Probability is the likelihood or chance that an event will occur. The probability of P(AUB) is 1/2
Conditional probabilityProbability is the likelihood or chance that an event will occur. Given the following parameters
If P(A) = 1/6
P(B) = 5/12
P(A\B) + P(B\A) = 7/10
Required
p(AUB)
Recall that:
P(A|B)=P(AnB)/P(B)
P(B|A) = P(BnA)/P(A)
P(AnB)/P(B) + P(BnA)/P(A) = 7/10
12/5P(AnB) + 6P(BnA) = 7/10
42/5P(BnA) = 7/10
6/5P(BnA) = 1/10
6P(BnA) = 1/2
P(BnA) = 1/12
Determine P(AUB)
P(AUB) = P(A) + P(B) - P(AnB)
P(AUB) = 1/6 + 5/12 - 1/12
P(AUB) = 1/6 + 4/12
P(AUB) = 2+4/12
P(AUB) = 1/2
Hence the probability of P(AUB) is 1/2
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100 points!!!!!
If the area of C is
400 ft2 and the
perimeter of B is 64 ft,
what is the side length
of square A?
[tex]\\\text{Side length of square A = a \text{ft}}\\\\\text{Side length of square B = b \text{ft}}\\\\ \text{Side length of square C = c \text{ft}}\\\\ \text{Given that,}\\\\\text{Area of square C} = 400 ~ \text{ft}^2\\\\\implies c^2=400~~~~~~......(i)\\\\\\\text{Perimeter of square B } = 64~ \text{ft}\\\\\implies 4b = 64\\\\\implies b = \dfrac{64}4\\\\\implies b = 16\\\\\implies b^2 = 256~~~~~~~.....(ii)\\\\\\[/tex]
[tex]\text{Applying Pythagorean theorem,}\\ \\~~~~~c^2 =a^2 +b^2\\\\\implies a = \sqrt{c^2 - b^2}\\ \\\implies a = \sqrt{400-256}\\\\\implies a = \sqrt{144}\\\\\implies a = 12[/tex]
[tex]\text{Hence, the side length of square A is 12 ft.}[/tex]
A group of 8 friends arrive at a party.
They increase numbers by 20%. How
many people now at the party?
The number of people at the party now is 23.
The percentage of a number is the fraction of that number multiplied by 100. Percentages are represented with this sign: %.
3 friends arrive at a party. The percentage of people increase by 20%.This can be represented with this equation:
p x 20% = 3 people
where p is the number of people at the party before the friends arrived.
p = 3 / 20%
p = 3 / 0.20
p = 15 people
The total number of people at the party now : 15 + 8 = 23.
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Matt mixes 4 pints of ice cream and 1 1/2 pints of milk to make a milkshake. He drinks 2 cups of the milkshake. How many cups are left? Will give brainliest
Answer:
7 1/2 cups
Step-by-step explanation:
First, convert the measure of ice cream from pints to cups:
1 pint = 2 cups
⇒ 4 pints = 4 × 2 = 8 cups
Therefore,
Milkshake = 8 cups of ice cream + 1 1/2 cups of milk
= 9 1/2 cups
If he drinks 2 cups of milkshake:
Remaining milkshake = 9 1/2 - 2
= 7 1/2 cups
1pint=2cups
icecream=4(2)=8cupsmilk=1 1/2=3/2cupsTotal cups:-
3/2+88+1.5=9.5cupsCups left:-
9.5-2=7.5cupsThe chocolate candy below is being wrapped in a cardboard box. How many square centimeters area needed for the box?
The total area of cardboard needed is equal to 121.34 square centimeters.
How many square centimeters area needed for the box?This is equal to the surface of the given chocolate.
First, we will have two sides that are rectangles measuring 16cm by 2.6cm, so the area is:
[tex]A = 16cm*2.6cm = 41.6cm^2[/tex]
Then we have another rectangular side which is the bottom one, that is a rectangle of 2.2cm by 16cm, so the are is:
[tex]A' = 2.2cm*16cm = 35.2cm^2[/tex]
Finally, we have the areas of the two triangular faces, the areas of these are:
[tex]A'' = 2.2cm*3cm/2 = 1.47cm^2[/tex]
Then the total area of cardboard needed is:
[tex]area = 2*A + A' + 2*A'' = 2*41.6cm^2 + 35.2cm^2 + 2* 1.47cm^2 = 121.34 cm^2[/tex]
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i will give you brainliest i swear
Answer:
step 1: 45:82, unsimplified
step 2: 67:90, unsimplified
Step 3: 1:10 simplified
Step-by-step explanation: Using the property of retrostatistical Ratios, we understand that the answers above are correct.
Joey recorded his heart rate in beats per minute (bpm) after doing different numbers of jumping jacks His results are shown in the table below
The linear regression equation that estimates the heart rate per number of jumping jacks is: y=1.72x + 69.4; the correlation coefficient of the linear regression equation is 0.97.
Linear regression equation and correlation coefficienta. Linear regression equation:
We would make used of graphing calculator in order to determine the linear regression equation by plugging the below given data and then click on stats so as to perform a linear regression.
Given table:
(x, y), (0, 68), (10, 84), (15, 104), (20, 100), (30, 120)
Hence:
a = 1.72
b = 69.4
Equation
y = ax + b
y = 1.72x + 69.4
b. Correlation coefficient :
Correlation coefficient = 0.967
Correlation coefficient=0.97 (nearest hundredth)
Analysis:
The above correlation coefficient shows a strong positive correlation between the number of jumping jacks and the heart rate.
Therefore the linear regression equation that estimates the heart rate per number of jumping jacks is: y=1.72x + 69.4; the correlation coefficient of the linear regression equation is 0.97.
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area of r ctangle formula with l 8.5. and b 3.4
Answer:
28.9 units²
Step-by-step explanation:
The area of a rectangle formula with L being 8.5 units and B being 3.4 units, is 28.9 units². make sure to add the units squared, otherwise, it's wrong.
Always remember for area:
rectangle = length * widthtriangle = [tex]\frac{base * width}{2}[/tex]trapezoid = [tex]\frac{base_{1}*base_{2} }{2} *height[/tex]circle = π * radius ² (The most accurate is to just square the radius and keep it as ___π, but not all teachers like that.)Hope this helps, if it is the best, mark brainliest, if not, hope it helps anyway.
what is the volume of Francisco’s water bottle?
Answer:
Anything known? I mean the lenght of bottle or anything like that?
Samara is purchasing gas at the Gas n' Sip. The gas costs $2.469 per gallon. How much did Samara
pay in gas if she purchased 7 gallons?
A. $0.35
B. $9.47
C. $14.82
D. $17.28
Answer:
D. $17.28
Step-by-step explanation:
Multiply the price of gas per gallon by the number of gallons purchased to get your answer
2.469 x 7 = 17.28
Let g(x) = 3x+ 2 and f(x) = x-2/ 3 Find the value.
f(g(0))
0
-2/3
1
-1
Explanation needed please!! I'm confused on how to solve.
Answer:
0** (READ BELOW)
Step-by-step explanation:
First, solve for g(0). Since g(0) = 3x +2, we plug in 0 for x.
So,
g(0) = 3(0) + 2 = 0 + 2 = 2.
Now that we have an answer for g(0), we can plug it into f(x).
So,
f(x) = (x-2)/3
f(x) = f(g(0)) = f(2).
f(2) = (2-2)/3 = 0/3 = 0.
Thus, f(g(0)) = 0.
Essentially, you first solve for g(0) and use the answer from that to solve for f(x) where x is your answer from g(0).
**I was unsure of what the equation was for f(x) based on how you wrote it in the question, but I assumed it was f(x) = (x-2)/3.
A triangular prism is 18 yards long and has a triangular face with a base of 18 yards and a height of 12 yards. The other two sides of the triangle are each 15 yards. What is the surface area of the triangular prism?
Answer:
I really don't know happy
What is a formula for the nth term of the given sequence? 15, 24, 33
Answer:
The nth terms: 15,24,33,42,51,60,69,78,87,96,105...
Step-by-step explanation:
The nth term of an arithmetic sequence is given by an = a + (n – 1)d. So, to find the nth term, substitute the given values a = 2 and d = 3 into the formula
Order the numbers from least to greatest -4 -4.35 -4.9 -5 and -4.3
Answer:
-5,-4.9,-4.35,-4.3,-4
Step-by-step explanation:
Hope this helps :)
The typical school day lasts 420
minutes. If Lisa has science class for 105
minutes, what fraction, decimal, and
percent of the school day does she
spend in her science class?
what is 1/2 - 1/3 = in simplest form
Answer:
1/6
Step-by-step explanation:
he area of each figure.
. 5x-4 x+1 3x-4
Answer:
Find each product.
1. (q + 6)(q + 5) 2. (x + 7)(x + 4)
q2 + 11q + 30 x2 + 11x + 28
3. (n - 4)(n - 6) 4. (a + 5)(a - 6)
n2 - 10n + 24 a2 - a - 30
5. (4b + 6)(b - 4) 6. (2x - 9)(2x + 4)
4b2 - 10b - 24 4x2 - 10x - 36
7. (6a - 3)(7a - 4) 8. (2x - 2)(5x - 4)
42a2 - 45a + 12 10x2 - 18x + 8
9. (3a - b)(2a - b) 10. (4g + 3h)(2g + 3h)
6a2 - 5ab + b2
8g2 + 18gh + 9h2
11. (m + 5)(m2 + 4m - 8) 12. (t + 3)(t2 + 4t + 7)
m3 + 9m2 + 12m - 40 t
3 + 7t
2 + 19t + 21
13. (2h + 3)(2h2 + 3h + 4) 14. (3d + 3)(2d2 + 5d - 2)
4h3 + 12h2 + 17h + 12 6d3 + 21d2 + 9d - 6
15. (3q + 2)(9q2 - 12q + 4) 16. (3r + 2)(9r2 + 6r + 4)
27q3 - 18q2 - 12q + 8 27r3 + 36r2 + 24r + 8
17. (3n2 + 2n - 1)(2n2 + n + 9) 18. (2t2 + t + 3)(4t2 + 2t - 2)
6n4 + 7n3 + 27n2 + 17n - 9 8t
4 + 8t
3 + 10t
2 + 4t - 6
19. (2x2 - 2x - 3)(2x2 - 4x + 3) 20. (3y2 + 2y + 2)(3y2 - 4y - 5)
4x4 - 12x3 + 8x2 + 6x - 9 9y4 - 6y3 - 17y2 - 18y - 10
GEOMETRY Write an expression to represent the area of each figure.
21.
4x + 2
2x - 2
22.
3x + 2
5x - 4
x + 1
23. NUMBER THEORY Let x be an even integer. What is the product of the next two
consecutive even integers?
24. GEOMETRY The volume of a rectangular pyramid is one third the product of the area of
its base and its height. Find an expression for the volume of a rectangular pyramid
whose base has an area of 3x2 + 12x + 9 square feet and whose height is x + 3 feet.
x3 + 7x2 + 15x + 9 ft3
Step-by-step explanation:
Find the total surface area
Answer:
3.4cm
Step-by-step explanation:
Multiply the 2 numbers 5x24=120 then u will solve trhe surface and V=bxh so then u U will get that
It cost Luis $5 to park his car at a parking meter for 2 hours. What is the price to park for 1 hour? Draw mode or write a word sentence to help you solve the problem. Then write and solve a multiplication
Answer: 2.5$
Step-by-step explanation: Since 1 hour is half of 2 hours and the price to park for 2 hours is 5. We can take half of the 2 hour parking price to find the 1 hour price.
5$/2 Hours = 2.5$ per hour
The diagram shows a cube with edges of length x cm and a sphere of radius 3cm
The surface area of circle of radius 3 cm and cube of edge length x cm being equal implies [tex]x = \sqrt{k\pi}[/tex] integer (k = 6).
How to find the surface area of a sphere?Suppose that radius of the considered sphere is of 'r' units.
Then, its surface area S would be:
[tex]S = 4\pi r^2 \: \rm unit^2[/tex]
Given that:
Side length of considered cube = x cmRadius of considered sphere = 3 cmSurface area of the considered cube = surface area of the considered sphere.Finding the surface area of the considered cube and sphere:
Surface area of cube with x cm edge length = [tex]\rm 6 \times side^2 = 6(x)^2 \: \rm cm^2[/tex]Surface area of sphere with radius r = k cm is [tex]4 \pi r^2 = 4\pi (3)^2 = 36\pi \: \rm cm^2[/tex]Thus, we get:
[tex]6x^2 = 36\pi\\\\\text{Dividing both the sides by 6}\\\\x^2 = 6\pi\\\\\text{Taking root of both the sides}\\\\x = \sqrt{6\pi} \: \rm cm[/tex]
(took positive value out of the root since x cannot be negative as it represents length of the edge of a cube which cannot be a negative quantity).
Thus, the surface area of circle of radius 3 cm and cube of edge length x cm being equal implies [tex]x = \sqrt{k\pi}[/tex] integer (k = 6).
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what is 25percent of 50
Answer:
12.5
Step-by-step explanation:
25% means the 1/4th part of the whole number and in the case if 50 it's 1/4th part is 12.5
3. If Jessie worked 36 hours at $6 per hour at a coffee bar last week and got $188 in tips, how much did she earn? (1) $216 (2) $288 (3) $296 (4) $404 (5) $1,467
Answer:
The answer is 404
Step-by-step explanation:
multiply 36 by 6= 216
add 188= 404
she got $404.00
PLEASE HELP PLEASE PLEASE
Answer:
21
Step-by-step explanation:
Yes, since 21 has more than two factors i.e. 1, 3, 7, 21. In other words, 21 is a composite number because 21 has more than 2 factors.
Mia is designing a cake for a birthday party. She plans for a total of 12 guests, each of whom may eat a piece of cake that has a volume of 8 cubic inches. Which of the following cakes would provide enough cake for each guest to have one piece of cake, with the least amount left over?
Square cake: side = 8 in., height = 2 in.
Round cake: diameter = 6 in., height = 3 in.
Round cake: diameter = 8 in., height = 3 in.
