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The vector parametric equation for the line passing through points P and Q with r(6) = P and r(10) = Q is r(t) = (-3,-1,1) + t(-1,-1,1).

To find the vector parametric equation of the line passing through points P and Q, we need to first find the direction vector d. We can find this by subtracting the coordinates of P from Q, i.e., d = Q - P = (-8,-4,5) - (-3,-1,1) = (-5,-3,4).  Now, we need to find the equation of the line in vector parametric form, which can be written as r(t) = P + td, where t is a scalar parameter. We are given that r(6) = P and r(10) = Q, which means that r(6) = (-3,-1,1) + 6d and r(10) = (-3,-1,1) + 10d.

We can now set these two equations equal to each other to solve for d:

(-3,-1,1) + 6d = (-3,-1,1) + 10d

4d = (-3,-1,1) - (-3,-1,1)

4d = (0,0,0)

d = (0,0,0)

This means that the line passing through P and Q is actually a point, which is not possible. However, we know that the direction vector is not zero, so there must be an error somewhere. Looking back at our calculations, we realize that we made a mistake when finding d. The correct value of d is actually (-5,-3,4), which means that the vector parametric equation of the line is r(t) = (-3,-1,1) + t(-5,-3,4), or equivalently, r(t) = (-3 - 5t, -1 - 3t, 1 + 4t).

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The exact value of the given integral is -10592/2197.

The given problem involves a double integral of two different expressions over a region in the xy-plane. The first expression is simply a constant function, while the second one involves a quadratic polynomial in x and y. The integral is to be evaluated over the region bounded by the x-axis and the curve y = (7/13)x² - 6x + 4. The exact answer is to be written in terms of radicals and/or integers or fractions.

To evaluate the given integral, we need to first find the limits of integration. The curve y = (7/13)x² - 6x + 4 intersects the x-axis at the points where 0 = (7/13)x² - 6x + 4, which yields x = 2 and x = 26/7. Therefore, the region of integration is the rectangle bounded by x = 0, x = 2, y = 0, and y = (7/13)x² - 6x + 4.

Now we can set up the double integral and evaluate it using iterated integration. First, we integrate with respect to x, treating y as a constant:

∫_0^(7/13)x²-6x+4 ∫_0² (1 + 6y/13) dx dy + ∫_0^(7/13)x²-6x+4 ∫_2^(7/13)x²-6x+4 (1 + 6y/13) dx dy

The inner integral with respect to x is straightforward to evaluate, and we get:

(1/2)x² + (6/13)xy |_0² = 2 + (12/13)y

(1/2)x² + (6/13)xy |_2^(7/13)x²-6x+4 = (36/169)x² + (84/169)xy - (332/169)x - (24/13)y + 83/169

Substituting these values back into the original integral and integrating with respect to y, we get:

∫_0² (2 + (12/13)y) dy + ∫_0² ((36/169)x² - (24/13)y + (84/169)xy - (332/169)x + 83/169 + (6/13)y) dy

= (26/13) + (8/3)x - (196/169)x²

Therefore, the exact value of the given integral is (26/13) + (8/3)(7/13) - (196/169)(39/2) = -10592/2197.

Therefore, the exact value of the given integral is -10592/2197.

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Its scale factor of 3

Answer:

-2

Step-by-step explanation:

you answer the brackets first then add 9 then add 8

(a)  The equation of the function is y = x/4

(b) The value of y = 2

Given,

Suppose that y varies directly with x, and y = 5 when x = 20 .

(a) To Write a direct variation that relates x and y.

(b) Find y when x = 8.

Now, According to the question:

(a) Based on the given conditions;

y = kx

Substitute y = 5 and x = 20 into y = kx

5 = k x 20

Swap the sides

k x 20 = 5

Divide both sides of the equation by the coefficient of variable

k = 5/20

Cross out the common factor

k = 1/4

Varies directly means the relationship is linear.

Find the equation of the function:

y = x/4

(b)  Based on the given conditions;

y = kx

We have find the equation of function in part (a)

Now, Substitute x = 8 into y = x/4

y = 8/4

Cross out common factor

y = 2

Hence, (a)  the equation of the function is y = x/4

             (b) The value of y = 2

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The probability that exactly 18 out of the 20 selected calculators are nonfunctional is approximately 0.071, or 7.1%.

To calculate the probability that exactly 18 out of 20 selected calculators are nonfunctional, we can use the hypergeometric probability formula. The hypergeometric distribution is appropriate in this case because we are sampling without replacement from a finite population (the 30 hand-held calculators).

The formula for the hypergeometric probability is:

P(X = k) = (C(N-K, n-k) * C(K, k)) / C(N, n)

Where:

N = Total population size (30 calculators)

K = Number of nonfunctional calculators in the population (22 calculators)

n = Sample size (20 calculators)

k = Number of nonfunctional calculators in the sample (18 calculators)

C(a, b) represents the combination of "a choose b."

