2(3y-1)3(y-4)=13 please show step by step

The variables as length are L and width is W and the system of equations is L = 2W - 3 and 42 = 2(L + W) and the length and width are 13 feet and 8 feet respectively.

A rectangle is a geometrical figure in which opposite sides are equal.

The angle between any two consecutive sides will be 90 degrees.

Area of rectangle = length × width.

As per the given total fencing = 42 feet

Let's say the length is L and the width is W.

As per the given,

L = 2W - 3

Perimeter = 2(length + width)

42 = 2(L + W)

21 = 2W - 3 + W

21 + 3 = 3W

W = 8 feet

And, L = 2(8) - 3 = 13 feet

Hence "The variables as lengths are L and width is W and the system of equations is L = 2W - 3 and 42 = 2(L + W) and the length and width are 13 feet and 8 feet respectively".

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The Last one is your answer

Answer:

The last one i did this before

Step-by-step explanation:

The amount of salt that is in the tank after 20 minutes is;

A(20) = 267.56 Oz

Initial amount of salt in tank; A(0) = 40 Ounces

A solution containing 4 oz salt per gallon is pumped into the tank at a rate of 5 gal/min.

This means rate in oz/min = 4/1 × 5/1 = 20 oz/min

A'(t) = 20 - [(A(t)/(100)) × 5/1]

A'(t) = 20 - A(t)/20

Rearranging gives;

A'(t) + A(t)/20 = 20

Multiplying through by the integrating factor gives;

A'(t) [tex]e^{t/20}[/tex] + (A(t)/20) [tex]e^{t/20}[/tex] = 20[tex]e^{t/20}[/tex]

A(t) [tex]e^{t/20}[/tex] = 400[tex]e^{t/20}[/tex]  + C

Divide through by [tex]e^{t/20}[/tex] to get;

A(t) = 400 + C [tex]e^{-t/20}[/tex]

At initial condition of A(0) = 40, we have;

40 = 400 + C

C = -360

Thus; at time (t), the amount of salt left is given by;

A(t) = 400 - 360 [tex]e^{-t/20}[/tex]

A(20) = 400 - 360 [tex]e^{-20/20}[/tex]

A(20) = 400 - 132.44

A(20) = 267.56 Oz

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The slope of the line that points M and N lies on is [tex]-\frac{3}{4}[/tex]

Given:

[tex]M(1, 3)\\N(5, 0)[/tex]

Formula for slope of a line is:

[tex]slope (m) = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Let,

[tex]M(1, 3) = (x_1, y_1)\\N(5, 0) = (x_2, y_2)[/tex]

Substitute

[tex]Slope(m) = \frac{0-3}{5-1} \\= \frac{-3}{4} \\= -\frac{3}{4}[/tex]

Therefore, the slope of the line that contains M(1, 3) and N(5, 0) is: [tex]-\frac{3}{4}[/tex]

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To solve the equation 3x = 42, divide both sides by 3, which results in x = 14. This means you would pay $14. The process is similar to isolating a variable in quadratic equations, where different methods may be employed.

Given the equation 3x = 42, we need to isolate the variable x to find its value. This is accomplished by dividing both sides of the equation by 3, which is the coefficient of x. Therefore, the equation becomes x = 42 / 3.

By performing this simple division, we find that x equals 14. So, if x represents the amount you must pay, then you would pay $14.

The process of isolating the variable is essential for solving not only simple equations but also more complex ones, such as quadratic equations which take the form ax² + bx + c = 0.

When dealing with quadratic equations, you can employ the quadratic formula or other methods like factoring or completing the square, depending on the nature of the coefficients and the terms present in the equation.

To construct a 95% confidence interval, use the formula: Confidence Interval = sample mean ± (critical value * (sample standard deviation / sqrt(sample size))). The confidence interval for the true mean cholesterol content is approximately 190.37 to 207.63 milligrams.

To construct a 95% confidence interval for the true mean cholesterol content of all chicken eggs, we can use the formula:

Confidence Interval = sample mean ± (critical value * (sample standard deviation / sqrt(sample size)))

Given that the sample mean is 199 milligrams, the sample standard deviation is 16.5 milligrams, and the sample size is 12, we need to determine the critical value for a 95% confidence level. Since we have a small sample size, we need to use the t-distribution.

Using a t-table or a statistical calculator, we find that the critical value for a 95% confidence level with a sample size of 12 is approximately 2.179.

Substituting the values into the formula, we get:

Confidence Interval = 199 ± (2.179 * (16.5 / sqrt(12)))

Simplifying and calculating, the confidence interval is approximately 190.37 to 207.63 milligrams.

To construct a 95% confidence interval for the mean cholesterol content of chicken eggs, we use the sample data provided, along with the t-distribution for a sample size less than 30, and apply the standard formula for confidence intervals.

The question asks to construct a 95% confidence interval for the true mean cholesterol content of chicken eggs based on the given sample data. To calculate this, we first need to use the sample mean (μ), which is 199 milligrams, and the standard deviation (s), which is 16.5 milligrams. Since the sample size is less than 30, we will use the t-distribution to find the critical value. With n=12, the degrees of freedom (df) are 11.

First, look up the critical t-value for df=11 at a 95% confidence level. Let's assume it is approximately 2.201. Next, calculate the standard error (SE) of the mean by dividing the sample standard deviation by the square root of the sample size. That's SE = 16.5 / sqrt(12).

Now, we can construct the confidence interval using the formula: mean ± (t-value * SE). Plugging in the numbers, we get 199 ± (2.201 * SE).

d. A 95 percent confidence interval means that if we took many samples and built a confidence interval from each of them, we'd expect about 95 percent of those intervals to contain the true mean cholesterol level of all such eggs. Because of sample variability, the interval provides a range of values within which we are 95% confident the true mean lies.

Answer:

Option B is correct, i.e. -2 x^8 y^18.

Step-by-step explanation:

To find the equivalent expression to (10)(x^6)(y^12) / (-5)(x^-2)(y^-6)

Step 1: simplify numerical terms

(10) / (-5) = -2

Step 2: simplify exponents of x-terms

(x^6) / (x^-2) = (x^6) * (x^2) = x^(6+2) = x^8

Step 3: simplify exponents of y-terms

(y^12) / (y^-6) = (y^12) * (y^6) = y^(12+6) = y^18

It means (10)(x^6)(y^12) / (-5)(x^-2)(y^-6) = -2 x^8 y^18

Hence, option B is correct, i.e. -2 x^8 y^18.

Answer:

the answer on edge is D. 66^2

Step-by-step explanation:

Answer:

The length of the radius of this circle is 14 inches.

Step-by-step explanation:

Circumference of the circle = [tex]28\pi[/tex]

Let's take the length of the radius of the circle as [tex]a[/tex]

Circumference of a circle = [tex]2\pi r[/tex]

Where,

r is the radius of the circle.

Therefore,

[tex]2\pi a=28\pi[/tex]

[tex]2a=28[/tex]

[tex]a=14[/tex]

Therefore, the length of the radius of this circle is 14 inches.

To determine the function which has the largest value at x=3,

We will calculate the value of each function by substituting the value of x=3 in each of the given function.

Let us consider the first function,

[tex] c(x)=3x^{2}+5x+22 [/tex]

[tex] c(3)=3\times 3^{2}+5 \times 3+22 [/tex]

[tex] c(3)=27+15+22 [/tex]

[tex] c(3)=64 [/tex]

Let us consider the second function,

[tex] j(x)=12x [/tex]

[tex] j(x)=12 \times 3 =36 [/tex]

Let us consider the third function,

[tex] a(x)=9x [/tex]

[tex] a(x)=9 \times 3=27 [/tex]

Therefore, the function c(x) has the largest value at x=3.

The answer is 3

To determine which function has the largest value when x = 3, we need to substitute x with 3 into each function and calculate their values.

c(x) = 3x2 + 5x + 22 => c(3) = 3(3)2 + 5(3) + 22 = 27 + 15 + 22 = 64

j(x) = 12x => j(3) = 12(3) = 36

a(x) = 9x => a(3) = 9(3) = 27

The function c(x) has the largest value of 64 when x = 3.

The total surface area of a cone can be found using the formula A = πr(r + l), where A is the total surface area, r is the radius of the base, and l is the slant height. In this case, the correct answer is 115π cm².

The total surface area of a cone can be found using the formula A = πr(r + l), where A is the total surface area, r is the radius of the base, and l is the slant height.

In this case, the correct answer is 115π cm². Let's calculate it:

Therefore, the correct answer is 115π cm².