what is the prime factorization of 55^5 x 65 x 9^15 and why? A. 3^15 * 5^6 *11^5*13 B. 3^30 *5^6 *11^5 *13 C.3^30 * 5^6 *11 * 13 D. 3^30 *5^5*11^5*13

Answer:

If something is guaranteed, it has a probability of 100%, or 1.

Step-by-step explanation:

A standard deck has 52 cards. Of these, half are red cards (diamonds and hearts) and half are black cards (clovers and spades)

Half of the deck is 26 cards (52 ÷ 2 = 26), so you have 26 red and 26 black cards.

What this means in our context is, if we draw 27 cards, even if we drew all 26 black cards, we would still have 1 red card.

So the probability is 100%, or 1, of drawing a red card when we pick 27 cards from a deck, no matter how it's shuffled

The probability of getting a red card is 1.

No matter how you shuffle the cards, the no of cards will remain the same.

Therefore, it will not affect the probability.

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

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Answer:

A

Step-by-step explanation:

Answer:

Children = 150

Students = 98

Adults = 75

Step-by-step explanation:

C + S + A = 323

5C + 7S + 12A = 2336

A = 1/2C

C = 150

S = 98

A = 75

Answer:

a feature of the universe

Step-by-step explanation:

Math is a feature of the universe because what we call math is just a way of explaining how things work.

Answer:

d. An optimal solution to linear programming problem can be found at an extreme point of the feasible region for the problem.

Step-by-step explanation:

A feasible solution satisfies all the constraints of the problem in linear programming. The constraints are the restrictions on decision variable. They limit the value of decision variable in linear programming. Optimal solutions occur when there is feasible problem in the programming.

Answer:

4

Step-by-step explanation:

Plug in 3 as x in the expression:

10 - 2x

10 - 2(3)

10 - 6

= 4

Answer:

4

Step-by-step explanation:

10 - 2x

Let x =3

10 -2(3)

10 -6

4

Answer:

Step-by-step explanation:

Given the total number of students in the school to be 2229 students. If among a sample of 452 students from this school district, 163 have mathematics scores below grade level, then we can determine the number of students in this school district with mathematics scores below grade level based on the sample scores using ratio.

Let the number of students in this school district with mathematics scores below grade level be x. The ratio of the students with math score below grade level to total population will be x:2229

Also, the ratio of the sample students with math score below grade level to sample population will be 163:452

On equating both ratios, we will have;

x:2229 =  163:452

[tex]\dfrac{x}{2229} = \dfrac{163}{452}\\ \\cross\ multiplying;\\\\\\452*x = 2229*163\\\\x = \dfrac{2229*163}{452}\\ \\x = \frac{363,327}{452}\\ \\x = 803.8\\\\x \approx 804[/tex]

Hence the estimate of the number of students in this school district with mathematics scores below grade level based on the sample is 804

Answer:

Step-by-step explanation:

xy = 2y + xy = 0

Hence, 2y + xy = 0 ---------(1)

Differentiating equation (1) n times by Leibnitz theorem, gives:

2y(n) + xy(n) + ny(n - 1) = 0

Let x = 0: 2y(n) + ny(n - 1) = 0

2y(n) = -ny(n - 1)

∴ y(n) = -ny(n - 1)/2 for n ≥ 1

For n = 1: y = 0

For n = 2: y(1) = -y

For n = 3: -3y(2)/2

For n = 4: -2y(3)

Answer:

1.86

Step-by-step explanation:

Given the following :

X : - - - - 0 - - - - 1 - - - - 2 - - - - - 3 - - - - 4

P(x) - 0.37 - - 0.28 - - 0.22 - - 0.22 - - 0.12

The mean of the distribution can be calculated by evaluated by determining the expected value of the distribution given that the data above is a discrete random variable. The mean value can be deduced multiplying each possible outcome by the probability of it's occurrence.

Summation of [P(x) * X] :

(0.37 * 0) + (0.28 * 1) + (0.22 * 2) + (0.22 * 3) + (0.12 * 4)

= 0 + 0.28 + 0.44 + 0.66 + 0.48

= 1.86

Answer:

The answer is 18 feet

Step-by-step explanation:

To find the diameter of a circle given it's radius we use the formula

diameter = radius × 2

From the question

radius = 8

So the diameter is

Hope this helps you

Answer:

18

Step-by-step explanation:

Hey there!

Well radius is half the diameter so,

D = r*2

Plug in 9

D = 9*2

D = 18

Hope this helps :)

Answer:

12.5 minutes

Step-by-step explanation:

When working together,It takes two computers 10 minutes to send out an email

It takes the slower computer 50 minutes to send out an email

Let x represent the time taken by the faster computer to do the job in its own

Therefore, the time required by the faster computer can be calculated as follows

1/x + 1/50= 1/10

Collect the like terms

1/x= 1/10-1/50

1/x= 4/50

Cross multiply both sides

4 × x = 50×1

4x=50

Divide both sides by the coefficient of x which is 4

4x/4=50/4

x= 12.5

Hence the time taken by the faster computer to finish the job on its own is 12.5 minutes

Hey there! I'm happy to help!

When graphing a system of equations, the solution is the point where the two lines meet. We see that they intersect at (-2,4).

Therefore, the solution to the system of equations is (-2,4).

Have a wonderful day! :D

Answer:

A

Step-by-step explanation:

edge 2020 Dec 9

Answer:

10

Step-by-step explanation:

Solution 1: At first, you might think that because there are 5 ways to choose the first store and 4 ways to choose the second store, the answer is 5 * 4 = 20 but this is over-counting by a factor of 2. Say that two of the stores are A and B. If she went to A then B, that's the same as going to B then A since you still go to the same stores, therefore, the answer is 20 / 2 = 10.

Solution 2: We need to find the number of ways to choose 2 stores from 5, we can do this by calculating ₅C₂ which equals:

5! / 2!  * 3!

= 5 * 4 * 3 * 2 * 1 / 2 * 1 * 3 * 2 * 1

= 5 * 4 / 2 * 1

= 10

1: 8 faces and 9 with the base 9 vertices and 16 edges

2: 3 faces and 5 with the bases 6 vertices and 9 edges

3: 3 faces and 4 with the base 4 vertices and 6 edges

Hope this can help you.

1: 8 faces and 9 with the base 9 vertices and 16 edges

2: 3 faces and 5 with the bases 6 vertices and 9 edges

3: 3 faces and 4 with the base 4 vertices and 6 edges

Answer:

(d-4)(c-9)

Step-by-step explanation:

cd-9d-4c+36

d(c-9)-4(c-9)

pull out the (c-9),

(d-4)(c-9)

Answer:

A. 9

C. 16  

E. 169

F. 625

Step-by-step explanation:

First pair of equations :

[tex]\dfrac{1}{2}x+y=15\ ..(i)\\\\-x-\dfrac{1}{3}y=-6\ ..(ii)[/tex]

Multiply 2 to equation (i), we get

[tex]x+2y=30\ ..(iii)[/tex]

By Elimination Method, Add (i) and (ii) (term with x eliminate), we get

[tex]2y-\dfrac{1}{3}y=30-6\\\\\Rightarrow\ \dfrac{5}{3}y=24\\\\\Rightarrow\ y=\dfrac{24\times3}{5}=14.4[/tex]

put y= 14.4 in (iii), we get

[tex]x+2(14.4)=30\Rightarrow\ x=30-28.8=1.2[/tex]

hence, x=1.2 and y =14.4

Second pair of equations :

[tex]\dfrac{5}{6}x+\dfrac13y=0\ ..(i)\\\\ \dfrac12x-\dfrac{2}{3}y=3\ ..(ii)[/tex]

Multiply 2 to equation (i), we get

[tex]\dfrac{5}{3}x+\dfrac{2}{3}y=0\ ..(iii)[/tex]

Elimination Method, Add (i) and (ii) (term with y eliminate) , we get

[tex]\dfrac53x+\dfrac12x=3\Rightarrow\ \dfrac{10+3}{6}x=3\\\\\Rightarrow\ \dfrac{13}{6}x=3\\\\\Rightarrow\ x=\dfrac{18}{13}[/tex]

put [tex]x=\dfrac{18}{13}[/tex]   in (i), we get

[tex]\dfrac{5}{6}(\dfrac{18}{13})+\dfrac{1}{3}y=0\\\\\Rightarrow\ \dfrac{15}{13}+\dfrac{1}{3}y=0\\\\\Rightarrow\ \dfrac{1}{3}y=-\dfrac{15}{13}\\\\\Rightarrow\ y=-\dfrac{45}{13}[/tex]

hence, [tex]x=\dfrac{18}{13}[/tex]   and [tex]y=\dfrac{-45}{13}[/tex] .

Answer: 0.584

Step-by-step explanation:

We have:

5 discs

6 jump ropes

3 balls

12 pieces of sidewalk.

5 + 6 + 3 + 12 = 26

If all of them have exactly the same probability of being removed, then:

in the first selection, we do not want to remove a jump rope, so we can remove one disc, one ball or one piece of sidewalk.

The total number of those objects is:

5 + 3 + 12 = 20.

Then the probability of removing one of those objects is:

P1 = 20/26 = 0.769

Now in the second selection, we have the same situation, but now we have 25 objects in total, and because in the previous selection we removed one ball, or one disc, or one piece of sidewalk, the total number of these things now is 19.

So the probability of removing another object of that set is:

P2 = 19/25 = 0.76

The joint probability is equal to the product of the individual probabilities, so we have:

P = P1*P2 = 0.769*0.76 = 0.584

Answer: It's B

Step-by-step explanation:

The table that represents the double number line is (b)

On the double number line, we have the following points

x: 0    1

y: 0    25

This means that as x increases by 1, y increases by 25.

So, we have:

x: 0  1    2    3   4

y: 0 25  50 75 100

The above is represented by the second table

Hence, the table that represents the double number line is (b)

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[tex]2.232\approx2.32[/tex]

Answer:

32.5%

Step-by-step explanation:

Hey there!

To find the probability we first need to find the amount of prime numbers in the 1-40 set.

Prime - 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37

That’s 13 prime numbers.

Fraction - 13/40

Simplified is just 13/40.

13 / 40 = .325

Percent - 32.5%

Hope this helps :)

Complete Question

It has been found that 26% of men 20 years and older suffer from hypertension (high blood pressure) and 31.5% of women are hypertensive. A random sample 150 of each gender was selected from recent hospital records, and the following results were obtained.

Men. 43 patients had high blood pressure

Woman. 52 patients had high blood pressure.

Answer:

The  95% confidence interval is  

      [tex]- 0.1651 < p_m - p_f <0.0451[/tex]

This mean that there is a 95 % confidence that the difference between the true proportions of male and  female that are hypertensive  is within this interval and given that the interval contains zero then there is no statistically significant difference between the genders that are hypertensive        

Step-by-step explanation:

From the question we are told that

    The  sample size for male is  [tex]n_1 = 150[/tex]

    The  number of male that are hypertensive is  [tex]m = 42[/tex]

    The  sample size of female is  [tex]n_2 = 150[/tex]

     The  number of female that are hypertensive is [tex]q = 52[/tex]

The proportion of male that are hypertensive is mathematically represented as

         [tex]\r p_m = \frac{43}{150}[/tex]

         [tex]\r p_m = 0.287[/tex]          

The proportion of female that are hypertensive is mathematically represented as

       [tex]p_f = \frac{52}{150}[/tex]

      [tex]p_f = 0.347[/tex]

From the question we are told that confidence level is 95%, hence the level of significance is mathematically represented as

       [tex]\alpha = 100 -95[/tex]

      [tex]\alpha =5\%[/tex]

     [tex]\alpha =0.05[/tex]

Next we obtain the critical value of  [tex]\frac{ \alpha }{2}[/tex] from  the normal distribution table, the value is  

           [tex]Z_{\frac{ \alpha }{2} } = 1.96[/tex]

Generally the margin of error is mathematically represented as

          [tex]E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{ \r p_m (1- \r p_m )}{n_1} + \frac{ \r p_f (1- \r p_f )}{n_2} }[/tex]

substituting value

         [tex]E = 1.96 * \sqrt{\frac{ 0.287 (1- 0.287 )}{150} + \frac{ 0.347 (1- 0.347 )}{150} }[/tex]

         [tex]E = 0.1051[/tex]

The  95% confidence interval is mathematically represented as  

           [tex](\r p_m - \r p_f ) - E < p_m - p_f < (\r p_m - \r p_f ) + E[/tex]

substituting values

          [tex]( 0.287 - 0.347 ) - 0.1051 < p_m - p_f <( 0.287 - 0.347 ) + 0.1051[/tex]    

           [tex]- 0.1651 < p_m - p_f <0.0451[/tex]

This mean that there is a 95 % confidence that the difference between the true proportion is within this interval and given that the interval contains zero then there is no statistically significant difference between the genders that are hypertensive.

Answer:

The equation 1+0=1

Step-by-step explanation:

Other options are not eligible because

1 option -Natural numbers cannot be closed under subtraction

2 option-The equation is not having proper rational numbers, they are decimals

3 option-Whole numbers cannot be closed under subtraction

Thank you!

Answer:

  1/10

Step-by-step explanation:

There are 5 numbers in the range that are multiples of 10: 10, 20, 30, 40, 50. The probability of choosing one of those at random from the set of 50 numbers is ...

  5/50 = 1/10

Answer: The slope of the line that passes through (2, 12) and (4, 20) is 4.

The value of the y-intercept is 9.

Step-by-step explanation:

Slope of line passing through (a,b) and (c,d) = [tex]\dfrac{d-b}{c-a}[/tex]

Then, the slope of the line that passes through (2, 12) and (4, 20) = [tex]\dfrac{20-12}{4-2}[/tex]

[tex]=\dfrac{8}{2}=4[/tex]

So, the slope of the line that passes through (2, 12) and (4, 20) is 4.

To find the y-intercept of 3x + 2y = 18, first write in slope intercept form y=mx+c ( where c= y-intercept ).

[tex]2y=-3x+18\\\\\Rightarrow\ y=-\dfrac{3}{2}x+9[/tex]

By comparison,  c= 9

Hence, the value of the y-intercept is 9.

Answer:

-15

Step-by-step explanation:

If it fell 3 deg every hour for 5 hours so the equation is 3*5 plus a - sign because it dropped degrees

Answer: 512 cm³

Explanation: Since the length, width, and height of a cube are all equal,

we can find the volume of a cube by multiplying side × side × side.

So we can find the volume of a cube using the formula v = s³.

In the cube in this problem, we have a side length of 8 cm.

So plugging into the formula, we have (8 cm)³

or (8 cm)(8 cm)(8 cm), which is 512 cm³.

So the volume of the cube is 512 cm³.

Answer:512[tex]cm^{3}[/tex]

Step-by-step explanation:

All sides are equal. Hence, volume =[tex]l^{3} = 8^{3} =512cm^{3}[/tex]

Answer:

(1+y^2) /2y

Step-by-step explanation:

arithmetic mean is the average of x and y

(x+y)/2

Using the equation

xy = 1

and solving for x

x = 1/y

Replacing x in the first equation

(1/y + y) /2

Multiply by y/y

(1/y + y) /2 * y/y

(1/y + y)*y /2y

(1+y^2) /2y

Answer:

a. Mean = 20

Sd = 4

b. Probability of X = 20 = 0.1960

Step-by-step explanation:

we have

n = 25

p = 80% = 0.8

mean = np

= 0.8 * 25

= 20

standard deviation = √np(1-p)

= √25*0.8(1-0.8)

=√4

= 2

probability that exactly 20 favours ban

it follows a binomial distribution

= 25C20 × 0.8²⁰ × 0.2⁵

= 53130 × 0.01153 × 0.00032

= 0.1960

Probability of X = 20 = 0.1960