The probabilities are given as follows:
P(964.6 < X < 1000.1) = 0.071 = 7.1%.P(964.6 < M < 1000.1) = 0.338 = 33.8%How to obtain probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation given by the equation presented as follows: [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The mean and the standard deviation for this problem is given as follows:
[tex]\mu = 957, \sigma = 193[/tex]
The probability is the p-value of Z when X = 1000.1 subtracted by the p-value of Z when X = 964.6, hence:
Z = (1000.1 - 957)/193
Z = 0.22.
Z = 0.22 has a p-value of 0.5871.
Z = (964.6 - 957)/193
Z = 0.04.
Z = 0.04 has a p-value of 0.5160.
Hence:
0.5871 - 0.5160 = 0.0711.
For the sample of 58, the standard error is obtained as follows:
s = 193/sqrt(58) = 25.34.
Hence:
Z = (1000.1 - 957)/25.34
Z = 1.7.
Z = 1.7 has a p-value of 0.9554.
Z = (964.6 - 957)/25.34
Z = 0.3.
Z = 0.3 has a p-value of 0.6179.
Hence:
0.9554 - 0.6179 = 0.338.
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Consider the graph of function f below. A diagonal curve declines through (negative 6, 7), (negative 5, 5), (negative 4, 3), (negative 3, 1), (3, negative 1, negative 3), (0, negative 5) and (1, negative 7) on the x y coordinate plane. The function g is a transformation of f. If g has a y-intercept at -1, which of the following functions could represent g? A. g(x) = f(x) - 1 B. g(x) = f(x + 4) C. g(x) = f(x - 1) D. g(x) = f(x) + 4
The function g(x) is defined as follows:
D. g(x) = f(x) + 4.
What is a translation?A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.
The four translation rules for functions are defined as follows:
Translation left a units: f(x + a).Translation right a units: f(x - a).Translation up a units: f(x) + a.Translation down a units: f(x) - a.The y-intercept for each function is given as follows:
f(x): y = -5.g(x): y = -1.Meaning that g(x) is a translation up four units of function f(x), hence it is defined as follows:
g(x) = f(x) + 4.
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Answer: D
Step-by-step explanation:
The function g(x) is defined as follows:
D. g(x) = f(x) + 4.
What is a translation?
A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.
The four translation rules for functions are defined as follows:
Translation left a units: f(x + a).
Translation right a units: f(x - a).
Translation up a units: f(x) + a.
Translation down a units: f(x) - a.
The y-intercept for each function is given as follows:
f(x): y = -5.
g(x): y = -1.
Meaning that g(x) is a translation up four units of function f(x), hence it is defined as follows:
g(x) = f(x) + 4.
find 15x2 2/3 using the distributive property
Evaluate each expression using the graphs of y=f(x) and y=g(x) shown below.
The composition of functions is solved and the expressions are
a) ( g o f ) ( -1 ) = 1
b) ( g o f ) ( 0 ) = 4
c) ( f o g ) ( -1 ) = -2
d) ( f o g ) ( 4 ) = -1
Given data ,
Let the composition of function be represented as A
Now , the value of A is
a)
( g o f ) ( -1 ) = g ( f ( -1 ) )
On simplifying the function , we get
when x = -1 , f ( -1 ) = 2
g ( 2 ) = 1
So , ( g o f ) ( -1 ) = 1
b)
( g o f ) ( 0 ) = g ( f ( 0 ) )
On simplifying the function , we get
when x = 0 , f ( 0 ) = 0
g ( 0 ) = 4
So , ( g o f ) ( 0 ) = 4
c)
( f o g ) ( -1 ) = f ( g ( -1 ) )
On simplifying the function , we get
when x = -1 , g ( -1 ) = 2
f ( 2 ) = -2
So , ( f o g ) ( -1 ) = -2
d)
( f o g ) ( 4 ) = f ( g ( 4 ) )
On simplifying the function , we get
when x = 4 , g ( 4 ) = 1
f ( 1 ) = -1
So , ( f o g ) ( 4 ) = -1
Hence , the composition of function is solved
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What is the output for x = -1
Answer:
f(-1) = 16
Step-by-step explanation:
"output" and the f(x) setup just means to plug in -1 in place of x and calculate.
For the function f(x) = 12(3/4)ˣ you have to already know that once you put that -1 in place of x that the -1 power only goes to the 3/4, not the 12 and also what to do with a negative exponent.
Exponent rules are just shortcuts. The shortcut to know here is that the -1 exponent will flip the 3/4 over and make it 4/3 (there are math reasons for this, it's not random. But that's how it works)
So now you have
f(-1) = 12(3/4)⁻¹ which becomes
f(-1) = 12(4/3)
Now you need to know how to multiply with fractions. Here you have a whole, big number times a fraction, which is:
"big num×top all over bottom"
So multiply the 12 times the 4 and put it over the 3
f(-1) = 48/3 = 16
(or you can "cancel" the 12 with the 3 and get 4×4, which is 16, so it comes out the same)
[SKIP TO HERE IF YOU DON'T CARE WHY]
f(x) = 12(3/4)ˣ
f(-1) = 12(3/4)⁻¹
f(-1) = 12(4/3)
f(-1) = 16
Suppose that the function g is defined, for all real numbers, as follows.
The graph of the piecewise function is given by the image presented at the end of the answer.
What is a piece-wise function?A piece-wise function is a function that has different definitions, depending on the input of the function.
All the three definitions of the function in this problem are constant, hence the graph will be composed by horizontal lines.
The definitions are given as follows:
y = 2 to the left of x = 0.y = -1 at x = 0.y = -3 to the right of x = 0.More can be learned about piece-wise functions at brainly.com/question/19358926
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What is the numerical expression that represents the sun of eight squared and thirty two
The numerical expression that represents the sum of eight squared and thirty two will be 96.
A numerical expression is a mathematical expression that consists of numbers and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation.
The numerical expression that represents the sum of eight squared and thirty two is
= 8² + 32
= 64 + 32
= 96.
The question is incomplete and the complete question is '' What is the numerical expression that represents the sum of eight squared and thirty two''.
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34 Points! Multiple choice algebra question. Photo attached. Solve e^x>2.7. Thank you!
Answer:
B
Step-by-step explanation:
not good at explaining this concept but keep the signal its X|X and its near the square root so tadaaa
The line plots represent data collected on the travel times to school from two groups of 15 students.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 4, 6, 14, and 28. There are two dots above 10, 12, 18, and 22. There are three dots above 16. The graph is titled Bus 47 Travel Times.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9, 18, 20, and 22. There are two dots above 6, 10, 12, 14, and 16. The graph is titled Bus 18 Travel Times.
Compare the data and use the correct measure of center to determine which bus typically has the faster travel time. Round your answer to the nearest whole number, if necessary, and explain your answer.
Bus 18, with a median of 13
Bus 47, with a median of 16
Bus 18, with a mean of 13
Bus 47, with a mean of 16
The correct option regarding which bus has the least spread among the travel times is given as follows: Bus 14, with an IQR of 6.
How to solveThe interquartile range is a better measure of spread compared to the range of a data-set, as it does not consider outliers.
For groups of 15 students, we have that:
The first half is composed by the first seven students, hence the first quartile is the fourth dot, which is the median of the first half.
The second half is composed by the last seven students, hence the first quartile is the eleventh dot, which is the median of the first half.
The quartiles for Bus 14 are given as follows:
Q1 = 12.
Q3 = 18.'
Hence the IQR is of:
IQR = Q3 - Q1 = 18 - 12 = 6.
The quartiles for Bus 18 are given as follows:
Q1 = 9.
Q3 = 16.
Hence the IQR is of:
IQR = Q3 - Q1 = 16 - 9 = 7.
Hence Bus 14 is the more consistent bus, due to the lower IQR.
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In a shipment of 1,750 seeds of each type, how many more defective bean seeds would be expected than pumpkin seeds?
There would be 35 more defective bean seeds than pumpkin seeds in the shipment.
How to solveCalculate the number of defective bean seeds:
Defective bean seeds = Total bean seeds * Defect rate for bean seeds
Defective bean seeds = 1,750 * 0.05 = 87.5
Since we can't have half a seed, we'll round it up to the nearest whole number.
Defective bean seeds = 88
Calculate the number of defective pumpkin seeds:
Defective pumpkin seeds = Total pumpkin seeds * Defect rate for pumpkin seeds
Defective pumpkin seeds = 1,750 * 0.03 = 52.5
Similarly, we'll round it up to the nearest whole number.
Defective pumpkin seeds = 53
Calculate the difference in defective seeds:
Difference in defective seeds = Defective bean seeds - Defective pumpkin seeds
Difference in defective seeds = 88 - 53 = 35
So, there would be 35 more defective bean seeds than pumpkin seeds in the shipment.
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In a shipment of 1,750 seeds of each type, with a defect rate of 5% for bean seeds and 3% for pumpkin seeds, how many more defective bean seeds would be expected than pumpkin seeds?
In a lottery game, a player picks six numbers from 1 to 22. If the player matches all six numbers, they win 40,000 dollars. Otherwise, they lose $1.
To find the probability of winning the lottery game, we can use the formula for combinations:
nCk = n! / (k! * (n - k)!)
where n is the total number of choices (22 in this case) and k is the number of choices we make (6 in this case).
So, the number of possible combinations of six numbers from 22 is:
22C6 = 22! / (6! * 16!) = 13,983,816
Therefore, the probability of winning the lottery game is 1 in 13,983,816.
The expected value of playing the lottery game can be calculated as follows:
Expected value = (Probability of winning * Amount won) - (Probability of losing * Amount lost)
Expected value = (1/13,983,816 * $40,000) - (13,983,815/13,983,816 * $1)
Expected value = $0.5709
This means that on average, the player can expect to win about 57 cents per game played. However, it is important to note that this is just an average and the actual outcome of any single game can vary widely.
Baristas at Hot Cocoa Coffee Shop tested their new hot chocolate machine. The following table shows the number of seconds the machine was turned on and the amount of hot chocolate that filled up the cup. Time (seconds) 4 8 12 16 20 24 Hot Chocolate Amount (fluid ounces) 5 7.5 9 11 13 16 Which representation is most appropriate for displaying and describing what is happening to the amount of hot chocolate over time? scatter plot titled New Machine with the x axis labeled hot chocolate amount in fluid ounces going from 0 to 18 and the y axis labeled time in seconds going from 0 to 26, with points at 5 comma 4, 7 and a half comma 8, 9 comma 12, 11 comma 16, 13 comma 20, and 16 comma 24 line graph titled New Machine with the x axis labeled hot chocolate amount in fluid ounces going from 0 to 18 and the y axis labeled time in seconds going from 0 to 26, with points at 5 comma 4, 7 and a half comma 8, 9 comma 12, 11 comma 16, 13 comma 20, and 16 comma 24, with line segments connecting each point to the next scatter plot titled New Machine with the x axis labeled time in seconds going from 0 to 28 and the y axis labeled hot chocolate amount in fluid ounces going from 0 to 18, with points at 4 comma 5 and 8 comma 7 and a half and 12 comma 9 and 16 comma 11 and 20 comma 13 and 24 comma 16 line graph titled New Machine with the x axis labeled time in seconds going from 0 to 28 and the y axis labeled hot chocolate amount in fluid ounces going from 0 to 18, with points at 4 comma 5 and 8 comma 7 and a half and 12 comma 9 and 16 comma 11 and 20 comma 13 and 24 comma 16, with line segments connecting each point to the next
The most appropriate representation for displaying and describing what is happening to the amount of hot chocolate over time is a scatter plot titled New Machine.
Which representation is most appropriate for displaying and describing what is happening to the amount of hot chocolate over time?
The most appropriate representation for displaying and describing what is happening to the amount of hot chocolate over time is a scatter plot titled New Machine with the x-axis labeled time in seconds going from 0 to 28 and the y-axis labeled hot chocolate amount in fluid ounces going from 0 to 18, with points at 4 comma 5 and 8 comma 7 and a half and 12 comma 9 and 16 comma 11 and 20 comma 13 and 24 comma 16.
A scatter plot is a useful way to show the relationship between two variables, in this case, the amount of hot chocolate and time. Each point on the scatter plot represents a pair of values for time and hot chocolate amount. A line graph with line segments connecting each point to the next would not be appropriate because the data is not continuous, and there is no reason to assume that the relationship between time and hot chocolate amount is linear.
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What linear function equation is represented by this graph?
ANSWER: 1
3
x−4 just took the test
Answer:
The linear function is y = (1/3)x - 4.
Step-by-step explanation:
The y-intercept is -4. Starting at (0, -4), go up 1 unit and then right 3 units. You will end at (3, -1). So the slope of this line is 1/3, and it follows that the function is
y = (1/3)x - 4.
Two points on the path of a planet are A and B. The points A and B have coordinates (1, 4, 2) and (2, –1, 3) respectively.
The line l has equation r= (2i-j+3k)+µ(i-j+k)
(a) Calculate the distance between the points A and B .
(b) The line AB makes an acute angle θ with l. Calculate θ.
(c) The point P on the line l is where λ = p.
(i) for the vector AP how that :
AP. (i-j+k)=7+3p
(ii) Hence find the coordinates of the foot of the perpendicular from the point
A to the line l.
(c) Determine the cartesian equation of line l.
(d) Determine the cartesian equation of line A
Answer:
Step-by-step explanation:
(a) The distance between two points A(x1, y1, z1) and B(x2, y2, z2) is given by the formula: AB = √((x2-x1)² + (y2-y1)² + (z2-z1)²). Substituting the coordinates of points A and B into this formula gives: AB = √((2-1)² + (-1-4)² + (3-2)²) = √(14).
(b) The direction vector of line l is given by the vector (i-j+k). The direction vector of line AB is given by the vector AB = (2-1)i + (-1-4)j + (3-2)k = i - 5j + k. The cosine of the angle between two vectors is given by the dot product of the vectors divided by the product of their magnitudes. Therefore, cos(θ) = (AB.(i-j+k)) / (|AB|.|i-j+k|) = ((i - 5j + k).(i-j+k)) / (√14.√3) = -3/√42. Hence θ = cos⁻¹(-3/√42).
©(i) Let P be the point on line l where λ = p. Then P has position vector r = (2i-j+3k)+p(i-j+k) = (2+p)i + (-1-p)j + (3+p)k. The vector AP is given by AP = r - a = ((2+p)i + (-1-p)j + (3+p)k) - (i+4j+2k) = pi - (5+p)j + pk. Taking the dot product of AP with (i-j+k), we get AP.(i-j+k)=7+3p.
©(ii) The foot of the perpendicular from point A to line l is the point on line l that is closest to point A. This point is obtained when AP is perpendicular to the direction vector of line l, which is (i-j+k). Therefore, AP.(i-j+k)=0. Substituting the expression for AP.(i-j+k), we get 7+3p=0, so p=-7/3. Substituting this value of p into the expression for r, we get r = (2-7/3)i - 8/3j + 2k. Hence, the coordinates of the foot of the perpendicular from point A to line l are (1/3,-8/3,2).
(d) The cartesian equation of a line with direction vector d and passing through a point with position vector a is given by r=a+λd. For line l, d=(i-j+k), a=(2i-j+3k), so its cartesian equation is r=(2i-j+3k)+λ(i-j+k).
How many triangles exist with the given side lengths?
3in , 4in , 2in
Step-by-step explanation:
Only ONE .....there are three sides to a triangle and you supplied 3 sides.
Suppose you have a 4 foot sub and you have to feed 10 people ,how many cuts will you make?
Answer: Cut 3 inch per person
Step-by-step explanation:
there is a 4 foot sub you take the quadrilatiral and divide it by 10 and you get 3 inches per person remember to multiply the reciprocal by 12 as there are 12 inches in a foot and you have 4 foot so the product of that reciprocal will be equal to 4 divided by your sum from adding the recriptorcal into the quadrilateral remember a quadrilateral not a duolateral or a triolatiral as there is 4 feet in the sub. >:)
Answer:
7 Cuts
Step-by-step explanation:
This is because if you do 48 inches / 6 inches = 8 sections Since each cut will create two sections, you need to make 7 cuts (one fewer than the number of sections) to get 8 equal portions.
Your friend has a bag of yellow and purple candy. He wants to use them to play a game with you.
Purple is worth 2 points and yellow is worth three points. Pick 9 candies from the bag
Create a system of equations where the combination of the candies gives you a total of 22 points. Make sure you label and define your variables.
The system of equations where the combination of the candies gives you a total of 22 points are:
x + y = 9
2x + 3y = 22
How can we create system of equations?To create the equations, we shall first define the variables:
x = the number of purple candies
y = the number of yellow candies
Next, we shall use the given information that purple candies are worth 2 points and yellow candies are worth 3 points.
Then, we would make sure that the total number of candies selected is 9.
The first equation represents the total number of candies selected:
x + y = 9
The second equation represents the total number of points obtained:
2x + 3y = 22
Therefore, the system of equations is:
x + y = 9
2x + 3y = 22
This is a system of linear equations.
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I arrived home to discover that my 50-foot by 40-foot basement has 18 inches of water in it! There are about 7.5 gallons in 1 cubic foot of water. How much water is in the basement?
Calculate using the most appropriate units to describe the amount of water, and state your answer in a meaningful sentence.
The amount of water in the basement is V = 22,500 gallons
Given data ,
To calculate the amount of water in the basement, we need to determine the volume of water in cubic feet and then convert it to the most appropriate units to describe the amount of water.
First, we need to convert the dimensions of the basement to feet, since the depth of the water is given in inches. 18 inches is equal to 1.5 feet, so the volume of water in cubic feet can be calculated as:
50 feet x 40 feet x 1.5 feet = 3,000 cubic feet
There are 7.5 gallons in 1 cubic foot of water, so the amount of water in the basement in gallons can be calculated as:
3,000 cubic feet x 7.5 gallons per cubic foot = 22,500 gallons
Hence , there are 22,500 gallons of water in the basement
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Find the missing value on the table below:
x y
2 4
? 6
4 8
Question is in the image. Please help me solve these
Answer:
Step-by-step explanation:
A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 106, and the sample
standard deviation, s, is found to be 10.
(a) Construct a 95% confidence interval about u if the sample size, n, is 16.
(b) Construct a 95% confidence interval about u if the sample size, n, is 11.
(c) Construct a 90% confidence interval about μ if the sample size, n, is 16.
(d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed?
In light of this, the 95% confidence interval for is (100.67, 111.33) as s is the sample standard deviation, n is the sample size.
what is standard deviation ?A collection of information's values' standard deviation serves as a gauge for how much variance or dispersion there is. It is a statistical word used to describe the degree to which the individual data points depart as from mean or average value that is contained in the data set. By taking taking square root of the variance—the sum of the squared deviations amongst each point in the data and the mean—we can determine the standard deviation. While a high standard deviation suggests that the data points are widely dispersed, a modest standard deviation suggests that the statistics are close to the mean.
given
(a) When the sample size, n, is 16, we can apply the following formula to create a 95% confidence interval regarding the population mean, :
x ± tα/2 * (s/√n)
where t/2 is the crucial value from the t-distribution with n-1 degrees of freedom and a confidence level of 95%, and x is the sample mean, s is the sample standard deviation, n is the sample size.
We determine that t0.025,15 = 2.131 using a t-distribution table or calculator.
When we enter the values, we obtain:
106 ± 2.131 * (10/√16)
which is equivalent to:
106 ± 5.33
In light of this, the 95% confidence interval for is (100.67, 111.33) as s is the sample standard deviation, n is the sample size.
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Which of these are statistical questions? Select ALL that Apply Question 1: How many minutes does it usually take each teacher to get from home to work? Question 2: During the past year did you work for more than 50 weeks? Question 3: During the past year how many hours did each teacher usually work each week? Question 4: How many extra hours did each doctor work each week?
The statistical questions are:
Question 1: How many minutes does it usually take each teacher to get from home to work?Question 3: During the past year how many hours did each teacher usually work each week?Question 4: How many extra hours did each doctor work each week?What is a statistical question?
A statistical question is a question that can be answered by collecting and analyzing data. It is a question that expects a variability in the response, meaning different individuals may give different answers. Statistical questions usually ask about a population, a group of individuals or objects that share a common characteristic or feature, and seek to understand a pattern or trend within that population.
In general, a statistical question is open-ended, does not have a single correct answer, and requires data analysis to arrive at a reasonable conclusion.
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Caroline fills 3 quarts pint glasses with grape juice they grape juice container si too heavy so she uses a smaller 1 quart pint pitcher yo pour the juice how many times does she have to full the smaller pitcher un order to fill 3 of the glasses with grape juice?
Caroline needs to fill the 1-quart pitcher four and a half times in order to fill all 3 pint glasses.
Calculating how to fill a container rightSince Caroline has 3 pint glasses to fill, she needs to use the 1-quart pitcher multiple times. Each time she fills the pitcher, she can pour it into 2 pint glasses
From this, we can say that Caroline needs to pour a total of 3 x 1.5 = 4.5 quarts of juice.
What is a Pitcher
Pitcher is a container with a spout and handle, used for holding and pouring liquids. It is typically used for serving beverages such as water, juice, milk, or iced tea. Pitchers can be made from a variety of materials, including glass, ceramic, metal, or plastic.
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inverse statement of M implies N
The inverse statement of M implies N is a negation of both the conclusion and the hypothesis.
What is an inverse statement?An inverse statement is one in which both the hypothesis and the conclusion are negated. Let us assume a statement with the hypothesis and conclusion as follows: If they annul the law, we will drive carelessly.
The inverse of this statement will be: If they do not annul the law, we will not drive carelessly. So, both the hypothesis and the conclusion are rewritten in negative terms.
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The number of lattes sold daily by two coffee shops is shown in the table.
Shop A Shop B
55 45
52 42
56 57
48 48
57 11
40 10
45 46
41 43
Based on these data, is it better to describe the centers of distribution in terms of the mean or the median? Explain.
A. Mean for both coffee shops because the data distribution is symmetric
B. Median for both coffee shops because the data distribution is not symmetric
C. Mean for shop B because the data distribution is symmetric; median for shop A because the data distribution is not symmetric
D. Mean for shop A because the data distribution is symmetric; median for shop B because the data distribution is not symmetric
Based on the data given in the table, B. Median for both coffee shops because the data distribution is not symmetric
Why is the median better ?It is better to describe the centers of distribution in terms of the median rather than the mean for both coffee shops because the data distribution is not symmetric.
The median is a better measure of central tendency in this case because it is not influenced by outliers or extreme values, which may exist in the data.
The mean, on the other hand, is sensitive to outliers and may not provide an accurate representation of the data distribution.
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Can the sides of a right triangle have lengths 7,9 and the square Root of 155
Answer:
No
Step-by-step explanation:
In order for a triangle to be a right angle, the sum of the squares of the two legs (a and b) must be equal the square of the longest side, known as the hypotenuse (c):
[tex]a^2+b^2=c^2[/tex]
The square root of 155 is the longest side as it is approximately 12.45. Thus, if the triangle is a right triangle, the square root of 155 must be the hypotenuse.
We can now check to see whether the sum of the squares of 7 and 9 equal the square of the square root of 155:
[tex]7^2+9^2=(\sqrt{155})^2\\ 49+81=155\\130=155[/tex]
The equation is not true since 130 is less than and not equal to 155. Therefore, a triangle with side lengths 7, 9, and the square root of 155 cannot be a right triangle.
Write the equation of a line that is perpendicular and passes through the midpoint of AB with A(-3, 5) and B(1, -1).
The given line AB is having endpoints A(-3,5) & B(1,-1).
To find the equation of line AB it can be written as[tex]y-y_1=(x-x_1){(y_2-y_1)/(x_2-x_1)}\\[/tex]
Substituting the given points
[tex]y-(-1)=(x-1){(5-(-1))/(-3-1)}\\[/tex]
y=-(3/2)x+1/2
For two perpendicular lines [tex]m_1*m_2=-1[/tex]
Therefore, (-3/2)*[tex]m_2[/tex]=-1
or [tex]m_2[/tex] = 2/3
Also, the midpoint of AB will be [tex]{1-(-3)}/2, {5-(-1)}/2[/tex] = (2,3).
The line passing through (2,3) & perpendicular to y=-3/2x+1/2 will be given as follows
(y-3)=(2/3)(x-2)
3y-9=2x-4
3y=2x+5 is the required equation of the line.
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Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2
PLEASE ANSWER FAST!!!! NEED TO UNDERSTAND!!!
Step-by-step explanation:
X component = 4.5 - 2.1 = 2.4
Y component = 7.8 - 2.1 = 5.7
Find magnitude using Pythagorean theorem
m^2 = 2.4^2 + 5.7^2
magnitude = 6.18 units
Remember for a right triangle tangent Φ = opposite leg / adjacent leg
angle = arctan ( 5.7 / 2.4 ) = 67.2 degrees
if you increase your current quality score of 85% by 7%, you will have a score of?
Answer:
90.95%
Step-by-step explanation:
85 * 0.07 = 5.95 5.95 + 85= 90.95
Answer:
The answer to your problem is, 90.95%
Step-by-step explanation:
Calculation:
In order to find the answer we need to
= Old score + New Score
= 85 + 7% of 85
= 85 + ( [tex]\frac{7}{100}[/tex] x 85 )
= 85 + ( 0.07 x 85 )
= 85 + 5.95
= 90.95
Which 90.95% is our answer.
Thus the answer to your problem is, 90.95%
Four data sets are shown below. Set 1: {10, 19, 38, 50, 51} Set 2: {5, 21, 26, 39, 51} Set 3: {9, 38, 50, 50, 51} Set 4: {5, 28, 28, 28, 51} Which data set has the largest standard deviation? * Set 1 Set 2 Set 3 Set 4
Answer:
Set 1: {10, 19, 38, 50, 51}
Step-by-step explanation:
To calculate the standard deviation of a data set, we first find the mean of the data set. The mean is simply the sum of all the values in the data set divided by the number of values. For example, the mean of Set 1 is:
(10+19+38+50+51)/5=33.6
Next, we find the variance of the data set. The variance is the average of the squared differences between each value in the data set and the mean. For example, the variance of Set 1 is:
((10−33.6)^2+(19−33.6)^2+(38−33.6)^2+(50−33.6)^2+(51−33.6)^2)/5=323.84
Finally, we take the square root of the variance to get the standard deviation. For example, the standard deviation of Set 1 is:
[tex]\sqrt{323.84}[/tex]=17.99
We can repeat this process for each of the four data sets and find that Set 1 has the largest standard deviation.