Answer:
a. The first six terms are:
-7, -4, -1, 2, 5, 8
b. The first six terms are:
0, 2, 0, 2, 0, 2.
c. The first six terms are:
4, 8, 24, 96, 480, 2880
Step-by-step explanation:
a. an - 3n - 10
For n = 1
a1 = 3(1) - 10
= -7
For n = 2
a2 = 3(2) - 10
= -4
For n = 3
a3 = 3(3) - 10
= -1
For n = 4
a4 = 3(4) - 10
= 2
For n = 5
a5 = 3(5) - 10
= 5
For n = 6
a6 = 3(6) - 10
= 8
The first six terms are:
-7, -4, -1, 2, 5, 8
b. an= (1+(-1)^n)^n
For n = 1
a1 = (1+(-1)^1)^1
= 0
For n = 2
a2 = (1+(-1)^2)^1
= 2
For n = 3
a3 = (1+(-1)^3)^1
= 0
For n = 4
a4 = (1+(-1)^4)^1
= 2
For n = 5
a5 = (1+(-1)^5)^1
= 0
For n = 6
a6 = (1+(-1)^6)^1
= 2
The first six terms are:
0, 2, 0, 2, 0, 2.
c. an= 2n! (2)
For n = 1
a1 = 2(1!)(2)
= 4
For n = 2
a2 = 2(2!)(2)
= 8
For n = 3
a3 = 2(3!)(2)
= 24
For n = 4
a4 = 2(4!)(2)
= 96
For n = 5
a5 = 2(5!)(2)
= 480
For n = 6
a6 = 2(6!)(2)
= 2880
The first six terms are:
4, 8, 24, 96, 480, 2880
The radius of circle C is 7 cm. ∠BCA (the non shaded region) has a measure of 1.36 radians. Find the length of arc BEA. Show your setup and your work for full credit. Round your answer to two decimal places.
Answer: 9.52cm
Step-by-step explanation:
The data we have is:
Radius = 7cm
Angle of the arc = 1.36 rads
Now, the perimeter of a full circle is equal to:
P = 2*pi*r
Where 2*pi = 6.28 rads
Then the length of an arc of angle A is
P = A*r
then in our case:
P = 1.36*7cm = 9.52cm
An experiment involves 17 participants. From these, a group of 3 participants is to be tested under a special condition. How many groups of 3 participants can
be chosen, assuming that the order in which the participants are chosen is irrelevant?
Answer: 680
Step-by-step explanation:
When order doesn't matter,then the number of combinations of choosing r things out of n = [tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
Given: Total participants = 17
From these, a group of 3 participants is to be tested under a special condition.
Number of groups of 3 participants chosen = [tex]^{17}C_3=\dfrac{17!}{3!(17-3)!}\[/tex]
[tex]^{17}C_3=\dfrac{17!}{3!(17-3)!}\\\\=\dfrac{17\times16\times15\times14!}{3\times2\times14!}\\\\=680[/tex]
Hence, there are 680 groups of 3 participants can be chosen,.
Find the area of the shaded region if the dimensions of the unshaded region are 12ft x 20ft . Use 3.14 for π as necessary. - - - no lengthy explanation needed! all I need is the answer! first answer gets brainliest!
Answer:
810.66 ft²
Step-by-step explanation:
Short answer:
Shaded region:
(12+2*7)*20 - 12*20 + 3.14*((12+2*7)/2)² =14*20 + 530.66 = 810.66 ft²Answer: 810.66 ft²
I agree.
Sam weights 51kg. What is this weight to the nearest stone?. Use this conversion, 1kg= 2.2 pounds and 14 pounds= 1 stone
Sam's weight to the nearest stone is equal to 8.0 stone.
Given the following data:
Sam's weight = 51 kg.1 kg = 2.2 pounds.14 pounds = 1 stone.To determine Sam's weight to the nearest stone:
How to convert the units of measurement.In this exercise, you're required to determine Sam's weight to the nearest stone. Thus, we would convert his weight in kilograms to pounds and lastly to stone as follows:
Conversion:
1 kg = 2.2 pounds.
51 kg = [tex]51 \times 2.2[/tex] = 112.2 pounds.
Next, we would convert the value in pounds to stone:
14 pounds = 1 stone.
112.2 pounds = X stone.
Cross-multiplying, we have:
[tex]14X = 112.2\\\\X=\frac{112.2}{14}[/tex]
X = 8.01 ≈ 8.0 stone.
Read more on weight here: brainly.com/question/13833323
A newsletter publisher believes that 71q% of their readers own a personal computer. Is there sufficient evidence at the 0.010.01 level to refute the publisher's claim.
Required:
State the null and alternative hypotheses for the above scenario.
Answer:
Null - p= 71%
Alternative - p =/ 71%
Step-by-step explanation:
The null hypothesis is always the default statement in an experiment. While the alternative hypothesis is always tested against the null hypothesis.
Null hypothesis: 71% of their readers own a personal computer- p = 71%
Alternative hypothesis: Not 71% of their readers own a personal computer - p =/ 71%
Crime and Punishment: In a study of pleas and prison sentences, it is found that 45% of the subjects studied were sent to prison. Among those sent to prison, 40% chose to plead guilty. Among those not sent to prison, 55% chose to plead guilty.
(A) If one of the study subjects is randomly selected, find the probability of getting someone who was not sent to prison.
(B) If a study subject is randomly selected and it is then found that the subject entered a guilty plea, find the probability that this person was not sent to prison.
Answer:
(a) The probability of getting someone who was not sent to prison is 0.55.
(b) If a study subject is randomly selected and it is then found that the subject entered a guilty plea, the probability that this person was not sent to prison is 0.63.
Step-by-step explanation:
We are given that in a study of pleas and prison sentences, it is found that 45% of the subjects studied were sent to prison. Among those sent to prison, 40% chose to plead guilty. Among those not sent to prison, 55% chose to plead guilty.
Let the probability that subjects studied were sent to prison = P(A) = 0.45
Let G = event that subject chose to plead guilty
So, the probability that the subjects chose to plead guilty given that they were sent to prison = P(G/A) = 0.40
and the probability that the subjects chose to plead guilty given that they were not sent to prison = P(G/A') = 0.55
(a) The probability of getting someone who was not sent to prison = 1 - Probability of getting someone who was sent to prison
P(A') = 1 - P(A)
= 1 - 0.45 = 0.55
(b) If a study subject is randomly selected and it is then found that the subject entered a guilty plea, the probability that this person was not sent to prison is given by = P(A'/G)
We will use Bayes' Theorem here to calculate the above probability;
P(A'/G) = [tex]\frac{P(A') \times P(G/A')}{P(A') \times P(G/A') +P(A) \times P(G/A)}[/tex]
= [tex]\frac{0.55 \times 0.55}{0.55\times 0.55 +0.45 \times 0.40}[/tex]
= [tex]\frac{0.3025}{0.4825}[/tex]
= 0.63
Explain how to find the range of a data set. What is an advantage of using the range as a measure of variation? What is a disadvantage?
Answer:
The range is found by subtracting the minimum data entry from the maximum data entry.
Step-by-step explanation:
The range is found by subtracting the minimum data entry from the maximum data entry.
It is easy to compute.
It uses only two entries from the data set.
Scatter plot show which type of correlation
Answer:
It is a negative correlation
Step-by-step explanation:
As the x value increases the y value decreases. This causes it to be a negative.
Please help. I’ll mark you as brainliest if correct!
Answer:
8lb of the cheaper Candy
17.5lb of the expensive candy
Step-by-step explanation:
Let the cheaper candy be x
let the costly candy be y
X+y = 25.5....equation one
2.2x +7.3y = 25.5(5.7)
2.2x +7.3y = 145.35.....equation two
X+y = 25.5
2.2x +7.3y = 145.35
Solving simultaneously
X= 25.5-y
Substituting value of X into equation two
2.2(25.5-y) + 7.3y = 145.35
56.1 -2.2y +7.3y = 145.35
5.1y = 145.35-56.1
5.1y = 89.25
Y= 89.25/5.1
Y= 17.5
X= 25.5-y
X= 25.5-17.5
X= 8
Which of the following is false? Correlation measures the strength of linear association between two numerical variables. If the correlation between two variables is close to 0.01, then there is a very weak linear relation between them. Correlation coefficient and the slope always have the same sign (positive or negative). If the correlation coefficient is 1, then the slope must be 1 as well.
