find the directional derivative of f(x, y, z) = xy2z3 at p(3, 1, 1) in the direction of q(0, −5, 7).

Answer:

14 or 0.14

Step-by-step explanation:

3 1/2 ÷ 1/4

1/4 = 25

3 1/2 ÷ 25 = 0.14 or 14

This is correct answer can you mark me brainliest

There is a 1/3 chance that random variable will have a value higher than 5.

For the variable t, which follows uniform probability distribution.

0 ≤ t ≤ 8

Total variables = 9.

For the probability of value greater than 5 for the random variable.

P(t > 5) = P(t = 6) + P(t = 7) + P(t = 8)

P(t > 5) = 1/9 + 1/9 + 1/9

P(t > 5) = 3/9

P(t > 5) = 1/3

Thus, there is a 1/3 chance that random variable will have a value higher than 5.

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The population decreased by 5,400 people from 2015 to 2020.

Also known as population decline, means the reduction in a human population size

Population in 2015 = Population in 2010 + Growth from 2010 to 2015

Population in 2015 = 167,000 + (8% of 167,000)

Population in 2015 = 167,000 + 13,360

Population in 2015 = 180,360

Population in 2020 = Population in 2015 - Decrease from 2015 to 2020

Population in 2020 = 180,360 - (3% of 180,360)

Population in 2020 = 180,360 - 5,411.8

Population in 2020 = 174,948.2

The population decrease from 2015 to 2020 is:

= Population in 2015 - Population in 2020

= 180,360 - 174,948.2

= 5,411.8

= 5,400 to nearest 100 people.

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Answer:

add 358 with itself 45 times

Step-by-step explanation:

Answer: multiply 45 with 357, or 385 x 5 x 9

Step-by-step explanation:

Answer: Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.

(13×55)+(25×33)=?

Complete the multiplication and the equation becomes

515+615=?

The two fractions now have like denominators so you can add the numerators.

Then:

5+615=11/15

This fraction cannot be reduced.

Therefore:

13+25=11/15

Step-by-step explanation: hope this helps!!!!

Answer:The answer would be 11/15 mile

Step-by-step explanation:

The august precipitation (in inches) and longitude (in degrees) were plotted for 50 American cities. a linear pattern was observed. a regression line to predict august precipitation was computed to be: 0.2034

What is regression?

Regression is a statistical technique used in the fields of finance, investing, and other disciplines that aim to establish the nature and strength of the connection between a single dependent variable (often represented by Y) and a number of independent variables (known as independent variables).

The most popular variation of this method is linear regression, which is also known as simple regression or ordinary least squares (OLS). Based on a line of best fit, linear regression determines the linear connection between two variables. The slope of a straight line used to represent linear regression, therefore, indicates how changing one variable effects changing another. In a linear regression connection, the value of one variable when the value of the other is zero is represented by the y-intercept.

The regression equation is \($\hat{y}=8.128-0.054 x$\);

Allendale\($Y=3.69$ inches.\) August was

The fitted value of Allendalis August precipitation when longitude

\($=85.96$\)

\($$\begin{aligned}\hat{y} &=8.128-0.054 \times 85.96 \\&=3.4862 .\end{aligned}$$$\therefore$ The residual for Allendali's Augurs rainfall is$$y-\hat{y}=3.69-3.4862=0.20384$$\)

Hence,

the august precipitation (in inches) and longitude (in degrees) were plotted for 50 American cities. a linear pattern was observed. a regression line to predict august precipitation was computed to be: 0.20384

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The contractor would have to work for 20 hours on the site to earn $555 total pay

What is total cost function?

Total cost function is the sum of the fixed charge, which is fixed cost to the person paying the contractor when the contractor visits the site and charge per hour multiplied by the number of hours spent working

TC=a+bX

TC=total cost=$555

a=fixed charged=$55

b=charge per hour=variable element of contractor's pay=$25

X=number of hours spent working=unknown

$555=$55+$25X

$555-$55=$25X

$500=$25*X

X=$500/$25

X=20

The contractor needs to work for 20 hours in order to earn a total pay of $555

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Answer:

Step-by-step explanation:

step 1: multiply both sides by 9π to get V9πr³=2

step 2: divide both sides by V9π to get r³=2/(V9π)

step 3: take the cubed root of both sides to get r=∛[2/(V9π)]

Answer:

Part a is \(A_n=2*3^{n-1}\)

Step-by-step explanation:

Step 1: Recall

Okay, so the formula for an explicit formula is \(A_{n} = a r^{n-1}\).

Step 2: Plug values in

\(A_n\) This is the term you are solving for? In this case, you are not solving for a time. \(a\) In this problem is the first term. In this case, two so let's plug that in. \(A_n = 2r^{n-1}\)

The next time is \(r\) . r for ratio or standard ratio. The common ratio is the number that is being multiplied or added. In this equation, each number is tripled so we can plug in 3 for r. \(A_n = 2*3^{n-1}\). So this is your explicit formula.

I forgot function form.. But I hope this poster my teacher made for me can help!

I think I used the wrong formula...

Answer:

The pattern is that each number is being multiplied by 3.

a: x * 3

b: 54 = 2 + (4 - 1)17.3

Step-by-step explanation:

a: x * 3

b: it's basically asking you to put it in function form and the image i attached explains it.

an = a + (n - 1)d

an = 54 because it's the last number

a = 2 because it's the first number

n = 4 because that's how many numbers there are in the sequence

d = 17.3, when you subtract the value between each number you get 52 and then divide that buy 3 and you get 17.3

subtract between the values:

6 - 2 = 4

18 - 6 = 12

54 - 18 = 36

then add all the numbers:

4 + 12 + 36 = 52

then divide by 3 since you subtracted 3 times:

52 / 3 = 17.3

An annual payment is found approximately $617.34. The correct option is e.. $617.34.

To find the size of your payments, you can use the formula for calculating the equal installments on a loan.

First, calculate the annual payment by dividing the borrowed amount ($2,000) by the present value factor of an annuity due with 4 periods at a 9% interest rate.

Using a financial calculator or spreadsheet, the present value factor of an annuity due with 4 periods at 9% interest rate is 3.2403.

Dividing $2,000 by 3.2403 gives us an annual payment of approximately $617.34.
Therefore, the correct answer is e. $617.34.

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Answer:

5c2 + 3c + 9

Step-by-step explanation:

Answer:

no entiendo :C

Step-by-step explanation:

The definite integral that represents the area of the region enclosed by the polar curve r = 1 sin θ is ∫[a, b] 1/2 r^2 dθ

To determine the definite integral that represents the area of the region, we integrate the expression 1/2 r^2 with respect to θ over the interval [a, b], where a and b are the limits of the region.

In this case, the polar curve r = 1 sin θ represents a circle with radius 1 centered at the origin. As θ varies from 0 to π, the curve traces half of the circle in the positive direction. To find the area of the region enclosed by this curve, we integrate the expression 1/2 r^2 over this interval.

The expression 1/2 r^2 represents the area of a sector of the circle with radius r and central angle θ. Integrating this expression with respect to θ gives us the total area enclosed by the curve.

By evaluating the definite integral over the interval [a, b], we can find the area of the region enclosed by the polar curve r = 1 sin θ.

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The equations of the lines are y = 3x - 5 and y = (1/2)x - 7

An equation is an expression that shows how numbers and variables are related to each other.

A linear function is in the form:

y = mx + b

Where m is the rate of change and b is the initial value

Two lines are parallel if they have the same slope

1) y = 3x + 6; (4, 7)

The parallel line would have a slope of 3 and pass through (4, 7), hence:

y - 7 = 3(x - 4)

y = 3x - 5

2) y = (1/2)x + 5; (4, -5)

The parallel line would have a slope of 1/2 and pass through (4, -5), hence:

y - (-5) = (1/2)(x - 4)

y = (1/2)x - 7

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Answer:

\(y = \frac{1}{8}(x + 4)^2 + 4\)

Step-by-step explanation:

Given:

Focus of parabola: (-4, 6)

Directrix: y = 2

Required:

Equation for the parabola

Using the formula, \( y = \frac{1}{2(b - k)}(x - a)^2 + \frac{1}{2}(b + k) \) , the equation for the parabola can be derived.

Where,

a = -4

b = 6

k = 2

Plug these values into the equation formula

\( y = \frac{1}{2(6 - 2)}(x - (-4))^2 + \frac{1}{2}(6 + 2) \)

\(y = \frac{1}{2(4)}(x + 4)^2 + \frac{1}{2}(8)\)

\(y = \frac{1}{8}(x + 4)^2 + \frac{8}{2}\)

\(y = \frac{1}{8}(x + 4)^2 + 4\)

If there are n men and n women in the group, we can first arrange the men and women separately in alternate positions. We can treat the men as a single group and arrange them in n! ways, and similarly, we can treat the women as a single group and arrange them in n! ways.

