Answer:
30 sets of model B20 sets of model AStep-by-step explanation:
To maximize profit, the greatest possible number of the most profitable item should be manufactured. Remaining capacity should be used for the less-profitable item.
Up to 30 of model B, which has the highest profit, can be made each day. The remaining amount (20 sets) of the daily capacity of 50 sets should be used to make model A sets.
A mechanic sells a brand of automobile tire that has a life expectancy that is normally distributed, with a mean life of 34 , 000 miles and a standard deviation of 2500 miles. He wants to give a guarantee for free replacement of tires that don't wear well. How should he word his guarantee if he is willing to replace approximately 10% of the tires?
Answer:
He should word his statement as "Free replacement for tires that wear before 30875 miles."
Step-by-step explanation:
If he is willing to replace 10% of tires he should find the life of tires that gives an area of 10% in the normal distribution graph.
Now for 10% of area standard normal deviate Z can be obtained from normal distribution table
Using normal distribution table for 10% area we have Z = -1.28
Thus we have [tex]Z=\frac{X-\overline{X}}{\sigma }\\\\\therefore X=\sigma Z+\overline{X}[/tex]
Applying given values we get
[tex]X=-1.28\times 2500+34000\\\\X=30875miles[/tex]
The mechanic would replace the tires that spoil without covering up to 30800 miles.
What is z score?Z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:
z = (raw score - mean) / standard deviation
For a mean of 34000 miles and standard deviation of 2500. The probability of 10% correspond with a z score of -1.28. Hence:
-1.28 = (x - 34000)/2500
x = 30800
The mechanic would replace the tires that spoil without covering up to 30800 miles.
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Stacy rolls a pair of six-sided fair dice.
The probability that the sum of the numbers rolled is either a multiple of 3 or an even number is
, and the two events are exclusive.
Answer:
Pr(the sum of the numbers rolled is either a multiple of 3 or an even number)=[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
Let A be the event "sum of numbers is multiple of 3"
and B be the event "sum is an even number".
As our dice has six sides, so the sample space of two dices will be of 36 ordered pairs.
|sample space | = 36
Out of which 11 pairs have the sum multiple of 3 and 18 pairs having sum even.
So Pr(A)= [tex]\frac{11}{36}[/tex]
and Pr(B)= [tex]\frac{18}{36}[/tex]
and Pr(A∩B) = [tex]\frac{5}{36}[/tex], as 5 pairs are common between A and B.
So now Pr(A or B)= Pr(A∪B)
= Pr(A)+Pr(B) - Pr(A∩B)
= [tex]\frac{11}{36}[/tex] + [tex]\frac{18}{36}[/tex] - [tex]\frac{5}{36}[/tex]
= [tex]\frac{24}{36}[/tex]
= [tex]\frac{2}{3}[/tex]
Answer:
2/3 and NOT mutually exclusive
Step-by-step explanation:
plato
What is the value of P for the following solid figure?
PLEASE HELP ME SOLVE. So lost rn
Answer:
Step-by-step explanation:
yes 30
A square has side length of 9 in. If the area is doubled, what happens to the side length?
Answer:
The side length is multiplied by [tex]\sqrt{2}[/tex]
Step-by-step explanation:
we know that
The area of the original square is equal to
[tex]A=9^{2}=81\ in^{2}[/tex]
If the area is doubled
then
The area of the larger square is
[tex]A1=(2)81=162\ in^{2}[/tex]
Remember that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
Let
z ----> the scale factor
x ----> the area of the larger square
y ---> the area of the original square
so
[tex]z^{2}=\frac{x}{y}[/tex]
we have
[tex]x=162\ in\^{2}[/tex]
[tex]y=81\ in\^{2}[/tex]
[tex]z^{2}=\frac{162}{81}[/tex]
[tex]z^{2}=2[/tex]
[tex]z=\sqrt{2}[/tex] ------> scale factor
therefore
The side length is multiplied by [tex]\sqrt{2}[/tex]
Answer:
sq root of 2
Step-by-step explanation:
that's how Mr. Burger says it is, lol.
because the area is doubled then both side lengths are multiplied by the sq root of 2.
Suppose a 95% confidence interval for µ turns out to be (1,000, 2,100). To make more
useful inferences from the data, it is desired to reduce the width of the confidence
interval. Which of the following will result in a reduced interval width?
A. Increase the sample size.
B. Decrease the confidence level.
C. Both increase the sample size and decrease the confidence level.
D. Both increase the confidence level and decrease the sample size.
Answer:
A. Increase sample size
Step-by-step explanation:
From the formula for estimating the confidence level interval for the mean:
X - Z × s/sqrt n where; X = sample mean; Z = z value corresponding to 95%;
s = standard deviation and n = sample size
It is evident from the equation that the confidence interval for the mean is inversely proportional to the sample size (n), hence increasing the sample size will result in a reduced interval width.
Two sides of an isosceles triangle have lengths 7 and 14. Find the length of the third side.
PLS HELP
Answer:
14
Step-by-step explanation:
An isosceles triangle has two sides that are the same. If one side is 7 and another is 14, then the two possibilities are 7, 7, and 14, or 14, 14, and 7.
It can't be 7, 7, and 14, because the sum of the shortest sides of a triangle must be greater than the longest side.
Therefore, it must be 14, 14, and 7. So the third leg is 14.
The length of third side of the isosceles triangle is 14.
What is an isosceles triangle ?An isosceles triangle is a triangle that has two sides of equal length. Also the property of isosceles triangle states that the base angle of the isosceles triangle subtends angle of equal measure.
How to find the length of third side of given isosceles triangle ?It is given that the two sides of the triangle have lengths 7 and 14.
Thus for the triangle to be isosceles, the third side of the triangle will have the length as 7 or 14.
We know that the sum of any two sides of a triangle must be greater than the third side.
Thus if the third side is 7, then the sum of the sides will be (7 + 7) = 14 which is not greater than the other side. So, third side will not be of length 7 units.
The third side of the isosceles triangle is of 14 units .
Therefore, the length of third side of the isosceles triangle is 14.
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The weights of steers in a herd are distributed normally. the variance is 40,000 and the mean steer weight is 800lbs. find the probability that the weight of a randomly selected steer is between 917 and 980lbs. round your answer to four decimal places.
Answer:
0.0952 or 9.52%.
Step-by-step explanation:
The standard deviation = √(40,000) = 200.
Z-scores are 917 - 800 / 200 = 0.585 and
980 - 800 / 200 = 0.90..
From the tables the required probability =
0.81594 - 0.72072
= 0.09522 (answer).
The probability of the steer's weight falling between 917lbs and 980lbs can be determined by first calculating their respective z-scores based on given mean and variance. The difference in probabilities associated with these z-scores will give the desired probability.
Explanation:In this case, we are dealing with a normal distribution which is important when we are considering mean and variance. To find the probability that the weight of the steer falls between 917lbs to 980lbs, we need to first convert these weights into z-scores, because a z-score helps us understand if a data point is typical or atypical within a distribution.
Z-score is given by z = (x - μ) / σ, where μ is the mean and σ is the standard deviation, which is the square root of variance. Given that the mean (μ) is 800lbs and variance is 40,000, the standard deviation (σ) is √40,000=200.
So, the z-scores for 917 and 980 lbs are z1 = (917 - 800) / 200 = 0.585 and z2 = (980 - 800) / 200 = 0.90 respectively.
The probability that the weight of a randomly selected steer is between 917lbs and 980lbs is the probability that the z-score is between 0.585 and 0.90. We can find these values using a z-table or statistical software. The difference between these probabilities will give us the probability of a steer's weight falling between 917 and 980 lbs.
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A marble is dropped from a height of 1m a. How long will the ball be in the air before it strikes the ground? b. What was the average velocity of the ball during its flight c. How fast was the ball going the instant before it hit the ground
Answer:
about 452 msabout 2.214 m/sabout 4.427 m/sStep-by-step explanation:
a. We assume the appropriate equation for ballistic motion is ...
h = -4.9t^2 +1
Then h = 0 when ...
0 = -4.9t^2 +1
49t^2 = 10 . . . . . add 4.9t^2, multply by 10
7t = √10 . . . . . . . take the square root
t = (√10)/7 . . . . . . divide by the coefficient of t
The marble will be in the air about (√10)/7 ≈ 0.451754 seconds.
__
b. The average velocity is the ratio of distance to time:
v = (1 m)/((√10)/7 s) = 0.7√10 m/s ≈ 2.214 m/s
__
c. Under the influence of gravity, the velocity is linearly increasing over the time period, so its instantaneous value when the marble hits the ground will be twice the average value:
When it hits, the marble's velocity is 1.4√10 m/s ≈ 4.427 m/s.
Which of the following statements about Pascal’s Triangle are true? It is symmetrical. The first diagonal is all 1’s. The second diagonal is the counting numbers. Any number in the triangle is the sum of the two numbers directly above it. Each row adds to a power of 2.
Answer: The following statements are true:
It is symmetrical.
The first diagonal is all 1’s.
The second diagonal is the counting numbers.
Any number in the triangle is the sum of the two numbers directly above it.
Each row adds to a power of 2.
Answer:
They are all correct
Step-by-step explanation:
The revenue (in thousands of dollars) from producing x units of an item is modeled by R(x) = 12x -0.005x^2.
Find the average rate of change in revenue as x changes from 1001 to 1008.
The average rate of change in revenue is ____ dollars per unit.
(Do not round until the final answer. Then round to the nearest integer as needed.)
I just need to know how to solve this problem, I know the answer. Thank you!
Answer:
See below.
Step-by-step explanation:
Average rate of change =( R(1008) - R(1001) ) / (1008 - 1001)
=[ 12(1008) - 0.005(1008)^2 - (12(1001) - 0.005(1001)^2) ] / 7
Answer:
2
Step-by-step explanation:
Average rate of change is just the slope.
You want to find the slope of the line that goes through x=1001 and x=1008 while on R(x)=12x-0.005x^2.
So y=R(x)... R(x) will give your corresponding y values for the x's mentioned.
Just plug them in.
R(1001)=12(1001)-0.005(1001)^2=7001.995
R(1008)=12(1008)-0.005(1008)^2=7015.68
So now the question just becomes find the slope of the line that goes through
(1001,7001.995) and (1008,7015.68).
To find the slope of a line given two points: I just lined the points up and subtract vertically. Afterwards I put the second number on top of the first number.
So let's do that!
(1008 , 7015.68)
-(1001, 7001.995)
------------------------------
7 13.685
So the slope also known as the average rate of change here is 13.685/7.
Putting 13.685 divided by 7 into my calculator returns the value 1.955.
This rounded to the nearest integer is 2.
The employees of a company were surveyed on questions regarding their educational background (college degree or no college degree) and marital status (single or married). Of the 600 employees, 400 had college degrees, 100 were single, and 60 were single college graduates. The probability that an employee of the company is married and has a college degree is?
Answer:0.68
Step-by-step explanation:
Given
Total of 600 employees out of which 400 had college degree ,100 are single
and 60 were single graduates
therefore out of 100, 60 were single and rest 40 are single undergraduate
and out of 400, 60 were single graduates thus 340 are married graduate.
Now out of 600, 100 were single i.e. 500 is married
thus Probability that an employee is married and has a college degree is
=[tex]\frac{Favourable outcome }{Total outcome}[/tex]
P=[tex]\frac{340}{500}[/tex]=0.68
On March 1, 2018, Mandy Services issued a 3% long-term notes payable for $15,000. It is payable over a 3-year term in $5,000 principal installments on March 1 of each year, beginning March 1, 2019. Each yearly installment will include both principal repayment of $5,000 and interest payment for the preceding one-year period. What is the amount of total cash payment that Mandy will make on March 1, 2019?
Answer:
amount of total cash payment is $5450
Step-by-step explanation:
Given data
amount = $15000
principal = $5000
rate = 3% = 0.03
to find out
the amount of total cash payment
solution
we know according to question is Each yearly installment will include both principal repayment of $5,000 and interest payment for the preceding one-year period
so first we calculate interest i.e.
interest = rate × amount
interest = 0.03 × 15000
interest = 450
so interest is $450 for 1 year
now we calculate the amount of total cash payment i.e.
interest + principal
so the amount of total cash payment = 450 +5000 = 5450
amount of total cash payment is $5450
Mandy will make total cash payment of [tex]\fbox{\begin{minispace}\\\$\text{ }5450\end{minispace}}[/tex] on March 1, 2019.
Further explanation:
Mandy issued a 3% long-term notes payable for [tex]\$\text{ }15000[/tex] over a 3-year term in [tex]\$\text{ }5000[/tex] principal installments on March 1 each year.
Then the interest payment for the first year will apply on total amount of [tex]\$\text{ }15000[/tex].
The formula for simple interest at principal value [tex]P[/tex] and rate percentage of [tex]R[/tex] in the time of [tex]T[/tex] years is,
[tex]\fbox{\begin{minispace}\\ \math{I}=\dfrac{P\times R\times T}{100}\\\end{minispace}}[/tex]
So, the interest amount payable at the end of one year is calculated as,
[tex]I=\dfrac{15000\times 3\times 1}{100}\\I=150\times 3\\I=450[/tex]
The total cash payment to be done by Mandy after a year on March 1, 2019, is the sum of the principal installment of [tex]\$\text{ }5000[/tex] and the interest applied on the total amount.
Hence the total cash payment is obtained as,
[tex]\fbox{\begin{minispace}\\\text{Total cash payment}=5000+450=5450\end{minispace}}[/tex]
Therefore, Mandy has to make a total payment of [tex]\fbox{\begin{minispace}\\\$\text{ }5450\end{minispace}}[/tex] on March 1, 2019.
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Answer details
Grade: High school
Subject: Mathematics
Chapter: Simple Interest
Keywords: installments, one year, Mandy, principal, long-term, payable, March 1, amount, total cash, total cash payments, each year, payments, simple interest, rate percentage, sum, total amount, time, interest applied.
To be considered as a menu item for Gloria's new restaurant an item must have scored in the top 15% by the food critics in the area. The average item's score is 7 with a standard deviation of 2. Assuming that the variable is normally distributed, find the lowest score possible for a menu item to still be considered?
Answer:
Lowest score needed=4.92
Step-by-step explanation:
Using the standard normal distribution table we find the value of standard normal deviate corresponding to area of 15%
For area of 15% we have Z= -1.04
Thus we have
[tex]Z=\frac{X-\overline{X}}{\sigma }\\\\\therefore X=\sigma Z+\overline{X}\\\\[/tex]
Applying values we get
[tex]X=-1.04\times 2+7\\\\X=4.92[/tex]
Thus lowest score needed = 4.92
You start your shift at 3:00 pm. On nursing assessment rounds, you find that Mr. Johnson has an IV of D5W that is infusing at 32 gtt/min. The IV tubing is calibrated for 15 gtt/mL. How many mL will Mr. Johnson receive during your 8-hr shift?
Answer:
Mr Johnson will receive 1024 mL IV in 8 hours.
Step-by-step explanation:
Mr Johnson has an IV that is infusing at 32 gtt per minute.
So in 1 hour patient will get the drug = 32×60 = 1920 gtt
Now in 8 hours drug received by the patient = 1920 × 8
= 15360 gtt
Since IV tube is calibrated for 15 gtt per mL which means in 1 mL amount of drug is 15gtt.
Therefore, total volume of infusion (in mL) will be
= [tex]\frac{\text{Total drug infused}}{\text{Total drug in 1 mL}}[/tex]
= [tex]\frac{15360}{15}[/tex]
= 1024 mL.
Therefore, 1024 mL IV will be infused in 8 hours.
NEED HELP NOW!!
Select the correct answer.
A sphere with a radius of 4.8 centimeters is carved out of a right cone with a base radius of 8 centimeters and a height of 15 centimeters. What is the approximate volume of the remaining portion of the cone in terms of ?
Answer:
c. 172.54 pi cm^3
Step-by-step explanation:
i got it right on plato
Answer:
c. 172.54 pi cm^3
Step-by-step explanation:
PLATO
Describe how to derive the quadratic formula from a quadratic equation in standard form.
Answer:
The quadratic formula is derived from a quadratic equation in standard form when solving for x by completing the square.
Step-by-step explanation:
Answer:
The quadratic formula is derived from a quadratic equation in standard form when solving for x by completing the square. The steps involve creating a perfect square trinomial, isolating the trinomial, and taking the square root of both sides. The variable is then isolated to give the solutions to the equation.
Step-by-step explanation:
A phone company offers two monthly plans. Plan A costs $11 plus an additional $0.17
for each minute of calls. Plan B costs $16 plus an additional $0.13 for each minute of calls.
For what amount of calling in minutes do the two cost the same?
What is the cost when the two plans cost the same?
Answer:
125 minutes of calling
It will cost $32.25 when the plans cost the same.
Step-by-step explanation:
The first plan's expression would be:
11+.17x x being the number of minutes
The second plan's expression would be:
16+.13x
You must set the expressions equal to one another. So:
11+.17x=16+.13x
Then solve for x:
.17x=5+.13x
.04x=5
x=125
So the plans will cost the same after 125 minutes. To find the cost of the plans at that time, substitute 125 in for the x in one of the equations.
11+.17(125)=y y being the overall cost of the plan
11+21.25=y
32.25=y
To check your answer, you can substitute again in the other equation:
16+.13(125)=y
16+16.25=7
32.25=7
A dentist sees patients each day to clean their teeth. The function g(x) represents the number of teeth cleaned, where x is the number of people who saw the dentist. Does a possible solution of (20, 20) make sense for this function? Explain your answer.
A.) Yes. The input and output are both possible.
B.) No. The input is not possible.
C.) No. The output is not possible.
D.) No. Neither the input nor output is possible.
A.) Yes. The input and output are both possible.
Explanation:In this problem, a dentist sees patients each day to clean their teeth. So we represent this function as [tex]g(x)[/tex] where:
x: Represents the number of people who saw the dentist.
g(x): Represents the number of teeth cleaned.
So we are given a point that is solution to our function, which is [tex](20, 20)[/tex] but what does this point represent? This tells us that the dentist saw 20 patients and cleaned 20 teeth, that is, he cleaned an only teeth per patient. So this will make sense under the conditions that make it possible, for example, a volunteer dentist can see more people than a common dentist and it is likely that that volunteer person sees fewer teeth. However, it's very difficult that that dentist finds 20 people with an only tooth each. So this situation is possible, but not realistic in the real world.
if sin(x) = squareroot 2 over 2 what is cos(x) and tan(x)
Answer:
cos(x) = square root 2 over 2; tan(x) = 1
Step-by-step explanation:
[tex]\frac{\sqrt{2} }{2}[/tex]
was, before it was rationalized,
[tex]\frac{1}{\sqrt{2} }[/tex]
Therefore,
[tex]sin(x)=\frac{1}{\sqrt{2} }[/tex]
The side opposite the reference angle measures 1, the hypotenuse measures square root 2. That makes the reference angle a 45 degree angle. From there we can determine that the side adjacent to the reference angle also has a measure of 1. Therefore,
[tex]cos(x)=\frac{1}{\sqrt{2} }=\frac{\sqrt{2} }{2}[/tex] and
since tangent is side opposite (1) over side adjacent (1),
tan(x) = 1
1.The reflection image of figure 1 with respect to line m is
PLEASE HELP!!!
2.For which pair of figures is the second figure a translation image of the first:
Figures 4 and 2
Figures 1 and 3
Figures 1 and 4
Figures 2 and 1
1) The reflection image of figure 1 with respect to line m is figure 2.
2) The pair of figures for which the second figure a translation image of the first is: Figures 1 and 3
How to find the transformation?
There are different types of transformation such as:
Translation
Rotation
Reflection
Dilation
1) The reflection transformation is a mirror image of the original image.
Thus, the reflection image of figure 1 with respect to line m is figure 2.
2) The pair of figures for which the second figure a translation image of the first is:
Figures 1 and 3
Convert the Cartesian equation x^2 + y^2 = 16 to a polar equation.
Convert the Cartesian equation x^2 + y^2 + 2y = 0 to a polar equation.
Convert the Cartesian equation y = 3 to a polar equation.
Will someone tell me a good calculator to use for these equations?
Answer:
Problem 1: [tex]r=4[/tex]
Problem 2: [tex]r=-2\sin(\theta)[/tex]
Problem 3: [tex]r\sin(\theta)=3[/tex]
Step-by-step explanation:
Problem 1:
So we are going to use the following to help us:
[tex]x=r \cos(\theta)[/tex]
[tex]y=r \sin(\theta)[/tex]
[tex]\frac{y}{x}=\tan(\theta)[/tex]
So if we make those substitution into the first equation we get:
[tex]x^2+y^2=16[/tex]
[tex](r\cos(\theta))^2+r\sin(\theta))^2=16[/tex]
[tex]r^2\cos^2(\theta)+r^2\sin^2(\theta)=16[/tex]
Factor the [tex]r^2[/tex] out:
[tex]r^2(\cos^2(\theta)+\sin^2(\theta))=16[/tex]
The following is a Pythagorean Identity: [tex]\cos^2(\theta)+\sin^2(\theta)=1[/tex].
We will apply this identity now:
[tex]r^2=16[/tex]
This implies:
[tex]r=4 \text{ or } r=-4[/tex]
We don't need both because both of include points with radius 4.
Problem 2:
[tex]x^2+y^2+2y=0[/tex]
[tex](r\cos(\theta))^2+(r\sin(\theta))^2+2(r\sin(\theta))=0[/tex]
[tex]r^2\cos^2(\theta)+r^2\sin^2(\theta)+2r\sin(theta)=0[/tex]
Factoring out [tex]r^2[/tex] from first two terms:
[tex]r^2(\cos^2(\theta)+\sin^2(\theta))+2r\sin(\theta)=0[/tex]
Apply the Pythagorean Identity I mentioned above from problem 1:
[tex]r^2(1)+2r\sin(\theta)=0[/tex]
[tex]r^2+2r\sin(\theta)=0[/tex]
or if we factor out r:
[tex]r(r+2\sin(\theta))=0[/tex]
[tex]r=0 \text{ or } r=-2\sin(\theta)[/tex]
r=0 is actually included in the other equation since when theta=0, r=0.
Problem 3:
[tex]y=3[/tex]
[tex]r\sin(\theta)=3[/tex]
A Cartesian equation can be converted to a polar equation using trigonometric relations. For example, the equations [tex]x^2 + y^2 = 16, x^2 + y^2 + 2y = 0,[/tex] and y = 3 can be transformed into the polar forms r = 4, r = -2sin(θ), and r = 3/cos(θ) respectively. The TI-84 calculator is recommended for these conversions.
Explanation:In Mathematics, specifically in the conversion of Cartesian equations to polar equations, we have two basic formulas from trigonometry. These are r2 = x2 + y2 and tan(θ) = y/x. But for regions where x might be zero, it is advisable to remember the Cartesian-polar relations which are x = rcos(θ), y = rsin(θ).
For x2 + y2 = 16, by substituting the first relation r2 = x2 + y2 we can get the polar equation r = 4. For x2 + y2 + 2y = 0, we complete the square on the left side then apply our formulas, resulting in a polar equation of r = -2sin(θ). For y = 3, this is a horizontal line in the Cartesian coordinate system, so we use y = rsin(θ) and solve for r to give the polar equation r = 3/cos(θ).
As for a suitable calculator, the TI-84 would be a good option for these conversions as it has the functionality to convert between these forms easily.
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. You deposit $10,000 in an account that pays 6.92% annual interest. Find the balance after 5 years if the interest is compounded with the given frequency.
a. Monthly
b. Daily
c. Quarterly
d. Weekly
a. Monthly: $14,185.30 b. Daily: $14,185.50 c. Quarterly: $14,320.00 d. Weekly: $14,372.70.
To find the balance after 5 years with different compounding frequencies, we'll use the compound interest formula:
[tex]\[A = P \left(1 + \frac{r}{n}\right)^{nt}\][/tex]
Where:
- [tex]\(A\)[/tex] is the amount of money accumulated after \(n\) years, including interest.
- [tex]\(P\)[/tex] is the principal amount (the initial amount of money).
- [tex]\(r\)[/tex] is the annual interest rate (in decimal).
- [tex]\(n\)[/tex] is the number of times that interest is compounded per year.
- [tex]\(t\)[/tex] is the time the money is invested for, in years.
Given:
- [tex]\(P = $10,000\)[/tex]
- [tex]\(r = 6.92\% = 0.0692\)[/tex]
Let's calculate each scenario:
a. Monthly compounding (12 times per year):
[tex]\[n = 12\][/tex]
[tex]\[A = 10000 \left(1 + \frac{0.0692}{12}\right)^{12 \times 5}\][/tex]
[tex]\[A = 10000 \left(1 + \frac{0.0692}{12}\right)^{60}\][/tex]
[tex]\[A[/tex] ≈ [tex]10000 \times (1.005766)^{60}[/tex]
[tex]\[A \approx10000 \times 1.41853\][/tex]
b. Daily compounding (365 times per year):
[tex]\[n = 365\][/tex]
[tex]\[A = 10000 \left(1 + \frac{0.0692}{365}\right)^{365 \times 5}\][/tex]
[tex]\[A = 10000 \left(1 + \frac{0.0692}{365}\right)^{1825}\][/tex]
[tex]\[A[/tex] ≈ [tex]10000 \times (1.000189)^{1825}[/tex]
[tex]\[A[/tex] ≈ [tex]10000 \times 1.41855[/tex]
[tex]\[A[/tex] ≈ [tex]\$14,185.50\][/tex]
c. Quarterly compounding (4 times per year):
[tex]\[n = 4\][/tex]
[tex]\[A[/tex] = [tex]10000 \left(1 + \frac{0.0692}{4}\right)^{4 \times 5}[/tex]
[tex]\[A[/tex] = [tex]10000 \left(1 + \frac{0.0692}{4}\right)^{20}[/tex]
[tex]\[A[/tex] ≈ [tex]10000 \times (1.0173)^{20}[/tex]
[tex]\[A[/tex] ≈ [tex]10000 \times 1.432[/tex]
[tex]\[A[/tex] ≈ [tex]\$14,320.00[/tex]
d. Weekly compounding (52 times per year):
[tex]\[n = 52\][/tex]
[tex]\[A = 10000 \left(1 + \frac{0.0692}{52}\right)^{52 \times 5}\][/tex]
[tex]\[A = 10000 \left(1 + \frac{0.0692}{52}\right)^{260}\][/tex]
[tex]\[A \approx 10000 \times (1.0013308)^{260}\][/tex]
[tex]\[A \approx10000 \times 1.43727\][/tex]
[tex]\[A \approx \$14,372.70\][/tex]
So, after 5 years, the balances would be:
a. Monthly compounding: [tex]\$14,185.30[/tex]
b. Daily compounding: [tex]\$14,185.50[/tex]
c. Quarterly compounding: [tex]\$14,320.00[/tex]
d. Weekly compounding: [tex]\$14,372.70[/tex]
Identify the values of a, b, and c.
a=
b=
C=
Given y = (2x + 3)? choose the standard form of
the given quadratic equation
0 = 25x2
0 = 4x2 +9
0 = 4x2 + 10x + 6
✓ 0 = 4x2 + 12x + 9
COMPLETE
RETRY
Answer:
a=4b=12c=9You have correctly selected the standard form.Step-by-step explanation:
(2x +3)² = (2x)² + 2(2x)(3) +(3)²
= 4x² +12x +9
Comparing that to ax² +bx +c, we can identify ...
a = 4b = 12c = 9The values of a, b, and c are:
a = 4
b = 12
c = 9
The given quadratic equation is:
y = (2x + 3)²
A quadratic equation is of the form:
y = ax² + bx + c
Expand the equation y = (2x + 3)²
y = (2x + 3)(2x + 3)
y = 4x² + 6x + 6x + 9
y = 4x² + 12x + 9
Comparing y = 4x² + 12x + 9 with y = ax² + bx + c
a = 4
b = 12
c = 9
Learn more here: https://brainly.com/question/17210919
Determine whether the sequence converges or diverges. If it converges, give the limit.
60, -10, 5/3, -5/18
Diverges
Converges; 11100 (this is definitely the wrong answer.)
Converges; 72
Converges; 0
Answer:
Converges; 51 3/7
Step-by-step explanation:
The common ratio is -10/60 = (5/3)/-10 = (-5/18)/(5/3) = -1/6.
Then the sum of the sequence is given by ...
S = a1/(1 -r) = 60/(1 -(-1/6))
S = 60/(7/6) = 360/7
S = 51 3/7
_____
If you erroneously evaluate the formula for the sum using +1/6 as the common ratio, then you will get S=60/(1-1/6) = 60·6/5 = 72.
what is the slope of the line
A: -3
B: 1
C:0
D: undefined
Answer:
A. -3
Step-by-step explanation:
Answer:
Its undefined or D
Step-by-step explanation:
A undefined slope is something that is vertical or horizontal. The provided images explains it! Hope it helps!
The number N = 100 + 100^2 + 100^3 + ... + 100^n . Find the least possible value of n such that the number N is divisible by 11. NEED QUICKLY! Thanks!!!
Answer:
Step-by-step explanation:
very interesting question. The temptation is to say that n should be 11 and that likely is divisible by 11 but it may not be the smallest.
100 + 100^2 = 100 + 10000 = 10100
The pattern of the series goes 101010101 ... 00...
100 / 11 = The remainder is 1/11
10100 / 11 = the remainder is 2/11
1010100 /11 the remainder is 3/11
The pattern suggests that the remainder will be 0 then n = 11
There might be other ways of doing this, but I don't know them.
Solve the formula for converting temperature from degrees celsius to degrees fahrenheit for c? F=9/5C+32
Final answer:
To convert Fahrenheit (F) to Celsius (C), subtract 32 from the Fahrenheit value, then multiply by 5/9 to get the Celsius value; the formula is C = (5/9)(F - 32).
Explanation:
Converting Fahrenheit to Celsius
To solve the formula for converting temperature from degrees Fahrenheit (F) to degrees Celsius (C), we are given the formula F = (9/5)C + 32. The student needs to find the value of C. To do this, we'll follow these steps:
Isolate the term containing C by subtracting 32 from both sides of the equation, which gives us F - 32 = (9/5)C.
Then, to solve for C, multiply both sides of the equation by the reciprocal of (9/5), which is (5/9), resulting in (5/9)(F - 32) = C.
Therefore, the converted equation for Celsius is C = (5/9)(F - 32), which can be used to find the Celsius temperature corresponding to a given Fahrenheit temperature.
Please give an example of another function whose inverse is only defined if we restrict the domain of the original function.
(In general, a function must be one-to-one in order to have an inverse function. Some functions, though, have inverses that are very useful but require us to restrict the original function to an interval where it IS one-to-one. This is the case with all of our trigonometric functions.)
Answer:
f(x) = x^2
Step-by-step explanation:
The square root function is defined to have a non-negative range only. That corresponds to restricting the domain of f(x) = x^2 to positive values of x.
_____
The attached graph shows the domain-restricted f(x)=x² in solid red and the corresponding f⁻¹(x) = √x in solid blue. The other halves of those curves are shown as dotted lines (and are inverse functions of each other, too). The dashed orange line is the line of reflection between a function and its inverse.
Answer:
OH NANANA
Step-by-step explanation:
Find all real numbers $x$ such that $3x - 7 \le 5x +9$. Give your answer as an interval.Find all real numbers $x$ such that $3x - 7 \le 5x +9$. Give your answer as an interval.Find all real numbers $x$ such that $3x - 7 \le 5x +9$. Give your answer as an interval.Find all real numbers $x$ such that $3x - 7 \le 5x +9$. Give your answer as an interval.Find all real numbers $x$ such that $3x - 7 \le 5x +9$. Give your answer as an interval.Find all real numbers $x$ such that $3x - 7 \le 5x +9$. Give your answer as an interval.Find all real numbers $x$ such that $3x - 7 \le 5x +9$. Give your answer as an interval.Find all real numbers $x$ such that $3x - 7 \le 5x +9$. Give your answer as an interval.
Select the correct answer.
Given: BC || DE, and ∠GAC ≅ ∠AFD.
----------------------------------------------------------
What is the missing step in the proof?
Answer:
B
Step-by-step explanation:
In step 1, we found ∠GAC ≅ ∠AFD.
In step 2, we found ∠GAC ≅ ∠AFE.
Therefore, by transitive property of equality, ∠AFD ≅ ∠AFE.
The ceiling function maps any number to the least integer that is _[blank]_ the number.
Which phrase correctly fills in the blank of the previous statement?
A less than or equal to
B less than
C greater than or equal to
D greater than
Answer:
C. greater than or equal to
Step-by-step explanation:
For example,
ceiling(5) = 5
ceiling(5.1) = 6
ceiling(-5) = -5
ceiling(-5.1) = -5