Answer:
If the correlation coefficient is 1, then the slope must be 1 as well.
Step-by-step explanation:
Coefficient of correlation is used in statistics to determine the relationship between two variables. Correlation coefficient and slope always have same sign. It measures the strength of linear relation between two variables. The values of correlation coefficient ranges between 0 to 1. where 0 determines that there is no relationship between two variables.
Assume that there is a 6% rate of disk drive failure in a year. a. If all your computer data is stored on a hard disk drive with a copy stored on a second hard disk drive, what is the probability that during a year, you can avoid catastrophe with at least one working drive? b. If copies of all your computer data are stored on independent hard disk drives, what is the probability that during a year, you can avoid catastrophe with at least one working drive? four a. With two hard disk drives, the probability that catastrophe can be avoided is . (Round to four decimal places as needed.) b. With four hard disk drives, the probability that catastrophe can be avoided is . (Round to six decimal places as needed.)
Answer: 0.9964
Step-by-step explanation:
Consider,
P (disk failure) = 0.06
q = 0.06
p = 1- q
p = 1- 0.06,
p = 0.94
Step 2
Whereas p represents the probability that a disk does not fail. (i.e. working entire year).
a)
Step 3
a)
n = 2,
let x be a random variable for number...
Continuation in the attached document
A car travels 133 mi averaging a certain speed. If the car had gone 30 mph faster, the trip would have taken 1 hr less. Find the car's average speed.
Answer:
49.923 mph
Step-by-step explanation:
we know that the car traveled 133 miles in h hours at an average speed of x mph.
That is, xh = 133.
We can also write this in terms of hours driven: h = 133/x.
If x was 30 mph faster, then h would be one hour less.
That is, (x + 30)(h - 1) = 133, or h - 1 = 133/(x + 30).
We can rewrite the latter equation as h = 133/(x + 30) + 1
We can then make a system of equations using the formulas in terms of h to find x:
h = 133/x = 133/(x + 30) + 1
133/x = 133/(x + 30) + (x + 30)/(x + 30)
133/x = (133 + x + 30)/(x + 30)
133 = x*(133 + x + 30)/(x + 30)
133*(x + 30) = x*(133 + x + 30)
133x + 3990 = 133x + x^2 + 30x
3990 = x^2 + 30x
x^2 + 30x - 3990 = 0
Using the quadratic formula:
x = [-b ± √(b^2 - 4ac)]/2a
= [-30 ± √(30^2 - 4*1*(-3990))]/2(1)
= [-30 ± √(900 + 15,960)]/2
= [-30 ± √(16,860)]/2
= [-30 ± 129.846]/2
= 99.846/2 ----------- x is miles per hour, and a negative value of x is neglected, so we'll use the positive value only)
= 49.923
Check if the answer is correct:
h = 133/49.923 = 2.664, so the car took 2.664 hours to drive 133 miles at an average speed of 49.923 mph.
If the car went 30 mph faster on average, then h = 133/(49.923 + 30) = 133/79.923 = 1.664, and 2.664 - 1 = 1.664.
Thus, we have confirmed that a car driving 133 miles at about 49.923 mph would have arrive precisely one hour earlier by going 30 mph faster
81^x^2=27^x solve for x
Step-by-step explanation:
81^x² = 27^x
(3^4)^x² = (3^3)^x
3^(4x²) = 3^(3x)
4x² = 3x
4x² − 3x = 0
x (4x − 3) = 0
x = 0 or ¾
A subcommittee is randomly selected from a committee of eight men and seven women. What is the probability that all three people on the subcommittee are men
Answer:
The probability that all three people on the subcommittee are men
= 20%
Step-by-step explanation:
Number of members in the committee = 15
= 8 men + 7 women
The probability of selecting a man in the committee
= 8/15
= 53%
The probability of selecting three men from eight men
= 3/8
= 37.5%
The probability that all three people on the subcommittee are men
= probability of selecting a man multiplied by the probability of selecting three men from eight men
= 53% x 37.5%
= 19.875%
= 20% approx.
