Write the equation for the translation of the graph of y = x + 7 one unit to the left.

Therefore , the solution of the given problem of inequality comes out to be the solutions x = -6 or x = -10 would be acceptable.

Algebra, which lacking a symbol for this difference, can represent it using a pair or group of numbers. Equity usually comes after equilibrium. Inequality is bred by the persistent gap of standards. Equality and disparity are not the same thing. As was my least preferred symbol, notwithstanding knowing that the pieces are often not connected or close to one another. (). No matter how small the variations, they all affect value.

Here,

Finding values of x that cause the left side of the inequality to be bigger than the right side is necessary to make the inequality -2x > 10 true. Divide both sides by -2 and invert the inequality sign to achieve this:

=> -2x > 10

=> x < -5

The inequality is therefore true for any value of x that is less than -5. For instance, the solutions x = -6 or x = -10 would be acceptable.

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Evaluating an exponential function A(x) = 160*(1.03)ˣ we can see that in 30 years she will have:

$388.36

We know that the initial investment is 160, and the rate per year is 3%.

Then after x years, the value is given by the exponential function.

A(x) = 160*(1.03)ˣ

The amount of money in the account after 30 years is what we get if we evaluate the equation in x = 30, then we will get:

A(30) = 160*(1.03)³⁰

A(30) = 388.36

In 30 years she will have a total amount of 388.36 dollars.

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Acellus is a powerful tool for students looking to achieve academic success and gain the skills they need to succeed in today's competitive world.

Acellus is an online learning management system designed to provide students with personalized, self-paced education. The system offers a wide range of courses in subjects such as mathematics, science, language arts, and social studies. The courses are designed to be interactive, engaging, and challenging, providing students with a comprehensive education in each subject area.

Acellus utilizes advanced technology to provide students with an adaptive learning experience. The system uses data analytics to track student progress and adapt the coursework to meet the needs of each individual student. This allows students to learn at their own pace, and to receive personalized instruction that is tailored to their specific needs.

In addition to providing high-quality educational content, Acellus also offers a number of other features and tools to support student learning. These include assessments, quizzes, and interactive games, as well as a student dashboard that allows students to track their progress and stay on top of their coursework.

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The rate of change for the water level between Weeks 2 and 3 is: D. 3 7/8.

In Mathematics and Geometry, the gradient, rate of change, or slope of any straight line can be determined by using the following mathematical equation;

Rate of change (slope) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Rate of change (slope) = rise/run

Rate of change (slope) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the formula for the slope of a line, we have the following;

Rate of change (slope) = (y₂ - y₁)/(x₂ - x₁)

Rate of change (slope) = (1 5/8 + 2 1/4)/(3 - 2)

Rate of change (slope) = (13/8 + 9/4)/(1)

Rate of change (slope) = 3 7/8

Based on the table, the rate of change is the change in y-axis with respect to the x-axis and it is equal to 3 7/8.

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Hello!

This shape is a "Strange" shape, but if you look closer at it, you can see that it can be divided into "normal shapes" like rectangles and squares

On the bottom on the "polygon" we can dived it into 2 squares

One square would have the dimensions of 6 and 6

The other one would have 4 and 6

The formula of area is: Base*Height

So the first square would have an area of 36

The second square would have an area of 24

Now we solve for the big rectangle

On first thought, it may seem like the dimensions are 16 and 25, but it is actually 10 and 25. Because 16 is the whole height of the polygon.

So we subtract it by 6

So the big rectangle is 250

=================

Now we add the areas together to get a total result of 310

If you have questions, feel free to ask

Answer:

I think it's 8...

Step-by-step explanation:

8x8 = 64

since each side is the same.

sorry if I'm wrong though-

Answer: 16 cm long

Step-by-step explanation:

Since we already have given the Area of the Square i.e. 64cm²

So, putting values into the Formulae, we get-

Area of the Square = side X side

64 = 8 x 8

since the sides have to be equal because the square has 4 equal sides, we multiply it by 4, it has to be 4 x 4 = 16

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A. 8(p, phi, theta) = 8p sin(phi) cos(theta) / (1 + p^2 + 2p cos(phi))^(3/2)

B. ∫0^(2π) ∫0^π ∫0^1 8p sin(phi) cos(theta) / (1 + p^2 + 2p cos(phi))^(3/2) p^2 sin(phi) dp d(phi) d(theta)

C. the mass of the solid 8 enclosed within the sphere is approximately 8.378.

(a) Using the conversion formulas for spherical coordinates, we have:

x = p sin(phi) cos(theta)
y = p sin(phi) sin(theta)
z = p cos(phi)

Substituting these expressions into the given density function, we get:

8(x, y, z) = 8(p sin(phi) cos(theta), p sin(phi) sin(theta), p cos(phi))
            = 8p sin(phi) cos(theta) / (1 + p^2 + 2p cos(phi))^(3/2)

Therefore, the density 8 as a function of spherical coordinates is:

8(p, phi, theta) = 8p sin(phi) cos(theta) / (1 + p^2 + 2p cos(phi))^(3/2)

(b) Since the solid 8 is enclosed within a sphere of radius 1 centred at 2 the origin, we have:

0 ≤ p ≤ 1
0 ≤ theta ≤ 2π
0 ≤ phi ≤ π

Therefore, the bounds of integration in spherical coordinates are:

∫0^(2π) ∫0^π ∫0^1 8p sin(phi) cos(theta) / (1 + p^2 + 2p cos(phi))^(3/2) p^2 sin(phi) dp d(phi) d(theta)

(c) Evaluating the triple integral using a computer algebra system or numerical integration, we get:

M = 8π/3

Therefore, the mass of the solid 8 enclosed within the sphere is approximately 8.378.

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Jonah's mom's would have to spend $45.878 to fill up her tank after the 40% increase in gas prices if her car takes 14 1/2 gallons of gas to fill up.

To find the cost that Jonah's mom would have to spend after the 40% increase in gas prices to fill up her 14 1/2 gallon tank, we need to follow these steps:

1. Find the increased price per gallon by multiplying last summer's price ($2.26) by 1.40 (since there's a 40% increase): $2.26 x 1.40 = $3.164 per gallon.
2. Convert 14 1/2 gallons to a decimal: 14.5 gallons.
3. Multiply the increased price per gallon ($3.164) by the number of gallons needed to fill up the tank (14.5 gallons): $3.164 x 14.5 = $45.878.

So, after the 40% increase in gas prices, Jonah's mom would have to spend $45.878 to fill up her 14 1/2 gallon tank.

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Option A) Cannot tell with the given information as the question doesn't provide any information about the relationship between having a dog and having a cat.

Without additional information, we cannot determine if these events are independent, dependent, disjoint, or have any other relationship. Independent events are events in which the occurrence or non-occurrence of one event does not affect the occurrence or non-occurrence of the other event.

In other words, the probability of one event happening does not depend on whether or not the other event happens.

Formally, events A and B are independent if and only if:

P(A ∩ B) = P(A) * P(B)

Where P(A) is the probability of event A occurring, P(B) is the probability of event B occurring, and P(A ∩ B) is the probability of both events A and B occurring simultaneously.

If the above equation holds true, then we can say that events A and B are independent. If not, then events A and B are dependent.

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Answer: range=9 mode=3 mean=9

Step-by-step explanation:

The third side that we can not see in the image that is shown has a size of 15.

The hypotenuse of a right triangle can be found using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

If c^2 = a^2 + b^2

c = √a^2 + b^2

c = √12^2 + 9^2

c = 15

Thus the missing side is 15 from the calculation.

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The difference in overall gain is $280.10. OPtion C

We have to first find the gains for Stock A and Stock B at high and low prices:

Stock A:

High price gain: 115 * ($105.19 - $90) = $1,747.85

Low price gain: 115 * ($103.25 - $90) = $1,523.75

Stock B:

High price gain: 30 * ($145.18 - $145) = $5.40

Low price gain: 30 * ($143.28 - $145) = -$51.60

Calculate total gains:

High price total gain: $1,747.85 + $5.40 = $1,753.25

Low price total gain: $1,523.75 + (-$51.60) = $1,472.15

Difference in overall gain: $1,753.25 - $1,472.15 = $280.10

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Based on the given information that angles a and d are equal, the value of x is determined to be -6.

To find the value of x in the given scenario, we can equate the measures of the angles using the given information:

m< a = 3x

m< d = 4x + 6

Since angles a and d are stated to be equal, we can set up the equation:

3x = 4x + 6

To solve for x, we subtract 3x from both sides:

0 = x + 6

Next, we subtract 6 from both sides:

-6 = x

Therefore, the value of x is -6.

In conclusion, based on the given information that angles a and d are equal, the value of x is determined to be -6.

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Answer:

B. ∠FBG

Step-by-step explanation:

When an angle is in the three letter form, the first letter is the first line that forms the angle, the second letter is where the angle is located, and third letter is the line that forms the angle with the first line.

Thus, we can see that line E combines with line F, and the actual angle is located at point B.

The two angles adjacent to ∠EBF are ∠DBE and ∠FBG.  Only ∠FBG is one of the answer choices so this is our final answer.

If Sabina and the pole are proportional, then the pole’s shadow will be 35/4 feet tall.

Since Sabrina is 4 feet tall and casts a 3.5-foot shadow, we can set up a proportion comparing the heights and shadow lengths: Sabrina's height (4 feet) / her shadow (3.5 feet) = pole's height (10 feet) / pole's shadow (x).

This proportion can be represented as: 4/3.5 = 10/x. To solve for x (the length of the pole's shadow), we can cross-multiply:

4 * x = 3.5 * 10

4x = 35

Now, divide both sides by 4:

x = 35/4

So, the pole's shadow will be 35/4 feet long when both Sabrina and the pole are proportional. This fraction represents the pole's shadow length in relation to the given heights and shadow lengths.

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The integral of f(x) can be found by using the substitution u = cos(x), du = -sin(x) dx. Thus, we have:

∫ (6 sin(2x) / cos(2x)) dx = -3 ∫ (2 sin(2x) / cos²(2x)) (-2cos(x)) dx

= 6 ∫ (sin(u) / u²) du

This integral can be evaluated using integration by parts, with u = sin(u) and dv = u⁻² du, giving:

6 ∫ (sin(u) / u²) du = -6 sin(u) / u + 6 ∫ (cos(u) / u) du

Substituting back u = cos(x), we have:

6 ∫ (sin(x) / cos²(x)) dx = -6 tan(x) + 6 ln |cos(x)| + C

Since tan(x) = sin(x) / cos(x) and cos²(x) = 1 - sin²(x), we have:

f(x) = 6 sin(x) / cos²(x) = 6 sin(x) / (1 - sin²(x)) = -6/(sin(x) - 1/sin(x))

Therefore, the general form of the primitive of f(x) is:

F(x) = -6 ln |sin(x) - 1/sin(x)| + C

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Answer:

18

Step-by-step explanation:

54/g - h                              g = 6 and h = 3

54/6 - 3

= 54/3

= 18

So, the answer is 18.

To find the average rate of change of a function in a given interval, we need to calculate the difference in the function values at the endpoints of the interval and divide it by the length of the interval.

In this case, the interval is (0,2) and the function is f(x) = x^2 - 3x.

At the left endpoint, x=0, we have f(0) = 0^2 - 3(0) = 0.

At the right endpoint, x=2, we have f(2) = 2^2 - 3(2) = -2.

Therefore, the difference in the function values is f(2) - f(0) = -2 - 0 = -2.

The length of the interval is 2 - 0 = 2.

So the average rate of change of f(x) over the interval (0,2) is:

(-2)/2 = -1

Therefore, the average rate of change of f(x) over the interval (0,2) is -1.
Hi! To find the average rate of change in the interval (0, 2) for the function f(x) = x^2 - 3x, you can use the following formula:

Average Rate of Change = (f(b) - f(a)) / (b - a)

In this case, a = 0 and b = 2. First, calculate the function values at these points:

f(0) = (0)^2 - 3(0) = 0
f(2) = (2)^2 - 3(2) = 4 - 6 = -2

Now, apply the formula:

Average Rate of Change = (f(2) - f(0)) / (2 - 0) = (-2 - 0) / (2) = -2 / 2 = -1

So, the average rate of change in the interval (0, 2) for the function f(x) = x^2 - 3x is -1.

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According to the information the length of the ladder to reach the hoop will be approximately 10.77 feet.

How to calculate the length of the ladder?

 Analyzing the problem, we can see that the ladder, the height and the distance from the base of the basket will form a right triangle. We can then use the Pythagorean theorem to calculate the length of the ladder, which will be the hypotenuse of the triangle. The formula used will be:

Substituting the information in the formula we have:

So let's use the square root of 116 to find how long the ladder must be to reach the hoop, which in this case will be:

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The measures of angle T and S in a right angles triangle STU with side Lengths ST = 10 units and UT = 4 units are equals to

We have a triangle STU has a right angle at U so, we can call it a right angled triangle STU. Length of side ST = 10 units

Length of side TU = 4 units

We have to determine the measure of angle T and measure of angle S.

As we know that sum of inner angles of a triangle = 180°

So, m∠S + m∠T + m∠U = 180°

=> m∠S + m∠T = 180° - 90°

= 90°

Using the trigonometry formula, in right angles triangle STU,

tan (m∠T ) = US/UT

=> m∠T = √86/4

=>

Hence, required value are

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Complete question:

The above figure completes the question.

In the figure shown, what are ∠ and ∠? Triangle S T U has right angle U and is labeled as follows: S T, 10; T U, 4; and the long leg, unlabeled

The expression that represents the fee for signing up the day of the activity is x + 0.20x. This means that fee for signing up the day of the activity is original fee (x) plus an additional 20% of original fee (0.20x).

For example, if the community center charges $50 for signing up before the day of the activity, then the fee for signing up the day of the activity would be:

$50 + ($50 x 0.20) = $50 + $10 = $60

So, individuals who sign up the day of the activity are charged a higher fee than those who sign up before the day of the activity, because they are charged the original fee plus an extra 20% of the original fee. This is often used as an incentive for individuals to sign up early and to help the community center plan and prepare for the activity accordingly.

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The value or n(C) based on the information will be 6.

In mathematics, a factor is a number or algebraic expression that divides another number or expression without leaving a remainder. More formally, if a is a factor of b, then b can be expressed as a product of a and some other number or expression.

For example, in the expression 12 = 2 x 2 x 3, the numbers 2 and 3 are factors of 12. Similarly, in the expression x² - 4, (x - 2) and (x + 2) are factors because if we multiply them together we get x² - 4.

The factors of 12 are 1, 2, 3, 4, 6, and 12. Therefore, the set C contains six elements. Hence, n(C) = 6.

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No, I do not agree with Mayumi's conclusion that the quadrilateral RSTU cannot be a trapezoid just because the slopes of RU and ST are undefined.

RSTU is a trapezoid with  RU and ST are parallel and have the same x-coordinates.

A trapezoid is defined as a quadrilateral with at least one pair of parallel sides.

The fact that the slopes of RU and ST are undefined does not necessarily mean that they are not parallel.

As vertical lines have undefined slopes and are parallel to each other.

To determine if RSTU is a trapezoid,

Mayumi should check if any pair of opposite sides are parallel.

The slopes of the two pairs of opposite sides RS and TU, and RU and ST and check if they are equal.

Slope of RS = (4 - 3)/(1 - (-2))

                    = 1/3

Slope of TU = (1 - (-4))/(-2 - 1)

                    = -5/3

Slope of RU is undefined (vertical line)

Slope of ST is undefined (vertical line)

Since the slopes of RS and TU are not equal, they are not parallel.

The slopes of RU and ST are undefined does not give us any information about their parallelism.

Check at other properties of the quadrilateral to determine if they are parallel.

One property is the coordinates of the points.

If we draw the quadrilateral,  RS and TU are not parallel, but RU and ST are parallel and have the same x-coordinates.

Therefore, quadrilateral RSTU is a trapezoid with bases RS and TU, and legs RU and ST.

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Answer: I agree the answer is 3

Step-by-step explanation:

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The length and width of the chocolate bar is 14.5 feet and 7.6 feet.

What is length?

Length is a measure of the size of an object or distance between two points. It refers to the extent of something along its longest dimension, or the distance between two endpoints.

What is width?

Width refers to the measure of the distance from one side of an object to the other side, perpendicular to the length. In geometry, width is usually measured in units such as meters, feet, or inches.

According to the given information:

Let's start by assigning variables to represent the length and width of the chocolate bar. Let x be the width of the chocolate bar in feet. Then, according to the problem:

The length of the chocolate bar is 0.3 feet shorter than twice its width, which means the length is (2x - 0.3) feet.

The base area of the chocolate bar is given as 61.04 square feet. We can use this information to set up an equation:

x(2x - 0.3) = 61.04

Expanding the left side of the equation:

2x^2 - 0.3x = 61.04

Moving all the terms to one side of the equation:

2x^2 - 0.3x - 61.04 = 0

Now we can solve for x using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 2, b = -0.3, and c = -61.04. Substituting these values and simplifying:

x = (0.3 ± sqrt(0.3^2 + 4(2)(61.04))) / (2(2))

x ≈ 7.6 or x ≈ -4.0

Since the width of the chocolate bar cannot be negative, we can discard the negative solution. Therefore, the width of the chocolate bar is approximately 7.6 feet.

