Answers
Answer:
61.76 ft^2
Step-by-step explanation:
First find the area of the rectangle without the circle
A = l*w = 14*8 =112
Then find the area of the circle
The diameter is 8 so the radius is 8/2 =4
A = pi r^2 = 3.14 * 16 =50.24
The shaded region is the rectangle minus the circle
112-50.24 =61.76 ft^2
Related Questions
If the measure of angle 2 is (5 x + 14) degrees and angle 3 is (7 x minus 14) degrees, what is the measure of angle 1 in degrees?
2 lines intersect to form 4 angles. From top left, clockwise, the angles are 1, 2, 3, 4.
88 degrees
89 degrees
90 degrees
91 degrees
Answers
Answer:
89 degrees
Step-by-step explanation:
The angle 1 is the same as angle 3.
Angle 2 is the same as angle 4.
The sum of these four angles is 360 degrees.
We have that:
Angle 2 = Angle 4 = 7x - 14
Angle 3 = Angle 1 = 5x + 14
Finding x:
Angle 1 + Angle 2 + Angle 3 + Angle 4 = 360
2*(5x + 14) + 2*(7x - 14) = 360
10x + 28 + 14x - 28 = 360
24x = 360
x = 15
Angle 1:
5x + 14 = 5*15 + 14 = 89 degrees
Answer:
I think it is B
Step-by-step explanation:
A cylindrical metal pipe has a diameter of 8.4 millimeters and a height of 10 millimeters. A hole cut out of the center has a diameter of 6 millimeters.
A smaller cylinder is cut out of a larger cylinder. The smaller cylinder has a diameter of 6 millimeters. The larger cylinder has a diameter of 8.4 millimeters. Both cylinders have a height of 10 millimeters.
What is the volume of metal in the pipe? Use 3.14 for and round the answer to the nearest tenth of a cubic millimeter.
Answers
Answer:
[tex]271.3 mm^3\\[/tex]
Step-by-step explanation:
We have to find the volume of the hole and subtract it from the volume of the cylinder.
The volume of a cylinder is given as:
[tex]V = \pi r^2h[/tex]
where r = radius
h = height
A cylindrical metal pipe has a diameter of 8.4 mm and a height of 10 mm.
Its radius is 4.2 mm. Therefore, its volume is:
[tex]V = 3.14 * 4.2^2 * 10 = 553.9 mm^3[/tex]
A hole cut out of the center has a diameter of 6 mm. Its height is also 10 mm.
Its radius is 3 mm. Therefore, its volume is:
[tex]V = 3.14 * 3^2 * 10 = 282.6 mm^3[/tex]
Therefore, the volume of metal in the pipe is:
[tex]553.9 - 282.6 = 271.3 mm^3[/tex]
Answer:
B
Step-by-step explanation:
7. How much alcohol must be added to 480 grams of hand sanitizer that is 24% alcohol to
make it a hand sanitizer that is 40% alcohol? Correct your answer to the nearest whole
number
Answers
Answer:
the amount of alcohol to be added is 128 grams
Step-by-step explanation:
Given that:
The initial mass of the hand sanitizer = 480 grams
The initial strength of the hand sanitizer = 24 %
The new strength of the hand sanitizer = 40%
The objective here is to determine the final amount of alcohol that is to be added to get the new strength of the alcohol
First; let's find the mass of alcohol in the initial hand sanitizer;
SO;
= 24 % of 480
[tex]=\dfrac{24}{100}*480[/tex]
= 115.2 grams
If y should represent the mass of the alcohol added to have 40%; we have
The new amount of the alcohol to be[tex](115.2 + y) \ grams[/tex]
The new amount of the hand sanitizer will be[tex](480 + y) grams[/tex]
∴
For the new strength of sanitizer:
40 % of (480 + y) = (115.2 + y)
[tex]0.4 *(480 + y) = (115.2 + y) \\ \\ 192 + 0.4 y = 115.2 + y \\ \\ y (1 - 0.4) = 192 - 115.2 \\ \\ y= \dfrac{76.8}{0.6} \\ \\ y = 128 \ grams[/tex]
Thus ; we can conclude that the amount of alcohol to be added is 128 grams
In the transmission of digital information, the probability that a bit has high, moderate, and low distortion is 0.02, 0.07, and 0.91, respectively. Suppose that three bits are transmitted and that the amount of distortion of each bit is assumed to be independent. Let and denote the number of bits with high and moderate distortion out of the three, respectively. Determine the following:
A. fxy(x,y).
B. fx(x).
C. E(X).
D. Are X and Y independent?
Answers
Answer:
A. (Table Attached)
B. (See Step 3)
C. 0.06 (See Step 4)
D. NOT independent (See Step 5)
Step-by-step explanation:
STEP 1:Name the probabilities:
p₁ = 0.02, p₂ = 0.07, p₃ = 0.91
q₁ = 1-p₁ = 0.98 , q₂ = 1-p₂ = 0.93 , q₃ = 0.09
Let X and Y be the number of bits with high and moderate distortion out of three.
STEP 2:A.
The function will follow multinomial distribution:
[tex]f_{XY}(x,y) = P(X=x, Y=y) = \frac{3!}{x!y!(3-x-y)!} (p_1^x)(p_2^y)(p_3^{3-x-y})[/tex]
Substitute the values and make a table.
TABLE IN ATTACHMENT
STEP 3:
B.
We calculate marginal distribution by:
[tex]P (X=x)=[/tex] ∑ [tex]P(X=x,Y=y)[/tex]
[tex]fx(x)[/tex] can be found by adding all the probabilities in each row for different value of X
For X=0 , ∑P = 0.94157441
For X=1 , ∑P = 0.057624
For X=2 , ∑P = 0.001176
For X=3 , ∑P =0.000008
STEP 4:C.
The mathematic expectation E is the sum of product of each possibility with its probabiity.
[tex]E(X)=[/tex]∑ [tex]xP(X=x)[/tex]
Find E(X):
[tex]E(X)= (0*0.9415744)+(1*0.057624)+(2*0.001176)+(3*0.000008)[/tex]
[tex]E(X)=0.06[/tex]
STEP 5:
Condition probability states:
[tex]P(A|B)=\frac{P(A,B)}{P(B)}[/tex]
It can also be written as:
[tex]f_{Y|X=1}(y)=\frac{f_{XY}(1,y)}{f_x(1)}[/tex]
Where [tex]f_x(1)\\[/tex] = 0.057624
Calculate the quotient:
[tex]Y|_{x=1}[/tex] = 0 , [tex]f_{Y|_X=1[/tex] = 0.862245
[tex]Y|_{x=1}[/tex] = 1 , [tex]f_{Y|_X=1[/tex] = 0.132653
[tex]Y|_{x=1}[/tex] = 2 , [tex]f_{Y|_X=1[/tex] = 0.000510
[tex]Y|_{x=1}[/tex] = 3 , [tex]f_{Y|_X=1[/tex] = 0
Find the dependency:
[tex]f_{XY}(y)=f_X(x)f_Y(y)[/tex]
We found that
[tex]f_{Y|_X=1[/tex] = 0.862245
Calculate [tex]f_Y(1)[/tex] from summing the column from the table
[tex]f_Y(1)=0.17428341+0.007644+0.000084\\f_Y(1)=0.18201141[/tex]
Which are not equal.
Conclusion:
X and Y are NOT Independent
Composition of the function is commuatative
Answers
Answer:
The functions g and f are said to commute with each other if g ∘ f = f ∘ g. Commutativity is a special property, attained only by particular functions, and often in special circumstances. For example, |x| + 3 = |x + 3| only when x ≥ 0. ... The composition of one-to-one functions is always one-to-one.
\
PEOPLE! THIS IS URGENT! PLEASE HELP ME!!!! If the product 3/2 · 4/3 · 5/4 · 6/5 ·…· a/b =9, what is the sum of a and b?
Answers
Answer:
35
Step-by-step explanation:
3/2 · 4/3 · 5/4 · 6/5 ·…· a/b =9
a+b=?
------
all numbers get cancelled apart from the first denominator and the last numerator:
1/2*a= 9
a= 18then
b= a-1= 18-1= 17a+b= 18+17= 35
Marcus states that angle ORP and angle LRP are a linear pair. Which best describes his statement?
Answers
Answer:
He is incorrect. Ray RO and ray RL are not opposite rays.
Step-by-step explanation:
Two angles are linear pair if they are supplementary and share a leg.
∠ORP and ∠LRP are not supplementary, because ray RO and ray RL are not opposite rays.
Therefore, ∠ORP and ∠LRP are not linear pair.
correct me if this is wrong
I wanted to compare my 5 hamsters’ average intelligence to see if they are different from the average intelligence of the 6 hamsters of another faculty member at a different university. Assume α = .01, then the cutoff for my hypothesis testing is ______.
Answers
Answer:
Step-by-step explanation:
The test to use is the t-test of independent means.
To determine the cutoff for the study then you need to find the degree of freedom and the alpha level. After the hypothesis testing, the calculated t value is then compared to the critical t value from the t distribution table using the degrees of freedom.
Do You Understand?
D
4.
1. Essential Question How does an equation
show the relationship between variables and
other quantities in a situation?
Answers
Answer:
An equation is basically a way to show a relationship of variables (x,y,a,b, etc) and numbers.
Step-by-step explanation:
Answer:
Shown by explanation.
Step-by-step explanation:
An equation shows a relationship between variables and other factors by defining the variables that are dependent and independent and how these dependent variables are related to the independent variables, this is usually as a result of a prescribed experiment where the relationship of this variables are investigated.
Also remember conditions that favour this experiment must be taken into consideration. And the experiment must always be performed under such conditions.
Solve for w: 2w<9+5w
Answers
Answer:
w > -3
Step-by-step explanation:
2w<9+5w
Subtract 5w from each side
2w-5w<9+5w-5w
-3w <9
Divide each side by -3 remembering to flip the inequality
-3w/-3 > 9/-3
w > -3
Answer:
w>-3
Step-by-step explanation:
Which of the following is the solution to 1 x1 +9 $7?
A XS -2
B. All values are solutions
C. 3-2 and 2-16
D. No solution
Answers
Answer:
d. no solution
Explanation:
Step 1 - Subtract nine from both sides of the equation
[tex]|x| + 9 \leqslant 7 \\ |x| + 9 - 9 \leqslant 7 - 9 \\ |x| \leqslant - 2[/tex]
Step 2 - Remove the absolute value
[tex] |x| \leqslant - 2 \\ 2 \leqslant x \leqslant - 2 \\ 2 \leqslant - 2[/tex]
Therefore, since positive two is not less than or equal to negative two, there is no solution.
The data from the data sample o 10 paired observations are shown:
Pair Population 1 Population 2
1 19 24
2 25 27
3 31 36
4 52 53
5 49 55
6 34 34
7 59 66
8 47 51
9 17 20
10 51 55
1. If you wish to test whether these data are sufficient to indicate that the mean for population 2 is larger than that for population 1, what are the appropriate null and alternative hypotheses?
2. Assuming that the within-pair differences are approximately normally distributed, conduct
the test using α = 0.1. What is your decision.
3. Find a 90% confidence interval for µd.
Answers
Answer:
Step-by-step explanation:
Corresponding means for population 1 and population 2 form matched pairs.
The data for the test are the differences between the mean for population 1 and mean for population 2.
μd = the mean for population 1 minus the mean for population 2.
Population 1 population 2 diff
19 24 - 5
25 27 - 2
31 36 - 5
52 53 - 1
49 55 - 6
34 34 0
59 66 - 7
47 51 - 4
17 20 - 3
51 55 - 4
Sample mean, xd
= (- 5 - 2 - 5 - 1 - 6 + 0 - 7 - 4 - 3 - 4)/10 = - 3.7
xd = - 3.7
Standard deviation = √(summation(x - mean)²/n
n = 10
Summation(x - mean)² = (- 5 + 3.7)^2 + (- - 2 + 3.7)^2 + (- 5 + 3.7)^2+ (- 1 + 3.7)^2 + (- 6 + 3.7)^2 + (0 + 3.7)^2 + (- 7 + 3.7)^2 + (- 4 + 3.7)^2 + (- 3 + 3.7)^2 + (- 4 + 3.7)^2 = 73.7
Standard - eviation = √(73.7/10
sd = 2.71
For the null hypothesis
H0: μd ≥ 0
For the alternative hypothesis
H1: μd < 0
The distribution is a students t. Therefore, degree of freedom, df = n - 1 = 10 - 1 = 9
The formula for determining the test statistic is
t = (xd - μd)/(sd/√n)
t = (- 3.7 - 0)/(2.71/√10)
t = - 4.32
We would determine the probability value by using the t test calculator.
p = 0.00097
Since alpha, 0.1 > than the p value, 0.00097, then we would reject the null hypothesis. Therefore, at 0.1 level of significance, we can conclude that these data are sufficient to indicate that the mean for population 2 is larger than that for population 1.
3) for population 1,
Mean = (19 + 25 + 31 + 52 + 55 + 34 + 59 + 47 + 17 + 51)/10 = 38.4
Summation(x - mean)² = (19 - 38.4)^2 + (25 - 38.4)^2 + (31 - 38.4)^2+ (52 - 38.4)^2 + (49 - 38.4)^2 + (34 - 38.4)^2 + (59 - 38.4)^2 + (47 - 38.4)^2 + (17 - 38.4)^2 + (51 - 38.4)^2 = 2042.4
Standard deviation, s1 = √2042.4/10 = 14.3
for population 2,
Mean = (24 + 27 + 36 + 53 + 55 + 34 + 66 + 51 + 20 + 55)/10 = 42.1
Summation(x - mean)² = (24 - 42.1)^2 + (27 - 42.1)^2 + (36 - 42.1)^2 + (53 - 42.1)^2 + (55 - 42.1)^2 + (34 - 42.1)^2 + (66 - 42.1)^2 + (51 - 42.1)^2 + (20 - 42.1)^2 + (55 - 42.1)^2 = 2248.9
Standard deviation, s2 = √2248.9/10 = 15
The formula for determining the confidence interval for the difference of two population means is expressed as
Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)
For a 90% confidence interval, we would determine the z score from the t distribution table because the number of samples are small
Degree of freedom =
(n1 - 1) + (n2 - 1) = (10 - 1) + (10 - 1) = 18
z = 1.734
x1 - x2 = 38.4 - 42.1 = - 3.7
√(s1²/n1 + s2²/n2) = √(14.3²/10 + 15²/10)
= 6.55
Margin of error = 1.734 × 6.55 = 11.4
The 90% confidence interval is
- 3.7 ± 11.4
In a game of cards, a bridge is made up of 13 cards from a deck of 52 cards. What
is the probability that a bridge chosen at random contains
6 of one suit, 4 of another, and 3 of another?
Answers
Answer:
Probabilty= 4.171. *10^-4
Step-by-step explanation:
bridge is made up of 13 cards
probability that a bridge chosen at random contains
6 of one suit, 4 of another, and 3 of another
Probabilty of 6 = 13C6
Probabilty of 4 = 13C4
Probabilty of 3 = 13C3
Then total= 53C13
Probabilty =( 13C6*13C4*13C3)/53C13
Probabilty=( 1716*715*286)/53C13
Probabilty= 4.171. *10^-4
What’s the correct answer for this?
Answers
Answer:
34°
Step-by-step explanation:
According to the theorem, "any two angles in the same segmant are congruent"
<BED = <BCD
So
<BED = 34°
ANSWER QUICK!!! Need 2 people to answer with the same answer to make sure! in the fridge there are 7 apples and 5 oranges. which of the following does NOT represent a ratio in the fridge? 7:5 5:7 5:12 7:12 6:7
Answers
You have two numbers to work with 7 and 5.
To keep the ratios the same using different numbers they would have to increase or decrease by the same multiple.
The answers would be 5:12, 7:12 and 6:7 do not represent a ratio in the fridge.
two lines intersect is more than one point
Answers
Answer:
FALSE
Step-by-step explanation:
two lines can be parallel- no intersectstwo lines intersect- one pointwhat is an example of a literal question
Answers
Answer:
an example of a literal question is "what size do you wear", "what time does the show start", "who was the protagonist in your story" etc
Step-by-step explanation:
Does coordinate s or coordinate t represent a greater number?
Answers
Answer:
t
Step-by-step explanation:
both t and s represent x axis value, t is greater as is on the right side from s
Answer: t
Step-by-step explanation: khan academy
Patricia can buy individual songs for $1.00 to download. Also, an entire album costs $10.00 to download. She can spend no more than a total of $80. She wants to buy no more than four albums, and at least 30 individual songs. The following system of inequalities represents this situation, where x is the number of individual songs and y is the number of albums.
Answers
Answer:
The system of inequalities is:
[tex]x\geq30\\\\y\leq4\\\\10x+1y\leq80[/tex]
Step-by-step explanation:
We will write each of the conditions stated in this problem
Patricia wants to buy at least 30 individual songs.
[tex]x\geq30[/tex]
She wants to buy 4 albums at most.
[tex]y\leq4[/tex]
The total expenditure has to be equal or less than $80, when each album cost $10 and each individual song cost $1.
[tex]10x+1y\leq80[/tex]
The system of inequalities is:
[tex]x\geq30\\\\y\leq4\\\\10x+1y\leq80[/tex]
A physicist examines 25 water samples for nitrate concentration. The mean nitrate concentration for the sample data is 0.165 cc/cubic meter with a standard deviation of 0.0783. Determine the 80% confidence interval for the population mean nitrate concentration. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Answers
Answer:
The 80% confidence interval for the the population mean nitrate concentration is (0.144, 0.186).
Critical value t=1.318
Step-by-step explanation:
We have to calculate a 80% confidence interval for the mean.
The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.
The sample mean is M=0.165.
The sample size is N=25.
When σ is not known, s divided by the square root of N is used as an estimate of σM:
[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{0.078}{\sqrt{25}}=\dfrac{0.078}{5}=0.016[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=25-1=24[/tex]
The t-value for a 80% confidence interval and 24 degrees of freedom is t=1.318.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_M=1.318 \cdot 0.016=0.021[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M-t \cdot s_M = 0.165-0.021=0.144\\\\UL=M+t \cdot s_M = 0.165+0.021=0.186[/tex]
The 80% confidence interval for the population mean nitrate concentration is (0.144, 0.186).
what is tan B enter your answer as a simplified fraction in the box
Answers
Answer:
7/24
Step-by-step explanation:
Tangent is opposite over adjacent. You know that the opposite leg is 14 but you don't know the adjacent.
To find the unknown leg, use Pythagorean theorem so that 50^2-14^2= leg. The length is 48.
14/48= tan B
7/24= tan B
if a propane tank has the shape of a cylindrical tank with a height of 4.2m and a radius of 1.3m how many cubic metres of propane is in the tank if it's only 50% full
Answers
Answer:
11.1 cm³
Step-by-step explanation:
V=πr²h / 2 (for half full)
V = (3.14)(1.3)²(4.2)/2
V = 11.1 cm³
The functions f(x) and g(x) are graphed.
On a coordinate plane, a curved red line with an upward arc, labeled g of x, crosses the y-axis at (0, 4) and the x-axis at (2, 0). A straight blue line with a negative slope, labeled f of x, crosses the y-axis at (0, 4) and the x-axis at (2, 0).
Which represents where f(x) = g(x)?
f(2) = g(2) and f(0) = g(0)
f(2) = g(0) and f(0) = g(4)
f(2) = g(0) and f(4) = g(2)
f(2) = g(4) and f(1) = g(1)
Answers
Answer: first answer choice
Step-by-step explanation:
They give us that f(0) and g(0) = 4 and f(2) = g(2) = 0, so the answer is simply the first one. When x=0, y=4 for both and when x=2, y=0 for both.
Hope that helped,
-sirswagger21
Answer:
A
Step-by-step explanation:
on edge
Two positive, consecutive, odd integers have a product of 143.
Complete the equation to represent finding x, the greater integer.
x(x –
) = 143
What is the greater integer?
Answers
Answer:
The answer is 13
Step-by-step explanation:
Two positive and consecutive old numbers are x and x - 2.
=> x(x - 2) = 143
=> x^2 - 2x - 143 = 0
=> x^2 + 11x - 13x - 143 = 0
=> x(x + 11) - 13(x + 11) = 0
=> (x + 11)(x - 13) = 0
=> x = -11 (invalid)
or x = 13 (valid), the remaining number is 13 - 2 = 11
=> The two numbers are 11 and 13, and the greater number is 13.
Hope this helps!
:)
Answer:
top: 2
bottom: 13
Step-by-step explanation:
step
by
step
explanation
HELP! Let f(x) = x + 1 and g(x)=1/x The graph of (fg)(x) is shown below.
Answers
Answer:
Step-by-step explanation:
all numbers except y = 1
because (f*g)(x) = 1+1/x
and 1/x cannot be equal to 0
A box on a 20 degree incline is shown with vectors radiating from a point in the center of the box. The first vector points up and parallel to the surface of the incline, labeled F Subscript f s Baseline. A second vector points toward the center of the earth, labeled F Subscript g Baseline = 735 N. A third vector is perpendicular to and away from the surface of the incline from the point, labeled F Subscript N Baseline. A fourth vector is broken into 2 components, one parallel to the surface and down the incline, labeled F Subscript g x Baseline, and one perpendicular to the surface and into the surface, labeled F Subscript g y Baseline.
A box at rest on a ramp is in equilibrium, as shown.
What is the force of static friction acting on the box? Round your answer to the nearest whole number. N
What is the normal force acting on the box? Round your answer to the nearest whole number.
Answers
The images to solve this problem is in the attachment.
Answer: [tex]F_{fs}[/tex] = 671.0 N; [tex]F_{N}[/tex] = 300 N
Step-by-step explanation: From the image in the attachment and knowing that the box is in equilibrium, i.e., the "sum" of all the forces is 0, it is possible to conclude that:
[tex]F_{fs}[/tex] = [tex]F_{gx}[/tex] and [tex]F_{N}[/tex] = [tex]F_{gy}[/tex]
Using trigonometry, shown in the second attachment, the values for each force are:
Force of Static Frictionsin 20° = [tex]\frac{F_{gx} }{F_{g} }[/tex]
[tex]F_{gx}[/tex] = [tex]F_{g}[/tex]. sin(20)
[tex]F_{gx}[/tex] = 735.0.913
[tex]F_{gx}[/tex] = 671.0
Normal Forcecos 20° = [tex]\frac{F_{gy} }{F_{g} }[/tex]
[tex]F_{gy}[/tex] = [tex]F_{g}[/tex]. cos (20)
[tex]F_{gy}[/tex] = 735.0.408
[tex]F_{gy}[/tex] = 300
The force of static friction is 671N and normal force is 300N
Answer:
Static force is 251 and the Normal force is 691.
Step-by-step explanation:
Hope this helps!! Have a great day!! :)
Find the point of diminishing returns (x comma y )for the function R(x), where R(x) represents revenue (in thousands of dollars) and x represents the amount spent on advertising (in thousands of dollars).
Answers
Complete Question
The complete question is shown on the first uploaded image
Answer:
The point of diminishing returns (x , y ) is (11, 21462)
Step-by-step explanation:
From the question we are told that
The function is [tex]R(x) = 10,000 -x^3 - 33x^2 + 800x , \ \ 0 \le x \le 20[/tex]
Here R(x) represents revenue (in thousands of dollars) and x represents the amount spent on advertising (in thousands of dollars).
Now differentiating R(x) we have
[tex]R'(x) = -3x^2 +66x + 800[/tex]
Finding the second derivative of R(x)
[tex]R''(x) = -6x +66[/tex]
at inflection point [tex]R''(x) = 0[/tex]
So [tex]-6x +66 = 0[/tex]
=> [tex]x= 11[/tex]
substituting value of x into R(x)
[tex]R(x) = 10,000 -(11)^3 - 33(11)^2 + 800(11) ,[/tex]
[tex]R(x) = 21462[/tex]
Now the point of diminishing returns (x , y ) i.e (x , R(x) ) is
(11, 21462)
I need help please help
Answers
Answer:
Step-by-step explanation:
Note that 28 + 110 + 42 = 180, and that 28 + 42 + 110 = 180 also.
Since all three angles of one triangle are the same as the corresponding angles of the other triangle, the triangles are similar.
An article reported the following data on oxidation-induction time (min) for various commercial oils:87 105 130 160 180 195 135 145 213 105 145151 152 136 87 99 92 119 129(a) Calculate the sample variance and standard deviation. (Round your answers to three decimal places.)s^2 = ________. min^2s = ________. min(b) If the observations were reexpressed in hours, what would be the resulting values of the sample variance and sample standard deviation? Answer without actually performing the reexpression. (Round your answer to three decimal places.)s^2 =______ hr^2s = ______hr
Answers
Answer:
Step-by-step explanation:
Mean = (87 + 105 + 130 + 160 + 180 + 195 + 135 + 145 + 213 + 105 + 145 + 151 152 + 136 + 87 + 99 + 92 + 119 + 129)/19 = 129
Variance = (summation(x - mean)²/n
Standard deviation = √(summation(x - mean)²/n
n = 19
Variance = [(87 - 129)^2 + (105 - 129)^2 + (130 - 129)^2+ (160 - 129)^2 + (180 - 129)^2 + (195 - 129)^2 + (135 - 129)^2 + (145 - 129)^2 + (213 - 129)^2 + (105 - 129)^2 + (145 - 129)^2 + (151 - 129)^2 + (152 - 129)^2 + (136 - 129)^2 + (87 - 129)^2 + (99 - 129)^2 + (92 - 129)^2 + (119 - 129)^2 + (129 - 129)^2]/19 = 23634/19 1243.895 min
Standard deviation = √1243.895 = 35.269 min
60 minutes = 1 hour
Converting the variance to hours,
Each division would have been divided by 60². 60² can be factorized out
Variance = 23634/60² = 6.565 hours
Converting the standard deviation to hours, it becomes
√6.565 = 2.562 hours
Kyle is making a frame for a rectangular piece of art. The length of the frame is 3 times the width, as shown below.
TIME REMAINING
54:06
3x
x
If Kyle uses 10 feet of wood to make the frame, what is the length of the frame? Write the answer in decimal form,
0.75
4.60
0.00
Answers
Answer:
3.75 feet
Step-by-step explanation:
The length of the frame is 3 times the width.
Let the width be x.
The length will be 3x.
Kyle uses 10 feet of wood to make the frame. This means that the perimeter is 10 feet.
The perimeter of a rectangle is:
P = 2(L + W)
=> 10 = 2(3x + x)
=> 10/2 = 4x
5 = 4x
=> x = 5/4 = 1.25 feet
The width is 1.25 feet. The length is therefore:
1.25 * 3 = 3.75 feet
