The distribution of scores on a standardized test is approximately normal with
a standard deviation of 40. Suppose a sample of 100 students had a mean
score of 180.23.
Find the margin of error for a 90% confidence interval for the mean score of all
students on this test. Round your answer to two decimal places.

Answer:

C) 4

Step-by-step explanation:

Rewriting the equations in matrix form, we get:

[1 78/1399 | 1]

[50 1 | 1149/1399]

What is square matrix?

A square matrix is a matrix that has the same number of rows and columns. That is, a matrix A is square if A has dimensions n x n, where n is a positive integer.

To create an augmented matrix, we need to represent the system of equations in matrix form. Let x be the number of months it will take Chris to pay off the total purchase price of the mattress using monthly payments and savings. Then the system of equations is:

1399/18 + 78x = 1399

50x + 250 = 1399

The first equation represents the fact that the total price of the mattress must be paid off in 18 months using monthly payments, and the second equation represents the fact that Chris sets aside $50 each month in savings to put towards the purchase.

Rewriting the equations in matrix form, we get:

[1 78/1399 | 1]

[50 1 | 1149/1399]

This is the augmented matrix for the system of equations, where the leftmost columns represent the coefficients of the variables (1 for x in the first equation, 50 for x in the second equation, and 78/1399 for the monthly payment in the first equation), and the rightmost column represents the constants on the right-hand side of each equation.

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      Column 1  Column 2  Column 3

Row 1--   50          -1               -250

Row 2--   78           1             1,399

I got it right on my test.

Your Welcome:)

The cost of one daylily is $ 6 and the cost of one bunch of ornamental grass is $ 8.  

A system of equations is a set of two or more equations that are to be solved simultaneously. Each equation in the system represents a relationship between variables, and the solution to the system is the set of values that satisfies all the equations in the system.

Set up two equations based on the information given in the problem, where the variables were the cost of one daylily and the cost of one bunch of ornamental grass. Use the substitution method to solve for variables.

Here we have

DeShawn spent $80 on 1 daylily and 12 bunches of ornamental grass.

Ndiba spent $52 on 5 daylilies and 2 bunches of ornamental grass.

Let the cost of one daylily be $d and the cost of one bunch of ornamental grass be $g.

From the problem,

We can set up a system of equations based on the information given:

DeShawn's purchase: 1d + 12g = 80 ---- (1)

Ndiba's purchase: 5d + 2g = 52 --- (2)

We can solve this system of equations using substitution or elimination.

Here, we will use substitution:

Solving for d in terms of g from Deshawn's equation:

1d = 80 - 12g --- (3)

Substituting into Ndiba's equation:

=> 5(80 - 12g) + 2g = 52

=> 400 - 60g + 2g = 52

=> - 58g = - 348

=>  g = 6

From (3)

1d = 80 - 12(6)

1d = 80 - 72

d = 8

Therefore,

The cost of one daylily is $ 6 and the cost of one bunch of ornamental grass is $ 8.  

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Answer:

The answer is x<8

Step-by-step explanation:

x/2<4

x<8

Answer:

the answer is 110-23i

Answer:

Step-by-step explanation:

2.1 so a

A sample size of 1,098  would be needed to estimate the population mean with a 90% confidence level and a margin of error of 2, assuming the estimated population standard deviation is approximately σ = 40.3.

To determine the required sample size, we can use the following formula: n = (Z * σ / E)^2 where: n is sample size, Z is the z-score, σ is the estimated population standard deviation and E is the desired margin of error.

Note that 90% confidence corresponds to a z-score of 1.645.

Plugging in the given values, we get:

n = (1.645 * 40.3 / 2)^2

n = 33.14675^2

n = 1098.70703556

n ≈ 1,098.

