Answer:
[tex]\left(-\dfrac{7}{2},\dfrac{7\sqrt{3}}{2}\right)[/tex].
Step-by-step explanation:
The given point is
[tex]\left(7,\dfrac{2\pi}{3}\right)[/tex]
We need to find the rectangular coordinates of the given point.
If a polar coordinate is [tex](r,\theta)[/tex], then
[tex]x=r\cos theta[/tex]
[tex]y=r\sin theta[/tex]
In the given point [tex]\left(7,\dfrac{2\pi}{3}\right)[/tex],
[tex]r=7,\theta=\dfrac{2\pi}{3}[/tex]
Now,
[tex]x=7\cos \dfrac{2\pi}{3}[/tex]
[tex]x=7\cos \left(\pi-\dfrac{\pi}{3}\right)[/tex]
[tex]x=-7\cos \left(\dfrac{\pi}{3}\right)[/tex]
[tex]x=-7\left(\dfrac{1}{2}\right)[/tex]
[tex]x=-\dfrac{7}{2}[/tex]
and,
[tex]y=7\sin \dfrac{2\pi}{3}[/tex]
[tex]y=7\sin \left(\pi-\dfrac{\pi}{3}\right)[/tex]
[tex]y=7\sin \left(\dfrac{\pi}{3}\right)[/tex]
[tex]y=7\left(\dfrac{\sqrt{3}}{2}\right)[/tex]
[tex]y=\dfrac{7\sqrt{3}}{2}[/tex]
Therefore, the required point is [tex]\left(-\dfrac{7}{2},\dfrac{7\sqrt{3}}{2}\right)[/tex].
Find the distance between the points (-3, -2) and (-1, -2). 2 √6 4
Answer:
Let the distance be AB.
So, by using distance formula, we get
AB=√(x^2-x^1)^2+(y^2-y^1)^2
AB=√[-1-(-3)]^2+[-2-(-2)]^2
AB=√(-1+3)²+(-2+2)²
AB=√2²+0²
AB=√4
AB=2 units
hope it helps u...
plz mark as brainliest...
Answer: The distance between the points (-3, -2) and (-1, -2). is 2
The number of cars sold annually by used car salespeople is normally distributed with a standard deviation of 17. A random sample of 470 salespeople was taken and the mean number of cars sold annually was found to be 69. Find the 95% confidence interval estimate of the population mean
Answer: Estimate mean is between 67.463 and 70.537
Step-by-step explanation: A 95% Confidence interval of a sample mean:
mean ± [tex]z.\frac{s}{\sqrt{n} }[/tex]
α = 1 - 0.95
α = 0.05
α/2 = 0.025
z-score of α/2 = 1.96
Knowing that mean = 69, sd = 17 and there were 470 salespeople in the sample:
69 ± [tex]1.96.\frac{17}{\sqrt{470} }[/tex]
69 ± [tex]1.96.\frac{17}{21.68}[/tex]
69 ± [tex]1.96.0.78[/tex]
69 ± 1.537
lower limit: 69 - 1.537 = 67.463
upper limit: 69 + 1.537 = 70.537
With a confidence of 95%, the estimate mean number of cars sold is between 67.463 and 70.537
A candidate for political office wants to determine if there is a difference in his popularity between men and women. To test the claim of this difference, he conducts a survey of voters. The sample contains 250 men and 250 women, of which 44% of the men and 52% of the women favor his candidacy. Do these values indicate a difference in popularity?Use a 0.01 significance level.
What are the hypothesis statements?
a) H0:pm=pw
HA:pm
b) H0:pm=pw
HA:pm>pw
c) H0:pm=pw
HA:pm≠pw
Answer:
c) H0:pm=pw
HA:pm≠pw
Step-by-step explanation:
We formulate our hypothesis as
H0: pm = pw " probability of men = probabilityof women" meaning there's no difference in the probabilityof the men and women in favor of his candidacy.
Alternate Hypothesis HA :pm≠pw " probability of men ≠ probabilityof women" meaning there's a difference in the probability of the men and women in favor of his candidacy.
the significance level α= 0.01
The test statistic under H0 is
Z = pm- pw/ √p`q` ( 1/n.m + 1/n.w)
pm= probability of men= 0.44
pw= probability of women = 0.52
p`= n.m pm+ n.w pw/ n.m + n.w
p`= 250 *0.44 + 250 *0.52/ 250 + 250
p`= 110 + 130 /500 = 240 /500 = 0.48
q`= 1- p`= 1-0.48= 0.52
Putting the values
Z= 0.44- 0.52/ √ 0.48 * 0.52
z= 0.08 / √0.2496
z= 0.08/ 0.4995
z= 0.1601
The critical region for α= 0.01 is Z= ± 2.58
Conclusion: Since the calculated z = 0.1601 does not fall in the critical region , so we accept the null hypothesis H0:pm=pw and conclude that the data does not appear to indicate that the tow probabilities are different.
Using the z-distribution, it is found that since the absolute value of the test statistic is less than the critical value, there values do not indicate a difference in popularity.
At the null hypothesis, it is tested if the proportions are equal, that is, their subtraction is of 0, hence:
[tex]H_0: p_w - p_m = 0[/tex]
At the alternative hypothesis, it is tested if they are different, that is, their subtraction is different of 0, hence:
[tex]H_1: p_w - p_m \neq 0[/tex]
The proportions and standard errors are:
[tex]p_m = 0.44, s_m = \sqrt{\frac{0.44(0.56)}{250}} = 0.0314[/tex]
[tex]p_w = 0.52, s_w = \sqrt{\frac{0.52(0.48)}{250}} = 0.0316[/tex]
For the distribution of the differences, the mean and the standard error are given by:
[tex]\overline{p} = p_w - p_m = 0.52 - 0.44 = 0.08[/tex]
[tex]s = \sqrt{s_m^2 + s_w^2} = \sqrt{0.0314^2 + 0.0316^2} = 0.0445[/tex]
The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{s}[/tex]
In which p = 0 is the value tested at the null hypothesis.
Hence:
[tex]z = \frac{0.08}{0.0445}[/tex]
[tex]z = 1.795[/tex]
The critical value, for a two-tailed test, as we are testing if the mean is different of a value, with a significance level of 0.01, is of [tex]|z^{\ast}| = 2.5758[/tex]
Since the absolute value of the test statistic is less than the critical value, there values do not indicate a difference in popularity.
A similar problem, also involving an hypothesis test for a proportion, is given at https://brainly.com/question/24302053
According to a study done by the Gallup organization, the proportion of Americans who are satisfied with the way things are going in their lives is 0.82. What is the probability the sample proportion who are satisfied with the way things are going in their life is greater than 0.85
Complete Question
According to a study done by the Gallup organization, the proportion of Americans who are satisfied with the way things are going in their lives is 0.82. Suppose a random sample of 100 Americans is asked "Are you satisfied with the way things are going in your life?"
What is the probability the sample proportion who are satisfied with the way things are going in their life is greater than 0.85
Answer:
The probability is [tex]P(X > 0.85 ) = 0.21745[/tex]
Step-by-step explanation:
From the question we are told that
The population proportion is [tex]p = 0.82[/tex]
The value considered is x = 0.85
The sample size is n = 100
The standard deviation for this population proportion is evaluated as
[tex]\sigma = \sqrt{\frac{p(1-p)}{n} }[/tex]
substituting values
[tex]\sigma = \sqrt{\frac{0.82(1-0.82)}{100} }[/tex]
[tex]\sigma = 0.03842[/tex]
Generally the probability that probability the sample proportion who are satisfied with the way things are going in their life is greater than x is mathematically represented as
[tex]P(X > x ) = P( \frac{X - p }{ \sigma } > \frac{x - p }{ \sigma } )[/tex]
Where [tex]\frac{X - p }{ \sigma }[/tex] is equal to Z (the standardized value of X ) so
[tex]P(X > x ) = P( Z> \frac{x - p }{ \sigma } )[/tex]
substituting values
[tex]P(X > 0.85 ) = P( Z> \frac{ 0.85 - 0.82 }{ 0.03842 } )[/tex]
[tex]P(X > 0.85 ) = P( Z> 0.78084)[/tex]
from the standardized normal distribution table [tex]P( Z> 0.78084)[/tex] is 0.21745
So
[tex]P(X > 0.85 ) = 0.21745[/tex]
Use z scores to compare the given values. The tallest living man at one time had a height of 249 cm. The shortest living man at that time had a height of 120.2 cm. Heights of men at that time had a mean of 176.55 cm and a standard deviation of 7.23 cm. Which of these two men had the height that was more extreme?
Answer:
Step-by-step explanation:
Average height = 176.55 cm
Height of tallest man = 249 cm
Standard deviation = 7.23
z score of tallest man
= (249 - 176.55) / 7.23
= 10.02
Average height = 176.55 cm
Height of shortest man = 120.2 cm
Standard deviation = 7.23
z score of smallest man
= ( 176.55 - 120.2 ) / 7.23
= 7.79
Since Z - score of tallest man is more , his height was more extreme .
