Answer:
A typical example would be when a statistician wishes to estimate the ... by the standard deviation ó) is known, then the standard error of the sample mean is given by the formula: ... The central limit theorem is a significant result which depends on sample size. ... So, the sample mean X/n has maximum variance 0.25/ n.
Step-by-step explanation:
Help me please thank y’all
x= 30 degrees
Step-by-step explanation:
there's 180 degrees in a triangle. You can see 60 degrees right there. Theres a 90 degree angle right next to it. 180-150=30
You have found the following ages (in years) of all 666 lions at your local zoo: 13,2,1,5,2,7 What is the average age of the lions at your zoo? What is the standard deviation? Average age: _____ years old Standard deviation: ____ years
Answer:
[tex]Mean = 5[/tex]
[tex]S_x = 4.123[/tex]
Step-by-step explanation:
Given
Number of Lions, n: 6
Ages: 13, 2, 1, 5, 2, 7
Required
Determine the:
1. Mean
2. Standard Deviation
Mean is calculated as;
[tex]Mean = \frac{\sum x}{n}[/tex]
[tex]Mean = \frac{13+2+1+5+2+7}{6}[/tex]
[tex]Mean = \frac{30}{6}[/tex]
[tex]Mean = 5[/tex]
Standard Deviation is calculated as follows
[tex]S_x = \sqrt{\frac{\sum (x_i - Mx)^2}{N}}[/tex]
Where Mx represent mean
Substitute values for x, Mean and Land
[tex]S_x = \sqrt{\frac{(13 - 5)^2+(2 - 5)^2+(1 - 5)^2+(5 - 5)^2+(2 - 5)^2+(7 - 5)^2}{6}}[/tex]
[tex]S_x = \sqrt{\frac{(8)^2+(- 3)^2+(-4)^2+(0)^2+(-3)^2+(2)^2}{6}}[/tex]
[tex]S_x = \sqrt\frac{64+9+16+0+9+4}{6}}[/tex]
[tex]S_x = \sqrt\frac{102}{6}}[/tex]
[tex]S_x = \sqrt{17}[/tex]
[tex]S_x = 4.123[/tex]
The mean and standard deviation is 5 and 4.123 respectively
We want to find the mean or average and the standard deviation of the given set.
The average age is 5 years old and the standard deviation is 4.52 years old.
We know that for a general set of N elements {x₁, x₂, ..., xₙ} the average or mean is given by:
[tex]M = \frac{x_1 + x_2 + ... + x_n}{N}[/tex]
And the standard deviation is given by:
[tex]S = \sqrt{\frac{(x_1 - M)^2 + ... + (x_n - M)^2}{N - 1}[/tex]
The given set is:
{13, 2, 1, 5, 2, 7}
Now we just need to use the two given formulas for our set.
The mean is:
[tex]M = \frac{13 + 2 + 1+ 5 + 2 +7}{6} = 5[/tex]
And the standard deviation is:
[tex]S = \sqrt{\frac{(13 - 5)^2 + (2 - 5)^2 + (1 - 5)^2 + (5 - 5)^2 + (2 - 5)^2 + (7 - 5)^2}{6 - 1} } = 4.52[/tex]
So the average age is 5 years old and the standard deviation is 4.52 years old.
If you want to learn more you can read:
https://brainly.com/question/12402189
The sum of 8 times a number and 7 equals 9!
Answer:
0.25*8+7=9
Step-by-step explanation:
8x+7=9
2/8=x
0.25=x
confidence interavls for a population proportion. suppose that a random sample of 1000 mortgage loans that were defaulted within the first year reveals 410 of these loans were approved on hte basis of falsified applications. what is point estiamte of and a 95% confidence interval for p, the proportion of all first year defaults that are approved on the basis of flsified application
Answer:
The 95% confidence interval is [tex]0.3795 < p < 0.4405[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 1000[/tex]
The number of approved loan is k = 410
Generally the sample proportion is mathematically represented as
[tex]\r p = \frac{k}{n}[/tex]
substituting values
[tex]\r p = \frac{410}{1000}[/tex]
[tex]\r p = 0.41[/tex]
Given that the confidence level is 95% then the level of significance is mathematically represented as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5\%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table,the value is
[tex]Z_{\frac{\alpha }{2} } =Z_{\frac{0.05 }{2} }= 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\r p(1- \r p)}{n} }[/tex]
substituting values
[tex]E = 1.96 * \sqrt{\frac{ 0.41(1- 0.41)}{1000} }[/tex]
[tex]E = 0.03048[/tex]
The 95% confidence interval for p is mathematically represented as
[tex]\r p - E < p < \r p + E[/tex]
substituting values
[tex]0.41 - 0.03048 < p < 0.41 + 0.03048[/tex]
[tex]0.3795 < p < 0.4405[/tex]
Find the fourth roots of 16(cos 200° + i sin 200°).
Answer:
See below.
Step-by-step explanation:
To find roots of an equation, we use this formula:
[tex]z^{\frac{1}{n}}=r^{\frac{1}{n}}(cos(\frac{\theta}{n}+\frac{2k\pi}{n} )+\mathfrak{i}(sin(\frac{\theta}{n}+\frac{2k\pi}{n})),[/tex] where k = 0, 1, 2, 3... (n = root; equal to n - 1; dependent on the amount of roots needed - 0 is included).
In this case, n = 4.
Therefore, we adjust the polar equation we are given and modify it to be solved for the roots.
Part 2: Solving for root #1
To solve for root #1, make k = 0 and substitute all values into the equation. On the second step, convert the measure in degrees to the measure in radians by multiplying the degrees measurement by [tex]\frac{\pi}{180}[/tex] and simplify.
[tex]z^{\frac{1}{4}}=16^{\frac{1}{4}}(cos(\frac{200}{4}+\frac{2(0)\pi}{4}))+\mathfrak{i}(sin(\frac{200}{4}+\frac{2(0)\pi}{4}))[/tex]
[tex]z^{\frac{1}{4}}=2(cos(\frac{5\pi}{18}+\frac{\pi}{4}))+\mathfrak{i}(sin(\frac{5\pi}{18}+\frac{\pi}{4}))[/tex]
[tex]z^{\frac{1}{4}} = 2(sin(\frac{5\pi}{18}+\frac{\pi}{4}))+\mathfrak{i}(sin(\frac{5\pi}{18}+\frac{\pi}{4}))[/tex]
Root #1:
[tex]\large\boxed{z^\frac{1}{4}=2(cos(\frac{19\pi}{36}))+\mathfrack{i}(sin(\frac{19\pi}{38}))}[/tex]
Part 3: Solving for root #2
To solve for root #2, follow the same simplifying steps above but change k to k = 1.
[tex]z^{\frac{1}{4}}=16^{\frac{1}{4}}(cos(\frac{200}{4}+\frac{2(1)\pi}{4}))+\mathfrak{i}(sin(\frac{200}{4}+\frac{2(1)\pi}{4}))[/tex]
[tex]z^{\frac{1}{4}}=2(cos(\frac{5\pi}{18}+\frac{2\pi}{4}))+\mathfrak{i}(sin(\frac{5\pi}{18}+\frac{2\pi}{4}))\\[/tex]
[tex]z^{\frac{1}{4}}=2(cos(\frac{5\pi}{18}+\frac{\pi}{2}))+\mathfrak{i}(sin(\frac{5\pi}{18}+\frac{\pi}{2}))\\[/tex]
Root #2:
[tex]\large\boxed{z^{\frac{1}{4}}=2(cos(\frac{7\pi}{9}))+\mathfrak{i}(sin(\frac{7\pi}{9}))}[/tex]
Part 4: Solving for root #3
To solve for root #3, follow the same simplifying steps above but change k to k = 2.
[tex]z^{\frac{1}{4}}=16^{\frac{1}{4}}(cos(\frac{200}{4}+\frac{2(2)\pi}{4}))+\mathfrak{i}(sin(\frac{200}{4}+\frac{2(2)\pi}{4}))[/tex]
[tex]z^{\frac{1}{4}}=2(cos(\frac{5\pi}{18}+\frac{4\pi}{4}))+\mathfrak{i}(sin(\frac{5\pi}{18}+\frac{4\pi}{4}))\\[/tex]
[tex]z^{\frac{1}{4}}=2(cos(\frac{5\pi}{18}+\pi))+\mathfrak{i}(sin(\frac{5\pi}{18}+\pi))\\[/tex]
Root #3:
[tex]\large\boxed{z^{\frac{1}{4}}=2(cos(\frac{23\pi}{18}))+\mathfrak{i}(sin(\frac{23\pi}{18}))}[/tex]
Part 4: Solving for root #4
To solve for root #4, follow the same simplifying steps above but change k to k = 3.
[tex]z^{\frac{1}{4}}=16^{\frac{1}{4}}(cos(\frac{200}{4}+\frac{2(3)\pi}{4}))+\mathfrak{i}(sin(\frac{200}{4}+\frac{2(3)\pi}{4}))[/tex]
[tex]z^{\frac{1}{4}}=2(cos(\frac{5\pi}{18}+\frac{6\pi}{4}))+\mathfrak{i}(sin(\frac{5\pi}{18}+\frac{6\pi}{4}))\\[/tex]
[tex]z^{\frac{1}{4}}=2(cos(\frac{5\pi}{18}+\frac{3\pi}{2}))+\mathfrak{i}(sin(\frac{5\pi}{18}+\frac{3\pi}{2}))\\[/tex]
Root #4:
[tex]\large\boxed{z^{\frac{1}{4}}=2(cos(\frac{16\pi}{9}))+\mathfrak{i}(sin(\frac{16\pi}{19}))}[/tex]
The fourth roots of 16(cos 200° + i(sin 200°) are listed above.
logx-log(x-l)^2=2log(x-1)
Answer:
x = 1.00995066776
x = 2.52925492433
Step-by-step explanation:
This sort of equation is best solved using a graphing calculator. For that purpose, I like to rewrite the equation as a function whose zeros we're seeking. Here, that becomes ...
[tex]f(x)=\log{(x)}-\log{(x-1)}^2-2\log{(x-1)}[/tex]
The attached graph shows zeros at
x = 1.00995066776 and 2.52925492433
_____
Comment on the equation
Note that we have taken the middle term to be the square of the log, rather than the log of a square. For the latter interpretation, see mberisso's answer at https://brainly.com/question/17210068
Comment on the answer refinement
We have used Newton's method iteration to refine the solutions to this equation. The solution near 1.00995 requires the initial guess be very close for that method to work properly. Fortunately, the 1.01 value shown on the graph is sufficient for the purpose.
The graph of F(x), shown below, has the same shape as the graph of
G(x) = x, but it is shifted up 2 units. What is its equation?
Greetings from Brasil...
We know that the translations are established as follows:
→ Horizontal
F(X + k) ⇒ k units to the left
F(X - k) ⇒ k units to the right
→ Vertical
F(X) + k ⇒ k units up
F(X) - k ⇒ k units down
G(X) = X and F(X) is G(X) shifted up 2 units.
In the statement it is said that there was a translation of 2 units upwards, so
F(X) = G(X) + k where k = 2 units up
F(X) = X + 2woman has 7 coworkers' man. How many different possible groups of four people could do the project, if one out of three is women? g
Answer: 24ways
Step-by-step explanation:
Given data:
No of men in the workplace = 7
No of women in the workplace = 1
How many ways can a group of 4 people carry out a project if on out of the 3 must be a woman.
Solution.
A group of 4 can carry out the project with one be a woman
This means there must be 3 males and 1 female in the group
= 4p3
= 24ways
The project can be carried out by 4 groups in 24 ways
Suppose that you borrow $1000.00 from a friend and promise to pay back $1390.00 in 2 years. What simple interest rate will you pay?
The simple interest rate is % (Round to the nearest tenth as needed.)
Answer:
19.5%
Step-by-step explanation:
Use the formula I = prt, where I is the interest money, p is the starting amount of money, r is the interest rate, and t is the time that the money was borrowed.
Plug in the values and solve for r:
390 = (1000)(r)(2)
390 = 2000r
0.195 = r
r = 19.5%
Answer:
19.5%
Step-by-step explanation:
Simple Interest = Principal x Time x Rate in % / 100
SI = 1000 x 2 x a / 100
=> SI = 10 x 2 x a
=> SI = 20a
Total Amount = SI + Principal
=> 1390 = 20a + 1000
=> 1390 - 1000 = 20a +1000 - 1000
=> 390 = 20a
=> 390/20 = 20a/20
=> 19.5 = a
Let's recheck
=> 1000 x 2 x 19.5 /100
=> 10 x 2 x 19.5
=> 195 x 2
=> 390
1390 = 390 + 1000
=> 1390 = 1390
So, the interest rate is 19.5 %
(16 points) Find the radius of convergence and the interval of convergence of the power series. g
Answer:
The equation to be solved is missing in the question.
I will explain power series and ways to find the radius and interval of convergence of a powers series in the attached image.
Step-by-step explanation:
Understand the power seriesFind radius of convergenceDetermine interval of convergenceWhat is the volume of a rectangular prism with a length, width,
2
1
5
and height of
cm, -
cm, and
cm, respectively?
3
4
6
Step-by-step explanation:
Hey, there!!
It's so simple,
Given,
length (l)= 2/3cm
Breadth (b) = 1/4cm
and height (h)=5/6cm
now, we use the formula for volume of rectangular prism is,
v = l× b× h
or, v= (2/3 × 1/4 × 5/6)^3
By simplifying it we get,
The volume is 5/36cm^3.
Hope it helps...
Combine like terms. What is a simpler form of each expression? 4c-4d+8c-3d
Answer:
12c-7d
Step-by-step explanation:
[tex]4c-4d+8c-3d=0\\4c+8c=3d+4d\\12c=7d\\12c-7d[/tex]
===============================================
Explanation:
The terms 4c and 8c are one pair of like terms that combine to 4c+8c = 12c. We add 4 and 8 to get 12, then tack a 'c' at the end
The other pair of like terms are -4d and -3d. They combine to -7d for similar reasoning.
12c and -7d are not like terms, so we can't combine them and we stop here.
-----------
One way to think of combining like terms is consider simplifying 2c+3c. You could say that 2c represents having 2 cups while 3c is having 3 cups. Writing 2c+3c means we start with 2 cups and add on 3 more getting a total of 2+3 = 5 cups. Symbolically we would then write 5c. Therefore 2c+3c = 5c.
Find the measure of A.
A. 50
B. 70
C. 100
D. 90
Answer:
D
Step-by-step explanation:
I don't know how to eliminate the wrong answers.
Two line segments which have one end at a diameter and the other end meeting at a common point, make a 90 degree angle.
A is made that way, so A is 90 degrees.
Answer:
Step-by-step explanation:
I believe it is 90
(01.01 MC) Monica earned $60 from a bonus plus $8.50 per hour (h) she worked this week. Which of the following expressions best represents Monica's income for the week? 8.50h + 60 8.50 + 60 8.50 + 60h 8.50 + h + 60
Answer:
Option (1)
Step-by-step explanation:
Monica earned a bonus = $60
Per hour earning in addition to bonus = $8.50
Let she worked for 'h' hours this week.
Then total earning from the hourly rate = $8.50h
Total earning for the week = Earning of 'h' hours + Bonus earned
= $(8.50h + 60)
Therefore, Option (1) will represent Monica's earnings for the week.
Answer:
8.50h + 60
Step-by-step explanation:
A quality control manager is concerned about variability of the net weight of his company’s individual yogurt cups. To check the consistency, he takes a random sample of sixteen 6-ounce yogurt cups and finds the mean of the sampled weights to be 5.85 ounces and the sample standard deviation to be 0.2 ounce.
Requried:
a. Test the hypotheses H0: µ ≥ 6 Ha: µ < 6 at the 5% level of significance. Assume the population of yogurt-cup net weights is approximately normally distributed.
b. Based on the results of the test, will the manager be satisfied that the company is not under-filling its cups?
c. State the decision rule, the test statistic, and the manager’s decision.
Answer:
a) We reject H₀
b) The manager won´t be satisfied with nominal filling its cup
c) See step-by-step explanation
Step-by-step explanation:
Normal distribution n < 30, therefore, we should use t - student table
Sample size n = 16
degree of freedom = df = n - 1 df = 15
Sample mean μ = 5,85 ou
Sample standard deviation is s = 0,2 ou
Hypothesis test
Null hypothesis H₀ μ >= μ₀
Alternative hypothesis Hₐ μ < μ₀
CI = 95 % then α = 5 % α = 0,05 α/2 = 0,025
Then in t-student table we find t(c) = 1,753
To calculate t(s)
t(s) = ( μ - μ₀ ) s/√n
t(s) = ( 5,85 - 6 ) / 0,2/√16
t(s) = - 0,15* 4 / 0,2
t(s) = - 3
To compare t(s) and t(c)
|t(s)| > |t(c)| 3 > 1,753
Then t(s) is in the rejection region. We should reject H₀. Data indicate that at 95 % of CI μ seems to be smaller than 6 ou
b) The manager won´t be satisfied with nominal filling its cup
Hi i need help on this im not that smart sorry, what is the x-intercept of the graph that is shown below
Answer:
(3, 0)
Step-by-step explanation:
x-intercept is where the line touches the x-axis
It is the point on the line where y=0
Answer:
3,0
Step-by-step explanation:
the point where the line cuts the x axis is the x-intecept
What is the 25th term in the following arithmetic sequence? -7, -2, 3, 8, ...
Answer:
108.
Step-by-step explanation:
-7, -2, 3, 8 is an arithmetic sequence with a1 (first term) = -7 and common difference (d) = 5.
The 24th term = a1 + (24 - 1)d
= -7 + 23 * 5
= -7 + 115
= 108.
HELP ME ILL GIV ROBUX Identify the property shown by the equation. 14 × 6 = 6 × 14 A. Commutative Property B. Associative Property C. Identity Property D. Distributive Property PLEASE HELP ME
Answer:
A. Commutative Property
Step-by-step explanation:
Hello!
This is the Commutative property which is when you can change the order of the numbers and the result does not change.
Hope this helps!
Can someone help I would really appreciate
Answer:
18/a
Step-by-step explanation:
quotient means divide
18/a
What is a categorical variable
It's a variable that deals with various labels, rather than the usual type of numeric variable you may be used to.
One example of a categorical variable is color. You could have red, green, blue, yellow, and orange as the five choices for your categorical variable. Each color is a label or category.
This is an example of a qualitative variable. We don't have any numeric data attached to color. They're simply names or labels. In contrast, a quantitative variable is something like a person's height since a number is attached here (more specifically its a continuous quantitative variable).
Word phrase for algebraic expression 15-1.5/d
Answer: 1.5 less than 15 is divided by a number d.
Step-by-step explanation:
Please help!
Explain how changes in the dimensions of a cube dimensions affect the volume of a cube. Be specific, explaining how much the volume will change with each increase of 1 unit on the side lengths.
Answer:
when each side length of a cube increases by 1 unit, the volume increases by 3x² + 3x + 1 (units)³
Step-by-step explanation:
Let the initial length of the sides of the cube = x unit
when the length of the cube = x ; volume of the cube = length × breadth × height = x × x × x = x³ (unit)³
when the length increased by 1 unit,
new length = (x + 1) unit
New volume = (x + 1) × (x + 1) × (x + 1)
multiplying the first two brackets
New volume = (x² + 2x + 1 ) (x + 1)
espanding the brackets
New volume = x³ + 2x² + x + x² + 2x + 1
New volume = x³ + 3x² + 3x + 1 (unit)³
Change in volume:
(New volume) - (old volume)
(x³ + 3x² + 3x + 1) - (x³)
x³ + 3x² + 3x + 1 - x³
collecting like terms:
(x³ - x³) + 3x² + 3x + 1
0 + 3x² + 3x + 1
change in volume = 3x² + 3x + 1
Therefore, when each side length of a cube increases by 1 unit, the volume increases by 3x² + 3x + 1 (units)³
Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable? (Enter your answers from smallest to largest. Enter NONE in any unused answer blanks.) f(x) = x + 3 x2 − 2x − 15
Answer:
-3 (removable), +5
Step-by-step explanation:
Maybe you have ...
[tex]f(x)=\dfrac{x+3}{x^2-2x-15}=\dfrac{x+3}{(x+3)(x-5)}=\dfrac{1}{x-5}\quad x\ne-3[/tex]
This will have discontinuities (points where the function is undefined) at ...
x = -3x = 5The discontinuity as x = -3 is removable by defining f(-3) = -1/8.
Was is a macroeconomics
Answer:
Macroeconomics is a study that deals with the whole economy and everything pertaining to it.
Step-by-step explanation:
when we talk about Macroeconomics, we mean the whole economy. It can be related to a country's import or export, governance, how resources are accurately allocated to people in the country and the like.
What is the correct standard form of the equation of the parabola? Enter your answer below. Be sure to show each step of your work.
Answer:
Step-by-step explanation:
eq. of directrix is y=4 or y-4=0
perpendicular distance of (x,y) from directrix =distance of (x,y) from focus (-3,2)
[tex]| \frac{y-4}{1}|=\sqrt{(x+3)^2+(y-2)^2} \\squaring~both~sides\\y^2-8y+16=(x+3)^2+(y-2)2\\(x+3)^2=y^2-8y+16-(y-2)^2\\(x+3)^2=y^2-8y+16-(y^2-4y+4)\\(x+3)^2=y^2-8y+16-y^2+4y-4\\(x+3)^2=-4y+12\\(x+3)^2=-4(y-3)[/tex]
the grasshopper population in Georgia is currently 4,000. It's growing by 2.3% each year. Write an equation that models the situation.
Answer:
[tex]4000(1.023)^t\\\\[/tex]
Step-by-step explanation:
Using this exponential growth equation we can get an equation that models the situation.
A= Principal Amount
R= Rate of Growth
T= Amount of time
[tex]A=4000\\R=2.3/100=.023\\T= Non[/tex]
[tex]A(1+R)^t\\4000(1+0.23)^t\\4000(1.023)^t\\\\[/tex]
Find the total area of all the shaded rectangles.
4
The total area of all the shaded rectangles is
(Simplify your answer. Type an expression using x as the variable
Answer:
25x^2 + 40x + 16
Step-by-step explanation:
area = 5x * 5x + 5x * 4 + 5x * 4 + 4 * 4
area = 25x^2 + 40x + 16
25x² + 40x + 16 is the required equation in variable x.
What is mensuration ?
Mensuration is a branch of mathematics where we calculate length, width, area, volume, lateral surface area, total surface area.
The sum of the areas of the shaded rectangles is the total area.
By observation we can see that the four shaded rectangles together form a square.
We all know that the area of the square is (side)²
= (5x + 4)²
= 25x² + 40x + 16 this is the required equation.
learn more about mensuration here :
https://brainly.com/question/23877107
#SPJ2
Jesse bought 3 T-shirts for $6 each and 4 T-shirts for $5 each. What expression can you use to describe what Jesse bought?
Can some body write a word problem using these numbers
Answer:
Mr Singh was travelling from England to Punjab, India. He arrived 5 hours after 0:00. When he was on the plane, there was a delay which caused the whole flight to be pushed 4 hours ahead. This would mean that he would arrive 9 hours after 0:00. Mr Singh was also with his son and he had some homework to do. He had to order the numbers [tex]-4,-2\frac{1}{3} ,0, \frac{3}{4} ,\sqrt{5},5[/tex] from lowest to highest.
PLEASE ANSWER ASAP!!
How many cubic centimeters (
[tex] {cm}^{3} [/tex]
) are there in a 5 gallon jug of water?
Must show your work!!!
any unrelated answer will be reported
Answer:
[tex]\boxed{\sf A}[/tex]
Step-by-step explanation:
[tex]\sf 1 \ gallon = 3785.41 \ cm^3[/tex]
[tex]\sf 5 \ gallon = \ ? \ cm^3[/tex]
[tex]\sf Multiply \ the \ gallon \ value \ by \ 3785.41.[/tex]
[tex]5 \times 3785.41 = 18927.1[/tex]
[tex]\sf Approximate \ the \ value.[/tex]
[tex]18927.1 \approx 19000[/tex]
