45.75 + 4.85=? Plzzzz help

a) P(X+Y = 12) = p6r6

b) True

Using the convolution formula, where X and Y are the outcomes of rolling the two dice, we can find the probability distribution of their sum for k=2, 7, and 12.

P(X+Y = k) = Σ P(X=i)P(Y=k-i)

For k = 2, we have:

P(X+Y = 2) = P(X=1)P(Y=1) = p1r1

For k = 7, we have:

P(X+Y = 7) = P(X=1)P(Y=6) + P(X=2)P(Y=5) + P(X=3)P(Y=4) + P(X=4)P(Y=3) + P(X=5)P(Y=2) + P(X=6)P(Y=1)

= p1r6 + p2r5 + p3r4 + p4r3 + p5r2 + p6r1

For k = 12, we have:

P(X+Y = 12) = P(X=6)P(Y=6) = p6r6

To show that P(S = 7) > P(S = 2)r6/r1 + P(S = 12)r1/r6, we can use the formulae we derived in part (a).

Substituting k=7, we have:

P(S = 7) = p1r6 + p2r5 + p3r4 + p4r3 + p5r2 + p6r1

Substituting k=2 and k=12, we have:

P(S = 2) = p1r1

P(S = 12) = p6r6

Substituting these into the inequality, we get:

p1r6 + p2r5 + p3r4 + p4r3 + p5r2 + p6r1 > p1r1(r6/r1) + p6r6(r1/r6)

p1r6 + p6r6 > p1r6 + p6r6

which is true. Therefore, P(S = 7) > P(S = 2)r6/r1 + P(S = 12)r1/r6.

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The probability that a randomly selected point within the circle falls in the red-shaded square is: 0.50

The formula for the area of a circle is:

A = πr²

where:

A is area

r is radius

Thus:

A = π * 4²

A = 50.265 unit²

Area of square = side * side

Area = 5 * 5

Area = 25 unit²

Thus:

P(selected area falls in the read square) = 25/50.265

P(selected area falls in the read square) = 0.497 ≈ 0.50

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The required answer is f(x) = ceil(x/3) is a valid function that satisfies the given conditions.

To find a function from the set {1, 2,..., 30} to {1, 2,..., 10} that is a 3-to-1 correspondence, you can use the ceiling function along with division. The ceiling function, denoted by ⌈x⌉, rounds a number up to the nearest integer. Here's the step-by-step explanation:
This ensures that each group of three numbers is assigned the same value in the target set.
1. Define a function f(x) that takes an input from the set {1, 2,..., 30}.
2. Divide the input (x) by 3, so the result is x/3.
3. Apply the ceiling function to the result, so you have ⌈x/3⌉.
4. The output of the function f(x) = ⌈x/3⌉ will be in the set {1, 2,..., 10}.
The division operation is used to group every three numbers together, and the ceiling operation is used to round up the result to the nearest integer.
Now you have a function f(x) = ⌈x/3⌉ that is a 3-to-1 correspondence from the set {1, 2,..., 30} to {1, 2,..., 10}.

The division and ceiling operations ensure that each element in the range set {1, 2,..., 10} corresponds to exactly three elements in the domain set {1, 2,..., 30}.

Therefore, f(x) = ceil(x/3) is a valid function that satisfies the given conditions.

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\(8 \sqrt{5} is \: the \: length\)

Step-by-step explanation:

\(( {16})^{2} = ( {x})^{2} - ( {8})^{2} \\ 256 = {x}^{2} - 64 \\ 256 + 64 = {x}^{2} \\ \sqrt{320} = \sqrt{ {x}^{2} } \\ 8 \sqrt{5} = x\)

Answer:

1/2h+9=17

We move all terms to the left:

1/2h+9-(17)=0

Domain of the equation: 2h!=0

h!=0/2

h!=0

h∈R

We add all the numbers together, and all the variables

1/2h-8=0

We multiply all the terms by the denominator

-8*2h+1=0

Wy multiply elements

-16h+1=0

We move all terms containing h to the left, all other terms to the right

-16h=-1

h=-1/-16

h=1/16

Answer:

1/3

Step-by-step explanation:

P(Sport utility vehicle) = 2/6 = 1/3

Answer:

13 containers of coleslaw

12 teammates

13÷12= 1,08 containers of coleslaw per teammate

The minimum sample size needed to estimate μ for the given values of c, o, and E is 100

The minimum sample size needed to estimate μ for the given values of c, o, and E is 100

We use the formula

n= (zc/E)2σ2

Where,

n = sample size

zc = The minimum sample size needed to estimate μ for the given values of c, o, and E is 100

E = margin of error

σ = standard deviation

Substituting the given values,

n= [(1.96*0.95)/1]2*5.72

n= 95.29

Therefore, the minimum sample size n equals 96 (rounded up to the nearest whole number).

The minimum sample size needed to estimate μ for the given values of c, o, and E is 100

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Answer:

Option (D)

Step-by-step explanation:

Let the equation of the line be,

y = mx + b

where m = slope of the line

b = y-intercept

Slope of the line passing through two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by,

m = \(\frac{y_2-y_1}{x_2-x_1}\)

Since, line 'l' is passing through two points (0, 1) and (-1, 0),

Therefore, slope 'm' = \(\frac{1-0}{0+1}\) = 1

y-intercept 'b' = 1

Therefore, equation of the line will be,

y = 1(x) + 1

y = x + 1

Option (D). will be the answer.

Answer:

??

Step-by-step explanation:

For given survey of 62 customers was taken at a bookstore regarding the types of books purchased,

a) The number of customers surveyed who purchased only science fiction = 9

b) The number of customers surveyed who purchased mysteries and science fiction, but not romance novels = 13

c) The number of customers surveyed who purchased mysteries or science fiction = 51

d) The number of customers surveyed who purchased mysteries or science fiction, but not romance novels = 46

e) The number of customers surveyed who purchased exactly two types of books = 2

In this question,

we have been given a survey of 62 customers was taken at a bookstore regarding the types of books purchased.

38 customers purchased mysteries,

31 purchased science fiction,

21 purchased romance novels,

18 purchased mysteries and science fiction,

12 purchased mysteries and romance novels,

9 purchased science fiction and romance novels,

and 5 purchased all three types of books.

Let S represents the set of customers who purchased science fiction books,

R represents the set of customers who purchased romance novels books and

M represents the set of customers who purchased mysteries books.

From given information,

n(S) = 31

n(R) = 21

n(M) = 38

n(M ∩ S) = 18

n(M ∩ R) = 12

n(S ∩ R) = 9

n(M ∩ R ∩ S) = 5

a) we need to find the number of customers surveyed who purchased only science fiction.

= n(S) - n(M ∩ S) - n(S ∩ R) - n(M ∩ R ∩ S)

= 31 - (18 - 5) - (9 - 5) - 5

= 31 - 13 - 4 - 5

= 9

b)  we need to find the number of customers surveyed who purchased mysteries and science fiction, but not romance novels

= n(M ∩ S) - n(M ∩ R ∩ S)

= 18 - 5

= 13

c) we need to find the number of customers surveyed who purchased mysteries or science fiction

n(M ∪ S) = n(M) + n(S) - n(M ∩ S)

              = 38 + 31 - 18

              = 51

d) we need to find the number of customers surveyed who purchased mysteries or science fiction, but not romance novels

= n(M ∪ S) - n(M ∩ R ∩ S)

= 51 - 5

= 46

e)  we need to find the number of customers surveyed who purchased exactly two types of books

=  n(M ∩ S) - n(S ∩ R) - n(M ∩ R)

= (18 - 5) - (9 - 5) - (12 - 5)

= 13 - 4 - 7

= 2

Therefore, for given survey of 62 customers was taken at a bookstore regarding the types of books purchased,

a) The number of customers surveyed who purchased only science fiction = 9

b) The number of customers surveyed who purchased mysteries and science fiction, but not romance novels = 13

c) The number of customers surveyed who purchased mysteries or science fiction = 51

d) The number of customers surveyed who purchased mysteries or science fiction, but not romance novels = 46

e) The number of customers surveyed who purchased exactly two types of books = 2

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Answer:

3) The exact side length is 3.87

4) 8.66

5) 49

6) 1.69

Step-by-step explanation:

3) \(\sqrt{15}\)

4) \(\sqrt{75}\)

5) \(7^{2}\)

6) \(1.3^{2}\)

Answer:

3:√15 in

4: 5√3 m

5: 49 m²

6: 1.69 in²

Step-by-step explanation:

To find the area of a square you take the lenght and multiply it by its width

The special thing about a square is that all sides are equal meaning length=width so we only need one side to get all the information we need

For this question x will be the side of a square

3: Area= x²

15=x²

√15=x

4: same deal as 3

75=x²

√75=5√3

5: This is even easier then the other two

we adjust our equation to look like the following

area=side²

so area=7²=49

49

6: same deal as before

1.3²=1.69

Step-by-step explanation:

BD is bisecting the angle ABC.

that means both split angles are the same size (half of the main angle).

so,

9x = 8x + 3

x = 3

Answer:

the y intercept is 0

Step-by-step explanation:

y=5x

there is a 0 as y inter

Answer:

0

Step-by-step explanation:

The equation of a line can always be represented as \(y=kx+b\).

We know the slope is 5, but this doesn't matter right now as we're looking for the y-intercept.

If there is nothing added to the slope, you always assume the y-intercept is (0, 0). It would have stated otherwise, like if the equation was \(y=5x+6\), then the y-intercept would be (0, 6).

So the y-value of the y-intercept of this equation is 0.

Hope this helped!

sarah used 8 centimeters of tape to wrap 4 presents. how many presents did sarah wrap is she used 18 centimeters of tape?​

Applying proportion

we have that

8/4=18/x

solve for x

x=18*4/8

x=9 presents

Answer:

$5.25

Step-by-step explanation:

The total cost of the paint is $15.40.

The first step is to find the volume of the bucket.

The volume of a cylinder is given by the formula:

V = πr²h

where V is the volume, r is the radius, and h is the height.

Plugging in the values, we get:

V = π(3.5 inches)²(8 inches)

V = 308 cubic inches

The total cost of the paint can then be found by multiplying the volume of the bucket by the cost per cubic inch:

Total cost = 308 cubic inches × $0.05/cubic inch

Total cost = $15.40

Therefore, the total cost of the paint is $15.40.

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Answer:

\(x = 2\)

Step-by-step explanation:

Using the pythagorean theorem in the right triangle:

\(1^2 + 2^2 = c^2\\1 + 4 = c^2\\c = \sqrt5\)

Using the pythagorean theorem in the left triangle:

\(x^2 + (\sqrt5)^2 = 3^2\\x^2 + 5 = 9\\x^2 = 4\\x = 2\)

The length of the segment in the complex plane is 5.

The length of a segment in the complex plane can be found using the distance formula. To find the length of the segment with endpoints at 4+2i and 7-2i, we can use the formula:

Distance formula = sqrt((x2 - x1)^2 + (y2 - y1)^2)

In this case, the coordinates of the first endpoint are x1 = 4 and y1 = 2i, while the coordinates of the second endpoint are x2 = 7 and y2 = -2i.

Plugging these values into the formula, we have:

Distance = sqrt((7 - 4)^2 + (-2 - 2)^2)
         = sqrt(3^2 + (-4)^2)
         = sqrt(9 + 16)
         = sqrt(25)
         = 5

Therefore, the length of the segment in the complex plane is 5.

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Answer:

A. Negative

Step-by-step explanation:

This line cannot have a slope of zero or undefined because it's a linear negative line. This line is not positive because it's not heading to the right, it's heading to the left which is the negative side, the slope Rise/Run goes up 1 and left 1, which means the slope for this equation is possibly -1x.

Answer:

Negative

Step-by-step explanation:

We can see that as x increases, y decreases. Therefore, the change in y over the change in x is negative. The line goes down from left to right.

angleD=(7b+1)angle E=(2b+1)and angle F=(b+8)

Answer:

<E = 35

Step-by-step explanation:

7b + 1 + 2b + 1 + b + 8 = 180

combine like terms

7 + 2 + 1 = 10

10b

1 + 1 + 8 = 10

10b + 10 = 180

substract 10 from 180

= 170

10b = 170

170 divided by 10

= 17

now plug in for b for angle E

2 (17) + 1

= 35

Data triangulation is a research method that involves using multiple data sources or methods to gather and analyze information, enhancing the validity and comprehensiveness of findings.

Data triangulation is a research method that involves using multiple sources or methods to gather and analyze data on a particular topic or research question. By combining different data sources, researchers aim to enhance the validity, reliability, and comprehensiveness of their findings.

Two real-world examples of data triangulation are:

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Answer:

A≈660.52cm²

Step-by-step explanation:

i used the formulassss A=πr2

d=2r

Answer:

solution

Step-by-step explanation:

The value of the variable for which the equation is satisfied is called the solution of the equation.

Answer:

c = -2

Step-by-step explanation:

6c-8-2c = -16

4c -8 =-16

4c = -16 +8

4c = -8

4c/4 = -8/4

c = -2

Answred by Gauthmath

The solution of the equation 6c - 8 - 2c = -16 is -2 calculated by combining like terms and isolating the variable then dividing the equation by coefficient of the c variable.

To solve the equation 6c - 8 - 2c = -16, isolate the variable c on one side of the equation.

Combine like terms on the left side of the equation:

6c - 2c = 4c

The equation now becomes:

4c - 8 = -16

Take constant term on the right side of the equation by adding 8 to both sides:

4c - 8 + 8 = -16 + 8

The equation simplifies to:

4c = -8

To find the value of c, divide both sides of the equation by 4:

4c / 4 = -8 / 4

c = -2

Hence, the value of c is -2 in the equation  6c - 8 - 2c = -16.

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The mode is 18.5.

What is mode?

In statistics, there  are most repeated value among the given set of data. Those are called mode. Among the given set of data, mode is the value which has the maximum frequency. Sometimes, it may be possible to have more than one value which has the equal maximum frequency.

Formula for mode for grouped data is given by:

Mode = l + [(f₁-f₀)/(2f₁-f₀-f₂)]×h.-------------------(1)

Where, l = lower class limit of modal class, h = class size, f₁ = frequency of modal class, f₀ = frequency of class preceding to modal class, f₂ = frequency of class succeeding to modal class.

In the given problem l= 15.5

                                   f₀= 8

                                  f₁= 10

                                  f₂= 8

                                  h= 6

Putting all the values in equation (1) we obtain mode

                     mode= 15.5 +{(10-8)/(2×10-8-8)} ×6

                              = 15.5+(2/4)×6

                              = 15.5+ 3

                               = 18.5

Hence, the mode is 18.5.

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To solve this problem, we can use the Pythagorean theorem to find the distance between the two cyclists at any given time. Let's assume the time it takes for the distance between the two cyclists to be 75 miles is "t" hours.

The distance traveled by the cyclist traveling north is given by the formula: distance = speed × time.

Therefore, the distance traveled by the northbound cyclist after time "t" is 15t miles.

Similarly, the distance traveled by the cyclist traveling east is distance = speed × time.

So, the distance traveled by the eastbound cyclist after time "t" is 20t miles.

According to the Pythagorean theorem, the distance between the two cyclists is given by the square root of the sum of the squares of their respective distances traveled:

distance = sqrt((distance north)^2 + (distance east)^2)

Using the distances we found earlier, we can substitute them into the formula:

75 = sqrt((15t)^2 + (20t)^2)

Now, let's solve for "t" by squaring both sides of the equation:

5625 = (15t)^2 + (20t)^2

5625 = 225t^2 + 400t^2

5625 = 625t^2

t^2 = 5625 / 625

t^2 = 9

t = sqrt(9)

t = 3

Therefore, it will take 3 hours for the distance between the two cyclists to be 75 miles.

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On the board, Ms. Sofia scrawled a list of numerals. 57,58,64,63,58,62,60. She then requested that a pupil write a number on the board. If the student added 65 to the list, the median would not change.

To find the median of the given list of numbers, we need to arrange them in order from smallest to largest:

57, 58, 58, 60, 62, 63, 64

The median is the middle number in this list, which is 60.

Now let's consider what will happen if the student adds 65 to the list. The new list of numbers will be:

\(57, 58, 58, 60, 62, 63, 64, 65\)

To find the new median, we need to arrange these numbers in order:

\(57, 58, 58, 60, 62, 63, 64, 65\)

The new median will be the middle number in this list, which is still 60.

Therefore, the answer is D. The median will not change if the student adds 65 to the list.

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