do i use mean and standard deviation or median and interquartile range?

We need to know the concept of mean and standard deviation to solve the problem.The standard deviation of the data set is 18.36

The given dataset is 1,2,3,3,4,4,4,4,5,5,6,70, inorder to find the standard deviation of the data set we need to first find the mean of the dataset. Mean of a dataset means the average of the set of numbers. We divide the sum of all the numbers in the data set by the size of the set. We represent mean by μ.

μ=\(\frac{1+2+3+3+4+4+4+4+5+5+6+70}{12} =\frac{111}{12} =9.25\)

Standard deviation measures the dispersion of a dataset relative to it's mean, the square of standard deviation is variance.

The formula for standard deviation is :

σ=\(\sqrt{\frac{(1-9.25)^{2}+(2-9.25)^{2} +...+(70-9.25)^{2} }{12} } =\sqrt{\frac{68.0625+52.5625+78.125+110.25+36.125+10.5625+3690.5625}{12} } \\=\sqrt{\frac{4046.25}{12} } =\sqrt{337.1875} =18.36\)

Thus we found the standard deviation of the data set to be 18.36

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The median of the given set of data is 24.

We have a set of data given in the figure.

We have to determine its median.

The median is defined as the middle number in an ordered data set.

According to question, we have the following data set -

0, 12, 20, 28, 33, 40

The total number of elements (N) = 6 - which is even

The Median of a set of even number of elements is the average of the two middle values.

The two middle values are -  X[3] = 20 and X[4] = 28

Therefore -

Median = \(\frac{X[3]+X[4]}{2}\)= \(\frac{20+28}{2}\) = 24

Hence, the median of the given set of data is 24

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Answer:

The coordinates of D is;

Explanation:

The question can be illustrated diagramatically as;

The drawing is not to scale. it is just a way of explainuing the scenario.

To find the coordinates of the end point D(x,y).

Let us apply the mid point formula;

The same applys to y coordinates.

Given;

Substituting we have;

Also,

Therefore, the coordinates of D is;

Michael needs to analyze the population data, demographics of the city, and the competition in the area to determine whether or not to open a new store.

Michael is trying to determine where to open two new store locations. He has population data to determine the amount of revenue he will receive for each location.

He is charged a $1000 fee for opening a new store at a certain location. However, he is unsure whether the population of the city would be large enough to warrant opening a new store at that location.

The first step that Michael needs to take is to analyze the population data that he has.

Based on the population data, he needs to make an informed decision about whether or not to open a new store at that location. This would require him to take into consideration the average income of the population as well as the demographics of the city.

Another important factor that Michael needs to take into consideration is the competition in the area. If there are already several stores in the area, then opening a new store might not be a good idea.

This is because the competition would be too high and he would not be able to generate enough revenue to make up for the cost of opening a new store.

However, if there are no stores in the area, then Michael might consider opening a new store. This would require him to invest a significant amount of money, but he could also generate a significant amount of revenue in return.

Additionally, he needs to take into consideration the cost of opening a new store and whether or not he can generate enough revenue to make up for that cost.

Overall, Michael needs to carefully analyze all the data that he has before making an informed decision about where to open new store locations.

In conclusion, Michael needs to analyze the population data, demographics of the city, and the competition in the area to determine whether or not to open a new store. If the population is large enough and there is no competition in the area, then he should consider opening a new store. However, if there is already a significant amount of competition in the area, then he should avoid opening a new store.

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Answer:

True

Step-by-step explanation:

Answer:

83/100

Step-by-step explanation:

Decimals to fractions

Answer:

y = 13x + 86

Step-by-step explanation:

y−8 =13(x+6); distribute the 13

y - 8 = 13x + 78; now add 8 to both sides

y = 13x + 86; this is the slope intercept form

The correct hypothesis statement for this golfer to prove his claim would be:

\(H_{0} :u\geq 90\)

\(H_{1} :u < 90\)

The golfer claims that his average score is less than 90.

Therefore, the null hypothesis is the opposite of what he claims

Null hypothesis \(H_{0}\) is average score \(u\) is greater than or equal to 90:

\(u \geq 90\)

\(H_{0} :u\geq 90\)

Alternative hypothesis \(H_{1}\) is then the opposite of null hypothesis.

Hence alternate hypothesis \(H_{1}\) is u< 90

\(H_{1} :u < 90\)

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$420

Step-by-step explanation:

$7,563/18

=$420.1667

=$420.17 (to the nearest dollar means to the nearest full dollar and since 17 cents is not up to 50, you remove it )

= $420

Answer:

Step-by-step explanation:

-8 > 4 +2v ; subtract 4 from both sides

-8-4 > 4-4 +2v; calculate

-12 > 2v; divide both sides by 2

-6 > v

TO Know:

apply the same operation to both sides of inequality

if the operation is dividing or multiplying by a negative number change the direction of the inequality

Answer:

B. No, Hannah should have used the ratio \( \frac{adjacent}{opposite} \)

Step-by-step explanation:

✍️The formula for calculating cotangent of an angle is given as:

\( cot = \frac{adjacent}{opposite} \).

The ratio, \( \frac{opposite}{adjacent} \), used by Hannah is the formula for calculating tangent of an angle.

Therefore, Hannah did not calculate the cotangent of the angle correctly.

She should have used, the ratio, \( \frac{adjacent}{opposite} \) instead.

Answer: $ 27.27

Step-by-step explanation:

Answer:

62.59

Step-by-step explanation:

Answer:no slope

Step-by-step explanation:

m = rise / run

m = (-7-3)/4-4

m = -10/0 = no slope

The one-sample chi-square test is used to determine whether the distribution of a single categorical variable significantly differs from what would be expected by chance. The statement is True.

The one-sample chi-square test is a statistical test used to determine if there is a significant difference between the observed frequency and the expected frequency in a single categorical variable. It compares the observed frequency distribution of a variable to the expected frequency distribution, assuming that the null hypothesis is true.

This test compares observed frequencies to expected frequencies and calculates a chi-square statistic to assess the significance of the difference.

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The correct substitution of the values a, b, and c from the equation 0 = − 3x² - 2x + 6 into the quadratic formula is x = -(-2) ± √((-2)²-4(-3)(6))/2(-3).

The given equation is 0 = − 3x² - 2x + 6.

Here, a = -3, b = -2, and c = 6, which we substitute into the quadratic formula x = -b± √b²-4ac/2a.

Substituting the values, we get:

x = -(-2) ± √((-2)²-4(-3)(6))/2(-3)

x = 2 ± √(4+72)/(-6)

x = 2 ± √(76)/(-6)

x = -1 ± (1/3)√(19)

Therefore, the two solutions are x = -1 + (1/3)√(19) and x = -1 - (1/3)√(19).

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Answer:

2

Step-by-step explanation:

Taylor: x

Jim: x + 18

Andre: 2x

Sum: x + (x + 18) + 2x = 26 ↔ x = 2

Answer: y=4x-2

Step-by-step explanation:

Since you are looking for y-intercept, the point has to be on the vertical line and the slope is 4 so it has to go up 4 to the right 1

The approximate value of b in the coordinates for the y - intercept would be 40.

The approximate slope of the estimated line of best fit would be 1. 5

The y - intercept of a line refers to where the line crosses the y - axis. Seeing as the y - axis crosses x - axis at 0, the coordinates would be ( 0, point on y - axis ). This point on the y - axis is shown to be 40 so the value of b is 40 so the coordinates are ( 0, 40 ).

The slope of the estimated line of best fit using ( 0, 40 ) and ( 20, 70) :

= Change in y / Change in x

= ( 70 - 40 ) / ( 20 - 0)

= 30 / 20

= 1. 5

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Answer:

4.3

Step-by-step explanation:

Answer:

y = 13/13

helpful??

A simplification of the expression 4³ + 4 · 5 is: B. 84.

In order to evaluate and solve this expression, we would have to apply the PEMDAS rule, where mathematical operations within the parenthesis (grouping symbols) are first of all evaluated, followed by exponent, and then multiplication or division from the left side of the expression to the right. Lastly, the mathematical operations of addition or subtraction would be performed from left to right.

Based on the information provided, we have the following mathematical expression:

Expression = 4³ + 4 · 5

By taking the exponent, we have:

Expression = 64 + 4 · 5

By multiplying, we have:

Expression = 64 + 20

From the addition, we have:

Expression = 84

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Answer:

A

Step-by-step explanation:

There are two correct statements regarding a 5 by 5 matrix with three eigenvalues, one of which has a three-dimensional eigenspace.

First, there must be at least two linearly independent eigenvectors associated with the eigenvalue that has a three-dimensional eigenspace. Second, the sum of the dimensions of the eigenspaces must be equal to the size of the matrix, which is 5 in this case.

To understand the first statement, recall that the dimension of an eigenspace is equal to the multiplicity of the associated eigenvalue, which is the number of times it appears as a root of the characteristic equation. Since one of the eigenvalues has a three-dimensional eigenspace, its multiplicity must be at least 3. This means there are at least 3 linearly independent eigenvectors associated with this eigenvalue, which is necessary to span a three-dimensional space. However, the sum of the multiplicities of all eigenvalues cannot exceed the size of the matrix, which is 5. Therefore, the remaining two eigenvalues must have a combined multiplicity of 2 at most, which implies that there are at most 2 linearly independent eigenvectors associated with each of them.

To understand the second statement, note that the sum of the dimensions of the eigenspaces is equal to the sum of the multiplicities of all eigenvalues. This follows from the fact that the eigenspaces associated with distinct eigenvalues are linearly independent. Since there are three distinct eigenvalues in this case, the sum of their multiplicities is at most 5, which means the sum of the dimensions of their eigenspaces is also at most 5. Since one of the eigenspaces has dimension 3, the sum of the dimensions of the other two eigenspaces must be at least 2, which means each of them has at least one linearly independent eigenvector.

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Answer:

144 in^2

Step-by-step explanation:

Using the A = s^2 and the text says that s= 12in

 the answer is 12 in * 12 in = 144 in^2

Mrs. Marina requires 5/2 or 2.5 cups of sugar to make  one and one half of the recipe.

What is proportion ?

A proportion is an equation based on the equality of two ratios.

Here it is given that :

A recipe requires 1 (2/3) cups of sugar.

That is 1 recipe requires = 1(2/3) cups of sugars

                                        = 5/3 cups of sugar

Now, Marina is going to make one and one half of the recipe and to find the sugar he needed we simply multiply 1(1/2) both the sides :

1 recipe requires = 5/3 cups of sugar

1(1/2) recipe requires = (5/3) x 1(1/2) cups of sugar

3/2 recipe requires = (5/3) x (3/2) cups of sugar

3/2 recipe requires = 5/2 cups of sugar or 2.5  cups of sugar.

Therefore, Mrs. Marina requires 5/2 or 2.5 cups of sugar to make  one and one half of the recipe.

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The measure which changes the most is the mean and the new value is 84°

The correct answer option is option B

Given data set: 58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57

Median = (100 + 105) / 2

= 205/2

= 102.5°

Mean = (58 + 61 + 71 + 77 + 91 + 100 + 105 + 102 + 95 + 82 + 66 + 57) / 12

= 965 /12

= 80.4°

Range = Highest value - lowest value

= 105 - 57

= 48°

Interquartile range = Third quartile - First quatile

= 88.5° - 74°

= 14.5°

101, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57

Median = (100 + 105) / 2

= 205/2

= 102.5°

Mean = (101 + 61 + 71 + 77 + 91 + 100 + 105 + 102 + 95 + 82 + 66 + 57) / 12

= 1008 /12

= 84°

Range = Highest value - lowest value

= 105 - 57

= 48°

First quartile = (71 + 77) / 2

= 148/2

= 74°

Third quartile = (95 + 82)/2

= 177/2

= 88.5°

Interquartile range = Third quartile - First quatile

= 88.5° - 74°

= 14.5°

Therefore, the new mean is 84°

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The postfix expression of "7+5-3*2(6*7)/4" is "7 5 + 3 2 * 6 7 * 2 * - 4 /". Evaluating the postfix expression gives the result of the expression. The prefix expression for the given infix expression is "/ - + 7 5 * 3 * 2 ( * 6 7 ) 4".

