The number of minutes is 8.52 minutes to find a parking space at 9 A.M.
Given data:
To find the number of minutes it takes to find a parking space more than 80% of the time, we need to determine the corresponding z-score and use it to find the value in the normal distribution.
First, determine the z-score corresponding to the desired percentile (80%). Since the normal distribution is symmetrical, the z-score for the upper tail is from a standard normal distribution table.
The z-score corresponding to 80% is approximately 0.84.
Next, the z-score formula to find the corresponding value in the distribution:
z = (x - mean) / standard deviation
Rearranging the formula to solve for x (the number of minutes):
x = z * standard deviation + mean
Plugging in the values,:
x = 0.84 * 3 + 6
x ≈ 8.52
Hence, more than 80% of the time, it takes more than approximately 8.52 minutes to find a parking space at 9 A.M.
To learn more about z-score, refer:
https://brainly.com/question/15016913
#SPJ12
Please answer this correctly
Answer:
First box is 4This is because 2 is the stem and the leaves are 1, 2, 4, and 5
so the numbers are 21, 22, 24, and, 25
Second box is 3This is because 2 is the stem for the leaves 6 and 7
3 is the stem for the leaf 0
So the numbers are 26, 27, and 30
Hope this helped
Answer:
As you know about the stem and leaf plot
1 |7 7 7 8 => 17, 17, 17, 18
2|1 2 4 5 6 7 => 21, 22, 24, 25, 26, 27
3|0 2 5 5 6 7 7 8 9 => 30, 32, 35, 35, 36, 37, 37, 38, 39
4|1 2 => 41, 42
Now we count to complete the table:
16-20 | 4 {17, 17, 17, 18}
21-25 | 4 {21, 22, 24, 25}
26-30 | 3 {26, 27, 30}
31-35 | 3 {32, 35, 35}
36-40 | 5 {36, 37, 37, 38, 39}
41-45 | 2 {41, 42}
Hope this helps!
Use the given degree of confidence and sample data to construct a confidence interval for the population mean μ. Assume that the population has a normal distribution. Thirty randomly selected students took the calculus final. If the sample mean was 95 and the standard deviation was 6.6, construct a 99% confidence interval for the mean score of all students.
A. 91.68
Answer:
B) 92.03 < μ < 97.97
99% confidence interval for the mean score of all students.
92.03 < μ < 97.97
Step-by-step explanation:
Step(i):-
Given sample mean (x⁻) = 95
standard deviation of the sample (s) = 6.6
Random sample size 'n' = 30
99% confidence interval for the mean score of all students.
[tex]((x^{-} - Z_{0.01} \frac{S}{\sqrt{n} } , (x^{-} + Z_{0.01} \frac{S}{\sqrt{n} })[/tex]
step(ii):-
Degrees of freedom
ν = n-1 = 30-1 =29
[tex]t_{0.01} = 2.462[/tex]
99% confidence interval for the mean score of all students.
[tex]((95 - 2.462 \frac{6.6}{\sqrt{30} } , 95 + 2.462\frac{6.6}{\sqrt{30} } )[/tex]
( 95 - 2.966 , 95 + 2.966)
(92.03 , 97.97)
Final answer:-
99% confidence interval for the mean score of all students.
92.03 < μ < 97.97
The graphs below have the same shape. What is the equation of the blue
graph?
Consider random samples selected from the population of all female college soccer players in the United States. Assume the mean height of female college soccer players in the United States is 66 inches and the standard deviation is 3.5 inches. Which do you expect to have less variability (spread): a sampling distribution with sample size n
Answer:
Option C is correct.
The sampling distribution with sample size n=100 will have less variability.
Step-by-step explanation:
Complete Question
Consider random samples selected from the population of all female college soccer players in the United States. Assume the mean height of female college soccer players in the United States is 66 inches and the standard deviation is 3.5 inches. Which do you expect to have less variability (spread): a sampling distribution with sample size n = 100 or a sample size of n = 20.
A. Both sampling distributions will have the same variability.
B.The sampling distribution with sample size n=20 will have less variability
C. The sampling distribution with sample size n =100 will have less variability
Solution
The central limit theorem allows us to say that as long as
- the sample is randomly selected from the population distribution with each variable independent of each other and with the sample having an adequate enough sample size.
- the random sample is normal or almost normal which is guaranteed if the population distribution that the random sample was extracted from is normal or approximately normal,
1) The mean of sampling distribution (μₓ) is approximately equal to the population mean (μ)
μₓ = μ = 66 inches
2) The standard deviation of the sampling distribution or the standard error of the sample mean is related to the population standard deviation through
σₓ = (σ/√N)
where σ = population standard deviation = 3.5 inches
N = Sample size
And the measure of variability for a sampling distribution is the magnitude of the standard deviation of the sampling distribution.
For sampling distribution with sample size n = 100
σₓ = (3.5/√100) = 0.35 inch
For sampling distribution with sample size n = 20
σₓ = (3.5/√20) = 0.7826 inch
The standard deviation of the sampling distribution with sample size n = 20 is more than double that of the sampling distribution with sample size n = 100, hence, it is evident that the bigger the sample size, the lesser the standard deviation of the sampling distribution and the lesser the variability that the sampling distribution shows.
Hope this Helps!!!
Write the equation represents the line.
Answer:
y = 3/4x+2
Step-by-step explanation:
The change in y over change in x of the two points given is 3/4, which is the slope. The line intersects with the y axis at 2, making 2 the y-int
Solve -6x + 3 > 21.
A. Xs3
B. x2 3
C. x2-3
D. xs-3
s the last book a person in City Upper A read a discrete random variable, continuous random variable, or not a random variable? A. It is a continuous random variable. B. It is a discrete random variable.
Answer:
Not a random variable
Step-by-step explanation:
The last book a person read in City A is not a random variable because it is not a number as there is no numerical description for the outcome of this experiment.
Thus, the last book read by someone in City A is not a random variable.
Answer:
not random
Step-by-step explanation:
A committee of 15 members is voting on a proposal. Each member casts a yea or nay vote. On a random voting basis, what is the probability that the final vote count is unanimous?
Answer:
0.006% probability that the final vote count is unanimous.
Step-by-step explanation:
For each person, there are only two possible outcomes. Either they vote yes, or they vote no. The probability of a person voting yes or no is independent of any other person. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Random voting:
So 50% of voting yes, 50% no, so [tex]p = 0.5[/tex]
15 members:
This means that [tex]n = 15[/tex]
What is the probability that the final vote count is unanimous?
Either all vote no(P(X = 0)) or all vote yes(P(X = 15)). So
[tex]p = P(X = 0) + P(X = 15)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{15,0}.(0.5)^{0}.(0.5)^{15} = 0.00003[/tex]
[tex]P(X = 15) = C_{15,15}.(0.5)^{15}.(0.5)^{0} = 0.00003[/tex]
So
[tex]p = P(X = 0) + P(X = 15) = 0.00003 + 0.00003 = 0.00006[/tex]
0.006% probability that the final vote count is unanimous.
Find the zeros of the function
m (x) = x+6x?
find the 0 multiplicity
Answer:
6x^2 Denadaaaaaaaaaaaaaaaaa
Please answer this correctly
Answer:
P(odd) = 50%
Step-by-step explanation:
Odd numbers in the spinner:
1, 3, 5, 7 - 4 numbers
There are a total of 8 numbers, therefore:
[tex]\frac{odd}{total} = \frac{4}{8} = \frac{1}{2} =[/tex]
Convert fraction to percentage:
(1 ÷ 2) × 100 = 50%.
P(odd), the probability of an odd number, is 50%.
50 % is the answer bro
coz the odd is exactly half of the total element
We claim that the average weight of our "product" is 50 pounds, with a standard deviation of 2 pounds. We take a sample of 50 units, with a mean of 49.95 pounds and a standard deviation of 1.9999 pounds. What is a 95% prediction interval for the mean weight of the NEXT unit of production from our process? Use Z for ease of calculation.
Answer:
49.95+/-0.5543
= ( 49.3957, 50.5043) pounds
the 95% confidence interval (a,b) = ( 49.3957, 50.5043) pounds
And to 2 decimal points;
the 95% confidence interval (a,b) = ( 49.40, 50.50) pounds
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
Given that;
Mean x = 49.95 pounds
Standard deviation r = 1.9999 pounds
Number of samples n = 50
Confidence interval = 95%
z value(at 95% confidence) = 1.96
Substituting the values we have;
49.95+/-1.96(1.9999/√50)
49.95+/-1.96(0.282828570338)
49.95+/-0.554343997864
49.95+/-0.5543
= ( 49.3957, 50.5043) pounds
Therefore, the 95% confidence interval (a,b) = ( 49.3957, 50.5043) pounds
An account with $250 balance accrues 2% annually. If no deposits or withdrawals are made, which graphs can be used to determine approximately how many years will it take for the balance to be $282?
An account with a $250 balance accrues 2% annually. If no deposits or withdrawals are made so, to take the balance to $282 requires 6.4 years and this can be determined by using the simple interest formula.
Given :
An account with a $250 balance accrues 2% annually.No deposits or withdrawals are made.Final amount = $282SImple interest formula can be used to determine the total number of years will it take for the balance to be $282.
The formula of simple interest is given by:
[tex]\rm A = P(1+rt)[/tex]
where A is the final amount, P is the initial principal balance, r is the annual interest rate and t is the time in years.
Now, put the known values in equation (1).
[tex]\rm 282 = 250(1+0.02t)[/tex]
[tex]\rm 282=250+5t[/tex]
32 = 5t
t = 6.4 years
So, 6.4 years will it take for the balance to be $282.
So, the graph correct graph is shown by option D).
For more information, refer to the link given below:
https://brainly.com/question/24432090
Answer:
D
Step-by-step explanation:
1.expand and simplify 2(x-4) -3 (x-2)
2.factorise a^2 + a
Answer:
Step-by-step explanation:
1 2(x-4)-3(x-2)
=2x-4x-3x+6
=2x-7x+6
2 a²+a
=a(a+1)
Brainliest to whoever gets this correct Which of the following is equal to the rational expression when x ≠ -3? x^2-9/x+3
Answer:
see below
Step-by-step explanation:
We presume you want to simplify ...
[tex]\dfrac{x^2-9}{x+3}=\dfrac{(x-3)(x+3)}{x+3}=\boxed{x-3}[/tex]
__
The numerator is the difference of squares, so is factored accordingly. One of those factors cancels the denominator.
A survey shows that 10% of the population is victimized by property crime each year. A random sample of 527 older citizens (65 years or more of age) shows a victimization rate of 12.35%. Are older people more likely to be victimized
Answer:
We conclude that older people are more likely to be victimized.
Step-by-step explanation:
We are given that a survey shows that 10% of the population is victimized by property crime each year.
A random sample of 527 older citizens (65 years or more of age) shows a victimization rate of 12.35%
Let p = population proportion of people who are victimized.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]p \leq[/tex] 10% {means that older people are less likely to be victimized or remains same}
Alternate Hypothesis, [tex]H_A[/tex] : p > 10% {means that older people are more likely to be victimized}
The test statistics that would be used here One-sample z-test for proportions;
T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of older people who are victimized = 12.35%
n = sample of older citizens = 527
So, the test statistics = [tex]\frac{0.1235-0.10}{\sqrt{\frac{0.10(1-0.10)}{527} } }[/tex]
= 1.798
The value of z-test statistics is 1.798.
Since in the question, we are not given with the level of significance so we assume it to be 5%. Now at 5% level of significance, the z table gives a critical value of 1.645 for right-tailed test.
Since our test statistics is more than the critical value of z as 1.798 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Therefore, we conclude that older people are more likely to be victimized.
Any help would be great
Answer:
15
Step-by-step explanation:
38=10+13+c
c=38-10-13=15
Hope this helps!
