which of the following is a false statement? a. 29% of 1,390 is 403. b. 296 is 58% of 510. c. 49 is 75% of 63. d. 14% of 642 is 90.

The volume of the solid formed by rotating the region inside the first quadrant enclosed by the curves y = x and y = 5x about the x-axis is (250π/7) cubic units. When finding the volume of a solid of revolution, we use the method of cylindrical shells.

To calculate the volume, we integrate the area of each cylindrical shell formed by rotating an infinitesimally small strip about the x-axis. The height of each shell is the difference between the y-values of the two curves, which is (5x - x²). The circumference of each shell is given by 2πx, and the thickness is dx. Therefore, the volume of each shell is 2πx(5x - x²)dx.

To find the total volume, we integrate this expression over the interval where the two curves intersect. Setting\(y = x^2\)and y = 5x equal to each other, we get x² = 5x. Solving this equation, we find two intersection points: x = 0 and x = 5. Thus, the limits of integration are from 0 to 5.

Integrating the expression \(2\pi x(5x - x^2)dx\) from 0 to 5 gives us the volume of the solid formed by rotating the region inside the first quadrant. Evaluating this integral, we find the volume to be (250π/7) cubic units.

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The resulting dilated triangle is as attached and it has the coordinates; (2, 4), (4, -2) and (-6, -2).

When a triangle is dilated, it means that each vertex of the figure has it's coordinates multiplied by the scale factor of the dilation. Now, due to the fact that multiplication operation is involved, it means that the original triangle and the dilated triangle are not congruent, as their side lengths are different.

The vertices of the triangle are given as follows:

(1, 2), (2, -1) and (-3, -1).

The dilation has a scale factor of 2, meaning that each coordinate of the vertices will be multiplied by 2 and as such, the coordinates of the dilated triangle are given as follows:

(2, 4), (4, -2) and (-6, -2).

The new triangle is as attached

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The length of BC as shown in the diagram is 6.32units

The formula for calculating the distance between two points is expressed as:

D = √(x2-x1)²+(y2-y1)²

Given the following coordinate points (3, 6) and (5, 0)

Substitute

BC = √(0-6)²+(5-3)²

BC = √(36+4)

BC = √40

BC = 6.32 units

Hence the length of BC as shown in the diagram is 6.32units

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Answer: The total number of stamps is 132.

Step-by-step explanation:

We know that Erin has 36 stamps.

Given that information, we can calculate how many stamps Julia has which is 2/3 as many stamps as Erin.

2/3 * 36 = 24

Julia has 24 stamps.

Julia also has 1/3 as many stamps as Robert.

24 = 1/3 * Robert

Robert = 72 stamps

Add the three numbers together to get your final answer

24 + 72 + 36 = 132

Julia must sell 21 tacos to meet the requirement .

Given: Price of each taco = $ 3.75

Price of each burrito = $ 6

Total amount of money she needs to earn = $ 330

Also the number of burritos sold= 42.

So the total amount earned on selling these burritos= 42× 6 = $ 252

And as it is given that total money she needs to earn is $ 330 .

so required money= $ 330- $ 252

=$ 78

Thus the total number of tacos she needs to sell = 78/ price of 1 taco

= 78/ 3.75

= 20.8 ≈ 21

Thus Julia must sell 21 tacos to meet the requirement .

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Answer:

360 miles

Step-by-step explanation:

to find the distance, multiply speed and time

120*3= 360

Can I have brainliest plz

Answer:

hi! you have 2 points! this means slope formula! y2-y1/x2-x1

okay all you do now is plugin! (x1 1,y1 3) (x2 3,y2 7) what I did was label your x1 y1 x2 y2! now just follow the formula and that / is division or basically a fraction

7-3/3-1

that equals -5! and that's your slope! memorize the formula it helpss!                                      

The composite method for determining the location of the center of gravity of a composite body requires integration.

So, the answer is A.

The center of gravity is the point at which the entire weight of a body appears to act when the body is in equilibrium.

The concept of a center of gravity is used to calculate the behavior of a body when subjected to external forces. The composite method for determining the location of the center of gravity of a composite body involves integration.

The center of gravity is found by dividing the sum of the products of individual masses with their corresponding distance from an arbitrary reference line by the total mass of the system. When there is more than one weight distribution involved, the composite method is employed.

Hence, the answer of the question is A.

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Answer:

A relation is defined as the collection of inputs and outputs which are related to each other in some way. In case, if each input in relation has accurately one output, then the relation is called a function.

Based on the given relation, we found that it is not a function because it has repeating x-values. Remember, for a relation to be a function, each input (x-value) must correspond to exactly one output (y-value).

To determine if a relation is a function, you need to check if each input (x-value) corresponds to exactly one output (y-value). You can use the following steps:

1. Identify the given relation as a set of ordered pairs, where each ordered pair represents an input-output pair.

2. Check if there are any repeating x-values in the relation. If there are no repeating x-values, move to the next step. If there are repeating x-values, the relation is not a function.

3. For each unique x-value, check if there is only one corresponding y-value. If there is exactly one y-value for each x-value, then the relation is a function. If there is more than one y-value for any x-value, then the relation is not a function.

Let's consider an example relation: {(1, 2), (2, 3), (3, 4), (2, 5)}.

Step 1: Identify the relation as a set of ordered pairs: {(1, 2), (2, 3), (3, 4), (2, 5)}.

Step 2: Check for repeating x-values. In our example, we have a repeating x-value of 2. Therefore, the relation is not a function.

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A conclusion which can be inferred about an individual score that corresponds to a z-value of 1.0 is that: c.) it is likely to come from the healthy distribution.

A z-value is also referred to as a z-score or standard score and it can be defined as a measure of the distance between a raw score and the mean, when standard deviation units are used.

In Statistics, z-values can either be positive or negative and it can be calculated by using this formula:

\(Z=\frac{x\;-\;u}{\delta}\)

Where:

Since the individual score that corresponds to a z-value of 1.0, we can reasonably infer and logically conclude that an individual score is likely to come from the healthy distribution.

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Complete Question:

Scores of healthy adults on a neurological test form a normal distribution with mean = 100 and SD = 15. What conclusion can be inferred about an individual score that corresponds to a z value of 1.0?

a.) it falls in the general region of the population

distribution

b.) it falls in the common region of the distribution

c.) it is likely to come from the healthy distribution

d.) it is unlikely to come from the healthy distribution

Answer:

y = 3x -3

Step-by-step explanation:

Find the slope first

Givens

y2 = 3

y1 = - 3

x2 = 3

x1 = 1

Equation

m= (y2 - y1)/(x2 - x1)

Solution

m = (3 - - 3) / (3 - 1)

m = (3 + 3) / 2

m = 3

Find the y intercept next

Use either point to find the y intercept

y = 3x + b

x = 3

y = 3

y = 3*3 + b

3 = 6 + b

-3 = b

Answer

y = 3x - 3

the 20 bags of mulch will cover an area of 17,280 square inches when spread in a rectangular layer that is 3 inches thick.

To determine how much area the mulch will cover, you need to know the volume of mulch you have. Assuming each bag of mulch contains the same amount, you can find the total volume by multiplying the volume of one bag by the number of bags:

Total volume = volume of one bag x number of bags

To find the volume of one bag, you need to know the dimensions of the bag. Assuming the bag is roughly rectangular in shape, you can measure its length, width, and height, and then use the formula for the volume of a rectangular prism:

Volume of one bag = length x width x height

Let's say that the dimensions of one bag are 2 feet by 1.5 feet by 0.5 feet. Converting to inches, we get:Length = 2 x 12 = 24 inches

Width = 1.5 x 12 = 18 inches

Height = 0.5 x 12 = 6 inches

Volume of one bag = 24 x 18 x 6 = 2,592 cubic inches

If you have 20 bags of mulch, then the total volume is:

Total volume = 2,592 x 20 = 51,840 cubic inches

To find the area the mulch will cover, you need to know the area of the rectangle that will be covered by the mulch layer. Assuming the layer will be a uniform thickness of 3 inches, you can use the formula for the volume of a rectangular prism to find the area:

Volume = length x width x height

In this case, the height is the thickness of the layer, which is 3 inches. Solving for the area:

Area = Volume / Height

Area = (51,840 cubic inches) / (3 inches)

Area = 17,280 square inches

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Suspension bridges are significant structures that are supported by cables that are attached to towers. To support the deck of the bridge, the cables are placed at a higher elevation than the deck.

A cable of a suspension bridge has its supports at the same level, separated by a distance of 500 feet. The support structures are 100 feet taller than the lowest point of the cable. If the cable is of uniform density and has negligible weight,To determine the slope of the cable on the supports, we need to find the equation for the parabola formed by the cable.

The equation of the parabola will help us find the slope of the cable on the supports.Let the center of the cable be at the origin. We will use x and y as the variables. We know that the supports are separated by a distance of 500 feet. Therefore, the maximum height of the cable is 100 feet.

We will use the vertex form of the equation of a parabola to model the shape of the cable:y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. Since the vertex is at the origin, the equation of the parabola becomes:y = ax^2The highest point of the parabola is at (250, 100). Therefore, we can write:a(250)^2 = 100

a = 100/(250)^2The equation of the cable is:

y = (1/62500)x^2To find the slope of the cable on the supports, we need to differentiate the equation:

y' = (2/62500)xThe slope of the cable on the supports is:

y'(250) = (2/62500) x 250

= 1/625Therefore, the slope of the cable on the supports is 1/625.

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Answer:

b= (3z-6)/(1+3z)

Step-by-step explanation:

z=(-b+6)/(3b-3)

cross multiple

z(3b-3)=-b+6

open the bracket

3bz-3z=-b+6

make -b the subject of the formula

-b = 3bz-3z-6

-b - 3bz = -3z - 6

factorize the left hand side...

-b(1+3z) = -3z-6

make -b the subject of the formula again

-b = -(3z-6)/(1+3z)

cancel the minus at both sides...

b = (3z-6)/(1+3z)

Answer:

b = \(\frac{3z + 6}{3z+1}\)

Step-by-step explanation:

Simply solve for "b" , so the formula will be

b = .....

z = \(\frac{-b+6}{3b-3}\) ( b > 0 )

z(3b - 3) = - b + 6

3zb - 3z = - b + 6

3zb + b = 3z + 6

b( 3z + 1 ) = 3z + 6

b =  \(\frac{3z + 6}{3z+1}\)

Answer: The maximum height of Scott’s and Eric’s javelins were the same

Step-by-step explanation: bc I put it as my answer and I got it right

Answer: sin L= 3 cos L= 3 tan L= 3 sin M= 5 cos M= 5 tan M= 5

Step-by-step explanation:

im just like that

(a) The number of distinguishable arrangements of the word "acbens" is 180.

(b) The number of distinguishable arrangements of the word "baaben" is 60.

(c) The number of distinguishable arrangements of the word "aabbba" is 15.

(a) The word "acbens" has 6 letters, but two of them ("a" and "b") are repeated. We can use the formula for the number of permutations of n objects with k1, k2, ..., km indistinguishable objects of types 1, 2, ..., m, respectively:

P(n; k1, k2, ..., km) = n! / (k1! k2! ... km!)

For this word, we have k1 = 2 (for the two "a"s) and k2 = 1 (for the "b"). Plugging these values into the formula, we get

P(6; 2, 1) = 6! / (2! 1!) = 360 / 2 = 180

Therefore, there are 180 distinguishable arrangements of the word "acbens."

(b) The word "baaben" also has 6 letters, but this time there are three "a"s and two "b"s. Using the same formula as before, we have k1 = 3 and k2 = 2, so

P(6; 3, 2) = 6! / (3! 2!) = 720 / 12 = 60

Therefore, there are 60 distinguishable arrangements of the word "baaben."

(c) The word "aabbba" has 6 letters, but this time there are four "a"s and two "b"s. Using the same formula as before, we have k1 = 4 and k2 = 2, so

P(6; 4, 2) = 6! / (4! 2!) = 720 / 48 = 15

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False. The statement "sampling error increases when we increase sample size" is incorrect.

In fact, the opposite is true.

Sampling error typically decreases as the sample size increases.
Sampling error refers to the difference between a sample statistic (such as the mean or the percentage) and the true population value.

A larger sample size generally leads to a more accurate representation of the population because it includes more data points, reducing the impact of random fluctuations or outliers.
To better understand this concept, let's consider an example.

Suppose you are conducting a survey on the average height of people in a certain region.

If you only collect data from a small sample (e.g., 10 people), your estimate may be significantly off from the true population mean because your sample might not be representative of the entire population.

However, if you increase your sample size to 1,000 people, the sample is more likely to represent the overall population, and the estimate will be closer to the true population mean.

In this case, the sampling error will decrease as the sample size increases.
In summary, sampling error typically decreases when we increase sample size because larger samples are more likely to represent the true population, leading to more accurate estimates.

Always remember to use an appropriate sample size in your research to minimize sampling error and obtain more reliable results.

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Answer:

infinetely many salutions

Answer:

D

Step-by-step explanation:

infinitely many solutions

Answer:

13. (B). False

Explanation

in the image

(a) The company's break-even point in total sales dollars is $69,249,800. At the break-even point, the sales mix is as follows: Sale of mail pouches and small boxes: $55,399,840 and Sale of non-standardized boxes: $13,849,960

(b) If the company shifts its sales mix so that 60% of its revenue comes from the delivery of non-standardized boxes, the new break-even sales would be $46,166,533. The amount of sales provided by each service type would be as follows:

Sale of mail pouches and small boxes: $18,466,613

Sale of non-standardized boxes: $27,699,920

Explanation and Calculation:

(a) To calculate the company's break-even point, we use the weighted-average contribution margin ratio to find the total sales dollars at which the company's total contribution margin equals its fixed costs. The contribution margin ratio for mail pouches and small boxes is 20% (0.20), and for non-standardized boxes, it is 70% (0.70).

Let X be the total break-even sales, Y be the sales of mail pouches and small boxes, and Z be the sales of non-standardized boxes.

Based on the given information, we set up the following equations:

0.20Y + 0.70Z = X (equation 1) [Total contribution margin equals fixed costs]

Y + Z = X (equation 2) [Total sales dollars equals X]

From equation 2, we get:

Y = X - Z

Substituting Y = X - Z into equation 1, we have:

0.20(X - Z) + 0.70Z = X

0.20X - 0.20Z + 0.70Z = X

0.50Z = 0.80X

Z = 1.6X

Substituting Z = 1.6X into equation 2, we get:

Y + 1.6X = X

Y = -0.6X

Since Y represents the sales of mail pouches and small boxes, which cannot be negative, we ignore the negative solution and take Y = 0. Therefore, Z = X.

Substituting Z = X into equation 2, we find the break-even point:

Y + X = X

Y = 0

Thus, at the break-even point, the sales of mail pouches and small boxes are $0, and the sales of non-standardized boxes are equal to the total break-even sales, X.

(b) To find the break-even sales with the new sales mix, where 60% of the revenue comes from the delivery of non-standardized boxes and the remainder from mail pouches and small boxes, we can calculate the sales dollars based on the weighted-average contribution margin ratio.

Let Y2 be the new break-even sales, and let Y3 be the sales of mail pouches and small boxes with the new sales mix.

Using the weighted-average contribution margin ratio, we have:

0.60(0.70)Y2 + 0.40(0.20)Y2 = 13,824,900

0.42Y2 + 0.08Y2 = 13,824,900

0.50Y2 = 13,824,900

Y2 = 27,649,800

Therefore, the company's break-even sales with the new sales mix would be $27,649,800. The amount of sales provided by each service type would be:

Sale of mail pouches and small boxes: 40% of 27,649,800 = $11,059,920

Sale of non-standardized boxes: 60% of 27,649,800 = $16,589,880

Conclusion:

(a) The company's break-even point in total sales dollars is $69,249,800. At the break-even point, the sales mix is as follows:

Sale of mail pouches and small boxes: $55,399,840

Sale of non-standardized boxes: $13,849,960

(b) If the company shifts its sales mix so that 60% of its revenue comes from the delivery of non-standardized boxes, the new break-even sales would be $46,166,533. The amount of sales provided by each service type would be as follows:

Sale of mail pouches and small boxes: $18,466,613

Sale of non-standardized boxes: $27,699,920

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Answer:

5

Step-by-step explanation:

Answer:

  rectangle

Step-by-step explanation:

You want to know the name of the polygon with vertices D(3, 1), E(1, 5), F(9, 9), and G(11, 5).

It can be informative to look at the diagonal vectors DF and EG.

  DF = F -D = (9, 9) -(3, 1) = (6, 8)

  EG = G -E = (11, 5) -(1, 5) = (10, 0)

The lengths of these are found by the Pythagorean theorem:

  DF = √(6²+8²) = √(36 +64) = √100 = 10

  EG = √(10²+0²) = 10

The diagonals are the same length.

The midpoints of the diagonals are ...

  midpoint DF = (D +F)/2 = ((9, 9) +(3, 1))/2 = (12, 10)/2 = (6, 5)

  midpoint EG = (E +G)/2 = ((11, 5) +(1, 5))/2 = (12, 10)/2 = (6, 5)

The midpoints of the diagonals are the same point. This means the figure is a parallelogram.

A quadrilateral that has congruent diagonals that bisect each other is a rectangle.

__

Additional comment

Looking at the graph, we see the slopes of the line segments are 1/2 and -2, opposite reciprocals. This means they are perpendicular, another indication the figure is a rectangle.

The diagonal vectors do not have opposite reciprocal slope, so this is not a rhombus or square or kite.

Answer:

It is one row by two columns.

Step-by-step explanation:

48 ft

A  = 144ft² = l²

144 = l²

l = √144

l = 12 ft

P = 4l

= 4×12ft

= 48 ft

Answer:

It should be ≈ 6,6

calculated the angle <CAB and both are 90°. But that would mean BC is wrong

Using proportions, the costs are given as follows:

a) Total Labor Cost: $2,505,600.

b) Total Product Cost: $1,950,000.

c) Total Cost = $4,455,600.

d) Cost per home = $461.77.

e) Cost per week = $99,013.33.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

For item a, the labor cost is found using the earnings of the workers, as follows:

45 weeks x 5 days x 8 hours x 58 per hour x (12 + 8 + 4 workers)

Hence:

Total Labor Cost = 45 x 5 x 8 x 58 x 24 = $2,505,600.

For item b, the product cost is the cost of the boards, hence:

(175 + 150 + 50 boards) x 5,200

Total Product Cost = 375 x 5,200 = $1,950,000.

For item c, the total cost is the sum of the product cost and the labor cost, hence:

Total Cost = 2,505,600 + 1,950,000 = $4,455,600.

For item d, the cost per home is found dividing the total cost by the 9,649 homes, hence:

Cost per home = 4455600/9649 = $461.77.

For item e, the cost per week is found dividing the total cost by the 45 weeks, hence:

Cost per week = 4455600/45 = $99,013.33.

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Answer:

g(x) = 6 * 3^x

Step-by-step explanation:

This is the answer because the question states that the graph is vertically stretched by a factor of 6. Since the parent function of an exponential function is f(x) = a * 3^(k(x-d)) + c, we plug in 6 for a, where we get g(x) = 6 * 3^x.