Answer:
Option (3)
Step-by-step explanation:
From the picture attached,
Bar graph sketched shows the grades earned by the students in an exam.
Number of students who achieved the grade A = 17
Number of students who achieved grade B = 14
Number of students with grade C = 5
Number of students with grade D = 9
Total students who took the exam = 17 + 14 + 5 + 9 = 45
Option (1)
"[tex]\frac{1}{5}[/tex] of the students earned a C"
Fraction of students who earned C = [tex]\frac{\text{Students who earned C}}{\text{Total students}}[/tex]
= [tex]\frac{5}{45}[/tex]
= [tex]\frac{1}{9}[/tex]
Therefore, this option is incorrect.
Option (2)
"3% more students earned an A then B"
Percentage of students who earned A = [tex]\frac{\text{Students got A}}{\text{Total students who took the exam}}\times 100[/tex]
= [tex]\frac{17}{45}\times 100[/tex]
= 37.78%
Percentage of students who earned B = [tex]\frac{\text{Students got B}}{\text{Total students who took the exam}}\times 100[/tex]
= [tex]\frac{14}{45}\times 100[/tex]
= 31.11%
Difference in percentage = 37.78 - 31.11
= 6.67%
Therefore, this option is not correct.
Option (3)
"20% of the students earned a D"
Percentage of students who earned D = [tex]\frac{\text{Students got D}}{\text{Total students who took the exam}}\times 100[/tex]
= [tex]\frac{9}{45}\times 100[/tex]
= 20%
Option (3) is the correct option.
Option (4)
" [tex]\frac{1}{4}[/tex] of the class earned a B"
Fraction of class who earned B = [tex]\frac{\text{Students got B}}{\text{Total students who took the exam}}[/tex]
= [tex]\frac{14}{45}[/tex]
Therefore, Option (4) is not correct.
4(x/2-2) > 2y-11 which of the following inequalities is equivalent to the inequality above?
1) 4x+2y-3 > 0
2) 4x-2y+3 > 0
3) 2x+2y-3 > 0
4) 2x-26+3 > 0
4) 2x-2y+3 > 0
although it is spelt "26" on the choices
limit chapter~ anyone can help me with these questions?
please gimme clear explanation :)
Step-by-step explanation:
I(S) = aS / (S + c)
As S approaches infinity, S becomes much larger than c. So S + c is approximately equal to just S.
lim(S→∞) I(S)
= lim(S→∞) aS / (S + c)
= lim(S→∞) aS / S
= lim(S→∞) a
= a
As S approaches infinity, I(S) approaches a.
A United Nations report shows the mean family income for Mexican migrants to the United States is $26,500 per year. A FLOC (Farm Labor Organizing Committee) evaluation of 24 Mexican family units reveals a mean to be $30,150 with a sample standard deviation of $10,560. State the null hypothesis and the alternate hypothesis.
Answer:
The null hypothesis [tex]\mathtt{H_0 : \mu = 26500}[/tex]
The alternative hypothesis [tex]\mathtt{H_1 : \mu \neq 26500}[/tex]
Step-by-step explanation:
The summary of the given statistics is:
Population Mean = 26,500
Sample Mean = 30,150
Standard deviation = 10560
sample size = 24
The objective is to state the null hypothesis and the alternate hypothesis.
An hypothesis is a claim with insufficient information which tends to be challenged into further testing and experimentation in order to determine if such claim is significant or not.
The null hypothesis is a default hypothesis where there is no statistical significance between the two variables in the hypothesis.
The alternative hypothesis is the research hypothesis that the researcher is trying to prove.
The null hypothesis [tex]\mathtt{H_0 : \mu = 26500}[/tex]
The alternative hypothesis [tex]\mathtt{H_1 : \mu \neq 26500}[/tex]
The test statistic can be computed as follows:
[tex]z = \dfrac{\overline X - \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \dfrac{30150 - 26500}{\dfrac{10560}{\sqrt{24}}}[/tex]
[tex]z = \dfrac{3650}{\dfrac{10560}{4.8989}}[/tex]
[tex]z = \dfrac{3650 \times 4.8989 }{{10560}}[/tex]
z = 1.6933
simplify each expression 17x + 4 - 3x
Answer:
14x+4
Step-by-step explanation:
17x-3x=14x
Find the midpoint of the segment between the points (8,−10) and (−10,−8) A. (−1,−9) B. (0,−6) C. (0,0) D. (−1,2)
Answer:
Hey there!
We can use the midpoint formula to find that the midpoint is (-1, -9).
Let me know if this helps :)
The midpoint of the segment between the points (8,−10) and (−10,−8) will be (−1, −9). Then the correct option is A.
What is the midpoint of line segment AB?
Let C be the mid-point of the line segment AB.
A = (x₁, y₁)
B = (x₂, y₂)
C = (x, y)
Then the midpoint will be
x = (x₁ + x₂) / 2
y = (y₁ + y₂) / 2
The midpoint of the segment between the points (8,−10) and (−10,−8)
x = (8 – 10) / 2
x = –1
y = (– 10 – 8) / 2
y = –9
Then the correct option is A.
More about the midpoint of line segment AB link is given below.
https://brainly.com/question/17410964
#SPJ5
which polynomial correctly combines the like terms and expresses the given polynomial in standard form? 9xy³ -4y⁴ -10x²y² + x³y + 3x⁴ + 2x²y² - 9y⁴
Answer:
3x^4+(x^3)y-8x^2y^2+9xy^3-13y^4
Step-by-step explanation:
3x^4+(nothing)=3x^4
x^3y+(nothing)=x^3y
-10x^2y^2=2x^2y^2=-8x^2y^2
9xy^3+(nothing)=0
-4y^4-9y^4=-13y^4
Add it all up and write the terms by descending order of exponent value, and u get my answer.
graph the solution set to the inequality
Graphed using the given range equation. The shaded area is the possible range, extending to infinity, infinity from 0, -1.
When a number is doubled and the
result is decreased by 4 the answer
is 19. Find the number.
Answer:
7.5
Step-by-step explanation:
what does 7g equal in like a verbal form
Answer:
see below
Step-by-step explanation:
7g can be "split" as 7 * g. The "*" means multiplication so a verbal form of this expression could be "7 times a number g" or "The product of 7 and a number g".
A couple has a total household income of $84,000. The husband earns $18,000 less than twice what the wife earns. How much does the wife earn? Select the correct answer below:
Answer:
$34000
Step-by-step explanation:
We can set up a systems of equations, assuming [tex]h[/tex] is the husbands income and [tex]w[/tex] is the wife's income.
h + w = 84000
h = 2w - 18000
We can substitute h into the equation as 2w - 18000:
(2w - 18000) + w = 84000
Combine like terms:
3w - 18000 = 84000
Add 18000 to both sides
3w = 102000
And divide both sides by 3
w = 34000
Now that we know how much the wife earns, we can also find out how much the husband earns by substituting into the equation.
h + 34000 = 84000
h = 50000
Hope this helped!
Find the sum to infinity of the series 2+5/4+11/16+23/64+..........up to the infinity.
infinity
We have
[tex]2+\dfrac54+\dfrac{11}{16}+\dfrac{23}{64}+\cdots=\displaystyle\sum_{n=0}^\infty\frac{3\cdot2^n-1}{4^n}[/tex]
(notice that each denominator is a power of 4, and each numerator is one less than some multiple of 3, in particular 3 times some power of 2)
Recall for [tex]|x|<1[/tex], we have
[tex]\displaystyle\frac1{1-x}=\sum_{n=0}^\infty x^n[/tex]
So we have
[tex]\displaystyle\sum_{n=0}^\infty\frac{3\cdot2^n-1}4=3\sum_{n=0}^\infty\left(\frac12\right)^n-\sum_{n=0}^\infty\left(\frac14\right)^n=\frac3{1-\frac12}-\frac1{1-\frac14}=\boxed{\frac{14}3}[/tex]
please answer this question please
Step-by-step explanation:
C = Amount (A) - Principal (P)
Where
C is the compound interest
To find the amount we use the formula
[tex]A = P ({1 + \frac{r}{100} })^{n} [/tex]
where
P is the principal
r is the rate
n is the period / time
From the question
P = Rs 12, 000
r = 5%
n = 3 years
Substitute the values into the above formula
That's
[tex]A = 12000 ({1 + \frac{5}{100} })^{3} \\ A = 12000(1 + 0.05)^{3} \\ A = 12000 ({1.05})^{3} [/tex]
We have the answer as
Amount = Rs 13891.50Compound interest = 13891.50 - 12000
Compound interest = Rs 1891.50Hope this helps you
Which option is correct and how would one solve for it?
