Answer:
Step-by-step explanation:
We would apply the formula for determining compound interest which is expressed as
A = P(1 + r/n)^nt
Where
A = total amount in the account at the end of t years
r represents the interest rate.
n represents the periodic interval at which it was compounded.
P represents the principal or initial amount deposited
From the information given,
P = 1100
A = 1900
n = 4 because it was compounded 3 times in a year and n = 12/3 = 4
t = 10 years
Therefore,.
1900 = 1100(1 + r/4)^4 × 10
1900/1100 = (1+ r/4)^40
1.73 = (1+ r/4)^40
Taking log to base 10 of both sides, it becomes
Log 1.73 = 40log(1 + 0.25r)
0.238 = 40log(1 + 0.25r)
Log(1 + 0.25r) = 0.238/40 = 0.00595
Take exponent of both sides, it becomes
10^log(1 + 0.25r) = 10^0.00595
1 + 0.25r = 1.0138
0.25r = 1.0138 - 1 = 0.0138
r = 0.0138/0.25
r = 0.0552
The The required annual interest rate is
0.0552 × 100 = 5.5%
A trust fund eels is 6% simple interest divide into its members accounts every month if a member has $5000 in the funds account how much money would be in that account after three months
Answer:
$5073.37
Step-by-step explanation:
We can use the simple interest rate (appreciation) formula: A = P(1 + r)^t
Because it gives us 3 months, we need to put it in terms of years. That will give us 1/4 of a year:
A = 5000(1 + 0.06)^0.25
When you plug that into the calc, you should get 5073.37 as your final answer!
SIMPLIFY THE EXPRESSION -4 X 4 X 4 X 4 X4 X 4 X 4 X4
Answer:
-4 · [tex]4^{7}[/tex]
Step-by-step explanation:
The height of water in a bathtub ,h, is a function of time ,t, let p represent this function height is measured in inches and time in minutes
The complete question is;
The height of water in a bathtub,h, is a function of time,t. Let P represent this function. Height is measured in inches and time in minutes.
Match each statement in function notation with a description.
A: P(0) = 0
B: P(4) = 10
C: P(10) = 4
D: P(20) = 0
1:After 20 minutes, the bathtub is empty.
2:The bathtub starts out with no water.
3:After 10 minutes, the height of the water is 4 inches.
4:The height of the water is 10 inches after 4 minutes.
Answer:
-option D is the correct answer for sentence 1.
-option A is the correct answer for sentence 2.
-option C is the correct answer for sentence 3.
-option B is the correct answer for sentence 4
Step-by-step explanation:
The height of water in a bathtub h is a function of time t.
-If t = 20 minutes, then height of water represented by P is empty so, P(20) = 0. Thus, option D is the correct option for sentence 1.
-The bath tub starts out with no water. Thus, P(0) = 0. So option A is the correct option for sentence 2.
-After 10 minutes, the height of the water is 4 inches. Thus, P(10) = 4. So, option C is the correct option for sentence 3.
- The height of the water is 10 inches after 4 minutes. Thus, P(4) = 10. So option B is the correct answer for sentence 4
if you’re probability surveys in math 30 please help it’s simple but i don’t remember how to do it!!
Answer:
4 C, 5 C
Step-by-step explanation:
4) Sum of all candies = 14
Total number of cherry candies = 5
probability of not getting a cherry candy = 14-5 / 14 = 9/14
5) Number of supporters for Lyshon = 14
Total number of supporters = 100
Probability that a student chosen at random will vote vote for lyshon =
14/100 = 7/50
The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation. Recently, Southwest Air had the best rate with 80 % of its flights arriving on time. A test is conducted by randomly selecting 18 Southwest flights and observing whether they arrive on time.
(a) Find the probability that at least 13 flights arrive late .
Answer:
The probability that at least 13 flights arrive late is 2.5196 [tex]\times 10^{-6}[/tex].
Step-by-step explanation:
We are given that Southwest Air had the best rate with 80 % of its flights arriving on time.
A test is conducted by randomly selecting 18 Southwest flights and observing whether they arrive on time.
The above situation can be represented through binomial distribution;
[tex]P(X = x) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r} ; x = 0,1,2,3,.........[/tex]
where, n = number of trials (samples) taken = 18 Southwest flights
r = number of success = at least 13 flights arrive late
p = probability of success which in our question is probability that
flights arrive late, i.e. p = 1 - 0.80 = 20%
Let X = Number of flights that arrive late.
So, X ~ Binom(n = 18, p = 0.20)
Now, the probability that at least 13 flights arrive late is given by = P(X [tex]\geq[/tex] 13)
P(X [tex]\geq[/tex] 13) = P(X = 13) + P(X = 14) + P(X = 15) + P(X = 16) + P(X = 17) + P(X = 18)
= [tex]\binom{18}{13}\times 0.20^{13} \times (1-0.20)^{18-13}+ \binom{18}{14}\times 0.20^{14} \times (1-0.20)^{18-14}+ \binom{18}{15}\times 0.20^{15} \times (1-0.20)^{18-15}+ \binom{18}{16}\times 0.20^{16} \times (1-0.20)^{18-16}+ \binom{18}{17}\times 0.20^{17} \times (1-0.20)^{18-17}+ \binom{18}{18}\times 0.20^{18} \times (1-0.20)^{18-18}[/tex]
= [tex]\binom{18}{13}\times 0.20^{13} \times 0.80^{5}+ \binom{18}{14}\times 0.20^{14} \times 0.80^{4}+ \binom{18}{15}\times 0.20^{15} \times 0.80^{3}+ \binom{18}{16}\times 0.20^{16} \times 0.80^{2}+ \binom{18}{17}\times 0.20^{17} \times 0.80^{1}+ \binom{18}{18}\times 0.20^{18} \times 0.80^{0}[/tex]
= 2.5196 [tex]\times 10^{-6}[/tex].
Which statement could be an interpretation of the graph’s x-intercept or y-intercept?
On a coordinate plane, a line goes through points (0, 800) and (400, 0).
Answer:
[tex] m=\frac{y_2 -y_1}{x_2 -x_1} =\frac{0-800}{400-0}= -2[/tex]
And then we can find the y intercept using one point for example (0,800) and we have:
[tex] 800= -2*0+ b[/tex]
[tex] b= 800[/tex]
And our model would be:
[tex] y = -2x +800[/tex]
And the x intercept would be if y=0 then
[tex] 0 =-2x +800[/tex]
[tex] x =400[/tex]
x intercept =400 represent the value of x when y =0
y intercept = 800 represent the value of y when x =0
Step-by-step explanation:
We have the following points given:
(0, 800) and (400, 0)
If we want to find the x intercept and y intercept we need to remember that we need to set a linear model given by:
[tex] y=mx +b[/tex]
Where
[tex] m=\frac{y_2 -y_1}{x_2 -x_1} =\frac{0-800}{400-0}= -2[/tex]
And then we can find the y intercept using one point for example (0,800) and we have:
[tex] 800= -2*0+ b[/tex]
[tex] b= 800[/tex]
And our model would be:
[tex] y = -2x +800[/tex]
And the x intercept would be if y=0 then
[tex] 0 =-2x +800[/tex]
[tex] x =400[/tex]
x intercept =400 represent the value of x when y =0
y intercept = 800 represent the value of y when x =0
Answer:
And then we can find the y intercept using one point for example (0,800) and we have:
And our model would be:
And the x intercept would be if y=0 then
x intercept =400 represent the value of x when y =0
y intercept = 800 represent the value of y when x =0
Step-by-step explanation:
We have the following points given:
(0, 800) and (400, 0)
If we want to find the x intercept and y intercept we need to remember that we need to set a linear model given by:
Where
And then we can find the y intercept using one point for example (0,800) and we have:
And our model would be:
And the x intercept would be if y=0 then
x intercept =400 represent the value of x when y =0
y intercept = 800 represent the value of y when x =0
Step-by-step explanation:
The grid shown below is in the shape of a rectangle. What is the area, in square units, of the shaded part of the rectangle? a 14 b 24 c 28 d 48
The correct answer is B. 24
Explanation:
If you consider the shaded part of the rectangle is a triangle the best way to calculate the area of this is by calculating the total area or space occupied by this triangle. This can be done if you multiply the base by the height and divide the result in 2 or b x h / 2.
6 squares (base) x 8 squares (height) = 48 / 2 = 24 squares
Also, the shaded area is approximately the half area of all the rectangle, in this case, you can calculate the area of the rectangle by multiplying side x side or length by width. This means 6 squares x 8 squares = 48 squares (total area), which divided by 2 (shaded area) is also equal to 24.
Answer:
B, 24.
Step-by-step explanation:
I solved it with my teacher
Assume Shelley Kate decides to take her social security at age 63. What amount of social security benefit will she receive each month, assuming she is entitled to $720 per month
She will receive a lot more money because she is already retired from work already and will win as bit more money
Fertilizer must be mixed with water in a 1:4 ratio. If you use 3
cups of fertilizer how much water do you need?
Answer:
12
Step-by-step explanation:
1:4 = 3:12
Answer:
12 cups of water
Step-by-step explanation:
The ratio of fertilizer is 1. To get to 3 you times it by 3. Therefore to find how much water you need you'd have to do the same to the other side of the ratio, times it by three. So it would be 3:12
An electrician charges $40 per visit, and $20 per hour of work. On a particular day, he made 3 visits and calculated that his average earnings were $50 per hour. Use this information to complete the statement. He worked hours that day.
Answer:
4 hours
Step-by-step explanation:
For three visits, the electrician earned $40 × 3 = $120 in "per-visit" charges. For working x hours, he earned 20x in "per-hour" charges. The total of these came to 50x:
120 +20x = 50x
120 = 30x . . . . . . . . subtract 20x
4 = x . . . . . . . . . . . . . divide by 30
The electrician worked 4 hours that day.
Which type of reasoning allows you to use observation to find the next three
values in the number pattern 1,4,7,10....?
A. Deduction
B. Induction
C. Decision making
D. Proof
Plz help me
Answer:
Induction
Step-by-step explanation:
Induction reasoning refers to conjectures which is what you will need for this
The Inductive reasoning allows to use observation to find the next three
values in the number pattern 1, 4, 7, 10, . . .
The correct answer is option (B)
What is inductive reasoning?It is a reasoning that is based on patterns you observe. By observing the pattern in the sequence, we can use inductive reasoning to decide the next successive terms of the sequence.A conclusion you reach using inductive reasoning is called a conjectureFor given example,
We have been given the number pattern 1, 4, 7, 10, . . .
Here, 4 - 1 = 3 ..................(i)
7 - 4 = 3 ..................(ii)
10 - 7 = 3 ..................(iii)
From (i), (ii) and (iii),
the common difference between consecutive terms is 3.
The next three values would be,
10 + 3 = 13
13 + 3 = 16
16 + 3 = 19
So, the number pattern would be 1, 4, 7, 10, 13, 16, 19, . . .
Therefore, an Inductive reasoning allows to use observation to find the next three values in the number pattern 1, 4, 7, 10, . . .
The correct answer is option (B)
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Stanford University conducted a study of whether running is healthy for men and women over age 50. During the first eight years of the study, 1.5% of the 451 members of the 50 Plus Fitness Association died. We are interested in the proportion of people over 50 who ran and died in the same eight year period.
Construct a 97% confidence interval for the population proportion of people over 50 who ran and died in the same eight–year period.
Define the random variable in X and P in words.
Which distribution should you use in this problem?
Answer:
Step-by-step explanation:
a) Confidence interval is written as
Sample proportion ± margin of error
Margin of error = z × √pq/n
Where
z represents the z score corresponding to the confidence level
p = sample proportion. It also means probability of success
q = probability of failure
q = 1 - p
p = x/n
Where
n represents the number of samples
x represents the number of success
From the information given,
n = 451
x = 1.5/100 × 451 = 7
p = 7/451 = 0.02
q = 1 - 0.02 = 0.98
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.97 = 0.1
α/2 = 0.01/2 = 0.03
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.03 = 0.97
The z score corresponding to the area on the z table is 2.17. Thus, Thus, the z score for a confidence level of 97% is 2.17
Therefore, the 97% confidence interval is
0.02 ± 2.17√(0.02)(0.98)/451
= 0.02 ± 0.014
b) x represents the number of members of the 50 Plus Fitness Association who ran and died in the same eight–year period.
P represents the proportion of members of the 50 Plus Fitness Association who ran and died in the same eight–year period.
The distribution that should be used is the normal distribution
For each of the sequences below, find a formula that generates the sequence. (a) 4, 10, 16, 22, 28, 34, 40, . . . (b) 5, 15, 45, 135, 405, . . . (c) 10, 20, 10, 20, 10, 20, 10
Answer:
[tex](a) \: 6n-2\\(b)\: 5 \times 3^{n-1}\\(c)\: 5({-1^n}+3)[/tex]
Step-by-step explanation:
[tex]6(1)-2=4[/tex]
[tex]6(2)-2=10[/tex]
[tex]5 \times 3^{(3)-1}=45[/tex]
[tex]5 \times 3^{(4)-1}=135[/tex]
[tex]5(-1^{(5)}+3)=10[/tex]
[tex]5(-1^{(6)}+3)=20[/tex]
a) The formula that generates the sequence 4, 10, 16, 22, 28, 34, 40 is an = 4 + 6 * (n - 1)
b) The formula that generates the sequence 5, 15, 45, 135, 405 is an = 5 * 3ⁿ⁻¹
c) The formula that generates the sequence 10, 20, 10, 20, 10, 20, 10 is an = 10 + 10 * ((n + 1) % 2)
(a) The sequence increases by 6 at each step. To generate the sequence, we can use the formula: an = 4 + 6 * (n - 1), where "an" represents the nth term in the sequence, and "n" is the position of the term in the sequence.
(b) The sequence is a geometric progression with a common ratio of 3. To generate the sequence, we can use the formula: an = 5 * 3ⁿ⁻¹ where "an" represents the nth term in the sequence, and "n" is the position of the term in the sequence.
(c) The sequence alternates between 10 and 20. To generate the sequence, we can use the formula: an = 10 + 10 * ((n + 1) % 2), where "an" represents the nth term in the sequence, and "%" represents the modulo operation, which results in 0 when n is even and 1 when n is odd. So, when n is even, an = 10, and when n is odd, an = 10 + 10 = 20.
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Suppose a simple random sample of size n= 11 is obtained from a population with u = 62 and a = 14.
(a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities regarding the sample me
(b) Assuming the normal model can be used, determine P(x < 65.8).
(c) Assuming the normal model can be used, determine P(x 2 64.2).
Click here to view the standard normal distribution table (page 1).
Click here to view the standard normal distribution table (page 2).
(a) What must be true regarding the distribution of the population?
O A. Since the sample size is large enough, the population distribution does not
need to be normal.
B. The population must be normally distributed and the sample size must be large.
OC. The population must be normally distributed.
OD. There are no requirements on the shape of the distribution of the population.
Answer:
a) C. The population must be normally distributed.
b) P(x < 65.8) = 0.8159
c) P(x > 64.2) = 0.3015
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use 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
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question:
[tex]\mu = 62, \sigma = 14, n = 11, s = \frac{14}{\sqrt{11}} = 4.22[/tex]
(a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities regarding the sample me
n < 30, so the distribution of the population must be normal.
The correct answer is:
C. The population must be normally distributed.
(b) Assuming the normal model can be used, determine P(x < 65.8).
This is the pvalue of Z when X = 65.8. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{65.8 - 62}{4.22}[/tex]
[tex]Z = 0.9[/tex]
[tex]Z = 0.9[/tex] has a pvalue of 0.8159.
So
P(x < 65.8) = 0.8159
(c) Assuming the normal model can be used, determine P(x > 64.2).
This is 1 subtracted by the pvalue of Z when X = 64.2. So
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{64.2 - 62}{4.22}[/tex]
[tex]Z = 0.52[/tex]
[tex]Z = 0.52[/tex] has a pvalue of 0.6985.
1 - 0.6985 = 0.3015
So
P(x > 64.2) = 0.3015
The perimeter of the shape is 28 cm. Find the value of radius.
Answer:
r = 4.2805cm
Step-by-step explanation:
ok first the shape its made of two slant height and and an arc of degree 70°
The total perimeter = 28cm
The formula for the total perimeter= 2l + 2πl(70/360)
Where l is the radius of the shape.
But l = 2r
So
= 2l + 1.2217l
= 3.2217l
28 = 3.2217l
l = 28/3.2217
l = 8.691
Recall that l = 2r
8.691= 2r
r = 8.691/2
r = 4.2805cm
A bookstore charges $4 for shipping, no matter how many books you buy. Irena makes a graph showing the shipping cost for I to 5 books. She claims that the points she graphed lie on a line. Does her statement make sense? Explain
Answer:
Yes
Step-by-step explanation:
1 book = $4
2 books = 2*$4
3 books = 3*$4
4 books = 4*$4
5 books = 5*$4
This can be shown as: y=4x
y=ax+b is linear function, Irena is right
eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Solution,
Radius=2 m
Area =pi r^2
= 3.142*(2)^2
=12.568 m^2
hope it helps
Good luck on your assignment
Results of 99% confidence intervals are consistent with results of two-sided tests with which significance level? Explain the connection. A 99% confidence interval is consistent with a two-sided test with significance level alphaequals nothing because if a two-sided test with this significance level does not reject the null hypothesis, then the confidence interval ▼ contains does not contain the value in the null hypothesis.
Answer:
Yes, they are consistent.
A 99% confidence interval is consistent with a two-sided test with significance level alpha=0.01 because if a two-sided test with this significance level does not reject the null hypothesis, then the confidence interval does contains the value in the null hypothesis.
Step-by-step explanation:
Yes, they are consistent.
A 99% confidence interval is consistent with a two-sided test with significance level alpha=0.01 because if a two-sided test with this significance level does not reject the null hypothesis, then the confidence interval does contains the value in the null hypothesis.
The critical values of the confidence level are equivalent to the critical values in the hypothesis test. In the case that the conclusion of the test is to not reject the null hypothesis, the test statistic falls within the acceptance region: its value is within the critical values of the two-sided test.
Then, it is also within the critical values of the confidence interval and the sample mean (or other measure) will be within the confidence interval bounds.
find the mean of x,2x,3x,4x,5x
Answer:
Mean = 3x
Step-by-step explanation:
Mean = [tex]\frac{SumOfObservations}{No. OfObservations}[/tex]
Mean = [tex]\frac{x+2x+3x+4x+5x}{5}[/tex]
Mean = [tex]\frac{15x}{5}[/tex]
Mean = 3x
The mean, also known as the average of x, 2x, 3x, 4x, and 5x is 3x as per the concept of Simplifying.
To find the mean of x, 2x, 3x, 4x, and 5x, we need to add up all the values and divide by the total number of values.
In this case, we have five values.
Mean = (x + 2x + 3x + 4x + 5x) / 5
Simplifying the numerator:
Mean = (15x) / 5
Mean = 3x
Therefore, the mean of x, 2x, 3x, 4x, and 5x is 3x.
The mean, also known as the average, represents the central tendency of a set of values. In this case, the mean is 3x, which indicates that on average, the values x, 2x, 3x, 4x, and 5x are three times the value of x.
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Will pick brainliest! I need help with this, actual effort in answering is much appreciated.
Answer:
option 2
Step-by-step explanation:
4^2=16/8=2. 4^2=16/16=1. 2-1=1
Please help! Correct answer only, please! The following information matrices show how many of each vehicle type sold and the bonus amount each salesperson receives for selling that type of vehicle for the car dealership for the week. Which salesperson sold the most vehicle for the week described?A. Scott B. Each sold the same number of vehicles C. Kelly D. Mark
Answer: b) Each sold the same number of vehicles
Step-by-step explanation:
This question is only asking for the quantity of vehicles (not the total amount earned) so we can disregard the second matrix and find the sum of each row in the first matrix.
Kelly: 8 + 2 + 6 = 16
Scott: 7 + 8 + 1 = 16
Mark: 10 + 4 + 2 = 16
The total number of vehicles sold by each person is the same
If Aizuddin borrowed RM 6.300 from a bank which offers an interest of 8%
compounded annually, find.
(a) the future value
(b) the amount of interest charged
Answer:
(a) The formula to calculate the amount of money (A) that Aizuddin must pay the bank after n years, with the original amount of borrowed money is 6300 RM, interest of 8%, compounded annually, is described as following:
A = principal x (1 + rate)^(time in year)
A = 6300 x (1 + 8/100)^n
(b) The amount of interest charged (AC) that Aizuddin must pay after n years:
AC = A - 6300
AC = 6300 x (1 + 8/100)^n - 6300
AC = 6300 x [(1 + 8/100)^n - 1]
Hope this helps!
which of the following expressions is equal to 2X^2 +8
Answer:
The question is not clear.
Step-by-step explanation:
Normally it helps to rewrite 8 as
8 = 2 * 2 * 2 = 2³
However the question is not clear.
There are no following expressions given...
By 2X^2 +8,
do you mean 2*x² + 8, or do you mean 2*x^(2 + 8)
or did you perhaps mean 2^(x+8)
Next time, please add a picture.
Answer:
(2x-4i)(x+2i)
work out the value of 7^2+4^3 divided by 2^5
113/32
Step-by-step explanation:
7 squared is 49, 4 cubed is 64, 2 to the 5th power is 32.
49 plus 64 is 113 divided by 32
3.53125
Step-by-step explanation:
7^2+4^3/2^5
= 49+64/32
= 113/32
= 3.53125
What’s the correct answer for this question?
Answer
A. 18(3/4)π
Explanation
In the attached file
According to a recent census, 16% of the people in the United States are of Hispanic origin. One county supervisor believes her county has a different proportion of Hispanic people than the nation as a whole. She looks at their most recent survey data, which has a random sample of 437 county residents, and found that 44 of those surveyed are of Hispanic origin.Randomization condition:Choose the correct statement.Select one:a. The 437 county residents were a voluntary response sample of all county residents.b. The 437 county residents is a systematic response sample of all county residents.c. The 437 county residents were a random sample of all county residents.
Answer:
Option C is correct.
The 437 county residents were a random sample of all county residents.
a) If p is the proportion of Hispanics in the county,
The null hypothesis is represented as
H₀: p = 0.16
The alternative hypothesis is represented as
Hₐ: p ≠ 0.35
b) The model of the test is two-tailled, one-proportion test. And it satisfies all of the required conditions for an hypothesis test.
c) The sketch of the region of acceptance is presented in the attached image to this answer. (z < -4.09 and z > 4.09).
Test statistic = -4.09
p-value = 0.000043
d) We can conclude that the proportion of the county that are Hispanics is different from the proportion of the country that are Hispanics.
Step-by-step explanation:
According to the question, it was clearly stated that the 437 county residents are a random sample of the residents in the county, hence, it is evident that option C is the right statement.
a) For hypothesis testing, the first thing to define is the null and alternative hypothesis.
The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.
While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.
For this question, the county supervisor wants to check if proportion of the county that are Hispanics is different from the proportion of the whole nation that are Hispanics. (0.16).
Hence, the null hypothesis is that there isn't enough evidence to conclude that the proportion of the county that are Hispanics is different from the proportion of the whole nation that are Hispanics. That is, there is no significant difference between the proportion of the county that are Hispanics and the proportion of the whole nation that are Hispanics. (0.16).
The alternative hypothesis will now be that enough evidence to conclude that the proportion of the county that are Hispanics is different from the proportion of the whole nation that are Hispanics (0.16).
Mathematically,
The null hypothesis is represented as
H₀: p = 0.16
The alternative hypothesis is represented as
Hₐ: p ≠ 0.16
b) To do this test, we will use the z-distribution because although, no information on the population standard deviation is known, the sample size is large enough.
Hence, the model of this test is two-tailled, one-proportion test.
And the major conditions for an hypothesis test is that
- The sample must be a random sample extracted from the population, with each variable in the sample independent from one another. This is already clearly given in the question.
- The sample must be a normal distribution sample or approximate a normal distribution.
The conditions to check this is that
np ≥ 10
and
np(1-p) ≥ 10
p = sample proportion = (44/437) = 0.101
np = 437×0.101 = 44 ≥ 10
np(1-p) = 437×0.101×(1-0.101) = 39.7 ≥ 10
The two conditions are satisfied, hence, we can conclude that this distribution at least approximates a normal distribution.
c) So, we compute the t-test statistic
z = (x - μ)/σₓ
x = sample proportion = 0.101
μ = p₀ = The proportion we are comparing against = 0.16
σₓ = standard error = √[p(1-p)/n]
where n = Sample size = 437
σₓ = √[0.101×0.899/437] = 0.0144145066 = 0.0144
z = (0.101 - 0.16) ÷ 0.0144
z = -4.093 = -4.09
checking the tables for the p-value of this z-statistic
Degree of freedom = df = n - 1 = 437 - 1 = 436
Significance level = 0.05 (when the significance level isn't stated, 0.05 is used)
The hypothesis test uses a two-tailed condition because we're testing in both directions (greater than or less than).
p-value (for z = -4.09, at 0.05 significance level, df = 436, with a two tailed condition) = 0.000043
The sketch of the region of acceptance is presented in the attached image to this answer. (z < -4.09 and z > 4.09).
d) The interpretation of p-values is that
When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.
So, for this question, significance level = 0.05
p-value = 0.000043
0.000043 < 0.05
Hence,
p-value < significance level
This means that we reject the null hypothesis, accept the alternative hypothesis & say that there is enough evidence to conclude that the proportion of the county that are Hispanics is different from the proportion of the whole nation that are Hispanics.
Hope this Helps!!!
A cylinder with a base diameter of x units has a volume of
cubic units
Which statements about the cylinder
options.
The radius of the cylinder is 2x units.
The area of the cylinder's base is ax? square units.
The area of the cylinder's base is nx square units.
The height of the cylinder is 2x units.
The height of the cylinder is 4x units.
Corrected Question
A cylinder with a base diameter of x units has a volume of [tex]\pi x^3[/tex] cubic units
Which statements about the cylinder are true? Check all that apply.
The radius of the cylinder is x units. The radius of the cylinder is 2x units. The area of the cylinder’s base is [tex]\dfrac{1}{4}\pi x^2[/tex] square units. The area of the cylinder’s base is [tex]\dfrac{1}{2}\pi x^2[/tex] square units. The height of the cylinder is 2x units. The height of the cylinder is 4x units.Answer:
The area of the cylinder’s base is [tex]\dfrac{1}{4}\pi x^2[/tex] square units. The height of the cylinder is 4x units.Step-by-step explanation:
If the Base Diameter = x
Therefore: Base radius [tex]=\dfrac{x}{2}$ units[/tex]
Area of the base [tex]=\pi r^2 =\pi (\dfrac{x}{2})^2 =\dfrac{\pi x^2}{4}$ square units[/tex]
Volume =Base Area X Height
[tex]\pi x^3 =\dfrac{\pi x^2}{4} X h\\$Height, h = \pi x^3 \div \dfrac{\pi x^2}{4}\\=\pi x^3 \times \dfrac{4}{\pi x^2}\\h=4x$ units[/tex]
Therefore:
The area of the cylinder’s base is [tex]\dfrac{1}{4}\pi x^2[/tex] square units. The height of the cylinder is 4x units.
On a number line, b, is located the same distance from 0 as another number, a, but in the opposite direction. The number b varies directly with number a. For example b= 11/4 when a= -11/4
A) b=-a
B) -b=-a
C) b-a=0
D) b(-a)=0
Answer:
B and A
Step-by-step explanation:
So based on the facts given, we know that b and a both have the same abasolute value. It does not matter whether a or b is negative or positive.
How can you convert the Heun’s Method into the Implicit Heun’s Method? Show an example
Answer:
Heun's method is also known by its other name called Modified Euler methods. This method is used in computational or mathematical science.
Step-by-step explanation:
Euler method is the method that is also pronounced in two similar stages such as Runge- Kutta methods. This method has been named after Dr. Heun.
This method is used for the solution of ordinary differential equations with its given values. There is some method to calculate this method. The improved Runge Kutta methods are also called the Butcher tableau method, the other methods are also called the Ralston methods.
The average of 12, 25 , 33 , and N is 120. Find N.
Answer:
So the formula for mean is you add up all of the numbers and divide by the number of numbers, that will give you the mean/average. So that means that (12+25+33+N)/4 = 120. We can simplify by first adding all of the numbers and multiplying both sides by 4 which will cancel out the four on the right side.
70+N/4 = 120
480 = 70+N
So then we subtract 70 from both sides. Then we get 410 = N.
The answer is
410 is Answer