Find the volume common to two spheres, each with radius r, if the distance between their centers is r/2.
(given information: A cap of a sphere with radius r = 5 and height h = 2.)

The sustainable growth rate is calculated by subtracting the payout ratio from the ROE.

The sustainable growth rate is calculated by subtracting the payout ratio from the ROE. To calculate the sustainable growth rate for Gold Corp., we must first calculate the retention ratio. The retention ratio is calculated by subtracting the payout ratio from 100%. In this case, the retention ratio would be 100% - 20% = 80%. The sustainable growth rate is then calculated by multiplying the retention ratio by the ROE. In this case, the equation would be 80% * 12% = 9.6%. The sustainable growth rate for Gold Corp. is 9.6%, which can be rounded to 9.6%.

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The square root of 7 is approximately 2.65 when rounded to the nearest hundredth.

The graph of the function is attached

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

f(x) = square root 4x

This can be expressed as

f(x) = √(4x)

Take the square root of 4

So, we have the following representation

f(x) = 2√x

This means that the graph f(x) = √(4x) and f(x) = √(4x) are the same

Next, we plot the graph

See attachment for the graph of f(x)

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The expression showing the distance between point J and point K is |-9|-|-2|

Distance between two points is the length of the line segment that connects the two given points.

Given that, two points J(6, -2) and k(6, -9), we need to find the distance between them,

The distance between two pints is given by,

D = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Here, the points are, (6, -2) and (6, -9)

Therefore,

|JK| = [tex]\sqrt{(0-0)^2+(-9+2)^2}[/tex]

|JK| = √7²

|JK| = 7 units

Therefore, the expression showing the distance between point J and point K is |-9|-|-2|

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The range of the given data is 15, the sum is 110, variance is 37.

The sample variance is a value that measures the variability of values in the data set and how much the observed values deviate from the value of the mean or central value of the data set.

X=[23,17,15,30,25]

(a)

The value of the range is the difference between the maximum value and minimum value:

range=30-15=15

(b)

Sum(x)= 23+17+15+30+25=110

the sum of x2 = [tex]23^2+17^2+15^2+30^2+25^2=2568[/tex]

(c)

from part (b)

[tex]s^2=\sum x_i-nX^2]/[n-1]\\\\=[2568-5(22)^2][5-1]\\\\=37[/tex]

(d)

Using the definition of the variance, first we calculate the mean,

u=110/5=22

u=22

[tex]v^2=\frac{1}{n-1}\sum (x_i-u)^2\\\\=148/4\\=29.6\\s=6.083.[/tex]

e)

The value of population variance is v =5.44

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hola i can help... all you have to do is grab a calculator and add 100 to each number, them sbract them by 302

The tenth term of the second sequence is 80 and sequence 2 is formed by multiplying by 2 to sequence 1. Then the correct option is C.

Let a₁ be the first term and d be a common difference. Then the nth term of the arithmetic sequence is given as,

aₙ = a₁ + (n - 1)d

From the table, the first term of the first sequence is 4 and the first term of the second sequence is 8. If the first sequence is multiplied by 2 then we obtain the second sequence.

The common difference of the second sequence is given as,

d = 16 - 8

d = 8

Then the tenth term of the second sequence is given as,

a₁₀ = 8 + (10 - 1) x 8

a₁₀ = 8 + 72

a₁₀ = 80

The tenth term of the second sequence is 80 and sequence 2 is formed by multiplying by 2 to sequence 1. Then the correct option is C.

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The complete question is attached below.

For x ≤ -1, the function is given by f(x) = 4x + 1. This is a linear function with a slope of 4 and y-intercept of 1. The graph of this part of the function is a straight line passing through (0, 1) with a steep slope, extending towards negative x-values.

In mathematics, a function is a rule that associates each element in one set (called the domain) to a unique element in another set (called the range). Functions are one of the most important concepts in mathematics and have a wide range of applications in various fields.