Substituting the given values into the formula, we can calculate the probability:

P(X = 18) = (C(22, 18) * C(8, 2)) / C(30, 20)

P(X = 18) = (77 * 28) / 30,045

P(X = 18) ≈ 0.071

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Answer:

The type of number that represents -4/2 is:

Choice B) Integer

Choice C) Rational

Step-by-step explanation:

The number -4/2 is an integer because it represents a whole number (-2) and it is also a rational number because it can be expressed as a fraction of two integers.

-4/2 is an :

Solution:

Before we make any decisions about the type of number -4/2 is, let's simplify it first.

It's the same as -2. Now, let's familiarize ourselves with the sets of numbers out there. Where does -2 fit in?

______________

This set incorporates only positive numbers and zero. So -2 doesn't belong here.

This set incorporates whole numbers and negative numbers. So -2 belongs here.

This set has integers, fractions, and decimals. So -2 does belong here too.

This is a set for numbers that cannot be written in fraction form (a/b, where b ≠ 0). So -2 doesn't belong here.

-4/2 belongs in the integer and rationals set.

Answer:

y = 2.5x - 8

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 2.5 and c = - 8 , then

y = 2.5x - 8 ← equation of line

Answer:

25

Step-by-step explanation:

Answer:

x=10

Step-by-step explanation:

5x-10 and 3x+10

+10 +10

5x and 3x+20

-3x -3x

2x and 20

divide by 2 on both sides

x=10

Answer:

The margin of error for a 98% confidence interval around the sample mean is approximately 6.679 minutes.

Margin of error (E) = Zα/2 × σ/√n

Here,α = (1 - confidence level)/2

            = (1 - 0.98)/2

            = 0.01/2

            = 0.005

Zα/2 is the Z-score that corresponds to the given level of confidence (0.98).

Zα/2 can be calculated using a Z-table, which gives a value of

2.33.σ = population standard deviation = 15.7 minutes

n = sample size = 30

Putting the given values in the formula:

Margin of error (E) = 2.33 × 15.7/√30

                               ≈ 6.679

Therefore, the margin of error for a 98% confidence interval around the sample mean is approximately 6.679 minutes.

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By comparing symbol we can compare number and evaluate answer we get that \(-1\frac{3}{4} \leq -1\frac{1}{4}\) .So \(-\frac{7}{4}\) is less than \(-\frac{5}{4}\) .It is our requried answer.

How do we compare fractions?

If the denominator are equal, then the fraction with the bigger numenators is the bigger  fraction. The fractions are equal if the numerators and denominators of both fractions are equal.  

A fraction is a number of consisting one or more equal parts of a unit .It is denoated by a/b where a and \(b\neq 0\) are integers.The numenator a of a/b denotes the number of parts taken of the unit ; is divided by the number of the parts equal to the number appearing as the denomenator b.

 \(-1\frac{3}{4} \leq -1\frac{1}{4}\)

\(-\frac{7}{4}\leq -\frac{5}{4}\)

Hence, \(-\frac{7}{4}\) is less than \(-\frac{5}{4}\).

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The missing Value, x, that when multiplied by 5/3^4 gives the result of 5^4 is 13125.

The missing value that, when multiplied by 5/3^4, gives the result of 5^4, we can set up the equation:

(5/3^4) * x = 5^4

To solve for x, we can simplify both sides of the equation. First, let's simplify the right side:

5^4 = 5 * 5 * 5 * 5 = 625

Now, let's simplify the left side:

5/3^4 = 5/(3 * 3 * 3 * 3) = 5/81

Now we have:

(5/81) * x = 625

To solve for x, we can multiply both sides of the equation by the reciprocal of 5/81, which is 81/5:

(81/5) * (5/81) * x = (81/5) * 625

On the left side, the fraction (81/5) * (5/81) simplifies to 1, leaving us with:

1 * x = (81/5) * 625

Simplifying the right side:

(81/5) * 625 = 13125

Therefore, the missing value, x, that when multiplied by 5/3^4 gives the result of 5^4 is 13125.

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According to the question, the given rational expression can be simplified which is as shown below:

Rational expression = \(\frac{12-4x}{x^{2} -9}=\frac{4(3-x)}{(x-3)(x+3)}\)

For the simplification of the given expression, calculate the factors of the numerator as well as denominator terms and divide them from each other. In this change the sign of the expression before dividing with each other.

Rational expression = \(\frac{-4}{(x+3)}\)

The rational expression are also known as polynomial expression. The highest degree of these expression is two. And these expression uses concept of factor rule.

Therefore, the final expression is \(\frac{-4}{(x+3)}\)

What is polynomial expression?

Polynomial expression are those equation whose highest degree is two. It is also called as quadratic equation. And it is simplified by performing the factors on the given expressions.

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"a ≡ b(mod0) means that a and b are equal."

Given, a≡b(mod0)To find what a≡b(mod0) means, we need to understand the definition of congruence.

Two integers are said to be congruent modulo n if their difference is divisible by n.

That is, a ≡ b(mod n) if n divides a-b where n is a positive integer.

Now, substituting 0 in place of n, we get, a ≡ b(mod 0) if 0 divides a-b or in other words a-b = 0. Hence, a ≡ b(mod 0) if a = b.

Since the difference between a and b must be divisible by n, and since 0 is divisible by every integer, the only way for a ≡ b(mod 0) is when a = b.

So, a ≡ b(mod0) means that a and b are equal.

Hence, the answer is "a ≡ b(mod0) means that a and b are equal."

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Answer:

the answer is on google

the Domain of f divided by g of x  (-∞, -2) to (-2 , ∞)

A function is described as a relation among a fixed of inputs having one output every. In easy words, a feature is dating among inputs in which every entry is associated with precisely one output.

Given, The function f(x) = 20x + 80 represents the distance in miles a drone flew.

The function g(x) = x + 2 represents the time the drone flew in hours

Part A:

f(x) = 20x + 80

F(2) = 20*2 + 80

F(2) = 120

g(x) = x + 2

g(2) = 2 + 2

g(2) = 4

Part B: f(x) divided by g(2)

=> f(x) / g(2)

=> (20x + 80 ) /4

=> 5x + 20 (since, g(2) is 4)

Part C:  the domain of f divided by g of x

So,

f(x) / g(x ) = (20x + 80)/(x +2)

=>  (20x + 80)/(x +2)

Since Denominator can not be zero.

Therefore, the Domain of f divided by g of x  (-∞, -2) to (-2 , ∞).

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Answer:

Is there specific topic/topics you are working on?

Also, if you are struggling Khan Academy has some informative videos all you have to do is search up a topic on their site and a video will come up with practice questions to try after the video as well!

good luck on your test!!

The total mortgage payment for the house is $557.51. This amount includes the monthly payments for both the first and second mortgages. Option B.

To calculate the total mortgage payment for the house, we need to consider the monthly payments for both the first (80%) mortgage and the second (20%) mortgage. Let's break down the steps to find the total mortgage payment:

Step 1: Calculate the loan amounts for each mortgage:

The first mortgage covers 80% of the house price, which is $100,000. Therefore, the loan amount for the first mortgage is 0.8 * $100,000 = $80,000.

The second mortgage covers the remaining 20% of the house price, which is $100,000. Therefore, the loan amount for the second mortgage is 0.2 * $100,000 = $20,000.

Step 2: Calculate the monthly payment for each mortgage:

To calculate the monthly payment for a fixed-rate mortgage, we can use the loan amount, interest rate, and loan term in months with the following formula:

Monthly Payment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Loan Term in Months))

For the first mortgage, the interest rate is 4.75% (or 0.0475 in decimal form) and the loan term is 30 years (or 360 months). Plugging these values into the formula, we find the monthly payment for the first mortgage is approximately $417.32.

For the second mortgage, the interest rate is 7.525% (or 0.07525 in decimal form) and the loan term is also 30 years (or 360 months). Using the formula, we find the monthly payment for the second mortgage is approximately $140.19.

Step 3: Add the monthly payments of both mortgages to find the total mortgage payment:

Total Mortgage Payment = Monthly Payment (First Mortgage) + Monthly Payment (Second Mortgage)

Total Mortgage Payment = $417.32 + $140.19 = $557.51

Therefore, the correct option is $557.51, which represents the total mortgage payment for this house. SO Option B is correct.

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Answer:

It looks like the angle between C and D are the same as between D and E, so the correct answer would be:

E. ∠CFD and ∠DFE

Brainliest? ;)

It helps a lot!

Answer:

A, C, E.

Step-by-step explanation:

Hope it helps. :)

Two lines are perpendicular if the multiplication of their slopes is equal to -1.

Isolating y from the equation:

The slope of this line is 2. Therefore, the slope of the line perpendicular to this one will be:

Answer:

the mode number of hours is 4 because is the hour spent mostly on the computer

therefore the mode number of hours is 4 hours

Answer:

k=-5

Step-by-step explanation:

-12=4.7k+11.5

switch sides - 4.7k+11.5=-12

multiply both sides by 10 - 4.7k times 10 +11.5 times 10=-12 times 10

refine - 47k+115=-120

subtract 115 from both sides - 47k+115-115=-120-115

simplify it - 47k=-235

divide both sides by 47 - 47k/ 47= -235/ 47

simplify - k =-5

Answer:

\(\textsf{A.} \quad g(x)=\sqrt{4x}-2\)

Step-by-step explanation:

Transformations

For a > 0

\(f(x)+a \implies f(x) \: \textsf{translated $a$ units up}\)

\(f(x)-a \implies f(x) \: \textsf{translated $a$ units down}\)

\(a\:f(x) \implies f(x) \: \textsf{stretched parallel to the $y$-axis (vertically) by a factor of $a$}\)

\(f(ax) \implies f(x) \: \textsf{stretched parallel to the $x$-axis (horizontally) by a factor of $\dfrac{1}{a}$}\)

Given parent function:

\(f(x) = \sqrt{x}\)

1.  Horizontal stretch by a factor of 4:

f(4x) is a horizontal stretch by a factor of 1/4.

So f(1/4x) is a horizontal stretch by a factor of 4.

\(f\left(\frac{1}{4}x\right)\implies g(x)=\sqrt{\frac{1}{4}x}\)

2. Vertical shift by 2 units down:

\(f\left(\frac{1}{4}x\right)-2\implies g(x)=\sqrt{\frac{1}{4}x}-2\)

There were 128 children and 155 adults.

Let us first set up our system by assigning x and y to mean something. Let x = the number of children and y = the number of adults.

First equation: Children cost $1.50 and Adults cost $4.00. In order to find the amount of money a group of children will cost, we multiply the number of children, x, by 1.5.

This is represented by 1.5x. For adults, who cost 4 dollars to enter, we will use 4y. The total amount of money made on the given day was $632. To get this amount, we must add 1.5x and 4y.

1.5x+4y=632 --------(1)

Second equation: Total amount of people on the given day is 238. To get this number, we must add together x and y, or the number of children and adults.

x + y = 238-----(2)

System of equations:

1.5x+4y=632

x+y = 238

Let's use the substitution of the x variable to solve the system.

x+y=238.

y=238-x

Substitute y = 238 - x into the first equation.

1.5x + 4 (238 - x) =632

1.5x + 952 - 4x = 632  

952- 2.5x = 632

-2.5x = -320

x = 128

Substitute x =128 back into y = 238 - x

y = 283-128

y=155

There were 128 children and 155 adults.

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Answer: 2,306,973.7 rounded... 2,306,974

900,000(1+.04)^24

So, the vector parametric equation of the line is x = 1 + 2t and y = -2 - 5t and z = 3 + t.

To find the vector parametric equation of the line that is perpendicular to the plane 2x - 5y + z - 4 = 0 and passes through the point P = (1, -2, 3), follow these steps:

Step 1: Find the normal vector of the plane.
The coefficients of x, y, and z in the equation of the plane represent the normal vector. So, the normal vector of the plane is n = (2, -5, 1).

Step 2: Find the direction vector of the line.
Since the line is perpendicular to the plane, the direction vector of the line will be parallel to the normal vector of the plane. So, the direction vector of the line is d = (2, -5, 1).

Step 3: Write the vector parametric equation.
The vector parametric equation of the line passing through point P and with direction vector d is:
r = P + t * d, where t is a parameter.

Substituting the values, we have:
r = (1, -2, 3) + t * (2, -5, 1).

So, the vector parametric equation of the line is:
x = 1 + 2t
y = -2 - 5t
z = 3 + t.

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P(X = 7), λ = 6: The Poisson probability of X = 7, with a parameter (λ) value of 6, is 0.1446. P(X = 11), λ = 12: The Poisson probability of X = 11, with a parameter (λ) value of 12, is 0.0946. P(X = 6), λ = 8: The Poisson probability of X = 6, with a parameter (λ) value of 8, is 0.1206.

The Poisson probability is used to calculate the probability of a certain number of events occurring in a fixed interval of time or space, given the average rate of occurrence (parameter λ). The formula for Poisson probability is P(X = k) = (e^-λ * λ^k) / k!, where X is the random variable representing the number of events and k is the desired number of events.

To calculate the Poisson probabilities in this case, we substitute the given values of λ and k into the formula. For example, for the first case (a), we have λ = 6 and k = 7: P(X = 7) = (e^-6 * 6^7) / 7!

Using a calculator, we can evaluate this expression to find that the probability is approximately 0.1446. Similarly, for case (b) with λ = 12 and k = 11, and for case (c) with λ = 8 and k = 6, we can apply the same formula to find the respective Poisson probabilities.

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Answer:

6

Step-by-step explanation:

4- -2

Answer:

6

Step-by-step explanation:

Answer:

6 /19

≅ 0.3157895

Step-by-step explanation:

Answer:

6/19

Step-by-step explanation:

This is your answer because first you have to make the to mixed fractions to improper fraction 6/5 and 22/5 are your improper fractions from there you divide them and that's how you get your answer

Hope this helps:)

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