Find P(AUB) of P(A)=2/5,P(B)=2/7 and A and B are Independent

Answer:

16

Step-by-step explanation:

The x's go up by 1 (1, 2, 3, 4, 5)

The y's go up by 4's. 0, 4, 8, 12, 16

There is a rule to find the y's from the x's instead:

times by 4 and minus 4.

y = 4x - 4

y = 4(5) - 4

y = 20 - 4

y = 16

By evaluating in x = 0, we can see that the function with the greater y-intercept is the first one:

y=-x+6

For any function y = f(x), we define the y-intercept as the value that y takes when we evaluate the function in x = 0.

For the first function:

y = -x + 6

The y-intercept is:

y = -0 + 6 = 6

While for the second function:

y = 2x - 3

Evaluating in 0 we get:

y = 2*0 - 3 = -3

So the y-intercept of the first function is 6, and the one of the second function is -3.

Then the first function has the greater y-intercept.

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The length and width of the rectangle with a perimeter of 64m are 19m and 13m respectively.

The perimeter of a rectangle is expressed as;

P = 2( l + w )

Where l is length and w is width.

Given the data in the question;

Let x represent the width be represented by variable x.

Plug the values into the equation above above.

P = 2( l + w )

64 = 2( (x + 6 ) + x )

64 = 2( 2x + 6 )

64 = 4x + 12

64 - 12 = 4x

52 = 4x

x = 52/4

x = 13

Hence, the dimensions of the rectangle are;

Width = x = 13m

Length = x + 6 = 13 + 6 = 19m

Therefore, the dimension of the rectangle are 13m by 19m.

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the equation of the perpendicular line is x = 4, as the line vertical and the slope is undefined

The point-slope formula is expressed as

y - y₁ = m( x - x₁ )

The slope intercept formula is expressed as;

y = mx + b

Where m is the slope and b is y-intercept.

Given the data in the question;

First, we determine the slope of the initial line by comparing to the slope intercept form y = mx + b

y = -2

Hence

Slope of initial line m = 0

Slope of the perpendicular line will be negative reciprocal of the initial line

m = -1/0

Slope m is undefined

Therefore, the perpendicular line is vertical and the slope is undefined

Hence.

x = 4.

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The given system of linear equations has no solution. By solving the equations using substitution method we get (11, 0) where no solution exists.

How many solutions can a system of linear equation can have?

A system of linear equations is usually a set of two linear equations with two variables.

The solution to a system of linear equations is the point at which the lines representing the linear equations intersect.

With linear systems of equations, there are three possible outcomes in terms of number of solutions:

How to identify the number of solutions?

Rewrite both equations in slope-intercept form, y = mx + b.

Compare the slopes of the lines, m, and their y-intercepts, b, to determine the number of solutions.

According to the given question:

Given system of linear equation are: y = -x + 11 and -4x -4y = 44

Rewriting the equations in slope-intercept form

        Simplifying further by dividing the equation with -4 on both side

        y = x - 11 ------ 2)

Clearly, both the equation have different m-values.

Hence the system of equation have one solution.

Now solving by substitution method

Substituting 2) in 1)

x - 11 = -x + 11 (since y = x -11 from 2))

2x = 22

∴ x = 11

Now substituting x = 11 in equation 2) to get the value of y

y = 11 - 11

∴ y = 0

So, the system of equation has no solution at (11, 0).

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Answer: The quotient is 3y² + 2y - 1.

Step-by-step explanation:

You can use long division to solve this expression by setting the dividend under the roof and the divisor outside as you would normally do when dividing numbers.

1) Look at the first term of the dividend, 15y³, and the first term of the divisor, 5y. Determine what value multiplied by 5y would give you 15y³. The answer is 3y², and given the number, you multiply it by the WHOLE divisor.

3y²(5y + 6) = 15y³ + 18y² <-- subtract this from the dividend.

2) Continue this process and make sure to drag down the next term for each new value you form after subtracting. Keep in mind of any negative values! When you reach up to -5y, determine what value multiplied by 5y would give you the value of -5y, which would be -1.

3) You should be left with a remainder of 0, leaving you with a quotient of 3y² + 2y - 1.

$2322.2 more the account be worth after 9 years by calculating interest compounded quarterly versus calculating simple interest.

Given that, principal = $1700, rate of interest = 2.7% and time period = 9 years.

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.

Simple interest is calculated with the following formula: S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years.

Here, simple interest = (1700×2.7×9)/100

= 41310/100

= $413.10

Amount = Principal + Simple interest

= 1700+413.10

= $2113.1

Compound interest:

[tex]Amount=P(1+\frac{R}{100} )^{nt}[/tex]

[tex]=1700(1+\frac{2.7}{100} )^{4\times9}[/tex]

[tex]=1700(1.027)^{36}[/tex]

= 1700×2.609

= $4435.3

Now, 4435.3-2113.1=$2322.2

Therefore, $2322.2 more the account be worth after 9 years by calculating interest compounded quarterly versus calculating simple interest.

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The numbers matched with its divisibility numbers is

for 60 the divisibility numbers are 2,3,5,10 .

for 48 the divisibility numbers are 2,3    and

for 81 the divisibility numbers are 3,9 .

In the question ,

three numbers are given as 60 , 48 and 81

we need to match them with their , respective divisibility numbers that are given in the option  

For the first number 60 ,

we see that 60 is divisible by 2 , 3 , 5 and 10 because

30*2 [tex]=[/tex] 60  , 3*20 [tex]=[/tex] 60 , 5*12 [tex]=[/tex] 60 and 10*6 [tex]=[/tex]60 ,

So, for 60 the divisibility numbers are 2,3,5,10

that is option(c)

For the second number 48 ,

we see that 48 is divisible by 2 and 3  because

2*24 [tex]=[/tex] 48 , 3*16 [tex]=[/tex] 48 ,

So , for 48 the divisibility numbers are 2,3

that is option(b)

For the third number 81

we see that 81 is divisible by 3 and 9  because

3*27 [tex]=[/tex] 81 , 9*9 [tex]=[/tex] 81

So , for 81 the divisibility numbers are 3 an 9

that is option(a)

Therefore , The numbers matched with its divisibility numbers is

for 60 the divisibility numbers are 2,3,5,10 .

for 48 the divisibility numbers are 2,3    and

for 81 the divisibility numbers are 3,9 .

The given question is incomplete , the complete question is

Match the numbers 60 , 48 and 81  with its divisibility numbers

(a) 3,9

(b) 2,3

(c) 2,3,5,10

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Answer:

38.8333333

sorry if it's wrong.

The simple interest on $1,200, 3.9%, 8 months is $31.356.

From the informationm, we want to calculate the simple interest of the amount that is given.

The simple interest is calculated thus:

Simple interest = PRT / 100

where

P = Principal = $1200

R = Rate = 3.9%

T = Time = 8 months = 8/12 = 0.67 years

The interest will be:

Simple interest = PRT / 100

Simple interest = (1200 × 3.9 × 0.67) / 100

Simple interest = 31.356

The interest is $31.356.

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Complete question

Calculate the simple interest on $1,200, 3.9%, 8 months

The value of 32/25 as mixed number is 1 7/25

A fraction represented with its quotient and remainder is a mixed fraction. For example, 2 1/7 is a mixed fraction, where 2 is the quotient, 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.

A mixed fraction can be obtained wen there is improper fraction. Improper fraction is a fraction that it's numerator is larger than denominator for example 32/25.

To convert to mixed fraction we find the number of times 25 can go in 32, which is 1 and the remainder is 7

Therefore 32/25 = 1 7/25.

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Equation of the perpendicular line in slope intercept form is [tex]y = \frac{5}{2}x + 2[/tex]

Option A is correct

What is equation of line in slope intercept form?

The most general form of equation of line in slope intercept form is given by y = mx + c

Where m is the slope of the line and c is the y intercept of the line.

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If  [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m = [tex]tan\theta[/tex]

The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.

The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.

Here, the given line is

2x + 5y = 10

5y = -2x + 10

[tex]y = -\frac{2}{5}x + \frac{10}{5}\\y = -\frac{2}{5}x + 2[/tex]

Slope of the given line is [tex]-\frac{2}{5}[/tex]

Slope of the line perpendicular to this given line is [tex]\frac{5}{2}[/tex]

The line passes through (-2, -3)

Equation of the required line

[tex]y - (-3) = \frac{5}{2}(x - (-2))\\y + 3 = \frac{5}{2}(x + 2)\\2y + 6 = 5x + 10\\2y = 5x + 10 - 6\\2y = 5x + 4\\y = \frac{5}{2}x + \frac{4}{2}\\y = \frac{5}{2}x + 2[/tex]

Equation of the perpendicular line in slope intercept form is [tex]y = \frac{5}{2}x + 2[/tex]

Option A is correct

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Dilation entails altering a figure's size.

Because the is larger than, Isaiah's assertion is untrue.

Although dilation is not a hard transformation, the angles of the figures it dilates remain unchanged.

The aforementioned claim suggests that,

The dimensions of and should be equal.

However, it is evident that;

are not equivalent.

In reality

greater than

Therefore, Isaiah's assertion is false.

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The probability of tossing a six-sided die with sides numbered 1 through 6 and getting a 5 is 0.166666 or 1/6.

Here in the question, we see that a six-sided die is tossed. So there will be a total of 6 outcomes.

So the sample space will be {1,2,3,4,5,6}

Of which the possible outcome of getting a 5 is 1

Let A be the event of getting a 5 on tossing a six-sided die

∴ the probability of getting a 5 on tossing a six-sided die is P(A)=1/6

∵ we know that the probability of an event is the possible outcome of the event divided by the total outcomes of that event.

So here the probability of getting a 5 is 0.166666 or 1/6.

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Using the Fundamental Counting Theorem, the number of plates for each case is obtained as follows:

The Fundamental Counting Theorem is a theorem that states that if there are n independent trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, the total number of outcomes is calculated by the multiplication of the factorials as presented as follows:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

With the Latin letters, it is found that for the letters, there are 26 outcomes, hence:

[tex]n_1 = n_2 = n_3 = 3[/tex]

With one number, the number of outcomes for the digit is:

[tex]n_4 = 9[/tex]

(as the digit cannot be zero).

With two numbers, the number of outcomes for the digit are:

[tex]n_4 = 9, n_5 = 10[/tex]

With three numbers, the parameters are:

[tex]n_4 = 9, n_5 = 10, n_6 = 10[/tex]

Hence the total number of plates is obtained as follows:

T = 26³ x (9 + 9 x 10 + 9 x 10 x 10) = 17,558,424.

With the extra letters, each letter can assume 29 outcomes, hence the number of plates is:

T = 29³ x (9 + 9 x 10 + 9 x 10 x 10) = 24,364,611.

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Answer:

A is shown in the attached image.

B. 5/6

C.  P(A or B)

Step-by-step explanation:

B. 1/2 + 2/3 - 1/3 = 5/6 or 3/6 + 4/6 - 2/6 = 5/6

C. P(A or B) = 5/6. P(A) + P(B) - P(A and B) = 5/6. Therefore, P(A) + P(B) - P(A and B) = P(A or B).

Answer:

Strings packs cost $14 each

Step-by-step explanation:

Lenny and Lashae are shopping for new guitar strings in a music store. Lenny buys 2 packs of strings. Lashae buys 2 packs of strings and a music book. The book cost $16. Their total cost is $72. How much is 1 pack of strings?

Lenny: 2s

Lashae: 2s + b

when b = $16 then these equations are:

Lenny: 2s

Lashae: 2s + 16

together they spent $72 so:

lenny + Lashae = $72 or:

2s + 2s + 16 = 72

subtract 26 from both sides:

2s + 2s + 16 - 16 = 72 - 16

2s + 2s = 56

combine s terms:

4s = 56

divide both sides by 4:

4s/4 = 56/4

s = $14

a. Jays total income is $93.50 and total spending is $103.25.

b. Jays Spending is greater than income.

c. Total saving is -9.75

d. Jays savings are negative. Since Jays spending is greater than income it does not make sense.

Two or more expressions with an Equal sign is called as Equation.

Given,

Jays Income:

Part time job: $83.50

Allowance: $10

Spending:

Clothing: $32.50

Lunches: $19.75

Entertainment: $29.00

Transportantion: $22.50

a. Jays total income and total spending

Total income = $83.50+$10.00

=$93.50

Total spending = $32.50+$19.75+$29.00+$22.50

=$103.25

b. Spending is greater than income.

c. Jays saving=Total income - Total spending

=93.50-103.25

=-9.75

d. Jays savings are negative. Since Jays spending is greater than income it doesnt make sense.

Hence,

a. Jays total income is $93.50 and total spending is $103.25.

b. Jays Spending is greater than income.

c. Total saving is -9.75

d. Jays savings are negative. Since Jays spending is greater than income it doesnt make sense.

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The solution to the expression is -31.5

An algebraic expression in mathematical is statement that comprises of  numbers, variables, symbols and mathematical operators.

Given, when a= 0.25 and b = -1

Step 1: Substitute the given into the expression 36a + 42b - 18a +6

we have;  36(0.25) + 42(-1) - 18(0.25) +6

= 9 - 42 - 4.5 +6

Step 2; use BODMAS  to evaluate

we have; 9 - 42 - 4.5 +6= -31.5

Therefore the solution to the expression is -31.5

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The interest on the borrowed amount after 7 years is $486.

The compound interest is a form of interest where the rate of interest is applied on the amount obtained after every interval of time.

Given that,

The amount borrowed is  P = $200.

Rate of interest is r = 18% per annum compounded quarterly.

Total time is t = 7 years

Then, the rate of interest for quarterly compounding is given by,

r  = 18 / 4%

  = 4.5%

And, total time period for compounding is,

n = 7 × 4

  = 28

The formula for compound interest is given as,

P[(1 + r / 100)ⁿ - 1]

Substitute the respective values to get,

200 × [(1 + 4.5 / 100)²⁸ - 1]

= 200 × 2.43

= 486

Hence, the interest due on the loan is given as $486.

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The linear function of the table is a) g(x)=x-7

What is linear function?

 If the largest power of the variables in a function is 1, then that function is linear. A line across these two points with a straightedge is needed to complete the graph because two points determine a line. When m and b are real numbers, the slope of a linear function has the form f(x)=mx+b. To find the x-intercept, set f(x)=0 and solve for x. Because y=f(x), we can use y and f(x) interchangeably.

Here let us take g(x) as y values. In given table take any two points ,

[tex](x_1,y_1)=(0,-7)\\(x_2,y_2)=(2,-5)[/tex]

Now using slope formula ,

=> slope m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

=> slope m = 2/2 = 1

Now using equation formula,

=> [tex]y-y_1=m(x-x_1)[/tex]

=> y+7=1(x-0)

=> y+7=x

=> y =x-7

Then y=g(x)

=> g(x) = x-7

Therefore the linear function of the given table is g(x)=x-7 .

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Here ya are hope this helps! :]]

Answer:

2 1/5

Step-by-step explanation:

8 4/5=44/5

(44/5)/(4)=(44/5)*(1/4)

(44/5)*(1/4)=44/20

44/20=2 1/5

The last sample range in this table is missing,the missing value is 2.

Given:

The Henry family has 5 children: Abby (age 15), Brian (age 10), Colin (age 9), Deena (age 7), and Elise (age 5).

Sample(n = 2)    A, B      A, C    A, D    Α, Ε  B, C ........ D,E

Ages                 15, 10    15,9    15,7    15, 5  10,9 .......  7,5

Sample range      5          6         8       10      1  ...........  

Let x be the sample range missing.

sample range = ages difference

= Age of D - Age of E

= 7 - 5

= 2

Therefore The last sample range in this table is missing,the missing value is 2.

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Answer:

answer is 2 i did it and got it right

Step-by-step explanation:

1) The probability that a randomly chosen penny weighs less than 2.4 grams is; 0.00621.

2) The probability that the mean weight of 15 pennies is less than 2.4 grams is; 0

The central limit theorem in statistics tells us that the sampling distribution of the mean will usually be normally distributed, provided that the sample size is large enough.

We are given the following parameter;

Population mean; μ = 2.4 grams

Standard deviation; σ = 0.04 grams

1) The probability that a randomly chosen penny weighs less than 2.4 grams is: P(X < 2.4)

Formula for z-score is;

z = (X - μ)/σ

z = (2.4 - 2.5)/0.04

z = -2.5

The p-value from z-score calculator is; p = 0.00621.

2) The standard deviation for these 15 pennies will now be;

σ' = 0.04/√15

σ' = 0.0103

The probability that the mean weight of 15 pennies is less than 2.4 grams is expressed as;

P(X' < 2.4)

z = (2.4 - 2.5)/0.0103

z = -9.709

The p-value from z-score calculator is; p = 0

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Answer:

It will take 7.5 days to complete the job.

Step-by-step explanation:

First, find how many total hours the ten men worked to complete the job

10 x 6 = 60 hours a day

12 x 60 = 720 hours total

Now compare that with the 8 men's hours

8 x 12 = 96 hours a day

720 / 96 = 7.5 days

An inequality of the form |x-al<k so that the inequality has the given solution set (-5,5) is |x|<10.

In the given question,

We have to write an inequality of the form |x-a|<k so that the inequality has the given solution set (-5,5).

We first learn about modulus,

A modulus function is a function that determines a number or variable's absolute value. It generates the size of the variable count. A function with absolute values is another name for it. No matter what input was provided to this function, the outcome is always positive.

The given set is (-5,5).

For x<(-5,5)

The mean value of x should be between -5 and 5.

-5<x<5

|x|<10

Hence, an inequality of the form |x-a l<k so that the inequality has the given solution set (-5,5) is |x|<10.

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Answer:

9 quarters and 26 dimes

Step-by-step explanation:

your welcome :)

Answer:

  DNE

Step-by-step explanation:

You want to know the y-intercept of x = -4.

The y-intercept is the point where a graph crosses the y-axis.

The line x=-4 is a vertical line parallel to the y-axis, so does not cross the y-axis.

There is no y-intercept. It does not exist (DNE).