Solve: StartFraction 20 Over x EndFraction = 2 a. x = 40 c. x = 20 b. x = 10 d. x = 15

The points that have a distance of 6 units between them are A(-12, 2) and B(-6, 2); B(-6, 2) and C(-6, -4).

The distance between two points P(x₁, y₁) and Q(x₂, y₂) is given by  

Here we have

A (-12, 2) and B(-6, 2)

B (-6, 2) and C(-6, -4)

C (-6, -4) and D(6, 2)

D (6, 2) and E(6, 4)

E (6, 4) and F(-12, 4)  

Here we will find the distance between given points to find the point which has 6 units between them.

As we know Distance = [tex]\sqrt{(x_{2} -x_{1})^{2} +(y_{2} - y_{1})^{2} }[/tex]

For Option A

A (-12, 2) and B(-6, 2)

Distance = √(-6 + 12)² + (2 - 2)²

= √[(6)² + (0)²] = √36 = 6

For Option B

For  B (-6, 2) and C(-6, -4)

Distance = √(-6 - (-6))² + ( - 4 - 2)²

= √[(0)² + (-6)²] = √36 = 6  

For Option C

For C (-6, -4) and D(6, 2)

Distance =√(6 - (-6))² + (2 - (-4))²

= √(12)² + (6)² = √180 = 6√5

For Option D

For D (6, 2) and E(6, 4)

Distance = √(4 - 2)² + ( 6 - 6)²

= √[(2)² + (0)²] = √4 = 2      

For Option E

For E (6, 4) and F(-12, 4)  

Distance = √(-12 - 6)² + (4 - 4)²

= √[(18)² + (0)²] = √18² = 18

Therefore,

The points that have a distance of 6 units between them are A(-12, 2) and B(-6, 2); B(-6, 2) and C(-6, -4).

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Answer: 15 / 18

Step-by-step explanation:

9 / 18 + 1/3

1/3 = 6 / 18

9 / 18 + 6/ 18

15 / 18

Answer:

5/6.

Step-by-step explanation:

Step 1: Rewrite 9/18

9/18 = 1/2

Step 2: Rewrite problem

1/2 + 1/3

Step 3: Find (Greatest common denominator)

6

Step 4: Rewrite fractions

3/6 + 2/6

Step 5: Add

5/6

1. This is not wrong at all, but there is a problem. In this case, the target parameter is not mentioned. Average in this case is not the most valid conclusion.

2. Not FALSE as in option #1, but the same problem occurs if the statement does not express a conclusion about the parameter of interest (mean) in this case.

3. This is not the case at all, as the statement refers to possible samples and not confidence levels or parameters of interest. So it's not the best option in this case.

4. true average number of chocolate chips per cookie.

This is the best interpretation, because confidence levels are used to construct the intervals. The most complete answer in this case, as the result is related to the parameter of interest.

Confidence Interval:

A confidence interval is "a range of values ​​that is likely to encompass the values ​​of a population with some degree of confidence. Often expressed as a percentage. The error bar is the range of values ​​above and below the sample statistic in the confidence interval

Normal Distribution:

"A probability distribution that is symmetric about the mean and indicates that data close to the mean are more common than data far from the mean."

X : represents sample mean

μ: population mean (variable of interest)

s : represents sample standard deviation

n : represents sample size

2) The mean confidence interval is given by the formula:

X ± [tex]t_{\alpha /2} \frac{s}{\sqrt{n} }[/tex]                    --------------------------- (1)

The 95% confidence interval obtained in this case is (18.6; 21.3)

Based on this, the statements can be analyzed individually as :

1: We are 95 years old We believe that each cookie from this brand contains approximately 18.6 to 21.3 chocolate chips.

This is not wrong at all, but there is a problem. In this case, the target parameter is not mentioned. Average in this case is not the most valid conclusion.

2: His 95% of cookies are expected to contain 18.6 to 21.3 chocolate his chips.

Not FALSE as in option #1, but the same problem occurs if the statement does not express a conclusion about the parameters of interest in this case.

3: About 95% of all possible sample means from this population are expected to be between 18.6 and 21.3 chocolate chips. This is not the case at all, as you are not referring to some parameter. So it's not the best option in this case.

4: 95% confident that the confidence interval of 18.6 to 21.3 contains the true average number of chocolate chips per cookie.

This is the best interpretation because of the confidence level used to construct the interval. The most complete answer in this case, as the result is related to the parameter of interest.

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The independent variable in the following hypothesis: interstate migration in the united states lowers state poverty levels is IV (  Interstate migration ) and DV ( State poverty level ) .

Given :

identify the independent variable in the following hypothesis: interstate migration in the united states lowers state poverty levels.

Independent variable :

An independent variable is exactly what it sounds like. It is a variable that stands alone and isn't changed by the other variables you are trying to measure.

Here in the given statement the independent variable is :

IV = Interstate migration

DV = State poverty level

Unit of Analysis = U.S. states

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The height of the pile increasing when the pile is 16 feet high is 5/32 ft/min.

We are given dV/dt=10 cubic ft/min and we want to find dh/dt. Therefore, first we need to write a formula relating v and h.

V=pi*r^2*h/3  since d=h at any moment, we know that r=h/2 at any moment and if we substitute h/2 for r, we get

V=pi(h/2)^2*h/3 and if we simplify this,  we get

V=pi*(h^3)/12

Now we need to take the derivative of both sides with respect to t

dV/dt = pi * ( 3 * h^2 ) */12 * dh/dt

= pi * h^2 / 4 * dh/dt, substitute 40 for dV/dt and 16 for h and solve for dh/dt and we get

40 = pi * 16^2/4*dh/dt

dh/dt = 40 * 4 / ( 256 * pi )

= 40/(256*pi) ft/min,

= 10/64

= 5/32 ft/min

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Answer: 36.4

Step-by-step explanation:

Just convert the percentage to decimal and multiply.

70 x 0.52 = 36.4

The following conditions must be met in order to test hypotheses using proportions: np ≥ 5 and nq ≥ 5

To test hypotheses using proportions, the following requirements are necessary:

np ≥ 5 and nq ≥ 5: It is necessary to have a sufficient number of samples in each group being compared.

The rule of thumb is to have at least 5 observations in each group, where n is the sample size and p is the proportion in that group.

This ensures that the sampling distribution of the proportion is approximately normal, which is necessary for hypothesis testing.

Hence, the correct answer would be an option (A).

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Answer: Religion reinforces and promotes social inequality and social conflict. It helps convince the poor to accept their lot in life, and it leads to hostility and violence motivated by religious differences. This perspective focuses on the ways in which individuals interpret their religious experiences.

Step-by-step explanation:

[tex]a_n = 11n + 91[/tex] is the nth term arithmetic progression for the following term.

The difference between any two successive integers in an arithmetic progression (AP) sequence of numbers is always the same amount. It also goes by the name Arithmetic Sequence.

For instance, the sequence 1, 2, 3, 4, 5, 6,... The standard progression in mathematics is a, (a + d), (a + 2d), and (a + 3d).

Given that,

the first five terms given in the table with position.

Denoted as: a₁ = 102, a₂ = 113, a₃ = 124, a₄ = 135, and a₅ = 146

Thus, the nth term for the arithmetic sequence is given as:

[tex]a_n = a_1 + (n-1)d[/tex]

here, d = (113-102) = 11

[tex]a_1 = 102[/tex]

d is the common difference

So, [tex]a_n = 102 + (n-1)11[/tex]

or, [tex]a_n = 102 +11n-11[/tex]

or, [tex]a_n = 11n + 91[/tex]

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A savings account with just an APR of 5.2% compounded quarterly on a balance of $2,000 will yield $16.61 more interest than a similar account with just an APR of 4.8% compounded monthly on the same balance.

Assume we had two different sorts of savings accounts, each with a deposit of $2,000 in it.

We must now determine the earnings for both accounts.

The following formula will be used to determine the earning:

Here,

Put the values for Account A now.

5.2 % in decimal form = 5.2/100= 0.052

v = 2000 x ( 1 + (0.052/4) )^(4*2)

v = 2217.71

Total earning for account A =  $ 2217.71.

For Account B:

4.8 % in decimal form = 4.8/100= 0.048

v = 2000*( 1 + (0.048/12) )^(12*2)

v = 2201.10

Total earning for account A = $ 2201.10

We will now deduct B's earnings from A's earnings to see how much more A earned than B.

2217.71 - 2201.10 = $16.61

Consequently, account A made $16.61 more so than account B.

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Option a) 90% confidence interval for the population proportion of successes = 0.402

Option b) 90% confidence interval for the population proportion of failures = 0.598

According to the question given,

Critical values of Standard deviations are to be used to construct the proportions for the confidence interval.

The formula of a confidence interval that we will be using for the solution will be,

p = [tex]z_{a} * \sqrt{\frac{p(1-p)}{n} }[/tex]

In the above expression,

p = observed population.

n = sample size

[tex]z_{a}[/tex] = critical value of confidence interval

Now the given observations in question = 115

That result in success = 46

The resultant sample proportion = [tex]\frac{46}{115}[/tex]

⇒ 0.40 and it is for both success and failure

Here we can see that the answer for both parts will be identical.

The critical value of z at 90% confidence = 1.64

a) Lower bound = [tex]0.4 - 1.64 * \sqrt{\frac{0.4(1-0.4)}{90} }[/tex]

⇒ 0.402

b) Upper bound = [tex]0.4 + 1.64 * \sqrt{\frac{0.4(1-0.4)}{90} }[/tex]

⇒ 0.598

Confidence interval = 0.402 to 0.598

Therefore,

Option a) 90% confidence interval for the population proportion of successes = 0.402

Option b) 90% confidence interval for the population proportion of failures = 0.598

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The probability that their mean length is less than 17.4 inches is 28.26%

Given :

A manufacturer knows that their items have a normally distributed length, with a mean of 19.7 inches, and standard deviation of 4 inches , If 25 items are chosen at random .

z = ( X - μ ) / σ, where X = date , μ = mean , σ = standard deviation .

substitute the values

z = 17.4 - 19.7 / 4

= -2.3 / 4

= -0.575

P - value at z = -0.575 is 0.2826

Converting into percentage :

= 0.2826 * 100%

= 28.26 %

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Definitions:

The given angles are:

Eric typed 15 words more than Dae per minute.

Linear equations are equations whose highest power of the variables is 1. The graph of a linear equation is a straight line. A nonlinear equation is an equation whose highest power of the variables is not 1 and the graph is not a straight line.

To find the amount of words typed in 1 minute for both;

Dae = 333/9

Dae = 27 words per minute

Eric = 252/6

Eric = 42 words per minute

Therefore 42 - 27 = 15 words per minute

Eric typed 15 more words per minute.

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There is a 90% probability that Abby and Bridget are seated adjacent to each other in the same row or the same column.

There are 10 total seating positions, and Abby and Bridget can be seated in any of these positions. There are two rows, and in each row there are 3 possible seating positions for Abby and 3 possible seating positions for Bridget, for a total of 6 possible seating arrangements in each row. There are also 3 possible seating positions for Abby and 3 possible seating positions for Bridget in the same column, for a total of 3 possible seating arrangements in the same column. Therefore, there are a total of 6+3=9 possible seating arrangements in which Abby and Bridget are seated adjacent to each other in the same row or the same column.

Out of all the possible seating arrangements, the probability that Abby and Bridget are seated adjacent to each other in the same row or the same column is therefore 9/10. This can be expressed as a fraction or as a decimal:

[tex]\frac{9}{10}[/tex] = 0.9

This means that there is a 90% probability that Abby and Bridget are seated adjacent to each other in the same row or the same column.

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The reasons that complete the statements are:

From the question, we have the following parameters that can be used in our computation:

Triangles = RST, and TUR

From the question, we have the following given parameters

∠SRT ≅ ∠UTR

This means that

Statement 2: ∠SRT ≅ ∠UTR ------ Given

At this point, we have

RS ≅ TU --- Congruent side (S)

∠SRT ≅ ∠UTR ------ Congruent angle (A)

RT ≅ TR --- Congruent side (S)

When these congruent sides and angles are combined, we have

SAS congruence property

The SAS congruent theorem implies that the corresponding sides of the triangles in question are congruent and the angles between the corresponding sides are also congruent

Hence, the additional information on the congruency of the triangles are Given and SAS congruence property

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Answer: To simplify the expression (x - 4)(4x^2 + x - 6), you can use the distributive property, which states that you can multiply a number or expression by each term inside a set of parentheses.

Here is the process for simplifying the expression:

Multiply the first term, "x - 4", by the first term inside the second set of parentheses, "4x^2": (x - 4)(4x^2) = 4x^3 - 16x^2

Multiply the first term, "x - 4", by the second term inside the second set of parentheses, "x": (x - 4)(x) = x^2 - 4x

Multiply the first term, "x - 4", by the third term inside the second set of parentheses, "-6": (x - 4)(-6) = -6x + 24

Add the three products together: 4x^3 - 16x^2 + x^2 - 4x - 6x + 24 = 4x^3 - 16x^2 + x^2 - 10x + 24 = 4x^3 - 15x^2 - 10x + 24

The simplified expression is: 4x^3 - 15x^2 - 10x + 24

So, (x - 4)(4x^2 + x - 6) = 4x^3 - 15x^2 - 10x + 24.

Answer:

5x+x=90

Step-by-step explanation:

5 times the other = 5x

the other piece is x

Answer: the small pipe is 15 inches long

Step-by-step explanation: since the larger pipe is 5 times larger than the small pipe, the 90 inch pipe would have too be divided by 6 to make sure the 5 times of the large pipe and the 1 small pipe. so, you would do 90/6=15. so the small pipe is 15 inches long. the large pipe is 75 inches long.

The line AC in the figure is the diameter of the circle also it is a chord.

The chord of a circle is a straight path that connects two locations on the circle's circumference. The chord is one of the line segments whose ends are on the perimeter of a circle that can be drawn.

As per the information obtained from the figure,

The line AC in the given diagram is the diameter of the circle, but it is also a chord of the circle because another definition of diameter is as a chord that runs across the center of the circle.

Note the point that every diameter can be said as a chord, but every chord cannot be the diameter of the circle.

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The average rate change of the function is -4.

What is a function?

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Given function is f(x) = 1x² + 1x - 8.

Find the average rate change of the function in the interval [-4, -1]

For this compute the value of f(x) at x = -4 and x = -1.

Then find the difference the value of f(x) and divide it by the difference the value of x.

The average rate change of function f(x) in the interval [a,b] is [f(b) - f(a)]/(b-a).

Putting x = -4 in the given function:

f(-4) = 1(-4)² + 1(-4) - 8

f(-4) = 4

Putting x = -1 in the given function:

f(-1) = 1(-1)² + 1(-1) - 8

f(-1) = -8.

The rate change of x is -1 - (-4) = 3

The average rate change of the function is

[f(-1) - f(-4)] /3

= -8 - 4/3

= - 12/3

= -4

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At least means less than or equal to.

Fewest means the smallest number of boxes.

12 3/4 +x ≥ 29 5/8

x ≥ 16 7/8

The fewest number of boxes would be almost ≅ 42 boxes

Part A:

Let x denote the amount of fudge at the shop.

Helena prepares 12 3/4 pounds of fudge containing nuts.

Mathematically, the total amount of fudge on Monday will be

12 3/4 +x

Of this amount of fudge  there are at least 29 5/8 pounds of fudge containing nuts at the fudge shop on Monday

12 3/4 +x ≥ 29 5/8

Part B:

The inequality can be solved

12 3/4 +x ≥ 29 5/8

x ≥ 29 5/8- 12 3/4

x ≥  29- 12     5/8- 3/4    

The whole numbers are subtracted and the fractions are solved separately to avoid long calculations.

x ≥  17  (5-6)/8

x ≥  17 - 1/8

x ≥  (136-1)/8

x ≥  (135)/8

x ≥  16 7/8

Part C :

To find the number of boxes we divide the equal number of pounds .

12 3/4 + 29 5/8

12 + 29   3/4 + 5/8

41  11/8

42 3/8

The fewest number of boxes would be almost ≅ 42 boxes

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The measures of angles x, y and z are 40°, 50° and 130° and measures of the segments are AY = 16, IY = 9, FG = 30, AP = 24

Centroid is the point in a triangle where all the medians of the triangle intersects.

Given are two triangles, in first we have to find the missing angles and in the second one we need to find the asked segments,

1) We know that, in a right triangle, one angle is 90° and the sum of other two sides is 90°,

Therefore, 40°+y = 90°

y = 50°

x+y = 90°

x = 90°-50°

x = 40°

z = 180°-50° (linear pair)

z = 130°

2) we know that, the centroid divides the medians into 2:1

AY = 2YP

AY = 16

IY = TY/2

IY = 9

FG = GY+YF   (segment addition postulate)

GY = YF/2

GY = 10

FG = 10+20 = 30

PA = AY+YP  (segment addition postulate)

PA = 8+16

PA = 24

Hence. the measures are x, y and z are 40°, 50° and 130° and  AY = 16, IY = 9, FG = 30, AP = 24

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The equation of the regression line is y = 4 + x and the regression analysis of the given data need not be done.

Straight line equation is y = a + bx.

The normal equations are

∑y = a·n + b ∑x ∑ xy = a ∑x + b∑x² Hence the regression analysis of the data :

The values are calculated using the following table

x y x²             x⋅y

58 62 3364 3596

47 51 2209 2397

84 88 7056 7392

62 66 3844 4092

57 61 3249 3477

72 76 5184 5472

69 73 4761 5037

hence :

∑x = 449

∑y = 477

∑x² = 29667

∑x⋅y = 31463

Substituting these values in the normal equations

7a+449b=477

449a+29667b=31463

Solving these two equations using Elimination method,

7a+449b=477

and 449a+29667b=31463

7a+449b=477→(1)

449a+29667b=31463→(2)

equation(1)×449

⇒3143a+201601b=214173

equation(2)×7

⇒3143a+207669b=220241

Substracting

⇒-6068b = -6068

⇒6068b = 6068

⇒b = 1

Putting b = 1 in equation (1), we have

7a+449(1) = 477

⇒7a = 477  - 449

⇒7a = 28 or a  = 4.

Now Estimate y for x=50

y = a + bx , we get

y = 4 + 1×50

y = 4 + 50

y = 54

At x equals 50 we get the value of y as 54 .

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The radius of the sphere B is 3 times greater than the radius of the sphere A or radius of the sphere A is 1/3 times greater than the radius of the sphere B.

A sphere is a three dimensional shape formed by the set of all points which are at equidistance from a point called the center of the sphere.

Volume of a sphere = [tex]\frac{4}{3}[/tex] π r³

Let the volume and radius of sphere A is V₁ and r₁ respectively and the volume and radius of sphere B be V₂ and r₂ respectively.

We have,

V₁ × 27 = V₂

[tex]\frac{4}{3}[/tex] π r₁³ × 27 = [tex]\frac{4}{3}[/tex] π r₂³

Common terms [tex]\frac{4}{3}[/tex] π get cancelled.

⇒ 27r₁³ = r₂³

⇒ r₁³ / r₂³ = 1 / 27

Taking cube root on both sides,

⇒ r₁ / r₂ = 1 / 3

⇒ 3r₁ =  r₂

⇒ r₁ = [tex]\frac{1}{3}[/tex] r₂

Hence the radius of the sphere A is 1/3 times greater than the radius of the sphere B.

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Answer:

Step-by-step explanation:

Explanation:

As you know, each electron that's part of an atom has its own unique set of four quantum numbers that describes its position and spin.

This means that looking for the number of unique sets of quantum numbers is equivalent to looking for the number of electrons that can occupy the third energy level.

As you know, the number of orbitals you get per energy level is given by the equation

no. of orbitals

=

n

2

, where

n

- the principal quantum number, the ones that gives the energy level.

So, if you're dealing with the third energy level, you can say that it will contain a total of

no. of orbitals

=

3

2

=

9

distinct orbitals.

Now, each orbital can contain a maximum of

2

electrons of opposite spins. This means that the third energy level will contain a maximum number of

no. of electron

=

9

⋅

2

=

18 e

−

So, if each electron is described by an unique set of quantum numbers, you can conclude that

18

sets of quantum numbers are possible for the third energy level.

ok maybe that will help!

The 3rd term of (4 - 5g) is -1050000g5

An arithmetic sequence is a set of integers that are ordered and have a common difference between each following word. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6. An arithmetic progression is another name for an arithmetic sequence.

It is simple to establish a series by starting with a number and repeatedly adding a fixed constant (d). An arithmetic sequence is this kind of sequence.

Given,

(4 - 5g)  simplifying

-1

So that is -1050000g5

The 3rd term of (4 - 5g) is -1050000g5

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By using proportions, it is discovered that 67% of voters who are female and vote for Candidate J to win.

A percentage is a component of a total amount, and the three-step rule is used to relate the measurements.

The percentage of voters who select Candidate J is:

60% of x are voters are female

30% of (1 - x), who vote are male

If the total of these percentages is larger than 50% = 0.5, Candidate J will be elected; therefore:

0.6x + 0.3(1 - x) > 0.5

0.6x + 0.3 - 0.3x > 0.5

0.3x > 0.2

x > 2/3

x > 0.667

x > 67%

By using proportions, it is discovered that 67% of voters who are female and vote for Candidate J to win.

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Answer: You must give more points for questions that are this long

sincerely,

A Friend

Step-by-step explanation:

The number of hours it will take the student to complete the project is 5 / 6 hours.

A student completes ⅘ of a math project in ⅔ hour. If the student continues at the same rate,  the time it will take the student to complete the project can be calculated as follows:

Therefore,

let

x = time it will take the student to complete the project

Hence

if 4 / 5 x = 2 / 3 hours

x = ? hours

cross multiply

Therefore,

number of hours to complete the whole math project = x × 2 / 3 ÷ 4 / 5 x

number of hours to complete the whole math project = 2 / 3 x × 5 / 4x

number of hours to complete the whole math project = 10x / 12x

number of hours to complete the whole math project = 10 / 12

number of hours to complete the whole math project = 5 / 6 hours

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