The double number line shows that a water park allows 18 people to go down a giant water slide in three minutes. Select the double number line that correctly label the number of people that can go down the slide in one, two, and four minutes.

Answer:

a) 99.73% probability that a randomly selected person does not have a birthday on March 14.

b) 96.71% probability that a randomly selected person does not have a birthday on the 2 nd day of a month.

c) 98.08% probability that a randomly selected person does not have a birthday on the 31 st day of a month.

d) 92.33% probability that a randomly selected person was not born in February.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

A non-leap year has 365 days.

​(a) Compute the probability that a randomly selected person does not have a birthday on March 14.

There are 365-1 = 364 days that are not March 14. So

364/365 = 0.9973

99.73% probability that a randomly selected person does not have a birthday on March 14.

​(b) Compute the probability that a randomly selected person does not have a birthday on the 2 nd day of a month.

There are 12 months, so there are 12 2nds of a month.

So

(365-12)/365 = 0.9671

96.71% probability that a randomly selected person does not have a birthday on the 2 nd day of a month.

​(c) Compute the probability that a randomly selected person does not have a birthday on the 31 st day of a month.

The following months have 31 days: January, March, May, July, August, October, December.

So there are 7 31st days of a month during a year.

Then

(365-7)/365 = 0.9808

98.08% probability that a randomly selected person does not have a birthday on the 31 st day of a month.

(d) Compute the probability that a randomly selected person was not born in February.

During a non-leap year, February has 28 days. So

(365-28)/365 = 0.9233

92.33% probability that a randomly selected person was not born in February.

The probability that a person does not have a birthday on March 14, on the 2nd day of a month, on the 31st day of a month, or is not born in February is approximately 0.9973, 0.9671, 0.9808, and 0.9233 respectively. These probabilities were computed by subtracting the fraction of the year representing the specific days or month from 1. These solutions are based on a standard non-leap year of 365 days.

To solve the probability questions, we will assume a non-leap year with 365 days.

(a) Probability that a randomly selected person does not have a birthday on March 14:

There is only one day out of the year that is March 14. Therefore, the probability that a person does have a birthday on March 14 is:

P(March 14) = 1/365

Consequently, the probability that a person does not have a birthday on March 14 is:

P(Not March 14) = 1 - 1/365 = 364/365 ≈ 0.9973

(b) Probability that a randomly selected person does not have a birthday on the 2nd day of a month:

Since there are 12 months in a year, there are 12 days which fall on the 2nd day of each month.

P(2nd day) = 12/365

Therefore, the probability that a person does not have a birthday on the 2nd day of any month is:

P(Not 2nd day) = 1 - 12/365 = 353/365 ≈ 0.9671
(c) Probability that a randomly selected person does not have a birthday on the 31st day of a month:

There are only 7 months with 31 days (January, March, May, July, August, October, December).

P(31st day) = 7/365

Therefore, the probability that a person does not have a birthday on the 31st day of any month is:

P(Not 31st day) = 1 - 7/365 = 358/365 ≈ 0.9808
(d) Probability that a randomly selected person was not born in February:

February has 28 days out of the year.

P(February birthday) = 28/365

Therefore, the probability that a person was not born in February is:

P(Not February) = 1 - 28/365 = 337/365 ≈ 0.9233

Answer:

Calculated value t = 1.3622 < 2.081 at 0.05 level of significance with 42 degrees of freedom

The null hypothesis is accepted .

Assume the population variances are approximately the same

Step-by-step explanation:

Explanation:-

Given data a random sample of 20 turkeys sold at the chain's stores in Detroit yielded a sample mean of 17.53 pounds, with a sample standard deviation of 3.2 pounds

The first sample size  'n₁'= 20

mean of the first sample 'x₁⁻'= 17.53 pounds

standard deviation of first sample  S₁ = 3.2 pounds

Given data a random sample of 24 turkeys sold at the chain's stores in Charlotte yielded a sample mean of 14.89 pounds, with a sample standard deviation of 2.7 pounds

The second sample size  n₂ = 24

mean of the second sample  "x₂⁻"= 14.89 pounds

standard deviation of second sample  S₂ =  2.7 pounds

Null hypothesis:-H₀: The Population Variance are approximately same

Alternatively hypothesis: H₁:The Population Variance are approximately same

Level of significance ∝ =0.05

Degrees of freedom ν = n₁ +n₂ -2 =20+24-2 = 42

Test statistic :-

   [tex]t = \frac{x^{-} _{1} - x_{2} }{\sqrt{S^2(\frac{1}{n_{1} } }+\frac{1}{n_{2} } }[/tex]

   where         [tex]S^{2} = \frac{n_{1} S_{1} ^{2}+n_{2}S_{2} ^{2} }{n_{1} +n_{2} -2}[/tex]

                      [tex]S^{2} = \frac{20X(3.2)^2+24X(2.7)^2}{20+24-2}[/tex]

             substitute values and we get  S² =  40.988

    [tex]t= \frac{17.53-14.89 }{\sqrt{40.988(\frac{1}{20} }+\frac{1}{24} )}[/tex]

    t =  1.3622

  Calculated value t = 1.3622

Tabulated value 't' =  2.081

Calculated value t = 1.3622 < 2.081 at 0.05 level of significance with 42 degrees of freedom

Conclusion:-

The null hypothesis is accepted

Assume the population variances are approximately the same.

We want to find a recursive formula for f(n) = 64 + 6n

The recursive formula is f(n) = f(n - 1) + 6

First, a recursive formula is a formula that gives the value of f(n) in relation to the value of f(n - 1) or other previous terms on the sequence.

We know that:

f(n) = 64 + 6n

f(n - 1) = 64 + 6*(n - 1) = 64 + 6*n - 6

Then we can rewrite:

f(n) = 64 + 6n + 6 - 6

f(n) = ( 64 + 6n - 6) + 6

And the thing inside the parenthesis is equal to f(n - 1)

Then we have:

f(n) = f(n - 1) + 6

This is the recursive formula we wanted to get.

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The most expensive type of life insurance is cash-value (whole) life insurance due to its integrated savings component, investment aspect, and the management involved. These features add complexity and cost to the policy, making it more expensive than term life insurance, which only offers a death benefit.

The most expensive type of life insurance is typically cash-value (whole) life insurance. This kind of policy not only provides a death benefit to beneficiaries upon the insured individual's death but also includes a savings component known as the cash value. Over time, the policy accumulates a cash value that the policyholder can borrow against or even withdraw. Part of the premium goes towards life insurance, while another part is invested by the company, often in a conservative mix of investments. This investment aspect and the management involved make whole life insurance more expensive compared to term life insurance which only provides a death benefit without a savings component.

It is also worth noting that individuals purchasing life insurance are likely to have more knowledge about their own health risks than the insurance company. This information asymmetry can impact the pricing of life insurance policies. Moreover, the fundamental law of insurance states that the average person's premium payments over time must cover the claims, the insurer's costs, and profits. Therefore, insurance premiums, particularly for policies with cash values, reflect the cost of investment management and the integrated savings aspects, which can contribute to their higher costs.

Answer:

x = 12

Step-by-step explanation:

20° + (6x - 2) = 90°

18° + 6x = 90°

6x = 90° - 18°

6x = 72°

x = 72°/6

x = 12

Answer:

Hope it helps buddy! Mark as brainlist please.

Answer:

9.9166667

Step-by-step explanation:

All of the numbers equal 59.5 then divide by 6 equals the answer above.

To calculate the mean of the given data set, sum all the data values and divide by the number of values. The mean of this data set is 9.9167.

To find the mean of the given data set: 2.5, 6.5, 9, 19, 20, 2.5,  follow these steps:

Hence, the mean of the data set is 9.9167.

Answer:

[tex]t=\frac{435-430}{\frac{29}{\sqrt{23}}}=0.827[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=23-1=22[/tex]  

And the p value taking in count that we have a bilateral test we got:

[tex]p_v =2*P(t_{(22)}>0.827)=0.417[/tex]  

Since the p value is higher than the significance level of 0.05 we have enough evidence to conclude that the true mean is not significantly different from 430 the required value

Step-by-step explanation:

Information given

[tex]\bar X=435[/tex] represent the mean for the weight

[tex]s=\sqrt{841}=29[/tex] represent the sample standard deviation

[tex]n=23[/tex] sample size  

[tex]\mu_o =430[/tex] represent the value that we want to verify

[tex]\alpha=0.05[/tex] represent the significance level

t would represent the statistic

[tex]p_v[/tex] represent the p value

System of hypothesis

We are trying to proof if the filling machine works correctly at the 430 gram setting, so then the system of hypothesis for this case are:

Null hypothesis:[tex]\mu = 430[/tex]  

Alternative hypothesis:[tex]\mu \neq 430[/tex]  

In order to cehck the hypothesis the statistic for a one sample mean test is given by

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

Replacing the info given we have this:

[tex]t=\frac{435-430}{\frac{29}{\sqrt{23}}}=0.827[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=23-1=22[/tex]  

And the p value taking in count that we have a bilateral test we got:

[tex]p_v =2*P(t_{(22)}>0.827)=0.417[/tex]  

Since the p value is higher than the significance level of 0.05 we have enough evidence to conclude that the true mean is not significantly different from 430 the required value

The type of hypothesis test used in this scenario is a two-tailed t-test for a single sample mean.

Step 1: State the hypotheses

- Null hypothesis H₀: The mean weight of the bags is 430 grams [tex]\mu = 430[/tex]

- Alternative hypothesis H₁: The mean weight of the bags is not 430 grams [tex]\mu \neq 430[/tex]

Step 2: Select the significance level

- The level of significance [tex]\alpha[/tex] is 0.05.

Step 3: Calculate the test statistic

- Sample mean [tex]\bar{x}\)[/tex] = 435 grams

- Population mean [tex]\mu\)[/tex] = 430 grams

- Sample size n = 23

- Sample variance s² = 841

- Sample standard deviation s = √841 = 29

The test statistic (t) is calculated using the formula:

[tex]\[ t = \frac{\bar{x} - \mu}{s / \sqrt{n}} \][/tex]

[tex]\[ t = \frac{435 - 430}{29 / \sqrt{23}} \][/tex]

[tex]\[ t = \frac{5}{6.048} \][/tex]

t ≈ 0.8266

Step 4: Determine the degrees of freedom and critical value

- Degrees of freedom [tex](\(df\)) = \(n - 1[/tex]

= 23 - 1

= 22

- For a two-tailed test at [tex]\(\alpha = 0.05\)[/tex] with 22 degrees of freedom, the critical t-values are approximately [tex]\(\pm 2.074[/tex].

Step 5: Make a decision

- Compare the calculated test statistic 0.8266 with the critical t-values [tex]\pm 2.074[/tex].

- If the test statistic is within the range -2.074 to 2.074, fail to reject the null hypothesis.

- If the test statistic is outside this range, reject the null hypothesis.

Since 0.8266 is within the range -2.074 to 2.074, we fail to reject the null hypothesis.

Conclusion:

- There is not enough evidence to suggest that the mean weight of the bags is different from 430 grams at the 0.05 significance level.

Answer:

6

Step-by-step explanation:

The mode is the number which appears most often in a set of numbers in this case that would be 6 because it appears twice

The mode of a set of values is the one that appears most frequently. In your list: 9, 10, 6, 5, 6 - the number 6 appears twice, more than any other number, making 6 the mode.

In statistics, the mode of a set of values is the value that appears most frequently. An easy way to find the mode is to count the frequency of each number. Looking at your list of numbers: 9, 10, 6, 5, 6. The number 6 is the only number that appears more than once.

So, the mode of the given set of numbers is 6 because it appears more frequently than the other numbers.

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Answer:

Step-by-step explanation:

This is a test of a single population mean since we are dealing with mean.

From the information given,

Null hypothesis is expressed as

H0:μ=1.5

The alternative hypothesis is expressed as

Ha:μ>1.5

This is a right tailed test

The decision rule is to reject the null hypothesis if the significance level is greater than the p value and accept the null hypothesis if the significance level is less than the p value.

p value = 0.052

Significance level, α = 0.05

Since α = 0.05 < p = 0.052, the true statement would be

At the α=0.05 significance level, you have proven that H0 is true. B.

Final answer:

The P-value of 0.052 provides some evidence against the null hypothesis H0, although not enough to reject it at the α = 0.05 significance level. A study with a larger sample size may be worthwhile to investigate the true mean nicotine content further.

Explanation:

With a P-value of 0.052 for the hypothesis test, comparing it against a significance level alpha (α) = 0.05 determines whether the null hypothesis (H0) is rejected or not. Despite the P-value being slightly above the significance level, the correct interpretation is Option C: 'There is some evidence against H0, and a study using a larger sample size may be worthwhile.' This suggests that while there isn't enough evidence to reject the null hypothesis at α = 0.05, the result is close enough to warrant further investigation.

We cannot claim that the null hypothesis has been proven true as statistical hypothesis testing never proves a hypothesis, but only provides evidence against it (Option A is incorrect). The data suggests that further investigation could be useful, instead of being unfruitful (Option B is an incorrect view). Lastly, there is evidence pointing towards the alternative hypothesis (Ha), it's not that there's no evidence at all (Option D is incorrect).

Answer

it is 0

Step-by-step explanation: you have to add 6 yto negative six so it is zero

Answer:

its is the option that shows the first line at six then 0

Answer:

B

Step-by-step explanation:

For one-way ANOVA test results to be reliable, it has to be assumed that standard deviations of populations are equal. Here standard deviations of populatinos are not mentioned.

Answer:

It’s c I got a 100

Step-by-step explanation:

e d g e n u I  ty

Answer:

M(Mx, My), R(Rx, Ry), S(Sx, Sy)

M is midpoint of RS

=> Rx + Sx = 2Mx => Rx = 2Mx - Sx = 2 x 8 - 9 = 7

=> Ry + Sy = 2My => Ry = 2My - Sy = 2 x 7 - 5 = 9

=> R(7, 9)

Hope this helps!

:)

Answer:

(7,9)

Step-by-step explanation:

Let R:(x,y)

(x+9)/2, (y+5)/2 = 8 ,7

x + 9 = 16

x = 7

y + 5 = 14

y = 9

R: (7,9)

Answer: Michelle's conclusion is wrong, he sells 8214.3 songs per day

Step-by-step explanation:

Sell 115000 songs every 2 weeks

Sell 115000 songs every 14 days

Sell (a) songs for 1 day

(a) =(115000x1) ➗ 14

(a) =115000 ➗ 14

(a) =8214.3

Answer:

The second one is the correct answer

Step-by-step explanation:

The third one is incorrect as she stated, I tried it and got it wrong when I did the retry I put the second one and I got it correct.

Answer:

mArc A B = 120° (C)

Step-by-step explanation:

Question:

In circle O, AC and BD are diameters.

Circle O is shown. Line segments B D and A C are diameters. A radius is drawn to cut angle D O C into 2 equal angle measures of x. Angles A O D and B O C also have angle measure x.

What is mArc A B?

a)72°

b) 108°

c) 120°

d) 144°

Solution:

Find attached the diagram of the question.

Let P be the radius drawn to cut angle D O C into 2 equal angle measures of x

From the diagram,

m Arc AOC = 180° (sum of angle in a semicircle)

∠AOD + ∠DOP + ∠COP = 180° (sum of angles on a straight line)

x° +x° + x° =180°

3x = 180

x = 180/3

x = 60°

m Arc DOB = 180° (sum of angle in a semicircle)

∠AOB + ∠AOD = 180° (sum of angles on a straight line)

∠AOB + x° = 180

∠AOB + 60° = 180°

∠AOB = 180°-60°

∠AOB = 120°

mArc A B = 120°

Answer:

c

Step-by-step explanation:

Answer:

The answer to this question can be described as follows:

Step-by-step explanation:

In the outcome of Jackson isn't legitimate as product A and product B were n’t considered equal in watering the plants. It is the preparation for all two to be compared, Product A with only a region of the backyard, which receives direct energy, and Product B will be maintained regularly by the very same area of the yards, that is in minimal lighting.

No, The conclusion done by Jackson's is not valid for this situation.

Effective Soiling depth is the depth of soil material  which is above the layer that impedes movement of air and water and growth in plant roots.

According to outcome of Jackson that isn't legitimate as product A and product B were considered equal in watering the plants. Then it is the preparation of two to be compare with product B, Product A with only a region of the backyard, which receives direct energy, and Product B will  maintained regularly very same area of the yards, that is with minimal lighting.

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Answer:

You should claim 10.5325 years on your warranty.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

[tex]\mu = 13, \sigma = 1.5[/tex]

Want's to replace no more than 5% of the products.

This means that the warranty should be 5th percentile, that is, the value of X when Z has a pvalue of 0.05. So X when Z = -1.645.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-1.645 = \frac{X - 13}{1.5}[/tex]

[tex]X - 13 = -1.645*1.5[/tex]

[tex]X = 10.5325[/tex]

You should claim 10.5325 years on your warranty.

We have been given a function [tex]h(x)=\frac{1}{8}x^3-x^2[/tex]. We are asked to find the average rate of change of our given function over the interval [tex]-2\leq x\leq 2[/tex].

We will use average rate of change formula to solve our given problem.

[tex]\text{Average rate of change}=\frac{f(b)-f(a)}{b-a}[/tex]

[tex]\text{Average rate of change}=\frac{h(2)-h(-2)}{2-(-2)}[/tex]

[tex]\text{Average rate of change}=\frac{\frac{1}{8}(2)^3-2^2-(\frac{1}{8}(-2)^3-(-2)^2)}{2+2}[/tex]

[tex]\text{Average rate of change}=\frac{\frac{1}{8}(8)-4-(\frac{1}{8}(-8)-(4))}{4}[/tex]

[tex]\text{Average rate of change}=\frac{1-4-(-1-4)}{4}[/tex]

[tex]\text{Average rate of change}=\frac{-3-(-5)}{4}[/tex]

[tex]\text{Average rate of change}=\frac{-3+5}{4}[/tex]

[tex]\text{Average rate of change}=\frac{2}{4}[/tex]

[tex]\text{Average rate of change}=\frac{1}{2}[/tex]

Therefore, the average rate of change over the interval [tex]-2\leq x\leq 2[/tex] is [tex]\frac{1}{2}[/tex].

The average rate of change of h over the interval -2 ≤ x ≤ 2 in the equation h(x)=1/8x³-x² is 3/8.

To find the average rate of change of h over the interval -2 ≤ x ≤ 2, we need to calculate the difference in the values of h at the endpoints of the interval and divide it by the change in x.

First, let's find the value of h at x = -2: h(-2) = (1/8) * (-2)^3 - (-2)^2 = -(1/2).

Next, let's find the value of h at x = 2: h(2) = (1/8) * (2)^3 - (2)^2 = 1.

The change in x is 2 - (-2) = 4. So, the average rate of change of h over the interval -2 ≤ x ≤ 2 is (1 - (-1/2))/4 = 3/8.

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Answer:

Check the explanation

Step-by-step explanation:

Number of transactions in a day is sum of number of withdrawals and number of deposits. So,

Number of transactions in a day, Z = X + Y

Moment Generating function of Z is,

T+1

Expected number of transactions in a day = E[Z]

[tex]= \frac{\mathrm{d} }{\mathrm{d} t}_{t=0}M_Z(t) = (r+1)\left ( \frac{p}{1-qe^t} \right )^{r} * \frac{-p}{(1-qe^t)^2} * (-qe^t) for t = 0[/tex]

[tex]= (r+1)\left ( \frac{p}{1-qe^0} \right )^{r} * \frac{-p}{(1-qe^0)^2} * (-qe^0)[/tex]

[tex]= (r+1)\left ( \frac{p}{1-q} \right )^{r} * \frac{-p}{(1-q)^2} * (-q)[/tex]

[tex]= (r+1)\left ( \frac{p}{p} \right )^{r} * \frac{-p}{(p)^2} * (-q)[/tex]

[tex]= \frac{(r+1)q}{p}[/tex]

Answer:

Zoe, at about the 96th percentile.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Zoe:

Zoe scored 82 on the History test. So X = 82.

The History test had a mean score of 68 with a standard deviation of 8. This means that [tex]\mu = 68, \sigma = 8[/tex]

Then, we find the z-score to find the percentile.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{82 - 68}{8}[/tex]

[tex]Z = 1.75[/tex]

[tex]Z = 1.75[/tex] has a pvalue of 0.9599.

So Zoe was at abouth the 96th percentile.

Joseph:

Joseph scored 82 on the Calculus test. This means that [tex]X = 82[/tex]

The Calculus test had a mean score of 70 with a standard deviation of 7.2. This means that [tex]\mu = 70, \sigma = 7.2[/tex]

Z-score

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{82 - 70}{7.2}[/tex]

[tex]Z = 1.67[/tex]

[tex]Z = 1.67[/tex] has a pvalue of 0.9525.

Joseph scored in the 95th percentile, which is below Zoe.

So the correct answer is:

Zoe, at about the 96th percentile.

Answer:

10 (3x+7)

Step-by-step explanation:

factor out 10

10 (3x+7)

Answer:

A

C

D

Step-by-step explanation:

Answer: I think c,e

Step-by-step explanation:Sorry if it wrong

Answer:

C

Step-by-step explanation:

IM DORA

Answer:

6 Years

Step-by-step explanation:

Orlando invests $1000 at 6% annual interest compounded daily.

Orlando's investment = [tex]A=1000(1+\frac{0.06}{365})^{(365\times t)}[/tex]

Bernadette invests $1000 at 7% simple interest.

Bernadette's investment = A = 1000(1+0.07×t)

By trail and error method we will use t = 5

Bernadette's investment will be after 5 years

1000(1 + 0.07 × 5)

= 1000(1 + 0.35)

= 1000 × 1.35

= $1350

Orlando's investment after 5 years

[tex]A=1000(1+\frac{0.06}{365})^{(365\times 5)}[/tex]

   = [tex]1000(1+0.000164)^{1825}[/tex]

  = [tex]1000(1.000164)^{1825}[/tex]

  = 1000(1.349826)

  = 1349.825527 ≈ $1349.83

After 5 years Orlando's investment will not be more than Bernadette's.

Therefore, when we use t = 6

After 6 years Orlando's investment will be = $1433.29

and Bernadette's investment will be = $1420

So, after 6 whole years Orlando's investment will be worth more than Bernadette's investment.

We have been given that a huge ice glacier in the Himalayas initially covered an area of 45 square kilo-meters. The relationship between A, the area of the glacier in square kilo-meters, and t, the number of years the glacier has been melting, is modeled by the equation [tex]A=45e^{-0.05t}[/tex].

To find the time it will take for the area of the glacier to decrease to 15 square kilo-meters, we will equate [tex]A=15[/tex] and solve for t as:

[tex]15=45e^{-0.05t}[/tex]

[tex]\frac{15}{45}=\frac{45e^{-0.05t}}{45}[/tex]

[tex]\frac{1}{3}=e^{-0.05t}[/tex]

Now we will switch sides:

[tex]e^{-0.05t}=\frac{1}{3}[/tex]

Let us take natural log on both sides of equation.

[tex]\text{ln}(e^{-0.05t})=\text{ln}(\frac{1}{3})[/tex]

Using natural log property [tex]\text{ln}(a^b)=b\cdot \text{ln}(a)[/tex], we will get:

[tex]-0.05t\cdot \text{ln}(e)=\text{ln}(\frac{1}{3})[/tex]

[tex]-0.05t\cdot (1)=\text{ln}(\frac{1}{3})[/tex]

[tex]-0.05t=\text{ln}(\frac{1}{3})[/tex]

[tex]t=\frac{\text{ln}(\frac{1}{3})}{-0.05}[/tex]

[tex]t=\frac{\text{ln}(\frac{1}{3})\cdot 100}{-0.05\cdot 100}[/tex]

[tex]t=\frac{\text{ln}(\frac{1}{3})\cdot 100}{-5}[/tex]

[tex]t=-\text{ln}(\frac{1}{3})\cdot 20[/tex]

[tex]t=-(\text{ln}(1)-\text{ln}(3))\cdot 20[/tex]

[tex]t=-(0-\text{ln}(3))\cdot 20[/tex]

[tex]t=20\text{ln}(3)[/tex]

Therefore, it will take [tex]20\text{ln}(3)[/tex] years for area of the glacier to decrease to 15 square kilo-meters.

Answer:

m1 = 62°, m2 = 118°

Step-by-step explanation:

The definition of a linear pair of angles is a pair of angles that are adjacent and add up to 180°.

Then, we have the following equation

[tex]x-9+x+47 =180 [/tex]

Then,

[tex]2x+38=180[/tex]

Subtracting 38 on both sides

[tex] 2x = 180-38 = 142[/tex]

Dividing by two, we get x = 71. Then m1 = 71-9 = 62, m2 = 71+47=118[/tex]

In response to the question, we may say that the height of the cylinder is 6.

A cylinder is a three-dimensiοnal geοmetric shape made up οf twο parallel cοngruent circular bases and a curving surface cοnnecting the twο bases. The bases οf a cylinder are always perpendicular tο its axis, which is an imaginary straight line passing thrοugh the centre οf bοth bases. The vοlume οf a cylinder is equal tο the prοduct οf its base area and height.

A cylinder's volume is computed as V = r²h,

where

"V" represents the volume,

"r" represents the radius of the base, and

"h" represents the height of the cylinder.

Thus,  

307.9 = 7²h

307.9 = 49h

h = 307.9/49

h 6.283

h = 6     (rounding to the nearest whole)

Thus, The height of the cylinder is 6.

To know more about cylinder visit:

brainly.com/question/16134180

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The easy answer: If, say, B is the zero matrix, i.e.

[tex]B=\begin{bmatrix}0&0\\0&0\end{bmatrix}[/tex]

then

[tex]2A=\begin{bmatrix}5&0\\-1&2\end{bmatrix}\implies A=\begin{bmatrix}\dfrac52&0\\\\-\dfrac12&1\end{bmatrix}[/tex]