Please help! Image below

Answer:

x=29

Step-by-step explanation:

Just as simple as substitution:

We will substitute in 16 for y

So the equation will look like 16=x-13

Isolate x:

Add 13 to both sides isolate the variable

-13+13=0

16+13=29

The new equation:

29=x

29-13 is 16.

Answer:

B

Step-by-step explanation:

Sphere Surface Area = 4 • π • r²

For it to equal 16 PI, then radius must equal 2

4*PI*2*2 = 16 PI

Sphere Volume = 4/3 • π • r³

Sphere Volume = 4/3 • π • 2^3

Sphere Volume = 4/3 *PI * 8

Sphere Volume = 32 / 3 PI

Sphere Volume = 10.666 PI cubic feet AND I think that is answer B

which SHOULD read 10 (2/3) PI ft^3

Step-by-step explanation:

political behaviour consists of activities that are

not required as part of one's formal

role in the organization

Answer:

How much compound interest is earned at 35 years? 850

How much simple interest is earned at 35 years? 600

How much more compound interest than simple interest is earned after 35 years? 250

Answer:

1: the balance after 8 years is approximately $151.78.

2:  is approximately 7%.

Step-by-step explanation:

1: The balance after t years with continuous compounding can be calculated using the formula:

B = Pe^(rt)

Where:

P = 120 dollars (initial deposit)

r = 2.5% = 0.025 (interest rate in decimal form)

t = 8 years

Substituting these values into the formula, we get:

B = 120e^(0.025*8) ≈ 151.78

Therefore, the balance after 8 years is approximately $151.78.

2: The interest rate can be found using the formula:

A = Pe^(rt)

Taking the natural logarithm of both sides and solving for r, we get:

r = ln(A/P) / t

Where:

A = 4055 dollars (final amount)

P = 1000 dollars (initial investment)

t = 20 years

Substituting these values into the formula, we get:

r = ln(4055/1000) / 20 ≈ 0.0774

Converting to a percentage and rounding to the nearest whole number, we get:

r ≈ 7%

Therefore, the interest rate, if compounded continuously, is approximately 7%.

Answer:

1. $146.57

2. 7%.

Step-by-step explanation:

1.

The formula for continuous compounding is:

A = Pe^(rt)

Where:

A = the balance after t years

P = the principal amount

r = the annual interest rate (expressed as a decimal)

t = the time in years

To use this formula, we first need to convert the annual interest rate to a decimal:

r = 2 1/2 = 2.5%

r = 2.5/100 = 0.025

Now we can plug in the values:

A = 120e^(0.025*8)

A ≈ $146.57

Therefore, the balance after 8 years is approximately $146.57

2.

The formula for continuous compounding is: A = Pe^(rt)

Where:

A = the balance after t years

P = the principal amount

r = the annual interest rate (expressed as a decimal)

t = the time in years

We can rearrange this formula to solve for the interest rate:

r = ln(A/P)/t

Where ln represents the natural logarithm.

Now we can plug in the given values:

r = ln(4055/1000)/20

r ≈ 0.069or 7.1%

Therefore, the interest rate, rounded to the nearest whole number, is 7%.

Answer:

The angle is approximately \(31^{o}\).

Step-by-step explanation:

The description i the given question can be represented with the sides of a right angled triangle.

Applying the appropriate trigonometric function, we have;

Tan θ = \(\frac{opposite}{adjacent}\)

In the question, opposite side = 60 feet, and adjacent side = 100 feet.

Tan θ = \(\frac{60}{100}\)

         = 0.6

θ = \(Tan^{-1}\) 0.6

  = \(30.964^{o}\)

θ = \(31^{o}\)

The angle of elevation from the end of the shadow to the top of the pole is \(31^{o}\).

The probability that either event will occur is P ( C ) = 0.89

Given data ,

Let the probability that either event will occur  be P ( C )

P ( A ) = 20/36

P ( B ) = 12/36

where P ( A or B ) = P ( C )

P ( C ) = P ( A ) + P ( B )

P ( C ) = 32/36

P ( C ) = 0.88888

Hence , the probability is P ( C ) = 0.89

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Answer:

1. 11 married females because out of the 19 married, only 8 had more than 15 years of service and 19 - 8 = 11.

2. 10 married males because of out the 18 married with more than 15 years of service, 8 were females and 18 - 8 = 10.

3. 9 single females because out of the 17 with more than 15 years of service, 8 were married and 17 - 8 = 9.

4. 8 married females because it literally says, "8 married female with more than 15 years of service".

gotta go hope this helps sry

Answer:

0.32989690721

Step-by-step explanation:

Answer:

rounded to the nearest hundred: 0.33

Step-by-step explanation:

hope this helps :3

The total income and expenditure of Agri-small business limited in September is R 299596 and expenditure is R 193236.

We have to find the total income and expenditure in September.

The equation for insurance is mathematically given as :

Insurance = 42% of the balance

Insurance=0.42*0.64A

Insurance=0.2688A.

Total expenditure after all other expenditures = 0.64A-0.2688A

Total expenditures after all other expenditures = 0.3712A.

Total expenditures after all other expenditures is as 111210 (106360 +4850)

Equating both the equation and value:

111210 = 3712 A

A = 299596

Thus The total income is 299596.

Therefore the calculation of expense is given as:

Expense=0.25A+0.11A+0.2688A+4850

Expense=0.6288A+4850

=0.6288*299596+4850

=193236

The expense is 193236.

Hence, the total income and expenditure in September are "Income is R 299596 and expenditure is R 193236.

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Apply the slope (m) formula:

where:

(x1,y1) = (-6,2)

(x2,y2) = (8,-3)

Replace:

slope = -5/14

Solution :

Let the three places be 1, 2, 3, 4, 5, 6, 7, 8

a). Number of the cases when a general manager is the next to a vice president is equal to 7 and the these 2 can be arranged in 21 ways. So the total number of ways = 7 x 2

                  = 14

[(1,2)(2,1) (2,3)(3,2) (3,4)(4,3) (4,5)(5,4) (5,6)(6,5) (6,7)(7,8) (8,7)(7,6)]

Therefore the required probability is

  \($=\frac{14}{8!}$\)

 = \($\frac{14}{40320} = 0.000347$\)

b). The probability that the marketing director to be placed in the leftmost position is

   \($=\frac{7!}{8!}$\)

  \($=\frac{1}{8} = 0.125$\)

c). The two events are not independent because

   \($P(A \cap B) \neq P(A) \times P(B)$\)

  \($\frac{12}{8!} \neq \frac{14}{8!} \times \frac{1}{8}$\)

where A is the case a and B is the case b.

(a) The possibility of the general manager is next to the vice president is \(\frac{1}{4}\).

(b) The possibility of the marketing director is in the leftmost position is \(\frac{1}{8}\).

(c) So, the two events are dependent on each other.

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e. how likely they are to happen, using it. The probability of all the events in a sample space adds up to 1.

Total people in company A and company B is \(=8\)

Overall ways in which these \(8\) people can be lined up\(=8!\)

                                                                                        \(=40320\)

(a) The probability that the general manager is next to the vice president is\(=P(A)\)

Now, we can combine the general manager and vice president as one, then the total people in both the company will become \(7\).

by arranging these \(7\) people in one line \(=7!\)

                                                                \(=5040\)

Again, combine the general manager and vice president in one line\(=2!\)

                                                                                                                \(=2\)

Therefore, \(P(A)=\frac{5040\times 2}{40320}\)

                          \(=\frac{10080}{40320}\)

\(P(A)=\frac{1}{4}\)

(b) The probability that the marketing director is in the leftmost position is\(=P(B)\)

Now, fixing the position of marketing director in the leftmost.

arranging the \(7\) other people in \(7!\) ways \(=5040\)

Therefore,\(P(B)=\frac{5040}{40320}\)

                          \(=\frac{1}{8}\)

\(P(B)=\frac{1}{8}\)

(c) Assuming event B already occurred which means that the position of marketing director is already fixed in the leftmost position.

Now, trying to find out the probability of the general manager next to the vice president is event A. it comes different because we are not allowed to arrange rest \(7\) people, we have to fix the position of one person that causes the repetition of probability.

So, the two events are dependent on each other.

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An expression for given sequence of operations is: j + 3^9

In this question, we need to write an expression for the sequence of operations described below.

raise 3 to the 9th power, then add the result to j

Consider the part of given statement,

raise 3 to the 9th power

We write this as: 3^9

then we add this result to j.

So, we get an expression: 3^9 + j

Therefore, an expression for given sequence of operations is: j + 3^9

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Answer:

um whats m or y?

Step-by-step explanation:

Answer:

\(x=3m+y\)

Step-by-step explanation:

Let's solve for \(x\).

\(m=\frac{x-y}{3}\)

Step 1: Flip the equation.

\(\frac{1}{3}x+\frac{-1}{3}y=m\)

Step 2: Add \(\frac{1}{3}y\) to both sides.

\(\frac{1}{3}x+\frac{-1}{3}y+\frac{1}{3}y=m+\frac{1}{3}y\)

\(\frac{1}{3}x=m+\frac{1}{3}y\)

Step 3: Divide both sides by \(\frac{1}{3}\).

\(\frac{\frac{1}{3}x }{\frac{1}{3} } ={\frac{m+\frac{1}{3}y }{\frac{1}{3} }\)

\(x=3m+y\)

Answer:

\(x=3m+y\)

The probability that a person who tests positive actually has the disease is approximately 0.194.

What exactly is probability?

Probability is a measure of an event's possibility or chance of occurring. It is stated as a number between 0 and 1, with 0 indicating an impossible event and 1 indicating a certain event. Probabilities ranging from 0 to 1 reflect occurrences that are probable but not guaranteed.

P(A) denotes the probability of an event A as the ratio of the number of possibilities that favour event A to the total number of potential outcomes. In other words, it is the number of possible outcomes for event A divided by the total number of possible outcomes.

Now,

To compute the probability that a person who tests positive actually has the disease, we can use Bayes' theorem, which states that:

P(A|B)=P(B|A)*P(A)/P(B)

where A and B are events, P(A | B) is the probability of event A when event B has occurred, P(B | A) is the probability of event B when event A has occurred, P(A)= prior probability of event A, and P(B) = prior probability of event B.

In this case, let A be the event of having the disease and B be the event of testing positive.

The incidence rate of the disease is 0.8%, which means that P(A) = 0.008.

The false negative rate is 6%, which means that P(B' | A) = 0.06 (where B' is the complement of event B, i.e., testing negative given that the person has the disease).

The false positive rate is 3%, which means that P(B | A') = 0.03 (where A' is the complement of event A, i.e., not having the disease).

We can compute P(B) using the law of total probability:

P(B) = P(B|A)*P(A) + P(B|A')*P(A')

= (1-P(B'|A))*P(A)+P(B|A')*(1-P(A))

= (1 - 0.06) * 0.008 + 0.03 * (1 - 0.008)

= 0.0328

Now we can use Bayes' theorem to compute P(A | B):

P(A | B) = P(B | A) * P(A) / P(B)

= (1 - P(B' | A)) * P(A) / P(B)

= (1 - 0.06) * 0.008 / 0.0328

= 0.194

Therefore,

                 the probability will be 0.194.

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Answer:

Below in bold.

Step-by-step explanation:

12.054 is about 0.9612 of 12.54.

12.054 is 12.54 - 12.054 = 0.486 less than 12.54.

Answer:

The point-slope form is y - 1 = -2 (x-1)

Step-by-step explanation:

A study based on a population sample that includes 2000 respondents would be the most reliable out of the given options.

In statistical analysis, the reliability of a study depends on the representativeness and size of the sample.

A larger sample size generally provides more reliable results as it reduces the sampling error and increases the precision of the estimates.

Given that the population contains 20,000 people, we need to consider which number of respondents would yield the most reliable study.

Option A: 200 respondents

This represents only 1% of the population.

While it is better than having just 2 respondents, it may not be sufficient to accurately capture the characteristics of the entire population.

Option B: 20 respondents

This represents only 0.1% of the population.

With such a small sample size, the study would likely suffer from a high sampling error and may not provide reliable results.

Option C: 2000 respondents

This represents 10% of the population.

While it is a larger sample size compared to the previous options, it still only captures a fraction of the population.

The study may provide reasonably reliable results, but there is room for potential sampling error.

Option D: 2 respondents

This represents an extremely small sample size, accounting for only 0.01% of the population.

With such a small sample, the study would be highly susceptible to sampling bias and would likely yield unreliable results.

Based on the options provided, option C with 2000 respondents would be the most reliable study.

Although it does not include the entire population, a sample size of 2000 respondents provides a larger representation of the population and reduces the potential for sampling error.

However, it's important to note that the reliability of a study depends not only on sample size but also on the sampling method, data collection techniques, and other factors that ensure representativeness.

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Answer:

The coefficient of variation (CV)= 9.83

Step-by-step explanation:

look at the attachment above ☝️

Answer:

each cup cost 1.25 on Tuesday

Answer:

A) 21

Step-by-step explanation:

3 x 7 = 21

Hope this helps! Pls give brainliest!

Answer:

50.75

Step-by-step explanation:

We have:

\(E[g(x)] = \int\limits^{\infty}_{-\infty} {g(x)f(x)} \, dx \\\\= \int\limits^{1}_{-\infty} {g(x)(0)} \, dx+\int\limits^{6}_{1} {g(x)\frac{2}{x} } \, dx+\int\limits^{\infty}_{6} {g(x)(0)} \, dx\\\\= \int\limits^{6}_{1} {g(x)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {(4x+3)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {(4x)\frac{2}{x} } \, dx + \int\limits^{6}_{1} {(3)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {8} \, dx + \int\limits^{6}_{1} {\frac{6}{x} } \, dx\\\\\)

\(=8\int\limits^{6}_{1} \, dx + 6\int\limits^{6}_{1} {\frac{1}{x} } \, dx\\\\= 8[x]^{^6}_{_1} + 6 [ln(x)]^{^6}_{_1}\\\\= 8[6-1] + 6[ln(6) - ln(1)]\\\\= 8(5) + 6(ln(6))\\\\= 40 + 10.75\\\\= 50.74\)

Answer:

26 meters

Step-by-step explanation:

To solve the perimeter you need to know the formula which is 6 + 7 x 2 and you get 26 meters

The correct options applied for the question are-

B.The solution's exponent is -12.

C.The solution's coefficient ≥ 1 but < than 10.

D 3.0×10⁻¹² is the quotient.

As, per the given question,

The equation stated can be written as;

= (9.6×10⁻⁸)/(3.2×10⁴)

Use the power rule of exponents;

= (9.6×10⁻⁸×10⁻⁴)/(3.2)

Add both the power of base 10 with sign as the same base is there.

= ((9.6×10⁻⁸⁻⁴)/(3.2)

= (9.6×10⁻¹²)/(3.2)

Divide the numerator by 3.2

= 3.0×10⁻¹²

The following conclusions are possible:

B.The solution's power of ten is -12, which is the difference of the original exponential function.

C.The coefficient is 3, which is greater than one but less than ten.

D. 3.0×10⁻¹² is the quotient.

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The complete question is-

What conclusions can be drawn about finding the quotient in scientific notation? Check all that apply. Start Fraction (9.6 times 10 Superscript negative 8 Baseline) Over (3.2 times 10 Superscript 4 Baseline) End Fraction

A.The coefficient of the solution is 6.4, the difference of the original coefficients.

B.The exponent of the solution is –12, the difference of the original exponents.

C.The coefficient of the solution must be greater than or equal to one but less than 10.

D.The quotient is 3.0 × 10-12

E.The solution is a very large number.

Answer: ur mom

Step-by-step explanation:

The numeric value of the function f(x) = 14/[3 + ae^(kx)] at x = 2 is given as follows:

f(2) = 0.172.

The function for this problem is defined as follows:

f(x) = 14/[3 + ae^(kx)]

When x = 0, y = 2, hence we can obtain the coefficient a as follows:

2 = 14/(3 + a)

6 + a = 14

a = 8.

Hence:

f(x) = 14/[3 + 8e^(kx)]

When x = 1, y = 1/2, hence the coefficient k is given as follows:

0.5 = 14/(3 + 8e^k)

1.5 + 4e^k = 14

4e^k = 12.5

e^k = 12.5/4

k = ln(12.5/4)

k = 1.14.

Hence:

f(x) = 14/[3 + 8e^(1.14x)]

Then the numeric value of the function at x = 2 is given as follows:

f(2) = 14/[3 + 8e^(1.14(2))]

f(2) = 0.172.

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There is not enough evidence to conclude that the mean time in changing a muffler is less than 13 minutes.

To determine whether there is enough evidence to conclude that the mean time in changing a muffler is less than 13 minutes, we can conduct a one-sample t-test with the following hypotheses:

Null hypothesis: The true mean time in changing a muffler is equal to 13 minutes.

Alternative hypothesis: The true mean time in changing a muffler is less than 13 minutes.

Use the formula to calculate the test statistic,

\(t = \dfrac{(x - \mu)} { \dfrac{s} { \sqrt{n}}}\)

where x is the sample mean, μ is the hypothesized population mean (13 minutes), s is the sample standard deviation, and n is the sample size (6).

Plugging in the numbers, we get:

t = (12.3 - 13) / (2.3 / √6) = -0.72

Using a t-distribution table with 5 degrees of freedom (n - 1), we find that the critical value for a one-tailed test with α = 0.05 is -2.571. Since our calculated t-value (-0.72) is greater than the critical value, we fail to reject the null hypothesis.

Therefore, there is not enough evidence to conclude that the mean time in changing a muffler is less than 13 minutes.

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Answer:

76

Step-by-step explanation:

6+13=19

19/2=9.5

9.5x8=76