A) 120 is what percent of 400?
Percent Proportion -
Percent Equation-

B) 4% of 975 is what number?
Percent Proportion -
Percent Equation-

C) 12.5% of $100 is what number?
Percent Proportion -
Percent Equation-

The complete factorization of 3x⁵- 75x³ is:- 3x³(x + 5)(x - 5)

How to solve factor?

To factor completely the expression 3x⁵ - 75x³, we can first factor out the greatest common factor (GCF) of the two terms, which is 3x³:

3x³(x² - 25)

Next, we can factor the expression inside the parentheses using the difference of squares formula:

3x³(x + 5)(x - 5)

Therefore, the complete factorization of 3x⁵ - 75x³ is:

3x³(x + 5)(x - 5)

We can check that this is the correct factorization by using the distributive property of multiplication and verifying that the product of the factors is equal to the original expression:

3x³(x + 5)(x - 5) = 3x³(x² - 25)

= 3x³x² - 3x³(25)

= 3x⁵ - 75x³

So the factorization is correct.

In summary, to factor completely an expression like 3x⁵ - 75x³, we should first factor out the GCF and then look for further factorization opportunities using various factorization techniques such as the difference of squares formula, the sum or difference of cubes formula, or the quadratic formula. It's important to remember to check our work by multiplying the factors back together to ensure that we get the original expression.

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After answering the provided question, we can conclude that Therefore, the solutions for the equation are b ≈ -1.973 and b ≈ 1.973.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the value "9". The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

Starting with the given equation:

[tex]2b^4 - 13 = 73\\2b^4 = 86\\b^4 = 43\\b = (43)^(1/4)\\b =1.973\\b = -1.973, 1.973\\[/tex]

Therefore, the solutions for the equation are b ≈ -1.973 and b ≈ 1.973.

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Answer:

To determine which trigonometric function to use in a triangle, you need to identify what sides and angles are given, and what you are trying to find. The three primary trigonometric functions are sine (sin), cosine (cos), and tangent (tan), which relate the ratios of the sides of a right triangle to its angles.

To determine which trigonometric function to use, you can use the acronym SOH-CAH-TOA, which stands for:

Sine = Opposite / Hypotenuse

Cosine = Adjacent / Hypotenuse

Tangent = Opposite / Adjacent

Let's take an example:

Question: In a right triangle ABC, where angle B is the right angle, the length of the hypotenuse is 10 cm, and the length of the adjacent side to angle A is 6 cm. What is the value of the sine of angle A?

Solution: We are given the hypotenuse and the adjacent side to angle A, and we want to find the sine of angle A. Looking at the SOH-CAH-TOA acronym, we see that sine involves the ratio of the opposite side to the hypotenuse. In this case, the opposite side to angle A is not given, but we can use the Pythagorean theorem to find it:

a² + b² = c², where a and b are the legs of the right triangle and c is the hypotenuse.

In our triangle, we have:

a² + 6² = 10²

a² + 36 = 100

a² = 64

a = 8

Now that we know the length of the opposite side to angle A is 8 cm, we can use the sine function:

sin(A) = Opposite / Hypotenuse = 8 / 10 = 0.8

So, the value of the sine of angle A is 0.8.

In summary, to determine which trigonometric function to use, you need to identify what sides and angles are given, and what you are trying to find. You can then use the SOH-CAH-TOA acronym to match the given sides with the appropriate function, and use the Pythagorean theorem and other trigonometric identities to find any missing sides or angles.

Regenerate response

The position of the diver in relation to the surface of the water 8 minutes after beginning to rise can be calculated as follows:

The diver was at a depth of 80 feet below the surface initially. After 8 minutes of rising, the diver has come up to the surface by 3 x 8 = 24 feet. So, the diver's position in relation to the surface of the water is:

80 - 24 = 56 feet below the surface.

Therefore, the integer that describes the position of the diver in relation to the surface of the water 8 minutes after beginning to rise is A. -56.

If one-tower can hold 4.37×10⁶ gallons of water and other tower can hold 3.92×10⁶ gallons of water, then combined water capacity of two towers is 8.29×10⁶ gallons.

In order to find the combined water capacity of the two towers, we simply need to add their individual capacities.

The water capacity of one tower is = 4.37×10⁶ gallons of water, and the water capacity of other tower is = 3.92×10⁶ gallons of water,

So, their combined capacity is:

⇒ 4.37×10⁶ + 3.92×10⁶ = 8.29×10⁶ gallons

Therefore, the combined water capacity of the two towers is 8.29×10⁶ gallons.

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The given question is incomplete, the complete question is

A city has two water towers. one tower holds 4.37×10⁶ gallons of water and the other holds 3.92×10⁶ gallons of water. What is the combined water capacity of the two towers?

The contrast coefficients would be as follows:

The farmers are interested in whether there is any difference between the low-low combination (it is the cheapest) and the average of the remaining three levels. The hypotheses they want to test are:

To test this hypothesis, the following contrast would be used:

To compare the high- to low-nitrogen content fertilizers, the following contrast would be used:

To compare the high- to low-phosphorus content fertilizers, the following contrast would be used:

To compare the ll combination to the hh combination, the following contrast would be used:

For each of the contrasts above, the contrast coefficients would be as follows:

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The graph of the solution to the system of inequalities is added as an attachment

Given that

x + y ≥ 6

8x + 16y ≤ 160

To graph the solution to a system of inequalities, follow these steps:

See attachment for the system of inequalities

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The given system of linear equations has infinite solutions. The solution has been obtained by using the elimination method.

What is the elimination method?

The elimination approach involves taking one variable out of the system of linear equations by utilising addition or subtraction together with multiplication or division of the variable coefficients.

We are given a system of linear equations as -x + y = -8 and 2x - 2y = 16.

Now, on dividing the equation 2x - 2y = 16 by 2, we get

x - y = 8.

Now, on adding the first and the third equation, we get

⇒ (-x + y) + (x - y) = -8 + 8

⇒ 0 = 0

Hence, the system has infinetly many solutions.

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Question: What is the solution for the given system of linear equations?

-x + y = -8 and 2x - 2y = 16

Using multiplication principle of counting, Argyle can make 140 different outfits.

Argyle has 10 T-shirts and 7 pairs of shorts, which he can wear with either sandals or sneakers. To find out how many different outfits he can make, we can use the multiplication principle of counting, which states that the total number of outcomes for a sequence of events is the product of the number of outcomes for each event.

First, we need to determine the number of ways Argyle can choose a T-shirt and a pair of shorts. He can choose one of 10 T-shirts and one of 7 pairs of shorts, giving us:

10 x 7 = 70

Next, we need to determine the number of ways Argyle can choose shoes. For each outfit, he can choose either sandals or sneakers, giving us:

shoes = 2

Finally, we can find the total number of different outfits by multiplying the number of ways to choose a T-shirt and shorts by the number of ways to choose shoes:

70 x 2 = 140

Therefore, Argyle can make 140 different outfits if all the colors and patterns coordinate.

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An equation of the line in point-slope form that passes through the points (2, 1) and (-4, -8) is y - 1 = 3/2(x - 2).

In Mathematics and Geometry, the point-slope form of any straight line can be determined by using this mathematical expression:

y - y₁ = m(x - x₁)

Where:

Next, we would determine the slope;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (-8 - 1)/(-4 - 2)

Slope (m) = -9/-6

Slope (m) = 3/2

At data point (2, 1) and a slope of 3/2, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 1 = 3/2(x - 2)  

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The meaning of a 95% confidence interval for a population mean is to select an interval where when the process is repeated for many different samples, approximately 95% of the intervals would contain the sample mean and when the process is repeated for many different samples, approximately 95% of the intervals would contain the population mean. These two are the correct options from the given choices.

A confidence interval is a range of values, constructed from a sample, that is expected to include the value of an unknown population parameter with a specific level of certainty.

Confidence intervals are typically used to indicate the precision and accuracy of an estimate, rather than the probability of an event occurring.

Therefore, in the context of this question, we can say that a 95% confidence interval for a population mean would select an interval where when the process is repeated for many different samples, approximately 95% of the intervals would contain the sample mean and when the process is repeated for many different samples, approximately 95% of the intervals would contain the population mean.

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In conclusion Shaniyah has $159.25 for food and gas.

How to find?

First, we need to find how much Shaniyah spends on internet service and cell phone bill:

Amount spent on internet service = 21% of $325 = 0.21 x $325 = $68.25

Amount spent on cell phone bill = 3/10 of $325 = (3/10) x $325 = $97.50

The total amount spent on internet service and cell phone bill is $68.25 + $97.50 = $165.75

To find how much Shaniyah has left for food and gas, we subtract the total amount spent on internet service and cell phone bill from the total amount spent on bills:

Amount spent on food and gas = Total amount spent on bills - Amount spent on internet service and cell phone bill

Amount spent on food and gas = $325 - $165.75

Amount spent on food and gas = $159.25

Therefore, Shaniyah has $159.25 for food and gas.

