Alex is making a nut mixture to sell at the local farmer's market. He mixes 2 pounds of cashews with a nut mixture that is 40% cashews. The resulting mixture is 52% cashews. How many pounds of nut mixture does Alex make?
Mr. Martinez mixes a 90% sugar cinnamon flavored solution with a 75% sugar cherry flavored solution to make 12 gallons of a new product. The new product is 85% sugar. How much of the cherry flavored solution did he use?
Mr.Acosta works in the lab at a pharmaceutical company. He needs 26 liters of a 36% acid solution to test a new product. His supplier only ships a 42% and a 29% solution. How much of the 42% solution will Mr.Acosta need to use?
PLEASE SHOW WORK!!
Answers
Mr.Acosta works in the lab at a pharmaceutical company. He needs 26 liters of a 36% acid solution to test a new product. His supplier only ships a 42% and a 29% solution. How much of the 42% solution will Mr.Acosta need to use?
We would use the relation c1v1+c2v2=cv
where
v=26 L
c=36%
c1=42%
c2=29%
v1=x
v2=v-x=26-x L
Applying relationship:
42%*x + 29%*(26-x) = 36%*26
Expand
13x+754=936
13x=936-754=182
x=182/13=14 L
Answer: Mr. Acosta will need 14 L of 42% solution, and 12 L of 29% solution to make 26 L of 36% solution.
1. The percentages of cashews available are 100% and 40%. We want to mix these to make 52%. We know that we have used 2 lbs of 100%, and we want to find how much 40% we need.
The first diagram shows the ratio of 40% to 100% will be 48:12. Dividing both terms of this ratio by 6, we get 8:2. This means we will use 8 lbs of 40% cashews with the 2 lbs of 100% cashews, for a total of 10 lbs of mix.
2. The second diagram tells us that 5 out of 15 or 1/3 of the mixture will be cherry-flavored. Of the 12 gallons total, 4 gallons will be cherry-flavored solution.
3. The third diagram shows that 7 of 13 liters will be 42% solution, so to make twice as much mixture, 14 L of 42% solution are needed.
_____
In each diagram, the right-side numbers are the differences between the middle number and the left-side number.
Related Questions
If cos B = 7 over 22, then which of the following is correct?
a. csc B = 7 over 22
b. csc B = 22 over 7
c.sec B = 7 over 22
d.sec B = 22 over 7
Answers
Hope this helped : )
A student's saving account has a balance of $4900 on September 1. Each month the balance declines by $350. What is the slope
Answers
Answer:
The slope is [tex]-\frac{350}{month}\[/tex]
Step-by-step explanation:
This saving account is declining a fixed amount every month, this means that the function that represents this decline is linear.
The other thing we know is that originally (september 1), the account has a balance of $4900, and this is the intercept.
Therefore, for a linear function depending of the variable "x", we can write that
[tex]f(x)= (-\frac{350}{month}x+4900)\[/tex]
where the units were factored. Then the slope is
[tex]-\frac{350}{month}\[/tex]
The measure of is 126. What is the measure of ABC, the tangent-chord angle?
A. 126
B. 66
C. 63
D. 152
Answers
Use the theorem above to find the measure of angle formed by the intersection of the tangent that intersects chord AC.
By the theorem, the measure of angle is half of the intercepted arc which is 126.
Then, (1/2) · 126 = 63;
The correct answer is C. 63;
Answer:63
Step-by-step explanation:
someone help? Which graph most likely shows a system of equations with two solutions?
Answers
Answer:
Option D is correct.
The fourth graph shows a system of equation with two solutions.
Step-by-step explanation:
From the given figure,
we can see that we have a parabola and a straight line.
Since, the line is touching the parabola at two points, one point and no point.
In the first graph, the line touches the parabola at one point.
In the second graph, the line does not touches the parabola at no point.
also,In the third graph,the line touches the parabola at one point and
In fourth graph, the lines touches the parabola at two points.
For the system of equations :
For one solution, the two equations will touch at one point.For Two solution, the two equation will touch at two point.For no solution, the two equation will not touch at no point.Therefore, the graph which is most likely shows a system of equation with two solutions is: In fourth graph
Answer:
Two solution to a system of equation means when we look at the graph of the function the graph of the two equations must intersect at exactly two points.
The graph satisfying such condition is attached to the answer.
in this graph the curve that is downward parabola and a line intersect at exactly two points and hence result in two solutions.
Which graph represents a phase shift of pi/2 units right for the graph of y=cos x
Answers
Solution:
we are given that [tex]y=cos x[/tex]
Here we are going to plot two curves one for cosx and the othere also of cosx but after making a phase shift of [tex]\pi/2[/tex]
When we do a phase shift by an angle of theta , in that case actaully we add angle negative theta .
For example when we shift the phase of sinx by [tex]\pi/2[/tex] we get [tex]sin(x-\pi/2).[/tex]
Hence we are going to plot the curve of
[tex]y=cosx\\ \\ y=cos(x-\pi/2)=sinx\\[/tex]
Hence the correct option is B.
Calculate each mountain path grade to the nearest percent. Path A for every 31 meters of horizontal distance, the vertical change is 11 meters Path B for every 4.25 meters of horizontal distance, the vertical change is 3 meters?
Answers
We have then:
Path A
m = (11/31) * (100) = 35.48387097%
m = 36%
Path B
m = (3 / 4.25) * (100) = 70.58823529%
m = 71%
Answer:
Path A = 36%
Path B = 71%
Route A is less inclined than route B.
The grades of Path A and Path B are calculated by dividing the vertical change by the horizontal distance. Path A has a grade of approximately 35%, while Path B has a grade of approximately 71%.
Explanation:The grade of a path or road is calculated by taking the vertical rise and dividing it by the horizontal distance, typically expressed as a percentage. In Path A, the vertical change is 11 meters and the horizontal distance is 31 meters. Therefore, the grade of Path A is calculated as follows:
(11 / 31) x 100 = 35.48%So, Path A has a grade of approximately 35% when rounded to the nearest percent.
For Path B, the vertical change is 3 meters and the horizontal distance is 4.25 meters. Therefore, the grade of Path B is calculated as follows:
(3 / 4.25) x 100 = 70.59%So, Path B has a grade of approximately 71% when rounded to the nearest percent.
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Goran runs 6 miles in 57 minutes how many miles does he run per minute?
Answers
57 = 6x
x = 0.11 miles per minute
what are two numbers that when multiplied equal 54, and also when added equals -15
Answers
6 + (-9) = -3
x2 - 3x - 54 = 0
(X + 6 ) (X - 9)
x2 - 3x - 54 = (X + 6 ) (X - 9)
=
6 & -9
I need help with this
Answers
=-0.22(1.8) is -0.22 times 1.8
= -0.396
The answer is -0.396
Hope this helps! :)
The larger triangle is a dilation of the smaller triangle with a center of dilation at
(2,???1)
.
What is the scale factor of the dilation?
A. 1/3
B. 1/2
C. 2
D. 3
Answers
Four consecutive integers sum to 70. What is the least of the 4 integers?
Answers
I dont know on this one, its complicated
Answers
so a = 11
answer
11 inches
.. (11 in)^2 = 121 in^2
The side length is 11 inches.
_____
A square is a special rectangle. Its length is equal to its width. The area of any rectangle is the product of length and width, but because those are the same for a square, its area is the square of the side length. (square ... square, do you see any relation?)
Finding a square root is the process of finding a number that multiplies by itself to give a particular result. You want to find the square root of 121, so you will know the value (11) that multiplies by itself to give 121. If you don't already know this number, your calculator will find it for you.
Answers from anybody please??
Answers
.. (27 in^2)*(8/12)^2 = 27*(4/9) in^2 = 12 in^2
What is the x- intercept of the line with the equation 4x+2y=12?
Answers
set y=0
4x+2(0)=12
4x+0=12
4x=12
divide by 4
x=3
(x,y)
(3,0)
make me brainleast plz
x-intercept: (−3,0)(-3,0)y-intercept: (0,6)
How long is the base of a parallelogram if it has an area of 100 m2 and a height of 5 m? Enter your answer in the box.
Answers
Area = Base x Height
We have two values which are given;
Area = 100 m²
Height = 5 m
Now, we have to plug in the given values to find the missing, which in this case, is the base
100 = Base x 5
To find the value of base, we have to bring 5 to the other side, since it is multiplied, we do the reverse function, which is division.
[tex] \frac{100}{5} = \frac{5(Base)}{5} [/tex]
5 and 5 cancels out in the right hand side
20 = Base
The base is 20 m long
Math question help :)
Answers
Use corresponding parts of the two triangles.
If two triangles are similar, then the lengths of corresponding parts are proportional.
The small triangle has a vertical side that measures 6 ft. That side corresponds to the height of the tree, h, in the large triangle.
The small triangle has a horizontal side that measures 10 ft. That side corresponds to the side of the large triangle that measures 40 ft.
