please answer 10-13 and show work please

Therefore, Thabo will get R18, Patrick will get R24, and Lucas will get R30.

In mathematics, a ratio is a comparison between two quantities or numbers, indicating how many times one quantity is contained within another. Ratios are often expressed in the form of a fraction, with the first quantity as the numerator and the second quantity as the denominator. Ratios can also be simplified by dividing both the numerator and denominator by their greatest common factor. Ratios are used in many areas of mathematics, science, and everyday life, such as in finance, cooking, and sports. They are particularly useful for comparing two quantities of different units or scales, as they provide a standardized way to express the relationship between them.

Here,

To determine how much each person will get, we first need to find the total of the ratios which is:

3 + 4 + 5 = 12

This means that the total amount of money is divided into 12 equal parts.

To find out how much each person gets, we need to multiply their share of the ratio by the total amount of money:

Thabo's share = 3/12 x R72 = R18

Patrick's share = 4/12 x R72 = R24

Lucas's share = 5/12 x R72 = R30

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Answer:

\(4.5x - 4 = 14 \\ 4.5x = 14 + 4 \\ 4.5x = 18 \\ x = \frac{18}{4.5} \\ x = 4\)

Answer: x=4

Step-by-step explanation:  4.5x-4=14

4.5x−4+4=14+4

4.5x/4.5=18/4.5

x=4

The standard deviation of the sample of 14 measurements is 4.8.

Given data: A sample of 12 measurements has a mean of 33 and a standard deviation(SD) of 5. Suppose that the sample is enlarged to 14 measurements, by including two additional measurements having a common value of 33 each. A. Find the mean of the sample of 14 measurements. The mean of the sample of 14 measurements= 33.B. Find the standard deviation of the sample of 14 measurements.  

Let's determine the population standard deviation of 12 measurements:

Population SD formula:σ=√((Σ(X−μ)^2)/N)

Where,σ = standard deviation Σ = the sum of X = each value μ = mean N = the number of values

σ=√((Σ(X−μ)^2)/N)= √((Σ(X−33)^2)/12)= √((2097)/12)= √(174.75) = 13.2

To calculate the standard deviation of the sample of 14 measurements, we must use the following formula for the sample SD:

$$s=\sqrt{\frac{1}{n-1}\sum_{i=1}^{n}(x_i-\overline{x})^2}$$

We have n = 14 and 2 of them are the same (33), so:

$$s=\sqrt{\frac{1}{14-1}\left[(12\times 5^2)+(2\times 0^2)\right]}$$$$s=\sqrt{\frac{1}{13}\left[300\right]}$$$$s=\sqrt{23.08}$$$$s=4.8$$

Therefore, the standard deviation of the sample of 14 measurements is 4.8.

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The mean of the sample of 14 measurements is 33

The standard deviation of the sample of 14 measurements is 1.34

From the question, we have the following parameters that can be used in our computation:

Mean = 33

Standard deviation = 5

Sample size = 12

The sample mean is always equal to the population mean

So, we have

Mean = 33

Here, we have

SD = σ/√n

So, we have

SD = 5/√14

Evaluate

SD = 1.34

Hence, the standard deviation is 1.34

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The presence of casomorphins and the stimulation of dopamine release, contribute to the addictive nature of cheese, making it difficult to resist for many individuals.

Cheese possesses two properties that contribute to its addictive nature. Firstly, cheese contains casein, a protein found in milk, which breaks down during digestion to produce casomorphins. Casomorphins are opioid-like substances that can bind to the brain's opioid receptors, leading to feelings of relaxation and pleasure. This mechanism is similar to the effects of addictive drugs, reinforcing the craving for cheese.

Secondly, cheese is rich in fat, particularly saturated fats. These fats have been shown to stimulate the release of dopamine, a neurotransmitter associated with pleasure and reward, in the brain. The combination of the creamy texture and the release of dopamine creates a pleasurable sensory experience, further enhancing the appeal of cheese.

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The general solution is given by: y = c1cos(5x) + c2sin(5x) + 1/25(- cos(ln(sec5x))) + 5xsin(5x)

The most general solution to the original nonhomogeneous differential equation can be found by adding the homogeneous solution and the particular solution together. That is,

y = y_h + y_p

= c1cos(5x) + c2sin(5x) + 1/25(- cos(ln(sec5x))) + 5xsin(5x)

This is the most general solution to the original nonhomogeneous differential equation. We can use the arbitrary constants c1 and c2 to find specific solutions for different initial conditions. The general solution is given by:

y = c1cos(5x) + c2sin(5x) + 1/25(- cos(ln(sec5x))) + 5xsin(5x)

This is the final answer. Note that we have used the terms "general solution" and "arbitrary constants" in our answer, as instructed.

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Answer:

6x

Step-by-step explanation:

3x/y=x/2y

Since 2y is 2X greater than y, 6x is 2X greater than 3x.

So,

The answer is 6x.

To draw a line through each point using a slope of "m," you can follow these steps: Choose a value for "m" to represent the slope of the straight line.. Plot the given points on a coordinate plane. Use the slope-intercept form of a linear equation, y = mx + b, where "m" is the slope and "b" is the y-intercept.

For each point, substitute the x- coordinate plane into the equation and solve for the y-coordinate. Connect the points on the graph using a straight line.

In this graph, the points (1, 2), (2, 3), (3, 4), and (4, 5) are connected by a straight line with a slope of 1/4.

  |

4 |            x

  |        x

3 |    x

  |x

2 |

  |

1 |

  |

0 |_________________________

    0  1  2  3  4  5  6  7  8

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Answer:

trinomial

Step-by-step explanation:

-x² - 1/2 + x

if you are asking for the specific name, it is a trinomial because there are 3 terms.

To determine the minimum score needed to ensure that you are in the top 7%, we need to find the z-score associated with the top 7% and then convert it back to the raw score.

The top 7% corresponds to an area of 0.07 under the standard normal distribution curve. To find the z-score associated with this area, we can use a standard normal distribution table or a calculator.

Using a standard normal distribution table or calculator, we find that the z-score corresponding to an area of 0.07 is approximately 1.4051.

To convert this z-score back to the raw score, we can use the formula:

x = z * standard deviation + mean

Substituting the values into the formula, we get:

x = 1.4051 * 100 + 500

x ≈ 140.51 + 500

x ≈ 640.51

Therefore, the minimum score needed to ensure that you are in the top 7% is approximately 640.51.

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The two tables, Able a and Table b, show the conversion between Celsius and Fahrenheit temperatures. The tables provide a convenient way to convert temperatures between the two scales.

The relationship between the two functions is that the ordered pairs (x, y) for one function correspond to the ordered pairs for the other function. In other words, the Celsius temperature in Able a corresponds to the Fahrenheit temperature in Table b, and vice versa. This demonstrates the relationship between the Celsius and Fahrenheit scales, where there is a direct correlation between the two.

The tables provide a convenient way to convert temperatures between the two scales.

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Answer:

Timespan is 1 hour(s) and 35 minute(s).

Step-by-step explanation:

Hope this helps

Answer for question 1 is Percentage Calculator: 6 is what percent of 15? = 40.

Answer for question 2 is What is 18 percent (calculated percentage %) of number 32? Answer: 5.76.

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Answer:

1. 40%

2. 56.25%

Step-by-step explanation:

1. N% of 15 = 6

N/100 x 15 =6

N = (6 × 100)/15

N = 40

2.N% of 32 = 18

N/100 x 32 = 18

N = (18 x 100) /32

N= 56.25

17(quarters)

10(dimes)

Hi there !

dimes = 0.1$ = 10c

quarters = 0.25$ = 25c

d + q = 27 => d = 27 - q

10d + 25q = 525

replace d

10(27 - q) + 25q = 525

270 - 10q + 25q = 525

25q - 10q = 525 - 270

15q = 255

q = 255 : 15

q = 17(quarters)

d = 27 - q

= 27 - 17

d = 10(dimes)

Good luck !

The length of a standard basketball court is 94 feet (28.65 meters), and the width is 50 feet (15.24 meters).

A standard basketball court is rectangular in shape and follows certain dimensions specified by the International Basketball Federation (FIBA) and the National Basketball Association (NBA). The length and width of a basketball court may vary slightly depending on the governing body and the level of play, but the most commonly used dimensions are as follows:

The length of a basketball court is typically 94 feet (28.65 meters) in professional settings. This length is measured from baseline to baseline, parallel to the sidelines.

The width of a basketball court is usually 50 feet (15.24 meters). This width is measured from sideline to sideline, perpendicular to the baselines.

These dimensions provide a standardized playing area for basketball games, ensuring consistency across different courts and facilitating fair play. It's important to note that while these measurements represent the standard dimensions, there can be slight variations in court size depending on factors such as the venue, league, or specific regulations in different countries.

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The standard error of the average sample weight when 15 participants are randomly selected for the sample is 9.05 (rounded to two decimal places).

The standard error of the average sample weight when 15 participants are randomly selected for the sample can be calculated using the formula given below:SE = σ/√nWhere,σ = standard deviation of the populationn = sample sizeSE = standard error of the meansubstituting the given values,SE = 35/√15 = 9.05

Note:When using the given formula, it is important to note that it assumes a normal distribution of sample means. The standard error is used to estimate the true value of the mean from the sample data. The larger the sample size, the smaller the standard error. The smaller the standard error, the more precise the estimate of the true value of the mean.

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Answer:

Less than

Step-by-step explanation:

To see how 3/4 compares to 3/8, give em the same denominator. The simplest way is to multiply 3/4 by 2. Multiply each the numerator and denominator by 2. That gives you 6/8. She needs 6/8 but only has 3/8, so less than a pizza.

It is correct to say that any point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment.

Any point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment. What is a perpendicular bisector? A perpendicular bisector is a line that intersects a line segment and forms a 90-degree angle. It divides the line segment into two equal halves.Each point on the perpendicular bisector of a line segment is equidistant from the endpoints of the segment. This means that the distance from any point on the line to one endpoint of the segment is the same as the distance to the other endpoint of the segment.

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The cartesian coordinates of the given polar coordinates are

(A) (2, π); (X, Y) = (-2, 0)

(B) (6, -2π/3); (X, Y) = (-3, -3√3)

The cartesian coordinates for the polar coordinates are calculated by the formulae,

x = rcosθ, and y = rsinθ

Where the polar coordinates are (r, θ).

The cartesian coordinates for the given polar coordinates are as follows:

(A) (r, θ) = (2, π)

Then,

x = r cosθ = 2 cos(π) = 2(-1) = -2

y =r sinθ = 2 sin(π) = 2(0) = 0

Therefore, the cartesian coordiantes are (X, Y) = (-2, 0).

(B) (r, θ) = (6, -2π/3)

Then,

x = r cosθ = 6 cos(-2π/3) = 6(-1/2) = -3

y =r sinθ = 6 sin(-2π/3) = 6(-√3/2) = -3√3

Therefore, the cartesian coordinates are (X, Y) = (-3, -3√3)

The plot for the given polar coordinates on a polar grid is shown below:

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So, \(\frac{1}{y-x}-\frac{1}{x-y}\) is equivalent to \(\frac{2}{y-x}\).

We can simplify \(\frac{1}{y-x}-\frac{1}{x-y}\) algebraically to evaluate the expression.

The difference between these two terms is that the sign in front of each term is reversed.

Let's look at the terms one by one:

Term 1: \(\frac{1}{y-x}\)

Term 2: \(\frac{1}{x-y}\)

Let's simplify the terms, starting with Term 1:

\(\frac{1}{y-x}\)

can be simplified to \(\frac{-1}{x-y}\).

Now, we can rewrite the expression as:

\(\frac{1}{y-x}-\frac{1}{x-y}

= \frac{1}{y-x} + \frac{1}{y-x}

= \frac{2}{y-x}\)

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Thus, the unique solution to the given differential equation with the initial condition y(1) = 13 is \(y = 1 / (- (1/4) * x^4 + 17/52).\)

To solve the given differential equation, we'll use the method of separation of variables.

First, we rewrite the equation in the form\(dy/dx = y^2 * x^3\)

Separating the variables, we get:

\(dy/y^2 = x^3 * dx\)

Next, we integrate both sides of the equation:

\(∫(dy/y^2) = ∫(x^3 * dx)\)

To integrate \(dy/y^2\), we can use the power rule for integration, resulting in -1/y.

Similarly, integrating \(x^3\) dx gives us \((1/4) * x^4.\)

Thus, our equation becomes:

\(-1/y = (1/4) * x^4 + C\)

where C is the constant of integration.

Given the initial condition y(1) = 13, we can substitute x = 1 and y = 13 into the equation to solve for C:

\(-1/13 = (1/4) * 1^4 + C\)

Simplifying further:

-1/13 = 1/4 + C

To find C, we rearrange the equation:

C = -1/13 - 1/4

Combining the fractions:

C = (-4 - 13) / (13 * 4)

C = -17 / 52

Now, we can rewrite our equation with the unique solution:

\(-1/y = (1/4) * x^4 - 17/52\)

Multiplying both sides by -1, we get:

\(1/y = - (1/4) * x^4 + 17/52\)

Finally, we can invert both sides to solve for y:

\(y = 1 / (- (1/4) * x^4 + 17/52)\)

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Answer:

i cant see what u attached please reupload

Step-by-step explanation:

D. 45,000 ft,²

As per the scale given,

1 in. = 15 ft.

10 in. = 10×15 ft. = 150 ft.

20 in. = 20×15 ft. = 300 ft.

So, area = 150 ft. × 300 ft. = 45,000 ft.²

Answer: The domain of a function refers to the set of all possible input values for which the function is defined. In the case of the function y = 2x - 6, the domain is all real numbers since the function is defined for any value of x.

The range of a function, on the other hand, refers to the set of all possible output values that the function can produce. To find the range of the function y = 2x - 6, we need to determine the lowest and highest values that the function can produce.

Since the coefficient of x in the function is positive (i.e. 2), the function is increasing as x increases. This means that as x increases, the value of y also increases without bound. Similarly, as x decreases, the value of y also decreases without bound.

Therefore, the range of the function y = 2x - 6 is all real numbers.

Step-by-step explanation:

Answer:

x = -1 and y = 3     x = 3 and y = -1

Step-by-step explanation:

Answer:

A: 120

Step-by-step explanation:

5! means 5 factorial

the factorial of a number is the number times every whole number until 1

in this case,

5 * 4 * 3 * 2 * 1

5 * 4 = 20 , 3 * 2 * 1 = 6

20 * 6 = 120 (option A)

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Answer:

a 120

Step-by-step explanation:

Answer: \(y=-\frac{1}{2}x-3\)

Step-by-step explanation:

The slope of the line is

\(\frac{-4-(-3)}{2-0}=\frac{-1}{2}\)

The y-intercept is (0,-3), meaning the equation is \(y=-\frac{1}{2}x-3\)

Answer:

This is a geometric sequence, and the common difference/ratio is 0.5

Step-by-step explanation:

The difference between 4 and 2 is * 0.5, or 1/2, which is the same between 2 and 1. This means that we are dividing.

Remember that arithmetic means plus or minus, while geometric means multiplication or division. Because we are dividing, this is a geometric sequence.

The common difference/ratio in this is divided by 2, which is the same as being multiplied by 0.5.

Answer:

x = 27/5

Step-by-step explanation:

5x - 1 = 26

Add 1 to each side

5x - 1 = 26

5x-1+1 = 26+1

5x = 27

Divide each side by 5

5x/5 = 27/5

x = 27/5

Answer:

Option D. All of the above