Answer:
The answer is below
Step-by-step explanation:
Let B₁ represent box 1, B₂ represent box 2, E₁ represent the event of selecting box 1, E₂ represent the event of selecting box 2 and R represent the event of selecting a red ball.
Given that:
Probability of selecting box 2 P(E₂) = 2/3, Probability of selecting box 1 = P(E₁) = 1/3
Probability of selecting red ball from box 1 = P(R | E₁) = 4/6 [4 red balls out of 4 red, 2 green]
Probability of selecting red ball from box 2 = P(R | E₂) = 2/6 [2 red balls out of 2 red, 4 green]
a)
Given the ball is red, the probability it was selected from the first box is:
[tex]P(E_1|R)=\frac{P(R|E_1)P(E_1)}{P(R|E_1)P(E_1)+P(R|E_2)P(E_2)} =\frac{2/3*1/3}{(2/3*1/3)+(1/3*2/3))} =\frac{1}{2}[/tex]
b)
Given the ball is red, the probability it was selected from the second box is:
[tex]P(E_2|R)=\frac{P(R|E_2)P(E_1)}{P(R|E_2)P(E_2)+P(R|E_1)P(E_1)} =\frac{1/3*2/3}{(1/3*2/3)+(2/3*1/3))} =\frac{1}{2}[/tex]
c)
We can see that both probabilities are equal. Although we have more red balls in box 1 (twice as much) than in box 2 but the probability of selecting from box 2 (is twice as much) than from selecting from box 1.
The probability that the ball selected is red and it is selected from the first box is 1/2 and the probability that the ball selected is red and it is selected from the second box is 1/2.
Given :
One of the two boxes contains 4 red balls and 2 green balls and the second box contains 4 green and two red balls. By design, the probabilities of selecting box 1 or box 2 at random are 1/3 for box 1 and 2/3 for box 2.a) The probability that the ball selected is red and it is selected from the first box is:
[tex]P(E_1|R)=\dfrac{P(R|E_1)P(E_1)}{P(R|E_1)P(E_1)+P(R|E_2)P(E_2)}[/tex]
[tex]P(E_1|R)=\dfrac{\dfrac{2}{3}\times \dfrac{1}{3}}{\dfrac{2}{3}\times \dfrac{1}{3}+\dfrac{1}{3}\times \dfrac{2}{3}}[/tex]
[tex]P(E_1|R)=\dfrac{1}{2}[/tex]
b) The probability that the ball selected is red and it is selected from the second box is:
[tex]P(E_2|R)=\dfrac{P(R|E_2)P(E_2)}{P(R|E_1)P(E_1)+P(R|E_2)P(E_2)}[/tex]
[tex]P(E_2|R)=\dfrac{\dfrac{2}{3}\times \dfrac{1}{3}}{\dfrac{2}{3}\times \dfrac{1}{3}+\dfrac{1}{3}\times \dfrac{2}{3}}[/tex]
[tex]P(E_2|R)=\dfrac{1}{2}[/tex]
c) The probability that the ball selected is red and it is selected from the first box and the probability that the ball selected is red and it is selected from the second box is the same.
For more information, refer to the link given below:
https://brainly.com/question/795909
What is equivalent to the equation y=3x+z/4?
For each ordered pair, determine whether it is a solution to 7x - 4y= -5.
A ladder is standing on horizontal ground and rests against a vertical
wall. The ladder is 4.5 m long and its foot is 1.6 m from the wall.
Calculate how far up the wall the ladder will reach. Round your
answer to three decimal places. (Show your working)
Answer:
I don't know how to tell you the answer on this one because you need to know how tall the wall is for this one
Step-by-step explanation:
What is the end behavior for the graph of the function
f(x)=9/10 log [-(x + 9)] + 10?
Answer:If you draw a graph or look it up on Desmos, it curves down around y = 10. It only hits the second and third quadrant. B is the only situation that describes this.
Step-by-step explanation:g
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OMG PLEASE HELP MEEEEEEE
Which expression could represent the additive inverse property?
A) −9 + 0
B) −9 −9
C) −9 + 1
D) −9 + 9
19.8.EE.6 Find the missing RISE given the similar triangles below:*
8.
14
4
Answer:
7
Step-by-step explanation:
Given that these triangles are similar, their sides are in ratio. Let x denote the missing RISE.
Top triangle : bottom triangle
14/8 = x/4
1.75 = x/4
x=7
(c+4)^2(4-c)^2 i need help
Answer
c^4-32c^2+256 (Simplified)
Y’all help meeeee :(
A bread recipe calls for 1/3 cup of white flour and 5 1/3 cups of whole wheat flour. How much flour do I need in total of my recipe?
Answer:
5 2/3
Step-by-step explanation:
A person's systolic blood pressure, which is measured in millimeters of mercury (mm Hg), depends on a person's age, in years. The equation: P = 0.006 y 2 − 0.02 y + 121 gives a person's blood pressure, P , at age y years. A.) Find the systolic pressure, to the nearest tenth of a millimeter, for a person of age 40 years. B.) If a person's systolic pressure is 130.74 mm Hg, what is their age (rounded to the nearest whole year)?
Answer:
129.8 mmHg
42 years
Step-by-step explanation:
Given the relation :
P = 0.006 y² − 0.02 y + 121
Systolic blood pressure, P
Age, y
A.)
Find P when age y = 40
P = 0.006(40)² − 0.02(40) + 121
P = 9.6 - 0.8 + 121
P = 129.8 mmHg
B)
P = 130.74 mmHg
y =?
130.74 = 0.006y² − 0.02y + 121
130.74 - 121 = 0.006y² − 0.02y
9.74 = 0.006y² − 0.02y
0.006y² − 0.02y - 9.74 = 0
Using a quadratic equation solver :
The roots are 41.99 and - 38.66
Age cannot be negative ;
Hence age = 41.99 = 42 years
A student received a coupon for 12% off the total purchase price at a clothing store. Let b be the
original price of the purchase. Use the expression below for the new price of the purchase. Write an
1. equivalent expression by combining like terms.
b-0.12b
Answer:
the equivalent expression is 0.88(x)
Step-by-step explanation:
Given that
There is 12% off on the total purchase price
Based on the above information
The expression that used the given terms i.e.
b - 0.12b
i.e.
1 - 0.12
= 0.88(x)
Hence, the equivalent expression is 0.88(x)
Which is the graph of f(x)= 1 4 (4)^ x ?
Answer:
it is the last graph/D
Step-by-step explanation:
Suzanna uses a 1/4 cup measuring scoop to make her coffee. If she needs to fill her coffee filter with 2 cuos of coffe grounds,how many 1/4 cups scoops will she need to use
Answer:
8
Step-by-step explanation:
1/4 times 8 is 2
If Siny = x Sin (a+y). Prove that
dy/dx=[Sin²(a+y)]/Sina
Answer:
Use Trigonometric formulae to simplify expressions
Step-by-step explanation:
Re-order to group the x and y,
Sin(y) / Sin(a+y) = x
to differentiate apply d/dx to both sides
[tex]\frac{d}{dx}[/tex]Sin(y) / Sin(a+y) = [tex]\frac{d}{dx}[/tex]x
use division rule on left side which will give
[tex]\frac{dy}{dx}[/tex]Cos(y)Sin(a+y) - [tex]\frac{dy}{dx}[/tex]Cos(a+y)Sin(y) / Sin²(a+y) = 1
Group them so dy/dx is on the left hand side:
[tex]\frac{dy}{dx}[/tex] = Sin²(a+y) / Cos(y)Sin(a+y) - Cos(a+y)Sin(y)
Apply trigonometric sum formula to expand Sin(a+y) and Cos(a+y),
[tex]\frac{dy}{dx}[/tex] = Sin²(a+y) / Cos(y)[Sin(a)Cos(y) + Cos(a)Sin(y)] - Sin(y)[Cos(a)Cos(y) - Sin(a)Sin(y)]
Simplify it
[tex]\frac{dy}{dx}[/tex] = Sin²(a+y) / (Cos²(y) + Sin²(y))(Sin(a))
[tex]\frac{dy}{dx}[/tex] = Sin²(a+y) / (1)(Sin(a))
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Answer:
B. 128
Step-by-step explanation:
Answer:
by using Pythagoras law
hypotenuse ²=perpendicular ²+base²
h²=100²+80²
h²=10000+6400
h=√16400=128.06m
128m is the required answer.
PLEASE SOMEONE ANSWER A REAL ANSWER WILL GIVE BRAINLIST
Answer:
a I think please be right
NEED HELP MY GRADE DEPENDS ON THIS QUESTION!!!
Write a congruence statement that describes the figures below.
Answer:
✓ triangle GSP = triangle RKF
Step-by-step explanation:
have a great day!
WILL GIVE BRAINLIEST
Find the area of the shaded region. Round to the tenths place. SHOW YOUR WORK
https://d3rqz33hmpm7kb.cloudfront.net/2021-01-15/5f6e19a9f9b9f1c16c230aae/6001f53de589b94a3a0f092f_rich-text-file-2021-01-15T20-04-46-084Z.imagepng
Find the inverse of the function, f(x)=5(x-4)^3 +6
trade x and y
Answer:
y=[(x-6)/5]^(1/3)+4
Step-by-step explanation:
f(x)=5(x-4)^3 +6
trade x and y
x=5(y-4)^3 +6
x-6=5(y-4)^3
(x-6)/5=(y-4)^3
[(x-6)/5]^(1/3)=y-4
y=[(x-6)/5]^(1/3)+4
4. Mrs. Hodges made 144 muffins for a bake sale. She puts them into tins of 5 muffins each. How many tins of muffins can she make?
how many solutions does this problem have 2x – 4 = 2(x – 2)
Answer:
= 0
Step-by-step explanation:
Let's solve your equation step-by-step.
2x−4=2(x−2)
Step 1: Simplify both sides of the equation.
2x−4=2(x−2)
2x+−4=(2)(x)+(2)(−2)(Distribute)
2x+−4=2x+−4
2x−4=2x−4
Step 2: Subtract 2x from both sides.
2x−4−2x=2x−4−2x
−4=−4
Step 3: Add 4 to both sides.
−4+4=−4+4
0=0
Find the circumference and area of the circle. Use 3.14 for π. Round to the nearest hundredth if necessary. r = 2m
The answer is 12.57
But rounded to the nearest tenth is 12.6
6. (09.04 LC)
For the equation y = 6x2 – 9x + 22, choose the correct application of the quadratic formula. (5 points)
X
-6+1(6)- 4(-9)(22)
2(-9)
X
6 + (6)- 4-9)(22)
21-9)
--9 +1(-99) - 4(6)(22)
X
2(6)
X
9+(-9) - 4(6)(22)
2(6)
Given:
The quadratic equation is
[tex]y=6x^2-9x+22[/tex]
To find:
The correct application of the quadratic formula.
Solution:
If a quadratic equation is [tex]ax^2+bx+c=0[/tex], then the quadratic formula is
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
We have,
[tex]y=6x^2-9x+22[/tex]
Putting [tex]y=0[/tex], we get
[tex]6x^2-9x+22=0[/tex]
Here, [tex]a=6,b=-9,c=22[/tex]. Using the quadratic formula, we get
[tex]x=\dfrac{-(-9)\pm \sqrt{(-9)^2-4(6)(22)}}{2(6)}[/tex]
The correct application of the quadratic formula is [tex]x=\dfrac{-(-9)\pm \sqrt{(-9)^2-4(6)(22)}}{2(6)}[/tex].
Note: The options are not in proper format.
Prove that the figure is a parallelogram. If so, classify the parallelogram. Be specific and justify your answer.
What is the perimeter and area?
Answer:
Step-by-step explanation:
If it is a parallelogram the opposite sides will a have the same slope.
Using the diagram we see from the coordinates of A and B:
Slope of AB = (5 - -1)/(-1 - -5)
= 6/4
= 3/2.
In the same way
slope of CD = (2 - -4) / (1 - -3)
= 3/2.
So AB and CD can be shown to be parallel.
Similarly the lines BC and AD are parallel.
So the figure is a parallelogram
Finding the perimeter (counting the units between the points):
Perimeter = 2AB + 2BC
By Pythagoras:
AB = sqrt (6^2 + 4^2) = sqrt 52
BC = sqrt (3^2 + 2^2) = sqrt 13
So Perimeter = 2sqrt52 + 2sqrt13
= 4sqrt13 + 2 sqrt13
= 6sqrt13
or 21.63 unit^2 to 2 decimal places.
Area = sqrt52 * perpendicular distance between the lines AB and CD.
Researchers published a study in which they considered the incidence among the elderly of various mental health conditions such as dementia, bi-polar disorder, obsessive compulsive disorder, delirium, and Alzheimer's disease. In the U.S., 45% of adults over 65 suffer from one or more of the conditions considered in the study. Calculate the probability that fewer than 320 out of the n
Answer:
The step-by-step procedure to solve this question is given, using the normal approximation to the binomial distribution.
Step-by-step explanation:
We use the normal approximation to the binomial distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In the U.S., 45% of adults over 65 suffer from one or more of the conditions considered in the study.
This means that [tex]p = 0.45[/tex]
Mean and standard deviation for the approximation, for a sample of n:
[tex]\mu = E(X) = np = 0.45n[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{0.45*0.55n}[/tex]
Calculate the probability that fewer than 320 out of the n
Using continuity correction, this is [tex]P(X < 320 - 0.5) = P(X < 319.5)[/tex], which is the pvalue of Z when X = 319.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{319.5 - 0.45n}{\sqrt{0.45*0.55n}}[/tex]
Just have to replace the value of n, find Z, and then find its pvalue.
what is the answer of 17x12
Answer:
204
Step-by-step explanation:
17x12=204
A circular park has a circumference of 94 ft. find d, the diameter of the garden in feet
Answer:
94 / π = 29.9211293...
Step-by-step explanation:
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Determine the equation of circle A.
(x - 1)2 + (y + 2)2 = 9
(x + 1)2 + (y-2)2 = 9
(x-1)2 + (y + 2)2 = 3
(x + 1)2 + (y-2) = 3
I'm not sure but if you have photomath or Microsoft mathematics use it to solve your problem
-3(p-7) ≥ 21 sovleplzzz
Answer:
-3p+21≥21
Step-by-step explanation: