How are the ordered pairs (,) and (,−) similar, and how are they different? Are the two points related by a reflection over an axis in the coordinate plane? If so, indicate which axis is the line of symmetry between the points. If they are not related by a reflection over an axis in the coordinate plane, explain how you know.

One chocolate chip cookie costs $0.50. This is found by setting up two equations using the given information and solving for the cost of one cookie.

To solve this problem, we can assume that the cost of one jumbo popcorn is P and the cost of one chocolate chip cookie is C. We can then set up two equations based on the given information.

The first equation comes from Julia's purchase, which includes one jumbo popcorn and two chocolate chip cookies. We know the total cost is $5.0, so we can write:

1P + 2C = 5.0

The second equation comes from Marvin's purchase, which includes one jumbo popcorn and four chocolate chip cookies. We know the total cost is $6.0, so we can write:

1P + 4C = 6.0

To solve for the cost of one chocolate chip cookie, we can eliminate P by adding the two equations. This gives us:

2P + 6C = 11.0

Dividing both sides by 2, we get:

P + 3C = 5.5

We can then substitute the value of P in terms of C from either of the two original equations into this equation, and solve for C. In this case, it's easier to use the first equation:

1P + 2C = 5.0

P = 5.0 - 2C

Substituting into the equation we just obtained:

(5.0 - 2C) + 3C

= 5.5

Simplifying and solving for C, we get:

C = 0.5

Therefore, one chocolate chip cookie costs $0.50.

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Part A: The greatest common factor of [tex]10x2 + 25x − 15[/tex]  is 5.

Part B:[tex]10x2 + 25x − 15[/tex] can be factored as [tex]5(2x2 + 5x − 3)[/tex].

Part C: The factoring from Part B is correct, as multiplying the two binomials in the parentheses yields [tex]2x2 + 5x − 3[/tex].

Part A: The greatest common factor of [tex]10x2 + 25x − 15[/tex] is 5. The greatest common factor (GCF) of a set of numbers is the largest number that is a factor of all numbers in the set. To find the GCF, first list all the factors of each number. The common factors among the numbers are the ones that are found in each list of factors. The largest number in the list of common factors is the GCF.

Part B:[tex]10x2 + 25x − 15[/tex] can be factored as [tex]5(2x2 + 5x − 3)[/tex]. To factor this expression, first identify the GCF, which is 5. Then divide the expression by 5 and factor the result. Since the result is a binomial, use the difference of squares formula, (x + a)(x − a). The resulting expression is then[tex]5(2x2 + 5x − 3[/tex]).

Part C: To check the factoring from Part B, multiply the two binomials in the parentheses. The result is [tex]2x2 + 5x − 3[/tex], which is the same as the original expression. To multiply, use the FOIL method. Multiply the First terms [tex](2x2 and 2x2)[/tex], the Outer terms[tex](2x2 and -3)[/tex], the Inner terms (5x and 2x), and the Last terms [tex](5x and -3)[/tex]. The resulting expression is [tex]2x2 + 5x − 3.[/tex]

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The function in Excel that we should use to find a measurement M given a right-tail probability (or area) A is = NORM.INV(1-A, mu, sigma)

In order to find a measurement M given a right-tail probability A in Excel, we can use the NORM.INV function. The NORM.INV function in Excel returns the inverse of the normal cumulative distribution for a given probability.

The formula for NORM.INV function is:

= NORM.INV(1-A, mu, sigma)

where:

A is the right-tail probability (or area)

mu is the mean of the distribution

sigma is the standard deviation

The function returns the measurement M such that the right-tail area from M to infinity under the normal curve is equal to A.

Note - In some versions of Excel, the function may be called NORM.INV.RT instead of NORM.INV.

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In a simple linear regression model we use the normal quantile plot of the residuals to evaluate if it is reasonable to assume the error term come from a normal distribution.

In a simple linear regression model, the normal quantile plot of the residuals is a graphical tool used to assess the normality assumption of the error term (also known as the residual). The error term represents the difference between the actual value of the dependent variable and the predicted value by the model.

Assuming that the error term follows a normal distribution is important for various reasons. Firstly, the normal distribution is a very common assumption in statistics, and many statistical methods rely on it. Secondly, a normal distribution of the error term is essential for making reliable predictions and for computing valid confidence intervals.

The normal quantile plot of the residuals compares the distribution of the residuals against a theoretical normal distribution. The plot consists of a straight line if the residuals are normally distributed. However, if the plot shows deviations from the straight line, it indicates non-normality in the residuals.

If the normality assumption is not satisfied, we need to explore the reasons for the non-normality and consider alternative methods to analyze the data, such as non-parametric methods.

Therefore, the normal quantile plot of residuals is an essential diagnostic tool in simple linear regression, as it allows us to evaluate the assumption of normality and make appropriate adjustments to the model.

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Answer:

27, 36

Explanation:

To find the possible two-digit numbers that meet the criteria, we can use algebra. Let x be the original two-digit number, and let y be the reverse of x. Then, we have:

x - y = 18

We can also write y in terms of x:

y = x % 10 * 10 + x / 10

Substituting the expression for y into the equation x - y = 18, we get:

x - (x % 10 * 10 + x / 10) = 18

Expanding and simplifying the right side of the equation, we get:

9x = 180 + 10

Dividing both sides of the equation by 9, we get:

x = 20

Since x must be a two-digit number, 20 is not a valid solution. However, we can check the two numbers that are close to 20, which are 18 and 21.

For x = 18, we have y = 81, which is a two-digit number, so 18 is a valid solution.

For x = 21, we have y = 12, which is a two-digit number, so 21 is also a valid solution.

Therefore, the possible two-digit numbers that meet the criteria are 27 and 36.

The value of correlation cofficient between the number of people who complete successfully complete each jump, y and height of jump, x is equals to the - 0.091.

We have a table which consists height ( in feet ), x and completions, y present above figure. We have to calculate the correlation coefficient for variables x and y. Correlation coefficients are used to measure how strong the relationship is between two variables. The commonly used cofficient in linear regression is Pearson's correlation (also called Pearson's R) coefficient . Formulas return a value between -1 and 1, where,

Formula used to determine the cofficient is r = (n∑ xy - (∑x)(∑y))/√[ n∑x² - (∑x)²][n∑y² - (∑y)²]

Here, n = 6, ∑xy = 375.8 , ∑ x =22.4, ∑y

= 102, ∑ x² = 96.5, ∑y² = 1978

so, r = 6×(375.8) - 102(22.4))/√[(6×96 - (22.4)²)(6×1978 - 102²)]

= -30/329.68

= - 0.091

Hence, required value of r is - 0.091.

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Complete question:

The above table shows the heights (in feet) of a high jump bar and the number of people who successfully complete each jump. Identify the correlation of coefficient. Round your answer to three decimal places.

Answer:

C.

Step-by-step explanation:

area = length × width

5/8 = 1/6 × w

w = (5/8) / (1/6)

Answer: C.

Answer: 47.20cm

Step-by-step explanation:

She paid $0.1282051282 per yard - $0.13 ( rounded ).

Answer:

[tex]10x^2+28x+15[/tex]

Step-by-step explanation:

[tex](2x^2+3)(4x+5)-8x(x^2-2)\\\\=(2x^2)(4x)+(2x^2)(5)+(3)(4x)+(3)(5)-8x^3+16x\\\\=8x^3+10x^2+12x+15-8x^3+16x\\\\=10x^2+28x+15[/tex]

A. The functions are not inverse of each other.

B.  The domain of the composition using interval notation is (-∞, ∞)

Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).

A. To show that two functions are inverses of each other, we need to show that their compositions are equal to the identity function, which is denoted as f(x) = x.

That is, we need to show that:

(f ∘ g)(x) = x

(g ∘ f)(x) = x

where ∘ denotes function composition.

First, we'll find the composition (f ∘ g)(x):

(f ∘ g)(x) = f(g(x))

             = f(9x+1)

             = (9x+1) - 3

             = 9x - 2

Next, we'll find the composition (g ∘ f)(x):

(g ∘ f)(x) = g(f(x))

             = g(x-3)

             = 9(x-3) + 1

             = 9x - 26

Since (f ∘ g)(x) ≠ x and (g ∘ f)(x) ≠ x, the functions f(x) and g(x) are not inverses of each other.

B. To find the domain of (f ∘ g)(x), we need to ensure that the input to g(x) is within its domain, which it is for all real numbers. To find the domain of (g ∘ f)(x), we need to ensure that the input to f(x) is within its domain, which it is for all real numbers.

Therefore, the domains of (f ∘ g)(x) and (g ∘ f)(x) are both all real numbers, and we can express this using interval notation as:

Domain of (f ∘ g)(x) and (g ∘ f)(x):

(-∞, ∞)

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Answer:

Solution to system of inequalities is y≥ 3x-2

Graph attached

Step-by-step explanation:

We have the following two inequalities:
y>-3x-5

y≥ 3x-2

To get the solution and graph

1. Graph each inequality separately

2. Choose a test point to determine which side of the line needs to be shaded

3. The solution will be the area where the shadings from each inequality overlap one another

The graph is attached. The heavily shaded region is the set of all points which satisfy all inequalities

We see that any point that satisfies y≥ 3x-2  also satisfies y>-3x-5

In other words, the solution set for y≥ 3x-2 is a subset of the solution set for   y>-3x-5

For the equation 3 = (g/-4) - 5, the value of g is g = -32.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The given equation is -

3 = (g/-4) - 5

The equation contains a fractional component.

Simplify the equation to get the value of g.

First collect all the like terms -

g/-4 = 3 + 5

Then use arithmetic operation of addition -

g/-4 = 8

Then move the denominator of the fraction to right hand side of the equation -

g = 8 × -4

Then use arithmetic operation of multiplication -

g = -32

Therefore, the value of g is -32.

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The surface area of the sphere is 113.2 ft².

The area that a sphere's outer surface covers in three dimensions is known as the surface area of the Sphere. A sphere is a three-dimensional solid that resembles a circle in shape and is round.

The formula for a sphere's total surface area is given by

Here we have

The formula for the radius of a sphere r = 1/2 [√S/π]    

Diameter of the Moeraki boulder radius = 3 feet

=> 3 feet =  1/2 [√S/π]    

=> 6 = [√S/π]

Squaring on both sides

=> 36 = [√S/π]²  

=> S/π = 36

=> S = 36π  

=> S = 113.2  

Therefore,

The surface area of the sphere is 113.2 ft².

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Answer:

C. Addition Property of Equality

Step-by-step explanation:

From step 4 to step 5, 20 is added to both sides.

Answer: Addition Property of Equality

Answer:

slope = 1

Step-by-step explanation:

[tex]m=\frac{0-3}{7-10} =\frac{-3}{-3} =1[/tex]

Hope this helps.

Answer:

{y l y > 9}

Step-by-step explanation:

Given function:

[tex]f(x)=3^x+9[/tex]

The given function is an exponential function.

The parent function is the basic equation before the function has undergone any transformation(s).  Therefore, the parent function of the given function is:

The range of the parent function is restricted to positive real numbers as it never takes a negative value.  Furthermore, it never reaches zero (although it approaches y = 0 as x → -∞).  Therefore, the range of the parent function is {y | y > 0}.

As the given function has been translated up 9 units (by the addition of "+ 9"), the range of the given function is translated 9 units up.  So as x approaches negative infinity, y approaches (but never reaches) 9. Therefore, the range of the given function is:

Using an equation, the bride-to-be and her maid of honor will each have made 25 favors in 5 minutes.

An equation is a mathematical statement showing that two or more mathematical expressions are equal or equivalent.

Equations are depicted using the equal symbol (=), while mathematical expressions, which combine variables, constants, and values only use mathematical operands.

The total number of wedding favors assembled by the bride-to-be = 15

The bride's assembling rate per minute = 2 favors

The maid of honor's assembling rate per minute = 5 favors

Let x = the number of minutes used

Let the number of favors assembled by the bride = 15 + 2x

Let the total number of favors assembled by the maid of honor = 5x

For the two to assemble the same number of favors, 15 + 2x = 5x

15 = 3x

5 = x

Thus, in 5 minutes the bride-to-be and her maid of honor will have assembled 25 favors each.

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The two lines have the same slope and different y-intercepts, thus, the lines are parallel.

Here we want to find the relation between the two lines:

8x = 3y + 3

-24x + 9y = 3

First, we need to write these two as lines in the slope-intercept form. We will get:

3y = 8x - 3

y = (8/3)*x - 3/3

y = (8/3)*x - 1

And the other one:

9y = 3 + 24x

y = (3/9) + (24/9)*x

y = (1/3) + (8/3)*x

So, we can see that both lines have the same slope (and different y-intercept), thus, the lines are parallel lines.

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Answer: To find the total change in pounds of fruit in the basket, we need to subtract the amount taken out from the amount added.

First, let's convert all the fractions to decimals:

1 1/4 = 1.25

2 3/8 = 2.375

Now, we can subtract:

1.25 - 2.375 = -1.125

So, the total change in the fruit basket was -1.125 pounds, meaning the basket had 1.125 pounds less fruit after the removal.

Step-by-step explanation:

The prediction about what might happen if you have ten birds will be 5. You'll have either seven or eight angry neighbors

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

In this case, it should be noted that as the number of birds increase, the number of angry neighbor increased too. Therefore, the prediction about what might happen if you have ten birds will be that you'll have either seven or eight angry neighbors.

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The vertex form of the function is  [tex]y = (x+4)^{2} - 19[/tex]

Vertex form of function:

The vertex of the function is located at (h,k) of its vertex form, and will be located at the peak or trough of the parabola on a graph. This is the highest or lowest point of the function, depending on its direction.

The vertex form of the equation is written as,

[tex]y = (x+h)^{2} + k[/tex]

Given function is,

y = x² + 8x + 16 - 3 -16

It is observed that,  

x² +8x + 16 = (x+4)²

So that, we can write as above function,

y = x² + 8x + 16 - 3 -16 = (x+4)² - 3 -16

or

y =  (x+4)² - 19

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Step-by-step explanation:

suppose you brought 45 shares of telecommunications company 4 years ago at a price of $63.00 per share. you just sold it for $71.50 per share. how much did you make

(a) The percentage of people that left the event in the afternoon is 8%

(b) The total number of people that were there at the start of the fund-raising event were 68.

Let x be the number of people at the start of the event. Then, 0.6x were males and 0.4x were females.

In the afternoon, 0.2 * 0.4x = 0.08x females left the event.

So, there were 0.4x - 0.08x = 0.32x females left at the event.

In the evening, 33 + 35 = 68 people left the event, and x - 68 people were left.

Out of the x - 68 people, 0.6(x - 68) were males.

So, we have 0.75 * (x - 68) = 0.6 * (x - 68).

We can now solve for x:

0.75 * (x - 68) = 0.6 * (x - 68)

0.15 * (x - 68) = 0

x - 68 = 0

x = 68

Thus, there were 68 people at the start of the fund-raising event.

(a) The percentage of people who left the event in the afternoon was 0.08x / x * 100% = 0.08 * 100% = 8%.

(b) There were 68 people at the start of the fund-raising event.

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3. The amount that should be returned to Meenaski for buying 12 books worth R250.75 each and giving the shopkeeper R4,000, using mathematical operations, is R991.

4. The number of crayon sets that can be bought for R2,750 if one set costs R25, using division operation, is 110.

5. Manu will pay R1,700, exchanging his old bike for a new bike.

The four basic mathematical operations include addition, subtraction, division, and multiplication.

These mathematical operations are performed to solve algebraic problems using the relevant mathematical operands and rules.

The number of books bought = 12

The unit cost of each book = R250.75

The total cost of the 12 books = R3,009 (R250.75 x 12)

The amount advanced to the cashier = R4,000

The balance to be returned = R991 (R4,000 - R3,009)

The cost of a set of crayon = R25

The amount of money for the purchase = R2,750

The number of crayon sets that can be bought with R2,750 = 110 (R2,750/R25).

The price of the new bicycle = R2,500

The value of the old bike for exchange = R800

The amount to be paid = R1,700 (R2,500 - R800)

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The price of the new bicycle is R2,500. The bike on exchange is worth R800.  How much does he pay for his new bike?

The total cost of the cement rings for the water well is RS. 70,000. This cost is only for the cement rings and does not include the cost of labour for digging the well.

The cost of each cement ring is given as RS. 2500. Since there are 28 cement rings used in the water well, the total cost of the cement rings can be calculated as follows:

Total cost of cement rings = Cost of each cement ring x Number of cement rings used

Total cost of cement rings = 28 x 2500 = RS. 70,000

Volume of the well = [tex]\mathrm{ \pi r^2h = \pi (0.7)^2(5.6) = 9.768m^3 }[/tex]

Cost of digging out the well = 500 x 9.798 = RS. 4,899

Total cost of the well = RS. 74,899

Total cost of cement rings = 2500 x 28 = RS. 70,000

Therefore, the total cost of the cement rings for the water well is RS. 70,000. This cost is only for the cement rings and does not include the cost of labour for digging the well.

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