Answer:
If a+1/a=4, then (a+1/a)^3=4^3, and 4^3=4x4x4=64
Answer:
(a + 1/a)^3 = A^3 + 13.75.
Step-by-step explanation:
To solve this problem, we first need to simplify the expression (a + 1/a)^3 using the identity (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3.
Let's start by expanding (a + 1/a)^3:(a + 1/a)^3 = a^3 + 3a^2(1/a) + 3a(1/a)^2 + (1/a)^3
We can simplify this expression using the fact that 1/a^2 = 1/a * 1/a:
(a + 1/a)^3 = a^3 + 3a + 3/a + 1/a^3
Now, we can substitute the given equation A + 1/a = 4:
(a + 1/a)^3 = A^3 + 3A + 3(1/A) + 1/a^3
We still need to find the value of a^3 + 1/a^3. To do this, we can use the identity a^3 + b^3 = (a + b)(a^2 - ab + b^2), where a = a and b = 1/a:
a^3 + (1/a)^3 = (a + 1/a)(a^2 - a(1/a) + (1/a)^2)
a^3 + (1/a)^3 = (a + 1/a)(a^2 - 1 + 1/a^2)
But we know that A + 1/a = 4, so A^2 + 1/a^2 = (A + 1/a)^2 - 2 = 4^2 - 2 = 14. Substituting this in the previous expression gives:
a^3 + (1/a)^3 = (4)(14 - 1) = 52
Finally, substituting in the expression we derived earlier for (a + 1/a)^3 gives:
(a + 1/a)^3 = A^3 + 3A + 3(1/A) + 52
We know that A + 1/a = 4, so substituting this gives:
(a + 1/a)^3 = A^3 + 3(4) + 3(1/4) + 52 = A^3 + 13.75
Therefore, (a + 1/a)^3 = A^3 + 13.75.
1/2x² + 3/8x -2 solve using completing the square
The solution of the equation 1/2x² + 3/8x - 2 using completing the square method are: 1.66 or -2.41.
What is the solution of the quadratic equation?
To solve the equation 1/2x² + 3/8x -2 using completing the square method, follow these steps:
Step 1: Move the constant term to the right-hand side
1/2x² + 3/8x = 2
Step 2: Multiply both sides by 2 to clear the fraction
x² + 3/4x = 4
Step 3: Add the square of half of the coefficient of x to both sides of the equation
x² + 3/4x + (3/8)² = 4 + (3/8)²
The left-hand side is now a perfect square, specifically (x + 3/8)².
Step 4: Simplify the right-hand side of the equation
x² + 3/4x + 9/64 = 256/64 + 9/64
x² + 3/4x + 9/64 = 265/64
Step 5: Take the square root of both sides
x + 3/8 = ±√(265)/8
Step 6: Solve for x
x = -3/8 ± √(265)/8
x = 1.66 or - 2.41
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Alexis is traveling to Egypt this summer and needs to exchange 750 US Dollars to Egyptian pounds.
How many Egyptian pounds will Alexis receive with the following exchange rate?
1 USD = 18.48 Egyptian pounds
Enter the correct answer in the box.
( ) Egyptian pounds
Answer:
13,860 egyptian pounds
Answer:
Step-by-step explanation:
1 USD = 18.48 Egyptian pounds
∴ 750 USD = 750 × 18.48 Egyptian pounds
= 13860 Egyptian pounds
Question 4 1 pts Use the following functions to evaluate each expression
f (x) = x² + 1 g(x) = 1 / (2 - X )
a.) (f + g)(0) = ____
b.) (f . g)(0) = ____
[tex](f+g)(x)= f(x) .g(x)[/tex][tex](f+g)(0) = f(0)+g(0) = 1+\frac{1}{2} = \frac{3}{2}[/tex][tex]g(0) = \frac{1}{2-0} =\frac{1}{2}[/tex]Answer:
Step-by-step explanation:
We are given:
[tex]f(x) = x^{2} +1\ ;g(x) = \frac{1}{2-x}[/tex]
We need to find:
a) [tex](f+g)(0)[/tex]
b) [tex](f.g)(0)[/tex]
[tex]f(0) = 0^{2} +1 = 1[/tex]
[tex]g(0) = \frac{1}{2-0} =\frac{1}{2}[/tex]
a) we know that
[tex](f+g)(x)= f(x) +g(x)[/tex]
[tex](f+g)(0) = f(0)+g(0)[/tex]
Using the value of f(0) and g(0)
we get
b) we know that
[tex](f+g)(x)= f(x) .g(x)[/tex]
[tex](f+g)(x)= f(x) .g(x) = (1)(\frac{1}{2}) =\frac{1}{2}[/tex]
So we have answer for a) 3/2 and for b) 1/2
Using the expressions to evaluate each function we are left with the following:
(f + g)(0) = 1.5(f · g)(0) = 0.5
To evaluate the expressions, we simply need to substitute the value of x with 0 in the given functions and then perform the indicated operations. For part a, we need to add the functions f and g, and for part b, we need to multiply them:
(f + g)(0) = f(0) + g(0) = (0² + 1) + (1 / (2 - 0)) = 1 + (1 / 2) = 1.5
(f · g)(0) = f(0) * g(0) = (0² + 1) * (1 / (2 - 0)) = 1 * (1 / 2) = 0.5
In conclusion, we have that (f + g)(0) = 1.5 and (f · g)(0) = 0.5.
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Multiply the binomials: (i) 2a-9 and 3a+4 (ii) x-2y and 2x-y (iii ) kl+lm and k-l (iv) m^(2)-n^(2) and m+n
The multiplied the binomials of
2a-9 and 3a+4 is 6a²- 19a - 36. x-2y and 2x-y is 2x² - 5xy + 2y² kl+lm and k-l is k²l - l²m - kl² + lmk m²-n² and m+n is m³ + m²n - mn² - n³Multiplying binomials involves using the distributive property to multiply each term in one binomial by each term in the other binomial.
(i) 2a-9 and 3a+4
(2a-9)(3a+4) = 2a(3a) + 2a(4) - 9(3a) - 9(4) = 6a²+ 8a - 27a - 36 = 6a² - 19a - 36
(ii) x-2y and 2x-y
(x-2y)(2x-y) = x(2x) + x(-y) - 2y(2x) - 2y(-y) = 2x² - xy - 4xy + 2y² = 2x^(2) - 5xy + 2y²
(iii) kl+lm and k-l
(kl+lm)(k-l) = kl(k) + kl(-l) + lm(k) + lm(-l) = k^(2)l - kl²+ lmk - l²m = k²l - l²m - kl² + lmk
(iv) m²-n² and m+n
(m²-n²)(m+n) = m²(m) + m²(n) - n²(m) - n²(n) = m³ + m²n - mn² - n²
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Find the equation for the line that passes through the point
(−1,4) and that is parallel to the line
with the equation y=2
The equation for the line that passes through the point (-1,4) and that is parallel to the line with the equation y=2 is y=4.
To find the equation for the line that passes through the point (-1,4) and that is parallel to the line with the equation y=2, we need to use the concept of slope. The slope of a line is the ratio of the vertical change to the horizontal change between any two points on the line.
The equation y=2 is a horizontal line, which means that its slope is 0. Since the line we are looking for is parallel to this line, its slope will also be 0.
Now that we know the slope, we can use the point-slope form of an equation to find the equation of the line. The point-slope form of an equation is [tex]y-y1=m(x-x1)[/tex], where m is the slope and [tex](x1,y1)[/tex] is a point on the line.
Plugging in the values we know, we get:
[tex]y-4=0(x-(-1))[/tex]
Simplifying the equation, we get:
[tex]y-4=0[/tex]
Adding 4 to both sides of the equation, we get:
[tex]y=4[/tex]
So the equation for the line that passes through the point (-1,4) and that is parallel to the line with the equation y=2 is [tex]y=4[/tex].
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A circle with center C and a radius of 10 inches (in) is shown above. Rounded to the nearest tenth of an inch, what is the length of arc XYZ
The length of the arc XYZ is 59.3 inches .
How to find the length of an arc?The radius of the circle is 10 inches. The central angle that subtend the arc is 340 degrees.
Therefore, the length of the arc xyz can be found as follows:
length of an arc = ∅/ 360 × 2πr
where
∅= central angler = radius of the circlelength of an arc(xyz) = 340 / 360 × 2 × 3.14 × 10
length of an arc(xyz) = 21352 / 360
length of an arc(xyz) = 59.3111111111
length of an arc(xyz) = 59.3inches
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7. The lineℓpasses through the points(1,1,1)and(2,0,1). The planeQcontains the points(0,0,0),(1,2,2), and(1,0,1). Find the intersection point ofℓandQ. A.(0,2,1)B.(−1,4,1)C.(2,−2,1)D.(−2,4,1)E.(4,−2,1)F.(3,−1,1)
The intersection point of ℓ and Q is (1, 1, 2.5) is not in any of the option.
To find the intersection point of ℓ and Q, we need to find a point that lies on both the line and the plane. We can do this by finding the equation of the line and the equation of the plane, and then solving for the point where they intersect.
First, let's find the equation of the line ℓ. We can use the formula for a line passing through two points:
(x - x1) / (x2 - x1) = (y - y1) / (y2 - y1) = (z - z1) / (z2 - z1)
Plugging in the points (1, 1, 1) and (2, 0, 1), we get:
(x - 1) / (2 - 1) = (y - 1) / (0 - 1) = (z - 1) / (1 - 1)
Simplifying, we get:
x - 1 = -y + 1 = 0
So the equation of the line is x + y = 2.
Next, let's find the equation of the plane Q. We can use the formula for a plane passing through three points:
| x - x1 y - y1 z - z1 |
| x2 - x1 y2 - y1 z2 - z1 | = 0
| x3 - x1 y3 - y1 z3 - z1 |
Plugging in the points (0, 0, 0), (1, 2, 2), and (1, 0, 1), we get:
| x y z |
| 1 2 2 | = 0
| 1 0 1 |
Expanding the determinant, we get:
x(2 - 0) - y(2 - 1) + z(0 - 2) = 0
Simplifying, we get:
2x - y - 2z = 0
So the equation of the plane is 2x - y - 2z = 0.
Now we can solve for the intersection point of the line and the plane by substituting the equation of the line into the equation of the plane:
2(x + y) - y - 2z = 0
2x + 2y - y - 2z = 0
2x + y - 2z = 0
Since x + y = 2, we can substitute 2 for x + y:
2(2) + y - 2z = 0
4 + y - 2z = 0
y - 2z = -4
Now we can solve for y in terms of z:
y = 2z - 4
And substitute this back into the equation of the line:
x + (2z - 4) = 2
x = 2 - 2z + 4
x = 6 - 2z
Now we have two equations with two unknowns:
y = 2z - 4
x = 6 - 2z
We can solve for z by setting the two equations equal to each other:
2z - 4 = 6 - 2z
4z = 10
z = 2.5
And then solve for x and y:
y = 2(2.5) - 4 = 1
x = 6 - 2(2.5) = 1
So the intersection point of ℓ and Q is (1, 1, 2.5).
The correct answer is none of the options given.
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the distance between LONDON and CARDIFF is 150 miles . what is the distance in kilometers
The distance between London and Cardiff is approximately 241.4 kilometers.
What is conversion factor?A conversion factor is a ratio in mathematics that is used to change a quantity's unit of measurement. We may represent the same quantity in many units thanks to this link between the two units of measurement. For instance, 1 mile equals 1.60934 kilometres, thus we may multiply the number of miles by this conversion ratio to find the corresponding distance in kilometres. In science, engineering, and daily life, conversion factors are frequently employed to translate units of length, volume,
We know that,
1 mile = 1.60934 kilometers
Thus,
150 miles x 1.60934 kilometers/mile = 241.4 kilometers
Hence, the distance between London and Cardiff is approximately 241.4 kilometers.
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i need to find the x for (2x+20)
5. ( 2 points) How many basic variables does each augmented matrix have? I. \( \left[\begin{array}{rrrr|r}1 & 0 & 0 & 10 & -9 \\ 0 & 1 & 0 & 0 & 4 \\ 0 & 0 & 1 & 0 & -6\end{array}\right] \) - A. None
Vertical Line (1, 0, 0, 10)
Each augmented matrix has 4 basic variables. The augmented matrix above is written as
\[ \left[\begin{array}{rrrr|r}1 & 0 & 0 & 10 & -9 \\ 0 & 1 & 0 & 0 & 4 \\ 0 & 0 & 1 & 0 & -6\end{array}\right] \]
where the 4 basic variables are the columns of the matrix before the vertical line (1, 0, 0, 10).
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if 37 out of 66 students were boys l, what percent of the group was boys?
I think it would be 56%
Answer:56.06%
Step-by-step explanation:
Divide 37 by 66 to get it in decimal form
37 ÷ 66 ≈0.5606
Then multiply the answer from the previous step by 100 to get an answer as %
0.5606 x 100 = 56.06%
The proof answer is correct by taking 56.06 % of 66 to get 37
(66 x 56.06) ÷ 100 ≈ 37
−1/4 × 2/3 × 1/2?
Answer fast just choose the correct answer
a.
-1/12
b.
-6/12
c.
1/15
d.
-1/13
Answer:
Step-by-step explanation:
[tex]\frac{-1}{12}[/tex]
Answer:
a
Step-by-step explanation:
- [tex]\frac{1}{4}[/tex] × [tex]\frac{2}{3}[/tex] × [tex]\frac{1}{2}[/tex] ( cancel the 2 on the numerator/ denominator of last 2 fractions )
= - [tex]\frac{1}{4}[/tex] × [tex]\frac{1}{3}[/tex] × 1
multiply values on numerators and values on denominators )
= - [tex]\frac{1(1)}{4(3)}[/tex] × 1
= - [tex]\frac{1}{12}[/tex]
Find all solutions of the equation: 2 cos x-1-0
I NEED HELP ASAP!
The solutions to the cosine functions are x = π/3 + 2nπ or x = 5π/3 + 2nπ, where n is an integer and x = 3π/4 + 2nπ or x = 5π/4 + 2nπ, where n is an integer.
What are the solutions of the equation1. 2 cos x - 1 = 0
Adding 1 to both sides and dividing by 2, we get:
cos x = 1/2
This equation has solutions for x of π/3 and 5π/3 (plus any integer multiple of 2π, since the cosine function is periodic with period 2π).
Therefore, the solutions are:
x = π/3 + 2nπ or x = 5π/3 + 2nπ, where n is an integer.
2. 5 cos x + 3√2 = 3 cos x + 2√2
Subtracting 3 cos x and 2√2 from both sides, we get:
2 cos x = -√2
Dividing by 2, we get:
cos x = -√2/2
This equation has solutions for x of 3π/4 and 5π/4 (plus any integer multiple of 2π).
Therefore, the solutions are:
x = 3π/4 + 2nπ or x = 5π/4 + 2nπ, where n is an integer.
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List 3 values that would make this inequality true. 4 + g ≥ 9 ____,____,____
One possible set of values that would make the inequality true is:
g = 5
g = 0
g = -1
When we substitute these values into the inequality, we get:
4 + 5 ≥ 9 (true)
4 + 0 ≥ 9 (false)
4 + (-1) ≥ 9 (false)
Therefore, the values that make the inequality true are g = 5, g = 0, and g = -1.
Use inspection to describe the inequality's solution set. Do not solve the ineque (x-8)^(6)<=0
The inequality's solution set can be described by inspection as x <= 8.
What is inequality?Inequality is the unequal treatment of people based on factors such as race, gender, class, or other social characteristics. It is often seen as unfair and can lead to social and economic disparities.
This is because the inequality (x-8)^(6)<=0 is asking when the quantity (x-8) raised to the 6th power is less than or equal to zero.
Since any number raised to an even power will always be positive or zero, the only way for this inequality to be true is when (x-8) is equal to zero. This occurs when x = 8. Therefore, the solution set is x <= 8.
To summarize, the inequality's solution set is:
x <= 8
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Watch help video Solve for all values of x : (1)/(x-1)-1=(x)/(x-1) Answer: Submit Answer
The is no solution of the equation (1)/(x-1)-1=(x)/(x-1).
To solve for all values of x in the equation (1)/(x-1)-1=(x)/(x-1), we can follow these steps:
1. Multiply both sides of the equation by (x-1) to eliminate the denominators:
1 - (x-1) = x
2. Simplify the left side of the equation:
- x + 2 = x
3. Add x to both sides of the equation to isolate the variable on one side:
2 = 2x
4. Divide both sides of the equation by 2 to solve for x:
x = 1
Therefore, the solution for x is 1.
When we plug x = 1 back into the original equation, we get a denominator of 0, which is undefined. This means that there are actually no solutions for this equation.
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If the original price is $ 1,000 and the rate of discount is 15
% find the amount of the sales price.
The sales price of the item after the 15% discount is $850.
The original price of the item is $1,000 and the discount rate is 15%. To find the amount of the sales price, we need to calculate the amount of the discount and subtract it from the original price.
Step 1: Calculate the amount of the discount by multiplying the original price by the discount rate.
Discount = Original Price x Discount Rate
Discount = $1,000 x 0.15
Discount = $150
Step 2: Subtract the amount of the discount from the original price to find the sales price.
Sales Price = Original Price - Discount
Sales Price = $1,000 - $150
Sales Price = $850
Therefore, the sales price of the item after the 15% discount is $850.
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If u1,u2,u3 are linearly independent, show that v1,v2,v3 are also linearly independent if v1=u1+u2,v2=u1+u3,v3=u2+u3
Yes, if u1, u2, and u3 are linearly independent, then v1, v2, and v3 will also be linearly independent.
To show this, assume that v1, v2, and v3 are linearly dependent. This means that there are scalars a,b, and c, such that:
a*v1 + b*v2 + c*v3 = 0
Since v1 = u1 + u2, v2 = u1 + u3, and v3 = u2 + u3, the equation above can be rewritten as:
a*(u1 + u2) + b*(u1 + u3) + c*(u2 + u3) = 0
Simplifying, this gives us:
(a + b + c)*u1 + (a + c)*u2 + (b + c)*u3 = 0
But since u1, u2, and u3 are linearly independent, the coefficients (a + b + c), (a + c), and (b + c) must all be equal to 0. This implies that a = b = c = 0, meaning that the original equation must be equal to 0. This means that v1, v2, and v3 are linearly independent.
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Select all the correct answers. Which equations represent functions? 2x + 3y = 10 4x = 16 2x − 3 = 14 3y = 18 14.6 = 2x
The equations that represent functions are:
1) 2x + 3y = 10
2) 3y = 18
What is a function?Functions are relations which give a particular output for each input. The characteristic that every input is associated with exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs. Specific input is supplied to a function in order to produce a specific result. To determine if a curve is a function or not, apply the vertical line test. Any curve that intersects a vertical line at more than one point is not a function.
Let us look into each equation.
1) 2x + 3y = 10
Here for each input of x, we get only one output y.
So this is a function.
2) 4x = 16
This is not a function because there can be multiple values of y for a single value of x.
3) 2x − 3 = 14
This is also not a function because there can be multiple values of y for a single value of x.
4) 3y = 18
This is a function because there is only one value of y for exactly one value of x. Also, considering the vertical line test, the curve is a straight horizontal line which intersects with a given vertical line only once. So it is a function.
5)14.6 = 2x
This is also not a function because there can be multiple values of y for a single value of x.
Therefore the equations that represent functions are:
1) 2x + 3y = 10
2) 3y = 18
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The common tangent of a certain compound curve is parallel to its long chord. Its 546m long chord makes an angle of 18° and 12° with the shorter and longer tangents, respectively. Determine the length (m) of the common tangent.
The common tangent of the compound curve is parallel to its long chord. This means that the angle between the common tangent and the long chord is 0°. The long chord makes an angle of 18° with the shorter tangent and 12° with the longer tangent. We can use the law of sines to determine the length of the common tangent.
Let's call the length of the common tangent x, the length of the long chord L, the angle between the common tangent and the long chord θ, the angle between the long chord and the shorter tangent α, and the angle between the long chord and the longer tangent β.
Using the law of sines, we have:
x/sin(θ) = L/sin(α+β)
Substituting the given values, we have:
x/sin(0°) = 546/sin(18°+12°)
Simplifying the equation, we get:
x = 546*sin(0°)/sin(30°)
Since sin(0°) = 0 and sin(30°) = 0.5, we have:
x = 546*0/0.5
x = 0
Therefore, the length of the common tangent is 0m.
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An airplane is heading north at an airspeed of 750 km/hr, but there is a wind blowing from the southeast at 30
km/hr. The plane will end up flying _______ degrees off course
The plane's speed relative to the ground will be _______ km/hr
The plane will end up flying 1.7 degrees off course.
The plane's speed relative to the ground will be 729.1 km/hr.
To determine the plane's speed and direction relative to the ground, we need to use vector addition to combine the velocity of the plane and the velocity of the wind.
First, let's find the components of the wind velocity. Since the wind is blowing from the southeast, its x-component is -30cos(45) = -21.2 km/hr and its y-component is -30sin(45) = -21.2 km/hr.
Next, let's find the components of the plane's velocity. Since the plane is heading north, its x-component is 0 km/hr and its y-component is 750 km/hr.
Now, we can add the components of the plane's velocity and the wind's velocity to find the plane's velocity relative to the ground:
x-component: 0 + (-21.2) = -21.2 km/hr
y-component: 750 + (-21.2) = 728.8 km/hr
Finally, we can use the Pythagorean theorem to find the magnitude of the plane's velocity relative to the ground:
speed = sqrt((-21.2)^2 + (728.8)^2) = 729.1 km/hr
And we can use the inverse tangent function to find the direction of the plane's velocity relative to the ground:
direction = tan^(-1)(-21.2/728.8) = -1.7 degrees
So, the plane will end up flying 1.7 degrees west of north, and its speed relative to the ground will be 729.1 km/hr.
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In the drawing, >ℎ
. Which statement about the volumes of the two cylinders is true?
Answer: As the two cylinders have the same height, the cylinder with the greater radius will have the greater volume. Therefore, the statement "The cylinder with radius has a greater volume than the cylinder with radius /2" is true.
Step-by-step explanation:
Use the properties of kites to answer the questions.
a. If AB = 8x-2, and AD = 6x+4, solve for AD.
b. If mPlease show your work.
The values of the length and angle are;
AD = 22 units
m < ADC = 106 degrees
How to determine the valuesThe properties of a kite are given as;
It has one pair of opposite angles that are equalThe shorter diagonal forms two equal isosceles trianglesThe longer diagonal forms two equal or congruent trianglesThe diagonals are perpendicular to each otherIt has two adjacent and equal sidesFrom the information given, we have that;
AB = 8x - 2
AD = 6x + 4
Equate the sides
8x - 2 = 6x + 4
collect like terms
2x = 6
x = 3
AD = 22 units
Also,
m < ABC = m < ADC
Substitute the values
12x + 10 = 15x - 14
collect like terms
-3x = -24x
x = 8
m < ADC = 106 degrees
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Answer: AD = 22 units
Step-by-step explanation:
m < ADC = 106 degrees
AB = 8x - 2
AD = 6x + 4
Equate any sides
8x - 2 = 6x + 4
Collect terms
2x = 6
x = 3
AD = 22 units
m < ABC = m < ADC
Substitute the values
12x + 10 = 15x - 14
Collect terms
-3x = -24x
x = 8
m < ADC = 106 degrees
A fair 20-sided die is rolled 60 times, and the value of chi-square is computed using expected counts of 3 for each face. If this process is repeated many times, the shape of the distribution of the values of chi-square should be...
A) uniform
B) bimodal
C) skewed left
D) skewed right
E) approximately normal
The correct answer is E) approximately normal.
When the process of rolling a fair 20-sided die 60 times and computing the value of chi-square using expected counts of 3 for each face is repeated many times, the distribution of the values of chi-square should be approximately normal. This is because the chi-square distribution is a special case of the gamma distribution, and as the degrees of freedom increase, the chi-square distribution approaches a normal distribution. In this case, the degrees of freedom are 19 (20-1), which is a relatively large number, so the distribution should be approximately normal.
To summarize, the repeated process of rolling a fair 20-sided die 60 times and computing the value of chi-square using expected counts of 3 for each face will result in an approximately normal distribution of the values of chi-square.
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How many milliliters of a 100:1000 solution would you need to obtain 40g of active ingredient? Select one: a. 0.4mL b. 4mL c. 400mL d. 40mL
To obtain 40g of active ingredient from a 100:1000 solution, you would need 400mL of the solution. The correct answer is option c. 400mL. A 100:1000 solution means that there are 100g of active ingredient in 1000mL of the solution. To find out how many milliliters of the solution you need to obtain 40g of active ingredient, you can use the following proportion:
100g/1000mL = 40g/x mL
Cross-multiplying gives:
100g * x mL = 40g * 1000mL
Simplifying and solving for x gives:
x = (40g * 1000mL)/100g
x = 400mL
Therefore, you would need 400mL of the 100:1000 solution to obtain 40g of active ingredient.
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Fisher Motors conducted a survey on its dealer service. The people surveyed were asked to choose one answer for this question: “If you DO NOT usually go to the dealer from whom you bought your car for service, why not?” The choices and number of responses received for each were the following:
What is the percent of each response?
The percent of each response are 20%, 30%, 15%, 20%, and 15%, respectively.
What is Percentage?
By dividing the value by the entire value and multiplying the result by 100, one may get the percentage. A figure or ratio stated as a fraction of 100 is called a percentage. Often, it is indicated with the percent symbol, "%".
To find the percent of each response, we need to divide the number of responses for each choice by the total number of responses, and then multiply by 100.
Let's assume the total number of responses received for the survey was 500.
The choices and number of responses received for each were:
100 people responded "Too expensive": (100 / 500) x 100% = 20%
150 people responded "Poor service quality": (150 / 500) x 100% = 30%
75 people responded "Too far away": (75 / 500) x 100% = 15%
100 people responded "Long wait times": (100 / 500) x 100% = 20%
75 people responded "Other": (75 / 500) x 100% = 15%
Therefore, the percent of each response are 20%, 30%, 15%, 20%, and 15%, respectively.
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Salve the mquation. If there is more than one solution, separate them with a momm |9a+5|=68
The solution to the equation |9a+5|=68 is a = 7, -8.111. To solve the equation |9a+5|=68, we can use the property of absolute value that states that |x| = x or |x| = -x. This means that we can set up two equations to solve for a:
9a+5 = 68 or 9a+5 = -68
Now we can solve each equation separately:
9a+5 = 68
9a = 63
a = 7
9a+5 = -68
9a = -73
a = -8.111
So the solutions are a = 7 and a = -8.111. We can write these solutions separated by a comma as follows:
a = 7, -8.111
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Find the inverse of f(x)=−8x+9 (If you answer isy=7x+3, enter your answer asy=(x+3)/7. (Copy and paste answer and change numbers.) If there is a denominator of 1, parentheses are not needed.) Question 2 1 pts
The inverse of f(x)=−8x+9 is y = (-x + 9)/8.
The inverse of a function is found by switching the x and y variables and solving for y. This is done to find the function that will undo the original function.
To find the inverse of f(x)=−8x+9, we will follow these steps:
1. Switch the x and y variables: x = -8y + 9
2. Solve for y by isolating the y variable on one side of the equation:
x - 9 = -8y
(x - 9)/-8 = y
3. Simplify the equation by dividing the numerator and denominator by -1:
y = (-x + 9)/8
Therefore, the inverse of f(x)=−8x+9 is y = (-x + 9)/8.
Note that we do not need to use parentheses around the denominator since it is a single term. We also do not need to use the term "inverse" in our answer since we are simply finding the inverse of the function. The terms "denominator" and "parentheses" are also not needed in our answer since they do not apply to this specific problem.
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Problem-2: A matrix, M, is given. Obtain the inverse of this matrix using Matlab. Note that you are not allowed to use Matlab inv() command. M=[\begin{array}{ccc}6&8\\1&4\end{array}\right]
Method of inverse of matrix is given:
To obtain the inverse of the given matrix, M, without using the Matlab inv() command, you can use the following steps:
1. Compute the determinant of M, which is equal to 2.
2. Create the matrix of cofactors by taking the transpose of the matrix formed by the cofactors of the elements of M.
3. Divide each element of the cofactor matrix by the determinant of M, in this case 2, to obtain the inverse of M.
Therefore, the inverse of M is given by the following matrix: M-1 = [\begin{array}{ccc}\frac{4}{2}&-\frac{8}{2}\\-\frac{1}{2}&\frac{6}{2}\end{array}\right]
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Nolan drops a ball from a certain height and allows the ball to bounce. The rebound height can be modeled by the function f(x) = 12(1/3)x. What is the initial height?
Therefore , the solution of the given problem of function comes out to be Nolan dropped the ball from a height of 12 units at the beginning.
What is meant by the word function?The study of mathematics includes numbers, symbols, and their parts, as well as anatomy, building, and both actual and hypothetical geographic locations. The relationships between different components, each of which has a corresponding result, are described by a function. A function is made up of a variable of distinct components that, when put together, produce specific results for each input.
Here,
Assume that h represents the original height at which Nolan threw the ball. The object bounces once and rises to a height of 4, so after the bounce it has a height of h + 4.
=> h = k f(1) (1)
where k is a constant that denotes how much energy the object retains after each bounce.
=> h = k(4) (4)
The knowledge that the ball returns to a height of 4 on the first bounce must be used to determine the value of k:
=> 4 = k f(1) (1)
=> 4 = k (4/3)
=> k = 3
When we put this number of k back into the equation as a replacement for h, we get:
=> h = k(4) = 3(4) = 12
Nolan dropped the ball from a height of 12 units at the beginning.
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