Answer:
Means:
1.55
1.73
Standard Deviation:
0.1434
0.1338
Coefficient of variation:
9.2
7.7
the limited data listed here shows evidence of stealing by the security service company's employees.
Step-by-step explanation:
Given data:
security Service Company Other Companies
x₁ x₂
1.5 1.8
1.7 1.9
1.6 1.6
1.4 1.7
1.7 1.8
1.5 1.9
1.8 1.6
1.4 1.5
1.4 1.7
1.5 1.8
n₁ = 10 n₂ = 10
To find:
coefficient of variation for each of the two samples
Solution:
The formula for calculating coefficient of variation of sample is:
Coefficient of Variation (CV) = (Standard Deviation / Mean) * 100%
Calculate Mean for Security Service Company data:
Mean = (Σ x₁) / n₁
= (1.5 + 1.7 + 1.6 + 1.4 + 1.7 + 1.5 + 1.8 + 1.4 + 1.4 + 1.5) / 10
= 15.5 / 10
Mean = 1.55
Calculate Standard Deviation for Security Service Company data:
Standard Deviation = √∑(x₁ - Mean)²/n₁-1
= √∑(1.5-1.55)² + (1.7-1.55)² + (1.6-1.55)² + (1.4-1.55)² + (1.7-1.55)² + (1.5-1.55)² + (1.8-1.55)² + (1.4-1.55)² + (1.4-1.55)² + (1.5-1.55)² / 10-1
=√∑ (−0.05)² + (0.15)² + (0.05)² + (−0.15)² + (0.15)² + (−0.05)² + (0.25)² + (−0.15)² + (−0.15)² + (−0.05)² / 10 - 1
= √∑0.0025 + 0.0225 + 0.0025 + 0.0225 + 0.0225 + 0.0025 + 0.0625 + 0.0225 + 0.0225 + 0.0025 / 9
= √0.185 / 9
= √0.020555555555556
= 0.14337208778404
= 0.143374
Standard Deviation = 0.143374
Coefficient of Variation for Security Service Company:
CV = (Standard Deviation / Mean) * 100%
= (0.143374 / 1.55) * 100
= 0.09249935 * 100
= 9.249935
CV = 9.2
CV = 9.2%
Calculate Mean for Other Companies data:
Mean = (Σ x₂) / n₂
= (1.8 + 1.9 + 1.6 + 1.7 + 1.8 + 1.9 + 1.6 + 1.5 + 1.7 + 1.8) / 10
= 17.3 / 10
Mean = 1.73
Calculate Standard Deviation for Other Companies data:
Standard Deviation = √∑(x₂-Mean)²/n₂-1
= √∑[(1.8-1.73)² + (1.9-1.73)² + (1.6-1.73)² + (1.7-1.73)² + (1.8-1.73)² + (1.9-1.73)² + (1.6-1.73)² + (1.5-1.73)² + (1.7-1.73)² + (1.8-1.73)²] / 10 - 1
= √∑ [(0.07)² + (0.17)² + (-0.13)² + (-0.03)² + (0.07)² + (0.17)² + (-0.13)² + (-0.23)² + (-0.03)² + (0.07)²] / 9
= √∑ (0.0049 + 0.0289 + 0.0169 + 0.0009 + 0.0049 + 0.0289 + 0.0169 + 0.0529 + 0.0009 + 0.0049) / 9
= √(0.161 / 9)
= √0.017888888888889
= 0.13374935098493
= 0.13375
Standard Deviation = 0.13375
Coefficient of Variation for Other Companies:
CV = (Standard Deviation / Mean) * 100%
= (0.13375 / 1.73) * 100
= 0.077312 * 100
= 7.7312
CV = 7.7
CV = 7.7%
Yes, the limited data listed here shows evidence of stealing by the security service company's employees because there is a significant difference in the variation.
please show me step by step
Answer:
Step-by-step explanation:
Picture
Find the measure of F. A. 44 B. 88 C. 90 D. 46
Answer:
A. 44º
Step-by-step explanation:
The sum of internal angles in a triangle is equal to 180 degrees, whereas the sum for a square is equal to 360 degrees. Given that three triangles depicted on figure constructs a square, it is to conclude that each is an isosceles triangle. The following relations are presented:
1) [tex]e + 92^{\circ} = 180^{\circ}[/tex] Given
2) [tex]a = b[/tex], [tex]c = d[/tex] Given
3) [tex]a + b + 92^{\circ} = 180^{\circ}[/tex] Given.
4) [tex]c + d + e = 180^{\circ}[/tex] Given.
5) [tex]b + c = 90^{\circ}[/tex] Given.
6) [tex]2\cdot a + 92^{\circ} = 180^{\circ}[/tex] 2) in 3)
7) [tex]a = 44^{\circ}[/tex] Algebra
8) [tex]b = 44^{\circ}[/tex] By 2)
9) [tex]b= f[/tex] Alternate internior angles.
10) [tex]f = 44^{\circ}[/tex] By 8). Result
Hence, the answer is A.
34% of working mothers do not have enough money to cover their health insurance deductibles. You randomly select six working mothers and ask them whether they have enough money to cover their health insurance deductibles. The random variable represents the number of working mothers who do not have enough money to cover their health insurance deductibles.
Required:
Construct a binomial distribution using n= 0.6 and p=0.34
Answer:
solution below
Step-by-step explanation:
The question says 6 working mother's were selected so n = 6 not 0.6
We are expected to find
P(X = 0,1,2,3,4,4,6)
1. When x = 0
6C0*(0.34)⁰*(0.66)⁶
= 1 *1* 0.827
= 0.0827
2. When X = 1
6C1*(0.34)¹*(0.66)⁵
= 6 x 0.34 x 0.252
= 0.2555
3. When X = 2
6C2*(0.34)²*(0.66)⁴
= 15 x 0.1156 x 0.1897
= 0.3289
4. When x = 3
6C3*(0.34)³*(0.66)³
20 x 0.039304 x 0.2875
= 0.2599
5. When X = 4
6C4*(0.34)⁴*(0.66)²
= 15 x 0.01336 x 0.4356
= 0.8729
6. When x = 5
6C5*(0.34)⁵*(0.66)¹
= 6 x 0.0045 x 0.66
= 0.01782
7. When x = 6
6C6*(0.34)⁶*(0.66)⁰
1 x 0.0015 x 1
= 0.0015
Jupiter orbits the sun at a rate of 8 miles per second. How far does Jupitertravel in one day? Tip: There are 86400 seconds in a day.
Answer:
Jupiter travels 691200 miles a day
Step-by-step explanation:
I just did 86400 x 8
Plz give brainliest
(-1, 4) and (-2, 2).
Answer:
Slope : 2
slope-intercept: y = 2x + 6
Point-slope (as asked): y - 4 = 2 (times) (x + 1)
standered: 2x - y = -6
Step-by-step explanation:
What number comes next in this series 7,10,10,13,16,16,
Given the central angle, name the arc formed.
Major arc for ∠EQD
A. EQDˆ
B. GDFˆ
C. EGDˆ
D. EDˆ
9514 1404 393
Answer:
C. EGD
Step-by-step explanation:
A major arc is typically named using the end points and a point on the arc. Here, the end points are E and D, and points on the major arc include C, G, and F. The major arc ED could be named any of
arc ECDarc EGD . . . . choice Carc EFDOf course, the reverse of any of these names could also be used: DCE, DGE, DFE.
4. Write 3x(x + 4)(x - 1) in standard form.
3x3 + 9x2 - 12x
3x3
- 12x + 9x2
3x3 + 9x2 - 12x + 1
1 - 12x + 9x2 + 3x3
Answer:
i thank the ans id 450
Step-by-step explanation:
If you want to turn a ball into a giant water balloon, how many cubic feet of lake water can you fill it with if the radius of this balloon is 1.5 feet?
Answer:
14.13 cubic feet of lake water can fill the given balloon.
Step-by-step explanation:
concept used:
volume of sphere = 4/3 [tex]\pi r^3[/tex]
where r is the radius of sphere
we take [tex]\pi[/tex] = 3.14
_____________________________________
shape of balloon can be taken as spherical.
Amount water filled in the balloon will be equal to capacity of balloon which is equal to volume of spherical balloon.
Given radius of balloon = 1.5 feet
Thus, volume of balloon = 4/3 [tex]\pi[/tex] 1.5^3 = 4/3*3.14*1.5^3
volume of balloon = 42.39/3 = 14.13 cubic feet
Thus, 14.13 cubic feet of lake water can fill the given balloon.
Suppose that 10% of all steel shafts produced by a process are nonconforming but can be reworked (rather than having to be scrapped). Consider a random sample of 200 shafts, and let X denote the number among these that are nonconforming and can be reworked. What is the (approximate) probability that X is:
a. Less than 30?
b. Between 15 and 25 (inclusive)?
Answer:
a?
Step-by-step explanation:
r-(-4x - (y + y)); use x = -4, and y = -3 evaluate
Answer:
insert values of x and y
r - ( -4(-4) - ( -3-3))
r - ( 16 +6 )
r - 22
Doneeeeeeeeeeeeeeeeee3
One of two small restaurants is chosen at random with equally likely probability, and then an employee is chosen at random from the chosen restaurant. Restaurant #1 has 10 full-timers and 6 part-timers. Restaurant #2 has 7 full-timers and 9 part-timers. What is the probability that Restaurant #1 was chosen at random, given that a full-time employee was chosen? Your answers should be rounded to 4 digits after the decimal.
Answer:
P(1 |F) = 10/17
Step-by-step explanation:
Let events
1 = restaurant 1
2 = restaurant 2
F = full-time worker chosen
P = part-time worken chosen
P(1 and F) = 1/2 * 10/16 = 5/16
P(2 and F) = 1/2 * 7/16 = 7/32
P( (1 or 2) and F ) = P(F) = 5/16+7/32 = 17/32
P(1 | F) Probability of choosing restaurant 1 given a full-time was chosen
= P(1 and F) / P(F)
= 5/16 / (17/32)
= 5/16 * 32/17
= 10 / 17
The sum of two numbers is 21. Five times the first number added to 2 times the second number is 66. Find the two numbers.
What is the slope of the line shown below?
A. -3/2
B. 3/2
C. 2/3
D. -2/3
Answer:
2/3
Step-by-step explanation:
We can find the slope using the slope formula
m = ( y2-y1)/(x2-x1)
= (1- -7)/(9 - -3)
= ( 1+7)/( 9+3)
= 8/12
Simplifying
= 2/3
Answer:
C. 2/3
Step-by-step explanation:
You can use the equation: [tex]y_{2} - y_{1}/x_{2} - x_{1}[/tex] to find the slope.
y2 is equal to the y coordinate of the second point: 1
y1 is equal to the y coordinate of the first point: -7
x2 is equal to the x coordinate of the second point: 9
x1 is equal to the x coordinate of the first point: -3
So if you plug these values into the equation, you will get:
1 - (-7)/ 9- (-3)
= 1 + 7/ 9 + 3
= 8/12
= 2/3
What is the y value when x is -5? What about 5?
I’ve done all three functions and the answers are -9, 24 and -4 but I don’t know which one to answer as the y value with. Please help.
A state lottery sells instant-lottery scratch tickets. 12% of the tickets have prizes. Neil goes to the store and buys 10 tickets. What is the probability that exactly three of Neil's tickets will have prizes?
Answer:
The probability of success is .12
The probability of failure is .88
According to the binomial theorem the probability of 3 success is
10! / (3! * 7!) * .12^3 * .88^7 = .085
a sheet metal worker earns $26.80 per hour after receiving a 4.5% raise. what was the sheet metal worker's hourly pay before raise? Round your answer to the nearest cent
Answer
$25.59
Step-by-step explanation:
subtract by percentage or you can also do:
100% - 4.5% = 95.5%
95.5% x $26.80 = $25.594
IF ROUNDED: $25.59
Answer:
$25.65
Step-by-step explanation:
Let the original hourly rate be r.
Then 1.045r + $26.80/hr.
Dividing both sides by 1.045, we get:
$26.80/hr
r = ------------------ = $25.65 This was the before-raise pay rate.
1.045
Which, if any, pair of sides are parallel? AB II DC and AD II BC Cannot be determined AB II DC only AD II BC only
Answer:
120%
Step-by-step explanation:
Identify the inverse function of f(x) = VX - 2 + 3.
