If P(A) = 2/3, P(B) = 4/5 and P(AnB) = 3/5, what is P(AuB)?

Answers

Answer 1

Answer:

13/15

Step-by-step explanation:

P(A∪B) = P(A) + P(B) – P(A∩B)

            = 2/3 + 4/5 - 3/5

 Getting a common denominator

            2/3 *5/5 + 4/5*3/3  - 3/5 *3/3

             10/15 + 12/15 - 9/15

             13/15

Answer 2

Answer:

[tex] \frac{13}{15} [/tex]

Step-by-step explanation:

We know that,

P(AUB) = P(A) + P(B) - P(A n B)

So,

[tex]P(AUB) = P(A) + P(B) - P(A n B) \\ = \frac{2}{3} + \frac{4}{5} - \frac{3}{5} \\ = \frac{10 + 12 - 9}{15} \\ = \frac{22 - 9}{15} \\ = \frac{13}{15} [/tex]

hope this helps you.

Have a nice day!


Related Questions

Quadrilateral A B C D is shown. All sides are congruent. Angle C is a right angle.
Which statements are true regarding quadrilateral ABCD? Check all that apply.

ABCD has congruent diagonals.
ABCD is a rhombus.
ABCD is not a rectangle.
ABCD is not a parallelogram.
ABCD has four congruent angles.

Answers

Answer:

The first one and last one

Step-by-step explanation:

Answer:

1,2,5

Step-by-step explanation:

got it right on edge

Lorraine computed a confidence interval for µ based on a sample of size 41. Since she did not know σ, she used s in her calculations. Lorraine used the normal distribution for the confidence interval instead of a Student's t distribution. Will her interval be longer or shorter than one obtained by using an appropriate Student's t distribution? Explain.

Answers

Answer:

Shorter

Step-by-step explanation:

When given the population standard deviation, σ, the normal distribution should be used. However, if the sample standard deviation is being used, the t distribution should be used. The implication of using a normal distribution in Lorraine's case when using the sample standard deviation which requires the use of the T - distribution is that, the interval beacjbea smaller as the critical value obtained is smaller than the T critical value with degree of freedom, n - 1 ; 41 - 1 = 40

At α = 0.05 ;

Tcritical, df = 40 = 2.02

Zcritical = 1.96

Find the constant of proportionality (r) in the equation y=rx

Answers

Answer:

0.1

Step-by-step explanation:

r = y/x

r = 1.4 / 14 = 0.1


find the angles of the triangle if they are proportional to the following 3 4 5

Answers

Answer:  90,  and 1600 degrees.2500

Step-by-step explanation:

If the angles are proportional to 3, 4, 5,Then the angle measures are 3x, 4X and 5X

Step-by-step explanation:

Answer:

45  60  75

Step-by-step explanation:

Let's call the angles 3 x , 4 x and 5 x

They must add up to 180 o in a triangle, so:

3 x + 4 x + 5 x = 12 x = 180 → x = 180 / 12 = 15 So the angles are:

3 ⋅ 15 = 45 o 4 ⋅ 15 = 60 o 5 ⋅ 15 = 75 o Check answer:

45 + 60 + 75 = 180

Find the scale factor of the dilation. Then tell whether the
dilation is a reduction or an enlargement

Answers

Answer:

Enlargement

k =[tex]\frac{18}{4}[/tex] =  [tex]\frac{9}{2}[/tex]

Step-by-step explanation:

k = [tex]\frac{new}{old}[/tex]

If k > 1 then its an enlargement.

If k < 1 then its a reduction

A 15 foot pole extends t feet below ground and 10 feet above ground. Choose the linear equation that models the situation.

Answers

No options are given for the question :

Answer:

t + 10 = 15

Step-by-step explanation:

Given that :

Length of pole = 15 feet

Height below the ground = t

Height above the ground = 10

Tge linear equation which represents the scenario can be modeled as :

Entire length of pole = 15 feets

Length above ground = 10

Length below ground = t

Length below + length above = total length

t + 10 = 15

-3/11 + 5/9 can you pls explain this step by step

Answers

Answer:

[tex]\frac{28}{9}[/tex]

Step-by-step explanation:

[tex]\frac{-3}{11} +\frac{5}{9}[/tex]

[tex]=\frac{-27}{99} +\frac{55}{99}[/tex]

[tex]=\frac{-27+55}{99}[/tex]

[tex]=\frac{28}{99}[/tex]

28/9 but I’m not quite sure

Use the elimination method to solve the system of equations.
3x + 2y = 16
2x - 2y = 4

Answers

Answer:

D (4, 2)

Step-by-step explanation:

adding equation 1 and 2,

5x = 20

x = 4

Hence y = 2

Hence its D

Answer:

b (5,3)

Step-by-step explanation:

Which of the following is most likely the next step in the series?
А.
B.
C.
D.

Answers

Answer:

D

Step-by-step explanation:

The answer is D because the pattern adds one angle every one shape. Ex. Triangle, Rectangle, Pentagon, Hexagon

What is the answer to this question

Answers

Answer:

24 [tex]m^{2}[/tex]

Step-by-step explanation:

Area of parallelograms is :

A = b x h

The height must be a line perpendicular to the base.

The slant measuring 5 is not perpendicular to the base.

A = 6 x 4

A = 24

The answer is 24 m^2

HELP ASAP PLEASE!! calculate the expected gain or loss for stock jkl

Answers

Answer: $8.50

Step-by-step explanation:

The expected gain (loss) is a weighted average of the probability of the different gains (losses) and the gains or losses.

Expected gain or loss for stock JKL:

= (Probability of losing $25 * -25) + ( Probability of gaining $5 * 5) + ( Probability of gaining $45 * 45)

= (15% * -25) + (65% * 5) + (20% * 45)

= -3.75 + 3.25 + 9

= $8.50

Answer:8.50$

Step-by-step explanation:

plz help ASAP with explanation

Answers

Answer:

19.5 cm

Step-by-step explanation:

the remaining height = 1200 /(12×8)

= 1200/96 = 12.5 cm

so, the height of the tank = 7+ 12.5 = 19.5 cm

[tex]\displaystyle\bf \boxed{V=abh \ ; \ 1dm^3=1litre=1000cm^3} \\\\a=12cm \ ; \ b=8 cm ;\: h_1=7 \; ; \ h_0=h_1+h_2=?\\\\abh_2=1,2litre=1,2dm^3\ = 1200cm^3\\\\ 8\cdot 12 h_2=1200\\\\h_2=12.5 cm\: then \\\\h_0= 7+12,5=19,5 \\\\Answer : the \ height \ of \ the \ tank \ is \ 19,5 cm[/tex]

PLS HELP (algebra 1)

solve -19d + 8(7d - 14)

Answers

Answer:

[tex]\huge\boxed{-19d + 8(7d - 14)=37d-112}[/tex]

Step-by-step explanation:

[tex]-19d + 8(7d - 14)[/tex]

use the distributive property: a(b + c) = ab + ac

[tex]-19d + (8)(7d)+(8)(- 14)=-19d+56d-112[/tex]

combine like terms

[tex]=(-19d+56d)-112=37d-112[/tex]

find x. need help w these 2, thanksss!

Answers

Answer:

f) 11

g) 75

please correct me if I am wrong

f) x = 52 degrees. g) x = 28 degrees

which relation is a function?

Answers

the first one because there is only one y value for every x value. you can also use the vertical line test in which you draw vertical lines and make sure the function only passes through it once at each point

The first one because there is only one y value for every x value. The correct option is first.

To determine if a relation is a function, use the vertical line test: If any vertical line intersects the graph of the relation at more than one point, then the relation is not a function. On the other hand, if every vertical line intersects the graph of the relation at most once, then the relation is a function.

In first relation is considered a function, because each input x-value is associated with exactly one output y-value. In other words, for every x-value in the domain of the relation, there can be only one corresponding y-value in the range. Each x-value should not have more than one y-value associated with it.

Therefore, each x-value should not have more than one y-value associated with it. The correct option is first.

Learn more about Function here:

https://brainly.com/question/31062578

#SPJ6

Find the integer that lies between [tex]$\sqrt[3]{-45}$ and $\sqrt[3]{-101}$[/tex]

Answers

∛(-45) = ∛((-1) × 45) = ∛(-1) × ∛45 = -∛45

Similarly,

∛(-101) = - ∛101

Now,

• 3³ = 27 and 4³ = 64, and 27 < 46 < 64, so ∛27 < ∛45 < ∛64, which places ∛45 between 3 and 4

• 5³ = 125, so ∛101 would similarly fall between 4 and 5

So to summarize, we have

3 < ∛45 < 4 < ∛101 < 5

so that

-5 < ∛(-45) < -4 < ∛(-101) < -3

so the integer between these numbers is -4.

Work out the height of this triangle with base, b = 8mm and
area, A = 218.8mm?,

Answers

Answer:

54.7 mm

Step-by-step explanation:

use the formula area= 1/2 base time height

A=1/2bh

Answer:

54.7mm

Step-by-step explanation:

Area=1/2b×h

218.8=0.5×8×h

218.8=4h

h=218.8÷4

h=54.7

75% of bis 12. What is b?

Answers

Answer:

9

Step-by-step explanation:

Answer: 16

Step-by-step explanation:

75=75/100=3/4

3/4*b=12

b=12/1*4/3

Martin can travel 174 miles in 3 hours. At this rate, how far can he travel in 7 hours.

Answers

Answer:

406

Step-by-step explanation:

all you have to do is divide 174 by 3 and multiply 58 by 7

simplify please help me
[tex] \frac{x - 4}{x + 6} - \frac{x - 6}{x + 4} [/tex]

Answers

Answer:

[tex]\frac{20}{x^2 + 10x+24}[/tex]

Step-by-step explanation:

common denominators : (x+6)(x+4)

numerators become difference of squares

[tex]x^2 -16[/tex]   and   [tex]x^2-36[/tex]  

[tex]x^2 -16[/tex]   -   [tex]x^2-36[/tex]   = 20

(x+6)(x+4) = [tex]{x^2 + 10x+24}[/tex]

Answer:

i hope it will help you thank u

Mary wants to send some packages to her uncle. It costs her $25 to send 5 packages through a certain shipping company. Consider the number of packages per dollar. Write an equation to represent the relationship.

Answers

Answer:

25 divided by 5 equals 5

it cost 5 dollars per package

Hope This Helps!!!

please someone help I know the answer but I don't know how to place it on the scales below. (15 Points)

Answers

Given:

a. 35% of 150 g

b. 113% of $55

To find:

The correct values for the given blanks.

Solution:

a. 35% of 150 g

Here, the percent part is 35% and percent whole is 100%.

35% of 150 g is:

[tex]\dfrac{35}{100}\times 150=52.5[/tex]

So, the number part is 52.5 g and the whole number is 150 g.

Therefore, the percent part is 35%, number part is 52.5 g and the whole number is 150 g.

b. 113% of $55 g

Here, the percent part is 113% and percent whole is 100%.

113% of $55 is:

[tex]\dfrac{113}{100}\times 55=62.15[/tex]

So, the number part is $62.15 and the whole number is $55.

Therefore, the percent part is 113%, number part is $62.15 and the whole number is $55.

Find the length of side xx in simplest radical form with a rational denominator.

Answers

Answer:

x = 2[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Using the sine ratio in the right triangle and the exact value

sin30° = [tex]\frac{1}{2}[/tex] , then

sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{\sqrt{2} }{x}[/tex]  = [tex]\frac{1}{2}[/tex] ( cross- multiply )

x = 2[tex]\sqrt{2}[/tex]

Answer:

Solution given:

Relationship between perpendicular and hypotenuse is given by sin angle

Sin 30°=opposite/hypotenuse

½=[tex]\frac{\sqrt{2}}{x}[/tex]

x=2*[tex]\sqrt{2}[/tex]

The value of x is 2[tex]\sqrt{2}[/tex]

HELPsjskskksksksksnxhxhxjsjsns

Answers

your answer would be A. -15/2 < x < 0

x² -23n +132 pls help​

Answers

Answer:

(x-11)(x-12)

Step-by-step explanation:

To clarify, there was a likely typo written in your question since it is impossible to solve two unknown values with only one equation. I'm supposing that the equation was supposed to be

[tex] {x}^{2} - 23x + 132[/tex]

The first step is to split the term into factorable terms.

Since the highest power is power of 2, the equation would look like this if factorized:

[tex](ax + b)(cx + d)[/tex]

If the terms were added properly, the expanded equation would be:

[tex](ac \times {x}^{2} ) +( (ad + bc) \times x) + (bd)[/tex]

Generally, we do not see decimal values or fractions in factorization with some exceptions. Otherwise, the equation could get very complicated.

In this case, we can determine the following:

[tex]a \times c = 1[/tex]

[tex](a \times d) + (b \times c) = - 23[/tex]

[tex]b \times d = 132[/tex]

First, we can determine a and c to be one since one only has one factor, which is itself.

This leaves us with two equations left

[tex]b + d = - 23[/tex]

[tex]b \times d = 132[/tex]

There are two ways to solve the remaining two terms. We can either find the factors or do quadratic equation. Finding the factors is the easier way out here.

b and d will add up to negative values but multiplying these values give positive values. The most likely reason is that b and d are negative values.

Now, we can find the factors of 132.

The factors are 1, 2, 3, 4 , 6, 11, 12, 22, 33, 44, 66 and 132. However, the values flip around.

In fact, the "factors" we are looking for are the negative values of the actual factors. To solve this, we should find two factors that add up to 23.

In this case, 11+12=23.

To verify, 11*12 is also 132.

Since we are looking for the negative values, the values we are looking for are -11 and -12.

The values can be plugged in anywhere in b or d.

After cleaning up, we can plug in the values into our factorization and we will get:

[tex](1x - 11)(1x - 12)[/tex]

or

[tex](x - 11)(x - 12)[/tex]

answer : (x-11) (x-12)


1. Another way to think of your net earnings is
the overtime request
the employee discount
the quota that is filled
the amount of your paycheck

Answers

Answer:

amount of your paycheck is the correct answer because the summation of all check paid to me will be my net earning.

What is the value of x in the equation 4 . 10 X+52 3 +35x+1 5 ?

:)​

Answers

Answer:

[tex]x=-3[/tex]

Step-by-step explanation:

Given:

[tex]4\frac{3}{10}-(2\frac{2}{5}x+5\frac{1}{2})=\frac{1}{2}(-3\frac{3}{5}x+1\frac{1}{5})[/tex]

Distribute to remove parentheses:

[tex]4\frac{3}{10}-2\frac{2}{5}x-5\frac{1}{2}=-\frac{18}{10}x+\frac{6}{10}[/tex]

For simplification and clarity, reduce all mixed numbers to simplified common fractions:

[tex]\frac{43}{10}-\frac{12}{5}x-\frac{11}{2}=-\frac{9}{5}x+\frac{3}{5}[/tex]

Combine like terms:

[tex]-\frac{12}{5}x-\frac{6}{5}=-\frac{9}{5}x+\frac{3}{5}[/tex]

Add 6/5 to both sides, then add 9/5x to both sides:

[tex]-\frac{3}{5}x=\frac{9}{5}[/tex]

Divide both sides by -3/5 to isolate x (recall dividing by a number is equal to multiplying by its reciprocal):

[tex]x=\frac{9}{5}\cdot -\frac{5}{3}, \\x=\frac{-9}{3},\\x=\boxed{-3}[/tex]

Find the measure of the missing angle using exterior angle sum theorm

Answers

35 degrees.

Assuming 145 is the exterior angle, the interior is 35. 180-145=35
Add 110 to 35 and get 145 degrees. Which leads the remaining angle 35 degrees

Answer:

35

Step-by-step explanation:

The exterior sum theorem states the exterior angle is equal to the sum of the opposite interior angles

145 = ?+110

145 - 100 = ?

35 = ?

PLEASE HELP ASAP!!!
solve for the given variable and show your work. 3a-12b=30. solve for b.

Answers

Answer:

b=(-10-a)/4

First factor out the common number:3

Then divide both sides by 3

Then simplify 30/3 to 10

Then subtract a to get your answer

PLEEAASSEEEE HELP ME. IM ABOUT TO GET A REALLY BAD GRADE AND MY PARENTS WILL GET SO MAD I REALLY NEED HELK PLEASW

Answers

An absolute value graph looks like a V. If the number attached to the x is positive, then the graph opens upwards. If the number attached to the x is negative, then the graph opens downwards.

In this case, the graph opens downwards.

To find the vertex, look at the |x - 1| part of the equation. This tells us that x is shifted 1 to the right (opposite of the sign). And, the 3 outside of the absolute value bars tells us that the graph is also shifted up 3. Therefore, the vertex is (1, 3).

Next, we need to figure out how to graph it. That's where the -2 in front comes in. We know the graph faces downwards already. So, from the vertex, we will go down 2 spaces and left or right 1 depending on the side you are working on. Continue this pattern just like you would graphing the slope of a regular line, but this one is two sided.

If you need to view the graph for further help, I would recommend an online graphing calculator such as Desmos.

Hope this helps!

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