Answer:
{HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}
Step-by-step explanation:
To find the sample space of flipping a quarter three times, we need to list all possible outcomes or combinations of heads (H) and tails (T) when flipping the quarter.
Since we are flipping the quarter three times, we can use a tree diagram to help visualize the different possible outcomes.
Starting with the first flip, we have two possible outcomes: H or T. Each of these outcomes will have two possible outcomes for the second flip (H or T), resulting in four possible outcomes so far: HH, HT, TH, TT.
For the third flip, each of the four outcomes from the second flip will have two possible outcomes (H or T), resulting in a total of eight possible outcomes for the third flip.
Combining all of the outcomes from each flip, we get the following sample space:
{HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}
This is the complete list of all possible outcomes when flipping a quarter three times.
a professor has two lightbulbs in her garage. when both are burned out, they are replaced, and the next day starts with two working lightbulbs. suppose when both are working, one of the two will go out with probability 0.03, and we cannot lose both lightbulbs on the same day. however, when only on lightbulb works, it will burn out with probability 0.07. what is the long-run fraction of time that there is exactly one lightbulb working?
The long-run fraction of time that there is exactly one lightbulb working (event O) is: 0.228.
Let's use the following notation:
Let W denote the event that both lightbulbs are working,
let O denote the event that one lightbulb is working, and
let B denote the event that both lightbulbs are burnt out.
We are given that when both lightbulbs are working (event W), one of them will go out with probability 0.03.
Therefore, the probability that both lightbulbs will still be working on the next day is 1 - 0.03 = 0.97.
On the other hand, when only one lightbulb is working (event O), it will burn out with probability 0.07, and the other lightbulb is already burnt out.
Hence, the probability of moving from O to B is 1.
We can set up the following system of equations to model the probabilities of being in each state on the next day:
P(W) = 0.97P(W) + 0.5P(O)
P(O) = 0.03P(W) + 0.93P(O) + 1P(B)
P(B) = 0.07P(O)
Note that in the first equation, we use 0.97 because the probability of staying in W is 0.97, and the probability of moving to O is 0.5 (because there are two ways for one of the lightbulbs to go out).
Simplifying the system of equations, we get:
0.03P(W) - 0.5P(O) = 0
-0.03P(W) + 0.07P(O) - 1P(B) = 0
0P(W) - 0.07P(O) + 1P(B) = 0
Solving for P(O), we get:
P(O) = 0.3P(W)
Substituting this into the second equation, we get:
-0.03P(W) + 0.07(0.3P(W)) - P(B) = 0
Simplifying, we get:
P(B) = 0.004P(W)
We also know that the sum of the probabilities of being in each state must be 1:
P(W) + P(O) + P(B) = 1
Substituting the expressions for P(O) and P(B), we get:
P(W) + 0.3P(W) + 0.004P(W) = 1
Solving for P(W), we get:
P(W) = 0.762
Therefore, the long-run fraction of time that there is exactly one lightbulb working (event O) is:
P(O) = 0.3P(W) = 0.228.
Approximately 22.8% of the time, there will be exactly one lightbulb working.
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find the surface area of a sphere with a radius of 4m.
________________________________________
solve for the surface are of a cylinder with a height of 8cm and a radius of 3cm.
_______________________________________
Answer: 207.338[tex]cm^2[/tex] or 66[tex]\pi[/tex]
Step-by-step explanation:
Lateral Area of a cylinder : 2[tex]\pi[/tex](radius)(height)
Surface Area of a cylinder : Lateral Area + 2 (base area)
LA= 48[tex]\pi[/tex]
= 150.79
SA= 150.79 + (2([tex]\pi[/tex]([tex]3^2[/tex])
= 207.338 [tex]cm^2[/tex]
: )))
if the pile contains only 25 quarters but at least 50 of each other kind of coin, how many collections of 50 coins can be chosen? collections
The number of collections of 50 coins that can be chosen from this pile is: C(125, 25) = 177,100,565,136,000
This is a very large number, which shows that there are many possible collections of 50 coins that can be chosen from the pile.
If the pile contains only 25 quarters but at least 50 of each other kind of coin, then the total number of coins in the pile must be at least 50 + 50 + 50 = 150. Let's assume that there are 150 coins in the pile, including the 25 quarters.
To choose a collection of 50 coins from this pile, we need to exclude the 25 quarters and choose 25 coins from the remaining 125 coins. We can do this in C(125, 25) ways, which is the number of combinations of 25 items chosen from a set of 125 items.
Therefore, the number of collections of 50 coins that can be chosen from this pile is:
C(125, 25) = 177,100,565,136,000
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There are 351 possible collections of 50 coins that can be chosen, considering the given conditions.
To find the number of collections of 50 coins that can be chosen, we will consider the given conditions:
The pile contains only 25 quarters.
There are at least 50 of each other kind of coin (pennies, nickels, and dimes).
Now, let's break this down step by step:
Determine the minimum number of coins from each kind required to make a collection of 50 coins.
- 25 quarters (as it's the maximum available)
- The remaining 25 coins must be a combination of pennies, nickels, and dimes.
Find the different combinations of pennies, nickels, and dimes that can be chosen to make a collection of 50 coins.
- We need 25 more coins, so we can divide them into three groups:
a) Pennies (P)
b) Nickels (N)
c) Dimes (D)
Calculate the combinations for the remaining 25 coins.
- Using the formula for combinations with repetitions: C(n+r-1, r) = C(n-1, r-1)
Where n is the number of types of coins (3) and r is the number of remaining coins (25)
- C(3+25-1, 25) = C(27, 25) = 27! / (25! * 2!) = 351.
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1. In adult smokers, a recent survey of randomly selected smokers indicated that 34% had tried to quit. If the survey had a 4% margin of error, how many people were surveyed?
If the survey had a 4% margin of error, 602 people were surveyed for a recent survey of randomly selected smokers indicating that 34% had tried to quit.
To solve this problem, we can use the margin of error formula:
Margin of error = z × √(p × (1-p) / n)
where z is the z-score corresponding to the desired level of confidence (let's assume 95% confidence, so z = 1.96), p is the proportion of smokers who tried to quit (p = 0.34), and n is the sample size.
We can rearrange the formula to solve for n:
n = (z / margin of error)² × p × (1-p)
Plugging in the values, we get:
n = (1.96 / 0.04)² × 0.34 × (1 - 0.34) = 601.96
Rounding up to the nearest whole number, the sample size is 602. Therefore, the survey included 602 adult smokers.
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What exactly do you do? I think it’s F honestly, just wanted to know you guys opinions
Hence correct option or expression are D and F.
What is the algebraic expression?its branches of mathematics. The arithmetic deals with numbers and mathematical procedures. Math think how to add, subtract, multiply, and divide two or more numbers. Shapes are the main focus in geometry, which involves creating them with various instruments including a compass, ruler, and pencil. Another fascinating area of study is algebra, where we use numbers and variables to represent the circumstances we encounter every day.
What is the exponential function?A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth, and so forth. You will discover the formulas, guidelines, characteristics, graphs, derivatives, exponential series, and examples of exponential functions in this article.
use,
[tex]\frac{a^{m} }{a^{n} } =a^{m-n}[/tex]
so,
[tex]\frac{b^{-2} }{b^{-6} } =b^{-2+6}\\=b^{4} or \frac{1}{b^{-4} }[/tex]
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0.2v = 1.2; v=10 is it a solution or not a solution?
Answer: To check if v=10 is a solution to the equation 0.2v = 1.2, we can substitute v=10 into the equation and see if the equation holds true:
0.2v = 1.2
0.2(10) = 1.2
2 = 1.2
This is not true, since 2 is not equal to 1.2. Therefore, v=10 is not a solution to the equation 0.2v = 1.2.
Step-by-step explanation:
Answer:
solution
Step-by-step explanation:
when a researcher uses the pearson product moment correlation, two highly correlated variables will appear on a scatter diagram as what?
When a researcher uses the Pearson product-moment correlation, two highly correlated variables will appear on a scatter diagram as a tightly clustered group of points that form a linear pattern.
The scatter diagram is a visual representation of the correlation between two variables, where one variable is plotted on the x-axis, and the other variable is plotted on the y-axis. If the two variables have a high positive correlation, then the points on the scatter diagram will form a cluster that slopes upwards to the right.
On the other hand, if the two variables have a high negative correlation, then the points will form a cluster that slopes downwards to the right. The tighter the cluster of points, the higher the correlation between the variables.
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Becca is construction triangle d e f using the following angles 50°, 65°, 65°,
what mistake did she make?
Becca made a mistake while constructing triangle DEF by using the angles 50°, 65°, and 65°. The mistake she made was violating the triangle inequality theorem.
According to the theorem, the sum of any two sides of a triangle must be greater than the third side. In other words, if we add the lengths of two sides of a triangle, it must be greater than the length of the third side.
Since Becca only used angles to construct the triangle, she did not consider the side lengths of the triangle. Therefore, there is a possibility that the triangle she constructed does not satisfy the triangle inequality theorem, and it may not be a valid triangle.
In order to ensure the triangle is valid, Becca needs to consider the side lengths while constructing the triangle. She could use trigonometric ratios or a ruler and protractor to measure the side lengths and angles accurately.
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7(x + 2) = 7x + 14 i dont get this someone pls help
Answer:
7
(
x
−
2
)
−
7
x
−
14
=
0
7
(
x
−
2
)
−
7
x
−
14
=
07
(
x
−
2
)
−
7
x
−
14
=
0
Step-by-step explanation:
Answer: 0 = 0
Step-by-step explanation: i showed the steps with these screen shots
The base of a square pyramid has a side length of 15 feet. The height of the square pyramid is 3.5 feet. What is the volume of the square pyramid in cubic feet? 15
Answer:52.5
Step-by-step explanation:
Multiply
The ratio of the books in the sample above is representative of the books in a bookcase in the library. If there are 35 yellow books in the bookcase, then how many green books are in the bookcase?
There are 15 green books in the bookcase.
How many green books are in the bookcase?The ratio of yellow books to green books in the sample is 7:3. This means that for every 7 yellow books, there are 3 green books.
If there are 35 yellow books in the bookcase, we can use the ratio to find the number of green books:
7 yellow books : 3 green books
35 yellow books : x green books (where x is the number of green books)
To solve for x, we can use cross-multiplication:
7 yellow books * x green books = 35 yellow books * 3 green books
7x = 105
x = 15
Therefore, there are 15 green books in the bookcase.
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1) Choose all of the common denominators of 2/3 and 7/9.
2) Choose all of the common denominators of 1/9 and 1/2
Please help me in both if you can. If not then only 1 answer is fine :). Thank you.
1) The common denominators of 2/3 and 7/9 are: 9, 18, 27, 36, 45, 54, 63, ...
2) The common denominators of 1/9 and 1/2 are: 18, 36, 54, 72, 90, 108, ...
To find the common denominators of 2/3 and 7/9, we need to find the least common multiple (LCM) of the denominators 3 and 9.
Prime factorization of 3: 3 = 3^1
Prime factorization of 9: 9 = 3^2
To find the LCM, we take the highest power of each prime factor that appears in either factorization. So, LCM(3, 9) = 3^2 = 9.
Therefore, the common denominators of 2/3 and 7/9 are all multiples of 9.
2) To find the common denominators of 1/9 and 1/2, we need to find the LCM of the denominators 9 and 2.
Prime factorization of 9: 9 = 3^2
Prime factorization of 2: 2 = 2^1
To find the LCM, we take the highest power of each prime factor that appears in either factorization. So, LCM(9, 2) = 2 x 3^2 = 18.
Therefore, the common denominators of 1/9 and 1/2 are all multiples of 18.
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What is the answer to this question? (Please i need help)
A statement that is best supported by the data in the box plots include the following: H. the interquartile range of the data for the community college is greater than the interquartile range of the data for the university.
What is a box-and-whisker plot?In Mathematics and Statistics, a box plot is a type of chart that can be used to graphically represent the five-number summary of a data set with respect to locality, skewness, and spread.
How to calculate the interquartile range (IQR)?Mathematically, interquartile range (IQR) of a data set is typically calculated as the difference between the first quartile (Q₁) and third quartile (Q₃):
Interquartile range (IQR) of university = Q₃ - Q₁
Interquartile range (IQR) of university = 15 - 9
Interquartile range (IQR) of university = 6.
For the community college, we have;
Interquartile range (IQR) = 15 - 6
Interquartile range (IQR) = 9.
Therefore, 9 is greater than 6.
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express 135km/h in m/s
To convert km/h (kilometers per hour) to m/s (meters per second), we need to divide the speed by 3.6.
Therefore, 135 km/h = (135/3.6) m/s ≈ 37.5 m/s
So, 135 km/h is approximately equal to 37.5 m/s.
state the nameof this quadrilateral...70 points
Answer:
Step-by-step explanation:
its a rectanlge
a company pays its employees an average of $5.25 per hour with a standard deviation of 60 cents. if the wages are approximately normally distributed: (a.) what percentage of the workers receive wages between $4.75 and $5.69 per hour? (b.) the highest 5% of the hourly wages are greater than what amount?
Using the standard normal distribution, we find that approximately 73.8% of workers receive wages between $4.75 and $5.69 per hour. Using the inverse of the standard normal distribution, we find that the highest 5% of hourly wages are greater than approximately $6.09.
Using a standard normal distribution table or calculator with a mean of 5.25 and a standard deviation of 0.60, we can find that approximately 79.42% of workers receive wages between $4.75 and $5.69 per hour.
Using a standard normal distribution table or calculator, we can find the z-score corresponding to the highest 5% of wages, which is approximately 1.645.
Then, we can solve for x in the equation z = (x - μ) / σ, where z is the z-score, μ is the mean of 5.25, and σ is the standard deviation of 0.60. This gives us x = zσ + μ, which is approximately $6.09 per hour. Therefore, the highest 5% of hourly wages are greater than $6.09 per hour.
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What is the approximate mean and standard deviation of the normal distribution below?
In a normal distribution with a mean of 75 and a standard deviation of 5, the approximate value of the median is 75 and approximately 68% of the scores fall between 70 and 75 while 95.45% of the scores lie between two standard deviations below and two standard deviations above the mean.
What is standard deviations?Standard deviation is a measure of how much variation exists in a set of data. It is used to measure the spread of the data, or how far the data is dispersed from the average. A low standard deviation indicates that data points are close to the average, while a high standard deviation means that the data points are spread out over a wide range of values. Standard deviation is calculated by taking the square root of the variance of the data.
1) The approximate value of the median in a normal distribution with a mean of 75 and a standard deviation of 5 is 75.
2) Approximately 68% of the scores fall between 70 and 75. This can be calculated by using the cumulative probability function for a normal distribution, which is given by: P(x) = 1/2[1 + erf( (x - μ) / (σ*sqrt(2)) ] where μ is the mean, σ is the standard deviation, and erf is the error function. In this case, the cumulative probability of 70 is 0.5 and the cumulative probability of 75 is 0.8413, so the difference of 0.3413 gives the approximate percentage of scores between 70 and 75.
3) Approximately 95.45% of the scores would lie between two standard deviations below and two standard deviations above the mean. This can be calculated by using the cumulative probability function for a normal distribution, which is given by: P(x) = 1/2[1 + erf( (x - μ) / (σ*sqrt(2)) ] where μ is the mean, σ is the standard deviation, and erf is the error function. In this case, the cumulative probability of two standard deviations below the mean is 0.02275 and the cumulative probability of two standard deviations above the mean is 0.97725, so the difference of 0.9545 gives the approximate percentage of scores between two standard deviations below and two standard deviations above the mean.
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Complete questions as follows-
Given a normal distribution with a mean of 75 and a standard deviation of 5, answer the following questions:
1) What is the approximate value of the median?
2) What percentage of scores fall between 70 and 75?
3) What percentage of the scores would lie between two standard deviations below and two standard deviations above the mean?
Using the graph, determine the coordinates of the y-intercept of the parabola.
Answer:
The y-intercept is at (0, 8).
Answer: (0,8)
Step-by-step explanation: The line only touches the Y-axis Once and its on 8
There is 6/8 of a cake
leftover after a birthday
party. How many 1/4
pieces can be made from
the leftover cake?
Answer: 3 pieces
Step-by-step explanation:First, 6/8 can be converted into fourths by dividing the numerator and the denominator by 2 and we get 3/4. if we want 1/4 slices we divide 3/4 by 1/4 and get 3.
The rate of consumption of oil in the United States during the 1980s (in billions of barrels per year) is modeled by the function C(t) = 27.08e', where t is the number of years after January 1, 1980. Find the total consumption of oil in the United States from January 1, 1980 to January 1, 1990.
the total consumption of oil in the United States from January 1, 1980, to January 1, 1990 is approximately 596,533.7 billion barrels.
To find the total consumption of oil in the United States from January 1, 1980 to January 1, 1990, we need to integrate the given function[tex]C(t) = 27.08e^t[/tex]with respect to time t, over the interval [0, 10], where t is measured in years.
The integral of the function is:
∫[tex](27.08e^t) dt[/tex]
To solve this integral, we use the fact that the integral of[tex]e^t[/tex] is [tex]e^t[/tex]itself. Thus, we get:
27.08∫[tex]e^t dt = 27.08e^t[/tex]
Now, we need to evaluate the definite integral over the interval [0, 10]:
[tex]27.08e^t[/tex]| from 0 to 10 =[tex]27.08(e^{10} - e^0)[/tex]
As e^0 = 1, the expression simplifies to:
[tex]27.08(e^{10} - 1)[/tex]
Now, we can calculate the value of the expression:
[tex]27.08(e^{10} - 1) =27.08(22026.47 - 1) = 27.08 * 22025.47 =596533.7[/tex]
Thus, the total consumption of oil in the United States from January 1, 1980, to January 1, 1990 is approximately 596,533.7 billion barrels.
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why would you use a trigonometric function to set-up an application problem instead of a non-trigonometric function
Trigonometric functions are used to model relationships between angles and sides of a right triangle. They are particularly useful in solving problems that involve angles, distances, heights, and lengths that are difficult to measure directly.
For example, consider a problem that involves finding the height of a building. By measuring the length of the shadow cast by the building at a particular time of day, the angle of the sun's rays can be calculated using trigonometry. Once the angle is known, the height of the building can be determined using the tangent function.
In contrast, a non-trigonometric function may not be able to model the relationship between the given quantities in such problems, and may not provide an accurate solution. Therefore, when a problem involves angles or distances that are not directly measurable, trigonometric functions are typically the best tool for setting up and solving the problem.
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URGENT
Emma doesn’t have experience using credit cards. In fact, she just got her first one. She is also about to start her first year of college. She uses her new credit card to purchase textbooks for her classes. The total comes to $300. These are the terms of her credit card:
It has a 15% annual interest rate.
The interest is compounded monthly.
The card has $0 minimum payments for the first four years it is active.
The expression that models this situation is P(1+r/n)^nt , where P represents the initial, or principal, balance; r represents the interest rate; t represents the time in years; and n represents the number of times the interest is compounded per year.
Part A
Question
Identify the values of P, r, and n in the expression P(1+r/n)^nt based on Emma’s situation. Then substitute those values into the formula to write a simplified exponential expression in terms of time.
Replace the variables a, b, and c to write the expression.
Part B
Question
Since the card has $0 minimum payments for the first 4 years it is active, Emma wonders how much it will cost her if she doesn't pay off the $300 balance until after college. How much will she owe in 4 years?
Type the correct response in the box. Use numerals instead of words. Round your answer to the nearest dollar.
In 4 years, Emma will owe about $
.
Part C
Question
Emma also wonders how long it will take her balance of $300 to reach $450, assuming she doesn’t make any payments toward it. Write the equation to represent the situation, and solve it using the inverse relationship between exponential and logarithmic expressions.
Type the correct response in the box. Use numerals instead of words. Round your answer to the nearest tenth.
It will take about
years for Emma’s balance to reach $450.
Part D
Question
Emma notices that since her credit card balance compounds monthly, she is charged more than 15% of her initial loan amount in interest each year. She wants to know how much she would pay if the card were compounded annually at a rate of 15%. What expression could Emma use to evaluate her balance with an annual compounding interest rate?
Part E
Question
How would the situation change if the interest on Emma’s credit card were compounded annually rather than monthly, and she didn’t make any payments toward the balance?
Select the correct answer from each drop-down menu.
After 4 years, Emma would owe approximately $
for her original purchase of $300.
It would take around
years for her balance to increase from $300 to $450
Emma has a credit card with 15% annual interest compounded monthly. The exponential expression is 300(1+0.15/12)^(12*t). She owes $509 in 4 years. It's about $464. Time it will take for her balance to reach $450, which is about 5.6 years. The expression to evaluate her balance with an annual compounding interest rate is 300(1+0.15)^t = 300(1.15)^t. If the card were compounded annually, she would owe about $459 in 4 years and it would take about 6.5 years for her balance to reach $450.
P = $300 (initial balance)
r = 0.15 (annual interest rate)
n = 12 (monthly compounding)
The simplified exponential expression is
300(1+0.15/12)^(12*t)
Using the formula from Part A with t = 4
300(1+0.15/12)^(12*4) ≈ $509
Emma will owe approximately $509 in 4 years if she doesn't make any payments toward the balance.
The equation for the situation is
300(1+0.15/12)^(12*t) = 450
Taking the logarithm of both sides and solving for t:
t = log(450/300) / (12*log(1+0.15/12)) ≈ 5.6 years
It will take about 5.6 years for Emma's balance to reach $450 assuming she doesn't make any payments toward it.
The expression Emma could use to evaluate her balance with an annual compounding interest rate is
300(1+0.15)^t = 300(1.15)^t
After 4 years, Emma would owe approximately $459 for her original purchase of $300.
It would take around 6.5 years for her balance to increase from $300 to $450.
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Solve the given right triangle for its missing angle and side measures.
Note: Figure not drawn to scale
A.
m∠D = 55°, DE ≈ 4. 40 units, DF ≈ 13. 65 units
B.
m∠D = 55°, DE ≈ 8. 40 units, DF ≈ 14. 65 units
C.
m∠D = 35°, DE ≈ 8. 40 units, DF ≈ 13. 65 units
D.
m∠D = 35°, DE ≈ 8. 40 units, DF ≈ 14. 65 units
The missing angle D is 55 degrees, and the lengths of DE and DF are approximately 8.40 units and 14.65 units, respectively. Therefore, the correct option is (B) m∠D = 55°, DE ≈ 8. 40 units, DF ≈ 14. 65 units
We can start by using the trigonometric ratios of the angles in a right triangle. In particular, we can use the tangent function to find the measure of angle D
tan(D) = DE / FE
tan(D) = DE / 12
We know that angle F is 35 degrees, so angle D must be
D = 90 - F
D = 90 - 35
D = 55 degrees
Now that we know the measure of angle D, we can use the sine and cosine functions to find the lengths of DE and DF, respectively. We know that
sin(F) = DE / DF
cos(F) = FE / DF
Substituting the given values
sin(35) = DE / DF
cos(35) = 12 / DF
Solving for DE and DF
DE = DF × sin(35)
DE = DF × 0.574
DE ≈ 0.574 × DF
DF = 12 / cos(35)
DF ≈ 14.65 units
DE ≈ 0.574 × 14.65
Multiply the numbers
DE ≈ 8.40 units
Therefore, the correct option is (B) m∠D = 55°, DE ≈ 8. 40 units, DF ≈ 14. 65 units
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The given question is incomplete, the complete question is:
Solve the given right triangle for its missing angle and side measures
A. m∠D = 55°, DE ≈ 4. 40 units, DF ≈ 13. 65 units
B. m∠D = 55°, DE ≈ 8. 40 units, DF ≈ 14. 65 units
C. m∠D = 35°, DE ≈ 8. 40 units, DF ≈ 13. 65 units
D. m∠D = 35°, DE ≈ 8. 40 units, DF ≈ 14. 65 units
if i randomly sample two cities from this group (consider these 45 the 'population' if you will) then what is the probability that at least one of the cities i select will have a commute time greater than 30 minutes?
The probability of at least 10 cities out 45 have a commute time greater than 30 minutes is 0.893 or 89.3%
Apply the complement rule.
Probability that at least one of the 10 cities you select will have a commute time greater than 30 minutes,
The complement of the event is 'none of the 10 cities have a commute time greater than 30 minutes'.
The probability of the complement event can be calculated by ,
Multiplying probabilities of selecting a city with a commute time less than or equal to 30 minutes for each of 10 selections.
P(none of 10 cities have a commute time > 30 minutes) = (35/45) x (35/45) x ... x (35/45) (10 times)
Because there are 35 cities out of the total 45 that have a commute time less than or equal to 30 minutes.
So the probability that at least one of the 10 cities has a commute time greater than 30 minutes is,
1 - P(none of the 10 cities have a commute time greater than 30 minutes)
= 1 - (35/45) x (35/45) x ... x (35/45) (10 times)
= 1 - 0.1073
= 0.8926
Therefore, the probability that at least one of the 10 cities you select will have a commute time greater than 30 minutes is 0.893 or 89.3%.
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The above question is incomplete, the complete question is:
If i randomly sample two cities from this group (consider these 45 the 'population' if you will) then what is the probability that at least one of the 10 cities i select will have a commute time greater than 30 minutes?
Given the quadratic equation x^(2)+4x+c=0, what must the value of c be in order for the equation to have solutions at x=-3 and x=-1 ?
Answer:
Step-by-step explanation:
If the solutions are x = -3 and x = -1, then (x - 3) (x - 1) will give us our answer. Using the FOIL method,
(x - 3) (x - 1)
x^2 - x - 3x + 3
x^3 - 4x + 3 = 0
Your answer is 3
Leila and Kai watch a movie that is 3.
hours long. Leila says the movie is less
than 10,000 seconds. Kai says the movie is
more than 10,000 seconds. Which friend is
correct? Explain.
Answer:
Kai is correct and Leila is incorrect. The movie is actually 10,800 seconds long.
Step-by-step explanation:
1 hour = 60 minutes
1 minute = 60 seconds
Therefore, 1 hour = 60 x 60 = 3600 seconds
So, the movie's length in seconds is:
3 hours x 3600 seconds/hour = 10,800 seconds
Leila says the movie is less than 10,000 seconds, which is not correct, since the movie is actually longer than 10,000 seconds.
Kai says the movie is more than 10,000 seconds, which is correct.
suppose you enter a raffle. there are a total of 100 entries. the winner of the raffle will win $500 if they can also guess the favorite season of the raffle organizer. there is a 0.01 chance of winning the raffle, and a 0.25 chance of guessing the organizer's favorite season. what is the chance that you will both win the raffle and win $500?
The chance that you will both win the raffle and win $500 is 0.0025, or 0.25%.
To find the chance of both winning the raffle and correctly guessing the organizer's favorite season, you need to multiply the probabilities of these two independent events.
Step 1: Determine the probability of winning the raffle.
The probability of winning the raffle is given as 0.01.
Step 2: Determine the probability of correctly guessing the favorite season.
The probability of correctly guessing the favorite season is given as 0.25.
Step 3: Multiply the probabilities of the two independent events.
To find the probability of both events happening, you multiply their probabilities: 0.01 (winning the raffle) * 0.25 (correctly guessing the favorite season).
0.01 * 0.25 = 0.0025
So, the chance that you will both win the raffle and win $500 is 0.0025, or 0.25%.
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The probability of both winning the raffle and correctly guessing the organizer's favorite season to win the $500 prize is 0.0025 or 0.25%.
To find the probability of both winning the raffle and guessing the organizer's favorite season correctly, you'll need to multiply the individual probabilities of each event.
Probability of winning the raffle: 0.01 (given in the question)
Probability of guessing the organizer's favorite season: 0.25 (given in the question)
Now, multiply these probabilities together:
0.01 * 0.25 = 0.0025.
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ANSWER ASAP AND PLEASE BE CORRECT FOR BRAINLIST
Question 12
A recent conference had 750 people in attendance. In one exhibit room of 70 people, there were 18 teachers and 52 principals. What prediction can you make about the number of principals in attendance at the conference?
There were about 193 principals in attendance.
There were about 260 principals in attendance.
There were about 557 principals in attendance.
There were about 680 principals in attendance.
Question 13
A college cafeteria is looking for a new dessert to offer its 4,000 students. The table shows the preference of 225 students.
Ice Cream Candy Cake Pie Cookies
81 9 72 36 27
Which statement is the best prediction about the number of cookies the college will need?
The college will have about 480 students who prefer cookies.
The college will have about 640 students who prefer cookies.
The college will have about 1,280 students who prefer cookies.
The college will have about 1,440 students who prefer cookies.
Question 14
A random sample of 100 middle schoolers were asked about their favorite sport. The following data was collected from the students.
Sport Basketball Baseball Soccer Tennis
Number of Students 17 12 27 44
Which of the following graphs correctly displays the data?
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
Question 15
The line plots represent data collected on the travel times to school from two groups of 15 students.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 4, 6, 14, and 28. There are two dots above 10, 12, 18, and 22. There are three dots above 16. The graph is titled Bus 47 Travel Times.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9, 18, 20, and 22. There are two dots above 6, 10, 12, 14, and 16. The graph is titled Bus 18 Travel Times.
Compare the data and use the correct measure of center to determine which bus typically has the faster travel time. Round your answer to the nearest whole number, if necessary, and explain your answer.
Bus 18, with a median of 13
Bus 47, with a median of 16
Bus 18, with a mean of 13
Bus 47, with a mean of 16
Below is the answer to the questions:
Q 12.
The prediction is that there were about 260 principals in attendance at the conference.
Q13.
The best prediction is that the college will have about 480 students who prefer cookies.
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What is the value or arc PQ? Only enter numerical values.
The length of arc PQ is 110 degrees
How to find arc PQKnowing that the arc lengths are in degrees and the total for a circle is 360 degrees then we have the equation
8x - 10 + 6x + 10x + 10 = 360
To solve the equation 8x - 10 + 6x + 10x + 10 = 360 for x, we first need to simplify the left side of the equation by combining like terms:
8x + 6x + 10x - 10 + 10 = 24x
Now the equation becomes:
24x = 360
To solve for x, we need to isolate x on one side of the equation by dividing both sides by 24:
24x/24 = 360/24
x = 15
Therefore, the solution for x is 15.
Arc PQ = 8x - 10
= 8 * 15 - 10
= 110 degrees
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Find the exact value of sin a, given that cos a=-5/9 and a is in quadrant 3
Since cosine is negative and a is in quadrant III, we know that sine is positive. We can use the Pythagorean identity to solve for sine:
sin^2(a) + cos^2(a) = 1
sin^2(a) + (-5/9)^2 = 1
sin^2(a) = 1 - (-5/9)^2
sin^2(a) = 1 - 25/81
sin^2(a) = 56/81
Taking the square root of both sides:
sin(a) = ±sqrt(56/81)
Since a is in quadrant III, sin(a) is positive. Therefore:
sin(a) = sqrt(56/81) = (2/3)sqrt(14)