The mean length of time, per week, that students at a certain school spend on their homework is 24.3 hours, with a standard deviation of 1.4 hours. Assuming the distribution of study times is normal, what percent of students study between 22.9 and 25.7 hours
Answer:
Approximately 68% of students study between 22.9 and 25.7 hours.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean of 24.3 hours, standard deviation of 1.4 hours.
What percent of students study between 22.9 and 25.7 hours?
22.9 = 24.3 - 1.4
25.7 = 24.3 + 1.4
Within 1 standard deviation of the mean, so:
Approximately 68% of students study between 22.9 and 25.7 hours.
Barnes and Nobles buy a book for $12.22. They mark up the price of the book by 35%.
Which equation can be used to find how much they sell the book for?
x = .35 (12.22)
x = 1.35 (12.22)
x = .65 (12.22)
x = .035 (12.22)
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Answer:
x = 1.35 (12.22)
Step-by-step explanation:
The selling price x is ...
x = cost + markup
x = cost + 0.35 × cost = cost(1 +0.35)
x = 1.35(12.22)
please help
Question: 6b = 18
Answer: ?
Answer:
6b=18
b=18/6
b=3
.
.
.
.
.
.
Answer:
6b=18
b=18/6
b=3
.
Step-by-step explanation:
A welding drawing shows that the weld-root reinforcement cannot exceed
" in thickness. Your weld measurement tools are metric, so this value needs to be converted to millimeters. You know that one inch equals 2.54 centimeters. What is the maximum weld-root reinforcement allowed in millimeters? Round your answer to the nearest tenth of a millimeter.
Answer:
3.2 millimeters
Step-by-step explanation:
1/8*2.54 *10 = 3.175
= 3.2 millimeter. (rounded to nearest tenth)
Help me with this please.
Answer:
the answer should be B
Step-by-step explanation:
take the total of people who got the flu(63) and the amount of them who were vaccinated(35) and write it as a fraction. 35/63 in its simplest form is 5/9
round 32.68 to the nearest hundredth
Answer:
32.70
Step-by-step explanation:
round up
Insurance companies are interested in knowing the population percentage of drivers who always buckle up before riding in a car. When designing a study to determine this population proportion, what is the minimum number of drivers you would need to survey to be 95% confident that the population proportion is estimated to within 0.04
Answer:
The minimum number of drivers you would need to survey is 601.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
What is the minimum number of drivers you would need to survey to be 95% confident that the population proportion is estimated to within 0.04?
The number is n for which M = 0.04.
We don't have an estimate for the proportion, so we use [tex]\pi = 0.5[/tex]. Then
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.04 = 1.96\sqrt{\frac{0.5*0.5}{n}}[/tex]
[tex]0.04\sqrt{n} = 1.96*0.5[/tex]
[tex]\sqrt{n} = \frac{1.96*0.5}{0.04}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96*0.5}{0.04})^2[/tex]
[tex]n = 600.25[/tex]
Rounding up:
The minimum number of drivers you would need to survey is 601.
find the volume of the following figure round your answer to the nearest tenth if necessary and make sure to use pi
Answer:
524cm^2
Step-by-step explanation:
Formula for Volume of sphere= 4/3 πr^2
We have,
r=5cm
Now,
Volume(v)=4/3 πr^2 = 4/3π 5^3= 4/3π 125 = 166.666666667π = 523.598775599
Rounding to the nearest tenth,
Volume=524cm^2
This semester, the tuition fee increased to $5,871. If this represents an increase by 14%, what was the original fee?
Part C
Based on feedback from an independent research firm, the flashlight manufacturer has decided to change the design of the flashlight. The reflector now needs to extend 4 centimeters past the center of the bulb, as shown in the diagram. In the new design, how wide will the reflector (CD) be at its widest point? Show your work.
Answer:
The answer is "18".
Step-by-step explanation:
In the given graph by concluding we observe that on the x-axis, one step is 2 units, and when we half each of the steps it will= 1 unit
[tex]\therefore\\\\CD = distance\ from\ -(8+1)\ to\ (8+1)\ = \text{distance between} -9 \ to\ 9\ = 18[/tex]
solve for x please help (show work)
Answer:
x=-2
Step-by-step explanation:
3x+8x - 3 = -25
Combine like terms
11x -3 = -25
Add 3 to each side
11x -3+3 = -25+3
11x = -22
Divide by 11
11x/11 = -22/11
x = -2
[tex]\large\bf{\pink{ \longrightarrow \: }} \tt \:3x \: + \: 8x \: - \: 3 \: = \: - 25[/tex]
[tex]\large\bf{\pink{ \longrightarrow \: }} \tt \:11x \: - \: 3 \: = \: - 25[/tex]
[tex]\large\bf{\pink{ \longrightarrow \: }} \tt \:11x \: = \: - 25 \: + \: 3[/tex]
[tex]\large\bf{\pink{ \longrightarrow \: }} \tt \:11x \: = \: - 22[/tex]
[tex]\large\bf{\pink{ \longrightarrow \: }} \tt \: x \: = \: {\cancel\frac{ {- 22} \:^{ - 2} }{11}} \\ [/tex]
[tex]\large\bf{\pink{ \longrightarrow \: }} \tt \:x \: = \: - 2[/tex]
Look at the pattern below. If the
pattern continues, what will be
the tenth number?
3. 11, 9, 17, 15, 23, 21...
Answer:
35
Step-by-step explanation:
We are adding 8 and then subtracting 2
3, 11, 9, 17, 15, 23, 21
The 8th number is 21+8 = 29
The 9th number
Subtract 2
29-2 = 27
10th number
Add 8
27+8 = 35
First is adding 8 to get the next number then subtract 2 to get the number after.
21 is the 7th number.
8th number = 21 + 8 = 29
9th number = 29-2 = 27
10th number = 27 + 8 = 35
Answer: 35
find the equation of the line
Four randomly chosen Nevada students were asked how many times they drove to Arizona last year. Their replies were 4,5,6,7. The geometric mean is
Group of answer choices
5.31
5.38
4.98
3.95
The geometric mean of the numbers is 5.38
Given the values a, b, c and d
The geometric mean of the values will be expressed as:
[tex]GM = (abcd)^{1/4}[/tex]
Given the values 4, 5, 6, and 7, the geometric mean will be expressed as:
[tex]GM = (4\times5\times6\times7)^{1/4}\\[/tex]
[tex]GM = (840)^{1/4}\\GM=\sqrt[4]{840} \\GM = 5.38[/tex]
Hence the geometric mean of the numbers is 5.38.
Learn more: https://brainly.com/question/23875011
? Question
Use the drawing tools to form the correct answer on the graph.
Graph this step function:
Answer:
start on (0,1) and go up two and left three. keep going until you run out of room. then, draw a line through the points.
Step-by-step explanation:
Translate and solve: fife less than z is 4
Answer:
z=9
Step-by-step explanation:
z-5=4. /+5
z=4+5
z=9
Answer:
z<-1
Step-by-step explanation:
5<z=4
collect like terms
z=<4-5
z<-1
explain how you determined which operation was needed to write the equation. 9 divided by 3/4
9/ (3/4)
= (9/1)/(3/4)
=(9x4)/(1x3)
=36/3
=12
Answer:
division:
divided means division (:)
9:3/4
And the answer is 12:))))))))))
Step-by-step explanation:
2kg of chicken
61.5 g left
How many kg of chicken were eaten
Answer:
1.9385 kilograms were eaten
1.9385 kg
Step-by-step explanation:
because 2 kg=2000 g
Subtracting 2000
- 61.5
1938.5
Converting 1938.5 in kg is 1.9385 kg
I need help this is confusing to me
Answer:i think it is b not really sure
Step-by-step explanation:
A lawyer commutes daily from his suburban home to his midtown office. The average time for a one-way trip is 24 minutes, with a standard deviation of 3.8 minutes. Assume the distribution of trip times to be normally distributed.
(a) What is the probability that a trip will take at least ½ hour?
(b) If the office opens at 9:00 A.M. and he leaves his house at 8:45 A.M. daily, what percentage of the time is he late for work?
(c) If he leaves the house at 8:35 A.M. and coffee is served at the office from 8:50 A.M. until 9:00 A.M., what is the probability that he misses coffee?
(d) Find the length of time above which we find the slowest 10% of trips.
(e) Find the probability that 2 of the next 3 trips will take at least one half
1/2 hour.
Answer:
Step-by-step explanation:
a) Probability-Above 30 min = 5.72% = .0572
b) Probability-Above 15 min = 99.11% = .9911
c) *Probability-Between 1 - 59.49% = .4051
d) 19.136 minutes z = -1.28
a) The probability that trip will take at least 1/2 hour will be 0.0606.
b) The percentage of time the lawyer is late for work will be 99.18%.
c) The probability that lawyer misses coffee will be 0.3659.
d) The length of time above which we find the slowest 10% of trips will be 0.5438.
e) The probability that exactly 2 out of 3 trips will take at least one half
1/2 hour is 0.0103.
What do you mean by normal distribution ?
A probability distribution known as a "normal distribution" shows that data are more likely to occur when they are close to the mean than when they are far from the mean.
Let assume the time taken for a one way trip be x .
x ⇒ N( μ , σ ²)
x ⇒ N( 24 , 3.8 ²)
a)
The probability that trip will take at least 1/2 hour or 30 minutes will be :
P ( x ≥ 30)
= P [ (x - μ) / σ ≥ (30 - μ) / σ ]
We know that , (x - μ) / σ = z.
= P [ z ≥ (30 - 24) / 3.8)]
= P [ z ≥ 1.578 ]
= 1 - P [ z ≤ 1.578 ]
Now , using the standard normal table :
P ( x ≥ 30)
= 1 - 0.9394
= 0.0606
b)
The percentage of the time the lawyer is late for work will be :
P ( x ≥ 15)
= P [ z ≥ -2.368 ]
= P [ z ≤ 2.368]
= 0.9918
or
99.18%
c)
The probability that lawyer misses coffee :
P ( 15 < x < 25 ) = P ( x < 25 ) - P ( x < 15)
= P [ z < 0.263] - P ( z < -2.368)
or
= 0.3659
d)
The length of time above which we find the slowest 10% of trips :
P( x ≥ X ) ≤ 0.10
= 0.5438
e)
Let's assume that y represents the number of trips that takes at least half hour.
y ⇒ B ( n , p)
y ⇒ B ( 3 , 0.0606)
So , the probability that exactly 2 out of 3 trips will take at least one half
1/2 hour is :
P ( Y = 2 )
= 3C2 × (0.0606)² × ( 1 - 0.0606)
= 0.0103
Therefore , the answers are :
a) The probability that trip will take at least 1/2 hour will be 0.0606.
b) The percentage of time the lawyer is late for work will be 99.18%.
c) The probability that lawyer misses coffee will be 0.3659.
d) The length of time above which we find the slowest 10% of trips will be 0.5438.
e) The probability that exactly 2 out of 3 trips will take at least one half
1/2 hour is 0.0103.
Learn more about normal distribution here :
https://brainly.com/question/26822684
#SPJ2
Wesley is making a patio from stones of two sizes, 5 inch wide and 10 inch wide. He wants to begin and end his pattern with a 10 inch stone so there will be one more of the 10 inch stones than of 5inch stones. His patio will be 130 inches wide.
How many 10 inch stones will Wesley need for one row?
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Answer:
9
Step-by-step explanation:
If x is the number of 10-inch stones, then (x-1) is the number of 5-inch stones, and the total width is ...
10x +5(x-1) = 130
15x -5 = 130 . . . . . . . eliminate parentheses
15x = 135 . . . . . . add 5
x = 9 . . . . . . . divide by 15
Wesley will need 9 10-inch stones for one row.
3. In A PQR, MZP=(4x-5),
m2Q=(8x-50), and MZR=(3x+10).
Which of the following best describes
APQR?
® Right triangle
® Isosceles triangle
© Equlateral triangle
Scalene triangle
Answer:
B
Step-by-step explanation:
The sum of all of them will result in 180. 15x-45=180. x=15. P=55, Q=70 and R=55. It's an isosceles triangle
Answer:
b
Step-by-step explanation:
its b
Solve for the unknown variable
4y-2=8-2y+4y
y=?
Step-by-step explanation:
I hope it helped and it is easy to understand i hope it was helpful
1)4y-2=8-2y+4y
=4y-2y+4y=8-2
2y +4y=8-2
6y+6
12
if PQR measures 75° , what is the measure of SQR
Answer:
PQR+SQR=180°(angles in a triangle)
75°+SQR=180°
SQR=180°-75°
SQR=105°
Average person who drives car in United States drives 15, 350 miles which is 50% more than an average driver in Europe. We assume that the number of yearly miles by U.S. drivers is approximately a normal random variable of standard deviation of 4200 miles. Calculate percent of drivers who traveled between 10,000 to 12,000 miles in a year.
Answer:
7,675
that is your answer
Consider the graph below, and identify the piecewise function that describes it.
Answer:
f(x)=-x when x belongs to (-infinity, 3)
f(x)=-2 when x belongs to [3, 6]
f(x)=2x-7 when x belongs to (6, infinity)
What is the are of the polygon below!help please!
Answer:
Area= 525
Step-by-step explanation:
14x9=126
3x7=21
14x27=378
126+21+378=525
A nurse is preparing to administer cefaclor 40 mg/kg/day PO divided in equal doses every 8 hr to a child who weighs 48 lb. Available is cefactor
suspension 375 mg/5 ml. How many mL should the nurse administer per dose? (Round the answer to the nearest tenth. Use a leading zero if it
applies. Do not use a trailing zero.)
This question is solved by proportions.
Step 1:
A nurse is preparing to administer cefaclor 40 mg/kg/day.
This means that the first step is finding the baby's weight in kg.
The child weighs 48lb. Each lb has 0,453592kg.
So the child weighs 48*0.453592 = 21.7724kg.
Step 2:
Here, we find the daily dose.
For each kg, the baby is administered 40 mg.
Since the baby weighs 21.7724 kg, the daily dose is of 40*21.7724 = 870.896 mg.
Step 3:
Here, we find how many mL in a day.
For 375 mg, 5 mL are administered. How many mL for 870.896 mg?
375 mg - 5 mL
870.896 mg - x mL
Applying cross multiplication:
[tex]375x = 5*870.896[/tex]
[tex]x = \frac{5*870.896}{375}[/tex]
[tex]x = 11.6[/tex]
Step 4:
Here, we find how many mL per dose.
Equal doses every 8 hours, so 24/8 = 3 doses per day.
11.6/3 = 3.9
Thus, the nurse should administer 3.9 mL per dose.
For more on proportional variables, you can check https://brainly.com/question/23536327.
Answer:
x = 3.9 ml quantity of ml / dose
Step-by-step explanation:
The child weighs 48 lbs.
Then the weigh in kgs is 48 * 0.454 = 21.792 kgs (since 1000 lbs = 454 kgs)
If the nurse has to prepare doses according to 40 mg/kg/day then for a child of 21.792 kgs it is needed 21.792*40 mg or 871.68 mg/day, and the fact that he or (she) need to take three doses then each dose will be of
871.68/3 = 290.56 mg
So far we know that each dose should contain 290.56 mg, now we have the cefactor in a suspension wich density is 375 mg/5 ml or 75 mg/ml
Then by rule of three
if 75 mg ⇒ 1 ml
290.56 mg ⇒ x (ml)
x = 290.56/75 ( mg*ml)/ mg
x = 3.87 ml round to the nearest tenth
x = 3.9 ml
10. In a group of 50 people, there are two types of professionals, engineers and managers. If 36 of them are engineers and 24 of them are managers, how many persons are both managers and engineers?
Step-by-step explanation:
The photo above is the Venn diagram
Now, the number of persons that are both managers and engineers= n
Since, Total number of persons is 50
Therefore, 50= M+n+E
M only = 36-n
E only = 24-n
Therefore, 50= 36 - n + n + 24 - n
50 = 36+24-n
50 = 60 - n
60 - n = 50
-n = 50 - 60
-n = - 10
Therefore, n = 10
Therefore, the number of persons that are both Managers and Engineers is 10persons.
The mean output of a certain type of amplifier is 102102 watts with a standard deviation of 1212 watts. If 6363 amplifiers are sampled, what is the probability that the mean of the sample would differ from the population mean by greater than 3.43.4 watts
Answer:
0.0244 = 2.44% probability that the mean of the sample would differ from the population mean by greater than 3.4 watts.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes 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.
Mean of 102, standard deviation of 12:
This means that [tex]\mu = 102, \sigma = 12[/tex]
Sample of 63:
This means that [tex]n = 63, s = \frac{12}{\sqrt{63}}[/tex]
What is the probability that the mean of the sample would differ from the population mean by greater than 3.4 watts?
Below 102 - 3.4 = 98.6 or above 102 + 3.4 = 105.4. Since the normal distribution is symmetric, these probabilities are equal, and thus, we find one of them and multiply by two.
Probability the mean is below 98.6.
p-value of Z when X = 98.6. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{98.6 - 102}{\frac{12}{\sqrt{63}}}[/tex]
[tex]Z = -2.25[/tex]
[tex]Z = -2.25[/tex] has a p-value of 0.0122.
2*0.0122 = 0.0244
0.0244 = 2.44% probability that the mean of the sample would differ from the population mean by greater than 3.4 watts.
