Bruce wants to make 50 ml of an alcohol solution with a 12% concentration. He has a 10% alcohol solution and a 15% alcohol solution. The equation 0.10x + 0.15(50 – x) = 0.12(50) can be used to find the amount of 10% alcohol solution Bruce should use. How much of the 10% alcohol solution should Bruce use? mL How much of the 15% alcohol solution should Bruce use?
Answer:
0.10x + 0.15(50 – x) = 0.12(50)
Step-by-step explanation:
8.find the result when 40 is INCREASED by 85%
10.find the result when 350 is DECREASED by 10%
28.find the result when 24 is INCREASED by 75%
30.find the result when 30 is DECREASED by 85%
Is 6.5 greater than 6.417
The shortest distance from the curve xy=4 to the origin is... ...?
The shortest distance [tex]x + y = 4[/tex] that is closest to the origin is [tex]\boxed{2\sqrt 2 {\text{ units}}}.[/tex]
Further explanation:
The formula for distance between the two points can be expressed as follows,
[tex]\boxed{{\text{Distance}} = \sqrt {{{\left( {{x_2} - {x_1}} \right)}^2} + {{\left( {{y_2} - {y_1}} \right)}^2}} }[/tex]
Given:
The line is [tex]x + y = 4.[/tex]
Explanation:
The coordinate of the origin is [tex]\left( {0,0} \right).[/tex]
The first point is [tex]\left( {x,y} \right)[/tex] and the second point is [tex]\left( {0,0} \right).[/tex]
The distance between the two points can be calculated as follows,
[tex]\begin{aligned}{\text{Distance}}&= \sqrt {{{\left( {x - 0} \right)}^2} + {{\left( {y - 0} \right)}^2}}\\&= \sqrt {{x^2} + {{\left( {4 - x} \right)}^2}}\\&= \sqrt {{x^2} + {x^2} - 8x + 16}\\&= \sqrt {2{x^2} - 8x + 16}\\\end{aligned}[/tex]
Differentiate the above equation with respect to [tex]x[/tex].
Substitute the first derivative equal to zero.
[tex]\begin{aligned}\frac{d}{{dx}}\left( {{\text{Distance}}} \right) &= 0\\\frac{{\left( {2x - 4} \right)}}{{\sqrt {2{x^2} - 8x + 16} }} &= 0\\2x - 4 &= 0\\2x &= 4\\x&= 2\\\end{aligned}[/tex]
Substitute [tex]x = 2[/tex] in equation [tex]x + y = 4[/tex] to obtain the value of [tex]y[/tex].
[tex]\begin{aligned}2 + y &= 4\\y&= 4 - 2\\y&= 2\\\end{aligned}[/tex]
The point is [tex]\left( {2,2} \right).[/tex]
The shortest distance can be obtained as follows,
[tex]\begin{aligned}{\text{Distance}} &= \sqrt {{2^2} + {2^2}}\\&= \sqrt {4 + 4}\\&= 2\sqrt 2\\\end{aligned}[/tex]
The shortest distance [tex]x + y = 4[/tex] that is closest to the origin is [tex]\boxed{2\sqrt 2 {\text{ units}}}.[/tex]
Learn more:
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Application of derivatives
Keywords: Derivative, shortest distance, curve, origin, attains, maximum, value of x, function, differentiate, minimum value, closest point, line, y+x = 4.
Given the function f(x) = −2x + 8, find x if f(x) = 14 ...?
Is a line is represented by a straight narrow segment with arrow signs at the end? ...?
Is 4√5 rational or irrational
Which coordinate pair is in the solution set for y < 1 − 6x?
To find the coordinate pair in the solution set for y < 1 - 6x, substitute x and y values into the inequality and check if it is satisfied.
Explanation:The question asks for a coordinate pair that is in the solution set for the inequality y < 1 - 6x. To find the solution set, we need to find the values of x and y that satisfy the inequality. Let's pick a few coordinate pairs and substitute the values into the inequality to see if they satisfy it.
For example, let's try the coordinate pair (1, 0). Substituting x = 1 and y = 0 into the inequality, we get 0 < 1 - 6(1), which simplifies to 0 < 1 - 6, and further simplifies to 0 < -5. Since this statement is false, the coordinate pair (1, 0) is not in the solution set.
Similarly, we can try other coordinate pairs and substitute the values into the inequality to check if they satisfy it. The coordinate pair that satisfies the inequality will be in the solution set.
The ratio of peaches to plums is 3:8. If there are 99 fruits how many plums are there?
Three largest earthquakes ever recorded took place in chile, russia, and alaska. they measured 9 1/10, 9.5, & 9 1/5 on the richter scale. the largest earthquake was in chile. the earthquake in russia was smaller than the one alaska. what did the three earthquakes measure on the richter scale
Final answer:
The largest earthquakes recorded in Chile, Russia, and Alaska measured 9.5, 9.1, and 9.2 on the Richter scale respectively, with Chile's earthquake being the largest and Russia's the smallest.
Explanation:
The three largest earthquakes ever recorded took place in Chile, Russia, and Alaska. Based on the information provided, the earthquake in Chile was the largest, measuring 9.5 on the Richter scale. The earthquake in Alaska, being larger than the one in Russia but not as large as the one in Chile, would measure 9 1/5, or 9.2, on the Richter scale. Lastly, the earthquake in Russia was the smallest of the three, measuring 9 1/10, or 9.1, on the Richter scale.
These seismic events, marked by their enormity on the Richter scale, underscore the geological dynamics in different regions of the world. The specific magnitudes assigned to each earthquake provide a quantitative measure of their intensity, offering valuable insights for understanding and preparing for such natural phenomena.
Casey is making a flower arrangement with roses(r) and carnations(c). The cost of each rose is $0.50 and the cost of each carnation is $0.10. The arrangement has a total of 80 flowers and the flower cost was $20. How many of each flower did Casey put in her arrangement?
Boys and girls, we love to teach. The students love it. Teaches a student is to be grateful (pleasing). We love to teach the disciples of the history of the Roman letter ("by means of Literature", abl. Of means). In the game a lot (many) are students. * * To mature to learn the use of Latin in the disciples
What conversion factor can be used to convert the number of blocks to the weight of the blocks, in pounds?
The correct answer is:
The conversion factor would be the number of blocks multiplied by the weight of 1 block.
Explanation:
Consider the following example:
Suppose 1 block weighs 3 pounds. If there are 15 blocks, to find the total weight of the blocks, we multiply 3 by 15: 3(15) = 45. This means the total weight would be 45 pounds.
For any given number of blocks and any given weight of 1 block, to find the total weight of the blocks we would multiply the number of blocks by the weight of 1 block.
How do i convert 16/5 to a mixed number?
Answer: 3 and 1/5
Step-by-step explanation: To write an improper fraction as a mixed number, divide the denominator into the numerator.
[tex]\sqrt[5]{16}[/tex] = 3 with a remainder of 1
Therefore, 14/5 can be written as the mixed number 3 and 1/5.
Which is a true statement about any two chords that are the same distance from the center of a circle?
A. They are parallel.
B. They are perpendicular.
C. They are congruent.
D. They are similar.
Answer C. If two chords are the exact same distance from the center of the circle then those two chords must be congruent.
in a carnival drawing,a green ticket wins $1,a yellow ticket wins $5,and a blue ticket wins $10. There are 100 green tickets, 25 yellow tickets and 5 blue tickets. in simplest form, what are the odds in favor of winning $5 or more?
What is 8.5 divided by 520?
200x50 mathematics problem
Answer:
10,000
Step-by-step explanation:
2 x 5= 10 then add 3 more zeros
Which of the following has the most inertia, four kilograms of iron or four kilograms of cork? ...?
Answer:
Both will have same inertia.
Step-by-step explanation:
The inertia of a body is defined as its property to oppose the state of rest or uniform motion. In this question, we have to write out of four kilograms of iron and four kilograms of cork which will have maximum inertia. Inertia of a body is also equal to measure of its mass.
In this case, the masses of both iron and cork are same i.e. 4 kg. So, it is clear that the inertia of both iron and cork are same due to their same masses.
4/9 multiplied by 1/8
List 5 numbers with 6 in the tens place
The list of 5 numbers with 6 in the tens place are [tex]\boxed{265,{\text{ 67, 163, 969, 2165, 31462}}}.[/tex]
Further explanation:
Explanation:
The whole numbers is the series of numbers that starts from zero.
The natural numbers are those numbers that start from one.
The place values are only natural numbers.
The base ten systems represent the position of a place value.
After decimal the first place is the tenth place, the second place is the hundredth and the third place is the thousandth.
Consider a number as [tex]265.[/tex]
Here, number 5 is on the ones place, number 6 is on the tens place and 2 is on the hundreds place.
Hence, the list of 5 numbers with 6 in the tens place are [tex]\boxed{265,{\text{ 67, 163, 969, 2165, 31462}}}.[/tex]
Learn more:
Learn more about inverse of the functionhttps://brainly.com/question/1632445. Learn more about equation of circle brainly.com/question/1506955. Learn more about range and domain of the function https://brainly.com/question/3412497
Answer details:
Grade: Middle School
Subject: Mathematics
Chapter: Decimals
Keywords: list of 5 numbers, numbers, hundreds place, tens place, whole number, decimal, compare, contrast, methods, base ten system, place value, decimal expansion, natural numbers, real numbers.
Final answer:
Five numbers with 6 in the tens place are 60, 61, 62, 63, and 64. Each has the digit 6 immediately to the left of the ones place.
Explanation:
To list 5 numbers with 6 in the tens place means that each number must have its second digit from the right as a 6. Here are five numbers that meet this criterion:
60
61
62
63
64
Each of these numbers has a 6 in the tens place, which we can confirm by looking at the digit immediately to the left of the ones place.
What is 3.99999..... converted into a fraction?
Write unit rate for 1.98 for 6
Multivariable: Assume there is an opaque ball of radius 1 centered at the origin.
Suppose that you stand at the point (2,3,0) and look in the direction of a point that is not visible because it is behind the ball. You will then be looking at a point on the sphere.
Find the point on the sphere at which you look if you are looking in the direction of (−2,−3,2).
To find the point on the sphere at which you are looking in the direction of (-2, -3, 2), we need to find the intersection of the line passing through (2, 3, 0) and the direction (-2, -3, 2) with the sphere of radius 1 centered at the origin. By substituting the parametric equations of the line into the equation of the sphere and solving for t, we can find the two points on the sphere where you will be looking.
Explanation:To find the point on the sphere at which you look when you are looking in the direction of (-2, -3, 2), we need to find the intersection of the line passing through (2, 3, 0) and the direction (-2, -3, 2) with the sphere of radius 1 centered at the origin.
The equation of the line passing through (2, 3, 0) and in the direction (-2, -3, 2) can be expressed as:
x = 2 - 2t
y = 3 - 3t
z = 2t
Substitute these equations into the equation of the sphere, we get:
(2 - 2t)2 + (3 - 3t)2 + (2t)2 = 1
Simplifying the equation:
17t2 - 14t + 2 = 0
Using the quadratic formula:
t = (-b ± √(b2 - 4ac))/(2a)
Substituting the values, we get two possible values of t: t ≈ 0.23 and t ≈ 0.1.
Substituting these values back into the parametric equations of the line:
For t ≈ 0.23:
x ≈ 1.54
y ≈ 1.31
z ≈ 0.46
For t ≈ 0.1:
x ≈ 1.8
y ≈ 2.1
z ≈ 0.2
So, the points on the sphere at which you look when you are looking in the direction of (-2, -3, 2) are approximately (1.54, 1.31, 0.46) and (1.8, 2.1, 0.2).
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Which expression has a value of 23?
A.
7 – (–16)
B.
–3 – 20
C.
10 – 13
D.
–18 – (–5)
The product of two rational numbers is _________rational.
sometimes
always
never
Which expression is equaivalent to mn+z
nm+n
z+mz
mz+n
z+nm
Answer:
D. z+nm
Step-by-step explanation:
Equaivalent to mn+z: Just switch the letters around and you get z+nm
How do you write 317 in words?
1. A circle has a center at (3,5). The point (3,8) is on the circle. What is the circumference of the to the nearest tenth of a unit?
A. 9.4 units
B. 18.8 units
C. 28.3 units
D. 56.5 units
2. A triangle has a perimeter of exactly 24 units. Which of the following could be the vertices of the triangle?
A. (-1 ,3 ), (2,-1), (-1,-1)
B. (6,0), (6,7), (0,7)
C. (-1,-1), (-6,-13), (-9,-9)
D.(-3,-4) (-3,4), (3,4)
3. A circle has an area of approximately 78.5 square units. If the center of the circle is at (2,4). Which of the following points is on the circle?
A. (-6,4)
B. (2,-1)
C.(-4,-4)
D. (2,-9)
4. The end point of a diameter of a circle are A (2,1) and B (5,5). Find the area of the circle in terms of pi.
A. 25/4 pi square units
B. 10 pi square units
C 25 pi square units
D. 5 pi units
Answer:
1. B
2. D
3. B
4. A
Step-by-step explanation:
Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate. If there is no solution, enter NO SOLUTION.)
2 sin^2 θ − sin θ − 1 = 0 ...?
Answer: 30°, 300° and 330°
Step-by-step explanation:
This is a quadratic equation in trigonometry format.
Given 2 sin^2 θ − sin θ − 1 = 0
Let a constant 'k' = sin θ...(1)
The equation becomes
2k²-k-1 =0
Factorizing the equation completely we have,
(2k²-2k)+(k-1) = 0
2k(k-1)+1(k-1)=0
(2k+1)(k-1)=0
2k+1=0 and k-1=0
2k = -1 and k=1
k=-1/2 and 1
Substituting the value of k into equation 1 to get θ
sin θ = 1
θ = arcsin1
θ = 90°
Similarly
sin θ = -1/2
θ = arcsin-1/2
θ = -30°
This angle is negative and falls in the 3rd and 4th quadrant
In the third quadrant, θ = 270 +30 = 300° and
in the 4th quadrant, θ = 360 - 30° = 330°
Therefore the values of θ are 30°, 300° and 330°
I hope you find this helpful?
Final answer:
The trigonometric equation is transformed into a quadratic equation by substituting sin θ with x. Then, the quadratic formula is applied to find x, which is then used to find the solutions for θ in radians, considering the periodic nature of the sine function. The solutions are then verified.
Explanation:
To solve the trigonometric equation 2 sin^2 θ − sin θ − 1 = 0, treat it as a quadratic equation by setting x = sin θ. The reformed equation is 2x^2 - x - 1 = 0. Now, factor this equation or use the quadratic formula to find the values of x, and subsequently the values of θ.
Using the quadratic formula:
x = [-(-1) ± √((-1)^2 - 4(2)(-1))]/(2*2)x = (1 ± √(1 + 8))/4x = (1 ± √9)/4x = (1 ± 3)/4Therefore, the solutions for x are:
x = 1x = -0.5Convert these back into solutions for θ by finding θ such that sin θ = x. Use units of radians for angles and remember to consider the periodic nature of the sine function.
Answer:
For x = 1: θ = ½π + 2πkFor x = -0.5: θ = −⅓π + 2πk or θ = −&frac43;π + 2πk, for all integers k.Check if the answers are reasonable by substituting back into the original equation and verifying that they produce true statements.
Which of the following tables shows the correct steps to transform x^2 + 10x + 24 = 0 into the form (x - p)^2 = q? [p and q are integers]
Answer: D
Step-by-step explanation:
The correct transformation of the equation is achieved by completing the square to obtain the form (x + 5)^2 = 1, which gives the values of p = -5 and q = 1.
The transformation of the quadratic equation x^2 + 10x + 24 = 0 into the form (x - p)^2 = q involves completing the square. To complete the square, one must find a number that, when added to x^2 + 10x, completes a perfect square trinomial. This number is calculated by taking half of the x-coefficient (b/2), squaring it, and adding it to both sides of the equation. In this case, (10/2)^2 = 25. We then have x^2 + 10x + 25 on the left and 25 - 24 on the right, which simplifies to (x + 5)^2 = 1. The values of p and q are thus -5 and 1, respectively.