Given the sample data x: 23 17 15 30 25
(a) Find the range.
(b) Verify that sum of x= 110 and sum of x^2= 2568
(c) Use the results of part (b) and appropriate computation formulas to compute the sample variances s^2 and sample standard deviation s.
(d) Use the defining formulas to compute the sample variance s^2 and sample standard deviation s.
(e) Suppose the given data comprise the entire population of all x values. Compute the population variance ơ^2 and population standard deviation ơ.

The conjugates of z1 and z2 are given below:

In mathematics, a pair of binomials with identical phrases that part opposite arithmetic operators in the midst of these similar terms are referred to as conjugates.

For instance, the conjugate of p + q is p - q.

'

With this in mind, the conjugate which is the same number with the imaginary part negated is given as:

The conjugate of 7+2i is 7-2i;

the conjugate of -3-i is -3+i.

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Answer:

  (a)  6a³ +22a² +14a -10

Step-by-step explanation:

You want the product of (3a +5) and (2a² +4a -2).

The distributive property is used to eliminate the parentheses when simplifying the product.

  (3a +5)(2a² +4a -2) = 3a(2a² +4a -2) +5(2a² +4a -2)

  = 6a³ +12a² -6a +10a² +20a -10

  = 6a³ +(12+10)a² +(-6+20)a -10

  = 6a³ +22a² +14a -10

__

Additional comment

The leading coefficient of the product is the product of the leading coefficients: 3·2 = 6. This eliminates the last two answer choices.

The first two answer choices differ only in the "a" term, so you only need to find that one. It will be the sum of terms (3a)(-2) and (5)(4a), so is -6a+20a = 14a.

You can also "guess" that the "a" term will be 14a, because that appears the most often among the answer choices.

The first answer choice is the correct one.

The exact terms are 1 (13 i +3 j) V178 u = 1 (3 i + 13 j) V178 u =

To find two unit vectors in a 2-space that make an angle of 45° with 8i+ 5j, we must first convert the given vector into its unit vector form. A unit vector is a vector with a magnitude of 1, so we can divide the vector 8i+ 5j by its magnitude to convert it into its unit vector form.

The magnitude of the vector 8i+ 5j can be calculated using the Pythagorean theorem as √(82 + 52) = √89 = 9.46. Therefore, the unit vector form of 8i+ 5j is (8/9.46)i+ (5/9.46)j, which can be simplified to (13/17.78)i+ (3/17.78)j.

Now, to find two unit vectors that make an angle of 45° with (13/17.78)i+ (3/17.78)j, we can use the formula for the unit vector of a vector making an angle θ with another vector u.

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The required angle is 35 degrees whose supplementary angle is 35 degrees more than twice its complementary angle.

The definition of a supplementary angle is that it adds up to 180 degrees.

Let's represent the required angle as "x".

We know that the supplementary angle to "x" is 180 - "x".

Similarly, the definition of a complementary angle is that it adds up to 90 degrees, so we know that the complementary angle to "x" is 90 - "x".

Given that the supplementary angle to "x" is 35 degrees more than twice its complementary angle, so we can write this as an equation:

180 - x = 2(90 - x) + 35

Simplifying this equation, we get:

180 - x = 180 - 2x + 35

Adding x to both sides, we get:

x = 35

Therefore, the required angle is 35 degrees.

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The numerator is 4 and the denominator is 7. It is a proper fraction.

A fraction represents the part of a set of objects. It has two parts separated by a dividing line, generally written

a/b

Where

There are 3 types of fraction. They are

1. Proper fraction

A proper fraction is a fraction whose numerator is less than the denominator. It makes the value is less than 1.

Example: 3/4, 2/5.

2. Improper fraction

An improper fraction is a fraction whose numerator is more than the denominator. The value is more than 1.

Example: 9/8, 7/5.

3. Mixed fraction

A mixed fraction is a combination of a whole number and a proper fraction. It is the quotient and the remainder of improper fraction.

Example:

From the explanation above, the fraction of 4/7 has the numerator of 4 and the denominator of 7. The numerator 4 is less than the denominator 7, so the fraction is a proper fraction.

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Answer:

Step-by-step explanation:

To find the result of increasing 24,312 by 22,211, you would simply add the two numbers:

24,312 + 22,211 = 46,523

So, the result of increasing 24,312 by 22,211 is 46,523.

Answer: 46,523

Step-by-step explanation:

Line up the two numbers by their number places (making sure to put the larger number on top). The add the digits that are on top of each other until you get your answer.

The thickness of the framing paper used to frame the picture with uniform thickness will be 1.13 inches.

