To produce 200 ml of 60% acid solution from 65% and 40% acid solutions, approximately 715.8 ml of the 65% acid solution must be mixed with approximately 484.2 ml of the 40% acid solution.
Since the resulting solution is 200 ml and is a 60% acid solution, we know that the amount of acid in the solution will be:
0.6 * 200 ml = 120 ml
For the quantity 65% acid solution, the amount of acid is 0.65x ml.
For the quantity 40% acid solution, the amount of acid is 0.4y ml.
Since we want to end up with a total of 200 ml of solution, we know that:
x + y = 200
We also know that the amount of acid in the final solution is the sum of the amounts of acid in the two solutions we're mixing together:
0.65x + 0.4y = 120
Solve the second equation for y:
0.4y = 120 - 0.65x
y = (120 - 0.65x) / 0.4
x + (120 - 0.65x) / 0.4 = 200
Solve for x:
1.6x + 120 - 0.65x = 800
0.95x = 680
x = 715.8 ml
So we need to mix approximately 715.8 ml of the 65% acid solution with approximately 484.2 ml of the 40% acid solution to get 200 ml of 60% acid solution.
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What’s the answer to this question?
There are 9 green apples and 5 red apples in a basket (a) what is the ratio of green apples to all the apples in the basket (b) what is the ratio of red apples to all apples in the bag 
After answering the provided question, we can conclude that So the ratio of red apples to all the apples in the basket is 5:14.
What is ratio?In mathematics, ratios show how frequently one number is contained in another. For example, if there are 8 oranges and 6 lemons in a fruit dish, the ratio of oranges to lemons is 8 to 6. In a similar vein, the orange-to-whole-fruit ratio is 8, while the lemon-to-orange ratio is 6:8. A ratio is an ordered pair of numbers a and b expressed as a / b, where b is not zero. A ratio is an equation that equates two ratios. For example, if there is one boy and three girls (for every boy she has three girls), 3/4 are girls and 1/4 are boys.
(a) The ratio of green apples to all the apples in the basket is:
Green apples : Total apples = 9 : (9+5) = 9 : 14
So the ratio of green apples to all the apples in the basket is 9:14.
(b) The ratio of red apples to all apples in the basket is:
Red apples : Total apples = 5 : (9+5) = 5 : 14
So the ratio of red apples to all the apples in the basket is 5:14.
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I was given this question on a review assignment but was never taught this. Please help!
You need to use the formula
pi r squared times the height and all you need to do is plug it in and you’ll have your answer
Talk about any similarities and differences you detect between the groups, as well as what conclusions you can draw from the side-by-side boxplots.
1. To compare, we have to use the matched test.
2. n = 57
3. Sample mean difference = -0.4681
3b. Sample standard deviation of difference = 1.2824
What is the Null Hypothesis?In statistics, the null hypothesis is a statement that suggests there is no significant difference between two groups, samples, or variables being compared. It is a starting point for statistical analysis, and the goal is to either reject or fail to reject this hypothesis based on the evidence from the data.
The images below contains the histogram of differences, the comparison data and the calculation
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use π ≈3.14 5mm and round your answer to the nearest hundredth
Answer:
113.04cm2
Step-by-step explanation:
6cm is the radius, right?
If so, 12*3.14 = 37.68cm is the circumference and 6^2*3.14 = 113.04cm2 is the area.
HOPES THIS HELPS
Do you want points? Comment below! Then Ill do another question!
Answer:
Step-by-step explanation: ???
A theater has 424 seats there are eight sections of seats in the theater each section has the same number of seats how many seats are in each section
Answer:
53.
Step-by-step explanation:
a backpack that normally sells for $40 is on sale for $30. find the percentage of a change.
Answer:It would be 40•.25=10
Step-by-step explanation: which means 40-10=30 so it’d be .25 and you’d move the decimal over 2 spots so it’d be 25% off
Given that co-factor matrix M=16-12-4-5-33 - 12-3 find the adjoint M
The answer of the given question based on the finding the adjoint of M is 16 -4 -33
-12 -5 -12.
What is Co-factor?In linear algebra, a cofactor is a scalar value that can be computed for each element of a square matrix. To find the cofactor of a specific element of a matrix, we first remove the row and column containing that element, and then compute the determinant of the remaining matrix. The sign of the cofactor depends on the position of the element within the matrix: it is positive if the sum of the row and column indices is even, and negative if the sum is odd.
The cofactor matrix of a given matrix is obtained by replacing each element of the matrix with its corresponding cofactor. Cofactor matrices are useful in computing the inverse of a matrix and in solving systems of linear equations.
The adjoint of matrix is transpose of its co-factor matrix.
First, we need to find the transpose of the co-factor matrix:
16 -12
-4 -5
-33 -12
Therefore, the adjoint of M is:
16 -4 -33
-12 -5 -12
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This question was on my study guide for a big pre algebra test. Only problem, I’m in algebra and never took pre-algebra. Please explain
use the distance formula and the converse of the pythagorean theorem to determine whether the points are vertices of a right triangle 22. (1,1), (4,4), (1,4) 23. (6, 0), (6,4), (2,4) 24_ (-2, 1), (3,5), (6, -2'
Using the distance formula and the converse of the pythagorean theorem to determine whether the points are vertices of a right triangle :
22. The points (1,1), (4,4), and (1,4) form a right triangle.
23. The points (6,0), (6,4), and (2,4) form a right triangle.
24. The points (-2,1), (3,5), and (6,-2) does not form a right triangle.
The points (1,1), (4,4), and (1,4) form a triangle. We can use the distance formula to find the lengths of the three sides, and then use the converse of the Pythagorean theorem to determine whether it is a right triangle. The distance formula is:
d = √((x₂-x₁)² + (y₂-y₁)²)
So the lengths of the three sides are:
d₁ = √((4-1)² + (4-1)²) = √(27)
d₂ = √((1-1)² + (4-1)²) = √(9)
d₃ = √((1-4)² + (4-1)²) = √(18)
To check if it is a right triangle, we need to see if any of the sides squared equals the sum of the squares of the other two sides. If that is the case, then it is a right triangle. Otherwise, it is not. Checking the three possible combinations, we see that:
d₁² = 27
d₂² + d₃² = 9 + 18 = 27
Therefore, the triangle formed by the points (1,1), (4,4), and (1,4) is a right triangle.
Similarly for points (6,0), (6,4), and (2,4), the lengths of the three sides are:
d₁ = √((6-6)² + (4-0)²) = 4
d₂ = √((2-6)² + (4-4)²) = 4
d₃ = √((6-2)² + (0-4)²) = 4√2
To check :
d₁² + d₂² = 16 + 16 = 32
d₃² = 32
Therefore, the triangle formed by the points (6,0), (6,4), and (2,4) is a right triangle.
For points (-2,1), (3,5), and (6,-2) the lengths of the three sides are:
d₁ = √((3-(-2))² + (5-1)²) = √(41)
d₂ = √((6-3)² + (-2-5)²) = √(58)
d₃ = √((6-(-2))² + (-2-1)²) = √(73)
To check :
d₁² + d₂² = 41 + 58 = 99
d₃² = 73
Therefore, the triangle formed by the points (-2, 1), (3,5), and (6, -2) is not a right triangle.
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need help with these two questions when anyone can do so, thanks.
The area of the composite shapes are:
1) A = 22 cm²
2) A = 91.5cm²
How to find the area of the composite shape?1) The formula for area of a trapezium is:
A = ¹/₂(sum of parallel sides) * height
Area of rectangle = Length * width
Thus:
Total Area of composite shape is:
A = (7 * 2) + ¹/₂(6 + 2)*2
A = 14 + 8
A = 22 cm²
2) Area of square = side * side
Area of semi circle = ¹/₂π(r²)
Total area of composite shape is:
A = (5 * 5) + (21 * 3) + ¹/₂π(1.5²)
A = 91.5cm²
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Prove the following theorem (Euclid's Proposition I.28) and its converse.
ℎ. ′ ,, ℎ ℎ ,ℎ ′
Answer:
Step-by-step explanation:
If a straight line falling on two other straight lines makes the interior angles on the same side less than two right angles
Please help me find the arc!
Answer:
33
Step-by-step explanation:
135/360 × 2 × 22/7 × 14
= 33
Write a phrase that could be modeled by the expression n +2n.
Answer:
Let age of mine be n years.
Age of my father is twice of mine -2 n years.
Find the sum of age of me and my father.
= n+2n
Step-by-step explanation:
if it helped you please mark me a brainliest :))
The expression n + 2n is an example of multiplication, where 2n is two times n. Adding n and 2n together results in 3n, which is three times n.
Write the expression using only positive exponents. Assume no denominator equals zero
Using the laws of exponents, we can simplify the given expression as:
-(¹/₂₇)(1/x¹²)y²¹
How to use laws of exponents?Some of the laws of exponents are:
1) When multiplying like bases, keep the base the same and add the exponents.
2) When raising a base with a power to another power, keep the base the same and multiply the exponents.
3) When dividing like bases, keep the base the same and subtract the denominator exponent from the numerator exponent.
The expression is given as:
(-3x⁴y⁻⁷)⁻³
Using the power to power rule of exponents, we have:
-3⁻³x⁻¹²y²¹
Using the reciprocal law of exponents, we have:
(-1/3³)(1/x¹²)y²¹
= -(¹/₂₇)(1/x¹²)y²¹
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The Sugar Sweet Company needs to transport sugar to market. The graph below shows the transporting cost (in dollars) versus the weight of the sugar being
transported (in tons).
Use the graph to answer the questions.
Cost (S)
Weight (tons)
(a) How much does the cost increase for each ton of
sugar being transported?
$0
(b) What is the slope of the line?
0
X
The cost increases by $10 for each ton of sugar being transported. This can be seen from the fact that for every 1 ton increase in weight, the cost increases by $10. And the slope of the line is $10/ton.
(a) To calculate the cost increase per ton of sugar being transported, we need to find the change in cost when the weight of sugar increases by 1 ton.
Looking at the graph, we can see that the cost increases from $20 to $30 as the weight of sugar increases from 1 ton to 2 tons. Therefore, the cost increase per ton of sugar is:
$30 - $20 = $10
So the cost increases by $10 for each ton of sugar being transported.
(b) The slope of the line can be calculated using the formula:
slope = (change in y) / (change in x)
where y is the cost and x is the weight of sugar being transported.
Since the line is perfectly horizontal, the change in y is zero for any change in x. Therefore, the slope is:
slope = 0 / (change in x) = 0
So the slope of the line is zero, which means that the cost does not change as the weight of sugar being transported changes.
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Complete the square to slice the quadratic equations
1. x2(x square) -10x = -100
2. x2(x square) +7x-16=0
The solution for the equation x^2 - 10x = -100 is
x = 5 + 5√3i and x = 5 - 5√3i.The solution for the equation x^2 + 7x - 16 = 0 is
x = -8 and x = 1How to solve the equation by completing the squareTo complete the square for the equation x^2 - 10x = -100, we need to add and subtract (b/2a)^2 = (10/2)^2 = 25 to both sides of the equation:
x^2 - 10x + 25 = -100 + 25
(x - 5)^2 = -75
x - 5 = ±√75i
x = 5 ± √(75)i
x = 5 ± 5√3 i
Therefore, the solutions are x = 5 + 5√3i and x = 5 - 5√3i.
For the equation x^2 + 7x - 16 = 0, we need to add and subtract (7/2)^2 = 49/4 to both sides of the equation:
x^2 + 7x + 49/4 - 49/4 - 16 = 0
(x + 7/2)^2 = 81/4
x + 7/2 = ±9/2
x = -7/2 ± 9/2
x = -8 or x = 1
Therefore, the solutions are x = -8 and x = 1.
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A piece of art is in the shape of a rectangular pyramid like the figure shown.
A rectangular pyramid with a base of dimensions 7 feet by 6 feet. The two large triangular faces have a height of 7.79 feet. The two small triangular faces have a height of 8 feet.
How much glass is needed to cover the entire pyramid?
After answering the provided question, we can state that As a result, 145.62 square feet of glass are required to cover the entire pyramid.
what is pyramid?A pyramid is a polygon formed by connecting points known as bases and polygonal vertices. For each hace and vertex, a triangle known as a face is formed. A cone with a polygonal shape. A pyramid with a floor and n pyramids has n+1 vertices, n+1 vertices, and 2n edges. Every pyramid is dual in nature. A pyramid contains three dimensions. A pyramid is made up of a flat tri face and a polygonal base that come together at a single point known as the vertex. A pyramid is formed by connecting the base and peak. The base's edges form triangle faces known as sides that connect to the top.
To determine how much glass is required to cover the entire pyramid, we must first determine the total surface area of the pyramid, including the base.
The formula for calculating the surface area of each triangular face is:
(1/2) x width x height
27.31 square feet = (1/2) x 7 feet x 7.79 feet
24 square feet = (1/2) x 6 feet x 8 feet
Simply multiply the length and width to find the area of the rectangular base:
7 feet by 6 feet equals 42 square feet
As a result, the total surface area of the pyramid is:
145.62 square feet = 2 (27.31 square feet) + 2 (24 square feet) + 42 square feet
As a result, 145.62 square feet of glass are required to cover the entire pyramid.
