Answer:
270 mL of pure alcohol is needed.
Step-by-step explanation:
In 540 mL of the mixture, you have 540*10% = 54 mL of pure alcohol.
If you add x mL pure alcohol, then you have (540 + x) mL solution, in it there is (54 + x) mL of pure alcohol
so (54 + x)/(540 + x) = 40%
Then
54 + x = 0.4(540 + x)
54 + x = 216 + 0.4 x
0.6x = 216 - 54 = 162
x = 162/0.6 = 270 mL
How do you do this question?
Answer: Convergent; converges to 9/5 = 1.8
======================================================
Explanation:
The expression 8/(n^2-1) is the same as 8/( (n+1)(n-1) )
Use partial fraction decomposition to get
8/( (n+1)(n-1) ) = A/(n+1) + B/(n-1)
8 = (n+1)(n-1)*( A/(n+1) + B/(n-1) )
8 = A(n-1) + B(n+1)
8 = An-A + Bn+B
0n + 8 = (A+B)n + (-A+B)
We can see that
[tex]\begin{cases}A+B = 0\\-A+B = 8\end{cases}[/tex]
Use elimination to get 2B = 8 which leads to B = 4
Plug B = 4 into either equation of that system to solve for A getting A = -4
Therefore,
8/( (n+1)(n-1) ) = A/(n+1) + B/(n-1)
8/( (n+1)(n-1) ) = -4/(n+1) + 4/(n-1)
--------------------------------------------
Why do all this? Because it'll be helpful to set up the telescoping sum
Let's plug in a few values of n. Let's say from n = 5 to n = 10
If we do so, then we have...
-4/(5+1)+4/(5-1) = -4/6 + 4/4
-4/(6+1)+4/(6-1) = -4/7 + 4/5
-4/(7+1)+4/(7-1) = -4/8 + 4/6
-4/(8+1)+4/(8-1) = -4/9 + 4/7
-4/(9+1)+4/(9-1) = -4/10 + 4/8
-4/(10+1)+4/(10-1) = -4/11 + 4/9
I'm not evaluating or simplifying further because we'll have cancellations as shown in the diagram below. The left panel is what you see before cancelling happens, and the right hand panel is what happens after the terms pair up and cancel (since those pairs add to 0).
Note the color coding so you can see what terms pair up and cancel. The only stuff left is the 4/4 and the 4/5
So,
4/4 + 4/5 = 1 + 4/5 = 5/5+4/5 = 9/5 = 1.8
is what the infinite sum converges to. You can use a tool like wolfram alpha to confirm this answer.
5 2/3 multiplied by 4 1/2
Answer:
[tex] 25\frac{1}{2} [/tex]
Step-by-step explanation:
[tex]5 \frac{2}{3} \times 4 \frac{1}{2} \\ \\ = \frac{5 \times 3 + 2}{3} \times \frac{4 \times 2 + 1}{2} \\ \\ = \frac{15 + 2}{3} \times \frac{8 + 1}{2} \\ \\ = \frac{17}{3} \times \frac{9}{2} \\ \\ = \frac{17}{1} \times \frac{3}{2} \\ \\ = \frac{51}{2} \\ \\ = 25 \frac{1}{2} [/tex]
Using synthetic division, what is the factored form of this polynomial
x^3+3x^2-13x-15
Answer:
D.
Step-by-step explanation:
(x-3)(x+1)(x+5)
The factored form of this polynomial x³ + 3x² - 13x - 15 will be (x - 3), (x + 5) and (x + 1).
What is factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
The polynomial is given as,
⇒ x³ + 3x² - 13x - 15
Factorize the polynomial, then we have
⇒ x³ + 3x² - 13x - 15
⇒ x³ - 3x² + 6x² - 18x + 5x - 15
⇒ x²(x - 3) + 6x(x - 3) + 5(x - 3)
⇒ (x - 3)(x² + 6x + 5)
⇒ (x - 3)(x² + 5x + x + 5)
⇒ (x - 3)[x(x + 5) + 1(x + 5)]
⇒ (x - 3)(x + 5)(x + 1)
The factored form of this polynomial x³ + 3x² - 13x - 15 will be (x - 3), (x + 5) and (x + 1).
More about the factorization link is given below.
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Jeannie has a cell phone plan that charges $60 per month. It includes unlimited calling but
only the first 500 text messages are free, For every extra text message that Jeannie sends,
she must pay $0.15. If Jeannie's bill at the end of a month is $70.80, how many extra text
messages did she send/receive?
Answer:
Jeannie sent/received 572 text messages
Step-by-step explanation:
60$ are payed at the beginning
0.15$ is payed for every extra text.
the total is 70.80$
if t is the number of extra text messages, then
60 + 0.15t = 70.80
subtract 60 from both sides
0.15t = 70.80 - 60
0.15t = 10.80
divide both sides by 0.15
t = 10.80/0.15
t = 72
remember, Jeannie was able to send 500 free texts at the beginning.
so, her total texts would be 572
let me know if I did something wrong!
05.02)One triangle on a graph has a vertical side of 7 and a horizontal side of 12. Another triangle on a graph has a vertical side of 28 and a horizontal side of 48.
Could the hypotenuses of these two triangles lie along the same line?
Yes, because they are similar triangles
Yes, because all triangles can fit along this line
No, because they need to be the same size
No, because they are not similar triangles
Answer:
B
Step-by-step explanation:
7 x 4 = 28
12 x 4 = 48
The higher numbers might be higher on the line but still in the same line :)
Answer:
A
Yes, because they are similar triangles
Step-by-step explanation:
Each angle increases by four
Triangle one is 7 and 12
Triangle two is 28 and 48
7 x 4 = 28
12 x 4 = 48
5(2y + 3)
can’t find any answers from this question
Answer:
10y + 15
Step-by-step explanation:
5(2y + 3)
= 5x2y + 5x3
= 10y + 15
Given the parent function f(x)=x^2 in red, write the equation for the transformed function g(x) in green.
Answer:
g(x) = 2x² + 1
Step-by-step explanation:
The parabola got thinner, so to show that, you put a 2 before x² to show that the graph was dilated (or thinned) by a factor of 2 (Note: this number can also be negative, so if the dilation factor is negative, it's okay). Since the parabola shifts up by 1, you then add + 1 after x² to show the positive upward shift.
Your full equation would look like this: g(x) = 2x² + 1
Dilation: this just means that every point on the parent function was double (or whatever the factor is) in the transformed function.
what % is 3% of 5%?
200m - 100m + 48,250 = 50,250 - 150m
Answer:
Ok sorry but I have a very strong feeling that this isn't a college question because I am in an 8th grader taking Algebra 1 and this is sooooo simple.
Step-by-step explanation:
the answer is
8=m
The Hindu Arabic Numeral for XCIS ? is 111 or 90 or 91 or 1000?
Answer:
there's no S .X=1 ,Xc=9.So 91
PLs Help me I will give brainliest
Answer:
i cant see the pic srry dude
Step-by-step explanation:
Answer:
it c
Step-by-step explanation:
it is c because it does cost less by 3.01 per pound and because i did it and got it correct plase mark me as brainliest
find the rate of change from the equation y=-x-1 will mark braniest
Answer:
-1
Step-by-step explanation:
slope=m
(keep in mind your equation is written in the form y=mx+b)
Answer:
-1Step-by-step explanation:
rate of change for y = -x - 1
so its the inverse of -x - 1 = -1 - x
therefore, the rate of change = -1
90% of babies are born with a certain ailment recover fully.
Hello! Your answer to this question is Yes!
Step-by-step explanation:
About 90% of babies born with a certain ailment recover fully. A hospital is caring for sixsix babies born with this ailment. The random variable represents the number of babies that recover fully. Decide whether the experiment is a binomial experiment.
Bodytemperatures ofhealthy koalasarenormally distributed with a mean of 35.6°C and a standard deviation of 1.3°C. a.What is the probability that a health koalahas a body temperature lessthan 35.0°C? (1pt)b.Veterinarians at a nature preserve in Australiathought a population of koalas might be infected with a virus, so they chose a random sample of n=30koalas and measured their body temperatures. If they got a sample mean body temperature less than 35.0°C, do you think that this population of koalas is healthy? Why/why not?Be specific.(4pt)c.List a potential confounding variable for this study and briefly how it might have impactedthe results. (2pt)2.
Answer:
a
[tex]P(X < 35) = 32.3 \%[/tex]
b
[tex]P(\= X < 35) = 0.6 \%[/tex]
Here the probability of koalas mean temperature being less than 35 °C is very small hence the koalas are not healthy
c
A potential confounding variable for this study is the population of the koalas because in the first question the population was not taken into account and the probability was [tex]P(X < 35) = 32.3 \%[/tex] but when the population was taken into account (i.e n = 30) the probability became
[tex]P(\= X < 35) = 0.6 \%[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 35.6^oC[/tex]
The standard deviation is [tex]s = 1.3^oC[/tex]
The sample size is n = 30
Generally the probability that a health koala has a body temperature less than 35.0°C is mathematically represented as
[tex]P(X < 35) = P(\frac{X - \mu }{s} < \frac{35 - 35.6}{1.3} )[/tex]
Here [tex](\frac{X - \mu }{s} = Z (The \ standardized \ value \ of \ X )[/tex]
So
[tex]P(X < 35) = P(Z < -0.46)[/tex]
From the z-table P(Z < -0.46) = 0.323
So
[tex]P(X < 35) = 0.323 [/tex]
Converting to percentage
[tex]P(X < 35) = 0.323 * 100 [/tex]
[tex]P(X < 35) = 32.3 \%[/tex]
considering question b
The sample mean is [tex]\= x = 35[/tex]
Generally the standard error of the mean is mathematically represented as
[tex]\sigma_{\= x} = \frac{s}{\sqrt{n} }[/tex]
=> [tex]\sigma_{\= x} = \frac{1.3}{\sqrt{30} }[/tex]
=> [tex]\sigma_{\= x} = 0.2373 [/tex]
Generally the probability of the mean body temperature of koalas being less than 35.0°C is mathematically represented as
[tex]P(\= X < 35) = P(\frac{\= X - \mu }{\sigma_{\= x }} < \frac{35 -35.6}{0.2373 } )[/tex]
[tex]P(\= X < 35) = P(Z< -2.53 )[/tex]
From the z-table we have that
[tex]P(Z< -2.53 ) = 0.006[/tex]
So
[tex]P(\= X < 35) = 0.006 /tex]
Converting to percentage
[tex]P(\= X < 35) = 0.006 * 100 [/tex]
[tex]P(\= X < 35) = 0.6 \%[/tex]
Here the probability of koalas mean temperature being less than 35 °C is very small hence the koalas are not healthy
A potential confounding variable for this study is the population of the koalas because in the first question the population was not taken into account and the probability was [tex]P(X < 35) = 32.3 \%[/tex] but when the population was taken into account (i.e n = 30) the probability became
[tex]P(\= X < 35) = 0.6 \%[/tex]
A coordinate plane with 2 lines. The first line is labeled y equals f(x) and passes through (negative 1, 2), (0, 2), and (2, 2). The second line is labeled y equals g(x) and passes through (negative 0.5, negative 2), points at (0, negative 1), and (1, 1). The lines intersect at (1.5, 2).
Use the graph to determine the input value for which f(x) = g(x) is true.
x = 0.5
x = 1
x = 1.5
x = 2
Answer:
C) x=1.5
Step-by-step explanation:
Hope This Helps!
Answer:
it is c!
Step-by-step explanation:
top one is correct
The ticket prices at a movie theater are shown in the table. A family purchased tickets for 2 adults and 3 children, and the family purchases 3 boxes of popcorn of the same size. The family spent a total of $40.25 how much did each box of of popcorn cost
Answer:
$2.25
Step-by-step explanation:
The first thing you do is multiply the prices of tickets by how many they bought.
$8.50 x 2= $17
$5.50 x 3= $16.50
You then add these two numbers together and subtract that from $40.25.
$17+$16.50=$33.50
$40.25-$33.50=$6.75
You then divide $6.75 by 3 to find the answer
$6.75/3=$2.25
Triangle ABC has a horizontal sido AC, and AB in perpendicular to BC. A vertical line is drawn from a point labeled Don AC to the point 8.
Which of the following statements are true? Select the two correct answers.
Answer:
Option (3)
Step-by-step explanation:
Given:
Horizontal side of a triangle ABC is side AC.
AB and BC are the perpendicular lines.
BD is perpendicular to side AC.
Solution:
Option (1).
Slopes of AB and BC are reciprocal.
False.
Option (2)
Angle DAB and BCD are equal.
False.
Option (3).
Since, sides AB and BC are perpendicular lines,
Slopes of AB and BC will be negative reciprocals.
True.
Option (4).
Triangles ABD and BCD are similar.
False.
Therefore, Option (3) will be the answer.
please just answer at least one
I’LL GIVE BRAINLY IF UR CORRECT!!!!!! Plus 25 points
what is the best estimate of the sum of the fractions? 31/4 + 17/3 + 8/18
13.86 would be about how much that is
Answer:it’s 13
Step-by-step explanation:
if johnny had 6 apples and ava took 3 how many would she have left
Answer: johnny will beat up ava and take his three apples back
Answer:
I'm assuming you mean how many would Johnny have left. If not I am providing both answers. Johnny has 3 apples leftover. Ava has 3 apples, now.
Step-by-step explanation:
Johnny's apples: 6-3 = 3
Ava's apples: 0+3 = 3
Jenny began her pizza delivery route with 1/2 of a tank of gas in her car. When she made it
back to the pizzeria, 2/5 of a tank of gas was left. How much gas did Jenny use?
Write your answer as a fraction or as a whole or mixed number.
Given that the polynomial f(x) has degree 8, which of the following most accurately describes the number of turning points of f(x)?
Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients. The polynomial f(x) that has a degree of 8 will have 7 turning points.
What is a polynomial?Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.
For any polynomial equation, the number of turning points is always less than or equal to the degree of the polynomial.
Generally, the number of turns is one less than the degree of the polynomial.
Hence, the polynomial f(x) that has a degree of 8 will have 7 turning points.
Learn more about Polynomials:
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Which expression is equivalent to one over fivem − 20?
one over five(m − 4)
one over five(m − 100)
5(m − 4)
5(m − 100)
Answer:
one over five (m-100)
Step-by-step explanation:
the answer to your question is the 2nd one
Answer:
1 / [ 5(m - 4) ] is equivalent to one over five m -20
Step-by-step explanation:
one over five(m − 4)
5(m − 4)
Factor the denominator:
1 / [ 5m - 20 ] = 1 / [ 5(m - 4) ]
Use elimination to solve for x and y:
9x - 4y = 11
x + 4y = 19
Select one:
a. (7,3)
b. (4,3)
c. (-1,5)
d. (3,4)
Answer:
multiply second eqyation by 9
Step-by-step explanation:
then subtract with 1 st eqn
A gallon of milk cost 1.99. A half-gallon cost 3.89. Is this proportional or nonproportional?
Answer:
Non Proportional
Step-by-step explanation:
A proportional figure relates to two or more figures that correspond in size or amount to one another. The gallon of milk which costs 1.99 is nonproportional to the half-gallon which costs 3.89.
On the other hand, a nonproportional figure does not correspond to in size or amount to one another.
From the given information;
A gallon of milk cost = 1.99A half-gallon cost 3.89
i.e.
[tex]\mathbf{= \dfrac{1}{2} \times 3.89}[/tex]
= 1.945
Therefore, we can conclude that the gallon of milk which cost 1.99 is nonproportional to the half-gallon which cost 3.89.
Learn more about proportionality here:
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List the next even number after 149
Answer:
150
Step-by-step explanation:
Answer:
152
Step-by-step explanation:
you want to be my friend
4 Nestor works at a garden center where he pots plants. It takes him 2 1··2hours to pot 15 plants. Part A How many plants can Nestor pot in 1 hour? Fill in the blanks to complete the equation and the statement.15 5 Nestor can pot plants in 1 hour. Part B If Nestor continues working at the same rate, how many plants will he be able to pot in 3 1··2hours? Show your work. Answer: plants
Answer:
plants sbbsjdjdhdhhs
818 divided by 34 in standard althriam
Find the value of the variables
PLZZZZZ HELP ME ILL MAKE YOU BRAINLIEST ANSWER PLZZZZZZ THANKYOUUU!!!!!!
Answer:
4) x=110º
5) x=90º (so does y)
6) x=109
7) x=15º and y=5º
8) x=7
9) x=95
10) x=33
Step-by-step explanation:
4), 5) and 6) were a little hard to read but they were mostly simple to solve from what I saw. Using the verticle angles theorem and corresponding theorem you can easily find the values.
7) I plugged in the two first equations to solve x which is (3x+60)=(6x+15)
and for y I had to plug in x to find one of the angles' values to plug in with 15y and then created a second equation which should look like this 105+15y=180º (Since they should be supplementary angles)
8) This one's similar to 7) and even a little simpler. The equation should look like this 4x=3x+7
9) The equation to solve it that I used is x + (x-10)=180º
10) The equation to solve it that I used is (4x+5)=137
Hope this was helpful and (to other people too) if I made any mistakes or didn't explain properly feel free to let me know! :)
What fraction is 0.16% equivalent to? (16 is repeating)
Answer:
[tex]\frac{16}{10000}[/tex]
Step-by-step explanation:
Answer:
4/25
Step-by-step explanation: