data set 1 has a mean of 54 and a mad of 4. data set 2 has a mean of 60 and a mad of 2. what can be concluded about the two distributions? select each correct answer. responses the means-to-mad ratio is 3. the means-to-mad ratio is 3. the distributions are somewhat similar. the distributions are somewhat similar. the means-to-mad ratio is 1.5. the means-to-mad ratio is 1.5. the distributions are similar.

The MVT guarantees the existence of at least one point c in (0, π) where

f'(c) = -2 sin 2c, which is equal to -2 sin 1.00229.

To apply the Mean Value Theorem (MVT) to the function f(x) = cos 2x on

the interval [0, π], we need to verify the two conditions:

f(x) is continuous on [0, π]

f(x) is differentiable on (0, π)

To check the continuity of f(x) on [0, π], we need to verify that the

function does not have any breaks or jumps on this interval. The cosine

function is continuous everywhere, so f(x) = cos 2x is also continuous on

[0, π].

To check the differentiability of f(x) on (0, π), we need to take the

derivative of f(x) and verify that it exists and is finite on this interval.

The derivative of f(x) = cos 2x is f'(x) = -2 sin 2x. This function is also

continuous everywhere, so it is differentiable on (0, π).

Since both conditions are satisfied, we can apply the MVT to f(x) on the

interval [0, π]. The theorem guarantees the existence of at least one

point c in (0, π) such that:

f'(c) = [f(π) - f(0)] / (π - 0)

Substituting the values for f(x) and f'(x), we get:

-2 sin 2c = [cos 2π - cos 2(0)] / π

-2 sin 2c = (-1 - 1) / π

sin 2c = 1 / π

Since the sine function is positive on (0, π), we know that 0 < 2c < π/2. Therefore, the only solution to sin 2c = 1 / π on this interval is:

2c ≈ 1.00229

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Suppose that you wanted to predict the price of a house based on where the house was located (northeast, northwest, southeast, or southwest) as well as square footage, then the northwest indicator variable would be set to 1, and the other three indicator variables would be set to 0.

Indicator variable An indicator variable is a binary variable that indicates whether or not a specific condition or category is present. Indicator variables are typically used in statistical models to represent categorical data or conditions, and they are also known as dummy variables or binary variables.

Example suppose you want to conduct a statistical analysis to determine the impact of location and size on the price of a house. There are four possible locations: northeast, northwest, southeast, and southwest. We can use four indicator variables (one for each location) to represent this information.

For instance, if a house is in the northeast, the northeast indicator variable would be set to 1, while the other indicator variables would be set to 0. Similarly, if the house is in the northwest, the northwest indicator variable would be set to 1, and the other three indicator variables would be set to 0. We would use similar logic for the other two locations.

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Step-by-step explanation:

You can factor out a '10' from each of the terms

10 ( -6 + 6n^2 + 5 n^3 )        

If you meant    - 60 n + 60 n^2 + 50 n^3

   you can factor out a 10 n

     10n ( -6 + 6n + 5n^2)

f(2) = 3

f(2) simply denotes that the x value of the function is 2. The table shows that when x = 2, y = 3.

Answer:

x = 2

Step-by-step explanation:

The given series is convergent under the condition that\(\sqrt{n^{4-1}/ n^{5 +3}}\)

To determine whether the series is convergent or divergent, we can use the limit comparison test.
Let's compare the given series with the series 1/n^2.

lim n→∞ (√\(n^{4-1}/ n^{5 +3})\)  / (1/n²)

= lim n→∞ (√ \(n^{4-1 }* n^2\) / (\(n^{5 +3}\)))

= lim n→∞ (√ 1 - 1/n⁴)

= 1
Here, the limit is finite and positive, both series converge or diverge together. Since the series 1/n^2 converges (p-series with p = 2 > 1), the given series also converges.

Therefore, the given series is convergent.

The limit comparison test is a convergence test applied in calculus to determine the convergence or divergence of a series. This test involves comparing the given series, (sum a_ {n}), to a preferred convergent series, (sum b_ {n}), through the limit of the ratio (a_ {n} / b_ {n}) as n approaches infinity. If the limit is finite and positive, then both series converge or diverge together.
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Answer:

A. -4

Step-by-step explanation:

−6 − (−2) = -6 + 2

              = -4

Hope this helped :)

Answer:

560

Step-by-step explanation:

1=160

2=320

3=480

4=640

5=800

6=960

7=1120

8=1280

9=1440

JUST ADD 160 EACH TIME

hope this is what your looking for   :)

Answer:

188

Step-by-step explanation:

10*5*4 - 6*2

Answer:

\((-1) \times (-2) \times (-3) \times (-4) \times (-5) = - 120\)

Step-by-step explanation:

By the rule of Integer multiplications,

\((-1) \times (-2) \times (-3) \times (-4) \times (-5) = [ (-1) \times (-2) ] \times [(-3) \times (-4)] \times (-5)\)

                                                      \(= [2] \times [12] \times (-5)\)

                                                      \(= -120\)

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Answer:

Step-by-step explanation:

Answer:

y = \(\frac{7}{6}\) x - 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (9, 2 ) and (x₂, y₂ ) = (3, - 5 )

m = \(\frac{-5-2}{3-9}\) = \(\frac{-7}{-6}\) = \(\frac{7}{6}\)

• Parallel lines have equal slopes , so

m = \(\frac{7}{6}\) is the slope of the parallel line

the line crosses the y- axis at (0, - 3 ) ⇒ c = - 3

y = \(\frac{7}{6}\) x - 3 ← equation of parallel line

Hey there!

\( \\ \)

\( \green{\boxed{\red{\bold{\sf{y = \dfrac{7}{6}x - 3}}}}}\)

\( \\ \)

To find the equation of a line, we first have to determine its slope knowing that parallel lines have the same slope.

Let the line that we are trying to determine its equation be \( \: \sf{d_1} \: \) and the line that is parallel to \( \: \sf{d_1} \: \) be \( \: \sf{d_2} \: \) .

\( \sf{d_2} \:\) passes through the points (9 , 2) and (3 , -5) which means that we can find its slope using the slope formula:

\( \sf{m = \dfrac{\Delta y}{\Delta x} = \dfrac{\green{y_2} - \orange{y_1}}{\red{x_2} - \blue{x_1 }}} \)

\( \\ \)

⇒Subtitute the values :

\( \sf{(\overbrace{\blue{9}}^{\blue{x_1}}\: , \: \overbrace{\orange{2}}^{\orange{y_1}}) \: \: and \: \: (\overbrace{\red{3}}^{\red{x_2}} \: , \: \overbrace{\green{-5}}^{\green{y_2}} )} \)

\( \implies \sf{m = \dfrac{\Delta y}{\Delta x} = \dfrac{\green{-5} - \orange{2}}{\red{ \: \: 3} - \blue{9 }} = \dfrac{ - 7}{ - 6} = \boxed{ \bold{\dfrac{7}{6} }}}\)

\( \sf{\bold{The \: slope \: of \: both \: lines \: is \: \dfrac{7}{6}}} \).

Assuming that we want to get the equation in Slope-Intercept Form, let's substitute m = 7/6:

Slope-Intercept Form:

\( \sf{y = mx + b} \\ \sf{Where \: m \: is \: the \: slope \: of \: the \: line \: and \: b \: is \: the \: y-intercept.} \)

\( \implies \sf{y = \bold{\dfrac{7}{6}}x + b} \) \( \\ \)

We know that the coordinates of the point (0 , -3) verify the equation since it is on the line \( \: \sf{d_1} \: \). Now, replace y with -3 and x with 0:

\( \implies \sf{\overbrace{-3}^{y} = \dfrac{7}{8} \times \overbrace{0}^{x} + b} \\ \\ \implies \sf{-3 = 0 + b} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \sf{\boxed{\bold{b = -3}} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \)

Therefore, the equation of the line \( \: \bold{d_1} \: \) is \( \green{\boxed{\red{\bold{\sf{y = \dfrac{7}{6}x - 3}}}}} \)

\( \\ \)

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It's difficult to say whether the conditions for constructing a t-confidence interval are met based on the information provided. To construct a t-confidence interval, three conditions must be met:

The sampling method must be random. It's not specified in the problem whether the method of selecting the vehicles was random or not, so it's impossible to say whether this condition is met.

The sample size must be large enough. A sample size of 100 vehicles is considered to be large enough for the normal/large sample condition to be met.

The population must be approximately normally distributed or the sample size must be large. Since the problem does not specify anything about the distribution of the population, it is not clear if this condition is met.

Given that the information provided does not give enough details to state whether the conditions for constructing a t-confidence interval are met or not.

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Answer:

d)the observations expressed in standard units

Step-by-step explanation:

The average will change and hence, consequently, so will the deviations from the average and also the standard deviation. so, the only option left is d)

Answer:

no

Step-by-step explanation:

The points will  meet x when it is folded are C or E

A point is a location of an object by taking reference of origin, In general case we consider it at (0,0), At the origin value of both the coordinate position is considered as Zero, In simple words point indicates how much it is above or below from the coordinate axes.

Vertical distance from the x axis is known as y coordinate and horizontal distance from the y axis is known as x coordinate.

Given that,

A green colored Net,

After folding x point will  meet the points = ?

When we start folding,

First step,

Side ABCD and DEFG will be folded,

C and E will meet with each other

Second Step,

Side ABCD and AGHI will be folded,

B and I will meet with each other

Third step,

Side DEFG and AGHI will be folded,

F and H will meet each other

Fourth step,

Upper portion AHI will cover the upper portion BCF of the box

X will at position of C or E

Hence, the X will meet C or E

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Answer:

Look down below!

Step-by-step explanation:

Fist, make your inequality:

-x + 5y > -10

5y > x - 10

y = .2x - 2

Now, plug in any value of x to find y!

Ex:  x = 5...

y = .2 (5) - 2

y = -1

Your first coordinate could be (5, -1)

Hope this helps!

Answer:

Step-by-step explanation:

Consider a utlity bill which shows a minimum initial cost plus variable costs dependent upon how many units are sold.

Then:  total cost ≥ (fixed cost) + (unit cost)(number of units sold)  

This involves the "equal to or greater than" concept.

Answer:

x = 5

Step-by-step explanation:

given B is the midpoint of AC , then

AB = BC ( substitute values )

4x - 3 = 2x + 7 ( subtract 2x from both sides )

2x - 3 = 7 ( add 3 to both sides )

2x = 10 ( divide both sides by 2 )

x = 5

Answer:

tan A  = 12/ 35

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp / adj

tan A = CB/ AB

tan A  = 12/ 35

we can reject the null hypothesis at the 5% significance level since the p-value is less than 0.05.

To calculate the p-value, we need to perform a hypothesis test.

Let's assume the null hypothesis is that the proportion of defective systems produced by x-game is equal to or less than the industry standard of 0.02, while the alternative hypothesis is that the proportion is greater than 0.02.

We can use the normal approximation to the binomial distribution since we have a large sample size (n=120) and np and n(1-p) are both greater than or equal to 10.

The test statistic can be calculated as:

\(z = (p_hat - p) / \sqrt{(p*(1-p)/n)}\)

where \(p_hat\)  is the sample proportion of defective systems, p is the hypothesized proportion under the null hypothesis, and n is the sample size.

Using the values given in the question, we have:

\(p_hat = 6/120 = 0.05\)

p = 0.02

n = 120

Plugging these values into the formula, we get:

\(z = (0.05 - 0.02) / \sqrt{(0.02*(1-0.02)/120) = 2.041}\)

The p-value can be calculated as the probability of getting a test statistic as extreme or more extreme than 2.041 under the null hypothesis.

Since this is a one-tailed test (the alternative hypothesis is one-sided), we look up the area in the right tail of the standard normal distribution table.

Using a standard normal distribution table, we find that the area to the right of 2.041 is 0.0207.

Therefore, the p-value is 0.0207.

Therefore, we can reject the null hypothesis at the 5% significance level since the p-value is less than 0.05.

This means that there is strong evidence that the proportion of defective systems produced by x-game exceeds the industry standard of 0.02.

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The required length of the missing side is 9.28 units for the given triangle.

As shown triangle:

∠A = 104°

∠B = 47°

∠C = 29°

Side c = 7 units

Let's denote the length of the missing side as x.

Using the Law of Sines:

sin(A)/a = sin(B)/b = sin(C)/c

We know the values of angles A, B, and C, as well as the length of side c. Plugging in these values, we get:

sin(104°)/x = sin(47°)/7

To find x, we can rearrange the equation and solve for x:

x = (7 × sin(104°)) / sin(47°)

Using a calculator, to get the value of x:

x ≈ 9.28

Therefore, the length of side a (in front of angle A) is approximately 9.28 units.

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The sum of all the number cards in a deck of 52 playing cards is 36.

A standard deck of playing cards comprises 13 ranks in each of the four French suits: clubs (♣), diamonds (♦), hearts (♥) and spades (♠). Each suite has thirteen cards: ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen and king. Thus the entire deck has 52 cards total.

We shall calculate the sum of the number cards as follows;

numbered clubs (♣) = 9 cards

numbered diamonds (♦) = 9 cards

numbered hearts (♥) = 9 cards

numbered spades (♠) = 9 cards

The four suits multiplied by 9;

4 × 9 = 36

Therefore, there are 36 number cards in a deck of cards.

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Answer:

a) Table:

Time required in hours to produce a unit of good

          shoe      slipper

A machine   1          0.5

B machine   1          1

Worker      2          2

Let x be the number of shoes produced and y be the number of slippers produced in a day.

The mathematical model for the best sales revenue is:

Maximize:

60x + 20y   (selling price)

Subject to:

x ≤ 20A         (machine A limit)

x ≤ 15B         (machine B limit)

2x + 2y ≤ T   (worker limit)

where T is the number of hours the workers work in a day.

Also, x and y must be non-negative.

b) To solve the mathematical model, we need to use linear programming. The standard form of the model is:

Maximize:

60x + 20y + 0s1 + 0s2 + 0s3

Subject to:

x − 20A + s1 = 0

x − 15B + s2 = 0

2x + 2y − T + s3 = 0

x, y, s1, s2, s3 ≥ 0

We can use a software or a calculator to find the optimal solution. The solution is:

x = 10

y = 30

A = 10

B = 10

T = 40

s1 = 0

s2 = 0

s3 = 0

Revenue = $2,400

c) The solution means that the factory should produce 10 shoes and 30 slippers in a day to maximize the revenue. Machine A and B should be used for 10 hours each per day. The workers should work for 20 hours to complete the production. The revenue earned per day would be $2,400.

The conclusion is that to maximize the revenue, the factory needs to produce more slippers than shoes. This is because the selling price of slippers is lower than that of shoes, but they require less time and resources to produce. Machine A is more efficient than machine B in producing shoes, but for slippers, both machines have the same efficiency. The workers will work for 12 hours or more, depending on the demand for the products.

Step-by-step explanation:

The simplified form of the expression (x² - 4x -21)/4(x-7) is (x + 3)/4

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

x²-4x-21 over 4(x-7)

Express properly

So, we have

(x² - 4x -21)/4(x-7)

Factor the numerator

This gives

(x + 3)(x - 7)/4(x-7)

Cancel out the common factors

This gives

(x + 3)/4

Hence, the simplified form of the expression is (x + 3)/4

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Approximately, the value of the series is -7,619,287 to within an error of at most \(10^-5.\)

The series is

\((-1)^(n+1) * n^6 n=1.\)

We have to approximate the value of the series to within an error of at most 10^-5.

To obtain an approximation for the series, let us evaluate the sum S6.

Hence, the series S is given as:

\(S = (-1)^(1+1)*1^6 + (-1)^(2+1)*2^6 + (-1)^(3+1)*3^6 + ... + (-1)^(n+1)*n^6\)

To obtain an approximation to this series, we will use the Alternating Series Estimation Theorem, which is given by:

|SN - S| <= |Rn|, where Rn is the remainder when SN is used to approximate the sum S.

Therefore, we have to determine the sum S6, the alternating series SN6, and the remainder R6.

|S6 - SN6| = R6

= |-7,605,967|

≈\(7.61 x 10^6.\)

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A null hypothesis is directly opposed by an alternative hypothesis. As a result, if either one of the two theories is accurate, the other is untrue.

In statistical hypothesis testing, null and alternate hypotheses are utilized. The null hypothesis of a test always predicts no effect or no association between variables, but the alternative hypothesis reflects the effect or relationship that your research predicts.

A null hypothesis is directly opposed by an alternative hypothesis. As a result, if either one of the two theories is accurate, the other is untrue.

Based on the study question or issue that they are attempting to solve, the analyst or researcher develops a null hypothesis. The null may be distinguished in many ways depending on the question.

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approximately 50 % of the values in a normal distribution will lie below the mean, and the remaining 50 % will lie above the mean.

In a normal distribution, approximately 50 % of the values lie below the mean.

A normal distribution is symmetric around its mean, with the mean located at the center. Since the distribution is symmetric, half of the values will fall below the mean and the other half will fall above the mean.

Therefore, approximately 50 % of the values in a normal distribution will lie below the mean, and the remaining 50 % will lie above the mean.

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Approximately 50% of the values lie below the mean in a normal distribution.

In a normal distribution, the mean is located at the center of the distribution. The distribution is symmetric, meaning that there are an equal number of values on both sides of the mean. To determine the percentage of values below the mean, we need to find the area under the curve to the left of the mean.

In a standard normal distribution, which has a mean of 0 and a standard deviation of 1, approximately 50% of the values lie below the mean. This means that if we were to calculate the area under the curve to the left of the mean, it would be approximately 0.5 or 50%.

It's important to note that in a normal distribution with a different mean and standard deviation, the percentage of values below the mean may vary. However, the concept remains the same - the area under the curve to the left of the mean represents the percentage of values below the mean.

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Answer:

>

Step-by-step explanation:

b is clearly negative

- - = +

so therefore, subtracting the negative will result in a larger answer than adding a small positive to a negative

According to the model, -9 (7v + 9.7) = -63v - 87.3. The solution has been obtained by using area model.

What is an area model?

An area model is a rectangular graphic used in mathematics to multiply and divide two numbers or expressions. The length and breadth of the rectangle are determined by the factors, also known as the quotient and divisor.

We are given an expression as -9 (7v + 9.7).

Using area model,

-9 * 7v = -63v

Similarly,

-9 * 9.7 = -87.3

On combining both, we get

-9 (7v + 9.7) = -63v - 87.3

Hence, the value for the expression is -63v - 87.3.

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