which of the following is not one of the measures of variability with each measure providing its own unique version of information that helps to describe the diversity of responses? question 8 options: range frequency distribution mode standard deviation

Answer:

The solution to the recurrence relation is given by an = 2^(n+1) - 1.

Step-by-step explanation:

(a) To solve the recurrence relation an = an-2 + 4, with initial conditions a1 = 3 and a2 = 5, we'll consider two cases: one for when n is even and one for when n is odd.

For n even:

Substituting n = 2k (where k is a positive integer) into the recurrence relation, we get:

a2k = a2k-2 + 4

Now let's write out a few terms to observe the pattern:

a2 = a0 + 4

a4 = a2 + 4

a6 = a4 + 4

...

We notice that a2k = a0 + 4k for even values of k.

Using the initial condition a2 = 5, we can find a0:

a2 = a0 + 4(1)

5 = a0 + 4

a0 = 1

Therefore, for even values of n, the solution is given by an = 1 + 4k.

For n odd:

Substituting n = 2k + 1 (where k is a non-negative integer) into the recurrence relation, we get:

a2k+1 = a2k-1 + 4

Again, let's write out a few terms to observe the pattern:

a3 = a1 + 4

a5 = a3 + 4

a7 = a5 + 4

...

We see that a2k+1 = a1 + 4k for odd values of k.

Using the initial condition a1 = 3, we find:

a3 = a1 + 4(1)

a3 = 3 + 4

a3 = 7

Therefore, for odd values of n, the solution is given by an = 3 + 4k.

(b) To solve the recurrence relation an = 2an-1 + 1, with initial condition a1 = 1, we'll find a general expression for an.

Let's write out a few terms to observe the pattern:

a2 = 2a1 + 1

a3 = 2a2 + 1

a4 = 2a3 + 1

...

We can see that each term is one more than twice the previous term.

By substituting repeatedly, we can express an in terms of a1:

an = 2(2(2(...2(a1) + 1)...)) + 1

= 2^n * a1 + (2^n - 1)

Using the initial condition a1 = 1, we have:

an = 2^n * 1 + (2^n - 1)

= 2^n + 2^n - 1

= 2 * 2^n - 1

Therefore, the solution to the recurrence relation is given by an = 2^(n+1) - 1.

The required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Let 'a' be the cost per gallon of fuel in the year 2000, and 'b' be the inflation rate per year. If the rate of inflation is constant then
After 7 year inflation = 7b
Cost of fuel in 2007 = a + 7b

Now,
according to the question
Change in cost of fuel
= cost in 2007 - cost in 2000
= a + 7b - a
= 7b

Thus, the required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

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Answer:

I will assume the second equation is y=2x^3.  If it is y=2x+3 or y=2x-3, the lines will never intersect:  they have the same slope (2):

Step-by-step explanation:

2x – y = 7 can be rewritten as:  y = 2x -7.  It has a slope of 2.  The second equation, y = 2x 3, isn't clearly written.  If the 3 has a plus or minus sign, then the lines will never intersect:  they have the same slope, 2.

I'll assume the second equation is y=2x^3.

See attached graph.

Answer:

9/14 dividend

27/28 quotient

Step-by-step explanation:

Dividend is the one being divided by the divisor

quotient is the answer

Answer:

B: ^5Г16x^4

Step-by-step explanation:

simplify the radical by breaking the radicand up into a product of known factors.

Answer:

42,195

Step-by-step explanation:

The set of polynomials of the form \(p(t) = at^2\), where \(a\) belongs to the set of real numbers, is a subspace of P. It is determined that the given set is a subspace of P for an appropriate value of \(n\).

To determine if a set is a subspace of P, it must satisfy three conditions: closure under addition, closure under scalar multiplication, and containing the zero vector. For the set of polynomials of the form \(p(t) = at^2\), where a belongs to the set of real numbers, we can see that it satisfies these conditions.

Closure under addition: Let \(p_1(t) = a_1t^2\) and \(p_2(t) = a_2t^2\) be two polynomials from the given set. If we add these two polynomials, we get \(p(t) = (a_1+ a_2)t^2\). Since the sum of two real numbers is also a real number, \(p(t)\) belongs to the set.

Closure under scalar multiplication: Let \(p(t) = at^2\) be a polynomial from the given set, and c be a scalar. If we multiply \(p(t)\) by \(c\), we get \(cp(t) = (ca)t^2\). Since the product of a real number and a scalar is still a real number, \(cp(t)\) belongs to the set.

Zero vector: The zero polynomial, \(p(t) = 0t^2\), where the coefficient a is zero, is in the set.

Therefore, the set of polynomials of the form \(p(t) = at^2\), where a belongs to the set of real numbers, satisfies all the conditions and is a subspace of P.

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An equation in point-slope form that can be used to describe the relationship between x and y is y - (-1) = 3/4(x - 1).

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (2 + 1)/(5 - 1)

Slope (m) = 3/4

At data point (1, -1) and a slope of 3/4, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - (-1) = 3/4(x - 1)  

y + 1 = 3/4(x - 1)  

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Answer: The answer would be x = -3 + 0.5y.

Step-by-step explanation: pls give me brainliest. may help w/ my depression.

Answer:

\(d = \frac{29}{10} \)

Step-by-step explanation:

\(d = 2 \frac{9}{10} \)

d = 2.9

Answer:

zero

Step-by-step explanation:

the projection of vector RS onto vector PQ is zero

please find the attachment for detail

Answer:

-14

Step-by-step explanation:

A T-score of -3.6 indicates that the individual has a severe case of osteoporosis

A T-score is a standard score used to compare an individual's bone mineral density (BMD) to that of a healthy young adult population. A T-score of -3.6 on a BMD test indicates that the individual's BMD is significantly lower than that of a healthy young adult. Specifically, it means that the individual's BMD is 3.6 standard deviations below the average BMD of a healthy young adult.

A T-score of -2.5 or lower is considered to indicate osteoporosis, which is a condition characterized by low bone density and an increased risk of fractures. Therefore, a T-score of -3.6 indicates that the individual has a severe case of osteoporosis, and the doctor will likely recommend treatment such as medication and lifestyle changes to help increase bone density and reduce the risk of fractures.

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Answer:

f(3)= -1

Step-by-step explanation:

1. f(3)= 3x - 10

f(3) means that where x is in the equation you put a 3

2. f(3)= 3(3) - 10

3. f(3)= 9 - 10

4. f(3)= -1

The rate of change for each set of ordered pairs is:

a. 1/2

b. 3

c. 7

The average rate of change = change in y / change in x.

Average rate of change for (2,3.5), (6,5.5):

Average rate of change = (5.5 - 3.5)/(6 - 2) = 2/4 = 1/2

Average rate of change for (-1,0), (0, 3):

Average rate of change = (3 - 0)/(0 - (-1)) = 3/1 = 3

Average rate of change for (3,-3), (4,4):

Average rate of change = (4 -(-3))/(4 - 3) = 7/1 = 7

Therefore, the rate of change for each set of ordered pairs is:

a. 1/2

b. 3

c. 7

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Answer:

-52

Step-by-step explanation:

Answer:

-116

Step-by-step explanation:

-84-(-32) it's simple

Answer:

19.5 miles

Step-by-step explanation:

6.5 x 3 = 19.5

Answer:

need to work out how long it would take 1 person first.

9 X 5 = 45

1 person will take 45 hours

45/3= 15 hours

Blake can purchase approximately 60.75 pounds of Cheese Filled Lizards and 10 dozen of Fried Frog Skins with the $432 he saved by recycling old aluminum cans.

First we need to set up some equations.

Let's denote the amount of Cheese Filled Lizards in pounds as "c" and the number of dozen Fried Frog Skins as "f". We can then set up the following system of equations:

8c + 6f = 432 (the total cost of the party is $432)

12f = k (the number of Fried Frog Skins in individual pieces, k is an unknown constant)

To solve for "c" and "f", we need to eliminate one of the variables. We can do this by solving the second equation for "f" and substituting it into the first equation:

f = k/12

8c + 6(k/12) = 432

8c + (1/2)k = 432

16c + k = 864

Now we have a single equation in two variables. We can choose one of the variables and solve for it in terms of the other. For example, solving for "k" in terms of "c", we get:

k = 864 - 16c

Substituting this expression for "k" into the equation 12f = k, we get:

12f = 864 - 16c

f = (72/4) - (4/3)c

f = 18 - (4/3)c

So we have expressed the number of Fried Frog Skins in terms of the amount of Cheese Filled Lizards. We can now substitute this expression into the cost equation:

8c + 6(18 - (4/3)c) = 432

Solving for "c", we get:

8c + 108 - 8c/3 = 432

16c/3 = 324

c = 60.75

So, Blake can purchase approximately 60.75 pounds of Cheese Filled Lizards and 10 dozen of Fried Frog Skins with the $432 he saved by recycling old aluminum cans.

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Answer:

2.5*10^7

Step-by-step explanation:

Standard form is always a number between 1 and 10 (but never exactly 10) multiplied by 10 to the power of something. Just divide the 25 by 10, so it can be used in standard form, and increase the power by 1. Hope this helped! :^)

Answer:

Step-by-step explanation:

40(12/100)

480/100

$4.80

Answer: $4.80

Step-by-step explanation:

%10 = $4.00

%12 = $4.80

%14 = $5.60

Answer:

The total cost, c(p), to purchase sugar is equal to the product of the pound cost equal to $0.59 and the number of pounds of sugar, p. Thus, the answer to this item is,

                                c(p) = ($0.59)p

Step-by-step explanation:

The total cost, c(p), to purchase sugar is equal to the product of the pound cost equal to $0.59 and the number of pounds of sugar, p. Thus, the answer to this item is C(p)=0.59p

Jay's error is that he misinterpreted the concept of the mean of the data set. The mean, also known as the average, is the sum of all numbers in a data set divided by the total number of data points. In this case, we do not know the context of the data set, so we cannot assume it refers to weight or the weight of a couch.

Jay's interpretation of the mean as "half the couch weight less than 7.76 pounds and half weighed more" is incorrect because it assumes that the data follows a symmetrical distribution, which may not be the case. The mean can be influenced by the values on either side of it, and it does not necessarily divide the data set in half.

If we assume that the data set refers to the weight of couches, then Jay's interpretation is incorrect because it is impossible for half the weight of a couch to be less than its weight. Rather, weight is always a positive value, so it would be more appropriate to describe the data in terms of a range or distribution rather than in terms of half and half.

In conclusion, Jay's error was in misinterpreting the meaning of the mean, assuming a symmetrical distribution, and making assumptions about the data set without the necessary context. It is important to understand the context and statistical properties of data before making any conclusions or interpretations.

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Answer:

15.6 and

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

Hope this helps :)

The answer is H0: At the 10% significance level, we conclude that the CFA designation is more lucrative than an MBA.

a. Set up the hypotheses to test if a CFA designation is more lucrative than an MBA at the 10% significance level.

The null hypothesis is: H0: μ1 ≤ μ2

The alternative hypothesis is: H1: μ1 > μ2So, the answer is (c) H0: μ1 − μ2 ≤ 0; HA: μ1 − μ2 > 0. b-1. Calculate the value of the test statistic.

The formula to find the test statistic is given by,

\[{\rm{T}} = \frac{{\left( {{\overline X _1} - {\overline X _2}} \right) - \left( {{\mu _1} - {\mu _2}} \right)}}{{\sqrt {\frac{{{\rm{s_1}^2}}}{n} + \frac{{{\rm{s_2}^2}}}{n}} }}\]Substituting the given values,\[{\rm{T}} = \frac{{\left( {146 - 133} \right) - \left( 0 \right)}}{{\sqrt {\frac{{{{\left( {53} \right)}^2}}}{41} + \frac{{{{\left( {26} \right)}^2}}}{52}} }} = 2.417\]

So, the value of the test statistic is 2.417.b-2. Find the p-value.

We need to find the p-value for a one-tailed test at a 10% significance level.

Since the alternative hypothesis is μ1 > μ2, the p-value is the area to the right of the test statistic.

Using a t-distribution table with 91 degrees of freedom (rounded to the nearest integer), we get the p-value as 0.010.

Since the p-value is less than the significance level, we reject the null hypothesis and conclude that the CFA designation is more lucrative than an MBA.

Therefore, the answer is H0: At the 10% significance level, we conclude that the CFA designation is more lucrative than an MBA.

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Answer:

A.

Step-by-step explanation:

Just find the lowest common multiple of 51 and 85.

51 = 3 * 17

85 = 5 * 17

3 * 5 * 17 = 255

The lowest common denominator for the fractions is 17.

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

Given:

fraction = 8/51 and 19/ 85

Now, LCM of 51 and 85.

51 = 17 x 3

85= 17 x 5

So, the least common multiple is 17.

Hence, the lowest common denominator for the fractions is 17.

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H0: p1 ≥ p2 (Null hypothesis: Proportion of ADHD-diagnosed students in School A is equal to or greater than in School B)

Null Hypothesis: The proportion of students diagnosed with ADHD in School A is equal to or greater than the proportion of students diagnosed with ADHD in School B.

Symbolically, the null hypothesis can be stated as:

H0: p1 ≥ p2

Where:

H0: Null Hypothesis

p1: Proportion of students diagnosed with ADHD in School A

p2: Proportion of students diagnosed with ADHD in School B

In other words, the null hypothesis assumes that there is no significant difference or that School A may have an equal or higher proportion of students diagnosed with ADHD compared to School B.

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Answer:

C

Step-by-step explanation:

Given that:

- Your sister will give you $15 for heads and $25 for tails.

- Your mother will give you $6 times the number that the spinner lands on.

you must calculate the Expected Value of each game:

- Game 1:

When you through the coin, the probability of getting a head is 50% and the probability of getting a tail is 50%.

You need to use the following formula for calculating the Expected Value:

Where "x" is the random variable, and p(x) is the probability obtained.

Therefore, for Game is:

- Game 2:

When you spin the spinner with six different outcomes. Therefore:

Then:

Hence, the answer is:

- Expected Value of your sister's game:

- Expected Value of your mother's game:

- You should take your mother's offer, because it has the greatest Expected Value.