Which expression is equivalent to the given expression? Assume the denominator does not equal zero. Please give a detailed explanation and not just the answer; explain the concept to me, step by step what to do to solve this problem. Thank you.

Unit conversion is the conversion of one unit to another unit with its standard conversion.

The distance traveled in 15 minutes at a speed of 12m/s is 10800 m.

It is the conversion of one unit to another unit with its standard conversion.

Example:

1 minute = 60 seonds

1 km = 100 m

1 m = 100 cm

We have,

Speed = 12 m/s

This means,

1 second = 12 m

Now,

1 minute = 60 seconds

15 minutes = 15 x 60 seconds

15 minutes = 900 seconds

So,

1 sec = 12 m

Multiply 900 on both sides.

900 x 1 sec = 900 x 12m

900 seconds = 10800 m

Thus,

The distance traveled in 15 minutes at a speed of 12m/s is 10800 m.

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The point-slope form of the line with slope 3/1 and passing through the point (-8, 7) is y = 3x + 31.

The point-slope form of a linear equation is given by y - y1 = m(x - x1), where (x1, y1) represents a point on the line and m represents the slope.

Given that the slope is 3/1 and the line passes through the point (-8, 7), we can substitute these values into the point-slope form:

y - 7 = (3/1)(x - (-8))

Simplifying:

y - 7 = (3/1)(x + 8)

y - 7 = 3(x + 8)

Expanding:

y - 7 = 3x + 24

Finally, rearranging the equation to the point-slope form:

y = 3x + 31

Therefore, the point-slope form of the line with slope 3/1 and passing through the point (-8, 7) is y = 3x + 31.

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Option B is not true with respect to a homogeneous system Ax = 0, where A is an m x n matrix. The system has nontrivial solutions if and only if there exist one or more free variables in the system.

A homogeneous system Ax = 0, where A is an m x n matrix, is a system of linear equations where all constants on the right-hand side are zero. The system is consistent since it has at least one (trivial) solution x = 0. If the system has nontrivial solutions, then there exist one or more free variables, and we can represent the solution set in parametric vector form as a span of a set of vectors in \(R^n\), where the free variables are used as parameters. The system has only the trivial solution, x = 0, if and only if all columns of A are pivot columns, or equivalently, if and only if rank(A) = n. If the system has exactly one free variable, then the solution set geometrically represents a line in \(R^n\) with a parametric equation x = tv, where v is a nonzero vector in \(R^n\)

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If a student population of 1200 was estimated to increase by 15% in the next five years but the population actually increased by 20%, then the most estimated and actual student populations are equal to 1380 and 1440 students respectively, and the percent error is equal to 4.2%.

The estimated and actual student populations can be calculated as follows,

Estimated increase = 15% = 15 / 100 = 0.15

Initial population = 1200

0.15 × 1200 = 180

Estimated population in the next five years = 1200 + 180 = 1380

Actual increase = 20% = 20 / 100 = 0.2

Initial population = 1200

0.2 × 1200 = 240

Actual population in the next five years = 1200 + 240 = 1440

We can find the percentage error as follows,

percentage error = [(actual value - estimated value) / actual value] × 100

percentage error = [(1440 - 1380) / 1440] × 100

percentage error = [60 / 1440] × 100

percentage error = 0.042 × 100 = 4.2%

Hence the estimated and actual student populations is calculated to be 1380 and 1440 respectively and the percentage error is equal to 4.2%.

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Answer:

A. (2,5), (3,6), (6,9)

Step-by-step explanation:

In order to be a function, all inputs (x values) must go to only one output (y value). List A is the only list that obeys this rule. Therefore, List A is a function.

