p (x) = (x^2+6x+9) (x+3) how many distinct real number roots does p have? what is the smallest real root of p?

Answer:

The value would be 100

Step-by-step explanation:

The final solution is: u(x,t) = Σ (-1)^n (2L)/(nπ)^2 sin(nπx/L) exp(-k n^2 π^2 t/L^2).

To solve the heat equation:

k ∂²u/∂x² = ∂u/∂t

subject to boundary conditions u(0,t) = 0, u(L,t) = 0, and initial condition u(x,0) = x,

we can use separation of variables method as follows:

Assume a solution of the form: u(x,t) = X(x)T(t)

Substitute the above expression into the heat equation:

k X''(x)T(t) = X(x)T'(t)

Divide both sides by X(x)T(t):

k X''(x)/X(x) = T'(t)/T(t) = λ (some constant)

Solve for X(x) by assuming that k λ is a positive constant:

X''(x) + λ X(x) = 0

Applying the boundary conditions u(0,t) = 0, u(L,t) = 0 leads to the following solutions:

X(x) = sin(nπx/L) with n = 1, 2, 3, ...

Solve for T(t):

T'(t)/T(t) = k λ, which gives T(t) = c exp(k λ t).

Using the initial condition u(x,0) = x, we get:

u(x,0) = Σ cn sin(nπx/L) = x.

Then, using standard methods, we obtain the final solution:

u(x,t) = Σ cn sin(nπx/L) exp(-k n^2 π^2 t/L^2),

where cn can be determined from the initial condition u(x,0) = x.

For this problem, since the initial condition is u(x,0) = x, we have:

cn = 2/L ∫0^L x sin(nπx/L) dx = (-1)^n (2L)/(nπ)^2.

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The total number of sides of a regular polygon with each exterior angle of measure 30 degrees is equal to 12.

Let us consider 'n' be the number of sides of the regular polygon.

Let 'y' be the measure of each of the exterior angle of regular polygon.

y = 30 degrees

Measure of each of the exterior angle of regular polygon 'y'

= ( 360° ) / n

⇒ n = ( 360° / y )

Substitute the value we get,

⇒ n = ( 360° / 30° )

⇒ n = 12

Therefore, the number of sides of a regular polygon with each of the exterior angle 30 degrees is equal to 12.

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The above question is incomplete, the complete question is:

How many sides does a regular polygon have when each exterior angle measures 30 degrees?

Answer:

y=2x-5

Step-by-step explanation:

Slope intercept form is y=mx+b, with m being the slope and b being the y-intercept.

Slope is found through (y2-y1)/(x2-x1) and when the values are plugged in you get (-3-1)/(1-3) which equals -4/-2 or 2.

y=2x+b

Since b is the y-intercept, you plug in the value of the point where the line crosses over the y axis. In this case, that value is -5, so you get y=2x-5.

The salvage value of the PS 5 system after 6 years will be $640.

The formula for the depreciation;

Depreciation per year = (cost of asset - salvage value)/ (useful life of assets)

For the stated question-

12 = (712 - salvage value)/ (6)

salvage value = 712 - 12x6

salvage value = $640.

Thus, the salvage value of the PS 5 system after 6 years will be $640.

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The 3-sigma limits for a process whose distribution conforms to the normal distribution include 99.74% of the observed values, in the long run. This means that if you have a process that is normally distributed, then, in the long run, 99.74% of the values will fall within three standard deviations of the mean.

This is an important concept to understand because it can be used to help control a process. For example, if you know that 99.74% of the values will fall within three standard deviations of the mean, then you can set up control limits that correspond to those values. This can help you ensure that your process stays within the desired range.

Understanding the 3-sigma limits can help you better control your process and ensure that it produces the desired results.

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What is the question?

Answer:

\(=\frac{27}{125}\)

Step-by-step explanation:

\(0.216\)

\(\mathrm{Multiply\:and\:divide\:by\:10\:for\:every\:number\:after\:the\:decimal\:point.}\)

\(\mathrm{There\:are\:}3\mathrm{\:digits\:to\:the\:right\:of\:the\:decimal\:point,\:therefore\:multiply\:and\:divide\:by\:}1000\)

\(=\frac{0.216\cdot \:1000}{1000}\)

\(=\frac{216}{1000}\)

\(216,\:1000\)

\(\mathrm{The\:GCD\:of\:}a,\:b\mathrm{\:is\:the\:largest\:positive\:number\:that\:divides\:both\:}a\mathrm{\:and\:}b\mathrm{\:without\:a\:remainder}\)

\(2,\:3\mathrm{\:are\:all\:prime\:numbers,\:therefore\:no\:further\:factorization\:is\:possible}\)

\(=2\cdot \:2\cdot \:2\cdot \:3\cdot \:3\cdot \:3\)

\(2,\:5\mathrm{\:are\:all\:prime\:numbers,\:therefore\:no\:further\:factorization\:is\:possible}\)

\(=2\cdot \:2\cdot \:2\cdot \:5\cdot \:5\cdot \:5\)

\(\mathrm{The\:prime\:factors\:common\:to\:}216,\:1000\mathrm{\:are\:}\)

\(=2\cdot \:2\cdot \:2\)

\(\mathrm{Multiply\:the\:numbers:}\:2\cdot \:2\cdot \:2=8\)

\(=8\)

\(=\frac{8\cdot \:27}{8\cdot \:125}\)

\(\mathrm{Cancel\:the\:common\:factor:}\:8\)

\(=\frac{27}{125}\)

Hence, the correct answer is \(=\frac{27}{125}\)

Answer:28 if I’m not mistaken

Step-by-step explanation:

Answer:

(3x+2)(3x−2)

Step-by-step explanation:

Answer:

x ≈ 17

Step-by-step explanation:

using the cosine ratio in the right triangle

cos62° = \(\frac{adjacent}{hypotenuse}\) = \(\frac{8}{x}\) ( multiply both sides by x )

x × cos62° = 8 ( divide both sides by cos62° )

x = \(\frac{8}{cos62}\) ≈ 17 ( to the nearest whole number )

Answer: False

Step-by-step explanation:

In Boolean algebra, the symbol "+" represents logical OR operation, not regular addition as in linear algebra. The logical OR operation is used to combine two or more logical statements into a single statement that is true if at least one of the statements is true.

For example, if A and B are two logical statements, then A+B is true if A is true, or B is true, or both A and B are true.

Therefore, it is important to understand the context in which the symbol "+" is being used, whether it is in the context of regular addition or logical OR operation.

Answer:

a) 18 students per teacher

b) 9 students per tutor

c) 7 tutors

Step-by-step explanation:

An arts academy requires there to be 6 teachers for every 108 students and 5 tutors for every 45 students.

a) How many students does the academy have per​ teacher?

6 teachers = 108 students

1 teacher = x

Cross Multiply.

6x = 108

x = 108/6

x = 18 students per teacher

b) Per​ tutor?

5 tutor = 45 students

1 tutor = x

Cross Multiply

5x = 45

x = 45/5

x = 9 students

= 9 students per tutor

c) How many tutors does the academy need if it has 63 students​?

45 students = 5 tutors

63 students = x

Cross Multiply

45x = 63 × 5

x = 63 × 5/45

x = 7 tutors

Answer:

9000 panels

Step-by-step explanation:

See attached for detailed explanation.

Remember that percent means division by a 100.

The unit rate for each shirt if 24 shirts cost $259.36 as required to be determined is; $10.81.

It follows from the task content that the unit rate is to be determined if 24 shirts cost $259.36.

On this note, it follows that; the unit rate is given by the quotient;

Unit rate = Total cost / No. of units

Unit rate = 259.36 / 24

Unit rate = 10.80667.

Ultimately, the unit rate of the shirts as required is; $10.81.

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Answer: 6/36

Step-by-step explanation:

When tossing two number cubes, you can get such sample space

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

There are 36 possible outcomes. Only (1,1), (2,2), (3,3), (4,4), (5,5), and (6,6) use the same number twice.

Hence, the probability that you roll two numbers that are the same in a row is 6/36, or in simplified form, 1/6.

Hope that helps! :)

Answer:

First, in standard notation, we must define our zero.

In this case, would make sense to define the zero in the surface of the water.

(below is a number line so you can see the process to think this)

Then if the whale is swimming 60ft bellow the surface of the water, then the first position of the whale is:

-60

Now the whale goes up 30ft, then the new position of the whale is:

-60ft + 30ft = -30ft.

The correct option is A:

The equation is -60 + 30 = -30. The whale is 30 feet below the water's surface.

(you wrote that the equation was equal to +30 instead of -30 in the option A, i supposed that it was a typo)

Answer:

I belive the answer is A.

Step-by-step explanation:

Answer:

\(800~cm^3\)

Step-by-step explanation:

\(Volume ~of A=(10*(12-5)*5=\)

\(Volume~ of ~B= 5*8(10-4)=\)

\(Total ~volume= A+B\)

\(560+240=\)

\(800~cm^3\)

-----------------------------

hope it helps...

have a great day!!

