Answer:
Null hypothesis :
[tex]H_o:p_1-p_2 = 0[/tex]
Alternative hypothesis:
[tex]H_1:p_1-p_2 \neq 0[/tex]
Decision Rule:
To reject the null hypothesis if z < -1.65 and z > 1.65
Conclusion:
Failed to reject null hypothesis if z > -1.65 or z < 1.65
z -value = 0.33022
P-value = 0.7414
Decision Rule:
Since the P-value is higher than the level of significance , therefore do not reject the null hypothesis at the level of significance of 0.1
Conclusion: we failed to reject null hypothesis, Therefore, the data does not believe that the true percentage of those in the first group who suffer a second episode is different from the true percentage of those in the second group who suffer a second episode
Step-by-step explanation:
From the summary of the given statistical data sets.
Let consider to [tex]p_1[/tex] represent percentage of the first group ; &
[tex]p_2[/tex] represent percentage of the second group
The null and the alternative hypothesis can be stated s follows:
Null hypothesis :
[tex]H_o:p_1-p_2 = 0[/tex]
Alternative hypothesis:
[tex]H_1:p_1-p_2 \neq 0[/tex]
At the level of significance ∝ = 0.1; the two tailed critical value from the z-table
[tex]z_{\alpha/2} = 1.65[/tex]
Decision Rule:
To reject the null hypothesis if z < -1.65 and z > 1.65
Conclusion:
Failed to reject null hypothesis if z > -1.65 or z < 1.65
However; from the question:
There are 55 people in the first group and this group will be administered the new drug.
There are 45 people in the second group and this group will be administered a placebo.
After one year, 11% of the first group has a second episode and 9% of the second group has a second episode.
The test statistic for the for the first group who suffered from the second episode can be denoted as :
[tex]\hat p_1 = \dfrac{\overline x_1}{n_1}=0.11[/tex]
The test statistic for the for the second group who suffered from the second episode can be denoted as :
[tex]\hat p_2 = \dfrac{\overline x_2}{n_2}=0.09[/tex]
where;
[tex]n_1[/tex] = sample size of group 1 = 55
[tex]n_2[/tex] = sample size of group 2 = 45
The total probability of both group is :
[tex]\hat p = \dfrac{n_1 \hat p_1 + n_2 \hat p_2}{n_1 + n_2}[/tex]
[tex]\hat p = \dfrac{55*0.11+ 45 * 0.09}{55+45}[/tex]
[tex]\hat p = \dfrac{6.05+ 4.05}{100}[/tex]
[tex]\hat p = \dfrac{10.1}{100}[/tex]
[tex]\hat p = 0.101[/tex]
The standard error of the statistic [tex]\hat p_1 - \hat p_2[/tex] an be computed as follows:
[tex]S.E(\hat p_1 - \hat p_2)= \sqrt{ p_1 (1 - \hat p)( \dfrac{1}{n_1}+\dfrac{1}{n_2})}[/tex]
[tex]S.E(\hat p_1 - \hat p_2)= \sqrt{0.101 (1 - 0.101)( \dfrac{1}{55}+\dfrac{1}{45})}[/tex]
[tex]S.E(\hat p_1 - \hat p_2)= \sqrt{0.101(0.899)(0.0404)}[/tex]
[tex]S.E(\hat p_1 - \hat p_2)= \sqrt{0.0036682796}[/tex]
[tex]S.E(\hat p_1 - \hat p_2)=0.060566[/tex]
Now; The test statistics is determined to be :
[tex]z = \dfrac{(\hat p_1 - \hat p_2 ) - (p_1-p_2)}{SE(\hat p_1 - \hat p_2)}[/tex]
[tex]z = \dfrac{(0.11-0.09) - 0}{0.060566}[/tex]
z = 0.33022
Hence; the value for the test statistics = 0.33022
the value for the test statistics = 0.33
From the z value; The P-value for the test statistics can be computed as:
P-value = 2P(Z ≥ |z|)
P-value = 2P(Z ≥ 0.33022)
P-value = 2 × P (Z ≤ - 0.33022)
From the z table Z ≤ - 0.33022 = 0.3707
P-value = 2 × 0.3707
P-value = 0.7414
Decision Rule:
Since the P-value is higher than the level of significance , therefore do not reject the null hypothesis at the level of significance of 0.1
Conclusion: we failed to reject null hypothesis, Therefore, the data does not believe that the true percentage of those in the first group who suffer a second episode is different from the true percentage of those in the second group who suffer a second episode
from $2003$ onward, the number of daily visitors to a website increased by $200\%$ every two years. So, for example, the number of visitors in $2011$ was $200\%$ more than the number of visitors in $2009$.
In what year was the number of daily visitors $800\%$ more than the number of daily visitors in $2003$? Explain, in words, why your answer is correct.
Answer:
2007
Step-by-step explanation:
If the number of visitors was, say, 100 people in 2003, then in 2005 that number would have gone up to 300 people, which is a 200% increase. And that number would have gone up to 900 people in 2007, which is an 800% increase.
Answer:
2007
NOT YOU TRYING TO GET THE AOPS PREALGEBRA 2 ANSWER
I stan though :D
Find the equation of the line: parallel to 3x−y=11 through (−2, 0).
Answer:
[tex]\huge\boxed{y=3x+6\to 3x-y=-6}[/tex]
Step-by-step explanation:
[tex]\text{Let}\ k:y=m_1x+b_1;\ l:y=m_2x+b_2\\\\k\ ||\ l\iff m_1=m_2\\k\ \perp\ l\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\===========================[/tex]
[tex]\text{We have the equation of a line in the standard form:}\ 3x-y=11.\\\text{Convert it to the slope-intercept form:}\ y=mx+b\\\\3x-y=11\qquad\text{subtract}\ 3x\ \text{from both sides}\\-y=-3x+11\qquad\text{change the signs}\\y=3x-11\to \boxed{m_1=3}\\\\\text{Let}\ k:y=3x-11\ \text{and}\ l:y=mx+b.\\\\l\ ||\ k\Rightarrow l:y=3x+b\\\\\text{Substitute the coordinates of the point}\ (-2;\ 0)\ \text{to the equation of}\ l:\\\\0=3(-2)+b\\0=-6+b\qquad\text{add 6 to both sides}\\6=b\to\boxed{b=6}[/tex]
[tex]\text{Finally}\ l:y=3x+6\\\\\text{Convert to the standard form:}\\\\y=3x+6\qquad\text{subtract}\ 3x\ \text{from both sides}\\-3x+y=6\qquad\text{change the signs}\\l:\ 3x-y=-6[/tex]
Find the present value of an investment that is worth $19,513.75 after earning 3% simple interest for 512 years.
Answer:
$16,750.00
Step-by-step explanation:
Simple interest:
I = Prt
Value of an investment of value P over t years at r interest rate:
F = P + Prt
F = P(1 + rt)
19,513.75 = P(1 + 0.03 * 5.5)
1.165P = 19,513.75
P = 16,750
Answer: $16,750.00
The present value of the investment was $16,750 which is worth $19,513.75 after earning 3% simple interest for 512 years.
What is the simple interest?Simple interest is defined as interest paid on the original principal and calculated with the following formula:
S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years. The rate of interest is in percentage r% and is to be written as r/100
We have been given data as:
Rate of Interest (R) = 3% = 3/100 = 0.03
Time (T) = 512 years
Value of an investment of value P over t years at r interest rate:
A = P + Prt
A = P(1 + rt)
19,513.75 = P(1 + 0.03 × 5.5)
19,513.75 = 1.165P
1.165P = 19,513.75
P = 19,513.75/1.165
P = 16,750
Thus, the present value of the investment was $16,750 which is worth $19,513.75 after earning 3% simple interest for 512 years.
Learn more about the simple interest here:
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What formula could you use to help find the area of the given triangle?
Answer:
Since it is a right triangle, you can use pythagorean theorem to find the missing side.
Step-by-step explanation:
Marguerite wants to rent a carpet cleaner. Company A rents a carpet cleaner for $15 per day. Company B rents a carpet cleaner for $100 per week, with a one-time fee of $5. The following functions represent the rate structures of the two rental companies: x = the number of weeks Company A f(x) = 15(7x) Company B g(x) = 100x + 5 The function h(x) = f(x) – g(x) represents the difference between the two rate structures. Determine which statements about h(x) and about renting a carpet cleaner are true. Check all that apply. If Marguerite rents for 2 weeks, it will cost her more if she rents from Company B. If Marguerite rents for 2 weeks, it will cost her less if she rents from Company B. If Marguerite rents for 1 week, it will cost her the same at either company. If Marguerite rents for 1 week, it will cost her more if she rents from Company A. h(x) = 5x – 5 h(x) = 5x + 5
Answer:
see below
Step-by-step explanation:
Company A f(x) = 15(7x)
Company B g(x) = 100x + 5
If Marguerite rents for 2 weeks, it will cost her more if she rents from Company B
A = 105(2) = 210
B = 100(2) + 5 = 205 B costs less False
f Marguerite rents for 2 weeks, it will cost her less if she rents from Company B
A = 105(2) = 210
B = 100(2) + 5 = 205 B costs less True
If Marguerite rents for 1 week, it will cost her the same at either company
A = 105(1) = 105
B = 100(1) +5 = 105 True
If Marguerite rents for 1 week, it will cost her more if she rents from Company A
A = 105(1) = 105
B = 100(1) +5 = 105 False
h(x) = 5x – 5
h(x) = f(x) – g(x)
=15(7x) - ( 100x + 5)
= 105x - 100x -5
= 5x-5 True
h(x) = 5x + 5 False
Answer:
If Marguerite rents for 2 weeks, it will cost her less if she rents from Company B.
If Marguerite rents for 1 week, it will cost her the same at either company.
h(x) = 5x - 5.
Step-by-step explanation:
Company A: f(x) = 15(7x)
Company B: g(x) = 100x + 5
h(x) = f(x) - g(x)
So, the function h(x) is the difference between Company A's rental and Company B's rental.
h(x) = (15(7x)) - (100x + 5)
= (105x) - (100x + 5)
= 105x - 100x - 5
= 5x - 5
h(x) = 5x - 5.
Let's say that Marguerite rents for 1 week. In Company A, that will cost her 15 * 7 = 105. In Company B, it will cost her 100 + 5 = 105. So, if Marguerite rents for 1 week, it will cost her the same at either company.
Let's say that Marguerite rents for 2 weeks. In Company A, that will cost her 15 * 7 * 2 = 30 * 7 = 210. In Company B, it will cost her 100 * 2 + 5 = 200 + 5 = 205. So, if Marguerite rents for 2 weeks, it will cost her less if she rents from Company B.
Hope this helps!
You are flying a kite on a line that is 350 feet long. Let's suppose the line is perfectly straight (it never really is) and it makes an angle of 65 degrees with the horizontal direction. The kite is flying at an altitude of feet.
Answer:
We can think that the line of the kite is the hypotenuse of a triangle rectangle, and the altitude is one of the cathetus of the triangle.
And we know that it makes an angle of 65° with the horizontal (i guess this is measured between the hypotenuse and the horizontal adjacent to the kite.
This angle is complementary to the top angle of our triangle rectangle, such that A + 65° = 90°
A = 90° - 65° = 25°
Then the altitude of the kite is the adjacent cathetus to this angle.
We can use the relation:
sin(A) = Adjacent cathetus/hypotenuse.
Sin(25°) = X/350ft
Sin(25°)*350ft = X = 147.9m
The kite is flying at an altitude of approximately 317.20 feet.
The situation will form a right angle triangle.
The hypotenuse of the triangle is the will be the line of the kite which is 350 ft long.
The line makes an angle of 65° with the horizontal direction. The horizontal direction is the adjacent of the triangle formed.
Using trigonometric ratio, the altitude of the kite can be found below.
The altitude of the kite is the height/ opposite side of the triangle.
Therefore,
sin 65° = opposite / hypotenuse
sin 65° = opposite / 350
cross multiply
opposite = 350 × sin 65
altitude of the kite = 350 × 0.90630778703
altitude of the kite = 317.207725463
altitude of the kite ≈ 317.20 ft
read more; https://brainly.com/question/13835041?referrer=searchResults
"An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 4.1 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 260 engines and the mean pressure was 4.2 pounds/square inch. Assume the standard deviation is known to be 0.9. A level of significance of 0.02 will be used. Determine the decision rule. Enter the decision rule."
Answer:
H₀ is accepted, we don´t have evidence to claim valves produces more than 4,1 pounds/square inch
Step-by-step explanation:
Normal Distribution
Population mean μ₀ = 4.1
Population standard deviation σ = 0,9
Sample size n = 260
Sample mean μ = 4,2
Level of significance 0,02 α = 0,02 form z-table we find z score
z(c) = 2,05 (critical value)
Test hypothesis
Null hypothesis H₀ μ = μ₀
Alternative hypothesis Hₐ μ > μ₀
Is a one tail-test ( to the right. Values have a mean over the population mean)
z(s) = ( μ - μ₀ )/ σ /√n
z(s) = 4,2 - 4,1 / 0,9/√260
z(s) = 0,1 *16,1245 / 0,9
z(s) = 1,7916
To compare z(s) and z(c)
z(s) < z(c)
Then z(s) is in the acceptance region, we accept H₀
Two trains leave New York at the same time heading in opposite directions. Train A travels at 4/5 the speed of train one. After seven hours they are 693 miles apart. What was the speed of train A? Can you pls help me fast
=============================================
Work Shown:
x = speed of train A
y = speed of train B
"train A travels 4/5 the speed of train B" (I'm assuming "train one" is supposed to read "train B"). So this means x = (4/5)y
distance = rate*time
d = x*7
d = (4/5)y*7 = (28/5)y represents the distance train A travels
d = y*7 = 7y represents the distance train B travels
summing those distances will give us 693
(28/5)y + 7y = 693
5*( (28/5)y + 7y ) = 5*693
28y + 35y = 3465
63y = 3465
y = 3465/63
y = 55
Train B's speed is 55 mph
4/5 of that is (4/5)y = (4/5)*55 = 4*11 = 44 mph
Train A's speed is 44 mph
What is 24-(-6) because in confused
Answer:
30
Step-by-step explanation:
24 - (-6)
Apply rule : -(-a) = a
Negative (-) times a negative (-) is positive (+).
24 + 6
= 30
Answer:
-6 is in parentheses because it is a negative number. this prevents the equation from looking like a too long subtraction sign (24--6); therefore it is written as 24 - (-6).
this simplifies to 24 + 6 = 30
to negatives = a positive
1.
ai. What is respiration?
ii. Distinguish between self-pollination and cross pollination.
bi. Define force?
ii. State three effect of force.
ci. Define any two types of energy.
Answer:
Respiration:
1)Energy giving process. (Cell respiration...)
2) The act of inhaling or exhaling.
Self-pollination:
The transmission of pollen grain from anther to stigma which takes place at a single flower.
Cross-pollination:
The transmission of pollen grain from anther to stigma which takes place between two different flowers of the same species.
Force:
Any push or pull exerted by a body.
Contact Force, Magnetic force, Gravitational force
Kinetic energy and Potential energy.
Kinetic energy:
A kind of energy which an object possesses due to its motion.
Potential energy:
A kind of energy which an object possesses due to its height or position.
Hope this helps ;) ❤❤❤
What is the degree of the polynomial?
Answer:
2
Step-by-step explanation:
The degree of this polynomial is 2, since a parabola is drawn. A parabola is a graph of a quadratic equation which has the highest degree of 2.
PLEASE HELP!!! QUICKLY
Practice
Question 1: Choose the number that will complete this Pythagorean triple.
15, 17
Question 2: Choose the number that will complete this Pythagorean triple.
9,
41
Question 3: Choose the number that will complete this Pythagorean triple.
12, 35,
Reset
Submit
Answer:
1. = 8
2. =40
3. =37
Step-by-step explanation:
1. x = √(17² - 15²) = 8
2. x =√(9² +41²) = 40
3. x =√(12² + 35²) = 37
please mark brainliest
6th grade math , helpp:D
Answer:
a) 30%
b) 45%
Step-by-step explanation:
a) Laura rolls it '4' 12/40 times, you need to convert that to a percent, so 12/40=6/20= 30% or 30/100
b) Basically the same thing: 18/40 = 45% or 45/100
Hope this helped XD
Circle the numbers divisible by 2.
320;5,763; 9,308; 5,857;3,219; 5,656; 83,001;53,634
If while playing Blackjack if you receive the 6 of hearts and the 8 of diamonds, what are the odds that you will bust if you hit? (If you receive another card what are the odds that their sum will add to 22 or higher with Aces counting as 1 and royal cards counting as 10?)
Answer:
Winning odd = 3.4
Loosing odd = 4.3.
Step-by-step explanation:
So, from this particular Question or problem we have the following data or information or parameters which is going to aid or help us in solving this particular Question;
=> Given 6 of hearts and the 8 of diamonds.
We know that there are 8 types of cards.
Also, we know that the total number of the cards is equal to fifty-two(52).
From cards of six(6) to ten(10) a bust will surely occur.
Therefore, 8 × 4 / 52= 32/52 = 0.62.
If an ace is pulled, then the chance of winning bis surely 4 out of 52 deck of cards.
Giving you a Winning odd = 3.4 and a
Loosing odd = 4.3.
A researcher compares the effectiveness of two different instructional methods for teaching anatomy. A sample of 146 students using Method 1 produces a testing average of 51.6. A sample of 180 students using Method 2 produces a testing average of 62.7. Assume the standard deviation is known to be 9.42 for Method 1 and 14.5 for Method 2. Determine the 98% confidence interval for the true difference between testing averages for students using Method 1 and students using Method 2. Step 1 of 2: Find the critical value that should be used in constructing the confidence interval.
Answer:
The confidence interval is [tex]-11.34 < \mu_1 -\mu_2 < -10.86[/tex]
Step-by-step explanation:
From the question we are told that
The first sample size is [tex]n_1 = 146[/tex]
The second sample size is [tex]n_2 = 180[/tex]
The first sample mean is [tex]\= x_1 = 51.6[/tex]
The second sample mean is [tex]\= x_2 = 62.7[/tex]
The first standard deviation is [tex]\sigma _1 = 9.42[/tex]
The second standard deviation is [tex]\sigma _2 = 14.5[/tex]
Given that the confidence level is 98% then the significance level is mathematically evaluated as
[tex]\alpha = (100 -98 )\%[/tex]
[tex]\alpha = 2 \%[/tex]
[tex]\alpha = 0.02[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the z-table , the value is [tex]Z_{\frac{\alpha }{2} } = 2.33[/tex]
The reason we are obtaining critical value of
[tex]\frac{\alpha }{2}[/tex]
instead of
[tex]\alpha[/tex]
is because
[tex]\alpha[/tex]
represents the area under the normal curve where the confidence level interval (
[tex]1-\alpha[/tex]
) did not cover which include both the left and right tail while
[tex]\frac{\alpha }{2}[/tex]
is just the area of one tail which what we required to calculate the margin of error
NOTE: We can also obtain the value using critical value calculator (math dot armstrong dot edu)
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{\sigma_1^2}{n_1^2} + \frac{\sigma_2^2}{n_2^2} }[/tex]
substituting values
[tex]E = 2.33 * \sqrt{ \frac{9.42^2}{146^2} + \frac{14.5^2}{180^2} }[/tex]
substituting values
[tex]E = 2.33 * \sqrt{ \frac{9.42^2}{146^2} + \frac{14.5^2}{180^2} }[/tex]
[tex]E = 0.2405[/tex]
The 98% confidence interval is mathematically represented as
[tex](\= x _ 1 - \= x_2 ) - E < \mu_1 -\mu_2 < (\= x _ 1 - \= x_2 ) + E[/tex]
substituting values
[tex](51.6 - 62.7) - 0.2405 < \mu_1 -\mu_2 < (51.6 - 62.7) + 0.2405[/tex]
[tex]-11.34 < \mu_1 -\mu_2 < -10.86[/tex]
Write a formula for the nth term of the arithmetic sequence
1, -3, -7, - 11, - 15...
The formula for the nth term of the sequence is an
Answer:
Step-by-step explanation:
[tex]a_{1}=1\\d=-3-1=-4\\a_{n}=a_{1}+(n-1)d\\a_{n}=1+(n-1)(-4)\\a_{n}=1-4n+4\\a_{n}=5-4n[/tex]
What’s 6(x – 1) = 9(x + 2) ?
Answer:
-8=x
Step-by-step explanation:
6x-6=9x+18
-6-18=9x-6x
-24=3x
x=-8
hope i helped
brainliest pls
im trying to level up
Answer:
x=-8
Step-by-step explanation:
(08.05 LC)The histogram shows the number of prizes won by different numbers of students at a quiz competition. Which of the following statements is correct regarding the number of students and the number of prizes won? A histogram titled Prizes Won is shown. The horizontal axis is labeled Number of Prizes with bins 0 to 5, 6 to 11, 12 to 17, and 18 to 23. The vertical axis labeled Students with values from 0 to 10 at intervals of 1. The first bin goes to 2, the second goes to 7, the third goes to 4, and the last goes to 10. A) A total of 10 students won all the prizes. B) Four students won 12, 13, 14, 15, 16, or 17 prizes. C) A total of 10 prizes were won by all the students. D) Four prizes were won by 12, 13, 14, 15, 16, or 17 students.
Answer: B.
Four students won 12, 13, 14, 15, 16, or 17 prizes
Answer:
Four students won 12, 13, 14, 15, 16, or 17 prizes!
Step-by-step explanation:
Alex has built a garden shed in the shape shown.
(A) Alex plans to paint the outside of the shed, including the roof but not the floor. One can of paint can cover 6m^2 . How many cans of paint will Alex need.
(B)If one can of paint costs $25.50, what will the cost be including 13% tax.
Answer:
A) 22 cans required to paint
B) Including 13% tax, cost of painting = $633.93
Step-by-step explanation:
As we check the figure, we have a composite figure.
Cuboid on the base and a pyramid on the top of it.
To find the area to be painted, we have 4 rectangular faces of cuboid with dimensions 6m [tex]\times[/tex] 3m.
And 4 triangular faces of pyramid with Base = 6m and Height 5m.
So, total area to be painted = 4 rectangular faces + 4 triangular faces
Area of rectangle = Length [tex]\times[/tex] Width = 6 [tex]\times[/tex] 3 = 18 [tex]m^2[/tex]
Area of triangle = [tex]\frac{1}{2}\times Base \times Height =\frac{1}{2}\times 6 \times 5 = 15\ m^{2}[/tex]
Total area to be painted = 4 \times 18 + 4 \times 15 = 72 + 60 = 132 [tex]m^2[/tex]
A) Area painted by 1 can = 6 [tex]m^2[/tex]
Cans required to paint 132 [tex]m^2[/tex] = [tex]\frac{132}{6} = 22\ cans[/tex]
B)
Cost of 1 can = $25.50
Cost of 22 can = $25.50 [tex]\times[/tex] 22 = $561
Including tax of 13% = $561 + $561 [tex]\times \frac{13}{100}[/tex] = $561 + $72.93 = $633.93
So, the answers are:
A) 22 cans required to paint
B) Including 13% tax, cost of painting = $633.93
Solve application problems using radical equations. A baseball diamond is a square that is 90 feet on each side. What is the distance a catcher has to throw the ball from home to second base?
Answer:
c=127.279
Step-by-step explanation:
c²=a²+b²
c²=90²+90²
c=√90²+90²
c=127.279 feet
Help ! Inductive and deductive reasoning differ in which way? A) Conclusions drawn using deductive reasoning are always false, while conclusions drawn using inductive reasoning are always true. B) Conclusions drawn using inductive reasoning are always valid, while conclusions drawn using deductive reasoning may or may not be valid. C) Conclusions drawn using inductive reasoning are always false, while conclusions drawn using deductive reasoning are always true. D) Conclusions drawn using deductive reasoning are always valid, while conclusions drawn using inductive reasoning may or may not be valid.
Answer:
B) Conclusions drawn using inductive reasoning are always valid, while conclusions drawn using deductive reasoning may or may not be valid.
Step-by-step explanation:
Inductive reasoning uses logic and uses more evidence to draw conclusions. In deductive reasoning, WE decide whether a deductive statement is true by assessing the strength of the link between the premises and the conclusion. But some deductive reasoning may appear to make sense without pointing to a truth
Answer:
The answer is D. Conclusions drawn using deductive reasoning are always valid, while conclusions drawn using inductive reasoning may or may not be valid.
Step-by-step explanation:
I took the test
For questions 13-15, Let Z1=2(cos(pi/5)+i Sin(pi/5)) And Z2=8(cos(7pi/6)+i Sin(7pi/6)). Calculate The Following Keeping Your Answer In Polar Form. 13. z1z2 14. z2 15. z1/z2
Answer:
Step-by-step explanation:
Given the following complex values Z₁=2(cos(π/5)+i Sin(πi/5)) And Z₂=8(cos(7π/6)+i Sin(7π/6)). We are to calculate the following complex numbers;
a) Z₁Z₂ = 2(cos(π/5)+i Sin(πi/5)) * 8(cos(7π/6)+i Sin(7π/6))
Z₁Z₂ = 18 {(cos(π/5)+i Sin(π/5))*(cos(7π/6)+i Sin(7π/6)) }
Z₁Z₂ = 18{cos(π/5)cos(7π/6) + icos(π/5)sin(7π/6)+i Sin(π/5)cos(7π/6)+i²Sin(π/5)Sin(7π/6)) }
since i² = -1
Z₁Z₂ = 18{cos(π/5)cos(7π/6) + icos(π/5)sin(7π/6)+i Sin(π/5)cos(7π/6)-Sin(π/5)Sin(7π/6)) }
Z₁Z₂ = 18{cos(π/5)cos(7π/6) -Sin(π/5)Sin(7π/6) + i(cos(π/5)sin(7π/6)+ Sin(π/5)cos(7π/6)) }
From trigonometry identity, cos(A+B) = cosAcosB - sinAsinB and sin(A+B) = sinAcosB + cosAsinB
The equation becomes
= 18{cos(π/5+7π/6) + isin(π/5+7π/6)) }
= 18{cos((6π+35π)/30) + isin(6π+35π)/30)) }
= 18{cos((41π)/30) + isin(41π)/30)) }
b) z2 value has already been given in polar form and it is equivalent to 8(cos(7pi/6)+i Sin(7pi/6))
c) for z1/z2 = 2(cos(pi/5)+i Sin(pi/5))/8(cos(7pi/6)+i Sin(7pi/6))
let A = pi/5 and B = 7pi/6
z1/z2 = 2(cos(A)+i Sin(A))/8(cos(B)+i Sin(B))
On rationalizing we will have;
= 2(cos(A)+i Sin(A))/8(cos(B)+i Sin(B)) * 8(cos(B)-i Sin(B))/8(cos(B)-i Sin(B))
= 16{cosAcosB-icosAsinB+isinAcosB-sinAsinB}/64{cos²B+sin²B}
= 16{cosAcosB-sinAsinB-i(cosAsinB-sinAcosB)}/64{cos²B+sin²B}
From trigonometry identity; cos²B+sin²B = 1
= 16{cos(A+ B)-i(sin(A+B)}/64
= 16{cos(pi/5+ 7pi/6)-i(sin(pi/5+7pi/6)}/64
= 16{ (cos 41π/30)-isin(41π/30)}/64
Z1/Z2 = (cos 41π/30)-isin(41π/30)/4
Answer:
13. 16(cos(41 π/30)+ isin(41 π/30))
14. Mine asked for z2 magnitude so I got 8 (magnitude is the same as modulus which is r)
15. 1/8 (cos(29 π/30)+ isin(29 π/30))
Step-by-step explanation:
13. Since we’re multiplying z1, and z2, use De Moivre’s theorem by multiplying the r values (2 and 8) and adding the theta values (π/5 and 7π/6). Adding the angle values should lead you to have 41 π/30, and the rest is self-explanatory.
14. Explanation is in the answer, just take the r value from z2 for magnitude (at least that’s what’s on my practice assignment)
15. Use De Moivre’s theorem again, this time with division, so you will divide the r values (2 divided by 8) and subtract the theta values (π/5 minus 7π/6). 2/8 simplifies to 1/8 and when subtracting with 6π/30 - 35π/30 (finding common denominators) you should get 29π/30.
Multicollinearity may cause problems if the absolute value of the sample correlation coefficient for two of the independent variables exceeds what value? a. .7 b. 1 c. .5 d. .05
Answer: a. .7
Step-by-step explanation:
Multicollinearity means the two or more explanatory variables in a multiple regression model are highly linearly related to each other.
Multicollinearity is a problem because
it weaken the statistical significance of an independent variable. Larger the standard error of a regression coefficient, the less likely it is that this coefficient will be statistically significant.Multicollinearity may cause problems if the absolute value of the sample correlation coefficient for two of the independent variables exceeds 0.7.
So, the correct option is a. .7 .
In a soccer league, the ratio of boys to girls is 4 to 6. There are a total of 50 players in the soccer league. Determine how many girls play in the soccer league.
Answer:
30
Step-by-step explanation:
We can call the number of boys 4x and girls 6x so we can write:
4x + 6x = 50
10x = 50
x = 5, therefore the number of girls is 6x = 6 * 5 = 30.
Answer:
30
Step-by-step explanation:
In the ratio 4:6, we can think of this like 4 boys and 6 girls out of 10 team members.
We can find how many girls play by multiplying 6 by 5, since 50 divided by 10 is 5.
6(5) = 30, so 30 girls play in the soccer league.
Find the measure of the indicated angle to the nearest degree. Thanks.
Answer:
θ ≈ 40°
Step-by-step explanation:
Since, sinθ = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
cosθ = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
tanθ = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
In the picture attached,
Measures of adjacent side and opposite side of the triangle have been given. Therefore, tangent rule will be applied in the given triangle.
tanθ = [tex]\frac{19}{23}[/tex]
θ = [tex]\text{tan}^{-1}(\frac{19}{23})[/tex]
θ = 39.56
θ ≈ 40°
Which linear function represents the line given by the point-slope equation y-8 = {(x - 4)?
O f(x)=x+4
Of(x)= x+6
O fx) = x-10
O f(x) = {x-12
Answer:
[tex]f(x) = x + 4[/tex]
Step-by-step explanation:
[tex]y - 8 = x - 4[/tex]
Add 8 to both sides to isolate the y
[tex]y = x - 4 + 8[/tex]
then you're left with y = x + 4
Please help!! Geometry is my weakness!!
Answer:
Hey there!
Opposite angles in a parallelogram must be congruent, so T=R.
Hope this helps :)
Answer:
∠T ≅ ∠R
Step-by-step explanation:
We know that the angles are equal because they are opposite sides in the parallelogram.
hi there help me please
Hello!
Answer:
Choice 1.
Step-by-step explanation:
We can go through each answer choice and examine whether it represents the question:
1) This does not represent the question because 10% of 6 is 0.6. The question is asking to find a number that 6 = 10% of, not finding 10% of 6.
2) Correct because a number multiplied by 10%, or 0.1, should be equal to 6 to answer the question.
3) Correct because 6 is equivalent to 10% of the answer, which is stated in this answer choice.
4) Correct because 6 should be 10% of the answer.
Therefore, the incorrect choice would be Choice 1.
Dion recorded his heart rate as 204 beats in 3 minutes. How many beats does his heart make in 1 minute?
Answer:
68
Step-by-step explanation:
Answer:
The answer is
68 beatsStep-by-step explanation:
To solve this problem we use ratio and proportion
For 3 minutes his heart rate was 204 beats
So 1 minute will be
[tex] \frac{204 \: beats}{3} \times 1[/tex]
= 68 beatsHope this helps you