Answers
Answer:
Step-by-step explanation:
D. possible angle is 60 degrees out out 360
60/360 = .1666 = 16.7%
P(D)=16.7%
P(B or C) = (30+90)/360 = .333 =33.3% Or means add your probabilities
P(A)=180/360=.5 = 50.0%
P(not A)= 180/360=.5= 50.0%
Related Questions
Chen and Megan have a parcel Chen’s parcel weighs 1 1/2kg Megan’s parcel weighs 1. 2kg how many more grams does Chen’s parcel weigh than Megan’s parcel
Answers
Chen’s parcel weighs 0.3 kg more than Megan’s parcel
What is the difference in fraction?When working with fractions and decimals, it is good to use only one unit for ease of solving.
We are given the weights as:
Weight of Chen’s Parcel = 1¹/₂ kg
Weight of Megan's Parcel = 1.2 kg
Now, let us convert the weight of Chen’s Parcel from fraction to decimal to get 1.5 kg
Thus:
Difference in weight = 1.5 kg - 1.2 kg
= 0.3 kg
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find the equation of a circle passing through the points (1, 2), (0, 3)and (-2, 7)
Answers
(x - h)^2 + (y - k)^2 = r^2
where (h, k) is the center of the circle, and r is the radius.
We can find the center and radius of the circle by solving a system of equations using the three given points. Here's how:
First, we can find the equations of the perpendicular bisectors of the line segments connecting the three points. The intersection of these bisectors will be the center of the circle.
The midpoint of the line segment connecting (1, 2) and (0, 3) is:
((1+0)/2, (2+3)/2) = (1/2, 5/2)
The slope of the line segment is:
(3-2)/(0-1) = -1
The slope of the perpendicular bisector is the negative reciprocal of the slope of the line segment, which is:
1/(-1) = -1
So the equation of the perpendicular bisector is:
y - (5/2) = (-1)(x - 1/2)
y = -x + 6
The midpoint of the line segment connecting (0, 3) and (-2, 7) is:
((0-2)/2, (3+7)/2) = (-1, 5)
The slope of the line segment is:
(7-3)/(-2-0) = -2
The slope of the perpendicular bisector is the negative reciprocal of the slope of the line segment, which is:
1/(-2) = -1/2
So the equation of the perpendicular bisector is:
y - 5 = (-1/2)(x + 1)
y = (-1/2)x + (11/2)
The intersection of these two lines is the center of the circle. Solving for x and y, we get:
-x + 6 = (-1/2)x + (11/2)
x = 1
Substituting x = 1 into either equation, we get:
y = -1 + 6 = 5
So the center of the circle is (1, 5).
To find the radius of the circle, we can use the distance formula between one of the given points and the center of the circle. Let's use (1, 2):
r^2 = (1 - 1)^2 + (2 - 5)^2
r^2 = 9
r = 3
Therefore, the equation of the circle passing through the points (1, 2), (0, 3), and (-2, 7) is:
(x - 1)^2 + (y - 5)^2 = 9
a team of soccer players spend an average of 15 minutes on weight weight training per practice session.how many minutes of weight trainingon an average would they have to complete in 116 practise?
Answers
Answer:
The answer to your problem is, 1,740 minutes
Step-by-step explanation:
The time period of 116 trainings solutions;
The time period of 1 weight training that we know is 15 minutes. Time period of 116 weight is 5 x 116 = 1,740
Thus the answer to your problem is, 1,740
Answer:1,740 minutes
Step-by-step:
I first saw that I need to take 15 minutes and x it be the 116 Practices.
So 15 x 116 is 1,740.
1,740 minutes is your answer.
Solve the system of equations using substitution 6x-9=y and y=-3x
Answers
Answer:
y = -3
x = 1
Step-by-step explanation:
To solve the system of equations using substitution, we need to isolate one variable in terms of the other in one of the equations and substitute this expression into the other equation. We can then solve for the remaining variable.
In this case, we are given two equations:6x - 9 = y
y = -3x
We can substitute the expression for y from the second equation into the first equation to get:
6x - 9 = -3x
Now we can solve for x:
6x + 3x = 9
9x = 9
x = 1
We can substitute this value of x back into one of the original equations to solve for y. Using the second equation, we have:
y = -3(1) = -3
Therefore, the solution to the system of equations is x = 1 and y = -3.
To verify the solution, we can substitute the values of x and y into the original equations and check if they are satisfied:
6x - 9 = y
6(1) - 9 = -3
-3 = -3
This equation is true, so x = 1 and y = -3 satisfy the first equation.
y = -3x
-3 = -3(1)
This equation is also true, so x = 1 and y = -3 satisfy the second equation.
Since x = 1 and y = -3 satisfy both equations, they are the solution to the system of equations using substitution.
PLEASE HELP, NEED IT BY TODAY
Write three equations. Each equation must include the numbers 3 and 30.3 and must be easy to solve by inspection. Solve your equations.
Answers
The three equations are:
3x = 30.3
30.3 - x = 27.3
3x + 30.3 = 63.6
We have,
Equation 1:
3x = 30.3
Solving for x, we can divide both sides by 3:
x = 10.1
Equation 2:
30.3 - x = 27.3
Solving for x, we can subtract 27.3 from both sides:
x = 3
Equation 3:
3x + 30.3 = 63.6
Solving for x, we can first subtract 30.3 from both sides:
3x = 33.3
Then, we can divide both sides by 3:
x = 11.1
Thus,
The three equations are:
3x = 30.3
30.3 - x = 27.3
3x + 30.3 = 63.6
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consider the data about the number of blocked intrusions in exercise 8.1, p. 240. (a) construct a 95% confidence interval for the difference between the average number of intrusion attempts per day before and after the change of firewall settings (assume equal variances). (b) can we claim a significant reduction in the rate of intrusion attempts? the number of intrusion attempts each day has approximately normal distribution. compute pvalues and state your conclusions under the assumption of equal variances and without it. does this assumption make a difference?
Answers
The 95% confidence interval for the difference between the average number of intrusion attempts per day before and after the change of firewall settings is (3.36, 13.78).
To construct a 95% confidence interval for the difference between the average number of intrusion attempts per day before and after the change of firewall settings, we can use a two-sample t-test with equal variances.
Let x₁ be the number of blocked intrusions per day before the change of firewall settings, and let x₂ be the number of blocked intrusions per day after the change of firewall settings. We have
x₂ = (56+47+49+37+38+60+50+43+43+59+50+56+54+58)/14 = 50.36
x₂ = (53+21+32+49+45+38+44+33+32+43+53+46+36+48+39+35+37+36+39+45)/20 = 40.95
s₁ = standard deviation of x₁ = 8.23
s₂ = standard deviation of x₂ = 8.98
The pooled standard deviation, sp, is given by
sp = √(((n₁-1)s₁² + (n₂-1)s₂²)/(n₁+n₂-2))
where n₁ and n₂ are the sample sizes. Since we assume equal variances, we use the formula for the pooled standard deviation. Substituting the values, we get:
sp = √(((14-1)8.23² + (20-1)8.98²)/(14+20-2)) = 8.63
The t-statistic for the difference between the means is given by
t = (x₁ - x₂) / (sp × √(1/n₁ + 1/n₂))
Substituting the values, we get
t = (50.36 - 40.95) / (8.63 × √(1/14 + 1/20)) = 2.28
We can use a t-distribution with degrees of freedom = n₁ + n₂ - 2 = 32 and a significance level of α = 0.05 to find the confidence interval. The confidence interval is given by
(x₂ - x₂) ± tsp√1/n₁ + 1/n₂)
Substituting the values, we get
(50.36 - 40.95) ± 2.0458.63√(1/14 + 1/20) = 8.57 ± 5.21
= (3.36, 13.78)
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The given question is incomplete, the complete question is:
The numbers of blocked intrusion attempts on each day during the first two weeks of the month were 56,47,49,37,38,60,50,43,43,59,50,56,54,58 After the change of firewall settings, the numbers of blocked intrusions during the next 20 days were 53,21,32,49,45,38,44,33,32,43,53,46,36,48,39,35,37,36,39,45. construct a 95% confidence interval for the difference between the average number of intrusion attempts per day before and after the change of firewall settings (assume equal variances).
the professor for a different section of the multi-section course reported his students’ exam scores as z-scores. a student in this section, katie, received a z-score of 2.2. what percentage of the students in her section did katie outscore?
Answers
Katie outscored approximately 1.39% of the students in her section.
How to calculate percentage of the students in her section did katie outscore?If Katie received a z-score of 2.2, this means that her score was 2.2 standard deviations above the mean of the exam scores for her section.
We can use a standard normal distribution table or calculator to find the percentage of scores that fall above a z-score of 2.2.
Using a standard normal distribution table, we can find the proportion of scores that fall below a z-score of 2.2, and then subtract this from 1 to find the proportion of scores that fall above a z-score of 2.2.
The table value for a z-score of 2.2 is approximately 0.9861, which means that approximately 98.61% of the scores fall below a z-score of 2.2. Therefore, approximately:
1 - 0.9861 = 0.0139, or 1.39%
of the scores fall above a z-score of 2.2.
This means that Katie outscored approximately 1.39% of the students in her section.
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Circumference of circle Q
Answers
The circumference of circle be 60 in.
Give that,
Angle of sector = 60 degree
Arc length = 10 inch
Arc length of circle = (Θ/360) x 2πr
Put the values
10 = (60/360)x2πr
⇒ r = 60/2π
Since circumference of circle = 2πr
Therefore,
circumference of the given circle = 2π x (60/2π)
= 60 in.
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The cost of 36 watches is ₹179100. Find the cost of one watch
Answers
The cost of one watch is ₹4975. The answer we got was obtained by dividing the total amount for 36 watches by the number of watches
To find the price of one watch, we can divide the total fee of 36 watches by way of the quantity of number of watches:
Price of 1 watch = general cost of 36 watches / 36
We are given that the price of 36 watches is about ₹179100, so we can now do the replacement of this value in to the formulation:
Value of one watch Is = ₹179100 / 36
When we will Simplify this expression, we get:
Value of 1 watch = ₹4975
Therefore, the cost of one watch is ₹4975.
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Find the probability of exactly 4 successes in 6 trials of a binomial experiment in which the probability of success is 40%
Answers
Answer:
0.13824
Step-by-step explanation:
You want the probability of exactly 4 successes in 6 trials if the probability of success in each trial is 0.4.
Binomial probabilityThe probability of k successes in n trials with each having a probability of success of p is given by the formula ...
P(k of n) = nCk·p^k·(1-p)^(n-k)
P(4 of 6) = 6C4·0.4^4·0.6^2 = 15·0.0256·0.36 = 0.13824
The probability of exactly 4 successes is 0.13824.
__
Additional comment
The binomial coefficient nCk is computed as ...
nCk = n!/(k!(n-k)!)
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How to find the perimeter of a composite shape with missing sides(rectangles)
Answers
Answer: You have to add up the lengths.
Dave drove 6,000 miles in his car last year. The total of fixed costs was $1,250.00 and of variable costs was $1,000.00.
Answers
Total annual cost for Dave's car driving 6,000 miles last year is $2,250.00 with fixed cost of $1,250.00 plus variable cost of $1,000.00.
Based on the given information, we can use the formula for total cost
Total Cost = Fixed Cost + (Variable Cost per unit x Number of units)
In this case, we know the fixed cost is $1,250.00, and the variable cost per mile is $1,000.00 / 6,000 miles = $0.1667/mile. Therefore, we can calculate the total annual cost as
Total Cost = $1,250.00 + ($0.1667/mile x 6,000 miles)
Total Cost = $1,250.00 + $1,000.20
Total Cost = $2,250.20
So, Dave's total annual cost of driving his car for 6,000 miles is $2,250.20.
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--The given question is incomplete, the complete question is given
" Dave drove 6,000 miles in his car last year. The total of fixed costs was $1,250.00 and of variable costs was $1,000.00. What is the total annual cost?"--
Jim and Avery compare the number of points they scored during a game. Explain your answer mathematically
Jim notices that when he doubles his number of points, then subtracts 10 from that number, the result is the same as the number of points Avery scored. Write an expression representing the number of points
Avery scored, in terms of the number of points Jim scored, j. Enter your expression in the response box
Answers
The expression representing the number of points Avery scored in terms of the number of points Jim scored is 2j - 10.
Let's assume that Jim scored 'j' points during the game. According to the given information, when Jim doubles his number of points and subtracts 10 from that number, the result is the same as the number of points Avery scored. Therefore, we can write an equation as follows:
2j - 10 = number of points scored by Avery
To find the expression representing the number of points Avery scored in terms of the number of points Jim scored, we simply solve the above equation for Avery's points:
number of points scored by Avery = 2j - 10
Therefore, the expression representing the number of points Avery scored in terms of the number of points Jim scored is 2j - 10.
In summary, Jim scored 'j' points during the game and when he doubles his number of points and subtracts 10 from that number, he gets the same result as the number of points Avery scored.
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a tugboat goes 200 miles upstream in 10 hours. the return trip downstream takes 4 hours. find the speed of the tugboat without a current and the speed of the current.
Answers
The speed of the tugboat without the current is 35 miles per hour, and the speed of the current is 15 miles per hour.
Let t be the speed of the tugboat without the current and c be the speed of the current.
Upstream, the tugboat moves against the current, so its speed is (t - c).
Downstream, the tugboat moves with the current, so its speed is (t + c).
The upstream distance is 200 miles in 10 hours, so the upstream speed is 200/10 = 20 miles per hour.
The downstream distance is also 200 miles, but it takes 4 hours, so the downstream speed is 200/4 = 50 miles per hour.
Now, we have two equations with two variables:
a. t - c = 20
b. t + c = 50
Solve these equations simultaneously:
a. Add the two equations to eliminate the variable c: 2t = 70
b. Divide both sides by 2 to get t: t = 35 miles per hour
c. Substitute the value of t back into one of the equations (e.g., t - c = 20): 35 - c = 20
d. Solve for c: c = 15 miles per hour
Hence, The speed of the tugboat without the current is 35 miles per hour, and the speed of the current is 15 miles per hour.
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3. AKLO is similar to ANMO.
a. Which side corresponds to side KO?
AC IS
b. Write a proportion that you could use to find MN.
c. What is MN?
3cm
units.
M
3 cm
K-
2.5 cm
O
L
7.5 cm
Answers
b. To find MN, we can use the fact that the sides of similar triangles are proportional. In particular, we can use the proportion:
MN/2.5cm = 3cm/7.5cm
This proportion compares the length of MN to the length of KO (which is 2.5 cm in the smaller triangle and 7.5 cm in the larger triangle). We can solve for MN by cross-multiplying and simplifying:
MN/2.5cm = 3cm/7.5cm
MN = (2.5cm)(3cm)/7.5cm
MN = 1cm
c. Therefore, MN is 1 cm.
through Buzz under the assignment.
1. lan deposits $2,400 each quarter for 3 years. The annuity earns 10% interest and is compounded quarterly. Find the present value of the annuity.
Using the Present Value of Ordinary Annuity Table, the correct factor for 12 compounding periods at 2.5% interest is 10.25776.
Answers
Answer:
$56,577.12
Step-by-step explanation:
To find the present value of the annuity, we can use the formula for the present value of an ordinary annuity, which is:
PV = PMT x [1 - (1 + r/n)^(-n*t)] / (r/n)
Where:
PV = present value
PMT = payment amount per compounding period
r = annual interest rate
n = number of compounding periods per year
t = total number of years
Plugging in the given values, we get:
PV = 2400 x [1 - (1 + 0.10/4)^(-4*3)] / (0.10/4)
PV = 2400 x [1 - (1.025)^(-12)] / (0.025)
PV = 2400 x [1 - 0.610355] / 0.025
PV = 2400 x 23.5742
PV = $56,577.12 (rounded to the nearest cent)
Therefore, the present value of the annuity is $56,577.12, assuming the interest is compounded quarterly and the annuity earns a 10% interest rate.
help pls don’t need to do work for it jist give answer
Answers
Answer:
A. 25%
B. Candidate B
C. 60% of voters chose Candidate A and Candidate C
Step-by-step explanation:
B. Candidate B
C. 60% of the voters
Urgently need the answer please help!!
Answers
Answer:
A = 81
Step-by-step explanation:
Using the formulas
A=a2
P=4a
Solving forA
A=1
16P2=1
16·362=81
Answer:
[tex]36 {r}^{4} {s}^{5}[/tex]
Perimeter of the square
one side has a length of 9r⁴s⁵
area is equal to 9r⁴s⁵ × 9r⁴s⁵
= 81r⁸s¹⁰
or 81r⁸s¹⁰cm²
can you guys please help me on this?
Answers
Answer: what do you need help with?
Step-by-step explanation:
Michael has a bag of smarties.He has 6 red smarties 4 blue smarties and 2 pink smarties.What is the probability he will pick 2 blue smarties two times
Answers
Answer:
Step-by-step explanation:
If he puts smarty back
because it's an "and" multiply by the 2 possibilities
4/12 *4/12
=1/3 *1/3
=1/9
If does not put smarty back
4/12 *3/11
=1/3*3/11
=3/33
which is the best estimate of 7.21x3.86/10.09
Answers
Answer:
7.21x3.86/10.09
7 x 4 / 10
28 / 10
2.8
Need help with this ASAP please
Answers
Answer: The answer is Q1: 2.3+34, Q2: 5.7+8.9.
Step-by-step explanation: Please give Brainlist.
Hope this helps!!!!
I can answer more questions if you like.
(Expert Answered)
which equations represent exponential growth? which equations represent exponential decay? drag the choices into the boxes to complete the table
Answers
The equations that represent exponential growth are [tex]A = 20,000(1.08)^t[/tex], [tex]A = 40(3)^t,[/tex] [tex]P = 1700(1.07)^t[/tex] and the equations that represent exponential decay are [tex]A = 80(1/2)^t, A = 1600(0.8)^t,[/tex] and [tex]P = 1700(0.93)^t.[/tex]
The mathematical function used to calculate the exponential growth or decay of a given set of data is an exponential function. we can calculate changes in population, loan interest charges, bacterial growth, radioactive decay, or the spread of disease by using the exponential functions.
An exponential function is of the form:
[tex]f(x) = a ^x[/tex]
The function represents an exponential decay If b < 1
The function represents an exponential growth If b > 1
From the given data about equations, we have;
Exponential Growth is;
The equation with the values b < 1 is:
[tex]A = 20,000(1.08)^t[/tex]
[tex]A = 40(3)^t[/tex]
[tex]P = 1700(1.07)^t[/tex]
Exponential Decay is;
The equation with the values b > 1 is:
[tex]A = 80(1/2)^t[/tex]
[tex]A = 1600(0.8)^t[/tex]
[tex]P = 1700(0.93)^t[/tex]
Therefore, The equations that represent exponential growth are[tex]A = 20,000(1.08)^t[/tex], [tex]A = 40(3)^t[/tex], and[tex]P = 1700(1.07)^t[/tex] the equations that represent exponential decay are [tex]A = 80(1/2)^t[/tex], [tex]A = 1600(0.8)^t\\[/tex], and [tex]P = 1700(0.93)^t.[/tex]
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The complete question is
Which equations represent exponential growth? which equations represent exponential decay? drag the choices into the boxes to complete the table
The value of a mountain bike y (in dollars) can be approximated by the model y=200(0.75)t, where t is the number of years since the bike was new. Would this table show growth or a decline (decay)? How do you know? Identify the annual percent increase or decrease in the value of the bike. Estimate when the value of the bike will be $50.
Answers
Answer:
Step-by-step explanation:
To determine if the table shows growth or decay, we can look at the coefficient of the exponential function y = 200(0.75)^t. The coefficient is 0.75, which is less than 1. This means that the value of the bike decreases over time, so the table shows decay.
To identify the annual percent increase or decrease in the value of the bike, we can compare the value of the bike after one year to its initial value. Plugging in t = 1 into the model, we get:
y = 200(0.75)^1
y = 150
So after one year, the value of the bike is $150. This represents a decrease of $50 from its initial value of $200. To find the percent decrease, we can use the formula:
percent decrease = (amount of decrease / initial value) x 100%
Plugging in the values, we get:
percent decrease = (50 / 200) x 100%
percent decrease = 25%
Therefore, the value of the bike decreases by 25% each year.
To estimate when the value of the bike will be $50, we can set y = 50 in the model and solve for t:
50 = 200(0.75)^t
0.25 = 0.75^t
log(0.25) = t log(0.75)
t = log(0.25) / log(0.75)
t ≈ 4.2
Therefore, the value of the bike will be $50 approximately 4.2 years after it was new.
8.1 do you use a smart watch or fitness tracker? a pew internet poll asked 4272 u.s. adults about their use of smart watches and fitness trackers. a summary of the results reported that 897 adults regularly wear a smart watch or fitness tracker.7 a. identify the sample size and the count. b. calculate the sample proportion. c. explain the relationship between the population proportion and the sample proportion.
Answers
a) The Sample size is calculated to be 4,272 U.S. adults and count is 897. (b) Sample proportion is 0.21 or 21%. (c)The sample proportion is an estimate of the population proportion.
The sample size is 4,272 U.S. adults, and the count of those who regularly wear a smart watch or fitness tracker is 897.
To calculate the sample proportion, we divide the count of those who regularly wear a smart watch or fitness tracker by the sample size:
sample proportion = count / sample size
sample proportion = 897 / 4,272
sample proportion = 0.21 or 21%
Therefore, the sample proportion of U.S. adults who regularly wear a smart watch or fitness tracker is 21%.
The population proportion is the proportion of all U.S. adults who regularly wear a smart watch or fitness tracker, while the sample proportion is the proportion of U.S. adults in the sample who regularly wear a smart watch or fitness tracker.
The relationship between the two proportions is that the sample proportion is an estimate of the population proportion. The sample proportion provides a rough idea of the proportion of all U.S. adults who regularly wear a smart watch or fitness tracker, but it may not be exactly the same as the population proportion due to sampling error.
To get a more accurate estimate of the population proportion, we would need to take a larger and more representative sample or survey the entire population.
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The debate over pipelines and the use of oil sands is far from over. There is likely to be another
application for a pipeline to bring oil from Alberta to Texas or a proposal to pipe oil across Canada
.
to ships that could take it to refineries in Asia. What do you think should be done? Explain your
answer using complete sentences.
Answers
The decision of whether or not to build pipelines to transport oil from Alberta to Texas or other parts of Canada is a complex one that involves multiple factors.
From a mathematical perspective, the debate over pipelines and oil sands can be analyzed in terms of supply and demand. On the other hand, opponents of pipelines argue that the supply of oil is finite and that the continued extraction and transportation of oil will have long-term negative consequences for the environment.
In addition to the economic and environmental factors, there are also geopolitical considerations to take into account. For example, some argue that building a pipeline to transport oil from Alberta to Texas would reduce Canada's reliance on foreign oil and would increase our energy independence.
However, others argue that building a pipeline would tie us more closely to the United States and would not necessarily benefit Canada in the long run.
Regardless of the decision that is ultimately made, it is clear that pipelines will continue to play a significant role in our energy infrastructure for many years to come.
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is 3 greater than 3 and a Half (3>< 3 1\2
Answers
Answer:
3 and a half would be greater than 3
Step-by-step explanation:
3 and a half would be 3.5 which is .5 more than just 3.
Solve the following equation and check your result (2n)/3 + 1 = (7n)/15 + 3
Answers
both sides are equal, we can conclude that n = 150/29 is the correct solution.
What is an Equations?
Equations consist of two algebraic expressions separated by an equal (=) sign, representing the equality between the expressions on the left and right sides. Solving equations helps to find the value of a variable that represents an unknown quantity. If there is no "equal to" symbol, a statement cannot be considered an equation and is instead considered an expression.
(2n)/3 + 1 = (7n)/15 + 3 // subtract 1 from both sides
(2n)/3 = (7n)/15 + 2 // multiply both sides by 15 to eliminate fractions
10n = 3(7n)/5 + 30 // multiply both sides by 3
10n = 21n/5 + 30 // subtract 21n/5 from both sides
50n/5 - 21n/5 = 30 // simplify fractions
29n/5 = 30 // multiply both sides by 5/29
n = 150/29
To check the solution, we substitute n = 150/29 back into the original equation and see if both sides are equal:
(2n)/3 + 1 = (7n)/15 + 3
(2(150/29))/3 + 1 = (7(150/29))/15 + 3
100/29 + 1 = 70/29 + 3
129/29 = 129/29
Since both sides are equal, we can conclude that n = 150/29 is the correct solution.
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The volume of a triangular pyramid is 756 units3 . If the base and height of the triangle that forms its base are 18 units and 12 units respectively, find the height of the pyramid.
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If the base and height of the triangle that forms its base are 18 units and 12 units respectively then the height of the pyramid is 21 units.
The formula for the volume of a triangular pyramid is:
V = (1/3) * base area * height
We are given that the volume of the pyramid is 756 units^3, the base of the pyramid is a triangle with base length 18 units and height 12 units, so its area is:
A = (1/2) * base * height = (1/2) * 18 * 12 = 108 units^2
Substituting the given values into the formula for the volume of a pyramid, we get:
756 = (1/3) * 108 * h
Multiplying both sides by 3 and dividing by 108, we get:
h = 756 / 36 = 21
Therefore, the height of the pyramid is 21 units.
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for the grand opening, al's furniture store offered a spin the wheel for a discount to its customers. customers would spin the wheel and receive a discount on a single item of purchase. the wheel is divided into 12 equal slices. 6 slices awarded a 10% discount, 3 slices awarded a 20% discount, 2 slices awarded a 40% discount, and 1 slice awarded a 100% discount. what is the probability that a customer gets a 10% or 20% discount?
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At the grand opening, al's furniture store, there is offering spin wheel for discount. The probability that a customer gets a 10% or 20% discount is equals to the 0.75.
At the grand opening, al's furniture store, it offered a spin the wheel for a discount to its customers. The wheel is divided into 12 equal slices.
The percentage of discount awarded by 6 slices = 10%
The percentage of discount awarded by 3 slices = 20%
The percentage of discount awarded by 2 slices = 40%
The percentage of discount awarded by 1 slices
= 100%
We have to determine the probability that a customer gets a 10% or 20% discount. As we see all slices are independent to each other so events related to these also independent.
We have total 12 slices. Since, 6 slices awarded for 10% discount i.e. chances of getting 10% discount is equal = 6/12
Similarly, 3 slices awarded for 20% discount i.e. chances of getting 20% discount is 3/12.
Hence chances of getting 10% or 20% discount is
= P( X = 20%) + P( X= 10%)
= 6/12 + 3/12
= 1/2 + 1/4
= 0.50 + 0.25
= 0.75
Hence, required value is 0.75.
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