Given x varies inversely with y and xy = 2, what is the value of x when y = 1?
-1
One-half
1
2

So Reena has ran a distance of 5 kilometers while only covering one-sixth of the distance.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical phrase with two equal sides separated by an equal sign is called an equation. An example of an equation is 4 + 6 = 10.

Here,

If Reena has completed one sixth of the 30 km run,

30 km / 6 = 5 km.

So, Reena has run a distance of 5 km so far when she had run one sixth of the distance.

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The value of x include the following: B. 52/3.

In Mathematics, the basic proportionality theorem states that when any of the two (2) sides of a triangle is intersected by a straight line which is parallel to the third (3rd) side of the triangle, then, the two (2) sides that are intersected would be divided proportionally and in the same ratio.

By applying the basic proportionality theorem to the given triangle, we have the following:

3x/4x = (3x + 7)/(5x - 8)

By cross-multiplying, we have the following:

3x(5x - 8) = 4x(3x + 7)

15x² - 24x = 12x² + 28x

3x² = 52x

3x = 52

x = 52/3.

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The probability of getting at least one question wrong on a 7 question multiple-choice test with two answers for each question is 1 - (1/4)^7, which is approximately 99.2%.

The probability of getting one question wrong on a 7 question multiple-choice test with two answers for each question is 1/4. This is because there are two options for each question, and if you choose the wrong one, you get the question wrong. Therefore, the probability of getting all 7 questions wrong is (1/4)^7, or one in 16,384. The probability of getting at least one question wrong on the test is 1 - (1/4)^7, which is equal to 1 - 1/16,384, or approximately 99.2%. To calculate the probability of getting at least one question wrong, you subtract the probability of getting all 7 questions correct from 1. This is because if you do not get all 7 questions correct, then you must have gotten at least one question wrong.

The complete question: On a 7 question multiple-choice test, where each question has 4 answers, what would be the probability of getting at least one question wrong? Give your answer as a fraction

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Vito can not use same amount of water for 40 flower pots, as it would take 15 liters of water.

Vito uses 9 liters of water 24 flower pots.

To find: the amount of liters of water (w) it would take to water 40 flower pots.

This means, 9 liters is to 24 pots as w liters is to 40 pots

We write above statement as :

9:24::w:40

So, we get an a proportion,

9/24 = w/40

We solve above equation for w.

24w = 9(40)

24w = 360

w = 360/24

w = 15 liters

Therefore, 15  liters of water it would take to water 40 flower pots.

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The complete question is:

Vito uses 9 liters of water 24 flower pots. He is wondering how many liters of water (w) it would take to water 40 flower pots. He assumes he'll use the same amount of water on each pot. Which portion could Vito use to model this situation? Solve the proportion how many liters of water it takes to water 40 flower pads

The likelihood of drawing an average even number first, followed by a number that is a multiple of 3, is frac1850 cdot[tex]$frac1649 = $frac2882450$[/tex].

Since the two events are independent of one another, the likelihood of drawing an even number first and then a multiple of 3 equals the product of the probabilities of the two events. In a deck of 50 cards, there are 18 even numbers and 16 multiples of 3, hence the likelihood of getting an even number is [tex]$frac$[/tex]1850 and the likelihood of drawing a multiple of 3 is frac1650. The likelihood of drawing an even number first, followed by a multiple of 3, is frac1850 cdot frac1650 = frac2882450 because these are separate events

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All the correct expression in each steps are,

⇒ Step 1; (m³ + m²n + mn² - m²n - mn² - n³)

( By multiplication distributor )

⇒ Step 2;  m³ - n³

( By combine like terms)

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The expression to prove is,

⇒ (m - n) (m² + mn + n²)

Now, We can simplify as;

⇒ (m - n) (m² + mn + n²)

Step 1;

⇒ (m³ + m²n + mn² - m²n - mn² - n³)

( By multiplication distributor )

Step 2;

⇒ m³ - n³

( By combine like terms)

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The domain and range of function f(x) = 2/3x² are respectively, real numbers and non-negative numbers

The domain of a function is the set of all input values (independent variable) for which the function is defined and produces a valid output (dependent variable).

The range of a function is the set of all possible output values of the function. It represents the set of all possible values of the dependent variable.

Given that,

The domain of the function f(x) = 2/3x² is all real numbers except x = 0, since division by 0 is undefined.

The function f(x) = 2/3x²

The range of the function f(x) = 2/3x² is all non-negative real numbers.

It is because for any real number x,

the value of 2/3x² will always be non-negative.

To see this, consider the case where x > 0.

In this case, 2/3x² is positive,

and for x < 0, 2/3x² is still positive.

So, the domain of the function f(x) = 2/3x² is all real numbers except x = 0 and the range of the function is all non-negative real numbers.

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So there are two possible triangles:

(10.5, 35.5, 37) and (35.5, 10.5, 37).

Let's call the length of the shorter leg x. Then, the longer leg would be 3x - 3, and the hypotenuse would be 4x - 7.

Using the Pythagorean theorem, we have:

x^2 + (3x - 3)^2 = (4x - 7)^2

Expanding and simplifying, we get:

x^2 + 9x^2 - 18x + 9 = 16x^2 - 56x + 49

Combining like terms, we have:

7x^2 - 74x + 40 = 0

Using the quadratic formula, we find the solutions for x:

x = (74 ± √(74^2 - 4 * 7 * 40)) / (2 * 7)

x = (74 ± √(2744 - 560)) / 14

x = (74 ± √2184) / 14

x = (74 ± 46.56)/14

x = (35.5, 10.5)

So there are two possible triangles:

(10.5, 35.5, 37) and (35.5, 10.5, 37).

These are the two solutions for the lengths of the sides of the triangle.

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The surface area and weight of the cylinder is 45.1805 in² and 11.107 lbs respectively.

A cylinder is a three-dimensional geometric shape that has two parallel circular bases and a curved lateral surface connecting the bases. The bases are located at opposite ends of the cylinder, and they have the same diameter. The lateral surface is a rectangle that has been bent around the circumference of the circular bases.

The height of a cylinder is the distance between the two bases, and the diameter of the bases is the distance across the circle through its center. The volume of a cylinder can be calculated by multiplying the area of one of its bases by its height. The formula for the volume of a cylinder is:

V = πr²h

where r is the radius of the circular base and h is the height of the cylinder.

Cylinders are commonly used in many real-world applications, such as in the design of pipes, cans, and other containers. They are also commonly used in mathematics and physics, where they can serve as models for objects with cylindrical symmetry, such as pipes and wires.

In summary, a cylinder is a three-dimensional shape with two parallel circular bases and a curved lateral surface connecting the bases. The height of the cylinder is the distance between the bases, and its volume can be calculated using the formula V = πr²h. Cylinders are commonly used in real-world applications and in mathematics and physics.

The following formula can be used to determine the cylinder's volume:

V = π × r² × h = π × (d/2)² × h = π × (1.35²) × 7.45 = 42.63374 in³

The following formula can be used to get the cylinder's surface area:

A = 2πr² + 2πrh = 2π × r² + 2π × r × h = 2π × (1.35²) + 2π × 1.35 × 7.45 = 45.1805 in²

The cylinder's weight can be determined using the formula below:

W = d × V = 0.259 lbs/in³ × 42.63374 in³ = 11.107 lbs.

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Answer:

Both Jill and John are correct.

Step-by-step explanation:

Triangle A and B are both similar to the triangle in question. They all have angles of 30, 60, and 90 degrees. We can infer this because all triangles have 180 degrees and the square in the corner means that it is a right angle (90 degrees).

The top of the ladder slips down the wall at the rate of 5.6 ft/sec.

What is a rate?

The ratio of two related quantities expressed in several units is known as a rate. The numerator of the ratio indicates the rate of change in the other (dependent) variable if the denominator of the ratio is written as a single unit of one of these quantities, and if it is assumed that this quantity may be modified systematically (i.e., is an independent variable).

Here, we have

Given: A ladder 15ft in length leans against a vertical wall, with the bottom of the ladder 5ft from the wall on the horizontal floor. If at that time the bottom end of the ladder is being pulled away at the rate of 2ft/s .

Let: x = the distance from the base of the ladder to the base of the wall

y = the distance from the tip of the ladder to the base of the wall, we have:

x² + y² = 15²

y² = 15² - 5² = 225 - 25 = 200 => y = 14.14 ft

2x dx/dt + 2y dy/dt = 0

2 * 5 * dx/dt + 2 * 14.14 * (-2) = 0

10 dx/dt = 56.56

dx/dt = 5.6 ft/sec

Hence, the top of the ladder slips down the wall at the rate of 5.6 ft/sec.

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Shoe Town provides the finest ultimate price, so Raven should purchase the boots there.

possessing an identical or consistent ratio or connection between two quantities: If y/x = k, in which k is the proportionality constant, then the numbers y and x are proportionate.

To determine which one is the best store for Raven let's calculate the price in each case.

Shoe Town

Total price:

Initial price - Mark down  + Sales tax

85.95 - 15% + 7.16 %

85.95 - 12.89 + 7.16 %

73.06 + 7. 16%

73.06 + 5.23 = 78.29

Lace Up

Total price:

Initial price - Mark down - Coupon + Sales tax

85.95 - 10% - 5 + 7.15%

89.95 - 8.99 - 5 + 7.15%

80.96 - 5 + 7.15%

75.96 + 7.15%

75.96 + 5.43 = 81.39

Run, Don't Walk

Total price:

Initial price + shipping

71.99 + 6.50 = 78.45

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The inequality for the given data can be written as 24x + 60y ≤ 2400 pounds.

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.

Given that A freight elevator can hold a maximum weight of 2,500 pounds. A 180-pound person has a load of boxes to deliver. Some of the boxes weigh 25 pounds each and some weigh 60 pounds each.

The inequality can be written as:-

24x + 60y ≤ 2400 pounds

The graph of the inequality is attached with the answer below.

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A scale model of a regulation-sized gymnasium that is 12 inches long would be 10 inches wide.

To determine the width of a scale model of a regulation-sized gymnasium, you need to determine the scale factor used to create the model. The scale factor is the ratio of the size of the model to the size of the actual object.

In this case, the length of the model is 12 inches, while the length of the actual gymnasium is 100 feet, or 1200 inches. So, the scale factor is: 12/1200 = 1/100.

To find the width of the model, you would multiply the width of the actual gymnasium, 80 feet, by the scale factor, 1/100. This gives you a width of:

80 × 1/100 = 0.8 feet = 10 inches.

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The probability that this ball is red after the jar is then shaken and one ball is randomly selected is 11/18.

There are four red balls and two white balls in a jar

P(white removed and then red is chosen)'

P = 2/6 * 5/6

= 10/36

P= 5/18

Probability that the white removed and then red is chosen is 5/18.

P(red removed and then white is chosen)

P = 4/6 * 1/2

= 4/12

= 1/3

P = 6/18

Probability that the red removed and then white is chosen is 6/18.

The probability that this ball is red,

P(red is chosen) = 5/18 +6/18 = 11/18

Therefore, The probability that this ball is red is 11/18.

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Answer:

B(1,-2)

Step-by-step explanation:

b is the answer from the above explanation

Answer:

x = 3 + √5 /  2

Step-by-step explanation:

4x²-12x+9=5

4(x²-3x+1=0)

x²-3x+1=0

(quadratic formula)

a=1  b=-3  c=1

x= -(-3)+√(-3)²-4x1x1 / 2x1

simplify:

x = 3+√5 / 2  

Danielle would most likely use the mean as a central tendency to describe her test scores because the mean would be her average

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Given that  the tests are out of twenty points, and she has gotten the following scores. 17, 19, 20, 14, 16

The mode of a set of data is the value that occurs most frequently. In this case, Danielle's scores are: 17, 19, 20, 14, 16.

There is no mode value.

Danielle would most likely use the mean as a central tendency to describe her test scores because the mean would be her average.

Hence, Danielle would most likely use the mean as a central tendency to describe her test scores because the mean would be her average.

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The Central Limit Theorem states that the distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the shape of the underlying population distribution.

If the sample size is large enough (typically, n >= 30), we can assume that the sample mean is approximately normally distributed with mean equal to the population mean and standard deviation equal to the population standard deviation divided by the square root of the sample size.

Therefore, if we know the population mean and standard deviation, we can calculate the probability that the sample mean will be greater than 3,011.76 or less than 2,988.24. Let's denote the population mean as mu and the population standard deviation as sigma. Then, the standard deviation of the sample mean is sigma / sqrt(n), where n = 1000 is the sample size.

We can standardize the sample mean using the z-score formula:

z = (x - mu) / (sigma / sqrt(n))

where x is the sample mean.

For the sample mean to be greater than 3,011.76, we have:

z = (3,011.76 - mu) / (sigma / sqrt(n)) > 0

And for the sample mean to be less than 2,988.24, we have:

z = (2,988.24 - mu) / (sigma / sqrt(n)) < 0

To find the probability, we need to find the area under the standard normal curve to the right of z for the first case, and to the left of z for the second case. These probabilities can be found using a standard normal table or a statistical software package.

Unfortunately, without knowledge of the population mean and standard deviation, it is not possible to determine the probability that the sample mean will be greater than 3,011.76 or less than 2,988.24.

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You have 7 lemons, by the consideration that you have 21 cuts available to divide the lemons.

What is the division?

A division is a process of splitting a specific amount into equal parts. For example, we can divide a group of 20 members into 4 groups of 5 members each or 5 groups of 4 members each, and so on.

To find out how many lemons you have, you need to take into consideration that you have 21 cuts available to divide the lemons.

With each cut, you can divide one whole lemon into two pieces or divide one section of lemon into two smaller pieces.

So, with 21 cuts, you can have a maximum of 2²¹ (2097152) pieces of lemon.

Since you have 30 jugs and each jug needs to have a piece of lemon, you would need at least 30 pieces of lemon.

To get 30 pieces of lemon with the minimum number of whole lemons, you would need 7 whole lemons (7 * 2 = 14 pieces, 14 * 2 = 28 pieces, 28 * 2 = 56 pieces, 56 - 30 = 26 pieces left over).

Therefore, you have 7 lemons, by the consideration that you have 21 cuts available to divide the lemons.

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The cash price of the refrigerator is $408.

A discount is the reduction of either the monetary amount or a percentage of the normal selling price of a product or service.

Given that, a new refrigerator has a price of $480.00.

The store will discount the price by 15% if the purchaser pays in cash.

Now, the discount is

15% of 480

= 15/100 ×480

= 0.15×480

= 72

Now, 480-72

= $408

Therefore, the cash price of the refrigerator is $408.

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The solution to the system of equations in this problem is given as follows:

x = 1.16, y = 3.71.

The system of equations for this problem is defined as follows:

Multiplying the first equation by 2, we have that:

x + 4y = 16

x = 16 - 4y.

Replacing into the second equation, the solution for y is obtained as follows:

3(16 - 4y) - 0.67y = 1

48 - 12y - 0.67y = 1

12.67y = 47

y = 47/12.67

y = 3.71.

Then the solution for x is of:

x = 16 - 4(3.71)

x = 1.16.

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What will the dimensions of some cross-sections of a cuboid be when cutting depends on the viewpoint.

We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.

Suppose we have a cuboid shape of a wooden block.

The height of the wooden block is h, the width of the wooden block is w and the length of the wooden block is l.

Now if we cut the wooden block along the red line a look at it from the top it will look like a rectangle width width 'w' and length 'l'.

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Answer: A. A rectangle 4 inches by 2 inches

Step-by-step explanation:

The graph represents the function that maps the area of the original figure to the area of the dilated figure. If the original area is 9 square units and the dilated area is x square units, then the equation y = √√x represents the relationship between the two areas. Points (B), (F), (G), and (H) are on the graph because they satisfy the equation y = √√x. Points (A), (C), and (E) are not on the graph because they do not satisfy the equation.

The scatter plot is given in the attached image below.

The correct option is D.

The straight line on a scatter plot closest to the points is called a trend line. Two points on a trend line can create an equation in slope-intercept form.

Given:

The data are shown in the table.

From the table:

When the value of x = 1, then y = 11.

And when x = 3, then y = 30.

Similarly, all the values are placed as per the data.

The scatter plot is given in the attached image.

Therefore, the plot is given below.

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Therefore , the solution of the given problem of expression comes out to be  there is no value of x which can make equation true.

Mathematical operations like addition, multiplication, variables and proliferation, and division are necessary. They result in the following when combined: An equation, some information, and a mathematical operator Values, parameters, and operations like additions, subtraction, multiplication, and division are all included in a statement of fact. Different sentences and words can be contrasted and compared.

Here,

Given :

Expression  is :

=> (1/64)ˣ / 2 + 1 = (1/16)ˣ / 3  -3

=>  (1/64)ˣ / 2 + 4 = (1/16)ˣ / 3

=> ( (1/64)ˣ  + 8  ) / 2  = (1/16)ˣ / 3

=> (1/64)ˣ  + 8   = (1/16)ˣ 2 / 3

=> (1/4)³ˣ + 8 = (1/4)²ˣ * 2/3

=> 8 = (1/4)²ˣ ( 2/3 + (1/4)ˣ )

So,

We found that there is no value of x which can make equation true.

Therefore , the solution of the given problem of expression comes out to be  there is no value of x which can make equation true.

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Answer:

158.29 m²

Step-by-step explanation:

A = πr²

A = 3.14 × 7.1 m × 7.1 m

A = 158.29 m²

Answer: The regular price is $9

Step-by-step explanation: We do 35/5 to find the cost of each book. You get 7,then add 2 to get 9

(35/5)+2

The components of the vector in rectangular form given magnitude and angle can be found as : x= |56| cos83°, y = |56| sin 83° .

Let be a vector in rectangular form, that is, a vector of the form (x, y). The magnitude can be found by applying the square root of the dot product of the vector or the Pythagorean theorem and the direction is determined by applying inverse trigonometric functions:

here, we have,

Magnitude (linear algebra approach)

|r|=√(x,y). (x.y)     (1)

Magnitude (algebra approach)

|r|=√(x²+y²)    (2)

Direction

θ = tan⁻¹ (y/x)     (3)

And the components of the vector can be found by applying the following formulas:

|r|=xcos θ   (4)

|r|=  y sinθ (5)

The components of the vector in rectangular form given magnitude and angle can be found as: x= |56| cos83°, y = |56| sin 83° ., .

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