Sophie
- The formula for continuously compounded interest is given by:
[tex]A=Pe^{rt}[/tex]Where:
A is the amount after t years.
P is the principal.
r is the annual interest rate.
Therefore the equation is:
P = $3500
r = 7.05% = 0.0705
[tex]A=3500e^{0.0705t}[/tex]- Money in Sophie’s account after 3 years:
t = 3
[tex]A=3500e^{0.0705(3)}=3500e^{0.2115}=4324.35[/tex]This is $4324.35
- Money in Sophie’s account after 10 years:
t = 10
[tex]A=3500e^{0.0705(10)}=3500e^{0.705}=7083.46[/tex]This is $7083.46
Answer
Describe the type of equation that models Sophie’s situation: exponential growth model.
Create that equation of Sophie’s situation:
[tex]A=3500e^{0.0705t}[/tex]Money will be in Sophie’s account after 3 years: $4324.35
Money will be in Sophie´s account after 10 years: $7083.46
What is the length of the hypotenuse of a right triangle with legs of length 70 feet and 240 feet?
For a right-angled triangle, Pythagoras theorems hold
Pythagoras theorem states that the square of the hypotenus is equal to the sum of the square of the other two sides
[tex]\begin{gathered} h^2=70^2+240^2 \\ h^2=4900+57600 \\ h^2=62500 \\ h=\sqrt[]{62500} \\ h=250 \end{gathered}[/tex]The hypotenuse is 250 feet
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
600
Step-by-step explanation:
[tex]R(1)=400 \\ \\ R(2)=1000 \\ \\ R(2)-R(1)=600[/tex]
Round 21.897 to the nearest hundredth. Underestimate
Answer:
21.9
Step-by-step explanation:
it rounds up
Write three sentences that compare the values 12 and 3 in different ways
Given data:
The numbers given are 12 and 3.
The 12 and 3 are both positive integers in which 12 is greater than 3.
The 12 and 3 both lie on the right side of the number line in which 12 comes after 3, so 12 is bigger number than 3.
The 12 and 3 are both natural as well as rational number, 12 is nine more than 3.
To analyze the variation of vitamin supplement tablets, you randomly select and weigh 14 tablets. The results are shown below: 500.000 499.995 500.010 499.997 500.015 499.988 500.000 499.996 500.020 500.002 499.998 499.996 500.003 500.000 a. Assume this sample is taken from a normally distributed population. Construct a 90% level of confidence for the population variance and population standard deviation. b. For quality control, the population standard deviation of the tablets weights should be less than 0.015 milligrams. Does the confidence interval you constructed for the population standard deviation suggest that it is at an acceptable level? Explain your reasoning.
Answer:
a.
[tex]\begin{gathered} 0.000041\leq\sigma^2\leq0.00015 \\ 0.0064\leq\sigma\leq0.0125 \end{gathered}[/tex]b. The standard deviation is at an acceptable level
Explanation:
The confidence interval for the variance can be calculated as:
[tex]\frac{(n-1)s^2}{\chi^2_{\frac{\propto}{2}}}\leq\sigma^2\leq\frac{(n-1)s^2}{\chi^2_{1-\frac{\propto}{2}}}[/tex]Where n is the size of the sample, s² is the variance of the sample, (1-∝) is the level of confidence, and χ² is the value of chi-square with n-1 degrees of freedom.
In this case, we get that n is 14 tablets, s² is 0.000071, and 1-∝ = 90%, so ∝ is 10%.
Then, the values of chi-square with 13 (14 -1) degrees of freedom is:
[tex]\begin{gathered} \chi^2_{\frac{\propto}{2}}=22.36 \\ \chi^2_{1-\frac{\propto}{2}}=5.89 \end{gathered}[/tex]Therefore, the interval of confidence for the population variance is:
[tex]\begin{gathered} \frac{(14-1)(0.000071)}{22.36}\leq\sigma^2\leq\frac{(14-1)(0.000071)}{5.89} \\ 0.000041\leq\sigma^2\leq0.00015 \end{gathered}[/tex]Then, the standard deviation is the square root of the variance, so the interval of confidence for the population standard deviation is:
[tex]\begin{gathered} \sqrt[]{0.000041}\leq\sigma\leq\sqrt[]{0.00015} \\ 0.0064\leq\sigma\leq0.0125 \end{gathered}[/tex]Finally, since the upper limit of the interval for the standard deviation is less than 0.15 milligrams, we can say that the population standard deviation is at an acceptable level with a confidence level of 90%
Carlos builds a robot that moves with small wheels. each wheel has six 5 inch long metal spokes that meet in the center what is the length of the arc
Answer:
Explanation:
a)
The formula for calculating the length of an arc is expressed as
Length of arc = θ/360 x 2πr
where
θ is the angle subtended at the center of the circle.
r is the radius of the circle
From the information given,
diameter = 5(length of each metal spoke)
r =diameter/2 = 5/2 = 2.5
Recall, the total angle in the circle is 360 degrees. There are 8 partitions. Angle between consecutive spokes is
360/8 = 45. Thus,
θ = 45
Length of are between consecutive spokes = 45//360 x 2 x π x 2.5
Length of are between consecutive spokes = 5π/8
b) The formula for calculating the area of a sector is expressed as
area of a sector = θ/360 x πr^2
By substituting the values,
area of a sector = 45/360 x π x 2.5^2
Area of sector = 25π/32 square inches
if 5% more than A is B, and B is 15% less than C, what is the ratio of A to C?
For the given condition when B is 5% more than A and B is 15% less than C then ratio of A to C is equal to 17 : 21.
As given in the question,
Let value of A is equal to 100
As per given condition we have,
B is 5% more than A
5% of 100
= (5/100) × 100
= 5
So B is equal to
= 100 +5
= 105
A:B = 100/105
= 20/21
B is 15% less than C
let C= 100
15 % of 100
= (15/100) × 100
= 15
Value of B is equal to
= 100 - 15
= 85
B:C = 85 : 100
= 17 : 20
Ratio A : B : C
= 340 : 357 : 420
Ratio A : C = 340 : 420
= 17 :21
Therefore, for the given condition when B is 5% more than A and B is 15% less than C then ratio of A to C is equal to 17 : 21.
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A price-taking firm makes air conditioners. The market price of one of its new air conditioners is $125. The firms total cost information is given in the table below
1. Calculating the marginal cost per day yields the following results:
Air conditioners Total cost Marginal cost
per day ($ per day) ($ per day)
1 100 100
2 150 50
3 220 70
4 310 90
5 405 95
6 510 105
7 650 140
8 800 150
2. To maximize profits, the price-taking firm should produce 6 air conditioners per day.
What is the profit-maximizing point?The profit-maximizing point or units is the output and price interaction that ensures that the marginal revenue equals the marginal cost.
The marginal revenue (MR) is the revenue earned from an additional unit. The marginal cost (MC) is the production cost per additional unit.
For price-taking firms, the maximum profit is achieved at the level of output where MC equals MR.
Market Price for one unit = $125
Air conditioners Total cost Marginal cost
per day ($ per day) ($ per day)
1 100 100 (100 - 0)
2 150 50 (150 - 100)
3 220 70 (220 - 150)
4 310 90 (310 - 220)
5 405 95 (405 - 310)
6 510 105 (510 - 405)
7 650 140 (650 - 510)
8 800 150 (800 - 650)
Thus, profit is not maximized where the MC exceeds the MR. Instead producing at that unit reduces profit.
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Question Completion:Total Cost Information
Air conditioners Total cost
per day ($ per day)
1 100
2 150
3 220
4 310
5 405
6 510
7 650
8 800
1. Calculate marginal cost per day, and enter your responses as whole numbers.
2. How many air conditioners should the firm produce per day if its goal is to maximize its profit? air conditioners per day.
y=-2/3x+5 and goes through (0, -2)
with steps please
The equation of the line with coordinate (0, -2) that goes through y = -²/₃x + 5 is; y = -²/₃x - 2
What is the Equation of the Line?We know that the general formula for an equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
Now, from the given equation of y = -²/₃x + 5, we can say that;
Slope; m = -²/₃
y-intercept = 5
Thus, equation of the new line would be;
y - (-2) = -²/₃(x - 0)
y + 2 = -²/₃x
y = -²/₃x - 2
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The proportional relationship between cost and pints of blueberries is shown in the table.
Blueberries (in pints) 2 5
Cost (in dollars) 6.80 17
Describe what a graph of the proportional relationship would look like.
A coordinate plane with the x-axis labeled Cost (in dollars) and the y-axis labeled Blueberries (in pints) shows a line going through (0, 0) and (5, 17).
A coordinate plane with the x-axis labeled Cost (in dollars) and the y-axis labeled Blueberries (in pints) shows a line going through (0, 0) and (2, 6.80).
A coordinate plane with the x-axis labeled Blueberries (in pints) and the y-axis labeled Cost (in dollars) shows a line going through (0, 0) and (5, 17).
A coordinate plane with the x-axis labeled Blueberries (in pints) and the y-axis labeled Cost (in dollars) shows a line going through (0, 0) and (6.80, 2).
A graph of what the proportional relationship would look like is: C. a coordinate plane with the x-axis labeled Blueberries (in pints) and the y-axis labeled Cost (in dollars) shows a line going through (0, 0) and (5, 17).
What is a graph?In Mathematics, a graph is commonly used for the graphical representation of data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis).
Generally speaking, the graph of a proportional relationship between two variables is always characterized by a straight line with its data points passing through the origin (0, 0).
In this context, the x-axis of this graph would be labeled Blueberries (in pints) while the y-axis would be labeled Cost (in dollars), with the data points starting from the origin (0, 0) and passes through (5, 17) as shown in the image attached below.
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Answer:
C. a coordinate plane with the x-axis labeled Blueberries (in pints) and the y-axis labeled Cost (in dollars) shows a line going through (0, 0) and (5, 17).
Step-by-step explanation:
Paving stones: 174 paving stones were examined for cracks, and 16 were found to be cracked. The same 174 stones were examined for discoloration, and 21were found to be discolored. A total of 3 stones were both cracked and discolored. One of the 174 stones is selected at random. Round all answers to fourdecimal places.Part 1 of 4(a) Find the probability that it is cracked.The probability that it is cracked is 0.0919SPart 2 of 4(b) Find the probability that it is discolored.The probability that it is discolored is 0.1207Part: 2/4Part 3 of 4(c) Find the probability that it is not cracked.The probability that it is not cracked is
We are given the following information:
• 174 paving stones total (examined)
,• 16, paving stones ,cracked
,• 21, paving stones ,discolored
,• 3, paving stones ,both cracked and discolored
We are trying to find the probability of paving stones that are not cracked.
SolvingSince we know from our given that 16 paving stones were cracked plus an additional 3 paving stones were both cracked and discolored, the total amount of cracked stones out of the 174 paving stones is equal to 19.
Therefore, we know that there will be 155 paving stones that aren't cracked. In order to find the probability, we will need to divide this number over the total amount of stones present:
[tex]\text{Probability of not cracked paving stones}=\frac{155}{174}[/tex]If we evaluate this fraction, we should obtain our answer.
AnswerThe probability that a paving stone isn't cracked is equal to 0.890805.
Tom invested $2500 a year in a mutual fund for 15 years. If the market value of the fund increases 5% per year, what will be the value of the fund after 15 deposits?
The value of the mutual fund of Tom after 15 deposits will be $5197.320 .
In the question ,
it is given that , Tom invested $2500 in mutual fund for 15 years ,
So,
the investment amount(P) = $2500 .
time for investment(x) = 15 years
rate of increase(r) = 5% = 0.05
The amount of fund after 15 deposits can be calculated using the formula
amount = P*(1+r)ˣ
Substituting the values of P, x and r , we get
amount = 2500*(1 + 0.05)¹⁵
= 2500*(1.05)¹⁵
= 5197.320
Therefore , The value of the mutual fund of Tom after 15 deposits will be $5197.320 .
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Solve the following system of inequalities graphically on the set of axes below. State the coordinates of a point in the solution set.y < 2x - 5 y ≤ -x - 2
First, we need to graph the lines:
[tex]\begin{gathered} y=2x-5\text{ (slope = 2 and y-intercept = -5)} \\ y=-x-2\text{ (slope = -1 and y-intercept = -2)} \end{gathered}[/tex]In the solution of the first inequality, the points on the line are not included, then this line must be dashed. On the other hand, in the solution of the second inequality, the points on the line are included, then this line must be solid.
In both cases, the solution to each inequality is the area below each line.
Combining this information we get the next graph:
where the solution is the orange area.
From the above graph, one point in the solution set is (1, -7). We can check if this point is part of the solution by replacing it into the inequalities, as follows:
[tex]\begin{gathered} -7<2(1)-5 \\ -7<-3\text{ (True)} \\ \text{And} \\ -7\le-1-2 \\ -7\le-3\text{ (True)} \end{gathered}[/tex]Given that the point satisfies both inequalities, then it is part of the solution set.
Write about a time you have used numbers and operations in your everyday life (outside ofmath class).
When going to the movies and we pay the ticket, most of the times (if we pay in cash) we will receive change for the bill we use.
For example, if the ticket costs $7 and we pay with $10, we will receive 10-7 = $3 as change.
We then have used math to know that the change we receive is correct.
I SEEN HELP ASAP. are these following triangles similar? Yes or no and explain
Given data:
The given length of the EC is CD=9.
The given length of the CD is CD=10.
The given length of TV is TV=27.
The given length of TU is TU=30.
The ratio of the corresponding sides is,
[tex]\frac{EC}{CD}=\frac{TV}{TU}[/tex]Susbtitute the given values in the above expression.
[tex]\begin{gathered} \frac{9}{10}=\frac{27}{30} \\ =\frac{9}{10} \end{gathered}[/tex]Thus, the ratio of the corresponding sides is equal so they are similar.
want is the constant out if these options 16.2 - 3(4) + 14/2
Given the expression :
[tex]16.2-3\mleft(4\mright)+\frac{14}{2}[/tex]so, the result will be as following:
[tex]\begin{gathered} 16.2-3\mleft(4\mright)+\frac{14}{2} \\ \\ =16.2-12+7 \\ \\ =11.2 \end{gathered}[/tex]the term 16.2 is a constant
Hey there!
Whenever, you hear or see the word “constant” think of the definition ‘a specific number or value that never changes in a particular equation’
16.2 - 3(4) + 14/2
= 16.2 - 12 + 14/2
= 16.2 - 12 + 7
= 4.2 + 7
= 11.2
Now, that we have that information out the way, we can answer your equation
Your CONSTANTS aren’t:
• -3(4) because we had to simplify it and convert it to: -12
• 14/2 because we had to simplify that as well and it converted it to: 7
(That’s how we figured out to make the equation much easier to breakdown)
(By the way, you can use PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, & Subtraction) to solve for the overall problem, like how I did for you :))
This leaves the constant to: 16.2 because we didn’t have to anything to it.
Therefore, your answer should be:
16.2
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
DUE IN 40 MIN PLEASE HELP
Answer:
[tex]f(x) = $\begin{cases}3x-4 & -2\le x < 1\\x + 3 & 1 \le x \le 5\\8 & 5 \le x \le 8 \end{cases}$[/tex]
Step-by-step explanation:
The permissible values of x for a function is called the domain of the function. Permissible values mean that the function is real and defined.
The range of a function is the set of all y values for the domain
If a point on a graph is a filled circle, that point is included in the domain(x-value) and represents a ≤ or a ≥ inequality
If a point on a graph is an unfilled or hollow circle, that point is not included in the domain(x-value) and represents a < or a >inequality
Let's look at the three parts of the given piecewise graph
Piecewise part A
We see that the minimum and maximum values of x for this function are x = -2 and x = 1 respectively. The point corresponding to x= 1 is a hollow circle so it is not included in the domain whereas the point corresponding to x = -2 is included
Let's find the equation of this line:
Take 2 points on the line. We choose points (0, -4) and (1, -1)
Slope of this line is -1 -(-4)/(1-0) = (-1 + 4)/1 = 3
The y-intercept is -4
So equation of the line is y = 3x -4 for -2 ≤ x < 1
Proceeding in a similar manner we can determine the domain and function equation for the other two pieces, B and C
Piecewise part B
Domain of x : 1 ≤ x ≤5
Slope = (8-4)/(5-1) = 4/4 = 1
Equation is of the form y = 1x + b
To calculate b, plug in values of x = 1, y = 4 to get
4 = 1(1) + b
b = 3
Equation of this piecewise function is
y = x + 3 for 1 ≤ x ≤ 5
Piecewise Part C
This is a flat horizontal line at y = 8
So that is the equation of the line
The domain of this piece is 5 ≤ x ≤ 8
So we get y = 8 for [tex]$\begin{cases}3x-4 & -2\le x < 1\\x + 3 & 1 \le x \le 5\\8 & 5 \le x \le 8 \end{cases}$[/tex]
Normally, instead of using y we use f(x)
Putting all this together we get the piecewise function defined as
[tex]f(x) = $\begin{cases}3x-4 & -2\le x < 1\\x + 3 & 1 \le x \le 5\\8 & 5 \le x \le 8 \end{cases}$[/tex]
Is y=x(x+1) a valid equation?
y = x(x + 1)
Yes, it's a valid equation, there are 2 values for x and two values for y.
In my opinion it's a continuous function because if we graph it there would not be gaps on it.
help me on my hw! I don't understand (answers are already there but mine doesn't match any)
The answer is d. 82.1
Explanation:
Tan 75 = x/22
A golf lesson lasts from 10:00 a.m. – 11:15 a.m. and includes a 15-minute break with equal lengths of time before and after the break. At what time should the break start?
A golf lesson lasts from 10:00 am - 11:15 am and includes a 15 minutes break with equal lengths of time before and after the break is at 10:30 am.
Total lesson time is 1 hour and 15 minutes (10:00 - 11:15)
There is 15 minutes break with equal lengths of time before and after break.
The lesson before the break is from 10 - 10:30
Therefore , break is at 10:30 am
Lesson resumes at 10:45 when break is over then lesson runs another 30 minutes until 11:15 am (10:45 - 11:15).
Therefore, the break is at 10:30 am in mid of 10:00 am - 11:15 am.
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how do I find the correct answer? ( the top says "Triangles ABC and DEF are right triangles, as shown, ABC is similar DEF.)
The cosine relation is defined by the length of the adjacent side over the length of the hypotenuse.
So, for triangle ABC, the cosine of B is defined as:
[tex]\cos (B)=\frac{BC}{AB}[/tex]And for triangle DEF, since the triangles are similar, the cosine of B is equal the cosine of its corresponding angle E:
[tex]\cos (E)=\frac{EF}{DE}[/tex]So the correct options are the first and fifth ones.
If n = 100 and p= 1/5, what is the mean and standard deviation of this binomial distribution?
The most appropriate choice for binomial distribution will be given by-
Mean of binomial distribution= 20
Standard deviation of binomial distribution = 16
What is binomial distribution?
Let there are n number of success or failure experiment called Bernouli trial and let p be the probability of success. Binomial distribution with parameters n and p is the probability distribution of p successes in n number of Bernouli trials.
Probability mass function of Binomial distribution
P(x = k) = [tex]n \choose k[/tex][tex]p^k(1-p)^k[/tex]
Here,
n = 100,
p = [tex]\frac{1}{5}\\[/tex]
1 - p = [tex]1 - \frac{1}{5}[/tex]
= [tex]\frac{5-1}{5}[/tex]
= [tex]\frac{4}{5}[/tex]
Mean of binomial distribution = np
= [tex]100 \times \frac{1}{5}\\[/tex]
=20
Standard deviation of binomial distribution =
[tex]100 \times \frac{1}{5}(1- \frac{1}{5})\\100 \times \frac{1}{5} \times \frac{4}{5}\\16[/tex]
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Meals in a hospital cafeteria are discounted 15% for all hospital employees what will an employee pay for the grilled chicken lunch which cost a non employee $8.00
Given that the meals in a hospital cafeteria are discounted 15% for all hospital employees,
The price an employee will pay for the grill chicken lunch worth of $8.00 will be,
[tex]\text{ \$8.00}-(15\text{ \% of \$8.00)}[/tex][tex]\begin{gathered} \text{ \$8.00-(}\frac{\text{15}}{100}\times\text{ \$8.00)} \\ \text{ \$8.00-(0.15}\times\text{ \$8.00)}=\text{\$8.00- \$1.2=\$6.8} \end{gathered}[/tex]Hence, the hospital employee will pay $6.8 for the grilled chicken lunch.
describe the transformation from f to g where f(x)=x² and g(x)=(1/3)x²
describe the transformation from f to g where f(x)=x² and g(x)=(1/3)x²
In this problem we have a dilation of the y-coordinate
so
the rule is
(x,y) -------> (x,ay)
where
the scale factor a=1/3
Write each trinomial in factored form (as the product of two binomials) by showing the steps used to factor.
You have the following trinomial given in the exercise:
[tex]p^2-8p+7[/tex]Notice that is is a trinomial because it is a polynomial that has three terms.
In order to factor it (as the product ot two binomials) you can find two numbers whose sum is -8 and whose sum is 7. These numbers would be -1 and -7, because:
[tex]\begin{gathered} -1-7=-8 \\ \\ \\ (-1)(-7)=7 \end{gathered}[/tex]Then, you can factor it
[tex](p-1)(p-7)[/tex]The answer is:
[tex](p-1)(p-7)[/tex]Cuanto es 1 1/4 + 1/2 + 3 1/2 =?
Ayudaaa
Answer:
es 1 1/4 + 2/4 +3 2/4 = 5 1/4
5 1/4
find the measure of Angel A? (Round your answer to the nearest whole number)
Answer:
Concept:
To figure out the measure of angle A, we will use the sine rule below
[tex]\begin{gathered} \frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC} \\ where, \\ a=37cm \\ c=29cm \\ C=50^0 \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} \frac{a}{sinA}=\frac{c}{sinC} \\ \frac{37}{sinA}=\frac{29}{sin50^0} \\ \end{gathered}[/tex]Cross multiply, we will have
[tex]\begin{gathered} \frac{37}{s\imaginaryI nA}=\frac{29}{s\imaginaryI n50^0} \\ 29\sin A=37\times sin50^0 \\ sinA=\frac{37sin50^0}{29} \\ sinA=0.9774 \\ find\text{ the arcsin} \\ A=\sin^{-1}0.9774 \\ A=77.79^0 \\ A\approx78^0(nearest\text{ whole number\rparen} \end{gathered}[/tex]Hence,
The measure of angle A to the nearest whole number is
[tex]\Rightarrow78^0[/tex]Solve the system. Tell how many solutions the system has.-2x + 6y = 8x-3y=-3solution(s).The system has (select)(select)onenoinfinitely many
We have
-2x + 6y = 8 ...(1)
x-3y=-3 ....(2)
we need to solve the system of equations
we will multiplicate the second equation by 2
[tex]2x-6y=-6[/tex]then we sum the equation above with the first equation
[tex]-2x+2x+6y-6y=8-6[/tex]we sum similar terms, and we obtain
[tex]0=2[/tex]that's an inconsistency
so we don't have a solution
the answer is no
Task 3: Solve the following quadratic equation by extracting the square root.
Given -
(2s - 1)² = 225
To Find -
s =?
Step-by-Step Explanation -
(2s - 1)² = 225
Now, on removing square =
(2s - 1) = √225
2s - 1 = 15
2s = 15 + 1
2s = 16
s = 16/2
s = 8
Final Answer -
s = 8
2,361÷59
What is the answer with a remainder
Answer:
40 R 1.
Step-by-step explanation: