Answer:
D. Confidence interval decreases.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes 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]
When sample size increases:
The standard deviation of the sample mean is:
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
That is, it is inversely proportional to the sample size, so if the sample size incerases, the standard deviation decreases, and so does the confidence interval.
This means that the correct answer is given by option D.
The top of the Boulder Dam has an angle of elevation of 1.2 radians from a point on the Colorado River. Measuring the angle of elevation to the top of the dam from a point 155 feet farther down river is 0.9 radi- ans; assume the two angle measurements are taken at the same elevation above sea level. How high is the dam?
Answer:
382.925 feets
Step-by-step explanation:
The solution diagram is attached below :
Converting radian measurement to degree :
radian angle * 180/π = degree angle
1.2 * 180/π = 68.755°
0.9 * 180/π = 51.566°
Height of dam is h:
Using trigonometry :
Tan θ = opposite / Adjacent
Tan 68.755° = h / x
h = x Tan 68.755° - - - (1)
Tan 51.566° = h / (155+x)
h = (155+x) tan 51.566° - - - (2)
Equate (1) and (2)
x Tan 68.755 = (155+x) Tan 51.566
x Tan 68.755 = 155tan 51.566 + x tan 51.566
x Tan 68.755 = 195.32311 + x Tan 51.566
x Tan 68.755 - x Tan 51.566 = 195.32311
x(tan 68.755 - tan 51.566) = 195.32311
x * 1.3120110 = 195.32311
1.3120110x = 195.32311
x = 195.32311 / 1.3120110
x = 148.87307
Using :
h = x Tan 68.755
h = 148.87307 * tan(68.755)
h = 382.92539
h = 382.925 feets
(View attachment)
a) Write ordered pairs.
b) Write the domain and range.
c) Why isn't the relation a function?
d) Which ordered pair should be removed to make the relation a function?
Answer:
in a relationship that maps elements from one set (the inputs) into elements from another set (the outputs), the usual notation for the ordered pairs is:
(x, y), where x is the input and y is the output.
In this case, the point where the arrow starts is the input, and where the arrow ends is the output.
a)
The ordered pairs are:
(28, 93)
(17, 126)
(52, 187)
(34, 108)
(34, 187)
b) The domain is the set of the inputs, in this case the domain is the set where all the arrows start, then the domain is:
{17, 28, 34, 52}
And the range is the set of the outputs, in this case the range is:
{93, 108, 126, 187}
c) A function is a relationship where the elements from the domain, the inputs, can be mapped into only one element from the range.
In this case, we can see that the input {34} is being mapped into two different outputs, then this is not a function.
d) We can remove one of the two ordered pairs where the input is {34},
So for example, we could remove:
(34, 108)
And then the relation would be a function.
Solve the exponential equation: 210 = 42x
Answer:
to get x you need to divide
210/42= 5
x=5
210 = 42x
210/42=5
42*5=210
so remove the x it'd be 210 = 42(5)
x = 5
What is the slope of the line represented by the equation f(x) = -3x + 7?
A -7
B -3
C 3
D 7
Answer:
-3
Step-by-step explanation:
in these equations the slope is multiplied by x which is -3 in this one.
Answer:
[tex]-3[/tex]
Step-by-step explanation:
The equation of a line is [tex]y=mx+b[/tex], and m is the gradient which is the slope. Hence, the number with x is the slope, which is [tex]-3[/tex].
Hope that helped.
please help me with this question.
Answer:
I think it's 18.1539073013
i'm not sure sorry
Write the equation for a parabola with a focus at ( 7, 2) and a directrix at y = -2
y = ?
PLEASE HELP MEEEEEEE EMERGENCY :(
Answer:
Ok ☺️✌️✌️✌️Ok ok ok ok
help me find the answer
Answer:
? = 9.4 cm
Step-by-step explanation:
we do the full calculation, as the missing side length is simply the full perimeter minus all the other sides (as the perimeter is the sum of all side lengths).
? = 113.6 - 39.8 - 5.6 - 5.6 - 11.1 - 11.1 - 11.1 - 19.9 = 9.4 cm
DIC A student has a total of $3000 in student loans that will be paid with a 48-month installment loan with monthly payments of $73.94. Determine the APR of the loan to the nearest one-half of a percent
Answer:
The APR of the loan was 18.30%.
Step-by-step explanation:
Given that a student has a total of $ 3000 in student loans that will be paid with a 48-month installment loan with monthly payments of $ 73.94, to determine the APR of the loan to the nearest one-half of a percent the following calculation must be done:
3,000 = 100
(73.94 x 48) = X
3,000 = 100
3,549.12 = X
3,549.12 x 100 / 3,000 = X
354,912 / 3000 = X
118.30 = X
118.30 - 100 = 18.30
Therefore, the APR of the loan was 18.30%.
Find the length of the third side. If necessary, round to the nearest tenth
[tex]\huge\bold{Given:}[/tex]
Length of the base = 8
Length of the hypotenuse = 17
[tex]\huge\bold{To\:find:}[/tex]
The length of the third side ''[tex]x[/tex]".
[tex]\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}[/tex]
[tex]\longrightarrow{\purple{x\:=\: 15}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
Using Pythagoras theorem, we have
(Perpendicular)² + (Base)² = (Hypotenuse)²
[tex]\longrightarrow{\blue{}}[/tex] [tex]{x}^{2}[/tex] + (8)² = (17)²
[tex]\longrightarrow{\blue{}}[/tex] [tex]{x}^{2}[/tex] + 64 = 289
[tex]\longrightarrow{\blue{}}[/tex] [tex]{x}^{2}[/tex] = 289 - 64
[tex]\longrightarrow{\blue{}}[/tex] [tex]{x}^{2}[/tex] = 225
[tex]\longrightarrow{\blue{}}[/tex] [tex]x[/tex] = [tex]\sqrt{225}[/tex]
[tex]\longrightarrow{\blue{}}[/tex] [tex]x[/tex] = [tex]15[/tex]
Therefore, the length of the missing side [tex]x[/tex] is [tex]15[/tex].
[tex]\huge\bold{To\:verify :}[/tex]
[tex]\longrightarrow{\green{}}[/tex] (15)² + (8)² = (17)²
[tex]\longrightarrow{\green{}}[/tex] 225 + 64 = 289
[tex]\longrightarrow{\green{}}[/tex] 289 = 289
[tex]\longrightarrow{\green{}}[/tex] L.H.S. = R. H. S.
Hence verified.
[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♨}}}}}[/tex]
You will need the same dataset used for problem 3 in homework 1 (the dataset obtained from the yahoo website with the company you selected). Use Excel to calculate the average and standard deviation of the close data column. Assume that these two numbers represent the population (parametric mean and population standard deviation, respectively, for the variable length (in cm) in a population printout of the data to your homework and write down the ticker code on it.
a. Calculate the probability of sampling at random a fish that is smaller in size than the value you would obtain by subtracting half the standard deviation from the average [x will be equal to: -(6/2)]
b. Calculate the probability of sampling at random a fish that is greater in size than the value you would obtain by adding half the standard deviation from the average [x = u + (0/2)]
c. Calculate the probability of sampling at random a fish that has a size between the two values [x = -(6/2), x=u +(6/2)) used in parts "a" and "b," respectively
d. Calculate the 25th and 75 percentiles of fish size for the population using the normal distribution table. e. Imagine that 5 individuals are sampled at random from this fish population. Calculate the probability that the average calculated will be less than the value: -(6/3)
Answer:
a) The probability of sampling at random a fish that is smaller in size than the value you would obtain by subtracting half the standard deviation from the average is 0.3085.
b) The probability of sampling at random a fish that is greater in size than the value you would obtain by adding half the standard deviation from the average is 0.3085.
c) The probability of sampling at random a fish that has a size between the two values is 0.383.
d) The 25th and 75 percentiles of fish size for the population using the normal distribution table is 5.69 and 5.87 respectively.
e) The probability that the average calculated will be less than the value is 0.3707.
Step-by-step explanation:
For the given data set mean [tex](\mu) = 5.75913[/tex]
Standard deviation [tex](\sigma) = 0.172229[/tex]
Variance [tex](\sigma2) = 0.0296[/tex]
Here we get is
a)
[tex]P(x < \mu - \sigma/2) = p(x < 5.673) \\\\ = 0.3085[/tex]
b)
[tex]P(x < \mu + \sigma/2) = p(x < 5.845) \\\\= 0.3085[/tex]
c)
[tex]P(\mu - \sigma/2 < x < \mu + \sigma/2) = p(5.673 < x < 5.845) \\\\= 0.383[/tex]
d)
25th percentile:-
[tex]= 25*[(n+1)/100]th term \\\\= 5.69[/tex]
75the percentile:-
[tex]= 75*[(n+1)/100]th term\\\\ = 5.87[/tex]
e)
[tex]p(x < \mu - \sigma/3) = p(x < 5.7017) \\\\= 0.3707[/tex]
What are the coordinates of the point that is 1/6 of the way from A to B? 6 A(-2, 3) 4+ B (10.3) ---- 4 4 O A. (6,0) O B. (3,0) O c. (0,6) O D. (0,3) O
Answer:
ITS C. (0, 3)
Step-by-step explanation:
I JUST ASKED THE TEACHER ;)
In 8 days, a group of workers can plant 72 acres.
