Answer:
x + y = 200
0.08x + 0.24y = 0.18(200)
Step-by-step explanation:
x + y = 200
0.08x + 0.24y = 0.18(200)
The equations which describes the amount of 8% solution used and the amount of 24% solution used are: x+ y=200 and x+3y=450.
What is equation?An equation is a relationship between two or more variables. They are mostly present in equal to form and are equated to find the value of variables present in them.
How to form equation?let the amount of 8% solution used be x and the amount of 24% solution used be y.
According to question the amount of total solution will be 200ml, So, the equation will be:
x +y=200
Now we have been said that the solution will be 18% saline and 8% saline mixture and 24% saline mixtures are used, So the next equation will be:
0.08x+ 0.24y=0.18*200
8x/100+24/100=18/100*200
8x+24y=3600
8(x+3y)=3600
x+3y=450
Hence the equations which shows the amount of solutions will be x+y=200 and x+3y=450.
Learn more about equations at https://brainly.com/question/2972832
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Excel:In cell B13, create a formula using the VLOOKUP function that looks up the value from cell A11 in the range A5:B7, returns the value in column 2, and specifies an exact match.
Answer:
=Vlookup'B13' A11' 7'false
Press enter.
Step-by-step explanation:
Vlookup is a technique in excel which enables users to search for criterion values. It is vertical lookup function in excel which return a value from a different column. The formula for Vlookup function is:
=Vlookup'select cell you want to look up in' select cell you want to lookup from' select column index number' true/false.
where true is approximate match and false is exact match.
Answer:=VLOOKUP(J2,A2:G23,2,FALSE)
Step-by-step explanation:
a. In cell J3, begin to enter a formula using the VLOOKUP function.
b. Use the Project ID (cell J2) as the lookup value.
c. Use the Projects table (range A2:G23) as the table_array.
d. Use the Project Name column (column 2) as the col_index_num.
e. Specify an exact match (FALSE) for the range_lookup.
Emily thinks the perfect tomato sauce has 8 cloves of garlic in every 500 mL, of sauce. Raphael's tomato sauce has 121 cloves of garlic in every 900 mL of sauce. What will Emily think of Raphael's tomato sauce? Choose 1 answer: Choose 1 answer: (Choice A) A It is too garlicky. (Choice B) B It is not garlicky enough. (Choice C) C It is perfect.
Answer:
A
Step-by-step explanation:
Let's find the ml per garlic for each sauce. Emily's has 1 clove of garlic for 62.5 ml. Raphael's has 1 clove of garlic for 7.438... ml. So, A, it will be too garlicky.
Write the polar form of a complex number in standard form for [tex]8[cos(\frac{\pi}{2}) + isin(\frac{\pi}{2})][/tex]
Answer:
Solution : 8i
Step-by-step explanation:
We can use the trivial identities cos(π / 2) = 0, and sin(π / 2) = 1 to solve this problem. Let's substitute,
[tex]8\left[cos\left(\frac{\pi }{2}\right)+isin\left(\frac{\pi \:}{2}\right)\right][/tex] = [tex]8\left(0+1i\right)[/tex]
And of course 1i = i, so we have the expression 8(0 + i ). Distributing the " 8, " 8( 0 ) = 0, and 8(i) = 8i, making the fourth answer the correct solution.
About % of babies born with a certain ailment recover fully. A hospital is caring for babies born with this ailment. The random variable represents the number of babies that recover fully. Decide whether the experiment is a binomial experiment. If it is, identify a success, specify the values of n, p, and q, and list the possible values of the random variable x. Is the experiment a binomial experiment?
Answer:
This is a binomial experiment .
Step-by-step explanation:
As the percent is not indicated the success is the amount of percent (if given) say it is 10 % . So p will be equal to = 0.1 and q will be = 1-0.1= 0.9
and n would be five or any number as a binomial experiment is repeated for a fixed number of times.
And x would take any value of n i.e.
X= 0,1,2,3,4,5
If it is 20 % . So p will be equal to = 0.2 and q will be = 1-0.2= 0.8
The probability is the number of the percent indicated. But as it is not indicated we assume it to be 10 % or 20 % .Or suppose any number for it to be a binomial experiment.
The number of trials n would be fixed .
The success remains constant for all trials.
All trials are independent.
Twice one number added to another number is 18. if the 2nd number is equaled to 12 less than 4 times the 1st number, find the two numbers
2x + y= ? ; y= ?x - ?
Answer:
8
Step-by-step explanation:
Math Word Problem: Twice one number added to another number is 18. Four times the first number minus the other number is 12. Find the number.?
Let the two numbers be x and y
As per statement twice one number added to another number is 18.
2x + y = 18
y = 18 - 2x…Eq..1
Four times the first number minus the other number is 12.
4x - y = 12…Eq..2
Now substituting the value of y from Eq..1 to Eq..2
4x - y = 12
4x - (18 - 2x) = 12
4x - 18 + 2x = 12
4x + 2x = 12 + 18
6x = 30
x = 30 / 6
x = 5
Thus one number is 5. Now calculating the other number by putting the value of x in Eq. 1
y = 18 - 2x
y = 18 - 2×5
y = 18 - 10
y = 8
Other number is 8
Answer the two numbers are 5 and 8
Let us check the correctness of answer by putting the value of x and y in Eq. 1
y = 18 - 2x
8 = 18 - 2 × 5
8 = 18 - 10
8 = 8
Means answer is correct
Solve the following system of equations.
2x + y = 3
x = 2y-1
ANSWER: ______
plz help me
(1,1) is your answer.
Work is shown below.
Any questions? Feel free to ask.
Answer: (1,1)
Step-by-step explanation:
I require someone to answer this question for me ASAP please?
Answer:
x has to be less than 3
Step-by-step explanation:
Answer:
x < 3
I hope this helps!
If is an angle bisector of ∠QOR and ∠QOP = 71°, then find the angle measure of ∠QOR. Question 8 options: A) 71° B) 142° C) 35.5° D) 35°
Answer: B. 142°.
Step-by-step explanation:
Given: OP is an angle bisector of ∠QOR and ∠QOP = 71°.
We know that an angle bisector divides an angle into two equal parts.
So, if OP is an angle bisector of ∠QOR and ∠QOP = 71°.
Then, the angle measure of ∠QOR = Twice of ∠QOP
⇒ Angle measure of ∠QOR = 2 (71°)
⇒ Angle measure of ∠QOR = 142°
Hence, correct option is B. 142°.
Hi everyone how to solve this question
$2x+7$
according to the flow chart,
1. multiply [tex] x[/tex] by $2$, so $2x$
and then add seven to it so $2x+7$
note, if the order was reverse, i.e. first add seven ($x+7$). then multiply by two ($2(x+7)$)
the answer would be $2x+14$
use the product of powers property to simplify the numeric expression.
4 1/3 • 4 1/5 = _____
Answer:
The value of [tex]4^{\dfrac{1}{3}} {\cdot} 4^{\dfrac{1}{5}[/tex] is [tex]4^{\dfrac{8}{15}}[/tex] .
Step-by-step explanation:
We need to simplify the numeric expression using property. The expression is as follows :
[tex]4^{\dfrac{1}{3}} {\cdot} 4^{\dfrac{1}{5}[/tex]
The property to be used is : [tex]x^a{\cdot} x^b=x^{a+b}[/tex]
This property is valid if the base is same. Here, base is x.
In this given problem, x = 4, a = 1/3 and b = 1/5
So,
[tex]4^{\dfrac{1}{3}} {\cdot} 4^{\dfrac{1}{5}}=4^{\dfrac{1}{3}+\dfrac{1}{5}}\\\\=4^{\dfrac{5+3}{15}}\\\\=4^{\dfrac{8}{15}}[/tex]
So, the value of [tex]4^{\dfrac{1}{3}} {\cdot} 4^{\dfrac{1}{5}[/tex] is [tex]4^{\dfrac{8}{15}}[/tex] .
12. Consider the function ƒ(x) = x^4 – x^3 + 2x^2 – 2x. How many real roots does it have?
options:
A) 2
B) 1
C) 3
D) 4
Answer:
Step-by-step explanation:
Hello, let's factorise as much as we can.
[tex]x^4-x^3 + 2x^2-2x\\\\=x(x^3-x^2+2x-2)\\\\=x(x-1)(x^2+2)[/tex]
So, the solutions are
[tex]0, \ 1, \ \sqrt{2}\cdot i, \ -\sqrt{2}\cdot i[/tex]
There are only 2 real roots.
Thank you.
Answer:
So, the solutions are
There are only 2 real roots.
Step-by-step explanation:
slope of -4/3x with point (7,20) find equation
Answer:
y= -4/3x+10 2/3
Step-by-step explanation:
To do this, just put the equation in point slope form and then rearrange it to y=mx+b, or slope intercept form. Slope point form is arranged like this, y-y1=m(x-x1). Now, just insert in the variables (x1=x coordinate of point, y1= y coordinate of point, m=slope). So your equation is now y-20=-4/3(x-7), which simplifies to y-20=-4/3x-9 1/3. Now rearrange it so that y in by itself, and all like terms are combined, making it look like this: y=-4/3x+10 2/3. Now its in slope intercept form and you've got your answer.
I hope my explanation wasn't confusing and that my answer helped.
show that an integer is divisible by 11 if and only if the alternating sum (add first digit, subtract the second, add the third, subtract the fourth etc) of its digits is divisible by 11
Need an answer by tomorrow if possible please
Answer and Step-by-step explanation:
Suppose that we have a number y which is a positive integer and that:
y = [tex]x_n...x_5x_4x_3x_2x_1x_0[/tex]
Where;
[tex]x_{0}[/tex] = digit at 10⁰ => one's place (units place)
[tex]x_1[/tex] = digit at 10¹ => 10's place (tens place)
[tex]x_{2}[/tex] = digit at 10² => 100's place (hundreds place)
[tex]x_{3}[/tex] = digit at 10³ => 1000's place (thousands place)
.
.
.
[tex]x_{n}[/tex] = digit at 10ⁿ place
Then;
y = [tex]x_{0}[/tex] * 10⁰ + [tex]x_1[/tex] * 10¹ + [tex]x_{2}[/tex] * 10² + [tex]x_{3}[/tex] * 10³ + [tex]x_{4}[/tex] * 10⁴ + [tex]x_5[/tex] * 10⁵ + . . . + [tex]x_{n}[/tex] * 10ⁿ
Since 10⁰ = 1, let's rewrite y as follows;
y = [tex]x_{0}[/tex] + [tex]x_1[/tex] * 10¹ + [tex]x_{2}[/tex] * 10² + [tex]x_{3}[/tex] * 10³ + [tex]x_{4}[/tex] * 10⁴ + [tex]x_5[/tex] * 10⁵ + . . . + [tex]x_{n}[/tex] * 10ⁿ
Now, to test if y is divisible by 11, replace 10 in the equation above by -1. Since 10 divided by 11 gives -1 (mod 11) [mod means modulus]
y = [tex]x_{0}[/tex] + [tex]x_1[/tex] * (-1)¹ + [tex]x_{2}[/tex] * (-1)² + [tex]x_{3}[/tex] * (-1)³ + [tex]x_{4}[/tex] * (-1)⁴ + [tex]x_5[/tex] * (-1)⁵ + . . . + [tex]x_{n}[/tex] * (-1)ⁿ
=> y = [tex]x_{0}[/tex] - [tex]x_1[/tex] + [tex]x_{2}[/tex] - [tex]x_{3}[/tex] + [tex]x_{4}[/tex] - [tex]x_5[/tex] + . . . + [tex]x_{n}[/tex] (-1)ⁿ (mod 11)
Therefore, it can be seen that, y is divisible by 11 if and only if alternating sum of its digits [tex]x_{0}[/tex] - [tex]x_1[/tex] + [tex]x_{2}[/tex] - [tex]x_{3}[/tex] + [tex]x_{4}[/tex] - [tex]x_5[/tex] + . . . + [tex]x_{n}[/tex] (-1)ⁿ is divisible by 11
Let's take an example
Check if the following is divisible by 11.
i. 1859
Solution
1859 is divisible by 11 if and only if the alternating sum of its digit is divisible by 11. i.e if (1 - 8 + 5 - 9) is divisible by 11.
1 - 8 + 5 - 9 = -11.
Since -11 is divisible by 11 so is 1859
ii. 31415
Solution
31415 is divisible by 11 if and only if the alternating sum of its digit is divisible by 11. i.e if (3 - 1 + 4 - 1 + 5) is divisible by 11.
3 - 1 + 4 - 1 + 5 = 10.
Since 10 is not divisible by 11 so is 31415 not divisible.
Two basketball players average the same number of points per game. What information would be most helpful in
determining which player's game performances show the least variability?
the most and least points each player has scored in a game
the number of games each player has played
the average number of points each player's team scores per game
O the total number of points each player has scored
Answer:
number of games each player has played
the average number of points each player's team scores per
Step-by-step explanation:
number of games each player has played
the average number of points each player's team scores per
(Algebra) PLZ HELP ASAP!
Answer: Its everthing except irrational
Step-by-step explanation:
In this triangle, which of the following is true?
We know that this is a right triangle, so one of the sides has to be 90 (indicated by the square on the corner) The angles of all triangles must add to exactly 180. Subtract 90 and 35 from 180
If we do that, we get 55. We know that the unknown angle is 55 now. Now, it asks us for b. We can pythagoras theorem which states that (a^2 + b^2 = c^2) We already know c (c is 20) It does not tell us 2 of the sides but we do know that the answer is either B or D.
The side opposite of 90* should be the largest. The size opposite of 55 would be the second largest one. The side opposite of 35 would be the smallest one. Using pythagoras theorem again, I can try plugging in both 11.47 and 16.38 with c^2 - b^2 = a^2
11.47:
400 - 132 =268 (sq root now = 16.37) this would mean that A is larger than B. B should be larger than A. Try the other one
16.37:
400 -268 = 132 (sq root = 16.37) this would mean that B is larger than A which is what we want.
Thus, 16.37 = B and the last option would be correct (D)
Hope this helps, give an honest rating for me please
What are the solutions to the system of equations? {y=2x2−8x+5y=x−2 (3.5, 0.5) and (1, −1) (7, 5) and (0.5, −1.5) (3.5, 1.5) and (1, −1) (3.5, 1.5) and (−1, −3)
Answer:
[tex](1,-1)[/tex] and [tex](3.5,1.5)[/tex]
Step-by-step explanation:
Given
[tex]y = 2x^2 - 8x+5[/tex]
[tex]y = x - 2[/tex]
Required
Determine the solution
Substitute x - 2 for y in [tex]y = 2x^2 - 8x+5[/tex]
[tex]x - 2 = 2x^2 - 8x+5[/tex]
Collect like terms
[tex]0 = 2x^2 - 8x - x + 5 + 2[/tex]
[tex]0 = 2x^2 - 9x + 7[/tex]
Expand the expression
[tex]0 = 2x^2 - 7x - 2x+ 7[/tex]
Factorize
[tex]0 = x(2x - 7) -1(2x - 7)[/tex]
[tex]0 = (x-1)(2x - 7)[/tex]
Split the expression
[tex]x - 1 = 0[/tex] or [tex]2x - 7 = 0[/tex]
Solve for x in both cases
[tex]x = 1[/tex] or [tex]2x = 7[/tex]
[tex]x = 1[/tex] or [tex]2x/2 = 7/2[/tex]
[tex]x = 1[/tex] or [tex]x = 3.5[/tex]
Recall that
[tex]y = x - 2[/tex]
When [tex]x = 1[/tex]
[tex]y = 1 -2[/tex]
[tex]y = -1[/tex]
When [tex]x = 3.5[/tex]
[tex]y = 3.5 - 2[/tex]
[tex]y = 1.5[/tex]
Hence, the solution is;
[tex](1,-1)[/tex] and [tex](3.5,1.5)[/tex]
Find the doubling time of an investment earning 8% interest if interest is compounded continuously. The doubling time of an investment earning 8% interest if interest is compounded continuously is ____ years.
Answer:
8.66 years
Step-by-step explanation:
Given that:
Interest rate = 8%
Using the exponential growth function:
A = Ao * e^(rt)
Where A = final amount
Ao = Initial amount
r = growth rate
t = time
Here we are to calculate the time it takes an investment earning 8% interest to double;
rate (r) = 8% = 0.08
2A = A * e^(rt)
Divide both sides by A
2 = e^(rt)
2 = e^(0.08 * t)
2 = e^(0.08t)
In(2) = 0.08t
0.6931471 = 0.08t
Divide both sides by 0.08
0.6931471 / 0.08 = 0.08t / 0.08
8.6643397 = t
t = 8.66 years
Answer:
symbolically, the answer would be t= ln(2)/(.08)
Step-by-step explanation:
start by writing out your variables:
rate= .08
*dont forget the investment doubles too, thats where 2P is in the bottom equation
equation should look like:
[tex]2P=Pe^{.08t}[/tex]
then you solve, so divide P on the right and left:
[tex]\frac{2p}{p} = \frac{Pe^{.08t}}{p}[/tex]
now it looks like: [tex]2=e^{.08t}[/tex]
you can take the natural log (ln) of 2 to get the exponent by itself .08t
ln(2)=.08t
then divide .08 to get t by itself
[tex]\frac{ln(2)}{.08} =\frac{.08t}{.08}[/tex]
so symbolically, your equation should be:
[tex]t=\frac{ln(2)}{.08}[/tex]
to get t as your answer you can plug this equation into your calculator to get:
t=8.66 years so approximently 8 years
What is numbers 1-30 added all together
Answer:
465
Step-by-step explanation:
The sum of consecutive numbers has a formula, and it's
[tex]\frac{n(n+1)}{2}[/tex].
Where n is the amount of numbers.
From 1-30, it's 30 numbers, so:
[tex]\frac{30(30+1)}{2} \\\\\frac{30(31)}{2} \\\\\frac{930)}{2} \\\\\\465[/tex]
Hope this helped!
Using minutes as the unit of measurement on the left-hand side of a constraint and using hours on the right-hand side is acceptable since both are a measure of time.
a. True
b. False
Answer:
True
Step-by-step explanation:
write 32 1/2 in radical form
Answer:
Nothing further, the simplest answer is 32 1/2
Step-by-step explanation:
Perimeter =68 Length (L) is 4 less than twice the width (W)
Answer:
Length = 21.3333333333; Width: 12.6666666667
Step-by-step explanation:
Perimeter = 68
Perimeter of a rectangle:
2 (L +W)
Length (L) = 2W - 4
Width = W
2 ( 2W -4 +W) = 68
=> 2 (3W - 4) = 68
=> 6w -8 = 68
=> 6w = 76
=> w = 12.6666666667
Length = (12.6666666667 X 2) - 4
=> 21.3333333333
How many cabinets must he sell to break even?
Answer: He must sell 7 cabinets.
Step-by-step explanation:
So it gives us the equations y= 400x + 1400 and the equations y=600x and to find the break even point we need to set the two equations equal each other to solve for x.
400x + 1400 = 600x
-400x -400x
1400 = 200x
x = 7
Which, if any, pair of sides are parallel? AB II DC and AD II BC Cannot be determined AB II DC only AD II BC only
Answer:
120%
Step-by-step explanation:
When x€Q, what is the solution of 3x-2/2=x-1/2 ?
Answer:
x = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
[tex]\frac{3x-2}{2}[/tex] = [tex]\frac{x-1}{2}[/tex]
Cross-multiply:
2(3x-2) = 2(x-1)
Simplify:
6x - 4 = 2x - 2
Subtract 2x from both sides:
4x - 4 = -2
Add 4 to both sides:
4x = 2
Divide both sides by 4:
x = [tex]\frac{1}{2}[/tex]
Match each function name with its equation.
Answer:
a. Quadratic--[tex]y=x^{2}[/tex]
b. Absolute Value--[tex]y=|x|[/tex]
c. Linear--[tex]y=x[/tex]
d. Reciprocal Squared--[tex]y=\frac{1}{x^{2} }[/tex]
e. Cubic--[tex]y=x^{3}[/tex]
f. Square Root--[tex]y=\sqrt{x}[/tex]
g. Reciprocal--[tex]y=\frac{1}{x}[/tex]
h. Cube root--[tex]y=\sqrt[3]{x}[/tex]
Answer:
Step-by-step explanation:
y=[tex]x^{2}[/tex] is quadratic
y=x is an absolute value
y= |x| os linear
y= [tex]\frac{1}{x}[/tex] is reciprocal
y= [tex]x^{3}[/tex] is cubic
y= [tex]\sqrt{x}[/tex] is square root
y= [tex]\frac{1}{x^{2} }[/tex] is reciprocal squared
y= [tex]\sqrt[3]{x}[/tex] is cube root
Annie tried to solve an equation step by step. Find Annie's mistake. *
Answer:
Hi, sorry, please could you resend the question again this isn't clear enough to properly answer your question .
maybe you should type in the steps before it is answered. thanks
Answer:
answer= C
Step-by-step explanation:
Suppose that y varies directly with x and y=20 when x=2 Find y when x=8
Answer:
80
Step-by-step explanation:
x y
2 = 20
8 = x
cross multiply( 8*20)/2
= 4 * 20
= 80
I buy 6 CDs costing £6.99.
How much change do I get from
£50?
Answer:
subtract the 6.99 from 50 and you get your answer
Step-by-step explanation:
Answer:
8.06
Step-by-step explanation:
Take the cost of a cd and multiply by 6
6.99 *6
41.94
Subtract this from 50.00
50.00 - 41.94
8.06
You will get 8.06 back
4x + 1 -5x =2x +4(x-5)
Answer:
x = 3
Step-by-step explanation:
To answer for x first distribute the 4 in the parenthesis
4x + 1 - 5x = 2x +4x - 20
Next add or subtract the x's
-x + 1 = 6x - 20
Now subtract 6x and 1 on both sides to get x on the left and the rest on the right
-7x = -21
Lastly, divide -7 on both sides
x = 3
