Barry and Robin walk to Dunkin' Donuts each Saturday to meet for coffee and donuts. Barry walks the 2 miles from his house in 30 minutes and Robin walks the 3 miles from his house in 36 minutes. Find the unit rate in minutes per mile for Barry. Find the unit rate in minutes per mile for Robin. Who walks faster, Barry or Robin

Answer:

The probability that a sample mean is less than 14.99mm=0.066808

Step-by-step explanation:

We are given that

Mean,[tex]\mu=15 mm[/tex]

Standard deviation,[tex]\sigma=0.04 mm[/tex]

n=36

We have to find the probability that a sample mean is less than 14.99mm.

We know that

[tex]P(\bar{x}<a)=P(Z<\frac{\bar{x}-a}{\frac{\sigma}{\sqrt{n}}})[/tex]

Using the formula

[tex]P(\bar{x}<14.99)=P(Z<\frac{14.99-15}{\frac{0.04}{\sqrt{36}}})[/tex]

[tex]P(\bar{x}<14.99)=P(Z<-1.5)[/tex]

=[tex]1-P(Z\geq -1.5)[/tex]

[tex]=1-0.93319[/tex]

=0.066808

Hence,  the probability that a sample mean is less than 14.99mm=0.066808

Answer:

0.2061 = 20.61% probability, given a class size of 30 students, the average time to complete the test is less than 48.5 minutes

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 50 minutes and a standard deviation of 10 minutes.

This means that [tex]\mu = 50, \sigma = 10[/tex]

Class size of 30 students

This means that [tex]n = 30, s = \frac{10}{\sqrt{30}}[/tex]

What is the probability, given a class size of 30 students, the average time to complete the test is less than 48.5 minutes.

This is the p-value of Z when X = 48.5. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{48.5 - 50}{\frac{10}{\sqrt{30}}}[/tex]

[tex]Z = -0.82[/tex]

[tex]Z = -0.82[/tex] has a p-value of 0.2061

0.2061 = 20.61% probability, given a class size of 30 students, the average time to complete the test is less than 48.5 minutes

Answer:

A is the equation in standard form

Step-by-step explanation:

Answer:

0.1317 = 13.17% probability of no successes.

Step-by-step explanation:

For each toss, there are only two possible outcomes. Either there is a success, or there is not. The probability of a success on a toss is independent of any other toss, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

A die is rolled 5 times.

This means that [tex]n = 5[/tex]

5 or 6 is considered a success.

2 out of 6 sides are successes, so:

[tex]p = \frac{2}{6} = 0.3333[/tex]

Find the probability of no success:

This is P(X = 0). So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{5,0}.(0.3333)^{0}.(0.6667)^{5} = 0.1317[/tex]

0.1317 = 13.17% probability of no successes.

Answer:

altitude = 30 cm

lateral surface area = 301 cm² (approximately)

Step-by-step explanation:

let the altitude be x,

240=6*4*x/3

or, x=30 cm

Lateral surface area,

=l×√(w/2)²+h²]+w×√[(l/2)²+h²]

=6×√[(4/2)²+30²]+4×√[(6/2)²+30²]

≈300.99806

≈ 301 cm²

Answered by GAUTHMATH

Answer: The answer would be D

Step-by-step explanation:

Answer:

Step-by-step explanation:

19.

The numbers are m and n

Sum of m and n = m + n

Sum is multiplied by 91 = 91 x ( m + n )

20.

Let the number be = m

Six subtracted from the number = m - 6

41 times the difference = 41 x ( m - 6)

21.

Let the number be = r

Difference between 83 and 10 = 83 - 10 = 73

[tex]The \ number\ divided \ by\ the \ difference \ = \frac{r}{73}[/tex]

22.

Total of p and 23 = p + 12

[tex]Total \ divided \ by \ 18 = \frac{p + 12 }{18}[/tex]

23.

The product of c and 3  = 3c

Sum of 9 and 12 = 21

Product is more than Sum = 3c + 21

24.

Sum of y  and 10 = y + 10

Number x decreased by 5 = x - 5

[tex]Sum \ divided \ by \ difference = \frac{ y + 10 }{x - 5}[/tex]

Answer:

The probability is P = 0.08

Step-by-step explanation:

We have:

2 pink balls

7 purple balls

6 white balls

So the total number of balls is just:

2 + 7 + 6 = 15

We want to find the probability of randomly picking 3 purple balls (without replacement).

For the first pick:

Here all the balls have the same probability of being drawn from the urn, so the probability of getting a purple one is equal to the quotient between the number of purple balls (7) and the total number of balls (15)

p₁ = 7/15

Second:

Same as before, notice that because the balls are not replaced, now there are 6 purple balls in the urn, and a total of 14 balls, so in this case the probability is:

p₂ = 6/14

third:

Same as before, this time there are 5 purple balls in the urn and 13 balls in total, so here the probability is:

p₃ = 5/13

The joint probability (the probability of these 3 events happening) is equal to the product between the individual probabilities, so we have:

P = p₁*p₂*p₃ = (7/15)*(6/14)*(5/13)  = 0.08

Answer:

Step-by-step explanation:

Answer:

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60

Step-by-step explanation:

1x120, 2x60, 3x40, 4x30, 5x24, 6x20, 8x15, 10x12, 12x10,15x8, 20x6, 24x5, 30x4, 40x3, 60x2

Answer:

-1.28 AND 2.61

Step-by-step explanation:

[tex]10= -4x+3x^2\\ 3x^2 -4x - 10 = 0\\\\[/tex]

use quadratic formula

x =  [tex]\frac{-b+\sqrt{b^{2} -4ac} }{2a}[/tex]   x =  [tex]\frac{-b-\sqrt{b^{2} -4ac} }{2a}[/tex]

Solution/X-Intercepts: -1.28 AND 2.61    

Answer:

18x^(2)-69x-55

Step-by-step explanation:

dont have the time to rn

Answer:

[tex]{ \bf{(9x + 5) - ( - 2x + 10)(9x + 5) - ( - 2x + 10)}} \\ = { \tt{(9x + 5) - ( - {18x}^{2} + 80x + 50) - ( - 2x + 10)}} \\ = { \tt{(9 - 80 + 2)x + {18x}^{2} + 5 - 50 - 10 }} \\ = { \tt{ {18x}^{2} - 69x - 55}}[/tex]

Consider the below figure attached with this question.

Given:

The transformation is:

[tex]f(x,y)=(-2x,-3y+1)[/tex]

The range is (4,-2), (2, −5), (−6, 4).

To find:

The domain of the transformation.

Solution:

We have,

[tex]f(x,y)=(-2x,-3y+1)[/tex]

For the point (4,-2),

[tex](-2x,-3y+1)=(4,-2)[/tex]

On comparing both sides, we get

[tex]-2x=4[/tex]

[tex]x=\dfrac{4}{-2}[/tex]

[tex]x=-2[/tex]

And,

[tex]-3y+1=-2[/tex]

[tex]-3y=-2-1[/tex]

[tex]-3y=-3[/tex]

[tex]y=\dfrac{-3}{-3}[/tex]

[tex]y=1[/tex]

So, the domain of (4,-2) is (-2,1).

Similarly,

For the point (2,-5),

[tex](-2x,-3y+1)=(2,-5)[/tex]

On comparing both sides, we get [tex]x=-1,y=2[/tex]. So, the domain of (2,-5) is (-1,2).

For the point (-6,4),

[tex](-2x,-3y+1)=(-6,4)[/tex]

On comparing both sides, we get [tex]x=3,y=-1[/tex]. So, the domain of (-6,4) is (3,-1).

So, the domain of the given transformation is (-2, 1), (-1, 2), (3, -1).

Therefore, the correct option is A.

Answer:

This is a Categorical variable and the measurement scale is ordinal scale.

Step-by-step explanation:

The measurement scale that is being used to classify sleep is the ordinal measurement. In this question, the variable that is called sleep quality is a categorical variable. categorical variables are variables that have the data representing groups. sleep quality has been given this categorical order extremely low very low low and extreme high.

The ordinal scale is a scale that denotes order it has all variables in a specific order.

Answer:

The standard error of the distribution of sample proportions is of 0.014.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Consider random samples of size 1200 from a population with proportion 0.65 .

This means that [tex]n = 1200, p = 0.65[/tex]

Find the standard error of the distribution of sample proportions.

This is s. So

[tex]s = \sqrt{\frac{0.65*0.35}{1200}} = 0.014[/tex]

The standard error of the distribution of sample proportions is of 0.014.

Answer:

There are no shortcuts to scaling successfully. It takes just as much — or more — work as it did to start the company in the first place. Take control of the transition. Get organized with tools that support your employees in their day-to-day roles, making it easier for them to get more done as the company grows.

Answer:

A

Step-by-step explanation:

Midpoints are found by averaging the coordinates.

Averaging " add all the numbers and divide by the number of numbers.

Here, there are only 2 numbers. So, you divide by 2.

(1,2) (1,-5)

[tex]\frac{1 +1}{2}[/tex] , [tex]\frac{2 + (-5)}{2}[/tex]

[tex]\frac{2}{2}[/tex] , [tex]\frac{-3}{2}[/tex]

(1, [tex]\frac{-3}{2}[/tex] )

Answer:

LCD????

[tex]2v^2x^3[/tex]

Step-by-step explanation:

Answer:

66 m

Step-by-step explanation:

First, lets add up the numbers you know. It should be:

16, 8, 17, and 7.

Add them all up, and you will get:

48.

For the last two sides, subtract 7 from 16 to get 9.

For the last slide, subtract 8 from 17 to get 9.

Add them all up, and get 66.

Answer: 30 mph is the answer.

Step-by-step explanation:

s = 3 miles

t = 6 minutes

so,

60 minute = 1 hour

1 minute = 1/60 hour

6 minutes = 1/60 * 6 = 0.1 hour

so

average speed = s/t

= 3/0.1 = 30 mph

Answer:

1. 766,536cm^3

2. 29,680,948cm^3

3. 41,620.8cm^3

Step-by-step explanation:

1. 123×82 = 10,086 10,086×76 = 766,536

2. 422×278 = 117,316 117,316×253 = 29,680,948

3. 87×2.3 = 200.1 200.1×208 = 41,620.8

Hope this helps! :)

Answer:72 [tex]cm^{2}[/tex]

Solution 1:

Step 1: Find EF use Pythagorean theorem

[tex]EF^{2} = EB^{2} + BF^{2}[/tex]

[tex]EF^{2} = 6^{2} + 6^{2}[/tex]

EF = [tex]\sqrt{6^{2} + 6^{2} }[/tex] = 6[tex]\sqrt{2}[/tex] cm

Step 2: The area of EFGH = [tex]EF^{2}[/tex]= [tex](6\sqrt{2} )^{2}[/tex] = 72

Solution 2: See that the area of EFGH is equal [tex]\frac{1}{2}[/tex] the area of ABCD

The area of ABCD = 12x12 = 144

Thus, the area of EFGH = 144: 2 = 72:)

Have a nice day!

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Explanation:

The phrasing "no less than" means the same as "at least".

Saying "at least 37" means 37 is the lowest we can go.

If x is the number of disconnected calls, then [tex]x \ge 37[/tex] and we want to find the probability of this happening (the max being 295).

We could use the binomial distribution to find the answer, but that would require adding 295-37+1 = 259 different values which could get tedious. So we could use the normal approximation to make things relatively straight forward.

Assuming this binomial meets the requirements of the normal approximation, then we'd look under the normal curve for the area to the right of 36.5; which is why the answer is choice A.

Why 36.5 and not 37? This has to do with the continuity correction factor when translating from a discrete distribution (binomial) to a continuous one (normal).

If we used 37, then we'd be missing out on the edge case. So we go a bit beyond 37 to capture 36.5 instead. It's like a fail safe to ensure we do account for that endpoint of 37. It's like adding a buffer or padding.

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

Side notes:

Answer:

B. 200 cu. units

Step-by-step explanation:

Volume of the triangular prism = ½*b*h*l

Where,

b = 8 units

h = 5 units

l = 10 units

Plug in the values

Volume of the prism = ½*8*5*10

= 4*5*10

= 200 cu. units

Step-by-step explanation:

There was originally 8 pieces of pie.

Answer:

if you have 3/8 of one pie, the denominator tells you that the pie was divided into 8 piece.

Answer:

The probability of this event is represented by a value of 1.

Step-by-step explanation:

Probability of a certain event:

The probability of an event that is considered to be certain, that is, guaranteed to happen, is 100% = 1.

You are certain to get a heart, diamond, club, or spade when selecting cards from a shuffled deck.

This means that the probability of this event is represented by a value of 1.

Answer:

-10

Step-by-step explanation:

Step-by-step explanation:

hope it helps