Simplify : 3a(6a²-4ab?) + 8a²b2 - 2b

Answer:

yes it can. If you look it up it will show you a link to see photos

Answer:

Step-by-step explanation:

Yes this is possible

ʕ◉ᴥ◉ʔ gimme crown please?

To determine the points of intersection we first equate the expressions, then we solve for x. Once we have the values of x for which the functions are equal we plu them on one of the function to find its corresponding value of y.

a)

Let's equate the functions and solve for x:

Now we find the corresponding values of y for each value of x; to do this we use the second equation.

When x=3:

Hence the functions intersect at (3,11)

When x=2:

Hence the functions intersect at (2,6)

Therefore the function intersect at the points (3,11) and (2,6).

b)

Let's equate the functions and solve for x:

Now we find the corresponding values of y for each value of x; to do this we use the second equation.

When x=7:

Hence the functions intersect at (7,-26)

When x=-1:

Hence the functions intersect at (-1,-2)

Therefore the function intersect at the points (7,-26) and (-1,-2).

She ran a total distance of 28 miles in 5 hours.

We can solve this problem by using the formula: distance = rate × time

First, we need to calculate the distance traveled during the first 3 hours at 6 mph. Using the formula, we have:

distance = rate × time

distance = 6 mph × 3 hours

distance = 18 miles

Next, we need to calculate the distance traveled during the last 2 hours at 5 mph. Using the same formula, we have:

distance = rate × time

distance = 5 mph × 2 hours

distance = 10 miles

Finally, we can add the distances traveled during the first 3 hours and the last 2 hours to get the total distance:

total distance = 18 miles + 10 miles

total distance = 28 miles

Therefore, the runner ran a total distance of 28 miles in 5 hours.

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Answer:

190

Step-by-step explanation:

(120*2) - 10 = 190

hope this helped !!

Therefore, Mario's winnings of 177 dollars is approximately 2.92 standard deviations below the mean.

We can calculate the number of standard deviations that Mario's winnings of 177 dollars is from the mean using the formula:

z = (x - μ) / σ

where x is the value we want to convert to standard deviations, μ is the mean of the distribution, and σ is the standard deviation of the distribution.

In this case, Mario's winnings of 177 dollars is the value we want to convert to standard deviations, the mean is μ = 323 dollars, and the standard deviation is σ = 50 dollars. Substituting these values into the formula, we get:

z = (177 - 323) / 50

= -2.92

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The statement that  Vector field F = (3×2, 1) is a gradient field for both ®/(x, y) = x3 + y and z(x, y) = y + x3 + 138. O is False

A vector field F = (3x², 1) is a gradient field for both  $R(x,y)=x³+y$ and $z(x,y)=y+x³+138$ can be true or false. Let's first take a look at a vector field.

The term "vector field" refers to a group of vectors that are drawn from every point in space, with each vector changing over time. The components of the vector are functions of the x and y coordinates of each point in space, so the components of the vector field are defined at each point in the plane.

Using a scalar potential function, a vector field is generated. Gradient fields are vector fields that result from a scalar potential function being differentiated with respect to two independent variables, resulting in two differentials.

The gradient vector field of a function is a vector field that points in the direction of the maximum rate of increase of the function and has a magnitude equal to the maximum rate of increase. According to the question, Vector Field is: F = (3x², 1)

Scalar Potential function are: R(x,y) = x3 + yz(x,y) = y + x3 + 138

Using the concept, A vector field F is said to be a gradient field for a scalar function f if and only if F=grad(f), i.e., F is the gradient of a scalar function f.

let's find the gradients of given scalar potential functions:$$grad(R(x,y))=<3x²,1>$$$$grad(z(x,y))=<3x²,1>$$. Comparing the gradients with the vector field F, we see that grad(R(x, y)) = F and grad(z(x, y)) = F, so F is a gradient field for both R(x, y) = x³ + y and z(x, y) = y + x³ + 138.

Therefore, the statement is False.

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After reducing all the book prices by 50%, the new median price is determined to be $7.70 (B)

To find the new median price after reducing all the book prices by 50%, we first need to calculate the reduced prices. By reducing each given price by 50%, we get $6.375, $7.40, $9.995, $4.975, $8.00, and $8.975 respectively.

Next, we arrange these reduced prices in ascending order: $4.975, $6.375, $7.40, $8.00, $8.975, and $9.995. The median is the middle value in this ordered list. Since there are six prices, the middle two values are $7.40 and $8.00.

To find the median, we take the average of these two values, which gives us ($7.40 + $8.00) / 2 = $7.70.

Therefore, the new median price, after reducing all the book prices by 50%, is $7.70 (B). This means that the median price of the books, after the reduction, is $7.70.

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Gregs's mom baked 24 cookies, while Vinnie's mom baked 36 cookies. Brad's mom baked twice as much as Greg's mom, resulting in a total of 48 cookies. The total number of cookies that were baked is found by adding the number of cookies that each mom baked:

24 + 36 + 48 = 108.

The cookies can be divided into 3 groups of 36, 4 groups of 27, 6 groups of 18, 9 groups of 12, 12 groups of 9, 18 groups of 6, 27 groups of 4, or 36 groups of 3 cookies. Since there are more than 100 words required, let's talk about the importance of fractions and equivalent ratios.

In conclusion, Greg's mom baked 24 cookies, Vinnie's mom baked 36 cookies, and Brad's mom baked 48 cookies, resulting in a total of 108 cookies. The cookies can be divided into fractions or equivalent ratios to distribute them evenly among the children.

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If m = 3/2, the two equations in the system are dependent and have an infinite number of solutions.

To do this, we can set the coefficients of x and y in the two equations equal to each other:

6 - 4m = 2k(2m - 1)

2n - 7 = 3k

Simplifying these equations, we get:

8m - 6 = 4km

2n - 7 = 3k

We can solve the first equation for k:

k = (8m - 6)/(4m)

Substituting this into the second equation and solving for n, we get:

n = (16m - 29)/(8m - 12)

Now we need to check if there are any values of m for which the equations are proportional. We can do this by checking if the expressions for k and n are the same for all values of m.

We find that the expressions for k and n are the same for m = 3/2.

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Complete Question:

Determine the values of m and n so that the following system of linear equations have infinite number of solutions:

(2m−1)x+3y−5=0

3x+(n−1)y−2=0

Answer:

5inches in all angles 2 right 2 obtuse 1 acute

Step-by-step explanation:

To determine the change in angular momentum (ΔL) of a cylinder from t = 0 to t = t0, a student can use the equation:

ΔL = I * Δω

where ΔL is the change in angular momentum, I is the moment of inertia of the cylinder, and Δω is the change in angular velocity.

To calculate Δω, the student needs to know the initial and final angular velocities, ω0 and ωt0, respectively. The change in angular velocity can be calculated as:

Δω = ωt0 - ω0

Once Δω is determined, the student can use the moment of inertia (I) of the cylinder to calculate ΔL using the equation mentioned earlier.

The moment of inertia (I) depends on the mass distribution and shape of the cylinder. For a solid cylinder rotating about its central axis, the moment of inertia is given by:

I = (1/2) * m * r^2

where m is the mass of the cylinder and r is the radius of the cylinder.

By substituting the known values for Δω and I into the equation ΔL = I * Δω, the student can calculate the change in angular momentum (ΔL) of the cylinder from t = 0 to t = t0.

It's important to note that this method assumes that no external torques act on the cylinder during the time interval. If there are external torques involved, the equation for ΔL would need to include those torques as well.

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Answer:

The descriptions that apply are E and F.

Step-by-step explanation:

Let's graph both functions, attached the result:

A: No. The graph is not reflected across x-axis. For this to happen, there should be a negative sign: g(x) = -x, for example

B: No, the graph doesn't translate. The graph only translates if there is: g(x) = a(x-c)+b, where b defines the vertical translation, and c the horizontal one.

C: No. This would happen for g(x)=x/2, for example.

D: No. Check the explanation of B.

E: Yes. The graph rotates due to the factor of 10. This rotation only applies for straight lines.

F: Yes. It stretched.

The 99% confidence interval for the mean score of all students is constructed as (85.497, 96.5026).

Given,

Sample size, n = 30

Sample mean, x = 91

Standard deviation, s = 11.7

The 99% confidence interval for the mean score of all students can be calculated as,

x ± z \(\frac{s}{\sqrt{n} }\)

z value for 99% confidence interval = 2.576

Confidence interval = (91 ± (2.576 × 11.7/√30)

                                 = (91 ± 5.5026)

                                 = (85.497, 96.5026)

Hence the confidence interval is (85.497, 96.5026).

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Based on the t-test assuming equal variances a. Examining the ratio of the variances, it is reasonable to conclude that the variances are unequal."

It is vital to establish whether or not the variances of the two groups being compared are indeed identical before performing a t-test under the assumption of equal variances. This is significant since the t-calculation statistic depends on the assumption that variances are equal.

One can look at the ratio of the variances between the two groups to evaluate the assumption of equal variances. Typically, it is acceptable to infer that the variances are not equal if the ratio of the variances is more than two or lower than half. One can presume that the variances are equal in the absence of such proof. Since the variances are not equal, it is not logical to infer that they are.

Complete and correct Question:

Based on the t-test assuming equal variances on the T-Test Equal worksheet, is it reasonable to assume that the variances are equal?
a. Examining the ratio of the variances, it is reasonable to conclude that the variances are unequal.
b. Whether the variances are equal or not is not relevant for this situation.
c. Examining the ratio of the variances, it is reasonable to conclude that the variances are equal.
d. It is impossible to determine if the variances are equal given the data we have.

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Answer:

check the pdf .

Step-by-step explanation:

Answer:

\(\dfrac{2}{3x-2} + \dfrac{1}{x+2}\)

Step-by-step explanation:

Use partial fraction decomposition to split up the following complex fraction.

\(\dfrac{5x+2}{3x^2+4x-4}\\\\\\\hrule\)

Here's a step-by-step guide on how to perform partial fraction decomposition:

Step 1: Determine the proper form of the fraction

Step 2: Factor the denominator

Step 3: Write the partial fraction decomposition equation

\(\dfrac{A_1}{factor_1}+ \dfrac{A_2}{factor_2} + ... + \dfrac{A_n}{factor_n}\)

Step 4: Determine the unknown coefficients

Step 5: Express the unknown coefficients

Step 6: Write the final partial fraction decomposition

Step 7 (Optional): Simplify and evaluate if necessary

\(\hrulefill\)

Step 1 -

The degree is determined by the highest power of x that appears in the expression.

\(\dfrac{5x+2}{3x^2+4x-4}\)

Observing our given expression, we see that the degree of the numerator is 1 and the degree of the denominator is 2. Thus, we can proceed with partial fractions.

Step 2 -

We have,

\(3x^2+4x-4\)

We can factor the denominator using grouping.

\(\Longrightarrow 3x^2+4x-4\\\\\\\Longrightarrow 3x^2+(-2+6)x-4\\\\\\\Longrightarrow 3x^2-2x+6x-4\\\\\\\Longrightarrow x(3x-2)+2(3x-2)\\\\\\\Longrightarrow (3x-2)(x+2)\)

Now we have,

\(\dfrac{5x+2}{3x^2+4x-4} \Longrightarrow \dfrac{5x+2}{(3x-2)(x+2)}\)

Step 3 -

For step three, instead of writing "A_1, A_2, ..." I will use "A, B, ..."

\(\dfrac{5x+2}{(3x-2)(x+2)}=\dfrac{A}{3x-2} + \dfrac{B}{x+2}\)

Step 4 and 5 -

\(\dfrac{5x+2}{(3x-2)(x+2)}=\dfrac{A}{3x-2} + \dfrac{B}{x+2} \Big](3x-2)(x+2)\\\\\\\\\Longrightarrow 5x+2=A(x+2)+B(3x-2)\\\\\\\\\Longrightarrow 5x+2=Ax+2A+3Bx-2B\\\\\\\\\Longrightarrow 5x+2=(A+3B)x+(2A-2B)\)

Using the method of comparison. We get the following system of equations,

\(\left \{ {{5=A+3B} \atop {2=2A-2B}} \right.\)

After solving the system we get A=2 and B=1.

Step 6 -

\(\dfrac{5x+2}{(3x-2)(x+2)}=\boxed{\boxed{\dfrac{2}{3x-2} + \dfrac{1}{x+2}}}\)

Thus, the problem is solved.

a) The solution for b in the equation 2b × 3 = 6 is b = 1.

b) The solution for b in the equation 32 - 3b = 2 is b = 10.

c) The solution for b in the equation 6 + 7b = 41 is b = 5.

d) The solution for b in the equation 100/5b = 2 is b = 10.

a) To solve for b in the equation 2b × 3 = 6, we can start by dividing both sides of the equation by 2 to isolate b.

2b × 3 = 6

(2b × 3) / 2 = 6 / 2

3b = 3

b = 3/3

b = 1

Therefore, the solution for b in the equation 2b × 3 = 6 is b = 1.

c) To solve for b in the equation 6 + 7b = 41, we can start by subtracting 6 from both sides of the equation to isolate the term with b.

6 + 7b - 6 = 41 - 6

7b = 35

b = 35/7

b = 5

Therefore, the solution for b in the equation 6 + 7b = 41 is b = 5.

b) To solve for b in the equation 32 - 3b = 2, we can start by subtracting 32 from both sides of the equation to isolate the term with b.

32 - 3b - 32 = 2 - 32

-3b = -30

b = (-30)/(-3)

b = 10

Therefore, the solution for b in the equation 32 - 3b = 2 is b = 10.

d) To solve for b in the equation 100/5b = 2, we can start by multiplying both sides of the equation by 5b to isolate the variable.

(100/5b) × 5b = 2 × 5b

100 = 10b

b = 100/10

b = 10.

Therefore, the solution for b in the equation 100/5b = 2 is b = 10.

In summary, the solutions for b in the given equations are:

a) b = 1

c) b = 5

b) b = 10

d) b = 10

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Answer:

Step-by-step explanation:

interval in mathematics stands for a set of real numbers,

denoted by [a,b] where a and b are the starting and ending real numbers both inclusive respectively.

thus, interval [a,b] is the set of real numbers starting from a to b both are real numbers and are included.

Answer:

Step-by-step explanation:

If X is 3 then it is

3 times 3 times 3 times 3 times 3

I don't know what is x or black sorry (-.-)

The ratio of the Volume of the sphere whose radius are in ratio 1:2 is 1:8.

A sphere is a three dimensional figure, it is made of set of points that are all equidistant from the center.

The ratio of radii of two spheres is 1:2

Volume of a sphere is given by

V = (4/3) πr³

The ratio of two sphere is given by

V₁ / V₂ = (r₁/r₂)³

V₁ / V₂ = (1/2)³

V₁ / V₂ = 1/8

Therefore, the ratio of the Volume of the sphere whose radius are in ratio 1:2 is 1:8.

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Answer:

\(\frac{2}{15}\)

Step-by-step explanation:

1. There are 9 balls in total in the first box, and 6 red balls in there so we would represent this as \(\frac{6}{9}\) and that can be simplified to \(\frac{1}{3}\) .

2. There are 5 balls in total in the second box, and 2 blue balls in there, so we would represent this as \(\frac{2}{5}\) . This can't be simplified, so we leave it like that.

3. Because it's a consecutive event we multiply the probabilities, which gives us \(\frac{2}{15}\) . This can't be simplified, and that gives us our answer.

The value of x for the given tangent line is 13 cm.

An extended straight line that intersects only one point on a curve and nowhere else is called a tangent. A circle's tangent is always perpendicular to its radius.

Here, two tangents to the same circle, A (x) and B (13), are subtended from two points on the circle.

So, if two tangents are drawn from a point outside the circle, they will both have the same length when they reach the point of contact inside the circle.

The two tangents in this instance have the same outside point of origin. Thus, based on the above calculation, x = 13 cm.

Hence, the value of x for the given tangent line is 13 cm.

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Answer:

The equivalent ratio to the given ratio is;

Explanation:

Given the ratio;

We want to select an equivalent ratio from the given options.

Let's divide the ratio all through by 3;

Therefore, the equivalent ratio to the given ratio is;

Answer:

The answer is

Step-by-step explanation:

The midpoint M of two endpoints of a line segment can be found by using the formula

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

C (4,6) and D(-1, -1)

The coordinates of the midpoint is

We have the final answer as

Hope this helps you

Using the four-step process,  f'(1) = 10, f'(2) = 12, and f'(3) = 14.

To identify f'(x), the derivative of f(x), using the four-step process, we can follow these steps:

1: Identify the function.
The given function is f(x) = x^2 + 8x - 6.

2: Apply the power rule.
Differentiate each term of the function separately.
The derivative of x^2 is 2x.
The derivative of 8x is 8.
The derivative of -6 is 0 (constant term).

3: Simplify.
Combine the derivatives obtained in step 2.
So, f'(x) = 2x + 8.

4: Evaluate f'(1), f'(2), and f'(3).
Substitute x = 1, 2, and 3 into the derived equation to identify the respective values.
f'(1) = 2(1) + 8 = 10.
f'(2) = 2(2) + 8 = 12.
f'(3) = 2(3) + 8 = 14.

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The area and circumference of the given circle are 200.96 cm2 200.96 c m 2 and 50.24 cm 50.24 c m respectively.

Circumference of circle:

In geometry, a circumference is the circumference of a circle or an ellipse. That is, the circumference will be the length of the arc of the circle as if it were open and straight to the line segment. More generally, the perimeter is the length of the curve around any closed figure. The circumference can also designate the circle itself, the trajectory corresponding to the edge of a disk. The circumference of a sphere is the circumference or length of one of its great circles.

Area of circle:

The area of ​​a circle is the space the circle occupies in a two-dimensional plane. Alternatively, the space occupied inside the boundary/perimeter of a circle is called the area of ​​the circle. The formula for the area of ​​a circle is A = πr2, where r is the radius of the circle. Area unit is square unit, such as m2, cm2, in2, etc.

According to the Question:

The circumference C of a circle with radius r is given by

C = 2πr

where the units of C will be the same as the unit of R.

The problem tells us that the radius r = 8m.

And, we will say π = 3.14

So,

C = 2(3.14)(8) = 50.24m

The units are meters.

Now, the area A of a circle with radius r is given by

A = πr², where the units of A will be the units of r squared.

Again,

we know r = 8,π = 3.14, so

A= 3.14(8²)

8² = 8⋅8 = 64,

Thus,

A= 64(3.14) = 200.96m²

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Answer:

multiple

Step-by-step explanation:

I think the answer is "multiple" Since a multiple of a number is that number multiplied by another.

Example: 10 is a multiple of 5 because 5 x 2 = 10

               48 is a multiple of 8 beacuse 8 x 6 = 48

Hope this helps :)

multiple of a number is that number times any whole number.

The following information should be considered:

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