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One side of a rectangle is 3 inches shorter than the other side, and the perimeter is 54 inches. What are the dimensions of the rectangle?

Answer:

The answer is...

Step-by-step explanation:

Purplea

Answer:

1. Cardinal Number

2. Ordinal number

3. Integer

4. Counting Number

5. Fraction

6. Base

7. Exponent

8. Factor

9. Prime factor

Step-by-step explanation:

A cardinal number is a number denoting quantity.

Ordinal numbers denote position, like first and second.

Integers are all whole numbers that are negative, and positive. It also includes 0.

Counting numbers are only positive integers.

Fractions always consist of a numerator and denominator.

Bases are always the number below the superscript of an exponent

Exponents are always the superscript of an exponent, such as 9^3. 3 would be the exponent.

A factor is a number that evenly divides into another number. For example, 2 and 4 are factors of the number 8.

Prime factors are factors of a number that are prime. Prime numbers are numbers that have the factors as themselves and the number 1. One example of a prime factor is 3. When given the number 9, 3 is a prime number, and factor of 9.

a) The relevant population is the heavy soft-drink users in the given case, and the appropriate sampling design that should be used is  stratified random sampling. The list of all heavy soft-drink users is the sampling frame.

b) Cluster sampling refers to a sampling design where population is divided into naturally occurring groups and a random sample of clusters is chosen.

The advantages are efficient, easy to perform, and used when the population is widely dispersed. The disadvantages are sampling errors, have lower level of precision, and have the standard error of the estimate.

a) The relevant population for the public relations research department to investigate the initial reactions of heavy soft-drink users to a new all-natural soft drink is heavy soft-drink users. The appropriate sampling design that can be used to investigate the issues is stratified random sampling.

Stratified random sampling is a technique of sampling in which the entire population is divided into subgroups (or strata) based on a particular characteristic that the population shares. Then, simple random sampling is done from each stratum. Stratified random sampling is appropriate because it ensures that every member of the population has an equal chance of being selected.

Moreover, it ensures that every subgroup of the population is adequately represented, and reliable estimates can be made concerning the entire population. The list of all heavy soft-drink users can be the sampling frame.

b) Cluster sampling is a type of sampling design in which the population is divided into naturally occurring groups or clusters, and a random sample of clusters is chosen. The elements within each chosen cluster are then sampled.

The advantages of cluster sampling are:

The disadvantages of cluster sampling are:

A situation where cluster sampling would be appropriate is in investigating the effects of a new medication on various groups of people. In this case, the population can be divided into different clinics, and a random sample of clinics can be selected. Then, all patients who meet the inclusion criteria from the selected clinics can be recruited for the study. This way, the study will be less expensive, and it will ensure that the sample is representative of the entire population.

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No, X or y-axis scale does not have to always start at zero. In a line chart, it's OK to start the axis at a number other than zero

A line that is used to take or mark measurements is known as an axis in mathematics. Two crucial axes of the coordinate plane are the x and y axes. A horizontal number line is the x-axis, while a vertical number line is the y-axis. The coordinate plane is created by the perpendicular intersection of these two axes.

Given,

No, X or y-axis scale does not have to always start at zero.

A line chart encodes data using location (x, y coordinates), whereas a bar chart represents data using length. In a line chart, it's OK to start the axis at a number other than zero despite many claims that they are always misleading since this minute difference influences how a reader utilizes the chart.

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The given statement "In performing a lower-tailed z-test for one mean, the value of the test statistic was z=0.51, which would yield a p-value of 0.695." is true because we perform null hypothesis.

In a lower-tailed z-test for one mean, we test a null hypothesis that the population mean (μ) is greater than or equal to a certain value, against an alternative hypothesis that the population mean is less than that value.

To perform the test, we calculate the z-test statistic using the sample mean, sample standard deviation, sample size, and the hypothesized population mean. If the calculated z-test statistic falls in the rejection region (below the critical value), we reject the null hypothesis and conclude that the population mean is less than the hypothesized value.

In this case, the calculated z-test statistic is 0.51, which falls in the non-rejection region (above the critical value) for a lower-tailed test with a significance level of 0.05. Therefore, the p-value is greater than 0.05, and we do not reject the null hypothesis. The statement that the p-value is 0.695 is consistent with this conclusion.

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Answer:

x = 0

y = 2

z = 2

Step-by-step explanation:

-5x + 5y - 5z = 0

               -5x = -5y + 5z

                   x = y - z

10x + 2y - 5z = -6

10(y - z) + 2y - 5z = -6

10y - 10z + 2y - 5z = -6

               12y - 15z = -6

                       12y = 15z - 6

                          y = \(\frac{5}{4} z - \frac{1}{2}\)

-5x + 2y + 3z = 10

-5(y - z) + 2(5/4z - 1/2) + 3z = 10

     -5y + 5z + 5/2z - 1 + 3z = 10

     -5y + 21/2z - 1 = 10

          -5y + 21/2z = 11

                   21/2z = 11 + 5y

                      21z = 22 + 10y

                            z = \(\frac{22 + 10y}{21}\)

_________

  x = y - z

 y = \(\frac{5}{4} z - \frac{1}{2}\)

  z = \(\frac{22 + 10y}{21}\)

y = \(\frac{5}{4} (\frac{22 + 10y}{21} ) - \frac{1}{2}\) = \(\frac{110 + 50y}{84} - \frac{1}{2}\) = \(\frac{110 + 50y - 42}{84}\) = \(\frac{68 + 50y}{84}\) = \(\frac{17}{21} + \frac{25}{42} y\)

y - \(\frac{25}{42} y\) = \(\frac{17}{21}\)

\(\frac{42}{42} y - \frac{25}{42} y = \frac{17}{21}\)

\(\frac{17}{42} y = \frac{17}{21}\)

17y = \(\frac{714}{21}\)

17y = 34

y = 2

z = \(\frac{22 + 10y}{21}\) = \(\frac{22 + 10(2)}{21} = \frac{42}{21}\)

z = 2

x = y - z = 2 - 2

x =  0

The correct option: A. 12.78% of the variability of verbal score that can be explained by the linear regression on the math score.

Students majoring in statistics at Prosperity University responded to a survey that requested their Verbal as well as Math SAT scores. Depending on the math score, they sought to anticipate the verbal score.

Stated values:

We must first comprehend what a correlation coefficient is, claims the assertion.

Here, depending on the survey results, they seek to determine the verbal score using the math number (independent variable).

r² = 0.1278

r = √0.1278

Statement(1): - 12.78% of the verbal score variability that the linear regression on the mathematics score can account for.

TRUE. The provided model accounts for 12.78% of the variability and the verbal and mathematical scores.

Statement #2: A linear regression just on verbal score can account for 12.78% of the variance in math scores.

FALSE, Since the verbal score rather than the numerical score is the dependent variable.

Statement 3: The verbal significant dimension by 12.78 points for every 1 point improvement in math scores.

FALSE, the determination coefficient does not accurately capture the slope of the a linear model.

Statement (4): A math score increases up 12.78 points for every 1 point that the verbal score goes up on average.

FALSE—the determination coefficient does not accurately capture the slope of the a linear model.

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The correct question is-

A survey of Statistics undergraduate at Prosperity University completed a survey that asked for their Verbal and Math SAT scores. They wanted to predict the verbal score based on the math score. The value of R-Squared was 12.78%. Interpret R-squared.

Group of answer choices

A. 12.78% of the variability of verbal score that can be explained by the linear regression on the math score.

B. 12.78% of the variability of math score that can be explained by the linear regression on the verbal score.

C. As the math score increases by 1 point on average, the verbal score increases by 12.78 points.

D. As the verbal score increases by 1 point on average, the math score increases by 12.78 points.

Answer:

less than 3/4 pound of watermelon

Step-by-step explanation:

half of 3/4 is 3/8, which is less than 3/4 clearly

Answer:

1. No

2. Yes

3. No

Explanation:

Statistical questions are questions that require statistical data to solve.

It will require collecting data from various samples and analyzing.

From the given options, let us identify the statistical and non-statistical questions.

1. what is your favorite food?

This is not a statistical question because it does need collecting any data it is a personal question and Non-statistical.

2. what is your favorite color of the sixth-grade students at your school?

This is a statistical question because it would involve collecting data samples from various sixth-grade students at your school and analyzing such data. So, it is a Statistical question.

3. what is the height of the Empire State Building?

There is only one empire state building, therefore it is a direct question that has a specific answer and does not require statistical data to solve. So, it is not a statistical question.

We can see that the first component of the vector equation is always zero, so the parabola lies in the xz-plane.

Moreover, the second component is a quadratic function of t, which gives us a vertical parabola when plotted in the yz-plane. The third component is a linear function of t, so the curve extends infinitely in both directions. Therefore, we have a vertical parabola in the xz-plane.

This statement is referring to a specific vector-valued function, which we can write as:

f(t) = (0, t^2, ct)

where c is a constant.

The second component of this vector function is t^2, which is a quadratic function of t. When we plot this function in the yz-plane (i.e., we plot y = t^2 and z = 0), we get a vertical parabola that opens upward. This is because as t increases, the value of t^2 increases more and more quickly, causing the curve to curve upward.

The third component of the vector function is ct, which is a linear function of t. When we plot this function in the xz-plane (i.e., we plot x = 0 and z = ct), we get a straight line that extends infinitely in both directions. This is because as t increases or decreases, the value of ct increases or decreases proportionally, causing the line to extend infinitely in both directions.

