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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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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 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?

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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[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]

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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Answer:

C. -3x + 2y = 20

Step-by-step explanation:

Since the slope of line P is -2/3, and line Q is perpendicular to line P, the slopes of lines P and Q will be negative reciprocals. So the slope of line Q is 3/2. Since (-6, 1) is on line Q, we have:

1 = (3/2)(-6) + b

1 = -9 + b

b = 10

y = (3/2)x + 10

2y = 3x + 20

-3x + 2y = 20, so the correct answer is C.

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 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:

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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.

The activity rate for Cost Pool A is $7.97 per unit of Product A, and the activity rate for Cost Pool B is $6.06 per unit of Product B.

The activity rate is a cost accounting term that refers to the cost that a company incurs for each unit of a particular activity or process. It is calculated by dividing the total cost of an activity or process by the total number of units produced or processed.

The purpose of calculating activity rates is to allocate the cost of a particular activity or process to the products or services that use that activity or process. This helps to determine the true cost of producing a product or service and to make informed decisions about pricing, profitability, and resource allocation.

In order to calculate the activity rate for each cost pool, we need to know the total cost for each cost pool.

Let's assume that there are two cost pools: Cost Pool A and Cost Pool B.

If we know the total cost for each cost pool, we can calculate the activity rate for each cost pool by dividing the total cost by the total number of units produced.

For example, if the total cost for Cost Pool A is $100,000 and 12,539 units of Product A were produced, then the activity rate for Cost Pool A would be:

Activity Rate for Cost Pool A = Total Cost for Cost Pool A / Total Units of Product A

Activity Rate for Cost Pool A = $100,000 / 12,539 units

Activity Rate for Cost Pool A = $7.97 per unit of Product A

Similarly, if the total cost for Cost Pool B is $50,000 and 8,254 units of Product B were produced, then the activity rate for Cost Pool B would be:

Activity Rate for Cost Pool B = Total Cost for Cost Pool B / Total Units of Product B

Activity Rate for Cost Pool B = $50,000 / 8,254 units

Activity Rate for Cost Pool B = $6.06 per unit of Product B

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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:

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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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:

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:

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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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

Answer:

Step-by-step explanation:

To solve the problem, we need to add the two distances Tom jogged:

4 1/6 + 5 4/5

To add the two mixed numbers, we need to convert them into improper fractions:

4 1/6 = (6 x 4 + 1) / 6 = 25 / 6

5 4/5 = (5 x 5 + 4) / 5 = 29 / 5

Now we can add the two fractions:

25/6 + 29/5

To add the fractions, we need to find a common denominator:

LCM of 6 and 5 = 30

25/6 x 5/5 = 125/30

29/5 x 6/6 = 174/30

Now we can add the fractions:

125/30 + 174/30 = 299/30

The sum of the distances in improper fraction form is 299/30 miles. To write the answer as a mixed number in simplest form, we need to divide the numerator by the denominator:

299 / 30 = 9 29/30

Therefore, Tom has jogged 9 29/30 miles in all.

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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+) tri1 = 2×3 = 6 (cm²)

+) tri2 = 3×4 = 12 (cm²)

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

Ans: 18cm²

ok done. Thank to me >:333

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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Answer:

4.5

Step-by-step explanation:

uh

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.

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:

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.

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.

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 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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