Answer:
[tex]\huge\boxed{f^{-1}(x) = (x-3)^2+2}[/tex]
Step-by-step explanation:
[tex]f(x) = \sqrt{x-2} + 3[/tex]
Replace y = f(x)
[tex]y = \sqrt{x-2} + 3[/tex]
Exchange x and y
[tex]x = \sqrt{y-2}+3[/tex]
Solve for y
[tex]x = \sqrt{y-2}+3[/tex]
Subtracting both sides by 3
[tex]x - 3 = \sqrt{y-2}[/tex]
Taking square on both sides
[tex](x-3)^2 = y -2[/tex]
Adding 2 to both sides
[tex]y = (x-3)^2+2[/tex]
Substitute y = [tex]f^{-1}(x)[/tex]
[tex]f^{-1}(x) = (x-3)^2+2[/tex]
Answer:
[tex] \boxed{ {f}^{ - 1} (x) = {(x - 3)}^{2} + 2}[/tex]Option D is the correct option
Step-by-step explanation:
[tex] \mathsf{f(x) = \sqrt{x - 2} + 3}[/tex]
Replace f(x) with y
[tex] \mathsf{y = \sqrt{x - 2} + 3}[/tex]
Interchange variables
[tex] \mathsf{x = \sqrt{y - 2} + 3}[/tex]
[tex] \mathsf{{(x - 3)}^{2} = {( \sqrt{y - 2)} }^{2} }[/tex]
[tex] \mathsf{ {(x - 3)}^{2} = y - 2}[/tex]
[tex] \mathsf{ y = {(x - 3)}^{2} + 2}[/tex]
Replace y with f ⁻¹( x )
[tex] \mathsf{ {f}^{ - 1} (x) = {(x - 3)}^{2} + 2}[/tex]
Hope I helped!
Best regards!
Each Friday, the sixth grade students in Mr. Shin's physical education class spend the first five minutes doing crunches. Instead of keeping track of the weekly total number of crunches, Mr. Shin keeps track of how they do compared to the week before, and then records the result as a positive or negative number. Record the number for each of the following:
Ben did 10 more crunches this week than last week. What number would Mr. Shin record?
Gail did 8 less crunches this week than last week. What number would Mr. Shin record?
Nathaniel did the same number of crunches this week as last week. What number would Mr. Shin record?
awnser asap
Answer:
Mr. Shim would record the number +10 or 10 for Ben because of the word "more".
For Gail, Mr. Shin would record the number -8 because of the word, "less''.
Since Nathaniel did not improve or decrease the number of crunches, Mr. Shin would record the number 0.
I hope this helps better
The radar system beeps once every second. How many times will it beep in 3 days?
Answer:
259200
Step-by-step explanation:
so there are 86400 in one day. multiply by 3.
Answer:
259200
Step-by-step explanation:
60x24x3x60=
Use Green's Theorem to evaluate the line integral along the given positively oriented curve. ∫C (3y +5e√x)dx + (10x + 3 cos y2)dy C is the boundary of the region enclosed by the parabolas y = x2 and x = y2
By Green's theorem, the line integral
[tex]\displaystyle \int_C f(x,y)\,\mathrm dx + g(x,y)\,\mathrm dy[/tex]
is equivalent to the double integral
[tex]\displaystyle \iint_D \frac{\partial g}{\partial x} - \frac{\partial f}{\partial y} \,\mathrm dx\,\mathrm dy[/tex]
where D is the region bounded by the curve C, provided that this integrand has no singularities anywhere within D or on its boundary.
It's a bit difficult to make out what your integral should say, but I'd hazard a guess of
[tex]\displaystyle \int_C \left(3y+5e^{-x}\right)\,\mathrm dx + \left(10x+3\cos\left(y^2\right)\right)\,\mathrm dy[/tex]
Then the region D is
D = {(x, y) : 0 ≤ x ≤ 1 and x ² ≤ y ≤ √x}
so the line integral is equal to
[tex]\displaystyle \int_0^1\int_{x^2}^{\sqrt x} \frac{\partial\left(10x+3\cos\left(y^2\right)\right)}{\partial x} - \frac{\partial\left(3y+5e^{-x}\right)}{\partial y}\,\mathrm dy\,\mathrm dx \\\\ = \int_0^1 \int_{x^2}^{\sqrt x} (10-3)\,\mathrm dy\,\mathrm dx \\\\ = 7\int_0^1 \int_{x^2}^{\sqrt x} \mathrm dy\,\mathrm dx[/tex]
which in this case is 7 times the area of D.
The remaining integral is trivial:
[tex]\displaystyle 7\int_0^1\int_{x^2}^{\sqrt x}\mathrm dy\,\mathrm dx = 7\int_0^1y\bigg|_{y=x^2}^{y=\sqrt x}\,\mathrm dx \\\\ = 7 \int_0^1\left(\sqrt x-x^2\right)\,\mathrm dx \\\\ = 7 \left(\frac23x^{3/2}-\frac13x^3\right)\bigg|_{x=0}^{x=1} = 7\left(\frac23-\frac13\right) = \boxed{\frac73}[/tex]
In a recent survey of drinking laws, a random sample of 1000 women showed that 65% were in favor of increasing the legal drinking age. In a random sample of 1000 men, 60% favored increasing the legal drinking age. Test the claim that the percentage of men and women favoring a higher legal drinking age is different at (alpha 0.05).
Answer:
Step-by-step explanation:
Given that:
Let sample size of women be [tex]n_1[/tex] = 1000
Let the proportion of the women be [tex]p_1[/tex] = 0.65
Let the sample size of the men be [tex]n_2[/tex] = 1000
Let the proportion of the mem be [tex]p_2[/tex] = 0.60
The null and the alternative hypothesis can be computed as follows:
[tex]H_0: p_1 = p_2[/tex]
[tex]H_0a: p_1 \neq p_2[/tex]
Thus from the alternative hypothesis we can realize that this is a two tailed test.
However, the pooled sample proportion p = [tex]\dfrac{p_1n_1+p_2n_2 } {n_1 +n_2}[/tex]
p =[tex]\dfrac{0.65 * 1000+0.60*1000 } {1000 +1000}[/tex]
p = [tex]\dfrac{650+600 } {2000}[/tex]
p = 0.625
The standard error of the test can be computed as follows:
[tex]SE = \sqrt{p(1-p) ( \dfrac{1} {n_1}+ \dfrac{1}{n_2} )}[/tex]
[tex]SE = \sqrt{0.625(1-0.625) ( \dfrac{1} {1000}+ \dfrac{1}{1000} )}[/tex]
[tex]SE = \sqrt{0.625(0.375) ( 0.001+0.001 )}[/tex]
[tex]SE = \sqrt{0.234375 (0.002)}[/tex]
[tex]SE = \sqrt{4.6875 * 10^{-4}}[/tex]
[tex]SE = 0.02165[/tex]
The test statistics is :
[tex]z =\dfrac{p_1-p_2}{S.E}[/tex]
[tex]z =\dfrac{0.65-0.60}{0.02165}[/tex]
[tex]z =\dfrac{0.05}{0.02165}[/tex]
[tex]z =2.31[/tex]
At level of significance of 0.05 the critical value for the z test will be in the region between - 1.96 and 1.96
Rejection region: To reject the null hypothesis if z < -1.96 or z > 1.96
Conclusion: Since the value of z is greater than 1.96, it lies in the region region. Therefore we reject the null hypothesis and we conclude that the percentage of men and women favoring a higher legal drinking age is different.
Help me with this question for 10 points please
9514 1404 393
Answer:
(a) 10 cm
Step-by-step explanation:
Since C is the midpoint of AB, the triangle shown is 1/4 of the rectangular area shown. When the tank is sitting horizontally on its 100 cm side, the water height will be 1/4 of the 40 cm height of the tank. It will be 10 cm.
__
More elaborate explanation
Triangle area = 1/2(AD)(AC) = 1/2(AD)(1/2(AB)) = 1/4(AD)(AB)
Whole tank area = (AD)(AB)
So, the triangle area is 1/4 the whole tank area. When the tank is tipped back to horizontal, the water area will still be 1/4 the whole tank area, so will be ...
water area = (1/4(AD))(AB)
and the height will be 1/4(AD) = 1/4(40 cm) = 10 cm
An individual is teaching a class on Excel Macros. The individual plans to break the class up into groups of 4 and wants each group to have 2 exercises to practice on, with no group doing the same exercise. The individual wants to know how many exercises he will need. Solve for the dependent variable (y) if the independent variable is 16.
Answer:
32
Step-by-step explanation:
If there are 16 independent variables (groups) then there would need to be 2 unique exercises x 16 groups = 32 exercises. If the independent variable is the number of students, then they would only need 8.
The Total Exercises each group will do 2x/4
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Total exercises individual need is y = 4x/2
y - 4x/2
The No. of groups = 4
Each group has to do exercises = 2
Total no. of exercises individual need is y
Total Exercises each group will do 2x/4
Total exercises individual need
y = 2x/4 (4)
y - 4x/2
Learn more about the unitary method, please visit the link given below;
https://brainly.com/question/23423168
#SPJ2
Express the quotient of z1 and z2 in standard form given that [tex]z_{1} = 6[cos(\frac{2\pi }{5}) + isin(\frac{2\pi }{5})][/tex] and [tex]z_{2} = 2\sqrt{2} [cos(\frac{-\pi }{2}) + isin(\frac{-\pi }{2})][/tex]
Answer:
Solution : - 2.017 + 0.656i
Step-by-step explanation:
The quotient of the two expressions would be the following,
[tex]6\left[\cos \left(\frac{2\pi }{5}\right)+i\sin \left(\frac{2\pi \:}{5}\right)\right][/tex] ÷ [tex]2\sqrt{2}\left[\cos \left(\frac{-\pi }{2}\right)+i\sin \left(\frac{-\pi \:}{2}\right)\right][/tex]
So if we want to determine this expression in standard complex form, we can first convert it into trigonometric form, then apply trivial identities. Either that, or we can straight away apply the following identities and substitute,
( 1 ) cos(x) = sin(π / 2 - x)
( 2 ) sin(x) = cos(π / 2 - x)
If cos(x) = sin(π / 2 - x), then cos(2π / 5) = sin(π / 2 - 2π / 5) = sin(π / 10). Respectively sin(2π / 5) = cos(π / 2 - 2π / 5) = cos(π / 10). Let's simplify sin(π / 10) and cos(π / 10) with two more identities,
( 1 ) [tex]\cos \left(\frac{x}{2}\right)=\sqrt{\frac{1+\cos \left(x\right)}{2}}[/tex]
( 2 ) [tex]\sin \left(\frac{x}{2}\right)=\sqrt{\frac{1-\cos \left(x\right)}{2}}[/tex]
These two identities makes sin(π / 10) = [tex]\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}[/tex], and cos(π / 10) = [tex]\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}[/tex].
Therefore cos(2π / 5) = [tex]\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}[/tex], and sin(2π / 5) = [tex]\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}[/tex]. Substitute,
[tex]6\left[ \left\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}+i\left\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\right][/tex] ÷ [tex]2\sqrt{2}\left[\cos \left(\frac{-\pi }{2}\right)+i\sin \left(\frac{-\pi \:}{2}\right)\right][/tex]
Remember that cos(- π / 2) = 0, and sin(- π / 2) = - 1. Substituting those values,
[tex]6\left[ \left\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}+i\left\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\right][/tex] ÷ [tex]2\sqrt{2}\left[0-i\right][/tex]
And now simplify this expression to receive our answer,
[tex]6\left[ \left\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}+i\left\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\right][/tex] ÷ [tex]2\sqrt{2}\left[0-i\right][/tex] = [tex]-\frac{3\sqrt{5+\sqrt{5}}}{4}+\frac{3\sqrt{3-\sqrt{5}}}{4}i[/tex],
[tex]-\frac{3\sqrt{5+\sqrt{5}}}{4}[/tex] = [tex]-2.01749\dots[/tex] and [tex]\:\frac{3\sqrt{3-\sqrt{5}}}{4}[/tex] = [tex]0.65552\dots[/tex]
= [tex]-2.01749+0.65552i[/tex]
As you can see our solution is option c. - 2.01749 was rounded to - 2.017, and 0.65552 was rounded to 0.656.
Which of the following is the correct notation of the complex number?
Answer:
-84 + 10i
Step-by-step explanation:
Standard Complex Form: a + bi
Step 1: Evaluate
√-100 = √-1 x √100 = i x 10 = 10i
-84 = -84
Step 2: Combine
10i - 84
Step 3: Rearrange
-84 + 10i
Answer:
Last Option
Step-by-step explanation:
√-100 - 84
(√(100×-1)) - 84
(√100)(√-1)-84
√-1 = i
10i - 84 or -84 + 10i
A researcher at the University of Washington medical school believes that energy drink consumption may increase heart rate. Suppose it is known that heart rate (in beats per minute) is normally distributed with an average of 70 bpm for adults. A random sample of 25 adults was selected and it was found that their average heartbeat was 73 bpm after energy drink consumption, with a standard deviation of 7 bpm. In order to test belief at the 10% significance level, determine P-value for the test.
Answer:
Step-by-step explanation:
Given that:
mean μ = 70
sample size = 25
sample mean = 73
standard deviation = 7
level of significance = 0.10
The null hypothesis and the alternative hypothesis can be computed as follows:
[tex]\mathtt{H_o : \mu = 70} \\ \\ \mathtt{H_1 : \mu > 70 }[/tex]
The z score for this statistics can be calculated by using the formula:
[tex]z = \dfrac{X- \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \dfrac{73- 70}{\dfrac{7}{\sqrt{25}}}[/tex]
[tex]z = \dfrac{3}{\dfrac{7}{5}}[/tex]
[tex]z = \dfrac{3 \times 5}{{7}{}}[/tex]
z = 2.143
At level of significance of 0.10
degree of freedom = n -1
degree of freedom = 25 - 1
degree of freedom = 24
The p - value from the z score at level of significance of 0.10 and degree of freedom of 24 is:
P - value = 1 - (Z < 2.143)
P - value = 1 - 0.9839
P - value = 0.0161
Decision Rule: since P value is lesser than the level of significance, we reject the null hypothesis.
Conclusion: We conclude that energy drink consumption increases heart rate.
A simple random sample of 28 Lego sets is obtained and the number of pieces in each set was counted.The sample has a standard deviation of 12.65. Use a 0.05 significance level to test the claim that the number of pieces in a set has a standard deviation different from 11.53.
Answer:
Step-by-step explanation:
Given that:
A simple random sample n = 28
sample standard deviation S = 12.65
standard deviation [tex]\sigma[/tex] = 11.53
Level of significance ∝ = 0.05
The objective is to test the claim that the number of pieces in a set has a standard deviation different from 11.53.
The null hypothesis and the alternative hypothesis can be computed as follows:
Null hypothesis:
[tex]H_0: \sigma^2 = \sigma_0^2[/tex]
Alternative hypothesis:
[tex]H_1: \sigma^2 \neq \sigma_0^2[/tex]
The test statistics can be determined by using the following formula in order to test if the claim is statistically significant or not.
[tex]X_0^2 = \dfrac{(n-1)S^2}{\sigma_0^2}[/tex]
[tex]X_0^2 = \dfrac{(28-1)(12.65)^2}{(11.53)^2}[/tex]
[tex]X_0^2 = \dfrac{(27)(160.0225)}{132.9409}[/tex]
[tex]X_0^2 = \dfrac{4320.6075}{132.9409}[/tex]
[tex]X_0^2 = 32.5002125[/tex]
[tex]X^2_{1- \alpha/2 , df} = X^2_{1- 0.05/2 , n-1}[/tex]
[tex]X^2_{1- \alpha/2 , df} = X^2_{1- 0.025 , 28-1}[/tex]
From the chi-square probabilities table at 0.975 and degree of freedom 27;
[tex]X^2_{0.975 , 27}[/tex] = 14.573
[tex]X^2_{\alpha/2 , df} = X^2_{ 0.05/2 , n-1}[/tex]
[tex]X^2_{\alpha/2 , df} = X^2_{0.025 , 28-1}[/tex]
From the chi-square probabilities table at 0.975 and degree of freedom 27;
[tex]X^2_{0.025 , 27}=[/tex] 43.195
Decision Rule: To reject the null hypothesis if [tex]X^2_0 \ > \ X^2_{\alpha/2 , df} \ \ \ or \ \ \ X^2_0 \ < \ X^2_{1- \alpha/2 , df}[/tex] ; otherwise , do not reject the null hypothesis:
The rejection region is [tex]X^2_0 \ > 43.195 \ \ \ or \ \ \ X^2_0 \ < \ 14.573[/tex]
Conclusion:
We fail to reject the null hypothesis since test statistic value 32.5002125 lies between 14.573 and 43.195.
Write the expression (x4)8 in simplest form.
Answer:
the 4 and 8 are exponents
Step-by-step explanation: