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A survey was conducted that asked 1012 people how many books they had read in the past year. Results indicated that
x= 10.4 books and s= 16.6 books. Construct a 95% confidence interval for the mean number of books people read. Interpret
the interval.
Click the icon to view the table of critical t-values.
Construct a 95% confidence interval for the mean number of books people read and interpret the result. Select the correct
choice below and fill in the answer boxes to complete your choice.
(Use ascending order. Round to two decimal places as needed.)
OA. There is 95% confidence that the population mean number of books read is between
OB. If repeated samples are taken, 95% of them will have a sample mean between
OC. There is a 95% probability that the true mean number of books read is between
and
and
and

Answer: C - 3a - 27

Step-by-step explanation:

We start with 2.5 + 3a - 20 - 9.5, and first solve for variables:

3a

Then we solve for constants:

2.5 - 20 - 9.5 = 2.5 - 29.5 = -27

Add the two together:

3a - 27

1/2% is read as 1.2 out of one hundred

so divide 100/1.2 which the answer would be 83.33333333 or 83.3

Answer:

The answer is x<8

Step-by-step explanation:

x/2<4

x<8

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:

0.077

Step-by-step explanation:

By the principle of mathematical induction, we have shown that

M(2k) = k  2k for all k ∈ N.

The principle of mathematical induction is a proof technique used to prove a statement that holds for all positive integers.

It consists of two steps:

Base case: Show that the statement is true for the smallest possible value of the positive integer, usually n = 1.

Inductive step: Assume that the statement is true for an arbitrary positive integer k, and then use this assumption to show that the statement must also be true for k + 1.

Here we have

The following recursive function computes the number of comparisons used in the worst case of merge sort.

M (1) = 0

M (2k) = 2M (2k−1) + 2k for all k > 0

To prove that M(2k) = k × 2k for all k ∈ N using mathematical induction, we will first show that the base case holds:

Base case: When k = 1,

we have M(2) = 2M(1) + 2¹ = 2(0) + 2 = 2, and k × 2k = 1 × 2¹ = 2.

Therefore, the base case holds.

Inductive hypothesis:

Assume that M(2k) = k × 2k holds for some positive integer k.

Inductive step:

We need to show that M(2k+1) = (k+1) × 2k+1.

Using the recursive definition of M, we have:

M(2k+1) = 2M(2k) + 2(2k+1)

= 2(k × 2k) + 2(2k+1) (using the inductive hypothesis)

= 2k(2k+2) + 2(2k+1)

= 2k(2(k+1)) + 2(2k+1)

= 2(k+1) × 2k + 2(2k+1)

= (k+1) × 2(2k+1)

Therefore, the inductive step holds.

Hence,

By the principle of mathematical induction, we have shown that

M(2k) = k  2k for all k ∈ N.

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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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Answer:

55°

Step-by-step explanation:

the total sum of a triangle is 180.

75+50= 125

180-125= 55

& since x is an acute angle we know x is less than 90.

The volume of the solid figure is  1795.5 metres squared. Therefore, the answer is d.

The volume of the figure is the area of the base multiplied by the height of the figure.

Therefore, let's find the volume of the figure as follows:

volume of the figure = area of the base × height of the figure

area of the base =1 / 2 (a + b)h

where

Therefore,

area of the base =1 / 2 (a + b)h

area of the base = 1 / 2 (11 + 16)9.5

area of the base = 128.25

Therefore,

volume of the figure = area × height

volume of the figure = 128.25 × 14

volume of the figure = 1795.5 metres squared

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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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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:)

Answer:

270 counter clockwise I think I'm not sure though

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:

Answer:

C) 4

Step-by-step explanation:

Answer:

Step-by-step explanation:

2.1 so a

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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The number of price increases that would be needed to cause zero profit as shown on the graph, is C) 87.

The point on the graph that would show the number of price increases necessary for the company to record zero profit would be the point on the x - axis where the line crosses the x-axis. This is because this would show the 0 profit mark.

This point on the graph is shown to be 87. This means that if the company increases the price of the wood chairs they sell, 87 times, they will experience zero profit.

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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]

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

Answer:

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

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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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 side length of the the rectangular garden are 20 feet by 5 feet.

Let

s = side length of the square garden

l = length of the rectangular garden

w = width of the rectangular garden

From the problem statement,

area of the square garden = area of the rectangular garden

Since the area of a square is just the side length squared, we can write:

s² = l * w

We also know that the length of the rectangular garden is 10 feet longer than the side of the square garden, and that the width of the rectangular garden is 5 feet shorter than the side of the square garden. We can express them as:

l = s + 10

w = s - 5

Now we can substitute these expressions for l and w into our first equation:

s² = (s + 10) * (s - 5)

Expanding the right-hand side, we get:

s² = s² + 5s - 50

0 = 5s - 50

5s = 50

Dividing both sides by 5, we get:

s = 10

Since the side length of the square garden is 10 feet.

We can use this to find the dimensions of the rectangular garden:

l = s + 10 = 10 + 10 = 20

w = s - 5 = 10 - 5 = 5

So the dimensions of the rectangular garden are 20 feet by 5 feet.

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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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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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Answer: He could be 47 or 46

Step-by-step explanation: I need the exact date of the time he was born (just the month and the day) to tell you how old he really is, but with the information given, he could be 47 or 46.

He would be 47 years                       [tex]1945\\-\\1898\\=\\47\\[/tex]