In an experiment, college students were given either four quarters or a $1 bill and they could either keep the money or
spend it on gum. The results are summarized in the table. Complete parts (a) through (c) below.

The equivalent value to 2.76 is C. two and nineteen twenty-fifths.

An equivalent value is an amount or numerical expression possessing the same value as the other.

Equivalent values are expressed as equations, using the equation symbol (=).

Equations are a class of the properties of mathematical expressions, including numbers and variables.

Two and nineteen twenty-fifths = 2¹⁹/₂₅.

When expressed as a decimal, 2¹⁹/₂₅ = 2.76.

Thus, 2.76%, 27.6%, or twenty-five over nineteen are not equivalent values of 2.76 but 2¹⁹/₂₅.

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Set A ={q, g, c, z, b}

What is a Venn diagram?

What is a roaster form?

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1.4 repeating as a simple fraction is 13/9

Simple fraction is a fraction with whole number as the numerator and denominator. The top term is called numerator and the bottom term is called denominator.

Decimal number is a number that consist of one whole number and a fractional part and those are  separated by a decimal point

The repeating decimal = 1.4444

Consider the value x = 1.4444

Then multiply 10 on both side of the equation

We get

10x = 14.444

Subtract x from the 10x

10x-x = 14.444-1.4444

Subtract the like terms in the equation

9x = 13

Move 9 to the right hand side

x = 13/9

Hence, 1.4 repeating as a simple fraction is 13/9

The complete question is

1.4 repeating as a fraction in simplest form

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Rewrite the limit as

[tex]\displaystyle \lim_{x\to0} \frac{x\cos(5x)}{\sin(5x)} = \lim_{x\to0} \frac{5x}{\sin(5x)} \cdot \lim_{x\to0} \frac{\cos(5x)}5[/tex]

Then using the known limit,

[tex]\displaystyle \lim_{x\to0} \frac{\sin(x)}x = 1 \implies \frac1{\lim\limits_{x\to0}\frac{\sin(x)}x} = \lim_{x\to0}\frac x{\sin(x)}=1[/tex]

it follows that

[tex]\displaystyle \lim_{x\to0} \frac{x\cos(5x)}{\sin(5x)} = 1 \cdot \frac{\cos(0)}5 = \boxed{\frac15}[/tex]

The finishing time would Ms. Lantz need in order to qualify for the Houston Marathon is 50.28 minutes in Rocket Run 5k.

The formula for calculating the z-score is;

z = (x - μ)/σ

x = sample size

μ = mean of the sample

σ = standard deviation of the sample

The given values are-

μ =  57 minutes

σ = 8 minutes

Probability = 20% = 0.20

Find the z-score from the negative z table for 0.20

z score = -0.84

Put the values in z formula and find x.

z = (x - μ)/σ

-0.84 = (x - 57)/8

Simplifying;

x = -6.72 + 57

x = 50.28 minutes

Thus, finishing time would Ms. Lantz need in order to qualify for the Houston Marathon is 50.28 minutes Rocket Run 5k.

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Ek, this is the solution:

Step 1: Let's review the information provided to us to answer the problem correctly.

Sales of the new toy = 2,000 per day

Price of the toy when sales are 2,000 per day = $ 6

Ther

The value of  [tex]f^{-1}(-7)[/tex] is given by -57/8.

Given that:-

f(x) = (x + 1)/(x + 8)

We have to find the value of [tex]f^{-1}(-7)[/tex].

Let f(x) = y

Hence,

[tex]f^{-1}(y) = x[/tex]

Now, we will find the inverse of the given function.

Hence, we can write,

y = (x + 1)/(x + 8)

We can rewrite it as:-

y = (x + 8 - 7)/(x + 8) = (x + 8)/(x + 8) - 7/(x + 8) = 1 - 7/(x + 8).

1 - y = 7/(x + 8)

x + 8 = 7/(1 - y)

x = 7/(1 - y) - 8

x = 7/(1 - y) - 8(1 - y)/(1 - y)

x = (7 - 8(1 - y))/(1 - y)

x = (7 - 8 + 8y)/(1 - y)

[tex]f^{-1}(y) = \frac{(8y - 1)}{( 1 - y)}[/tex]

Replacing y with x in the above equation, we can write,

[tex]f^{-1}(x) = \frac{(8x - 1)}{( 1 - x)}[/tex]

The above equation is the inverse of the function.

Putting x = -7 in the above equation, we get,

[tex]f^{-1}(-7) = \frac{(8(-7) - 1)}{( 1 - (-7))}[/tex]

= (-56 - 1)/ (1 + 7) = - 57/8

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In a case whereby Apollo Spas services 298 hot tubs and each hot tub needs 175 mL of muriatic acid,number of liters of acid that are needed for all of the hot tubs is 52.15 litres.

The unit conversion can be described as the changing of bone unit to another.

We can calculate the number of liters of acid that are needed as (298 * 175)= 52150ml

This can be converted to liter by dividing  52150ml by 1000 which  can be done as (52150ml/1000) = 52.15 litres of acid.

Therefore, the  liters of acid are needed for all of the hot tubs can be expressed as the 52.15 litres

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Using multiplication of matrices, it is found that the values of a and b are given as follows:

To multiply matrices, we multiply the rows of the first matrix by the columns of the second matrix.

Hence, the element of the row 1 and column 1 of the product matrix is given by the multiplication of the row 1 of the first matrix by the column 1 of the second matrix, then:

3(-1) -2(2) + a(3) = 5

-3 - 4 + 3a = 5

3a = 12

a = 4.

The element of the row 2 and column 2 of the product matrix is given by the multiplication of the row 2 of the first matrix by the column 2 of the second matrix, then:

4(3) - 1(b) + 2(-2) = 2

12 - b - 4 = 2

8 - b = 2

b = 8 - 2

b = 6.

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Answer:

A: Reflection over the y-axis

B: Translation 3 right

C: Translation 4 down

D: Reflection over the x-axis

Step-by-step explanation:

A: This is a reflection over the y axis because we can tell it has been flipped to the other side, vertically.

B: Count the spaces between the two 'P's, getting 3 to the right. This is not a reflection because it is facing the same way.

C: Count the spaces between the two 'P's, getting 4 down. Again, this is not a reflection because it is facing the same way.

D. This is a reflection over the x axis because we can tell it has been flipped to the other side, horizontally.

Hope it helps!

The equation of the line that has the given features is y = -1/3x - 4

Linear equations are equations that have constant average rates of change.

Note that the constant average rates of change can also be regarded as the slope or the gradient

From the question, the given parameters are

Slope, m = -2

y-intercept, c = 9

As a general rule:

A linear equation is represented as

y = slope * x + y-intercept

This can be rewritten as

y = mx + c

Next, we substitute the known values in the above equation

So, we have the following equation

y = -2x + 9

The above equation cannot be further simplified

So, we have

y = -2x + 9

However, it can also be expressed as

y = 9 - 2x

Hence. the linear equation is y = -1/3x - 4

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Possible question

What is the equation of a linear equation that has the following features

Y-intercept 9 and slop -2

Using the normal distribution, the upper boundary, in inches, of a symmetric and centered interval of the sample averages with n = 167 that are within 0.92 standard deviation s of the mean is of:

67.21 inches.

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 given as follows:

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

Considering samples of 167, with the mean and standard deviation of the population given in the problem, the parameters are given as follows:

[tex]\mu = 66.9, \sigma = 4.33, n = 167, s = \frac{4.33}{\sqrt{167}} = 0.335[/tex]

The desired height is X when Z = 0.92, because it is 0.92 standard deviations from the mean and we want the upper limit, hence:

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

By the Central Limit Theorem

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

0.92 = (X - 66.9)/0.335

X - 66.9 = 0.92 x 0.335

X = 67.21 inches.

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Answer:

I hope this helps. Four is greater than six times a number t in inequality form is 4 › 6 * t

⇒Plug in places the given values in the expression x-2c and simplify

given that x=3 and c =-3

⇒[tex]=(3)-2(-3)\\=3+6\\=9[/tex]

The expression evaluated at the given variables is equal to 9.

Answer:

The answer to your question is A "In an Old House"  I hope this helps

Sorry if I am wrong

Answer: It would be "In an Old House"

Step-by-step explanation:

The interpretation of the transformation of the given functions are;

f([tex]x + \frac{1}{4}[/tex]) means translated by 1/4 units to the left.

f(x) + 1/4 means that f(x) is translated by 1/4 units upwards

There are different ways of function transformations such as translation, reflection, dilation, compression e.t.c

Now, the function written can be said to translated by 1/4 units to the left . This is because when we translate a function by say "a" units to the left, we are simply going to add a units to the x - variable.

To translate a graph upwards, it simply means we will add the number of units to the function; for example, f (x) + 3 moves the graph of the function f (x) upward by 3 units.

Thus, the given function f(x) + 1/4 means f(x) is translated by 1/4 units upwards

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Answer:

[tex]x = \frac{20}{91}[/tex]

Step-by-step explanation:

Since this is a proportion, first you need to cross multiply.

[tex]\frac{20}{7}[/tex] × [tex]\frac{2}{25}[/tex] = [tex]\frac{40}{175}[/tex]

[tex]\frac{26}{25} x = \frac{40}{175}[/tex]

Now multiply both sides by the reciprocal of 26/25 which is 25/26.

[tex]\frac{25}{26} (\frac{26}{25} )x=\frac{40}{175} (\frac{25}{26} )\\[/tex]

Cancel on the right side, 25 and 175, by 25.  Then cancel 40 and 26 by 2.

[tex]x = \frac{20}{7} (\frac{1}{13} )[/tex]

[tex]x = \frac{20}{91}[/tex]

The value of x is 1 , -5 and y is 3 , -3

A[tex]x^{2}[/tex] + bx + c = 0 is the form of a quadratic equation, which is an expression in second-degree algebra. Square-sounding "quad" is the root of the term "quadratic," which signifies "quadratic." An "equation of degree 2" is another way to describe a quadratic equation. A quadratic equation is utilized in a wide variety of situations. You may be surprised to learn that a quadratic equation accurately predicts a rocket's trajectory after launch. Additionally, a quadratic equation is useful in many fields, including physics, engineering, astronomy, etc.

Given that : the linear-quadratic system of equations is y = [tex]x^{2}[/tex] +5x - 3 and y -x=2 .

y = [tex]x^{2}[/tex] +5x - 3 .....(i)

y = 2+ x.....(ii)

put the value of y in equation i

2 + x = [tex]x^{2}[/tex] +5x - 3

[tex]x^{2}[/tex] +4x - 5 = 0

[tex]x^{2}[/tex] +(5-1)x - 5 = 0

x(x + 5) -1(x + 5) = 0

(x -1)(x + 5)=0

x=1

x=-5

now put value of x in equation ii

y = 2+ x.....(ii)

y = 3 (when x = 1)

y = -3(when x = -5)

The value of x is 1 , -5 and y is 3 , -3

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Answer:

261

Step-by-step explanation:

The measure of the vertically opposite angle ∠A = 136°

From the given question;

∠A and ∠B are vertical angles.

Thus, ∠A = ∠B

The values are given as;

∠A = (2x +26)°

∠B = (3x − 29)°

Equating both;

(2x +26)°  =  (3x − 29)°

Simplyfying;

2x + 26 = 3x − 29

3x - 2x = 26 + 29

x = 55

Put the value of x in ∠A = (2x +26)°

∠A = (2x +26)° = 2x55 +26

∠A = 136°

Thus, the measure of the vertical angle ∠A = 136°.

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The table representing the exact values of y from the function is attached below.

In mathematics, a function from a set X to a set Y assigns each element of X exactly one element of Y. The sets X and Y are referred to as the function's domain and codomain, respectively.

The given function is of the form y = 2x .

Now let us find the respective values of y for the given values of x.

At x = -2

y = 2x = 2 × (-2) = -4

At x = -1

y = 2x = 2 × (-1) = -2

At x = 0

y = 2x = 2 × (0) = 0

At x = 1

y = 2x = 2 × (1) = 2

At x = -2

y = 2x = 2 × (2) = 4

Therefore the table to represent this y-values of the function is [tex]\begin{table}[]\begin{tabular}{lllll} & & & & \\ & & & & \\ & & & & \\ & & & & \end{tabular}\end{table}[/tex][tex]\begin{table}[]\begin{tabular}{ll} & \\ & \\ & \\ & \\ & \end{tabular}\end{table}[/tex]attached below.

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a) quotient = 23 and remainder = 14

b)  quotient = 28 and remainder = 12.

c) quotient = 20 and remainder = 10.

a) Here in the first question we have to divide 405 by 17.

405 is not completely divisible by 17.

So when we divide 405 by 17 we get 23 as quotient and 14 as remainder.

we can cross check this by the formula;

Dividend= Divisor × Quotient + Remainder.

So in here the dividend is 405 and the divisor is 17 which when multiplied by the quotient 23 and added by the remainder that is 14 gives us 405.

Thus quotient = 23 and remainder = 14

b) Here dividend = 656 and divisor = 23

Thus when we divide 656 by 23 we get:

we get quotient as 28 and remainder as 12.

c) Given dividend is 1990 and divisor is 98.

Thus we divide 1990 by 98 we get:

Quotient = 20 and remainder = 10.

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Answer:

If you have earned 20 points, this means you have passed 25 levels.

Step-by-step explanation:

25 =  5 (20/4)

Answer:

Slope-intercept form is given as y = mx + c where m is the slope and c is the y-intercept.

Since slope = 2, equation is y = 2x + c.

Substitute (-1,2) into the equation to find c.

2 = 2(-1) + c

c = 4

Hence, equation is y = 2x + 4

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.

We graph both equations in the same coordinate system in order to visually solve a system of linear equations. The intersection of the two lines is where the system's answer will be found.

Any two ordered pairs can be used to create a solution set on a graph by connecting them with a straight line. Thus, any point along this graphed line would be included in the solution set.

There is only one solution that holds true for both equations if the equations' graphs cross. There are no solutions that hold for both equations if the equations' graphs do not meet (for instance, if they are parallel).

The answer for this graph is -4.

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Answer:

x = 3

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Shop work on the customer's computer for 5.5 hours.

Given,

Charge is flat fee of $ 10.95

and, then $24.50 per hour.

And, to find the number of hours if customer paid $147.90.

Now, According to the question:

Let shop work on computer for x hours .

Then, Amount paid = 10.95 + 24.90x

So, if customer paid $147.90

then, 147.90 = 10.95 + 24.90x

24.90x = 147.90 - 10.95

24.90x = 136.95

x = 136.95/ 24.90

x = 5.5

Hence, Shop work on the customer's computer for 5.5 hours.

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Let the Length of the rectangle be l and the width of the rectangle be w

The width of a rectangular field is 3 meters less than its length, this can be represented as

w = l - 3

Given the perimeter = 58meters

Perimeter of the rectangle = 2(l + w)

58 = 2(l + l-3)

58 = 2(2l - 3)

58 = 4l - 6

58 + 6 = 4l

64 = 4l

4l = 64

l = 64/4

l = 16

w = l - 3

w = 16 - 3

w = 13

Hence, the length of the rectangle is 16 meters while the width is 13 meters.