A function is usually denoted by a letter, such as f(x), where x is an element in the domain and f(x) is the corresponding element in the range. The domain of a function is the set of all possible values of x for which the function is defined, and the range is the set of all possible values of f(x).

To graph the piecewise function f(x), we will graph each part of the function separately.

For -1 < x < 2, the function is given by f(x) = -2x - 3. This is also a linear function with a slope of -2 and y-intercept of -3. The graph of this part of the function is a straight line passing through (-1, 1) with a gentle slope, extending towards positive x-values until it reaches x=2.

For x ≥ 2, the function is given by f(x) = 5. This is a horizontal line at y=5, which is a constant function. The graph of this part of the function is a horizontal line at y=5 starting from x=2.

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If Sam is not an expert sailor, then he will not be allowed on Signe's racing boat. and If Sam is allowed on Signe's racing boat, then he is an expert sailor.

are both correct if-then forms of the given statement, with the first being the contrapositive of the second. The other options are not correct if-then forms.

The original statement is "Sam will be allowed on Signe's racing boat only if he is an expert sailor." This statement can be rewritten in if-then form using the formal definition of "only if," which means "if and only if" or "implies and is implied by."

One possible if-then form is "If Sam is not an expert sailor, then he will not be allowed on Signe's racing boat." This is the contrapositive of the original statement, which means that it is logically equivalent to the original statement. It asserts that if Sam is not an expert sailor, then he cannot be on Signe's racing boat.

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The actual dimensions of the rectangular garden are 17.5 cm by 12.5 cm

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

Scale: 1.6 cm = 2 cm

A scale is the ratio of the size of the drawing to the size of the actual object.

Given that the dimension is

14 cm by 10 cm

Using the above as a guide, we have the following equation

Actual = 14 * 2/1.6 cm by 10 * 2/1.6 cm

Evaluate

So, we have the following representation

Actual = 17.5 cm by 12.5 cm

Hence, the actual is 17.5 cm by 12.5 cm

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Answer: 63

63-15=48

Step-by-step explanation:

Brandon have a total of $32 originally

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

When he spends $24, he has 3/4 of the original amount left

Using the above as a guide, we have the following:

24 = Original * 3/4

Make "Original" the subject of the formula

So, we have the following representation

Original = 24/(3/4)

Evaluate the expression

Original = 32

Hence, the amount is $32

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To eliminate the x-variable using addition in this system of equations we must multiply 3(2x + 3y = 25) and 2(- 3x + 4y = 22).

If a system of equations only contains two linear equations with two variables, the system's equation can be graphed, the graph will have two straight lines, and the intersection point(s) of those lines will be the system's solution.

There are only three matching forms of solution for a given system of equations because there are only three different ways that two straight lines in the plane can graph.

Given, A system of equations 2x + 3y = 25 and - 3x + 4y = 22.

Now, To eliminate the x-variable using addition we have to multiply equation (i) by 3 and equation (ii) by 2 which results in,

6x + 9y = 75 and - 6x + 8y = 44,        (6x + (-6x) would cancel out).

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Biography, as it provides a brief overview of the life and career of Emest Cline.

What is Biography ?

A biography is a written account of another person's life, typically written by someone else. It often includes information about the person's background, education, career, accomplishments, and other significant events and experiences throughout their life. Biographies can also provide insights into a person's personality, character, and motivations, as well as the historical or cultural context in which they lived.

Given ,

Emest Cline is an American Screenwriter and author. Emest was born in 1972. He started his writing career in 1992

doing spoken word poetry. His best known works include 'Dance Monkey Dance' and 'When I Was a Kid. He then moved to film, as the screenwriter of the film Fanboys. He then released one of the most entertaining novels of all time, Ready Player One. Today Cline is still working, writing for many projects.

The type of informational text that this paragraph is is A.

Therefore, Biography, as it provides a brief overview of the life and career of Emest Cline.

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The linear equation is y = $25 + $10*w, and its graph is on the image at the end.

Here we know that he started with $25 He adds $10 to the cookie jar each week. Then we can model this with a linear equation:

y = $25 + $10*w

Where w is the number of weeks.

Now we want to graph this, to do so, we just need to find two points on the line.

if w = 0

y = $25 + $10*0 = $25

if w = 6

y = $25 + $10*6 = $85

So we need to graph the points (0, 25) and (6, 85) and connect them witha  line.

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Mean absolute deviation of the data is 1.

The mean absolute deviation of a dataset is the average distance between each data point and the mean. It gives us an idea about the variability in a dataset.

Given, In bar chart

Number of artists n = 4

Number of albums for Lil Shane x₁ = 7

Number of albums for Ben Raises x₂ = 9

Number of albums for Nicky x₃ = 6

Number of albums for Underdog x₄ = 6

Mean of the number of albums

μ = (7 + 9 + 6 + 6)/4 = 28/4 = 7

|μ - x₁| = |7 - 7| = 0

|μ - x₂| = |7 - 9| = |-2| = 2

|μ - x₃| = |7 - 6| = 1

|μ - x₄| = |7 - 6| = 1

Mean absolute deviation = ∑|x - μ|/n

= (0 + 2 + 1 + 1)/4

= 1

Hence, 1 is the mean absolute deviation (MAD) of the data in the bar chart.

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The solution is,

-2A = (-6, -8, 0, 8, 2, -8)

B - 2A = (2, -7, -4, 3, 4, -12)

AC is undefined.

CD = (3, 2, 12, 5)

In mathematics, a matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.

here, we have,

Given the matrices:

A = (3 4 0 -4 -1 4)

B = (8 1 -4 -5 2 -4)

C = (1 -1 3 1)

D = (3 -2 4 5)

We are required to compute the following

-2A, B - 2A, AC, CD

For -2A:

-2(3 4 0 -4 -1 4)

= (-6, -8, 0, 8, 2, -8)

For B - 2A:

Because B - 2A = B + (-2A),

we have:

(8 1 -4 -5 2 -4) + (-6, -8, 0, 8, 2, -8)

(2, -7, -4, 3, 4, -12)

For AC:

(3 4 0 -4 -1 4)(1 -1 3 1)

This is undefined.

For CD:

(1 -1 3 1)(3 -2 4 5)

= (3, 2, 12, 5)

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The value of h such that the matrix is the augmented matrix of a consistent linear system is 2

For the given matrix to be the augmented matrix of a consistent linear system, we need to check whether the matrix is in row echelon form or not. If the matrix is in row echelon form and the last row is not all zeros, then the linear system is consistent.

We can use elementary row operations to transform the matrix into row echelon form.

[tex]\left[\begin{array}{ccc}1&h&4\\3&6&8\end{array}\right][/tex]

R2 <- R2 - 3R1

[tex]\left[\begin{array}{ccc}1&h&4\\0&6-3h&-4\end{array}\right][/tex]

The matrix is in row echelon form. Now, we need to check whether the last row is all zeros or not.

If 6-3h = 0, then the last row will be all zeros, which implies that the linear system is inconsistent.

If 6-3h ≠ 0, then the last row will not be all zeros, which implies that the linear system is consistent.

Therefore, we need to solve the equation 6-3h = 0 to determine the value of h that makes the linear system consistent.

6-3h = 0

3h = 6

h = 2

So, the value of h that makes the matrix the augmented matrix of a consistent linear system is h = 2.

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When the interpreting the covariance between X and Y , a positive value of covariance indicates that , on average ,if x below its mean then y tends to be below its mean.

Covariance is a statistical measure that indicates how two variables are related to each other. Specifically, covariance measures the degree to which the values of two variables vary together. If two variables have a positive covariance, it means that they tend to increase or decrease together. Conversely, if two variables have a negative covariance, it means that they tend to move in opposite directions.

Mathematically, covariance is calculated as the average of the products of the deviations of each value from their respective means, for two variables. A positive covariance indicates that the two variables tend to be above or below their respective means together, while a negative covariance indicates that one variable tends to be above its mean when the other is below its mean, and vice versa.

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a) 90% confident that the true population mean μ is between 91.01 and 102.99.

b) 90% confident that the true population mean μ is between 92.26 and 101.74.

c) 80% confident that the true population mean μ is between 93.79 and 100.21.

d) Using Central Limit Theorem to approximate the population mean as normally distributed, the confidence intervals can still be computed using the same formula as before.

(a) To construct a 90% confidence interval about μ when n = 27, we use the formula:

x ± z × (s/√n)

where x is the sample mean, s is the sample standard deviation, n is the sample size, and z is the z-score that corresponds to the desired confidence level (in this case, z = 1.645 for a 90% confidence level). Plugging in the values given, we get:

97 ± 1.645 × (13/√27)

which simplifies to:

(91.01, 102.99)

Therefore, we are 90% confident that the true population mean μ is between 91.01 and 102.99.

(b) To construct a 90% confidence interval about μ when n = 18, we use the same formula as before, but with a different z-score (since the sample size is smaller). In this case, we use z = 1.734, and we get:

97 ± 1.734 × (13/√18)

which simplifies to:

(92.26, 101.74)

Therefore, we are 90% confident that the true population mean μ is between 92.26 and 101.74.

(c) To construct an 80% confidence interval about μ when n = 27, we use the same formula as before, but with a different z-score (since the confidence level is different). In this case, we use z = 1.282, and we get:

97 ± 1.282 × (13/√27)

which simplifies to:

(93.79, 100.21)

Therefore, we are 80% confident that the true population mean μ is between 93.79 and 100.21.

(d) The confidence intervals in parts (a)-(c) assume that the population is normally distributed. If the population is not normally distributed, we cannot rely on these intervals to accurately estimate the true population mean. However, if the sample size is sufficiently large (usually n > 30), we can use the Central Limit Theorem to approximate the population mean as normally distributed, and the confidence intervals can still be computed using the same formula as before. If the sample size is small and the population is not normally distributed, other methods may be needed to construct a confidence interval, such as bootstrapping or using a non-parametric approach.

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The signficant changes that are happening as per the information provided in the question will be as follows:

1. The p-value for Factor A is 0.4194 option e. greater than 0.10.

2. The conclusion with respect to Factor A will be option b. Factor A is not significant.

3. The conclusion with respect to Factor B will be option b. Factor B is not significant.

4. The p-value for the interaction of factors A and B is 0.1621 option e. greater than .10

5. There is no effect of decreasing the waiting time and changing the loading and unloading methods  between the rides.

Here, we are going to perform two-way ANOVA Observation

A       B               C                

41, 43, 49 52, 44, 46 50, 46, 48

49, 50, 48 50, 46, 48 48, 44, 46          

Sums of row and column

A      B        C          Row total (xa)

133     142   144                    419

147     144   138                    429

Col total (xb)

280   286 282                    848

For A,

∑x²=412+432+492+...+482+442+462=40088

∑x²b/ra =1/3⋅2(280²+286²+282²)

=1/6(78400+81796+79524)

=1/6(239720)

For B,

=39953.3333

∑x²a/rb=1/3⋅3(419²+429²)

=1/9(175561+184041)

=1/9(359602)

For C,

=39955.7778

∑∑x²ab/r=  1/3(133²+142²+144²+147²+144²+138²)

=1/3(17689+20164+20736+21609+20736+19044)

=1/3(119978)

=39992.6667

For D,

(∑x)²/rab

=(848)²/3⋅2⋅3

=719104/18

=39950.2222

Sum of squares total

SST=∑x²-(∑x)²/n

Now we subtract A and D

=(A)-(D)

=40088-39950.2222

=137.7778

Sum of squares between rows will be,

SSA=∑x²a/rb-(∑x)²/n

Now, we subtract C and D

=(C)-(D)

=39955.7778-39950.2222

=5.5556

Sum of squares between columns

SSB=∑x²b/ra- (∑x)²/n

Now, we subtract B and D

=(B)-(D)

=39953.3333-39950.2222

=3.1111

Sum of squares between columns

SSAB=∑∑x²ab/r-(∑x)²/n-SSA-SSB

Now we subtract B, D and Sum of squares between columns

=(B)-(D)-SSA-SSB

=39992.6667-39950.2222-5.5556-3.1111

=33.7778

The residual value of sum of squares Error,

SSE=SST-SSA-SSB-SSAB

=137.7778-5.5556-3.1111-33.7778

=95.3333

ANOVA table

Source. Sums    Degrees Mean Squares Square

of squares of freedom variation freedom

                       SS              DF          MS              F        

A         SSA=5.5556     a-1=1 MSR=5.5556    0.6993   0.4194 (p-value)

B            SSB=3.1111      b-1=2 MSC=1.5556    0.1958

0.8247 (p-value)

AB       SSAB=33.7778   2   MSAB=16.8889   2.1259 0..1621 (p-value)

Error (residual) SSE=95.33      12         MSE= 7.9444            

Total of SST=137.7778      will be    17  

In conclusion,

1. F for between columns, the critical value F(1,2) at 0.05 level of significance will be 4.7472. As computed that FR=0.6993<4.7472

H0 has been accepted, thus, there is no significant difference between rows.

P value is 0.4194 > 0.05. Hence, we fail to reject H0

2. F for between columns, the critical value F(2,2) at 0.05 level of significance will be 3.8853. As computed, FC=0.1958<3.8853. Thus, H0 is accepted and there is no significant difference between columns. P value is 0.8247 > 0.05. Hence, we fail to reject H0

3. The interaction between the Factors AB, there is no sufficient evidence to support the claim of interaction between the factors. Thus, P value is 0.1621 > 0.05. Hence, we fail to reject H0.

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Note that the full question is:

An amusement park studied methods for decreasing the waiting time (minutes) for rides by loading and unloading riders more efficiently. Two alternative loading/ unloading methods have been proposed. To account for potential differences due to the type of ride and the possible interaction between the method of loading and unloading and the type of ride, a factorial experiment was designed. Use the following data to test for any significant effect due to the loading and unloading method, the type of ride, and interaction. Use α = .05. Use both p-Value and Critical-Value approaches.Type of Ride

Roller Coaster Screaming Demon Log Flume

Method 1 41 52 50

43 44 46

49 46 48

Method 2

49 50 48

51 46 44

47 48 46

1. The p-value for Factor A is:__________.

a. less than .01

b. between .01 and .025

c. between .025 and .05

d. between .05 and .10

e. greater than .10Item 18

2. What is your conclusion with respect to Factor A?

a. Factor A is significant

b. Factor A is not significant

3. The p-value for Factor B is:_______.

a. less than .01

b. between .01 and .025

c. between .025 and .05

d. between .05 and .10

e. greater than .10

3. What is your conclusion with respect to Factor B?

a. Factor B is significant

b. Factor B is not significant

4. The p-value for the interaction of factors A and B is:_______.

a. less than .01

b. between .01 and .025

c. between .025 and .05

d. between .05 and .10

5. What is your recommendation to the amusement park?

We can see from a t-table with right-tail probabilities that the probability value that is closest to 2.5% is 0.0250, which is represented by a t-score.

The row in the table that corresponds to the number of degrees of freedom (df) must be found before the column that corresponds to the desired level of significance or alpha value in order to use the t-table to determine a t-score that cuts off a specific percentage in the upper tail for a t-distribution with a given number of df.

Since there are 24 degrees of freedom in this situation, we need to identify the t-score that removes 2.5% of the upper tail. We will be looking at the column for the right-tail probabilities because this test has one tail (upper tail), making it a one-tailed test.

Therefore, We can see from a t-table with right-tail probabilities that the probability value that is closest to 2.5% is 0.0250, which is represented by a t-score.

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The amount to be paid by Bo is 0.82B

A percent of a number is the 100th part of it.

Given that, the board game costs B dollars. Price is reduced by 18%.  we need to calculate the final bill.

Cost of game = B dollars

Discount = 18% = 0.18

Discount amount = 0.18B

Final cost = B-0.18B

Amount to pay = 0.82B

Hence, the amount to be paid by Bo is 0.82B

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The complete question is:-

Bo is buying a board game which usually costs B dollars. The game is on sale, and the price has been reduced by 18% There are different ways of thinking about how to calculate Bo's final bill. Match the expressions to their meanings.

Answer: It is D.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The notation is not what I am used to, but I think that I understand.  To go from the large figure to the smaller figure.  You need to dilate your figure by 1/3 .  The length of the big figure is 6 and 1/3 of that is a length of 2.  The width of the big figure is 3.  !/3 of that is 1 and that is what I see on the smaller figure.

Assuming the center of the dilation is point J.  If you move the shrunken figure 2 to the left and 5 down, it would fit right on top of the smaller figure.

The correct translation rule is given as -

(D_1/3 . T_<-2,-5> ) JKLM.

Translation is defined as the movement of graphical image over the two

dimensional plane. In genera, we can write the translation as -

(x, y) → (x ± k, y ± a)

here, we have,

Given is the composition of transformations that maps JKLM to PQRS.

Firstly →

The image is first translated according to the rule -

(x, y) → (x - 2, y - 5).

Secondly -

The image is then dilated by the scale factor -

{K} = 1/3.

Therefore, the correct translation rule is given as -

(D_1/3 . T_<-2,-5> ) JKLM.

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To find the surface area of the composite figure, we need to break it down into simpler shapes and add up their surface areas. From the given dimensions, we can see that the composite figure consists of two rectangular prisms and a triangular prism.

The dimensions of the rectangular prism are 10 cm (length), 8 cm (width), and 24 cm (height). Therefore, its surface area is:

SA1 = 2lw + 2lh + 2wh

SA1 = 2(10 cm)(8 cm) + 2(10 cm)(24 cm) + 2(8 cm)(24 cm)

SA1 = 160 cm^2 + 480 cm^2 + 384 cm^2

SA1 = 1024 cm^2

The dimensions of the triangular prism are 5 cm (base), 12 cm (height), and 8 cm (length). Therefore, its surface area is:

SA2 = lb + 2[(1/2)bh + lh]

SA2 = (8 cm)(5 cm) + 2[(1/2)(5 cm)(12 cm) + (8 cm)(12 cm)]

SA2 = 40 cm^2 + 240 cm^2 + 96 cm^2

SA2 = 376 cm^2

The dimensions of the rectangular prism on top are 4 cm (length), 5 cm (width), and 12 cm (height). Therefore, its surface area is:

SA3 = 2lw + 2lh + 2wh

SA3 = 2(4 cm)(5 cm) + 2(4 cm)(12 cm) + 2(5 cm)(12 cm)

SA3 = 40 cm^2 + 96 cm^2 + 120 cm^2

SA3 = 256 cm^2

To find the total surface area of the composite figure, we add the surface areas of the three shapes:

Total surface area = SA1 + SA2 + SA3

Total surface area = 1024 cm^2 + 376 cm^2 + 256 cm^2

Total surface area = 1656 cm^2

Therefore, the surface area of the composite figure is 1656 cm^2.

The probability that heads would be obtained 15 or fewer times when this coin is flipped 25 times is 0.370

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

"Information available from the question"

The parameters are:

Sample size, n = 25

Probability of success, p = 0.65

Number of success, x ≤ 15

The probability is represented using the following binomial formula:
[tex]P(x) =n_C_x*p^x*(1-p)^n^-^x[/tex]

Using the above formula, we have:

P(x ≤ 15) = 0.370

Hence, the probability is 0.370

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Answer:

Step-by-step explanation:

if we simplify both of them,

5/10=1/2

and

6/12=1/2

then it means they are equal