Which statement implies that A and B are independent events?
O A. P(B|A)= P(B and A)
OB.P(B|A)= P(B)
P(A)
OC. P(B|A)= P(A)
OD. P(B|A)= P(B)
Answer:
Option B
Step-by-step explanation:
When A and B are independent events:
P(A and B) = P(A) * P(B)
OR
P(A|B) = P(A) * P(B)
What is the solution y=-2x+4 and y=x-2
Answer:
Look below
Step-by-step explanation:
Please answer this correctly
Answer:
9 people
Step-by-step explanation:
37, 39, 41, 46, 61, 63, 69, 77, 80
9 people waited more than 36 minutes.
Alice skated 3.4 miles on Monday and 2.6 miles on Wednesday. How much farther did she skate on Monday ?
Answer:
.8 miles further on Monday
Step-by-step explanation:
Take the miles on Monday and subtract the miles on Wednesday
3.4 - 2.6 =.8 miles
Find value of 397 x 17 + 397 x 3 *
Answer:
7940
Step-by-step explanation:
=> 397 * 17 + 397 * 3
=> 6749 + 1191
=> 7940
You are building a model sailboat. The plans show that the base of the main sail is 9 cm, the bottom acute angle in the sail is 52°, and the distance between the base of the sail and the deck is 2 cm. What is the height of the mast? a. 12.5 cm b. 11.2 cm c. 13.5 cm d. 11.5 cm
Answer:
c. 13.5 cm
Step-by-step explanation:
In the right triangle formed by the main sail.
Using the trigonometric function
[tex]\tan \theta =\dfrac{\text{Opposite}}{\text{Adjacent}} \\\tan 52^\circ =\dfrac{x}{9} \\x=9 \times \tan 52^\circ\\x=11.52$ cm[/tex]
Therefore:
Height of the mast = 2+11.5=13.5 cm
The height of the mast is 13.5 cm.
Suppose a jar contains 20 red marbles and 10 blue marbles. If you reach in the jar and pull out 2 marbles at random at the same time, find the probability that both are red.
Answer:
The probability that both are red is 2/9Step-by-step explanation:
Given the sample space
20 red marbles and
10 blue marbles
the sample size is
S= 20+10= 30
The probability that both are red if two marbles are pulled at once is
[tex]\frac{20}{30} *\frac{10}{30} \\\\=\frac{2}{3}*\frac{1}{3} = \frac{2}{9}[/tex]
Jaden had 2 7/16 yards of ribbon. He used 1 3/8 yards of ribbon to make a prize ribbon. How much does he have now?
EASY!
Answer: 17/16 or 1 1/16
Step-by-step explanation:
BRO IT'S ELEMANTARY FRACTIONS!!!!
If a/b = c/d, which of the following is not true?
1) ad=bc
2) a/c=b/d
3) a+b/b=c+d/d
4) a/d=c/b
5) b/a=d/c
Answer:
Option 4 is not true
Step-by-step explanation:
[tex]\frac{a}{b}=\frac{c}{d}\\\\[/tex]
1)Cross multiply,
ad = bc
So, true
2) a/ c = b/d also true
3) a+b/b = c+d/d also true
For example:
[tex]\frac{1}{4}=\frac{2}{8}\\\\\frac{1+4}{4}=\frac{2+8}{8}\\\\\frac{5}{4}=\frac{10}{8}\\\\[/tex]
When simplifying 10/8, it is 5/4.
5) b/a = d/c is also true
How did the temperature change if: at first it increased by 25 % and then decreased by 40% ?
Please help!!
Answer:
At first it increases by 25%, then you have 1.25x the original temp. A drop of 40% gives you .6 x 1.25, or 75% of the original temperature
Step-by-step explanation:
found that on the web for yuh. I really hope it helped.
Answer:
decreased by 25%
Step-by-step explanation:
Please answer this correctly
Answer:
There are 10 teams.
Step-by-step explanation:
Given that the question wants at least 48 swimmers so any numbers above 47 are counted.
In this diagram, there are 10 teams consisting 48 swimmers and above, 48, 52, 53, 63, 76, 79, 82, 84, 85 and 86.
Answer:
10 teams have 48 or more swimmers.
Step-by-step explanation:
If we look at stem 4 there is one team with 48 members.
So counting from there we have:
1 + 2 + 1 + 2 + 4
= 10 teams.
The number of hours of daylight, H, on day t of any given year (on January 1, tequals1) in a particular city can be modeled by the function :
H(t)=11+8.5 sin[2π/365 (t-83)]
Required:
a. On March 24, the 83rd day of the year, is the spring equinox. Find the number of hours of daylight in the city on this day. (Round to one decimal place as needed.)
b. On June 24, the 175th day of the year, is the summer solstice, the day with the maximum number of hours of daylight. Find the number of hours of daylight in the city on this day. (Round to one decimal place as needed.)
c. On December 24, the 358 day of the year, is the winter solstice, the day with a minimum number of hours of daylight. Find the number of hours of daylight in the city on this day. (Round to one decimal place as needed.)
Answer:
(a)11 hours
(b)19.5 hours
(c)2.5 hours
Step-by-step explanation:
The number of hours of daylight, H, on day t of any given year in a particular city can be modeled by the function :
[tex]H(t)=11+8.5\sin\left(\dfrac{2\pi}{365}(t-83)\right)[/tex]
(a)When t=83
[tex]H(83)=11+8.5\sin\left(\dfrac{2\pi}{365}(83-83)\right)\\=11+8.5\sin 0\\=11$ hours[/tex]
(b)When t=175
[tex]H(175)=11+8.5\sin\left(\dfrac{2\pi}{365}(175-83)\right)\\=11+8.5\sin\left(\dfrac{2\pi}{365}\times 92 \right)\\=11+8.5\\=19.5$ hours[/tex]
(b)When t=358
[tex]H(175)=11+8.5\sin\left(\dfrac{2\pi}{365}(358-83)\right)\\=11+8.5\sin\left(\dfrac{2\pi}{365}\times 275 \right)\\=11-8.5\\=2.5$ hours[/tex]
Based on a poll, 40% of adults believe in reincarnation. Assume that 6 adults are randomly selected, and find the indicated probability. Complete parts (a) through (c) below.
a. What is the probability that exactly 5 of the selected adults believe in reincarnation? Round to 3 decimal places.
b. What is the probability that all of the selected adults believe in reincarnation?
c. What is the probability that at least 5 of the selected adults believe in reincarnation?
Answer:
a. 3.686 %
b. 0.41 %
c. 4.096%
Step-by-step explanation:
We make use of the binomial probability equation, which is as follows:
P = [n! / (n - r)! r!] p ^ r * q ^ (n - r)
where,
n total number samples = 6
r is the selected number, depends on each point (a, b, c)
p is the of believing in reincarnation = 0.40
q = 1 - p = 0.60
to. What is the probability that exactly 5 of the selected adults believe in reincarnation?
So we use r = 5
P = [6! / ((6 - 5)! * 5!)] * [0.40 ^ 5 * 0.60 ^ (6 - 5)]
P = 6 * 0.006144
P = 0.0368 = 3.686%
b. What is the probability that all of the selected adults believe in reincarnation?
So we use r = 6
P = [6! / ((6 - 6)! * 6!)] * [0.40 ^ 6 * 0.60 ^ (6 - 6)]
P = 1 * 0.004096
P = 0.004096 = 0.41%
c. What is the probability that at least 5 of the selected adults believe in reincarnation?
So we use r = 5 to 6
P (r = 5) = [6! / ((6 - 5)! * 5!)] * [0.40 ^ 5 * 0.60 ^ (6 - 5)]
P (r = 5) = 6 * 0.006144
P (r = 5) = 0.0368 = 3.686%
P (r = 6) = [6! / ((6 - 6)! * 6!)] * [0.40 ^ 6 * 0.60 ^ (6 - 6)]
P (r = 6) = 1 * 0.004096
P (r = 6) = 0.004096 = 0.41%
The total is the sum of all:
P (total) = 3.686% + 0.41%
P (total) = 4.096%
what are the possible values of x in 8x^2+4=-1 a. 2+-iroot/3 b. -1+-i/6 c.-1+-i/4 d.1+-i/4 e. 1+-i root 2/4
Answer:
x = ± i sqrt(5/8)
Step-by-step explanation:
8x^2+4=-1
Subtract 4 from each side
8x^2+4-4=-1-4
8x^2 = -5
Divide by 8
8/8x^2=-5/8
x^2 = -5/8
Take the square root of each side
sqrt(x^2) = ±sqrt(-5/8)
x = ±sqrt(-5/8)
x = ±sqrt(5/8) sqrt(-1)
x = ± i sqrt(5/8)
if f(x) =2x-1 and g(x)=x^2-3x-2, fins (f+g)(x)
Answer:
[tex](f+g)(x)=x^2-x-3[/tex]
Step-by-step explanation:
If [tex]f(x)=2x-1[/tex], and [tex]g(x)=x^2-3x-2[/tex], then the addition [tex](f+g)(x)[/tex] equals:
[tex](f+g)(x)=2x-1+x^2-3x-2=x^2-3x+2x-2-1=x^2-x-3[/tex]
1. The Wall Street Journal reported that bachelor’s degree recipients with majors in business average starting salaries of $53,900 in 2012 (The Wall Street Journal, March 17, 2014). The results for a sample of 100 business majors receiving a bachelor’s degree in 2013 showed a mean starting salary of $55,144 with a sample standard deviation of $5,200. Conduct a hypothesis test to determine whether the mean starting salary for business majors in 2013 is greater than the mean starting salary in 2012. Use a = .01 as the level of significance
Answer:
The calculated value t = 4.976 > 2.6264 at 0.01 level of significance
Null hypothesis is rejected
Alternative hypothesis is accepted
The mean starting salary for business majors in 2013 is greater than the mean starting salary in 2012
Step-by-step explanation:
Given Mean of the population μ = $53,900
Given sample size 'n' = 100
Mean of the sample size x⁻ = 55,144
Sample standard deviation 'S' = 5200
Null hypothesis:H₀: There is no difference between the means
Alternative Hypothesis :H₁: The mean starting salary for business majors in 2013 is greater than the mean starting salary in 2012
Test statistic
[tex]t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }[/tex]
[tex]t = \frac{55144-53900}{\frac{5200}{\sqrt{100} } }[/tex]
t = 4.976
Degrees of freedom
ν = n-1 = 100-1 =99
t₀.₀₁ = 2.6264
The calculated value t = 4.976 > 2.6264 at 0.01 level of significance
Null hypothesis is rejected
Alternative hypothesis is accepted
Final answer:-
The mean starting salary for business majors in 2013 is greater than the mean starting salary in 2012
Answer:
We conclude that the mean starting salary for business majors in 2013 is greater than the mean starting salary in 2012.
Step-by-step explanation:
We are given that the Wall Street Journal reported that bachelor’s degree recipients with majors in business average starting salaries of $53,900 in 2012.
A sample of 100 business majors receiving a bachelor’s degree in 2013 showed a mean starting salary of $55,144 with a sample standard deviation of $5,200.
Let [tex]\mu[/tex] = mean starting salary for business majors in 2013.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\leq[/tex] $53,900 {means that the mean starting salary for business majors in 2013 is smaller than or equal to the mean starting salary in 2012}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > $53,900 {means that the mean starting salary for business majors in 2013 is greater than the mean starting salary in 2012}
The test statistics that would be used here One-sample t-test statistics because we don't know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean starting salary = $55,144
s = sample standard deviation = $5,200
n = sample of business majors = 100
So, the test statistics = [tex]\frac{55,144-53,900}{\frac{5,200}{\sqrt{100} } }[/tex] ~ [tex]t_9_9[/tex]
= 2.392
The value of t-test statistic is 2.392.
Now, at 0.01 significance level the t table gives a critical value of 2.369 at 99 degree of freedom for right-tailed test.
Since our test statistic is more than the critical value of t as 2.392 > 2.369, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that the mean starting salary for business majors in 2013 is greater than the mean starting salary in 2012.
Carpetland salespersons average $8000 per week in sales. Steve Contois, the firm's vice president, proposes a compensation plan with new selling incentives. Steve hopes that the results of a trial selling period will enable him to conclude that the compensation plan increases the average sales per salesperson.a. Develop the appropriate null and alternative hypotheses.: - Select your answer -: - Select your answer -b. In this situation, a Type I error would occur if it was concluded that the new compensation plan provides a population mean weekly sales - Select your answer - when in fact it does not.What are the consequences of making this error
Answer:
The null and alternative hypothesis are:
[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2> 0[/tex]
where μ1 is the population mean sales with compensation plan, and μ2 is the populatiojn mean sales without compensation plan.
A Type I error is made when a true null hypothesis is rejected. In this case, it would be concluded that the compensation plan increases sales, when in fact it does not (at least, not significantly).
The consequences of this error would be that the compensation plan would have evidence to be implemented in the company when in fact it will not bring the results it is expected to have.
Step-by-step explanation:
This hypothesis test will test the claim that the compensation plan increases the average sales per salesperson. This claim will be stated in the alternative hypothesis, and will state that, with the compensation plan, the sales are significantly higher than without the compensation plan.
The null hypothesis, that Steve wants to falsify, will state that the sales will not differ with or withour compensation plan.
We can write this hypothesis as:
[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2> 0[/tex]
where μ1 is the population mean sales with compensation plan, and μ2 is the populatiojn mean sales without compensation plan.
A Type I error is made when a true null hypothesis is rejected. In this case, it would be concluded that the compensation plan increases sales, when in fact it does not (at least, not significantly).
The consequences of this error would be that the compensation plan would have evidence to be implemented in the company when in fact it will not bring the results it is expected to have. The sales would be expected to increase due to this implementation, and they will not increase, at least, not for the compensation plan.
What is the area of the trapezoid below? Select one: a. 88 cm2 b. 44√3 cm2 c. 65 cm2 d. 36√3 cm2
Answer: D
Step-by-step explanation:
Since we are not given the height of the trapezoid, we can split this into a triangle and a rectangle. We find the area of each and then add them together. In order to do so, we must use Pythagorean Theorem to find the missing length so that we can find the area.
a²+b²=c²
a²+4²=8²
a²+16=64
a²=48
a=√48
a=4√3
Now that we know the missing length of the triangle, we can find the area of the triangle and the rectangle.
Triangle
A=1/2bh
A=1/2(4)(4√3)
A=8√3
-----------------------------------------------------------------------------------------
Rectangle
A=lw
A=7(4√3)
A=28√3
With our areas, we can add them together.
4√3+28√3=36√3 cm²
Suppose f(x)=x^2. Find the graph of f(x-2)
The answer is
Answer:
f(x-2) = (x-2)²
or
f(x-2) = x² -4x + 4
Step-by-step explanation:
Simply plug in (x - 2) into f(x) to find your graph.
Edit (With Picture):
You are moving the graph right 2.
Answer:
Step-by-step explanation:
f(x) = x²
f(x - 2) = (x - 2)²
f(x - 2) = x² - 4x + 4
The grafic is below.
I hope I've helped you.
Graph g(x)=-2|x-5|-4
Answer:
Step-by-step explanation:
A driver travels a distance of 119 miles between 09:50 and 11:35. Work out the average speed of the driver
Answer:
68 miles per hour.
Step-by-step explanation:
The time taken for the driver to drive 119 miles is 105 minutes.
The average speed is equal to distance divided by the time taken.
105 minutes is equal to 1.75 hours.
[tex]S=119/1.75[/tex]
[tex]S =68[/tex]
The driver's average speed is 68 miles per hour.
Answer:
Speed = 68 mph
Step-by-step explanation:
Given:
Distance = 119 miles
Time = 1 hour 45 minutes = 1.75 hours
Required:
Speed = ?
Formula:
Average Speed = Total Distance Covered / Total Time Taken
Solution:
Speed = 119/1.75
Speed = 68 mph
Seven new employees, two of whom are married to each other, are to be assigned seven desks that are lined up in a row. If the assignment of employees to desks is made randomly, what is the probability that the married couple will have adjacent desks
Answer:
2/7
Step-by-step explanation:
Seven employees can be arranged in 7! ways. n(S) = 7!
Two adjacent desks for married couple can be selected in 6 ways viz.,(1, 2), (2, 3), (3,4), (4, 5), (5,6),(6,7).
This couple can be arranged in the two desks in 2! ways. Other five persons can be arranged in 5! ways.
So, number of ways in which married couple occupy adjacent desks
= 6×2! x 5! =2×6!
so, the probability that the married couple will have adjacent desks
[tex]\frac{n(A)}{n(s)} =\frac{2\times6!}{7!} \\=\frac{2}{7}[/tex]
Halfway through the season, a soccer player has made 15 penalty kicks in 19 attempts. Based on her performance to date, what is the relative frequency probability that she will make her next penalty kick?
Answer:
[tex]\dfrac{15}{19}[/tex]
Step-by-step explanation:
The soccer player so far has made 15 penalty kicks in 19 attempts.
Therefore:
Total Number of trials =19
Number of Successes =15
Therefore, the relative frequency probability that she will make her next penalty kick is:
[tex]=\dfrac{\text{Number of Successes}}{\text{Total Number of Trials}} \\=\dfrac{15}{19}[/tex]
You deal a pile of cards, face down, from a standard 52-card deck. What is the least number of cards the pile must have before you can be assured that it contains at least five cards of the same suit
Answer:
we need at least 17 - card deck
Step-by-step explanation:
From the information given :
We can attempt to solve the question by using pigeonhole principle;
"The pigeonhole principle posits that if more than n pigeons are placed into n pigeonholes some pigeonhole must contain more than one pigeon"
Thus; the minimum number of pigeon; let say at least n pigeons sit on at least one same hole among m hole can be represented by the formula:
m( n - 1 ) + 1
where ;
pigeons are synonymous to card
pigeonholes are synonymous to suits
So; m = 4 ; n = 5
∴ 4 (5 -1 ) + 1 ⇒ 4 (4) + 1
= 16 + 1
= 17
Hence; we need at least 17 - card deck
The product of Holly's savings and 3 is 39.
Use the variable h to represent Holly's savings.
Answer:
3h = 39Step-by-step explanation:
The question is incomplete. Here is the complete question.
Translate this sentence into an equation. The product of Holly's height and 3 is 39. Use the variable h to represent Holly's height.
Let holly's savings be h. If the product of Holly's savings and 3 is 39, this can be represented mathematically as h*3 = 39
To get holly's savings "h', we will divide both sides of the equation by 3
h*3 = 39
h*3/ 3= 39/3
h = 13*3/ 3
h = 13 * 3/3
h = 13*1
h = 13
Holly's savings is 13 and the required equation is 3h =39
The 2003 Zagat Restaurant Survey provides food, decor, and service ratings for some of the top restaurants across the United States. For 15 top-ranking restaurants located in Boston, the average price of a dinner, including one drink and tip, was $48.60. You are leaving on a business trip to Boston and will eat dinner at three of these restaurants. Your company will reimburse you for a maximum of $50 per dinner. Business associates familiar with the restaurants have told you that the meal cost at 5 of the restaurants will exceed $50. Suppose that you randomly select three of these restaurants for dinner.
Required:
a. What is the probability that none of the meals will exceed the cost covered by your company?
b. What is the probability that one of the meals will exceed the cost covered by your company?
c. What is the probability that two of the meals will exceed the cost covered by your company?
d. What is the probability that all three of the meals will exceed the cost covered by your company?
Answer:
a. P(x=0)=0.2967
b. P(x=1)=0.4444
c. P(x=2)=0.2219
d. P(x=3)=0.0369
Step-by-step explanation:
The variable X: "number of meals that exceed $50" can be modeled as a binomial random variable, with n=3 (the total number of meals) and p=0.333 (the probability that the chosen restaurant charges mor thena $50).
The probabilty p can be calculated dividing the amount of restaurants that are expected to charge more than $50 (5 restaurants) by the total amount of restaurants from where we can pick (15 restaurants):
[tex]p=\dfrac{5}{15}=0.333[/tex]
Then, we can model the probability that k meals cost more than $50 as:
[tex]P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{3}{k} 0.333^{k} 0.667^{3-k}\\\\\\[/tex]
a. We have to calculate P(x=0)
[tex]P(x=0) = \dbinom{3}{0} p^{0}(1-p)^{3}=1*1*0.2967=0.2967\\\\\\[/tex]
b. We have to calculate P(x=1)
[tex]P(x=1) = \dbinom{3}{1} p^{1}(1-p)^{2}=3*0.333*0.4449=0.4444\\\\\\[/tex]
c. We have to calcualte P(x=2)
[tex]P(x=2) = \dbinom{3}{2} p^{2}(1-p)^{1}=3*0.1109*0.667=0.2219\\\\\\[/tex]
d. We have to calculate P(x=3)
[tex]P(x=3) = \dbinom{3}{3} p^{3}(1-p)^{0}=1*0.0369*1=0.0369\\\\\\[/tex]
Alex has 5 pieces of paper, each with a different math problem. In how many ways can he give these problems to his 10 friends (he can give each friend more than one problem)
Answer:
100,000 ways
Step-by-step explanation:
For each note, assign a number of friends
This can be repeated among the notes.
This is a 5 digit base 10 number
thus there are 10^5 = 100,000
There are 100,000 ways to distribute the problems among his 10 friends
Christian Iris and Morgan each get an equal share of 1/2 of pizza which model represent the fraction of the pizza each person gets
Answer:
CICI
Step-by-step explanation: NO cici
Christian, Iris and Morgan each get an equal share of 1/2 of the pizza and the model 1/6 represent the fraction of the pizza each person gets.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
Given:
Christian, Iris and Morgan each get an equal share of 1/2 of the pizza.
To find the fraction of the pizza each person gets:
Divide the amount of pizza by the number of people.
There are 3 people and 1/2 pizza.
The fraction of the pizza each person gets
= The amount of pizza / number of people
The fraction of the pizza each person gets
= (1/2) / 3
Simplifying into multiplication,
The fraction of the pizza each person gets = 1/2 x 1/3
The fraction of the pizza each person gets
= 1/(2x3)
= 1/6
Therefore, the model that represents the requirement is 1/6.
To learn more about the division;
https://brainly.com/question/13263114
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I'm lost with this problem please help. Write answers as a fractions
Answer: 8/3 and -9/4
Step-by-step explanation:
1. [tex]\frac{2^{3}}{3} = \frac{2 * 2 * 2}{3} = \frac{8}{3}[/tex]
2. In this problem, when raising a whole fraction to a power, you must both raise the numerator and denominator to that power.
[tex]-(\frac{3}{2})^2 = -(\frac{3^2}{2^2}) = -(\frac{9}{4}) = -\frac{9}{4}[/tex]
Graph the function f(x) = 21(0.5)x.
Answer:
is m= 10.5 espero que te ayude