Consider a sample with data values of 6, 17, 14, 7, and 16. Compute the variance. (to 1 decimal) Compute the standard deviation.

Answer: $42.65

Step-by-step explanation: multiply

$8.63 by 5

Answer:

42.65$

Hope this helps!

Step-by-step explanation:

1 box = 8.53

5 boxes = 8.53 * 5

8.53 * 5 = 42.65

Answer:

17.6

Step-by-step explanation:

70.40 divided by 4= 17.6.

The standard deviation is best described as a measure of the spread of a distribution around its mean or expected value.

What is standard deviation?

Standard deviation (SD) is a numerical measurement of how spread out or dispersed a set of data is. It can be expressed as the square root of variance (s²), which is the average deviation of a data point from the mean.

What is the formula for standard deviation?

The formula for standard deviation can be written as:

s = √(Σ (Xi - µ)² / (n - 1))

where:s = standard deviation

           Σ = sum

           Xi = each data point

           µ = the mean of the data points

           n = number of data points

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6 teenagers liked "Space Jam 2" but not "Fast and Furious 9".

16 teenagers liked "Fast and Furious 9" only.

The coordinates of the reflected points based on the given isometries are given below.

We have,

To solve this problem, we can use the principles of set theory and Venn diagrams.

a. To find the number of teenagers who liked "Space Jam 2" but not "Fast and Furious 9", we need to consider the set difference between the set of teenagers who liked "Space Jam 2" (S) and the set of teenagers who liked both "Fast and Furious 9" and "Space Jam 2" (F ∩ S).

The formula for the set difference is:

|S - (F ∩ S)| = |S| - |F ∩ S|

Given that |S| = 17 and |F ∩ S| = 11, we can calculate:

|S - (F ∩ S)| = 17 - 11 = 6

Therefore, 6 teenagers liked "Space Jam 2" but not "Fast and Furious 9".

b. To find the number of teenagers who did not like any of the three movies, we need to consider the complement of the union of the three sets (F ∪ S ∪ A) with the total number of teenagers (n = 50). The formula for the complement is:

|n - (F ∪ S ∪ A)| = n - |F ∪ S ∪ A|

Given that |F ∪ S ∪ A| can be calculated using the principle of inclusion-exclusion as:

|F ∪ S ∪ A| = |F| + |S| + |A| - |F ∩ S| - |F ∩ A| - |S ∩ A| + |F ∩ S ∩ A|

Given the values provided:

|F| = 16

|S| = 17

|A| = 11

|F ∩ S| = 11

|S ∩ A| = 6

|F ∩ A| = 5

|F ∩ S ∩ A| = 0

We can calculate:

|n - (F ∪ S ∪ A)| = 50 - (16 + 17 + 11 - 11 - 5 - 6 + 0)

= 50 - 22

= 28

Therefore, 28 teenagers did not like any of the three movies.

c. To find the number of teenagers who liked "Fast and Furious 9" only, we need to consider the set difference between the set of teenagers who liked "Fast and Furious 9" (F) and the intersection of all three sets (F ∩ S ∩ A).

The formula for the set difference is:

|F - (F ∩ S ∩ A)| = |F| - |F ∩ S ∩ A|

Given that |F| = 16 and |F ∩ S ∩ A| = 0, we can calculate:

|F - (F ∩ S ∩ A)| = 16 - 0 = 16

Therefore, 16 teenagers liked "Fast and Furious 9" only.

IV. Isometries:

Reflecting the figure given the vertices below into the x-axis, y-axis,

y = x, and y = -x:

A(-12, 5)

B(-12, 2)

C(-8, 5)

D(-5, 2)

E(-8.5, 0.5)

F(-10.5, 3)

To reflect a point (x, y) across the x-axis, we change the sign of the y-coordinate.

To reflect across the y-axis, we change the sign of the x-coordinate.

To reflect across the line y = x, we swap the x and y coordinates.

To reflect across the line y = -x, we change the sign of both the x and y coordinates.

Applying these reflections to each vertex, we get:

a. Reflection across the x-axis:

A'(-12, -5)

B'(-12, -2)

C'(-8, -5)

D'(-5, -2)

E'(-8.5, -0.5)

F'(-10.5, -3)

b. Reflection across the y-axis:

A'(-12, 5)

B'(-12, 2)

C'(8, 5)

D'(5, 2)

E'(8.5, 0.5)

F'(10.5, 3)

c. Reflection across the line y = x:

A'(5, -12)

B'(2, -12)

C'(5, -8)

D'(2, -5)

E'(0.5, -8.5)

F'(3, -10.5)

d. Reflection across the line y = -x:

A'(12, -5)

B'(12, -2)

C'(8, -5)

D'(5, -2)

E'(8.5, -0.5)

F'(10.5, -3)

These are the coordinates of the reflected points based on the given isometries.

Thus,

6 teenagers liked "Space Jam 2" but not "Fast and Furious 9".

16 teenagers liked "Fast and Furious 9" only.

The coordinates of the reflected points based on the given isometries are given.

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Answer:

Mrs. Taylor bought 200 oranges ;) .

Answer:

200

Step-by-step explanation:

If 30% of the oranges were bad, then that means 0.3 * total number of oranges, were bad. so if 0.3 * total = 60, then 60/0.3 = total number of oranges.

The closed form of the second relation is:

aₙ = 1

To find the closed form of the recursive relations, we'll solve them iteratively.

For the first relation:

a₀ = 1

aₙ = 9 - aₙ₋₁

We can start by finding the values of a₁, a₂, a₃, and so on, based on the recursive formula:

a₁ = 9 - a₀ = 9 - 1 = 8

a₂ = 9 - a₁ = 9 - 8 = 1

a₃ = 9 - a₂ = 9 - 1 = 8

We observe that the values of aₙ alternate between 1 and 8:

a₀ = 1, a₁ = 8, a₂ = 1, a₃ = 8, ...

Thus, the closed form of the first relation is given by:

aₙ = 8^(n mod 2)

For the second relation:

a₀ = 1

aₙ = 3aₙ₋₁ - 2aₙ₋₂

Again, we can start by finding the values of a₁, a₂, a₃, and so on:

a₁ = 3a₀ - 2a₋₁ = 3 - 2 = 1

a₂ = 3a₁ - 2a₀ = 3 - 2 = 1

a₃ = 3a₂ - 2a₁ = 3 - 2 = 1

We observe that all the values of aₙ are 1.

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Explanation:

Inequalities are solved just like regular equations. The difference is that you need to take care to reverse the direction when multiplying or dividing negative numbers.

The simplest way to solve an inequality is to first solve it as an equality, and then CHECK the value to find out which way the sign should point.

x

3

<

6

; multiply both sides by 3;

x

<

18

As an equality:

x

3

=

6

;

x

=

18

CHECK one value higher (19): ;

19

3

<

6

;

6.333

<

6

NOT TRUE! So, the value of x must be LESS than 18, as found originally.

x

<

18

Answer:

x<9

Step-by-step explanation:

Answer:

Option A, E ,F are correct

Step-by-step explanation:

f(x).g(x)=(8x^2+4)(-x^2+12x+10)

=(-8x^4+96x^3+80x^2-4x^2+48x+40)

= -8x^4+96x^3+76x^2+48x+40

Leading term is -8x^4. The x term has coefficient 48. The x^2 term has coefficient +76

Answer:

4(3x - 5)

Step-by-step explanation:

12x - 20 ← factor out 4 from each term

= 4(3x - 5)

There are 10 cars with 4 doors and red color.

Given:

So,

Therefore, there are 10 cars with 4 doors and red color.

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Answer:

Step-by-step explanation:

\(\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\\\\\left(x_1,\:y_1\right)=\left(-1,\:2\right),\:\left(x_2,\:y_2\right)=\left(5,\:4\right)\\\\m=\frac{4-2}{5-\left(-1\right)}\\\\m = \frac{2}{5+1}\\ \\m = \frac{2}{6} \\\\m = \frac{1}{3}\)

Answer:

4 to the power of 13

Step-by-step explanation:

Answer:

Visual artifacts are anomalies apparent during visual representation as in digital graphics and other forms of imagery, especially photography and microscopy.

The median price from the given data is 648,303.

To find the median price from the given data, we need to arrange the prices in ascending order and then locate the middle value. If there is an odd number of data points, the median will be the middle value. If there is an even number of data points, the median will be the average of the two middle values.

Let's arrange the data in ascending order:

181,386,243,922,355,008,406,791,542,820,648,303,782,200,845,053,924,494,1,089,774,1,175,704,1,274,928,1,308,954

There are a total of 13 data points, which is an odd number. So, the median price is the middle value.

The middle value is the 7th value:

Median Price = 648,303

Therefore, the median price from the given data is 648,303.

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Answer:

3.=300%

0.35=35%

4.=400%

0.812=81.2%

Answer:

30%.34  81%.02

Step-by-step explanation:

Answer:

x < -7

Step-by-step explanation:

to isolate x we need to subtract 2 from both sides. -5-2 is -7, so the answer is x < -7

Answer:

x< −7

Step-by-step explanation:

Rearrange:

Rearrange the equation by subtracting what is to the right of the greater than sign from both sides of the inequality :

                    x+2-(-5)<0

Step by step solution :

STEP 1:

Solve Basic Inequality :

1.1      Subtract  7  from both sides

           x < -7

Inequality Plot :

1.2      Inequality plot for

        x  + 7.000  <  0

Answer:

32

Step-by-step explanation:

The inequality which best represents the possible combinations of cupcakes and cakes Nancy decorated is 4x + 32y > 224

Given:

Time to decorate cupcake = 4 minutes

Time to decorate cake = 32 minutes

Total time spent decorating last week = more than 224 minutes

number of cupcakes = x

number of cakes = y

The inequality:

4x + 32y > 224

4x + 32(4) > 224

4x + 128 > 224

4x > 224 - 128

4x > 96

x > 96/4

x > 24

4x + 32y > 224

4(32) + 32(3) > 224

128 + 96 > 224

224 > 224

Therefore, it is possible that Nancy decorated 3 cakes and 32 cupcakes last week

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Answer:

\(\textsf{a)} \quad \textsf{Recursive Rule}: \quad a_n=5n-2\)

     \(\textsf{Explicit Rule}: \quad \begin{cases}a_1=3\\a_n=a_{n-1}+5\end{cases}\)

b)  4998

c)  explicit rule (see below for explanation)

d)  see below

Step-by-step explanation:

An explicit formula for an arithmetic sequence allows you to find the nth term of the sequence.

A recursive formula for an arithmetic sequence allows you to find the nth term of the sequence provided you know the value of the previous term in the sequence.

Explicit Formula

\(a_n=a+(n-1)d\)

where:

Given sequence:  3, 8, 13, 18, 23, ...

To find the common difference, subtract one term from the next term.

Therefore:

Substituting the found values of a and d into the formula to create a explicit rule for the given sequence:

\(\implies a_n=3+(n-1)5\)

\(\implies a_n=3+5n-5\)

\(\implies a_n=5n-2\)

Recursive Formula

\(a_n=a_{n-1}+d \quad \textsf{for }n\geq 2\)

where:

We already know the common difference our previous calculations.

Therefore:

\(\implies a_n=a_{n-1}+5\)

When giving a recursive rule we also have to define the first term of the sequence, as it is not part of the formula.  Therefore, the full recursive rule for the given sequence is:

  \(\begin{cases}a_1=3\\a_n=a_{n-1}+5\end{cases}\)

To find the 1000th term of the sequence, use the explicit rule and substitute n = 1000:

\(\implies a_{1000}=5(1000)-2\)

\(\implies a_{1000}=5000-2\)

\(\implies a_{1000}=4998\)

Therefore, the 1000th term of the sequence is 4998.

We used the explicit rule to find the 1000th term as this rule allows us to find the nth term of the sequence without having to know any previous terms.

The disadvantage of a recursive rule when compared to an explicit rule is that we need to know the previous term to find the nth term, whereas the explicit rule doesn't need this information.

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The base of triangle will be 12 cm.

A triangle is a three-sided polygon.

The area of a rectangle is commonly known to be b*h, where b is the base and h is the height. Using the formula for a rectangle, we can get the area of a triangle.

A rectangle is split into two congruent triangles by a diagonal. The area of each triangle is equal to half the size of the rectangle.

As a result, the triangle's area A may be calculated using the equation A=1/2*b*h, where b denotes the triangle's base and h its height.

AREA OF TRIANGLE = 1/2*b*h

base = area of triangle * 2 / h

         = 30 * 2 / 5

         = 12 cm.

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The number of people who prefer eggs is 35.

In mathematics, a ratio is a comparison of two or more numbers that indicates their sizes in relation to each other. A ratio compares two quantities by division, with the dividend or number being divided termed the antecedent and the divisor or number that is dividing termed the consequent. A ratio might be formatted as a Part to Part or Part to Whole comparison. A Part to Part comparison looks at two individual quantities within a ratio of greater than two numbers, such as the number of dogs to the number of cats in a poll of pet type in an animal clinic. A Part to Whole comparison measures the number of one quantity against the total, such as the number of dogs to the total number of pets in the clinic.

Let the number of people who prefer eggs be x.

21 people said they prefer oatmeal.

The ratio of people who prefer oatmeal to those who prefer eggs is 3 to 5.

∴ \(\frac{21}{x} = \frac{3}{5} \\x = \frac{21*5}{3}\\ x = \frac{105}{3} \\x = 35\)

Thus, the number of people who prefer eggs is 35.

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The amount of teaspon cinnamon he would need to serve is 33.33

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

Number of people = 20

Using the teaspon cinnamon, we have

teaspon cinnamon = 3/5

So, we have

Amount = People/teaspon cinnamon

Substitute the known values in the above equation, so, we have the following representation

Amount = 20/(3/5)

Evaluate

Amount = 33.33

Hence, the amount is 33.33

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Given that `z` is a standard normal random variable, we are to calculate the following probabilities using the appropriate appendix table or technology:

(a) `P(z ≤ -2.0)` (b) `P(Z > -2)` (c) `P(Z < 1.7)` (d) `P(-2.3 ≤ Z ≤ 2)` (e) `P(-3 < Z < -1.5)`.

From the normal distribution table, we can read the probability of a `z-score`. Using this table, we can calculate the following probabilities:

(a) P(z ≤ -2.0). The standard normal distribution table shows that the area to the left of a `z-score` of `2.0` is `0.0228`. Hence, P(z ≤ -2.0) = 0.0228.

Answer: `0.0228`

(b) P(Z > -2)P(Z > -2) = 1 - P(Z ≤ -2) = 1 - 0.0228 = 0.9772

Answer: `0.9772`

(c) P(Z < 1.7)P(Z < 1.7) = 0.9554

Answer: `0.9554`

(d) P(-2.3 ≤ Z ≤ 2)P(-2.3 ≤ Z ≤ 2) = P(Z ≤ 2) - P(Z ≤ -2.3)

We need to find `P(Z ≤ 2)` and `P(Z ≤ -2.3)` by referring to the standard normal distribution table:

P(Z ≤ 2) = 0.9772P(Z ≤ -2.3) = 0.0107

Therefore, P(-2.3 ≤ Z ≤ 2) = 0.9772 - 0.0107 = 0.9665

Answer: `0.9665`

(e) P(-3 < Z < -1.5)P(-3 < Z < -1.5) = P(Z < -1.5) - P(Z < -3)

We need to find `P(Z < -1.5)` and `P(Z < -3)` by referring to the standard normal distribution table:

P(Z < -1.5) = 0.0668P(Z < -3) = 0.0013

Therefore, P(-3 < Z < -1.5) = 0.0668 - 0.0013 = 0.0655

Answer: `0.0655`.

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Answer:

C

Step-by-step explanation:

Answer:

7 days

Step-by-step explanation:

We need to find bracelets per day.

1 day 2 days

5 bracelets 10 bracelets

since we know how many bracelets she can make per day, all we have to do is divide 35 by 5.

to get 7 days.

Answer:

Step-by-step explanation:

Given that:

Keiko sold 3 less than three-fourths of his sister's sale.

To find:

Expression that represents what Keiko sold ?

\(1.\ \dfrac{3}{4} x - 3 \\2.\ \dfrac{3}{4} x + 3 \\ 3.\ 3 x + \dfrac{3}{4} \\4.\ 3x - \dfrac{3}{4}\)

Solution:

First of all, let the sales done by Keiko's sister = \(x\)

Now, let us consider the Keiko's sale word by word.

3 less than three-fourths of his sister's sale.

i.e. subtract 3 from the expression obtained in 1st line.

\(\dfrac{3}{4}x-3\)

So, sales done by Keiko = \(\dfrac{3}{4}x-3\)

So, correct answer is:

\(1.\ \dfrac{3}{4}x-3\)

\(\frac{3}{4}x-3\)

An algebraic expression is one that is obtained by performing a finite number of algebraic operations on symbols that represent numbers.

Any of the common arithmetic operations, such as addition, subtraction, multiplication, division, raising to a whole number power, and taking roots, is a basic algebraic operation.

Let \(x\) denotes sale of sister of Keiko.

As Keiko sold \(3\) less than three-fourths of his sister's sales,

Sales of Keiko \(=\frac{3}{4}x-3\)

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Answer:

0.008.

Step-by-step explanation:

10^-3 basically tells you to move the decimal point to the left by three digits.

Right now, you have 8. If the decimal point were to move left by three digits, you can visualize 8 as 0008. Move left by three digits, and you get 0.008.

Hope this kind of helps!

Answer:

0.008.

hope this helps :)

Ticket sales at this performance fell $1,100 below the goal of $2,350

Let's start by setting up a system of equations based on the given information. We know that the total revenue from ticket sales for one performance is $2,350. We also know that the number of adult tickets sold is d, and the number of student tickets sold is s. The price of an adult ticket is $6.50, and the price of a student ticket is $3.50. Finally, we know that the total number of tickets sold is 500.

Using this information, we can write the following system of equations:

d + s = 500 (equation 1)

6.5d + 3.5s = 2350 (equation 2)

We can use equation 1 to solve for one of the variables in terms of the other. For example, if we solve for s, we get:

s = 500 - d

We can then substitute this expression for s into equation 2:

6.5d + 3.5(500 - d) = 2350

Simplifying and solving for d, we get:

6.5d + 1750 - 3.5d = 2350

3d = 600

d = 200

So, 200 adult tickets were sold. We can use equation 1 to find the number of student tickets sold:

s = 500 - d

s = 500 - 200

s = 300

So, 300 student tickets were sold.

Now, let's consider the second part of the question. We know that at one performance, there were two times as many student tickets sold as adult tickets. Let's call the number of adult tickets sold at this performance a, and the number of student tickets sold b. Then we can write:

b = 2a (equation 3)

a + b = 300 (equation 4)

We can use equation 3 to substitute for b in equation 4:

a + 2a = 300

3a = 300

a = 100

So, 100 adult tickets were sold at this performance. We can use equation 3 to find the number of student tickets sold:

b = 2a

b = 2(100)

b = 200

So, 200 student tickets were sold at this performance.

To find out how much below the goal of $2,350 ticket sales fell, we can use equation 2 to calculate the total revenue from ticket sales at this performance:

6.5a + 3.5b = revenue

6.5(100) + 3.5(200) = 1250

So, ticket sales at this performance fell $1,100 below the goal of $2,350.

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Step-by-step explanation:

Since the initial fee is fixed, we can assume it is a constant and the succeeding mile fee is the variable as it changes for every mile covered.

Let x = distance (mile)

let y = total charge (dollars)

Yellowcab company equation for cost calculation;  3.50 + 2.5x = y

laxicab company equation for cost calculation;  4.54+2.3x = z

the two companies charge the same amount when y = z

; 3.50 + 2.5x = 4.54+2.3x

x = 5.2 miles

COST CALCULATION

;3.50 + 2.5x = ?

if x = 5.2;

; 3.50 + 2.5(5.2) =$16.50

OR

; 4.54+2.3x = ?

; 4.54 + 2.3(5.2) = $16.50

Answer:

wheres the table

Step-by-step explanation:

I dont see a picture so I cant help u sorry

a) The probability that Dwight signs 6 new clients in a randomly selected week is approximately 0.1047

b) The probability that Dwight signs at least 3 new clients in a randomly selected week is approximately 0.7227.

Let X be the number of new clients that Dwight signs in a randomly selected week. Since X follows a Poisson distribution with an average rate of 3.7 new clients per week, we can write:

P(X = x) = \((e^{-\lambda} \times \lambda ^x)\) / x!, x = 0, 1, 2, ...

where λ is the average rate and e is the mathematical constant e ≈ 2.71828.

a) Probability that Dwight signs 6 new clients:

To calculate this probability, we need to substitute x = 6 and λ = 3.7 into the above formula:

P(X = 6) = (\(e^{-3.7}\) x 3.7⁶) / 6! ≈ 0.1047

b) Probability that Dwight signs at least 3 new clients:

To calculate this probability, we need to sum the probabilities of signing 3, 4, 5, 6, and so on, new clients. Since the Poisson distribution is a discrete probability distribution, we can use the cumulative distribution function (CDF) to compute this probability:

P(X ≥ 3) = 1 - P(X < 3) = 1 - P(X = 0) - P(X = 1) - P(X = 2)

Substituting λ = 3.7 into the Poisson probability formula, we get:

P(X = 0) = \(e^{-3.7}\) x 3.7⁰ / 0! ≈ 0.0240

P(X = 1) = \(e^{-3.7}\) x 3.7¹ / 1! ≈ 0.0890

P(X = 2) = \(e^{-3.7}\) x 3.7² / 2! ≈ 0.1643

Therefore,

P(X ≥ 3) = 1 - 0.0240 - 0.0890 - 0.1643 ≈ 0.7227

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