You are given two functions, f: RR, f (x) = 3x and g:R+R, 9(r) = x+1 a. Find and record the function created by the composition of f and g, denoted gof. b. Prove that your recorded function of step (a.) is both one-to-one and onto. That is prove, gof:R R; (gof)(x) = g(f (r)). is well-defined where indicates go f is a bijection. For full credit you must explicitly prove that go f is both one-to-one and onto, using the definitions of one-to-one and onto in your proof. Do not appeal to theorems. You must give your proof line-by-line, with each line a statement with its justification. You must show explicit, formal start and termination statements as shown in lecture examples. You can use the Canvas math editor or write your math statements in English. For example, the statement to be proved was written in the Canvas math editor. In English it would be: Prove that the composition of functions fand g is both one-to-one and onto.

The force F = r^2k(r^) is not conservative because its curl is nonzero. The force is central because it depends only on r and acts along the radial direction. Since it is not conservative, there is no potential energy function V(r) associated with this force

To determine whether the force F = r^2k(r^) is conservative and central, let's analyze its properties.

A force is conservative if it satisfies the condition ∇ × F = 0, where ∇ is the gradient operator. In Cartesian coordinates, the force can be written as F = Fx i + Fy j + Fz k, where Fx, Fy, and Fz are the components of the force in the x, y, and z directions, respectively. The curl of F is given by:

∇ × F = (∂Fz/∂y - ∂Fy/∂z)i + (∂Fx/∂z - ∂Fz/∂x)j + (∂Fy/∂x - ∂Fx/∂y)k.

Calculating the components of F = r^2k(r^):

Fx = 0, since there is no force component in the x-direction.

Fy = 0, since there is no force component in the y-direction.

Fz = r^2kr^.

Taking the partial derivatives, we have:

∂Fz/∂x = ∂/∂x (r^2kr^) = 2rkr^2(∂r/∂x) = 2rkr^2(x/r) = 2xkr^3.

∂Fz/∂y = ∂/∂y (r^2kr^) = 2rkr^2(∂r/∂y) = 2rkr^2(y/r) = 2ykr^3.

Substituting these values into the curl equation, we get:

∇ × F = (2ykr^3 - 2xkr^3)k = 2k(r^3y - r^3x).

Since the curl of F is not zero, ∇ × F ≠ 0, we conclude that the force F = r^2k(r^) is not conservative.

Now let's determine if the force is central. A force is central if it depends only on the distance from the origin (r) and acts along the radial direction (r^).

For F = r^2k(r^), the force is indeed central because it depends solely on r (the magnitude of the position vector) and acts along the radial direction r^. Hence, it can be written as F = Fr(r^), where Fr is a function of r.

Since the force is not conservative, it does not possess a potential energy function. In conservative forces, the potential energy function V(r) can be defined, and the force can be expressed as the negative gradient of the potential energy, i.e., F = -∇V. However, since F is not conservative, there is no potential energy function associated with it.

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Answer:

40 magazines.

Step-by-step explanation:

She gets $200 from the book store the week she needs $280 for the school trip. Therefore, she only needs $80 in order to go.

$80 ÷ $2 = 40

40 magazines.

Answer:

40 is the answer.....  your welcome

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

When we talk of the range, that means the difference between the highest and the lowest figure in the data set

The mean refers to the sum of the values in the data set divided by the count of the value in the data set.

let’s take a look at data set option A;

mean = [4(14) + 2(7)]/6 = (56 + 14)/6 = 70/6 which is definitely not 14 which makes the option wrong

Let’s take a look at option C

mean = {13(3) + 15)3)}/6 = (39 + 45)/6 = 84/6 = 14

While the range is 15-13 = 2 which does not make it right too

Now, a look at option D

mean = (13 + 12 + 15 + 15 + 11 + 18)/6 = 84/6 = 14

range = 18-11 = 7 (highway number in the set minus lowest number)

This makes option D our answer

Answer:

They are 12, 13, 14 and 15.

Step-by-step explanation:

If the least integer is x, then:

x + x + 1 + x + 2 + x + 3 = 54

4x + 6 = 54

4x = 48

x = 12.

The expected value of z, e(z), is 12 and the variance of z, v(z), is 90. The expected value of the random variable z, defined as z = 2x - 3y + 5, can be determined using the properties of expected values. The value of e(z) is calculated as 2e(x) - 3e(y) + 5.

Similarly, the variance of the random variable z, denoted as v(z), can be determined using the properties of variances. The value of v(z) is calculated as 2^2v(x) + (-3)^2v(y), since x and y are independent random variables.

Given e(x) = 8, e(y) = 3, v(x) = 9, and v(y) = 6, we can calculate the expected value and variance of z.

e(z) = 2e(x) - 3e(y) + 5

    = 2(8) - 3(3) + 5

    = 16 - 9 + 5

    = 12.

Therefore, the expected value of z, e(z), is 12.

v(z) = 2^2v(x) + (-3)^2v(y)

    = 2^2(9) + (-3)^2(6)

    = 4(9) + 9(6)

    = 36 + 54

    = 90.

Therefore, the variance of z, v(z), is 90.

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Answer:

see below

Step-by-step explanation:

in words f_0=0 and f_1=1

and f_n=f_(n-1)+f_(n-2)

The probability that Kwan randomly selects a sugar cookie from the bag, eats it, and then randomly selects another sugar cookie is 12 / 22C2.

The probability that Kwan randomly selects a sugar cookie from the bag, eats it, and then randomly selects another sugar cookie can be calculated by dividing the number of ways to select two sugar cookies by the total number of ways to select any two cookies.
Step-by-step explanation:
1. Determine the number of ways to select two sugar cookies: There are 4 sugar cookies in the bag, so the number of ways to select the first sugar cookie is 4. After eating the first sugar cookie, there are 3 sugar cookies left, so the number of ways to select the second sugar cookie is 3. Therefore, there are 4 * 3 = 12 ways to select two sugar cookies.
2. Determine the total number of ways to select any two cookies: There are a total of 6 + 5 + 4 + 7 = 22 cookies in the bag. So, the number of ways to select any two cookies is calculated by choosing 2 cookies out of 22, which is denoted as 22C2.
3. Calculate the probability: To find the probability, divide the number of ways to select two sugar cookies by the total number of ways to select any two cookies.
  Probability = (Number of ways to select two sugar cookies) / (Total number of ways to select any two cookies)
  Probability = 12 / 22C2
So, the probability that Kwan randomly selects a sugar cookie from the bag, eats it, and then randomly selects another sugar cookie is 12 / 22C2.

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So, by fraction, number of times he will have to fill the smaller measuring cup to equal 1 3/4 cups is 7 times.

Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.

Glass holds = 1(3/4) cups of water

One cup holds = 1/4 cup of water

number of 1/4 cups needed to fill the 1(3/4) cups of water glass.

\(\frac{1}{4xC}=1(\frac{3}{4})\\\\\frac{C}{4} = \frac{7}{4} \\\\C=\frac{7}{4x4}\\ \\C= 4\)

number of times the smaller cup fills the glass is 7.

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Complete Question: Quentin is filling a glass that holds 1 3/4 cups of water. he is using 1/4 cup measuring cup. how many times will he have to fill the smaller measuring cup to equal 1 3/4 cups?

Answer:

yes it's rotated 180 degree angle

Answer:

3

Step-by-step explanation:

Step 1:

x + 5 = 8

Step 2:

x = 8 - 5

Answer:

x = 3

Hope This Helps :)

Answer:

x = 3

Step-by-step explanation:

Step 1: Write equation

x + 5 = 8

Step 2: Subtract 5 on both sides

x = 3

Step 3: Check

Plug in x to verify if it's a solution.

3 + 5 = 8

8 = 8

If Liam buys a laptop for Rs 840 (including 15% VAT) then the price of the laptop without VAT could be Rs 730.

Let the price of the laptop be 100 rupees.

After including 15% VAT, the price of the laptop would be 115 rupees.

The original price = (100 × 840)/115 = 730.

Hence the price of the laptop could be Rs 730.

This problem is the concept of discount and tax. In mathematics, the tax calculation is related to the selling price and income of taxpayers. It is a charge imposed by the government on the citizens for the collection of funds for public welfare and expenditure activities. There are two types of taxes: direct tax and indirect tax. In this lesson, we will study the tax computation when the selling price or price before tax is given. We calculate tax on a product by multiplying the tax rate with the product's net selling price.

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Answer:

x=0 or x=pi / x=πn

Step-by-step explanation:

cos2x + 3 = 4

subtract 3 from both sides

cos2x = 1

take the inverse cos/arccos of both sides

arccos(cos2x) = arccos(1)

2x=0 or 2x=2pi

divide both sides by 2

x=0 or x=pi

beyond (0,2pi) for every possible answer you should do x=(pi)n since any multiple of pi gives you the same answer

Answer:

(0 , 25)

Step-by-step explanation:

y = 4x + 25 is our equation.

The formula used is y = mx + b where:

m = slope

x = independent variable

b = constant/y - intercept

Based on that knowledge we can tell that 25 is our y intercept.

The correct answer is False because, If the sample size is large enough (n greater than or equal to 30) the sampling distribution is approximately normal regardless of the shape of the population.

The sample fraction, often called the "p-hat", is the ratio of the number of sample successes to the size of the sample. The standard deviation of (p) decreases as the sample size n increases. This is because n is included in the denominator of the standard deviation formula. That is, (p has) has fewer variables for larger samples. The P-hat (must be a lowercase p with a caret (^) circumflex) indicates the percentage of the sample (this is the x-bar, the average of the samples).

A p-hat (proportion) sampling distribution is a collection of equal-sized repeated sample proportions drawn from the same population to represent it. According to the central limit theorem, the sampling distribution of p-hat is approximately normally distributed for large sample sizes.

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Answer:

27.7 (rounded)

Step-by-step explanation:

Answer:

im on the same one if i get it right i will comment and tell u k?

Step-by-step explanation:

kk

Answer:

A

Step-by-step explanation:

The half-life of a radioactive material is the time it takes for half of its atoms to decay. The half-life of the given radioactive material is approximately 4.5 hours.

To calculate the half-life of the given radioactive material, we need to use the formula:
Nt = N0 \((1/2)^{(t/T)}\)
Where Nt is the number of radioactive atoms at time t, N0 is the initial number of radioactive atoms, T is the half-life of the material, and t is the time elapsed since the initial measurement.
Using the given data, we can set up two equations:
1450 = N0 \((1/2)^{(0/T)}\)
380 = N0 \((1/2)^{(8/T)}\)
Dividing the second equation by the first equation, we get:
380/1450 = \((1/2)^{(8/T)} / (1/2)^{(0/T)}\)
Simplifying this expression, we get:
380/1450 = \((1/2)^{(8/T)}\)
Taking the natural logarithm of both sides, we get:
ln(380/1450) = ln\((1/2)^{(8/T)}\)
Simplifying this expression, we get:
T = -8ln(380/1450)/ln(1/2) ≈ 4.5 hours

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Answer:

Rest of the part will be = x - 5x/10- x/10

solution will be 4x/10 i.e 4/10 part of the garden

Step-by-step explanation:

Let the sum total of parts of garden be x

If it is divided into 10 equal parts then

one part will be equal to x/10

Given carrots are planted on 5/10 of the garden

parts on which garden is planted = 5/10 * total part of garden = 5x/10

Given peas are planted on 1/10 of the garden

parts on which peas are is planted = 1/10 * total part of garden = x/10

On rest of the part corn is planted.

Rest of the part will be = total parts of garden - part on which carrots are planted - part on which carrots are planted

Rest of the part will be = x - 5x/10- x/10 = (10x-5x-x)/10 = 4x/10

Model will be

Rest of the part will be = x - 5x/10- x/10

solution will be 4x/10 i.e 4/10 part of the garden

The doctor is deciding whether or not to provide treatment to use a null or an alternative hypothesis.

Also test's power would drop and the likelihood of a Type II error would rise.

The null hypothesis or the alternative hypothesis are two statements that make up the hypothesis test. The test statistic and critical value are two more components, and they together give us the P-value or the rejection region (), respectively.

An analyst performs hypothesis testing on a statistical sample with the intention of demonstrating the plausibility of a null hypothesis. A sample of the people being studied is measured and examined by statistical analysts in order to test a hypothesis.

The test's power would drop and the likelihood of a Type II error would ;rise.

Hence, the probability of a Type II error would increase and the power of the test would decrease.

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We have proven that ∠JKM = ∠NKL.

To prove that ∠JKM = ∠NKL,

       J

      / \

     /   \

    /     \

   K-------N

  / \       / \

 /    \     /     \

/      \   /         \

M-------K-------L

To prove that JKM is congruent to NKL, we need to show that all corresponding sides and angles are equal.

First, we know that KM bisects JKN, so angle JKM is congruent to angle NKM (by the angle bisector theorem). Similarly, KN bisects MKL, so angle LKN is congruent to angle MKN.

Also, we know that JK is equal to KN (by the definition of a bisector), and KM is equal to ML (since KM bisects the side KL).

we will use the given information that KM bisects ∠JKN and KN bisects ∠MKL.
Since KM bisects ∠JKN, it means that it divides ∠JKN into two equal angles.

So, ∠JKM = ∠KJN. (Definition of angle bisector)
Similarly, since KN bisects ∠MKL, it divides ∠MKL into two equal angles.

So, ∠KJN = ∠NKL. (Definition of angle bisector)
Now, we can use the transitive property of equality: if ∠JKM = ∠KJN and ∠KJN = ∠NKL, then ∠JKM = ∠NKL.

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Answer:

3811

Step-by-step explanation:

37X100= 3700

37X3=111

so 3700+ 111= 3811

Players no longer need commitment strategies to reach a mutually-beneficial cooperative equilibrium when games are repeated.

This is an exercise related to Game Theory.

The extended form is typically used to depict repeated games, commonly referred to as supergames, in game theory since they occur repeatedly across time.

The potential of collaborating means that we may choose to compromise in order to continue earning a payout over time, knowing that if we do not fulfill our part of the bargain, our adversary may decide not to either.

As contrast to one-shot games, recurring games provide a new set of incentives.

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The chi-square test of independence is typically used to analyze the relationship between two variables when both variables are nominal, the two variables have been measured on different individuals and the observations on each variable are within-subjects in nature. The answer is  D. all of the above

The chi-square test of independence is a statistical test that is used to determine if there is a significant association between two categorical variables. It is commonly used when both variables are nominal, meaning they consist of categories or groups rather than numerical values.

When conducting the chi-square test of independence, the data is typically collected by measuring the two variables on different individuals or units.

For example, researchers may collect data on the gender (nominal variable) and political affiliation (nominal variable) of different individuals and analyze whether there is a relationship between the two variables.

The test examines the observed frequencies of the different categories in a contingency table and compares them to the expected frequencies under the assumption of independence. If the observed and expected frequencies significantly differ, it suggests that there is an association between the two variables.

Therefore, the chi-square test of independence is applicable when both variables are nominal and the data is collected on different individuals. This allows researchers to investigate the relationship between the variables and determine if they are associated or independent.

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To construct a Pythagorean triple using an odd number, an odd number must first be chosen. Here 5, 12, and 13 form a Pythagorean triple.

To generate Pythagorean triples using an odd number, follow these steps:

Choose any odd number, say n.

Calculate (n^2-1)/2 and n. These two numbers will form a Pythagorean triple.

Check if the numbers obtained in step 2 are indeed a Pythagorean triple. The two numbers should satisfy the Pythagorean theorem, i.e., a^2 + b^2 = c^2, where a and b are the smaller numbers, and c is the largest number.

If the numbers in step 2 do not form a Pythagorean triple, choose a different odd number and repeat the process.

For example, let's choose the odd number 5:

(n^2-1)/2 = (5^2-1)/2 = 12

n = 5

Now, we can check if 5, 12, and 13 form a Pythagorean triple:

5^2 + 12^2 = 13^2

25 + 144 = 169

Therefore, 5, 12, and 13 form a Pythagorean triple.

We can repeat this process with different odd numbers to generate more Pythagorean triples.

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Answer:

the ansewr is b

Step-by-step explanation:

Okay, let's solve this step-by-step:

1) The equations for the two curves are:

r = sin(θ)  and  r = cos(θ)

2) We need to find the intersection points of these two curves. This is done by setting them equal and solving for θ:

sin(θ) = cos(θ)

=>  θ = π/4

3) The intersection points are (1, π/4) and (1, 3π/4). The region lies between θ = π/4 and θ = 3π/4.

4) To find the area, we use the formula:

A = ∫θ=3π/4 θ=π/4 2πr dθ

5) Substitute r = sin(θ) or r = cos(θ):

A = ∫θ=3π/4 θ=π/4 2πsin(θ) dθ

= 2π ∫θ=3π/4 θ=π/4 sin(θ) dθ

6) Integrate:

A = 2π(cos(θ) - sin(θ) )|π/4  to  3π/4

= 2π(0 - 1) = 2π

7) Therefore, the area of the region is 2π square units.

Let me know if you have any other questions!

Answer:

$48

Step-by-step explanation:

23+25=48

The value of the probability P(AnB) will be 0.11

The given parameters are:

P(A)=0.43, P(B)=0.55 and P(A/B)=0.23

we have A, B be defined on the same sample space S

The value of P(AnB) is calculated using:

P(AnB) = P(a|b) * P(b)

Substitute the known values;

P(AnB) = 0.55 * 0.23

Evaluate the product;

P(AnB) = 0.11

Hence, the value of the probability P(AnB) is equal to 0.11

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The complete question is;

Let A, B be defined on the same sample space S such that P(A)=0.43, P(B)=0.55 and P(A/B)=0.23, find the value of P(ANB).

Answer:

m∠FAL = 119°

Step-by-step explanation: