The claim of Miguel is correct, as the two events are independent because P(NF|PB) = P(NF).
What is conditional probability?The conditional probability is the happening of an event, when the probability of occurring of other event is given.
[tex]P(A|B)=\dfrac{P(A\cap B)}{P(B)}[/tex]
The probability of event A, given that the event B is occurred.
Independent events are those events whose occurrences do not depend on the other events.
The two-way table shows the distribution of book style to genre is given as,
The first column has entries paperback, hardcover, total.
The second column is labeled Fiction with entries 20, 10, 30.
The third column is labeled nonfiction with entries 60, 30, 90.
The fourth column is labeled total with entries 80, 40, 120.
Miguel claims that given that the book is paperback (PB) does not affect the outcome that the book is nonfiction (NF).
Suppose that two events are denoted by A and B. They are said to be an independent event if and only if:
[tex]P(A \cap B) = P(A)P(B)[/tex]
Put the values as,
[tex]\dfrac{60}{120}=\dfrac{80}{120}\times\dfrac{90}{120}\\\dfrac{1}{2}=\dfrac{1}{2}[/tex]
As both the values are equal. Thus, the claim of Miguel is correct because the two events are independent because P(NF|PB) = P(NF).
Learn more about the probability here;
https://brainly.com/question/24756209
Learn more about the independent events here;
https://brainly.com/question/12700357
Answer:
The correct answer is option A. :)
Step-by-step explanation:
Just got it right on edge - the above answer helped and is correct :D
Brainliest would be greatly appreciated!
A soccer ball has a radius of 11 cm. Using π ≈ 3.14 , what is the approximate volume of the soccer ball in cubic centimeters?
It can be noted that the volume of the ball which is a sphere will be 5572.45 cm³.
How to calculate volumeFrom the information given, the soccer ball has a radius of 11 cm. This will be calculated by using the volume of a sphere.
Volume = 4/3πr³
= 4/3 × 3.14 × 11³
= 5572.45 cm³
In conclusion, the correct option is 5572.45 cm³.
Learn more about volume on:
https://brainly.com/question/1972490
What’s the correct one? I have no idea please help
Answer:
22π cm³
Step-by-step explanation:
Let's start with the formulas for volume:
volume of cylinder = πr²h
volume of cone = (1/3)πr²h
Notice the formulas above for the volume of a cylinder and the volume of a cone. The only difference is that the volume of the cone has the fraction 1/3 multiplying the rest, and the rest is exactly the same as in the volume of the cylinder.
That means that if a cylinder and a cone have the same radius and height, the volume of the cone is 1/3 the volume of the cylinder.
Here, the cylinder and cone do have the same radius and height. That means the volume of the cone is 1/3 the volume of the cylinder.
The volume of the cylinder is 66π cm³.
The volume of the cone is 1/3 of that volume, so divide 66π cm³ by 3 to find it.
volume of cone = 66π cm³ / 3 = 22π cm³
Answer: 22π cm³
You need to paint your house to sell it. You can choose between two different painters, George and Henry. George will charge 90$ for the paint, and then $40 per hour. Henry will charge $120 for the paint and then $35 per hour.
After how many hours will the cost be the same?
If you estimate it will take about 10 hours to paint the room, who should you choose?
Answer:
At 6 hours the cost is the same. At 10 hours of service Henry is cheaper.
Step-by-step explanation:
This is simple. Follow my lead!
First we must create an equation for George
He charges $90 initially and then $40 per hour
So George's equation is:
[tex]y = 40x + 90[/tex]
Now let's find Henry's equation!
He charges $120 initially and then $35 per hour
So Henry's equation is:
[tex]y = 35x + 120[/tex]
1) To find when they will be the same, just set them equal to each other and solve for x.
[tex]40x + 90 = 35x + 120 \\ - 35x \\ 5x + 90 = 120 \\ - 90 \\ 5x = 30 \\ \div 5 \\ x = 6[/tex]
This means that when x = 6 or at 6 hours in the cost is the same!
2) Just solve both equations with x = 10
[tex]y = 40(10) + 90 \\ y = 400 + 90 \\ y = 490[/tex]
At 10 hours George's service costs $490!
[tex]y = 35(10) + 120 \\ y = 350 + 120 \\ y = 470[/tex]
At 10 hours Henry's service costs $470!
$470 is less than $490 so that means Henry is more cheaper!
Yay! We did it!
Brainliest Appreciated! If you have questions please don't hesitate to comment.
Which polynomials are prime? Check all that apply. X2 4 x2 – 5x 2 x2 10x – 24 x2 – x 27 2x3 – 4x 5x2 – 10.
If the polynomial is having only two factors then the polynomial is a prime polynomial that is shown below.
[tex]\rm x^{2} +4\\\\ x^{2} -5x +2\\\\ x^{2} -x + 27 \\\\2x^{3} -4x + 5\\\\[/tex]
What is a prime polynomial?The polynomial that has only two factors is known as a prime polynomial.
The polynomials are
[tex]\rm 1. \ \ x^{2} +4\\\\2. \ \ x^{2} -5x +2\\\\3. \ \ x^{2} +10x -24 \\\\4. \ \ x^{2} -x + 27 \\\\5.\ \ 2x^{3} -4x + 5\\\\6. \ \ 5x^{2} - 10[/tex]
The factor of the given polynomial will be
1. [tex]\rm x^{2} + 4[/tex] is a prime factor. Because it has only two factors.
2. [tex]\rm x^{2} -5x + 2[/tex] is a prime factor. Because it has only two factors.
3. [tex]\rm x^2 + 10 x - 24[/tex] is not a prime factor. Because it has more than two factors.
4. [tex]\rm x^2 - x + 27[/tex] is a prime factor. Because it has only two factors.
5. [tex]\rm 2x^3 - 4x + 5[/tex] is a prime factor. Because it has only two factors.
6. [tex]\rm 5x^2 - 10[/tex] is not a prime factor. Because it has more than two factors.
More about the prime polynomial link is given below.
https://brainly.com/question/17490039
g(x) = 3/(x - 2) - 1
Find the inverse function
Answer:
2
Step-by-step explanation:
g(3)=3/(3-2)-1
3/1-1
3-1
2
Simplify the expression below. (10x+1)3x+5(5x)
Answer:
38x
Step-by-step explanation:
{(10x+1)3x}+5(5x)
10x+3x+25x=38x
Answer:
2x*(15x+14)
Step-by-step explanation:
First Step:
(3 • (10x + 1) • x) + 25x
Second Step:
3x • (10x + 1) + 25x
Third Step:
.....
Fourth Step:
Pull out like factors :
30 x 2 + 28x = 2x • (15x + 14)
Final result :
2x • (15x + 14)
5+8 divided by 2
Someone pls tell me
Answer:
it's 6.5 5+8=13 divided by 2 is 6.5
Step-by-step explanation:
1. Solve: 3x42• (56 = 8x3)
Answer:126
Step-by-step explanation:40+40+40=120. 2x3 6. So 120+6= 126
A number is the same as 16 less than 3 times itself. What is the number?
Answer:
-8
Step-by-step explanation:
-8 x 3 = -24
-24 is 16 units less than -8
simplify, the fraction 24/36
Step-by-step explanation:
24/36
=2/3
Hope it helps
Answer:
2/3
Step-by-step explanation:
12×2 = 24
&
12×3 = 36
=2/3
(would appreciate it if you could mark me the brainliest :))
Quadrilateral JKLM is a parallelogram. What is the m kjn
Answer:
solution: KL-2ML. LKIN=63x2=126*
Step-by-step explanation:
Mark me brainliest!!
first answer = brainliest
Answer:
e = -4
step-by-step explanation:
2e + 3 + 7 = 2
2e + 10 = 2
2e = 2 - 10
2e = -8
e = -8/2
e = -4
verification:
2e + 3 + 7
2(-4) + 3 + 7
-8 + 10
2 ... Therefore proved.
Answer:
e = -4
Step-by-step explanation:
2e + 3 + 7 = 2
2e + 7 = -1
2e = -8
e = -4
First I subtracted the 3 off both sides to keep the equation equal getting me -1. Then i subtracted off the 7 from both sides getting me -8. Finally, i divide both sides by 2 and get -4. E will equal -4.
Have an amazing day!!!
PLEASE RATE!!
What is the domain of 2x+4/x^2-4
Answer:
(2*(x^3-2x^2+2))/(x^2)
What is the perimeter?
Answer:
19.25 inches
Step-by-step explanation:
x^2 + 5^2 = 8^2= 64
25+ x^2 = 64
x^2 = 64-25= 39
x = 6.24
perimeter = 19.24
[tex] \\ [/tex]
BC = 5 inAC = 8inAB = x (in)[tex] \\ [/tex]
☆To find :[tex] \\ [/tex]
Perimeter of triangle[tex] \\ [/tex]
☆Solution:[tex] \\ [/tex]
So to find perimeter of triangle first we have to find value of x.
[tex] \\ [/tex]
As it's Given one angle is 90°
So we can find value of x by using this formula:-
[tex] \\ [/tex]
Hypotenuse ² = Base² + perpendicular ²
[tex] \\ [/tex]
Where :-
Hypotenuse is AC
Base is BC
Perpendicular is AB
[tex] \\ [/tex]
So:-
[tex] \\ [/tex]
⇢AC² = BC² + AB²
[tex] \\ [/tex]
⇢8² = 5² + x²
[tex] \\ [/tex]
⇢64 = 5² + x²
[tex] \\ [/tex]
⇢64 = 25 + x²
[tex] \\ [/tex]
⇢25 + x² = 64
[tex] \\ [/tex]
⇢x² = 64 - 25
[tex] \\ [/tex]
⇢x² = 39 in.
[tex] \\ [/tex]
⇢x = √(39)
[tex] \\ [/tex]
⇢x = 6.2
[tex] \\ [/tex]
Now Let's find perimeter of triangle.
We know :-
Perimeter of triangle = Side one + side two + side 3
[tex] \\ [/tex]
So:-
[tex] \\ [/tex]
⇢Perimeter of triangle = AB + BC + AC
[tex] \\ [/tex]
⇢Perimeter of triangle = 5 + 8 + 6.2
[tex] \\ [/tex]
⇢Perimeter of triangle = 13 + 6.2
[tex] \\ [/tex]
⇢Perimeter of triangle = 19.2 in.
*PLS HELP*
The Question Is In The Attachment
Answer:
Step-by-step explanation:
Rhombus:
Base = b = 14 in
altitude = h = 12 in
Area of rhombus = b*h = 14 * 12 = 168 in²
Triangle:
base = b = 12 in
Height = h = 14 in
[tex]Area \ of \ triangle = \dfrac{1}{2}bh=\dfrac{1}{2}*12*14=12*7=84 \ in^{2}[/tex]
Area of the figure = area of the rhombus + area of the triangle
= 168 + 84
= 252 in²
15. When x =9, which number is closest to the value of y on the line of best fit in the graph below?
12
1
9
17
James is seeking a loan with a simple interest rate of 3% per year. If he wants to borrow $8,000, then how much will he be charged in interest after 4 years?
Answer:
960
Step-by-step explanation:
I used a calculator but its 3% of $8,000 (which I'm pretty sure is 8,000 divided by 3) x 4 so in that's 240x4 which equals 960. Hope this helps have a good day!
Answer:
$960
Step-by-step explanation:
Simple interest is interest that goes up the same amount each period. The formula for simple is A=P(1+rt), where is A is the total amount, P is the principal (aka initial amount), r is the rate (in decimal form), and t is the time.
So, to solve we can use the equation, A=8000(1+0.03*4). In this equation A=8960, meaning that in 4 years the total amount owed, including the initial loan, will be $8960. Since the difference between the principal and the total amount is 960, $960 is the amount paid in interest.
CORRECT ANSWER GETS BRAINLIEST
Answer:
Plug in the 12 into the x's and find the ordered pair
Step-by-step explanation:
Avery bought 23 rainbow and balloon stickers for her little sister. The rainbow stickers cost 1 cent apiece and the balloon stickers cost 6 cents apiece. If Avery spent exactly 113 cents, how many of each type of sticker did she buy?
