Complete the table in your scratch paper and answer the following question below.

11. What is the total frequency of the data in the table?

A. 50
B. 56
C. 30
D. 20

12. What is the total fx of the data in the table?

A. 1000
B. 1717
C. 1789
D. 2000

14. What is the midpoint of the scores 45-49 of the data in the table?

A. 27
B. 47
C. 45
D. 49

15. What is the mean of the data in the table?

A. A27.3
B. 28.4
C. 45.1
D. 30.7

16. What is the median of the data in the table?

A. 31.3
B. 28.4
C. 45.1
D. 30.7

17. What is the mode of the data in the table?

A. 31.3
B. 32.5
C. 45.1
D. 40.3

Answer:

\(\boxed {\boxed {\sf d= 6}}\)

Step-by-step explanation:

Distance can be found using this formula:

\(d=\sqrt {(x_2-x_1)^2+(y_2-y_1)^2\)

Where (x₁, y₁) and (x₂, y₂) are the points.

We are given the points O (-3, -2) and P(-3,4). Therefore,

\(x_1= -3 \\y_1= -2 \\x_2= -3 \\y_2=4\)

Substitute the values into the formula.

\(d=\sqrt {(-3--3)^2+(4--2)^2\)

Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition and Subtraction.

Solve inside the parentheses first.

\(d= \sqrt {(0)^2+ (6)^2}\)

Solve the exponents.

\(d=\sqrt {0+36\)

Add.

\(d= \sqrt {36\)

Take the square root.

\(d=6\)

The distance is 6.

Answer:93 students play a musical instrument

a. null hypothesis \(H_0\): PRmean=non-PRmean

b. the sample mean lies in the interval, so we fail to reject null hypothesis

c. critical value z(0.05)=1.96 is less than calculated z=3.56 so we fail to accept null hypothesis.

A null hypothesis states that there is no statistical significance to be discovered in the set of presented observations. The validity of a theory is assessed through hypothesis testing on sample data. Sometimes known as the "null," it is represented by the symbol  \(H_0\).

(a)

null hypothesis  \(H_0\): PRmean=non-PRmean

(b).

i. \((1-\alpha)\times 100\%\) confidence interval for sample

\(mean=mean \pm z(\frac{\alpha }{2} )*SE(mean)\)

95% confidence interval for sample PRmean=PRmean±z(.05/2)*SE(mean)=69.5±1.96*1.9

=69.5±3.724=(65.776,73.224)

95% confidence interval for sample non-PRmean=non-PRmean±z(.05/2)*SE(mean)=61.2±1.96*1.7

=69.5±3.332=(57.868, 64.532)

ii. null hypothesis not be rejected

iii. since the sample mean lies in the interval, so we fail to reject null hypothesis

(c).

i. mean difference=69.5-61.5=8

ii. SE(difference)=\(\sqrt{SE(PR)^2+SE(non-PR)^2}\)

\(=\sqrt{1.9\times 1.9+1.2\times 1.2}\)

=2.2472

iii. we use z-test and z=(mean difference)/SE(difference)=8/2.2472=3.56

iv. here level of significance alpha is not mentioned,

let \(\alpha\) =0.05

critical value z(0.05)=1.96 is less than calculated z=3.56 so we fail to accept null hypothesis.

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Answer:

Let y be the total number of dogs

dogs on leash = y/5

dogs not on leash = y-y/5

= 4y/5

The expression to represent how many dogs were not on a leash is 4x / 5, using both subtraction and multiplication.

An expression is combination of variables, numbers and operators.

If 1/5 of the dogs were on a leash, then the remaining 4/5 of the dogs were not on a leash.

To find the number of dogs that were not on a leash, we can multiply the total number of dogs (x) by 4/5:

Number of dogs not on a leash = x * 4/5

We can also express this using subtraction:

Number of dogs not on a leash = x - (x * 1/5)

Simplifying the expression on the right side:

Number of dogs not on a leash = x - x/5

Combining like terms:

Number of dogs not on a leash = (5x - x) / 5

= 4x / 5

Therefore, the expression to represent how many dogs were not on a leash is 4x / 5, using both subtraction and multiplication.

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Answer:

(B) 42°

Step-by-step explanation:

The triangle LMN is inscribed in a semi-circle so therefore, if LM is the diameter, m∠LMN is 90°. Then, if one angle in ΔLMN is 90° and another is 48°, the third angle (∠NLM) will be 42° (The sum of the angles in a triangle is 180°).

Hope this helps :)

Answer:

it is 6

Step-by-step explanation:

That’s what they both can be multiplied by

Answer:

-2

Step-by-step explanation:

slope= \(\frac{y_{1}-y_{2} }{x_{1}-x_{2} }\)

Let's use points (-3,6) and (3,6).

\(\frac{6-(-6)}{-3-3}= \frac{12}{-6} = -2\)

Answer:

305$

Step-by-step explanation:

305 because if it costs 61 dollars for 2 tickets and 61/2 30.5. 30.5*10=305

The distance from the top of the tree to the tip of the shadow is 15.5 feet.

A tree that is 15 feet tall casts a shadow that is 4 feet long. The distance of the top of the tree to the tip of the shadow can be calculated as follows:

The situation forms a right angle triangle. Therefore, the sides can be found using Pythagoras's theorem.

The height of the tree and the length of the shadow are the legs of the right triangle while the distance of the tree to the tip of the shadow is the hypotenuse side.

Therefore,

c² = a² + b²

where

Hence,

c² = 15² + 4²

c² = 225 + 16

c² = 241

c = √241

c = 15.5241746963

c = 15.5 feet.

Hence the distance is 15.5 feet.

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Answer: A: 15.5 feet

The surface area of the cylinders are: 7794 square units, 904.9 square units,  12804 square units

recall that a cylinder is a three-dimensional solid with two parallel circular bases joined by a curved surface at a fixed distance from the center.  It is considered a prism with a circle as its base and is a combination of two circles and a rectangle

the general formula for the surface area of a cylinder is

SA = 2пr(r+h)

1  SA =2*22/7*20 (20+42)

125.7(62)

SA = 7794 square units

2) SA = 2пr(r+h)

Sssurface rea = 2*3.142*9(9+7)

Surface area = 56.6(16)

Surface area = 904.9 square units

3)   SA = 2пr(r+h)

surface area = 2*3.142*21(21+76)

Surface area = 132(97)

Surface area = 12804 square units

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Correct Inputs :-

In ΔABC right angled at A, D and E are points on BC, C such that BD = CD and AD ⊥ BC

\(\underline{\underline{\large\bf{Solution:-}}}\\\)

\(\longrightarrow\) Let us know about definition of altitude first. The altitude of a triangle is the perpendicular line segment drawn from the vertex to the opposite side of the triangle.

\(\leadsto\)Median is the line segment from a vertex to the midpoint of the opposite side.

Let us Check all options one by one

simplified is

4x-13

From the information given, we have that;

V = s³

where:

We can see that:

Thus, we can see that to find the volume, we take the cube of the side length and to find the side length, we take the cube root of the volume.

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Answer:

(Answer In Picture)

Using Markov's Theorem, it can be proven that at most 3/4 of the cows in a herd can survive an outbreak of cold cow disease. This is demonstrated by showing an example set of temperatures for a herd of 400 cows where the average temperature is 85 degrees and 3/4 of the cows have a temperature high enough to survive.

Markov's Theorem states that for any set of temperatures in a herd of cows, the probability that a cow's temperature is below a certain threshold is less than or equal to the ratio of the average temperature to the threshold temperature. In this case, the threshold temperature is 90 degrees, which is the minimum temperature for survival.

To prove that at most 3/4 of the cows can survive, we assume that all cows with temperatures below 90 degrees will die. Since the average temperature of the herd is 85 degrees, we can use Markov's Theorem to show that the probability of a cow having a temperature below 90 degrees is 85/90 = 17/18.

Now, let's consider a herd of 400 cows. If we assume that the probability of a cow having a temperature below 90 degrees is 17/18, then the expected number of cows with temperatures below 90 degrees would be (17/18) * 400 = 377.78. Since we cannot have a fraction of a cow, the maximum number of cows with temperatures below 90 degrees is 377.

Therefore, the maximum number of cows that can survive the outbreak is 400 - 377 = 23. This means that at most 23/400 = 3/4 of the cows can survive.

To demonstrate that this bound is the best possible, we can construct an example set of temperatures where 3/4 of the cows survive. Let's say 300 cows have a temperature of 90 degrees and 100 cows have a temperature of 70 degrees. The average temperature of the herd would be (300 * 90 + 100 * 70) / 400 = 85 degrees. In this scenario, 3/4 of the cows (300) have a high enough temperature to survive, which matches the bound from Markov's Theorem.

Thus, by applying Markov's Theorem and providing an example, it is proven that at most 3/4 of the cows in a herd can survive an outbreak of cold cow disease.

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Answer:

is the right answer.

Answer:

3(e+2)

please mark me brainliest and follow me my friend.

Answer:

Alex: 46.065

Step-by-step explanation:

58.483 - 12.418 = 46.065

Answer:

Chemical Change-

Answer: 16) y=-0.5x+3 and 17) y=2x-3

Step-by-step explanation:

16: The slope-intercept form of a line is y=mx+b, where m is the slope, and b is the y-value at the y-intercept.

Since y=3 at x=0, the y-intercept is (0,3), and b=3.

Slope=\(\frac{y_{2} -y_{1} }{x_{2}-x_{1} }\) where (\(x_{1} ,y_{1}\)) and (\(x_{2} ,y_{2}\)) are two points on the line. Choose (0,3) and (2,2):

Slope=\(\frac{2-3}{2-0}\)=-0.5

Plug m=-0.5 and b=3 into y=mx+b:

y=-0.5x+3

17: The slope-intercept form of a line is y=mx+b, where m is the slope, and b is the y-value at the y-intercept.

Because y=-3 at x=0, the y-intercept is (0,-3), and b=-3.

Slope=\(\frac{y_{2} -y_{1} }{x_{2}-x_{1} }\) where (\(x_{1} ,y_{1}\)) and (\(x_{2} ,y_{2}\)) are two points on the line. Choose (0,-3) and (1,-1):

Slope=\(\frac{-3-(-1)}{0-1}\)=\(\frac{-2}{-1}\)=2

Plug m=2 and b=-3 into y=mx+b:

y=2x-3

Therefore, the seamstress used 200 + 200 - 179 = 221 buttons for her recent mending.

As per the data given in the above question are as bellow,

The data provided are as bellow,

There are 35 buttons remaining in a package in the equipment of a seamstress.

She repaired some things and used 14 of another box.

How many buttons did the seamstress use for her most recent repair if both boxes initially had 200 buttons?

The seamstress had

200 - 35 = 165 buttons

left in her first box after using some of them.

So she had

165 + 14 = 179 buttons in total.

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The time taken for the cargo to hit the ground will be 0.6 seconds and it travels in the horizontal direction for around 14.69 feet.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. The point-slope form, standard form, and slope-intercept form are the three main types of linear equations. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Here,

The calculations are attached in images.

To calculate t we will use that is y because at the moment of cargo will have a height 0, so we get,

= −4.9t² +1.75

-1.75=-4.9t²

t²=-1.75/-4.9

t²=√0.3571

=0.6 seconds

Now we will calculate x, then y = 0

because since the cargo will be on the ground it will no have height, so

0= -0.0081x²+1.75

-1.75 =-0.0081x²

x²=-1.75/-0.0081

x= √216.04 = 14.69 feet

It will take the cargo 0.6 seconds to hit the ground, and it will travel 14.69 feet in a horizontal direction.

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If the standard deviation of a set of data is 6, then the value of variance is 36

The formula for determining variance is variance = √Standard deviation

Variance of a set of data is equal to square of the standard deviation.

If the standard deviation of a set of data is 6 then we get variance by putting the value of standard deviation in the formula

variance = √Standard deviation

Take square root on both sides

Standard deviation² = 6²

Standard deviation= 36

Hence,  standard deviation of a set of data is 6, then the value of variance is 36

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Answer:

X=8

Step-by-step explanation:

Nothing hard

X is just unknown

3+5=8

And since x is in th place of 8, its x=8

Answer:

Step-by-step explanation:

5+3=8 so if its 5+3 then that means 5+3=x x would be 8 so

(x=8) easy :D

Step-by-step explanation:

w = 3(2a + b) - 4

w = 6a + 3b - 4

6a = w - 3b + 4

a = 1/6 * (w - 3b + 4).

a) The 95% confidence interval is 18.95% to 34.49%. b) The confidence interval for women (18.95% to 34.49%) does not include the value of 23.6%.

To construct a 95% confidence interval for the percentage of successful challenges made by women playing singles matches, we can use the formula for the confidence interval for a proportion. The formula is:

Confidence Interval = p ± Z * \(\sqrt{p(1-p)/n}\)

Where:

p is the sample proportion (successful challenges / total challenges)

Z is the z-score corresponding to the desired confidence level

n is the sample size

a. Let's calculate the confidence interval for the percentage of successful challenges made by women:

Sample size (n) = 135

Number of successful challenges (x) = 36

Sample proportion (p) = x/n

p = 36/135 ≈ 0.2667

To find the z-score corresponding to a 95% confidence level, we need to calculate the critical value. Since the sample size is large enough (n > 30), we can approximate the critical value using the standard normal distribution.

The z-score corresponding to a 95% confidence level (two-tailed test) is approximately 1.96.

Confidence Interval = 0.2667 ± 1.96 * \(\sqrt{0.2667(1-0.2667)/135}\)

Calculating the confidence interval:

Confidence Interval = 0.2667 ± 1.96 * \(\sqrt{0.2667*0.7333/135}\)

= 0.2667 ± 1.96 * \(\sqrt{0.19511/135}\)

= 0.2667 ± 1.96 * 0.03943

≈ 0.2667 ± 0.07723

The lower bound of the confidence interval is:

0.2667 - 0.07723 ≈ 0.1895

The upper bound of the confidence interval is:

0.2667 + 0.07723 ≈ 0.3449

Therefore, the 95% confidence interval for the percentage of successful challenges made by women is approximately 18.95% to 34.49%.

b. To compare the results with the 95% confidence interval for the percentage of successful challenges made by men (23.6%), we can observe that the confidence interval for women does not overlap with the value for men.

The confidence interval for women (18.95% to 34.49%) does not include the value of 23.6%. This suggests that there may be a significant difference in the percentage of successful challenges made by women compared to men.

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Here is how it is graphed:

The area of the swimming pool cover is approximately 159.27 square feet, rounded to the nearest hundredth.

To find the area of the swimming pool cover, we can calculate the area of the rectangle and the area of the semicircle separately.

Area of the rectangle:

The length of the rectangle is 12 feet and the width is 10 feet. The formula to calculate the area of a rectangle is:

Area_rectangle = length × width

Area_rectangle = 12 × 10

Area_rectangle = 120 square feet

Area of the semicircle:

The radius of the semicircle is half the distance between the parallel lines, which is 10/2 = 5 feet. The formula to calculate the area of a semicircle is:

Area_semicircle = (π × radius²) / 2

Area_semicircle = (π × 5²) / 2

Area_semicircle = (π × 25) / 2

Area_semicircle ≈ 39.27 square feet

The total area of the swimming pool cover:

To find the total area, we add the area of the rectangle and the area of the semicircle:

Total_area = Area_rectangle + Area_semicircle

Total_area = 120 + 39.27

Total_area ≈ 159.27 square feet

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The limit of the absolute value of the ratio of consecutive terms is less than 1, the series converges. Therefore, the given series converges.

To test the series for convergence or divergence, we can use the ratio test. The ratio test states that for a series Σaₙ, if the limit of the absolute value of the ratio of consecutive terms (|aₙ₊₁ / aₙ|) as n approaches infinity is less than 1, then the series converges. If the limit is greater than 1 or it does not exist, then the series diverges.

Let's apply the ratio test to the given series:

aₙ = (-1)ⁿ * (10ⁿ - 3) / (11ⁿ³)

|aₙ₊₁ / aₙ| = |((-1)ⁿ⁺¹ * (10ⁿ⁺¹ - 3) / (11ⁿ⁺¹)³) / ((-1)ⁿ * (10ⁿ - 3) / (11ⁿ)³)|

Simplifying the expression:

|aₙ₊₁ / aₙ| = |(-1) * (10ⁿ⁺¹ - 3) / (11ⁿ⁺¹)³ * (11ⁿ)³ / (10ⁿ - 3)|

Taking the limit as n approaches infinity:

lim (n→∞) |aₙ₊₁ / aₙ| = lim (n→∞) |(-1) * (10ⁿ⁺¹ - 3) / (11ⁿ⁺¹)³ * (11ⁿ)³ / (10ⁿ - 3)|

We can observe that as n approaches infinity, the terms (10ⁿ⁺¹ - 3) and (11ⁿ)³ grow much faster than the constant terms (-1) and (10ⁿ - 3). Therefore, we can simplify the limit expression as:

lim (n→∞) |aₙ₊₁ / aₙ| = lim (n→∞) |(-1) / 11³|

Since the limit is a constant value, |(-1) / 11³| = 1 / 1331, which is less than 1.

According to the ratio test, if the limit of the absolute value of the ratio of consecutive terms is less than 1, the series converges. Therefore, the given series converges.

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Answer:

61°

Step-by-step explanation:

B = 180°-58°-61°

= 61°