Domain and range of
[tex]x = {2}^{y} [/tex]
​

The equation that shows a proportional relationship is y = 12x; where the constant of proportionality is 12

An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.

A proportion relationship  is in the form:

y = kx; where x is the constant of proportionality

Let y represent the number of paper towel rolls and x represent the number of cases. Hence:

y = kx

From the table, using the point (1, 12):

12 = k(1)

k = 12

The equation is y = 12x

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A table that represents a linear function include the following: A.

x −4 −2 0 2 4

y   5 1 −3 −7 −11

In Mathematics, a linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.

This ultimately implies that, a linear function has the same (constant) slope and it is typically used for uniquely mapping an input variable to an output variable, which both increases simultaneously.

Next, we would determine the slope by using the points contained in the table as follows;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (1 - 5)/(-2 + 4) = (-3 - 1)/(0 + 2) = (-7 + 3)/(2 - 0)

Slope (m) = -2.

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Answer:

a

Step-by-step explanation:

[tex]\textit{area of a circular ring}\\\\ A=\pi (R^2 - r^2) ~~ \begin{cases} R=\stackrel{outer}{radius}\\ r=\stackrel{inner}{radius}\\[-0.5em] \hrulefill\\ R=4\\ r=2 \end{cases}\implies A=\pi (4^2 - 2^2) \\\\\\ A=12\pi \implies A\approx 37.70~in^2[/tex]

Answer:

12πin² = 37.7in² (3sf)

Step-by-step explanation:

area of whole circle = π(4)² = 16π

area of small circle = π(2)² = 4π

area of shaded = 16π - 4π = 12π

12π = 37.6991... ≈ 37.7in² (3sf)

We can estimate that 84 eighth graders in the school spend 2 hours each night on homework.We can use the proportion of students in the sample who spend 2 hours each night on homework to estimate the number of students in the school who spend the same amount of time on homework.

We are given that a random sample of 50 eighth-grade students was taken, and 15 of them spent 2 hours each night on homework. Therefore, the proportion of students in the sample who spend 2 hours each night on homework is:

15/50 = 0.3

We can use this proportion to estimate the number of eighth graders in the school who spend 2 hours each night on homework. If we assume that the sample is representative of the larger population, we can multiply the proportion by the total number of eighth graders in the school:

0.3 x 280 = 84

Therefore, we can estimate that 84 eighth graders in the school spend 2 hours each night on homework. It's important to note that this is just an estimate and the actual number may differ due to sampling variability.

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Answer:

1. 4, 28, 80

2. P(x)=4x

3. P(9.1)=36.4

The perimeter is 36.4 and the side length is 9.1

Step-by-step explanation:

To find perimeter you multiple a squares side length by 4.

Answer:

look below

13,800

The financial product described is an annuity.

An annuity is a contract offered by insurance companies, where the buyer makes a lump-sum payment or a series of payments in exchange for regular payments made over time, usually until the end of the buyer's life. An annuity can be either fixed or variable, depending on the type of investment chosen by the buyer.

In a fixed annuity, the payments are predetermined and do not change over time, while in a variable annuity, the payments are based on the performance of the underlying investments. An annuity is often used as a retirement income stream.

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Since 4 and 5 have a least common denominator of 20, we can convert both fractions to have a denominator of 20:

-17/4 * 5/5 = -85/20, 32/5 * 4/4 = 128/20, -85/20 - 128/20 = -213/20

A fraction is referred to as the portion of a whole in mathematics. For instance, if a pizza is cut into four equal pieces, each one is represented by a quarter. Fractions make calculations quicker and easier by making it easier to distribute and judge numbers. The depiction of fractions appears easier than when decimal values are used.

A fraction is used to denote a portion or component of a whole. It stands for the proportionate pieces of the whole. The numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.

To simplify:

-4 and 1/4 - 6 and 2/5

For the two mixed integers, we must identify a common denominator. The least frequent multiple of 4 and 5 is 20 since their prime components are 2 and 5. Both mixed numbers can be transformed into improper fractions with a denominator of 20 as follows:

-4 and 1/4 = -17/4

6 and 2/5 = 32/5

Now we can subtract these fractions:

-17/4 - 32/5

We must locate a common denominator in order to subtract fractions. Since 4 and 5 have a least common denominator of 20, we can convert both fractions to have a denominator of 20:

-17/4 * 5/5 = -85/20

32/5 * 4/4 = 128/20

We can now take the two fractions apart:

-85/20 - 128/20 = -213/20

Therefore, -4 and 1/4 - 6 and 2/5 simplify to -213/20.

So, the answer is negative 213 over 20.

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Answer:

240

Step-by-step explanation:

15% of 54=8.1

15% of 240=36

15% of 360=54

15% of 540=81

so the answer is 240

36 is 15 percent of 240.

We have,

To find out what number 36 is 15% of, we can set up the equation:

36 = 0.15x

Here, x represents the unknown number we are trying to find.

To solve for x, we divide both sides of the equation by 0.15:

36 / 0.15 = x

Simplifying the right side gives:

240 = x

Therefore,

36 is 15 percent of 240.

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Answer:

6%

Step-by-step explanation:

0.06 is 6% as a decimal

Answer:3/2

Step-by-step explanation:

[tex]\frac{9}{6} = \frac{\frac{9}{3} }{\frac{6}{3} }=\frac{3}{2}[/tex]

The value of the tip she left is $42.53.

Sales tax is a compulsory amount levied by the government on the sales price of a good or service. Sales price increase the cost of a good or service.

The first step is to determine the total bill after the sales tax has been included.

Total bill after sales tax = (1 + percent sales tax/100) x total bill

(1 + 7/100) x $265

(1 + 0.07) x $265

1.07 x $265

= $283.55

Now, multiply the total bill after sales tax by the percentage value of the tip.

Value of the tip = 15% x $283.55

0.15 x $283.55 = $42.53

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The best applicant to fill the only position available based on the test score is Vincent as he scored highest. The method for determining which applicant performed the best on the aptitude test is to use z-scores, which are measurements of how far from the mean a test score falls in standard deviation units.

Since the test is not on the same scale, it is impossible to compare raw test scores. What are Z-scores?A z-score, also known as a standard score, is a score that indicates the number of standard deviations from the mean a raw score is. In other words, a z-score tells you how far from the mean the score is in terms of standard deviations.

In other words, we can use the following formula to calculate the z-score for each person's test result.$$Z = \frac {x - \mu}{\sigma}$$where x is the test score, μ is the test mean, and σ is the standard deviation.The Z-scores for each of the candidates based on their test results are as follows: Demetria:$$Z = \frac {85.1 - 61.1}{12} = 2.00$$,Vincent:$$Z = \frac {299.2 - 264}{22} = 1.6$$,Tobias:$$Z = \frac {7.26 - 7.1}{0.4} = 0.4$$. From the calculations, Vincent has the highest z-score, indicating that he outperformed the other candidates. The candidate with the highest z-score is the best performer, thus Vincent is the best candidate for the job.

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The calculated equation that represents a line parallel to y = -2x + 4 is (c) -2x - y = 3.

The equation of a line that is parallel to y = -2x + 4 will have the same slope as -2 since parallel lines have the same slope.

Therefore, we need to look for an equation that has a slope of -2.

(a) 1/2x + y = 1 has a slope of -1/2, which is not equal to -2. Thus, it is not parallel to y = -2x + 4.

(b) -2x + y = 8 has a slope of 2, which is not equal to -2. Thus, it is not parallel to y = -2x + 4.

(c) -2x - y = 3 can be rearranged to y = -2x - 3, which has a slope of -2, so it is parallel to y = -2x + 4.

(d) -1/2x + y = 5 has a slope of 1/2, which is not equal to -2. Thus, it is not parallel to y = -2x + 4.

Therefore, the equation that represents a line parallel to y = -2x + 4 is (c) -2x - y = 3.

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Answer:

the vertex of∠5 is point M

Step-by-step explanation:

Answer: M

Step-by-step explanation: M represents the vertex. Think of the vertex almost like the starting point of an angle.

By dividing the diameter by 2, one may get the radius of the cone's base:[tex]r = d/2 = 11.9/2 = 5.95 ft[/tex] The volume of a cone is calculated as follows: V = (1/3)πr^2h Inputting the values provided yields.

[tex]V = (1/3)π(5.95^2)(35) (3.5) V equals 138.2 cubic feet[/tex]. Using tenths of a cubic foot increments, we obtain: V ≈ 138.2 ft^3 Hence, the right circular cone has a volume of around 138.2 cubic feet. some further data on the volume of the cone. The formula: can also be used to express a cone's volume in terms of its height and slant height. V is equal to (1/3)r2h plus (1/3)r2(h2 + r2). where the square root symbol is represented by. Since we already know the height and radius, we can use the Pythagorean theorem to get the slant height.

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Answer:

150 Lanterns

Step-by-step explanation:

Total lanterns : 300

[tex]\frac{2}{6} * 300 = 100[/tex]
[tex]\frac{1}{6} * 300 = 50[/tex]

so He sold 150 lanterns in total , leaving 300-150 = 150 Lanterns left.

The length of side 2 of the given triangle is 16.22.

The Law of Cosines is a mathematical formula that is used to calculate the length of sides and angles in a triangle. It is based on the Pythagorean theorem, which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides

The Law of Cosines helps to solve for the side length in triangles when we are given two sides and the angle between them. In this triangle we are given side 1 (15) and the angle between the two sides (33°). To find side 2, we will use the formula:

c² = a² + b²- 2ab*cosC

Where c is the length of the unknown side, a is the length of the given side, b is the length of the other given side, and C is the angle between the two given sides.

In this case, c is side 2, a is 15, b is unknown, and C is 33°. We will plug in the known values and solve for b:

b² = 15² + c² - 2*15*c*cos(33°)

b² = 225 + c² - 30c*cos(33°)

We can solve this equation for c:

c = (225 + b² - 30b*cos(33°))/2

Now, we can solve for b using the values for c and a given in the problem:

b²= 225 + 27² - 30*27*cos(33°)

b² = 225 + 729 - 690.8

b²= 264.2

b = 16.22

Therefore, the length of side 2 is 16.22.

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Answer:

slope is -2/3, and the y intercept is 1.

Step-by-step explanation:

Using y=Mx+b (slope intercept form), where M=slope, and B = Y intercept , you can find which valurs are which.

Answer:

[tex]x = -2[/tex]

Step-by-step explanation:

[tex] \frac{(x + 8)}{[(x + 3) (x + 4)]} = \frac{3}{(x + 3)}[/tex]

Multiplying both sides by (x + 3) (x + 4), we get:

[tex](x + 8) = 3 (x + 4)[/tex]

Expanding the right-hand side, we get:

[tex]x + 8 = 3x + 12[/tex]

Subtracting x and 8 from both sides, we get:

[tex]2x = -4[/tex]

Dividing both sides by 2, we get:

[tex]x = -2[/tex]

Therefore, the solution to the given equation is x = -2. We can check this solution by substituting x = -2 into the original equation and verifying that both sides are equal.

After deducting a commission of 1.5%, Brian will receive 155.71 pounds in exchange for R2100.

To find out how many pounds Brian will get, we first need to calculate the amount of commission he will pay. The commission is 1.5% of R2100, which is equal to 0.015 x R2100 = R31.50.

The amount of money he will actually receive in pounds is the remaining R2100 minus the commission, which is R2068.50. To convert this to pounds, we multiply by the exchange rate of R1 = 0.075199 pound:

2068.50 x 0.075199 = 155.706675 pounds

Therefore, Brian will get 155.71 pounds for R2100 after paying the agent commission.

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My answer:

There are 4 cards of number eight in a deck of 52 cards, namely: 8 Spades, 8 Diamond, 8 Clubs, and 8 Hearts. So the probable outcomes are 4 and the total cards are 52. So, x 100 = 1/13. So there is a 1/13 chance for getting an eight, i.e, for every 13 cards, one card will be an eight.

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The equation of the given circle is: (x - 5)² + (y+ 1)² = 256

The center-radius form (most formally called the standard form) of a circle is usually expressed as;

(x - h)² + (y - k)² = r²

where (h, k) is the center and r is the radius.

We are given a circle with center T(5,-1) and a radius of 16 units

The equation then becomes:

(x - 5)² + (y - (-1))² = 16²

(x - 5)² + (y+ 1)² = 256

Thus, we can conclude that is the equation of the circle.

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Around 62.47% of the data population is situated between a z-score of -1.5 and 0.5.

Assuming a standard normal distribution, the percentage of the data population that falls between a z-score of -1.5 and 0.5 can be calculated using a standard normal table or a calculator.

Using a standard normal table, we can find the area under the curve between z = -1.5 and z = 0.5.

The area to the left of z = 0.5 is 0.6915, and the area to the left of z = -1.5 is 0.0668. Therefore, the area between z = -1.5 and z = 0.5 is:

0.6915 - 0.0668 = 0.6247

So, approximately 62.47% of the data population falls between a z-score of -1.5 and 0.5.

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Answer:

a. An absolute value inequality that represents the possible actual temperature t is:

|t - 72| < 2

b. To find the range of possible actual temperatures, we can solve the inequality:

|t - 72| < 2

We can split this into two separate inequalities, one for when t is greater than 72 and one for when t is less than 72:

t - 72 < 2 and -(t - 72) < 2

Simplifying these inequalities, we get:

t < 74 and t > 70

Therefore, the range of possible actual temperatures is 70°F < t < 74°F.

Step-by-step explanation:

(a) When [tex]x=-2, 2^x = 2^(-2) = 1/2^2 = 1/4[/tex]. So, the expression 2^x when x=-2 is 1/4.

(b) When [tex]x=3, 2^x = 2^3 = 8[/tex]. So, the expression 2^x when x=3 is 8.

The expression 2^x represents exponential growth, where the base 2 is multiplied by itself x number of times. When x is a negative number, the expression becomes a fraction because we are dividing 1 by the base raised to the absolute value of x. In this case, 2^(-2) is equivalent to 1/2^2, which is equal to 1/4. On the other hand, when x is a positive number, the expression grows exponentially. When x=3, the expression becomes 2^3, which is equal to 2x2x2 = 8.

In summary, the evaluation of 2^x when x is a negative number produces a fraction, whereas when x is a positive number, it produces a positive integer.

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