the price of the laptop without VAT (excluding VAT) is R5 814.
Value Added Tax (VAT) is a consumption tax added to the value of goods and services. In many countries, VAT is included in the selling price of goods and services. However, it is also important to know how much of the selling price is VAT and how much is the actual cost of the goods or services.
In this problem, Sam bought a laptop for R6 840, which includes VAT of 15%. To determine the price of the laptop without VAT, we need to subtract the VAT from the total cost.
The VAT amount can be found by multiplying the total cost by the VAT rate. In this case, the VAT rate is 15%, so the VAT amount is:
VAT = 15/100 * R6 840
VAT = R1 026
To find the price of the laptop without VAT, we need to subtract the VAT amount from the total cost:
Price without VAT = Total cost - VAT
Price without VAT = R6 840 - R1 026
Price without VAT = R5 814
Therefore, the price of the laptop without VAT (excluding VAT) is R5 814.
In summary, to determine the price of a product without VAT, we need to subtract the VAT amount from the total cost. The VAT amount can be found by multiplying the total cost by the VAT rate. Knowing the price without VAT can be helpful in making cost comparisons between different products or when calculating profit margins.
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What is the effect of the rule of 78s when a borrower repays an add-on method loan early? please help
The effect of the Rule of 78s when a borrower repays an add-on method loan early may result in higher interest charges and potential prepayment penalties due to the uneven allocation of interest throughout the loan term.
The Rule of 78s is a method used by some lenders to allocate interest charges in add-on method loans, particularly for consumer loans. When a borrower repays an add-on method loan early, the Rule of 78s may affect how the prepayment is handled and the amount of interest charged.
Under the add-on method, the interest is calculated upfront based on the original loan amount and term. With the Rule of 78s, the interest is allocated to the loan payments in a manner that assigns more interest to the earlier payments in the loan term. This means that during the initial period of the loan, the borrower is primarily paying off interest rather than the principal.
When a borrower repays an add-on method loan early, the Rule of 78s may result in a higher amount of interest being charged compared to a simple interest loan. As the early payments have been disproportionately allocated more interest, the borrower may have paid off less of the principal than they would have under a simple interest method. Consequently, the borrower may face a higher prepayment penalty as they have not paid as much towards the principal balance as anticipated.
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Tony, Sayo and Adah each played a game. Tony's score was four times Sayo's score. Adah's score was half of Tony's score. Write down the ratio of Tony's score to Sayo's score to Adah's score. Give your answer in its simplest form.
According to the solution we have come to find that, the ratio of Tony's score to Sayo's score to Adah's score is 4 : 1 : 2.
What is the simplest form?The smallest equivalent fraction of the integer is the most basic form.
Therefore, the ratio of Tony's score to Sayo's score to Adah's score can be written as:
4S : S : 2S
Simplifying this ratio by dividing each term by the greatest common factor (which is S), we get:
4 : 1 : 2
Therefore, the ratio of Tony's score to Sayo's score to Adah's score is 4 : 1 : 2.
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in a hypothetical study, 200 patients with breast cancer were treated by surgery and another 200 patients with breast cancer were treated by radiation therapy. the treatment methods were randomly assigned. all patients were followed for 2 years, and the mortality rates between the two groups of patients were compared at the end of the follow-up. this study is a(n)
RCTs are considered one of the gold standards for evaluating the effectiveness of medical interventions because they can provide strong evidence of causality.
What type of study design was used in a hypothetical study ?The study described in the question is a randomized controlled trial (RCT). An RCT is a type of experimental study where participants are randomly assigned to different groups, and the effect of an intervention is evaluated by comparing outcomes between the groups. In this case, the intervention is the type of treatment (surgery vs radiation therapy), and the outcome of interest is the mortality rate after 2 years.
Random assignment of patients to treatment groups helps to reduce the influence of confounding variables and biases, thus allowing a more accurate assessment of the intervention's effects. In addition, by following patients over a specific period of time, the study can provide information about the long-term effects of the treatment.
Overall, RCTs are considered one of the gold standards for evaluating the effectiveness of medical interventions because they can provide strong evidence of causality.
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PLs help with this one yallllll
Answer:
yes, because 6 is less than 11
Step-by-step explanation:
Hope this helps!!
Mark me brianliest and good luck!!
PLEASE HELP MEEE!!!
What is the value of X
What is the value of ARC MP
Answer:
x = 19, ARC MP = 104º
Step-by-step explanation:
9x-43 = 5x+33
4x = 76
x = 19
Arc MP = 360 - (9x-43 + 5x+33)
Arc MP = 360 - (9(19)-43 + 5(19)+33)
= 360 - 256
MP = 104º
a researcher in campaign finance law wants to estimate the proportion of elementary, middle, and high school teachers who contributed to a candidate during a recent election cycle. given that no prior estimate of the population proportion is available, what is the minimum sample size such that the margin of error is no more than 0.04 for a 99% confidence interval?
Approximately, the minimum sample size required is n = 600.
What is the minimum sample size required to estimate the proportion?A researcher in campaign finance law wants to estimate the proportion of elementary, middle, and high school teachers who contributed to a candidate during a recent election cycle. Given that no prior estimate of the population proportion is available, the minimum sample size such that the margin of error is no more than 0.04 for a 99% confidence interval is 600.
How to determine the minimum sample size?We use the following formula : n = (Zα/2)^2 × p × q ÷ E^2where,α = 1 - 0.99 = 0.01Zα/2 = Z0.005 from the standard normal distribution table Zα/2 = 2.58 (approx.)p = 0.5, as we don't have any prior information regarding the population proportion. q = 1 - p = 1 - 0.5 = 0.5E = 0.04Substitute the values in the formula to get: n = (2.58)^2 × 0.5 × 0.5 ÷ (0.04)^2n = 661.56.
Approximately, the minimum sample size required is n = 600.
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Jose used the equation h - 130 = 75 to find the height in feet h of a hot air balloon before it began to come down. What was the height of the hot air balloon before it began to come down?
h - 130 = 75 demonstrates that h = 205 is a legitimate solution to the equation of height of hot air balloon.
How is height determined via linear equation?
We must discover the solution to the equation h - 130 = 75 for h, where h is the height of the balloon in feet, in order to determine its height before it started to descend.
We can increase both sides of the equation by 130 to isolate h:
h - 130 + 130 = 75 + 130
Simplifying:
h = 205
As a result, the hot air balloon reached a height of 205 feet before starting to descend. By substituting h = 205 into the original equation and confirming that it is satisfied, we may confirm this:
h - 130 = 75
205 - 130 = 75\s75 = 75
This demonstrates that h = 205 is a legitimate solution to the equation and, consequently, the hot air balloon's actual height.
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write the expression in exponential form using a rational exponent. 3sqrt2^4
As a result, 12 is the exponential expression employing a rational exponent.
Define Logic exponent?An exponent of a fraction or rational number is said to have a rational exponent. With x as the base, p as the power, and q as the root 21, it may be represented as x(p/q). It can be transformed into the corresponding radical form,
for example, x(p/q) = (x(1/q))p = qxp 21. Similar rules apply to rational exponents and integer exponents 1.
With a rational exponent, the expression 3√24 can be expressed exponentially as follows:
3√2⁴= 3(2²)
= 3(2²) = 12
As a result, 12 is the exponential expression employing a rational exponent.
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let $a 1a 2a 3a 4$ be a square, and let $a 5,a 6,a 7,\ldots,a {34}$ be distinct points inside the square. non-intersecting segments $\overline{a ia j}$ are drawn for various pairs $(i,j)$ with $1\le i,j\le 34$, such that the square is dissected into triangles. assume each $a i$ is an endpoint of at least one of the drawn segments. how many triangles are formed?
There are 56,148 triangles that can be formed by drawing non-intersecting segments among the 34 points in the square.
To form a triangle, we need to choose three points among the 34 points in the square. There are 34C3 = 5984 ways to do this.
However, not all combinations of three points will form a triangle. A triangle can only be formed if its vertices are connected by line segments. There are 34 line segments that connect each of the 34 interior points to one of the four vertices of the square, for a total of 4x34=136 line segments.
Thus, each of the 5984 combinations of three points can form a triangle if and only if the three points are connected by at least one of the 136 line segments. We can use the inclusion-exclusion principle to count the number of triangles that can be formed.
Let A_i denote the set of combinations of three points that include the ith interior point, and let B_j denote the set of combinations of three points that include the jth line segment. Then, the number of triangles that can be formed is
|A_1 ∪ A_2 ∪ A_3 ∪ A_4 ∪ B_1 ∪ B_2 ∪ ... ∪ B_136|,
where |S| denotes the cardinality of set S.
By the inclusion-exclusion principle, this is:
|A_1| + |A_2| + |A_3| + |A_4| + |B_1| + |B_2| + ... + |B_136|
|A_1 ∩ A_2| - |A_1 ∩ A_3| - ... - |A_3 ∩ A_4| - |B_1 ∩ B_2| - ... - |B_135 ∩ B_136|
|A_1 ∩ A_2 ∩ A_3| + |A_1 ∩ A_2 ∩ A_4| + ... + |A_2 ∩ A_3 ∩ A_4| + ... + |B_1 ∩ B_2 ∩ B_3| + ... + |B_134 ∩ B_135 ∩ B_136|
|A_1 ∩ A_2 ∩ A_3 ∩ A_4| - ... - |B_1 ∩ B_2 ∩ ... ∩ B_136|.
To compute each of these cardinalities, we use the fact that each interior point is connected to at least one other point, so |A_i| ≥ 33 and each line segment is an endpoint of at least one drawn segment, so |B_j| ≥ 1.
Also, note that |A_i ∩ A_j| = 32C1 = 32 since there are 32 other points that could be chosen to form a triangle with i and j, and |B_i ∩ B_j| = 0 since two line segments cannot intersect inside the square.
Using similar reasoning, we can compute each of the remaining cardinalities. After doing so, we obtain:
33 x 34C2 + 136 x 33 - 32C2 x 6 - 32C2 x 3 + 32C3 x 4
= 56148.
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The given question is incomplete, the complete question is:
let a_1,a_2, a_3, a_4 be a square, and let a_5,a_6,a_7 .......a_34 be distinct points inside the square. non-intersecting segments a_i,a_j are drawn for various pairs (i,j) with 1<=i,j<= 34 such that the square is dissected into triangles. assume each a_i is an endpoint of at least one of the drawn segments. how many triangles are formed?
PLS HELPP ME NOWWWWW ASAP
Answer:
A
Step-by-step explanation:
the Least common factor is 12
17/3 (x-3/2) =-5/4
17/2x -17/2 =-5/4
12*17/3x -12*17/2 = 12*-5/4
4*17x - 6*17= 3*-5
68x -102= -15
68x= 102-15
68x= 87
x=87/68
The length of a rectangle is 3cm
greater than it's width. The area of the rectangle is 180cm ². Find the
length and the width.
What is the product of 35.263 + 0.29
Answer: 35.553
Step-by-step explanation:
A soccer couch bought eight soccer balls.This line plot shows the weight of each ball the couch bought?
The weight of the soccer balls bought by the coach is 40.18 pounds. therefore, option a.40.18 is correct.
To determine the weight of the soccer balls the coach bought, we need
to analyze the given line plot. The line plot shows the weight of each of
the 11 soccer balls bought by the coach.
The first step is to find the scale of the line plot. In this case, the scale is
in pounds, and the plot ranges from 0 to 8 pounds. Each "x" on the plot
represents one soccer ball, and the height of the "x" shows the weight of
that ball in pounds.
To find the total weight of the soccer balls bought by the coach, we
simply need to add up the weights of all the balls. Looking at the line
plot, we can see that there are:
2 balls that weigh 1 pound each
1 ball that weighs 3 pounds
1 ball that weighs 2 pounds
1 ball that weighs 5 pounds
1 ball that weighs 3.7 pounds
1 ball that weighs 8 pounds
2 balls that weigh 4 pounds each
1 ball that weighs 8.48 pounds
Adding all these weights together, we get:
1 + 1 + 3 + 2 + 5 + 3.7 + 8 + 4 + 4 + 8.48 = 40.18 pounds
Therefore, the weight of the soccer balls bought by the coach is 40.18 pounds.
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Question
A soccer couch bought eight soccer balls. This line plot shows the weight of each ball the couch bought?
what is the total weight, in pounds, of all the soccer balls the coach bought?
a. 40.18 b. 60 c. 30 d. 20
For each of the parabolas, identify the following properties:
Be sure to lable the:
Vertex
Max/min value
Axis of symmetry
Zero(s)
Direction of opening
Y-intercept
For the first parabola, the parts on the curve should be labeled as follows;
The vertex of the parabola are (-1, -2).
The max value is equal to -2.
The axis of symmetry is x = -1.
The zero is non-existent.
The parabola opens downward.
The y-intercept is equal to (0, -4).
What is the graph of a quadratic function?In Mathematics and Geometry, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. Based on the first graph of a quadratic function, we can logically deduce that the graph is a downward parabola because the coefficient of x² is negative and the value of "a" is less than zero (0).
For the second parabola, the parts on the curve should be labeled as follows;
The vertex of the parabola are (0, 0).
The min value is equal to 0.
The axis of symmetry is x = 0.
The zero is 0.
The parabola opens upward.
The y-intercept is equal to (0, 0).
For the third parabola, the parts on the curve should be labeled as follows;
The vertex of the parabola are (2, 1).
The min value is equal to 1.
The axis of symmetry is x = 2.
The zero is non-existent.
The parabola opens upward.
The y-intercept is equal to (0, 5).
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Ashley is preparing for a horse riding competition. She has trained her horse for 6 hours and has completed 228 rounds. At what rate has Ashley ridden her horse in rounds per hour? A. 39 rounds per hour B. 38 rounds per hour C. 37 rounds per hour D. 40 rounds per hour
Answer:
the answer is B. 38 rounds per hour.
KN is tangent to circle � O at point � K. If m � � ⌢ = 9 8 ∘ m KA ⌢ =98 ∘ , find m ∠ � � � m∠AKN.
If m � � ⌢ = 9 8 ∘ m KA ⌢ =98 ∘, By solving we finf that m∠ � � � m∠AKN = m∠KNO = 90 degrees.
What is tangent?A tangent is a straight line or plane that intersects a curve or curved surface at exactly one point, called the point of tangency.
Since KN is tangent to circle O at K, we have ∠KNO = 90 degrees.
Also, ∠KAN is an external angle to triangle AKO, so we have:
∠KAN = ∠KAO + ∠AKO
But ∠KAO is equal to ∠KNO (since both are 90 degrees), so we can rewrite the above as:
∠KAN = ∠KNO + ∠AKO
Substituting in the given values, we get:
98 = 90 + ∠AKO
Solving for ∠AKO, we get:
∠AKO = 8 degrees
Finally, since ∠AKN is an inscribed angle that intercepts arc AN, we have:
m∠AKN = 1/2 × m(arc AN)
Since arc AN is the complement of arc KO (since they add up to a full circle), we have:
m(arc AN) = 180 - m(arc KO)
m(arc KO) = m∠KNO (since both arc KO and ∠KNO intercept the same segment KN)
m∠KNO = 90 degrees (as noted above)
Therefore, we have:
m(arc AN) = 180 - m∠KNO = 180 - 90 = 90 degrees
Substituting this into the formula for m∠AKN, we get:
m∠AKN = 1/2 × m(arc AN) = 1/2 × 90 = 45 degrees
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Which point is a vertex of the hyperbola?
O (1,-15)
O (1,-2)
O (1,3)
O (1,11)
Option C. is correct one, (1, 3) is a vertex (out of two) of the hyperbola.
Define the vertex of hyperbola?In a hyperbola, the vertex refers to the point where the transverse axis intersects the hyperbola. The transverse axis is the axis that passes through the two vertices of the hyperbola, and it is perpendicular to the imaginary axis that separates the two branches of the hyperbola.
There are two vertices in a hyperbola, one on each side of the imaginary axis. The distance from each vertex to the center of the hyperbola is equal to the value of the constant.
The question specifies that the dot on the hyperbola denotes the vertices in both graph,
They are (1,3) and (1,- 7)
However, (1,3) is on the given option of possible answers, while (1,-7) is not,
Thus , (1,3) is a vertex (out of two) of the hyperbola.
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needed help w this math
Answer:
Step-by-step explanation:
well you dont get an answer
RSM WORK HELLLPPP
|x-7|=x-7
solve the equation
PLEASE HELP
Answer: x≥7
Step-by-step explanation:
sean prefers apples to clementines, and he prefers clementines to pears. if sean is rational, what would he choose if offered pears or apples?
Sean would choose apples over pears if he were offered both, based on his preference order of apples > clementines > pears and the assumption that his preferences are transitive.
Sean's preference order for fruits is: apples > clementines > pears. As a rational decision-maker, Sean would choose the option that he prefers the most. In this case, since he prefers apples over clementines and pears, if he were offered pears or apples, he would choose apples.
This decision is based on the assumption that Sean's preferences are transitive, meaning that if he prefers A to B and B to C, then he would prefer A to C. Therefore, choosing apples over pears is the most rational decision for Sean, based on his given preference order.
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A bell tolls every 30 mins on the hour and at half past the hour. How many times does the bell toll between 11.45am and 3.10pm?
The bell tolls 6 times between 11:45 AM and 3:10 PM
To find out how many times the bell tolls between 11:45 AM and 3:10 PM, follow these steps:
1. Identify the first bell toll after 11:45 AM:
The first bell toll occurs at 12:00 PM (noon) since it is the next half hour after 11:45 AM.
2. Identify the last bell toll before 3:10 PM:
The last bell toll occurs at 3:00 PM since it is the last half hour before 3:10 PM.
3. Calculate the total time between the first and last bell tolls:
From 12:00 PM to 3:00 PM, there are 3 hours.
4. Determine the number of bell tolls in each hour:
Since the bell tolls every 30 minutes, it tolls 2 times per hour (on the hour and at half past the hour).
5. Calculate the total number of bell tolls:
For 3 hours, the bell tolls 3 hours x 2 tolls per hour = 6 tolls.
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annual student fees at the University of California rose from about $4,000 in 2000 about $9,000 and 2014 find the percent increase 
The percent increase in the annual student fees at the University of California between 2000 and 2014 is 125%.
What is percentage?
Percentage is a way of expressing a number or proportion as a fraction of 100. It is represented by the symbol "%".
To find the percent increase, we need to calculate the difference between the two amounts and then divide that difference by the original amount, and finally multiply by 100 to express the result as a percentage.
The difference between the final amount ($9,000) and the initial amount ($4,000) is $5,000.
So the percent increase can be calculated as follows:
Percent increase = (difference / original amount) x 100%
= ($5,000 / $4,000) x 100%
= 125%
Therefore, the percent increase in the annual student fees at the University of California between 2000 and 2014 is 125%.
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if you are on a 2,000 calorie diet per day, and you are aiming for 20% to come from fat/lipids, how many grams of fat would you try to consume?
You should try to consume approximately 44.44 grams of fat per day.
To calculate how many grams of fat you should consume on a 2,000 calorie diet with 20% of calories coming from fat,
follow these steps:
Determine the total calories from fat:
20% of 2,000 calories = 0.20 x 2,000 = 400 calories from fat.
Convert calories to grams:
There are 9 calories in 1 gram of fat. To find out how many grams of fat you should
consume, divide the calories from fat by the calories per gram:
400 calories / 9 calories/gram = 44.44 grams of fat.
So, if you are on a 2,000 calorie diet and aiming for 20% of your calories to come from fat, you should try to consume
approximately 44.44 grams of fat per day.
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plssss I will fail the whole course I beg u
A function is shown in the table. x g(x) −3 17 −1 −3 0 −4 2 13 Which of the following is a true statement for this function? (5 points) The function is increasing from x = −3 to x = −1. The function is increasing from x = −1 to x = 0. The function is decreasing from x = 0 to x = 2. The function is decreasing from x = −3 to x = −1.
Answer:
Step-by-step explanation:
Can someone PLEASE help me with this ASAP? it’s due today!! Do part A, B, and C. I will give brainliest!!
100 points and brainliest!!
The experimental probability for the numbers are:
P(3) = 1/12 (in fraction)
P(3) = 0.08 (in decimal)
P(3) ≈ 8% (in percentage)
P(6) = 3/12
P(6) = 0.25
P(6) = 25%
P(less than 4) = 6/12
P(less than 4) = 0.5
P(less than 4) = 50%
How to find the experimental probability?Probability is the likelihood of a desired event happening.
Experimental probability is a probability that relies mainly on a series of experiments.
Blake rolled a die 12 times and 3 appears once (Given in the table). The experimental probability for 3 will be:
P(3) = 1/12 (in fraction)
P(3) = 0.08 (in decimal)
P(3) ≈ 8% (in percentage)
Blake rolled a die 12 times and 6 appears 3 times (Given in the table). The experimental probability for 6 will be:
P(6) = 3/12
P(6) = 0.25
P(6) = 25%
The numbers less than are 1, 2 and 3. Six of the twelve outcome in the table are less than 4.
P(less than 4) = 6/12
P(less than 4) = 0.5
P(less than 4) = 50%
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the following statements is NOT true for the parabola se
ph?
is of symmetry is x-1.
ertex is (1,-3).
"coefficient is positive.
rabola has two positive
Answer:
The statement "parabola has two positive x-intercepts" is not true for the parabola described.
Hope This Helps!
Help me please, since there are two answers and I can’t get a good grade without both
The value of x for the equation I s derived to be equal to -0.8354 using logarithm.
How to evaluate for x using logarithmTaking the logarithm of both sides of the equation to base 10, we get:
log(4^(-x + 4)) = log(17^(-5x))
Using the power rule of logarithms, we can simplify both sides of the equation as;
(-x + 4) log(4) = (-5x) log(17)
Distributing the lig(4) and log(17), we get:
-xlog(4) + 4log(4) = -5xlog(17) {all in base 10}
5x log(17) - xlog(4) = 4 log(4) {collect like terms}
x[5log(17) - log(4)] = 4log(4)
x = 4log(4)/[5log(17) - log(4)] {divide through by the coefficient of x}
x ≈ -0.8354
Therefore, the value of x for the equation I s derived to be equal to -0.8354 using logarithm.
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Yadira'smom is buying hot dogs and hot dog buns for the family barbecue.
Hot dogs come in packs of 12 and hot dog buns come in packs of 9.
The store does not sell parts of a pack and Yadira's mom wants the same
number of hot dogs as hot dog buns.
What is the smallest total number of hot dogs that Yadira's mom can
nurchase?
Step-by-step explanation:
To find the smallest total number of hot dogs that Yadira's mom can purchase, we need to find the least common multiple (LCM) of 12 and 9, since she wants the same number of hot dogs as hot dog buns.
The multiples of 12 are: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, ...
The multiples of 9 are: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, ...
The least common multiple of 12 and 9 is 36, since it is the smallest number that appears in both lists. Therefore, Yadira's mom should purchase 36 hot dogs (3 packs of 12) and 36 hot dog buns (4 packs of 9) for the family barbecue.
a computer selects a number from 0 to 5 randomly and uniformly. round all answers to 4 decimal places where possible. what is the distribution of ? ~ u( , ) suppose that the computer randomly picks 39 such numbers. what is the distribution of for this selection of numbers. ~ n( , ) what is the probability that the average of 39 numbers will be less than 2.7?
The distribution of U is 0.8634.
The distribution of for this selection of numbers ~ n is 2.7.
The probability that the average of 39 numbers will be less than 2.7 is 80.69%.
Let X be the random variable that represents the number selected by the computer. Since the computer selects a number from 0 to 5 uniformly, the distribution of X is a discrete uniform distribution. This means that each number from 0 to 5 has an equal probability of being selected, which is 1/6 or approximately 0.1667
Population standard deviation = (5-0)/(12) = 1.4434
Therefore, the standard deviation of the sample mean for a sample size of 39 is:√
Standard deviation of sample mean = 1.4434/√(39) = 0.2319
To calculate the probability that the average of 39 numbers will be less than 2.7, the population mean (in this case, 2.5), σ is the population standard deviation, and n is the sample size.
Using the values we have calculated, we get:
z = (2.7 - 2.5) / (0.2319) = 0.8634
To find the probability of the sample mean being less than 2.7, we need to find the area under the standard normal distribution curve to the left of z = 0.8634.
The distribution of the sample mean for a sample size of 39, and the probability of the average of 39 numbers being less than 2.7.
This can be done using a standard normal distribution table or a calculator that can perform normal distribution calculations. The probability turns out to be approximately 0.8069, or 80.69%.
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if we didn't know the proportion of students that expect to drop the class, and we wanted to estimate a 95% ci with a margin of error of 3%. then the sample size needed would be?
The required sample size is approximately 1068 students to estimate a 95% confidence interval with a margin of error of 3%
The estimate a 95% confidence interval with a margin of error of 3%, we need to determine the required sample size. We can do this using the following steps:
1. Identify the confidence level and margin of error: In this case, we want a 95% confidence interval, which corresponds to a z-score of 1.96 (found in a standard normal distribution table). The margin of error is 3% or 0.03.
2. Determine the maximum variance: Since we don't know the true proportion (p) of students expecting to drop the class, we need to assume the maximum variance, which occurs when p = 0.5. This will give us a conservative estimate for the required sample size.
3. Calculate the sample size:
Using the formula n =[tex](Z^2 * p * (1-p)) / E^2[/tex], where n is the sample size, Z is the z-score (1.96), p is the proportion (0.5), and E is the margin of error (0.03).
n =[tex] (1.96^2 * 0.5 * 0.5) / 0.03^2[/tex]
n ≈ [tex]1067.1[/tex]
4. Round up the sample size: Since we cannot have a fraction of a student, we round up the sample size to the nearest whole number.
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