A sample of n = 64 scores has a mean of M = 68. Assuming that the population mean is μ = 60, find the z-score for this sample:
If it was obtained from a population with σ = 16
z =
If it was obtained from a population with σ = 32
z =
If it was obtained from a population with σ = 48
z =

The line an illustrates a linear function. Line a's slope is thus 1. Y = x + 2 is the equation for the line 'a'.

The steepness or slant of a line may be determined by looking at its slope. The slope is defined as the ratio of any two points on the line's vertical change (rise) to its horizontal change (run). The letter "m" is typically used to indicate slope.

The slope of a line connecting the coordinates (x1, y1) and (x2, y2) may be determined mathematically using the following formula:

[tex]m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]

Now, Evaluating slope of line 'a';

[tex]m=\frac{4-2 }{2-0 } = \frac{2}{2} =1[/tex]

Hence, the slope of line 'a' is 1.

Final Plotted Graph is mentioned in image 3 attached.

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Complete Question : Draw a vertical y-axis on the left-hand side of your graph and label it. Then draw a horizontal x-axis at the bottom of your graph. Then label the coordinates of each corner of the sign on your graph(Refer to image attached). Draw line a on your graph. What is the slope of line a?

Answer:

X = -8 X= -4

Step-by-step explanation:

x² + 12x = -32

(x + 12/2)² = -32 + (12/2)²

(x + 6)²= 4

square root both sides

x + 6 = 2

x + 6 = -2

x=-8 x=-4

The measure of the angle ∠6 is 102 degrees for the given parallel lines.

Two angles are said to be supplementary if their sums equal 180 degrees. In other words, if angles A and B are complementary, then the sum of the two angles is 180 degrees. Four angles are created when two lines intersect; if two of these angles are supplementary, the other two are likewise supplementary.

Since 70 + 110 = 180 degrees, 70 degrees and 110 degrees serve as an illustration of a pair of supplementary angles. Another illustration is a pair of vertical angles, which are always supplementary and are generated by the intersection of two lines.

The measure of angle of a straight line is given as 180 degrees.

Thus,

∠6 + 78 = 180

∠6 = 180 - 78

∠6 = 102

Hence, the measure of the angle ∠6 is 102 degrees for the given parallel lines.

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The given rational numbers are marked on number line below.

The given numbers are [tex]-2\frac{1}{6}[/tex] and 11/6.

We need to plot the given numbers on number line.

A number line is a visual representation of numbers on a straight line. This line is used to compare numbers that are placed at equal intervals on an infinite line that extends on both sides, horizontally or vertically.

Hence, the given rational numbers are marked on number line below.

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Answer:

170.52

Step-by-step explanation:

Let x be the original price

Then,

129.60 = 76% of x

129.60 = 76/100 * x

12960/76 = x

x = 170.52

Answer:

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The correct representations of the inequality –3(2x – 5) < 5(2 – x) are x > 5 and x > 5

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

–3(2x – 5) < 5(2 – x)

Open the brackets

So, we have

-6x + 15 < 10 - 5x

Evaluate the like terms

So, we have

-x < -5

This gives

x > 5

Hence, the correct representations of the inequality are x > 5 and x > 5

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The dimensions of the cubicle are 31.97 and 16.5 respectively.

We make diagram of rectangular office and AB is diagonal

let L be length and E be width

From the information, the diagonal of the floor of a rectangular office cubicle is 4 ft longer than the length of the cubicle and 3ft longer than twice the width.

As given  diagonal of the floor of a rectangular office cubicle is 4 ft longer than the length L.

So D = l + 4

D² = L² + W²

(D - 4)² + (D - 3)² / 4 = D²

Simplifying further, the dimensions of the cubicle are 31.97 and 16.5 respectively.

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Expected frequency of each face value is 20 and we can reject the null hypothesis that the die is fair.

To conduct a goodness-of-fit test for the fairness of the die, we need to first determine the expected frequency of each face value assuming the die is fair. Since there are six equally likely outcomes for a fair die, the expected frequency of each face value is 120/6 = 20.

Thus, we can complete the expected frequency column in the table as follows:

Face Value            Frequency          Expected Frequency

1                                  15                                20

2                                 29                               20

3                                 16                                20

4                                 15                                20

5                                 30                                20

6                                  15                                20

We can then calculate the chi-squared statistic using the formula:

χ² = Σ[(O - E)² / E]

where O is the observed frequency and E is the expected frequency.

