From 1994 to 2003, the amount of athletic equipment E (in millions of dollars) sold domestically can be modeled by E(t) = -10t^3 + 140t^2 - 20t + 18,150where t is the number of years since 1994. Use the following steps to find the year when about $20,300,000,000 of athletic equipment was sold. a. Write a polynomial equation that can be used to find the answer. b. List the possible whole-number solutions of the equation in part (a) that are less than 10.c. Use synthetic division to determine which of the possible solutions in part (b) is an actual solution. Then calculate the year which corresponds to the solution.

Answer:

We dissect each statement from the problem above to fully understand it.

the sum of a number and 7 is (x + 7)

3 times this is 3(x + 7)

is means the equal sign here 3(x + 7) =

Two less then 5 times the number is 5x - 2.

Therefore, the answer is B, 3(x + 7) = 5x - 2

The temperature drop between noon and 10 PM is 14.4° F.

Celsius to Fahrenheit is the conversion of temperature from Celsius unit to Fahrenheit unit. Temperature scales provide a way of measuring how hot or cold a body is. Fahrenheit and Celsius are temperature scales.

The formula to convert Celsius to Fahrenheit is given by: °F = °C × (9/5) + 32.

Given that, Maha checked the outside temperature at noon one day and found it was 26° C.

So, the temperature in Fahrenheit is °F =26° ×(9/5)+32

= 46.8+32

= 78.8° F

At 10 PM when she checked, the outside temperature was 18° C.

So, the temperature in Fahrenheit is °F =18° ×(9/5)+32

= 32.4+32

= 64.4° F

Difference in temperature =78.8-64.4

= 14.4° F

Therefore, the temperature drop between noon and 10 PM is 14.4° F.

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The largest value of x is 13.

A closed shape's perimeter is the sum of the lengths of its outside boundaries. The lengths of all the sides are added to determine the measurement.

Given:

The size of a pentagon are given as x, x+1,x+3,x-2 and 6.

The perimeter is less than 78 cm and x is an integer.

The perimeter of the pentagon = the sum of all the sides.

x + x+1 + x+3 + x-2 + 6 < 78

4x + 10 - 2 < 78

4x < 70

x < 14

The largest value of x is 13.

Therefore, the largest value of x is 13.

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The correct answer is, the figure is a line segment.

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

here, we have,

from the given figure,

we get,

AB is a line segment.

Hence, The correct answer is, the figure is a line segment.

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The sum of the first seven terms is given by -2186

Any progression in which the ratio of adjacent terms is fixed is a Geometric Progression. The general form of representation of a geometric sequence is a, ar, ar², ar³, ...

The geometric sequence is given here by -2,-6,-18...

We can observe that the common ratio is r=3

thus the sequence of upto 7 terms is given by

-2,-6,-18,-54,-162,-486.-1458

Thus the sum of all seven terms is given by

S=-2-6-18-54-162-486-1458

=-2186

Hence, The sum of the first seven terms is given by -2186

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A graph of the resulting image after a dilation by a factor of 1/4 centered at the origin is shown in the image attached below.

In Geometry, dilation simply refers to a type of transformation which typically changes the size of a geometric object, but not its shape.

Next, we would have to dilate the coordinates of the pre-image by using a scale factor of 1/4 centered at the origin as follows:

Ordered pair T (8, 8) → Ordered pair T' (8 × 1/4, 8 × 1/4) = Ordered pair T' (2, 2).

Ordered pair R (-8, -4) → Ordered pair R' (-8 × 1/4, -4 × 1/4) = Ordered pair R' (-2, -1).

Ordered pair S (4, -8) → Ordered pair S' (4 × 1/4, -8 × 1/4) = Ordered pair S' (1, -2).

Lastly, we would use an online graphing calculator to plot the resulting data points.

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Answer:

Step-by-step explanation:

1/2 is your answer

A diagram of a pyramid with the given measurements is not possible to generate.

But we can calculate he base length, side length and height of a pyramid using the Pythagorean theorem.

In a pyramid, the slant height (rmid) can be found using the Pythagorean theorem. If the base length (b) and the height (h) of the pyramid are known, the slant height (rmid) can be calculated using the formula:

rmid = sqrt(b^2 + h^2)

In this case,

rmid = sqrt(8^2 + 12^2) = sqrt(64 + 144) = sqrt(208) = 14.4

You can also use this information to find the side length of the pyramid, which is the length of one of the triangular faces. Using the Pythagorean theorem again:

side length = sqrt(rmid^2 - (b/2)^2)

In this case,

side length = sqrt(14.4^2 - (8/2)^2) = sqrt(207.36 - 16) = sqrt(191.36) = 6.56

So, based on the information provided, the base length of the pyramid is 8 feet, the side length is 6.56 feet and the height is 12 feet and the slant height is 14.4 feet.

