If a and b are two events defined on the same sample space, given that p(a) = 0.28 and p(aub) = 0.51, find the p(b) such that a and b are mutually exclusive

Answer:

Step-by-step explanation:

gas mileage = miles covered/gallons used

but:

miles covered = [tex]35\frac{1}{2}[/tex]

                        = 35.5

gallons used     = 1[tex]\frac{1}{2}[/tex]

                           = 1.5

gas mileage = 35.5/1.5

gas mileage = 23.667 miles/gallon (to 3 decimal places)

gas mileage = miles covered/gallons used

but:

miles covered = [tex]27\frac{1}{5}[/tex]

                        = 27.2

gallons used     = [tex]\frac{4}{5}[/tex]

                         = 0.8

gas mileage = 27.2/0.8

gas mileage = 34 miles/gallon

c)

gas mileage of blue: 23.667 miles/gallon implies the blue car will travel 23.667 miles on 1 gallon

gas mileage of silver: 34 miles/gallon implies the silver car will travel 34 miles on 1 gallon

Hence the silver car would travel a greater distance on 1 gallon than the blue car.

Answer: g/15 = 3 ; g = 45 gifts.

Step-by-step explanation: You would basically have to multiply 15 by 3, and it equal 45. This answer choice shows an equation that will make the answer 45, so it is right.

g/15 will equal 3.

Then, you would break them apart and do the denominator (15) multiplied by the numerator (3).

This will get you the answer 45.

So, you will get the answer choice A.

Answer:

Step-by-step explanation:

[tex]\frac{y}{\sqrt{x} }[/tex] - [tex]\frac{\sqrt{x} }{x}[/tex] = [tex]\frac{y\sqrt{x} }{\sqrt{x} \sqrt{x} }[/tex] - [tex]\frac{\sqrt{x} }{x}[/tex] = [tex]\frac{y\sqrt{x} }{x}[/tex] - [tex]\frac{\sqrt{x} }{x}[/tex] = [tex]\frac{y\sqrt{x} -\sqrt{x} }{x}[/tex]    

Answer:

P+380=312

Step-by-step explanation:

The total, meaning addtion, and equals meaning equals sign. P+380=312

Answer: x=17

Step-by-step explanation:

Simplifying

5x = 85

Solving

5x = 85

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Divide each side by '5'.

x = 17

Simplifying

x = 17

The value of x in the equation is 17 .

Given,

5x = 85

Solving

5x = 85

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Divide each side by '5'.

x = 17

Simplifying

x = 17

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Answer:

125

Step-by-step explanation:

71.47 rounded to the nearest whole number would be 71.

54.357 rounded to the nearest whole number would be 54.

Now, when we add 71 and 54, we get:

71+54=

125

The total would be 125

Yes , there can be a Right triangle with two side lengths as simple fraction and other side length as an integer .

In the question ,

we have to find , whether a Right Triangle can be made by two fractions and an integer length .

yes, we can make a Right Triangle with two lengths as fractions and other length as integer .

let us prove it with the help of an example .

Consider the triplet 7 , 24 , 25 .

let the two fractions side be 7/25 and 24/25 , and the hypotnuse of the right triangle be  1 .

We know that for the Right Triangle

(side1)² + (side2)² = hypotnuse²

(7/25)² + (24/25)² = 1²

49/625 + 576/625 = 1

(49+576) / 625 =1

625/625 = 1

1 = 1

hence ,it is a Right Triangle .

Therefore , Yes , there can be a Right triangle with two side lengths as simple fraction s and other side length as an integer .

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Answer

A) f(w) = 80w + 30

B) w represents the number of weeks and f(w) the number of flowers that bloomed

C) 2830 flowers

Step-by-step explanation

A) To find the function f, which represents the number of flowers that bloomed, as a function of w, the number of weeks, we have to evaluate f(s) with s = s(w) = 40w, as follows:

B) w represents the number of weeks and f(w) the number of flowers that bloomed, like before.

C) Substituting w = 35 weeks into f(w), we get:

Consider that a rotation of 90° clockwise is given by:

T(x,y) => (y,-x)

The coordintates of the point L is L(0,1), the, after the rotation you have:

T(0,1) => (1,0)

answer:

D. L(1,0)

The structure must be designed so that there are no risks to the health and safety of the patients, staff, and general public. The main goal of layout exists to make clear that work, materials, and information flow through a system smoothly.

Layout design generally seeks to arrange organizational units inside a building so that the space is used to its fullest potential and total distances are kept to a minimum.

The structure must be designed so that there are no risks to the health and safety of the patients, staff, and general public. It must be able to endure the pressure and environmental conditions that they might encounter.

A facility's layout and design are crucial to a company's overall operations because they may both suit the needs of employees and maximize the efficiency of the production process. The main goal of layout exists to make clear that work, materials, and information flow through a system smoothly.

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Answer:

Step-by-step explanation:

Since City a is an equation, you would have to solve it for its population, which is 280000, and since City B is 1,620,000 and City C is double city B, 3,240,000/280000 would get you the population, which is:

11.57, you would round up after that, which would get you the answer:

12

The required correct answer is,

The area under P2 is 1, the area under P1 depends on the standard deviation of the dataset

i.e., Option d. is correct.

What is density curve ?

A density curve is a curve that illustrates the general shape of a data distribution. It is always above the x-axis; the area beneath it is always equal to one whole; the area beneath shows the percentage of all observations that fall in a given range. It is statistically easier to deal with a smooth curve than a histogram.

The bell-shaped density curve, which symbolizes the normal distribution, is the most well-known.

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Answer: 0.3

5/10 x 6/10 = 30/100 = 3/10 = 0.3

Answer:

8/15(-2/3)

we simply multiply them

-8*2/15*3

as we know that+*-=-

-16/30

so simply divided by 2 because it whole decide them 16/2and30/2

-8/15

The number with 3,4 and 8 as its factors is 24

The least common multiple(LCM) can be defined as the smallest multiple that two or more numbers have in common

The Lowest Common Multiples of 3 are:3, 6, 9, 12, 15, 18, 21, 24, 27 and 30

The Lowest Common Multiples of 4 are:  4, 8, 12, 26, 20, 24, 28, 32, ...

The Lowest Common Multiples of 8 are: 8, 16, 24, 32, 40, 48, ...

From the Lowest Common Multiples above, 24 is the only number that is common among the multiples of 3,4 and 8

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The ordered pairs that could be included in the set so that the relation remains a function of x is  (-6, 1), (-1, 1).

For the given relation that is a function of x.

{(-5, 1), (-4, 1), (−3, 1), (−2, 1)}

As, from the definition of the function, the domain of the function will not repeat in the set.

Thus, (-6, 1), (-1, 1) is the ordered pairs that could be included in the set so that the relation remains a function of x.

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The equation

has slope -3/7.

The product of perpendicular lines must be -1, so the slope of the new equation must be:

The line with that slope and that passes throught (1,6) is:

The following graph shows both equations:

ANSWER :

The answer is B. y = (x + 4)^2 + 9

EXPLANATION :

From the problem, we have :

Group the terms in which the constant term and the terms with variables are separated.

add and subtract a variable m to the parenthesis to maintain equivalency.

Calculate the value of m using b^2/4a^2 with a = 1 and b = 8

Then :

The first parenthesis will be a perfect square trinomial.

Factor and simplify :

The result of 34+(12+14)2.2 in the mixed fraction is  [tex]91\frac{1}{5}[/tex]

The expression is

34+(12+14)2.2

The mixed fraction is defined as the fraction that consist of one whole number part and a simple fraction part. simple fraction is the fraction that consist of numerator and denominator as whole numbers. The top term of  the simple fraction is called numerator and bottom term of the simple fraction is called denominator.

The expression is

=34+(12+14)2.2

First do the arithmetic operation in the bracket

= 34 + 26×2.2

Do the Multiplication

= 34+57.2

= 91.2

Convert the decimal form to simple fraction

91.2 = 456/5

Convert the simple fraction to the mixed fraction

456/5 = [tex]91\frac{1}{5}[/tex]

Hence, The result of 34+(12+14)2.2 in the mixed fraction is  [tex]91\frac{1}{5}[/tex]

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The total price of that Ingrid has to pay is $52.90.

From the Latin word "per centum," which meaning "by the hundred," the word "percentage" was borrowed. The denominator of percent's is 100, making them fractions. In other words, it is the relationship between a component and a whole in which the value of the entire is consistently set to 100. The value of the entire is always 100 in a percentage, which is a ratio or fraction. Sam, for instance, would have received a score of 30 out of 100 on his arithmetic test if he received a 30%. When expressed as a ratio, it is written as 030:10 and as a fraction, 30/100. An quantity or part that is contained in each hundred is known as a percentage. The symbol "%" signifies that it is a fraction with 100 as the denominator.

Sales price = $48.90

Amount needed to be paid = 8.5% of $48.90 + $48.90

= 4.15 + $48.90

= $52.90

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Answer:

The answers are all below.

Step-by-step explanation:

7. Yes

Plug 10 in for t

10-3 ≥ 2

7 ≥ 2

8. No

Plug 1 in for w

6(1) < -2

6 < -2 (Nope)

9. Yes

Plug 5 in for p

5 + 1.6 ≤ 4

6.6 ≤ 4

10. Yes

Plug 0 in for d

[tex]\frac{1}{2}[/tex](0) > -3

0 > -3

11.

1(------------------>k

12.

n<------------------]2.5

13.

In order to try out for one of the parts in a play at the local theater, you must be at most 12 years old. Write an inequality that represents this situation.

x≤12

x<-----------------]12

14. Yes

Plug 2 in for h

3(2) - 7 < 2

Simplify

6 - 7 < 2

-1 < 2

15. No

Plug -12 in for q

-12 + 8 ≥ [tex]\frac{-12}{4}[/tex]

Simplify

-4 ≥ -3 (Nope)

16.

    a. Yes

    Plug 0 in for x

    -2(0) < 10

    and

    -6 < -2(0)

    Simplify

    0 < 10

    and

    -6 < 0

    b. No

    Plug 4 in for x

    -2(4) < 10

    and

    -6 <  -2(4)

    Simplify

    -8 < 10

    -6 < -8 (Nope)

    c. -1

    Plug -1 in for x

    -2(-1) < 10

    and

     -6 < -2(-1)

    Simplify

    2 < 10

    and

    -6 < 2

We know the domain is the set of all x when is represented by ordered pairs: (x, y)

In this case {(-8,-12),(4,-8), (2, -10),(-10.-16) } we can observe that there are four x (the first number of each pair):

Domain = { -8, 4, 2, -10}

Inequality involving the sum of the angles of a triangle i.e,

[tex]\alpha +\beta +y > \pi[/tex]

The area of a spherical triangle ABC with angles a, B, Y are

AABC = ([tex]\alpha[/tex] + [tex]\beta[/tex]+ Y- [tex]\pi[/tex] ) [tex]R^{2}[/tex]

The AA'B'C' = AABC (by sss) as we discuss move.

We just need to demonstrate that IACI = IAC' and C'L IBCI = 1BC '1 will proceed similarly.

since AC & ATC resulted in the same.

the middle.

We now have external proof that the surface and their mon- are real. As of (ABCA) and LA'B'C) cover. A overlapping sphere with appropriate angles for each letter of the alphabet Las offered my first figure of $ segments that are completely separate from one another, so we may write -

( AABC A ) + ( A A'B'C' )A + ( An -x ) + ( Ax-B ) + ( An-V ) = [tex]4\pi R^{2}[/tex]

2 ( A ABC A ) =[tex]4\pi R^{2}[/tex] - 2 ( [tex]\pi -\alpha[/tex] ) [tex]R^{2}[/tex]- 2 ( [tex]\pi -\beta[/tex])[tex]R^{2}[/tex]-2([tex]\pi -Y[/tex])[tex]R^{2}[/tex]

AABCA = [tex](\alpha +\beta +Y-\pi )R^{2}[/tex]

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The area of the rectangle is 104 inches²

Define Area of Rectangle

The area of a rectangle is the space occupied by the rectangle inside its perimeter.

Given that, the perimeter is 42 inches

we know, the formula of perimeter of rectangle = 2(L + W)

so, the first equation will be

2(L + W) = 42

or, 2L + 2W = 42       ----------eq(i)

Next, the length of a rectangle is 5 inches longer than its width, so

L = W + 5

or, L - 5 = W              --------------eq(ii)

Now, the eq(i) is

2L + 2W = 42

Put W value from eq(ii),

2L + 2(L- 5) = 42

=> 2L + 2L - 10 = 42

=> 4L - 10 = 42

=> 4L = 52

=> L = 13

We got, L = 13 put this value in any of the equation

I'm putting the value in eq(ii) as it easy for to solve

=> 13 - 5 = W

=> W = 8

If you want to cross verify the values of L and W , then simply put the values in both the equation and LHS = RHS like that

2(13) + 2(8) = 42  (correct)

13 - 5 = 8 (correct)

Now, we got length and width so now just put the values of L and W in area of rectangle formula,

Area of rectangle = Length * width

                            = 13 * 8

Area of rectangle = 104 inches²

Hence, The area of the rectangle is 104 inches²

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Answer:

Equation of line is given as y = mx + c, where m is the slope and c is the y-intercept.

Since line has a slope of -3, equation is y = -3x + c.

Substitute (-3,1) into the equation to find c.

1 = -3(-3) + c

c = -8

Hence, equation of line is y = -3x - 8.

Answer:

(g ∘ f)(6) = 216

Step-by-step explanation:

We are given the functions f(x) = 2x - 6 and g(x)=x³

We want to find the value of (g∘f)(6), where we first find the value of f(6), and then substitute that value into g(x).

Substitute 6 as x in f(x)=2x-6.

f(6)=2(6)-6

Multiply

f(6)=12-6

Subtract

f(6)=6

Now substitute 6, which is the value of f(6) as x in g(x) = x³.

g(6)=6³ = 6 * 6 * 6 = 36 * 6 = 216

The value of g(6) is the same as the value of (g ∘ f)(6), as the 6 that we plugged into g(x) is the value of f(6).

Therefore, (g ∘ f)(6) = 216.

The equations are solved to give;

46. x = 5

48. h = 1

50. The inequality is 7 ≤ d/ -5

An algebraic expression is described as a mathematical expression that is composed of terms, factors, coefficients, constants and variables.

They are described as expressions made up of arithmetic operations which includes;

Given the expression;

46.  |2x + 5| = 3x

Take the absolute value, we have;

2x + 5 = 3x

collect like terms

2x - 3x = - 5

-x = -5

x = 5

48.  (3h + 8) + 2 = 13

expand the bracket

3h + 8 + 2 = 13

collect like terms

3h = 13 - 10

3h = 3

Make 'x' the subject of formula

h = 1

50. Seven is at most the quotient of a number d and -5.

This is expressed as;

7 ≤ d/ -5

Hence, the values are x = 5, h = 1 and 7 ≤ d/ -5

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The given equation is expressed as

The value of expression 4 1/5 + 3 2/3 + 1 1/6  is 9 1/30

Given that,

to  simplify: 4 1/5 + 3 2/3 + 1 1/6

Mixed fraction definition?

It is a type of fraction, and those that have both a fraction and a whole number are considered to be it.

How to convert Improper fraction to a mixed fraction?

Divide the fraction's numerator by its denominator, or 15/7, in step one.

Second Step: Since 2 is an integer, the answer's integer component will be a mixed fraction.

Step 3: The original denominator of seven will be used as the denominator.

Step 4: The incorrect fraction 15/7 is now a mixed fraction with the value 2 (1/7)

To simplify ,

4 1/5 + 3 2/3 = 7 13/15

7 13/15 + 1 1/6 = 9 1/30

Therefore the correct answer is 9 1/30

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