The lower limit is 72.1 and the upper limit is 78.5.
The sample mean is 75.3, and the standard error is 1.613.
What is standard deviation?The standard deviation is a measurement of how differently distributed a set of data values are from their mean or average. Finding the square root of the variance, which is the sum of the squared deviations between each data point and the mean, is how it is determined.
To find the confidence interval, we can use the formula:
Confidence interval = sample mean ± (critical value) x (standard error)
where the standard error is the standard deviation of the sample mean and the critical value is based on the desired confidence level and the sample size.
Since we want a 95% confidence interval and the sample size is 50, we can find the critical value from a t-distribution with 49 degrees of freedom (n-1). Using a t-distribution instead of a normal distribution is appropriate here because the population standard deviation is not known.
From a t-distribution table or calculator, the critical value for a 95% confidence interval with 49 degrees of freedom is approximately 2.009.
The standard error can be found using the formula:
standard error = standard deviation / sqrt(sample size)
Substituting the given values, we get:
standard error = 11.4 / sqrt(50) = 1.613
Now we can plug in the values into the formula for the confidence interval:
Confidence interval = 75.3 ± 2.009 x 1.613 = (72.14, 78.46)
Therefore, the lower limit is 72.1 and the upper limit is 78.5. The sample mean is 75.3, denoted by X-bar and the standard error is 1.613, denoted by Ś.
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The acts in a talent competition consist of 10 instrumentalists, 12 singers, and 8 dancers. If the acts are ordered randomly, what is the probability that a dancer performs first?
Answer:
P=4/15
Step-by-step explanation:
P(dancer first) = 8/30=4/15
Triangle ABC is being enlarged using a scale factor of and centre (2,9) to
give triangle A'B'C'.
a) What are the coordinates of the vertex C'?
b) What is the length of the side A’B’
a) The coordinates of the vertex C' are C'(x, y) = (5, 5).
b) The length of the side A'B' is equal to 4.
In this problem we find the case of a right triangle, whose image must be found by a kind of rigid transformation known as dilation. The dilation formula for a vertex is introduced below:
P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)]
Where:
k - Dilation factor
O(x, y) - Center of dilation
P(x, y) - Original vertex
P'(x, y) - Resulting vertex
And the dilation formula for a formula is:
L' = k · L
Where:
L - Original length.
L' - Resulting length.
Please notice that side lengths can be found by Pythagorean theorem.
we know that O(x, y) = (2, 9), k = 1 / 2, A(x, y) = (6, 7), B(x, y) = (10, 7) and C(x, y) = (6, 1), then the resulting vertices and sides are:
C'(x, y) = (2, 9) + (1 / 2) · [(6, 1) - (0, 9)]
C'(x, y) = (2, 9) + (1 / 2) · (6, - 8)
C'(x, y) = (2, 9) + (3, - 4)
C'(x, y) = (5, 5)
And the length of the side A'B' is:
AB = 8
A'B' = (1 / 2) · AB
A'B' = 4
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Please if you know the answer put the steps in there thank you.
Answer:
The market trader should sell each of the remaining 20 packs of muffins for £1.30 to meet his target.
Step-by-step explanation:
To find out how much the market trader needs to sell the remaining 20 packs of muffins, we first need to calculate his total cost and his target revenue.
The cost of the loaves of bread is:
100 loaves x 84p/loaf = £84
The cost of the packs of muffins is:
60 packs x £1.10/pack = £66
Therefore, the total cost for the trader is:
£84 + £66 = £150
To make a 40% profit, the trader needs to make £150 x 40/100 = £60 in profit.
His target revenue is, therefore:
£150 + £60 = £210
The revenue from the loaves of bread is:
100 loaves x £1.20/loaf = £120
The revenue from the 40 packs of muffins sold at £1.60 per pack is:
40 packs x £1.60/pack = £64
So the total revenue from the loaves of bread and the 40 packs of muffins is:
£120 + £64 = £184
This means that the trader needs to make:
£210 - £184 = £26
from the sale of the remaining 20 packs of muffins.
To sell 20 packs of muffins to make £26, he needs to sell each pack for:
£26/20 = £1.30 per pack
Therefore, the market trader should sell each of the remaining 20 packs of muffins for £1.30 to meet his target.
Correct answer gets brainliest!!!!
Answer:is b
A line segment has both of its end-points fixed and so it has a definite length.
Step-by-step explanation:
pl z give me brianlieyst and have a good day
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Riley runs a stable that boards a range of horses.
white 3
bay 2
palomino 9
black 1
Considering this data, how many of the next 20 horses that come to board should you expect to be white horses?
