Answer:
a) The mean of the data set is 58.3.
b) The standard deviation of the data-set is of 10.8.
c) 50% of presidents' ages fall within one standard deviation of the mean
Step-by-step explanation:
Question a:
Sum of all values divided by the number of values.
[tex]M = \frac{69 + 64 + 46 + 54 + 47 + 70}{6} = 58.3[/tex]
The mean of the data set is 58.3.
Question b:
Square root of the sum of the difference squared between each value and the mean, divided by the number of values subtracted by 1. So
[tex]S = \sqrt{\frac{(69-58.3)^2 + (64-58.3)^2 + (46-58.3)^2 + (54-58.3)^2 + (47-58.3)^2 + (70-58.3)^2}{5}} = 10.8[/tex]
The standard deviation of the data-set is of 10.8.
Question c:
Between 58.3 - 10.8 = 47.5 and 58.3 + 10.8 = 69.1.
3 out of 6(Reagan, Bush and W. Bush), so:
3*100%/6 = 50%
50% of presidents' ages fall within one standard deviation of the mean
What is the conversion factor from meters to centimeters?
10,000 meters per centimeter
100 meters per centimeter
100 centimeters per meter
10,000 centimeters per meter
Answer: there are 100 centimeters in 1 meter. Meters to centimeters multiply by 100. Centimeters to meters divide by 100.
Step-by-step explanation:
Meters to centimeters multiply by 100
(10,000 m ) (100) = 1,000,000 cm.
(100 m) (100) = 10,000 cm.
Centimeters to meters divide by 100.
100 cm / 100 = 1 meter
10,000 cm /100 = 100 m
A sample tested the claim that heights of men and heights of women have difference variances, with s=7.42388 cm for women and 7.14974 cm for men. The sample sizes are n1=144 and n2=156. When using the F test with these data, is it correct to reason that there is no need to check for normality because n1>30 and n2>30?
No. The F test has a requirement that samples be from the normally distributed populations, regardless of how large the samples are.
The F-test simply shows whether the variances that are in the numerator and the denominator are equal. The F-test can be applied on a large sampled population.
One main assumption of the F test is that the populations where the two samples are drawn are normally distributed.
Regarding the question, it's important to note that when using the F test with these data, it's not correct to reason that there is no need to check for "normality".
It should be noted that the F test has a requirement that samples are from the normally distributed populations, regardless of how large such samples are.
Read related link on:
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Find perpendicular,hypotenuse and base
Step-by-step explanation:
In right angled triangle ABC,
Taking alpha as reference angle,
By pythagoras theorem,
p=BC,h=AB,b=AC
Taking thita as reference angle,
p=AC,h=AB,b=BC
Keep smiling and hope u are satisfied with my answer.Have a good day :)
which expression is equivalent to c^2 - 4 / c + 3 /
Step-by-step explanation:
[tex] \frac{ {c}^{2} - 4 }{c + 3} [/tex]
[tex] \frac{(c - 2)(c + 2)}{(c + 3)} [/tex]
-1/12 to the second power? Halp me plz
Answer:
1/144
Step-by-step explanation:
(-1/12)^2
(-1/12)*(-1/12)
1/144
I NEED HELP PLEASE!!!!
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Answer:
A. 1/2
Step-by-step explanation:
The points on a unit circle are (cos(θ), sin(θ)), where θ is the angle from the +x axis to to the ray from the origin through that point.
If the point is (√3/2, 1/2), then sin(θ) = 1/2.
Ben consumes an energy drink that contains caffeine. After consuming the energy drink, the amount of caffeine in Ben's body decreases exponentially. The 10-hour decay factor for the number of mg of caffeine in Ben's body is 0.2722. What is the 5-hour growth/decay factor for the number of mg of caffeine in Ben's body
Answer:
The 5-hour decay factor for the number of mg of caffeine in Ben's body is of 0.1469.
Step-by-step explanation:
After consuming the energy drink, the amount of caffeine in Ben's body decreases exponentially.
This means that the amount of caffeine after t hours is given by:
[tex]A(t) = A(0)e^{-kt}[/tex]
In which A(0) is the initial amount and k is the decay rate, as a decimal.
The 10-hour decay factor for the number of mg of caffeine in Ben's body is 0.2722.
1 - 0.2722 = 0.7278, thus, [tex]A(10) = 0.7278A(0)[/tex]. We use this to find k.
[tex]A(t) = A(0)e^{-kt}[/tex]
[tex]0.7278A(0) = A(0)e^{-10k}[/tex]
[tex]e^{-10k} = 0.7278[/tex]
[tex]\ln{e^{-10k}} = \ln{0.7278}[/tex]
[tex]-10k = \ln{0.7278}[/tex]
[tex]k = -\frac{\ln{0.7278}}{10}[/tex]
[tex]k = 0.03177289938 [/tex]
Then
[tex]A(t) = A(0)e^{-0.03177289938t}[/tex]
What is the 5-hour growth/decay factor for the number of mg of caffeine in Ben's body?
We have to find find A(5), as a function of A(0). So
[tex]A(5) = A(0)e^{-0.03177289938*5}[/tex]
[tex]A(5) = 0.8531[/tex]
The decay factor is:
1 - 0.8531 = 0.1469
The 5-hour decay factor for the number of mg of caffeine in Ben's body is of 0.1469.
A trader sold 90 oranges at 3 for GHC 0.75.
How much did she get from selling all the
oranges?
Answer:
GHC22.5
Step-by-step explanation:
90/3=30
30=0.75
30×0.75
=22.5
Which of the following lines is perpendicular to y = -2x +3?
A. y= 2x +3
B.
1
y=-x+3
2
C. y=-2x +2
D.
1
= --X-2
2
y=1/2x-2 is perpendicular to y=2x+3
Find two consecutive even numbers whose sum is 758.
Answer:
378 and 380
Step-by-step explanation:
The two even consecutive numbers that add up to 758 are going to be very close to half of 758. This is because two half of 758 are going to be the most similar addends of 758. This is important because the answers will be consecutive and therefore, must also be very similar. To solve, first, divide 758 by 2. This is 379, which is not an even number. So, to find the needed addends subtract and add 1 to 379. Both of these will be even and consecutive. These two numbers are 378 and 380. Then, to check you, can add them and see that they do sum 758.
Answer:
Step-by-step explanation:
Let the first number = x
Let the second number = x + 2
x + x + 2 = 758 Collect like terms
2x + 2 = 758 Subtract 2
2x = 758 - 2 Combine
2x = 756 Divide by 2
2x/2 = 756/2
x = 378
The first number is 378
The second number 380
If your teacher is really fussy, you can do it this way.
Let the first number = 2x
Let the second number = 2x + 2
The reason for this is to guarantee that both numbers were even to start with.
2x + 2x+2 = 758 Combine like terms
4x + 2 = 758 Subtract 2
4x = 756 Divide by 4
x = 756/4
x = 189
Therefore 2x = 378
2x + 2 = 380 Just as before.
please help.
find the missing side or angle and each problem .
Jacqueline will spend a fair spinner with the numbers 0 1 2 3 and 4 a total of three times if event a spinner lands on numbers are greater than 2 and event be total sum of 9 which of the following best describes event A and B
Events are said to be INDEPENDENT if the occurence of one does not rest or depend on the outcome of another. Therefore, since the outcome of event A and B does not depend on each other, then both events are INDEPENDENT
Giving a brief description of the options given :
• Dependent events are simply events where the outcome of one event affects the occurence of the other. This is usually related to selection without replacement, where the number of subjects changes after each selection.
• Mutually Exclusive events simply refers to a scenario whereby two events cannot occur simultaneously. For instance, obtaining a head and a tail simultaneously during a single coin throw.
• Complement events describes two exactly opposite events. For instance, the Complement of obtaining a 4 on a 6 - sided die roll is (1, 2, 3, 5, 6)
For the event described above , the occurrence of A does not hinder the occurrence of the other (not a dependent event ) and it is possible to have both events simultaneously (not Mutually exclusive) (If we have 3 in all throws then both events have occurred )
Therefore, the best description for events A and B is that both events are INDEPENDENT.
Learn more about independent events :
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Answer: the answer is dependent
Step-by-step explanation:
Events are independent if the knowledge of one event occurring does not affect the chance of the other event occurring. In this case, the chance of Event B occurring is greater if Event A occurs, so these events are dependent. Since the spinner could land on 3, 3, and 3, the events are not mutually exclusive.
Find COS Instructions: Find the value of the trigonometric ratio. Make sure to simplify the If needed
Answer:
Sin X = 12 / 37
Step-by-step explanation:
Given a right angled triangle, we are to obtain the Sin of the angle X ;
Using trigonometry, the sine of the angle X , Sin A is defined as the ratio of the angle opposite X to the hypotenus of the right angle triangle.
In the right angle triangle :
Sin X = opposite / hypotenus
Opposite = 12 ; hypotenus = 37
Sin X = 12 / 37
Is the function f(x) = 1/8 ^x an exponent function? If so , identify the base , if not why not ?

Yes , the base is 1/e
yes, the base is e
No, there is no base that is a positive real number not equal to 1 raised to a variable exponent.
No, the base is the reciprocal of e, a number smaller than 1.
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Answer:
(a) Yes , the base is 1/e
Step-by-step explanation:
The variable is in the exponent, so this is an exponential function.
The base is the number that has the exponent. The base is (1/e).
Answer:
Step-by-step explanation:
bvxbvxbvxbvcvbbb cv
Find the measure of angle x in the figure below:
A triangle is shown. At the top vertex of the triangle is a horizontal line aligned to the base of the triangle. The angle formed between the horizontal line and the left edge of the triangle is shown as 57 degrees, the angle formed between the horizontal line and the right edge of the triangle is shown as 61 degrees. The angle at the top vertex of the triangle is labeled as y, and the interior angle on the right is labeled as 67 degrees. The interior angle on the left is labeled as x.
35°
47°
51°
62°
Your answer iss...
It is 51º
A regular 2016-gon with all vertices on the unit circle is given. Find its perimeter, as a decimal to the nearest hundredth. (I have been stuck on this problem for half a hour I need help asap)
Answer:
6.28 unitsStep-by-step explanation:
Interior angle opposite to each side of the polygon is:
(360/2016)°Since the circle is unit circle, its radius is 1 unit.
Let the side is a, then as per definition of sine we have:
sin ((360/2016)/2) = (a/2)/1a = 2 sin (180/2016)°a = 0.00311665811The perimeter is:
P = 2016a = 2016(0.00311665811) ≈ 6.28 unitsWhat is the 11th term of this geometric sequence?: 16384, 8192, 4096, 2048
Answer:
16
Step-by-step explanation:
1) Find out r of the sequence. The first term(a1) is 16384, the second term (a2) is 8192.
8192=16384*r. r= 0.5
2) Use the rule that an=a1*r^(n-1)
a11=a1*r^10
a11= 16384*((0.5)^10)= 16384/ (2^10)=16.
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
the question is in the photo
9514 1404 393
Answer:
108.8 km/h at 84.3°
Step-by-step explanation:
The law of cosines can be used to find the resultant ground speed. In the attached diagram, the length of interest is OR. It will be found as ...
OR² = OP² +PR² -2·OP·PR·cos(P)
OR² = 130² +26² -2×130×26×cos(32°) ≈ 11843.19
OR = √11843.19 ≈ 108.8
__
The angle POR can be found from the law of sines.
sin(POR)/PR = sin(OPR)/OR
sin(POR) = PR/OR×sin(32°) ≈ 0.12660
∠POR ≈ arcsin(0.12660) ≈ 7.27°
Then the bearing of the ground track of the airplane is 77° +7.27° = 84.27°.
The airplane is traveling at about 108.8 km/h on a bearing of 84.3°.
An article reported that, in a study of a particular wafer inspection process, 356 dies were examined by an inspection probe and 244 of these passed the probe. Assuming a stable process, calculate a 95% (two-sided) confidence interval for the proportion of all dies that pass the probe. (Round your answers to three decimal places.)
Answer:
The 95% confidence interval for the proportion of all dies that pass the probe is (0.637, 0.733).
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].
356 dies were examined by an inspection probe and 244 of these passed the probe.
This means that [tex]n = 356, \pi = \frac{244}{356} = 0.685[/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 limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.685 - 1.96\sqrt{\frac{0.685*0.315}{356}} = 0.637[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.685 + 1.96\sqrt{\frac{0.685*0.315}{356}} = 0.733[/tex]
The 95% confidence interval for the proportion of all dies that pass the probe is (0.637, 0.733).
Viết các số 1,2,..,100 theo một thứ tự nào đó, được dãy a1, a2,..,a100. CMR: Tổng S= |a1 - 1| + |a2 -2| + .. +|a100 -100|. Hãy tổng quát hóa bài toán
Plz help’
!
I’ll be giving extra points
because it's value will always be same
Answer:
This value doesn't depend on x or y
It'll be the same things always
find the solution of the general equation of the differential equation:
(1-cosx)y' - ysinx =0, x ≠ k2π
Notice that the condition x ≠ 2πk for (presumably) integer k means cos(x) ≠ ±1, and in particular cos(x) ≠ 1 so that we could divide both sides by (1 - cos(x)) safely. Doing so lets us separate the variables:
(1 - cos(x)) y' - y sin(x) = 0
==> (1 - cos(x)) y' = y sin(x)
==> y'/y = sin(x)/(1 - cos(x))
==> dy/y = sin(x)/(1 - cos(x)) dx
Integrate both sides and solve for y. On the right, substitute u = 1 - cos(x) and du = sin(x) dx.
∫ dy/y = ∫ sin(x)/(1 - cos(x)) dx
∫ dy/y = ∫ du/u
ln|y| = ln|u| + C
exp(ln|y|) = exp(ln|u| + C )
exp(ln|y|) = exp(ln|u|) exp(C )
y = Cu
y = C (1 - cos(x))
e) Three friends were each given 25% of pie. What fraction of the pie was given altogether?
Answer:
3/4 or 75% or .75
Step-by-step explanation:
You would multiply 3 * .25 because there are three people getting 25% of a pie. All of the answers above are equivalent
I need help completing this problem ASAP
Answer:
[tex]4\sqrt{5}[/tex]
Step-by-step explanation:
Prime factorize 20 and 45
[tex]\sqrt{20}=\sqrt{2*2*5}=2\sqrt{5}\\\\\\\sqrt{45}= \sqrt{5*3*3}=3\sqrt{5}[/tex]
[tex]\sqrt{20}-\sqrt{5}+\sqrt{45}=2\sqrt{5}-\sqrt{5}+3\sqrt{5}[/tex]
[tex]=(2-1+3)\sqrt{5}\\\\\\= 4\sqrt{5}\\[/tex]
Question 8 of 10
If f(x) = 4x2 and g(x) = x+1, find (f•g)(x).
A. 4X2 + 1
B. 4x2 + 4x2
C. 4(x+1)
D. 4x(x)
SURVIT
Answer:
option c is the answer for your question
Choose the best answer from the choices below:
If a radius of a circle bisects a chord which is not a diameter, then ____.
Answer: the radius is perpendicular to the chord.
If a radius of a circle bisects a chord which is not diameter, then the radius is perpendicular to the chord.
Answered by Gauthmath must click thanks and mark brainliest
The radius is perpendicular to the chord.
Does the radius of the circle bisect the string?If the radius of the circle is perpendicular to the chord of the circle, the radius bisects the chord. The two strings are congruent only if they are equidistant from the center of the circle.
No, not all strings in a circle are diameters because the diameter passes through the center of the circle. Therefore, all the diameters of a circle are also strings, not all the strings of a circle.
Learn more about chord at
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Need the value of P please
Answer:
B. 35°
Step-by-step explanation:
First, find the two interior angles that are adjacent to angles 90° and 125° respectively.
Thus:
Interior angle 1: 180° - 90° = 90° (linear pair)
Interior angle 2: 180° - 125° = 55° (linear pair)
P + 90° + 55° = 180° (sum of interior angles in a triangle)
P + 145° = 180°
Subtract 145° from each side
P = 180° - 145°
P = 35°
Find an equation for the perpendicular bisector of the line segment whose endpoints are (8,9) and (4,−3).
x + 3y -15 = 0
Step-by-step explanation:
let (x,y) be the coordinate of bisector,
so (x,y) should be equal distance from point (8,9) and (4,-3)
(x-8)^2 + (y-9)^2 = (x-4)^2 + (y-(-3))^2
or, (x^2 - 16x + 64) + (y^2 - 18y + 81 )= (x^2 -8x + 16) + (y^2 + 6y + 9)
After cancelling x^2 and y^2 from both side, we get
-16x - 18y +145 = -8x +6y + 25
or, -16x + 8x - 18y - 6y +145 -25 = 0
or, -8x - 24y + 120 = 0
or -8 ( x + 3y - 15) = 0
or, x + 3y - 15 = 0 ------ this is the equation of the perpendicular bisector of line segment with endpoints (8,9) and (4,-3)
At the end of 2 years, P dollars invested at an interest rater compounded annually increases to an amount, A dollars, given by the following formula.
A = P(1+r)?
Find the interest rate if $192 increased to $363 in 2 years. Write your answer as a percent..
-
Annual compound interest rate = % (Type an integer or a decimal.)
Answer:
37.5%
Step-by-step explanation:
A=P(1+r)^t
363=192*(1+r)^2
1.375=1+r, r=0.375=37.5%
