f(x)=3-2x g(x)=x+1\4 find fg(x) note: 4 is denominator for x+1​

The dot product of two vectors u and v is given by the formula u · v = |u||v|cos(theta). The angle theta between the vectors u and v is approximately 2.356 radians or 135 degrees.

1. The dot product of two vectors u and v is defined as u · v = |u||v|cos(theta), where |u| and |v| represent the magnitudes of vectors u and v, respectively, and theta is the angle between the vectors.

2. In this case, the vectors u = 8i + 4j + k and v = 4i - 8j are given. To calculate the dot product, we need to find the magnitudes of u and v. The magnitude of a vector is calculated using the formula |u| = sqrt(u₁² + u₂² + u₃²), where u₁, u₂, and u₃ are the components of the vector.

3. For vector u, the magnitude |u| = sqrt(8² + 4² + k²) = sqrt(64 + 16 + k²) = sqrt(80 + k²). For vector v, the magnitude |v| = sqrt(4² + (-8)²) = sqrt(16 + 64) = sqrt(80).

4. Now, we can calculate the dot product of u and v by taking the sum of the products of their corresponding components:

u · v = (8 * 4) + (4 * -8) + (k * 0) = 32 - 32 = 0.

5. Using the dot product formula u · v = |u||v|cos(theta), we can solve for cos(theta):

0 = sqrt(80 + k²) * sqrt(80) * cos(theta).

6. Since the magnitudes |u| and |v| are positive, we can ignore the absolute values in the equation. Simplifying the equation further, we have:

0 = sqrt(80 + k²) * 8 * cos(theta).

7. To find the angle theta, we need to solve for cos(theta). Since the dot product is zero, the only way for the equation to hold is if cos(theta) = 0. This occurs when theta is equal to pi/2 radians or 90 degrees.

8. Therefore, the angle theta between the vectors u and v is approximately 2.356 radians or 135 degrees.

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The dot product of two vectors u and v is given by the formula u · v = |u||v|cos(theta). The angle theta between the vectors u and v is approximately 2.356 radians or 135 degrees.

1. The dot product of two vectors u and v is defined as u · v = |u||v|cos(theta), where |u| and |v| represent the magnitudes of vectors u and v, respectively, and theta is the angle between the vectors.

2. In this case, the vectors u = 8i + 4j + k and v = 4i - 8j are given. To calculate the dot product, we need to find the magnitudes of u and v. The magnitude of a vector is calculated using the formula |u| = sqrt(u₁² + u₂² + u₃²), where u₁, u₂, and u₃ are the components of the vector.

3. For vector u, the magnitude |u| = sqrt(8² + 4² + k²) = sqrt(64 + 16 + k²) = sqrt(80 + k²). For vector v, the magnitude |v| = sqrt(4² + (-8)²) = sqrt(16 + 64) = sqrt(80).

4. Now, we can calculate the dot product of u and v by taking the sum of the products of their corresponding components:

u · v = (8 * 4) + (4 * -8) + (k * 0) = 32 - 32 = 0.

5. Using the dot product formula u · v = |u||v|cos(theta), we can solve for cos(theta):

0 = sqrt(80 + k²) * sqrt(80) * cos(theta).

6. Since the magnitudes |u| and |v| are positive, we can ignore the absolute values in the equation. Simplifying the equation further, we have:

0 = sqrt(80 + k²) * 8 * cos(theta).

7. To find the angle theta, we need to solve for cos(theta). Since the dot product is zero, the only way for the equation to hold is if cos(theta) = 0. This occurs when theta is equal to pi/2 radians or 90 degrees.

8. Therefore, the angle theta between the vectors u and v is approximately 2.356 radians or 135 degrees.

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Answer:

Option A  and D

Step-by-step explanation:

A polynomial is the combined form of expression that contains variables, operations and exponents. It cannot be divided by a variable.Polynomial does not have fractional exponent.

Option A is a polynomial because it contains variables x  and y and operators like + and division

Option B is not a polynomial because it have x in the denominator . Polynomial cannot be divided by a variable.

Option C is not a polynomial because it has a fractional exponent 1/3

Option D is a polynomial because it contains variables x  and y

Answer:

c

Step-by-step explanation:

Using the binomial probability function formula, the probability that the sample contains exactly 2 graduate students is 0.215.

The probability that the sample of 5 students contains exactly 2 graduate students using the binomial probability function can be determined by using the formula below:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

where n is the sample size, k is the number of successes, p is the probability of success, and (n choose k) = n! / (k! * (n - k)!) denotes the number of ways to choose k items from a set of n items.

Using the formula above and the information given, the probability of the sample containing exactly 2 graduate students can be calculated as follows:

P(X = 2) = (5 choose 2) * (0.32)² * (1 - 0.32)^(5 - 2) = 0.215

Where (5 choose 2) = 5! / (2! * (5 - 2)!) = 10 is the number of ways to choose 2 graduate students from a sample of 5 students.

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The probability that exactly 1 of the chosen Californians were born outside the US when 4 Californians are chosen randomly where 27% of California residents were born outside the united states is 0.42.

This is a case of Binomial distribution where there is 0.27 probability a resident of California were born outside US and 0.73 probability they were born inside the US.

In this case of Binomial distribution, the total number of successful trial(n) is the number of Californian residents chosen that is n = 4. Probability that exactly 1 of the chosen resident is

P = 4C1 × (0.27)¹ × (0.73)⁽⁴⁻¹⁾

= 4!/ ((4-1)! × 1!) × 0.27 × 0.73³

= 4 × 0.27 × 0.389017

= 0.42013836

≈ 0.42

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Answer:

2,075 = 5 × 5 × 83

√2,075 = 5√83 = about 45.55

It is not a function. cuz the x doesn't have unique image in y .

- 1 and 1 has same image.

I HOPE IT WILL HELP YOU.

Have a great day ahead.

Thank you.

^ - ^

Answer:

The diagram is omitted--please sketch it to confirm my answer.

Set your calculator to degree mode.

\( \tan( \alpha ) = \frac{110}{450} \)

\( \alpha = {tan}^{ - 1} \frac{11}{45} = 13.74 \: degrees\)

The angle of elevation is 13.74°.

Answer:

a) BOC = 80⁰

b) COD = 60⁰

Step-by-step explanation:

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

Answer:

BOC is 80 and COD is 60

Step-by-step explanation:

If DOF is 120 you subtract 40 from it because of of AOB then COD is the remaining of 180

The average cost in terms of quantity is given as C(q) =q²-3q+100, and the marginal profit is given as MP(q) = 3q-1. The revenue is given by R(q) = [4q² - 3q + 100]/q.

The average cost in terms of quantity is C(q) = q² - 3q + 100 and the marginal profit is MP(q) = 3q - 1. We have to identify the revenue. In order to identify the revenue, we have to use the relation among revenue, cost, and profit which is Revenue = Cost + Profitor, R(q) = C(q) + P(q)

Now, we have to calculate the Revenue, therefore we first need to identify the Cost and Profit. Cost is,

C(q) = q² - 3q + 100

For calculating profit, we use the relation: MP(q) = R'(q) = P(q)

Where MP(q) is the marginal profit and P(q) is the profit. R'(q) = P(q) = 3q - 1.

Putting this value in relation to Cost, we get

C(q) = C(q)/qR (q) = C(q) + P(q)

R(q) = [q² - 3q + 100]/q + [3q - 1]

Now, we simplify the above expression as follows: R(q) = [(q² - 3q + 100) + (3q² - q)]/qR(q) = [4q² - 3q + 100]/q

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Answer:

2

Step-by-step explanation:

There are two turning points, therefore this is a cubic function. The degree is 3

Answer:

EZ LOOK AT YOUR MATH PROBLEM AND COPY WHAT MATH PROBLEM DO

Answer:

its easy use magnetic field for math calculations towards the mass and volume coming out of the decrease reaction in the magnet calculations if i am right

Step-by-step explanation:

The standardized measure of the degree to which the independent variable caused a change in the dependent variable is a standard change.

A dependent variable is what is determined in an experiment or test and is the one that is influenced throughout the experiment. The dependent variable is affected by the independent variable.

In mathematical modeling, statistical modeling, and experimental sciences, dependent and independent variables are variables. Dependent variables are so named because their values are explored in an experiment under the assumption or requirement that they are dependent, by some law or rule, on the values of other variables.

In conclusion, the standard change illustrates the change.

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The student covers a total distance of 22.05 kilometers in a week's time, walking between the park and the house each day.

To find the total distance covered by the student in a week's time, we need to calculate the distance covered in one round trip (from the house to the park and back) and then multiply it by the number of round trips in a week.

Given that the difference between the park and house is 1 kilometer and 575 meters, we can convert it to a total distance of 1.575 kilometers.

In a round trip, the student covers twice the distance between the park and the house, which is 1.575 kilometers * 2 = 3.15 kilometers.

Now, we need to determine how many round trips the student makes in a week. Let's assume the student makes one round trip each day.

Since there are 7 days in a week, the total distance covered by the student in a week's time is 3.15 kilometers * 7 = 22.05 kilometers.

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Answer:

3

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The number of tickets the airline still sells will be 88. Then the correct graph is A.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

An airplane can seat up to 175 passengers.

The airline has already sold 87 tickets for a flight on the airplane.

Then the graph represents the solution to the inequality that the number of tickets the airline still sells will be

Let x be the number of the ticket which need to sell. Then the inequality equation will be

x + 87 ≤ 175

       x ≤ 175 - 87

       x ≤ 88

Thus, the correct option is A.

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Answer:

option d is the correct answer

Step-by-step explanation:

use formula for finding sum of all interior angles of regular polygon i.e. (n-2)×180 where n is no of sides of regular polygon then divide it by no. of sides of regular polygon to find measure of one angle of regular polygon and then subtract it from 180° to find the answer

The value of the fourth element of the series is 13.

In this problem we must use a recurrence formula and a initial value to derive the fourth element of the series. Recurrence formulas are expressions that calculate succesive elements of a series in terms of its previous elements.

Now we proceed to find the value of the fourth element of the series:

n = 2

a₂ = a₁ + 1

a₂ = 10 + 1

a₂ = 11

n = 3

a₃ = a₂ + 1

a₃ = 11 + 1

a₃ = 12

n = 4

a₄ = a₃ + 1

a₄ = 12 + 1

a₄ = 13

The value of the fourth element of the series is 13.

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Answer:

Step-by-step explanation:

The value of the fourth element of the series is 13.

How to determine the value of an element of the series by using recurrence formulas

In this problem we must use a recurrence formula and a initial value to derive the fourth element of the series. Recurrence formulas are expressions that calculate succesive elements of a series in terms of its previous elements.

Now we proceed to find the value of the fourth element of the series:

n = 2

a₂ = a₁ + 1

a₂ = 10 + 1

a₂ = 11

n = 3

a₃ = a₂ + 1

a₃ = 11 + 1

a₃ = 12

n = 4

a₄ = a₃ + 1

a₄ = 12 + 1

a₄ = 13

The value of the fourth element of the series is 13.

Answer:

SSS

Step-by-step explanation:

We can see that 2 sides are equal already, and because they share a side, that side is also equal. So, side side side.

Answer:

See explanation

Step-by-step explanation:

for -2x+4=4 the slope is y=2x-4

for -3x+2y=6 the slope is y=3/2x+3

for -3x+2y=6 the y-intercept is y=3 or (0,3)

(you can plug into desmos to check :) )

The probability that exactly 4 total launches will be performed until an unsuccessful launch occurs is approximately 0.0720 or 7.2%

The probability of exactly 4 total launches being performed until an unsuccessful launch occurs, we can use the geometric probability formula.

In this case, the probability of a successful launch (p) is 0.7 (since the probability of an unsuccessful launch is 0.3). We want to find the probability of 4 successful launches followed by an unsuccessful launch.

The probability of exactly 4 successful launches followed by an unsuccessful launch can be calculated as follows:

P(4 successful launches followed by an unsuccessful launch) = (p⁴) × (1-p)

P(4 successful launches followed by an unsuccessful launch) = (0.7⁴) × (1-0.7)

P(4 successful launches followed by an unsuccessful launch) = 0.7⁴ × 0.3

P(4 successful launches followed by an unsuccessful launch) = 0.2401 × 0.3

P(4 successful launches followed by an unsuccessful launch) ≈ 0.0720

Therefore, the probability that exactly 4 total launches will be performed until an unsuccessful launch occurs is approximately 0.0720 or 7.2%

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In a two-way ANOVA, the sum of squares can be calculated for each of the factors and their interaction. The sum of squares for each factor represents the variation in the dependent variable that can be attributed to that particular factor. Therefore, the sum of squares for a two-way ANOVA can be found by calculating the sum of squares for each factor and their interaction.

To find the sum of squares for a two-way ANOVA, follow these steps:

Calculate the grand mean, which is the overall mean of the dependent variable.

Calculate the sum of squares for each factor. This can be done by calculating the sum of the squared deviations of each level of the factor from the grand mean, and then summing these squared deviations across all levels of the factor. The sum of squares for factor A (SSA) and factor B (SSB) can be calculated as follows:

SSA = Σ(∑Xij – (∑Xj/n))^2 / (r * n)

SSB = Σ(∑Xij – (∑Xi/n))^2 / (c * n)

Where Xij is the value of the dependent variable for the ith level of factor A and the jth level of factor B, n is the total number of observations, r is the number of levels for factor A, and c is the number of levels for factor B.

Calculate the sum of squares for the interaction between factor A and B (SSAB) by summing the squared deviations of each cell mean from the corresponding row mean, column mean, and grand mean, and then summing these squared deviations across all cells. The formula for SSAB is as follows:

SSAB = ΣΣ(Xij – Xi – Xj + X)^2 / ((r-1) * (c-1))

Where Xij is the value of the dependent variable for the ith level of factor A and the jth level of factor B, Xi is the mean of the ith level of factor A, Xj is the mean of the jth level of factor B, and X is the grand mean.

Calculate the residual sum of squares (SSE) by subtracting the sum of squares for factor A, factor B, and their interaction from the total sum of squares (SSTO):

SSE = SSTO – SSA – SSB – SSAB

Verify that the sum of squares for each factor and their interaction, plus the residual sum of squares, equals the total sum of squares:

SSTO = SSA + SSB + SSAB + SSE

Therefore, to find the sum of squares in a two-way ANOVA, calculate the sum of squares for each factor and their interaction, and the residual sum of squares using the above steps.

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Answer:

Option: D is the correct answer.

D) 20.455 <= X <= 20.545

Step-by-step explanation:

We are given The ideal length of a particular metal rod is 20.5 cm.

It is given that:

The measured length may vary from the ideal length by at most 0.045 cm.

By atmost we mean either less than or equal to that amount but not more than that.

It means that:

|X-20.5|≤ 0.045

⇒  -0.045  ≤ X-20.5 ≤ 0.045

⇒    -0.045+20.5 ≤ X ≤ 20+0.045

⇒   20.455 ≤ X ≤ 20.545.

Hope this helped! <3

Answer:

4b +3r

The student did not subtract both terms in the second parentheses

Step-by-step explanation:

(6b + 4r) – (2b + r)

Distribute the minus sign to all terms in the second parentheses

6b + 4r – 2b - r

Combine like terms

6b -2b   +4r -r

4b +3r

The student did not subtract both terms in the second parentheses

Answer:

4b+3r

Step-by-step explanation:

(6b+4r)-(2b+r)

Distribute the negative symbol across the second set of parenthesis.

6b+4r-2b-r

Add like terms

4b+3r

Error: the student added r instead of subtracting it. They most likely only distributed the negative to the 2b.

Length of MKL is 15.71 m.

If MK = 10 m, find the length of MKL. Round to the nearest hundredth.

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The number of days, d, after which there will be 14 cookies remaining in

the jar is 9.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Number of cookies in the jar = 32

Number of cookies eaten each day = 2

The expression for the number of days d after which the number of cookies is 14.

32 - 2d = 14

32 - 14 = 2d

18 = 2d

d = 9

Thus,

The number of days is 9.

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Answer:

A=30.24

Step-by-step explanation:

A=1/2h(b1 +b2)

A =1/2×4.2×(6.3+8.1)

A =1/2x4.2(14.4)

A=30.24

Answer:

SA = 94 ft²

Step-by-step explanation:

To find the surface area of a rectangular prism, you can use the equation:

SA = 2 ( wl + hl + hw )

SA = surface area of rectangular prism

l = length

w = width

h = height

In the image, we are given the following information:

l = 4

w = 5

h = 3

Now, let's plug in the information given to us to solve for surface area:

SA = 2 ( wl + hl + hw)

SA = 2 ( 5(4) + 3(4) + 3(5) )

SA = 2 ( 20 + 12 + 15 )

SA = 2 ( 47 )

SA = 94 ft²

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