Answer:
5 rainbows and 18 ballons
Step-by-step explanation:
113 ÷ 6 = 18.83333
18 balloons
6×18 = 108 ( total amount of balloons)
113 - 108 = 5
What is an equation of the line that passes through the points (-5, -6) and (5, 6)?
Answer:
It would be -5 + -6 = 65
Step-by-step explanation:
Add it up to together by removing the -
Henry saved 25% of his paycheck last week. If his paycheck was $800, how much did he save?
this is almost due so i really need the help thank you
π = 3.142 and r = 3cm. find the volume of the sphere
Answer:
113.112 cm³
Step-by-step explanation:
Volume (sphere) = 4/3πr³
= 4/3 x 3.142 x 27
= 36 x 3.142
= 113.112 cm³
10(x-2)=-2(4/3+7x)
help please
Answer:
13/18 is the correct answer to 10(x-2)=-2(4/3+7x)
Step-by-step explanation:
Hope this helps!!!
What is the future value if $18733 is invested at 5.1% for 10 years, compounded quarterly
Answer:
Step-by-step explanation:
The compound interest formula is [tex]P(1+r/n)^{nt}[/tex]
P: the initial amount of cashr: interest raten: # of times that interest is compounded per time periodt: # of time periodsKnown information:
P: 18733r: 5.1% or 0.051n: quarterly or 4t: 10 yrsNow let's set up the equation:
Future amount: [tex]18733 (1+\frac{0.051}{4} )^{4*10}[/tex] [tex]=31,095.49[/tex]
Thus the future amount is $31.095.49.
Hope that helps!
please hurry! will give brainliest
Answer:
Step-by-step explanation:
If we think about a right triangle, we get that the hypotenuse is 24ft or the length of the ladder. The base of the ladder is 15ft away from the building which is the leg of the right triangle. The screenshot is the diagram (my drawing isn't that good lol:))
Thus we can use cosine function with the angle between the ladder and the ground since we need to find the angle and we get
[tex]cos\alpha = \frac{15}{24}[/tex]
and [tex]\alpha = 51.3 degrees[/tex]
The angle is 51.3 degrees hope that helps!
Simplify 7 + (−3). Please hurry
-10
-4
4
10
Answer: The answer is 4. 7+(-3) is like 7 minus 3.
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
since the 3 is negative, you need to take 3 away from 7 = 4
A crew of highway workers paved 2/15 mile in 20 min
If they work at the same rate what portion of a mile will the pave in one hour
(Please explain your answer)
Answer:
6/15 or simplified 2/5
Step-by-step explanation:
id.k if this is right :))
What are the dimensions of a rectangle with an area of 18 square inches and a perimeter of 18 inches? A) 9 in. x 2 in.B) 5 in. x 4 in.C) 6 in. x 3 in.D) 8 in. x 1 in.
Answer:
C
Step-by-step explanation:
Area: [tex]6 \times 3 = 18[/tex]
Perimeter: [tex]2 \times (6 + 3) = 18[/tex]
Answer:
C) 6 in. x 3
Step-by-step explanation:
area of rectangle: length * widthperimeter of rectangle: 2(length + width)using the formula:
area:
6 * 3
18 in²
perimeter:
2( 6 + 3)
2(9)
18 in
Hence proved that C is the right answer.
Solve each system by using substitution.
Answer:
1: I think 14
Step-by-step explanation:
Answer:
See below.
(-1,-3), (1,-4), (1,-2)
Step-by-step explanation:
See the attached image. One may also graph the equations and find the point they intersect (attached).
Identify two examples from different sources of how the ancient Inca benefited from their skills as stonemason and master builders. Explain each example benefited ancient Inca society. Cite the source for each example by title or number
The ways that the Inca benefitted from their skills as stonemasons and master builders were:
They built walls to defend them from enemies.They constructed buildings for shelter. What were the benefits of Ancient Inca stonemasonry?Thanks to their skills as master builders and stonemasons, the ancient Inca were able to construct large walls around their cities which protected them during times of conflict.
Their construction skills also allowed them to build great houses that gave them shelter from the weather elements thereby ensuring their survival and growth as a civilization.
Find out more on Inca buildings at https://brainly.com/question/1036358.
