1) Evaluate the following expressions.show your work
a) 7(m - 8) for m = -4

Answer:

A insects and plants

Step-by-step explanation:

the decaying things are used as fertilizer for plants to grow and insects to eat

a) We have the function given by; y = 8x + 3We need to find the arclength of the curve between the limits of x = 2 and x = 8.The arclength L of the curve is given by; L = ∫(2,8) sqrt(1 + f'(x)²)dx Here, f(x) = 8x + 3 Differentiate f(x) with respect to x;f'(x) = 8Now, substitute f'(x) in the above equation; L = ∫(2,8) sqrt(1 + 8²)dx L = ∫(2,8) sqrt(65)dxL = sqrt(65)∫(2,8)dxL = sqrt(65) [x]₂⁸L = sqrt(65) [8 - 2]L = 6sqrt(65)Therefore, the arclength L of this curve is 6sqrt(65).

b) We are given the function y = 8x + 3We need to rotate this curve by 2π radians about the x-axis to get the required surface of revolution. The formula for the surface area of the surface of revolution generated by revolving the curve y = f(x) between x = a and x = b about the x-axis is given by;A = ∫(a,b) 2πf(x) sqrt(1 + f'(x)²)dx Here, f(x) = 8x + 3f'(x) = 8We know that the limits of integration are from x = 2 to x = 8.

Substitute the values in the above equation; A = ∫(2,8) 2π(8x + 3) sqrt(1 + 8²)dxA = 16π ∫(2,8) (8x + 3) sqrt(65)dxA = 16π [∫(2,8) (8x sqrt(65))dx + ∫(2,8) (3 sqrt(65))dx]A = 16π [2/3(8sqrt(65))² - 2/3(2sqrt(65))² + 3sqrt(65)(8 - 2)]A = 16π [2/3(8sqrt(65))² - 2/3(2sqrt(65))² + 3sqrt(65)(6)]A = 192πsqrt(65)

Therefore, the area of the surface of revolution, A that is obtained when the curve is rotated by 2π radians about the x-axis is 192πsqrt(65) square units.

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a. Critical value, t∗, for a 99% Confidence Interval, n=16 is given by t∗=2.921. 

b. The margin of error is 0.97.

a) Critical Value, t∗ for a 99% Confidence Interval: Critical value, t∗, for a 99% Confidence Interval, n=16 is given by t∗=2.921. 
Note: t-table, with 15 degrees of freedom is used to determine the critical value for the given confidence interval. 

b) Margin of Error for a 99% Confidence Interval:Margin of error for a 99% confidence interval, n=16 is given by E = t∗× s/√n, where s is the standard deviation. 
E = 2.921 × 1.4/√16 = 0.97 (rounded off to two decimal places). 
Hence, the margin of error is 0.97.

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Find the critical value, t∗, for a 99% Confidence interval.

The sample size is 16.The degree of freedom (df) = n - 1 = 16 - 1 = 15.

From t-table for 15 degrees of freedom (df) and 99% level of confidence (α = 0.01) (two-tail) t* = 2.947.a) t* = 2.947.

b) Find the margin of error for a 99% Confidence interval.

The margin of error (E) for a 99% confidence interval is given by:

E = t* × s / √n

Where s is the sample standard deviation.

s = 1.4 (given)E = 2.947 × 1.4 / √16E = 0.7285 or ≈ 0.73

Therefore, the margin of error for a 99% confidence interval is approximately 0.73.

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Answer:

0.000173611 miles is 11 inches

15.22359 miles is 24.5km

Step-by-step explanation:

Answer:

x = 5,-2

Step-by-step explanation:

Multiply the whole equation by 3(x+1) to get rid of the denominator.

[tex] \large{ \frac{x + 2}{3} \times 3(x + 1) = \frac{2(x + 2)}{x + 1} \times 3(x + 1)} \\ \large{(x + 2)(x + 1) = 2(x + 2) \times 3} \\ \large{ {x}^{2} + 3x + 2 = 6(x + 2)} \\ \large{ {x}^{2} + 3x + 2 = 6x + 12}[/tex]

Then we solve the equation.

[tex] \large{ {x}^{2} + 3x + 2 - 6x - 12 = 0} \\ \large{ {x}^{2} - 3x - 10 = 0} \\ \large{(x - 5)(x + 2) = 0} \\ \large{x = 5, - 2}[/tex]

Since we are also solving rational equation, make sure that x ≠ -1 for this problem. Because if x = -1, the denominator is 0 which is undefined. Since our solutions are x = 5,-2 and not -1. Therefore the answer is x = 5,-2

Answer:

a.  70°

Step-by-step explanation:

m∠BDC + m∠CDA = m∠BDA

-3x + 34 - 2x + 56 = 150

-5x + 90 = 150

-5x = 60

x = -12

m∠BDC = -3x + 34 = -3(-12) + 34

              = 36 + 34 = 70°

True. et a be square real matrix if v is an eigenvector for eigenvalue λ then v is an eigenvector for eigenvalue λ

In linear algebra, if a is a square real matrix and v is an eigenvector of a corresponding to eigenvalue λ, then v is also an eigenvector of a corresponding to the same eigenvalue λ. The definition of an eigenvector states that it remains unchanged (up to scaling) when multiplied by the matrix, and this property holds regardless of whether the eigenvalue is repeated or not. Therefore, if v satisfies the equation a * v = λ * v, it will still satisfy the same equation when considering the eigenvalue λ.

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The velocity of the stream is approximately 2.13 feet per second.

To calculate the velocity of the stream, we can use the formula:

Velocity = Distance / Time

Given that the drop of food coloring travels 32 feet in 15 seconds, we can plug in these values into the formula:

Velocity = 32 feet / 15 seconds

To find the velocity, we divide 32 by 15:

Velocity ≈ 2.13 feet per second

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Answer:

36

Step-by-step explanation:

sara had 27 peaches when she left the stand. when she returns the total number of peaches is 63. So to find the answer you take 63 and subtract it by 27 to get your answer.

Answer:

Solution x=16

Step-by-step explanation:

Answer:

with atleast two right angles in rectangle and it do not describe unique because it is simple

Answer: 3.75 liters

Step-by-step explanation:

Zoe uses 250 milliliters of milk to make a loaf of bread.

If she needed to make 15 loaves therefore, she would do the following:

= 250 * 15 loaves

= 3,750 milliliters of milk

Then convert the above quantity to liters.

1 Liter = 1,000 milliliters.

3,750 milliters to liters is:

= 3,750 / 1,000

= 3.75 liters

Answer:

Following are the solution to these question:

Step-by-step explanation:

Please find the complete question in the attachment file.

Formula:

[tex]\to \tan \theta= \frac{Perpendicular}{Base}[/tex]

[tex]\to \tan R = \frac{45}{28} \\\\ \to \tan S = \frac{28}{45}[/tex]

The equilibrium vector for the given transition matrix is approximately (0.359, 0.359, 0.284).

To find the equilibrium vector, we need to solve the equation [tex]T * v = v[/tex], where T is the transition matrix and v is the equilibrium vector.

Let's denote the equilibrium vector as (x, y, z). Setting up the equation, we have:

[tex]0.47x + 0.19y + 0.34z = x\\0.45x + 0.55y + 0z = y\\0x + 0y + 1z = z[/tex]

Simplifying the equations, we get:

[tex]0.46x - 0.19y - 0.34z = 0\\-0.45x + 0.45y = 0\\0x + 0y + 1z = z[/tex]

From the second equation, we can see that x = y. Substituting x = y in the first equation, we have:

[tex]0.46x - 0.19x - 0.34z = 0\\0.27x - 0.34z = 0[/tex]

Simplifying further, we get:

[tex]0.27x = 0.34z\\x = (0.34/0.27)z\\x = 1.259z[/tex]

Since the equilibrium vector must sum to 1, we have:

[tex]x + y + z = 1\\1.259z + 1.259z + z = 1\\3.518z = 1\\z - 0.284[/tex]

Substituting the value of z back into x, we get:

[tex]x = 1.259 * 0.284=0.359[/tex]

Therefore, the equilibrium vector is approximately (0.359, 0.359, 0.284).

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The degree of precision of the quadrature formula with an error term of 24 f‴() is 2.

To know more about the degree of precision of a quadrature formula, refer here:

The degree of precision of a quadrature formula represents the highest power of x that the formula can integrate exactly. In this case, the error term of the formula is given as 24 f‴(), where f‴() denotes the third derivative of the function f(x). The degree of precision is determined by the highest power of x that appears in the error term.

In a quadrature formula, the error term typically has the form K * h^p, where K is a constant, h is the step size, and p is the degree of precision. In this case, the error term is 24 f‴(). We can see that there is no dependence on the step size h, which implies that h^p = h^0 = 1. Therefore, the highest power of x in the error term is determined by the highest power of x that appears in f‴().

Since the error term is 24 f‴(), it indicates that the highest power of x in f‴() is 1. Thus, the degree of precision of the quadrature formula is 2, as the highest power of x in the error term is two degrees less than the highest power of x that the formula can integrate exactly.

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Answer:

2

Step-by-step explanation:

You set up and equation:

5+6x = 17

You solve it and get 2.

Step-by-step explanation:

17-5 = 12

Answer:

Yes, that is correct.

Step-by-step explanation:

The area of the surface obtained by rotating the curve x = y² − 2y + 1, 0 ≤ y ≤ 2 about the y-axis isπ ∫_0^2 [(y-1)^2+1] √[1+4(y-1)^2] dy.Let's work out the solution. We need to apply the formula of surface area by revolving around the y-axis.The surface area is generated by the revolving the curve about y-axis, given as,x = y² − 2y + 1, 0 ≤ y ≤ 2.

Now, we must derive the formula to calculate the area of a surface obtained by rotating a curve around the y-axis. We use the formula given below, which involves integration of the function involved.

Let's see the formula for rotating around the y-axis:Area = 2π ∫_a^b xf(x)dxWe have given x = y² − 2y + 1, 0 ≤ y ≤ 2,To apply the above formula, we need to rearrange the given curve in terms of x,Let x = y² − 2y + 1We can obtain the value of y as, y = 1 ± √(x − 1).The limits of integration of y-axis are 0 and 2.Therefore, the area of the surface obtained by rotating the curve x = y² − 2y + 1, 0 ≤ y ≤ 2 about the y-axis isπ ∫_0^2 [(y-1)^2+1] √[1+4(y-1)^2] dy.

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Step-by-step explanation:

area of rhombus =1/2×d1×d2

area of rhombus =1/2×9cm×5cm

area of rhombus =22.5cm²

area of rhombus = 1/2×d1×d2

area of rhombus =1/2×8in×17in

area of rhombus= 68in²

Answer:

yes

Step-by-step explanation:

no

Answer:

5 hours or 300 mins

Step-by-step explanation:

Answer:

arc XY = 46°

Step-by-step explanation:

The inscribed angle XZY is half the measure of its intercepted arc , then

arc XY = 2 × 23° = 46°

Answer:  8 pupils are absent

Step-by-step explanation:

20 percent * 40 =

(20* 40)/100 =

(800)100 =

 =8

The correct answer is option B. 0.6 mL which is the powder volume in the vial.

To determine that 0.6 mL of powder volume in the vial, we need to subtract the volume of the sterile water used for reconstitution from the final volume.

The vial states that it needs to be reconstituted with 3.4 mL of sterile water for a final volume of 4 mL. This means that 3.4 mL of sterile water will be added to the vial to make a total volume of 4 mL.

To find the powder volume, we subtract the volume of the sterile water (3.4 mL) from the final volume (4 mL):

Powder volume = Final volume - Volume of sterile water

Powder volume = 4 mL - 3.4 mL

Powder volume = 0.6 mL

Therefore, the powder volume in the vial is 0.6 mL.

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Answer:

16 2/3 yards

Step-by-step explanation:

Hope this helps and have a wonderful day!!!!

The side lengths of the given triangle are 3 m, 10 m, and 10 m.

Let's assume the length of the third side of the triangle is x.

According to the given information, the two equal sides of the triangle are each 8 m less than six times the third side. Therefore, the lengths of the two equal sides can be expressed as:

6x - 8

6x - 8

The perimeter of a triangle is the sum of all three sides. In this case, the perimeter is given as 23 m:

x + (6x - 8) + (6x - 8) = 23

Simplifying the equation:

x + 6x - 8 + 6x - 8 = 23

13x - 16 = 23

13x = 23 + 16

13x = 39

x = 39 / 13

x = 3

Now that we have the value of x, we can find the lengths of the two equal sides:

Equal side 1 = 6x - 8 = 6 * 3 - 8 = 10 m

Equal side 2 = 6x - 8 = 6 * 3 - 8 = 10 m

Therefore, the side lengths of the triangle are 3 m, 10 m, and 10 m.

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The flux of the vector field F across the surface S in the indicated direction is 8π/3.

So, the flux of the given vector field F across the surface S can be calculated by the surface integral as follows:

Φ = ∫∫S F · dS = ∫∫S (xi + yj + z2k) · n(x, y, z) dS= ∫∫S (2x/z + 2y/z + z2(-1/2)) dS= ∫∫S (2x + 2y) / z dS= ∫0²∫2π 2rcosθ / z √(r² + z²)  dr dθ= 8π/3.

The flux of the vector field F across the surface S in the indicated direction is 8π/3.

Given, vector field F = xi + yj + z2k,

S is the portion of the cone z = 2√(x² + y²) between z = 2 and z = 4 and the direction is outward.

The flux of the vector field F is given by the surface integral:Φ = ∫∫S F · dS .

Here, dS is the outward pointing unit normal vector of the surface S. Hence the flux Φ will be positive if F points outward, otherwise negative. The surface S can be parameterized as r(x, y, z) = xi + yj + zk, where z varies from 2 to 4 and (x² + y²) = (z²/4).

Then, the unit normal vector to the surface is given by n(x, y, z) = (2x/z)i + (2y/z)j - k/2.

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Answer:

[911,∞)

Step-by-step explanation:

Given: S be the number of cans collected by Shane.

Since,  Abha collected 178 more cans than Shane did.

Then, the number of cans collected by Abha = S+178

Also, Shane and Abha earned a team badge that required their team to collect no less than 2000 cans for recycling.

So,  

Hence, the solution set of the inequality will be [911,∞)

Answer:

75 times.

Step-by-step explanation:

Well there are 12 months and 3 of them start with the letter J, so theoretically, 25% of the months chosen will start with the letter J because [tex]\frac{3}{12}=\frac{1}{4}[/tex], which is 25%. 25% of 300 (or [tex]\frac{300}{4}[/tex], for those who like fractions) is 75, so theoretically, we can expect a month that starts with the letter J 75 times.

Hope this helps!

P.S: Please mark me as brainliest!

Answer:

Step-by-step explanation:

2(4x - 3) = 9 + 2x + 6               Combine the like terms on the right

2(4x - 3)  = 2x + 15                   The distributive property gets rid of the brackets

8x - 6 = 2x + 14                        Add 6 to both sides

     6              6

8x = 2x + 20                            Subtract 2x from both sides

-2x   -2x        

6x = 20

Step 2 is the error. It is a very common error. You multiply 2 and - 3 together. as well as 2 and 4 together. If you are going to forget something that will be it.