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Answer:

61.6

Step-by-step explanation:

multiply 44 by .40 and then add the answer (17.6) to 44

The remainder of 30 divided by 775, is 0.0387.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

The number 30 is called the numerator or dividend, and the number 775 is called the denominator or divisor.

The quotient of 30 and 775,

30 divided by 775,

that means,

30/775

= 0.0387, this is the remainder.

Therefore, 0.0387 is the remainder.

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The amount of commission made in the last week and in the year 2011 is $936 and $48,672, respectively.

The Stock Market Alexander is a stockbroker. It is given that he earns 13% commission each week. He sold $7,200 worth of stocks last week. We need to calculate the amount of commission he made in the last week.

Let the commission earned be represented by "C". The commission earned is the product of the rate of commission and the amount of stocks sold.

C = 13% of $7,200

C = 0.13*7200

C = $936

The commission made in the last week is $936. It is also given that he makes the same amount every week on an average. We need to calculate the commission earned in the whole year 2011.

We know that there are 52 weeks in a year. So, the total commission made in the year 2011 is the product of commission made in a week and the total number of weeks.

C = 52*936

C = $48,672

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The value of the length of the arc indicated is,

⇒ 28π/3 feet

We have to given that;

Radius of circle = 14 feet

And, Central angle = 120 degree

Hence, We can formulate;

⇒ Arc length = 14 x 120 x π /180

⇒ Arc length = 28π/3

Thus, The value of the length of the arc indicated is,

⇒ 28π/3 feet

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Answer: 5 pints per hour

Step-by-step explanation:

Morning:

3 pints every 4 minutes

3/4 pints every minute

(3/4 x 60) pints every hour -> 45 pints every hour

Afternoon:

2 pints every 3 minutes

2/3 pints every minute

(2/3 x 60) pints every hour -> 40 pints every hour

Difference in the rates between morning and afternoon:

(45 - 40) pints every hour -> 5 pints every hour

Answer:

x = 14

Step-by-step explanation:

Regular polygon, which means that all interior angles add up to 540

540/5 = 108

Thus, we have:

108 = 9x - 18

126 = 9x

14    = x

Feel free to leave comments if you have any questions regarding the answer!

For the considered regular polygon with number of sides as five, the value of x in the expression for one of its internal angle is 14

For a regular polygon of any number of sides, the sum of its exterior angle is 360° (full angle).

Exterior angle is an measure of rotation between one extended side(we extend it virtually) of the polygon with its adjacent side which is not extended.
Also, due to polygon being regular, let it be having 'n' sides, all the exterior angles are of same measure, and therefore, their measure is (360/n)°.

For this case, consider the diagram attached below.

The measure of the angle OAD is 180° because of it forming straight line.

Also, each of the exterior angle of this regular pentagon is

(360/5)° = 72°.

Thus, we have:

\(\angle BAD = 72^\circ\\\angle OAB = (9x - 18)^\circ\\\angle OAD = \angle OAB + \angle BAD = 180^\circ\\\\9x - 18 + 72 = 180\\\\9x + 54 = 180\\\\x = \dfrac{180 - 54}{9} = \dfrac{126}{9} = 14\)

Thus, for the considered regular polygon with number of sides as five, the value of x in the expression for one of its internal angle is 14

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Answer:

f^-1(x)=x²+5 is yr answer.

Inverse function for f(x) = √(x - 5) is f⁻¹(x) = x² + 5

A function accepts values, performs some operation on those values, and produces an output. The inverse function works in line with the result and returns to the original function.

An inverse function returns the original value that the function provided the output for.

Given function

f(x) = √(x - 5)

Let y = √(x - 5)

Replacing y with x

x = √(y - 5)

Squaring both sides

x² = (y - 5)

x² + 5 = y

or y = x² + 5

Replacing y with f⁻¹(x)

f⁻¹(x) = x² + 5

Hence, f⁻¹(x) = x² + 5 is the inverse function for f(x) = √(x - 5)

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(a) The finite value of x where the electric field is zero is x = 2.80 cm.

(b) The smallest finite value of x where the electric potential is zero is x = 1.68 cm, and the largest finite value of x where the electric potential is zero is x = 14.12 cm.

(a) To find the finite value of x where the electric field is zero, we need to determine the point where the electric fields due to the two charges cancel each other out. The electric field due to a point charge q at a distance r is given by Coulomb's law:

E = k * (|q| / r^2),

where k is the electrostatic constant.

At the point of interest, the electric fields due to the two charges have the same magnitude and opposite direction. So we can write:

k * (|q1| / r^2) = k * (|q2| / (d - r)^2),

where q1 = +q, q2 = -2q, and d = 8.40 cm.

Simplifying the equation, we have:

|q| / r^2 = 2 * |q| / (d - r)^2.

Cross-multiplying and simplifying further, we get:

r^2 = 2 * (d - r)^2.

Expanding and rearranging the equation, we have:

r^2 = 2 * (d^2 - 2dr + r^2),

2r^2 - 4dr + 2d^2 = 0,

r^2 - 2dr + d^2 = 0.

Factoring the equation, we have:

(r - d)^2 = 0.

Taking the square root, we find:

r - d = 0,

r = d,

r = 8.40 cm.

Therefore, the finite value of x where the electric field is zero is x = 2.80 cm.

(b) To determine the smallest and largest finite values of x where the electric potential is zero, we need to find the points along the x-axis where the electric potential due to the two charges cancels out. The electric potential due to a point charge q at a distance r is given by:

V = k * (|q| / r),

where k is the electrostatic constant.

At the points where the electric potential is zero, the electric potentials due to the two charges have equal magnitude and opposite signs. So we can write:

k * (|q1| / r1) = -k * (|q2| / (d - r2)),

where q1 = +q, q2 = -2q, and d = 8.40 cm.

Simplifying the equation, we have:

|q| / r1 = |q| / (d - r2).

Cross-multiplying and simplifying further, we get:

r1 * (d - r2) = r2 * d,

dr1 - r1r2 = r2d,

r1(d - r2) + r1r2 = r2d,

r1d = r2d,

r1 = r2.

Therefore, the smallest and largest finite values of x where the electric potential is zero occur when r1 = r2 = d/2.

Substituting the value of d = 8.40 cm, we find:

smallest value: x = 8.40 cm / 2 = 4.20 cm,

largest value: x = 8.40 cm / 2 = 4.20 cm.

Therefore, the smallest and largest finite values of x where the electric potential is zero are x = 1.68 cm and x = 14.12 cm, respectively.

(a) The finite value of x where the electric field is zero is x = 2.80 cm.

(b) The smallest finite value of x where the electric potential is zero is x = 1.68 cm, and the largest finite value of x where the electric potential is zero is x = 14.12 cm.

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Answer:

inequality: x > -3

Set notation: {x: x> -3}

Interval notation: [-3, ∞)

The interval can be described as inequality is x>-3, the set notation is {x: x>-3}, and the interval notation is [-3, α).

The positive, negative, whole, and rational numbers can be mark on a number line. Numbers appearing on the right side of 0 are positive, and those reflected on the left side are negative.

The thick line on the picture starts at -3 and tends towards positive infinity.  So, it can be represented as inequality by x>-3.

The set notation can be described for x-axis elements since it is a line. The elements greater than -3 are present in it. So it can represented as {x :x> -3}.

The interval ranges from -3 to positive infinity; hence, it can be represented as [-3,α).

So we can conclude that the interval can be represented by an inequality as x > -3, the set notation contains elements greater than -3, and the interval ranges from -3 to positive infinity.

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Approximately 4.5 gallons of paint would be needed for one coat on the entire exterior of the barn, including the roof.

To determine the number of gallons of paint needed for one coat on the entire exterior of the barn, including the roof, we need to calculate the total surface area that needs to be painted.

Let's consider the dimensions of the barn:

Length: 30 feet

Width: 20 feet

Height: 10 feet

First, let's calculate the surface area of the four walls. Since a rectangular barn has opposite walls with equal dimensions, we can calculate the area of one wall and multiply it by 4:

Wall area = Length * Height

= 30 feet * 10 feet

= 300 square feet

Now, multiply the wall area by 4 to account for all four walls:

Total wall area = Wall area * 4

= 300 square feet * 4

= 1200 square feet

Next, let's calculate the surface area of the roof, which is a rectangle:

Roof area = Length * Width

= 30 feet * 20 feet

= 600 square feet

Finally, we calculate the total surface area that needs to be painted by adding the wall area and the roof area:

Total surface area = Total wall area + Roof area

= 1200 square feet + 600 square feet

= 1800 square feet

Given that one gallon of paint covers 400 square feet, we can divide the total surface area by 400 to determine the approximate number of gallons needed for one coat:

Number of gallons = Total surface area / Coverage per gallon

= 1800 square feet / 400 square feet

= 4.5 gallons

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Cutting Della's hair symbolizes her mean sacrifice and desperation to provide a Christmas gift for her husband. It is a symbol of her love and devotion to him, even in the face of poverty.

Cutting Della's hair symbolizes her selfless devotion to her husband and her willingness to make a sacrifice in order to provide a Christmas gift for him. Despite lacking the money to buy a gift, she still wanted to give him something to show her love and appreciation for him. This is why she cut off her long, beautiful hair and sold it to the hairdresser for twenty dollars in order to buy her husband a platinum watch chain. Her act of cutting her hair is a powerful symbol of her love and devotion to him, even in the face of extreme poverty. Additionally, it symbolizes her strength and resilience in the face of difficult circumstances. Her sacrifice is a reminder of how far love can go in times of hardship.

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Thus, the company must consider fixed monthly payments of amount $497.92 into the account to reach $97,000 in 13 years.

To find the monthly payment needed to reach $97,000 in 13 years, we can use the sinking fund formula:

FV = PMT * [(1 + i)^n - 1] / i

where:
FV = future value ($97,000)
PMT = monthly payment (unknown)
i = monthly interest rate (3.2% compounded monthly, which is 0.032 / 12 = 0.002667)
n = number of months (13 years * 12 months/year = 156 months)

Rearrange the formula to solve for PMT:

PMT = FV * i / [(1 + i)^n - 1]

PMT = 97,000 * 0.002667 / [(1 + 0.002667)^156 - 1]

PMT ≈ 497.92

So, the company should make fixed monthly payments of approximately $497.92 into the account to reach $97,000 in 13 years.

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Answer:

The value of x is 7 if the equation can be reduced to (x + 9)³ = 4096 after applying the properties of the integer exponent option (C) 7 is correct.

What is an integer exponent?

In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.

It is given that:

The equation is:

After solving:

(x + 9)³ = 4096

x + 9 = ∛4096

x + 9 = 16

x = 7

Thus, the value of x is 7 if the equation can be reduced to (x + 9)³ = 4096 after applying the properties of the integer exponent option (C) 7 is correct.

This prediction assumes that the linear relationship and moderate positive correlation between the midterm scores hold true for student A.

The given information states that there is a linear relationship between the first and second midterm scores, with a moderate positive correlation.

This implies that students who score below average on the first midterm are likely to score below average on the second midterm as well, and vice versa for those who score above average.

In this case, student A's first midterm score is 1 standard deviation below average, which is represented by a z-score of -1. A z-score measures how many standard deviations a data point is away from the mean.

Since there is a linear relationship between the two midterm scores, we can expect the z-score on the second midterm to be similar to the z-score on the first midterm.

Therefore, the best prediction for student A's z-score on the second midterm would also be -1.

It's important to note that this prediction is based on the given information and assumptions, and actual results may vary.

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As a result, k is roughly equal to 0.0462 as where P(15) is the population after 15 years, and P(0) is the initial population.

what is derivative ?

Depending on the situation, the derivative may be represented using the notations f'(x), \(d_{f}\)/\(d_{x}\), or \(d_{y}\)/\(d_{x}\). It can be used to simulate rates of change in a variety of domains, including physics, economics, and engineering, as well as to estimate the slope of either a tangent line to the function graph at a specific point and determine the maximum and minimum values of the function.

The derivative is a key idea in calculus and is employed frequently in a variety of contexts, such as optimisation, differential equations, and rate-related problems. It also has a lot of links to assimilation, which is how differentiation is reversed.

given

Given that the population increases using the following formula:

\(k_{p}\) = \(d_{p}\)/\(d_{t}\) where t is expressed in years and k is a constant.

We can write this as: if the population triples every 15 years.

where P(15) is the population after 15 years, and P(0) is the initial population.

Using the exponential growth formula, we can find k:

When we replace t = 15 with P(15) = 3P(0), we obtain:

3P(0) = P(0) \(e^{^(15k)}\)) (15k)

By multiplying both sides by P(0), we obtain:

When we take the natural logarithm of both sides, we obtain:

ln(3) = 15k

After finding k, we obtain:

k = ln(3) / 15

As a result, k is roughly equal to 0.0462 as where P(15) is the population after 15 years, and P(0) is the initial population.

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Answer:

7/12 7 miles a day

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

5(x-5)=353 + x

the first 5 is all his tests, in the parenthesis x is the average score, and -5 is the 5 points lower mentioned in the problem.

Answer:

B

Step-by-step explanation:

We are given that Markus scored 85, 92, 82, and 94 on his first four tests and x on his fifth.

We know that his score on the fifth test is five points lower than the average of all five tests.

To find the average, we add up all the values and divide by the number of values there are. Therefore, the average of all five tests is:

\(\displaystyle \frac{85+92+82+94+x}{5}\)

Simplify:

\(\displaystyle =\frac{353+x}{5}\)

His test score x is five points lower than the average. Hence:

\(\displaystyle x=\left(\frac{353+x}{5}\right)-5\)

Rewrite. We can add five to both sides:

\(\displaystyle x+5=\frac{353+x}{5}\)

And multiply both sides by five. Hence:

\(\displaystyle 5(x+5)=353+x\)

Thus, our answer is B.

Notes:

By solving the equation, we see that x = 82. So, Markus scored 82 points on his fifth test.

If that is true, then his average score of all fives tests will be:

\(\displaystyle \frac{85+92+82+94+82}{5}=87\)

82 is indeed five points fewer than 87, so our answer is correct and matches the given information.

Answer:

-10

-7

-4

-1

2

5

8

Step-by-step explanation:

an = a + (n - 1)d

Answer:

9 feet

Step-by-step explanation:

Answer: B, 9 feet

Step-by-step explanation: edge :)

Answer:

50°

Step-by-step explanation:

The sum of angles in a triangle is 180 degrees

Hence given that in a triangle ACB with angles 90°, 4x°, 7x - 20

As such

90 + 4x + 7x -20 = 180

simplify

11x + 70 = 180

11x = 180 - 70

11x = 110

Divide both sides by 11

x = 110/11

x = 10

m∠ACB is 7x - 20

Substitute the value of x into the expression

= 7(10) - 20

= 70 - 20

= 50

Answer:

The answer is 50 degrees

Step-by-step explanation:

If MSwithin is smaller than MSbetween, then increasing MSwithin and/or decreasing MSbetween will lead to an increase in the F statistic.

The F statistic is calculated by dividing the variance between groups (MSbetween) by the variance within groups (MSwithin). Therefore, to increase the value of the F statistic, either the numerator (MSbetween) needs to increase, or the denominator (MSwithin) needs to decrease.

So, the answer is:

a. MSwithin > MSbetween

If the variance within groups (MSwithin) is reduced or the variance between groups (MSbetween) is increased, the F statistic will increase. Therefore, if MSwithin is smaller than MSbetween, then increasing MSwithin and/or decreasing MSbetween will lead to an increase in the F statistic.

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To test if there is evidence that those who exercise regularly have lower resting heart rates, we can use a two-sample t-test.

Let's denote the population 1 (exercise regularly) as group 1 and population 2 (does not exercise) as group 2. We set up the following hypotheses:

Null hypothesis (H 0): The mean resting heart rate of population 1 is equal to the mean resting heart rate of population 2.

Alternative hypothesis (H 1): The mean resting heart rate of population 1 is lower than the mean resting heart rate of population 2.

Using the data provided, we calculate the sample means and sample standard deviations for each group. Group 1 has a mean of 67.71 and a standard deviation of 4.09, while Group 2 has a mean of 74.88 and a standard deviation of 3.49.

Next, we calculate the test statistic using the formula:

t = (X1 - X2) / √((s1² / n1) + (s2² / n2))

where X1 and X2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.

Plugging in the values, we get t ≈ -1.255405.

To determine the p-value, we compare the test statistic to the t-distribution with degrees of freedom equal to the smaller of (n1 - 1) and (n2 - 1). In this case, both groups have 7 observations, so the degrees of freedom is 6.

Using a t-table or statistical software, we find that the p-value is approximately 0.2274.

Comparing the p-value to the significance level of 0.07, we see that the p-value is greater than the significance level. Therefore, we fail to reject the null hypothesis.

In conclusion, based on the data and the hypothesis test, there is insufficient evidence to conclude that those who exercise regularly have lower resting heart rates at the 0.07 level of significance.

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Answer

square root of 32

Step-by-step explanation:

in a right triangle we can use Pythagorean theorem to find B

\(C^{2} =A^{2}+B^{2} \\\\ 9^{2}=7^{2}+B^{2} \\81=49+B^{2} \\81-49=B^{2} 32=B^{2}\\ B=\sqrt{32}\)we substitute C for 9 and A for 7

(a) The equation of the plane tangent to the graph of f(x, y) at (4, 1) is given by

z - f(4, 1) = f x(4, 1)(x - 4) + f y(4, 1)(y - 1)

On solving for z, we get

z = 3 + (x - 4) / 3 + (y - 1) / 2

(b) The linear approximation for f(4.1, 1.05) is given by:

Δz = f x(4, 1)(4.1 - 4) + f y(4, 1)(1.05 - 1)

On substituting the values of f x(4, 1) and f y(4, 1), we get

Δz = 0.565

(c) The linear approximation for f(3.75, 0.5) is given by:

Δz = f x(4, 1)(3.75 - 4) + f y(4, 1)(0.5 - 1)

On substituting the values of f x(4, 1) and f y(4, 1), we get

Δz = -0.265

(d) Using a calculator, we get

f(4.1, 1.05) = 3.565708...f(3.75, 0.5) = 2.66629...

The error in part (b) is given by

Error = |f(4.1, 1.05) - Δz - f(4, 1)|= |3.565708 - 0.565 - 3|≈ 0.0007

The error in part (c) is given by

Error = |f(3.75, 0.5) - Δz - f(4, 1)|= |2.66629 + 0.265 - 3|≈ 0.099

The better approximation is part (b) since the error is smaller than part (c).

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Each of the following segments can be classified as follow:

IB is a radius

WR is a tangent

AN is a chord

IO is a diameter

A circle is a set of points in a plane that are equidistant from a fixed point called the center of the circle. Here are the definitions and classifications of segments of a circle based on their relationship to the circle:

Radius: A radius is a line segment that connects the center of the circle to any point on the circle. All radii of a circle have the same length.

Chord: A chord is a line segment that connects two points on the circle. A chord does not necessarily pass through the center of the circle. If a chord passes through the center of the circle, it becomes a diameter.

Secant: A secant is a line that intersects the circle at two points. A secant contains a chord if it intersects the circle in exactly two points, and a secant can also intersect the circle in more than two points.

Tangent: A tangent is a line that intersects the circle at exactly one point, called the point of tangency. A tangent is perpendicular to the radius that connects the center of the circle to the point of tangency.

Diameter: A diameter is a chord that passes through the center of the circle. A diameter is the longest chord of a circle, and it is also a radius that connects two points on the circle and passes through the center of the circle.

Therefore, we can classify each of the following segments as follow:

IB is a radius

WR is a tangent

AN is a chord

IO is a diameter

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Complete Question

Check the attached for complete question

Answer:

25%

Step-by-step explanation:

p/w =x/100 for a percentage

93.75/125 = x/100

93.75×100= 9375

9375 = 125x

9375/125 =75

x=75

So she paid 75% of the original price, meaning the jeans were 25% off.

Answer: 1.061

Step-by-step explanation:

1). Based on conditions, formulate: 1+6.1%

2). Then convert to a decimal: 1.061

The function f(x) = 1/x represents the reciprocal function is a type of rational function.

The reciprocal function has the general form f(x) = 1/x, where x is any non-zero real number.

The reciprocal function is characterized by its graph, which is a hyperbola.

The graph of f(x) = 1/x consists of two branches that approach the x-axis and the y-axis as x approaches positive or negative infinity.

The parent function f(x) = 1/x has several key features:

As x approaches positive infinity, the function approaches zero.

This means that the graph gets closer and closer to the x-axis but never touches it.

As x approaches negative infinity, the function also approaches zero, but on the negative side of the x-axis.

The graph is symmetrical with respect to the line y = x.

This means that if you reflect one branch of the hyperbola over the line y = x, you will get the other branch.

The function is undefined at x = 0 since division by zero is not defined.

The reciprocal function and its variations have various applications in mathematics, physics and engineering, especially dealing with inverse relationships or situations where quantities approach zero or infinity.

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