after calculating both the expressions we can conclude that both expressions represent the same value of 12.
what is expression ?Mathematical operations including multiplication, division, addition, and subtraction are possible. The construction of an expression looks like this: Expression, number, and mathematical operator Numbers, variables, and functions are the elements of a mathematical expression (such as addition, subtraction, multiplication, and division, etc.). Expressions and phrases can be contrasted. Expressions are any equations that comprise numbers, variables, and an arithmetic operation. They are occasionally referred to as algebraic expressions. For instance, the value of m in the computation of 4m + 5 is the same as the word m in the provided equation, which has been separated from the figures 4m and 5 by the mathematical symbol +.
given,
Since subtracting a negative integer is equivalent to adding its positive counterpart, the expressions "10 - (-2)" as well as "-10 + 2" have the same meaning.
To be more precise, "10 - (-2)" denotes starting with a value of 10 and then deducting a negative value of -2. The positive value of an amount that is negative may be subtracted without affecting it, and vice versa. Therefore, "10 - (-2)" equals "10 + 2," making 12 the result.
The expression "-10 + 2" on the opposite hand suggests that we start with an amount of -10 and subsequently add a value of 2.
A positive number is equal to its negative counterpart when added to a negative number. Because of this, "-10 + 2" equals "-10 - (-2)", which also equals 12.
Therefore, both expressions represent the same value of 12.
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(T/F) If the size of a sample is at leastâ 30, then you can useâ z-scores to determine the probability that a sample mean falls in a given interval of the sampling distribution.
The statement "If the size of a sample is at least 30, then you can use a z-scores to determine the probability that a sample mean falls in a given interval of the sampling distribution." is true because when the sample size is at least 30, the Central Limit Theorem applies and the sampling distribution of the sample mean can be approximated by a normal distribution.
If the size of a sample is at least 30, the Central Limit Theorem (CLT) applies, which states that the distribution of sample means is approximately normal, regardless of the underlying distribution of the population, as long as the sample size is sufficiently large.
When the sample size is at least 30, the sampling distribution of the sample mean can be approximated by a normal distribution, and z-scores can be used to calculate probabilities of sample means falling in a given interval.
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Toshi predicted that he will perform a card trick successfully 95% of the time. He went on to perform the card trick successfully 24 out of 30 times. How did Toshi’s prediction compare with his actual results?
Toshi's actual results were significantly different from his prediction. Specifically, his actual success rate of 80% was lower than his predicted success rate of 95%.
What is probability?Probability is a way to gauge how likely or unlikely something is to happen. It is denoted by a number between 0 and 1, with 1 denoting a certain event and 0 denoting an impossibility.
According to question:Toshi's prediction was that he would perform the card trick successfully 95% of the time. This means that out of 100 card tricks, he expects to perform the trick successfully in 95 of them. We can represent this mathematically by:
P(success) = 0.95
This is the probability of success for one card trick.
Toshi actually performed the card trick 30 times and was successful in 24 of them. We can represent this as:
P(actual success) = 24/30 = 0.8
This is the proportion of successful card tricks that Toshi actually performed.
To compare Toshi's prediction with his actual results, we can use probability theory. The probability of getting exactly x successes in n trials when the probability of success is p is given by the binomial distribution formula:
P(x) = (n choose x) * pˣ * [tex](1-p)^(n-x)[/tex]
In this case, we can use the formula to calculate the probability of getting exactly 24 successes in 30 trials if Toshi's prediction of 95% success rate is accurate. This is given by:
P(24 successes) = (30 choose 24) * 0.95²⁴ * 0.05⁶ ≈ 0.0045
This means that if Toshi's prediction is accurate, the probability of getting exactly 24 successes in 30 trials is very low (less than 0.5%).
Therefore, we can conclude that Toshi's actual results were significantly different from his prediction. Specifically, his actual success rate of 80% was lower than his predicted success rate of 95%.
