Answer:
[tex]\bar{x}= 200[/tex]
Step-by-step explanation:
We are given the following in the question:
Population mean = 200
Population standard deviation = 50
Sample size, n = 100
We have to estimate the expected value of the sample mean.
The best point estimate for the sample mean is the population mean.
Thus, we can write:
[tex]\bar{x}= \mu = 200[/tex]
Thus, the expected value of the sample mean is 200.
For this distribution, which is the BEST estimate for the mean, given that the median is shown to be 6.6?
A) 2.3
B) 4.1
C) 9.1
D) 12.3
Answer: Its C, 9.1
Step-by-step explanation: Did it on usa prept :)
Margo must sell at least 38 tubs of cookie dough to support the student council fundraiser. She has already sold
19 tubs of cookie dough. Which inequality best represents the number of tubs of cookie dough Margo still
needs to sell?
Answer:
19 + x ≥ 38
Step-by-step explanation:
Margo must sell at least 19 more tubs of cookie dough to meet her goal for the student council fundraiser, represented by the inequality x ≥ 19
The question asks to find an inequality that represents the number of tubs of cookie dough Margo still needs to sell.
Margo needs to sell at least 38 tubs of cookie dough and has already sold 19, so we subtract the tubs sold from the total needed:
38 - 19 = 19
Now, let x represent the number of tubs Margo still needs to sell.
The inequality that best represents this situation is:
x ≥ 19
This inequality shows that Margo needs to sell at least 19 more tubs to meet her minimum goal for the fundraiser.
A circular swimming pool has a tacius of 28 ft. There is a path all the way around the pool that is 4 ft wide. A fence is going to
be built around the outside edge of the pool path
About how many feet of fencing are needed to go around the pool path? Use 3.14 for
SS
1001
1761
2010
Marks and
Save and Exit
Next
Submit
Step-by-step explanation:
A circular swimming pool has a tacius of 28 ft. There is a path all the way around the pool that is 4 ft wide. A fence is going to be built around the outside edge of the pool path
WE need to find the circumference of the circle
radius of circular swimming pool is 28 feet
path is 4 ft wide
so we add 4 with radius
radius of the pool with path is 28+4= 32
[tex]circumference =2\pi (r)[/tex]
where r is the radius
r=32
[tex]circumference =2\pi (r)\\circumference =2\pi (32)=200.96=201[/tex]
Answer:
201 feet
The probability of winning the shell games if you
randomly pick is 1 in 3. What would be the
approximate probability of winning 4 games in a row?
A.) 33.3%
B.) 1.2%
C.) 16.7%
D.) 1.5%
Final answer:
The approximate probability of winning 4 games in a row when each game has a 1/3 chance of winning is 1.23%.
(Option B)
Explanation:
To find the approximate probability of winning 4 games in a row, we need to multiply the probabilities of winning each game. Since the probability of winning each game is 1/3, we can calculate the overall probability as [tex](1/3)^4[/tex]. Using a calculator, this comes out to be approximately 0.0123 or 1.23%.
Multiplying the individual probabilities of winning each game, given as 1/3, results in the overall probability of winning 4 games in a row, expressed as [tex](1/3)^4[/tex]. Using a calculator, this evaluates to approximately 0.0123, or 1.23%, highlighting the cumulative nature of independent events.
The endpoints of one side of a regular octagon are (-2,-4) and (4.-6). What 6
is the perimeter of the octagon? *
To find the perimeter of the regular octagon, we use the distance formula to calculate the length of one side given the endpoints and then multiply that length by eight, as there are eight equal sides in a regular octagon.
Explanation:The question revolves around finding the perimeter of a regular octagon given the coordinates of one of its sides. First, we must determine the length of the side using the distance formula between the two given endpoints (-2,-4) and (4,-6). The distance formula is √((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) and (x2, y2) are the coordinates of the endpoints. After calculating the length of one side, we multiply this by 8 (since an octagon has eight equal sides) to get the perimeter.
The calculation is as follows:
Calculate the length of one side: √((4 - (-2))^2 + (-6 - (-4))^2) = √((6)^2 + (-2)^2) = √(36 + 4) = √40Multiply this length by 8 to find the perimeter: 8 * √40 = 8 * 2√10 = 16√10The perimeter of the octagon is 16√10 units.
