Answer: a) 8.779 years
b) 8.664 years
Step-by-step explanation:
a)
[tex]A=P\bigg(1+\dfrac{r}{n}\bigg)^{nt}[/tex]
A: accumulated amount (balance)P: principal amount (original/initial investment)r: interest rate (convert to a decimal)n: number of times compounded per yeart: number of yearsGiven: A = 1800, P = 900, r = 8% = 0.08, n = 3, t = unknown
[tex]1800=900\bigg(1+\dfrac{0.08}{3}\bigg)^{3t}\\\\\\2=\bigg(1+\dfrac{0.08}{3}\bigg)^{3t}\\\\\\ln\ 2=ln \bigg(1+\dfrac{0.08}{3}\bigg)^{3t}\\\\\\ln\ 2=3t\ ln\bigg(1+\dfrac{0.08}{3}\bigg)\\\\\\\dfrac{ln\ 2}{3\ ln\bigg(1+\dfrac{0.08}{3}\bigg)}=t\\\\\\\large\boxed{8.779=t}[/tex]
b)
[tex]A=Pe^{rt}[/tex]
[tex]1800=900e^{0.08t}\\\\\\2=e^{0.08t}\\\\\\ln\ 2=0.08t\\\\\\\dfrac{ln\ 2}{0.08}=t\\\\\\\large\boxed{8.664=t}[/tex]
NEED UGANT HELP pls help me
An event that is impossible has a probability of 0
An event that is certain to happen has a probability of 1
The probability scales from 0 to 1, referring from no chance to will happen.
A company is divided into 50,000 shares. An investor purchases 1,000 shares. What percent of the company does the investor own?
Answer:
Step-by-step explanation:
percentage is per 100.
If we have to find x as percentage of y then
formula for percentage is given by = x/y*100
_______________________________________________
Given
total no. of shares = 50,000
Share bought by investor = 1,000
Percentage of share bought by investor
= Share bought by investor/total no. of shares *100
= (1000/50000)*100 = 2%.
It means that if there are 100 shares for company then investor owns 2 shares of the company. This makes the qualitative analysis easy.
2% percent of the company does the investor own.
Crane Company reports the following for the month of June.
Date
Explanation
Units
Unit Cost
Total Cost
June 1 Inventory 150 $4 $600
12 Purchase 450 5 2,250
23 Purchase 400 6 2,400
30 Inventory 80
Assume a sale of 500 units occurred on June 15 for a selling price of $7 and a sale of 420 units on June 27 for $8.
Calculate cost of goods available for sale.
Calculate Moving-Average unit cost for June 1, 12, 15, 23 & 27. (Round answers to 3 decimal places, e.g. 2.525.)
Answer:
Crane CompanyJune Financial Reports
a) Cost of goods available for sale = $5,250
b) Moving-Average unit cost for:
i) June 1: = $5
ii) 12: = $4.75
iii) 15: = $4.75
iv) 23: = $5.75
v) 27: = $5.25
Step-by-step explanation:
a) Calculations:
Date Explanation Units Unit Cost Total Cost Moving Average Cost
June 1 Inventory 150 $4 $600 $4.000
12 Purchase 450 5 2,250 4.750
15 Sale 500 7 3,500 4.750
23 Purchase 400 6 2,400 5.750
27 Sale 420 8 3,360 5.250
30 Inventory 80
Cost of goods available for sale = Cost of Beginning Inventory + Cost of Purchases = $5,250 + ($600 + 2,250 + 2,400)
b) Moving-Average unit cost for:
i) June 1: Cost of goods available/Units of goods available = $5 ($600/150)
ii) 12: Cost of goods available/Units of goods available = $4.75 ($600 + 2,250/600)
iii) 15: Cost of goods available/Units of goods available = $4.75 ($475/100)
iv) 23: Cost of goods available/Units of goods available = $5.75 ($475 + 2,400)/500
v) 27: Cost of goods available/Units of goods available = $5.25 ($420/80)
4x+1/15=2x/10 PLEASE HELP
Answer:
[tex]x=-1[/tex]
Step-by-step explanation:
Cross multiply.
10(4x + 1) = 15(2x)
Expand brackets.
40x + 10 = 30x
Add -30x and 10 on both sides.
40x - 30x = -10
10x = -10
Divide both sides by 10.
10/10x = -10/10
x = -1
Please answer this correctly
Answer:
12.5
Step-by-step explanation:
This is the answer!
Answer:
50%
Step-by-step explanation:
Total Cards = 4
6 or even cards = 2
P( 6 or even) = 2/4
=> 1/2
In %age:
50%
4. Parking fees at IIUM are RM 5.00 for IIUM students and RM 7.50 for non-IIUM students. At the
end of each day, the total number of vehicles parked that day and the gross receipts for the day are
recorded, but the number of vehicles in each category is not. The following table contains the relevant
information for a recent 4-day period:
Day
Vehicles Parked
Gross Receipts
Monday
1,200
RM 7,125
Tuesday
1.550
RM 9,825
Wednesday Thursday
1.740
1,400
RM 11,100 RM 8,650
(a) How many vehicles in each category used the IIUM parking facilities on Wednesday? (1 point]
(b) If 1,200 vehicles are parked in one day, is it possible to take in gross receipts of RM 10,000?
Explain. [1 point]
(c) Describe all possible gross receipts on a day when 1,200 vehicles are parked. [1 point]
(3 points)
Answer:
(a) 780 students and 960 non-students
(b) No. The maximum revenue is RM9000 from 1200 non-students.
(c). Revenue is maximum of RM9000 at 1200 non-students, decreasing by RM2.50 per student to a minimum of RM6000 at 1200 students
Step-by-step explanation:
Let x = IIUM students and
and y = non-IIUM students
You have two conditions
(a) x + y = total vehicles parked
(b) 5.00x + 7.50y = total gross receipts
(a) Wednesday
From your table,
x + y = 1740
5.00x + 7.70y = RM11 100
Solve the simultaneous equations
[tex]\begin{array}{rrcrl}(1) & x + y & = &1740&\\(2) & 5.00x + 7.50y & = & 11 100\\(3)& 5.00x + 5.00y & = & 8700 & \text{Multiplied (1) by 5}\\&2.50 y & = &2400 &\text{Subtracted (3) from (2)}\\(4)&y& = &\mathbf{960} &\text{Divided each side by 2.50}\\& x +960& = &1740& \text{Substituted (4) into (1)}\\& x& = &\mathbf{780}& \\\end{array}\\\text{There are $\large \boxed{\textbf{780 students and 960 non-students}}$}[/tex]
(b) Can 1200 vehicles bring in RM10000?
No. Even if all the cars were from non-students, the most you could get is
1200 × 7.50 = RM9000
(c) Possible combinations for 1200 vehicles
Revenue = 5.00x + 7.50y = 5.00x + 7.50(1200 -x) = 5.00x + 9000 - 7.50x =
Revenue = 9000 - 2.50x
The maximum revenue of RM9000 occurs when there are no student cars and 1200 non-student cars.
For each student car that enters and displaces a non-student, the revenue drops by RM2.50.
Finally. when there are 1200 student cars and no non-students, the revenue has dropped to a minimum of RM6000.
An electrical engineer wishes to compare the mean lifetimes of two types of transistors in an application involving high-temperature performance. A sample of 60 transistors of type A were tested and were found to have a mean lifetime of 1827 hours and a standard deviation of 168 hours. A sample of 180 transistors of type B were tested and were found to have a mean lifetime of 1658 hours and a standard deviation of 225 hours. Find a 95% confidence interval for the difference between the mean lifetimes of the two types of transistors.
Answer:
(115.2642, 222.7358).
Step-by-step explanation:
Given data:
type A: n_1=60, xbar_1=1827, s_1=168
type B: n_2=180, xbar_2=1658, s_2=225
n_1 = sample size 1, n_2= sample size 2
xbar_1, xbar_2 are mean life of sample 1 and 2 respectively. Similarly, s_1 and s_2 are standard deviation of 1,2.
a=0.05, |Z(0.025)|=1.96 (from the standard normal table)
So 95% CI is
(xbar_1 -xbar_2) ± Z×√[s1^2/n1 + s2^2/n2]
=(1827-1658) ± 1.96×sqrt(168^2/60 + 225^2/180)
= (115.2642, 222.7358).
HELP WITH THESE QUESTIONS!!
The table below shows the distance a car travels and the amount of gasoline left in the tank of the car. Distance Traveled and Gas Left in Tank Distance Traveled (in miles) 0 90 180 270 Amount of Gas Left in Tank (in gallons) 15 12 9 6 PLZ HELP How many gallons of gasoline does the car have left after it has traveled 330 miles? 2 4 6 8
Answer:
b: 4
Step-by-step explanation:
i took the test on edge 2020
The gallons of gasoline the car has left after it has traveled 330 miles is 4 gallons so option (B) will be correct.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
In other words, an equation is a set of variables that are constrained through a situation or case.
Given the table of the number of miles and gallons.
If we take two points of the number of miles and gallons.
Then,
1 st point = ( 0 ,15 )
2 nd point = ( 90 , 12)
Now since the relation is linear which can be seen by data.
So,
Linear equation joining points 1st and 2nd is
y - 15 = [(12-15)/(90-0)](x - 0)
y - 15 = -x/30
y = (450 - x)/30
So,
At x = 330 miles
y = (450 - 330 )/30
y = 4 gallons
Hence "The gallons of gasoline the car has left after it has traveled 330 miles is 4 gallons".
For more about the equation,
https://brainly.com/question/10413253
#SPJ2
Answer in POINT-SLOPE FORM:
Complete the point-slope equation of the line through (1,3) and (5,1) Use exact numbers!
Answer:
y - 3 = (1/2)(x - 1)
Step-by-step explanation:
As we go from (1, 3) to (5, 1), we see that x (the run) increases by 4 and y (the rise) decreases by 2. Hence, the slope is m = rise / run = 2/4, or m = 1/2.
Then the desired point slope equation is y - 3 = (1/2)(x - 1).
Find the exact value of sin(u-v) given that sin u= 5/13 and sin v= 12/13
with u and vin quadrant I.
sin(u - v) =
(Type an integer or a simplified fraction.)
Answer:
Sin(u-v)= (-119/169)
Step-by-step explanation:
Sin(a-b)= Sinacosb-cosasinb
Sin(u-v)= sinucosv-cosusinv
Sinu= 5/13
U = sin^-1(5/13)
U= 22.62
Sinv= 12/13
V= sin^-1(12/13)
V= 67.38
Fr right angle triangle
If sin u = 5/13
Cos u = 12/13
If sin v = 12/13
Cos v= 5/13
Sin(u-v)= sinucosv-cosusinv
Sin(u-v)=(5/13)*(5/13) -(12/13)*(12/13)
Sin(u-v)= 25/169 - 144/169
Sin(u-v) = (25-144)/169
Sin(u-v)= (-119/169)
Pls somebody can help me?
What is the domain of f(x) = (1/2)^x ?
Answer:
all real numbers
Step-by-step explanation:
Answer:
C. All real numbers
Step-by-step explanation:
x goes forever in both the positive and negative directions, so the domain is all real numbers.
Determine the relation of AB and CD given the following points: A (3,-4), B (5.-7), C (8,3), and D (6,6).
Answer:
Step-by-step explanation:
To find the relationship between the given lines, we have to find the slope of both lines using slope formula, which is
So for AB, we will get
And for CD , we will get
Since the slopes of the two lines are equal , and when slopes are equal , lines are parallel .
What is the slope of the line on the graph below? On a coordinate plane, a line goes through points (negative 2, negative 3), (negative 1, negative 1), (0, 1) and (1, 3). –One-half One-half 1 2 plz
Answer:
slope = 2
Step-by-step explanation:
All four points lie on the same line.
Taking the first and fourth points, the slope can be found by the formula
slope, m = (y2-y1)/(x2-x1) = (3- -3) / (1- -2) = 6/3 =2
See attached diagram.
Answer:
2
Step-by-step explanation:
edge 2020
Nadine mixes a juice solution that is made from 3 gallons of an 80% juice solution and 1 gallon of a 20% juice solution. What is the percent concentration of the final solution?
Answer:
65%
Step-by-step explanation:
Nadine mixes a juice solution that is made from 3 gallons of an 80% juice solution and 1 gallon of a 20% juice solution. What is the percent concentration of the final solution?
3 gallons of 80% juice solution contains this amount of juice:
80% * 3 gal = 0.8 * 3 gal = 2.4 gal
1 gallon of 20% juice solution contains this amount of juice:
20% * 1 gal = 0.2 * 1 gal = 0.2 gal
The total amount of juice in the final juice solution is
2.4 gal + 0.2 gal = 2.6 gal
The total amount of juice solution made is 3 gal + 1 gal = 4 gal
The 4 gal juice solution contains 2.6 gallons of juice.
2.6 gallons is what percent of 4 gallons?
2.6/4 * 100% = 0.65 * 100% = 65%
Answer: 65%
Answer:
65% i got the answer right on the question
Step-by-step explanation:
Lisa surveyed 60 students at her school and found that 0.85 of the students she surveyed said their favorite class is math. Another 15% of the students she surveyed reported that their favorite class is science. How many more students in the survey prefer math over science?
Answer:
42
Step-by-step explanation:
Number of students whose favorite class is Math:
60*0.85=51
Number of students whose favorite class is Science:
15% is equal to 0.15.
60*0.15=9
Subtract number of students who like science from number of students who like math.
51-9=42
42 more students in the survey prefer math over science.
Answer:
42
Step-by-step explanation:
85% math
15% science
Subtract
85-15 = 70
The difference is 70 %
70% of 60 students
.70 * 60 = 42
There is a 42 student difference
In a certain online dating service, participants are given a 4-statement survey to determine their compatibility with other participants. Based on the questionnaire, each participant is notified if they are compatible with another participant. Each question is multiple choice with the possible responses of "Agree" or "Disagree," and these are assigned the numbers 1 or −1, respectively. Participant’s responses to the survey are encoded as a vector in R4, where coordinates correspond to their answers to each question. Here are the questions:
The question is incomplete. Here is the complete question.
In a certain online dating service, participants are given a 4-statement survey to determine their compatibility with other participants. Based on the questionnaire, each particpant is notified if they are compatible with another participant. Each question is multiple choice with the possible responses of "Agree" or "Disagree", and these are assigned the numbers 1 or -1, respectively. pArticipnat's responses to the survey are encoded as a vector in R4, where coordinates coreespond to their answers to each question. Here are the questions:
Question #1: I prefer outdoor activities, rather than indoor activities.
Question #2: I prefer going out to eat in restaurants, rahter than cooking at home.
Question #3: I prefer texting, rather than talking on the phone.
Question #4: I prefer living in a small town, rather than in a big city.
Here are the results for the questionaire, with a group of 5 participants:
Question1 Question2 Question3 Question4
participant A 1 1 -1 -1
participant B -1 1 1 1
participant C -1 -1 1 1
participant D 1 -1 -1 -1
participant E 1 -1 1 1
Two participants are considered to be "compatible" with each other if the angle between their compatibility vectors is 60° or less. Participants are considered to be "incompatible" if the angle between their compatibility vectors is 120° or larger. For angles between 60° or 120°, pairs of participants are warned that they "may or may not be compatible".
(a) Which pairs of paricipants are compatible?
(b) Which pairs of participants are incompatible?
(c) How would this method of testing compatibility change if the questionnaire also allowed the answer "Neutral", which would correspond to the number zero in a participant's vector? Would this be better than only
allowing "Agree" or "Disagree"? Could anything go wrong if we allowed "Neutral" as an answer?
Answer: (a) Participants A and D; B and C; C and E.
(b) Participants A and B; A and C; A and E; B and D; C and D;
Step-by-step explanation: Vectors in R4 are vectors in a 4 dimensional space and are determined by 4 numbers.
Vectors form angles between themselves and can be found by the following formula:
cos α = [tex]\frac{A.B}{||A||.||B||}[/tex]
which means that the cosine of the angle between two vectors is equal the dot product of these vectors divided by the product of their magnitude.
For the compatibility test, find the angle between vectors:
1) The vectors magnitude:
Magnitude of a vector is given by:
||x|| = [tex]\sqrt{x_{i}^{2} + x_{j}^{2}}[/tex]
Since all the vectors have value 1, they have the same magnitude:
||A|| = [tex]\sqrt{1^{2} + 1^{2} + (-1)^{2} + (-1)^{2}}[/tex] = 2
||A|| = ||B|| = ||C|| = ||D|| = ||E|| = 2
2) The dot product of vectors:
A·B = 1(-1) + 1(1) + (-1)1 + (-1)1 = -2
cos [tex]\alpha_{1}[/tex] = [tex]\frac{-2}{4}[/tex] = [tex]\frac{-1}{2}[/tex]
The angle that has cosine equal -1/2 is 120°, so incompatible
A·C = 1(-1) + 1(-1) + (-1)1 + (-1)1 = -4
cos [tex]\alpha _{2}[/tex] = -1
Angle = 180° --------> incompatible
A·D = 1(1) + 1(-1) + (-1)(-1) + (-1)(-1) = 2
cos [tex]\alpha _{3}[/tex] = 1/2
Angle = 60° ---------> COMPATIBLE
A·E = 1.1 + 1(-1) + (-1)1 + (-1)1 = -2
cos [tex]\alpha_{4}[/tex] = -1/2
Angle = 120° --------> incompatible
B·C = (-1)(-1) + 1(-1) + 1.1 + 1.1 = 2
cos [tex]\alpha _{5}[/tex] = 1/2
Angle = 60° -------------> COMPATIBLE
B·D = (-1)1 + 1(-1) + 1(-1) + 1(-1) = -4
cos[tex]\alpha_{6}[/tex] = -1
Angle = 180° -----------> incompatible
B·E = (-1)1 + 1(-1) + 1.1 + 1.1 = 0
cos[tex]\alpha _{7}[/tex] = 0
Angle = 90° -------------> may or may not
C·D = (-1)1 + (-1)(-1) + 1(-1) + 1(-1) = -2
cos[tex]\alpha_{8} =[/tex] -1/2
Angle = 120° ---------------> Incompatible
C·E = (-1)1 + (-1)(-1) + 1.1 + 1.1 = 2
cos [tex]\alpha_{9}[/tex] = 1/2
Angle = 60° ---------------> COMPATIBLE
D·E = 1.1 + (-1)(-1) + (-1)1 + (-1)1 = 0
cos [tex]\alpha_{10}[/tex] = 0
Angle = 90° -----------------> may or may not
(c) Adding zero (0) as a component of the vectors would have to change the method of compatibility because, to determine the angle, it is necessary to calculate the magnitude of a vector and if it is a zero vector, the magnitude is zero and there is no division by zero. So, unless the service change the method, adding zero is not a good option.
A defunct website listed the "average" annual income for Florida as $35,031. What is the role of the term average in statistics? Should another term be used in place of average? Choose the correct answer below. A. The term average is not used in statistics. The term median should be used for the result obtained by adding all of the sample values and dividing by the total number of sample values. B. The term average is often used in statistics to represent the mean. C. The term average is not used in statistics. The term mean should be used for the result obtained by adding all of the sample values and dividing by the total number of sample values. D. The term average is often used in statistics to represent the median.
Answer:
C. The term average is not used in statistics. The term "mean" should be used for the result obtained by adding all of the sample values and dividing by the total number of sample values.
Step-by-step explanation:
In colloquial language, the average is the result obtained when we add all the sample values and divide by the total number of sample values.
However, in statistics, the term which is used to represent this calculation is the "mean" of the sample data. The term average is not used.
The correct option is C.
A softball pitcher has a 0.626 probability of throwing a strike for each curve ball pitch. If the softball pitcher throws 30 curve balls, what is the probability that no more than 16 of them are strikes
Answer:
19.49% probability that no more than 16 of them are strikes
Step-by-step explanation:
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 = 30, p = 0.626[/tex]
So
[tex]\mu = E(X) = np = 30*0.626 = 18.78[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{30*0.626*(1-0.626)} = 2.65[/tex]
What is the probability that no more than 16 of them are strikes
Using continuity correction, this is [tex]P(X \leq 16 + 0.5) = P(X \leq 16.5)[/tex], which is the pvalue of Z when X = 16.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{16.5 - 18.78}{2.65}[/tex]
[tex]Z = -0.86[/tex]
[tex]Z = -0.86[/tex] has a pvalue of 0.1949
19.49% probability that no more than 16 of them are strikes
Create a bucket by rotating around the y axis the curve y=5 ln(x-2) from y=0 to y=4. If this bucket contains a liquid with density 760 kg/m3 filled to a height of 3 meters, find the work required to pump the liquid out of this bucket (over the top edge). Use 9.8 m/s2 for gravity.
Answer:
The work will be "1909212.015 J". The further explanation is given below.
Step-by-step explanation:
The given values are:
Liquid's density
= 760 kg/m³
Height
= 3 meters
Gravity
g = 3.8 m/s²
Value of y is:
y = 5 log (x-2)
y = 0
y = 4
As we know,
⇒ [tex]\Delta V=\pi r^2 \Delta y[/tex]
⇒ [tex]y =5log(x-2)[/tex]
⇒ [tex]\frac{y}{5} =log (x-2)[/tex]
⇒ [tex]e^{\frac{y}{5}}=(x-2)[/tex]
⇒ [tex]x=e^{\frac{y}{5}}+2[/tex]
Now,
[tex]\Delta F=ma[/tex]
[tex]=760 \pi (e^{\frac{y}{5}}+2)^2(9.8)\Delta y[/tex]
So that,
⇒ [tex]\Delta W = \Delta F.distance[/tex]
[tex]=\Delta F(4-y)[/tex]
The required work will be:
⇒ [tex]W=760\times 9.8 \pi \int_{3}^{0}(e^{\frac{y}{5}}+2)^2 (\Delta-y)dy[/tex]
[tex]=760\times 9.8 \pi[{-20(y-9)^{e^{\frac{y}{5}}}-2(y-8)y}][/tex]
[tex]=760\times 9.8 \pi[81.455][/tex]
[tex]=1909212.015 \ J[/tex]
Refer to the figure and find the volume generated by rotating the given region about the specified line. ℛ1 about AB
Answer:
I guess that the area we care about is the yellow area, delimited by the functions.
f(x) = 8*(x)^(1/4)
and the line with the slope s= 8/1 = 8 (as the line goes through the points (0,0) and (1, 8)).
g(x) = 8*x
then we want tofind the area between x = 0 and x = 1, of f(x) - g(x)
then we have:
[tex]I = \int\limits^1_0 {f(x)} \, dx = \int\limits^1_0 {8*\sqrt[4]{x} )} \, dx = (8*(4/5)*\sqrt[4]{1^5} - 8*(4/5)*\sqrt[4]{0^5}) = 6.4[/tex]
now, for the area under the g(x) we have:
[tex]I2 = \int\limits^1_0 {g(x)} \, dx = \int\limits^1_0 {8x} \, dx = (8/2)*1^2 - (8/2)*0^2 = 4.[/tex]
then I - I2 = 6.4 - 4 = 2.4
The yellow area is 2.4
And then, if we rotate this about the line AB, the volume will be:
B = 2*pi*2.4 = 2*3.14*2.4 = 15.075
The figure will be something like a half spheroid, with a hole in the shape of a cone inside of it.
13) BRAINLIEST &10+ POINTS!
Answer:
- 220° and 500°
Step-by-step explanation:
To find the coterminal angles add / subtract 360°, that is
140° - 360° = - 220°
140° + 360° = 500°
Answer:
- 220° and 500°
Step-by-step explanation:
50 random teenagers were asked how many hours a day they use their phone. They spent an average of 7 hours a day with a standard deviation of 1.3. Based on the results, what is the margin of error for the true mean number of hours a teenager spends on their phone?your margin of error on a 95% confidence level, round your answer to the nearest tenth
Answer:
The margin of error for the true mean number of hours a teenager spends on their phone is of 0.4 hours a day.
Step-by-step explanation:
We have the standard deviation of the saple, so we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 50 - 1 = 49
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 49 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2\frac{1.3}{\sqrt{50}} = 0.4[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The margin of error for the true mean number of hours a teenager spends on their phone is of 0.4 hours a day.
Tanya can wash a car and vacuum its interior in 2 hours. Pat needs 5 hours to do this same job. If Tanya and Pat work together, how many hours will it take them to clean a car??
Answer:
It will take 1.43 hours for them to clean the car.
Step-by-step explanation:
The together rate is the sum of each separate rate.
In this problem:
Together rate: 1/x
Tanya's rate: 1/2
Pat's rate: 1/5
Together rate = Tanya's rate + Pat's rate
[tex]\frac{1}{x} = \frac{1}{2} + \frac{1}{5}[/tex]
[tex]\frac{1}{x} = \frac{5 + 2}{10}[/tex]
[tex]\frac{1}{x} = \frac{7}{10}[/tex]
[tex]7x = 10[/tex]
[tex]x = \frac{10}{7}[/tex]
[tex]x = 1.43[/tex]
It will take 1.43 hours for them to clean the car.
I will give brainliest and thanks
Answer: 8.6602540378
Step-by-step explanation:
Based on pythagorean’s theorem we have:
[tex]\sqrt{14^{2}-11^{2} } =\sqrt{75}=8.66025[/tex]
The amount of soda a dispensing machine pours into a 12-ounce can of soda follows a normal distribution with a mean of 12.45 ounces and a standard deviation of 0.30 ounce. Each can holds a maximum of 12.75 ounces of soda. Every can that has more than 12.75 ounces of soda poured into it causes a spill and the can must go through a special cleaning process before it can be sold. What is the probability that a randomly selected can will need to go through this process?
Answer:
0.1587
Step-by-step explanation:
According to the situation, the solution and the data provided is as follows
mean = 12.45 ounces
Standard deviation = 0.30 ounces
maximum = 12.75 ounces
More than ounces of soda = 12.75
Based on the above information, the probability is
[tex]Z=\frac{X-\mu }{\sigma } \\\\Z=\frac{12.75-12.45 }{0.30 } \\\\\Z=\frac{0.30 }{0.30 } \\\\Z= 1 \\\\P(X> 12.75)=1-P(X< 12.75) \\\\\P(X> 12.75)=1-P(Z< 1) \\\\[/tex]
As we know that
P(Z<1) = 0.8413
So,
P (X > 12.75) = 1 - 0.8413
= 0.1587
1. Define: Denominator
Answer:
This is an arithmetic fraction written under the line that indicates the equal part, the divisor.
Step-by-step explanation:
Answer:denominator is the lower part of a fraction.
Step-by-step explanation:
Feel pleasure to help u...
What are the side of triangle PWR
Answer:
PR, PW, RW
Step-by-step explanation:
The sides of a triangle are named by naming the vertices at either end.
Triangle PWR has vertices P, W, R. The sides connecting these are named ...
PW, WR, RP
Any name can have the letters reversed. That is, PR names the same segment that RP does.
If x is a binomial random variable with n trials and success probability p , then as n gets smaller, the distribution of x becomes
Answer:
If the value of n gests smaller then the distribution of X would be more skewed, that's a property of the binomial distribution
Step-by-step explanation:
For this problem we are assumeing that the random variable X is :
[tex] X \sim Bin(n,p)[/tex]
If the value of n gests smaller then the distribution of X would be more skewed, that's a property of the binomial distribution and if we don't satisfy this two conditions:
[tex] n p>10[/tex]
[tex]n(1-p) >10[/tex]
Then we can't use the normal approximation
The diagram shows the first four patterns of a sequence. Find an expression for the numbers of squares in the nth pattern of the sequence.
Answer:
n^2+3
Step-by-step explanation:
As we can see in the diagram
1st pattern consists from 1 square 1x1 +3 squares 1x1 each
2nd pattern consists from 1 square 2x2 +3 squares 1x1 each
3-rd pattern consists from 1 square 3x3 +3 squares 1x1 each
4-th pattern consists from 1 square 4x4 + 3 squares 1x1 each
We can to continue :
5-th pattern consists from 1 square 5x5+3 squares 1x1 each
So the nth pattern consists from 1 square nxn+3 squares 1x1 each
Or total amount of 1x1 squares in nth pattern N= n^2+3
The expression for the numbers of squares in the nth pattern of the sequence is [tex]n^{2} +3[/tex].
What is nth term of a sequence?"The nth term of a sequence is a formula that enables us to find any term in the sequence. We can make a sequence using the nth term by substituting different values for the term number(n) into it."
From the given diagram
We can see that every term is made up with a square which side is n and three small square side is 1.
So,
1st term is 1 × 1 + 3 = 4
2nd term is 2 × 2 + 3 = 4
3rd term is 3 × 3 + 3 = 12
4th term is 4 × 4 + 3 = 19
So, nth term is [tex]n^{2} +3[/tex]
Hence, The expression for the numbers of squares in the nth pattern of the sequence is [tex]n^{2} +3[/tex].
Learn more about nth term of a sequence here
https://brainly.com/question/24306119
#SPJ2