In the united states, the number of children under age 18 per family is skewed right with a mean of 1.9 children and a standard deviation of 1.1 children.

analyst 1 wants to calculate the probability that a randomly selected family from the united states has at least 2 children.

analyst 2 wants to calculate the probability that if 40 families from the united states are randomly selected, the mean number of children per family is at least 2 children.

what sample size does analyst 1 plan to use?

enter an integer. what sample size does analyst 2 plan to use?

enter an integer.

To use Holt's method with smoothing constants of 0.3 for alpha and 0.6 for gamma, we first need to calculate the initial values for the level and slope.

Let L0 be the initial level and B0 be the initial slope. We can estimate these using the following equations:

L0 = y1

B0 = y2 - y1

where y1 and y2 are the first two observed values in the time series.

Once we have the initial values, we can use the following recursive equations to calculate the level and slope at each time period t:

Lt = alpha * yt + (1 - alpha) * (Lt-1 + Bt-1)
Bt = gamma * (Lt - Lt-1) + (1 - gamma) * Bt-1

where yt is the observed value at time t.

Using these equations and the given smoothing constants, we can find the equation of the forecast line as:

Ft+1 = Lt + Bt

and the mean squared error (MSE) as:

MSE = (1 / n) * sum((yt - Ft)^2)

where n is the number of observed values.

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Answer: 3, 3, 1

Step-by-step explanation:

(x+1)³= (x+1)(x+1)²

=(x+1)(x²+2x+1)

=x³+ 3x²+3x+1

Step-by-step explanation:

Question 1:

Question 2:

Answer:

0.64y = 40.

Question 2:

0.45z = 72

z = 72 * (1/0.45) = 160.

Step-by-step explanation:

Therefore, the correct inequality to find the domain is simply x - 3 < 0, which simplifies to x < 3.

To find the domain of a function, we need to determine all the values of the independent variable (usually represented by x) that the function is defined for. In this case, the function is defined as f(x) = x - 3, which means we can plug in any value of x into the expression x - 3 to get a corresponding value of f(x).

However, there are some values of x that would cause the expression x - 3 to be undefined. For example, if we were trying to find f(x) when x = 2, we would get f(2) = 2 - 3 = -1, which is a valid output. But if we were trying to find f(x) when x = 3, we would get f(3) = 3 - 3 = 0/0, which is undefined.

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Answer:

Step-by-step explanation:t55

An octagon has 8 sides. If each of them has a length of x, then the perimeter is 8x which is twice the perimeter of the square. (The square has a perimeter of 4x)

A dodecagon is a 12 sided regular polygon. It will have 12 sides all of which are equal to x. Since the square has a perimeter of 4x and the dodecagon has a perimeter of 12x the perimeter of the dodecagon is 3 times that of the given square.

Answer: sqrt(61)

Step-by-step explanation:

For parts a) and c1), refer to the attached picture.

For part b), the distance formula is:

d = sqrt[(x2 - x1)^2 + (y2 - y1)^2]

Using x1 = -1, y1 = -4, x2 = -6, y2 = 2:

d = sqrt[(-6 + 1)^2 + (2 + 4)^2] = sqrt[25 + 36] = sqrt(61)

Part c2) Another way to find the length of AB without using the distance formula is by drawing the line and measuring it according to the scale.

Part d) This will only work as long as the graph paper is accurately made, and the scale computation is done correctly. However, this will only give approximations, and will not give an exact answer when radicals are involved.

The area of the expression  2 1/2 x 1/3 Using an area model is 5/6.

The area model is a method of calculating area by parts.

Given that, we are asked to find the area of the expression 2 1/2 x 1/3 Using an area model,

Area =

\(= (2\frac{1}{2}) . (\frac{1}{3}) \\\\= 2.\frac{1}{3}+\frac{1}{2}.\frac{1}{3}\\\\= \frac{2}{3}+\frac{1}{6}\\\\= \frac{15}{18}\\\\= \frac{5}{6}\)

Hence, the area of the expression  2 1/2 x 1/3 Using an area model is 5/6.

