A sample of n = 9 scores is obtained from a population with μ = 70 and σ = 18. If the sample mean is M = 76, what is the z-score for the sample mean?
a. z = 0.33
b. z = 0.50
c. z = 1.00
d. z = 3.00

Answer:

0= 30

Step-by-step explanation:

-7(3x+5) +20=5)3-5x)+4x

-21x-35+20=5)3-5x)+4x

Add the numbers

-21x-35+20=5)3-5x)+4x

-21x-15=5)3-5x)+4x

Rearrange terms

-21x-15=5)3-5x)+4x

-21x-15=5(-5x+3)+4x

Distribute

-21x-15=-25x+15+4x

Combine like terms

-21x-15=-21x+15

Add 15 to both sides of the equation

-21x-15+15=-21x+15+15

Simplify

Add the numbers

-21x=-21x+30

add 21 to both sides of the equation

-21x+21x= 21x+30+21x

Simplify

combine like terms

0=30

Complete Question

The complete question is shown on the first uploaded image

Answer:

The result of the rotation is Ali the Alien having the same orientation before the rotation.

The center of rotation is the same as the center of Ali the Alien.

Step-by-step explanation:

Let's take the center of Ali the Alien as the center of rotation, so when Ali the Alien is rotated through 180° we will discover that Ali the Alien will have the same orientation as he did before the rotation.

The probability of the mean height of the sample of boys being at least 6 cm higher than the mean height of the sample of girls can be calculated using a two-sample t-test. The t-test compares the means of two samples and determines whether they are different from one another. The t-test requires the assumption of equal variances and normal distribution of the data.

What does the math term "probability" mean?

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

Given that the variances are equal, the t-test statistic can be calculated as:

t = (mean_boys - mean_girls - 6) / (sqrt(variance/n))

where n is the sample size of each group (8 in this case).

The probability of observing a t-value as extreme or more extreme than this value can be calculated using the cumulative distribution function (CDF) of a t-distribution with n1 + n2 - 2 degrees of freedom.

Because you are looking for the probability that the mean height of the sample of boys is at least 6cm higher than the mean height of the sample of girls, this is a one-tailed test. The probability of a one-tailed test can be calculated by subtracting the probability of a two-tailed test from 1.

The probability can be calculated using a t-distribution table with 14 d.f. or using software such as R or excel.

It is important to note that the sample size is very small, with 8 boys and 8 girls, which may not be representative of the population. As sample size increases the probability of getting a significant difference increases.

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Answer:

f(x)=x-6 is your answer.

when x=0

f(0)=0-6=-6

similarly other too

Answer:

Step-by-step explanation:

3x+23/54

Answer: 0.67

Step-by-step explanation:

Answer:16 baths

Step-by-step explanation:

A model can help you solve surface area and volume problems because shows faces and helps you find the volume or area.

These problems can be challenging for some students because it implies imaging or visualizing 3-d objects to understand the dimensions of the figure, the number of faces, and then to calculate the volume or surface area.

This can be solved by using a model such as a graph or drawing that will help you to get a better idea of the object that is being analyzed.

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Answer:

Step-by-step explanation:

A

Answer:

219.8 inches

Step-by-step explanation:

Calculating the circumference of circle on which the unicycle travel :

\( \rightarrow{\bold{C = 2\pi r}}\)

Putting all the given values in the formula:

\(\begin{gathered}\mapsto{\sf{C = 2\pi r}} \\ \\ \mapsto{\sf{C = 2 \times 3.14 \times 7}} \\ \\ \mapsto{\sf{C = 6.28 \times 7}} \\ \\ \mapsto{\sf{C = 43.96 \: {} }}\end{gathered}\)

Thus, the circumference of circle is 43.96 inches.

\(\begin{gathered}\end{gathered}\)

Now, we know that unicycle covers 43.96 inches in one revolution. So, calculating the path travel in 5 inches:

\(\begin{gathered} \leadsto\sf{5 \times 43.96} \\ \\ \leadsto\sf{219.8}\end{gathered}\)

Hence, the unicycle will travel 219.8 inches in 5 revolution.

Answer:

y ≤ 1

Step-by-step explanation:

Range is the values of y that the graph can have

For part (a), we are asked to describe the set {5} ∪ {10} ∪ {15} ∪ {20} ∪ {25} using set builder notation, where each set is Ai = {ix : i ∈ Z+}.

To do this, we can simply list out all the elements of the set and use set builder notation to describe it. The set contains the elements {5, 10, 15, 20, 25}, so we can describe it as:

{ix : i ∈ Z+ and i = 1, 2, 3, 4, or 5}

Alternatively, we could also use interval notation to describe the set:

{ix : i ∈ Z+ and i ∈ [1, 5]}

For part (b), we are asked to describe the set (Ů4) Ai ∩ {x : 1 < x < 20} using roster notation, where each set is Ai = {ix : i ∈ Z+}.

To do this, we first need to find the union of the first 4 sets, which is given by:

{1, 2, 3, 4, 5} ∪ {2, 4, 6, 8, 10} ∪ {3, 6, 9, 12, 15} ∪ {4, 8, 12, 16, 20}

We can then take the intersection of this set with the set {x : 1 < x < 20}, which gives us the elements {2, 3, 4, 6, 8, 12, 16}, so we can describe the set using roster notation as:

{2, 3, 4, 6, 8, 12, 16}
Hi! I'm happy to help you with Exercise 3.3.2 regarding unions and intersections of sequences of sets.

(a) Using set builder notation, you can describe the set 5 ∪ Ai (i=1) as:

{ x ∈ Z+ : x is a positive integer multiple of any i where 1 ≤ i ≤ 5 }

(b) To describe the set (∪4 Ai) ∩ {Z: 1 < x < 20} using roster notation, first list the elements of each Ai for i = 1 to 4, and then find the elements that are also in the set {Z: 1 < x < 20}.

A1: {2, 4, 6, 8, 10, 12, 14, 16, 18}
A2: {3, 6, 9, 12, 15, 18}
A3: {4, 8, 12, 16}
A4: {5, 10, 15, 20}

Now, find the union of these sets:

∪4 Ai = {2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20}

Finally, find the intersection with the set {Z: 1 < x < 20}:

(∪4 Ai) ∩ {Z: 1 < x < 20} = {2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 18}

So the roster notation for this set is:

{2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 18}

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A statistic can never be larger than a parameter is not a correct statement. The correct statement among the following is as follows: IV Only. The statement "A statistic can be calculated whereas a parameter can never be established" is the correct statement.

Statistics and parameters are two fundamental concepts in statistical analysis. Both of these concepts are widely used in various researches and surveys.

A statistic is a numerical value that represents a particular characteristic of the sample and is used to estimate an unknown parameter. A parameter is a numerical value that represents a particular characteristic of a population.Statistics can be larger, smaller, or equal to parameters. A statistic is a value that is calculated from a sample, whereas a parameter is a value that represents a population characteristic and is estimated from the sample.A parameter can be established, but it is only possible if the entire population is considered for analysis. In contrast, a statistic is calculated from a sample of the population and represents only the characteristics of the sample.

:A statistic can never be larger than a parameter is not a correct statement. The correct statement is IV Only. The statement "A statistic can be calculated whereas a parameter can never be established" is the correct statement.

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9 meters cost P600

Step-by-step explanation:

3×3 = 9

p200×3 =P600

Answer:

1,2.

Step-by-step explanation:

.

Answer:

y+1=4(x-1)

Step-by-step explanation:

Point slope form is:  y-y₁=m(x-x₁)

Answer:

it would be 60

Step-by-step explanation

4*5= 20

8*5=40

12*5=  60

We multiply by 5 because if we divide 20/4=5, 40/8=5, 60/12=5.

Answer:

  2x^2 -2x +1 remainder 6

Step-by-step explanation:

Long Division

Perhaps you want the steps of long division. Those are shown in the first attachment.

Synthetic Division

The division can also be done using synthetic division. It gets you to the same place with a lot less writing. That method is shown in the second attachment.

Graphing Calculator

A method I sometimes use when solving cubic equations is shown in the third attachment. We find the remainder value by evaluating the polynomial at x=2 (remainder theorem). Subtracting that remainder from the given polynomial gives one that is evenly divisible by (x -2). The result of that division is a quadratic that describes a parabola.

The vertex of the parabola is easily found from its graph, so the vertex form equation can be written more or less directly from the graph. Expanding that gives the quotient. (We know the leading coefficient of the quadratic is 2, because that is the leading coefficient of the given polynomial, and the leading coefficient of the divisor is 1.) For leading coefficient c and vertex (h, k), the vertex-form quadratic is ...

  c(x -h)² +k

  2(x -1/2)² +1/2 = 2(x² -x +1/4) +1/2 = 2x² -2x +1 . . . quotient

  we already know the remainder is 6

_____

Additional comment

At each step of the long division, you multiply the quotient term by the divisor and subtract that product. The net result is that the highest-degree dividend term is cancelled.

Synthetic division makes this a little easier by doing two things. It ignores the arithmetic with the most-significant terms of quotient and divisor, because the result of that arithmetic is always zero. And, it uses the opposite of the binomial divisor constant for doing the multiplication, so the result can be added instead of subtracted. (Addition is generally easier to do without making mistakes.) You notice the number at upper left in the synthetic division is 2, not -2, for division by (x-2).

The steps are explained below.

Factorization of the given polynomial to find the product is as follows;

(x² + 3x + 2)/(x² + 6x + 5) = (x + 1)(x + 2)/(x + 1)(x + 5)

(x² + 7x + 10)/(x² + 4x + 4) = (x + 2)(x + 5)/(x + 2)(x + 2)

Expressing the product in terms of the factors

(x² + 3x + 2)/(x ^ 2 + 6x + 5) × (x² + 7x + 10)/(x² + 4x + 4) = (x + 2)(x + 5)/(x + 2)(x + 2) × (x + 1)(x + 2)/(x + 1)(x + 5)

The steps arranged in the order in which they would be performed are;

First step;

(x² + 3x + 2)/(x² + 6x + 5) × (x² + 7x + 10)/(x² + 4x + 4)

Second step (factorizing) =

(x + 1)(x + 2)/(x + 1)(x + 5) × (x + 2)(x + 5)/(x + 2)(x + 2)

Third step (dividing out common terms) =

(x+5)/(x+2) × (x+2)/(x+5)

Fourth step (rearranging and removing terms that cancel each other)

= 1

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If the confidence level were increased to 99%, the width of the confidence interval increases, when decreased to 80%, the width of the confidence interval decreases.

A confidence interval provides a range of estimated values for a population parameter's real value. A confidence level is connected to confidence intervals. The width of the confidence interval grows as the confidence level increases. The width of the confidence interval reduces as the confidence level goes down.

Since the margin of error grows as the confidence level does as well, the confidence interval will be bigger. Hence it increases for 99% and decreases for 80%.

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Take both mixed numbers (a whole number plus a fraction) and turn them into improper fractions ( a numerator (top number) bigger than the denominator (bottom number).

To do this, multiply the denominator by the whole number, and add the result to the numerator.

5 5/8 will become 45/8

1 1/2 will become 3/2.

Area is length * width, so width would be Area/ length. So 45/8 is the area and 3/2 is the length. Now you have (45/8)/(3/2). To divide fractions, take the second fraction and flip the numerator and denominator, forming the reciprocal (2/3). Now multiply 45/8 and 2/3

The result is 90/24, and simplifying would get 15/4, or 3 3/4. This is the width(or length)

Answer:

the volume will be (20-2x)(20-2x)(x)

Step-by-step explanation:

assuming its a square

Answer:

Total cost = $5h + $3s

Step-by-step explanation:

total cost of hot dog = price of hot dog x quantity of hot dog = 5 x $h

total cost of softdrink = price of softdrink x quantity of softdrink = $3s

total cost = $5h x $3s

Answer:

He got 4 bolts and 3 washers

Step-by-step explanation:

Because 0.55 · 4 = 2.2

0.07 · 3 = .21

and put it together, 2.2 + .21 = 2.41

The necessary components to describe a rotation on a coordinate plane include the center of rotation, the shape of the figure, and the number of degrees of rotation.

To describe a rotation of a figure on a coordinate plane, the necessary components include the center of rotation, the shape of the figure, and the number of degrees of rotation.

a. The center of rotation is a fixed point around which the figure rotates. It serves as the anchor for the rotation and determines the position of the figure after the rotation is applied.

b. The shape of the figure refers to its size, proportions, and geometric characteristics. This information is crucial as the figure retains its original shape during the rotation.

c. The number of degrees of rotation determines the magnitude of the rotation. It specifies how much the figure is rotated around the center of rotation. Positive angles indicate counterclockwise rotations, while negative angles represent clockwise rotations.

d. The direction of rotation is not necessary to describe a rotation on a coordinate plane. The rotation can be defined solely by the center, shape, and angle of rotation.

In summary, the essential components to describe a rotation on a coordinate plane include the center of rotation, the shape of the figure, and the number of degrees of rotation. The direction of rotation is not required to define the rotation.

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Answer:

\(a_{n}\) = 5n + 5

Step-by-step explanation:

The nth term of an arithmetic progression is

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 10 and d = a₂ - a₁ = 15 - 10 = 5 , then

\(a_{n}\) = 10 + 5(n - 1) = 10 + 5n - 5 = 5n + 5

Answer:

D

Step-by-step explanation:

factor the denominators of both fractions

x² - 16 ← is a difference of squares

= (x - 4)(x + 4)

8x + 2x² ← factor out 2x from each term

= 2x(4 + x) = 2x(x + 4)

then expression is

\(\frac{x^2}{(x-4)(x+4)}\) + \(\frac{9x}{2x(x+4)}\)

with LCD of 2x(x + 4)(x - 4)

Answer:

40° or 40.03 degrees or 25 inches as nilla mentioned.

Answer:

Step-by-step explanation:

a. 20,000 people because the more people you ask the more likely it is that you get a more accurate answer

b. because it would be more difficult to ask 20,000 people a question than 100 or 2000 people. it would take more time/effort/energy/resorces.

Answer: C 78 units

Step-by-step explanation:

If two quadrilaterals are similar, that means that they must have a scale factor that makes one of the figures bigger proportionally, so we can find the scale factor by taking to corresponding sides and dividing the bigger one over the smaller one...

YZ/QS = 13/4 = 3.25 (scale factor)

Now we can multiply the smaller sides by 3.25 to find any sides that we don't know the size of (for the bigger quadrilateral).

PQ * 3.25 = 9 x 3.25 = 29.25 (XY)

PR * 3.25 = 3 x 3.25 = 9.75 (XW)

Add the lengths together to get the perimeter...

XY + XW + WZ + YZ = 29.25 + 9.75 + 26 + 13 = 78 units

*remember to use scale factor to find the lengths or measurements for proportionally bigger figures... :D