is the linear relationship represented by the table a proportional relationship?
Tickets
Cost
0
$0
The linear relationship
the point (0, 0)
2
$14.50
Choose
4
$29
6
$43.50
a proportional relationship because the ratios between each pair of values are equivalent and the graph
Choose...
through

a) The function is P = 500e^0.4t

b) The count after 10 hours is 27299

c) it would reach 80000 in 13 hours

We know that at this time we are dealing with the population of the bacteria and we have to invoke the exponential growth ideology and we would have;

P = Poe^rt

P = population at time t

Po = Initial population

r = Population growth rate
t = Time taken

Then we have;

P = 500e^0.4t

After ten hours;

P= 500e^0.4 * 10

P = 27299

The count would reach 80000 when;

80000 = 500e^0.4 t

80000/500 = e^0.4 t

160 = e^0.4 t

ln160 = e^0.4 t

ln160 = 0.4t

t = ln160/0.4

t = 13 hours

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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 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 p-value is the chance of finding a t-value with an absolute value at least as great as the one we actually observed in the sample data assuming the null hypothesis is actually true. The t-value is a way to measure the difference between the population means.

We reject the null hypothesis of the test if the p-value is less than a predetermined threshold (for example, 0.05). We are primarily concerned with the p-value for each form of t-test, and we merely employ the t-value as a first step in that process.

You'll see that we merely used the t-value as a first step before determining the p-value. The genuine value in which we were most interested was the p-value, but first, we had to determine the t-value.

Therefore the p-value is the likelihood that, if the null hypothesis is correct, each test will result in a t-value with an absolute value at least as great as the one we actually observed in the sample data. The t-value is a way to measure the difference between population means.

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If a particular sample has 36 participants and the other sample has 40 participants, the total degrees of freedom for the study is

In Mathematics, the degrees of freedom in a sample are typically used to correct a possible bias that exists between the alternative and null hypotheses.

Mathematically, total degrees of freedom for the study can be calculated by using this mathematical expression:

v = n - k

Where:

Note: k is equal to 2 in this scenario.

Total degrees of freedom, v = n₁ + n₂ - k

Total degrees of freedom, v = 36 + 40 - 2

Total degrees of freedom, v = 74.

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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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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?

There may be a correlation, but there is no direct link. This is because it is more likely that you will get shoes in the color you want.

It's likely that the preferred color and the color of the shoes are related. A person's favorite color may or may not match the color of their shoes, so there is no direct correlation. Particularly, the color of the shoes may have influenced the preferred color.

There may be a correlation, but there is no direct link.

Correlation is a method for figuring out how two variables relate to each other. You learned that putting two variables on a "scatter plot" can help you figure out if they are usually connected. Despite the fact that there are other measures of association for variables measured at the ordinal or higher level of measurement, correlation is the strategy that is utilized the most frequently.

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The proportion of students that had a grade at least 5 points greater than the 25th percentile is given as follows:

0.7054 = 70.54%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for this problem are given as follows:

[tex]\mu = 78, \sigma = 36[/tex]

The 25th percentile is X when Z = -0.675, hence:

-0.675 = (X - 78)/36

X - 78 = -0.675 x 36

X = 53.7

The proportion of students with a grade of at least 58.7 is one subtracted by the p-value of Z when X = 58.7, hence:

Z = (58.7 - 78)/36

Z = -0.54

Z = -0.54 has a p-value of 0.2946.

1 - 0.2946 = 0.7054 = 70.54%.

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In a case whereby a right triangle, sin(7x+5)=cos(8x-5),  the smaller of the triangles two acute angles is 43°.

The concept that will be used is  right triangle. An acute angle is one that is smaller than 90 degrees in length. The correct angle is larger than this angle (which is equal to 90 degrees).

We can see  that sin(7x+5)=cos(8x-5)

An it implies that 7x+5 -8x-5  =90°

15x=90

x= 6

Then 7(6)+5= 47°     8(6)-5 = 43°

Hence the smaller of the triangles two acute angle is 43°

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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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Answer:

Step-by-step explanation:

The slope's simplest form is 1/2.

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 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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166158  is the break-even point for the manual process

An expression is combination of variables, numbers and operators.

Given that The manual process will have a fixed cost of $36,234 and a variable cost of $2.14 per bag.

Let the number of bags will be x

36234+2.14x..(1)

The mechanized process would have a fixed cost of $84,420 and a variable cost of $1.85 per bag.

84420+1.85x..(2)

From equation 1 and 2

36234+2.14x=84420+1.85x

2.14x-1.85x=84420-36234

0.29x=48186

Divide both sides by 0.29

x=166158

Hence, 166158  is the break-even point for the manual process

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The equation that can be used to find how many hours, x, the second part of the trip will take is:

distance = rate x time

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The fraction that voted for the gym is calculated as: 5/28.

To find out what fraction voted for the gym, you have to subtract the fractions that voted for the restaurant and the library from 1, which represents the total number of people surveyed.

You can do this by adding the fractions that voted for the restaurant and the library and then subtracting the sum from 1.

(1/4) + (4/7) = (7/28) + (16/28) = (23/28)

so 1 - (23/28) = (5/28)

Therefore, 5/28 of the people surveyed voted for the gym.

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The fractions with different numerators and denominators but the same value are said to be equivalent fractions.

For instance, since 2/4 and 3/6 both equal the 1/2, they are equivalent fractions. An element of a whole is a fraction. The same amount of the whole is represented by equivalent fractions.

A rule that says the result of multiplying the numerator and denominator of a fraction by the same nonzero number is a fraction equal to the original fraction.

Equivalent fractions are those that, despite their visual differences, represent the same value. For instance, if you have a cake and cut it into two equal pieces, you will have consumed half of the cake.

In this case, it should be noted 1/2 is the same as 3/6.

Note that an overview was given as your information is incomplete.

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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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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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In trigonometry it is important that the right triangles (reference triangles) have a consistent orientation. the reference triangles always have a leg perpendicular to the y-axis , the value of the hypotenuse is positive , and is the angle adjacent to the y-axis and hypotenuse.

A right angle triangle has six trigonometric ratios: Sin, Cos, Tan, Cosec, Sec, and Cot. They represent, successively, Sine, Cosine, Tangent, Cosecant, Secant, and Cotangent.

So, when we graph a right angle triangle, we draw a side of triangle perpendicular to y-axis and another side will be on y-axis. The remaining side left would be hypotenuse that will always be positive and is adjacent to the side perpendicular to y-axis and the side on the y-axis.

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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 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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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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The total area of the garden is given as follows:

32.1 m².

The total area of the garden is obtained applying the proportions in the context of this problem.

The area of native plants is given as follows:

107/4 = 26.75 m².

This area of 26.75 m² represents a fraction of 5/6 of the total area g of the garden, hence the total area of the garden is obtained applying the proportion as follows:

5g/6 = 26.75.

g = 26.75 x 6/5

g = 32.1 m².

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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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The number of years that it will it have about 100 students is 11 years.

Final population = Initial population * (1-0.04)^years

Where 0.04 is the percentage decrease (4%) converted to decimal form, and "years" is the number of years in the future.

We can use this formula to find the number of years it will take for the senior class to have about 100 students:

Final population = 100

Initial population = 160

100 = 160 * (1-0.04)^years

We can solve for "years" by taking the natural logarithm of both sides:

ln(100) = ln(160 * (1-0.04)^years)

ln(100) = ln(160) + ln((1-0.04)^years)

and then we can solve for the power of (1-0.04)

ln(100) - ln(160) = ln((1-0.04)^years)

now we can get the value of years

years = (ln(100) - ln(160)) / ln(1-0.04)

which is around 10.72 , so it would take about 11 years for the senior class to have about 100 students.

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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 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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