Answer:
d/t=speed
Step-by-step explanation:
Suppose that $10,083 is invested at an interest rate of 6.8% per year, compounded continuously.
a) Find the exponential function that describes the amount in the account after time t, in years.
b) What is the balance after 1 year? 2 years? 5 years? 10 years?
c) What is the doubling time?
Answer:
a) The exponential function is [tex]A(t) = 10083(1.068)^t[/tex]
b)
The balance after 1 year is of $10,768.644
The balance after 2 years is of $11,500.91
The balance after 5 years is of $14,010.25.
The balance after 10 years is of $19,467.15
c)
The doubling time is of 10.54 years.
Step-by-step explanation:
Continuously compounded interest:
The amount of money earning after t years, with interest compounded continuously, is given by:
[tex]A(t) = A(0)(1+r)^t[/tex]
In which A(0) is the amount of the initial investment and r is the growth rate, as a decimal.
a) Find the exponential function that describes the amount in the account after time t, in years.
Suppose that $10,083 is invested at an interest rate of 6.8% per year
This means, respectively, that [tex]A(0) = 10083, r = 0.068[/tex]
So
[tex]A(t) = A(0)(1+r)^t[/tex]
[tex]A(t) = 10083(1+0.068)^t[/tex]
[tex]A(t) = 10083(1.068)^t[/tex]
b) What is the balance after 1 year? 2 years? 5 years? 10 years?
After 1 year:
[tex]A(1) = 10083(1.068)^{1} = 10,768.644[/tex]
The balance after 1 year is of $10,768.644
After 2 years:
[tex]A(2) = 10083(1.068)^{2} = 11,500.91[/tex]
The balance after 2 years is of $11,500.91.
After 5 years:
[tex]A(5) = 10083(1.068)^{5} = 14,010.25[/tex]
The balance after 5 years is of $14,010.25.
After 10 years:
[tex]A(10) = 10083(1.068)^{10} = 19,467.15[/tex]
The balance after 10 years is of $19,467.15.
c) What is the doubling time?
This is t for which [tex]A(t) = 2A(0)[/tex]. So
[tex]A(t) = A(0)(1.068)^t[/tex]
[tex](1.068)^t = 2[/tex]
[tex]\log{(1.068)^t} = \log{2}[/tex]
[tex]t\log{1.068} = \log{2}[/tex]
[tex]t = \frac{\log{2}}{\log{1.068}}[/tex]
[tex]t = 10.54[/tex]
The doubling time is of 10.54 years.
PLS HELP I WILL MARK BRAINLIEST
Four more than 5 times the number x is less than 50. Write an inequality for this statement.
Answer:
5x<50
Step-by-step explanation:
Answer:
Step-by-step explanation:
5n < 50 <--- subtracts 4 from both sides
n < 10 <--- divides both sides by 5
Check: testing n=0, we have 4 + 5(0) = 4 + 0 = 4 < 54, so yes it works
testing n=10, 4 + 5(10) = 4 + 50 = 54.
testing n=11, 4 + 5(11) = 4 + 55 = 59 <--- fails as expected.
X < 10, proven, verified, correct
21 and 22 are complementary angles. The measure of Z1 is 60°. The
measure of 22 is 5(x - 1)º. Find the value of x.
Answer:
The value of x is 7
Step-by-step explanation:
Complementary angles have a sum of 90°, therefore the equation to solve for x is:
∠1+∠2=90°
60°+5(x-1)°=90°
5(x-1)=30°
x-1=6
x=7
So the value of x is 7
13 points Please help 8th grade math
Answer:
4.2
Step-by-step explanation:
Answer:
Volume of the sphere is 2065.24
I have no idea how to calculate the slope of that.
Step-by-step explanation:
3·π·7.93≈2065.23693
I need help if right I will mark you
Answer:
B
Step-by-step explanation:
Find (-5)(-2)(5)( - 1)(-4)
PLEASE HELP ASAP!
Classify the polynomial, 8m^3–10m^2– 7, by degree and number of terms.
Answer:
Step-by-step explanation:
The answer is m • (2m - 3) • (4m + 1)
What is the solution to
−12x≤−72
Solve each equation MUST SHOW WORK!!!! 10 points.
Answer:
1. x=34
2. c=8
3. x=9
4. m=32
That the answer for all 4.
Step-by-step explanation: Hope this help :D
12 cm
16 cm
find the lateral area surface area is each regular pyramid round to the nearest 10th if necessary
Which statement is true about the relationship between the height of the plant and the number of days? This relationship is a function because the plant can only be one height at a time. This relationship is not a function because the plant can only be one height at a time. This relationship is a function because the plant can be more than one height at a time. This relationship is not a function because the plant can be more than one height at a time.
Answer:
This relationship is a function because the plant can only be one height at a time.
Step-by-step explanation:
Functions occur when the recorded x-value is varied each time. Since the height of the plant (the x-value) varies each day, it is a function.
How many different 5-letter words can be made
a. if the first letter must be A or Y and no letter may be repeated?
b. if repeats are allowed (but the first letter is A or Y)?
c. How many of the 5-letter words (starting with A or Y) with no repeats end
in H?
Help me please this is due tonight!
Here is a photo of the problem. I’m a little blank on my math tonight, any help is appreciated!
9514 1404 393
Answer:
A
Step-by-step explanation:
The applicable rules of exponents are ...
(a^b)(a^c) = a^(b+c)
(ab)^c = (a^c)(b^c)
(a^b)^c = a^(bc)
__
Using these rules, along with the distributive property, we can simplify the given expression.
[tex]\displaystyle 9a^3b^6(3a^3b^2+7a^2b^2)-(5a^4b^4)^2\\\\=\displaystyle 9a^3b^6(3a^3b^2+7a^2b^2)-(5^2a^{4\cdot2}b^{4\cdot2})\\\\=(9)(3)a^{3+3}b^{6+2}+(9)(7)a^{3+2}b^{6+2}-25a^8b^8=27a^6b^8+63a^5b^8-25a^8b^8\\\\=\boxed{-25a^8b^8+27a^6b^8+63a^5b^8}\qquad\text{matches A}[/tex]
33
3
Solve the proportion.
р
28
Answer:
p = 308
Step-by-step explanation:
Find the measure of 26.
4 6 = [?]
249
46
Answer:
Solution given:
<6+24=180[co- interior angle]
<6=180-24=156°
<6=156°
Marie bicycled 15 miles at 5 miles per
hour. How long did Marie bicycle?
Answer:
3 hours
Step-by-step explanation:
15÷5=3 so that's ot
HELP! WILL GIVE BRANLIEST!
Answer:
Z = 80 degrees and X = 8 degrees
Step-by-step explanation:
The reason Z = 80 degrees is because a flat line always has a measure of 180 degrees.
I forget the term, but we know that 6x + 52 is equal to 100 due to some angle theorem. (Once again, I do not remember the term.)
We then subtract 52 from 100 to get the equation 6x = 48. Divide them both by 6 and you get X = 8!
Hope this helped!
Mr. & Mrs. Dargen spent $46.25 on a meal, about how much should they
leave for a 18% tip?
Answer:
$8.32
Step-by-step explanation:
I found one percent of 46.25 ( which was 0.4625) by dividing it by 100 then i multiplied that number by 18 in order to get how much the 18% tip would be. From that I got 8.325 but since this is in a currency the answer would be 8.32
thats just how I do it there's other ways
A worldwide organization of academics claims that the mean IQ score of its members is 118, with a standard deviation of 17. A randomly selected group of 40 members of this organization is tested, and the results reveal that the mean IQ score in this sample is 115.8. If the organization's claim is correct, what is the probability of having a sample mean of 115.8 or less for a random sample of this size
Answer:
0.2061 = 20.61% probability of having a sample mean of 115.8 or less for a random sample of this size
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
A worldwide organization of academics claims that the mean IQ score of its members is 118, with a standard deviation of 17.
This means that [tex]\mu = 118, \sigma = 17[/tex]
A randomly selected group of 40 members
This means that [tex]n = 40, s = \frac{17}{\sqrt{40}} = 2.6879[/tex]
What is the probability of having a sample mean of 115.8 or less for a random sample of this size?
This is the pvalue of Z when X = 115.8.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{115.8 - 118}{2.6879}[/tex]
[tex]Z = -0.82[/tex]
[tex]Z = -0.82[/tex] has a pvalue of 0.2061
0.2061 = 20.61% probability of having a sample mean of 115.8 or less for a random sample of this size
Tucker purchased $4,600 in new equipment for a catering business. He estimates that the value of the equipment is reduced by approximately 40% every two years. Tucker states that the function V(t)=4,600(0.4)2t could be used to represent the value of the equipment, V, in dollars, t, years after the purchase of the new equipment. Explain whether the function Tucker stated is correct, and, if not, determine the correct function that could be used to find the value of the equipment purchased.
Fort his problem what is the correct answer?
Answer:
its b have a nice day
Step-by-step explanation:
Answer:
I think its D.
Step-by-step explanation:
Simplify the expression -3 devided by -2/5. A. -7 1/2 B. -1 1/5 C. 1 1/5 D. 7 1/2
Answer:
D. 7 1/2
Step-by-step explanation:
-3 divided by -2/5
-(-3(-5/2)
-(-3 x 5/2)
-15/2
7 1/2
Hope it helps
  help needed pls
There are two cylinders.
The first has a radius of 7 and height of 5.
The second has a radius of 6 and height of 7.
Which cylinder has the larger surface area?
A-The first cylinder
B-The second cylinder
Answer:
b
Step-by-step explanation:
HELPPPP. QUICKK. PLEASEE AND TY :))
Answer: D
Step-by-step explanation:
D
100 points What is the equation of the line that goes through (1,-1) and is parallel to y =
3x-3?
A. y+ 1 = 3(x - 1)
B. y+1=-}(-1)
C. y = 3x + 1
OD. y+1-}(x-1)
How is x = 5 mathematically different from x > 5?
Answer:
in x>5 x is larger than 5
Step-by-step explanation:
x=5 means x is equal to 5
x>5 means x is greater than 5
Answer:
X=5 means that the unknown variable in the equation is equal to the number 5, while x > 5 means that the unknown variable is larger then the number 5.
Step-by-step explanation:
Write the standard equation of a circle with its center at the origin and radius 3.
Answer:
9 = x^2+y^2
Step-by-step explanation:
3^2 = (x-0)^2 + (y-0)^2
9 = x^2+y^2
The weight of an object on the moon, m, is about of the object's weight on Earth, e
Which equation represents the approximate weight of an object on the moon in terms
of the object's weight on Earth?
A m =
Bm
8
Gm6e
Dm66
Students crew anywhere on this side
Answer:
wdDW
Step-by-step explanation:
WDDwdWD
= REAL NUMBERS Evaluating a quadratic expression: Integers Evaluate the expression when n=4. n2-5n+6
Answer:
-2
Step-by-step explanation:
I got it wrong and it told me negative 2 was the correct answer lol
