the u.s. labor department reported an average hourly wage of $17.52 for hourly workers in 2022 in south carolina. assume the standard deviation for this population is $6.00 per hour. what is the mean of the sampling distribution of the means for a random sample of 35 workers from this group?

The equation of the line tangent to the curve at the point corresponding to the given value of t.

x = t²-23 and y = t³ + t, at t = 5 is

38x - 5y + 574 = 0

Given, a curve with the points represented by

x = t²-23 and y = t³ + t, at t = 5

we have to find an equation of the line tangent to the curve at the given point on the curve.

so, the given point is (x , y) = (5² - 23 , 5³ + 5)

(x , y) = (2 , 130)

Now, the slope of the curve at that point be,

dy/dx = (3t² + 1)/(2t)

dy/dx = 76/10

Now, on using the slope-intercept form, we get

(y - 130)/(x - 2) = 38/5

5(y - 130) = 38(x - 2)

5y - 650 = 38x - 76

38x - 5y + 574 = 0

Hence, the equation of the line tangent to the curve at the point corresponding to the given value of t.

x = t²-23 and y = t³ + t, at t = 5 is

38x - 5y + 574 = 0

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The  inequality represents the values of x is

-1.8x^2 – 1.61x + 217.55 > 255. Option  A

This is further explained below.

Generally,  Considering that Pattie's Produce sells a box of strawberries for $2.29, and each day they are capable of producing 95 packages. The daily money received is $2.29 multiplied by 95 shipments, which equals $217. Given that a twenty-cent increase results in nine fewer packages.

One may determine the number of increases in the price of a package of strawberries by 20 cents based on the following factors:

(2.29 + 0.2x)(95 - 9x) > 255

217.55 - 20.61x + 19x - 1.8x^2 > 255

-1.8x^2 - 1.61x + 217.55 > 255

In conclusion, The  inequality represents the values of x is

-1.8x^2 - 1.61x + 217.55 > 255

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CQ

Pattie's Produce charges $2.29 for a package of strawberries. On average, Pattie's Produce sells 95 packages of strawberries daily. They estimate that for each 20-cent increase in the cost of a package of strawberries, 9 fewer packages will be sold each day. Let x represent the number of 20-cent increases in the cost of a package of strawberries.

Which inequality represents the values of x that would allow Pattie's Produce to have a daily revenue of at least $255 from selling the packages of strawberries?

A. B. -1.872 – 1.615 + 217.55 > 255

B -1.812 + 21.61r + 217.55 > 255

C -1.8r2 – 21.611 + 217.55 < 255

D. -1.812 + 1.61x + 217.55 < 255​

The investment problem is modeled by an initial value problem (IVP) where the rate of change of the investment is determined by the initial investment, monthly deposits, and the interest rate.

a) The investment problem can be modeled by an initial value problem where the rate of change of the investment, y(t), is given by the initial investment, monthly deposits, and the interest rate. The IVP can be written as:

dy/dt = 0.09y + 200, y(0) = 500.

b) To solve the IVP, we can use an integrating factor to rewrite the equation in the form dy/dt + P(t)y = Q(t), where P(t) = 0.09 and Q(t) = 200. Solving this linear first-order differential equation, we obtain the solution for y(t).

c) To find the value of the investment after 2 years, we substitute t = 2 into the obtained solution for y(t) and calculate the corresponding value.

d) After 2 years, the monthly deposit increases to $300. To find the value of the investment a year later, we substitute t = 3 into the solution and calculate the value accordingly.

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Using the given graph we can answer the questions:

a. The parabola opens upward.

b. The coordinates of the vertex, which is the point at the bottom of the parabola, are (2,1).

c. The equation of the axis of symmetry is x=2.

d. The y intercept is 5.

The graph has no x intercepts.

The equation T = 2π√(L/g) satisfies dimensional consistency, indicating that it is a valid relationship for the periodic time T of a simple pendulum.

To test the validity of the equation x = x₀ + v₀t + (1/2)at², we can check if the dimensions on both sides of the equation are consistent.

Breaking down the dimensions of each term:

x: Displacement has dimensions of length (L).

x₀: Initial displacement has dimensions of length (L).

v₀t: Velocity times time has dimensions of (L/T) * T = L.

(1/2)at²: Acceleration times time squared has dimensions of (L/T²) * T² = L.

Since the dimensions on both sides of the equation are consistent (L = L), the equation x = x₀ + v₀t + (1/2)at² is valid.

Now, let's use dimensional analysis to find the relationship of the periodic time T of a simple pendulum using the factors affecting it: mass of the bob (m), length (L) of the pendulum, and acceleration due to gravity (g).

The factors affecting the periodic time T of a simple pendulum are:

Mass (m): Denoted by [M].

Length (L): Denoted by [L].

Acceleration due to gravity (g): Denoted by [LT⁻²].

The periodic time T of a simple pendulum is expected to depend on these factors in some way.

By applying dimensional analysis, we can determine the relationship between these factors. The equation is given as T = 2π √(L/g), where T is the periodic time, π is a constant, L is the length, and g is the acceleration due to gravity.

Breaking down the dimensions of each term:

T: Periodic time has dimensions of time (T).

2π: A constant, so it is dimensionless.

√(L/g): The square root of the ratio of length to acceleration due to gravity has dimensions of √([L]/[LT⁻²]) = √(T²) = T.

Therefore, the equation T = 2π√(L/g) satisfies dimensional consistency, indicating that it is a valid relationship for the periodic time T of a simple pendulum.

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Answer:

3/8

change to an improper fraction

1 1/8=9/8

3/4 times 2 equals

6/8

9/8-6/8

3/8

Answer: I think the answer is 3/8 or it can be 5/8.

explanation: I hope this helps.

8 7/12

Step-by-step explanation:

Hi there!  

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I believe your answer is:  

\(x - 6 = 5\)

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

I am assuming that '3=x divided by 3' is supposed to be \(3 = \frac{x}{3}\).

⸻⸻⸻⸻

The first, second, and fourth equations have x divided by a number. To isolate x, we would have to use the multiplication property of equality.

⸻⸻⸻⸻

For the third one (\(x-6=5\)), the variable 'x' is being subtracted by 6. We would have to use the addition property of equality to isolate x.

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

These thoughts show you that AAS theorem is straight extension of ASA theorem.

A triangle is a simple polygon with 3 sides and 3 interior angles. It is one of the basic shapes in geometry in which the 3 vertices are joined with each other and it is denoted by the symbol △. There are various types of triangles that are classified on the basis of the sides and angles.

ASA congruence theorem: If two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.

AAS congruence theorem: If two angles and the non-included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.

Consider two triangles ΔABC and ΔA'B'C' .

If        m∠A = m∠A'

and   m∠B = m∠B'

         AB = A'B'

then two triangles ΔABC and ΔA'B'C' are congruent by AAS theorem.

Thus, these thoughts show you that AAS theorem is straight extension of ASA theorem.

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Answer:  The Sample Response is the answer Edge uses as a correct answer. Answer varies depending on your response.

Step-by-step explanation:

This answer is correct I got it right on Edge 2022. The proof is down below.

Sample Response: The interior angle measures of a triangle add up to 180 degrees. Thus, if you are given angle-angle-side, you can solve for the third angle measure and essentially have angle-side-angle because the given side will now be the included side.

As long as you explain and include these in your answer it should be correct: (If you decide to answer using your own words)

Hope this helps someone. Good luck! :)

The value for the hotspots of the similar triangles ∆ABC and ∆PWR are:

(1). angle B = 68°

(2). PQ = 5cm

(3). BC = 19.5cm

(4). area of ∆PQR = 30cm²

Similar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.

(1). angle B = 180 - (22 + 90) {sum of interior angles of a triangle}

angle B = 68°

Given that the triangle ∆ABC is similar to the triangle ∆PQR.

(2). PQ/7.5cm = 12cm/18cm

PQ = (12cm × 7.5cm)/18cm {cross multiplication}

PQ = 5cm

(3). 13cm/BC = 12cm/18cm

BC = (13cm × 18cm)/12cm {cross multiplication}

BC = 19.5cm

(4). area of ∆PQR = 1/2 × 12cm × 5cm

area of ∆PQR = 6cm × 5cm

area of ∆PQR = 30cm²

Therefore, the value for the hotspots of the similar triangles ∆ABC and ∆PWR are:

(1). angle B = 68°

(2). PQ = 5cm

(3). BC = 19.5cm

(4). area of ∆PQR = 30cm²

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Answer:

Triangular inequality:  Length of third side must be less than the sum of the lengths of the other 2 sides.

x < 18 + 29

x < 47

so Maximum length of third side is 46 units.

Also 29 < 18 + x

x > 11    so minimum length = 12

Difference  = 46-11 = 35

Answer:

Step-by-step explanation:

To find the width, you have to divide the height and length by the volume

When firing a handgun , you should hold the handgun (d) at arm's length , from the body .

When firing a handgun, it is recommended to hold it at arm's length, from your body. This allows for proper control and aim of the firearm, as well as providing a buffer between you and the potential dangers of the discharge.

Holding the handgun too close to your body can also interfere with accuracy and control, as your arms may obstruct the movement of the gun. It's important to follow manufacturer guidelines and seek proper training and follow all safety procedures when handling handgun to ensure responsible and safe use.

The given question is incomplete , the complete question is

When firing a handgun, how far should you hold it from your body?

(a) 9 inches

(b) one foot

(c) eighteen inches  

(d) at arm's length

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Answer:

The slope is -2 and the y-intercept is (0,1)

The amount of interest for the year was 3,770 cents, and the regular price of the electric drill that Pamela bought before the discount was 21,927 cents

Interest = P x R x T.

Where:

P = Principal amount (the beginning balance).

R = Interest rate

T = Number of time periods

In this case, we are given that;

Principal amount (P) = $580

Interest rate (R) = 6,5 %

Time = 1 year

Hence, The amount of the interest = 6,5% of $580

                                                     = 0.065 × $580

                                                     = $37.7

1 dollar = 100 cents

Hence, $37.7 = 37.7 × 100 cents equal to 3,770 cents

P = (1 – d) x

Where,

P = Price after discount

D = discount rate

X = regular price

In this case, we are given that:

P = $32.89

D = 85% = 0,85

Hence, the regular price:

P = (1 – D) x

32.89 = (1 – 0.85) X

32.89 = 0.15X

X = 32.89/0.15

X= 219.27

1 dollar = 100 cents

Hence, $219.27 = 219.27 × 100 cents equal to 21,927 cents

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The vertex form of the equation is y = (x - 3)² - 4, which corresponds to option OD.

To convert the given equation from standard form to vertex form, we need to complete the square.

The vertex form of a parabola's equation is y = a(x-h)² + k, where (h, k) represents the vertex of the parabola.

Given equation: y = x² - 6x + 14

Move the constant term to the right side:

y - 14 = x² - 6x

Complete the square by adding and subtracting the square of half the coefficient of x:

y - 14 + 9 = x² - 6x + 9 - 9

Group the terms and factor the quadratic:

(y - 5) = (x² - 6x + 9) - 9

Rewrite the quadratic as a perfect square:

(y - 5) = (x - 3)² - 9

Simplify the equation:

y - 5 = (x - 3)² - 9

Move the constant term to the right side:

y = (x - 3)² - 9 + 5

Combine the constants:

y = (x - 3)² - 4

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Lake Okeechobee has a surface area of 5329 square miles, as determined by solving the given values.

The area of a square unit, such as a square mile, is calculated by multiplying two lengths. Each length in the case of square miles is measured in miles.

Given: The Okeechobee lake is 7.3 * 10 to the second power square miles in area.

We need to figure out how many square miles Lake Okeechobee covers.

Area covered in square miles = (7.3 × 10)²

                                                 = 73²

                                                 = 5329 square miles

Therefore, Lake Okeechobee covers an area of 5329 square miles which was calculated by solving the given values.

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The given summation expression ∑i=29​(i−8) has the index of summation (i), the upper bound (29), and the lower bound (unspecified).

The index of summation, denoted by the letter in the summation notation, represents the variable that takes on different values as the sum is computed.

In this case, the index of summation is "i". The upper bound specifies the last value of the index for which the summation is performed. In this case, the upper bound is 29.

However, the lower bound is not specified in the given expression. The lower bound represents the starting value of the index for which the summation begins. Without a specified lower bound, we cannot determine the full range of values over which the summation is computed.

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Answer:

\(a = x(2x - 3) + 5 x - 2x ^{2} = \\ a = x - 1x + 5x + 4x ^{2} = \\ a = 1x - 1x + 5x + 4x ^{2} = \\ a = 5x + 4x ^{2} \)

Je pense que c'est la réponse

All the attatchments include the directions below:

Prepare a two-way table as shown below.

Enter the number 50 in the two-way table

Prepare a column total and enter 68 for the total number of people who split the check.

The total number of people who do not eat desert are 56, and the total number of people who took the survey are 122. Enter both values.

The remaining values can be found out as shown below.

The two way table shows the characteristics of the given information,

having a sum which is the number of people surveyed.

The completed two-way table is presented as follows;

\(\begin{tabular}{l|c|c|}&Order desert & No desert\\Split the check&50&18\\One person pays&16&38\end{array}\right]\)

Reasons:

Number of people that responded to the survey, U = 122 people

Number of the respondents that ordered dessert and split the check, DS = 50

Number of respondent that prefer splitting the check, S = 68 people

Number that prefer to skip dessert, ND = 56 people

Therefore;

Number that split the check and no dessert, S/ND = S - DS

S/ND = 68 - 50 = 18

Number that do not split the check and no dessert, NS/ND = ND - S/ND

NS/ND = 56 - 18 = 38

Only one person pays, and orders desert, NS/D = The rest of the respondent not excluding the respondent sorted above

Therefore, NS/D = U - S - NS/ND

Which gives

NS/D = 122 - 68 - 38 = 16

The completed two-way table is therefore;

\(\begin{tabular}{l|c|c|}&Order desert & No desert\\Split the check&50&18\\One person pays&16&38\end{array}\right]\)

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The volume of an irregular object, such as garden soil, can be measured using the water displacement method. By measuring the amount of water displaced when the object is submerged, the volume of the irregular object can be determined.

To measure the volume of an irregular object like garden soil, the water displacement method is commonly used. First, obtain a known volume of water in a container and record its initial level. Then, carefully submerge the irregular object into the water, ensuring it is fully immersed. As the object displaces water, the water level in the container will rise. Record the final water level after the object is submerged.

To calculate the volume of the irregular object, subtract the initial water level from the final water level. The difference in water levels represents the volume of water displaced by the object. Since the object and the garden soil have the same volume, this displaced water volume is equal to the volume of the irregular object, i.e., the garden soil.

By employing the water displacement method, the volume of irregular objects like garden soil can be accurately measured, providing valuable information for various purposes such as gardening, construction, or scientific research.

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To fill the rectangular prism we need 1 cube.

To find the number of cubes needed to fill the rectangular prism, we can calculate the volume of the prism and divide it by the volume of a single cube.

The volume of the rectangular prism is given by the formula:

Volume = Length × Width × Height

Substituting the given values:

Volume = 8 in. × 4 in. × 21 in.

Volume = 672 in³

The volume of a cube is given by the formula:

Volume = Edge Length³

Substituting the given edge length:

Volume of a cube = (14 in.)³

Volume of a cube = 2744 in³

Now, we can divide the volume of the prism by the volume of a single cube to find the number of cubes needed:

Number of cubes = Volume of prism / Volume of a single cube

Number of cubes = 672 in³ / 2744 in³

Calculating this division gives:

Number of cubes ≈ 0.245

Since we cannot have a fraction of a cube, we need to round up to the nearest whole number. Therefore, we would need 1 cube to fill the rectangular prism.

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We must find the length of one side of the new square.

Step one

The area of the square is 64. We know that the is of a rectangle is given by n x n, so:

The value of n is a number that multiplied by itself gives us 64, that number is 8, so we have:

Step two

The length of one side of the new square is obtained by multiplying the original length 8 by the scale factor 3/2, which gives us:

Answer

The amount of the annual depreciation has been $90.

The statement provides us with the following data:

The yearly depreciation of the table saw can be calculated by subtracting the depreciated value from the original cost and dividing by the number of years.

Yearly depreciation = (Original cost - Depreciated value) / Number of years

Yearly depreciation = ($810 - $450) / 4

Yearly depreciation = $360 / 4

Yearly depreciation = $90

Therefore, the amount of yearly depreciation for the table saw is $90.

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All three options involve conducting a survey using random sampling, which is the most appropriate method for creating an estimate of the percentage of district residents who support the building of a new middle school. The correct answer would be A, B, or C, depending on the availability of resources.

The most appropriate method for creating an estimate of the percentage of district residents who support the building of a new middle school would likely be a survey using random sampling.

Random sampling is a statistical method in which a representative sample of a larger population is selected, in order to make inferences about the population as a whole. When conducting a survey, random sampling helps to ensure that the sample is representative of the population, reducing the potential for bias.

There are several different types of surveys that could be used to estimate the level of support for a new middle school, including telephone surveys, online surveys, and in-person surveys.

Complete question:

The superintendent of a large school district wants to estimate the percentage of district residents who support the building of a new middle school. To gather data, the superintendent will select a random sample of district residents. What is the most appropriate method for the superintendent to estimate the percentage of district residents who support the building of a new middle school?

A. Telephone survey using random sampling

B. Online survey using random sampling

C. In-person survey using random sampling

D. Observing the behavior of district residents

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Answer:

x = 18 cm

Step-by-step explanation:

(4x)^2 = 3(4x)(x+6)

16x^2=3(4x)(x+6)

divide both sides by 4x

4x = 3(x+6)

4x=3x+18

x = 18

Answer:

-5 or 5

Step-by-step explanation:

2x^2-50=0

add 50 on both sides

2x^2=50

divide both sides by 2

x^2=25

so x can be 5 or -5

Hope that helps :)

The correct answer to the given question is d. 2n+1. The other options, such as 1n, 3n, 2n-1, and 2n+2, do not accurately represent the chromosome number of a trisomic organism.

A trisomic organism is one that has an extra copy of a chromosome in its genome. This means that it has three copies of a particular chromosome instead of the usual two, which can have significant implications for the organism's development and health.

In terms of algebraic notation, the chromosome number of a trisomic organism would be denoted as 2n+1, where "n" represents the normal diploid number of chromosomes for that organism. The "2n" represents the normal two sets of chromosomes, and the "+1" represents the extra chromosome.

Therefore, the correct answer to the given question is d. 2n+1. The other options, such as 1n, 3n, 2n-1, and 2n+2, do not accurately represent the chromosome number of a trisomic organism. It is important to note that trisomies can occur for any chromosome, not just the sex chromosomes, and can have varying effects depending on which chromosome is affected.

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