Answer:
[tex]A(t) = 600(1.035)^8[/tex]
The ending balance is of $790.1.
Step-by-step explanation:
Compound interest:
The amount of money earned after t years, in compound interest, is given by:
[tex]A(t) = A(0)(1+r)^{t}[/tex]
In which A(0) is the initial amount of money and r is the interest rate, as a decimal.
$600 that earns 3.5% compound interest over 8 years
This means, respectively, that:
[tex]A(0) = 600, r = 0.035, t = 8[/tex]
So, the formula is:
[tex]A(t) = A(0)(1+r)^{t}[/tex]
[tex]A(t) = 600(1+0.035)^{8}[/tex]
[tex]A(t) = 600(1.035)^8[/tex]
Ending balance:
The ending balance is:
[tex]A(t) = 600(1.035)^8 = 790.1[/tex]
The ending balance is of $790.1.
g Based on historical data, your manager believes that 32% of the company's orders come from first-time customers. A random sample of 146 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is greater than than 0.43
Answer:
0.0022 = 0.22% probability that the sample proportion is greater than than 0.43
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 zscore 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 pvalue, 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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Based on historical data, your manager believes that 32% of the company's orders come from first-time customers.
This means that [tex]p = 0.32[/tex]
Mean and standard deviation:
Sample of 146 means that [tex]n = 146[/tex]
[tex]\mu = p = 0.32[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.32*0.68}{146}} = 0.0386[/tex]
What is the probability that the sample proportion is greater than than 0.43?
This is 1 subtracted by the pvalue of Z when X = 0.43. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.43 - 0.32}{0.0386}[/tex]
[tex]Z = 2.85[/tex]
[tex]Z = 2.85[/tex] has a pvalue of 0.9978
1 - 0.9978 = 0.0022
0.0022 = 0.22% probability that the sample proportion is greater than than 0.43
Write the equation of the line passing through (2,0) and (0,-5)
Answer:
y=5/2x+2
Step-by-step explanation:
To get the slope,
(-5-0) /(0-2)=-5/-2=5/2
Introduce points (x,y) (0,2) i.e one of the given points ,it should give same answer either way
(0,2)(x,y)
y-2/x-0=5/2
Cross multiplication,2(y-2)=5(x-0)
2y-4=5x-0
2y=5x-0+4
2y=5x +4
Divide both sides by 2 to get
y=5/2x+2.
A manufacturing company with 350 employees is changing the employee health insurance plan to either plan A or plan B. The company wants to know if employees have a preference between the two plans and whether or not preference differs between those employees who have family members covered under the current plan (group 1) and those who do not (group 2). The human resources office takes a simple random sample from each of the two groups, sends information about both plans to the employees in each sample, and asks them whether they prefer plan A or plan B. The table summarizes the responses received, with expected cell counts in parentheses.
Plan A Plan B Total
Yes (group 1) 40 (32.5) 20 (27.5) 60
No (group 2) 6 (13.5) 19 (11.5) 25
Total 46 39 85
Which statement is true about whether the conditions for the chi-square test for homogeneity have been met?
a. A simple random sample should have been taken from all the employees, and then each employee in the sample should have been asked their plan preference and whether or not they have family members covered under the current health insurance plan.
b. The expected cell counts are not large enough to apply the chi-square test for homogeneity.
c. The total sample size is not large enough to apply the chi-square test for homogeneity.
d. The total sample size is too large to apply the chi-square test for homogeneity.
e. All conditions necessary to apply the chi-square test for homogeneity are satisfied here.
Answer: D. The total sample size is too large to apply the chi-square test for homogeneity.
Step-by-step explanation: When sampling without replacement, the sample size should not exceed 10 percent of the population size. Here, the sample size of 85 is just over 24 percent of the population of 350 company employees.
The total sample size is too large to apply the chi-square test for homogeneity.
We have given that,
A manufacturing company with 350 employees is changing the employee health insurance plan to either plan A or plan B.
Plan A Plan B Total
yes(group 1) 40(32.5) 20(27.5) 60
No (group 2) 6 (13.5) (11.5) 25 25
Total 46 39 85
We have to find which statement is true,
What is sampling without replacement?Each sample unit of the population has only one chance to be selected in the sample. we can select one sample only way and after selection we cannot pot this sample in the sample space again.
The sample size should not exceed 10 percent of the population size.when we use sampling without replacement,
Here, the sample size of 85 is just over 25 percent of the population of 350 company employees.
Therefore,the total sample size is too large to apply the chi-square test for homogeneity.
To learn more about the sample space replacement and without replacement visit:
https://brainly.com/question/17042101
please help me with this math project (photo linked). (7th grade unit 3) check my other questions plsss (last one)
1. -3x - 17
2. -24x + 25
3. 2x + 4
4. -9x -9
5. 7x - 2
?????????????????????
Answer: A 128
Step-by-step explanation:
PLEASE HELP 20 POINTS!
which model shows 1/4 ÷ 3?
Answer:
A
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
A
in a school of 40 students 10% are boys. How many boys are there
Answer:
4boys
Step-by-step explanation:
40 of 10% 40×10/100 =4 remember percentage is always over 100
Find the exact perimeter of the circle with a radius of 5 and round your answer to 2 decimal places
Answer:
31.42
Step-by-step explanation:
This Question: 1 pt
17 of 29
Emma has $160 cash to spend at a music store. How much can she spend on items if there is a 7% sales tax?
Emma can spend on items.
(Round to the nearest cent as needed.)
Answer:
i would say $148.80
Step-by-step explanation:
tax would amount to 11.20 so when you subyract that from the total then the rest is what she can spend.
Please help I’ll give brainalist + 10 points to whoever helps and get this 100% right
Answer:
its C
Step-by-step explanation:
because 180⁰-40⁰=140⁰
Answer:
∠m = 140°
Step-by-step explanation:
∠1 and ∠m are adjacent angles, so they add up to 180°.
∠1 + ∠m = 180
40 + ∠m = 180
∠m = 180 - 40
∠m = 140°
Help
solve 2x+4=10
Brainliest
❤️ The answer is attached
achievements.
Answer:
x=3
Step-by-step explanation:
2x+4=10
subtracting both side by 4.
2x+4-4=10-4
2x=6
x=6/2=3
3 tons = ________ how many pounds
Answer:
6000 pounds
Step-by-step explanation:
calculator
Answer:
6000lbs
Step-by-step explanation:
3*2000=6000
A shoe box is 4 inches wide, 3 inches deep, and 12 inches long. What is the volume?
I know it's 144 but 144 what?
Answer:
144in square
Step-by-step explanation:
How many planes are shown in the figure?
Answer:
5
Step-by-step explanation:
5
Answer:
5
Step-by-step explanation:
a rectangular banner has an area of 36.75 square feet, The length of the banner is 15 feet. What is its width
Answer:
w=A
l=36.75
15=2.45ft
Step-by-step explanation: there you go :>
Answer:
2.45ft
Step-by-step explanation:
w=A
l=36.75
15=2.45ft
solve[5x-6/7] = -8 for x
please help
Answer:
7=7
Step-by-step explanation:
1 Let x=\frac{13}{5}x=
5
13
.
5\times \frac{13}{5}-6=7
5×
5
13
−6=7
2 Cancel 55.
13-6=7
13−6=7
3 Simplify 13-613−6 to 77.
7=7
7=7
hope this helps.
The ratio of adults to children at a museum is 2:7 which table represents this ratio.
refer to pictures
Answer:
D
Step-by-step explanation:
Find the graph that has equivalent ratios to 2:7 make sure your order is right.
2:7 equals 6:21 for example; 2 x 3=6 7 x 3=21
D
âp3x
is
TRASH
ãp3x didnt even give us a SPRING BREAK WHICH WE ARE ENTITLED TO!!!!
answer if u wanna
yup I use it. it gets anoying
5x -30 = 3x + 60
How many solutions are there
Answer:
one solution
Step-by-step explanation:
5x - 30 = 3x + 60
2x - 30 = 60
2x = 90
x = 45
I’ll give 35 points and brainliest answer asap please it’s due tomorrow
Answer:
try 72.2
Step-by-step explanation:
surface area is 3.8x3.8x6
but minus one side is 3.8x3.8x5 = 72.2
Answer:
72.2 square metersStep-by-step explanation:
multiply the length by the width
3.8 x 3.8 = 14.44
in a cube there are 6 sides; however, it says Sarah is painting all the sides except for one so she is only painting 5 sides
14.44 x 5 = 72.2
Louis has a bag of 2510 shells each pen shell is 18 cm long what is the combine length of the pen shells in meters
Answer:
45180cm
Step-by-step explanation:
You have to multiply the amount of shells by the length on one shell to get the length of all of them combined so, 2510 multiplied by 18 is 45180.
Together, Dien and Jane can eat 2/3 of a pizza in 4 seconds. How long would it take each of them to eat the whole pizza alone if Jane can eat a pizza 5 seconds faster than Dien?
Answer:
Dien - 15 seconds, Jane - 10 secondsStep-by-step explanation:
Together:
2/3 of pizza ⇒ 4 secondsFull pizza ⇒ 4 ÷ 2/3 = 6 secondsDien needs x seconds to eat pizza
Jane needs x - 5 seconds to eat pizza
In one second, Dien can eat 1/x, Jane can eat 1/(x - 5), together 1/6 of a pizza
1/x + 1/(x - 5) = 1/6x(x - 5) = 6(x + x - 5)x² - 5x - 12x + 30 = 0x² - 17x + 30 = 0(x - 15)(x - 2) = 0x = 15 (x = 2 is discounted as not realistic)Dien can eat a pizza in 15 seconds, Jane can eat a pizza in 10 seconds
Solve for x Enter the solutions from least to greatest . (x - 4)(- 5x + 1) = 0 lesser x = greater x =
The first three terms of a sequence are given. Round to the nearest thousandth (if necessary). 16, 8,4,... 16,8,4,... \text{Find the 10th term.} Find the 10th term.
Answer:
0.03125
To the nearest thousandth = 0.031
Which expression is equivalent to 16 + 2 ⋅ 36?
Please no links!! Can’t open them! Thanks
A: 49
B: 33
C: 57
D: 16
Answer:
d
Step-by-step explanation:
i believe its 49 - 33= answer bc 49=49
Answer:
16°
Step-by-step explanation:
The two angles are vertical, meaning that they are the same
33 + 16 = 49
what is the value of x ?
Answer:
the letter "x" is often used in algebra to mean a value that is not known yet. It is called a 'varaible' or sometimes unknown.
Answer:
It is 65, B
Step-by-step explanation: because 180-115=65 tell me if you dont get it
Is the ratios 2.5 : 8 and 7.5 : 24 are they equivalent?
Answer:
Yes, they are equivalent.
Step-by-step explanation:
To get from 2.5 : 8 to 7.5 : 24, you have to multiply by both sides by 3.
So they are equivalent.
(2a^3 b^4) ^4=
What is the answer to this problem ?
Answer: 16a^12 b^16
Step-by-step explanation:
Everything in the parenthesis to the 4th power.
2a^4= 16a
3*4=12
b^4*4=b^16