This is the same as:
The probability of selecting 3 men from the 15 member-committee
= 3/15
= 20%
Which of the following is best described as sets of three whole numbers (a, b, and c) that satisfy the equation ?
A.
The Pythagorean theorem
B.
Prime numbers
C.
Pythagorean triples
D.
Perfect squares
Answer:
Option C
Step-by-step explanation:
The whole numbers a,b and c such that [tex]a^2+b^2 = c^2[/tex] are Pythagorean triples satisfying the Pythagorean theorem.
Answer:
C
Step-by-step explanation:
a, b, and c are side lengths of the triangle.
The three side lengths that make up a right triangle are most commonly known as Pythagorean triples.
A triangle has interior measures of 32° and 90°. What is the measure of the third angle?
Answer:
58°Step-by-step explanation:
Let the measure of third angle be X
The sum of interior angle of triangle = X
Let's create an equation
[tex]x + 32 + 90 = 180[/tex]
Add the numbers
[tex]x + 122 = 180[/tex]
Move constant to R.H.S and change its sign
[tex]x = 180 - 122[/tex]
Subtract the numbers
[tex]x = 58[/tex] °
Hope this helps...
Best regards!!
In the search to determine if car 1 is slower to accelerate than car 2, the mean time it takes to accelerate to 30 miles per hour is recorded (Note: a car is slower to accelerate if it takes more time to accelerate). Twenty trials of the acceleration time for each car are recorded, and both populations have normal distributions with known standard deviations. What are the hypotheses used in this test
Answer:
Step-by-step explanation:
The happiest used in a test in statistics are the null and the alternative hypothesis. The null hypothesis is usually the default statement while the alternative hypothesis is thevopposite of the null hypothesis.
In this case study, the null hypothesis is u1 = u2: the average mean time it takes to accelerate to 30 miles per hour for car 1 is the same as that for car 2.
The alternative hypothesis is u1 > u2: the mean time it takes to accelerate to 30 miles per hour is greater than that for car 2 thus car 1 is slower to accelerate as it takes more time.
In which table does y vary inversely with x? A. x y 1 3 2 9 3 27 B. x y 1 -5 2 5 3 15 C. x y 1 18 2 9 3 6 D. x y 1 4 2 8 3 12
Answer:
In Table C, y vary inversely with x.
1×18 = 18
2×9 = 18
3×6 = 18
18 = 18 = 18
Step-by-step explanation:
We are given four tables and asked to find out in which table y vary inversely with x.
We know that an inverse relation has a form given by
y = k/x
xy = k
where k must be a constant
Table A:
x | y
1 | 3
2 | 9
3 | 27
1×3 = 3
2×9 = 18
3×27 = 81
3 ≠ 18 ≠ 81
Hence y does not vary inversely with x.
Table B:
x | y
1 | -5
2 | 5
3 | 15
1×-5 = -5
2×5 = 10
3×15 = 45
-5 ≠ 10 ≠ 45
Hence y does not vary inversely with x.
Table C:
x | y
1 | 18
2 | 9
3 | 6
1×18 = 18
2×9 = 18
3×6 = 18
18 = 18 = 18
Hence y vary inversely with x.
Table D:
x | y
1 | 4
2 | 8
3 | 12
1×4 = 4
2×8 = 16
3×12 = 36
4 ≠ 16 ≠ 36
Hence y does not vary inversely with x.
A city council consists of eight Democrats and eight Republicans. If a committee of six people is selected, find the probability of selecting two Democrats and four Republicans.
(Type answer a fraction Simplify your answer.)
Answer:
The probability is [tex]P[ D n R] = 0.196[/tex]
Step-by-step explanation:
From the question we are told that
The number of Democrats is [tex]D = 8[/tex]
The number of republicans is [tex]R = 8[/tex]
The number of ways of selecting selecting two Democrats and four Republicans.
[tex]N = \left {D} \atop {}} \right. C_2 * \left {R} \atop {}} \right. C_1[/tex]
Where C represents combination
substituting values
[tex]N = \left {8} \atop {}} \right. C_2 * \left {8} \atop {}} \right. C_1[/tex]
[tex]N = \left {8} \atop {}} \right. C_2 * \left {8} \atop {}} \right. C_1 = \frac{8!}{(8-2)! 2!} * \frac{8! }{(8-4)! 1 !}[/tex]
=> [tex]N = \left {8} \atop {}} \right. C_2 * \left {8} \atop {}} \right. C_1 = \frac{8!}{(6)! 2!} * \frac{8! }{(6)! 1 !}[/tex]
=> [tex]N = \left {8} \atop {}} \right. C_2 * \left {8} \atop {}} \right. C_1 = \frac{8 * 7 * 6!}{(6)! 2!} * \frac{8*7 *6! }{(6)! 1 !}[/tex]
=> [tex]N = \left {8} \atop {}} \right. C_2 * \left {8} \atop {}} \right. C_1 = \frac{8 * 7 }{ 2*1 } * \frac{8*7 }{ 1 *1 }[/tex]
=> [tex]N = 1568[/tex]
The total number of ways of selecting the committee of six people is
[tex]Z = \left {D+R} \atop {}} \right. C_6[/tex]
substituting values
[tex]Z = \left {8+8} \atop {}} \right. C_6[/tex]
[tex]Z= \left {16} \atop {}} \right. C_6[/tex]
substituting values
[tex]Z= \left {16} \atop {}} \right. C_6 = \frac{16! }{(16-6) ! 6!}[/tex]
[tex]Z= \left {16} \atop {}} \right. C_6 = \frac{16 *15 *14 * 13 * 12 * 11 * 10! }{10 ! 6!}[/tex]
[tex]Z= \left {16} \atop {}} \right. C_6 = \frac{16 *15 *14 * 13 * 12 * 11 }{6* 5 * 4 * 3 * 2 * 1}[/tex]
[tex]Z= \left {16} \atop {}} \right. C_6 = 8008[/tex]
The probability of selecting two Democrats and four Republicans is mathematically represented as
[tex]P[ D n R] = \frac{N}{Z}[/tex]
substituting values
[tex]P[ D n R] = \frac{1568}{8008}[/tex]
[tex]P[ D n R] = 0.196[/tex]
please help all i need is the slope in case the points are hard to see here they are problem 1. (-2,2) (3,-3) problem 2. (-5,1) (4,-2) problem 3. (-1,5) (2,-4)
Answer: 1. [tex]-\dfrac{5}{6}[/tex] 2. [tex]-\dfrac{1}{3}[/tex] . 3. [tex]-3[/tex]
Step-by-step explanation:
Formula: Slope[tex]=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
1. (-2,2) (3,-3)
Slope [tex]=\dfrac{-3-2}{3-(-2)}[/tex]
[tex]=\dfrac{-5}{3+2}\\\\=\dfrac{-5}{6}[/tex]
Hence, slope of line passing through (-2,2) (3,-3) is [tex]-\dfrac{5}{6}[/tex] .
2. (-5,1) (4,-2)
Slope [tex]=\dfrac{-2-1}{4-(-5)}[/tex]
[tex]=\dfrac{-3}{4+5}\\\\=\dfrac{-3}{9}\\\\=-\dfrac{1}{3}[/tex]
Hence, slope of line passing through (-2,2) and (3,-3) is [tex]-\dfrac{1}{3}[/tex] .
3. (-1,5) (2,-4)
Slope [tex]=\dfrac{-4-5}{2-(-1)}[/tex]
[tex]=\dfrac{-9}{2+1}\\\\=\dfrac{-9}{3}\\\\=-3[/tex]
Hence, slope of line passing through (-1,5) and (2,-4) is -3.
Scores turned in by an amateur golfer at the Bonita Fairways Golf Course in Bonita Springs, Florida, during and are as follows: Season: 7377787674727476 Season: 7069747684797078a. Calculate the mean (to the nearest whole number) and the standard deviation (to decimals) of the golfer's scores, for both years.MeanStandard deviationMeanStandard deviationb. What is the primary difference in performance between and
Complete question is;
Scores turned in by an amateur golfer at the Bonita Fairways Golf Course in Bonita Springs, Florida, during 2005 and 2006 are as follows:
2005 Season: 73 77 78 76 74 72 74 76
2006 Season: 70 69 74 76 84 79 70 78
A) Calculate the mean (to the nearest whole number) and the standard deviation (to decimals) of the golfer's scores, for both years.
B) What is the primary difference in performance between 2005 and 2006? What improvement,
if any, can be seen in the 2006 scores?
Answer:
A) 2006 mean = 75
2005 mean = 75
2006 standard deviation = 5.2644
2005 standard deviation = 2.0702
B)The primary difference is that variation is higher in the 2006 season than the 2005 season.
Step-by-step explanation:
A) Mean is the sum of all scores divided by the number of scores.
Thus;
μ_2005 = (73 + 77 + 78 + 76 + 74 + 72 +74 + 76)/8 = 75
Similarly;
μ_2006 = (70 + 69 + 74 + 76 + 84 + 79 + 70 + 78)/8 = 75
Now, variance is calculated by the sum of the square of mean deviations divided by (n - 1)
Thus;
2005 Variance = ((73-75)² + (77-75)² + (78-75)² + (76-75)² + (74-75)² + (72-75)² + (74-75)² + (76-75)²)/(8-1) = 4.2857
2006 Variance = ((70-75)² + (69-75)² + (74-75)² + (76-75)² + (84-75)² + (79-75)² + (70-75)² + (78-75)²)/(8 - 1) = 27.7143
Now, standard deviation is the square root of variance.
Thus;
2005 standard deviation = √4.2857 = 2.0702
2006 standard deviation = √27.7143 = 5.2644
B) The primary difference is that variation is higher in the 2006 season than the 2005 season.
Also,
the value of 4^-1+8^-1÷1/2/3^3
Answer:
1.9375.
Step-by-step explanation:
To solve this, we must use PEMDAS.
The first things we take care of are parentheses and exponents.
Since there are no parentheses, we do exponents.
4^-1+8^-1÷1/2/3^3
= [tex]\frac{1}{4} +\frac{1}{8} / 1/ 2/ 27[/tex]
= 1/4 + (1/8) / 1 * (27 / 2)
= 1/4 + (27 / 8) / 2
= 1/4 + (27 / 8) * (1 / 2)
= 1/4 + (27 / 16)
= 4 / 16 + 27 / 16
= 31 / 16
= 1.9375.
Hope this helps!
Find the area of the kite below. POSSIBLE ANSWERS: 168 mm 2 or 216 mm 2 or 195 mm 2 or 228 mm 2
Answer:
168 mm²
Step-by-step explanation:
Let A be the area of this shape
the kite is made of two triangles
Let A' and A" be the areas of the triangles
let's calculate A' and A" :
The area of a triangle is the product of the base and the height over 2
A' = [tex]\frac{(12+12)*5}{2}[/tex] = 60 mm² A"= [tex]\frac{(12+12)*9}{2}[/tex] = 108 mm²Let's calculate A
A = A' + A" A = 108+ 60 A = 168 mm²need answers (ASAP!!!) with equations, please!!
Answer:
a=6, b=5.5
Step-by-step explanation:
By looking at the sides of the triangles it can easily be seen that some of the sides match up. Side b is similar to the side of 11 and same with side a and the side of 3. Since one side is 16 and the other side on the smaller triangle is 8, the bigger triangle is twice as large than the smaller one. So 3 x 2 = 6 and 11 / 2 = 5.5
You will note the wheel has 38 slots. There are two green slots (labeled
0,00) and 36 slots which alternate red/black and are numbered 01-36. A
player participates by tossing a small ball around the wheel as the wheel
spins, and the ball lands in one of the 38 slots. The goal is for the ball to
land in a slot that the player predicted it would, and bet money on
happening. Define the following events:
E = The ball lands in an even numbered slot
M = The ball lands in a slot that is numbered a multiple of three (3,6,9,
12, etc...)
Use the given information to calculate the conditional probability M|E.
Round your answer to four decimal places.
