Lucy and Daniela sat on a see-saw . Lucy weighs 50kg,sat 3.5metres away from the pivot on the other side . find the mass of Daniela if the see-saw was balanced .

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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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 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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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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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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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 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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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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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.

Answer: $350

Step-by-step explanation:

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 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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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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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  

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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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

Answer:4x−6

That's one

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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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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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 equation of the line that is parallel to this line and passes through the point (6, -3) is y = x/2.

The equation of the line that is perpendicular to this line and passes through the point (6, -3) is y = -2x + 9.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

From the information provided above, we have the following slope and data points on the line:

In Geometry, two (2) lines are parallel under the following conditions:

m₁ = m₂ ⇒ 1/2 = 1/2

At data point (6, -3), a linear equation of this line can be calculated by using the point-slope form as follows:

y - (-3) = 1/2(x - 6)

y + 3 = x/2 - 3

y = x/2 - 3 + 3

y = x/2

In Mathematics, a condition that must be met for two lines to be perpendicular is given by:

m₁ × m₂ = -1

1/2 × m₂ = -1

m₂ = -2

At data point (6, -3), a linear equation of this line can be calculated by using the point-slope form as follows:

y - (-3) = -2(x - 7)

y + 3 = -2(x - 6)

y = -2x + 12 - 3

y = -2x + 9.

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Answer:

  x ≈ -2.803

Step-by-step explanation:

You want to use the iterative formula x = ∛(5x -8) to find a solution to x³ -5x +8 = 0, starting with x₁ = -3.

Your iterator appears to be found by solving for x:

  x³ -5x +8 = 0

  x³ = 5x -8 . . . . . . add 5x-8

  x = ∛(5x -8) . . . . take the cube root

The attached table shows some iterations using this formula. To 3 dp, the solution is x ≈ -2.803.

__

Additional comment

Using a faster-converging iteration technique, we find the solution to be about ...

  x ≈ -2.8025​887521

The solution above is accurate to 3 dp.

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 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 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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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).

Answer:

B(1,-2)

Step-by-step explanation:

b is the answer from the above explanation

Answer:

158.29 m²

Step-by-step explanation:

A = πr²

A = 3.14 × 7.1 m × 7.1 m

A = 158.29 m²