Answer:
0.18
Step-by-step explanation:
1/8 as a decimal is 0.125
1/8 un-simplified is 3/24
0.525 as a fraction is 21/40
So 0.18 is the only one that doesn't belong
0.18 is not equal to 0.525 or 1/8. Therefore Option (A) is the correct answer.
We need to find which of the decimals or fractions are not equal to 0.525 or 1/8.
How do convert decimals to fractions?The decimal numeral system is the standard system for denoting integer and non-integer numbers.
To convert decimal to fraction follow these steps
Step 1: Make a fraction with the decimal number as the numerator (top number) and a 1 as the denominator (bottom number).
Step 2: Remove the decimal places by multiplication. First, count how many places are to the right of the decimal. Next, given that you have x decimal places, multiply the numerator and denominator by \(10^{x}\).
Step 3: Reduce the fraction. Find the Greatest Common Factor (GCF) of the numerator and denominator and divide both numerator and denominator by the GCF.
Step 4: Simplify the remaining fraction to a mixed number fraction if possible.
Now, from option (A)
0.18=18/100=9/25
From option (B)
0.125=125/1000=5/40=1/8
From option (C)
3/24=1/8
From option (D)
21/40=0.525
Therefore, option (A) is the correct answer.
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for f− f − , enter an equation that shows how the anion acts as a base. express your answer as a chemical equation. identify all of the phases in your answer.
The anion acts as a base as shown by the equation below:As a base, an anion is a compound that accepts a hydrogen equation ion (H+),
thus, the equation for f− acting as a base can be given as:F⁻ + H₂O ⟷ OH⁻ + HF (aq)The phases in this equation are aqueous (aq), and as such, can be represented as:F⁻(aq) + H₂O(l) ⟷ OH⁻(aq) + HF(aq)Note that the reversible arrow (↔) indicates that the reaction is not complete and can proceed in either direction, depending on the conditions of the reaction.
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Tierra is making steps for a doll houseshe has cut a piece of wood that measures 1.5 centimeters wide and 30 centimeters longeach step will measure 15 millimeters by 4 millimetersshe will make 21 steps for her doll housewhich are the dimensions of the wood that remains after tierra finishes making the 21 steps?
The dimensions of the wood that remains after Tierra finishes making the 21 steps is 1.185 cm by 21.6 cm
How to determine the remaining dimensions?The given parameters are:
Wood = 1.5 cm by 30 cm
Each cut = .15 mm by 4 mm
Steps = 21
The remaining dimension is calculated as:
Remaining = 1.5 cm - 21 * .15 mm by 30 cm - 21 * 4 mm
Express mm as cm
Remaining = 1.5 cm - 21 * .015 cm by 30 cm - 21 * 0.4 cm
Evaluate the difference
Remaining = 1.185 cm by 21.6 cm
Hence, the dimensions of the wood that remains after Tierra finishes making the 21 steps is 1.185 cm by 21.6 cm
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there are 5 red marbles, 7 green marbles, 4 black marbles, and 8 blue marbles in a bag. find green or black
Answer:
11/24
Step-by-step explanation:
Answer:
11/24
Step-by-step explanation:
A system of two linear equations is graphed. The lines have the same slope, but different intercepts. How many solutions does the system have?. A. 0. B. 1. C. 2. D. infinite
Answer:
D
Step-by-step explanation:
I hope this is correct and have a great day
Find the absolute maximum and minimum values at the function over the indicated interval, and indicate the x-values at which they occur.
F(x) = x^2 - 4x - 9 ; [-1,3]
the absolute maximum value is ___ at x=___
the absolute minimum value is ___ at x=____
The absolute maximum value is 8 at x=3, and the absolute minimum value is -16 at x=-1.
To find the absolute maximum and minimum values of the function F(x) = x^2 - 4x - 9, we need to calculate the function's critical points and calculate the function at these points.
The critical points can be found by setting the first derivative of the function equal to zero and solving for x:
F'(x) = 2x - 4 = 0
2x = 4
x = 2
We now need to calculate the function at x=-1, x=2, and x=3 to find the absolute maximum and minimum values:
F(-1) = (-1)^2 - 4(-1) - 9 = -16
F(2) = 2^2 - 4(2) - 9 = -3
F(3) = 3^2 - 4(3) - 9 = 8
Therefore, the absolute maximum value is 8 at x=3, and the absolute minimum value is -16 at x=-1.
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bob thinks the inverse of y=2x-5 is y =5x-2 identify his error and find the correct inverse
Answer:
yea he is wrong
Step-by-step explanation:
He is wrong because you cant not just switch the variable. If you move the variable the value will change.
Write without negative exponents: (3xy^−3)^−2
The expression \((3xy^{-3})^{-2}\) without negative exponents is \(\frac{y^6}{9x^2}\).
What are some rules of exponents?Some common rules of exponents are
xᵃ×xᵇ = xᵃ⁺ᵇ.
xᵃ/xᵇ = xᵃ⁻ᵇ.
Addition and subtraction of exponents are only possible for the same base value and when the base is different and both have the same exponent we just multiply the bases and write the exponent.
Given, An expression in exponents \((3xy^{-3})^{-2}\).
Now, Changing the place of exponents from the numerator to the denominator or vice versa changes its sign.
Therefore, \((3xy^{-3})^{-2} = 3^{-2}x^{-2}y^{6}\).
\(3^{-2}x^{-2}y^{6} = \frac{y^6}{3^2x^2}\).
\(\frac{y^6}{3^2x^2} = \frac{y^6}{9x^2}\).
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Describe the solution of f(x) shown in the graph. a parabola opening up passing through 0 comma 2, 1 comma zero and 2 comma zero All real solutions All solutions that lie on f(x) All positive solutions All whole number solutions
A quadratic equation is in the form of ax²+bx+c. The correct option is C, All the positive solutions.
What is a quadratic equation?A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.
The graph of the question is given below. Since a quadratic equation has only two solutions, and this two solutions can be found by observing the graph. The coordinate at which the graph of the equation intersect the x-axis are the solution of the equation.
As it can be observed in this graph, that the graph intersect the x-axis at (1,0) and (2,0).Therefore, the solutions of the graph are 1 and 2.
Thus, both the solutions are positive or it can be concluded that all the solutions are positive.
Hence, the correct option is C, All the positive solutions.
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Answer:
B. All solutions that lie on f(x)
Step-by-step explanation:
Hope this helps!
If not, I am sorry.
3n³ - 12n²-30n what Is the answer
Step-by-step explanation:
Factor 3n³−12n²−30n
3n³−12n²−30n
=3n(n²−4n−10)
Which point represents the value of –(–2) on the number line?
Point A
Point B
Point C
Point D
Answer:
yo where is it
Step-by-step explanation:
2.6 I’m a improper fraction
Answer:
26/10 is your answer
Step-by-step explanation:
2 6/10 = 26/10
2 is your whole and 6 is your numerator and 10 is your denominator since 6 is in the TENTHS place.
Which are steps in the process of completing the square used to solve the equation 3 – 4x = 5x2 – 14x? Check all that apply.
3 = 5(x2 + 2x)
3 = 5x2 – 10x
4 = 5(x2 – 2x + 1)
8 = 5(x2 – 2x + 1)
3 = 5(x – 1)2
4 = 5(x – 1)2
StartFraction 8 Over 5 EndFraction = (x – 1)2
Answer:
1. 3 = 5x2 – 10x
2. 8 = 5(x2 – 2x + 1)
3. StartFraction 8 Over 5 EndFraction = (x – 1)2
Step-by-step explanation:
3-4x=5x^2-14x
3=5x^2-14x+4x
3=5x^2-10x
5x^2-10x-3=0
1. 3 = 5x2 – 10x
2. 8 = 5(x2 – 2x + 1)
8=5x^2-10x+5
8-5=5x^2-10x
3=5x^2-10x
3. StartFraction 8 Over 5 EndFraction = (x – 1)2
8/5=x^2-2x+1
Cross product
8=5(x^2-2x+1)
8=5x^2-10x+5
8-5=5x^2-10x
3=5x^2-10x
Answer:
3 - 4x = 5x2 - 14x
= 3 - 5x2 = - 14x + 4x
= 3 - 10 = 10x
= 7 = 10x
= x = 7/10
= x = 0.7
Step-by-step explanation:
I was wondering what these lines mean? and if so can you guys help me calculate the perimeter of the rhombus?
Thank you :)
anthony uses 8 fluid ounces of lemon juice in one batch of lemonade. How many batches can he mane with 1 pint of lemon juice
Answer:
Therefore, he can make 2 batches of lemonade with 1pint of lemon juice
Anthony can make 2 batches of lemonade with 1 pint of lemon juice.
In this problem, we'll determine how many batches of lemonade Anthony can make using a given amount of lemon juice. We'll be using the fact that 1 pint is equivalent to 16 fluid ounces.
Step 1: Convert Pints to Fluid Ounces
Since 1 pint is equal to 16 fluid ounces, we need to convert the given 1 pint of lemon juice into fluid ounces.
1 pint = 16 fluid ounces
Step 2: Calculate Batches
Now that we know 1 pint is equal to 16 fluid ounces, we can find out how many batches of lemonade Anthony can make using 8 fluid ounces of lemon juice per batch.
Number of batches = Total fluid ounces / Fluid ounces per batch
Substitute the values:
Number of batches = 16 fluid ounces / 8 fluid ounces per batch
Number of batches = 2 batches
Therefore, Anthony can make 2 batches of lemonade using 1 pint of lemon juice, given that he uses 8 fluid ounces of lemon juice in each batch.
This calculation ensures that he has enough lemon juice for the desired number of batches without any wastage.
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Which ordered pairs are solutions to the inequality 2x - y > -4? Check all that apply.
Answer:
(1,-6)
(-2,-5)
(8,2)
(4,0)
Given the following differential equation, dx
dy
=2+ y−2x+3
Find the following: (a) The substitution u= (b) The transformed differential equation dx
du
= (c) The implicit solution, given that c is a constant of integration, is x+c=
The correct options are: (a) The substitution u = y - x. (b) The transformed differential equation \($\frac{dx}{du} = 2 + u + 3 - \frac{dy}{du}$\).
(c) The implicit solution, given that c is a constant of integration, is \(x + c = $\frac{y^2}{2} - \frac{3}{2}y + x + \frac{u^2}{2} - \frac{3}{2}u + C$.\)
Given differential equation:
\($ \frac{dx}{dy} = 2 + y - 2x + 3$.$ \frac{dx}{dy} = 2 + y - 2x + 3$.\)
The substitution \($u = y - x$\)
The transformed differential equation:
\($\frac{dx}{du} + \frac{dy}{du} = 2 + u + 3$$\frac{dx}{du} = 2 + u + 3 - \frac{dy}{du}$\)
The implicit solution, given that c is a constant of integration, is:
\(x + c = $\frac{y^2}{2} - \frac{3}{2}y + x + \frac{u^2}{2} - \frac{3}{2}u + C$\)
So, the correct options are:
(a) The substitution u = y - x
(b) The transformed differential equation \($\frac{dx}{du} = 2 + u + 3 - \frac{dy}{du}$\)
(c) The implicit solution, given that c is a constant of integration, is \(x + c = $\frac{y^2}{2} - \frac{3}{2}y + x + \frac{u^2}{2} - \frac{3}{2}u + C$.\)
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Prove, or disprove by means of a counterexample, each of the following statements. (i) The sum of a finite number of convex subsets of R n is convex. (ii) The collection of all convex subsets of R 2 a linear space. (iii) The sum of two closed subsets of R n is closed. (iv) Does the sentence in (iii) above make sense if (X,d) is substituted for R n ? If so, prove it. If not, justify the claim that it is incoherent. (v) The projection onto any particular coordinate of a closed subset of a metric space R n is closed. [Recall that for any A⊆R n , its projection on to the i th -cordinate, i=1,⋯,n, is denoted by proj i A={y i ∈R:(y 1 ,y 2 ,⋯,y n )∈A}.]
(i) The statement is true. The sum of a finite number of convex subsets of R^n is convex.
(ii) The statement is false. The collection of all convex subsets of R^2 is not a linear space.
(iii) The statement is false. The sum of two closed subsets of R^n is not necessarily closed.
(iv) The sentence in (iii) does not make sense if (X, d) is substituted for R^n.
(v) The statement is true. The projection onto any particular coordinate of a closed subset of a metric space R^n is closed.
(i) The statement is true. The sum of a finite number of convex subsets of R^n is convex.
Proof: Let A_1, A_2, ..., A_k be convex subsets of R^n. We want to show that the set B = A_1 + A_2 + ... + A_k (which is the set of all possible sums of elements from each A_i) is convex.
Let x, y ∈ B and let α ∈ [0, 1]. Since x and y are in B, there exist vectors a_1, a_2, ..., a_k and b_1, b_2, ..., b_k such that x = a_1 + a_2 + ... + a_k and y = b_1 + b_2 + ... + b_k, where a_i, b_i ∈ A_i for each i = 1 to k.
Now consider the point z = αx + (1 - α)y. We need to show that z is also in B.
z = αx + (1 - α)y
= α(a_1 + a_2 + ... + a_k) + (1 - α)(b_1 + b_2 + ... + b_k)
= (αa_1 + (1 - α)b_1) + (αa_2 + (1 - α)b_2) + ... + (αa_k + (1 - α)b_k)
Since each A_i is convex, we have αa_i + (1 - α)b_i ∈ A_i for all i = 1 to k. Therefore, z belongs to the set B = A_1 + A_2 + ... + A_k.
Hence, the sum of a finite number of convex subsets of R^n is convex.
(ii) The statement is false. The collection of all convex subsets of R^2 is not a linear space.
Counterexample: Consider two convex subsets of R^2, A = {(x, y) ∈ R^2 : x > 0} (the right half-plane excluding the y-axis) and B = {(x, y) ∈ R^2 : x < 0} (the left half-plane excluding the y-axis). Both A and B are convex subsets of R^2.
Now, let's consider their sum, A + B. For any point (x, y) in A + B, there exist points (a, b) from A and (c, d) from B such that (x, y) = (a, b) + (c, d). However, (a + c, b + d) must lie on both the right half-plane and the left half-plane simultaneously, which is not possible. Therefore, A + B is not a valid convex subset of R^2.
Hence, the collection of all convex subsets of R^2 is not a linear space.
(iii) The statement is false. The sum of two closed subsets of R^n is not necessarily closed.
Counterexample: Consider the closed subsets A = [0, 1] and B = [2, 3] of R. Both A and B are closed intervals in R.
The sum A + B = [0, 1] + [2, 3] = [2, 4]. However, [2, 4] is not closed since it does not contain its limit points, specifically the point 3.
Therefore, the sum of two closed subsets of R^n is not always closed.
(iv) The sentence in (iii) does not make sense if (X, d) is substituted for R^n.
The concept of "closed" subsets relies on the notion of limits and convergence, which is defined in the context of metric spaces. If (X, d) is a general metric space, the idea of closed subsets and their properties may vary depending on the specific metric and topology of the space. Therefore, it is not meaningful to discuss the closure of subsets in a general metric space without further specifying the properties of that particular space.
Hence, the claim is incoherent unless additional information about the specific metric space (X, d) is provided.
(v) The statement is true. The projection onto any particular coordinate of a closed subset of a metric space R^n is closed.
Proof: Let A be a closed subset of R^n, and consider its projection onto the i-th coordinate, proj_i(A) = {y_i ∈ R : (y_1, y_2, ..., y_n) ∈ A}.
We need to show that proj_i(A) is closed. To do this, we can show that its complement, proj_i(A)^c, is open.
Let x ∈ proj_i(A)^c. This means that x is not in proj_i(A), so there exists some (a_
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There are four students named A,B,C, and D. All four of them are loss averse over money, with the same value function for money: v(x dollars )={√x x ≥ 0
{-2√-x x < 0
All three of them are also loss averse over mugs, with the same value function for mugs:
v(y mugs)={3y y ≥ 0
{4y y < 0
Total utility is the sum of the gain/loss utility for mugs and the gain/loss utility for money. The reference point is the status quo, that is, a person's initial endowment. Student A owns a mug and is willing to sell it for a price of a dollars or more. Student B does not own a mug and is willing to pay up to b dollars for buying it. Student C does not own a mug and is indifferent between getting a mug and getting c dollars. Student D is indifferent between losing a mug and losing d dollars.
1. Solve for a,b,c, and d.
2. Instead, suppose A, B, C, and D are only loss averse over mugs, but not over money. That is, their value function for money is instead:
v(x dollars)={√x x ≥ 0
{-√-x x < 0
and their value function for mugs remains:
v(y mugs)={3y y ≥ 0
{4y y < 0
Solve for a,b,c, and d.
3. Instead, suppose A,B,C, and D are not loss averse:
v(x dollars)={√x x ≥ 0
{-√-x x < 0
and v(y mugs)=3y
Solve for a,b,c, and d.
4. Suppose A, B, C, and D are not loss averse (as in the previous question), but their value for a mug varies with ownership. Specifically, the value of the mug is 3 for someone who does not currently own the mug, and 4 for someone who currently owns a mug. Solve for a,b,c, and d.
As per the question, All four students A, B, C, and D are loss-averse over money and have the same value function as below:v(x dollars)={√x x ≥ 0 {-2√-x x < 0They are also loss averse over mugs and have the same value function.
v(y mugs)={3y y ≥ 0
{4y y < 0
Now, we have to find the values of a, b, c and d as below:
- Student A owns a mug and is willing to sell it for a price of a dollars or more. i.e v(a) = v(0) + v(a-A), where A is the initial endowment of A. According to the given function, v(0) = 0, v(a-A) = 3, and v(A) = 4.
So, a ≥ A+3/2
- Student B does not own a mug and is willing to pay up to b dollars for buying it. i.e v(B-b) = v(B) - v(0), where B is the initial endowment of B. According to the given function, v(0) = 0, v(B-b) = -4, and v(B) = -3.
So, b ≤ B+1/2
- Student C does not own a mug and is indifferent between getting a mug and getting c dollars. i.e v(c) = v(0) + v(c), where C is the initial endowment of C. According to the given function, v(0) = 0, v(c) = 3.
So, c = C/2
- Student D is indifferent between losing a mug and losing d dollars. i.e v(D-d) = v(D) - v(0), where D is the initial endowment of D. According to the given function, v(0) = 0, v(D-d) = -3.
So, d = D/2
2) In this case, value function for money changes to:v(x dollars)={√x x ≥ 0
{-√-x x < 0
However, the value function for mugs remains the same:v(y mugs)={3y y ≥ 0
{4y y < 0
Therefore, values for a, b, c, and d will remain the same as calculated in part (1).
3) In this case, students are not loss-averse. Value function for money:v(x dollars)={√x x ≥ 0
{-√-x x < 0
Value function for mugs:v(y mugs)={3y y ≥ 0
The reference point is the status quo, i.e initial endowment. So,
- Student A owns a mug and is willing to sell it for a price of a dollars or more. The value of mug for A is 3 initially and he would sell it for 3 or more.
So, a ≥ A+3/2
- Student B does not own a mug and is willing to pay up to b dollars for buying it. The value of mug for B is 3 initially and he would buy it for 3 or less.
So, b ≤ B+3/2
- Student C does not own a mug and is indifferent between getting a mug and getting c dollars. The value of the mug for C is 3 initially.
So, c = 3
- Student D is indifferent between losing a mug and losing d dollars. The value of the mug for D is 3 initially.
So, d = 3
4) In this case, value function for money:v(x dollars)={√x x ≥ 0
{-√-x x < 0
Value function for mugs: Mug will have a value of 4 for someone who owns it and 3 for someone who does not own it.
The reference point is the status quo, i.e initial endowment. So,
- Student A owns a mug and is willing to sell it for a price of a dollars or more. The value of mug for A is 4 initially and he would sell it for 4 or more.
So, a ≥ A+2
- Student B does not own a mug and is willing to pay up to b dollars for buying it. The value of mug for B is 3 initially and he would buy it for 3 or less.
So, b ≤ B+3/2
- Student C does not own a mug and is indifferent between getting a mug and getting c dollars. The value of the mug for C is 3 initially and he would like to buy it for 3.
So, c = 3
- Student D is indifferent between losing a mug and losing d dollars. The value of the mug for D is 3 initially.
So, d = 3.
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what is the mean? No working out needed, just an honest answer please.
Answer:
2.333333..... (2.3 repeating)
question content area top part 1 find a polynomial function of degree 3 with the given numbers as zeros. assume that the leading coefficient is 1.
The polynomial function of degree 3 with the given numbers as zeros is x³ - x² - 18x + 24.
Assume that the leading coefficient is 1. The given numbers as zeros are 2, -3, and 4. To find a polynomial function of degree 3 with these given numbers as zeros, we use the zero product property. So, we will have
(x - 2)(x + 3)(x - 4) = 0
Multiplying the terms within the parentheses, we have
(x - 2)(x + 3)(x - 4) = (x² - 2x + 3x - 6)(x - 4)
= (x³ - 4x² + 3x² + 12x - 6x - 24)
Expanding, we get
= (x³ - x² - 18x + 24)
Thus, the polynomial function of degree 3 with the given numbers as zeros is x³ - x² - 18x + 24.
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Which storm is likely to cause quick destruction along a narrow path?
hurricane
thunderstorm
tornado
Answer:
tornado bc they are narrow and can cause great destruction :) hope I helped !
A tornado is the storm that is likely to cause quick destruction along a narrow path.
What is storm?A storm is any disturbed state of the natural environment or the atmosphere of an astronomical body.
Tornadoes are characterized by their rapidly rotating column of air that extends from the base of a thunderstorm to the ground.
They can cause widespread damage and destruction within a very short period, along a narrow path that can be just a few meters wide.
While hurricanes can produce powerful winds and storm surge that can cause significant damage and destruction, their effects are spread over a larger area, including a broad swath of coastal areas.
Thunderstorms can also produce damaging winds, hail, and flash flooding, but they usually affect smaller areas compared to hurricanes or tornadoes.
Hence, tornado is the storm that is likely to cause quick destruction along a narrow path.
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how many bit strings of length 8 start with a 11 or end with 000? (you do not need to compute the final value. you just need to write down the combination, e.g., x^a y^b)
There are 92 bit strings of length 8 that start with a 11 or end with 000.
We can solve this problem using the principle of inclusion-exclusion. Let A be the set of bit strings of length 8 that start with 11, and let B be the set of bit strings of length 8 that end with 000. We want to find the size of the union of A and B.
The number of bit strings of length 8 that start with 11 is 2^6, since there are 6 remaining bits that can be either 0 or 1. The number of bit strings of length 8 that end with 000 is also 2^5, since there are 5 remaining bits that can be either 0 or 1.
However, we have counted the bit strings that both start with 11 and end with 000 twice. To correct for this, we need to subtract the number of bit strings of length 8 that start with 11000, which is 2^2.
Therefore, the number of bit strings of length 8 that start with a 11 or end with 000 is:
|A ∪ B| = |A| + |B| - |A ∩ B|
= 2^6 + 2^5 - 2^2
= 64 + 32 - 4
= 92
So there are 92 bit strings of length 8 that start with a 11 or end with 000.
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There are 88 bit strings of length 8 that start with "11" or end with "000."
To determine the number of bit strings of length 8 that start with "11" or end with "000," we can use the principle of inclusion-exclusion.
Let's consider the two conditions separately:
Bit strings that start with "11":
In this case, the first two bits are fixed as "11." The remaining 6 bits can be either 0 or 1, giving us 2^6 = 64 possibilities.
Bit strings that end with "000":
Similarly, the last three bits are fixed as "000." The first 5 bits can be either 0 or 1, resulting in 2^5 = 32 possibilities.
However, we have counted some bit strings twice because they satisfy both conditions (start with "11" and end with "000"). These bit strings have a length of at least 5 (3 bits in the middle), and there are 2^3 = 8 possibilities for these middle bits.
By using the principle of inclusion-exclusion, we can compute the total number of bit strings satisfying either condition as follows:
Total = Bit strings starting with "11" + Bit strings ending with "000" - Bit strings satisfying both conditions
= 64 + 32 - 8
= 88
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About how many feet of fencing are needed to go around the pool path? Use 3.14 for Pi. 88 ft 100 ft 176 ft 201 ft
Complete question :
A circular swimming pool has a radius of 28 ft. There is a path all around the pool that is 4 ft wide. A fence is going to be built around the outside edge of the pool path.
About how many feet of fencing are needed to go around the pool path
Answer:
201 feets
Step-by-step explanation:
The Circumference of a circle, C :
C = 2 * pi * r
r = Radius ; pi = 3.14
The entire Radius = pool radius + pathnaroind the pool = 28 + 4 = 32
Hence, the Circumference, which gives the value of fencing required is :
C = 2 * 3.14 * 32
C = 200.96 ft
C = 201 feets
Answer:
D. 201
Step-by-step explanation:
how many ways are there to select a committee of five members of the department if at least one woman must be on the committee?
Answer: 16
Step-by-step explanation:
A student walks 1/4 miles from her home to the store on her way to a friends house. If the store is 1/3 of the way to her friends house, how far is her friends house from her home?
Answer:
4/12 I think
Step-by-step explanation:
Answer:
3/4 of a mille.
Step-by-step explanation:
1/3 * 1/4
x=1/4*1/3
x=3/4
3/4 of a mile
Express 2cos^(2) x + 4sin(x) cos(x) in the form a sin2x + b cos2x + c, then determine the values of a, b, c.
The values of a, b, and c are a = -1, b = 1, c = 2. The double angle identities and the Pythagorean identity.
To express the expression 2cos^2(x) + 4sin(x)cos(x) in the form a sin^2(x) + b cos^2(x) + c, we can use the double angle identities and the Pythagorean identity.
Starting with the expression:
2cos^2(x) + 4sin(x)cos(x)
Using the double angle identity for cosine, cos^2(x) = (1 + cos(2x))/2, we can rewrite the expression as:
2(1 + cos(2x))/2 + 4sin(x)cos(x)
Simplifying, we have:
1 + cos(2x) + 2sin(x)cos(x)
Using the double angle identity for sine, sin(2x) = 2sin(x)cos(x), we can rewrite the expression further:
1 + cos(2x) + sin(2x)/2
Using the Pythagorean identity, sin^2(x) + cos^2(x) = 1, we can rewrite cos(2x) as:
cos(2x) = 1 - sin^2(x)
Substituting this into the expression, we have:
1 + (1 - sin^2(x)) + sin(2x)/2
Simplifying, we get:
2 - sin^2(x) + sin(2x)/2
Now, let's simplify further:
2 - sin^2(x) + sin(2x)/2
= 2 - sin^2(x) + (2sin(x)cos(x))/2
= 2 - sin^2(x) + sin(x)cos(x)
Finally, we can rearrange the terms to match the desired form:
2 - sin^2(x) + sin(x)cos(x)
= -sin^2(x) + sin(x)cos(x) + 2
Therefore, the values of a, b, and c are:
a = -1
b = 1
c = 2
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reg gets a hit 24% of the times he is at bat. If he got 18 hits this season, how many at-bats did he have?
Answer:
He had a total of 75 at-bats
Step-by-step explanation:
24% of his at bats are hit
Let the number of hits be x
24% of x = 18
24/100 * x = 18
24x = 100 * 18
x = (100 * 18)/24
x = 75
2x3(5-4)/6.2
Algebra
6/6.2 OR 0.627
Step-by-step explanation:
\( \frac{2 \times 3(5 - 4)}{6.2} \)
6(1)/6.2 = 6/6.2 OR 0.627
If two lines intersect, then the vertical angles formed must be? both equal in measure both acute angles complementary angles
If two lines intersect, then the vertical angles formed must be both equal in measure.
What is intersection of a line?The intersection of a line can be described as when two or more lines cross each other in a plane as a result of this they are been referred to as intersecting lines.
Therefore, intersecting lines share a common point, hence , If two lines intersect, then the vertical angles formed must be both equal in measure.
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A designer decides to create a larger scale model of a smart phone so that his team can work more easily on the design. The length of the screen of his model is 60 centimeters, which is 2.5 times longer than it is wide. The designer asked his team to build the screen of the actual phone with a width of 6 centimeters. What is the scale factor of the model phone to the actual phone?
Answer:
The length of the model is 250% of the width and is 60 centimeters, and the width of the actual phone is 6 so it has a scale factor of 4:1.
Hope this helps!