Pls help need it right now :((
If the standard deviation of of the values 2,4, 6,8 is 2.236, the the standard deviation of the values 4, 8, 12, 20 is?
Answers
Answer:
5.916
count N : 4
Sum, Ex : 44
Mean , M
Variance , o2 : 35
Step-by-step explanation:
we are creating the mean value of the squares of the differences of each data point to the mean value (variance), and then we pull the square root to bring the differences back to the same dimension as the basic data points.
and since we are dealing with the whole "population" of data points and not only with a sample of a much larger set of data points, that mean value of the differences is a true mean value (divide by n = the number of data points). if we would deal with a sample of a much larger population, we would divide by n-1.
so, how does this work in practice ?
let's go first for the given example :
2, 4, 6, 8.
the mean value is : (2+4+6+8)/4 = 20/4 = 5.
the variance (mean value of the squared differences of each data point to the mean value) :
((2-5)² + (4-5)² + (6-5)² + (8-5)²)/4 = (9+1+1+9)/4 = 20/4 = 5.
the standard deviation is the square root of the variance.
so,
SD = sqrt(5) = 2.236067977...
now for the given problem :
4, 8, 12, 20
the mean value is : (4+8+12+20)/4 = 44/4 = 11.
the variance (mean value of the squared differences of each data point to the mean value) :
((4-11)² + (8-11)² + (12-11)² + (20-11)²)/4 = (49+9+1+81)/4 = 140/4 = 35.
the standard deviation is the square root of the variance.
so,
SD = sqrt(35) = 5.916079783... ≈ 5.916
Related Questions
Find the local linear approximation L(x) of the function f(x) = 5−x^2 at x = 2.
Use this to estimate f(2.1).
Answers
Answer:
L(x)=-4x+9
L(2.1)=0.6
Step-by-step explanation:
It's asking us to find the tangent line to curve f(x) = 5−x^2 at x = 2.
Theb use this to estimate f(2.1).
To find slope of tangent line, we must differentiate and then plug in 2 for x.
f'(x)=0-2x by constant and power rule.
f'(x)=-2x
So the slope of the tangent line is -2(2)=-4.
A point on this tangent line shared by the curve is at x=2. We can find it's corresponding y-value using f(x)=5-x^2.
f(2)=5-(2)^2
f(2)=5-4
f(2)=1
So let's rephrase the question a little.
What's the equation for a line with slope -4 and goes through point (2,1).
Point-slope form y-y1=m(x-x1) where m is slope and (x1,y1) is a point on the line.
Plug in our information: y-1=-4(x-2).
Distribute: y-1=-4x+8
Add 1 on both sides: y=-4x+9
Let's call this equation L(x), an expression to approximate value for f near x=2.
L(x)=-4x+9
Now the appropriation at x=2.1:
L(2.1)=-4(2.1)+9
L(2.1)=-8.4+9
L(2.1)=0.6
If we did plug in 2.1 into given function we get 5-(2.1)^2=0.59 . This is pretty close to our approximation above.
A contributor for the local newspaper is writing an article for the weekly fitness section. To prepare for the story, she conducts a study to compare the exercise habits of people who exercise in the morning to the exercise habits of people who work out in the afternoon or evening. She selects three different health centers from which to draw her samples. The 57 people she sampled who work out in the morning have a mean of 5.2 hours of exercise each week. The 70 people surveyed who exercise in the afternoon or evening have a mean of 4.5 hours of exercise each week. Assume that the weekly exercise times have a population standard deviation of 0.6 hours for people who exercise in the morning and 0.4 hours for people who exercise in the afternoon or evening. Let Population 1 be people who exercise in the morning and Population 2 be people who exercise in the afternoon or evening.
Step 1 of 2: Construct a 95% confidence interval for the true difference between the mean amounts of time spent exercising each week by people who work out in the morning and those who work out in the afternoon or evening at the three health centers. Round the endpoints of the interval to one decimal place, if necessary.
Answers
Answer:
The 95% confidence interval for the true difference between the mean amounts of time spent exercising each week by people who work out in the morning and those who work out in the afternoon or evening at the three health centers is (0.5, 0.9).
Step-by-step explanation:
Before building the confidence intervals, we need to understand the central limit theorem and subtraction of normal variables.
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.
