How many possible birth orders with respect to gender are possible in a family with six ​children

Answer:

160/100+60+0/one hundred sixty

OR JUST 160 LIKE YOU ASKED

The product of thirty-two and five will be equal to 160.

A product is the result of multiplication or an expression that indicates factors that are to be multiplied, in mathematics.

The multiplication will be given as:-

32  x  5  =  160

Or we can also do it like the addition of 32 five times:-

32  +  32  + 32  +  32  +  32 = 160

Therefore products of thirty-two and five will be equal to 160.

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Finding the z-value in a standard normal distribution for certain proportions involves using a standard normal (Z-score) table. For (a) the z-value is -0.36, and for (b), the z-value is 0.36.

To find the value of z that allows for a proportion of observations less or greater than it in a standard normal distribution, you need to use a standard normal (Z-score) table, or use an online calculator that allows you to find the Z-score associated with a specific proportion.

(a) For the proportion of observations that are less than z = 0.36, you would look up this proportion in the body of a standard normal table to find the associated Z-score. Alternatively, using a Z-score calculator, the z value is approximately -0.36.

(b) For the proportion of observations that are greater than Z = 0.36, it would be equivalent to looking for the proportion that is less than Z = 1 - 0.36 = 0.64 in the standard normal table. The z value here is approximately 0.36.

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Answer:

[22.57 ± 2.776]

Step-by-step explanation:

Hello!

You have the 95% Confidence Z-interval (21.182;23.958), the mean X[bar]= 22.57 and the sample size n=25.

The formula for the Z interval is

[X[bar] ± [tex]Z_{1-\alpha /2} *( \frac{Sigma}{\sqrt{n} } )[/tex]]

The value of Z comes from tha standard normal table:

[tex]Z_{1-\alpha /2} = Z_{0.975}= 1.96[/tex]

The semiamplitude (d) or margin of error (E) of the interval is:

E or d= (Upperbond- Lowerbond)/2 = (23.958-21.182)/2 = 2.776

[X[bar] ± E]

[22.57 ± 2.776]

I hope it helps!

Answer:

y(x)=C_1·e^{2x} + C_2·e^{-6x}

Step-by-step explanation:

From Exercise we have the differential equation

y''+4y'-12=0.  

This is a characteristic differential equation and we are solved as follows:

y''+4y'-12=0

m²+4m-12=0

m_{1,2}=\frac{-4±\sqrt{16+48}}{2}

m_{1,2}=\frac{-4±\sqrt{64}}{2}

m_{1,2}=\frac{-4±8}{2}

m_1=2

m_2=-6

The general solution of this differential equation is in the form

y(x)=C_1·e^{m_1 ·x} + C_2·e^{m_2 ·x}

Therefore, we get

y(x)=C_1·e^{2x} + C_2·e^{-6x}

The correct values of the constant [tex]\( r \)[/tex] for which [tex]\( y = e^{rx} \)[/tex] is a solution of the differential equation [tex]\( y'' + 4y' - 12y = 0 \)[/tex] are [tex]\( r = 2 \)[/tex] and [tex]\( r = -6 \).[/tex]

To find the values of [tex]\( r \)[/tex], we substitute [tex]\( y = e^{rx} \)[/tex] into the differential equation. First, we find the first and second derivatives of [tex]\( y \)[/tex]:

[tex]\[ y' = \frac{d}{dx}(e^{rx}) = re^{rx} \][/tex]

[tex]\[ y'' = \frac{d}{dx}(re^{rx}) = r^2e^{rx} \][/tex]

Now, we substitute [tex]\( y \)[/tex], [tex]\( y' \)[/tex], and [tex]\( y'' \)[/tex] into the differential equation:

[tex]\[ y'' + 4y' - 12y = 0 \][/tex]

[tex]\[ r^2e^{rx} + 4re^{rx} - 12e^{rx} = 0 \][/tex]

Since [tex]\( e^{rx} \)[/tex] is never zero, we can divide through by [tex]\( e^{rx} \)[/tex] to get the characteristic equation:

[tex]\[ r^2 + 4r - 12 = 0 \][/tex]

Now, we solve this quadratic equation for [tex]\( r \)[/tex]:

[tex]\[ r^2 + 6r - 2r - 12 = 0 \][/tex]

[tex]\[ r(r + 6) - 2(r + 6) = 0 \][/tex]

[tex]\[ (r - 2)(r + 6) = 0 \][/tex]

Setting each factor equal to zero gives us the possible values for [tex]\( r \)[/tex]:

[tex]\[ r - 2 = 0 \quad \Rightarrow \quad r = 2 \][/tex]

[tex]\[ r + 6 = 0 \quad \Rightarrow \quad r = -6 \][/tex]

Therefore, the values of [tex]\( r \)[/tex] for which [tex]\( y = e^{rx} \)[/tex] is a solution of the given differential equation are [tex]\( r = 2 \)[/tex] and [tex]\( r = -6 \).[/tex]

Answer:

x+2a-b=5x+5a-2*3a+2*b

x+2a-b=5x+5a-6a+2b

x+2a-b=5x-a+2b

5x-x=2a-b+a-2b

4x=3a-3b

4 x=3(a-b)

x=3/4(a-b)

The answer of the vector x in the form of a and b is 3/4(a-b).

"A vector is an object that has both a magnitude and a direction. Geometrically, we can picture a vector as a directed line segment, whose length is the magnitude of the vector and with an arrow indicating the direction. The direction of the vector is from its tail to its head."

Here,

[tex]x + 2a - b = 5(x + a) - 2(3a - b) x[/tex]

[tex]x+2a-b=5x+5a-6a+2b\\\\x+2a-b=5x-a+2b\\\\5x-x=2a-b+a-2b\\\\4x=3a-3b\\\\4 x=3(a-b)\\\\x=3/4(a-b)\\[/tex]

Hence the vector x = 3/4(a-b)

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Answer:

16/52 or 4/13 when reduced.

Step-by-step explanation:

4/52 is for the Jack card since there are 4 jack cards out of a total of 52 cards.

12/52 is for the face cards since there are 12 face cards out of a total of 52 cards.

Since the problem says OR, this means one or the other, so you will be adding those two fractions together. If the problem said AND, this would mean that you have to multiply since both would have to occur.

The probability of selecting a heart or a face card from a standard deck of cards is 22/52.

To calculate the probability of selecting a heart or a face card from a standard deck of cards, we must consider the total number of heart cards and face cards in the deck, mindful not to double-count any cards that are both. A standard deck has 52 cards, 12 of which are face cards (3 face cards per suit, and there are 4 suits in total). Besides these 12 face cards, there are 13 heart cards, but since three of them are face cards, which we have already counted, we subtract those, leaving us with 10 additional heart cards. Thus, the total number of favorable outcomes is 12 (face cards) + 10 (non-face-card hearts) = 22.

The probability of drawing a heart or face card is then 22 favorable outcomes divided by 52 possible outcomes, which simplifies to 11/26 or about 42.31%.

To understand if this outcome is more or less likely than selecting a heart suit face card, we consider that there are only 3 face cards in the hearts suit. Hence, the probability of drawing a heart suit face card is 3/52 or about 5.77%. Clearly, drawing a heart or a face card is more likely than drawing a heart suit face card alone, as 42.31% > 5.77%.

Answer:

L.A. = 80 + 16√13

Step-by-step explanation:

the lateral area is the area of the vertical faces.

So, for the given prism = The sum of the area of the vertical rectangles.

                                      = height * perimeter of the right triangle.

The hypotenuse of the right triangle = [tex]\sqrt{6^2+4^2} = \sqrt{36+16} =\sqrt{52} =\sqrt{4*13} =2\sqrt{13}[/tex]

So, the sides of the triangle are 4 , 6 and 2√13

The perimeter of the right triangle = 4 + 6 + 2√13 = 10 + 2√13

Height = 8

The lateral area for the prism = 8 * ( 10 + 2√13 ) = 80 + 16√13

Answer:

The correct answer is 80 + 16√13 feet²

Step-by-step explanation:

Like we can see in the plot, the prism has three rectangular sides, that are its lateral area. For calculating the area, we need to add up the three sides, this way:

Height of the prism (h) = 8 ' or 8 feet

Area of the first side = 8 * 4 = 32 feet²

Area of the third side = 8 * 6 = 48 feet²

Area of the third side = 8 * Hypotenuse of the triangle

Hypotenuse of the triangle² = 4² + 6² = 52

Hypotenuse of the triangle =√52 = √13 * 4 = 2√13 feet

Area of the third side = 8 * 2√13 feet = 16√13 feet²

Area lateral of the prism = 32 + 48 + 16√13 = 80 +  16√13 feet²

Answer:

a) Permutations

b) combination

Step-by-step explanation:

a)

Since the order of 15 most important artwork pieces matter, with most popular at first and then at N0.2, 3,4, and so on. Whenever we are dealing with "order of placement" the question at hand is of permutations.

b)

Out of 320 pieces, 125 pieces are to be "selected" and displayed, the process of selection incurs Combinations in which the order in which we select does not matter.  

Scenario a) represents a permutation and the 15 popular pieces can be arranged in 15! ways.

Scenario b) represents a combination and the 125 pieces can be selected in 320 choose 125 ways.

a) This scenario is an example of a permutation. In a permutation, the order of the items matters. In this case, the 15 popular pieces can be arranged in 15! (15 factorial) ways.
b) This scenario is an example of a combination. In a combination, the order of the items does not matter. In this case, the 125 pieces can be selected from the total of 320 pieces in a total of 320 choose 125 ways.

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Answer:

a). [tex]4.86\times 10^{-15}[/tex] m

b). [tex]4.21\times 10^{-2}[/tex] m³

c). [tex]7.00\times 10^{3}[/tex] N²

Step-by-step explanation:

In this question we have to convert each option into SI units.

a). [tex]4.86(10^{-6})^{2}[/tex] mm

= [tex]4.86\times (10^{-12})\times (10^{-3} )[/tex] m

= [tex]4.86\times 10^{-15}[/tex] m

b). (348 mm)³

= [tex](348)^{3}\times (10^{-3})^{3}[/tex] m³

= [tex]42144192\times 10^{-9}[/tex] m³

= [tex]4.21\times 10^{-2}[/tex] m³

c). [tex](83700)^{2}\times (10^{-3})^{2}[/tex] N²

= [tex]700569\times 10^{4}\times 10^{-6}[/tex] N²

= [tex]7.00\times 10^{9}\times 10^{-6}N^{2}[/tex]

= [tex]7.00\times 10^{3}[/tex] N²

The decision rule in hypothesis testing is the criteria used to decide whether to accept or reject the null hypothesis. Given our level of significance and sample data, we reject the null hypothesis if the Z score (calculated as -1.92) is less than the critical value (-1.645). Hence, our decision rule is: if Z is less than -1.645, reject the null hypothesis.

The decision rule in hypothesis testing is the criteria that determines what the decision should be. In this case, the null hypothesis (H0) is that the mean weight of the chocolate chip bags is 439.0 grams, and the alternative hypothesis (H1) is that the mean weight is less than 439.0 grams because the machine is believed to be underfilling the bags.

Given a level of significance of 0.05 and a standard deviation of 21.0, we can calculate the z-score of the sample mean. Z = (Sample Mean - Population Mean) / (Standard Deviation / sqrt(Sample Size)), thus Z = (433.0 - 439.0) / (21.0 / sqrt(47)) = -1.92.

For a one-tailed test at a 0.05 level of significance, the critical value from the Z table is -1.645. The rule is to reject the null hypothesis if the calculated Z score is less than the critical value.

So the decision rule is: if Z is less than -1.645, reject the null hypothesis. In this case, as -1.92 is less than -1.645, we reject the null hypothesis. Hence, based on the sample, it can be said that the machine is underfilling the bags.

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Answer:

a.

Step-by-step explanation:

A and B both are greater than mean and so A and B lies on the right side of mean. Further it is stated that A is more away from the mean than B. It means that A is greater than B. So, in order to find the area between A and B we have to subtract the area of mean to B from area of mean to A. It can be explain in the notations as

P(B<X<A)=P((B-μ)/σ<z<(A-μ)/σ)

P(B<X<A)=P(z<(A-μ)/σ)-P(z<(B-μ)/σ)

Hence, we find the area from mean to A and subtract the area from mean to B.

Answer:

The best option is to phone a friend which will yield a total earnings of $ 806,400

Step-by-step explanation:

From the analysis of the question, there is the probability of success and failure.

if he choose not to answer which is the probability of success, his earnings = $500,000.

if he he answers the question correctly, his earnings = $1,000,000 which in the end, is still a success for him

if he answers the question wrongly, his earnings = $32,000

the last option is to phone a friend and he will either choose option a or option b

Probability of choosing option A = 0.6

Probability of choosing option B = 0.4

expected earnings = P(choosing A) x his earnings if correct +  P(choosing B) x his earnings if wrong

= 0.6 x 1,000,000 + 0.4 x 32,000

= $612,000 will be his earning by second option

if he picks the option b = P (choosing B) x his earnings if correct + P(choosing A) x earnings if wrong = 0.4 x 1,000,000 + 0.6 x 32,000

= $419,000

from the P(success) + P( failure) =1

His earnings = Probability of success x earnings if correct + Probability of failure x earnings if incorrect = 0.8 x 1,000,000 + 0.2 x 32,000

= $806,400

from the calculation done, it is apparent that his best option is to go by phoning a friend since that will yield more earnings for him which is greater than his earnings by going for the second options hence the best option is phoning a friend as this will accrue his expected earning to be $ 806,400

The best strategy is to select an answer (a or b). The expected payout for this option is $600,000.

To find the best strategy, we can create a decision tree. The decision tree will consider the options of not answering, selecting an answer, and phoning a friend. The expected payout for each option can be calculated by multiplying the probability of that option with the payout associated with that outcome. After calculating the expected payout for each option, we can compare them to determine the best strategy.

The decision tree shows that the best strategy is to Select an answer (a or b).

The expected payout for this option is calculated by multiplying the probability of choosing (a) and winning with the payout of $1,000,000, and adding it to the probability of choosing (b) and winning with the payout of $32,000.

The expected payout for this option is $600,000.

Therefore, by selecting an answer, you can expect to win $600,000 on average.

Answer:the constant of proportionality is 2.5 hours per day.

The equation is y = 2.5x

Step-by-step explanation:

Let x represent the number of days that Bruno listens to podcasts.

Let y represent the total number of hours that Bruno listens to podcasts.

Bruno listens to podcasts for

two and a half hours a day.

Let k represent the constant of proportionality. Therefore,

y = kx

k = y/x

So k = 2.5/1 = 2.5 hours/day

The equation is expressed as

y = 2.5x

So if you want to fit the y-intercepts or "b", on the y-axis you should go by 25's [0, 25, 50, 75, 100...]

If the x-axis does not have to follow the same pattern (25's), you should go by 5's  [0, 5, 10, 15, 20...]

y = 7x + 50

y = 2x + 175

First I would plot the y-intercepts for each equation, then plot a few points with x = 5, 10, 15      Then draw a straight line.

The point where the two lines meet/cross paths is your solution. It should be (25, 225)  The x-axis is the number of miles, and the y-axis is the total cost. So Truck driver A and B would arrive/be at the same place/meet in 25 miles at the same cost of $225

Answer:

D. Yes, because the probabilities sum to 1 and are all between 0 and 1, inclusive.

Step-by-step explanation:

0.21 + 0.28 + 0.02 + 0.28 + 0.21 = 1

All individual data are between 0 and 1. Data added up = 1

The true statement is (d) Yes, because the probabilities sum to 1 and are all between 0 and 1, inclusive.

For a distribution to be a discrete probability distribution, the following must be true

[tex]\sum P(x) =1[/tex]

So, we have:

[tex]\sum P(x) = 0.21 + 0.28 + 0.02 + 0.28 + 0.21[/tex]

Evaluate the sum

[tex]\sum P(x) =1[/tex]

The above statement shows that the distribution is a discrete probability distribution

Hence, the true statement is (d) Yes, because the probabilities sum to 1 and are all between 0 and 1, inclusive.

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Answer:

∫(x+25x)dx=13x²

Step-by-step explanation:

From Exercise, we want  calculate integral for x + 25 x dx.  

But this not required  a substitution to express the integrand as a rational function. We can calculte integral, and we get

∫(x+25x)dx= ∫x dx+25∫x dx=x²/2+ \frac{25}{2} · x^2=\frac{26}{2}·x^2=13x²

Therefore, we get that is  

∫(x+25x)dx=13x².

Answer:

a) 25446.90 ft²

b) 101787.60 ft²

c) 407150.41 ft²

d) 2025πt²

Step-by-step explanation:

Data provided in the question:

Rate of spread radially = 45 feet per day

a) Radius of spread after 2 days

= 45 × 2

= 90 feet

Therefore,

Area affected = πr²

= π(90)²

= 25446.90 ft²

b) Radius of spread after 2 days

= 45 × 4

= 180 feet

Therefore,

Area affected = πr²

= π(180)²

= 101787.60 ft²

c) Radius of spread after 2 days

= 45 × 8

= 360 feet

Therefore,

Area affected = πr²

= π(360)²

= 407150.41 ft²

a) Radius of spread after t days

= 45 × t ft

Therefore,

Area affected = πr²

= π(45t)²

= 2025πt²

The area affected by the fungal disease, which spreads radially at a constant speed, can be calculated by using the formula for the area of a circle, where the radius is the product of the spread speed and time. After 2, 4, and 8 days, the areas affected are 25,446 square feet, 101,784 square feet, and 407,150 square feet, respectively.

The given scenario represents a real-world application of the mathematical concept involving growth in a circular pattern where the growth happens at a constant rate. Here, the representation of the disease spread through the farm is in form of a circle increasing in radius over time. To calculate the area affected on any given day (t), we apply the formula for the area of a circle (πr^2) where the radius is the rate of spread multiplied by the number of days.

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Answer:

[tex]z=\frac{0.427 -0.5}{\sqrt{\frac{0.5(1-0.5)}{110}}}=-1.531[/tex]  

[tex]p_v =P(z<-1.531)=0.0629[/tex]  

If we compare the p value obtained and using the significance level given [tex]\alpha=0.1[/tex] we have that [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 10% of significance the proportion of tails is significantly less than 0.5.  

Step-by-step explanation:

1) Data given and notation

n=110 represent the random sample taken

X=47 represent the number of tails obtained

[tex]\hat p=\frac{47}{110}=0.427[/tex] estimated proportion of tails

[tex]p_o=0.5[/tex] is the value that we want to test

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

Confidence=90% or 0.90

z would represent the statistic (variable of interest)

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

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the proportion of tails is lower than 0.5:  

Null hypothesis:[tex]p\geq 0.5[/tex]  

Alternative hypothesis:[tex]p < 0.5[/tex]  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

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

The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].

3) Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

[tex]z=\frac{0.427 -0.5}{\sqrt{\frac{0.5(1-0.5)}{110}}}=-1.531[/tex]  

4) Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level provided [tex]\alpha=0.1[/tex]. The next step would be calculate the p value for this test.  

Since is a left tailed test the p value would be:  

[tex]p_v =P(z<-1.531)=0.0629[/tex]  

If we compare the p value obtained and using the significance level given [tex]\alpha=0.1[/tex] we have that [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 10% of significance the proportion of tails is significantly less than 0.5.  

Answer:

Step-by-step explanation:

Hello!

Missing Questions:

1) The probabylity of P(121 < X ≤ 129) is:

You can rewrite it as:

P(X ≤ 129) - P(X < 121)

Now the expression " P(X < 121)" does not include 121 so to calculate this interval you have to substract the cummulative probability to the previoous value of the variable " P(X ≤ 120)"

Then the interval is

P(X ≤ 129) - P(X ≤ 120)= 0.978 - 0.533= 0.445

2) The approximation to normal (without correction of continuity) of P(121 < X ≤ 129) is:

To use the normal approximation you have to calculate the mean and variance of the variable.

E(X)= np= 150*0.8= 120

V(X)= np(1-p)= 150*0.8*0.2= 24

Now you can standardize the given interval:

P(X ≤ 129) - P(X < 121)= P(Z ≤ (129-120)/√24) - P(Z < (121-120)/√24)

P(Z ≤ 1.84) - P(Z < 0.20) = 0.967 - 0.579= 0.388

3) The approximation to normal (with correction of continuity) of P(121 < X ≤ 129) is:

P(121 < X ≤ 129)

Applying the correction of continuity:

For X ≤ n + 0.5

For X > n + 0.5

P(121.5 < X ≤ 129.5) = P(X ≤ 129.5) - P(X < 121.5)

P(Z ≤ (129.5-120)/√24) - P(Z < (121.5-120)/√24)

P(Z ≤ 1.94) - P(Z < 0.31) = 0.974 - 0.622= 0.352

4) The approximation of poisson of P(121 < X ≤ 129) is:

First define the rate of successes of the distribution λ= np= 150*0.8= 120

Then you look at the individual cummulative probabilities using the tables of the distribution:

P(X ≤ 129;  λ= 120)= 0.808

P(X < 121;  λ= 120)= P(X ≤ 120;  λ= 120)= 0.524

P(121 < X ≤ 129) =  P(120 ≤ X ≤ 129)= P(X ≤ 129) - ≤ 129)= 0.808 - 0.524= 0.284

I hope it helps!

Answer:

  (a) 4.00×10^7 m

  (b) 5.10×10^14 m^2

  (c) 1.083×10^21 m^3

Step-by-step explanation:

Put the given value of radius into the various formulas and do the arithmetic. Your scientific calculator can show you the results in scientific notation.

  C = 2πr = 2π·6.37×10^6 m ≈ 4.00×10^7 m* . . . circumference

  A = 4πr^2 = 4π(6.37×10^6 m)^2 ≈ 5.10×10^14 m^2 . . . area

  V = (4/3)πr^3 = (4/3)π(6.37×10^6 m)^3 ≈ 1.083×10^21 m^3 . . . volume

_____

* An early definition of the meter was 10^-7 times the distance from the North Pole to the Equator as measured through Paris, France.

Answer:

We calculate that is CD=4.

Step-by-step explanation:

From Exercise we have that

AB=AC=3

BC=6

BD=2

AD=1.  

From Axioms D-1 and D-3, we have  

D-1: ∀ A, B∈ S,  there is a unique AB ∈ R

D-3: ∀ A, B∈ S, AB=BA.

We use the  Axioms D-1 and D-3, and we get that

AC=CA=3

AD=1

because are the points is collinear, we get

CA+AD=CD

3+1=CD

CD=4

We calculate that is CD=4.

Final answer:

To find the length of segment CD, we assume points on a collinear path as A-D-B-C, and subtract the length of BD from BC, resulting in CD = 4 units.

Explanation:

The student has asked for the length of segment CD when given a set of collinear points A, B, C, and D, with various distances between them. Since we have point B between points A and C, and points A and D, and knowing AB, AC, BC, and BD, we can determine the length of AD by subtracting from AC the length of BC, since AB equals AC. Therefore, AD = AC - BC = 3 - 6 = -3, which does not make sense geometrically since lengths cannot be negative. This might imply a typo or a misinterpretation of the points' arrangement. If assuming points in a line segment: A-D-B-C, CD can be found by subtracting BD from BC, CD = BC - BD = 6 - 2 = 4.

The population after one year would be 42 deer.

And, the population after two years would be 59 deer.

Used the concept of compound interest where the amount A after t years, starting from an initial value P and growing at a rate r is:  

[tex]A = P(1+r)^t[/tex]

Given that,

A population of 30 deer is introduced into a wildlife sanctuary.

Hence, After one year we have;

P₁ = 30 (1 + 0.40)¹  

= 42

After two years;

P₂ = 30 (1 + 0.40)²

= 59

Thus, the population after one year = 42 deer.

And, the population after two years = 59 deer.

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Answer:

Step-by-step explanation:

a) C(x) = 6x+350

b) Function for total revenue, R(x) = 15x & charge per lawn is $15.

c) Jimmy must mow approx 39 lawns before he begins making a profit.

Consider the initial cost of lawnmower is $350,

Gasoline and maintenance cost are $6 per lawn.

(a) To formulate a function C(x) for the total revenue of mowing x lawn, we use the given values than the function C(x) will be given by

C(x) = 6x+350

Find the function for the total revenue from moving x lawns.

Recollect: P(x) = R(x)-C(x)

So, R(x) = P(x)+C(x)  ..............(1)

Substitute, P(x) = 9x-350 & C(x) = 6x+350 in (1) we get,

R(x) = 9x-350+6x+350

      = 15x

So, the total revenue = 15x

∴ Charge per lawn = R(x)/x = 15x/x = $15

To find the number of lawn jimmy must mow before begins making a profit, we use P(x) = 0

∴ 9x-350=0

⇒x = 350/9

⇒x ≈ 39

Hence, the solution is x = 39 (approx)

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The possible values of net winnings in this coin flipping game range from -5 to 5 dollars. The individual probabilities of these outcomes can be calculated using a binomial probability distribution. The game is symmetric because of the fairness of the coin, resulting in the probability of winning and losing $5 being equal.

In this coin flipping game

, we have five independent trials (flips) each having two possible outcomes (heads or tails). This implies

a binomial distribution

is expected. In each trial, 'success' can be defined as getting heads, and 'failure' as getting tails. Number of successes (X) can range from 0 to 5, that is your net winnings can be from -5 to 5 dollars.

The Probability Mass Function (PMF) of X can be calculated using the binomial distribution formula, which is: P(X=k) = (5 choose k) * (0.5)^k * (0.5)^(5-k), where k represents number of 'successes' (heads), (5 choose k) is the number of combinations of getting k successful outcomes in 5 trials, and (0.5) is the probability of getting heads or tails.

PMF will give you the probability of each possible outcome (from -5 to 5 dollars), which in this specific scenario is symmetric due to the coin being fair. So for instance, winning $5 and losing $5 both have a probability of (0.5)^5 = 0.03125.

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Answer:

P(Sum of the two dice is 7) = 6/36

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this problem, we have that:

A fair dice can have any value between 1 and 6 with equal probability. There are two fair dices, so we have the following possible outcomes.

Possible outcomes

(first rolling, second rolling)

(1,1), (2,1), (3,1), (4,1), (5,1), (6,1)

(1,2), (2,2), (3,2), (4,2), (5,2), (6,2)

(1,3), (2,3), (3,3), (4,3), (5,3), (6,3)

(1,4), (2,4), (3,4), (4,4), (5,4), (6,4)

(1,5), (2,5), (3,5), (4,5), (5,5), (6,5)

(1,6), (2,6), (3,6), (4,6), (5,6), (6,6)

There are 36 possible outcomes.

Desired outcomes

Sum is 7, so

(1,6), (6,1), (5,2), (2,5), (3,4), (4,3).

There are 6 desired outcomes, that is, the number of outcomes in which the sum of the two dice is 7.

Answer

P(Sum of the two dice is 7) = 6/36

Final answer:

The probability of getting a sum of 7 while rolling two fair dice is 1/6.

Explanation:

In the rolling of two fair dice, the probability of getting a sum of 7 is:

There are 6 ways to get a sum of 7: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1).

There are a total of 36 possible outcomes when rolling two dice, each with a probability of 1/36.

Therefore, the probability of rolling a sum of 7 is 6/36 or 1/6.

Answer:

a number produced from a subset of the group of interest.

Step-by-step explanation:

This problems is, basically, about the difference of concepts between a statistic and a parameter.

When something is taken from a sample and estimated to the entire population, it is a statistic. For example, if you survey 200 Central New York residents, an 60% of them say they are Buffalo Bills fans, the 60% is a statistic.

When something is true to the entire population, it is a parameter. If i study the voting preference of all 53 players on the Buffalo Bills active roster, and 83% are Democrats, the 83% is an parameter.

So the correct answer is:

a number produced from a subset of the group of interest.

This subset is the sample, for example, and the group of interest is the population.

Answer:

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

[tex]df=n-1=21-1=20[/tex]  

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

[tex]p_v =P(t_{(20)}<-0.024)=0.4905[/tex]  

And we can use the following excel code to find it: "=T.DIST(-0.024,20,TRUE)"

Step-by-step explanation:

Data given and notation  

[tex]\bar X[/tex] represent the mean

[tex]s[/tex] represent the sample standard deviation

[tex]n=21[/tex] sample size  

[tex]\mu_o =140[/tex] represent the value that we want to test

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

t=-0.024 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 for the widths of tornadoes is lower than 140 yd, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \geq 140[/tex]  

Alternative hypothesis:[tex]\mu < 140[/tex]  

If we analyze the size for the sample is < 30 and 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

The statistic is given by: [tex] t = -0.024[/tex]

P-value

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

[tex]df=n-1=21-1=20[/tex]  

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

[tex]p_v =P(t_{(20)}<-0.024)=0.4905[/tex]  

And we can use the following excel code to find it: "=T.DIST(-0.024,20,TRUE)"

Based on the p value obtained we can conclude that we FAIL to reject the null hypothesis at any significance level selected [tex]\alpah=0.01,0.05,0.1[/tex]

Answer:

Mean of the 11th observations = 46.809

Step-by-step explanation:

The step by step explanations is given in the attached file.

What is appled is mean or average which is the total number of observation divided by the sum of the frequencies of each observaton .

Answer:

8(5) + 8(25) + 8(125) + 8(625) +8(3125)= 10(3125 - 1)=31240

Hence proved Conjecture is correct

L.H.S=R.H.S

Step-by-step explanation:

Consider the pattern:

8(5)=10(5-1)=40

8(5) + 8(25) = 10(25 - 1) =240

8(5) + 8(25) + 8(125) = 10(125 - 1) =1240

8(5) + 8(25) + 8(125) + 8(625) = 10(625 - 1)=6240

According to inductive reasoning next term of pattern will become:

8(5) + 8(25) + 8(125) + 8(625) +8(3125)= 10(3125 - 1)=31240

Checking whether conjecture is correct or not:

Consider L.H.S:

8(5) + 8(25) + 8(125) + 8(625) +8(3125)

40+200+1000+5000+25000

31240

R.H.S:

31240

Hence proved Conjecture is correct

L.H.S=R.H.S

Answer:

The weight of concrete column is 1039 Newton.

Step-by-step explanation:

We are given the following in the question:

Diameter of column = 350 mm = 0.35 m

[tex]\text{Radius} = \dfrac{\text{Diameter}}{2} = \dfrac{0.35}{2} = 0.175 ~m[/tex]

Length of column = 2 m

Density of column = 2.45 Mg per meter cube

Volume of column =

[tex]\text{Volume of cylinder}\\= \pi r^2h\\\text{where r is the radius and h is the height}\\V = \dfrac{22}{7}\times (0.175)^2\times 2\\\\V = 0.1925\text{ cubic meter}[/tex]

Mass of column =

[tex]\text{Volume of column}\times \text{Density of cone}\\= 2.45\times 0.1925\\=0.4716~ Mg\\=0.4716\times 10^3~Kg\\= 471.6~Kg[/tex]

Weight of column =

[tex]\text{Mass}\times g\\= 471.6\times 9.8\\= 4621.68~ N[/tex]

Weight in pounds =

[tex]1 \text{ pound} = 4.4482 ~N\\\\\Rightarrow \dfrac{4621.68}{4.4482} = 1039\text{ pounds}[/tex]

The weight of concrete column is 1039 Newton.

Final answer:

To determine the weight of the concrete column in pounds, calculate its mass using the density formula and then convert it using the conversion factor. The weight of the column is approximately 1.882π lb.

Explanation:

To determine the weight of the concrete column in pounds, we need to calculate its mass and then convert it to pounds using the conversion factor. First, let's find the volume of the column by using the formula for the volume of a cylinder: V = πr^2h, where r is the radius and h is the height.

The radius is half the diameter, so r = 350mm / 2 = 175mm = 0.175m. The height is given as 2m. Thus, the volume is: V = π(0.175m)^2 * 2m = 0.1925π m³.

Next, we can calculate the mass of the concrete using the density formula: mass = density * volume. Plugging in the given density of concrete (2.45 Mg/m³) and the calculated volume, we get: mass = 2.45 Mg/m³ * 0.1925π m³ = 0.425π Mg.

To convert the mass to pounds, we need to multiply by the conversion factor of 4.4482 N / 1 lb. Using this conversion factor, the weight of the concrete column is: weight = 0.425π Mg * 4.4482 N / 1 lb = 1.882π lb.