What is their rate in acres per day
Helppp fastttt
Answer:
Step-by-step explanation:
72/8 = 9 acres per day
If an average-sized man with a parachute jumps from an airplane, he will fall
12.5(0.2t − 1) + 21t feet
in t seconds. How long will it take him to fall 150 feet? (Round your answer to two decimal places.)
Answer:
It will take him 5.85 seconds.
Step-by-step explanation:
12.5 (0.2t - 1) + 21t = 150
Use Distributive Property:
2.5t - 12.5 + 21t = 150
Combine like terms:
23.5t - 12.5 = 150
Subtract 12.5 from both sides:
23.5t = 137.5
Divide both sides by 23.5 to isolate variable t:
5.851063.....
Round to two decimal places (hundredths place):
5.85
Your roommate asks to borrow $500 and agrees to pay it in 45 days with interest rate of 4%. How much interest will you earn?
Answer:
$20
Step-by-step explanation:
500 x .04 = 20
For a certain river, suppose the drought length Y is the number of consecutive time intervals in which the water supply remains below a critical value y0 (a deficit), preceded by and followed by periods in which the supply exceeds this critical value (a surplus). An article proposes a geometric distribution with p = 0.365 for this random variable. (Round your answers to three decimal places.)
a. What is the probability that a drought lasts at most 3 intervals?
b. What is the probability that the length of a drought exceeds its mean value by at least one standard deviation?
Solution :
a). P(X = x)
= [tex]$p(1-p)^x$[/tex] for x = 0, 1, 2, ....
P(x ≤ 3) = 0.837
b). Expectation = [tex]$\frac{(1-p)}{p}$[/tex]
= 1.7397
Variance = [tex]$\frac{(1-p)}{p^2}$[/tex]
= 4.7663726
Standard deviation = 2.1832
Therefore, mean + standard deviation
= 1.7397 + 2.1832
= 3.9229
[tex]$P(x > 3.9229) = 0.1626$[/tex]
So the required P = 2 x 0.1626
= 0.325
A real estate broker acting as a property manager leased a building for 10 years at an annual rent of 48,000. They will receive a commission of 7.5% for the first five years, 5% for the next three years, and 3.5% for the final two years. What will the broker's gross income be from this commission over the life of the lease
Answer:
Question... is the commission given 10 times or 3?
If the commission is 10 then
5*(48,000 * .075) + 3*(48,000 * .05) +2*(48,000 * .035)
5*(3600) + 3*(2400) +2*(1680)
= 28560
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
If the commission is 3 then (once for first five years, once for the next three,
and once for the last two
(48,000 * .075) + (48,000 * .05) +(48,000 * .035)
=7680
Step-by-step explanation:
The system of equations y = negative one-fifth x minus 6 and y = –2x + 3 is shown on the graph below.
On a coordinate plane, 2 lines intersect at (5, negative 7).
According to the graph, what is the solution to this system of equations?
(5, –7)
(–7, 5)
(5, 7)
(7, 5)
Answer:
It is A (5, -7)
Step-by-step explanation:
Answer:
A 5,-7
Step-by-step explanation:
Verify that a÷(b+c)=(a÷b)+(a ÷c), a=10 , b=5 , 6=2
Answer:
a÷(b+c)≠(a÷b)+(a ÷c)
Step-by-step explanation:
To verify that a÷(b+c)=(a÷b)+(a ÷c)
Using the values ;
a=10 , b=5 , 6=2
plugging the values into a÷(b+c) should give the same result as (a÷b)+(a ÷c) ;
That is, right hand side = left hand side
a÷(b+c) = 10 ÷ (5+ 2)
a÷(b+c) = 10 / 7
Also;
(a÷b)+(a ÷c) = (10/5) + (10/2) = 2 + 5 = 7
Given the result, it can be seen that ;
RHS ≠ LHS
10/7 ≠ 7
Pls solve this question:
it is about Square and square roots
if u answer, then I will mark you as brilliant
Answer:
the answer is 2.3
Step-by-step explanation:
bc if u take the square root of 2.3 it would be 1.516575089 in the decimal form then u multiply it by that decimal and get 2.3. hope this help
Answer:
2.3
Step-by-step explanation:
[tex]\sqrt{2.3}[/tex] * [tex]\sqrt{2.3}[/tex]
it means
[tex](\sqrt{2.3})^2[/tex]
root and square gets cancel so,
2.3
I’ll give brainliest to the first answer
Answer:
52
Step-by-step explanation:
4 1/2 x + 2x
Let x = 8
4 1/2 (8) + 2(8)
Change to an improper fraction
9/2(8) +2(8)
36+16
52
Kyle was trying to decide which type of soda to restock based on popularity: regular cola or diet cola. After studying the data, he noticed that he sold less diet cola on weekdays and weekends. However, after combing through his entire sales records, he actually sold more diet cola than regular cola. Which paradox had Kyle encountered?
Answer:
Simpson's Paradox
Step-by-step explanation:
Answer:
Simpson's Paradox
Step-by-step explanation:
Got it right on the test.
Find x and then find the measure of the exterior angle
Answer:
x = 32
exterior = 104
Step-by-step explanation:
The exterior angle is equal to the sum of the opposite interior angles
40 + 2x = x+72
Subtract x from each side
40+2x-x = x+72-x
x+40 = 72
Subtract 40 from each side
x+40-40 =72-40
x = 32
The exterior angle
x+72 = 32+72 = 104
Aball has a density of 0.5 g/ml and a mass of 125 grams. What is the volume of the ball?
Answer:
250
Step-by-step explanation:
Density = mass / volume
density = 0.5 g / mL
mass = 125 g
0.5 = 125 / V Multiply both sides by V
0.5 * V = 125 Divide by 0.5
0.5V 0.5 = 125/0.5
V = 250
When doing these kinds of ratios make sure that you get the numbers all on one side before you actually do the division or multiplication. That way you won't get confused.
Tìm giá trị lớn nhất và giá trị nhỏ nhất của hàm số
y=40[tex]\sqrt{(x-1)x^{3 }[/tex]- 3x-3
si 8888888888888888888888888888
How much would $100 invested at 8% interest compounded continuously be
worth after 15 years? Round your answer to the nearest cent.
A(t)=Poet
O A. $332.01
O B. $220.00
O C. $317.22
D. $285.67
Answer:
Step-by-step explanation:
A = [tex]pe^{rt}[/tex]
A = 100[tex]e^{.08 *15}[/tex]
A=. $332.01
The value of the investment after 15 years is $332.01.
Option A is the correct answer.
What is compound interest?It is the interest we earned on the interest.
The formula for the amount earned with compound interest after n years is given as:
A = P [tex](1 + r/n)^{nt}[/tex]
P = principal
R = rate
t = time in years
n = number of times compounded in a year.
We have,
The continuous compounding formula is given by:
[tex]A = Pe^{rt}[/tex]
Where:
A = the ending amount
P = the principal (initial investment)
e = the mathematical constant (approximately equal to 2.71828)
r = the interest rate (as a decimal)
t = the time period (in years)
Using this formula, we can find the value of the investment after 15 years:
A = 100 \times e^{0.08 \times 15} ≈ $332.01
Therefore,
The value of the investment after 15 years is $332.01.
Learn more about compound interest here:
https://brainly.com/question/13155407
#SPJ7
what is equal to -10> ?
Answer:
It's answer is - 9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4......
Can someone please help me ?
Answer:
5x+3y=6
Step-by-step explanation:
Use the slope intercept form then rearrange
2) O número 6 e divisor de qual número a seguir ? Faça as divisões por 6 e verifique qual é exata
A) 64
B)72
C)128
D)80
POR FAVOR ME AJUDEM EU NÃO ESTOU COSENGUINDO !!!!!!!
Answer:please write in english
Step-by-step explanation:
At a movie rental machine the movies rent for $3.00 except on Tuesdays when they rent for $0.49 Appoximately what percent of the regular cost is saved by renting a movie on a Tueday
Answer:
16%
Step-by-step explanation:
To find what percent of the regular cost is saved by renting a movie on a Tuesday, we must do 0.49/3.00. This helps us find the decimal point to convert into a percentage. 0.49/3.00 is equal to 0.163333333333 . And 0.163333333333 converted into a percentage is approximately 16%.
Hope this helps and if it does, don't be afraid to rate my answer as well as maybe give it a "Thanks"? (Or even better a "Brainliest")