Answer:

Equation I believe is the answer

let me know if not

Choose:

Increase the likelihood of rejecting the null hypothesis and increase measures of effect size.

The t statistic is the ratio of the calculated deviation of a parameter from its hypothesized value with its standard error.

In general, the likelihood of discovering a significant difference increases as the variance of the difference scores increases. A limited variation for the difference scores in a repeated-measures study suggests that the treatment has little or no effect.

Increasing the number of scores within each sample reduces the predicted standard error of the mean difference. This increases the size of the observed t, making it easier to reject the null hypothesis H0. In other words, when sample size increases, statistical power increases.

Higher t-value corresponds to a lower p-value, indicating that the difference between sample-mean (Χ) and population-mean (μ) is statistically significant (hence we reject the null hypothesis).

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Answer:

-3

Step-by-step explanation:

     Let x = the number

Then 3x = its triple, and the condition is:

x - 8 < 3x

Subtract x from each side

-8 < 2x

Divide each side by 2

-4 < x

Reverse the inequality

x > -4

The smallest integer greater than -4 is -3.

Check:

-3 - 8 < 3(-3)

-11 < -9

It checks.

Answer: 34.2 pounds

Step-by-step explanation:

First, convert 15 4/5 into an improper fraction. You should get 79/5. Then, convert 50 into a fraction that has a denominator of 5. Right now, 50= 50/1 so just multiply the top and bottom by 5 to make it 250/5. Then, subtract 79/5 from 250/5. You should get 171/5. Lastly, simplify. You should get 34.2 pounds as your final answer. Hope this helps!

Answer:

hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

Step-by-step explanation:

Answer:

40%

Step-by-step explanation:

Total girls

= 12 + 18

= 30

Girls who prefer soccer =

12

Percentage =

12/30

= 0.4

= 40%

Answer:

Solution is in attached photo.

Step-by-step explanation:

Do take note for this question, since PQ and RS are parallel, they have the same slope.

Answer:it’s D

Step-by-step explanation:

The proof of mathematical induction is; d( k+1) is only true when d(k) is true , also d(1) should also be true.

Mathematical induction is a method that is used to prove that a statement P(n) holds true for every natural number n.

For each and every natural number n, mathematical induction is a method of demonstrating a statement, theorem, or formula that is presumed to be true.

It is given that the statement is true for n = k. Thus we can say that from the principle of Mathematical Induction;

Let d(n) be a statement involving Natural Number n such that;

d(1) is true

d(m) is true

d(m + 1) is true

So, the statement d(n) is true for all the n natural numbers.

According to the second principle of Mathematical Induction, let d(n) be a statement involving Natural number n such that;

d(1) is true

d(m) is true when d(n) is true for all n where 1 ≤ n ≤m .

Then the statement d(n) is true for all n (natural numbers)

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It will take approximately 32.11 years for the elephant population to double from the number in 1980.

Let's set up the differential equation to model the population growth. We assume that the rate of change of the population is proportional to the difference between the maximum capacity (200 elephants) and the current population (y elephants) with a growth constant of 0.01. This can be expressed as:

dy/dt = k(200 - y),

where dy/dt represents the rate of change of the population with respect to time, and k is the growth constant.

To solve this differential equation, we separate the variables and integrate:

∫(dy / (200 - y)) = ∫k dt.

Using partial fraction decomposition and integrating, we find

- ln|200 - y| = kt + C,

where C is the constant of integration.

Next, we can solve for y(t) by isolating y in the equation:

200 - y = Ce^(-kt).

Given that y(0) = 30 (number of elephants in 1980), we can substitute the initial condition into the equation:

200 - 30 = Ce^(-k * 0),

170 = C.

Plugging this value back into the equation, we have:

200 - y = 170e^(-kt).

Simplifying, we obtain the equation for the number of elephants as a function of time:

y(t) = 200 - 170e^(-0.017t).

To determine how long it will take for the population to double from the number in 1980 (30 elephants), we solve the equation y(t) = 2 * y(0):

200 - 170e^(-0.017t) = 2 * 30,

170e^(-0.017t) = 140,

e^(-0.017t) = 140/170,

e^(-0.017t) = 0.8235.

Taking the natural logarithm of both sides, we get:

-0.017t = ln(0.8235),

t ≈ -ln(0.8235)/0.017,

t ≈ 32.11.

Rounding to 2 decimal places, it will take approximately 32.11 years for the elephant population to double from the number in 1980.

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