(07.04 MC)
Given the expression: 4x¹0-64x²
Part A: Rewrite the expression by factoring out the greatest common factor. (4 points)
Part B: Factor the entire expression completely. Show the steps of your work. (6 points)

STEPS PLEASE

Wyatt's calculated total earnings for the month of February is 1374.75

To find out how much Wyatt earned in all in February, we need to add up his earnings for each week.

Wyatt earned 316.50 each week for the first three weeks, so his total earnings for those three weeks were:

3 × 316.50 = 949.50

Wyatt earned 425.25 the last week of February, so his total earnings for that week were:

1 × 425.25 = 425.25

To find Wyatt's total earnings for February, we can add up his earnings for each week:

949.50 + 425.25 = 1374.75

Therefore, Wyatt earned a total of 1374.75 in February.

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The width of the garden is 18 feet. In this case, the length of the diagonal of the rectangular garden is the hypotenuse, and the length and width of the garden are the other two sides. Let's denote the width of the garden as "w".

Given:

Length of the garden = 24 feet

Diagonal of the garden = 30 feet

Using the Pythagorean theorem, we can set up the following equation:

[tex]24^2[/tex] + [tex]w^2[/tex] = [tex]30^2[/tex]

Simplifying:

576 + [tex]w^2[/tex] = 900

Subtracting 576 from both sides:

[tex]w^2[/tex] = 900 - 576

[tex]w^2[/tex] = 324

Taking the square root of both sides:

w = √324

w = 18

So, the width of the garden is 18 feet.

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we have:24² + w² = 30²Solve the equation:576 + w² = 900Subtract 576 from both sides:w² = 324 Take the square root of both sides:w = √324w = 18So, the width of the rectangular garden is 18 feet.

Using the Pythagorean theorem, we can find the width of the garden. If the length is 24 feet and the diagonal is 30 feet, then the width can be found by taking the square root of (30^2 - 24^2), which is approximately 18.97 feet.

Therefore, the garden is about 18.97 feet wide. We can use the Pythagorean theorem to find the width of the rectangular garden.

The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the diagonal across the garden is the hypotenuse, and the length and width of the garden are the other two sides.

The diagonal is 30 feet, and the length is 24 feet. We need to find the width (w).

The Pythagorean theorem formula is:a² + b² = c²Where 'a' and 'b' are the two shorter sides, and 'c' is the hypotenuse.

In this case, we have:24² + w² = 30²Solve the equation:576 + w² = 900Subtract 576 from both sides:w² = 324Take the square root of both sides:w = √324w = 18So, the width of the rectangular garden is 18 feet.

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Answer: 12 inches is one foot

Step-by-step explanation: hope that this is what you were asking ;)

Recall the equation provided in the pdf:

   (125x ^ 3 * y ^ - 12) ^ (- 2/3) = (y ^ [A])/([B] * x ^ [c])

find A B and C.

The answer will be:

We can solve this problem using the rules of exponents and algebraic manipulation.

Starting with the left-hand side of the equation:

(125x^3 * y^-12)^(-2/3)

Using the rule that (a * b)^c = a^c * b^c, we can rewrite the expression as:

125^(-2/3) * x^(-2) * y^(8)

Simplifying further, we can use the fact that a^(-n) = 1/(a^n) to get:

1/(5^2 * x^2 * y^8/3)

Now, we can see that the denominator on the right-hand side of the equation must be 5^2 * x^2 * y^8/3. To find the numerator, we need to simplify the expression y^A. Comparing exponents, we see that:

y^A = y^(8/3)

Therefore, we need to find a value of A such that A = 8/3. Solving for A, we get:

A = 8/3

Now, we can write the equation as:

y^(8/3)/(5^2 * x^2 * y^8/3) = y^(8/3)/(25 * x^2 * y^(8/3))

Comparing exponents again, we see that we need to find values of B and C such that:

B * C = 2

and

-8/3 = -C

Solving for C, we get:

C = 8/3

Substituting this value of C into the first equation, we get:

B * 8/3 = 2

Solving for B, we get:

B = 3/4

Therefore, the solution is:

A = 8/3

B = 3/4

C = 8/3

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Answer:

sorry did not mean to answer this

Step-by-step explanation:

Answer:

Domain: (0, ∞)

Range: (-∞, ∞)

Step-by-step explanation:

Domain solution: x > 0

Range solution: -∞ < f(x) < ∞

Hope this helps.