Answer:
28
Step-by-step explanation:
We need to find the value of [tex]\Sigma_{x=0}^3\ 2x^2[/tex]
We know that,
[tex]\Sigma n^2=\dfrac{n(n+1)(2n+1)}{6}[/tex]
Here, n = 3
So,
[tex]\Sigma n^2=\dfrac{3(3+1)(2(3)+1)}{6}\\\\\Sigma n^2=14[/tex]
So,
[tex]\Sigma_{x=0}^3\ 2x^2=2\times 14\\\\=28[/tex]
So, the value of [tex]\Sigma_{x=0}^3\ 2x^2[/tex] is 28. Hence, the correct option is (d).
Which option is correct and how would one solve for it?
Answer:
2+4+6+8
Step-by-step explanation:
We have the sum of 2n where n runs from 1 to 4
n=1 2(1) = 2
n=2 2(2) = 4
n=3 2(3) = 6
n=4 2(4) = 8
The sum is add
2+4+6+8
A librarian needs to package up all of the children's books and move them to a different location in the library. There are 625 books, and she can fit 25 books in one box. How many boxes does she need in order to move all of the books? 5 B. 25 C. 125 D. 600 E. 650
Answer: B. 25
Step-by-step explanation:
Given: Total books = 625
Number of books can fit in one box = 25
Now, the number of boxes she need to move all of the books = (Total books) ÷ (Number of books can fit in one box )
= 625÷25
= 25
hence, she requires 25 boxes in order to move all of the books.
So, correct option is B. 25.
f(x)=3x2+10x-25 g(x)=9x2-25 Find (f/g)(x).
Answer:
[tex](f/g)(x) = \frac{x + 5}{3x + 5} [/tex]
Step-by-step explanation:
f(x) = 3x² + 10x - 25
g(x) = 9x² - 25
To find (f/g)(x) divide f(x) by g(x)
That's
[tex](f/g)(x) = \frac{3 {x}^{2} + 10x - 25 }{9 {x}^{2} - 25 } [/tex]
Factorize both the numerator and the denominator
For the numerator
3x² + 10x - 25
3x² + 15x - 5x - 25
3x ( x + 5) - 5( x + 5)
(3x - 5 ) ( x + 5)
For the denominator
9x² - 25
(3x)² - 5²
Using the formula
a² - b² = ( a + b)(a - b)
(3x)² - 5² = (3x + 5)(3x - 5)
So we have
[tex](f/g)(x) = \frac{(3x - 5)(x + 5)}{(3x + 5)(3x - 5)} [/tex]
Simplify
We have the final answer as
[tex](f/g)(x) = \frac{x + 5}{3x + 5} [/tex]
Hope this helps you
Because she has limited shelf space, she can't put out all her copies of the CD at once. On Monday morning, she stocked the display with 40 copies. By the end of the day, some of the copies had been sold. On Tuesday morning, she counted the number of copies left and then added that many more to the shelf. In other words, she doubled the number that was left in the display. At the end of the day, she discovered that she had sold the exact same number of copies as had been sold on Monday. On Wednesday morning, the manager decided to triple the number of copies that had been left in the case after Tuesday. Amazingly, she sold the same number of copies on Wednesday as she had on each of the first two days! But this time, at the end of the day the display case was empty.
Now, it look like there is some information missing in the answer. The whole problem should look like this:
Alicia Keys's new album As I Am is climbing the charts, and the manager of Tip Top Tunes expects to sell a lot of copies. Because she has limited shelf space, she can't put out all her copies of the CD at once. On Monday morning, she stocked the display with 40 copies. By the end of the day, some of the copies had been sold. On Tuesday morning, she counted the number of copies left and then added that many more to the shelf. In other words, she doubled the number that was left in the display. At the end of the day, she discovered that she had sold the exact same number of copies as had been sold on Monday. On Wednesday morning, the manager decided to triple the number of copies that had been left in the case after Tuesday. Amazingly, she sold the same number of copies on Wednesday as she had on each of the first two days! But this time, at the end of the day the display case was empty. How many copies of the As I Am CD did she sell each day?
Answer:
She sold 24 copies of the cd each day.
Step-by-step explanation:
In order to solve this problem we must first set our variable up. In this case, since we need to know what the number of sold cd's per day is, that will just be our variable:
x= Number of copies sold.
So we can start setting our equation up. So we take the first part of the problem:
"On Monday morning, she stocked the display with 40 copies. By the end of the day, some of the copies had been sold."
This can be translated as:
40-x
where this expression represents the number of copies left on the shelf by the end of monday.
"On Tuesday morning, she counted the number of copies left and then added that many more to the shelf."
so we represent it like this:
(40-x)+(40-x)
"In other words, she doubled the number that was left in the display."
so the previous expression can be simplified like this:
2(40-x)
"At the end of the day, she discovered that she had sold the exact same number of copies as had been sold on Monday."
so the expression now turns to:
2(40-x)-x this is the number of copies left by the end of tuesday.
"On Wednesday morning, the manager decided to triple the number of copies that had been left in the case after Tuesday."
this translates to:
3[2(40-x)-x]
This is the number of copies on the shelf by the begining of Wednesday.
"Amazingly, she sold the same number of copies on Wednesday as she had on each of the first two days! But this time, at the end of the day the display case was empty."
this piece of information lets us finish writting our equation:
3[2(40-x)-x] -x = 0
since there were no copies left on the shelf, then the equation is equal to zero.
So now we proceed and solve the equation for x:
3[2(40-x)-x] -x = 0
We simplify it from the inside to the outside.
3[80-2x-x]-x=0
3[80-3x]-x = 0
we now distribute the 3 so we get:
240-9x-x=0
we combine like terms so we get:
240-10x=0
we move the 240 to the other side of the equation so we get:
-10x=-240
and divide both sides into -10 so we get:
x=24
so she sold 24 copies each day.
Change the polar coordinates (r, θ) to rectangular coordinates (x, y):(-2,sqrt2pi
Step-by-step explanation:
x=rcosθandy=rsinθ,. 7.7. r2=x2+y2andtanθ=yx. 7.8. These formulas can be used to convert from rectangular to polar or from polar to rectangular coordinates.
An economist is interested in studying the income of consumers in a particular region. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in an average income of $15,000. What is the width of the 90% confidence interval
Answer:
The width is [tex]w = 282.8[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 50
The population standard deviation is [tex]\sigma = \$ 1000[/tex]
The sample size is [tex]\= x = \$ 15,000[/tex]
Given that the confidence level is 90% then the level of significance can be mathematically represented as
[tex]\alpha = 100 - 90[/tex]
[tex]\alpha = 10 \%[/tex]
[tex]\alpha = 0.10[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table, the value is
[tex]Z_{\frac{0.10 }{2} } = 1.645[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{0.10}{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]E = 1.645 * \frac{1000 }{\sqrt{50 }}[/tex]
=> [tex]E = 141.42[/tex]
The width of the 90% confidence level is mathematically represented as
[tex]w = 2 * E[/tex]
substituting values
[tex]w = 2 * 141.42[/tex]
[tex]w = 282.8[/tex]
Greg is 10 years older than his brother gabe. He is also 3 times as old as gabe. How old is Greg?
Answer: 30 i think 10x3=30
Step-by-step explanation:
What is the equation of the parabola that has its vertex at (8,-1) and a y-intercept of (0,-17)?
y = a(x + 1.5)^2 - 12.5
y intercept is (0,-8) so:-
-8 = a(0+1.5)^2 - 12.5
-8 = 2.25a - 12.5
a = 4.5/ 2.25 = 2
so we have
y = 2 ( x +1.5)^2 - 12.5
solving for x when y = 0:-
(x + 1.5)^2 = 12.5/2 = 6.25
taking sqrt's x + 1.5 = +/- 2.5
x = -4, 1
so the x intercepts are (-4,0) and (1,0)
Answer:
y = –1∕4(x – 8)^2 – 1
Step-by-step explanation:
I took the exam and got it right.
Each power smoothie that Theo makes has 3 scoops of mango, 1 scoop of strawberries, and 1 scoop of spinach. If Theo makes 7 power smoothies, how many scoops will he use in all?
Answer: 35 scoops total!
Step-by-step explanation: FIrst, you would add the number of scoops in total which is 3+1+1=5 scoops.
Now you would do 7*5=35
Therefore, Theo uses 35 scoops in all. I hope this helps you!
Please help me guys :)
Question:
In exercises 1 through 4, find the one-sided limits lim x->2(left) f(x) and limx-> 2(right) from the given graph of f and determine whether lim x->2 f(x) exists.
Step-by-step explanation:
For a left-hand limit, we start at the left side and move right, and see where the function goes as we get close to the x value.
For a right-hand limit, we start at the right side and move left, and see where the function goes as we get close to the x value.
If the two limits are equal, then the limit exists. Otherwise, it doesn't.
1. As we approach x = 2 from the left, f(x) approaches -2.
lim(x→2⁻) f(x) = -2
As we approach x = 2 from the right, f(x) approaches 1.
lim(x→2⁺) f(x) = 1
The limits are not the same, so the limit does not exist.
lim(x→2) f(x) = DNE
2. As we approach x = 2 from the left, f(x) approaches 4.
lim(x→2⁻) f(x) = 4
As we approach x = 2 from the right, f(x) approaches 2.
lim(x→2⁺) f(x) = 2
The limits are not the same, so the limit does not exist.
lim(x→2) f(x) = DNE
3. As we approach x = 2 from the left, f(x) approaches 2.
lim(x→2⁻) f(x) = 2
As we approach x = 2 from the right, f(x) approaches 2.
lim(x→2⁺) f(x) = 2
The limits are equal, so the limit exists.
lim(x→2) f(x) = 2
4. As we approach x = 2 from the left, f(x) approaches 2.
lim(x→2⁻) f(x) = 2
As we approach x = 2 from the right, f(x) approaches infinity.
lim(x→2⁺) f(x) = ∞
The limits are not the same, so the limit does not exist.
lim(x→2) f(x) = DNE
Your job in a company is to fill quart-size bottles of oil from a full -gallon oil tank. Then you are to pack quarts of oil in a case to ship to a store. How many full cases of oil can you get from a full -gallon tank of oil?
Answer:
See below.
Step-by-step explanation:
1 gal = 4 qt
With a full gallon oil tank, you can fill 4 1-qt bottles.
The problem does not mention the number of quarts that go in a case, so there is not enough information to answer the question.
Also, is the full tank really only 1 gallon, or is there a number missing there too?
Two balls are drawn in succession out of a box containing 5 red and 4 white balls. Find the probability that at least 1 ball was red, given that the first ball was (Upper A )Replaced before the second draw. (Upper B )Not replaced before the second draw. (A) Find the probability that at least 1 ball was red, given that the first ball was replaced before the second draw. StartFraction 24 Over 49 EndFraction (Simplify your answer. Type an integer or a fraction.) (B) Find the probability that at least 1 ball was red, given that the first ball was not replaced before the second draw.
Answer:
The answer is below
Step-by-step explanation:
The box contains 5 red and 4 white balls.
A) The probability that at least 1 ball was red = P(both are red) + P(first is red and second is white) + P(first is white second is red)
Given that the first ball was (Upper A )Replaced before the second draw:
P(both are red) = P(red) × P(red) = 5/9 × 5/9 = 25/81
P(first is red and second is white) = P(red) × P(white) = 5/9 × 4/9 = 20/81
P(first is white and second is red) = P(white) × P(red) = 4/9 × 5/9 = 20/81
The probability that at least 1 ball was red = 25/81 + 20/81 + 20/81 = 65/81
B) The probability that at least 1 ball was red = P(both are red) + P(first is red and second is white) + P(first is white second is red)
Given that the first ball was not Replaced before the second draw:
P(both are red) = P(red) × P(red) = 5/9 × 4/8 = 20/72 (since it was not replaced after the first draw the number of red ball remaining would be 4 and the total ball remaining would be 8)
P(first is red second is white) = P(red) × P(white) = 5/9 × 4/8 = 20/72
P(first is white and second is red) = P(white) × P(red) = 4/9 × 5/8 = 20/72
The probability that at least 1 ball was red = 20/72 + 20/72 + 20/72 = 60/72
Researchers recorded that a certain bacteria population declined from 450,000 to 900 in 30 hours at this rate of decay how many bacteria will there be in 13 hours
Answer:
30,455
Step-by-step explanation:
Exponential decay
y = a(1 - b)^x
y = final amount
a = initial amount
b = rate of decay
x = time
We are looking for the rate of decay, b.
900 = 450000(1 - b)^30
1 = 500(1 - b)^30
(1 - b)^30 = 0.002
1 - b = 0.002^(1/30)
1 - b = 0.81289
b = 0.1871
The equation for our case is
y = 450000(1 - 0.1871)^x
We are looking for the amount in 13 hours, so x = 13.
y = 450000(1 - 0.1871)^13
y = 30,455
Calcule o valor de x nas equações literais: a) 5x – a = x+ 5a b) 4x + 3a = 3x+ 5 c) 2 ( 3x -a ) – 4 ( x- a ) = 3 ( x + a ) d) 2x/5 - (x-2a)/3 = a/2 Resolva as equações fracionárias: a) 3/x + 5/(x+2) = 0 , U = R - {0,-2} b) 7/(x-2) = 5/x , U = R - {0,2} c) 2/(x-3) - 4x/(x²-9) = 7/(x+3) , U = R - {-3,3}
Answer:
1) a) [tex]x = \frac{3}{2}\cdot a[/tex], b) [tex]x = 5-3\cdot a[/tex], c) [tex]x = -a[/tex], d) [tex]x = \frac{5}{2}\cdot a[/tex]
2) a) [tex]x = -\frac{3}{4}[/tex], b) [tex]x = -5[/tex], c) [tex]x = 3[/tex]
Step-by-step explanation:
1) a) [tex]5\cdot x - a = x + 5\cdot a[/tex]
[tex]5\cdot x - x = 5\cdot a + a[/tex]
[tex]4\cdot x = 6\cdot a[/tex]
[tex]x = \frac{3}{2}\cdot a[/tex]
b) [tex]4\cdot x + 3\cdot a = 3\cdot x + 5[/tex]
[tex]4\cdot x - 3\cdot x = 5 - 3\cdot a[/tex]
[tex]x = 5-3\cdot a[/tex]
c) [tex]2\cdot (3\cdot x - a) - 4\cdot (x-a) = 3\cdot (x+a)[/tex]
[tex]6\cdot x -2\cdot a -4\cdot x +4\cdot a = 3\cdot x +3\cdot a[/tex]
[tex]6\cdot x -4\cdot x -3\cdot x = 3\cdot a -4\cdot a +2\cdot a[/tex]
[tex]-x = a[/tex]
[tex]x = -a[/tex]
d) [tex]\frac{2\cdot x}{5} - \frac{x-2\cdot a}{3} = \frac{a}{2}[/tex]
[tex]\frac{6\cdot x-5\cdot (x-2\cdot a)}{15} = \frac{a}{2}[/tex]
[tex]\frac{6\cdot x - 5\cdot x+10\cdot a}{15} = \frac{a}{2}[/tex]
[tex]2\cdot (x+10\cdot a) = 15 \cdot a[/tex]
[tex]2\cdot x = 5\cdot a[/tex]
[tex]x = \frac{5}{2}\cdot a[/tex]
2) a) [tex]\frac{3}{x} + \frac{5}{x+2} = 0[/tex]
[tex]\frac{3\cdot (x+2)+5\cdot x}{x\cdot (x+2)} = 0[/tex]
[tex]3\cdot (x+2) + 5\cdot x = 0[/tex]
[tex]3\cdot x +6 +5\cdot x = 0[/tex]
[tex]8\cdot x = - 6[/tex]
[tex]x = -\frac{3}{4}[/tex]
b) [tex]\frac{7}{x-2} = \frac{5}{x}[/tex]
[tex]7\cdot x = 5\cdot (x-2)[/tex]
[tex]7\cdot x = 5\cdot x -10[/tex]
[tex]2\cdot x = -10[/tex]
[tex]x = -5[/tex]
c) [tex]\frac{2}{x-3}-\frac{4\cdot x}{x^{2}-9} = \frac{7}{x+3}[/tex]
[tex]\frac{2}{x-3} - \frac{4\cdot x}{(x+3)\cdot (x-3)} = \frac{7}{x+3}[/tex]
[tex]\frac{1}{x-3}\cdot \left(2-\frac{4\cdot x}{x+3} \right) = \frac{7}{x+3}[/tex]
[tex]\frac{x+3}{x-3}\cdot \left[\frac{2\cdot (x+3)-4\cdot x}{x+3} \right] = 7[/tex]
[tex]\frac{2\cdot (x+3)-4\cdot x}{x-3} = 7[/tex]
[tex]2\cdot (x+3) -4\cdot x = 7\cdot (x-3)[/tex]
[tex]2\cdot x + 6 - 4\cdot x = 7\cdot x -21[/tex]
[tex]2\cdot x - 4\cdot x -7\cdot x = -21-6[/tex]
[tex]-9\cdot x = -27[/tex]
[tex]x = 3[/tex]
It is advertised that the average braking distance for a small car traveling at 65 miles per hour equals 122 feet. A transportation researcher wants to determine if the statement made in the advertisement is false. She randomly test drives 38 small cars at 65 miles per hour and records the braking distance. The sample average braking distance is computed as 116 feet. Assume that the population standard deviation is 21 feet. (You may find it useful to reference the appropriate table: z table or t table) a. State the null and the alternative hypotheses for the test.
Complete Question
The complete question is shown on the first uploaded image
Answer:
the null hypothesis is [tex]H_o : \mu = 122[/tex]
the alternative hypothesis is [tex]H_a : \mu \ne 122[/tex]
The test statistics is [tex]t = - 1.761[/tex]
The p-value is [tex]p = P(Z < t ) = 0.039119[/tex]
so
[tex]p \ge 0.01[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 122[/tex]
The sample size is n= 38
The sample mean is [tex]\= x = 116 \ feet[/tex]
The standard deviation is [tex]\sigma = 21[/tex]
Generally the null hypothesis is [tex]H_o : \mu = 122[/tex]
the alternative hypothesis is [tex]H_a : \mu \ne 122[/tex]
Generally the test statistics is mathematically evaluated as
[tex]t = \frac { \= x - \mu }{\frac{ \sigma }{ \sqrt{n} } }[/tex]
substituting values
[tex]t = \frac { 116 - 122 }{\frac{ 21 }{ \sqrt{ 38} } }[/tex]
[tex]t = - 1.761[/tex]
The p-value is mathematically represented as
[tex]p = P(Z < t )[/tex]
From the z- table
[tex]p = P(Z < t ) = 0.039119[/tex]
So
[tex]p \ge 0.01[/tex]
Find the slope of the line whose x-intercept is 4 and the y- intercept is -9
Answer:
y = (9/4)x - 9
Step-by-step explanation:
The x-intercept is (4, 0) and the y-intercept is (0, -9).
As we move from (0, -9) to (4, 0), x (the 'run' increases by 4 and y (the 'rise' increases by 9. Thus, the slope of the line connecting these two points is m = rise/run = 9/4, from which we can write the desired equation in the form y = mx + b:
y = (9/4)x - 9
An Internet service provider is implementing a new program based on the number of connected devices in each household currently,customers are charged a flat rate of $175 per month.the new plan would charge a flat rate of $94 plus an additional $4.50 per device connected to the network.find the number of devices,x,for which the cost of the new plan is less than the cost of the current plan.
Answer:
(x=6) is less than 18 which would give you the cost of the current plan
Step-by-step explanation:
If you take six, first you must multiply 4.50 by 6, ($27) then add it, to $94, giving you $121. Now we have to find which phone will give us the same cost, for this I choose 18. if you do 18 x 4.50, you get $81, and if you add this to 94, it gives you 175.