a scale on a map reads 2in 150ft find the actual distance if the length on a map is 4.5 inches ​

The 90% confidence interval for the difference in the population means is -2.51 to 0.31

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

xˉ₁ = −17.1

s₁² = 8.4

n₁ = 22

​xˉ₂ = −16.0

s₂² = 8.7

n₂ = 24

Calculate the pooled variance using

P = (df₁ * s₁² + df₂ * s₂²)/df

Where

df₁ = 22 - 1 = 21

df₂ = 24 - 1 = 23

df = 22 + 24 - 2 = 44

So, we have

P = (21 * 8.4 + 23 * 8.7)/44

P = 8.56

Also, we have the standard error to be

SE = √(P/n₁ + P/n₂)

So, we have

SE = √(8.56/22 + 8.56/24)

SE = 0.86

The z score at 90% CI is 1.645, and the CI is calculated as

CI =  (x₁ - x₂) ± z * SE

So, we have

CI = (-17.1 + 16.0) ± 1.645 * 0.86

This gives

CI = -1.1 ± 1.41

Expand and evaluate

CI = (-2.51, 0.31)

Hence, the confidence interval is -2.51 to 0.31

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Answer:21 tree cards

Step-by-step explanation:

Answer:

4th option

Step-by-step explanation:

the absolute value function always gives a positive result, however, the expression inside can be positive or negative, that is

\(\frac{x}{2}\) = 8 or - \(\frac{x}{2}\) = 8

solving each equation

\(\frac{x}{2}\) = 8 ( multiply both sides by 2 to clear the fraction )

x = 2 × 8 = 16

or

- \(\frac{x}{2}\) = 8 ( multiply both sides by 2 )

- x = 16 ( multiply both sides by - 1 )

x = - 16

then x = - 16 , x = 16

1) In the context of statistics, the term "normal" is referred to a distribution of the data that follows the characteristic of the Normal distribution: symmetrical and bell shaped.

It was named "normal" distribution because it represents many distributions of measures in nature. But it does not represent what is normal or not in all the possible contexts.

2) If we graph the histogram of the data, we can check if the distribution is normal-like byb looking at those two characteristics: how symmetric is the distribution of the data around the mean (the more symmetric, the closer to the normal distribution) and the shape of the distribution (it should be bell-shaped, with more data around the mean and less on the tails).

This gives us a total of 1,583,616 ft-lbs of work required to pump the water out of the pool.

Amount is a numerical value that refers to the total sum of money or other type of payment due. It is used to quantify the size of a transaction, the cost of goods or services, or any other type of financial transaction. Amounts can be expressed in a variety of different currencies, and they can be negative (owing) or positive (owed).

To calculate the amount of work required to pump all the water from the rectangular swimming pool into a drain at the top edge, we must first calculate the volume of the water in the pool. Volume is calculated by multiplying the length, width, and depth of the pool, which in this case is 20 ft x 20 ft x 8 ft = 3,200 cubic ft. Since the pool is filled to 1 ft below the top, the volume of water is 3,200 ft3 - 20 ft3 = 3,180 ft3.

Next, we must calculate the weight of the water, which is the volume multiplied by the weight density of water (62.4 lb/ft3). The weight of the water in the pool is 3,180 ft3 x 62.4 lb/ft3 = 197,952 lbs.

Finally, to calculate the amount of work required to pump the water from the pool into a drain at the top edge, we must multiply the weight of the water (197,952 lbs) by the height of the drain (8 ft). This gives us a total of 1,583,616 ft-lbs of work required to pump the water out of the pool.

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Under any circumstances, the imaginary number i = √-1. We use i to represent the square root of a negative number because negative numbers cannot have square roots (ex: 2^2 = 4, -2^2 = 4).

So, we have a complex number 2 + i. The absolue value? Simple.