The equation that relates time and rate of travel is time = distance / rate, so for the given scenario, the equation would be time = 1525 miles / rate.

The equation that relates time and rate of travel is:

time = distance / rate

Where:

time is the time taken to travel the distance

distance is the distance between two places (in this case, from Chicago to Las Vegas)

rate is the rate of travel (the average speed)

So, for this specific case, the equation would be:

time = 1525 miles / rate

where rate is the average speed at which you travel from Chicago to Las Vegas.

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The minimum number of coin flips required to obtain a 98% confidence interval width of at most 0.15 is 188.

Hence option d is correct.

We'll use the formula for the confidence interval of a proportion, which is given by:
CI = p-hat ± (z * sqrt(p-hat * (1-p-hat) / n))
Here, p-hat represents the sample proportion (observed proportion of heads), z is the z-score for the desired confidence level (98% in this case), and n is the number of coin flips.
We want to find the minimum number of coin flips (n) needed to obtain a confidence interval width of at most 0.15. Since we suspect that the coin is fair, we'll assume p-hat = 0.5.
For a 98% confidence interval, the z-score (rounded to three decimal places) is 2.576.

Now, we'll set up the inequality:
0.15 >[tex]= 2 * (2.576 * \sqrt{(0.5 * (1-0.5) / n))}[/tex]
Squaring both sides and solving for n, we get:
n >= [tex]((2.576 * \sqrt{(0.25))^2) / (0.15/2)^2}[/tex]
n >= 188.423
Since the number of coin flips must be a whole number, we'll round up to the nearest integer, which is 188.

Hence option d is correct.

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As Kenisha packs three crates of merchandise having masses of 65kg , 72 kg and 42 kg, he or she packs total of 179 kg of merchandise.

Kenisha has 3 crates of merchandise.

Each of the crates have different masses, those  are as : first crate has mass 65 kg, second has mass of72 kg and third case has mass of 42 kg.

By simple addition rule we get,

The total masses of three crates is =  (65 + 72 + 42) kg

=179 kg

Thus, Kenisha has packed 179 kg of merchandise as he or she has packed three crates having masses 65 kg, 72kg and  42kg.

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When the applet selects random samples from the town's population of babies, we assume that the population is large enough and diverse enough to accurately represent the characteristics and traits of the entire population.

We assume that the selection of the random samples is unbiased and that every member of the population has an equal chance of being selected for the sample.

Based on your question, we are discussing random samples taken from a town's population of babies this year. When selecting random samples from this population, we assume the following:

1. The population of babies is well-defined and includes all babies born in the town within the specified year.
2. The random samples are representative of the entire population, meaning that each baby has an equal chance of being selected in the sample.
3. The samples are independent, meaning that the selection of one baby does not influence the selection of another.

These assumptions ensure that the results obtained from the random samples can be generalized to the entire population of babies in the town for this year.

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By assuming these conditions are met, we can perform statistical analyses on the random samples and make valid inferences about the entire population of babies in the town.

When an applet is selecting random samples from a town's population of babies this year, we typically assume the following about the population:
Independence:

Each baby selected in the sample is independent of the others, meaning that the outcome of one selection does not affect the outcome of another selection.
Randomness:

The applet chooses babies from the population in a random manner, ensuring that every baby has an equal chance of being selected.

Representativeness:

The random samples selected are representative of the entire population, meaning that the samples accurately reflect the characteristics of the town's population of babies as a whole.

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Thus, the total surface area of cylinder is found to be 480π sq. cm.

A cylinder's surface area is made up of its two congruent, parallel circular sides added together with its curved surface area. You must determine the Base Area (B) and Curved Surface Area in order to determine the surface area of a cylinder (CSA).

As a result, the base area multiplied by two and the area of a curved surface add up to the surface area or total surface of a cylinder.

Given data:

radius r = 8 cm

Height h = 22 cm

Total surface area of cylinder = 2*area of circle + area of curved cylinder

TSA = 2πr² + 2πrh

TSA = 2π(8)² + 2π(8)(22)

TSA = 2π(64) + 2π(176)

TSA = 128π + 352π

TSA = 480π sq. cm.

Thus, the total surface area of cylinder is found to be 480π sq. cm.

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Complete question-

Find the surface area of the cylinder with radius of 8 cm and height of 22 cm. write the answer in terms of pi and round the answer to the nearest hundredths place.

Answer: it is 3/2x x + 0

Step-by-step explanation:

you do rise over run which is 3 up and 2 over in this case. and the 0 is the y intercept but its at the center also known as the origin so its 0

Answer:

Step-by-step explanation:

b) The power of the given problems is: Power = 30556 J/s

c) The Force is:  500 N

The power is:  625 J/s

Power is defined as the rate at which work is done. That is workdone over time taken.

b) The formula for power when given force and velocity is:

Power = Force * velocity

We are given:

Force = 1000 N

Velocity = 110 km/h = 30.556 m/s

Thus:

Power = 1000 * 30.556

= 30556 J/s

c) The formula for workdone is:

W = Force * distance

Thus:

Force = Work/distance

Force = 25000J/50 m

Force = 500 N

The power = wordkdone/time taken

= 25000/40

= 625 J/s

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The correct graph is: bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44

Since the data is categorical and discrete, a bar graph is appropriate to display the data. The bars should be labeled with the sports, and their heights should correspond to the number of students who chose each sport.

A histogram is not appropriate because the data is not continuous. Also, the order of the bars does not matter in this case since the data is not ordinal.

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Thus, the interval estimate of the number of drivers under the age of 19 in 2008, together with its margin of error of 0.0245.

An unknown population parameter's value is likely to be within the bounds of a confidence interval (CI), which is a range of values. Given the qualities of your sample data, these intervals reflect a likely domain for the parameter.

Confidence intervals are computed using a predetermined degree of confidence and are obtained from sample statistics.

Margin of error ME = z(α/2)√[p(1-p)/n]

confidence interval = 95%

z(α/2) value for the 95% confidence interval = 1.96 (taken from attached table)

P = 75% = 0.75

1-p = 1 - 0.75 = 0.25

n = 1200

Put the values in formula:

ME = (1.96)*√[0.75*0.25 / 1200]

ME = (1.96)*√0.00015625

ME = 0.0245

Thus, the interval estimate of the number of drivers under the age of 19 in 2008, together with its margin of error of 0.0245.

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Complete question:

Fewer young people are driving. In 1983, 87% of 19-year-olds had a driver’s license. Twenty-five years later (in 2008) that percentage had dropped to 75%. Suppose these results are based on a random sample of 1200 19-year-olds in 1983 and again in 2008.  At a 95% confidence, what is the margin of error and the interval estimate of the number of 19-year-old drivers in 2008?

The height of the hill in the triangle is approximately 460.1 feet, which corresponds to option 1.

Angles are used to define how an object is situated in respect to an observer. These angles include the angle of elevation and the angle of depression. The angle of elevation is the angle formed between the horizontal and a line connecting an item above eye level and the observer. In other words, it is the angle created while gazing up at an item from the ground. On the other hand, the angle of depression is the angle formed by the horizontal and a line drawn from the observer to an object that is below their level.

For the given triangle, applying the trigonometric function we have:

tan(49°) = h / 400

h = 400 * tan(49°) ≈ 460.1 ft

Hence, the height of the hill is approximately 460.1 feet, which corresponds to option 1.

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The statement or reason to each box which complete the proof are;

Subtraction Property of Equality

Division Property of Equality

4z + 5 = 17

Then z = 3

4z + 5 = 17

subtract 5 from both sides (Subtraction Property of Equality)

4z = 17 - 5

4z = 12

divide both sides by 4 (Division Property of Equality)

z = 12/4

Therefore, the value of z = 3

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The fraction of the total vote he should expect to get is 23/75.