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Answer: 102.53
Step-by-step explanation: I calculated all the numbers you gave me and then added them to get 102.53
The radius of a cone's circular base is 3.5 inches. The height of the cone is twice the base's diameter.
What is the volume of the cone?
Use π≈3.14.
Enter your answer rounded to the nearest whole number in the box.
in³
Answer: It is 180
Step-by-step explanation:
The vοlume οf the cοne is apprοximately 205.9 cubic inches.
What is cοne?A cοne is a shape fοrmed by using a set οf line segments οr the lines which cοnnects a cοmmοn pοint, called the apex οr vertex, tο all the pοints οf a circular base(which dοes nοt cοntain the apex). The distance frοm the vertex οf the cοne tο the base is the height οf the cοne.
The diameter οf the base is twice the radius, sο:
Diameter = 2 x Radius = 2 x 3.5 inches = 7 inches
The height οf the cοne is twice the diameter, sο:
Height = 2 x Diameter = 2 x 7 inches = 14 inches
The vοlume οf a cοne can be fοund using the fοrmula:
Vοlume = (1/3) x π x Radius² x Height
Substituting the given values, we get:
Vοlume = (1/3) x π x (3.5 inches)² x (14 inches)
Simplifying, we get:
Vοlume = (1/3) x π x 12.25 inches² x 14 inches
Vοlume = 205.9 cubic inches (rοunded tο οne decimal place)
Therefοre, the vοlume οf the cοne is apprοximately 205.9 cubic inches.
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Directions: Simplify by combining like terms in each of the following expressions.
1. 1s2 + 10s2 - 21st =
2. 5st - st - t2 =
3. x^{2} + x^{2} + x^{3} =
4. 6x - 4x + 2=
5. 9x - 3s - 2t=
6. 87x + 8x - 1 =
7. 3x + 6x - 2 =
8. 8s - 4s + 3s =
9. 12 + x - 11x =
10. 12x + 24x - 3x - 4 =
11. 14t + 8t - 12t =
12. 17g + 14g - 6g + g =
13. 13 + 12 - 12 + 13x =
14. 17s - 3s + 3s =
15. 14t - 12t + t =
Answer:
1. 11s2 - 21st
2. 4st - t2
3. 2x² + x³
4. 2x + 2
5. 9x - 3s - 2t
6. 95x - 1
7. 9x - 2
8. 7s
9. 12 - 10x
10. 33x - 4
11. 10t
12. 26g
13. 13 + 13x
14. 17s
15. 3t
Find the value of the ratio: x : 16 = 9 : 24.
Answer: 18/27 or 2/3
Step-by-step explanation: trust me
I need help with this question
Answer:
the answer is very simple the answer would be, 5 giga horse power every hour, 5/60*360= 30, the answer is 30m/s2
Step-by-step explanation:
according to formula
3/4 of the bolts in the marina are white 4/7
of the remaining bolts are blue, and the rest are red. If there are nine red boats, how many boats are in the marina.
The majority of the marina's bolts are white. The remaining bolts are divided into 4/7 blue and the remainder red. There are 84 vessels at the marina if there are nine red boats.
Let's start by finding the fraction of bolts that are not red:
Fraction of white bolts: 3/4
Fraction of bolts that are not white: 1 - 3/4
Fraction of bolts that are not white = 4-3/4
Fraction of bolts that are not white = 1/4
Fraction of blue bolts: 4/7 of 1/4
Fraction of blue bolts = 4/28
Fraction of blue bolts = 1/7
Fraction of red bolts: 1/4 - 1/7
Fraction of red bolts = 7-4/28
Fraction of red bolts = 3/28
We know that there are nine red boats, which is equal to 3/28 of the total number of bolts. So we can set up an equation to solve for the total number of bolts:
3/28x = 9
Multiplying both sides by (28/3), we get:
x = (28/3) * 9
x = 28 * 3
x = 84
Therefore, there are 84 boats in the marina.
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square root of 98 . simifiy
We can simplify the square root of 98 by factoring 98 into its prime factors:
98 = 2 * 7 * 7
Now, we can take out one factor of 7 from the square root and simplify it:
√98 = √(2 * 7 * 7)
√98 = √2 * √7 * √7
√98 = 7√2
Therefore, the simplified form of the square root of 98 is 7√2.
Please Someone Help
Brainliest+30 Points
Answer:8
Step-by-step explanation:
if x>7 it means x is have to be bigger than 7
in this case,
6<7
5<7
8>7
which is answer.
can you solve this question?
f(x)=?
a=?
Using derivative of a function
f(x) = cosx and a = πWhat is the derivative of a function?The derivative of a function is its limit as the change in the independent variable tends to zero.
Now, since we have the [tex]\lim_{h \to 0}\frac{cos(\pi + h) - (- 1)}{h}[/tex].
We know that the definition of the derivative of a function f(x) is
[tex]f'(x) =\lim_{h \to 0}\frac{f(x + h) - f(x)}{h}[/tex]
Now, comparing both equations, we see that
f(x + h) = cos(x + h), f(x) = -1
Now, since f(x + h) = cos(x + h), we notice that f(x) must be a cosine function.
So, f(x) = cosx
Now, f(a) = -1
cosa = -1
a = cos⁻¹(-1)
= π
So, substituting this into the derivative equation, we have
[tex]f'(x) =\lim_{h \to 0}\frac{f(x + h) - f(x)}{h}[/tex]
[tex]f'(x) =\lim_{h \to 0}\frac{cos(x + h) - (-1)}{h}\\=\lim_{h \to 0}\frac{cos(x + h) - cos(x)}{h}\\=\lim_{h \to 0}\frac{cos(\pi + h) - cos(\pi )}{h}\\= -sin\pi \\= 0[/tex]
So,
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Hi hello I just want the answer to this picture. Thanks!
If the average is 85 minutes, then on the seventh day he skated for 115 minutes.
How long he skated the seventh day?For a set of N values {x₁, x₂, ..., xₙ} we define the average as:
A = (x₁ + ... + xₙ)/N
Here we know that for four days, he skated for 1hr + 25min = 85 min
Then for 2 days he skated for 1hr + 10min = 70 min
And the seventh day he skated x minutes.
We know that the average is 85 min, then we can write the equation:
(4*85 + 2*70 + x)/7 = 85
x = 85*7 - 2*70 - 4*85
x = 115
He scated for 115 minutes.
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really need help with this question don’t get it at all
Answer:
v = 40 cm
w = 126
x = 30
y = 63 cm
Step-by-step explanation:
So are given that ΔBIG is similar to ΔMOP. This means that their respective angles are the same measurements, but different side lengths. By definition of similar triangles, their respective side lengths are equal in proportion.
∠I corresponds to ∠O, so their measurements are equal. w = 126°.
∠B corresponds to ∠M, so their measurements are also equal. We don't know the angle measurement for x, but we have all the angles for two similar triangles, so we can find the measure of the third angle. The total angle measure for any triangle is 180°.
x = 180 - 24 - 126
x = 30°
Now that we have all the angle measurements, we can proportions to calculate the lengths of the unknown sides. The proportion of ΔBIG to ΔMOP can be calculated using the corresponding side length for each triangle.
Segment BG corresponds to segment MP. The proportion of BG to MP is:
48/72. Proportions are fractions, so this ratio can be simplified to 2/3 (divide by 24 on top and bottom).
Now we know that the ratio of ΔBIG to ΔMOP is 2/3.
Segment BI (aka v) = (2/3) * 60 cm
v = 40 cm
Segment PO (aka y) * (2/3) = 42 cm
y = 42 * 1.5
y = 63 cm
Calculate the amount of money you'll have at the end of the indicated time period.
You invest $4000 in an account that pays simple interest of 6% for 8 years.
Answer:
$5920.00
Step-by-step explanation:
1. (6% ÷ 100)×4000
=240.
2. 240 interest per year
240×8 years
= $1920
3. $1920 + $4000= $5920.00
The amount of money you'll have at the end of the indicated time period is $5920.
Given
You invest $4000 in an account that pays a simple interest of 6% for 8 years.
The amount of money you'll have at the end of 8 years.
What is the interest owed for the use of the money?We know the formula of simple interest, substitute the values in it,
[tex]\text{Simple interest}=\dfrac{\text{P}\times\text{R}\times\text{T}}{100}[/tex]
Substitute all the values in the formula
[tex]\text{Simple interest}=\dfrac{\text{P}\times\text{R}\times\text{T}}{100}[/tex]
[tex]\text{Simple interest}=\dfrac{\text{4000}\times\text{6}\times\text{8}}{100}[/tex]
[tex]\text{Simple interest}=40\times6\times8[/tex]
[tex]\text{Simple interest}=1920[/tex]
Therefore,
The amount of money you'll have at the end of the indicated time period is:
[tex]= \$1920 + \$4000 = \$5920[/tex]
Hence, the amount of money you'll have at the end of the indicated time period is $5920.
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