1/7 is the probability of getting both lights to be red.
In this problem, we want the conditional probability that both showed red, given that they both showed the same color, hence the outcomes are given as follows:
Desired outcomes: same color and red.
Total outcomes: same color.
The outcomes which result in the same color are given as follows:
Red - red, with 6/7 x 1/6 = 1/7 probability.
Green - green, with 1/7 x 3/10 = 3/70 probability.
Meaning that the conditional probability is calculated as follows:
p =1/7.
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Which numbers are 4 units from -2 on this number line?
Drag and drop the two numbers that are 4 units from -2 to their correct position on the number line.
Answer:
-6 and 2
Step-by-step explanation:
See attached worksheet.
Which of the following can be used to show that these triangles are congruent?
It is 2,966 miles round trip to Craig's aunt's house. If he travels to her house 6 times this year, how many miles did he travel in all?
If there are 8 boys and 56 girls in a room, fill out all of the possible ratios of boys to girls that could be made.
Answer:
1:7 , 2:14, 4:28, 8:56
Step-by-step explanation:
Ratios act just like fractions, because of this, you can simplify ratios just as you would simplify a fraction. In addition, because they asked for the ratio of boys to girls, we know that they want the (number of boys): (number of girls)
HOPE THIS HELPS!!!
Help please anything
Answer:
36 ft
Step-by-step explanation:
The ratio of the lengths of the sides is the same as the ratio of the perimeters.
Just like one side (15 ft) of triangle ABC is 3 times as long as the corresponding side (5 ft) of triangle DEF, the perimeter of triangle ABC is also 3 times the perimeter of triangle DEF.
15/5 = x/12
3 = x/12
x = 36
Answer: 36 ft
Please see attachment below, 40 points!!!
Answer: I would say 68 i believe this because if i do remember correctly you have to make it equal 192 and 68 did that.
Step-by-step explanation: Sorry if im wrong.
Self-confidence is an attitude about your skills and abilities. It means you accept and trust yourself and have a sense of control in your life. You know your strengths and weakness well, and have a positive view of yourself. You set realistic expectations and goals, communicate assertive
The work that Ryan did to find the greatest common factor of 48 and 72 is shown below.
Prime factorization of 48: 2 x 2 x 2 x 2 x 3
Prime factorization of 72: 2 x 2 x 2 x 3 x 3
The greatest common factor is 2 ´ 2 ´ 2 ´ 3 x 3
What is Ryan’s error?
Answer:
there will only be one 3
Step-by-step explanation:
see cause the first 3 of both numbers are 2 but only the last one of both numbers are 3 .
If you put $2,000 in an account at an annual simple interest rate of 5%, how long will it take your balance
to grow to $2,600? (Hint: How many years will it take to earn $600 worth of interest?)
Answer:
After investing for 10 years at 5% interest, your $2,000 investment will have grown to $3,258
Step-by-step explanation:
Your welcome
An amusement park opened at 10:00 a.m. In the first hour,
480 people purchased admission tickets. In the second hour,
40% more people purchased admission tickets than in the
first hour. Each admission ticket cost $24.50.
What was the total amount of money paid for all the tickets
purchased in the first two hours?
A) $16,464.00
B) $4,704.00
C) $18,816.00
D) $28,224.00
Answer:
D) $28,224.00
Step-by-step explanation:
1st hour: 480 ticket sales
2nd hour: 480 + 40% of 480 = 480 + 0.4 × 480 = 480 + 192 = 672
Total ticket sales in first 2 hours: 480 + 672 = 1152
Ticket price: $24.50
Total sales: 1152 × $24.50 = $28,224
Raina deposits $6000 into an account that pays simple interest at a rate of 2% per year. How much interest will she be paid in the first 5 years
Answer:
She will have $600 in the first five years
Step-by-step explanation:
6000 - 10% = 5400 so it takes 600 and 2% in each year = 10% every 5 years so it is 600
Use the Distributive Property to complete the equivalent expression. 4(y-3)=___-___? Please answer quickly!!!
Answer:
4y-12
Step-by-step explanation:
ok in distributive propertie you multiply the number or term on the outside of the parenthesis with the terms in the inside in other words. 4 ×y and 4× 12
Answer:
4y-12
Step-by-step explanation:
I did something just like this
Is y=-x proportional?
Answer:
Yea
Step-by-step explanation:
two brothers were talking about how the older they get, the less significant the difference in their ages seems to be. specifically, they noticed that, 20 years ago, the ratio of their ages (in years) was 1:2; now, the ratio is 5:6; and, 20 years from now, the ratio will be 9:10.
The current ages of the two brothers are A = 25 and B = 30.
To solve the problem, let's denote the current ages of the two brothers as A and B, where A is the older brother and B is the younger brother.
From the given information, we have three time points to consider: 20 years ago, the present, and 20 years from now. Let's analyze each of these time points:
20 years ago:
At this time point, the ratio of their ages was 1:2. This can be expressed as (A-20)/(B-20) = 1/2.
Present:
Currently, the ratio of their ages is 5:6. This can be expressed as A/B = 5/6.
20 years from now:
In the future, the ratio of their ages will be 9:10. This can be expressed as (A+20)/(B+20) = 9/10.
Now, we have three equations based on the given information. We can solve this system of equations to find the ages of the brothers.
Equation 1: (A-20)/(B-20) = 1/2
Equation 2: A/B = 5/6
Equation 3: (A+20)/(B+20) = 9/10
Solving this system of equations will yield the values of A and B, representing the current ages of the two brothers.
2(A-20) = B-20
2A - 40 = B - 20
2A - B = 20
Now, let's solve the system of equations using a method like substitution
From Equation 2, we have A/B = 5/6. We can rewrite it as A = (5/6)B.
Substituting this value of A into Equation 1:
2((5/6)B) - B = 20
(10/6)B - B = 20
(4/6)B = 20
(2/3)B = 20
B = (3/2) × 20
B = 30
Now, we can substitute the value of B back into Equation 2 to find A:
A/B = 5/6
A/30 = 5/6
A = (5/6) × 30
A = 25
Therefore, the current ages of the two brothers are A = 25 and B = 30.
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Let f(x) be a function that is defined for all real numbers. Select EVERY true statement (there may be more than one). If f(x) is continuous on (a,b), then f(x) attains an absolute maximum value f(c) and an absolute minimum value f(d) for some numbers cand d in (a,b). If f(x) has a critical point at x = c, then f'(c) = 0. If f(x) has a local minimum value at x = c, then f'(c) = 0. If f'(c) = 0, then f(x) has a local maximum or minimum at x = c. o If f'(c) is undefined, then x = c is a critical point of f(x).
All options are true except option iii)
Given function is f(x) which is defined for all real numbers.
What is a critical point? A critical point of a function is a point where the derivative of the function equals zero or fails to exist. For a given function f(x), select the true statements:
i) If f(x) is continuous on (a,b), then f(x) attains an absolute maximum value f(c) and an absolute minimum value f(d) for some numbers c and d in (a,b).
ii) If f(x) has a critical point at x=c, then f'(c)=0.
iii) If f(x) has a local minimum value at x=c, then f'(c)=0.
iv) If f'(c)=0, then f(x) has a local maximum or minimum at x=c.
v) If f'(c) is undefined, then x=c is a critical point of f(x). From the above all options, all options are true except option iii). Option iii is incorrect because if f(x) has a local minimum or maximum value, then f'(c)=0 is not necessary. The necessary condition is f'(c)=0 but the converse is not true.
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Your Stats teacher tells you your test score was the 3rd quartile for the class. Which is true?
I. You got 75% on the test.
II. Youcan'treallytellwhatthismeanswithoutknowingthestandarddeviation.
III. You can't really tell what this means unless the class distribution is nearly Normal.
Find two consecutive odd numbers such that the sum of the larger number and twice the smaller number is 27 less then foir times the smaller number
Answer:
29 and 31Step-by-step explanation:
x - some integer
2x+1 - an odd integer (the smaller one)
2x+1+2=2x+3 - the next odd integer consecutive to 2x+1 (the larger)
2×(2x+1) - twice the smaller number
2x+3+2•(2x+1) -the sum of the larger number and twice the smaller number
4•(2x+1) - four times the smaller number
4•(2x+1)-27 - 27 less then four times the smaller number
2x + 3 + 2•(2x + 1) = 4•(2x + 1) - 27
2x + 3 + 4x + 2 = 8x + 4 - 27
6x + 5 = 8x - 23
-5 -5
6x = 8x - 28
-8x -8x
-2x = - 28
÷(-2) ÷(-2)
x = 14
2x+1 = 2•14 + 1 = 29
2x+3 = 2•14 + 3 = 31
Check: 31+2•29=31+58=89; 4•29-27=116-27=89
help please and thank you.
Answer:
the answer is C 7/4
Step-by-step explanation:
goes up 7 and over 4
Decide whether the function defined as follows is a probability density function on the indicated interval. If not, tell why. f(x) = 35 70 12,9) lo
No, the function f(x) = 35/(70-12.9) is not a probability density function on any interval, since it violates the non-negativity requirement of probability density functions.
A probability density function is a non-negative function that integrates to 1 over its defined interval. This means that the function must take non-negative values for all possible values of x, and its integral over the entire interval must equal 1.
In this case, the denominator (70-12.9) is equal to 57.1, which means that the value of the function f(x) is greater than 1 for any value of x. This violates the non-negativity requirement of probability density functions.
In conclusion, f(x) = 35/(70-12.9) is not a probability density function since it takes values greater than 1, violating the non-negativity requirement.
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A family buys 6 tickets to a show. They also pay a $3 parking fee. They spend $27 to see the show.
Answer:
27 -3= 24
24 /6= 4
Tickets were $4 each
Step-by-step explanation:
Ashley and Rod cleaned the house in 4 hours. Rod can clean the houre alone in 2 hours how long will it take for ashley to clean the house alone?
It will take 4 hours for Ashley to clean the house alone.Answer: Ashley will take 4 hours to clean the house alone.
Given:Ashley and Rod cleaned the house in 4 hours. Rod can clean the house alone in 2 hours.To find:How long will it take for Ashley to clean the house alone?Solution:Let's suppose the time Ashley takes to clean the house alone is x hours.Then, Ashley and Rod can clean the house in 4 hours.Thus, using the concept of work, we have:\begin{aligned} \text { Work done by Ashley in 1 hour } + \text { Work done by Rod in 1 hour } &= \text { Work done by Ashley and Rod in 1 hour } \\ \Rightarrow \frac {1}{x} + \frac {1}{2} &= \frac {1}{4} \\ \Rightarrow \frac {2 + x}{2x} &= \frac {1}{4} \\ \Rightarrow 8 + 4x &= 2x \\ \Rightarrow 2x - 4x &= -8 \\ \Rightarrow x &= 4 \end{aligned}Therefore, it will take 4 hours for Ashley to clean the house alone.Answer: Ashley will take 4 hours to clean the house alone.
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What is the difference between a rectangle and a cube? A rectangle is a 3-dimensional and a cube is a 2-dimensional. A rectangle and a cube are both 2-dimensional. A rectangle is a 2-dimensional and a cube is a 3-dimensional A rectangle and a cube are both 3-dimensional.
Answer: A rectangle is a 2-dimensional and a cube is a 3-dimensional
Step-by-step explanation:
Which expression is equivalent to 25x â€" 45y?
A. 25(5x â€" 20y)
B. 5(5x - 9y)
C. 70(x â€" y)
D. 10(15x â€" 35y)
Answer:
D
Step-by-step explanation:
Somehting bknbye3uehnfhnjun Español uno, como sulfhídrica
consider a 10-year 3% coupon bond with annual payments and face value of $1,000. if it is currently trading at $901, what is its yield to maturity? answer in percent, rounded to one decimal place.
7.0% is the maturity yield. It is computed by taking into account the present value of the bond's future cash flows, the face value, and the current market price.
A bond's yield to maturity is a measure of the expected return on investment. It takes into account the bond's face value as well as the current market price and future cash flows. In this case, the bond has a 10-year maturity period, a 3% coupon rate, annual payments, and a $1,000 face value. If it is currently trading at $901, the can be calculated. To begin, we must compute the present value of the bond's future cash flows, which include coupon and principal payments. The YTM is used in this case. The in this case is 7.0%, implying that an investor will earn a 7.0% return.
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Last season he scored 179 touchdowns. This season he scored 253 touchdowns.
What was the percent increase in the number of touchdowns Frank scored?
Round to the nearest percent.
A member of the sales team earns 30% commission on any sales. A salesperson sold $450 worth of merchandise.
How much was the salesperson's commission on the sale?
Answer:
The answer to this is B, $135.
Step-by-step explanation:
I took the test.
Answer:
$135 is the correct answer, I took the test and got it right
Step-by-step explanation:
Need 6 and 7 done please and thank you
Answer:
black
black
Step-by-step explanation:
Please help!!
1. If the cost, C(×), for manufacturing x units of a certain product is given by C(x) = x^2 - 15x + 50, find the number of units manufactured at a cost of $9,500.
2. While hovering near the top of the Ribbon Falls in Yosemite National Park at 1,600 feet, a helicopter pilot accidentally drops his sunglasses. The height h(t) of the sunglasses after tseconds is given by the polynomial function h(t) =- 16t + 1600. When will the sunglasses hit the ground?
3. After t seconds, the height h(t) of a model rocket launched from the ground into is given by the function h(t) =- 16t? + 80t. Find how long it takes the rocket to r height of 96 feet.
4. 5. The floor of a shed has an area of 90 square feet. The floor is in the shape of a rectangle whose length is 3 feet less than twice the width. Find the length and the width of the floor of the shed.
The number of units manufactured at a cost of $9,500 is approximately 141.75 units.
The sunglasses will hit the ground after 100 seconds
The rocket reaches a height of 96 feet at t = 2 seconds or t = 3 seconds.
The width of the floor is 6 feet, and the length is 9 feet.
How to calculate the valueNow we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
where a = 1, b = -15, and c = -9,450.
Plugging these values in:
x = (-(-15) ± √((-15)² - 4(1)(-9,450))) / 2(1)
x = (15 ± √(15 + 18,960)) / 2
x = (15 ± √19,185) / 2
x ≈ 141.75
In order to find when the sunglasses will hit the ground, we need to find the time t when h(t) = 0.
h(t) = -16t + 1600 = 0
Solving for t:
-16t = -1600
t = 100
Therefore, the sunglasses will hit the ground after 100 seconds.
h(t) = -16t² + 80t
96 = -16t² + 80t
0 = -16t² + 80t - 96
0 = -t² + 5t - 6
0 = (t - 2)(t - 3)
The rocket reaches a height of 96 feet at t = 2 seconds or t = 3 seconds.
2w² - 3w - 90 = 0
(2w + 15)(w - 6) = 0
If w - 6 = 0, then w = 6, which is a valid solution.
Therefore, the width of the floor is 6 feet, and the length is 2(6) - 3 = 9 feet.
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A chemist has three different acid solutions,
The first solution contains 20 % acid, the second contains 35 % acid, and the third contains 55%
acid.
She created 108 liters of a 40 % acid mixture, using all three solutions. The number of liters of
55 % solution used is 3 times the number of liters of 35 % solution used.
How many liters of each solution was used?
The chemist used
liters of 20% solution,
liters of 35 % solution, and
liters of 55 % solution.
Question Help: Message
instructor
Calculator
9514 1404 393
Answer:
36 liters of 20%18 liters of 35%54 liters of 55%Step-by-step explanation:
Let a, b, c represent the quantities of 20%, 35%, and 55% solutions, respectively. Then for the given mix, we have ...
a + b + c = 108 . . . . . total number of liters
.20a +.35b +.55c = 0.40·108 . . . . . liters of acid
0a - 3b + c = 0 . . . . . 55% solution was 3 times 35% solution
__
Solving these three equations by your favorite method gives ...
(a, b, c) = (36, 18, 54)
The chemist used 36 liters of 20%, 18 liters of 35%, and 54 liters of 55%.
_____
Comment on alternate approach
Since the ratio of 55% to 35% is 3 : 1, that mix will have an acid content of ...
(3(.55) +1(.35))/4 = 0.50 = 50%
So, the final mix is equivalent to some quantity of 50% mix being added to some quantity of 20% mix. The fraction that is 50% mix* will be (40-20)/(50-20) = 2/3 of the total, or (2/3)(108 L) = 72 L.
Now we know that (1/3)(108 L) = 36 L of 20% solution is needed and (1/4)(72 L) = 18 L of 35% solution is needed. 3 times that is 54 L of 55% solution.
__
* After you work a few mixture problems, you can see the pattern. If we start with an equation for x = fraction of 50% to use with 20% to make 40%, we get ...
x(50%) +(1 -x)(20%) = 40%
x(50% -20%) = 40% -20% . . . . . subtract 1(20%) and factor out x
x = (40% -20%)/(50% -20%)
The key here is to see where the numbers 20%, 40%, and 50% show up in the fraction.
A man trying to improve his health wanted to see if there was a linear relationship between how many miles he ran and his heart rate in beats per minute. After recording how many miles he ran and his heart rate for 12 different days he created this 95% confidence interval for 3 miles (160,180). The twelve different days could be considered a random sample of all of his run days. Which of these options below is the best interpretation of the confidence interval?
a. It can be stated with 95% confidence that his average heart rate after running 3 miles is between 160 and 180 beats per minute.
b. 95% of all people who run 3 miles will have a heart rate between 160 and 180 beats per minute.
c. It can be stated with 95% confidence that of the 12 days sampled every time he ran 3 miles his heart rate was between 160 and 180 beats per minute
d. It can be stated with 95% confidence that every time he has a heart rate between 160 and 180 beats per minute he will have just run 3 miles
A man wanted to investigate the linear relationship between how many miles he ran and his heart rate in beats per minute. After recording how many miles he ran and his heart rate for 12 different days, he created this 95% confidence interval for 3 miles (160,180). The twelve different days could be considered a random sample of all of his run days. The best interpretation of the confidence interval is Option a) It can be stated with 95% confidence that his average heart rate after running 3 miles is between 160 and 180 beats per minute.
Given that the 12 different days could be considered a random sample of all of his run days, the sample statistics of the study can be used to make inferences about the population parameters. Therefore, the 95% confidence interval for 3 miles of (160,180) can be interpreted as There is a 95% chance that the true population average heart rate after running 3 miles is between 160 and 180 beats per minute. Or It can be stated with 95% confidence that his average heart rate after running 3 miles is between 160 and 180 beats per minute.
Option a. It can be stated with 95% confidence that his average heart rate after running 3 miles is between 160 and 180 beats per minute is the best interpretation of the confidence interval.
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= 2 - 4
Drawing Tools
Click on a tool to begin drawing
3 peate
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Select
Line
10-
8-
6-
4
-10
-8
-5
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8
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it
B
a
Answer:
Please find attached the required inverse of a function chart
Step-by-step explanation:
The inverse of a function is found by reversing the operations of the function
The inverse of the function f(x) = 2·x - 4 is found as follows;
x = 2·x - 4
x + 4 = 2·x
x = (x + 4)/2 = x/2 + 2
Therefore, the inverse of the function f(x) = 2·x - 4 is f(x) = x/2 + 2
The inverse function is plotted by generating data points as follows;
\({}\)x \({}\) f(x)
0 2
1 2.5
2 3
3 3.5
4 4
5 4.5
6 5
7 5.5
8 6
9 6.5
10 7
11 \({}\) 7.5
12\({}\) 8
13 8.5
14 9
15 9.5
16 10