A fraction is a mathematical unit used to represent a portion of a whole or a ratio of two integers. They are shown as the top number, or numerator, and the bottom number, or denominator, separated by a line. The denominator is the total number of pieces that make up the whole, whereas the numerator is the number of shares or parts.

For instance, you may write 3/8 for the portion of pizza you consumed if there were 8 pieces and you only ate 3. This indicates that you consumed three of the pizza's eight equally sized portions.

From the given table we can determine the total number of votes are:

13 + 9 + 10 + 8 + 10 + 14 + 5 + 6 = 75.

Now, Jamal received 13 + 10 = 23 votes.

Thus, the fraction of the total vote he should expect to get is 23/75.

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To prepare for a benefits bid, Sally should census gather data on the age, marital status, and number of children of the 20 full-time employees.

This information will help Sally determine what types of benefits would be most appealing to the employees and what types of benefits might be necessary to attract and retain talent.

Additionally, Sally should gather data on the tenure and education levels of the employees to help her understand what types of benefits might be necessary to incentivize employees to stay with the company long-term and to attract highly educated candidates.

Finally, Sally should consider gathering data on disability and veteran status to ensure that the company is providing adequate support for those employees who may require additional assistance.

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The answer is (11. 845)

The Vieth-Müller Circle is an imaginary circle that passes between both retinae and the fixation point.

The Vieth-Müller Circle is an ophthalmology concept that depicts an imaginary circle that passes across the foveas (the primary points of the retinae that are responsible for acute, detailed vision) and the fixation point (the point at which the eyes are directed).

The Vieth-Müller Circle is significant because it helps to explain the phenomenon of binocular vision, which is the ability to perceive depth and three-dimensional space using both eyes together. The circle aids in the definition of the equivalent locations on the two retinae, which are sites that receive visual field information and are critical in combining the images from the two eyes into a single, three-dimensional perception.

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The imaginary circle that passes through both retinae and the fixation point is called the horopter. The horopter is important in visual perception as it represents the set of points in space that stimulate corresponding points on each retina, which is necessary for binocular vision and depth perception.

The Horopter is an imaginary circle that passes through both retinae and the fixation point. In this context:

1. "Imaginary" refers to the fact that the Horopter is a theoretical concept rather than a physical object.
2. "Retinae" are the light-sensitive layers at the back of both eyes, which play a crucial role in processing visual information.
3. "Fixation" is the point where both eyes are focused on a single object in the visual field.

In brief, the Horopter represents a collection of points in the 3D space that are perceived as having the same depth or distance as the fixation point. It helps in understanding binocular vision and depth perception, as points on the Horopter contribute to forming a single, fused image from both eyes.

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1. The area of the semi circle is 56.52ft²

2. The area of the rectangle is 228ft²

3. The total area is 284.52ft²

The area of a shape is the space occupied by the boundary of a plane figures like circles, rectangles, and triangles.

The area of a semi circle is expressed as;

A = 1/2 πr²

r = d/2 = 12/2 = 6ft

A = 1/2×3.14 × 6²

A = 56.52ft²

therefore the area of the semicircle is 56.52ft²

The area of a rectangle is expressed as;

A = l×w

= 19×12

= 228ft²

therefore the area of the rectangle is 228ft²

The total area = (228+56.52)ft²

= 284.52ft²

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Answer:

To find out how many points Nicky needs to score in her next game, we can use the formula for the mean (also known as the average) of a set of numbers:

mean = (sum of all numbers) / (number of numbers)

We know that Nicky has played three games and scored, and points in them. So the sum of all her points is:

sum=18+22+28

sum=68

We also know that Nicky wants to have a mean of 25 points per game, and she has played three games already. If we add the score from her next game to the sum, we will have the total number of points she has scored in four games.

The probability of detecting this shift on the first sample following the shift would be 68.3%.

The probability of detecting can be calculated by taking the difference between the sample mean and the new process mean (92-100 = -8) and dividing it by the process standard deviation (6).

The result is -1.33, which is then used to calculate the probability of a sample mean falling within the three-sigma control limits.

The difference between the sample mean and the new process mean (92-100 = -8).

The difference by the process standard deviation (6).

The result is -1.33.

The number to calculate the probability of a sample mean falling within the three-sigma control limits.

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Answer:

they have the same volume

Step-by-step explanation:

in order to find the volume of a rectangular prism you have to multiply the width,height and length.

2 × 3 × 5 = 30.since both prisms have the same numbers ,they have the same volume.

hope this helps :)

Answer:

The volumes of the two rectangular prisms are the same.

Step-by-step explanation:

For the first rectangular prism, the area of the base is 6 square meters, and the height is 5 meters, so the volume is 30 cubic meters.

For the second rectangular prism, the area of the base is 15 square meters, and the height is 2 meters, so the volume is 30 cubic meters, the same volume as the first rectangular prism.

the total weight of all the tablets in the box is 4,000 grams or 4 kilograms.

What is net weight mean?

The weight of a product or item that does not include the weight of its packing or container is known as its "net weight."

Given, number of tablets = 2,00,000 and weight of each tablet = 20 mg.

To convert from milligrams to grams, we divide by 1000. Therefore, the weight of each tablet in grams is:

20 mg ÷ 1000 = 0.02 g

Total weight of all the tablets in the box in grams is:

2,00,000 tablets × 0.02 g/tablet = 4,000 g

To convert from grams to kilograms, we divide by 1000. Therefore, the weight of all the tablets in the box in kilograms is:

4,000 g ÷ 1000 = 4 kg

Therefore, the total weight of all the tablets in the box is 4,000 grams or 4 kilograms.

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In contrast, open-ended questions allow for more in-depth and nuanced responses but can be more difficult to analyze due to the variability of responses.

A survey researcher is most likely to use a closed-ended question when the dimensions of the variables are well defined. Closed-ended questions provide respondents with a list of predefined response options to choose from, which allows for easier categorization and analysis of the data. This type of question is ideal for measuring specific and clearly defined variables, such as demographic information or attitudes towards a particular issue. In contrast, open-ended questions allow for more in-depth and nuanced responses but can be more difficult to analyze due to the variability of responses.

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(a) Two points: y = 2x + 1 and y = -2x - 1 (where the line intersects the parabola at (1,1) and (-1,1))

(b) One point: y = 2x - 1 (where the line intersects the parabola at (1,1))

(c) No point: y = 2x + 2 (the line does not intersect the parabola)

A parabola is a U-shaped symmetrical curve. In mathematics, it is a type of quadratic function that can be described as y = ax² + bx + c, where a, b, and c are constants and x is the variable. The graph of a parabola is symmetric about a vertical line called the axis of symmetry, which passes through the vertex of the parabola.

In the given question,

(a) When the graph of the line intersects the graph of the parabola at two points, it means that the discriminant of the quadratic equation is positive. Let the two intersection points be (x1, y1) and (x2, y2), where x1 < x2. Then we have:

y1 = x1² and y2 = x2²

The slope of the line passing through these two points is:

m = (y2 - y1)/(x2 - x1) = (x2² - x1²)/(x2 - x1) = x1 + x2

The equation of the line can then be written as:

y - y1 = m(x - x1)

y - x1^2 = (x1 + x2)(x - x1)

(b) When the graph of the line intersects the graph of the parabola at one point, it means that the discriminant of the quadratic equation is zero. Let the intersection point be (x0, y0), then we have:

y0 = x0^2

The equation of the line can be written as:

y - y0 = m(x - x0)

y - x0² = m(x - x0)

(c) When the graph of the line does not intersect the graph of the parabola, it means that the discriminant of the quadratic equation is negative. In this case, there is no solution for the system of equations y = x² and y = mx + b, where m and b are constants. Therefore, there is no equation of the line that satisfies this condition.

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