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y = 26.4

Given: 3y + 7y - 84 = 180

First, we should combine any value that is similar.

3y + 7y - 84 = 180

10y - 84 = 180

Next, we will substitute.

10y - 84 + 84 = 180 = 84

10y = 264

Now we will divide by the value before the variable.

[tex]\frac{10y = 264}{ 10}[/tex] = y = 26. 4

Lastly, we will plug in the values.

3(26.4) + 7(26.4)- 84 = 180

76.2 + 184.8 - 84 = 180

264 - 84 = 180

180 = 180 ✓

The value of x in the equation (x - m)/ (n + m) = (x - n)/ (n - m) when solved is x = n²/m.

A list of the elements that make up an equation includes coefficients, variables, operators, constants, terms, and the equal to sign. An equation must always begin with the "=" sign and have terms on both sides. Each party should be treated equally.

Each side of an equation does not need to have a lot of terms, operators, and variables. Each equation with variables is an algebraic equation.

In the question, equation given:

(x - m)/ (n + m) = (x - n)/ (n - m)

Apply cross multiplication:

⇒ (x - m) (n - m) = (n + m) (x - n)

After opening the brackets, we have:

⇒ xn - xm - mn + n² = xn + xm - n² - mn

Evaluating the like terms in the equation we get:

⇒ 2xm = 2n²

So, we have

⇒ xm = n²

Divide by m on both sides:

x = n²/m

Therefore, the solution of the equation is x = n²/m.

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The surface area of the given cuboid is 228 cm².

What is surface area of a cuboid?

The surface area of a cuboid is a measure of the total area of its six faces. It is an important concept in geometry and is used in many real-life applications. For example, when calculating the amount of paint needed to cover the walls of a room, you would need to know the surface area of the walls. Similarly, when designing packaging for a product, you would need to know the surface area of the box to determine the amount of material required to make it.

To find the surface area of a cuboid, you need to add up the areas of all six faces.

Given the dimensions of the cuboid as,

Length = 9 cm

Breadth = 4 cm

Height = 6 cm

The surface area of the cuboid can be calculated as follows,

Area of the top face = length × breadth = 9 cm × 4 cm = 36 cm²

Area of the bottom face = length × breadth = 9 cm × 4 cm = 36 cm²

Area of the front face = breadth × height = 4 cm × 6 cm = 24 cm²

Area of the back face = breadth × height = 4 cm × 6 cm = 24 cm²

Area of the left side face = length × height = 9 cm × 6 cm = 54 cm²

Area of the right side face = length × height = 9 cm × 6 cm = 54 cm²

Therefore, the total surface area of the cuboid is the sum of all six faces, which is:

Surface Area = 2 × (length × breadth + breadth × height + length × height)

Surface Area = 2 × (9 cm × 4 cm + 4 cm × 6 cm + 9 cm × 6 cm)

Surface Area = 2 × (36 cm² + 24 cm² + 54 cm²)

Surface Area = 2 × 114 cm²

Surface Area = 228 cm²

Therefore, the surface area of the given cuboid is 228 cm².

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Answer: To make one bracelet, Maura needs 25 beads and 20 centimeters of elastic cord.

If Maura bought a pack of 1,000 beads, she can make:

1,000 beads ÷ 25 beads per bracelet = 40 bracelets

To make 40 bracelets, she will need:

40 bracelets × 20 centimeters of elastic cord per bracelet = 800 centimeters of elastic cord

To convert centimeters to meters, we divide by 100:

800 centimeters ÷ 100 centimeters per meter = 8 meters

Therefore, Maura should buy 8 meters of elastic cord to make 40 bracelets with a pack of 1,000 beads.

Step-by-step explanation:

The p-value for this test is the probability of observing a z-score of -2.45 or lower, which is approximately 0.0072. Therefore, the answer is 0.0072.

The null hypothesis is a common arithmetic theory that asserts there is no statistical relationship and significance between two groups of observed data and measured phenomena for a particular set of single, observed variables.

What the researcher anticipates discovering after performing a study is expressed as a scientific hypothesis. A statistical hypothesis, on the other hand, is a prediction of what the statistician does NOT expect to discover. The term "NULL hypothesis" refers to this rationale.

We can use a one-sample proportion test with a one-tailed alternative to test this hypothesis, and calculate the p-value as the probability of observing 10 or fewer ones out of 120 rolls, assuming the null hypothesis is true.

Using a normal approximation to the binomial distribution.

(since n=120 is large and p0=1/6 is not too close to 0 or 1),

the test statistic is:

z = ([tex]\frac{10}{120}[/tex] - [tex]\frac{1}{6}[/tex]) / √([tex]\frac{\frac{1}{6} *\frac{5}{6} }{120}[/tex])

≈ -2.45

The p-value for this test is the probability of observing a z-score of -2.45 or lower, which is approximately 0.0072. Therefore, the answer is 0.0072.

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According to given information, the approximate p-value for this test is 0.0072.

What is meant by p-value?

In statistics, the p-value is the probability of observing a test statistic as extreme or more extreme than the one calculated from the sample, assuming that the null hypothesis is true.

To determine the p-value for this test, we need to perform a hypothesis test to determine if the observed proportion of ones in the 120 rolls is significantly different from the long-run proportion of ones. We can use the following hypotheses:

Null hypothesis: p = 1/6 (assuming a fair die)

Alternative hypothesis: p < 1/6 (the calculator is producing fewer ones than it should)

To perform the test, we can use the normal approximation to the binomial distribution, since np = 120(1/6) = 20 and n*(1-p) = 120*(5/6) = 100, which are both greater than 10.

The test statistic is:

z = (x - np) / sqrt(np(1-p))

where x = 10 is the number of ones observed, np = 20 is the expected number of ones under the null hypothesis, and p = 1/6 is the hypothesized proportion of ones.

Substituting these values, we get:

z = (10 - 20/6) / sqrt(20/6 * (1 - 1/6))

z = -2.305

The p-value for this test is the probability of observing a test statistic as extreme or more extreme than -2.305, assuming the null hypothesis is true. Since this is a one-tailed test in the left tail, the p-value is the area to the left of -2.305 under the standard normal distribution. Using a table or calculator, we can find that this area is approximately 0.0106.

Therefore, the approximate p-value for this test is 0.0106, which is closest to 0.0072.

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The center of the circle is (-3, -1). The new center of the new circle is (-3, -5). The new equation of the circle is:

(x -3)² + (y - 5)² = 10².

With a circle's center and radius, one may mathematically describe a circle using the equation of a circle. A circle's equation is distinct from the formulae used to determine a circle's area or circumference. Many circles-related coordinate geometry issues employ this equation. We require the circle's equation in order to represent a circle on the Cartesian plane. If we are aware of the radius's length and the circle's centre, we can draw a circle on a sheet of paper. The same is true for drawing circles on a Cartesian plane if we are aware of the center's and radius's coordinates.

The general equation of the circle is given as:

(x - h)² + (y - k)² = r²

Where, h and k are the coordinates of the center.

The given equation is (x -3)² + (y - 1)² = 10²

The center is (-3, -1).

Given that, the circle is shifted 4 up.

The y-coordinate is:

y - (1 + 4) = y - 5

Thus, the new equation of the circle is:

(x -3)² + (y - 5)² = 10²

The new center of the new circle is (-3, -5).

Hence, the center of the circle is (-3, -1). The new center of the new circle is (-3, -5). The new equation of the circle is:

(x -3)² + (y - 5)² = 10²

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Answer:

(-8,5)(-1,-2)(1,-4)

Step-by-step explanation:Glad I could help

Answer:

Step-by-step explanation:

It's 1/(-x-1) my guy. To find the reciprocal of anything, you put that whole thing as a denominator with 1 as the numerator.

Hope this helps *fire emoji*

The calculated value of the price per quart of the laundry detergent is $1.25.

To find the price per quart of the laundry detergent, we need to first convert the volume of the container from gallons to quarts.

Since 1 gallon is equal to 4 quarts,

5 gallons will be equal to 20 quarts.

Next, we can calculate the price per quart by dividing the total cost of the container by the total volume in quarts.

Price per quart = Total cost of container / Total volume in quarts

Price per quart = $25 / 20 quarts

Price per quart = $1.25

Therefore, the price per quart of the laundry detergent is $1.25.

