What is the number of possible permutations of 6 objects taken 3 at a time?

Answer: The expression 2√2 + √50 is equivalent to 7√2.

Step-by-step explanation: When 2√2 + √50 is added together, the result if 7√2.

Answer:

(4,5)

Step-by-step explanation:

To find the x coordinates of the midpoint, add the x coordinates together and divide by 2

(x1+x2)/2 = (0+8)/2 = 8/2 = 4

To find the y coordinates of the midpoint, add the y coordinates together and divide by 2

(y1+y2)/2 = (2+8)/2 = 10/2 = 5

The midpoint is (4,5)

Answer:

(4,5)

Step-by-step explanation:

Midpoint: (0+8)/2, (2+8)/2

8/2, 10/2

4,5

Answer:

The overall expected grade point average for the semester is 3.16/3.1 or 3.2 if you round it up.

Step-by-step explanation:

To get the average, you need to add up all the numbers then divide the sum by how many numbers you added.

3.5 + 3.0 + 3.0 = 9.5

9.5 / 3 = 3.16

Given Information:

expected grade in two-credit course = 3.5

expected  grade in three-credit course = 3.0

expected grade in four-credit course = 3.0

Required Information:

Expected overall grade point average = ?

Answer:

The expected overall grade point average of this college student is 3.11

Step-by-step explanation:

The overall expected grade point average is given by

E(X) = Sum of grades/Total number of credit hours

Sum of grades = ∑ weightage*expected grades

Sum of grades = 2*3.50 + 3*3.0 + 4*3.0 = 28

Total number of credit hours = 2 + 3 + 4 = 9

E(X) = Sum of grades/Total number of credit hours

E(X) = 28/9

E(X) = 3.11

Therefore, the expected overall grade point average of this college student is 3.11 .

Answer:

[tex] p =\frac{Possible}{Total}[/tex]

Where possible represent the possible cases on this case 5 since we have 5 balls and the total is the size of the sample space on this case 12. And replacing we got:

[tex] p =\frac{5}{12}= 0.417[/tex]

And rounded to the tenths place we got:

[tex] p=0.4[/tex]

And the best answer is:

B. 0.4

Step-by-step explanation:

For this case the size of the sampel space is 5+4+3= 12 representing the total of balls used.

We select a random ball from the total and we want to find the probability of selecting a blue ball. And for this case the can use the empirical definition of probability from Laplace given by:

[tex] p =\frac{Possible}{Total}[/tex]

Where possible represent the possible cases on this case 5 since we have 5 balls and the total is the size of the sample space on this case 12. And replacing we got:

[tex] p =\frac{5}{12}= 0.417[/tex]

And rounded to the tenths place we got:

[tex] p=0.4[/tex]

And the best answer is:

B. 0.4

Answer:

102, 78

Step-by-step explanation:

angle 1= x

angle 2= x-24

x+x-24=180

x=102

x-24=78

102+78=180

The measure of the angles are 102 and 78 degrees

If the difference of two supplementary angles is 24 degrees, then;

x - y = 24

y = x - 24

Taking the sum of the angles and equating to 180 degrees since they are supplementary

x + y = 180

x + x - 24 = 180

2x = 180 + 24

2x = 204

x = 102

Since y = 180 - x

y = 180 - 102

y = 78 degrees

Hence the measure of the angles are 102 and 78 degrees

Learn more on supplementary angles here: https://brainly.com/question/404323

Answer:

[tex]5cm^{3}[/tex]

Step-by-step explanation:

from the formula of cylinder and cone we can see that the volume of a cone is 3 times smaller than that of a cylinder

[tex]volume=\pi r^{2} h[/tex]....................cylinder

[tex]volume= \frac{1}{3} \pi r^{2}h[/tex].................cone

assuming all units in (cm)

Given data.

Volume of cylinder  =  [tex]15cm^{3}[/tex]

Diameter d=  [tex]2cm[/tex]

Radius r =   [tex]\frac{d}{2}[/tex][tex]= \frac{2}{2} = 1cm[/tex]

Height h=  ??

we know that the expression for the volume of a cylinder is

[tex]volume=\pi r^{2} h[/tex]

we can substitute our given data to find the height h

[tex]15= 3.142*1^{2}*h\\15= 3.142h[/tex]

divide both side by 3.142 we have

[tex]h= \frac{15}{3.142}\\ h= 4.77cm[/tex]

We can now use this height[tex]4.77cm[/tex] and radius [tex]1cm[/tex] to find the equivalent  volume of a cone.

the expression for the volume of a cone is

[tex]volume= \frac{1}{3} \pi r^{2}h[/tex]

substituting our data into the expression  we have

[tex]volume= \frac{3.142*1^{2*} 4.77}{3} \\volume= \frac{15}{3} \\voulume = 5cm^{3} \\[/tex]

Answer: I think the answer is 3.

Step-by-step explanation:

Kim's team scored the same number of innings to win the game and Kim's team already had 6 points so four times a number has to be greater than 17.

4* 3 + 6= 18

which means the minimum number can't be less than three so they may have scored three or more points in  each of the four innings that was left.

Answer:

x = 0

Step-by-step explanation:

[tex]\frac{1}{3} x+\frac{3}{10}x=0[/tex]

x = 0

Answer:4

Step-by-step explanation:

464565=753

Answer:

5 hours

Step-by-step explanation:

5.6 all you have to use is .6 times 5hours to make 3kmapart

Answer:

d

Step-by-step explanation:

did da math

Answer:

The mode is gymnastics

Step-by-step explanation:

The mode of a data set is the number that occurs most frequently in the set. To easily find the mode, put the numbers in order from least to greatest and count how many times each number occurs. The number that occurs the most is the mode!

hope his helps!!!!!!!!!!!!

Answer: 20 quarts of peanut oil worth 19 cents a quart must be mixed.

Step-by-step explanation:

Let x represent the number of quarts of peanut oil worth 19 cents a quart that would be in the mixture.

The total number of quarts in the mixture would be x + 100

The cost of the x quarts would be x × 19 = 19x cents

The cost of 100 quarts of the other peanut oil would be 25 × 100 = 2500 cents

The cost of the mixture would be

24(x + 100) = 24x + 2400

Therefore, the equation would be

19x + 2500 = 24x + 2400

24x - 19x = 2500 - 2400

5x = 100

x = 100/5

x = 20

Answer:

20 quarts

Step-by-step explanation:

Answer:

166 legos are required

Step-by-step explanation:

In this case, let's analyze the data. We need 3 trophies, using at most 324 legos in total. The big trophy requires 220 legos, the smallest requires 135, so we need to know how much will be used in the medium trophy. This number should be 135 < X < 220

Now, if we know that the total legos to be used are 324, then, we can make a difference and sum for all the legos, and then, calculate the number of legos used.

Total legos = A + B + C

324 = 220 + 135 + C

324 = 355 + C

C = -31

This means that there is difference of 31 legos between the smallest and biggest trophy, therefore, this difference should be used and added to the smallest trophy and see how much Tristen use in the final trophy:

135 + 31

= 166 legos

So we need to use 166 legos to build the final trophy.

Answer:

he already used 355 so 166

Step-by-step explanation:

Answer:

about 225-250 million years:

Answer:

0.1 probability of Matt picking a red fish

6 of the fish are red.

Step-by-step explanation:

We have these following probabilities:

70% = 0.7 probability that the fish is blue.

20% = 0.2 probability that the fish is green.

p probability that the fish is red.

The sum of all these probabilities is 100% = 1. So

0.7 + 0.2 + p = 1.

p = 0.1

0.1 probability of Matt picking a red fish

There are 60 fish in the fish bowl. How many of the fish are red?

n trials with p probability of sucess. The expected value is

[tex]E(X) = np[/tex]

Here we have [tex]n = 60, p = 0.1[/tex]. So

[tex]E(X) = np = 60*0.1 = 6[/tex]

6 of the fish are red.

The probability of Matt at the time of picking a red fish is 0.1.

And, The number of fish that should be red is 6.

Since

There is a 70% probability when the fish is blue

And, 20% probability when the fish is green.

Now

Here we assume p be the probability in the case when the fish is red.

So,

Here the sum of probabilities should be 100% i.e. equal to 1.

Now

The following calculation is to be done

0.7 + 0.2 + p = 1

0.9 + p = 1

So,

p = 0.1

Now for the red one it should be

= 60 (0.1)

= 6

Hence, The probability of Matt at the time of picking a red fish is 0.1.

And, The number of fish that should be red is 6.

Learn more about probability here: https://brainly.com/question/10695144

Answer:

Option A. The volume of the sphere is multiplied by 1/343.

Step-by-step explanation:

The volume of a sphere can be obtained by the following formula:

V = 4/3πr^3

Let the initial volume (V1) of the sphere be:

V1 = 4/3πr^3 = (4πr^3)/3

Now, if we multiply the radius by 1/7, then the new volume (V2) of the sphere will be:

V2 = 4/3 x π x (1/7r)^3

V2 = 4/3 x π x 1/343r^3

V2 = (4πr^3)/1029

Now we determine the ratio of V2 : V1 as shown below:

V2/V1 = (4πr^3)/1029 ÷ (4πr^3)/3

V2/V1 = (4πr^3)/1029 × 3/(4πr^3)

V2/V1 = 3/1029

V2/V1 = 1/343

V2 = 1/343 x V1

Therefore, the volume of the sphere is multiplied by 1/343.

Answer:

The roles can be assigned in 15120 ways.

Step-by-step explanation:

The parts, which means that the order in which the people are selected is important. So we use the permutations formula to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

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

In this question:

5 people chosen from a set of 9. So

[tex]P_{(9,5)} = \frac{9!}{(9-5)!} = 15120[/tex]

The roles can be assigned in 15120 ways.

Answer:

162

Step-by-step explanation:

54 * 3 = 162

hope it's helpful

Answer:

162

Step-by-step explanation:

54 x 3 = 162

54+ 54+ 54= 162

Answer:

[tex]P(X = 3) = C_{7,3}.(0.7)^{3}.(0.3)^{4} = 0.0972[/tex]

Step-by-step explanation:

For each day there are only two possible outcomes. Either it rains, or it does not. The probability of rain on a day is independent of any other day. So we use the binomial probability distribution 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.

In a state park where the probability of rain on any given day is 0.7.

This means that [tex]p = 0.7[/tex]

Which expression can be used to find the probability that it will rain on exactly 3 of the seven days they are there

We have to find [tex]P(X = 3)[/tex] when [tex]n = 7[/tex]

So

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

[tex]P(X = 3) = C_{7,3}.(0.7)^{3}.(0.3)^{4} = 0.0972[/tex]

Hello!

[tex]\boxed{ \bf The~approximate~area~of~the~circle~is~D.~380~m^2}[/tex]

___________________________________________

We must use a certain formula to find the area of a circle.

A = πr²

Let's plug in the radius.

A = π × 11²

A = π × 121

A = 380

Step-by-step explanation:

the length s of the arc AC is given as :

s = r. 0

where

r = 10 is radius

0 = 90°

= π/2 rad is angle

s = 10. π/2

= 5π

= 5.3.14

= 15.7 ~ 16

Answer:

Radius, r = 10.64 m

Step-by-step explanation:

The formula of a spherical shaped object is given by :

[tex]V=\dfrac{4}{3}\pi r^3[/tex]

r is radius of a sphere

[tex]r=(\dfrac{3V}{4\pi })^{1/3} \\\\r=(\dfrac{3\times 5044}{4\times 3.14 })^{1/3} \\\\r=10.64\ m[/tex]

So, the radius of a sphere is 10.64 m.

Answer:

5x -20

Step-by-step explanation:

p(x) = r(x) - c(x)

      = 11x - (6x+20)

Distribute the minus sign

     = 11x -6x -20

Combine like terms

     = 5x -20

Answer:

x=7

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

12 bars --- 2 boxes

42 bars --- x boxes

x = 42*2/12 = 7

Answer:-8

Step-by-step explanation: you add -1+ -1, to get -2, then -2+-2, to get -4 and so forth.

The missing term is -8.

The complete sequence is –1, –2, –4, -8, –16, –32.

A unique kind of sequence called a geometric sequence has a constant ratio between every two succeeding terms. This ratio is regarded as one of the geometric sequence's common ratios.

aₙ=a₁(r)ⁿ⁻¹

Given:

–1, –2, –4, ?, –16, –32.

The sequence is a geometric sequence.

So, we will find the common ratio,

r = -2/-1 = 2

The general formula of geometric sequence,

aₙ = a₁(r)ⁿ⁻¹

a₄ = (-1)(2)⁴⁻¹

a₄ = (-1)(8)

a₄ = -8

Therefore, the missing term is -8.

To learn more about the geometric sequence;

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Answer:

Isosceles

Step-by-step explanation:

An isosceles triangle is a triangle in which the length of at least two sides are same.

The triangle which Seth has two sides of same length that is 20 inches.

Third side is different.

Hence. the triangle which Seth has is  isosceles.

Answer:

[tex]a_{n} = 27 - 3(n-1)[/tex]

Step-by-step explanation:

Arithmetic sequences concepts:

The general rule of an arithmetic sequence is the following:[tex]a_{n+1} = a_{n} + d[/tex]

In which d is the common diference between each term.

We can expand the general equation to find the nth term from the first, by the following equation:

[tex]a_{n} = a_{1} + (n-1)*d[/tex]

And also:

[tex]a_{n} = a_{m} + (n-m)*d[/tex]

In this question:

[tex]a_{4} = 18, a_{7} = 9[/tex]

Finding the common ratio:

[tex]a_{n} = a_{m} + (n-m)*d[/tex]

[tex]a_{7} = a_{4} + (7-4)*d[/tex]

[tex]9 = 18 + 3d[/tex]

[tex]3d = -9[/tex]

[tex]d = \frac{-9}{3}[/tex]

[tex]d = -3[/tex]

Finding the first term:

[tex]a_{4} = a_{1} + (4-1)*d[/tex]

[tex]18 = a_{1} + 3*(-3)[/tex]

[tex]a_{1} = 27[/tex]

General rule:

[tex]a_{n} = a_{1} + (n-1)*d[/tex]

[tex]a_{n} = 27 - 3(n-1)[/tex]

Answer:

1) There is enough evidence to support the claim that the average hospital stay for men is longer than the average hospital stay for women. (P-value = 0.00051).

2) zc=2.33

Step-by-step explanation:

1) This is a hypothesis test for the difference between populations means.

The claim is that the average hospital stay for men is longer than the average hospital stay for women.

Then, the null and alternative hypothesis are:

H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2> 0

The significance level is 0.01.

The sample 1, of size n1=37 has a mean of 5.6 and a standard deviation of 1.2.

The sample 2, of size n2=35 has a mean of 4.5 and a standard deviation of 1.6.

The difference between sample means is Md=1.1.

[tex]M_d=M_1-M_2=5.6-4.5=1.1[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{1.2^2}{37}+\dfrac{1.6^2}{35}}\\\\\\s_{M_d}=\sqrt{0.039+0.073}=\sqrt{0.112}=0.335[/tex]

Then, as we know the population standard deviation of both, we can calculate the z-statistic as:

[tex]z=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{1.1-0}{0.335}=\dfrac{1.1}{0.335}=3.29[/tex]

This test is a right-tailed test, with z=3.29, so the P-value for this test is calculated as:

[tex]P-value=P(z>3.29)=0.00051[/tex]

As the P-value (0.00051) is smaller than the significance level (0.01), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the average hospital stay for men is longer than the average hospital stay for women.

2. The critical values for this right tail test are calculated from the z-table and the significance level (α=0.01)

[tex]P(z>z_c)=0.01[/tex]

This happens for zc=2.33:

[tex]P(z>2.33)=0.01[/tex]