Integrate both sides of the differential equation you found for dp to obtain an equation for p. Your equation should then include a constant that depends on initial conditions. Determine the value of this constant by assuming that the pressure at some reference height y0 is p0. Express your answer in terms of quantities given in the problem introduction along with y0 and p0.
Answers
Answer:
Step-by-step explanation:
FIND THE SOLUTION BELOW
Related Questions
please help asap thanks in advance.
Answers
Answer:
hope this helps
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2.
1. A small town's population is growing at
an exponential rate. In 2010, there were
700 residents in the town. In 2011 there
were 770 residents and in 2012, there
were 847 residents. What equation can
be used to determine p, the number of
residents in 2018?
Answers
Answer:
[tex]P(8)=700\cdot(1.1)^8\approx 1500[/tex], where t is the number of years since 2010.
Step-by-step explanation:
See my attached image for an explanation!
Add a cell phone assembly plant, 80% of the cell phone keypad pass inspection. A random sample of 181 keypads is analyzed. Find the probability that less than 76 in the sample keypads pass inspection.
Answers
Answer:
0% probability that less than 76 in the sample keypads pass inspection.
Step-by-step explanation:
I am going to use the normal approximation to the binomial 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 samples 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 this problem, we have that:
[tex]n = 181, p = 0.8[/tex]
So
[tex]\mu = E(X) = np = 181*0.8 = 144.8[/tex]
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{181*0.8*0.2} = 5.38[/tex]
Find the probability that less than 76 in the sample keypads pass inspection.
Using continuity correction, this is [tex]P(X < 76 - 0.5) = P(X < 75.5)[/tex], which is the pvalue of Z when X = 75.5.
So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{75.5 - 144.8}{5.38}[/tex]
[tex]Z = -12.88[/tex]
[tex]Z = -12.88[/tex] has a pvalue of 0
0% probability that less than 76 in the sample keypads pass inspection.
Of the 100 students enrolled at the dance studio, 50 take ballet and 24 take tap dancing. Eight of the students who take ballet also take tap dancing. If a student at the studio is chosen at random, find the probability that they take ballet, if it is known that they do not take tap dancing
Answers
Answer:
42 over 100
Step-by-step explanation:
Answer:21/38
Step-by-step explanation:
A woman puts $1 million dollars into a savings account that she is not going to touch. She isn’t going to work either but she will live off the interest. If the rate of interest on the account is 6 1/2% what is the amount she will make in interest? If her totally expenses last year is $47,000 will she be able to live off the interest? Justify your answer
Answers
Answer:
i. The amount made in interest is $65,000.
ii. Yes, because her expenses is lesser that her interest.
Step-by-step explanation:
i. The woman puts $1,000,000 in a savings account with an interest rate of 6[tex]\frac{1}{2}[/tex]%.
Interest rate = 6[tex]\frac{1}{2}[/tex]% = [tex]\frac{13}{200}[/tex]
The amount she would make in interest = [tex]\frac{13}{200}[/tex] × 1,000,000
= 65,000
The amount made in interest is $65,000.
ii. The total of her expenses last year is $47,0000 which is lesser than the amount made in inerest.
After her total expenses, should would have a remainder of;
= $65,000 - $47,0000
= $18,000
Therefore, she would be able to live off the interest.
A grain silo is shaped like a cylinder with a cone-shaped top. The cylinder is 30 feet tall. The volume of the silo is 1152 cubic feet. Find the radius of the silo.
Answers
Answer:
The radius of the silo is 3.49 m.
Step-by-step explanation:
We have,
Height of the cylinder, h = 30 ft
Volume of cylindrical shaped grain silo, [tex]V=1152\ ft^3[/tex]
It is required to find the radius of silo. The formula of volume of cylinder is given by :
[tex]V=\pi r^2h[/tex]
r is radius
[tex]r=\sqrt{\dfrac{V}{\pi h}} \\\\r=\sqrt{\dfrac{1152}{\dfrac{22}{7}\times 30 }} \\\\r=3.49\ m[/tex]
So, the radius of the silo is 3.49 m.
What is the interquartile range of the data ? 0,2,4,0,2,3,8,6
Answers
(arrange the data set from least to greatest)
0, 0, 2, 2, 3, 4, 6, 8
(find the median: *the middle number*)
Median: 2.5
Lower quartile: 1
Upper quartile: 5
Interquartile range : upper quartile - lower quartile = answer
Interquartile range: 5 - 1 = 4
So the IQR or interquartile for the following data set is 4.
Which best explains why the expression plus or minus StartRoot b squared minus 4 a c EndRoot cannot be rewritten as b plus or minus StartRoot negative 4 a c EndRoot during the next step?
Answers
Answer:
Step-by-step explanation:
let the quadratic eq. be ax²+bx+c=0
or x²+b/a x+c/a=0
or x²+b/ax=-c/a
to complete the square add both sides (b/2a)²or b²/4a²
x²+b/a x+(b/2a)²=b²/4a² -c/a
(x+b/2a)²=(b²-4ac)/(4a²)
taking square root
[tex]x+\frac{b}{2a} =\pm \frac{\sqrt{b^2-4ac} }{2a} \\or\\x=-\frac{b}{2a} \pm\frac{\sqrt{b^2-4ac} }{2a} \\or\\x=\frac{-b \pm\sqrt{b^2-4ac} }{2a}[/tex]
now you must know why -b and not +b
Final answer:
The expression ± √(b² - 4ac) in the quadratic formula refers to the discriminant and cannot be rewritten as b ± √(-4ac) because it would incorrectly separate b from the discriminant and alter the expression's meaning, leading to incorrect solutions.
Explanation:
The student is asking about the quadratic formula, which is used to find the solutions to a quadratic equation of the form at² + bt + c = 0. The formula for the solutions is given by:
-b ± √(b² - 4ac) / 2a
The term ± √(b² - 4ac) cannot be rewritten as b ± √(-4ac) because it alters the original expression's meaning. The square root is taken of the entire expression b² - 4ac, which represents the discriminant of the quadratic equation. It provides information on the nature and number of roots of the equation. Separating b from the discriminant before taking the square root would calculate a different value and therefore lead to incorrect solutions.
Example:
When you substitute the given values, say a = 1, b = 0.0211, and c = -0.0211, into the quadratic formula, you will get:
-0.0211 ± √((0.0211)² - 4(1)(-0.0211)) / (2(1))
Changing the formula to b ± √(-4ac) incorrectly suggests that you can separate b from the discriminant and take the square root of -4ac alone, which would not yield a correct solution.
Hector took out a loan of $900 for 18 months at a rate of 5.5% annually. How much will he pay in interest on the loan?
Answers
Answer:
Hector will pay $74.25 interest on the loan.
Step-by-step explanation:
Hector took out a loan of $900 for 18 months at a rate of 5.5% annually.
Principal amount = $900
Rate of interest = 5.5%
Time = 18 months = 1.5 years
Formula for interest :
[tex]I=\frac{P\times R\times T}{100}[/tex]
[tex]=\frac{900\times 5.5\times 1.5}{100}[/tex]
= 74.25
Hector will pay $74.25 interest on the loan.
Birdseed costs $0.52 a pound and sunflower seeds cost $0.82 a pound. Angela Leinenbachs' pet store wishes to make a 40-pound mixture of birdseed and sunflower seeds that sells for $0.72 per a pound. How many pounds of each type of seed should she use?
Answers
Answer: she should use 13 pounds of birdseed and 27 pounds of sunflower seeds.
Step-by-step explanation:
Let x represent the number of pounds of birdseed that she should use.
Let y represent the number of pounds of sunflower seeds that she should use.
Angela Leinenbachs' pet store wishes to make a 40-pound mixture of birdseed and sunflower seeds. It means that
x + y = 40
Birdseed costs $0.52 a pound and sunflower seeds cost $0.82 a pound. If the mixture would sell for $0.72 per a pound, then the total cost of the mixture would be 0.72 × 40 = $28.8
The equation would be
0.52x + 0.82y = 28.8- - - - - - - - - -1
Substituting x = 40 - y into equation 1, it becomes
0.52(40 - y) + 0.82y = 28.8
20.8 - 0.52y + 0.82y = 28.8
- 0.52y + 0.82y = 28.8 - 20.8
0.3y = 8
y = 8/0.3 = 27
x + y = 40
x + 27 = 40
x = 40 - 27
x = 13
i’ll mark brainlist the first personify gets it
Answers
I am going to assume 10.42 is 10 minutes 42 secons.
10 min * 60 seconds / per minute, = 600 seconds
600 + 42 = 642 seconds starting
-
8 min * 60 seconds / per minute, = 480 seconds objective
To solve for how long this will take set up an equation,
642 - 1.6t = 480
162 = 1.6t
t = 101.25 days
Since time has a decial, it needs to be rounded up in order for her to be fully below 8 minutes.
Therefore the answer is 102 days.
What are the quotient and remainder of (3x^4+ 2x^2 - 6x + 1) = (x + 1)
Answers
Answer: Im 75% sure the answer is A. Its either A or B.
Step-by-step explanation:
The ordered pairs in the table below represent a linear function.
What is the slope of the function?
One-fourth
One-half
2
4
Answers
Answer:
2Step-by-step explanation:
The ordered pairs are
x | y 2 | 3 5 | 9The slope is:
m = (y2 - y1)/(x2 - x1) m = (9 - 3)/(5 - 2)= 6/3 = 2Answer is 2
Answer:
4
Step-by-step explanation:
The graph is:
x y
1/4 2
1/2 4
Slope formula is (y2-y1/x2-x1)
4-2/0.5-0.25
2/0.25
4
Best of Luck!
A relation is a special type of function.
A. True
B. False
(30) points
Answers
The probability that Linda receives spam e-mail is 4 percent. If she receives 520 e-mails in a week, about how many of them can she expect to be spam?
Answers
Answer:21 (2 sf)
Step-by-step explanation:
10%0f 520=52
1%0f 520=52 divide by 10 =5.2
5.2x4=20.8
=21 to 2sf
A right triangle whose hypotenuse is StartRoot 18 EndRoot18 m long is revolved about one of its legs to generate a right circular cone. Find the radius, height, and volume of the cone of greatest volume that can be made this way.
Answers
Answer:
V = [tex]\frac{1}{3}[/tex]π(8 - [tex]\frac{8}{3}[/tex])[tex]\sqrt{\frac{8}{3} }[/tex] = 9.11 [tex]m^{3}[/tex]
r = 4[tex]\frac{\sqrt{3} }{3}[/tex]
h = [tex]\sqrt{\frac{8}{3} }[/tex]
Step-by-step explanation:
Given that the right triangle whose hypotenuse is [tex]\sqrt{8}[/tex]
Let r is the radius of the cone Let h is the height of the coneWe know that:
[tex]r^{2} + h^{2} = 8[/tex]
<=> [tex]r^{2} = 8 - h^{2}[/tex]
The volume of the cone is:
V = π[tex]r^{2} \frac{1}{3} h[/tex]
<=> V = π[tex]\frac{1}{3}(8 - h^{2} )h[/tex]
Differentiate w.r.t h
[tex]\frac{dV}{dh}[/tex] = π [tex]\frac{1}{3}[/tex] (8 - [tex]3h^{2}[/tex])
For maximum/minimum: [tex]\frac{dV}{dh}[/tex] = 0
<=> π [tex]\frac{1}{3}[/tex] (8 - [tex]3h^{2}[/tex]) = 0
<=> [tex]h^{2}[/tex] = [tex]\frac{8}{3}[/tex]
<=> h = [tex]\sqrt{\frac{8}{3} }[/tex]
=> [tex]r^{2}[/tex] = [tex]\frac{16}{3}[/tex]
<=> r = 4[tex]\frac{\sqrt{3} }{3}[/tex]
So the volume of the cone is:
V = [tex]\frac{1}{3}[/tex]π(8 - [tex]\frac{8}{3}[/tex])[tex]\sqrt{\frac{8}{3} }[/tex] = 9.11 [tex]m^{3}[/tex]
Use the two-point form of the linear equation. Fill in the missing blanks using (1, 1) for (x1, y1). You will need both points to determine the slope, y2 − y1 x2 − x1 . y − 1 = − 2 3 − 1 6 − 1 x −
Answers
Answer: (-2, 3)
Step-by-step explanation:
Answer:
The point-slope form of a linear equation is a formula that allows a person to calculate the slope and point of intercept of a line, and then once you calculate the linear equation, you can calculate the x and y coordinate of any point on the line!
1. Choose two points on a line.
2. Indicate the y1 (the y coordinate of the first point) and y2 (the y coordinate of the second point).
3. Indicate the x1 (the x coordinate of the first point) and the x2 (the x coordinate of the second point)
4. Plug the previously identified variables into the slope formula where the slope is equal to (y2-y1)/(x2-x1)
5. Subtract y2 and y1.
6. Subtract x2 and x1.
7. Divide the quantity in #5 by the quantity in #6. This is your slope.
8. Observe the equation: y=mx+b where "m" is the slope calculated in #7.
9. Plug in the slope for "m"
10. Using one of the points identified earlier, plug in y1 into "y" and x1 into "x". Rearrange and solve for b.
11. Then plug in the value "b" into y=mx+b. Make sure to leave the unknown variables "x" and "y", but make sure to still plug in the "m" calculated earlier!
Which loan is likely to have the highest Annual Percentage Rate (APR)? All of the loans are $500 and include a finance charge of $20.
a. Term of 5 days
b. Term of 10 days
c. Term of 20 days
d. Term of 30 days
e. Term of 90 days
Answers
The loan with the shortest term, which is 5 days in this case, is likely to have the highest APR because the finance charge would have less time to be spread out.
Explanation:The loan that is likely to have the highest Annual Percentage Rate (APR) is the one with the shortest term when all other factors are equal. In this scenario, that would be the loan with a term of 5 days. This is due to the fact that APR is calculated by the annualizing the interest and fees associated with a loan, meaning the shorter the term of a loan, the higher the APR. For instance, a $500 loan with a $20 finance charge has a much higher APR over 5 days as compared to 30 days or 90 days as the finance charge would have lesser time to be spread out.
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What’s the value of Y?
Answers
Answer:
44
Step-by-step explanation:
if 88 is the right angle degree, that means the acute angle would be half of 88.
88÷2=44
Lily built a rectangular prism with cubes. The area of the base is 16 connecting cubes. It is 6 layers high what is the volume of his rectangular prism?
Answers
Answer:
Volume of prism is equal to [tex]96[/tex] units
Step-by-step explanation:
let the side of the cube be of one unit.
Then, the area of the base is equal to [tex]16[/tex] connecting cubes
Assuming a square base of the rectangular prism.
Length of one side of the base of rectangular prism [tex]= 4[/tex] units
Similarly, width of the base of rectangular prism [tex]= 4[/tex] units
The height of the rectangular prism is [tex]6[/tex] units
Volume of the prim [tex]=[/tex] Length [tex]*[/tex] Width [tex]*[/tex] Height
Substituting the given values in above equation, we get -
[tex]V = 4* 4* 6\\V = 96[/tex]
Volume of prism is equal to [tex]96[/tex] units
Final answer:
To find the volume of a rectangular prism, multiply the base area by the height. In this case, the volume of Lily's rectangular prism would be 96 cubic units.
Explanation:
The volume of a rectangular prism is calculated by multiplying the length, width, and height of the prism.
For this specific rectangular prism with a base area of 16 connecting cubes and 6 layers high, we can calculate the volume as follows:
Volume = Base Area x Height
Volume = 16 x 6
Volume = 96 cubic units
What is the surface area of this square pyramid
Answers
Answer 144 ft2
Step-by-step explanation:
Answer:
The surface area is 81 feet squared
Step-by-step explanation:
IM SO SORRY! the answer is 33 feet squared
Hayden is 59 inches tall and is standing on top of a ladder that is 2 yards y’all in inches what is the distance from the top of Hayden’s head to the ground
Answers
Answer:
131 inches
Step-by-step explanation:
1 yard = 36 inches
36 x 2 = 72
72 + 59 = 131
c:
Suppose Frances is a researcher at Beaded Gemsz, a company that makes beaded jewelry. She wants to evaluate whether using better equipment during the current year has increased jewelry-making productivity. The company's reporting team estimated an average daily production yield of 105 units per store from previous years. Frances conducts a one-sample z - test with a significance level of 0.08 , acquiring daily unit yield data from each of the stores' databases for 45 randomly selected days of the year. She obtains a P -value of 0.06 . The power of the test to detect a production increase of 12 units or more is 0.85 . What is the probability that Frances concludes that the new equipment increases the average daily jewelry production when in fact the new equipment has no effect
Answers
Answer:
There is 8% (P=0.08) that Frances concludes that the new equipment increases the average daily jewelry production when in fact the new equipment has no effect.
Step-by-step explanation:
We have one-sample z-test with a significance level of 0.08 and a power ot the test of 0.85.
In this test, the null hypothesis will state that the new equipment has the same productivity of the older equipment. The alternative hypothesis is that there is a significative improvement from the use of new equipment.
The probability that Frances concludes that the new equipment increases the average daily jewelry production when in fact the new equipment has no effect is equal to the probability of making a Type I error (rejecting a true null hypothesis).
The probability of making a Type I error is defined by the level of significance, and in this test this value is α=0.08.
Then, there is 8% that Frances concludes that the new equipment increases the average daily jewelry production when in fact the new equipment has no effect.
Two components in a rocket operate independently, and the probability that for every component to fail on a launch is p. Let X denote the number of launches required to have a failure of the first component, and let Y denote the number of launches required to have a failure of the second component, X, Y
Answers
Answer: p = X/(1-X)X + Y/(1-Y)Y
Step-by-step explanation:
How many one-third cubes are needed to fill the gap in the prism shown below?
A. 4
B. 8
C. 16
D. 24
Answers
The one-third cubes which are needed to fill the gap in the prism shown below are [tex]976[/tex].
What is cube ?Cube is a [tex]3D[/tex] solid object bounded by six square faces, facets or sides, with three meeting at each vertex.
Here we have,
Length [tex]=4\frac{2}{3}[/tex]
Breadth [tex]=4[/tex]
Height [tex]=2[/tex]
Here, we have the side of cube [tex]=\frac{1}{3}[/tex],
So, Total volume of the prism [tex]=l*b*h[/tex]
[tex]=2*4*4\frac{2}{3}[/tex]
[tex]=\frac{112}{3}[/tex]
Volume of a cube [tex]= a^{3}[/tex]
[tex]=(\frac{1}{3} )^{3}=\frac{1}{27}[/tex]
Total number of cubes [tex]= \frac{\frac{112}{3}}{\frac{1}{27} } =1008[/tex]
Volume of given cubes in prism [tex]= 32*\frac{1}{27} =\frac{32}{27}[/tex]
So, the gap left in the prism [tex]=\frac{112}{3} -\frac{32}{27} =\frac{976}{27}[/tex]
So, the number of cubes required [tex]=\frac{\frac{976}{27} }{\frac{1}{27} }=976[/tex]
Hence, we can say that the one-third cubes which are needed to fill the gap in the prism shown below are [tex]976[/tex].
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Suppose that $20,000 is invested in an account for which interest is compounding continuously at 3.14%. What is the value after 5 years? After 10 years? (Round your answers to two decimal places.) After how many years will the original investment be doubled? (Round your answer to two decimal places.)
Answers
Answer:
value after 5 years = $23,399.91
after 10 years = $27,377.79
Time it takes for the amount to double = 22.07 years
Step-by-step explanation:
For amounts that are compounded continuously, it means that the interest rate is is added to the investment amount at an infinite number of time, and the formula is given as:
A = P [tex]e^{r.t}[/tex], where:
A = Future value
P = present value
e = constant ≈ 2.7183
r = interest rate in decimal form
t = years
Now for value after 5 years;
A = ???
P = $20,000
r = 3.14% = 0.0314
t = 5 years
∴ A = P [tex]e^{r.t}[/tex]
= 20,000 [tex]e^{0.0314*5}[/tex]
= 20,000 × [tex]e^{0.157}[/tex] = 20,000 × 1.169995 = $23,399.91 ( to 2 decimal places)
(Note that the function '[tex]e[/tex]' can be punched directly from the calculator)
value after 10 years;
A = ???
P = $20,000
r = 3.14% = 0.0314
t = 10 years
∴ A = P[tex]e^{r.t}[/tex]
= 20,000 × [tex]e^{0.0314 * 10}[/tex]
= 20,000 × [tex]e^{0.314}[/tex] = $27,377.79 ( to 2 decimal places)
Time it will take to double the original investment;
A = P [tex]e^{r.t}[/tex]
where;
A = 40,000
P = 20,000
r = 0.0314
t =???
40,000 = 20,000 × [tex]e^{0.0314 * t}[/tex]
[tex]\frac{40,000}{20,000} = \frac{20,000}{20,000} * e^{0.0314*t}[/tex] (divide both sides by 20,000)
2 = [tex]e^{0.0314 * t}[/tex]
Next take the natural logarithm of both sides
㏑(2) = ㏑[tex]e^{0.0314 *t}[/tex] (㏑[tex]e[/tex] = 1; and the exponent can be brought down )
= 0.6931 = 0.0314 × t × 1
∴ t = [tex]\frac{0.06931}{0.0314}[/tex] = 22.07 years ( to 2 decimal places)
Calculate the value of an investment after 5 and 10 years with continuous compounding at a certain interest rate. Determine the time needed for an investment to double using the continuous compounding formula.
When calculating the future value of an investment with compound interest, we can use the formula A = Pert, where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial sum of money), r is the annual interest rate (as a decimal), t is the time the money is invested for in years, and e is the base of the natural logarithm.
Applying this formula, the future value of a $20,000 investment at a 3.14% interest rate compounded continuously for 5 years would be
After 5 years: $20,000 × [tex]e^{(0.0314 \times 5)[/tex] ≈ $23,914.83After 10 years: $20,000 × [tex]e^{(0.0314 \times 10)[/tex] ≈ $28,717.83Time to double: $20,000 × [tex]e^{(0.0314 \times t)[/tex] = $40,000 ⇒ t ≈ 22.10 yearsFind the arc length of the shaded region. Multiply through by #(3.14) Round solution to
tenth place. Ex. 1.2
90°
Answers
Given:
The radius of the circle is 12 units.
The central angle of the shaded region is 90°
We need to determine the arc length of the shaded region.
Arc length:
The arc length of the shaded region can be determined using the formula,
[tex]Arc \ length=(\frac{\theta}{360} ) 2 \pi r[/tex]
substituting [tex]\theta=90[/tex] and r = 12, we get;
[tex]Arc \ length=(\frac{90}{360} ) 2 (3.14)(12)[/tex]
Multiplying the terms, we have;
[tex]Arc \ length=\frac{6782.4}{360}[/tex]
Dividing, we get;
[tex]Arc \ length=18.84[/tex]
Rounding off to the nearest tenth, we get;
[tex]Arc \ length =18.8[/tex]
Thus, the arc length of the shaded region is 18.8 units.
Two functions are shown in the table below.
~
Complete the table on your own paper, then select the value that is a solution to f(x) = g(x). (2 points)
Group of answer choices
A. x = 2
B. x = 3
C. x = 5
D. x = 6
Answers
Answer:
D
Step-by-step explanation:
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HELP ME PLEASE!!
I WILL MARK AS BRANLIEST!!
16 POINTS!!
Answers
Answer:
y = 1.8x + 32
or
y = 9/ 5x + 32
Step-by-step explanation:
Used a slope calculator
The wait times in line at a grocery store are roughly distributed normally with an average wait time of 7.6 minutes and a standard deviation of 1 minute 45 seconds. What is the probability that the wait time is less than 7.9 minutes
Answers
Answer:
[tex]0.56749[/tex].
Step-by-step explanation:
We have been given that the wait times in line at a grocery store are roughly distributed normally with an average wait time of 7.6 minutes and a standard deviation of 1 minute 45 seconds. We are asked to find the probability that the wait time is less than 7.9 minutes.
First of all, we will convert 45 seconds into minutes by dividing by 60 as:
[tex]45\text{ Seconds}=\frac{45}{60}\text{ minutes}=0.75\text{ minutes}[/tex]
So 1 minute 45 seconds will be equal to 1.75 minutes.
Now, we will find z-score corresponding to 7.9 minutes using z-score formula.
[tex]z=\frac{x-\mu}{\sigma}[/tex]
z = z-score,
x = Random sample score,
[tex]\mu[/tex] = Mean,
[tex]\sigma[/tex] = Standard deviation.
[tex]z=\frac{7.9-7.6}{1.75}[/tex]
[tex]z=\frac{0.3}{1.75}[/tex]
[tex]z=0.17142\approx 0.17[/tex]
Now we will use normal distribution to find area under normal curve that corresponds to a z-score of 0.17 that is [tex]P(z<0.17)[/tex].
[tex]P(z<0.17)=0.56749[/tex]
Therefore, the probability that wait time is less than 7.9 minutes would be 0.56749.