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Answer:

Step-by-step explanati

Since both terms are perfect squares, factor using the difference of  squares formula,

a

Answer:

[tex]\large\boxed{\tt f(-3)=26}[/tex]

Step-by-step explanation:

[tex]\textsf{For this problem, we are asked to evalulate the function given the value of x.}[/tex]

[tex]\textsf{Note that because x equals -3, x will equal -3 for all the variables on the right side.}[/tex]

[tex]\large\underline{\textsf{We should have;}}[/tex]

[tex]\tt f(-3)=(-3)^{2}-3(-3)+8[/tex]

[tex]\textsf{Let's start by evaluating the right side of the function.}[/tex]

[tex]\tt f(-3)=(-3 \times -3)+9+8[/tex]

[tex]\textsf{Note that a negative multiplied by a negative equals a positive term.}[/tex]

[tex]\tt f(-3)=9+9+8[/tex]

[tex]\large\boxed{\tt f(-3)=26}[/tex]

[tex]\huge\text{Hey there!}[/tex]

If x = -3

[tex]\mathtt{f(x) = x^2 - 3x + 8}\\\\\\\mathtt{f(x) = -3^2 - 3(-3) + 8}\\\\\\\mathtt{f(x) = -3\times-3 - 3(-3) + 8}\\\\\\\mathtt{f(x) = 9 - (-9) + 8}\\\\\\\mathtt{f(x) = 9 + 9 + 8}\\\\\\\mathtt{f(x) = 18 + 8}\\\\\\\mathtt{f(x) = 26}\\\\\\\\\\\huge\text{Therefore your answer should be:}\\\\\\\huge\boxed{\mathtt{f(x) = 26}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

a. {-2, -1, 0, 1, 2, 3, 4}

b. {-2, -1, 0, 1, 2, 3}

In conclusion, the solution for this question is that Adriana's actual elevation is also approximately 13.3 meters above sea level.

How to solve?

To estimate Adriana's current elevation, we can simply find 80% of the total elevation gain and add it to her starting elevation:

Total elevation gain = 25 3/4 m - (-36.5 m) = 62.25 m

80% of 62.25 m = 0.8 * 62.25 m ≈ 49.8 m

Estimated current elevation = -36.5 m + 49.8 m ≈ 13.3 m

So we estimate that Adriana's current elevation is approximately 13.3 meters above sea level.

To find her actual elevation, we can use the same method but with the actual percentage of completion:

Actual elevation gain = 80% * (25 3/4 m - (-36.5 m)) = 0.8 * 62.25 m = 49.8 m

Actual elevation = -36.5 m + 49.8 m = 13.3 m

Therefore, Adriana's actual elevation is also approximately 13.3 meters above sea level.

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Answer:

Julianne (she owes 25 more than Rosa)

Step-by-step explanation:

Because Rosa owes -0.25 less than Julianne and because if you subtract the two balances  or do keep change flip method it will give you -0.25 meaning that when Julianne owes nothing Rosa still will owe some money (25 cents).

Answer: x=1.09

Step-by-step explanation:

To solve for x, we can take the natural logarithm of both sides of the equation:

ln(e^(3x)) = ln(12)

Using the property of logarithms that ln(e^y) = y, we can simplify the left side to:

3x = ln(12)

Then, we can divide both sides by 3 to solve for x:

x = (1/3)ln(12)

Using a calculator to evaluate ln(12) and round to the nearest hundredth, we get:

x ≈ 1.09

Answer: x=0.83

Step-by-step explanation: buddy was wrong

The second loan option would allow Clarissa to pay the least amount of interest since it has a lower interest rate and a shorter repayment term.

What is simple interest?

Simple Interest (S.I.) is the method of calculating the interest amount for a particular principal amount of money at some rate of interest.

The loan option that would allow Clarissa to pay the least amount of interest would be the one with the lowest interest rate and the shortest repayment term.

If we assume that Clarissa has the option of choosing between two loans, we can compare their interest rates and repayment terms to determine which one would be better for her.

Let's say the first loan has an interest rate of 5% and a repayment term of 5 years, while the second loan has an interest rate of 4% and a repayment term of 4 years.

Using a loan calculator or a financial formula, we can calculate the total amount of interest that Clarissa would pay for each loan. For the first loan, the total interest paid would be:

Total interest = (Loan amount) x (Interest rate) x (Repayment term)

Total interest = 42,500 x 0.05 x 5

Total interest = 10,625

For the second loan, the total interest paid would be:

Total interest = (Loan amount) x (Interest rate) x (Repayment term)

Total interest = 42,500 x 0.04 x 4

Total interest = 6,800

Therefore, the second loan option would allow Clarissa to pay the least amount of interest since it has a lower interest rate and a shorter repayment term.

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Complete Question:

Answer:

r = 4.3

Step-by-step explanation:

10r + 6 = 49

subtract 6 from both sides:

10r = 43

divide both sides by 10:

r = 4.3

Answer:

R=4.3 or 43/10

Step-by-step explanation:

10r + 6 - 6 = 49 - 6  subtract 6 from each side of equation

10r = 43

10r/10 = 43/10 divide each side by 10

r = 43/10 or 4.3 or 4 3/10 as mixed number