Euclid’s root beer mug is shaped basically like a cylinder that is eight inches tall with a radius of three inches. Aristotle’s root beer glass is shaped basically like a cone that is 18 inches tall with a diameter of four inches. Which vessel holds the most root beer?


Complete Question:

a) Is it plausible that X is normally distributed?

b) For a random sample of 50 such pairs, what is the (approximate) probability that the sample mean courtship time is between 100 min and 125 min?

Answer:

a) It is plausible that X is normally distributed

b) probability that the sample mean courtship time is between 100 min and 125 min is 0.5269

Step-by-step explanation:

a)X denotes the courtship time for the scorpion flies which indicates that is a real - valued random variable, and since normal distribution is a continuous probability distribution for a real valued random variable, it is plausible that X is normally distributed.

b) Probability that the sample mean courtship time is between 100 min and 125 min

[tex]\mu = 120\\n = 50[/tex]

[tex]P(x_{1} < \bar{X} < x_{2} ) = P(z_{2} < \frac{x_{2}- \mu }{SD} ) - P(z_{1} < \frac{x_{2}- \mu }{SD})[/tex]

[tex]SD = \sqrt{\frac{\sigma^{2} }{n} } \\SD = \sqrt{\frac{110^{2} }{50} } \\SD = 15.56[/tex]

[tex]P(100 < \bar{X} <125 ) = P(z_{2} < \frac{125- 120 }{15.56} ) - P(z_{1} < \frac{100- 120 }{15.56})\\P(100 < \bar{X} <125 ) = P(z_{2} < 0.32 ) - P(z_{1} < -1.29)[/tex]

From the probability distribution table:

[tex]P(z_{2} < 0.32 ) = 0.6255\\ P(z_{1} < -1.29) = 0.0986[/tex]

[tex]P(100 < \bar{X} <125 ) = 0.6255 - 0.0986\\P(100 < \bar{X} <125 ) =0.5269[/tex]

Answer:

Step-by-step explanation:

hello :

let: A = 3√16+√-9

16=4²   and  -9 = 9i² =(3i)²   .... ( i² = -1)

√16 =√4² = 4     and  √-9 = √9i²= √(3i)² ± 3i

A= 12  ± 3i

Answer:

The answer is 1 : 3 : 2

Step-by-step explanation:

First, you have to make them into same unit by converting it into km or m :

1 km = 1000 m

0.007 km = 7 m

0.021 km = 21 m

7 : 21 : 14

OR

14 m = 0.014 km

Then you can simplify it by 7 :

m,

7 : 21 : 14

= 1 : 3 : 2

OR

km,

0.007 : 0.021 : 0.014

= 0.001 : 0.003 : 0.002

= 1 : 3 : 2

(take note: in ratio, it is better to put it in whole number form rather than decimal form)

Answer:

There are 36 dogs in the shelter.

Step-by-step explanation:

(Draw a model)

(3 boxes for dogs and 7 boxes for cats)

10 units = 120

1 unit = 120÷10

= 12

3 units = 12×3

= 36

(I hope you understand the question. A gentle reminder, always draw the model according to the ratio. From there you will understand.)

Step-by-step explanation:

a(n) = a ( n - 1) - 17

a(1) = 20

a(2) = a ( 2 - 1) - 17

= a (1) - 17

= 20 - 17

= 3

Now

a(3) = a ( 3 - 1 ) - 17

= a (2) - 17

= 3 - 17

= - 14

Hope it will help you.

Answer:

$36

Step-by-step explanation:

You are going to want to use the simple interest formula for this. The one below is modified for solving the interest earned.

[tex]I = Prt[/tex]

I = interest amount

P = principal amount

r = interest rate (decimal form)

t = time (years)

First, change 4% into a decimal:

4% -> [tex]\frac{4}{100}[/tex] -> 0.04

Now, plug the values into the equation:

[tex]I=300(0.04)(3)[/tex]

[tex]I=36[/tex]

The interest earned is $36

Please consider the complete question.

A parking lot in the shape of a trapezoid has an area of 12,052.1 square meters. The length of one base is 82.4 meters and the length of the base is 108.6 meters. What is the width of the parking lot

We will use area of trapezoid to formula to solve our given problem.

[tex]\text{Area of trapezoid}=\frac{1}{2}(a+b)\times h[/tex], where

a and b represents parallel sides of trapezoid,

h = height of trapezoid.

Width of the trapezoid will be equal to height.

Upon substituting our given values in above formula, we will get:

[tex]12,052.1=\frac{1}{2}(82.4+108.6)\times h[/tex]

[tex]12,052.1\cdot 2=2\cdot \frac{1}{2}(82.4+108.6)\times h[/tex]

[tex]24104.2=(191)\times h[/tex]

[tex]\frac{24104.2}{191}=\frac{(191)\times h}{191}[/tex]

[tex]126.2=h[/tex]

Therefore, the width of the parking lot is 126.2 meters.

Answer:

The best interpretation of one of the values of the function is that the rate  increases by 12% each day.

Step-by-step explanation:

Given:

F(x)=245(1.12)^x

To Find:

statement is the best interpretation of one of the values of the function

Solution:

Depending upon the values given the statement can be developed

As the function is itself the exponential growth structure ,

In this the statement ,Growth can be significantly depends on all factor

Such as time period initial value and rate.

But here the formula is simplified as ,

[tex]P=A(1+r)^t[/tex]

Here A= initial value r=rate and t =time period

Here A=245 and 1+r=1.12

i.e r=0.12 i.e 12%

Hence the rate give the best interpretation and more information about the function and scenario.

The function f(x)=245(1.12)^x models the exponential growth of bacteria in a sample over x days, with the base 245 being the initial number and 1.12 representing the daily growth rate.

The function f(x)=245(1.12)^x describes the exponential growth of bacteria, where the base number (245) represents the initial amount of bacteria and 1.12 indicates the growth rate per day.

For example, if we want to determine the number of bacteria at the end of the first day (x=1), we substitute 1 into the function to get f(1)=245(1.12)^1, which would give us the total number of bacteria at the end of day one.

The exponent x stands for the number of days and shows how the population grows at an increasing rate over time, which is a signature characteristic of an exponential function in a context like bacterial growth.

Answer:

The answer to your question is t = 1.3 s

Step-by-step explanation:

Data

Equation    h(t) = -4.9t² + v₀t + h₀

v₀ = 0 m/s

h₀ = 8 m

t = ?

h = 0 m

Process

1.- Substitute the values in the formula

                  0 = -4.9t² + 0t + 8

2.- Simplification

                  0 = -4.9t² + 8

3.- Solve for t

                 4.9t² = 8

                      t² = 8/4.9

                      t² = 1.63

4.- Result

                      t = 1.27 ≈ 1.3 s

Answer: 10.2

Step-by-step explanation:

Area of a circle is

A= pixr^2

327= 3.14r^2

Divide by 3.14

= 104.14

Get the sq rat of 104.14

= 10.2

Answer:

The correct answer is 52 squats.

Step-by-step explanation:

An exercise routine requires 24 crunches for every 16 squats.

Therefore the routine would require 1 crunch for every [tex]\frac{16}{24}[/tex] squats.

And by the use of unitary method, the routine would require 78 crunches for every [tex]\frac{16}{24}[/tex] × 78 squats = 52 squats.

Thus for every 78 crunches attempted, the exercise routine would requires 52 squats to be done.

Answer:

B.14 m

Step-by-step explanation:

We are given that

Height of tree=12 m

[tex]\theta=40^{\circ}[/tex]

We have to find the distance between the spotlight and the base of tree.

In triangle ABC

AB=12 m

[tex]tan\theta=\frac{perpendicular\;side}{base}[/tex]

Using the formula

[tex]tan 40=\frac{AB}{BC}=\frac{12}{BC}[/tex]

[tex]BC=\frac{12}{tan 40}=14.3\approx 14 m[/tex]

Hence, option B is true.

Answer:

14m

Step-by-step explanation:

I took the test

Answer:

Heres the anwser my man 128

Step-by-step explanation:

hope you got it right.

Answer:

The first one is correct

Step-by-step explanation:

You can multiply the base and perpendicular height to find the area.

Answer:

A) 1/2 - there are 2 sides - just as likely to occur as not to occur

B) 0% - it's never going to happen (impossible)

C) 0/0 - it's never going to happen (impossible)

D) 1/2 simplified from 2/4 - that was 2 out of the four balls. - just as likely to occur as not to occur

Answer:

[tex]\pi \: = \frac{22}{7} \: \: \: \: or \: \: \: \: \: \: 3.14 \\ \\ [/tex]

Answer:

$2

Step-by-step explanation:

She earns 5%  of $40 each year. To find how much she makes in 1 year, multiply 5% and 40

40*5%

Convert 5% to a decimal by dividing by 100

5%/100=0.05

40*0.05=2

So, in one year, the account earns $2 in interest

Answer:

8 to 25

Step-by-step explanation:

The total number of lunches sold i

220+120+160 =500

We want the ratio of salads to total lunches

salads: lunches

160:    500

Divide each side by 20

160/20 : 500/20

8:25

Answer:

its D the last one i just took the assignment

Step-by-step explanation:

Answer:

The answer is D.

Step-by-step explanation:

I took the assignment.

Answer:

116

Step-by-step explanation: You would have to split the figure into a square and a triangle as you can see in the picture. You then find the area of each figure.

Area of Square : 8 * 8 = 64

Area of Triangle : 8 * 13 /2 = 52

Then, you add the areas of both figures together to get 116.

Answer: The third option.

Step-by-step explanation:

This is an equation because it has an equals sign that can be solved for, making it an equation.

Answer:

x + 3 = 12

Step-by-step explanation:

This is an equation because it contains an equal sign, if it does not contain an equal sign then it is an expression.

Answer:

Step-by-step explanation:

Well first you have to find what the total amount of all the interior angles. In Oder to do that you count how many sides the shape has the subtract two from that number. Take the number you get from that and multiply it by 180. That number is total amount of all the interior angles including the angle x. Take the angles you do know and add them together. Take the number you get from that and subtract it from the total amount of all interior angles. The number you get from that is your answer. The answer to this problem is 103.

The value of angle x in a pentagon is 103 degrees.

In a pentagon, the sum of the interior angles is always 540 degrees. To find the value of angle x, we can subtract the given angles from 540 degrees and then divide by the number of missing angles.

Given angles: 117, 100, 105, 115

Sum of given angles: 117 + 100 + 105 + 115 = 437 degrees

Sum of missing angles: 540 - 437 = 103 degrees

Since there is only one missing angle x in the pentagon, the value of x must be 103 degrees.

Answer: C.

Simple random sampling

Step-by-step explanation:

A simple random sample in statistics, is a subset of individuals chosen from a larger set. Each individual is chosen randomly and entirely by chance, such that each individual has the same probability for the entire larger set.

Answer:

C

Step-by-step explanation:

The computer randomly selects 500 names without any bias, Thus, it is simple random sampling because each name has equal chance of getting selected.

Answer:15

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

5=1

10=2

15=3

Given:

Desmond deposits $ 50 monthly.

Yearly he deposits = $50×12 = $ 600

Rate of interest compounded monthly = 4.7%

To find the amount he will receive after 10 years and the rate of change the value of his account after 10 years.

Formula

[tex]A = P(1+\frac{r}{(n)(100)} )^{nt}[/tex]

where,

A be the final amount

P be the principal

r be the rate of interest

t be the time and

n be the number of times the interest is compounded.

Now,

Taking,

P = 600, r = 4.7, n = 12, t = 10 we get,

[tex]A = 600(1+\frac{4.7}{(12)(100)}) ^{(12)(10)}[/tex]

or, [tex]A = 600(1.0039)^{120}[/tex]

or, [tex]A = 959.1[/tex]

Now,

At starting he has $ 600

At the end of 10 years he will be having $ 959.1

So,

The amount of change in his account = $ (959.1-600) = $ 359.1

Therefore the rate of change = [tex](\frac{359.1}{600} )(100) %[/tex]

= 59.85%

Hence,

a) His account will contain $ 959.1 after 10 years.

b) The rate of change in his account is 59.85% after 10 years.

Answer:

$48 green tokens

Step-by-step explanation:

please check the attached file for explanation

Answer:

48

Step-by-step explanation:

Answer:

30:15 (simplified is 2:1)

Step-by-step explanation:

Out of the 45 times Eric flipped a coin, 30 of them landed on heads. Tails is the the only other probable occurance, so since we know that there are 15 trials left, this means that the coin landed on tails 15 times. This would give a heads to tails ratio of 30:15, but the simplified ratio would be 2:1, because that's the smallest it can be divided evenly.

45-30=15

30:15=2:1

Answer:

1/9= 2/18=3/27=4/36

Step-by-step explanation:

To find equivalent ratios to 1/9, both the numerator and the denominator are multiplied by the same number. Thus, 2/18, 3/27, and 4/36 are all equivalent ratios to 1/9.

Ratios are equivalent if they represent the same relationship between numbers. To find equivalent ratios for 1/9, you need to multiply both the numerator and the denominator by the same number. Here are three examples:

So, 2/18, 3/27, and 4/36 are ratios equivalent to 1/9.

https://brainly.com/question/4916861?referrer=searchResults

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Answer:

6 pineapple, 6 melons, 8 grapefruits

Step-by-step explanation:

3.25P + 2.75M + 0.5G = 40

P = M

6M + 0.5G = 40

Let M = 6

6(6) + 0.5G = 40

0.5G = 4

G = 8

P = 6

M = 6

G = 8