Dina has a mass of 50 kilograms and is waiting at the top of a ski slope that’s 5 meters high. The maximum kinetic energy she can reach when she skis to the bottom of the slope is joules. Use pe = m × g × h and g = 9. 8 m/s2. Ignore air resistance and friction

Answer:

15

Step-by-step explanation:

To solve 1/3 (-2x + 9 +3x) = 8, you need to follow these steps:

Multiply both sides by 3 to get rid of the fraction: -2x + 9 + 3x = 24

Simplify by combining like terms: x + 9 = 24

Subtract 9 from both sides: x = 15

Check your answer by plugging it back into the original equation: 1/3 (-2(15) + 9 + 3(15)) = 8

Simplify: 1/3 (9 + 45) = 8

Simplify: 1/3 (54) = 8

Simplify: 18 = 8

Since this is true, the answer is correct.

The solution is x = 15.

In terms of i the imaginary root of √−13 is √13i as we know that √(-1) is represented by 'i'.

In mathematics, an imaginary root (also known as a complex root) is a root of a polynomial equation that involves the imaginary unit 'i'. The imaginary unit is defined as the square root of -1, and it is represented by the letter 'i'. A polynomial equation can have either real roots, imaginary roots, or both.

To write √(-13) in terms of 'i', we can start by expressing it as:

√(-1) x √(13) x √(1)

We know that √(-1) is represented by 'i', so we can substitute it in the expression:

'i' x √(13) x √(1)

Since √(1) is equal to 1, we can remove it from the expression:

'i' x √(13)

Therefore, the answer for √(-13) in terms of 'i' is 'i'√(13), which is the simplified form.

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The question is -

Write in terms of i. Simplify your answer as much as possible √−13.

The solution of the given problem of expression comes out to be  9x³.

There is a need for calculations like variable multiplying, splitting, joining, and currently removing. If they were combined, it would read: A mathematical formula, some data, and an equation. Values, elements, and mathematical operations like additions, subtractions, mistakes, subdivisions, but also arithmetic formulas all make up a declaration of truth. It is possible to assess and analyse words and sentences.

Here,

The following is the provided sentence's algebraic expression:

=> 9x³

where x is a numerical symbol.

Therefore , the solution of the given problem of expression comes out to be  9x³.

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Complete question:

Represent the following sentence as an algebraic expression, where "a number" is the letter x. You do not need to simplify.

{Nine times the difference of 8 and a number.}

Nine times the difference of 8 and a number.

Answer:

See below.

Step-by-step explanation:

First, we know that area = length times width. so the first step is to figure out how we got 8[tex]x^{2}[/tex]-12x. factor out 4x  from the equation to get the length of the rectangular length. 4x(2x-3). so the length of the rectangle is 2x-3. to prove your answer, FOIL the two numbers, 4x and 2x-3, to get 8[tex]x^{2}[/tex]-12x. This equation is in standard form. The final answer is 8[tex]x^{2}[/tex]-12x

Answer:

Assuming you're referring to a product of two numbers, if one number is decreased by a factor of two and the other is decreased by a factor of eight, the overall effect on the product will depend on the relative values of the two numbers.

Let's say the product is given by P = a * b, where a and b are the two numbers. If we decrease one number by a factor of two, we can write it as 0.5a. Similarly, if we decrease the other number by a factor of eight, we can write it as 0.125b. So the new product, P', can be written as:

P' = (0.5a) * (0.125b)

= 0.0625ab

So the new product will be 1/16th (0.0625) of the original product. This means that the product will be decreased by a factor of 16.

In other words, if you decrease one number by a factor of two and the other by a factor of eight, the resulting product will be 16 times smaller than the original product.

The 95% confidence interval for the population mean IQ score is (99.62, 111.98), therefore option(A) use normal distribution

Since the sample size is greater than 30 (n=20), we can use the normal distribution to construct a confidence interval for the population mean.

We can use the formula:

Confidence Interval = sample mean ± z (standard error)

where z is the critical value from the standard normal distribution corresponding to the desired level of confidence, and the standard error is calculated as:

standard error = o / sqrt(n)

where o is the sample standard deviation and n is the sample size.

Assuming a 95% confidence level, we can find the critical value z from the standard normal distribution table or using a calculator. The critical value for a 95% confidence level is 1.96.

Substituting the values in the formula, we get:

Confidence Interval = 105.8 ± 1.96 × (15 / sqrt(20))

Confidence Interval = 105.8 ± 6.18

Therefore, the 95% confidence interval for the population mean IQ score is (99.62, 111.98).

Therefore, we can use the normal distribution to construct a confidence interval for the population mean IQ score.

Therefore, the correct option is (A) Use normal distribution.

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Since opposite angles of a parallelogram are equal, angle A = angle C and angle B = angle D where x is 35.

What is parallelogram?

A parallelogram is a four-sided flat shape in which opposite sides are parallel and have the same length. It is a type of quadrilateral, which means it has four sides.

The opposite angles of a parallelogram are also equal, which means that if angle A is equal to angle C, then angle B is equal to angle D. Moreover, the adjacent angles of a parallelogram are supplementary, which means that if angle A and angle B are adjacent angles, then angle A + angle B = 180 degrees.

According to the question:
Since AB = CD and angle A is 60 degrees, it means that opposite sides AB and CD are parallel and have the same length. Therefore, the figure ABCD is a parallelogram.

To determine the value of angle B, we can use the fact that the opposite angles in a parallelogram are equal. That is, angle B = angle D.

Since angle A + angle B + angle C + angle D = 360 degrees for any quadrilateral, we can write:

angle A + angle B + angle C + angle D = 60 + (3x+15) + angle C + angle D = 360

Simplifying this equation, we get:

4x + 75 + angle C + angle D = 360

angle C + angle D = 360 - 4x - 75 = 285 - 4x

Since angle B = angle D, we have:

angle B + angle D = 2 angle D = (3x+15)

Therefore, we can solve for angle D:

2 angle D = (3x+15)

angle D = (3x+15)/2

Now, we can substitute this into the equation for angle C + angle D:

angle C + (3x+15)/2 = 285 - 4x

Multiplying both sides by 2, we get:

2 angle C + 3x + 15 = 570 - 8x

Simplifying and solving for angle C, we get:

2 angle C = 555 - 11x

angle C = (555 - 11x)/2

Therefore, the angles of the parallelogram ABCD are:

angle A = 60 degrees

angle B = (3x+15) degrees

angle C = (555 - 11x)/2 degrees

angle D = (3x+15)/2 degrees

Note that since opposite angles of a parallelogram are equal, angle A = angle C and angle B = angle D.


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Q. Determine the figure given below which has Angle A= 60 and Angle B=(3x+15)

An adult male hippopotamus can weight from 3,500 pounds to 9,920 pounds, which is equivalent to 1.75 tons to 4.96 tons.

Weight is a measure of the force exerted on an object by gravity. It is typically measured in units of mass, such as pounds or kilograms, but is commonly referred to as "weight" in everyday language. The weight of an object can vary depending on its location and the strength of the gravitational field in that location.

To convert pounds to tons, we need to divide the weight in pounds by 2,000 (since there are 2,000 pounds in a ton). So, we have:

Minimum weight: 3,500 pounds / 2,000 = 1.75 tons (rounded to the nearest hundredth)

Maximum weight: 9,920 pounds / 2,000 = 4.96 tons (rounded to the nearest hundredth)

Therefore, an adult male hippopotamus can weigh approximately 1.75 to 4.96 tons.

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The probability of coffee or cookies is 0.456, and the probability of tea given that it contains mugs is 0.727.

The probability of an event occurring is the number of successful outcomes divided by the total number of possible outcomes. In this case, we are asked to find the probability of two different combinations: coffee or cookies, and tea given that it contains mugs.

Part 1 of 3:

(a) Coffee or cookies

To find the probability of coffee or cookies, we need to add the probability of coffee and the probability of cookies, and then subtract the probability of both occurring. The probability of coffee is 16/79, and the probability of cookies is 20/79.

The probability of both occurring is 0, since there are no gift baskets that contain both coffee and cookies. So, the probability of coffee or cookies is:

P(coffee or cookies) = P(coffee) + P(cookies) - P(coffee and cookies)
P(coffee or cookies) = 16/79 + 20/79 - 0
P(coffee or cookies) = 36/79
P(coffee or cookies) ≈ 0.456

Part 2 of 3:

(b) Tea, given that it contains mugs

To find the probability of tea given that it contains mugs, we need to use the formula for conditional probability:

P(A|B) = P(A and B)/P(B)
In this case, A is the event of tea, and B is the event of mugs. The probability of tea and mugs is 16/79, and the probability of mugs is 22/79. So, the probability of tea given that it contains mugs is:

P(tea| mugs) = P(tea and mugs)/P(mugs)
P(tea| mugs) = (16/79)/(22/79)
P(tea| mugs) = 16/22
P(tea| mugs) = 8/11
P(tea| mugs) ≈ 0.727

Therefore, the probability of coffee or cookies is 0.456, and the probability of tea given that it contains mugs is 0.727.

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Answer:

Step-by-step explanation:

At least 88.88% of islanders have blood pressure that falls between 47 and 101 millimetres of mercury using Chebyshev's Theorem.

For each data distribution, Chebyshev's Theorem gives a lower constraint on the percentage of data that is within a given range of standard deviations of the mean. It specifically asserts that at least 1-1/k2 of the data will fall within k standard deviations of the mean for each dataset, regardless of its shape. In this instance, we're trying to determine the percentage of islanders whose blood pressure is between 47 and 101 millimetres of mercury.

We must determine the upper and lower range boundaries' standard deviations from the mean in order to use Chebyshev's Theorem. The lowest and upper limits are both 27 mmHg below and above the mean, respectively. As we want to know what percentage of the data falls within three standard deviations of the mean, we set k=3 and the range to be 6 standard deviations broad (27 mmHg / 9 mmHg per standard deviation).

By using Chebyshev's Theorem, we can determine that at least 88.88% of the islanders have blood pressure that is within three standard deviations of the mean (1-1/32 = 8/9 = 0.8888). We can infer that at least 88.88% of islanders have blood pressure in the range of 47 mmHg to 101 mmHg as the range we are interested in is within three standard deviations of the mean.

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Answer:

A rectangle park is 45m long and 30m wide. A path 2.5m wide is constructed outside the park. Find the area of the path

Step-by-step explanation:

A rectangle park is 45m long and 30m wide. A path 2.5m wide is constructed outside the park. Find the area of the path

Answer:

yes

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer: 10,000

Step-by-step explanation:

10^5 = 100000 and 10^-1 = 1/10, so the answer is 10000

Answer: 24 green

Step-by-step explanation:

3 red for every 4 green, so three goes into 18 six times. Multiply four (green) by six, and you get 24. Sorry if the explanation doesn't help

The ant must crawl 454.48 mm upwards to get from the base of the cone to the top of the hill. Inserting the values of h (447.68 mm) and r (20 mm) into the equation gives h = 8792/(3.14*202))*3 = 447.68 mm.

A cone is a three-dimensional geometric form with a smooth taper from a flat cylindrical base to a singular spot known as the tip. A cone has a curved surface that stretches from the base to the tip and an axis that runs through the base and apex.

The formula for the height of the cone is: Height = 3/πr2 (where r is the radius of the base of the cone). In this case, the radius is 20 mm, so the height is equal to: Height = 3/π(20)2 = 60/π mm.  The slant height, s, is equal to the square root of the height squared plus the radius squared. the distance the ant has to crawl from the base of the cone to the top of the hill, we can use the Pythagorean theorem to find.

1. To find the height of the cone, the formula for the volume of a cone can be used, where V = (1/3)πr2h. Rearranging this formula gives h = (V/(πr2))*3, where V is the volume of the anthill (8792 mm3), π is 3.14, and r is the radius of the anthill (20 mm).

2. The slant height of a cone is the distance from the center of the circle at the base of the cone to the apex of the cone. It is equal to the square root of the sum of the squared height of the cone and the squared radius of the cone. This can be expressed using the Pythagorean Theorem, where s = √h2 + r2.

A cone is a three-dimensional geometric shape with a circular base and a pointed apex. It is one of the two basic forms of a solid in geometry, the other one being a sphere.  

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Therefore , the solution of the given problem of triangle comes out to be triangle's length, rounded to two decimal places, is roughly 33.33 units.

A polygon is a hexagon if it has not less than one extra segment. It has a straightforward rectangle-shaped structure. Only edges A and B can differentiate something like this from an ordinary triangular shape. Despite the exact collinearity of the borders, Euclidean geometry only produces a part of the cube. Three edges and three angles make up a triangle.

Here,

Finding the length of each side and adding them together will allow us to determine the perimeter of the triangle whose points are E(12,-5), D(-1,-1), and F(7,-4).

The length of EF is given below using the distance formula:

=> √((7 - 12) ² + (4 - (- 5))² = √(25 + 81) = √(106) =  10.30

The ED is as follows:

=>  sqrt((-1 - 12)2 + (-1 - (-5))2) = sqrt(169 + 16) = sqrt(185), which is 13.60.

And DF is this long:

=>  √((7-1))² + (4-1))² = √(64+25) = √(89) = 9.43

As a result, the triangle's circumference is:

=>  10.30 + 13.60 + 9.43 ≈ 33.33

The triangle's length, rounded to two decimal places, is roughly 33.33 units.

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Answer:

960

Step-by-step explanation:

In this case, the value of x is 9 Degrees.

From the given information, we know that ∠A is equal to 5x - 15 degrees. Now, we can use this equation to find the value of x. To do this, we need to rearrange the equation and solve for x. We can do this by adding 15 degrees to both sides of the equation, which gives us:

∠A + 15 = 5x

Now, we can divide both sides of the equation by 5 to isolate x, which gives us:

x = (∠A + 15) / 5

Therefore, we have found the value of x in terms of ∠A. If we know the value of ∠A, we can substitute it into this equation to find the value of x. For example, if ∠A is equal to 30 degrees, then:

x = (30 + 15) / 5
x = 9

So, in this case, the value of x is 9 degrees. I hope this helps you with your question. If you have any further questions or need any additional help, please let me know.

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If a restaurant makes smoothies in batches of 6.4 litres. the maximum number of batches of smoothie that can be made from 42 litres of lime juice is 50.

If the ratio of ice cream to mixed fruit juice is 5:3, then,

Fraction of the smoothie that is ice cream =5/(5+3) = 5/8

Fraction that is mixed fruit juice =  3/(5+3) = 3/8

If 35% of the mixed fruit juice is lime juice, then,

Fraction of the mixed fruit juice that is lime juice=  35/100 = 7/20

Fraction of the smoothie that is lime juice = (3/8) x (7/20) = 21/160

To make one batch of smoothie, we need 6.4 litres of mixed fruit juice, of which (21/160) x 6.4 = 0.84 litres is lime juice.

To make 42 litres of lime juice, we nee:

42/0.84 = 50 batches of smoothie.

Therefore, the maximum number of batches of smoothie that can be made from 42 litres of lime juice is 50.

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Answer:

3. [tex]\frac{3}{4}[/tex] and [tex]\frac{6}{8}[/tex]  4.[tex]\frac{8}{2}[/tex] and [tex]\frac{4}{1}[/tex]

5. [tex]\frac{10}{50}[/tex]   6.[tex]\frac{1}{4}[/tex]  7.[tex]\frac{45}{50}[/tex]

8. x=1  9.x=30  10.x=16

11. [tex]\frac{8}{12} \frac{4}{6} \frac{2}{3}[/tex]  

12.   red pencils=[tex]\frac{4}{10}[/tex]   black pencils=[tex]\frac{6}{10}[/tex]

total pencil = 4+6 =10

13. no es claramente visible, pero la respuesta podría ser [tex]\frac{1}{3}[/tex] y [tex]\frac{2}{6}[/tex]

Answer:17/4

Step-by-step explanation:

Solution:

Your problem → 2((1/8)+ 4) - ((3/6)*8)

2((18)+4)-((36)⋅8)

=2⋅(1/8)+4-((36)⋅8)

=2⋅(1+4×8)/8-((36)⋅8)

=2⋅(1+32)/8-((36)⋅8)

=2⋅(33/8)-((36)⋅8)

=2⋅(33/8)-((36)⋅8)

=(33/4)-((36)⋅8)

=(33/4)-(36⋅8)

=(33/4)-(12⋅8)

=(33/4)-12⋅8

=(33/4)-4

=(33/4)-4

=(33-4×4)/4

=(33-16)/4

=17/4

=4.25 (in decimal)

Step-by-step explanation:

The interquartile range for the masses of adult men is 6.75 kg (1 decimal place).

The probability that an adult man, chosen at random, will have a mass greater than 77.5 kg is 0.4 (4 decimal places). The probability that an adult man, chosen at random, will have a mass between 76.6 kg and 83.5 kg is 0.2366 (4 decimal places). 62% of adult men have a mass greater than 78.45 kg (1 decimal place).

Let X be the mass of an adult man, then X ~ N(75, 5^2).

P(X > 77.5) = P(Z > (77.5 - 75) / 5) where Z is the standard normal random variable.

P(Z > 0.5) = 1 - P(Z ≤ 0.5) ≈ 0.3085

Therefore, the probability that an adult man, chosen at random, will have a mass greater than 77.5 kg is approximately 0.3085.

P(76.6 < X < 83.5) = P[(76.6 - 75) / 5 < Z < (83.5 - 75) / 5]

P(1.32 < Z < 1.7) = P(Z < 1.7) - P(Z < 1.32) ≈ 0.0932

Therefore, the probability that an adult man, chosen at random, will have a mass between 76.6 kg and 83.5 kg is approximately 0.0932.

Let p be the proportion of adult men with a mass greater than some value x, then we want to find x such that p = 0.62.

By standardizing and using the standard normal distribution table, we get:

P(Z > (x - 75) / 5) = 0.62

P(Z < (75 - x) / 5) = 0.38

Using the standard normal distribution table, we find that Z ≈ 0.2533

Therefore, (x - 75) / 5 ≈ 0.2533

x ≈ 76.267 kg (rounded to 1 decimal place)

Therefore, 62% of adult men have a mass greater than 76.3 kg.

The interquartile range (IQR) is a measure of spread and is defined as the difference between the 75th percentile and the 25th percentile of the distribution. For a normal distribution, the IQR is approximately 1.35 times the standard deviation.

IQR ≈ 1.35 * 5 ≈ 6.75 kg (rounded to 1 decimal place)

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Answer: 6/13-2/13

I'm correct cause I always am hehe

The researcher is not conducting non-random sampling.

Random sampling is a sampling technique in which every individual or element of the population of interest has an equal opportunity of being selected for the sample. Each member of the population has an equal chance of being selected for the sample. Random sampling helps to ensure that the sample is representative of the population.

Non-random sampling, on the other hand, is a sampling technique in which the individuals or elements of the population of interest are not randomly selected. In other words, not every member of the population has an equal chance of being selected. This sampling method is biased and can lead to an unrepresentative sample.

The researcher is not conducting a non-random sampling technique because she is observing every child in the population of interest. The population of interest, in this case, is the children on the playground.

The researcher is not conducting non-random sampling because random sampling is a sampling technique in which every individual or element of the population of interest has an equal opportunity of being selected for the sample.

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Finding a line segment parallel to another segment and passing through a given point is true.

A line segment is a finite portion of a line that is bounded by two distinct points.

The statement is asking whether the following method is true or false for finding a line segment parallel to another segment and passing through a given point:

This method is called the "fold-and-copy" method, and it is a valid way to construct a segment parallel to another segment and passing through a given point. The reason this works is because when the paper is folded along the given point, the fold line is perpendicular to the original segment. When the segment is copied onto the paper on both sides of the fold, the resulting segments are also perpendicular to the fold line. Since two lines that are both perpendicular to the same line are parallel, the resulting segment is parallel to the original segment. The resulting segment also passes through the given point, since it was copied from the original segment which passes through the given point. Therefore, the statement is true.

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Answer:

Scalene; right triangle

Step-by-step explanation:

See picture attached.

Circle 1:

    R- 3cm

    D- 6cm

    C- 18.84cm

Circle 2:

    R- 6in

    D- 12in

    C- 37.68in

Circle 3:

    R- 9mm

    D- 18mm

    C- 56.52mm

your welcome :)

The solution to the equation √(-2x - 5) - 4 = x are x = -7 and x = -3

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

√(-2x - 5) - 4 = x

So, we have

-2x - 5 = x + 4

Take the square of both sides

so, we have the following representation

x² + 8x + 16 = -2x - 5

Evalyate the like terms

x² + 10x + 21 = 0

When factorized, we have

(x + 7)(x + 3) = 0

This means that

x = -7 and x = -3

Hence, the solutions are x = -7 and x = -3

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