How do you multiply fractions with a common denominator?

The graph of the linear equation is attached

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

A bowling alley charges $6 for shoe rental and $2 for each game.

This means that

Intial value = 6

Rate = 2

The function is then represented as

f(x) = Initial + Rate * x

So, we have

f(x) = 6 + 2x

See attachment fr the graph

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Answer: midpoint is 4,5

Step-by-step explanation:

The y-intercept will be at (0, 22,995) and the x -intercept at (9, 0).

The y-axis is calibrated in dollars and the x-axis in years.

The graph is a straight line which starts  on the positive y axis and ends on the positive x-axis and has a negative slope .

Y - intercept:

The point of intersection is the point on the Y-axis through which the slope of the straight line passes. This is the y-coordinate of the point where the line or curve intersects the y-axis. This is shown when writing the equation for the y = mx + c straight line. where m is the slope and c is the intersection with the y-axis.

X- Intercept:

The x-intercept is the point at which the graph of the equation intersects the x-axis, and the y-value must be 0 for the point to intersect the x-axis. Consequently, the x segment can always be represented as (x, 0). The x value indicates where the graph intersects the x-axis.

According to the question:

When X = 0, y = 22995

And, X = 9  and Y = 0.

So the intercepts are (0,22995) and (9,0) which are shown on the right.

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Answer:

The value of [tex]r[/tex] is 24 cm.

Option C. 24 cm

Step-by-step explanation:

We can use the Pythagorean theorem to evaluate the missing side.

Here is the formula for the Pythagorean theorem.

[tex]a^2+b^2=c^2[/tex]

[tex]a[/tex] and [tex]b[/tex] are the legs of the triangle

[tex]c[/tex] is the hypotenuse

In this example we are given the value of 1 leg and the hypotenuse.

Knowing 2 of the 3 sides, we can evaluate the missing leg.

Let [tex]a=r[/tex]

We are given

[tex]b=10\\c=26[/tex]

Inserting our values into the Pythagorean theorem gives us

[tex]r^2+10^2=26^2[/tex]

Lets solve for [tex]r[/tex].

[tex]r^2+10^2=26^2[/tex]

Evaluate [tex]10^2[/tex].

[tex]r^2+100=26^2[/tex]

Evaluate [tex]26^2[/tex].

[tex]r^2+100=676[/tex]

Subtract [tex]100[/tex] from both sides of the equation.

[tex]r^2=576[/tex]

Take the square root of both sides to eliminate the exponent.

[tex]r=\sqrt{576}[/tex]

[tex]r=24[/tex]

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Answer: 250

Step-by-step explanation:

It says in the question that the first round was -350 but the second round she score 250 and the question wants to know how many points she scored in the second round with would be 250.

The markup is $6.47 and the selling price is $31.87

percentage, a relative value indicating hundredth parts of any quantity.

A markup is the amount added to the cost price of a product to determine the selling price.

Let the cost price of a box of copy paper is $25.4 and the markup is 25.4%

Now let us find the selling price by given formula.

Selling price = Cost price + (Cost price x Markup percentage)

Selling price = $25.4 + ($25.4 x 25.4%)

Selling price = $25.4 + ($25.4 x 0.254)

Selling price = $25.4 + $6.47

Selling price = $31.87

So, the markup is $6.47 and the selling price is $31.87.

Hence,  the markup is $6.47 and the selling price is $31.87

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The value of x from the given figure is 15°.

An exterior angle is an angle which is formed by one of the sides of any closed shape structure such as polygon and the extension of its adjacent side. The sum of the measures of the exterior angles of a polygon is equal to 360 degrees, irrespective of the number of sides in the polygons.

In the given figure, we have 7x°, 83°, 33°, 6x° and 49°.

Now, 7x°+83°+33°+6x°+49°=360°

13x+165=360

13x=360-165

13x=195

x=195/13

x=15

Now, 6x=90° and 7x=105°

Therefore, the value of x is 15°.

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The probability that a student is in 4th grade given that they did not choose popular as the most important trait is 0.5 or 50%.

The probability is a concept used in statistics that measures the likelihood of an event occurring.

Let's call the event of a student being in 4th grade as A and the event of a student not choosing popular as the most important trait as B. We can find the probability of A and B happening together by dividing the number of students who are in 4th grade and did not choose popular by the total number of students. This can be represented as

P(A and B) = P(A | B) = (75 / 250) = 0.3.

Next, we can find the probability of B happening by dividing the number of students who did not choose popular by the total number of students. This can be represented as

P(B) = (150 / 250) = 0.6.

Finally, we can use Bayes' theorem to find the probability of A given B. Bayes' theorem states that

=> P(A | B) = P(A and B) / P(B).

Therefore,

=> P(A | B) = (75 / 250) / (150 / 250) = 0.3 / 0.6 = 0.5.

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A library has 2500 books.40% of the books are fiction, number of not fiction books are 1500.

A percentage is a relative figure that represents one tenth of a quantity. Since one percent (symbolised as 1%) is equal to one tenth of anything, 100 percent stands for everything, while 200 percent refers to double the amount specified.

Total amount of book in library are 2500 ,

Out of that 40% are fiction so the number of the non fiction books are 60%

so 60% of 2500 will give us the value of non fiction books,

Number of non fiction = 2500 x 60%

= 2500 x 60/100

= 25 x 60

= 1500

Therefore,  Number of non fiction books are 1500.

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Answer:

5.3

Step-by-step explanation:

sin24 = x/13

x = sin24(13) = 5.3

Answer:

Amy is 14 years old and Sam is 10 years old.

Step-by-step explanation:

Let's represent Amy's current age as "A".

Since Sam is four years younger than Amy, his current age can be represented as (A - 4).

Five years ago, Amy's age was A - 5 and Sam's age was (A - 4) - 5 = A - 9.

At that time, Sam was half of Amy's age, so we can write the following equation:

(A - 9) = (A - 5) / 2

Expanding and simplifying the equation, we get:

A - 9 = 2A / 2 - 5 / 2

A - 9 = A - 5 / 2

7 = A / 2

A = 14

So, Amy is 14 years old and Sam is (14 - 4) = 10 years old.

Answer: yes

Step-by-step explanation:

7^2+24^2 = 625

[tex]\sqrt{625}[/tex] = 25

Answer:

[tex]158[/tex][tex]cm^2[/tex]

Step-by-step explanation:

Since the formula is [tex]2(wl+hl+hw)[/tex], we can simply plug in the lengths.

Once calculated, the answer is [tex]158cm^2[/tex].

Hope it helped!

Answer:

  158 cm²

Step-by-step explanation:

You want the surface area of a rectangular prism whose net is shown.

The surface area of the prism is the area of the net. That area is the sum of the areas of the rectangles that make it up. The rectangles come in pairs that have the same area.

Down the middle we have two pairs of rectangles. One pair is 8 cm wide and 3 cm high; the other is 8 cm wide and 5 cm high. Together the area of those four rectangles is ...

  2(8 cm)(3 cm +5 cm) = 2(64 cm²) = 128 cm²

The "wings" of the net are rectangles that are 3 cm by 5 cm, so their total area is ...

  2(3 cm)(5 cm) = 30 cm²

The area of the net is then ...

  surface area = 128 cm² +30 cm²

  surface area = 158 cm²

__

Additional comment

If you like, you can use the area formula. It will tell you the same thing for this 3 × 5 × 8 cm prism.

  SA = 2(LW +H(L +W)) = 2(3·5) +8(3 +5)) = 2(15 +8·8) = 2(79) = 158 . . . cm²

Liliana's next step is to find the area of each of the two trapezoids.

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

Given that she has broken the polygon into two trapezoids, the next step ti so calculate the area of each trapezoid

This is done using

Area = 1/2 * (sum of parallel sides) * height

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Complete question

Area of Trapezoids and Other Figures quick check

Liliana wants to find the area of a polygon. First, she breaks apart the polygon into two trapezoids. What is Liliana's next step?

A high standard deviation indicates greater variability in the data set. A low standard deviation indicates lower variability in the data set.

A standard deviation is a measure of how spread out the values in a data set are. It is calculated by taking the square root of the variance, which is the average of the squared differences from the mean. A high standard deviation indicates that the values in the data set are far from the mean and spread out over a large range of values. This suggests that there is a large amount of variation and diversity in the data. On the other hand, a low standard deviation indicates that the values in the data set are close to the mean and spread out over a smaller range of values. This suggests that there is less variability and diversity in the data. A standard deviation of zero indicates that all values in the data set are the same. This suggests that there is no variation or diversity in the data. No one set of data is more accurate than another; accuracy depends on the context and purpose of the data. For example, if the goal is to identify trends or outliers, a data set with a high standard deviation may be more useful than one with a low standard deviation.

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The numbers have been matched accordingly as below.

Rational numbers are numbers which can be written in the form of a/b, b ≠ 0, and a and b are integers.

Irrational numbers cannot be written in this form.

√30 is not a perfect square. So it is real, irrational root.

-26 is a negative real integer. So it is a real rational integer.

√64 is actually a perfect square root, 8, which is a whole number. So it is a real, rational root, whole number.

1/4 is of the form a/b. So it is also real, rational.

0.363363336.... is a real irrational decimal.

0.424242..... is a real rational decimal, since it is repeating in nature.

[tex]\sqrt{-7}[/tex] or [tex]7i[/tex] is an imaginary number.

Hence the numbers has been matched according to the properties.

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Step-by-step explanation:

the distance from a vertex of the quadrilateral to the touching points on the two sides emanating from the vertex is the same.

and that applies to each of the 4 vertices.

so, AB splits into the distance a (from A to the circle touching point on AB) and b (from the touching point on AB to B).

b = AB - a

in the same way, BC splits into b (B to circle touching point on BC) = AB - a, and c (circle touching point on BC to C).

c = BC - (AB - a) = BC - AB + a

CD splits into c (C to circle touching point on CD) = BC - AB + a, and d (circle touching point on CD to D).

d = CD - (BC - AB + a) = CD - BC + AB - a

DA now splits into d (D to circle touching point on DA) = CD - BC + AB - a, and into ... a (the circle touching point on DA to A).

a = DA - (CD - BC + AB - a) = DA - CD + BC - AB + a

0 = DA - CD + BC - AB

DA = CD - BC + AB = 8 - 5 + 4 = 7

An expression which best represents the value of pi include the following: D. C/7.

Mathematically, the circumference of a circle can be calculated by using this mathematical expression:

C = 2πr or C = πD

Where:

Making π the subject of formula, we have the following:

π = C/D

Substituting the given parameters into the circumference of a circle formula, we have;

π = C/7.

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Complete Question:

A circular pond has a circumference of about C feet. The diameter of the pond is 7 feet. Which expression best represents the value of pi?

A. C/14

B. 7/C

C. 14/C

D. C/7

The number of possibilities are 20,160. Therefore, the option A is the correct answer.

Factorials is defined as the mathematical expression that is the product of the given number down to 1. It is denoted with the symbol n! which means that is n is given as 4, then it's factorial would be = 4×3×2×1 = 24.

Factorials is used in mathematics or statistics to denote the possibilities of an event in an outcome.

The number of specialty pizzas that is being offered by pizza parlor = 8

The number of specialty that Almeida's family wants to order = 2

To calculate the number of possibilities;

= 8!/2!

= 8×7×6×5×4×3×2×1/2×1

= 20,160.

Therefore, the option A is the correct answer.

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As a result, the ratio of eighth students to seventh graders is 4:1.

A ratio is a comparison of two or more values, often expressed as a fraction or a colon-separated set of numbers. Ratios can be used to compare quantities of similar items, such as the ratio of the number of apples to the number of bananas in a basket. Ratios can also be used to describe the relationship between different aspects of a system, such as the ratio of length to width of a rectangle, or the ratio of time spent working to time spent sleeping. Ratios are a useful tool for making comparisons and understanding relationships between different values.

Here,

Out of the 15 students in the yearbook club, 3 are in 7th grade, and the rest are in 8th grade, which means there are 15 - 3 = 12 students in 8th grade.

The ratio of 8th graders to 7th graders can be calculated by dividing the number of 8th graders by the number of 7th graders:

12/3 = 4:1

So, the ratio of 8th graders to 7th graders is 4:1.

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The elements in (D∩B)' is A,B,D.

A set is defined as collection of well-defined object. It is denoted by capital letters and their elements are denoted by small letters.

Given that ,

In venn diagram, B is the swamp portion and D is the rainforest portion.

C represents the intersection of B and D. i.e., C= (D∩B)

A is the universal set.

(D∩B)' = A - (D∩B)

          = A - C

Hence, (D∩B)' contains  A, B, D.

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The root of the equation are x² + x − 5 = 0 are 2.85 and --3.85

quadratic equation is a second-order polynomial equation in a single variable x ax²+bx+c=0. with a ≠ 0 . Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

We can use the formula x =-b±√b²-4ac/2a to find the root of a quadratic equation

a = 1, b = 1 and c = -5

x= -(1) ± √ 5²-4× -5×1)/2

x = -1±√25+20)/2

x = -1±√45)/2

x = -1+6.7/2 or -1-6.7/2

x = 5.7/2or -7.7/2

x = 2.85 or -3.85

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There are 11,838,890 ways to arrange 7 elves and 5 goblins in a row without any goblins standing next to each other.

This can be calculated using the formula for combinations, n!/(r!(n-r)!), where n is the total number of elves and goblins (12) and r is the number of goblins (5). The calculation is written as 12!/(5!(12-5)!) = 11,838,890.

To illustrate, one possible arrangement is EE EG EEG EEG EGEE EG. Here, E stands for elf and G stands for a goblin. The arrangement starts with two elves, followed by an elf and a goblin, followed by three elves, followed by an elf and a goblin, followed by two elves, and finally ending with an elf.

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Total number of students that like chicken nuggets is 4/7 x G + 40/100 x B.

The percentage of entire student body that like chicken nuggets are (4/7 x G + 40/100 x B) / T x 100.

Given that 4/7 of the girls like chicken nuggets, if there are G girls, then the number of girls who like chicken nuggets is 4/7 x G.

Given that 40% of the boys like chicken nuggets, if there are B boys, then the number of boys who like chicken nuggets is 40/100 x B.

The total number of students who like chicken nuggets is 4/7 x G + 40/100 x B.

To find the percentage of the entire student body that likes chicken nuggets, divide the number of students who like chicken nuggets by the total number of students, and multiply by 100.

Let's say there are T total students.

The percentage of the entire student body that likes chicken nuggets is (4/7 x G + 40/100 x B) / T x 100.

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Answer:

I would recommend taking practice quizzes online for the level of math you are taking to find what areas you understand well and what areas you are struggling in. From there, you can review that specific area of math and refine your knowledge. Taking practice quizzes repeatedly until you are confident both in the mathematics and the test taking itself(if you struggle with test taking in general) will help a lot.

Answer:

Step-by-step explanation:

Study Time: I suggest you study over a period of time and try to understand the topic. For example, try to include breaks to help yourself relax. DO NOT cram lots of math into your head on an overnight studying marathon. Many people try that, and unless you have a photographic memory, it does not help at all.

Topics: Try to study one topic at a time so the information does not get mixed up in your head. Try to remember things with variables.

Resources: Ask your teacher what topics the test will cover and how many questions will be on the test. You can find lots of worksheets online and review explanations to similar questions on websites.

Morning before the test: Sleep early and wake up early. Try to relax and eat a healthy breakfast.

I wish you luck on your test!

A quadrilateral with two sets of parallel sides and 4 congruent sides is called a parallelogram. A parallelogram is a quadrilateral with two sets of parallel sides and 4 congruent sides.

A parallelogram is a four-sided polygon with two pairs of opposite sides that are parallel to each other and equal in length. This means that the shape has two sets of parallel sides and all of its sides have the same length.

Parallelograms have several key properties, including opposite sides that are equal in length and parallel, and opposite angles that are equal in measure. Additionally, the diagonals of a parallelogram bisect each other, meaning they split each other in half.

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By using the x- and y-intercepts, a graph of the function modeling the total number of tickets sold is shown in the image attached below.

The domain and range of each function is {-∞, ∞}.

The meaning of the x-intercept is that the initial number of student tickets sold is 600 tickets.

The meaning of the y-intercept is that the initial number of adult tickets sold is 300 tickets.

The slope of the function is 0.5 and it represents the number of tickets sold per week.

You can use the graph to determine a combination of ticket sales to meet the goal of $3,000 by adding each ordered pair (s, a) or (x, y) together.

Felina's graph is correct because it has the same x-intercept and y-intercept with the original graph.

In order to write a linear equation to describe this situation, we would a assign variable to the number of student tickets sold and the adult tickets sold respectively, and then translate the word problem into a linear equation as follows:

Since student are paying $5 while adults are paying $10 for a ticket and the athletic association need to raise $3000 by selling tickets, a linear equation that models the situation is given by:

5s + 10a = 3000

When s = 0, the value of a is given by:

5(0) + 10a = 3000

a = 300

When a = 0, the value of s is given by:

5a + 10s = 3000

s = 600

For the total number of tickets, we have this linear equation:

s + a = 450

In conclusion, we would use an online graphing calculator to plot the system of linear equations in order to determine the solution (point of intersection), which is at the ordered pair (300, 150).

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Complete Question:

The Marshall High School Athletic Association sells tickets for the weekly football games. Students pay $5 and adults pay $10 for a ticket. The athletic association needs to raise $3000 selling tickets to send the team to an out-of-town tournament.

1. Use x- and y-intercepts to graph the function modeling the total number of tickets sold on each coordinate plane.

2. Determine the domain and range of each function

The exact area of the circle would be = 36πcm². That is option B.

The area of a circle can be calculated through the use of the formula = πr²

Where,

radius (r) = 6 cm

area = π × 6²

= 36π cm² ( in the terms of π)

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The value of the angle 4 is 96 degrees as shown in the diagram.

A line is an object in geometry that is indefinitely long and has neither breadth nor depth nor curvature. Since lines can exist in two, three, or higher dimensional environments, they are one-dimensional things.

From the given diagram, the measure of angle 1 and 3 are equal as well as 2 and 4.

Given the following angles

m<3 = 84 degrees

Since the measure of <3 and <4 lies on the same straight line, hence:

m<3 + m<4 = 180

84 + m<4 = 180

m<4 = 180 - 84

m<4 = 96 degrees

Hence the measure of angle 4 from the figure is 96 degrees

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137 is not a term in this sequence due to the fact that  7n +2= 137 gives n = 19.285 which is not a whole number.

We have to use the formula

tn = a + ( n - 1) d

where we have tn = 137

a is the first term = 9

n i unknown

d is the difference = 16 - 9 = 7

We have to put these values in the formula such that

137 = 9 + (n - 1) 7

then we have to expand this

137 = 9 + 7n - 7

take the like terms

137 = 9 - 7 + 7n

137 = 2 + 7n

137 - 2 = 7n

135 = 7n

divide through by 7

135 / 7 = 7n / 7

n = 19.28571...

This is not a whole number, hence 137 is not a term in the sequence that we have here

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