What is simplest radical form in math?

The equivalent exponential expression to 10^5/10² is given as follows:

10³.

The exponential expression for this problem is defined as follows:

10^5/10².

When two terms with the same base and different exponents are divided, we keep the base and subtract the exponents.

The subtraction of the exponents in this problem is given as follows:

5 - 2 = 3.

Hence the equivalent exponential expression to 10^5/10² is given as follows:

10³.

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The price of a t-shirt is $43.50.

Let's call the price of a t-shirt "t" and the price of a pair of jeans "j".

For David:

4t + 3j = 181

For Jennifer:

t + 2j = 94

We can use these two equations to solve for t and j. Subtracting the second equation from the first, we have:

3t + j = 87

Next, we can substitute the second equation into the third equation to eliminate t:

3(t + 2j) = 3 * 94 = 282

Expanding the left side, we have:

3t + 6j = 282

Subtracting j from both sides:

3t + 5j = 282 - j

Combining like terms:

3t + 6j = 282

Subtracting the first equation from the third equation:

2t = 181 - 94

Combining like terms:

2t = 87

Finally, solving for t:

t = 87 / 2 = 43.5

The price of a t-shirt is $43.50.

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The price of a t-shirt is $43.50.

Let's call the price of a t-shirt "t" and the price of a pair of jeans "j".

For David:

4t + 3j = 181

For Jennifer:

t + 2j = 94

We can use these two equations to solve for t and j. Subtracting the second equation from the first, we have:

3t + j = 87

Next, we can substitute the second equation into the third equation to eliminate t:

3(t + 2j) = 3 * 94 = 282

Expanding the left side, we have:

3t + 6j = 282

Subtracting j from both sides:

3t + 5j = 282 - j

Combining like terms:

3t + 6j = 282

Subtracting the first equation from the third equation:

2t = 181 - 94

Combining like terms:

2t = 87

Finally, solving for t:

t = 87 / 2 = 43.5

The price of a t-shirt is $43.50.

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the function is defined on the interval [0,1], we must have 0 ≤ x ≤ 1. Therefore, the value of x for which[tex]f'(x)=0 is x = 0.[/tex]

To find the value of x for which[tex]f'(x)=0[/tex], we need to differentiate the given function.

[tex]f'(x) = (e-1)(π/2)(ex)(cos(π/2x)) - (sin(π/2x))[/tex]

Now, set [tex]f'(x) = 0[/tex]and solve for x.

[tex](e-1)(π/2)(ex)(cos(π/2x)) - (sin(π/2x)) = 0(e-1)(π/2)(ex) = (sin(π/2x))ex = (sin(π/2x))/(e-1)(π/2)[/tex]

Taking natural log on both sides

[tex]xln(e) = ln(sin(π/2x)) - ln((e-1)(π/2))xln(e) = ln(sin(π/2x)) - ln(e-1) - ln(π/2)x = (ln(sin(π/2x)) - ln(e-1) - ln(π/2))/ln(e)[/tex]

Since the function is defined on the interval [0,1], we must have 0 ≤ x ≤ 1.

Therefore, the value of x for which [tex]f'(x)=0 is x = 0.[/tex]

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The mean, median, standard deviation, and interquartile range for each data set is given below.

The IQR is a measure of the middle 50% of values when they are organized from lowest to highest. To get the interquartile range, find the median (middle value) of the lower and upper half of the data (IQR).

These are the values for the quartiles 1 (Q1) and 3 (Q3). The IQR is the distinction between Q3 and Q1.

Using the statistical tool, the following were arrived at for Manuel:

Standard Deviation = 3.13961

Mean = 8

Median = 8

IQR = Q3-Q1 = 10 - 6 = 4

Using the statistical tool, the following were arrived at for Gretchen:

Standard Deviation = 4.68737.

Mean = 9.6

Median = 9

IQR = IQR = Q3-Q1 = 12 - 7 = 5.

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1.6256 Meters in 5 foot 4 inches

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There are 1.6256 Meters in 5 foot 4 inches

As a result, multiplying a measurement by 12 will convert it from feet to inches. Since it is an exact number, there will be no restrictions on utilising significant figures.

Conversion of feet to inches where both length measurement units are in the imperial system. the standard unit for centimetre length measurements. Twelve inches are equivalent to one foot.

This is also how tall I am because I'm 5'7". I would first convert the feet to inches using the closest I can remember conversion factor of 2.54 centimetres to 1 inch.

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It's definitely one of the more rewarding survival experiences that has hit the platform.

Is Into the Radius VR worth it?

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if |v| = 4 and |w| = 7, what are the smallest and the largest possible values of |v − w|

smallest and the largest possible values of v · w

v and w are vectors, not numbers. v*w indicates the dot product of these vectors and l v l and l w l their magnitudes.

Assuming v and w are vectors with any direction but with definite magnitudes

||v − w|| ≤ ||v|| + ||w|| = 11

and ||v − w|| ≥ ||v|| − ||w||| = 3,

while

|v · w| = ||v||||w|| cos θ ≤ ||v|| · ||w|| = 28,

so −28 ≤ v · w ≤ 28.

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The probability of X being greater than Y is equal to 1 minus the probability of X being less than or equal to Y multiplied by the probability of Y being less than or equal to X, which can be expressed as 1 minus (1 - e^(-(λ1 + λ2)t))/2, or e^(-(λ1 + λ2)t)/2.

P(X > Y) = 1 - P(X ≤ Y) = 1 - (1 - e^(-(λ1 + λ2)t))/2 = e^(-(λ1 + λ2)t)/2

1. P(X > Y) = 1 - P(X ≤ Y)

2. P(X ≤ Y) = P(X ≤ Y ∩ Y ≤ X)

3. P(X ≤ Y ∩ Y ≤ X) = P(X ≤ Y)P(Y ≤ X) (Since X and Y are independent)

4. P(X ≤ Y) = 1 - P(X > Y)

5. P(Y ≤ X) = 1 - P(Y > X)

6. P(X > Y) = 1 - P(X ≤ Y)P(Y ≤ X)

7. P(X > Y) = 1 - (1 - e^(-(λ1 + λ2)t))/2

8. P(X > Y) = e^(-(λ1 + λ2)t)/2

The probability of X being greater than Y is equal to 1 minus the probability of X being less than or equal to Y. Since X and Y are independent, the probability of X being less than or equal to Y and Y being less than or equal to X is equal to the product of the probabilities of X being less than or equal to Y and Y being less than or equal to X. The probability of X being less than or equal to Y is equal to 1 minus the probability of X being greater than Y, and the probability of Y being less than or equal to X is equal to 1 minus the probability of Y being greater than X. Therefore, the probability of X being greater than Y is equal to 1 minus the probability of X being less than or equal to Y multiplied by the probability of Y being less than or equal to X, which can be expressed as 1 minus [tex](1 - e^(-(λ1 + λ2)t))/2, or e^(-(λ1 + λ2)t)/2.[/tex]

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When it is simpler to describe an angle as the sum or difference of distinct angles (0°, 30°, 45°, 60°, 90°, and 180°), the sum and difference formulae in trigonometry are used to determine the value of the trigonometric functions at those particular angles.

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The two choices that reflect one for the center and one for the spread are:

A. Better measure of spread: the interquartile range (IQR)

B. Better measure of center: the median

For the first data set, the values appear to be unordered, so it would be difficult to determine the mean. The median is a more appropriate measure of center for this data set, as it would provide a value that separates the data into two halves.

The interquartile range (IQR) is a better measure of spread for this data set, as it provides a robust measure of spread that is less sensitive to outliers. The IQR is the difference between the 75th percentile and the 25th percentile of the data, and it provides a measure of the spread of the middle 50% of the data.

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The component that is missing from the biologist's process is:

c) The biologist did not randomly assign each of the bats to the treatment groups.

When carrying out a research study where you have groups created that you want to study, differences between and within groups can be satisfactory ensuring that they are not systematic when subjects are randomly assigned to groups.

Given, A biologist wonders if the life span of bats will be affected by two new food sources from invasive species moving into an area.

a group where the diet will not include invasive species (control), a group where the diet will include one invasive species (treatment group 1), and another group where the diet will include the other invasive species (treatment group 2).

Thus, it gives the researcher the confidence that groups are the same in terms of variables, and any differences can be confidently ascribed to experimental treatments.

Therefore, the component that is missing from the biologist's process is: c. The biologist did not randomly assign each of the bats to the treatment groups.

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As the y variable tends to increase when the x variable increases, we say the variables have a positive correlation. When the y variable tends to decrease as the x variable rises, we say there is a negative correlation between the variables.

A graph is a visual representation or diagram that displays facts or values in an organized manner in mathematics.

The points on a graph are typically used to depict the relationships between two or more things.

Making a diagram that shows the link between two or more objects is known as developing a graph.

Scatterplots frequently reveal relationships or trends.

We say there is a positive correlation between the variables when the y variable tends to rise when the x variable rises.

We say there is a negative correlation between the variables when the y variable tends to decline as the x variable rises.

Therefore, a y variable tends to increase when the x variable increases, we say the variables have a positive correlation. When the y variable tends to decrease as the x variable rises, we say there is a negative correlation between the variables.

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When written in reduced row echelon​ form, any 3 ×2 matrix will have at least one row of all zeros. When solving Ax=b​, that row will represent an equation with a zero on the left side and a possibly nonzero entry of b on the right side.

This means that there is no solution for the equation Ax=b for that specific b, making the system inconsistent.

Generalizing this argument to the case of an arbitrary A with more rows than columns, if the number of rows in A is greater than the number of columns, the reduced row echelon form of A will have at least one row of all zeros, and the corresponding equation in Ax=b will have no solution, making the system inconsistent for that specific b.

Hence, the correct answer is B.

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--The given question is incomplete; the complete question is

"Let A be a 3 times ×2 matrix. Explain why the equation Ax=b cannot be consistent for all b in a set of real numbers R3.

Generalize your argument to the case of an arbitrary A with more rows than columns.

Why is the equation Ax=b not consistent for all b in a set of real numbers R3​?

A. When written in reduced row echelon​ form, any 3 ×2 matrix will have at least one column of all zeros. Since there is not a pivot in every​ column, the matrix cannot be consistent.

B. When written in reduced row echelon​ form, any 3 ×2 matrix will have at least one row of all zeros. When solving Ax=b​, that row will represent an equation with a zero on the left side and a possibly nonzero entry of b on the right side.

C. When written in reduced row echelon​ form, any 3 ×2 matrix will have at least one row of all zeros. When solving Ax=b​, that row will represent an equation with infinitely many solutions.

D. When written in reduced row echelon​ form, any 3 ×2 matrix will have a pivot in every row. Because there are more rows than​ columns, this is too many​ pivots, and the system will be inconsistent."--

The length of the rectangular swimming pool is, 50 m.

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

We have to given that;

A rectangular swimming pool has a perimeter of 150 m.

And, The length of the pool is twice the width of the pool.

Now, Let the width of the pool = x

Then, The length of the pool = 2x

We know that;

Perimeter of rectangle = 2 (Length + Width)

Substitute all the given values, we get;

⇒ 150 = 2 (2x + x)

⇒ 150 = 2 × 3x

⇒ 150 = 6x

⇒ x = 150 / 6

⇒ x = 25

Thus, The length of the rectangular swimming pool = 2x

                                                                               = 2 × 25

                                                                               = 50 m

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For the first question, the percentage of the usual price that Elena's mom paid is 60%, and for the second question, the price that Elena's dad paid is $187.50.

For the first question, to find the percentage of the usual price Elena's mom paid, you can divide the actual price by the usual price and multiply by 100:

$150 ÷ $250 × 100 = 60%

So, Elena's mom paid 60% of the usual price for the cell phone.

For the second question, you can use the percentage of the usual price to find the actual price:

$250 × 75/100 = $187.50

So, Elena's dad paid $187.50 for the other type of cell phone, which is 75% of the usual price.

