12,10,15, 13.18.16.21.19 what comes next .





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The surge tank is a vital component of a system in which the flow rate fluctuates significantly. The flow rate entering the tank varies significantly, causing the fluid level in the tank to fluctuate as a result of the compressibility of the liquid. The surge tank is utilized to reduce pressure variations generated by a rapidly fluctspace uating pump flow rate. To determine the matrices A,B,C, and D using state-space notation, here are the steps:State representation is given by:dx/dt = Ax + Bu; y = Cx + DuWhere: x represents the state variablesA represents the state matrixB represents the input matrixC represents the output matrixD represents the direct transmission matrixThe equation can be written asA = [ -1/R₁ 0; 1/R₁ -1/R₂]B = [1/A₁; 0]C = [0 1/R₂]D = 0Thus, the matrices A,B,C and D assuming that the level deviations are the state variables: h'₁ and h'₂. The input variable is q'ᵢ, and the output variable is the flow rate deviation, q'₂ are given by A = [ -1/R₁ 0; 1/R₁ -1/R₂]B = [1/A₁; 0]C = [0 1/R₂]D = 0.Hence, the required matrices are A = [ -1/R₁ 0; 1/R₁ -1/R₂], B = [1/A₁; 0], C = [0 1/R₂], and D = 0 using state-space notation for the given system of equations for two liquid surge tanks.

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Answer:

1. x=-283/60

2. x=21/4

3. x=43/4

4. x= -10

5. x= -16.1

Step-by-step explanation:

Answer:

Find the diameter or radius of a circle using the formulas: C = πd; C = 2πr

Step-by-step explanation:

Answer:

You can discover the diameter and radius when the circumference is given by using: C = πd; C = 2πr

Step-by-step explanation:

The 29.9-ounce package has a lower unit price of $0.2669 per ounce, making it the better buy.

To determine the unit price for the 10.5-ounce package, you would divide the cost of the package ($2.99) by the weight of the package (10.5 ounces). So:

$2.99 ÷ 10.5 ounces = $0.2847 per ounce

To find the unit price for the 29.9-ounce package, you would divide the cost of the package ($7.98) by the weight of the package (29.9 ounces). So:

$7.98 ÷ 29.9 ounces = $0.2669 per ounce

So, the 29.9-ounce package has a lower unit price of $0.2669 per ounce, making it the better buy.

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Answer:

112

Step-by-step explanation:

Divide 1111 By 999 and you get 1.1121121121121

So 112 is repeating over and over in the decimal.

112 is repeated  4 times and starts to repeat again.

Hope that helps!

a. The number of student surveyed is = 12 + 7 - 4 + 47 = 62

b. The number of student that are math major but not biology major = 7

c. The number of student that are neither math major nor biology major = 47

d. The number of student that are both math and biology major = 4

Answer:

Adding 12 to the circle area is equal to the square area.

Or

s2 = 12 + A

Where

s = side of square

A = area of circle

So

s2 = 12 + 36

s2 = 48

Solve this for s to get the side length

The probability that the sum will be an even number on the toss of two dice is  5/9 .

In the question ,

it is given that ,

the numbers on the faces of the dice are 1, 2, 3, 5, 7, and 8 .

the probability of getting an odd number first is = 4/6 = 2/3,

the probability of getting an even number first is = 2/6 = 1/3,

To get an even, we must get either 2 odds or 2 evens.

The probability of getting 2 odds is 4/6 × 4/6 = 16/36 .

The probability of getting 2 evens is 2/6 × 2/6 = 4/36.

If we add them together,

we get ,

= 16/36 + 4/36

= 20/36

= 10/18 = 5/9

Therefore , the required probability is 5/9  .

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Answer:

The width and length of the old card are 2 inches and 4 inches respectively.

Step-by-step explanation:

The given scale factor, \(C=\frac{5}{4}\)

She draws is a rectangle by using the scale factor of C.

The width of her drawing, \(b=2\frac{1}{2}\) \(=\frac{5}{2}\) inch, and

the length of the drawing, \(a=5\) inch.

Let \(a'\) and \(b'\) be the length and width of her reference business card (the old one as mentioned).

\(\text{Scale factor}=\frac{\text{New dimension}}{\text{Reference dimention}}\)

Here, the dimension is the length of the sides of rectangular cards.

So, \(C=\frac{a}{a'}\) and \(C=\frac{b}{b'}\)

\(\Rightarrow \frac{5}{4}=\frac{5}{a'}\)

\(\Rightarrow a'=4\) inch

and  \(\frac{5}{4}=\frac{5/2}{b'}\)

\(\Rightarrow b'=2\) inch

So, the old business card is of the dimensions 2 inches by 4 inches, which are the correct dimensions.

Actually, the print shop multiplied he scale-factor, C, with the new scaled length to get the reference length (lengths of original old card), which was the error. In, fact, as already described earlier, the new dimensions can be obtained by multiplying the scale-factor, C, with the reference dimensions.

Answer:

C. The scale factor is a fraction so the scale drawing is a reduction, and the original card is 2 inches by 4 inches.

Step-by-step explanation:

Given that a linear function f(x) has an x-intercept of (−6,0) and it intersects the x-axis at an angle of 67∘. We have to find the y-intercept (0,b) of f.

Since the function has an x-intercept of (-6,0), we can write the equation of the function in the form of: f(x) = m(x + 6)
where m is the slope of the function.
Now, we know that the function intersects the x-axis at an angle of 67 degrees. Since x-axis has an angle of 0 degree, this means the angle of the slope of the function with the x-axis is 67 degrees.
Therefore, the slope m of the function can be calculated as: tan(67) = m m = tan(67) m = 2.364
Now, we can write the equation of the function as: f(x) = 2.364(x + 6)

To find the y-intercept (0,b) of the function, we put x = 0 in the equation of the function: f(0) = 2.364(0 + 6) f(0) = 2.364(6)
f(0) = 14.184 Hence, the y-intercept (0,b) of the function is (0, 14.18) (rounded to two decimal places).

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There are a total of 56 possible committees.

Given data,

From 8 names on a ballot, a committee of 5 will be elected to attend a political national convention.

To know how many different committees are possible;

From the given data,

By using the combinations we get,

⇒ ⁸C₅

⇒ ⁸C₅ = \(\frac{8!}{5!*(8-5)!}\)

 = 56

Therefore, a total of 56 different committees is possible.

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Answer: $640

Step-by-step explanation:

100%-65%=35%

$224/35%=6.4

6.4*100%=$640

To check the solution

$640*65%=$416

$224+$416=$640

since we know that M is the midpoint of the AB segment, that simply means that the two halves it makes are congruent, namely AM = BM.

\(\stackrel{AM}{4x+13}~~ = ~~\stackrel{BM}{3x+17}\implies x+13=17\implies x=4~\hfill \stackrel{3(4)~~ + ~~17}{BM=29}\)

The required length of the side BM is 29.

Algebra is a study of mathematical expressions, in which numbers and quantities are represented in formulas and equations by letters and other universal symbols.

In the given question,

Point M is the midpoint of line AB.

AM = 4x + 13,

and BM = 3x + 17

To find the length of MB, use midpoint property.

Since, Point M is the midpoint of AB,

Therefore, AM = MB

4x + 13 = 3x + 17

4x - 3x = 17 - 13

x = 4

The length of MB = 3x + 17 = 3 × 4 + 17 = 12 + 17 = 29.

The length of MB, where M is midpoint of AB, is 29.

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Step-by-step explanation:

that is totally easy.

in the slope intercept form of a line equation the factor of x is always the slope.

in general

y = ax + b

a = the slope.

so, in our case here

y = 5x - 7

5 is the slope.

and -7 is the y intercept (at what point does the line intercept the y-axis; that is the y value when x = 0).

Depending on the size and thickness of the box, a certain amount of metal is required to cast a cubical metal box.

Depending on the size and thickness of the box, a certain amount of metal is required to cast a cubical metal box. In general, more metal is required for larger, thicker boxes. One must first calculate the box's volume in order to determine how much metal is required. The box's length, width, and height can be multiplied together to get this. The thickness of the metal must next be determined. The total amount of metal required can be estimated by multiplying the volume of the box by the thickness of the metal once the volume and thickness of the metal have been established. For instance, consider a box with dimensions of 6 inches long, 6 inches wide, and 6 inches high and a metal thickness.

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The frog's probability of being on lily pad B after an hour (or in the long run) is around 0.2975 or 29.75%.

To calculate the probability that the frog will be on lily pad B after an hour, we can start by calculating the long-run distribution or steady-state probabilities of the frog's movement between the two lily pads.

Let p represent the probability that the frog is on lily pad B at any given time. We may develop two equations based on the probabilities given in the problem:

p = 0.85(1-p) (the frog moves from point A to point B with a probability of 0.85 and stays on point B with a probability of 1-p).

1-p = 0.65p (the frog moves from B to A with the probability of 0.65 and stays on A with the probability of 1-p).

Simplifying the equation, we get:

p = 0.85 - 0.85p + 0.65p

p = 0.85(1 - 0.65) = 0.2975

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Company A has a higher risk percentage (55%) compared to Company B (3%).

To compute the Coefficient of Variation (CV) for each company, we need to use the formula:

CV = (Standard Deviation / Mean) * 100

Let's calculate the CV for each company:

For Company A:

Risk Percentage = 55%

Return = 14%

For Company B:

Risk Percentage = 3%

Return = 14%

Since we don't have the standard deviation values for each company, we cannot calculate the exact CV. However, we can still compare the riskiness of the two companies based on the provided information.

The Coefficient of Variation measures the risk relative to the return. A higher CV indicates higher risk relative to the return, while a lower CV indicates lower risk relative to the return.

In this case, Company A has a higher risk percentage (55%) compared to Company B (3%), which suggests that Company A is riskier. However, without the standard deviation values, we cannot make a definitive conclusion about the riskiness based solely on the provided information. The CV would provide a more accurate measure for comparison if we had the standard deviation values for both companies.

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the local time in Anchorage when the image was taken was 5:00 PM, and the local day was Dec. 2, 2011.

To determine the local time and day in Anchorage when the satellite image was taken, we need to consider the time difference between the Prime Meridian (0 degrees longitude) and Anchorage, Alaska (approximately 150 degrees west longitude).

Each time zone is approximately 15 degrees wide, representing a one-hour difference in local time. Anchorage is in the Alaska Standard Time (AKST) zone, which is typically UTC-9 (nine hours behind UTC) during standard time.

Given that Anchorage is about 150 degrees west of the Prime Meridian, we can calculate the time difference as follows:

150 degrees / 15 degrees per hour = 10 hours

Therefore, when the image was taken at 0300Z (3:00 AM), Dec. 3, 2011, at the Prime Meridian, the local time and day in Anchorage were:

3:00 AM - 10 hours = 5:00 PM, Dec. 2, 2011

So, the local time in Anchorage when the image was taken was 5:00 PM, and the local day was Dec. 2, 2011.

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The F-test statistic for the given data is 2.09. At a significance level of 0.05, the mean rates of return for the three industries are not significantly different.

To perform the F-test to compare the means of three populations, we need to calculate the sum of squares between groups (SSB), sum of squares within groups (SSW), and the degrees of freedom for each. Then, we can use these values to calculate the F-test statistic and compare it to the critical value of the F-distribution with degrees of freedom (dfB = k - 1) and (dfW = N - k), where k is the number of groups and N is the total sample size.

Using technology, we can calculate the SSB, SSW, and degrees of freedom, as shown below:

SSB = [(n1)(X1 - X)^2 + (n2)(X2 - X)^2 + (n3)(X3 - X)^2]/(k - 1)

= [(8)(11.19 - 11.03)^2 + (8)(12.85 - 11.03)^2 + (8)(9.86 - 11.03)^2]/(3 - 1)

= 12.93

SSW = [(n1 - 1)s1^2 + (n2 - 1)s2^2 + (n3 - 1)s3^2]/(N - k)

= [(7)(4.28^2) + (7)(5.23^2) + (7)(5.31^2)]/(24 - 3)

= 20.91

dfB = k - 1 = 2

dfW = N - k = 21

where X is the overall mean, X1, X2, and X3 are the sample means, n1, n2, and n3 are the sample sizes, s1, s2, and s3 are the sample standard deviations, and k is the number of groups.

Using these values, we can calculate the F-test statistic:

Fo = SSB/dfB / SSW/dfW

= 12.93/2 / 20.91/21

= 6.19

Using a significance level of 0.05, and with dfB = 2 and dfW = 21, the critical value of the F-distribution is 3.14 (found using a calculator or a table).

Since Fo = 6.19 is greater than the critical value of 3.14, we reject the null hypothesis and conclude that the mean rates of return are different at the 0.05 level of significance.

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_____The given question is incomplete, the complete question is given below:

Use technology to find the F-test statistic for this data set. Fo=(Round to two decimal places as needed.) accompanying table e. - Х X Rates of Return the means and Hya and H, H Financial 10.73 15.05 17.21 5.07 19.50 8.16 10.45 6.52 Energy 12.89 13.91 6.43 11.23 18.79 20.73 9.60 17.40 the samp Utilities 11.88 5.86 13.46 9.90 3.95 3.44 7.11 15.70 Are the mean rates of return different at the a = 0.05 level of significance?

The expression of ⁴√(81x³y⁴z⁸) with rational exponents is: 3x(¾)yz²

The 8 laws of exponents can be listed as follows:

Zero Exponent Law: a^(0) = 1.

Identity Exponent Law: a^(1) = a.

Product Law: a^m × a^n = a^(m+n)

Quotient Law: a^m/a^n = a^(m - n)

Negative Exponents Law: a^(-m) = 1/a^(m)

Power of a Power: (a^m)^n = a^(mn)

Power of a Product: (ab)^m = a^m*b^m

Power of a Quotient: (a/b)^m = a^m/b^m

We are given the algebra expression as:

⁴√81x³y⁴z⁸

This gives us:

81^(1/4) * x^(3/4) * y^(4/4) * z^(8/4)

= 3x^(3/4)yz²

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Answer:

67

Step-by-step explanation:

we have a gap between 1st and 2nd terms of 4. a gap between 2nd and 3rd of 8. 16 for next gap. the gap doubles every time.

so we expect gap between 4th and 5th terms to be 2 X 16 = 32.

35 + 32 = 67. that is the next number in the sequence.

Answer:

Yes what is the question I would surely love to help u

Step-by-step explanation:

The derivative of y = (5x6 − 3x4 + 2x2 − 1)(4x9 + 3x7 − 5x2 + 4x) is (30x^5 - 12x^3 + 4x)(4x^9 + 3x^7 - 5x^2 + 4x) + (5x^6 - 3x^4 + 2x^2 - 1)(36x^8 + 21x^6 - 10x + 4).

Using the product rule of differentiation, we have:

y' = (5x^6 - 3x^4 + 2x^2 - 1)'(4x^9 + 3x^7 - 5x^2 + 4x) + (5x^6 - 3x^4 + 2x^2 - 1)(4x^9 + 3x^7 - 5x^2 + 4x)'

Taking the derivative of the first term using the power rule, we get:

(5x^6 - 3x^4 + 2x^2 - 1)' = 30x^5 - 12x^3 + 4x

Taking the derivative of the second term using the product rule, we get:

(4x^9 + 3x^7 - 5x^2 + 4x)' = 36x^8 + 21x^6 - 10x + 4

Therefore, we have:

y' = (30x^5 - 12x^3 + 4x)(4x^9 + 3x^7 - 5x^2 + 4x) + (5x^6 - 3x^4 + 2x^2 - 1)(36x^8 + 21x^6 - 10x + 4)

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Answer:

3/4

Step-by-step explanation:

With regards to the above, since 1/4 of the volunteers are teenagers, the fraction of the volunteers would be

= 1 - 1/4

= 3/4

It therefore means that 3/4 of the volunteers are teenagers.

Answer:

1.73, 2.24, 3 1/7,4

Step-by-step explanation:

You do the whole numbers  first, and then the decimal or fraction.

Answer:

Below in bold.

Step-by-step explanation:

Radius of the pizza = 1/2 * 8 = 4 in.

Area of the whole pizza = π r^2

=  π * 4^2

= 8 π

So if you take 1/8 away

the area left = 7/8 * 8 * π

= 7π

Taking π to be 22/7:

= 7 * 22/7

= approximately 22 in^2.