Rectangular cake: length = 6 in., width = 9 in., height = 2 in.
The square cake can be distributed in such a way that each person out of 15 guest may get 8 [tex]inch^{3}[/tex], with the least amount left over .
The Correct option is (1).
What is Volume of any shape?The volume of an object is the amount of space occupied by the object or shape, which is in three-dimensional space. It is usually measured in terms of cubic units.
First find the volume of square cake,
Volume = l x b x h= 8 x 8 x 2
=128 [tex]inch^{3}[/tex]
Now there are total 15 guests, Each of get
=[tex]\frac{128}{15}[/tex]
= 8.533 [tex]inch^{3}[/tex]
2.Volume of round cake (d= 6 inch, r=3 inch, h= 3 inch)
Volume= [tex]\frac{1}{3} \pi r^{2} h[/tex]
= [tex]\frac{1}{3} *3.14 *3^{2}* 3[/tex]
=[tex]3.14*9[/tex]
=28.26 [tex]inch^{3}[/tex]
Now there are total 15 guests, Each of get
=[tex]\frac{28.26}{15}[/tex]
= 1.884[tex]inch^{3}[/tex]
3.Volume of round cake (d= 8 inch, r=4inch, h= 3 inch)
Volume= [tex]\frac{1}{3} \pi r^{2} h[/tex]
= [tex]\frac{1}{3} *3.14 *4^{2}* 3[/tex]
=[tex]3.14*16[/tex]
=50.24 [tex]inch^{3}[/tex]
Now there are total 15 guests, Each of get
=[tex]\frac{50.24}{15}[/tex]
= 3.349 [tex]inch^{3}[/tex]
4. Volume = l x b x h
= 6 x 9 x 2
=108 [tex]inch^{3}[/tex]
Now there are total 15 guests, Each of get
=[tex]\frac{108}{15}[/tex]
= 7.2[tex]inch^{3}[/tex]
According to question each person may get 8 [tex]inch^{3}[/tex].
Only the square cake can be distributed in such a way that each person may get 8 [tex]inch^{3}[/tex], with the least amount left over .
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You attend a working dinner with four other colleagues. Since alcohol
is not reimbursed by your company. your party receives two separate
bills: One for food ($156.65) and one for alcohol ($49.50). Each
needs to be split 5 ways.
How much do you owe for each bill?
$3.13 for food and $9.90 for alcohol
$31.33 for food and $0.99 for alcohol
$31.33 for food and $99.0 for alcohol
Using proportions, it is found that the amount owed for each bill are given as follows:
$31.33 for food $9.90 for alcohol.
What is a proportion?A proportion is a fraction of a total amount.
In this problem, each of the bills are split equally among the five people, hence the fraction is 1/5.
Thus:
1/5 x 156.65 = $31.33
1/5 x 49.50 = $9.90.
Hence the amount owed for each bill are given as follows:
$31.33 for food $9.90 for alcohol.
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what is the sum of the degree measures of the complement and the supplement of a 16 degree angle
Answer:
270
Step-by-step explanation:
I need help with this question please
Answer:
option b is the correct answer of given statement
Step-by-step explanation:
percent of SSSSD strings
10 1/2 gal = __ qt
brainliest will be given
Answer:
10 1/2 gallons = 42 quarts:)
m stuck, i dont know where i went wrong. Will brain list, pls help. Evaluate x³-2x²+3x-7/x-1
Answer: hii
Its A. x2−x+2−5x−1
Step-by-step explanation:
Divide using polynomial division.
Hopefully this helps you
- Matthew
Meeko insurance offers an annuity with a minimum interest rate of 4% for the next five years. You decide to invest 1000 into his account. what type of annuity is this?
a.single-payment fixed annuity
b.recurring-payment fixed annuity
c. recurring-payment variable annuity
D.single-payment variable annuity
Answer:
single payment variable annuity
Step-by-step explanation:
Given : ABC Insurance offers an annuity with 4.5% APR for the next 5 years. You decide to invest $1000 each year into this account.
To find : What type of annuity is this?
Solution :
Annuity is the form of insurance in which some of the money is paid each year to secure for future.
There are two types of annuity:
Single payment variable annuity - In this annuity the payment is made at the end of each period over a fixed length of time. Also in this annuity payments are made monthly, quarterly, semi-annually or annually.
Annuity due - is the opposite of single payment variable annuity as in this the payment is made at the beginning of each period.
In the given situation the annuity is single payment variable annuity because the investment is done each year for 5 years.
Find the surface area of this cube. Be sure to include the correct unit in your answer.
Answer: 54 inch²
Step-by-step explanation:
The total surface area of the cube can simply be found by finding the area of one face and multiplying by 6 because the cube has 6 faces
Area of one face = 3 inch x 3 inch = 9 inch²
Total surface area of the cube = 9 inch² x 6 = 54 inch²