) If Daniella opens a mutual fund account with a deposit of $15,000 and it promises to
pay an annual interest rate of r%, compounded on a monthly basis.
(i) Derive a function B, which shows the balance on Daniella′
s account the end of 6 years.
(ii) Make a comparison of the rates of change in B with resect to the interest rate when r is
8% , 10% and 12%.
(b) A virus is believed to be spreading through a sheep farm according to that equation
N = 450 (
1
1 + 249e
−0.1t ) where
N is the number of sheep infected and t is the number of days.
(i) How many sheep are infected at t = 0?
(ii) Using a spreadsheet calculate the number of sheep infected after 0, 10, 30 , 50, 70, 100 days)
(iii) Will all the sheep become infected eventually? Give reasons to support your answer.
Answers
Step-by-step explanation:
(a)(i) The formula for compounded interest is:
A = P (1 + r/n)^(nt)
where A is the final amount,
P is the initial amount,
r is the annual interest rate,
n is the number of compoundings per year,
and t is the number of years.
In this case, P = 15000, n = 12, and t = 6.
B = 15000 (1 + r/12)⁷²
(a)(ii) Take derivative with respect to r using power rule and chain rule.
dB/dr = 90,000 (1 + r/12)⁷¹
Evaluate at different values of r:
\(\left[\begin{array}{cc}r&dB/dr\\0.08&144253.51\\0.10&162231.56\\0.12&182414.79\end{array}\right]\)
(b)(i) N(t) = 450 [1 / (1 + 249e^(-0.1t))]
N(0) = 450 [1 / (1 + 249)]
N(0) = 1.8
(b)(ii) Evaluate N at different values of t.
\(\left[\begin{array}{cc}t&N\\0&1.8\\10&4.9\\30&33.6\\50&168.1\\70&366.7\\100&445.0\end{array}\right]\)
(b)(iii) As t approaches infinity, N approaches 450. So yes, eventually all 450 sheep will be infected.
Related Questions
Which of them belongs in the places.
Answers
Answer:
a belongs at b.
b belongs at c
c belongs at a
a.k.a
a - > b
b - > c
c - > a
Step-by-step explanation:
i used visual representation
Help I need help I have 20 missing assignments
Answers
each function
f(x)=-4x-5;
ion for
Find ƒ(1)
for the given
Answers
When x is equal to 1, the Function f(x) = -4x - 5 yields a value of -9.
The find ƒ(1) for the function f(x) = -4x - 5, we need to substitute x = 1 into the function and evaluate the expression.
Replacing x with 1, we have:
ƒ(1) = -4(1) - 5
Simplifying further:
ƒ(1) = -4 - 5
ƒ(1) = -9
Therefore, when x is equal to 1, the value of the function f(x) = -4x - 5 is ƒ(1) = -9.
Let's break down the steps taken to arrive at the solution:
1. Start with the function f(x) = -4x - 5.
2. Replace x with 1 in the function.
3. Evaluate the expression by performing the necessary operations.
4. Simplify the expression to obtain the final result.
In this case, substituting x = 1 into the function f(x) = -4x - 5 gives us ƒ(1) = -9 as the output.
It is essential to note that the notation ƒ(1) represents the value of the function ƒ(x) when x is equal to 1. It signifies evaluating the function at a specific input value, which, in this case, is 1.
Thus, when x is equal to 1, the function f(x) = -4x - 5 yields a value of -9.
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Fill in the blank to complete the trigonometric formula.
sin(u-v)=
i need to know what to put in on the outher side
Answers
Answer
=sin (u -v)
Step-by-step explanation:
sin ( u-v): sin(u-v)
The rate constant for first-order degradation of a N2O2 in a solution (1.0 mg/ml) at 40°C
is 0.00351 hr-1, activation energy is 2000 cal/mol, and R = 1.987 cal/mol/degree.
Calculate
a. The rate constant for first-order degradation of N2O2 at room temperature (25°C).
Answers
The 0.0035 hr⁻¹ first-order degradation rate constant in the 40 °C, 1.0 mg/ml solution, where R = 1.987 cal/mol/degree and 2,000 cal/mol activation energy indicates;
a. The rate constant for first-order degradation of N₂O₂ at room temperature is approximately 4.12595 × 10⁻² hr⁻¹
What is a first-order reaction?A first order reaction is one that has a rate that varies linearly with the concentration of one reactant
The given parameters are;
Temperature of the solution = 40°C
T₁ = 40 °C + 273.15 = 313.15 K
The rate constant, K₁ = 0.00351 hr⁻¹
Concentration of the solution = 1.0 mg/ml
Activation energy, Eₐ = 2000 Cal/mol
R = 1.987 cal/mol/degree
The formula by which the rate constant can be found is presented as follows;
\(log\dfrac{k_2}{k_1} =\dfrac{E_a}{2.303\times R} \times \dfrac{T_2-T_1}{T_1\cdot T_2}\)
a. Room temperature = 25 °C
T₂ = 25 °C + 273.15 = 298.15 K
Therefore;
\(log\dfrac{k_2}{0.00351} =\dfrac{2000}{2.303\times 1.987} \times \dfrac{313.15-298.15}{313.15 \times 298.15}\)
\(k_2=0.00351 \times 10^{\left(\dfrac{2000}{2.303\times 1.987} \times \dfrac{313.15-298.15}{313.15 \times 298.15}\right)} \approx 4.12595\times 10^{-2}\)
The rate constant for first-order degradation of N₂O₂ at room temperature is k₂ ≈ 4.12595 × 10⁻² hr⁻¹Learn more about the rate constant for first-order degradation here:
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Martha’s clubhouse is shaped like
a square pyramid with four congruent equilateral triangles for its sides. All of the edges are 6 feet
long. What is the total surface area of the clubhouse including the floor? Round your answer to the nearest hundredth.
A=
Answers
The total surface area of the clubhouse including the floor is approximately 95.98 square feet.
We have,
The surface area of a square pyramid can be found by adding the area of the base to the sum of the areas of the four triangular faces.
Since the base is a square, its area is 6^2 = 36 square feet.
Each triangular face is an equilateral triangle with a side length of 6 feet, so its area can be found using the formula.
A = (√(3)/4) x s²,
where s is the length of a side.
The area of each triangular face.
A = (√(3)/4) x 6² = 9 √(3) square feet.
The total surface area is then:
A = 4 x 9 √(3) + 36
A = 36 √(3) + 36 ≈ 95.98 square feet
(rounded to the nearest hundredth)
Therefore,
The total surface area of the clubhouse including the floor is approximately 95.98 square feet.
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FOR 100 POINTS!!!!!!!!!!!
A food truck did a daily survey of customers to find their food preferences. The data is partially entered in the frequency table. Complete the table to analyze the data and answer the questions:
Likes hamburgers Does not like hamburgers Total
Likes burritos 29 41
Does not like burritos 54 135
Total 110 205
Part A: What percentage of the survey respondents liked neither hamburgers nor burritos? Show all work. (3 points)
Part B: What is the marginal relative frequency of all customers who like hamburgers? Show all work. (3 points)
Part C: Is there an association between liking burritos and liking hamburgers? Use ratios of joint and marginal frequencies to support your answer. (4 points)
Answers
Answer:
Part A:
To find the percentage of survey respondents who liked neither hamburgers nor burritos, we need to calculate the frequency in the "Does not like hamburgers" and "Does not like burritos" categories.
Frequency of "Does not like hamburgers" = Total in "Does not like hamburgers" category = 135
Frequency of "Does not like burritos" = Total in "Does not like burritos" category = 54
Total respondents who liked neither hamburgers nor burritos = Frequency of "Does not like hamburgers" + Frequency of "Does not like burritos" = 135 + 54 = 189
Percentage of survey respondents who liked neither hamburgers nor burritos = (Total respondents who liked neither hamburgers nor burritos / Total respondents) x 100
Percentage = (189 / 205) x 100 = 92.2%
Therefore, 92.2% of the survey respondents liked neither hamburgers nor burritos.
Part B:
To find the marginal relative frequency of all customers who like hamburgers, we need to divide the frequency of "Likes hamburgers" by the total number of respondents.
Frequency of "Likes hamburgers" = 110 (given)
Total respondents = 205 (given)
Marginal relative frequency = Frequency of "Likes hamburgers" / Total respondents
Marginal relative frequency = 110 / 205 ≈ 0.5366 or 53.66%
Therefore, the marginal relative frequency of all customers who like hamburgers is approximately 53.66%.
Part C:
To determine if there is an association between liking burritos and liking hamburgers, we can compare the joint and marginal frequencies.
Joint frequency of "Likes hamburgers" and "Likes burritos" = 29 (given)
Marginal frequency of "Likes hamburgers" = 110 (given)
Marginal frequency of "Likes burritos" = 70 (calculated by adding the frequency of "Likes burritos" in the table)
To assess the association, we compare the ratio of the joint frequency to the product of the marginal frequencies:
Ratio = Joint frequency / (Marginal frequency of "Likes hamburgers" x Marginal frequency of "Likes burritos")
Ratio = 29 / (110 x 70)
Ratio ≈ 0.037 (rounded to three decimal places)
TIME REMAINING
44:54
The table below shows the number of cars sold each month for 5 months at two dealerships.
Cars Sold
Month
Admiral Autos
Countywide Cars
Jan
4
9
Feb
19
17
Mar
15
14
Apr
10
10
May
17
15
Which statements are supported by the data in the table? Check all that apply.
The mean number of cars sold in a month is the same at both dealerships.
The median number of cars sold in a month is the same at both dealerships.
The total number of cars sold is the same at both dealerships.
The range of the number of cars sold is the same for both dealerships.
The data for Admiral Autos shows greater variability.
Answers
The statements supported by the data in the table are:
The mean number of cars sold in a month is the same at both dealerships.
The total number of cars sold is the same at both dealerships.
The data for Admiral Autos shows greater variability.
To determine which statements are supported by the data in the table, let's analyze the given information:
The mean number of cars sold in a month is the same at both dealerships.
To calculate the mean, we need to find the average number of cars sold each month at each dealership.
For Admiral Autos:
(4 + 19 + 15 + 10 + 17) / 5 = 65 / 5 = 13
For Countywide Cars:
(9 + 17 + 14 + 10 + 15) / 5 = 65 / 5 = 13
Since both dealerships have an average of 13 cars sold per month, the statement is supported.
The median number of cars sold in a month is the same at both dealerships.
To find the median, we arrange the numbers in ascending order and select the middle value.
For Admiral Autos: 4, 10, 15, 17, 19
Median = 15
For Countywide Cars: 9, 10, 14, 15, 17
Median = 14
Since the medians are different (15 for Admiral Autos and 14 for Countywide Cars), the statement is not supported.
The total number of cars sold is the same at both dealerships.
To find the total number of cars sold, we sum up the values for each dealership.
For Admiral Autos: 4 + 19 + 15 + 10 + 17 = 65
For Countywide Cars: 9 + 17 + 14 + 10 + 15 = 65
Since both dealerships sold a total of 65 cars, the statement is supported.
The range of the number of cars sold is the same for both dealerships.
The range is determined by subtracting the lowest value from the highest value.
For Admiral Autos: 19 - 4 = 15
For Countywide Cars: 17 - 9 = 8
Since the ranges are different (15 for Admiral Autos and 8 for Countywide Cars), the statement is not supported.
The data for Admiral Autos shows greater variability.
To determine the variability, we can look at the range or consider the differences between each data point and the mean.
As we saw earlier, the range for Admiral Autos is 15, while for Countywide Cars, it is 8. Additionally, the data points for Admiral Autos are more spread out, with larger differences from the mean compared to Countywide Cars. Therefore, the statement is supported.
Based on the analysis, the statements supported by the data are:
The mean number of cars sold in a month is the same at both dealerships.
The total number of cars sold is the same at both dealerships.
The data for Admiral Autos shows greater variability.
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drag a the right word or number
Answers
Answer:
Step-by-step explanation:
1. 2
2. Variable
3. Variable Term
4. 5
5. 5 more than the product of 8 times g.
Evaluate 2+8m if m = 4
Answers
Answer: 34
Step-by-step explanation:
The first step is if you multiply 8x4 you get 32
And then if you add 32+2 you get 34
According to PEMDAS
P=Parenthesis
E=Exponents
M=Multiplication
D=Division
A=Addition
S=Subtraction
Thus, you have to multiply, then add. If not you will get a way off answer. Also, because M comes before A.
Answer:
34
Step-by-step explanation:
To evaluate the expression 2 + 8m when m = 4, we can simply substitute 4 for m in the expression and simplify:
2 + 8m = 2 + 8 * 4
= 2 + 32
= 34
So, when m = 4, the value of the expression 2 + 8m is 34.
If you have 6 eggs and 2 bananas for 4 people, how many eggs and bananas would you need for 10 people?
Answers
Answer:
15 eggs
5 bananas
Step-by-step explanation:
6/4=x/10
6(10)=4x
60=4x
/4. /4
15=x
We need 15 eggs
2/4=x/10
2(10)=4x
20=4x
5=x
We need 5 bananas
Or
6/4=1 1/2
Now we make 1 and 1/2 have a denominator of 10
1 5/10=15/10
Meaning 15 eggs
2/4=1/2=5/10
Meaning 5 bananas
Hopes this helps please mark brainliest
Answer:you would need 15 eggs and 5 bananas for 10 people
Step-by-step explanation:multiply the 6 eggs and 2 bannanas by 2 then add half more of each
sorry if this confuses you im not a good explainer
help pleaseeeeeeee :$))$$$$
Answers
Answer:6
Step-by-step explanation: I don't really know how to explain this...
Answer:
6
Step-by-step explanation:
hi! absolute value is defined as the number of units away from zero on the number line. distance is always positive, so absolute value is always positive. therefore, the answer is 6 since you just take the negative sign away.
hope this helps!
Please kindly help
According to a newspaper article 15% more home remodeling was done in 1985 than in 1984. Professionals performed 75% of all remodeling. If $80.4 billion was spent on residential remodeling in 1985 what was the value of the work done by professionals in 1985?
(1) $ 8.4 billion
(2) $12.06 billion
(3) $20.1 billion
(4) $60 billion
(5) $60.3 billion
Answers
Answer:
(3) $20.1 billion
Step-by-step explanation:
hope it help
Answer:
(5) $60.3 billion
Step-by-step explanation:
3.3.4 Practice: Angle Relationships in Triangles
Practice
Math 8 Sem 2
Tips for Success
Read the assignment carefully and make sure you answer each part of the question or questions.
Check your work when you're done.
Your Assignment
Answer the questions to find the measures of ∠2 and ∠3.
1. What is the measure of ∠4? Explain how you know.
Write your answer in the space below.
2. What is the sum of the measures of the angles in a triangle?
Write your answer in the space below.
3. ∠1 is in a triangle with ∠4 and a 53° angle. What is the sum of the measures of those two angles?
Write your answer in the space below.
4. What is the measure of ∠1? Explain.
Write your answer in the space below.
5. Find the measure of ∠2. Explain how you found its measure.
Write your answer in the space below.
6. What is the measure of ∠3? Explain.
Write your answer in the space below.
Answers
For question 1 and 2, you should keep in mind that the sum of all angles in a triangle is 180°. 1. If the measure of one angle of a triangle is 90 degrees, you can assume that the sum of the other two triangles should be 90 degrees. Because
180 - 90 = 90
The sum of the three angles of any triangle is equal to 180 degrees.
Angle 2=127 because 180-53=127.
Angle 3=23 because 180-30-127=53
Angle 1=37 because 90-53=37
Angle 4=90
Angle 1+4=127
The measure of ∠1 is 125° .
Next x+64=110. The reason why you can do this is because ∠R is going to be an opposite interior angle. Subtract 64 from the left and right sides. x=46
Answer:
Good luck!
Step-by-step explanation:
HELP ME PLEASEEEEEEEEE
Answers
Answer:
perimeter is 34
area is 72
Step-by-step explanation:
side lengths are 8,8,9,9
add all 4 up to get perimeter of 34
area is 9x8 which is 72
show in form of p by q 0.235
Answers
Answer:
p = 235, q = 1000
Step-by-step explanation:
\( \frac{p}{q} = \frac{235}{1000} \\ \)
WRITE Math Consider 7 X 10 x 10 x 10 x 10.
Write a pattern to find the value of the expression.
Answers
Answer:
I dont know if I'm wrong but I think its
Step-by-step explanation:
7×10=70
70×10=700
700×10=7000
7000×10=70000
I MIGHT BE WRONG AND IF I AM IM SORRY
The number 55 is attached to a two-digit number to its left and the formed 4-digit number is divisible by 24. What could be the 2-digit number? List all options.
Answers
Given:
The number 55 is attached to a two-digit number to its left and the formed 4-digit number is divisible by 24.
To find:
The 2-digit numbers.
Solution:
Let the two digit number be \(ab\). Then the 4 digit number will be \(55ab\).
We know that the number \(55ab\) lies in the range 5500 to 5599.
Now,
\(5500=229\times 24+4\)
It means, \(5500-4=5496\) is divisible by 24. So, the numbers lie in the range 5500 to 5599 and divisible by 24 are:
\(5496+24=5520\)
\(5520+24=5544\)
\(5544+24=5568\)
\(5568+24=5592\)
Therefore, the possible 2-digit numbers are 20, 44, 68, 92.
Please Help!
Select the equation for a graph that is the set of all points in the plane that are equidistant from the point F(6, 0) and line x = -6.
a. x = 1/24y^2
b. x = 1/2y^2
c. x = -1/24y^2
d. x = -1/12y^2
Answers
Answer:
Letter:C
Step-by-step explanation:
#CARRY ON LEARNING
15. The length of a rectangle is 5 cm more than 4 times the width. If the perimeter of the rectangle is 50 cm,what are its dimensions? (The perimeter of a rectangle is twice the sum of the length and the width.)
Answers
Step 1: Write out the formula for the perimeter of a rectangle
\(\begin{gathered} P=2(l+w) \\ \text{ Where} \\ P=\text{ the perimeter} \\ l=\text{ the length} \\ w=\text{ the width} \end{gathered}\)Step 2: Write out the given value and substitute them into the formula above
\(\begin{gathered} \text{ The length of the rectangle is 5cm more than 4 times the width} \\ \text{therefore} \\ l=4w+5----(1) \\ \text{ the perimeter is 50cm} \\ \text{Hence} \\ 2(l+w)=50 \\ l+w=25---(2) \end{gathered}\)Substituting equation (1) into equation (2), we have
\(\begin{gathered} (4w+5)+w=25 \\ 4w+w=25-5 \\ 5w=20 \\ \frac{5w}{5}=\frac{20}{5} \\ w=4cm \end{gathered}\)Substituting the value of w into equation(1), we have
\(l=4(4)+5=16+5=21\operatorname{cm}\)Hence, the length is 21 cm and the width is 4cm
Which of the following expressions represents the distance between \dfrac52 2 5 start fraction, 5, divided by, 2, end fraction and 4\dfrac{7}{8}4 8 7 4, start fraction, 7, divided by, 8, end fraction on a number line?
Answers
Answer:
Please re word your question.
Step-by-step explanation:
It seems that the scan system has tripped up your question please repost!
Answer:
it is B
Step-by-step explanation:
Which of the following expressions represents the distance between \dfrac52
2
5
start fraction, 5, divided by, 2, end fraction and 4\dfrac{7}{8}4
8
7
4, start fraction, 7, divided by, 8, end fraction on a number line
When 58,511 is divided by 21, the quotient is 2,786 R ___.
Numerical Answers Expected!
Answer for Blank
Answers
If you take the answer, 2786 and multiple by 21
You get 58,506
Which if you subtract from 58,511 you would get 5
Which is r
WILL GIVE BRAINLYEST!!!. Clara visits the aquarium while on vacation. The aquarium is 2 1/2 miles from her hotel. She walks 1/4 mile to the bus stop, takes the bus for 1 3/4 miles, and walks the rest of the way to the aquarium. HOW FAR DID CLARA WALK AFTER GETTING OFF THE BUS? PLZ help...
Answers
Answer:
1/2 mile
Step-by-step explanation:
its 2 1/2 miles right? so u just have to find the difference.
2.5-0.25=2.25
2.25-1.75=0.5
0.5 miles is left
Angle ADB and CD are straight lines. angle ADC = 5 x angle CDB Work out the size of angle ADC.
Answers
Answer:
Step-by-step explanation:
9. Use the graph of the function f(x) = x³ – 7x² + 10x to
x`
identify its relative maximum and minimum.
da
-4
8
8
2
K
T
2
da
y
8
+w
8
maximum = 4.1, minimum = -8.2
maximum = 0.9, minimum = 3.8
Answers
The extremas of the function f(x) = x³ - 7x² + 10x are given as follows:
Relative maximum: (0.88, 4.061).Relative minimum: (3.786, -8.209).What are the relative minimums and the relative maximums of a function?The relative minimums of a function are given by the points in which the function's behavior changes from decreasing to increasing, that is, where the function curves down.The relative maximums of a function, meanwhile, are given by the points in which the function's behavior changes from increasing to decreasing, that is, where the function curves up.More can be learned about extremas of a function at https://brainly.com/question/9839310
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Really need the answers
Answers
Answer:
Of what???? what question?
What is the measure of angle AED?
Answers
Answer:
Step by step explanation:
well this is simble you just do it
Which part of a flower grows into the fruit?
the stigma
the anther
the ovule
the ovary
Answers
Answer:
ovary
Step-by-step explanation:
What is .7899 rounded 4 decimal places
Answers
Hope this helped. :)
A - on the po boyds at a emase the foot, 1, of building. He. Observes an obje- et on the top, P of the building at an angle of ele- building of 66 Aviation of 66 Hemows directly backwards to new point C and observes the same object at an angle of elevation of 53° · 1P) |MT|= 50m point m Iame horizontal level I, a a
Answers
Answer:
53\(x_{123}\) == 134 cf
Step-by-step explanation:
A - on the po boyds at a emase the foot, 1, of building. He. Observes an obje- et on the top, P of the building at an angle of ele- building of 66 Aviation of 66 Hemows directly backwards to new point C and observes the same object at an angle of elevation of 53° · 1P) |MT|= 50m point m Iame horizontal level I, a a
The height of the building is approximately 78.63 meters.
The following is a step-by-step explanation of how to solve the problem. We'll need to use some trigonometric concepts and formulas to find the solution.
Draw a diagram of the situation described in the problem to get a better understanding of the problem. The diagram would have a right-angled triangle with angle of elevation of 66° at the bottom left vertex and another angle of elevation of 53° at the bottom right vertex. The object on top of the building is at the vertex of the triangle. Point M and I on the diagram are points on the horizontal line of sight and on the ground respectively. We can label the diagram with the following values:Angle of elevation from point A = 66°Angle of elevation from point P = 53° Length of line segment AM = h Length of line segment MP = x Length of line segment IP = y Length of line segment MT = 50m. We'll use these values to calculate the length of h, which is the height of the building.Use the tangent ratio to find x:tan 66° = h / x => x = h / tan 66°. Use the tangent ratio to find y:tan 53° = h / y => y = h / tan 53°.We know that x + y = 50, so substituting the expressions for x and y from step 3 gives:h / tan 66° + h / tan 53° = 50h = 50 tan 66° tan 53° / (tan 53° + tan 66°) ≈ 78.63 m.Therefore, the height of the building is approximately 78.63 meters.
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