Answer:
point form (-3, -1)
equation form x=-3, y=-1
Step-by-step explanation:
consider the following data for two independent random samples taken from two normal populations. sample 1 10 7 14 7 9 7 sample 2 9 7 8 4 5 9
a. Compute the two sample means.
Sample 1: Answer 9
Sample 2: Answer 7
b. Compute the two sample standard deviation (to 2 decimals).
Sample 1: Answer 2.28
Sample 2: Answer 1.79
c. What is the point estimate of the difference between the two population means? Answer
d. What is the 90% confidence interval estimate of the difference between the two population means (to 2 decimals - - use 9 degrees of freedom)? Answer
C. The point estimate of the difference between the two population means is 2.
D. The 90% confidence interval estimate of the difference between the two population means is (1.748, 0.867)
Given that:
Sample 1 mean (x1) = 9
Sample 2 mean (x2) = 7
Sample 1 standard deviation (σ1^2) = 2.28
Sample 2 standard deviation (σ2^2) = 1.79
C. To find point estimate of the difference between the two population means.
sample mean(x1) - sample mean(x 2)
= 9 - 7
= 2
Therefore, point estimate = 2
D. To find 90% confidence interval estimate of the difference between the two population means
90% confidence for 't'
df = (n1 + n2) - 2
= 12-2
= 10
90% confidence with df = 10 is t
t = 1.812
point estimate + 1 - t * [tex]\sqrt{\frac{s^2_{1} }{n_{1} } + \frac{s^2_{2} }{n_{2} } }[/tex]
2 + 1 - 1.812*[tex]\sqrt{\frac{2.28^2}{6} + \frac{1.79^2}{6} }[/tex]
3 - 1.812 *[tex]\sqrt{0.866 + 0.534}[/tex]
1.188 * 0.9305 + 0.7307
(1.748, 0.867)
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based on his past record, luke, an archer for a college archery team, has a probability of 0.90 of hitting the inner ring of the target with a shot of the arrow. assume that in one practice luke will attempt 5 shots of the arrow and that each shot is independent from the others. let the random variable x represent the number of times he hits the inner ring of the target in 5 attempts. the probability distribution of x is given in the table. P(X) 0 000001 0,00045 0.00810 0.07290 03280S 0.59049
What is the probability that the number of times Luke will hit the inner ring of the target out of the 5 attempts is less than the mean of X?
(A) 0.40951
(B) 0.50000
(C) 0.59049
(D) 0.91854
(E) 0.99144
The probability that Luke will touch the target's inner ring fewer times than the mean of X out of five attempts is 0.40951.
What is probability ?Probability refers to possibility.
A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.
Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.
According to our question-
P(target) equals 0.90
Let the random variable X stand in for the number of times the arrow is fired at the target's ring.
The probability distribution of X is
x: 0 1 2 3 4 5
P(x): 0.00001 0.00045 0.00810 0.07290 0.32805 0.59049
Hence, The probability that Luke will touch the target's inner ring fewer times than the mean of X out of five attempts is 0.40951.
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Jill is going to make weekly deposits of $100 into an account for 3 years. The account earns 5.2%/a compounded weekly. How much money will she have in her account at the end of 3 years? How much money did she make on this investment?
Answer:
every week jill is going to make 5.20 dollars then you do 5.20 x 1095 days in 3 years = $5694 a year
Step-by-step explanation:
Emma has $140 cash to spend at a music store. How much can she spend on items if there is %7 sales tax?
Answer:
$130.84
Step-by-step explanation:
If a 7% sales tax is applied, the cost of the item (including tax) will be 107% of the original price.
To calculate how much Emma can spend if she has $140 cash to spend, divide $140 by 107%:
[tex]\implies \dfrac{140}{107\%}[/tex]
[tex]\implies \dfrac{140}{\frac{107}{100}}[/tex]
[tex]\implies 140 \times \dfrac{100}{107}[/tex]
[tex]\implies \dfrac{14000}{107}[/tex]
[tex]\implies 130.84[/tex]
Therefore, Emma can spend $130.84 on items if there is a 7% sales tax.
take the van der pol equation . (a) set and . convert the above second order differential equation to a two dimensional system of differential equations:
The van der Pol equation which is a second-order differential equation is given by
d²x/dt² - μ(1 - x²)dx/dt + x = 0
Here we are asked to convert it to a two-dimensional system.
Here we need to set y = dx/dt, where y represents the system's velocity.
Hence we will rewrite it as
d²x/dt² = μ(1 - x²)y + x
Now if we set the derivatives of x and y with respect to time to be equal to different variables we get
dx/dt = y
dy/dt = μ(1 - x²)y + x
Hence we get the above systems of equations as the 2-dimensional representation of the Van der Pol equation where x and y represent the system's position and velocity respectively.
If we set μ = 1 and x = 0, then we get
dx/dt = y
dy/dt = y
Hence we get the system of differential equations representing the behavior of the van der Pol equation with μ = 1 and x = 0 in two dimensions.
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I don’t understand number 2
Answer:
x=-6.-3.0.3.6
y=6.3.0.-3.-6
Step-by-step explanation:
So in this problem you're given the table at the top for your values of X is going across their corresponding P of X values and their corresponding Q of X values. So in part A we want to find P fq of X. So first off we're gonna start when X is equal to zero. So that would mean we want to find p. of Q. of zero. So remember you start with your inside function. Well Q of zero is equal to zero. So now we need to find P. Of zero which is equal to three. Alright so next we want to find when X is one. So we have P of Q of one. Well Q of one is equal to one and I'm sorry that would leave us with PS one and PS one happens to also be one. So that'll be value for one. Next for one. X. is to so api of Q of two. Well Q two is equal to four and then P. Of four. That would leave us a pr four and pr four is equal to five. So that will be our answer for the next one. It will be five. Alright, next for three. So we have p. of Q. of three. So we have two of three which is equal to two. So now sorry that should be a P. Then we find P. F two which is also to So that'll be the answer to the 3rd 1 Next we need it for four. So we're looking for p of Q of four. Well looking according to our thing. Q4 is equal to five and then we have to find P. Of five which is zero. And lastly for five. So first we'll start with p. of Q. of five. So Q. A. Five we're told is three. So then we have to find pf three which is equal to four. So that's how you would find your first values. Okay, So now part B. We want to find sfx but no, this is the opposite way this time it's Q. A. P. Of X. So when X zero, we're going to be looking for Q. Of P. Of zero. Well no this P. Of zero is equal to three. So then we have to find Q. of three which is equal to two. It'll be our first answer. Next we'll do one. So we're gonna have Q. Of P. Of one. Well p. of one is equal to one. So then we find Q. Of one which is also one. So bring that down. All right, so now for two. First we're gonna start with Q. A. P. F. Two. Well P. F two is two. So that means we're essentially just finding Q. Of two which is four. Alright, next for three. So you're gonna have cute Of p. of 3? Well p of three is equal to four And Q four is equal to five. So I'll be your answer there. I'll do a new color because I think we're running out of room here. So next we're doing for, so I'm gonna go right here. So we're gonna have Q. A. P. Of four. Well if you four is equal to five, so that means we have to find Q. Of five which is three. And lastly for five. So we're gonna have Q. A. P. Of five. So first we'll find PFE which is zero. So that means now we need Q. Of zero which is zero. And now we filled out both of your tables.
given sales for the year of $218,000, cash expenses of $92,000 and depreciation expense of $23,000, net cash flow for the year is blank . multiple choice question. $195,000 $126,000 $103,000 $218,000
Answer:
$126,000
Step-by-step explanation:
The net cash flow for the year is $103, 000.
What is Net cash flow?After all debts have been settled, net cash flow can represent either a gain or a loss in money over a time period. A company is said to have positive cash flow if, after paying all of its operational expenses, it still has cash left over.
We have,
Sales for the year = $ 218, 000
Cash expenses = $92, 000
Depreciation Expenses = $23, 000
So, the Net cash flow is
= 218,000 - (92, 000 + 23, 000)
= $ 103, 000.
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The length of a rectangle is three times its width. If the perimeter of the rectangle is 40 m, find its length and width.
Answer:
The width would be 5, and the length would be 15.
Step-by-step explanation:
To solve this problem, first look at the perimeter. If the perimeter of the rectangle is 40m, then we can now solve the problem.
Since we don't know the width or the length, first, say that the width is w.
Width=w
Now, since the length is three times the width, we can write 3w for the length.
Length=3w.
Now, combine like terms.
w+3w+w+3w=40
8w=40
Divide by 8 on both sides.
40/8=5
w=5.
Since now we know that the width is 5, plug in 5 for w.
3(5)=15
w=5
The width would be 5, and the length would be 15.
Hope this helps! Have a great day! :D
Answer:
Length = 15 m Width = 5 mStep-by-step explanation:
Let us assume that,
→ Perimeter = 40 m
→ Width = x
→ Length = 3x
Perimeter of rectangle formula,
→ P = 2(l + w)
Forming the equation,
→ 2(3x + x) = 40
Now the value of x will be,
→ 2(3x + x) = 40
→ 2(4x) = 40
→ 8x = 40
→ x = 40/8
→ [ x = 5 ]
Then the length and width is,
→ Width = x = 5 m
→ Length = 3x = 3(5) = 15 m
Hence, these are the answers.
find a forumla for the general term an ( not the partial sum) of the infinte series (starting with a1
A forumla for the general term an ( not the partial sum) of the infinte series (starting with a1) is [tex]a_n=\left(\frac{1}{2}\right)^n[/tex]
[tex]We rewrite $a_1, a_2, a_3, a_4$ in the sequence so that we can find a formula for the nth term of the sequence.$$\begin{aligned}& a_1=\frac{1}{2}=\left(\frac{1}{2}\right)^1 \\& a_2=\frac{1}{4}=\left(\frac{1}{2}\right)^2 \\& a_3=\frac{1}{8}=\left(\frac{1}{2}\right)^3 \\& a_4=\frac{1}{16}=\left(\frac{1}{2}\right)^4\end{aligned}[/tex]
Based on the pattern of the first four terms, we know this sequence is a geometric sequence, and the nth term of the sequence is given by the formula[tex]a_n=\left(\frac{1}{2}\right)^n[/tex]
Geometric Sequence
A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant. We can write a formula for the nth term of a geometric sequence in the form
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which of the following are defined? you can assume that all vector fields have 3 components and f(x,y,z)f(x,y,z) is a scalar field.
div( curl( grad f )) - scalar field; the divergence of a vector field is a scalar field
What is vector ?A quantity with both direction and magnitude, particularly when used to depict the distance between two points in space.
What is Scaler Field ?In a scalar field, each point in a space—possibly actual space—is assigned a single integer.
According to the given information
(a) You can only determine the curl of a vector field; curl f is meaningless.
(b) grad f - vector field; when you take a gradient of something , it results in a vector field
(c) div F - scalar field; take the divergence of a vector field, it results in a scalar field
(d) A vector field is produced by the operation curl(grad f) on a vector field.
(e) grad F - meaningless; gradients are only used for scalar fields
(f) grad( div F ) - vector field; the gradient of a scalar field is a vector field
(g) div( grad f ) - scalar field; if you take divergence of a vector field, the result is a scalar field
(h) Grad (div f) is useless; one cannot take a scalar field's divergence into account.
(i) vector field; a vector field is a vector field's curl (curl F).
(j) div(div F) is useless; it is impossible to calculate a scalar field's divergence.
(k) ( grad f ) x ( div F ) - meaningless; you cant cross a scalar field by a vector field !
(l) The divergence of a vector field is a scalar field, and its formula is div(curl(grad f))
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Ashu's mother is three times as old as Ashu. After 5 years if Ashu's age would be 25. How old is Ashu's mother today?
Answer:
60 years old
Step-by-step explanation:
A=Ashu's age. M=Ashu's Mother's Age
M=A*3
M/3 = (A*3)/3 ==> divide 3 on each side to solve for A
A = M/3
A+5 = M/3 + 5 ==> A+5=25 since that'll be Ashu's age 5 years from now
25 = M/3 + 5 => plug in 25 for A+5
25-5 = M/3 + 5 - 5 ==> solve for M
20 = M/3
M = 20 * 3
M = 60 years old
2. A bond quote of 75.65 is equal to ___ in dollars
A. $765.50
B. $75.65
C. $756.50
D. $760.00
A bond quote of 75.65 is equal to $75.65 in dollars. The correct option is B.
What is a bond quote?A bond quote is the most recent price at which a bond traded, converted to a point scale and expressed as a percentage of par value. Par value is typically set at 100, or 100% of a bond's $1,000 face value. If a corporate bond is quoted at 99, for instance, it is currently trading at 99% of its face value. In this instance, each bond costs $990 to purchase.
The most recent price at which a bond traded is referred to as a bond quote.
Bond quotes are converted to a point scale and expressed as a percentage of par (face value). The standard par value is 100, which equals 100% of a bond's $1,000 face value. Bond quotes can include fractional values.
Therefore, based on the information given, the correct option is B.
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(Graphing Proportional Relationships LC)
The table shows a proportional relationship.
x 15 9 21
y 5 3 7
Describe what the graph of the proportional relationship would look like.
A line passes through the point (0, 0) and continues through the point (15, 5).
A line passes through the point (0, 0) and continues through the point (7, 21).
A line passes through the point (0, 0) and continues through the point (5, 15).
A line passes through the point (0, 0) and continues through the point (3, 9).
The graph of the given proportional relation shows that the line passes through the point (0, 0) and continues through the point (15, 5). The relation is represented by the equation y = -0.33x. So, option A is correct.
What is the proportional relationship of the given table of proportions?The given table shows the x and y coordinates of a line.
So, we can find the relationship among them by writing an equation from the given points as
y - y₁ = {(y₂ - y₁)/(x₂ - x₁)} × (x - x₁)
Here we have (x₁, y₁) = (15, 5); (x₂, y₂) = (9, 3)
⇒ y - 5 = (3 - 5)/(9 - 15) × (x - 15)
⇒ y - 5 = (-2)/(-6) × (x - 15)
⇒ y - 5 = 1/3 × (x - 15)
⇒ 3y - 15 = x - 15
⇒ 3y = x + 0
∴ y = 0.33x
Thus, the equation for the given proportions is y = 0.33x.
Since the line is in the form of y = mx, it passes through th point (0, 0) and continues through the point (15, 5).
So, option A is correct.
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The Maryland Department of Transportation reported the following data on driving Speed (miles per hour, mph) and fuel efficiency or Mileage (miles per gallon, mpg), for ten mid-size automobiles: 1 23 4 5 6 7 89 10 Automobile Speed (mph 30 50 40 55 30 25 60 25 50 55 Mileage (mpg)2 25 25 2330 32 2 32625 a. Compute the sample bivariate correlation coefficient. b. Interpret the strength (magnitude) and sign (direction) of the sample bivariate correlation coefficient. Test whether the population bivariate correlation coefficient difers significantly from zero at α-0.01. c.State the null and alternative hypotheses associated with the test. d. What is the calculated value of the associated test statistic? e. What is the critical value of the associated test statistic? f.State your decision regarding the null hypothesis. g. State your conclusion (meaning, describe what the decision means in this problem)
On solving the provided question we can say that - correlation coefficient of the question is r = [tex]\frac{S_{xy} }{\sqrt{S_{xx} S_{yy} } }[/tex] = -0.91
What is correlation coefficient ?The Pearson's correlation coefficient, also known as the Pearson's r, Pearson's product-moment correlation coefficient, bivariate correlation, or simply correlation coefficient, is a statistical indicator of the linear relationship between two sets of data.
[tex]S_{xx} =[/tex]∑[tex]x^2[/tex] - (∑x[tex])^2[/tex] /n = 19300- ((420)^2 /10)= 1660
[tex]S_{yy} =[/tex] ∑[tex]y^2[/tex] (∑y[tex])^2[/tex]/n = 7454- ((270)^2 /10) = 164
[tex]S_{xy} =[/tex]∑[tex](xy)^2[/tex]/n -475
The correlation coefficient is:
r = [tex]\frac{S_{xy} }{\sqrt{S_{xx} S_{yy} } }[/tex] = -0.91
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solve the problem. in terms of effective interest rate, order the following nominal rate investments from lowest to highest: i 4.87% compounded quarterly ii 4.85% compounded monthly iii 4.81% compounded daily (365 days) iv 4.79% compounded continuously ii, iii, iv, i iv, iii, ii, i iii, iv, i, ii i, ii, iii, iv
The nominal rate investment ranges from 4.90%, 4.92%, 4.95%, and 4.96%.
Part (c), or IV, III, II, and I, is therefore the right response to the question.
We must now determine the effective interest rate [tex]R_{e}[/tex] , we'll use the formula:-
[tex]R_{e} = (1 + i)^{k} - 1[/tex]
where, i = r / k
Here,
r = interest rate,
I = the nominal interest rate,
k = is the number of times that interest is compounded annually.
(i) 4.87% compounded quarterly
Then i = (4.87 / 100) * 4 =
i = 0.0487 * 4 = 0.012
So, [tex]R_{e}[/tex] = (1 + 0.012)⁴ - 1
[tex]R_{e}[/tex] = 0.0496 = 4.96 %
Therefore, the effective Interest Rate = 4.96%
(ii) 4.85% compounded monthly
Then i = (4.85 / 100) * 12
i = 0.0485 * 12 = 0.0040
So, [tex]R_{e}[/tex] = (1 + 0.0040)⁴ - 1
[tex]R_{e}[/tex] =0.04959 = 4.95 %
(iii) 4.81% compounded daily (365 days)
Then i = (4.81 / 100) * 365
i = 0.0481 * 365 = 0.00013
So, [tex]R_{e}[/tex] = (1 + 0.00013)⁴ - 1
[tex]R_{e}[/tex] = 0.0492 = 4.92 %
(iv) 4.79% compounded continuously
Then i = (4.79 / 100)
i = 0.0479
So, [tex]R_{e}[/tex] = (1 + 0.0479)⁴ - 1
[tex]R_{e}[/tex] = 0.0490 = 4.90 %
Therefore, the nominal rate investment is as follows: 4.90%, 4.92%, 4.95%, and 4.96%.
The right response to the question is section (c), which is IV, III, II, and I.
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What are some possible solutions for the following inequality? 2f - 8 ≤ 6f + 4
-4.5
-8
-1
4
0
Answer:
Solutions: -1, 4, and 0
Step-by-step explanation:
f= -4.5
2f - 8 ≤ 6f + 4
2 (-4.5) -8 ≤ 6 (-4.5) + 4
-9 - 8 ≤ -27 + 4
-17 ≤ -23
Not True
f= -8
2f - 8 ≤ 6f + 4
2 (-8) - 8 ≤ 6 (-8) + 4
-16 - 8 ≤ -48 + 4
-24 ≤ -44
Not true
f= -1
2f - 8 ≤ 6f + 4
2 (-1) - 8 ≤ 6 (-1) + 4
-2 - 8 ≤ -6 + 4
-10 ≤ -2
True
f= 4
2f - 8 ≤ 6f + 4
2 (4) - 8 ≤ 6 (4) + 4
8-8 ≤ 24 + 4
0 ≤ 28
True
f= 0
2f - 8 ≤ 6f + 4
2 (0) - 8 ≤ 6 (0) + 4
0 - 8 ≤ 0 + 4
-8 ≤ 4
True
The LA Lakers had a PCT of 583 in the 2020-21 season. What does this mean in practical terms?
The meaning when LA Lakers had a PCT of 58.3 in the 2020-21 season is that the percentage of winning is 58.3%.
How to illustrate the percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
From the information given, the LA Lakers had a PCT of 58.3 in the 2020-21 season. It should be noted that PCT simply means percentage. Therefore, it denotes 58.3 percent.
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Complete question
The LA Lakers had a PCT of 58.3 in the 2020-21 season. What does this mean in practical terms
courtney borrows $38,100 to make improvements to her new house. the loan is a 6-year loan with an apr of 4%. find her monthly payment to the nearest dollar.
2. The box and whisker plot below shows the starting salaries for 120 graduates of a small college.
a) What is the range of the starting salaries?
b) About 30 graduates make below what amount?
c) How many graduates have a salary above $33,000 ?
d) $25 of the graduates make above what amount?
The range of the starting salaries is 53,000
Given,
The box and whisker plot below shows the starting salaries
The number of graduates in a small college = 120
We have to find the range of the starting salaries;
Range of a data;
The difference between the highest and lowest values for a given data collection is the range in statistics. For instance, the range will be 10 - 2 = 8 if the given data set is 2, 5, 8, 10, and 3. As a result, the range may alternatively be thought of as the distance between the highest and lowest observation.
Here,
Lowest value = 19,000
Highest value = 72,000
Then,
Range of the set = 72,000 - 19,000 = 53,000
That is,
The range of the given data set is 53,000
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If y = -x - 4 is horizontally stretched by a factor of 5, what is the equation after the transformation?
Answer:
y = - 1/5x - 4------------------------------
The function f(x) is horizontally stretched when the function f(bx) has the value of b between 0 and 1.
We have a function y = - x - 4.
If we need to find the equation of horizontally stretch of this function by a factor of 5, then our b = 1/5.
So the function is:
y = - 1/5x - 4The Daily Total Number Of Students Who Used The State University Swimming Pool On 40 Days During The Summer Is As follows:
The frequency table with the classes is:
Category Frequency
85 99 7
100-114 8
115-129 13
130-144 7
145-159 5
In the given question,
The daily total number of students who used the state university swimming pool on 40 days during the summer is given.
A frequency table with the classes is 85 99, 100-114, 115-129, 130-144, and 145-159.
First we make table of given frequency and write the given number who lies in between that numbers.
Category Numbers in interval
85-99 90, 93, 98, 89, 86, 97, 98
100-114 110, 107, 108, 110, 102, 105, 109, 104
115-129 121, 119, 128, 129, 128, 115, 120, 129, 118, 122, 126, 118, 116
130-144 142, 132, 139, 137, 131, 132, 131
145-159 145, 149, 149, 152, 159
As we know that the frequency is the total numbers that cones between given interval.
Now the frequency is:
Category Frequency
85 99 7
100-114 8
115-129 13
130-144 7
145-159 5
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The right question is:
The daily total number of students who used the state university swimming pool on 40 days during the summer is as follows:
90 98 137 108 128 115 152 122 110 132 149 131 102 109 118 126 121 145 89 149 86 120 97 118 142 139 128 110 105 104 131 159 93 119 107 129 132 129 98 116
For a frequency table with the classes 85 99, 100-114, 115-129, 130-144, and 145-159.
Which of these relations on the set of all people are equivalence relations? Determine the properties of an equivalence relation that the others lack.
a) {(a, b) | a and b are the same age}
b) {(a, b) | a and b have the same parents}
c) {(a, b) | a and b share a common parent}
d) {(a, b) | a and b have met} e) {(a, b) | a and b speak a common language}
Relations in the options (a), (b) and (e) are the Equivalence relations as, the relations are reflexive, symmetric and transitive all.
Given, five relations as,
a) {(a, b) | a and b are the same age}
b) {(a, b) | a and b have the same parents}
c) {(a, b) | a and b share a common parent}
d) {(a, b) | a and b have met}
e) {(a, b) | a and b speak a common language}
we have to find which of them are equivalence relations
a) as, (a , a) ∈ R ∀ a hence, Reflexive.
also, if (a , b) ∈ R then (b , a) ∈ R ∀ a, b. Hence, Symmetric.
and if (a , b) ∈ R & (b , c) ∈ R then (a , c) ∈ R ∀ a, b, c. Hence, Transitive.
So, R = {(a, b) | a and b are the same age} is an equivalence relation.
b) as, (a , a) ∈ R ∀ a hence, Reflexive.
also, if (a , b) ∈ R then (b , a) ∈ R ∀ a, b. Hence, Symmetric.
and if (a , b) ∈ R & (b , c) ∈ R then (a , c) ∈ R ∀ a, b, c. Hence, Transitive.
So, R = {(a, b) | a and b have the same parents} is an equivalence relation.
c) as, (a , a) ∈ R ∀ a hence, Reflexive.
also, if (a , b) ∈ R then (b , a) ∈ R ∀ a, b. Hence, Symmetric.
and if (a , b) ∈ R & (b , c) ∈ R then (a , c) need not to be in R for some a, b, c. Hence, Non - Transitive.
So, R = {(a, b) | a and b share a common parent} is not an equivalence relation.
d) as, (a , a) ∈ R ∀ a hence, Reflexive.
also, if (a , b) ∈ R then (b , a) ∈ R ∀ a, b. Hence, Symmetric.
and if (a , b) ∈ R & (b , c) ∈ R then (a , c) need not to be in R for some a, b, c. Hence, Non - Transitive.
So, R = {(a, b) | a and b have met} is not an equivalence relation.
e) as, (a , a) ∈ R ∀ a hence, Reflexive.
also, if (a , b) ∈ R then (b , a) ∈ R ∀ a, b. Hence, Symmetric.
and if (a , b) ∈ R & (b , c) ∈ R then (a , c) ∈ R ∀ a, b, c. Hence, Transitive.
So, R = {(a, b) | a and b speak a common language} is an equivalence relation.
Hence, the relations in options (a) , (b) and (e) are the equivalence relations.
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the base of s is a circular disk with radius 5r. parallel cross-sections perpendicular to the base are squares.
The volume of the solid is 250r³ when the base of s is a circular disk with radius 5r.
Given that,
We have to discover the described solid's volume, v. The parallel cross-sections perpendicular to the base of s are squares, and the base of s is a circular disk with radius 5r.
We know that,
A cylinder is a solid with square cross sections parallel to the bases and circular bases. Its height is equal to the base circle's diameter.
The radius = 5r,
So the height = diameter = 10r
Volume of the cone is base × height= πr²×h
=π(5r)²×(10r)
=250πr³
Therefore, The volume of the solid is 250r³ when the base of s is a circular disk with radius 5r.
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Which of the following expressions represent the difference of 3 times a number and 10?
A. 3n-10 B. 3n+10 c. 3(n-10) D. 3n-2(10)
help me solve this please
Thus, the required trig values corresponding to the cosФ = -3/5 have been shown,
What are trigonometric equations?These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.
Here,
cosФ = -3/5
cosФ = -3/5 = base / hypotenuse,
perpendicular = √5² - 3² = 4
sinФ = perpendicular / hypotenus
= 4/5
Simultaneously,
cosecФ = 5/4
secФ = -5/4
tanФ = -4/3
cotФ = -3/4
Here,
sin and cosec are positive because this function as a positive positive value between π/2 and π, while else trigonometric function as a negative value for π/2 to π.
Thus, the required trig values are shown above.
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For the general solution of the differential equation in X use A and B for your constants and list the functions in alphabetical order, for example y=????cos(x)+????sin(x)y=Acos(x)+Bsin(x). For the differential equation in T use the C and D.For the variable ????λ type the word lambda and type alpha for ????α,otherwise treat them as you would any other variable.
Use the prime notation for derivatives, so the derivative of ????X is written as ????′X′. Do NOT use ????′(x)X′(x)
The longitudinal displacement u(x,t) of a vibrating elastic bar can be modeled by a wave equation with free-end conditions
????2∂2????∂x2=∂2????∂????2,00a2∂2u∂x2=∂2u∂t2,00
∂????∂x∣∣∣x=0=0,∂????∂x∣∣∣x=????=0,????>0∂u∂x|x=0=0,∂u∂x|x=L=0,t>0
????(x,0)=x∂????∂????∣∣∣????=0=−2,0
This differential equation's general answer is
u(x,t)=Acos(αx−ωt)+Bsin(αx−ωt)+Cx+D
The wave equation with free-end conditions is a differential equation of the form
????2∂2????∂x2=∂2????∂????2,00a2∂2u∂x2=∂2u∂t2,00
where ???? is the longitudinal displacement of a vibrating elastic bar, and x and t are the spatial and temporal variables, respectively.
∂????∂x∣∣∣x=0=0,∂????∂x∣∣∣x=????=0,????>0∂u∂x|x=0=0,∂u∂x|x=L=0,t>0
and the initial condition is
????(x,0)=x∂????∂????∣∣∣????=0=−2,0
u(x,0)=x,∂u∂t|t=0=-2,0
To solve this differential equation, we use the method of separation of variables. We first rewrite the equation as
a2∂2u∂x2=∂2u∂t2,
and then we assume that u can be written as a product of two functions, one of x and one of t. That is,
u(x,t)=X(x)T(t).
Substituting this into the wave equation and rearranging, we obtain two equations for X and T:
a2X″(x)=−ω2T(t)
a2T″(t)=−ω2X(x).
X(x)=Acos(αx)+Bsin(αx).
T(t)=Ccos(ωt)+Dsin(ωt).
Therefore, the general solution of the wave equation with free-end conditions is
u(x,t)=Acos(αx−ωt)+Bsin(αx−ωt)+Cx+D.
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A 20 cm nail ,just fit inside cylindrical can.Three identical spherical balls need to fit entirely within the can.What is the maximum radius os each ball?
A radius is a part of a circle that doubles to form its diameter. The radius of each sphere is 3.34 cm.
A circle is a shape bounded by curved line known as circumference. some of its parts of a circle are; diameter, radius, arc, chord etc.
A radius is that part of the circle that is half of its diameter. This implies that;
radius = [tex]\frac{diameter}{2}[/tex]
Such that;
diameter = 2*radius
A sphere is an object that can be derived from the volume of a circle.
Given that the height of the cylindrical can is 20 cm, and three identical spherical balls would fit entirely within the can.
Then;
diameter of each spherical balls = [tex]\frac{20}{3}[/tex]
= 6.67 cm
Thus;
the radius of each of the spherical balls = [tex]\frac{diameter}{2}[/tex]
= [tex]\frac{6.67}{2}[/tex]
radius of each of the spherical balls = 3.335 cm
Therefore, the maximum radius of each ball is 3.34 cm.
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A four-wheel-drive vehicle is transporting an injured hiker to the
hospital from a point that is 30 km from the nearest point on a straight
road. The hospital is 50 km down that road from that nearest point. If
the vehicle can drive at 30 kph over the terrain and at 120 kph on the
road, how far down the road should the vehicle aim to reach the road
to minimize the time it takes to reach the hospital?
The final distance is 31 km.
Time, t = Distance, d/Velocity, v
Let's assume the ambulance drives a distance of x along the road, which leaves us 50-x on the road, after which it has reached the road.
It forms a triangle, after which we can use Pythagoras Theorem.
Using it, we get distance down the hill, d1, and we can calculate distance on the road remaining till the hospital, d2.
t = d1/v1 + d2/v2
= [tex]\frac{\sqrt{x^{2} + 30^{2} } }{30} + \frac{50 - x}{120}[/tex]
We need to minimise t. Therefore, we have to differentiate.
On differentiating and equating it to 0, we get the value of x as [tex]\sqrt{60} = 7.75[/tex]
How far down the road should the vehicle aim to reach the road to reach the hospital at the minimum time?
[tex]= \sqrt{900 + 7.75^{2} } = 31 km[/tex]
Thus, the final distance is 31 km.
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Please help me!!!!!!!!!!!!
Answer:
A
Step-by-step explanation:
change 'its' to it's which is a contraction for 'it is'
Graph: y ≤ 3x + 4
A. Is (1,7) a solution? yes or no
B. Is ( 0,0) a solution? yes or no
A.
[tex]7 \leqslant 3(1) + 4 \\ 7 \leqslant 3 + 4 \\ 7 \leqslant 7[/tex]
B.
[tex]0 \leqslant 3(0) + 4 \\ 0 \leqslant 0 + 4 \\ 0 \leqslant 4[/tex]
BOTH ARE TRUE
Answer:
A. yes
B. yes
Step-by-step explanation:
You want a graph of y ≤ 3x +4 and an indication whether (1, 7) and (0, 0) are solutions.
GraphThe graph is attached. The boundary line is solid because points on that line are in the solution set. Points in the shaded area are also in the solution set.
A. (1, 7)This point is on the boundary line. It is a solution.
B. (0, 0)This point is in the shaded area of the graph. It is a solution.
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