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Isotopes are creation of a chemical element with specific properties. They are different nuclear species (or nuclides) of the same element.

They are generated by the same atomic number (number of protons in their nuclei) and their position in the periodic table (and hence belong to the same chemical element), but they are different in nucleon numbers (mass numbers) due to different numbers of neutrons in their nuclei.

The periodic table is considered a space which comprises a table of the chemical elements which are arranged in order of atomic number, generally in rows, so that elements with similar atomic structure appear in vertical columns.
It is globally used in chemistry, physics, and other sciences, and is generally seen as an icon of chemistry. The periodic table is sub divided into four blocks, reflecting the filling of electrons into types of subshell. Here, the table columns are referred as groups, and the rows are referred as periods.
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Therefore , the solution to the given problem of equation comes out to be p=7/4.

A mathematical language stating the equality of two variables or mathematical expressions is known as an equation. Noticing how the weights on the left and right are equal, respectively When indicating equality between two numbers or mathematical equations, we use the equal sign.For instance, the equation for the scenario above is 5 kg + 2 kg = 4 kg + 3 kg.

Here,

Given : -8p + 14 =0

thus ,

For finding the value of p

=> -8p = -14

=> 8p =14

=> p = 14/8

=> p=7/4

Therefore , the solution to the given problem of equation comes out to be p=7/4.

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Both options a. A = 129.9° and b. A = 53.1° are correct.

To find the possible values for angle A in triangle ABC, we can use the Law of Sines, which states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant.

Using the Law of Sines, we have sin(A)/a = sin(B)/b. Plugging in the given values, we get sin(A)/36 = sin(51°)/35.

To find the two possible values for angle A, we can solve the equation sin(A)/36 = sin(51°)/35. Taking the arcsine of both sides, we have A = arcsin((sin(51°)/35)*36).

Calculating this expression, we find two possible values for angle A:

A ≈ 53.1° (rounded to the nearest tenth)

A ≈ 129.9° (rounded to the nearest tenth)

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Answer:15x3 /=divide 5 = 9

Step-by-step explanation:

because if you do 15x3 it is 45 then you divide it by 5 and get 9 as your answer!

Answer:    The price per foot will be 2.74$

Step-by-step explanation:

what is the relation between yard and foot?

The value of one yard is  equal to3 feet.

That is given by ,

1 yard =3 feet.

we have 2 yards piece of aluminium wire

Firstly,we have to find the cost of 2 pieces of aluminium wire.

2×3=6

The cost is 16.44

16.44/6=2.74.

Therefore the price per foot will be $2.74.

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Answer:2.74

4. f(x,y) is homogeneous of degree 2.

5. a) f(x,y) is homothetic with h(x,y) = xy and g(x) = x-1

4. Show that f(x,y)=\(x^2\)y is homogeneous, and find its degree of homogeneity:

A function is said to be homogeneous of degree k, if it satisfies the condition:

f(tx,ty) = \(t^k\)f(x,y)

We have f(x,y) = \(x^2\)y. Let’s check if it satisfies the above condition:

f(tx,ty) = \((tx)^2(ty) = t^3x^2y = t^2(x^2y\)) = \(t^2\)f(x,y)

Hence f(x,y) is homogeneous of degree 2.

5. Which of the following functions f(x,y) are homothetic? Explain.

(a) f(x,y)=\((xy)^2\)+1

(b) f(x,y)=\(x^2+y^3\)

Let us first understand the meaning of homothetic transformation.

A homothetic transformation is a non-rigid transformation of the Euclidean plane that preserves the direction of the straight lines but not their length. It stretches or shrinks the plane by a constant factor called the dilation.

Let’s now find out whether the given functions are homothetic or not.

(a) f(x,y)=\((xy)^2\)+1

In order to check if f(x,y) is homothetic or not, we need to check if the function satisfies the following condition:

f(x,y) = g(h(x,y))

where g is a strictly monotonic function and h is a homogeneous function with degree 1

We have

f(x,y) = \((xy)^2\)+1

Let’s assume g(x) = x - 1, then g(x+1) = x

Similarly, let’s assume h(x,y) = (xy), then h(tx,ty) = \(t^2\)h(x,y)

Now, we have

g(h(x,y)) = h(x,y) - 1 = (xy) - 1

Thus f(x,y) is homothetic with h(x,y) = xy and g(x) = x-1

(b) f(x,y)=\(x^2+y^3\)

We can’t write this function in the form f(x,y) = g(h(x,y)) where h(x,y) is a homogeneous function with degree 1. Hence this function is not homothetic.

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Answer:

\(\fbox {True}\)

Step-by-step explanation:

Trigonometric ratios apply to only right triangles, and not to oblique triangles. There various ratios of angles less than or equal to 90 degrees is taken.

Step-by-step explanation:

hope you can understand

Answer:

C. $200 over $999 = x% over 100

Step-by-step explanation:

200/999 = 0.2002002002 about 20%

that's how much it decreases since they have a difference of 200.

1. (-1,1) type the equation for the graph of the quadratic to the left (the graph thingy is up):

The equation for the quadratic with the vertex at (-1, 1) and facing upwards would be: y = a(x + 1)^2 + 1.

2. (3,2) type the equation of the graph of the quadratic to the left (its facing down):

The equation for the quadratic with the vertex at (3, 2) and facing downwards would be: y = a(x - 3)^2 + 2.

3. (-2,5) type the equation of the graph of the quadratic to the left (facing down):

The equation for the quadratic with the vertex at (-2, 5) and facing downwards would be: y = a(x + 2)^2 + 5.

Please note that the "a" in the equations represents the coefficient that determines the width and direction of the quadratic graph. Without additional information or specific values for "a," the equations provide the general form for the given vertex and orientation.\(\)

A plasmid used in both yeast and bacteria requires two different selection markers because the same selection may not work for both hosts and bacteria and yeast recognize different promoters.

When using a plasmid in both yeast and bacteria, it is important to have two different selection markers for several reasons. First, the same selection, such as the presence of an antibiotic, may not be effective in both hosts. Different organisms have varying sensitivities to antibiotics, so a marker that works in bacteria may not work in yeast or vice versa. Therefore, two different selection markers are needed to ensure successful selection in both hosts.

Additionally, bacteria and yeast recognize different promoters, which are DNA sequences that control the initiation of gene expression. Promoters are specific to each organism and play a crucial role in regulating gene expression. By incorporating two different selection markers into the plasmid, each marker can be driven by a promoter recognized specifically by the corresponding host. This ensures that the selection marker is effectively expressed in the appropriate host organism, enabling accurate selection and maintenance of the plasmid.

In summary, using two different selection markers in a plasmid intended for both yeast and bacteria is necessary because the same selection may not be effective in both hosts, and different promoters are recognized by bacteria and yeast. This approach allows for successful selection and maintenance of the plasmid in both organisms.

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Answer:

$9.50

Step-by-step explanation:

If there are 8 tickets and they all add up to $76, you have to divide 76 by 8 (the number of tickets)

Answer:

no because she would get the same total if she added it before or after

Step-by-step explanation:

Anthony's "hiring process" or "recruitment period" was 30 days.

The blank can be filled with "hiring process" or "recruitment period" to indicate the duration between placing the advertisement for a new assistant on November 1 and hiring Marquis on December 1. This period represents the time it took Anthony to evaluate applicants, conduct interviews, and make the decision to hire Marquis.

The hiring process typically involves several steps, such as advertising the job opening, reviewing applications, conducting interviews, and finalizing the selection. The duration of this process can vary depending on various factors, including the number of applicants, the complexity of the position, and the efficiency of the hiring process.

In this case, the hiring process took 30 days, indicating the length of time it took for Anthony to complete the necessary steps and choose Marquis as the new assistant. This duration provides insight into the timeframe Anthony needed to assess candidates and make a hiring decision.

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Answer:

B.) 15 Feet

Step-by-step explanation:

So how you would sove this problem is to see that 15/5=3, so then you will take 45 and divide that by 3 and get 15 Feet which brings your answer to be "B"!

I hope this helped you:)

Answer:

(-6)

Step-by-step explanation:

I just did the assignment lol

Answer:

Step-by-step explanation:

Step-by-step explanation:

Given

-45 < 5(p-2)

Dividing both sides by 5

9 < p - 2

Adding two on both sides

9 + 2 < p - 2 + 2

11 < p

or

p > 11

Hope it will help :)❤

Answer:

AB = \(\left[\begin{array}{ccc}0&-2\\4&-12\\\end{array}\right]\)

Step-by-step explanation:

To obtain the first row of AB

Sum the products of corresponding elements in row 1 of A with elements in column 1 and 2 of B

To obtain the second row of AB

Sum the corresponding elements in row 2 of A with elements in column 1 and 2 of B, that is

AB = \(\left[\begin{array}{ccc}0(-1)+2(0)&0(3)+2(-1)\\-4(-1)+0(0)&-4(3)+0(-1)\\\end{array}\right]\)

      = \(\left[\begin{array}{ccc}0+0&0-2\\4+0&-12+0\\\end{array}\right]\)

      = \(\left[\begin{array}{ccc}0&-2\\4&-12\\\end{array}\right]\)

Answer:

1. AC = 11

2. CD = 5

3. AD = 15

4. CD = 6

Step-by-step explanation:

hope that will help you

if u need more explanation text me