Answer:
~0.3158
Step-by-step explanation:
Number of even numbers in the range of 1 - 38 is 38/2 = 19
=> P(E) = 19/38 = 1/2
Having: 38 = 3 x 12 + 2, then the number of numbers that is a multiple of 3 in the range of 1 - 38 is 12
=> P(M) = 12/38 = 6/19
Having: 38 = 6 x 6 + 2, then the number of numbers that is a multiple of 6 (or multiple of 2 and 3) is 6
=> P(E and M) = 6/38 = 3/19
Applying the conditional probability formula:
P(M|E) = P(E and M)/P(E) = (3/19)/(1/2) = 6/19 = ~0.3158
A regression model between sales (y in $1000), unit price (x1 in dollars), and television advertisement (x2 in dollars) resulted in the following function: Ŷ = 7 - 3x1 + 5x2 For this model, SSR = 3500, SSE = 1500, and the sample size is 18. If we want to test for the significance of the regression model, the critical value of F at the 5% level of significance is a. 3.29. b. 3.24. c. 3.68. d. 4.54.
Answer: C. 3.68
Step-by-step explanation:
Given that;
Sample size n = 18
degree of freedom for numerator k = 2
degree of freedom for denominator = n - k - 1 = (18-2-1) = 15
level of significance = 5% = 5/100 = 0.05
From the table values,
the critical value of F at 0.05 significance level with (2, 18) degrees of freedom is 3.68
Therefore option C. 3.68 is the correct answer
5x - y = -7
4x + 2y = – 14
Answer:
[tex]\boxed{\sf \ \ x=-2, \ y=-3 \ \ }[/tex]
Step-by-step explanation:
Hello,
I assume that you want to solve this system of two equations
(1) 5x - y = -7
(2) 4x + 2y = -14
We will multiply (1) by 2 and add to (2) so that we can eliminate the terms in y
2*(1)+(2) gives
10x - 2y + 4x + 2y = -7*2 -14 = -14 - 14 = -28
<=>
14x = - 28 we can divide by 14 both parts
x = -28/14 = -2
and then we replace x in (1)
5*(-2)-y=-7
-10-y=-7 add 7
-10-y+7=0
-3-y=0 add y
-3 = y
which is equivalent to y = -3
do not hesitate if you have any question
Answer:
x = -2, y = -3
Step-by-step explanation:
5x - y = -7
4x + 2y = – 14
Multiply the first equation by 2
2(5x - y) = 2*-7
10x -2y = -14
Add this to the second equation to eliminate y
10x -2y = -14
4x + 2y = – 14
---------------------------
14x = -28
Divide by 14
14x/14 = -28/14
x = -2
Now find y
4x+2y = -14
4*-2 +2y = -14
-8+2y = -14
Add 8 to each side
2y = -6
Divide by 2
2y/2 = -6/2
y = -3
Historically, the proportion of students entering a university who finished in 4 years or less was 63%. To test whether this proportion has decreased, 114 students were examined and 51% had finished in 4 years or less. To determine whether the proportion of students who finish in 4 year or less has statistically significantly decreased (at the 5% level of signficance), what is the critical value
Answer:
z(c) = - 1,64
We reject the null hypothesis
Step-by-step explanation:
We need to solve a proportion test ( one tail-test ) left test
Normal distribution
p₀ = 63 %
proportion size p = 51 %
sample size n = 114
At 5% level of significance α = 0,05, and with this value we find in z- table z score of z(c) = 1,64 ( critical value )
Test of proportion:
H₀ Null Hypothesis p = p₀
Hₐ Alternate Hypothesis p < p₀
We now compute z(s) as:
z(s) = ( p - p₀ ) / √ p₀q₀/n
z(s) =( 0,51 - 0,63) / √0,63*0,37/114
z(s) = - 0,12 / 0,045
z(s) = - 2,66
We compare z(s) and z(c)
z(s) < z(c) - 2,66 < -1,64
Therefore as z(s) < z(c) z(s) is in the rejection zone we reject the null hypothesis
a 12- inch ruler is duvided into 3 parts. the large part is 3 times longer than the small. the meddium part is times longer than then small, the medium part is 2 times long as the smallest .how long is the smallest part?
Answer:
2 inches
Step-by-step explanation:
x= smallest
3x=largest
2x=medium
x+3x+2x=12
6x=12
x=2
so smallest is 2
largest is 6 (3x)
medium is 4 (2x)
2+6+4=12
Compute the following values when the log is defined by its principal value on the open set U equal to the plane with the positive real axis deleted.
a. log i
b. log(-1)
c. log(-1 + i)
d. i^i
e. (-i)^i
Answer:
Following are the answer to this question:
Step-by-step explanation:
The principle vale of Arg(3)
[tex]Arg(3)=-\pi+\tan^{-1} (\frac{|Y|}{|x|})[/tex]
The principle value of the [tex]\logi= \log(0+i)\ \ \ \ \ _{where} \ \ \ x=0 \ \ y=1> 0[/tex]
So, the principle value:
a)
[tex]\to \log(i)=\log |i|+i Arg(i)\\\\[/tex]
[tex]=\log \sqrt{0+1}+i \tan^{-1}(\frac{1}{0})\\\=\log 1 +i \tan^{-1}(\infty)\\\=0+i\frac{\pi}{2}\\\=i\frac{\pi}{2}[/tex]
b)
[tex]\to \log(-i)= \log(0-i ) \ \ \ x=0 \ \ \ y= -1<0\\[/tex]
Principle value:
[tex]\to \log(-i)= \log|-i|+iArg(-i) \\\\[/tex]
[tex]=\log \sqrt{0+1}+i(-\pi+\tan^{-1}(\infty))\\\\=\log1 + i(-\pi+\frac{\pi}{2})\\\\=-i\frac{\pi}{2}[/tex]
c)
[tex]\to \log(-1+i) \ \ \ \ x=-1, _{and} y=1 \ \ \ x<0 and y>0[/tex]
The principle value:
[tex]\to \log(-1+i)=\log |-1+i| + i Arg(-1+i)[/tex]
[tex]=\log \sqrt{1+1}+i(\pi+\tan^{-1}(\frac{1}{1}))\\\\=\log \sqrt{2} + i(\pi-\tan^{-1}\frac{\pi}{4})\\\\=\log \sqrt{2} + i\tan^{-1}\frac{3\pi}{4}\\\\[/tex]
d)
[tex]\to i^i=w\\\\w=e^{i\log i}[/tex]
The principle value:
[tex]\to \log i=i\frac{\pi}{2}\\\\\to w=e^{i(i \frac{\pi}{2})}\\\\=e^{-\frac{\pi}{2}}[/tex]
e)
[tex]\to (-i)^i\\\to w=(-i)^i\\\\w=e^{i \log (-i)}[/tex]
In this we calculate the principle value from b:
so, the final value is [tex]e^{\frac{\pi}{2}}[/tex]
f)
[tex]\to -1^i\\\\\to w=e^{i log(-1)}\\\\\ principle \ value: \\\\\to \log(-1)= \log |-1|+iArg(-i)[/tex]
[tex]=\log \sqrt{1} + i(\pi-\tan^{-1}\frac{0}{-1})\\\\=\log \sqrt{1} + i(\pi-0)\\\\=\log \sqrt{1} + i\pi\\\\=0+i\pi\\=i\pi[/tex]
and the principle value of w is = [tex]e^{\pi}[/tex]
g)
[tex]\to -1^{-i}\\\\\to w=e^(-i \log (-1))\\\\[/tex]
from the point f the principle value is:
[tex]\to \log(-1)= i\pi\\\to w= e^{-i(i\pi)}\\\\\to w=e^{\pi}[/tex]
h)
[tex]\to \log(-1-i)\\\\\ Here x=-1 ,<0 \ \ y=-1<0\\\\ \ principle \ value \ is:\\\\ \to \log(-1-i)=\log\sqrt{1+1}+i(-\pi+\tan^{-1}(1))[/tex]
[tex]=\log\sqrt{2}+i(-\pi+\frac{\pi}{4})\\\\=\log\sqrt{2}+i(-\frac{3\pi}{4})\\\\=\log\sqrt{2}-i\frac{3\pi}{4})\\[/tex]