Which statement regarding polynomials and their zeros is true?

The Mean Absolute Deviation of the given data set, 58, 38, 54, 48, 26, 36 is 10

From the question, we are to calculate the mean absolute deviation of the given data set

The given data set is:

58, 38, 54, 48, 26, 36

First, we will determine the mean of numbers

Mean = (58 + 38 + 54 + 48 + 26 + 36) / 6

Mean = 260 / 6

Mean = 43.33

To calculate the MAD, we will determine the absolute deviation of each data from the mean

|58 - 43.33| = 14.67

|38 - 43.33| = 5.33

|54 - 43.33| = 10.67

|48 - 43.33| = 4.67

|26 - 43.33| = 17.33

|36 - 43.33| = 7.33

Now, we will calculate the mean of the absolute deviations

MAD = (14.67 + 5.33 + 10.67 + 4.67 + 17.33 + 7.33) / 6

MAD = 60/6

MAD = 10

Hence, the MAD is 10

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Answer:

0 they cancel each other out..

Step-by-step explanation:

The expression -4x + 4x simplifies to zero:

-4x + 4x = (-4 + 4)x = 0x = 0

Therefore, the result is zero.

The absolute value of f(24) is 25165824 for the given recurrence relation.

As per the question, the recurrence relation as:

f(n) = 2 × f(n-1)

f(1) = 3

As we know that the geometric series is described as a series representing the sum of the terms in a finite or infinite geometric sequence.

This is a geometric sequence with a = 3 and r = 2.

The formula for the nth term of a geometric sequence is:

f(n) = ar⁽ⁿ⁻¹⁾

Substitute a = 3 and r = 2, we get:

f(n) = 3×2⁽ⁿ⁻¹⁾

So, the absolute value of f(24):

|f(24)| = 3 × 2⁽²⁴⁻¹⁾

|f(24)| = 3 × 2²³

|f(24)| = 25165824

Therefore, the absolute value of f(24) is 25165824.

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The required there are 120 ways to choose a team captain, an assistant captain, and an equipment manager from a team of 10.

The number of ways 3 people can be selected from a team of 10 is given by the combination formula:

C(10, 3) = 10! / (3! (10 - 3)!)
            = (10 x 9 x 8) / (3 x 2 x 1)
            = 120

Thus, there are 120 ways to choose a team captain, an assistant captain, and an equipment manager from a team of 10.

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Answer:

600.5%

Step-by-step explanation:

6.005 × 100 is 600.5%

"per cent" means per hundred, so TIMES by 100 to change a number to a percent. DIVIDE by 100 to change a percent to a decimal number.

Some people memorize this as move the decimal two places to the right (decimal to percent) or left (percent to decimal)

Answer:

25%

Step-by-step explanation:

The equivalent expression is log (yz/x²)

We have,

Using the logarithmic concept.

log a + log b = log ab

log a - log b = log (a/b)

log x² = 2 log x

Now,

We will use,

log_2 x = log x

Now,

-2 log x + 4 log y + 4 log z

= (4 log y + 4 log z) -2 log x

= log (yz) - log x²

= log (yz/x²)

Thus,

The equivalent expression is log (yz/x²)

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The equation that shows the point-slope form of the line which passes through (3, 2) is: y - 2 = (x - 3).

The equation of any straight line on a coordinate plane can be expressed in point-slope form as:

y - b = m(x - a), where (a, b) is a point and m is the slope of the line.

Given the point a line goes through as (3, 2), which also has a slope (m) of 1, to find the equation of the line in point-slope form, substitute a = 3, b = 2 and m - 1 into y - b = m(x - a):

y - 2 = 1(x - 3)

y - 2 = (x - 3)

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Answer: The monthly payment for the sailboat is $348.14, and the total interest paid over the 12-year period is $13,080.16.

Step-by-step explanation: To calculate the monthly payment and interest for the sailboat, we can use the formula for the present value of an annuity due:

PV = PMT * [(1 - (1 + r)^(-n)) / r] * (1 + r)

where PV is the present value, PMT is the monthly payment, r is the monthly interest rate, and n is the total number of payments.

First, we need to calculate the present value of the sailboat after the down payment:

PV = $35,000 - (0.2 * $35,000) = $28,000

Next, we can plug in the values and solve for PMT:

$28,000 = PMT * [(1 - (1 + 0.0875/12)^(-12*12)) / (0.0875/12)] * (1 + 0.0875/12)

Simplifying this equation, we get:

PMT = $348.14

Therefore, your monthly payment for the sailboat would be $348.14.

To calculate the total interest paid, we can multiply the monthly payment by the total number of payments (12 years * 12 months/year = 144 payments) and subtract the principal amount:

Total Interest = (PMT * n) - PV

Total Interest = ($348.14 * 144) - $28,000

Total Interest = $13,080.16

Therefore, you would pay a total of $13,080.16 in interest over the 12-year period.

The length of the missing side is 3 < x < 13.

We have, two measurement of triangle is 9 and 6 unit.

Also, we know that the length of third side of a triangles lies in between the sum of sides and difference of sides.

So, Sum of sides = 9 + 6= 13 unit

Difference of side= 9-6 = 3 unit

Then, the measure of third side is 3 < x < 13.

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The solution is, the profit is 18.

If the profit of a company made by the company is in the form a quadratic expressions but in the different forms as given in the question.

a). The prices that give a profit of zero dollars.

   Expression that is most useful,

   Factored form: -2(p - 3)(p - 9) = 0

   p = 3, 9

b). The profit when the price is zero .

   Standard form:

   Profit = -2p² + 24p - 54 = 0

   -p² + 12p - 27 = 0

   -p² + 3p + 9p - 27 = 0

   -p(p - 3) + 9(p -3) = 0

    (-p + 9)(p - 3) = 0

    p = 3, 9

c). The price that gives the maximum profit.

  Vertex form: -2(p - 6)² + 18

  Vertex of the given expression → (6, 18)

  Maximum profit will be at p = 6.

  Therefore, profit = -2(6 - 6)² + 18 = 18

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complete question:

The profit that a company makes selling an item (in thousands of dollars) depends on the price of the item (in dollars). If p is the price of the item, then three equivalent forms for the profit are

Standard form: - 2 p^2 + 24p - 54

Factored form: -2(p - 3)(y-9)

Vertex form: -2(p-6)^2 + 18.

Which form is most useful for finding a. The prices that give a profit of zero dollars?

b. The profit when the price is zero?

c. The price that gives the maximum profit?​

I'm assuming you mean y = [3x+5], wherein the brackets signify the biggest integer function (also known as the floor function).

What exactly are function and example?

A function was a type of rule that produces one output for one input. Alex Federspiel provided the image. y=x2 is an example of this. If you enter something for x, you will only get a single result for y. Because x represents the input value, we can say as y represents a function of x.

To graph this formula, we must plot points which satisfy the conditions, where y is the largest integer that is equal or less than to 3x+5.

Let's begin by examining some specific x values:

When x equals -2, y equals [3(-2)+5]. = [-1] = -1

When x equals -1.5, y equals [3(-1.5)+5]. = [-0.5] = -1

When x equals -1, y equals [3(-1)+5]. = [2] = 2

y = [3(-0.5)+5] for x = -0.5. = [3.5] = 3

When x = 0, y equals [3(0)+5]. = [5] = 5

When x equals 0.5, y equals [3(0.5)+5]. = [6.5] = 6

When x equals 1, y equals [3(1)+5]. = [8] = 8

When x equals 1.5, y equals [3(1.5)+5]. = [9.5] = 9

When x equals 2, y equals [3(2)+5]. = [11] = 11

We can draw points on a chart and link them to construct a line using these values:

        |

  12    |

        |

  11    |             x=2

        |

  10    |

        |

   9    |             x=1.5

        |

   8    |             x=1

        |

   7    |

        |

   6    |             x=0.5

        |

   5    |             x=0

        |

   4    |

        |

   3    |

        |

   2    |             x=-1

        |

   1    |

        |

   0____|_____________

       -2   -1   0   1   2

It's worth noting that the graph is made up of a succession of horizontal lines with "jump" points wherein 3x+5 is a number.  The graph meets the x-axis at the following locations: (-5/3), where the biggest integer was -2, and each subsequent intersection happens at x & (-5/3) + (1/3) & (-4/3), (-5/3) + (2/3) & (-1/3), (-5/3) + (3/3) & 0, (-5/3) + (4/3) & (1/3), and so on.

