If qr = 20 in., rs = 7 in., and sq = 24 in., what is pn? 3 in. 7 in. 20 in. 24 in.

Answer:

6(p + 5)(p + 10)

Step-by-step explanation:

6p² + 90p + 300 ← factor out 6 from each term

= 6(p² + 15p + 50) ← factor the quadratic

consider the factors of the constant term (+ 50) which sum to give the coefficient of the p- term (+ 15)

the factors are + 5 and + 10 , then

p² + 15p + 50 = (p + 5)(p + 10)

and

6p² + 90p + 300

= 6(p + 5)(p + 10)

The mean is 65 inches and the standard deviation is 3 inches.

Given,

In a group of women, the distribution of heights is roughly normal. Women who are shorter than 62 inches in height make up 16% of the population.

The empirical rule, less than μ - σ of 16% of the data is accurate.

P (x < μ - σ) = 16%

μ - σ = 62 → (I)

Approximately 97.5% of the women are under 71 inches in height,

P (x < μ + 2σ) = 97.5%

μ + 2σ = 71 → (II)

By solving (I) & (II);

μ - σ = 62

μ + 2σ = 71

3σ = 9

σ = 3

From (I);

μ - σ = 62

μ - 3 = 62

μ = 65

Hence, Mean = 65 inches

            Standard deviation = 3 inches

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The vertex is (-2, 5) and The range is [5, ∞)

The correct option is (D) i.e.,  (−2, 5); 5 ≤ y < ∞

Given:

The Function is :

y =  |2x + 4| + 5

To find the vertex and range of the function.

What is vertex and range ?

The vertex is given by the coordinates (h, k), so all we need to consider is the k. For example, consider the function f(x)=3(x+4)2−6. a is positive and the vertex is at (−4,−6), so the range is all real numbers greater than or equal to −6.

Now, According to the question:

The function is given as:

y =   |2x + 4| + 5

So, According to the above statement is:

The vertex in y = |2x + 4| + 5

The vertex is (-2, 5)

The range in y =   |2x + 4| + 5

The range is all real numbers

The range is [5, ∞)

Hence, The vertex is (-2, 5) and The range is [5, ∞)

The correct option is (D) i.e.,  (−2, 5); 5 ≤ y < ∞

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(D) - (−2, 5); 5 ≤ y < ∞

The dimensions of the scale drawing is length = 168 inches and width = 126 inches

Scale drawing helps to represent surfaces on earth in a paper by either enlarging its dimension, reducing its dimension by a constant factor called the scale factor.

The conversion or scale factor is 21 inches = 4 meters

If 21 inches = 4 meters,

then 1 meter = 21/4 inches

32 meters inches = 32 x 21/4 = 168 inches

24 meters = 24 x 21/4 = 126 inches.

In conclusion, length of the scale drawing is 168 inches and width of the scale drawing iss 126 inches

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Use of the two-tailed test is advised. In order to compare the average across two years,

A random sample of 25 national capitals had their air quality measured in 2013, and the same cities had been visited again in 2014. We want to compare the average air quality between the two years using this data.

A one-sided or two-sided test should be used, right? Describe your thinking.

The two-tailed test should be used. We want to contrast the average across two years. If the test parameter calculated for the two years differs, it would be interesting to know. (There is no exact comparison to show if one year is better or worse than the other.)

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Answer:

Step-by-step explanation:

Let the missing part be x.

According to triangle proportionality theorem we have:

The required side is 28.

Similarity of a triangle is the ratio of their corresponding sides or angles which are equal .

Given that AB=35, AE=12 and CE=3.

Let BD=x ⇒ AD = 35-x

Triangle ΔABC and ΔADE are similar,

By using property of similarity,

AB/AC=AD/AE

35/15=35-x/3

x=28

value of side x=28.

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The value of "a" for which the given equation has an infinite number of solutions is 2x.

We are given an equation. The equation is linear in nature. An equation is a mathematical statement that includes the sign "equal to" between two expressions with equal values. We need to find the value of the variable "a" such that the equation has infinite solutions. A variable is a quantity that can change in the context of a mathematical problem or experiment. The equation is : 2(x + 3) = a + 6. If an equation has infinite solutions, then the equation is called an identity. Identity is an equation that is true regardless of the values used.

2(x + 3) = a + 6

2x + 6 = a + 6

a = 2x

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Based on the information provided, the equation that can be used to find how much money, c, each charm bracelet cost at full price is 5(c – 4) = 45.

An equation is its simplest form in algebra, refers to a mathematical statement that represents that two mathematical expressions are equal. For example, 2x + 6 = 14 is an equation, where 2x + 6 and 14 are two expressions that are separated by an equal sign. In the given case, as each bracelet cost is reduced by $4 from the full price, and the total cost of 5 identical charm bracelets is $45, the equation that can be used is given by:

5(c – 4) = 45

Solving the equation,

5(c – 4) = 45

c – 4 = 9

c = 9 + 4 = $13

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Answer:

g(t - 1) = t² - 3t + 2

Step-by-step explanation:

substitute x = t - 1 into g(x) , that is

g(t - 1)

= (t - 1)² - (t - 1) ← expand squared factor using FOIL

= t² - 2t + 1 - t + 1 ← collect like terms

= t² - 3t + 2

The monthly deposit for the amount to compound monthly would be $1515.15.

What is compounding?

Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit. It is considered to be the 8th wonder of  the world as it has great power in terms of money.

Main Body:

formula for compound interest monthly(C.I.)  =[tex]P(1+\frac{R}{12})^{12t} -P[/tex]

Here R- 3.7% = 0.037   ,  T=22 years  , C.I. = 500000    P=?

Calculating ,

500000 = P(1+[tex]\frac{0.037}{12}^{12*22}[/tex]) -P

500000 = P(1.25)

P= 400000 but it is for all time period.

so monthly deposit = P/12*22

                                = 400000/264

                                = 1515.15

Hence the answer is $1515.15.

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Answer:

-4

Step-by-step explanation:

Simplifying

8(x + 12) = 64

Reorder the terms:

8(12 + x) = 64      (12 * 8 + x * 8) = 64      (96 + 8x) = 64

Solving

96 + 8x = 64

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-96' to each side of the equation.

96 + -96 + 8x = 64 + -96

Combine like terms: 96 + -96 = 0

0 + 8x = 64 + -96

8x = 64 + -96

Combine like terms:

64 + -96 = -32

8x = -32

Divide each side by '8'.

x = -4

Simplifying

x = -4

Answer:

x = 19/2 (or) 9.5

Step-by-step explanation:

The equation is,

→ (8x - 12) = 64

Now the value of x will be,

→ (8x - 12) = 64

→ 8x = 64 + 12

→ x = 76/8

→ x = 19/2

→ [ x = 9.5 ]

Hence, the value of x is 9.5.

The probability that a randomly selected CD player will have a replacement time of fewer than 8.0 years is 0.7389

P(X<8) = P((X-mean)/s <(8-7.1)/1.4)

= P(Z<0.64) = 0.7389 (from standard normal table)

= P(X>c)=0.02

= P(Z<(c-7.1)/1.4) = 1-0.02 = 0.98

= (c-7.1)/1.4 =2.05 (from the standard normal table)

= c = 7.1+2.05*1.4 = 9.97

Probability sampling alludes to the choice of an example from a populace when this determination depends on the rule of randomization, that is to say, irregular determination or possibility. Probability sampling is more intricate, additional tedious, and normally more exorbitant than non-probability sampling.

While picking a probability test plan, the objective is to limit the inspecting blunder of the evaluations for the main study factors, while at the same time limiting the time and cost of leading the review. A few functional limitations can likewise affect that decision, for example, the qualities of the survey frame.

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x = 24

y = 58

Step-by-step explanation:

5x+20 = 6x-4 ( vertically opposite angles)

20+4 = 6x-5x(collect like terms)

x = 24

(y-18)+(5x+20) = 180 (sum of angles on a straight line)

(y-18)+(5×24+20) = 180

(y-18)+140 = 180

y-18 = 180-140(collect like terms)

y-18 = 40

y = 40+18

y=58

The probability is 0.0132.

Here we have mean and standard deviations for air samples from large cities.

According to large samples, the law sample average calculated from large samples is approximately equal to the population average.  

As here sample is taken from a large city, the sample is considered a large sample. Hence mean is approximately equal to the population mean. Also, it is considered a random sample is representative of the population and the sample standard deviation is approximate to the population standard deviation. Hence we can say that carbon monoxide concentrations in air samples from this city are normally distributed.

So here we have

μ = 12

σ = 9 , n = 100

Hence here we need to find,

= p (x > 14)

= p((x-μ /(σ/√n)) > 14-12/9/√100)

= p ( z > 2.22 )

= 1 - p ( z < 2.22 )

= 1 - 0.9868 (using excel formula = norm.s.dist(2.22,1))

= 0.0132

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The average salary is s(x) = 117400 x + 138600

The average salary in 2005 is $1899600

The average salary in 2010 is $2486600

What is average salary ?

The mean wage earned by a country's working population is known as the national average salary (or national average wage). It is computed by adding together the yearly wages of everyone who is employed and dividing the total by the number of employees.

Let s(x) = mx + b →Linear model in slope-intercept form

at s(1) = $256,000

   s(11) = $1430000

slope [tex]m = \frac{s(11) - s(1)}{11-1}[/tex]

           = (1430000-256000) / 10

           = 117400

To find b we can write

s(1) = 117400 (1) +b

256000 = 117400 + b

b = 256000 - 117400

 = 138600

s(x) = 117400 x + 138600

(b) s(15) = 117400 (15) + 138600

            = $1899600

(c) s(20) =  117400 (20) + 138600

             = $2486600

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The legend chart element will tells the category of data that each line represents the lines.

Lines:

Lines refers a one-dimensional figure, which has length but no width.

Given,

suppose that a line chart includes several lines.

Here we need to identify the chart element will tell you the category of data that each line represents.

Basically, chart is a visual representation of numeric data in a worksheet. And it helps you to identify trends, make comparisons, and recognize patterns in the numbers.

In order to get the clear information that appears in your chart, you can add a chart title, axis titles, and data labels.

The element legend or data table is used to represents the category of the data.

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Answer:

(11x + 17) = 116°

(13x - 1) = 116°

Step-by-step explanation:

(11x + 17) and (13x - 1) are equal because they are vertically opposite angles.

11x + 17 = 13x - 1

2x = 18

x = 9

Substitute x = 9 into angle measures.

11(9) + 17 = 116°

Since both angles are equal, (13x - 1) is also 116°.

13 72/99 is rational number.

A rational number is a number that can represented in the form p/q where p, q are integers and q ≠ 0. E.g. 3/1, 5/12.

An irrational number is the opposite of a rational number that cannot be represented in the form p/q where p, q are integers and q ≠ 0. E.g. √2

Given, number = 13 72/99

It is a mixed fraction. It can be converted into proper fraction :

(13×99 + 72)/99 = 1359/99

1359/99 is a rational number since numerator and the denominator are both integers.

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The value of f(2) when f(x) = [tex]-x^{2} +6[/tex] will be 2.

According to the question,

We have the following expression:

f(x) = [tex]-x^{2} +6[/tex]

Now, we can easily find the value of f(2) by putting the value of x in the given expression as 2.

So, we will have the following expression:

f(2) = [tex]-(2)^{2} +6[/tex]

f(2) = -4+6

(More to know: the two integers with different signs are subtracted but the sign in the final result remains that of the larger integer. So, in this case, the sign will be positive in the final result.)

f(2) = 2

Hence, the value of f(2) when f(x) = [tex]-x^{2} +6[/tex] will be 2.

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The local gym per month fees is $44.92

Define Division

Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

What do you mean by Cost ?

It's given that,

One year membership cost is = $539

So, per month cost will be = 539 / 12

                                            = 44.91666 or 44.92

Hence, the local gym per month fees is $44.92

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Answer:

[tex]\frac{1}{2}[/tex]x

Step-by-step explanation:

3/5  is the same as 6/10

[tex]\frac{6}{10}[/tex] x - [tex]\frac{1}{10}[/tex]x

[tex]\frac{5}{10}[/tex]x = [tex]\frac{1}{2}[/tex]x

By using addition of integers, it has been calculated that

On drawing a yellow card, the player has to move 2 block backward

What is addition of integers?

At first it is important to know about integers

To find the sum total of two or more integers, addition operator is used on the integers

Here addition operator will be required

Let going forward be denoted by a positive sign and going backward be denoted by a negative sign

A blue card means move forward 4 squares.

A red card means move back 6 squares.

So we assign +4 to blue card and we assign -6 to red card

Now, drawing a yellow card is equivalent to drawing a blue card followed by a red card

Number of spaces moved by a player = (+4) + (-6)

                                                               = 4 - 6

                                                               = -2

So on drawing a yellow card, the player has to move 2 block backward

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Answer:

m = -96/7

Step-by-step explanation:

5(m - 6) = 10 - 4[2(m - 7) - 5m]

5m - 30 = 10 - 4[2m - 14 - 5m]

5m - 30 = 10 - 4(-3m - 14)

5m - 30 = 10 + 12m + 56

-7m = 96

m = -96/7

The length of AC in triangle BAC is equal 10.7 units

In trigonometry, the cosine rule says that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.

The formula is given as

AC² = AB² + BC² - 2(AB)(BC) cos AC

AC² = 6² + 7² - 2(6)(7)cos110

AC = 10.7

Using cosine rule, the length of AC is 10.7 unit.

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Answer: A. The researcher computes difference scores to compute a t statistic

B. If the researcher has n number of participants to use in the experiment, then the degrees of freedom will be the same in a repeated-measures experiment or in a matched-subjects experiment

C. The researcher must compute an estimated standard error for the mean difference score to compute a t statistic.

D. Participants in both types of experiments are all measured the same number of times

A matched-subjects experiment produced a t statistic with a df of 9. How many subjects participated in this study?

A. 20

B. 10

C. 18

D. 9

For a repeated-measures experiment comparing two treatment conditions, the t statistic has a df of 11. How many subjects participated in this study?

A. 12

B. 22

C. 24

D. 11

Step-by-step explanation:

Answer:

Step 2

Step-by-step explanation:

He messed up because while changing the denominator (number on the bottom), he forgot to change the numerator (number on top).

It should be 2/8 instead of 1/8.