which of the following groups of numbers is ordered from least to greatest?

A. 1/5, 3/8, 4/10, 0.45, 0.6
B. 1/5, 3/8, 0.45, 4/10, 0.6
C. 0.6, 0.45, 4/10, 3/8, 1/5
D. 0.6, 4/10, 0.45, 1/5, 3/8

Answers

Answer 1

ans.(a) is correct

only in option (a) numbers are arranged from least to greatest.


Related Questions

if r=11 units and x = 15 units, then what is the volume of the cylinder shown above?

Answers

The volume of the cylinder  V = πr²h. Therefore, we need to have more information about the cylinder's height in order to solve this problem.

To find the volume of the cylinder, we first need to know the height of the cylinder. However, the height is not given in the question. Therefore, we cannot determine the volume of the cylinder with the given information.

We can use the formula for the volume of a cylinder, which is V = πr²h, where V is the volume, r is the radius, and h is the height.

Since r = 11 units and x = 15 units, we can find the diameter of the base of the cylinder by multiplying r by 2, which gives us 22 units. However, we still do not know the height of the cylinder.
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Find the prime factorization of each number. Record without and then with exponents. 75​

Answers

Answer:

5*5*3

5²*3

Step-by-step explanation:

Assuming that we have to find prime factorization of 75:

75 = 25 * 3

75 = 5*5*3

FILL IN THE BLANK. Determine the direction in which f has maximum rate of increase from P. f(x,y,z) x²y√ z, P= (-1,7,9) = (Give your answer using component form or standard basis vectors. Express numbers in exact form. Use symbolic notation and fractions where needed.) direction of maximum rate of increase:_______ Determine the rate of change in that direction. (Give an exact answer. Use symbolic notation and fractions where needed.) rate of change:_______

Answers

Direction of maximum rate of increase: (-14, 3, 7/3).

The rate of change in that direction:√(196 + 9 + 49/9).

To determine the direction in which f has a maximum rate of increase from point P(-1, 7, 9):

We need to find the gradient of the function f(x, y, z) = x²y√z.

The gradient is given by the vector of partial derivatives with respect to x, y, and z:

∇f = (df/dx, df/dy, df/dz)

First, find the partial derivatives:

df/dx = 2xy√z
df/dy = x²√z
df/dz = (1/2)x²y*z^(-1/2)

Now, evaluate the gradient at point P(-1, 7, 9):

∇f(P) = (2(-1)(7)√9, (-1)²√9, (1/2)(-1)²(7)*(9^(-1/2)))
∇f(P) = (-14, 3, 7/3)

The direction of maximum rate of increase is given by the gradient at point P, which is (-14, 3, 7/3).

To determine the rate of change in that direction:

The rate of change is given by the magnitude of the gradient vector:

Rate of change = ||∇f(P)|| = √((-14)^2 + (3)^2 + (7/3)^2)
Rate of change = √(196 + 9 + 49/9)

The rate of change is the square root of this value, which is an exact representation of the rate of change in the direction of maximum increase.

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The difference between the record high and low temperatures in Chicago, Illinois is 109°F. The record low temperature was -5°F. Use an equation to find the record high temperature.

Answers

The value of the record high temperature is 114°F

Using an equation to find the record high temperature.

From the question, we have the following parameters that can be used in our computation:

The difference between the record high and low temperatures in Chicago, Illinois is 109°F. The record low temperature was -5°F.

This means that

High - Low = 109

Substitute the known values in the above equation, so, we have the following representation

High - 5 = 109

Add 5 to both sides

High = 114

Hence, the record high temperature is 114°F

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Frank needs to find the area enclosed by the figure. The figure is made by


attaching semicircles to each side of a 54-m-by-54-m square. Frank says the area


is 1,662. 12 m2. Find the area enclosed by the figure. Use 3. 14 for it. What error


might Frank have made?


The area enclosed by the figure is


m2


(Round to the nearest hundredth as needed. )

Answers

To find the area enclosed by the figure, we first need to find the area of  the square and the  area of each semicircle.

The area of the square is simply the length of one of its sides squared, which is:

54 m x 54 m = 2,916 m²

The area of each semicircle is half the area of a full circle with the same radius as the side of the square. The radius of each semicircle is 54 m/2 = 27 m.