Activity 1:
Q\Circle the coefficient of each of these terms:
14d f) 3.5g
11k +4 g) W
5.3e +67 h) X
918273k + 87 I) k + 455
-5g j) 3X +1
Answer:
e) 14
f) 3.5 and 11
g) 1 and 5.3
h) 1 and 918273
i) 1 and -5
j) 3
Step-by-step explanation:
A coefficient is the number or constant that multiplies a variable in an algebraic expression. It is placed before a variable.
We are to find the coefficient of each of the terms.
e) 14d
Considering the above definition, d is the variable. The coefficient to be circled is 14
f) 3.5g + 11k +4
Considering the above definition, g and k are variables respectively.
The coefficient to be circled are 3.5 and 11 respectively
g) w + 5.3e +67 = 1w + 5.3e +67
Considering the above definition, w and e are variables respectively.
The coefficient to be circled are 1 and 5.3 respectively
h) x + 918273k + 87 = 1x + 918273k + 87
Considering the above definition, x and k are variables respectively.
The coefficient to be circled are 1 and 918273 respectively
I) k + 455 -5g = 1k + 455 -5g
Considering the above definition, k and g are variables respectively.
The coefficient to be circled are 1 and -5 respectively
j) 3x +1
Considering the above definition, x is the variable. The coefficient to be circled is 3
Note the answer to (f), (g) and (h) would be slightly different if the signs are opposite. That is if we have: x - 918273k + 87. Coefficient = -918273
If 3.5g - 11k +4, Coefficient = 3.5 and -11
For w - 5.3e +67, Coefficient = -5.3 and 67
You can used the formula to find the omitted questions(a to d)
What is the sum? 3k/k^2+k-7/4K
Answer:
[tex]\dfrac{k^2+5k}{4k^2}[/tex]
Step-by-step explanation:
A suitable common denominator is 4k^2. (This eliminates the first and last choices.)
[tex]\dfrac{3k}{k^2}+\dfrac{k-7}{4k}=\dfrac{4(3k)}{4(k^2)}+\dfrac{k(k-7)}{k(4k)}\\\\=\dfrac{12k+k^2-7k}{4k^2}=\boxed{\dfrac{k^2+5k}{4k^2}}[/tex]
The college student senate is sponsoring a spring break Caribbean cruise raffle, with proceeds going to the local homeless shelter. A local travel agency donated the cruise, worth an estimated $3000. The students sold 2900 tickets at $5 per ticket. Find the mathematical expectation of a student who purchases 10 tickets.
Answer:
The mathematical expectation of a student who purchases 10 tickets is -$39.65.
Step-by-step explanation:
A student that purchases 10 tickets out of 2900 has a probability of winning the cruise that can be calculated as:
[tex]p=10/2900\approx0.00345[/tex]
Each ticket cost $5, so he has spent $50 for the 10 tickets.
Then, the expected value of this operation is equal to the expected value of the earnings (probability of winning the prize multiplied by the value of the prize), minus the costs:
[tex]E(X)=p\cdot R-C\\\\E(X)=0.00345\cdot3000-50=10.35-50=-39.65[/tex]
The mathematical expectation of a student who purchases 10 tickets is -$39.65.
Select the correct answer.
Four-thirds times the sum of a number and 8 is 24. What is the number?
A.
40
B.
26
O c.
24
OD.
10
Answer: D. 10
Step-by-step explanation:
4/3 (x + 8) = 24
Multiply both sides by 3/4....
x + 8 = 18
x = 10
Brian set a goal to horseback ride more than 6 miles. The horse he rode averaged a speed of 4.6 miles per hour. A 2-column table with 4 rows titled Brian's Activity time (hours). Column 1 has entries hiking, mountain biking, horseback riding, cross-country skiing. Column 2 has entries 3, 1.45, 1.2, 0.75. Brian rode miles. Did he reach his goal?
Answer:
BRIAN DID NOT REACH HIS GOAL! Brian rode 5.52 miles!
Step-by-step explanation:
Answer:
he didn't reach his goal. he rode 5.52 miles
Step-by-step explanation:
−
50
54
−
100
40
+1.65=minus, start fraction, 54, divided by, 50, end fraction, minus, start fraction, 40, divided by, 100, end fraction, plus, 1, point, 65, equals
Answer:
[tex]\frac{-50}{54} - \frac{40}{100} +1.65 = 0.32[/tex]
Step-by-step explanation:
First of all, let us lay out the problem clearly:
[tex]\frac{-50}{54} - \frac{40}{100} +1.65[/tex]
This can be solved using a calculator, by first simplifying the individual fractions first, to decimals, then computing the addition and subtraction.
using your calculator, punch (-50 ÷ 54), your results should be:
-50 ÷ 54 = -0.93
Next, punch ( 40 ÷ 100), you should get 0.4
Now, join the individual results together to get:
- 0.93 - 0.40 + 1.65
Finally, still using the calculator, input the values as shown:
- 0.93 - 0.40 + 1.65 = 0.32
I need 100,000,000$ for my vacation. I only have 90,000,000. How many do I need?
Answer:
10,000,000.
Step-by-step explanation:
Because 10,000,000+90,000,000=100,000,000!
and 100,000,000-90,000,00= 10,000,000! and
100,000,000-10,000,000=90,000,000!
Answer:
$ 10 000 000
Step-by-step explanation:
100 000 000-90 000 000=10 000 000
What is the solution to the linear function? 2/3x - 1/2 = 1/3 + 5/6x
Answer:
x = -5
Step-by-step explanation:
You are often told to start a problem like this by clearing fractions. Multiply the equation by the least common denominator of the fractions. Here, that value is 6.
4x -3 = 2 +5x . . . . multiply the equation by 6
-5 = x . . . . . . . . . . . add -2-4x to both sides
The solution is x = -5.
_____
If you're comfortable with arithmetic using fractions, you can "cut to the chase." Subtract 2/3x+1/3 from both sides:
(2/3x -1/2) -(2/3x +1/3) = (1/3 +5/6x) -(2/3x +1/3)
-1/2 -1/3 = 5/6x -2/3x . . . . simplify a little
-5/6 = 1/6x . . . . . . . . . . . . .simplify more
-5 = x . . . . . . multiply by 6
a) A large hotel in Miami has 900 rooms (all rooms are equivalent). During Christmas, the hotel is usually fully booked. However, as it is possible for a customer to cancel their reservation, the hotel overbooks its rooms. 1000 people were given assurance of a room. Let us assume that each customer cancels their reservation with a probability of 0.1. If the total number of customers who still keep their booking is more than 900, the hotel has to unfortunately send some customers to other accommodation. What is the probability that this happens, as per the Central Limit Theorem
Answer:
14.69% probability that this happens
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use 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.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
1000 people were given assurance of a room.
This means that [tex]n = 1000[/tex]
Let us assume that each customer cancels their reservation with a probability of 0.1.
So 0.9 probability that they still keep their booking, which means that [tex]p = 0.9[/tex]
Probability more than 900 still keeps their booking:
[tex]n = 1000, p = 0.9[/tex]
So
[tex]\mu = 0.9, s = \sqrt{\frac{0.9*0.1}{1000}} = 0.0095[/tex]
901/1000 = 0.91
So this is 1 subtracted by the pvalue of Z when X = 0.91.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{0.91 - 0.9}{0.0095}[/tex]
[tex]Z = 1.05[/tex]
[tex]Z = 1.05[/tex] has a pvalue of 0.8531
1 - 0.8531 = 0.1469
14.69% probability that this happens
which equation is an identity?
Answer:
Option (3).
Step-by-step explanation:
Option (1).
3(x - 1) = x + 2(x + 1) + 1
3x - 3 = x + 2x + 2 + 1
3x - 3 = 3x + 3 [Not True]
Therefore, this equation is not an identity.
Option (2).
x - 4(x + 1) = -3(x + 1) + 1
x - 4x - 4 = -3x - 3 + 1
-3x - 4 = -3x - 2 [Not true]
Therefore, this equation is not an identity.
Option (3).
2x + 3 = [tex]\frac{1}{2}(4x + 2) + 2[/tex]
2x + 3 = 2x + 1 + 2
2x + 3 = 2x + 3 [True]
Therefore, this equation is an identity.
Option (4).
[tex]\frac{1}{2}(6x-3)=3(x+1)-x-2[/tex]
3x - 1.5 = 3x + 3 - x - 2
3x - 1.5 = 2x + 1 [Not true]
Therefore, this equation is not an identity.
Answer:
2x + 3 = 1/2(4x + 2) + 2
Step-by-step explanation:
Which of the following is the solution to 9|x-1|=-45
Answer:
No solutions.
Step-by-step explanation:
9|x-1|=-45
Divide 9 into both sides.
|x-1| = -45/9
|x-1| = -5
Absolute value cannot be less than 0.
Answer:
No solution
Step-by-step explanation:
=> 9|x-1| = -45
Dividing both sides by 9
=> |x-1| = -5
Since, this is less than zero, hence the equation has no solutions
A group of 50 people were asked their gender and if they liked cats. The data from the survey are shown in the Venn diagram. Determine the value for each variable in the two-way table.
Answer:
a = 13,
b = 28,
c = 6,
d = 22,
e = 31
Step-by-step explanation:
E = 15 +16 = 31
6 males like cats ( the middle section) so C = 6
d = 6 +16 = 22
a = 19-6 = 13
b = 50-22 = 28
so in order: a = 13, b = 28, c = 6, d = 22, e = 31
Bob can row 12 mph in still water. The total time to travel downstream and return upstream to the starting point is 4 hours. If the total distance downstream and back is 36 miles, determine the speed of the river (current speed).
Answer:
[tex]\boxed{\sf \ 6 \ mph \ }[/tex]
Step-by-step explanation:
when Bob travels downstream his speed is 12 + x
where x is the speed of the river
he travels 36/2 = 18 miles
it takes
[tex]\dfrac{18}{(12+x)}[/tex]
hours to do it
when Bob travels upstream his speed is 12 - x
it takes
[tex]\dfrac{18}{(12-x)}[/tex]
hours to do it
finally, it takes
[tex]\dfrac{18}{(12+x)}+\dfrac{18}{(12-x)}=4[/tex]
[tex]<=> 18(12-x+12+x)=4(12+x)(12-x)\\\\<=> 18*24=4(12^2-x^2)\\<=> 4x^2=576-432=144\\<=> 2x=12\\ <=> x = 6[/tex]
So the current speed is 6mph
it takes 1 hour to downstream and 3 hours to upstream
hope this helps
The speed of the river will be 6 mph.
What is Speed?
Speed of any object is defined by dividing the distance from the given time.
It can be written as;
Speed = Distance / Time
Given that;
Bob can row 12 mph in still water.
The total time to travel downstream and return upstream to the starting point is 4 hours.
The total distance downstream and back is 36 miles.
Let x is the speed of the river.
Then, Bob speed when it travel downstream = 12 + x
And, Distance = 36 / 2 = 18 miles
Hence, Time taken by Bob = 18 / (12 + x)
And, Bob speed when it travel upstream = 12 - x
And, Distance = 36 / 2 = 18 miles.
Hence, Time = 18 / (12 - x)
Since, Total time = 4 hours.
So, we can formulate;
18 / (12 + x) + 18 / (12 - x) = 4
18 (1/ (12 + x) + 1 / (12 - x)) = 4
18 ( 12 - x + 12 + x ) / (12- x)(12 + x) = 4
18 × 24 = 4 (12² - x²)
18 × 6 = 144 - x²
x² = 144 - 108
x² = 36
x = 6
Thus, The speed of the river will be 6 mph.
Learn more about the speed visit:
https://brainly.com/question/14719933
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What is the formula for area of a trapezuim??
Answer:
The formula is 1/2h(a+b)
h stands for the perpendicular height
a and b stand for the two horizontal lengths which are parallel to each other
