Answer:
The percentage of growth is of 9.05%.
The amount of money in the account after t years is given by [tex]P(t) = 330(1.0905)^t[/tex]
Step-by-step explanation:
Amount of money after t years:
The amount of money in an account after t years is given by:
[tex]P(t) = P(0)(1+r)^t[/tex]
In which P(0) is the initial deposit and r is the growth rate, as a decimal.
Money doubles every 8 years.
This means that [tex]P(8) = 2P(0)[/tex]. So
[tex]P(t) = P(0)(1+r)^t[/tex]
[tex]2P(0) = P(0)(1+r)^8[/tex]
[tex](1+r)^8 = 2[/tex]
[tex]\sqrt[8]{(1+r)^8} = \sqrt[8]{2}[/tex]
[tex]1 + r = 2^{\frac{1}{8}}[/tex]
[tex]1 + r = 1.0905[/tex]
[tex]r = 1.0905 - 1[/tex]
[tex]r = 0.0905[/tex]
The percentage of growth is of 0.0905 = 9.05%.
Person invested $330
This means that [tex]P(0) = 330[/tex]
So
[tex]P(t) = P(0)(1+r)^t[/tex]
[tex]P(t) = 330(1+0.0905)^t[/tex]
[tex]P(t) = 330(1.0905)^t[/tex]
The amount of money in the account after t years is given by [tex]P(t) = 330(1.0905)^t[/tex]
Find the area of a circle that has a diameter of 11 inches. Approximate ar as 3.14. Round your answer to the
nearest hundredth.
A
in 2
in
Answer:
94.99
Step-by-step explanation:
Hi,
The formula to find the area of a circle is: A = πr²
So...
A = 3.14 (r)²
The radius of the circle is 5.5 because half of the diameter is the radius.
A = 3.14 (5.5)²
A = 3.14 (30.25)
A = 94.985 rounded is 94.99
I hope this helps :)
let f(x)=ln(x^2) and g(x)=√e^3x. find fog(x) and its domian
Answer:
[tex](f\ o\ g)(x) = 3x[/tex]
[tex]-\infty < x < \infty[/tex]
Step-by-step explanation:
Given
[tex]f(x) = ln(x^2)[/tex]
[tex]g(x)=\sqrt{e^{3x}}[/tex]
Solving (a): (f o g)(x)
This is calculated as:
[tex](f\ o\ g)(x) = f(g(x))[/tex]
We have:
[tex]f(x) = ln(x^2)[/tex]
[tex]f(g(x)) = \ln((g(x))^2)[/tex]
Substitute: [tex]g(x)=\sqrt{e^{3x}}[/tex]
[tex]f(g(x)) = \ln(\sqrt{e^{3x}})^2[/tex]
Evaluate the square
[tex]f(g(x)) = \ln(e^{3x})[/tex]
Using laws of natural logarithm:
[tex]\ln(e^{ax}) = ax[/tex]
So:
[tex]f(g(x)) = \ln(e^{3x})[/tex]
[tex]f(g(x)) = 3x[/tex]
Hence:
[tex](f\ o\ g)(x) = 3x[/tex]
Solving (b): The domain
We have:
[tex]f(g(x)) = 3x[/tex]
The above function has does not have any undefined points and domain constraints.
Hence, the domain is: [tex]-\infty < x < \infty[/tex]
The histogram below shows the number of push-ups the students in Hayley's class can do.
Select all of the true statements about the data.
The majority of students can do more than 15 push-ups.
The data distribution is skewed to the right.
More students did 6-10 push-ups than 11-15 push-ups.
The students in Hayley's class can do between 1 and 25 push-ups.
The data distribution is skewed to the left.
300 is what percent less than 599
Answer:
59.8%
Step-by-step explanation:
599 - 300 = 299. Now we need to find the percentage 299 is of 500.
299 / 500 = 0.598
0.598 as a percent is 59.8%.
Answer: 59.8%
Hope this helps!
what is the value of x?
Answer:
33
Step-by-step explanation:
if you set it as an equation equal to 180 its easier to tackle
According to the Labor Department, the average duration of unemployment for adults ages 20 to 24 was 34.6 weeks during a recent month. Assume that the standard deviation for this population is 10.2 weeks. A random sample of 36 adults in this age group was selected. What is the probability that the average duration of unemployment was between 30 and 37 weeks
Answer:
0.9173 = 91.73% probability that the average duration of unemployment was between 30 and 37 weeks.
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.
Mean of 34.6, standard deviation of 10.2
This means that [tex]\mu = 34.6, \sigma = 10.2[/tex]
Sample of 36
This means that [tex]n = 36, s = \frac{10.2}{\sqrt{36}} = 1.7[/tex]
What is the probability that the average duration of unemployment was between 30 and 37 weeks?
This is the pvalue of Z when X = 37 subtracted by the pvalue of Z when X = 30.
X = 37
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{37 - 34.6}{1.7}[/tex]
[tex]Z = 1.41[/tex]
[tex]Z = 1.41[/tex] has a pvalue of 0.9207
X = 30
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{30 - 34.6}{1.7}[/tex]
[tex]Z = -2.71[/tex]
[tex]Z = -2.71[/tex] has a pvalue of 0.0034
0.9207 - 0.0034 = 0.9173
0.9173 = 91.73% probability that the average duration of unemployment was between 30 and 37 weeks.
A punch bowl has 1/3 of a gallon of Rainbow sherbet, 1/2 of a gallon of Sprite, and 1/6 of a gallon of Sundrop. After the punch is split equally among two serving bowls how much of each ingredient is in one serving bowl. How much Rainbow Sherbet will be in the bowl if it is split equally between two bowls?
Answer:
1/6
Step-by-step explanation:
To solve this, multiply the denominator by 2, which would be 2x3 which would be 6.
At a party, if 1/5 of one sheet
cake is uneaten and Tom eats
1/6 of the uneaten cake, what
fraction of the original cake
did Tom eat?
Answer:
Step-by-step explanation:
He eats 1/6 or 1/5 of the original cake.
All you need to do to get the answer is multiply the denominators.
1/5 * 1/6 = 1/30
If there was something in the numerators. you would multiply them too.
So suppose the two fractions were 3/5 and 2/7
The answer would be 3 * 2 / 5 * 7 = 6 / 35
General rule
When multiplying two fractions, multiply numerator * numerator / (denominator * denominator).
3. A rectangular prism has dimensions of , 2, and in.
(a) Determine the edge length of the largest unit cube that you could use to pack the prism. Explain.
(b) What is the volume of the prism? Explain.
(c) How many cubes with the edge length from part (a) will fit into the prism? Explain.
Answer:
Answer:
(b). 3.5
(c). 28 cubes
Step-by-step explanation:
Bob took out a 5 year loan for $4000 and paid 3% annual simple interest
Bill took out a 4 year loan for $4000 and paid 5% annual simple interest
What is the sum of amounts of interest bob and bill paid for their loans
Jenny ran 6,715 meters in 8.3 minutes. Johnny ran 1,455 meters in 2.1 minutes. Who was faster and by how much?
Answer: Jenny was faster by 116.17
Step-by-step explanation: Jenny: 809.03 meters a minute
Johnny: 692.86 meters a minute
I need find the value of x
Answer:
x = 115
Step-by-step explanation:
The chord- chord angle x is half the sum of the arcs intercepted by the angle and its vertical angle, then
x = [tex]\frac{1}{2}[/tex] (145 + 85 ) = 0.5 × 230 = 115
Step-by-step explanation:
answer is 115 you should solve it also your answer will be same
Michael and Themba are travelling from Cape town to Johannesburg by car.They travel 30km in 18 minutes and they continue at this constant speed.how far will they have travelled in 1 hour 48 minutes
Answer:
180km
Step-by-step explanation:
1hour48mins =108mins
108÷18=6
6×30=180km
A triangle has a 90° angle and two sides that measure 5 cm in length. Which statements are true about this triangle?
Answer:
what are the statements
Step-by-step explanation:
One number is five less than a second number. Five times the first is 2 more than 2 times the second. Find the numbers.
find the missing variables pythagorean theorem
Answer:
y = 12 x = 12√2 z = 12√3
Step-by-step explanation:
The 45° triangle will also have a height of y so....
y² + y² = x² 2y² = x² y² = x²/2 y = √(x²/2)
The 30° triangle
y² + z² = 24² y² = 24² - z² y = √(24² - z²)
sin 30 = y/24 1/2 = y/24 y = 12
y² = x²/2
12² = x²/2²
2(144) = x² x = √(288) x = 12√2
y² + z² = 24²
z² = 24² - y²
z² = 24² - 12²
z² = 576 - 144
z² = 432
= √(16·9·3)
z = 4·3√3
z = 12√3
y² + z² = 24²
12² + (12√3)² = 24²
144 + 144·3 = 576
2y² = x²
2(12)² = x²
288 = (12√2) = 144·2 = 288
Calculate the exact value of cos(a−b) given that sin a=12/13 with π/2
Answer:
Step-by-step explanation:
[tex]sin ~a=\frac{12}{13} ,\frac{\pi}{2} <a<\pi\\a ~is~in~2nd~quadrant.\\sin~b=\frac{3}{5} ,0<b<\frac{\pi}{2} \\b~is~in~1st~quadrant.\\cos~b=\sqrt{1-sin ^2b} \\=\sqrt{1-(\frac{3}{5} )^2} \\=\sqrt{\frac{25-9}{25} } \\=\sqrt{\frac{16}{25} } \\=\frac{4}{5} ,\\cos~a=-\sqrt{1-sin^2 a} \\=-\sqrt{1-(\frac{12}{13} )^2} \\=-\sqrt{\frac{169-144}{169} } \\=-\sqrt{\frac{25}{169} } \\=-\frac{5}{13} \\cos(a-b)=cos~acos~b+sin~a sin~b\\=\frac{-5}{13}* \frac{4}{5} +\frac{12}{13}* \frac{3}{5} \\=?[/tex]
What is 1/2 plus 1/3 plus 5/6 ??
Answer:
10/6 or 5/3
Step-by-step explanation:
1/2 ---> 3/6
1/3 ---> 2/6
5/6 ---> 5/6
Add those new fractions together:
(3/6) + (2/6) + (5/6) = 10/6 or 5/3
Answer:
10/6 or 5/3
Step-by-step explanation:
Hope it help's :)
H) Cole worked 20 hours and
earned $500. How many hours must Cole work in order to earn $700?
Please help me :)
Answer:
he would have to work 28 hours
Step-by-step explanation:
Answer:
Cole have to work 28 hours
5. Translate each of these statements into logical expressions using predicates, quantifiers, and logical connectives. The domain is all people on Earth. a) No one is perfect. b) Not everyone is perfect. c) All your friends are perfect. d) At least one of your friends is perfect. e) Everyone is your friend and is perfect. f) Not everybody is your friend or someone is not perfect.
Solution :
A logical expression may be defined as those equation or expression which is either viable or inviable.
In the context, translating each statement into a logical expression using the predicates, the quantifiers, and the logical connectives.
Let P(x) be the propositional function "x is perfect"
Let F(x) be the propositional function "x is your friend"
And the domain is all the people
a). No one is perfect
[tex]$\forall \ x \rightharpoondown P(x)$[/tex]
b). Not everyone is perfect.
[tex]$\rightharpoondown \forall \ x\ P(x)$[/tex]
c). All your friends are perfect.
[tex]$\forall \ x (F(x)\rightarrow P(x))$[/tex]
d). At least one of your friends is perfect.
[tex]$\exists \ x \ (F(x) \wedge P(x))$[/tex]
e) Everyone is your friend and is perfect.
[tex]$\forall \ x \ F(x) \wedge \ \forall \ x \ P(x)$[/tex]
f). Not everybody is your friend or someone is not perfect.
[tex]$(\rightharpoondown \ \forall \ x \ F(x) ) \ \wedge (\exists \ x \ \rightharpoondown \ A (x))$[/tex]
Please help I'll give brainliest
Answer:
angle A = 130°
x=65°
I hope it's helps you
Answer:
(2x - 30°) + 50° = 180° (linear pair angles)
2x + 20° = 180°
2x = 180° - 20°
2x = 160°
x = 160°/2 = 80°
Now, A = 2x - 30° = 160°-30° = 130°
Help me please it’s due tonight!
Answer:
B.
[tex] \frac{5}{8} [/tex]
Josh cycled 8 laps on a bicycle path surrounding a lake. Each lap was the same length. If he cycled a total of 26.4mi, what was the length of each lap around the lake? Write your answer in feet. Use the table of conversion facts as necessary, and do not round your answer. ft
Answer:
The length of each lap around the lake was of 3.3 miles.
Step-by-step explanation:
Given that Josh cycled 8 laps on a bicycle path surrounding a lake, and each lap was the same length, to determine what was the length of each lap around the lake if he cycled a total of 26.4 miles, the following calculation must be performed:
26.4 / 8 = X
3.3 = X
Thus, the length of each lap around the lake was 3.3 miles.
Find the slope of the line passing through the points (2,-9) and )1,-3)
Answer:
5
Step-by-step explanation:
Slope = (-3 - 2) / (1 - 2) = -5 / -1 = 5
Hi there!
[tex]\large\boxed{\text{slope =} 6}[/tex]
We can calculate slope using the following formula:
[tex]slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Plug in the corresponding points:
[tex]slope = \frac{-9-(-3)}{2-1}[/tex]
Simplify:
[tex]slope = \frac{-6}{1} = -6[/tex]
Please help me with this for 20 points !!!!
Answer:
A (the first answer)
Step-by-step explanation:
Please help meeeeeeeeeeeeeeeee
Answer:
1436.8 in³
Step-by-step explanation:
Volume of sphere = (4/3)πr³
r = 7
---> (4/3)π(7)³ = 1436.8 in³
Have a great day :)
Answer:
The volume of the sphere is A.
Which of the following is true regarding the Central Limit Theorem (CLT)?
• A. If your sample size is n = 30 exactly, then you are guaranteed to have an approximately normal sampling distribution of the sample mean.
• B. As the sample size n increases, the data distribution should become approximately normal.
• C. The Central Limit Theorem states that the sampling distribution of the sample mean should always have the same shape as the population distribution.
D. none of the above
Answer:
im sure its c
Step-by-step explanation:
:)
part 2
If we used the quadratic expression below to complete a diamond, what value would go at the very BOTTOM of the diamond?
x^2 - 4x + 5
a. -4
b. 4
c. 1
d. 5
9514 1404 393
Answer:
a. -4
Step-by-step explanation:
When using the "diamond method" for factoring quadratics, the bottom number is the coefficient of the linear term. In this quadratic, it is -4.
The bottom number is -4.
Violet is taking a computer-adaptive test, where each time she answers a question
correctly, the computer gives her a more difficult question. Let Q be the number of
questions Violet answers correctly before she misses one.
What type of variable is Q?
Algebraic
None of them.
Geometric
Binomial
Answer: Neither
Step-by-step explanation:
find the missing length
Answer:
PQ=36
Step-by-step explanation:
If the triangles are similar, then they must have a common ratio between them.
RQ corresponds with CB, so [tex]\frac{84}{18}=\frac{14}{3}[/tex]
If the ratio is [tex]\frac{14}{3}[/tex], then [tex]\frac{168}{\frac{14}{3}}=36[/tex], so PQ=36.
