Using the concept of volume, 700 milliliters of Solution B was used.
What is volume?Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.
When dealing with unknowns, the first step is to represent the unknowns using variables, draw up equations based on the available data, and then solve those equations to account for the unknowns.
Volumes of solutions A and B are here which is unknown.
Put these factors in place for us
Let x = the amount of solution A that was mixed in milliliters.
Let y= the amount of solution B that was mixed in milliliters.
The amount of volume utilized for A is 400 ml less than the amount used
for B.
This can be expressed mathematically as y - x = 400.
Or,
- x + y = 400 [1]
The ratios of alcohol in A and B are provided to us.
A contains 12% alcohol, hence its real alcohol content is 12% of x ml.
= 0.12x (12% = 12/100 = 0.12)
Similar to A, B has an alcohol content of 0.20x.
If x of A and y of B are combined, the total alcohol by volume is 0.12x + 0.20y.
and it is said that this amount is 176 ml.
Our second equation is therefore set up as 0.12x + 0.20y = 176 [2].
We create an equation containing only the other term by using both equations and removing either the x or y terms.
We should remove the x term from both equations to create a single equation that just contains the y term because the question only asks us to compute the volume of Solution B that was used.
Review the equations now:
- x + y = 400 [1]
0.12x + 0.20y = 176 [2]
x's coefficients should all be the same:
Increase [1] by 0.12
=> -0.12x + 0.12y =
= 0.12 x 400
=> 0.12x + 0.12y = 48 [3]
By adding [2] and [3], the x word is removed.
0.12x + 0.20y = 176+( -0.12x) + 0.12y = 48
0x + 0.32 y = 224
=> 0,32y = 224
Subtract 0.32 from both sides to get[tex]\frac{0.32y}{0.32}[/tex] = [tex]\frac{224}{0.32}[/tex]
==> y = 700
Therefore, 700 cc of Solution B was utilized.
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Help with part B please
a) The opposite of the numbers 3, 7.5, and -2(2/3) will be 0.33, 0.133, and -0.375.
b) The sum of the given number and its opposite will be 7.928.
What is an irrational number?It is defined as the numbers in all real numbers which cannot be represented as rational numbers, in other words, the irrational number cannot be expressed in the form of p/q form.
A rational number is a sort of real number that has the form p/q and does not equal zero.
The given number is as,
3, 7.5, and -2(2/3)
a)
The opposite number is obtained as 1 by dividing the given number,
⇒ 1 / 3 = 0.33
⇒ 1 / 7.5 = 0.133
⇒ 1 / -2(2/3) = -0.375
b)
The sum of the given number and its opposite is,
= 3+0.33 + 7.5 + 0.133+ (-2(2/3) ) + (-0.375)
= 7.928
Thus, the opposite of the numbers 3, 7.5, and -2(2/3) will be 0.33, 0.133, and -0.375.and the sum of the given number and its opposite will be 7.928.
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a woman can hike 2mph faster down a trail to Archuletta Lake then she can on the return trip uphill. it takes her 2 hours to get to the lake and 4 hours to return. what is her speed hacking down to the late?
Answer:
4 mph
Explanation :
Let us call x, the woman speed as she goes uphill
Now, we know that it took the woman 2 hours to go uphill; therefore, the distance covered is
4* (x)
shortly afterwards, when the woman returns she is walking at x + 2 mph; therefore, the distance she covers is
D = 4 (x +2 )
Since the uphill and the downhill distances ar the same, we have
4x = 2 (x +2 )
4x = 2x + 4
x = 2
Hence, going to the hill, the woman speed is 2 miles per goo
g(x) = x2 − 5x
h(x)= 4x + 4
Find (g ◦ h) (x)
Answer:
(g ◦ h) (x) = 16x² + 12x -4
Step-by-step explanation:
We have
g(x) = x² − 5x
h(x)= 4x + 4
(g ◦ h) (x) = g(h(x))
h(x) = 4x + 4
g(h(x)) = g(4x + 4)
= (4x + 4)² - 5(4x+4) //substitute 4x + 4 wherever there is an s-term in
(4x + 4)² = 16x² + 32x + 16
5(4x + 4) = 20x + 20
(4x + 4)² - 5(4x+4) = 16x² + 32x + 16 -(20x + 20)
= 16x² + 32x + 16 - 20x - 20
= 16x² +(32x - 20x) + (16-20)
= 16x² + 12x -4
Help , stuck on this one .
Answer:
D. -87 + 33i
Step-by-step explanation:
(7 + 5i)(-6 + 9i)
7(-6 + 9i) + 5i(-6 + 9i)
-42 + 63i + -30i + 45i²
-42 + 33i + 45(-1)
-42 + 33i - 45
-87 + 33i
I hope this helps!
the retail price of a television set is $4500. if the buyer pays cash, the price 10% below the retail price. if the set is bought on hire purchasr, the buyer pays a downpayment of $675 and 24 monthly instalments of $212.50.(a) Determine the difference between the hire purchase price and the cash price.(b) Calculate the difference as a percentage of the retail price.
Data:
Retail price: $4500
Pays cash: -10%
hire purshast: $675 + 24(212.50)
-----------------------------------
The cash price is: $40501. Find the 10% of 4500:
[tex]4500\cdot\frac{10}{100}=450[/tex]2. Substract the 10% to the retail price:
[tex]4500-450=4050[/tex]-------------------------------------
Hire purchase price is: $57751. Add 675 and (24*212.50):
[tex]\begin{gathered} 675+(24\cdot212.50) \\ =675+5100 \\ =5775 \end{gathered}[/tex]-----------------------------------------
Difference between hire purchase and cash price is: $1725[tex]5775-4050=1725[/tex]----------------------------
Difference as a percentage of the retail price is: 38.33%As the retail price 4500 is 100% which percent is 1725:
[tex]1725\cdot\frac{100}{4500}=38.33[/tex]helpppp plsssssssss
..........................................
Answer:
D. An infinite number of real solutions
Step-by-step explanation:
3(2x + 1) = 2(3x + 5) - 7
6x + 3 = 6x + 10 - 7
6x + 3 = 6x + 3
I hope this helps!
Hello, I need some assistance with this homework question, please? This is for my precalculus homework. Q11
Explanation
The vertical asymptote
[tex]\begin{gathered} \mathrm{For\:rational\:functions,\:the\:vertical\:asymptotes\:are\:the\:undefined\:points,\:} \\ \mathrm{also\:known\:as\:the\:zeros\:of\:the\:denominator,\:of\:the\:simplified\:function.} \end{gathered}[/tex]for the given function
[tex]T(x)=\frac{x^3}{x^4-81}[/tex]According to the formula
The denominator will be undefined when
[tex]\begin{gathered} x^4-81=0 \\ x=\sqrt[4]{81} \\ x=3,\text{ x=-3} \\ x= \end{gathered}[/tex]The vertical asymptotes are
[tex]x=-3,3[/tex]For the horizontal function
[tex]\mathrm{If\:denominator's\:degree\:>\:numerator's\:degree,\:the\:horizontal\:asymptote\:is\:the\:x-axis:}\:y=0.[/tex]Since the denominator degree is higher than the numerator
Then
The horizontal asymptote is
[tex]y=0[/tex]For the oblique asymptote
Since the degree of the numerator is not one degree greater than the denominator, then there are no slant asymptotes.
There are no oblique asymptote
Find the slope of the line that passes through the following points: (5,4) (-2,0)
Answer: slope = 4/7
Step-by-step explanation:
you can plug the coordinates into the slope formula. y2 - y2/x2 -x1.
if you have x - 4 and subtract 1 / 4 x + 5 from it the result is
Answer
(3x/4) - 9
[tex]\frac{3x}{4}-9[/tex]Explanation
We are told to subtract (¼x + 5) from (x - 4)
We just simply do this step by step
(x - 4) - (¼x + 5)
[tex]\begin{gathered} (x-4)-(\frac{1}{4}x+5) \\ =x-4-\frac{1}{4}x-5 \\ =x-\frac{x}{4}-4-5 \\ =\frac{4x}{4}-\frac{x}{4}-9 \\ =\frac{4x-x}{4}-9 \\ =\frac{3x}{4}-9 \end{gathered}[/tex]Hope this Helps!!!
Jeriel is going to invest $640 and leave it in an account for 5 years. Assuming the
interest is compounded annually, what interest rate, to the nearest tenth of a percent,
would be required in order for Jeriel to end up with $760?
Using the compounding formula we can conclude that approximately a 3% of interest rate would be required in order for Jerial to end up with $760.
What is a compound interest?Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit. It occurs when interest is reinvested, or added to the loaned capital rather than paid out, or when the borrower is required to pay it so that interest is earned the following period on the principal amount plus any accumulated interest. In finance and economics, compound interest is common.So, the principal amount is $640 and the obtained amount is $760.
Compounded annually for 5 years.Then the interest rate will be:
3.497%Rounding off to the nearest tenths: 3%(Refer to the image attached below for calculation)
Therefore, using the compounding formula we can conclude that approximately a 3% of interest rate would be required in order for Jerial to end up with $760.
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the cost of 12 hot dogs and 8 fry portions is £52. The cost of 8 hot dogs and 12 fry portions is £48. What is the total cost of a hot dog and a portion of fries?
Answer:
Hot dogs cost £3 and fry's cost £2.
Total cost £5.
Step-by-step explanation:
Let a hot dog cost £x and a portion of fry's cost £y.
Then:
12x + 8y = 52
8x + 12y = 48
Simplifying these 2 equations we get:
3x + 2y = 13 ---------- (A)
2x + 3y = 12...............(B)
multiply the first equation by 2 and the second by 3:
6x + 4y = 26
6x + 9y = 36
Subtracting:
0 - 5y = -10
y = -10/-5 = 2.
Now, substituting in equation (A):
3x + 2(2) = 13
3x = 9
x = 3.
luke ran 3/4 as much as much as he did on thursday then he did on wendsday how many miles did luke run on thrurday
The number of miles that Luke ran on Thursday will be 3 miles.
How to calculate the fraction?From the information given, it was illustrated that Luke ran 4 miles on Wednesday and then ran 3/4 as much as much as he did on Thursday.
It should be noted that the distance that he ran on Thursday will be:
= 3/4 × Distance on Wednesday
= 3/4 × 4
= 3 miles.
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Luke ran 4 miles on Wednesday. Luke ran 3/4 as much as much as he did on thursday than he did on wendsday how many miles did luke run on thrurday
What is the value of this expression when x = -6 and y= 1/2 ?
4(x2 + 3) − 2y
Answer: -37
Step-by-step explanation:
Select the correct answer from each drop-down menu. Consider parallelogram ABCD, where m∠ABC = 135° and the length of diagonal AC is 41 units. A parallelogram ABCD has two diagonals AC and BD, intersects each other at a point E inside it. The length of side AD is 35 units and length of side AB is 7 units. An arc is marked on angle B. Note: figure not drawn to scale Use the figure and given information to complete the statements. m∠BCD = ° The length of segment CD is units. The length of segment AE is units.
The length of segment CD is 7 units. The length of segment AE is 20.5 units. The m∠BCD is 45 degrees.
What is a parallelogram?A parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.
Given that parallelogram ABCD, has m∠ABC = 135° and the length of diagonal AC is 41 units.
The measure of length of side AD is 35 units and length of side AB is 7 units.
WE know that the opposite side of a parallelogram are same. Thus,
The length of segment CD = AB = 7 units.
Also, the length of diagonal AC = 41 units. Then;
The length of segment AE = 1/2 AC = 41/2 = 20.5 units.
Therefore, m∠BCD + m∠ABC = 180
m∠BCD + 135 = 180
m∠BCD = 180 - 135
m∠BCD = 45 degrees.
Hence, The length of segment CD is 7 units. The length of segment AE is 20.5 units. The m∠BCD is 45 degrees.
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Answer:
45
7
20.5
Step-by-step explanation:
Consider the equation 2 (ax+ 3) = 4x- 3 (4x+ 8). For what value of a is there no solution to the equation?
The equation given is,
[tex]2(ax+3)=4x-3(4x+8)[/tex]Solving for a
Expand the terms
[tex]\begin{gathered} 2\times ax+2\times+3=4x-3\times4x-3\times+8 \\ 2ax+6=4x-12x-24 \\ 2ax+6=-8x-24 \end{gathered}[/tex]Comparing the two sides of the equation
[tex]2ax=-8x[/tex]Divide both sides by 2x
[tex]\begin{gathered} \frac{2ax}{2x}=-\frac{8x}{2x} \\ a=-4 \end{gathered}[/tex]Hence, the value of a for which there is no solution to the equation is
[tex]a=-4[/tex]simplify the expression. Write the answer using scientific notation. (4x10^8) ^-2
Given:
[tex](4\times10^8)^{-2}[/tex]Aim:
We need to write the given expression in scientific notation.
Explanation:
[tex]Use\text{ \lparen a}\times b)^n=a^n\times b^n.[/tex][tex](4\times10^8)^{-2}=4^{-2}\times(10^8)^{-2}[/tex][tex]Use\text{ \lparen a}^n)^m=a^{n\times m}.[/tex][tex](4\times10^8)^{-2}=4^{-2}\times10^{-16}[/tex][tex]Use\text{ a}^{-n}=\frac{1}{a^n}[/tex][tex](4\times10^8)^{-2}=\frac{1}{4^2}\times10^{-16}[/tex][tex](4\times10^8)^{-2}=\frac{1}{16}\times10^{-16}[/tex][tex](4\times10^8)^{-2}=0.0625\times10^{-16}[/tex][tex]Use\text{ -16=2-18.}[/tex][tex](4\times10^8)^{-2}=0.0625\times10^{2-18}[/tex][tex](4\times10^8)^{-2}=0.0625\times100\times10^{-18}[/tex][tex](4\times10^8)^{-2}=6.25\times10^{-18}[/tex]Final answer:
[tex](4\times10^8)^{-2}=6.25\times10^{-18}[/tex]You drive 3 hours to reach the waterpark. Driving home along the same route, you increase your
speed by 20 miles per hour, reducing your drive time by 1 hour. Write and solve an equation to find
how fast you were driving to the waterpark.
The initial speed to the waterpark is 40 miles/hr.
The return speed is 60 miles/hr.
How to find the speed?
Given,
t = 3hr
Return speed = s +20m
Return time = 3 -1 = 2hrs
Solution:
s = d/t
s = d/3
d = 3s----1
s + 20 = d/t - 1
s + 20 = d/3-1
s + 20 = d/2
2s + 40 = d------2
Equating equations 1 and 2,
3s = 2s + 40
s = 40 miles/hr
The initial speed to the waterpark is 40 miles/hr.
Return speed = s +20
= 40+20
= 60 miles/hr
The return speed is 60 miles/hr.
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You borrow $90,000 for college at an APR of 6.25%. You plan to elect 25-year repayment. How much more must you repay in total if your loan is unsubsidized, as opposed to being subsidized?
Answer:
Step-by-step explanation:
What is twelve hundredths as a fraction
ANSWER
[tex]\frac{12}{100}[/tex]EXPLANATION
Now, imagine you are to divide something into 100 equal sections;
the 12th section of those sections is the twelve hundredths.
To represent this as a fraction we have 12/100.
Hence, the twelve hundredths as a fraction is 12/100.
what is the rate if the base is 244 and the portion 50
SOLUTION
Step1:Write out the formula
[tex]\frac{\text{portion}}{base}=\frac{rate\text{ }}{100}[/tex]Step2; write out the parameters
[tex]\begin{gathered} portion=50 \\ \text{Base}=244 \end{gathered}[/tex]Step3: Substitute into the formula and simplify
[tex]\frac{50}{244}=\frac{rate}{100}[/tex]Step4: simplify the expression above
[tex]\begin{gathered} \text{ Multiply both side by 244} \\ \text{rate}\times244=100\times50 \\ \text{then} \\ \text{ Rate=}\frac{100\times50}{244} \end{gathered}[/tex]Then the rate becomes
[tex]20.49\text{ }[/tex]Therefore the rate is 20.49
What is the negation of "Everybody loves somebody sometime"
Answer:
Everybody hates somebody sometimes.
Or Not everybody loves somebody sometime
Step-by-step explanation:
The company with the common equity accounts shown here has declared a stock dividend of 20 percent at a time when the market value of its stock is $30 per share. Common stock ($1 par value) $ 460,000 Capital surplus 861,000 Retained earnings 3,870,800 Total owners' equity $ 5,191,800 What would be the number of shares outstanding, after the distribution of the stock dividend? (Do not round intermediate calculations.)
1110800. Equity Account will be after stock dividends
What is stock dividend ?Similar to a cash dividend, however instead of cash, stocks are given out. A stock dividend will increase the number of shares outstanding while lowering the stock price.
In this issue, there are 460000 shares outstanding at a price of $30, which equals 13800000
Equity's total market value is $13800000.
Each shareholder will get a 20% increase in stock, and the number of existing shares will increase as a result of the 20% stock dividend.
Shares outstanding after dividend announcement total 460000 + 46000 ×20% =552000.
The number of outstanding common shares will rise to 552000 as a result of the issuance of 92000 more shares.
Common stock only contains the par value; for example, if the market price of a share is $30 and the par value is $1, the excess amount of $29×92000:2668000 is added to the capital surplus account. It will total 861000 + 2668000=3529000.
Due to the absence of any monetary transactions, the total owners' equity is unaltered.
The retained earnings will be decreased by 92000 × 30 = 2760000, resulting in 3870800 – 2760000=1110800.
Equity Account will be after stock dividends.
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Solve for r: S= 4 pie r^2
we have
S= 4*(pi)*r^2
solve for r
That means ------> isolate the variable r
step 1
Divide by 4*(pi) both sides
so
S/(4*pi)=r^2
step 2
Square root both sides
so
[tex]\begin{gathered} r=\sqrt[]{\frac{S}{4\pi}} \\ \text{simplify} \\ r=\frac{1}{2}\sqrt[]{\frac{S}{\pi}} \end{gathered}[/tex]I am doing principle rate and time and trying to figure out how to find out what the missing number is whether it be rate time or principle
Generally, the equation representing the simple interest on a deposited amount is;
[tex]I\text{ = }\frac{PRT}{100}[/tex]where ;
I is the simple interest
R is the rate
T is the time
We have other varaints of this formula, depending on the term missing
All we have to is to make the missing term the subject of the equation and input the other given values to get the missing term
We can have the variants of this formula as follows
a) Missing Principal
[tex]P\text{ = }\frac{100I}{RT}[/tex]b) Missing Rate
[tex]R\text{ = }\frac{100I}{PT}[/tex]c) Missing Time
[tex]T\text{ = }\frac{100I}{PR}[/tex]Postage Stamp A square postage stamp has area 1,260 mm². About how long is each side?
Answer: 35.9166 mm (the square root of 1290)
Step-by-step explanation:
angela spends $95 to buy 7 cakes for the office party. she cuts each cake into quarters, then cuts each quarter into 3 pieces. if kevin eats 5 pieces of cake during the party, how much did engela spend on just kevins share of the cake
If Angela spent $95 to buy 7 cakes for her office party, and she then cut each cake into quarters and each quarter into further 3 pieces, of which Kevin ate 5 pieces, then Angela had spent $5.65 on just the share of the cake that Kevin had.
As per the question statement, Angela spends $95 to buy 7 cakes for her office party, and she then cuts each cake into quarters and each quarter into further 3 pieces, of which Kevin ate 5 pieces.
We are required to calculate the amount Angela had spent on just the share of the cake that Kevin had.
To solve this question, first let us calculate the total number of pieces, did Angela cut all the 7 pieces of the cake into.
Considering one piece, that it was first cut into a quarter and then each quarter into further 3 pieces, one single piece out of original 7 pieces was cut into a total of [(4 * 3) = 12] pieces.
Therefore, all the 7 original pieces were altogether cut into a total of
[(7 * 12) = 84] pieces.
Now, since Angela spent $95 to buy the original 7 pieces,
Or, Angela actually spent $95 to buy 84 pieces of cake,
Then, 1 piece of the 84 costs $(95/84) = $1.13.
Now, since Kevin ate 5 such pieces of the 84, those 5 pieces cost
$(1.13 * 5) = $5.65.
Therefore, Angela had spent $5.65 on just the share of the cake that Kevin had.
Quarter: In Mathematics, when one whole of anything is divided into 4 equal parts, every part is known as a quarter.To learn more about Quarters, click on the link below.
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I confused on this would be grateful if any one could help
Answer:
126
Step-by-step explanation:
a+b=d
9x being d, 4x being a and 70 being b
4x+70=9x
70=5x
x=14
9(14)=126
please help asap!!! will appreciate it
H=16.4
Step-by-step explanation:
1.2x4=4.8
3.9x4=15.6
so
4.1x4=16.4
You have 7/8 of a cup of tomato sauce. You must fill small containers with exactly 1/4 of a cup of tomato sauce How many containers can you fill completely?
Using division, If you have 7/8 of a cup of tomato sauce and you must fill small containers with exactly 1/4 of a cup of tomato sauce, then number of containers can fill completely is 3 containers
The total quantity of tomato sauce that you have = 7/8 of a cup
The quantity of tomato sauce with you must fill small containers = 1/4 of a cup
To find the number of containers that you can fill completely, you have to use division
Number of containers can fill completely = The total quantity of tomato sauce that you have / The quantity of tomato sauce with you must fill small containers
= 7/8 ÷ 1/4
= 7/8 × 1/4
= 7/2
= 3.5
≈ 3 containers
Hence, using division, if you have 7/8 of a cup of tomato sauce and you must fill small containers with exactly 1/4 of a cup of tomato sauce, then number of containers can fill completely is 3 containers
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Sixth grade > FF.24 Surface area of pyramids 5XW
Science
1 yd
What is the surface area of this rectangular pyramid?
Submit
1 yd
1 yd
Surface Area of rectangular pyramid is lw + l√[(w ÷ 2)² + h²] + w√[(l ÷ 2)² + h²].
The area of a rectangular pyramid is equal to the sum of the areas of the sides and faces of the rectangular pyramid. A quadrilateral pyramid is a three-dimensional shape with only a rectangular base and triangles on either side of the base.
The area of the base of the rectangle is calculated by multiplying the length of the rectangle by the width of the rectangle.
The area of a rectangle with a pyramidal formula is determined by observing the width, length, and height of the base,
S.A. = lw + l√[(w ÷ 2)² + h²] + w√[(l ÷ 2)² + h²],
where l is the length of the bottom of the rectangle, w is the width of the bottom of the rectangle, and h is the height.
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