Answer:
a)[tex]A(t)=2000e^{0.085t}[/tex]
b)[tex]A'(t)=170e^{0.085t}[/tex]
c)$3059.1808
d)t=4.77 years
e) The balance growing is $254.99/year
Step-by-step explanation:
We are given that Two thousand dollars is deposited into a savings account at 8.5% interest compounded continuously.
Principal = $2000
Rate of interest = 8.5%
a) What is the formula for A(t), the balance after t years?
Formula [tex]A(t)=Pe^{rt}[/tex]
So,[tex]A(t)=2000e^{0.085t}[/tex]
B)What differential equation is satisfied by A(t), the balance after t years?
So, [tex]A'(t)=2000 \times 0.085 e^{0.085t}[/tex]
[tex]A'(t)=170e^{0.085t}[/tex]
c)How much money will be in the account after 5 years?
Substitute t = 5 in the formula "
[tex]A(t)=2000e^{0.085t}\\A(5)=2000e^{0.085(5)}\\A(5)=3059.1808[/tex]
d)When will the balance reach $3000?
Substitute A(t)=3000
So, [tex]3000=2000e^{0.085t}[/tex]
t=4.77
The balance reach $3000 in 4.77 years
e)How fast is the balance growing when it reaches $3000?
Substitute the value of t = 4.77 in derivative formula :
[tex]A'(t)=170e^{0.085t}\\A'(t)=170e^{0.085 \times 4.77}\\A'(t)=254.99[/tex]
Hence the balance growing is $254.99/year
Use Green's Theorem to evaluate ?C F·dr. (Check the orientation of the curve before applying the theorem.)
F(x, y) =< x + 4y3, 4x2 + y>
C consists of the arc of the curve y = sin x from (0, 0) to (p, 0) and the line segment from (p, 0) to (0, 0).
Answer:
Step-by-step explanation:
given a field of the form F = (P(x,y),Q(x,y) and a simple closed curve positively oriented, then
[tex]\int_{C} F \cdot dr = \int_A \frac{dQ}{dx} - \frac{dP}{dy} dA[/tex] where A is the area of the region enclosed by C.
In this case, by the description we can assume that C starts at (0,0). Then it goes the point (pi,0) on the path giben by y = sin(x) and then return to (0,0) along the straigth line that connects both points. Note that in this way, the interior the region enclosed by C is always on the right side of the point. This means that the curve is negatively oriented. Consider the path C' given by going from (0,0) to (pi,0) in a straight line and the going from (pi,0) to (0,0) over the curve y = sin(x). This path is positively oriented and we have that
[tex] \int_{C} F\cdot dr = - \int_{C'} F\cdot dr[/tex]
We use the green theorem applied to the path C'. Taking [tex] P = x+4y^3, Q = 4x^2+y[/tex] we get
[tex] \int_{C'} F\cdot dr = \int_{A} 8x-12y^2dA[/tex]
A is the region enclosed by the curves y =sin(x) and the x axis between the points (0,0) and (pi,0). So, we can describe this region as follows
[tex]0\leq x \leq \pi, 0\leq y \leq \sin(x)[/tex]
This gives use the integral
[tex] \int_{A} 8x-12y^2dA = \int_{0}^{\pi}\int_{0}^{\sin(x)} 8x-12y^2 dydx[/tex]
Integrating accordingly, we get that [tex]\int_{C'} F\cdot dr = 8\pi - \frac{16}{3}[/tex]
So
[tex] \int_{C} F cdot dr = - (8\pi - \frac{16}{3}) = \frac{16}{3} - 8\pi [/tex]
Hee lllp!!! Now 70 points
Answer:
[tex]\huge\boxed{Option \ 1}[/tex]
Step-by-step explanation:
Since, AE = CE and BE = DE , then E is the midpoint of AC and BD. Causius can use that to show that AC and BD bisect each other which means that they both are the diagonals of a parallelogram bisecting each other. Hence, It will be proved that ABCD is a || gm.
Hope this helped!
~AnonymousHelper1807Can someone please explain how to do this problem? The websites instructions are very poor. Rewrite [tex]\frac{2}{x^{2} -x-12}[/tex] and [tex]\frac{1}{x^{2}-16 }[/tex] as equivalent rational expressions with the lowest common denominator.
Answer: x = -5
Step-by-step explanation:
If you factor each denominator, you can find the LCM.
[tex]\dfrac{2}{x^2-x-12}=\dfrac{1}{x^2-16}\\\\\\\dfrac{2}{(x-4)(x+3)}=\dfrac{1}{(x-4)(x+4)}\\\\\\\text{The LCM is (x-4)(x+4)(x+3)}\\\\\\\dfrac{2}{(x-4)(x+3)}\bigg(\dfrac{x+4}{x+4}\bigg)=\dfrac{1}{(x-4)(x+4)}\bigg(\dfrac{x+3}{x+3}\bigg)\\\\\\\dfrac{2(x+4)}{(x-4)(x+4)(x+3)}=\dfrac{1(x+3)}{(x-4)(x+4)(x+3)}\\[/tex]
Now that the denominators are equal, we can clear the denominator and set the numerators equal to each other.
2(x + 4) = 1(x + 3)
2x + 8 = x + 3
x + 8 = 3
x = -5
In triangle ABC, the measure of angle A is half the measure of angle B, and the measure of angle C is 50° less than the measure of angle B. Find the measure of the smallest angle. (Recall that the sum of the measures of the angles in a triangle is 180°.)
Answer:
42º
Step-by-step explanation:
You can start by setting up the equations that are given in the stem of the problem: a=.5b, c=b-50, a+b+c=180. Then plug in the values of b in relation to the other values into the equation a+b+c=180. This will give you (.5b)+b+(b-50)=180. By expanding this and combining like terms, we will get 2.5b=230. By dividing each side by 2.5, we get b=92. Then, referencing the first equations, a=.5(92)=46, and c=92-50=42. The smallest of all of these is c, 42.
What is the general form of the equation of the line shown? 2 x - y + 3 = 0 2 x - y - 3 = 0 x - 2 y - 3 = 0
Answer:
2x - y - 3 = 0
Step-by-step explanation:
Find slope-intercept form first: y = mx + b
Step 1: Pick out 2 points
In this case, I picked out (2, 1) and (0, -3) from the graph
Step 2: Using slope formula y2 - y1/x2 - x1 to find slope
-3 - 1/0 - 2
m = 2
Step 3: Place slope formula results into point-slope form
y = 2x + b
Step 4: Plug in a point to find b
-3 = 2(0) + b
b = -3
Step 5: Write slope-intercept form
y = 2x - 3
Step 6: Move all variables and constants to one side
0 = 2x - 3 - y
Step 7: Rearrange
2x - y - 3 = 0 is your answer
solve for x
2x/3 + 2 = 16
Answer:
2x/3 + 2= 16
=21
Step-by-step explanation:
Standard form:
2
3
x − 14 = 0
Factorization:
2
3 (x − 21) = 0
Solutions:
x = 42
2
= 21
A woman has a collection of video games and anime. she has 50 anime DVDs, and she has 70 video games. which it adds up to 120 items. if you divide them by 5, how many items does she have all together?
Answer:
24
Step-by-step explanation:
Since you are given almost everything, you just simply divide by 5=>
120/5 = 24
Hope this helps
what is 7/9 x 5 2/5 please!
Answer:
[tex]4\frac{1}{5}[/tex]
Step-by-step explanation:
=>[tex]\frac{7}{9} * 5 \frac{2}{5}[/tex]
=> [tex]\frac{7}{9} * \frac{27}{5}[/tex]
=> [tex]\frac{7*3}{5}[/tex]
=> [tex]\frac{21}{5}[/tex]
=> [tex]4\frac{1}{5}[/tex]
Answer:
[tex]4\frac{1}{5}[/tex]
Step-by-step explanation:
[tex]\frac{7}{9} \times 5 \frac{2}{5}[/tex]
[tex]\frac{7}{9} \times \frac{27}{5}[/tex]
[tex]\frac{7 \times 27}{9 \times 5 }[/tex]
[tex]\frac{189}{45}[/tex]
[tex]\frac{21}{5}[/tex]
[tex]=4\frac{1}{5}[/tex]
is 614 divisible by both 2 and 6?
Answer:
No
Step-by-step explanation:
It is not divisible by 6, for if you divide by 6, you will get a non natural number,
It is obviously divisible by 2.
So, No.
Answer:
no
Step-by-step explanation:
only by 2
614/2 = 307
614/6 = 102.33
HELP ME Answer it from the forst one to the last one with the rght answer please.This is Urgent so do it Faster if u now the answers
Step-by-step explanation:
2) 63
3) 7000
4) 10
These are some answers
SOMEONE PLEASE HELP ME ASAP PLEASE!!!
Answer:
plane
Step-by-step explanation:
Answer:
D. Plane
Step-by-step explanation:
A plane extends in two dimensions. This figure is a plane. It is not a point, a segment or a ray.
In a certain community, eight percent of all adults over age 50 have diabetes. If a health service in this community correctly diagnosis 95% of all persons with diabetes as having the disease and incorrectly diagnoses ten percent of all persons without diabetes as having the disease, find the probabilities that:
Complete question is;
In a certain community, 8% of all people above 50 years of age have diabetes. A health service in this community correctly diagnoses 95% of all person with diabetes as having the disease, and incorrectly diagnoses 10% of all person without diabetes as having the disease. Find the probability that a person randomly selected from among all people of age above 50 and diagnosed by the health service as having diabetes actually has the disease.
Answer:
P(has diabetes | positive) = 0.442
Step-by-step explanation:
Probability of having diabetes and being positive is;
P(positive & has diabetes) = P(has diabetes) × P(positive | has diabetes)
We are told 8% or 0.08 have diabetes and there's a correct diagnosis of 95% of all the persons with diabetes having the disease.
Thus;
P(positive & has diabetes) = 0.08 × 0.95 = 0.076
P(negative & has diabetes) = P(has diabetes) × (1 –P(positive | has diabetes)) = 0.08 × (1 - 0.95)
P(negative & has diabetes) = 0.004
P(positive & no diabetes) = P(no diabetes) × P(positive | no diabetes)
We are told that there is an incorrect diagnoses of 10% of all persons without diabetes as having the disease
Thus;
P(positive & no diabetes) = 0.92 × 0.1 = 0.092
P(negative &no diabetes) =P(no diabetes) × (1 –P(positive | no diabetes)) = 0.92 × (1 - 0.1)
P(negative &no diabetes) = 0.828
Probability that a person selected having diabetes actually has the disease is;
P(has diabetes | positive) =P(positive & has diabetes) / P(positive)
P(positive) = 0.08 + P(positive & no diabetes)
P(positive) = 0.08 + 0.092 = 0.172
P(has diabetes | positive) = 0.076/0.172 = 0.442
Using formula:
[tex]P(\text{diabetes diagnosis})\\[/tex]:
[tex]=\text{P(having diabetes and have been diagnosed with it)}\\ + \text{P(not have diabetes and yet be diagnosed with diabetes)}[/tex]
[tex]=0.08 \times 0.95+(1-0.08) \times 0.10 \\\\=0.08 \times 0.95+0.92 \times 0.10 \\\\=0.076+0.092\\\\=0.168[/tex]
[tex]\text{P(have been diagnosed with diabetes)}[/tex]:
[tex]=\frac{\text{P(have diabetic and been diagnosed as having insulin)}}{\text{P(diabetes diagnosis)}}[/tex]
[tex]=\frac{0.08\times 0.95}{0.168} \\\\=\frac{0.076}{0.168} \\\\=0.452\\[/tex]
Learn more about the probability:
brainly.com/question/18849788
If an image of a triangle is congruent to the pre-image, what is the scale factor of the dilation?
0.1
1/2
1
10
How many solutions does 6-3x=4-x-3-2x have?
Answer:
no solutions
Step-by-step explanation:
6-3x=4-x-3-2x
Combine like terms
6-3x =1 -3x
Add 3x to each side
6 -3x+3x = 1-3x+3x
6 =1
This is not true so there are no solutions
Answer:
No solutions.
Step-by-step explanation:
6 - 3x = 4 - x - 3 - 2x
Add or subtract like terms if possible.
6 - 3x = -3x + 1
Add -1 and 3x on both sides.
6 - 1 = -3x + 3x
5 = 0
There are no solutions.
Which of the following is not an undefined term?
point, ray, line, plane
Answer:
Step-by-step explanation:
Ray
Answer:
ray
Step-by-step explanation:
ray is a part of a line that has an endpoint in one side and extends indefinitely on the opposite side. hence, the answer is ray
hope this helps
Find the product of
3/5 × 7/11
Answer:
21/55
Step-by-step explanation:
Simply multiply the top 2 together:
3 x 7 = 21
And the bottom 2 together:
5 x 11 = 55
21/55 is your answer!
If the terms of a polynomial do not have a GCF, does that mean it is not factorable?
Keith Rollag (2007) noticed that coworkers evaluate and treat "new" employees differently from other staff members. He was interested in how long a new employee is considered "new" in an organization. He surveyed four organizations ranging in size from 34 to 89 employees. He found that the "new" employee status was mostly reserved for the 30% of employees in the organization with the lowest tenure.
A) In this study, what was the real range of employees hired by each organization surveyed?
B) What was the cumulative percent of "new" employees with the lowest tenure?
Answer:
a) Real range of employees hired by each organization surveyed = 56
b) The cumulative percent of "new" employees with the lowest tenure = 30%
Step-by-step explanation:
a) Note: To get the real range of employees hired by each organization, you would do a head count from 34 to 89 employees. This means that this can be done mathematically by finding the difference between 34 and 89 and add the 1 to ensure that "34" is included.
Real range of employees hired by each organization surveyed = (89 - 34) + 1
Real range of employees hired by each organization surveyed = 56
b) It is clearly stated in the question that the "new" employee status was mostly reserved for the 30% of employees in the organization with the lowest tenure.
Therefore, the cumulative percent of "new" employees with the lowest tenure = 30%
How many different triangles can you make if you are given
these three lengths for sides?
Answer:
Step-by-step explanation:
i think its 3
Answer:
0
Step-by-step explanation:
You cannot make any triangles with this angle
1. A door of a lecture hall is in a parabolic shape. The door is 56 inches across at the bottom of the door and parallel to the floor and 32 inches high. Sketch and find the equation describing the shape of the door. If you are 22 inches tall, how far must you stand from the edge of the door to keep from hitting your head
Answer:
See below in bold.
Step-by-step explanation:
We can write the equation as
y = a(x - 28)(x + 28) as -28 and 28 ( +/- 1/2 * 56) are the zeros of the equation
y has coordinates (0, 32) at the top of the parabola so
32 = a(0 - 28)(0 + 28)
32 = a * (-28*28)
32 = -784 a
a = 32 / -784
a = -0.04082
So the equation is y = -0.04082(x - 28)(x + 28)
y = -0.04082x^2 + 32
The second part is found by first finding the value of x corresponding to y = 22
22 = -0.04082x^2 + 32
-0.04082x^2 = -10
x^2 = 245
x = 15.7 inches.
This is the distance from the centre of the door:
The distance from the edge = 28 - 15.7
= 12,3 inches.
Please answer this correctly
Answer:
Hiking: 28%
Canoeing: 16%
Swimming: 24%
Fishing: 32%
Step-by-step explanation:
21 + 12 + 18 + 24 = 75 (there are 75 campers)
21 out of 75 = 28%
12 out of 75 = 16%
18 out of 75 = 24%
24 out of 75 = 32%
Hope this helps!
Please mark Brainliest if correct
Suppose that prices of recently sold homes in one neighborhood have a mean of $225,000 with a standard deviation of $6700. Using Chebyshev's Theorem, what is the minimum percentage of recently sold homes with prices between $211,600 and $238,400
Answer:
[tex] 211600 = 225000 -k*6700[/tex]
[tex] k = \frac{225000-211600}{6700}= 2[/tex]
[tex] 238400 = 225000 +k*6700[/tex]
[tex] k = \frac{238400-225000}{6700}= 2[/tex]
So then the % expected would be:
[tex] 1- \frac{1}{2^2}= 1- 0.25 =0.75[/tex]
So then the answer would be 75%
Step-by-step explanation:
For this case we have the following info given:
[tex] \mu = 225000[/tex] represent the true mean
[tex]\sigma =6700[/tex] represent the true deviation
And for this case we want to find the minimum percentage of sold homes between $211,600 and $238,400.
From the chebysev theorem we know that we have [tex]1 -\frac{1}{k^2}[/tex] % of values within [tex]\mu \pm k\sigma[/tex] if we use this formula and the limit given we have:
[tex] 211600 = 225000 -k*6700[/tex]
[tex] k = \frac{225000-211600}{6700}= 2[/tex]
[tex] 238400 = 225000 +k*6700[/tex]
[tex] k = \frac{238400-225000}{6700}= 2[/tex]
So then the % expected would be:
[tex] 1- \frac{1}{2^2}= 1- 0.25 =0.75[/tex]
So then the answer would be 75%
for a sample size of 115 and a population parameter of 0.1,what is the standard deviation of the normal curve that can be used to approximate the binomial probability histogram. Round your answer to three decimal places
A.0.028
B.0.054
C.0.043
D.0.035
Answer:
A) 0.028
Step-by-step explanation:
Given:
Sample size, n = 115
Population parameter, p = 0.1
The X-Bin(n=155, p=0.1)
Required:
Find the standard deviation of the normal curve that can be used to approximate the binomial probability histogram.
To find the standard deviation, use the formula below:
[tex]\sigma = \sqrt{\frac{p(1-p)}{n}}[/tex]
Substitute figures in the equation:
[tex]\sigma = \sqrt{\frac{0.1(1 - 0.1)}{115}}[/tex]
[tex]\sigma = \sqrt{\frac{0.1 * 0.9}{115}}[/tex]
[tex]\sigma = \sqrt{\frac{0.09}{115}}[/tex]
[tex] \sigma = \sqrt{7.826*10^-^4}[/tex]
[tex] \sigma = 0.028 [/tex]
The Standard deviation of the normal curve that can be used to approximate the binomial probability histogram is 0.028
According to a Harris Poll in 2009, 72% of those who drive and own cell phones say they use them to talk while they are driving. If you wish to conduct a survey in your city to determine what percent of the drivers with cell phones use them to talk while driving, how large a sample should be if you want your estimate to be within 0.02 with 95% confidence.
Answer:
We need a sample of at least 1937.
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 zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
For this problem, we have that:
[tex]\pi = 0.72[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
How large a sample should be if you want your estimate to be within 0.02 with 95% confidence.
We need a sample of at least n.
n is found when M = 0.02. So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.02 = 1.96\sqrt{\frac{0.72*0.28}{n}}[/tex]
[tex]0.02\sqrt{n} = 1.96\sqrt{0.72*0.28}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.72*0.28}}{0.02}[/tex]
[tex](\sqrt{n})^{2} = (\frac{1.96\sqrt{0.72*0.28}}{0.02})^{2}[/tex]
[tex]n = 1936.16[/tex]
Rounding up to the nearest number.
We need a sample of at least 1937.
finding angle measures between intersecting lines.
Answer: x=45°
Step-by-step explanation:
Angles opposite from each other are equal. The angle 160 degrees in red on the bottom encompasses two angles: BEG and CEG. Angle BEG is on the opposite side as FEA which means it is equal to x.
Since angle FED on the other side is 115, you subtract 115 from 160 to get 45 degrees.
Answer: x=45°
The angle BEG, which is opposite to the angle FEA, is determined to be 45 degrees.
According to the information provided, in a figure with an angle of 160 degrees (red angle on the bottom), there are two angles labeled as BEG and CEG. It is stated that the angle BEG is opposite to the angle FEA, making them equal, so we can represent this angle as x.
Additionally, it is mentioned that the angle FED on the other side measures 115 degrees.
To find the value of x, we subtract 115 degrees from the angle of 160 degrees.
=160-115
= 45
Thus, the solution is x = 45°.
For more details about the angle visit the link below: https://brainly.com/question/16959514
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PLEASE HELP ME WITH THIS, HELP NEEDED ASAP
Answer:
x = 16.5
Step-by-step-explanation:
The height of the larger triangle is 11, and the height of smaller triangle is 2. Which means that the larger triangle height is 5.5 times greater than the smaller triangle's height.
If the base of the smaller triangle is 3, that means that base of the whole/larger triangle is 16.5 because 3 * 5.5 = 16.5
A human resource manager for a large company takes a random sample of 60 employees from the company database. Based on the sample she calculates a 95% confidence interval for the mean time of employment for all employees to be 8.7 to 15.2 years. Which of the following will provide a more informative (i.e., narrower) confidence interval than the 95% confidence interval?
A. Using a 90% confidence level (instead of 95%)
B. Using a 99% confidence level (instead of 95%)
C. Using a sample size of 40 employees (instead of 60)
D. Using a sample size of 90 employees (instead of 60)
Answer:
A. Using a 90% confidence level (instead of 95%)
D. Using a sample size of 90 employees (instead of 60)
Step-by-step explanation:
The margin of error of a confidence interval is given by:
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which z is related to the confidence level, [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
The higher the margin of error, the less precise the confidence interval is.
We have:
A 95% confidence interval, with a sample of 60.
We want to make it more precise:
Two options, decrease z(decrease the confidence level), or increase n(increase the sample size).
So the correct options are:
A. Using a 90% confidence level (instead of 95%)
D. Using a sample size of 90 employees (instead of 60)
For what values (cases) of the variables the expression does not exist: a / a−b
Answer:
a=b
Step-by-step explanation:
When the denominator is zero, the expression is undefined
a-b=0
a=b
Please answer this correctly
Answer:
101-120=4
Step-by-step explanation:
All that you need to do is count how many data points fall into this category. In this case, there are four data points that fall into the category of 101-120 pushups
111111105113Therefore, the answer to the blank is 4. If possible, please mark brainliest.
Answer:
There are 4 numbers between 101 and 120.
Step-by-step explanation:
101-120: 105, 111, 111, 113 (4 numbers)
Which graph shows a function whose domain and range exclude exactly one value?
Answer:
C (the third graph)
Step-by-step explanation:
This graph's function has a domain and range that both exclude one value, which is 0. The x and y values are never 0 in the function, as it approaches 0 but never meets it.
Answer:
see below
Step-by-step explanation:
This graph has an asymptote at y = 0 and x=0
This excludes these values
The domain excludes x =0
The range excludes y=0