Answer:
- At 95% confidence interval, the true mean is ( 13.5245 < μ < 15.0755 )
- the time allowed will be 0.50 hours or 30 minutes
Step-by-step explanation:
Given the data in the question;
sample size; n = 28
mean; x" = 14.3 miles
standard deviation; S = 2 miles.
degree of freedom DF = n - 1 = 28 - 1 = 27
confidence interval = 95%
level of significance = 1 - 95% = 1 - 0.95 = 0.05
so
[tex]t_{\alpha /2, df[/tex] = [tex]t_{0.025, df=27[/tex] = 2.0518
Hence, we have;
x" + [tex]t_{\alpha /2, df[/tex]( S/√n ) = 14.3 + 2.0518( 2/√28 )
= 14.3 + 0.7755
= 15.0755 { Upper Limit }
Also,
x" - [tex]t_{\alpha /2, df[/tex]( S/√n ) = 14.3 - 2.0518( 2/√28 )
= 14.3 - 0.7755
= 13.5245 { Lower Limit }
Therefore, at 95% confidence interval, the true mean is ( 13.5245 < μ < 15.0755 )
b)
If a manager wants to be sure that the employees are not late, then he/she should consider the upper bound of the confidence interval as the permissible distance range.
Now given that the average speed were 30 miles per hour
suggested time will be;
t = Upper limit / speed
t = 15.0755 / 30
t = 0.50 hours or 30 minutes
Therefore, the time allowed will be 0.50 hours or 30 minutes
A college admissions officer takes a simple random sample of 90 entering freshman and computes their mean mathematics sat score to be 436. assume the population standard deviation is σ = 101. Based on a 99% confidence interval for the mean mathematics SAT score, is it likely that the mean mathematics SAT score for entering freshmen class is greater than 460?
Answer:
460 is part of the confidence interval, which means that we cannot say that there is significant evidence that the mean mathematics SAT score for entering freshmen class is greater than 460
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.99}{2} = 0.005[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.005 = 0.995[/tex], so Z = 2.575.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 2.575\frac{101}{\sqrt{90}} = 27.4[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 436 - 27.4 = 408.6.
The upper end of the interval is the sample mean added to M. So it is 436 + 27.4 = 463.4.
460 is part of the confidence interval, which means that we cannot say that there is significant evidence that the mean mathematics SAT score for entering freshmen class is greater than 460
The resale value V, in thousands of dollars, of a boat is a function of the number of years t since the start of 2011, and the formula is
V = 12.5 − 1.3t.
(a) Calculate V(3).
(b) In what year will the resale value be 7.3 thousand dollars?
(c) Solve for t in the formula above to obtain a formula expressing t as a function of V.
(d) In what year will the resale value be 3.4 thousand dollars?
Answer:
a) V(3) = 8.6.
b) The resale value will be 7.3 thousand dollars at the start of 2015.
c) [tex]t(V) = \frac{12.5 - V}{1.3}[/tex]
d) 2017
Step-by-step explanation:
We are given the following function:
[tex]V(t) = 12.5 - 1.3t[/tex]
(a) Calculate V(3).
This is V when t = 3. So
[tex]V(3) = 12.5 - 1.3(3) = 8.6[/tex]
So
V(3) = 8.6.
(b) In what year will the resale value be 7.3 thousand dollars?
t years after the start of 2011, and t is found when [tex]V(t) = 7.3[/tex]. So
[tex]V(t) = 12.5 - 1.3t[/tex]
[tex]7.3 = 12.5 - 1.3t[/tex]
[tex]1.3t = 5.2[/tex]
[tex]t = \frac{5.2}{1.3}[/tex]
[tex]t = 4[/tex]
2011 + 4 = 2015
The resale value will be 7.3 thousand dollars at the start of 2015.
(c) Solve for t in the formula above to obtain a formula expressing t as a function of V.
[tex]V(t) = 12.5 - 1.3t[/tex]
[tex]1.3t(V) = 12.5 - V[/tex]
[tex]t(V) = \frac{12.5 - V}{1.3}[/tex]
(d) In what year will the resale value be 3.4 thousand dollars?
t years after 2011, and t is found t when [tex]V = 3.4[/tex]. So
[tex]V(t) = 12.5 - 1.3t[/tex]
[tex]3.9 = 12.5 - 1.3t[/tex]
[tex]1.3t = 8.6[/tex]
[tex]t = \frac{8.6}{1.3}[/tex]
[tex]t = 6.62[/tex]
2011 + 6.62 = 2017
So the year is 2017.
Select the statements that describe exponential growth.
a. Exponential growth is common in many circumstances throughout nature.
b. Exponential growth is the rapid and unrestricted increase of a population.
c. Exponential growth is population growth limited by natural resources in the environment.
d. Exponential growth occurs when populations level off and stop growing.
e. Exponential growth occurs when a population increases at a fixed percentage of every generation.
Answer:
the answer is B
Step-by-step explanation:
cause exponensial means like a crazy amount very quickly
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Answer:
e. Exponential growth occurs when a population increases at a fixed percentage of every generation.
Step-by-step explanation:
Exponential growth occurs when the amount of increase is proportional to the population. That is, the increase is a fixed percentage of the population in any given time period (generation).
__
Many populations appear to have exponential growth when resources are effectively unlimited. The growth can be rapid, but isn't always. At some point, the population generally finds a limit to its growth, which then ceases to be exponential.
A function describing population growth that is jointly proportional to population and available resources is called a logistic function. It has an exponential component, but is not an exponential function.
The Table below shows the number of hours ten students spent studying for a test and their svores
Answer:
Step-by-step explanation:
By using linear regression calculator,
Linear regression equation representing the data set will be,
y = 7.79x + 34.27
Correlation coefficient of the line will be,
R = 0.98
Since, correlation coefficient of the line is (+0.98), relation between the two variables is a strong linear relationship.
That means hours spent studying has the strong relation with test scores obtained.
santino is renting a canoe from a local shop that charges a $10 fee, plus an hourly rate of $7.50. For how long can santino rent a canoe if he pays a total of $70
Answer:
Santino rented the canoe for 8 hours.
Step-by-step explanation:
The total bill is represented by the formula r(h) = $10 + ($7.50/hour)h,
where h is the number of hours over which the canoe is rented.
If the total bill is $70, then $70 = $10 + ($7.50/hour)h.
Solve this for h. Start by subtracting $10 from both sides, obtaining:
$60 = ($7.50/hour)h.
Dividing both sides by ($7.50/hour), we get:
$60
h = --------------------- = 8 hours
($7.50/hour)
Santino rented the canoe for 8 hours.
A baseball is hit and its height at different one-second intervals is recorded (See attachment)
Answer:
[tex]h(t)[/tex] is likely a quadratic function.
Based on values in the table, domain of [tex]h(t)[/tex] : [tex]\lbrace 0,\, 1,\, 2,\, 3,\, 4,\, 5,\, 6,\, 7,\, 8\rbrace[/tex]; range of [tex]h(t)\![/tex]: [tex]\lbrace 0,\, 35.1,\, 60.1\, 75.2,\, 80.3,\, 75.3,\, 60.2,\, 35.0 \rbrace[/tex].
Step-by-step explanation:
By the power rule, [tex]h(t)[/tex] is a quadratic function if and only if its first derivative, [tex]h^\prime(t)[/tex], is linear.
In other words, [tex]h(t)[/tex] is quadratic if and only if [tex]h^\prime(t)[/tex] is of the form [tex]a\, x + b[/tex] for some constants [tex]a[/tex] and [tex]b[/tex]. Tables of differences of [tex]h(t)\![/tex] could help approximate whether [tex]h^\prime(t)\![/tex] is indeed linear.
Make sure that values of [tex]t[/tex] in the first row of the table are equally spaced. Calculate the change in [tex]h(t)[/tex] over each interval:
[tex]h(1) - h(0) = 35.1[/tex].[tex]h(2) - h(1) = 25.0[/tex].[tex]h(3) - h(2) = 15.1[/tex].[tex]h(4) - h(3) = 5.1[/tex].[tex]h(5) - h(4) = -5.0[/tex].[tex]h(6) - h(5) = -15.1[/tex].[tex]h(7) - h(6) = -25.2[/tex].[tex]h(8) - h(7) = -35.0[/tex].Consecutive changes to the value of [tex]h(t)[/tex] appears to resemble a line with slope [tex](-10)[/tex] within a margin of [tex]0.2[/tex]. Hence, it is likely that [tex]h(t)\![/tex] is indeed a quadratic function of [tex]t[/tex].
The domain of a function is the set of input values that it accepts. For the [tex]h(t)[/tex] of this question, the domain of [tex]h(t)\![/tex] is the set of values that [tex]t[/tex] could take. These are listed in the first row of this table.
On the other hand, the range of a function is the set of values that it outputs. For the [tex]h(t)[/tex] of this question, these are the values in the second row of the table.
Since both the domain and range of a function are sets, their members are supposed to be unique. For example, the number "[tex]0[/tex]" appears twice in the second row of this table: one for [tex]t = 0[/tex] and the other for [tex]t = 8[/tex]. However, since the range of [tex]h(t)[/tex] is a set, it should include the number [tex]0\![/tex] only once.
Which step in the solution contains the first error ?? Please helpp
Answer:
step 4 I believe
Step-by-step explanation:
In a geometric sequence, the term an+1 can be smaller than the term ar O A. True O B. False
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Answer:
True
Step-by-step explanation:
In a geometric sequence, the terms a[n+1] and a[n] are related by the common ratio. If the sequence is otherwise unspecified, two sequential terms may have any a relation you like.* Either could be larger or smaller than the other.
__
* If one is zero, the other must be as well. Multiplying 0 by any finite common ratio will give zero as the next term.
Sonia took a loan of $10 000 from ABC bank tob pay for a renovation at home. The bank offered her a period of 30 months at a rate of 10.5%. to repay the loan:
a) Calculate the Simple Interest she would pay in 30 months.
b) Calculate the Total amount Sonia would have to repay the bank.
Answer:
a. Simple interest, S.I = $2,625
b. Total amount = $12,625
Step-by-step explanation:
Given the following data;
Principal = $10,000
Interest rate = 10.5%
Time = 30 months to years = 2.5 years
a. To find the simple interest;
Mathematically, simple interest is calculated using this formula;
[tex] S.I = \frac {PRT}{100} [/tex]
Where;
S.I is simple interest. P is the principal. R is the interest rate. T is the time.Substituting into the formula, we have;
[tex] S.I = \frac {10000*10.5*2.5}{100} [/tex]
[tex] S.I = \frac {262500}{100} [/tex]
Simple interest, S.I = $2,625
b. To calculate the total amount Sonia would have to repay the bank;
Total amount = simple interest + principal
Total amount = 2625 + 10000
Total amount = $12,625
These box plots show daily low temperature for a sample of days in two different towns
Answer:
The interquartile range (IQR) for town A, 15° is less than the IQR for town B, 20°.
Step-by-step explanation:
From the boxplot Given ;
Town A :
The first quartile, Q1 = 15
Third quartile, Q3 = 30
The interquartile range, IQR = Q3 - Q1 = 30 - 15 = 15°
TOWN B :
The first quartile, Q1 = 20
Third quartile, Q3 = 40
The interquartile range, IQR = Q3 - Q1 = 40 - 20 = 20°
The interquartile range (IQR) for town A, 15° is less than the IQR for town B, 20°.
Rounding in the calculation of monthly interest rates is discouraged. Such rounding can lead to answers different from those presented here. For long-term loans, the differences may be pronounced.
To buy a car, you borrow $27,000 with a term of five years at an APR of 6%. What is your monthly payment? (Round your answer to the nearest cent.)
$
How much total interest is paid? (Round your answer to the nearest cent.)
$
Answer:
The correct answer is -
monthly payment = 521.99
total pain intrest = 4319.14
Step-by-step explanation:
Given:
a or the borrowed amount = 27000
r or the interest rate = 6%
n = 5 years or 60 months
Monthly payment = ?
total intreset = ?
Formula:
The formula for the monthly payment is -
[tex]\frac{a}{\frac{{[(1+r)^n]-1}}{[r(1+r)^n]}} = P[/tex]
or, [tex]\frac{ar}{[1-(1+r)^{-60}}[/tex] = P
Where, the amount of the loan = a
r = 0.005 (6% annual rate—expressed as 0.06—divided by 12 monthly payments per year)
n = 60 months
Solution:
Putting all the values in the either of the following formula will give monthly payments:
[tex]\frac{27000}{\frac{{[(1+0.005)^{60}]-1}}{[0.005(1+0.005)^{60}]}} = P[/tex] or [tex]\frac{ar}{[1-(1+r)^{-60}}[/tex]
= 521.9856 or to the nearest cent 521.99.
The total intrest would be -
= (monthly payment*number of month) - amount borrowed
= 521.99*12-27000
= 31319.14-27000
= 4319.14
En una escuela hay 200 estudiantes. Si la razón entre hombres estudiantes y mujeres
estudiantes es de 3:5, ¿cuántos estudiantes son hombres y cuántas son mujeres?
Answer:
75 hombres y 125 mujeres
Step-by-step explanation:
lo siento, yo no hablo español bien
SOMENE PLS PLS HELP IL GIVE OYU A KISS AND A COOKIE FI YOU HHELP E IM BEGGING
Answer:
B
Step-by-step explanation:
SOH CAH TOA
sin theta = opp/hyp
csc theta = hyp/opp
csc theta = 10/8 = 5/4
cos theta = adj/hyp
sec theta = hyp/adj
sec theta = 10/6 = 5/3
Answer: B
Which of the following question is not considered a statistical question?
Answer:
B. How many total customers were at the story today?
Step-by-step explanation:
Option 'B' is not a statistical question because there is not more than one answer.
There is only one answer to this question.
Option 'A,' 'C,' and 'D' are statistical questions because there is more than one answer.
What amounts did each person at the store spend on their purchase?
This question has more than one answer.
How long did each customer spend shopping at the store?
What are the heights of each customer who entered the store?
These questions have more than one answer as well.
Statistical questions are questions that have more than one answer. This means you can collect data.
I, therefore, believe that option 'B' is not a statistical question.
Ahmed packs 8 text books each of mass x grams. And two dictionaries each mass y grams into a box of mass 250 grams. What is total mass of the box now?
Answer:
8x + 2y + 250 grams
Step-by-step explanation:
The box contains
8 text books each with a mass of x grams = 8x
2 dictionaries each with a mass of y grams = 2y
1 box = 250 grams
Total = 8x + 2y + 250
What is the value of x in the triangle?
3/2
X
help please<3
Answer:
x = 3
Step-by-step explanation:
Assuming the acute angle are 45degrees
Hypotenuse = 3√2
Opposite = x
According to SOH CAH TOA
Sin 45 = opposite//hypotenuse
Sin 45 = x/3√2
1/√2 = x/3√2
Cross multiply
√2x = 3√2
x = 3
Hence the value of x is 3
The square root of -2 rounded to nearest 100th?
Answer:
√-2 ≈ 1.41i
Step-by-step explanation:
√-2 = i√2 = i × 1.414.. ≈ 1.41i
what does the equation inverse of the function found in part b represent in the contract of the problem ? explain your answer .
context to question - At a carnaval , you pay $15 for admission plus $3 for each ride that you go on .
Answer:
[tex]f^{-1}(x) =\frac{x}{3} - 5[/tex]
The inverse function is to calculate the number of rides; given the amount paid
Step-by-step explanation:
Given
[tex]Admission = 15[/tex]
[tex]Ride = 3[/tex] per ride
Required
Explain the inverse function
First, we calculate the function
Let x represents the number of rides
So:
[tex]f(x) = Admission + Ride * x[/tex]
[tex]f(x) = 15 + 3 * x[/tex]
[tex]f(x) = 15 + 3x[/tex]
For the inverse function, we have:
[tex]y = 15 + 3x[/tex]
Swap x and y
[tex]x = 15 + 3y[/tex]
Make 3y the subject
[tex]3y = x - 15[/tex]
Make y the subject
[tex]y =\frac{x}{3} - 5[/tex]
Replace y with the inverse function
[tex]f^{-1}(x) =\frac{x}{3} - 5[/tex]
The above is to calculate the number of rides; given the amount paid
given the function f(x) = 2x^2 - 6x +4. calculate the following values
Answer:
x^1 = 1, x^2 =2
Step-by-step explanation:
its hard to explain but there's the answer
Maria's Pizza Palace offers 4 types of crust, 7 toppings, and 6 kinds of cheese for the mega calzone. How many different mega calzones can be made if a mega calzone contains 5 different toppings and 3 different cheeses
Answer:
210 different mega calzones can be made.
Step-by-step explanation:
Fundamental counting principle:
States that if there are p ways to do a thing, and q ways to do another thing, and these two things are independent, there are p*q ways to do both things.
Additionally:
The order in which the toppings and the cheeses are chosen is not important, which means that the combinations formula is used to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Toppings:
5 from a set of 7. So
[tex]C_{7,5} = \frac{7!}{5!2!} = 21[/tex]
Cheeses
3 from a set of 6. So
[tex]C_{6,3} = \frac{6!}{3!3!} = 20[/tex]
How many different mega calzones can be made if a mega calzone contains 5 different toppings and 3 different cheeses?
Toppings and cheeses are independent, and thus, by the fundamental counting principle:
21*20 = 210
210 different mega calzones can be made.
What is the common ratio of the sequence?
-2, 6, -18, 54,...
-3
-2
3
8
Answer:
-3
Step-by-step explanation:
can anyone help me in this questions
Answer:
Step-by-step explanation:
Write the following as an algebraic expression. Then simplify.
The total amount of money (in cents) in x nickles, (x+3) quarters, and 3x dimes. (Hint: The value of a nickel is 5 cents, the value of a quarter is 25 cents, and the value of a dime is 10 cents.)
The total amount of money is ___ cents.
(Simplify your answer. Do not factor.)
Answer:
[tex]60x+75[/tex]
Step-by-step explanation:
We want to find the total amount of money (in cents) of the expression:
[tex]\text{$x$ nickels, $(x+3)$ quarters, and $3x$ dimes}[/tex]
Since each nickel is worth five cents, each quarter 25 cents, and each dime ten cents, we can write that:
[tex]\displaystyle \text{Total}=5(x)+25(x+3)+10(3x)[/tex]
Simplify. Distribute:
[tex]T=5x+25x+75+30x[/tex]
Combine like terms. Therefore, the total amount of money (in cents) is represented by:
[tex]T=60x+75[/tex]
Five children have to form a queue. In how many different ways can they be arranged?
A. 120
B. 100
C. 60
D. 80
Answer:
120 different ways
The total number of ways to do this is the product because of the fundamental counting principle[1]. So 5x4x3x2x1 = 5! (read as “5 factorial”[2]) = 120 different ways to line up those 5 people. Five people lining up essentially means 5 people sorting into 5 positions.
3384/24 step by step ......I really need help
WILL MARK BRAINLIEST TO THE FIRST PERSON OR WHO IS RIGHT!!!!
The work of a student to solve a set of equations is shown:
Equation 1: m = 8 + 2n
Equation 2: 6m = 4 + 4n
Step 1: −6(m) = −6(8 + 2n) [Equation 1 is multiplied by −6.]
6m = 4 + 4n [Equation 2]
Step 2: −6m = −48 − 12n [Equation 1 in Step 1 is simplified.]
6m = 4 + 4n [Equation 2]
Step 3: −6m + 6m = −48 − 12n + 4n [Equations in Step 2 are added.]
Step 4: 0 = −48 − 8n
Step 5: n = −6
In which step did the student first make an error?
Step 3
Step 5
Step 4
Step 2
Answer:
Step 3
Step-by-step explanation:
Step 3 should be:
−6m + 6m = −48 − 12n + 4n + 4
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Answer:
Step 3
Step-by-step explanation:
When the equations are added in step 3, the result should be ...
-6m +6m = -48 -12n +4 +4n
In the work shown, the (+4) was left out in Step 3.
__
When the work is properly continued, it becomes ...
Step 4: 0 = -44 -8n . . . . [step 3 is simplified]
Step 5: n = -5.5 . . . . . . . [step 4 is divided by -8 and 5.5 subtracted]
Step 6: m = -3 . . . . . . . . . [n is substituted into Equation 1]
And the solution is (m, n) = (-3, -5.5).
Practice: Write and Evaluate Expressions - Practice --- Level
Which answer matches this description?
half of the difference of 25 and 7
* * (25 – 7)
3+ (25 – 7)
3 - (25 + 7)
* * (25+7)
There are 4 teams. Each team plays each other team once. How many games are played?
A 3
B 4
C. 6
D. 12
E 16
Answer:
E) 16
Step-by-step explanation:
4 * 4 = 16
Hope this helps
The solution is Option C.
The number of games played by 4 teams if they play each other only once is given by combinations and is 6 games
What are Combinations?
The number of ways of selecting r objects from n unlike objects is:
ⁿCₓ = n! / ( ( n - x )! x! )
where
n = total number of objects
x = number of choosing objects from the set
Given data ,
Let the total number of teams be n = 4 teams
Each team plays the other team only once , so x = 2
The number of games played by 4 teams if they play each other only once is given by Combination
ⁿCₓ = n! / ( ( n - x )! x! )
Substituting the values in the equation , we get
⁴C₂ = ( 4! ) / 2! x 2!
On simplifying the equation , we get
⁴C₂ = ( 4 x 3 ) / 2 x 1
⁴C₂ = 2 x 3
⁴C₂ = 6 games
Therefore , the value of ⁴C₂ =6
Hence , the number of games is 6 games
To learn more about combinations click :
https://brainly.com/question/28065038
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Find the value of the missing coefficient a in the equation y = a(x - 3)(x + 5) if the graph goes through the point (1, -6)
Plz help I will mark brainliest
Answer:
3
Step-by-step explanation:
you have to solve for x then you can find the coeeffiecnt
Leila is arranging 11 cans of food in a row on a shelf. She has 4 cans of corn, 1 can of peas, and 6 cans of beets. In how many distinct orders can the cans be arranged if two cans of the same food are considered identical.
Given:
Leila is arranging 11 cans of food in a row on a shelf. She has 4 cans of corn, 1 can of peas, and 6 cans of beets.
To find:
The distinct orders can the cans be arranged if two cans of the same food are considered identical.
Solution:
Total number of cans = 11
Cans of corn = 4
Cans of Peas = 1
Cans of beets = 6
We need to find divide total possible arrangements (11!) by the repeating arrangements (1!, 4!, 6!) to find the distinct orders can the cans be arranged if two cans of the same food are considered identical.
[tex]\text{Distinct order}=\dfrac{11!}{1!4!6!}[/tex]
[tex]\text{Distinct order}=\dfrac{11\times 10\times 9\times 8\times 7\times 6!}{1\times (4\times 3\times 2\times 1)\times 6!}[/tex]
[tex]\text{Distinct order}=\dfrac{55440}{24}[/tex]
[tex]\text{Distinct order}=2310[/tex]
Therefore, the total number of distinct orders is 2310.
