Given:
Standard error = 4
Population standard deviation = 16
To find:
The value of n.
Solution:
The formula of standard error is:
[tex]SE=\dfrac{\sigma}{\sqrt{n}}[/tex]
Where, SE is standard error , [tex]\sigma[/tex] is population standard deviation and n is the total number of elements.
Substituting [tex]SE=4,\sigma=16[/tex] in the above formula, we get
[tex]4=\dfrac{16}{\sqrt{n}}[/tex]
[tex]\sqrt{n}=\dfrac{16}{4}[/tex]
[tex]\sqrt{n}=4[/tex]
Taking square on both sides, we get
[tex]n=4^2[/tex]
[tex]n=16[/tex]
Therefore, the value of n is 16.
Find the remainder when f(x) = –2x3 + x2 - 4x + 1 is divided by x + 3.
Answer:
Step-by-step explanation:
The remainder when f(x) is divided by x + 3 would be 76.
What is remainder theorem for polynomials?If there is a polynomial p(x), and a constant number 'a', then
[tex]\dfrac{p(x)}{(x-a)} = g(x) + p(a)[/tex]
where g(x) is a factor of p(x).
We have been given a function;
[tex]f(x) = -2x^3 + x^2 - 4x + 1[/tex]
We need to find the remainder when f(x) is divided by x + 3.
So, Let p(x) = x + 3
p(x) = 0
x + 3 = 0
x = -3
Substitute in the given function f(x);
[tex]f(x) = -2x^3 + x^2 - 4x + 1\\\\f(-3) = -2(-3)^3 + (-3)^2 - 4(-3) + 1\\\\f(-3) = 54 + 9 + 12 + 1\\\\f(-3) = 76[/tex]
Thus, the remainder when f(x) is divided by x + 3 would be 76.
Learn more about remainder;
https://brainly.com/question/16394707
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find the missing side lengths
this is a special triangle so v = 17
u = 17√2
Answer:
v = 17
u = 17[tex]\sqrt{2}[/tex]
Step-by-step explanation:
If v = 17 (it is because it is a right triangle, so the pythagorean theorum works, and triangles are 180 degrees, so 180 - 90 = 90, so the other two angles are 45 degrees, meaning that v is the same length as 17.) then
17 ^ 2 = u ^2
289 = u^2
17 root to 2
I need this please pleaseeee nowww
Answer:
y = 3x - 5
Step-by-step explanation:
Slope = 3
x-intercept (what the value of y is when its 0) = -5 so y = 3x - 5
Answer:
y = 3x - 5
Step-by-step explanation:
Find the slope of the line between (0,−5)(0,-5) and (3,4)(3,4) using m=y2−y1x2−x1m=y2-y1x2-x1, which is the change of yy over the change of xx.
m=3m=3
Use the slope 33 and a given point (0,−5)(0,-5) to substitute for x1x1 and y1y1 in the point-slope form y−y1=m(x−x1)y-y1=m(x-x1), which is derived from the slope equation m=y2−y1x2−x1m=y2-y1x2-x1.
y−(−5)=3⋅(x−(0))y-(-5)=3⋅(x-(0))
Simplify the equation and keep it in point-slope form.
y+5=3⋅(x+0)
Add xx and 00.
y+5=3xy+5=3x
Subtract 55 from both sides of the equation.
y=3x−5
A plumber had two pipes. The ratio of the length of the longer pipe to the
shorter pipe was 9 : 2. When he
cut 1.65 m from the longer pipe, the
remaining length was 3 times that of the shorter
pipe. Find the length of
the shorter pipe in metres.
Answer:
4.95m
Step-by-step explanation:
Let the length of longer and shorter pipe be x and y respectively..
given,
x/y=9/2...(i)
x-1.65=3y ...(ii)
in eqn ii..
x-1.65=3y
or, x/y - 1.65/y = 3
or, 9/2-1.65/y =3
or, 4.5-3 = 1.65/y
or, y=1.65/1.5
•°• y = 1.1m
now,
x/y = 9/2
or, x/1.1 = 4.5
x= 4.5×1.1
•°• x= 4.95m
thus, the length of the longer pipe is 4.95m
Please help me with this on the picture
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Answer:
(-5, 4)
Step-by-step explanation:
The inside corner moves from (2, -2) to (-3, 2). That is 5 is subtracted from the x-coordinate, and 4 is added to the y-coordinate. (x, y) ⇒ (x -5, y +4)
The translation vector can be written horizontally as (-5, 4), or vertically as ...
[tex]\displaystyle\binom{-5}{4}[/tex]
Help me this question
Answer:
(a) 218.6 N
(b) 97.14 N
Step-by-step explanation:
When the system is in equilibrium, the net torque on the system is zero.
AC = 1.5 m, CD = 2.3 m, DB = 5 - 1.5 - 2.3 = 1.2 m
Let the centre of gravity of plank is at G.
AG = 2.5 m, CG = 2.5 - 1.5 = 1 m, GB = 2.5 m
(a) Let the reaction at C is R and at D is R'.
R + R' = 29 x 9.8 = 284.2 N ... (1)
Take the torque about C.
29 x 9.8 x CG = R' x GD
29 x 9.8 x 1 = R' x 1.3
R' = 218.6 N
(b) Take the torque about D.
6 x 9.8 x AD = R x CD
6 x 9.8 x (1.5 + 2.3) = R x 2.3
R = 97.14 N
WILL MARK BRAINLIEST PLEASE SHOW WORK :)
Answer:
(1). A = 18 cm² ; (2). TR = 18 units
Step-by-step explanation:
Please help me to find this answer
Answer:
Look in Step by Step Explanation
Step-by-step explanation:
3)SOHCAHTOA
tan=opposite/adjacent
tan(20)=x/83
83tan(20)=x
x=30.209
2) SOHCAHTOA
Tangent=opposite/adjacent
Tan(62)=x/8
8tan(62)=x
x=15.04
3)SOHCAHTOA
Sin=opposite/hypotonouse
sin(25)=30/x
x=30/sin(25)
x=70.986
2. What is the number 643,581 rounded off
to the thousands place?
(1) 640,000
(2) 643,000
(3) 643,600
(4) 644,000
(5) 644,600
Answer:
(4) 644,000
Step-by-step explanation:
643,581
The 3 is in the thousands place
We look at the hundreds place
5
It is 5 or greater so we round the thousands place up 1
644000
I want to know how to solve this equation
Answer:
B
Step-by-step explanation:
5³.5^×
simply means
5³×5^×
using indices rule,
multiplication is addition
5 is common
so 5(³+×)
hence 5^3+×
an international company has 27,100 employees in one country. if this represents 18.4% of the company's employees, how many employees does it have in total? round to nearest whole number
According to government data, the probability than an adult never had the flu is 19%. You randomly select 70 adults and ask if he or she ever had the flu. Decide whether you can use the normal distribution to approximate the binomial distribution, If so, find the mean and standard deviation, If not, explain why. Round to the nearest hundredth when necessary.
Answer:
Since [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], the normal distribution can be used to approximate the binomial distribution.
The mean is 13.3 and the standard deviation is 3.28.
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed 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.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex], if [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex].
The probability than an adult never had the flu is 19%.
This means that [tex]p = 0.19[/tex]
You randomly select 70 adults and ask if he or she ever had the flu.
This means that [tex]n = 70[/tex]
Decide whether you can use the normal distribution to approximate the binomial distribution
[tex]np = 70*0.19 = 13.3 \geq 10[/tex]
[tex]n(1-p) = 70*0.81 = 56.7 \geq 10[/tex]
Since [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], the normal distribution can be used to approximate the binomial distribution.
Mean:
[tex]\mu = E(X) = np = 70*0.19 = 13.3[/tex]
Standard deviation:
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{70*0.19*0.81} = 3.28[/tex]
The mean is 13.3 and the standard deviation is 3.28.
Dưới đây là bảng CĐKT gần đây nhất của VNA:
ĐVT: tỷ đồng
TÀI SẢN
NGUỒN VỐN
Tài sản lưu động
Tài sản cố định
Tổng tài sản
11.30
21.35
32.65
Nợ ngắn hạn (NH)
Nợ dài hạn
Vốn cổ phần ưu đãi
Vốn cổ phần thường
Tổng nguồn vốn
10.69
9.46
2.50
10.00
32.65
Biết: Nợ NH không chịu bất kỳ khoản phí nào, chi phí trung bình nợ NH sau thuế là 5.5%;
Chi phí nợ dài hạn trước thuế là 11.5%;
Tỷ suất sinh lời cần thiết trên vốn cổ phần ưu đãi là 13.5%; hệ số beta = 1,25
Tỷ suất lợi nhuận cho rủi ro thị trường là 8%; tỷ lệ lãi suất trái phiếu cũng 8%
Thuế TNDN là 32%.
Yêu cầu:
Tính chi phí vốn của mỗi nguồn nợ ngắn hạn, nợ dài hạn, vốn cổ phần ưu đãi, vốn cổ phần phổ thông?
Tính chi phí bình quân gia quyền vốn WACC của VNA?
True or false?
A function assigns each value of the independent variable to exactly one
value of the dependent variable.
A. True
B. False
SUB
Answer:
This statement would be true.
Step-by-step explanation:
Find the measure of x. X=8, x=7, x=9, x=11
Answer:
[tex]\frac{135}{15} =\frac{15(x+2)}{15}[/tex]
[tex]9=x+2[/tex]
[tex]x=7[/tex]
OAmalOHopeO
A manufacturer knows that their items have a normally distributed length, with a mean of 18.2 inches, and standard deviation of 3.9 inches. If 2 items are chosen at random, what is the probability that their mean length is less than 21.9 inches
Answer:
0.9099 = 90.99% probability that their mean length is less than 21.9 inches.
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 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.
Mean of 18.2 inches, and standard deviation of 3.9 inches.
This means that [tex]\mu = 18.2, \sigma = 3.9[/tex]
2 itens:
This means that [tex]n = 2, s = \frac{3.9}{\sqrt{2}}[/tex]
What is the probability that their mean length is less than 21.9 inches?
This is the p-value of Z when X = 21.9. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{21.9 - 18.2}{\frac{3.9}{\sqrt{2}}}[/tex]
[tex]Z = 1.34[/tex]
[tex]Z = 1.34[/tex] has a p-value of 0.9099.
0.9099 = 90.99% probability that their mean length is less than 21.9 inches.
Solve 3 - 5(a - 4) any one who can answer in the next 3 mins plz answer
Answer:
[tex]3-5\left(a-4\right)[/tex]
[tex]-5(a-4)=-5a+20[/tex]
[tex]=3-5a+20[/tex]
[tex]=-5a+23[/tex]
OAmalOHopeO
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\text{3 - 5(a - 4)}\\\\\huge\text{\underline{\underline{DISTRUBUTE -5 within the parentheses}}}\\\\\large\text{3 - 5(a) - 5(-4)}\\\large\text{= 3 - 5a + 20}\\\\\huge\text{\underline{\underline{COMBINE the LIKE TERMS}}}\\\large\text{-5a + (3 + 20)}\\\large\text{= \bf -5a + 23}\\\\\\\boxed{\boxed{\huge\text{Therefore, your answer is: \bf -5a + 23}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!} \\\\\\\frak{Amphitrite1040:)}[/tex]
Help me please thanks guys
Answer:
B, D, F
Step-by-step explanation:
In a rational exponent, the numerator is an exponent, and the denominator becomes the index of the root.
[tex]a^{\frac{m}{n}} = \sqrt[n] {a^m}[/tex]
Answer: B, D, F
Yooooo HELPPP
with this question plz
Answer:
Step-by-step explanation:
(x-2)(x+4)=x^2+4x-2x-8=0=> x =2, x=0
Answer:
A
Step-by-step explanation:
Find COS Instructions: Find the value of the trigonometric ratio. Make sure to simplify the If needed
Answer:
Sin A = 15 / 17
Step-by-step explanation:
Given a right angled triangle, we are to obtain the Sin of the angle A ;
Using trigonometry, the sin of the angle A, Sin A is the ratio of the angle opposite A to the hypotenus of the right angle triangle.
Hence. Sin A = opposite / hypotenus
Opposite = 15 ; hypotenus = 17
Sin A = 15 / 17
How many numbers multiple of 3 are in the range [2,2000]?
Answer: so there are 666 multiples of 3 between 2 and 2000.
Step-by-step explanation:
the smallest number = 3 which is 3*1. The largest number is = 1998 = 3*666
multiples of 3 between {2,2000} = 666-1+1 = 666
A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 409 gram setting. It is believed that the machine is underfilling the bags. A 21 bag sample had a mean of 401 grams with a standard deviation of 26. A level of significance of 0.1 will be used. Assume the population distribution is approximately normal. Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.
Answer:
The decision rule is to Reject H0 if Z ≤ -1.282
Step-by-step explanation:
We are given;
Population mean; μ = 409 g
Sample mean; x¯ = 401 g
Sample size; n = 21
Standard deviation; s = 26
Let's define the hypotheses;
Null hypothesis; H0: μ = 409 g
Alternative hypothesis; Ha : μ ≠ 409 g
Formula for test statistic is;
z = (x¯ - μ)/(s/√n)
z = (401 - 409)/(26/√21)
z = -1.410
z-value is negative and thus this is a lower tail test.
At significance level of 0.1, the critical value is -1.282.
Thus, the decision rule is;
Reject H0 if Z ≤ -1.282
jane drove 50 miles more then her husband jim. the total distance traveled was 230 miles. find the number of miles that each of them traveled. (let jim be x and jane be x+50)
Answer:
115
Step-by-step explanation:
You divide 230 by 2 cause there are two peoples. I hope that helps :)
PLZ ANSWER QUESTION IN PICTURE
Answer: [tex](\frac{2}{5},0) ; (0,2)[/tex]
Step-by-step explanation:
(to find the x-intercept, plug in 0 for y)
(to find the y-intercept, plug in 0 for x)
[tex]0=-5x+2\\5x=2\\x=\frac{2}{5}\\(\frac{2}{5},0)\\y=-5(0)+2\\y=2 \\(0,2)[/tex]
Let f(x) = e ^3x/5x − 2. Find f'(0).
Answer:
Step-by-step explanation:
Our friend asking what the actual function is has a point. I completed this under the assumption that what we have is:
[tex]f(x)=\frac{e^{3x}}{5x-2}[/tex] and used the quotient rule to find the derivative, as follows:
[tex]f'(x)=\frac{e^{3x}(5)-[(5x-2)(3e^{3x})]}{(5x-2)^2}[/tex] and simplifying a bit:
[tex]f'(x)=\frac{5e^{3x}-[15xe^{3x}-6e^{3x}]}{(5x-2)^2}[/tex]and a bit more to:
[tex]f'(x)=\frac{5e^{3x}-15xe^{3x}+6e^{3x}}{(5x-2)^2}[/tex] and combining like terms:
[tex]f'(x)=\frac{11e^{3x}-15xe^{3x}}{(5x-2)^2}[/tex] and factor out the GFC in the numerator to get:
[tex]f'(x)=\frac{e^{3x}(11-15x)}{(5x-2)^2}[/tex] That's the derivative simplified. If we want f'(0), we sub in 0's for the x's in there and get the value of the derivative at x = 0:
[tex]f'(0)=\frac{e^0(11-15(0))}{(5(0)-2)^2}[/tex] which simplifies to
[tex]f'(0)=\frac{11}{4}[/tex] which translates to
The slope of the function is 11/4 at the point (0, -1/2)
A person on the top of a tall building looks through his binoculars at his friend that is 300 ft away from the building on the ground. If the angle of depression from the person on the building is 30°, how tall is the building?
Answer:
520 feets
Step-by-step explanation:
The height of the building, h can be obtuined using trigonometry ;
From the attached diagram, opposite side = 300 feets ; height, h = adjacent side
Hence,
Tan θ = opposite / Adjacent
Tan 30° = 300 / height
0.5773502 = 300 / height
Height = 300 / 0.5773502
Height = 519.615
Height = 520 feets
The average mileage per gallon for cars built since 1940 approximates to the following curve 0.0075*t^2-.2672*t+14.8 where t is year -1940.
Answer the following questions:
What is the expected MPG in 2025?
How about 2050?
Is this a valid function?
Is there a top end to MPG?
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Answer:
46.3 in 202576.2 in 2050Step-by-step explanation:
The attached shows the predicted mileage for cars built in 2025 to be 46.3 mpg, 76.2 mpg for cars built in 2050.
__
No doubt, the function is valid over the time period used to derive it. It may or may not be valid for predicting MPG beyond that period.
Virtually any function that predicts future increases without bound will turn out to be unreliable at some point. In this universe, there are always limits to growth.
what expression is equivalent to (-7²-x-5)-(3x²+x)
Answer:
-3x² - 2x - 54
Step-by-step explanation:
(-7²-x-5)-(3x²+x)
-7² - x - 5 - 3x² - x
-49 - x - 5 - 3x² - x
-3x² - x - x - 49 - 5
-3x² - 2x - 54
Which of the answer choices has matrix multiplication defined?
Answer:
AB
Step-by-step explanation:
For the multiplication of two matrices to be defined then the number of columns of the first matrix must be equal to the number of rows of the second matrix. For example, 2*3 and 3*2 matrices can be multiplied since the number of columns of the first matrix must be equal to the number of rows of the second matrix.
Matrix A = 2*2
Matrix B = 2*3
Matrix C = 3*3
Matrix D = 1 * 3
From the matrices given, we can see that the matrices that can be multiplied together are AB and BC since the number of columns of the first matrix must be equal to the number of rows of the second matrix. Hence the correct option is AB
To solve the system of linear equations 3 x minus 2 y = 4 and 9 x minus 6 y = 12 by using the linear combination method, Henry decided that he should first multiply the first equation by –3 and then add the two equations together to eliminate the x-terms. When he did so, he also eliminated the y-terms and got the equation 0 = 0, so he thought that the system of equations must have an infinite number of solutions. To check his answer, he graphed the equations 3 x minus 2 y = 4 and 9 x minus 6 y = 12 with his graphing calculator, but he could only see one line. Why is this?
A. because the system of equations actually has only one solution
B. because the system of equations actually has no solution
C.because the graphs of the two equations overlap each other
D. because the graph of one of the equations does not exist
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Answer:
C. because the graphs of the two equations overlap each other
Step-by-step explanation:
When a system of linear equations has an infinite number of solutions, the equations are "dependent." That means they both describe the same line. The graph will appear to be one line because the lines overlap each other.
__
Additional comment
The Desmos graphing calculator lets the texture of the graph be varied, so we can see that the two lines overlap. In the attached, one equation is graphed as a dotted red line, the other as a solid blue line.