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The height is 114.83 ft and the distance of the ø if someone is observing below is 84.8.

The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.

Given that at a given point of 67.7ft at the ground level of a covered court, the angle of elevation of a roof worker from the bottom is 38.6⁰ and the angle of elevation of the roof from the top is 42.4 degrees.

The base will be calculated as:-

tan(38.6) = P / B

tan(38.6) = 67.7 / B

B = 67.7 / tan(38.6)

B = 54.8 ft

The height will be calculated as:-

Cos(42.4) = B / H

H = 84.8 / Cos(42.4)

H = 114.83 ft

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A one-sigma uncertainty criterion means that if a theoretical value falls within one standard deviation of the measured data, it is considered consistent with the data.

Using this criterion, we can rule out theoretical value D. 19.7, since it is outside the range of measured values.

The other theoretical values A. 15.6, B. 15.9, and C. 19.5 fall within one standard deviation of the measured data, so they cannot be ruled out by this criterion.

Therefore, the only theoretical value that can be ruled out by our usual     1-sigma uncertainty criterion is D. 19.7

It's worth noting that this method just gives a rough idea of the consistency of a theoretical value with the data.

Other methods, such as the chi-squared test, or Bayesian analysis could be used to find the best-fit theoretical value and its uncertainty, and confirm or rule out other theoretical values.

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The solution to the equation on the interval is x = π/6 + 2πn, where n is any non-negative integer less than 2.

From the question, we have the following parameters that can be used in our computation:

3 sin x = sin x + 1

Interval = [0, 2π).

To solve the equation 3sin(x) = sin(x) + 1, we first subtract sin(x) from both sides to get 2sin(x) = 1.

So, we have

2sin(x) = 1

Then, we divide both sides by 2

sin(x) = 1/2.

Therefore, x = arcsin(1/2) + 2πn, where n is any integer.

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The sampling distribution of a statistic is the distribution of values taken by the statistic in all possible samples of the same size from the same population.

The population parameter is the true value of the statistic for the entire population. The probability that the statistic is obtained is the probability that it will be obtained in a single sample from the population. The variance of the values is the amount of variation among the values of the statistic in the sample. The formula for calculating the variance is the sum of the squared deviations from the mean, divided by the number of values in the sample. This can be written mathematically as: Variance = Σ (x - X)2/ n, where x is each value in the sample, X is the mean value, and n is the number of values in the sample.

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The value of  PQ / BD of given parallelogram where Diagonal BD intersects line CM and line CN at P and Q, respectively  = 1/3

Let's consider the two triangles BMP and DCP.
Here,
∠DPC = ∠BPM (because they are vertically opposite angles)
∠DCP = ∠BMP (because they are alternate interior angles of transversal CM with DC // BM)
∴△BMP∼△DCP (By AA theorem)
Thus,
ABCD is a parallelogram. Therefore AB = DC and AD = BC.
It is given that M is the midpoint of AB
BD  = DQ  + BQ                BD = BP  + PD

BD = 2BQ  + BQ               BD = 2PD + PD

BD  = 3BQ                        BD = 3PD

therefore

BQ  = PD And

Since DQ  = 2BQ  then  DQ  = 2PD and

PD + PQ = 2PD   subtract PD from each side

PQ  = PD

so BQ = PD  = PQ

BD = PD + PQ + BQ

BD  = PQ  + PQ  + PQ

BD  = 3PQ

Therefore the value of  PQ / BD of given parallelogram is PQ / BD  = 1/3.

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The best grade that can be earned is given as 0.8575

If he is able to get the sum of 100 percent in the final exam, trhis would count as 25 percent of the total grade that he has

100 - 25 = 75%

Then we would have

0.75 * 81 + 25 / 100

= 85.75 / 100

= 0.8575

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Question

A friend has a 81% average before the final exam for a course. That score includes everything but the final, which counts for 15% of the course grade.

What is the best course grade your friend can earn?

If we take a sample of 50 Reece's Pieces candies, we would expect about 20 of them to be orange.

The manufacturer says that exactly 40% of the candies are orange. We can use this information to find the expected value of the number of orange candies in a sample of 50 candies.

Expected value is found by multiplying the number of trials (in this case, 50) by the probability of success (in this case, 40% or 0.40)

x = (50)(0.40) = 20 candies.

So, if we take a sample of 50 Reece's Pieces candies, we would expect about 20 of them to be orange.

It's worth noting that this is an expectation, the actual number of orange candies in the sample of 50 candies may be different from the expected value.

The correct question of the following problem is:

If a sample of 1000 Reese's Pieces contains 40% orange candies, and a random sample of 50 Reese's Pieces is selected, how many orange candies can be expected to be in the sample of 50 Reese's Pieces?  Let x be the number of orange candies in the sample of 50 Reese's Pieces.

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A manufacturer buys a new machine costing $180000 dollars. The value of the machine at the end of 10 years is $6000.

Calculate the annual depreciation of the machine.

Depreciation = (Purchase Price - Salvage Value) / Useful Life

Depreciation = (180000 - 6000) / 10

Depreciation = 174000 / 10

Depreciation = $17400 per year

Calculate the value of the machine at the end of each year.

Year 1: 180000 - 17400 = $162600

Year 2: 162600 - 17400 = $1452000

Year 3: 1452000 - 17400 = $1277600

Year 4: 1277600 - 17400 = $1103200

Year 5: 1103200 - 17400 = $928800

Year 6: 928800 - 17400 = $754400

Year 7: 754400 - 17400 = $580000

Year 8: 580000 - 17400 = $405600

Year 9: 405600 - 17400 = $231200

Year 10: 231200 - 17400 = $6000

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The expanded value of the given equation is a²+2bx = b² + x ²+ h² .

Multiplication distributes over addition, so an expansion of a product of sums represents it as a sum of products.

Expansion is a scale-increasing affine transformation, sometimes known as enlargement or dilatation. It is also frequently referred to as an enlargement and is the polar opposite of a geometric contraction. An expansion and a translation are equivalent to a central dilation.

We must multiply out the brackets in order to expand and simplify an expression, and we must then collect like words in order to simplify the resulting expression.

Given : a^2= (b-x)^2 +h^2

          a² = (b-x)² + h²

we know that (c-d)² = c²+d² + 2cd

So,    a² = b² + x² -2bx + h²

         a²+2bx = b² + x ²+ h²

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The number of payments for the ordinary annuity that pays $1,000 quarterly for two years is 8.

An ordinary annuity's cash flows or payments occur at the end of the period, unlike an annuity due.

For quarterly payments, in a year, payments are made 4 times, that is, every three months.

For two years, the payments will be made 8 times (4 x 2).

Thus, we expect the ordinary annuity to pay $8,000 ($1,000 x 2 x 4).

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now, the assumption being that your granpa's are depositing the money at the beginning of the month.

[tex]~~~~~~~~~~~~\stackrel{\textit{deposits at the beginning of the period}}{\textit{Future Value of an annuity due}} \\\\ A=pmt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right]\left(1+\frac{r}{n}\right)[/tex]

[tex]\begin{cases} A=\textit{accumulated amount} \\ pmt=\textit{periodic deposits}\dotfill & 100\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &18 \end{cases}[/tex]

[tex]A=100\left[ \cfrac{\left( 1+\frac{0.03}{12} \right)^{12 \cdot 18}-1}{\frac{0.03}{12}} \right]\left(1+\frac{0.03}{12}\right) \\\\\\ A=100\left[ \cfrac{(1.0025)^{216}-1}{0.0025} \right](1.0025) \implies \boxed{A \approx 28665.52}[/tex]

Answer:

The answer to your questionis 3.65

Answer:

3.25, 3.50, 3.50, 3.50, 3.65, 4.00, 4.00, 7.50, 7.99

3.65 is the median.

Step-by-step explanation:

You're welcome.

The average rate of change on the interval [2, 2 + h] is r = 2.

Wewant to find the average rate of change of p(x) = 2x + 5 on the interval [2, 2 + h]

Remember that the average rate of change on an interval [a, b] is:

r = ( p(b) - p(a))/(b - a)

So on this case, we have:

r = ( p(h + 2) - p(2))/(2 + h - 2)

r = ( 2*(x + h) + 5 - 2*x - 5)/h

r = (2h)/h

r = 2

The average rate of change is 2.

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Answer:

The height of the building is 43.7 feet.

Step-by-step explanation:

Attached is a sketch of the problem.

We can use SOH CAH TOA to find our answer.

In this acronym, O is the opposite side, A is the adjacent side, and H is the hypotenuse. S is for the SIN function. C is for the COS function. T is for the TAN function.

We can calculate the height of the building by using the TAN function.

So we can say the tangent of angle x is the opposite side divided by the adjacent side.

[tex]tan(x)=\frac{O}{A}[/tex]

Lets solve for [tex]O[/tex].

Multiply both sides by [tex]A[/tex].

[tex]tan(x)*A=\frac{O}{A}*A[/tex]

Simplify the right side by cancelling the common factor of [tex]A[/tex].

[tex]tan(x)*A=O\\O=A*tan(x)[/tex]

Now lets evaluate the height of the building.

In this example we are given

[tex]x=17\\A=143[/tex]

[tex]O=143*tan(17)[/tex]

[tex]O=43.7195[/tex]

The amount of work that the laborer has done, given the weight of the bricks and the laborer is 4, 577 Joules .

To calculate the amount of work done by the laborer, we can use the formula:

work = force x distance x

where:

force is the force applied,

distance is the distance moved,

The force applied by the laborer is the combined weight of the laborer and the bricks:

= 895N + 575N

= 1, 470N

Therefore, the work done by the laborer is:

Work = 1, 470N x 3.1m

= 4577 Nm or Joules (J)

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The factorised for. of the given Polynomial expression using the greatest common factor is; 2 (14x - 1).

It follows from the task content that the factorised form of the given Polynomial expression is to be determined using the greatest common factor.

Since the given expression is; 28x - 2.

By careful observation of the two terms (28x and -2) in the polynomial expression; the greatest common factor is; 2.

Hence, the factorised form of the polynomial expression as required is; 2 (14x - 1).

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The linear regression equation for this data is given as follows:

y = x - 6.

The projected grade for a student with homework grade of x = 79 is given as follows:

73.

The equation for the line of fit is obtained inserting the points of the data-set into a linear regression calculator.

The points from this data-set are given as follows:

(70, 55), (89, 92), (79, 81), (84, 74), (84, 77), (70, 65) and (64, 68).

Inserting these points into a calculator, the regression equation is given as follows:

y = x - 6.

The projected grade for a student with homework grade of x = 79 is obtained as follows:

y = 79 - 6

y = 73.

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Answer:

4

Step-by-step explanation:

because its the factor

The scale factor of the dilation of triangles is k = 4/3

Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent

The result of dilation is that the shapes and boundaries of objects in the input image are expanded or thickened. It is often used in conjunction with other morphological operations such as erosion, opening, and closing to manipulate and enhance images.

Given data ,

Let the scale factor of the dilation be represented as k

Now , the measure of leg of the first triangle is a = 3 units

The measure of leg of the second triangle is b = 4 units

So , the dilated triangle is given by

3 k = 4

Divide by 3 on both sides , we get

k = 4/3

Hence , the dilation factor is k = 4/3

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The boxes are split in halves, and there is 4 boxes. The answer is 4 / 1/2.

What is division?

Division is a mathematical operation that involves dividing one number (the dividend) by another (the divisor). The result of this operation is called the quotient. Division is the inverse of multiplication, meaning that the product of a number divided by itself is equal to one. Division can also be used to find the number of times one number is contained in another. Division can be expressed in a variety of ways, such as by using fractions, decimals, or by using a long division algorithm.

When you look at the diagram, The boxes are split in halves, and there is 4 boxes. The answer is 4 / 1/2.

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No, we cannot conclude that pedestrians are safer in San Francisco than in Los Angeles based on the data provided. The number of pedestrian fatalities in a given county is only one factor in determining the safety of pedestrians in that county.

Other factors, such as the number of pedestrians in each county, the number of vehicles in each county, the number of traffic laws in each county, and the number of traffic enforcement officers in each county, all play a role in determining the safety of pedestrians in a given county.

We would also need to consider other factors such as the number of pedestrian-friendly infrastructure in each county, the number of pedestrian-friendly policies in each county, and the number of pedestrian-friendly initiatives in each county. With this additional data, we would be able to make a more informed conclusion about which county is safer for pedestrians.

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The value of x is found to be 3 and the arithmetic sequence is found to be 4, -2, -8, ... .

What is arithmetic sequence?

The nth term of an arithmetic progression is determined using the arithmetic sequence formula. The series where the common difference between any two next words stays constant is known as an arithmetic sequence.

The arithmetic sequence is 3x - 5, x - 5, 2x - 14, ....

If the numbers are in an arithmetic sequence, then the difference between the first and second term must be the same as the difference between the second and third term.

(x - 5) - (3x - 5) = (2x - 14) - (x - 5)

x - 5 - 3x + 5 = 2x - 14 - x + 5

-2x = x - 9

-2x - x = -9

-3x = -9

x = 3

The first three terms can be obtained by substituting the value of x in the terms -

The first term - 3(3) - 5 = 4

The second term - 3 - 5 = -2

The third term = 2(3) - 14 = -8

Therefore, the arithmetic sequence is 4, -2, -8, .....

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