Frankie is practicing for a 5 km race is normal time is 31 minutes 17 seconds yesterday it's a king only 29 minutes 49 seconds how much faster was Frankie yesterday then his normal time

By using the concept of probability, it can be calculated that

a) State space S(x) = {-1, 0, 1, 2}

b) The required probability mass function is

    P(X = -1) = \(\frac{125}{216}\)

    P(X = 0)  \(= \frac{25}{72}\)

    P(X = 1)  \(= \frac{5}{72}\)

    P(X = 2)  \(= \frac{1}{216}\)

c) Expected value of X  = -0.5

d) the stake of the gambler in  order to make this a fair game is $0.5

What is probability?

Probability gives us the information about how likely an event is going to occur

Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.

Probality of any event is greater than or equal to zero and less than or equal to 1.

Probability of sure event is 1 and probability of unsure event is 0.

a) Let a number n be chosen between 1 and 6

Three fair six sided dice are thrown

The following cases can occur

1) Number n occur on none of the three dice

2) Number n occur on one dice

3) Number n occur on two dice

4) Number n occur on three dice

Let X denote your net win after one round of gambling (i.e., the payment received from the casino minus your stake)

1) X = 0  -1 = -1

2) X = 1 - 1 = 0

3) X = 2 - 1 = 1

4) X = 3 - 1 = 2

State space S(x) = {-1, 0, 1, 2}

b) P(X = -1) = \({3 \choose 0}(\frac{1}{6})^0(\frac{5}{6})^3 = (\frac{5}{6})^3 = \frac{125}{216}\)

    P(X = 0) = \({3 \choose 1})(\frac{1}{6})(\frac{5}{6})^2 = \frac{25}{72}\)

    P(X = 1) = \({3 \choose 2}(\frac{1}{6})^2\frac{5}{6} = \frac{5}{72}\)

    P(X = 2) = \({3 \choose 3}(\frac{1}{6})^3(\frac{5}{6})^0 = \frac{1}{216}\)

    The required probability mass function is

    P(X = -1) = \(\frac{125}{216}\)

    P(X = 0)  \(= \frac{25}{72}\)

    P(X = 1)  \(= \frac{5}{72}\)

    P(X = 2)  \(= \frac{1}{216}\)

c) Expected value of X = \(-1 \times \frac{125}{216} + 0 \times \frac{25}{72} + 1 \times \frac{5}{72} + 2\times \frac{1}{216}\)

                                      = \(\frac{-125 + 0 + 15 +2}{216}\\\)

                                      = \(-\frac{108}{125}\)

                                      = -0.5

d) The gambler looses $0.5 on a average

   So this is not a fair game

   Let the stake of the gambler in  order to make this a fair game be t

   By the problem,

   -0.5 + t = 0

     t = 0 + 0.5

     t = $0.5

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Answer:

a

Step-by-step explanation:

Answer:

x≥6

Step-by-step explanation:

The  p-value is approximately 0.027 (rounded off to two decimal places).

To determine whether there is strong evidence that more than 15% of college students in America have at least one sibling, we can use a hypothesis test with a significance level of 0.05.

Let p be the proportion of college students in America who have at least one sibling. The null hypothesis is that p ≤ 0.15, and the alternative hypothesis is that p > 0.15.

Under the null hypothesis, the number of students in a sample of 100 who have at least one sibling follows a binomial distribution with parameters n = 100 and p = 0.15. We can use this distribution to calculate the probability of observing 20 or more students with at least one sibling in a sample of 100 if the null hypothesis is true.

The p-value is the probability of observing a test statistic as extreme or more extreme than the observed value, assuming the null hypothesis is true. In this case, the test statistic is the number of students with at least one sibling in a sample of 100.

Using a binomial distribution calculator or software, we find that the probability of observing 20 or more students with at least one sibling in a sample of 100 if p = 0.15 is approximately 0.027.

Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is strong evidence that more than 15% of college students in America have at least one sibling.

Therefore, the p-value is approximately 0.027 (rounded off to two decimal places).

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The inequality solved to give a solution of x ≥ 1 and x ≤ -3 is |x + 1| ≥ 2.

b = 1, ≥

From the diagram, the solution to the inequality is x ≥ 1 and x ≤ -3

Hence:

|x + b| ≥ 2

x + b ≥ 2 or -(x + b) ≥ 2

x ≥ 2 - b or x ≤ -2 - b

2 - b = 1 and -2 - b = -3

b = 1

Hence |x + 1| ≥ 2

The inequality solved to give a solution of x ≥ 1 and x ≤ -3 is |x + 1| ≥ 2. b = 1, ≥

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The points that would be plotted after transforming the data using the natural logarithm function would be: A. (1.690, 3.891), (2.535, 5.840), (3.380, 7.785)

To transform the data, we need to take the natural logarithm of the second coordinate (y) for each point. Using the formula log(e)y = ln(y), we can find the natural logarithm of each y-value:

log(49) = 3.891
log(343) = 5.840
log(2401) = 7.785

Then, we plot each point with the transformed coordinates (x, log(y)):

(2, 3.891)
(3, 5.840)
(4, 7.785)

However, the question asks us to round log(y) to three decimal places, so our final answer is: A. (1.690, 3.891), (2.535, 5.840), (3.380, 7.785)

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If they charges a one-time fee of $45, plus $25 per hour, then the the slope of this situation is $25 per hour.

The situation described can be represented by the linear equation

Cost = $45 + $25 × hours

where "Cost" is the total cost of the tour and "hours" is the number of hours for which the tour is taken.

The slope of this equation represents the rate of change in the cost of the tour with respect to the number of hours.

In other words, it tells us how much the cost increases for each additional hour of the tour.

The slope of this equation is simply the coefficient of the "hours" variable, which is $25.

Therefore, the slope of this situation is $25 per hour.

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Answer:

$25 per hour.

Step-by-step explanation:

The probability that a woman has endometrial cancer has a partner who smokes is 0.2

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.

Probability(Event) = Favorable Outcomes/Total Outcomes = x/n

                                        OR

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

Where,

P(A) is the probability of an event “A”

n(A) is the number of favorable outcomes

n(S) is the total number of events in the sample space.

According to the question,

50 women has endometrial cancer because 5 of them reports that their partner smokes cigerate.

According to the probability formula:

            P(A) = n(A)/ n(s)

                    = 10/50

                    = 0.2

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Answer:

$75 - $15 - $20 = $40

Step-by-step explanation:

Given that:

Money owed by Preston to his brother = $15

Money owed by Preston to his sister = $20

Total money earned by Preston = $75

Now, the money is paid back that he owed to his sister and brother.

To find:

The expression to represent the amount of money left with Preston after clearing all his dues?

Solution:

Once Preston pays back the money that he owed to his brother and sister, he will not have all $75 left with him.

He will have lesser amount of money.

Money left with Preston = Total money earned by Preston - Money owed to brother - Money owed to sister

Putting the values given as per the question statement, we get:

Money left with Preston = $75 - $15 - $20 = $40

Therefore, the expression to represent the amount of money left with Preston = $75 - $15 - $20 = $40

Answer:

\(3\frac{3}{4}\)

Step-by-step explanation:

6 1/8 - 2 3/8

=(8 x 6)+1/8  -  (8 x 2)+3/8

=49/8 - 19/8

=30/8

=15/4

=3 3/4

Answer: The width of the remaining piece of the board is \(\frac{15}{4}\) inches

Step-by-step explanation:

let us find the width of the remaining piece

Given that

                         width of remaining piece =\(\frac{49}{8}\)-\(\frac{19}{8}\)  = \(\frac{15}{4}\)      

Answer:

The dimensions of the field is 185 yards by 48 yards

Step-by-step explanation:

Here, we are interested in calculating the dimensions of the field.

Let the width of the field be x yards

From the question, we are made to know that the length of the field is 7 yards less than quadruple ( 4 times) the width

So mathematically, the length of the field will be ;

(4x -7) yards

The perimeter of the field mathematically is:

2(l + b)

Thus;

2(x + 4x- 7) = 466

2(5x -7) = 466

divide both side by 2

5x - 7 = 466/2

5x - 7 = 233

5x = 233 + 7

5x = 240

x = 240/5

x = 48 yards

Length of field is; 4x -7 = 4(48) -7 = 192 - 7 = 185 yards

Answer:

2a³

Step-by-step explanation:

2a³ can divide all these without living a remainder

The radius of convergence for the given power series is to be found. Therefore, the radius of convergence for the given power series is infinite.

It is given that the power series is:

$$ch\ \(E((n!)^2)x^2\)

\(={sum_{n=0}^{\infty}}{(n!)^2x^2)^n}{(2n)}\)}$$

For finding the radius of convergence, we use the ratio test:

\begin{aligned} \lim_{n \rightarrow \infty}\bigg|\frac{a_{n+1}}{a_n}\bigg|&

=\(\lim_{n \rightarrow\infty}\frac{(((n+1)!)^2x^2)^{n+1}}{(2n+2)!}\frac{(2n)!}{((n!)^2x^2)^n}\\\) &

=\(\lim_{n \rightarrow \infty}\frac{(n+1)^2x^2}{4n+2}\\ &=\frac{x^2}{4}\)$$

Since the limit exists and is finite, the radius of convergence $R$ of the given series is given by:$

R=\(\frac{1}{\lim_{n \rightarrow \infty}\sqrt[n]{|a_n|}}\\\)&

=\(\frac{1}{\lim_{n \rightarrow \infty}\sqrt[n]{\bigg|\frac{((n!)^2x^2)^n}{(2n)!}\bigg|}}\\\) &

=\(\frac{1}{\lim_{n \rightarrow \infty}\frac{(n!)^2|x^2|}{(2n)^{\frac{n}{2}}}}\\\)&

=\(\frac{1}{\lim_{n \rightarrow \infty}\frac{n^ne^{-n}\sqrt{2\pi n}|x^2|}{2^nn^{n+\frac{1}{2}}e^{-n}}}, \text

{ using Stirling's approximation}\\\)&

=\(\frac{1}{\lim_{n \rightarrow \infty}\frac{\sqrt{2\pi n}\\|x^2|}{2^{n+\frac{1}{2}}}}\\\)\\ &

=\(\frac{2}{|x|}\lim_{n \rightarrow \infty}\sqrt{n}\\\)R&

=\(\boxed{\infty}, \text{ for } x \in \mathbb{R} \end{aligned}\)$$

Therefore, the radius of convergence for the given power series is infinite.

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Answer:

B

Step-by-step explanation:

y+1>2(x-2)

distribute the right side

y+1>2x-4

minus 1 on both sides

y>2x-5

slope is 2/1

y intercept is -5

> means dotted line and shaded in to the left

:)

Answer:

Step-by-step explanation:

-5 is bigger because it’s closer to 0 in a number line

Answer:

-5 because it is closer to 0 and -15 is farther away from 0 .

Step-by-step explanation:

ANSWER: p^2 - 2p + 2

Step-by-step explanation:

Total age of three = p + p-2 + (p-2)^2

= 2p-2 + p^2-4p+4

= p^2 - 2p + 2

(a) The critical values of a function are the values of x. (b) function increasing for +ve vice versa,(c) Relative extrema occur at the critical values (d) occur where the second derivative changes

To find the critical values, we need to find the values of x where the derivative of the function is equal to zero or undefined. These critical values can be potential points of relative extrema or points of inflection

To determine the intervals where the function is increasing or decreasing, we analyze the sign of the derivative. If the derivative is positive, the function is increasing, and if the derivative is negative, the function is decreasing.

The relative extrema occur at the critical values where the function changes from increasing to decreasing or vice versa. These points can be either a local minimum or a local maximum.

Points of inflection occur where the second derivative changes sign or where the second derivative is undefined. At these points, the concavity of the function changes.

To determine the intervals of concave up or concave down, we analyze the sign of the second derivative. If the second derivative is positive, the function is concave up, and if the second derivative is negative, the function is concave down.

By examining the critical values, intervals of increasing/decreasing, relative extrema, points of inflection, and intervals of concavity, we can obtain a comprehensive understanding of the behavior of the function.

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As per the mathematical operation both Jillian and Samuel are correct.

Given expression = 30+40+70,

The methodology by Jillian = added 30 and 40 and then 70

The methodology by Samuel = added 30 and 70 and then 40.

Determining the result of the given equation:

30 + 40 + 70

= 140

Reviewing the operations of both Jillian and Samuel

Jillian

He added 30 and 40 and then 70:

30 + 40 = 70

70 + 70 = 140

Samuel

He added 30 and 70 and then 40

30 + 70 = 100

100 + 40 = 140

The result of both mathematical operations is 140. Thus, it can be stated that both are correct.

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Answer: The general form of a sine function is:

y = A sin (Bx + C) + D

Where:

A = amplitude

B = 2π/period

C = phase shift

D = vertical shift or midline

Given the values in the problem, we can substitute and simplify:

A = 3

midline = 2, so D = 2

period = 8π/7, so B = 2π/(8π/7) = 7/4

y = 3 sin (7/4 x + C) + 2

To find the phase shift, we need to use the fact that the sine function is at its maximum when the argument of the sine function is equal to π/2. That is:

Bx + C = π/2

We can solve for C:

C = π/2 - Bx

C = π/2 - (7/4) x

Substituting back the value of C in the equation, we get:

y = 3 sin (7/4 x + π/2 - 7/4 x) + 2

y = 3 sin (7/4 x - 7π/8) + 2

Therefore, the sine function with an amplitude of 3, a midline of y=2, and a period of 8π/7 is:

y = 3 sin (7/4 x - 7π/8) + 2

Answer:

Step-by-step explanation:

Answer:

b. interaction effect

Step-by-step explanation:

In a regression model, the interaction effect is present when a predictor variable changes the effect of another predictor variable on the outcome.

In a regression model, the interaction effect exists when one predictor variable impacts the outcome of another predictor variable differently than when examined individually. It refers to the interaction between two or more predictor variables and their influencers on an outcome or response variable. For example, in a regression model, studying and having a quiet place may individually contribute to a better score on a test, but perhaps studying in a quiet place provides a significantly better effect than the sum of those two effects separately. This would be considered an interaction effect.

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Answer:

11

Step-by-step explanation:

On a fair six-sided die, there is a \(\frac{1}{6}\) chance of rolling each number. Therefore, for each of the rolls, the number 6 has a \(\frac{1}{6}\) chance of being rolled. This can be read as for every 6 rolls, one 6 should appear.

Since the die is being rolled 66 times, we have the following proportion:

\(\frac{1}{6}=\frac{x}{66}\), where \(x\) is the theoretical number of times a roll of "6" occurs.

Multiply both sides by 66:

\(x=\frac{1}{6}\cdot 66=\boxed{11}\)

The Expected value of M is 65

The Standard error of M is 5

Given,

The sample score, n = 9

The Standard deviation, σ = 15

Population mean, μ = 65

Then,

The Expected value of M = μ

∴ The Expected value of M = 65

The Standard error of M = σ/\(\sqrt{n}\)

                                          \(=\frac{15}{\sqrt{9} } \\\\=\frac{15}{3} \\=5\)

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Answer:

Rewrite it in the form {a}^{2}+2ab+{b}^{2}a

​2

​​ +2ab+b

​2

​​ , where a={x}^{2}a=x

​2

​​  and b=5b=5.

{({x}^{2})}^{2}+2({x}^{2})(5)+{5}^{2}(x

​2

​​ )

​2

​​ +2(x

​2

​​ )(5)+5

​2

​​

2 Use Square of Sum: {(a+b)}^{2}={a}^{2}+2ab+{b}^{2}(a+b)

​2

​​ =a

​2

​​ +2ab+b

​2

​​ .

{({x}^{2}+5)}^{2}(x

(x^2 + 5)^ 2

​​

Step-by-step explanation:

Answer:

Step-by-step explanation:

Denise now has $365 and wants to increase those savings to $635 or more.

We can immediately write    $365 + d ≥ $635.

Solving for d, we get d ≥ $635 - $365, or d ≥ $270.

Denise needs to save at least $270.

The volume enclosed by the sphere\(x^{2}\)+\(y^{2}\) +\(z^{2}\)=\(R^{2}\), where R > 0, can be found using spherical coordinates. The volume is given by V = (4/3)π\(R^{3}\).

In spherical coordinates, a point (x, y, z) can be represented as (ρ, θ, φ), where ρ is the radial distance from the origin, θ is the azimuthal angle in the xy-plane, and φ is the polar angle from the positive z-axis.

To find the volume enclosed by the sphere, we integrate over the entire region in spherical coordinates. The radial distance ρ ranges from 0 to R, the azimuthal angle θ ranges from 0 to 2π (a complete revolution around the z-axis), and the polar angle φ ranges from 0 to π (covering the entire sphere).

The volume element in spherical coordinates is given by dV = ρ^2 sin(φ) dρ dθ dφ. Integrating this volume element over the appropriate ranges, we have:

V = ∫∫∫ dV

 = ∫[0 to 2π] ∫[0 to π] ∫[0 to R] ρ^2 sin(φ) dρ dθ dφ

Simplifying the integral, we get:

V = (4/3)πR^3

Therefore, the volume enclosed by the sphere \(x^{2}\)+ \(y^{2}\) +\(z^{2}\)=\(R^{2}\) is given by V = (4/3)π\(R^{3}\).

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Step-by-step explanation:

= 3/5 × 1/6

= (3 × 1)/(5 × 6)

= 3/30

= 1/10

Answer:

\( \sf \frac{1}{10} \)

Step-by-step explanation:

\( \sf = \frac{3}{5} \times \frac{1}{6} \)

\( \sf = \frac{3 \times 1}{5 \times 6} \)

\( \sf = \frac{1 \times 1}{5 \times 2} \)

\( \sf = \frac{1}{10} \)

Answer: $78 for 19 months

Step-by-step explanation:

$40 for sig-up

$2 monthly fee

Duration: 19 months

Total cost

 \(= 40 + 2(19)\\= 40 + 38\\= 78\)

Answer: The number is 2

Step-by-step explanation: Suzie says that \(\frac{1}{2}\), which is half of a whole, is equal to only \(\frac{1}{4}\) of the unknown number. This means that to find the value of the unknown number, you need to multiply \(\frac{1}{2}\) by 4 so that it equals to \(\frac{4}{4}\) of the mystery number.

Simply put, multiply \(\frac{1}{2}\) by 4. Then reduce for the answer, and this gives us these equations.

\(x=4(\frac{1}{2} )\)

\(x=\frac{4}{2}\)

\(x=2\)

Hope that this helps!

Simplification of ( 11/24) - ( 1/4) is 5/24 after finding its lowest common multiple.

As given in the question,

Given expression is ( 11/24) - ( 1/4)

Find the lowest common multiple (L.C.M) of the denominators 24, and 4

L.C.M of ( 24 , 4 ) = 24

Equivalent fractions are:

( 11 /24 ) × ( 1 /1 )  =  11 / 24

( 1 / 4 ) × ( 6 / 6 ) = 6 / 24

Simplify by subtracting 6 / 24 from 11 / 24 we get,

( 11 / 24 ) - ( 6 / 24 )

= ( 11 - 6 ) / 24

= 5 / 24

Therefore, the simplified form of the expression ( 11/24) - ( 1/4) is equal to 5 /24.

The complete question is:

Find the lowest common denominator (multiple) of ( 11/24) - ( 1/4). Type the equivalent fractions. Then, add or subtract. Simplify your answer.

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