A rectangle has length 4 inches and width 2 inches. If the length and width of the rectangle are
reduced by 50 percent, by what percent will the area of the rectangle be reduced?
40 percent
50 percent
60 percent
75 percent
Answer:
75%
Step-by-step explanation:
First we can solve the area of the rectangle originally the answer is:
4 × 2 = 8
Then we decrease both measurements by 50% to get the dimensions 1 and 2. The new area will be 1 × 2 which is 2.
2 is 25% of 8 which means that the area of the rectangle has been reduced by 75%.
Translate the sentence into an equation seven times the sum of a number and 5 is 4
Answer:
7(x+5) = 4
Step-by-step explanation:
"A number" refers to a variable. Seven is multiplied to the sum of a number and 5, meaning they must be in parentheses, indicating it is the sum.
Change Y - 4X = 0 to the slope-intercept form of the equation of a line.
Answer:
y=4x
Step-by-step explanation:
Add 4x to both sides to get y=mx+b
0 is y-intercept.
4x is the slope.
Tristan wants to buy a car and has a choice between two different banks. One bank is offering a simple interest rate of 3% and the other bank is offering a rate of 2.5%
compounded annually. If Tristan decides to deposit $7,000 for 4 years, which bank would be the better deal?
Answer:
The better deal would be simple interest rate of 3%
Step-by-step explanation:
In order to calculate which bank would be the better deal If Trsitam decides to deposit $7,000 for 4 years, we would have to make the following calculation:
simple interest rate of 3%.
Therefore, I= P*r*t
=$7,000*3%*4
I=$840
FV= $7,000+$840
FV=7,840
compound interest rate of 2.5%
Therefore, FV=PV(1+r)∧n
FV=$7,000(1+0.25)∧4
FV=$17,089
The better deal would be simple interest rate of 3%
Please answer this correctly without making mistakes
Answer:
Centerville is 13 kilometers away from Manchester
Step-by-step explanation:
26.1 - 13.1 = 13
A manufacturer knows that on average 20% of the electric toasters produced require repairs within 1 year after they are sold. When 20 toasters are randomly selected, find appropriate numbers x and y such that (a) the probability that at least x of them will require repairs is less than 0.5; (b) the probability that at least y of them will not require repairs is greater than 0.8
Answer:
(a) The value of x is 5.
(b) The value of y is 15.
Step-by-step explanation:
Let the random variable X represent the number of electric toasters produced that require repairs within 1 year.
And the let the random variable Y represent the number of electric toasters produced that does not require repairs within 1 year.
The probability of the random variables are:
P (X) = 0.20
P (Y) = 1 - P (X) = 1 - 0.20 = 0.80
The event that a randomly selected electric toaster requires repair is independent of the other electric toasters.
A random sample of n = 20 toasters are selected.
The random variable X and Y thus, follows binomial distribution.
The probability mass function of X and Y are:
[tex]P(X=x)={20\choose x}(0.20)^{x}(1-0.20)^{20-x}[/tex]
[tex]P(Y=y)={20\choose y}(0.20)^{20-y}(1-0.20)^{y}[/tex]
(a)
Compute the value of x such that P (X ≥ x) < 0.50:
[tex]P (X \geq x) < 0.50\\\\1-P(X\leq x-1)<0.50\\\\0.50<P(X\leq x-1)\\\\0.50<\sum\limits^{x-1}_{0}[{20\choose x}(0.20)^{x}(1-0.20)^{20-x}][/tex]
Use the Binomial table for n = 20 and p = 0.20.
[tex]0.411=\sum\limits^{3}_{x=0}[b(x,20,0.20)]<0.50<\sum\limits^{4}_{x=0}[b(x,20,0.20)]=0.630[/tex]
The least value of x that satisfies the inequality P (X ≥ x) < 0.50 is:
x - 1 = 4
x = 5
Thus, the value of x is 5.
(b)
Compute the value of y such that P (Y ≥ y) > 0.80:
[tex]P (Y \geq y) >0.80\\\\P(Y\leq 20-y)>0.80\\\\P(Y\leq 20-y)>0.80\\\\\sum\limits^{20-y}_{y=0}[{20\choose y}(0.20)^{20-y}(1-0.20)^{y}]>0.80[/tex]
Use the Binomial table for n = 20 and p = 0.20.
[tex]0.630=\sum\limits^{4}_{y=0}[b(y,20,0.20)]<0.50<\sum\limits^{5}_{y=0}[b(y,20,0.20)]=0.804[/tex]
The least value of y that satisfies the inequality P (Y ≥ y) > 0.80 is:
20 - y = 5
y = 15
Thus, the value of y is 15.
An object is moving at a speed of 7300 inches every 3 seconds. Express this speed in miles per day.
Answer:
≈3318 miles per day....
Step-by-step explanation:
Suppose that you expect SugarCane stock price to decline. So you decide to ask your broker to short sell 2000 shares. The current market price is $40. The proceeds from the short sale $80,000 is credited into your account. However, a few days later the market price of the stock jumps to $80 per share and your broker asks you close out your position immediately. What is your profit or loss from this transaction?
Answer:
Loss = $80000
Step-by-step explanation:
To determine if it's a profit or loss is simple.
He predicted the sugar cane stock to fall so he sold , but few days later the stock grew and went bullish.
He sold at$ 40 for 2000 shares
=$ 80000
But the stock went up to $80 per share that is gaining extra $40
So it was actually a loss.
The loss is =$40 * 2000
The loss = $80000
1. What is the length of the shortest side if the perimeter of the rectangle is
56 inches?
3х
5х – 4
Answer:
Length of Shortest Side = 12 inches
Step-by-step explanation:
Length of Shortest Side = L = 3x
Length of Longest Side = W = 5x-4
Condition:
2L+2W = Perimeter
2(3x)+2(5x-4) = 56
6x+10x-8 = 56
16x-8 = 56
Adding 8 to both sides
16x = 56+8
16x = 64
Dividing both sides by 14
=> x = 4
Now,
Length of the Shortest Side = L = 3(4) = 12 inches
Length of the Longest Side = W = 5(4)-4 = 16 inches
Answer:
12 inches
Step-by-step explanation:
The length is the longest side.
The width is the shortest side.
Length : [tex]l=5x-4[/tex]
Width : [tex]w=3x[/tex]
Apply formula for the perimeter of a rectangle.
[tex]P=2l+2w[/tex]
[tex]P=perimeter\\l=length\\w=width[/tex]
Plug in the values.
[tex]56=2(5x-4)+2(3x)[/tex]
[tex]56=10x-8+6x[/tex]
[tex]56=16x-8[/tex]
[tex]64=16x[/tex]
[tex]4=x[/tex]
The shortest side is the width.
[tex]w=3x[/tex]
Plug in the value for x.
[tex]w=3(4)[/tex]
[tex]w=12[/tex]
Section 8
Find the mean of these numbers:
24 18
37
82 17
26
Answer:
[tex]\boxed{Mean = 34.33}[/tex]
Step-by-step explanation:
Mean = Sum of Observations / No. Of Observations
Mean = (24+18+37+82+17+26)/6
Mean = 206 / 6
Mean = 34.33
WILL MARK AS BRAINLIEST!!! 5. A 2011 study by The National Safety Council estimated that there are nearly 5.7 million traffic accidents year. At least 28% of them involved distracted drivers using cell phones or texting. The data showed that 11% of drivers at any time are using cell phones . Car insurance companies base their policy rates on accident data that shows drivers have collisions approximately once every 19 years. That’s a 5.26% chance per year. Given what you know about probability, determine if cell phone use while driving and traffic accidents are related. Step A: Let DC = event that a randomly selected driver is using a cell phone. What is P(DC)? (1 point) Step B: Let TA = event that a randomly selected driver has a traffic accident. What is P(TA)? Hint: What is the probability on any given day? (1 point) Step C: How can you determine if cell phone use while driving and traffic accidents are related? (1 point) Step D: Given that the driver has an accident, what is the probability that the driver was distracted by a cell phone? Write this event with the correct conditional notation. (1 point) Step E: What is the probability that a randomly selected driver will be distracted by using a cell phone and have an accident? (2 points) Step F: For a randomly selected driver, are the events "driving while using a cell phone" and "having a traffic accident" independent events? Explain your answer. (2 points)
Answer:
Step-by-step explanation:
Hello!
Regarding the reasons that traffic accidents occur:
28% are caused by distracted drivers using cell phones or texting
11% of the drivers' user their phones at any time
The probability of a driver having an accident is 5.26%
a)
DC = event that a randomly selected driver is using a cell phone.
P(DC)= 0.11
b)
TA = event that a randomly selected driver has a traffic accident.
P(TA)= 0.0526
c) and f)
If both events are related, i.e. dependent, then you would expect that the occurrence of one of these events will affect the probability of the other one. If they are not related, i.e. independent events, then their probabilities will not be affected by the occurrence of one or another:
If both events are independent P(TA|DC)= P(TA)
If they are dependent, then:
P(TA|DC)≠ P(TA)
P(TA|DC)= 0.28
P(TA)= 0.0526
As you can see the probability of the driver having an accident given that he was using the cell phone is different from the probability of the driver having an accident. This means that both events are related.
d) and e)
You have to calculate the probability that "the driver was distracted with the phone given that he had an accident", symbolically P(DC|TA)
P(DC|TA) = [tex]\frac{P(DCnTA)}{P(TA)}[/tex]
[tex]P(TA|DC)= \frac{P(TAnDC}{P(DC)}[/tex] ⇒ P(DC∩TA)= P(TA|DC)*P(DC)= 0.28 * 0.11= 0.0308
P(DC|TA) = [tex]\frac{0.0308}{0.0526}= 0.585= 0.59[/tex]
I hope this helps!
among a group of students 50 played cricket 50 played hockey and 40 played volleyball. 15 played both cricket and hockey 20 played both hockey and volleyball 15 played cricket and volley ball and 10 played all three. if every student played at least 1 game find the no of students and how many students played only cricket, only hockey and only volley ball
Answer:
Cricket only= 30
Volleyball only = 15
Hockey only = 25
Explanation:
Number of students that play cricket= n(C)
Number of students that play hockey= n(H)
Number of students that play volleyball = n(V)
From the question, we have that;
n(C) = 50, n(H) = 50, n(V) = 40
Number of students that play cricket and hockey= n(C∩H)
Number of students that play hockey and volleyball= n(H∩V)
Number of students that play cricket and volleyball = n(C∩V)
Number of students that play all three games= n(C∩H∩V)
From the question; we have,
n(C∩H) = 15
n(H∩V) = 20
n(C∩V) = 15
n(C∩H∩V) = 10
Therefore, number of students that play at least one game
n(CᴜHᴜV) = n(C) + n(H) + n(V) – n(C∩H) – n(H∩V) – n(C∩V) + n(C∩H∩V)
= 50 + 50 + 40 – 15 – 20 – 15 + 10
Thus, total number of students n(U)= 100.
Note;n(U)= the universal set
Let a = number of people who played cricket and volleyball only.
Let b = number of people who played cricket and hockey only.
Let c = number of people who played hockey and volleyball only.
Let d = number of people who played all three games.
This implies that,
d = n (CnHnV) = 10
n(CnV) = a + d = 15
n(CnH) = b + d = 15
n(HnV) = c + d = 20
Hence,
a = 15 – 10 = 5
b = 15 – 10 = 5
c = 20 – 10 = 10
Therefore;
For number of students that play cricket only;
n(C) – [a + b + d] = 50 – (5 + 5 + 10) = 30
For number of students that play hockey only
n(H) – [b + c + d] = 50 – ( 5 + 10 + 10) = 25
For number of students that play volleyball only
n(V) – [a + c + d] = 40 – (10 + 5 + 10) = 15
Answer:
Cricket only= 30
Volleyball only = 15
Hockey only = 25
Explanation of the answer:
Number of students that play cricket= n(C)
Number of students that play hockey= n(H)
Number of students that play volleyball = n(V)
From the question, we have that;
n(C) = 50, n(H) = 50, n(V) = 40
Number of students that play cricket and hockey= n(C∩H)
Number of students that play hockey and volleyball= n(H∩V)
Number of students that play cricket and volleyball = n(C∩V)
Number of students that play all three games= n(C∩H∩V)
From the question; we have,
n(C∩H) = 15
n(H∩V) = 20
n(C∩V) = 15
n(C∩H∩V) = 10
Therefore, number of students that play at least one game
n(CᴜHᴜV) = n(C) + n(H) + n(V) – n(C∩H) – n(H∩V) – n(C∩V) + n(C∩H∩V)
= 50 + 50 + 40 – 15 – 20 – 15 + 10
Thus, total number of students n(U)= 100.
Note;n(U)= the universal set
Let a = number of people who played cricket and volleyball only.
Let b = number of people who played cricket and hockey only.
Let c = number of people who played hockey and volleyball only.
Let d = number of people who played all three games.
This implies that,
d = n (CnHnV) = 10
n(CnV) = a + d = 15
n(CnH) = b + d = 15
n(HnV) = c + d = 20
Hence,
a = 15 – 10 = 5
b = 15 – 10 = 5
c = 20 – 10 = 10
Therefore;
For number of students that play cricket only;
n(C) – [a + b + d] = 50 – (5 + 5 + 10) = 30
For number of students that play hockey only
n(H) – [b + c + d] = 50 – ( 5 + 10 + 10) = 25
For number of students that play volleyball only
n(V) – [a + c + d] = 40 – (10 + 5 + 10) = 15
▬▬▬▬▬▬▬▬▬▬▬▬
find the maximum value of c=6x+2y
Answer:
∞
Step-by-step explanation:
c can have any value you like.
There is no maximum. We say it can approach infinity.
__
Additional comment
There may be some maximum imposed by constraints not shown here. Since we don't know what those constraints are, we cannot tell you what the maximum is.
helpppppp pleaseeee me helpppp
Answer:
$10 + $10 + $1 + 25¢ + 5¢
or
$20 + $1 + 25¢ + 5¢
Step-by-step explanation:
Each one must pay $21.30
um aluno tinha uma quantidade de questoes para resolver se ja resolveu a quinta parte da sua tarefa então a razão entre o numero de questoes resolvidas e o numero restante de questoes nessa ordem é a) 1/20 b)1/5 c)1/4 d)4 e)5
Answer:
can you please simplify that in English?
Find the probability of each event. A six-sided die is rolled seven times. What is the probability that the die will show an even number at most five times?
Answer:
[tex]\dfrac{15}{16}[/tex]
Step-by-step explanation:
When a six sided die is rolled, the possible outcomes can be:
{1, 2, 3, 4, 5, 6}
Even numbers are {2, 4, 6}
Odd Numbers are {1, 3, 5}
Probability of even numbers:
[tex]\dfrac{\text{Favorable cases}}{\text{Total cases }} = \dfrac{3}{6} = \dfrac{1}{2}[/tex]
This is binomial distribution.
where probability of even numbers, [tex]p =\frac{1}{2}[/tex]
Probability of not getting even numbers (Getting odd numbers) [tex]q =\frac{1}{2}[/tex]
Probability of getting r successes out of n trials:
[tex]P(r) = _nC_r\times p^r q^{n-r}[/tex]
Probability of getting even numbers at most 5 times out of 7 is given as:
P(0) + P(1) +P(2) + P(3) +P(4) + P(5)
[tex]\Rightarrow _7C_0\times \frac{1}{2}^0 \frac{1}{2}^{7}+_7C_1\times \frac{1}{2}^1 \frac{1}{2}^{6}+_7C_2\times \frac{1}{2}^2 \frac{1}{2}^{5}+_7C_3\times \frac{1}{2}^3 \frac{1}{2}^{4}+_7C_4\times \frac{1}{2}^4 \frac{1}{2}^{3}+_7C_5\times \frac{1}{2}^5 \frac{1}{2}^{2}[/tex]
[tex]\Rightarrow (\dfrac{1}{2})^7 (_7C_0+_7C_1+_7C_2+_7C_3+_7C_4+_7C_5)\\[/tex]
[tex]\Rightarrow (\dfrac{1}{2})^7 (1+7+\dfrac{7 \times 6}{2}+\dfrac{7 \times 6 \times 5}{3\times 2}+\dfrac{7 \times 6 \times 5}{3\times 2}+\dfrac{7 \times 6}{2})\\\Rightarrow \dfrac{120}{128} \\\Rightarrow \dfrac{15}{16}[/tex]
Find m<1 .Triangle Angle-Sum Theorem.
Answer:
m<1 = 30
Step-by-step explanation:
To find m<1, we can do 180 - 75 - 75, which will give us 30 degrees, so m<1 = 30
determine the polynomial equivalent to this expression.
x^2-9/x-3
A. x-3
B. -3x-9
C. x+3
D. x^2+3x
Answer:
[tex]\dfrac{x^2-9}{x-3}= \Large \boxed{x+3}[/tex]
Step-by-step explanation:
Hello,
We need to work a little bit of the expression to see if we can simplify.
Do you remember this formula?
for any a and b reals, we can write
[tex]a^2-b^2=(a-b)(a+b)[/tex]
We will apply it.
For any x real number different from 3 (as dividing by 0 is not allowed)
[tex]\dfrac{x^2-9}{x-3}=\dfrac{x^2-3^2}{x-3}=\dfrac{(x-3)(x+3)}{x-3}=x+3[/tex]
So the winner is C !!
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
In a study of the accuracy of fast food drive-through orders, Restaurant A had 302accurate orders and 59that were not accurate.a. Construct a 95%confidence interval estimate of the percentage of orders that are not accurate.b. Compare the results from part (a) to this 95%confidence interval for the percentage of orders that are not accurate at Restaurant B: 0.143less thanpless than0.219.What do you conclude?
Answer:
(a) A 95% confidence interval estimate of the percentage of orders that are not accurate is [0.125, 0.201].
(b) We can conclude that both restaurants can have the same inaccuracy rate due to the overlap of interval areas.
Step-by-step explanation:
We are given that in a study of the accuracy of fast food drive-through orders, Restaurant A had 302 accurate orders and 59 orders that were not accurate.
Firstly, the pivotal quantity for finding the confidence interval for the population proportion is given by;
P.Q. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of orders that were not accurate = [tex]\frac{59}{361}[/tex] = 0.163
n = sample of total orders = 302 + 59 = 361
p = population proportion of orders that are not accurate
Here for constructing a 95% confidence interval we have used a One-sample z-test for proportions.
So, 95% confidence interval for the population proportion, p is ;
P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5% level
of significance are -1.96 & 1.96}
P(-1.96 < [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < 1.96) = 0.95
P( [tex]-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < [tex]{\hat p-p}[/tex] < [tex]1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.95
P( [tex]\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < p < [tex]\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.95
95% confidence interval for p = [ [tex]\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] , [tex]\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ]
= [ [tex]0.163 -1.96 \times {\sqrt{\frac{0.163(1-0.163)}{361} } }[/tex] , [tex]0.163 +1.96 \times {\sqrt{\frac{0.163(1-0.163)}{361} } }[/tex] ]
= [0.125, 0.201]
(a) Therefore, a 95% confidence interval estimate of the percentage of orders that are not accurate is [0.125, 0.201].
(b) We are given that the 95% confidence interval for the percentage of orders that are not accurate at Restaurant B is [0.143 < p < 0.219].
Here we can observe that there is a common area of inaccurate order of 0.058 or 5.85% for both the restaurants.
So, we can conclude that both restaurants can have the same inaccuracy rate due to the overlap of interval areas.
Suppose the weather forecast calls for a 60% chance of rain each day for the next 3 days. What is the probability that it will NOT rain during the next 3 days
Answer:
Probability that it'll not rain during the next three days = 0.064
Step-by-step explanation:
Given
Let:
P(R) represent the probability that it'll rain each day
P(R') represent the probability that it'll not
[tex]P(R) = 60\%[/tex]
Required
Probability that it'll not rain during the next three days
From concept of probability;
[tex]P(R) + P(R') = 1[/tex]
Substitute 60% for P(R)
[tex]60\% + P(R') = 1[/tex]
Subtract 60% from both sides
[tex]60\% - 60\% + P(R') = 1 - 60\%[/tex]
[tex]P(R') = 1 - 60\%[/tex]
Convert % to decimal
[tex]P(R') = 1 - 0.6[/tex]
[tex]P(R') = 0.4[/tex]
The probability that it'll not rain during the next 3 days is:
[tex]P(R') * P(R') * P(R')[/tex]
[tex]P(R') * P(R') * P(R') =0.4 * 0.4 * 0.4[/tex]
[tex]P(R') * P(R') * P(R') = 0.064[/tex]
Use spherical coordinates. Find the volume of the solid that lies within the sphere x2 + y2 + z2 = 16, above the xy-plane, and below the cone z = x2 + y2 .
The volume is given by the integral,
[tex]\displaystyle\int_0^{2\pi}\int_0^{\cos^{-1}((\sqrt{65}-1)/8)}\int_0^4\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\varphi\,\mathrm d\theta[/tex]
That is, [tex]\rho[/tex] ranges from the origin to the sphere of radius 4. The range for [tex]\varphi[/tex] starts at the intersection of the cone [tex]z=x^2+y^2[/tex] with the sphere [tex]x^2+y^2+z^2=16[/tex], which gives
[tex]z+z^2=16\implies z^2+z-16=0\implies z=\dfrac{\sqrt{65}-1}2[/tex]
and
[tex]z=4\cos\varphi\implies\varphi=\cos^{-1}\left(\dfrac{\sqrt{65}-1}8\right)[/tex]
and extends to the x-y plane where [tex]\varphi=\frac\pi2[/tex]. The range for [tex]\theta[/tex] is self-evident.
The volume is then
[tex]V=\displaystyle\int_0^{2\pi}\int_0^{\cos^{-1}((\sqrt{65}-1)/8)}\int_0^4\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\varphi\,\mathrm d\theta[/tex]
[tex]V=\displaystyle\left(\int_0^{2\pi}\mathrm d\theta\right)\left(\int_0^{\cos^{-1}((\sqrt{65}-1)/8)}\sin\varphi\,\mathrm d\varphi\right)\left(\int_0^4\rho^2\,\mathrm d\rho\right)[/tex]
[tex]V=2\pi\left(\dfrac{\sqrt{65}-1}8\right)\left(\dfrac{64}3\right)=\boxed{\dfrac{16\pi(9-\sqrt{65})}3}[/tex]
A sphere is a three-dimensional object with a round form. The volume of the sphere is [16π(9-√65)]/3 unit³.
What is a sphere?A sphere is a three-dimensional object with a round form. A sphere, unlike other three-dimensional shapes, has no vertices or edges. Its centre is equidistant from all places on its surface. In other words, the distance between the sphere's centre and any point on its surface is the same.
We know that the volume of the given sphere can be given by the integral,
[tex]{\rm Volume} = \int^{2\pi}_0\int^{cos^{-1}(\frac{\sqrt{65}-1}{8})} \int_0^4\rho^2sin\varphi\ d\rho\ d\varphi\ d\theta[/tex]
where ρ ranges from the origin of the plot to the sphere of radius 4 while the range of φ starts at the intersection of the cone z=x²+y² with the sphere x²+y²+z²=16.
Now, the value of z and φ can be written as,
[tex]x^2+y^2+z^2 = 16\\\\(x^2+y^2)+z^2 = 16\\\\z+z^2 = 16\\\\z^2+z-16=0 \implies z=\dfrac{\sqrt{65}-1}{2}[/tex]
And
[tex]z =4\ cos\ \varphi \implies \varphi =cos^{-1}(\dfrac{\sqrt{65}-1}{8})[/tex]
Further, the volume of the sphere can be written as,
[tex]{\rm Volume} = \int^{2\pi}_0\int^{cos^{-1}(\frac{\sqrt{65}-1}{8})} \int_0^4\rho^2sin\varphi\ d\rho\ d\varphi\ d\theta\\\\\\{\rm Volume} = (\int^{2\pi}_0\ d\theta)(\int^{cos^{-1}(\frac{\sqrt{65}-1}{8})} sin\varphi\ d\varphi)(\int_0^4\rho^2 d\rho)\\\\\\V = 2\pi(\dfrac{\sqrt{65}-1}{8})(\dfrac{64}{3}) = \dfrac{16\pi(9-\sqrt{65})}{3}[/tex]
Hence, the volume of the sphere is [tex]\dfrac{16\pi(9-\sqrt{65})}{3}[/tex].
Learn more about Sphere:
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VW=40in. The radius of the circle is 25 inches. Find the length of CT.
Answer:
The answer is B. 40 inches.
Step-by-step explanation:
The question starts by telling you that line VW is equal to 40 in. If you look at the picture you can see it is divided into 2 equal parts of 20 in each. If you look at line CT, you can see that there are the same marks meaning that those segments are also 20 in. That means that line CT and line VW are equal and that line CT is equal to 40 in.
Examine the system of equations. y = 3 2 x − 6, y = −9 2 x + 21 Use substitution to solve the system of equations. What is the value of y? y =
Answer:
its 3/4
Step-by-step explanation: i got it right trust me
The solution to the system of equations will be x= 9 / 2 and y= 3 / 4.
What is a system of equations?A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.
An equation is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
The given equations are y=(3/ 2 )x-6 and y=(-9/2)x+21 to calculate the values of x and y using the substitution method.
Since both equations are equated to y, you just need to use substitution to create the equation below:
(3/ 2 )x-6 =(-9/2)x+21
Solve the equation for x:
(3/ 2 )x + (9/2)x = 27
x = 27 / 6 = 9 / 2
Plug x into any one of the given equations to find the value of y:
y=(3/ 2 )x-6
Solve for the value of y.
y=(3/2) x (9 / 2)-6
y = ( 27 / 4 ) - 6
y = ( 27 - 24 ) / 4
y = 3 / 4
Hence, the solution for the equation will be x = 9 / 2 and y = 3 / 4.
To know more about the system of linear equations follow
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Using traditional methods it takes 109 hours to receive an advanced flying license. A new training technique using Computer Aided Instruction (CAI) has been proposed. A researcher believes the new technique may lengthen training time and decides to perform a hypothesis test. After performing the test on 190 students, the researcher decides to reject the null hypothesis at a 0.02 level of significance.
What is the conclusion?
a. There is sufficient evidence at the 0.020 level of significance that the new technique reduces training time.
b. There is not sufficient evidence at the 0.02 level of significance that the new technique reduces training time.
I think the answer is option B.
Because while researchers research they believed that it will lengthen the time and it don't reduced the time.
Hope it's correct..
WILL GIVE BRAINLIEST IF CORRECT!! Please help ! -50 POINTS -
Answer:
i think (d) one i think it will help you