A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 40% salt and Solution B is 65% salt. She wants to obtain 150 ounces of a mixture that is 55% salt. How many ounces of each solution should she use
Answers
Since she wants to obtain 150 ounces of the mixture of A and B, then
Add A and B, then equate the sum by 150
\(A+B=150\rightarrow(1)\)Since 40% of A is salt
Since 65% of B is salt
Since 150 ounces has 55% salt, then
\(\begin{gathered} \frac{40}{100}A+\frac{65}{100}B=\frac{55}{100}(150) \\ \\ 0.40A+0.65B=82.5\rightarrow(2) \end{gathered}\)Now, we have a system of equations to solve it
Multiply equation (1) by -0.40 to make the coefficients of A equal in values and opposite in signs
\(-0.40A-0.40B=60\rightarrow(3)\)Add equations (2) and (3)
\(\begin{gathered} (0.40A-0.40A)+(0.65B-0.40B)=(82.5-60) \\ \\ 0+0.25B=22.5 \\ \\ 0.25B=22.5 \end{gathered}\)Divide both sides by 0.25
\(\begin{gathered} \frac{0.25B}{0.25}=\frac{22.5}{0.25} \\ \\ B=90 \end{gathered}\)Substitute B in equation (1) by 90 to find A
\(A+90=150\)Subtract 90 from each side
\(\begin{gathered} A+90-90=150-90 \\ \\ A=60 \end{gathered}\)There are 60 ounces of A and 90 ounces of B
Related Questions
Y=3x-7 complete the missing value in the solution to the equation (1,
Answers
Answer: (1, -4) or y = -4
Step-by-step explanation:
Given:
y = 3x - 7
Plug in the value of 1 for x - given to us by "(1, ?)
y = 3x - 7
y = 3(1) - 7
Multiply:
y = 3 - 7
Subtract:
y = -4
y = -4
Nine people go to a show. The adult tickets are $15 and the children tickets are $7. The total cost was $87, How many children and adults are there?
Answers
Answer:
2 adults, 8 children.
Step-by-step explanation:
just add the prices together.
Match each decimal to its equivalent percent.
12.5%
1
0.8
8%
0.125
80%
0.25
1%
0.5%
50%
0.01
100%
0.5
0.08
25%
0.005
Answers
Answer:
12.5%=.125, 1= 100%, .8=80% 8%=.08 .25= 25% .5 = 50% .01= 1% .005= 0.5%
Step-by-step explanation:
On the Decimal numbers just move the decimal place over 2 to the right
and add a percent
What is the lower limit of the confidence interval for the proportion of millennials that care about the Education? Write your answer as a proportion (decimal) and NOT as a percent. Do not Round.
2. What is the confidence interval for the proportion of millennials that care about Jobs/Economy?
1) (0.20, 0.30)
2) (0.24, 0.26)
3) (0.22, 0.28)
4) (0.16, 0.22)
Answers
The confidence interval for the proportion of millennials that care about Jobs/Economy is (0.22, 0.28).
The term confidence interval refers statistical measure used to indicate the range of estimates within which an unknown statistical parameter is likely to fall.
Here we have given that Jobs/Economy 25%, Immigration 17%, Healthcare 16%, Education 16%, Environment 12%.
And we need to find the confidence interval for the proportion of millennials that care about Jobs/Economy.
As per the formula of confidence interval,
CI = x ± Z× s/√n
CI = 25 ± 1.9600 × 0.03/ √50
CI = 25 ± 0.00832
When we simplify this one then we get the confidence interval for the proportion of millennials that care about Jobs/Economy as
=> (0.22, 0.28)
Therefore, option (3) is correct.
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The Recreation CPI index number was 93.0 in 1994 and 95.6 in 1995. What was the
percent increase in the prices of recreation goods and services for 1995, to the nearest tenth percentage?
Answers
Answer:
2.7957
Step-by-step explanation:
To calculate percentage increase we- the final value by the starting value so in 1994 we have 93 and in 1995 we have 95.6.
95.6 - 93 = 2.6
We then divide 2.6 by the absolute value of value 1(93) so 2.6 divided by 93=0.02795698924
Then use a calculator if you would like you don't have to but times that answer 0.02795698924 by 100. and you get the percent increase.
0.02795698924 x 100=2.7957.
Hope it helps have a great day:)
Five less than twice the value of a number is equal to three times the quantity of 4 more than 1/2 the number what is the number let x be the number right and solve an equation to find x show your work.
Answers
The value of the number is x = 34.
Let's break down the problem and solve it step by step.
1. "Five less than twice the value of a number": This can be represented as 2x - 5, where x is the number.
2. "Three times the quantity of 4 more than 1/2 the number": This can be represented as 3 * (x/2 + 4).
According to the problem statement, the two expressions are equal. We can set up the equation as follows:
2x - 5 = 3 * (x/2 + 4)
Now, let's solve the equation:
2x - 5 = 3 * (x/2 + 4)
Distribute the 3 to both terms inside the parentheses:
2x - 5 = (3/2)x + 12
Multiply through by 2 to eliminate the fraction:
2(2x - 5) = 2((3/2)x + 12)
4x - 10 = 3x + 24
Next, let's isolate the x term by moving the constant terms to the other side of the equation:
4x - 3x = 24 + 10
Simplify:
x = 34
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based on the graph how many tiles are im figure 0
Answers
For figure {0}, the number of tiles will be equal to 2.
What is a mathematical function, equation and expression?Function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function
Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators
Equation : A mathematical equation is used to equate two expressions.
Given is a graph as shown in the image.
The line passes through point -
(3, 8) and (4, 10)
So, the slope of the line will be -
m = (10 - 8)/(4 - 3)
m = 2
y = 2x + c
For the point (3, 8), we can write -
8 = 6 + c
c = 2
For figure {0}, the number of tiles will be equal to 2.
Therefore, for figure {0}, the number of tiles will be equal to 2.
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don't have to answer all just at least 1 pls and write yes if the statement is a proportion or no if it is not a proportion.
2:3 = 9:4
3/8 = 12/32
10/12 = 20/25
4/9 = 17/38
Answers
Answer:
3/8 = 12/32 is a proportion
Step-by-step explanation:
2:3 and 9:4 is not a proportion, 10/12 and 20/25 is not a proportion, 4/9 and 17/38 is not a proportion
How to do this problem
Answers
Answer:
a. geometric series
b. r_n = 100 × (0.75)^n ft
c. 400
Step-by-step explanation:
a.
Start: 100 ft
After 1 hour: 75% of 100ft = 100 ft × 0.75
After 2 hours: 75% of 100ft × 0.75 = 100 ft × 0.75²
After 3 hours: 75% of 100 ft × 0.75² = 100 ft × 0.75³
Notice what is happening to the radius as the hours pass.
With each passing hour, the radius is 0.75 times the previous radius.
Since each new term is the previous term multiplied by a constant, 0.75, this is a geometric series.
b.
At each hour, multiply 100 ft by 0.75 raised to the number of the hour.
a_n = 100 × (0.75)^n ft
The nth term is 100 times 0.75 to the nth power.
c.
The sum of all the radii is the sum of a series that has 100 as its first term, and each subsequent term is 0.75 times the previous term.
r_n = 100(0.75)^n
Since the constant ratio has an absolute value less than 1, the series has a sum.
S = a_1/(1 - r)
S = sum of infinite series
a_1 = first term
r = constant ratio
S = 100/(1 - 0.75)
S = 100/0.25
S = 400
MATH
Systems of Linear Equations
1. Determine if each system of equations below is linear or nonlinear.
A. -9x+8y = 9x 7y+8=8x
Linear or nonlinear?
D. 6y+x=12 y-x=1-x
B.
2.3y+1.2x = 0
1.1x+0.1y 1.2
C.
2 7-3y=- 2x+9= 3y
Linear or nonlinear?
Linear or nonlinear?
E. 45x + y = 12 y+x² = 1-x²
Linear or nonlinear?
G
0.2x+9.1y9.1√x
7x+1=8√y
Linear or nonlinear?
F. x+8y = 81 x-7y = 32
Linear or nonlinear?
H.
98317y= 1010 + 2965x
-71389y=5692x - 1001
3 xx y-5= 1 zy+3x=-21
Linear or nonlinear?
Linear or nonlinear?
Linear or nonlinear?
2. Find the solution, if one exists, for each of the graphs shown below that are representing different systems of linear equations.
A.
B.
Solution:
Solution:
C.
D.
Solution:
Solution:
2. Find the solution, if one exists, for each of the graphs shown below that are representing different systems of linear equations.
A.
B.
Solution:
Solution:
C.
D.
Solution:
Solution:
Answers
The system of equations -9x+8y = 9x and 7y+8=8x is linear.
A system of equations is considered linear if each equation in the system is linear, meaning that the highest power of any variable in each equation is 1.
In this case, the first equation -9x+8y = 9x is linear because the highest power of any variable is 1 (x is raised to the first power).
Similarly, the second equation 7y+8=8x is also linear because the highest power of any variable is 1 (x is raised to the first power and y is not raised to any power).
Therefore, the system of equations is linear.
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Abcd is a cyclic quadrilateral. o is the center of the circle ∠bad = 40°,then angle BCD=?,m(arc BCD) =?,m( arc BAD)=?
Answers
Answer:
m∠BCD = 140°
m(arc BCD) = 80°
m(arc BAD) = 280°
Step-by-step explanation:
In the cyclic quadrilateral, every two opposite angles are supplementary.The measure of the subtended arc to an inscribed angle equals twice the measure of this angleLet us use these facts to solve the question
∵ ABCD is a cyclic quadrilateral in circle O
∵ ∠BAD and ∠BCD are opposite angles
→ By using the 1st fact above
∴ m∠BAD + m∠BCD = 180°
∵ m∠BAD = 40°
∴ 40° + m∠BCD = 180°
→ Subtract 40° from both sides
∴ 40° - 40° + m∠BCD = 180° - 40°
∴ m∠BCD = 140°
∵ Arc BCD subtended the inscribed ∠BAD
→ By using the 2nd fact above
∴ m(arc BCD) = 2(m∠BAD)
∵ m∠BAD = 40°
∴ m(arc BCD) = 2(40°)
∴ m(arc BCD) = 80°
∵ Arc BAD subtended the inscribed ∠BCD
→ By using the 2nd fact above
∴ m(arc BAD) = 2(m∠BCD)
∵ m∠BCD = 140°
∴ m(arc BAD) = 2(140°)
∴ m(arc BAD) = 280°.
•Taylorann Johnson 3/6/23 3td pero For each parabola, label all parts on the curve. Circle if it is a max or a min. Fill in the points or lines. 1 Name 1. y = x² Opens up or down? Positive Vertex (0.0) Max/Min Axis of Symmetry: x=__ y-intercept (,0) x-intercept(s) or the zeros ( ) [ Parabola Review Domain: (0₁2) Range: (1,8)
Answers
For the given parabola, the parts on the curve should be labeled as follows;
The parabola with the equation y = x² opens up.The vertex of the parabola are (0, 0).The max/min value are equal to (0, 0).The axis of symmetry is x = 0.The y-intercept is equal to (0, 0).The x-intercept or the zeros is (0, 0).The domain is equal to (-∞, ∞).The range is equal to (0, ∞).How to calculate the vertex and axis of symmetry of a quadratic function?In Mathematics, the axis of symmetry of a quadratic function can be calculated by using the following mathematical expression:
Axis of symmetry, Xmax = -b/2a
Where:
a and b represents the coefficients of the first and second term in the quadratic function.
For the given quadratic function f(x) = y = x², we have the following:
Axis of symmetry, Xmax = -b/2a
Axis of symmetry, Xmax = -(0)/2(1)
Axis of symmetry, Xmax = 0/1 = 0.
Vertex (h, k) = (0, 0).
In conclusion, the domain of this quadratic function f(x) = y = x² are all the x-values that are located on the x-axis of the graph, which include {-∞, ∞} or all real numbers.
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For the function f(x) = -x^3 + 2x^2 + x - 2
a. Show that (x - 1) is a factor of f(x).
b. Find other factors.
c. Sketch the graph of f(x) = -x^3 + 2x^2 x - 2
Answers
Answer:
Step-by-step explanation:
a)
\(f(1)=-1^3+2*1^2+1-2=-1+2+1-2=0\\\\\)
b)
Rationnel roots are divisor of -2: -1,1,-2,2
\(f(-1)=-(-1)^3+2*(-1)^2+(-1)-2=1+2-1-2=0\\\\\begin{array}{c|cccc}&x^3&x^2&x&1\\---&---&---&---&---\\&-1&2&1&-2\\x=1&&-1&1&2\\&-1&1&2&0\\\\x=-1&&1&-2\\&-1&2&0\\---&---&---&---&---\\\end {array}\\\\\\f(x)=-x^3+2x^2+x-2=(x-1)(x+1)(-x+2)\\\\\)
c) see picture
Select the correct answer.
It costs $480.00 to rent an apartment on the Gold Coast for a weekend. Last year it cost $400.00.
What method below shows how you would calculate the % increase?
Answers
The method is: Find the increase and find the ratio of the increase and the old price.
The percentage increase is 20%
What method below shows how you would calculate the percentage increase?A percentage is defined as the ratio that can be expressed as a fraction of 100.
The method below shows how you would calculate the % increase.
First step: Find the increase:
increase = 480 - 400 = $80
Second step: Find the ratio of the increase and the old price and multiply by 100 to express in percentage:
80/400 * 100 = 20%
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8.5 x 6.5 i need help with this question
Answers
Answer:
55.25
Step-by-step explanation:
So, all you gotta do is get rid of the decimal, times them both, then add the decimal back into it, and how you do that is you see how many numbers are behind a decimal point in the first place, in this case, it's two (8.5, 6.5) and you got your answer!
Hope this helps! <D
Evaluate the expression, writing the result as a simplified complex number.
To earn full credit be sure to show all steps and calculations. You may wish to do the work on paper and submit an image of that written work.
\frac{(2+i)(4-2i)}{1+i}
Answers
The simplified expression involving complex numbers is given as follows:
5 + 5i.
What are complex numbers?Complex numbers are number that have a real and an imaginary part, and are defined as follows:
z = a + bi.
In which:
a is the real part.b is the imaginary part.The basic relation of complex numbers is given as follows:
i² = -1.
The fraction for this problem is given as follows:
(2 + i)(4 - 2i)/(1 + i).
The numerator is simplified as follows:
(2 + i)(4 - 2i) = 8 - 4i + 4i - 2i² = 8 + 2 = 10.
Hence the fraction is of:
10/(1 + i).
To remove the complex number from the denominator, the entire fraction is multiplied by the conjugate of the denominator, hence:
10/(1 + i) x (1 - i)/(1 - i) = 10(1 + i)/(1 - i²) = 10(i + 1)/2 = 5 + 5i.
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Approximately how many times greater is 374,000 than 22,000?
Answers
Answer:
352,000
Step-by-step explanation:
Subtract 374,000 by 22,000 and you will get 352,000 as your answer
The number 374000 is greater then 22000 by exactly 25200 amount.
What is mathematic expression?
A mathematical expression is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Here, to find out by how much times the number 374000 is greater then the number 22000 we simply subtract the number 374000 by 22000 which comes out be 35200.
It should be noted that, To cross verify the answer we can add 35200 with 22000 it must be equal to 374000.
374000 - 22000 = 352000
Therefore, the number 374000 is greater then 22000 by exactly 25200 amount.
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after much experimentation, john discovers a which says that the wavelengths of light absorbed by hydrogen gas fit into a pattern which he is able to express in a mathematical formula.
Answers
After much testing, John comes up with a "law" that states that the light wavelengths absorbed as hydrogen gas follow a pattern that can be expressed mathematically.
Explain about the wavelengths of light for hydrogen gas?When hydrogen gas is placed in the discharge tube as well as the light released on the passing electrical discharges at low pressure is inspected using a spectroscope.
The emission spectrum or line spectrum for hydrogen is formed. It is discovered to be made up of numerous lines divided into various series.Four wavelengths with in visible spectrum of hydrogen light—410 nm, 434 nm, 486 nm, then 656 nm—are associated with photon emissions by excited electrons transitioning towards the quantum level denoted by the primary quantum number n = 2.Thus, John comes up with a "law" that states that the light wavelengths absorbed as hydrogen gas follow a pattern that can be expressed mathematically.
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The correct question is-
after much experimentation, john discovers a _____ which says that the wavelengths of light absorbed by hydrogen gas fit into a pattern which he is able to express in a mathematical formula.
if you could help that would be greatly appreciated
Answers
Answer: search
Step-by-step explanation: look up the question on your browser and the answer will pop up
arsenia has 90 movie posters and 60 band posters she plans to sell 27 movie poster she says that if she's also sells 27 band posters the ratio of movie posters to band poster says the same is that true why or why not complete the explanation
Answers
if anyone know the answers to this question i really need help.
Answers
Answer:
b.) 6
Step-by-step explanation:
2^6 = 64 because 2 * 2 * 2 * 2 * 2 * 2 = 64.
This is a hard question can you help me
Answers
Answer:
1: 6
2: 20
3: 4
4: 2
Step-by-step explanation:
Poppy gets semi-monthly paycheck of $2,375. What is her annual income?
Answers
Answer:
57,000
Step-by-step explanation:
(2375*2)*12
not sure what semi monthly is but i assume it’s 2 times every month, times 12 months in a year, boom
I will give brainiest to whoever answers correctly !!
Answers
Answer:
15,894.06
Step-by-step explanation:
HI there!
This is a compound interest question, so we will use the formula
\(x = p(1+\frac{r}{n})^n^t\)
P being our principle amount, $15,000 in this case,
R being our rate, or 1.25
N being our compound rate, which is semiannually, or twice a year.
T is our time, being 3.
After plugging these values in, we get
15,894.06
I hope this helps!
15,894.06
If need step by step please message me! And yes this is the right answer!
What is the sum of this expression?
Answers
Answer:
B. 9\(\frac{1}{2}\)
Step-by-step explanation:
Rewriting the two fractions in the expression:
=\(\frac{[(8)(2)]+1}{8} + \frac{[(8)(7)]+3}{8}\)
=\(\frac{17}{8} + \frac{59}{8}\)
Since the denominators of both the fractions is the same, then the denominator of the resulting simplified fraction will also be the same. In addition, everything written in the numerator level will be copied down as it is:
=\(\frac{17 + 59}{8}\)
=\(\frac{76}{8}\)
Divide the numerator and denominator by the Highest Common Factor '4':
= \(\frac{19}{2}\)
Apply Long Division since:
The numerator is greater than the denominator and The numerator and the denominator cannot be further reduced or simplifiedChoose the highest quotient to be multiplied by 2 to give a number closest to 19 but still less than 19. The quotient turns out to be 9. The remainder is 1
∴ Sum of the expression = 9\(\frac{1}{2}\)
3. Which of the following
shows a list of values in
decreasing order?
A. -6.007, -211, -V48
C. -27, -6.007,-48
B.-21, -148,-6.007
D. -6.007, -148, -27
please help. :/
Answers
Answer:
C. is seeing as decreasing order
Ganesh spends 60% of his income every month and saves Rs 11120 in a month. Find his monthly income and expenditure.
Answers
Monthly income and expenditure of Ganesh will be-16680
Let Ganesh's monthly income be x
The problem can be solved using linear equation
The amount of 60% of his salary is spent which can be written as 60% of x or 0.6x
The amount of money saved by Ganesh = total salary - amount spent
= x - 0.6x
= 0.4x
The amount of savings made by Ganesh as per the question = 11120
Lets equate both the equation
0.4x = 11120
x = (11120 × 100)/ 40
x = 27800
Hence, Ganesh's monthly salary comes out to be 27800
Ganesh's monthly expenditure = 0.6 x= 0.6 × 27800 =16680
What is a linear equation in math?
A linear equation only has one or two variables. No variable in a linear equation is raised to a power greater than 1 or used as the denominator of a fraction. When you find pairs of values that make a linear equation true and plot those pairs on a coordinate grid, all of the points lie on the same line
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2. center (5, -6), radius 4
Answers
Answer:
(x - 5)² + (y + 6)² = 16
Step-by-step explanation:
assuming you require the equation of the circle
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
here (h, k ) = (5, - 6 ) and r = 4 , then
(x - 5)² + (y - (- 6) )² = 4² , that is
(x - 5)² + (y + 6)² = 16
A map has a scale of 1cm: 4 kilometres.
The actual distance between two cities is 52 kilometres.
What is the distance between the cities on the map?
Answers
Answer:
Step-by-step explanation:
You can use conversion to solve for cm
52 km x 1 cm / 4 km = 13 cm
where km cancels out leaving your answer in cm.
the actual distance on the map would be 13 cm
graph the equation y=-3x-1
Answers
The graph of y=-3x-1 is given in the attachment.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The given equation is y=-3x-1
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
In the given equation slope is -3.
Let us find few values of x and y.
x 0 1 2 3 4
y -1 -4 -7 -10 -13
Hence, the graph of y=-3x-1 is given in the attachment.
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