determine the minimum sample size required when you want to be be
90​%
confident that the sample mean is within one unit of the population mean and
σ=12.2.
Assume the population is normally distributed.

Answer:

Step-by-step explanation:

I assume your expression is:

6x^3-60x^2+144x.

I'll use that information.

Factor 6x^3−60x^2+144x

6x^3−60x^2+144x

=6x(x−4)(x−6)

Answer:

Step-by-step explanation:

245

Answer:

Step-by-step explanation:

There will be a vertical stretch with a factor of 3.

Answer:

4x-20

Step-by-step explanation:

(x-5) + (x-5) + (x-5) + (x-5) = 4x-20

or

(4)(x-5) = 4x-20

The expression x² - 10x + 25 will represent the a square with side (x-5) units.

A square is a geometrical figure in which we have four sides each side must be equal and the angle between two adjacent sides must be 90 degrees.

Area of square = Side²

The perimeter of square = 4× side

Length of diagonal of square = √(2) × side

Given,

Side of square = (x - 5)

The area of a square is given by = Side²

So,

Area = (x - 5)²

Area = x² - 10x + 25

Hence,The expression x² - 10x + 25 will represent the a square with side (x-5) units.

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Answer: Ian is 25 and craig is 20

Step-by-step explanation:

(45 - 5) /2 +5 to one of them

Answer:

Craig is 20 and Ian is 25 years old.

Step-by-step explanation:

I = Ian

C = Craig

I = C + 5

45 = C + I

45 = C + C + 5

45 - 5 = C + C

40 = 2C

C = 20

I = 20 + 5

Craig is 20 and Ian is 25.

The pair of figures having same volume are:

a. The cylinder has a radius of 3 units and a height of 8 units ; The cone has a radius of 6 units and a height of 6 units.

b. The cone has a radius of 8 units and a height of 9 units ; The cylinder has a radius of 4 units and a height of 12 units.

c. The rectangular prism length is labeled 16 units, width of 6 units, and height of 6 units ; The rectangular prism length is labeled 8 units, width of 8 units, height of 9 units.

What is volume of a figure?

Volume is a unit of measurement for three-dimensional space. It is usually stated quantitatively in terms of a number of imperial or US-standard units as well as SI-derived units.

i. The cone has a radius of 4 units and a height of 12 units.

⇒ Volume = π\(r^{2} \frac{h}{3}\)

⇒ Volume = π\(4^{2} \frac{12}{3}\)

⇒ Volume = 64 π

⇒ Volume = 201 cubic units

ii. The rectangular prism has a length of 18 units, a width of 6 units, a height of 6 units.

⇒ Volume = length * width * height

⇒ Volume = 18 * 6 * 6

⇒ Volume = 648 cubic units

iii. The rectangular prism length is labeled 16 units, width of 6 units, and height of 6 units.

⇒ Volume = length * width * height

⇒ Volume = 16 * 6 * 6

⇒ Volume = 576 cubic units

iv. The cylinder has a radius of 3 units and a height of 8 units.

⇒ Volume = π\(r^{2}\)h

⇒ Volume = π\(3^{2}\) * 8

⇒ Volume = 72 π

⇒ Volume = 226 cubic units

v. The cone has a radius of 8 units and a height of 9 units.

⇒ Volume = π\(r^{2} \frac{h}{3}\)

⇒ Volume = π\(8^{2} \frac{9}{3}\)

⇒ Volume = 192 π

⇒ Volume = 603 cubic units

vi. The rectangular prism length is labeled 8 units, width of 8 units, height of 9 units.

⇒ Volume = length * width * height

⇒ Volume = 8 * 8 * 9

⇒ Volume = 576 cubic units

vii. The cylinder has a radius of 4 units and a height of 12 units.

⇒ Volume = π\(r^{2}\)h

⇒ Volume = π\(4^{2}\) * 12

⇒ Volume = 192 π

⇒ Volume = 603 cubic units

viii. The cone has a radius of 6 units and a height of 6 units.

⇒ Volume = π\(r^{2} \frac{h}{3}\)

⇒ Volume = π\(6^{2} \frac{6}{3}\)

⇒ Volume = 72 π

⇒ Volume = 226 cubic units

Hence, three pairs have the same volume.

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The missing figures have been attached below.

Carrie will have $15,481.24 after taxes for a year assuming she works 52 weeks.

First, let's calculate the total taxes she pays each week:

Federal income tax rate = 10% of $350.15 = $35.02

State income tax rate = 5% of $350.15 = $17.51

Total taxes per week = $35.02 + $17.51 = $52.53

Now, we can calculate the total amount of taxes she pays for a year:

Total taxes for a year = $52.53 x 52 weeks = $2,731.56

Amount Carrie will have after taxes for a year:

Annual income before taxes = $350.15 x 52 weeks = $18,212.80

Net income after taxes = Annual income before taxes - Total taxes for a year

Net income after taxes = $18,212.80 - $2,731.56 = $15,481.24

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--The complete Question is, Carrie Burnside is single, earns $350.15 weekly, and claims 1 allowance. If the federal income tax rate is 10% plus an additional 5% state income tax rate, how much will Carrie have after taxes for a year assuming she works 52 weeks? --

The first table is a quadratic function, while the second table is an exponential function

Table 1

On this table, we can see that:

As x increases by 1, the value of y do not change constantly

This means that the table is a non-linear function

The y values on the table are

-5   -4    -1   4   11

Calculate the first difference

So, we have

-5   -4    -1     4    11

   1      3     5     7

Calculate the second difference

So, we have

-5   -4    -1     4    11

   1      3     5     7

       2     2     2

Since the second differences are equal, then the table is a quadratic table

Table 2

On this table, we can see that:

As x increases by 1, the value of y do not change constantly

This means that the table is a non-linear function

However, we can see that the y values have a common rate of 2

This means that the table is an exponential table

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Answer:

A

Step-by-step explanation:

x= -2

none of the provided options (a, b, c, d) appear to be accurate or close to the minimum space required.

To determine the minimum space required for a male restroom design with the given plumbing requirements, we need to consider the minimum space required for water closets and lavatories.

The minimum space required for water closets is typically around 30-36 inches per unit, and for lavatories, it is around 24-30 inches per unit.

Since the design requires a minimum of 12 water closets and 13 lavatories, we can estimate the minimum space required as follows:

Minimum space required for water closets = 12 water closets * 30 inches = 360 inches

Minimum space required for lavatories = 13 lavatories * 24 inches = 312 inches

Adding these two values together, we get a total minimum space requirement of 672 inches.

Among the given options, the closest value to 672 inches is option d) 249. However, this value seems significantly lower than the expected minimum space requirement.

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9)

The constant of proportionality is 3.

10)

The measure of YC is 12.

We have,

9)

YHC and WTD are similar triangles.

This means,

The ratio of the corresponding sides is equal.

Now,

TD/HC = TW/HY

Substituting the values,

150/50 = 162/54

3 = 3

This means,

3 is the constant of proportionality.

And,

10)

MRC and WYC are similar triangles.

This means,

The ratio of the corresponding sides are equal.

MR/WY = CR/YC

14/6 = 28/YC

YC = 28/14 x 6

YC = 4/2 X 6

YC = 4 x 3

YC = 12

Thus,

The constant of proportionality is 3.

The measure of YC is 12.

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If the mean seasonal factor for June was 96.9, and the sum for all twelve months is 1195, the adjusted seasonal index for June is 8.11

To calculate the adjusted seasonal index for June, we need to divide the mean seasonal factor for June by the sum of the seasonal factors for all twelve months and then multiply the result by 100.

Adjusted seasonal index for June = (Mean seasonal factor for June / Sum of seasonal factors for all twelve months) × 100

Adjusted seasonal index for June = (96.9 / 1195) × 100 ≈ 8.11

The adjusted seasonal index for June is approximately 8.11.

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A relative frequency histogram was constructed for the given data, and it was observed that the distribution is skewed to the right.

A relative frequency histogram provides a visual representation of the distribution of a dataset by displaying the relative frequencies of observations in each interval or bin.

In this case, the data is not normally distributed, as most of the observations are concentrated towards the lower end of the range and there are a few high values that skew the distribution to the right.

This can be observed by noticing that the histogram bars are taller on the left side and shorter on the right side, with a long tail towards the higher values.

Therefore, it can be concluded that the distribution is skewed to the right. This type of distribution is also known as a positively skewed distribution.

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Answer:

Below.

Step-by-step explanation:

Left side = 2 cos^2 ( π/4 - A/2) - 1

= 2 ( cos π/4  cos A/2 + sin π/4  sin A/2)^2 - 1

Now sin π/4 and cos π/4 = 1 /√2 so:

= 2 ( 1/√2 cos A/2 + 1/√2 sin A/2)^2 - 1

= 2  * 1/2( cos^2 A/2 + sin^2 A/2 + 2 sin A/2 cos A/2) - 1

But cos^2 a/2 + sin^2 A/2 = 1 so we have:

2 * 1/2( 1 +  2sin A/2 cos A/2) - 1

= 1  + 2 sin A/2 cos A/2 - 1

=  2 sin A/2 cos A/2

Using the identity 2 sin A cos A = sin 2A

2 sin A/2 cos A/2 = sin A  = right side.

So left side = right side and the identity is proved.

Answer:  see proof below

Step-by-step explanation:

Use the Double Angle Identity:  cos 2A = 2cos²A - 1

Use the Difference Identity:  cos (A - B) = cosA · cosB + sinA · sinB

Use the Unit Circle to evaluate:  cos (π/2) = 0   &     sin (π/2) = 1

Proof  LHS → RHS

\(\text{Given:}\qquad \qquad \qquad \qquad 2\cos^2\bigg(\dfrac{\pi}{4}-\dfrac{A}{2}\bigg)-1\\\\\\\text{Double Angle Identity:}\quad \cos2\bigg(\dfrac{\pi}{4}-\dfrac{A}{2}\bigg)\\\\\\\text{Simplify:}\qquad \qquad \qquad \quad \cos\bigg(\dfrac{\pi}{2}-A\bigg)\\\\\\\text{Difference Identity:}\qquad \cos\dfrac{\pi}{2}\cdot \cos A+\sin \dfrac{\pi}{2}\cdot \sin A\\\\\\\text{Unit Circle:}\qquad \qquad \qquad 0\cdot \cos A+1\cdot \sin A\\\\\\\text{Simplify:}\qquad \qquad \qquad \qquad \sin A\)

LHS = RHS:   sin A = sin A   \(\checkmark\)

Answer:

801.66

Step-by-step explanation:

calculator

Answer:

801.6632653061

Step-by-step explanation:

.......

Answer:

Step-by-step explanation:

There are 6 possibilities for each roll: 1, 2, 3, 4, 5 and 6. Each of these has a probability of 1/6.

If you roll the die 30 times, the probability of getting a 6 would be 30 x (1/6) = 5. The answer is 5.

Answer:There are 6 numbers on a die.

The probability of rolling a 6 would be 1/6 for each time you roll the die.

Multiply the number of rolls by 1/6.

30 rolls x 1/6 probability = 5 times.

Step-by-step explanation:

The values of ∂z/∂r and ∂z/∂s. These partial derivatives will depend on the specific function F(u, v, w) provided.

To find ∂z/∂r and ∂z/∂s, we need to differentiate z = F(u, v, w) with respect to r and s.
Given that u = r^2, v = -2s^2, and w = ln(r) + ln(s), we can substitute these values into z = F(u, v, w).
So, z = F(r^2, -2s^2, ln(r) + ln(s)).
To find ∂z/∂r, we differentiate z with respect to r while treating s as a constant. This gives us:
∂z/∂r = ∂F/∂u * ∂u/∂r + ∂F/∂w * ∂w/∂r.
Similarly, to find ∂z/∂s, we differentiate z with respect to s while treating r as a constant. This gives us:
∂z/∂s = ∂F/∂v * ∂v/∂s + ∂F/∂w * ∂w/∂s.
Since we don't have the specific function F(u, v, w) mentioned in the question, we cannot determine the values of ∂z/∂r and ∂z/∂s. These partial derivatives will depend on the specific function F(u, v, w) provided.

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Answer:

what?

Step-by-step explanation:

the amount in the account after $800 is invested for 1 year at 9% compounded monthly would be $875.03 (rounded to two decimal places).

Assuming an annual interest rate of 9% compounded monthly, the amount in the account after one year can be calculated using the formula:

A = P(1 + r/n)^(nt)

where:
A = the amount in the account after one year
P = the principal amount (initial investment) = $800
r = the annual interest rate (as a decimal) = 0.09
n = the number of times the interest is compounded per year = 12 (for monthly compounding)
t = the time period in years = 1

Plugging in these values, we get:

A = 800(1 + 0.09/12)^(12*1)
A = 800(1.0075)^12
A = 800(1.0938)
A = 875.03

Therefore, the amount in the account after $800 is invested for 1 year at 9% compounded monthly would be $875.03 (rounded to two decimal places).

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Answer:

y varies inversely with x is written as

y = k /x

where k is the constant of variation

y = 8 x = 1.55

8 = k / 1.55

Multiply through by 1.55

k = 12.4

The formula is

y = 12.4 / x

when y = - 0.62

- 0.62 = 12.4/x

- 0.62x = 12.4

Divide both sides by - 0.62

x = 12.4/-0.62

x = - 20

When y = - 0.62 x = - 20

Hope this helps

Answer:

Radius=7.5cm

Diameter=15cm

Step-by-step explanation:

The radius is half of the diameter which is the length of the circle measured across (or through I guess), so the radius is what is shown 7.5, and the radius doubled (x2) is the diameter so 7.5x2 = 15.

HOPE THAT HELPS AND MAKES SENSE! :)

d. dV/dt = -0.15V³ is a differential equation that could describe the relationship between the rate of change of the volume V with respect to time t of water leaking from a tank, and the cube of the volume.

A differential equation is an equation that relates a function and its derivatives. In this case, the function is the volume V of water in the tank, and the variable is time t. The problem states that the rate of change of the volume V with respect to time t is proportional to the cube of the volume. This means that the rate at which the volume is changing is directly proportional to the cube of the volume, and the proportionality constant is a negative number.

The differential equation that describes this relationship is dV/dt = -0.15V³, where dV/dt represents the rate of change of the volume with respect to time, and -0.15V³ represents the proportionality constant times the cube of the volume. The negative sign indicates that the volume is decreasing over time, as water is leaking out of the tank. This differential equation can be used to model the behavior of the water leaking from the tank, and can be used to determine the volume of water remaining in the tank at any given time.

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The probability that a randomly selected firm will earn less than 96 million dollars is 0.8907

The given data is that the mean income of firms in the industry for a year is 80 million dollars with a standard deviation of 13 million dollars. Now, it is required to find the probability that a randomly selected firm will earn less than 96 million dollars if incomes for the industry are distributed normally.

The probability is calculated by the Z-score formula which is given as below:

z = (x - μ) / σ

Where,μ = 80 (Mean),  x = 96 (Randomly selected firm income),  σ = 13 (Standard deviation)

Putting the values in the formula we have,

z = (96 - 80) / 13z = 1.23

Now we will use the Z-table to find the probability value. From the Z-table, we can say that the probability of Z-score = 1.23 is 0.8907.

Therefore, the probability that a randomly selected firm will earn less than 96 million dollars is 0.8907 (approx) when rounded off to four decimal places.

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Hello!

The first step is to subtract 1 from both sides.

\(\bf{3x+1=38}\)

\(\bf{3x=37}\)

Now, divide both sides by 3:

\(\bf{\displaystyle\frac{37}{3} }\)

Can this fraction be simplified? Nope.

Why? Because 37 and 3 do not have any common factors, except 1 (and what's the point of dividing by 1?)

Hence, the answer is

\(\huge\boxed{\text{Answer:{\boxed{\circ\star{\frac{37}{3} }}}}}\)

Hope everything is clear.

Let me know if you have any questions!

#KeepOnLearning

\(\boxed{An~Emotional~Helper!}\)

To solve the equation:

We meed to remember the identity:

Plugging this identity in the equation we have:

Hence we have the quadratic equation in the cotangent:

To solve it let:

Then we have the quadratic equation:

let's use the general formula to solve it:

Once we know the value of w we can find the value of x, remember the definition of w, then we have:

Since it is easier to work with the tangent function we will use the fact that:

Hence our equations take the form:

Finally to solve the equations we need to remember that the tangent function has a period of pi, therefore we have that:

where n is any integer number. To find the solutions in the interval given we plug n=0 and n=1 in each expression for x; therefore, the solutions in the interval are:

Statement: {x ∣ x ∈ N and 25 < x < 30} ⊆ {x ∣ x ∈ N and 10 < x ≤ 29} is a true statement.

{x ∣ x ∈ N and 25 < x < 30} ⊆ {x ∣ x ∈ N and 10 < x < 30}.

We have to check whether this statement is true or false and to modify it, if it is not correct.

We know that N represents a set of natural numbers and this set is countable.

{x ∣ x ∈ N and 25 < x < 30} represents the set of natural numbers that are between 25 and 30.

These elements are 26, 27, 28 and 29. {x ∣ x ∈ N and 10 < x < 30} represents the set of natural numbers that are between 10 and 30.

These elements are 11, 12, 13, …, 28 and 29.

If we compare the two sets, we see that the first set is a subset of the second set.

Therefore, we can conclude that the given statement is true.

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The numeric value of the function when x = 0 is found replacing each instance of x by zero in the definition of the function.

If a graph is given, then the numeric value is given as the value of y when the function crosses the y-axis.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

Supposing we have a function definition, then the numeric value at x = 0 is found replacing each instance of x by zero.

On graph, x = 0 is when the graph of the function touches or crosses the y-axis.

The problem is incomplete, hence the general procedure to obtain the numeric value at x = 0 was presented.

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