The amounts of time per workout an athlete uses a stairclimber are normally​ distributed, with a mean of 24 minutes and a standard deviation of 7 minutes. Find the probability that a randomly selected athlete uses a stairclimber for​
(a) less than 19 ​minutes,
(b) between 24 and 33 ​minutes, and​
(c) more than 40 minutes.

Which event is unusual?

Answer:

  360π

Step-by-step explanation:

Put the given numbers in the volume formula and do the arithmetic.

  V = πr²h . . . . . r is the radius; h is the height

  V = π(6²)(10)

  V = 360π

The volume is 360π cubic units.

Answer:

X=0 and Y= 4(2i-1)/5

Step-by-step explanation:

Here is my solution, assuming that the equation equals 0. For y, just remember the definition of complex numbers and multiply by its conjugate.

The value of x and y are -8/7 and -4 respectively if (x + yi) + 2(3x - y) + 4i = 0.

It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.

We have a complex number:

(x + yi) + 2(3x - y) + 4i = 0

After arranging:

x + yi + 6x - 2y + 4i = 0

7x - 2y + yi + 4i = 0

7x - 2y + (y + 4)i = 0

7x - 2y = 0

y + 4 = 0

This is the linear equation in two variables:

Plug y = -4 in the other equation:

7x - 2(-4) = 0

7x = -8

x = -8/7

y = -4

Thus, the value of x and y are -8/7 and -4 respectively if (x + yi) + 2(3x - y) + 4i = 0.

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Answer: angle A = 72 and angle C = 72

Step-by-step explanation:

Angle A and C are opposites so they have to equal each other so do the equation 3y+27=5y-3. y would come out to be 15 and so to find the angles you would replace y with 15.

Answer:

8.62% probability that all have the same color

Step-by-step explanation:

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

The order in which the marbles are selected is not important. So we use the combinations formula to solve this question.

Combinations formula:

[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]

What is the probability that all have the same color?

Desired outcomes:

Either all red(from a set of 9), all white(from a set of 9) or all blue(from a set of 8). So

[tex]D = C_{9,3} + C_{9,3} + C_{8,3} = \frac{9!}{3!6!} + \frac{9!}{3!6!} + \frac{8!}{3!5!} = 224[/tex]

Total outcomes:

3 marbles, from a set of 9 + 9 + 8 = 26. So

[tex]T = C_{26,3} = \frac{26!}{3!23!} = 2600[/tex]

Probability:

[tex]p = \frac{D}{T} = \frac{224}{2600} = 0.0862[/tex]

8.62% probability that all have the same color

Answer:

The axis of symmetry is  -b/2a

The x-intercept shown is 3 units away from the axis of symmetry.

The other x-intercept also must be 3 units away from the axis of symmetry but on the opposite side.

Subtract 3 from the axis of symmetry.

The other x-intercept is  (-b/2a-3,0)

Step-by-step explanation:

Answer:

60y

where y is the number of houses each volunteer can build

Step-by-step explanation:

I'll assume this is a complete question and i'll try to solve it the best way i can mathematically.

Let us assume that one volunteer can build a certain number of houses, say y houses.

Also, it is stated that the amount of houses that can be built varies directly as the with the number of volunteers. Therefore, it will be mathematically logical to say that if 1 volunteer can build y number of houses, then 60 volunteers will build 60y houses

Answer:

5 km.

Step-by-step explanation:

We have to calculate the distance if we apply the speed formula that would be the distance in a given time:

v = d / t

therefore, if we solve for distance it would be:

d = v * t

Now the speed is 6 km / h but the time must be calculated, it leaves at 9:15 and returns at 10:05, that is, there is no exact time but 50 minutes, one hour equals 60 minutes, therefore:

50 min * 1 h / 60 min = 0.833 h, that is, the child took 0.833 hours to get to school, now if we replace:

d = 6 * 0.8333

d = 5

In other words, the distance between the school and the house is 5 km.

Answer: 133 m^2

Step-by-step explanation:

The area of the parallelogram is:

[tex]A = b\times h=9.5\times14=133 m^2[/tex]

Answer:

Step-by-step explanation:

The probability that the forester does not get the seedlings is 1/2 if the mean density of seedlings is 5 per square metre.

Density means the area within which a substance is collected or taken.

We have been given the mean density =5 square metre.

And we  have to calculate the probability that the forester will not get any seedlings.

So the probability that he will get the seedlings will be=5/10

which is 1/2

So the probability that he will not get the seedlings will be 1-1/2

that is 1/2.

Hence the probability that he will not get seedlings will be 1/2.

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Answer:

Step-by-step explanation:

Since; the density function diagrams were not included in the question; we will be unable to determine the  best which depicts this problem.

However;

Let use X to represent the time required for the delivery.

Then X~N(3.8 ,0.8)

i.e

E(x) = 3.8

s.d(x) = 0.8

NOW; P(x>4) = P(X-3.8/0.8 > 4-3.8/0.8)

= P(Z > 0.25)

= 1-P(Z < 0.25)

=1 - Φ (0.25)

= 1 - 0.5987  ( from Normal table  Φ (0.25) = 0.5987 )

= 0.4013

Thus;  the probability a single delivery would take more than 4 hours is 0.4013

What is the z value corresponding to the interval boundary?

The z value is calculated as:

[tex]z = \dfrac{X- \mu}{\sigma}[/tex]

[tex]z = \dfrac{4- 3.8}{0.8}[/tex]

z = 0.25

Answer:

The standard error of the proportion is 0.0367.

Step-by-step explanation:

The Central Limit Theorem estabilishes 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 standard error is [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

In this question:

[tex]p = 0.16, n = 100[/tex]

So

[tex]s = \sqrt{\frac{0.16*0.84}{100}} = 0.0367[/tex]

The standard error of the proportion is 0.0367.

Answer:

m = 3

Step-by-step explanation:

Assuming these shapes are similar, you can set up a proportion:

[tex]\frac{8}{12} =\frac{2}{m}[/tex]

→Cross multiply:

[tex]\frac{8m}{24}[/tex]

→Divide 24 by 8:

m = 3

Answer:

  x^2 +16 is prime

Step-by-step explanation:

A prime polynomial is one that cannot be factored using integers.

Answer:

I got 35

Step-by-step explanation:

Answer:

40 minutes

Step-by-step explanation:

Let's take the average playing time as u, and let the standard deviation be [tex] \sigma [/tex].

Thus,

[tex] u = 34 [/tex]

[tex] \sigma = 6 [/tex]

To find the value of 1 standard deviation above the mean, we have:

[tex] u + 1\sigma [/tex]

Since u = 34 minutes and [tex]1\sigma [/tex] = 6 minutes, we now have:

[tex] = 34 + 6 = 40 [/tex]

The value (in minutes) of 1 standard deviation above the mean is 40 minutes.

Answer:

40 minutes

Step-by-step explanation:

Given that:

The average time playing time of compact disc in a large collection= 34 minutes and the standard deviation = 6 minutes.

Let [tex]\mu[/tex] represent the average playing time and [tex]\sigma[/tex] to be the standard deviation.

So;

[tex]\mu = 34 \\ \\ \sigma = 6[/tex]

The value for 1 standard deviation above the mean is;

[tex]x+1 s= 34+6 \\ \\ = 40[/tex]

Answer:

35

Step-by-step explanation:

Given

Sample of rat

Population = 36

Required

Find the degree of freedom.

Given that the sample is a single-sample t test;

A single-sample t test has just one parameter has its estimate;

And its degree of freedom is calculated as thus;

[tex]df = n - 1[/tex]

Where df represents the degree of freedom and n represents the sample size;

By substituting n = 36;

[tex]df = 36 - 1[/tex]

[tex]df = 35[/tex]

Hence, the degree of freedom of the sample of 36 rats for a single-sample t test is 35

Answer:

The degrees of freedom if we are conducting a test about the true mean are given by:

[tex] df =n-1[/tex]

And replacing the info given we got:

[tex] df = 36-1=35[/tex]

And the best option would be:

35

Step-by-step explanation:

For this case we know that the sample size is n=36.

The degrees of freedom if we are conducting a test about the true mean are given by:

[tex] df =n-1[/tex]

And replacing the info given we got:

[tex] df = 36-1=35[/tex]

And the best option would be:

35

Answer:

Step-by-step explanation:i really am lost,

The work rate for the associate is 5.3 hours.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Given; Jane can paint the office by herself in 7 hours.

with an associate, she can paint the office in 3 hours.

The combined work rate is 3 hours per office.

WE need to find the work rate for the associate

Let the expression for the work rate be;

1/A+1/B= 1/T

1/7+1/B=1/3

1/B=1/3-1/7

1/B= 8-4/21

1/B= 4/21

B= 21/4

B=5.3 hours

Therefore, the work rate for the associate is 5.3 hours.

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Answer:

18

Step-by-step explanation:

Do 72 divided by 4 because it is a square so all sides are equal

Hiya! ✌.ʕʘ‿ʘʔ.✌

Okay, so with a square, ALL sides are EQUAL.

To find the perimeter of a shape, you just need to add the measure of all sides together.

What you can do, is since all sides are equal, and a square has four sides, just get the measure of ONE side and multiply that by 4! (ﾉ◕ヮ◕)ﾉ*:･ﾟ✧

The perimeter is 72 meters and if we find the value of u, we get the value of all sides.

Let's set this up as an equation:

P = 4u where P = perimeter and u = measure of one side

Let's insert the given value (72) into the equation for perimeter

72 = 4u

Now we have to solve for u, and to do that, we have to get it by itself on that side of the equation. u is being multiplied by 4, so do the opposite by dividing both sides of the equation by 4!

72/4=18

4u/4=u

Now our equation looks like this:

18 = u

So the value of u is 18! (✿◠‿◠)

To prove it, insert it into the formula... P = 4(18)... P = 72.

Boom! :D

Have a lovely day~ ≧◡≦

Answer:

The three numbers are 1, 2, and 4.

Step-by-step explanation:

[tex]x+y+z=7\\3x+1=z\\z+x=5[/tex]

From these equations, we get:

[tex]x=1\\y=2\\z=4[/tex]

Which fits all the equations we have written.

Answer:

a.

Network             CBS   NBC   FOX   ABC

f                           9          9         1           6

Relative f          0.36     0.36    0.04     0.24

Percent f            36          36       4          24

b.

CBS and NBC have done best in presenting top-rated television shows.

The most top rated shows are from CBS and NBC while ABC network also has top rated shows but CBS and NBC percentages are higher.

Step-by-step explanation:

a.

Network        f Relative f  Percent f

CBS          9         0.36 36

NBC       9         0.36 36

FOX        1         0.04 4

ABC       6         0.24 24

"f" represents the frequency of network.

"Relative  f" represents relative frequency of Network.

"Percent f" represents percent frequency of Network.

Frequency is computed by counting the number of times value repeated in the data. So, the frequency distribution is

Network  Frequency

CBS         9

NBC         9

FOX         1

ABC         6

Relative frequency is computed by dividing the frequency to the sum of frequencies.

sum of frequencies=9+9+1+6=25.

So, the relative frequency distribution is

Network  Relative frequency

CBS          9/25=0.36

NBC         9/25=0.36

FOX         1/25=0.04

ABC         6/25=0.24

Percent frequency is computed by multiplying relative frequencies to 100.

So, the Percent frequency distribution is

Network    Percent frequency

CBS             0.36*100=36

NBC             0.36*100=36

FOX             0.04*100=4

ABC             0.24*100=24

b.

From frequencies, relative frequencies and percent frequencies we can see the CBS and NBC have equally higher cont of top rated shows comparative to ABC and  FOX. ABC has second highest top rated shows while Fox has least top rated shows among other networks.

Answer:

A.

Step-by-step explanation:

Since VA and BC are equal in length so their central angles would also be equal.

So

<VWA = <BWC

32x-27 = 120

32x = 120+27

32x = 147

Dividing both sides by 32

x ≈ 4.6

Answer:

4.6

Step-by-step explanation:

3x-27=120

32x=147

x=147/32

x=4.59

x≈4.6

Answer:

Since Interquartile Range consider the middle values in the data set, i.e. 50%, it is not affected by outliers or extreme values. While other statistics mean, standard deviation and range are all affected by outliers or extreme values.

Step-by-step explanation:

hope this helps you :) can you help me please northc04 :(

Answer:

The answer is Interquartile Range. I know this is the right answer is because I got it right on a quiz.

Answer:

-3

Step-by-step explanation:

5-8

-3

Answer:

=-3

Step-by-step explanation:

we have to find the difference when 8 is subtracted from 5

difference=5-8

the digit after from will come first

=-3

i hope it will help you

Answer:

2 doughnut boxes

Step-by-step explanation:

6+6=12

12=1 box

and the other 3 can go in a different box which would be 2 boxes

Answer:

76 % of babies will be born out of​ wedlock in the [tex]81^{st}[/tex] year

Step-by-step explanation:

Given:  In​ 1990, 28 % of babies in the United States were born to parents who were not married. This increased by approximately 0.6 % per year.

To find: year when 76 % of babies born out of​ wedlock

Solution:

A sequence is said to be in arithmetic progression if the difference between the terms is same.

For a sequence with first term as 'a' and common difference as 'd', the nth term is given by [tex]a_n=a+(n-1)d[/tex]

The given situation also forms an arithmetic progression with  [tex]a=28\,,\,d=0.6[/tex]

Also, put [tex]a_n=76[/tex]

So,

[tex]a_n=a+(n-1)d\\76=28+(n-1)(0.6)\\76-28=0.6(n-1)\\48=0.6(n-1)\\\frac{48}{0.6}=n-1\\\\80=n-1\\n=80+1\\n=81[/tex]

So, 76 % of babies will be born out of​ wedlock in the [tex]81^{st}[/tex] year

Answer:

D = 24 units

Step-by-step explanation:

Using Distance Formula

Distance Formula = [tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]

D = [tex]\sqrt{(1-25)^2+(-3+3)^2}[/tex]

D = [tex]\sqrt{(-24)^2+(0)^2}[/tex]

D = [tex]\sqrt{576}[/tex]

D = 24 units

Answer:

24

Step-by-step explanation:

Y is 60% of 40

Equation: Y = P% * X

Solving our equation for Y

Y = P% * X

Y = 60% * 40

Converting percent to decimal:

p = 60%/100 = 0.6

Y = 0.6 * 40

Y = 24