Answer:
2±√13
Step-by-step explanation:
9/x=x-4
x² -4x - 9=0
x² -4x +4- 13=0
(x -2)²=13
x-2= ±√13
x= 2±√13
Which set of ordered pairs does NOT represent a function ?
Answer:
The answer is C.
Step-by-step explanation:
For a function, we do a vertical line test. If there is more than one point in one single x-position, it is not a function. Example, the ordered pairs (1, 1) and (1, 2) do NOT describe a function because there are more than one point on x=1.
What are the next two numbers in the pattern of numbers 45,15,44,17,40,20,31,25
Answer:
14, 32
Step-by-step explanation:
45,15,44,17,40,20,31,25
this is combination of 2 series:
45-44-40-31- ?15-17-20-25-?In the first series we can see the pattern as:
-1, -4, -9 = -1², -2², -3² so next difference must be -4², which is 31- 16= 14In the second series we can see the pattern as:
2, 3, 5 prime numbers, so next difference must be 7, which is 25+7=32The series will continue as:
45, 15, 44, 17, 40, 20, 31, 25, 14, 32Answer:
14, 32
Step-by-step explanation:
lol :D
Two students, A and B, are working independently on homework (not necessarily for the same class). Student A takes X = Exp(1) hours to finish his or her homework, while B takes Y = Exp(2) hours. (a) Find the CDF of X/Y , the ratio of their problem-solving times. (b) Find the probability that A finishes his or her homework before B does.
Answer:
a) The CDF of X/Y is calculated as:
[tex]F_{z} (\zeta) = \frac{\zeta}{\zeta + 2}[/tex] for [tex]0 < \zeta < \infty[/tex]
[tex]F_{z} (\zeta) = 0[/tex] for [tex]\zeta \leq 0[/tex]
Note: Z = X/Y
b) Probability that A finishes before B = 1/3
Step-by-step explanation:
For clarity and easiness of expression, this solution is handwritten and attached as a file. Check the complete solution in the attached file.
For a hyperbolic mirror the two foci are 42 cm apart. The distance of the vertex from one focus is 6 cm and from the other focus is 36 cm. Position a coordinate system with the origin at the center of the hyperbola and with the foci on the y-axis. Find the equation of the hyperbola.
Answer:
[tex]\dfrac{y^2}{225} -\dfrac{x^2}{216}=1[/tex]
Step-by-step explanation:
For a hyperbolic mirror the two foci are 42 cm apart.
The distance between the foci = 2c.
Therefore:
2c=42c=21The distance of the vertex from one focus = 6 cm
The distance of the vertex from the other focus = 36 cm
2a=36-6=30
a=15Now:
[tex]c^2=a^2+b^2\\21^2=15^2+b^2\\b^2=21^2-15^2\\b^2=216\\b=6\sqrt{6}[/tex]
If the transverse axis lies on the y-axis, and the hyperbola is centered at the origin. Then the hyperbola has an equation of the form:
[tex]\dfrac{y^2}{a^2} -\dfrac{x^2}{b^2}=1[/tex]
Therefore, the equation of the hyperbola is:
[tex]\dfrac{y^2}{225} -\dfrac{x^2}{216}=1[/tex]
Find the area of a rectangle with base 4ft and height 4 in.
Hey there!
Answer:
A = 192 in²
Step-by-step explanation:
Base = 4 ft
Height = 4 in
Convert the length of the base to inches:
4 ft = 4 ×12 = 48 in
Formula for the area of a rectangle: A = l × w (in this instance, 'l' is the height)
4 × 48 = 192 in²
Answer:
A =192 in^2
Step-by-step explanation:
Change the 4 ft to inches
4 * 12 = 48 inches
A = l*w
A = 48*4
A =192 in^2
If you put all of the bean sprouts together end to end what
would be the total length of all the objects?
inches
Answer:
5.625 = 45/8 = 5 5/8
Step-by-step explanation:
Use variation of parameters to find a general solution to the differential equation given that the functions y1 and y2 are linearly independent solutions to the corresponding homogeneous equation for t > 0. ty" + (2t - 1 )y' - 2y = 6t^2 e^-2t​; y1 = 22t −​1, y2 = e^-2t
Answer:
[tex]y_g(t) = c_1*( 2t - 1 ) + c_2*e^(^-^2^t^) - e^(^-^2^t^)* [ t^3 + \frac{3}{4}t^2 + \frac{3}{4}t ][/tex]
Step-by-step explanation:
Solution:-
- Given is the 2nd order linear ODE as follows:
[tex]ty'' + ( 2t - 1 )*y' - 2y = 6t^2 . e^(^-^2^t^)[/tex]
- The complementary two independent solution to the homogeneous 2nd order linear ODE are given as follows:
[tex]y_1(t) = 2t - 1\\\\y_2 (t ) = e^-^2^t[/tex]
- The particular solution ( yp ) to the non-homogeneous 2nd order linear ODE is expressed as:
[tex]y_p(t) = u_1(t)*y_1(t) + u_2(t)*y_2(t)[/tex]
Where,
[tex]u_1(t) , u_2(t)[/tex] are linearly independent functions of parameter ( t )
- To determine [ [tex]u_1(t) , u_2(t)[/tex] ], we will employ the use of wronskian ( W ).
- The functions [[tex]u_1(t) , u_2(t)[/tex] ] are defined as:
[tex]u_1(t) = - \int {\frac{F(t). y_2(t)}{W [ y_1(t) , y_2(t) ]} } \, dt \\\\u_2(t) = \int {\frac{F(t). y_1(t)}{W [ y_1(t) , y_2(t) ]} } \, dt \\[/tex]
Where,
F(t): Non-homogeneous part of the ODE
W [ y1(t) , y2(t) ]: the wronskian of independent complementary solutions
- To compute the wronskian W [ y1(t) , y2(t) ] we will follow the procedure to find the determinant of the matrix below:
[tex]W [ y_1 ( t ) , y_2(t) ] = | \left[\begin{array}{cc}y_1(t)&y_2(t)\\y'_1(t)&y'_2(t)\end{array}\right] |[/tex]
[tex]W [ (2t-1) , (e^-^2^t) ] = | \left[\begin{array}{cc}2t - 1&e^-^2^t\\2&-2e^-^2^t\end{array}\right] |\\\\W [ (2t-1) , (e^-^2^t) ]= [ (2t - 1 ) * (-2e^-^2^t) - ( e^-^2^t ) * (2 ) ]\\\\W [ (2t-1) , (e^-^2^t) ] = [ -4t*e^-^2^t ]\\[/tex]
- Now we will evaluate function. Using the relation given for u1(t) we have:
[tex]u_1 (t ) = - \int {\frac{6t^2*e^(^-^2^t^) . ( e^-^2^t)}{-4t*e^(^-^2^t^)} } \, dt\\\\u_1 (t ) = \frac{3}{2} \int [ t*e^(^-^2^t^) ] \, dt\\\\u_1 (t ) = \frac{3}{2}* [ ( -\frac{1}{2} t*e^(^-^2^t^) - \int {( -\frac{1}{2}*e^(^-^2^t^) )} \, dt] \\\\u_1 (t ) = -e^(^-^2^t^)* [ ( \frac{3}{4} t + \frac{3}{8} )] \\\\[/tex]
- Similarly for the function u2(t):
[tex]u_2 (t ) = \int {\frac{6t^2*e^(^-^2^t^) . ( 2t-1)}{-4t*e^(^-^2^t^)} } \, dt\\\\u_2 (t ) = -\frac{3}{2} \int [2t^2 -t ] \, dt\\\\u_2 (t ) = -\frac{3}{2}* [\frac{2}{3}t^3 - \frac{1}{2}t^2 ] \\\\u_2 (t ) = t^2 [\frac{3}{4} - t ][/tex]
- We can now express the particular solution ( yp ) in the form expressed initially:
[tex]y_p(t) = -e^(^-^2^t^)* [\frac{3}{2}t^2 + \frac{3}{4}t - \frac{3}{8} ] + e^(^-^2^t^)*[\frac{3}{4}t^2 - t^3 ]\\\\y_p(t) = -e^(^-^2^t^)* [t^3 + \frac{3}{4}t^2 + \frac{3}{4}t - \frac{3}{8} ] \\[/tex]
Where the term: 3/8 e^(-2t) is common to both complementary and particular solution; hence, dependent term is excluded from general solution.
- The general solution is the superposition of complementary and particular solution as follows:
[tex]y_g(t) = y_c(t) + y_p(t)\\\\y_g(t) = c_1*( 2t - 1 ) + c_2*e^(^-^2^t^) - e^(^-^2^t^)* [ t^3 + \frac{3}{4}t^2 + \frac{3}{4}t ][/tex]
Scientists think that robots will play a crucial role in factories in the next several decades. Suppose that in an experiment to determine whether the use of robots to weave computer cables is feasible, a robot was used to assemble 507 cables. The cables were examined and there were 9 defectives. If human assemblers have a defect rate of 0.035 (3.5%), does this data support the hypothesis that the proportion of defectives is lower for robots than humans
Answer:
The data support the hypothesis that the proportion of defectives is lower for robots than humans.
Step-by-step explanation:
To know if the proportion of defectives is lower for robots than humans so as to prove if the hypothesis is true.
From the data given:
Total number of cables a robot assembled = 507
Defectives = 9
To get the defect rate = the number of defects divided by the total number of cables, multiplied by 100.
Defect rate = (9 / 507) x 100 = 0.01775 x 100
Defect rate for the robot = 1.775%
From the question, a robot was used and the defect rate after the calculation is 1.775%. While for humans, the defect rate is 3.5%. This implies, if humans were used to assembling the same 507 cables, there will be 17.745 defectives.
x / 507 = 3.5%
x (defectives) = 17.745
Therefore, the data support the hypothesis that the proportion of defectives is lower for robots than humans.
There are 225 students at March middle school. On Friday, 135 students wore spirit shirts. What percent of the students did Not wear spirit shirts on Friday?
Answer:
40%
Step-by-step explanation:
To find the answer to this, you first can find out what percentage of students did wear spirit shirts. To do this you can divide 135 by 225 to give you 0.6. To convert the decimal into a percentage you can simply multiply by 100, giving you 60%. Then to find the percentage of students that did not wear spirit shirts, you can subtract 60 from 100, giving you 40%.
Which shows one way the equation can be represented in words?
Z-6=1.4
Answer:
6 less than a number is equal to 1 and 4 tenths
Step-by-step explanation:
Do not answer or report What is -6 plus -6
Answer:
-12Step-by-step explanation:
it is -12 because -6 plus -6 is also like 6 plus 6
and then you have to add the negative Sign.
pls brainliest me
-6 - 6 = - 12
Happy to help! Please mark as the brainliest!
What are two possible measures of the angle below?
The smaller angle, inside the bold lines, is -90 degrees.
The larger angle, outside the bold lines, is 270 degrees.
Angles can be measured in increments between -90° and 630°.
What angles are created when two lines cross one other?Two straight lines are considered to be intersecting if they come together at the same point. The intersection of two lines is known as the junction point. When two lines intersect, four angles are produced. The sum of the four angles is always 360 degrees.
Two straight lines that cross one other and produce right angles are called perpendicular lines. There are four right angles created when two perpendicular lines cross.
There are two types of angle connections produced when lines intersect:
Congruent opposite angles
Nearby angles are helpful
The information is
Let O (0, 0) be the origin, where the y and x axes must connect.
Thus, the angles on the four quadrants of the axis are produced.
The fourth quadrant's crossing lines create an angle that is given by For, the anticlockwise measure, A = -90°.
B = 360n - 180° for the clockwise measure, and n = 3 in this case.
Hence, when we simplify, we obtain
The second angle has a length of = 630°.
As a result, the angles are 90° and 630°.
Go here to find out more about angles created by intersecting lines.
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Express the function G in the form f∘g. (Enter your answers as a comma-separated list. Use non-identity functions for
f(x) and g(x).)
Answer:
i dont really know what it is
I don’t know how to do this can someone help?
Answer:
67
Step-by-step explanation:
Using triangle property
127+x=180
x=53
53+60+y=180
113+y=108
y=67
y
The figure shows A XYZ. XW is the angle
bisector of ZYXZ.
8
6.5
W
What is W Z?
Enter
your answer in the box. Do not round
your answer.
x
Z
6
units
Basic
Answer:
3.84 units
Step-by-step explanation:
By the properties of angle bisectors, ...
WZ/ZX = WY/YX
Solving for WY, we have ...
WY = (YX)(WZ)/(ZX) = (6.5/6)(WZ)
The length YZ is ...
YZ = 8 = WY +WZ
8 = (6.5/6)(WZ) +WZ = 12.5/6(WZ) . . . . substitute for WY
WZ = 8(6/12.5) . . . . multiply by 6/12.5
WZ = 3.84
Answer:
The correct answer is indeed 3.84 units
Step-by-step explanation:
I just took the test and got it correct hope this helps ☺
Find the point of diminishing returns (x comma y )for the function R(x), where R(x) represents revenue (in thousands of dollars) and x represents the amount spent on advertising (in thousands of dollars).
Complete Question
The complete question is shown on the first uploaded image
Answer:
The point of diminishing returns (x , y ) is (11, 21462)
Step-by-step explanation:
From the question we are told that
The function is [tex]R(x) = 10,000 -x^3 - 33x^2 + 800x , \ \ 0 \le x \le 20[/tex]
Here R(x) represents revenue (in thousands of dollars) and x represents the amount spent on advertising (in thousands of dollars).
Now differentiating R(x) we have
[tex]R'(x) = -3x^2 +66x + 800[/tex]
Finding the second derivative of R(x)
[tex]R''(x) = -6x +66[/tex]
at inflection point [tex]R''(x) = 0[/tex]
So [tex]-6x +66 = 0[/tex]
=> [tex]x= 11[/tex]
substituting value of x into R(x)
[tex]R(x) = 10,000 -(11)^3 - 33(11)^2 + 800(11) ,[/tex]
[tex]R(x) = 21462[/tex]
Now the point of diminishing returns (x , y ) i.e (x , R(x) ) is
(11, 21462)
graph the equation in a coordinate plane, x+2y=4
Hope this helps!
Stay safe, have a good day :D
Please answer this question I give brainliest thank you! Number 9
Answer:
B
The mode is 11 and 3
The Median is 10
The mean is 12
Find the function value. cos150°
Answer:
[tex]cos150 = -\frac{\sqrt{3} }{2}[/tex]
Step-by-step explanation:
Recall the unit circle. At 150 deg, the point value is (-sqrt3/2, 1/2)
Remember the cosine is always the x-value, and sine is always the y-value.
This means that cosine will be -sqrt3/2.
Determine whether the following procedure is a binomial experiment.
If it is not, explain why. Drawing 5 marbles from a bag with 10 red, 8 green and 12 yellow marbles without replacement and finding out how many of these five are green.
a. Yes, this is a binomial experiment.
b. No, the outcomes cannot be classified into two categories.
c. No, the trials are not independent
Answer:
C. The trails are not independent.
The probability of drawing one marble will not be independent of others thus option (c) is correct.
What is probability?The probability of an event occurring is defined by probability.
Probability is also called chance because if you flip a coin then the probability of coming head and tail is nothing but chances that either head will appear or not.
As per the given,
Drawing 5 marbles from a bag with 10 red, 8 green, and 12 yellow marbles without replacement.
In without replacement, the remaining balls in each draw will go to be decreased thus they will be dependent events so binomial distribution will not be applied.
Hence "One marble's likelihood of being drawn won't be independent of the other marbles".
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Which of the following linear equations has the steepest slope?
A. Y = -2x +11
B. y=+x+4
C. y - x +7
D. y - 7+2
Answer:
A --- unless d is supposed to be "y= -7x + 2"
Step-by-step explanation:
The slope is m in y=mx + b
So:
a. y= -2x + 11 slope= -2
b. y= x + 4 slope= 1
c. y= -x + 7 slope= -1
d. y= -7 + 2 (I don's see an x but if there were an x I assume that the slope would equal -7)
The higher the m value, the steeper the slope because it is m/1
So, -2/1 is steeper than 1/1 or -1/1
Really in need of help :( please !
Answer:
A
Step-by-step explanation:
(2,1) - only one in the table. Remember (x,y)
What preserves a shapes orientation?
a. Vertical translation
b. Reflection across the shapes base
c. Rotation about its center
Answer:
a.vertical translation
A marketing consultant was hired to visit a random sample of five sporting goods stores across the state of California. Each store was part of a large franchise of sporting goods stores. The consultant taught the managers of each store better ways to advertise and display their goods. The net sales for 1 month before and 1 month after the consultant's visit were recorded as follows for each store (in thousands of dollars):_________.
Before visit: 57.1 94.6 49.2 77.4 43.2After visit: 63.5 101.8 57.8 81.2 41.9Do the data indicate that the average net sales improved? (Use a= 0.05)
Answer:
Step-by-step explanation:
Corresponding net sales before 1 month and after 1 month form matched pairs.
The data for the test are the differences between the net sales before and after 1 month.
μd = the net sales before 1 month minus the net sales after 1 month.
Before after diff
57.1 63.5 - 6.4
94.6 101.8 - 7.2
49.2 57.8 - 8.6
77.4 81.2 - 3.8
43.2 41.9 1.3
Sample mean, xd
= (- 6.4 - 7.2 - 8.6 - 3.8 + 1.3)/5 = - 4.94
xd = - 4.94
Standard deviation = √(summation(x - mean)²/n
n = 5
Summation(x - mean)² = (- 6.4 + 4.94)^2 + (- 7.2 + 4.94)^2 + (- 8.6 + 4.94)^2+ (- 3.8 + 4.94)^2 + (1.3 + 4.94)^2 = 60.872
Standard deviation = √(60.872/5
sd = 3.49
For the null hypothesis
H0: μd ≥ 0
For the alternative hypothesis
H1: μd < 0
The distribution is a students t. Therefore, degree of freedom, df = n - 1 = 5 - 1 = 4
2) The formula for determining the test statistic is
t = (xd - μd)/(sd/√n)
t = (- 4.94 - 0)/(3.49/√5)
t = - 3.17
We would determine the probability value by using the t test calculator.
p = 0.017
Since alpha, 0.05 > than the p value, 0.017, then we would reject the null hypothesis. Therefore, at 5% significance level, the data indicate that the average net sales improved.
What’s the correct answer for this question?
Answer: Choice C
Step-by-step explanation:
Events A and B are independent if the equation P(A∩B) = P(A) · P(B) holds true.
3/10≠3/5*1/4
so event A and B are not independent.
On a residential single lane road there was a wreck that backed up traffic for 5 miles. 80% of the traffic consists of cars and 20% of the traffic consists of trucks. The average distance between vehicles is 3 feet. The average length of a car is 13.5 feet and the average length of a truck is 20 feet. Estimate how many vehicles are stuck in the traffic jam. (Hint: There are 5280 feet in 1 mile.) A. 853 vehicles B. 1510 vehicles C. 2103 vehicles D. 2320 vehicles
Answer: b) 1510 vehicles
Step-by-step explanation:
Total: 5 miles x 5280 ft per mile = 26,400
Cars: 80% of vehicles are cars with a length of 13.5 = 0.8(13.5)v = 10.8v
Trucks: 20% of vehicles are trucks with length of 20 = 0.2(20)v = 4v
Between: Distance between two vehicles is 3: (3/2)v = 1.5v
Total = Cars + Trucks + Between
26,400 = 10.8v + 4v + 1.5v
26,400 = 16.3v
1619.6 = v
the closest number of all of the options is (b) 1510
A train is traveling at a constant speed and has traveled 67.5 miles in the last 11 hours.
Which equation shows the proportional relationship between the distance, d, and the time, t,
that the train has traveled?
A.d=45t
B.d=50t
C.d = 690
D.d=67.5t
Answer:
A. d= 45t
Step-by-step explanation:
(assuming that you meant 67.5 in the last 1.5 hours)
67.5 miles = distance
1.5 hours = time
therefore:
[tex]\frac{d}{t\\}[/tex] = 67.5/1.5
making your answer 45
leaving a as your correct answer:
d= 45t
The proportion relationship between the distance d, and the time t, that the train has travelled is, d = 45t. So the correct option is A).
What is a proportion relationship?Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other.
Given that, A train travels at a constant speed and has travelled 67.5 miles in the last 1.5 hours. (assuming that you meant 67.5 in the last 1.5 hours)
67.5 miles = distance
1.5 hours = time
We know that, speed = distance / time
s = 67.5/1.5
s = 45 mph
Now, distance = speed × time
d = 45t
Hence, the proportion relationship between the distance d, and the time t, that the train has travelled is, d = 45t. So the correct option is A).
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Statistics show that about 42% of Americans voted in the previous national election. If three Americans are randomly selected, what is the probability that none of them voted in the last election
Answer:
19.51% probability that none of them voted in the last election
Step-by-step explanation:
For each American, there are only two possible outcomes. Either they voted in the previous national election, or they did not. The probability of an American voting in the previous election is independent of other Americans. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
42% of Americans voted in the previous national election.
This means that [tex]p = 0.42[/tex]
Three Americans are randomly selected
This means that [tex]n = 3[/tex]
What is the probability that none of them voted in the last election
This is P(X = 0).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{3,0}.(0.42)^{0}.(0.58)^{3} = 0.1951[/tex]
19.51% probability that none of them voted in the last election
how do you add 9 1/6 + 2 1/12
Answer:
11 1/4
Step-by-step explanation:
first make the fractions equal. So 9 1/6 would be 9 2/12 so that we canadd them together.
9 2/12 + 2 1/12 = 11 3/12
but u can simplify the answer so itll be 11 1/4
[tex]answer = 11 \ \frac{3}{12} \\ solution \\ 9 \ \frac{1}{6} + 2 \ \frac{1}{12} \\ = \frac{55}{6} + \frac{25}{12} \\ = \frac{55 \times 2 + 25}{12} \\ = \frac{110 + 25}{12} \\ = \frac{135}{12} \\ = 11 \ \ \frac{3}{12} \\ hope \: it \: helps[/tex]
Antonio burns 75 calories for every 15 minutes
Answer is 5 calories/min
75 divided by 15 is 5
Answer:five cal per min.15 in five groups equals ''75''