining sandwich contents provided they both possess a shared 4/8 numerator?

Four sandwiches were prepared by Mrs. Ericson, each identical in size, for her offspring: Matt, Elisa, Carl, and Riley.

The children consumed varying portions of their respective sandwiches during the shared midday meal.

Post-lunch investigations denoted different fractions residual from each child's original sandwich quantity.

Matt kept 7/8 of his portion while Elisa held on to 3/4 of hers. Meanwhile, two halves (2/4) constitute what remained of Carl's sandwich with Riley retaining 4/8 for himself.

Given this gridlock, which child between Matt and Riley still had more proportionate remaining sandwich contents provided they both possess a shared 4/8 numerator?

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The question in English is:

Mrs. Ericson made sandwiches for her 4 children. All the sandwiches had

The same size. After lunch, each child had a fraction left.

different from your sandwich. Matt had, Elisa had

7

3, Carl was 2, and Riley was 8

8

4

Use this information to write a problem comparing two fractions

with the same numerator.

Answer:

8.604 in.

Step-by-step explanation:

We can use the formula for compound interest to find the height of domino #9:

A = P(1 + r)^n

where A is the final amount, P is the initial amount, r is the growth rate, and n is the number of compounding periods. In this case, P is the height of domino #0, r is 15% or 0.15, and n is 9 (since we want to find the height of domino #9).

Substituting the given values:

A = 3.00 in * (1 + 0.15)^9

Simplifying:

A = 3.00 in * 2.86797199

A ≈ 8.604 in

Therefore, the height of domino #9 is approximately 8.604 inches.

The total cost of the art supplies without the coupon is:

2 paint brushes x $10.50 per brush = $21.00

1 dozen colored pencils x $7.88 per dozen = $7.88

1 sketch book x $16.12 per book = $16.12

Total cost without coupon = $21.00 + $7.88 + $16.12 = $45.00

With the $15.00 off coupon, the total cost becomes:

$45.00 - $15.00 = $30.00

The amount saved by using the coupon is:

$45.00 - $30.00 = $15.00

The percentage saved can be calculated as:

Percentage saved = (Amount saved / Total cost without coupon) x 100%

Percentage saved = ($15.00 / $45.00) x 100%

Percentage saved = 33.33%

Therefore, the customer saved 33.33% by using her coupon.

Answer:

Step-by-step explanation:

Answer: 1/2

Step-by-step explanation:

The fraction equivalent of 0.5 is 1/2.

To convert it into a mixed number, we can divide the numerator by the denominator:

1 ÷ 2 = 0 with a remainder of 1

So, the mixed number is 0 1/2.

The circles are similar because you can translate Circle 1 using the transformation rule (0, -7) and then dilate it using a scale factor of 3/5.

Translation involves moving an object in a straight line without changing its size or shape. In this case, we can translate Circle 1 7 units down to match the y-coordinate of Circle 2. The transformation rule for this translation is (0, -7), since we are not changing the x-coordinate.

Dilation involves uniformly scaling an object, either making it larger or smaller. We can dilate Circle 1 by a scale factor of 3/5 to make it have the same radius as Circle 2. The scale factor is determined by taking the ratio of the radii:

scale factor = radius of Circle 2 / radius of Circle 1

scale factor = 9 / 15

scale factor = 3/5

The center of dilation is the center of Circle 1, since we want to preserve its position.

Therefore, we can transform Circle 1 into Circle 2 by translating it 7 units down and dilating it by a scale factor of 3/5. The transformation rule is:

(0, -7) followed by dilation with a scale factor of 3/5

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Evaluating the expression (x - 2)/(x - 1) = (x - 1 + 2)/(x + 1)(x - 1), we get x = 1

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

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

Evaluating the like terms, we have

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

Cancel out the common factors

So, we have

(x - 2) = 1

Add 2 to both sides

x = 3

Hence, the solution is 3

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Answer:

Step-by-step explanation:

Let A(-2,-3), B(-4,-4).

