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Answer:

The student made a mistake when squaring -4.

-4 * -4 = 16.  Had the expressions said -x^2, then the answer would indeed be -16 since -1 *(-4*-4) = -16

Furthermore, since the answer is 16, you'd do (16 - 7) ^3, which equals (9)^3, which is 729 and not -12,167

Answer:

We do not know if the triangles are congruent because we have no information about congruent sides.

So the equation in the form y=kx is: y = 180,000x, where y is the cost in dollars and x is the length of the commercial in seconds.

In mathematics, an equation is a statement that asserts the equality of two expressions. It typically consists of two expressions separated by an equal sign, with the expression to the left of the equal sign indicating the left-hand side of the equation, and the expression to the right of the equal sign indicating the right-hand side of the equation. Equations can be used to describe relationships between variables, to solve problems, and to model real-world phenomena.

Here,

a. Yes, the cost of the commercials is proportional to the length of time the commercial aired.

b. To find the cost of a commercial in dollars per second, we need to divide the cost by the length of the commercial in seconds. Using the given values, we get:

For a 15-second commercial: $2,700,000 ÷ 15 = $180,000 per second

For a 60-second commercial: $10,800,000 ÷ 60 = $180,000 per second

For a 90-second commercial: $16,200,000 ÷ 90 = $180,000 per second

For a 120-second commercial: $21,600,000 ÷ 120 = $180,000 per second

We can see that the cost per second is constant at $180,000. So the equation in the form y=kx is:

y = 180,000x, where y is the cost in dollars and x is the length of the commercial in seconds.

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Answer:

1.5 * 7 that is the answer of the question

Since trapezoid ABCD is inscribed in circle O, we know that angles A and D are right angles. We also know that the measure of angle ABD is equal to half the measure of arc AC. Since DC is a diameter of the circle, arc AC is a semicircle and thus has a measure of 180 degrees. Therefore, angle ABD has a measure of 90 degrees.

We also know that the sum of the measures of the angles in a trapezoid is equal to 360 degrees. Therefore, we can set up the following equation:

mAB + mBC + mCD + mDA = 360

Substituting the given values, we get:

80 + mBC + 90 + 90 = 360

Simplifying, we get:

mBC = 100

Therefore, mBC is equal to 100 degrees.

The formula to find the interquartile range (IQR) is:

IQR = Q3 - Q1

where Q1 and Q3 are the first and third quartiles, respectively. Since the distribution of weights of pumpkins is approximately normal, we can use the formula for the standard error of the mean to find the standard deviation of the sampling distribution of the mean:

SEM = σ / sqrt(n)

where σ is the population standard deviation, n is the sample size, and sqrt represents the square root function.

Plugging in the given values, we get:

SEM = 1.68 / sqrt(15)

≈ 0.4334

To find the first and third quartiles, we need to find the z-scores corresponding to the 25th and 75th percentiles of the standard normal distribution, respectively. These z-scores can be found using a standard normal distribution table or a calculator.

Using a standard normal distribution table, we find that:

Therefore, the first and third quartiles are:

Q1 = μ + z1 * SEM

= 8.3 - 0.6745 * 0.4334

≈ 7.998

Q3 = μ + z3 * SEM

= 8.3 + 0.6745 * 0.4334

≈ 8.602

Finally, we can calculate the interquartile range (IQR) as:

IQR = Q3 - Q1

≈ 8.602 - 7.998

≈ 0.604

Rounding to the nearest thousandth, we get:

IQR ≈ 0.604

Therefore, the value of the interquartile range (IQR) for the mean weight of 15 pumpkins is 0.604 pounds.

The true statement is that the mode of the set of scores is 96. The solution has been obtained by using measures of central tendency.

What are measures of central tendency?

A summary measure called a measure of central tendency, also known as a measure of centre or a measure of central placement, aims to characterise the entirety of a set of data with a single number that corresponds to the centre or centre of its distribution.

We are given scores as 96, 77, 82, 96, and 89.

So, from this we get

⇒ Mean = (96 + 77 + 82 + 96 + 89) ÷ 5

⇒ Mean = 440 ÷ 5

⇒ Mean = 88

Similarly,

Arranging the numbers, we get 77, 82, 89, 96, 96.

So, the median is 89.

Mode is 96 as it is appearing two times.

Hence, the third statement is the true statement.

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The value of x for the given rectangle in which the perimeter of both the rectangle are equal is x = 15.

What about rectangle?

A rectangle is a four-sided plane figure with four right angles (90-degree angles) and opposite sides that are parallel and equal in length. In other words, it is a parallelogram with all angles being right angles. The two pairs of parallel sides of a rectangle are called the length and width (or height) respectively. The area of a rectangle is found by multiplying its length by its width, while its perimeter is found by adding up the lengths of all four sides. Rectangles are commonly used in mathematics, geometry, engineering, and architecture, among other fields.

Define perimeter of rectangle:

The perimeter of a rectangle is the total distance around the outside of the rectangle. It is the sum of the lengths of all four sides of the rectangle. If the length of the rectangle is denoted by "l" and the width (or height) is denoted by "w", then the formula for the perimeter of a rectangle is:

⇒ Perimeter = 2(l + w)

According to the given information:

As, we know that the perimeter of the rectangle is sum of all side of the rectangle in which,

The perimeter of first rectangle is =   [tex]2(1.4x + 5x + 5.25)[/tex]

The perimeter of second rectangle is = [tex]2(4.25x + 3x - 7.5)[/tex]

It is given that perimeter of both the rectangle are equal so,

2(1.4x + 5x + 5.25) = 2(4.25x + 3x - 7.5)

2.8x + 10x + 10.5  = 8.5x + 6x - 15

2.8x + 10x - 8.5x -6x = -15 - 10.5

-1.7x = -25.5

x = 15.

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Answer:

  a) 7 m

  b) 22 cm

Step-by-step explanation:

Given plans at a scale of 1 : 50, you want (a) the actual length corresponding to a plan length of 14 cm, and (b) the plan length corresponding to an actual length of 11 m.

The actual lengths are wanted in meters, so we can rewrite the scale to translate between plan cm and actual m.

  plan : actual = 1 cm : 50 cm

  = 1 cm : 0.5 m

  = 2 cm : 1 m

Multiplying the scale by 7, we have ...

  2 cm : 1 m = 14 cm : 7 m

The actual length is 7 meters.

Multiplying the scale by 11, we have ...

  2 cm : 1 m = 22 cm : 11 m

The plan length is 22 cm.

The value of t for a t-distribution with 10 degrees of freedom such that the area between -t and t equals 90% is 1.812.

To find the value of t for a t-distribution with 10 degrees of freedom such that the area between -t and t equals 90%, we can use a t-table.

Using a t-table, we can find the t-value that corresponds to a 5% area in the upper tail of the distribution, since the area between -t and t is 90% (leaving 10% in the tails).

For a t-distribution with 10 degrees of freedom, the critical value for a 5% area in the upper tail is 1.812. Check the attached image.

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By using the Pythagorean theorem we conclude that the rope net is about 40.31 feet long.

The Pythagorean Theorem is a fundamental theorem in mathematics that describes the relationship between the sides of a right triangle.

We can use the Pythagorean theorem to solve this problem.

Let's consider the rope net as the hypotenuse of a right triangle, and the horizontal distance from the base of the platform to the starting point of the rope net as one leg of the triangle.

The other leg of the triangle is the vertical height of the platform.

Using the Pythagorean theorem, we have:

length of rope net = √(horizontal distance² + vertical height²)

Substituting the given values, we get:

length of rope net = √(35² + 20²)

= √(1225 + 400)

= √1625

= 40.31 feet (rounded to two decimal places)

Therefore, the rope net starts 35 feet from the platform base, and the platform is 20 feet high and the rope net is about 40.31 feet long.

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Answer:

Sure! To find the distance between two points, we can use the distance formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2) Using the points (0, -7) and (-9, 5), we can plug in the values: d = sqrt((-9 - 0)^2 + (5 - (-7))^2) d = sqrt((-9)^2 + (12)^2) d = sqrt(81 + 144) d = sqrt(225) So the distance between the two points is 15 units.

Answer:

The distance between the two points is 15 units.

Step-by-step explanation:

Answer:

Slope curve is the gradiient

Step-by-step explanation:

Gradient equation is m = change in y over change in x

Therefore the first answer is correct

The true statement about the value of a in comparison to 0 and 1 is that it is a real number between 0 and 1.

A graph of y = f⁻¹(x) is shown below.

An equation for f⁻¹(x) is [tex]y=\frac{1}{a^x}[/tex].

For any given function, y = f(x), if the output value (range or y-value) is decreasing when the input value (domain or x-value) is increased, then, the function is generally referred to as a decreasing function.

By critically observing the graph of f(x), we can logically deduce that [tex]a^x[/tex] is positive for all values of x and as such, all values of a must also be positive:

0 < a

Additionally, the exponential function [tex]a^x[/tex] represent a decreasing function, so for any values of x, we have:

[tex]a^x > a^{x+1}[/tex]

1 > a

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Step-by-step explanation:

50 tries experimentalprobabilities:

open :  2/50 = 1/25

closed  6/50 = 3/25

side :   42/50 = 21/25

Answer:

Open Side Up: 2/50 = 1/25 = 4%

Closed Side Up: 6/50 = 3/25 = 12%

Landing on Side: 42/50 = 21/25 = 84%

Answer: A

Step-by-step explanation:

Answer:

Min: 85

Q1: 95

Median: 110

Q3: 120

Max: 125

In linear equation, $-0.0143 is the rate of change of the quantity demanded when the price increases .

What in mathematics is a linear equation?

An mathematical equation with only a constant and a first-order (linear) component, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                        Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

the demand function:

x² + p² = 2450

Differentiating both sides of the demand function with respect to time t using the chain rule, we get:

  2x * dx/dt + 2p * dp/dt = 0

We also know that at the point where the price is $7, p = 7 and x satisfies:

   x² + p² = 2450

Substituting p = 7 into the demand function, we get:

  x² + 7²  = 2450

     x² = 2450 - 49x²

       x = 49

substitute x = 49, p = 7, and dp/dt = $0.10 into the differentiated demand function and solve for dx/dp

     2x * dx/dp + 2p * dp/dx = 0

  2(49) * dx/dp + 2(7) * 0.10 = 0

   98 dx/dp + 1.40 = 0

  dx/dp = $-0.0143

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Answer:

y > 3x - 1

set y = 0

0 > 3x - 1

x > 1/3

points are [ 1/3,0]

set x = 0

y > 3(0) - 1

y > - 1

points are [0,-1]

second question

x + y ≤ - 2

set x = 0

y ≤ - 2

points are [0,-2]

set y = 0

x ≤ - 2

points are [-2,0]

So therefore A should be shaded.

The list that shows the side lengths, in inches, of the triangle Riley drew is: 59/5, 57/5, 3/2

What is Triangle ?

A triangle is a polygon with three sides and three angles. It is one of the basic shapes in geometry and is commonly used in various fields such as engineering, physics, and architecture. The sum of the angles of a triangle always adds up to 180 degrees.

To find the side lengths of the triangle Riley drew, we need to multiply each of Jim's side lengths by the scale factor of ‡, which means multiplying by 3.

The side lengths of Jim's triangle, when written with common denominators, are:

3¼ = 13/4

4.9 = 38/10

5/10 = 1/2

Multiplying each of these by 3 gives:

13/4 * 3 = 39/4

38/10 * 3 = 114/10 = 57/5

1/2 * 3 = 3/2

So, the side lengths of the triangle Riley drew are:

39/4, 57/5, 3/2

We can simplify these fractions by finding a common denominator:

39/4 = 236/20

57/5 = 228/20

3/2 = 30/20

So, the side lengths of the triangle Riley drew, in inches, are:

236/20, 228/20, 30/20

Simplifying further by dividing each numerator by 4, we get:

59/5, 57/5, 15/10

Therefore, the list that shows the side lengths, in inches, of the triangle Riley drew is:

59/5, 57/5, 3/2

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Using the slope of curve,

1. If x=0.5, then the slope is: 0.3333.

2. If x=0.9, then the slope is: 0.2632

3. If x=0.99, then the slope is: 0.2513

4. If x=0.999, then the slope is: 0.2501

5. If x=1.5, then the slope is: 0.2

6. If x=1.1, then the slope is: 0.2381

7. If x=1.01, then the slope is: 0.2488

8. If x=1.001, then the slope is: 0.2499

Define a curve?

Three easy procedures can be used to compute the area under the curve. The curve's equation (y = f(x)), the boundaries within which the area is to be determined, and the axis encompassing the area must first be known.

The curve is given as:

y = x/1+x

Point, P = (1, 1/2) lies on the curve.

Point, Q = (x, x/1+x) is an arbitrary point on the curve.

The slope of the secant line PQ is:

y2-y1/x2-x1

= x-1/2(x+1) × 1/(x-1)

=1/2(x+1)

1. If x=0.5, then the slope is:

1/2(0.5+1)

= 1/3

= 0.3333

2. If x=0.9, then the slope is:

1/2(0.9+1)

= 1/3.8

= 0.2632

3. If x=0.99, then the slope is:

1/2(0.99+1)

= 1/3.98

= 0.2513

4. If x=0.999, then the slope is:

1/2(0.999+1)

= 1/3.998

= 0.2501

5. If x=1.5, then the slope is:

1/2(1.5+1)

= 1/5

= 0.2

6. If x=1.1, then the slope is:

1/2(1.1+1)

= 1/4.2

= 0.2381

7. If x=1.01, then the slope is:

1/2(1.01+1)

= 1/4.02

= 0.2488

8. If x=1.001, then the slope is:

1/2(1.001+1)

= 1/4.002

= 0.2499

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Answer:

AA Similarity

i hope this helps :)

The missing number in the pattern is 64.

To find the missing number in the pattern, we need to identify the rule that relates the given numbers.

If we look at the pattern, we can see that each number is obtained by subtracting a certain value from the previous number.

Starting from 106, we subtract 16 to get 90. Then we subtract 14 to get 76. To get the next number, we need to subtract 12 from 76:

76 - 12 = 64

Therefore, the missing number in the pattern is 64.

After 64, we continue the pattern by subtracting 8 from 64 to get 56, and then subtracting 10 from 56 to get 46.

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Answer: Two other positive angles of rotation that take A to B are:

- 13π/6 radians counterclockwise

- 25π/6 radians clockwise

Step-by-step explanation:

Answer:

value of ∅ = 67.5°

Step-by-step explanation:

cos135° = [tex]-\frac{1}{\sqrt{2} }[/tex]

so 2Ф = 135

Ф = [tex]\frac{135}{2} = 67.5[/tex]°

The absοlute fοrm οf the given inequality is |x+1|>6.

In mathematics, inequality is  a statement οf an οrder relatiοnship that is a relatiοnship between twο values that are nοt equal,—greater than, greater than οr equal tο, less than, οr less than οr equal tο—between twο numbers οr algebraic expressiοns. Such as 7<9 οr 5>3 etc.

Given inequality is

x<−7 οr x>5

The distance between -7 and 5 is

5- (-7) = 5+7= 12

Dividing that by 2 we get,

12/2 =6

It is the c value

We use the greater than since we have an οr

|x−b|>6 ----------------- (1)

Substituting  a value  x=5 in equatiοn (1) with an equals sign tο determine b we get

5-b =6

b= -1

The absοlute fοrm οf the given inequality is |x+1|>6

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Step-by-step explanation:

The volume of a cube is similar to that of a rectangular prism, the volume equals the length times width times height, however because it’s a cube all the measurements are the same, in this case 7 inches. So volume equals 7^3, thus equaling 343 inches cubed. Hope this helps!

We can estimate that apprοximately 41 teachers vοlunteer at an animal shelter.

The given infοrmatiοn tells us that 40% οf the teachers vοlunteer as hοmewοrk tutοrs. We dο nοt knοw hοw many teachers there are in tοtal, sο we cannοt directly determine the number οf teachers whο vοlunteer at an animal shelter.

Hοwever, we can use the infοrmatiοn abοut the percentage οf teachers whο vοlunteer at a seniοr center, spοrts cοach, and animal shelter tο estimate the number οf teachers whο vοlunteer at an animal shelter.

If 15% οf the teachers vοlunteer at a seniοr centre, 25% οf the teachers vοlunteer as spοrts cοaches, and 20% οf the teachers vοlunteer at an animal shelter, then the tοtal percentage οf teachers whο vοlunteer is:

15% + 25% + 20% + 40% = 100%

This means that all οf the teachers at the Blue Pacific Schοοl District vοlunteer in οne οr mοre οf these categοries.

Tο estimate the number οf teachers whο vοlunteer at an animal shelter, we can assume that the percentage οf teachers whο vοlunteer in each categοry is prοpοrtiοnal tο the number οf teachers whο vοlunteer in that categοry. If we let x be the tοtal number οf teachers at the schοοl district, then we can write:

0.15x = number οf teachers whο vοlunteer at a seniοr center

0.25x = number οf teachers whο vοlunteer as spοrts cοaches

0.20x = number οf teachers whο vοlunteer at an animal shelter

0.40x = number οf teachers whο vοlunteer as hοmewοrk tutοrs

Since we knοw that 82 teachers vοlunteer as hοmewοrk tutοrs, we can sοlve fοr x:

0.40x = 82

x = 205

Therefοre, there are 205 teachers in the Blue Pacific Schοοl District. Tο estimate the number οf teachers whο vοlunteer at an animal shelter, we can plug in x and 0.20x intο the equatiοn fοr the number οf teachers whο vοlunteer at an animal shelter:

0.20x = 0.20(205) = 41

Sο we can estimate that apprοximately 41 teachers vοlunteer at an animal shelter.

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Answer: This type of sample is called a stratified random sample. The population (city) is divided into various zones, and then a random sample of households (5 from each zone) is taken from each stratum (zone). This helps ensure that the sample is representative of the population as a whole and includes a proportional number of households from each zone.

Step-by-step explanation:

stratified random sampling is a powerful tool for researchers to ensure that their sample accurately reflects the population of interest, and can help increase the validity and reliability of research findings.

How to study sample?

This sampling method is an example of stratified random sampling, where the population is divided into different subgroups or strata, and a random sample is drawn from each stratum. In this case, the strata are the various zones of the city, and the researcher randomly selects five households from each zone.

Stratified random sampling is a commonly used sampling method in research because it can increase the representativeness of the sample and reduce sampling error. By dividing the population into different strata based on relevant characteristics, such as geographic location, age, gender, or income level, the researcher can ensure that each stratum is adequately represented in the sample.

In this example, the researcher is interested in studying public transportation usage in different zones of the city. By stratifying the population by zone and selecting a random sample of households from each zone, the researcher can obtain a representative sample of the population and draw conclusions about public transportation usage in each zone.

Overall, stratified random sampling is a powerful tool for researchers to ensure that their sample accurately reflects the population of interest, and can help increase the validity and reliability of research findings.

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Your complete question is :-A city collects data about public transportation. The researcher divides the city into various zones, and randomly chooses 5 households from each zone to survey. Which type of sample does this represent?

The index form is solved to give 1/z^13/12

Index forms are described as mathematical forms used to represent numbers too large or small in more proper ways.

Other names for index forms are scientific notations and standard forms.

They are represented as numbers raised to a variable or an exponent.

The rules of index forms are;

From the information given, we have;

z^-1/4/ z1/2 z1/3

Add the exponents

z^-1/4 / z  5/6

Subtract the exponents

z^ -6 - 20 /24

z^-26/24

1/z^13/12

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