The standard deviation for the given data items is 2.6
The standard deviation of the given data items can be calculated by taking the square root of the variance.
Variance is a measure of variability and it is calculated by taking the average of squared deviations from the mean.
Hence, we will first determine the mean of the given data items.
Mean is simply the average of the numbers.
Therefore mean of the given data items is
[tex]Mean = \frac{9+11+11+16}{4}[/tex]
[tex]Mean = \frac{47}{4}[/tex]
Mean = 11.75
Now, for the variance of the data
[tex]Variance = \frac{(9-11.75)^{2}+(11-11.75)^{2}+(11-11.75)^{2}+(16-11.75)^{2} }{4}[/tex]
[tex]Variance = \frac{(-2.75)^{2}+(-0.75)^{2}+(-0.75)^{2}+(4.25)^{2} }{4}[/tex]
[tex]Variance = \frac{7.5625+0.5625+0.5625+18.0625}{4}[/tex]
[tex]Variance = \frac{26.75}{4}\\[/tex]
∴ Variance = 6.6875
But,
Standard deviation [tex]= \sqrt{Varinace}[/tex]
∴Standard deviation [tex]=\sqrt{6.6875}[/tex]
Standard deviation = 2.586
Standard deviation ≅ 2.6
Hence, the standard deviation for the given data items is 2.6
Learn more on standard deviation here: https://brainly.com/question/18562832
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!! Part 2.
2. What is a determinant and what role does it play with matrices (Hint: What does a determinant of 0 mean)? How can this be used when solving systems of equations?
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Explanation:
Definition
The determinant of a square matrix is a single number that is computed (recursively) as the sum of products of the elements of a row or column and the determinants of their cofactors. The determinant of a single element is the value of that element.
The cofactor of an element in an n by n matrix is the (n-1) by (n-1) matrix that results when the row and column of that element are deleted. The "appropriate sign" of the element is applied to the cofactor matrix. The "appropriate sign" of an element is positive if the sum of its row and column numbers is even, negative otherwise. (Rows and columns are considered to be numbered 1 to n in an n by n matrix.)
Uses
The inverse of a square matrix is the transpose of the cofactor matrix, divided by the determinant. Hence if the determinant is zero, the inverse matrix is undefined. This means any system of equations the matrix might represent will have no distinct solution. (There may be zero solutions, or there may be an infinite number of solutions. The determinant by itself cannot tell you which.)
Cramer's Rule for the solution of linear systems of equations specifies that the value of any given variable is the ratio of the determinants of two matrices. The numerator matrix is the original matrix with the coefficients of the variable replaced by the constants in the standard-form equations; the denominator matrix is the original coefficient matrix. This rule lets you solve a system of 3 equations in 3 variables by computing 3+1 = 4 determinants, for example.
Let's look at an example.
If we wanted to solve this system of equations
[tex]\begin{cases}2x-y = 2\\x+y = 7\end{cases}[/tex]
Then it's equivalent to solving this matrix equation
[tex]\begin{bmatrix}2 & -1\\1 & 1\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}2\\7\end{bmatrix}[/tex]
We can then further condense that into the form
[tex]Aw = B[/tex]
Where,
[tex]A = \begin{bmatrix}2 & -1\\1 & 1\end{bmatrix}\\\\w = \begin{bmatrix}x\\y\end{bmatrix}\\\\B = \begin{bmatrix}2\\7\end{bmatrix}[/tex]
------------------------------------------
To solve the matrix equation Aw = B, we could compute the inverse matrix [tex]A^{-1}[/tex] and left-multiply both sides by this to isolate w.
So we'd go from [tex]Aw=B[/tex] to [tex]w = A^{-1}*B[/tex]. The order of multiplication is important.
For any 2x2 matrix of the form
[tex]P = \begin{bmatrix}a & b\\c & d\end{bmatrix}[/tex]
its inverse is
[tex]P^{-1} = \frac{1}{ad-bc}\begin{bmatrix}d & -b\\-c & a\end{bmatrix}[/tex]
Notice the expression ad-bc in the denominator of that fractional term outside. This [tex]ad-bc[/tex] expression represents the determinant of matrix P. Some books may use the notation "det" to mean "determinant"
[tex]P^{-1} = \frac{1}{\det(P)}\begin{bmatrix}d & -b\\-c & a\end{bmatrix}[/tex]
or you may see it written as
[tex]P^{-1} = \frac{1}{|P|}\begin{bmatrix}d & -b\\-c & a\end{bmatrix}[/tex]
Those aren't absolute value bars, even if they may look like it.
Based on that, we can see that the determinant must be nonzero in order to compute the inverse of the matrix. Consequently, the determinant must be nonzero in order for Aw = B to have one solution.
If the determinant is 0, then we have two possibilities:
There are infinitely many solutions (aka the system is dependent)There are no solutions (the system is inconsistent)So a zero determinant would have to be investigated further as to which outcome would occur.
------------------------------------------
Let's return to the example and compute the inverse (if possible).
[tex]A = \begin{bmatrix}2 & -1\\1 & 1\end{bmatrix}\\\\A^{-1} = \frac{1}{2*1 - (-1)*1}\begin{bmatrix}1 & 1\\-1 & 2\end{bmatrix}\\\\A^{-1} = \frac{1}{3}\begin{bmatrix}1 & 1\\-1 & 2\end{bmatrix}\\\\[/tex]
In this case, the inverse does exist.
This further leads to
[tex]w = A^{-1}*B\\\\w = \frac{1}{3}\begin{bmatrix}1 & 1\\-1 & 2\end{bmatrix}*\begin{bmatrix}2\\7\end{bmatrix}\\\\w = \frac{1}{3}\begin{bmatrix}1*2+1*7\\-1*2+2*7\end{bmatrix}\\\\w = \frac{1}{3}\begin{bmatrix}9\\12\end{bmatrix}\\\\w = \begin{bmatrix}(1/3)*9\\(1/3)*12\end{bmatrix}\\\\w = \begin{bmatrix}3\\4\end{bmatrix}\\\\\begin{bmatrix}x\\y\end{bmatrix} = \begin{bmatrix}3\\4\end{bmatrix}\\\\[/tex]
This shows that the solution is (x,y) = (3,4).
As the other person pointed out, you could use Cramer's Rule to solve this system. Cramer's Rule will involve using determinants and you'll be dividing over determinants. So this is another reason why we cannot have a zero determinant.
Some friends are sharing a pizza. If each person gets 1/8 of the pizza, what percent of the pizza does each person get?
Answer:
1/8=12.50%
Step-by-step explanation:
Take the pizza as a whole = 100
Then consider 1/8 of 100
or 1/8 * 100
= 1/4 * 50
= 1/2 * 25
= 12.50
Therefore it is 12.50%
billy joe purchased a 60 gallon pool. at 1 pm he stared filling the pool at the rate of 3 gallons per hour. after 10 hours the horses started drinking the water at the rate of 1 gallon per hour. five hours after that he notices the animal and place a second hose in the pool which filled at the rate of 2 gallons per hour. at what time was the pool finally filled
Answer:
3*10=30 gallons after 10 hours
minus 1 gal/hr for 5 hours=25 gallons.
If the animals are still drinking, the pool is effectively filling at 1 gal/hr, 2-1, and it will take 35 more hours to fill.
If the animals aren't drinking, the pool will fill at 2 gal/hour and it will be full in 35/2 hours or 17.5 hours.
Step-by-step explanation:
In the figure, ∆BAT ≅ ∆CAT. Which statement is not true by CPCTC? ∠BTA ≅ ∠CTA ∠BAT ≅ ∠CAT
Answer:
Both are true.
Step-by-step explanation:
Meena's family took a road trip to Niagara Falls. Meena slept through
the last 49% of the trip. If the total length of the trip was 500 miles, how many miles had they travelled when Meena fell asleep?
245 miles
49/100*500 i guess it's the answer
Answer: 255 miles
Explanation:
Total length of the trip = 500 miles
Then 49% = 49/100×500
= 245 miles
Therefore she slept for 245 miles
How many miles had they travelled when meena fell asleep
= 51%
= 51/100×500
= 255 miles
Or
500 - 245
= 255 miles
Answered by Gauthmath must click thanks and mark brainliest
show that the line x-y+2=0 and the line joining the points (4,6) and (10,12) are parallel to each other
x-y+2=0
-y= -x-2
y=x+2
In order for the other line to be parallel, the slope has to be the same.
(12-6)/(10-4)= 6/6= 1
Both slopes are the same, meaning it is parallel.
PLEASE HELP THIS IS DUE ASAP (answer in decimal!!!!)
Which of the following fractions is closest to 0? 5/12 , 2/3, 5/6,3/4
Answer:
5/12
Step-by-step explanation:
5/12 , 2/3, 5/6,3/4
Get a common denominator of 12
5/12, 2/3 *4/4, 5/6*2/2, 3/4 *3/3
5/12, 8/12, 10/12, 9/12
The numerator closest to 0 is the fraction closest to 0
5/12
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
(B) An airline knows from experience that the distribution of the number of suitcases that get lost each week on a certain route is normal with μ (mean) = 15.5 and σ (standard deviation) = 3.6. What is the probability that during a given week the airline will lose between 11 and 19 suitcases?
Answer:
The correct answer is "0.7289".
Step-by-step explanation:
The given values are:
Mean,
[tex]\mu = 15.5[/tex]
Standard deviation,
[tex]\sigma = 3.6[/tex]
As we know,
⇒ [tex]z = \frac{(x - \mu)}{\sigma}[/tex]
The probability will be:
⇒ [tex]P(11< x< 19) = P(\frac{11-15.5}{3.6} <z<\frac{19-15.5}{3.6})[/tex]
[tex]=P(z< 0.9722)-P(z< -1.25)[/tex]
By using the z table, we get
[tex]=0.8345-0.1056[/tex]
[tex]=0.7289[/tex]
100.331 divide 99.355
Answer:
1.009823361
Step-by-step explanation:
Just divide like this:
[tex] \frac{100.331}{99.355} = 1.009853361[/tex]
a group of workers can plant 3/5 acres in 5/6 days. what is the unit rate per day?
Answer:
Workers can plant 0.72 acres per day.
I need to know the answer ASAP thank you
Answer:
Step-by-step explanation:
The lengths of two sides of the right triangle ABC shown in the illustration given
a= 7cm and b= 24cm
Answer:
25 cm.
Step-by-step explaination:
Given,
Two sides of a triangle:
a = 7cm
b = 24 cm
To find,
Third side:
c = ?
By Pythagorean Theorem;
a² + b² = c²
[where c is the longest side,hypotenuse]
Putting the value of a and b;
we get,
7² + 24² = c²
49 + 576 = c²
625 = c²
25² = c² (square root)
25 = c
c = 25
Therefore, the length of the third side will be equal to 25 cm.
The lengths of two sides of the right triangle ABC shown in the illustration given
a= 7cm and b= 24cm
Given,> a= 7cm
> b= 24cm
To find?Side c (third side)
Solution:-Using Pythagoras theorem,
▶️ a² + b² = c
▶️ 7cm ² + 24cm² = c²
▶️ 49cm + 576cm = c²
▶️ 625cm = c²
▶️ 25² = c² (25×25 = 625)
▶️ c = 25
The value of c is 25 cm.
Find the value of term a14 in the sequence.
3, 1, –1, –3, –5, . . .
–23
–11
–9
–25
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Answer:
(a) -23
Step-by-step explanation:
The sequence is arithmetic with first term 3 and common difference -2. Then the general term is ...
an = a1 +d(n -1)
an = 3 -2(n -1)
and the 14th term is ...
a14 = 3 -2(14 -1) = 3 -2(13) = 3 -26
a14 = -23
If the nominal rate of interest is 10% per annum and there is quarterly compounding, the effective rate of interest will be: a) 10% per annum b) 10.10 per annum c) 10.25%per annum d) 10.38% per annum
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Answer:
d) 10.38%
Step-by-step explanation:
The multiplier for four quarters of quarterly compounding is ...
(1 +10%/4)^4 = 1.025^4 = 1.103812890625
This is about 1 + 10.38%.
The effective rate of interest is about 10.38% per annum.
Find the circumference of the circle.
10.1 in
Hint: C = xxd
x= 3.14
A.15.857 in
B.31.714 in
C.63.428 in
D.13.24 in
Step-by-step explanation:
c=3.14×3.14×10.1
=99.58196
Find the lengths of the other two sides of the isosceles right triangle
Answer:
h²=p²+b²
(7√2)²=x²+x²
(49×2)=2x²
2x²=49ײ
x²=49×2/2
x²=49
x=√49=7
x=7
OAmalOHopeO
Write an equation in slope-intercept form for the line with slope -3/2
and y-intercept 5.
Answer: y = -3/2x + 5
Step-by-step explanation:
Slope-intercept form: y = mx + b
m = slope = -3/2b = y-intercept = 5y = -3/2x + 5
Answer:
y = -3/2x + 5 totally
Step-by-step explanation:
a fair coin is flipped. if the flip results in a head, then a fruit is selected from a basket containing 8 apples, 2 bananas, and 6 cantaloups. if the flip results in a tail, then a fruit is selected from a basket containing 6 apples and 4 bananas. what is the probability that the flip resulted in tails, given that the fruit selexted is a banana g
Solution :
We have given two baskets :
[tex]$H_1$[/tex] : 8 apples + 2 bananas + 6 cantaloupes = 16 fruits
[tex]$H_2$[/tex] : 6 apples + 4 bananas = 10 fruits
A fair coin is made to flipped. If the [tex]\text{flip}[/tex] results is head, then the fruit is selected from a basket [tex]$H_1$[/tex].
If the flip results in tail, then the fruit is selected from the basket [tex]$H_2$[/tex].
Probability of head P(H) = [tex]1/2[/tex]
Probability of tail P(T) = [tex]1/2[/tex]
if given event is :
B = selected fruit is BANANA
We have to calculate : P(T|B)
Probability of banana if the flip results is head P(B|H) = [tex]$\frac{2}{16}$[/tex]
Probability of banana if the flip results is tail P(B|T) = [tex]$\frac{4}{10}$[/tex]
From the Bayes' theorem :
Probability of flip results is tail when selected fruit is BANANA.
[tex]$P(T|B) = \frac{P(B|T)\ P(T)}{P(B|T) \ P(T) + P(B|H)\ P(H)}$[/tex]
[tex]$=\frac{\frac{4}{10} \times \frac{1}{2}} {\frac{4}{10} \times \frac{1}{2} + \frac{2}{16} \times \frac{1}{2}}$[/tex]
[tex]$=\frac{\frac{1}{5}}{\frac{1}{5}+\frac{1}{16}}$[/tex]
[tex]$=\frac{\frac{1}{5}}{\frac{21}{80}}$[/tex]
[tex]$=\frac{16}{21}$[/tex]
∴ [tex]$P(\ T|B\ )=\frac{16}{21}$[/tex]
You are skiing down a mountain with a vertical height of 1250 feet. The distance that you ski as you go from the top down to the base of the mountain is 3350 feet. Find the angle of elevation from the base to the tep of the mountain. Round your answer to a whole number as necessary.
Step-by-step explanation:
here is the answer to your question
Exhibit 10-7 In order to estimate the difference between the average hourly wages of employees of two branches of a department store, two independent random samples were selected and the following statistics were calculated. Downtown Store North Mall Store Sample size 25 20 Sample mean $9 $8 Sample standard deviation $2 $1 Refer to Exhibit 10-7. A 95% interval estimate for the difference between the two population means is _____. Selected Answer: b. .071 to 1.928
Answer:
[tex]E(x)=1[/tex]
Step-by-step explanation:
From the question we are told that:
Sample mean 1 [tex]\=x_1=$9[/tex]
Sample mean 1 [tex]\=x_2=$8[/tex]
Sample standard deviation 1 [tex]\sigma_1 = $2[/tex]
Sample standard deviation 1 [tex]\sigma_2 = $1[/tex]
Generally the equation for Point estimate is mathematically given by
[tex]E(x)=\=x_1-\=x_2[/tex]
[tex]E(x)=9-8[/tex]
[tex]E(x)=1[/tex]
A. Use the appropriate formula to determine the periodic deposit.
B. How much of the financial goal comes from deposits and how much comes from interest?
Periodic Deposit: $? at the end of each year
Rate: 7% compounded annually
Time: 18 years
Financial Goal: $130,000
The periodic deposit is? $
Answer:
A. Periodic deposit:
The goal is to make $130,000 by depositing a set amount every year.
This set amount is an annuity. The $130,000 is therefore the future value of the annuity after 18 years.
Future value of annuity = Annuity * Future value of annuity factor, 7%, 18 years
130,000 = Annuity * 33.9990
Annuity = 130,000 / 33.9990
= $3,823.64
B. Sources of the financial goal.
Money from deposits = Periodic deposit * no. of years
= 3,823.64 * 18
= $68,825.52
Money from interest:
= Financial goal - Money from deposits
= 130,000 - 68,825.52
= $61,174.48
Measure and record the lengths of the sides of ABC and FGH.
