Answer:
(a) [tex]f(n)= 900n -100[/tex]
(b) [tex]f(1) = 800[/tex]; [tex]f(n) = f(n-1) +900[/tex] for [tex]n \ge 2[/tex]
Step-by-step explanation:
Given
[tex]f(1) = 800[/tex] --- first month
[tex]d = 900[/tex] --- difference in distance covered each month
Required
Find f(n)
To do this, we have:
[tex]a_n = a_1 +d(n -1)[/tex]
Where
[tex]a_1 = f(1) = 800[/tex]
This gives:
[tex]a_n = 800 +900(n -1)[/tex]
[tex]a_n = 800 + 900n - 900[/tex]
Collect like terms
[tex]a_n= 900n +800-900[/tex]
[tex]a_n= 900n -100[/tex]
So, we have:
[tex]f(n)= 900n -100[/tex]
As a recursion, we have:
[tex]f(1) = 800[/tex]
For every other month i.e. [tex]n \ge 2[/tex]
We have:
[tex]f(n) = f(n-1) +900[/tex] for [tex]n \ge 2[/tex]
Which means 900 miles plus distance covered in previous month
i would love a little help
Step-by-step explanation:
36A) AB = 4/ sin 30° = 4/ 0.5 = 8 cm
36B) AC = 4/ tan 30° = 4/ 0.577 = 6.9 cm
36C) BD = 4/sin 45° = 4/ 0.707 = 5.7 cm
36D) area of ∆ABC = ½×6.9×4= 13.8 cm²
36E) sin A = sin 30° = 0.5
A car salesman will make $1400 salary this month and will earn an extra $500 each time he sells a car. Write an equation for the situation. Determine how much money he will make if he sells 7 cars.
Given:
Fixed salary = $1400
Additional salary = $500 each time he sells a car.
To find:
The equation for the situation and how much money he will make if he sells 7 cars.
Solution:
Let y be the total salary of the salesman after selling x cars.
He will earn an extra $500 each time he sells a car. So, extra money earned by him after selling x cars is 500x.
Total salary = Fixed salary + Additional salary
[tex]y=1400+500x[/tex]
Substituting [tex]x=7[/tex], we get
[tex]y=1400+500(7)[/tex]
[tex]y=1400+3500[/tex]
[tex]y=4900[/tex]
Therefore, the required equation for the given situation is [tex]y=1400+500x[/tex] and the salesman will earn $4900 if he sells 7 cars.
Your class earned $110.00 Saturday afternoon by washing cars to raise money for a class trip. This is 14 of the money needed for the trip. What is the total amount needed?
Answer: $1,540.00 is the total amount needed for the class trip
Step-by-step explanation:
Data: $110.00 earned for class trip
14th of the money needed
Money needed: x
Step one, Make the equation
110x14=x
Reason: Since we know 110.00 is a 14th of the money needed, we know multipling it by 14 will get us the money needed for the class trip. Having it in an equation will make it easier to solve.
Step two, Evaluate the equation
110x14=x=1540=x
Reason: The only thing that was left to do was to multiply 110 by 14 to get 1540 since the x was already isolated to begin with. That leaves us with the answer of x=1540.
However, since this is a real world problem, we have to make the answer more realistic so the final answer is '$1,540.00 is the total amount needed for the class trip'
I hope this helps!
In a survey of 802 U.S. adult drivers, 265 state that traffic is getting worse in their community. Construct a 95% confidence interval for the proportion of residents who think traffic is getting worse in their community.
Answer:
The 95% confidence interval for the proportion of residents who think traffic is getting worse in their community is (0.2978, 0.3630).
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].
In a survey of 802 U.S. adult drivers, 265 state that traffic is getting worse in their community.
This means that [tex]n = 802, \pi = \frac{265}{802} = 0.3304[/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].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3304 - 1.96\sqrt{\frac{0.3304*0.6669}{802}} = 0.2978[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3304 + 1.96\sqrt{\frac{0.3304*0.6669}{802}} = 0.3630[/tex]
The 95% confidence interval for the proportion of residents who think traffic is getting worse in their community is (0.2978, 0.3630).
please help me i really need help please help me
9514 1404 393
Answer:
735.6 in³
Step-by-step explanation:
The formula for the volume of a sphere is ...
V = 4/3πr³ . . . . where r is the radius
The radius is half the diameter, so we can write this in terms of diameter as ...
V = (4/3)π(d/2)³ = (π/6)d³
Using the given diameter, the volume is ...
V = (π/6)(11.2 in)³ ≈ 735.6186 in³
The volume is about 735.6 cubic inches.
Last semester, Mr. Dean had 8 students who built a sailboat in 160 working hours. The time that
takes for a group of students to build a sailboat varies inversely as the number of students s working on the
sailboat. How many hours would it take 12 students to build the bout?
Answer:
106.67 hours
Step-by-step explanation:
Total hours
160 * 8 = 1,280
Hours for group of 12
1280 / 12 = 106.6666666667
Slove it step by step
Answer:
17is the truth
Step-by-step explanation:
I need the answer fast
The answer is the first one, A = 0.5bh. I hope this helps, have a good day!
An electronics store advertises that one lucky customer will be given a television at the store's 10th anniversary celebration on the day of the
celebration, 150 customers, of which 82 are less than 30 years old and 68 are 30 years old or more, complete a form to enter for the chance to win
the television. The manager of the store wants to select the winner by drawing a form out of a box, but the box can only hold 100 forms.
Which method ensures both that the manager can use the box for the selection and that each customer has a fair chance of winning?
A. Divide the forms into two lots based on age. Then, randomly select one of the lots and place it in the box Randomly select the
winning customer's form out of the box.
B. Randomly divide the 150 forms into three equal-sized lots. Then, randomly select two of the lots and place them in the box
Randomly select the winning customer's form out of the box
c. Sort the forms alphabetically by last name Then, place the first 100 forms into the box Randomly select the winning customer's
form out of the box
D. Randomly divide the 150 forms into five equal-sized groups. Then randomly select 4 of the groups and place them in the box
Randomly select the winning customer's form out of the box
Answer:
the answer to this question is"B"
B. Randomly divide the 150 forms into three equal-sized lots. Then, randomly select two of the lots and place them in the box
Randomly select the winning customer's form out of the box
What a in electronics?AMPERE - A unit of measure for the flow of current in a circuit. One ampere is the amount of current flow provided when one volt of electrical pressure is applied against one ohm of resistance.
What is the use of electronics?Electronics uses active devices to control electron flow by amplification and rectification, which distinguishes it from classical electrical engineering, which only uses passive effects such as resistance, capacitance and inductance to control electric current flow.
To learn more about Electronics, refer
https://brainly.com/question/18569581
#SPJ2
Distance on a Coordinate Plane
Determine the distance between the two points.
Answer:
The distance between the points is five for the first one and 7 for the second one.
Step-by-step explanation:
Find the volume of a cone with a height of 13 cm and a radius of 5 cm.
Answer:
V≈340.34
Step-by-step explanation:
V=πr2h
3=π·52·13
3≈340.3392
how to put 10x - 3y= -6 in slope intercept form
Answer:
y=10/3x+2
HOPE THIS HELPS
- Todo ❤️
Step-by-step explanation:
10x-3y=-6
-10x. -10x
-3y=-6-10x
/-3. /-3
y=10/3x+2
what is the volume of the aquarium?
Answer:
3000 in3 ? I haven't actually done this i-ready before- but I believe it's
Width x Length x Height = Final result?
Step-by-step explanation:
I need Help!
+9 - (+12) =?
Answer:
+9-12
==3
Step-by-step explanation:
when u multiply - and + it will always be -
Answer:
To simplify this, it is simply.
9 - 12
Because the + means its a positive.
9 - 12 = - 3
I need help plz
urgent
Answer:
B
Step-by-step explanation:
An art class is planning to paint a mural on an outside wall.The figure below is a scale
drawing of the wall. What is the area of the actual wall?
Answer:
Step-by-step explanation:
I dont see The figure to hepl you
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PLLS
DUE RN
WILL
GIVE BRAINLIST
X
X
X
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Answer:
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Step-by-step explanation:
41/8 = 5.125
The probability that a birth in the United States is male during 2018 is 0.511. Suppose a random number generator from 1 to 1,000 is used as a statistical model to create simulated results for births in the United States during 2018. Suppose the numbers 1 to 511 represent a male birth in the United States during 2018 and 512 to 1,000 represent a female birth in the United States during 2018. Explain whether the following results are consistent with the model, and if not, explain the expected number of male births and the expected number of female births for 300
trials.
In 300
simulated trials, 171 of the births are female and 129 are male.
Answer:
Step-by-step explanation:
The probability that a birth in the United States is male during 2018 is 0.511. So there are slightly more males than females born.
In 300 simulated trials, 171 of the births are female and 129 are male. More females are born so it is not consistent with the model.
The expected number of male birth for 300 trials should be 300*0.511 = 153.
The expected number of female = 300-153 = 147
Cos 0 =
I need this as fast as I can please
Step-by-step explanation:
I hope you understand what I wrote
Answer:
cos=Adjacent / hypotenuse
[tex] \cos = \frac{35}{37} [/tex]
choose B.
The expense ratio (in percentage) for large-cap growth mutual funds have the following sample data0.52, 1.06, 1.26, 2.17, 1.55, 0.99, 1.10, 1.07, 1.81, 2.05 0.91, 0.79, 1.39, 0.62, 1.52, 1.02, 1.10, 1.78, 1.01, 1.15The data is believed to be normally distributed.a. Is there compelling evidence for concluding that the population mean expense ratio exceeds 1%? Carry out a test of the relevant hypothesis using a significance level 0.01.b. Referring back to part (a), describe in context type I and II errors and say which error you might have made in reaching your conclusion. The source from which the data was obtained reported that ? = 1.33 for the population of all 762 such funds. So did you actually commit an error in reaching your conclusion?c. Suppose that ? = 0.5, determine and interpret the power of the test in part (a) for the actual value of ? stated in (b).
Answer:
Part a: Since the calculated value of t = 2.412 does not fall in the critical region t > ± 2.539 we conclude that population mean expense ratio does not exceed 1% at 0.01 significance level.
Part b: Yes we accepted the null hypothesis when it is false so we made a type II error.
Part c: Power = 0.6591=0.66
Step-by-step explanation:
Part a:
Let the null and alternate hypotheses be
H0: u ≤ 1 against the claim Ha: u > 1
The significance level is ∝=0.01
As the standard deviation of the population is not given we use t- test which has n-1= 20-1= 19 degrees of freedom
This is one tailed test the critical region is t > ± 2.539
The mean is calculated to be 1.24 and standard deviation of the sample = s= 0.4486
We take population mean = u= 1
The test statistic is
t = x`-u/ s/ √n
t= 1.24-1 / 0.445/√20
t= 0.24/0.0995
t= 2.412
Since the calculated value of t = 2.412 does not fall in the critical region t > ± 2.539 we conclude that population mean expense ratio does not exceed 1% at 0.01 significance level.
Part b:
Type I errors are those errors when the null hypothesis is true and is rejected.
Type II errors are those in which the null hypothesis is false and is accepted.
If we had rejected the null hypothesis as it was true then we would have made a type I error.
Population mean = u = 1.33
And our null hypothesis is u= 1
Yes we accepted the null hypothesis when it is false so we made a type II error.
Part c:
When σ= 0.5
For Part a: μ= 1.33
Power = P (reject H0/ H0 is false)
= 1-β
P (reject H0/ H0 is false) = P (z > 2.539+ (u`-u0) / σ*√n)
= P (z > 2.539+ (1-1.33) /0.5 *√20)
=P (z > 2.539-2.9516)
= P (z > 0.4126)
= 0.5 - P (z= 0.2938) from the area of table.
= 0.5- 0.1591
=0.3409
Power = 1-β = 1- 0.3409= 0.6591=0.66
BRAINLIEST PLEASSEEEEE HELP
7TH GRADE MATH
10PTSSSSS EASYYY
PLEASE HELP
What will be the perimeter and the area of the rectangle below if it is enlarged using a scale factor of 4.5?
Perimeter = 46 cm, area = 131.25 cm2
Perimeter = 126 cm, area = 972 cm2
Perimeter = 46 cm, area = 972 cm2
Perimeter = 126 cm, area = 131.25 cm2
Answer:
B
Step-by-step explanation:
Segment AB, with endpoints A(-6,9) and B(12, -3), is dilated by a scale factor of 2/3 centered at the origin. What are the coordinates of A'?
9514 1404 393
Answer:
A'(-4, 6)
Step-by-step explanation:
When dilation is about the origin, the image points are the preimage points multiplied by the scale factor.
A' = (2/3)A = (2/3)(-6, 9)
A' = (-4, 6)
Answer:
(-4, 6)
Step-by-step explanation:
How do I multiply 73.458 × 0.39
Let X and Y denote the latitude and longitude of a person who is thought to be lost in a certain part of a forest. If we assume that the density of X is uniform for 2 < X < 8.2 and the density of Y is also uniform for 3.01 < Y < 6.3, and we assume that X and Y are independent, then the joint density of X and Y is
Answer:
P(X, Y) = 1/(20.398 ) if X ∈ (2, 8.2) and Y ∈ (3.01, 6.3)
P(X, Y) = 0 if X ∉ (2, 8.2) and Y ∉ (3.01, 6.3)
Step-by-step explanation:
We know that the possible values of X (all with the same probability) are:
2 < X < 8.2
And for Y we have the range (also uniform):
3.01 < Y < 6.3
Then we have a rectangle of area.
(8.2 - 2)*(6.3 - 3.01) = 20.398
Such that the probability for all the points inside the rectangle should be exactly equal, then we will have:
P(X, Y) = 1/(20.398 ) if X ∈ (2, 8.2) and Y ∈ (3.01, 6.3)
Such that if we integrate this in the given region, the integral will be equal to 1, as we should expect.
And zero if the point is outside that region, this is:
P(X, Y) = 0 if X ∉ (2, 8.2) and Y ∉ (3.01, 6.3)
For each of the regions D in R^2 below, fill in the blank so that the statements are true:
A continuous function on D= {(x,y) ∈ R^2 | 2x^4+6y^2 >= 152} __________ have an absolute maximum.
a. must
b. might or might not
c. must not
Answer:
b. might or might not
Step-by-step explanation:
Theorem:
If f is a continuous function in a bounded interval, it must have an absolute maximum.
In this question:
The interval is 2x^4+6y^2 >= 152, which goes to infinite, meaning it is not bounded, and so the function might or might not have an absolute maximum, and the correct answer is given by option b.
Answer:
b. might or might not
Step-by-step explanation:
For each of the regions D in R^2 below, fill in the blank so that the statements are true: might or might not
1 hundredth + 3 tenths =?hundredths
Answer:
.01 + .3 = 0.31
Step-by-step explanation:
Solve for x
3x−2=4x+5
Answer:
the answer for x equal negative 7
What is the length of the sink using the red line on the tape measure?
Answer:
A.
Step-by-step explanation:
Need help asap!! What is the circumference of the circle shown?
Answer:
56.5
Step-by-step explanation:
Circumference = [tex]\pi d[/tex]
C = 3.14(18) = 56.52
which fraction is equivalent to 0.63? A. 7/11 B. 19/30 C. 63/100 D. 63/1000
Answer:
C. 63/100
hope this helps
have a good day :)
Step-by-step explanation: