There are 3 seniors who take Math and Spanish, but not Physics.
What is Venn Diagram?
A diagram representing mathematical or logical sets pictorially as circles or closed curves within an enclosing rectangle (the universal set), common elements of the sets being represented by the areas of overlap among the circles.
To solve this problem, we can use a Venn diagram to organize the information given about the students.
First, we know that there are 150 seniors in total, so we can label the outer rectangle of the Venn diagram as having a total of 150 students.
Next, we can label the three circles as Math, Spanish, and Physics, with the numbers given in the problem:
80 seniors take Math, so we label the Math circle with 80.
41 seniors take Spanish, so we label the Spanish circle with 41.
54 seniors take Physics, so we label the Physics circle with 54.
We also know that 10 seniors take Math and Spanish, 19 take Math and Physics, 12 take Physics and Spanish, and 7 take all three. We can label these overlaps in the Venn diagram as follows:
The overlap of Math and Spanish is 10.
The overlap of Math and Physics is 19.
The overlap of Physics and Spanish is 12.
The overlap of all three is 7.
To find the number of seniors who take Math and Spanish, but not Physics, we need to subtract the number of seniors who take all three (because they are counted in all three circles) and the number of seniors who take Math, Spanish, and Physics (because they are counted in the overlap of all three circles). Then we add the number of seniors who take only Math and Spanish (because they are not counted in the Physics circle).
Using the formula for the number of elements in the union of three sets, we have:
Math or Spanish or Physics = Math + Spanish + Physics - (Math and Spanish) - (Math and Physics) - (Spanish and Physics) + (Math and Spanish and Physics)
So, the number of seniors who take Math and Spanish, but not Physics is:
Math and Spanish - (Math and Spanish and Physics) + (Math or Spanish or Physics - (Math + Spanish + Physics) + (Math and Spanish and Physics))
= 10 - 7 + (80 + 41 + 54 - 2(10) - 2(19) - 2(12) + 7)
= 3
Therefore, there are 3 seniors who take Math and Spanish, but not Physics.
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2) The table shows the number of minority officers in the U.S. military in 2000.
Army
Marines
Air Force Total
9162
1341
4282
18309
2105
914
1518
7269
4075
599
3823
11150
15342
2854
9623
36728
Assume that one person will be randomly selected from the group described in the table. Find the
probability of selecting an officer who is in the Navy, given that the officer is African American. (Do
not reduce.)
3524
A)
8909
African Americans
Hispanic Americans
Other Minorities
Total
B)
Navy
3524
2732
2653
8909
8909
18,309
C).
3524
18,309
3542
14785
D).
2)
The probability of selecting an officer who is in the Navy given that the officer is African American is 0.192.
What is the probability?Probability calculates the likelihood that an event would happen. The likelihood that an event would occur has a value that lies between 0 and 1 or 0 and 100. The more likely an event would happen, the closer the probability value would be to 1 or 100.
The probability of selecting an officer who is in the Navy given that the officer is African American = number of African Americans that are in the Navy / total number of African Americans
Total number of African Americans = 9162 + 3524 + 1341 + 4282 = 18,309
The probability = 3524 / 18,309 = 0.192
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A simple random sample of size n is drawn. The sample mean, x, is found to be 18.1, and the sample standard deviation, s, is found to be 4.1.
(a) Construct a 95% confidence interval about u if the sample size, n, is 34.
Lower bound: Upper bound:
(Use ascending order. Round to two decimal places as needed.)
In response to the stated question, we may state that Hence, the 95% CI function for u is (16.72, 19.48), rounded to two decimal places in increasing order.
what is function?In mathematics, a function is a connection between two sets of numbers in which each member of the first set (known as the domain) corresponds to a single element in the second set (called the range). In other words, a function takes inputs from one set and produces outputs from another. Inputs are commonly represented by the variable x, whereas outputs are represented by the variable y. A function can be described using an equation or a graph. The equation y = 2x + 1 represents a linear function in which each value of x yields a distinct value of y.v
We use the following formula to create a confidence interval around the population mean u:
CI = x ± z*(s/√n)
where x represents the sample mean, s represents the sample standard deviation, n represents the sample size, z represents the z-score associated with the desired degree of confidence, and CI represents the confidence interval.
Because the degree of confidence is 95%, we must calculate the z-score that corresponds to the standard normal distribution's middle 95%. This is roughly 1.96 and may be determined with a z-table or calculator.
CI = 18.1 ± 1.96*(4.1/√34)
CI = 18.1 ± 1.96*(0.704)
CI = 18.1 ± 1.38
Hence, the 95% CI for u is (16.72, 19.48), rounded to two decimal places in increasing order.
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The equation of the line in slope-intercept form is y = 2.5x + 210.
What is slope intercept form?y = mx + b, where m is the line's slope and b is its y-intercept, is the equation of a line in slope-intercept form. This version of the equation is advantageous since it makes it simple to determine a line's slope and y-intercept and to utilise its equation to graph the line.
We may first apply the formula for the slope to get the slope of the line in order to calculate the equation of a line given two points. Next, we solve for the y-intercept using the slope-intercept version of the problem, substituting the slope and one of the supplied locations.
The given coordinates of the line are (46, 325) and (64, 370).
The slope is given by:
m = (y2 - y1) / (x2 - x1)
Substituting the values we have:
m = (370 - 325) / (64 - 46)
m = 45 / 18
m = 2.5
The slope intercept form of the line is given as:
y = mx + b
here, b is the y-intercept.
325 = 2.5(46) + b
b = 325 - 115
b = 210
Hence, the equation of the line in slope-intercept form is y = 2.5x + 210.
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Let f(x)=-3x-1 and g(x)=x - 4 Find (fxg)(-1).
The value of the equation (fxg)(-1) is 10.
What is Equation?An equation is a mathematical statement that shows that two expressions are equal. It usually includes variables, which are represented by letters or symbols, and constants, which are fixed values.
What are the different types of Equations?There are several types of equations in mathematics. Here are some of the most common types:
Linear equation: An equation of the form "ax + b = c", where "a", "b", and "c" are constants and "x" is the variable. The graph of a linear equation is a straight line.Quadratic equation: An equation of the form "ax² + bx + c = 0", where "a", "b", and "c" are constants and "x" is the variable. The graph of a quadratic equation is a parabola.
Cubic equation: An equation of the form "ax³ + bx² + cx + d = 0", where "a", "b", "c", and "d" are constants and "x" is the variable. The graph of a cubic equation is a curve that can have one or two humps.
In the given question,
To find (f x g)(-1), we need to evaluate the product of f(-1) and g(-1).
First, we find f(-1):
f(-1) = -3(-1) - 1 = 2
Next, we find g(-1):
g(-1) = -1 - 4 = -5
Now, we can find the product (f x g)(-1):
(f x g)(-1) = f(-1) x g(-1) = 2 x (-5) = -10
Therefore, (f x g)(-1) = -10.
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A carpenter has a box of nails of various
different lengths. You decide to practice your
weighted averaging skills to figure out the
average length of a nail in the box. You grab
two handfuls of nails and count out the
number of each type of nail. You record your
data in the table below.
Sample
Type
Short nail
Medium nail
Long nail
Number Abundance
of Nails
(%)
67
18
10
[?]
Nail Length
(cm)
2.5
5.0
7.5
What is the percent abundance of the
medium nails in your sample?
The percent abundance of medium nails in the sample is approximately 18.95%.
What is weighted averaging?An average value for a collection of data is calculated statistically via weighted averaging, where each data point is assigned a weight based on its relative relevance or frequency. This method is frequently applied when certain data points are more important than others or when the sample sizes for several sets of data vary. Each data point is multiplied by its weight in weighted averaging, and the resulting products are added up and divided by the overall weight.
The number of each type of nail is:
Abundance = 67 + 18 + 10 = 95
The weighted average is:
Weighted Average = (Abundance1 x Value1 + Abundance2 x Value2 + ... + AbundanceN x ValueN) / Total Abundance
For different types of nails we have:
Short nail: Abundance1 = 67, Value1 = 2.5
Medium nail: Abundance2 = 18, Value2 = 5.0
Long nail: Abundance3 = 10, Value3 = 7.5
Substituting the values:
Weighted Average = (67 x 2.5 + 18 x 5.0 + 10 x 7.5) / 95
Weighted Average ≈ 3.53
The percent abundance is:
Percent Abundance = (Abundance2 / Total Abundance) x 100%
Substituting the values:
Percent Abundance = (18 / 95) x 100%
Percent Abundance ≈ 18.95%
Hence, the percent abundance of medium nails in the sample is approximately 18.95%.
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Help quick! Timed
Let f(x) = ex and g(x)=x-3. What are the domain and range of (fog)(x)?
domain: x > 0
range: y < 0
O domain: x>3
range: y > 0
O domain: all real numbers
range: y < 0
domain: all real numbers
range: y > 0
Answer:
To find the domain and range of (fog)(x), we need to first find (fog)(x):
(fog)(x) = f(g(x)) = f(x-3) = e^(x-3)
The domain of (fog)(x) is all real numbers because there are no restrictions on the input x that would make e^(x-3) undefined.
To find the range of (fog)(x), we need to determine the possible outputs of e^(x-3). Since e^x is always positive, e^(x-3) is positive for all x. Therefore, the range of (fog)(x) is y > 0.
So, the answer is: D. domain: all real numbers | range: y > 0
Trigonometric Functions
pls help and be sure to show all your work !! the second pic is the graph that needs to be plotted for the first question.
A) Values of y will be 1, 0, -1, 0, 1
B) and C) plot the values as shown in below figure.
Define the term Trigonometric Function?Trigonometric functions are a set of mathematical functions that relate the angles and sides of right triangles.
A) for f(x) = cos x; the values of x-y chart are:
x y = f(x)
0 1
[tex]\frac{\pi }{2}[/tex] 0
[tex]\pi[/tex] -1
[tex]\frac{3\pi }{2}[/tex] 0
[tex]2\pi[/tex] 1
B) the points are plotted as given figure below.
C) Connects the dots to show the graph of y = cos x; sown in figure below please check it.
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A sample of 245 high school students from grades 9-10 and 11-12 were asked to choose the kind of band to have play at a school dance
Let's break down this question. How many students were in each grade? In grades 9-10, there were 122 students, and in grades 11-12, there were 123 students. What kind of bands were the students asked to choose from? Were they given a list of bands to choose from, or were they simply asked to suggest a band they would like to see?
a string composed of positive integers, in which every prefix contains at least as many positive integers i as integers i 1.
Lattice permutation is a string composed of positive integers, in which every prefix contains at least as many positive integers i as integers i + 1.
In mathematics, a lattice permutation group is a type of permutation group, also known as a Coxeter group, which acts on a set of vectors in a lattice.
A lattice permutation group is a special type of finite group that can be used to generate symmetries in a lattice structure. They are related to Coxeter groups, which are groups that act on a set of points in a Euclidean space, and are generated by reflections.
Lattice permutation groups are generated by permutations of the lattice points, and can be used to study the symmetry of a lattice. These groups are important in the study of crystallography, and can be used to classify the symmetry of a lattice.
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The complete question is:
______ is a string composed of positive integers, in which every prefix contains at least as many positive integers i as integers i + 1.
A mail-order company business has six telephone lines. Let X denote the number of lines in use at a specified time. Suppose the pmf of X is as given in the accompanying table.
x 0 1 2 3 4 5 6
p(x) 0.10 0.15 0.20 0.25 0.20 0.05 0.05
Calculate the probability of each of the following events.
(a) {at most three lines are in use}
(b) {fewer than three lines are in use}
(c) {at least three lines are in use}
(d) {between two and five lines, inclusive, are in use}
(e) {between two and four lines, inclusive, are not in use}
(f) {at least four lines are not in use}
The probability of each of the events of {at most three lines are in use}, {fewer than three lines are in use}, {at least three lines are in use, {between two and five lines, inclusive, are in use}, {between two and four lines, inclusive, are not in use} and {at least four lines are not in use} are 0.70, 0.45, 0.55, 0.80, 0.35 and 0.40 respectively.
The problem involves finding probabilities of different events for a mail-order company with six telephone lines. The probability mass function (pmf) is given, and we use it to calculate the probabilities of different events such as "at most three lines are in use" or "between two and five lines, inclusive, are in use".
To calculate these probabilities, we use basic probability formulas such as the addition rule, subtraction rule, and the complement rule.
P(X ≤ 3) = 0.10 + 0.15 + 0.20 + 0.25 = 0.70
P(X < 3) = 0.10 + 0.15 + 0.20 = 0.45
P(X ≥ 3) = 1 - P(X < 3) = 1 - (0.10 + 0.15 + 0.20) = 0.55
P(2 ≤ X ≤ 5) = P(X ≤ 5) - P(X < 2) = (0.10 + 0.15 + 0.20 + 0.25 + 0.20) - 0.10 = 0.80
P(2 ≤ X ≤ 4) = 0.20 + 0.25 + 0.20 = 0.65, so P(2 ≤ X ≤ 4)ᶜ = 1 - 0.65 = 0.35
P(X ≥ 4) = 0.20 + 0.05 + 0.05 = 0.30, so P(X ≤ 3) = 1 - P(X ≥ 4) = 0.70 - 0.30 = 0.40
These formulas are applied based on the given events to determine the probabilities.
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Converting
What is 3.4 hours in hours and minutes?
By answering the presented questiοn, we may cοnclude that 0.4 οf an expressiοns hοur is 0.4 x 60 = 24 minutes in this situatiοn. As a result, 3.4 hοurs equals 3 hοurs and 24 minutes.
What is expressiοn ?An expressive in mathematics is a collection of numbers, variables, and complicated mathematical operations (such as addition, subtraction, multiplication, division, multiplicands, and others) that convey a quantity's value. Expressions can be as straightforward as "3 + 4" or as complex as "(3x2 - 2) / (x + 1)". They could also include functions like "sin(x)" or "lg(y)".
The real way to evaluate an expression is to insert the variables with their values and carry out the arithmetic operations in the order specified. For instance, the phrase "3x + 5" means 3(2) + 5 = 11 if x = 2. In mathematics, expressions are typically used to describe actual situations, build equations, and decompose challenging mathematical diagrams.
3 hοurs and 24 minutes is cοmparable tο 3.4 hοurs.
Yοu may separate the full number (which represents the hοurs) frοm the decimal tο cοnvert decimal hοurs tο hοurs and minutes (which represents the fractiοn οf an hοur in minutes).
0.4 οf an hοur is 0.4 x 60 = 24 minutes in th
is situation. As a result, 3.4 hours equals 3 hours and 24 minutes.
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I will mark you brainiest!
What is the measure of angle R?
A) 17 degrees
B) 25 degrees
C) 34 degrees
D) 65 degrees
Answer: D) Angle R is 65 degrees
Step-by-step explanation:
In the given figure, we have a right-angled triangle PQR.
Using the property of angles in a triangle, we know that the sum of angles in a triangle is 180 degrees. Therefore,
∠QRP + ∠QPR + ∠PRQ = 180 degrees
Since ∠PRQ is a right angle (90 degrees), we have:
∠QRP + ∠QPR = 90 degrees
Now, we are given that ∠QPR is 25 degrees. Substituting this in the above equation, we get:
∠QRP + 25 = 90 degrees
Solving for ∠QRP, we get:
∠QRP = 90 - 25 = 65 degrees
Therefore, the measure of angle R is 65 degrees, which is option (D).
Answer:
Answer is D
Step-by-step explanation:
SPiDerMom is so hot bTw
Please answer these questions correctly :)
Find the percent of each number :-
1.) 64% of 75 tiles :
[tex] \implies \sf \: \dfrac{64}{100} \times 75 \\ \\\implies \sf \:0.64 \times 75 \\ \\ \implies \sf \: 48 \\ [/tex]
Hence, 64% of 75 tiles is 48 tiles.
2.) 20% of 70 plants.
[tex] \implies \sf \: \dfrac{20}{100} \times 70 \\ \\\implies \sf \:0.2 \times 70 \\ \\ \implies \sf \: 14 \\ [/tex]
Hence, 20% of 70 plants is 14 plants.
3.) 32% of 25 pages .
[tex] \implies \sf \: \dfrac{32}{100} \times 25 \\ \\\implies \sf \: 0.32 \times 25 \\ \\ \implies \sf \: 8 \\ [/tex]
Hence, 32% of 25 pages is 8 pages.
4.) 85% of 40 e -mails.
[tex] \implies \sf \: \dfrac{85}{100} \times 40 \\ \\\implies \sf \:0.85 \times 40 \\ \\ \implies \sf \: 34 \\ [/tex]
Hence, 85% of 40 e -mails is 34 e-mails.
5.) 72% of 350 friends.
[tex] \implies \sf \: \dfrac{72}{100} \times 350 \\ \\\implies \sf \:0.72 \times 350 \\ \\ \implies \sf \: 252 \\ [/tex]
Hence, 72% of 350 friends is 252 friends.
6.) 5% of 220 files.
[tex] \implies \sf \: \dfrac{5}{100} \times 220 \\ \\\implies \sf \:0.05 \times 220 \\ \\ \implies \sf \: 11 \\ [/tex]
Hence, 5% of 220 files is 11 files.
In a certain company, employees contribute to a welfare fund at the rate of 4% of the first $1000 earned, 3% of the next $1000, 2% of the next $1000 and 1% of any extra monies. How much will an employee who earned $20,000 contribute to the fund?
The employee will contribute 4% of the first $1000, which is $40. Then, the employee will contribute 3% of the next $1000, which is $30. Following that, the employee will contribute 2% of the next $1000, which is $20. Finally, the employee will contribute 1% of the remaining $17,000, which is $170. Therefore, the employee will contribute a total of $260 to the fund.
An employee who earned $20,000 will contribute $260 to the welfare fund.
To calculate the contribution to the welfare fund for an employee who earned $20,000, we can break down the earnings into different tiers based on the given rates.
The first $1000 will have a contribution rate of 4%.
Contribution for the first $1000 = 4% of $1000 = $40.
The next $1000 will have a contribution rate of 3%.
Contribution for the next $1000 = 3% of $1000 = $30.
The next $1000 will have a contribution rate of 2%.
Contribution for the next $1000 = 2% of $1000 = $20.
The remaining amount above $3000 ($20,000 - $3000 = $17,000) will have a contribution rate of 1%.
Contribution for the remaining amount = 1% of $17,000 = $170.
Now, let's sum up the contributions for each tier:
$40 + $30 + $20 + $170 = $260.
Therefore, an employee who earned $20,000 will contribute $260 to the welfare fund.
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please identify from the following choices which has the shape of the resultant matrix of multiplication of a 2 by 4 and 4 by 3 matrices.
The shape of the resultant matrix of the multiplication of a "2 by 4" matrix and a "4 by 3" matrix will be a "2 by 3" matrix, the correct option is (d).
We know that the general rule for matrix multiplication, which is If matrix A is "m by n" matrix (it has m rows and n columns) and the matrix B is "n by k" matrix (it has n rows and k columns),
Then the product AB is an "m by k" matrix, which means, that the resulting matrix will have "m" rows and "k" columns.
In this case, the "2 by 4" matrix means that matrix has 2-rows and 4-columns, and
The "4 by 3" matrix means the matrix has 4-rows and 3-columns.
Since the number of columns in the first matrix (4) matches the number of rows in the second matrix (4), we can perform the multiplication.
The resulting matrix will have 2 rows and 3 columns,
Therefore, the shape of the resultant matrix is (d) 2 by 3.
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The given question is incomplete, the complete question is
Please identify from the following choices which has the shape of the resultant matrix of multiplication of a "2 by 4" and "4 by 3" matrices.
(a) 3 by 2
(b) 2 by 4
(c) 4 by 4
(d) 2 by 3
Pleasee help!
Highlight the vertex, and name the angle on the image below
Answer:
Highlight "x" then it's an acute angle
Step-by-step explanation:
The retail price of a television set is $4,500. If the buyer pays by cash, the price is 10% below the retail price. If the set is bought on higher purchase, the buyer pays a down payment of $675 and 24 monthly installments of $212.50. Calculate for the television the:
cash price to the buyer, if he pays by cash.
amount payable.
outstanding balance.
hire purchase price.
interest.
difference between the hire purchase and the cash price.
percentage interest charged.
Cash price to the buyer, if he pays by cash:
The cash price would be 10% less than the retail price of $4,500:
Cash price = $4,500 - (10% * $4,500)
Cash price = $4,500 - $450
Cash price = $4,050
Amount payable:
If the buyer chooses to purchase the TV on higher purchase, the amount payable would be the sum of the down payment and the total amount of monthly installments:
Amount payable = Down payment + (24 * Monthly installment)
Amount payable = $675 + (24 * $212.50)
Amount payable = $5,175
Outstanding balance:
The outstanding balance would be the difference between the amount payable and the down payment:
Outstanding balance = Amount payable - Down payment
Outstanding balance = $5,175 - $675
Outstanding balance = $4,500
Hire purchase price:
The hire purchase price would be the sum of the down payment and the outstanding balance:
Hire purchase price = Down payment + Outstanding balance
Hire purchase price = $675 + $4,500
Hire purchase price = $5,175
Interest:
The interest charged on the hire purchase would be the difference between the hire purchase price and the cash price:
Interest = Hire purchase price - Cash price
Interest = $5,175 - $4,050
Interest = $1,125
Difference between the hire purchase and the cash price:
The difference between the hire purchase price and the cash price would be the interest charged:
Difference = Interest
Difference = $1,125
Percentage interest charged:
To calculate the percentage interest charged, we can divide the interest by the hire purchase price and multiply by 100:
Percentage interest charged = (Interest / Hire purchase price) * 100
Percentage interest charged = ($1,125 / $5,175) * 100
Percentage interest charged = 21.74%
Therefore, the cash price to the buyer is $4,050, the amount payable is $5,175, the outstanding balance is $4,500, the hire purchase price is $5,175, the interest charged is $1,125, the difference between the hire purchase and the cash price is $1,125, and the percentage interest charged is 21.74%.
What does the point (5, 10) represent on the
graph?
Answer:
It means the point x = 5 and y = 10
Answer: The place 5 units right and 10 units up from the center of the graph (the origin).
Step-by-step explanation:
Starting at the origin, the 5 represents moving right 5, and the 10 represents going up 5.
Bill buys candy that costs $5 per pound. He will spend at least $40 on candy. What are the possible numbers of pounds he will buy? Use p for the number of pounds Bill will buy. Write your answer as an inequality solved for p.
Answer: 5p = 40
Step-by-step explanation:
5 X p = 40
5/5 40/5
p = 8
a coin is toosed and a number cube is rolled. sketch a list or tree digrams to represnts the sample space
The first of these two events is the number displayed on the cube. The result of the coin toss is the second. There should be two columns in this tree, one for each occurrence.
a list or tree digrams to represnts the sample space in the given below figure . Observe the first column first. Let the number cube's result be. The following six values are possible:. Six branches, one for each outcome, result from that proceed to the following column. Let the result of the coin toss be. There would always be two possible results for, regardless of the number obtained for.
The first of these two events is the number displayed on the cube. The result of the coin toss is the second. There should be two columns in this tree, one for each occurrence.
Observe the first column first. Let N represent the number cube's result. Six values are possible: 1, 2, 3, 4, 5, and 6. Six branches, one for each outcome, result from that. proceed to the following column. Let the result of the coin toss be. There would always be two possible results for, regardless of the number obtained for.
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the actual question is :
The number cube is rolled and a coin is tossed . How can you sketch a tree diagram to represent the sample space ?
find the point(s) on the surface which are closest to the point . list points as a comma-separated list, (e.g., (1,1,-1), (2, 0, -1), (2,0, 3)).
The points on the surface z² = xy+ 1 which are closest to the point
(7, 11, 0) is x = 2 and y = 10.
The distance of any point on the surface from the point (7, 11, 0) is
D(x, y) = { [ x -7]2 + [ y -11 ]2 + [ z -0 ]2 } 1/2
D(x, y) = { [ x -7]2 + [ y -11 ]2 + z 2 } 1/2
D(x, y) = { [ x -7]2 + [ y -11 ]2 + z 2 } 1/2
D(x, y) = { [ x -7]2 + [ y -11 ]2 + x y +1 } 1/2
Now,
To minimize D suffices to minimize
d (x ,y ) = [ x -7]2 + [ y -11 ]2 + x y +1
∂ d / ∂ x =2 x + y - 14
∂ d / d y = 2 y +x - 22
Solving the system:
2x + y - 14 = 0 and 2y +x - 22 = 0 we get for
x = 2 and for y = 10
The Hessian being 3 > 0 and d²x and d²y positive makes sure that the points ( 2 , 10, √21 ) and ( 2 , 10, -√21 ) are the points of interest
Complete Question:
Find the point(s) on the surface z2=xy+1 which are closest to the point
(7, 11, 0). List points as a comma-separated list, (e.g., (1,1,-1), (2, 0, -1),
(2,0, 3)).
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Locate the absolute extrema of the function on the closed interval
Answer:
The absolute extrema is minimum at (-1, 2/9)
Step-by-step explanation:
Absolute extrema is a logical point that shows whether a the curve function is maximum or minimum.
Forexample a curve in the image attached. A, B and C are points of absolute maxima or absolute maximum. and P and Q are points of absolute minima or minimum.
Remember A, B, C, P, Q are critical points or stationary points.
How do we find absolute extrema?
The find the sign of the second derivative of the function.
From the question;
[tex]{ \sf{g(x) = \sqrt[3]{x} }} \\ \\ { \sf{g(x) = {x}^{ \frac{1}{3} } }} \\ [/tex]
Find the first derivative of g(x)
[tex]{ \sf{g {}^{l}(x) = \frac{1}{3} {x}^{ - \frac{2}{3} } }} \\ [/tex]
Find the second derivative;
[tex]{ \sf{g {}^{ll} (x) = ( \frac{1}{3} \times - \frac{2}{3}) {x}^{( - \frac{2}{3} - 1) } }} \\ \\ { \sf{g {ll}^{(x)} = - \frac{2}{9} {x}^{ - \frac{5}{3} } }}[/tex]
Then substitute for x as -1 from [-1, 1]
[tex]{ \sf{g {}^{ll}(x) = - \frac{2}{9} ( - 1) {}^{ - \frac{5}{3} } }} \\ \\ = \frac{ - 2}{9} \times - 1 \\ \\ = \frac{2}{9} [/tex]
Since the sign of the result is positive, the absolute extrema is minimum
You have three dice in your pocket, one is 4 -sided and two are 6-sided. You randomly select two of the dice, roll them, and record the sum. a. What's the probability the sum is 7 ? b. Given that the sum of the dice is 7 , what's the probability both dice are 6 -sided?
The probability that sum of two randomly selected dice is 7 is 1/2. The given that the sum of the dice is 7, the probability that both dice are 6-sided is 1/3.
a. Each pair has a probability of being selected of 1/3 * 1/2 = 1/6. Now sum of the probabilities of the three pairs that have a sum of 7: P = P(4-6) + P(6-4) + P(6-6) = 1/6 + 1/6 + 1/6 = 1/2
b. Given that the sum of the dice is 7, there are three possible pairs that could have been rolled: (1-6), (2-5), or (3-4). Of these, only one pair has both dice as 6-sided.
P = (1/3 * 1/2) / (1/2) = 1/3
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The graph of triangle has coordinates E(1,4) F(-1,1) and G(2,-1). Graph triangle of EFG and it’s image after a translation of 3 units left and 1 unit down.
Answer:
Step-by-step explanation:1.4 -1, 1 2, -1
Find the 16th term of the arithmetic sequence described below.
ak = 3 + 4 (k − 1)
Show your work here
Answer: 63
Step-by-step explanation:
The given arithmetic sequence is defined by the formula:
ak = 3 + 4(k - 1)
To find the 16th term, we can substitute k = 16 into this formula and simplify:
a16 = 3 + 4(16 - 1)
a16 = 3 + 4(15)
a16 = 3 + 60
a16 = 63
Therefore, the 16th term of the arithmetic sequence is 63.
Suppose that your mass is 86 kg How fast (in m/s) would vou have t0 run to have the same linear momentum as 1490 kg car moving at 2.7 km/h? Number Azo Units mfs The number of _ significant digits is set to 2; the tolerance is +/-3%/
The velocity with which we have to move to have the momentum equal to the car is 46.78 km/h.
Linear momentum is the vector quantity and described as the product of the mass of an object, m, and its velocity, v. It is represented by the symbol "p," which is also used to denote momentum. Please be aware that the body's momentum always points in the same direction as its vector of motion.
We are given:-
The mass of the car (M1) = 1490kg.
The velocity of the car (V1V1)= 2.7 km/h.
The formula to calculate linear momentum:- linear momentum= mass of the body* Velocity of the body (P= mvmv)
therefore, the momentum (P1) of the car = M1V1
P1= 1490*2.7= 4023
let momentum of yourself is P2 which is equal to P1 according to the question, Hence P2= 4023.
M2= 86 kg.
V2= ?
P2= M2V2
V2= P2/M2
V2 = 4023/86
V2= 46.78 km/h.
hhence toto the velocity with which we have to run to get momentum equal to the car is 46.78 km/h.
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[tex]y = ( \sqrt{47 + \sqrt{9 - \sqrt{25} } } )[/tex]
find the value of y ~
The simplification of the given expression
[tex]y = ( \sqrt{47 + \sqrt{9 - \sqrt{25)} } } [/tex]
is y = 7
How to simplify expressions?[tex]y = ( \sqrt{47 + \sqrt{9 - \sqrt{25)} } } [/tex]
find the square root of 25
[tex]y =( \sqrt{47 + \sqrt{9 - 5} } [/tex]
simplify root 9 - 5
[tex]y = ( \sqrt{47 + \sqrt{4} } [/tex]
find the square root of 4
[tex]y = ( \sqrt{47 + 2)} [/tex]
Add root 47 and 2
[tex]y = ( \sqrt{49} )[/tex]
Find the square root of 49
y = 7
Therefore, the solution to the given expression is y = 7
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what is the range of function m?
The range of the function m is [1, ∞). Thus, B is correct option.
What are a function's range and domain?The dοmain οf a functiοn is the cοllectiοn οf values that can be plugged intο it. This set represents the x values in a functiοn like f. (x). A functiοn's range is the set οf values that the functiοn can take οn. This is the set οf values returned by the functiοn when we enter an x value.
Tο determine the range οf functiοn m, we must first determine the set οf all pοssible functiοn οutput values.
Looking at the function graph, we can see that the lowest point is (3, 1) and the highest point is (∞, ∞).
As a result, the function m has a range of [1, ∞).
We can write: in interval notation:
m ∈ [1, ∞) range.
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Which expression is equivalent to 14m2n2/ 7mn? Assume that the denominator does not equal to zero.
A. 7/mn
B.2mn/7
C.7mn
D.2mn
Answer: D: 2mn
Step-by-step explanation:
To simplify the expression 14m^2n^2 / 7mn, we can cancel out the common factors in the numerator and denominator.
We can cancel out 7 in both the numerator and denominator to get:
14m^2n^2 / 7mn = 2m * n / 1 = 2mn
Therefore, the expression 14m^2n^2 / 7mn is equivalent to 2mn. The answer is option D.
We are working on a survey that shows what 100 insurance holders claim for that survey. We find that 40 are fire claims (FIRE), 16 of which are fraudulent (FRAUD). Also, there are a total of 40 fraudulent claims.
(a) Let us construct a contingency table summarizing the claims data. Use the pairs of Events FIRE and FIRE, FRAUD and FRAUD as shown below:
The probability of a claim being both fire and fraudulent is:
P(Fire and Fraud) = number of claims that are both fire and fraudulent/total number of claims
= 16 / 100
= 0.16
We can use the information given to construct a contingency table as follows:
Fraud No Fraud Total
Fire 16 24 40
No Fire 24 36 60
Total 40 60 100
This table shows the number of insurance claims that fall under each combination of the FIRE and FRAUD events. For example, 16 claims are both fire and fraudulent, and 24 claims are fire but not fraudulent.
We can also calculate some probabilities from this table. For example, the probability of a claim being fraudulent is:
P(Fraud) = number of fraudulent claims / total number of claims
= 40 / 100
= 0.4
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Question:-We are working on a survey that shows what 100 insurance holders claim for that survey. We find that 40 are fire claims (FIRE), 16 of which are fraudulent (FRAUD). Also, there are a total of 40 fraudulent claims.
(a) Let us construct a contingency table summarizing the claims data. Use the pairs of
Events FIRE and, FRAUD and as shown below:
Fraud No Fraud Total
Fire 16 24 40
No Fire 24 36 60
Total 40 60 100