Dane is using two differently sized water pumps to clean up flooded water. The larger pump can remove the water alone in 240 min240min240, start text, m, i, n, end text. The smaller pump can remove the water alone in 400 min400min400, start text, m, i, n, end text. How long would it take the pumps to remove the water working together?

The measure of the angle MSP, m∠MSP, obtained using the relationship between linear pair angles is 80°

Linear pair angles are angles that have a sum of 180°. Linear pair angles come together to form a straight line.

The specified measure of the angle NSM is m∠NSM = 100°

The angles ∠NSM and ∠MSP are linear pair angles therefore;

m∠NSM + m∠MSP = 180°

Plugging in the known value of the angle NSM, we get;

100° + m∠MSP = 180°

Therefore; m∠MSP = 180° - 100° = 80°

The measure of the angle MSP, m∠MSP is 80°

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Rewriting 11,000,000 as a power of 10 using scientific notation is: 1.1 * 10⁷

A number is written in scientific notation whenever a number between 1 and 10 is multiplied by a power of 10. For example, 650,000,000 can be written in scientific notation as 6.5 * 10^8.

Now, we want to write the number 11000000 as a power of 10. Using the concept of scientific notation, we have:

11000000 = 1.1 * 10⁷

That is the final expression of the given number as a power of 10

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Answer:

In geometry, congruent segments are segments that have the same length. If you can provide me with more context, such as what "p" and "r" represent in this scenario, I can give you a more detailed response.

Step-by-step explanation:

The coordinates for the image after the translation of EFG would be E'(-2, 3), F'(-4, 0), and G'(-1, -2).

To translate a point, you simply add or subtract the specified units from its x and y coordinates. In this case, you are asked to translate the points 3 units left and 1 unit down.

To translate 3 units left, subtract 3 from the x-coordinate, and to translate 1 unit down, subtract 1 from the y-coordinate.

For point E (1, 4):

E' = (1 - 3, 4 - 1) = (-2, 3)

For point F (-1, 1):

F' = (-1 - 3, 1 - 1) = (-4, 0)

For point G (2, -1):

G' = (2 - 3, -1 - 1) = (-1, -2)

The translated points are E'(-2, 3), F'(-4, 0), and G'(-1, -2).

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Answer:

(d + 1) (2d + 9)

Step-by-step explanation:

2d² + 11d + 9

First, we rewrite 11d as 2d + 9d, we have the equation:

2d² + 2d + 9d + 9

We group them, so the equation will be

(2d² + 2d) + (9d + 9)

Factor out the GCF of each group

2d (d + 1) + 9 (d + 1)

Factor the polynomial by factoring out the greatest common factor, d+1

(d + 1) (2d + 9)

So, the answer is (d + 1) (2d + 9)

Answer: in2

Step-by-step explanation:

answerd

Buying bulk topsoil is less expensive than buying bags of topsoil in this case.

Volume is a measure of the amount of space occupied by a three-dimensional object. It is typically measured in cubic units, such as cubic meters (m³), cubic centimeters (cm³), or cubic feet (ft³).

To find the volume of a simple object such as a cube, rectangular prism, or cylinder, you can use a formula that involves multiplying the length, width, and height of the object. For example, the formula for the volume of a rectangular prism is V = lwh, where V is the volume, l is the length, w is the width, and h is the height.

For more complex objects, such as irregular shapes or those with curved surfaces, you can use techniques such as integration or approximation to find the volume.

First, we need to determine how many cubic feet of topsoil Austin needs to cover his backyard with a 4 inch layer. We can start by calculating the volume of his backyard in cubic feet:

Volume = length x width x depth

Volume = 70 ft x 60 ft x (4 in / 12) ft

Volume = 1400 ft³

So Austin needs 1400 cubic feet of topsoil to cover his backyard with a 4 inch layer.

Option 1: Bags of Topsoil

Each bag of topsoil covers 3 cubic feet, so Austin needs 1400 / 3 = 466.67 bags of topsoil. Since he can only buy whole bags, he will need to buy 467 bags. Each bag costs $2.50, so the total cost of the topsoil would be:

Total cost = number of bags x cost per bag

Total cost = 467 x $2.50

Total cost = $1167.50

Since delivery is free, the total cost of the topsoil is $1167.50.

Option 2: Bulk Topsoil

Bulk topsoil costs $22.00 per cubic yard, and Austin needs 1400 / 27 = 51.85 cubic yards. Since he can only buy whole yards, he will need to buy 52 yards. The cost of the topsoil itself would be:

Cost of topsoil = volume of topsoil x cost per cubic yard

Cost of topsoil = 52 yd³ x $22.00/yd³

Cost of topsoil = $1144.00

There is also a $20 delivery fee, so the total cost of the topsoil would be:

Total cost = cost of topsoil + delivery fee

Total cost = $1144.00 + $20.00

Total cost = $1164.00

Therefore, buying bulk topsoil is less expensive than buying bags of topsoil in this case.