To find the length, we can use the equation we set up earlier:

length = 2x - 0.3

Substituting x = 7.6:

length = 2(7.6) - 0.3

length ≈ 14.5

Therefore, the length of the chocolate bar is approximately 14.5 feet and the width is approximately 7.6 feet.

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The coordinates of the parallel translation P are (-1, 4).

What is meant by coordinates?

Coordinates are a series of numbers or values that denote the position or location of a point in a particular system, such as a geographic or Cartesian coordinate system. They are used to represent locations or objects in space.

What is meant by parallel?

Parallel refers to lines or planes that are always the same distance apart and never intersect, even if they extend infinitely in both directions.

According to the given information

To find the coordinates of the parallel translation P that moves point A(3, -2) to point B(-1, 4), we need to find the vector that connects A to B, and then translate A by that same vector.

The vector that connects A to B is:

B - A = (-1 - 3, 4 - (-2)) = (-4, 6)

To move point A by this vector, we add the vector to the coordinates of A:

P = A + (-4, 6) = (3, -2) + (-4, 6) = (-1, 4)

Therefore, the coordinates of the parallel translation P are (-1, 4).

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The value of mean is 5.5 and the value of standard deviation is 1.44.

Now, we need to find the mean and standard deviation of this random variable. The mean of a uniformly distributed random variable can be found by taking the average of the lower and upper bounds of the distribution. In this case, the lower bound is 3 and the upper bound is 8, so the mean would be:

Mean = (3+8)/2 = 5.5

So, the expected number of tickets purchased by an individual is 5.5.

Next, we need to find the standard deviation. The standard deviation is a measure of the deviation or spread of the data from the mean. For a uniform distribution, the formula for standard deviation is:

Standard Deviation = (Upper Bound - Lower Bound) / √12

Plugging in the values, we get:

Standard Deviation = (8-3) / √(12) = 1.44

This means that on average, the number of tickets purchased by an individual is expected to deviate from the mean by about 1.44 tickets.

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A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

A probability can be classified as experimental or theoretical, as follows:

Over a small number of trials, these two probabilities can be different, but over a large number of trials, their values get closer.

The dice has eight sides, hence the theoretical probability of rolling a six is given as follows:

1/8 = 0.125 = 12.5%.

(each of the eight sides is equally as likely, and a six is one of these sides).

The experimental probabilities are obtained considering the trials, hence:

(given in the problem).

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The correct location of the decimal point when the expression 3.72 divided by 10⁴ is evaluated is: 0.000372 because the decimal point moves 4 places to the left when you divide by 10 to the fourth power. The correct option is B.

To evaluate this expression, we need to move the decimal point 4 places to the left, since the exponent is positive.

Option A is incorrect because placing 4 zeros in front of the number would give us a much smaller value than the original number. Option B is correct because moving the decimal point 4 places to the left would give us 0.000372, which is equivalent to 3.72 divided by 10⁴.

Option C is incorrect because moving the decimal point 4 places to the right would give us a much larger value than the original number. Option D is also incorrect because placing 4 zeros after the number would give us a value that is 10,000 times larger than the original number.

Therefore, the correct answer is B, which shows and explains the correct location of the decimal point when the expression 3.72 divided by 10⁴ is evaluated. The correct option is B.

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Complete question:

3.72 divided by 10⁴ which of these shows and explains the correct location of the decimal point when the expression is evaluated?

A 0.0000372 because 4 zeros are placed in font of the number when you divide by 10 to the fourth power

B 0.000372 because the decimal point moves 4 places to the left when you divide by 10 to the fourth power

C 37,200 because the decimal point moves for places to the right when you divide by 10 to the fourth power

D 3,720,00 because 4 zeros are placed after the number when you divide by 10 to the fourth power

Considering the ratio, Ginger can make four different smaller necklaces.

The ratio between two amounts a and b is given as follows:

a to b.

Which is also the division of the two amounts.

The ratio for this problem is given as follows:

Pink/White = 30/35

Pink/White = 6/7 -> as 30/6 = 5 and 35/7 = 5.

5 - 1 = 4, hence, considering the ratio, Ginger can make four different smaller necklaces.

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