Answer:
[tex](a)\ k(r) = \ln(1+r)[/tex]
[tex](b)\ r(T_2) = 2^{1/T_2}-1[/tex]
[tex](c)\ T_2(k) = \frac{\ln(2)}{k}[/tex]
Step-by-step explanation:
Given
[tex]y(t) = y_0e^{kt}[/tex]
[tex]y(t) = y_0(1+r)^t[/tex]
[tex]y(t) = y_02^{t/T_2}[/tex]
Solving (a): k(r)
Equate [tex]y(t) = y_0e^{kt}[/tex] and [tex]y(t) = y_0(1+r)^t[/tex]
[tex]y_0e^{kt} = y_0(1+r)^t[/tex]
Cancel out common terms
[tex]e^{kt} = (1+r)^t[/tex]
Take ln of both sides
[tex]\ln(e^{kt}) = \ln((1+r)^t)[/tex]
Rewrite as:
[tex]kt\ln(e) = t\ln(1+r)[/tex]
Divide both sides by t
[tex]k = \ln(1+r)[/tex]
Hence:
[tex]k(r) = \ln(1+r)[/tex]
Solving (b): r(T2)
Equate [tex]y(t) = y_02^{t/T_2}[/tex] and [tex]y(t) = y_0(1+r)^t[/tex]
[tex]y_0(1+r)^t = y_02^{t/T_2}[/tex]
Cancel out common terms
[tex](1+r)^t = 2^{t/T_2}[/tex]
Take t th root of both sides
[tex](1+r)^{t*1/t} = 2^{t/T_2*1/t}[/tex]
[tex]1+r = 2^{1/T_2}[/tex]
Make r the subject
[tex]r = 2^{1/T_2}-1[/tex]
Hence:
[tex]r(T_2) = 2^{1/T_2}-1[/tex]
Solving (c): T2(k)
Equate [tex]y(t) = y_02^{t/T_2}[/tex] and [tex]y(t) = y_0e^{kt}[/tex]
[tex]y_02^{t/T_2} = y_0e^{kt}[/tex]
Cancel out common terms
[tex]2^{t/T_2} = e^{kt}[/tex]
Take ln of both sides
[tex]\ln(2^{t/T_2}) = \ln(e^{kt})[/tex]
Rewrite as:
[tex]\frac{t}{T_2} * \ln(2) = kt\ln(e)[/tex]
[tex]\frac{t}{T_2} * \ln(2) = kt*1[/tex]
[tex]\frac{t}{T_2} * \ln(2) = kt[/tex]
Divide both sides by t
[tex]\frac{1}{T_2} * \ln(2) = k[/tex]
Cross multiply
[tex]kT_2 = \ln(2)[/tex]
Make T2 the subject
[tex]T_2 = \frac{\ln(2)}{k}[/tex]
Hence:
[tex]T_2(k) = \frac{\ln(2)}{k}[/tex]
Internet providers: In a survey of 961 homeowners with high-speed Internet, the average monthly cost of a high-speed Internet plan was $74.54 with standard deviation $11.08. Assume the plan costs to be approximately bell-shaped. Estimate the number of plans that cost between $52.38 and $96.7. Round to the nearest whole number. The number of plans that cost between $52.38 and $96.7 is .
Answer:
The number of plans that cost between $52.38 and $96.7 is 913.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean of $74.54, standard deviation of $11.08
Percentage of plans that cost between $52.38 and $96.7.
52.38 = 74.54 - 2*11.08
96.7 = 74.54 + 2*11.08
Within 2 standard deviations of the mean, so by the Empirical Rule, 95%.
The number of plans that cost between $52.38 and $96.7 is .
95% of 961. So
0.95*961 = 913
The number of plans that cost between $52.38 and $96.7 is 913.
Which inequality is graphed below?
3x + 2y < –6
3x + 2y > –6
3x – 2y > 6
3x – 2y < 6
Answer:
3x-2y > 6
Step-by-step explanation:
3x-2y > 6
see attached figure.
please answer both thank you
Answer:
7.
Solution given;
male=15
female=27
1st term=5*3
2nd term=3*3*3
now
Highest common factor=3
So
The maximum number of groups that the teacher can make is 3.
and each team contains 5 male and 9 female.
The number of cars sold in May m was 60 less than four times the number of cars sold in April a. Which equation shows the
relationship between m and a?
Answer:
m = 4a - 60, option b
Step-by-step explanation:
Number of cars sold in May:
This was m.
60 less than four times the number of cars sold in April a
Four times the number of cars sold in April was 4a.
m was 60 less than 4a, that is, m is given by 4a subtracted by 60. So
m = 4a - 60, and the correct answer is given by option b.
A doctor at a local hospital is interested in estimating the birth weight of infants. How large a sample must she select if she desires to be 90% confident that her estimate is within 4 ounces of the true mean
Answer:
The minimum sample size needed is [tex]n = (\frac{1.96\sqrt{\sigma}}{4})^2[/tex]. If n is a decimal number, it is rounded up to the next integer. [tex]\sigma[/tex] is the standard deviation of the population.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
How large a sample must she select if she desires to be 90% confident that her estimate is within 4 ounces of the true mean?
A sample of n is needed, and n is found when M = 4. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]4 = 1.96\frac{\sigma}{\sqrt{n}}[/tex]
[tex]4\sqrt{n} = 1.96\sqrt{\sigma}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{\sigma}}{4}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96\sqrt{\sigma}}{4})^2[/tex]
[tex]n = (\frac{1.96\sqrt{\sigma}}{4})^2[/tex]
The minimum sample size needed is [tex]n = (\frac{1.96\sqrt{\sigma}}{4})^2[/tex]. If n is a decimal number, it is rounded up to the next integer. [tex]\sigma[/tex] is the standard deviation of the population.
reggie withdrew $175 from his bank account to go shopping. after his withdrawal, there was $234 left in reggies account. how much money did reggie have in his account before his withdrawal
Answer:
409
Step-by-step explanation:
You add 234 with 175.
If f(x)=4x and g (x)= 3x^3-6x^2+9x-3 then what is f(f(-3))?
Answer:
https://www.wyzant.com/resources/answers/64459/if_f_x_3x2_4x_and_g_x_3x_2_then_which_of_the_following_is_equal_to_f_x_183_g_x#answer-79706
Step-by-step explanation:the link tells you heheh
Tony is watching a bird feeder on Monday and sees a chickadee take four seeds and a cardinal take six seeds. On Tuesday, Tony sees the chickadee take eight seeds and the cardinal take twelve seeds. On Wednesday, the chickadee takes twelve seeds and the cardinal takes eighteen seeds. On Thursday, the chickadee takes sixteen seeds and the cardinal takes twenty-four seeds. If this pattern continues, how many total seeds did each bird take in a week? How many seeds did each bird take on the last day of three weeks? Show all of your mathematical thinking.
Find the area of this figure
Answer:
90ft²
Step-by-step explanation:
Figure shown is a triangle
Area of a triangle = ( base length times height ) divided by 2
The triangle has a given height of 12 ft and a given base length of 15 ft
Hence area = ( 12 * 15 ) / 2
12 * 15 = 180
180 / 2 = 90
area = 90ft²
Answer:
Area is 90 degrees.
Step-by-step explanation:
The formula for the area of a triangle is (h*b)/2=A
We know height is 12.
We know base is 15.
So lets plug these in:
(12*15)/2=A
180/2=A
90=A
So 90 is our answer!
Hope this helps!
A culture started with 5,000 bacteria. After 4
hours, it grew to 5,500 bacteria. Predict how
many bacteria will be present after 13 hours.
Round your answer to the nearest whole
number.
P = Aekt
Answer:
5000 * (e^((1 /4) * ln(55 / 50) * (13))) = 6,815.47
Step-by-step explanation:
Find the simple interest. $1,540, 8.25%, 2 years
Answer:
[tex]simple \: interest = \frac{ptr}{100} \\ si = \frac{1540 \times 2 \times 8.25}{100 } \\ = 254.1[/tex]
If g(x)=4x^2-16 were shifted 5 units to the right and 2 down hat would the new equation be
Answer:
This is the answer
Step-by-step explanation:
This is the solution, hope it helps
(06.01)
The tables below show four sets of data:
Set B
Set A
x[1 2131415161718
19
y3 45161718 91011
X 1 |2|3|4|5161
y 10
817161514317
Setc
Set D
1234 5 6 7 189
718165143.532.522
< 1 2 3 415
12.52.53456789
For which set of data will the scatter plot represent a negative linear association between x and y? (4 points)
Set A
a
Ob
Set B
Set
od
Set D
Answer:
Set A
Step-by-step explanation:
A negative linear association will always have a negative slope , a negative association can also be be detected from the data given, as the y value will decrease as the x values increases or vice versa.
The plot of the set A is attached Below with a correlation of - 1, meaning a strong negative relationship exists between the x and y variables.
PLS HURRY IM BEING TIMED
Answer:
A
Step-by-step explanation:
I think it's A because that how many miles shes walking not hours not secound or minutes miles. Sry if i'm wrong.
Which of these is always the largest?
A. acute angle
B. obtuse angle
C. right angle
D. straight angle
Answer:
Step-by-step explanation:
B
Answer:
obtuse angle
Step-by-step explanation:
8. Are these ratios equvalent?
9: 3 arid 15:5 and 3:1
Answer:
Yes
Step-by-step explanation:
3:1 x 3 = 9:3
3:1 x 5 = 15:5
5 pts
Question 6
Write the first five terms of the geometric sequence where Q1
Sand r = 3
O {8, 24, 72, 216, 648}
O {8, , , ,
O {3, 24, 192, 1536, 9216}
O {8, 11, 14, 17, 20}
5 pt
Question 7
Answer:
{8, 24, 72, 216, 648}
Step-by-step explanation:
Geometric sequence:
In a geometric sequence, the quotient of consecutive terms is always the same, that is, each term is the previous term multiplied by the common ratio.
In this question:
First element is 8, common ratio of 3. So
Second term: 8*3 = 24
Third term: 24*3 = 72
Fourth term: 72*3 = 216
Fifth term: 216*3 = 648
So the answer is {8, 24, 72, 216, 648}
Jeremy needs to buy three pieces of wood to make a triangular frame. If the wood is cut in 1 l- foot increments, which set of wood length will form a triangle?
Need help finding constant rate of change!
Answer:
[tex]m = \frac{4}{7}\\[/tex]
Step-by-step explanation:
Given
The attached graph
Required
The constant rate of change (m)
This is calculated as:
[tex]m = \frac{y_2 -y_1}{x_2 - x_1}[/tex]
From the graph, we have:
[tex](x_1,y_1) = (3,4)[/tex]
[tex](x_2,y_2) = (10,8)[/tex]
So, the formula becomes:
[tex]m = \frac{8-4}{10 - 3}[/tex]
[tex]m = \frac{4}{7}\\[/tex]
What is the square root of -1?
Assume that y varies inversely with x. If y = 7 when x = 2/3, find y when x = 7/3.
y = [?]
Answer:
y = 2
Step-by-step explanation:
varies inversely
xy = k
y = 7 when x = 2/3
(2/3)7 = k
14/3 = k
k = 14/3
--------------------
find y when x = 7/3
(7/3)y = 14/3
multiply both sides by 3/7
y = 14/3 * 3/7
y = 2
Answer: y = 2
Step-by-step explanation: When we have two sets of inversely related coordinates, x₁ and y₁, and x₂ and y₂, we can use the product rule, shown below, to find the missing value.
x₁y₁ = x₂y₂Since we know that y = 7 when x = 2/3, one set of coordinates will be 7 and 2/3 and since we want to find the value of y when x = 7/3, our other coordinates will be 7/3 and y.
(2/3)(7) = (7/3)(y)
So we have 14/3 = 7/3y and solving for y from here, we find that y = 2.
A car dealership marks up all new automobiles by 15%. What was the original wholesale cost of a car with a sticker price of $22,500 at this dealership?
Answer:
$19,565.22
Step-by-step explanation:
15% of 22,500 = 3375 as we multiply by 0.15
but, 15% of an initial is still whole 1 + 0.15 = 1.15 but when using sale prices to find initial we DIVIDE
= 22500 / 1.15 = 19565.2174
and round up by 2dp currency.
= $19565.22
The way to remember is the opposite finds the original
Which sequence can be defined by the recursive formula f(1) = 4, f (n + 1) = f(n) - 1.25 for n 2 1?
O 1,-0.25,-1.5, -2.75, -4,...
O 1, 2.25, 3.5, 4.75, 6, ...
O 4,2.75, 1.5, 0.25,-1, ...
O 4,5.25, 6.5, 7.75, 8, ...
Answer:
the third option
4, 2.75, 1.5, 0.25, -1, -2.25, ...
Step-by-step explanation:
the first value in the sequence is 4.
that eliminates already answer options 1 and 2.
and the values are going down, as we continuously subtract 1.25 from the previous sequence number.
but answer option 4 shows a sequence, where the values go up.
so, only option 3 remains and is correct
4-1.25 = 2.75
2.75-1.25 = 1.5
1.5-1.25 = 0.25
0.25-1.25 = -1
...
Write the equation 8 is 5 less than a number n
Answer:
n=13
Step-by-step explanation:
the equation 8 is 5 less than a number n
n-5=8
n=?
n=8+5
=13
n=13
Answer:
13
Step-by-step explanation:
the equation 8 is 5 less than a number n
n-5=8
n=?
n=5+8
=13
X Cube - 5x Square - 2 x + 24
Answer:
(x+2)(x-4)(x-3)
(x²-4x+2x-2)(x-3)
(x²-2x-2)(x-3)
=x³-5x²-2x+24
So the answer true
can you explain
pls now later
What is the product of 4x2/3
[tex]\sf\purple{2.667}[/tex] ✅
Step-by-step explanation:
[tex]4 \times \frac{2}{3} \\ = \frac{4 \times 2}{ 3} \\ = \frac{8}{3} \\ = 2.667 [/tex]
[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]
Find three consecutive integers such that the sum of the first two is three times the third.
Answer:
-3, -4, -5
Step-by-step explanation:
x = 1st integer
x+1 = 2nd integer
x+2 = 3rd integer
x+x+1 = 3(x+2)
2x + 1 = 3x + 6
1 = x + 6
-5 = x
-4 = x+1
-3 = x+2
If the graphs of the linear equations shown below are perpendicular, what is the value
of a?
y = 3x +8
2y = ax - 5
Answer:
[tex]a=-\frac{2}{3}[/tex]
Step-by-step explanation:
We are given the lines, [tex]y=3x+8[/tex] and [tex]2y=ax-5[/tex]. For the latter equation, we can isolate the variable y to have the same format as the first. We want to create a y=mx+b equation where m represents the slope of the line. We now have the equations:
[tex]y=3x+8[/tex] and
[tex]y=\frac{a}{2}x-2.5[/tex]
The definition of perpendicular lines is that their slopes must be the negative reciprocal of each other. Thus:
[tex]-\frac{1}{3}=\frac{a}{2} \\\\a=-\frac{2}{3}[/tex]
I hope this helps! Let me know if you have any questions :)
G P
2 3
S I
2 8
Q E
2 ??
Answer:
yea i dont know this one bro gp 23 si 28
Step-by-step explanation: