Mathematics College

Use the given information to find the indicated probability. a and b are mutually exclusive. p(a) = .8, p(b) = .1. find p((a ∪ b)').

Answers

Answer 1
If [tex]A[/tex] and [tex]B[/tex] are mutually exclusive, then

[tex]\mathbb P(A\cup B)=\mathbb P(A)+\mathbb P(B)=0.8+0.1=0.9[/tex]

Then [tex]\mathbb P((A\cup B)')=1-\mathbb P(A\cup B)=0.1[/tex].

Related Questions

As viewed from above, a swimming pool has the shape of the ellipse x24900+y22500=1, where x and y are measured in feet. the cross sections perpendicular to the x-axis are squares. find the total volume of the pool. v = cubic feet

Answers

4900>2500, the major axis of the ellipse is along x-axis
a=sqrt(4900)=70
b=sqrt2500=50

The squares are parallel to the y-axis, thus their sides extend in the y-axis direction, hence the length of the sides are:
y=+/-50sqrt(1-x^2/4900))
The area of the square 
=y^2=[2500-2500(x^2/4900)

Thus, the volume will be sum along the x-axis from one of the ends of the ellipse to the other. by definition, the limits are (-a to a)=(-70 to 70)
But since the ellipse is symmetrical we can go from (0 to 70) and double the integral.
thus
V=2*int(0 to 70)[2500-2500(x^2/4900)]dx
=int(0 to 70)[5000-(50/49)x^2]dx
=[5000x-50/147x^3] (0 to 70)
=233,333 1/3 ft^3

what is the domain and range of
y=-2(x-3)(x+4)

Answers

The domain of any polynomial is "all real numbers."

The vertex of this function is (-0.5, 24.5), so the range of y=-2(x-3)(x+4) is
  -∞ < y ≤ 24.5

the width of a rectangle is shown below:

Answers

The difference between the y-coordinates is 7 units. If the area is to be 42 square units, the missing coordinates must be 42/7 = 6 units to the right of those shown.
B = A +(6, 0) = (-4, 4) +(6, 0) = (-2, 4)

D = C +(6, 0) = (-4, -3) +(6, 0) = (-2, -3)

The appropriate choice is the last one, ...
  (-2, 4) and (-2, -3)

Factor completely 56a2b3 − 35ab.
7ab(8ab2 − 5)
7a(8b2 − 5ab)
Prime
7a(8ab3 − 5b)

Answers

A. 

Both numbers have a factor of 7ab. Pull that out by dividing. 

Answer:

7 ab ( 8 ab² - 5 ) .

Step-by-step explanation:

Given  : 56 a²b³ − 35 ab.

To find : Factor completely.

Solution : We have given 56 a²b³ − 35 ab.

Taking 7ab common form both terms .

7 ab ( 8 ab² - 5 ) .

Therefore, 7 ab ( 8 ab² - 5 ) .

find the length of the side f .

Answers

I am pretty sure the answer is 10. Someone correct me if I'm wrong
[tex]10 {}^{2} + 15 {}^{2} = 18 {}^{2} \\ 100 + 225 = 325 \\ \sqrt{325} = 18 [/tex]
The length of side "f" would be about 9.95.

Using Pythagorean Theorem, you have the hypotenuse or side "c" (18) which is longest side. You also have side "b" (15).
Since the equation is "a^2 + b^2 = c^2”, fill in for "b" and "c" giving "a^2 + 15^2 = 18^2"
Solve for "a". Square each known value, leaving "a^2 + 225 = 324". Subtract 225 from each side, leaving "a^2 = 99" then use the square root on each side. Thus getting "a = 9.94987..., which rounded up is 9.95.

I hope this helps!

HURRY PLEASE ITS TIMED
In the year 2000, Franklintown had a population of 30,000 people. Its population had decreased by 3% each year since then. Part A: Can this situation be modeled by an exponential decay function, an exponential growth function, or neither? Explain. Part B: If the population continues to decrease at the same rate, what would you expect the approximate population to be in 2016? Show your work.

Answers

Part A:
 For this case we have a function of the form:
 y = A * (b) ^ t
 Where,
 A: initial amount
 b: decrease rate
 t: time
 Substituting values we have:
 y = 30000 * (0.97) ^ t
 Answer:
 this situation can be modeled by an exponential decay function.

 Part B:

 We have the following function:
 y = 30000 * (0.97) ^ t
 For the year 2016 we have to:
 t = 16
 Substituting values:
 y = 30000 * (0.97) ^ 16
 y = 18427.6096
 Rounding:
 y = 18428
 Answer:
 The approximate population for 2016 is:
 y = 18428

is this correct if not help me

Answers

So far, so good.

You have properly counted squares and circles.

Marcus baked a loaf of banana bread for a party. He cut the loaf into equal size pieces. At the end of the party, there 6 pieces left. Explain how you can find the number of pieces in the whole loaf if Marcus told you that 1/3 of the loaf was left.

Answers

Marcus is left with 6 pieces and 1/3 of the loaf. so  by the problem if x is the whole loaf 1x/3 =6 x =18 . The total pieces of loaves  were 18

Each square is one square meter

Answers

36 square meters i believe

please help me with this if you can

Answers

The worst error will be where the prediction is farthest away from the actual value. Since the actual value corresponds to predictions in the 2nd column, the prediction at the far right (22.8) is the farthest away. The greatest error is ...
(22.8 -22.3)/22.3 * 100% ≈ 2.2%

in the plane figure shown below. if the degree measures of the angle are as shown, then x+y=

Answers

we know that

the sum of the internal angles in the figure shown is 360 degrees
so
360°=100°+60+70°+y+80°+x
360°=(x+y)+310°
(x+y)=360°-310°-----> 50°

the answer is
x+y is 50°

hello can you please help me posted picture of question

Answers

B. Seven as your answer
:)
For this question we need to make a Venn Diagram as shown below.

Start from the inner most circle.

5 patrons like all 3 drinks. 
8 patrons like Latte and Espresso. From these 8, 5 like all 3 drinks, so the patrons which only like Latte and Espresso will be 3.

Fill all the regions this way and you will get a diagram similar to the one given below. 

Count all the numbers inside the circles. These add up to 47. This means 47 patrons like the drinks.

Total number of patrons was 50. So there are 7 such patrons which do not like any of these drinks.

So, the correct answer is option B


The amount of money that a student at harvard university carries on his/her person is normally distributed with a mean of $25 and a standard deviation of $15. what is the probability that a randomly selected sample of 25 harvard university students will have an average amount of less than $22 on his/her person?

Answers

Mean, m = $25
Standard deviation, s = $15
Sample size, n = 25 students
X <$22

Now,
Z = [(X - m)*Sqrt (n)]/s = [(22-25)*Sqrt(25)]/15 = -1

From Z tables,
P(X) = P(Z = -1) = 0.1587 = 15.87%

Therefore, probability that the selected sample has an average of less than $22 is 15.87%.

When subtracted, what is the simplified form of (5 − 3i) − (4 + 6i)? Write the answer in standard form, a + bi, where a and b are real numbers.

Answers

(5 - 3i) - (4 + 6i)      Remove the brackets. Be careful with those on the right.
5 - 3i - 4 - 6i            Did you notice how the second set worked. That - sign affected both terms inside the brackets. Now collect your like terms.

5 - 4 - 3i - 6i   The - 3i and - 6i  act like money. You are three dollars in the hold and you spend another 6. Where does that put you ?
1 - 9i              You are now 9 dollars in the whole.


Find the midpoint of the segment with the given endpoints. P(–2, 1) and Q(–3, 2)

Answers

Answer:

  (-5/2, 3/2)

Step-by-step explanation:

The midpoint is the average of the coordinates of the endpoints:

  (P +Q)/2 = ((-2, 1) +(-3, 2))/2 = (-2-3, 1+2)/2 = (-5/2, 3/2)

a game has a deck of cards with 10 red cards, 4 blue cards, and 2 yellow cards. you randomly choose two cards(choose one and choose the second one without replacement) find the probability of choosing a blue card and a yellow card

Answers

[tex] \displaystyle
|\Omega|=\binom{16}{2}=\dfrac{16!}{2!14!}=\dfrac{15\cdot16}{2}=120\\
|A|=4\cdot2=8\\\\
P(A)=\dfrac{8}{120}=\dfrac{1}{15}\approx7\% [/tex]

hey can you please help me posted picture of question

Answers

The inverse of 7x ix x/7

The composition of the function and its inverse must be zero. So the composition of 7x with x/7 is:

[tex](F( F^{-1}x)) \\ \\ =F( \frac{x}{7}) \\ \\ = 7(\frac{x}{7}) \\ \\ = x [/tex]

Thus, 7x and x/7 are inverse of each other.

So the answer to this question is option B

One serving of Mike’s crackers has 150 calories and a mass of 30 grams. How many calories are in 6 grams of the crackers?

Answers

The amount of calories that are in 6 grams of crackers is 30 grams.

What is the amount of calories in the crackers?

Division is the mathematical operation that is used to determine the quotient of a number.  It is the process of grouping a number into equal parts using another number.

Calories in 6 grams = (150 / 30) x 6 = 30 grams

To learn more about division, please check: https://brainly.com/question/13281206

#SPJ2

Final answer:

To find the calories in 6 grams of Mike's crackers, divide the total calories by the total mass of one serving to get the unit rate (5 calories/gram) and then multiply by the mass in question (6 grams) to obtain 30 calories.

Explanation:

The question asks how many calories are in 6 grams of Mike's crackers, given that one serving of 30 grams has 150 calories. To find the calories in 6 grams of the crackers, we can use unit rate and proportions.

Step-by-Step Calculation

First, determine the calories per gram of the crackers by dividing the total calories by the total mass (in grams) of one serving. This gives us the unit rate: 150 calories / 30 grams = 5 calories per gram.

Next, since we're asked about the calories in 6 grams, we multiply the calories per gram (unit rate) by the mass: 5 calories/gram × 6 grams = 30 calories.

Therefore, there are 30 calories in 6 grams of Mike's crackers. This calculation illustrates the utility of understanding proportions and unit rates in everyday applications such as determining caloric intake from portions of food.

if 12 1/2% of a sum of money is $40 what is the total sum of money?

Answers

12 1/2% = 12.5%

12.5% = $40

1% = 40 ÷ 12.5 = $3.20

100% = $3.20 x 100 = $320

Answer: $320

The total sum of money will be $320.

Let the total sum of money be represented by x.

Based on the information given, the equation to solve the question will be:

12 1/2% × x = 40

0.125x = 40

Divide by 0.125

x = 40/0.125.

x = 320

Therefore, the total sum of money will be $320.

Read related link on:

https://brainly.com/question/2805223

what is the area of a square with a radius of 9 cm

Answers

the answer would be 254.34
squares don’t have radius’, circles do. If you mean the length of one side is 9, then the area would be 81cm squared.

If you mean the area of a circle with a 9cm radius, then it would be 254.34 cm squared.

Which graph best represents the equation -4x + 5y = 10?

Answers

Do you have a photo to show the separate graphs?

Answer: these are the graphs and i need the answer

Step-by-step explanation:

with an 18% discount, George was able to save 13.23 what was the original price

Answers

The original price is 74! Hope this helps!

18% = $13.23

1% = $13.25 ÷ 18 = $0.7361

100% = $0.7361 x 100 = $73.61

Answer: $73.61

hey can you please help me posted picture of question

Answers

The correct answer is the option B.To solve this problem you must apply the proccedure shown below:

 1. You have the following expression:

 (11-7i)-(16-11i)

 2. If you want to substract both terms, you  need to substract the real numbers and the complex numbers. Then, you obtain:

 11-7i-16+11i
 (11-16)+(-7+11)

 3. Then, you obtain the following result:

 -5+4i

 4. Therefore, as you can see, the correct answer is the second option (option B), which is:

 B. -5+4i
Correct answer is option B.

Solution is shown below:

To add or subtract two complex numbers, the real part is added or subtracted from real part and the complex part is added to or subtracted from complex part as shown below:

(11 - 7i) - (16 - 11i)

= 11 - 7i - 16 + 11i

= -5 + 4i

So, the answer to this question is option B

A soccer ball is kicked from the ground in an arc defined by the function, h(x) = -2x 2 + 8x. At what point does the ball hit the ground?

Answers

check the picture below.  That's about what a parabola for an "initial velocity" case would look like.

anyhow, it hits the ground at two points, when it began, and when it came back down, and that happens when y = 0.

[tex]\bf h(x)=-2x^2+8x\implies \stackrel{h(x)}{0}=-2x^2+8x\implies 0=-2x(x-4)\\\\ -------------------------------\\\\ 0=-2x\implies 0=x\qquad \impliedby \textit{when it began}\\\\ -------------------------------\\\\ 0=x-4\implies \boxed{4=x}\qquad \impliedby \textit{when it came back down}[/tex]

Answer:

4 seconds

Step-by-step explanation:

h(t) = -3t^2 + 12t

0 = -3t^2 + 12t

0 = -3t(t - 4)

0 = t - 4

t = 4

Therefore, it takes 4 seconds for the rocket to hit the ground.

hope it helps :)

mark brainliest!

A listing of all possible outcomes of an experiment and their corresponding probability of occurrence is called

Answers

A listing of all possible outcomes of an experiment and their corresponding probability of occurrence is called Probability distribution

The listing of all possible outcomes for an experiment is known as a probability distribution.

The following information is related to the probability distribution is:

It is the table or an equation that is connected with each and every result of the statistical experiment along with the probability of occurrence.Also, it is the list of all possible experiment results.

Therefore we can conclude that the listing of all possible outcomes for an experiment is known as a probability distribution.

Learn more: brainly.com/question/22174871

I have two bags. bag 1 contains 1010 blue marbles, while bag 2 contains 1515 blue marbles. i pick one of the bags at random, and throw 66 red marbles in it. then i shake the bag and choose 55 marbles (without replacement) at random from the bag. if there are exactly 22 red marbles among the 55 chosen marbles, what is the probability that i have chosen bag 1

Answers

55 blue or red marbles,

55-22 = 33 blue marbles

bag1+bag2= 2525

bag1=.4 

33/55=.6  blue marbles

bag 2=.6

so it is 40% that U choose bag 1 















Under what circumstances is a t statistic used instead of a z score for a hypothesis test

Answers

If you know the population standard deviation sigma, then you'd use the z score. Otherwise, you would use a t statistic. However, if n is large enough (usually n > 30), then you can approximate the T distribution with the normal Z distribution. Some stats textbooks will allow the use of a z score if n > 30. Though it will depend on your specific book and/or your teacher. 

if you flip a coin four times what is the probability of flipping tails four times

Answers

There are 16 possible outcomes.
Out of all 16 outcomes, there is only one way to get the result T T T T.
Therefore, the probability is 1/16 or 0.0625




How do you evaluate this equation: a number decreased by the difference of m and 7? Please help and quick!!

Answers

Let n be the number. 

A number decreased by the difference of m and 7 can be translated into mathematical expression as

     [tex]n-\left(m-7\right)[/tex]

all I drink 3/4 of a 16 fluid ounce bottle of juice how many fluid ounces of juice are left in the bottle

Answers

4 fluid ounces. 16 * 1/4 is 4
STEP 1:
multiply 16 oz. by 3/4 to find how many ounces are 3/4 of the bottle

=16 * 3/4
=(16*3)/4
=48/4
=12 ounces


STEP 2:
subtract step 1 answer from the whole 16 oz. to find number of ounces left

=16 - 12
=4 ounces left


CHECK:
multiply the whole 16 oz. by the fraction that would be left (4/4 - 3/4= 1/4). There are several ways to check this problem; this is just one way.

=16 * 1/4
=(16*1)/4
=16/4
=4


ANSWER: 4 ounces would be left

Hope this helps! :)
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