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A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 45% salt and Solution B is
95% salt. She wants to obtain 60 ounces of a mixture that is 85% salt. How many ounces of each solution should she use?
we know A is 45% salt, so the amount of salt in A is (45/100)*A or 0.45A.
likewise we know that B is 95% salt, so the salt amount in it is (95/100)*B or 0.95B.
[tex]\begin{array}{lcccl} &\stackrel{solution}{quantity}&\stackrel{\textit{\% of }}{amount}&\stackrel{\textit{oz of }}{amount}\\ \cline{2-4}&\\ A&x&0.45&0.45x\\ B&y&0.95&0.95y\\ \cline{2-4}&\\ mixture&60&0.85&51 \end{array}~\hfill \begin{cases} x+y=60\\ 0.45x+0.95y=51\\[-0.5em] \hrulefill\\ y = 60 -x \end{cases}[/tex]
[tex]\stackrel{\textit{substituting on the 2nd equation}}{0.45x+0.95(60-x) = 51}\implies 0.45x+57-0.95x=51 \\\\\\ 0.45x-0.95x=-6\implies -0.5x=-6\implies x = \cfrac{-6}{-0.5} \\\\\\ \boxed{x = 12}~\hfill \stackrel{\textit{we know that}}{y = 60 -x}\implies \boxed{y=48}[/tex]
In a survey of 280 adults over 50, 75% said they were taking vitamin supplements. Find the margin of error for this survey if we want a 99% confidence in our estimate of the percent of adults over 50 who take vitamin supplements. (Round to the nearest thousandths.)
The margin of error for this survey if we want a 99% confidence in our estimate of the percent is 0.067
The formula for calculating the margin of error is expressed as:
[tex]e= z \cdot \sqrt{\frac{p(1-p)}{n} }[/tex]
p is the proportion
n is the sample size
Given the following parameters;
p = 75% = 0.75
n = 280
z = 2.576
Substitute into the formula
[tex]e=\sqrt{\frac{0.75(1-0.75)}{280} }\\e=\sqrt{\frac{0.1875}{280} } \\e=\sqrt{0.0006964} \\e=0.0258 \times 2.576\\e \approx 0.067[/tex]
Hence the margin of error for this survey if we want a 99% confidence in our estimate of the percent is 0.067
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venere madona de mihai eminescu particularitatile textului literar și poetic
The product of .010 and .001 is
Answer:
its 0.00001
I hope this helps
A Norman window is a window with a semi-circle on top of regular rectangular window. What should be the dimensions of the rectangular part of the norman window to allow in as much light as possible, if there are only 12 ft of the frame material.
Answer:
the answer is 12 feet
Step-by-step explanation:
Alvin’s family used 18.5 gallons of gas to drive 518 miles. How many miles did they drive per gallon of gas?
Please help me
Answer:
the answer is 1.2
Step-by-step explanation:
The number of miles Alvin’s family drive per gallon of gas is 28 miles.
Given that, Alvin’s family used 18.5 gallons of gas to drive 518 miles.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Number of miles drive per gallon of gas = Total number of miles ÷ Total number of gallons
= 518 ÷ 18.5
= 28 miles
Hence, the number of miles Alvin’s family drive per gallon of gas is 28 miles.
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(X-2)(5x+6)
Multiply using Distributive property
[tex](x-2)(5x+6)\\\\=x(5x+6) -2(5x+6)\\\\= 5x^2 +6x -10x -12 \\\\=5x^2 -4x-12[/tex]
5x-10x+6x-12
-`9x-12
i believe so
Driveway pavers are 6 inches by 10 inches. If your driveway is 21840 square inches, how many pavers do you need for your driveway?
Answer:
364 pavers are needed.
Step-by-step explanation:
6 x 10= 60
21840/60= 364
Pythagorean theorem
How do you visualize it and and solve it drawn out
Answer:
so using the Pythagorean theorem is simple. what you want o do for this question is to make a graph to visualize it. since the top of the ladder is 7 feet up the house, you would go up 7 points, and its 2 1/2 feet from the house, you would move out 2 1/2 points. The ladders length is the hypotenuse, or the longer side that you get when you connect those two points.
Step-by-step explanation:
Determine whether a quadratic model exists for the set of values below. If so, write the model. f(0) = -4, f(3) = -19, f(-1) = -11
Select the correct choice below:
A) A quadratic model does exist. It is f(x)= ?
B) A quadratic model does not exist.
Answer:
A) The model exists: f(x) = -3x^2 +4x -4
Step-by-step explanation:
A quadratic model will always exist for 3 given points, provided they are not on a line. In that case, a linear model is appropriate.
Here, the slope between -1 and 0 is positive, and the slope between 0 and 3 is negative. Thus, we know these points are not collinear, and a model must exist.
The model is most easily found using a quadratic regression tool. Such is shown in the attachment. It tells us that ...
f(x) = -3x^2 +4x -4
geomtry plzz help 15 points
Answer:
False.
Step-by-step explanation:
The sides of a triangle rule asserts that the sum of the lengths of any two sides of a triangle has to be greater than the length of the third side. However, 8+6=14 is less than 15. Hence, the triangle cannot be formed.
Local Internet service costs $685 for 24 months. This includes a one-time installation fee of
$85. What is the monthly fee?
Answer:
25
Step-by-step explanation:
685-85 = 600
600 divided by 24 = 25
Hope this helps!
Simplify the ratio 25 :15
Answer:
5/3
Step-by-step explanation:
Find the GCD (or HCF) of numerator and denominator
GCD of 25 and 15 is 5
Divide both the numerator and denominator by the GCD
25 ÷ 5
15 ÷ 5
Reduced fraction:
5
3
Therefore, 25/15 simplified to lowest terms is 5/3.
brailiest pls hope it helps
What is the answer for 14.8 x -2.5
Answer:
-37
Step-by-step explanation:
The answer is -37
Hope this is the answer u needed have a great rest of ur day
Answer:
the answer is -37
Step-by-step explanation:
hope this helps have a good rest of your night :)❤
Zoin is reading a 300-page book.He is 41% finshed. How many pages of the book has he read so far?
Answer: 41% of 300 is 123
this was a basic answer
He has read 123 pages of the book so far.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
Given that Zoin is reading a 300-page book.He is 41% finshed.
Therefore, we get;
41% of 300
41% x 300
0.41 x 300
= 123
Hence,
The number of pages is 123
Learn more about the unitary method, please visit the link given below;
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Suppose you roll a pair of six-sided dice and add their totals, What is the probability that the sum of the numbers on your dice is a number other than 11
Answer:
17/18
Step-by-step explanation:
total number of outcomes=6×6=36
favorable outcomes for a total of 11=56,65
number of favorable items for a total of 11=2
P(a total of 11)=2/36=1/18
P(for a total other than 11=1-1/18=(18-1)/(18)=17/18
Can anyone help me with this question?
Answer: Here you go
Explanation:
Raduis is 2.5cm
Diameter 5cm
Circumference 15.70796cm or 16 rounded up because 2 times pie time 2.5 because 2.5 is the radius which if you calculate is 15.7 because 2 x 3.1415 x 2.5 = 15.7
simplify _4x+2y+z_3x+2y_2z
Answer:
maybe 3xz + 4yz + 4x + 2y
Step-by-step explanation:
I tried my best!
I would really appreciate help with this. I will give brainliest
Can any of you tell me the types of frequencies in math and explain how to find each one? It would be really really helpful if you answered:)
Answer:
Grouped Frequenct Distribution
UnGrouped Frequency Distribution
Step-by-step explanation:
Figures or numbers collected for some definite purpose is called data. Frequency is the value in numbers that shows how often a particular item occurs in the given data set. There are two types of frequency table - Grouped Frequency Distribution and Ungrouped Frequency Distribution. Data can be shown using graphs like histograms, bar graphs, frequency polygons, and so on.Find the product. Simplify your answer.
(m+2)(3m+2)
there you go the answer is in the picture
write the domain and rang of h using interval notation
We can write the domain and range in interval notation, which uses values within brackets to describe a set of numbers. In interval notation, we use a square bracket [ when the set includes the endpoint and a parenthesis ( to indicate that the endpoint is either not included or the interval is unbounded.
study the visual fraction below. Is it A,B,C, or D?
Answer: B
Step-by-step explanation: the pic shows this
if there are 60 houses and every house have one kid and there's 30 parts how much kids will have to go to each Park
Answer:
2 parks
Step-by-step explanation:
Answer:
20
Step-by-step explanation:
There would be 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20
Find c
[tex]a+a=10\\a+b=35\\b-z=5\\z+a+b+c= 10[/tex]
Answer= -50
a= 5
b= 30
z= 25
c= -50
Write (-3,-9) and (4,-2) in slope intercept form
Answer:
Slope intercept form is y = x - 6 (you don't write 1 in front of x in this case btw)
Slope = 1
Y-intercept = -6
Step-by-step explanation:
Slope intercept form looks like this y=mx+b, where m is slope and b is y-intercept.
To find slope, we will do y2 - y1 over x2 - x1.
This is how coordinates are written btw (x,y)
So we will do:
-2 - (-9) = -2 + 9 = 7
4 - (-3) = 4 + 3 = 7
Since 7/7 is the same as 7÷7, the slope is going to be 1. (It's also a positive slope btw)
Now, in order to find what the y-intercept is, you should use the point slope formula⤵⤵⤵:
[tex]y - y _{1} = m(x - x _{1})[/tex]
We'll use point (4,-2) for this:
y + 2 = 1 (x - 4)
Now we solve:
Distribute the 1 among everything inside the parenthesis to get y + 2 = x - 4, then subtract 2 on both sides to get y = x - 6.
Hope this helps :)
Nina brought 25 cupcakes to school for her friends. There were two flavors, chocolate and vanilla. For every 2 chocolate cupcakes she brought, Nina brought 3 vanilla cupcakes.
How many vanilla cupcakes did Nina take to school? Explain.
The number of vanilla cupcakes that Nina took to school is; 15 vanilla cupcakes
We are given;
Number of cake Nina bought for her friends = 25 cupcakes
There are two flavors namely chocolate and vanilla.
Now, we are told that for every 2 chocolate cupcakes she bought, she bought 3 vanilla cupcakes. Thus;
Fraction of chocolate cupcakes of the total = 2/(2 + 3) = 2/5
Fraction of vanilla cupcakes of the total = 3/5
Thus;
Number of the chocolate cupcakes she bought = 2/5 × 25 = 10 chocolate cupcakes
Number of the vanilla cupcakes she bought = 3/5 × 25 = 15 vanilla cupcakes
Read more at; https://brainly.com/question/14777115
expand 6(7+11x)
,,,,
Answer:
It would be 41+66x
Step-by-step explanation:
is there a way to place 29 books on shelves so that each shelf has the same number of books with more than one book on each shelf explain
Answer:
No, 29 is prime
Step-by-step explanation:
find the slope from the pair of points (0,-5) (2,5)
Step-by-step explanation:
given points,
(0,-5) and (2,5)
we know,
slope = y2 - y1 / x2 - x1
→ 5 - (-5) / 2 - 0
→ 5+5/2 = 10/2
→ 5
therefore, slope of the line is 5.
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Plz help!!!!! Need theses as soon as possible. No links plz!!!!
Answer:
1. 3
2. 0, 620
3. Positive
4. 2006
5. 2637