The probability that both the balls are red = [tex]\bold{\frac{11}{20}}[/tex]
What is probability?"Probability is a branch of mathematics which deals with finding out the likelihood of the occurrence of an event."
Formula of the probability of an event A is:P(A) = n(A)/n(S)
where, n(A) is the number of favorable outcomes, n(S) is the total number of events in the sample space.
What is the formula of combination?"[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]"
For given question,
a bag contains 12 red, 3 white and 1 blue balls.
Total balls = 12 + 3 + 1
Total = 16
Two balls are drawn from a bag.
The number of possible ways of drawing 2 balls from the bag are:
Using combination formula,
[tex]^{16}C_2\\\\=\frac{16!}{2!(16-2)!}\\\\ =\frac{16!}{2!\times 12!}\\\\ =120[/tex]
So, n(S) = 120
Two balls are drawn with replacement from a bag.
We need to find the probability that both are red.
Let event A: both the balls are red
[tex]\Rightarrow n(A)=^{12}C_2[/tex]
Using combination formula,
[tex]^{12}C_2\\\\=\frac{12!}{2!\times (12-2)!}\\\\= \frac{12!}{2!\times 10!}\\\\ =66[/tex]
Using probability formula,
[tex]\Rightarrow P(A)=\frac{n(A)}{n(S)}\\\\\Rightarrow P(A)=\frac{66}{120}\\\\\Rightarrow P(A)=\frac{11}{20}[/tex]
Therefore, the probability that both the balls are red = [tex]\bold{\frac{11}{20}}[/tex]
Learn more about probability here:
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Find the imagine of (x-1 ,y -8 )
Answer:
triangle KLM
Step-by-step explanation:
x-1 meaning subtractikn so u subtract l from its original x cord making it move left 1
y-8 same thing but for the y making it move down 8 spaces
ayúdenme por favor, es de matemática.
Answer:welcome to brainly
Step-by-step explanation:
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The top and bottom ends of a windshield wiper blade are R = 24 in. and r = 14 in., respectively, from the pivot point. While in operation, the wiper sweeps through 135°. Find the area swept by the blade. (Round your answer to the nearest whole number.)
Answer:
Area swept by the blade = 448[tex]in^{2}[/tex]
Step-by-step explanation:
The arc the wiper wipes is for 135 degrees angle.
So, find area of sector with radius 24 inches. And the find area of arc with r=14 inches.
Then subtract the area of sector with 14 inches from area of sector with radius as 24 inches.
So, area of sector with r=24 in =[tex]\frac{135}{360} *\pi *24^{2}[/tex]
Simplify it,
=216[tex]\pi[/tex]
Now, let's find area of sector with radius 14 inches
Area of sector with r=14 in = [tex]\frac{135}{360} *\pi *14^{2}[/tex]
Simplify it
=73.5[tex]\pi[/tex]
So, area swept by the blade = 216[tex]\pi[/tex] -73.5[tex]\pi[/tex]
Simplify it and use pi as 3.14.....
Area of swept =678.584 - 230.907
=447.6769
Round to nearest whole number
So, area swept by the blade = 448[tex]in^{2}[/tex]
A philosophy professor assigns letter grades on a test according to the following scheme. A: Top 12% of scores B: Scores below the top 12% and above the bottom 57% C: Scores below the top 43% and above the bottom 19% D: Scores below the top 81% and above the bottom 5% F: Bottom 5% of scores Scores on the test are normally distributed with a mean of 66.5 and a standard deviation of 9.9. Find the minimum score required for an A grade. Round your answer to the nearest whole number, if necessary.
Answer:
The minimum score required for an A grade is 80.
Step-by-step explanation:
According to the Question,
Given That, A philosophy professor assigns letter grades on a test according to the following scheme.A: Top 12% of scores
B: Scores below the top 12% and above the bottom 57%
C: Scores below the top 43% and above the bottom 19%
D: Scores below the top 81% and above the bottom 5%
F: Bottom 5% of scores Scores on the test
And The normally distributed with a mean of 66.5 and a standard deviation of 9.9.
Now,
In a set with mean and standard deviation, the Z score of a measure X is given by Z = (X-μ)/σwe have μ=66.5 , σ=9.9
Find the minimum score required for an A grade.Top 12%, so at least the 100-12 = 88th percentile, which is the value of X when Z has a p-value of 0.88. So it is X when Z = 1.175.
⇒ Z = (X-μ)/σ
⇒ 1.175×9.9 = X-66.5
⇒ X=78.132
Rounding to the nearest whole number, the answer is 80.
The minimum score required for an A grade is 80.
There are 16 tablespoons in one cup. Which table correctly relates the number of cups to the number of tablespoons?
Answer:
The first table.
Step-by-step explanation:
1 cup = 1 * 16 = 16 tablespoons
2 = 2 * 16 = 32
3 = 3*16 = 48
4 = 4*16 = 64 and so on....
Finding probabilities associated with distributions that are standard normal distributions is equivalent to _______.
Answer:
finding the area of the shaded region representing that probability.
Step-by-step explanation:
In a normal distribution, standardardized probability is usually represented digramatically by a sketch which covers the area which always has a mean of 0 and a standard deviation of 1. The mean value is the midpoint of the area under the curve and has an equal difference of 1 to either side of graph which represents the standard deviation. The area of the shaded region under a normal probability curve represents the probability of associated with that particular standardized value.
Find the distance between the two points.
(3,-9) and (-93,-37)
Answer:
d(A,B)=100
Step-by-step explanation:
The distance between two points A([tex]x_A,y_A[/tex]) and B=([tex]x_B,y_B[/tex]) is:
d(A,B)=[tex]\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}[/tex]
In this case:
[tex]x_B = - 93\\x_A = 3\\y_B = -37\\y_A = -9[/tex]
In this case:
[tex]d(A,B)=\sqrt{( - 93 -3)^2+( - 37 - (-9))^2} =\\=\sqrt{( - 96)^2+(-28)^2} =\\=\sqrt{9.216+784} \\=\sqrt{10000}=\\=\sqrt{10^4} =\\=100[/tex]
work out the area of this shape
Answer:
75.5
Step-by-step explanation:
First, the picture is not to scale.
The Area of the bottom (2) rectangle is 33
base x height = A
11 x 3 = 33 (where did I get 3? Total height of shape is 8. Trapezoid is 5)
(8-5 = 3)
Area of the trapezoid:
A = [tex]\frac{h (B_{1} + B_{2}) }{2}[/tex]
= [tex]\frac{(5)(6 + 11)}{2}[/tex]
= [tex]\frac{5(17)}{2}[/tex]
= [tex]\frac{85}{2}[/tex]
= 42.5
42.5 + 33 = 75.5
Which statement about y=x^2-14x+45 is true
Instructions: Drag and drop the correct name for each angle. Each angle has more than one name so be sure to identity all the correct names
Answer/Step-by-step explanation:
Recall: an angle can be named in three different ways:
i. Using one letter which is the vertex of the angle. i.e. if the vertex of the angle is A we can name the angle as <A.
ii. Using the number of the labelled angle. i.e. is the angle is labelled 2, we can name it <2
iii. Using the three letters of the angles with the vertex angle in the middle. i.e. if the three points that form an angle are A, B, C and the vertex is B, we can name the angle as <ABC.
✔️Let's name the each angle given according:
1. <G, <3, and <FGH
2. <D, <4, and <CDE
3. <S and <TSR (the number seems blur and difficult to read. Whatever number is used to label the angle is what you'd use in naming the angle)
If anyone could help me figure out this problem I’d really appreciate it and I’ll give you brainliest
Answer:
A={Delaware, Pennsylvania, New Jersey}
|B|=3
Step-by-step explanation:
B={New Hampshire, Virginia, New York}
p{x:x is a natural number x (9
Answer:
you need a photo my dude
Step-by-step explanation:
Select the two values of x that are roots of this equation 2x^2+5x-3=0
Answer:
A and D are the answer.
Step-by-step explanation:
We can factor this by grouping
[tex]2 {x}^{2} + 5x - 3[/tex]
[tex]2 {x}^{2} + 6x - x - 3[/tex]
[tex]2x(x + 3) -1 (x + 3)[/tex]
The roots are
[tex](x + 3) = 0[/tex]
and
[tex]2x - 1 = 0[/tex]
Let solve for zero in each roots.
[tex]x = - 3[/tex]
[tex]2x = 1[/tex]
[tex]x = \frac{1}{2} [/tex]
7r - 3s =26
2r - 6s =8
Answer:
r = 3 2/3
s = -0.444333
Step-by-step explanation:
Multiply the top equation by 2
14r - 6s = 52
2r - 6s = 8 Subtract the two equations
12r = 44 Divide by 12
r = 44/12
r = 3 8/12
r = 3 2/3
2r - 6s = 8
2*(2 2/3) - 6s = 8
2*2.6667 - 6s = 8
5.3334 - 6s = 8 Subtract 5.3334 from both sides.
- 6s = 2 2/3 Divide by - 6
s = - 0.4443333
Speedy Oil provides a single-server automobile oil change and lubrication service. Customers provide an arrival rate of 2.5 cars per hour. The service rate is 5 cars per hour. Assume that arrivals follow a Poisson probability distribution and that service times follow an exponential probability distribution. What is the average number of cars in the system
Answer:
the average number of car(s) in the system is 1
Step-by-step explanation:
Given the data in the question;
Arrival rate; λ = 2.5 cars per hour
Service time; μ = 5 cars per hour
Since Arrivals follows Poisson probability distribution and service times follows exponential probability distribution.
Lq = λ² / [ μ( μ - λ ) ]
we substitute
Lq = (2.5)² / [ 5( 5 - 2.5 ) ]
Lq = 6.25 / [ 5 × 2.5 ]
Lq = 6.25 / 12.5
Lq = 0.5
Now, to get the average number of cars in the system, we say;
L = Lq + ( λ / μ )
we substitute
L = 0.5 + ( 2.5 / 5 )
L = 0.5 + 0.5
L = 1
Therefore, the average number of car(s) in the system is 1
8th Grade Which expression is equivalent to 1/27
Answer:
[tex]( \frac{1}{3})^{3} [/tex]
Step-by-step explanation:
There are many expressions that can be equivalent to 1/27.
For example, 2/54, 3/81 etc
But I think the expression you are looking for is
[tex] \frac{1}{27} = \frac{1 \times 1 \times 1}{3 \times 3 \times 3} = \frac{ {1}^{3} }{ {3}^{3} } = ( \frac{1}{3} )^{3} [/tex]
Hope this is helpful
Given that Q(x)=2x^2 +5x-3 find and simplify Q(a+h)-Q(a-h)
Step-by-step explanation:
here is the answer. Feel free to ask for more.
Use the quadratic formula to find the solutions to the equation.
3x^2-10x+5=0
Answer:
option a is correct by using quadratic formula
Peter organizes morning hikes for his friends every Saturday. When the hiking trail is 3 km long, 19 friends join him and when the trail is 5 km long, only 7 friends tag along. There exists a linear relationship between the distance of the hiking trail (in km) and the number of friends who tag along. The number of friends depend on the distance of the trail. Determine how many friends will tag along to a hiking trail of 2 km.
Answer:
25
Step-by-step explanation:
x = distance of the hike
y = number of friends coming along
so, we are looking for a linear relationship between these two.
y = ax + b
we need to find the factor a and the constant offset b.
19 = a×3 + b
7 = a×5 + b
7 - b = a×5
a = (7-b)/5
19 = (7-b)×3/5 + b
19 = (21 - 3b)/5 + b
95 = 21 - 3b + 5b
74 = 2b
b = 37
a= (7-37)/5 = -30/5 = -6
so, the relationship is
y = -6x + 37
for 2km hiking
y = -6×2 + 37 = -12 + 37 = 25 friends
If the domain of a function that is rotated 90 degrees counter-clockwise is (0, 0), (3, 5), (-1, 4), what is the range?
A. (0, 0), (5, 3), (4, -1)
B. (0, 0), (5, -3), (4, 1)
C. (0, 0), (-3, -5), (1, -4)
D. (0, 0), (-5, 3), (-4, -1)
Answer:
the answer is B. (0,0) (5,-3) (4,1)
please mark me brainlist
Step-by-step explanation:
Answer:
Your answer is
Step-by-step explanation:
Your answer is B.(0, 0), (5, -3), (4, 1)
the angle of elevation of the top of the mast from a point 53m to its base on level ground is 61°. find the height of the mast to the nearest meter
the answer Is 95.61465. If you approximate you get 10.
A woman had 88 goats.20 of them died.how many did he remains with.
Answer:
68 i think..........
Step-by-step explanation:
(⌒_⌒;)
a. 23 = -11 - 4x
b. 23 = -11 + (-4x)
C. 23 + 11 = -11 + (-4x) + 11
d. 23 + 11 = -11 + 11 +(-4x)
e. 34 = - 4x
f. 34/-4 = -4x/ -4
g. -8.5 = x
Which properties of equality justify steps c and f?
A.) addition property of equality; subtraction property of equality B.) addition property of equality; division property of equality C.) subtraction property of equality; multiplication property of equality D.) multiplication property of equality; division property of equality
Answer:
B.) addition property of equality; division property of equality
What is the factored form of 125a^6-64?
Answer:
(5 a^2 - 4) (25 a^4 + 20 a^2 + 16)
Step-by-step explanation:
Since both terms are perfect cubes, factor using the difference of cubes formula,
a^3 − b^ 3 = (a − b) (a^2 + a b + b^2) where a = 5a^2 and b = 4 .
8 9 13. Jenny bought kg of berries from the market and another 3 kg of berries from a fruit stall. How much berries did she buy altogether? 3 3
Answer:
she bought 5 berries in total
Step-by-step explanation:
3+2=5
Find the value of x in each case
The answer is 36 degrees
Step 1
Angle GEH=180-2x (angles on a a straight line are supplementary)
Step 2
4x= G^+GE^H(sum of exterior angle)
4x=x+(180-2x)
4x=180-x
4x+x=180
5x=180
x=36 degrees
help pls, i need help pls
9514 1404 393
Answer:
no
Step-by-step explanation:
For lines to be parallel, any obtuse angle where a transversal crosses must be supplementary to any acute angle at that transversal. Here the sum of the obtuse and acute angles is 105° +65° = 170°, so it is not possible for this geometry to include parallel lines.
(c) Construct a 99% confidence interval for u if the sample
size, n, is 35.
Answer:
The confidence interval is [tex](\overline{x} - 1.99\frac{\sigma}{\sqrt{35}}, \overline{x} + 1.99\frac{\sigma}{\sqrt{35}})[/tex], in which [tex]\overline{x}[/tex] is the sample mean and [tex]\sigma[/tex] is the standard deviation for the population.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.99}{2} = 0.005[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.005 = 0.995[/tex], so Z = 2.575.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
In this question:
[tex]M = 1.99\frac{\sigma}{\sqrt{35}}[/tex]
The lower end of the interval is the sample mean subtracted by M, while upper end of the interval is the sample mean added to M. Thus, the confidence interval is [tex](\overline{x} - 1.99\frac{\sigma}{\sqrt{35}}, \overline{x} + 1.99\frac{\sigma}{\sqrt{35}})[/tex], in which [tex]\overline{x}[/tex] is the sample mean and [tex]\sigma[/tex] is the standard deviation for the population.
PLEASE HELP ASAP !! WILL MARK BRAINLIEST
I think it might be the 3rd option
Step-by-step explanation:
2 The product of two numbers is 5425. If one of them is 25. What is the other 2 number
Answer:
217
Step-by-step explanation:
5425/25 = 217