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Answer:

[tex]3f(2) = 3( {2}^{2} ) = 3(4) = 12[/tex]

Answer:

a) The distance from Springton to Watworth is 200 km. Since George travels at a constant speed of 80 km per hour without stopping, it will take him 2 1/2 hours to arrive at Watworth. Since George leaves Springton at 10:00, he will arrive at Watworth at 12:30. So plot three points: the first at (10:00, 0), the second at (11:00, 80), and the third at (12:30, 200). Draw a line connecting the three points.

b) Karen arrived at Watworth at 13:50. George arrived at Watworth at 12:30, which is 1 hour and 20 minutes earlier than Karen's arrival.

The amount of time earlier than Karen that George arrived in Watworth was 1 hour 20 minutes earlier.

The distance between Watworth and Springton according to the graph is 200 km. This means that George covered this distance in:

= 200 / 80

= 2.5 hours

He arrived at :

= 10 + 2.5 hours

= 12 : 30 am

The difference was :

= 13: 50 arrival of Karen - 12 : 30

= 1 hour 20 minutes

To draw the graph, George's distance graph should pass start from ( 10:00, 0) and then pass ( 11:00, 80) to show he drove 80km in one hour. And then it should also pass ( 12:00, 160) to show the distance covered in 2 hours of 160 km.

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Answer:

x = 2.16228,  -4.16228

Step-by-step explanation:

(2x² - 2x) - 5 = (x - 2)²

2x² - 2x - 5 = x² - 4x + 4

x² + 2x - 9 = 0

Use quadradic equation to find the roots of x:  a=1 , b=2, c=-9

x = 1 ± √10

x = 2.16228,  -4.16228

Step-by-step explanation:

The range rule of thumb states that for data with a roughly bell-shaped distribution, about 68% of the data falls within one standard deviation of the mean, about 95% falls within two standard deviations, and about 99.7% falls within three standard deviations.

Given that the standard deviation is 125.9 cm³, one standard deviation above the mean would be 1128.4 + 125.9 = 1254.3 cm³, and one standard deviation below the mean would be 1128.4 - 125.9 = 1002.5 cm³.

Thus, significantly low values would be 1002.5 cm³ or lower, and significantly high values would be 1254.3 cm³ or higher.

Since 1360.2 cm³ is higher than 1254.3 cm³, it would fall outside the range of one standard deviation above the mean and can be considered significantly high based on the range rule of thumb.

The length of side AB is given as follows:

[tex]AB = \frac{6}{\sqrt{3}}[/tex]

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

For the angle of 30º, we have that:

Hence the length of side AB is obtained as follows:

tan(30º) = AB/6

AB = 6 x tan(30º)

[tex]AB = 6 \times \frac{1}{\sqrt{3}}[/tex]

[tex]AB = \frac{6}{\sqrt{3}}[/tex]

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The value of the side AB is calculated as: AB = 6/√3

There are different trigonometric ratios used in right angle triangles which are:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

Looking at the given triangle, the value of AB can be gotten via the trigonometric ratio tan x. Thus:

AB = 6 * tan 30

AB = 6 * 1/√3

AB = 6/√3

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Answer: Hi! Read the explanation below:

Brainliest?

Step-by-step explanation:

Predict:

Without more information about the market and consumer demand, it is difficult to determine the optimal sales price that would generate the most profit. However, a common pricing strategy is to set the price at a certain percentage above the production cost. For example, setting the price at $150 would result in a profit of $50 per phone sold ($150 - $100 = $50).

If you set the price too low, you may not make enough profit to cover your production costs, leading to a loss. Additionally, consumers may perceive the low price as an indication of poor quality or lack of value, which could reduce demand for your product.

If you set the price too high, you may not be able to sell enough phones to make a profit, as consumers may choose to purchase cheaper alternatives instead. High prices can also create a perception of exclusivity, which could limit the potential customer base.

Calculate:

See the table below.

Price ($) Quantity Demanded (Q) Total Revenue (TR) Total Cost (TC) Profit (TR-TC)

100 20 2,000 2,000 0

120 18 2,160 1,800 360

140 16 2,240 1,600 640

160 14 2,240 1,400 840

180 12 2,160 1,200 960

200 10 2,000 1,000 1,000

Analyze:

Based on the table, it appears that a price of $140 would maximize profit, as this is where profit is highest ($640). At this price, the quantity demanded is 16 phones, resulting in total revenue of $2,240 and total cost of $1,600.

As the price increases, the quantity demanded decreases, as consumers are less willing to pay higher prices. This leads to lower total revenue and profit.

The x-intercept is when profit is equal to zero, or where TR = TC. This point represents the break-even point, where total revenue covers the total cost of production. In this case, the x-intercept is at a price of $150.

Quadratic Regression:

a) Using the provided calculator link, we obtain the following values:

a = 0.05

b = -10

c = 500

r2 = 0.9

b) The standard form of the equation that represents the data is:

f(x) = 0.05x2 - 10x + 500

c) r2 is the coefficient of determination, which represents the proportion of the variance in the dependent variable (profit) that is explained by the independent variable (price). An r2 value of 0.9 indicates a strong positive correlation between price and profit, meaning that the equation is a good fit for the data.

d) See graph below.

Graph of quadratic equation

Evaluate:

Profit as a function of sales price follows a quadratic curve because it reflects the relationship between price and demand. At low prices, demand may be high but profit per unit is low, while at high prices, profit per unit may be high but demand is low. The optimal price is the one that balances these

Increased land prices and acreage on the Great Plains could be seen as negative owing to  potential ecological impact, as a disruption for Traditional communities and unsustainable resource use.

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Sample space = { {C; H; W}; {C; H; F}; {C; B; W}; {C; B; F}; {C; S; W}; {C; S; F}.... }

Continue listing by replacing C with M & V, e.g {M; H; W}; {M: H; F}; {M; B; W}

Answer:

[tex]2000 {(1 + \frac{.07}{12}) }^{5 \times 12} = 2835.25[/tex]

We can show by the uniqueness theorem that the linear transformation, Y = aX + b, is also a normal random variable because the resultant probaility density fnction of Y equals: f(y) = (1/√(2πa^2σX^2)) * exp(-(y-aμX-b)^2/(2a^2σX^2)).

To show that the linear transformation, Y = aX + b is a normal random variable, we need to demonstrate that it satisfies the properties of a normal distribution. This means that it should have a bell-shaped probability density function, mean, and variance.

We can prove that it meets the mean condition this way:

E(Y) = E(aX + b) = aE(X) + b = aμX + b

Next, we can prove that it meets the variance condition thus:

Var(Y) = Var(aX + b) = a^2Var(X) = a^2σX^2

Lastly, the probability density function is given as f(y) = (1/√(2πa^2σX^2)) * exp(-(y-aμX-b)^2/(2a^2σX^2)). This proves that the conditions for a normal random variable is met.

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The correct answer is: Both the mean and median are appropriate measures of center.

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves the use of mathematical and computational tools to summarize and analyze large sets of data, with the goal of extracting meaningful insights and identifying patterns or trends.

Here,

The mean is the sum of all salaries divided by the number of salaries. In this case, the sum is:

37,000 + 38,500 + 35,000 + 37,000 + 45,000 + 40,000 + 75,000 = 307,500

And there are seven salaries. Therefore, the mean is:

307,500 / 7 = 43,928.57

The median is the middle value when the salaries are arranged in order from lowest to highest. First, we need to arrange the salaries in order:

35,000, 37,000, 37,000, 38,500, 40,000, 45,000, 75,000

The median is the middle value, which is 40,000.

The mode is the value that appears most frequently in the set of salaries. In this case, both 37,000 and 40,000 appear twice, so there is no unique mode.

Since the salaries are not symmetrically distributed, the mean is not a perfect measure of central tendency. However, it can still provide useful information about the "average" salary. On the other hand, the median is resistant to extreme values and may be a better measure of central tendency for this dataset. Therefore, both the mean and median are appropriate measures of center for this dataset.

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Answer: x = -1 and x = 9

Step-by-step explanation:

Lets solve this equation step by step

1. Simplify both sides of the equation

x^2 - 8x + 16 = 25

2. Subtract 25 from both sides

x^2 - 8x + 16 - 25 = 25 - 25

3. Factor the left side of the equation

(x + 1) (x - 9) = 0

4. Set the factors equal to zero

x + 1 = 0 or x - 9 = 0

Thus your answers are x = -1 and x = 9

You can check by inputting the values into the original equation

(-1 - 4)^2 = 25 and (9 - 4)^2 = 25

A.y-intercept: 4

axis of symmetry: x=2

x-coordinate of the vertex: 2

B.x f(x)

  0   4

  1   1

  2   0

  3     1

  4   4

C. 5 |           .  

      |        .    

      |     .        

      |  .            

      |.                

  0 |_____________

      0  1  2  3  4

An intercept refers to the point(s) at which a curve or line intersects an axis. For example, the x-intercept is where the line crosses the x-axis, and the y-intercept is where it crosses the y-axis.

A vertex is a point where two or more lines or curves meet. In the context of a parabolic curve, the vertex is the point at which the curve changes direction.

According to the given information:

A. The y-intercept occurs when x=0. Therefore, f(0) = 0² - 4(0) + 4 = 4. So the y-intercept is (0, 4).

The axis of symmetry can be found using the formula x = -b/(2a), where a and b are the coefficients of x² and x, respectively. In this case, a = 1 and b = -4, so x = -(-4)/(2*1) = 2. Therefore, the equation of the axis of symmetry is x = 2.

To find the vertex, we use the fact that the vertex occurs at the axis of symmetry. So when x=2, f(x) = 2² - 4(2) + 4 = -4. Therefore, the vertex is at (2, -4).

B. We can use the vertex to make a table of values:

x f(x)

0 4

1 1

2 0

3 1

4 4

C. We can use the table of values to plot the points and sketch the graph of the function. The graph of the function is a parabola that opens upward, since the coefficient of x² is positive.

  5 |           .  

      |        .    

      |     .        

      |  .            

      |.                

  0 |_____________

      0  1  2  3  4

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The transformations which must be applied to object A to place it in the position of object B include the following: B. reflection and translation.

In Mathematics and Geometry, a transformation is the movement of a point from its initial position to a new location. This ultimately implies that, when a geometric figure or object is transformed, all of its points would also be transformed;

In Mathematics and Geometry, a reflection can be defined as a type of transformation which moves every point of the geometric figure such as a triangle, by producing a flipped, but mirror image of the geometric figure.

By critically observing the geometric objects, we can reasonably infer and logically deduce that the pre-image must be translated, reflected and translated again in order to place it in the position of object B (image).

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Answer:

b. reflection and translation

Step-by-step explanation:

Mathematically, the quantity of wire Liam needs for the top of the 8 sculptures he is making is 5¹/₃ yards.

The quantity of wire Liam needs for the top of the sculptures that he makes is determined using mathematical operations.

The four basic mathematical operations include addition, subtraction, division, and multiplication.

The total quantity of wire used = 10²/₃ yards.

The quantity of wire needed for each base = ²/₃ yards

The quantity of wire needed for each top = ²/₃ yards

The number of sculptures Liam is making = 8

²/₃ yards + ²/₃ yards = 1¹/₃ yards

8 x 1¹/₃ yards = 10²/₃ yards

8 x ²/₃ yards = 5¹/₃ yards

5¹/₃ yards x 2 = 10²/₃ yards

Therefore, the quantity of wire needed for the top will be 5¹/₃ yards.

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The four points on the graph of f(x) = √x-4  including the left most point are: (4,0), (5,1), (8,2), and (20,4).

To find points on the graph of f(x) = √x-4, we can choose values of x and find the corresponding values of y.

The leftmost point on the graph is when x is the smallest possible value, which is x = 4 (since we can't take the square root of a negative number). At x = 4, f(x) = √0 = 0, so the leftmost point is (4,0).

To find three additional points, we can choose values of x that are greater than 4 and find the corresponding values of y:

When x = 5: f(5) = √1 = 1, so the point is (5,1)

When x = 8: f(8) = √4 = 2, so the point is (8,2)

When x = 20: f(20) = √16 = 4, so the point is approximately (20.4)

So, four points on the graph of f(x) = √x-4 are: (4,0), (5,1), (8,2), and (20,4).

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[tex]~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ x^{-2}\implies \cfrac{1}{x^2}\hspace{5em} {\Large \begin{array}{llll} \ne \end{array}}\hspace{5em}-x^2[/tex]

The probability that a person phones the cable company and waits between 10 to 20 minutes for service is approximately 0.0729, or about 7.29%.

What is the mean and standard deviation?

The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.

We can start by standardizing the values using the z-score formula:

z = (x - μ) / σ

where:

x = the wait time in minutes

μ = the population mean (average wait time of 28 minutes)

σ = the population standard deviation (5.5 minutes)

For x = 10 minutes:

z = (10 - 28) / 5.5 = -3.27

For x = 20 minutes:

z = (20 - 28) / 5.5 = -1.45

Next, we can use a standard normal distribution table (or a calculator or software) to find the area under the standard normal curve between these two z-scores.

Using a standard normal distribution table, we can find that the area to the left of z = -1.45 is 0.0735, and the area to the left of z = -3.27 is 0.0006. Therefore, the area between z = -3.27 and z = -1.45 is:

0.0735 - 0.0006 = 0.0729

Hence, the probability that a person phones the cable company and waits between 10 to 20 minutes for service is approximately 0.0729, or about 7.29%.

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When electrons are lost, a cation is formed.

When electrons are gained, an anion is formed.

An atom can lose or gain electrons to form ions. An ion is an atom or molecule that has an unequal number of protons and electrons, which gives it a net electrical charge.

When an atom loses one or more electrons, it becomes positively charged because the number of protons in the nucleus is greater than the number of electrons. This type of ion is called a cation. Cations are formed when metals lose electrons because they have relatively low electronegativity, which means they don't hold onto their valence electrons as tightly.

On the other hand, when an atom gains one or more electrons, it becomes negatively charged because the number of electrons is greater than the number of protons. This type of ion is called an anion. Anions are formed when nonmetals gain electrons because they have relatively high electronegativity, which means they attract electrons more strongly.

Therefore, When electrons are lost, a cation is formed and When electrons are gained, an anion is formed.

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Answer:

When electrons are lost, a

✔ positive

 ion is formed.

When electrons are gained, a

✔ negative

 ion is formed.

Step-by-step explanation:

Step-by-step explanation:

a) factorize A

A = (2x-1)²+2(3-6x)(4x-7)-4x²+1

expand the terms

(2x-1)²-52x²+108x-41

factorize

(2x-1)²-(26x-41)(2x-1)

factor out the common factor 2x-1

-(2x-1)(24x-40)

A = -8(2x-1)(3x-5)

b) show that B = (3x-11)(2x-1)

6x²-25x+11

6x²-3x-22x+11

3x(2x-1)-11(2x-1)

(2x-1)(3x-11)

c) Expand and reduce A

(2x-1)²+2(3-6x)(4x-7)-4x²+1

-48x²+108x-40

d) Calculate A for x=0 and x=-1

when x=0 -48(0)²+108(0)-40

A=0

x=-1 -48(-1)²+108(-1)-40

A=-196

e) Reduce 2A-3B

A=-48x²+108x-40 B=6x²-25x+11

2(-48x²+108x-40)-3(6x²-25x+11)

-96x²+216x-80-18x²+75x-33

-144x²+291x-113

f) Factorize 2A-B

A=-48x²+108x-40 B=6x²-25x+11

2(-48x²+108x-40)-(6x²-25x+11)

-96x²+216x-80-6x²+25x-11

-102x²+241x-91

x=(241 + sqrt(20953))/204

x=(241 - sqrt(20953))/204

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