the polynomial below is a perfect square trinomial of the form A^2-2AB+B^2. 9x^2 - 30x + 25

A p-value for correlation which is statistically significant implies the correlation is due to random chance. The correct solution to this is False.

A p-value for correlation which is statistically significant implies that it is unlikely that the observed correlation is due to random chance alone. In other words, it suggests that there is evidence to support the presence of a true correlation between the two variables being studied. The p-value is a measure of the strength of evidence against the null hypothesis (i.e., that there is no correlation between the two variables), and a smaller p-value indicates stronger evidence against the null hypothesis.

Interpretation of the intercept: The intercept in a linear regression model represents the value of the dependent variable when all independent variables are equal to zero. It is the value of the dependent variable when there is no effect of the independent variable(s) on it. For example, in a regression model predicting height based on age, the intercept would represent the expected height of a person at age zero (which is not a realistic scenario).

Interpretation of a residual: A residual is the difference between the actual observed value of the dependent variable and the predicted value of the dependent variable based on the regression model. It represents the part of the dependent variable that the model was not able to explain. A positive residual means that the actual value is greater than the predicted value, while a negative residual means that the actual value is smaller than the predicted value.

Interpretation of r-squared: R-squared is a measure of how much of the variation in the dependent variable is explained by the independent variable(s) in the regression model. It ranges from 0 to 1, with higher values indicating a better fit of the model to the data. Specifically, it represents the proportion of the total variation in the dependent variable that is explained by the independent variable(s) in the model. For example, if r-squared is 0.75, it means that 75% of the variability in the dependent variable is explained by the independent variable(s) in the model.

Interpretation of the slope: The slope in a linear regression model represents the change in the dependent variable that is associated with a one-unit increase in the independent variable, holding all other variables constant. It reflects the average change in the dependent variable for each unit change in the independent variable. For example, in a regression model predicting height based on age, the slope would represent the average change in height for each additional year of age.

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At the rate of 45(3/5) pages per hour Nolan reads the book.

As per the question,

Nolan read 7(3/5) pages in (1/6) of an hour.

Total number of pages read by the Nolan = \(7\frac{3}{5} = \frac{38}{5}\)

Time taken by her = (1/6) Hour

We have to determine the rate per page per hour with which she is reading the book.

As rate can be calculated by dividing the total number of pages read by Nolan by the time she takes her to read the page.

So, for calculating the rate we will divide (38/5) pages by (1/6) Hour.

So, the rate of Nolan will be

\(\frac{\frac{38}{5}}{\frac{1}{6}}\\\\=\frac{38 \times 6}{5} \\\\= \frac{228}{5} = 45.6 = 45\frac{3}{5}\)

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Answer:

90 hope this helps~!

Step-by-step explanation:

====================================

\(\large \sf \underline{Problem:}\)

Is the following linear or nonlinear?

m = n 2 - 7n - 54

a) linear

b) nonlinear

====================================

\(

\large \sf \underline{Answer:}\)

A. Linear

====================================

\(\large \sf \underline{Explanation:}\)

The standard form for linear equations in two variables is Ax+By=C. For example, 2x+3y=5 is a linear equation in standard form. When an equation is given in this form, it's pretty easy to find both intercepts (x and y).

====================================

Answer:

x = 46°

Step-by-step explanation:

Angles on a straight line sum to 180°.

Therefore, the interior angle of the triangle that forms a linear pair with the exterior angle marked 130° is:

⇒ 180° - 130° = 50°

The interior angle of the triangle that forms a linear pair with the exterior angle marked 96° is:

⇒ 180° - 96° = 84°

The interior angles of a triangle sum to 180°. Therefore:

⇒ 50° + 84° + x = 180°

⇒ 134° + x = 180°

⇒ 134° + x - 134° = 180° - 134°

⇒ x = 46°

Therefore, the size of angle x is 46°.

Answer:

4

Step-by-step explanation:

3/9 is the same as 1/3 so 1/3 or 12 is 4

Answer:

4

Step-by-step explanation:

Answer & Step-by-step explanation:

On a six-sided die, there are 4 numbers less than 5. So, we can write this as a fraction.

\(\frac{4}{6}\) or we can write this fraction as \(\frac{2}{3}\)

So, the probability of rolling a number less than 5 is \(\frac{2}{3}\)

Answer:

1 unit, there's only a difference of 1 in the x values

Step-by-step explanation:

Answer:

12x - 8y

Step-by-step explanation:

Combine like terms.

10x - 5y + 2x -3y =

= 10x + 2x - 5y - 3y

= 12x - 8y

Answer:

140

Step-by-step explanation:

one exterior = the sum of two interior

Answer:

2x + 2.50

Step-by-step explanation:

A game costs 2.50 to start, which is a constant, The 2x is how many players will be playing.

Answer:

6.28

Step-by-step explanation:

½ × 3.47²

So our set of numbers is  5,8,b,9,4 . And we know the average is 7. So first, you have to add all the numbers in the set : 5+8+9+4 which gives you 26. We also know that to get the average of a set of numbers you have to add all the numbers and divide that sum by the how many numbers you have, in thsi case we have 5 numbers including b . So our equation now is : 26+b÷5=7. And if you plug in 9 for b you get 26+9÷5=7 and 26+9÷5  does equal 7 so therefore A is your answer

Answer:

B. 4

Step-by-step explanation:

the sum of two sides of a triangle should be longer than one other side

The probability that at least one cell phone is defective when selecting a random sample of 6 cell phones, with a defect probability of 0.13, can be calculated as 0.745.

To find the probability that at least one cell phone is defective, we can calculate the probability of the complement event (no defective cell phones) and subtract it from 1.

The probability of selecting a non-defective cell phone in one trial is (1 - 0.13) = 0.87.

Since the sample is selected randomly and independently, the probability of selecting all 6 cell phones as non-defective is \((0.87)^6\).

Therefore, the probability of at least one cell phone being defective is \((0.87)^6\) ≈ 0.745.

This means that there is a 74.5% chance of encountering at least one defective cell phone when randomly selecting 6 cell phones from Electronics Unlimited's manufacturing line with a defect probability of 0.13.

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12) There were about 557 principals in attendance. 13) Option A: The college will have about 480 students who prefer cookies. 14) Option C: bar graph, title favorite sport and the x axis labeled sport and the y axis.

The relationship between two quantities that are measured on the same scale and in the same units is known as a percentage. The relative size or magnitude of one thing in comparison to another is represented by proportions, which are frequently stated as ratios, fractions, or percentages. For instance, if there are 8 girls and 12 boys in a class, the girl-to-boy ratio is 8:12, or 2:3, which indicates that there are 3 guys for every 2 girls. Statistics, geometry, and physics are just a few of the mathematical and scientific disciplines that use proportions. Proportions are frequently used in statistics to describe the distribution of a population or a sample.

12) For the number of principals in conference we set up a proportionality with total people as follows:

We know that, 52 principals out of 70 people thus:

52/70 = x/750

Now,

x = (52/70) * 750

x = 557.14

Hence, we can predict that there were about 557 principals in attendance at the conference.

13) Given that, out of 225 students 27 prefer cookies thus,

27/225 = 0.12

That is 12% students like cookies.

Now, for the total number of students we have:

0.12 * 4000 = 480

Thus, option A: The college will have about 480 students who prefer cookies.

14) For the collected data the best representation is option C: bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44.

15) For the given description of the line plot the median is:

For Bus 47 = 16

For Bus 18 = 13

The faster bus is Bus 47, with a median of 16.

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The margin of error corresponding to the 95% confidence interval for a sample mean constructed from a sample of size 53 is 7.94.

Margin of error is defined as the degree of the sampling errors in statistics. It can be calculated using the formula below.

MOE = z x (SD / √n)

where MOE = margin of error

z = found by using a z-score table

SD = sample standard deviation = 29.5

n = sample size = 53

At 95% confidence level, the area in each tail of the standard normal curve is 2.5, and the cumulative area up to the second tail is 97.5.

(100 - 95) / 2 = 2.5

100 - 2.5 = 97.5

Find 0.975 in the z-table to get the value of z.

At p = 0.975, z = 1.96

Plug in the values to the formula and solve for the margin of error.

MOE = z x (SD / √n)

MOE = 1.96 x (29.5/√53)

MOE = 7.94

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From the graph and the given information, the value of the given function, fg(-3), is 9

From the question, we are to determine the value of the function, fg(-3).

First , we will determine the value of g(-3)

From the given information,

g(x) = 1/(2 + x)

Substitute x = -3 in the function to determine the value of g(-3)

g(-3) = 1/(2 + (-3))

g(-3) = 1/(2 - 3)

g(-3) = 1/-1

g(-3) = -1

Now,

fg(-3) = f(g(-3))

Thus,

fg(-3) = f(-1)

Now, we will determine the value of f(-1) from the given graph.

From the graph, we can read that the value of f(-1) is 9

Hence,

The value of fg(-3) is 9

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Answer: The range is  \(\{y \in \mathbb{R}\ | \ y \le -6\}\)

Explanation:

The parabola opens down, forming a "frowny face" in a way (just without the eyes). Or you can think of it as a hill or mountain. This means that the vertex (-3,-6) is at the top of that mountain. It's the highest point of that parabola.

The range is the set of all possible y values. We see that y = -6 is the largest it can get. So y = -6 or y is smaller than this. We would then write \(y \le -6\) to describe all the possible y values.

Therefore, the range is \(\{y \in \mathbb{R}\ | \ y \le -6\}\)

This translates to "y is a real number such that y is -6 or smaller".

So the second answer you wrote is close, but you forgot the "or equal to" portion of the inequality sign.

See below for a visual example of what's going on.

The probability density function is defined as the derivative of the cumulative distribution function. It represents the relative likelihood of a continuous random variable taking on a specific value. The total area under the probability density curve is always equal to 1.

For a continuous random variable X, the probability density function f(x) satisfies the following properties:

1. Non-negativity: f(x) ≥ 0 for all x.

2. Integrates to 1: The integral of the probability density function over the entire range of X is equal to 1:

  ∫[−∞, ∞] f(x) dx = 1

This integral represents the total area under the probability density curve, which must be equal to 1.

To calculate the probability of X falling within a certain interval [a, b], we can use the probability density function as follows:

P(a ≤ X ≤ b) = ∫[a, b] f(x) dx

This integral gives the probability that X takes on a value between a and b.

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K has the dimension of [T^2/L^2] to ensure dimensional correctness of the equation t = ka√(rt).

To determine the value of K in the equation t = ka√(rt), we can analyze the dimensions of each variable involved.

Dimensions:

t: time

a: acceleration

r: distance

k: constant

The dimension of time is denoted as [T], the dimension of acceleration is denoted as [L/T^2], and the dimension of distance is denoted as [L].

Let's break down the given equation and analyze the dimensions:

t = ka√(rt)

The square root of (rt) has the dimension √([L] * [L]) = [L].

Therefore, the dimensions of both sides of the equation become:

[T] = [L] * [L/T^2]

To make both sides of the equation compatible, the dimensions must be the same. We can see that the right side has a dimension of [L^2/T^2].

To match the dimensions on both sides, the constant k should have the dimension [T^2/L^2].

Therefore, K = [T^2/L^2].

In summary, K has the dimension of [T^2/L^2] to ensure dimensional correctness of the equation t = ka√(rt).

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Answer:

d

Step-by-step explanation:

Answer:

A. 45.23

Step-by-step explanation:

25.65 + 13.23 + 6.35 equals 45.23.

Hey there! I'm happy to help!

A step function is a function that looks like stairs when you graph it. Normally the end of one line will be graphed as an open circle (less or greater than, not equal to) while the other end would be a closed circle. This allows for a new line of the function to start directly above it without it not being a function (an input cannot have two outputs)

The function f(x)=4 is just a horizontal line as it has a slope of 0 (there is no x on the right side of the equation), so this doesn't resemble a step function.

Have a wonderful day and keep learning! :D

Answer:

The second and third expressions

nThe Middle East has been an important source of musical instruments for other parts of the world. Bagpipes, guitar, lute, oboe, tambourine, viols, and most zithers have a Middle Eastern origin.

The similarity is that both of them place value on the use of instrumental music. The South Asian and the Middle East is known to have a lot of musical instruments when compared to other parts of the world.

The musical Instruments that can be seen in Hindustani classical music are known to be the sitar, sarod, tambura, and others.

The instruments that is said to be used in Karnatak classical music are known to be the vina, mrdangam, violin and others

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In general, the limit will reach infinity or negative infinity when you take a limit and the denominator is equal to zero (depending on the sign of the function).

The number zero is not a real number. It is a mathematical notion used to symbolize an extremely huge value that is theoretically impossible to obtain. Limit solutions imply that the equation you are getting the limit of will continue to go in that direction indefinitely. The graph approaches but never touches the y-axis (represented by x = 0) because you have a vertical asymptote there. g(x) = 1/(x2) will continue to rise as you approach x = 0 from the right or left. You can picture it continuing upwards after it leaves the page. In other words, because g(x) keeps increasing indefinitely as x approaches 0, its limit is infinity.

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The value after double integration is 45.73

We can evaluate rectangle integrals in any order we like in Cartesian coordinates. We treat the other integral as a constant regardless of which integral we assess first; this is something to keep in mind while choosing the order of integration.

We want that x to be constant; we can easily integrate with respect to y. So we will evaluate y first. We get:

\(\int\limits^ \int\limits^ \frac{6x}{1+xy} dA=6\int\limits^6_0 \int\limits^1_0 {\frac{x}{1+xy} } \, dydx\)

\(or, 6\int\limits^6_0 {[In(1+xy)}_{0} ^{1} ]} \, dx\)

\(or, 6\int\limits^6_0 {In(1+x)} } \, -In 1dx\)

\(or, 6\int\limits^6_0 {In(1+x)} } \, dx\)

\(or,[(1+x)In(1+x)-(1-x)]^{6} _{0}\)

\(or,[7In7-In1-7+1]\\or,6(7In7-6)\\or,45.73\)

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`To get the total number of iterations in a nested loop, add the number of iterations in the inner loop to the number in the outer loop, Which is a False statement.

Loops inside the loops are known to be "nested".These nested loops are used for working with two dimensions which are printing stars in rows and columns.

When a loop is nested inside another loop, the inner loop will run many times inside the outer loop. In every iteration of the outer loop, the inner loop will be re-started.

The inner loop should be finished with all of its iterations before the outer loop can continue to its next. In a nested loop, the external loop goes through all of its iterations for each iteration of the inner loop.

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