How many bitstrings of length 10 contain three consecutive 0’s or 4 consecutive 1’s? How many bitstrings of length 10 contain two sets of 3 consecutive 0’s or two sets of 3 consecutive 1’s?

The expected value for the amount of money made selling all of the candy in one bag is $15, and the standard deviation is approximately $24.33.

The standard deviation is a measurement of how widely apart a set of numbers or statistics are from their mean.

The expected value for the amount of money made selling all of the candy in one bag can be found by;

Expected value = mean number of candy bars per bag x price per candy bar

Expected value = 12 x $1.25 = $15

Formula for the standard deviation of a product of random variables:

\(SD (XY) = \sqrt{((SD(X)^2)(E(Y^2)) + (SD(Y)^2)(E(X^2)) + 2(Cov(X,Y))(E(X))(E(Y)))}\)

where X and Y are random variables, SD is the standard deviation, and Cov is the covariance.

X is the number of candy bars in a bag, which has a mean of 12 and a standard deviation of 2. Y is the price per candy bar, which is a constant $1.25. So we have:

E(Y²) = $1.25² = $1.5625

E(X²) = (SD(X)²) + (E(X)²) = 2² + 12² = 148

Cov (X,Y) = 0 (because X and Y are independent)

Using these values, we can calculate the standard deviation for the amount of money made selling all of the candy in one bag:

\(SD = sqrt((2^{2} )(148) + (0)(12)(1.25)^{2} + 2(0)(2)(12)(1.25))\)

SD = √(592)

SD ≈ $24.33

Therefore, the expected value for the amount of money made selling all of the candy in one bag is $15, and the standard deviation is approximately $24.33.

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The expression representing the perimeter of the polygon is given as follows:

7mn³/3 + 4m² + 3mn².

The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.

Hence the perimeter for the polygon in this problem is given as follows:

mn³(1/3 + 2) + m²(1 + 3) + mn²(1 + 2) = 7mn³/3 + 4m² + 3mn².

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Work Shown:

LCM = (product of two numbers)/(HCF of the two numbers)

LCM = 1536/16

LCM = 96

The total amounts paid are displayed in the image below:

The amount of interest due each period expressed as a percentage of the amount lent, deposited, or borrowed is known as an interest rate.

The total interest on a loaned or borrowed sum is determined by the principal amount, the interest rate, the frequency of compounding, and the period of time the loan, deposit, or borrowing took place.

How to calculate interest rates

Using S.I:

Simple Interest: The formula for simple interest is I = P x R x T, where I is the interest, P is the principal amount, R is the rate of interest, and T is the time period.

For example, if you borrow $1,000 at a simple interest rate of 5% per year for 3 years, the interest would be calculated as follows: I = $1,000 x 5% x 3 = $150.

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Answer:

Every book is 8 dollars but you have to subtract 10, so like this:

Step-by-step explanation:

p(x) = 8x - 10 Lets say you sell 2 books

p(2) = 8(2) - 10

p(2) = 16 - 10

p(2) = 6  You would make 6 dollars.

The solution to the system of equations is x = 6 and  y = -5, which is the same as we obtained using the elimination method.

A system of equations is a collection of one or more equations that are considered together. The system can consist of linear or nonlinear equations and may have one or more variables. The solution to a system of equations is the set of values that satisfy all of the equations in the system simultaneously. The given system of equations is:

2x + y = 7 ---(1)

x + y = 1 ---(2)

To solve this system, we can use the method of elimination or substitution.

Method 1: Elimination

In this method, we eliminate one of the variables by adding or subtracting the two equations. To do this, we need to multiply one or both equations by a suitable constant so that the coefficients of one of the variables become equal in magnitude but opposite in sign.

Let's multiply equation (2) by -2, so that the coefficient of y in both equations becomes equal in magnitude but opposite in sign:

-2(x + y) = -2(1) --

Multiplying equation

(2) by -2-2x - 2y = -2

Now we can add the two equations (1) and (-2x - 2y = -2) to eliminate y:

2x + y = 7(-2x - 2y = -2)0x - y = 5

We now have a new equation in which y is isolated.

To solve for y, we can multiply both sides by -1:

-1(-y) = -1(5)y = -5

Now that we know y = -5, we can substitute this value into equation (2) to find x:x + y = 1x + (-5) = 1x = 6

Therefore, the solution to the system of equations is (x,y) = (6,-5).

Method 2: Substitution

In this method, we solve one of the equations for one variable in terms of the other variable and substitute this expression into the other equation to get an equation with only one variable.

From equation (2), we can solve for y in terms of x:y = 1 - x

We can then substitute this expression for y into equation (1):2x + y = 72x + (1 - x) = 7 --Substituting y = 1 - xx + 1 = 7x = 6

Now that we know x = 6, we can substitute this value into equation (2) to find y:x + y = 16 + y = 1 --Substituting x = 6y = -5

Therefore, the solution to the system of equations is (x,y) = (6,-5), which is the same as we obtained using the elimination method.

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Hubble's constant in units of km/s/million LY is approximately 21.47.

what is  approximately ?

Approximately means close to or nearly, but not exactly. It is used to indicate that a value or number is an estimation or approximation, rather than an exact value. It is often used when a precise value is not necessary or when the exact value is unknown or difficult to determine.

In the given question,

To convert Hubble's constant from km/s/Mpc to km/s/million LY, we need to multiply it by a conversion factor that accounts for the difference in distance units. We can use the fact that 1 Mpc is equal to 3.26 million LY:

1 Mpc = 3.26 million LY

Therefore, to convert Hubble's constant from km/s/Mpc to km/s/million LY, we can use the following conversion factor:

1 Mpc / 3.26 million LY

Multiplying Hubble's constant by this conversion factor gives:

H = 70 km/s/Mpc x (1 Mpc / 3.26 million LY) = 21.47 km/s/million LY

Therefore, Hubble's constant in units of km/s/million LY is approximately 21.47.

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The equation of the line passing through the points (-7, -3) and (1, 2) is \(y = \frac{5}{8}x + \frac{11}{8}\).

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

First, we determine the slope of the line.

Given the two points are (-7, -3) and (1, 2)

We can find the slope of the line by using the slope formula:

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values, we get:

m = (2 - (-3)) / (1 - (-7))

m = 5/8

Using the point-slope form, plug in one of the given points and slope m = 5/8 to find the equation of the line.

Let's use the point (-7, -3:

y - y₁ = m(x - x₁)

\(y - (-3) = \frac{5}{8}( x - (-7) ) \\\\y + 3 = \frac{5}{8}(x + 7 )\\\\y + 3 = \frac{5}{8}x + \frac{35}{8} \\ \\y = \frac{5}{8}x + \frac{35}{8} - 3\\\\y = \frac{5}{8}x + \frac{11}{8}\)

Therefore, the equation of the line is \(y = \frac{5}{8}x + \frac{11}{8}\).

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Based on the given histogram, the data is skewed with a maximum range of 49.

This is because the frequency bars are not evenly distributed across the x-axis intervals, indicating that the data is not symmetric. The lack of a shaded bar for the 40 to 49 interval also suggests that there were fewer donations in that range compared to the other intervals.

One possible explanation for this skewness could be that the charity had suggested donation levels, with a minimum of $10, resulting in a large number of donations in the 10 to 19 interval. Additionally, the shaded bar stopping at 1 for the 30 to 39 and 50 to 59 intervals suggests that there were fewer donations in those ranges. This could be due to a variety of reasons, such as donors being more likely to give in the suggested $10 increments, or the charity's fundraising efforts being more effective at attracting donors in certain age or income brackets.

Overall, the histogram does not suggest a bimodal distribution, as there is not a clear separation between two distinct modes. The maximum range of 49 also indicates that there were no extreme outliers or large donations that would skew the data towards a higher range. Therefore, it is likely that the data represents a typical distribution of donations to a charity, with most donors giving smaller amounts and fewer donors giving larger amounts.

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Answer: El índice de refracción del vidrio flint es mayor que el del aire. Cuando la luz pasa de un medio con un índice de refracción menor (como el aire) a un medio con un índice de refracción mayor (como el vidrio), experimenta un cambio de dirección. Este fenómeno se conoce como refracción.

Cuando observamos el bloque de vidrio flint desde arriba, la luz que proviene del bloque sufre refracción al pasar del vidrio al aire. Debido a la refracción, los rayos de luz se desvían y parecen venir de una posición más alta dentro del vidrio de lo que realmente están. Esto crea una ilusión óptica que hace que el espesor aparente del bloque de vidrio se vea más delgado de lo que realmente es.

La cantidad exacta de adelgazamiento aparente depende del ángulo de incidencia de la luz y de los índices de refracción del vidrio y el aire. Sin más información, no es posible determinar el espesor aparente específico del bloque de vidrio flint cuando se ve desde arriba.

Step-by-step explanation:

Answer:

What is the diagram?

Step-by-step explanation:

The expected total dollar net operating Income for next year = $70,000

1) The contribution format income statement for the game last year, and the degree of operating leverage is computed below:

Contribution format income statement for the game last year Sales (15,000 × $20) = $300,000

Variable expenses (15,000 × $6) = $90,000

Contribution margin = $210,000

Fixed expenses = $182,000Net operating income = $28,000

Degree of operating leverage = Contribution margin / Net operating income= $210,000 / $28,000= 7.5 2)

The expected percentage increase in net operating income for next year:

The expected sales in next year = 18,000

games selling price per game = $20

Therefore, Total sales revenue = 18,000 × $20 = $360,000

Variable expenses = 18,000 × $6 = $108,000

Fixed expenses = $182,000

Expected net operating income = Total sales revenue – Variable expenses – Fixed expenses

= $360,000 – $108,000 – $182,000= $70,000

The expected percentage increase in net operating income = (Expected net operating income - Last year's net operating income) / Last year's net operating income*100= ($70,000 - $28,000) / $28,000*100= 150%

The expected total dollar net operating income for next year = $70,000

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Answer:

A translation is a transformation that occurs when a figure is moved from one location to another location without changing its size, shape or orientation. In the coordinate plane we can draw the translation if we know the direction and how far the figure should be moved.

Step-by-step explanation:

Answer:

A translation is converting another language into English

Step-by-step explanation:

Answer:

\(3x^{4}\)

Step-by-step explanation:

I suggest looking lessons on it online if you don't understand... It's hard to do your work especially if you don't understand it. Or if your online, go to past lessons or something.

Answer:

The answer is 3x^4

Step-by-step explanation:

\(2 \times |12-14|=2 \times |-2| =2\times 2=\boxed{4}\)

Answer:

The ratio of sides in a 30-60-90 triangle is 1:√3:2. Since the shortest side is the 1 in this case the other lengths are 15√3 and 30.

The point (-√2,1) can also be represented as (√3, 5.18) in polar coordinates.

To find the polar coordinates of the rectangular coordinates (-√2,1), we can use the following formulas:

r = √(x² + y²)

θ = tan^⁻1(y/x)

Plugging in the given values of (-√2,1), we get:

r = √((-√2)² + 1²) = √(2 + 1) = √3

θ = tan^⁻1(1/(-√2)) ≈ 2.0344 radians

Note that since the point (-√2,1) is in the second quadrant, we need to add π to the value of θ obtained from the inverse tangent in order to obtain an angle in the interval [0,2π). Thus, we have:

θ ≈ 2.0344 + π ≈ 5.1779 radians

Rounding to 2 decimal places as needed, we get the polar coordinates of (-√2,1) as (r,θ) ≈ (√3, 5.18).

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Answer:

Nicolas is closer to the surface

PLZ TELL ME IF IM WRONG

Answer:

Nicolas is closer to the surface, he is 7 feet closer to the surface than Jerome

Step-by-step explanation:

The simplified solution of the expression 5x²+6x+4+x²+x is 6x²+7x+4.

The given expression is 5x²+6x+4+x²+x

Simplifying the given expression

5x²+6x+4+x²+x

Firstly, put the similar terms together

5x²+x²+6x+x+4

Adding the similar terms

6x²+7x+4

∵ The expression cannot be solved further, 6x²+7x+4 is the final solution.

Therefore, the simplified solution of the expression 5x²+6x+4+x²+x is 6x²+7x+4.

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Answer:

the explanatory variable is "the amount of practice every year" while the response variable is "the improvement in his game"

Step-by-step explanation:

In simple terms, the difference between explanatory and random variable is that the response variable is usually the focus of a question in a study/experiment while an explanatory variable is a variable that explains changes in the response variable. Which means that the explanatory variable is simply any variable that may affect the response variable.

Now, in this question, the golfer wants to determine if the amount of practice every year can be used to predict the amount of improvement in his game.

This means that the amount of practice every year explains how much he improves every year.

Thus, the explanatory variable is "the amount of practice every year" while the response variable is "improvement in his game"

The type of model that best fits the situation of a $500 raise in salary each year is a linear model.

In a linear model, the dependent variable changes a constant amount for constant increments of the independent variable.

In the given case, the dependent variable is the salary and the independent variable is the year.

You may build a table to show that for increments of 1 year the increments of the salary is $500:

Year         Salary        Change in year         Change in salary

2010           A                           -                                       -

2011           A + 500     2011 - 2010 = 1          A + 500 - 500 = 500

2012          A + 1,000   2012 - 2011 = 1          A + 1,000 - (A + 500) = 500

So, you can see that every year the salary increases the same amount ($500).

In general, a linear model is represented by the general equation y = mx + b, where x is the change of y per unit change of x, and b is the initial value (y-intercept).              

In this case, m = $500 and b is the starting salary: y = 500x + b.

Answer:

10^20

Step-by-step explanation:

So in this word problem, we have to multiply 10^13 bacteria cells on a single person by the 10^7 of people.

Always remember this, when you have exponenets with the same bases, and the question asks for multiplying and dividing exponents, you just need to add and subtract the exponent.

So in this case, we will just add since it calls for multipactation.

So we need to solve:

10^13+7

This will just equal:

10^20 power

Hope this helps ;)

Answer:

110

Step-by-step explanation:

90 + 10

Answer:

Megavolt used a Systematic sampling method.

Step-by-step explanation:

From the information given:

For every 100th evil light bulbs tested, he starts with the 42nd. This implies that;

The first bulb tested is the 142nd bulb, the second bulb tested is the 242nd...

The sequence is as follows:

142nd, 242nd, 342nd, 442nd, 542nd, 642nd .... etc

From the starting point of manufacturing the evil light bulb, the sequence is derived from sampling where each nth unit is known to be a sample, and this is only feasible in systematic sampling.

3. The factored polynomial is p(x) = (x - 1)(x - 5)

4. The factored polynomial is p(x) = (x + 3)²

A polynomial is a mathematical expression in which the power of the unknown is greater than or equal to 2.

3. To factorize the polynomial using the graph, we see that the polynomial cuts the x - axis at x = 1 and x = 5.

This implies that its factors are (x - 1) and (x - 5)

So, the factored polynomial is p(x) = (x - 1)(x - 5)

4. To factorize the polynomial using the graph, we see that the polynomial touches the x - axis at only one point x = -3. So,it has repeated roots

This implies that its factors are (x - (-3)) = (x + 3) twice

So, the factored polynomial is p(x) = (x + 3)²

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In the expression, there are 3 terms.

3x and 4x are like terms because the variables are identical.

Also, we have a constant term which is -3.

Answer: 243

Step-by-step explanation:

It’s going up by the square roots of 3 so therefore the fourth term is 3 to the fourth power which is 243.

Answer:

C.    AA

Step-by-step explanation:

Since m<Y = 27°, then m<W = 27°.

We have two angles of one triangle (A and B) congruent to two angles of the other triangle (W and X).

Answer: C.   AA