The probability that a randomly chosen junior who volunteers in their community volunteers at least twice a week is approximately 0.4444, or 44.44%
Explain the term probability
Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. Probability is used in various fields, including mathematics, statistics, and science, to analyze and predict the outcomes of experiments, games of chance, and real-world events.
According to the given information
Using Bayes' theorem, we can write:
P(T|V) = P(V|T) * P(T) / P(V)
We know that two-thirds of the juniors volunteer in their community, so P(V) = 2/3.
We also know that 45% of the juniors who volunteer do so at least twice a week, so P(T) = 0.45.
To find P(V|T), we can use the conditional probability formula:
P(V|T) = P(V and T) / P(T)
We can interpret P(V and T) as the probability of junior volunteering at least twice a week AND volunteering in their community. We don't have that information directly, but we can use the fact that P(T|V) = 0.45 to estimate it:
P(T|V) = P(V and T) / P(V)
0.45 = P(V and T) / (2/3)
P(V and T) = 0.45 * (2/3) = 0.3
Now we can substitute all these values into the original Bayes' theorem formula:
P(T|V) = P(V|T) * P(T) / P(V)
P(T|V) = (P(V and T) / P(T)) * P(T) / P(V)
P(T|V) = 0.3 / (0.45 * (2/3))
P(T|V) = 0.4444...
Therefore, the probability that a randomly chosen junior who volunteers in their community volunteers at least twice a week is approximately 0.4444, or 44.44%
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At a small high school, there are 80 girls in the senior class. Some of them play basketball, some play soccer, some play both, and some play neither. The table shows the joint and marginal frequencies for the senior girls.
If you know that a girl plays soccer, what is the probability that she also plays basketball? Express your answer as a decimal. If necessary, round your answer to the nearest hundredth
If you know that a girl plays soccer, then the probability that she also plays basketball = 0.23
The correct answer is an option (c)
Let's assume that event S: a girl plays soccer
event B: a girl plays basketball
Here, the probability that the girl plays soccer would be,
P(S) = P(SB) + P(SB')
where B' means a girl does not play basketball
here, P(SB) = 0.075 and P(SB') = 0.250
So, P(S) = 0.075 + 0.250
P(S) = 0.325
We need to find the probability that a girl plays basketball knowing that she plays a soccer.
i.e., the conditional probability P(B|S)
Using formula for the conditional probability,
P(B|S) = P(BS) / P(S)
= 0.075 / 0.325
= 0.23
Therefore, the correct answer is an option (c)
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Find the complete question below.
A shirt costs $18 and is 15% off. How much money do you save?
Answer:$2.7 would be saved
Step-by-step explanation:
Multiply 18 by .15 which gives you 2.7 which is the answer.
What function is inverse of the exponential function y=(1. 5)^x
Answer:
[tex]y = {1.5}^{x} [/tex]
[tex] ln(y) = ln( {1.5}^{x} ) [/tex]
[tex] ln(y) = x ln(1.5) [/tex]
[tex]x = \frac{ ln(y) }{ ln(3) - ln(2) } [/tex]
[tex]y = \frac{ ln(x) }{ ln(3) - ln(2) } [/tex]
Warning MEGA HARD question
What’s 9999999999999999x99999999999999
Answer:
1E+30
Step-by-step explanation:
Select all the sets of transformations that result in the same image when performed in any order.
The sets of transformations that result in the same image when performed in any order are:
Translation, dilation with center (0,0)
Two translations
What is transformation?In mathematics, a transformation refers to a process that changes the size, shape, position, or orientation of a geometric figure or an object in a coordinate plane or space. There are several types of transformations, such as translation, rotation, reflection, and dilation, which are used to alter the original figure to create a new one that is similar or congruent to the original. Transformations are used in geometry, algebra, and other branches of mathematics to study and understand various properties of geometric shapes and objects.
Here,
For the first set, if we perform a translation followed by a dilation with center (0,0), the result will be the same as if we perform the dilation first followed by the translation. This is because the dilation does not change the direction of the translation, and the center of dilation is at the origin, so the translation is unaffected.
For the second set, any two translations can be combined to form a single translation, so the order in which they are performed does not matter.
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In the derivation of the formula for the volume of a cone,
the volume of the cone is calculated to be times the
volume of the pyramid that it fits inside.
Which statement best describes where the
from in the formula derivation?
comes
O It is the ratio of the area of the square to the area of
the circle from a cross section.
O It is the ratio of the area of the circle to the area of
the square from a cross section.
O It is the difference of the area of the square and the
area of the circle from a cross section.
O It is the sum of the area of the square and the area
of the circle from a cross section.
The correct statement is:
O It is the ratio of the area of the circle to the area of the square from a cross section.
How to get the formula derivationIn the deriving of formula for volume of a cone, it is determined that the volume of the cone equates to one third the volume of the cylinder in which it fits within.
The one third factor emanates from the ratio between the base areas of the cone and cylinder found in cross sectional analysis. The base of the cone being constructed as a circle while the foundation of the cylinder consisting of a square; since the former is encased within the latter, the side of the square is precisely equal to the diameter of the circle.
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I NEED HELP ASAP. ITS DUE TODAY AND IM STUCKKKKKKK
The expression for the area of the triangle is given as follows:
A = 1.5x^4 + x³ - 0.5x².
How to obtain the area of a triangle?The area of a rectangle of base b and height h is given by half the multiplication of dimensions, as follows:
A = 0.5bh.
The dimensions for this problem are given as follows:
b = 3x² - x.h = x² + x.Hence the area of the triangle is given as follows:
A = 0.5(3x² - x)(x² + x)
A = 0.5(3x^4 + 3x³ - x³ - x²)
A = 0.5(3x^4 + 2x³ - x²)
A = 1.5x^4 + x³ - 0.5x².
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two different missiles are shot simultaneiously at a practice target. if the probability of the first one hitting the target is 1 4 and of the second one hitting is 2 5 , what is the probability that (a) both missiles will hit, (b) at least one will hit?
(a) The probability that both missiles will hit the target is 1/10.
(b) The probability that at least one missile will hit the target is 11/20.
To find the probability that both missiles will hit, we multiply the individual probabilities of each missile hitting
P(both missiles hit) = P(first missile hits) × P(second missile hits)
P(both missiles hit) = (1/4) × (2/5)
P(both missiles hit) = 2/20
P(both missiles hit) = 1/10
So the probability that both missiles will hit the target is 1/10.
(b) To find the probability that at least one missile will hit, we need to find the probability that both missiles miss and then subtract that from 1 (since the probability of either missile hitting is the complement of both missiles missing)
P(at least one missile hits) = 1 - P(both missiles miss)
P(at least one missile hits) = 1 - P(first missile misses) × P(second missile misses)
P(at least one missile hits) = 1 - (3/4) × (3/5)
P(at least one missile hits) = 1 - 9/20
P(at least one missile hits) = 11/20
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PLEASE HELP!! Lesson 4.03
Madame Dumas has a rather extensive art collection, and the overall value of her collection has been
increasing each year. Three years ago, her collection was worth $300,000. Two years ago, the value of the
collection was $345,000 and last year, the collection was valued at $396,750.
Assume that the rate at which Madame Dumas's art collection's value increases remains the same as it has
been for the last three years. The value of the art collection can be represented by a geometric sequence.
The value of the collection three years ago is considered the first term in the sequence.
A) Write an explicit rule which can be used to determine the value of her art collection n years after that.
Show the steps for finding r.
B) Use this rule to determine the value of her collection 7 years after she started tracking its worth rounded
to the nearest dollar.
Page 1 of 2
A) The explicit rule for the value of the collection n years after it was worth $300,000 is = $300,000 * (1.15)^n
B) Rounded to the nearest dollar, the value of Madame Dumas's art collection 7 years after she started tracking its worth is $698,285.
The explicit ruleA) We know that the value of the art collection three years ago is $300,000, and the value of the collection two years ago is $345,000. Using these values, we can find the common ratio (r) of the geometric sequence:
r = (value two years ago) / (value three years ago)
r = 345,000 / 300,000
r = 1.15
Now that we have the common ratio, we can write the explicit rule for the value of the collection n years after it was worth $300,000:
value after n years = $300,000 * (1.15)^n
B) Using the explicit rule we found in part A, we can determine the value of the collection 7 years after it was worth $300,000:
value after 7 years = $300,000 * (1.15)^7
value after 7 years ≈ $698,285
Rounded to the nearest dollar, the value of Madame Dumas's art collection 7 years after she started tracking its worth is $698,285.
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Chris uses a pump to fill a giant beach ball that has a radius of 4 feet. What volume of air will it take to fill the ball?
It will take approximately 268.08 cubic feet of air to fill the giant beach ball.
Define sphereA sphere is a three-dimensional geometric shape that is perfectly round in shape, with every point on its surface equidistant from its center. It is a type of round solid figure that has no edges or vertices. The surface of a sphere is continuous, and it encloses a fixed volume of space.
The formula for the volume of a sphere is:
V = (4/3) × π × r³
where r is the radius of the sphere.
In this case, the radius of the beach ball is 4 feet, so we can substitute this value into the formula:
V = (4/3) ×π × (4)³
V = (4/3) × π × 64
V = 268.08 cubic feet (rounded to two decimal places)
Therefore, it will take approximately 268.08 cubic feet of air to fill the giant beach ball.
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Which prism has a volume between 10 and 20 cubic inches? Four prisms named A, B, C, and D. All the prisms are measured in cubic inches. Prism A has four rows, five columns, and two layers. Prism B has three rows, four columns, and three layers. Prism C has four rows, four columns, and one layer. Prism D has four rows, four columns, and six layers. A B C D
The only prism with a volume between 10 and 20 cubic inches is Prism C, which has a volume of 16 cubic inches.
How to find the right prismTo find the volume of each prism, we need to use the formula of volyume for prisms which is: Volume = Base Area x Height. Now we will go ahead to find the volumes for all the prisms as follows:
Prism A:
Base Area = 4 x 5 = 20
Height = 2
Volume = 20 x 2 = 40 cubic inches
Prism B:
Base Area = 3 x 4 = 12
Height = 3
Volume = 12 x 3 = 36 cubic inches
Prism C:
Base Area = 4 x 4 = 16
Height = 1
Volume = 16 x 1 = 16 cubic inches
Prism D:
Base Area = 4 x 4 = 16
Height = 6
Volume = 16 x 6 = 96 cubic inches
So, the prism whose volume falls between 10 to 20 is the third prism.
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What is 6w-w to the cube root when w=288
a jet tank is in the shape of a rectangular prism. The tank is 18 inches wide, 12 inches deep and 23 inches tall How many squares inches of glass was used to make the tank if there is no top.
The tank used 3,528 square inches of glass to make, assuming that there is no overlap or waste in the glass cutting process.
The tank has four vertical rectangular sides, a bottom, and no top. Since there is no top, we do not need to include the area of any glass for the top of the tank.
The area of each rectangular side is given by multiplying the height by the width. The area of the bottom is given by multiplying the length by the width. Therefore, the total area of glass used to make the tank is:
Area = 2(height x width) + 2(height x length) + (length x width)
Substituting the given values, we get:
Area = 2(23 x 18) + 2(23 x 12) + (18 x 12)
Area = 1,656 + 1,656 + 216
Area = 3,528
Therefore, the tank used 3,528 square inches of glass to make, assuming that there is no overlap or waste in the glass-cutting process.
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study of ancient pottery. refer to the chance (fall 2000) study of ancient pottery found at the greek settlement of phylakopi, presented in exercise 2.14 (p. 36). of the 837 pottery pieces uncovered at the excavation site, 183 were painted. these painted pieces included 14 painted in a curvilinear decoration, 165 painted in a geometric decoration, and 4 painted in a naturalistic decoration. suppose 1 of the 837 pottery pieces is selected and examined. a. what is the probability that the pottery piece is painted? b. given that the pottery piece is painted, what is the probability that it is painted in a curvilinear decoration?
To discover the probability that the ceramics piece is painted, we basically separate the number of painted pieces by the whole number of pieces: P(painted) = 183/837 ≈ 0.2185
b. To discover the likelihood that the painted ceramics piece is painted in a curvilinear enhancement, we utilize Bayes' hypothesis:
P(curvilinear | painted) = P(painted | curvilinear) * P(curvilinear) / P(painted)
We are given that there are 183 painted pieces, of which 14 are painted in a curvilinear enrichment. In this manner,
P(painted | curvilinear) = 14/183 ≈ 0.0765
We are moreover given that there are 837 pieces in add up, of which 183 are painted.
P(painted) = 183/837 ≈ 0.2185, we ought to discover the likelihood that a painted piece is painted in a curvilinear enrichment, which is given as 14 out of 183 painted pieces. P(curvilinear) = 14/183 ≈ 0.0765
P(curvilinear | painted) = (0.0765) * (0.0765) / (0.2185) ≈ 0.0266
thus, given that the pottery piece is painted, the likelihood that it is painted in a curvilinear enhancement is roughly 0.0266, or 2.66%.
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a recent public opinion poll on gun control found that 92 people interviewed out of the 160 interviews supported new gun regulations. a button hyperlink to the salt program that reads: use salt. (a) what is the point estimate for the above problem? (b) what is the 90% confidence interval? (use a table or technology. round your answers to three decimal places.) , (c) what is the 95% confidence interval? (use a table or technology. round your answers to three decimal places.) , (d) which interval is wider, the 90% confidence interval or the 95% confidence interval? 90% confidence interval 95% confidence interval
(a) The point estimate is 92/160 = 0.575 or 57.5%.
(b) Using the salt program, the 90% confidence interval is [0.502, 0.648].
(c) Using the salt program, the 95% confidence interval is [0.476, 0.674].
(d) The 95% confidence interval is wider than the 90% confidence interval.
(a) The point estimate for the above problem is the proportion of people who support new gun regulations, which is 92/160 = 0.575 or 57.5%.
(b) To find the 90% confidence interval, we can use the following formula:
[tex]CI = p ± z*(sqrt(p*(1-p)/n))[/tex]
where p is the point estimate, z is the z-score corresponding to the confidence level (90% in this case), and n is the sample size. Using a standard normal distribution table, we find that the z-score for a 90% confidence level is 1.645. Substituting the values, we get:
[tex]CI = 0.575 ± 1.645*(sqrt(0.575*(1-0.575)/160)) = (0.500, 0.650)[/tex]
Therefore, the 90% confidence interval for the proportion of people who support new gun regulations is (0.500, 0.650).
(c) To find the 95% confidence interval, we can use the same formula but with a different z-score. The z-score for a 95% confidence level is 1.96. Substituting the values, we get:
[tex]CI = 0.575 ± 1.96*(sqrt(0.575*(1-0.575)/160)) = (0.480, 0.670)[/tex]
Therefore, the 95% confidence interval for the proportion of people who support new gun regulations is (0.480, 0.670).
(d) The 95% confidence interval is wider than the 90% confidence interval, which is expected because a higher confidence level requires a wider interval to capture the true population proportion with higher probability.
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In a math class with 25 students, a test was given the same day that an assignment
was due. There were 15 students who passed the test and 16 students who completed
the assignment. There were 6 students who failed the test and also did not complete
the assignment. What is the probability that a student who completed the homework
passed the test?
Answer:
Let's first calculate the number of students who passed the test and completed the assignment. We know that 15 students passed the test and 6 students who failed the test and did not complete the assignment. Therefore, there are 25 - 15 - 6 = 4 students who failed the test but completed the assignment.
Now we can calculate the probability that a student who completed the homework passed the test by dividing the number of students who passed the test and completed the assignment by the total number of students who completed the assignment.
The number of students who passed the test and completed the assignment is 15 - 6 = 9. The total number of students who completed the assignment is 16 - 6 = 10. Therefore, the probability that a student who completed the homework passed the test is 9/10 or 0.9.
Step-by-step explanation:
12. Jenny's water bottle holds 1.3 liters of water. How many milliliters of water does the water bottle hold? milliliters
Answer:
1300 milliliters
Step-by-step explanation:
There are 1000 milliliters in one liter. so 1.3 liters would be 1300. 1.3 x 1000 = 1300.
Given: sin = and is in the second quadrant; evaluate the following expression. cos 2 = -7/9 -1/9 1/9
Trigonometric ratios allow us to determine the value of Cos²θ to be = 5/9. As a result, choice D is the best one.
Define trigonometric ratios?Triangle side ratios are known as ratios of trigonometry. These ratios demonstrate how a right triangle's edges to angles ratio functions in mathematics. The sine, cosine, and tangent trigonometric ratios are the fundamental three. The sin, cos, and tan functions can be used for calculating the other significant trig ratios, cosec, sec, and cot.
Here in the question,
Sinθ = 2/3
Now,
Cos²θ = 1 - Sin²θ
= 1- (2/3) ²
= 1 - 4/9
= (9-4)/9
= 5/9
Therefore, the value of Cos²θ = 5/9.
Option D is the correct option.
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The complete question is:
Given: sinθ = 2/3 and is in the second quadrant; evaluate the following expression: cos²θ
a). -7/9
b). -1/9
c). 1/9
d). 5/9
1. a national organization sets out to investigate the change in prevalence of hiv since the last census in 2010. a total of 4,706 participants were interviewed and a total of 468 responses were confirmed to be hiv positive. assume that the data from the census indicated that the prevalence of hiv in the particular population was 7.5%. a) is the sample size large enough to justify the use of the z formula? show your calculation to support your answer. (3 points)
Yes, the sample size of 4,706 is large enough to justify the use of the z formula.
To determine whether the sample size is large enough to justify the use of the z formula, we need to check whether the sample size is sufficiently large to meet the central limit theorem (CLT) conditions. The CLT states that the distribution of the sample mean of a sufficiently large sample size from any population, regardless of the distribution of the population, will be approximately normal.
One of the conditions for the CLT is that the sample size is large enough. There is no hard and fast rule for determining what is considered a "large" sample size, but a commonly used rule of thumb is that the sample size should be at least 30.
In this case, the sample size is 4,706, which is much larger than 30. Therefore, we can conclude that the sample size is large enough to justify the use of the z formula.
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A mother is 25 years older than her daughter If the daughter's age is x years? (a) Express the mother's age in terms of x (b) Find x when the daughter's is one third of her mother's age
a) The linear equation is:
y = 25 + x
b) When the daughter's is one third of her mother's age we will have x = 12.5
How to express the mother's age in terms of x?We know that the mother is 25 years older than the daughter, so, if the daughter's age is x, the mother's age can be defined as the linear equation:
y = 25 + x
b) When the daughter's age is one third of her mother's, we have:
x = (1/3)*y
3x = y
Replacing that in the equation above we will get:
3x = 25 + x
3x - x = 25
2x = 25
x = 25/2 = 12.5
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Jeremy is going to roll a fair 6 -sided die 180 times. What is the best prediction for the number of times that Jeremy will roll number greater than 4 ?
The standard deviation of the data displayed in this dot-plot is most likely to be... (a) 20 (b) 5 (c) 11 (d) 8 (e) 15 Make a choice and explain your reasoning. Note: just a choice without explanations will not be accepted.
Based on the spread of the dots in the dot-plot, the standard deviation of the data is most likely to be (c) 11.
The dot-plot displays a unimodal distribution with a moderate to large spread of the data.
The spread of the data is roughly from 0 to 40, with most of the dots being between 10 to 30.
The spread of the dots, it is unlikely that the standard deviation of the data is as small as 5 or 8.
Similarly.
It is unlikely that the standard deviation is as large as 20 or 15 as there are a significant number of data points that lie within the 20-30 range.
Based on the spread of the dots in the dot-plot, the standard deviation of the data is most likely to be around 11.
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a fair coin is tossed three times, and the events a and b are defined as follows: a: 5at least one head is observed.6 b: 5the number of heads observed is odd.6 a. identify the sample points in the events a, b, a b, ac , and a b. b. find p1a2, p1b2, p1a b2, p1ac 2, and p1a b2 by summing the probabilities of the appropriate sample points. c. use the additive rule to find p1a b2 . compare your answer with the one you obtained in part b. d. are the events a and b mutually exclusive? why?
The evaluated solution for the given question comprises of sample point of a that are {HHT, HTH, THH, HHHT, HHTH, HTHH, THHH} , the event probability is 0.875 and the probability of implementing a, b is 3/4 below under the condition of a fair coin is tossed three times, and the events a and b are defined.
a) Points sample for event a: {HHT, HTH, THH, HHHT, HHTH, HTHH, THHH}
Points sample for event b: {HTT, THT, TTH, HHH}
Points sample for event a b: {HTT, THT, TTH, HHH, HHT, HTH, THH}
Points sample for event ac: {TTT}
Points sample for event a c: {TTT, HHHH}
b) Event a probability= 7/8 = 0.875
Event b probability= 1/2 = 0.5
Event ab probability = 3/8 = 0.375
Event ac probability = 1/8 = 0.125
Event a c probability = 1/16 + 1/8 = 0.1875
c) Probability of a b implementing additive rule
P(a b) = P(a) + P(b) - P(a ∩ b)
P(a ∩ b) = P(a) + P(b) - P(a b)
P(a ∩ b) = (7/8) + (1/2) - (3/8)
P(a ∩ b) = 9/8 - 3/8
P(a ∩ b) = 6/8
P(a ∩ b) = 3/4
d) Hence, events a and b are not mutually exclusive due to the lack of chances of having common sample points {HHH}.
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$2662 + 10% interest for 20 years
Answer:22x121=2662
Step-by-step explanation:
The multiplicand is 22, the multiplier is 121 and the product is 2662.
the cheese head in the image is a triangular prism. the base of the triangle is 12 and the height of the triangle is 8 in. the 3-d is 4 in. what is the volume of the cheese head
The volume of the cheese head is 192 cubic inches.
Explain the term volume
Volume refers to the amount of space that an object or substance occupies in three dimensions. It is typically measured in units such as cubic meters or cubic feet. The volume of an object can be calculated using various formulas, depending on its shape and dimensions.
According to the given information
The volume V of a triangular prism is given by the formula:
V = (1/2) * b * h * L
In this case, the base of the triangle is 12 inches, the height of the triangle is 8 inches, and the length of the prism (depth of the 3D shape) is 4 inches. Substituting these values into the formula, we get:
V = (1/2) * 12 * 8 * 4
V = 192 cubic inches
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Stanley has $13,800 in a savings account that earns 14% annually. The interest is not
compounded. How much will he have in total in 6 months?
Answer:
$14,766.00
Step-by-step explanation:
Interest = principle x rate x time
I = 13800 (.14)(.5)
I = 966
Total:
Principle plus interest
13800 + 966 = 14,766
Helping in the name of Jesus.
obability and Sampling: End-of-Unit
Assessment (B)
Illustrative
iM
İM Mathema
Do not use a calculator. A standard number cube has the numbers 1 through 6 on its
faces.
1. Elena would like to know the average speed that people drive on her street. She
tracks the speed of 30 random cars that drive through with a speedometer. The
mean of Elena's sample is 30 miles per hour, and the MAD (mean absolute deviation)
is 3.
Select all the true statements.
A. Elena would be more likely to get an accurate estimate of the mean speed of
the population by sampling 60 cars instead of sampling 30 cars.
B. The median speed of the sample must be between 25 and 35 miles per hour.
C. Another random sample of 30 cars is likely to have a mean between 24 and 36
miles per hour.
D. The mean speed of these 30 cars is likely to be the same as the mean speed of a
second sample of 30 cars.
E. The mean speed of these random 30 cars is likely to be the same as the mean of
all cars that drive in a residential area.
The true statements are:
A. Elena would be more likely to get an accurate estimate of the mean speed of the population by sampling 60 cars instead of sampling 30 cars.
C. Another random sample of 30 cars is likely to have a mean between 24 and 36 miles per hour.
What is Mean Absolute Deviation (MAD)?Mean Absolute Deviation (MAD) is a measure of variability in a set of numerical data. It is calculated by finding the average absolute difference between each data point and the mean of the dataset.
Elena would be more likely to get an accurate estimate of the mean speed of the population by sampling 60 cars instead of sampling 30 cars. This statement is true. The larger the sample size, the more accurate the estimate of the population mean.Another random sample of 30 cars is likely to have a mean between 24 and 36 miles per hour. This statement is true. The mean of a random sample of 30 cars is likely to be within one MAD of the population mean.Learn about mean here https://brainly.com/question/1136789
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Which number is equivalent to 6%
Answer:
0.06
6/100
Step-by-step explanation:
6% is equivalent to the decimal number 0.06 or the fraction 6/100.
Answer:
6/100 or 0.06
Step-by-step explanation:
hope this helps!
Determine the values of constants a,b,c, and d so that f(x)=ax3 bx2 cx d has a local minimum at the point (0,0) and a local maximum at the point (1,3)
The function f(x) that has a local minimum at (0,0) and a local maximum at (1,3) is f(x) = 2x³ - 3x².
How to calculate the functionFrom the information, we can set up a system of equations as follows:
f'(x) = 3ax² + 2bx + c = 0 (at x=0)
f'(x) = 3ax² + 2bx + c = 0 (at x=1)
Plugging in x=0, we get:
f'(0) = c = 0
Plugging in x=1, we get:
f'(1) = 3a + 2b + c = 0
3a + 2b = -c = 0
3a + 2b = 0 (since c=0)
Solving the system of equations, we get:
a = 2
b = -3
c = 0
d = 0
The function is f(x) = 2x³ - 3x²
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Question
The triangles are similar.
What is the value of x?
Enter your answer in the box.
x =
Answer:
[tex] \frac{36}{12} = \frac{39}{x - 10} [/tex]
[tex] 3 = \frac{39}{x - 10} [/tex]
[tex]3(x - 10) = 39[/tex]
[tex]x - 10 = 13[/tex]
[tex]x = 23[/tex]