To convert the infix expression "7+5-3*2(6*7)/4" into postfix expression, we follow the rules of operator precedence and associativity. The postfix expression is obtained by placing operators after their operands.

The postfix expression for the given infix expression is:

"7 5 + 3 2 * 6 7 * 2 * - 4 /"

To evaluate the postfix expression, we use a stack data structure. We scan the postfix expression from left to right and perform the corresponding operations.

Starting with an empty stack, we encounter the operands "7" and "5". We push them onto the stack. Then we encounter the operator "+", so we pop the last two operands from the stack (5 and 7), perform the addition operation (7 + 5 = 12), and push the result back onto the stack.

We continue this process for the remaining operators and operands in the postfix expression. Finally, after evaluating the entire expression, the result left on the stack is the final answer.

To convert the infix expression into prefix expression, we follow similar rules but scan the expression from right to left. The prefix expression is obtained by placing operators before their operands.

The prefix expression for the given infix expression is:

"/ - + 7 5 * 3 * 2 ( * 6 7 ) 4"

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Answer:

3 = 3 (infinitely many solutions)

Step-by-step explanation:

Answer:

16642.8

Step-by-step explanation:

tan 31°=10000/x

x=10000/tan31°

x=16642.8

To solve the quadratic equations you provided, we can use various methods depending on the equation's form and complexity.

Here's the best method for each equation:

1. x^2 - 3x = 10:

We can rearrange the equation and set it equal to zero:

x^2 - 3x - 10 = 0

This equation can be factored as:

(x - 5)(x + 2) = 0

Therefore, the solutions are x = 5 and x = -2.

2. 4x^2 + 29x - 60 = 0:

This equation doesn't factor easily, so we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For this equation, a = 4, b = 29, and c = -60.

Plugging these values into the formula, we get:

x = (-29 ± √(29^2 - 4 * 4 * -60)) / (2 * 4)

Simplifying further, we find:

x = (-29 ± √(841 + 960)) / 8

x = (-29 ± √1801) / 8

These are the two solutions to the equation.

3. x^2 - 6x = 0:

Here, we can factor out the common term x:

x(x - 6) = 0

This equation will be true if either x = 0 or x - 6 = 0.

Therefore, the solutions are x = 0 and x = 6.

4. 5x^2 + 5 = 9x:

Rearranging the equation, we get:

5x^2 - 9x + 5 = 0

This equation doesn't factor easily, so we can again use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

Here, a = 5, b = -9, and c = 5.

Plugging these values into the formula, we have:

x = (-(-9) ± √((-9)^2 - 4 * 5 * 5)) / (2 * 5)

Simplifying further, we get:

x = (9 ± √(81 - 100)) / 10

x = (9 ± √(-19)) / 10

Since the discriminant is negative, the solutions to this equation are complex numbers.

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Ok, so

We have that, for option 1:

The total cost of the service will be:

20x + 45. Where x is the number of months.

Fot option 2, the total cost will be:

35x + 0. Where x is the number of months.

If we equal both equations, we obtain:

20x + 45 = 35x.

Now, we have to solve this equation to find the number of months in which the cost will be the same for two options.

Then, 45 = 15x and x=3.

So, the number of months is 3.

Then, that cost can be found, if we replace x=3 in any equation. For example, in equation 2:

Cost = 35x which is equal to 35*3 and this is 105.

So, after 6 months:

Option 1 will be equal to: 20(6) + 45 and this is: 165$.

Option 2 will be equal to 35(6) and this is: 210$.

Then, Option 1 will be the cheaper option.