Substituting the values from the table, we get:

χ² = [(15-20)²/20] + [(29-20)²/20] + [(16-20)²/20] + [(15-20)²/20] + [(30-20)²/20] + [(15-20)²/20]

χ² = 4.75 + 2.25 + 1 + 4.75 + 5 + 4.75

χ² = 22.25

The degrees of freedom for this test is (6-1) = 5. Using a chi-squared distribution table with 5 degrees of freedom and a significance level of 0.05, we find the critical value to be 11.07.

Since the calculated chi-squared value of 22.25 is greater than the critical value of 11.07, we can reject the null hypothesis that the die is fair. Therefore, we have evidence to suggest that the die may be biased.

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Answer: a) The amount saved each year will be 10% of the annual salary, which is:

10% x $31,800 = $3,180

b) the monthly deposit will be $265.

c) the amount in the account after 24 years will be $76,046.92.

Step-by-step explanation:

a. From the graph a = 1 and b = 1

b. f(x) = -x/4 + 5

c. The area under the graph is 9 units²

a. First to find the area under the graph, we find the values of a and b. From the graph, a = 1 and b = 3

b. To find f(x), we note that f(x) is a straight line. So, using the equation of a

in slope form, we have that

(y - y')/(x - x') = (y" - y')/(x" - x') where

So, substituting the values of the variables into the equation, we have that

(y - y')/(x - x') = (y" - y')/(x" - x')

(y - 5)/(x - 0) = (4 - 5)/(4 - 0)

(y - 5)/x = -1/4

y - 5 = -x/4

y = -x/4 + 5

So, f(x) = -x/4 + 5

c. To find the area under the curve, we notice that ∫f(x)dx = area

So, ∫f(x)dx = ∫₁³(-x/4 + 5)dx

= ∫₁³(-xdx/4) +  ∫₁³5dx

= [-x²/(2 × 4)]₁³ + [5x]₁³

= [-x²/8]₁³ + [5x]₁³

= [-3²/8 - (-1)³/8] + 5[3 - 1]

= [-9/8 + 1/8] + 5[2]

= -8/8 + 10

= -1 + 10

= 9 units²

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Answer:

Hilltop

Step-by-step explanation:

Convert all to meters,

Mammoth- 8005 meters

Brookside- 8700 meters

Wild Rose- 8080 meters

Hilltop- 8800 meters.

Hilltop has the most meters, it is the longest.

Answer:

$705.71

Step-by-step explanation:

Let's assume the regular price of the sofa is "x".

According to the problem statement, the sale price is 65% off the regular price, which means the sale price is equal to 35% of the regular price.

We can write this relationship as:

0.35x = $247

To find the value of "x", we need to solve for "x" in the above equation.

Dividing both sides by 0.35, we get:

x = $247 ÷ 0.35

x = $705.71

Therefore, the regular price of the sofa is $705.71.

If Mike scores two standard deviations above the mean then the Mike's percentile-score is 97.72 ≈ 98 percentile.

The percentile score corresponding to a raw test score, is the probability of the test score of a randomly chosen student to be less than or equal to the given test score.  To calculate this probability we find the value of the cumulative distribution function of the test score random variable at the given test score.

To calculate the percentile score of the given raw test score we have to find the value of the cumulative distribution function for the test score random variable at the given raw test score. if this random variable is X, then the linearly scaled random variable [tex]Z=\frac{X-\mu}{\sigma}[/tex], has standard normal-distribution. here [tex]\mu\textrm{ and }\sigma[/tex] are the mean and the standard deviation of the test score r.v respc. Also [tex]\textrm{P}(X\leq x_0) = \textrm{P}(Z\leq z_0),\textrm{ where }z_0=\frac{x_0-\mu}{\sigma}[/tex].  So instead of finding [tex]\textrm{P}(X\leq x_0)\textrm{, we can find } \textrm{P}(Z\leq z_0)[/tex] instead. [tex]z_0[/tex] is called the z-score corresponding to the [tex]x_0[/tex]. We can find [tex]\textrm{P}(Z < z_0)[/tex], using the table for the standard normal distribution.

For our question, we want to find [tex]\textrm{P}(X\leq \mu + 2\sigma)[/tex]. which is equal to [tex]\textrm{P}(Z\leq \frac{\mu+2\sigma - \mu}{\sigma}) = \textrm{P}(Z\leq 2).[/tex] So the z-score = 2. From the table for the standard normal distribution we get [tex]\textrm{P}(Z\leq 2) = .9772[/tex]. So our percentile score is .9772 or 97.72% [tex]\sim[/tex] 98%.

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Rachel $8500 invested at 4% and $8800 invested at 2% interest rate.

Investment is the act of allocating money or resources with the expectation of generating income or profit in the future.

Let x be the amount invested in the second account (with a 4% interest rate).

Then, since Rachel invested $300 more in the first account, the amount invested in the first account (with a 2% interest rate) is (x + 300)

We know that the total interest income Rachel earned was $516. We can set up an equation using the interest formula: (2% means 0.02 and 4% means 0.04)

⇒ 0.02(x + 300) + 0.04x = 516
⇒ 0.02x + 6 + 0.04x = 516
⇒ 0.06x + 6 = 516
⇒ 0.06x = 510
⇒ x = 8500

So, Rachel invested $8500 in the second account (with a 4% interest rate)

and (x + 300) = (8500 + 300) = $8800 in the first account (with a 2% interest rate).

Therefore, Rachel $8500 invested at 4% and $8800 invested at 2%.

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+) tri1 = 2×3 = 6 (cm²)

+) tri2 = 3×4 = 12 (cm²)

+) area of this shape = tri1 + tri2 = 6+12 = 18 (cm²)

Ans: 18cm²

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The volume of the rectangular prism is 144 in³ with the area of the base is 24 square inches and the height is 6 inches.

Volume is a measure of the amount of physical space occupied by an object or a fluid.

This is because the volume of a rectangular prism can be calculated by the formula V = A x h, where V is the volume, A is the area of the base, and h is the height. In this problem, the area of the base is 24 square inches and the height is 6 inches.

Therefore, the volume of the rectangular prism can be calculated as follows:

V = 24 in² x 6 in

= 144 in³

It is important to note that the formula for calculating the volume of a rectangular prism can be used for any rectangular prism, regardless of the size of the area of the base and the height. The formula remains the same and the only thing that changes is the numbers that are used to calculate the volume.

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Answer:

3:5 or 3 to 5 or [tex]\frac{3}{5}[/tex]

Step-by-step explanation:

[tex]\frac{6}{10}[/tex] ÷[tex]\frac{2}{2}[/tex] = [tex]\frac{3}{5}[/tex]

Helping in the name of Jesus.

Answer:

4.5

Step-by-step explanation:

uh

[tex]\cfrac{9}{x}=\cfrac{6}{10}\implies \cfrac{9}{x}=\cfrac{3}{5}\implies 45=3x\implies \cfrac{45}{3}=x\implies 15=x[/tex]

Union will need to choose a random sample of at least 65 wages to be 90% confident that its estimate of the mean hourly wage of foodservice workers is within $0.45 of the true population mean.

To calculate the minimum sample size needed for the union to be 90% confident within $0.45 of the true population mean, we can use the formula which states n = (Z^2 * σ^2) / E^2

Z = 90% = 1.645

σ = $2.20

E = $0.45

Substituting the values, we get:

n = (1.645^2 * 2.20^2) / 0.45^2

n = 13.097161 / 0.2025

n = 64.6773382716

n = 64.678

n = 65

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Okay, let's list the 4 rational numbers from smallest to largest:

5/3

7/15

6/10

25/5

So:

5/3 is A

7/15 is B

6/10 is C

25/5 is D

Answer:

The answer is C. 24, 9, -11, -24, -33.

In this list, 24 is the greatest integer, followed by 9, then -11, then -24, and finally -33. The other options are not in order from greatest to least.

Step-by-step explanation:

Answer:

The answer is C. 24, 9, -11, -24, -33.

In this list, 24 is the greatest integer, followed by 9, then -11, then -24, and finally -33. The other options are not in order from greatest to least.

Step-by-step explanation:

Sarah's daily outgoings on wages are £892.50.

What is wages?

Wages refer to the payment made to an employee in exchange for their labor or services provided to an employer. It is usually paid on an hourly, daily, weekly or monthly basis, and the amount of wages earned is determined by the hours worked, rate of pay, and any applicable deductions or taxes. Wages can be paid for various types of work, such as manual labor, skilled trades, clerical work, or professional services. It is an essential component of an employee's compensation package and is regulated by labor laws to ensure that employees are fairly compensated for their work.

Each employee works for 8.5 hours a day (17:00 - 08:30 = 8.5). So, the total number of hours worked by 12 employees in a day is 12 employees × 8.5 hours/employee = 102 total hours

Sarah pays each employee £8.75 per hour, so her total daily outgoings on wages can be calculated as,

102 total hours × £8.75 per hour/employee = £892.50

Therefore, Sarah's daily outgoings on wages are £892.50.

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Answer:

1. 16

2. 9

3. 21.08

Step-by-step explanation:

1. (explanation) (x+b)^2 = x^2+2bx + b^2 ( square formula)

16, would make a square trinomial

Answer:

1.16

2.9

3.x=9+root of 146(12.08) or x=9-root of 146

The final product of the given algebraic expression is: b⁴ - 64

Algebraic expressions are defined as simply the idea of expression of numbers using letters without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as a, b, c, etc. These letters are referred to as variables. An algebraic expression can be a combination of both the variables and the constants. Any value that is placed before and multiplied by a variable is a coefficient.

The expression is given as:

(b² + 8)(b² - 8)

Expand the expression using (a + b)(a - b) = a² - b²

Thus:

(b² + 8)(b² - 8) = b⁴ - 64

Thus, that is the final product of the given algebraic expression.

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Answer:

14. D) x+25=50; when x=157, x+25=182, which is equal to 50.

15. a) 3; you can solve for r by isolating the variable on one side of the equation. First, add 21 to both sides to get 10g - 21 + 21 = 7r + 12 + 21. Simplify to get 10g = 7r + 33. Then, subtract 33 from both sides to get 10g - 33 = 7r. Finally, divide both sides by 7 to get r = (10g - 33)/7. Plugging in a value for g, such as 3, gives you r = 3.

16. C) 2; combine like terms on both sides of the equation to get r - 8 = 8r + 10. Then, isolate the variable by subtracting r from both sides to get -9r - 8 = 10. Next, add 8 to both sides to get -9r = 18. Finally, divide both sides by -9 to get r = -2.

17. a) -36; start by isolating the variable on one side of the equation. Add 18 to both sides to get m/3 = m + 24. Then, subtract m from both sides to get -2m/3 = 24. Next, multiply both sides by -3/2 to get m = -36.

Step-by-step explanation:

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Plug in 0 for 'x' to find the y-intercept:

[tex]7x - 3y = 21[/tex]

[tex]7(0) - 3y = 21[/tex]

[tex]0 - 3y = 21[/tex]

[tex]-3y = 21[/tex]

Divide -3 to both sides:

[tex]y = -7[/tex]

So the y-intercept is -7.

[tex]7x - 3y = 21[/tex]

Plug in 0 for 'y' to find the x-intercept.

[tex]7x - 3(0) = 21[/tex]

[tex]7x - 0 = 21[/tex]

[tex]7x = 21[/tex]

Divide 7 to both sides:

[tex]x = 3[/tex]

So the x-intercept is 3.

The perfect square is the integer that can be expressed as the square of another integer. Moreover, it is said to be the product of some integer with itself.

To see the percent of the perfect squares less than 1000 that end in a 6. Let us see the perfect squares under 1000.

Perfect squares  < 1000

0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256. 289, 324, 361, 400. 441. 484, 529. 576, 625, 676, 729, 784, 841, 900, 961

Hence, there are 32  perfect squares less than 1000 in which,

6  end  in a "6"

So

6  / 32 = 3/ 16   = 18.75 %

Therefore 18.75% percent of the perfect squares are less than 1000 that end in a 6.

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The matrix of A is [tex]A = \left[\begin{array}{ccc}0&0&-6\\9&0&0\\0&0&0\end{array}\right][/tex]

Let's start by considering the first standard basis vector [1 0 0]. Applying the transformation T to this vector gives:

T([1 0 0]) = [0 9 -6] * [1 0 0] = [0 0 0]

Therefore, the image of [1 0 0] under T is the zero vector [0 0 0]. Since the image of the first standard basis vector is the first column of the matrix A, we know that the first column of A is the zero vector.

We can follow the same process to find the image of the second standard basis vector [0 1 0]:

T([0 1 0]) = [0 9 -6] * [0 1 0] = [0 9 0]

Therefore, the image of [0 1 0] under T is the vector [0 9 0]. Since the image of the second standard basis vector is the second column of the matrix A, we know that the second column of A is [0 9 0].

Finally, we find the image of the third standard basis vector [0 0 1]:

T([0 0 1]) = [0 9 -6] * [0 0 1] = [-6 0 0]

Therefore, the image of [0 0 1] under T is the vector [-6 0 0]. Since the image of the third standard basis vector is the third column of the matrix A, we know that the third column of A is [-6 0 0].

Putting it all together, the matrix A of the linear transformation T (x) = v * x is:

[tex]A = \left[\begin{array}{ccc}0&0&-6\\9&0&0\\0&0&0\end{array}\right][/tex]

In conclusion, we can see that the matrix A captures how the linear transformation T maps each standard basis vector in R³. By applying this matrix to any vector in R³, we can efficiently compute the image of that vector under T.

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