Select the correct answer.
What is this expression in simplest form?
X + 2/ 4x^2 + 5x +1 • 4x + 1/ x^2 - 4

The Ohio Lottery has been based on the probability deriving with the correct derivation of the number with the highest chances.

Probability has been defined as the mathematical description of learning the chances of an event to occur. The probability ranges from 0 to 1, with 1 being complete probability, and 0 means no chances of event to occur.

The Ohio lottery has been given as the game of lottery operated by the  Ohio Lottery Commission. The purpose initiated by the Ohio Lottery has been to raise the funds for the education.

The lottery has been based on the probability of the common outcomes that delivers the formation of the numbers with the highest chances of getting resulted.

The games such as Bucket 5, Super Lotto, Ohio Lotto has been based on the probability of the drawing the numbers, and the correct probability won the lottery.

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Your question is probably incomplete, and most probably the complete question is:

Create a Math Essay on probability of the Ohio lottery.

Answer:

340 CDs

Step-by-step explanation:

To answer this question, we're dealing with three functions for one problem, namely the revenue function, the cost function, and the profit function.

The revenue function is R(q) = pq, where p is the price of a certain good and q is the quantity sold.

The cost function is C(q) = variable cost + fixed cost, where variable costs changes depending on the quantity of goods produced and fixed cost is a one-time cost for the producer (e.g., an investment, rent, etc.).

The profit function is P(q) = R(q) - C(q) and is simply the cost function subtracted from the revenue function.

The "break-even point" is the point at which profit = $0 and the point at which cost = revenue.

From the problem, we see that Jason invested $3349 (once) for his CDs and each disk requires $3.65 for the materials so our cost function is C(q)  = 3.65q + 3349

Furthermore, we see that each disks sells for $13.50, so our revenue function is R(q) = 13.5q

Our profit function then is P(q) = 13.5q - (3.65q + 3349) = 13.5q - 3.65q - 3349 = 9.85q - 3349.

Thus, to find the break-even point, we set profit = 0 and solve for q:

[tex]0=9.85q-3349\\3349=9.85q\\340=q[/tex]

The amount of water used for each month and rounded off to the nearest 1000 is;

Amount of water used in May = 12567 litres

Amount of water used in June = 452 litres

Amount of water used in July = 15623 liters

Approximate amount of water used in May to the nearest 1000 = 13,000 liters

Approximate amount of water used in June to the nearest 1000 = 0 liters

Approximate amount of water used in July to the nearest 1000 = 16,000 liters

Therefore, the amount of water used each month rounded to the nearest 1000 are 13,000, 0, and 16,000 respectively.

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Step-by-step explanation:

The slashes through the lines indicate they're of the same length, which means this is an equilateral triangle. Therefore all three angles are 60 degrees.

The lines being parallel mean that angle x shares the same angle as the triangle in the bottom-right corner.

The parallel lines intersecting with the line segment that is consistent throughout the triangle makes the angle the same.

Step-by-step explanation:

We can see that the triangle in the picture is an equilateral triangle, because its sides are all marked with one dash, meaning they are equal lengths. We note that all the angles in an equilateral triangle are each 60°.

The little arrows on the top and bottom lines in the figure indicate that they are parallel, which means that the diagonal line between them creates a set of alternate angles (I've attached a pic of what alternate angles generally look like to make this clearer).

Alternate angles are equal, which means x is equal to the angle at the bottom right of the triangle, which is 60°.

The required, each person can have 2/7 of a cake. This fraction cannot be simplified any further, so the answer is 2/7.

A fraction is a mathematical concept that can be used to express a portion of a whole or a number that can be written as the ratio of two integers.

here,
To divide the 2 cakes equally among 7 people, we can use division. We can think of the total amount of cake as 2 whole cakes or 2/1 cakes. To find out how much cake each person can have, we can divide the total amount of cake by the number of people:

2/1 cakes ÷ 7 people = 2/1 × 1/7 = 2/7 cakes per person

So each person can have 2/7 of a cake. This fraction cannot be simplified any further, so the answer is 2/7.

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Answer:

16.66667% increase

Step-by-step explanation:

100 x 350 - 300/ 300 = 50/3 = 16.66667% increase

Formula for percent increase is below↓

Answer:

Step-by-step explanation:

The probability of rolling a sum of 11 on the first roll of two dice is 1/36, as there is only one combination of dice that can add up to 11 (a 5 and a 6).

The probability of rolling a sum of 5 on the second roll of two dice is also 1/36, as there is only one combination of dice that can add up to 5 (a 1 and a 4).

The probability of two independent events occurring is equal to the product of their individual probabilities. So, the probability of rolling a sum of 11 on the first roll and a sum of 5 on the second roll is:

1/36 * 1/36 = 1/1296

So, the probability of rolling a sum of 11 on the first roll and a sum of 5 on the second roll is 1/1296.

The mean of the given data is 1744 days, median of the given data is 1460.5 days, mode of the given data is 1461 days & 4422 days.

To find the mean, median, and mode of the lengths of terms of the US Presidents that preceded Joe Biden:

Mean:

To find the mean, we add up all of the term lengths and divide by the total number of terms:

Mean = (4422 + 2922 + 2865 + 2840 + 2728 + 2041 + 2027 + 1886 + 1654 + 1503 + 1461 + 1460 + 1430 + 1419 + 1262 + 1036 + 969 + 895 + 881 + 492 + 199 + 31) / 44

Mean = 1743.77 days

Median:

To find the median, we need to arrange the term lengths in order from smallest to largest, and then find the middle term. In this case, since we have an even number of terms, we will take the average of the two middle terms:

31 199 492 881 895 969 1036 1262 1419 1430 1460 1461 1503 1654 1886 2027 2041 2728 2840 2865 2922 4422

Median = (1460 + 1461) / 2

Median = 1460.5 days

Mode:

The mode is the most frequently occurring term length. In this case, there are two modes: 1,461 days and 4,422 days.

Since the term length of FDR is much higher than all the other term lengths, it has pulled up the mean to a higher value than the other measures of central tendency. Additionally, the mode being a high value is likely due to the fact that FDR served for more than three terms, which is an outlier in the data set.

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Answer:

Planes

Step-by-step explanation:

You can think of a plane as a sheet of paper that goes on in all directions.

Answer:

B. planes

Step-by-step explanation:

The grammer makes sense

Answer:

Step-by-step explanation:

we have two rectangles side by side, the larger one measures 8m by 6m, the smaller one 5m by 4m, the 4 meters is the difference between the base  (10m) and the 6m side, so we find the areas and add them using the formula A = L x W, the result is not in the choices but it is right.

6 * 8 + 4 * 5 =                     remember PEMDAS

48 + 20 =

68 m²

The total value of $6800 compounded quarterly at 6% for 3 years is $8,123

From the question, we have

A = final amount

P = principal amount (initial investment) = $6800

r = annual interest rate = 0.06 ie. 6%

n = number of times interest is compounded per year = 4

t = time (in years) = 3

The total value is calculated as:

A = P(1 + r/n)^(nt)

substitute the known values in the above equation, so, we have the following representation

A = 6800(1 + 0.06/4)^(4*3)

Evaluate

A = 8130.2

Hence,, the value is $8130.2

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Answer:

11 bat and 8 helmets.

Step-by-step explanation:

Let x = the number of bats

Let y = the number of batting helmets

x + y = 19  Rewrite as y = 19 - x

18.25x + 24.50y = 369.75  Multiply by 100

1825x + 2450y = 36975  Substitute 19 - x for y

1825x + 2450(19 -x) = 39675   Distribute the 2450

1825x + 46550 - 2450x = 39675  combine like terms

-625x + 46550 = 39675  subtract 46550 from both sides

-625x = -6875  Divide both sides by -625

x = 11

He bought 11 bats

x + y = 19  Substitute 11 for x to solve for y

11 + y = 19  Subtract 11 from both sides

y = 8

He bought 8 helmets.

Answer:

Step-by-step explanation:

Here's a step by step solution with more details:

Let's call the length of the two equal sides of the triangle as x.

The third side, which is 1 1/3 cm longer, will have a length of x + 1 1/3 cm.

The perimeter of the triangle is 5 2/5 cm, so we can write an equation using the lengths of the sides:

x + x + (x + 1 1/3) = 5 2/5

Simplifying the equation:

2x + 1 1/3 = 5 2/5

Subtracting 1 1/3 from both sides:

2x = 4 1/5

Dividing both sides by 2:

x = 2 2/5

So the two equal sides of the triangle are 2 2/5 cm and the third side is 2 2/5 + 1 1/3 = 3 7/15 cm.

Answer:

One equal side = [tex]1\frac{16}{45}[/tex]cm and third side is [tex]2\frac{31}{45}[/tex]cm

Step-by-step explanation:

This is describing an isosceles triangle

1[tex]\frac{1}{3}[/tex] = [tex]\frac{4}{3}[/tex]

5[tex]\frac{2}{5}[/tex] = [tex]\frac{27}{5}[/tex]

Let

x = one of the two equal sides of the triangle

∴ Third side of triangle = [tex]\frac{4}{3} + x[/tex]

Perimeter of a triangle = Sum of all three sides:

[tex]\frac{27}{5}[/tex] [tex]= x + x + (\frac{4}{3} + x)[/tex]

Expand the parenthesis using the Distributive Law and bring all the like terms together:

[tex]=\frac{27}{5} = 2x + \frac{4}{3} + x[/tex]

[tex]= \frac{27}{5} = 3x + \frac{4}{3}[/tex]

[tex]= \frac{27}{5} -\frac{4}{3} = 3x[/tex]

The two denominators of the two fractions have to be manipulated to be made the same:

[tex]= (\frac{3}{3})(\frac{27}{5}) - (\frac{5}{5})(\frac{4}{3}) = 3x[/tex]

[tex]= \frac{81}{15} - \frac{20}{15} = 3x[/tex]

[tex]= \frac{81 - 20}{15} = 3x[/tex]

[tex]= \frac{61}{15} = 3x[/tex]

Cross-multiplication is added:

[tex]= (61)(1) = (15)(3x)[/tex]

[tex]= 61 = 45x[/tex]

Isolate x and make it the subject of the formula:

x = [tex]\frac{61}{45}[/tex]

x = One of the two equal sides = [tex]1\frac{16}{45}[/tex]cm

∴Third side:

= [tex]\frac{61}{45} + \frac{4}{3}[/tex]

= [tex]\frac{61}{45} + (\frac{15}{15})(\frac{4}{3})[/tex]

= [tex]\frac{61}{45} + \frac{60}{45}[/tex]

= [tex]\frac{61 + 60}{45}[/tex]

= [tex]\frac{121}{45}[/tex]

= [tex]2\frac{31}{45}[/tex]cm

Answer: no exact answer

Step-by-step explanation:

Answer: 6.7

Step-by-step explanation: 7^2-2^2=45

square 45 =6.7

The demonstration of magnitude of power given by 80 kg monkey by climbing a 15 meter tree in half a minute is equal to option b.  392 J/S.

Weight 'm' of the monkey is equal to 80kilogram

Height 'h' of the tree is equal to 15 meter

Time 't' taken by monkey to climb a tree = half a minute

                                                                    = 30 minutes

g = 9.8 m/s²

Magnitude of power = ( m × g × h )/ t

⇒ Magnitude of power = ( 80 × 9.8 × 15 )/ 30

⇒ Magnitude of power = 784 / 2

⇒ Magnitude of power = 392 J/S

Therefore, the magnitude of the power for the given weight , displacement and time is equal to option b. 392 J/S.

The above question is incomplete, the complete question is:

A 80 Kg monkey climbs a 15 meter tree in half a minute. What is the magnitude of power the monkey demonstrated?

a. 13.1 J/S

b. 392 J/S

c. 784 J/s

d. 11760 J/s​

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The y-coordinate for the solution to the system of equations is y = -3.

The substitution method is typically used in mathematics to solve an equation system. In this approach, you solve the equation for one variable first, then you enter its value into the other equation.

Simultaneous equations may usually be solved easily using the substitution method. There are direct ways that can give you the value of the unknown variables, such as cross-multiplication techniques. However, this method can be chosen over other algebraic methods for straightforward equations that don't require complicated calculations.

The system of equation is given as:

y = 1/2x - 4

y = -2x + 1

Substituting the value of y in equation 1 we have:

-2x + 1 = 1/2x - 4

-2x + 1 = x - 8 / 2

(-2x + 1)(2) = x - 8

-4x + 2 = x - 8

2 + 8 = x + 4x

10 = 5x

x = 2

Substituting the value of x in the second equation:

y = -2(2) + 1

y = -4 + 1

y = -3

Hence, the y-coordinate for the solution to the system of equations is y = -3.

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The value of f(3) is 2.

Option B is the correct answer.

A function has an input and an output with a relationship between them.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = 1/4 x [tex]2^x[/tex]

Substitute x = 3.

f(3) = 1/4 x 2³

f(3) = 1/4 x 8

f(3) = 2

Thus,

The value of f(3) is 2.

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On solving the provided question, we can say that By fraction, 3/4 times 5/7 is 15/28 and Action games are 15/28 of the apps.

Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.

By fraction,

3/4 times 5/7 is 15/28.

Action games are 15/28 of the apps.

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The quantity of cholesterol in an egg is 272 mg

The quantity of cholesterol in a cupcake is 18 mg

The quantity of cholesterol in a slice of pizza is 9 mg

Let the amount of egg be e

Let the amount of cupcake be c

Let the amount of pizza be p

By eating 1 egg, 1 cupcake, and 1 slice of pizza, a child consumes 299 mg of cholesterol

e + c + p = 299

The child eats 3 cupcakes and 4 slices of pizza, he or she takes in 90 mg of cholesterol

3c + 4p = 90

By eating 3 eggs and 1 cupcake, a child consumes 834 mg of cholesterol

3e + c = 834

e + c + p = 299

3c + 4p = 90

3e + c = 834

solving the simultaneous equation gives

e = 270

c = 18

p = 9

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Answer:

Step-by-step explanation:

To calculate the compound interest on Mary's savings account, we can use the formula:

A = P * (1 + r/n)^(nt)

Where:

A is the amount after t years

P is the initial principal (£12000)

r is the interest rate (1.5%)

n is the number of times the interest is compounded in a year (let's assume it's compounded annually)

t is the number of years (2)

So, plugging in the values, we get:

A = £12000 * (1 + 0.015/1)^(1 * 2)

A = £12000 * (1.015)^2

A = £12000 * 1.0302

A = £12363.84

So, after 2 years, Mary's £12000 investment would be worth £12363.84, including the compound interest.

Answer:t he autocorrelation of the time series X at lag 2 is approximately -0.018.

Step-by-step explanation:

To find the autocorrelation of the time series X at lag 2, we need to calculate the covariance between X(t) and X(t-2). This can be done using the following formula:

r(2) = cov(X(t), X(t-2)) / var(X(t))

where cov(X(t), X(t-2)) is the covariance between X(t) and X(t-2), and var(X(t)) is the variance of X(t).

To calculate the covariance, we'll use the following formula:

cov(X(t), X(t-2)) = sum((X(t) - mean(X(t))) * (X(t-2) - mean(X(t-2)))) / (n - 1)

where n is the number of observations in the time series. To calculate the variance, we'll use the following formula:

var(X(t)) = sum((X(t) - mean(X(t)))^2) / (n - 1)

First, let's calculate the mean of X(t):

mean(X(t)) = (47 + 64 + 23 + 71 + 38 + 64 + 55 + 41 + 59 + 48) / 10 = 51

Next, let's calculate the covariance between X(t) and X(t-2):

cov(X(t), X(t-2)) = sum((X(t) - 51) * (X(t-2) - 49)) / (10 - 1) = -10.3

Finally, let's calculate the variance of X(t):

var(X(t)) = sum((X(t) - 51)^2) / (10 - 1) = 563.7

Plugging in these values, we can find the autocorrelation at lag 2:

r(2) = cov(X(t), X(t-2)) / var(X(t)) = -10.3 / 563.7 = -0.018

So the autocorrelation of the time series X at lag 2 is approximately -0.018.

The total area of the shaded region for the region x = 5y³ , x = 5y² in the interval ( 5, 1 ) is equal to ( 5 / 12 ).

From the attached graph :

The area of the shaded region :

x = 5y³ , x = 5y² for the interval ( 5, 1 ) is equal to :

= [tex]\int\limits^1_0 {( 5y^{2 } - 5y^{3 }}) \, dy[/tex]

=  [ ( 5y³/3 ) - ( 5y⁴ / 4 ) ][tex]| \limits^1_0[/tex]

Substitute the lower limit and upper limit we get,

= (5 /3 )( 1 )³ - 0  - ( 5 / 4 )( 1⁴) + 0

= ( 5 / 3 ) - ( 5 / 4 )

= ( 20 - 15 ) / 12

= 5 / 12

Therefore, the total area of the shaded region in the given graph for the lower and upper limit is equal to ( 5 / 12 ) .

The given question is incomplete, I answer the question in general according to my knowledge:

Find the total area of the shaded region x = 5y³ , x = 5y² for the interval

( 5, 1 ).

Graph is attached.

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Answer:

Step-by-step explanation:

In the compound interest formula: A = P(1 + r)^t

A represents the amount of money in the account at the end of the term t, including interest.

P represents the initial principal, or the amount of money invested.

r represents the interest rate, usually expressed as a decimal.

t represents the number of time periods over which the interest is compounded.

In the continuously compounded interest formula: A = Pe^(rt)

A represents the amount of money in the account at the end of the term t, including interest.

P represents the initial principal, or the amount of money invested.

r represents the interest rate, usually expressed as a decimal.

t represents the number of time periods over which the interest is compounded.

So the variables in the formulas and their descriptions are:

A: the amount of money in the account at the end of the term t, including interest

P: the initial principal, or the amount of money invested

r: the interest rate, usually expressed as a decimal

t: the number of time periods over which the interest is compounded.

Answer:

the answer is 25c²

Step-by-step explanation:

(5c-3d)²-9d²

5²c²+3²d²-9d²

25c²+9d²-9d²

25c²

Answer:

= 25c² - 30cd

Step-by-step explanation:

(5c-3d)²-9d²

[tex](5c - 3d)(5c - 3d) - 9 {d}^{2} \\ 5c(5c - 3d) - 3d(5c - 3d) - 9{d}^{2} \ \\ 25 {c}^{2} - 15cd - 15cd + 9 {d}^{2} - 9 {d}^{2} \\25 {c}^{2} - 30cd[/tex]

A. The indifference curve of a consumer is negatively sloped to the right because it represents the consumer's preference for one good over another. As the consumer's income increases, their willingness to substitute one good for the other increases.

B. The indifference curve is convex to the origin because it shows the diminishing marginal rate of substitution of the two goods. As the consumer reaches the optimal combination of goods, the marginal rate of substitution between the two goods decreases.

C. Using the Lagrange method, the optimum combination of goods can be determined as follows:

Let L(X,Y) be the Lagrangian of this problem:

L(X,Y) = √X² + Y² - λ(200 - 3X - 4Y)

Where λ is the Lagrange multiplier.

The optimal solution is obtained by setting the derivatives of L with respect to X and Y to 0 and solving the equations simultaneously.

∂L/∂X = 0 -> X = 11.85

∂L/∂Y = 0 -> Y = 8.57

Therefore, the optimum combination of goods is X = 11.85 and Y = 8.57.

D. The slope of the indifference curve is equal to the slope of the budget line. This can be shown by comparing their respective equations and noting that their slopes are the same. The equation for the indifference curve is Y/X = (-2/3) and the equation for the budget line is Y/X = (-3/4). Since these equations are the same, it follows that the slopes of the two lines are equal.

Answer:  Weight of water in 1 cubic foot water (in pounds)

Weight of water in 1 cubic foot water (in ounces)=

Step-by-step explanation:

Given: One cubic foot holds 7.48 gallons of water.

One gallon of water weighs 8.33 pounds.

To find the weight of water in 1 cubic foot water in pounds we apply Unitary method.

Weight of water in 1 cubic foot water (in pounds)

⇒Weight of water in 1 cubic foot water (in pounds)

Since , 1 pound = 16 ounces .

Weight of water in 1 cubic foot water (in ounces)=

Step-by-step explanation:

Step-by-step explanation:

We can start by using an equation to represent the given information. Let's call the number p, and the number k, then:

k = (1/5)p + 6

So, "six more than one-fifth of a number p is equal to a number k" can be represented mathematically as k = (1/5)p + 6. To find the value of p, we can solve for p:

p = 5k - 30

So, p is equal to 5 times the value of k minus 30.

Answer: Scalene Right

Step-by-step explanation:

None of the side lengths are equal and there's a 90 degree angle