For the numbers below, find the area between the mean and the z-score: a) z = 1.17 b) z = -1.37 For the z-scores below, find the percentile rank (percent of individuals scoring below): a) -0.47 b) 2.2

(a) To show that 3i is a root of p(2), we substitute 3i into p(z) and check if it equals zero.

p(3i) = 24 - 2(3i)^3 + 7(3i)^2 - 9(3i) - 18

Using the properties of i:

(3i)^2 = -9

(3i)^3 = -27i

Substituting these values into the equation:

p(3i) = 24 - 2(-27i) + 7(-9) - 9(3i) - 18

= 24 + 54i - 63 - 27i - 18

= -57 + 27i

Since p(3i) is not equal to zero, 3i is not a root of p(2).

(b) As 3i is not a root of p(2), we need to find the four roots using other values.

p(2) = 24 - 2(2)^3 + 7(2)^2 - 9(2) - 18

= 24 - 16 + 28 - 18 - 18

= 0

This means that 2 is a root of p(z).

(c) To write rp(x) as a product of linear factors, we can factorize p(x) using synthetic division or other methods. Factoring p(x) gives:

p(x) = (x - 2)(x - a)(x - b)(x - c)

Where a, b, and c are the other three roots.

Since p(x) is a real polynomial, the other three roots must either be real or occur in conjugate pairs. Therefore, the four roots of p(x) are 2, a, b, and c.

The irreducible real factor can be determined by factoring p(x) further or by using numerical methods. Without additional information or calculations, we cannot determine the exact form of the irreducible real factor.

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Answer:

I think that the person who is right is Ryan because he used the all the proprieties in the right way

Step-by-step explanation:

Answer: Ryan's work is correct because if you Subtract 7 and 3 you would get 4. Then you add 2 you would get 6.

Step-by-step explanation: Step 1: (7 - 3 = 4) Step 2: (4 + 2 = 6)

Yes, the point (2,-1) lies on the curve y=1/(1-x) as when x=2, y=1/(1-2)=1/(-1)=-1, which is equal to -1.

y=1/(1-x)

y=1/(1-2)

y=1/(-1)

y=-1

Yes, the point (2,-1) lies on the curve y=1/(1-x). To prove this, we can substitute the x-coordinate of the point (2) into the equation. When x=2, the equation becomes y=1/(1-2). Simplifying this equation, we get y=1/(-1) which is equal to -1. Thus, y=-1, which is the same as the y-coordinate of the point (-1). This means that the point (2,-1) does indeed lie on the curve y=1/(1-x). This can be further verified by plotting the point (2,-1) on a graph and seeing that it is indeed located on the curve y=1/(1-x).

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Answer:

j : k : m = 4 : 12 : 15

Step-by-step explanation:

Given

j : k = 1 : 3 , then k = 3j

Given

k : m = 4 : 5

then expressing in fractional terms

\(\frac{k}{m}\) = \(\frac{4}{5}\) ( substitute k = 3j )

\(\frac{3j}{m}\) = \(\frac{4}{5}\) ( cross- multiply )

4m = 15j ( divide both sides by 4 )

m = \(\frac{15}{4}\) j , so

j : k : m = 1 : 3 : \(\frac{15}{4}\) ( multiply each part by 4 to clear the fraction )

            = 4 : 12 : 15

Answer:

12

Step-by-step explanation:

12 is the most number in the equation

Answer:

Mean Age: 13 years

Step-by-step explanation:

To find the mean or average in mathematics, add up all data in a set, and divide by the amount of individual values there are in the set.

Here's what I mean:

12+14+12+15+14+13+12+12 = 104 / 8 different ages in the set = 13

Hope this helped :) .

Answer:

44,10

Step-by-step explanation:

I think this is the answer

Answer:

$44.10

Step-by-step explanation:

tip = 35 x .20 = 7.00

tax = 35 x .06 = 2.10

9.10 + 35.00 = 44.10

Answer:

Rate: 36:3

Unit Rate: 12:1

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:1/6

Step-by-step explanation:

Answer:

D) 12 feet

Step-by-step explanation:

The formula for area of a rectangle is length x width. We have this information: length x 7 = 84. To solve for this, divide 7 from both sides to get: length = 12 feet.

Hope it helps!

Answer:

12 ft

Step-by-step explanation:

L = area / width

L = 84 / 7

L = 12

The times that the ball is 34 feet high to the nearest tenth of a second is equal to 4.61 and 0.39 seconds.

In order to determine the time or times for this ball at a height of 34 feet, we would simply substitute the value of the height into the function h(t) as follows;

h(t) = -16t² + 80t + 5

34 = -16t² + 80t + 5

Re-arranging the equation, we have:

16t² - 80t + 34 - 5 = 0

16t² - 80t + 29 = 0

Next, we would solve the quadratic equation by using the quadratic formula:

\(x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}\\\\x = \frac{-(-80)\; \pm \;\sqrt{-80^2 - 4(16)(29)}}{2(16)}\\\\x = \frac{80\; \pm \;\sqrt{6400 - 1856}}{32}\\\\x = \frac{80\; \pm \;\sqrt{4544}}{32}\)

x = (80 ± 8√71)/32

x = (80 + 8√71)/32  and  x = (80 - 8√71)/32

x = 4.61 and 0.39 seconds.

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Here are the steps to solve this problem:

1. Find the area of each face of the ramp.

The rectangular base is 2 meters by 1.5 meters, so the area is 2 x 1.5 = 3 square meters.

The triangular side is 0.5 meters by 1.5 meters, so we use the area of a triangle formula: (base x height)/2 = (0.5 x 1.5)/2 = 0.375 square meters

2. Add the areas of the faces together to find the total surface area that needs to be covered.

3 + 0.375 = 3.375 square meters

3. We need an additional amount for overlaps where the vinyl pieces meet. Let's assume a 10% overlap, or 0.338 square meters.

0.338 + 3.375 = 3.713 square meters

So Mathias needs about 3.7 square meters of vinyl to cover his bike ramp.

In summary:

Area of rectangular base = 2 x 1.5 = 3m^2

Area of triangular side = (0.5 x 1.5)/2 = 0.375m^2

Total area = 3 + 0.375 = 3.375 m^2

Additional 10% for overlap = 0.338m^2

Total vinyl needed = 0.338 + 3.375 = 3.713 m^2

Answer:

0,1

2,2

4,3

6,4

Step-by-step explanation:

Some Examples

4 = 1/2 (6) + 1

4 = 3 + 1

4=4

----------

2 = 1/2 (2) + 1

2 = 1 + 1

2 = 2

h

0

2

4

6

...................

Answer: 0.43

Step-by-step explanation: 43% = 43/100 = 0.43

Therefore, the depth of the water is changing at a rate of -7/3 ft/hour when the depth of the water is 6 ft.

a. To find the rate at which the depth of the water is changing, we can use related rates. Let's call the depth of the water "h" and the radius of the top of the water "r". We're given that dh/dt = -2 ft^3/hour (since the water is leaking). We want to find dr/dt when h = 6 ft.

Using similar triangles, we can set up the following relationship: h/6 = r/7. We can rearrange this equation to solve for r in terms of h: r = (7/6)h.Now, we can differentiate both sides of this equation with respect to time (t) to find the relationship between dh/dt and dr/dt: dr/dt = (7/6)(dh/dt).

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Answer:

A

Step-by-step explanation:

According to the given question.

Total number of shirts, n = 12

Number of shirts to be selected, r = 3

As we know, the total number of ways of selection of r objects from n objects at a time without replacement is given by

C(n, r) = n!/r!(n - r)!

Answer:

88

Step-by-step explanation:

4 pints = 8 cups

3 cups = 3 cups

8 cups + 3 cups = 11 cups

11 cups = 88 fl oz

Answer:

64 + 24 = 88 oz

Step-by-step explanation:

1 pint = 16 oz  (4 x 16 = 64)

1 cup = 8 oz (3 x 8 =24)

Answer:

x = 3.5

Step-by-step explanation:

By definition, congruent chords are equidistant from the center of a circle. We are given two congruent chords and their distances(the lines perpendicular), meaning those distances must be equal. We set set up an equation to model the situation:

x + 8 = 3x + 1

8 = 2x + 1

2x = 7

x = 3.5

1. In this context, the other variables that might be confounded with a mother's consumption of diet soda during pregnancy are the health of the mother during gestation period.

2. A sentences which can best describes a completely randomized design for this experiment on "Diet soda and pregnancy" is "adverse effect of intake of soda drinks on pregnancy".

Basically, completely randomized design is a type of experimental design in which the experimental units are assigned to the various treatments at random. When the experimental units are thought to be "uniform," that is, when there is no uncontrolled factor in the experiment, it is used.

It is a design where the treatments are assigned completely at random so that each experimental unit has the same chance of receiving any one treatment. For the CRD, any difference among experimental units receiving the same treatment is considered as experimental error.

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Since Quadrilateral CDEF is inscribed in Circle A, the value of x is equal to: B. 33.

Since Quadrilateral CDEF is inscribed in Circle A, we can reasonably infer and logically deduce that line segment DF is the chord of Circle A. Mathematically, an equation which can be used to solve for the value of x in this circle is given by:

m∠DEF + m∠DCF = 180°

Substituting the given parameters into the formula above, we have the following;

(3x + 7)° + (2x + 8)° = 180°

3x + 2x + 8 + 7 = 180°

5x + 15 = 180°

5x = 180° - 15

5x = 165

x = 165/5

x = 33.

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The numerical limits for a D grade would be 78% for the top and 7% for the bottom.

To calculate this, you would need to use the z-score formula.

The z-score formula is (x-µ)/σ, where x is the score in question, µ is the mean, and σ is the standard deviation. In this case, 78% would be the score of x.

We can plug in the given mean of 67.3 and standard deviation of 7.2 into the formula and solve for x.

Doing this, we find that x would be equal to 78.48, which rounds up to 78. Therefore, the numerical limits for a D grade are 78% for the top and 7% for the bottom.

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a) U is subspace of R^3.

b) The set {(3, -2, 0), (0, 1/2, 1)} is a basis for U.

c) 2.

a) To show that U is a subspace of R^3, we need to verify the following three conditions:

i) The zero vector (0, 0, 0) is in U.

ii) U is closed under addition.

iii) U is closed under scalar multiplication.

i) The zero vector is in U since 0 + 2(0) - 3(0) = 0.

ii) Let (x1, y1, z1) and (x2, y2, z2) be two vectors in U. Then we have:

x1 + 2y1 - 3z1 = 0 (by definition of U)

x2 + 2y2 - 3z2 = 0 (by definition of U)

Adding these two equations, we get:

(x1 + x2) + 2(y1 + y2) - 3(z1 + z2) = 0

which shows that the sum (x1 + x2, y1 + y2, z1 + z2) is also in U. Therefore, U is closed under addition.

iii) Let (x, y, z) be a vector in U, and let c be a scalar. Then we have:

x + 2y - 3z = 0 (by definition of U)

Multiplying both sides of this equation by c, we get:

cx + 2cy - 3cz = 0

which shows that the vector (cx, cy, cz) is also in U. Therefore, U is closed under scalar multiplication.

Since U satisfies all three conditions, it is a subspace of R^3.

b) To find a basis for U, we can start by setting z = t (where t is an arbitrary parameter), and then solving for x and y in terms of t. From the equation x + 2y - 3z = 0, we have:

x = 3z - 2y

y = (x - 3z)/2

Substituting z = t into these equations, we get:

x = 3t - 2y

y = (x - 3t)/2

Now, we can express any vector in U as a linear combination of two vectors of the form (3, -2, 0) and (0, 1/2, 1), since:

(x, y, z) = x(3, -2, 0) + y(0, 1/2, 1) = (3x, -2x + (1/2)y, y + z)

Therefore, the set {(3, -2, 0), (0, 1/2, 1)} is a basis for U.

c) Since the basis for U has two elements, the dimension of U is 2.

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Answer:

A. Payday Lending

Explanation:

Payday Lending is common for small lending companies and not banks. They assist clients who have a minimal amount of salary to borrow a small amount of money with a high interest. The amount of money he can borrow will depend on the amount of salary he receives per month. The client will not be required to give any form of collateral for the borrowed money, thus, the client is said to be high-risk. However, he will have to return the money over a short period of time with an interest rate that is high. Though it is easy to get a loan with this kind of service, you have to make sure that you are employed.

Banks prefer to offer loans to people who have a steady income and a certain amount of salary.  

Answer:

a

Step-by-step explanation:

i think its correct

This sample would be considered A. Cluster sample. In a cluster sample, the researcher divides the population into groups or clusters, and then randomly selects some of these clusters to include in the sample.

In this case, the researcher is selecting nine counties as the clusters, and surveying all shoulder surgery patients within those counties. This is different from a stratified sample, in which the population is divided into subgroups or strata based on certain characteristics, and a representative sample is selected from each stratum. It is also different from a convenience sample, in which the researcher simply selects the individuals who are easiest to reach or who happen to be available at the time of the study. And it is different from a simple random sample, in which every member of the population has an equal chance of being selected for the sample.

The missing part in the question is shown below.

A medical researcher surveys all shoulder surgery patients

in each of 9 randomly selected counties in North Carolina.

Which type of sample does this represent?

A. Cluster sample.

B. Stratified sample.

C. Convenience sample.

D. Simple random sample.

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Step-by-step explanation:

= (8x² + 9) - (3x² + 2x + 5)

= 8x² + 9 - 3x² - 2x - 5

= 5x² - 2x + 4

C. (∃x)(A(x) ∧ B(x)) ⇔ (∃x)A(x) → (∀y)B(y)

This statement is incorrect. The left-hand side states that there exists an x such that both A(x) and B(x) are true.

Therefore, the incorrect statement is option C.

A = {{1, 2, 3}, {4, 5}, {6, 7, 8}}

Hence. Option D is wrong.

In set theory, a subset relation is denoted by ⊆, and a proper subset relation is denoted by ⊂. A subset relation indicates that all elements of one set are also elements of another set.

In this case, let's evaluate the options:

A. ∅ ⊆ A: This option is correct. The empty set (∅) is a subset of every set, including A.

B. {6, 7, 8} ⊂ A: This option is correct. The set {6, 7, 8} is a proper subset of A because it is a subset of A and not equal to A.

C. {{4, 5}} ⊂ A: This option is correct. The set {{4, 5}} is a proper subset of A because it is a subset of A and not equal to A.

D. {1, 2, 3} ⊂ A: This option is incorrect. The set {1, 2, 3} is not a subset of A because it is not included as a whole within A. The element {1, 2, 3} is present in A but is not a subset.

In conclusion, the incorrect option is D, {1, 2, 3} ⊂ A.

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Answer:

A campaign manager would like to show the distribution of individuals...

Step-by-step explanation:

goodness of fit can be used to compare observed and expected counts. The newspaper report would be the expected. The campaign manager's distribution is the expected.

Answer:

x=2

Step-by-step explanation:

You can simplify the equation with all the x's on one side and the numerical values on the other. After solving, the answer would be x=2

Answer:

x=2

Step-by-step explanation:

Distribute the 2.5 and 4 out

15x - 10 = 10 + 6 +2x

Add the constant variables together

15x - 10 = 16 +2x

Move the x on one side and the constant on the other

13x = 26

Divide both sides to find x

x=2