A state's labor department conducted a study regarding the mean yearly earnings per household in the state. The department randomly selected 533 households in the state to be the sample. The population mean is $49,829.00. The department also found the standard deviation to be $933.00. What is the approximate standard error of the mean, assuming a 99.7% confidence level? 1.75 40.41 17.45 23.09

Answer:

D. 3.25%

Step-by-step explanation:

The formula for simple interest is:

I = Prt

where I is the interest earned, P is the principal, r is the annual interest rate, and t is the time in years.

We are given that:

I = $1430

P = $5500

t = 8 years

Substituting the values:

$1430 = $5500 * r * 8

Simplifying, we get:

r = $1430 / ($5500 * 8)

r = 0.0325 or 3.25%

Therefore, the annual interest rate of the CD is 3.25%.

Answer: D. 3.25%

Θ(x) = tan⁻¹(5x / (4(x - 13))), and Θ is maximized when the distance the cow must stand from the billboard x₀ = 26.

To find Θ, use similar triangles. Let the distance from the cow to the top of the billboard be h. Then, using similar triangles:

h / x = 5 / (x - 13)

Solving for h:

h = 5x / (x - 13)

The vertical angle subtended by the billboard at the cow's eye is equal to the angle whose tangent is given by:

tan(Θ) = h / 4

Substituting for h:

tan(Θ) = 5x / (4(x - 13))

To maximize Θ, find the value of x that maximizes tan(Θ). Taking the derivative of tan(Θ) with respect to x and setting it equal to zero:

d/dx (tan(Θ)) = 5(52 - 26x) / (4(x - 13))² = 0

Solving for x:

x₀ = 26

Substituting x₀ into the expression for Θ:

Θ(x₀) = tan⁻¹(5(26) / 4(13)) = tan⁻¹(5/2)

Therefore, Θ(x) = tan⁻¹(5x / (4(x - 13))), and Θ is maximized when x₀ = 26.

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Answer:

CA - 144

AD - 98

ABD - 49

BC - 134

C - unsure

Step-by-step explanation:

Answer:

Step-by-step explanation:

so the entire angle sum is 180 degrees then subtract 61 from 180 and divide by 2. hope it helps :)

Answer: Therefore, the population will exceed 100,000 in the year 2005 + 10.73 ≈ 2016.

Step-by-step explanation:   a) The population of the town in 2005 is given by the formula, where t = 0 since 2005 is the starting year:

P = 50,000(1.15)^0 = 50,000

Therefore, the population of the town in 2005 was 50,000.

b) We need to find the value of t when the population P exceeds 100,000:

100,000 = 50,000(1.15)^t

Divide both sides by 50,000:

2 = 1.15^t

Take the natural logarithm of both sides:

ln 2 = ln (1.15^t)

Apply the power rule of logarithms:

ln 2 = t ln 1.15

Divide both sides by ln 1.15:

t = ln 2 / ln 1.15

Using a calculator, we get:

t ≈ 10.73

The expression without the absolute value symbol is:

|x + 5| = x + 5, if x > 5

|x - 5| = 0, if x = 5

|x - 5| = 5 - x, if x < 5

Since, An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

|(x + 3) | if x > 5

This can be written as,

= |x + 3|

Now,

|x + 5| = x + 5, if x > 5

|x - 5| = 0, if x = 5

|x - 5| = 5 - x, if x < 5

Thus,

The expression without the absolute value symbol is:

|x + 5| = x + 5, if x > 5

|x - 5| = 0, if x = 5

|x - 5| = 5 - x, if x < 5

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The reduced form of the matrix is [tex]\begin{bmatrix}1 &-\frac{4}{7} &\frac{4}{7} \\0& 11& 79\end{bmatrix}[/tex]

A matrix is a rectangular array of numbers arranged in rows and columns. In linear algebra, matrices can be used to represent linear transformations and solve systems of linear equations.

In the given matrix, we need to perform a row operation to get a 1 in row 1, column 1. Row operations are operations performed on the rows of a matrix to transform it into another matrix that is equivalent in terms of solutions to a system of linear equations.

The three types of row operations are:

Swapping two rows.

Multiplying a row by a non-zero constant.

Adding a multiple of one row to another row.

To perform this row operation, we first multiply row 1 by 12 to get a multiple of 12 in the first column of row 1:

[tex]\begin{bmatrix}84 &-48 &96 \\-12& 7& -13\end{bmatrix}[/tex]

Next, we add row 1 to row 2 multiplied by 2 to get a 0 in column 1 of row 2:

[tex]\begin{bmatrix}84 &-48 &96 \\0& 11& 79\end{bmatrix}[/tex]

Finally, we can divide row 1 by 84 to get a 1 in row 1, column 1:

[tex]\begin{bmatrix}1 &-\frac{4}{7} &\frac{4}{7} \\0& 11& 79\end{bmatrix}[/tex]

Now we have a 1 in row 1, column 1, and the matrix is in row echelon form.

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Answer:

Step-by-step explanation:

I'm sorry, but there isn't enough information to solve for the missing side of a triangle with just the perimeter given as 8x-6. We would need at least one more piece of information, such as the lengths of the other sides or angles of the triangle.

The initial velocity of the car before the brake was pulled is 30m/s

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

A car pulls the emergency hand brake, accelerating at -4.0 m/s2 for 7.5 seconds

This means that

Acceleration = -4.0m/s^2

Time = 7.5 seconds

Using the above as a guide, we have the following:

Initial velocity = -Acceleration  * Time

substitute the known values in the above equation, so, we have the following representation

Initial velocity = 4  * 7.5

Evaluate

Initial velocity = 30

Hence, the initial velocity is 30

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Answer: 1/2, the same as getting tails 5 times

Step-by-step explanation:

hope this helps

The expression that is equivalent to 5/4x +33-2+2 is 5x + 132/4. Option C

It is important to note that algebraic expressions are defined as expressions that consists of factors, variables, constants, coefficients and terms.

These expressions are also made up of arithmetic operations.

These operations are listed as;

From the information given, we have that;

5/4x +33-2+2

Add or subtract the values

5/4x + 33

Find the LCM, we have;

5x + 132/4

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Complete question:

Which expression is equivalent to 5/4x +33-2+2

5x + 132

6x + 132/4

5x + 132/4

6x + 132

Answer:

2(1/2)(11)(7) + 11(14) + 14(8) + 14(9) = 469 in.^2

The correct answer is A.

The value of the function is 136

It is important that we note that functions are described as expressions that are used to explain the relationship between two variables.

From the information given, we have that;

g(x)=2x

h(x)=x^(2)+4

To determine the composite function, we would need to substitute the value of h(-8) as x in the function g(x)

Then, we have that;

h(-8) = (-8)^2 + 4

Find the values

h(-8) = 68

Now, substitute the value as x , we have that;

g(h(-8)) = 2(68)

expand the bracket and multiply

g(h(-8)) = 136

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Answer:

Step-by-step explanation:

To calculate the monthly payment on a loan, you can use the formula for the monthly payment on an annuity: P = (r * PV) / (1 - (1 + r)^(-n)), where P is the monthly payment, r is the monthly interest rate, PV is the present value of the loan (i.e., the amount borrowed), and n is the total number of monthly payments.

In this case, the amount borrowed is $56,937 and the interest rate is 6.3% per year. To convert this to a monthly interest rate, we divide by 12: r = 0.063 / 12 = 0.00525. The loan term is 5 years, so the total number of monthly payments is n = 5 * 12 = 60.

Substituting these values into our formula for the monthly payment, we get: P = (0.00525 * 56937) / (1 - (1 + 0.00525)^(-60)) ≈ $1102.53. So, the monthly payment on this loan would be approximately $1102.53.

Answer:

The answer is going to 5

Step-by-step explanation:

I hope this helps you

P(both poodle) = (3/10)(3/10) = 9/100

Answer: The probability of choosing the same puppy is 9/100

The terminal point of 13π/6 is (-√3/2, 1/2) by using unit circle.

The quadrants of a graph are the four sections that divide the coordinate plane. The quadrants are numbered in a counterclockwise direction starting from the positive x-axis.

1. Quadrant I is located in the upper-right section and contains points with positive x and y-coordinates.

2. Quadrant II is located in the upper-left section and contains points with negative x-coordinates and positive y-coordinates.

3. Quadrant III is located in the lower-left section and contains points with negative x and y-coordinates.

4. Quadrant IV is located in the lower-right section and contains points with positive x-coordinates and negative y-coordinates.

The quadrants are useful for determining the signs of coordinates, angles, and for plotting points on a graph.

To find the terminal point of 13π/6, we can start by recognizing that this angle is greater than 2π, which is one complete revolution around the unit circle.

To bring the angle back within one revolution, we can subtract 2π, which gives us 13π/6 - 2π/1 = 13π/6 - 12π/6 = 1π/6.

The angle 1π/6 is in the standard position between the positive x-axis and the first quadrant. The reference angle is π/6, which is the angle between the terminal side and the x-axis.

Since the angle is in the 2nd quadrant, the x-coordinate will be negative and the y-coordinate will be positive. Using the unit circle, we can find the values of sine and cosine at π/6 and then negate the value of cosine since the angle is in the second quadrant.

cos(π/6) = √3/2

sin(π/6) = 1/2

Therefore, the terminal point of 13π/6 is (-√3/2, 1/2).

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The resulting arrow should end at -6 1/2. This is because -4 - 2 1/2 is equal to -6 1/2.

In mathematics, an expression is a combination of numbers, variables, and operators that can be evaluated to produce a value. Expressions can be simple or complex and are used to represent mathematical relationships and operations.

To find -4 - 2 1/2 expression on the number line by drawing an arrow, we need to start at -4 and then move left by 2 1/2 units.

To do this, we can draw an arrow starting at -4 and then mark off 2 1/2 units to the left. One way to represent 2 1/2 units is to divide the space between -4 and -5 into two equal parts, and then mark off one of those parts.

The resulting arrow should end at -6 1/2. This is because -4 - 2 1/2 is equal to -6 1/2.

Here's an example of what the arrow would look like:

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Hence, the darkened sector covers an area of roughly [tex]10.55 km^2[/tex] as circle's radius is 7 km, and the shaded sector's central angle is 154 degrees .

The radii of a circle in geometry is the separation between any two points on the circle's circumference. It is frequently used to describe how far apart two points are. One of a circle's most crucial characteristics is its radius, which is taken into account when calculating a circle's circumference, area, and diameter. The distance around a circle that passes through its centre, or its diameter, is equal to half of its radius. Other shapes like spheres, cylindrical, and cones can also be described using the radius. The radius here means the distance from the shape's centre to any point on its perimeter.

given

The following formula must be used to determine a sector's area:

A = (θ/360)[tex]\pi r^2[/tex]

where r is the circle's radius, is pi, or roughly 3.14, and is the sector's centre angle, expressed in degrees.

The circle's radius is 7 km, and the shaded sector's central angle is 154 degrees, according to the provided figure. When these values are added to the formula, we obtain:

[tex]A = (154/360)\pi (7)^2[/tex]

[tex]= 10.55 km^2[/tex]

Hence, the darkened sector covers an area of roughly [tex]10.55 km^2[/tex] as circle's radius is 7 km, and the shaded sector's central angle is 154 degrees .

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The complete question is:-  

154 degree

7 km

Find the area of the shaded sector.

A = __ km2

The number of cups of frozen strawberries that are needed to make 3 gallons of punch is equal to 48 cups.

In this exercise, you're required to determine the number of cups of frozen strawberries that are needed to make 3 gallons of punch.

Thus, we would apply direct proportion.

Note: There are 16 cups of frozen strawberries in a gallon.

By direct proportion:

16 cups = 1 gallon

X cups = 3 gallons

Cross-multiplying, we have:

X = 16 × 3

X = 48 cups of frozen strawberries.

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Answer:

The y-intercept of the graph of the equation is -9. This means that the graph crosses the y-axis at the point (0, -9).

Step-by-step explanation:

To solve this question, we need to plug in x = 0 into the given equation and simplify. We get:

y = 6(0 - 1/2)(0 + 3) y = 6(-1/2)(3) y = -9

Therefore, the y-intercept of the graph of the equation is -9. This means that the graph crosses the y-axis at the point (0, -9).

Answer: 87.964594300514 feet3 or 87.96 feet3

Step-by-step explanation:

πr^2 h

=  π×2^2×7

=  28π

=  87.964594300514 feet3

Answer:

7 seeds will go into each bag

Given:

56 flower seeds need to be put into 8 separate bags.

To find out how much go into each bag you will divide the number of seeds by the number of bags

56/8=7

So 7 seeds will go into each of the 8 bags

The difference between the adjustable-rate mortgage (ARM) and the  fixed-rate mortgage is $176,494.80.

First, find the total amount paid on the adjustable-rate mortgage would be :
= ( 5 years x 12 months x 2, 506.43 payment ) + ( 10 x 12 x 3, 059. 46 ) + ( 5 x 12 x 3, 646.76) + ( 5 x 12 x 3, 630.65 )

=  $ 1, 172, 971. 20

Then we can find the total payment for the fixed - rate mortgage :

= Monthly payment x Number of years

= 2, 767. 99 x 30 years x 12 months

= $ 996, 476. 40

The difference is:

= 1, 172, 971.20 - 996, 476. 40

= $ 176,494. 80.

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Answer:

I dont know the answer I dont know  what it is I just needed points bye

Step-by-step explanation:

Answer: 7 centimeters equals 70 millimeters :)

P(X=2) &= {14\choose 2}(0.08)^2(0.92)^{12} \

&= \frac{14!}{2!(14-2)!}(0.08)^2(0.92)^{12} \

[tex]\sf\implies\:&=\frac{14\times13}{2\times1}(0.08)^2(0.92)^{12}[/tex]

&= 91(0.08)^2(0.92)^{12} \

&\approx \boxed{0.2166

[tex]\begin{align}\huge\colorbox{black}{\textcolor{yellow}{\boxed{\sf{I\: hope\: this\: helps !}}}}\end{align}[/tex]

[tex]\begin{align}\colorbox{black}{\textcolor{white}{\underline{\underline{\sf{Please\: mark\: as\: brillinest !}}}}}\end{align}[/tex]

[tex]\textcolor{lime}{\small\textit{If you have any further questions, feel free to ask!}}[/tex]

[tex]\huge{\bigstar{\underline{\boxed{\sf{\color{red}{Sumit\:Roy}}}}}}\\[/tex]