To summarize, Elena's mom paid 60% of the usual price of $250 and paid $150, while Elena's dad paid $187.50, which is 75% of the usual price.

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Answer:

[tex] \red{ \boxed{\sf{c = 0.81s}}}[/tex]

Step-by-step explanation:

(total cos t) = k (songs)

total cost / songs = k

8.1/10 = k

0.81 = k

now substitute 0.81 in for k in your equation

c = 0.81s

follow..

The fourth vertex of the rectangle using the coordinate plane is; (4, 21)

The three coordinates of the rectangle are expressed as;

(21, 21)

(21, 1)

(4, 1)

Now, when we tal about a rectangle, it is pertinent to note that two points must have the same y coordinates while two points must also have the same x -coordinates because the two parallel sides of a rectangle are equal.

Thus, we already have two sides with 21 as x-coordinate but only one with 4 as x-coordinate and as such the fourth point will have 4 as x-coordinate.

Similarly, only one point has 21 as y-coordinate and as such the fourth point will have its' y-coordinate as 21.

(4, 21)

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The value of 'x' in x² - 50 = 0 is either - 7.07 or + 7.07.

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

Given, A quadratic equation x² - 50 = 0, where x belongs to R.

x² = 50.

x = ± √50.

x = ± 7.07.

So, The value of x can be - 7.07 or it can be + 7.07 squaring both numbers will result to approximately 50.

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The requried solution of the given expression is given as x = 7.07, -7.07.

Zeros of an equation are defined as the value of the independent variable where the equation or function gives zero.

Here,
Given expression,
x² - 50 = 0
x² = 50
x = √50
x = ±7.07

Thus, the requried solution of the given expression is given as x = 7.07, -7.07.

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The general solution to the differential equation d(r)/dt = 5tln(t) is: r = (5/2)t^2ln(t) - 5te^5 + C.

The general solution to the differential equation d(r)/dt = 5tln(t) can be found using the method of integrating factors.

First, we find the integrating factor:

I = e^∫5ln(t)dt = e^(5t - 5)

Next, we multiply both sides of the equation by the integrating factor:

I * d(r)/dt = I * 5tln(t)

Now, we can integrate both sides of the equation:

∫I * d(r)/dt = ∫I * 5tln(t)dt

Using the substitution u = r and du/dt = d(r)/dt, we can simplify the left side of the equation:

du/dt = I * d(r)/dt

And on the right side, we use integration by parts:

∫I * 5tln(t)dt = (5/2)t^2ln(t) - 5te^5 + C

Finally, we can solve for r:

r = (5/2)t^2ln(t) - 5te^5 + C

The general solution to the differential equation d(r)/dt = 5tln(t) is:

r = (5/2)t^2ln(t) - 5te^5 + C.

Note that C is an arbitrary constant and represents the freedom in choosing the initial conditions for the solution.

Therefore, The general solution to the differential equation d(r)/dt = 5tln(t) is: r = (5/2)t^2ln(t) - 5te^5 + C.

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The dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches.

The area of a square with sides of one inch is equal to one square inch (plural: square inches).

We have that:

Let the dimension of the paper be x and y.

Such that:

Length = [tex]x[/tex]

Width = [tex]y[/tex]

So:

Area = [tex]x*y[/tex]

Substitute 128 for Area

[tex]128=x*y[/tex]

Make x the subject.

[tex]x=\frac{128}{y}[/tex]

When 1 inch margin is at top and bottom

The Length becomes:

[tex]Length =x+1+1[/tex]

[tex]Length = x+2[/tex]

When 2-inch margin is at both sides

The width becomes:

[tex]Width = y+2+2[/tex]

[tex]Width = y+4[/tex]

The New Area (A) is then calculated as:

[tex]A = (x+2)*(y+4)[/tex]

Substitute [tex]\frac{128}{y}[/tex] for x

[tex]A = (\frac{128}{y}+2 )*(y+4)[/tex]

Open Brackets

[tex]A = 128 + \frac{512}{y} + 2y + 8[/tex]

Collect Like Terms

[tex]A = \frac{512}{y} + 2y + 8+128[/tex]

[tex]A = \frac{512}{y} +2y+136[/tex]

[tex]A = 512y^{-1} +2y + 136[/tex]

To calculate the smallest possible value of y, we have to apply calculus.

Differentiate A with respect to y

[tex]A' = -512y^{-2}+2[/tex]

Set

[tex]A' = 0[/tex]

This gives:

[tex]0=-512y^{-2}+2[/tex]

Collect Like Terms

[tex]512y^{-2} = 2[/tex]

Multiply through by [tex]y^{2}[/tex]

[tex]y^{2} *512y^{-2} = 2*y^{2}[/tex]

[tex]512 = 2y^{2}[/tex]

Divide through by 2.

[tex]256 = y^{2}[/tex]

Take square roots of both sides.

[tex]\sqrt{256= y^{2} }[/tex]

[tex]16 =y\\\\y=16[/tex]

Recall that:

[tex]x = \frac{128}{y}[/tex]

[tex]x = \frac{128}{16}[/tex]

[tex]x=8[/tex]

Recall that the new dimensions are:

[tex]Length = x+2[/tex]

[tex]Width = y+4[/tex]

So:

[tex]Length = 8+2[/tex]

[tex]Length = 10[/tex]

To double-check.

Differentiate A'

[tex]A' = -512y^{-2}+2[/tex]

[tex]A'' = -2 * -512y^{-3}[/tex]

[tex]A'' = 1024y^{-3}[/tex]

[tex]A'' = \frac{1024}{y^{3} }[/tex]

The above value is:

[tex]A'' = \frac{1024}{y^{3} } > 0[/tex]

In other words, the estimated numbers are at their lowest.

Hence, the dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches.

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The dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches.

The area of a square with sides of one inch is equal to one square inch (plural: square inches).

We have that:

Let the dimension of the paper be x and y.

Such that:

Length = x

Width = y

So:

Area = xy

Substitute 128 for Area

128 = xy

Make x the subject.

x=128/y

When 1 inch margin is at top and bottom

The Length becomes:

length = x+2

When 2-inch margin is at both sides

The width becomes:

width = y+4

The New Area (A) is then calculated as:

A = (x+2)(y+4)

Substitute  for x

A = (128/y +2)(y+4)

Open Brackets

A = 128 +512/y + 2y +8

Collect Like Terms

A = 512/y + 2y +136

To calculate the smallest possible value of y, we have to apply calculus.

Differentiate A with respect to y

A' = -512/y*y  +2

Set

A' = 0

This gives:

y = 16

Recall that:

x = 128/y

x = 8

Recall that the new dimensions are:

Length = x +2

Width = y+4

So:

Length = 10

To double-check.

Differentiate A'

A'' = 1024/y*y*y

The above value is greater than 0

In other words, the estimated numbers are at their lowest.

Hence, the dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches.

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Answer:

Below

Step-by-step explanation:

If you lose 5 %, you basically have 95 % remaining which is .95 in decimal

y = 1000 * (.95)^x       where x is the number of months  ( x = 9 in this case)

The 10-year to 3-month term premium will be 0.079%.

Now, According to the question:

The premiums that are the regularly scheduled installments that are finished to pay the inclusion of the insurance contract are less expensive in term life coverage than in real money life coverage as the term just covers the recipients for the period the contract is purchased for instance: a half year. On the off chance that the individual who claims the arrangement passes on in a half year, the insurance agency needs to pay the recipients the capital set in the strategy.

Anyway assuming the individual passes on after the a half year or doesn't bite the dust the insurance agency pay nothing to the buyer of the strategy.

In the money life coverage the individual gets one last installment though the individual lives or passes on as the strategy goes about as a saving arrangement.

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The complete question is:

What is the 10-year to 3-month term premium of the following yield curve?

Each of the following events result in a tax payment, an example of a direct tax is D. Javier owes money to the federal government based on job earnings.

A direct tax is one that is paid by an individual or group of individuals directly to the body that levied it. Taxes on assets, real estate, personal property, and income are a few examples that are all paid by an individual taxpayer directly to the government.

Direct taxes are those that you pay to the government directly. You have paid a direct tax, for instance, if you pay income tax, property tax, or capital gains tax. On the other side, an indirect tax is when you make a purchase and someone else subsequently pays the tax on your behalf through a sales tax.

Therefore, option D is correct.

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The yummy bakery sold 216 roles and oh so good bakery sold 523 roles.

Given is that yummy bakery and oh so good bakery had a contest with these results: yummy sold 9 fewer rolls than twice what oh so good sold. together they sold a total of 639 rolls.

We can write the relation as -

2x - 9 + x = 639

3x - 9 = 639

3x = 648

x = 216

So, we can write -

2x - 9 = 2 x 216 - 9 = 532 - 9 = 523

Therefore, the yummy bakery sold 216 roles and oh so good bakery sold 523 roles.

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A rhombus has 6 and 8 centimeter diagonals, 24 cm2 is the size of the rhombus.

The product of the lengths of the diagonals divided by two equals the area of a rhombus. The formula Area = (d1 d2)/2 sq. is used to determine the area of a rhombus using diagonals.

The product of the lengths of the diagonals divided by two equals the area of a rhombus.

Knowing that, First diagonal, d1=6 cm. Diagonal 2, d2 = 8 cm Rhombus surface area is given by A=d1d22 =682 =482 =24 cm2. So, the rhombus has a 24 cm2 surface area.

A rhombus has 6 and 8 centimeter diagonals, 24 cm2 is the size of the rhombus.                

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According to a report from the Neilson company,

a) The probability that exactly 20 of them used Search Engine is 0.068

b)  the probability that 15 or fewer used Search Engines is 0.0560

c) The probability that more than 20 of them used a Search Engine is 0.2484

d) Yes, it would be unusual if fewer than 12 used Search Engine.

a. The probability that exactly 20 of 25 searches used the Search Engine can be calculated using the binomial distribution formula:

b. The probability that 15 or fewer of 25 searches used the Search Engine can be calculated as the sum of the probabilities of 0 to 15 searches using the Search Engine:

c. The probability that more than 20 of 25 searches used the Search Engine can be calculated as the complement of the probability of 20 or fewer searches using the Search Engine:

d. The probability of fewer than 12 of 25 searches using the Search Engine can be calculated as the sum of the probabilities of 0 to 11 searches using the Search Engine:

So Yes, It would be unusual if fewer than 12 of 25 searches used the Search Engine if the probability is less than a certain threshold, such as 0.05, which is often used to determine statistical significance.

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Complete Question:

According to a report of the Nielsen company,76% of internet searches used the  search engine. Assume that a sample of 25 searches is studied.

a. What is the probability that exactly 20 of them used Search Engine?

b.What is the probability that 15 or fewer used Search Engine?

c.What is the probability that more than 20 of them used Search Engine?

d.Would it be unusual if fewer than 12 used Search Engine?

According to the information, the options that correspond to the possible scale copies of the original rectangle would be 4.5 in. by 1.5 in. yes, 13.5 in. by 4.5in. Yes, and 90 in. by 30in. Yeah.

To calculate the possible scales we must carry out the following procedure: First we must make a division between the two lengths of the sides of the rectangle:

9 / 3 = 3

So, the relationship between these two lengths would be 3. Now we just have to check which options follow this proportional relationship. According to this procedure they would be the following:

4.5in. by 1.5in

13.5in. by 4.5in

90 in. by 30in

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Divide the area value by 640 to get 1 Acre = 0.0016 Square Miles.

It is necessary to calculate how many times 640 is multiplied by the number of acres in order to get how many square miles. Each 640 acres equals 1 square mile. Calculators and hand division are both acceptable methods of division.

The result of multiplying two lengths is a square unit of area, such as a square mile. Given that each length in square miles is expressed in miles, miles2 is obtained by multiplying miles by miles.

The two-acre plot's circumference, if two square acres were placed side by side, would be 1252.26 feet, or almost four and a half times around, or a mile.

1Acre = 0.0015625

          = 0.0016Sq. miles

divide the area value by 640

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