_____ white horses
we should expect 4 white horses among the next 20 horses that come to board. we can solve by equation .
what is equation ?
An equation is a mathematical statement that uses symbols and variables to show that two expressions are equal. It typically consists of two sides separated by an equal sign (=). The expressions on each side of the equal sign can contain variables, constants, and mathematical operations such as addition
In the given question,
Out of the 15 horses currently boarded, 3 are white. This means that the proportion of white horses among the currently boarded horses is:
3 / 15 = 0.2 or 20%
Therefore, if we assume that the next 20 horses that come to board will have a similar distribution of coat colors, we can expect approximately 20% of them to be white.
So, the expected number of white horses among the next 20 horses that come to board is:
20 x 0.2 = 4
Therefore, we should expect 4 white horses among the next 20 horses that come to board.
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The students in Mr. Anderson's class are growing bean plants from seeds. The heights of the plants are measured after 7 days and recorded in the histogram below.
The average height of the bean plants in Mr. Anderson's class after 7 days is approximately 7.41 centimeters.
How to solveHeight (in centimeters) Frequency
0 - 3 | 5
4 - 6 | 10
7 - 9 | 15
10 - 12 | 7
13 - 15 | 3
To find the average height, we can follow these steps:
Determine the midpoint of each height range.
Multiply the midpoint of each range by the frequency.
Add up the products from step 2.
Add up the frequencies.
Divide the sum from step 3 by the sum from step 4.
Step 1: Determine the midpoint of each height range.
Height Range Midpoint
0 - 3 | 1.5
4 - 6 | 5
7 - 9 | 8
10 - 12 | 11
13 - 15 | 14
Step 2: Multiply the midpoint of each range by the frequency.
Height Range Frequency Midpoint Midpoint x Frequency
0 - 3 | 5 | 1.5 | 7.5
4 - 6 | 10 | 5 | 50
7 - 9 | 15 | 8 | 120
10 - 12 | 7 | 11 | 77
13 - 15 | 3 | 14 | 42
Step 3: Add up the products from step 2.
7.5 + 50 + 120 + 77 + 42 = 296.5
Step 4: Add up the frequencies.
5 + 10 + 15 + 7 + 3 = 40
Step 5: Divide the sum from step 3 by the sum from step 4.
296.5 / 40 = 7.4125
The average height of the bean plants in Mr. Anderson's class after 7 days is approximately 7.41 centimeters.
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The students in Mr. Anderson's class are growing bean plants from seeds. The heights of the plants are measured after 7 days and recorded in the histogram below.
What is the average height of the bean plants in Mr. Anderson's class after 7 days?
A man earned wages of 38,800 received 1600 in interest from savings account and contributed to 3200 to tax deferred retirement plan he was entitled to personal exemption of 2900 and had had deductions totaling 4950 find his gross income adjust gross income and taxable income
The gross income amount is $35,750
Given data ,
To find the gross income, we add up all of the man's income sources:
Gross Income = Wages + Interest + Retirement Plan Contribution
Gross Income = 38,800 + 1,600 + 3,200
Gross Income = 43,600
To find the Adjusted Gross Income (AGI), we subtract any eligible deductions from the gross income. In this case, the personal exemption and deductions are eligible.
AGI = Gross Income - Personal Exemption - Deductions
AGI = 43,600 - 2,900 - 4,950
AGI = 35,750
Finally, to find the taxable income, we subtract any additional deductions or exemptions from the AGI. We will assume that there are no additional deductions or exemptions in this case.
Taxable Income = AGI
Taxable Income = 35,750
Hence , the gross income is $43,600, the adjusted gross income is $35,750, and the taxable income is $35,750
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For the graph of a function y=f(x) shown to the right, find the absolute maximum and the absolute minimum, if they exist. Identify any local maxima or local minima.
Answer:
B) There is no absolute max for y=f(x)
Step-by-step explanation:
There is no absolute max as the function increases infinitely
However there is an absolute minimum at x=0
# 27
2
G
A
1 2 3
2
7.G.B.6
1,7
Johnny uses a wheelbarrow to move planting soil to a delivery truck. The
volume of planting soil that fits in the wheelbarrow measures 2 feet by 3 feet
by 1.5 feet. The delivery truck measures 11 feet by 8 feet and is 6 feet tall.
Johnny puts planting soil in the delivery truck until the truck is 70% full.
What is the minimum number of times Johnny needs to use the wheelbarrow
until the delivery truck is 70% full?
He will need to use the wheelbarrow at least 41 times to fill the delivery truck to 70% of its capacity.
Define volumeVolume is a measure of the amount of space that a substance or object occupies in three dimensions. It is typically measured in units such as cubic meters (m³), cubic centimeters (cm³), liters (L), or gallons (gal), depending on the system of measurement being used.
First, let's calculate the total volume of the delivery truck:
Volume of delivery truck = length x width x height
Volume of delivery truck = 11 ft x 8 ft x 6 ft
Volume of delivery truck = 528 cubic feet
To fill the delivery truck to 70% of its capacity, Johnny needs to put 0.7 x 528 = 369.6 cubic feet of planting soil in the truck.
Now, let's calculate the volume of planting soil that fits in the wheelbarrow:
Volume of wheelbarrow = length x width x height
Volume of wheelbarrow = 2 ft x 3 ft x 1.5 ft
Volume of wheelbarrow = 9 cubic feet
Number of loads = Total volume of planting soil needed / Volume of each load
Number of loads = 369.6 cubic feet / 9 cubic feet
Number of loads = 41.0666667
Since Johnny cannot use a fraction of a load, he will need to use the wheelbarrow at least 41 times to fill the delivery truck to 70% of its capacity.
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Solve the inequality and graph the solution on the line provided.
> ≤ ≥ or
Inequality Notation:
Number Line:
-12 -10
4x + 45 57
-4-2 0 24
Click and drag to plot line.
6
10 12
The solution of the given inequality is x ≤ 13/4
Since Inequality can be defined as the relation which makes a non-equal comparison between two given functions.
We are given the Inequality as;
4x + 45 ≤ 57
Solving;
4x + 45 ≤ 57
4x ≤ 57 - 45
4x ≤ 13
x ≤ 13/4
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A major credit card company is interested in whether there is a linear relationship between its internal rating of a customer’s credit risk and that of an independent rating agency. The company collected a random sample of 200 customers and used the data to test the claim that there is a linear relationship. The following hypotheses were used to test the claim.
H0:β1=0Ha:β1≠0
The test yielded a t
t
-value of 3.34 with a corresponding p
p
-value of 0.001. Which of the following is the correct interpretation of the p
p
-value?
The correct interpretation of the p-value is 3.34.
We are given that;
t-value=3.34
Number of customers= 200
Now,
The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed one, assuming that the null hypothesis is true. In this case, the p-value of 0.001 means that there is a 0.1% chance of getting a t-value of 3.34 or higher (or -3.34 or lower) if the true slope of the linear relationship between the two ratings is zero. The p-value is very small, which indicates that the data provide strong evidence against the null hypothesis and in favor of the alternative hypothesis.
The p-value of 0.001 means that there is a 0.1% chance of getting a t-value of 3.34 or higher (or -3.34 or lower) if there is no linear relationship between the two ratings.
Therefore, by probability the answer will be 3.34
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Kelly purchased a toaster for $115. She made a down payment of 10% and financed the rest for 9 months with payments of $16.78. Find (a) the down payment and (b) the total installment price of the toaster.
(A) The down payment of the toaster = $ 11.5
(B) The total installment price of the toaster = $151.02
(A) The down payment of the toaster made by Kelly is 10 % of $ 115
Down payment = 115 × 10/100
Down payment = 1150/100
Down payment = 11.5
The down payment of the toaster = $ 11.5
(B) Total installment price of the toaster for 9 months with payment of $ 16.78
Total installment price of toaster = 9 × 16.78
Total installment price of toaster = $ 151.02
The total installment price of the toaster = is $ 151.02
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HELP PLS 65.1 + WHAT = 100 !!!
Answer: 34.9
Step-by-step explanation: 100 - 65.1
A given distribution has a population mean, μ, of 144 and a population standard deviation, σ, of 9. Compute the raw, x-value associated with a Z-score of 0.21. Round to two decimal places, as needed.
The raw x-value associated with a Z-score of 0.21 for the given distribution is 145.89.
To compute the raw x-value associated with a Z-score of 0.21 for a distribution with a population mean, μ, of 144 and a population standard deviation, σ, of 9, we can use the formula for standardizing a variable:
Z = (x - μ) / σ
Rearranging the formula to solve for x, we get:
x = Zσ + μ
Substituting the given values, we get:
x = 0.21(9) + 144
Simplifying the expression, we get:
x = 145.89
A Z-score represents the number of standard deviations a value is from the mean, and it can be used to standardize values from different distributions. By standardizing values, we can compare them on a common scale and make more meaningful statistical inferences.
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f ( x ) = 12 ( 7 ) x using base e
HELP ME PLEASE!
Whoever answers right gets brainliest!
Therefore, the range of the relation shown is (1, 3, 4, 6, 7). Option C is the correct answer.
What is function?In mathematics, a function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range) with the property that each input is associated with exactly one output. In other words, a function is a rule that assigns a unique output value to each input value. Functions are used to model relationships between variables in many areas of mathematics and other fields such as physics, engineering, economics, and computer science. They are used to describe various phenomena, such as the growth of populations, the trajectory of a projectile, or the behavior of financial markets. Functions are also important tools in calculus, where they are used to study rates of change and continuity, among other things.
Here,
The range of a relation refers to the set of all possible output values or y-values of the relation. Looking at the image reference, we can see that the y-values or the outputs are 1, 3, 4, 6, and 7.
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campaign. Evaluate how community respond to women and children in (3x4)(12) light of the following aspects: Bill of Rights Discrimination Human Rights Violations ■ . B
The community's response to women and children in light of the Bill of Rights, Discrimination, and Human Rights Violations should prioritize the protection and promotion of their rights and freedoms.
Now, The evaluation of community response to women and children in the context of Bill of Rights, Discrimination, and Human Rights Violations can be done as follows:
Bill of Rights:
The Bill of Rights guarantees certain rights and freedoms to all individuals regardless of their gender or age. Therefore, any discrimination or violation of women and children's rights would be a direct violation of the Bill of Rights. The community must ensure that women and children are not denied their right to life, dignity, equality, and freedom from all forms of violence and exploitation.
Discrimination:
Discrimination against women and children is a prevalent issue in many societies. Women and children are often subjected to discrimination on the basis of their gender, age, race, religion, or socio-economic status. The community should work towards eliminating all forms of discrimination against women and children and provide them with equal opportunities in all spheres of life.
Human Rights Violations:
The community must also ensure that the human rights of women and children are protected. Human rights violations against women and children can include physical and emotional abuse, sexual harassment and assault, child labor, child marriage, and human trafficking, among others. The community must take a strong stance against such violations and work towards preventing and punishing the perpetrators.
In conclusion, the community's response to women and children in light of the Bill of Rights, Discrimination, and Human Rights Violations should prioritize the protection and promotion of their rights and freedoms. Any form of discrimination or violation of their rights should be condemned and punished to ensure that women and children are safe and empowered members of society.
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Triangle GFH has vertices G(2, –3), F(4, –1), and H(1, 1). The triangle is rotated 270° clockwise using the origin as the center of rotation. Which graph shows the rotated image?
On a coordinate plane, triangle G prime H prime F prime has points (negative 3, negative 2), (1, negative 1), (negative 1, negative 4).
On a coordinate plane, triangle G prime H prime F prime has points (3, 2), (negative 1, 1), (1, 4).
On a coordinate plane, triangle G prime H prime F prime has points (2, negative 3), (1, 1), (4, negative 1).
On a coordinate plane, triangle G prime H prime F prime has points (2, 3), (4, 1), (1, negative 1).
Check the picture below.
Answer:
b
Step-by-step explanation:
edge 2023
Using the GCF, what is the factored form of 75 - 3x?
please i need help!!!
u will get 100 points!!!
The GCF (Greatest Common Factor) is the largest number that divides evenly into two or more numbers. In this case, we can find the GCF of 75 and 3 by listing their factors and finding the largest one they have in common. The factors of 75 are 1, 3, 5, 15, 25, and 75. The factors of 3 are 1 and 3. The largest factor they have in common is 3. Therefore, the GCF of 75 and 3 is 3.
We can use the GCF to factor the expression 75 - 3x by dividing each term by the GCF and writing the expression as a product. In this case, we can divide both terms by 3 to get 75/3 - (3x)/3, which simplifies to 25 - x. We can then write the original expression as a product by multiplying this simplified expression by the GCF: 3(25 - x).
Therefore, the factored form of 75 - 3x using the GCF is 3(25 - x).
Answer:
3(25-x)
Step-by-step explanation:
First we find the GCF of 75 and -3x, which is 3
3 is the highest number we can divide both 75 and -3
Hence, the answer is 3(25-x)
Calculate the area of a circle 4ft ,2in,18ft,5.2in,7.3in,14cm,9m,3m,9.2cm,7m,5m,6m
Answer:
Step-by-step explanation:
It seems like you have provided multiple measurements for the radius of the circle. I'm sorry, but a circle can only have one radius, so I am not able to calculate its area with the given information.
Please provide the correct measurement for the radius of the circle, and I will be happy to help you calculate its area.
Husk takes out a 3200 student loan at 6.7% to help him
Part (a) find the total amount interest that will accrue for loan 1(community college )
Part (b) find the total amount of intrest that will a cure for loan 2 state university
Part (c) find the total amount intrest that accrues until payment begin
(c) Total interest accrued until payments begin = $1023.33 (loan 1) + $2362.33 (loan 2) ≈ $3385.66.
How to solve(a) For loan 1, $3200 at 6.7% for 4 years and 7 months (4 years in college + 3 months deferment), the simple interest = 3200 * 0.067 * (55/12) ≈ $1023.33.
(b) For loan 2, $12,000 at 7.3% for 2 years and 7 months (2 years in college + 3 months deferment), simple interest = 12000 * 0.073 * (31/12) ≈ $2362.33.
(c) Total interest accrued until payments begin = $1023.33 (loan 1) + $2362.33 (loan 2) ≈ $3385.66.
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Justine is enrolled in an SAT prep class at the Oakdale Community Center. The community
center is 1.4 miles away from Justine's house. On a map of Oakdale, this distance is
represented by 1 inch. What is the scale of the map?
Write your answer in simplest form using whole numbers.
inches:
miles
Answer:
1.4:1
= 14:10
= 7:5
Hence, ans is 7:5
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A graph has quantity on the x-axis and price on the y-axis. A supply line goes through (10, 25), (20, 30), (30, 35), (40, 40).A graph has quantity on the x-axis and price on the y-axis. A demand line goes through (10, 40), (20, 30), (30, 20), (40, 10). Based on the supply graph and the demand graph shown above, what is the price at the point of equilibrium? a. 20 b. 30 c. 40 d. There is not enough information given to determine the point of equilibrium. A graph has quantity on the x-axis and price on the y-axis. A supply line goes through (10, 25), (20, 30), (30, 35), (40, 40).A graph has quantity on the x-axis and price on the y-axis. A demand line goes through (10, 40), (20, 30), (30, 20), (40, 10). Based on the supply graph and the demand graph shown above, what is the price at the point of equilibrium? a. 20 b. 30 c. 40 d. There is not enough information given to determine the point of equilibrium. A graph has quantity on the x-axis and price on the y-axis. A supply line goes through (10, 25), (20, 30), (30, 35), (40, 40).A graph has quantity on the x-axis and price on the y-axis. A demand line goes through (10, 40), (20, 30), (30, 20), (40, 10). Based on the supply graph and the demand graph shown above, what is the price at the point of equilibrium? a. 20 b. 30 c. 40 d. There is not enough information given to determine the point of equilibrium.
Describe the following function
The transformation in the function y = -1/3f(x + 4) - 5 is described below
Describing the transformation in the functionFrom the question, we have the following parameters that can be used in our computation:
y = f(x)
The transformed function g(x) is given as
y = -1/3f(x + 4) - 5
The sequence of transformation on the transformed function is as follows
Horizontal shift to the left by 4 unitsVertical stretch by a factor of 1/3Reflection across the x-axisLastly, vertical shift down by 5 unitsRead more about transformation at
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An agency wanted to study annual-sales distribution of 500 cottage industries of the same standard. Since the industries are located in different regions, it will be expensive to collect data from all 500 industries. Thus, the study is to be based on the sales of 75 industries which are selected to represent the whole. a) The agency summarized the collected data in tabular form, displayed it in graph and further found the average annual sales to be 36 thousand birr. What type of statistical technique is used here? b) The average sale of the 500 cottage industries is estimated to be 36 thousand birr based on the sample average. What type of statistical technique is used here?
The type of statistical technique used here is inferential
We are given that;
Annual-sales distribution of cottage industries of the same standard=500
Number of industries=500
Now,
a) The type of statistical technique used here is descriptive statistics, which involves summarizing, organizing, and presenting data in a meaningful way. Descriptive statistics can use tables, graphs, and numerical measures such as mean, median, mode, range, standard deviation, etc. to describe the main features and patterns of a data set.
b) The type of statistical technique used here is inferential statistics, which involves drawing conclusions or making predictions about a population based on a sample. Inferential statistics can use methods such as estimation, hypothesis testing, confidence intervals, regression analysis, etc. to make inferences about the population parameters from the sample statistics.
Therefore, by statistics the answer will be inferential.
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12 A quality control inspector at a plant has found the probability of randomly selecting a defective
battery from a batch of batteries being produced is 0.02. The probability of rain that day has been
projected to be 0.75. If these two events are independent, what is the probability that on that particular
day, it rains, and the inspector chooses a defective battery from the batch being produced?
(1) 0.77
(3) 0.015
(2) 0.5
(4) 0.95
Answer:
The answer is (3) 0.015.
Step-by-step explanation:
This is because to find the probability of finding both independent events happening at the same time, we must multiply them.
The independent events are:
- Randomly selecting a defective battery: 0.02
- Raining tomorrow: 0.75
0.02 x 0.75 = 0.015
Therefore, the answer is (3) 0.015.
1.) The average student takes 5 classes a semester. The table represents the probability distribution of the number of classes an average student passes in a given semester.
x P(X=x)
0 0.001
1 0.098
2
3 0.175
4 0.419
5 0.195
a. Find the missing probability
b. Find the expected number of classes passed.
c. Is it unusual for an average student to pass at most 2 class in a given semester?
a. The missing probability is 0.112
b. The expected number of classes passed is 3.38.
c. Is it unusual for an average student to pass at most 2 classes in a given semester is 0.211
a. Since the whole of all probabilities must rise to 1, we are able to discover the lost likelihood by subtracting the whole of the given probabilities from 1:
1 - 0.001 - 0.098 - 0.175 - 0.419 - 0.195 = 0.112
Subsequently, P(X=2) = 0.112.
b. The anticipated number of classes passed can be found by increasing each possible value of X by its particular likelihood, and after that summing the items:
E(X) = 0(0.001) + 1(0.098) + 2(0.112) + 3(0.175) + 4(0.419) + 5(0.195)
= 3.38
Hence, the anticipated number of classes passed is 3.38.
c. To decide in case it is bizarre for an average student to pass at most 2 classes in a given semester, we have to calculate the likelihood of passing at most 2 classes:
P(X ≤ 2) = P(X=0) + P(X=1) + P(X=2)
= 0.001 + 0.098 + 0.112
= 0.211
Since this likelihood is more noteworthy than 0.05 (i.e., the commonly utilized threshold for determining whether an occasion is unordinary), it isn't abnormal for a normal understudy to pass at most 2 classes in a given semester.
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What is the correct answer for 17? Plsss help
If lines m and n are parallel, then the value of x must be 4.
How to find the value of x?
If lines m and n are parallel, then the measures of the angles in the correspondent quadrants must be the same ones.
Here we can see that the two angles are in the third quadrant, thus, these angles have the same measure. Then we can write this as:
6x² = 96
Now we can solve this for x, we will get:
x² = 96/6
x² = 16
x = √16
x = 4
That is the value of 4.
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Find cordinates of point of inter section
7x+4y=23
8x-10y=19
Answer:
To find the coordinates of the point of intersection between the two lines, we can solve the system of equations by elimination or substitution. Here, we will use the elimination method.
First, we will multiply the first equation by 10 and the second equation by 4, in order to eliminate the y term:
- 70x + 40y = 230
- 32x - 40y = 76
Adding these two equations, we get:
- 102x = 306
Dividing both sides by 102, we get:
- x = 3
Now we can substitute this value of x into either equation to find the value of y. Using the first equation:
- 7(3) + 4y = 23
- 21 + 4y = 23
- 4y = 2
- y = 1/2
Therefore, the point of intersection is (3, 1/2).
Answer:
Step-by-step explanation:
Solve the following quadratic equation by completing the square. Simplify the solutions and rationalize denominators, if necessary.
3x^2−30x=−2
The solutions to this quadratic equation are x = √(73/3) + 5 or x = -√(73/3) + 5.
What is a quadratic equation?In Mathematics and Geometry, the standard form of a quadratic equation is represented by the following equation;
ax² + bx + c = 0
Next, we would solve the given quadratic equation by using the completing the square method;
3x² - 30x = -2
By dividing all through by 3, we have:
x² - 10x = -2/3
In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:
x² - 10x + (-10/2)² = -2/3 + (-10/2)²
x² - 10x + 25 = -2/3 + 25
x² - 10x + 25 = 73/3
By simplifying, we have;
(x - 5)² = 73/3
x = √(73/3) + 5 or x = -√(73/3) + 5
Read more on quadratic functions here: brainly.com/question/14201243
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