Lisandro is using this diagram to find the equation of a circle. He notices that the radius, the blue line, and the red line form a right triangle. Which shows his correct reasoning and equation

a) The length of the red line is |x + h|.
The length of the blue line is |y + k|.
The equation of a circle is (x + h)2 + (y + k)2 = r2.


b) The length of the radius is r.
The area of a circle is πr2.
The equation of the circle is y = πr2x.


c) The length of the red line is |x – h|.
The length of the blue line is |y – k|.
The equation of a circle is (x – h)2 + (y – k)2 = r2.


d) The length of the red line is |x – h|.
The length of the blue line is |y – k|.
The equation of a circle is (x – h)2 + (y – k)2 = r.

Answer:

50

Step-by-step explanation:

add 5 to -25 to get -2/5x by itself.

Answer:

Step-by-step explanation:

Table(2) shows the relative frequency opted from the table(1).

It is defined as the number of waves that crosses a fixed point in one second known as frequency. The unit of frequency is per second.

We have a table in which data has shown:

To find the relative frequency:

For the first cell:

[tex]=\frac{67}{92} \times100 \approx 73\%[/tex]

For the second cell:

= 100 - 73 ⇒ 27%

For the third cell:  

[tex]\rm = \frac{46}{66} \times 100 \approx 70\%[/tex]

For the fourth cell:

= 100 - 70 = 30%

Thus, table(2) shows the relative frequency opted from table(1).

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Answer: 3(3x−4) is the answer

Answer:

3(3x-4) is the answer

Step-by-step explanation:

Answer: b. A 90% confidence level and a sample of 24 observations. 1.714 1.714 Correct

Step-by-step explanation:

Answer:

28.57% probability that the oldest is a girl and the youngest is a boy​, given that there is at least one boy and at least one girl.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

These are all the possible outcomes: from youngest to oldest, b is boy and g is girl

b - b - b - g

b - b - g - b

b - b - g - g

b - g - b - b

b - g - b - g

b - g - g - b

b - g - g - g

g - b - b - b

g - b - b - g

g - b - g - b

g - b - g - g

g - g - b - b

g - g - b - g

g - g - g - b

The nuber of total outcomes is 14.

Desired outcomes:

Oldest(last) girl, youngest(first) boy

b - b - b - g

b - b - g - g

b - g - b - g

b - g - g - g

So 4 desired outcomes

Probability:

4/14 = 0.2857

28.57% probability that the oldest is a girl and the youngest is a boy​, given that there is at least one boy and at least one girl.

Final answer:

The probability that a family with four children will have the oldest being a girl and the youngest being a boy, given that there is at least one boy and one girl, is 1/4.

Explanation:

To solve this probability question, we need to consider all possible combinations of children while adhering to the given conditions: the oldest child must be a girl (G), the youngest must be a boy (B), and there must be at least one boy and at least one girl in the family.

The possible genders for the four children can be represented as a sequence of G (girl) and B (boy) like this: G---B. There are two positions in the middle that can be either a boy or a girl. Since each position can be filled independently with either a boy or a girl, there are 2 options for each of the middle children, giving us 2 x 2 = 4 combinations: GBGB, GBBB, GGBB, GGBG.

To calculate the probability of any single one of these combinations occurring, we need to remember that the probability of giving birth to a boy or a girl is equal, which means each event (birth of a child) has a probability of 1/2. Thus, the probability of each combination is (1/2)^4 since there are four independent events (births). However, since we have 4 combinations that meet the criteria, we multiply this probability by 4. So, the probability is 4 * (1/2)^4 = 1/4.

Therefore, the probability that a family with four children will have the oldest being a girl and the youngest being a boy, given that there is at least one boy and at least one girl, is 1/4.

Answer:

Mean is 3.2

Median is 3.1

Step-by-step explanation:

a) mean

= (2.5+3.6+3.1+4.3+2.9+2.3+2.6+4.1+3.4)/9

= 28.8/9

= 3.2

b) median: we will arrange in ascending order and pick the middle term.

2.3 2.5 2.6 2.9 3.1 3.4 3.6 4.1 4.3

From the above order, 3.1 is the middle term and is the median

a) The mean reaction time of the 9 subjects is 3.2 seconds.