Answer:
can you please send the picture of the diagram.
Step-by-step explanation:
Answer:
ABC:
AB-5 units
BC-12.65 units
AC-15 units
FGH:
FG-5 units
GH-12.65 units
FH-15 units
Step-by-step explanation:
PLATO SAMPLE ANSWER
Plz help me i need this question solution
Answer:
your mom
Step-by-step explanation:
Insurance companies are interested in knowing the population percent of drivers who always buckle up before riding in a car. They randomly survey 401 drivers and find that 294 claim to always buckle up. Construct a 90% confidence interval for the population proportion that claim to always buckle up. Use interval notation, for example, [1,5].
Answer:
[0.6969, 0.7695]
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
They randomly survey 401 drivers and find that 294 claim to always buckle up.
This means that [tex]n = 401, \pi = \frac{294}{401} = 0.7332.
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.7332 - 1.645\sqrt{\frac{0.7332*0.2668}{401}} = 0.6969[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.7332 + 1.645\sqrt{\frac{0.7332*0.2668}{401}} = 0.7695[/tex]
The 90% confidence interval for the population proportion that claim to always buckle up is [0.6969, 0.7695]
At Dorcas's Hair Salon there are three hair stylists. 27% of the hair cuts are done by Martin, 30% are done by Jennifer, and 43% are done by Dorcas. Martin finds that when he does hair cuts, 6% of the customers are not satisfied. Jennifer finds that when she does hair cuts, 7% of the customers are not satisfied. Dorcas finds that when she does hair cuts, 3% of the customers are not satisfied. Suppose that a customer leaving the salon is selected at random. If the customer is not satisfied, what is the probability that their hair was done by Dorcas
Answer:
Dorcas's Hair Salon
If the customer is not satisfied, the probability that their hair was done by Dorcas is:
= 18.75%
Step-by-step explanation:
Number of hair stylists = 3
Martin Jennifer Dorcas Total
Percentage of haircuts
done 27% 30% 43% 100%
Percentage of dissatisfied
customers 6% 7% 3%
Proportion of dissatisfied
customers 37.5% (6/16) 43.75% (7/16) 18.75% (3/16)
If the customer is not satisfied, the probability that their hair was done by Dorcas
= 18.75%
Write the solution for x+5≤8 x + 5 ≤ 8 in set notation
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Answer:
{x ∈ ℝ | x ≤ 3}
Step-by-step explanation:
Subtracting 5 from both sides, we see the solution is ...
x ≤ 3
In set notation, this can be written ...
{x ∈ ℝ | x ≤ 3}
The graph represents two complex numbers, z1 and z2, as solid line vectors. Which points represent their complex conjugates?
Point A represents the complex conjugate z₁ and point L represents the complex conjugate of z₂ respectively
The reason the above values of the points of the complex conjugate are correct is as follows:
Definition:
The complex conjugate of a complex number is a complex number that
having equal magnitude in the real and imaginary part as the complex
number to which it is a conjugate, but the imaginary part of the complex
conjugate has an opposite sign to the original complex number
Graphically, the complex conjugate is a reflection of the
original complex number across the x-axis because the transformation for
a reflection of the point (x, y) across the x-axis is given as follows;
Preimage (x, y) reflected across the x-axis give the image (x, -y)
In a complex number, x + y·i. we have;
x = The real part
y = The imaginary part
The reflection of z₁(1, -2) across the x-axis gives the point A(1, 2), while the
reflection of z₂(6, -7) across the x-axis gives the point L(6, 7)
To summarize;
Point A(1, 2) is the reflection and therefore represents the complex
conjugate of z₁(1, -2) and point L(6, 7) is the reflection and therefore
represents the complex conjugate of z₂(6, -7)
Learn more about complex numbers here;
https://brainly.com/question/20365080
GIVING 25 POINTS AND BRAINIER IF ANSWERED!
What is one thing you would not do when finding the question in a word problem?
A. Look for a problem similar to the word problem you are trying to solve.
B. The question may not be directly stated.
C. So you can understand what the facts are in the word problem.
D. To define your strategy or game plan to solve the word problem.
Answer:
B. The question may not be directly stated.