Next, we need to arrange the two groups (men and women) in alternate positions to satisfy the given condition. Since we need to place the youngest person (who could be a man or a woman) at the beginning of the row, we have two cases:

Case 1: The youngest person is a man

In this case, the men must start the arrangement, followed by the women. Since there are n men and n women, there are n! ways to arrange the men and n! ways to arrange the women. We can fix the youngest man at the beginning of the row, so there are (n-1)! ways to arrange the remaining n-1 men. Similarly, there are (n-1)! ways to arrange the n-1 women. Therefore, the total number of arrangements in this case is:

n! * n! * (n-1)! * (n-1)!

Case 2: The youngest person is a woman

In this case, the women must start the arrangement, followed by the men. Since there are n women and n men, there are n! ways to arrange the women and n! ways to arrange the men. We can fix the youngest woman at the beginning of the row, so there are (n-1)! ways to arrange the remaining n-1 women. Similarly, there are (n-1)! ways to arrange the n-1 men. Therefore, the total number of arrangements in this case is:

n! * n! * (n-1)! * (n-1)!

To get the total number of arrangements that satisfy the given condition, we need to add the number of arrangements in Case 1 and Case 2:

n! * n! * (n-1)! * (n-1)! + n! * n! * (n-1)! * (n-1)!

= 2 * n! * n! * (n-1)! * (n-1)!

= 2 * (n!)^2 * (n-1)!

Therefore, the total number of ways to arrange the people in a row with alternating men and women, starting with the youngest person, is 2 * (n!)^2 * (n-1)!.

Step-by-step explanation:

Given, 3x−2<2x+1

⇒3x−2x<1+2

⇒x<3orx∈(−∞,3)

The lines y=3x−2 and y=2x+1 both will intersect at x=3

Clearly, the dark line shows the solution of 3x−2<2x+1.

Answer: the answer is 32:12

Step-by-step explanation: add 12+6+14 yw

Answer: C and D are the correct answers

Step-by-step explanation:

Answer:

the coordinates of the other corner are (-10/3, -1 3/4).

The four ordered pairs that represent the corners of Maya's rectangular driveway are (-1, 1), (1 1/2, -8 1/2), (-10/3, -1 3/4), and (1 1/2, -1 3/4).

Step-by-step explanation:

To plot the other two corners of Maya's rectangular driveway, we need to determine the coordinates of the points that are diagonally opposite to the points (-1, 1) and (1 1/2, -8 1/2).

Since the points (-1, 1) and (1 1/2, -8 1/2) are diagonally opposite, we can draw a line through the center of the rectangle that is perpendicular to the line connecting these two points. The center of the rectangle can be found by averaging the x-coordinates and the y-coordinates of the two points. The x-coordinate of the center is (-1 + 1 1/2)/2 = 1/4 and the y-coordinate of the center is (1 + -8 1/2)/2 = -3 3/4.

We can then use the center of the rectangle and the slope of the line connecting (-1, 1) and (1 1/2, -8 1/2) to find the coordinates of the other two corners. The slope of the line is (-8 1/2 - 1)/(1 1/2 - (-1)) = -17/3, so the slope of the line perpendicular to it is -3/17.

We can use this slope and the center of the rectangle to find one of the remaining corners by moving a fixed distance in the y-direction from the center. For example, if we move 2 units in the positive y-direction from the center, we will reach the point (1/4, -3 3/4 + 2) = (1/4, -1 3/4). We can then use the slope of the line to find the x-coordinate of the other corner by solving the equation y = mx + b for x, where m is the slope, x is the x-coordinate of the corner, y is the y-coordinate of the corner, and b is the y-intercept. The y-intercept is the y-coordinate of the center, so we can solve the equation as follows:

y = -3/17 * x + (-3 3/4)

x = (y - (-3 3/4))/(-3/17)

Substituting the coordinates of the corner we found earlier, we get:

x = (-1 3/4 - (-3 3/4))/(-3/17) = (2)/(-3/17) = -10/3

So, the coordinates of the other corner are (-10/3, -1 3/4).

The four ordered pairs that represent the corners of Maya's rectangular driveway are (-1, 1), (1 1/2, -8 1/2), (-10/3, -1 3/4), and (1 1/2, -1 3/4).

Answer:

0.79

Step-by-step explanation:

This value is the most opposite of the value above R, meaning that there is an association between the variables.

Answer:

.79

Step-by-step explanation:

Bc y not

The equation of the ellipse with foci at ​(39​,0) and ​(-39​,0) and a constant difference of 30 is given as follows:

x²/39² + y²/9² = 1.

The equation of an ellipse of center (h,k) is given by the rule presented as follows:

(x - h)²/a² + (y - k)²/b² = 1.

In which:

The coordinates of the foci are given as follows:

​(39​,0) and ​(-39​,0).

The center is the midpoint of these two coordinates, hence:

The coefficient a is given as follows:

a = |39 - 0| = |0 - 39| = 0.

Considering the constant difference of 30, the constant b is given as follows:

b = a - 30 = 39 - 30 = 9.

Thus the equation of the ellipse is given as follows:

x²/39² + y²/9² = 1.

The problem asks for the equation of the ellipse with the given features.

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Answer:

The angle marked E is 120 degrees

Step-by-step explanation:

Here, we want to get the value of the angle marked E

when two triangles are similar/congruent, we have equal angle measures

Using the markings, we can deduce the following relationships;

4y -28 = 83 + y

4y-y = 83 + 28

3y = 111

y = 111/3

y = 37

So, we have;

4y-28 as

4(37) - 28

= 120

The constant of proportionality 'k' is 90.

Therefore, the answer is option c. 90.

To find the constant of proportionality in this indirect variation problem, we can set up a proportion using the given information.

Let's denote the constant of proportionality as 'k'. We know that when Bartolo runs at an average speed of 15 feet/second, he finishes the race in 6 seconds. We can write this as:

15 feet/second x 6 seconds = k

Similarly, when Bartolo runs at an average speed of 18 feet/second, he finishes the race in 5 seconds:

18 feet/second x 5 seconds = k

Now we can solve for 'k' by setting the two expressions equal to each other:

15 feet/second x 6 seconds = 18 feet/second x 5 seconds

90 feet = 90 feet

This shows that the constant of proportionality 'k' is 90.

Therefore, the answer is option c. 90.

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The average speed for the first part of the trip is 60 miles.

Given:

1st leg DATA:

distance = 120 miles ;

rate = x mph ;

time = d/r = 120/x hrs

2nd leg DATA:

distance = 220 miles ;

rate = x-5 mph ;

time = 220/(x-5) hrs

hence the equation we frame is:

Equation:

120/x + 220/(x-5) = 6

120(x-5) + 220x = 6x(x-5)

120x - 600 + 220x = 6x² - 30x

-6x² + 340x + 30x - 600 =0

-6x² + 370x - 600 = 0

-3x² - 185x + 300 = 0

(3x-5)(x-60)

3x = 5 or x-60=0

x = 5/3 or x = 60

hence x-5 = 60-5

= 55 miles per hour.

Hence we get the answer as 60 miles.

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The displacement and distance traveled depend on the given time interval.

To find the displacement, we need to integrate the velocity function from 0 to 5 or 0 to 5π, depending on the given time interval.

If the time interval is [0,5], we have:

Displacement = ∫[0,5] v(t) dt
Displacement = ∫[0,5] 6cos(t) dt
Displacement = [6sin(t)] from 0 to 5
Displacement = 6sin(5) - 6sin(0)
Displacement ≈ 2.785 meters

If the time interval is [0,5π], we have:

Displacement = ∫[0,5π] v(t) dt
Displacement = ∫[0,5π] 6cos(t) dt
Displacement = [6sin(t)] from 0 to 5π
Displacement = 0 - 6sin(0)
Displacement = 0 meters

To find the distance traveled, we need to integrate the absolute value of the velocity function over the given time interval.

If the time interval is [0,5], we have:

Distance = ∫[0,5] |v(t)| dt
Distance = ∫[0,5] |6cos(t)| dt
Distance = ∫[0,π/2] 6cos(t) dt + ∫[π/2,5] -6cos(t) dt
Distance = [6sin(t)] from 0 to π/2 + [-6sin(t)] from π/2 to 5
Distance = 6 - 6sin(5) ≈ 2.215 meters

If the time interval is [0,5π], we have:

Distance = ∫[0,5π] |v(t)| dt
Distance = ∫[0,5π] |6cos(t)| dt
Distance = ∫[0,π] 6cos(t) dt + ∫[π,2π] -6cos(t) dt + ∫[2π,3π] 6cos(t) dt + ∫[3π,4π] -6cos(t) dt + ∫[4π,5π] 6cos(t) dt
Distance = [6sin(t)] from 0 to π + [-6sin(t)] from π to 2π + [6sin(t)] from 2π to 3π + [-6sin(t)] from 3π to 4π + [6sin(t)] from 4π to 5π
Distance = 0 meters

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Answer:

x = 12, y = 8

Step-by-step explanation:

They're congruent, just sub numbers