9514 1404 393
Answer:
common denominator: (x² -4)simplified complex fraction: (2x +1)/(9 -2x)Step-by-step explanation:
It is helpful to remember the factoring of the difference of squares:
a² -b² = (a -b)(a +b)
__
Your denominator of (x² -4) factors as (x -2)(x +2). You will note that one of these factors is the same as the denominator in the other fraction.
It looks like you want to simplify ...
[tex]\dfrac{\left(\dfrac{2}{x-2}-\dfrac{3}{x^2-4}\right)}{\left(\dfrac{5}{x^2-4}-\dfrac{2}{x+2}\right)}=\dfrac{\left(\dfrac{2(x+2)}{(x-2)(x+2)}-\dfrac{3}{(x-2)(x+2)}\right)}{\left(\dfrac{5}{(x-2)(x+2)}-\dfrac{2(x-2)}{(x-2)(x+2)}\right)}\\\\=\dfrac{2(x+2)-3}{5-2(x-2)}=\boxed{\dfrac{2x+1}{9-2x}}[/tex]
Answer:
c
Step-by-step explanation:
(x+2)^2(x-2)
Solve the following system of equations: y + 5 = x
y= x2 – 3x – 5
Answer:
X=0,y=-5
x=4,y=-1
Step-by-step explanation:
Replace all occurrences of y with x^2-3x-5
(x^2-3x-5)+5=x
x^2-3x=x
X^2-4x=0
so :x=0,4
enter the value of x in the equation then find y
y=-5,-1
find the equation of the line that is perpendicular to y=6x-2) and contains to the point (6-,2)
Answer:
y = -1/6x - 1.
Step-by-step explanation:
I am assuming that the point id (6, -2).
The slope of the required line = -1/6.
y - y1 = m(x - x1) where m = slope and x1,y1 is a point on the line so we have
y - (-2) = -1/6( x- 6)
y + 2 = -1/6x + 1
y = -1/6x - 1.
In the figure above, AABC is an equilateral
triangle and each circle is tangent to the other
two circles. If each circle has diameter 10, what
is the distance h?
(A) 103
(B) 1513
(C) 15+513
(D) 10+1013
(E) 10+5/5
Answer:
B
Step-by-step explanation:
Mila wants to buy a scooter for Rs 62,000 . She has only Rs 19,000 with her, so she decides to take a loan from a bank for the remaining amount. The bank offers Mini three loan schemes as shown below. Mini has to return the loan amount with interest in equal monthly instalments
1) How much money does mila take as loan from the bank?
a) Rs 62,000
b) Rs 44,000
c) Rs 45,000
d) Rs 43,000
Answer:
Scheme a 45000 is the answer
Consider the differential equation: 2y′′−13y′−7y = 0
a. Show that, for any constants A and B, the following is a solution to the above differential equation: y = Ae^(−9x)+Be^(x/3)
b. Find the values A and B that make the above general solution into a solution for the following initial value problem: 2y′′−13y′−7y = 0; y(0) = 3, y′(0) = −5
--------------------------------------------------
Just a correction, the characteristic roots of the equation are [tex]y = 7[/tex] and [tex]y = -\frac{1}{2}[/tex], thus, we should test for:
[tex]y = Ae^{7x} + Be^{-\frac{x}{2}}[/tex]
--------------------------------------------------
Question a:
First, we find the derivatives, thus:[tex]y = Ae^{7x} + Be^{-\frac{x}{2}}[/tex]
[tex]y^{\prime} = 7Ae^{-7x} - \frac{1}{2}Be^{-\frac{x}{2}}[/tex]
[tex]y^{\prime\prime} = 49Ae^{-7x} + \frac{1}{4}Be^{-\frac{x}{2}}[/tex]
Now, we replace into the equation:[tex]2y^{\prime\prime} - 13y^{\prime} - 7y = 0[/tex]
[tex]2(49Ae^{-7x} + \frac{1}{4}Be^{-\frac{x}{2}}) - 13(7Ae^{-7x} - \frac{1}{2}Be^{-\frac{x}{2}}) - 7(Ae^{7x} + Be^{-\frac{x}{2}}) = 0[/tex]
[tex]98Ae^{-7x} + \frac{1}{2}Be^{\frac{x}{2}} - 91Ae^{-7x} + \frac{13}{2}e^{-\frac{x}{2}} - 7Ae^{7x} - 7Be^{-\frac{x}{2}} = 0[/tex]
[tex]98Ae^{-7x} - 91Ae^{-7x} - 7Be^{-\frac{x}{2}} + \frac{1}{2}Be^{\frac{x}{2}} + \frac{13}{2}e^{-\frac{x}{2}} - 7Be^{-\frac{x}{2}} = 0[/tex]
[tex]0A + 0B = 0[/tex]
[tex]0 = 0[/tex], thus, we found the identity, and for each constant A and B, the following is a solution.
--------------------------------------------------
Question b:
[tex]y = Ae^{7x} + Be^{-\frac{x}{2}}[/tex]
Since [tex]y(0) = 3[/tex][tex]A + B = 3 \rightarrow B = 3 - A[/tex]
--------------------------------------------------
[tex]y^{\prime} = 7Ae^{-7x} - \frac{1}{2}Be^{-\frac{x}{2}}[/tex]
Since [tex]y^{\prime}(0) = -5[/tex][tex]7A - \frac{1}{2}B = -5[/tex]
Using [tex]B = 3 - A[/tex]
[tex]7A - \frac{3}{2} + \frac{A}{2} = -5[/tex]
[tex]\frac{14A}{2} + \frac{A}{2} = -\frac{10}{2} + \frac{3}{2}[/tex]
[tex]\frac{15A}{2} = -\frac{7}{2}[/tex]
[tex]15A = -7[/tex]
[tex]A = -\frac{7}{15}[/tex]
--------------------------------------------------
Then, B is given by:
[tex]B = 3 - A = 3 - (-\frac{7}{15}) = \frac{45}{15} + \frac{7}{15} = \frac{52}{15}[/tex]
Thus, the values are: [tex]A = -\frac{7}{15}, B = \frac{52}{15}[/tex]
A similar problem is given at https://brainly.com/question/2456414
solve for x please help (show ur work)
Answer:
x = -3
Step-by-step explanation:
12 -4x-5x = 39
Combine like terms
12 - 9x = 39
Subtract 12 from each side
12-9x-12 = 39-12
-9x = 27
Divide by -9
-9x/-9 = 27/-9
x = -3
Answer:
x = -3
Step-by-step explanation:
12 - 4x - 5x = 39
Combine like terms
12 - 9x = 39
Subtract 12 from both sides
12 - 12 - 9x = 39 - 12
-9x = 27
Divide both sides by -9
-9x/-9 = 27/-9
x = -3
Most brainiest for the right answer on this problem!
Answer:
82.8
Step-by-step explanation:
mean = sum of all points, over the total given number of points
84 * 26 = 2184
2184 + 69 + 66 = 2319
Now the total number of tests is 26 + 2 or 28
So divide 2319 by 28
2319/28 = 82.82142
rounded to the nearest tenth is 82.8
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Which of the following is NOT a requirement for testing a claim about two population standard deviations or variances? A. The populations are independent. B. One of the populations is normally distributed. C. The two samples are simple random samples. D. This test requires that both populations have normal distributions.
Answer:
B. One of the populations is normally distributed.
Step-by-step explanation:
To test a claim about two population standard deviation or variance, it is imperative that the data meets certain requirements which include :
Randomness : Data must not be biased as such it must be drawn as a random sample from a larger group.
The data must be independent. That is not related to one another, the outcome of one should not rely on the outcome or value of another.
Both groups must be drawn From a population which is normally distributed.
One group being normally distributed by stribuyed while the other isn't a requirement for hypothesis testing in this scenario.
Factor.
64x^12 + 27y^3
Answer:
answer is (4x^4+3y)(16x^8-12x^4y+9y^2)
Step-by-step explanation:
1. (02.01)
Solve -4(x + 10) - 6 = -3(x - 2). (1 point)
-40
-46
-52
52
Answer:
-52
Step-by-step explanation:
-4(x + 10) - 6 = -3(x - 2)
Distribute the left side to get:
(-4x + -40) - 6
Now distribute the right side to get:
-3x + 6
Arrange the equation as the following:
-4x - 40 - 6 = -3x + 6
Add the like terms on each side:
-4x - 46 = -3x + 6
Do the inverse operation of each term:
-x = 52
Now we need to get x to become a positive, so we just divide -x by -1 to get x.
And 52/-1 to get our final answer of -52.
Answer: -52
Step-by-step explanation:
-4(x + 10) - 6 = -3(x - 2)
Distribute the left side to get:
(-4x + -40) - 6
Now distribute the right side to get:
-3x + 6
Arrange the equation as the following:
-4x - 40 - 6 = -3x + 6
Add the like terms on each side:
-4x - 46 = -3x + 6
Do the inverse operation of each term:
-x = 52
Now we need to get x to become a positive, so we just divide -x by -1 to get x.
And 52/-1 to get our final answer of -52.
The fraction model below shows the steps that a student performed to find a quotient. Which statement best interprets the quotient? A: There are 5 1/5 five-sixths in 4 1/3. B: There 6 1/6 five sixths-in 4 1/3. C: There are 5 1/5 four and one-thirds in 5/6. D: There are 6 1/6 four and one-thirds in 5/6.
Answer:
The answer is D
Step-by-step explanation:
there are 8 1/6 five and one sixth in 2/3
The range is the set of________
A) First Coordinates
B) Ordered Pairs
C) Second coordinates
Answer:
The range is the set of first coordinates
Working for a car company, you have been assigned to find the average miles per gallon (mpg) for acertain model of car. you take a random sample of 15 cars of the assigned model. based on previous evidence and a qq plot, you have reason to believe that the gas mileage is normally distributed. you find that the sample average miles per gallon is around 26.7 with a standard deviation of 6.2 mpg.
a. Construct and interpret a 95% condence interval for the mean mpg, , for the certain model of car.
b. What would happen to the interval if you increased the condence level from 95% to 99%? Explain
c. The lead engineer is not happy with the interval you contructed and would like to keep the width of the whole interval to be less than 4 mpg wide. How many cars would you have to sample to create the interval the engineer is requesting?
Answer:
a) The 95% confidence interval for the mean mpg, for the certain model of car is (23.3, 30.1). This means that we are 95% sure that the true mean mpg of the model of the car is between 23.3 mpg and 30.1 mpg.
b) Increasing the confidence level, the value of T would increase, thus increasing the margin of error and making the interval wider.
c) 37 cars would have to be sampled.
Step-by-step explanation:
Question a:
We have the sample standard deviation, and thus, the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 15 - 1 = 14
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 14 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.1448
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.1448\frac{6.2}{\sqrt{15}} = 3.4[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 26.7 - 3.4 = 23.3 mpg.
The upper end of the interval is the sample mean added to M. So it is 26.7 + 3.4 = 30.1 mpg.
The 95% confidence interval for the mean mpg, for the certain model of car is (23.3, 30.1). This means that we are 95% sure that the true mean mpg of the model of the car is between 23.3 mpg and 30.1 mpg.
b. What would happen to the interval if you increased the confidence level from 95% to 99%? Explain
Increasing the confidence level, the value of T would increase, thus increasing the margin of error and making the interval wider.
c. The lead engineer is not happy with the interval you constructed and would like to keep the width of the whole interval to be less than 4 mpg wide. How many cars would you have to sample to create the interval the engineer is requesting?
Width is twice the margin of error, so a margin of error of 2 would be need. To solve this, we have to consider the population standard deviation as [tex]\sigma = 6.2[/tex], and then use the z-distribution.
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
How many cars would you have to sample to create the interval the engineer is requesting?
This is n for which M = 2. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]2 = 1.96\frac{6.2}{\sqrt{n}}[/tex]
[tex]2\sqrt{n} = 1.96*6.2[/tex]
[tex]\sqrt{n} = \frac{1.96*6.2}{2}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96*6.2}{2})^2[/tex]
[tex]n = 36.9[/tex]
Rounding up:
37 cars would have to be sampled.
Question 6 of 10
Which situation shows a constant rate of change?
A. The number of tickets sold compared with the number of minutes
before a football game
B. The height of a bird over time
C. The cost of a bunch of grapes compared with its weight
D. The outside temperature compared with the time of day
SUBMI
a) the cost of a bunch of grapes compared with its weight
GRAAAAAAAAAAAAAAAAAAAAAAAAAAAAPES!!!!!
Find the smallest number from which 3 is to be subtracted so that the difference is exactly divisible 18,24,36
Answer:
72
Step-by-step explanation:
look at the prime factors of each number.
18 = 2*3^2
24 = 2^3*3
36 = 2^2*3^2
The most factors of 2 in any of these numbers is 3: 2^3
The most factors of 3 in any of these numbers is 2: 3^2
2^3*3^2 is 8*9 or 72.
72 is the lowest number exactly divisible by 18, 24, and 36.
find the sum of (-260)+(-30)
Answer:
-290
Step-by-step explanation:
(-260) +(-30)
=-260-30
=-290
Answer:
the answer is -290
Step-by-step explanation:
it is telling us to add so we can see that both the numbers have the same sign which is negative
when the signs are all the same, we can add and we got -290
I need help ASAP please please please
Answer:
n=39/5
Step-by-step explanation:
24=5(n-3)
24=5n-15
-5n= -15-24
-5n=39
n= 39/5
Agyappng is three times as old as Atsu .three years ago ,he was four times as old as Atsu ..how old is each boy now
9514 1404 393
Answer:
Atsu is 9Agyappng is 27Step-by-step explanation:
Let x represent Atsu's current age. Then Agyappng is 3x. Three years ago the relationship was ...
(3x -3) = 4(x -3)
9 = x . . . . . . . . . . . . add 12-3x
Atsu is 9; Agyappng is 27.
5^3×25=
Simplify as much as possible
The distribution of widgets from a production line is known to be approximately normal with mean 2.7 inches and standard deviation 0.25 inches. About 95% of the distribution lies between what two values?
A. 2.45 inches and 3.2 inches
B. 2.45 inches and 2.95 inches
C. 2.2 inches and 3.2 inches
D. 1.95 inches and 3.45 inches
Option D is correct. 95% of the distribution lies between 1.9975inches and 3.4025inches.
To get the required range of values, we will have to first get the z-score for the two-tailed probability at a 95% confidence interval. According to the normal table, the required range is between -2.81 and 2.81
The formula for calculating the z-score is expressed as;
[tex]z=\frac{x-\overline x}{s}[/tex] where:
[tex]\overline x[/tex] is the mean
s is the standard deviation
z is the z-scores
Given the following
[tex]\overline x[/tex]=2.7 in
s = 0.25
if z = -2.81
[tex]-2.81=\frac{x-2.7}{0.25}\\x-2.7=-2.81*0.25\\x-2.7=-0.7025\\x=-0.7025+2.7\\x=1.9975[/tex]
Similarly:
[tex]2.81=\frac{x_2-2.7}{0.25}\\x_2-2.7=2.81*0.25\\x_2-2.7=0.7025\\x_2=0.7025+2.7\\x_2=3.4025[/tex]
Hence the 95% of the distribution lies between 1.9975inches and 3.4025inches.
Learn more on normal distribution here: https://brainly.com/question/23418254
From the figure, the cylinder glass has a height of 6 inches and a radius of the mouth of the glass 1.25 inches. Find the length of SK in inches.
Answer:
D. 6.5
Step-by-step explanation:
The diameter of the cylinder is 1.25 x 2 = 2.5
SK = √1.25² + 6² = √42.25 = 6.5
What is the area of a trapezoid.. base 14in and 7in height is 5in?
if the formula is [tex]\frac{(B+b)}{2} .h[/tex] we just need to plug in the values
21/2 = 10.5 x 5 = 52.5
hope it helps :)
Answer:
A = 52.5 in^2
Step-by-step explanation:
The area of a trapezoid is
A = 1/2 (b1+b2)h
where b1 and b2 are the bases and h is the height
A = 1/2 ( 14+7)*5
A = 105/2
A = 52.5 in^2
Stuck on this problem
9514 1404 393
Answer:
-8,257,536·u^5·v^10
Step-by-step explanation:
The expansion of (a +b)^n is ...
(c0)a^nb^0 +(c1)a^(n-1)b^1 +(c2)a^(n-2)b^2 +... +(ck)a^(n-k)b^k +... +(cn)a^0b^n
Then the k-th term is (ck)a^(n-k)b^k, where k is counted from 0 to n.
The value of ck can be found using Pascal's triangle, or by the formula ...
ck = n!/(k!(n-k)!) . . . . where x! is the factorial of x, the product of all positive integers less than or equal to x.
This expansion has 11 terms, so the middle one is the one for k=5. That term will be ...
5th term = (10!/(5!(10-5)!)(2u)^(10-5)(-4v^2)^5
= (252)(32u^5)(-1024v^10) = -8,257,536·u^5·v^10
Please help me with 9 I really need it
Answer:
605 boys.
Step-by-step explanation:
5:7 means 5 parts consists of boys and 7 parts consist of girls.
Since 7 parts = 847, 1 part = 121 and 5 parts = 605
Hence there are 605 boys.
Hope you have a nice day :)
Please help me determine the general equation for the graph above as well as solve for a. Thank you.
Observe that the x coords of the roots of a polynomial are,
[tex]x_{1,2,3,4}=\{-3,0,1,4\}[/tex]
Which can be put into form,
[tex]y=a(x-x_1)(x-x_2)(x-x_3)(x-x_4)[/tex]
with data
[tex]y=a(x-(-3))(x-0)(x-1)(x-4)=ax(x+3)(x-1)(x-4)[/tex]
Now if I take any root point and insert it into the equation I won't be able to solve for y because they will always multiply to zero (ie. when I pick [tex]x=-3[/tex] the right hand side will multiply to zero,
[tex]y=-3a(-3+3)(-3-1)(-3-4)=0[/tex]
and a will be "lost" in the process.
If we observed a non-root point that we could substitute with x and y and result in a non-loss process then you could find a. But since there is no such point (I don't think you can read it of the graph) there is no other viable way to find a.
Hope this helps :)
John has a rectangular garden with an area of 22.6 square feet. If the length of the garden is 5.2 feet, what is the length of the diagonal of the garden? Round to the nearest tenth.
Group of answer choices
6.1 feet
4.1 feet
8.1 feet
6.8 feet
Answer:
6.8 feet
Answer From Gauth Math
Width = area/length = 22.6/5.2 = 113 ≈/26
Diagonal = √[length² + width²] ≈ √23.0 feet
PLEASE HELP
select all the statistical questions.
A what is the typical amount of rainfall for the month of June in the galapagus islands
B how much did it rain yesterday at the Mexico City International airport
C why do you like to listen to music
D how many songs does the class usually listen to each day
E how many songs did you listen to today
F what is the capital of Canada
G how long does it typically take for 2nd graders to walk a lap around the track
The selected statistical questions are as follows:
A what is the typical amount of rainfall for the month of June in the Galapagos islands
D how many songs does the class usually listen to each day
G how long does it typically take for 2nd graders to walk a lap around the track
Statistical questions are known by these two main characteristics:
they are answered by the collection of datathere is always variability in the data collectedThis means that the data vary. They are not the same data. For example, "How old is Monday?" is not a statistical question because it has one answer.
Thus, statistical questions are not answered by a single number or answer, especially when the correct answer is just one.
Learn more examples of statistical questions here: https://brainly.com/question/15729334
Suppose that 25% of people own dogs If you pick three people at random, what
is the probability that they all three own a dog? (Let me add that we don’t know the
populations size so calculate the probability as if the population is infinite.)
Answer:
1/64
Step-by-step explanation:
25% own a dog, so picking one person has a probability of 1/4 (0.25) for that person to own a dog.
picking 3 people means combining (multiplying) the probabilities of the non-overlapping and non-depending events.
picking the third person has 1/4 chance of owning a dog (as the population is "infinite") combined with the chance that also the second pick owned a dog, which has to be combined with the chance of the first pick owning a dog.
so,
1/4 × 1/4 × 1/4 = 1/4³ = 1/64 = 0.015625
Students at a virtual school are allowed to sign up for one math class each year. The numbers of students signing up for various math classes for the next school
year are given in the following table:
Grade Geometry Algebra II Pre-Calculus AP Statistics Total
10th
150
75
25
5
255
11th
50
100
75
20
245
12th
10
50
100
65
225
Total 210
225
200
90
725
Part A: What is the probability that a student will take AP Statistics? (2 points)
Part B: What is the probability that a 12th-grader will take either Pre-Calculus or AP Statistics? (2 points)
Part C: What is the probability that a student will take Algebra II given that he or she is in the 11th grade? (2 points)
Part D: Consider the events "A student takes Algebra II and "A student is a 10th-grader. Are these events independent? Justify your answer. (4 points)
A well formatted table of the distribution is attached below :
Answer:
0.124
0.733
0.408
Step-by-step explanation:
Using the table Given :
1.) P(AP Statistics) = 90 / 725 = 0.124
2.) P(12th grade ; Precalculus or AP Statistics) = (100 + 65) / 225 = 165 /225 = 0.733
3.) P(Algebra 11 | 11th grade) = P(Algebara11 n 11th grade) / P(11th grade) = 100 / 245 = 0.408
I add 7 to a certain number. I double the result. My final answer is 34. What was my number?
Answer:
answer is 10
explanation
when u add 7 with 10 u get 17 then double of 17 is 34
I hope It helps
It is found that the unknown number was 10.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. The addition is one of the mathematical operations. then the addition of two numbers results in the total amount of the combined value.
Given that "I add 7 to a certain number. I double the result. My final answer is 34".
Let consider the number be 10.
When we add 7 with 10 we get;
7 + 10 = 17
then double the result of 17 = 34
Hence, the unknown number was 10.
Learn more about equations here;
https://brainly.com/question/25180086
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