6 ft corresponds to h
10 ft corresponds to 40 ft
[tex] \dfrac{6}{h} = \dfrac{10}{40} [/tex]
Answer:
Step-by-step explanation:
I think its D.
What is the name of a ray that divides an angle into two equal angles?
Answers
Write an expression for the following situation and solve. Mr. Simms bought 20 pencils. He used 1/4 of the pencils and then gave 4 to his students. How many total pencils does Mr.Simms use and give away? Show your work.
Answers
1/4 of 20 pencils are 5 pencils.
Since he gave away 4 pencils,
Total = 5 + 4 = 9
Mr. Simms use and give away total 9 pencils.
Mr. Simms used 1/4 of the 20 pencils he bought, which equals 5 pencils, and gave away an additional 4 pencils, totaling to 9 pencils used and given away.
To solve how many total pencils Mr. Simms uses and gives away, we first find out how many pencils he used by taking 1/4 of the 20 pencils he bought. To do this, we multiply 20 by 1/4:
20 times 1/4 = 5
Mr. Simms used 5 pencils. He also gave away 4 pencils to his students. To find the total number of pencils used and given away, we add the pencils used to the pencils given away:
5 (used) + 4 (given away) = 9
Therefore, Mr. Simms used and gave away a total of 9 pencils.
Select the correct product.
(2x + 9)(x + 1)
2x2 + 11x + 9
3x2 + 11x + 9
2x2 - 7x + 9
2x2 + 11x + 10
Answers
2x * x + 2x * 1 + 9 * x + 9 * 1
= 2x^2 + 2x + 9x + 9
= 2x^2 + 11x + 9
The answer would be the first option.
Hope this helps!
Final answer:
To find the product of (2x + 9) and (x + 1), we use the distributive property and combine like terms, resulting in 2x² + 11x + 9.
Explanation:
The student is asking for the correct product when multiplying the binomials (2x + 9) and (x + 1). This is a math problem involving algebraic multiplication.
To find the product, we apply the distributive property (also known as FOIL method in binomials):
Multiply 2x by x to get 2x².Multiply 2x by 1 to get 2x.Multiply 9 by x to get 9x.Multiply 9 by 1 to get 9.Combine the terms to get the final product: 2x² + 2x + 9x + 9, which simplifies to 2x² + 11x + 9.
The correct product of (2x + 9)(x + 1) is 2x² + 11x + 9.
The staff at Larry's Lawns spends their workday mowing lawns, raking, and bagging leaves. They work an average of nine hours per day. The mowing and raking typically takes six hours and an average of thirty-six bags of leaves are filled. Assuming the bags are filled at a constant rate, what is the average time it takes to fill one bag of leaves?
Answers
The average time it takes to fill one bag of leaves is approximately 0.17 hours.
Explanation:To find the average time to fill one bag of leaves, we use the formula
Average Time=Total Time÷Total Bags. In this scenario, the total time spent is the average workday hours, which is 9 hours, and the total number of bags filled is 36.
So,
Average Time=9hours÷36bags=0.25 hours/bag.
Therefore, the average time it takes to fill one bag of leaves is 0.25 hours or 15 minutes. This means, on average, it takes 15 minutes to fill each bag of leaves.
In summary, the staff at Larry's Lawns spends 9 hours a day on lawn-related tasks, with mowing and raking taking 6 hours. Since they fill an average of 36 bags of leaves in that time, each bag takes approximately 0.25 hours or 15 minutes to fill, assuming a constant rate of filling.
To find the average time it takes to fill one bag of leaves at Larry's Lawns, divide the total time spent filling bags by the number of bags filled. Time per bag = 1/6 hours per bag.
Explanation:To find the average time it takes to fill one bag of leaves, we need to divide the total amount of time spent filling bags by the number of bags filled. In this case, the staff at Larry's Lawns spend 6 hours mowing and raking and fill 36 bags of leaves. So to find the average time per bag, we divide 6 hours by 36 bags:
Time per bag = Total time / Number of bags = 6 hours / 36 bags
Since we want the average time per bag, we can simplify the fraction:
Time per bag = 1/6 hours per bag.
Suppose that an individual has a body fat percentage of 16.4% and weighs 153 pounds. how many pounds of her weight is made up of fat? round your answer to the nearest tenth.
Answers
So multiply 0.164 times 153 to get 25.1lbs of fat.
how many fluorine atoms are found in 1.92 grams of AsF3?
Answers
The molar mass of AsF3 is 131.918 g/mole so
1.92 g * (1 mole)/(131.918g) = .0146 moles AsF3
Each mole of AsF3 has 6.02 x10^23 molecules of AsF3 and each molecule of AsF3 has 3 flourines, so you need to convert from moles to molecules AsF3 to atoms of F
0.146 moles AsF3 * (6.02 x 10^23 molecules AsF3)/(1 mole AsF3) * (3 atoms F)/(1 molecule AsF3) = 2.64 x 10^22 atoms F
It takes 40 ink cartridges and 200 pages to print a book, and it takes 30 ink cartridges and 80 pages to print a magazine.
Sarah wants to print books and magazines with at most 300 ink cartridges and 1200 pages. Let B denote the number of books she prints and M the number of magazines she prints.
Write an inequality that represents the condition based on the number of ink cartridges.
Write an inequality that represents the condition based on the number of pages.
Answers
.. 40B +30M ≤ 300
It takes 200 pages to print a book and 80 pages to print a magazine and Sarah wants to use at most 1200 pages.
.. 200B +80M ≤ 1200
Answer:
40B+30M≤300
200B+80M≤1200
Step-by-step explanation:
A thief steals an ATM card and must randomly guess the correct three-digit pin code from a 10-key keypad. Repetition of digits is allowed. What is the probability of a correct guess on the first try?
Answers
The probability of a correct guess on the first try will be [tex]0.001[/tex] .
What is Probability ?Probability is the ratio of number of favorable outcome to the
i.e. Probability [tex]P(E)=\frac{number\ of\ favorable\ outcome}{Total\ number\ of\ outcomes.}[/tex]
We have,
An ATM Card having three-digit code.
Repetition of digits is allowed.
So,
As Repetition is allowed, and we have [tex]10-[/tex]key keypad, and have to guess [tex]3[/tex] digit code,
Then
Total number of outcomes [tex]=10*10*10=1000[/tex]
And
Number of favorable outcome [tex]=1[/tex]
So,
Probability [tex]P(E)=\frac{number\ of\ favorable\ outcome}{Total\ number\ of\ outcomes.}[/tex]
[tex]P(E)=\frac{1}{1000}[/tex]
[tex]P(E)=0.001[/tex]
So, the Probability of correct guess is [tex]0.001[/tex] .
Hence, we can say that the probability of a correct guess on the first try is [tex]0.001[/tex] .
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I need help ASAP I will give brainliest if correct
Answers
we know that
the property of cyclic quadrilaterals for which opposite angles are supplementary
then
m∠A°+43°=180°------------> m∠A=180°-43°=137°
the answer is m∠A=137°
Part 2) Quadrilateral ABCD is inscribed in a circle. What is the measure of angle A?
we know that
the property of cyclic quadrilaterals for which opposite angles are supplementary
then:
m∠A+m∠C=180∘
(2x+9)+(3x+1)=180---------------> 5x+10=180
x=(180-10)/5=34
m∠A=2x+9-------------> 2*34+9=77°
the answer is m∠A=77°
The domain of f(x) is the set of all real values except 7, and the domain of g(x) is the set of all real values except –3. What describes the domain of (gºf)(x)?
Answers
Therefore the Domain you are looking for in words is every x that can be put into f(x) and that gives you a value y that can be put in g(y).
Mathematically:
Dom (g°f) = {x ∈ Dom(f) | f(x) ∈ Dom(g)}
In your case:
Dom (g°f) = { x ∈ R - {7} | f(x) ∈ R - {-3} }
*Please answer*
Don't understand. Please help.
Answers
It is the third option, Product of Powers
I have attached an image that may help you
PLEASE HELP
If a = 1, find the values of b, c, and d that make the given expression equivalent to the expression below.
Answers
Once you have simplified the expression, you get
[tex] \dfrac{-x-9}{2x-4} [/tex].
But, the problem stipulates that a must equal 1. We can equivalently factor out the negative sign and put it on the denominator with no change to write
[tex] \dfrac{x+9}{-(2x-4)} = \dfrac{x+9}{-2x+4}[/tex].
So, seeing where each coefficient corresponds between the two expressions, you get a = 1, b = 9, c = –2, and d = 4.
Equivalent expressions are expressions with the same value.
The values of the variables are:
[tex]\mathbf{a = 1}[/tex] [tex]\mathbf{b = 9}[/tex] [tex]\mathbf{c = -2}[/tex] [tex]\mathbf{d = 4}[/tex]
The expression is given as:
[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49}}[/tex]
Expand
[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49 } = \frac{3x^2 + 9x - 7x - 21}{-2x^2 +4x -6x + 12} \cdot \frac{2x^2 + 14x + 9x + 63}{6x^2 + 21x - 14x - 49 } }[/tex]
Factorize
[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49 } = \frac{3x(x + 3) - 7(x + 3)}{-2x(x -2) -6(x - 2)} \cdot \frac{2x(x + 7) + 9(x + 7)}{3x(2x + 7) - 7(2x - 7) } }[/tex]
Factor out the terms
[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49 } = \frac{(3x - 7) (x + 3)}{(-2x -6)(x - 2)} \cdot \frac{(2x + 9)(x + 7)}{(3x - 7) (2x - 7) } }[/tex]
Cancel out 3x - 7
[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49 } = \frac{(x + 3)}{(-2x -6)(x - 2)} \cdot \frac{(2x + 9)(x + 7)}{ (2x - 7) } }[/tex]
Factor out -2
[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49 } = \frac{(x + 3)}{-2(x +3)(x - 2)} \cdot \frac{(2x + 9)(x + 7)}{ (2x - 7) } }[/tex]
Cancel out x + 3
[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49 } = \frac{1}{-2(x - 2)} \cdot \frac{(2x + 9)(x + 7)}{ (2x - 7) }}[/tex]
Rewrite as:
[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49 } = \frac{(2x + 9)(x + 7)}{ -2(x - 2)(2x - 7) } }[/tex]
Expand
[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49 } = \frac{2x^2 + 25x + 63}{ -4x^2 + 22x - 28}}[/tex]
Factorize again
[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49 } = \frac{(2x+ 7)(x + 9)}{(2x + 7)(-2x + 4)}}[/tex]
Cancel out common factors
[tex]\mathbf{\frac{3x^2 + 2x - 21}{-2x^2 -2x + 12} \cdot \frac{2x^2 + 25x + 63}{6x^2 + 7x - 49 } = \frac{x + 9}{-2x + 4}}[/tex]
From the question, we have:
[tex]\mathbf{\frac{ax + b}{cx + d}}[/tex]
So, we have:
[tex]\mathbf{\frac{ax + b}{cx + d} = \frac{x + 9}{-2x + 4}}[/tex]
By comparison, we have:
[tex]\mathbf{a = 1}[/tex]
[tex]\mathbf{b = 9}[/tex]
[tex]\mathbf{c = -2}[/tex]
[tex]\mathbf{d = 4}[/tex]
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What is the 7th term of the geometric sequence 4, −20, 100, …? −312,500 −12,500 62,500 1,562,500?
Answers
.. a[n] = 4*(-5)^(n -1)
Then
.. a[7] = 4*(-5)^6 = 62,500
The 3rd selection is appropriate.
Answer: The correct option is (C) 62500.
Step-by-step explanation: We are given to find the 7-th term of the following geometric sequence :
4, −20, 100, . . .
We know that
the n-th term of a geometric sequence with first term a and common ratio r is given by
[tex]a_n=ar^{n-1}.[/tex]
For the given geometric sequence, we have
first term, a = 4
and common ratio r is given by
[tex]r=\dfrac{-20}{4}=\dfrac{100}{-20}=~~.~~.~~.~~=-5.[/tex]
Therefore, the 7-th term of the given geometric sequence is
[tex]a_7=ar^{7-1}=4\times(-5)^6=4\times 15625=62500.[/tex]
Thus, the required 7-th term is 62500.
Option (C) is CORRECT.
What is the value of x to the nearest tenth?
x=2.1
x=3.4
x=9.6
x=13.1
Answers
x = (6 * 11.2) / 7 = 9.6 answer
The value of x is 9.6.
To find the value of x to the nearest tenth, we can use the angle bisector theorem, which states that in a triangle, an angle bisector divides the opposite side into two segments that are proportional to the other two sides of the triangle.
Given that:
[tex]\[\frac{6.3}{5.4} = \frac{11.2}{x}\][/tex]
We can solve for x by cross-multiplying:
[tex]\[6.3 \cdot x = 5.4 \cdot 11.2\][/tex]
[tex]\[6.3x = 60.48\][/tex]
Now, divide both sides by 6.3 to isolate x:
[tex]\[x = \frac{60.48}{6.3}\][/tex]
[tex]\[x \approx 9.6\][/tex]
So, the value of x to the nearest tenth is 9.6. Therefore, the correct option is x = 9.6.