Can someone help me with this problem

Given the following P(A) = 0.3, P(B) = 0.2, P(A) and P(B) 0.06. So, A and B are independent. This can be solved using probability concept.

The word "probability" derives from the Latin word "probitatem," which means "credibility, likelihood," from the noun probabilis in the 14th century (see probable). The phrase was first used in a mathematical meaning in 1718.

A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

Given that,

P(A) = 0.3

P(B) = 0.2

P(A and B) = 0.06

Now, P(A and B) = P(A) × P(B)

or, 0.06 = 0.3 × 0.2

So, A and B are independent.

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Answer:

101

Step-by-step explanation:

f(1) = 5 = 4*1 +1

f(9) = 37 = 4*9+1

f(6) = 4*6+1 = 25

f(f(6)) = f(25) = 4*25+1 =101

Answer:

  101

Step-by-step explanation:

Given the values of a linear function f(1) = 5 and f(9) = 37, you want the value of f(f(6)).

The given ordered pairs are (1, 5) and (9, 37). Using these, we can find the slope of the function to be ...

  m = (y2 -y1)/(x2 -x1)

  m = (37 -5)/(9 -1) = 32/8 = 4

The y-intercept is ...

  b = y -mx

  b = 5 -4(1) = 1

So the function in slope-intercept form is ...

  y = mx +b

  f(x) = 4x +1

The value of f(6) is ...

  f(6) = 4·6 +1 = 25

The value of f(f(6)) is ...

  f(f(6)) = f(25) = 4·25 +1 = 101

The value of f(f(6)) is 101.

Answer:

(7x + 5)(- x - 11)

Step-by-step explanation:

9(x - 1)² - 16(x + 2)² ← is a difference of squares and factors in general as

a² - b² = (a + b)(a - b)

9(x - 1)² - 16(x + 2)²

= [ 3(x - 1) ]² - [4(x + 2) ]² with a = 3(x - 1) and b = 4(x + 2)

= [ 3(x - 1) + 4(x + 2) ] [ 3(x - 1) - 4(x + 2) ] ← distribute parenthesis

= [ 3x - 3 + 4x + 8 ] [ 3x - 3 - 4x - 8 ]

= (7x + 5)(- x - 11 )

The inequality that describes this situation will be 6x + 2s ≤ 76

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.

x = number of group dance numbers

s = number of solo performances

The inequality will be 6x + 2s ≤ 76

This inequality can be read as "the total duration of the group dance numbers (6 minutes per group dance number) plus the total duration of the solo performances (2 minutes per solo performance) is less than or equal to 76 minutes."

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If the business owner wanted to make the case that the workers are paid well, she would use the range of central tendency.

The range, D

You are undoubtedly most familiar with the mean, which is the arithmetic average and a measure of central tendency. It is extremely easy to calculate the mean. Simple addition and division by the dataset's observation count are all that are required to calculate the values. All data values are included in the mean calculation.

Finding a variable's maximum observed value (also known as the range) and deducting its least observed value will yield the range (the minimum).

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If the Gasoline costs $3.58 per gallon and Karl paid $30.43 , the number of gallons Karl purchased is  8.5 gallons .

The Per unit cost of Gasoline is = $3.58  ;

the amount paid by Karl for gasoline is = $30.43   ;

we have to calculate the number of gallons of gasoline purchased by Karl,

the number of gallons can be calculated by the formula :

Number Of Gallons purchased = [tex]\frac{Total \; Amount }{Cost \; per \; Gallon}[/tex] ;

Substituting the values of amount and cost per gallon in the formula ,

we get ;

Number of gallons = [tex]\frac{30.43}{3.58}[/tex] ;

we get ; ⇒ 8.5 .

Therefore , Karl purchased 8.5 gallons of gasoline .

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Using the equation, the restaurant owner can determine how long it will take before the high-water mark is less than 30 cm from the base of the walkway. In this case, the answer is 40 years.

1. Subtract the desired end point from the current height of the walkway:

50 cm - 30 cm

= 20 cm

2. Divide the difference by the rate of submergence:

20 cm / 0.5 cm/yr

= 40 years

The restaurant owner can use the equation to calculate the number of years it will take for the high-water mark to be less than 30 cm from the base of the pier’s walkway. By subtracting the desired end point from the current height of the walkway, the owner can determine the difference in height. Then, by dividing this difference by the rate of submergence, the owner can calculate the number of years it will take before it is necessary to take action to protect the pier from flooding. In this case, the answer is 40 years.

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The area of the part of the plane 5x + 3y + z = 15 that lies in the first octant is 15x^3/6 + 45x^2y/2.

Area is a measure of the size of a surface or the amount of space it takes up. It can be measured in square units such as square feet, square meters, or acres. Area is used to describe the size of a two-dimensional object or shape, and is often used when discussing the size of a plot of land, a room, or other geographical area.

The first octant is defined as the area in the three-dimensional Cartesian coordinate system where all the coordinates are positive. In this case, the equation 5x + 3y + z = 15 can be rearranged to solve for z: z = 15 - 5x - 3y. This new equation can then be used to find the area of the plane that lies in the first octant by integrating the equation over the area of the octant.

To solve for the area, we must first find the boundaries of the octant. Since all coordinates must be positive, the boundaries of the octant are x = 0, y = 0, and z = 0. The area of the plane that lies in the first octant is then computed using the triple integral:

Area = ∫∫∫ 0 0 0 15-5x-3y dzdydx

= ∫∫ 0 0 (15x + 45y)dydx

= ∫ 0 (15x^2/2 + 45xy)dx

= 15x^3/6 + 45x^2y/2

Therefore, the area of the part of the plane 5x + 3y + z = 15 that lies in the first octant is 15x^3/6 + 45x^2y/2.

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Therefore , the solution to the given problem of number line comes out to be option 2 543 is correct.

An introduction to mathematics tool is the number line, which is a visual integer depiction of real numbers. It is a representation of an intensity line. Each actual figure is taken to symbolize a point on the real number, or each precise figure is taken to symbolize a position. On a number line, distances between increments are equal. A line's numbers can only be answered in the way that is specified by those numbers. The question that corresponds with the number will define how it is used. B: Speak your mind.

Here,

Given :

Number are as follows : 221 ,543,28492 and 92349

Thus,

To find that the number is divisible by 3 but not 9.

So , as we know that sum of individual number of that number is divisible by 3 .

Then thw hole number is divisible by 3 .

So , we see 543 is divisible by 3 but not 9 .

Therefore , the solution to the given problem of number line comes out to be option 2 543 is correct.

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a number is  divisible by 3 if the sum of its digits is divisible by 3.

a number is  divisible by 9 if the sum of its digits is divisible by 3.

the  number  divisible by 3 but not by 9 is 543,  

These two points on the number line describe that she descended by 70 units.

A number line is defined as the number marked on the line calibrated into an equal number of units. For example -1, 0, 1, and so on.

Here,
She started at –5 and descended to –75.
On the number line, the difference between  -75 and -5 is given as
= -5 - (-75)
= 70

Thus, these two points on the number line describe that she descended by 70 units.

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5-card hands have at least one club  2023203

5-card hands have at least two cards with the same rank 916,272

N[at least one club] = N[total ways] - N'[at least one club]

                               = N[total ways] - N[no clubs]

There are 39 cards without a club. So there are 39 choose 5 = 575757 ways to not get a club.

There are 2598960 possible hands, leaving us with 2598960-575757 ways.

Which is 2023203 hands.

How many 5 card hands will have (at least) two of the same number?

This is a standard deck. Take 2–10 to be what I mean by numbers.

N=∑k=24(91)(4k)⋅(125−k)(41)5−k+[(92)+(91)(41)](42)2⋅(111)(41)

+(91)(42)⋅(121)(43)+(91)(43)⋅(41)(42)

=(760,320+38,016+432)+114,048+2,592+864

=916,272

A standard deck of playing cards contains 13 unique ranks, each with 4 distinct suits. Since we are interested in only pairs from ranks 2 to 10, we shall define A be the collection of the 9 relevant ranks and B be the collection of the 4 ranks (ace, jack, queen, king) where pairs are not a consideration. Collection C is the union of A and B, which contains all 13 ranks.

When computing probabilities we need to select the ranks(s) from a collection and then choose a number of suits (cards). When ranks are chosen from either A or B they are also chosen from C. This is important since we might choose twice from the same collection. For example, we might choose a rank from A for a pair (9 choose 1) and later choose 3 ranks from C for singletons (12 choose 3).

To hopefully make understanding the logic easier, I have first chosen the ranks either from A, B, or C, and immediately following I have chosen the number of cards, which is always choosing from 4 suits. I have inserted a dot between different card selections.

We begin by computing the number of combinations with exactly 2, 3, and 4 of a kind from A. The singletons come from C.

N1=∑k=24(91)(4k)⋅(125−k)(41)5−k=760,320+38,016+432=798,768

We add the case of either two pairs from A or a pair from each of A and B. The singleton comes from C.

N2=[(92)+(91)(41)](42)2⋅(111)(41)=114,048

We add the case of a pair from A and 3 of a kind from C.

N3=(91)(42)⋅(121)(43)=2,592

Finally, we add the case of 3 of a kind from A and a pair from B. Note that the case of both 3 of a kind and a pair from A is the same as the case of both a pair and 3 of a kind from A, which has already been included.

N4=(91)(43)⋅(41)(42)=864

N=N1+N2+N3+N4=916,272

5-card hands have at least one club  2023203

5-card hands have at least two cards with the same rank 916,272

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Answer:

[tex]g(5)=-75[/tex]

Step-by-step explanation:

[tex]g(x)=-3x^{2} \\g(5)=-3(5)^{2} \\g(5)=-75[/tex]

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The total distance travelled on the cycle is 30.46m and the acceleration  is the last 8 seconds is 0.85 m/s².

"Acceleration is the measure of the speed at which velocity changes."

OR "Acceleration depends upon the velocity if the velocity continously increases or decreases the acceleration will be produced."

Positive acceleration results from continuously increasing velocity.

Negative acceleration will be negative if the velocity is continuously decreasing.

FORMULA

Acceleration is defined as a change in velocity divided by time, or a = (Vf-Vi)/t UNIT.

Meter/second+square, or m/S², is the SI unit of velocity in the MKS system.

a. Total distance = Hypotenuse₁ + mid distance + Hypotenuse₂

Hypotenuse₁ = [tex]$ \sqrt{10^2 + 6^2} $[/tex]

Hypotenuse₁ = 11.66m

mid distance = 12 - 6

                      = 6m

Hypotenuse₂ = [tex]$ \sqrt{10^2 + (20-12)^2} $[/tex]

Hypotenuse₂ = [tex]$ \sqrt{10^2 + (8)^2} $[/tex]

Hypotenuse₂ = 12.80m

Total distance = 11.66m + 6m + 12.80m

Total distance = 30.46m

b. Acceleration  [tex]{\displaystyle ={\frac { \text{v - u} }{t}}[/tex]

[tex]\displaystyle = {\frac { \text{12.80 - 6} }{8}[/tex]

[tex]\displaystyle = {\frac { 6.80 }{8}[/tex]

0.85 m/s²

Thus, the total distance travelled on the cycle is 30.46m and the acceleration  is the last 8 seconds is 0.85 m/s².

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The equation that represent the relationship between pounds of garbage y and of days x is y = 4.5x

Direct variation describes a simple relationship between two variables . We say y varies directly with x , then y=kx. for some constant k , called the constant of variation or constant of proportionality .

From the graph when y = 4.5 , x = 1 and when y = 9 , x = 2. we can take any of these values to find K

y = kx

9 = 2k

therefore K = 9/2 = 4.5

representing K for 4.5 in y = kx

then, y = 4.5x

therefore the equation of the relationship between y and x is y = 4.5x

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[tex]\angle 3[/tex] and [tex]\angle 6[/tex]

The smallest possible whole-number length for the third side is 12

Following the Pythagorean theorem which states that the hypotenuse square is equal to the sum of the squares of the other two sides in a triangle.

This is represented as;

a² = b² + c²

Given that;

From the information given, we have that;

14² = 6² + c²

Find the square values

196 = 36 + c²

collect like terms

c² = 196 - 36

subtract the values

c² = 160

Find the square root of both sides

c = √160

c = 12. 65

Thus, the value is 12

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The interval should be 12 hours and 25 minutes for the two high tides and two low tides.

What is interval ?

An interval refers to the amount of time it takes for a tide to go from high to low or low to high

The reason for two high tides and two low tides each day is due to the gravitational pull of the moon and the sun on Earth's oceans. These gravitational forces cause the water in the oceans to bulge, creating high tides. The gravitational pull of the moon is stronger than that of the sun, so the moon has a greater impact on tides.

The time it takes for the tide to go from high to low and back to high is called the tidal period, which is about 12 hours and 25 minutes. This is not exactly 24 hours because the Earth is also rotating on its axis, so the position of the Moon and the Sun relative to a specific location on the Earth's surface is constantly changing.

So, the interval should be 12 hours and 25 minutes for the two high tides and two low tides.

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Answer:

The communicative property does not apply to subtraction.

10 - 8 = 2

8 - 10 = -2

We do not get the same answer.  2 and -2 are not the same number.

Step-by-step explanation:

The distance Jon travels to work is 472.5 miles.

Let d be the distance Jon travels to work.

The time it takes to drive is 20 minutes and the time it takes to bike is 45 minutes.

The difference in speed between driving and biking is 14.5 mph.

We can set up the following equation:

20min * (14.5mph + x) = 45min * x

Solving for x gives us the average speed of Jon on the bike, which is 10.5 mph.

Now we can use the distance formula to solve for d:

d = rate * time

d = 10.5mph * 45min

d = 472.5 miles

Therefore, the distance Jon travels to work is 472.5 miles.

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Amy will earn $28.70 + $3.80 = $32.50.

Profit and loss:

A profit and loss (P&L) statement refers to a financial statement that summarizes the revenues, costs, and expenses incurred during a specified period, usually a quarter or fiscal year. These records provide information about a company’s ability or inability to generate profit by increasing revenue, reducing costs, or both. P&L statements are often presented on a cash or accrual basis. Company managers and investors use P&L statements to analyze the financial health of a company.

Amy will earn $28.70 from selling 7 large necklaces (7 x $4.10 = $28.70) and $3.80 from selling 1 small necklace, so in total, she will earn $28.70 + $3.80 = $32.50.

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The provided statement indicates that the regression line's equation is[tex]\hat{Y}[/tex] =  -0.06392X + 3.42231. Hence the formula for predicting the anticipated sepal size of a floral with panicle length 6.39 is [tex]\hat{Y}[/tex] = 3.01

More specifically, the nature and degree of the correlation between a variable y and a number of different independent variables are assessed using linear regression. It aids in the creation of models for making predictions, such as projecting the stock price of a corporation.

Let X represent the sepal's length, and Y represent its breadth. Next, we have the information below:

Cov (X, Y) = -0.0438254

[tex]$$\begin{aligned}& \bar{Y}=3.04966 \\& \sigma_Y=0.445429 \\& \bar{X}=5.829932 \\& \sigma_X=0.828054\end{aligned}$$[/tex]

The following provides the least squares estimates of the intercept and regression coefficient:

[tex]\hat{\beta_0}=\bar{Y}-\hat{\beta_1} \bar{X}[/tex]

[tex]$\hat{\beta_1}$[/tex] = Cov (X, Y)/[tex]$\sigma_X^2$[/tex]

[tex]\begin{aligned}& \hat{\beta}_1=\frac{-0.0438254}{0.828054^2} \\& \hat{\beta}_1=-0.06392\end{aligned}[/tex]

and,

[tex]$$\begin{aligned}& \hat{\beta_0}=3.04966-(-0.06392) *(5.829932) \\& \Rightarrow \hat{\beta}_0=3.42231\end{aligned}$$[/tex]

Thus, the regression line's equation is as follows:

[tex]\hat{Y}[/tex] =  -0.06392X + 3.42231

With a sepal length of 6.39, the following formula predicts the sepal breadth of a flower:

[tex]$$\begin{aligned}\hat{Y} & =-0.06392 * 6.39+3.42231 \\\Rightarrow \hat{Y} & =3.0138612 \simeq 3.01\end{aligned}$$[/tex]

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The complete question is-

The famous iris dataset (the first sheet of the spreadsheet linked above) Was first published in 1936 by Ronald Fisher. The dataset contains 50 samples from 3 iris species. setosa, virgiria, and versicolor. Four features are measured, all in cm sepal length, sepal with, petal length, and petal width.

What is the equation tor the least,square regressian line where the independen; or predictor variabie is pelat Iength and the dependent of response variable is petal width for iris versicolar?

What is the predicted petal width for iris versicolor for a flower with a pelal length of 4.1?

Step-by-step explanation:

now you should be able to dive these things yourself.

A no

(1/4)v = 4

4×(1/4)v = 4×4

v = 16

this is not v = 4

B no

n + 4 = 25

n + 4 - 4 = 25 - 4

n = 21

this is not n = 17

C yes

2z = 28

2z/2 = 28/2

z = 14

The area of the region enclosed by the inner loop of the curve can be calculated by integrating the function r = 6 + 12 sin θ over the interval of θ.

The area of the inner loop is given by Area = 1/2 ∫r^2 dθ = 1/2 ∫(6 + 12 sin θ)^2 dθ

We can solve this integral by breaking it into two parts: Area = 1/2 (∫(6 + 12 sin θ)^2 dθ) = 1/2(∫36 + 72sin θ + 144sin^2 θ dθ)

The first integral is simple and equals to 36*θ and the second one is equal to 48θ - 48cos(2θ)

The limits of integration are [0, 2π]

So the area of the inner loop is 1/2(36*2π + 48(2π) - 48(2)) = 72π

So the area of the region enclosed by the inner loop of the curve is 72π square units.

Answer: The answer is 0.25 inches every minute

Step-by-step explanation: The equation tells you that the pool started at 30 inches (0.25t+30). It says that the pool's depth rises 0.25 inches every minute. So the answer is that the pool started out as 30 inches (which is the y-intercept) and rose 0.25 inches every minute.

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If a student in stat 121 wants to estimate the average score on the stat 121 final exam from last semester. The sample is: The 200 students interviewed.

Sample can be defined as the data or information that are randomly collected from a group of population so as to reach or drawn a conclusion.

Based on the scenario the sample will be the 200 students who took the class last semester  as the 200 students were randomly selected from a larger population so as to reach a conclusion.

Therefore we can conclude that the sample is the 200 students interviewed.

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We can say that in geometry, Babylonian mathematicians were able to calculate the area of a trapezoid, suggesting that they were aware of the Pythagorean Theorem.

The Pythagorean Theorem, sometimes known as the Pythagorean Theorem, is the basic Euclidean geometry relationship between a right triangle's three sides. According to this rule, the area of a square with the hypotenuse side equals the sum of the areas of squares with the other two sides. The Pythagorean Theorem, often known as the generic algebraic notation a2 + b2 = c2, states that the square that crosses the hypotenuse of a right triangle opposite the right angle equals the sum of the squares that span the sides of a right triangle.

Other complex mathematical strategies were known to the Babylonians. For example, in geometry, Babylonian mathematicians were able to calculate the area of a trapezoid, suggesting that they were aware of the Pythagorean Theorem long before Pythagoras.

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Answer:

x (number of games) = 8

Step-by-step explanation:

We want these two to be equal, which means we want:

4.50x + 5 = 4.75x + 3

We will minus 4.50x and 3 from both sides, giving us:

2 = .25x

Then, multiply by 4 to get a whole number of x, which gives us:

x = 8

Now, we will check our answer. We have:

4.50 * 8 + 5 = 4.75 * 8 + 3

36 + 5 = 38 + 3

41 = 41

So this proves x = 8.

So, the amount of games where the price would be the same is 8, x = 8.

Hope this helped!

The sine function that intersects its midline at (0,-6) and then has a minimum point at (2.5,-9) is given as follows:

y = 3sin(0.6πx) - 6.

The standard definition of the sine function is given as follows:

y = Asin(Bx) + C.

For which the parameters are given as follows:

The midline is at y = -6, while the minimum point is at y = -9, hence the amplitude of the function is given as follows:

A = -6 - (-9)

A = 3.

A sinusoidal function with amplitude 3 should oscillate between -3 and 3, while it oscillates between -3 and -9, hence the vertical shift is given as follows:

C = -6.

The distance from the midline to the minimum value is of 3/4 of the period, hence the period is of:

3/4P = 2.5

P = 4 x 2.5/3

P = 10/3.

This means that the parameter b is obtained as follows:

2π/B = 10/3

10B = 6π

B = 0.6π

This means that the function is defined as follows:

y = 3sin(0.6πx) - 6.

The graph of the sinusoidal function is given by the image presented at the end of the answer, and the labeled points show that the desired features are present.

The complete problem is given as follows:

The graph of a sinusoidal function intersects its midline at (0,-6)(0,−6)left parenthesis, 0, comma, minus, 6, right parenthesis and then has a minimum point at (2.5,-9).

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