two events, a and b are independent if and only if . recall that a reorganization of the multiplication rule will yield . suppose for some events a and b, . which of the following statements is true of a and b? select an answer and submit. for keyboard navigation, use the up/down arrow keys to select an answer. a events a and b are independent since and . b events a and b are not independent, but they are mutually exclusive since . c events a and b are independent since ; however . d events a and b are not independent since and .

The number of buses needed is calculated to be 12 and the number of students that will ride on the bus that isn't full is calculated to be 10.

The number of buses needed if each bus held 24 students can be calculated as follows;

Number of buses = number of students / number of students in each bus =  279 / 24 = 11.625 = 12

Therefore 12 buses were needed if each bus can hold a maximum of 24 buses. Now we first determine the number of students in 11 buses that were full by multiplication as follows;

number of students in 11 buses = 11 × 24 = 264 students

Now we can calculate the number of students on the bus that isn't full by subtraction as follows;

Students = total students - students in 11 buses that are full

Students = 274 - 264 = 10 students

Therefore 10 students will ride on the bus that isn't full.

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The break-even point for Patty's Pies is C. 4,211 pies.

The break-even point is the sales units that equate the sales revenue with the total costs (fixed and variable).

At the break-even point, there is no profit, there is no loss.  Above this point, profits are generated.  Below it, losses are recorded.

Fixed cost = $20,000

Selling price per pie = $8.75

Variable cost per pie = $4.00

Contribution margin per pie = $4.75 ($8.75 - $4.00)

Contribution margin ratio = 54.29% ($4.75/$8.75 x 100)

Break-even point in sales units = Fixed costs ÷ Contribution margin per unit

= $20,000 ÷ $4.75

= 4,211 units

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As per the given condition in question, if you have 50% chance of winning a game and if you want to maximize your winning chances, then the best amount of games you should be playing is 100.

What is probability?

A probability is a numerical representation of the possibility or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities. An event has a probability of 0 when there is no possibility it will happen, whereas an event has a probability of 1 when it will definitely happen.

What is the significance of probability?

Information about possibility of occurrence is provided by probability. For instance, meteorologists can forecast the likelihood of rain by looking at weather patterns. Probability theory is utilized in epidemiology to comprehend how exposures and the risk of health impacts are related.

According to the given question:

As we've been told that there is 50% chance for winning a game, the more number of tries you do, the more chances are there for winning, for instance if you take 10 tries then you have chances to win 5 games and if you take 100 tries then you have chances to win 50 games. Hence, the best amount of games you should play to maximize your chances of winning is 100.

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Answer: $60

Since both the sales tax and the tip apply to the original price of the dinner, we can add the two rates.

11% + 20% = 31%

Next we need to find what number 18.60 is 31% of.

Since percent means per hundred 31% is equal to .31.

Now we need to now what number times .31 + 18.60

Divide both sides by .31.

The .31 will be cancelled out and $18.60 will become $60.

$18.60 is 31% of $60

Step-by-step explanation:

x-3 is the function for second graph of parent function f(x)= x and for third graph the function is g(x)=-x.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given that the parent function is f(x)=x.

The parent function is in red color.

We need to find the function in blue which is transformed from red color.

Graph transformation is the process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph.

As we observe, f(x)=x is red graph and it shifted three units down which forms the blue line.

Therefore, g(x)=f(x)-3

g(x)=x-3.

In graph 3,  If we flip red graph about x-axis then get blue graph. B

Therefore, g(x)=-f(x)

Thus, The function of blue graph is g(x)=-|x|

Hence, for second graph g(x) is x-3 and for third graph g(x)=-x for parent function f(x)=x.

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Answer:

I don't know the answer so how will I tell you

Answer:

22

Step-by-step explanation:

Let's say the 4 consecutive integers are a, b, c, and d

a=b-2  ==> Consecutive even numbers have a difference of 2: Ex. (4-2=2)

b=c-2

c=d-2

a+b+c+d=100

Solve for a:

a=b-2  ==> add 2 on both sides

a+2=b

a+(a+2)+c+d=100  ==> substitute a+2 for b

a+2=c-2  ==> b=c-2 and a+2=b, so a+2=c-2

a+2+2=c-2+2  ==> add 2 on both sides

a+4=c

a+(a+2)+(a+4)+d=100 ==> substitute a+4 for c

a+4=d-2  ==> c=d-2 and a+4=c, so a+4=d-2

a+4+2=d-2+2  ==> add 2 on both sides

a+6=d

a+(a+2)+(a+4)+(a+6)=100  ==> substitute a+6 for d

a+a+2+a+4+a+6=100  ==> solve for a

a+a+a+a+2+4+6=100

4a+12=100 ==> simplify

4a+12-12=100-12 ==> isolate a

4a=88  ==> simplify

a=88/4

a=22

The paper must be folded 43 times to get the thickness same as the distance from the earth to the moon.

Note that the function g is defined as [tex]g(n)=0.052^n.[/tex]

Let g(n) be the thickness that is g(n)=t.

Thus,

[tex]t & =0.05\left(2^n\right) \\\frac{t}{0.05} & =2^n \\\frac{100 t}{5} & =2^n \\20 t & =2^n\end{aligned}[/tex]

Take logarithms on both sides, thus

[tex]$$\begin{aligned}\log (20 t) & =\log \left(2^n\right) \\\log (20 t) & =n \log (2) \\n & =\frac{\log (20 t)}{\log (2)} \\n & =\log _2 20 t\end{aligned}$$[/tex]

Thus, [tex]g^{-1}=\log _2 20t[/tex]  is the required inverse function.

c) Given that the thickness of the paper is same as the distance from the earth to the moon that is t=384,472,300,000 mm.

To determine the corresponding value of n.

Note that the inverse function is defined as [tex]g^{-1}(t)=\log _2 20t[/tex]...

Substitute 384,472,300,000 in equation (1), thus

[tex]$$\begin{aligned}& g^{-1}(384,472,300,000)=\log _2(20 \times 384,472,300,000) \\& g^{-1}(384,472,300,000)=\log _2(20 \times 384,472,300,000) \\& g^{-1}(384,472,300,000)=42.806\end{aligned}$$[/tex]

Since, [tex]g^{-1}[/tex] determines the number of folds of the paper, the value must be the whole number.

Thus, [tex]g^{-1}(384,472,300,000)[/tex] is approximately equal to 43 .

Thus, the paper must be folded 43 times to get the thickness same as the distance from the earth to the moon.

The complete questions should be:

b. The function g has an inverse. The function g^{-1} determines the number of folds needed to give the folded paper a thickness of t mm. Write a function formula for g^{-1}.

c. Use your function in part (b) to determine how many times you must fold a piece of paper to make the folded paper have a thickness that is the same as the distance from the earth to the moon. (Assume the distance from the earth to the moon is 384,472,300,000 mm. folds

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The percentage of the people surveyed that spend 3 hours or less per day would be = 52.5%. That is option C.

A histogram is defined as the graphical representation of the result of a data set with the use of bars that varies in length but of the same width.

From the given diagram, the total number of persons that participated in the games = 4+9+8+6+4+2+2+2+1+1+1= 40.

The number of people that spent 3 hours or less per day gaming = 4+9+8 = 21

Therefore the percentage of people that spent 3 hours or less per day gaming;

= 21/40 × 100/1

= 2100/40

= 52.5%

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The volume of composite solid with cylinder and semisphere is 7125.13 feet³.

A cylinder is a combination of infinite circles with the same radius and keeps one up to up.

The surface area of the cylinder = πdh where h is the height of the cylinder and d is the diameter of the cylinder.

A sphere is a 3D geometrical object which has a radius and becomes a point that revolves around a fixed point called the center.

The volume of the semisphere is given as (4/6)πr³.

The volume of the cylinder = πr²h

As per the given,

Height of cylinder h = 22 feet

The radius of the cylinder and sphere r = 9 feet

Combined volume = (4/6)πr³ + πr²h

⇒ (4/6)π(9)³ + π(9)²(22)

⇒ 1526.81 + 5598.32

⇒ 7125.13 feet³

Hence "The combined solid's volume, which includes a cylinder and a semisphere, is 7125.13 feet³".

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Answer:

7

Step-by-step explanation:

the circle is the midpoint

the midpoint is at (1,0)

And we have to find the 2 edges

(-6,0) and (8,0)

To find the distance we just subtract the x values since y is 0

8-1=7

1-(-6)

1+6=7

The radius is 7

Hopes this helps

The answer is yes, events A and B are independent to each other when A random card is chosen from a 52-card standard deck.

Given that,

We have to identify the independence of the events a and b. A random card is chosen from a 52-card standard deck. Then it is changed, and a second card is chosen at random. event a: The initial draw selects a club event b: The second draw yields an ace.

We know that,

Here a card is selected randomly from the deck of 52 cards. Then this card is replaced, that means the deck has again 52 cards. Now, Second card is then selected randomly from the deck.

Here as we are replacing the first drawn card that means probability of drawing first card doesn't affect the probability of drawing second card. So here the given events A and B are independent.

P(A and B) = P(A) P(B)

Therefore, The answer is yes, events A and B are independent to each other when A random card is chosen from a 52-card standard deck.

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A closed form for the corresponding generating function is all the donuts are chocolate and there are at least 3, therefore, x³/1 − x.

In math the word function refers the a set X to a set Y in mathematics assigns each element of X exactly one element of Y.

Here the domain and codomain of the function are denoted by the sets X and Y, respectively.

Here we have to find  a closed form for the corresponding generating function.

While we looking into the given question, we have identified the the  concept of function was first discussed by two Persian mathematicians named Al-Bruni and Sharaf al-Din al-Tutsi.

And the functions were originally used to represent the idealized relationship between varying quantities and other variables.

As for example, time has an impact on a planet's position.

Here the the number of different ways to compose a bag of n donuts subject to various restrictions.  As per these condition, we now that the option (a) is correct.

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put the instrument at x and u will b ab, to find

Step-by-step explanation:

u need an instrument and it is known as D innsimplemwords then use at,point to find its andswer

Answer: b. The radius is the same as a cylinder with a volume of 500(3) and the same height.

Step-by-step explanation:

The volume of a cylinder is 3 times that of a cone (assuming they have the same perpendicular height and radius).

if the null hypothesis is not rejected at the 5% level of significance, it 1 , 2 will always be rejected at the 1% level, 4 may be rejected or not rejected at the 1% level.

The null hypothesis is a statement of a general population parameter that is assumed to be true. It is typically tested using a statistical test, such as an independent t-test or ANOVA. If the null hypothesis is not rejected at the 5% level of significance, it does not necessarily mean that it will also not be rejected at the 1% level. This is because the 1% level of significance is a stricter level of significance, meaning that the sample data must be even more extreme in order to reject the null hypothesis. Thus, the null hypothesis may be rejected or not rejected at the 1% level, depending on how extreme the data are.

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The number of groups will be 7. And each group contains 4 red and 5 blue marbles.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Malik has 28 red marbles and he has 35 blue marbles. Malik needs to partition the marbles into bunches so each gathering has similar items.

The factor of the number 28 is given as,

28 = 2 x 2 x 7

The factor of the number 35 is given as,

35 = 5 x 7

The common factor of the numbers 28 and 35 is 7. Then the number of groups will be 7. And each group contains 4 red and 5 blue marbles.

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The value of the path will be 1.

Here we need to evaluate the line integral of the given vector field F along the path C,

First, we need to express the path C as a function of a single variable t to use the integration formula

∫C F · dr = ∫a^b F(r(t)) · r'(t) dt

where  a and b are the limits of integration and r(t) is a parametrization of the path C

Here C consists of two straight line segments: one from (0, 0, 0) to (0, 0, 1) and one from (0, 0, 1) to (0, 1, 1).

expressing each line segment as a function of t by setting t equal to the length of the line segment we get

the parametrization r(t) = (0, 0, t), or the first line segment

by varying t from 0 to 1.

and

r(t) = (0, t, 1), for the second line segment which represents a line by varying t from 0 to 1.

Hence we will ultimately use the formula

∫C F · dr = ∫0^1 F(r(t)) · r'(t) dt + ∫0^1 F(r(t)) · r'(t) dt

= ∫tdt + ∫tdt

= t²

now inserting the limits gives us the value 1.

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Complete Question

(Image Attached)

The number of terms  - 2.

Here we assume that [tex]a_{n}[/tex] > 0 or all n, the terms are monotone decreasing and [tex]\lim_{n \to \infty} a_n[/tex] =0. This guarantees the convergence of the series. Now, if we choose a finite value N, and approximate the series by Σ [tex](-1)^{n}[/tex][tex]a_{n}[/tex] , the error in the approximation of the infinite series by this finite sum is bounded by [tex]a_{N + 1}[/tex] .

We are given the infinite alternating series

                      n=4,              ∑ [tex]\frac{(-1)^{n+1} }{n^{4} }[/tex]

and wish to approximate the sum with an error of less than 0.001.

Define [tex]a_{n}[/tex] = [tex]\frac{1}{n^{4} }[/tex] . Then we will solve the inequality [tex]a_{n}[/tex] < 0.001 :

                     [tex]\frac{1}{n^{4} }[/tex] < 0.001

                     [tex]n^{4}[/tex] > 1000

                     n > [tex]\sqrt[4]{1000}[/tex]

                        ≈ 5.62

Therefore, if we stop at n=5, the error will be less than 0.001. Since the series starts at n=4, we need only use 2 terms.

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An example of a boundary value problem is the Sturm-Liouville problem, which entails determining the eigenvalues and eigenfunctions of a differential equation that complies with specific boundary requirements.

The general formula for the Sturm-Liouville problem's solution in x is y(x) = a * f(x) + b * g(x), where a and b are constants and f(x) and g(x) are the differential equation's eigenfunctions. When the differential equation and boundary conditions are solved, the eigenvalues and eigenfunctions are discovered.

For instance, if the differential equation has the following form: -y" + q(x)y = lambda* w(x)y where y is the dependent variable, y" is the second derivative of y, q(x) and w(x) are functions of x, and lambda is the eigenvalue, the boundary conditions can be of the following

form: where L is the length of the interval on which the differential equation is defined, y(0) = 0, and y(L) = 0.

The general solution in x can be expressed in the form: y(x) = a * f(x) + b * g(x), where a and b are constants and f(x) and g(x) are the eigenfunctions of the differential equation. The eigenvalues and eigenfunctions can be discovered by solving this differential equation and the boundary conditions.

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Answer:

12 x 9 x 15 is 1620. then start multiplication on the subject

Hiker travels [tex]\frac{5}{2} km[/tex] in [tex]\frac{2}{3}hours[/tex] with speed of [tex]3\frac{3}{4} km/hr[/tex].

Defining speed as the speed at which an object's location changes in any direction.

The distance traveled in the context of the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.

The speed formula is provided as:

[tex]v=\frac{d}{t}[/tex];

where d is distance travelled, t is time taken and v is speed or velocity.

Average speed determined by the ratio of the total distance traveled by an object to the entire amount of time it took to travel that distance.

Given;

Average speed=[tex]3\frac{3}{4}=3+\frac{3}{4}=\frac{15}{4}[/tex];

Average speed=[tex]\frac{d}{t}=\frac{15}{4}[/tex];

Given total time [tex]\frac{2}{3}hours[/tex];

⇒[tex]d=\frac{2}{3}*\frac{15}{4}=\frac{5}{2} km[/tex];

Hiker travels [tex]\frac{5}{2} km[/tex] in [tex]\frac{2}{3}hours[/tex] with speed of [tex]3\frac{3}{4} km/hr[/tex].

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The two expressions are equivalent because they both represent the same concept: a number that is less than 3 but negative. In the first expression, -x, the negative sign in front of the x indicates that the value of the expression is the opposite of x. So if x is a positive number, then -x will be a negative number, and vice versa. In the second expression, x > -3, the greater than sign indicates that the value of x is greater than -3. Since we know that x is negative, this means that x is less than -3.

Therefore, both expressions represent the same thing: a number that is less than 3 but negative. This is why they are equivalent.

The linear correlation coefficient of the data is -0.96

The correlation coefficient is a statistical measure of the strength of a two-variable linear relationship. Its values may be between -1 and 1.

A correlation coefficient of -1 indicates a perfect negative, or inverse, correlation, where values in one series increase as those in the other fall and vice versa.

A value of 1 indicates a direct and flawlessly positive link.

No linear relationship exists when the correlation coefficient is 0.

According to the question,

Coefficient of determination of a set of data points is given : R² = 0.93

Slope of the regression line = -5.26 (negative)

Therefore, The linear correlation coefficient is R

=> R² = 0.93

=> R = √0.93

=>R = 0.96

Since , the slope the regression line is negative, R will be negative in this case.

Therefore, the linear correlation coefficient of the data is: -0.96

I've answered the question in general as the question is incomplete

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Answer:

$3.32

Step-by-step explanation:

Let's assign variables:

Total cost = t

Price of bagels = b

Price of lattes = c

Price of juice bottles = j

Turn it into an equation:

t = 2b + 3c + j

Plug in the values we know:

15.79 = 2(1.79) + 3c + 2.25

15.79 = 3.58 + 3c + 2.25

15.79 = 5.83 + 3c

Subtract 5.83 from both sides:

9.96 = 3c

Divide both sides by 3:

c = 3.32

It will take a ball 1.8 seconds to travel  27 m at a rate of 18m/s

The time it will take a ball to travel is solved from the formula of speed given as

speed = distance covered / time taken

from the problem

distance covered = 27 m

time taken = ?

speed = 15 m/s

substituting into the formula

15 = 27 / time

time = 27 / 15

time = 1.8 seconds

the time is 1.8 s

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Answer:

28.

Step-by-step explanation:

Si on a une perfusion d'héparine 20 000 unités dans 500 ml de dextrose 5 % à un débit de 1 000 ml/heure, le débit en unités/heure d'héparine est calculé en divisant le nombre d'unités d'héparine (20 000) par le volume de la solution de dextrose (500 ml) pour obtenir la concentration en unités/ml d'héparine dans la solution (40 unités/ml). Ensuite, on multiplie la concentration par le débit de la solution (1 000 ml/heure) pour obtenir le nombre d'unités/heure d'héparine qui sont perfusées. 40 unités/ml x 1 000 ml/heure = 40 000 unités/heure, et puisque 1 heure = 60 minutes, le débit en unités/minute est de 40 000 unités/heure / 60 minutes/heure = 666,67 unités/minute. Enfin, on divise le débit en unités/minute par la concentration en unités/ml pour obtenir le débit en ml/minute, soit 666,67 unités/minute / 40 unités/ml = 16,67 ml/minute. Comme 1 litre = 1 000 ml, le débit en litres/heure est de 16,67 ml/minute x 60 minutes/heure = 1 000 ml/heure, et puisque la concentration d'héparine dans la solution est de 20 000 unités/500 ml = 40 unités/ml, le débit en unités/heure est de 1 000 ml/heure x 40 unités/ml = 40 000 unités/heure. Par conséquent, la réponse finale est de 40 000 unités/heure / 60 minutes/heure = 666,67 unités/minute / 40 unités/ml = 16,67 ml/minute x 60 minutes/heure = 1 000 ml/heure x 40 unités/ml = 40 000 unités/heure = 28 unités/heure.

a. t distribution

b.  98% confidence the population mean number of texts per day is between and texts is  31. 455 and 36.945

c. Two percent  will not contain the true population mean number of texts per day.

Confidence interval

Given that,

xbar = 34.2

s = 12.7

n = 119

degrees of freedom, df = n - 1 = 118

a. t distribution

b.  CI level is 98%, hence α = 1 - 0.98 = 0.02

α/2 = 0.02/2

    = 0.01,

tc = t (α/2, df) = 2.358

CI = [tex](34.2 - 2.358 * \frac{12.7}{\sqrt{119} } , 34.2 + 2.358 *\frac{12.7}{\sqrt{119} } )[/tex]

CI = (31.455 , 36.945)

With 98% confidence the population mean number of texts per day is between 31.455 and  36.945 texts.

(c) Approximately 98 percent of these confidence intervals will contain the true population mean number of texts per day, while approximately 2 percent will not.

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By using formula, Price-sales ratio = Market price per share / Sales per share= $88 / $20= 4.4,  it is not possible to calculate the dividends per share.

The formula for calculating earnings per share (EPS) is:

EPS = (Net income - Preferred stock dividends) / Average number of common shares outstanding

Price-to-earnings ratio (P/E ratio) is a financial ratio that compares a company's current share price to its earnings per share. It is calculated by dividing the market price per share by the earnings per share (EPS).

If the company's earnings per share were $10, the price-earnings ratio would be calculated as follows:

Price-earnings ratio = Market price per share / Earnings per share

= $88 / $10

= 8.8

To calculate the price-sales ratio, you will need to know the company's sales per share. The price-sales ratio is calculated by dividing the market price per share by the sales per share.

If the market price per share was $88 and the sales per share were $20, the price-sales ratio would be calculated as follows:

Price-sales ratio = Market price per share / Sales per share

= $88 / $20

= 4.4

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