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Answer:

y=-2/5+33/5

Step-by-step explanation:

Answer:

y=-2/8x+5

Step-by-step explanation:

Answer:

\(y=-(1/2) x X-1= - x/2-1\)

Step-by-step explanation:

The equation showing the relation between shorter and longer skirt is 3s+4t = 140.

Given that the Scottish dance team used 140 yards of tartan to make dancing skirts.

The skirt pattern for the shorter members is 3- yards of fabric, and the skirt pattern for the taller members is 4 yards of fabric.

So, we need to find the equation represents the relationship between the number of short skirts and the number of long skirts that were made,

So, if there are s short skirts and t long skirts,

So,

The relation will be =

3s + 4t = 140

Hence the equation showing the relation between shorter and longer skirt is 3s+4t = 140.

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Answer:

y=2(x + 2))^2 - 9

Step-by-step explanation:

So, whenever two negative signs are right next to each other, they make a positive. However, when they are alone, they stay negative.

With this, y=2(x-(-2))^2 + (-9) --> y=2(x + 2))^2 -9

The value of x from the equation 8/9 = x + 1/3 (7) is -13/ 9

Algebraic expressions are defined as expressions composed of terms, factors, constants, variables and coefficients.

They also consist of mathematical operations such as;

Given the expression;

8/9 = x + 1/3 (7)

We have to take the following steps

expand the bracket

8/ 9 = x + 7/ 3

Now, collect like terms

8/ 9 - 7/ 3 = x

Find the LCM

8 - 21 / 9 = x

-13/ 9 = x

Thus, the value of x from the equation 8/9 = x + 1/3 (7) is -13/ 9

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The Markup percentage based on cost if the wholesaler paid $780 for the guitar is 79%

Given,

The cost price of the guitar = $780

The selling price of the guitar = $1396.20

We have to find the markup percent based on the cost;

Markup percentage;

The gross profit of a unit, which is its sales price less its cost to produce or acquire for resale, is divided by the unit's cost to determine the markup %.

Markup percent = (Selling price - cost price) / cost price x 100

= (1396.20 - 780) / 780 x 100

= 616.20 / 780 x 100

= 0.79 x 100

= 79%

That is,

The Markup percentage based on cost if the wholesaler paid $780 for the guitar is 79%

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Answer:5 3/8

Step-by-step explanation:

\(3\frac{1}{8} =\frac{25}{8}\\4\frac{7}{28} =4\frac{1}{4}=\frac{17}{4}\\1\frac{5}{6} =\frac{11}{6}=\frac{33}{18}\\\frac{\frac{25}{8}}{x-\frac{17}{4}}=\frac{17}{18}+\frac{33}{18}=\frac{50}{18}=\frac{25}{9}\\\frac{\frac{25}{8}}{x-\frac{17}{4}}=\frac{\frac{25}{9}}{1}\\\frac{25}{8}=\frac{25}{9}*(x-\frac{17}{4})\\(x-\frac{17}{4})=\frac{25}{8}:\frac{25}{9}=\frac{25}{8}*\frac{9}{25}=\frac{9}{8}\\x=\frac{9}{8}+\frac{17}{4}=\frac{9}{8}+\frac{34}{8}=\frac{43}{8}=5\frac{3}{8}\)

The required, Mmusi borrowed R3000 from Aggie as per the given conditions.

Simple interest is a quick and simple formula for figuring out how much interest will be charged on loan.

Amount = Principal [1 + rate×time]

Let's call the amount Mmusi borrowed from Aggie "P".

After two years, he has to pay back
= P + P * 18% * 2
= P + 0.18 * P * 2
= P + 0.36P
= 1.36P

So if he has to pay back R4080, we can set up an equation to solve for P:

1.36P = 4080

To find P, we can divide both sides by 1.36:

P = 4080 / 1.36 = 3000

So Mmusi borrowed R3000 from Aggie.

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Answer:

x=3

y=7

Step-by-step explanation:

3+yi=x-7i

equate real and imaginary parts

3=x

y=-7

The corresponding parts are:

The statement is given as:

△ABC was transformed using two rigid transformations.

The rigid transformations imply that:

The images of the triangle after the transformation would be equal

So, the corresponding parts are:

The results are true because rigid transformations do not change the side lengths and the angle measures of a shape

To do this, we simply make use any of the following congruent theorems:

The classmate's claim is that

Only two pairs of corresponding parts are enough to prove the congruent triangle

The above is true because of the following congruent theorems:

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Energy consumption is the amount of power used over time, measured in watt-hours (Wh) or kilowatt-hours (kWh). It is calculated by multiplying the power (measured in watts) by the time for which it is used.

To calculate energy consumption, you will need to know the amount of power being used and the time over which it is being used. Power is typically measured in watts (W), and energy is the product of power and time, so energy consumption is the number of watts used multiplied by the number of hours for which they are used.

For example, let's say you want to calculate the energy consumption of a light bulb that uses 60 W of power and is left on for 4 hours. The energy consumption would be:

Energy consumption = 60 W * 4 hours = 240 Wh (watt-hours)

This is the amount of energy that the light bulb used over the 4-hour period.

You can also convert watt-hours to other units of energy, such as kilowatt-hours (kWh). To do this, you would divide the watt-hours by 1,000. In the example above, the energy consumption would be 0.240 kWh.

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Answer: 25%

Step-by-step explanation:

From the question, we are informed that Allison earned $200 the first month she worked and $250 the second month she worked.

The percentage increase in her salary will be calculated as:

= Salary Increase / Old salary × 100

= (250 - 200) / 200 × 100

= 50/200 × 100

= 1/4 × 100

= 25%

The percentage increase is 25%

Answer

Solved Calculus AB, Semester 2 Assignment: Applications of ...

The population of a bacteria culture increases at the rate of 3 times the square root of the present population.

Answer:

9(x+3)

Step-by-step explanation:

9x + 27

Taking 9 as the common factor in the 2 terms

=> 9(x) + 9(3)

=> 9(x+3)

An example of a linear transformation whose kernel is the line spanned by the vector [-1, 2] in ℝ^3 is the transformation that projects every point in ℝ^3 onto the plane orthogonal to [-1, 2].

To find a linear transformation whose kernel is the line spanned by [-1, 2], we need to consider a transformation that maps vectors in ℝ^3 to the zero vector if and only if they lie on the line spanned by [-1, 2]. One way to achieve this is by projecting every point in ℝ^3 onto the plane orthogonal to [-1, 2].

The projection of a vector onto a plane can be computed by subtracting the orthogonal projection of the vector onto the normal vector of the plane from the original vector. In this case, the normal vector of the plane orthogonal to [-1, 2] is [-1, 2].

Therefore, the linear transformation that maps every vector in ℝ^3 to its projection onto the plane orthogonal to [-1, 2] has the line spanned by [-1, 2] as its kernel.

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In triangle ABC, with side lengths a = 2.5 cm, c = 3.6 cm, and angle A = 43 degrees, we can use the Law of Sines to solve for the remaining angles and side lengths.

First, let's sketch the triangle ABC. Label side a opposite angle A, side b opposite angle B, and side c opposite angle C.

Using the Law-of-Sines, we have the following ratio: sin(A) / a = sin(B) / b = sin(C) / c.

Given that angle A is 43 degrees, we can calculate sin(A) using a calculator: sin(43) ≈ 0.681.

We can now set up the ratios: sin(43) / 2.5 = sin(B) / b = sin(C) / 3.6.

To find angle B, we can solve for sin(B) using the ratio: sin(B) = (sin(43) / 2.5) * b.

Similarly, to find angle C, we can solve for sin(C) using the ratio: sin(C) = (sin(43) / 2.5) * 3.6.

Using the inverse sine function on a calculator, we can find the values of angle B and angle C.

Keep in mind that the Law of Sines can have multiple solutions. Therefore, when using the inverse sine function, we need to consider both the acute and obtuse angles.

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