The area of each semicircle is:

1/2 x π x 27 m² = 1/2 x 3.14 x 27 m x 27 m ≈ 1,442.31 m²

Since there are four semicircles, the total area of the semicircles is:

4 x 1,442.31 m² = 5,769.24 m²

Therefore, the total area enclosed by the figure is:

2,916 m² + 5,769.24 m² ≈ 8,685.24 m²

Frank's answer of 1,662.12 m² is significantly less than the actual area. He may have made the mistake of only calculating the area of one of the semicircles instead of all four, or he may have forgotten to include the area of the square.

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The revenue from selling q items is R(q)=625q−q2, and the total cost is C(q)=50+6q. Write a function that gives the total profit earned, and find the quantity which maximizes the profit.

Answers

To find the total profit earned, we need to subtract the total cost from the revenue. Therefore, the profit function is:

P(q) = R(q) - C(q)
P(q) = 625q - q^2 - (50 + 6q)
P(q) = -q^2 + 619q - 50

To find the quantity which maximizes the profit, we need to take the derivative of the profit function and set it equal to zero:

P'(q) = -2q + 619
0 = -2q + 619
2q = 619
q = 309.5

Therefore, the quantity which maximizes the profit is 309.5. To find the total profit earned at this quantity, we plug it back into the profit function:

P(309.5) = -(309.5)^2 + 619(309.5) - 50
P(309.5) = $95,268.25

So the total profit earned at the quantity which maximizes the profit is $95,268.25.

To find the total profit function, you'll want to subtract the total cost function, C(q), from the revenue function, R(q). So the profit function, P(q), is given by:

P(q) = R(q) - C(q) = (625q - q^2) - (50 + 6q)

Now, simplify the profit function:

P(q) = 625q - q^2 - 50 - 6q = -q^2 + 619q - 50

To find the quantity which maximizes the profit, you can take the first derivative of the profit function with respect to q, set it equal to 0, and solve for q:

P'(q) = -2q + 619

Set P'(q) to 0 and solve for q:

0 = -2q + 619
2q = 619
q = 309.5

Since you can't have a fraction of an item, consider checking q = 309 and q = 310 to find the maximum profit. Evaluate P(q) at both points:

P(309) = -309^2 + 619(309) - 50
P(310) = -310^2 + 619(310) - 50

P(309) = 95441
P(310) = 95439

Thus, the quantity which maximizes the profit is 309 items.

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Does the transformation appear to be a rigid motion?

Answers

The transformation appears to be a rigid motion because A. Yes, because the angle measures and the distances between the vertices are the same as the corresponding angle measures and distances in the preimage.

What is a rigid motion transformation ?

A rigid motion transformation, colloquially referred to as an isometry, preserves the conformation and magnitude of a geometric construct. This change consists of translations, rotations, and reflections.

For this particular example, the preimage happens to be a right triangle facing leftward, whilst the image is an inverted right triangle facing eastward. This transmutation can be realized through a conjunction of reflection and rotation while maintaining similar angle measurements and distances between vertices. As a result, it is evidently a rigid motion.

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Complete the proof that the point (, −3) does or does not lie on the circle centered at the origin and containing the point (5, 0).
the radius of the circle is

Answers

The radius of the circle is 5.

To complete the proof, we need to find the radius of the circle centered at the origin and containing the point (5, 0). We can use the distance formula to find the distance between the origin (0, 0) and the point (5, 0):

distance = √((5 - 0)^2 + (0 - 0)^2) = √25 = 5

Therefore, the radius of the circle is 5.

Now, to determine whether the point (, −3) lies on the circle, we need to find the distance between the origin and the point (, −3):

distance = √((-3 - 0)^2 + (0 - 0)^2) = √9 = 3

Since the distance between the origin and the point (, −3) is not equal to the radius of the circle, which is 5, we can conclude that the point (, −3) does not lie on the circle centered at the origin and containing the point (5, 0).

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Pls help and actually answer the question pls

Answers

Answer:

y = |x - 1|

Step-by-step explanation:

This is an absolute value function in the form g(x) = |x - h| + k, where

(h, k) is the vertex, (1, 0).  Substitute these values into the function to get the equation of the graph:

y = |x - 1| + 0 = |x - 1|

A construction company makes cement stairs from a wooden mold. The construction company must calculate the volume of the mold to determine how much cement they need to create the stairs. What is the volume of the wooden mold?

Answers

If the mold is not a rectangular prism, then the formula for its volume will be different, depending on its shape.

How to calculate the volume of the wooden mold?

To calculate the volume of the wooden mold, we need to know its dimensions. Let's assume that the mold is in the shape of a rectangular prism, with length (L), width (W), and height (H).

Then, the volume (V) of the wooden mold is given by the formula:

V = L x W x H

To find the values of L, W, and H, the construction company needs to measure the dimensions of the mold using a measuring tape or ruler. Once they have the measurements, they can plug them into the formula above to find the volume of the mold.

It's important to note that the units of measurement used for the dimensions of the mold should be consistent. For example, if the length and width are measured in feet, then the height should also be measured in feet, and the resulting volume will be in cubic feet.

If the mold is not a rectangular prism, then the formula for its volume will be different, depending on its shape.

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Cause then you'd only get one answer to study.


Now back to the


a collection of facts,


Numbers, measurements and things like that.


conclusion


estimate


data

Answers

A collection of information, such as numbers, measurements, or observations, is commonly referred to as data.

Data can be collected from a wide variety of sources, such as surveys, experiments, or observations, and can be analyzed to reveal patterns, trends, and relationships.

Data can be represented in many different ways, including tables, graphs, charts, or statistical summaries, and can be used to make informed decisions in a wide range of fields, including business, science, healthcare, and social sciences.

However, it is important to ensure that the data is accurate, reliable, and unbiased, and that appropriate statistical methods are used to analyze and interpret it.

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Full Question: What is a collection of information such as number measurement or observation called?

A supermarket has three options for purchasing a brand of cereal:
Standard $2. 49 for 220g
Economy $5. 00 for 725g
Supersize $11. 50 for 2kg
Compare the cost of each for 100g, and order the brands from cheapest to most expensive

Answers

A comparison of the cost of each for 100 g indicates that the standard which costs about $1.13 per 100 grams is more expensive than the supersize which costs about $0.69 per 100 g and the supersize is more expensive than the economy which costs $0.575 per 100 g.

The cost per 100 g the standard is more than the cost per 100 g of the supersizeThe cost per 100 g of the supersize is more than the cost of the economy brand per 100 grams.

The order of the cost of the brands from cheapest to most expensive can be presented as follows;

Supersize > Economy > Standard

What is a cost per unit?

The cost per unit is the cost of a number of items, divided by the number of units of the item.

The unit cost of the brands of cereal sold at the supermarket are therefore;

Unit cost per 100 gram for Standard = $2.49/220 g × 100 ≈ $1.13/g

Unit cost per gram for Economy = $5.00/725 g × 100 = $100/145/ g ≈ $0.69/g

Unit cost per gram for Supersize = $11.50/2kg × 100 = $1150/2,000 g ≈ $0.575/g

Based on the above unit cost, we get;

1.13 > 0.69 > 0.575

Therefore, the cheapest brand is the supersize with a cost per 100 gram of $0.575/g, followed by the economy, with a cost per 100 grams which is about $0.69/g then the most costly is the standard, with a cost per 100 gram of $1.13/g

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A community organization wishes to know the proportion of subjects who feel financially comfortable in a certain town.



Based on last year's census, 64% of the residents in this town felt financially comfortable. In this year's survey 56 out of 115 randomly chosen subjects felt financially comfortable. Comfortable.



If indeed the residents' economic opinions have NOT changed from last year, what's the probability of getting a survey of size n = 115, where 56 or fewer subjects say they feel financially comfortable?




a. 0. 0006




b. 0. 0003




c. 0. 3245




d. 0. 0927




e. 0. 9997

Answers

The probability of getting a survey of size n = 115, where 56 or fewer subjects say they feel financially comfortable is 0.0003. Therefore, the correct option is B.

To find the probability of getting a survey of size n = 115, where 56 or fewer subjects say they feel financially comfortable if the residents' economic opinions have not changed from last year, we can use the normal distribution as an approximation to the binomial distribution.

1. Calculate the mean (μ) and standard deviation (σ) of the binomial distribution using the proportion from the census (64%) and the sample size (n = 115).

Mean (μ) = n * p = 115 * 0.64 = 73.6

Standard deviation (σ) = √(n * p * (1-p)) = √(115 * 0.64 * 0.36) ≈ 6.45

2. Convert the observed value (56) to a z-score:

z = (x - μ) / σ = (56 - 73.6) / 6.45 ≈ -2.73

3. Find the probability of getting a z-score less than or equal to -2.73 using a z-table or an online calculator.

P(Z ≤ -2.73) ≈ 0.0032

The closest answer choice to this probability is 0.0003, so the correct answer is (b) 0.0003.

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In two or more complete sentences, describe the steps a consumer can take to become more knowledgeable.
uploa

Answers

There are several steps a consumer market can take to become more knowledgeable like research and asking questions.

Research The first step is to  probe the product or service that you're interested in. This involves looking at reviews, product descriptions, and comparing prices. You can also look for information from  dependable sources  similar as consumer reports or government websites.   Ask questions If you have any  dubieties or  enterprises, don't  vacillate to ask the  dealer or service provider.

Ask them about their experience and qualifications, and make sure to clarify any terms or conditions that are unclear.   Get a alternate opinion If you're  doubtful about a product or service, seek the advice of someone you trust or who has  moxie in that area. They can help you make an informed decision grounded on their knowledge and experience.

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A rectangle that is 7 feet wide has an area of 56 square feet

Answers

The length of the rectangle is 8 feet given it is 7 feet wide and has an area of 56 square feet.

A rectangle is a geometric figure with four straight sides and four right angles, where the opposite sides are parallel and equal in length. In this case, we are given that the rectangle has a width of 7 feet and an area of 56 square feet. The area of a rectangle is calculated by multiplying its length (L) and width (W), expressed as A = L × W.

We are provided with the width, W = 7 feet, and the area, A = 56 square feet. To find the length of the rectangle, we can rearrange the area formula:

L = A ÷ W

Substituting the given values, we have:

L = 56 ÷ 7

L = 8 feet

Hence, the length of the rectangle is 8 feet. To summarize, a rectangle with a width of 7 feet and an area of 56 square feet has a length of 8 feet. The dimensions of the rectangle are 7 feet by 8 feet.

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A rectangular box will have a square cross section and a volume of 500 cubic centimeters. A. Sketch the box and sketch a net for the box. Assume the box will have an open top. Label the dimensions. B. Using w for the width and h for the height, find an expression in h and w for w the surface area of the box. C. Find the width and height that will make the surface area as small as possible

Answers

The expression for the surface area of the box is if w is A = x² + 2(xh) + 2(h²) the width of the box and h is the height. The dimensions of the box that minimize the surface area are approximately 11.68 cm by 11.68 cm by 6.19 cm.

The sketch of the box and the sketch of the net of the box is attached below. The box has a square base of side length x, and height h. The volume of the box is given as 500 cubic centimeters, therefore

x × x × h = 500

The surface area of the box can be found by summing the areas of each of the six faces. The top face is a square of side length x, so its area is x². The other five faces are all rectangles. The area of each of these rectangles is given by its length times its width. Therefore, the surface area of the box is

A = x² + 2(xh) + 2(h²)

To find the dimensions that minimize the surface area, we can use calculus. We can first solve the equation for x in terms of h

x² = 500/h

x = √(500/h)

Substituting this expression for x into the equation for the surface area, we get

A = 500/h + 2h×√(500/h) + 2h²

We can find the derivative of this expression with respect to h

dA/dh = -500/h² + sqrt(500/h) - 4h

Setting this derivative equal to zero and solving for h, we get

-500/h² + sqrt(500/h) - 4h = 0

Using a calculator or computer, we can find that this value is approximately 6.19. Substituting this value back into the equation for x, we get

x = √(500/6.19) ≈ 11.68

Therefore, the dimensions of the box that minimize the surface area are approximately 11.68 cm by 11.68 cm by 6.19 cm.

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Please hurry I need it ASAP

Answers

To solve this problem, we can use something called the law of sines. This is a proportional relationship in which the sine of one angle over the opposite side is equal to the sine of another angle over its opposite side.

sin(a) / a = sin(b) / b = sin(c) / c

To use the law of sines, we will need to figure out the measure of angle C, however.

27 + 132 + C = 180

159 + C = 180

C = 21

Now that we have sides and their opposite angles, we can apply the law of sines.

sin(27) / AC = sin(21) / 26

AC x sin(21) = sin(27) x 26

AC = [ sin(27) x 26 ] / sin(21)

AC = 32.9375

AC (rounded) = 32.9

Answer: AC = 32.9 m

Hope this helps!

Pls
provide correct ans. Will upvote
Let C be the curve y = 3x3 for 0 < x < 3. 80 72 64 56 48 40 32 24 16 8 0.5 1 1.5 2 2.5 Find the surface area of revolution of C about the x-axis. Surface area =

Answers

The surface area of revolution of C about the x-axis is π/27 (81^(3/2) - 1) or approximately 478.48 units².

How to the surface area of revolution of a curve?

To find the surface area of revolution of C about the x-axis, we can use the formula:

Surface area = ∫2πy ds

where y is the function that defines the curve C, and ds is an element of arc length along the curve.

We can express ds in terms of dx as follows:

ds = √(1 + (dy/dx)²) dx

where dy/dx is the derivative of y with respect to x.

For the curve C, we have:

y = 3x³

dy/dx = 9x²

Substituting these into the expression for ds, we get:

ds = √(1 + (9x²)²) dx

= √(1 + 81x⁴) dx

Substituting y and ds into the formula for surface area, we get:

Surface area = ∫₂πy √(1 + (dy/dx)²) dx

= ∫₀³ 2π(3x³) √(1 + 81x⁴) dx

This integral can be evaluated using substitution:

Let u = 1 + 81x⁴

Then du/dx = 324x³

And dx = du/324x³

Substituting these into the integral, we get:

Surface area = ∫₁₀³ 2π(3x³) √(1 + 81x⁴) dx

= 2π/108 ∫₁₀³ (3x³) √u du

= π/54 ∫₁₀³ u^(1/2) du

= π/54 (2/3) u^(3/2) | from 1 to 81

= π/81 (2/3)(81^(3/2) - 1)

= π/27 (81^(3/2) - 1)

Therefore, To find the surface area of revolution of C about the x-axis, we can use the formula:

Surface area = ∫2πy ds

where y is the function that defines the curve C, and ds is an element of arc length along the curve.

We can express ds in terms of dx as follows:

ds = √(1 + (dy/dx)²) dx

where dy/dx is the derivative of y with respect to x.

For the curve C, we have:

y = 3x³

dy/dx = 9x²

Substituting these into the expression for ds, we get:

ds = √(1 + (9x²)²) dx

= √(1 + 81x⁴) dx

Substituting y and ds into the formula for surface area, we get:

Surface area = ∫₂πy √(1 + (dy/dx)²) dx

= ∫₀³ 2π(3x³) √(1 + 81x⁴) dx

This integral can be evaluated using substitution:

Let u = 1 + 81x⁴

Then du/dx = 324x³

And dx = du/324x³

Substituting these into the integral, we get:

Surface area = ∫₁₀³ 2π(3x³) √(1 + 81x⁴) dx

= 2π/108 ∫₁₀³ (3x³) √u du

= π/54 ∫₁₀³ u^(1/2) du

= π/54 (2/3) u^(3/2) | from 1 to 81

= π/81 (2/3)(81^(3/2) - 1)

= π/27 (81^(3/2) - 1)

Therefore, the surface area of revolution of C about the x-axis is π/27 (81^(3/2) - 1) or approximately 478.48 units².

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Lola is in a hot air balloon that has just taken off and is now floating 7 meters above its launching point. Julian is standing on the ground, 6 meters away from the launching point. How far apart are Lola and Julian? If necessary, round to the nearest tenth.

Answers

We can use the Pythagorean Theorem to find the distance between Lola and Julian. Let's draw a diagram to visualize the situation.

```
* Lola
|
| *
| 7 m
|
|
|
|
* Julian
6 m
```

The distance between Lola and Julian is the hypotenuse of a right triangle, with one leg being 7 meters (the height of the balloon) and the other leg being 6 meters (the distance between Julian and the launching point).

Using the Pythagorean theorem, we have:

```
distance^2 = 6^2 + 7^2
distance^2 = 36 + 49
distance^2 = 85
distance = sqrt(85)
distance ≈ 9.2 meters
```

Therefore, Lola and Julian are approximately 9.2 meters apart.

The rectangle has a perimeter of 62 millimeters. What is its area?

Answers

Let's assume that the length of the rectangle is x and the width is y.

The perimeter of the rectangle is given by:

P = 2x + 2y

Substituting P = 62, we get:

62 = 2x + 2y

Simplifying the above equation, we get:

x + y = 31

The area of the rectangle is given by:

A = xy

To find the area, we need to solve for one of the variables, either x or y. We can use the equation x + y = 31 to solve for y in terms of x:

y = 31 - x

Substituting this expression for y in the equation for the area, we get:

A = x(31 - x)

Expanding the above expression, we get:

A = 31x - x^2

To find the maximum area, we need to find the value of x that maximizes A. We can do this by completing the square:

A = - (x^2 - 31x)

A = - [(x - 15.5)^2 - 240.25]

A = 240.25 - (x - 15.5)^2

The maximum area occurs when x = 15.5, so the dimensions of the rectangle are:

x = 15.5 mm

y = 31 - x = 15.5 mm

The area of the rectangle is:

A = xy = 15.5 mm × 15.5 mm = 240.25 mm^2

Therefore, the area of the rectangle is 240.25 square millimeters.

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Bank Rate (RATE) has a closing price of $13.95 and earnings of $2.71. The company iStar Financial (STAR) has a closing price of $12.18 and earnings of $3.62. Determine which company is financially stronger using their PE ratios.

Answers

iStar Financial (STAR) has a lower PE ratio than Bank Rate (RATE), which suggests that it may be financially stronger

To determine which company is financially stronger using their PE ratios, we need to calculate the PE ratio for each company. PE ratio, or price-to-earnings ratio, is a financial metric used to measure the valuation of a company's stock. It is calculated by dividing the market price per share by the earnings per share.

For Bank Rate (RATE), the PE ratio can be calculated as:

PE ratio = market price per share / earnings per share

PE ratio = $13.95 / $2.71

PE ratio = 5.14

For iStar Financial (STAR), the PE ratio can be calculated as:

PE ratio = market price per share / earnings per share

PE ratio = $12.18 / $3.62

PE ratio = 3.37

A lower PE ratio indicates that a company's stock is relatively undervalued compared to its earnings. In this case, iStar Financial (STAR) has a lower PE ratio than Bank Rate (RATE), which suggests that it may be financially stronger.

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Question 7 Determine the way in which the line (x, y, z) = (2, -3, 0] + k[-1, 3, -1) intersects the plane [x, y, 2] = [4, -15, -8] + s[1, -3, 1] + t[2, 3, 1), if at all. [2T/2A] , - No text entered -

Answers

The line intersects the plane at the point (-4, 15, -6).

How to find the intersection of line in given plane?

The line (x, y, z) = (2, -3, 0) + k(-1, 3, -1) can be expressed parametrically as:

x = 2 - k

y = -3 + 3k

z = k

The plane [x, y, 2] = [4, -15, -8] + s[1, -3, 1] + t[2, 3, 1) can be expressed in scalar form as:

x + y - 2z = 14 + s - 2t

To find the intersection of the line and the plane, we can substitute the parametric equations of the line into the scalar equation of the plane:

(2 - k) + (-3 + 3k) - 2k = 14 + s - 2t

Simplifying this equation, we get:

-4k + 3 = 14 + s - 2t

We can also express the line and plane equations in vector form:

Line: r = (2, -3, 0) + k(-1, 3, -1) = (2-k, -3+3k, k)

Plane: r = (4, -15, -8) + s(1, -3, 1) + t(2, 3, 1) = (4+s+2t, -15-3s+3t, -8+s+t)

To find the intersection of the line and the plane, we need to find the values of k, s, and t that satisfy both equations simultaneously. We can do this by equating the vector forms of the line and plane and solving for k, s, and t:

2 - k = 4 + s + 2t

-3 + 3k = -15 - 3s + 3t

k = -8 - s - t

Substituting k into the first equation, we get:

2 + 8 + s + t = 4 + s + 2t

Simplifying this equation, we get:

t = 4

Substituting t = 4 and k = -8 - s - t into the second equation, we get:

-3 + 3(-8 - s - 4) = -15 - 3s + 3(4)

Simplifying this equation, we get:

s = -2

Substituting t = 4 and s = -2 into the first equation, we get:

k = 8 - s - t = 8 + 2 - 4 = 6

Therefore, the line intersects the plane at the point (x, y, z) = (2, -3, 0) + 6(-1, 3, -1) = (-4, 15, -6).

So the line intersects the plane at the point (-4, 15, -6).

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The time it takes Susan to drive to work each day is normally distributed with a mean of 42 minutes and a standard deviation of 4 minutes.



Approximately what percent of workdays does it take Susan between 38 and 46 minutes to drive to work?




50%



68%



95%



99. 7%

Answers

We can use the empirical rule to estimate the percentage of workdays it takes Susan between 38 and 46 minutes to drive to work. According to the empirical rule, for a normal distribution:

- About 68% of the data falls within one standard deviation of the mean

- About 95% of the data falls within two standard deviations of the mean

- About 99.7% of the data falls within three standard deviations of the mean

Since the mean is 42 minutes and the standard deviation is 4 minutes, one standard deviation below the mean is 38 minutes, and one standard deviation above the mean is 46 minutes. So, about 68% of the time it takes Susan between 38 and 46 minutes to drive to work.

Therefore, the answer is (B) 68%.

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6. How fast is each train traveling (km/h)? Round to the nearest whole number. a) Train A travels 520.4 km in 4.8 h b) Train B travels 72.1 km in 0.8 h​

Answers

Answer: a) To find the speed of Train A, we need to divide the distance traveled by the time taken:

Speed = Distance / Time

Speed = 520.4 km / 4.8 h

Speed ≈ 108.42 km/h

Rounding to the nearest whole number, we get:

Train A is traveling at 108 km/h (approximately).

b) To find the speed of Train B, we need to divide the distance traveled by the time taken:

Speed = Distance / Time

Speed = 72.1 km / 0.8 h

Speed ≈ 90.13 km/h

Rounding to the nearest whole number, we get:

Train B is traveling at 90 km/h (approximately).

Step-by-step explanation:

Solve x^2+6x=5 using any method. Round your solutions to the nearest hundredth

Answers

The solutions of the quadratic equation are:

x = - 3 ±√14

How to solve the quadratic equation?

Here we want to solve the equation:

[tex]x^2 + 6x = 5[/tex]

We can rewrite that to standard form:

[tex]x^2 + 6x - 5 = 0[/tex]

Completing squares we will get:

[tex](x^2 + 2*3*x + 3^2 - 3^2) - 5 = 0[/tex]

[tex](x + 3)^2 = 5 + 9[/tex]

x = - 3 ±√14

These are the two solutions of the quadratic equation.

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13. A colony of bacteria doubles in number every hour. The expression 250* 2h gives the number of
bacteria after h hours. What does the constant 250 in the expression represent?

Answers

Therefore, the expression 250 * [tex]2^h[/tex] gives the number of bacteria in the colony after h hours, assuming that the initial number of bacteria is 250.

What is expression?

In mathematics, an expression is a combination of numbers, variables, and mathematical operations, such as addition, subtraction, multiplication, and division. Expressions can also include parentheses, brackets, and other symbols to clarify the order of operations. Expressions can be evaluated to obtain a numerical result or can be simplified using mathematical rules and properties to make them easier to work with. In algebra, expressions are often used to represent relationships between variables and to solve equations and inequalities.

Here,

In the given expression 250*[tex]2^h[/tex], the constant 250 represents the initial number of bacteria in the colony.

Since the number of bacteria doubles every hour, if we start with 250 bacteria at the beginning, after one hour we will have 250 * 2 = 500 bacteria. After two hours, we will have 500 * 2 = 1000 bacteria, and so on.

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The diameter of a cylinder is 3 yd. the height is 12 yd. what is the first step to finding the volume of the​ cylinder? find the volume of the cylinder.

Answers

The volume of the given cylinder is 84.78 cubic yards.

The first step to finding the volume of a cylinder is to use the formula V = πr^2h, where r is the radius of the cylinder (which is half of the diameter). So, to find the radius, we divide the diameter (which is 3 yards) by 2, giving us a radius of 1.5 yards. Then, we can plug in the values for radius (1.5), height (12), and π (3.14) into the formula to find the volume:

V = πr^2h
V = 3.14 x 1.5^2 x 12
V = 84.78 cubic yards

Therefore, the volume of the cylinder is 84.78 cubic yards.
Hi! To find the volume of a cylinder with a diameter of 3 yards and a height of 12 yards, the first step is to find the radius.

Step 1: Since the diameter is 3 yards, you can find the radius by dividing the diameter by 2. Radius = Diameter / 2. So, the radius is 1.5 yards.

Step 2: Now, you can find the volume of the cylinder using the formula: Volume = π × (radius^2) × height. In this case, Volume = π × (1.5^2) × 12.

Step 3: Calculate the volume: Volume = π × 2.25 × 12. Using the value of π as approximately 3.14, the volume becomes 3.14 × 2.25 × 12.

Step 4: Multiply the numbers: Volume ≈ 84.78 cubic yards.

So, the volume of the cylinder is approximately 84.78 cubic yards.

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Last week, hayden rode his bike 5 times. each time, he biked a 3-mile path, a 2-mile path, and a 2 1 4 -mile path. which expression represents the total number of miles he biked? a. 5 × ( 3 2 2 1 4 ) b. 5 ( 3 × 2 × 2 1 4 ) c. 5 × ( 3 × 2 × 2 1 4 ) d. 5 ( 3 2 2 1 4 )

Answers

The correct expression to represent the total number of miles Hayden biked is A. 5 × (3 + 3 + 2 1/4)

This is because each time Hayden rode his bike, he biked a 3-mile path, a 2-mile path, and a 2 1/4 -mile path. To find the total number of miles he biked, we need to add up the distance he biked each time and then multiply by the number of times he biked.

Using the distributive property of multiplication over addition, we can rewrite the expression as:

= 5 × (3 + 3 + 2 1/4)

Therefore, Hayden biked a total of 41 1/4 miles. The correct answer is A

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Y’all pls help this is due

Answers

the answer would be 4.7

Answer: 4.7KL

Step-by-step explanation:

KL=DAL/100

KL=470/100

KL=4.7

The student council is planning for the prom. They have broken down their expenses in the graph below. If they decide they will spend $1200 in refreshments, then what is their total budget?

Answers

The total budget of the prom, using the percentage concept, is given by = $ 4000.

Hence the correct option is (D).

Let the total budget be $ 100x.

Spending on Entertainment is 25% of the Budget.

So the spending on Entertainment = 100x*(25/100) = $ 25x.

Spending on Refreshments is 30% of the Budget.

So the spending on Refreshments = 100x*(30/100) = $ 30x.

Spending on Decorations is 45% of the Budget.

So the spending on Decorations = 100x*(45/100) = $ 45x.

It is also given that the spending on refreshments in dollar is $ 1200.

According to information,

30x = 1200

x = 1200/30

x = 40

Hence the total budget is = $100x = $ 100*40 = $ 4000.

So the correct option is (D).

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The question is incomplete. The complete question will be -

"The student council is planning for the prom. They have broken down their expenses in the graph below. If they decide they will spend $1,200 on refreshments, then what is their total budget?

Prom Budget:

Entertainment: 25%

Refreshments: 30%

Decorations: 45%

Answer choices:

A. $3,600

B. $6,000

C. $7,200

D. $4,000"

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