When will n(A∩B)=0? Explain and give an example.

Answer:

Mean: 18.6 years old

Median: 18.5 years old

Step-by-step explanation:

Mean = average (add all numbers then divide by the number of numbers in the data set)

To find the mean, start by adding all of the numbers except for the outliers.

19 + 19 + 19 + 18 + 18 + 18 + 18 + 20 = 149

We added 8 numbers, so divide the sum by 8.

149/8 = 18.6

Therefore, the mean without outliers is 18.6 years old.

Median = middle (order numbers from least to greatest, then find the middle)

To find the median, order the numbers from least to greatest.

18, 18, 18, 18, 19, 19, 19, 20

Now, find the middle.

(Since there are an even number of numbers, select the two numbers in the middle.)

18, 18, 18, 18, 19, 19, 19, 20

Now, add these numbers and divide by 2.

18 + 19 = 37

37/2 = 18.5

Therefore, the median without outliers is 18.5 years old.

Answer:

X=70 :) Good Luck!!

Step-by-step explanation:

Using the concept of supplementary angles, it is found that the value of x is of 70 degrees.

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

Thus:

[tex]45 + 2x - 5 = 180[/tex]

[tex]2x + 40 = 180[/tex]

[tex]2x = 140[/tex]

[tex]x = \frac{140}{2}[/tex]

[tex]x = 70[/tex]

The value of x is of 70 degrees.

A similar problem is given at https://brainly.com/question/22826236

Answer:

Step-by-step explanation:

a)

Class limits       Frequency

38 - 63                  9

64 - 89                  7

90 - 115                 1

116 - 141                 1

142 - 167              2

Construct a histogram of these data(image attached)

b)

Frequency distribution table (also known as frequency table) consists of various components.

Classes: A large number of observations varying in a wide range are usually classified in several groups according to the size of their values. Each of these groups is defined by an interval called class interval. The class interval between 10 and 20 is defined as 10-20.

Class limits: The smallest and largest possible values in each class of a frequency distribution table are known as class limits. For the class 10-20, the class limits are 10 and 20. 10 is called the lower class limit and 20 is called the upper class limit.

Class limit: Class limit is the midmost value of the class interval. It is also known as the mid value.

Mid value of each class = (lower limit + Upper limit)2.  

If the class is 38 to 63 , lower limit is 38 and upper limit is 63. So the mid value is

[tex]\frac{(38+63)}{2} =50.5[/tex]

Class width is calculated using upper and lower value

Class width = (upper - lower) value /class

[tex]=\frac{ ( 163 - 38)}{5} \\\\=25[/tex]

Magnitude of a class interval: The difference between the upper and lower limit of a class is called the magnitude of a class interval.

Class frequency: The number of observation falling within a class interval is called class frequency of that class interval.

Answer:

2,4,2,4.

Step-by-step explanation:

Answer:

2,4,2,4.

Step-by-step explanation:

Answer: 82

Step-by-step explanation:

72 times 6 is equal to 432

6 plus 2 is 8

74.25 times 8 is equal to 594

If you minus 594 and 432 you get 162

162 is total marks for both subjects

162 minus 80 you get 82 which is the marks for the 8th subject

Hope it taught you something..

Answer:0.06

Step-by-step explanation:

Answer:

Step-by-step explanation:

m-(n+(p-(m+n-p)))

Final Result :

     2 • (m - p)

9514 1404 393

Answer:

  55.39 square units

Step-by-step explanation:

The formula for the area of a circle is ...

  A = πr²

Put the given numbers in place of the corresponding variables and do the arithmetic.

  A = 3.14 × 4.2² = 3.14 × 17.64 = 55.3896

Rounded to hundredths, the area is ...

  55.39 square units

Answer:

A =754 ft^2

Step-by-step explanation:

The area of a rectangle is given by

A = l*w

A = 58*13

A =754 ft^2

Answer:

Step-by-step explanation:

Part a

Exponential growth model for the frog population is given by

[tex]P=P_{0}b^{t}\texttt{ \ where} \ P_{0}=Population \ at \ t=0 \ and \ b=Base[/tex]

The population of frog at t=0 (2 years ago) is given as 46000 which implies

[tex]P_{0}=46000[/tex]

The population in the current year is given as 55200 which implies

 At,

t=2 years, P=55200

Therefore, substitute the above values to calculate the value of b

[tex]55200=46000b^{2} => b^2=\frac{55200}{46000}=1.2[/tex]

[tex]b=\sqrt{1.2}=1.095445[/tex]

Therefore, the model equation becomes

[tex]P=46000(1.095445)^{t}[/tex]

Part b

Since all the tags for this year have fallen off which implies no of tags for the next year can be calculated by calculating the population at t=3

[tex]P=46000(1.095445)^{3}\\\\=46000\times 1.3145\\\\=60467[/tex]

Answer:

b

Step-by-step explanation:

Answer:

Tina can select and answer the essay questions on her test in 35 ways.

Step-by-step explanation:

The order in which she chooses the questions is not important. For example, choosing questions 1, 3 and 7 is the same as choosing 7, 3 and 1. 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]

In this question:

Three questions from a set of 7. So

[tex]C_{7,3} = \frac{7!}{3!(7-4)!} = 35[/tex]

Tina can select and answer the essay questions on her test in 35 ways.

Tina can select and answer the essay question on her test in 35 ways.

     Number of ways to select 'r' objects out of 'n' objects is given by the expression,

Number of ways = [tex]^nC_r[/tex]

Since, [tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]

If n = 7 and r = 3,

Number of ways to select 3 essays out of 7 will be,

Number of ways = [tex]^7C_3[/tex]

                           [tex]=\frac{7!}{3!(7-3)!}[/tex]

                           [tex]=\frac{7\times 6\times 5\times 4!}{3\times 2\times 1\times 4!}[/tex]

                           [tex]=35[/tex]

  Therefore, Tina can select and answer the essay question on her test in 35 ways.

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Answer:

the only one that does is C

Step-by-step explanation:

doesn't= A, B, D, E

Answer:

a) [tex]f(t)=0.001155[\frac{2}{3}t(t-1980)^{3/2}-\frac{4}{15}(t-1980)^{5/2}]+264,034,000[/tex]

b) f(t=2015) = 264,034,317.7

Step-by-step explanation:

The rate of change in the number of hospital outpatient​ visits, in​ millions, is given by:

[tex]f'(t)=0.001155t(t-1980)^{0.5}[/tex]

a) To find the function f(t) you integrate f(t):

[tex]\int \frac{df(t)}{dt}dt=f(t)=\int [0.001155t(t-1980)^{0.5}]dt[/tex]

To solve the integral you use:

[tex]\int udv=uv-\int vdu\\\\u=t\\\\du=dt\\\\dv=(t-1980)^{1/2}dt\\\\v=\frac{2}{3}(t-1980)^{3/2}[/tex]

Next, you replace in the integral:

[tex]\int t(t-1980)^{1/2}=t(\frac{2}{3}(t-1980)^{3/2})- \frac{2}{3}\int(t-1980)^{3/2}dt\\\\= \frac{2}{3}t(t-1980)^{3/2}-\frac{4}{15}(t-1980)^{5/2}+C[/tex]

Then, the function f(t) is:

[tex]f(t)=0.001155[\frac{2}{3}t(t-1980)^{3/2}-\frac{4}{15}(t-1980)^{5/2}]+C'[/tex]

The value of C' is deduced by the information of the exercise. For t=0 there were 264,034,000 outpatient​ visits.

Hence C' = 264,034,000

The function is:

[tex]f(t)=0.001155[\frac{2}{3}t(t-1980)^{3/2}-\frac{4}{15}(t-1980)^{5/2}]+264,034,000[/tex]

b) For t = 2015 you have:

[tex]f(t=2015)=0.001155[\frac{2}{3}(2015)(2015-1980)^{1/2}-\frac{4}{15}(2015-1980)^{5/2}]+264,034,000\\\\f(t=2015)=264,034,317.7[/tex]

Answer:

C. 7, 14, 21, 28

Step-by-step explanation:

We want to find the multiples of 7

7*1= 7

7*2 = 14

7*3= 21

7*4 = 28

Answer:

The answer is, C. 7, 14, 21, 28

Answer:

a) In the step-by-step explanation.

b)  The null and alternative hypothesis are:

[tex]H_0: \mu=125000\\\\H_a:\mu> 125000[/tex]

c) P-value = 0.015

d) The conclusion, at a level of significance of 0.05, is that there is enough evidence to support the claim that that area residential property is available at a mean cost significantly higher than $125,000 per lot.

e) The claim of the chamber of commerce is false. We have statistical evidence against that claim and we can conclude that the mean prices are significantly higher than $125,000.

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim, expressed in the alternative hypothesis, is that area residential property is available at a mean cost significantly higher than $125,000 per lot.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=125000\\\\H_a:\mu> 125000[/tex]

The significance level is 0.05.

The sample has a size n=32.

The sample mean is M=130000.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=12500.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{12500}{\sqrt{32}}=2209.71[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{130000-125000}{2209.71}=\dfrac{5000}{2209.71}=2.26[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=32-1=31[/tex]

This test is a right-tailed test, with 31 degrees of freedom and t=2.26, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=P(t>2.26)=0.015[/tex]

As the P-value (0.015) is smaller than the significance level (0.05), the effect is  significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that that area residential property is available at a mean cost significantly higher than $125,000 per lot.

Answer:

C)

Step-by-step explanation:

3x+2>5

3x>3

x>1

I believe that you mistyped C so I think its C

Answer:

0.573 m

Step-by-step explanation:

a. To find the depth, x, we first solve the differential equation to find the expression for I  

dI/dx = (-1.21)I

dI = (-1.21)Idx

dI/I = -1.21dx

Integrating both sides, we have

∫dI/I = ∫-1.21dx

㏑I = -1.21x + C

I = exp(-1.21x + C)

I = exp(-1.21x)exp(C) Let exp(C) = A

I =Aexp(-1.21x)

when x = 0, I = L. Substituting these into the equation, we have

L = Aexp(-1.21 × 0)

L = Aexp(0)

L = A

So, I = Lexp(-1.21x)

we want to find x when I = L/2.

So, L/2 = Lexp(-1.21x)

1/2 = exp(-1.21x)

-1.21x= ㏑(1/2)

-1.21x= -㏑2

x = -㏑2/-1.21

x =  0.693/1.21

x = 0.573 m

Answer:

The 95% confidence interval for the proportion of all people in the United States who would indicate that their favorite sport to watch on television is American football is (0.34, 0.40). This means that we are 95% sure that the true proportion of all people in the United States who would indicate that their favorite sport to watch on television is American football is between (0.34 and 0.40).

The lower bound of the confidene interval is higher than 0.33. So it is not reasonable to believe that 33% is the actual percent of people in the United States whose favorite sport to watch on television is American football, this estimate should be higher than 33%.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 1000, \pi = 0.37[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.37 - 1.96\sqrt{\frac{0.37*0.63}{1000}} = 0.34[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.37 + 1.96\sqrt{\frac{0.37*0.63}{1000}} = 0.40[/tex]

The 95% confidence interval for the proportion of all people in the United States who would indicate that their favorite sport to watch on television is American football is (0.34, 0.40). This means that we are 95% sure that the true proportion of all people in the United States who would indicate that their favorite sport to watch on television is American football is between (0.34 and 0.40).

Based on your answer to the previous problem, is it reasonable to believe that 33 percent is the actual percent of people in the United States whose favorite sport to watch on television is American football

The lower bound of the confidene interval is higher than 0.33. So it is not reasonable to believe that 33% is the actual percent of people in the United States whose favorite sport to watch on television is American football, this estimate should be higher than 33%.

The 95% Confidence Interval we will found for given case is:

(0.34, 0.40)

It is Not reasonable to believe that  33 percent is the actual percent of people in the United States whose favorite sport to watch on television is American football

95% confidence interval for the proportion of all people in the United States who would indicate that their favorite sport to watch on television is American football.

When there is n sample size and the probability of success is p with level of significance [tex]\alpha[/tex]calculated as:

[tex]CI = p \pm z_0 \sqrt{\dfrac{p(1-p)}{n}[/tex]

Where [tex]z_0[/tex] is the z score  [tex]1- \dfrac{\alpha}{2}[/tex] .

1 -  [tex]\alpha[/tex] = 0.95 ( since it is given to find 95% CI)

Thus,  [tex]\alpha[/tex]  = 0.05

The z score at p value = 1 -  [tex]\alpha[/tex]/2 = 1 -0.025 = 0.975 is 1.96

Thus we have:

[tex]CI = p \pm z_0 \sqrt{\dfrac{p(1-p)}{n}}\\\\CI = 0.37 \pm 1.96 \sqrt{\dfrac{0.37 \times0.63 }{1000}}\\\\CI = 0.37 \pm 1.96 \times 0.0152 = 0.37 \pm 0.03\\[/tex]

Lower limit of CI = 0.34 and Upper limit of CI = 0.40.

The case to decide to believe that 33 percent is the actual percent of people in the United States whose favorite sport to watch on television is American football can be solved as:

33% = 0.33 probability of actually liking watching american probability.

Since 0.33 is lower than the lower limit of CI for 0.37 probability, thus we reject the null hypothesis that both 0.37 and 0.33 are approximately same, and thus decide that it is false that 0.33 percent believe that 33 percent is the actual percent of people in the United States whose favorite sport to watch on television is American football.

Thus it is not reasonable to believe that 33% is the actual percent of people in the United States whose favorite sport to watch on television is American football.

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Answer:

[tex]1+ 0i[/tex]

Step-by-step explanation:

A complex number is a number which has some real part and some imaginary part.

Standard form of a complex number is represented as

[tex]a +bi[/tex]

Where [tex]a[/tex] is the real part,

and [tex]bi[/tex] is the imaginary part.

And [tex]i = \sqrt{-1}[/tex]

Given complex number:

[tex]-4i+\dfrac{1}{4}-5i)-(-\dfrac{3}{4}+8i)+17i\\\Rightarrow -4i+\dfrac{1}{4}-5i + \dfrac{3}{4}-8i+17i\\\Rightarrow \dfrac{3}{4}+\dfrac{1}{4}-4i -5i-8i+17i\\\Rightarrow \dfrac{3+1}{4}-17i+17i\\\Rightarrow \dfrac{4}{4}+0i\\\Rightarrow 1 + 0i[/tex]

Hence, the standard form is [tex]1+ 0i[/tex].

Answer:

d 25

So 10 cans of orange Concentrate will be = 25 cans of water

Step-by-step explanation:

Andrea combines the orange concentrate and the water using a 2:5 ratio.

We are to find how many cans of water she needs to combine with 10 cans of concentrate

So using the ratio.

2 cans of orange Concentrate is to 5 cans of water.

So 10 cans of orange Concentrate will be =( 10*5)/2

So 10 cans of orange Concentrate will be = 50/2

So 10 cans of orange Concentrate will be = 25 cans of water

Answer:

1.2h / 72min

Step-by-step explanation:

Maria waxes her car in 2 hours. When she works with Susan, they can wax the car

in 45 mins. How long will it take Susan, working by herself, to wax the car?

:

Let x = time required by Susan by herself

:

Change 45 min to hrs: 45/60 = .75 hrs

:

Let the completed job = 1

:

Each will do a fraction of the job and will add up to 1

:

.75%2F2 + .75%2Fx = 1

Multiply equation by 2x to eliminate the denominators, solve for x

.75x + 2(.75) = 2x

:

.75x + 1.5 = 2x

:

1.5 = 2x - .75x

:

1.5 = 1.25x

x = 1.5%2F1.25

x = 1.2 hrs (72min), for Susan to do the job by herself

Answer:

Always true or 0 = 0

Step-by-step explanation:

This equation simplifies to 0 = 0 I will show in several steps.

1. (-15x - 10) - (x - 3) = (-16x - 20) + 13

2. -16x - 7 = -16x - 20 + 13

3. 0 = 7 - 20 + 13

4. 0 = 0

Hope this helps! (Please consider giving brainliest)

Answer:

all real value for x

Step-by-step explanation:

5(- 3x - 2) - (x - 3) = -4(4x + 5) + 13

Distribute

-15x -10 -x+3 = -16x -20 +13

Combine like terms

-16x-7 = -16x -7

Add 16x to each side

-16x-7 +16x= -16x -7+16x

-7 = -7

This is always true so x is all real values

Answer:

p = 1 and r = - 2

Step-by-step explanation:

Given the 2 equations

6p - 4r = 14 → (1)

p - 2r = 5 → (2)

Multiplying (2) by - 6 and adding to (1) will eliminate the term in p

- 6p + 12r = - 30 → (3)

Add (1) and (3) term by term to eliminate p

8r = - 16 ( divide both sides by 8 )

r = - 2

Substitute r = - 2 into either of the 2 equations and solve for p

Substituting into (2)

p - 2(- 2) = 5

p + 4 = 5 ( subtract 4 from both sides )

p = 1

Step-by-step explanation:

here is the answer u can get help from it.....

The solution to the equation (2x-4)/5 = 4 is x = 12.

To solve the equation (2x-4)/5 = 4, we will use the following steps.

Multiply both sides of the equation by 5 to eliminate the denominator as;

5[(2x-4)/5] = 5 x 4

This simplifies to:

2x - 4 = 20

Add 4 to both sides of the equation to isolate the term with x:

2x - 4 + 4 = 20 + 4

This simplifies to:

2x = 24

Divide both sides of the equation by 2 to solve for x:

(2x)/2 = 24/2

This simplifies to:

x = 12

Thus, the solution to the equation (2x-4)/5 = 4 is x = 12.

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Answer:

The answer is false already got this question wrong though D;

Step-by-step explanation:

The ratio of the volumes of two similar solid polyhedra is equal to the cube of the ratio between their edges is false.

The ratio of the corresponding edges or sides or lengths of given similar solids is called the linear scale factor.

The linear scale factor can be used to determine the area scale factor which is the ratio of the area of the similar solids.

The area scale factor is given as the square of the linear scale factor.

that is Area Scale Factor = (Linear Scale Factor)²

The linear scale factor can also be used to find the ratio of the volumes of similar solids, or what is called the volume scale factor such that the volume scale factor is given by the cube of the area scale factor.

Therefore the given statement is false

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Answer:

Step-by-step explanation:

The person receives 10000 every month

for one year total principal 10000 * 12 = 120000

r= 12%p.a and t is 1yr

simple interest= 120000*12*1/100 = 14400

total money received in present year 120000 + 14400 = 134400

for 20 yrs principal becomes 10000*12*20= $2400000

simple interest = 2400000*12*20/100= $5760000

total amount received for 20 yrs = 2400000+ 5760000=8160000.

present value of principal as money receive 10000 for 10 yrs = 10000*10 = 100000

si = 100000*10*12/100= 120000

amount = $220000

Answer:

  300 mL

Step-by-step explanation:

If one part is 100 mL, then 3 parts will be 300 mL.

300 mL of water should be added.