Sam and Adam share some money in the ratio 2 : 5.
Adam got £12 more than Sam.
Work out how much money Sam received.

The minimum sample size need for the given condition is 14

What is Confidence Level in Statistics?

The proportion of likelihood, or certainty, that the confidence interval will include the real population parameter when a random sample is drawn numerous times is referred to as the confidence level.

Solution:

The minimum sample sixe required when,

Confidence Level = 99%

Variance = 50%

Generally going through the table

Minimum sample size is

X = 14

To learn more about Confidence Level from the given link

https://brainly.com/question/24260117

#SPJ4

Information is needed to evaluate the project's financial viability, considering factors such as the initial investment, expected cash flows, cost of capital, and project duration.

To calculate the year 1 operating cash flows (OCF), we need to subtract the year 1 costs from the year 1 revenues:

OCF = Year 1 Revenues - Year 1 Costs

OCF = $192,000 - $125,000

OCF = $67,000

To find the depreciation expense in year 3, we need to determine the depreciation method. The provided information is incomplete regarding the depreciation method, so we cannot calculate the depreciation expense in year 3 without knowing the specific method.

The change in Net Working Capital (NWC) in year 2 can be determined by multiplying the Net Working Capital percentage (given as a percentage of t+1 revenues) by the year 1 revenues and subtracting the result from the year 2 revenues:

Change in NWC = (Year 2 Revenues - Net Working Capital percentage * Year 1 Revenues) - Year 1 Revenues

Without the specific Net Working Capital percentage or Year 2 Revenues values, we cannot calculate the exact change in NWC in year 2.

The net cash flow from salvage (ATSV) is calculated by multiplying the Salvage Value percentage by the Initial Cost:

ATSV = Salvage Value percentage * Initial Cost

ATSV = 28% * $390,000

ATSV = $109,200

To calculate the project's NPV, we need the cash flows for each year, the cost of capital, and the project duration. Unfortunately, the information provided does not include the cash flows for each year, so we cannot calculate the project's NPV.

To know more about investment visit:

https://brainly.com/question/29547577

#SPJ11

The complete question is:

Below are your numerical inputs for the problem: 4 & Initial Cost (\$) & 390000 5 & Year 1 Revenues (\$) & 192000 6 & Year 1 Costs (\$) & 125000  7 & Inflation & 2.75% 8 & Project Duration (years) & 6 9 & Depreciation Method & 10 & Tax Rate & 11 & Net Working Capital (\% oft+1 Revenues) & MACRS 12 & Salvage Value (\$) & 28.00% 13 & Cost of Capital & 15.00% & 245000 How much are the year 1 operating cash flows (OCF)? How much is the depreciation expense in year 3 ? What is the change in Net Working Capital (NWC) in year 2? What is the net cash flow from salvage (aka, the after-tax salvage value, or ATSV)? What is the project's NPV? Would you recommend purchasing the ranch? Briefly explain.

Answer:

(a) \(x=\dfrac{\pi}{8},\dfrac{3\pi}{8},\dfrac{9\pi}{8},\dfrac{11\pi}{8}\)

(b) \(x=\dfrac{3\pi}{2},\dfrac{\pi}{6},\dfrac{5\pi}{6}\)

Step-by-step explanation:

It is given that \(0\leq x\leq 2\pi\).

(a)

\(\sqrt{2}\sin 2x=1\)

\(\sin 2x=\dfrac{1}{\sqrt{2}}\)

\(\sin 2x=\dfrac{\pi}{4}\)

\(2x=\dfrac{\pi}{4},\dfrac{3\pi}{4},\dfrac{9\pi}{4},\dfrac{11\pi}{4}\)     \([\because \sin x=\sin y\Rightarrow x=n\pi+(-1)^ny]\)

\(x=\dfrac{\pi}{8},\dfrac{3\pi}{8},\dfrac{9\pi}{8},\dfrac{11\pi}{8}\)

(b)

\(\csc^2 x-\csc x-2=0\)

\(\csc^2 x-2\csc x+\csc x-2=0\)

\(\csc x(\csc x-2)+1(\csc x-2)=0\)

\((\csc x+1)(\csc x-2)=0\)

\(\csc x=-1\text{ or }\csc x=2\)

\(\sin x=-1\text{ or }\sin x=\dfrac{1}{2}\)         \([\because \sin x=\dfrac{1}{\csc x}]\)

\(x=\dfrac{3\pi}{2}\text{ or }x=\dfrac{\pi}{6},\dfrac{5\pi}{6}\)

Therefore, \(x=\dfrac{3\pi}{2},\dfrac{\pi}{6},\dfrac{5\pi}{6}\).

Answer:

17%of 23000

17/100×23000

1 yrs depreciation is 3910

then

after 4 years depreciation is 4×3910

=15640

the worth of after 4 yrs is 23000-15640

=Rs 7360

Answer:

90 degrees

Step-by-step explanation:

Assuming that this polygon is a square, x would be 90 degrees. In a square, all angles are right angles.

y=-1/5x+4 is the equation in slope-intercept form for the line with y-intercept 4 and slope -1/5

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Given,

y-intercept 4 and slope -1/5

Now y=-1/5x+4

Hence y=-1/5x+4 is the equation in slope-intercept form for the line with y-intercept 4 and slope -1/5

To learn more on slope of line click:

https://brainly.com/question/14511992

#SPJ1

The value of x is -4

When an integer by itself , the product obtained is a perfect square. Examples of perfect squares are 25 from 5×5, 36 from 6×6

The square root of the perfect square will give the original number.

Solving 4(x+7)^2-49=-13

collecting like terms

4( x+7)^2 = -13+49

4(x+7)² = 36

divide both sides by 4

(x+7)² = 9

Square both sides

x+7 = √9

x+7 = 3

x = 3-7

x = -4

therefore the value of x is -4

learn more about perfect square from

https://brainly.com/question/26119721

#SPJ1

Let's analyze the given information and the statements provided.

We are told that the integers r, s, and t all have the same remainder when divided by 5. This means that these integers can be written in the form:

r = 5n + k

s = 5m + k

t = 5p + k

where n, m, and p are integers representing quotients and k is the common remainder.

Statement (1) r + s = t:

If r + s = t, we can substitute the expressions for r and s:

(5n + k) + (5m + k) = 5p + k

Combining like terms:

10n + 10m = 5p

Dividing both sides by 5:

2n + 2m = p

From this equation, we can see that p must be an even number. However, we cannot determine the exact value of t based on this equation alone. Statement (1) is not sufficient to answer the question.

Statement (2) 20 ≤ t ≤ 24:

This statement provides a range for the possible values of t. Since t has the same remainder when divided by 5 as r and s, it must be congruent to k modulo 5. From the given range, the only number that satisfies this condition is t = 20.

However, we need to consider the combined information from both statements to reach a conclusion.

By considering both statements, we find that the only value that satisfies both conditions is t = 20.

the value of t is 20.

To know more about integers visit:

brainly.com/question/490943

#SPJ11

The number of total seats in the theater is 1287 seats.

The formula to find the sum in an arithmetic sequence will be:

= n/2 (a + l)

where n = total number

a = first term

l = last term

The last term which is the 22nd term will be:

= a + 21d

= 27 + 21(3)

= 27 + 63

= 90

The sum will be:

= n/2 (a + l)

= 22/2 ( 27 + 90)

= 11 × 117

= 1287 seats

Learn more about theater on:

brainly.com/question/13565425

#SPJ1

Step-by-step explanation:

Here we will, Provide index power 5 on both the sides, so that we can cancel out the 5th power root in the L.H.S

so we get as,

==> x+7 = (-2)^5

==> x+7 = -32

==> x = -32-7

==> x = -39

hence, x = -39

Option A.) is correct.

a. The alternative hypothesis (H1) specifies that is greater than 26, indicating a directed alternative, this is a one-tailed test.

b. The alternative hypothesis is one-sided and argues that > 26, hence the critical value is 1.645.

c. The value of the test statistic (z-score) is z ≈ 3.82.

d. We reject the null hypothesis (H0) because the test statistic (z = 3.82) is higher than the crucial value (1.645).

In this case, the p-value is the probability of observing a sample mean of 28 or greater, assuming the population mean is 26.

a. This is a one-tailed test because the alternative hypothesis (H1) states that μ is greater than 26, indicating a directional alternative.

b. The decision rule for a one-tailed test at a significance level of 0.05 is to reject the null hypothesis (H0) if the test statistic is greater than the critical value. In this case, the critical value is 1.645 because the alternative hypothesis is one-sided and states that μ > 26.

c. The value of the test statistic (z-score) can be calculated using the formula:

z = (x - μ) / (σ / √n)

where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

In this case:

x = 28

μ = 26

σ = 4

n = 34

Substituting the values into the formula:

z = (28 - 26) / (4 / √34) ≈ 3.82

d. Since the test statistic (z = 3.82) is greater than the critical value (1.645), we reject the null hypothesis (H0).

e-1. To calculate the p-value, we need to find the area under the standard normal distribution curve to the right of the test statistic (z = 3.82). We can use a standard normal distribution table or a calculator to find this area.

The p-value is the probability of observing a test statistic as extreme as the one calculated (or more extreme) under the null hypothesis.

e-2. Interpreting the p-value: The p-value represents the probability of obtaining a sample mean as extreme as the one observed (or more extreme) if the null hypothesis is true.

learn more about hypothesis from givn link

https://brainly.com/question/606806

#SPJ11

To convert 4.42 kg into pounds, the starting place in the conversion process is to understand the conversion factor between kilograms and pounds.

The conversion factor between kilograms (kg) and pounds (lbs) is 1 kg = 2.20462 lbs. This means that 1 kilogram is equal to approximately 2.20462 pounds. To convert a given weight in kilograms to pounds, you need to multiply the weight in kilograms by the conversion factor.

In this case, you want to convert 4.42 kg into pounds. The starting place in the conversion process is to use the conversion factor:

4.42 kg * 2.20462 lbs/kg = 9.7314044 lbs

By multiplying the given weight in kilograms (4.42 kg) by the conversion factor (2.20462 lbs/kg), you find that 4.42 kg is approximately equal to 9.7314044 pounds. Therefore, when converting kilograms to pounds, the first step is to apply the appropriate conversion factor by multiplying the weight in kilograms by the conversion factor.

Learn more about conversion  here:

https://brainly.com/question/23718955

#SPJ11

E⁣⁣⁣xplanation i⁣⁣⁣s i⁣⁣⁣n a f⁣⁣⁣ile

bit.\(^{}\)ly/3a8Nt8n

Answer: To find the probability of Janice making her next free throw, you can use the proportion of successful free throw shots out of the total number of free throw shots attempted so far.

First, we need to find the number of free throws made by Janice so far:

80% success rate * 15 free throws attempted = 12 free throws made

Then we add the number of free throws made today:

12 + 3 = 15

Then we add the number of free throws attempted today:

15 + 5 = 20

So the probability of Janice making her next free throw is:

15 free throws made / 20 free throws attempted = 75%

So, the probability that Janice will make her next free throw is 75%.

It's worth noting that this answer is based on the assumption that her success rate will remain the same and doesn't take into account any other variable or change in her performance.

Step-by-step explanation:

We have verified Chebyshev’s inequality for k = 2 and k = 3 when x ∼ binomial(50, 0.4).

Main answer :Using r’s "pbinom" function, we can verify Chebyshev’s inequality for k = 2 and k = 3 when x ∼ binomial(50, 0.4).The P(X ≤ μ + 2σ) and P(X ≤ μ + 3σ) values were obtained from the "pbinom" function for k = 2 and k = 3, respectively.

Supporting explanation :Chebyshev’s inequality states that for any data set, the proportion of the data within k standard deviations of the mean is at least 1 – 1/k^2, where k is a constant greater than 1. This holds true regardless of the shape of the distribution. To verify Chebyshev’s inequality for k = 2 and k = 3 when x ∼ binomial(50, 0.4), we first calculate the mean and standard deviation using the formula μ = np and σ = sqrt(npq), where n = 50, p = 0.4, and q = 0.6. Thus, μ = 20 and σ = 2.83.Then, we use the "pbinom" function in R to obtain the values of P(X ≤ μ + 2σ) and P(X ≤ μ + 3σ) for k = 2 and k = 3, respectively. For k = 2, P(X ≤ 25.66) = 0.9975, and for k = 3, P(X ≤ 28.49) = 0.9995.These values are greater than or equal to 1 – 1/k^2, where k = 2 and k = 3, respectively.

Know more about Chebyshev’s inequality here:

https://brainly.com/question/30928440

#SPJ11

Step-by-step explanation:

Probability of A  is  10 + 5  =15

Probability of B is   9 + 5   ( but you already counted the '5')  

 so just count   9

9+ 15 = 24

  this is  24 out of     16 + 10 + 5 + 9 = 40

      or    24/40   which reduces to 3/5   or  .6   or  60%

Using the equation given:

P(A) + P(B) - P(A and B)

  15  + 14    - 5    = 24       this is out of the entire number 40

               24/40 = same as above

Answer:

185.68 cm3

Step-by-step explanation:

SA = 2 (L x W) + 2 (L x H) + 2 (W x H)

     = 2 (8.2 x 3.4) + 2 (8.2 x 5.6) + 2 (3.4 x 5.6)

     = 2 (27.88)      + 2 (45.92)      + 2 (19.04)

     =     55.76       +     91.84         +     38.08

     SA = 185.68 cm3

sequence im sure for my answer

The Scale factor was used to enlarge the picture is 7/ 31.5.

A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size. It is used to find the missing length, area, or volume of an enlarged or reduced figure as well as to draw the enlarged or reduced shape of any given figure. It should be remembered that the scale factor only affects how big a figure is, not how it looks.

Given:

A picture is 7 inches wide and 9 inches long.

A photographer enlarges it so it is 31.5 inches wide and 40.5 inches long.

So, scale factor is

= Original dimension / Enlarged dimension

= 9/ 40.5

= 90/ 405

= 10/45

= 2/9

Now, simplifying the scale factor 7/31.5 because it has Nr < Dr.

= 7/ 3.15

= 70/31.5

= 2/9

Learn more about Scale Factor here:

https://brainly.com/question/30051525

#SPJ2

Answer:

f(x)=  - (x+4)/5

Step-by-step explanation:

sorry, i don't have time to explain..

If the sample has the same mix of people, in the same proportions, as the population being studied then sociologists know if the sample they are using is representative. So the option c is correct.

No subject is off-limits when sociologists use the sociological lens and start asking questions. Every facet of human behaviour has the potential to be studied. Sociologists cast doubt on the society that people have built and inhabit. They observe behavioral patterns as individuals navigate that world.

Sociologists have uncovered workplace patterns that have revolutionized industries, family patterns that have educated parents, and educational patterns that have supported structural changes in classrooms by using sociological methodologies, methodical research, and a scholarly interpretive approach.

To learn more about Sociology link is here

brainly.com/question/25099331

#SPJ4

The complete question is;

How do sociologists know if the sample they are using is representative?

a. If the people in the sample freely volunteered to serve as representatives

b. If the sample has an even number, decided by the researcher, of people from several different categories or backgrounds

c. If the sample has the same mix of people, in the same proportions, as the population being studied

d. If the participants have been interviewed to reveal possible bias.

Mean of the sampling distribution of X is 180 and the standard deviation is approximately 4.96, which represents the average variability in sample proportions. The sampling distribution of X is approximately normal due to the Central Limit Theorem. The probability that an SRS of 1500 American adults will contain between 155 and 205 African Americans can be calculated using the normal approximation to the binomial distribution. A polling organization can compare the observed proportion of African Americans in the sample with the known proportion to check for undercovering and other sources of bias, helping identify potential issues and improve sampling methodology.

To calculate the mean and standard deviation of the sampling distribution of X, we need to use the properties of a simple random sample (SRS). In an SRS, each individual has an equal chance of being selected.

Mean of the sampling distribution of X:

The mean of the sampling distribution of X is equal to the population proportion. In this case, the proportion of African Americans in the population is 0.12.

Mean = population proportion * sample size

Mean = 0.12 * 1500

Mean = 180

Therefore, the mean of the sampling distribution of X is 180.

Standard deviation of the sampling distribution of X:

The standard deviation of the sampling distribution of X is given by the formula:

Standard deviation = sqrt((population proportion * (1 - population proportion)) / sample size)

Standard deviation = sqrt((0.12 * (1 - 0.12)) / 1500)

Standard deviation ≈ 4.96

Interpretation of the standard deviation:

The standard deviation of the sampling distribution of X represents the average amount of variability or dispersion in the sample proportions that we would expect to see across different samples of the same size.

The sampling distribution of X is approximately normal due to the Central Limit Theorem (CLT). The CLT states that for a large enough sample size, regardless of the shape of the population distribution, the sampling distribution of the sample mean or proportion tends to follow a normal distribution.

To calculate the probability that an SRS of 1500 American adults will contain between 155 and 205 African Americans, we can use the normal approximation to the binomial distribution.

P(155 ≤ X ≤ 205) = P(X ≤ 205) - P(X ≤ 155)

Using the normal approximation, we can calculate the probability using the mean and standard deviation of the sampling distribution of X:

P(X ≤ 205) = P(Z ≤ (205 - 180) / 4.96)

P(X ≤ 205) ≈ P(Z ≤ 5.04)

Similarly, calculate P(X ≤ 155) using the same formula.

A polling organization can use the results from the previous question to check for undercoverage and other sources of bias by comparing the observed proportion of African Americans in the sample (based on the calculated probability) with the known proportion of 12% in the population. If the observed proportion significantly differs from 12%, it suggests the possibility of undercoverage or bias in the sample, indicating that certain groups might be underrepresented or overrepresented. This information can help identify potential sources of bias and improve the sampling methodology to obtain a more representative sample.

To know more about sampling distribution,

https://brainly.com/question/15030031

#SPJ11

Answer:

The height is 12.4 in

Making linear equations,  there are 27 chocolate bars in the vending machine.

What is the definition of a linear equation ?

A linear equation is an equation that describes a straight line in a coordinate system. It is an algebraic equation in which the highest power of the variable is 1 (i.e., the variable is not raised to any exponent other than 1). The general form of a linear equation having variable x is

ax + b = 0

where a and b are constants.

Now,

Let c be the number of chocolate bars and p be the number of bags of pretzels.

From the problem, we know that:

c + p = 41 (the total number of items in the vending machine is 41)

c = 2p - 1 ( given that the number of chocolate bars is one less than twice the number of bags of pretzels)

We can use the second equation to substitute for c in the first equation:

(2p - 1) + p = 41

Simplifying and solving for p:

3p - 1 = 41

3p = 42

p = 14

Now that we know p, we can use the second equation to find c:

c = 2p - 1

c = 2(14) - 1

c = 27

Therefore, there are 27 chocolate bars in the vending machine.

To know more about linear equations visit the link

brainly.com/question/29739212

#SPJ1

Answer: D is a function.

Step-by-step explanation:

A function need to have exactly one output to each input.

Answer: D. (2, 3), (4, 3), (-2, -3), (-4,-3)

Step-by-step explanation: This represents a function because they're the opposing of each other. Hope this helps happy holidays! :)

Answer:

The mean of a set of numbers, sometimes simply called the average, is the sum of the data divided by the total number of data.

The median of a set of numbers is the middle number in the set (after the numbers have been arranged from least to greatest) -- or, if there are an even number of data, the median is the average of the middle two numbers.

The mode of a set of numbers is the number which occurs most often.

Answer:

Step-by-step explanation:

12

Answer:

(x , y) ----> (-x , y)

Step-by-step explanation:

(x , y) ----> (-x , y)

Example for 1. :

(-4,2) ---> (4,2)

Answer:

i dont see it-

Step-by-step explanation:

Step-by-step explanation:

ok but what's the question