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
In the morning:
Sample of 57, mean of 5.2, standard deviation of 0.6, so:
[tex]\mu_1 = 5.2[/tex]
[tex]s_1 = \frac{0.6}{\sqrt{57}} = 0.0795[/tex]
In the afternoon/evening:
Sample of 70, mean of 4.5, standard deviation of 0.4, so:
[tex]\mu_2 = 4.5[/tex]
[tex]s_2 = \frac{0.2}{\sqrt{70}} = 0.0239[/tex]
Distribution of the difference:
[tex]\mu = \mu_1 - \mu_2 = 5.2 - 4.5 = 0.7[/tex]
[tex]s = \sqrt{s_1^2+s_2^2} = \sqrt{0.0795^2 + 0.0239^2} = 0.083[/tex]
Confidence interval:
The confidence interval is:
[tex]\mu \pm zs[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower bound of the interval is:
[tex]\mu - zs = 0.7 - 1.96*0.083 = 0.5[/tex]
The upper bound of the interval is:
[tex]\mu + zs = 0.7 + 1.96*0.083 = 0.9[/tex]
The 95% confidence interval for the true difference between the mean amounts of time spent exercising each week by people who work out in the morning and those who work out in the afternoon or evening at the three health centers is (0.5, 0.9).
A control variable is:
A. Measured to show the effect of a change.
B. Kept the same to make an experiment a fair test.
C. Collected to draw conclusions.
D. Changed to test a hypothesis.
It’s in between a and b, they’re both technically true no?
Answers
Answer:
B: kept the same to make an experiment a faith test
please help me asapp
Answers
Answer:
C. 12, 8, 5
Step-by-step explanation:Side lengths of any triangle must conform to the triangle inequality theorem, which says that the sum of the lengths of any of the two sides of the triangle is greater than the length of the third side.
This means:
a + b > c
a + c > b
b + c > a
Let's check each of the options to see which set are possible lengths for a triangle:
A. 6, 5, 11
6 + 11 > 5 ===> 17 > 5
5 + 11 > 6 ===> 16 > 6
6 + 5 > 11 ===> 11 > 11 (INCORRECT. Does not confirm to tye theorem)
Therefore, this set cannot be possible side lengths for a triangle.
B. 8, 1, 2
8 + 1 > 2 ===> 9 > 2
1 + 2 > 8 ===> 3 > 8 (INCORRECT)
8 + 2 > 1 ===> 10 > 1
This set cannot be possible side lengths for a triangle.
C. 12, 8, 5
12 + 8 > 5 ===> 20 > 5
8 + 5 > 12 ===> 13 > 12
12 + 5 > 8 ===> 17 > 8
All are correct, therefore these are possible side lengths for a triangle.
write your answer in simplest radical form
Answers
Answer:
a = 4[tex]\sqrt{3}[/tex]
Step-by-step explanation:
Using the cosine ratio in the right triangle and the exact value
cos60° = [tex]\frac{1}{2}[/tex] , then
cos60° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{2\sqrt{3} }{a}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
a = 4[tex]\sqrt{3}[/tex]
What is the length of AC?
a. 3ft
b. 4ft
c. 18ft
d. 12ft
plz hurry
Answers
d. 12ft
Answer:
Solution given:
∆ABC is similar to∆MBN
since their corresponding side are proportional.
so
AB/MB=AC/MN
[since AM=BM=4ft
AB=AM+BM=4+4=8ft]
8/4=AC/6
doing crisscrossed multiplication
2*6=AC
AC=12ft
PLEASE HELP FAST!! WILL GIVE FIRST PERSON THAT RESPONDS A HIGH RATING AND POINTS!
Answers
Answer:
Step-by-step explanation:
3
3. (02.01)
Solve for x:
wim
(x – 4) = 2x. (1 point)
2
-2
-8
-4
Answers
x = -4
Step-by-step explanation:
(x - 4) = 2x
We need an x that when is subtracted by 4 is equal to multiplying it by 2
((-4) - 4) = 2(-4)
(-8) = (-8)
Therefore x = -4
Solve x2 + 8x + 22 = 0 by completing the square.
Question 20 options:
A)
x = –4 + i√ 6 , x = –4 – i√ 6
B)
x = –4 + √ 14 , x = –4 – √ 14
C)
x = –4 + i√ 14 , x = –4 – i√ 14
D)
x = –4 + √ 6 , x = –4 – √ 6
Answers
Answer:
A)
Step-by-step explanation:
the solution of a squared equation is
x = (-b ± sqrt(b² - 4ac)) / (2a)
in our case
a = 1
b = 8
c = 22
x = (-8 ± sqrt(64 - 88))/2 = (-8 ± sqrt(-24))/2 =
= (-8 ± sqrt(4×-6))/2 = (-8 ± 2×sqrt(-6))/2 =
= -4 ± sqrt(-6) = -4 ± i×sqrt(6)
a. 1.5
b. 2.3
c. 2.4
d. 1.9
Answers
Answer:
2.3
Step-by-step explanation:
.5 - .3 = .2
.8 - .5 = .3
1.2 - .8 = .4
1.7 - 1.2 = .5
We should add .6 next
1.7+.6 = 2.3
Joel and Matt must together save at least $50.00 to buy a special present for their mother.
Joel saves twice as much as Matt. Which inequality best represents the situation if x
represents the amount of money that Matt saves?
Answers
Answer:
Option (2)
Step-by-step explanation:
Let the savings of Joel = $y
And the savings of Matt = $x
They jointly save at least $50 to buy a special present.
Therefore, equation for this condition will be,
x + y ≥ 50 --------(1)
Joel saves twice as much as Matt.
Equation for this condition will be,
y = 2x ------ (2)
By substituting the value of 'y' in the equation,
x + 2x ≥ 50
Therefore, Option (2) will be the answer.
For a standard normal distribution, find:
P(z > c) = 0.058
Find c.
Answers
Answer:
1.572
Step-by-step explanation:
For a standard normal distribution,
P(z > c) = 0.058
To obtain C ; we find the Zscore corresponding to the proportion given, which is to the right of the distribution ;
Using technology or table,
Zscore equivalent to P(Z > c) = 0.058 is 1.572
Hence, c = 1.572
1
What is the perimeter of a rectangle
whose length is 5 feet and whose width
is 3.5 feet?
O 8.5 ft.
O 16.5 ft.
O 17 ft.
O 17.5 ft.
Answers
Answer:
17ft
Step-by-step explanation:
5*2 + 3.5*2=17
Explanation
Perimeter of rectangle = 2(l+b)
As length = 5 ft and breadth/width = 3.5 ft
So,
=2 ( 5+3.5)
=2 ( 8.5 )
= 17 feet
I hope it helps!
pls mark me brainliest :)
i need help ON THIS PLS
Answers
Answer:
No, because the ratio of pay to hours is not the same for each pair of value.
A newspaper advertisement offers a $9,000 car for nothing down and for 36 easy monthly payments of $317.50 what is the simple interest rate?
Answers
Answer:
27%
Step-by-step explanation:
Let x = simple interest rate
$9000 / 36 = $250 per month
$250x = 317.5
Divide both sides by 250
250x/250 = 317.5/250
x = 1.27
Let's check
250 x 1.27 = 317.5
If you were to multiply by .27 then it would just go down
250 x .27 = 67.5
Which of the following graphs represents the line that passes through (–2, –3) and has a slope of 2/3?
Answers
Fourth graph
Step-by-step explanation:
It passes through the point (-2, -3) and has a slope of 2/3
Answer:
Step-by-step explanation:
−12x+y=10 in slope-intercept form
Answers
Answer:
y=12x+10
Step-by-step explanation:
Slope-intercept form is y=mx+b
1. Add -12x to both sides of the equation
A simple random sample of 400 individuals provides 112 Yes responses. (a) What is the point estimate of the proportion of the population that would provide Yes responses
Answers
Answer:
The point estimate of the proportion of the population that would provide Yes responses is 0.28.
Step-by-step explanation:
Point estimate of the proportion of the population that would provide Yes
The sample proportion of yes responses.
In the sample:
112 yes responses in the sample of 400, so:
[tex]p = \frac{112}{400} = 0.28[/tex]
The point estimate of the proportion of the population that would provide Yes responses is 0.28.
Mike wants to buy a scooter worth R10000 but cannot afford so he opts for the hire purchase agreement which requires a 13% deposit and a 24 equal monthly installments at a rate of 15% per annum compounded monthly
A.How much will his deposit be?
B.calculate how much does he still need to pay after the deposit
C.calculate the monthly installment
Answers
Answer: I think the answer is A
Step-by-step explanation:
What are the solutions of this quadratic equation?
4x2 + 3 = 4x + 2
Answers
Answer:
A. x = 1/2
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesAlgebra I
Terms/CoefficientsFactoringStandard Form: ax² + bx + c = 0Solving quadraticsStep-by-step explanation:
Step 1: Define
Identify
4x² + 3 = 4x + 2
Step 2: Solve for x
[Equality Property] Rewrite in standard form: 4x² - 4x + 1 = 0Factor: (2x - 1)² = 0Solve: x = 1/2Find the missing side of the triangle
Answers
Answer:
x = 15
Step-by-step explanation:
Pytago: a^2 + b^2 = c^2
x = [tex]\sqrt{25^{2} -20^{2} }[/tex] = 15
write your answer in simplest radical form.
Answers
9514 1404 393
Answer:
√3
Step-by-step explanation:
The ratio of the short sides to the hypotenuse in an isosceles right triangle is ...
1 : 1 : √2
This means ...
p·√2 = √6
p = (√6)/(√2) = √(6/2)
p = √3
What is the volume of the following rectangular prism?
Answers
Answer:
44/3
Step-by-step explanation:
V=L*W*H
WH=22/3
V=2*(22/3)
Find the area of the triangle with the given
Answers
Answer:
616.2442
area to the nearest whole number=616
Step-by-step explanation:
using formula 1/2absinx
where a =44,b=29 ,x=105
1/2x44x29xsin105
44x29=1276
1276÷2=638
638 x sin 105
the sin of 105 is 0.9659
if u are using a four figure table where u can't find 105 under sin of angle
u simply subtract 105 from 180=75
638 x 0.9659 =616.2442
approx.616
Six math books, four physics books and three chemistry books are arranged on a shelf.
How many arrangements are possible if all books of the same subject are grouped together?
Answers
Answer:
622,080
Step-by-step explanation:
The total number of subjects is 3
= 3×2×1
= 6
Six maths book
= 6×5×4×3×2×1
= 720
Four physics book
= 4×3×2×1
= 24
Three chemistry book
= 3×2×1
= 6
6×720×24×6
= 622,080
Hence if the books are grouped together 622,080 arrangement is possible
Which system of inequalities is shown in the graph?
36 > (x + 3)2 + (y – 2)2 and 16 > (x – 4)2 + y2
36 > (x – 2)2 + (y + 3)2 and 16 > (x – 4)2 + y2
36 < (x + 3)2 + (y – 2)2 and 16 > (x – 4)2 + y2
36 < (x – 2)2 + (y + 3)2 and 16 > (x – 4)2 + y2
Answers
Answer:
(x-2)^2 +(y+3)^2 >36 and (x-4)^2 +(y)^2 < 16
Step-by-step explanation:
The equation of a circle is (x-h)^2+(y-k)^2 = r^2
We are outside the yellow circle The yellow circle has a radius of 6 and a center at (2, -3)
(x-2)^2 +(y--3)^2 > 6^2
(x-2)^2 +(y+3)^2 > 36
We are also inside the blue circle which has a radius of 4 and a center of (4,0)
(x-4)^2 +(y-0)^2 < 4^2
(x-4)^2 +(y)^2 < 16
Answer:
D.) 36 < (x – 2)2 + (y + 3)2 and 16 > (x – 4)2 + y2
Step-by-step explanation:
Edge 2022
The pair of figures to the right are similar. The area of one figure is given. Find the area of the other figure to the nearest whole number. Area of larger triangle = 165 ft^2 Thank you!!
Answers
9514 1404 393
Answer:
73 ft²
Step-by-step explanation:
The ratio of areas is the square of the ratio of linear dimensions.
smaller area = larger area × ((10 ft)/(15 ft))² = 165 ft² × (4/9)
smaller area = 73 1/3 ft² ≈ 73 ft²
Answer:
Area of the smaller triangle = 73 square feet
Step-by-step explanation:
Area of the larger triangle = 165 square feet
Area of a triangle = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
[tex]\frac{1}{2}(\text{Base})(\text{Height})=165[/tex]
[tex]\frac{1}{2}(15)(\text{Height})=165[/tex]
Height = 22 ft
Since, both the triangles are similar.
By the property of similar triangles,
Corresponding sides of the similar triangles are proportional.
Let the height of smaller triangle = h ft
Therefore, [tex]\frac{h}{22}=\frac{10}{15}[/tex]
h = [tex]\frac{22\times 10}{15}[/tex]
h = 14.67 ft
Area of the smaller triangle = [tex]\frac{1}{2}(10)(14.67)[/tex]
= 73.33
≈ 73 square feet
A boat has a rip-hole in the bottom while 20 miles away from the shore. The water comes in at a rate of 1.5 tons every minute, and the boat would sink after 70 tons of water came in. How fast must the boat go in order to reach the shore before sinking?
Answers
Answer:
t = 70 tons/1.5 tons/min = 46.7 min = 2800 sec before boat sinks
S = V * t
V = S / t = 20 mi * 5280 ft/mi / 2800 sec = 37.7 ft/sec
Since 88 ft/sec = 60 mph
the speed is 60 * 37.7 / 88 = 25.7 mph
From quadrilateral ABCD is a quadrilateral with area of 48 square units, find the length of AC.
A. 48/5
B. 24
C. 24/5
D. 48
Answers
Step-by-step explanation:
I do hope that you understand through the steps in the attachment, if not kindly reach out!
What is the common ratio for this geometric sequence?
27, 9, 3, 1, ...
Answers
Answer:
1/3
Step-by-step explanation:
common ratio is
9÷27=1/3
3÷9=1/3
1÷3=1/3
therefore common ratio is 1/3
Answer: 1/3
Step-by-step explanation:
Let us confirm that this is a geometric sequence. 9/27 = 1/3 and 3/9 = 1/3. Thus, the common ratio is 1/3.
