Wendy is arranging books on the bookshelves in the school library. The total number of books she arranges is given by the equation b = 12r, where b is the total number of books and r is the number of rows. Each row contains the same number of books.
If Wendy arranged 16 rows, she arranged a total of

Answer:

3/10

Step-by-step explanation:

If homeroom 101 has 1/2 of the bulletin board, and 3/5 of their side is used.

To calculate the area that is using we multiply both values,

1/2 x 3/5 = 3/10

Which is our answer!

Scale Factor. To create a scaled copy, we multiply all the lengths in the original figure by the same number.

A 1.5 GPA, or Grade Point Average, is comparable to a D+ letter grade on a scale of 4.0 GPA. This corresponds to a grade of around 69%. The Scale Factor. To make a scaled replica, multiply all of the original figure’s lengths by the same number. This figure is known as the scaling factor. The scale factor in this case is 1.5 since 4(1.5)=6, 5(1.5)=7.5, and 6(1.5)=9.

An Over 1.5 Goals bet is simply a betting on there being two or more goals scored in a given game. The scoreboard is irrelevant; as long as the two sides collaborated for at least two goals, your bet will win.

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The triangle is a perfect right angle triangle  since it satisfies the Pythagoras theorem .

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or previously rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.

According to the definition of a right triangle, a triangle is referred to as a right-angled triangle or simply a right triangle if one of the angles is a right angle (90°). Triangle ABC is a right triangle in the illustration, consisting of the base, altitude, and hypotenuse. Here, the hypotenuse is BC, the height is AC, and the base is AB. The significant side of a right triangle is the hypotenuse, which is the longest side and sits in opposition to the triangle's right angle.

By using pythagoras theorem

[tex]\sqrt{24\x^{2} + 7\x^{2} } = 25[/tex]

The triangle si a perfect right angle triangle  since it satisfies the Pythagoras theorem .

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The base of an exponent is a number that is increased to a definite power. So, the base of an exponent defines the number that is multiplied by itself.

An exponent is a number or letter written above and to the right of a mathematical expression said the base. It indicates that the base is to be increased to a certain power.

In 2³ = 2 × 2× 2, 2 is the base number which is to be multiplied by itself thrice and could be also called “two to the power of three” or “two to the third power” In 2³= 2 × 2× 2, 3 is the exponent which represents the number of times 2 is to be multiplied by itself.

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Answer:

Step-by-step explanation:

V=(1/3)hπr^2

<=> 4487 = 1/3x21πxr^2

<=> r^2 = 641/π

<=> r = squrt( 641/π)

(x - 4) is a factor of the expression 5x³ − 7x² − ax − 28, when a = 28

Here we are given the expression 5x³ − 7x² − ax − 28

now we need to find a value of a for which (x - 4) is a factor of

5x³ − 7x² − ax − 28

This implies that 5x³ − 7x² − ax − 28.must be divisible by (x - 4)

On dividing 5x³ − 7x² − ax − 28. by x - 4 will give us

[tex]x-4) \overline{5x^{3}-7x^{2}-ax-28.}(5x^{2}+14x+(56-a)\\{\hspace{1cm} 5x^{3}-20x^{2}\\\\\hspace{2cm}\overline{14x^{2}-ax}\\{\hspace{2cm}14x^{2}-56x\\\\{\hspace{3cm} \overline{(56 - a)x - 28}\\{\hspace{3cm} (56-a)x-(56-a)\\{\hspace{5cm} \overline{28-a}[/tex]

Since (x - 4) is a factor of 5x³ − 7x² − ax − 28, there should not be any remainder left

Hence, 28 - a = 0

or, a = 28

Hence (x - 4) is a factor of 5x³ − 7x² − ax − 28, when a = 28

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Correct Question

Find the value of a such that (x−4) is a factor of 5x³ − 7x² − ax − 28.

The Wien Apetrol UC 20142000 was a unique and innovative venture that aimed to provide clean energy solutions to the people of Austria.

x = -7

ma = 54

m23 = 54

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We will convert between volume units by multiplication or division process depending on the standard metric units.

What is unit conversion?

Unit conversion is done either by multiplication or division process between numerical values. There are some standard metric units. By following the standard, we can convert one unit to another. As example we have a box that is 2 square feet area, now we want to know the area in inches. So, we will multiply it by 144 to convert in square inches.

How do we convert between volume units?

We convert between volume units either by multiplication or division process depending on the standard unit. If we find a volume in liter and we can convert it in cubic meter by multiplying the number by 0.001. Assume, we measured a volume in cubic feet, but someone want to know this volume in cubic meter that time we divide this value by 35.32 to convert in required unit.

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Answer:

As it is a right angle triangle, you can find a by Pythagoras Theorem.

[tex] {a}^{2} + {51}^{2} = {60}^{2} \\ a = \sqrt{( {60}^{2} - {51}^{2} )} \\ a = 31.63 \: yd[/tex]

The statement that must be true since the average rate of change T(d) for the interval d = 4 and d = 10 is 0 is this:

C: The same number of tickets was sold on the fourth day and tenth day.

The average rate of change is a measurement that shows how much the function of a unit changes over a given interval. In the above question, we can see that the average rate of change given the two intervals is zero and this means that there was no change among the variables.

Thus, we can conclude that the number of tickets that were sold on day 4 was also the number of tickets sold on day 10.

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The decision rule for is to reject null if critical value is higher than the test statistic, since there is insufficient evidence to show that the machines are underfilling the bag.

First we have to solve for the test statistic

t = x - u / s /√n

the variables are stated as:

where x = 444

u = 447

n = 24

s = 10

we would have the test statistic solved as :

444 - 447 / 10 / √24

-3 / 2.0412

= -1.4697

at 0.1 significance level, we would have:

degree of freedom

n - 1

= 24 - 1 = 23

the critical value is -1.3194.

Because the critical value is  greater than the test statistic, we are going  to  reject the null.

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Mia spend 1/4 of her money on a ticket, he has 30 pound left. Therefore the ticket was 120 pound.

Pound:

The sterling  is the currency of the United Kingdom and nine associated territories. The pound (symbol: £) is the primary unit of sterling, and the word "pound" is also commonly used to refer to British currency, and in international contexts is often British It is called pound or pound sterling.

The sterling is the world's oldest currency still in use and has been in continuous use since its creation. It is currently the fourth most traded currency in the foreign exchange market, after the US dollar, the euro and the Japanese yen. Together, these three currencies and the renminbi form a basket of currencies for calculating the value of the IMF's Special Drawing Rights. As of late 2022, the pound is the world's reserve currency and he is also the fourth most held reserve currency.

According to the question:

Since, 1/4 of her money is spent on the tickets.

Then , there left 3/4 part of money.

Therefore,

So she spent a total of 1/4 of her money in the tickets, and therefore had 3/4 of her money left at the end. So 3/4 of the money she started with is 30 pound.

Therefore she started with 30 * 4 = 120 pound.

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The change in profit for each owner is -$22.00c

You should be aware that change in profit in this regard talks about how much money each partner is going to loose over what he or she gains initially

The given parameters that will help us to understand the question are

This implies that the 100 dollars will be shared among the five partners in this way

110/5 = 22.00

In conclusion each partner gets a change in profit of $22.00

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The result after multiplication = 6/X, 1, 1/ 7

When one is divided by a number or value it is called the reciprocal of that number or value. It is also said the inverse form of the value or number. As example, reciprocal of 12 is written as 1/12.

What is the result?

There are four values 6, X, 6 and 42.

multiply the first number by the reciprocal of others.

reciprocal of X = 1/X

reciprocal of 6 = 1/6

reciprocal of 42 = 1/42

now we multiply, 6×1/X = 6/X

6×1/ 6 = 1

6×1/ 42 = 1 /7

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Therefore , the solution to the given problem of circle comes out to be  

572 yard^2.

Each point in the plane that is a certain distance from some other point forms a circle (center). Thus, it is an curve composed of spots that are spaced apart from one another in the plane. Additionally, at every angle, it is axis of rotation symmetric about the center. The closed, two-dimensional plane of a circle has every pair of points uniformly separated from the "center." With tracing a path through the circle, one can create a line of circular symmetry. Additionally, at every angle, it is radially symmetric about the center.

Here,

area=pi times

radius2 area=3.14 times 13.52

=>3.14 times diameter=2radius dameter/2

=>radius d=27 27/2=radius.

The answer, 182.25=572.265,

Area is 572 yards.

Therefore , the solution to the given problem of circle comes out to be  

572 yard^2.

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Integers are a type of real number that just includes positive and negative whole numbers and natural numbers. Real numbers can include fractions due to rational and irrational numbers, but integers cannot include fractions.

$75.50 and 18 cents - $35.50 and 8 cents = $40.00 and 10 cents per mile. For x miles, we multiply $40.00 and 10 cents by x miles.

Also, we could convert dollars to cents by multiply it by 100 Since $1 =100 cents.

7568 - 3558 cents = 4010 cents. For x miles, 4010X cents.

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The vertex of the parabola is at (0, 0), the focus of parabola is at (2, 0) and axis of symmetry of parabola is x-axis.

A parabola is an approximately U-shaped, mirror-symmetrical planar curve. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves.

One definition of a parabola includes a line and a point (the focus) (the directrix). The directrix is not the main focus. The locus of points in that plane that are equally spaced apart from the directrix and the focus is known as the parabola.

Given a horizontal parabola centered on the origin opens to the left,

the equation for a horizontal parabola,

(y − b)² = 4p(x − a), p≠0

a and b are the vertex of parabola,

since the parabola is centered on the origin, a and  b are (0, 0)

vertex of parabola is at (0, 0),

and for horizontal parabola axis of symmetry is the x-axis.

focus of parabola is at (a + p, b)

given p = 2

focus of parabola is at (0 + 2, 0) = (2, 0)

Hence vertex at (0, 0), focus at (2, 0), and symmetry with the x-axis.

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The circumference of circle B is 14 m

The circumference (or) perimeter of a circle = 2πr units. The area of a circle = πr2 square units. Where r is the radius of the circle. The circumference of the circle or the perimeter of the circle is the measurement of the boundary of the circle. Whereas the area of the circle defines the region occupied by the circle.

Given here: The circumference of circle A as 2²/₃ m and circumference of circle B as 1¹/2 times the diameter of circle A

let the radius of the circle A be r then we have

2πr=8/3

r=4/3×7/22

r=14/33 m

or diameter of the circle A= 28/33

Again let the circumference of the circle be x then we have

x=28/3 ×3/2

x=14

Hence, The circumference of circle B is 14 m

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Answer:

Step-by-step explanation:

15 tiles

The value of k are the graphs (equations) equal is k = -3/2

Equations are mathematical expressions that show the relationship between two variables.

Since we have the two equations  12y = -3x + 8 and 6y = kx -5, re-writing them, we have

12y = -3x + 8

3x + 12y - 8 = 0  (1)

Also, 6y = kx - 5

-kx + 6y + 5 = 0  (2)

For a pair of equations ax + bx + c = 0 (3) and a'x + b'x + c' = 0 (4) to be equal (or consistent), then

a/a' = b/b' = c/c'

Comparing with (1) and (2), with (3) and (4) above, we have that

So, using a/a' = b/b', we find k.

So, substituting the values of the variables into the equation, we have that

a/a' = b/b'

⇒ 3/-k = 12/6

Cross-multiplying, we have that

3 × 6 = -k × 12

k = -3 × 6/12

k = -3/2

So, the value of k = -3/2

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The expected value of Isabel's game is given as follows:

E(X) = 0.

The expected value of a discrete distribution is calculated as the sum of each outcome multiplied by it's respective probability.

The game is composed by choosing eight balls, which are equally as likely to be chosen.

Then the probability distribution of earnings is given as follows:

Hence the expected value of the price is given as follows:

E(X) = 1/8 x (1 + 2 + 5 + 6 + 8 + 10) - 16 x 2/8.

E(X) = 0.

The problem asks for the expected earnings.

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Step-by-step explanation:

82=−3(−4a+3)−5

Step 1: Simplify both sides of the equation.

82=−3(−4a+3)−5

82=(−3)(−4a)+(−3)(3)+−5 (Distribute)

82=12a+−9+−5

82=(12a)+(−9+−5) (Combine Like Terms)

82=12a+−14

82=12a−14

Step 2: Flip the equation.

12a−14=82

Step 3: Add 14 to both sides.

12a−14+14=82+14

12a=96

Step 4: Divide both sides by 12.

[tex]\frac{12a}{12} = \frac{96}{12}[/tex]

a=8

Angle 5 is congruent to angle 8 by (vertically opposite angle )

Angle 5 is also Congruent to Angle 4 (alternate Angles)

Angle 5 is also Congruent to Angle 1 ( corresponding Angles )

When two figures or things are similar in size and shape, or when one is the mirror image of the other, they are said to be congruent.

It states that two triangles are considered to be congruent if they are identical duplicates of one another and completely cover one another when superposed. In other words, two triangles are congruent if their corresponding sides and angles are equivalent to those of the first triangle.

Two line segments are said to be congruent if their lengths are identical. In addition, two congruent line segments have the same length. Two angles are congruent if they have the same measure.

Angle 5 is congruent to angle 8 by (vertically opposite angle )

Angle 5 is also Congruent to Angle 4 (alternate Angles)

Angle 5 is also Congruent to Angle 1 ( corresponding Angles )

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Angle 5 is congruent to angle 8 by (vertically opposite angle )

Angle 5 is also Congruent to Angle 4 (alternate Angles)

Angle 5 is also Congruent to Angle 1 ( corresponding Angles )

When two figures or things are similar in size and shape, or when one is the mirror image of the other, they are said to be congruent.

It states that two triangles are considered to be congruent if they are identical duplicates of one another and completely cover one another when superposed. In other words, two triangles are congruent if their corresponding sides and angles are equivalent to those of the first triangle.

Two line segments are said to be congruent if their lengths are identical. In addition, two congruent line segments have the same length. Two angles are congruent if they have the same measure.

Angle 5 is congruent to angle 8 by (vertically opposite angle )

Angle 5 is also Congruent to Angle 4 (alternate Angles)

Angle 5 is also Congruent to Angle 1 ( corresponding Angles )

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The probability of all 6 locations being in water is 0.9994.

The probability of a single location being in water is 0.71. When finding the probability of 6 locations all being in water, we can use the binomial probability formula:

P(x=6) = (n!/(x!(n-x)!)(p^x)(q^(n-x))

where n is the number of trials, x is the number of successes, p is the probability of success, and q is the probability of failure.

Plugging in the values, we get:

P(x=6) = (6!/(6!(6-6)!)(0.71^6)(0.29^(6-6))

P(x=6) = 0.9994

Therefore, the probability of all 6 locations being in water is 0.9994.

The probability of all 6 locations being in water is 0.9994.

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The table shows the temperature of a substance at the start of a science experiment which - 16.8°C and we were told that it changed by 3/4 of the value which therefore means that the final temperature at 2:35pm is - 29.4°C.

This is referred to as the degree of hotness or coldness of a substance and it is measured in Celsius, kelvin etc.

In this scenario we were told that the temperature - 16.8°C changed by 3/4 of the value which means that:

3/4 × - 16.8°C = - 12.6°C

The temperature at 2:35pm will therefore be  - 16.8°C - 12.6°C = - 29.4°C.

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Susie AnnaMarie spent 6 hours cutting grass

Let a represent the number of hours Susie AnnaMarie spent cutting grass

Let b represent the number of hours Susie AnnaMarie spent tutoring

a + b = 14..........equation 1

12a + 14b= 184.........equation 2

From equation 1

a + b= 14

a= 14-b

Substitute 14-b for a in equation 2

12(14-b) + 14b= 184

168 - 12b + 14b= 184

168 + 2b= 184

2b=  184-168

2b= 16

b= 16/2

b= 8

Substitute 8 for b in equation 1

a + b= 14

a + 8= 14

a= 14-8

a= 6

Hence Susie AnnaMarie spent 6 hours cutting the grass

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The horizontal line test is a procedure that can be used to determine if a function is a one-to-one function. This means that, for every y-value in the function, there is only one distinctive x-value.

The purpose of the horizontal line test is to decide whether or not a given function is one-to-one considering its graph. A function from one set to another is a relation between the two sets in which each element of the first set is assigned to a single element in the second.  In other words, a function f is one-to-one

                           [tex]f(x_{1}) = f(x_{2})[/tex]  ⇒ [tex]x_{1} = x_{2}[/tex]

for every [tex]x_{1} , x_{2}[/tex] n the domain of f.

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For y = 10x the constsnt of proportionality is 10

We know that the quantity m is proportional to quantity n if there is a constant p such that m = pn

Here, p is called as the constsnt of proportionality.

This means, the constsnt of proportionality is nothing but the ratio between two proportional quantities.

Two variables are proportonal to each others means, when the variable increase the other one would also increase at some rate and that rate is the constant of proportionality.

We have been given an equation y = 10x.

Comparing given equation y = 10x with y = kx (here k is the constsnt of proportionality)

we have k = 10

This means, the constsnt of proportionality is k = 10

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The height of a triangle if its base is 24 cm and its area is 216 cm² is 18 cm.

The area of triangle is calculated using the below mentioned formula -

Area = 1/2 × base × height. We will use the formula of area of triangle to calculate the height of triangle.

Keep the values in formula -

216 × 2 = 24 × height

Firstly multiplying the values given on Left Hand Side of the equation

height × 24 = 432

Shifting 24 to Right Hand Side of the equation

Height = 432/24

Now dividing the values

Height = 18 cm

Thus, the height of the triangle is 18 cm.

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