First, we have to find the perimeter of the picture. We know that the perimeter of a rectangle is 2(length + breadth). So, The perimeter of the picture will be :

⇒ 2(10 + 5)

⇒30 inches

Now, finding the area of the framing paper :

⇒ length x breadth

⇒ 8.5 x 4

⇒ 34 inch²

Now, we know that thickness x perimeter = area

∴ Thickness = area /  perimeter

⇒  34 / 30

⇒ 1.13 inch

Therefore, the thickness needed to frame the picture with uniform thickness using the fancy paper without wasting any paper is 1.13 inch.

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The complete question will be :

suppose you have another picture that is 10 inches by 5 inches, and are now using a fancy paper that is 8.5 inches by 4 inches to frame the picture. again, the frame is to be uniform in thickness all the way around. no fancy framing paper is to be wasted! Find out how thick the frame should be.

The correct answer is A. Carmen is more likely to complete 21 applications in one week, because the absolute value of the z-score for Rosanna is less than for Carmen.

Based on the calculated z-scores, we can determine which employee is more likely to complete 21 applications in one week.

The z-score for Carmen is -1.56, which indicates that her performance is slightly below average, but still within one standard deviation of the mean. On the other hand, the z-score for Rosanna is -2.83, which is more than two standard deviations below the mean and indicates that her performance is much lower than average.

Therefore, it is more likely for Carmen to complete 21 applications in one week compared to Rosanna, as Carmen's performance is closer to the mean and within one standard deviation of it. Hence, the correct answer is A. Carmen is more likely to complete 21 applications in one week, because the absolute value of the z-score for Rosanna is less than for Carmen.

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[tex]-\frac{21}{20}[/tex] or -1.05

Slope describes the rate of change for a line.

Finding the Slope

One way to find the slope when given 2 points is using the slope formula. The slope formula is as follows:

To find the slope, just plug in the x and y values from each coordinate pair. Remember that in a coordinate pair, the order is (x-value, y-value).

This shows that the slope is -21/20. This can be rewritten as -1.05.

Interpreting Slope

Slope is often described as rise over run. This means that slope is the change in y divided by the change in x. On a graph, a slope of -21/20 means that the graph goes down 21 units and right 20 units between each point. This can be seen in the points we are given. Point (14, -9) is 21 units below and 20 units to the right of (-6, 12)

Answer:

Step-by-step explanation:

There are 60 students who chose spaghetti and pizza over corn dogs, tacos, and cheeseburgers, as their favorite lunch.

A circular graph is also known as a pie chart. It is used to display a set of data. The data can be in percentages or degrees or radians.

The given data are as follows:

Pizza: 45%

Corn dogs: 10%

Cheeseburger: 8%

Tacos: 12%

Spaghetti: 25%

The total number of students is 150.

The total percentage of students who eat spaghetti and pizza is (25%+45%), that is, 70%.

The total percentage of students who eat corn dogs, tacos, and cheeseburgers is (10%+12%+8%), that is, 30%.

The percentage difference is (70%-30%), that is, 40%.

Now, calculate 40% of the total students, that is, 150.

150×40% = 150×40/100

= 60

Therefore, the obtained answer is 60.

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The complete question is given in the following chart.

Answer:

A

Step-by-step explanation:

There probably is a good explanation but I don't have it.

The proportion that could be used is (a) 2/5=13/2x

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

Scale = 1 inch: 2 1/2 feet

The proportion that can be used is:

actual length / length on the floor plan = scale factor

So, we can set up the proportion as follows:

actual length / 6 1/2 inches = 2 1/2 feet / 1 inch

Solving for actual length (x), we get:

x/(13/2) = 5/2

So, we have

2x/13 = 5/2

Rewrite as

13/2x = 2/5

Hence, the proporton is (a) 2/5=13/2x

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Answer:

High-powered money is the base for the expansion of Bank deposits and creation of money supply. The supply of money varies directly with changes in the monetary.

Step-by-step explanation:

have great day :)

The boxplots below summarize two data sets, I and II so Data set I and data set II have the same number of data points. so potion D.

The distribution of data is shown using a boxplot, which is a standardised method based on a five-number summary ("minimum," first quartile ("Q1"), median ("Q3"), and "maximum"). It can reveal information about your outliers' values. Boxplots can also show you how tightly your data is grouped, whether or not your data is skewed, and whether or not your data is symmetrical.

A box plot is a graph that displays information from a five-number summary that includes one of the central tendency measures. It does not clearly depict the distribution as a stem and leaf plot or histogram does. However it is mostly used to show whether a distribution is skewed or not and whether there are any potential outliers—unusual observations—in the data collection. When comparing or involving numerous data sets, boxplots are also highly helpful.

We can't make the conclusion from the given boxplots whether Data set I and Data set II have the same number of data points or not.

Hence,

Option D is correct.

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Complete question:

The boxplots shown below summarize two data sets, I and II. Based on the boxplots, which of the following statements about these two data sets CANNOT be justified? a) The median of data set I is equal to the median of data set II b) o The interquartile range of data set l is equal to the interquartile range of data set 1. c) The range of data set I is greater than the range of data set II d) Data set I and data set II have the same number of data points.

The camera must turn at a rate of about 53.67 degrees/s to follow the ball at an angle of 15 degrees.

In this issue, we are given the underlying speed of the football and the distance of the television camera from the way of the football. We really want to find the rate at which the camera should go to follow the ball at a specific point theta=15 degrees. We can utilize geometry to take care of this issue. The point between the way of the ball and the line associating the camera and the ball is given by 90 - 15 = 75 degrees. Utilizing the cosine capability, we can find the part of the speed of the football opposite to the camera, which is 56*cos(15) = 53.17 ft/s. Presently, utilizing the digression capability, we can find the rate at which the camera should go to follow the ball, which is (53.17/92)*tan(75) = 0.937 radians/s or roughly 53.67 degrees/s. In this manner, the camera should turn at a pace of around 53.67 degrees/s to follow the ball at a point of 15 degrees.

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The complete question is:

A football is thrown horizontally (very little arc) at 56 ft./s parallel to the sideline. A TV camera is 92 ft. from the path of the football. Find de/dt, the rate at which the camera must turn to follow the ball when θ = 15°. football TV camerao 92 ft.

Answer:

the two integers are 11 and -8

Step-by-step explanation:

Let's call the two integers we're trying to find "x" and "y".

From the problem statement, we know two things:

x + y = 3 (the sum of the two integers is three)

x^2 + y^2 = 185 (the sum of the squares is 185)

We can use the first equation to solve for one of the variables in terms of the other. For example, we can solve for "y" in terms of "x" by subtracting "x" from both sides:

y = 3 - x

Now we can substitute this expression for "y" into the second equation:

x^2 + (3 - x)^2 = 185

Expanding the square on the left-hand side, we get:

x^2 + 9 - 6x + x^2 = 185

Combining like terms, we get:

2x^2 - 6x - 176 = 0

We can simplify this equation by dividing both sides by 2:

x^2 - 3x - 88 = 0

Now we can solve for "x" using the quadratic formula:

x = (3 ± sqrt(3^2 - 4(1)(-88))) / 2(1)

Simplifying, we get:

x = (3 ± sqrt(361)) / 2

We can ignore the negative root, since it would give us a negative value for "y". So, taking the positive root, we get:

x = (3 + 19) / 2 = 11

Now we can use the first equation to solve for "y":

y = 3 - x = 3 - 11 = -8

Answer:

-5+6a-8-3a

=6a-3a-5-8

=3a-13

The best describes reason the proof is not correct is c. The proof violates the parity property.

The reason the attempted proof of the statement "The difference between any odd integer and any even integer is odd" is not correct is "The proof violates the parity property."

The student incorrectly subtracted an even integer from an odd integer and concluded that the result is odd. However, the difference between an odd integer and an even integer is always odd, which can be proven directly as follows:

Let n be any odd integer and m be any even integer. Then, by definition, n = 2k + 1 and m = 2j for some integers k and j. The difference between n and m is:

n - m = (2k + 1) - 2j

= 2k - 2j + 1

= 2(k - j) + 1

Since k and j are integers, k - j is also an integer. Therefore, the difference between any odd integer and any even integer is of the form 2x + 1, where x is an integer, which is an odd integer.

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The probability of  both cards are kings and first card isn't replaced after it's drawn and is a king is 0.00452

"Information available from the question"

Two cards are drawn from a shuffled deck of 52 cards.

To find the  probability that both cards are kings if the first card isn't replaced after it's drawn and is a king.

Now, According to the question:
The probability that the first card of a king is [tex]\frac{4}{52}[/tex] = [tex]\frac{1}{13}[/tex]

If you do not replace the card, there are only 51 cards left and only 3 kings left, so the probability of now drawing a king is [tex]\frac{3}{51}[/tex]

Multiply these probabilities:

[tex]\frac{4}{52}[/tex] × [tex]\frac{3}{51}[/tex] = 0.00452

Hence, The probability is 0.00452

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Answer:

To find the equation of the line passing through two points, we need to use the point-slope form of a line:

y - y1 = m(x - x1)

where m is the slope of the line, and (x1, y1) is one of the given points.

First, we can find the slope of the line using the two points:

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

m = (-3 - 1) / (4 - (-6))

m = -4/10

m = -2/5

Now, we can use one of the points and the slope to write the equation of the line:

y - y1 = m(x - x1)

y - 1 = (-2/5)(x - (-6))

y - 1 = (-2/5)(x + 6)

y - 1 = (-2/5)x - (2/5) * 6

y - 1 = (-2/5)x - 12/5

y = (-2/5)x - 12/5 + 1

y = (-2/5)x - 12/5 + 5/5

y = (-2/5)x - 7/5

Therefore, the equation of the line that passes through (-6, 1) and (4, -3) is y = (-2/5)x - 7/5.

Answer: y = 5x + 31

Step-by-step explanation:

You have to find the slope which is change in y over change in x. That would be (-6-4)/(1-3)    

that simplifies down to 5.

You equation for a linear equation is y=mx+b with m=slope and b=y-intercept

Take a point and plug in the values for x and y. I'm going to use (-6, 1) but it doesn't really matter

1=5(-6)+b

1=-30+b

+30 +30

31 = b

Now you have everything for your equation so when you put it all together, it is y=5x+31

The function is an exponential decay function. Then the correct option is B.

Let a be the initial value and x be the power of the exponent function and b be the increasing factor.

The exponent is given as,

y = a(b)ˣ

At (-1, 50), then the equation is given as,

50 = a / b           ...1

At (1, 2), then the equation is given as,

2 = ab                ....2

From equations 1 and 2, then we have

2 = 50b · b

b² = 1/25

b = 1/5

Then the value of 'a' is given as,

2 = a x 1/5

a = 10

The value of the variable 'b' is less than one that is 1/5. Then the function is an exponential decay function. Then the correct option is B.

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The given two ratios are not form a proportion.

Ratio is defined as the comparison of two quantities of the same kind by the method of division.

Proportion is an equation it is formed when two ratios are equivalent to each other.

The given two ratios are 4/8 and 1/7.

i.e., 4:8 and 1:7

By simplifying this ratio 4:8 we get 1:2

That is these two ratios are not equal.

proportion is formed only when the two ratios are equal.

Hence, the given two ratios are not form a proportion.

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The zeroes of the quadratic function f(x) = -2x² + 2 is -1 and +1 and the axis symmetry is x = 0.

Quadratic functions are polynomial functions consisting of variables and exponents and the degree of the variable is 2.

The general form of a quadratic function is f(x) = ax² + b x + c.

Given that,

a = -2, b = 0 and c = 2.

Substituting in the standard form, we get the quadratic function as,

f(x) = -2x² + 2

Let f(x) = 0.

-2x² + 2 = 0

-2x² = -2

x² = 1

x = ±1

So the two roots are +1 and -1.

Axis of symmetry is x = (1 + -1) / 2 = 0

x = 0 is the axis symmetry

The smaller zero is -1 and the larger zero is 1.

Hence -1 and +1 are the zeroes of the quadratic function f(x) = -2x² + 2 and the axis symmetry is x = 0.

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Answer:

1743.46[tex]\frac{meters}{min}[/tex]

Step-by-step explanation:

Two unit multipliers will be used here:

1 mile (mi)  = 1,609.344 meters

1 hour (hr) = 60 minutes (min)

65 [tex]\frac{mi}{hr}[/tex] = (65[tex]\frac{mil}{hr}[/tex])×([tex]\frac{1609.344 meters}{1 mile}[/tex])×([tex]\frac{1 hour}{60 minutes}[/tex])

The miles unit in the numerator and denominator will cannel each other out completely. In addition, the hour unit in the numerator and denominator will also cancel each other out completely:

         = 1743.46 [tex]\frac{meters}{min}[/tex]

Answer:

[tex]2\sqrt{22}[/tex]

Step-by-step explanation:

For any given positive real number x and natural number n, there exists a unique positive real number r such that [tex]x = r^n[/tex].

Let x be a positive real number and n be a natural number. We want to show that there exists a unique positive real number r such that [tex]x = r^n[/tex]. This can be expressed mathematically as [tex]x^(1/n) = r[/tex], where r is the unique positive real number we are looking for.

To solve for r, we can take the nth root of both sides of the equation. This gives us [tex]r = x^(1/n)[/tex]. Since x is a positive real number and n is a natural number, it follows that r is also a positive real number.

Furthermore, since x is a fixed value and n is a fixed value, we can conclude that the positive real number r is unique. In other words, for any given x and n, there is only one r that satisfies the equation [tex]x = r^n[/tex].

Therefore, for any given positive real number x and natural number n, there exists a unique positive real number r such that [tex]x = r^n[/tex].

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The data is qualitative, discrete, and at the nominal level of measurement.

The data is qualitative, as it describes the type of pizza ordered, which cannot be measured numerically.

The data is discrete, because there are only a finite number of possible values that the variable can take on, which in this case is one of the three types of pizza: Pepperoni, "Mushroom, or Black Olive.

The highest level of measurement for this data is nominal, because the numbers used to record the type of pizza do not imply any order or ranking between the categories. The numbers are simply a code to identify which type of pizza was ordered, and do not have any intrinsic numerical value or relationship between them. Therefore, the data falls into the nominal level of measurement, which is the lowest level of measurement that data can have.

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