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This is about hypothesis testing. The various steps required to determine whether elderly dementia patients really do take longer to fall asleep than average are given below.

The stages involved in testing a hypothesis are as follows:

1) First, state your hypotheses.

Elderly dementia sufferers fall asleep in the same length of time as the ordinary person (H0) (μ = 7)

An alternative hypothesis (Ha) is that elderly dementia patients sleep more slowly than the general population (μ  > 7)

2) Determine the degree of importance in step two.

The problem does not specify the degree of relevance (α). Assume that α = 0.05.

3) Calculate the test statistic in step three.

To compare the sample mean to the population mean, we may use a one-sample t-test. The t-test formula is as follows:

t = (x - μ) / (s / √n)

where:

x = sample  mean (7.2)

μ  = population mean  (7)

s =  sample standard  deviation (1.1)

n = sample  size  (8)

Plugging in the values,  we obtain the folowing:

t = (7.2  - 7) / (1.1 / √ 8) = 1.62

4) Determine the crucial value in step four.

We must use the t-distribution to ascertain the critical value because this is a one-tailed test with a sample size of fewer than 30, and the population standard deviation is unknown. n - 1 equals 7 degrees of freedom.

The crucial value is 1.895 when using a t-table with 7 degrees of freedom and a one-tailed test with = 0.05.

Step 5: Make a choice and analyze the outcomes

We are unable to reject the null hypothesis since the computed t-value (1.62) is lower than the critical value (1.895).


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0.8942 = 89.42% probability of the mean IQ score of people in the sample is less than 98.

The Normal (or Gaussian) distribution is the most common continuous probability distribution. The function calculates the likelihood that an event will occur between any two real number limits as the curve gets closer to zero on either side of the mean. The area beneath the normal curve is always one.

Problems of normal distributions can be solved using the z-score formula.

In a set with mean and standard deviation, the z-score of a measure X is:

[tex]\text{z}=\dfrac{\text{x}-\mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

This is the P-value of Z when X = 98.

[tex]\text{z}=\dfrac{\text{x}-\mu}{\sigma}[/tex]

[tex]\text{z}=\dfrac{(98 -100)}{15}[/tex]

[tex]\text{z}=-0.133[/tex]

z = -0.133 has a P-value of 0.8942

Hence, 0.8942 = 89.42% probability of the mean IQ score of people in the sample is less than 98.

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The factors are (x+6) (x-6), 3(x+4) (x-4), (x+3) (x+3) and 4(x+3)(x-5)

Given that are polynomial, we need to find their factors,

a) x²-36 =

We know that a²-b² = (a+b) (a-b)

So, x²-36 = x²-6² = (x+6) (x-6)

b) 3x²-12 =

3(x²-4²) = 3(x+4) (x-4)

c) x² + 6x + 9

= x² + 3x + 3x + 9

= x(x+3) + 3(x+3)

= (x+3) (x+3)

d) 4x² - 8x - 60

= 4(x²-2x-15)

= 4(x²-5x+3x-15)

= 4{x(x-5) +3(x-5)}

= 4(x+3)(x-5)

Hence, the factors are (x+6) (x-6), 3(x+4) (x-4), (x+3) (x+3) and 4(x+3)(x-5)

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Answer:

To find the sum of all integers between 18 and 75, we need to add up all the integers from 18 to 75. We can do this using the formula for the sum of an arithmetic series:

sum = (n/2) x (first term + last term)

where n is the number of terms in the series.

In this case, the first term is 18, the last term is 75, and we need to find the number of terms. We can do this by subtracting the first term from the last term and adding 1:

number of terms = last term - first term + 1

= 75 - 18 + 1

= 58

Now we can substitute these values into the formula:

sum = (n/2) x (first term + last term)

= (58/2) x (18 + 75)

= 29 x 93

= 2673

Therefore, the sum of all integers between 18 and 75 is 2673.

The radius of the barrel which has the shape of a cylinder would be = 5 ft. That is option C.

To calculate the radius of the barrel, the formula that should be used is the formula for the volume of a cylinder which is given below;

Volume of cylinder = πr²h

where;

π = 3.14

height = 10ft

radius = ?

Volume = 785.4 ft³

That is;3.

785.4 ft³ = 3.14× r² × 10

make r the subject of formula;

r² = 785.4/3.14×10

r = √ 785.4/3.14×10

= √ 785.4/31.4

= √25.01273885

r = 5ft

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1/5 ÷3 is equal to 1/15

I hope this helps

The exact value of x is √1156 and it follows the Pythagorean triple

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

Legs of the right triangle = 16 and 30

Using the pythagoras theorem, we have

Hypotenuse^2 = the sum of the squares of the other lengths

So, we have

x^2 = 16^2 + 30^2

When evaluated, we have

x^2 = 1156

This gives

x = √1156

Hence, the exact value is √1156

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Answer:

The statement that best defines a circle is:

C. The set of all points that are the same distance from a given point called the center.

A circle is a geometric shape consisting of all the points in a plane that are equidistant from a fixed point called the center. The distance from the center to any point on the circle is called the radius, and the distance across the circle through the center is called the diameter. Therefore, a circle is defined as the set of all points that are the same distance (equal to the radius) from a given point (the center).

Answer: The answer should be B

The probability that a student chosen randomly from the class has a brother is 13/30

From the attached two way table we can observe that the total number of students in the class = 20

To find the number of students having a brother, we need to add the number of students having a sister as well as brother i.e., 6 and the number of students having a brother but do not have a sister i.e.,7

so, we get the sum as 6 + 7 = 13

Let event A: a student chosen randomly from the class has a brother

n(A) = 13

The probability that a student chosen randomly from the class has a brother.

Using the definition of probability,

P(A) = n(A) / n(S)

P(A) = 13/20

This is the required probability.

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Find the complete question below.

Answer: $4,580

Step-by-step explanation:

First, we need to calculate the monthly payment for the 15-year, fixed-rate loan at the original rate of 5.05%. We can use the formula for the monthly payment of a mortgage loan:

P = L[c(1 + c)^n]/[(1 + c)^n - 1],

where P is the monthly payment, L is the loan amount, c is the monthly interest rate (which is the annual interest rate divided by 12), and n is the total number of payments (which is the number of years multiplied by 12).

Plugging in the given values, we get:

L = $137,000

c = 0.0505/12 = 0.0042083 (rounded to 7 decimal places)

n = 15 x 12 = 180

P = $1,071.18

Next, we need to calculate the monthly payment at the lower rate of 4.81% if the buyers purchase four points. Each point costs 1% of the loan amount, so four points will cost 4% of the loan amount.

The new rate after purchasing four points is:

5.05% - 0.24% = 4.81%

The new loan amount after purchasing four points is:

$137,000 - (4% x $137,000) = $131,920

Using the same formula for the monthly payment, but with the new values for the loan amount and monthly interest rate, we get:

L = $131,920

c = 0.0481/12 = 0.0040083 (rounded to 7 decimal places)

n = 15 x 12 = 180

P = $1,030.98

The monthly savings due to the lower interest rate is:

$1,071.18 - $1,030.98 = $40.20

To calculate the cost of the four points, we need to divide the upfront cost of the points by the monthly savings:

Cost of four points = ($40.20 x 180)/0.0024 = $3,015

Therefore, the cost of the four points is $3,015, which is closest to $4,580.

The four points that the homebuyers are purchasing to lower their rate from 5.05% to 4.81% will cost them D. $5,480.

The points purchased for loans are charges that the borrower pays upfront to lower their interest rates.

Each point equals a percentage of the loan amount.

For example, four points on a $137,000 loan are 4 percent of the loan amount, or $5,480.

The loan amount for the purchase of the condominium = $137,000

Fixed interest rate = 5.05%

Loan period = 15 years

Loan option rate = 4.81%

Hence, Four points =  $137,000 x 4%

                              = $5,480

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Answer: y + 6 = -4 (x+2)

Step-by-step explanation:

Answer:

To convert radians to degrees, we use the conversion factor which is:

1 radian = 180/π degrees

To convert 11π/12 radians to degrees, we can multiply by the conversion factor:

11π/12 radians × 180/π degrees/radian = 990/π degrees

This is the exact value in degrees. If we want a decimal approximation, we can use a calculator to evaluate:

990/π degrees ≈ 315.944 degrees

Therefore, 11π/12 radians is approximately equal to 315.944 degrees.

The class width is 0.3877.

In order to analyze data, it is often helpful to group it into categories, or intervals, and then determine how frequently each interval occurs. This process is known as frequency distribution.

To calculate the class width, you need to determine the range of each interval. The range is the difference between the upper and lower limits of the interval. For example, the first interval is 160-179, so the range is 179-160=19.

In mathematical terms, the formula for class width is:

Class Width = (Range of all intervals) / (Number of intervals)

In your case, the range of the intervals are:

19, 19, 19, 19, and 19

And the number of intervals is:

53 + 24 + 93 + 27 + 48 = 245

So, the class width can be calculated as follows:

Class Width = (19+19+19+19+19) / 245

Class Width = 95 / 245

Class Width = 0.3877

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Complete Question:

The data given below is for 245 randomly selected 10-minute intervals, where the number of people entering the atrium of a large mall were recorded. Calculate the class width.

Number of Guests         Frequency

160 - 179                                 53

180- 199                                 24

200 - 219                              93

220 - 239                              27

240 - 259                             48

Answer:

9 Prizes

Step-by-step explanation:

She begins with 420 tickets.

She goes on 2 rides for 75 tickets each so 420-75-75= 270

She then attends the concert for 180 tickets so 270-180= 90

Now she is left with 90 tickets. 10 tickets = 1 prize therefore you can do 90/10 = 9

9 PRIZES

Answer:

A confidence interval and hypothesis test will yield the same results when the null hypothesis value is outside the calculated confidence interval. In other words, if the null hypothesis falls outside the confidence interval, the null hypothesis is rejected at the same level of significance used to calculate the confidence interval. Conversely, if the null hypothesis falls inside the confidence interval, it cannot be rejected.

Null hypothesis: The proportion of college students who believe that freedom of the press is secure or very secure in this country has not changed from 2016.

Alternative hypothesis: The proportion of college students who believe that freedom of the press is secure or very secure in this country has changed from 2016.

We can test this hypothesis using a two-sample z-test for proportions, where the two proportions being compared are the proportion of students who believed freedom of the press was secure or very secure in 2016 and the proportion who believed this in 2017. The test statistic is calculated as:

z = (p1 - p2) / sqrt( p(1-p) * (1/n1 + 1/n2) )

where p1 is the proportion of students who believed freedom of the press was secure or very secure in 2016, p2 is the proportion who believed this in 2017, n1 is the sample size for 2016, n2 is the sample size for 2017, and p is the pooled proportion of successes.

If the test statistic falls outside the critical values for the chosen level of significance, the null hypothesis can be rejected and we can conclude that the proportion of college students who believe that freedom of the press is secure or very secure in this country has changed from 2016.

Step-by-step explanation:

Answer: 21

Step-by-step explanation:

The residual is equal to 6.5.

The given equation is y=5x-2.5 and the coordinate point is (3, 6).

The residual is the difference between the predicted value and the real value. Using the equation, we find for the value of y using the given value of x.

y = -2.5 + 5x

y = -2.5 + 5(3)

y = 12.5

Residual=actual y value−predicted y value,

The difference between this value and the given value of y is 12.5 - 6 = 6.5

Therefore, the residual is equal to 6.5.

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