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The given linear equation in slope intercept form is y = -1/4(x) - 2/7.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + c

Where:

By making "y" the subject of formula, we have the following:

1/4x + y = -2/7

y = -1/4(x) - 2/7

By comparison, we have the following:

Slope, m = -1/4.

y-intercept, c = -2/7.

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100% of the number is 100 times X.

A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.

If 10% of a number is X,

0.1 * number = X

number = X / 0.1

number = 10 * X

As a result, if X represents 10% of a number, the whole number is 10 times X. To get 100% of the answer, simply multiply X by 10 again:

100% of the number = 10 * X * 10 = 100 * X

So, 100% of the number is 100 times X.

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The equivalent expression for 6r in terms of s is 20s, which we obtain by substituting the value of r from the given equation and simplifying.

The given equation, r = (10/3)s, shows that there is a proportional relationship between the variables r and s. This means that when one variable changes, the other variable changes in direct proportion to it. In other words, if we increase r by a certain factor, s will increase by the same factor, and vice versa.

To find an expression that is equivalent to 6r, we can substitute the value of r from the given equation and simplify.

r = (10/3)s (given equation)

6r = 6(10/3)s (substitute 6r for r in the equation)

6r = 20s (simplify by multiplying 6 and 10/3)

Therefore, the expression that is equivalent to 6r in terms of s is 20s. This means that if we know the value of s, we can use this expression to find the value of 6r in a proportional relationship. For example, if s = 2, then 6r = 20s = 20(2) = 40.

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Answer:

e = - [tex]\frac{1}{2}[/tex] q + [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

- 12e = 6q - 4 ( divide through by - 12 )

e = [tex]\frac{6}{-12}[/tex] q - [tex]\frac{4}{-12}[/tex] , that is

e = - [tex]\frac{1}{2}[/tex] q + [tex]\frac{1}{3}[/tex]

Answer:

Step-by-step explanation:

The problem shows a 90° angle split by a ray, we know that both angles are equal to 90° because the whole is equal to the sum of its parts therefore adding 6b+7 and 7b-8 gives us 90° which is simplified as

13b°-1°= 90°

add 1  to both sides

13b°-1° + 1° = 90° +1°

13b° = 91°

divide by 13

13b°/13 = 91°/13

b= 7°

The solution is, 5.4 × 10⁻³ is the number in scientific notation.

Given:

The signal from a certain satellite takes approximately 0.0054 seconds to reach earth.

we will write the number in a scientific notation

The scientific notation is the number that is between 1 and 9 multiplied by 10 raised to an exponent

So, the given number will be:

0.0054

=54/10000

=54/10 * 1/1000

=5.4 × 10⁻³

Hence, The solution is, 5.4 × 10⁻³ is the number in scientific notation.

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As a result, the function's slope at [1, pi/2] is [-24] as where the derivative of y with respect to x is denoted by y'.

The slope of a line in mathematics serves as a gauge for how steep it is. Between any two locations on the line, it is the proportion of the shift in the vertical motion (y) to the shift in the horizontal position (x). If we take into account two points on a line, (x1, y1) and (x2, y2), we can use the following formula to get the slope of the line: slope equals (y2 - y1)/. (x2 - x1) . Depending on the line's direction, the inclination can be zero, positive, or negative. A line with a positive slope is moving upward from left to right, whereas one with a negative slope is moving downward.

given

Finding the derivative of the given function with respect to x can be our first step. By applying the quotient rule, we get:

F(x) = 8x 3 sin (y)

[tex][(sin(y))(-24x2)] = f'(x) - (-8x^3) (cos(y))(y')] / (sin(y))^2[/tex]

where the derivative of y with respect to x is denoted by y'.

We can change x=1 and y=pi/2 in the equation above since we are interested in the slope at the position [1, pi/2].

Due to the fact that cos(pi/2) = 0 and sin(pi/2) = 1, we can write:

[tex]f'(1) = [(1)(-24) (-24) - (-8)(1)(0)(y')] / (1)^2[/tex]

f'(1) = -24 + 0

f'(1) = -24

As a result, the function's slope at [1, pi/2] is [-24] as where the derivative of y with respect to x is denoted by y'.

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The volume of the rectangular prism for the given dimensions length , width , and the height is equal to 168 cubic inches.

