The sample space listing the eight simple events that are possible when a couple has three children is​ {bbb, bbg,​ bgb, bgg,​ gbb, gbg,​ ggb, ggg}. After identifying the sample space for a couple having four​ children, find the probability of getting three girls and one boy (in any order ).

Answer:

Step-by-step explanation:

The standard form of an exponential function is

[tex]y=a(b)^x[/tex] , where a is the initial value and b is the growth factor.

You will always find your initial value at the y value where x = 0.  From your table where x = 0 and y = 1/2:

[tex]\frac{1}{2}=a(b)^0[/tex]

Any number or variable raised to the power of 0 = 1, therefore

[tex]\frac{1}{2}=a(1)[/tex] which gives us an initial value, a, of 1/2.

Answer:

7) 6 is not a perfect square, sqrt(6) can't be written in a fraction form

8) 2 is not a perfect cube, cuberoot of 2 can't be written in a fraction form

9) 3/2 is already a fraction, so clearly rational

Answer:

1 : 3

Step-by-step explanation:

The ratio of strawberries : grapes = 6 : 18 ( divide both values by 6 )

ratio = 1 : 3 ← in simplest form

Answer:

1 : 3

Step-by-step explanation:

The ratio of strawberries : grapes = 6 : 18 ( divide both values by 6 )

ratio = 1 : 3 ← in simplest form

Answer:

[tex]t=\frac{70.1-65.2}{\frac{2.52}{\sqrt{30}}}=10.65[/tex]    

[tex]p_v =P(t_{(29)}>10.65)=7.76x10^{-12}[/tex]  

And the best conclusion for this case would be:

D. The p-value is less than 0.00001. There is sufficient data to reject the null hypothesis.

Step-by-step explanation:

Data given and notation  

[tex]\bar X=70.1[/tex] represent the sample mean

[tex]\sigma=2.52[/tex] represent the population standard deviation  

[tex]n=30[/tex] sample size  

[tex]\mu_o =65.2[/tex] represent the value that we want to test

[tex]\alpha[/tex] represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean is higher than 65.2, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \leq 65.2[/tex]  

Alternative hypothesis:[tex]\mu > 65.2[/tex]  

If we analyze the size for the sample is = 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic

We can replace in formula (1) the info given like this:  

[tex]t=\frac{70.1-65.2}{\frac{2.52}{\sqrt{30}}}=10.65[/tex]    

P-value

The first step is calculate the degrees of freedom, on this case:  

[tex]df=n-1=30-1=29[/tex]  

Since is a one side right tailed test the p value would be:  

[tex]p_v =P(t_{(29)}>10.65)=7.76x10^{-12}[/tex]  

And the best conclusion for this case would be:

D. The p-value is less than 0.00001. There is sufficient data to reject the null hypothesis.

The correct option is D. The p-value is less than [tex]0.00001.[/tex] There is sufficient data to reject the null hypothesis.

Hypotheses:

Null hypothesis [tex](\(H_0\)): \(\mu_1 = \mu_2\)[/tex] (the mean height of contemporary males is equal to the mean height of eighteenth-century males)

Alternative hypothesis [tex](\(H_1\)): \(\mu_1 > \mu_2\)[/tex] (the mean height of contemporary males is greater than the mean height of eighteenth-century males)

Given Data:

Sample mean for contemporary males [tex](\(\bar{x}_1\)) = 70.1 inches[/tex]

Sample standard deviation for contemporary males [tex](\(s_1\)) = 2.52 inches[/tex]

Sample size for contemporary males [tex](\(n_1\)) = 30[/tex]

Sample mean for eighteenth-century males [tex](\(\bar{x}_2\)) = 65.2 inches[/tex]

Sample standard deviation for eighteenth-century males [tex](\(s_2\)) = 3.51\ inches[/tex]

Sample size for eighteenth-century males [tex](\(n_2\)) = 30[/tex]

Test Statistic:

We use a two-sample t-test for the difference of means:

[tex]\[t = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}}\][/tex]

Substituting the given values:

[tex]\[t = \frac{70.1 - 65.2}{\sqrt{\frac{2.52^2}{30} + \frac{3.51^2}{30}}}\][/tex]

First, calculate the variances and their respective terms:

[tex]\[s_1^2 = 2.52^2 = 6.3504, \quad s_2^2 = 3.51^2 = 12.3201\][/tex]

[tex]\[\frac{s_1^2}{n_1} = \frac{6.3504}{30} = 0.21168, \quad \frac{s_2^2}{n_2} = \frac{12.3201}{30} = 0.41067\][/tex]

[tex]\[\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}} = \sqrt{0.21168 + 0.41067} = \sqrt{0.62235} = 0.7889\][/tex]

Now calculate the t-value:

[tex]\[t = \frac{70.1 - 65.2}{0.7889} = \frac{4.9}{0.7889} = 6.21\][/tex]

Degrees of Freedom:

Since the sample sizes are the same, we can use the following approximation for degrees of freedom [tex]df[/tex]

[tex]\[df = n_1 + n_2 - 2 = 30 + 30 - 2 = 58\][/tex]

P-value:

Using a t-distribution table or a calculator for a one-tailed test with [tex]58[/tex] degrees of freedom, we find that a t-value of [tex]6.21[/tex] corresponds to a p-value much less than [tex]0.00001.[/tex]

Answer:

C

Step-by-step explanation:

I think you missed attaching the picture, so hope my photo fits your questions well!

We must consider the median of the data sets, it may  represent the center of the dispersion measure. Then we see answer C is the most suitable one, this is because it's median is approximately to $60.

Answer:

The answer to the question is

The probability of winning second prize (that is, picking five of the six winning numbers) with a 6/44 lottery, as played in Connecticut, Missouri, Oregon, and Virginia is 3.49905×10⁻⁵≡ 0.00003 to five decimal places.

Step-by-step explanation:

The probability of winning the second prize or picking five of the six winning numbers) with a 6/44 lottery is given by

Number of 5 sets of numbers in 44 = ₄₄C₅ = 1086008 ways

Number of 5 set of winning numbers in 44 = 1

Number of ways of picking the last number to make it 6 numbers is given by

44 - 5 lucky numbers - The 1 winning number = 38

Therefore, there are 38 ways from 1086008 of selecting the 5 second place winning numbers

Therefore the probability of picking the 5 second place winning numbers is [tex]\frac{38}{1086008}[/tex] = 3.49905×10⁻⁵

Answer:

8 headbands can be made.

Step-by-step explanation:

dividing both sides by 16.5, the material needed for one, leaves the equation as h=8, because 132 divided by 16.5 equals 8

Brinley can make 8 hands from the elastic she has.

What is the unitary method?

The unitary method is a method in which you find the value of a unit and then the value of a required number of units. Suppose you go to the market to purchase 6 apples. The shopkeeper tells you that he is selling 10 apples for Rs 100. In this case, the apples are the units, and the cost of the apples is the value.

Given here, A headband needs 16 and a half inches of elastic and Brinley has 132 inches of elastic

Therefore the number of headbands that she could make is

= 132/16.5

=8 Headbands.

Hence, Brinley can make 8 hands from the elastic she has.

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Answer:

[tex]D(t)=100(0.4)^t[/tex]

Step-by-step explanation:

The temp is 100 at time t = 0

After 1 sec, the temp difference would be:

[tex]100-(\frac{100-60}{100})[/tex]

After 2 sec, the temp difference would be:

[tex]100-(\frac{100-60}{100})^2[/tex]

Similarly for 3 seconds, 4 seconds etc.

We notice that the parenthesis part is 40% of it, so we can also write:

100(40%)^t,

where

t is the time

40% can be written as 40/100  = 0.4

SO, the function is:

[tex]d(t)=100(0.4)^t[/tex]

Answer:

[tex]D(t)=100*0.4^t[/tex]

Step-by-step explanation:

Initially, the difference between the rod's and the water's temperatures is 100°

i.e D(t)=100 When t=0

After 1 seconds, the temp drops by 60%.

Therefore, the new value of D will be the old value multiplied by (100-60)%.

D(1)=100 X (100%-60%) = 100*0.4

After 2 seconds, the temp difference would be:

D(2)=100*0.4*0.4= [tex]100*0.4^2[/tex]

We notice that for any t, the percentage at which the difference is reduced is raised to the power of t.

Therefore, temperature difference in degrees Celsius, D(t), t seconds after the rod was plunged into the water is given as:

[tex]D(t)=100*0.4^t[/tex]

Answer:

The total amount spent during 2003 was $725.78.

Step-by-step explanation:

Given:

During the 2004 season, New York theater goers bought 11.3 million tickets for a total of $749.0 . Theater goers spent a total of 3.2% more than the year before.

Now, to find the total amount that was spent during 2003.

Let the amount spent during 2003 be [tex]x.[/tex]

The amount spent during 2004 = $749.0.

As, given theater goers spent a total of 3.2% more than the year before.

So, we put equation to get the amount spent during 2003:

[tex]x+3.2\%\ of\ x=749[/tex]

[tex]x+\frac{3.2}{100} \times x=749[/tex]

[tex]x+\frac{3.2x}{100}=749[/tex]

[tex]\frac{100x+3.2x}{100} =749[/tex]

[tex]\frac{103.2x}{100} =749[/tex]

Multiplying both sides by 100 we get:

[tex]103.2x=74900[/tex]

Dividing both sides by 103.2 we get:

[tex]x=\$725.78[/tex]

Therefore, the total amount spent during 2003 was $725.78.

Answer:

(b) 4 x = 4 5 is the needed expression to solve for the value of x.

Step-by-step explanation:

Here, the given proportion is simplified as:

[tex]\frac{4}{5} = \frac{9}{x}[/tex]

Now, to simplify any proportion of the form [tex]\frac{a}{b} = \frac{c}{d}[/tex]  the simplest way is CROSS MULTIPLICATION.

So, cross multiplying  [tex]\frac{a}{b} = \frac{c}{d} \implies ad = bc[/tex]

Similarly cross multiplying [tex]\frac{4}{5} = \frac{9}{x}[/tex], we get:

4 (x)  = (9) (5)

or, 4 x  = 45

Hence, 4 x = 45 is the needed expression to solve for the value of x.

Answer:

4x=45

Step-by-step explanation:

4/5=9/x, so first you would multiply 5×9 (because cross products are always equal) and you would get 45. Since 4x has to also equal 45, the answer is 4x=45.

Hope this helps (P.S. I got it right on the test)!

Answer: the power required to do the same work in 1 hour is 30 j/h

Step-by-step explanation:

If two variables vary inversely, an increase in one of the variables causes a decrease in the other variable and vice versa.

The power P required to do a fixed amount of work varies inversely as the time t. If we introduce a constant of variation, k, the expression would be

P = k/t

If a power of 15 J/h is required to do a fixed amount of work in 2 hours, it means that

15 = k/2

k = 15 × 2 = 30

The equation becomes

P = 30/t

Therefore, the power required to do the same work in 1 hour is

P = 30/1 = 30 j/h

Answer:

y will increase if x is increased,

y will decrease if x is decreased.

Step-by-step explanation:

1/F=1/X+ 1/Y

1/F-1/X=1/Y

X-F/FX=1/Y

FX/X-F=Y

Rearranging, Y=FX/X-F

So this is the function in terms of X, and F is just a constant

Therefore, the function becomes Y=65X/X-65

Explanation:

y = focusing distance

x = distance from lens

Focusing distance y will increase if the object x moves far away from the lens i.e. x is increased,

Similarly, focusing distance y will decrease if the object x moves closer and closer to the lens i.e. x is decreased.

An asymptote is a function that mimics a curve f(x) as x approaches infinity.

A vertical asymptote, however, cannot be crossed in a function.  Remember that a function cannot have multiple y values for a given x value, hence the vertical line test for a function.  If a function crossed a vertical asymptote and then went back to it, then it would have to go back over itself as it becomes arbitrarily close to the asymptote. Therefore, it is not possible to cross a vertical asymptote.

The focal point, F, the object distance from the lens, X, and the image distance from the the lens, Y, vary according to the lens formula

1. The value of the focusing distance, Y, is negative and increases in

magnitude, when X < 65, and positive and decreasing in magnitude when

X > 65, the line X = 65 is a vertical asymptote.

2. When X > 65, the value of Y is positive and increasing as the object

moves closer to the lens. At X = 65, there is no image when 0 ≤ X < 65, the

value of Y is negative and increasing towards 0.

3. A vertical asymptote is a discontinuity, where the function is not defined

Reasons:

Known;

[tex]\dfrac{1}{F} = \dfrac{1}{X} + \dfrac{1}{Y}[/tex]

Where;

F = The focal length

X = Object distance from lens

Y = Location of film = Image distance from lens

(a) Given that F = 65, we have;

[tex]\dfrac{1}{65} = \dfrac{1}{X} + \dfrac{1}{Y}[/tex]

[tex]\dfrac{1}{65} - \dfrac{1}{X} = \dfrac{1}{Y}[/tex]

[tex]Y = \dfrac{65 \cdot X}{X - 65}[/tex]

Given that 65·X > X - 65 When X > [tex]-\dfrac{65}{64}[/tex], we have;

As X is increased, Y is decreases, with the rate of decrease reducing as the

value of X gets larger.

(b) As the object moves closer to the lens, when X > 65, the value of Y

increases, at X = 65, the value of Y is infinity, which is a vertical asymptote,

as the object moves closer, the value of Y becomes negative, with the

value increasing (becoming less negative) and when X = 0, Y = 0

3. It is not possible to cross the asymptote because the function has a

discontinuity at the asymptote, which represent the point where the image

is at infinity, such that giving that the distance of the image increases as X

approaches the asymptote, crossing the asymptote results in the image

located further than infinity (which is impossible).

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Answer:

Veggie

Step-by-step explanation:

I corrected your question for a better situation.

At a party there were four large submarine sandwiches all the same size . During the party 2/3 of the chicken sandwich three over 4 of the tuna sandwich 7/12 of the roast beef sandwich and 5/6 of the veggie sandwich were eating which sandwich had the least amount left

Here is my answer:

So the sandwich had the least amount is Veggie

Answer:

Step-by-step explanation:

Given that the mean salary for a new teacher in your town is $48,000

You believe it is higher for new teachers in a neighboring town.

So to prove or disprove your claim you have to show statistical evidence.

For that hypothesis testing is necessary.

You must conduct a hypothesis test for comparing the mean of salary of new teacher with neighbouring places

The hypotheses wouldbe

[tex]H_0: \mu = 48000\\H_1: \mu >48000[/tex]

where mu is the average for neighbouring states.

Answer:

27/2

Step-by-step explanation:

Answer:

The answer is: 3

Step-by-step explanation:

1. At the begining of the program we start by declairing the variables:

 double x=1, double y=1 and int i=0.

2. The structure do...while is used to defined the loop. x<2.5 is the finalization condition of the loop. i is the counter of the loop.

y=x/2 is the first calculation

x=x+y is the second one. Here is where the values of the variable x changes.

a) for the first iteration, the values of y and x are shown below:

[tex]\\\\x=1\\y=1\\y=1/2=0.5\\x=1+0.5=1.5\\i=1[/tex]

The variable x is minor to 2.5 so the loop will continue computing.

b)   the second iteration, the values of y and x are shown below::

 [tex]y=0.5\\x=1.5\\y=\frac{1.5}{2}=0.75\\ x=1.5+0.75=2.25\\i=2[/tex]

The variable x is still minor to 2.5 so the loop will continue computing.

c) third iteration:

[tex]y=0.75\\x=2.25\\y=\frac{2.25}{2} =1.1125\\x=2.25+1.125=3.375\\i=3[/tex]

The condition x<2.5 is not true so the loop ends.

3. System.out.print(i + " "); displays the value of the variable i wich value is 3.

Therefore the number 3 is display.

Answer:

$58,544

Step-by-step explanation:

Given that Baylor charges tuition fees at $41,194, Room at $13038 and Required fees at $4598 p.a. We also know that the scholarship pays $44194 p.a.

#The additional money for the four years is the total  minus the scholarship  multiplied by 4 yrs:

[tex]C_{p.a}=Tution+Room+Required\\\\=41194+13038+4598\\\\=58830\\\\Scholarship=44194\\\\\bigtriangleup p.a=58830-44194\\\\=14636[/tex]

The additional cost to attend the college for the next four years is:

[tex]\bigtriangleup p.a=14636\\\\\sum{\bigtriangleup p.a _i}=4\times 14636\\\\=58544[/tex]

Hence, Amanda needs an additional $58,544 to attend Baylor for the 4 years.

Answer:

D

Step-by-step explanation:

Cause if you se it close you wil get it

Approximately 85.33% of the exam scores are between 68 and 77.99 points.

To find the proportion of exam scores between 68 and 77.99 points in a normally distributed set, we can use the Z-score formula:

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

where X is the score, [tex]\( \mu \)[/tex] is the mean, and [tex]\( \sigma \)[/tex] is the standard deviation.

Given:

- Mean [tex]\( \mu = 71.33 \)[/tex]

- Standard deviation [tex]\( \sigma = 3 \)[/tex]

- We need to find the proportion of scores between [tex]\( X_1 = 68 \)[/tex] and [tex]\( X_2 = 77.99 \)[/tex].

1. Calculate the Z-scores for [tex]\( X_1 = 68 \)[/tex]:

[tex]\[ Z_1 = \frac{68 - 71.33}{3} = \frac{-3.33}{3} = -1.11 \][/tex]

2. Calculate the Z-scores for [tex]\( X_2 = 77.99 \)[/tex]:

[tex]\[ Z_2 = \frac{77.99 - 71.33}{3} = \frac{6.66}{3} = 2.22 \][/tex]

Next, we look up these Z-scores in the standard normal distribution table or use a calculator to find the corresponding proportions:

- The proportion corresponding to [tex]\( Z_1 = -1.11 \)[/tex] is approximately 0.1335.

- The proportion corresponding to [tex]\( Z_2 = 2.22 \)[/tex] is approximately 0.9868.

The proportion of scores between [tex]\( X_1 = 68 \)[/tex] and [tex]\( X_2 = 77.99 \)[/tex] is the difference between these two proportions:

[tex]\[ P(68 < X < 77.99) = P(Z < 2.22) - P(Z < -1.11) \][/tex]

[tex]\[ P(68 < X < 77.99) = 0.9868 - 0.1335 = 0.8533 \][/tex]

Answer:

W = 15 ft. and L = 30 ft.

Step-by-step explanation:

Perimeter = 90 ft.

Twice as long as it is wide: L=2W

P = 2(L + W) = 2(2W + W) = 6W

90 = 6W

W = 15 ft. and L = 30 ft.

Answer:

The dimensions are: Width= 15ft

Length=30ft

Step-by-step explanation:

Perimeter of fence=90feet

He wants to make a rectangle with dimensions length and with.

The rectangle length is twice as long as the width= L= 2W

Perimeter of a rectangle = 2(L + W)

90= 2(2W +W)

90= 6W

90/6=W=15ft

L=2W= 2× 15=30ft

Answer:

16 possible ways

Step-by-step explanation:

Using the formular Cp,k= p!/I! (P-k)!

Where k= number of selected committee members

P= available number that can sit in the committee

For doctors,there are 5 doctors

C= 5!/2!(3)!= 120/12 = 10ways

For nurses,there are 4

C= 4!/2!(2)! = 24/4 =6ways

Total possible ways=10 + 6 = 16 ways

Answer:

60

Step-by-step explanation:

(2 out of 5 doctors) * (2 out of 4 nurses)

Answer: it would take them 40/13 hours

Step-by-step explanation:

If Naomi were to paint her living room alone, it would take 5 hours. it means that the rate at which she paint her living room alone is 1/5

Her sister Jackie could do the job in 8 hours. it means that the rate at which Jackie paint the living room is 1/8

If they work together, they would work simultaneously and their individual rates are additive. This means that their combined working rate would be

1/5 + 1/8 = (8 + 5)/40 = 13/40

Assuming it takes t hours for both of them to clean the room working together, the working rate per hour would be 1/t. Therefore,

13/40 = 1/t

t = 40/13 hours

Answer:

[tex]x = 2\,\frac{4}{5}\,ft[/tex]

Step-by-step explanation:

The equation of elevation for the dolphin is:

[tex]-\frac{67}{4} + 5\cdot x = -\frac{21}{4}[/tex]

[tex]5\cdot x = \frac{56}{4}[/tex]

[tex]x = 2\,\frac{4}{5}\,ft[/tex]

Answer:

5x -16 3/4 = -5 1/4

Note: This is based off of Study Island's multiple choice answers

Step-by-step explanation:

We're trying to figure out how far the dolphin travels with each kick. The dolphin starts at an elevation of -16 3/4 feet and ends up at an elevation of -5 1/4 feet. In other words, what can we add to -16 3/4 to get -5 1/4?

The elevation is our variable (x). The dolphin kicks 5 times to get from point a to point b. So we should add 5x to -16 3/4 to get -5 1/4. This equation will solve for the length in feet traveled per kick. Our equation is now:

5x + -16 3/4 = -5 1/4

Adding a negative is the same thing as subtracting a positive, so our final equation is:

5x - 16 3/4 = -5 1/4

If we want to solve this:

5x - 16.75 = -5.25

5x = 11.5

x = 2.3 feet per kick

Answer:

The new mean = 3 × (the old mean) = 150

The new standard deviation is also = 3 × (The old standard deviation) = 15

Step-by-step explanation:

µ = 50 and σ = 5

The mean is the sum of variables divided by the number of variables.

Mean = (Σx)/N = µ = 50

x = each variable

N = number of variables

If each variable changed to 3x

Mean becomes

Mean = (Σ(3x))/N = 3 (Σx)/N = 3 × µ = 3 × 50 = 150.

The standard deviation is the square root of variance. And variance is an average of the squared deviations from the mean.

The standard deviation measures the rate of spread of the data set around the mean.

Standard deviation = σ = √[Σ(x - µ)²/N]

x = each variable

µ = mean

N = number of variables

If each variable changed to 3x

Recall µ changed to 3µ

Standard deviation = σ = √[Σ(3x - 3µ)²/N]

σ = √[Σ 3² (x - µ)²/N] = √[(3²)Σ(x - µ)²/N] = 3×√[Σ(x - µ)²/N] = 3 × σ = 3 × 5 = 15

If every score is multiplied by 3, it is logical to reason that the average of the new set of numbers also is 3× the old average.

And the new set of numbers spread out similarly around this new mean, only that the new space of spread is now 3× the old one.

When every score in a population is multiplied by a constant, both the mean and the standard deviation are multiplied by that constant. So, in the given example, the new mean would be 150 and the new standard deviation would be 15.

In mathematics, when every score in a population is multiplied by a constant, both the mean (µ) and the standard deviation (σ) are also multiplied by that constant.

So, if every score in a population with µ = 50 and σ = 5 is multiplied by 3, the new mean (µ_new) would be 50 * 3 = 150, and the new standard deviation (σ_new) would be 5 * 3 = 15.

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Answer:

False

Step-by-step explanation:

We are told that there is a 33% probability that physics students belong to ethnic minorities, therefore if the sample is 10 people, the amount would be given as follows:

10 * 33% = 3.3 people would be from ethnic minorities. What means of those 10 no more than 4 (to round the number) people belong to an ethnic minority.

Therefore, this statement is false, because it does not represent exactly the probability established in the university.

It is possible to clarify that what affirmation is true part because it fulfills what it says, because the probability says that 4 or less, and the affirmation says that 6 or less, however, the affirmation mentions that it corresponds to the probability of 33% and that if it is false, to correspond it should be between 51% and 60%.

Answer:

what is the actual problem?

Step-by-step explanation:

The swimmer will travel a distance of 55.92 meters when swimming from one corner to the opposite corner of an Olympic-size swimming pool.

Given, the length and width of the pool form the two sides of the right-angled triangle, and the distance the swimmer will travel is the hypotenuse.

Using the Pythagorean theorem, we can calculate the distance as follows:

Distance² = Length² + Width²

Distance² = 50² + 25²

Distance² = 2500 + 625

Distance² = 3125

Distance = √3125

Distance = 55.90 meters

Therefore, a swimmer will travel approximately 55.92 meters.

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Final answer:

To determine the distance a swimmer travels across an Olympic-sized pool from corner to opposite, the Pythagorean theorem is used, giving approximately 55.90 meters as the distance.

Explanation:

The student's question entails calculating distances and speeds in different swimming and water current scenarios, which is a classic physics problem involving kinematics and geometry. However, since it involves calculations and applying formulae, particularly the Pythagorean theorem, and rate, time, and distance relationships, it falls under the subject of Mathematics.

To Calculate the Distance Swum Across an Olympic-sized Pool

For an Olympic-sized pool that is 50 meters in length and 25 meters in width, a swimmer traveling from one corner to the opposite would traverse a diagonal. To calculate this diagonal distance, we use the Pythagorean theorem:

Diagonal2 = Length2 + Width2

Diagonal = √(Length2 + Width2)

Substitute the given values:

Diagonal = √(502 + 252) = √(2500 + 625)

Diagonal = √(3125) meters

The swimmer will travel approximately √(3125) meters, which is about 55.90 meters.

Answer:

270725 different ways

Step-by-step explanation:

The problem tells us that the order of the letters does not matter. Therefore, in the combination the order is NOT important and is signed as follows:

C (n, r) = n! / r! (n - r)!

We have to n = 52 and r = 4

C (52, 4) = 52! / 4! * (52-4)! = 52! / (4! * 48!) = 270725

Which means that there are 270725 different ways in total to make that raffle

Answer:

Step-by-step explanation:

a)

Number of children under 5    Number of household   Relative frequency

      0                                                      17                           17 / 50 = 0.34

       1                                                      14                           14 / 50 = 0.28

       2                                                      14                           14 / 50 = 0.28

       3                                                       3                            3 / 50 = 0.06

       4                                                        2                            2 / 50 = 0.04

                                                                50

Note,

Relative frequency  = Class frequency / Total Frequency

b) Percentage of households has two children under the age of 5 ,

= [tex]\frac{14}{50}[/tex] x 100

= 0.28 x 100

= 28%

Final answer:

To calculate the percentage of households with two children under the age of 5, divide the frequency of 2 by the total number of households and multiply by 100.

Explanation:

To calculate the percentage of households with two children under the age of 5, we need to find the relative frequency of 2 in the given data. The relative frequency is calculated by dividing the frequency of 2 by the total number of households, which is 50 in this case. The frequency of 2 is 0.06, so the relative frequency of 2 is 0.06/50 = 0.0012. To convert it to percentage, we multiply by 100, so the percentage of households with two children under the age of 5 is 0.0012 * 100 = 0.12%.

Answer:

Option C) Quadratic regression model

Step-by-step explanation:

Quadratic regression model

where x is the independent variable and [tex]\hat{y}[/tex] is the dependent variable.

Thus, the correct answer is

Option C) Quadratic regression model

The (c) quadratic regression model is used to model a nonlinear relationship between the independent and dependent variables by including the independent variable and the square of the independent variable.

The correct answer to this question is C. Quadratic regression model. In statistics, a quadratic regression model is used to model a nonlinear relationship between the independent and the dependent variables. This is achieved by including the independent variable and the square of the independent variable in the model. For example, if 'x' is the independent variable, the model would include both 'x' and 'x²'. The quadratic term allows for the model to fit simple curved relationships between the dependent and independent variable. The other models listed, such as multiple regression model, least squares regression model and a simple regression model, tend to represent linear relationships.

Here is a simple illustrative example: suppose you wanted to model the relation between the amount of fertilizer used (independent variable 'x') and the height of a plant (dependent variable 'y'). If the relation isn't linear (meaning more fertilizer does not always result in more growth, and growth rate declines after a certain point, forming a curved pattern in the data), you could use a quadratic regression model

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