Answer:
(A) Probability that the port handles less than 5 million tons of cargo per week is 0.7291.
(B) Probability that the port handles 3 or more million tons of cargo per week is 0.9664.
(C) Probability that the port handles between 3 million and 4 million tons of cargo per week is 0.2373.
(D) The number of tons of cargo per week that will require the port to extend its operating hours is 3.65 million tons.
Step-by-step explanation:
We are given that the port of South Louisiana, located along 54 miles of the Mississippi River between New Orleans and Baton Rouge.
The U.S. Army Corps of Engineers reports that the port handles a mean of 4.5 million tons of cargo per week with a standard deviation of 0.82 million tons.
Let X = Number of tons of cargo handled per week
SO, X ~ Normal([tex]\mu=4.5,\sigma^{2}=0.82^{2}[/tex])
The z score probability distribution for normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean = 4.5 million tons
[tex]\sigma[/tex] = standard deviation = 0.82 million tons
(A) Probability that the port handles less than 5 million tons of cargo per week is given by = P(X < 5 million tons)
P(X < 5) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{5-4.5}{0.82}[/tex] ) = P(Z < 0.61) = 0.7291
The above probability is calculated by looking at the value of x = 0.61 in the z table which has an area of 0.7291.
(B) Probability that the port handles 3 or more million tons of cargo per week is given by = P(X [tex]\geq[/tex] 3 million tons)
P(X [tex]\geq[/tex] 3) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\geq[/tex] [tex]\frac{3-4.5}{0.82}[/tex] ) = P(Z [tex]\geq[/tex] -1.83) = P(Z [tex]\leq[/tex] 1.83)
= 0.9664
The above probability is calculated by looking at the value of x = 1.83 in the z table which has an area of 0.9664.
(C) Probability that the port handles between 3 million and 4 million tons of cargo per week is given by = P(3 million tons < X < 4 million tons)
P(3 million tons < X < 4 million tons) = P(X < 4) - P(X [tex]\leq[/tex] 3)
P(X < 4) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{4-4.5}{0.82}[/tex] ) = P(Z < -0.61) = 1 - P(Z [tex]\leq[/tex] 0.61)
= 1 - 0.7291 = 0.2709
P(X [tex]\leq[/tex] 3) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{3-4.5}{0.82}[/tex] ) = P(Z [tex]\leq[/tex] -1.83) = 1 - P(Z < 1.83)
= 1 - 0.9664 = 0.0336
The above probability is calculated by looking at the value of x = 0.61 and x = 1.83 in the z table which has an area of 0.7291 and 0.9664 respectively.
Therefore, P(3 < X < 4) = 0.2709 - 0.0336 = 0.2373
(D) Now, it is given that 85% of the time the port can handle the weekly cargo volume without extending operating hours, that means;
P(X > x) = 0.85 {where x is the required no. of tons of cargo}
P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{x-4.5}{0.82}[/tex] ) = 0.85
P(Z > [tex]\frac{x-4.5}{0.82}[/tex] ) = 0.85
In the z table, the critical value of x which represents top 85% area is given as -1.036, that is;
[tex]\frac{x-4.5}{0.82} = -1.036[/tex]
[tex]{x-4.5} = -1.036\times 0.82[/tex]
x = 4.5 - 0.85 = 3.65 million tons
Hence, the number of tons of cargo per week that will require the port to extend its operating hours is 3.65 million tons.
A bakery sold 100 mocha cupcakes in a day, which was 20% of the total number of cupcakes sold that day. How many total cupcakes did the bakery sell that day?
Answer:
500
Step-by-step explanation:
percentage is the quantitative way to express number of things out of 100 things.
For example : 20% of bananas are ripe.
it means that if there are 100 apples, 20 are ripe.
Let the total number of cupcakes sold that day be X
20% of total number of cupcakes sold = 20% of X = (20/100) * X __1
It is given that 20% of total number of cupcakes sold is equal to 100
Thus the equation 1 should be equal to 100.
Writing it mathematically we have
(20/100) * X = 100
=> 0.2X = 100
=> X = 100/0.2 = 500
500 cupcakes did the bakery sell that day.
A jar is 25 filled with water. If 750 ml more water is poured into the jar, it becomes full. What is the capacity of the jar?
Answer:
775 ml
Step-by-step explanation:
Answer:
775
Step-by-step explanation:
25 plus 50 equals 75.700 plus 75= 775 ml.
if 9 more than twice a number is 3 less than three times the same number, what is the number?
Answer:
the number is 12
Step-by-step explanation:
9+2x=3x-3
9+3=3x-2x
12=x
The required number is 12.
What are linear equation?A linear equation only has one or two variables. No variables in a linear equation is raised to power greater than 1 or used as denominator of a fraction.
Now it is given that,9 more than twice a number is 3 less than three times the same number.
Let the number be x.
So, 9 more than twice a number = 9 +2x
and, 3 less than three times the same number = 3x - 3
Hence we have,
9 + 2x = 3x - 3
Adding 3 both the side we get,
12 + 2x = 3x
Now substracting 2x both the side we get,
x = 12
Hence the number is 12.
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what is the mean of :20 20 20 22 22 24 26 26 26
The mean of a set of numbers is the sum divided by the number of terms.
Answer: 22.9
Answer:
YOU ADD AND DIVIDE FOR THE MEAN
Step-by-step explanation:
add 20 + 20 + 20 + 22 + 22 + 24 + 26 + 26 + 26 equaling to = 206
divide by 9 equaling to = 22.88
Use the given values of n and p to find the minimum usual value μ - 2σ and the maximum usual value μ + 2σ.
n = 2136, p = 3/7
Answers:
1. Minimum: 843.1; maximum: 987.75
2. Minimum: 961.17; maximum: 869.69
3. Minimum: 892.56; maximum: 938.3
4. Minimum: 869.69; maximum: 961.17
Answer:
[tex] \mu -2\sigma = 915.428 - 2* 22.87=869.69[/tex]
[tex] \mu +2\sigma = 915.428 + 2* 22.87=961.17[/tex]
And the best option would be:
4. Minimum: 869.69; maximum: 961.17
Step-by-step explanation:
We can assume that the variable of interst X is distributed with a binomial distribution and we can use the normal approximation.
For this case the mean would be given by:
[tex] E(X) = np = 2136 *(\frac{3}{7})= 915.428[/tex]
And the standard deviation would be:
[tex] \sigma = \sqrt{2136*(\frac{3}{7}) (1-\frac{3}{7})} =22.87[/tex]
And if we find the limits we got:
[tex] \mu -2\sigma = 915.428 - 2* 22.87=869.69[/tex]
[tex] \mu +2\sigma = 915.428 + 2* 22.87=961.17[/tex]
And the best option would be:
4. Minimum: 869.69; maximum: 961.17
5,-5/2,5/4,-5/8 what is the 5th term
Answer: your answer would be 5/16th :)
Answer:
5/16
Step-by-step explanation:
The common ratio is -5/2 / 5 = -1/2
Xn = 5 × (-1/2)^(n-1)
X5 = 5 × (-1/2)^(5-1)
X5 = 5 × (-1/2)^(4) = 5/16
ANYONE PLZZZ THIS IS DUE IN AN HOUR. Will mark the brainliest
Answer:
0.96 in^3
Step-by-step explanation:
Are those the only three choices? Anyway, I hope this helps
What's the answer please?
Answer:
1. 3
2. 2
3. 6
Step-by-step explanation:
1. 3 * 3 = 9
2. 5 - 2 = 3
3. 3 + 6 = 9
A new screening test for Lyme disease is developed for use in the general population. The sensitivity and specificity of the new test are 60% and 70%, respectively. Three hundred people are screened at a clinic during the first year the new test is implemented. Assume the true prevalence of Lyme disease among clinic attendees is 10%.
Calculate the following values:
The predictive value of a positive test
The predictive value of a negative test
Answer:
predictive value of a positive test = 18.18%
predictive value of a negative test = 94.03%
Step-by-step explanation:
Sensitivity = 60% = 0.6
Specificity = 70% = 0.7
Let True Positive = TP
True Negative = TN
False Negative = FN
[tex]Sensitivity = \frac{TP}{TP + FN} \\0.6 = \frac{TP}{TP + FN} \\0.6TP + 0.6FN = TP\\0.4TP = 0.6FN\\TP = 1.5 FN[/tex]
[tex]Specificity = \frac{TN}{TN + FP} \\0.7 = \frac{TN}{TN + FP} \\0.7TN + 0.7FP = TN\\0.7FP = 0.3 TN\\TN = 7/3 FP[/tex]
Prevalence = 10% = 0.1
Three hundred people are screened, [tex]T_{total} = 300[/tex]
Total number of people having the disease, [tex]T_{disease} = ?[/tex]
[tex]Prevalence = \frac{T_{disease} }{T_{total} } \\0.1 = \frac{T_{disease} }{300 }\\T_{disease} = 30[/tex]
[tex]T_{disease} = TP + FN\\30 = TP + FN[/tex]
But TP = 1.5 FN
30 = 1.5 FN + FN
30 = 2.5 FN
FN = 30/2.5
FN = 12
TP = 1.5 FN = 1.5 * 12
TP = 18
[tex]FP + TN = T_{total} - T_{disease} \\FP + TN = 300 - 30\\FP + TN = 270\\FP + \frac{7}{3} FP = 270\\\frac{10}{3} FP = 270\\FP = 27 * 3\\FP = 81[/tex]
81 + TN = 270
TN = 189
To calculate the Predictive value of positive test (PPT)
[tex]PPT = \frac{TP}{TP + FP} * 100\\PPT = \frac{18}{18+81} * 100\\PPT = \frac{18}{99} * 100\\PPT = 18.18 \%[/tex]
To calculate the Predictive value of negative test (PNT)
[tex]PPT = \frac{TN}{FN + TN} * 100\\PPT = \frac{189}{189+12} * 100\\PPT = \frac{189}{201} * 100\\PPT = 94.03 \%[/tex]
What is the circumference of the circle? Use 3.14 for Pi. A circle with radius 6.4 centimeters.
Answer:
C≈40.21cm
Step-by-step explanation:
Answer:
40.192
Step-by-step explanation:
the radius is half of the diameter so the diameter is 12.8 now 12.8 times pi / 3.14
59 people showed up to the party. There were 3 less men than women present. How many men were there?
Answer:
28 MEN
Step-by-step explanation:
X + X-3=59
2X-3=59
2X=62
X=31
MEN=31-3=28
Subtract and write in standard form
(8x – 6x3 + 5x2) - (2x2 + 2x - 7x3)
Answer:
x^3 +3x^2 +6x
Step-by-step explanation:
Eliminate parentheses using the distributive property. Collect terms. Standard form has the exponents decreasing.
= 8x -6x^3 +5x^2 -2x^2 -2x +7x^3
= x^3(-6 +7) +x^2(5 -2) +x(8 -2)
= x^3 +3x^2 +6x
mary had 1 3/4 pound of blackberries. Mary's friend ate 3/4 of the blackberries. How many pounds of blackberries did Mary friend eat?
Answer:
Shown in the explanation below,
Step-by-step explanation
Mary had 1 3/4 pounds
Mary friend eat 3/4 blackberry which is
3/4. × 7/4 = 21/ 16 = 1 5/16
What is 841,487 rounded to the nearest ten thousand?
Answer:
840,000
Step-by-step explanation:
841,487 sice the ten thousands place is under the number five you round down to 840,000
PLEASE ANSWER ASAP! WILL GIVE ~BRAINLIEST~ ANSWER (IF CORRECT)
Rewrite the expression in the form 9^n
9^7/9^5
Answer:
a^b/a^c = a^b-c
9^7/9^5=9^7-5
=9^2 ( ANSWER )
Step-by-step explanation:
please mark me BRAINLIEST
Use the definition of continuity and the properties of limits to show that the function
f(x) = x2 + 5(x - 2)7 is continuous at x = 3.
Answer:
Applied the definition and the limit.
They had the same result, so the function is continuous.
Step-by-step explanation:
At function f(x) is continuous at x = a if:
[tex]\lim_{x \to a} f(x) = f(a)[/tex]
In this question:
[tex]f(x) = x^{2} + 5(x-2)^{7}[/tex]
At x = 3.
[tex]\lim_{x \to 3} x^{2} + 5(x-2)^{7} = 3^{2} + 5(3-2)^{7} = 14[/tex]
[tex]f(3) = 3^{2} + 5(3-2)^{7} = 14[/tex]
Since [tex]\lim_{x \to 3} f(x) = f(3)[/tex], f(x) is continuous at x = 3.
The radius of the circle below intersects the unit circle at ( 3/5 • 4/5 What is the approximate value of e?
Answer:
12/25
Step-by-step explanation:
multiply the fractions.
multiply the numbers.
A school survey asked students which candidate they supported for class president. The survey data are shown in the relative frequency table. What percentage of females polled supported Wilson?
Answer:
D about 44%
Step-by-step explanation:
just took the tests
Using the percentage concept and the given table, it is found that about 39% of males supported Wilson.
What is a percentage?
The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:
[tex]P=\frac{a}{b}\times 100%[/tex]
In this problem, males are 46% of the sample, and 18% are males that supported Wilson,
[tex]P=\frac{18}{46} \times 100=39[/tex]
About 39% of males supported Wilson.
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Which expression is equivalent to (sf)(6)
Answer:
(st)(6)= s(6) * t(6)
Step-by-step explanation:
(st)(6)
(st)(x)= s(x) * t(x) we multiply it
(st)(6)= s(6) * t(6)
Hope this helps.
PLS HELP ASAP twenty points Find the value of c such that the expression is a perfect square trinomial.
x^2-14x+c
Answer:
49
Step-by-step explanation:
x^2-14x+c
Take the coefficient of x
-14
Divide by 2
-14/2 = -7
Square it
(-7)^2
49
This is the number you add
The Community College Survey of Student Engagement reports that 46% of the students surveyed rarely or never use peer or other tutoring resources. Suppose that in reality 40% of community college students never use tutoring services available at their college. In a simulation, we select random samples from a population in which 40% do not use tutoring. For each sample, we calculate the proportion who do not use tutoring. If we randomly sample 100 students from this population, the standard error is approximately 5%. Would it be unusual to see 46% who do not use tutoring in a random sample of 100 students?a) Yes, this would be unusual because 46% is more than one standard error from the mean. It is very rare for a sample to be more than one standard error from mean. b) Yes, this would be unusual because 46% is 6% higher than 40%. c) No, this would not be unusual because the error is only 6%. d) No, this would not be unusual because 46% is only 1.2 standard errors from 40%.
Answer:
d) No, this would not be unusual because 46% is only 1.2 standard errors from 40%.
Step-by-step explanation:
Problems of normally distributed samples are 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.
If the z-score is higher than 2 or lower than -2, X is unusual.
In this question:
Mean = 40%. So [tex]\mu = 0.4[/tex]
Standard error = 5%. So [tex]\sigma = 0.05[/tex]
Is 46% unusual?
We have to find Z when X = 0.46. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0.46 - 0.4}{0.05}[/tex]
[tex]Z = 1.2[/tex]
1.2 is lower than 2, that is, it is only 1.2 standard deviations from the mean. So 46% is not unusual.
So the correct answer is:
d) No, this would not be unusual because 46% is only 1.2 standard errors from 40%.
Determin The Constant of proportionality
l varies derectly as h; when l = 112,h = -16
Answer:
-7
Step-by-step explanation:
l = kh . . . . . l is proportional to h with proportionality constant k
112 = k·(-16) . . . . . . use the given numbers
k = -112/16 = -7 . . . divide by the coefficient of k
The constant of proportionality is -7.
This month you earned 8% more than last month write two different expressions to show this
Answer:
X+8/100x ; X+0.08x
Step-by-step explanation:
Let x = last month's earning
8% =8/100 or 0.08
8/100 of x= 8/100x 008 of x=0.08x
last month + 8/100 of last month:
x+8/100x
last month + 0.08 of last month:
x+0.08x
Those are your two answers. I am sorry if they are wrong. I am not the best at math, but I tried supplying the answers as best as I could.
x2 + y2 + 10x + 12y + 25 = 0
What is the center of this circle ?
What is the radius of this circle ?
units
Answer:
Center (- 5, - 6)
Radius 6 units
Step-by-step explanation:
x² + 10x + y² + 12y + 25 = 0
x² + 2*5*x + 5² + y² + 2*6*y + 6² - 5² - 6² + 25 = 0
(x + 5)² + (y + 6)² - 6² = 0
(x + 5)² + (y + 6)² = 6²
Center (- 5, - 6)
Radius 6 units
You have $125 in a savings account and you deposit an equal amount into your account each week. After 5 weeks the account holds $170. Write an equation that represents the amount y
(in dollars) of money in the account after x
weeks.
Answer:
The answer is 9
Step-by-step explanation:
if u 170-125= 45 then u divide 5 into 45 and u get 9
ASAP! GIVING BRAINLIEST! Please read the question THEN answer correctly! No guessing.
Answer:
Step-by-step explanation:
f(x) = x^2
reflect along the x-axis
g(x) = -x^2
expand vertilcally by a factor of 1/3
g(x) = (-1/3) x^2
move horizontally 4 units to the left
g(x) = (-1/3) (x+4)^2
hope this helps
Answer:
B. The graph of G(x) is the graph of F(x) stretched vertically, flipped over the x-axis, and shifted 4 units to the left.
Step-by-step explanation:
The [tex]\frac{-1}{3}[/tex] is less than one, making it stretch wider, and the (-) made it flip over the x-axis. The +4 in [tex](x+4)^2[/tex] made the function on the graph shift 4 units to the left.
This makes the correct answer be "B."
There were 128 participants in an online Fortnite tournament. The table below shows the number of people that were left in the tournament after each round. After each round the # decreases. Round 1=64,2=32,3=16,4=8. Determine how many more rounds until there’s a winner & explain
Answer:
7 rounds
Step-by-step explanation:
After the 5th round, 8 divide by 2 equals 4. After the 6th round, 4 divided by 2 equals 2. After the 7th round, 2 divided by 2 equals 1 determining a winner. After every round, the number of people is decreased by dividing by 2.
Hope this helps!!! PLZ MARK BRAINLIEST!!! GG’s
For a function p(x), as — then p(x) — 4. Which of the following graphs
could be p(x)?
The following options are available for a car wash
Standard wash £8
Deluxe wash £12
In one day 60 customers have their car washed. The ratio of customers choosing the standard car wash to those choosing the deluxe car wash is 3:2
What is the total takings at the car wash for the day?
Answer:
£576
(would really, reallly appreciate the brainliest)
Step-by-step explanation:
8 * 60 * 3/5 + 12 * 60 * 2/5
Find the equation for the line that passes through the point
(−3,−1) and that is parallel to the line with the equation
y=1/2x-3
Answer:
work is shown and pictured