Answer:
1) 5.9
2) 8.1
3) 54
Step-by-step explanation:
A is opposite, so we have sine 36=a/10
sine 36(10)=a
a=5.9
B is adjacent, so we have cosine 36=b/10
cosine 36(20)=b
b=8.1
Angles of a triangle add to 180
we have a angle of 36 and a right angle which is 90
36+90=126
180-126=54
Answer:
D. ("24.")
Step-by-step explanation:
it is D
In a box of chocolates, 1/5 of the chocolates contain nuts.
The rest of the chocolates do not contain nuts.
Write down the ratio of the number of chocolates that contain nuts to number of chocolates that do not contain nuts.
Give your answer in the form of 1:n
Answer:
1:4
Step-by-step explanation:
Ratios and Fractions
It's given 1/5 of the chocolates in a box contain nuts. The rest do not contain nuts. The portion that does not contain nuts is:
\(1 - \frac{1}{5}=\frac{4}{5}\)
We need to calculate the ratio of the number of chocolates that contain nuts to the number of chocolates that do not contain nuts.
This can be done by dividing 1/5 by 4/5:
\(\displaystyle \frac{\frac{1}{5}}{\frac{4}{5}}\)
Operating:
\(\displaystyle \frac{1}{5}\cdot\frac{5}{4}=\frac{1}{4}\)
Expressing it as a ratio: 1:4
If angle 1 = (2x+5) and angle 7 = (4x-17), find x
The value of x is 11
What is supplementary angle ?
Two angles are said to be supplementary if their sums total 180 degrees. A linear pair's two angles, like angles 1 and 2 in the illustration below, are always supplementary. But two angles don't have to be close to one another to be supplementary. In the following image, 3 and 4 are supplementary since their sums equal 180 degrees.
Angles ∠1 and ∠7 are alternate exterior angles where a transversal crosses parallel lines, so are congruent.
∠ 1 = ∠ 7
∴2x + 5 = 4x - 17
4x - 2x =17+5
2x = 22
x = \(\frac{22}{2}\)
x = 11
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A kite is flying at a height of 20 m vertically above the ground. Just below it, a fish is underwater at a
depth of 5 m. Find the vertical distance between kite and the fish
Answer:t a particular point it is exactly above the fish moving in a pond 3m below the ground level. Find the vertical distance between these two points.? is done on EduRev Study Group by Class 7 Students. The Questions and Answers of A kite is flying at a height of 10m above the ground level. At a particular point it is exactly above the fish moving in a pond 3m below the ground level.
Step-by-step explanation:
in a stem-and-leaf display, . a. a single digit is used to define each stem, and one or more digits are used to define each leaf b. one or more digits are used to define each stem, and a single digit is used to define each leaf c. a single digit is used to define each stem, and a single digit is used to define each leaf d. one or more digits are used to define each stem, and one or more digits are used to define each leaf
in a stem-and-leaf display: b. one or more digits are used to define each stem, and a single digit is used to define each leaf
What is stem-and-leaf plot?A stem and leaf plot, often known as a stem plot, is a method for categorizing discrete or continuous data. Data are organized as they are gathered using a stem and leaf plot. A stem and leaf plot resembles a bar graph in appearance. As each integer throughout the database is divided into a stem and a leaf, thus the name fits.
The last digit of each data point serves as the "leaf" in a stem and leaf plot, which divides the data into numerical points (the leading digit or digits).
Thus, in this case, correct option is:b
in a stem-and-leaf display: b. one or more digits are used to define each stem, and a single digit is used to define each leaf
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what is understand function
There are differnet definition from what a function is.
The most precisely definition of a function is that a function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
For example:
Let define the following function: y= 3x + 2
The graph for the function y=3x + 2 would be as follow:
As you can clearly see above, for example the number 1 in X would correspond to the number 5 in y.
during the last six years of his life, vincent van gogh produced 700 drawings and 800 oil paintings. write the ratio of drawings to oil paintings in three different ways. (select all that apply.)
The ratio of Vincent van Gogh's drawings to oil paintings during the last six years of his life can be represented in three different ways:
1. As a fraction: 700/800
2. As a simplified fraction: 7/8
3. As a ratio with a colon: 7:8
To express the ratio of Vincent van Gogh's drawings to oil paintings during the last six years of his life, we can use the given numbers: 700 drawings and 800 oil paintings.
1. As a fraction: To represent the ratio as a fraction, we simply place the number of drawings over the number of oil paintings:
700 drawings / 800 oil paintings
2. As a simplified fraction: To simplify the fraction, we can find the greatest common divisor (GCD) of the two numbers. In this case, the GCD of 700 and 800 is 100. We can then divide both the numerator (drawings) and the denominator (oil paintings) by 100:
=(700/100) / (800/100)
=7/8
The simplified fraction representing the ratio of drawings to oil paintings is 7/8.
3. As a ratio with a colon: To represent the ratio using a colon, we can simply use the numbers from the simplified fraction:
=7:8
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Determine whether each of these statements is true or false.a) 0 ∈ ∅ b) ∅∈{0}c) {0}⊂∅ d) ∅⊂{0}e) {0}∈{0} f ) {0}⊂{0}g) {∅} ⊆ {∅}
a) True, b) False, c) False, d) True, e) False, f) False, g) True
a) The statement is true. The symbol "∅" represents the empty set, which does not contain any elements. Since 0 is not an element of the empty set, the statement "0 ∈ ∅" is false.
b) The statement is false. The symbol "{0}" represents a set containing the element 0. The empty set, represented by "∅", does not contain any elements. Therefore, the empty set is not an element of the set {0}.
c) The statement is false. The symbol "{0}" represents a set containing the element 0. However, the empty set, represented by "∅", does not contain any elements. Therefore, the set {0} is not a subset of the empty set.
d) The statement is true. The empty set, represented by "∅", does not contain any elements. Every set is a subset of the empty set, including the set {0}.
e) The statement is false. The symbol "{0}" represents a set containing the element 0. In this case, {0} is not an element of itself. Therefore, the statement "{0}∈{0}" is false.
f) The statement is false. The symbol "{0}" represents a set containing the element 0. In this case, {0} is not a proper subset of itself. Therefore, the statement "{0}⊂{0}" is false.
g) The statement is true. The symbol "{∅}" represents a set containing the empty set. In this case, {∅} is a subset of itself because it contains the element ∅. Therefore, the statement "{∅} ⊆ {∅}" is true.
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the tree diagram below shows the probabilities for the simple events combining weather patterns and seasons of the year
The tree diagram illustrates the probabilities associated with different combinations of weather patterns and seasons of the year. The tree diagram is a visual representation that presents the probabilities of various outcomes resulting from the combination of weather patterns and seasons of the year.
It is a useful tool for understanding the likelihood of specific events occurring based on different factors.
The diagram is structured hierarchically, with the weather patterns forming the first level and the seasons of the year forming the second level. Each branch represents a specific combination, and the probability associated with that combination is indicated on the branch.
By analyzing the diagram, one can observe how the probabilities change depending on the weather patterns and seasons. For instance, certain weather patterns may be more prevalent during specific seasons, resulting in higher probabilities for certain combinations.
Overall, the tree diagram serves as a visual aid to comprehend the probabilities associated with simple events combining weather patterns and seasons of the year, enabling a better understanding of the likelihood of different outcomes based on these factors.
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Ash can dig 5 holes in 2 hours, and Bruce can dig 9 holes in 5 hours. How many holes can they dig in 15 hours if they work together?
If Ash can dig 5 holes in 2 hours, and Bruce can dig 9 holes in 5 hours. The number of holes they can dig is: 64.5 holes .
How to find the number of holes?Ash rate:
5 holes / 2 hours
= 2.5 holes per hour
Bruce rate
9 holes / 5 hours
= 1.8 holes per hour
Number of holes they can dig together in one hour
2.5 holes per hour + 1.8 holes per hour
= 4.3 holes per hour
Now let find the number of holes they can dig in 15 hours,
4.3 holes per hour x 15 hours
= 64.5 holes
Therefore, Ash and Bruce can dig 64.5 holes.
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In Figure 1.2, what is the measure of x? image done below
Answer:
73°, C
Step-by-step explanation:
This is due to the x being vertically opposite the 73° angle,
-1 -3x + 10x -6 -1 please help me
Answer:
-8+7x
Step-by-step explanation:
-1-6-1=-8
-3x+10x=7x
A television screen has a length of 33 ft and a width of 45 ft. A second television is similar to the first television. The second television is 51 ft. wide. What is the length of the second television? (Decimal Answer)
Length of the second television = ____ft
Answer:1683
Step-by-step explanation:33 ft x 51 ft = 1683
4. Emily ate dinner at Geisha. Her total was $17.50. A 8% sales tax was
added to her bill. After, Emily added a 20% tip on the total after tax. What
was Emily's final total?
*
Answer: $22.68
Step-by-step explanation:
17.50 times 0.08 = 1.40
17.50 + 1.40 = 18.90
Now the tip:
18.90 times .2 = 3.78
18.90 + 3.78 = 22.68
Chester rode his bike uphill 24 miles and then back downhill at 2 mph faster than his uphill. If it took him 2 hours longer to ride uphill than downhill, l, what was his uphill rate?
The uphill speed was x=4 miles per hour.
Let's say Chester's uphill speed is x miles per hour. Then his downhill speed would be x+2 miles per hour. According to the problem, he rode uphill for 24 miles and then rode back downhill, which would also be 24 miles. Let's now set up an equation based on the given information:
Upward journey: Time taken = Distance/Speed24/x
Downward journey: Time taken = Distance/Speed24/(x+2)
According to the problem, it took him 2 hours longer to ride uphill than downhill. Therefore, we can set up another equation:x+2 = (24/x)-2
We can simplify this equation and solve for
x:x+2 = 24/x - 2x² + 2x - 48
= 0x² - x - 24
= 0(x-4)(x+6)
= 0x = 4 or x = -6
Since the speed cannot be negative, we can discard the value x=-6. Hence, the uphill speed was x=4 miles per hour. Therefore, the answer is 4 miles per hour.
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the symbol μ ˆ p represents the proportion of a sample of size n, not the proportion of a sample of size n. true or false
The statement ''the symbol μ ˆ p represents the proportion of a sample of size n, not the proportion of a sample of size n.'' is false because the symbol "μ ˆ p" does not represent the proportion of a sample of size n.
In statistical notation, the symbol "μ ˆ p" typically represents the sample proportion, which is an estimate of the population proportion. The sample proportion is obtained by dividing the number of occurrences of a specific event in the sample by the sample size.
On the other hand, the population proportion, denoted by "p," represents the proportion of the entire population that exhibits a certain characteristic or has a specific attribute.
The symbol "μ ˆ p" could be a typographical error or a confusion between different symbols used in statistics. The correct symbol to represent the sample proportion is usually denoted as "p ˆ" or "p-hat." The symbol "μ" typically represents the population mean.
Therefore, it is incorrect to state that "μ ˆ p" represents the proportion of a sample of size n.
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is the bottled water you are drinking really purified water? a study of various brands of bottled water conducted by the natural resources defense council found that 25% of bottled water is just tap water packaged in a bottle (scientific american, july 2003).
Yes, there is a chance that the bottled water you are drinking is just tap water packaged in a bottle. According to a study by the Natural Resources Defense Council, 25% of bottled water is just tap water that has been packaged in a bottle. [Scientific American, July 2003]
What is bottled water?Bottled water is drinking water that has been packaged in bottles or containers for sale. Bottled water can come from a variety of sources, such as municipal supplies, springs, wells, and other sources. In some cases, bottled water is treated or purified to remove impurities and contaminants. However, not all bottled water is purified or treated, and some may be just tap water that has been packaged in a bottle.
What is purified water?Purified water is water that has been treated to remove impurities and contaminants. Purified water can come from any source, including municipal supplies, wells, and other sources. Purification methods may include filtration, reverse osmosis, distillation, or other methods. Purified water is commonly used in medical and industrial applications, as well as in homes for drinking and cooking.
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Please help me work out this
Answer:
226.5
Step-by-step explanation:
area=area of larger rectangle - area of smaller rectangle
Area= (16×17) - (6.5×7)
=226.5
which fraction is equivalent to 4/7?
Answer: 8/14
Step-by-step explanation:
Please help me im confused with this
Answer:
A
Step-by-step explanation:
Because it seems like that would be the right answer
And sorry if im wrong
Hi, please help with this circle geometry question (image attached)! It would be helpful if you show your working out/proof. You also need to use tangent properties of circles.
Thank you!
Given that ABC is a right-angled triangle and that AB, BC, and CA are tangents to the circle, the value of x is 2 cm.
what is triangle ?Since a triangle has three parts and three vertices, it is a polygon. It is a fundamental geometric shape. Triangle ABC is the moniker given to one triangle that has vertex shader A, B, and C. When the three principles are not collinear, a singular plane and triangle are found in Euclidean geometry. A triangle is a polygon if it has three sections and three corners. The points where the sides meet are known as the triangle's corners.
given
To find : radius 'r' of the incircle.
ABC is a right angled triangle
=100
⇒ BC= 100 =10cm
Since area of right anged triangle = 1/2×base×height
⇒ Area of △ABC= 1/2×6×8
=3×8=24cm 2
⇒ Area of △ABC=24cm 2 ....(1)
Also, Area of △ABC= area of △OAC+ area of △OBC+ area of △OBA
= 1/2 ×r×8+ 1/2 ×r×10+ 1/2 ×6×r= 1/2* r(8+10+6)= 1/2r(24)=12r....(2)
Equating (1) and (2) 12r=24
⇒ r= 12/24 =2cm
Given that ABC is a right-angled triangle and that AB, BC, and CA are tangents to the circle, the value of x is 2 cm.
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The complete question :- In fig. 4 triangle ABC is a right triangle with AB=6 cm, AC=8 cm and ∠A=90∘ . A circle with center O is inscribed inside the triangle. Find the radius 'r'
URGENT!
While playing a board game, Isaiah noticed that the die landed on the number 5 more often than usual.
Part A: Describe a simulation that could be run to test how many times out of 100 a fair die should land on the number 5. State the representations and possible outcomes. Be sure to give enough detail that another person could replicate your simulation. (7 points)
Part B: While running a simulation, the die landed on the number 5 a total of 29 times out of the 100 rolls. Construct and interpret a 95% confidence interval for the true proportion of rolls that will land on the number 5. Show all work. (7 points)
Part C: Does the confidence interval in part B support Isaiah's suspicions that the die is not fair? Explain your reasoning. (6 points)
Part A = The possible outcomes of each roll are the integers 1 to 6, with an equal chance of 1/6 for each number to appear.
Part B = Confidence Interval ≈ (0.201, 0.379)
Part C = The confidence interval does support Isaiah's suspicions that the die may not be fair, as it suggests a higher probability of landing on 5 compared to a fair die.
Explanation =
Part A: Simulation to Test Die Rolls :-
To simulate the rolling of a fair die, we can use a random number generator to mimic the outcomes.
Here's a step-by-step description of the simulation:
1) Representation: Let's represent each die roll as an integer from 1 to 6, with 1 representing a roll showing one dot, 2 for two dots, and so on, up to 6 for six dots.
2) Possible Outcomes: The possible outcomes of each roll are the integers 1 to 6, with an equal chance of 1/6 for each number to appear. For this simulation, we will specifically track how many times the die lands on the number 5.
3) Simulation Procedure:
a. Initialize a counter to zero, which will track the number of times the die lands on 5.
b. Repeat the following steps 100 times (representing 100 die rolls):
i. Generate a random number between 1 and 6, representing the result of the die roll.
ii. If the generated number is 5, increment the counter by 1.
4) Interpretation: After the simulation is completed, the value of the counter will represent the number of times the die landed on the number 5 out of the 100 rolls.
Part B: Constructing the 95% Confidence Interval :-
To construct the 95% confidence interval for the true proportion of rolls that will land on the number 5, we can use the formula for a confidence interval for proportions:
Confidence Interval = \(\pi \pm Z \times \sqrt{\frac{\pi(1-\pi)}{n}\)
Where,
π is the observed proportion of successes (rolling a 5) in the sample (total of 29/100).
Z is the critical value for a 95% confidence level (approximately 1.96 for a large sample size).
n is the sample size (100 rolls in this case).
Now, let's calculate the confidence interval:
π = \(\frac{29}{100}\)
π = 0.29
Z = 1.96
n = 100
Confidence interval = \(0.29 \pm 1.96 \times \sqrt{\frac{0.29(1-0.29)}{100}\)
= \(0.29 \pm 1.96 \times \sqrt{\frac{0.29 \times 0.71 }{100}\)
= \(0.29 \pm 1.96 \times \sqrt{\frac{0.2059}{100}\)
= \(0.29 \pm 1.96 \times 0.04537\)
Therefore,
Confidence Interval ≈ (0.201, 0.379)
Part C: Interpretation of the Confidence Interval :-
The 95% confidence interval for the true proportion of rolls landing on the number 5 is approximately (0.201, 0.379).
This means that based on the data from the simulation, we are 95% confident that the true proportion of rolls resulting in a 5 lies between 20.1% and 37.9%.
Isaiah's suspicion is that the die landed on the number 5 more often than usual. Since the lower bound of the confidence interval is 20.1%, which is above 0 (no rolls with a 5), it suggests that the true proportion of rolls resulting in a 5 could be higher than expected.
Therefore, the confidence interval does support Isaiah's suspicions that the die may not be fair, as it suggests a higher probability of landing on 5 compared to a fair die.
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Kendall puts 1,000.00 into an account to use for school expenses the account earns 9% interest compounded monthly how much will be in the account after 9 years
To calculate the total amount accrued when you deposit the money in an account that earns compound interest you have to use the following formula
\(A=P(1+\frac{r}{n})^{tn}\)A: amount accrued
P: principal amount
t: time, years
r: interest rate, expresed as a decimal value
n: number of coumpound periods
For this exericse
The principal amount is P=$1000
The time is t= 9 years
The interest rate is 9%/100=0.09
The compounding periods are 12/year (the interest is compounded monthly) so for the 9 year time period is 9*12=108
\(\begin{gathered} A=1000(1+\frac{0.09}{108})^{9\cdot108} \\ A=2247.15 \end{gathered}\)
the confidence interval for the mean amount of money spent per household on internet service
each month is $47.45 to $72.45. what is the estimated mean?
internet each
The estimated mean amount of money spent per household on internet service each month is $59.95 with confidence interval.
To calculate the estimated mean amount of money spent per household on internet service each month, we first need to find the lower and upper bounds of the confidence interval. The lower bound is $47.45 and the upper bound is $72.45. We then take the average of these two numbers to get the estimated mean. The average of $47.45 and $72.45 is
($47.45 + $72.45) / 2
= $59.95.
Therefore, the estimated mean amount of money spent per household on internet service each month is $59.95.
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through the years we all will be together if the fate allows
graham is hiking at an altitude of 14,040 feet and is descending 50 feet each minute. max is hiking at an altitude of 12,500 feet and is ascending 20 feet each minute. how many minutes will it take graham and max to meet at the same altitude? a. 18.5 minutes b. 36 minutes c. 51.3 minutes d. 22 minutes
Answer: D:22,
14,040-12,500=1540.
1540/70 = 22
What is the common ratio Between successive terms in the sequence? 1.5,1.2,0.96,0.768
Answer:
0.8
Step-by-step explanation:
0.768/0.96= 0.8
0.96/1.2 =0.8
a tank contains 1000 l of water and it flows out at the rate of 5 sec how much water is there in the tank after each second? write their numbers as sequence
Answer:
Step-by-step explanation:
10 becuae you have to subract it by 5 seonds everytime
use the laplace transform to solve the given system of differential equations. dx/dt + 7x + dy/dt = 1 dx/dt − x + dy/dt − y = eᵗ x(0) = 0, y(0) = 0
Therefore, the solution to the system of differential equations is:
x(t) = -e^(2t)/8 + (3/4) e^(-2t) + (1/2) e^(-t) - (1/8) e^(-4t)
y(t) = (1/8)e^(2t) - (1/4)e^(-2t) - (1/4)e^(-t) + (1/8)e^(-4t)
We can use Laplace transforms to solve this system of differential equations. Taking the Laplace transform of both sides of each equation, we get:
sX(s) + 7x(0) + sY(s) + y(0) - x(0) = 1/s (taking L.T. of first equation)
sX(s) - x(0) - sY(s) - y(0) + y(0) - x(0) = 1/(s-1) * 1/s * 1/(s-1)^2 (taking L.T. of second equation)
Using the initial conditions x(0)=y(0)=0 and simplifying, we get:
sX(s) + sY(s) = 1/s - 1/(s-1) * 1/s * 1/(s-1)^2
sX(s) - sY(s) = 1/(s-1) * 1/s * 1/(s-1)^2
Now, solving for X(s) and Y(s), we get:
X(s) = [(s-1)/(s-2)(s^2+6s+8)] * 1/s
Y(s) = [1/(s-2)(s^2+6s+8)] * 1/s
To find x(t) and y(t), we can take the inverse Laplace transform of X(s) and Y(s). However, the partial fraction decomposition of X(s) is somewhat complicated, so instead we can use a table of Laplace transforms to find the inverse Laplace transform of X(s). Specifically, we use the formula:
L⁻¹[F(s)/s] = ∫ f(t) dt
where F(s) = X(s) and f(t) is the inverse Laplace transform of X(s)/s.
Using partial fraction decomposition, we can write X(s) as:
X(s) = A/(s-2) + B/(s+2) + C/(s+1) + D/(s+4)
where A = -1/8, B = 3/8, C = 1/2, and D = -1/8. Therefore,
X(s)/s = (-1/8)/(s-2) + (3/8)/(s+2) + (1/2)/(s+1) - (1/8)/(s+4)
Taking the inverse Laplace transform of each term using the table of Laplace transforms, we get:
L⁻¹[(-1/8)/(s-2)] = -e^(2t)/8
L⁻¹[(3/8)/(s+2)] = (3/4) e^(-2t)
L⁻¹[(1/2)/(s+1)] = (1/2) e^(-t)
L⁻¹[(-1/8)/(s+4)] = -(1/8) e^(-4t)
Therefore, x(t) = -e^(2t)/8 + (3/4) e^(-2t) + (1/2) e^(-t) - (1/8) e^(-4t).
To find y(t), we can take the inverse Laplace transform of Y(s) using partial fraction decomposition or using the table of Laplace transforms directly. Either way, we get:
y(t) = (1/8)e^(2t) - (1/4)e^(-2t) - (1/4)e^(-t) + (1/8)e^(-4t)
Therefore, the solution to the system of differential equations is:
x(t) = -e^(2t)/8 + (3/4) e^(-2t) + (1/2) e^(-t) - (1/8) e^(-4t)
y(t) = (1/8)e^(2t) - (1/4)e^(-2t) - (1/4)e^(-t) + (1/8)e^(-4t)
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Which of the following is NOT a voluntary response sample? Choose the correct answer below O A. A survey is taken at a mall by asking passersby if they will fill out the survey O B. A radio station asks for call-in responses to a question concerning city recycling OC. A local dentist asks her patients to fill out a questionnaire and mail it back to determine the quality of the care received during an office visit OD. Quiz scores from a college level statistics course are analyzed to determine student progress State whether the data described below are discrete or continuous, and explain why. The number of donations a charity receives each month Choose the correct answer below. O A. The data are discrete because the data can only take on specific values. O B. The data are continuous because the data can take on any value in an interval. O C. The data are continuous because the data can only take on specific values. D. The data are discrete because the data can take on any value in an interval. O
The correct answer for the first question is D. The data are discrete because the data can take on any value in an interval.
Quiz scores from a college level statistics course are analyzed to determine student progress. This is not a voluntary response sample because the students taking the quiz are required to participate, and their scores are collected for the purpose of analyzing their progress.
For the second question, the data described, which is the number of donations a charity receives each month, is discrete. Discrete data can only take on specific values and cannot be divided into smaller, meaningful intervals. In this case, the number of donations can only be whole numbers, such as 0, 1, 2, and so on. It cannot take on any value in an interval or be represented by fractions or decimals. Therefore, the data is discrete.
It is important to distinguish between discrete and continuous data when analyzing and interpreting data, as different statistical methods and techniques are used for each type. Discrete data is usually counted or measured in whole numbers, while continuous data can take on any value within a given range or interval.
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a large group of people get together. each one rolls a die 120 times, and counts the number of aces (with a single dot). about what percentage of these people should get counts in the range 10 to 30? choose the closest answer. group of answer choices 68% 99% 28% 74%
Approximately 80.8% of the people should get counts in the range of 10 to 30 aces. The closest answer choice is 74%.
To estimate the percentage of people who would get counts in the range of 10 to 30 aces when rolling a die 120 times, we can use the normal distribution approximation.
The number of aces rolled by a person in 120 rolls of a fair die follows a binomial distribution with parameters n = 120 (number of trials) and p = 1/6 (probability of rolling an ace).
To apply the normal approximation, we need to check if the conditions are satisfied. When np ≥ 10 and n(1 - p) ≥ 10, we can approximate the binomial distribution with a normal distribution.
In this case, np = 120 * 1/6 = 20 and n(1 - p) = 120 * (5/6) ≈ 100, so the conditions are met.
Using the normal approximation, the distribution of counts will be approximately normal with mean μ = np = 20 and standard deviation σ = √(np(1 - p)) ≈ 4.32.
To find the percentage of people with counts in the range of 10 to 30, we can calculate the area under the normal curve between those values.
Using a standard normal distribution table or a calculator, we can find that the area under the curve between -1.74 and 1.74 is approximately 0.808, which corresponds to 80.8%.
Therefore, approximately 80.8% of the people should get counts in the range of 10 to 30 aces.
The closest answer choice is 74%.
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