John and Dawn have been married for over 20 years. They have lived in their home in Northville, MI (a suburb of Detroit) with their three children for most of those years. According to the Census Bureau, which type of household do they live in

Answer:

4,414,000,000

Step-by-step explanation:

4.414x10^9, move the decimal place 9 places to the left.

Answer:

4,414,000,000

Step-by-step explanation:

4.414 x 10⁹

= 4.414 x 1,000,000,000

= 4,414,000,000

Using the Sample size formula , the sample manufactuer of paints observations or sample size is 22 ton .

Sample size: It is defined as the number of participants or total observations in a study of sample.

we have provided that,

standard deviations of sample (σ)= 3 tons

mean of sample ( X) = 70 tons

confidence level = 98% = 0.98

Margin of error (M.E) = 1 ton

Using the sample size formula,

n = z²(σ)(1-σ) /( M.E)²[1+σ (1-σ)z²/(M.E)²X]

where, X---> population size

s.d --> standard deviations

M.E ---> margin of error

Z-value for confidence level

so, z-value corresponding to 98% of confidence level is 2.32 ..

putting all the values in above formula we get, n = (2.32)²(2)3/(1)²(1+ (2.32)²(6)70×1)

=> n= 32.29/(1+(0.46))= 32.29/ 0.46

= 22.1 ~ 22

Hence, sample size is 22 ton .

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Answer:

5

Step-by-step explanation:

The slope is 5 because the equation is y = 200-5x where 5 is the slope because it is the rate of change.

An angle that measures from the horizontal upward to an object is called the angle of elevation, whereas an angle that measures from the horizontal downward to an object is called the angle of depression.

The angle of elevation is commonly used in surveying, navigation, and construction to determine the height of objects, such as buildings, towers, and mountains.

To find the height of an object using the angle of elevation, one needs to measure the distance between the observer and the object and the angle between the horizontal and the line of sight from the observer to the top of the object. By applying trigonometry, one can then calculate the height of the object.

On the other hand, the angle of depression is often used to measure the depth of objects, such as wells, valleys, and caves.

To find the depth of an object using the angle of depression, one needs to measure the distance between the observer and the object and the angle between the horizontal and the line of sight from the observer to the bottom of the object. Again, by applying trigonometry, one can then calculate the depth of the object.

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To make a stem-and-leaf display, we will separate the ages into stems based on the tens digit and leaves based on the ones digit.

Therefore, the stem-and-leaf display of the age distribution is:

1 | 6

2 | 6 8 9

3 | 3 7 8

4 | 1 3 6 7 8 9

5 | 3 5

6 | 3 4 5 8

A stem-and-leaf display is a graphical representation of a set of data. It is a way to organize and display data in a way that allows for easy interpretation and comparison of the data.

In a stem-and-leaf display, the data is separated into two parts: the stem and the leaf. The stem represents the tens digit of each data point, and the leaf represents the ones digit. For example, the number 47 would be represented as a stem of 4 and a leaf of 7.

The stems are listed vertically, and the leaves are listed horizontally next to their respective stems. The leaves are usually listed in increasing order.

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The correct option is option (C) .

Cluster Sampling is a type of probability sampling and other options are non- probability sampling examples .

Sampling :

Sampling is defined as a technique that selects individual members or subsets from a population to help determine characteristics of the population as a whole.

Croach and Housden postulate that a sample is a finite number taken from a large group for testing and analysis, and that the sample can be taken as representative of the group as a whole.

There are two main types of sampling:

i) probability sampling

ii) Non-probability sampling

A) probability sampling:

It is defined as the sampling technique which researchers use a related method to draw probability theory samples from a larger population.

The most important requirement for probabilistic sampling is that everyone in the population has a known equal chance of being selected.

Probability Samples:

1. Stratified Sampling: Stratified sampling is a type of sampling technique that divides the total population into smaller groups or strata to complete the sampling process. Hierarchies are formed based on some common characteristics of demographic data.

2. Cluster Sampling: Cluster sampling is a probabilistic sampling technique in which researchers divide a population into multiple groups (clusters) for research purposes. Researchers then select random groups using simple sampling techniques for data collection and data analysis.

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Answer:

isn't it b i remember doing something almost the same as this

Answer:

24

Step-by-step explanation:

f(4) means you plug the 4 into the equation so 4 x 4= 16

then 3(4)= 12

16+12-4=24

The center of the face of a cube is the midpoint of the face and lies along the line that runs between the opposite vertices of the face.

This is the point of intersection of the two diagonals in a face. In other words, it is the point that is equidistant from all four corners of the face.

To visualize this, imagine dividing the face into four equal triangles by drawing lines from each corner to the center. The center of the face is at the intersection of these lines.

In three-dimensional space, the center of the face of a cube is also the center of the cube itself, as all faces of a cube are congruent (the same shape and size) and meet at the center of the cube.

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Answer:

(3,3) (-1,-3), you just have to look at the coordinates

Answer:

The penguins swan 2 2/5 miles in one hour

Step-by-step explanation:

The line integral ∫[C] (Pdx + Qdy) over the given curve C consisting of the arc of the parabola y = x² from (0,0) to (1, 1), and the line segment from (1,1) to (0,1) is equal to 2/5.

What is integral?

The value obtained after integrating or adding the terms of a function that is divided into an infinite number of terms is generally referred to as an integral value.

To evaluate the line integral using Green's theorem, we need to find a vector field F = (P, Q) such that ∇ × F = Qₓ - Pᵧ, where Qₓ represents the partial derivative of Q with respect to x, and Pᵧ represents the partial derivative of P with respect to y.

Let's consider F = (P, Q) = (x²y², xy).

Now, let's calculate the partial derivatives:

Qₓ = ∂Q/∂x = ∂(xy)/∂x = y

Pᵧ = ∂P/∂y = ∂(x²y²)/∂y = 2x²y

The curl of F is given by ∇ × F = Qₓ - Pᵧ = y - 2x²y = (1 - 2x²)y.

Now, let's find the line integral using Green's theorem:

∫[C] (Pdx + Qdy) = ∫∫[R] (1 - 2x²)y dA,

where [R] represents the region enclosed by the curve C.

To evaluate the line integral, we need to parameterize the curve C.

The arc of the parabola y = x² from (0, 0) to (1, 1) can be parameterized as r(t) = (t, t²) for t ∈ [0, 1].

The line segment from (1, 1) to (0, 1) can be parameterized as r(t) = (1 - t, 1) for t ∈ [0, 1].

Using these parameterizations, the region R is bounded by the curves r(t) = (t, t²) and r(t) = (1 - t, 1).

Now, let's calculate the line integral:

∫∫[R] (1 - 2x²)y dA = ∫[0,1] ∫[t²,1] (1 - 2t²)y dy dx + ∫[0,1] ∫[0,t²] (1 - 2t²)y dy dx.

Integrating with respect to y first:

∫[0,1] [(1 - 2t²)(1 - t²) - (1 - 2t²)t²] dt.

Simplifying:

∫[0,1] [1 - 3t² + 2t⁴] dt.

Integrating with respect to t:

[t - t³ + (2/5)t⁵]_[0,1] = 1 - 1 + (2/5) = 2/5.

Therefore, the line integral ∫[C] (Pdx + Qdy) over the given curve C consisting of the arc of the parabola y = x² from (0,0) to (1,1), and the line segment from (1,1) to (0,1) is equal to 2/5.

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The equation relating the total cost (y) to the number of balloons (x) is y = 0.8x.

We are given the following information:
1. The cost of the helium tank is $24.
2. The tank can inflate 30 balloons.

We need to write an equation relating the total cost (y) to the number of balloons (x).

Since the helium tank cost is a fixed amount, we can divide this cost by the number of balloons it can inflate to find the cost per balloon.

Cost per balloon = Total cost of the tank / Number of balloons
Cost per balloon = $24 / 30

Now, we can write the equation relating y and x as follows:

y = (Cost per balloon) * x

Plug in the value for the cost per balloon calculated above:

y = ($24/30) * x

Simplify the equation:

y = $0.8 * x

So, the equation relating the total cost (y) to the number of balloons (x) is:

y = 0.8x

This equation shows that the total cost (y) is equal to the cost per balloon ($0.8) multiplied by the number of balloons (x). It helps us calculate the total cost for inflating any number of balloons using the helium tank.

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The equation of the given curve is given by r2 cos(2θ) = 36.

To find the Cartesian equation of the curve, we need to convert the polar equation into its equivalent Cartesian form. This can be done by substituting x = r cos θ and y = r sin θ into the given equation, yielding:
x2cos(2θ) + y2cos(2θ) - 36 = 0
Using the identity cos(2θ) = cos2θ - sin2θ, the equation can be rewritten as:
x2(cos2θ - sin2θ) + y2(cos2θ - sin2θ) - 36 = 0
Simplifying, we get:
x2 - y2 - 36 = 0

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It will take approximately 6.2 years for the account to grow to $14500 when $9000 is invested at 8% interest compounded annually.

The compound interest formula is expressed as:

\(A = P( 1 + \frac{r}{t})^{nt}\)

\(t = \frac{In(\frac{A}{P} )}{n[In(1 + \frac{r}{n} )]}\)

Where A is accrued amount, P is the principal, r is the interest rate and t is time.

Given that:

Principal P = $9,000, compounded annually n = 1, interest rate r = 8%, Accrued amount A = $14500.

Plug these values into the above formula and solve for time t.

\(t = \frac{In(\frac{A}{P} )}{n[In(1 + \frac{r}{n} )]}\\\\t = \frac{In(\frac{14,500}{9,000} )}{1*[In(1 + \frac{0.08}{1} )]}\\\\t = \frac{In(\frac{14,500}{9,000} )}{[In(1 + 0.8 )]}\\\\t = \frac{In(\frac{14,500}{9,000} )}{[In(1.8 )]}\\\\t = 6.197 \ years\)

Therefore, the time required is 6.197 years.

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Answer:

64 square centimeters

Step-by-step explanation:

The surface are of a pyramid is found by finding the sum of the area of the four sides and the base.

Finding the triangular face:

Area of triangle = \(\frac{1}{2} b h\) = \(\frac{1}{2}*4*6 = 12\)

12 * 4 (4 sides) = 48 square cm

Finding the Base = \(w * l = 4 * 4 = 16\)

Finally, we add it together. 48 + 16 = 64

Answer:

y-4x=-2

Step-by-step explanation:

standard form is just putting both variables on the same side.

hope this helps :)

The elementary row operation \(R_i - R_j\) can be used to manipulate the rows of a matrix and is a fundamental tool in the process of row reduction (also known as Gaussian elimination) for solving systems of linear equations and computing matrix inverses.

A matrix is a rectangular array of numbers or other mathematical objects arranged in rows and columns. Matrices are used in many areas of mathematics, as well as in physics, engineering, and computer science. The dimensions of a matrix are given by the number of rows and columns it contains. For example, a matrix with three rows and two columns is called a 3x2 matrix.

The entries of a matrix can be any mathematical object, but they are usually real or complex numbers. Matrices can be added and multiplied, which leads to many useful operations and applications. Matrix addition and multiplication are defined element-wise, meaning that the corresponding entries of two matrices are added or multiplied. Matrices can also be used to represent transformations of geometric objects, such as rotations, translations, and scaling.

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Complete Question:

Xavier performs the elementary row operation represented by Ri - R, on matrix A.

Joshua should continue continue buying the coffee until the marginal benefit equals to the marginal cost.

The marginal benefit simply means the maximum amount that a consumer is willing to pay for an additional good or service.

From the complete information, Joshua should keep buying coffee through the evening until the marginal benefit of purchasing one more coffee equals the marginal cost.

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Answer:

The perimeter of the rectangle that contains the 3 squares is 24x + 36 units

Step-by-step explanation:

Here, we have a square with side length 2x + 3

The perimeter of this square would be calculated using the mathematical formula;

P = 4L

P = 4(2x + 3) = 8x + 12 units

Now, this particular rectangle is composed of three of these squares.

The expression which would represent the perimeter of the rectangle is equal to the sum of the perimeters of the 3 squares.

That would be 8x + 12 + 8x + 12 + 8x + 12 or simply 3(8x + 12) = 24x + 36

Answer:

B = 3

Step-by-step explanation:

3x + 15 = 4x + 12

= 15-12=4x-3x

= 3 = x

X = 3

The bounds for a 95% confidence interval could be option (B) 72 and 79

We know that the 98% confidence interval has bounds of 73 and 80. This means that if we were to repeat the same experiment many times, we would expect that 98% of the time, the true population mean would fall within this range.

To find the bounds for a 95% confidence interval, we can use the fact that a higher confidence level corresponds to a wider interval, and a lower confidence level corresponds to a narrower interval.

Since we want a narrower interval for a 95% confidence level, we can expect the bounds to be closer to the sample mean. We can calculate the sample mean as the midpoint of the 98% confidence interval

(sample mean) = (lower bound + upper bound) / 2 = (73 + 80) / 2 = 76.5

Next, we can use the formula for a confidence interval:

(sample mean) ± (z-score) × (standard error)

where the z-score depends on the desired confidence level, and the standard error depends on the sample size and sample standard deviation. Since we don't have this information, we can assume that the sample size is large enough (i.e., greater than 30) for the central limit theorem to apply, and we can use the formula

standard error = (width of 98% CI) / (2 × z-score)

For a 98% confidence interval, the z-score is 2.33 (found using a standard normal distribution table or calculator). Plugging in the values, we get

standard error = (80 - 73) / (2 × 2.33) = 1.70

Now, we can use this standard error to calculate the bounds for a 95% confidence interval

(sample mean) ± (z-score) × (standard error) = 76.5 ± 1.96 × 1.70

Simplifying, we get

(lower bound) = 76.5 - 3.33 = 73.17

(upper bound) = 76.5 + 3.33 = 79.83

Therefore, the correct option is (B) 72 and 79

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Answer:

8

Step-by-step explanation:

Answer is =8cm

Step-by-step explanation:

d=2r=2·4=8cm

Answer:

The base salary was £21,500.

Step-by-step explanation:

Giving the following information:

Increase rate (g)= 12%

New salary= £24,080

To calculate the base salary, we need to use the following formula:

Base salary= new salary / (1 + increase rate)

Base salary= 24,080 / (1.12)

Base salary= £21,500

The base salary was £21,500.

Considering the curve x³y + y³ = sin y - x, the final i is;\(\frac{dy}{dx} = \frac{-2x}{3y^2 - cos(y)} \div (x^3 - cos(y))\)

Implicit differentiation is a technique used to differentiate equations that are not explicitly expressed in terms of one variable. It is particularly useful when you have an equation that defines a relationship between two or more variables, and you want to find the derivatives of those variables with respect to each other.

To find dy/dx for the curve x³y + y³ = sin y - x², the implicit differentiation will be used which involves differentiating both sides of the equation with respect to x.

It is expressed as follows;

\(\frac{d}{dx} x^3y + \frac{d}{dx} y^3 = \frac{d}{dx} sin(y) - \frac{d}{dx} x^2\)

Then we'll differentiate each term:

For the first term, x^3y, we'll use the product rule

\(\frac{d}{dx} x^3y = 3x^2y + x^3 \frac{dy}{dx}\)

For the second term, y^3, we'll also use the chain rule

\(\frac{d}{dx} y^3 = 3y^2 \frac{dy}{dx}\)

For the third term, sin(y), we'll again use the chain rule

\(\frac{d}{dx} sin(y) = cos(y) \frac{dy}{dx}\)

For the fourth term, x², we'll use the power rule

\(\frac{d}{dx} x^2 = 2x\)

Substituting these expressions back into the original equation, we get:

3x²y + x³(dy/dx) + 3y²(dy/dx) = cos(y)(dy/dx) - 2x

Simplifying the equation:3x²y + x³(dy/dx) + 3y²(dy/dx) - cos(y)(dy/dx) = -2x

Dividing both sides by 3y² - cos(y), we get:(x³ - cos(y))(dy/dx) = -2x / (3y² - cos(y))

Hence, the final answer is;\(\frac{dy}{dx} = \frac{-2x}{3y^2 - cos(y)} \div (x^3 - cos(y))\)

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Answer:

9 cups!

Step-by-step explanation:

I cup = 1 liter

? cups = 9 liter

1 * 9 = 9

so ? * 1 = 9

? = 9

Answer:

The answer is

Step-by-step explanation:

59 cups

sry if im wrong

The first five terms of the arithmetic sequence with a1 = 28 and d = 10 are 28, 38, 48, 58, and 68. The first five terms of the arithmetic sequence with a1 = -34 and d = -10 are -34, -44, -54, -64, and -74.

The first five terms of the arithmetic sequence with a1 = 35 and d = 4 are 35, 39, 43, 47, 51.The first five terms of the arithmetic sequence with a1 = 2 and d = 3k are: 2, 2 + 3k, 2 + 6k, 2 + 9k, 2 + 12k.The first five terms of the arithmetic sequence with a1 = 1/6 and d = 1/2 are: 1/6, 1/6 + 1/2, 1/6 + 1, 1/6 + 3/2, 1/6 + 2.

To find the first five terms of an arithmetic sequence, we start with the given first term (a1) and add the common difference (d) successively to obtain the subsequent terms. In each case, we use the given values of a1 and d to calculate the corresponding terms by adding the appropriate multiples of d to a1.

The resulting sequence of terms represents the arithmetic sequence. By applying this process to each given scenario, we obtain the first five terms for each arithmetic sequence as listed above.

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