Standard deviation and median are less affected by extreme scores, while mode is not affected at all since it represents the most frequently occurring value.
The measure of variation affected most by a few extreme scores is the range, as it considers only the difference between the highest and lowest values in a dataset. However, the mean can also be influenced by extreme scores, causing it to deviate from the central tendency. Standard deviation and median are less affected by extreme scores, while the mode is not affected at all since it represents the most frequently occurring value.
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The measure of variation affected most by a few extreme scores is the range. The range is the difference between the
highest and lowest values in a data set. Extreme scores significantly increase the range, making it a sensitive measure
of variation.
The measure of variation that is affected most by a few extreme scores is the standard deviation.
The reason for this is that the standard deviation is calculated by taking the square root of the sum of squared
deviations from the mean, and the squared deviations from the mean are particularly sensitive to extreme scores.
On the other hand, the mode, range, median, and mean are less affected by a few extreme scores.
The mode is simply the most frequently occurring value in a dataset and is not affected by extreme scores.
The range is the difference between the highest and lowest values in a dataset and can be affected by extreme scores, but only to a limited extent.
The median is the middle value in a dataset, and it is also not affected by extreme scores unless they are extreme
enough to change the position of the middle value.
The mean is the average value in a dataset, and while it can be influenced by extreme scores, its effect is typically less
pronounced than on the standard deviation.
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if there are no other feasible solutions with a larger objective function value in the immediate neighborhood, then the feasible solution is known as
The feasible solution is known as a locally optimal solution.
It may not be the best possible solution for the entire optimization problem.
If there are no other feasible solutions with a larger objective function value.
The immediate neighborhood, then the feasible solution is known as a locally optimal solution.
This means that the solution is optimal within a particular region of the feasible space but may not necessarily be the globally optimal solution. Bhe best possible solution over the entire feasible space.
In other words, a locally optimal solution is the best possible solution. Among all feasible solutions in its immediate neighborhood or region.
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Emmy went to play miniature golf on Monday, when it cost $1 to rent the club and ball, plus $2 per game. Liam went Thursday, paying $1 per game, plus rental fees of $5. By coincidence, they played the same number of games for the same total cost. How many games did each one play?
Emmy and Liam each played 4 games according to the given statement.
What is an equation?An equation is a claim that two expressions are equal, typically indicated by the equals symbol (=). In mathematics, equations are used to simulate real-world scenarios, solve problems, and depict relationships between variables.
Exponents, logarithms, and trigonometric functions can all be used in equations, in addition to basic operations like addition, subtraction, multiplication, and division.
Let us suppose the number of games played = x.
Thus, for Emmy we have:
E = 1 + 2x
For Liam the equation is:
L = 5 + 1x
Equating the two equations we have:
1 + 2x = 5 + 1x
x = 4
Hence, Emmy and Liam each played 4 games according to the given statement.
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what is the answer of this question (please i need help)
Answer:
The answer is B ([tex]x=\frac{6}{5}[/tex])
Step-by-step explanation:
We start with creating labels for the shapes that represent what they value -at first I tried multiplying the 5x by 4 but there wasn't an answer for that.
[tex]5x+4=10[/tex]
First we just simplify,
[tex]5x (-4)=10(-4)[/tex]
[tex]5x=6[/tex]
then divide,
[tex]\frac{5x}{5} =\frac{6}{5}[/tex]
and we end up with:
[tex]x=\frac{6}{5}[/tex]
or
B
A container built for transatlantic shipping is constructed in the shape of a right
rectangular prism. Its dimensions are 4 ft by 9.5 ft by 13 ft. If the container is entirely
full and, on average, its contents weigh 0.05 pounds per cubic foot, find the total
weight of the contents. Round your answer to the nearest pound if necessary
Thus, the on average the contents weight for the transatlantic shipping is found as 24.7 pounds.
Explain about the rectangular prism:a solid, three-dimensional object with six rectangular faces.It is a prism due to its uniform cross-section along its whole length.Volume is a unit of measurement for the amount of 3-dimensional space a thing occupies. Cubic units are used to measure volume.Given dimension of rectangular prism
Length l = 4ft
width w = 9.5 ft
height h = 13 ft
Volume of rectangular prism = l*w*h
V = 4*9.5*13
V = 494 ft³
Now,
1 ft³ = 0.05 pounds
So,
weight of 494 ft³ = 494*0.05 pounds
weight of 494 ft³ = 24.7 pounds
Thus, the on average the contents weigh for the transatlantic shipping is found as 24.7 pounds.