\(|2 + i|\\2 + |\sqrt{-1} |\\2 + \sqrt{1} \\2 + 1\\3\)

If you need an explanation, look at it this way. The number cannot exist. Yet let's assume it did exist for a moment. What would be the absolute value of a negative square root if they could exist? Well, it would be the same as the square root of that number's opposite, it's positive counterpart!

So, what is the positive counterpart of -1? That would be 1. What's the square root of 1? 1! So, why don't we eliminate these steps? Instead of assuming √-1 can exist and then finding the absolute value of that, just skip those steps and instead take √1, or just 1.

So finally: |√-1| = 1

Answer: x=4

               x=12

Step-by-step explanation:

7x=28

divide 7 on both sides

28/7=4

x=4

4x=48

divide 4 on both sides

48/4=12

x=12

Answer:

\( d = 123 \)

Step-by-step explanation:

The given figure above is an inscribed quadrilateral with all four vertices lying on the given circle, thereby forming chords each.

Therefore, the opposite angles of the above quadrilateral are supplementary.

This means:

\( c + 31 = 180 \) , and

\( d + 57 = 180 \)

Find the measure of d:

\( d + 57 = 180 \)

Subtract 57 from both sides.

\( d + 57 - 57 = 180 - 57 \)

\( d = 123 \)

(a) The total degree of freedom of the experiment is 14.

(b) The total degree of freedom of the experiment is 4.

If two data points were collected at each combination of the factors, the total degrees of freedom of the experiment is given by the formula: (n-1)Total degrees of freedom = (k1 - 1) + (k2 - 1) + [(k1 - 1) × (k2 - 1)]

Where n is the number of data points collected at each combination of factors, k1 is the number of levels of the first factor, and k2 is the number of levels of the second factor.

a) In this problem, there are 3 levels for the first factor and 4 levels for the second factor.

Therefore, using the formula above, the total degrees of freedom of the experiment can be calculated as follows:

(2-1)(3-1)+[ (4-1)(3-1)] = 2(2) + 6(2) = 4 + 12 = 16 degrees of freedom.

However, since two data points were collected at each combination of the factors, 2 degrees of freedom should be subtracted from the total degrees of freedom.

Hence, the final answer is: Total degrees of freedom = 16 - 2 = 14 degrees of freedom.

b)In this problem, there are 2 levels for the first factor and 5 levels for the second factor. Therefore, using the formula given above, the total degrees of freedom of the experiment can be calculated as follows:

(3-1)(2-1)+[ (5-1)(2-1)] = 2 + 4(1) = 6 degrees of freedom.

However, since two data points were collected at each combination of the factors, 2 degrees of freedom should be subtracted from the total degrees of freedom. Hence, the final answer is:

Total degrees of freedom = 6 - 2 = 4 degrees of freedom.

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(a) The total degree of freedom of the experiment is 14.

(b) The total degree of freedom of the experiment is 4.

Given that,

a) The first factor has 3 levels, while the second factor has 4 levels.

b)  The first factor has 2 levels, while the second factor has 5 levels.

We know that,

When two data points were collected at each combination of the factors, the total degrees of freedom of the experiment is, (n-1)

Total degrees of freedom = (k₁ - 1) + (k₂ - 1) + [(k₁ - 1) × (k₂ - 1)]

Where n is the number of data points collected at each combination of factors, k₁ is the number of levels of the first factor, and k₂ is the number of levels of the second factor.

a) Since, there are 3 levels for the first factor and 4 levels for the second factor.

Therefore, the total degrees of freedom of the experiment can be calculated as follows:

(2 - 1)(3 - 1) +[ (4-1)(3-1)]

= 2(2) + 6(2)

= 4 + 12

= 16 degrees of freedom.

However, since two data points were collected at each combination of the factors, 2 degrees of freedom should be subtracted from the total degrees of freedom.

Hence, the final answer is:

Total degrees of freedom = 16 - 2

                                       = 14 degrees of freedom.

b) Since, there are 2 levels for the first factor and 5 levels for the second factor.

Therefore, the total degrees of freedom of the experiment can be calculated as follows:

(3-1)(2-1)+[ (5-1)(2-1)]

= 2 + 4(1)

= 6 degrees of freedom.

However, since two data points were collected at each combination of the factors, 2 degrees of freedom should be subtracted from the total degrees of freedom. Hence, the final answer is:

Total degrees of freedom = 6 - 2

                                        = 4 degrees of freedom.

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Answer:

the answer of v is -4.6 of the question

Answer:

Your question has already being answered.

I am just here to ask for brainliest please.

sorry for the interruption

The magnitude of the average velocity vector is approximately 3.651 m/s.

To find the magnitude of the average velocity vector, we need to calculate the displacement and divide it by the time taken.

Representation:

Initial position: D1 = (50 m North, 10 m East)

Final position: D2 = (5 m North, 35 m East)

Time taken: t = 15 seconds

Equations:

Displacement vector (ΔD) = D2 - D1

Average velocity vector (\(V_{avg}\)) = ΔD / t

Algebra work:

ΔD = D2 - D1

   = (5 m North, 35 m East) - (50 m North, 10 m East)

   = (-45 m North, 25 m East)

|ΔD| = √((-45)^2 + 25^2)  [Magnitude of the displacement vector]

\(V_{avg}\) = ΔD / t

       = (-45 m North, 25 m East) / 15 s

       = (-3 m/s North, 5/3 m/s East)

|\(V_{avg}\)| = √((-3)^2 + (5/3)^2)  [Magnitude of the average velocity vector]

Symbolic answer:

The magnitude of the average velocity vector is approximately 3.651 m/s.

Units check:

The units for displacement are in meters (m) and time in seconds (s). The average velocity is therefore in meters per second (m/s), which confirms the units are consistent with the calculation.

Therefore, the magnitude of the average velocity vector is approximately 3.651 m/s.

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The cost of the total fuel consumed can be determined by the conversion of the Euro into Dollars. The total cost of the fuel is 383 USD.

Significant Figure

Significant figures are the number of digits in a value, often a measurement, that contribute to the degree of accuracy of the value. We start counting significant figures at the first non-zero digit. Calculate the number of significant figures for an assortment of numbers.

Euro and Dollars:

The cost of the total fuel consumed can be determined by the conversion of the Euro into Dollars.

Given here,

Total distance = 5000 km

Average fuel consumption = 6 lit per 100 km = 0.06 lit / km

Average fuel cost = 1.063 EUR/lit

1 EUR  = 1.2 USD

So, Total fuel consumption,

⇒ 5000 km × 0.06 lit /km

⇒ 300 lit

Thus, Total fuel cost,

⇒ 300 lit × 1.063 EUR/lit

⇒ 318.9 EUR

⇒ 318.9 EUR × 1.2 USD

⇒ 383 USD

Therefore, the total cost of the fuel is 383 USD

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Answer:

The graph of y = a·f(x) will compress (or shrink) vertically when |a| < 1.

Step-by-step explanation:

A compression is a transformation that decreases the distance between corresponding points of a graph and a line.

A vertical compression (or shrink) by a factor of a , such that y = a·f(x), where 0 < a < 1. This means that when a is between 0 and 1, the parent graph tends to widen.

In the given problem where y = 0.1x², the a = 0.1, which made the graph wider. This represents the vertical shrink (toward the x-axis) by a factor of 0.1.

Answer:

\( \sf \: a = 5\)

Step-by-step explanation:

Now we have to,

→ find the required value of a.

The equation is,

→ 2 + a = 7

Then the value of a will be,

→ 2 + a = 7

→ a + 2 = 7

→ a = 7 - 2

→ [ a = 5 ]

Hence, the value of a is 5.

As per Mental hypothesis, the statistical inference procedures that we should use Chi-square test for goodness of fit.

Hypothesis

In probability, an idea or explanation that you then test through study and experimentation is known as hypothesis.

Given,

Here we have given that, an experiment involving peas results in 580 offspring, 152 of which peas have yellow pods. Mendel claimed that the proportion of peas with yellow pods should be 25%. we want to know if these data are consistent with Mendel's hypothesis.

And we need to find in which statistical inference procedures should we use.

According to the definition of Chi-square test for goodness of fit, the claim is that the proportion of peas with yellow pods should be 25%. And then here the researcher wants to check that the experimental and observed counts of yellow offspring peas shows significant difference or not.

So, the statistical procedure used to study this case is Chi-square test for goodness of fit . Hence, option (1) is correct.

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9514 1404 393

Answer:

  1. 2x +2y = 310; x -y = 55

  2. y = 50, x = 105

Step-by-step explanation:

Let the numbers be represented by x and y. Double the numbers would give 2x and 2y. We're told the sum of the doubled numbers is 310, so one equation is ...

  2x + 2y = 310

The difference of the numbers is (x-y). We're told that difference is 55, so the other equation is ...

  x - y = 55

__

We can divide the first equation by 2, and subtract the second.

  1/2(2x +2y) -(x -y) = 1/2(310) -(55)

  2y = 100 . . . . . . . simplify

  y = 50 . . . . . . . . . divide by 2

  x -50 = 55   ⇒   x = 105 . . . . use the second equation to find x

The two numbers are 105 and 55.

Answer:

A

Step-by-step explanation:

Comment

The first one. Such an expression requires an isolation plus or minus sign and two terms that are not alike.

Answer

A

Answer:

6x+4

Step-by-step explanation:

A term can be a constant(like 7,4,3 etc) or a variable (x,y etc) which is separated by a multiplication, division,addition or subtraction sign.

The ability for Nike to manufacture its own shoes and then build stores for distribution is an example of Forward Integration.

What is forward integration ?

In order to lower manufacturing costs and increase efficiency, a sort of vertical integration known as "forward integration" moves up the supply chain.

An operational competency is what?

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\(\text {Hi! Let's Solve this Problem!}\)

\(\text {The First Step is to Convert all Mixed Numbers into Improper Fractions:}\)

\(\text {Multiply 5*5 and get 15. Now add 1 and get 16.}\\\text {5 1/3 = 16/3}\)

\(\text {Multiply 2*5 and get 10. Now add 4 and get 14.}\\\text {2 4/5 = 14/5}\)

\(\text {Your new Problem should be: 16/3-14/5}\)

\(\text {The Next Step is to Subtract:}\)

\(\text {16/3-14/5=}\)

\(\text {Your Answer would be:}\)

\(\fbox {38/15}\)

\(\text {Your Final Step is to Convert 38/15 into a Mixed Number:}\)

\(\text {38/15=}\)

\(\text {Your Final Answer would be:}\)

\(\fbox {2 8/15}\)

\(\text {Best of Luck!}\)

\(\text {-LimitedX}\)

Answer:

Perimeter is 16x - 10

Step-by-step explanation:

\({ \sf{perimeter = 2(length + width)}} \\ p = 2 \{(5x - 7) + (3x + 2) \} \\ p = 2(8x - 5) \\ p = 16x - 10\)

Answer:

Ali ran 25.13 m more than bily

Step-by-step explanation:

From the diagram, we can see that bully runs with the inner track line while Ali runs with the outer track line.

Thus;

Diameter of inner semi circle = 20 m

Diameter of outer semi circle = 20 + 4 + 4 = 28 m

Perimeter of inner semi circle = πD/2 = 10π

Perimeter of outer semi circle = πD/2 = 14π

Now, perimeter of Billy = 80 + 80 + 10π + 10π = 222.83 m

Perimeter of Ali = 80 + 80 + 14π + 14π = 247.96 m

Thus, in one lap, difference in distance between Ali and billy = 247.96 - 222.83 = 25.13 m

Step-by-step explanation:

To dilate the figure by a factor of 2, I will multiply the x and y-value of each point by 2. I plotted all the new points to find the new triangle. To dilate the figure by a factor of 2, I will multiply the x-value of each point by 2.

Answer:

93

Step-by-step explanation:

87 + x = (90*2)

87 + x = 180

x = 180-87

x = 93

Answer:

93

Step-by-step explanation:

Given:

The area of a rectangle = 14 square units.

The side lengths are a and b.

\(a=2\dfrac{1}{3}\)

To find:

The value of b.

Solution:

We know that, the area of a rectangle is:

\(Area=Length\times Width\)

The area of the given rectangle is:

\(14=a\times b\)

\(14=2\dfrac{1}{3}\times b\)

\(14=\dfrac{2(3)+1}{3}b\)

\(14=\dfrac{6+1}{3}b\)

On further simplification, we get

\(14=\dfrac{7}{3}b\)

\(14\times 3=7b\)

\(42=7b\)

Divide both sides by 7.

\(\dfrac{42}{7}=b\)

\(6=b\)

Therefore, the value of b is 6 units.

The remainder when a positive integer x leaves a remainder of 2 when divided by 8 and x+9 is divided by 8 is 5.

If the positive integer x leaves a remainder of 2 when divided by 8, then we can say that x = 8k + 2, where k is an integer.

Now, if we divide x+9 by 8, we get:

(x+9)/8 = (8k + 2 + 9)/8
         = (8k + 11)/8
         = k + (11/8)

So, the remainder when x+9 is divided by 8 is 11/8. However, since we are dealing with integers, the remainder can only be a whole number between 0 and 7.

Therefore, we need to subtract the quotient (k) from the expression above and multiply the resulting decimal by 8 to get the remainder:

Remainder = (11/8 - k) x 8

Since k is an integer, the only possible values for (11/8 - k) are -3/8, 5/8, 13/8, etc. The closest whole number to 5/8 is 1, so we can say that:

Remainder = (11/8 - k) x 8 ≈ (5/8) x 8 = 5

Therefore, the remainder when x+9 is divided by 8 is 5.

If a positive integer x leaves a remainder of 2 when divided by 8, then x can be expressed as 8k + 2, where k is an integer. To find the remainder when x+9 is divided by 8, we divide x+9 by 8 and subtract the quotient from the decimal part. The resulting decimal multiplied by 8 gives us the remainder. In this case, the decimal is 11/8, which is closest to 1. Thus, we subtract the quotient k from 11/8 and multiply the result by 8 to get the remainder of 5.

The remainder when a positive integer x leaves a remainder of 2 when divided by 8 and x+9 is divided by 8 is 5.

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Answer:

2√21

Step-by-step explanation:

let the sides of bigger triangle be a, b and d.

then,

a²= b² + d² [ by Pythagoras theorem]

13² = 9² + d²

d² = 13² - 9²

d²= 169 - 81

d² = 88

d = √88

Now, the sides of smaller triangle are c, x, and d

by Pythagoras theorem,

d² = c²+x²

(√88)² = 2² + x²

88 - 4 = x²

x² = 84

x = √84

x= 2x2x3x7

x = 2√21

Therefore, the value of x is 2√21

Hope it's helpful..

Answer:

a= 130

Step-by-step explanation:

Since all angles of a triangle add up to 180

180= a+b+c

180= a+20+30

180=a+50

180-50= a

130= a

we get: y = (-2 - 3√3) x + 2(4 + 3√3)Hence, the slope of the tangent line at P is m = - (4 + 3√3) / 2 and equation of tangent line at P is y = (-2 - 3√3) x + 2(4 + 3√3).

Given: function y=f(x)= 4/(−2+x²), P(2,2)To find: Slope of the tangent line to its inverse function f⁻¹ at P, Equation of the tangent line to the graph of f⁻¹ at P.

Solution:

We have to find the inverse of f(x) first. Let's do that: y = f(x) => y = 4 / (-2 + x²) => x y - 2y = 4 / x => x²y - 2xy = 4 => x²y - 2xy - 4 = 0This is a quadratic equation in x y. Using the quadratic formula, we can get the value of  x y as: $$x y=\fraction{2 \pm \sqrt{20}}{2}$$$$x y=1 \pm \sqrt{5}$$Therefore, we have, x.f⁻¹(x) = x y = 1 ± √5 => f⁻¹(x) = (1 ± √5) / x

Let's find the slope of tangent of f⁻¹(x) at (2,2).m = d y/dx = 1 / (d y/dx of f(x) at x = f⁻¹(2))Let x = f⁻¹(2), then we have f⁻¹(2) = (1 ± √5) / 2Putting x = f⁻¹(2) in f(x), we get:2 = 4 / (-2 + (f⁻¹(2))²) => (f⁻¹(2))² - 2(f⁻¹(2)) - 2 = 0

Solving, we get f⁻¹(2) = 1 + √3 (We will take positive value as f⁻¹(2) > 0)Now, let's find d y/dx of f(x) at x = f⁻¹(2) using chain rule: d y/dx = d y/du . du/dx where, u = -2 + x²dy/du = -4 / (u²)du/dx = 2xUsing this, we get: d y /dx at x = f⁻¹(2) = -2 / (4 + 3√3)Putting this in slope equation of f⁻¹(x), we get: m = 1 / (d y/dx at x = f⁻¹(2)) = - (4 + 3√3) / 2Let's find the equation of the tangent line to f⁻¹(x) at (2,2) using point-slope form: y - y1 = m(x - x1)Putting the value of m and (x1, y1) = (f⁻¹(2), 2), we get:

y - 2 = - (4 + 3√3) / 2 (x - 2)

Simplifying, we get: y = (-2 - 3√3) x + 2(4 + 3√3)Hence, the slope of the tangent line at P is m = - (4 + 3√3) / 2 and equation of tangent line at P is y = (-2 - 3√3) x + 2(4 + 3√3).

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The equation of the tangent line at point `P(2,2)` is `x = -2`.

Given function is `f(x)= 4/(−2+x²)` and `P(2,2)`

a. Slope of the tangent line at that point:
m = 1/f'(f⁻¹(P)),

where `f⁻¹(P)` is the inverse of `f` at point `P`.

First, we need to find the inverse of the given function f(x).

So, `y = 4/(−2+x²)` can be written as `x² - 2 = 4/y`.

Then, `x² = 4/y + 2`Taking the reciprocal of both sides,

`1/x² = y/4 + 1/2`.

Then, `y = 4/(2x² - 4)`.

So, `f⁻¹(x) = 4/(2x² - 4)`Now, we will find the derivative of `f⁻¹(x)` using the chain rule.`

(f⁻¹)'(x) = (d/dx)(4/(2x² - 4))``= -8x/(2x² - 4)²

Hence, `f'(f⁻¹(P)) = f'(2) = 8/3`.

So, `m = 1/f'(f⁻¹(P)) = 3/8`.

Therefore, the slope of the tangent line at that point is `3/8`.

b. Equation of the tangent line at that point:

Let `y = f⁻¹(x)`.

So, `x = f(y)` is the equation of the tangent line to the graph of `f⁻¹` at point `P` using implicit differentiation.

`f(y) = 4/(2y² - 4)`

Differentiating with respect to `x`,

we get:`dx/dy = -8y/(2y² - 4)²

At point `P(2,2)`, the slope of the tangent line is `3/8`.

So, substituting the values, we get:`3/8 = dx/dy = -8y/(2y² - 4)²

Solving for `y`, we get `y = 2`.

Now, `x = f(y) = 4/(2y² - 4) = -2`.

So, the point on the graph of `f⁻¹` is `(-2,2)` which is the same as the point `(2,2)` on the graph of `f`.

The equation of the tangent line at point `P(2,2)` is `x = -2`.

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