(-3)^5 x (-3)^2 in single power

Answer:

0

Step-by-step explanation:

5(x+3) replace x with -3

5(-3+3)

5(0)

0

The statement "For all integers a, b, and c, if a is a factor of c and b is a factor of c then ab is a factor of c." is true.

To prove this statement directly from the definitions, we need to show that if a and b are factors of c, then ab is also a factor of c. By definition, a factor of a number divides that number evenly without any remainder.

Let's assume that a and b are factors of c, which means that c can be expressed as c = ma and c = nb, where m and n are integers. Multiplying these equations, we get:

c x c = (ma) x (nb)

Expanding the right-hand side of this equation, we get:

\(c^2\) = mnb x ab

Since m, n, and ab are all integers, we can conclude that ab is also a factor of \(c^2\). Now, we know that c is a factor of\(c^2\) , since any number is a factor of itself. Therefore, if we divide both sides of the equation \(c^2\) = mnb x ab by c, we get:

c = (mn) x ab

This shows that ab is also a factor of c, since c can be expressed as the product of (mn) and ab.

Therefore, we have shown that if a and b are factors of c, then ab is also a factor of c, which means the statement is true.

Counterexample: If we take a = 3, b = 5, and c = 7, we can see that a and b are both factors of c (since 7 is a prime number and its only factors are 1 and 7), but ab = 15 is not a factor of c. This provides a counterexample to the statement and shows that it is false in general.

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Answer:

The first one, 4x(-x+3)

According to the rate of change, it is found that the hourly rate of temperature change at the bottom of the mountain was of -2.5 ºC per hour.

The average rate of change of a function is given by the change in the output divided by the change in the input.

In this problem, it is stated that at the top of the mountain, the average rate of change is of -2.5 ºC per hour, and at the bottom of the mountain the rate is the same, hence the hourly rate of temperature change at the bottom of the mountain was of -2.5 ºC per hour.

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There is no evidence that adult Atlantic bluefin tuna weigh more than 800 lbs, on average.

The p-value represents the probability of obtaining a sample result as extreme as the one observed, assuming the null hypothesis is true.

In this case, the null hypothesis states that the average weight of adult Atlantic bluefin tuna is 800 lbs.

A p-value of 0.112 means that there is a 11.2% chance of observing a sample mean weight of 825 lbs or higher, assuming the true population mean is 800 lbs.

Since the p-value is greater than the commonly used significance level of 0.05, we do not have enough evidence to reject the null hypothesis.

Therefore, we cannot conclude that adult Atlantic bluefin tuna weigh more than 800 lbs, on average, based on the findings so far.

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Answer:

If m<AOC = 49°, m<BOC = 2x°+10°, and m<AOB = 4x°–15° find the degree measure of BOC and AOB.

mBOC = 18°; mAOB = 31°

mBOC = 28°; mAOB = 21°

mBOC = 21°; mAOB = 28°

mBOC = 31°; mAOB = 18°

Step-by-step explanation:

The value of the unknown variable [x] is 4.

Given is that -

m ∠AOC = 19 degrees

m ∠BOC = (2x+10) degrees

m ∠AOB = (4x - 15) degrees

It can be written from the image as -

m ∠AOC = m ∠AOB + m ∠AOC

19 = (2x + 10) + (4x - 15)

6x - 5 = 19

6x = 19 + 5

6x = 24

x = 4

Therefore, the value of the unknown variable [x] is 4.

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Answer:

-1/3

Step-by-step explanation:

Answer: 7.2 months

Step-by-step explanation:

Hi, to answer this question we have to substitute f(x) =500 in the equation given:

f(x) = 100(1.25)^x

500= 100(1.25)^x

Solving for x (number of months)

500/100 = 1.25^x

5 = 1.25^x

log 5 =log 1.25^x

log 5 =x (log 1.25)

log 5 /log 1.25 =x

x = 7.2 months

Feel free to ask for more if needed or if you did not understand something.  

Step-by-step explanation:

I cannot draw here, but I can show and tell you how to find 2 points of the individual lines that you can then mark on the chart and draw the line through them.

1)

y = 7/2 x - 2

so, the first and easiest point is the y-intercept (where x = 0).

x = 0, therefore, y = -2

so, the first point is (0, -2)

for the second point : what value of x would eliminate the fraction and make this whole integer number calculations ?

well, x = 2 !

so,

y = 7/2 × 2 - 2 = 7 - 2 = 5

and our second point is (2, 5)

2)

y = -6x + 3

the same principles. first x = 0, therefore y = 3

the first point is (0, 3)

for the second point we can choose any integer x, as all the other terms are integer too.

let's pick x = 1

y = -6×1 + 3 = -6 + 3 = -3

so, the second point is (1, -3)

3)

y = -5

this just means that for every possible value of x the resulting y value is -5.

that means it is a horizontal line through y = -5 or (0, -5)

4)

y = 6/5 x + 1

the same principles. x = 0, therefore y = 1

the first point is (0, 1)

for the second point, again, what x eliminates the fraction and makes all an integer operation ?

well, x = 5.

y = 6/5 × 5 + 1 = 6 + 1 = 7

ok, 7 is off the chart, so let's use x = -5 instead.

y = 6/5 × -5 + 1 = -6 + 1 = -5

so, the second point on the chart is (-5, -5)

Answer: 3 1/3 miles

Step-by-step explanation:

Answer:

no solution

Step-by-step explanation:

Answer:

Fungi

Step-by-step explanation:

By definition, the x-coordinate of the terminal point is equal to cos t and the y-coordinate is equal to sin t. This allows us to easily find the values of sin t and cos t. To find tan t, we use the formula tan t = sin t / cos t, which we can substitute with our previously found values for sin t and cos t.

First need to understand what is meant by the terms "terminal point" and "unit circle". The unit circle is a circle with a radius of 1, centered at the origin of the coordinate plane. The terminal point is the point where the circle intersects with a line that starts at the origin and passes through an angle t measured in radians.
To find sin t and cos t, we need to look at the coordinates of the terminal point. Let's call the x-coordinate of the terminal point x' and the y-coordinate y'. By definition, x' = cos t and y' = sin t. Therefore, sin t = y' and cos t = x'.
To find tan t, we use the formula tan t = sin t / cos t. Substituting in our values for sin t and cos t, we get:
tan t = y' / x'
So, to summarize:
- sin t = y'
- cos t = x'
- tan t = y' / x'
In summary, we can use the unit circle to determine the values of sin t, cos t, and tan t for any angle t measured in radians. The terminal point on the unit circle is the point where the circle intersects with a line passing through the origin at angle t.

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the potential at the center of the equilateral triangle is 3kq√3 / a.To find , we can use the formula for the electric potential due to a point charge:

V = kq / r

where k is the Coulomb constant, q is the charge, and r is the distance between the point charge and the center of the triangle.

Assuming the charges are all positive, the potential at the center due to each charge will be the same, so we can find the total potential by multiplying the potential due to one charge by three.

The distance from the center of the equilateral triangle to each charge is a/√3, since the height of the equilateral triangle is √3/2 times the side length.

Therefore, the potential at the center is:

V = 3(kq / (a/√3))

Simplifying:

V = 3kq√3 / a

Hence, the potential at the center of the equilateral triangle is 3kq√3 / a.

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To determine the equation of the tangent plane and normal line of the given curve at the point P(2, -3, 18), we need to find the partial derivatives of the function f(x, y, z) = x^2 + y^2 - 2xy - x + 3y - z - 4.

Taking the partial derivatives with respect to x, y, and z, we have:

fx = 2x - 2y - 1

fy = -2x + 2y + 3

fz = -1

Evaluating these partial derivatives at the point P(2, -3, 18), we find:

fx(2, -3, 18) = 2(2) - 2(-3) - 1 = 9

fy(2, -3, 18) = -2(2) + 2(-3) + 3 = -7

fz(2, -3, 18) = -1

The equation of the tangent plane at P is given by:

9(x - 2) - 7(y + 3) - 1(z - 18) = 0

Simplifying the equation, we get:

9x - 7y - z - 3 = 0

To find the equation of the normal line, we use the direction ratios from the coefficients of x, y, and z in the tangent plane equation. The direction ratios are (9, -7, -1).Therefore, the equation of the normal line passing through P(2, -3, 18) is:

x = 2 + 9t

y = -3 - 7t

z = 18 - t

where t is a parameter representing the distance along the normal line from the point P.

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the solution of the given rational equation is x = -1/7, which means the value of x is equal to negative one by seven when the equation is true.

Given Rational Equation

:

$\frac{4x - 1}{12} = \frac{11}{12} x$

We have to solve the above rational equation.So, let's solve it.

First of all, we will multiply each term of the equation by the LCD (Lowest Common Denominator), in order to remove

fractions from the equation.So, the LCD is 12

.Now, multiply 12 with each term of the equation.

$12 × \frac{4x - 1}{12} = 12 × \frac{11}{12}x$

Simplify the above equation by canceling out the denominator on LHS

.4x - 1 = 11x

Solve the above equation for x

Subtract 4x from both sides of the equation.-1 = 7x

Divide each term by 7 in order to isolate x. $x = -\frac{1}{7}$

Hence, the solution of the given rational equation is x = -1/7, which means the value of x is equal to negative one by seven when the equation is true.

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The solution to the rational equation is \($x = 3$\).

To solve the rational equation \($\frac{4x - 1}{12} = \frac{11}{12}$\) for \($x$\), we can follow these steps:

1. Start by multiplying both sides of the equation by 12 to eliminate the denominator: \($(12) \cdot \frac{4x - 1}{12} = (12) \cdot \frac{11}{12}$\).

2. Simplify the equation: \($4x - 1 = 11$\).

3. Add 1 to both sides of the equation to isolate the variable term: \($4x - 1 + 1 = 11 + 1$\).

4. Simplify further: \($4x = 12$\).

5. Divide both sides of the equation by 4 to solve for \($x$\): \($\frac{4x}{4} = \frac{12}{4}$\).

6. Simplify the equation: \($x = 3$\).

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To evaluate the triple integral 5(\(x^3\)yx\(y^2\)) dv in cylindrical coordinates, we first need to express the equation of the paraboloid z = \(x^2\) + \(y^2\) in cylindrical coordinates.

Using the conversion formulae, we have:

x = r cos(theta)

y = r sin(theta)

z = z

Substituting these values in the equation of the paraboloid, we get:

z = \(r^2\)

The limits of integration for r, theta, and z are:

0 ≤ r ≤ √z

0 ≤ theta ≤ π/2

0 ≤ z ≤ 1

Thus, the triple integral becomes:

∫∫∫ 5(\(r^5\)\(cos^3\)(theta)\(sin^3x^{2}\)(theta)) r dz dr d(theta)

Simplifying this expression and evaluating the integral, we get:

5/32

Therefore, the value of the given triple integral in cylindrical coordinates is 5/32.

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The expression given represents an exponential growth relation. The average rate of change is the average growth of the flower from day 1 to days 5

The rate of change of the flower can be deduced frommthe equation as :

Hence, the growth rate of the flower per day = 0.02

The number of days, n = 5

Therefore, the average growth rate is the average growth of the flower within the number of days given.

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Answer:

C

Step-by-step explanation:

I got it right

Answer:

\(i\sqrt4 ~ \text{and} ~ 2i\)

Step-by-step explanation:

\(\sqrt{-4}\\\\=\sqrt{-1} \sqrt4\\\\=i\sqrt4\\\\=2i\)

Answer: 27, 29

Step-by-step explanation:

Let's say that the 2 numbers are x and x+2

That means that: x+x+2=56

Simplify: 2x+2=56

Solve: 2x=54

x=27

27,29 are the 2 numbers

2 hours will pass before they meet.

"Information available from the question"

In the question:

Aaron starts riding a bike at a rate of 3 mi/h on a road toward a store 20 mi away.

Zhang leaves the store when Aaron starts riding his bike, and he rides his bike toward Aaron along the same road at 2 mi/h.

Now, According to the question:

Total distance = 20mi

Aaron starts riding a bike at a rate of  = 3mi/h

Zhang rides his bike toward Aaron along the same road at  = 2mi/h

Let y be the number of hours for them to meet.

The expression is given as

3y + 2y = 20

solving for y, we have

5y = 20

y = 20/5

y = 4hrs

Therefore, 2 hours will pass before they meet.

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Answer:

The median is 3.5!

Step-by-step explanation:

You either got it right, or you guessed! I arranged the data set from lowest to highest value, and then chose the middle one. For this one, there were two middle values : 3 and 4. So, the median would be in the middle, middle, which is 3.5 :)

Answer:

There are 2 solutions to square root x = 9

They are 3, and -3

Step-by-step explanation:

The square root of x=9 has 2 solutions,

The square root means, for a given number, (in our case 9) what number times itself equals the given number,

Or, squaring (i.e multiplying with itself) what number would give the given number,

so, we have to find the solutions to \(\sqrt{9}\)

since we know that,

\((3)(3) = 9\\and,\\(-3)(-3) = 9\)

hence if we square either 3 or -3, we get 9

Hence the solutions are 3, and -3

Answer:

y=-5x-3

Step-by-step explanation:

put -1 and 1 in equation and you will get the answer

The equation that best represents a line perpendicular will be y = - 5x - 3. Then the correct option is A.

Let the equation of the line be ax + by + c = 0. Then the equation of the perpendicular line that is perpendicular to the line ax + by + c = 0 is given as bx - ay + d = 0

The equation of the line passing through (-1, 2) and (1, -8). Then the equation of the line will be

y + 8 = [(-8 - 2) / (1 + 1)] (x - 1)

y + 8 = -5x + 5

y = - 5x - 3

The equation that best represents a line perpendicular will be y = - 5x - 3. Then the correct option is A.

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Answer:

2

Step-by-step explanation:

2x^2 + 8x + 8

factor the 2 out : 2(x^2 + 4x + 4)

2(x + 2)^2

x = -2

Answer:

{4,3,27}

the geometric mean is 6.86828545532

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

The geometric mean is the nth root of the terms multiplied by each other, with n being the total number of terms \(\sqrt[n]{4/3*27} \)

So we have \(\sqrt[2]{4/3 * 27} \), which is just the square root

4/3 * 27 is equal to 36

So the square root of 36 is 6

Best of luck

The support of (X, Z) is the triangular region in the square [0, 1] × [0, 2]. The PDF of Z is a constant 1 within the interval [0, 2].

To determine the support of the random variable Z = X + Y, where X and Y are independent random variables following a uniform distribution on [0, 1], we need to find the range of possible values for Z.

The support of (X, Z) represents the set of all possible values that the pair (X, Z) can take. In this case, X is restricted to the interval [0, 1], and Z is the sum of X and Y. Since X and Y are both uniformly distributed on [0, 1], their values can also range from 0 to 1. Therefore, the support of (X, Z) is the set of all pairs (x, z) such that x and z both lie in the interval [0, 1].

To visualize the support of (X, Z), we can plot a graph with the x-axis representing the values of X and the y-axis representing the values of Z. The plot will show the region in the square [0, 1] × [0, 2] where the pairs (x, z) can occur.

The plot will be a triangular region in the square, bounded by the lines z = 0, x = 0, x = 1, and z = 2. The height of the triangle represents the values of Z, which range from 0 to 2, and the base of the triangle represents the values of X, which also range from 0 to 1.

Now, let's consider the probability density function (PDF) of Z. The PDF represents the probability of Z taking a specific value. Since X and Y are independent random variables with uniform distributions, their PDFs are constant within their support, which is [0, 1].

The probability density function of Z can be obtained by convolving the PDFs of X and Y. Convolution is an operation that combines the distributions of independent random variables. In this case, since X and Y both have the same uniform distribution, the convolution simplifies to a triangular function.

The PDF of Z is given by:

fZ(z) = ∫fX(x)fY(z - x)dx

Since both fX(x) and fY(z - x) are constant within their support, the integral simplifies to the length of the interval over which the product of the PDFs is nonzero.

For 0 ≤ z ≤ 1, the PDF of Z is given by:

fZ(z) = ∫1 * 1 dx = 1

For 1 < z ≤ 2, the PDF of Z is given by:

fZ(z) = ∫1 * 1 dx = 1

Therefore, the PDF of Z is a constant 1 within the interval [0, 2], and it is zero outside this interval.

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Answer:

sin(5607) = 0.67641680533

sin(506)  = -0.202179403335

sin(702)  = -0.989367016834

sin(803) = -0.948263002181

sin(562) =  0.33827666045

Step-by-step explanation:

put sin into a calculator and then put in the number

hope this helps! :)

Step-by-step explanation:

f/p = p(1+i)^n

p= 2500

i=0.03 =3%

n=4

2500(1 + 0.03)^4