What is the diameter of a hemisphere with a volume of 2233\text{ cm}^3,2233 cm 3 , to the nearest tenth of a centimeter?
The diameter of the hemisphere is 20.4 centimeters.
Here's the breakdown of the calculation:
Formula for hemisphere volume: The volume of a hemisphere is equal to two-thirds the volume of a full sphere with the same radius (r).
V_hemisphere = (2/3) * (4/3) * π * r^3
Substituting known values: We know the volume of the hemisphere (V_hemisphere) is 2233 cm^3. Plugging this into the equation:
2233 cm^3 = (2/3) * (4/3) * π * r^3
Solve for radius (r): Isolate r:
r^3 = (2233 cm^3 * 3 / 8 * π) ≈ 1181.36 cm^3
r ≈ 10.3 cm
Calculate diameter: Diameter is twice the radius:
diameter = 2 * radius ≈ 20.6 cm
Therefore, the diameter of the hemisphere is approximately 20.4 centimeters to the nearest tenth of a centimeter.
A model rocket is launched with an initial upward velocity of 15 m the Rockets height is H equals 50 T minus 5T squared
Answer:
Step-by-step explanation:
What are you looking for as an answer?
The amount of flour needed to bake a cake is directly proportional to the size of the cake. If it
takes 2 cups of flour to bake an 8 inch cake, how many cups of flour is needed for a 12 inch
cake?
The 12 inch cake needs 3 cups of flour.
What is Unitary method?In order to solve a problem for two different values of a quantity, its unit value is first derived. This method is known as unitary method.
Given that,
The amount of cup of flour for 8 inch cake is 2 cups.
The given problem can be solved using unitary method as follows,
The 8 inch cake needs 2 cups.
Then, 1 inch cake needs 2/8 = 1/4 cups.
Thus, 12 inch cup requires 1/4 × 12 = 3 cups.
Hence, the number of cups needed for 12 inch cake is 3.
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George jogged downhill at 6 mph and then jogged back up at 4 mph. If the total jogging time was 1.25 hours, how far did he jog in all?
The total distance covered is 6 m
Step-by-step explanation:
Let the total distance be '2d'
Total time = 1.25hrs
Downhill speed = 6 mphr
Uphill speed = 4 mphr
(d/6) +(d/4) = 1.25
(2d + 3d) /12 = 1.25
5d/12 = 1.25
d = 3m
So, 2d = 6 m
The total distance covered is 6 m
Country A, Country B, and Country C won a total of 130 medals. Country B won 10 more medals than Country C. Country A won 38 more medals than the total amount won by the other two. How many medals did each of the top three countries win?
Answer:
Country A = 84
Country B = 28
Country C = 18
Step-by-step explanation:
Country A, Country B, and Country C won a total of 130 medals;
A + B + C = 130 ......1
Country B won 10 more medals than Country C;
B = C + 10 .......2
Country A won 38 more medals than the total amount won by the other two;
A = B + C + 38 ........3
Substituting equation 3 to 1;
(B+C+38) + B+C = 130
2B + 2C + 38 = 130 .......4
Substituting equation 2 into 4;
2(C+10) + 2C + 38 = 130
4C + 58 = 130
4C = 130-58 = 72
C = 72/4 = 18
B = C + 10 = 18 + 10 = 28
A = B + C + 38 = 18 + 28 + 38 = 84
Country A = 84
Country B = 28
Country C = 18
Regarding inferences about the difference between two population means, the sampling design that uses a pooled sample variance in cases of equal population standard deviations is based on:
A. research samples.
B. pooled samples.
C. independent samples.
D. conditional samples.
Option B, pooled samples, is the correct answer, as it relies on the homogeneity of variance assumption for a t-test comparing two means.
Regarding inferences about the difference between two population means, when both populations are assumed to have equal standard deviations (or variances), the sampling design that uses a pooled sample variance is based on independent samples. This method pools the sample variances into a single, blended variance estimate when conducting a t-test for comparing two means.
The correct answer to the original question is B.pooled samples. This approach uses the assumption that the population variances are equal, an assumption known as homogeneity of variance. The pooled variance is then used to calculate the test statistic which is crucial for the t-test to compare the means from the two populations accurately.
If the assumption of equal population variances is true, using pooled variance gives a more precise estimate of the population variance, which can lead to a more powerful statistical test. If the populations do not have equal variances, another test designed for unequal variances, like Welch's t-test, should be used instead.
the sampling design that uses a pooled sample variance in cases of equal population standard deviations is based on:pooled samples
The correct option is (B).
When making inferences about the difference between two population means, one common scenario is when the standard deviations of the two populations are equal. In such cases, the pooled sample variance approach is used.
Pooled sample variance involves combining the variances of the two samples into a single pooled estimate. This is done because when the standard deviations are equal, it's reasonable to assume that the underlying population variances are also equal.
The pooled sample variance approach is typically used in independent samples designs, where the samples are taken from two separate populations or groups. These samples are independent because the individuals in one sample are not related to the individuals in the other sample.
Therefore, the correct answer is B. pooled samples, as it accurately describes the sampling design used in cases of equal population standard deviations when making inferences about the difference between two population means.
Helpppp.
................
Answer:
1/x^2
Step-by-step explanation:
When you have a negative sign in the exponent, the integer will become fraction.
To illustrate the effects of driving under the influence of alcohol, a police officer brought a DUI simulator to a local high school. Student reaction time in an emergency was measured with unimpaired vision and also while wearing a pair of goggles to simulate the effects of alcohol on vision. For a random sample of nine teenagers, the time (in seconds) required to bring the vehicle to a stop of 60 miles per hour was recorded. Complete parts (a) and (b).Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers.Data table:Subj. 1 2 3 4 5 6 7 8 9Normal 4.49 4.24 4.58 4.56 4.31 4.80 4.59 5.00 4.79XiImpaired 5.86 5.85 5.45 5.32 5.90 5.49 5.23 5.63 5.63XiA. (pick one below)a. This is a good idea in designing the experiment because the sample size is not large enough.b. This is a good idea in designing the experiment because reaction times are different.c. This is a good idea in designing the experiment because it controls for any "learning" that may occur in using the simulator.B. Use 95% confidence interval to test if there is a difference in braking time with impaired vision and normal vision where the differences are computed as "impaired minus normal."The 95% confidence interval is (_, _). (Round to the nearest thousandth as needed.)State the appropriate conclusion. Choose the correct answer below.a. There is sufficient evidence to conclude there is a difference in braking time with impaired vision and normal vision.b. There is insufficient evidence to conclude there is a difference in braking time with impaired vision and normal vision.
Answer:
Check the explanation
Step-by-step explanation:
Here we have to first of all carry out dependent sample t test. consequently wore goggles first was selected at random for the reason that the reaction time in an emergency taken with goggles would be greater than the amount of reaction time in an emergency taken with not so weakened vision. So that we will get the positive differences d = impaired - normal
b)
To find 95% confidence interval first we need to find sample mean and sample sd for difference d = impaired minus normal.
We can find it using excel that is in the first attached image below,
Therefore sample mean [tex]( \bar{X}_{d} )[/tex] = 0.98
Sample sd [tex]( \bar{S}_{d} )[/tex] = 0.3788
To find 95% Confidence interval we can use TI-84 calculator,
Press STAT ----> Scroll to TESTS ---- > Scroll down to 8: T Interval and hit enter.
Kindly check the attached image below.
Therefore we are 95% confident that mean difference in braking time with impaired vision and normal vision is between ( 0.6888 , 1.2712)
Conclusion : As both values in the interval are greater than 0 , mean difference impaired minus normal is not equal to 0
There is significant evidence that there is a difference in braking time with impaired vision and normal vision at 95% confidence level .
Bringing a DUI simulator to a high school is a good idea as it controls for any "learning" that may occur. The 95% confidence interval shows that there is a difference in braking time with impaired vision and normal vision.
In designing the experiment, bringing a DUI simulator to a high school is a good idea because it controls for any "learning" that may occur in using the simulator. It allows the students to experience the effects of impaired vision due to alcohol and measure their reaction times under both normal and impaired conditions.
To test if there is a difference in braking time with impaired vision and normal vision, a 95% confidence interval is used. The 95% confidence interval is calculated by determining the mean difference in braking time and finding the range within which the true mean difference lies.
The 95% confidence interval for the difference in braking time with impaired vision and normal vision is (0.254, 1.088) seconds. Based on this interval, there is sufficient evidence to conclude that there is a difference in braking time with impaired vision and normal vision.
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Which of the following points lies on the graph of the function y = 3 Superscript x? a. (1, 0) c. (3, 1) b. (2, 9) d. (0, 3)
Answer:
Its b (2,9)
Step-by-step explanation:
I got it on edge
The points which line on the graph as per the given function will be (2, 9). Hence, option B is correct.
What is a graph?In math, graph science is the theory of geometric structures called graphs that are used to represent pairwise different objects. Vertices—also known as nodes or points—that are joined by edges make form a network in this sense.
Undirected graphs, where edges connect two vertices equally, and focused therapy, where edges connect two vertices unevenly, are distinguished.
As per the given information in the question,
The given function is,
y = 3ˣ
In this issue, we have to form points (x₀, y₀). All the function's points need to be replaced by y = 3ˣ.
Replace x₀ with x and y₀ with y.
Only when the right and left sides of the equality are equal does the point belong to the function.
Now, let's check the options one by one.
(a) (1, 0)
y = 3ˣ
0 = 3¹
0 = 3, it is incorrect.
(b) (2, 9)
y = 3ˣ
9 = 3²
9 = 9, it is correct.
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What is the solution to the system of equations graphed below?
y= -3/2x+12
y= 5x+ 28
Given:
The system of equations is [tex]y=-\frac{3}{2}x+12[/tex] and [tex]y=5x+28[/tex]
We need to determine the solution to the system of equations.
Solution:
The solution to the system of equations is the point of intersection of these two lines.
Let us solve the system of equations using substitution method.
Thus, we have;
[tex]5x+28=-\frac{3}{2}x+12[/tex]
Simplifying, we get;
[tex]\frac{13}{2}x+28=12[/tex]
[tex]\frac{13}{2}x=-16[/tex]
[tex]13x=-32[/tex]
[tex]x=-2.462[/tex]
Thus, the value of x is -2.462
Substituting x = -2.462 in the equation [tex]y=5x+28[/tex], we get;
[tex]y=5(-2.462)+28[/tex]
[tex]y=-12.31+28[/tex]
[tex]y=15.69[/tex]
Thus, the value of y is 15.69.
Therefore, the solution to the system of the equations is (-2.462, 15.69)
Stephen counted 17 heartbeats in 15 seconds. How many times does his heart beat in 1 minute?
Stephen's heart beats 68 times in one minute
Step-by-step explanation:
60 sec (one min) divided by 15 sec ( the unit of time we use to track the 17 heartbeats) = 4
4 times 17 =68
in the unted states, the height of men are normally distributed with the mean 69 inches and standard deviation 2.8 inches. If 16 men are randomly selected. what is the probability that their mean height is less than 68 inches
Answer:
Probability that their mean height is less than 68 inches is 0.0764.
Step-by-step explanation:
We are given that in the united states, the height of men are normally distributed with the mean 69 inches and standard deviation 2.8 inches.
Also, 16 men are randomly selected.
Let [tex]\bar X[/tex] = sample mean height
The z-score probability distribution for sample mean is given by;
Z = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean height = 69 inches
[tex]\sigma[/tex] = population standard deviation = 2.8 inches
n = sample of men = 16
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.
So, probability that the mean height of 16 randomly selected men is less than 68 inches is given by = P([tex]\bar X[/tex] < 68 inches)
P([tex]\bar X[/tex] < 68 inches) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{68-69}{\frac{2.8}{\sqrt{16} } }[/tex] ) = P(Z < -1.43) = 1 - P(Z [tex]\leq[/tex] 1.43)
= 1 - 0.9236 = 0.0764
Now, in the z table the P(Z x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 1.43 in the z table which has an area of 0.92364.
Therefore, probability that their mean height is less than 68 inches is 0.0764.
Suppose two radii of a circle determine a 45° angle, and the length of both radii is 64 yards. What is the arc length formed by the two radii
in yards? Round your answer to two decimal places.
The arc length formed by the 2 radio is 15.24 yards
Step-by-step explanation:
Angle between the 2 radio = 45°
Radius = 64 yards
Arc length = (45/360) (2π) (64)
= (1/8) (2π) (64
= 16π
= 16(3.14)
=15.24 yards
The arc length formed by the 2 radio is 15.24 yards
What is the equation of line I?
Answer:
N/A
Step-by-step explanation:
what is line l?
2. Connecticut is located between New York and Boston, so baseball fans in the state typically root for
either the Yankees or Red Sox. In a recent poll of 803 randomly selected baseball fans in Connecticut,
55% said their favorite team was the Yankees Calculate and interpret a 90% confidence interval for
the proportion of all Connecticut baseball fans who say their favorite team is the Yankees
We are 90% confident that the true proportion of all Connecticut baseball fans who say their favorite team is the Yankees is between 0.511 and 0.589.
What is a confidence interval?A confidence interval is a range of values that is likely to contain the true value of an unknown parameter, such as a population means or proportion, based on a sample of data from that population.
It is a statistical measure of the degree of uncertainty or precision associated with a statistical estimate.
We have,
To calculate a 90% confidence interval for the proportion of all Connecticut baseball fans who say their favorite team is the Yankees, we can use the formula:
CI = p ± z √((p(1-p))/n)
where:
p is the sample proportion (0.55)
z* is the critical z-value for a 90% confidence level (1.645)
n is the sample size (803)
Plugging in the values,
CI = 0.55 ± 1.645 √((0.55(1-0.55))/803)
CI = 0.55 ± 0.042
Therefore,
The 90% confidence interval for the proportion of all Connecticut baseball fans who say their favorite team is the Yankees is (0.508, 0.592).
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To calculate a 90% confidence interval for the proportion of Connecticut baseball fans who favor the Yankees, the standard error was computed and multiplied by the Z-score for 90% confidence. The confidence interval was found to be between 52.11% and 57.89%, meaning there is a 90% chance the true proportion falls within this range.
Explanation:The question requires the calculation of a 90% confidence interval for the proportion of all Connecticut baseball fans who favor the New York Yankees. A sample proportion (p-hat) of 803 Connecticut baseball fans showed that 55% (or 0.55) favored the Yankees. To calculate the confidence interval, we use the formula for the confidence interval of a proportion:
CI = p-hat ± Z*sqrt[(p-hat)(1-p-hat)/n], where Z is the Z-score that corresponds to the level of confidence and n is the sample size. For a 90% confidence level, the Z-score is approximately 1.645.
Calculating the standard error (SE):
SE = sqrt[(0.55)(0.45)/803] = sqrt[0.2475/803] = sqrt[0.000308344] = 0.017562
Then, the margin of error (ME):
ME = Z*SE = 1.645 * 0.017562 = 0.028894
The 90% confidence interval (CI) is:
CI = 0.55 ± 0.028894
CI = [0.521106, 0.578894]
Interpreting this confidence interval, we are 90% confident that the true proportion of all Connecticut baseball fans who favor the Yankees falls between 52.11% and 57.89%.
8x-3(-z-y)
X= 1
Y=3
Z=-2
Answer:
11
Step-by-step explanation:
8x - 3(-z - y)
Substitute
8(1) - 3(-(-2) - 3)
Simplify
8 - 3(-1)
Multiply
8 + 3
Add
11
Answer:
Here; 8x-3(-z-y) =
so your asking 8x-3(-z-y) right?
Let's simplify step-by-step.
8x−3(−z−y)
awnser again xD
=8x+3y+3z
The mean height of an adult giraffe is 18 feet. Suppose that the distribution is normally distributed with standard deviation 0.8 feet. Let X be the height of a randomly selected adult giraffe. Round all answers to two decimal places.What is the probability that a randomly selected giraffe will be shorter than 17 feet tall?What is the probability that a randomly selected giraffe will be between 16 and 19 feet tall? The 90th percentile for the height of giraffes is?
Answer:
1. the probability that giraffe will be shorter than 17 feet tall is equal to 0.1056
2. the probability that a randomly selected giraffe will be between 16 and 19 feet tall is equal to 0.8882
3. the the 90th percentile for the height of giraffes is 19.024
Step-by-step explanation:
To calculate the probability that a giraffe will be shorter than 17 feet tall, we need to standardize 17 feet as:
[tex]z=\frac{x-m}{s}[/tex]
Where x is the height of the adult giraffe, m is the mean and s is the standard deviation, so 17 feet is equivalent to:
[tex]z=\frac{17-18}{0.8}=-1.25[/tex]
Now, the probability that giraffe will be shorter than 17 feet tall is equal to P(z<-1.25). Then, using the standard normal distribution table, we get that:
[tex]P(z<-1.25)=0.1056[/tex]
At the same way, 16 and 19 feet tall are equivalent to:
[tex]z=\frac{16-18}{0.8}=-2.5\\z=\frac{19-18}{0.8}=1.25[/tex]
So, the probability that a randomly selected giraffe will be between 16 and 19 feet tall is equal to:
[tex]P(-2.5<z<1.25)=P(z<1.25)-P(z<-2.5)\\P(-2.5<z<1.25)=0.8944-0.0062\\P(-2.5<z<1.25)=0.8882[/tex]
Finally, to find the the 90th percentile for the height of giraffes, we need to find the value z that satisfy:
[tex]P(Z<z)=0.9[/tex]
Now, using the standard normal distribution table we get that z is equal to 1.28. Therefore, the height x of the giraffes that is equivalent to 1.28 is:
[tex]z=\frac{x-m}{s} \\1.28=\frac{x-18}{0.8} \\x=(1.28*0.8)+18\\x=19.024[/tex]
it means that the the 90th percentile for the height of giraffes is 19.024
Using Z-scores, the probability that a randomly selected giraffe is less than 17 feet tall is approximately 0.106, the probability that it is between 16 and 19 feet tall is approximately 0.888. The 90th percentile in height for giraffes is about 19.02 feet.
Explanation:These questions are related to normal distribution. The formula of normal distribution (Z-score) is Z = (X - μ)/σ, where X is the specific value, μ is the mean, and σ is the standard deviation.
For the first question, we want to find the probability that a randomly selected giraffe is less than 17 feet tall. The Z-score is calculated as Z = (17 - 18) / 0.8 = -1.25. Using the Z-table, the probability that a giraffe is less than 17 feet tall is approximately 0.106.
For the second question, we need to find the probability that a randomly selected giraffe will be between 16 and 19 feet tall. We calculate two Z-scores: Z1 = (16 - 18) / 0.8 = -2.5 and Z2 = (19 - 18) / 0.8 = 1.25. Using the Z-table, the probability that a giraffe is between 16 and 19 feet tall is approximately 0.894-0.006 = 0.888.
For the third question, we need to find the 90th percentile for the height of giraffes. It corresponds to the Z-score of 1.282 on the Z-table. Hence, X = μ + Zσ = 18 + 1.282*0.8 = 19.02 feet.
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Stefan was able to map \triangle ABD△ABDtriangle, A, B, D onto \triangle ABC△ABCtriangle, A, B, C. Stefan concluded: "I was able to map \triangle ABD△ABDtriangle, A, B, D onto \triangle ABC△ABCtriangle, A, B, C using a sequence of rigid transformations, so the figures are congruent." What error did Stefan make in his conclusion? Choose 1 answer: Choose 1 answer: (Choice A) A Stefan didn't use only rigid transformations, so the figures are not congruent. (Choice B) B It's possible to map \triangle ABD△ABDtriangle, A, B, D onto \triangle ABC△ABCtriangle, A, B, C using a sequence of rigid transformations, but the figures are not congruent. (Choice C) C There is no error. This is a correct conclusion.
Answer: Stefan didn’t use only rigid transformations, so the figures are not congruent
Step-by-step explanation:
Stefan didn’t use only rigid transformations, so the figures are not congruent.
What is Congruency?Two triangles are said to be congruent if their sides are equal in length, the angles are of equal measure, and they can be superimposed on each other.
In the given, Δ ABC and Δ ABD are not congruent triangles. if they are congruent then This means that the corresponding angles and corresponding sides in both the triangles are equal.
The following are the congruence theorems or the triangle congruence criteria that help to prove the congruence of triangles;
SSS (Side, Side, Side)
SAS (side, angle, side)
ASA (angle, side, angle)
AAS (angle, angle, side)
RHS (Right angle-Hypotenuse-Side or the Hypotenuse Leg theorem)
As, from the given cases the prediction of congruency of two triangles is incorrect. There is no error he made.
Hence, Stefan didn’t use only rigid transformations, so the figures are not congruent
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Why is the central limit theorem important in statistics? a) Because for a large sample size n, it says the population is approximately normal. b) Because for any population, it says the sampling distribution of the sample mean is approximately normal, regardless of the shape of the population. c) Because for a large sample size n, it says the sampling distribution of the sample mean is approximately normal, regardless of the shape of the population. d) Because for any sample size n, it says the sampling distribution of the sample mean is approximately normal. e) none of the above
Answer:
The correct option is (c).
Step-by-step explanation:
According to the Central Limit Theorem if we have a population with a known mean and standard deviation and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample means will be approximately normally distributed.
Then, the mean of the distribution of sample means is given by, the population mean.
And the standard deviation of the distribution of sample means is given by,
[tex]SD_{\bar x}=\frac{SD}{\sqrt{n}}[/tex]
So, the most basic and main objective of the Central limit theorem is to approximate the sampling distribution of a statistic by the Normal distribution even when we do not known the distribution of the population.
Thus, the correct option is (c).
The Central Limit Theorem is crucial in statistics because it provides a powerful tool for dealing with data from various populations by allowing us to rely on the normal distribution for making statistical inferences, even when the underlying population is not normally distributed. This property makes it a cornerstone of statistical theory and practice.
The correct answer is: c) Because for a large sample size n, it says the sampling distribution of the sample mean is approximately normal regardless of the shape of the population.
The Central Limit Theorem (CLT) is a fundamental concept in statistics with widespread applications.
It is important for several reasons:
Approximation of the Sampling Distribution:
The CLT states that for a sufficiently large sample size (n), the sampling distribution of the sample mean will be approximately normally distributed, regardless of the shape of the population from which the samples are drawn.
This is crucial because it allows statisticians to make inferences about population parameters based on the normal distribution, which simplifies statistical analysis.
Widespread Applicability:
The CLT is not limited to specific populations or data types.
It holds true for a wide range of data distributions, making it a versatile tool in statistical analysis.
Whether the underlying population distribution is normal, uniform, exponential, or any other shape, the CLT assures us that the distribution of sample means will tend to be normal for sufficiently large samples.
Foundation for Hypothesis Testing and Confidence Intervals:
Many statistical methods, including hypothesis testing and the construction of confidence intervals, rely on the assumption of a normal distribution.
The CLT's ability to transform non-normally distributed data into a normal sampling distribution is essential for these statistical techniques.
For similar question on Central Limit Theorem.
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What is the formula for this question?
Answer:
2.7
Step-by-step explanation:
This can be modeled using exponential growth/decay.
A = P (1 + r)ⁿ
where A is the final amount,
P is the initial amount,
r is the rate of growth/decay,
and n is the number of cycles.
For half life problems, r = -½, and n = t / T, where t is time and T is the half life.
A = P (1 − ½)^(t/T)
A = P (½)^(t/T)
Given that P = 9, t = 10000, and T = 5730:
A = 9 (½)^(10000/5730)
A ≈ 2.7
There are approximately 2.7 mg of ¹⁴C left.
Find an equation in standard form for the ellipse with vertical major axis of length 18 and minor axis length of 6
Answer:
The equation of the ellipse is standard form is expressed as:
x²/81 + y²/9 = 1
Step-by-step explanation:
General equation of an ellipse is expressed as shown below:
x²/a² + y²/b² = 1
Length of the major axis = 2a
Length of the Minor axis = 2b
Given length of major axis = 18
18 = 2a
a = 9
Similarly, if the length of the minor axis is 6, then
6 = 2b
b = 3
The equation of the ellipse becomes;
x²/9² + y²/3² = 1
x²/81 + y²/9 = 1
Finding the LCM
(x²+9y²)/81 = 1
x²+9y² = 81
A study was conducted to determine whether UH students sleep fewer than 8 hours. The study was based on a sample of 100 students. The sample mean number of hours of sleep was 7 hours and the sample standard deviation was 5 hours.
1. What is the value of the test statistic?
a. 0.5
b. 5.0
c. 1.2
d. -5.0
Answer:
The value of t test statistics is -2.
Step-by-step explanation:
We are given that a study was conducted to determine whether UH students sleep fewer than 8 hours.
The study was based on a sample of 100 students. The sample mean number of hours of sleep was 7 hours and the sample standard deviation was 5 hours.
Let [tex]\mu[/tex] = mean number of hours UH students sleep.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \geq[/tex] 8 hours {means that UH students sleep more than or equal to 8 hours}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 8 hours {means that UH students sleep fewer than 8 hours}
The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean number of hours of sleep = 7 hours
s = sample standard deviation = 5 hours
n = sample of students = 100
So, test statistics = [tex]\frac{7-8}{\frac{5}{\sqrt{100} } }[/tex] ~ [tex]t_9_9[/tex]
= -2
Hence, the value of t test statistics is -2.
In a large lecture class, the professor announced that the scores on a recent exam were normally distributed with a range from 51 to 87. Using the Empirical Rule μ ± 3σ to estimate σ, how many students would you need to sample to estimate the true mean score for the class with 90 percent confidence and an error of ±2?
Answer:
The standard deviation of the scores on a recent exam is 6.
The sample size required is 25.
Step-by-step explanation:
Let X = scores of students on a recent exam.
It is provided that the random variable X is normally distributed.
According to the Empirical rule, 99.7% of the normal distribution is contained in the range, μ ± 3σ.
That is, P (μ - 3σ < X < μ + 3σ) = 0.997.
It is provided that the scores on a recent exam were normally distributed with a range from 51 to 87.
This implies that:
P (51 < X < 87) = 0.997
So,
μ - 3σ = 51...(i)
μ + 3σ = 87...(ii)
Subtract (i) and (ii) to compute the value of σ as follows:
μ - 3σ = 51
(-)μ + (-)3σ = (-)87
______________
-6σ = -36
σ = 6
Thus, the standard deviation of the scores on a recent exam is 6.
The (1 - α)% confidence interval for population mean is given by:
[tex]CI=\bar x\pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]
The margin of error of this interval is:
[tex]MOE = z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]
Given:
MOE = 2
σ = 6
Confidence level = 90%
Compute the z-score for 90% confidence level as follows:
[tex]z_{\alpha/2}=z_{0.10/2}=z_{0.05}=1.645[/tex]
*Use a z-table.
Compute the sample required as follows:
[tex]MOE = z_{\alpha/2}\frac{\sigma}{\sqrt{n}}\\2=1.645\times \frac{6}{\sqrt{n}}\\n=(\frac{1.645\times 6}{2})^{2}\\n=24.354225\\n\approx 25[/tex]
Thus, the sample size required is 25.
The Empirical Rule guides estimating sample sizes with specific confidence levels and margins of error.
The Empirical Rule states that about 95 percent of the values lie within two standard deviations of the mean in a normal distribution.
To estimate the sample size needed to estimate the true mean score with 90 percent confidence and an error of ±2, we can use the formula for the margin of error.
By rearranging this formula and plugging in the required values, we can determine the sample size needed to achieve the desired confidence level and margin of error.
*) Name this triangle by looking at its side lengths.
Answer
equilateral
Step-by-step explanation:
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What is the difference in surface areas, in square feet, of the two boxes?
Rectangular Prism: 3 ft by 4.5 ft by 2 ft
Cube: 3 ft
Final answer:
The difference in surface areas of the two boxes is 3 square feet.
Explanation:
The difference in surface areas between two boxes is computed by first finding the surface area of each box and then subtracting the smaller surface area from the larger one.
Rectangular Prism:
For the rectangular prism with dimensions 3 ft by 4.5 ft by 2 ft, the surface area (SA) is calculated using the formula SA = 2lw + 2lh + 2wh.
The surface areas of the rectangular prism are:
Top and Bottom: 2(3 ft × 4.5 ft) = 27 ft²Front and Back: 2(3 ft × 2 ft) = 12 ft²Sides: 2(4.5 ft × 2 ft) = 18 ft²Total surface area of the rectangular prism = 27 ft² + 12 ft² + 18 ft² = 57 ft²
Cube:
For the cube with a side of 3 ft, the surface area is found using the formula SA = 6s².
Thus:
Total surface area of the cube = 6(3 ft × 3 ft) = 54 ft²
Difference in Surface Area:
Difference in surface areas = Surface area of the rectangular prism - Surface area of the cube = 57 ft² - 54 ft² = 3 ft².