A mean is an average of a set of values.

The mean is computed by summing the values and then dividing the sum by the number of subjects.

b) The median reaction time for the random sample of 9 subjects to a stimulant is 3.1 seconds.

The median is the middle number in an arranged list of values.  The arrangement takes into consideration their ascending or descending orders.

The median is simple to determine when the list of values is not too long and well-arranged.

Variables    Reaction Times

                       in seconds

1.                         2.5

2.                        3.6

3.                        3.1

4.                       4.3

5.                       2.9

6.                       2.3

7.                       2.6

8.                       4.1

9.                      3.4

Total               28.8

Mean = 3.2 (28.8/9)

6.                       2.3

1.                        2.5

7.                       2.6

5.                       2.9

3.                       3.1

9.                      3.4

2.                      3.6

8.                      4.1

4.                      4.3

Thus, the mean and the median have been calculated.

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Answer:

The answer is A.

Step-by-step explanation:

Answer:

0.0668

Step-by-step explanation:

Assuming the distribution is normally distributed with a mean of $75,

with a standard deviation of $12.

We can find the z-score of 78 using;

[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]

[tex]\implies z=\frac{78-75}{\frac{12}{36} } =1.5[/tex]

Using our normal distribution table, we obtain the area that corresponds to 0.25 to be 0.9332

This is the area corresponding to the probability that, the average is less or equal to 78.

Subtract from 1 to get the complement.

P(x>78)=1-0.9332=0.0668

The probability that the average sales per customer from a sample of 36 customers, taken at random from this population, exceeds $78 is 0.0668.

Since The average sales per customer at a home improvement store during the past year is $75 with a standard deviation of $12.

Here  we need to find out the z score

= [tex]78-75\div 12\div 36[/tex]

= 1.5

Here we considered normal distribution table, we obtain the area that corresponds to 0.25 to be 0.9332

So,  the average is less or equal to 78.

Now

Subtract from 1 to get the complement.

So,

P(x>78)=1-0.9332

=0.0668

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Answer:

10.0

Step-by-step explanation:

4.0+8.0=12.0-2.0=10.0

The volume of the cylinder is 401.92 cube m.

Step-by-step explanation:

Given,

A cylinder of height 2x inscribed in a sphere of radius 8 m.

The center of the sphere is the midpoint of the altitude that joins the centers of the bases of the cylinder.

To find the volume of the cylinder.

Formula

The volume of a cylinder with h as height and r as radius is = πr²h

Since,

The cylinder is inscribed in the sphere

The radius (r) of the cylinder = 4 m

The height (h) of the cylinder = 8 m

So,

The volume of the cylinder = π×4²×8 cube m

= 128π cube m [ taking π=3.14]

= 128×3.14 cube m

= 401.92 cube m

Hence,

The volume of the cylinder is 401.92 cube m.

The volume of the cylinder is 128πx.

The volume of a cylinder can be found using the formula V = πr²h, where r is the radius of the cylinder's base and h is the height of the cylinder. In this case, the cylinder is inscribed in a sphere with radius 8 meters and the center of the sphere is the midpoint of the altitude that joins the centers of the bases of the cylinder. Since the cylinder is inscribed in the sphere, the diameter of the cylinder is equal to the diameter of the sphere, which is twice the radius of the sphere. Thus, the diameter of the cylinder is 16 meters and the radius is 8 meters.

Since the height of the cylinder is given as 2x, we can substitute this value into the formula to find the volume:

V = π(8)²(2x) = 128πx

Therefore, the volume of the cylinder is 128πx.

Without sufficient data, we cannot calculate the probabilities or the cost for the 3% highest domestic airfares. The calculations require details about the total number of observed airfares and the number that falls in the specified price ranges.

I regret to inform you that I cannot provide a factual answer to your question regarding domestic airfares as you have not provided sufficient data. Probability depends on the sample space and given conditions which are not provided in your question. For instance:

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Answer:

C

Step-by-step explanation:

[tex]x^{2}[/tex]+[tex]y^{2}[/tex]= [tex]\sqrt{x^{2}+y^{2} }[/tex]+2y

Answer:

The equation of equivalent is,[tex]x^{4}+ y^{4} +3 y^{2} +2x^{2} y^{2} -4y^{3} -4 x^{2} y-x^{2} =0[/tex]

Step-by-step explanation:

If two systems of equations have the same solution, they are equivalent (s). This article explains how to determine whether two systems are equal. Equivalent systems are sets of equations that have the same solution.

Given, r = 1+2sinФ

[tex]r^{2} =r+2rsin[/tex]θ

[tex]x^{2}+ y^{2} =r+2y\\x^{2} + y^{2} -2y=r\\[/tex]

Squaring, both side:

[tex](x^{4} +y^{4} -2 y^{2}) = r^{2} \\x^{4}+ y^{4} + 4y^{2}+2 x^{2} y^{2} - 4y^{3} -4x^{2} y =x^{2} +y^{2} \\x^{4} + y^{4} +3 y^{2} +2 x^{2} y^{2} -4y^{3} -4x^{2} y^}-x^{2} =0[/tex]

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Answer:

We conclude that % of DC area adults who have traveled outside of the United States is different from 40%.

Step-by-step explanation:

We are given that 40% of DC area adults have traveled outside of the United States. Nardole wants to know if his customers are typical in this respect. He surveys 40 customers and finds 60% have traveled outside of the U.S.

We have to test is this result a statistically significant difference.

Let p = % of DC area adults who have traveled outside of the United States

SO, Null Hypothesis, [tex]H_0[/tex] : p = 40%  {means that 40% of DC area adults have traveled outside of the United States}

Alternate Hypothesis, [tex]H_a[/tex] : p [tex]\neq[/tex] 40%  {means that % of DC area adults who have traveled outside of the United States is different from 40%}

The test statistics that will be used here is One-sample z proportion statistics;

                  T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1- \hat p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = % of customers who have traveled outside of the United States

                  in a survey of 40 customers = 60%

          n  = sample of customers = 40

So, test statistics = [tex]\frac{0.60-0.40}{\sqrt{\frac{0.60(1-0.60)}{40} } }[/tex]

                             = 2.582

Since in the question we are not given with the significance level so we assume it to be 5%. So, at 0.05 level of significance, the z table gives critical value of 1.96 for two-tailed test. Since our test statistics is more than the critical value of z so we have sufficient evidence to reject null hypothesis as it will fall in the rejection region.

Therefore, we conclude that % of DC area adults who have traveled outside of the United States is different from 40%.

Answer:

Answer : D

Step-by-step explanation:

A school has two kindergarten classes. There are 21 children in Ms. Toodle's kindergarten class. Of these, 17 are "pre-readers" children on the verge of reading. There are 19 children in Mr. Grimace's kindergarten class. Of these, 13 are pre-readers. Using the plus four confidence interval method, a 90% confidence interval for the difference in proportions of children in these classes that are pre-readers is â0.104 to 0.336.  

Which of the following statements is correct?

A) This confidence interval is not reliable because the samples are so small.  

B)This confidence interval is of no use because it contains 0, the value of no difference between classes.  

C)This confidence interval is reasonable because the sample sizes are both at least 5.  

D) This confidence interval is not reliable because these samples cannot be viewed as simple random samples taken from a larger population.

The Answer is D - This confidence interval is not reliable because these samples cannot be viewed as simple random samples taken from a larger population.

In this setup, all the students are already involved in the data. This is not a sample from a larger population, but probably, the population itself.

Answer:

uhhh

Step-by-step explanation:

uh I don't see the graph

Answer:

D and B

Step-by-step explanation:

To calculate the probability that the sample mean would differ from the true mean by greater than $38, if a sample of 208 persons is randomly selected, we need to use the Central Limit Theorem. First, we determine the standard error of the mean (SEM) using the formula SEM = standard deviation / square root of sample size. Then, we calculate the Z-score using the formula Z = (sample mean - true mean) / SEM. Finally, we find the probability associated with the Z-score using a Z-table or calculator.

To calculate the probability that the sample mean would differ from the true mean by greater than $38, if a sample of 208 persons is randomly selected, we need to use the Central Limit Theorem.

According to the Central Limit Theorem, the distribution of sample means will be approximately normal regardless of the shape of the population distribution, as long as the sample size is large enough.

Since the sample size is greater than 30, we can assume that the distribution of sample means will be approximately normal.

To calculate the probability, we first need to determine the standard error of the mean (SEM), which is the standard deviation divided by the square root of the sample size. In this case, the SEM = $397 / √208.

Next, we calculate the Z-score using the formula Z = (sample mean - true mean) / SEM = ($38 - 0) / ($397 / √208). Finally, we can use a Z-table or calculator to find the probability associated with the Z-score.

In this case, it is the probability that Z is greater than the calculated Z-score. Hence, the probability that the sample mean would differ from the true mean by greater than $38 is the probability that Z is greater than the calculated Z-score.

Answer: 40in²

Step-by-step explanation:

To find the area of the shade region, considering the diagram, the diagonal of the rectangle has divided the figure into two equal half. So, one is shaded and the other not shaded. So the shaded region is a right angled triangle,. So the formula for finding the area of a triangle need to be applied.

Area. = 1/2 × b × h

= 1/2 × 10 × 8

= 40in²

Answer:Correct Answer: A

Explanation: Choice A is the correct answer. Let x be the number of hours that the babysitter worked. Since the babysitter earns money at a rate of $8 per hour, she earned 8x dollars for the x hours worked. If the babysitter gets both children to bed on time, the babysitter earns an additional $3 tip. Therefore, the babysitter earned a total amount of 8x + 3 dollars.

Choice B is incorrect since the tip and the rate per hour have been interchanged in the expression. Choices C and D are incorrect since the number of children is not part of how the babysitter’s earnings are calculated.

Answer:

840

Step-by-step explanation:

the volume of a rectangular prism is the base(width)height

Answer:

$15.6

Step-by-step explanation:

one bag= $1.95

8 bags = 8×1.95=15.6

so answer is $15.6.

Answer:

m=2/3

Step-by-step explanation:

your answer would be A.

Answer: A

Step-by-step explanation:

Answer:

the first opition is the correct answer

Answer:

The median of the following set of data is 9 since the question is implying, which is the center of the data distribution.

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

just did it on the assignment

Answer: G=21

Step-by-step explanation:

Solve for G by simplifying both sides of the equation, then isolating the variable.

The center of mass of the lamina is located at the point (0, (39/12) (1 / ln(4))).

To find the center of mass of the given lamina, we need to calculate the moment about the x-axis and the y-axis, and then divide them by the total mass of the lamina.

Given information:

- The boundary of the lamina consists of the semicircles y = sqrt(1 - x^2) and y = sqrt(16 - x^2), and the portions of the x-axis that join them.

- The density at any point is inversely proportional to its distance from the origin.

Find the total mass of the lamina.

Let the density function be [tex]\[ \rho(x, y) = \frac{k}{\sqrt{x^2 + y^2}} \][/tex], where k is a constant.

The total mass, M, is given by the double integral of the density function over the region of the lamina.

M = ∫∫ ρ(x, y) dA

To evaluate this integral, we need to express the lamina in polar coordinates.

The semicircles can be represented as:

0 ≤ r ≤ 1, 0 ≤ θ ≤ π

0 ≤ r ≤ 4, π ≤ θ ≤ 2π

The total mass can be calculated as:

[tex]\[ M = \int_{0}^{\pi} \int_{0}^{1} \frac{k}{r} r \, dr \, d\theta + \int_{\pi}^{2\pi} \int_{0}^{4} \frac{k}{r} r \, dr \, d\theta \]\[ M = k \left( \pi \ln(1) + 2\pi \ln(4) \right) \]\[ M = 2\pi k \ln(4) \][/tex]

Calculate the moment about the x-axis.

The moment about the x-axis, Mx, is given by:

[tex]\[ M_x = \int_{0}^{\pi} \int_{0}^{1} \frac{k}{r} r^2 \sin(\theta) \, dr \, d\theta + \int_{\pi}^{2\pi} \int_{0}^{4} \frac{k}{r} r^2 \sin(\theta) \, dr \, d\theta \]\[ M_x = k \left( \frac{\pi}{2} + \frac{32\pi}{3} \right) \]\[ M_x = \frac{39\pi}{6} k \][/tex]

Calculate the moment about the y-axis.

The moment about the y-axis, My, is given by:

My = ∫∫ x ρ(x, y) dA

In polar coordinates:

[tex]\[ M_y = \int_{0}^{\pi} \int_{0}^{1} \frac{k}{r} r^2 \cos(\theta) \, dr \, d\theta + \int_{\pi}^{2\pi} \int_{0}^{4} \frac{k}{r} r^2 \cos(\theta) \, dr \, d\theta \][/tex]

My = 0 (due to symmetry)

Find the coordinates of the center of mass.

The coordinates of the center of mass (x_cm, y_cm) are given by:

x_cm = My / M

y_cm = Mx / M

Substituting the values, we get:

x_cm = 0 / (2πk ln(4)) = 0

y_cm = (39π/6) k / (2πk ln(4)) = (39/12) (1 / ln(4))

Therefore, the center of mass of the lamina is located at the point (0, (39/12) (1 / ln(4))).

Complete question:

The boundary of a lamina consists of the semicircles y=sqrt(1 − x^2) and y= sqrt(16 − x^2) together with the portions of the x-axis that join them. Find the center of mass of the lamina if the density at any point is inversely proportional to its distance from the origin.

The center of mass of the lamina is at the origin (0, 0)

To find the center of mass of the lamina, we first need to find the mass and the moments about the  x- and  y-axes.

The mass  M of the lamina can be calculated by integrating the density function over the lamina. Since the density at any point is inversely proportional to its distance from the origin, we can express the density[tex]\( \delta \) as \( \delta(x, y) = \frac{k}{\sqrt{x^2 + y^2}} \)[/tex], where  k is a constant.

Let's denote [tex]\( \delta(x, y) \) as \( \frac{k}{\sqrt{x^2 + y^2}} \)[/tex]. Then the mass M  is given by the double integral of [tex]\( \delta(x, y) \)[/tex] over the region  R bounded by the semicircles and the portions of the x-axis:

[tex]\[ M = \iint_R \delta(x, y) \, dA \][/tex]

Where  dA  represents the differential area element.

To find the moments about the  x- and  y -axes, we calculate:

[tex]\[ M_x = \iint_R y \delta(x, y) \, dA \]\[ M_y = \iint_R x \delta(x, y) \, dA \][/tex]

Then, the coordinates [tex]\( (\bar{x}, \bar{y}) \)[/tex] of the center of mass are given by:

[tex]\[ \bar{x} = \frac{M_y}{M} \]\[ \bar{y} = \frac{M_x}{M} \][/tex]

Now, let's proceed to find [tex]\( M \), \( M_x \), and \( M_y \)[/tex]

First, let's express the density [tex]\( \delta(x, y) \)[/tex] in terms of k:

[tex]\[ \delta(x, y) = \frac{k}{\sqrt{x^2 + y^2}} \][/tex]

Now, we'll find the mass  M by integrating [tex]\( \delta(x, y) \)[/tex] over the region  R :

[tex]\[ M = \iint_R \frac{k}{\sqrt{x^2 + y^2}} \, dA \][/tex]

Since the region  R  is symmetric about the  x-axis, we can integrate over the upper half and double the result:

[tex]\[ M = 2 \iint_{R_1} \frac{k}{\sqrt{x^2 + y^2}} \, dA \][/tex]

Now, we'll switch to polar coordinates [tex]\( (r, \theta) \)[/tex]. In polar coordinates, the region [tex]\( R_1 \)[/tex]is described by [tex]\( 0 \leq \theta \leq \pi \) and \( 1 \leq r \leq 4 \).[/tex]

So, the integral becomes:

[tex]\[ M = 2 \int_{0}^{\pi} \int_{1}^{4} \frac{k}{r} \cdot r \, dr \, d\theta \]\[ = 2k \int_{0}^{\pi} \int_{1}^{4} 1 \, dr \, d\theta \]\[ = 2k \int_{0}^{\pi} (4 - 1) \, d\theta \]\[ = 2k \int_{0}^{\pi} 3 \, d\theta \]\[ = 6k \pi \][/tex]

For [tex]\( M_x \)[/tex], we integrate [tex]\( x \delta(x, y) \)[/tex] over the region R :

[tex]\[ M_x = \iint_R x \cdot \frac{k}{\sqrt{x^2 + y^2}} \, dA \]\[ = 2 \int_{0}^{\pi} \int_{1}^{4} r \cos(\theta) \cdot \frac{k}{r} \cdot r \, dr \, d\theta \]\[ = 2k \int_{0}^{\pi} \int_{1}^{4} \cos(\theta) \cdot r \, dr \, d\theta \]\[ = 2k \int_{0}^{\pi} \left[ \frac{1}{2} r^2 \cos(\theta) \right]_{1}^{4} \, d\theta \][/tex]

[tex]\[ = 2k \int_{0}^{\pi} \left( 8 \cos(\theta) - \frac{1}{2} \cos(\theta) \right) \, d\theta \]\[ = 2k \int_{0}^{\pi} \left( \frac{15}{2} \cos(\theta) \right) \, d\theta \]\[ = 2k \left[ \frac{15}{2} \sin(\theta) \right]_{0}^{\pi} \]\[ = 2k \cdot 0 \]\[ = 0 \][/tex]

Now, for[tex]\( M_y \)[/tex], we integrate [tex]\( y \delta(x, y) \)[/tex]over the region  R :

[tex]\[ M_y = \iint_R y \cdot \frac{k}{\sqrt{x^2 + y^2}} \, dA \\\[ = 2 \int_{0}^{\pi} \int_{1}^{4} r \sin(\theta) \cdot \frac{k}{r} \cdot r \, dr \, d\theta \\\[ = 2k \int_{0}^{\pi} \int_{1}^{4} \sin(\theta) \cdot r \, dr \, d\theta \\\[ = 2k \int_{0}^{\pi} \left[ \frac{1}{2} r^2 \sin(\theta) \right]_{1}^{4} \, d\theta \\[/tex]

[tex]\[ = 2k \int_{0}^{\pi} \left( 8 \sin(\theta) - \frac{1}{2} \sin(\theta) \right) \, d\theta \\\[ = 2k \int_{0}^{\pi} \left( \frac{15}{2} \sin(\theta) \right) \, d\theta \\\[ = 2k \left[ -\frac{15}{2} \cos(\theta) \right]_{0}^{\pi} \\\[ = 2k \cdot 0 \\\[ = 0 \][/tex]

Now, we have [tex]\( M = 6k \pi \), \( M_x = 0 \), and \( M_y = 0 \).[/tex]

Finally, we can find the coordinates of the center of mass [tex]\( (\bar{x}, \bar{y}) \):[/tex]

[tex]\[ \bar{x} = \frac{M_y}{M} = \frac{0}{6k \pi} = 0 \]\[ \bar{y} = \frac{M_x}{M} = \frac{0}{6k \pi} = 0 \][/tex]

So, the center of mass of the lamina is at the origin (0, 0) .

Answer:

4n-3=5

Step-by-step explanation:

If you read it step by step the product of and a number is basically 4* any variable.( In this case I use n.) Next the beginning part is 3 less than the product part so it is 4n-3. And finally the whole equation is equal to 5 so itis 4n-3=5.

Answer:

The old version awards 50 more points for each level

Step-by-step explanation:

Function Modeling

Two models are being compared: The old model relates the total number of points awarded in a computer game (y) with the number of levels completed (x) as

[tex]y=175x+150[/tex]

The new model is given as a graph. To find the equation of the line we must locate a couple of 'good' points. The graph is very clear, so we select the extreme points (1,250) (9,1250)

Find the equation of the line with the point-point formula

[tex]\displaystyle y-250=\frac{1250-250}{9-1}(x-1)[/tex]

[tex]\displaystyle y-250=\frac{1000}{8}(x-1)[/tex]

[tex]y=250+125x-125[/tex]

[tex]y=125x+125[/tex]

Comparing the new function with the old function we can note the coefficient of x (the slope of the line) is 50 points more in the old version than the points in the new version.

Thus the answer is

The old version awards 50 more points for each level

Answer: the answer is B

Step-by-step explanation: