solve for x: logx(16)=2

Answer:

B) median < mean

Step-by-step explanation:

To find the median, take away one of the frequencies until you have only one left. The median is 6.

To find the mean add up all of the numbers and divide by how many numbers are used. 3 + 4(3) + 6(8) + 8(3) + 10(2) + 11 = 118/17 = 6.94

This means that the mean is greater than the median.

If this answer is correct, please make me Brainliest!

Answer:

B) median < mean

To find the median, take away one of the frequencies until you have only one left. The median is 6.

Step-by-step explanation:

The corresponding 'x' value is an estimation of the median. If we divide a cumulative frequency curve into quarters, the value at the lower quarter is referred to as the lower quartile, the value at the middle gives the median and the value at the upper quarter is the upper quartile.

Answer:

The weight of an adult male who is 158 cm tall is 59.32 kg.

Step-by-step explanation:

The regression equation representing the relationship between height and weight of a person is:

[tex]\hat y=-105+1.04 x[/tex]

Here,

y = weight of a person (in kg)

x = height of a person (in cm)

The information provided is:

[tex]\bar x=167.77\ \text{cm}\\\bar y=81.54\ \text{cm}\\r(X, Y)=0.201\\p-value=0.045[/tex]

The significance level of the test is, α = 0.01.

The hypothesis to test the significance of the correlation between height and weight is:

H₀: There is no relationship between the height and weight, i.e. ρ = 0.

Hₐ: There is a relationship between the height and weight, i.e. ρ ≠ 0.

Decision rule:

If the p-value of the test is less than the significance level, then the null hypothesis will be rejected and vice-versa.

According to information provided:

p-value = 0.045 > 0.01

The null hypothesis will not be rejected at 1% level of significance.

Thus, concluding that there is no relationship between the height and weight.

Compute the weight of an adult male with height, x = 158 cm as follows:

[tex]\hat y=-105+1.04 x[/tex]

  [tex]=-105+(1.04\times 158)\\=-105+164.32\\=59.32[/tex]

Thus, the weight of an adult male who is 158 cm tall is 59.32 kg.

I suppose you're supposed to prove that set intersection is distributive across a union,

[tex]A\cap(B\cup C)=(A\cap B)\cup(A\cap C)[/tex]

Two sets are equal if they are subsets of one another. To prove a set [tex]X[/tex] is a subset of another set [tex]Y[/tex], you have to show that any element [tex]x\in X[/tex] also belongs to [tex]Y[/tex].

Let [tex]x\in A\cap(B\cup C)[/tex]. By definition of intersection, both [tex]x\in A[/tex] and [tex]x\in B\cup C[/tex]. By definition of union, either [tex]x\in B[/tex] or [tex]x\in C[/tex]. If [tex]x\in B[/tex], then clearly [tex]x\in A\cap B[/tex]; if [tex]x\in C[/tex], then [tex]x\in A\cap C[/tex]. Either way, [tex]x\in(A\cap B)\cup(A\cap C)[/tex]. Hence [tex]A\cap(B\cup C)\subseteq(A\cap B)\cup(B\cap C)[/tex].

The proof in the other direction uses the same sort of reasoning. Let [tex]x\in(A\cap B)\cup(A\cap C)[/tex]. Then either [tex]x\in A\cap B[/tex] or [tex]x\in A\cap C[/tex]. If [tex]x\in A\cap B[/tex], then both [tex]x\in A[/tex] and [tex]x\in B[/tex]; if [tex]x\in A\cap C[/tex], then both [tex]x\in A[/tex] and [tex]x\in C[/tex]. So certainly [tex]x\in A[/tex], and either [tex]x\in B[/tex] or [tex]x\in C[/tex] so that [tex]x\in B\cup C[/tex]. Hence [tex](A\cap B)\cup(A\cap C)\subseteq A\cap(B\cup C)[/tex].

Both sets are subsets of one another, so they are equal.

Answer:

P(A/D) = 0.5714

Step-by-step explanation:

Let's call A the event that a chip is produced by Plant A, B the event that a chip is produced by Plant B and D the event that the chip is defective

So, the likelihood or probability P(A/D) that a chip came from plant A given that the chip is defective is calculated as:

P(A/D) = P(A∩D)/P(D)

Where P(D) = P(A∩D) + P(B∩D)

Then, the probability P(A∩D) that a chip is produced by plant A and it is defective is calculated as:

P(A∩D) = 0.4*0.02 = 0.008

Because, Plant A produces 40% of the chips and 2% of the chips produced by plant A are defective.

At the same way, the probability P(B∩D) that a chip is produced by plant B and it is defective is calculated as:

P(B∩D) = 0.6*0.01 = 0.006

So, P(D) and P(A/D) are equal to:

P(D) = 0.008 + 0.006 = 0.014

P(A/D) = 0.008/0.014 = 0.5714

it means that if a randomly chosen chip produced by the company is defective, the likelihood that the chip came from plant A is 0.5714

Answer:

120 cm

Step-by-step explanation:

10 plus 6 equals 16.

16 times 15 equals 240

240 divided by 2 equals 120

Answer:

120cm

Step-by-step explanation:

got it right on edge

Answer:

It would be 4 hours and 22 minutes because from 1 to 5 would be 4 hours and then 22 because of the 44 so ur answer would be 4 hours and 22 minutes.

Step-by-step explanation:

Answer:

262 minutes

Step-by-step explanation:

4 hours and 22 minutes difference in time

4x60=240

240+22=262 minutes

Answer:

The base of the triangle = 9inches

Step-by-step explanation:

Explanation:-

The area of the triangle = [tex]\frac{1}{2} bh[/tex] square units

Given area of the triangle(A) = 54 square inches

Given the height of the triangle (h) = 12 inches

now  equating     [tex]\frac{1}{2} b h = 54[/tex]

                          [tex]\frac{1}{2} b (12) = 54[/tex]

now simplification, we get

                           6 b = 54

Dividing '6' on both sides, we get

                             b = 9

The base of the triangle = 9 inches

Conclusion:-

The base of the triangle = 9 inches

Answer:

-7 degrees Celsius

Step-by-step explanation:

You subtract 25 by 32 and get -7 degrees.

Answer:

-7 degrees celcius

Step-by-step explanation:

To do this we just need to subtract 32 from 25, indicated by "dropped."

25-32=-7

Answer:

This site is kinda sucky

Step-by-step explanation:

go to a different one

Answer:

After 15 years, the area will be of 775.3 km²

Step-by-step explanation:

The equation for the area of the forest after t years has the following format.

[tex]A(t) = A(0)(1-r)^{t}[/tex]

In which A(0) is the initial area and r is the yearly decrease rate.

A certain forest covers an area of 2600 km2.

This means that [tex]A(0) = 2600[/tex]

Suppose that each year this area decreases by 7.75%.

This means that [tex]r = 0.0775[/tex]

So

[tex]A(t) = 2600(1-0.0775)^{t}[/tex]

[tex]A(t) = 2600(0.9225)^{t}[/tex]

What will the area be like after 15 years?

This is [tex]A(15)[/tex]

[tex]A(t) = 2600(0.9225)^{t}[/tex]

[tex]A(15) = 2600(0.9225)^{15} = 775.3[/tex]

After 15 years, the area will be of 775.3 km²

Answer:

[tex] A(t) = 2600 (1-0.0775)^t = 2600 (0.9225)^t [/tex]

And since the question wants the value for the area at t = 15 years from know we just need to replace t=15 in oir model and we got:

[tex] A(15) = 2600 (0.9225)^{15} = 775.299[/tex]

So then we expect about 775.299 km2 remaining for the area of forests.

Step-by-step explanation:

For this case we can use the following model to describe the situation:

[tex] A = A_o (1 \pm r)^{t}[/tex]

Where [tex]A_o = 2600 km^2[/tex] represent the initial area

[tex] r =-0.0775[/tex] represent the decreasing rate on fraction

A represent the amount of area remaining and t the number of years

So then our model would be:

[tex] A(t) = 2600 (1-0.0775)^t = 2600 (0.9225)^t [/tex]

And since the question wants the value for the area at t = 15 years from know we just need to replace t=15 in oir model and we got:

[tex] A(15) = 2600 (0.9225)^{15} = 775.299[/tex]

So then we expect about 775.299 km2 remaining for the area of forests.

Answer:

The answer is (2u-1)(5u+1)=0

Step-by-step explanation:

Answer:

(2u-1)(5u+1)=0

Step-by-step explanation:

Answer:

Yes. They are Right Triangles

Step-by-step explanation:

To determine if the triangles are right triangles, all you need to do is verify whether or not the dimensions satisfy the Pythagoras Theorem.

Pythagoras Theorem:[tex]Hypotenuse^2=Opposite^2+Adjacent^2[/tex]

Note that in a right triangle, the longest side is always the hypotenuse.

Given the length of the sides 1.5 feet, 2.0 feet, 2.5 feet

[tex]2.5^2=1.5^2+2.0^2\\6.25=2.25+4\\6.25=6.25[/tex]

Since the Pythagoras theorem holds, the triangles are in fact right triangles.

Answer:

[tex]f(t) = \frac{1}{24}\cdot t^{4} + 5\cdot \sin t +\frac{1}{2}\cdot C \cdot t^{2} + D\cdot t + E[/tex]

Step-by-step explanation:

The second derivative is found by integrating it:

[tex]f''(t) = \frac{1}{2}\cdot t^{2} -5\cdot \sin t + C[/tex]

The first derivative is:

[tex]f' (t) = \frac{1}{6}\cdot t^{3}+5\cdot \cos t + C\cdot t + D[/tex]

Lastly, the function is:

[tex]f(t) = \frac{1}{24}\cdot t^{4} + 5\cdot \sin t +\frac{1}{2}\cdot C \cdot t^{2} + D\cdot t + E[/tex]

Given that,

f'''(t) = t — 5cos(t)

We want to find f(t) so we need to integrate this function three times to get f(t)

First anti derivative

∫ f'''(t) dt = ∫ (t —5cos(t)) dt

Note, the integral of cos(t) is sin(t), and the integral of sin(t) is —Cos(t)

Integrating third derivatives decreases it to second derivatives i.e. f'''(t) to f''(t)

f''(t) = t²/2 — 5sin(t) + C

Where C is the first anti derivative constant

Second anti derivative

f''(t) = t²/2 — 5sin(t) + C

∫ f''(t) = ∫ (t²/2 — 5sin(t) + C) dt

f'(t) = t³/6 + 5Cos(t) + Ct + D

Where D is the second anti derivative constant

Third anti derivative

f'(t) = t³/6 + 5Cos(t) + Ct + D

∫ f'(t) = ∫ t³/6 + 5Cos(t) + Ct + D) dt

f(t) = t⁴/24 + 5Sin(t) + Ct²/2 + Dt + E

Where E is the third anti derivative constant.

So the required f(t) function is

f(t) = t⁴/24 + 5Sin(t) + ½Ct² + Dt + E

Answer:

a. Dependent variable - fatalities

   Independent variable - age of the driver

b.  Dependent variable - grocery bills

   Independent variable - number of family members

c.  Dependent variable - insurance

   Independent variable - age of applicant

d.  Dependent variable - utility bill

   Independent variable - power consumption

e.  Dependent variable - crime rate

   Independent variable - higher education

Step-by-step explanation:

The independent variable is the variable that is used to predict the other variable, while the dependent variable is the variable that is been predicted.

The simple regression model comprises of one dependent variable (y)(y) and one independent variable (x)(x). It is used to predict the value of a dependent variable based on one independent variable.

Therefore,

a. The dependent variable is fatality and the independent variable is the age of the driver.

b. The dependent variable is grocery bills and the independent variable is the number of family members.

c. The dependent variable is insurance premium and the independent variable is the age of the applicant.

d. The dependent variable is the utility bill and the independent variable is power consumption.

e. The dependent variable is the crime rate and the independent variable is higher education.

Final answer:

a. Independent variable: age; Dependent variable: fatalities per 100,000 drivers.

b. Independent variable: number of family members; Dependent variable: weekly grocery bill.

c. Independent variable: age of applicant; Dependent variable: insurance premium.

d. Independent variable: power consumption; Dependent variable: utility bills.

e. Independent variable: higher education (years); Dependent variable: crime rates.

Explanation:

In the field of research, particularly in scientific and sociological studies, it's crucial to distinguish the independent variable (IV) from the dependent variable (DV). The independent variable is the condition that is manipulated or selected by the researcher to determine its effect on the dependent variable, which is the outcome that is measured. Here's the delineation between the IV and DV in given scenarios:

Each of these examples illustrates the relationship principle where the dependent variable changes in response to the independent variable, providing insight into the cause-effect dynamics at play.

Answer:

y=-6

Step-by-step explanation:

Divide -11 by 66 to isolate y to get 6

Answer:

the answer is y=-6

Step-by-step explanation:

you are welcome

Answer:

b. We can be 95% confident that the proportion of all nicotine patch users who would report no smoking incidents in the following year is between 17.4% and 24.8%.

Step-by-step explanation:

The confidence interval is an estimation for the true population parameter, calculated from the information of a sample of this population.

The parameter of the population will be within this interval with a certain degree of confidence.

a. There is a 95% probability that the proportion of all nicotine patch users who would report no smoking incidents in the following year is between 17.4% and 24.8%.

Incorrect. The confidence interval gives only the probability that the true proportion (or population proportion) is within 17.4% and 24.8%, not the proportion of individual samples.

b. We can be 95% confident that the proportion of all nicotine patch users who would report no smoking incidents in the following year is between 17.4% and 24.8%.

Correct.

c. We can be 95% confident that the proportion of the sample who would report no smoking incidents in the following year is between 17.4% and 24.8%.

Incorrect. The confidence interval does not give information about another samples.

d. 95% of samples will have between 17.4% and 24.8% who would report no smoking incidents in the following year.

Incorrect. The confidence interval does not give information about another samples or sampling distributions.

Answer:

Step-by-step explanation:

Here, 40 of the 69 who were served by a server wearing a red shirt left a tip. Of the 349 who were served by a server wearing a different colored shirt, 130 left a tip.

Therefore:

2.1 40 72 130

The sample sizes are:

721 69 722 349 2

Two proportions and their difference are:

400.580 0.580 p = =_= 69 130 1300.372 D =-= n2 349 p1-P2 = 0.580-0.372 = 0.208

------------------------------------------------------------------------------------------------------------------------

c) For 95% confidence level, critical value of z is 1.96.

The large-sample 95% confidence interval for the difference in proportions is:

n1 7l n2 0.580(1 - 0.580) 0.372(1- 0.372) 0.208 ± 1.96 0.208 t 0.127 or (0.081,0.335)

We are 95% confident that the difference in proportion of male customers left a tip who were served by a server wearing a red shirt and who were served by a server wearing a different colored shirt lies between 0.081 and 0.335. Since 0 does not lie in the confidence interval, we can conclude that higher proportion of male customers left a tip who were served by a server wearing a red shirt than those who were served by a server wearing a different colored shirt.

------------------------------------------------------------------------------------------------------------------------

d) The hypotheses are:

\\H_0:p_1=p_2 \\H_a:p_1\ne p_2

The pooled proportion is:

1240 +130 +n2 69+34 0.4067

The test statistic is:

pi-2 0.580 0.372 V mi-P)(4+4) ν/0 4067(1-04067) (かー = 3.20 ) 0.4067(1-0.4067) (69 т 349

The p-value is:

p-value = P(z <-3.20) + P(z > 3.20) = 0.0007 0.0007 = 0.00 1 4

Since p-value is less than 0.05, reject the null hypothesis. We can conclude that there is significant difference in proportion of male customers left a tip who were served by a server wearing a red shirt and who were served by a server wearing a different colored shirt.

Please see attachment for better indentation and formula input in the solution.

The 95% confidence interval provides a range where the true difference in tipping behavior may lie, while a large-sample significance test assesses if the difference is statistically significant.

For part a, the objective is to establish a 95% confidence interval for the difference in proportions. The proportion of individuals who tip when served by a server wearing a red shirt (p1) is 40/69, and the proportion of individuals who tip when served by a server wearing a different colored shirt (p2) is 130/349. The difference in proportions (p1 - p2) will give us the estimated difference. The standard error can then be calculated. Z is typically 1.96 for a 95% confidence interval.

For part b, a large-sample significance test is performed to test the null hypothesis that the two proportions are the same against the alternative hypothesis that the two proportions are not the same. Z score is calculated using the difference in proportions and standard error. P-value can then be derived from the z-score. The p-value will indicate whether the difference is statistically significant or not.

The confidence interval gives us the range of values within which the actual difference in proportions might fall 95% of the time, whereas the significance test helps determine if there is a substantial difference in the tipping habits depending on the color of the shirt worn by the server.

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Final answer:

The algebraic equation representing "The number of medals won by the United States is 26 more than three times the number of medals won by Italy" is U = 3I + 26, where U is the number of medals won by the United States, and I is the number of medals won by Italy.

Explanation:

The question requires us to write an algebraic equation based on the statement: "The number of medals won by the United States is 26 more than three times the number of medals won by Italy." Let's use U to represent the number of medals won by the United States and I for the number of medals won by Italy. Following the given statement, we can write the equation as:

U = 3I + 26

This equation signifies that to find the number of medals won by the United States, we need to multiply the number of medals won by Italy (I) by 3 and then add 26 to this total.

Answer:

1.6

Step-by-step explanation:

if you divide 16.8 by 4.5 you get 3.7 now 3.7 divided 2.3 = 1.6

Answer:

2) We are 95% confident that the difference between the average sales after the ad campaign and the average sales before the ad campaign is between-3.83 and 1.83

Step-by-step explanation:

The confidence interval is a estimation, from the information that the sample gives, about a parameter of the population. In this case, the difference of means.

The 95% is a measure of the confidence about the estimation about the difference of the means. There is a 95% probability that the difference of means (sales after and sales before the ad) is within the confidence interval.

Answer:

Infinite pairs of numbers

1 and -1

8 and -8

Step-by-step explanation:

Let x³ and y³ be any two real numbers. If the sum of their cube roots is zero, then the following must be true:

[tex]\sqrt[3]{x^3}+ \sqrt[3]{y^3}=0\\ \sqrt[3]{x^3}=- \sqrt[3]{y^3}\\x=-y[/tex]

Therefore, any pair of numbers with same absolute value but different signs fit the description, which means that there are infinite pairs of possible numbers.

Examples: 1 and -1; 8 and -8; 27 and -27.

Answer:

95% confidence interval for the actual proportion of Meridian Township residents who are in favor of the tax increase is [0.5228 , 0.6972].

Step-by-step explanation:

We are given that the Township Board of Meridian Township randomly surveyed a group of residents and found that 61% are in favor of the tax increase.

The estimated standard error of sample proportion is 0.0445.

Firstly, the pivotal quantity for 95% confidence interval for the population proportion is given by;

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

where, [tex]\hat p[/tex] = sample proportion of residents in favor of the tax increase = 61%

           n = sample of criminals

           p = population proportion

Here for constructing 99% confidence interval we have used One-sample z proportion test statistics.

The 95% confidence interval for the actual proportion of Meridian Township residents who are in favor of the tax increase is given by;

95% Confidence interval for p =  [tex]\hat p \pm Z_\frac{\alpha}{2} \times \sqrt{\frac{\hat p(1-\hat p)}{n} }[/tex]

Here, Standard error =  [tex]\sqrt{\frac{\hat p(1-\hat p)}{n} }[/tex] = 0.0445

And [tex]\alpha[/tex] = significance level

So,  [tex]Z_\frac{\alpha}{2} =Z_\frac{0.05}{2}[/tex] = 1.96

Hence, 95% Confidence interval for p =  [tex]0.61 \pm 1.96 \times 0.0445[/tex]

                                                           =  [[tex]0.61 -0.08722[/tex] , [tex]0.61 +0.08722[/tex]]

                                                           =  [0.5228 , 0.6972]

Therefore, 95% confidence interval for the actual proportion of Meridian Township residents who are in favor of the tax increase is [0.5228 , 0.6972].

Also, the upper bound for the 95% confidence interval is 0.6971.

Answer:

555

Step-by-step explanation:

Answer:

the edges only would be 16 pieces.

Step-by-step explanation:

Think of it as a square. The top row is 5 pieces, bottom row is 5 pieces.

The left vertical side is 3 and the right vertical side is 3. Because the corner pieces are already there, you don't count them twice.

Answer:

The salmon size is less than equal to 10.28 inches represent bottom 25% of all salmon.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 12.5 inches

Standard Deviation, σ = 3.3

We are given that the distribution of salmon size is a bell shaped distribution that is a normal distribution.

Formula:

[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]

We have to find the value of x such that the probability is 0.25

[tex]P( X < x) = P( z < \displaystyle\frac{x - 12.5}{3.3})=0.25[/tex]  

Calculation the value from standard normal z table, we have,  

[tex]\displaystyle\frac{x - 12.5}{3.3} = -0.674\\\\x = 10.2758\approx 10.28[/tex]  

Thus, the salmon size is equal to or less than 10.28 inches, they are considered small and young and represent bottom 25% of all salmon.

Answer:

a = 27400 ( borrow)

b = -21600  ( do not borrow)

c = -84600  ( do not borrow)

Step-by-step explanation:

a) Success probability = 88%

Expected payout = 88($430,000) +  0.12(-$270000) = $34600

Cost of borrowing = $270000(1+ 0.18) = 318600

EXPECTED PROFIT = 27400 you can borrow.

b) Probability of success  is 81%

Expected payout  = 0.18($430000) + 0.19(-$270000)  

= $297,000

Cost of borrowing  = $270000 (1+0.18) = 318600

Expected loss = -21600 do not borrow

c) Probability of of success = 72%

Expected payout = 0.72($430000) + 0.28(-$270000) = $234000

Cost of borrowing = $270000(1+ 0.18) = 318600

Expected loss = -84600 do not borrow

Answer:

(a)  Wilson Motors should borrow the money.

(b)  Wilson Motors should not borrow the money.

(c) Wilson Motors should not borrow the money.

Step-by-step explanation:

(a) If the probability of success is 91​%?

Expected return = 0.91*$430,000 + 0.09*(-$290,000)

                                = 391,000 - 26,100

                                = $364,900

Cost = $290,000*(1+12%)

        =  $324,800

Expected profit = Expected return - Cost

                         = $364,900 - $324,800

                         = $40,100

Since it results in profit, Wilson Motors should borrow the money.

(b) If the probability of success is 85​%?

Expected return = 0.85*$430,000 + 0.15*(-$290,000)

                                = 365500 - 43,500

                                = $322,000

Cost = $290,000*(1+12%)

        =  $324,800

Expected profit = Expected return - Cost

                         = $322,000 - $324,800

                         = -$2800

Since it results in loss, Wilson Motors should not borrow the money.

 c) If the probability of success is 75​%?      

Expected return = 0.75*$430,000 + 0.25*(-$290,000)

                                = 322500 - 72,500

                                = $250,000

Cost = $290,000*(1+12%)

        =  $324,800

Expected profit = Expected return - Cost

                         = $250,000 - $324,800

                         = -$74800

Since it results in loss, Wilson Motors should not borrow the money.

The decimal which is equal to [tex]\frac{4}{3}[/tex] is; Choice D: 1.333 option D is correct.

The accepted method for representing both integer and non-integer numbers is the decimal numeral system. It is the extension of the numeral system to non-integer numbers. Decimal notation is the term used to describe the method of representing numbers in the decimal system.

A decimal is a number that is divided into two parts: a whole and a fraction. Between integers, decimal numbers are used to express the numerical value of complete and partially whole quantities. For instance, there is one complete pizza and a half of another pizza in the photograph.

[tex]\frac{4}{3} =1.333[/tex]

Therefore, option D is correct.

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Answer:

6x(x+3)(x-2)=6x^3+6x^2-36x

3(x-2)(x +9)=3x^2+21x-54

Step-by-step explanation:

Answer:

6x(x+3)(x-2)=6x^3+6x^2-36x

3(x-2)(x +9)=3x^2+21x-54

Step-by-step explanation:

Answer:

  yes

Step-by-step explanation:

The 90-th percentile of a normal distribution corresponds to a z-score of 1.282. Bob's z-score is above that, so he is definitely in the top 10%.

_____

If you haven't memorized the percentiles associated with the normal distribution, it is convenient to use a calculator or table of values.

In this case, ob is correct in saying that his score is in the top 10 percent.

To determine if Bob's z-score corresponds to a score in the top 10 percent of the distribution, we need to find the percentile associated with his z-score.

We can then compare this percentile to 90%, as the top 10% corresponds to the highest scores.

Using a standard normal distribution table or a calculator, we find that a z-score of 1.52 corresponds approximately to the 93rd percentile.

This means that 93% of the scores are below Bob's score, indicating that he is indeed in the top 10% of the class.

So, Bob is correct in saying that his score is in the top 10 percent.

Answer:

Step-by-step explanation:

a) Your question supplies the formula for N(t):

  N(t) = N0·e^(kt)

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b) Given the initial population and doubling time (in months), the population function can also be written as ...

  N(t) = 10,000·2^(t/14) . . . . . t in months

Then in 4 years the population will be ...

  N(48) = 10,000·2^(48/14) ≈ 107,672.02

The population 4 years from now will be approximately 107,672 people.

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Comment on the formula for N(t)

In order to use the formula of the first part in answering the second part, we need to find the value of k. It will be an irrational number. In order to obtain accurate results in the second part, k would need to be good to at least 6 significant digits. Its value, for t in months, is ...

  k = ln(2)/14 ≈ 0.0495105

For t in years, it is 12 times this value, or ...

  k ≈ 0.594126

The advice not to do any rounding (even for the value of k) is appropriate.

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As we can see from the above, it is not necessary to determine k in order to answer the question in part b.

The population of a city with exponential growth can be expressed as [tex]N(t) = N0 * e^(^k^t^)[/tex]. The growth factor k is found to be approximately 0.592. Using this, the population 4 years later is found to be approximately 43609.

The population of a city showing exponential growth can be expressed as [tex]N(t) = N0 * e^(^k^t^)[/tex] where N(t) is the population at time t, N0 is the initial population, e is the natural logarithmic base (approx. 2.71828), and k is the growth rate.

Given that the population doubled in 14 months, which is about 1.17 years, we have: 2*N0 = N0 * [tex]e^(^1^.^1^7^k^)[/tex]. Solving this equation for k, we get k = ln(2)/1.17. Hence, the growth rate (k) is approximately 0.592.

To find the population 4 years from now, we substitute t=4 and k=0.592 into the equation. So, N(4) = 10000 * [tex]e^(^4^*^0^.^5^9^2^)[/tex]. After calculating, we get a population of approximately 43609.

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Answer:

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Step-by-step explanation:

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