Answer:
The correct option is (b) 0.3333.
Step-by-step explanation:
The standard deviation of the sampling distribution of sample mean [tex](\bar x)[/tex] is known as the standard error [tex](\sigma_{\bar x})[/tex].
The standard error is given as follows:
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
The information provided is:
[tex]\mu=8\\\\\sigma=2\\\\n=36[/tex]
Compute the standard deviation of the sample mean as follows:
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
[tex]=\frac{2}{\sqrt{36}}\\\\=\frac{2}{6}\\\\=\frac{1}{3}\\\\=0.3333[/tex]
Thus, the standard deviation of the sample mean is 0.3333.
Please give me the answer ASAP The average of 5 numbers is 7. If one of the five numbers is removed, the average of the four remaining numbers is 6. What is the value of the number that was removed Show Your Work
Answer:
The removed number is 11.
Step-by-step explanation:
Given that the average of 5 numbers is 7. So you have to find the total values of 5 numbers :
[tex]let \: x = total \: values[/tex]
[tex] \frac{x}{5} = 7[/tex]
[tex]x = 7 \times 5[/tex]
[tex]x = 35[/tex]
Assuming that the total values of 5 numbers is 35. Next, we have to find the removed number :
[tex]let \: y = removed \: number[/tex]
[tex] \frac{35 - y}{4} = 6[/tex]
[tex]35 - y = 6 \times 4[/tex]
[tex]35 - y = 24[/tex]
[tex]35 - 24 = y[/tex]
[tex]y = 11[/tex]
Okay, let's slightly generalize this
Average of [tex]n[/tex] numbers is [tex]a[/tex]
and then [tex]r[/tex] numbers are removed, and you're asked to find the sum of these [tex]r[/tex] numbers.
Solution:
If average of [tex]n[/tex] numbers is [tex]a[/tex] then the sum of all these numbers is [tex]n\cdot a[/tex]
Now we remove [tex]r[/tex] numbers, so we're left with [tex](n-r)[/tex] numbers. and their. average will be [tex]{\text{sum of these } (n-r) \text{ numbers} \over (n-r)}[/tex] let's call this new average [tex] a^{\prime}[/tex]
For simplicity, say, sum of these [tex]r[/tex] numbers, which are removed is denoted by [tex]x[/tex] .
so the new average is [tex]\frac{\text{Sum of } n \text{ numbers} - x}{n-r}=a^{\prime}[/tex]
or, [tex] \frac{n\cdot a -x}{n-r}=a^{\prime}[/tex]
Simplify the equation, and solve for [tex]x[/tex] to get,
[tex] x= n\cdot a -a^{\prime}(n-r)=n(a-a^{\prime})+ra^{\prime}[/tex]
Hope you understand it :)
I need help plotting this on number line
Answer:
Step-by-step explanation:
Find the distance between the points. Give an exact answer and an approximation to three decimal places.
(3.1,0.3) and (2.7. - 4.9)
The exact distance is
(Simplify your answer. Type an exact ans
Answer: sqrt(27.2) =approx 5.215
Step-by-step explanation:
The distance between 2 points can be calculated using Phitagor theorem
L= sqrt( (x1-x2)²+(y1-y2)²)
Where x1, y1 are the coordinates of the first point and x2, y2 are the coordinates of the 2-nd point.
L=sqrt((3.1-2.7)²+(0.3-(-4.9))²)= sqrt(0.4²+5.2²)=sqrt(27.2) - this is exact answer.
sqrt(27.2)=5.21536...=approx 5.215
Find the solution of the system of equations.
2x – 10y = -28
-10x + 10y = -20
GbA
Answer:
(6, 4 )
Step-by-step explanation:
Given the 2 equations
2x - 10y = - 28 → (1)
- 10x + 10y = - 20 → (2)
Adding (1) and (2) term by term eliminates the term in y, that is
- 8x = - 48 ( divide both sides by - 8 )
x = 6
Substitute x = 6 into either of the 2 equations and evaluate for y
Substituting into (1)
2(6) - 10y = - 28
12 - 10y = - 28 ( subtract 12 from both sides )
- 10y = - 40 ( divide both sides by - 10 )
y = 4
Solution is (6, 4 )
Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit. (If the quantity diverges, enter DIVERGES.) an = 1/sqrt(n)
This sequence converges to 0.
Proof: Recall that
[tex]\displaystyle\lim_{n\to\infty}\frac1{\sqrt n}=0[/tex]
is to say that for any given [tex]\varepsilon>0[/tex], there is some [tex]N[/tex] for which [tex]\left|\frac1{\sqrt n}-0\right|=\frac1{\sqrt n}<\varepsilon[/tex] for all [tex]n>N[/tex].
Let [tex]N=\left\lceil\frac1{\varepsilon^2}\right\rceil[/tex]. Then
[tex]n>\left\lceil\dfrac1{\varepsilon^2}\right\rceil\ge\dfrac1{\varepsilon^2}[/tex]
[tex]\implies\dfrac1n<\varepsilon^2[/tex]
[tex]\implies\dfrac1{\sqrt n}<\varepsilon[/tex]
as required.
HELP
PLSFind all the missing elements:
Answer:
a = 6.7 , c = 2.0
Step-by-step explanation:
For side aTo find the missing side a we use the sine rule
[tex] \frac{ |b| }{ \sin(B) } = \frac{ |a| }{ \sin(A) } [/tex]From the question
B = 58°
b = 6
A = 109°
Substituting the values into the above formula we have
[tex] \frac{6}{ \sin(58) } = \frac{ |a| }{ \sin(109) } [/tex][tex] |a| \sin(58) = 6\sin(109) [/tex]Divide both sides by sin 58°
[tex] |a| = \frac{6 \sin(108) }{ \sin(58) } [/tex]a = 6.728791
a = 6.7 to the nearest tenthFor side cTo find side c we use the sine rule
That's
[tex] \frac{ |b| }{ \sin(B) } = \frac{ |c| }{ \sin(C) } [/tex]C = 13°
[tex] \frac{6}{ \sin(58) } = \frac{ |c| }{ \sin(13) } [/tex][tex] |c| \sin(58) = 6 \sin(13) [/tex]Divide both sides by sin 58°
[tex] |c| = \frac{6 \sin(13) }{ \sin(58) } [/tex]c = 1.591544
c = 2.0 to the nearest tenthHope this helps you
Answer:
B=58 a=6.7 c=1.6
Step-by-step explanation:
It was right on Acellus
Sorry I cant give a better explanation but this unit is killing me.
3. The length of a rectangle is 4 inches more than its width. The area of the rectangle is equal to 5 inches more than 2 times the perimeter. Find the length and width of the rectangle.
PLEASE HELP IM SO LOST
1. Ted is working on his financial plan and lists all of his income and expenses in the spreadsheet below.
А
B
Net Pay
$5,000
2
Interest on Deposits $0
3 Income from Investments $225
4 Rent
$3,000
5 Utilities
$250
6 Satellite Dish
$175
7 Cell Phone Plan
$135
8 Car Payment
$385
9 Groceries
$200
10 Insurance
$380
11 Recreation
$400
What is Ted's net cash flow?
2. Tamara earns $8 an hour at her job working 25 hours per week. If her net pay is 78% of her paycheck
and she has no other sources of income, what is Tamara's monthly cash inflow? (Assume there are 4
pays per month.)
Answer: 1) $300 2) $624
Step-by-step explanation:
[tex]\begin{array}{l||l|l}\underline{\quad \text{Item}\qquad \qquad \qquad \qquad}&\underline{\text{Income} }&\underline{\text{Expense}}\\\text{Net Pay}&5000&\\\text{Interest on Deposits}&0&\\\text{Income from Investments}&225&\\\text{Rent}&&3000\\\text{Utilities}&&250\\\text{Satellite Dish}&&175\\\text{Cell Phone Plan}&&135\\\text{Car Payment}&&385\\\text{Groceries}&&200\\\text{Insurance}&&380\\\underline{\text{Recreation}\qquad \qquad \qquad}&\underline{\qquad \quad }&\underline{400\qquad}\\\end{array}[/tex]
TOTALS 5225 4925
Net Cash Flow = Income - Expenses
= 5225 - 4925
= 300
*************************************************************************************
[tex]\dfrac{25\ hours}{week}\times \dfrac{\$8}{hour}\times 4\ weeks\times 78\%\\\\\\=25\times \$8 \times 0.78\\\\= \$624[/tex]
Please answer this correctly without making mistakes
Answer:
[tex]\large \boxed{\mathrm{4/5 \ cups}}[/tex]
Step-by-step explanation:
Subtract 1/10 from 9/10 to find out how much is left.
9/10 - 1/10
8/10 = 4/5
Answer:
4/5 cupsStep-by-step explanation:
[tex]Volume\:of \: syrup \:in \:cup\:from\:jug = \frac{9}{10}\\\\ She \:took\: \frac{1}{10} from \:the\:cup\:into\:the \:jug \\\\Volume \:of syrup\:in\:cup=?\\\\\frac{9}{10} -\frac{1}{10} \\\\= \frac{4}{5} cups[/tex]
What is the domain of f(x)=2/5x+6
Answer:
Look at that picture
Step-by-step explanation:
You have $2,000 on a credit card that charges a 16% interest rate. If you want to pay off the credit card in 5 years, how much will you need to pay each month (assuming you don't charge anything new to the card)?
9514 1404 393
Answer:
$48.64
Step-by-step explanation:
The monthly payment amount is given by the amortization formula ...
A = P(r/n)/(1 -(1 +r/n)^(-nt))
where P is the loan amount, r is the annual interest rate compounded n times per year for t years.
Here, you have P=2000, r=0.16, n=12 (months per year), t=5 (years), so the payment is ...
A = $2000(0.16/12)/(1 -(1 +0.16/12)^(-12·5)) = $320/(12(0.54828942))
A ≈ $48.636 ≈ $48.64
You will need to pay $48.64 each month to pay off the charge in 5 years.
Suppose that Y1, Y2,..., Yn denote a random sample of size n from a Poisson distribution with mean λ. Consider λˆ 1 = (Y1 + Y2)/2 and λˆ 2 = Y . Derive the efficiency of λˆ 1 relative to λˆ 2.
Answer:
The answer is "[tex]\bold{\frac{2}{n}}[/tex]".
Step-by-step explanation:
considering [tex]Y_1, Y_2,........, Y_n[/tex] signify a random Poisson distribution of the sample size of n which means is λ.
[tex]E(Y_i)= \lambda \ \ \ \ \ and \ \ \ \ \ Var(Y_i)= \lambda[/tex]
Let assume that,
[tex]\hat \lambda_i = \frac{Y_1+Y_2}{2}[/tex]
multiply the above value by Var on both sides:
[tex]Var (\hat \lambda_1 )= Var(\frac{Y_1+Y_2}{2} )[/tex]
[tex]=\frac{1}{4}(Var (Y_1)+Var (Y_2))\\\\=\frac{1}{4}(\lambda+\lambda)\\\\=\frac{1}{4}( 2\lambda)\\\\=\frac{\lambda}{2}\\[/tex]
now consider [tex]\hat \lambda_2[/tex] = [tex]\bar Y[/tex]
[tex]Var (\hat \lambda_2 )= Var(\bar Y )[/tex]
[tex]=Var \{ \frac{\sum Y_i}{n}\}[/tex]
[tex]=\frac{1}{n^2}\{\sum_{i}^{}Var(Y_i)\}\\\\=\frac{1}{n^2}\{ n \lambda \}\\\\=\frac{\lambda }{n}\\[/tex]
For calculating the efficiency divides the [tex]\hat \lambda_1 \ \ \ and \ \ \ \hat \lambda_2[/tex] value:
Formula:
[tex]\bold{Efficiency = \frac{Var(\lambda_2)}{Var(\lambda_1)}}[/tex]
[tex]=\frac{\frac{\lambda}{n}}{\frac{\lambda}{2}}\\\\= \frac{\lambda}{n} \times \frac {2} {\lambda}\\\\ \boxed{= \frac{2}{n}}[/tex]
Yooo I just had MAD diarrhea D:
Review the example argument and reasoning below. Identify the form (inductive or deductive) of reasoning and the type (example, analogy, causal correlation, syllogism, sign, or causal generalization) of reasoning Raul uses to justify his argument. Then, apply the three tests of argumentative reasoning (quantity, quality, & opposition) to test this argument.
Raul believes that if someone’s eyes shift to the left when they are responding to a question it is evidence that they are lying. While interviewing Michael, Raul notices Michael's eyes shifting to the left frequently when answering questions. Later, Raul tells a coworker that Michael was not hired because Raul believed Michael had lied about his previous experience during the interview.
Answer:
inductive - . Inductive reasoning makes broad generalizations from specific observations.
casual correlation
quality ( i think)
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
i just did it
3x7-12-2=7?
I have no clue please help...
Answer:
X = 28/3, or 9 1/3 or 9.3
Step-by-step explanation:
Answer:
Step-by-step explanation:
How many solutions does the following equation have ?
−3x+9−2x=−12−5x
[tex]\text{Solve for x:}\\\\-3x+9-2x=-12-5x\\\\\text{Combine like terms}\\\\-5x+9=-12-5x\\\\\text{Add 5x to both sides}\\\\9=-12\\\\\text{Since that's not valid, there would be no solutions}\\\\\boxed{\text{No solutions}}[/tex]
4. Two unbiased coins are tossed. Calculate the probability that
(a) Two heads are obtained.
(b) One head and one tail is obtained.
Solving Equations by Dividing 2) 9x= -135 Solve for x. 0 -144 O 126 O 15 0 -15
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\boxed{\mathsf{9x = -135}}[/tex]
[tex]\huge\boxed{\text{DIVIDE 9 to BOTH SIDES}}[/tex]
[tex]\huge\boxed{\mathsf{\dfrac{9x}{9}= \dfrac{-135}{9}}}[/tex]
[tex]\huge\boxed{\mathsf{\bullet \ CANCEL: \dfrac{9}{9}\ because\ it \ gives\ you\ 1}}[/tex]
[tex]\huge\boxed{\bullet\ \mathsf{KEEP: \dfrac{-135}{9}\ because\ it\ helps\ solve \ for}}\\\huge\boxed{\mathsf{the\ x-value}}[/tex]
[tex]\huge\boxed{\mathsf{x = \dfrac{-135}{9}}}\\\\\huge\boxed{\mathsf{\dfrac{-135}{9}= x}}}[/tex]
[tex]\huge\boxed{Simplify \ it\uparrow}[/tex]
[tex]\huge\boxed{\mathsf{x = \bf -15}}[/tex]
[tex]\huge\boxed{\textsf{Therefore, your answer is: Option D. -15 }}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\huge\boxed{\frak{Amphitrite1040:)}}[/tex]
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!!
1. How can a matrix be used to solve a system of equations? Demonstrate by solving the following system. Show your work. In other words, use a problem of system of equations problem as an example.
Answer:
Step-by-step explanation:
Assuming the system is solvable in the first place, create an augmented matrix of coefficients from the equations. Then put the matrix into reduced row echelon form.
Example is attached.
"Demonstrate by solving the following system."
You need to provide the system of equations.
PLEASE HELP ASAP THANKS IN ADVANCE
Answer:
the answer to the question is "C"
Complete the point-slope equation of the line through (2,3)(7,4). Use exact numbers. y-4=
Please help me, I would really appreciate it!
Answer:
The answer is
[tex]y - 4 = \frac{1}{5} (x - 7)[/tex]Step-by-step explanation:
To find the equation of a line given two points first find the slope and use the formula
[tex] y - y_{1} = m(x - x_{1})[/tex]Where m is the slope
To find the slope we use the formula
[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]The slope of the line using points
(2,3)(7,4) is
[tex]m = \frac{4 - 3}{7 - 2} = \frac{1}{5} [/tex]Equation of the line using point (7,4) and slope 1/5 is
[tex]y - 4 = \frac{1}{5} (x - 7)[/tex]Hope this helps you
Answer:
y-4=1/5(x-3)
Step-by-step explanation:
We plug in the x's and the y's and find the slope with:
[tex](y-y_{1} )/ x-x_{1})=m[/tex]
If I get paid $100 a week but my car cost $4, 990 how long will I have to save to officially buy my car?
Answer:
50 weeks.
Step-by-step explanation:
Did the math like u should've
Write all the factors of 32
Matj
Answer
Answer: 1, 2, 4, 8, 16, and 32.
Step-by-step explanation:
Factors are what we can multiply to get the number.
Factors of 32:
1 x 32=32
2 x 16=32
4 x 8=32
Therefore, the factors of 32 are 1, 2, 4, 8, 16, and 32.
Please Help Me!!! (WORTH 60 POINTS) Will Give Extra points out
Answer:
√11 cm
Step-by-step explanation:
Pythagorean Thereom
a^2 + b^2= c^2
x^2 +5^2=6^2
x^2 + 25 = 36
subtract 25 from both sides
x^2=11
do the square root
x = √11
Decide all proper subsets of A { 8 ,7 ,6 ,5 ,4 ,3 ,2 ,1} = A 1- { 4 ,3 ,2 ,1} 2- { } 3- { 9 ,8 ,7 } 4- { 11 ,2} 5- { 5 }
Answer:
A, E
Step-by-step explanation:
There should be 2^8-1 proper subsets of A. Its every one besides { }
Calculate how many different sequences can be formed that use the letters of the given word. Leave your answer as a product of terms of the form C(n, r). HINT [Decide where, for example, all the s's will go, rather than what will go in each position.]
georgianna
A) C(10, 7)
B) C(2, 10)C(1, 8)C(1, 7)C(1, 6)C(1, 5)C(2, 4)C(2, 2)
C) C(10, 2)C(8, 1)C(7, 1)C(6, 1)C(5, 1)C(4, 1)C(3, 1)C(2, 1)C(1, 1)
D) 10 · C(10, 2)C(8, 1)C(7, 1)C(6, 1)C(5, 1)C(4, 2)C(2, 2)
E) C(10, 2)C(8, 1)C(7, 1)C(6, 1)C(5, 1)C(4, 2)C(2, 2)
Answer: E) C(10, 2)C(8, 1)C(7, 1)C(6, 1)C(5, 1)C(4, 2)C(2, 2)
Step-by-step explanation:
According to the combinations: Number of ways to choose r things out of n things = C(n,r)
Given word: "georgianna"
It is a sequence of 10 letters with 2 a's , 2 g's , 2 n's , and one of each e, o,r, i.
If we think 10 blank spaces, then in a sequence we need 2 spaces for each of g.
Number of ways = C(10,2)
Similarly,
1 space for 'e' → C(8,1)
1 space for 'o' → C(7,1)
1 space for 'r' → C(6,1)
1 space for 'i' → C(5,1)
1 space for 'a' → C(4,2)
1 space for 'n' → C(2,2)
Required number of different sequences = C(10,2) ×C(8,1)× C(7,1)× C(6,1)×C(5,1)×C(2,2).
Hence, the correct option is E) C(10, 2)C(8, 1)C(7, 1)C(6, 1)C(5, 1)C(4, 2)C(2, 2)
7.619 by 10^-3
7.254 by 10^2
Answer:
0.007619
0.07254
Step-by-step explanation:
1)7.619*10^-3
0.007619
2)7.254*10^2
0.07254
Explanation:
7.619*10^-3
The number here is 7.619 and the number written in scientific notation has minus 3 as its exponent.
.007.619
So the distance between the first decimal point and the second decimal is only three numbers.
Since it is exponent is minus three.
Another way to get the answer.
[tex]7.619 \times 10 {}^{ - 3} = \frac{7619}{1000} \times \frac{1}{1000} = \frac{7619}{1000000} = 0.007619 [/tex]
This applies to the second one too.
Hope this helps ;) ❤❤❤
Question 2b only! Evaluate using the definition of the definite integral(that means using the limit of a Riemann sum
Answer:
Hello,
Step-by-step explanation:
We divide the interval [a b] in n equal parts.
[tex]\Delta x=\dfrac{b-a}{n} \\\\x_i=a+\Delta x *i \ for\ i=1\ to\ n\\\\y_i=x_i^2=(a+\Delta x *i)^2=a^2+(\Delta x *i)^2+2*a*\Delta x *i\\\\\\Area\ of\ i^{th} \ rectangle=R(x_i)=\Delta x * y_i\\[/tex]
[tex]\displaystyle \sum_{i=1}^{n} R(x_i)=\dfrac{b-a}{n}*\sum_{i=1}^{n}\ (a^2 +(\dfrac{b-a}{n})^2*i^2+2*a*\dfrac{b-a}{n}*i)\\[/tex]
[tex]=(b-a)^2*a^2+(\dfrac{b-a}{n})^3*\dfrac{n(n+1)(2n+1)}{6} +2*a*(\dfrac{b-a}{n})^2*\dfrac{n (n+1)} {2} \\\\\displaystyle \int\limits^a_b {x^2} \, dx = \lim_{n \to \infty} \sum_{i=1}^{n} R(x_i)\\\\=(b-a)*a^2+\dfrac{(b-a)^3 }{3} +a(b-a)^2\\\\=a^2b-a^3+\dfrac{1}{3} (b^3-3ab^2+3a^2b-a^3)+a^3+ab^2-2a^2b\\\\=\dfrac{b^3}{3}-ab^2+ab^2+a^2b+a^2b-2a^2b-\dfrac{a^3}{3} \\\\\\\boxed{\int\limits^a_b {x^2} \, dx =\dfrac{b^3}{3} -\dfrac{a^3}{3}}\\[/tex]
A car dealer's markup on every car they sell is 20%. For what price did the dealership buy a car that they sold for $18,600?
Answer:
buying price = $15,500
Step-by-step explanation:
selling price 20% more than the buying price
let the buying price be 100% then;
selling price = 120%
120% = $18,600
100% = ?
(100 × 18600) ÷ 120
= $15,500
convert 407 in base 8 to decimal
[tex]4\cdot8^2+0\cdot8^1+7\cdot8^0=256+7=263[/tex]
[tex]407_8=263_{10}[/tex]