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A rectangular box has a volume of 3,840 cubic inches. The length of the box is 20 inches and the height of the box is 16 inches. Determine the width of the box. Question 4 options: 11 inches 12 inches 13 inches 14 inches
The width of the rectangular box is 12 inches.
How to determine the width of the rectangular box?Remember that the volume of a box of length L, width W, and height H is:
V = H*W*L
Here the volume is 3,840 cubic inches. The length of the box is 20 inches and the height of the box is 16 inches. Replacing that in the formula we will get:
3840 = 20*16*W
Solving that for W we will get:
3840/(20*16) = W
12 = W
The width is 12 inches.
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Vectors u and v are shown in the graph. vector u with initial point at the origin and terminal point at negative 10 comma negative 7 and vector v with initial point at the origin and terminal point at negative 8 comma 4 What is
[tex]proj _{v}u[/tex]
?
Answer:
im sorry i couldnt help myself
Step-by-step explanation:
How could you mathematically prove that the elevation on ramp B is steeper than ramp A? (without using logic)
Elevation on ramp B is more steep than ramp A.
What is elevation?"Elevation" typically refers to the height of a location above sea level. It is often used in geography and topography to describe the height of a mountain or the altitude of a city or other location. Elevation is usually measured in feet or meters, and it can have a significant impact on climate, weather patterns, and other environmental factors.
What is steep?"Steep" can have a few different meanings depending on the context. It can refer to a steep slope or incline, such as a steep hill or mountain. It can also mean a high price or cost, as in "the price is too steep for me." Additionally, "steep" can refer to the act of soaking something in hot water in order to extract flavor, as in steeping a tea bag in hot water.
For RampA:
tanα=36/30
tanα=1.2
For Ramp B:
tanβ=36/20
tanβ=1.8
Therefore for Ramp B angle is more than Ramp A and incase of tangent function value of angle increases with the angle measures.
So β>α.
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The diameters of cherry tomatoes produced by a large farm have an approximately Normal distribution, with a
mean diameter of 22 mm and a standard deviation of 2. 5 mm. After they are picked and washed, tomatoes with a
diameter of at most 15 mm or at least 30 mm are rejected and not sold. What proportion of such tomatoes are
rejected?
Find the z-table here.
O 0. 0033
O 0. 0201
O 0. 9799
O 0. 9967
The proportion of cherry tomatoes that are rejected based on their diameter is 0.0033. (option a).
To use the CDF, we need to standardize the diameter values using the z-score formula:
z = (x - μ) / σ
where z is the z-score, x is the diameter value, μ is the mean diameter, and σ is the standard deviation.
For tomatoes with a diameter of at most 15 mm, we have:
z = (15 - 22) / 2.5 = -2.8
For tomatoes with a diameter of at least 30 mm, we have:
z = (30 - 22) / 2.5 = 3.2
Next, we use the z-table to find the area under the Normal distribution curve that corresponds to these z-scores. For a z-score of -2.8, the area is 0.0026. For a z-score of 3.2, the area is 0.9993.
Finally, we add these two areas together to get the total proportion of rejected tomatoes:
proportion = 0.0026 + (1 - 0.9993) = 0.0033
Hence the correct option is (a).
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see the scatter plot of Wins compared to Free Throw Attempts per Game.
Then use the scatterplot to write your line of best fit and determine the correlation.
I'm confused what's being asked here...but if you're looking for someone to check it then:
The line of best fit is drawn correctly; there are about the same amount of dots on the top and bottom of the line.
And the correlation is positive
Que tanto mas alto era la calificacion mas alta del examen que la calificacion mas baja
As per the fraction, the lowest score in the examination is 44.
Let's consider the given information. We are told that the highest score and the lowest score in an examination differ by 55 marks. We can represent the highest score as x and the lowest score as y. Therefore, we have:
x - y = 55 ----- equation 1
We are also given that the higher score, which is x, is 9/4 times the lower score, which is y. This can be represented as:
x = (9/4)y
We can use this equation to substitute x in equation 1 and solve for y.
Substituting x in equation 1, we get:
(9/4)y - y = 55
Simplifying the above equation, we get:
(5/4)y = 55
Multiplying both sides by 4/5, we get:
y = 44
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Complete Question:
In an examination, the highest score and the lowest score are different by 55 and the higher one was 9/4 times the lower one. Find the lowest score.
Dylan is 11 3/4 years old. Camden is 1 3/8 years older than Dylan and Jane is 1 1/5 older than Camden. How old is Jane?
Answer: 14.325 years old
Step-by-step explanation:
Dylan is 11 3/4 you add 1 3/8 to get camdens age of 13 1/8 add 1 1/5 to get janes age of 14.325 or as a fraction is 573/40
Find the amount of money Lee can afford to borrow using the banker's rule. Lee makes $24,700 annually. What is the amount that can be borrowed?
Answer: $31,920.
Step-by-step explanation:
The banker's rule is a method used by lenders to determine the maximum amount of money that a borrower can afford to repay. According to this rule, the maximum amount of money that Lee can afford to borrow is determined by multiplying his annual income by a factor of 0.28.
Using this rule, the amount that Lee can afford to borrow can be calculated as:
Maximum affordable monthly payment = 0.28 x monthly income
Maximum affordable monthly payment = 0.28 x (24700/12)
Maximum affordable monthly payment = 0.28 x 2058.33
Maximum affordable monthly payment = 576.66
Therefore, Lee can afford to make monthly payments of up to $576.66. To calculate the total amount he can borrow, we need to determine the total cost of the loan, including principal and interest.
Assuming a 5-year loan with an interest rate of 4%, the total cost of the loan can be calculated using an online loan calculator or spreadsheet software.
Plugging in the numbers, the total amount that Lee can borrow is approximately $31,920.
It's important to note that this calculation is based on the banker's rule and assumes that Lee has no other debt obligations. Actual loan approval and loan amounts may vary depending on other factors such as credit score, debt-to-income ratio, and other lender-specific requirements.
Find the area.
Area =
6 m
10 m
square meters
Answer:
32m
Step-by-step explanation:
area= L×B
L= 10m ×2 =20m
B= 6m×2 =12m
Area= 20m + 12m = 32m
The probability that a contestant played an electric guitar is 0.8, the probability that a contestant was dressed in sequins is 0.4, and the probability that a contestant played an electric guitar or was dressed in sequins is 0.9.
What is the probability that a randomly chosen contestant played an electric guitar and was dressed in sequins?
By probability, the likelihood that a candidate chosen at random played an electric guitar and wore sequins is 0.3.
explain probability.Using probabilities, one can determine how likely something is to occur.. It is represented by a number between 0 and 1, with 1 denoting a certain event and 0 an impossibility.
For instance, you can get either heads or tails when you flip a coin. There is only one way to get heads and two outcomes, hence the probability of receiving heads is 0.52.
The likelihood that a competitor played an electric guitar is 0.8, the likelihood that they were wearing sequins is 0.4, and the combined likelihood that they both played an electric guitar and wore sequins is 0.91.
The following formula can be used to determine the likelihood that a competitor chosen at random played an electric guitar and wore sequins:
P(A and B) equals P(A) times P(B|A)
where there are two events, A and B.
In this instance, A stands for the competitor who played an electric guitar, and B is for the person who wore sequins.
P(A) is known to equal 0.8. and P(B) = 0.4.
We also know that P(A or B) = 0.9.
Using the following equation to determine the likelihood of two events occurring together:
P(A or B) = P(A) + P(B) - P(A and B)
we can find P(A and B):
P(A and B)
= 0.8 + 0.4 - 0.9
= 0.3
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Use inverse operations to solve each of the following quadratic equations. Put each of your responses in the simplest radical form possible.
The given quadratic equations by solving using inverse operations gives,
(a) x = ±2√2, (b) x = ±3√2 + 5, (c) x = ±4√2, (d) x = ±√90 - 2 and (e) x = 4 ±3√3.
Given are some quadratic equations.
We have to solve this using the inverse operations.
Inverse operations are operations which undo the operation which is done to the equation.
(a) 1/2 x² - 4 = 0
Adding both sides by 4,
1/2 x² = 4
Multiplying both sides by 2,
x² = 8
Taking the square root on both sides,
x = ±√8 = ±2√2
(b) (x - 5)² = 18
Taking the square root on both sides,
x - 5 = ±√18
x - 5 = ±3√2
Adding 5 on both sides,
x = ±3√2 + 5
(c) 2x² + 7 = 71
Subtracting by 7 on both sides,
2x² = 64
Dividing by 2 on both sides,
x² = 32
Taking the square root on both sides,
x = ±4√2
(d) 5 (x + 2)² + 37 = 487
Subtracting by 37 on both sides,
5 (x + 2)² = 450
Dividing by 5 on both sides,
(x + 2)² = 90
Taking the square root on both sides,
x + 2 = ±√90
Subtracting by 2 on both sides,
x = ±√90 - 2
(e) (x - 4)² /3 + 8 = 17
Subtracting by 8 on both sides,
(x - 4)² /3 = 9
Multiplying both sides by 3,
(x - 4)² = 27
Taking the square root on both sides,
x - 4 = ±3√3
Adding both sides by 4,
x = 4 ±3√3
Hence the values are found.
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0.305 in word form??
help me please
Answer:
three hundred five thousanths
Step-by-step explanation:
What is the period for the following graph?
A. 180
B. 270
C. 90
D. 360
The period for the following graph is 90 degrees. So correct option is C.
Describe Period?In mathematics, a period is a specific type of repetition in a function or a sequence. A period is the smallest positive value of a constant T for which a function or a sequence f(x + T) = f(x) for all x.
Periods are used to describe the behavior of functions and sequences that exhibit a repeating pattern. The length of the period determines the frequency of the pattern, and it is often used to describe the periodicity of functions in various applications, such as signal processing, harmonic analysis, and Fourier series.
For example, the sine function sin(x) is periodic with a period of 2π. This means that sin(x + 2π) = sin(x) for all x. Similarly, the cosine function cos(x) is also periodic with a period of 2π. Other common examples of periodic functions include the tangent function, cotangent function, and exponential function.
In addition to their applications in mathematics, periods also have practical applications in fields such as physics, engineering, and computer science, where they are used to model periodic phenomena such as waves and oscillations.
Overall, periods are an important concept in mathematics and are used to describe the repeating patterns that are found in many mathematical functions and sequences.
The period for the following graph is 90 degrees.
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Look at this set of 5 numbers:
32 52 29 32 25
Which value would change the most if the number 80 replaced the number 25 in the set?
The measure of central tendency that will change the most in the data set is: Mean
How to find the measure of central tendency?The mean is defined as the average value of a distribution which is obtained by dividing the sum of the values by the frequency.
The median is defined as the number at the middle of the distribution. It is obtained by arranging the values in ascending order and picking the mid value.
The mode is defined as the value which has the most number of occurrences in the distribution.
The set of numbers can be arranged as:
25, 29, 32, 32, 52
The mean = 34
Mode = 32
Median = 32
If we replace 25 with 80, we will have:
Mean = 45
Mode = 32
Median = 32
Thus, the mean will change the most
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The perimeter of a triangle is 73 inches. If the second side is 5 inches longer than twice the first side, and the third is 4 inches less than twice the first side how long is each side?
Using the formula for the perimeter of a triangle, x + (2x+5) + (2x-4) = 73. Solving for x, so the first side is 18 inches, the second side is 41 inches, and the third side is 32 inches.
What is perimeter?Perimeter is the total distance around the outside of a closed two-dimensional shape, such as a polygon or a circle. It is found by adding the lengths of all the sides of the shape.
What is equation?An equation is a mathematical statement that shows the equality of two expressions or values, often with one or more variables that can be solved for.
According to the given information :
Let the first side of the triangle be x.
Then, the second side is 2x + 5, and the third side is 2x - 4, according to the given conditions.
The perimeter of the triangle is the sum of the lengths of its sides, so we can write:
x + (2x + 5) + (2x - 4) = 73
Simplifying the equation:
5x + 1 = 73
5x = 72
x = 14.4
Therefore, the first side of the triangle is 14.4 inches, the second side is 2(14.4) + 5 = 33.8 inches, and the third side is 2(14.4) - 4 = 24.8 inches.
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Simon wants to fill 8 punch bowls for a birthday party. Each punch bowl holds 9 1/5 quarts of punch. How much punch will Simon need?
Write your answer as a fraction or as a whole or mixed number.
Punch that Simon needs in fraction is 73[tex]\frac{3}{5}[/tex] quarts.
What is fraction?
Part of a whole is a fraction. The quantity is written as a quotient in mathematics, where the numerator and denominator are divided. Each is an integer in a simple fraction. Whether it is in the numerator or denominator, a complex fraction contains a fraction. The numerator and denominator of a correct fraction are opposite each other.
Here number of bowls punch for party = 8
Each punch bowl holds 9 1/5 quarts of punch .
Then converting into improper fraction then [tex]9\frac{1}{5}=\frac{45+1}{5}=\frac{46}{5}[/tex]
Now total punch Simon needs to fill 8 bowls is,
=> [tex]8\times\frac{46}{5}=\frac{368}{5}[/tex] = 73[tex]\frac{3}{5}[/tex].
Hence Punch that Simon needs in fraction is 73[tex]\frac{3}{5}[/tex] quarts.
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50 POINTS
The average speed of a baseball line drive is 82 miles per hour. Josiah practiced a new technique to improve his hitting speed. His coach recorded the speed of 45 random hits during practice and found that his average speed using the new technique was 83.2 miles per hour, with a standard deviation of 4.6 miles per hour.
Part A: State the correct hypotheses if Josiah is trying to prove the new technique is an improvement over the old technique. (2 points)
Part B: Identify the correct test and check the appropriate conditions. (4 points)
Part C: Carry out the test and determine if there is sufficient evidence at the 0.01 level that Josiah's technique has improved his drive speed.
On solving the provided question, we can say that As a result, we lack sufficient data at the hypothesis 0.01 level to declare that Josiah's new strategy has increased his driving speed.
What is null hypothesis?A null hypothesis is a statistical hypothesis that states that a certain collection of observations has no statistical significance. Hypotheses are examined using sample data to determine their viability. It is also known as "zero" and is represented by the symbol H0. Researchers begin with the assumption that there is a relationship between the variables. The null hypothesis, on the other hand, asserts that there is no such link. Although the null hypothesis may not appear to be significant, it is an important component of research.
Part A: The following are the hypotheses for Josiah's test:
There is no statistically significant change in the average speed of Josiah's hits utilising the old and new techniques. In scientific notation: H0 = 1 - 2 = 0, where 1 represents the population mean speed of hits using the old approach and 2 represents the population mean speed of hits using the new technique.
Alternative hypothesis: There is a substantial difference in the average speed of Josiah's hits when employing the old and new techniques, with the new technique producing a faster average speed. In mathematical terms: Ha: 1 - 2 0.
Part B: We'll use a t-test because we're comparing two means and don't know the population standard deviation. We will assume that the sample sizes are big enough for the Central Limit Theorem to apply, and that the sample means have a normal distribution. We also suppose that the two samples are independent, which means that the speed of one strike is independent of the speed of the other.
Part C: To run the test, we must compute the test statistic and compare it to the critical value with 44 degrees of freedom (n1 + n2 - 2).
The test statistic is calculated as follows:
[tex]t = (x1 - x2 - 0) / (s / \sqrt(n1 + n2 - 2))[/tex]
where x1 represents the sample mean speed using the old approach, x2 represents the sample mean speed using the new technique, s represents the pooled standard deviation, and n1 and n2 represent the sample sizes.
When we plug in the values, we get:
[tex]t = (82 - 83.2 - 0) / (4.6 / \sqrt(45)) = -2.06[/tex]
At the 0.01 significance level, the critical value for a one-tailed t-test with 44 degrees of freedom is -2.681. We cannot reject the null hypothesis since our test statistic (-2.06) is bigger than the crucial threshold.
As a result, we lack sufficient data at the 0.01 level to declare that Josiah's new strategy has increased his driving speed.
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Describe his mistake
Answer:
In (-3)^2, Henry multiplied -3 by 2. That is not correct. (-3)^2 = (-3)(-3) = 9. Additionally, a^3 • a^4 = a^7, and so
[tex] {( - 5ab)}^{3} \times {( - 3 {a}^{2} {b}^{2} )}^{2} [/tex]
[tex] {( - 5)}^{3} {a}^{3} {b}^{3} \times ( { - 3)}^{2} {a}^{4} {b}^{4} [/tex]
[tex]( - 125 \times 9) {a}^{7} {b}^{7} = 1125 {a}^{7} {b}^{7} [/tex]
48 students took an arithmetic test. If 36 students passed the test, what percent of students have passed? Show your work using the
scratchpad.
The percentage of the students who passed the test is
Answer step by step due tmrw
The interior angles measure 160° and the exterior measure 200°
How to find the angles?The sum of the interior angles of a polygon of n sides is:
(n - 2)*180
here n = 18
(18 - 2)*180 = 2880
divide that by the number of sides
2880/18 = 160°
That is the measure of each interior angle, and the exteriors are such that the sum is 360, then:
a + 160 = 360
a = 360 - 160 = 200
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A group of medical professionals predicts that the number of yearly occurrences of a disease will decrease from the year 2008 to the year 2016. They constructed a spreadsheet with formulas to display their predictions. How many occurrences of the disease do they predict in the year 2016?
One way to predict occurrences of a disease for a future year based on previous years' data is to use exponential modeling.
How can we predict occurrences of disease for year mathematically based on previous years data?Specifically, the formula for exponential growth or decay can be used to project the number of cases for a future time period based on the growth or decline rate observed in the past.
For example, let's say that we have data on the number of cases of a certain disease for the past 10 years. We can use this data to fit an exponential model that describes the growth or decline rate of the disease over time.
Once we have this model, we can use it to predict the number of cases for a future year. For instance, if the model predicts that the disease will grow at a rate of 5% per year, we can use this rate to estimate the number of cases for the next year by multiplying the current number of cases by 1.05. By doing this, we can forecast the occurrence of the disease for the next year based on the previous years' data.
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you want to determine what uniform color shirt is the most preferred among 7th grade students. You survey 6 random students in your art class. 4 choose red, so you conlude that red us the preferred color of shirt. is your conclusion valid. explain.
The conclusion that red is the preferred color of shirt among 7th grade students based on a survey of 6 random students in an art class is not necessarily valid due to the small sample size, sampling bias, and lack of generalizability.
How to determine if the conclusion is valid.The sample size of six pupils is tiny and may not be typical of the overall seventh-grade population. It's probable that the six students in the art class have different preferences or biases than the other seventh-grade students.
Also, the sample of six pupils is drawn at random from an art class rather than from the total 7th grade population. Students who are interested in art may have different preferences than students who are not. This can add bias into the sample.
Finally, the language of the survey question is critical. If the survey question specifically asks about the most chosen color of shirt among 7th grade kids in general, the conclusion that red is the most preferred color of shirt follows.
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An estimator is consistent if as the sample size decreases, the value of the estimator approaches the value of the parameter estimated. (True or False)
The statement "An estimator is consistent if as the sample size decreases, the value of the estimator approaches the value of the parameter estimated" is False.
Consistency is an important property of estimators in statistics. An estimator is consistent if its value approaches the true value of the parameter being estimated as the sample size increases.
In other words, if we repeatedly take samples from the population and compute the estimator, the values we obtain will be close to the true parameter value.
This is an essential characteristic of a good estimator, as it ensures that as more data is collected, the estimation error decreases.
However, as the sample size decreases, the value of the estimator is more likely to deviate from the true value of the parameter. The reason for this is that a small sample size may not be representative of the population, and as a result, the estimation error may increase.
As a consequence, the statement is false. In conclusion, consistency is a property that an estimator possesses when its value converges to the true value of the parameter as the sample size grows.
As the sample size decreases, the estimator may become less reliable, leading to an increase in the estimation error.
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If you know a ratio, the inverse trig function gives you an...
Answer: angle
Step-by-step explanation:
If three staff of Chukwudi and Sons Ltd. agreed to share their salary arrears in the ration of their ages, which are 18 years, 20 years, 22 years respectively. If the sum of the money collected is ₦120,000.00K, How much does the second staff receive?
The second staff member receives ₦40,000.
what is Ratio?In mathematics, a ratio is a comparison of two or more quantities of the same kind or unit. It is expressed as the quotient or fraction of one quantity to another. Ratios are used to compare and express the relationship between different quantities, such as distance, time, weight, or money.
To solve this problem, we need to first determine the total ratio of the ages of the three staff, which is 18 + 20 + 22 = 60.
Next, we need to calculate the share of each staff member by multiplying their age ratio with the total amount of money collected:
The first staff member's share = (18/60) x ₦120,000 = ₦36,000
The second staff member's share = (20/60) x ₦120,000 = ₦40,000
The third staff member's share = (22/60) x ₦120,000 = ₦44,000
Therefore, the second staff member receives ₦40,000.
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Which number line shows the solution to the inequality n + 3 > 4?
The number line which correctly shows the solution to the given inequality as required is as attached.
What is the solution of the inequality represented on a number line?It follows from the task content that the number line which correctly shows the solution to the given inequality is to be determined.
First, we must solve the inequality as follows;
n + 3 > 4
n > 4 - 3
n > 1.e
Ultimately, the number line which represents the solution of the inequality as required is as in the attached image.
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a quality control inspector has drawn a sample of 17 light bulbs from a recent production lot. suppose 30% of the bulbs in the lot are defective. what is the probability that between 3 and 6 (both inclusive) bulbs from the sample are defective? round your answer to four decimal places.
Answer: This is a binomial distribution problem with parameters n = 17 and p = 0.3, where n is the sample size and p is the probability of a defective bulb. We need to find the probability that between 3 and 6 (both inclusive) bulbs from the sample are defective.
Let X be the number of defective bulbs in the sample. Then X has a binomial distribution with parameters n = 17 and p = 0.3, i.e., X ~ B(17, 0.3).
We want to find P(3 ≤ X ≤ 6). Using the binomial probability formula, we have:
P(3 ≤ X ≤ 6) = P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)
= (17 choose 3)(0.3^3)(0.7^14) + (17 choose 4)(0.3^4)(0.7^13) + (17 choose 5)(0.3^5)(0.7^12) + (17 choose 6)(0.3^6)(0.7^11)
≈ 0.1566 (rounded to four decimal places)
Therefore, the probability that between 3 and 6 (both inclusive) bulbs from the sample are defective is approximately 0.1566.
Step-by-step explanation:
In equation F=-kx, k is commonly called the
Answer:
k is usually called the spring constant
Step-by-step explanation:
sorry if its not right, that is just what i have learned.
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