9514 1404 393
Answer:
345 mL of 80%230 mL of 30%Step-by-step explanation:
Let x represent the amount of 80% alcohol. Then (575 -x) is the amount of 30% alcohol. The total amount of alcohol in the mix is ...
0.30(575 -x) +0.80(x) = 0.60(575)
172.5 +0.50x = 345
0.50x = 172.5 . . . . . . . . subtract 172.5
x = 345 . . . . . . . . . . . . multiply by 2; amount of 80% needed
575 -x = 230 . . . . amount of 30% needed
You should use 230 mL of 30% alcohol and 345 mL of 80% alcohol.
_____
Additional comment
You can work a problem like this by writing two equations in two unknowns. The variables would be the amounts of each solution (w=weak, s=strong), and the equations would reflect the total amount and the amount of alcohol in the mix.
w+s = 575.30w +.80s = .60(575)You will notice that if you solve this by substitution, substituting for the "weak" variable, you get ...
w = 575 -s0.30(575 -s) +0.80s = 0.60(575) . . . . substitute for wwhich is the same equation we used above.
When you simplify this and isolate the variable, the coefficient of the variable is positive. This makes the arithmetic less prone to error. If you substitute for the "strong" variable, then the coefficients come out negative. That still works, but you need to spend extra effort to get the signs right.
Essentially, our choice of a single variable for the "strong" solution results in a single 2-step equation that is easily solved. A lot of mixture problems can be solved with this approach.
Taylor wants to find the perimeter of a rectangular playground. The lenght of the playground measures (3x-20) metres. The width of the playground measures (2x+4) metres. What is the perimeter of the playground?
Answer:
Step-by-step explanation:
P = 2(3x-20) + 2(2x+4) = (6x-40) + (4x+8) = 10x-32
The required perimeter of the playground is 10x-32.
The length of the playground measures (3x-20) metres.
The width of the playground measures (2x+4) metres.
What is the perimeter?
Perimeter, is the measure of the figure on its circumference.
The Required perimeter is for the playground is given by
= 2(3x-20) + 2(2x+4)
= 10x-32
Thus the required perimeter of the playground is 10x-32.
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solve using the multiplication principle. Don't forget to perfom a check
-3/5x = 6/35
453,193 what is the value of the 5
Answer:
50,000
Step-by-step explanation:
3 is in the ones place so 3
9 is in the tens place (90)
1 is in the hundreds place (100)
3is in the thousands place (3,000
Write the equation in slope-intercept form. y=2(x−8)+4x
Answer:
y=6x-8
Step-by-step explanation:
y=2(x-8)+4x
y=2x+4x-8, y=6x-8
At a birthday party there were five more girls than boys. If the ratio of girls to boys was 4 to 3,
how many girls were at the party? (Make a chart to help you.)
Let number if boys be x
No of girls=x+5ATQ
[tex]\\ \sf\longmapsto \dfrac{x+5}{x}=\dfrac{4}{3}[/tex]
[tex]\\ \sf\longmapsto 3(x+5)=4x[/tex]
[tex]\\ \sf\longmapsto 3x+15=4x[/tex]
[tex]\\ \sf\longmapsto 4x-3x=15[/tex]
[tex]\\ \sf\longmapsto x=15[/tex]
Number of girls[tex]\\ \sf\longmapsto x+5=15+5=20[/tex]
QUESTION 5 - 1 POINT
An investment of $32,000 is worth $38,302 after being compounded monthly at 3%. How many years was the investment
for? (Round to the nearest whole year).
9514 1404 393
Answer:
6
Step-by-step explanation:
The compound interest formula tells you the future value of principal P invested at annual rate r compounded n times per year for t years is ...
A = P(1 +r/n)^(nt)
Solving for t, we get ...
t = log(A/P)/(n·log(1 +r/n))
Using the given values, we find t to be ...
t = log(38302/32000)/(12·log(1 +0.03/12)) ≈ 5.9997
The investment was for 6 years.
Answer the question you hopeless heathens
Monico recently hired a roofer to do some necessary work. On the final bill, Monico was charged a total of $605. The amount listed for parts was $285 and the rest of the bill was for labor. If the hourly rate for labor was $64, how many hours of labor was needed to complete the job?
(A) First write an equation you can use to answer this question. Use x as your variable. The equation is ___________________
(B) Solve your equation in part (A) to find the number of labor hours needed to do the job. Answer: The number of labor hours was ________________
Answer:
A) 64x + 285 = 605
B) 5 hours
Step-by-step explanation:
64x + 285 = 605
64x + 285-285 = 605 - 285
64x = 320
64x/64 = 320/64
x = 5
Double check
($605 Total - $285 parts) / $64 Hourly rate = Labor per hour
$320 Labor / $64 Hour = 5 hours
or 64x
What is the completely factored form of this polynomial? x3 + 3x2 - 6x – 18
A. (x - 2)(x - 3)(x + 3)
B. (x2 - 6)(x + 3)
C. (x2 + 3)(x-6)
D. (x + 6)(x - 1)(x + 3)
Answer:
(x+3) ( x^2 -6)
Step-by-step explanation:
x^3 + 3x^2 - 6x – 18
Factor by grouping
x^3 + 3x^2 - 6x – 18
Factor x^2 out of the first group and -6 out of the second group
x^2( x+3) -6(x+3)
Factor out x+3
(x+3) ( x^2 -6)
Question 26 of 58
Mr. Nguyen recorded the numbers of students in his homeroom class who
participated in spirit week.
The table shows the number of students who dressed up each day.
Day
Mon Tues. Wed. Thurs. Fri. Total
Number of students 2
2
5
5
6
20
Find the mean and the median of the data set.
Determine which of these values is greater.
O A. The mean, 5, is greater than the median, 4.
OB. The mean, 5, is greater than the median, 2.
O c. The median, 6, is greater than the mean, 2.
O D. The median, 5, is greater than the mean, 4.
Answer:
D
Step-by-step explanation:
The answer is D.
Solve for x
-3x = -15
A) x = -45
B) x = 5
C) x = -5
C-x=-5
Step-by-step explanation:
-3x=-15
or,-3x x =-15
or, x=-15÷3
therefore, x=-5
Solve this inequality: x+ 4< 16
Answer:
x < 12
Step-by-step explanation:
subtract 4 from both sides:
x + 4 < 16
- 4 -4
x < 12
Answer:
x<4
Step-by-step explanation:
x+4 <16
x < 16
4
x<4
I hope this will help you
reflect the x axis A B C D
Answer:
see explanation
Step-by-step explanation:
Under a reflection in the x- axis
a point (x, y ) → (x, - y ) , then
A (- 1, - 17 ) → A' (- 1, 17 )
B (0, - 12 ) → B' (0, 12 )
C (- 5, - 11 ) → C' (- 5, 11 )
D (- 6, - 16 ) → D' (- 6, 16 )
what is the volume of the container
Một miếng đất hình chữ nhật có chu vi 80 mét.Nếu kéo dài thêm 8 mét nữa thì diện tích tăng thêm là 72 mét vuông.Tính chiều dài và chiều rộng hình chữ nhật ban đầu ?
Answer:
Step-by-step explanation:
(D+R) = 80:2 = 40
D = 40-R
(D+8) * R = 72X
Thay D=40-R
(40-R+8)*R = 72X
R=1.55, D=38.45
Can I get help with this? Ez points
9514 1404 393
Answer:
(-1, -1), (-1, 5), (2, -1)
Step-by-step explanation:
All of the blanks are filled with -1. (see attached)
_____
The attachment also shows the solutions that maximize or minimize the value of z.
What is the value of 2 in 9,274
Answer:
200
Step-by-step explanation:
4 is in the ones place so 4 just 4
7 is in the tens place so it is 70
2 is the hundreds place so 200
9 is in the thousands place so 9.000
Suppose a six-sided die is tossed 1200 times and a 6 comes up 419 times. (a) Find the empirical probability for a 6 to occur. (Enter your probability as a fraction.) (b) On the basis of a comparison of the empirical probability and the theoretical probability, do you think the die is fair or biased
Answer:
Here both probabilities are not equal.
Therefore the die is not fair and biased.
Step-by-step explanation:
Now n= 1200 times and x = 419 times.
a) Empirical Probability:
[tex]=\frac{x}{n} \\\\= \frac{419}{1200}\\ \\=0.349[/tex]
Probability = 0.349
b) Theoretical Probability:
[tex]=\frac{1}{6}[/tex]
Here both probabilities are not equal.
Therefore the die is not fair and biased.
Which of the following algebraic equations models the English sentence, a number decreased by two is equal to
four?
A W + 2 = 4
B 2 -w = 4
C W-2 = 4
D w= 2-4
Answer:
The choose C. w–2=4
I hope I helped you^_^
Answer: C
Step-by-step explanation:
Jack is going to the fair. The fair charges $10 to enter and $0.25 per ticket. How much will be spent by Jack? t = tickets 0.25 + 10 10 + 0.25t
Answer:
10 + .25t
Step-by-step explanation:
The total amount spent is equal to the amount to get in plus the cost of the tickets times the number of tickets
cost = 10 + .25t
If the mean age of the managers in company is 52 years with a standard deviation of 2.5 years, what is the probability that a randomly chosen manager will be between 54.5 and 57 years old
Answer:
13.5 %
Step-by-step explanation:
For a normal distribution, the Empirical Rule states that 68% of values lie between 1 standard deviation of the mean, 95% of values lie between 2 standard deviations of the mean, and 99.7% of values lie between 3 standard deviations of the mean. Here, we can see that 54.5 is 1 standard deviation away from the mean and 57 is 2 standard deviations away. This means that we want to find the difference between 1 and 2 standard deviations from the mean (in the positive direction)
To find the difference, we can simply find (percent of values 2 standard deviations of the mean) - (percent of values 1 standard deviation from the mean) = percent of values between 1 and 2 standard deviations from the mean
= 95-68 = 27 %
Finally, this gives us the percent of values between 1 and 2 standard deviations from the mean on both sides. We want to only find the positive aspect of this, as we don't care how many values are between 49.5 and 47 years old. Because normal distributions are symmetric, or equal on both sides of the mean, we can simply divide by 2 to eliminate the half we don't want, resulting in 27/2 = 13.5
The probability that a randomly chosen manager will be between 54.5 and 57 years old is 0.8413.
Given that, average age managers = 52 years standard deviation = 2.5 years.
What is standard deviation?Standard deviation is the positive square root of the variance. Standard deviation is one of the basic methods of statistical analysis. Standard deviation is commonly abbreviated as SD and denoted by 'σ’ and it tells about the value that how much it has deviated from the mean value.
Considering the equation Z = (X−μ)/σ
Where, X is the lower or higher value, as the case may be μ is the average σ is standard deviation
Now, z1= (54.5 - 52)/2.5
= 1
z2= (57 - 52)/2.5
= 2
Now, z2-z1= 2-1
= 1
P(54.5>Z<57)= 0.8413
Therefore, the probability that a randomly chosen manager will be between 54.5 and 57 years old is 0.8413.
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Will give brainliest
mplete the equation describing how
x and y are related.
Х
0 1
2
3
4
Y -1 3 7
11 15
y = 4x + [? ]
Enter the answer that belongs in [?]
Answer:
y = 4x + -1
Step-by-step explanation:
clearly seen.
Which equation does the graph of the systems of equations solve?
two linear functions intersecting at 3, negative 2
−one thirdx + 3 = x − 1
one thirdx − 3 = −x + 1
−one thirdx + 3 = −x − 1
one thirdx + 3 = x − 1
Answer:
-1/3x+3 = x-1
Step-by-step explanation:
The solution is (3,-2)
Check and see if the point solves the equation
-1/3x+3 = x-1
-1/3(3) +3 = 3-1
-1+3 = 3-1
2=2 yes
Answer:
C
Step-by-step explanation:
At a time hours after taking a tablet, the rate at which a drug is being eliminated r(t)= 50 (e^-01t - e^-0.20t)is mg/hr. Assuming that all the drug is eventually eliminated, calculate the original dose.
Answer:
2500 mg
Step-by-step explanation:
Since r(t) is the rate at which the drug is being eliminated, we integrate r(t) with t from 0 to ∞ to find the original dose of drug, m. Since all of the drug will be eliminated at time t = ∞.
Since r(t) = 50 (e^-01t - e^-0.20t)
m = ∫₀⁰⁰50 (e^-01t - e^-0.20t)
= 50∫₀⁰⁰(e^-01t - e^-0.20t)
= 50[∫₀⁰⁰e^-01t - ∫₀⁰⁰e^-0.20t]
= 50([e^-01t/-0.01]₀⁰⁰ - [e^-0.20t/-0.02]₀⁰⁰)
= 50(1/-0.01[e^-01(∞) - e^-01(0)] - {1/-0.02[e^-0.02(∞) - e^-0.02(0)]})
= 50(1/-0.01[e^-(∞) - e^-(0)] - {1/-0.02[e^-(∞) - e^-(0)]})
= 50(1/-0.01[0 - 1] - {1/-0.02[0 - 1]})
= 50(1/-0.01[- 1] - {1/-0.02[- 1]})
= 50(1/0.01 - 1/0.02)
= 50(100 - 50)
= 50(50)
= 2500 mg
Use the discriminant to determine the number of solutions to the quadratic equation −40m2+10m−1=0
From the analysis of the discriminant, you obtain that the quadratic function has no real solutions.
In first place, you must know that the roots or solutions of a quadratic function are those values of x for which the expression is 0. This is the values of x such that y = 0. That is, f (x) = 0.
Being the quadratic function f (x)=a*x² + b*x + c, then the solution must be when: 0 =a*x² + b*x + c
The solutions of a quadratic equation can be calculated with the quadratic formula:
[tex]Solutions=\frac{-b+-\sqrt{b^{2} -4*a*c} }{2*a}[/tex]
The discriminant is the part of the quadratic formula under the square root, that is, b² - 4*a*c
The discriminant can be positive, zero or negative and this determines how many solutions (or roots) there are for the given quadratic equation.
If the discriminant:
is positive: the quadratic function has two different real solutions. equal to zero: the quadratic function has a real solution. is negative: none of the solutions are real numbers. That is, it has no real solutions.In this case, a= -40, b=10 and c= -1. Then, replacing in the discriminant expression:
discriminant= 10² -4*(-40)*(-1)
Solving:
discriminant= 100 - 160
discriminant= -60
The discriminant is negative, so the quadratic function has no real solutions.
Suppose that a population begins at a size of 100 and grows continuously at a rate of 200% per year. Give the formula for calculating the size of that population after t years.
A) A = 100 + te^2
B) A = 100 + e^2t
C) A = 100e^2t
D) A = 100 + 2e^t
Answer:
D)
Step-by-step explanation: Im not so sure ok i sorry if Im wrong
Grams in this equation
30 .650 pounds of gramsin vegetables
Jupiter orbits the sun at a rate of 8 miles per second. How far does Jupitertravel in one day? Tip: There are 86400 seconds in a day.
Answer:
Jupiter travels 691200 miles a day
Step-by-step explanation:
I just did 86400 x 8
Plz give brainliest
I need to know about rounding the numbers up to 100
Step-by-step explanation:
Rounding number are important in world-problem. They help us in many ways like counting class, food, etc. It's the same thing as estimating.
Tens Place:
50-99: round to 100
100th place:
150-101: round to 100
There is still a lot I'm missing out on, but you could say does are the lowest group that can be round to 100. I'm not a expert, but I hope I could help! You can also ask for the other numbers, but it just depends on where you place or how you use the 100.
what is the absolute value of -5/9
Answer:
5/9
Step-by-step explanation:
In short, the absolute value of a number turns that number into a positive value no matter what. Here is a small representation:
Negative -> Positive
Positive -> Positive
Since we are working with a negative value, it will turn positive.
Best of Luck!
Determine x&y
(2+i) (x+yi) = -7+3i
Answer:
x = -11/5 or -2.2
y = 13/5 or 2.6
Step-by-step explanation:
well, start by doing the multiplication. then we will see better.
2x + 2yi + xi + yii = -7 + 3i
2x + 2yi + xi - y = -7 + 3i
this is because, remember, i = sqrt(-1), and ii = -1.
now we group the i-factors and the terms without i and compare it to the corresponding parts on the right side.
2x - y = -7
2yi + xi = 3i
=> 2y + x = 3
x = 3 - 2y
and that we use ihr the first equation again
2×(3-2y) - y = -7
6 - 4y - y = -7
-5y = -13
y = 13/5
x = 3 - 2×13/5 = 3 - 26/5 = 15/5 - 26/5 = -11/5
