Some couples planning a new family would prefer at least one child of each sex. The probability that a couple’s first child is a boy is 0.512. In the absence of technological intervention, the probability that their second child is a boy is independent of the sex of their first child, and so remains 0.512. Imagine that you are helping a new couple with their planning. If the couple plans to have only two children: (a) What is the probability of getting one child of each sex?

Answer:

A= (0,0) and B = (6,3)

We can find the length AB with the following formula:

[tex] d = \sqrt{(x_B -x_A)^2 +(y_B -y_A)^2}[/tex]

And replacing we got:

[tex] d = \sqrt{(6-0)^2 +(3-0)^2} = \sqrt{45}= 3\sqrt{5}[/tex]

So then the length AB would be [tex] 3\sqrt{5}[/tex]

Step-by-step explanation:

For this case we have the following two points:

A= (0,0) and B = (6,3)

We can find the length AB with the following formula:

[tex] d = \sqrt{(x_B -x_A)^2 +(y_B -y_A)^2}[/tex]

And replacing we got:

[tex] d = \sqrt{(6-0)^2 +(3-0)^2} = \sqrt{45}= 3\sqrt{5}[/tex]

So then the length AB would be [tex] 3\sqrt{5}[/tex]

Answer:6.71

Step-by-step explanation: awesomeness

Answer:

Step-by-step explanation:

The smaller/closer the difference between observed and expected frequencies, the higher the probability of concluding that the probabilities specified in the null hypothesis are correct concluding that the data fits that particular distribution given.

Answer:

260

20

Step-by-step explanation:

speed of plane= p

speed of wind =w

and

added up the 2 equations we get:

then

Answer:

Range. The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain. In plain English, the definition means: The range is the resulting y-values we get after substituting all the possible x-values

Step-by-step explanation:

Answer:

$18,750

Step-by-step explanation:

Take the earnings per week times the number of weeks

50 * 375

18,750

Answer:

$18,750

Step-by-step explanation:

If we want to find the nurse's aide's earnings for the year, we have to multiply her weekly salary by the number of weeks she worked.

weekly salary * number of weeks

She earns $375 per week and she worked for 50 weeks.

$375*50 weeks

375*50

Multiply the 2 numbers

18,750

Her total earnings for the year are $18,750

Answer:

Solve   -x2+11xandg+6x-6  = 0

Step-by-step explanation:

Answer:

the correct option is D

Step-by-step explanation:

JK IS longer than JL

Answer:

30 students are in the science class and 3 students recieved a failing grade.

Answer:

30, 3

Step-by-step explanation:

a. Let's call the total students x. If 40% x = 12, 0.4x = 12, x = 12/0.4 = 30 students.

b. We know that 100 - 40 - 30 - 20 = 10% of all students failed. This is 10% * 30 = 0.1 * 30 = 3 students.

Answer:

[tex] z =\frac{50-64}{7}= -2[/tex]

[tex] z =\frac{43-64}{7}= -3[/tex]

We know that within two deviations from the mean we have 95% of the data from the empirical rule so then below 2 deviation from the mean we have (100-95)/2 % =2.5%. And within 3 deviations from the mean we have 99.7% of the data so then below 3 deviations from the mean we have (100-99.7)/2% =0.15%

And then the final answer for this case would be:

[tex] 2.5 -0.15 = 2.35\%[/tex]

Step-by-step explanation:

For this case we have the following parameters from the variable number of motnhs in service for the fleet of cars

[tex] \mu = 64, \sigma =7[/tex]

For this case we want to find the percentage of values between :

[tex] P(43< X< 50)[/tex]

And we can use the z score formula given by:

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

In order to calculate how many deviation we are within from the mean. Using this formula for the limits we got:

[tex] z =\frac{50-64}{7}= -2[/tex]

[tex] z =\frac{43-64}{7}= -3[/tex]

We know that within two deviations from the mean we have 95% of the data from the empirical rule so then below 2 deviation from the mean we have (100-95)/2 % =2.5%. And within 3 deviations from the mean we have 99.7% of the data so then below 3 deviations from the mean we have (100-99.7)/2% =0.15%

And then the final answer for this case would be:

[tex] 2.5 -0.15 = 2.35\%[/tex]

Answer:

Ignoring leap years, May has 31 days, a year has 365 days. 334 days of the year are NOT in May so the probability of a birthday not being in May = 334/365 = approximately 91.5%

Step-by-step explanation:

The probability of event A which represents that the man's birthday is not on New Year's Day is 0.99.

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur. Mathematically -

P(A) = n(A)/n(S)

Given is a person who is randomly selected.

Assume that Event A represents that the man's birthday is not on New Year's Day.

Total number of days in a year = n(S) = 365

Total number of days not on New Year's Day = n(A) = 364

Therefore, the probability that the man's birthday is in May will be -

P(A) = n(A)/n(S)

P(A) = 364/365

P(A) = 0.99

Therefore, the probability of event A which represents that the man's birthday is not on New Year's Day is 0.99.

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Answer:

4.4

4.40

Step-by-step explanation:

These two decimals above are equivalent to 4.400 because no matter the amount of zeroes, the numbers are the same. For example, 4.400 is also equivalent to 4.400000000000000000000000000000000.  As long as the  "4's" maintain the same place (ones place and tens place), the decimals will be congruent to one another.

Answer: They are not parallel, they are coincident

Step-by-step explanation:

If two lines have the same slope but a different y-intercept, the lines are parallel. If two lines have the same slope and the same y-intercept, the lines are coincident.

We can rewrite 5x−y=−5 adding -5x to both sides and multiplying by -1:

5x - y =-5

5x - y -5x = -5 - 5x (adding -5x to both sides)

-y = -5 - 5x

Multiplying by -1

y = 5x + 5

Both equations look the same so they are coincident. They have the same intercept y=5 and the same slope m=5.

Answer:

The interval that would represent weights of the middle 95% of all oranges from this orchard is from 5 oz to 7 oz.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 6

Standard deviation = 0.5

Middle 95% of weights:

By the Empirical Rule, within 2 standard deviations of the mean.

6 - 2*0.5 = 5

6 + 2*0.5 = 7

The interval that would represent weights of the middle 95% of all oranges from this orchard is from 5 oz to 7 oz.

The interval representing the weights of the middle 95% of all oranges from this orchard is from 5 oz to 7 oz.

The Empirical Rule states that for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

The empirical rule says that, in a standard data set, virtually every piece of data will fall within three standard deviations of the mean.

95% of the measures are within 2 standard deviations of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 6

Standard deviation = 0.5

Middle 95% of weights

By the Empirical Rule, within 2 standard deviations of the mean.

6 - 2*0.5 = 5

6 + 2*0.5 = 7

The interval representing the weights of the middle 95% of all oranges from this orchard is from 5 oz to 7 oz.

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Answer:

S(3)=22

Step-by-step explanation:

The rate of change of the number of squirrels S(t) that live on the Lehman College campus is directly proportional to 30 − S(t).

[tex]\dfrac{dS}{dt}=k(30-S(t))\\ \dfrac{dS}{dt}+kS(t)=30k\\$The integrating factor: e^{\int k dt}=e^{kt}\\$Multiply all through by the integrating factor\\ \dfrac{dS}{dt}e^{kt}+kS(t)e^{kt}=30ke^{kt}[/tex]

[tex](Se^{kt})'=30ke^{kt} dt\\$Integrate both sides\\ Se^{kt}=\dfrac{30ke^{kt}}{k}+C$ (C a constant of integration)\\Se^{kt}=30e^{kt}+C\\$Divide both sides by e^{kt}\\S(t)=30+Ce^{-kt}[/tex]

When t=0, S(t)=15

[tex]15=30+Ce^{-k*0}\\C=15-30\\C=-15[/tex]

When t = 2, S(t)=20

[tex]20=30-15e^{-2k}\\20-30=-15e^{-2k}\\-10=-15e^{-2k}\\e^{-2k}=\dfrac23\\$Take the natural log of both sides$\\-2k=\ln \dfrac23\\k=-\dfrac{\ln(2/3)}{2}[/tex]

Therefore:

[tex]S(t)=30-15e^{\frac{\ln(2/3)}{2}t}\\$When t=3$\\S(t)=30-15e^{\frac{\ln(2/3)}{2} \times 3}\\S(3)=21.8 \approx 22[/tex]

Answer:

18 units

Step-by-step explanation:

5+5=10

4+4=8

8+10=18 units

Answer:

14

Step-by-step explanation:

The perimeter of a rectangle is the sum of the lengths of the 4 sides of a rectangle. Since in a rectangle opposite sides are congruent, you just need to find the lengths of any two adjacent sides because adjacent sides cannot be opposite. Then add them and multiply the sum be 2 to account for the opposites sides.

Two find the distance between any two points, you can use the distance formula. If the two points lie on the same vertical line (both points have the same x-coordinate), or if the two points lie on the same horizontal line (both points have the same y-coordinate), then just subtract the different coordinates and take the absolute value.

PQ = |2 - 6| = |-4| = 4

QR = |2 - 5| = |-3| = 3

perimeter = 2(length + width)

perimeter = 2(4 + 3)

perimeter = 2(7)

perimeter = 14

Answer:

Scatter plots are used to plot data points on a horizontal and a vertical axis in the attempt to show how much one variable is affected by another. Each row in the data table is represented by a marker whose position depends on its values in the columns set on the X and Y axes

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The one dot that is a lot farther away from the rest of the points is an outlier so the answer is D.

Answer:

[tex]z=\frac{0.231 -0.2}{\sqrt{\frac{0.2(1-0.2)}{221}}}=1.152[/tex]  

The p avlue for this case is given by:

[tex]p_v =P(z>1.152)=0.125[/tex]  

The p value for this case is higher than the significance level so then we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true proportion is higher than 0.2 or 20%

Step-by-step explanation:

Information provided

n=221 represent the random sample taken

X=51 represent the people with nausea

[tex]\hat p=\frac{51}{221}=0.231[/tex] estimated proportion of people with nausea

[tex]p_o=0.21[/tex] is the value to test

[tex]\alpha=0.1[/tex] represent the significance level

z would represent the statistic

[tex]p_v[/tex] represent the p value

Hypothesis to verify

We want to check if the true population is higher than 0.20, the system of hypothesis are.:  

Null hypothesis:[tex]p \leq 0.2[/tex]  

Alternative hypothesis:[tex]p > 0.2[/tex]  

The statistic is given:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

Replacing the info given we got:

[tex]z=\frac{0.231 -0.2}{\sqrt{\frac{0.2(1-0.2)}{221}}}=1.152[/tex]  

The p avlue for this case is given by:

[tex]p_v =P(z>1.152)=0.125[/tex]  

The p value for this case is higher than the significance level so then we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true proportion is higher than 0.2 or 20%

Answer:

Height of the pennant is 30 inches.

Step-by-step explanation:

Given that:

Area of pennant = 180 sq inches

Base of pennant = z inches

Height of pennant = (2z + 6) inches

Also, it is a triangular pennant and area of a triangle can be given as:

[tex]A = \dfrac{1}{2} \times Base\times Height[/tex]

Putting the values in above formula:

[tex]180 = \dfrac{1}{2} \times z \times (2z+6)\\\Rightarrow 360 = 2z^{2} + 6z\\\Rightarrow 180 = z^{2} + 3z\\\Rightarrow z^{2} + 3z -180 = 0\\\Rightarrow z^{2} + 15z -12z -180 = 0\\\Rightarrow z(z + 15) -12(z+15) = 0\\\Rightarrow (z + 15) (z-12) = 0\\\Rightarrow z = 12\ or\ z=-15[/tex]

Value of z can not be negative, so value of Base, z = 12 inches.

Height is given as 2z + 6 so, height = 2[tex]\times[/tex]12 +6 = 30 inches

Answer:

C.30 inches

Step-by-step explanation:

Answer:

1680 is the answer.

Step-by-step explanation:

Here, we have 11 letters in the word MISSISSIPPI.

Repetition of letters:

M - 1 time

I - 4 times

S - 4 times

P - 2 times

As per question statement, we need a substring MISS in the resultant strings.

So, we need to treat MISS as one unit so that MISS always comes together in all the strings.

The resultant strings will look like:

xxxxMISSxxx

xxMISSxxxxx

and so on.

After we treat MISS as one unit, total letters = 8

Repetition of letters:

MISS - 1 time

I - 3 times

S - 2 times

P - 2 times

The formula for combination of letters with total of n letters:

[tex]\dfrac{n!}{p!q!r!}[/tex]

where p, q and r are the number of times other letters are getting repeated.

p = 3

q = 2

r = 2

So, required number of strings that contain MISS as substring:

[tex]\dfrac{8!}{3!2!2!}\\\Rightarrow \dfrac{40320}{6\times 2 \times 2}\\\Rightarrow 1680[/tex]

So, 1680 is the answer.

Answer:

The probability of observing between 9 and 15 (inclusive) swarms is 0.6639.

Step-by-step explanation:

The random variable X can be defined as the number of swarms of honeybees seen each spring.

The average value of the random variable X is, λ = 13.

A random variable representing the occurrence of events in a fixed interval of time is known as Poisson random variables.

For example, the number of customers visiting the bank in an hour or the number of typographical error is a book every 10 pages.

So, the random variable X follows a Poisson distribution with parameter λ = 13.

The probability mass function of X is as follows:

[tex]P(X=x)=\frac{e^{-\lambda}\ \lambda^{x}}{x!}; x=0,1,2,3...[/tex]

Compute the  the probability of observing between 9 and 15 (inclusive) swarms as follows:

P (9 ≤ X ≤ 15) = P (X = 9) + P (X = 10) + P (X = 11) + ... + P (X = 15)

                      [tex]=\sum\limits^{15}_{x=9}{\frac{e^{-\lambda}\ \lambda^{x}}{x!}}\\\\=0.06605+0.08587+0.10148+0.10994\\+0.10994+0.10209+0.08848\\\\=0.66385\\\\\approx 0.6639[/tex]

Thus, the probability of observing between 9 and 15 (inclusive) swarms is 0.6639.

The solution to the system of equations is (-1, 2, 4), which is equal to choice (c) (-1, 2, 4).

One or many equations having the same number of unknowns that can be solved simultaneously are called simultaneous equations. And the simultaneous equation is the system of equations.

To solve the system of equations, we can represent it in an augmented matrix and use row operations to find its reduced row-echelon form.

The augmented matrix for the system is:

[ 2  1  4 | 16 ]

[ 5 -2  2 | -1 ]

[ 1  2 -3 | -9 ]

We want to get the matrix in reduced row-echelon form.

We can start by using row operations to get a 1 in the upper left corner:

R(1/2) -> R1:

[ 1 1/2  2 |  8 ]

[ 5 -2  2 | -1 ]

[ 1  2 -3 | -9 ]

Now we want to get zeros in the first column below the pivot element (1). We can do this by subtracting 5 times the first row from the second row, and subtracting the first row from the third row:

-5R1 + R2 -> R2:

-R1 + R3 -> R3:

[ 1  1/2   2  |  8 ]

[ 0 -9/2  -8  | -41 ]

[ 0  3/2 -5  | -17 ]

R2 + R3 -> R3:

[ 1  1/2   2  |  8 ]

[ 0 -9/2  -8  | -41 ]

[ 0  -3    -13 | -58 ]

We can continue with row operations to get a 1 in the second row, second column:

(-2/9)R2 -> R2:

[ 1  1/2   2    |  8 ]

[ 0   1   16/9  |  82/9 ]

[ 0  -3    -13 | -58 ]

3R2 + R3 -> R3:

[ 1  1/2   2    |  8 ]

[ 0   1   16/9  |  82/9 ]

[ 0  0    -23/3 | -92/3 ]

Finally, we can get a 1 in the third row, third column:

(-3/23)R3 -> R3:

[ 1  1/2   2    |  8 ]

[ 0   1   16/9  |  82/9 ]

[ 0  0    1 | 4 ]

Now the matrix is in reduced row-echelon form.

We can read the solution directly from the last column:

x = 8 - (1 + 8) = -1

y = 82/9 - (16/9)(4) = 2

z = 4

Therefore, the solution to the system of equations is (-1, 2, 4).

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Answer:

95% confidence interval for p, the true fraction of crimes in the area in which some type of firearm was reportedly used.

(0.59445 , 0.67155)

Step-by-step explanation:

Explanation:-

Given random sample size 'n' = 600

sample proportion

                            [tex]p^{-} = \frac{x}{n} = \frac{380}{600} = 0.633[/tex]

95% of confidence interval for Population proportion is determined by

[tex](p^{-} - Z_{\frac{\alpha }{2} } \sqrt{\frac{p^{-} (1-p^{-} )}{n} } , p^{-} +Z_{\frac{\alpha }{2} } \sqrt{\frac{p^{-} (1-p^{-} )}{n} })[/tex]

Level of significance : α = 0.05

   [tex]z_{\frac{0.05}{2} } = Z_{0.025} =1.96[/tex]

[tex](0.633 - 1.96 \sqrt{\frac{0.633 (1-0.633 )}{600 }}, (0.633 + 1.96 \sqrt{\frac{0.633 (1-0.633 )}{600 }[/tex]

On calculation , we get

(0.633 - 0.03855 , (0.633 + 0.03855)

(0.59445 , 0.67155)

Conclusion:-

95% confidence interval for p, the true fraction of crimes in the area in which some type of firearm was reportedly used.

(0.59445 , 0.67155)

Answer:

241

Step-by-step explanation:

We want to evaluate the expression:

[tex]2^8-10-15\div3[/tex]

We follow the order of operations: PEMDAS

Since there are no parenthesis(P), we evaluate the exponents(E)

[tex]2^8-10-15\div3=256-10-15\div3[/tex]

Next is Division (D)

[tex]256-10-15\div3=256-10-5[/tex]

We can then simplify since we have only subtraction.(S)

[tex]256-10-5=241[/tex]

Therefore:

[tex]2^8-10-15\div3=241[/tex]

Answer:

rectangular prism

Step-by-step explanation:

A rectangular prism has 6 sides that are rectangles.

Answer:

a) It can be used because np and n(1-p) are both greater than 5.

Step-by-step explanation:

Binomial distribution and approximation to the normal:

The binomial distribution has two parameters:

n, which is the number of trials.

p, which is the probability of a success on a single trial.

If np and n(1-p) are both greater than 5, the normal approximation to the binomial can appropriately be used.

In this question:

[tex]n = 201, p = 0.45[/tex]

So, lets verify the conditions:

np = 201*0.45 = 90.45 > 5

n(1-p) = 201*(1-0.45) = 201*0.55 = 110.55 > 5

Since both np and n(1-p) are greater than 5, the approximation can be used.

Answer:

3 1/2 miles is 6160 yards and 3,520 yards is 2 miles

Step-by-step explanation:

Answer:

1600

please see the attached picture for full solution

Hope it helps...

Answer:

Chemical rocks form when minerals dissolve in a solution and crystalize.

Answer:

Chemical rocks don't form from solidification from a melt

Step-by-step explanation: