Let g(x)=x²-5 and h(x) = 3x + 2. Find (hog)(x)

If x and y are independent, then the covariance between x and y, cov(x, y), is equal to 0.

Covariance measures the linear relationship between two random variables. If x and y are independent, it means that the occurrence of one variable does not affect the occurrence of the other. In other words, there is no linear relationship between x and y.

The computational formula for covariance is given by:

cov(x, y) = E[(x - E[x])(y - E[y])],

where E[x] and E[y] are the expected values of x and y, respectively.

If x and y are independent, it implies that E[x] and E[y] are also independent, and therefore the term (x - E[x])(y - E[y]) will equal 0 for all possible values of x and y. Consequently, the expected value of this term will also be 0.    

Since cov(x, y) is defined as the expected value of (x - E[x])(y - E[y]), and this term is 0, it follows that cov(x, y) must be equal to 0.

Hence, if x and y are independent, their covariance cov(x, y) is always 0, indicating that there is no linear relationship between the variables.

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Step-by-step explanation:

Quadratic Zeros: One Only

Priya Ravindran

What are the zeros of f(x) = x² - 10x+25?

OA. x= -5 and x = 5

O B. x = 5 only

OC. x = -5 and x = 10

O D. x = -5 only

We can find the zeros of the quadratic function f(x) = x² - 10x + 25 by setting f(x) equal to zero and solving for x:

x² - 10x + 25 = 0

This quadratic equation can be factored as:

(x - 5)² = 0

Using the zero product property, we can see that this equation is true when:

x - 5 = 0

So the only zero of f(x) is x = 5.

Therefore, the correct answer is option B: x = 5 only.

Priya Ravindran

In a newspaper, it was reported that the number of yearly robberies in Springfield in 2013 was 100, and then went down by 11% in 2014. How many robberies were there in Springfield in 2014?

If there were 100 robberies in Springfield in 2013 and the number of robberies went down by 11% in 2014, we can calculate the number of robberies in 2014 as follows:

Number of robberies in 2014 = Number of robberies in 2013 - 11% of Number of robberies in 2013

Using this formula, we get:

Number of robberies in 2014 = 100 - 0.11(100)

Number of robberies in 2014 = 100 - 11

Number of robberies in 2014 = 89

Therefore, there were 89 robberies in Springfield in 2014.

Answer:

The total profit made when a person buys an item for $2.25 and then sells the item for $2.25.

Step-by-step explanation:

The item is bought for $2.25 and sold for the same rate. There is no profit.

        Final value is 0.

Answer:

slope 1 ; y int -3

slope -1 ; y int 3

slope 3 ; y int -1

slope -3 ; y int 1

Step-by-step explanation:

slope int formula is y=mx+b

The slope is mx and the y int is B

Answer:

x-3=y matches to m=1, b=-3

-x+3=y matches to m=-1, b=3

y=3x-1 matches to m=3, b=-1

y=1-3x matches to m=-3, b=1

Step-by-step explanation:

y=mx+b

m is the slope

b is the y-intercept

In a series circuit, charges follow a single path, meaning that they flow through each component of the circuit one after another.

What is series circuit?

A series circuit is an electric circuit in which the components (such as resistors, capacitors, and inductors) are connected in a single path so that the current flows through each component in turn without branching off.

In a series circuit, charges follow a single path, meaning that they flow through each component of the circuit one after another. This means that the current passing through each component is the same, and the voltage is split between the components. If one component fails, the circuit is broken, and no current can flow.

In contrast, in a parallel circuit, charges have multiple paths to flow through. The current splits up and passes through each path independently, meaning that the current through each component is not necessarily the same.

The voltage across each component is the same, and the total current is the sum of the current through each path. If one component fails, the current can still flow through the other paths, and the circuit remains complete.

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Answer:

75 + 17 = 92

Step-by-step explanation:

Given an LTI system that has an output y = 2te^-ul for the input x(t) = -(t). Here, e^-ul is the decay constant and is a real positive constant. The impulse response of the system can be found by considering the impulse input x(t) = δ(t).

The output of the system with an impulse input is given by y(t) = h(t), where h(t) is the impulse response of the system.We have,x(t) = -(t)..........(1)Applying derivative on both sides of the above equation, we get,y(t) = 2te^-ul, Applying derivative on both sides of the above equation, we get,

Plot of frequency response and Impulse response of the system Hence, the plot of frequency response and the impulse response of the LTI system is shown in the figure below:, the frequency response is given by H(jω) = (2/(-jω + ul)^2) where ω is the angular frequency. The impulse response of the system is given by h(t) = (2/ul^2)t.e^-ul.

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Answer:

It will be the 1st one that is The triangles are similar by AA

I can explain the process of finding the test statistic for testing the equality of variances for three brands. Please note that the exact calculation depends on the specific statistical test you are using.

To test the equality of variances among three brands, you can use the Bartlett's test or Levene's test. Here, I will explain the steps for performing Levene's test:

Step 1: Set up hypotheses

- Null hypothesis (H0): The variances of the three brands are equal.

- Alternative hypothesis (HA): The variances of the three brands are not equal.

Step 2: Calculate the test statistic

Levene's test statistic is based on the absolute deviations of each observation from the group mean. The test statistic is given by:

\[ W = \frac{(N-k)}{(k-1)} \times \frac{\sum_{i=1}^{k}N_i(\bar{Z_i} - \bar{Z})^2}{\sum_{i=1}^{k}\sum_{j=1}^{N_i}(Z_{ij} - \bar{Z_i})^2}\]

where:

- N is the total number of observations.

- k is the number of groups (in this case, three brands).

- Ni is the number of observations in the i-th group.

- Zi is the absolute deviation of each observation in the i-th group from the group mean.

- Z is the overall mean of all observations.

Step 3: Conclusion

Compare the calculated test statistic with the critical value from the appropriate distribution (e.g., F-distribution). If the calculated test statistic is greater than the critical value, you would reject the null hypothesis and conclude that the variances are not equal. Conversely, if the calculated test statistic is less than the critical value, you would fail to reject the null hypothesis and conclude that there is not enough evidence to suggest a difference in variances among the three brands.

Remember to round your answer to three decimal places as requested.

It's important to note that without specific data, I can't provide an actual calculation or conclusion. The above explanation provides a general overview of the steps involved in testing the equality of variances for three brands.

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Using the rule of exponents, the expression is 12x^4 × 35y^5

The rules of exponents are given as:

Given the expression;

3x^3 * 7y^2 * 4x * 5y ^3

collect the like bases

3x³ × 4x × 7y² × 5y³

Add the powers

12x^3 + 1 × 35^ 2 + 3

We then have;

12x^4 × 35y^5

Thus, using the rule of exponents, the expression is 12x^4 × 35y^5

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Answer:

c=15+25x

Step-by-step explanation:

From the information given, you can say that the total amount Tom's Landscaping charges for a job would be equal to the flat fee plus the result of multiplying the charge per hour for the number of hours and this would be:

c=y+25x (1), where:

c is the total cost

y is the flat fee

x is the number of hours

Now, as you know that Tom charged a customer $90 for a job that required 3 hours, you can replace c with 90 and x with 3 and solve for y to find the flat fee:

90=y+25(3)

90=y+75

90-75=y

y=15

Finally, as you know that the flat fee is 15, you can replace this value in (1) to establish the equation that would calculate the total amount that Tom's Landscaping charges for a job that requires x hours of work:

c=15+25x

The value of this golden ratio = 1/2 (1 + √5) = 1.618

Ratio:

Majority of the explanations for ratio and proportion use fractions. A ratio is a fraction that is expressed as a:b, but a proportion says that two ratios are equal. In this case, a and b can be any two integers. The foundation for understanding the numerous concepts in mathematics and science is provided by the two key notions of ratio and proportion. We apply the concepts of ratio and proportion every day, for example, while dealing with money in business or when preparing any meal, etc. Students occasionally struggle to understand the difference between ratio and proportion.

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Answer:

The answer is ≈3 to the nearest whole number

Step-by-step explanation:

using SOH CAH TOA

BCA

sin0=opp/hyp

sin0=7.9/11

0=sin‐¹(7.9/11)

0=46 to the nearest degree

<A=<D

so,<EDF=46°

tan0=adj/hyp

tan46=x/3.3

x=tan46×3.3

x=3 to the nearest whole number

The equivalent expression of this 19 - 6(-k + 4) will be 6k + 5.

Given that:

Expression, 19 - 6(-k + 4)

The equivalent is the expression that is in different forms but is equal to the same value.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less complicated.

Simplify the expression, then we have

⇒ 19 - 6(-k + 4)

⇒ 19 + 6k - 24

⇒ 6k - 5

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The instantaneous acceleration at any time t is given by 10t. The limit definition of a derivative is true because it allows us to find the instantaneous rate of change of a function at a specific point.

To use the limit definition of a derivative to calculate instantaneous acceleration, we need to find the derivative of the velocity function with respect to time. The derivative of velocity gives us acceleration.

The limit definition of a derivative is given by:

f'(x) = lim (h→0) [f(x+h) - f(x)] / h

To calculate instantaneous acceleration, we substitute the velocity function, v(t), into the limit definition. Let's say v(t) = 5t^2.

Using the limit definition, we have:

a(t) = lim (h→0) [v(t+h) - v(t)] / h

Substituting v(t) = 5t^2, we get:

a(t) = lim (h→0) [5(t+h)^2 - 5t^2] / h

Expanding and simplifying:

a(t) = lim (h→0) [10th + 5h^2] / h

Now, we can cancel out the h term:

a(t) = lim (h→0) 10t + 5h

Taking the limit as h approaches 0, we get:

a(t) = 10t

Therefore, the instantaneous acceleration at any time t is given by 10t.

The limit definition of a derivative is true because it allows us to find the instantaneous rate of change of a function at a specific point. By taking the limit as the change in input approaches zero, we are able to approximate the exact rate of change at that point. This concept is fundamental to calculus and is used in various applications such as physics, engineering, and economics.

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The arithmetic mean of the two fractions is 68/35.

The arithmetic mean can be calculated using the mentioned formula -

Arithmetic mean = sum of the numbers / frequency of numbers.

Sum of the fractions = 2/5 + 4/7

Performing division of the two numbers

Sum of the fractions = (14 + 20)/35

Sum of the fractions = 34/35

Arithmetic mean = (34/35)/2

Rewriting the average

Arithmetic mean = (34 × 2)/35

Performing multiplication on Right Hand Side of the equation

Arithmetic mean = 68/35

Hence, the Arithmetic mean is 68/35.

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The beetle population, growing linearly, has an explicit formula P(n) = 3 + 10n, and it will take 18 weeks for the population to reach 183.

(a) To find an explicit formula for the beetle population after n weeks, we can use the information given in the problem. Since the growth model is linear, we can assume that the population increases by a constant amount each week.

Let's denote the population after n weeks as P(n). We know that P(0) = 3 (initial population) and P(10) = 103 (population after 10 weeks).

Since the population increases by a constant amount each week, we can find the growth rate (or increase per week) by taking the difference in population between week 10 and week 0, and dividing it by the number of weeks:

Growth rate = (P(10) - P(0)) / 10 = (103 - 3) / 10 = 100 / 10 = 10

Therefore, the explicit formula for the beetle population after n weeks can be written as:

P(n) = P(0) + (growth rate) * n

P(n) = 3 + 10n

(b) To find how many weeks it will take for the beetle population to reach 183, we can set up an equation using the explicit formula and solve for n:

P(n) = 183

3 + 10n = 183

Subtracting 3 from both sides:

10n = 180

Dividing both sides by 10:

n = 18

Therefore, it will take 18 weeks for the beetle population to reach 183.

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We can solve this system of the linear equation as follows:

Substituting the value of x = 1/5 in the next equation, we have the value for y:

Then, we have that the solutions for this system are x = 1/5 and y = 6.

The expected variance of red balls chosen is 2/3 from the urn.

Six red balls and four green balls are in an urn.

Till a urn is empty, we take balls out of it one at a time without replacing them and noting their order of the colors.

The, the variance is found as-

Variance(X,Y) = E(XY) - E(X).E(Y).E(XY)

E(XY)  = 25×(6/10)(4/9)

E(X) = 5×(6/10)

E(Y) = 5×(4/10)

Thus,

Variance(X,Y) = 25(6/10)(4/9) - 25(6/10)(4/10)

Variance(X,Y) = 2/3

Thus, the variance for choosing red balls is 2/3.

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Answer:

\( \sqrt[3]{2y} = 6 - 4\)

2y=2³

2y=8

y=4

Answer:

line: a line that is straight, thin, and never ending.

line-segment: a line but instead of being endless it has two dots at the end stopping it.

ray: only has ONE ending instead of two (so one way doesn't end.)

angle: an angle is the figure formed by two rays.

plane: a flat 2d surface that extends infinitely.

straight angle:  the angle rays face in the opposite directions.

right angle: 90 degree angle.

acute angle: an angle that's greater than 0 and less than 90.

obtuse angle: bigger than 90 but less than 180.

Two Angles are Complementary: the two angles add up to 90.

Two Angles are supplementary: they are supplementary when adding up to 180.

intersecting lines: lines crossing paths.

parallel lines: lines that never touch .

perpendicular lines: similar to intersecting but they make a right angle.

Vertical Angles: angles that are opposite when two straight lines intersect

Bisector: a straight line that bisects an angle or a line segment.

Perpendicular Bisector: a line, line segment, or ray that is perpendicular to the middle.

Coplanar: set of points, line segments, rays, et cetera that are in the same plane.

Non-Coplanar: not in the same plane

Collinear: If two or more than two points are on a line close or far from each other, then they are considered collinear.

Non-Collinear: Non-collinear means it doesn't lie on a common line.

Skew Lines: (3d geometry) lines that don't intersect but are parallel  

Opposite Ray: two rays that have the same end and go in opposite directions.

Vertex: a point where more than one curves, edges, or lines meet.

Parallel Planes: planes that NEVER touch.

Intersecting Planes: planes that meet.

that it is important for likert-type scale response choices to be balanced at the ends of the response continuum. This means that there should be an equal number of positive and negative response options to avoid any bias or skew in the results.

An explanation for this is that if there are too many positive or negative response options, respondents may feel pressured to choose a certain option even if it doesn't accurately reflect their true opinion. This can result in inaccurate data and can skew the results of the survey or study.

balancing the response choices on a likert-type scale is crucial for obtaining accurate and unbiased data. By having an equal number of positive and negative options, respondents are more likely to provide honest and accurate responses.

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The area between z=1.1 and z=2.1 is approximately 0.982 - 0.864 = 0.118, rounded to three decimal places.

To find the area below z=1.04 for an Upper N(0,1) density, you will need to use the standard normal distribution table or a calculator with a z-table function. Here are the steps:

1. Locate the value of z=1.04 in the table or use the calculator's function.
2. Find the corresponding area value (which represents the probability or percentage of values below z=1.04).

The area below z=1.04 is approximately 0.851, rounded to three decimal places.

(b) To find the area above z=-1.4 for an Upper N(0,1) density, follow these steps:

1. Locate the value of z=-1.4 in the table or use the calculator's function.
2. Find the corresponding area value.
3. Since we need the area above z=-1.4, subtract the area value found in step 2 from 1.

The area above z=-1.4 is approximately 1 - 0.0808 = 0.919, rounded to three decimal places.

(c) To find the area between z=1.1 and z=2.1 for an Upper N(0,1) density, follow these steps:

1. Locate the values of z=1.1 and z=2.1 in the table or use the calculator's function.
2. Find the corresponding area values for both z=1.1 and z=2.1.
3. Subtract the area value of z=1.1 from the area value of z=2.1 to find the area between them.

The area between z=1.1 and z=2.1 is approximately 0.982 - 0.864 = 0.118, rounded to three decimal places.

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If Sabia and Arlan bought 45 books for rs 30, then at the rate of rs 24, they can buy 34 books.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

It is given that, Sabia and Arlan bought 45 books for rs 30, then at the rate of rs 24, how many books they can buy,

Rs 30 = 45 book

Rs 30 = 45

Rs 1 = 45 / 30

Rs 24 = 3/2 × 24

Rs 24 = 34 books

Thus, if Sabia and Arlan bought 45 books for rs 30, then at the rate of rs 24, they can buy 34 books.

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To find the volume generated by rotating the region bounded by the curves y = x, y = 0, and x = 1 about the y-axis, we can use the method of cylindrical shells.

First, let's consider a vertical strip of width Δy and height y within the region. This strip can be thought of as a cylindrical shell.

The radius of the cylindrical shell is given by the distance from the y-axis to the curve y = x, which is simply x. Since we are rotating about the y-axis, the radius is y.

The height of the cylindrical shell is Δy, which is the width of the strip.

The circumference of the cylindrical shell is given by 2πy, and the volume of the shell is the product of the circumference, height, and thickness.

Therefore, the volume of the entire solid can be obtained by integrating the volume of all the cylindrical shells over the range of y-values from 0 to 1.

V = ∫[0,1] 2πy Δy

Evaluating the integral gives us the volume of the solid generated by rotating the region about the y-axis.

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Answer:

The numbers are:

5, 12 and 4

Step-by-step explanation:

a + b + c = 21       Eq. 1

b = 2a +2             Eq. 2

b = 3c                   Eq. 3

From Eq. 2:

b - 2 = 2a

(b-2)/2 = a              Eq. 4

From Eq. 3:

c = b/3                     Eq. 5

Replacing Eq. 4 and Eq. 5 in Eq. 1:

(b-2)/2 + b + b/3 = 21

3(b-2)/6 + 6b/6 + 2b/6 = 126/6

3(b-2) + 6b + 2b = 126

(3*b + 3*-2) + 8b = 126

3b - 6 + 8b = 126

11b = 126 + 6

11b = 132

b = 132/11

b = 12

from Eq. 4

(b-2)/2 = a

(12-2)/2 = a

10/2 = a

a = 5

from Eq. 5

c = b/3

c = 12/3

c = 4

Check:

from Eq. 1

a + b + c = 21

5 + 12 + 4 = 21