[tex]3(x+2)^2-6=21[/tex]

The required table represents a two-column table for the given data is,
 x        y

30      45
45     67.5
50      75

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
Tamara read 30 pages in 45 minutes.

Tamara read 45 pages in 67.5 minutes.

Tamara read 50 pages in 75 minutes.

The table form of the above data is given as
let x be the time. y be the number of pages

Table,
 x        y

30      45
45     67.5
50      75

Thus,  the required table is shown above.

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Answer:

a)  D [y = 6x + 7]

Step-by-step explanation:

First, subtract 6x from both sides to isolate the -y by itself.

6x - y = -7 becomes

-y = -6x -7

Next, to get it into slope-intercept form, we must make the y positive.

To do this, we must multiply both sides of the equation by -1

The equation now becomes:

y = 6x + 7 [Giving us our final answer in y=mx+b form]
-------------------------------------------------------------------------------------------------------------

b) A [6]

The reason the slope is 6 is because in slope-intercept form, the coefficient in front of the x is the slope. That number is 6, as seen above, meaning that the slope is 6.

Hope this helped!

Answer:

y = -2/3x - 6

Slope is a measure of steepness of a line. In Algebra 1, It is how much the y-value changes when the x-value increases by 1.

Slope Formula:

Take any 2 points on the line and plug in:

[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

y-intercept is the y-value of the line when it intersects with the y-axis, or the y-value of the line when the x-value of the line is 0.

y = mx + b

y and x stay as variables when graphing the equation and are only substituted when solving for values such as the x-intercept.

m is the slope and b is the y-intercept.

First, examine the graph. When does the graph have an x-value of 0 and intersects the y-axis, what is the y-value of the line?

-6

y = mx - 6

Then, lets get 2 points from the graph. You can use any 2 points.

(-6,-2)

(0,-6)

Plug into the formula.

[tex]\frac{-6-(-2)}{0-(-6)}[/tex]

[tex]\frac{-4}{6}[/tex]

[tex]-\frac{2}{3}[/tex]

y = -2/3x - 6

The linear equation best estimate of the difference between the number of yellow and blue paper clips is option(b).

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables.

Number of yellow paper clips found in one box = 27955

Number of blue paper clips found in another box = 9427

We are asked to find the best estimate of the difference in the number of yellow and blue paper clips that Kimberly found.

The actual difference between the number of yellow and blue paper clips = 27955 - 9427 = 18528

An estimate of a number means the closest number that the actual number can be rounded off for simplifying calculations or understanding.

In this case, from the given options the closest number of 18528 is 19000.

Therefore option(b) is the best estimate of the difference between yellow and blue paper clips.

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Answer:

4

Step-by-step explanation:

the difference between 76 and 52 is 24

and the difference between 52 and 28 is 24

the difference between 28 and 24 is 4

Answer: 10 in just squash, 7 in just onions, Intersection is 4, Union is 21

Step-by-step explanation: 10 are by themselves in the squash circle. 7 are alone in onion circle. Intersection is where the circles cross and Union is all of them.

Step-by-step explanation:

this is a college level question ? elementary school students must be able to solve this.

the perimeter of a rectangle is

2×length + 2×width

as when you walk around a rectangle one full time, you have to walk the long side twice and the short side twice - it has 4 sides, you know.

other words for length : base, ...

other words for width : height, breadth, ...

so, we know

56 = 2×12 + 2×base = 24 + 2×base

now we can make it totally simple right away and divide everything by 2

28 = 12 + base

16 = base

the base (or length) is 16 cm.

The new coordinates of the triangle after the dilation by a factor of 2 would be (4,-6), (4, -12), (8,-6)

What is Dilation?

Dilation is a process for creating similar figures by changing the size.

A dilation by a factor of 2 means that each coordinate value will be multiplied by 2.

So the new coordinates of the point (2, -3) would be (2 x 2, -3 x 2) = (4, -6)

The new coordinates of the point (2, -6) would be (2 x 2, -6 x 2) = (4, -12)

The new coordinates of the point (4, -3) would be (4 x 2, -3 x 2) = (8, -6)

Thus, the new coordinates of the triangle would be (4,-6), (4, -12), (8,-6).

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The first sample's index and K (interval) value, which are both equal to 7 - 2 = 5, the 10th sample's index is 25 because 33 - 8 .

Probability theory, a subfield of mathematics, gauges the likelihood of an event or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a comprehensive set of equally likely outcomes that result in a certain occurrence compared to the total number of outcomes.

given

Decide on your sample size and multiply your population by your chosen sample size to find your interval, k.

the first sample's index and K (interval) value, which are both equal to 7 - 2 = 5, the 10th sample's index is 25 because 33 - 8

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On solving the provided question, we can say that coordinates are (-2,2) and (0,-2), inequality equation will be => y[tex]\leq[/tex] -2x + 2

An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal sign (). Different inequalities are used to contrast values, no matter how little or large. Many simple inequalities may be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.

as here,

coordinates are (-2,2) and (0,-2)

inequality equation will be

y[tex]\leq[/tex] -2x + 2

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On the map distance between two cities is 19.2 inches.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

The basic formula to find the scale factor of a figure is expressed as,

Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.

The actual distance between Danton and Crowley is 672 miles.

Here, the scale factor is 1 inch =35 miles

So, on map distance = 672/35

= 19.2 inches

Therefore, on the map distance between two cities is 19.2 inches.

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Following answers for transformation of f(x) to g(x) are:-

A. First transformation addition of value k in f(x)

    Second transformation subtraction of value k in g(x)

B.  Values of k in each transformation are respectively +18 & -18

C.  An equation for each type of transformation are respectively, f(x) = 3x-1 &  g(x) = 3x+17

The equation of a straight line is a relationship between x and y coordinates, The general equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept.

m = change in y coordinate/change in x coordinate = Δy/Δx

Given points,    

f(x) passes through, (0, -5) & (5, 14)

g(x) passes through, (-6, -1) & (-1, 14)

A.  By slope formula, we can calculate slope of both the lines

m₁ = 3

m₂ = 3

Slopes are equal, So changing intercepts we can transform f(x) into g(x)

we can do it by two ways,

First transformation addition of value k in f(x)

Second transformation subtraction of value k in g(x)

B. We can see in graph difference between intercepts is 18,

So in, First transformation addition of value +18 in f(x)

Second transformation subtraction of value -18 in g(x)

C.  we have given two points for each linear function, So by using two points form of straight line, we can write following equations

1.  f(x) = 3x-1

2. g(x) = 3x+17

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Answer:

49/300 or 0.163 recurring

Step-by-step explanation:

7x21=147

147/900=49/300=0.1633333

48 and 24 are the numbers that the ratio equivalent to 16:8. Its simplified form would 2:1 or simply 2.

By dividing two quantities of the same type, we can compare them. This process is known as a ratio. How many times one quantity is equal to the other is revealed by this relationship. The ratio is the number that can be used to represent one quantity as a percentage of another, to put it simply.

A ratio's two numbers can only be compared if they share the same unit. To compare two things, we use ratios. The ratio sign is represented by the letter ":".

To Find the number that makes the ratio equivalent to 16:8

Simply multiply any number with both 16 and 8 i.e.

16 × 3 = 48

8 × 3 = 24

When you simplify them you get 16:8,

Thus, 48 and 24 are the numbers that the ratio equivalent to 16:8.

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Graph B is a function because each value of x corresponds to exactly one y-value.

What is the graph of a function?

The graph of a function f is the set of all points in the plane of the form (x, f(x)). We could also define the graph of f to be the graph of the equation y = f(x). So, the graph of a function is a special case of the graph of an equation.

Using the function concept, it is found that:

Graph B is a function because each value of x corresponds to exactly one y-value.

In a function, one value of the input can be related to only one value of the output.

In a graph, it means that for each value of x(horizontal axis), there can be only one respective value of y(vertical axis).

In this problem, at Graph A, when x = 5, for example, a vertical line crosses the function 3 times, hence there are 3 respective values of y for x = 5, and the same is valid for other values of x, hence it is not a function.

In Graph B, for each value of x, there is only one value of y, hence it is a function.

Hence, Graph B is a function because each value of x corresponds to exactly one y-value.

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Note: The complete question is in the attached image.

Answer:

b

Step-by-step explanation:

Answer:b

Step-by-step explanation:

if a was a yellow banana and b a green one, and there was only one banana, (yellow). The green ones gone so its -b

The percentage under the density curve where x is more than 3 is given as follows:

100%.

A percentage under the density curve is obtained by the area under the density curve that respects the given features.

The area for which x is more than 3 is composed by all the area of the density curve that is to the right of 3.

The area to the right of 3 is composed as follows:

The area of a right triangle is given by half the multiplication of the sides, hence:

At = 0.5 x 1 x 0.4 = 0.2 units squared.

The area of a rectangle is given by the multiplication of dimensions, hence:

Ar = 2 x 0.8 = 0.8 units squared.

Meaning that the total area is given as follows:

A = At + Ar

A = 0.2 + 0.8

A = 1 unit squared.

Meaning that the percentage is of 1 x 100% = 100%.

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Answer:

-3y(5y^3 - 4y + 3)

Step-by-step explanation:

-15, 12, -9 have a common factor of -3.

y^4, y^2, y have a common factor of y.

Factor out -3y.

-3y(5y^3 - 4y + 3)

Answer: Divide the integer by 9 to equal 3/4

Step-by-step explanation:

Answer:

Step-by-step explanation:

The flat cost of Jim's Auto Shop is $15 dollars.

The flat cost of Danny's Wrecker Services is $10.

The per-mile cost for Jim's Auto Shop is .50

The per-mile cost for Danny's Wrecker Services is .75

Let's say that your vehicle needs to be towed for x number of miles.

15

The equation for the total cost would be:

flat cost x (per-mile cost × number of miles)

_____________________________________________________

Just use the above equation and substitute it with the information given to you in your question. Hopefully, this helps. If you need further help, please elaborate on your question and comment.

The total cost would be equal to ;75 dolar.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

Given that the flat cost of Jim's Auto Shop is $15 dollars.

The flat cost of Danny's Wrecker Services = $10.

The per-mile cost for Jim's Auto Shop = 0.50

The per-mile cost for Danny's Wrecker Services = 0.75

Let's say that vehicle needs to be towed for x number of miles.

15

The equation for the total cost would be as;

flat cost x (per-mile cost × number of miles)

10 x 0.50 x 15

= 75

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1. Proportional to Mikel's tip.

2. Not proportional to Mikel's tip.

3. Proportional to Mikel's tip.

What is a proportion?

A proportion is an equation that states that two ratios are equal. In other words, it is a statement that says two fractions are equivalent. The most common way to write a proportion is in the form of "a/b = c/d".

We are told that Mikel gave a $1.32 tip for an order that cost $8.80. We are asked to determine whether or not each given tip is proportional to Mikel's tip.  

Let us compare our given tip and order cost proportions with Mikel given tip and order cost proportion.

1) 1.32/8.80 = 2.22/14.80

   0.15 = 0.15

We can see that our given proportion is equal to Mikel's proportion, therefore, the tip given in the first option is proportional to Mikel's tip.

2) 1.32/8.80 = 1.86/10.50

   0.15 ≠0.177

We can see that tip given in the second option is greater than Mikel's tip, therefore, it is not proportional to Mikel's tip.

3) 1.32/8.80 = 0.78/5.20

   0.15 = 0.15

We can see that our both proportions are equal, therefore, a tip given in the third option is proportional to Mikel's tip.

Hence,

1. Proportional to Mikel's tip.

2. Not proportional to Mikel's tip.

3. Proportional to Mikel's tip.

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Answer:hi the question isnt rlly that clear i could give u an answer if u explain a bit thx !

Step-by-step explanation:

The first responder is exactly correct in order to find the answer you must divide the gas cost by the amount of gallons (which in this case is 5 gallons.

$17.50 / 5 = $3.50 per gallon.

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A. The confidence interval estimate of the expected value of y will be wider than the prediction interval is correct.

A confidence interval gives an estimated range of a population parameter based on a sample. It is calculated by taking a sample of the population and using statistical methods to estimate the range in which the true population parameter would fall, with a certain level of confidence.

On the other hand, a prediction interval gives an estimated range of a future observation based on a sample. It is calculated by taking a sample of the population and using statistical methods to estimate the range in which a future observation would fall, with a certain level of confidence.

Since a prediction interval includes the uncertainty of an unobserved future value, it will typically be wider than the confidence interval estimate of the expected value of y which is based on the sample and the estimation of the population parameter.

Therefore Option A is the correct answer.

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As Theresa write a 3,000-word article in 2 hours, her rate of payment dollars per hour is $45 per hour. The Option C is correct.

The payment rate relates to the amount of money paid to someone or the act of paying this money. The rate of pay of an employee is the amount of money they are paid over a period of time. Some employees who work more than 40 hours per week may be eligible for $30per hour.

Data

She is paid 3 cents per word

For 3,000-word article, she will be paid:

= 3,000 * 3

= 9,000 cent or $90.

Because it will take her 2 hours to write 3,000-word article, then, her her rate of payment dollars per hour equals to $45 ($90 / 2 hours).

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The best deal that Holly can choose, would be Store A.

The best deal that Holly can get from the various stores would be the deals that leads to a lower price per yard.

The store with the best deal would therefore be:

Store A :

= Cost of yards / Number of yards

= 16. 52 / 6

= $ 2.75 per yard

Store B :

= 13. 85 / 5

= $ 2.77

The cheaper store is therefore Store A.

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The deals are:

$16.52 per 6 yd

$13.85 per 5 yd

Answer:

No -- histograms are generally divided into range groups, as seen in this graph, and we therefore cannot separate the cars who got 20 mpg relative to cars who got, for example, 21 mpg

Answer: 70 cars.

Step-by-step explanation: At 0 - 5 miles per gallon there are 0 cars. At 5 - 10 miles per gallon there are 15 cars. At 10 - 15 miles per gallon there are 20 cars. At 15 - 20 miles per gallon there are 35 cars. So the total cars at 0 - 20 miles per gallon = 0 + 15 + 20 + 35 70 cars.