Line f(x) = y = ax + b (C)

The line passes through these points so when substituting their coordinates into (C), we get:

-3 = -2a + b

-4 = -4a + b

Solving this set of equations gives us a = 1/2; b = -2.

So the equation of this line is  [tex]f(x)=\frac{1}{2}x-2[/tex]

The number of players  who included red and purple as their favorite colors is 0.

option A.

The number of people who included red and purple as their favorite colors are calculated as follows;

We are going to determine this number based on the given Venn diagram.

Check the intersection of red and purple, you will notice it is empty, so there is volleyball team member who included red and purple as their favorite colors.

So the answer is zero (0) since the intersection or connection point between red and purple is empty.

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The value of the expression is 28 2/3

To determine the value of addition, we need to know that fractions are described as part of a whole number or variables.

From the information given, we have that;

1/9 times 3 to the 3rd power

This is represented as;

(1/9 × 3)³

Divide the values, we get

(3)³

Find the cube

27

Then, we have;

27 + 2(1/6+2/3)

Solve the bracket

27 + 2( 1+ 4 /6)

27 + 2(5/6)

Divide the values

27 + 5/3

81 + 5/3

86/3

Divide the values

28 2/3

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According to the information, the distance from your starting point to the library is 4 miles.

To calculate how far do you live from the library we have to assume that the distance from the starting point to the library is "x" miles.

According to the problem, when you are 75% of the way there, you realize you forgot a book. It means you have traveled 75% of the distance, which is 0.75x miles.

Now, you turn around and bike back. When you are 1/3 of the way back, you realize you don't need the book, so you turn around again and bike 3.2 miles to the library.

From the starting point, you have traveled 0.75x miles to the point where you forgot the book, and then you traveled back 1/3 of 0.75x miles, which is (1/3)*0.75x = 0.25x miles.

Now you turn around again and bike 3.2 miles to the library. It means that the distance between the point where you realized you don't need the book and the library is 3.2 miles.

Therefore, the total distance from your starting point to the library is:

Simplifying the equation:

Thus, the distance from your starting point to the library is 4 miles.

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The triangle with 2 angles as 90° is not possible and the statement is false.

Given data ,

Let the triangle be represented as ∠ABC

Now , the measures of the angles of the triangle are

A triangle has two 90° angles and a side 12 centimeters in length

So , ∠ABC = ∠BAC = 90°

And , For a Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

Therefore, a triangle cannot be formed with 2 angles as 90°

Hence, the statement, the third angle is 90° is False

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The probability which is selected randomly from a lot of people living alone in the area in the 25-34 age range is 0.1487

The total digit of individuals living independently in the area = 31.6

The digit of individuals living in the area who fall within the 25 - 34 age range = 4.7

The probability formula will be applied ed as

P = required outcome / Total possible outcomes

From the information that is provided above the given data is:

P(range 25 - 34) = 4.7 / 31.6

= 0.1487

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The question is incomplete, Complete question probably will be  is:

The table shows the​ distribution, by age and​ gender, of the 31.6 million people who live alone in a certain region. Use the data in the table to find the probability that a randomly selected person living alone in the region is in the 25-34 age range.

The probability is ___.

(Type an integer or decimal rounded to the nearest hundredth as needed.)

The water cooler tank has to be filled 18 times to quench the thirst of 1200 students.

We have

Number of students= 1200

Water consumption per student= 750 ml

So, Total water consumption

= Number of students × Water consumption per student

= 1200 × 750 ml

= 900000 ml

= 900 Liter

Now, the time cooler tank has to be filled to quench the thirst

= 900 / 50

= 18 times

Thus, the water cooler tank has to be filled 18 times to quench the thirst of 1200 students.

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Answer:

B)  6

Step-by-step explanation:

Calculate the value of c by substituting point (0, 15) into the quadratic equation formula:

[tex]f(x)=ax^2+bx+c[/tex]

[tex]\begin{aligned}f(0)=a(0)^2+b(0)+c&=15\\0+0+c&=15\\c&=15\end{aligned}[/tex]

Therefore:

[tex]f(x)=ax^2+bx+15[/tex]

Substitute the point (1, 22) into the formula and create an equation for a in terms of b:

[tex]\begin{aligned}f(1)=a(1)^2+b(1)+15&=22\\a+b+15&=22\\a+b&=7\\a&=7-b\end{aligned}[/tex]

Therefore:

[tex]f(x)=(7-b)x^2+bx+15[/tex]

Finally, substitute another point from the table (-3, 6) and solve for b:

[tex]\begin{aligned}f(-3)=(7-b)(-3)^2+b(-3)+15&=6\\(7-b)9-3b+15&=6\\63-9b-3b+15&=6\\78-12b&=6\\-12b&=-72\\b&=6\end{aligned}[/tex]

Therefore, the value of b is 6.

Answer:

6

Step-by-step explanation:

The equation for the translated function is the one in option D:

G(x) = (x - 6)² - 4

We start with the parent quadratic function:

F(x) = x²

We apply two translations, one of 6 units to the right which can be written as:

G(x) = F(x - 6)

And a translation of 4 units down, which is written as:

G(x) = F(x - 6) - 4

Replacing F(x) we will get:

G(x) = (x - 6)² - 4

The correct option is D.

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The solution set of the inequality 2.5x ≥ 20 is x ≥ 8 and as such, Sebastian is incorrect based on his graph.

The graph of the solution set of -48 < -8t is shown below.

In Mathematics and Geometry, a number line simply refers to a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

Next, we would determine the solution to the given inequality as follows;

2.5x ≥ 20

x ≥ 20/2.5

x ≥ 8 (Sebastian was wrong)

-48 < -8t

-48/-8 < -8t/-8

6 < t

t > 8

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The answer to the expression is  (x+3)/(x-1)

You should recall that a quadratic expression is an algebraic expression of the form ax2 + bx + c = 0, where a ≠ 0

The given expressions are

(x² - 3x - 18) / (x²- 7x +6

(x²-6x +3x +19) / (x²-x -6x +6)

This implies that {(x²-6x)+(3x-18)} / {(x²-x) -(6x+6)}

⇒[x(x-6)+3(x-6)] / [x(x-1) - 6(x-1)]

This means that [(x+3)(x-6)] / [(x-6)(x-1)]

Dividing by (x-6) to have

Therefore the value of the expression is (x+3)/(x-1)

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The probability that fewer than 30% of the rolls result in a two is given as follows:

0.3085 = 30.85%.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

2 out of the six faces are two, and there will be 50 trials, thus the parameters n and p are given as follows:

n = 50, p = 2/6 = 1/3 = 0.3333.

The mean and the standard error are given as follows:

The probability that fewer than 30% of the rolls result in a two is the p-value of Z when X = 0.3, hence:

Z = (0.3 - 0.3333)/0.0667

Z = -0.5

Z = -0.5 has a p-value of 0.3085.

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By translation, the image of the vertices of the figure A'B'C' are A''(x, y) = (1, - 3), B''(x, y) = (- 2, - 1) and C''(x, y) = (- 3, - 5), respectively.

In this problem we must determine the image of the figure A'B'C', whose vertices are A'(x, y) = (4, - 1), B'(x, y) = (1, 1), C'(x, y) = (0, - 3), by translation, whose definition is shown below:

P'(x, y) = P(x, y) + T(x, y)

Where:

If we know that T(x, y) = (- 3, - 2), then the image of the vertices of the figure A'B'C' are:

A''(x, y) = (4, - 1) + (- 3, - 2)

A''(x, y) = (1, - 3)

B''(x, y) = (1, 1) + (- 3, - 2)

B''(x, y) = (- 2, - 1)

C''(x, y) = (0, - 3) + (- 3, - 2)

C''(x, y) = (- 3, - 5)

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Answer:

0

Step-by-step explanation:

The concepts of percentage, rate, and base can be defined as follows:

In our daily lives, we utilize these three concepts in many different ways, some examples of which are outlined below:

When we go shopping, we frequently come across discounts or sale prices offered as percentages off the original price. For example, if an item was initially $40 but is now available at a discount of 20%, it will be priced at $32.

