how many bit strings of length 12 contain a) exactly three 1s? b) at most three 1s? c) atleastthree1s? d) an equal number of 0s and 1s?

Answer:

4,796 Meters

Step-by-step explanation:

Mary ran 4,796 more meters than she did on Tuesday.

6,491 - 1,695 = 4,796

The area of the training field will be 6933.06 square meters.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is 86 m long and 54 m wide.

Then the area of the training field will be

Area = area of a rectangle + area of a circle

Then we have

Area = 86 x 54 + 3.14 x 27 x 27

Area = 4644 + 2289.06

Area = 6933.06 m²

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There are two possible volumes for the rectangular prism: 36 cubic units or 25 cubic units.

To find the volume of the rectangular prism with a space diagonal of 13 units and integer unit dimensions, we can follow these steps:

1. Recall that the space diagonal of a rectangular prism can be found using the Pythagorean theorem in 3D: d² = l² + w² + h², where d is the space diagonal, and l, w, and h are the length, width, and height of the prism.

2. Given that the space diagonal is 13 units, we have: 13² = l² + w² + h².

3. Since the dimensions are integers, we need to find the combination of l, w, and h that satisfies this equation. Possible combinations are: (2, 3, 6) and (1, 5, 5), as these are the only sets of integers that satisfy the equation.

4. Now, we can calculate the volume of the rectangular prism using the formula: Volume = l × w × h.

For the combination (2, 3, 6), the volume is: 2 × 3 × 6 = 36 cubic units.
For the combination (1, 5, 5), the volume is: 1 × 5 × 5 = 25 cubic units.

So, there are two possible volumes for the rectangular prism: 36 cubic units or 25 cubic units.

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Work Shown:

(height)/(shadow length) = (height)/(shadow length)

(5 ft)/(6.5 ft) = (x ft)/(26 ft)

5/(6.5) = x/26

5*26 = 6.5*x

130 = 6.5x

6.5x = 130

x = 130/(6.5)

x = 20

The palm tree is 20 feet tall, which is the same height as a 2 story building (assuming each floor is 10 ft).

Answer:

Distributive Property

Step-by-step explanation:

16(4x -1) = 16 · 4x - 16·1
16 is distributed across both terms and multiplied by each term

Value of the k is -2 for the equation \(3x^{2} +2x + k = 0\).

Given equation is,

\(3x^{2} + 2x + k = 0\)

From the quadratic equation we get,

a = 3, b = 2, c = k

Let us consider roots of the equation are x₁ and x₂

We know that sum of roots is -b/a

x₁ + x₂ = - 2/3

and product of roots is c/a

x₁x₂ = k / 3

It is given that 2x₁ = -3x₂

                ⇒      x₁ = - 3/2 x₂

Putting value of x₁ in the first equation,

-3/2 x₂ + x₂ = - 2/3

-3x₂ + 2x₂ = -2/3

- x₂ = - 2/3

⇒ x₂ = 2/3

and x₁ = (- 3/2)(2/3)

       x₁ = -1

Therefore x₁x₂ = k/3 implies that,

-1(2/3) = k/3

- 2/3 = k/3

k = -2.

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1) The probability that all the marbles are red:

There are 8 red marbles out of a total of 20 marbles (8 + 5 + 7). The probability of drawing 4 red marbles without replacement is:

(8/20) * (7/19) * (6/18) * (5/17) = 0.0392
Rounded to 4 decimal places, the probability that all the marbles are red is 0.0392.

2) The probability that none of the marbles are red:

There are 12 non-red marbles out of 20 total marbles. The probability of drawing 4 non-red marbles without replacement is:

(12/20) * (11/19) * (10/18) * (9/17) = 0.2614
Rounded to 4 decimal places, the probability that none of the marbles are red is 0.2614.

a) The probability of getting all Tails when tossing a fair coin 4 times is calculated by multiplying the probability of getting a Tail in each toss (which is 0.5). So, the probability is:

0.5 * 0.5 * 0.5 * 0.5 = 0.0625
Rounded to 4 decimal places, the probability is 0.0625.

b) To find the probability of getting at least one Head, we can find the probability of not getting any Heads (i.e., getting all Tails) and then subtract it from 1:

1 - 0.0625 = 0.9375
Rounded to 4 decimal places, the probability of getting at least one Head is 0.9375.

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Answer:

..................

Step-by-step explanation:

\(2(3 + 16) \)

The steps in Mia's method were smaller than in Jenna's, which was an advantage.

The same result will be obtained by adding the products of multiplying the sum of two or more addends by a number as opposed to multiplying each addend separately by the number.

The direct algorithm process suggested in this paper is known as the direct calculation method (DCM), and it can deal with using confinement loss as an incremental step to simulate the effect of moving tunnel face excavation, calculating the stresses and displacements in each step, and drawing the results.

Jenna's technique:

\(\begin{aligned}&5(30+4) \\&=(5)(30)+(5)(4) \\&=150+20 \\&=170\end{aligned}\)

Mia's technique:

\(\begin{aligned}&5(30+4) \\&=(5)(34) \\&=170\end{aligned}\)

Both used the right approach, albeit in different ways.

One uses the distributive property, whereas the other uses direct calculation.

Consequently, Jenna and Mia came to the same conclusion.

However, Mia's approach has one advantage over Jenna's: it requires fewer steps.

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1. The x-intercepts are x=3 and x=1. Since 3 is greater than 1, the greatest x-intercept is x=3.

2. The y-intercept is -8.

3. g(x) has the greatest y-intercept.

1. The x-intercept of a function is found by setting f(x) = 0 and solving for x. So for f(x) = 2x²-8x+6, we have:

0 = 2x²-8x+6

0 = x²-4x+3

0 = (x-3)(x-1)

Therefore, the x-intercepts are x=3 and x=1. Since 3 is greater than 1, the greatest x-intercept is x=3.

2. The y-intercept of a function is found by setting x = 0 and evaluating f(x). So for f(x) = -x²-6x-8, we have:

f(0) = -(0)²-6(0)-8 = -8

Therefore, the y-intercept is -8.

For g(x), we have:

g(0) = 2(0)²+16(0)+31 = 31

Therefore, g(x) has the greatest y-intercept.

3. Similar to question 2, we find the y-intercept by setting x=0 and evaluating f(x):

f(0) = -(0)²-8(0)-12 = -12

Therefore, the y-intercept is -12.

4. To find the x-intercepts of f(x) = (x+8)²-4, we set f(x) = 0:

0 = (x+8)²-4

4 = (x+8)²

±2 = x+8

x = -8 ± 2

Therefore, the x-intercepts are x=-6 and x=-10. Since -6 is greater than -10, the greatest x-intercept is x=-6.

5. The axis of symmetry of a quadratic function in the form f(x) = ax²+bx+c is given by x = -b/(2a).

For f(x) = -2x²-12x-16, we have a = -2 and b = -12, so the axis of symmetry is x = -(-12)/(2*-2) = 3.

For g(x) = 2x²+16x+31, we have a = 2 and b = 16, so the axis of symmetry is x = -16/(2*2) = -4.

Therefore, f(x) has the greatest axis of symmetry.

6. To find the y-intercept, we set x=0 and evaluate the functions:

f(0) = 2(0-3)²+1 = 19

g(0) = 2(0+3)²+2 = 20

Therefore, g(x) has the greatest y-intercept.

7. To find the x-intercept, we set f(x) = 0:

0 = -(x+1)²+1

1 = (x+1)²

±1 = x+1

x = -1 ± 1

Therefore, the x-intercepts are x=-2 and x=0. Since -2 is greater than 0, g(x) has the greatest x-intercept.

8. Similar to question 6, we find the y-intercept by setting x=0 and evaluating the functions:

f(0) = -2(0+2)²+2 = -6

g(0) = 2(0+3)²-4 = 14

Therefore, g(x) has the greatest y-intercept.

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Step-by-step explanation:

20x12= 240cm^2 (the size of one brick)

If there are 5000 bricks then you multiply 240cm^2 by 5000

5000x240= 1,200,000cm^2

(it's a huge number so I'm not so sure about this)

Answer:

I believe it is 2 grams.

Step-by-step explanation:

there are 1000 grams in 1 kg, there are 500 crayons, therefore each crayon weighs 2 grams

Answer:

its C

Step-by-step explanation:

a P e X

Answer:

Step-by-step explanation:

You are given 6 numbers and asked to classify them with respect to the sets of Natural numbers, Integers, and Rational numbers.

The given numbers are ...

  -6; 6,3; -0,1277; 6,(6); -6,073992...; 197

Here, the comma (,) is used as the decimal separator, and the parentheses (6) indicate a repeating digit.

The sets you're asked to use for classification are ...

  (comma is used as a list separator)

The numbers you're asked to classify are ...

Then the sets of interest are ...

  1. (ℤ and not ℕ: negative integers) — {-6}

  2. (ℕ and not ℚ: irrational counting numbers) — N, no such numbers

__

Additional comment

All natural number are integers, and all integers are rational numbers. Any member of ℕ or ℤ is a member of ℚ.

  ℕ ⊂ ℤ

  ℤ ⊂ ℚ

Allie earns $817.4 in a week.

To find the probabilities for the given scenarios, we will use the normal distribution and Z-scores. The Z-score measures how many standard deviations an observation is away from the mean in a normal distribution.

Given:

Mean (μ) = $710

Standard Deviation (σ) = $124

a) Probability of earnings less than $760:

We need to find P(X < $760), where X is the weekly earnings.

First, we need to calculate the Z-score corresponding to $760:

Z = (X - μ) / σ

Z = ($760 - $710) / $124

Using a Z-table or calculator, we can find the probability corresponding to the Z-score, which represents the area under the normal distribution curve to the left of the Z-score.

b) Probability of earnings between $620 and $892:

We need to find P($620 < X < $892), where X is the weekly earnings.

We can calculate the Z-scores for both $620 and $892 using the formula mentioned above. Then, we can find the difference between their probabilities to get the desired probability.

c) If Summer works for the company and only 20% of the company gets paid more than she does, we need to find the earnings threshold that corresponds to the top 20% of the distribution.

We need to find the Z-score that corresponds to the 80th percentile (20% of the data falls below it). We can use a Z-table or calculator to find the Z-score corresponding to the 80th percentile.

Once we have the Z-score, we can calculate the earnings threshold using the formula:

X = Z * σ + μ

Let's calculate the probabilities and earnings threshold:

a) Probability of earnings less than $760:

Calculate the Z-score:

Z = ($760 - $710) / $124

b) Probability of earnings between $620 and $892:

Calculate the Z-scores for $620 and $892:

Z1 = ($620 - $710) / $124

Z2 = ($892 - $710) / $124

c) If 20% of the company gets paid more than Summer, find Allie's earnings:

Calculate the Z-score for the 80th percentile:

Z = Z-score corresponding to the 80th percentile (from the Z-table)

Calculate Allie's earnings:

X = Z * $124 + $710

Please note that to calculate the probabilities and earnings, you can either use a Z-table or a statistical calculator that provides the cumulative distribution function (CDF) of the normal distribution.

Therefore, from the z-table, z = 0.85.

Substituting the values of μ and σ gives;

0.85 = (x - 710)/124

Solving for x gives:

x = (0.85 * 124) + 710

= 817.4

Allie earns $817.4 in a week.

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The wholesale cost of bike is $96.15 and the price andre can buy after discount is $100

What is discount ?

An item's regular price is decreased when given a discount. A discount is frequently offered on them. 20% off is given to all full-time employees. Synonyms: cut, concession, cutback, decrease more words for "discount" the transitive verb.

The difference in price between the item's purchase price and par value is the discount. The cost price of a product can be reduced or subtracted in the form of a discount.

The cost of the bikes after the markup is $125. The markup was 30%. Assuming the wholesale price is x, the expression would be:

x + (x × 30%) = 125

x + 0.3x = 125

1.3x = 125

x = 125/1.3

x = $96.15

If Andre want to buy the bike at a discounted price of 20%, the price would be:

= Selling price x (1 - Discount rate)

= 125 x (1 - 20%)

= 125 x 0.8

= $100

In conclusion, the wholesale price was $96.15 and the amount Andre pays is $100.

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The equation for the amount, A, in dollars that the investment is worth as a function of time, n, in years is A=P(1+r/n)ˣᵇ.  The amount (A) after (i) 2 years $4,494.40, (ii) 10 years is $7,163.39 (iii) 20 years is $12,828.54  (c) the value of the function at n=o years is $4000.

How to determine the amount of an investment?

The amount of an investment is determined using the formula

bi  The amount the investment will worth in 2 years is

A=$4000(1+0.06)²

A=$4,494.40

ii. in 10 years

A=$4000(1+0.06)¹⁰

A=4000(1.06)¹⁰

A=$7,163.39

iii in 20 years time

A=$4000(1.06)²⁰

A=$12,828.54

The value and the meaning of the function at n=0 is $4000 and it means that there is no increase in the principal invested.

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A permutation is an arrangement of objects in a specific order

i.e. AB ≠ BA

In Permutation order is important.

Here there are 12 Letters and symbols

Out of which E is repeated.

here we are given that duplicates from the list of 12 are not allowed, and We see that letter E is repeated.

So There are 12 letters in all, out of which we need 7 letters and symbol, where order is important.

So formula for permutation is nPr = \(\frac{n!}{(n-r)!}\) where ! is called fractional symbol n! = n*(n-1)*(n-2)

*3*2*1x! = reputation of any word.

So Permutation with reputation of any letter or object is \(\frac{nPr}{x!}\)

for example 4! = 4*3*2*1 = 24

So the answer is,

12P7 = \(\frac{12!}{2!*(12-7)!} = \frac{12!}{5!*2!} = \frac{12*11*10*9*8*7*6*5!}{5!*2!}\) If we cancel 5! from both numerator and denominator.

12P7 = 12*11*10*9*8*7*3 = 1995840

So the answer is 1995840.

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The solution to the given differential equation is: x⁷ cos y = y + C

where C is the constant of integration

To solve the given differential equation:

\(\[7x^6\cos y dx - dy = 0\]\)

We can separate the variables and integrate both sides.

Separating variables, we can write the equation as:

\(\[7x^6\cos y dx = dy\]\)

Now, we can integrate both sides with respect to their respective variables:

\(\[\int 7x^6\cos y dx = \int dy\]\)

Integrating the left side:

\(\[\int 7x^6\cos y dx = 7 \int x^6 \cos y dx\]\)

To integrate \(\(x^6 \cos y\)\)with respect to x, we can use integration by parts.

Let's take u = x⁶ and \(\(dv = \cos y dx\)\).

Differentiating u with respect to \(\(x\) gives \(du = 6x^5 dx\).\)

Integrating dv with respect to x gives \(\(v = \int \cos y dx = \cos y \cdot x\).\)

Applying the integration by parts formula:

\(\[\int x^6 \cos y dx = u \cdot v - \int v \cdot du\]\)

Substituting the values:

\(\[\int x^6 \cos y dx = x^6 \cdot \cos y \cdot x - \int (\cos y \cdot x) \cdot (6x^5 dx)\]\)

Simplifying:

\(\[\int x^6 \cos y dx = x^7 \cos y - 6 \int x^6 \cos y dx\]\)

Moving the integral term to the left side:

\(\[7 \int x^6 \cos y dx = x^7 \cos y\]\)

Dividing both sides by 7:

\(\[\int x^6 \cos y dx = \frac{x^7 \cos y}{7}\]\)

Now, substituting this result back into our original equation:

\(\[7 \int x^6 \cos y dx = dy\]\)

\(\[\frac{7x^7 \cos y}{7} = dy\)

Simplifying:

x⁷ cos y = dy

Finally, the solution to the given differential equation is:

x⁷ cos y = y + C

where C is the constant of integration.

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Answer:

38

Step-by-step explanation:

Since he wants to have equal number of rows and columns..the number of plants must be a root number. 6203 is not a root number. 6241 is the closest root number

(√6241= 79)

So he needs a minimum of 6241 plants in total for it.

6241-6203= 38

Therefore he needs 38 more plants

The solution of the given inequality y ≤ -x² + 2x is (x,y) ≥ {(0,0) and (-2,-4)} obtained by plotting graph between axis.

A mathematical phrase in which the sides are not equal is referred to as being unequal. In essence, a comparison of any two values reveals whether one is less than, larger than, or equal to the value on the opposite side of the equation.

Given the inequality,

y ≤ −x² + 2x

The inequality consists of two functions,

y ≤ -x² and y ≤ 2x

Now if we plot both inequalities

x = 0 ⇒ y = 0

And,

2x ≤ -x²

-x²/x ≥ 2

x ≤ -2

So,

y ≤ 2(-2)

y ≤ -4

If we plot both as shown below then the bounded region is obtained towards the right therefore the solution will be greater than this.

Therefore (x,y) ≥ {(0,0) and (-2,-4)} will be solution.

Hence "The solution of the given inequality y ≤ -x² + 2x is (x,y) ≥ {(0,0) and (-2,-4)} obtained by plotting graph between axis".

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Answer:

I think it is 5m + 4....

Step-by-step explanation:

Still confusing... i-ready as always...

Answer:

5m + 4

Step-by-step explanation:

First distribute, so 5(m + 1) is 5m + 5 (5 times m a plus 5 times 1)

Then you are left with 5m + 5 - 1

You do 5 - 1 which is equal to 4

The final answer is 5m + 4

The mode of the given data values is N/A (not applicable).Hence, the mean, median, and mode of the given data values are:Mean = 54.36Median = 55.5Mode = N/A (not applicable)

Given data values are 55, 56, 70, 61, 53, 57, 50, 73, 52, 69, and 2. We need to calculate the mean, median, and mode of this sample.So, let's first arrange the data values in ascending order:2, 50, 52, 53, 55, 56, 57, 61, 69, 70, 73

Mean:The mean is the sum of all the data values divided by the total number of data values. So, we can use the following formula to calculate the mean:

Mean = (sum of all the data values) / (total number of data values)Sum of all the data values = 55 + 56 + 70 + 61 + 53 + 57 + 50 + 73 + 52 + 69 + 2 = 598Total number of data values = 11

Therefore,Mean = (sum of all the data values) / (total number of data values) = 598 / 11 = 54.36 (rounded to two decimal places)Therefore, the mean of the given data values is 54.36.

Median:The median is the middle value of a sorted data set. Since the data set has 11 data values, the median is the average of the 6th and 7th values (counting from smallest to largest).

Therefore, the median is :Median = (55 + 56) / 2 = 55.5Therefore, the median of the given data values is 55.5.

Mode:The mode is the data value that appears most frequently in the data set. In this case, there is no data value that appears more than once. So, there is no mode.

Therefore, the mode of the given data values is N/A (not applicable).Hence, the mean, median, and mode of the given data values are:Mean = 54.36Median = 55.5Mode = N/A (not applicable)

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The equation used in writing a partial fraction decomposition is given as:

Negative 15 x + 10 / (5 x - 2) = a / (5 x - 2) + b / (5 x - 2).

To determine the values of a and b, we can use a system of equations. This system of equations consists of two equations, one for a and one for b. The equation for a is: Negative 15 x + 10 = a * (5 x - 2). The equation for b is: 0 = b * (5 x - 2). We can solve these equations simultaneously to get the values of a and b.

For example, if x = 1, then the equation for a becomes: Negative 15 + 10 = a * (5 - 2), which simplifies to -5 = a * 9. Therefore, a = -5/9. The equation for b becomes: 0 = b * (5 - 2), which simplifies to 0 = b * 3. Therefore, b = 0.

In summary, the system of equations used to determine the values of a and b is:

Negative 15 x + 10 = a * (5 x - 2) and 0 = b * (5 x - 2). By solving these equations simultaneously, we can get the values of a and b.

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Answer:

B!!!

Right on Edge

Step-by-step explanation:

Answer:

Graph A

Step-by-step explanation:

\(-0.6x-3 < 1.8\\-0.6x -3+3 < 1.8+3\\-0.6x < 4.8\\-0.6x/-0.6 < 4.8/-0.6\\x > -8\)