Answer:
Step-by-step explanation:
1) The distance that Lauren drove to the coast is the same as the distance he drove back from the coast. It means that the total miles that Lauren drove in this round-trip is
75 + 75 = 150 miles
2) time = distance/speed
Time spent in driving to the coast is
75/75 = 1 hour
His return speed is 25 mph
Time spent in driving back from the coast is
75/25 = 3 hours
3) Average speed = total distance/total time
Total distance = 75 + 75 = 150 miles
Total time = 1 + 3 = 4 hours
Average speed = 150/4 = 37.5 mph
A sequence is defined recursively by the formula F (n+1)=-2f(n). The 1st term of the sequence is -1.5. What is the next term in the sequence
Answer:
F(2)=3
Step-by-step explanation:
The first term is -1.5= f(1).
So F(1+1)=-2*f(1)= (-1.5)*(-2)=3
Suppose you have a sample of 27 Syrian hamsters who were exposed to high levels of the hormone progesterone when they were pups, and who have an average gestation length of 17.4 days and a sample variance of 33.7 days. You want to test the hypothesis that Syrian hamsters who were exposed to high levels of the hormone progesterone when they were pups have a different gestation length than all Syrian hamsters.
Required:
Calculate the t- statistics.
Answer:
Test statistic t=1.2531.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that Syrian hamsters who were exposed to high levels of the hormone progesterone when they were pups have a different gestation length than all Syrian hamsters (P-value=0.11).
Step-by-step explanation:
The question is incomplete: We need the gestation length of the population to perform the hypothesis test. We assume it to be 16 days (μ=16).
This is a hypothesis test for the population mean.
The claim is that Syrian hamsters who were exposed to high levels of the hormone progesterone when they were pups have a different gestation length than all Syrian hamsters.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=16\\\\H_a:\mu> 16[/tex]
The significance level is 0.05.
The sample has a size n=27.
The sample mean is M=17.4.
The sample variance is s^2=33.7 days^2.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=33.7^(0.5)=5.81.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{5.81}{\sqrt{27}}=1.1172[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{17.4-16}{1.1172}=\dfrac{1.4}{1.1172}=1.2531[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=27-1=26[/tex]
This test is a right-tailed test, with 26 degrees of freedom and t=1.2531, so the P-value for this test is calculated as (using a t-table):
[tex]P-value=P(t>1.2531)=0.11[/tex]
As the P-value (0.11) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that Syrian hamsters who were exposed to high levels of the hormone progesterone when they were pups have a different gestation length than all Syrian hamsters.
Cuanto es 1× -1× es x o no?
Answer:
[tex]1^x[/tex] is always 1, so [tex]1^x-1^x=0[/tex]
es0
dame grasias
si soi nuevo
My rule is: y= 1/3x+ 11/15 Find x, if y=1.
Answer:
x=5/4
Step-by-step explanation:
First, plug in 1 for y. Since a common denominator for the right side is 3, multiply both sides by 3 to get 3=x+11/5. Then multiply both sides by 5 to get 15=5x+11. Subtract 11 on both sides to get 4=5x. Finally divide by 5 to get x by itself and get x = 5/4.
2x+8y=12. 3x-8y=11 solve
Answer:
x = 23/5 and y = 7/20
Step-by-step explanation:
2x + 8y = 12 and 3x - 8y = 11 are two given equations
Now,
Step 1:
2x + 8y = 12 ...(1)
3x - 8y = 11 ...(2)
Step 2:
From equation (2) we get the value of x
i.e.,
3x - 8y = 11
3x = 8y + 11
x = 8y + 11/3
Step 3:
Now,
Put the value of x = 8y + 11/3 in equation (1) we get,
i.e.,
2x + 8y = 12
2(8y + 11/3) + 8y = 12
16y + 22/3 + 8y = 12
16y + 22 + 8y(3)/3 = 12
16y + 22 + 24y/3 = 12
16y + 24y + 22 = 12 * 3
40y = 36 - 22
40y = 14
y = 14/40
y = 7/20
Step 4:
Now,
Substitute the value of y = 7/20 in equation (2) we get,
i.e.,
3x - 8y = 11
3x - 8(7/20) = 11
3x - 56/20 = 11
3x - 14/5 = 11
3x = 11 + 14/5
3x = 11 * 5 + 14/5
3x = 55 + 14/5
3x = 69/5
x = 69/3 * 5
x = 23/5
A study will be conducted to examine a new medicine intended to reduce high blood pressure in adult men who have high blood pressure. As part of the study, a random sample of 40 men with high blood pressure will have their blood pressure measured, and then they will take the new medicine every day for one month. At the end of the month, their blood pressure will be measured again. Of the following, which is the best procedure to investigate whether there will be convincing statistical evidence of a change, on average, in blood pressure for men with high blood pressure who take the new medicine? (A) A one-sample z-test for a proportion (B) A two-sample z-test for a difference between proportions (C) A two-sample i-test for the difference between two means (D) A matched-pairs t-test for a mean difference (E) A chi-square test of independence
Answer:
Option D
Step-by-step explanation:
A matched pairs t-test is appropriate for this experiment. It compares two means that are from the same individual; the before drug administration and the after drug administration. It compares the before-and-after observations on the same subjects.
The best and convincing statistical evidence of a change, on average, in blood pressure is the t test.
What is t test?The test is one of the kinds of inferential statistics. It is deployed in decision making. As such, it involves the test to see if there is significant difference between the means of two groups, which may be related.
Hence, in this study, the best and convincing statistical evidence of a change, on average, in blood pressure is the t test.
Learn more about t test:https://brainly.com/question/15870238
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The formula in cell B1 is= A$2. Autofill is used by dragging B1’s autofill box across to C1,D1, and E1. What formulas will appear in C1, D1, and E1, respectively?
Answer:
The formulas that will appear in
C1 is =B$2
D1 is = C$2
E1 is = D$2
Step-by-step explanation:
Given
Formula in B1 is = A$2
Required
Formulas in C1, D1 and E1 when dragged from B1.
In Microsoft Office Excel, this is called absolute reference.
But this type of absolute reference requires that only the cell name will be changed or altered, the row number will always remain the same no matter where it's been dragged to.
Since the initial column name is A and the Initial row number is 2 (from A$2),
Cell C1 will take the formula = B$2
Cell D1 will take = C$2
Cell E1 will take = D$2
Notice that only the column name changed for each formula; the row number remain unchanged.
Answer:
=B$2, C$2, D$2
Step-by-step explanation:
7×{(-150)÷(10-10-5)}
Answer:
[tex]=210[/tex]
Step-by-step explanation:
[tex]7\times \left(-150\right)\div \left(10-10-5\right)\\Follow\:the\:PEMDAS\:order\:of\:operations\\\mathrm{Calculate\:within\:parentheses}\:\left(10-10-5\right)\::\quad -5\\10-10-5\\\mathrm{Add\:and\:subtract\:\left(left\:to\:right\right)}\\10-10=0\\=0-5\\=0-5\\=-5\\=7\times \left(-150\right)\div \left(-5\right)\\\mathrm{Multiply\:and\:divide\:\left(left\:to\:right\right)}\:7\times \left(-150\right)\div \left(-5\right)\::\quad 210\\7\times \left(-150\right)\div \left(-5\right)[/tex]
[tex]\mathrm{Apply\:rule\:}-a\div \left(-b\right)\:=\:a\div \:b\\-1050\div \left(-5\right)=1050\div \:5=210\\=210[/tex]
Answer:
210
Step-by-step explanation:
7×{(-150)÷(10-10-5)}
remove the opposites
7×{(-150)÷(-5)}
divide
7×30
multiply
210
Spend some time looking at the vehicles on the road. Look at the first 40 vehicles that drive by. Take note of the number of vehicles that are cars (sedans). Use the data you collect to construct confidence interval estimates of the proportion of vehicles that are cars (rather than trucks, vans, etc). Report your confidence interval to the group. Why might people get different results? Is your sample likely a good representation of the total population of all vehicles? Why or why not?
Answer:
The confidence interval is ( 0.225952516, 0.474047484)
People will get different results because, the amount of sedans may be dependent on the area in which the data is taken.
No, the sample is not really a good representation of the whole population of vehicles, since only a certain area was sampled or experimented.
Step-by-step explanation:
Solution
Given that:
From the experiment we discovered that out of 40 vehicles, 14 of them were sedans.
Let us note that:
p^ = It is the point estimate of the population proportion
Where,
n=/n = 0.35
We also check for the standard error of p, sp:
which is,
sp =√{p^ (1-p^)/n] =0.075415516
Thus,
for the the critical z, we have the following:
α/2 = 0.05
So,
z (α)/2 = 1.644853627
Thus,
For lower bound = p^ - z(α/2) * sp = 0.225952516
For upper bound = p^ + z(α/2)* sp = 0.474047484
Hence,
The confidence interval becomes: ( 0.225952516, 0.474047484)
2. For the data in the table does Y very directly with X if it does write an equation for the direct variation
Answer:no it doesn’t vary
Step-by-step explanation:because if you count them up there is no possibility that they match
Quadrilateral QPRS is transformed by a dilation centered at the origin with a scale factor of 2 to create quadrilateral Q'P'R'S'. Which are the coordinates of quadrilateral Q'P'R'S'?
Q'(4, 4), P'(0, 0), R'(-4, -8), S'(8, -4)
Q'(1, 1), P'(0, 0), R'(-1, -2), S'(2, -1)
Q'(4, 4), P'(2, 2), R'(0, -2), S'(6, 0)
Q'(0, 0), P'(-2, -2), R'(-4, -6), S'(2, -4)
Answer:
B
Step-by-step explanation:
The coordinates of quadrilateral Q'P'R'S' is
Q'(4, 8), P'(0, 0), R'(-4, -8), S'(8, -4).
What is a scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object,
We have,
To perform a dilation centered at the origin with a scale factor of 2, we need to multiply the x and y coordinates of each vertex by 2.
So starting with the coordinates of quadrilateral QPRS:
Q(2, 4), P(0, 0), R(-2, -4), S(4, -2)
Multiplying each coordinate by 2, we get:
Q'(4, 8), P'(0, 0), R'(-4, -8), S'(8, -4)
Therefore,
The coordinates of quadrilateral Q'P'R'S' is
Q'(4, 8), P'(0, 0), R'(-4, -8), S'(8, -4).
Learn more about scale factors here:
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The complete question.
Quadrilateral QPRS is transformed by a dilation centered at the origin with a scale factor of 2 to create quadrilateral Q'P'R'S'. Which are the coordinates of quadrilateral Q'P'R'S'?
Where
The coordinates of PQRS are:
Q = (2, 4), P = (0, 0), R = (-2, -4), S = (4, -2).
The functions u and w are defined as follows. u(x)=2x-2 w(x)=-2x^2+1 Find the value of w(u(5)).
Answer:
-127
Step-by-step explanation:
u(x)=2x-2
w(x)= -2x^2+1
w(u(5))=?
---------
u(5)= 2*5-2= 8
W(8)= - 2*64+1= -127
Answer:
that was the wrong answer this site sucks
Which of the following is the absolute value parent function? A. F(X) = | x | + 1
B. F(x) = x^2
C. F(x) = | x |
D. F(x) = 1/x
Answer:
C. F(x) = | x |
Step-by-step explanation:
The parent function has no adornments, shifts, multipliers, offsets, reflections, or anything else.
The absolute value of x is written |x|. That is the parent absolute value function.
F(x) = |x|
Answer: C
Step-by-step explanation:
Mice and Pain Can you tell if a mouse is in pain by looking at its facial expression? A new study believes you can. The study1 created a "mouse grimace scale" and tested to see if there was a positive correlation between scores on that scale and the degree and duration of pain (based on injections of a weak and mildly painful solution.) The study's authors believe that if the scale applies to other mammals as well, it could help veterinarians test how well painkillers and other medications work in animals. 1"Of Mice and Pain", The Week, May 28, 2010, p. 21. 1. State the null and alternative hypotheses. 2.Since the study authors report that you can tell if a mouse is in pain by looking at its facial expression, do you think the data were found to be statistically significant? 3.If another study were conducted testing the correlation between scores on the "mouse grimace scale" and a placebo (non-painful) solution, should we expect to see a sample correlation as extreme as that found in the original study? 4. If another study were conducted testing the correlation between scores on the "mouse grimace scale" and a placebo (non-painful) solution, should we expect to see a sample correlation as extreme as that found in the original study, if the original study results showed no evidence of a relationship between mouse grimaces and pain?
Explanation:
1. a) Null hypothesis: There is no statistically significant relationship between the mouse grimace scale and the amount of pain felt by mouse.
b) Alternate hypothesis: There is a statistically-significant relationship between the mouse grimace scale and the amount of pain felt by mouse.
2. Yes, because a statistically significant data implies that there is sufficient evidence to believe the study, based on the results of the findings.
3. No, since the variables are different in this case. Here we are dealing with a non-painful solution so there may be no sample correlation as extreme as that found in the original study.
4. Possibly, because every hypothesis is an assumption until it is proven. Thus, in every statistical research, there may be different findings.
The ages of the winners of a cycling tournament are approximately bell-shaped. The mean age is 27.3 years, with a standard deviation of 3.4 years. The winner in one recent year was 22 years old.
(a) Transform the age to a z-score.
(b) Interpret the results.
(c) Determine whether the age is unusual.
Answer:
Convert the age to a z-score:
Step-by-step explanation:
Let X be the random variable with mean 27.2 and standard deviation 3.8.
Here, the observation, x is 24.
The z-score of the winner's age is -1.56.
A negative z-score indicates that the value is below the mean.
The age of the winner is not considered unusual.
What is z-score?
A z-score also called a standard score is a measure of how many standard deviations a data point is away from the given mean of a distribution.
It measures the unusual or extreme a particular data point is compared to the rest of the distribution
We have,
(a)
To transform the age of the winner into a z-score, we use the formula:
z = (x - μ) / σ
where x is the value we want to transform, μ is the mean, and σ is the standard deviation.
So,
Substituting the values given,
z = (22 - 27.3) / 3.4
z = -1.56
The z-score of the winner's age is -1.56.
(b)
A z-score represents the number of standard deviations a data point is from the mean.
In this case, the winner's age is 1.56 standard deviations below the mean age of the winners.
A negative z-score indicates that the value is below the mean.
(c)
Compare the z-score to a threshold value.
A commonly used threshold for unusual values is z = ±2.
If the absolute value of the z-score is greater than or equal to 2, then the value is considered unusual.
So,
The absolute value of the z-score is less than 2 (|z| < 2), which means that the age of the winner is not considered unusual in the context of the distribution of the ages of the winners.
Thus,
The z-score of the winner's age is -1.56.
A negative z-score indicates that the value is below the mean.
The age of the winner is not considered unusual.
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If a track has 219 miles and takes 108 minutes to get there. Is the average speed 104 miles per hour
Answer:
122 miles per hour.
Step-by-step explanation:
Time:108 min ÷60 =1.8 hours
Speed = distance /time = 219/1.8 =122 miles per hour.
Hope this helps..
Answer:
No its 121.67 mph.
Step-by-step explanation:
Speed in miles per minute is 219/108 miles per minute
To convert to miles per hour we multiply by 60:
= 219 * 60 / 108
= 121.67 m p h.
A nursery located in Florida uses a water meter to measure its water usage 1 point
in CCF. It is charged $0.36 per CCF of water. Its last meter reading was
123,692 and their present reading is 127,394. For this usage, the nursery was
charged $332.72*
True or false?
Answer:
Step-by-step explanation:
From the information given, their last meter reading was 123,692 and their present reading is 127,394. The difference between the last and the present meter reading is
127394 - 123692 = 3702
If the water meter measures its water usage in terms of 1 point in CCF, then the amount of CCF of water used is 3702. If the school is charged $0.36 per CCF of water, then for this usage, the charge would be
3702 × 0.36 = $1332.72
Therefore, it is false
what should be add to 7 3/5 to get 18
Answer:
[tex]10\frac{2}{5}[/tex]
Step-by-step explanation:
[tex]7\frac{3}{5} + x = 18\\[/tex]
transformation : [tex]7\frac{3}{5} = \frac{(5*7) + 3}{5} = \frac{38}{5}[/tex]
[tex]\frac{38}{5} + x = 18\\\\x = 18 - \frac{38}{5} = \frac{(5*18) - 38}{5} = \frac{52}{5}[/tex]
[tex]\frac{52}{5} = 10\frac{2}{5}[/tex]
Answer:
[tex]10\frac{2}{5}[/tex]
Step-by-step explanation:
What should be add to [tex]7\frac{3}{5}[/tex] to get [tex]18[/tex] ?
[tex]18-7\frac{3}{5}=\\ \\=17\frac{5}{5}-7\frac{3}{5}\\\\\\=(17-7)+(\frac{5}{5}- \frac{3}{5})\\ \\=10+\frac{2}{5}\\ \\=10\frac{2}{5}[/tex]
What is the sum of V-2 and V-18?
Answer:
=2v−20
Step-by-step explanation:
Let's simplify step-by-step.
v−2+v−18
=v+−2+v+−18
Combine Like Terms:
=v+−2+v+−18
=(v+v)+(−2+−18)
=2v+−20
Answer:
=2v−20
After several shares of the company stock was sold, a profit of $1320 was earned. The prophet was over 15% over 30 day period. How much were the shares worth when they were originally purchased
Answer:
$104430
Step-by-step explanation:
Let's recall the formula
PRT/100 = interest I
Where
P = principal/initial amount
R = rate
T= period or time
P =( 100*I)/(RT)
P =( 100*1320)/(15*(30/356))
P = 132000/1.264
P = $104430
3x - 7 = 8 looking for the answer to X
Answer:
[tex]x=5[/tex]
Step-by-step explanation:
[tex]3x - 7 = 8[/tex]
[tex]3x = 8+7[/tex]
[tex]3x=15[/tex]
[tex]x=5[/tex]
Answer:
x=5
Step-by-step explanation:
Let's solve your equation step-by-step.
3x−7=8
Step 1: Add 7 to both sides.
3x−7+7=8+7
3x=15
Step 2: Divide both sides by 3.
3x/3=15/3
x=5
7 over 4 times y equals 56
Answer:
[tex]y=32[/tex]
Step-by-step explanation:
[tex]\frac{7}{4}y=56\\\mathrm{Multiply\:both\:sides\:by\:}4\\4\cdot \frac{7}{4}y=56\cdot \:4\\\mathrm{Simplify}\\7y=224\\\mathrm{Divide\:both\:sides\:by\:}7\\\frac{7y}{7}=\frac{224}{7}\\Simplify\\y=32[/tex]
A certain car traveling 34.0 mph skids to a stop in 29 meters from the point where the brakes were applied. In approximately what distance would the car stop had it been going 105.4 mph?
Answer:
279 m
Step-by-step explanation:
Work by friction = change in kinetic energy
Fd = ½ mv²
d ∝ v²
d / 29 m = (105.4 mph)² / (34.0 mph)²
d = 279 m
which fraction is the largest 5/7 7/10 10/13 show how u worked out the answer
Answer:
[tex]3.1/13[/tex]
Step-by-step explanation:
[tex]1.5/7 =0.214286[/tex]
[tex]2.7/10=0.27[/tex]
[tex]3.1/13 =0.238462[/tex]
Use long division to find quotient below
the answer is in the photos
Another question (sorry)
Answer:
19.99
Step-by-step explanation:
First you would multiply .44 by 16 to get 7.04
then you would add 12.95 to get 19.99
f(x)=4x-8 and g(x)=5x+6, find (f+g)(x)
Answer:
9x-2
Step-by-step explanation:
Since you are adding the two functions, you should first start adding like terms. 4x + 5x is 9x. -8 + 6 is -2. Thus the value of (f+g)(x) is 9x-2.
The prior probabilities for events A1 and A2 are P(A1) = 0.20 and P(A2) = 0.80. It is also known that P(A1 ∩ A2) = 0. Suppose P(B | A1) = 0.25 and P(B | A2) = 0.05. (a) Are A1 and A2 mutually exclusive? They mutually exclusive. How could you tell whether or not they are mutually exclusive? P(B | A1) ≠ P(B | A2) P(A1) + P(A2) = 1 P(A1 ∩ A2) = 0 P(A1) ≠ P(A1 | A2) P(A2) ≠ P(A2 | A1) (b) Compute P(A1 ∩ B) and P(A2 ∩ B). P(A1 ∩ B) = P(A2 ∩ B) = (c) Compute P(B). (d) Apply Bayes' theorem to compute P(A1 | B) and P(A2 | B). (Round your answers to four decimal places.) P(A1 | B) = P(A2 | B) =
Answer:
(a) [tex]A_1[/tex] and [tex]A_2[/tex] are indeed mutually-exclusive.
(b) [tex]\displaystyle P(A_1\; \cap \; B) = \frac{1}{20}[/tex], whereas [tex]\displaystyle P(A_2\; \cap \; B) = \frac{1}{25}[/tex].
(c) [tex]\displaystyle P(B) = \frac{9}{100}[/tex].
(d) [tex]\displaystyle P(A_1 \; |\; B) \approx \frac{5}{9}[/tex], whereas [tex]P(A_1 \; |\; B) = \displaystyle \frac{4}{9}[/tex]
Step-by-step explanation:
(a)[tex]P(A_1 \; \cap \; A_2) = 0[/tex] means that it is impossible for events [tex]A_1[/tex] and [tex]A_2[/tex] to happen at the same time. Therefore, event [tex]A_1[/tex] and [tex]A_2[/tex] are mutually-exclusive.
(b)By the definition of conditional probability:
[tex]\displaystyle P(B \; | \; A_1) = \frac{P(B \; \cap \; A_1)}{P(B)} = \frac{P(A_1 \; \cap \; B)}{P(B)}[/tex].
Rearrange to obtain:
[tex]\displaystyle P(A_1 \; \cap \; B) = P(B \; |\; A_1) \cdot P(A_1) = 0.25 \times 0.20 = \frac{1}{20}[/tex].
Similarly:
[tex]\displaystyle P(A_2 \; \cap \; B) = P(B \; |\; A_2) \cdot P(A_2) = 0.80 \times 0.05 = \frac{1}{25}[/tex].
(c)Note that:
[tex]\begin{aligned}P(A_1 \; \cup \; A_2) &= P(A_1) + P(A_2) - P(A_1 \; \cap \; A_2) = 0.20 + 0.80 = 1\end{aligned}[/tex].
In other words, [tex]A_1[/tex] and [tex]A_2[/tex] are collectively-exhaustive. Since [tex]A_1[/tex] and [tex]A_2[/tex] are collectively-exhaustive and mutually-exclusive at the same time:
[tex]\displaystyle P(B) = P(B \; \cap \; A_1) + P(B \; \cap \; A_2) = \frac{1}{20} + \frac{1}{25} = \frac{9}{100}[/tex].
(d)By Bayes' Theorem:
[tex]\begin{aligned} P(A_1 \; |\; B) &= \frac{P(B \; | \; A_1) \cdot P(A_1)}{P(B)} \\ &= \frac{0.25 \times 0.20}{9/100} = \frac{0.05 \times 100}{9} = \frac{5}{9}\end{aligned}[/tex].
Similarly:
[tex]\begin{aligned} P(A_2 \; |\; B) &= \frac{P(B \; | \; A_2) \cdot P(A_2)}{P(B)} \\ &= \frac{0.05 \times 0.80}{9/100} = \frac{0.04 \times 100}{9} = \frac{4}{9}\end{aligned}[/tex].
Using probability concepts, along with conditional probability and Bayes Theorem, it is found that:
a) [tex]P(A1 \cap A2) = 0[/tex], thus yes, A1 and A2 are mutually exclusive.
b) The probabilities are: P(A1 ∩ B) = 0.05, P(A2 ∩ B) = 0.04.
c) The probability of event B is: P(B) = 0.09.
d) The probabilities are: P(A1|B) = 0.5555 and P(A2|B) = 0.4445.
-----------
Conditional Probability
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
P(B|A) is the probability of event B given that A. [tex]P(A \cap B)[/tex] is the probability of both A and B. P(A) is the probability of A.-----------
Bayes Theorem:
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]
-----------
Item a:
Two events A and B are mutually exclusive if they cannot happen together.Since [tex]P(A1 \cap A2) = 0[/tex], yes, it can be said that events A1 and A2 are mutually exclusive.Item b:
Using conditional probability.
A1 and B:
[tex]P(B|A1) = \frac{P(A1 \cap B)}{P(A1)}[/tex]
[tex]0.25 = \frac{P(A1 \cap B)}{0.2}[/tex]
[tex]P(A1 \cap B) = 0.25(0.2) = 0.05[/tex]
A2 and B:
[tex]P(B|A2) = \frac{P(A2 \cap B)}{P(A2)}[/tex]
[tex]0.05 = \frac{P(A1 \cap B)}{0.8}[/tex]
[tex]P(A1 \cap B) = 0.8(0.05) = 0.04[/tex]
Item c:
P(B) is given by:
[tex]P(B) = P(A1 \cap B) + P(A2 \cap B) = 0.05 + 0.04 = 0.09[/tex]
Item d:
Applying Bayes Theorem
[tex]P(A1|B) = \frac{P(A1)P(B|A1)}{P(B)} = \frac{0.25(0.2)}{0.09} = 0.5555[/tex]
[tex]P(A2|B) = \frac{P(A2)P(B|A2)}{P(B)} = \frac{0.8(0.05)}{9} = 0.4445[/tex]
A similar problem is given at https://brainly.com/question/22428992
Can someone please explain how to
find the mean , median , range, and interquartile range????
Jenny has $20 in a savings account. The interest rate is 5% compounded annually. To the nearest cent, how much interest will she earn in 2 years?
Answer:
22.05
Step-by-step explanation:
