Suppose that Drake works for a research institute in Greenland and is given the job of treating wild polar bears there for hypothyroidism using medicated darts. The appropriate dosage depends on the bear's mass. Eager to head into the wilderness, he prints out the statistics he needs and sets off, planning to prepare the darts along the way.

Two days into his trek, however, Drake spills a cup of coffee on the printout. Unwilling to admit to his boss what happened, he decides to estimate the polar bear mass with the information he has remaining. He knows the population standard deviation to be ?=60 kg, and he has data from a simple random sample of n = 10 polar bears from Greenland. Their masses, in kg, are

275,250,325,310,240,360,350,400,380,400

The sample mean polar bear mass is x (there is the line on top of x) =329 kg.

-First, determine if the requirements for a z?confidence interval are met.

A) The requirements are not met because the population standard deviation is not known.

B) The requirements are not met because there is an outlier in the sample, indicating that polar bear masses do not come from a normal distribution or that the sample was not a simple random sample.

C)The requirements are met because the sample is a simple random sample from a normal distribution with a known population standard deviation.

D) The requirements are met because the sample is a simple random sample from a normal distribution and the standard deviation can be estimated from the sample.

-Next, calculate the lower and upper limits (bounds) for a 99% confidence interval for the mean polar bear mass in Greenland. Give your answer precise to one decimal place.

lower limit= _________kg

upper limit=_________kg

-Finally, summarize the results.

A) There is 99% confidence that the polar bear mass sample mean is between the lower and upper limits of the confidence interval.

B) There is a 99% chance that a randomly selected polar bear in Greenland will have a mass between the lower and upper limits of the confidence interval.

C) There is a 99% chance that the Greenland polar bear mass population mean is between the lower and upper limits of the confidence interval.

D) There is 99% confidence that the lower and upper limits of the confidence interval contains the Greenland polar bear mass population mean.

Answer:

clearing picture

Step-by-step explanation:

Answer:

Orange juice bottle has greater percent of water.

Percent of water in apple juice bottle=40%

Step-by-step explanation:

We are given that

Total mass of apple juice bottle=80 ounce

Apple juice contains water=32 ounces

Total mass of orange juice bottle=64 ounce

Orange juice bottle contain water=48 ounces

We have to find that which juice has greater percent of water and find the percent of water in  the bottle of apple juice .

Percent of water in apple juice=[tex]\frac{water}{total\;mass}\times 100=\frac{32}{80}\times 100=[/tex]40%

Percent of water in orange juice bottle=[tex]\frac{48}{64}\times 100=[/tex]75%

Orange juice bottle has greater percent of water.

Answer:

Step-by-step explanation:

Z=-1.5

-1.5=2.5

Final answer:

To find the area under the standard normal curve between z = -1.5 and z = 2.5, subtract the area to the left of z = -1.5 from the area to the left of z = 2.5 to be 0.927.

Explanation:

To find the area under the standard normal curve between z = -1.5 and z = 2.5, we can subtract the area to the left of z = -1.5 from the area to the left of z = 2.5.

Using the z-table, we can find that the area to the left of z = -1.5 is approximately 0.0668 and the area to the left of z = 2.5 is approximately 0.9938.

Therefore, the area between z = -1.5 and z = 2.5 is approximately 0.9938 - 0.0668 = 0.927.

Answer:

a) 54 mph to 144 mph

Step-by-step explanation:

We don't know the shape of the distribution, so we use Chebyshev's Theorem to solve this question. It states that:

At least 75% of the measures are within 2 standard deviations of the mean.

At least 89% of the measures are within 3 standard deviations of the mean.

At least eight-ninths of the player's serves.

8/9 is approximately 89%

So

Mean: 99, standard deviation: 15

99 - 3*15 = 54

99 + 3*15 = 144

So the correct answer is:

a) 54 mph to 144 mph

Answer:

The factors that cause Earth to experience seasons are:

1. the tilt of Earth’s axis

2. the directness of the Sun’s rays

The factors that cause Earth to experience seasons are:

1. the tilt of Earth’s axis

2. the directness of the Sun’s rays

The reason why the Earth contains various seasons because it deals with the variation of the sun's rays angles and the earth titles to the 23.5 degrees on its axis. Also along with the earth rotation, the earth orbits should be around to the sun because of which various parts should be exposed to the different amount of lights

Therefore, the above two points should be considered.

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Answer:

[tex]A(t) = 48833e^{0.0389t}[/tex]

The exponential growth rate is r = 0.0389

Step-by-step explanation:

An exponential function for the number of women graduating from​ 4-yr colleges in t years after 1930 can be given by the following equation:

[tex]A(t) = A(0)e^{rt}[/tex]

In which A(0) is the initial amount, and r is the exponential growth rate, as a decimal.

1930​, when 48,833 women earned a​ bachelor's degree

This means that [tex]A(0) = 48833[/tex]

2004​, when approximately 870,000

2004 is 74 years after 1930, which means that [tex]A(74) = 870000[/tex]

Applying to the equation:

[tex]A(t) = A(0)e^{rt}[/tex]

[tex]870000 = 48833e^{74r}[/tex]

[tex]e^{74r} = \frac{870000}{48833}[/tex]

[tex]\ln{e^{74r}} = \ln{\frac{870000}{48833}}[/tex]

[tex]74r = \ln{\frac{870000}{48833}}[/tex]

[tex]r = \frac{\ln{\frac{870000}{48833}}}{74}[/tex]

[tex]r = 0.0389[/tex]

So

[tex]A(t) = A(0)e^{rt}[/tex]

[tex]A(t) = 48833e^{0.0389t}[/tex]

To find an exponential function that fits the given data, determine the values of the base and the exponent. The exponential function that fits the data is y = 2.311 * 1.049^x. The exponential growth rate is approximately 1.049.

To find an exponential function that fits the data, we need to determine the values of the base and the exponent. Let's let the year be the input, x, and the number of women graduating be the output, y. The general form of an exponential function is y = ab^x, where a is the initial value and b is the growth rate. Substituting the given data, we have the equation:

48,833 = a * b1930

870,000 = a * b2004

By dividing the second equation by the first equation, we can eliminate a:

870,000 / 48,833 = (a * b2004) / (a * b1930)

17.821 = b2004-1930

17.821 = b74

Taking the log base b of both sides, we get:

logb 17.821 = 74

Solving for b using logarithmic properties, we find:

b = 17.8211/74

b ≈ 1.049

Now that we have the value of b, we can substitute it into one of the original equations to find a:

48,833 = a * 1.0491930

Solving for a, we get:

a ≈ 2.311

Therefore, the exponential function that fits the data is y = 2.311 * 1.049x. The exponential growth rate is approximately 1.049.

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Answer:

100

Step-by-step explanation:

43+57=100

I added 3+7=10

Then 40+50=90 and added them

90+10=100

Answer: 100

Step-by-step explanation:

You know that 3+7=10

You know that 40+50=90

90+10=100

Answer:

84.13% of bottles will have volume greater than 994 mL

Step-by-step explanation:

Mean volume = u = 1000

Standard deviation = [tex]\sigma[/tex] = 6

We need to find the proportion of bottles with volume greater than 994. So our test value is 994. i.e.

x = 994

Since the data is normally distributed we will use the concept of z-score to find the required proportion. First we convert 994 to its equivalent z-score, then using the z-table we will find the corresponding value of proportion. The formula to calculate the z score is:

[tex]z=\frac{x-u}{\sigma}[/tex]

Substituting the values, we get:

[tex]z=\frac{994-1000}{6}=-1[/tex]

This means 994 is equivalent to a z score of -1. Now we will find the proportion of z values which are greater than -1 from the z table.

i.e. P(z > -1)

From the z-table this value comes out to be:

P(z >- 1) = 1 - P(z < -1) = 1 - 0.1587 = 0.8413

Since, 994 is equivalent to a z score of -1, we can write that proportion of values which will be greater than 994 would be:

P( X > 994 ) = P( z > -1 ) = 0.8413 = 84.13%

To find the proportion of bottles with more than 994 mL, calculate the z-score and use a z-table. Approximately 93.32% of bottles are filled with more than 994 mL.

To determine the proportion of bottles with volumes greater than 994 mL, we need to use the properties of the standard normal distribution. The mean volume of a bottle is given as 1000 mL with a standard deviation of 4 mL. We first calculate the z-score for 994 mL, which is the number of standard deviations 994 mL is from the mean.

Z = (X - μ) / σ = (994 mL - 1000 mL) / 4 mL = -1.5

Using a z-table or standard normal distribution calculator, we can find the proportion of the area to the right of z = -1.5, which represents the proportion of bottles filled with more than 994 mL. The area to the right of z = -1.5 is approximately 0.9332. Therefore, about 93.32% of the bottles are expected to have volumes greater than 994 mL.

Answer:

147.58 cm

Step-by-step explanation:

Circumference is represented by 2πr.

R is 23.5, and I'll approximate π to 3.14, as is common.

This creates 2 • 3.14 • 23.5

Simplify to: 147.58, which is your circumference

Answer:

148

Step-by-step explanation:

To find the circumference, use 2r*3.14 for a approximate answer. in this case, 23.5*2=47.

47*3.14=147.58.

Rounded to the nearest whole number, the answer is 148.

Answer:5000

Step-by-step explanation:

A kilometer is equal to 1000 meters.

5*1000=5000.

Answer:

5000 meters

Step-by-step explanation:

It is given that Monique ran in a 5 kilometer race.

Answer:

The number of ways she can select her lunches N ;

N = 10×10×10×10×3 = 30000 ways

Step-by-step explanation:

Number of week days = 5

Total number of dishes = 10

Number of vegetarian dishes = 3

Note; on other week days apart from Friday she can select any lunch she want vegetarian or not...

Therefore, on Monday to Thursday she has ten choices per day, and on Friday she has 3 choices

The number of ways she can select her lunches N ;

N = 10×10×10×10×3 = 30000 ways

Find the given attachments for complete answer

Answer:

The 95% confidence interval for the proportion for the American adults who believed in astrology is (0.23, 0.27).

This means that we can claim with 95% confidence that the true proportion of all American adults who believed in astrology is within 0.23 and 0.27.

Step-by-step explanation:

We have to construct a 95% confidence interval for the proportion.

The sample proportion is p=0.25.

[tex]p=X/n=501/2004=0.25[/tex]

The standard deviation can be calculated as:

[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.25*0.75}{2004}}=\sqrt{ 0.000094 }=0.01[/tex]

For a 95% confidence interval, the critical value of z is z=1.96.

The margin of error can be calculated as:

[tex]E=z\cdot \sigma_p=1.96*0.01=0.0196[/tex]

Then, the lower and upper bounds of the confidence interval can be calculated as:

[tex]LL=p-E=0.25-0.0196=0.2304\approx0.23\\\\UL=p+E=0.25+0.0196=0.2696\approx 0.27[/tex]

The 95% confidence interval for the proportion for the American adults who believed in astrology is (0.23, 0.27).

This means that we can claim with 95% confidence that the true proportion of all American adults who believed in astrology is within 0.23 and 0.27.

Lower Quartile: 2

Upper Quartile: 5.25

Median: 3

Final answer:

In the given data set 2, 2, 2, 4, 5, 6, the lower quartile is 2, the median is 3, and the upper quartile is 5.

Explanation:

To find the lower quartile, median, and upper quartile of the given data set 2, 2, 2, 4, 5, 6, we first need to organize it in ascending order, which is already done. Next, we compute the median, which is the middle value when the data set is listed in order. Since there are six numbers, the median will be the average of the third and fourth numbers, (2+4)/2, which is 3.

To find the first quartile (Q1) or lower quartile, we take the median of the lower half of the data set, not including the median. This would be the median of the first three numbers: 2, 2, and 2, which is simply 2. To find the third quartile (Q3) or upper quartile, we look at the upper half of the data set, again not including the median. The median of the last three numbers 4, 5, and 6 is 5.

Therefore, the lower quartile is 2, the median is 3, and the upper quartile is 5.

Answer:

the third one

Step-by-step explanation:

you can cross out parabola and hyperbola. the second graph is an exponential function because exponential functions go through (0,1), While logarithmic functions go through (1,0).

Answer:

Option 3

Step-by-step explanation:

Edge 2021

Answer:

1 hour 15 Minutes

Step-by-step explanation:

The glider begins its flight [tex]\dfrac{3}{4}[/tex] mile above the ground.

Distance above the ground after 45 minutes =[tex]\frac{3}{10} \:mile[/tex]

Change in height of the glider

[tex]=\frac{3}{4}-\frac{3}{10} \\\\=\frac{15-6}{20}\\\\=\frac{9}{20} miles[/tex]

Next, we determine how long the entire descent last.

Expressing the distance moved as a ratio of time taken

[tex]\frac{9}{20} \:miles : 45 \:minutes\\\\\frac{3}{10}\:miles:x \:minutes\\\\x=45X\frac{3}{10}\div\frac{9}{20} =30 Minutes[/tex]

Therefore: Total Time taken =45+30=75 Minutes

=1 hour 15 Minutes

Answer:

Half way in between negative 1 and negative 2.

Step-by-step explanation:

Answer:

21.77% probability that a randomly selected frog of this type has thumb length longer than 9.08 mm.

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 = 8.59, \sigma = 0.63[/tex]

Calculate the probability that a randomly selected frog of this type has thumb length longer than 9.08 mm.

This is 1 subtracted by the pvalue of Z when X = 9.08. So

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

[tex]Z = \frac{9.08 - 8.59}{0.63}[/tex]

[tex]Z = 0.78[/tex]

[tex]Z = 0.78[/tex] has a pvalue of 0.7823

1 - 0.7823 = 0.2177

21.77% probability that a randomly selected frog of this type has thumb length longer than 9.08 mm.

Answer:

The platform cannot hold both elephants.

Step-by-step explanation:

This problem is solved by conversion of units.

Elephant A weighs 11,028 pounds

Elephant B weighs 5 1/2 = 5.5 tons

The platform can hold 22,000 pounds

To see if the platform holds both elephants, the first step is converting the weigth of Elephant B to pounds.

Each ton has 2000 pounds.

So 5.5 tons have 5.5*2000 = 11000 pounds.

So Elephant B weighs 11000 pounds

Combined weights of Elephants A and B

11,028 + 11,000 = 22,028 > 22,000

The platform cannot hold both elephants.

Answer:

The fifth degree Taylor polynomial of g(x) is increasing around x=-1

Step-by-step explanation:

Yes, you can do the derivative of the fifth degree Taylor polynomial, but notice that its derivative evaluated at x =-1 will give zero for all its terms except for the one of first order, so the calculation becomes simple:

[tex]P_5(x)=g(-1)+g'(-1)\,(x+1)+g"(-1)\, \frac{(x+1)^2}{2!} +g^{(3)}(-1)\, \frac{(x+1)^3}{3!} + g^{(4)}(-1)\, \frac{(x+1)^4}{4!} +g^{(5)}(-1)\, \frac{(x+1)^5}{5!}[/tex]

and when you do its derivative:

1) the constant term renders zero,

2) the following term (term of order 1, the linear term) renders: [tex]g'(-1)\,(1)[/tex] since the derivative of (x+1) is one,

3) all other terms will keep at least one factor (x+1) in their derivative, and this evaluated at x = -1 will render zero

Therefore, the only term that would give you something different from zero once evaluated at x = -1 is the derivative of that linear term. and that only non-zero term is: [tex]g'(-1)= 7[/tex] as per the information given. Therefore, the function has derivative larger than zero, then it is increasing in the vicinity of x = -1

Answer:

4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Answer:

Answer: 600

Step-by-step explanation:

5x5=25

3x8=24

25x24=600

Answer:

a parallelogram, trapezium and rhombus

Step-by-step explanation:

The best-predicted pulse rate for a woman who is 66 inches tall, using the given regression equation 18.4 + 0.930x, is approximately 79.78 beats per minute.

To predict the pulse rate of a woman who is 66 inches tall using the given regression equation, we plug in the height (x = 66) into the equation:

ModifyingAbove y with caret = 18.4 + 0.930x

Substituting x = 66:

ModifyingAbove y with caret = 18.4 + 0.930(66)

Perform the calculation:

ModifyingAbove y with caret = 18.4 + 61.38

ModifyingAbove y with caret = 79.78

Therefore, the best-predicted pulse rate for a woman who is 66 inches tall is approximately 79.78 beats per minute. This prediction assumes that the relationship between height and pulse rate holds for this particular height value.

Answer:

3 x 0.50=1.5

6 x 0.50=3

10 x 0.50=5

Step-by-step explanation:

x 3, 6, 10

y 1.5, 3, 5

The charges are

For 3 Km the charges would be is $1.5

For 6 Km the charges would be is $3

For 10 Km the charges would be is $5

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For Example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

The passenger is charged $0.50 for each kilometer

For 3 Km the charges would be

=3 x 0.50

= $1.5

For 6 Km the charges would be

= 6 x 0.50

=$3

For 10 Km the charges would be

= 10 x 0.50

=$5

The complete Table is

x  3,      6,   10

y  1.5,    3,   5

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Answer:

$2,977.54

Step-by-step explanation:

You are going to use the compound interest formula:

[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]

P = initial balance

r = interest rate

n = number of times compounded annually

t = time

First, change 6% into the decimal form:

6% -> [tex]\frac{6}{100}[/tex] -> 0.06

Next, lets plug in the values:

[tex]A=2,500(1+\frac{0.06}{1} )^{3(1)}[/tex]

[tex]A=2,977.54[/tex]

Your answer will be $2,977.54

Answer:

We accept H₀ we don´t have enough evidence to conclude that a consumer group position is correct

Step-by-step explanation:

We have a case of test of proportion, as a consumer group is suspicious of the claim and think the proportion is lower we must develop a one tail test (left tail) Then

1.- Test hypothesis:

Null hypothesis  H₀                   P = P₀

Alternative hypothesis  Hₐ       P < P₀

2.- At significance level of α  = 0,05   Critical value

z(c)  =  -1,64

3.-We compute z(s) value as:

z(s)  =  ( P - P₀ )/ √P*Q/n      where   P = 44/80     P = 0,55   and Q = 0,45

P₀ = 0,6   and  n = 80

Plugging all these values in the equation we get:

z(s)  = ( 0,55 - 0,6 ) / √(0,2475/80)

z(s)  =  - 0,05/ √0,0031

z(s)  =  - 0,05/0,056

z(s)  =  - 0,8928

4.-We compare  z(s)  and  z(c)

z(s) > z(c)      -0,8928 on the left side it means that z(s) is in the acceptance region so we accept H₀

Answer:

7/25

Step-by-step explanation:

Just did on delta math