PLEASE HELP!

The following are the last 10 run scores Colin got in cricket: 31, 10, 26, 16, 28, 31, 9, 11, 8, 1 a) Work out Colin's mean score. b) Colin plays cricket again on Sunday. He gets 27 runs. What is his new mean score? Give your answers as decimals.

In conclusion  62 inches is equal to 157.48 centimeters (rounded to the nearest tenth).

How to solve?

Part 1 of 2:

The first method to convert 62 inches to centimeters involves using the conversion factor of 1 inch equals 2.54 centimeters. We can set up a proportion to solve for the number of centimeters in 62 inches:

1 in. x cm

----- = -----

2.54 62 in.

To solve for x, we can cross-multiply and simplify:

1 × x = 2.54 × 62

x = 157.48

Therefore, 62 inches is equal to 157.48 centimeters (rounded to the nearest tenth).

So the first method gives us 157.5 cm as the answer.

Part 2 of 2:

The second method to convert 62 inches to centimeters involves multiplying 62 by the conversion factor of 2.54 centimeters per inch:

62 in. × 2.54 cm/in = 157.48 cm

Therefore, using this method, we also get 157.5 cm as the answer (rounded to the nearest tenth).

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Answer: D

Step-by-step explanation:

A. \(y=2 \cdot 2^x\), which fails for x=1.

B. \(y=4x^2\), which fails for x=1.

C. \(y=3x\), which fails for x=2.

D. \(y=3x^2\). which is correct for x=1, 2, 3.

The values of x in each equation are;

1) 128

2) 1500

Forming an equation involves expressing a mathematical relationship or statement using mathematical symbols and symbols of equality. The goal is to represent a real-life situation, a mathematical problem, or a hypothesis in a clear and concise way that can be easily analyzed and solved.

We have that;

1) let the number be x

85/100 * x = 108.8

x = 108.8 * 100/85

= 128

2) Let the number of the kettle corn be x;

6/10 * 2500 = x

x = 1500

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The solution to the given initial-value problem is y(x) = -3ex + 5e5x + 4 + 20x + 4x^2.To solve the given initial-value problem, we start by finding the complementary solution to the homogeneous equation y''' - 2y'' + y' = 0.

The characteristic equation associated with this equation is r^3 - 2r^2 + r = 0, which can be factored as r(r-1)^2 = 0. Therefore, the complementary solution is y_c(x) = c1e^x + c2xe^x + c3x^2e^x.

Next, we find a particular solution to the non-homogeneous equation y''' - 2y'' + y' = 2 - 24ex + 40e5x. We assume a particular solution of the form y_p(x) = Aex + Be5x + C. By substituting this into the differential equation, we can determine the values of A, B, and C. After solving the resulting equations, we find A = -3, B = 5, and C = 4.

Finally, the general solution to the non-homogeneous equation is given by y(x) = y_c(x) + y_p(x). Plugging in the values of c1, c2, c3, A, B, and C, we obtain y(x) = -3ex + 5e5x + 4 + 20x + 4x^2. This represents the solution to the given initial-value problem.

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The interval of convergence is (-18/5, 18/5).

To express f(x) as a power series, we first need to decompose it into partial fractions:

f(x) = 11/(x^2 - 7x - 18) = 11/[(x - 9)(x + 2)]

Using partial fractions, we can write:

11/[(x - 9)(x + 2)] = A/(x - 9) + B/(x + 2)

Multiplying both sides by the denominator (x - 9)(x + 2), we get:

11 = A(x + 2) + B(x - 9)

Setting x = 9, we get:

11 = A(9 + 2)

A = 1

Setting x = -2, we get:

11 = B(-2 - 9)

B = -1

Therefore, we have:

f(x) = 1/(x - 9) - 1/(x + 2)

Now, we can write the power series of each term using the formula for a geometric series:

1/(x - 9) = -1/18 (1 - x/9)^(-1) = -1/18 * sigma^n=0 to infinity (x/9)^n

1/(x + 2) = 1/11 (1 - x/(-2))^(-1) = 1/11 * sigma^n=0 to infinity (-x/2)^n

So, putting everything together, we get:

f(x) = 1/(x - 9) - 1/(x + 2) = -1/18 * sigma^n=0 to infinity (x/9)^n + 1/11 * sigma^n=0 to infinity (-x/2)^n

The interval of convergence can be found using the ratio test:

|a_n+1 / a_n| = |(-x/9)^(n+1) / (-x/9)^n| + |(-x/2)^(n+1) / (-x/2)^n|

= |x/9| + |x/2|

= (|x|/9) + (|x|/2)

For the series to converge, we need |a_n+1 / a_n| < 1. This happens when:

(|x|/9) + (|x|/2) < 1

Solving for |x|, we get:

|x| < 18/5

Therefore, the interval of convergence is (-18/5, 18/5).

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Answer:

Charmaine earns $60.90 for 6h for mowing and 1h for babysitting.

Step-by-step explanation:

We must write the data problems.

Charmaine = $8.80/h mowing

Charmaine = $8.10/h babysitting

How much will Charmaine earn for 6 h mowing and 1 h babysitting?

1 h mowing ....................... $8.80

6 h mowing ....................... $x

x = 6 h mowing * $8.80

x = $52,8

To find the total earn of Charmaine, we have to gather the earns from mowing and babysitting.

$52,8 (from mowing) + $8.10 (from babysitting) = $60.90

Answer:14 ft

Step-by-step explanation: 50^2=x^2+48^2(Pythagorean theorem)

x^2=2500-2304

x^2=196

x=14

\(9 \geqslant w \\ \\ - 7 \leqslant w\)

"9 is greater than or equal to w" translates to \(9 \ge w\) which flips to \(w \le 9\). We swap both sides and flip the inequality sign as well.

"-7 is less than or equal to w" translates to \(-7 \le w\)

We have \(-7 \le w\) and \(w \le 9\) which then ultimately combine into the compound inequality \(-7 \le w \le 9\)

Sampling is the use of a subset of the population to represent the whole population or to inform about processes that are meaningful beyond the particular cases, individuals or sites studied.

In non-probability sampling, the sample is selected based on non-random criteria, and not every member of the population has a chance of being included. Common non-probability sampling methods include convenience sampling, voluntary response sampling, purposive sampling, snowball sampling, and quota sampling.

Using the given conditions that sin(20) = cos(2u) = tan(24) = 3, we can find the exact values of sin(2u), cos(2u), and tan(2u) using the double-angle formulas. By substituting the known values into the formulas, we can determine the exact values of these trigonometric functions.

Given sin(20) = 3, we can use the double-angle formula for sine to find sin(2u).

The double-angle formula for sine is sin(2u) = 2sin(u)cos(u). We know that sin(u) = -3/5, so we can substitute this value into the formula to calculate sin(2u).

Therefore, sin(2u) = 2(-3/5)(cos(u)).

Given cos(2u) = 3, we can use the double-angle formula for cosine to find cos(2u).

The double-angle formula for cosine is cos(2u) = cos^2(u) - sin^2(u). Since we already know sin(u) = -3/5 and cos(u) can be calculated using the Pythagorean identity (cos^2(u) = 1 - sin^2(u)), we can substitute these values into the formula to determine cos(2u).

Finally, given tan(24) = 3, we can use the double-angle formula for tangent to find tan(2u).

The double-angle formula for tangent is tan(2u) = (2tan(u))/(1 - tan^2(u)). By substituting the known value of tan(24) = 3 into the formula, we can calculate the exact value of tan(2u).

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Answer:

306m

Step-by-step explanation:

someone else asked the same question here! https://brainly.com/question/30091724

there are better explainations there :)

you're looking for the perimeter, so you need to add all the sides. that's 55+55+98+98, which is 306.

To evaluate the given integral using Green's theorem, we need to express it in the flux form.  The result of the integral is -r/6.

Green's theorem states that for a region R bounded by a simple closed curve C, the flux of the vector field F = (P, Q) across C is equal to the double integral of the curl of F over R.

In this case, we have the vector field F = (r^2xy, 1/2y^3), where r is the position vector (x, y).

The flux form of Green's theorem is:

\(∫∫R (curl F) · dA = ∫∫R (∂Q/∂x - ∂P/∂y) dA\)

Let's calculate the curl of F:

∂Q/∂x = 0

∂P/∂y = 2rxy

So, the curl of F is given by\((∂Q/∂x - ∂P/∂y) = 0 - 2rxy = -2rxy.\)

Now, let's evaluate the integral using the flux form of Green's theorem:

∫∫R (-2rxy) dA

Since the region R is a triangle with vertices (0,0), (1,0), and (0,1), we can express it as:

\(R = {(x, y) | 0 ≤ x ≤ 1, 0 ≤ y ≤ 1 - x}\)

Now, we can rewrite the integral:

\(∫₀^(1-x) (-2rxy) dy = -2rxy²/2 ∣₀^(1-x) = -rxy² ∣₀^(1-x) = -r(x-x²)\)

Let's evaluate the inner integral first:

\(∫₀^(1-x) (-2rxy) dy = -2rxy²/2 ∣₀^(1-x) = -rxy² ∣₀^(1-x) = -r(x-x²)\)

Now, evaluate the outer integral:

\(∫₀¹ -r(x-x²) dx = -r(x²/2 - x³/3) ∣₀¹ = -r(1/2 - 1/3) = -r(3/6 - 2/6) = -r(1/6) = -r/6\)

Therefore, the result of the integral is -r/6.

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The correct answer is that the probability of a cash flow being between $16,000 and $19,000 is approximately 18.59%.

To calculate the probability of a cash flow being between $16,000 and $19,000, we can use the standard deviation and assume a normal distribution.

We are given that the average cash flow is $14,000 with a standard deviation of $5,000. These values are necessary to calculate the probability.

The probability of a cash flow falling within a certain range can be determined by converting the values to z-scores, which represent the number of standard deviations away from the mean.

First, we calculate the z-score for $16,000 using the formula: z = (x - μ) / σ, where x is the cash flow value, μ is the mean, and σ is the standard deviation. Plugging in the values, we get z1 = (16,000 - 14,000) / 5,000.

z1 = 2,000 / 5,000 = 0.4.

Next, we calculate the z-score for $19,000: z2 = (19,000 - 14,000) / 5,000.

z2 = 5,000 / 5,000 = 1.

Now that we have the z-scores, we can use a standard normal distribution table or calculator to find the corresponding probabilities.

Subtracting the probability corresponding to the lower z-score from the probability corresponding to the higher z-score will give us the probability of the cash flow falling between $16,000 and $19,000.

Looking up the z-scores in a standard normal distribution table or using a calculator, we find the probability for z1 is 0.6554 and the probability for z2 is 0.8413.

Therefore, the probability of the cash flow being between $16,000 and $19,000 is 0.8413 - 0.6554 = 0.1859, which is approximately 18.59%.

So, the correct answer is that the probability of a cash flow being between $16,000 and $19,000 is approximately 18.59%.

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The probability of a cash flow between $16,000 and $19,000 is approximately 18.59%.

To calculate the probability of a cash flow being between $16,000 and $19,000, we can use the standard deviation and assume a normal distribution.

We are given that the average cash flow is $14,000 with a standard deviation of $5,000. These values are necessary to calculate the probability.

The probability of a cash flow falling within a certain range can be determined by converting the values to z-scores, which represent the number of standard deviations away from the mean.

First, we calculate the z-score for $16,000 using the formula: z = (x - μ) / σ, where x is the cash flow value, μ is the mean, and σ is the standard deviation. Plugging in the values, we get z1 = (16,000 - 14,000) / 5,000.

z1 = 2,000 / 5,000 = 0.4.

Next, we calculate the z-score for $19,000: z2 = (19,000 - 14,000) / 5,000.

z2 = 5,000 / 5,000 = 1.

Now that we have the z-scores, we can use a standard normal distribution table or calculator to find the corresponding probabilities.

Subtracting the probability corresponding to the lower z-score from the probability corresponding to the higher z-score will give us the probability of the cash flow falling between $16,000 and $19,000.

Looking up the z-scores in a standard normal distribution table or using a calculator, we find the probability for z1 is 0.6554 and the probability for z2 is 0.8413.

Therefore, the probability of the cash flow being between $16,000 and $19,000 is 0.8413 - 0.6554 = 0.1859, which is approximately 18.59%.

So, the correct answer is that the probability of a cash flow being between $16,000 and $19,000 is approximately 18.59%.

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An equation is formed of two equal expressions. The number of people that can sit at a table is 6.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the number of people that can be seated at a table be represented by x, while the number of people that can be seated in a booth is y.

The equation for the two floor plans can be written as,

24x + 11y = 254

12x + 17y = 242

Solving the above equations, by plotting the two of the given equations. Therefore, the number of people that can sit at a table is 6.

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The variables are evaluated to give;

1. 2

2. 6

An algebraic expression can be defined as an expression that is made up of terms, variables, coefficients, factors and constants.

These expressions are also thought to consist of mathematical or arithmetic operations such as;

From the information given, we have that;

A=1 b=2 c=3 x=3 y=2 z=1

1. ab

Let's substitute the values into the formula

1(2)

Multiply the values

2

2. Abc

Substitute the values

(1)(2)(3)

multiply the values

6

Hence, the values are 2 and 6

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The height to which the hollow sphere rolls up the incline is the same as the height to which the hollow cylinder rolls up, which is 1.0 m in this case.

To determine the height to which the hollow sphere rolls up the incline, we can use the principle of conservation of energy. The initial kinetic energy of both the hollow cylinder and hollow sphere is the same since they have the same mass and initial velocity. This kinetic energy is converted into potential energy as they roll up the incline. The potential energy gained by an object of mass m and height h is given by the formula:

PE = mgh

Since both the hollow cylinder and hollow sphere have the same mass, we can compare their potential energies. Let's assume the potential energy gained by the hollow cylinder is PE_cylinder and the potential energy gained by the hollow sphere is PE_sphere.

PE_cylinder = mgh_cylinder  ... (1)

PE_sphere = mgh_sphere  ... (2)

Since the initial velocity and mass are the same for both objects, we can equate their potential energies:

PE_cylinder = PE_sphere

mgh_cylinder = mgh_sphere

h_cylinder = h_sphere

Therefore, the height to which the hollow sphere rolls up the incline is the same as the height to which the hollow cylinder rolls up, which is 1.0 m in this case.

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A random variable is a quantitative outcome of a chance experiment.

A probability distribution includes the likelihood of each possible outcome.

A random variable is a variable whose value is determined by chance or randomness. It is often used to represent a numerical outcome of a chance experiment, such as the result of a coin toss, the roll of a die, or the outcome of a survey. Random variables can take on any numerical value, but it is often useful to assign probabilities to each possible value. This probability, known as a probability distribution or probability density function, describes the likelihood that a given value of the random variable will occur.

A normal distribution is a type of probability distribution that is symmetrical and bell-shaped, with the mean, median, and mode all equal. The values of the distribution are spread out around the mean, with the majority of the values within one standard deviation of the mean. A normal distribution is also known as a Gaussian distribution, as it was discovered by Carl Friedrich Gauss in the early 19th century.

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The side length of the square mat is 6 feet and the side length of the equilateral triangle mat is 8 feet, when x is equal to 3.

Let's solve for the side lengths of each game mat given the information provided.

For the square mat, the side length is given as x + 3 feet.

For the equilateral triangle mat, the side length is given as 3x - 1 feet.

To find the perimeters of the mats, we multiply the side length by the number of sides for each shape.

For the square mat:

Perimeter of square = 4 * (x + 3) = 4x + 12 feet

For the equilateral triangle mat:

Perimeter of triangle = 3 * (3x - 1) = 9x - 3 feet

Since both mats have the same perimeter, we can equate the two expressions:

4x + 12 = 9x - 3

To solve for x, let's simplify the equation:

12 + 3 = 9x - 4x

15 = 5x

Dividing both sides by 5, we find:

x = 3

Now that we have the value of x, we can substitute it back into the expressions for the side lengths of each mat:

For the square mat:

Side length = x + 3 = 3 + 3 = 6 feet

For the equilateral triangle mat:

Side length = 3x - 1 = 3(3) - 1 = 8 feet

Therefore, the side length of the square mat is 6 feet and the side length of the equilateral triangle mat is 8 feet, when x is equal to 3.

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There were approximately 13,333 gorillas 10 years ago. Rounded to the nearest thousand, there were 13,000 gorillas 10 years ago.

To find the approximate number of gorillas 10 years ago, we can use the information that the population declined by 70% over the last 10 years and that there are currently 4,000 gorillas left in the wild.

Let's assume the population of gorillas 10 years ago was "x."

The population 10 years ago declined by 70%, which means 30% of the population remains now (100% - 70% = 30%).

We can set up the equation:

30% of x = 4,000

To find 30% of x, we can multiply x by 0.30:

0.30 * x = 4,000

Now, solve for x:

x = 4,000 / 0.30

x ≈ 13,333.33

So, there were approximately 13,333 gorillas 10 years ago. Rounded to the nearest thousand, there were 13,000 gorillas 10 years ago.

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The rule of inference being used here is Modus Tollens. Modus Tollens is a valid deductive argument form that states if a conditional statement "If P, then Q" is true and the consequent Q is false, then the antecedent P must also be false.

In the given scenario, the conditional statement is "If the guard dog doesn't know a person, then it barks."

The observation that the dog didn't bark (Q is false) leads to the conclusion that the dog must have known the person (the antecedent P is false).

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The Value of the expression 2s³ - 4r² by substituting the given values into the expression is 246

Given the equation ; 2s³ - 4r²

To solve, substitute the values of r and s into the equation :

2(5)³ - 4(1)²

2(5 × 5 × 5) - 4(1 × 1)

2(125) - 4(1)

250 - 4

= 246

Therefore, the final value of the expression by substituting the value of r and s as 1 and 5 respectively is 246

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Answer:

because ur adding

Step-by-step explanation:

7+7=14

it's like adding as u always have

Answer:12 km

3 km per hour 3rd part i don't know 8 i don't know line means that is how fast in marks you re going

Step-by-step explanation:

With an off-course speed of 11 miles per hour, the ship will go 33 miles in 3 hours.

Multiplying in math is the same as adding equal groups. The number of items in the group grows as we multiply. Parts of a multiplication issue include the product, the two factors, and the product. The components in the multiplication problem 6 x 9 = 54 are the numbers 6 and 9, and the result is the number 54. One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual addition of sets of same size.

Here,

speed of ship= 11 miles/hour

time given= 3 hours

distance= speed * time

=11*3

=33 miles

The ship will cover 33 miles in 3 hours while moving at the speed of 11 miles/ hour off course.

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