Answer:

\(x=-14\)

Step-by-step explanation:

\(\frac{x+7-8x}{3}=-\frac{5x}{2}\\\mathrm{Apply\:fraction\:cross\:multiply:\:if\:}\frac{a}{b}=\frac{c}{d}\mathrm{\:then\:}a\cdot \:d=b\cdot \:c\\\left(x+7-8x\right)\cdot \:2=-3\cdot \:5x\\Simplify\\2\left(-7x+7\right)=-15x\\\mathrm{Expand\:}2\left(-7x+7\right):\quad -14x+14\\2\left(-7x+7\right)\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b+c\right)=ab+ac\\a=2,\:b=-7x,\:c=7\\=2\left(-7x\right)+2\cdot \:7\\\mathrm{Apply\:minus-plus\:rules}\\+\left(-a\right)=-a\\=-2\cdot \:7x+2\cdot \:7\)

\(\mathrm{Multiply\:the\:numbers:}\:2\cdot \:7=14\\=-14x+14\\-14x+14=-15x\\\mathrm{Subtract\:}14\mathrm{\:from\:both\:sides}\\-14x+14-14=-15x-14\\\mathrm{Simplify}\\-14x=-15x-14\\\mathrm{Add\:}15x\mathrm{\:to\:both\:sides}\\-14x+15x=-15x-14+15x\\\mathrm{Simplify}\\x=-14\)

Answer:

222222222/1000000000

Step-by-step explanation:

Ali will receive £10, and Ben will receive £25 when they divide £35 in the ratio of 2:5.

To divide £35 in the ratio of 2:5, we first need to calculate the total parts of the ratio:

Total parts = 2 + 5 = 7

Next, we divide the total amount (£35) into 7 equal parts:

£35 / 7 = £5

Now, we can allocate the amounts to Ali and Ben based on the ratio:

Ali's share = 2 parts * £5 = £10

Ben's share = 5 parts * £5 = £25

Therefore, Ali will receive £10, and Ben will receive £25 when they divide £35 in the ratio of 2:5.

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Gray's $3,500 tax-deductible contribution to his IRA will save him $980 on his taxes.

When Gray contributes $3,500 to his individual retirement account (IRA), it is considered a tax-deductible contribution. This means that the amount contributed is deducted from his taxable income, reducing the amount of taxes he owes.

Since Gray is in the 28 percent tax bracket, this means that for every dollar of taxable income, he pays 28 cents in taxes. To calculate the tax savings from his $3,500 IRA contribution, we need to multiply the contribution amount by his tax rate:

$3,500 (contribution) x 0.28 (tax rate) = $980 (tax savings)

In this case, Gray's $3,500 tax-deductible contribution to his IRA will save him $980 on his taxes. By contributing to his IRA, Gray not only invests in his future retirement but also takes advantage of the tax benefits associated with these accounts. In the end, he reduces his taxable income and, consequently, the amount of taxes he needs to pay.

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There will be 221 highway signs on the road trip.

What is Total Length?

Whole Length (TL) is the measurement taken in a straight line, with the fish lying on its side, from the tip of the snout to the end of the tail (caudal fin).

The total length of the road trip is 13.2 hours.

Highway signs are posted every 0.06 hours. To find out how many highway signs are on the road trip, we can divide the total length of the road trip by the interval between each sign and then add one more sign for the end of the road trip:

(number of signs) = (total length of road trip) / (interval between signs) + 1

Substituting the values, we get:

(number of signs) = 13.2 / 0.06 + 1

(number of signs) = 220 + 1

(number of signs) = 221

Therefore, there will be 221 highway signs on the road trip.

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A pentagonal prism is a 3-dimensional shape with two pentagons as its base, five rectangular faces, and nine edges. It has ten vertices, five on each pentagon.

A pentagonal prism is a 3-dimensional shape with two parallel pentagons as its base. It has five rectangular faces, each with a pentagon at each end, and nine edges which connect the five faces. The pentagonal prism has ten vertices in total; five on each pentagon. The pentagons are in the same plane, with the rectangular faces in between them extending outwards. The pentagonal prism is a polyhedron, meaning that it has flat faces and straight edges. The edges of a pentagonal prism are all the same length, and each of its rectangular faces has the same area. The height of the prism is the distance between the two pentagons. Pentagonal prisms can be used to make various objects such as boxes, and can also be used to make tessellations.

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Subtract the height of the dive from

The total distance he dove:

15 - 9 = 6

The pool is 6 meters deep

Answer:

463,185

Step-by-step explanation:

3.75% of 370,000 is 13875

370,000 + 13875 = 383,875

(end of first year)

3.75% of 383,875 is 14395.312, rounding it down to 14395

383,875 + 14,395 = 385,370

(end of second year)

3.75% of 385,370 is 14451.375, rounding it down to 14451

385,370 + 14,451 = 399,821

(end of third year)

3.75% of 399,821 is 14993.287499999999, but I'm rounding it down to 14,933

399,821 + 14,933 = 414,754

(end of fourth year)

3.75% of 414,754 is 15553.275, but I'm rounding it down to 15,553

414,754 + 15,553 = 430,307

(end of fifth year)

3.75% of 430,307 is 16136.512499999999, but I'm rounding it down to 16,136

430,307 + 16,136 = 446,443

(end of sixth year)

3.75% of 446,443 is 16741.6125, but I'm rounding it up to 16,742

446,443 + 16,742 = 463,185

(end of seventh year)

Hopefully, that helped :) I rounded to make the numbers easier to work with, rounding down with numbers below 5, and rounding up with numbers 5 and above.

Answer:

it's C

Step-by-step explanation:

pink or purple hamster plz :D

omg paint strips, that's the way to go

Observations consisting of pairs of variable data are required to construct a scatter plot chart. A scatter plot chart is a graphical representation of the relationship between two variables.

One variable is plotted on the horizontal axis, while the other variable is plotted on the vertical axis. Each point on the chart represents an observation or data point consisting of a pair of values for the two variables being plotted. The scatter plot chart is useful for identifying patterns, trends, and relationships between the variables. It can also be used to detect outliers or unusual observations that do not follow the general pattern of the data.

The scatter plot chart can be enhanced by adding regression lines or trend lines, which provide a visual representation of the linear relationship between the two variables. Overall, the scatter plot chart is a powerful tool for analyzing and understanding the relationship between two variables in a dataset.

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Observations consisting of pairs of variable data are required to construct a scatter chart.

A scatter chart is a graphical representation of a set of observations where one variable is plotted on the x-axis and the other variable is plotted on the y-axis. Scatter charts are useful in identifying patterns and relationships between the two variables. The strength and direction of the relationship between the variables can be determined by examining the pattern of the scatter chart. If the data points are tightly clustered around a straight line, then there is a strong linear relationship between the two variables. On the other hand, if the data points are scattered without any pattern, then there is no relationship between the two variables. Scatter charts are commonly used in scientific research, marketing analysis, and other fields where two variables need to be analyzed simultaneously.

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Answer:  

m<1 = 51

m<2 = 34

m<3 = 95

m<4 = 38

m<5 = 47

m<6 = 74

m<7 = 59

Step-by-step explanation: because to get angle 1 you take 180 (because its is a straight line) and subtract the angle 129 giving you m<1 witch is 51. the second one is 180 - (m<1 + 95) =m<2 witch is 34 so m<2 = 34. third is the angle 95 because the lines that intersect give equal opposite angles so m<3 = 95. Four is 180 - (m<3 + 47) =m<4 witch is 38. fifth is opposite angle so it is 47. sixth is m<5 +m<6 + m<7 = 180 so m<5 is 47 and we can find m>7 by subtracting from 180 the angle 121 giving us m<7 = 59 so we will add m<5 and m<7 and subtract from 180 giving us m<6 witch is 74.    

a) If 20 servers are available, they can serve approximately 114.29 tables in 20 minutes

b) To serve 160 tables in 20 minutes, the hotel would need approximately 35 servers

To answer these questions using the Service Capacity Excel template, we need to first determine the service rate (customers served per hour) and the arrival rate (customers arriving per hour).

Since it takes 4 minutes to get the meals and serve them to 10 guests (1018 seconds = 180 seconds = 3 minutes), the service time per table is 4 + 3 = 7 minutes. Therefore, the service rate is 60/7 tables per hour, or approximately 8.57 tables per hour per server. With 20 servers, the total service rate is 208.57 = 171.43 tables per hour.

Since we want to know how many tables can be served in 20 minutes, we need to convert this to an hourly arrival rate. There are 3 sets of 20 minutes in an hour, so the arrival rate is 160/3 = 53.33 tables per hour.

Using the Service Capacity Excel template, we enter the service rate of 171.43 tables per hour and the arrival rate of 53.33 tables per hour. We then select the "Number of servers" option and vary the number of servers until the utilization (or occupancy) is close to 100% (but not over). We find that the minimum number of servers needed to achieve this is 35. Therefore, the hotel needs 35 servers to be able to serve 160 tables in 20 minutes.

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The 98 percent confidence interval for the mean hours spent on personal tasks for 25-44 years olds will be (3.97, 4.11).

From the complete information, it should be noted that the mean is 4.04, the standard deviation is 0.81 and the number is 708.

Since the sample size is large, so the z-critical will be used. In this case, the critical value is 2.33.

The 98% confidence interval will be:

= 4.04 + 2.33(0.81/✓768)

= 4.11

Also, 4.04 - 2.33(0.81/✓768)

= 3.97

Therefore, the 98% confidence interval is (3.97, 4.11).

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\(r - 1\)

\(( - r - 5) - ( - 2r - 4) \\ ( - r - 5) + 2r + 4\)

\(( - r - 5) + 2r + 4 \\ - r - 5 + 2r + 4\)

\( - 3 \purple{ - 5} + 2r + \purple{4} \\ - r \purple{ - 1} + 2r\)

\( \purple{ - r } - 1 + \purple{2r} \\ \purple{1r} - 1\)

\(1r - 1 \\ r - 1\)

Hopefully it's help

I copy MissJoy2 answer cuz her/his answer is right

Answer:

Duh MeepMeepMeepMeep

Step-by-step explanation:

bc I said

Answer:

Meepmeepmeepmeep or Meeeeeeeep.

Step-by-step explanation:

Meeeeeeeep has all of the es. Meepmeepmeepmeep has everything.

Answer:

.6

Step-by-step explanation:

Ratios are just another way of writing fractions. 3:5 is just 3/5 which is .6 or 60%

Answer:

-12.6

Step-by-step explanation:

Answer:

12.6 this is the answer

Step-by-step explanation:

sporting get up in subtracting numbers

The type of water-based ecosystem that can be found in all regions of North Carolina are Ocean Pond

A tiny body of quiet, pure water is called a pond. It varies from a river or stream since there is no flowing water in it, and it differs from a lake because it is only a tiny area and only 1.8 meters deep.

About 71 percent of the surface of the Earth is covered by the ocean, a vast body of saltwater. Oceanographers and nations throughout the world have historically classified the planet's ocean into four separate regions: the Pacific, Atlantic, Indian, and Arctic seas.

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Answer: I would guess B

Step-by-step explanation: If I am wrong.... I am really sorry. :(

The volume of the solid is 243/2 cubic units. To find the volume of the solid, we need to integrate the function z = 9 - y - x^2 over the bounded region in the first octant.

The region is bounded by the coordinate planes, so we have the limits of integration as follows:

0 ≤ x ≤ √9-y
0 ≤ y ≤ 9

The solid is bounded, so the integral will give us a finite volume:

V = ∫∫z dA, where the double integral is taken over the bounded region.

V = ∫[0,√9-y]∫[0,9] (9-y-x^2) dx dy

We can simplify the integrand by integrating with respect to x first:

V = ∫[0,9] ∫[0,√9-y] (9-y-x^2) dx dy
V = ∫[0,9] (9y - y^2 - 3(9-y)^2/2) dy
V = ∫[0,9] (-3y^2 + 54y - 243/2) dy
V = [-y^3/3 + 27y^2 - 243/2 y] [0,9]
V = 243/2

Therefore, the volume of the solid is 243/2 cubic units.

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By looking at the table, you can see that we have an x

that is paired with two different y's so this does not fit the

definition of a function which states that each x must

be paired with exactly one y.

Answer:

Step-by-step explanation:

Option D is the correct answer

8 + D = 43

Answer:

The last one

Step-by-step explanation:

8 - (-d) = 43 is the same as 8 + d = 43

Answer:

Step-by-step explanation:

Step-by-step explanation:

5:15

=1/3

=0.333

=33.3%