Rates enable us to measure speed when we are driving or running with unit-based measurements. In addition, rates allow us to compare prices during grocery shopping, where we might need to know the cost per pound of apples and/or calculate interests on investments or loans.

Bases have utility while dealing with ratios or proportions. For instance, if we wish to prepare food for eight people instead of four, one can take the existing recipe as a base and adjust ingredient quantities proportionally.

The formulas P = B × R, B = P / R, and R = P / B are basic calculations that correspond to different values based on the given percentage, rate, or base. For instance, P = B × R allows us to obtain the value of P given the input of B and R.

Meanwhile, B = P / R enables us to get the value of B by punching in P and R much like calculating interest paid out each month in compound-interest cases.

Finally, R = P / B yields the value of R using inputs for P and B. These formulas find rampant use in fields like finance, economics, and mathematics.

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The width of the brochure is 3/2 inches and the height is 10 inches.

Let's assume that the width of the brochure is x and the height is y.

The area of the brochure is given as 30 square inches:

xy = 30

The perimeter of the brochure is given as 23 inches:

2x + 2y = 23

We can use the second equation to solve for one variable in terms of the other.

2x + 2y = 23

2x = 23 - 2y

x = (23 - 2y)/2

Now we can substitute this expression for x into the equation for the area:

xy = 30

[(23 - 2y)/2]y = 30

23y/2 - y^2 = 60/2

y^2 - 23y/2 + 30 = 0

We can solve for y using the quadratic formula:

y = [23/2 ± sqrt((23/2)^2 - 4(1)(30))]/(2)

y = [23/2 ± sqrt(529/4 - 120)]/2

y = [23/2 ± sqrt(289/4)]/2

y = [23/2 ± 17/2]/2

y = 10 or y = 3/2

Since the height must be greater than the width, we can eliminate y = 3/2 as a solution.

So, y = 10 and

x = (23 - 2y)/2 = (23 - 20)/2 = 3/2

Therefore, the width of the brochure is 3/2 inches and the height is 10 inches.

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We can solve this problem using the conservation of momentum and the law of conservation of energy. Here's how:

Let v be the velocity of the 105 kg player just before the tackle. Then the velocity of the 156 kg player just before the tackle is -6 m/s, since he is running south. After the tackle, the two players move at a velocity of 3 m/s north, so we have:

Total momentum before = Total momentum after

(105 kg)(v) + (156 kg)(-6 m/s) = (105 kg + 156 kg)(3 m/s)

Simplifying and solving for v, we get:

v = (105 kg + 156 kg)(3 m/s) + (156 kg)(6 m/s) / 105 kg

v = 2.85 m/s

Therefore, the velocity of the 105 kg player just before the tackle was 2.85 m/s north.

The measure of the obtuse angle with vertex P is 30 degrees.

We have,

If there is an acute angle with vertex Q measuring 60 degrees, then there must be a corresponding obtuse angle with vertex P that shares the same side as angle Q.

Let's call the measure of this obtuse angle x.

By the angle sum property of triangles, the sum of the measures of the three angles in any triangle is always 180 degrees.

Therefore, we can write the equation:

60 degrees + 90 degrees + x = 180 degrees

Simplifying this equation, we get:

x = 180 degrees - 60 degrees - 90 degrees = 30 degrees

Therefore,

The measure of the obtuse angle with vertex P is 30 degrees.

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Check the picture below.

Answer:

The Correct answer is D and F

The line of reflection of the graph is y = -3

The given graph is added as an attachment

From the graph, we can see that the shapes are symmetrical about the line y = -3

When shapes are symmetrical about a point or a line, then the point or the line is the point of reflection

This means that the line of reflection is y = -3

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Answer:

The calculated line of reflection of the graph is y = -3

Step-by-step explanation: