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? [5]
(b) What is the probability that at least one girl is born? [5]
(c) What is the probability that at least one boy is born? [5] and
(d) What is the probability that both children are the same sex? [5]

Answer:

D

Step-by-step explanation:

Answer:

the g's contributing term for the overall uncertainty of P is  [tex]dP_g = [\frac{dg}{g}][/tex]

Step-by-step explanation:

From the question we are told that

   The pressure is   [tex]P = P_o + \rho gh[/tex]

The first step in determining the uncertainty of P in by obtaining the terms in the equation contributing to it uncertainty and to do that we take the Ln of both sides of the equation

    [tex]ln P = lnP_o + ln(\rho gh )[/tex]

=>   [tex]ln P = lnP_o + ln \rho + ln g + ln h[/tex]

Then the next step is to differentiate both sides of the equation

    [tex]\frac{d(ln P)}{dP} = \frac{d(ln P_o)}{dP_o} + \frac{d(ln \rho)}{d\rho} +\frac{d(ln g)}{dg} + \frac{d(ln h)}{dh}[/tex]

=>    [tex]\frac{dP}{P} = \frac{dP_o}{P_o} + \frac{d \rho}{\rho} +\frac{d g}{g} + \frac{d h}{h}[/tex]

We asked to obtain the contribution of the term g to the uncertainty of P

This can deduced from the above equation as

     [tex]dP_g = [\frac{dg}{g}] P[/tex]

Answer:

Yes

Step-by-step explanation:

They both have only one base. They are different from prisms and cylinders.

Answer:

11 5/8

Step-by-step explanation:

Simply the 5/8 to 16th

5/8 equals to 10/16

Then add the 16ths together

The divide it by 16

Then add the whole numbers

Then add of them together to get your answer

Answer:

Exact Form:

93 /8

Decimal Form:

11.625

Mixed Number Form:

11  5 /8

Step-by-step explanation:

If you add every side together:

3 3/16 + 2 5/8 + 3 3/16 + 2 5/8 = 93/8

It's quite easy, just add everything together ;)

Answer:

C.)

Step-by-step explanation:

C.) Because it states the exact decimals rather than just stating about $2.36. Also, the other options were not specific. Hope this helps!  

Answer:

[tex]\boxed{\sf \ \ \ answer \ b. \ \ +5 \ \ \ }[/tex]

Step-by-step explanation:

Hello

let's assume that we are looking for x >=0

[tex]4x^2=100 <=> \dfrac{4x^2}{4}=x^2=\dfrac{100}{4}=25\\<=>\sqrt{x^2}=25\\<=> |x| = 5 <=> x = 5 \ or \ x=-5[/tex]

Let's assume that we are looking for x>=0

so the correct answer is 5

Answer:

Step-by-step explanation:

Confidence interval is written in the form,

(Sample mean - margin of error, sample mean + margin of error)

The sample mean, x is the point estimate for the population mean.

Margin of error = z × s/√n

Where

s = sample standard deviation = 21.8

n = number of samples = 17

From the information given, the population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the z score

In order to use the t distribution, we would determine the degree of freedom, df for the sample.

df = n - 1 = 17 - 1 = 16

Since confidence level = 99% = 0.99, α = 1 - CL = 1 – 0.99 = 0.01

α/2 = 0.01/2 = 0.005

the area to the right of z0.005 is 0.005 and the area to the left of z0.005 is 1 - 0.005 = 0.995

Looking at the t distribution table,

z = 2.921

Margin of error = 2.921 × 21.8/√17

= 15.44

The confidence interval for the mean wake time for a population with drug treatments is

90.3 ± 15.44

The upper limit is 90.3 + 15.44 = 105.74 mins

The lower limit is 90.3 - 15.44 = 74.86 mins

The result suggests that the mean wake time might have really reduced since the values barely fall above 100 minutes as in before treatment with a high degree of confidence. Therefore, the drug is effective.

Answer:

What we know about the p-value for the test is that it will be less than 0.05

Step-by-step explanation:

The complete question is as follows;

Suppose that you had consumer group wanted to test to see if weight of participants in a weight loss program changed (up or down). They computed a 95% confidence interval of the result (-4.977, -2.177). Suppose that we had a significance test with the following hypothesis:

H0: population mean weight loss = 0

Ha: population mean weight loss does not equal 0

What do we know about the p-value for the test?

solution;

Given the information in the question, we are concerned with saying what we know about the p-value for the test

To answer this question, we shall be looking at it from the angle of the confidence interval

The confidence interval given is 95%.

Now what does this indicate?

It indicates that 95% confidence interval contains only values which are less than 0.

What does this mean for the p-value?

This means that the p-value will be less than 0.05

Complete Question

1 Explain what is meant by the equation lim x → 8 f(x) = 9.

A If |x1 − 8| < |x2 − 8|, then |f(x1) − 9| < |f(x2) − 9|.

B The values of f(x) can be made as close to 8 as we like by taking x  sufficiently close to 9.

C  f(x) = 9 for all values of x.

D If |x1 − 8| < |x2 − 8|, then |f(x1) − 9|≤ |f(x2) − 9|.

E The values of f(x) can be made as close to 9 as we like by taking x sufficiently close to 8.

2  Is it possible for this statement to be true and yet f(8) = 6? Explain.

A Yes, the graph could have a hole at (8, 9) and be defined such that f(8) =6.

B Yes, the graph could have a vertical asymptote at x = 8 and be defined such that f(8) = 6.

C No, if f(8) = 6, then lim x→8 f(x) = 6.

D No, if lim x→8 f(x) = 9, then f(8) = 9.

Answer:

1

   The correct option is  D

2

    The correct option is   A

Step-by-step explanation:

Generally a a limit function  [tex]\lim_{n \to x } f(x) = L[/tex]

Tell us that as n tends toward x the values of  f(x) tends towards L hence for the first question E is the correct option

Now looking at the second question

  Yes it is possible for  lim x → 8 f(x) = 9.  to be true and  f(8) = 6 this is because the graph defined by this limit equation can have a hole the point

(8, 9) and created in such a way that f(8) = 6

Calculus's basic idea of limits in mathematics describes how a function behaves when its input approaches a specific value. No, if f(8) = 6, then lim x → 8 f(x) = 6. The correct option is C.

The statement "lim x → 8 f(x) = 9" means that as x approaches 8, the limit of f(x) is equal to 9. This implies that the function f(x) gets arbitrarily close to 9 as x gets arbitrarily close to 8.

If f(8) = 6, it means that the function f(x) has a specific value of 6 at x = 8. This contradicts the idea that f(x) gets arbitrarily close to 9 as x approaches 8.

Therefore, if f(8) = 6, it is not possible for the statement "lim x → 8 f(x) = 9" to be true.

To know more about equation limits follow

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Answer:

1,300,000,000

Step-by-step explanation:

 78    300   000

 550  400   000

 648  700   000

1  277  400   000

To the nearest million

1,2 | 77 400 000            more than 4, so +1

1,300,000,000

Answer:

[tex]z=\frac{0.81 -0.78}{\sqrt{\frac{0.78(1-0.78)}{900}}}=2.173[/tex]  

The p value for this case is given by this probability:

[tex]p_v =P(z>2.173)=0.0149[/tex]  

Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true proportion of people who favored te construction is significantly higher than 0.78 or 78%

Step-by-step explanation:

Information given

n=900 represent the random sample taken

[tex]\hat p=0.81[/tex] estimated proportion of residents who favored the construction

[tex]p_o=0.78[/tex] is the value to test

[tex]\alpha=0.02[/tex] represent the significance level

z would represent the statistic

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

Hypothesis to test

We want to test if the true proportion is more than 0.78 or not.:  

Null hypothesis:[tex]p\leq 0.78[/tex]  

Alternative hypothesis:[tex]p > 0.78[/tex]  

The statistic is given by:

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

Replacing the info we got:

[tex]z=\frac{0.81 -0.78}{\sqrt{\frac{0.78(1-0.78)}{900}}}=2.173[/tex]  

The p value for this case is given by this probability:

[tex]p_v =P(z>2.173)=0.0149[/tex]  

Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true proportion of people who favored te construction is significantly higher than 0.78 or 78%

Answer:

  y = -2

Step-by-step explanation:

A horizontal line has an equation of the form ...

  y = constant

In order for the line to go through a point with a y-coordinate of -2, the constant must be -2.

  y = -2 . . . . horizontal line through (-5, -2)

Answer:

3

Step-by-step explanation:

x^2 + y^2 = 9

The equation of a circle is

(x-h)^2 + (y-k)^2 = r^2

( h,k) is the center and r is the radius

x^2 + y^2 = 3^2

The radius is 3

Answer:

The answer is drawing the 6 of clubs or the 6 of spades because those are the only black 6's.

Answer:The answer for the first one is log2(.25)=-2

The answer for the second one is 8^3=512

Step-by-step explanation:

Answer:

20 ton

Step-by-step explanation:

We created a system of two separate equations to answer these questions.

"y" will be the total cost to transport the sugar

"x" will be the amount of sugar transported

Therefore, we have to:

y = 3995 + 225.50 * x

y = 6500 + 100.25 * x

We must establish these equations equal to each other because it asks how much of x is necessary to make the same amount of y, therefore:

3995 + 225.50 * x = 6500 + 100.25 * x

solved we have:

225.50 * x - 100.25 * x  = 6500 - 3995

125.25 * x = 2505

x = 2505 / 125.25

x = 20

which means that when the amount of sugar transported is 20 tons, the price is the same

Answer:

a

Step-by-step explanation:

increase the significance level to increase the probability of type 1 error

You can use the definition of type I and type II error to find the correct option.

To avoid the more consequential error, the researchers should do:
Option D: Decrease the significance level to decrease the probability of Type I error.

Firstly the whole story starts from hypotheses. The null hypothesis is tried to reject and we try to accept the alternate hypothesis.

The negative is just like the doctor's test getting negative means no disease. Similarly, if we conclude null hypothesis negative means it is accepted. If it is accepted wrongly means the negative test result was false, thus called false negative. This error is called type II error.

The probability of committing the type I error is called the significance level of the hypothesis test.

Since in the given context, by using the definitions of the type I error and the type II error, we have

More consequential error for educators : For the educators, the more consequential error would be that the program does not help children improve their reading skills but the test indicated that it does help.

Thus, the more consequential error for the educators is committing the type I error.

To prevent committing this error, they need to decrease type I error's probability which is denoted by level of significance, need to decrease the level of significance of the hypothesis test.

Thus,

Option D: Decrease the significance level to decrease the probability of Type I error.

Lear more about type I and type II error here:
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Answer:

2

Step-by-step explanation:

16 ^ (1/4)

Rewriting 16 as 2^4

2^4 ^ 1/4

We know that a^b^c = a^(b*c)

2 ^ (4*1/4)

2 ^1

2

The right answer is 2.

please see the attached picture for full solution

Hope it helps

Good luck on your assignment

Answer:

a) [tex] t_{\alpha/2}=\pm 2.447[/tex]

b) [tex] t_{\alpha/2}=\pm 2.718[/tex]

c) [tex] t_{\alpha/2}=\pm 2.779[/tex]

d) [tex] t_{\alpha/2}=\pm 2.650[/tex]

Step-by-step explanation:

Part a

The degrees of freedom are given by:

[tex] df=n-1= 7-1=6[/tex]

The confidence is 95% or 0.95 the significance would be [tex]\alpha=0.05[/tex] and the critical values would be:

[tex] t_{\alpha/2}=\pm 2.447[/tex]

Part b

The degrees of freedom are given by:

[tex] df=n-1=12-1=11[/tex]

The confidence is 98% or 0.98 the significance would be [tex]\alpha=0.02[/tex] and the critical values would be:

[tex] t_{\alpha/2}=\pm 2.718[/tex]

Part c

The degrees of freedom are given by:

[tex] df=n-1=27-1=26[/tex]

The confidence is 99% or 0.99 the significance would be [tex]\alpha=0.01[/tex] and the critical values would be:

[tex] t_{\alpha/2}=\pm 2.779[/tex]

Part d

The degrees of freedom are given by:

[tex] df=n-1=14-1=13[/tex]

The confidence is 98% or 0.98 the significance would be [tex]\alpha=0.02[/tex] and the critical values would be:

[tex] t_{\alpha/2}=\pm 2.650[/tex]

A value of a test statistic defines the upper bounds of a confidence interval, statistical significance in a test statistic is known as the crucial value.

For part a )

n = 7

Calculating the degrees of freedom [tex]= df = n - 1 = 7 - 1 = 6[/tex]

At [tex]95\%[/tex] the confidence level, the t:

[tex]\alpha = 1 - 95\% = 1 - 0.95 = 0.05\\\\\frac{\alpha}{ 2} = \frac{0.05}{ 2} = 0.025\\\\t_{\frac{\alpha}{ 2}}\\\\df = t_{0.025,6} = 2.447\\\\[/tex]

The critical value = 2.447

For part b )

n =12

Calculating the degrees of freedom[tex]= df = n - 1 = 12 - 1 = 11[/tex]

At [tex]98\%[/tex] the confidence level , the t:

[tex]\alpha = 1 - 98\% = 1 - 0.98 = 0.02\\\\\frac{\alpha}{ 2}= \frac{0.02}{ 2} = 0.01\\\\t_{\frac{\alpha}{ 2}}\\\\df = t_{0.01,11} =2.718\\\\[/tex]

The critical value =2.718

For part c )

n = 27

Calculating the degrees of freedom [tex]= df = n - 1 = 27 - 1 = 26[/tex]

At [tex]99\%[/tex] the confidence level, the t:

[tex]\alpha = 1 - 99\% = 1 - 0.99 = 0.01\\\\\frac{\alpha}{ 2} = \frac{0.01}{ 2} = 0.005\\\\t_{\frac{\alpha}{ 2}}\\\\df = t_{0.005,26}=2.779\\\\[/tex]

The critical value =2.779

For part d )

n = 14

Calculating the degrees of freedom [tex]= df = n - 1 = 14 - 1 = 13[/tex]

At [tex]98\%[/tex] the confidence level, the t:

[tex]\alpha = 1 - 98\% = 1 - 0.98 = 0.02\\\\\frac{\alpha}{ 2} = \frac{0.02}{ 2} = 0.01\\\\t_{\frac{\alpha}{ 2}} \\\\df = t_{0.01,13} =2.650[/tex]

The critical value =2.650

Find out more about the critical value here:

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Answer:

E(s) = 0.15s + 120

Step-by-step explanation:

She earns 15% of her weekly sales plus her $120 salary base.

Answer: Its the second option

Step-by-step explanation: I Promise its correct!

Answer:

a.

Vladivostok is three hours ahead of Bangkok.

Step-by-step explanation:

Time the train left Bangkok is 1:50am

It traveled for 16 hours 40 minutes.

If the train was to be in Bangkok.

The Time Will be 1+16 hours then 50+40 minutes

Which is 17 hours + 1 hour 30 minutes

Which is 18 hours and 30 minutes

And 18 hours = 6:00 pm

So if it was in Bangkok the time with be 6:30 pm

But in Vladivostok, it was 9:30 pm

It's clear that Vladivostok time is faster by 3 hours

Answer:

Step-by-step explanation:

Volume has three parameters and is three dimensional, thus needing a unit in the third power

In difference,

Area is two-dimensional and has only 2 parameters, thus needing a unit only in the second power

Answer:

see below

Step-by-step explanation:

Area is found by multiplying two dimensions  together ( l*w)

Volume is found by multiplying three dimensions together ( l*w*n)

Answer:

1 / 2,787,760,560

Step-by-step explanation:

The number of permutations is:

41 × 40 × 39 × 38 × 37 × 31 = 2,787,760,560

So the probability of winning the jackpot is 1 / 2,787,760,560.

Answer:

-The arrows should be a length of 6

-The arrows should point in the negative direction

-The arrows should start at zero

Step-by-step explanation:

Hope this helps!

Answer:

B

D

E

Step-by-step explanation:

Answer:

Step-by-step explanation:

a) Find the gradient

[tex]\nabla f(x,y) =f_x(x,y)\bold{i} +f_y (x,y)\bold{j}[/tex]

[tex]Also, sin(4x+3y)= sin(4x)cos(3y)+sin(3y)cos (4x)[/tex]

[tex]f_x(x,y) = 4cos(4x)cos(3y)-4sin(3y)sin(4x) = 4 cos(4x-3y)[/tex]

[tex]f_y(x,y) = -3sin(4x)sin(3y)+3cos(3y)cos(4x)=3cos(4x-3y)[/tex]

Hence

[tex]\nabla f(x,y) = 4cos(4x-3y)\bold{i}+3cos(4x-3y)\bold{j}[/tex]

b) At point (-6, 8) just replace the values in gradient to find it out. You can do it.

c) directional derivative in the direction u.

[tex]D_uf(x,y)=\nabla f(x,y). u[/tex]

I stuck with your 1 2 3 i -j . What does 1 2 3 mean? is it not 123 or 1 2/3 or else?

Answer: 3x^3 -8*x^2 + 8*x + 3

Step-by-step explanation:

The standard form for a plolynomial is:

a*x^n + b*x^(n-1) + c*x^(n - 2) ........

We have:

(x-1)(3x^2-5x-3)

this is equal to:

3*x^3 - 5*x^2 + 3*x - 3*x^2 +5*x + 3

where the thing that i did is distribute the multiplication

this is equal to:

3x^3 -8*x^2 + 8*x + 3

Answer:

15/4

Step-by-step explanation:

3/4:1/5= 3/4*5= 15/4

Answer:

Step-by-step explanation:

your question is

[tex]-3*1 + 10x = x+4[/tex]

-3+10x=x+4

9x=7

x = 7/9

Answer:

x=7/9

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

(−3)(1)+10x=x+4

−3+10x=x+4

10x−3=x+4

Step 2: Subtract x from both sides.

10x−3−x=x+4−x

9x−3=4

Step 3: Add 3 to both sides.

9x−3+3=4+3

9x=7

Step 4: Divide both sides by 9.

9x

9

= 7 /9

x= 7 /9

Answer:

P(X≥112) = 0.9495

The  percentage of the games that Easton bowls does  he score higher than 112 = 94.95%

Step-by-step explanation:

Given mean of the Population = 130

Given standard deviation of the Population = 11

Let X= 112

[tex]Z =\frac{x-mean}{S.D} =\frac{112-130}{11}=-1.636[/tex]

P(X≥112) = P(Z≥ z)

               = 1-P(Z≤z)

               = 1- ( P(Z≤-1.636)

             =  1- (0.5-A(-1.636)

            = 0.5 +A(1.636)

            = 0.5 + 0.4495

P(X≥112) = 0.9495

The  percentage of the games that Easton bowls does

he score higher than 112 = 94.95%