Find the sample variance and standard deviation.
23, 16, 5, 7, 11 q
OA. s² =
2
S
OB. 0²=

Answer:

See below for solution steps for parts (a) and (c)

Step-by-step explanation:

The trick here is to get all the roots to have the same radical. Each of the lowest radical is the square root pf a prime so cannot be reduced further

For example, in a, the lowest is [tex]\sqrt{3}[/tex]

So get all the others to this level a[tex]\sqrt{3}[/tex]  and then you can just add up the non-radicals and use the radical as the common expression

I will solve a couple and that will give you a general idea of solving the rest

Let's do a.
[tex]5\sqrt{3} , \sqrt{3}[/tex] are already at the lowest radical level of [tex]\sqrt{3}[/tex] so let's reduce 108 to have [tex]\sqrt{108}[/tex] to have [tex]\sqrt{3}[/tex] as one of its components

We can factor 108 as follows;

108/3 = 36

So 108 = 36 x 3

√108 = √36 × √3 = 6√3

Therefore the original expression becomes

[tex]5\sqrt{3} - 6\sqrt{3} + \sqrt{3} = (5 - 6 + 1)\sqrt{3} = 0 \sqrt{3} = 0[/tex]

[tex]-------------------------------[/tex]

c.
[tex]2\sqrt{20} - 7\sqrt{5} + \sqrt{45}[/tex]

Lowest radical is [tex]\sqrt{5}[/tex] whose coefficient is 7

Factor 20 = 4 x 5

[tex]2\sqrt{20} = 2\sqrt{4 \times 5} = 2\sqrt{4} \times \sqrt{5} = 2\times 2 \times \sqrt{5}\\= \bold{4\sqrt{5}}[/tex]

Factor 45:
45 = 9 x 5

[tex]\sqrt{45} = \sqrt{9} \times \sqrt{5} = \bold{3\sqrt{5}}[/tex]

Original expression becomes:
[tex]4\sqrt{5} - 7\sqrt{5} + 3\sqrt{5}\\\\=(4 - 7 + 3)\sqrt{5}\\\\= 0 \sqrt{5}\\\\= 0\\----------------------------[/tex]

I am sure you can do the rest. If not post them as another question. Maybe someone else will answer a few of the ones I did not.

All the best

Answer:

Step-by-step explanation:

heyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy

The algebraic equation for the statement is 21 = 2 x - 5

Algebraic equations can be written using mathematical symbols and operations to represent relationships between variables or quantities. Variables are the quantities that the equation is trying to represent or solve for.

There is only one variable here and we can call it x.

The number is doubled so the representation would be :

= 2 x

This is then decreased by 5 and becomes :

= 2 x - 5

This is equated to 21 to become:

21 = 2 x - 5

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The short-run total cost is TC is wL + rK and short-run average cost curve is TC/Q. The SMC is 4.01 and the SMC curve intersects the SAC curve at its lowest or minimum points because the average cost is a weighted average of the marginal cost and the fixed cost.

A. To calculate the firm’s short-run total cost curve, we need to calculate the total cost at each level of output. The short-run total cost can be represented as follows:

TC = wL + rK,

where w is the wage rate, L is the labor used, r is the interest rate, and K is the capital used. In this case, w = $4 and r = $1.

To calculate the short-run average cost curve, we need to divide the total cost by the level of output:

SAC = TC / Q

Where Q is the level of output.

B. The short-run marginal cost function can be calculated as the change in total cost for a small change in the level of output:

SMC = dTC / dQ

At a level of output of 25, the labor used is L = 25 / 2 = 12.5. The total cost can be calculated as follows:

TC = 4 * 12.5 + 1 * 100 = 50 + 100 = 150

So, the short-run average cost is SAC = 150 / 25 = $6 and the short-run marginal cost is SMC = dTC / dQ. To calculate the derivative, we need to use the production function given:

Q = 2 * sqrt(KL)

Taking the derivative with respect to L, we get:

dQ / dL = (1 / (2 * sqrt(KL))) * 2K = K / (sqrt(KL))

Substituting the values, we get:

SMC = 4 + (1 / (sqrt(100 * 12.5)))

At a level of output of 200, the labor used is L = 200 / 2 = 100. The total cost can be calculated as follows:

TC = 4 * 100 + 1 * 100 = 400

So, the short-run average cost is SAC = 400 / 200 = $2 and the short-run marginal cost is SMC = dTC / dQ. To calculate the derivative, we need to use the production function given:

Q = 2 * sqrt(KL)

Taking the derivative with respect to L, we get:

dQ / dL = (1 / (2 * sqrt(KL))) * 2K = K / (sqrt(KL))

Substituting the values, we get:

SMC = 4 + (1 / (sqrt(100 * 100)))

SMC = 4.01

C. To draw the graph for the SAC and SMC, we need to calculate the SAC and SMC for different levels of output. We can then plot the SAC and SMC against the level of output to obtain the graphs.

D. The SMC curve intersects the SAC curve at its lowest or minimum points because the average cost is a weighted average of the marginal cost and the fixed cost. When the level of output is low, the marginal cost is high and the fixed cost is a large portion of the total cost. As the level of output increases, the marginal cost decreases and the fixed cost becomes a smaller portion of the total cost. As a result, the average cost decreases and reaches a minimum at the point where the marginal cost intersects the average cost.

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The value of x that will make L||m is 9.

Geometry is a branch of mathematics that deals with shapes, angles, dimensions and sizes of different things we see in everyday life

The angle (4x²- 324)° is equal to 90°. That is:

(4x²- 324)° = 90°

4x²- 324 = 90

4x² = 90 + 324

4x² = 324

x² = 324/4

x² = 81

x = √81

x = 9

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Answer:

No

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180°

sum the 3 angles and equate to 180

x + 32 + 4x + 20 + 4x + 20 = 180

9x + 72 = 180  ( subtract 72 from both sides )

9x = 108 ( divide both sides by 9 )

x = 12

then the 3 angles are

x + 32 = 12 + 32 = 44°

4x + 20 = 4(12) + 20 = 48 + 20 = 68°

4x + 20 = 68°

an obtuse angle is greater than 90°

none of the 3 angles in the triangle are obtuse

Answer:

No

Step-by-step explanation:

All angles of a triangle add up to 180°.

4x + 20 + 4x + 20 + x + 32 = 180

1. Simplify

9x + 72 = 180

2. Subtract 72 from both sides.

9x = 108

3. Divide both sides by 9.

x = 12

Replace x by 12 in each angle.

-  12 + 32 = 44°

-  4(12) + 20 = 68°

-  4(12) + 20 = 68°

All of the angles are less than 90°, so they aren't obtuse.

The common difference of the given arithmetic sequence is 8.

An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same. The general form an arithmetic sequence is aₙ=a+(n-1)d.

The given arithmetic sequence is -1, 7, 15,....

Common difference = Second term - First term

= 7-(-1)

= 7+1=8

Common difference = Third term - Second term

= 15-7

= 8

Therefore, the common difference is 8.

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The solution is, the common differences are -3, -20, -10, -2, 5.

In an arithmetic sequence, the difference between any two consecutive terms must always be the same number, which is known as the common difference.

here, we have,

So we just need to take different pairs of consecutive terms and see if their difference is always the same:

1) The differences are:

32 - 35 = -3

29 - 32 = -3

26 - 29 = -3

So yes, this is an arithmetic sequence and the common difference is -3

2) The differences are:

-23 - (-3) = -20

-43 - (-23) = -20

-63 - (-43) = -20

This is an arithmetic sequence, and the common difference is -20

3) The differences are:

-64 -(-34) = -30

-94 -(-64) = -30

-124 -(-94) = -30

This is an arithmetic sequence and the common difference is -30

4) The differences are:

-40 -(-30) = -10

-50 - (-40) = -10

-60 - (-50) = -10

This is an arithmetic sequence and the common difference is -10

5) The differences are:

-9 - (-7) = -2

-11 - (-9) = -2

-13 - (-11) = -2

This is an arithmetic sequence, and the common difference is -2

6) The differences are:

14 - 9 = 5

19 - 14 = 5

24 - 19 = 5

This is an arithmetic sequence, and the common difference is 5.

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It's important to work through the problems yourself to improve your understanding and problem-solving skills.

For the unit 3 homework on parallel and perpendicular lines, you should have learned about the slope of lines, how to find the slope of a line given two points, and the relationship between parallel and perpendicular lines.

To find the slope of a line given two points, you can use the slope formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are the coordinates of the two points on the line.

To determine if two lines are parallel, you can compare their slopes. Parallel lines have the same slope.

To determine if two lines are perpendicular, you can use the fact that the product of their slopes is -1. That is, if m1 and m2 are the slopes of two lines, and m1 * m2 = -1, then the lines are perpendicular.

It's important to practice working through problems using these concepts and formulas to develop your skills and understanding. Additionally, you can seek assistance from your teacher or tutor if you have specific questions or concerns.

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The future value of the investment when interest is compounded continuously is; $3408.29

Compound interest is a method of calculating the interest charge. In other words, it is the addition of interest on interest.

Given Data

P= $1500, r = 3.95%, t = 5 yr

To Calculate the number of periods: in this case we have 5*12= 60 months.

- The monthly interest rate, we have to divide the annual nominal rate by 12 (the number of periods in the year).

Then, we can calculate the future value as:

A = P (1 + r/n)^nt

A = 1500(1 + 3.95/365)(365)^(5)

P = 1500/ (1 + 0.00010137)^(5)

P = $3408.29

The future value when compounded monthly is $3408.29.

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Answer:

Step-by-step explanation:

To find the two diameters that separate the top 3% and the bottom 3% of the bolts produced in the machine shop, we need to find the lower and upper bounds of the interval that contains the middle 94% of the data. This can be done using the standard normal distribution and the z-score.

First, we'll find the z-score that corresponds to the lower bound. To do this, we'll use the formula:

z = (x - μ) / σ

where x is the lower bound, μ is the mean of the data (6.48 mm), and σ is the standard deviation of the data (0.06 mm). We want to find the value of x such that the area to the left of x is equal to 3%:

z = (x - 6.48) / 0.06

z = -2.33

Next, we'll use the z-score to find the value of x (the lower bound). We'll use the standard normal distribution table to look up the value of -2.33 and find that it corresponds to a cumulative probability of 0.01. So, the lower bound is such that 1% of the data is less than or equal to this value. To find the value of x, we'll use the formula:

x = μ + zσ

x = 6.48 + (-2.33) * 0.06

x = 6.32

So, the lower bound of the interval that contains the middle 94% of the data is 6.32 millimeters. This is the diameter that separates the bottom 3% of the bolts from the rest.

Next, we'll find the upper bound in a similar way. To do this, we'll use the formula:

z = (x - μ) / σ

where x is the upper bound, μ is the mean of the data (6.48 mm), and σ is the standard deviation of the data (0.06 mm). We want to find the value of x such that the area to the left of x is equal to 97%:

z = (x - 6.48) / 0.06

z = 2.33

Using the standard normal distribution table, we find that the value of 2.33 corresponds to a cumulative probability of 0.99. So, the upper bound is such that 99% of the data is less than or equal to this value. To find the value of x, we'll use the formula:

x = μ + zσ

x = 6.48 + 2.33 * 0.06

x = 6.64

So, the upper bound of the interval that contains the middle 94% of the data is 6.64 millimeters. This is the diameter that separates the top 3% of the bolts from the rest.

Therefore, the two diameters that separate the top 3% and the bottom 3% of the bolts produced in the machine shop are 6.32 millimeters and 6.64 millimeters, rounded to the nearest hundredth.

Based on the information, we can infer that the graph would be a curve like the one shown in the attached image.

First of all, to graph the information about the body temperature of children, we must consult on the internet or other sources what is the body temperature of children. Below is the information:

According to the above, the graph should present a higher frequency at a temperature of 98.6, so the highest point on the graph would be at that temperature. On the other hand, the other temperatures would decrease because they are less frequent among children.

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Answer:

Let's call the number of cubic yards of mix A that the farmer buys "x", and the number of cubic yards of mix B that the farmer buys "y".

We can write the following constraints based on the minimum monthly requirements:

20x + 10y >= 460 (for acid)

30x + 30y >= 939 (for nitrogen)

5x + 10y >= 200 (for potash)

We also want to minimize the cost, which is given by 25x + 49y.

This is a linear programming problem, which can be solved using simplex method or the graphical method.

By using the graphical method, we find that the optimal solution occurs at x = 11.75 and y = 4.5. This means that the farmer should buy 11.75 cubic yards of mix A and 4.5 cubic yards of mix B to meet the minimum monthly requirements at a minimum cost.

So, the answer to the question is: If mix A costs $25 per cubic yard and mix B costs $40 per cubic yard, the farmer should blend 11.75 yd of mix A & 4.5 yd of mix B to meet the minimum monthly requirements at a minimum cost.

A = {f, k, m, y}

B' = {k, x, y}

[tex]A \cup B' = \{f, ~k, ~m, ~y, ~x\}[/tex]

(every element from A and any other element that B' has that A didn't)

A' = {q, x}

B' = {k, x, y}

[tex]A \cap B' = \{x\}[/tex]

(x is the only element that both sets have)

The set of ordered pairs of option A does not represent a function. The solution has been obtained using the properties of function.

What is a function?

A relationship between a number of inputs and one output per input is referred to as a function. Typically, a function is denoted by the notation f(x), where x is the input. Typically, a function is represented as y = f(x).

We know that for one input, a function can have only one output.

But, in option A, for the same input value 2, there are two output values 2 and 7. Whereas in other options, each input has only one output.

Hence, the set of ordered pairs of option A does not represent a function.

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The number of ways for the child to select 3 treats is given as follows:

455 ways.

The number of different combinations of x objects from a set of n elements is obtained with the formula presented as follows, using factorials.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The order in which the treats are chosen is not relevant, hence the combination formula is used to solve this question.

Three treats are chosen from a set of 15, hence the number of ways is given as follows:

C(15,3) = 15!/(3! x 12!) = 455 ways.

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Answer:

s = 13.6

m∠T = 35.7°

m∠U = 61.3°

Step-by-step explanation:

• Solving for side s:

To find the length of side s, we have to use the cosine rule:

[tex]\boxed{a^2 = b^2 + c^2 - 2bc \ cosA}[/tex],

where:

In this case, the unknown side is s, and the sides adjacent to it have lengths of 8 and 2. The angle opposite to s is ∠S = 83°. Therefore,

[tex]s^2 = 8^2 + 12^2 -2(8)(12) \cdot cos(83^{\circ})[/tex]

⇒ [tex]s = \sqrt{8^2 + 12^2 -2(8)(12)\cdot cos(83^{\circ})}[/tex]

⇒ [tex]s = \bf 13.6[/tex]

• Solving for m∠T:

In order to find m∠T, we can use the sine rule:

[tex]\boxed{\frac{sinA}{a}= \frac{sinB}{b} =\frac{sinC}{c}}[/tex],

which means that the ratios of the sines of angles and their opposite sides are equal for a triangle.

The side opposite to ∠T is US = 8. Therefore:

[tex]{\frac{sinT}{8} = \frac{sin(83^{\circ})}{13.6}}[/tex]

⇒ [tex]sinT= \frac{sin(83^{\circ})}{13.6} \times 8[/tex]

⇒ [tex]T = sin^{-1}( \frac{sin(83^{\circ})}{13.6} \times 8)[/tex]

⇒ [tex]T = \bf 35.7^{\circ}[/tex]

• Solving for m∠U:

Now that we know the values of two angles of the triangle, we can calculate the third angle using the fact that the angles in a triangle add up to 180°:

∠U + ∠S ∠T = 180°

⇒ ∠U + 83° + 35.7° = 180°

⇒ ∠U = 180° - 83° - 35.7°

⇒ ∠U = 61.3°

The angle of the base and the ladder is 69. 34 degrees

Note that the six trigonometric identities are;

From the information given, we have that;

Hypotenuse = 17 meters

Adjacent = 6 meters

The identity to use is the cosine

cos θ = adjacent/hypotenuse

Substitute the  values

cos θ = 6/17

cos θ =,0. 3529

Take inverse of cos

θ = 69. 34 degrees

Hence, the value is 69. 34 degrees

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Answer: To find the percent error, we can use the formula:

percent error = (estimated value - actual value) / actual value * 100

Plugging in the values:

percent error = (76 - 59) / 59 * 100 = 29.49%

Rounding to the nearest tenth of a percent:

percent error = 29.5%

So the percent error is 29.5%.

Step-by-step explanation:

Answer:

C) 0.24 kg

----------------------------

Find the weight of two loaves of bread:

Find the difference of weights of 2 loaves of bread and 6 muffins:

The matching choice is C.

The difference of weights of 2 loaves of bread and 6 muffins:

= 0.24 kg

We have to given that,

One loaf of bread weighs 0.68 kilogram.

And, Six muffins weigh 1.12 kilograms.

Now, We can Find the weight of two loaves of bread:

Here, One loaf of bread weighs 0.68 kilogram.

Hence, the weight of two loaves of bread:

0.68 x 2 = 1.36 kg

Hence, the difference of weights of 2 loaves of bread and 6 muffins:

= 1.36 kg - 1.12 kg

= 0.24 kg

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According to the given information the lateral surface area of given cylinder is 725.34 in².

In mathematics, a cylindrical is indeed a three-dimensional solid that retains two parallel bases spaced apart by a curving surface. These bases frequently have a circular shape (like a circle), and also an axis links their respective centers.

A cylinder is a three-dimensional form having two parallel, round sides on either end, one side that curves, no vertices or edges.

As we know that the lateral surface area of cylinder (A) = 2πrh

Given

D = [tex]16\frac{1}{2}[/tex]in

h = 14in

r = D/2

 = 33/4 in

A = (2 × 3.14 × 33 × 14) / 4

   = 2901.36 /4

   = 725.34 in²

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7.21 × 10⁻⁷

Step-by-step explanation:

(6.94 × 10⁻⁷) + (2.7 × 10⁻⁸) = 7.21 × 10⁻⁷

If A, B and C be events relative to the sample space S, then the Venn diagram of the representing event has been plotted

Let A, B and C be events relative to the sample space S.

The sample space is the set of all possible outcomes of the experiment.

The Venn diagram is the pictorial representation of the sample space of the experiment by using the circles and the overlapping of the circles.

Here we have to plot the each representing events using the Venn diagram representation

Part a

The event is (A ∩ B)'

Plot the Venn diagram

Part b

The event is (A ∪ B)'

Plot Venn diagram

Part c

The event is (A ∩ C) ∪ B

Plot the Venn diagram

Therefore, the Venn diagram of the each event has been plotted

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Answer: A. Parallelogram

Step-by-step explanation:  A parallelogram is a four-sided polygon with opposite sides that are parallel and equal in length.

Answer:

Step-by-step explanation:13x6

The Possible effects of incentives for political leaders includes options 1, 2, 3, and 4. These options elaborate the incentives of political leaders.

Favor programs with immediate benefits: Political leaders may be incentivized to prioritize policies or programs that provide immediate benefits to their constituents in order to increase their popularity and chances of reelection.

Implement policies that favor a small, powerful group: Incentives for political leaders may also lead them to implement policies or regulations that favor a small, powerful group, such as major donors or influential interest groups, at the expense of the general public.

Provide policies whose costs outweigh the benefits: Political leaders may be incentivized to implement policies that provide short-term benefits but have long-term costs or consequences, such as a large budget deficit or environmental degradation.

Favor programs with immediate costs: Alternatively, incentives may lead political leaders to prioritize programs or policies with immediate costs, such as increased taxes or reduced spending, to address pressing issues and avoid long-term consequences.

Therefore, options 1, 2, 3, and 4 describe possible effects of incentives for political leaders.

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____The given question is incomplete, the complete question is given below:

Select all the items that describe possible effects of incentives for political leaders. 1.favor programs with immediate benefits 2.implement policies that favor a small, powerful group 3.provide policies whose costs outweigh the benefits 4.favor programs with immediate costs

The equation for the graphed quadratic function is:

y = -1*(x - 3)^2 + 2

Here we have the graph of a quadratic equation. Remember that if the leading coefficient is a and the vertex is (h, k) then we can write:

y = a*(x - h)^2 + k

Here the vertex is at (3, 2) then we can write:

y = a*(x - 3)^2 + 2

We can see that it also passes through the point (1, -2), replacing these values we will get:

-2 = a*(1 - 3)^2 + 2

-2 = a*4 + 2

-2 - 2 = a*4

-4/4 = a = -1

Then the quadratic equation is:

y = -1*(x - 3)^2 + 2

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Answer:

=17 + 6n.

Step-by-step explanation:

[tex]4 \times 5 + 6n - 3 \\ = 20 + 6n - 3 \\ = 20 - 3 + 6n \\ = 17 + 6n[/tex]