Dimensions of the rectangular prism is equal to,

length of the rectangular prism = 12 inches

width of the rectangular prism = 8 inches

height of the rectangular prism = 1.75 inches

The formula for the volume of a rectangular prism is equal to,

Volume of the rectangular prism = length x width x height

Plugging in the given values of the dimensions , we have,

⇒ Volume of the rectangular prism  = 12 inches x 8 inches x 1.75 inches

Simplifying this expression to get the volume of rectangular prism, we get,

⇒ Volume of the rectangular prism = 168 cubic inches

Therefore, the volume of the rectangular prism is 168 cubic inches.

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Answer: 50

Step-by-step explanation
One method to estimate the number of fish in the pond is to use the mark-and-recapture method. This method assumes that the proportion of marked fish in the second sample is the same as the proportion of marked fish in the entire population. Using this assumption, we can estimate the total number of fish in the pond as follows:

Let N be the total number of fish in the pond.

Let M be the number of fish caught in the first sample (50 fish).

Let R be the number of marked fish caught in the second sample (8 fish).

Let r be the unknown total number of marked fish in the pond.

According to the mark-and-recapture method, we have the following proportion:

M/N = R/r

We can rearrange this equation to solve for N:

N = M * r / R

Substituting the values given in the problem, we have:

N = 50 * r / 8

Simplifying, we get:

N = 6.25 * r

This means that the estimated total number of fish in the pond is 6.25 times the number of marked fish in the second sample. Since we know that 8 fish were marked in the second sample, the estimate for the total number of fish in the pond is:

N = 6.25 * 8 = 50

Therefore, the estimated number of fish in the pond is 50

The length of the side w is 55mm. Option C

Note that the different trigonometric identities are;

From the triangle shown, we have;

x = 45mm

z = 80mm

We also have tangent where the star is located is 1

Then,

tan θ = 1

find the tangent inverse of the values

θ = 45 degrees

As given in the diagram, the diagrams are similar

So both angles are 45 degrees

However, we can deduce that since the angles are equal, then, the sides are equal

x = w = 55mm

w = 55mmm

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The equation that represents your balance after x years is: [tex]250 * (1.0725)^x[/tex]

what is interest ?

To calculate simple interest, multiply the principal by the rate of interest rates, the duration, and several other variables. The marketing formula is simple returns = capital + interests + hours.

Initial Value (a): $250

Rate (r): 7.25% per year (or 0.0725 as a decimal)

Time (x): x years

The formula for calculating the balance after x years is:

[tex]Balance = a * (1 + r)^x[/tex]

Plugging in the values, we get:

[tex]Balance = 250 * (1 + 0.0725)^x[/tex]

So the equation that represents your balance after x years is:

[tex]Balance = 250 * (1.0725)^x[/tex]

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The mean and standard deviation of a sampling distribution of sample means with sample size 249 are 71 and approximately 1.267 respectively when the population has a mean of 71 and standard deviation of 20.

We know that, if the population has mean [tex]=\mu[/tex] and standard deviation [tex]=\sigma[/tex] and if the sampling distribution has sample size of n then

mean of the sampling distribution will be [tex](\mu_{\bar{x}})=\mu[/tex]

and the standard deviation of sampling distribution will be [tex](\sigma_{\bar{x}})=\frac{\sigma}{\sqrt{n}}[/tex]

Here in this problem,

Mean of the population [tex](\mu)[/tex] = 71

Standard Deviation of the population [tex](\sigma)[/tex] = 20

And the sample size of the sampling distribution (n) = 249

So, the mean of sampling distribution [tex](\mu_{\bar{x}})=\mu[/tex] = 71

Standard Deviation of sampling distribution [tex](\sigma_{\bar{x}})=\frac{\sigma}{\sqrt{n}}=\frac{20}{\sqrt{249}} \approx 1.267[/tex] (Correct up to three decimal places)

Hence, the mean and standard deviation of the sampling distribution of sample means with sample size 249 are 71 and 1.267 (approximately) respectively.

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Juliana and Brody hiked a total distance of 6 1/2 miles, which is the sum of the distances of the two trails they hiked 3 2/3 miles and 2 5/6 miles.

To find the total distance hiked by Juliana and Brody, we need to add the distances of the two trails they hiked.

3 2/3 + 2 5/6 can be written as a common fraction by finding the least common multiple (LCM) of the denominators, which is 6.

3 2/3 can be written as 11/3, and 2 5/6 can be written as 17/6.

So, 3 2/3 + 2 5/6 = 11/3 + 17/6

We need to find a common denominator, which is 6

11/3 + 17/6 = 22/6 + 17/6

Adding the two fractions, we get

22/6 + 17/6 = 39/6

Simplifying the fraction, we get

39/6 = 6 3/6

Therefore, Juliana and Brody hiked a total distance of 6 3/6 or 6 1/2 miles.

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An equation that expresses the relationship between the lengths of the three sides is a^2 + b^2 = c^2.

In a right triangle, the side opposite the right angle is called the hypotenuse, while the other two sides are called the legs.

The relationship between the lengths of the three sides in a right triangle is described by the Pythagorean Theorem, which states that the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse.

Mathematically, this can be represented as:

a^2 + b^2 = c^2

where a and b are the lengths of the legs, and c is the length of the hypotenuse.

For the given right triangle with lengths 5, 2.2360679775, and 5.47722557505, we can plug in the values of a, b, and c to get:

5^2 + 2.2360679775^2 = 5.47722557505^2

which simplifies to:

25 + 5 = 30

This equation is true, indicating that the given lengths do indeed form a right triangle according to the Pythagorean Theorem.

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The height of the cuboid is 14cm.

What is the perimeter?

A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter. There are numerous uses in real life for perimeter calculations.

Here, we have

Given: Joe has 784 one-centimeter cubes.

He arranges all of the cubes into a cuboid.

The perimeter of the top of the cuboid is 30 cm.

Each side of the cuboid has a length greater than 2 cm.

We have to find the height of the cuboid.

1. a = 7, b = 8

V = 784

We know that

height = V/s

h = 784/56

h = 14cm

Hence, the height of the cuboid is 14cm.

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The area of the polygon containing the given triangle and rectangle is 45 square units.

What exactly is a rectangle?

A rectangle is a quadrilateral having four straight sides, four right angles, and parallel and equal-length opposing sides. A rectangle's opposing sides are also congruent, which implies they have the same length.

The formula A = lw gives the area of a rectangle, where A is the area, l is the length, and w is the width. A rectangle's perimeter is determined by the formula P = 2l + 2w, where P is the perimeter.

Now,

To find the area of the polygon containing the triangle and rectangle, we need to find the individual areas of the triangle and rectangle, and then add them together.

The area of a triangle

A = (1/2)bh

where b= base and h = height. Substituting the given values, we get:

A_triangle = (1/2)(9)(6) = 27 square units

The area of a rectangle is

A = lw

where l = length and w = width. Substituting the given values, we get:

A_rectangle = (9)(2) = 18 square units

Therefore, the total area of the polygon is:

A_polygon = A_triangle + A_rectangle

A_polygon = 27 + 18

A_polygon = 45 square units

Therefore, the area of the polygon containing the given triangle and rectangle is 45 square units.

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Answer:

parallelogram and rectangle

Step-by-step explanation:
the shape can’t be a rhombus or a square, because all sides of it are not the same length. it’s a parallelogram, because all 4 sides are parallel to each other, and it’s a rectangle, because it’s a parallelogram and all of its sides aren’t equal.

Kira will be paid $120 in interest in the first two years.

Simple interest is expressed as;

I = P × r × t

Where I is the interest, P is the principal amount, r is the interest rate per year, and t is the time in years.

Given that:

Substituting the given values, we get:

I = P × r × t

I = 2000 × 0.03 × 2

I = $120

Therefore, the interest in the first two years is $120.

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The number of Americans experience hearing loss sufficient to affect communication is: 1 in 4.

According to the National Institute on Deafness and Other Communication Disorders (NIDCD).

Approximately 1 in 4 adults in the United States aged 65 and older have hearing loss that is sufficient to affect communication.

This is based on data from a survey conducted by the NIDCD and the National Health Interview Survey.

NIDCD (National Institute on Deafness and Other Communication Disorders).

In the United States, 1 in 4 persons 65 and older suffer hearing loss severe enough to impair conversation.

This is based on information from surveys done by the National Health Interview Survey and the NIDCD.

The number of Americans who experience hearing loss sufficient to affect communication is: 1 in 4.

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The evaluated probability for chances of  randomly selecting an employee who will  have a starting salary of at least $31,000 is 11.51%. Here, we have to depend on the principles of standard normal distribution to find the percentage of probability,


Let us take  z-score for a starting salary of $31,000 as

z = (31000 - 25000) / 5000
= 1.2

Now after using a standard normal distribution table , the probability of a z-score of 1.2 or greater is approximately 0.1151
Converting it into percentage
0.1151 x 100
= 11.51%
The evaluated probability for chances of  randomly selecting an employee who will  have a starting salary of at least $31,000 is 11.51%.

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1. ∠B is the primage of ∠B'. They are similar triangles.

2. AC ≈AC'

CB ≈ CB'

AB ≈ AB'

When discussing angles, the preimage refers to the original angle before any transformation has occurred.

In geometry, a transformation refers to the process of moving or changing the position, shape, or size of an object. For example, if an angle is rotated or reflected, the resulting image of the angle would be the transformed angle.

The preimage is the angle before the transformation occurred. It is used to determine the relationship between the original angle and the transformed angle, such as whether they are congruent, similar, or related by another geometric property.

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