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You deposit $150 in an investment account that earns 6% annual interest compounded annually. You make no additional deposits or withdrawals. What is the balance of this account after 5 years
Answer:200.734
Step-by-step explanation:
150(1+0.06)^t
t=number of years
150(1.060)^5
200.73383664
round
200.734
The balance of this account after 5 years is $200.73
What is Compound interest?Compound interest is the interest earned on the principal and the interest previously accumulated. It is given by
Amount = [tex]P(1+r/n)^n^t[/tex] where P = Principal, r = annual rate of interest, n = number of times interest is compounded per year, & t = time in years.
The given principal is $150 for 5 years & annual interest rate is 6%.
To find the amount compunded annualy at 6% for 5 years substituting the given values in the above formula i.e.
Amount = [tex]P(1+r/n)^n^t[/tex]
Amount = $[tex]150(1+0.06)^5[/tex]
Amount = $200.73
Hence, the total amount accumulated for 5 years will be $200.73
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a random sample of n equal to 64 scores is selected from a normally distributed population with mu equal to 77 and sigma equal to 21. what is the probability that the sample mean will be less than 79? hint: this is a z-score for a sample.
The probability of the sample mean being less than 79 is 77.64%
In order to solve the given problem we have to take the help of Standard error mean
SEM = ∑/√(n)
here,
∑ = population standard deviation
n = sample size
hence, the z-score can be calculated as
z = ( x' - μ)/σ/√(n)
here,
x' = sample mean
μ = population mean
σ = population standard deviation
n = sample size
adding the values into the formula
SEM = σ / √(n)
= 21/√64
= 2.625
z = (x' - μ)/SEM
= (79-77)/2.625
= 0.76
now, using standard distribution table we find that probability of a z-score is less than 0.77 then converting it into percentage
0.77 x 100
= 77%
The probability of the sample mean being less than 79 is 77.64%
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Find the surface area and width of a rectangular prism with height of 6 cm, length of 5 cm, and the
volume of 240 cm³.
Answer:
236 cm^2 and 8 cm
Step-by-step explanation:
width=w
240=6(5)(w)
w=8 cm
area=2[(6)(5)+(6)(8)+(5)(8)]
area=236 cm^2
Use the law of sines to find the indicated side x. ( Assume a=160). Round answer to one decimal place. A= 102, B =28
Using the law of sines, the value of the indicated side x, is calculated to one decimal place as: 125.3.
What is the Law of Sines?The Law of Sines is a trigonometric formula used to relate the side lengths and angles of any triangle. It states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is equal for all three sides of the triangle. Mathematically, this can be represented as:
sin A/a = sin B/b = sin C/c
Thus, we have:
C = 180 - 102 - 28 = 50°
a = 160
A = 102°
c = x = ?
Applying the law of sines, we have:
sin 102/160 = sin 50/x
Cross multiply:
x = sin 50 * 160 / sin 102
x ≈ 125.3
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a rectangular prism has a square base with edge length . its volume is . what does the expression represent?
The expression represents the height of the, rectangular prism has a square base with edge length, which is 3 cm.
Explain in detail about what does the expression represent?The expression represents the height of the rectangular prism with a square base of edge length and volume .
To make this more concrete, let's assume some values for and . Let's say that the edge length of the square base is 4 cm, and the volume of the rectangular prism is 48 cubic cm.
Using the formula for the volume of a rectangular prism, we can write:
Volume = Base Area x Height
Since the base of the rectangular prism is a square with edge length 4 cm, its area is:
Base Area = 4 x 4 = 16 square cm
Substituting the given values into the formula for volume, we get:
48 cubic cm = 16 square cm x Height
To solve for the height, we can isolate it on one side of the equation by dividing both sides by 16 square cm:
48 cubic cm ÷ 16 square cm = Height
3 cm = Height
Therefore, in this scenario, the expression represents the height of the rectangular prism, which is 3 cm.
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a medical researcher wants to estimate , the mean weight of babies born to women over the age of 40. the researcher chooses a random sample of 100 pregnant women who are over 40. using the mean birth weight of the 100 babies in the sample, the researcher calculates the 95% confidence interval for . with 95% confidence, the researcher estimates the mean birth weight of all babies born to women who are over the age of 40 to be between 2935 and 3135 grams. the researcher wants to maintain the 95% level of confidence but report a confidence interval with a smaller margin of error. what should she do? group of answer choices redo the study and choose a different sample of size 100.
Maintain the 95% level of confidence but report a confidence interval with a smaller margin of error, the medical researcher should increase the sample size.
This will provide a more precise estimate of the mean birth weight of babies born to women over the age of 40.
Maintain the 95% level of confidence but report a confidence interval with a smaller margin of error, the researcher should increase the sample size.
The larger the sample size, the smaller the margin of error, which means that the estimated mean birth weight of all babies born to women over the age of 40 will be more precise.
Redoing the study and choosing a different sample of size 100 will not necessarily reduce the margin of error, as the variability in the sample may be the same.
To achieve a smaller margin of error, the researcher needs to increase the sample size.
With a larger sample size, the researcher will have a more representative sample of the population, which will lead to a more accurate estimate of the mean birth weight of all babies born to women over the age of 40.
However, the larger sample size may require more resources and time to collect the data.
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please read the phtot/picture its worth 18 ponits please help its worth 89 percent of my grade
2(4/3) represents the shaded area in the diagram as two rectangles of equal size, each with a length of 4 units and a width of 2/3 units.
4 * 2/3 represents the shaded area in the diagram as a rectangle with a length of 4 units and a width of 2/3 units.
4 * 2 * 1/3 represents the shaded area in the diagram as a rectangle with a length of 4 units, a width of 2 units, and a smaller rectangle with a length of 1 unit and a width of 1/3 units.
What is the area of the rectangle?
To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.
a. The diagram shows 3/5 by dividing the whole rectangle into 5 equal parts horizontally and shading 3 of those parts. This means that the shaded portion represents 3 out of 5 equal parts.
b. The diagram shows 3 * 1/5 by shading one-fifth of the rectangle, and then repeating this process three times. This means that the shaded portion represents three times one-fifth of the whole.
c. The value of 3/5 is equivalent to 0.6 or 60%. This means that if we divide a whole into 5 equal parts, and take 3 of those parts, we have 60% of the whole.
a. The expression 2(4/3) represents the shaded parts of the diagram by first finding the area of one shaded rectangle, which is 4/3. Then, we multiply this area by 2 because there are two shaded rectangles in the diagram. Therefore, 2(4/3) gives us the total shaded area.
b. The expression 4 * 2/3 represents the shaded parts of the diagram by multiplying the width of the shaded rectangle (2 units) by its height (2/3 units), and then multiplying that by the number of shaded rectangles (4). Therefore, 4 * 2/3 gives us the total shaded area.
c. The expression 4 * 2 * 1/3 represents the shaded parts of the diagram by multiplying the length of the shaded rectangle (4 units) by its width (2 units) by its height (1/3 units), and then multiplying that by the number of shaded rectangles (4). Therefore, 4 * 2 * 1/3 gives us the total shaded area.
Hence, 2(4/3) represents the shaded area in the diagram as two rectangles of equal size, each with a length of 4 units and a width of 2/3 units.
4 * 2/3 represents the shaded area in the diagram as a rectangle with a length of 4 units and a width of 2/3 units.
4 * 2 * 1/3 represents the shaded area in the diagram as a rectangle with a length of 4 units, a width of 2 units, and a smaller rectangle with a length of 1 unit and a width of 1/3 units.
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a researcher wants to determine if zinc levels are different between the top of a glass of water and the bottom of a glass of water. many samples of water are taken. from half, the zinc level at the top is measured and from half, the zinc level at the bottom is measured. would this be a valid matched pair test?
Yes, this would be a valid matched pair test. In a matched pair test, two samples are taken from the same group or individual, and the samples are matched on some criteria such as age, sex, or in this case, location in the glass of water.
The researcher is using a matched pair test, which is an acceptable method to account for individual variations and boost the statistical power of the test, by collecting samples from the top and bottom of the glass of water and matching them according to the position. Due to the fact that any additional changes (such as in the source of the water or pollution) should be uniformly distributed across the two groups, this design also enables the researcher to ascertain whether there is a substantial difference in zinc levels between the top and bottom of the glass of water.
A paired t-test will be used to conduct the test in order to see if there is a significant difference between the zinc levels at the top and bottom of the water glass.
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Find the volume of the trapezoidal prism 10m 8m 4m 5m
The volume of the trapezoidal prism is 180 cubic meters.
What are parallel lines?
Parallel lines are two lines in a plane that never intersect. This means that they maintain the same distance between each other at all points.
To find the volume of a trapezoidal prism, we need to multiply the area of the trapezoidal base by the height of the prism.
The trapezoidal base has a length of 10m and 8m, and a height of 4m. The formula for the area of a trapezoid is:
Area = (a + b) * h / 2
where a and b are the lengths of the parallel sides, and h is the height.
Using the formula, we can calculate the area of the trapezoidal base:
Area = (10m + 8m) * 4m / 2
Area = 36m²
Therefore, the volume of the trapezoidal prism is:
Volume = Area of base * Height
Volume = 36m² * 5m
Volume = 180 cubic meters
Therefore, the volume of the trapezoidal prism is 180 cubic meters.
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in a survey of 300 college graduates, 53% reported that they entered a profession closely related to their college major. if 9 of those survey subjects are randomly selected with replacement for a follow-up survey, what is the probability that 3 of them entered a profession closely related to their college major? round to four decimal places.
The probability that 3 of the 9 randomly selected subjects entered a profession closely related to their college major is approximately 0.1665, or 16.65%.
To find the probability that 3 out of 9 randomly selected subjects entered a profession closely related to their college major, we can use the binomial probability formula:
[tex]P(X = k) = (n choose k) * p^k * (1 - p)^{n - k}[/tex]
where:
- P(X = k) is the probability of k successes (in this case, 3 people entering a profession closely related to their major)
- n is the number of trials (9 subjects)
- k is the number of successes (3 people)
- p is the probability of success (53% or 0.53)
- (n choose k) is the number of combinations of n items taken k at a time, which can be calculated as C(n, k) = n! / (k! * (n - k)!)
Plugging in the values, we get:
[tex]P(X = 3) = C(9, 3) * (0.53)^3 * (1 - 0.53)^{9 - 3}[/tex]
First, calculate the combinations (n choose k):
C(9, 3) = 9! / (3! * (9 - 3)!)
C(9, 3) = 9! / (3! * 6!)
C(9, 3) = 362880 / (6 * 720)
C(9, 3) = 84
Now, calculate the probabilities:
[tex]P(X = 3) = 84 * (0.53)^3 * (0.47)^6[/tex]
P(X = 3) = 84 * 0.148877 * 0.013325
P(X = 3) ≈ 0.1665.
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mrs. blue wants her students to be able to write two column geometric proofs. which is the most appropriate way to determine their mastery?
a clinical trial is conducted studying the time it takes a certain allergy medication to be effective. a sample of patients in the trial report that it takes 23 minutes, on average, for them to feel the effects of the medication. the researchers report that their 99% confidence interval is: (19.728,26.272) what is the margin of error? round your answer to three decimal places.
Margin of error is equal to half of this width:
6.544 / 2 = 3.272
What is the margin of error?In a confidence interval, the margin of error is half of the width of the interval.
So, the width of the confidence interval is:
26.272 - 19.728 = 6.544
Margin of error is equal to half of this width:
6.544 / 2 = 3.272
Rounding to three decimal places, the margin of error is 3.272.
This means that the researchers are 99% confident that the true mean time for the medication to take effect falls between 19.728 and 26.272 minutes.
The margin of error tells us how much we can expect the sample mean (23 minutes) to differ from the true mean. So, we can say with 99% confidence that the true mean time it takes for the medication to take effect is within 3.272 minutes of the sample mean.
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The ratio of the weight to the mass is constant. Which statement describes the ratio of the weight to the mass and the value of x in the table?
The ratio of the weight to the mass and the value of x in the table is B) The ratio is 10/98, x = 110.
What is mass and weight?The quantity of matter in an object is measured by its mass, which is commonly expressed in kilogrammes or grammes. Since mass is a scalar quantity, the gravitational field has no effect on it. The force of gravity acting on an object is quantified by weight, which is commonly expressed in newtons or pounds. Weight is a vector quantity that is influenced by the strength of the gravitational field. While an object's mass is constant, its weight might vary depending on the gravitational field.
The ratio of weight to mass according to the given table is:
weight / mass = 196 / 20 = 98/10
The ratio is constant thus for x we have:
1078 / x = 98 / 10
Using cross multiplication we have:
x = 1078 (10) / 98 = 110
Hence, the ratio of the weight to the mass and the value of x in the table is B) The ratio is 10/98, x = 110.
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The complete question is:
i need help with this quick please help
Answer:
19.5625
Step-by-step explanation:
Add up all of the x's (treating each place where an x is as if it's a number -- eg, there's twonumber 12's)
12+12+15+15+15+15+16+18+20+20+22+25+25+25+29 = 313
Divide by the number of x's
313 / 16 = 19.5625
Evaluate the following. Write an exponential function of the form y=ab^x that has the given points 1. (1,5), (2, 7)
Answer:
Step-by-step explanation:
25
=
a
b
−
2
10
=
a
b
1
PLEASE HELP. Lesson 15.3 Tangents and Circumscribed Angles
Proof of Circumscribed Angle Theorem
Given: ZAXB is a circumscribed angle of circle C.
Prove: ZAXB and ZACB are supplementary.
Complete the proof.
A
B
C
If ZAXB is a circumscribed angle of circle C, XA and XB are
Select an answer to the circle
The assumption that AXB is a bounded angle is false, as a result, if AXB is a circumscribed angle of circle C, then AXB and ACB are supplementary.
How to prove circumscribed angles?To complete the proof of the Circumscribed Angle Theorem, use the fact that an inscribed angle of a circle is equal to half of the central angle that intercepts the same arc.
Since angle ∠AXB is circumscribed by the circle, point X lies on the circumference of the circle. Therefore, angles ∠CXA and ∠CXB are inscribed angles that intercept the same arc AB.
By the Inscribed Angle Theorem:
∠CXA = ½∠CAB
∠CXB = ½∠CAB
Adding these two equations:
∠CXA + ∠CXB = ½∠CAB + ½∠CAB
∠CXA + ∠CXB = ∠CAB
Now, observe that angles ∠CAB and ∠ACB form a linear pair, since they are adjacent angles that together make a straight line. Therefore, they are supplementary, which means:
∠CAB + ∠ACB = 180°
Substituting ∠CAB with ∠CXA + ∠CXB:
∠CXA + ∠CXB + ∠ACB = 180°
Finally, ∠AXB and ∠CXB form a linear pair, since they are adjacent angles that together make a straight line. Therefore, they are supplementary, which means:
∠AXB + ∠CXB = 180°
Substituting ∠CXB with ∠CAB - ∠CXA:
∠AXB + ∠CAB - ∠CXA = 180°
Adding ∠CXA to both sides:
∠AXB + ∠CAB = ∠ACB + 180°
Substituting ∠AXB + ∠CAB with 180° (since they are adjacent angles that together make a straight line):
180° = ∠ACB + 180°
Simplifying:
∠ACB = 0°
This is a contradiction, since we know that ∠ACB is a non-zero angle. Therefore, our assumption that ∠AXB is a circumscribed angle must be false. Hence, we have proved that if ∠AXB is a circumscribed angle of circle C, then ∠AXB and ∠ACB are supplementary.
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A researcher administers a treatment to a sample from a population with a mean of m = 60. If the treatment is expected to increase scores and a one-tailed test is used to evaluate the treatment effect, then the null hypothesis would state that m ³ 60.A) TrueB) False
For the given statement after evaluating both the options the correct option is true under the condition that scores increase and null hypothesis is used to find out Treatment effect.
Here, null hypothesis clearly states that there is no significant difference is observed in comparison of sample mean and population mean.
Null hypothesis refers to statistical process which takes certain assumptions regarding two sets of different variables. In the branch of science it is used to find credibility regarding a sample data.
For the given case, the null hypothesis presents that the population mean remains unchanged (m = 60) post treatment, doesn't matter if it is greater than or equal to 60. The alternative hypothesis will be increases the mean for the treatment (m > 60).
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True. Your statement is: A researcher administers a treatment to a sample from a population with a mean of m = 60. If the treatment is expected to increase scores and a one-tailed test is used to evaluate the treatment effect, then the null hypothesis would state that m ≥ 60.
The null hypothesis typically represents no effect or no difference. In this case, the null hypothesis would state that the population mean remains unchanged (m = 60) after the treatment, not that it is greater than or equal to 60. The alternative hypothesis would be that the treatment increases the mean (m > 60).
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true or false: a linear programming problem can have an optimal solution that is not a corner point. select one: true false
It is true that a linear programming problem can have an optimal solution that is not a corner point.
How given statement is true? Explain further?In linear programming, the optimal solution represents the point where the objective function is optimized while still satisfying all the constraints.
In some cases, the optimal solution may occur at a corner point of the feasible region, where two or more of the constraints intersect.
However, it is possible for the optimal solution to occur at a point that is not a corner point, but rather lies on an edge or a line segment of the feasible region.
This can occur when the objective function is parallel to one of the constraint lines or when there are redundant constraints that limit the feasible region.
Therefore, it is true that a linear programming problem can have an optimal solution that is not a corner point.
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19.
Solve the problem.
2
Find the critical value XR corresponding to a sample size of 5 and a confidence
level of 98%.
(1 point)
O11.143
00.297
13.277
00.484
The critical value of the chi-square distribution corresponding to a sample size of 5 and a confidence level of 98% is given as follows:
0.297 and 13.277.
How to obtain the critical value?To obtain a critical value, we need three parameters, given as follows:
Distribution.Significance level.Degrees of freedom.Then, with the parameters, the critical value is found using a calculator.
The parameters for this problem are given as follows:
Chi-square distribution.1 - 0.98 = 0.02 significance level.5 - 1 = 4 degrees of freedom.Using a chi-square distribution calculator, the critical values are given as follows:
0.297 and 13.277.
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Suppose that the miles-per-gallon (mpg) rating of passenger cars is a normally distributed random variable with a mean and a standard deviation of 33.8 and 3.5 mpg, respectively. Use Table 1.
a. What is the probability that a randomly selected passenger car gets more than 35 mpg?
b. What is the probability that the average mpg of four randomly selected passenger cars is more than 35 mpg?
c. If four passenger cars are randomly selected, what is the probability that all of the passenger cars get more than 35 mpg?
the probability that a randomly selected passenger car gets more than 35 mpg is approximately 0.3665.
the probability that the average mpg of four randomly selected passenger cars is more than 35 mpg is approximately 0.087
the probability that all of the passenger cars get more than 35 mpg is approximately 0.015.
We need to find [tex]P(X > 35),[/tex] where X is the mpg rating of a randomly selected passenger car.
The standard normal distribution and Table 1, we have:
[tex]z = (35 - 33.8) / 3.5 = 0.34[/tex]
[tex]P(X > 35) = P(Z > 0.34) = 0.3665[/tex]
[tex]P(\bar X > 35)[/tex], were [tex]\bar X[/tex] is the sample mean mpg rating of four randomly selected passenger cars.
The population standard deviation, we use the t-distribution with [tex]n-1[/tex] degrees of freedom (were [tex]n = 4[/tex]) and Table 1. We have:
[tex]t = (35 - 33.8) / (3.5 / \sqrt(4)) = 1.83[/tex]
Using Table 1 with 3 degrees of freedom ([tex]n-1 = 4-1[/tex]), we find:
[tex]P(T > 1.83) = 0.087[/tex]
We need to find [tex]P(X1 > 35[/tex] and [tex]X2 > 35[/tex] and [tex]X3 > 35[/tex] and [tex]X4 > 35[/tex]), where X1, X2, X3, and X4 are the mpg ratings of four randomly selected passenger cars.
Since the mpg ratings of the four cars are independent and identically distributed, we have:
[tex]P(X1 > 35[/tex]and[tex]X2 > 35[/tex] and [tex]X3 > 35[/tex] and [tex]X4 > 35[/tex]) =[tex]P(X > 35)^4[/tex]
From part (a), we know that[tex]P(X > 35) = 0.3665.[/tex]
[tex]P(X1 > 35[/tex]and [tex]X2 > 35[/tex] and[tex]X3 > 35[/tex] and [tex]X4 > 35) = 0.3665^4 \approx 0.015[/tex]
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Jack is running a 5-mile race with Jill. Jack's run is represented by the function d = 0.05t, where d is
distance traveled in miles and t is the minutes run. Jill's run is represented by d = 0.04t+ 0.5.
Part A
How do the graphs of Jack's representative function and Jill's representative function compare to the
graph of the linear parent function?
Part B
What do the effects of comparing Jack and Jill's functions to the linear parent function mean in the real-
world context?
A) Their graphs will be different from the graph of the linear parent function. B) In real-world context, comparing functions can be useful in many scenarios, such as predicting sales or analyzing trends.
What is y-intercept?The y-intercept is the point where the graph of a function intersects with the y-axis. It is the point at which the value of x is 0.
According to question:Part A:
The linear parent function is represented by y = mx + b, where m is the slope and b is the y-intercept. The slope of the linear parent function is constant, while the y-intercept can vary.
In Jack's function, d = 0.05t, the slope is 0.05, which means that for every minute he runs, he travels 0.05 miles. The y-intercept is 0, which means that he starts at 0 miles.
In Jill's function, d = 0.04t + 0.5, the slope is 0.04, which means that for every minute she runs, she travels 0.04 miles. The y-intercept is 0.5, which means that she starts at 0.5 miles.
Both functions are linear, but they have different slopes and y-intercepts. Therefore, their graphs will be different from the graph of the linear parent function.
Part B:
Comparing Jack and Jill's functions to the linear parent function can give us insights into their race. The fact that their functions are linear means that they are running at a constant rate. However, the different slopes and y-intercepts mean that they are running at different rates and starting at different distances.
For example, we can see from their functions that Jack is running faster than Jill since his slope is larger. We can also see that Jill has a head start since her y-intercept is larger. By comparing their functions, we can make predictions about who will win the race or how far ahead one person will be at a certain time.
In real-world context, comparing functions can be useful in many scenarios, such as predicting sales or analyzing trends. By understanding the relationship between variables, we can make informed decisions and predictions.
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Two friends, Julieta and Camila, had just bought their first cars. The equation
y = 38.8x represents the number of
miles, y, that Camila can drive her car for every a gallons of gas. Julieta uses 10 gallons of gas to drive 333 miles in her
car.
We can use the equation y = 38.8x to find how many miles Camila can drive her car for each gallon of gas, and then use that information to find how many gallons of gas she would need to drive the same distance as Julieta.
Julieta drives 333 miles using 10 gallons of gas, so her car can travel 333/10 = 33.3 miles per gallon.
To find how many miles Camila's car can travel per gallon, we can use the equation y = 38.8x, where x is the number of gallons of gas. If Camila uses 1 gallon of gas, then y = 38.8(1) = 38.8 miles. Therefore, Camila's car can travel 38.8 miles per gallon.
To travel 333 miles like Julieta, Camila would need to use:
333 miles / 38.8 miles per gallon = 8.58 gallons of gas
Therefore, Camila would need to use 8.58 gallons of gas to travel the same distance as Julieta.
The following table shows Jace's earnings based on the number of hours that he works.
Number of hours 111 222 333
Jace's Earnings \$20$20dollar sign, 20 \$30$30dollar sign, 30 \$40$40dollar sign, 40
Are Jace's earnings proportional to the number of hours that he works?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
Yes
(Choice B)
B
No
The correct answer to the given problem is choice B - No.
Jace's earnings are not proportional to the number of hours that he works because if he worked twice as many hours, he would earn twice as much but he is not earning twice the amount.
Jace's earnings are not proportional to the number of hours that he works. Proportional means that one quantity is a constant multiple of the other. In this case, if Jace's earnings were proportional to the number of hours he works, we would expect that if he worked twice as many hours, he would earn twice as much. However, we can see from the table that this is not the case.
For example, when Jace works 1 hour, he earns $20, but when he works 2 hours, he earns $30, which is not double his earnings for 1 hour of work.
Therefore, Jace's earnings are not proportional to the number of hours that he works.
Hence, the correct option is "B".
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Students made a craft project at camp. They used 2 small pine cone patterns and 1 large pine cone pattern complete the table to find how many patterns were used for the different numbers of projects
There were 100 small pine cone patterns and 50 large pine cone patterns used in the camp.
When 50 students constructed one craft project each using two little pine cone patterns and one giant pine cone pattern, it is the question of how many small and large pine cone patterns were utilised overall:
We can begin by figuring out how many little pine cone patterns were utilized overall to solve this.
Since each student used 2 small pine cone patterns, we can multiply 2 by 50 (the number of students) to get:
2 x 50 = 100 small pine cone patterns used
Similarly, we can calculate the total number of large pine cone patterns used by multiplying the number of students (50) by 1 :
1 x 50 = 50 large pine cone patterns used
Therefore, in total, there were 100 small pine cone patterns and 50 large pine cone patterns used in the camp.
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--The complete Question is, If a camp has 50 students and each student made one craft project using 2 small pine cone patterns and 1 large pine cone pattern, how many small and large pine cone patterns were used in total? --
Baseball Field Problem
Find the amount of fencing, dirt, and sod needed to rebuild the baseball field.
380 to the fence
Fencer
'Is'
Goss
Dit
Dirf
Cr=10¹
Grass
Grass
Fence
Dint
Note: Not drown to scale
S
15'
The baseball field's fence, soil and sod requirements will be-: Length of fencing ≈ 1410.5 feet, Area of the sod ≈ 118017.13 ft², Area of of the field covered with dirt ≈ 7,049.6 ft²
How to find the area of sector of Circle?To find the area of a sector of a circle:
The sector's central angle, expressed in degrees, can be measured or calculated.Calculate or measure the circle's radius (r).Use this equation: Sector area is equal to (θ/360) * r2 *.Insert the formula's values for r and θ.Apply the formula to the area to calculate it.Round the outcome to the required degree of precision.The amount of fencing, dirt, and sod can be found using the formula for finding the circumference of a circle and the area of a circle as follows;
Circle's Area can be given by, (A)= π × r²
Circle's Circumference can be given by, (C) = 2 × π × r
Where, 'r' denotes the radius of the circle
The area of a quarter of a circle is therefore= A ÷ 4
The perimeter of a quarter of a circle = C ÷ 4
Taking reference from the image,
Fencing; (1/4) × 2 × π × 380 + 2 × 15 + 2 × 380 + (1/4) × 2 × π × 15
Fencing = 190·π + 790 + 7.5·π = 197.5·π + 790 ≈ 1410.5
The fencing ≈ 1410.5 feet
Grass; π/4 × (380 - 6)² + 87² - π/4 × (87 + 30)² + 2 × 380 × 15 + π/4 × 15² - (3/4) × π × 10² - 25·π = 31528·π + 18969 ≈ 118017.13
The area covered by the sod is about 118017.13 square feet
Dirt; π/4 × 380² - π/4 × (380 - 6)² + π/4 × (87 + 30)²- 87² + π·100 = (18613·π - 30276)/4 ≈ 7049.6
The area occupied by the dirt is about 7049.6 square feet
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Complete Question:Find the amount of fencing, dirt, and sod needed to rebuild the baseball field?(refer to image attached for dimensions of field)
During a flood, there were 6000 acres of land under water. After 2 days, only 3375 acres of land were under water. Assume that the water receded at an exponential rate. Write a function to model this situation that has a B-value of 1.
where t is measured in days, and A(t) represents the amount of flooded land at time t. This function has a B-value of -0.3118.
To model the situation of the flood, we can use an exponential decay function, which represents the decreasing amount of flooded land over time. The function can be written as:
[tex]A(t) = A0 * e^{(-kt)}[/tex]
where A(t) is the amount of flooded land at time t, A0 is the initial amount of flooded land, k is a constant representing the rate of decay, and e is the mathematical constant approximately equal to 2.718.
To determine the value of k, we can use the given information that after 2 days, only 3375 acres of land were under water. Substituting t = 2 and A(t) = 3375 into the equation above, we get:
[tex]3375 = A0 * e^{(-2k)[/tex]
We also know that initially, there were 6000 acres of land under water. Substituting A0 = 6000 into the equation above, we get:
Dividing both sides by 6000, we get:
ln(0.5625) = -2k[tex]ln(0.5625) = -2k[/tex]
Taking the natural logarithm of both sides, we get:
[tex]ln(0.5625) = -2k[/tex]
Solving for k, we get:
[tex]k = -ln(0.5625)/2[/tex]
k ≈ 0.3118
Therefore, the function to model the situation of the flood is:
[tex]A(t) = 6000 * e^{(-0.3118t)}[/tex]
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