Answer:
Ground distance of Bob from his friends house = 61 ft (Approx)
Step-by-step explanation:
Given:
Length of string = 75 ft
Angle with the ground = 35°
Find:
Ground distance of Bob from his friends house.
Computation:
Using trigonometric application:
⇒ Cos [tex]\theta[/tex] = Base / Hypotenuse
⇒ Cos 35° = Base / 75
⇒ 0.819 = Base / 75
⇒ Base = 61.425 ft
Ground distance of Bob from his friends house = 61 ft (Approx)
The mean age of 5 people in a room is 40 years. A person enters the room. The mean age is now 35. What is the age of the person who entered the room?
Answer:
10 years.
Step-by-step explanation:
Let total age of five people be x;
x/5 = 40
x = 40*5
x = 200.
Let age of new person be y;
(200 + y)/ 6 = 35
200 + y = 210
y = 210-200
y= 10.
The age of the new person is 10.
See ya!
Hope it helps!
Answer:
[tex]\boxed{\sf \ \ \ 10 \ y\ old \ \ \ }[/tex]
Step-by-step explanation:
Hello,
let s note a, b, c, d, e the age of the 5 people
we can say that
[tex]\dfrac{a+b+c+d+e}{5}=40[/tex]
So [tex]a+b+c+d+e=5*40=200[/tex]
Now there is another person , let s note his age x
we can write
[tex]\dfrac{a+b+c+d+e+x}{6}=35\\<=> a+b+c+d+e+x=6*35=210\<=> x = 210 - (a+b+c+d+e)[/tex]
but we know that a+b+c+d+e = 200 so
x = 210 - 200 = 10
hope this helps
can someone help please
Answer:
A, B, C, D, and F are all solutions.
Step-by-step explanation:
All of the possible answers are correct except for E. Answer E is 0.001 less than -4 which would not make the equation true. Hope this helps!!
Which orderd pair is a solution of the equation-3x+5y = 2x + 3y
Answer:
2y=5x
Step-by-step explanation:
-3x+5y=2x+3y
5y=5x+3y
2y=5x
Construct an equation that has k = 4 as its solution. Use k on both sides of the equation.
______=______
[tex]\frac{3}{2}k - 7 = \frac{k}{4} - 2[/tex]
Since our fractions have two different denominators of 2 and 4 in this equation, we can get rid of the fractions by multiplying both sides of the equation by their common denominator, which is 4.
So we have [tex](4)(\frac{3}{2}k - 7) = (\frac{k}{4} - 2)(4)[/tex].
Make sure you distribute the 4 through both
terms on both sides of the equation.
On the left, (4)(3/2k) is 6k and (4)(-7) is -28.
On the right, (4)(k/4) is k and (4)(-2) is -8.
So we have 6k - 28 = k - 8.
Now subtract k from both sides to get 5k - 28 = -8.
Now add 28 to both sides to get 5k = 20.
Finally, dividing both sides by 5, we find that k = 4.
Bob collects stamps. Each day he adds 4 stamps to his collection. At the end of three days he has 50 stamps. How many stamps does he have at the end of 10 days? *
Answer:
78 stamps
Step-by-step explanation:
50 stamps collected after 3 days
4 stamps added a day
next 7 days added= 7*4= 28 stamps
Total after 10 days= 50+28= 78 stamps
What integers are plotted on the number line below?
0-3 and 3
08 and 8
0 -8 and -12
8 and -2
Answer:
0-3 and there
Step-by-step explanation:
1. if the person who is zero or a woman or woman would like
2. I think the same way I think it is a lot more minutes and more than a lot
Answer:
-8 and-2
Step-by-step explanation:
its because oe of the point is on the -2 and one is on the -8 also did it on edg 2020
Determine the measure of angle P if the measure of arc BD is 154 degrees and secant AD is a diameter of Circle C.
Complete Question
The complete question is shown on the first uploaded image
Answer:
The angle P is [tex]P = 26^o[/tex]
Step-by-step explanation:
From the question we are told that
The angle BD is [tex]BD = 154^o[/tex]
Now looking at the diagram we can deduce that angle [tex]B \r CD = 180 ^o[/tex]
Now looking at line AD we see that it is tangent to the circle this implies that line CD is perpendicular to line AD
So we can also deduce that
[tex]B \r C A + D \r C A = 180[/tex]
=> [tex]D \r C A = 180 - 154[/tex]
=> [tex]D \r C A = 26^o[/tex]
Now total angle in a triangle is 180 so
[tex]C\r DA + D\r A C + A \r C D = 180^o[/tex]
Now [tex]D \r A C = 90^o[/tex]
So
[tex]D \r AC = 180 - (90 + 26)[/tex]
=> [tex]P = D \r AC = 26^o[/tex]
hey! could you help me answer these questions? i really need them quick! i’ll mark u as the brainliest
Answer:
Hope this is correct
An isotope with a mass number of 193 has 116 neutrons. What is the atomic number of this isotope?
Answer:
Yttrium
Step-by-step explanation:
The atomic number of yttrium is 39. . An isotope with an atomic mass of 193 has 116 neutrons.
Answer:
77
number of protons is 77. Therefore atomic number atomic number is 77.
a 129$ golf club is on sale for 30% off. if sales tax is 6.25% what will be the final cost of the golf club with the discount and sales tax?
Answer:
approximately $95.94375
In order to accurately estimate the difference between the number of touchdowns scored by the Detroit Lions and the Seattle Seahawks in a particular string of n = 5 games, we must know that the standard deviations for the two teams are equal. Suppose that in this string of games the Lions score an average of x_1 = 2 touchdowns per game with a standard deviation of s_1 = 0.37, while the Seahawks score an average of x_2 = 2.8 touchdowns with standard deviation s_2 = 1.89. Can we assume, at the alpha = 0.1 significance level, that the standard deviations for these two teams are the same? a) Test Statistic: b) Critical Value: c) Conclusion: A. There is sufficient evidence to conclude that the standard deviations are different. B. There is insufficient evidence to conclude the standard deviations are different. We may assume they are equal.
Answer:
Step-by-step explanation:
Here,
[tex]H_0:\sigma _1 = \sigma _2\\\\H_1:\sigma_1 \neq \sigma_2[/tex]
a) Test Statistic
[tex]F = \frac{S_1^2}{S_1^2} \\\\=\frac{0.37^2}{1,89^2} \\\\=0.04[/tex]
b) Critical value for
[tex]\sigma = 0.1[/tex]
degrees of freedom is
[tex](n_1 - 1, n_2 -1)[/tex]
d.f =(5 - 1, 5 - 1)
d.f = (4, 4)
Fcritical=
[tex]F_{0.1},(4,4)\\\\[/tex]
Fcritical = 4.11
Critical value = 4.11
Here,
F test Statistic < critical value
so we fail to reject null hypothesis H₀
Conclusion
There is insufficient evidence to conclude the standard deviations are different.
we may assume they are equal.
A crop scientist is conducting research with a drought resistant corn hybrid. She is interested in determining if increasing the spacing between these plants will increase yield. She prepares 30 single acre plots and randomly assigns 15 to have normal spacing while the other 15 are planted with an expanded spacing. The resulting average yield for each group of 15 plots was recorded.
Select all that apply.
Select one or more:
a. The explanatory variable is whether the corn plants had normal spacing or expanded spacing.
b. The response variable is the yield of the crops.
c. The explanatory variable is the yield of the crops.
d. The response variable is whether the corn plants had normal spacing or expanded spacing.
e. This study is best described as an experiment.
f. This is best described as an observational study.
Answer:
A , B and E.
Step-by-step explanation:
the scientist can control and deal with the measure of manure that is given to a solitary corn plants. thus A is correct.
The reaction variable is the yield recorded for each plot due to the fact that the yield recorded in each plot is needed to check whether the compost is given or not. choice B is also correct
it's considered an experiment because the specialist is controlling the autonomous variable. then E is a right choice.
I need Help The question is Really complicated
Answer:
Graph A
Step-by-step explanation:
A linear association means that the dots form a line
Answer:
The answer is A
Step-by-step explanation:
A linear association is when the dots on the graph create a straight line. A creates a straight line therefore it is a linear association.
If you ordered ten 20” pizzas and you lined up all the crust, would it be shorter or longer than an 18-wheeler truck (48 ft long)?
Answer:
It would me shorter by about 31.4 inches
Step-by-step explanation:
Answer:
yes (longer)
Step-by-step explanation:
20π=62.83...
62.83...x10=628.31...
628.31.../12=52.35'
step one, finding circumference.
step two multiplying circumference by 10 pizzas
step three dividing 10x circumference by 12 inches to feet.
April and Blake went running. Blake
ran 4 miles farther than April. Added
together, they ran a total of 16 miles.
How far did April run?
X = April's distance
4 + x = Blake's distance
Answer:
6 miles
Step-by-step explanation:
From the information given you can write the following equation:
x+y= 16 (1), where
x= April's distance
y= Blake's distance
You also have that Blake ran 4 miles farther than April which means that y= 4+x and you can replace this in the first equation and isolate x:
x+(4+x)= 16
x+4+x=16
2x=16-4
x=12/2
x= 6
According to this, the answer is that April ran 6 miles.
Find the equation of the line that contains the point (4, -2) and is perpendicular to the line y= -2x+5
.
Answer:
y +2 = (1/2)(x -4)
Step-by-step explanation:
The given line's equation is in the slope-intercept form ...
y = mx + b
where m is the slope and b is the y-intercept. Matching your equation to this one, you see that m = -2. That is, the slope of the given line is -2.
The slope of the perpendicular line will be the opposite of the reciprocal of this slope, so will be ...
-1/(-2) = 1/2
__
We can use the desired slope and given point in the point-slope form of the equation of a line:
y -k = m(x -h) . . . . . . . line with slope m through point (h, k)
Filling in the values we want, m=1/2, (h, k) = (4, -2), gives us the equation ...
y +2 = (1/2)(x -4) . . . . the equation of your line
__
This can be rearranged to any of several other forms
y = 1/2x -4 . . . . . slope-intercept form
x -2y = 8 . . . . . . standard form
Answer:
y +2 = (1/2)(x -4) did it on college board
Step-by-step explanation:
If the quarter circle intersects the x-axis at the coordinate (- 3, 0) and is rotated around the y-axis what is the resulting 3 - D figure and determine its volume to the nearest cubic unit.
Answer:
Volume of the hemisphere will be 57 cubic units.
Step-by-step explanation:
A quarter circle which intersects the x-axis at (-3, 0) when rotated around the y-axis, 3-D figure formed will be a hemisphere.
As shown in the figure attached,
Radius of the hemisphere formed = 3 units
Volume of the hemisphere = [tex]\frac{1}{2}(\frac{4}{3})\pi (r)^{3}[/tex]
= [tex](\frac{2}{3})\pi (r)^{3}[/tex]
= [tex]\frac{2}{3}\pi (3)^{3}[/tex]
= 18π
= 56.55 cubic units
≈ 57 cubic units
Therefore, volume of the hemisphere will be 57 cubic units
A water storage tank has a cylindrical shape. The base has a diameter of
15 meters and the tank is 30 meters high. How much paint will be needed to cover the outside
of the tank, to the nearest meter squared unit?
Answer:
1761 square meters
Step-by-step explanation:no, thanks.
The quantities xxx and yyy are proportional. xxx yyy 777 353535 121212 606060 202020 100100100 Find the constant of proportionality (r)(r)left parenthesis, r, right parenthesis in the equation y=rxy=rxy, equals, r, x.
Answer: The constant of proportionality is r = 5.
Step-by-step explanation:
O, we know that x and y are proportional, this means that:
y = r*x
where r is the constant of proportionality.
we also have the table
x y
7 35
12 60
20 100
Now, we can replace those values in our equation and get, for the first pair:
35 = r*7
r = 35/7 = 5
for the second pair:
60 = r*12
60/12 = 5 = r
So we can conclude that the constant of proportionality is 5.
Answer:
5
Step-by-step explanation:
It was right for me on khan
A store finds that its sales revenue changes at a rate given by S'(t) = −30t2 + 420t dollars per day where t is the number of days after an advertising campaign ends and 0 ≤ t ≤ 30. (a) Find the total sales for the first week after the campaign ends (t = 0 to t = 7). $ (b) Find the total sales for the second week after the campaign ends (t = 7 to t = 14). $ g
Answer:
Step-by-step explanation:
Give the rate of change of sales revenue of a store modeled by the equation [tex]S'(t)= -30t^{2} + 420t[/tex]. The Total sales revenue function S(t) can be gotten by integrating the function given as shown;
[tex]\int\limits {S'(t)} \, dt = \int\limits ({-30t^{2}+420t }) \, dt \\S(t) = \frac{-30t^{3} }{3}+\frac{420t^{2} }{2}\\ S(t)= -10t^{3} +210t^{2} \\[/tex]
a) The total sales for the first week after the campaign ends (t = 0 to t = 7) is expressed as shown;
[tex]Given\ S(t) = -10t^{3} + 210t^{2}[/tex]
[tex]S(0) = -10(0)^{3} + 210(0)^{2}\\S(0) = 0\\S(7) = -10(7)^{3} + 210(7)^{2}\\S(7) = -3430+10,290\\S(7) = 6,860[/tex]
Total sales = S(7) - S(0)
= 6,860 - 0
Total sales for the first week = $6,860
b) The total sales for the secondweek after the campaign ends (t = 7 to t = 14) is expressed as shown;
Total sales for the second week = S(14)-S(7)
Given S(7) = 6,860
To get S(14);
[tex]S(14) = -10(14)^{3} + 210(14)^{2}\\S(14) = -27,440+41,160\\S(14) = 13,720[/tex]
The total sales for the second week after campaign ends = 13,720 - 6,860
= $6,860
A vegetable garden and surrounding path are shaped like a square that together are 10ft wide. The path is 3ft wide. Find the total area of the vegetable garden and path.
Answer:
256
Step-by-step explanation:
since the the path surounds both sides of the garden you have to add 2 x instead of just x
let me show you what i mean. 10=garden width and 3=path width=x
since it is a square, we can calculate the area by taking one side and squaring it so you get (10+2x)^2 which is 16^2 since x is 3, the width of the garden
to do simaler problems just use thei formula (garden length+2path length)^2 or (garden length+2path length)times(garden length+2path length)
A certain daily delivery route for Hostess breads and snack cakes includes eight grocery stores and four convenience stores. The historical mean tome to complete these deliveries (to the 12 stores) and return to the distribution center is 6.5 hours. A new deliver has been assigned to this route, and a random sample of his route completion times (in hours) was obtained. The data are given below:
6.61, 6.25, 6.40, 6.57, 6.35, 5.95, 6.53, 6.29
Required:
Assume the underlying population is normal. Is there evidence to suggest that the new driver has been able to shorten the route completion time, at the level of significance 0.01?
a. 0.05
b. 0.1 < p-value < 0.2: There is no evidence to suggest tha tthe new driver has been able to shorten the mean delivery time for this route.
c. 0.1 < p-value < 0.2: There is an enough evidence to suggest thatthe new driver has been able to shorten the mean delivery time for this route.
d. 0.05 < p-value < 0.1: There is no evidence to suggest tha tthe new driver has been able to shorten the mean delivery time for this route.
Answer:
d. 0.05 < p-value < 0.1: There is no evidence to suggest tha tthe new driver has been able to shorten the mean delivery time for this route.
Step-by-step explanation:
We calculate the mean and standard deviation of the sample:
[tex]M=\dfrac{1}{8}\sum_{i=1}^{8}(6.61+6.25+6.4+6.57+6.35+5.95+6.53+6.29)\\\\\\ M=\dfrac{50.95}{8}=6.369[/tex]
[tex]s=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{8}(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{7}\cdot [(6.61-(6.369))^2+...+(6.29-(6.369))^2]}\\\\\\s=\sqrt{\dfrac{0.3216875}{7}}=\sqrt{0.046}\\\\\\s=0.214[/tex]
This is a hypothesis test for the population mean.
The claim is that the new driver has been able to shorten the route completion time (significantly less than 6.5 hours).
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=6.5\\\\H_a:\mu< 6.5[/tex]
The significance level is 0.01.
The sample has a size n=8.
The sample mean is M=6.369.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=0.214.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{0.214}{\sqrt{8}}=0.08[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{6.369-6.5}{0.08}=\dfrac{-0.13}{0.08}=-1.73[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=8-1=7[/tex]
This test is a left-tailed test, with 7 degrees of freedom and t=-1.73, so the P-value for this test is calculated as (using a t-table):
[tex]P-value=P(t<-1.73)=0.063[/tex]
As the P-value (0.063) is bigger than the significance level (0.01), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the new driver has been able to shorten the route completion time (significantly less than 6.5 hours).
4x – 8 + 6x – 12 = 10
Step-by-step explanation:
4x+6x-8-12=10
10x-20=10
10x=10+20
10x=30
x=3
Answer:
x=3
Step-by-step explanation:
to find X first find the like terms
like terms: 4x and 6x
like terms: -12 and -8
combine the like the like terms
4x+6x=10x
-12-8=-20
10x-20=10
add 20 on both sides
10x-20+20=10+20
10x=30
divide both sides by 10
10x/10=30/10
x=3
ANSWER CHECK
substitute the variable
4(3) – 8 + 6(3) – 12 = 10
12-8+18-12
4+18-12
22-12 = 10
10=10
Write the statement as a proportion. Name the means and the extremes: a.2isto3as8isto12 b. 90isto36 as135isto54
Answer:
Step-by-step explanation:
The base of the triangle is 5 inches. The length of the rectangle is 15 inches. The height of the triangle is 10 inches. Find the surface area
Answer:
275 square inches
Step-by-step explanation:
Here we have to give us various measurements, but we do not know to which figure it corresponds since you do not attach it, but I have found an image where they asked the same questions and it makes sense that it is the question, the attached one.
We have that the rectangle is 15 inches long and the width corresponds to the same as the base of the triangle, that is, 5 inches, therefore, the area of the rectangle would be:
A = l * w
A = 15 * 5
A = 75
75 in ^ 2 but how are 3 rectangles would be:
75 * 3 = 225
225 in ^ 2 would be the area of the 3 rectangles, it would be necessary to add the area of the two triangles that would be:
A = b * h / 2
replacing:
A = 5 * 10/2
A = 25
25 in ^ 2 for the triangle, but being 2, they would be 50 ^ 2, now in total they would be:
225 + 50 = 275
In other words, the surface area of the figures is 275 square inches
Football and Cognitive Percentile A recent study1 examined several variables on collegiate football players, including the variable Years, which is number of years playing football, and the variable Percentile, which gives percentile on a cognitive reaction test. The regression line for predicting Percentile from Years is: . 1Singh R, et al., "Relationship of Collegiate Football Experience and Concussion with Hippocampal Volume and Cognitive Outcomes", JAMA, 311(18), 2014. Data values are estimated from information in the paper. Predict the cognitive percentile for someone who has played football for 11 years and for someone who has played football for 17 years. Enter the exact answers.
Complete Question:
Football and Cognitive Percentile A recent study1 examined several variables on collegiate football players, including the variable Years, which is number of years playing football, and the variable Percentile, which gives percentile on a cognitive reaction test. The regression line for predicting Percentile from Years is:
Percentile = 102 - 3.34(years)
1Singh R, et al., "Relationship of Collegiate Football Experience and Concussion with Hippocampal Volume and Cognitive Outcomes", JAMA, 311(18), 2014. Data values are estimated from information in the paper. Predict the cognitive percentile for someone who has played football for 11 years and for someone who has played football for 17 years. Enter the exact answers.
Answer:
cognitive percentile for someone who has played football for 11 years = 65.26
cognitive percentile for someone who has played football for 17 years = 45.22
Step-by-step explanation:
This is a very straight forward question. The regression line for predicting percentile from the number of years has been explicitly given in the question as:
Percentile = 102 - 3.34(years)
Therefore,
the cognitive percentile for someone who has played football for 11 years will be calculated as:
Percentile = 102 - 3.34(11)
Percentile = 102 - 36.74
Percentile = 65.26
the cognitive percentile for someone who has played football for 17 years will be calculated as:
Percentile = 102 - 3.34(17)
Percentile = 102 - 56.78
Percentile = 45.22
The range of the data: 7, 10, 30, 16, 8, 5, 3, 18, 35, and 1 tell the answer only
Range of data = [tex]\boxed{\sf{\red{Highest-lowest}}}\\[/tex]
Data = 1, 3 , 5 , 7 , 8 , 10 , 16 ,18 , 30, 35
Range = 35 - 1
Range of data is 34.
If one centimeter on the map above equals 30 miles, our vehicle gets 15 miles per gallon of gasoline, and gasoline costs $ 4.09 per gallon, how much will it cost to drive to the ski lodge
Answer:
[tex]\large \boxed{\$98.16}[/tex]
Step-by-step explanation:
Assume that your map looks like the one below.
1. Calculate the distance
It looks like the distance on the map is 12 cm.
[tex]\text{Distance} = \text{12 cm} \times \dfrac{\text{30 mi}}{\text{1 cm}} = \text{ 360 mi}[/tex]
2. Calculate the volume of gasoline
[tex]\text{Volume} = \text{ 360 mi} \times \dfrac{\text{1 gal}}{\text{15 mi}} = \text{24 gal}[/tex]
3. Calculate the cost of the gasoline
[tex]\text{Cost} = \text{24 gal} \times \dfrac{\$4.09}{\text{1 gal}} = \mathbf{\$98.16}\\\\\text{It will cost $\large \boxed{\mathbf{\$98.16}}$ to drive to the ski lodge.}[/tex]
A math teacher tells her students that eating a healthy breakfast on a test day will help their brain function and perform well on their test. During finals week, she randomly samples 46 students and asks them at the door what they ate for breakfast. She categorizes 26 students into Group 1 as those who ate a healthy breakfast that morning and 20 students into Group 2 as those who did not. After grading the final, she finds that 50% of the students in Group 1 earned an 80% or higher on the test, and 40% of the students in Group 2 earned an 80% or higher. Can it be concluded that eating a healthy breakfast improves test scores? Use a 0.05 level of significance.
Answer:
Step-by-step explanation:
Hello!
To test the claim that eating a healthy breakfast improves the performance of students on their test a math teacher randomly asked 46 students what did they have for breakfast before they took the final exam and classified them as:
Group 1: Ate healthy breakfast
X₁: Number of students that ate a healthy breakfast before the exam and earned 80% or higher.
n₁= 26
Group 2: Did not eat healthy breakfast
X₂: Number of students that did not eat a healthy breakfast before the exam and earned 80% or higher.
n₂= 20
After the test she counted the number of students that got 80% or more in the test for each group obtaining the following sample proportions:
p'₁= 0.50
p'₂= 0.40
The parameters of study are the population proportions, if the claim is true then p₁ > p₂
And you can determine the hypotheses as
H₀: p₁ ≤ p₂
H₁: p₁ > p₂
α: 0.05
[tex]Z= \frac{(p'_1-p'_2)-(p_1-p_2)}{\sqrt{p'(1-p')[\frac{1}{n_1} +\frac{1}{n_2}] } } }[/tex]≈N(0;1)
pooled sample proportion: [tex]p'= \frac{x_1+x_2}{n_1+n_2} =\frac{13+8}{46} = 0.46[/tex]
[tex]Z_{H_0}= \frac{(0.5-0.4)-0}{\sqrt{0.46(1-0.46)[\frac{1}{26} +\frac{1}{20}] } } }= 0.67[/tex]
p-value: 0.2514
The decision rule is:
If p-value ≤ α, reject the null hypothesis.
If p-value > α, do not reject the null hypothesis.
The p-value: 0.2514 is greater than the significance level 0.05, the test is not significant.
At a 5% significance level you can conclude that the population proportion of math students that obtained at least 80% in the test and had a healthy breakfast is equal or less than the population proportion of math students that obtained at least 80% in the test and didn't have a healthy breakfast.
So having a healthy breakfast doesn't seem to improve the grades of students.
I hope this helps!
The number of potholes in any given 1-mile stretch of freeway pavement in Pennsylvania has a Normal distribution. This distribution has a mean of 49 and a standard deviation of 9. Using the Empirical Rule, what is the approximate percentage of 1-mile long roadways with potholes numbering between 22 and 58?
Answer:
83.85% of 1-mile long roadways with potholes numbering between 22 and 58
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 49
Standard deviation = 9
Using the Empirical Rule, what is the approximate percentage of 1-mile long roadways with potholes numbering between 22 and 58?
22 = 49 - 3*9
So 22 is three standard deviations below the mean.
Since the normal distribution is symmetric, 50% of the measures are below the mean and 50% are above the mean.
Of those 50% which are below the mean, 99.7% of those are within 3 standard deviations of the mean, that is, greater than 22.
58 = 49 + 9
So 58 is one standard deviation of the mean.
Of those which are above the mean, 68% are within 1 standard deviation of the mean, that is, lesser than 58.
Then
0.997*0.5 + 0.68*0.5 = 0.8385 = 83.85%
83.85% of 1-mile long roadways with potholes numbering between 22 and 58
