Answer:
a) 0.3 = 30% probability of drawing a white chip.
b) 0.3333 = 33.33% probability that bowl B1 had been selected, given that a white chip was drawn.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
a. P(W), the probability of drawing a white chip.
1/3(one white out of 3) of 0.3(from B1).
1/2(two white out of 4) of 0.2(from B2).
1/5(one white out of 5) of 0.5(from B3). So
[tex]P(W) = 0.3333*0.3 + 0.5*0.2 + 0.2*0.5 = 0.3[/tex]
0.3 = 30% probability of drawing a white chip.
b. P(B1 Given W), the conditional probability that bowl B1 had been selected, given that a white chip was drawn.
The probability of drawing a white chip from B1 is 1/3 out of 0.3, so:
[tex]P(B1 \cap W) = 0.3\frac{1}{3} = 0.1[/tex]
Then the conditional probability is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.1}{0.3} = 0.3333[/tex]
0.3333 = 33.33% probability that bowl B1 had been selected, given that a white chip was drawn.
In the expression below, the
3 is the
of x.
3x + 2
A. Coefficient
B. Constant
C. Operator
D. Variable
A) Coefficient is the correct answer.
Step-by-step explanation:
The 3 is a coefficient. The x is the variable.
You will purchase some cds and dvds. If you purchase 13 cds and 5 dvds, it will cost you $96.70; if you purchase 5 cds and 12 dvds, it will cost you $134.50. Write and solve a system of equations to solve.
You will purchase some cds and dvds. If you purchase 13 cds and 5 dvds, it will cost you $96.70; if you purchase 5 cds and 12 dvds, it will cost you $134.50. Write and solve a system of equations to solve for the cost of each cd and the cost of each dvd.
Answer:Cost of cd = $3.72
Cost of dvd = $9.66
Step-by-step explanation:Let the cost of a cd be c
Let the cost of a dvd be d
From the second statement:
If you purchase 13 cds and 5 dvds, it will cost you $96.70
This means that
13c + 5d = 96.70 ----------------(i)
Also, from the third statement:
if you purchase 5 cds and 12 dvds, it will cost you $134.50
This means that;
5c + 12d = 134.50 ---------------------(ii)
The equations to solve are equations (i) and (ii)
13c + 5d = 96.70
5c + 12d = 134.50
Multiply the first equation by 5 and the second equation by 13. i.e
5 x (13c + 5d = 96.70)
13 x (5c + 12d = 134.50)
This will give
65c + 25d = 483.5
65c + 156d = 1748.5
Find the difference of the two equations
65c + 25d = 483.5
-
65c + 156d = 1748.5
0 - 131d = - 1265
This gives;
-131d = -1265
Divide both sides by -131
[tex]\frac{-131d}{-131} = \frac{-1265}{-131}[/tex]
d = 9.66
This means that the cost of a dvd which is d = $9.66
Now substitute the value of d = 9.66 into equation (i) as follows;
13c + 5(9.66) = 96.70
Expand the above and solve for c
13c + 48.3 = 96.70
13c = 48.4
c = [tex]\frac{48.4}{13}[/tex]
c = 3.72
This means that the cost of a cd which is c = $3.72
please answer both questions thanks
Answer:
8. cos(58) = 20/x
x · cos(58) = 20
x = 20/cos(58)
= 37.742
≈ 37.7
9. tan(69) = 324/x
x · tan(69) = 324
x = 324/tan(69)
= 124.372
≈ 124.4
There are two machines available for cutting corks intended for use in wine bottles. The first produces corks with diameters that are normally distributed with mean 3 cm and standard deviation 0.08 cm. The second machine produces corks with diameters that have a normal distribution with mean 3.04 cm and standard deviation 0.03 cm. Acceptable corks have diameters between 2.9 cm and 3.1 cm.
What is the probability that the first machine produces an acceptable cork? (Round your answer to four decimal places.)
What is the probability that the second machine produces an acceptable cork? (Round your answer to four decimal places.)
Please explain the math behind your answer so I am able to understand!(:
Answer:
0.7888 = 78.88% probability that the first machine produces an acceptable cork.
0.9772 = 97.72% probability that the second machine produces an acceptable cork.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
First machine:
Mean 3 cm and standard deviation 0.08 cm, which means that [tex]\mu = 3, \sigma = 0.08[/tex]
What is the probability that the first machine produces an acceptable cork?
This is the p-value of Z when X = 3.1 subtracted by the p-value of Z when X = 2.9. So
X = 3.1
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{3.1 - 3}{0.08}[/tex]
[tex]Z = 1.25[/tex]
[tex]Z = 1.25[/tex] has a p-value of 0.8944
X = 2.9
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2.9 - 3}{0.08}[/tex]
[tex]Z = -1.25[/tex]
[tex]Z = -1.25[/tex] has a p-value of 0.1056
0.8944 - 0.1056 = 0.7888
0.7888 = 78.88% probability that the first machine produces an acceptable cork.
What is the probability that the second machine produces an acceptable cork?
For the second machine, [tex]\mu = 3.04, \sigma = 0.03[/tex]. Now to find the probability, same procedure.
X = 3.1
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{3.1 - 3.04}{0.03}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a p-value of 0.9772
X = 2.9
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2.9 - 3.04}{0.03}[/tex]
[tex]Z = -4.67[/tex]
[tex]Z = -4.67[/tex] has a p-value of 0
0.9772 - 0 = 0.9772
0.9772 = 97.72% probability that the second machine produces an acceptable cork.
Helppppppp pleaseeeeeeeee
Answer:
x = 8
Step-by-step explanation:
m<PQR = (2x + 6)°
m<RPQ = (x - 7)°
m<QRS = (5x - 17)°
<PQR and <RPQ are interior angles opposite to the exterior angle <RPQ.
Therefore,
m<PQR + m<RPQ = m<QRS (Exterior Angle Theorem of a Triangle)
Substitute in the values
2x + 6 + x - 7 = 5x - 17
Add like terms
3x - 1 = 5x - 17
Collect like terms
3x - 5x = 1 - 17
-2x = -16
-2x/-2 = -16/-2
x = 8
Geometry, circles please help that'd be great.
Answer:
maybe the answer is 63cm...
Anquan's account balance is $29.96, and Will's account balance is -$29.96. Which of the following is true
Answer:
is there anymore to the question because this doesn't make sense
Step-by-step explanation:
15 POINTS! PLEASE HELP! BRAINLIEST!
What is the probability of flipping a coin 15 times and getting heads 6 times? Round your answer to the nearest tenth of a percent. O A. 19.6% O B. 9.2% O C. 4.2% O D. 15.3% SUBMIT
Answer:
D. 15.3%Step-by-step explanation:
Total number of outcomes:
2¹⁵ = 32768Number of combinations of getting 6 heads:
15C6 = 15!/6!(15-6)! = 5005Required probability is:
P(6 heads out of 15 flips) = 5005/32768 = 0.1527... ≈ 15.3%Correct choice is D
Answer:
option D
Step-by-step explanation:
Total sample space
= [tex]2^{15}[/tex]
Number of ways 6 heads can emerge in 15 flips
= [tex]15C_6[/tex]
Probability:
[tex]=\frac{15C_6}{2^{15}}[/tex] [tex]= 0.1527[/tex]
Probability to the nearest percent : 15.3%
What is the solution to the following system of equations?
[3x-2y = 12
16x-4y = 24
O It has infinitely many solutions.
It has no solution.
It has one solution (2, -3).
It has one solution (4,0).
Answer:
(0, -6)
Step-by-step explanation:
Given the following systems of linear equations;
3x - 2y = 12 ...... equation 1
16x - 4y = 24 ........ equation 2
We would solve for the solution using the elimination method;
Multiplying eqn 1 by 2, we have;
2 * (3x - 2y = 12)
6x - 4y = 24
16x - 4y = 24
Subtracting the two equations, we have;
(6x - 16x) + (-4y -[-4y]) = (24 - 24)
-10x - 0 = 0
-10x = 0
x = -0/10 = 0
Next, we would find the value of y;
3x - 2y = 12
3(0) - 2y = 12
0 - 2y = 12
-2y = 12
y = -12/2
y = -6
Check:
3x - 2y = 12
3(0) - 2(-6) = 12
0 - (-12) = 12
12 = 12
Note: the options provided for this questions are incorrect or inappropriate.
The London Eye Ferris wheel has a diameter of 120 meters. It completes one revolution in 30 minutes. About how far will a person travel along the arc of the Ferris wheel in 10 minutes while riding the London Eye?
Answer:
Step-by-step explanation:
the multiplicative inverse of 5 2/3
Answer:
Step-by-step explanation:
5[tex]\frac{2}{3}[/tex]
first chnge to improper or proper fraction
5*2/3
10/3
multiplicative inverse of 10/3 = 3/10
Michael and Sondra are mixing lemonade. In Michael’s lemonade, the ratio of lemons to water is 1:4. In Sondra’s lemonade, the ratio of lemons to water is 2:6. Several equivalent ratios for each mixture are shown in the ratio tables.
Michael
Lemons
Cups of Water
1 4
3 12
4 16
Sondra
Lemons
Cups of Water
2 6
4 12
6 18
Imagine that you want to compare Michael’s ratio to Sondra’s ratio. Which two ratios in the tables shown have a common denominator you could use to compare?
Answer:
1/4= 3/12 & 2/6 = 4/12
Step-by-step explanation:
Answer:
Its simply B
Step-by-step explanation:
If we are to express both ratios in their simplest form, we will have the ratio of Michael’s lemonade is 1:4 and that of Sondra is 1:3. The denominator that can be used in order to compare the ratios is that which can be divided by both ratios. For example, we have 12 as a denominator. The ratios can be expressed as 3/12 and 4/12. Also, the denominator can be 24 such that the ratios can be expressed as 6/24 and 8/24.
find t =?
please help me
Answer:
−7.361097448
Step-by-step explanation:
The sum of two integers is 1. Their difference is 7. What are
the two integers?
A
6 and -1
B 2 and -3
C 4 and -3
D
-10 and -3
Answer:
The two integers are C, 4 and -3.
Step-by-step explanation:
When you add 4 and -3 you get 1, when you subtract them you get 7.
Can someone please answer and explain this.
Answer:
x =74
Step-by-step explanation:
540 degrees is the sum of all the angles
90 +90 + 2x+10 + x + 2x-20 = 540
Combine like terms
5x+170=540
Subtract 170 from each side
5x = 370
Divide by 5
5x/5 = 370/5
x =74
Can y’all help me on question 2?!
Answer:
4.5
Step-by-step explanation:
18 divided by 4 equals 4.5
a cylinder water tank carries a volume of 150L when it is full. The water tank has a base surface with a diameter of 140 cm. what is the height of the water tank?
Answer:
9.74418019cm=h
~ 9.7442
Step-by-step explanation:
volume of a cylinder=πr²h
radius=½of diameter
=½×140cm
=70cm
1l=1000cm³
150l=150l/1l×1000cm³
=150000cm³
150000cm³=π(70cm)²×h
150000cm³=15393.8040cm²h
150000cm³/15393.8040cm²=15393.8040cm²h/15393.8040cm²
150000cm³/15393.8040cm²=h
9.74418019cm=h
Please help me with i ii iii
Step by step
(i) I used distributive property to get the x’s and y’s out of parentheses. I then combined like-terms to simplify until I could do no more. That is your final answer for (i) is -3x - 12y
(ii) This one is similar to the first one, just with no parentheses. I combined like terms again until not like terms were left. Your final answer for (ii) is -3k -2 -2n
(iii) I started by dividing 15 by 3 and got 5, and because the 15 had an x to it, you get 5x. I then moved onto the next term, 9. 9 divided by 3, to get 3. Your final answer for (iii) is 5x + 3
Determine the value of x.
The answer to this question is B) 44.78
Answer:
Step-by-step explanation:
x = 44.78
A store only sells 20-pound bags of ice. Over the weekend, the store sells 800 bags of ice, making $3,400. On Monday, the store sells 80 bags of ice. How much money does the store make selling ice on Monday?
The amount of money the store makes selling ice by the same ratio will be $340.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
As per the given,
The store sells 800 bags of ice, making $3,400.
Ratio = 3400/800
With the same ratio,
The store sells x amount of bags of ice,
x/80 = 3400/800
x = $340
Hence "The store will make $340 from selling ice using the same ratio".
For more information about ratios and proportions,
brainly.com/question/26974513
#SPJ2
Anya contributed $1,200 toward the purchase
of a $2,000 computer. Her brother contributed
$240 toward the same computer. Her parents
provided the rest of the money for the computer. What percentage of the total cost of the computer did Anya's parents pay?
Answer:
Parent's share would be : 28%
Step-by-step explanation:
Cost of the computer = $2000
Anya's share = $1200
Brother's share = $240
Parents paid rest. That will be : 2000 - 1200 - 240 = $560
Percentage of parents share :
[tex]\frac{560}{2000} \times 100 = 28 \%[/tex]
What is the probability that a randomly selected day in the summer will be rainy if it’s cloudy?
Answer:
0.872
Step-by-step explanation:
Given that :
P(cloudy) = P(C) = 0.94
P(cloudy and rainy) = P(C n R) = 0.82
Probability that a given day will be rainy if it is cloudy ; this is a conditional probability problem:
Recall ; P(A|B) = P(AnB) / P(B)
P(R|C) = P(C n R) / P(C) = 0.82 / 0.94 = 0.872
PLZ HELP ILL AWARD BRAINLIEST
PLSS HELP!! I NEED TO FIND THE SURFACE AREA OF THIS CYLINDER!!
Answer:
338π
Step-by-step explanation:
[tex]2\pi rh+2\pi r^2[/tex]
[tex]2\pi *7*20+2\pi *7^2=240\pi +98\pi[/tex]
Get brainiest if right!!
10 points
Answer:
the ordered list is x, x+2, x+4, x+6, x+8, x+10
formula is Tn = 2n - 2
5x + 3y = 17
-8x - 3y = 9
Answer:
1)x=−3/5y+17/5
2)x=−3/8y+−9/8
Step-by-step explanation:
Let's solve for x.
5x+3y=17
Step 1: Add -3y to both sides.
5x+3y+−3y=17+−3y
5x=−3y+17
Step 2: Divide both sides by 5.
5x/5=−3y+17/5
x=−3/5y+17/5
Answer:
x=−3/5y+17/5
Let's solve for x.
−8x−3y=9
Step 1: Add 3y to both sides.
−8x−3y+3y=9+3y
−8x=3y+9
Step 2: Divide both sides by -8.
−8x/−8=3y+9/−8
x=−3/8y+−9/8
Answer:
x=−3/8y+−9/8
I HOPE THIS IS CORRECT IF NOT TELL ME AND ILL FIX IT.
Complete each congruence statement by naming the corresponding angle or side. NO LINKS!!!
Answer:
Solution given:
19
<JKL=<KLS
20
FD=GD
9514 1404 393
Answer:
19) ∠JKL ≅ ∠SLK
20) FD ≅ GD
Step-by-step explanation:
It works well to identify the locations of the letters in the congruence statement, then use the letters in the same order from the other part of the congruence statement.
19) Letters JKL have the order 312 in the first part of the congruence statement ΔKLJ ≅ ....
The last part of the congruence statement is ... ≅ ΔLKS. The letters in order 312 from that part are SLK, so we want our angle congruence to read ...
∠JKL ≅ ∠SLK
__
20) The letters we're given (FD) are in positions 31 of the first part of the triangle congruence statement. The letters in those positions in the second part are GD, so our segment congruence is ...
FD ≅ GD
what is the slope of the line that passes through these two points?
Answer:
slope of the line is 0
Step-by-step explanation:
given points are:
(-3 , 2)=(x1 , y1)
(4 , 2)=(x2 , y2)
slope =y2 - y1/x2 - x1
=2-2/4-(-3)
=0/4+3
=0/7
=0
why are chiken nugget rw that come from plans
Answer:
because i decided that
Step-by-step explanation:
Question 2
Find the volume.
Answer:
Volume of cone = 686π/3 or 718.67 in³
Step-by-step explanation:
Given the following data;
Radius, r = 7 in
Height, h = 14 inches
From the diagram, we can see that the object is a cone
To find the volume of a cone;
Mathematically, the volume of a cone is given by the formula;
[tex] V = \frac{1}{3} \pi r^{2}h[/tex]
Where;
V is the volume of the cone.
r is the radius of the base of the cone.
h is the height of the cone.
Substituting into the equation, we have;
[tex] Volume = \frac{1}{3} * \frac {22}{7} *7^{2}*14 [/tex]
[tex] Volume = \frac{1}{3} * 22 * 7 * 14 [/tex]
[tex] Volume = \frac{1}{3} * 2156 [/tex]
[tex] Volume = 718.67 [/tex]
Volume of cone = 718.67 in³ or 686π/3 in³