Hellppp pls , need of help

The simplified form of the expression [8q² -2 [q²-2 (3q²-3q+5)​ is 18q² −12q + 20.

Reduce a fraction to its simplest form to simplify it. A fraction is said to be in its simplest form if both its numerator and denominator only contain the number one. As we attempt to solve fractional problems, the process of simplifying difficulties is crucial. Even after we simplify them, the fraction's value will not change. This shows that the true fraction and the simplified fraction are two equivalent fractions.

Lets Simplify

= [8q² -2 [q²-2 (3q²-3q+5)​

= [8q² -2(q²−6q² +6q−10)

= 8q² + 10q² −12q + 20

= 18q² −12q + 20

Thus, The simplified form of the expression [8q² -2 [q²-2 (3q²-3q+5)​ is 18q² −12q + 20.

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Answer:

The formula for the tripling time (t3) of an exponential growth model with relative growth rate k is: t3 = ln(3)/k

Step-by-step explanation:

To find the tripling time (t3) of an exponential growth model, we'll use the formula for exponential growth, which is:

P(t) = P0 * e^(k*t)

Here, P(t) represents the population at time t, P0 is the initial population, k is the relative growth rate, and t is the time.

To find the tripling time (t3), we want the population to triple, so we'll set P(t) = 3 * P0: 3 * P0 = P0 * e^(k*t3)

Now, we'll solve for t3:

1. Divide both sides by P0: 3 = e^(k*t3)

2. Take the natural logarithm (ln) of both sides: ln(3) = ln(e^(k*t3))

3. Use the logarithm property: ln(a^b) = b*ln(a): ln(3) = k*t3

4. Solve for t3: t3 = ln(3)/k

So, the formula for the tripling time (t3) of an exponential growth model with relative growth rate k is: t3 = ln(3)/k

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Answer:

3a + 18

Step-by-step explanation:

Answer: (1) 19x 4y

(2)3.8x 15y

(3) 3x 9.5y

(4) 5.5x 0y

The approximate distance from Town A to Town C is 12.5 miles.

What is the midpoint?

The midpoint of a line segment is a point that lies halfway between 2 points. The midpoint is the same distance from each endpoint.

To find the midpoint of Town A and Town B, you need to find the average of the x-coordinates and the average of the y-coordinates.

The x-coordinate of Town A is -8 and the x-coordinate of Town B is 10, so the average is (10 - (-8))/2 = 9/2 = 4.5.

The y-coordinate of Town A is 2 and the y-coordinate of Town B is 8, so the average is (8 - 2)/2 = 6/2 = 3.

Therefore, Town C is located at (4.5, 3).

To find the distance from Town A to Town C, you can use the distance formula, which is the square root of the difference in x-coordinates squared plus the difference in y-coordinates squared.

The distance from Town A to Town C = √((4.5 - (-8))^2 + (3 - 2)^2) = √(12.5^2 + 1^2) = √(156.25 + 1) = √(157.25) = 12.5 miles

Hence, the approximate distance from Town A to Town C is 12.5 miles.

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Let Cesar's, Carmen's and Dalila's amount be represented by x, y and z respectfully.

Since they're money sum up to $95.34, the first expression will be;

x+y+z=95.34

Carmen_y_ is $12.12 less than cesar_x, so the equation will be ;

y=x-12.12

Cesar_x_raised $35more than Dalila_z. So the equation will be;

x=z+35

making z the subject, z=x-35 .

Substituting the Second equation into the first one, we get;

x+x-12.12+z=95.34

Subtracting the third equation into the new equation we get;

x+x-12.12+x-35=95.34

Simplifying, we get 3x- 47.12= 95.34.

3x=142.46

The height of the 10th bounce of the ball will be 0.6 feet.

A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value.

The nth term of the geometric sequence is given by

\(\sf T_n=ar^{n-1}\)

Where,

According to the given question.

During the first bounce, height of the ball from the ground, a = 4.5 feet

And, the each successive bounce is 73% of the previous bounce's height.

So,

During the second bounce, the height of ball from the ground

\(\sf = 73\% \ of \ 10\)

\(=\dfrac{73}{100}(10)\)

\(\sf = 0.73 \times 10\)

\(\sf = 7.3 \ feet\)

During the third bounce, the height of ball from the ground

\(\sf = 73\% \ of \ 7.3\)

\(=\dfrac{73}{100}(7.3)\)

\(\sf = 5.33 \ feet\)

Like this we will obtain a geometric sequence 7.3, 5.33, 3.11, 2.23,...

And the common ratio of the geometric sequence is 0.73

Therefore,

The sixth term of the geometric sequence is given by

\(\sf T_{10}=10(0.73)^{10-1\)

\(\sf T_{10}=10(0.73)^{9\)

\(\sf T_{10}=10(0.059)\)

\(\sf T_{10}=0.59\thickapprox0.6 \ feet\)

Hence, the height of the 10th bounce of the ball will be 0.6 feet.

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The equation of the circle in the picture is

Information given in the question

center at the point (2, -1)

radius = 3

The equation of a circle with radius given as 3 is solved as below

Equation of a circle is given as

(x - h)² (y - k)² = r²

where h and k refers to points at the center, substituting the values gives

(x - 2)² (y - (-1))² = 3²

(x - 2)² (y + 1)² = 3²

(x - 2)² (y + 1)² = 9

hence option C represents the equation of the circle

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Based on the numbers being divided, the number of significant digits that the quotient should have is 4 significant digits.

The number of significant digits from a quotient where numbers divided each other should be the significant digits in the number with the smaller number of significant digits.

The number with the lower significant digits here is 2.058 × 10^9.

In this number, there are 4 significant digits because 0 is between non zero numbers.

The quotient would therefore have 4 significant digits.

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Answer:

9degrees Celsius

Step-by-step explanation:

Yesterday the temperature =( –9 degrees Celsius)

Today temperature= O degrees Celsius.

Hence there was increase in temperature from yesterday to today with [0 - (-9)]= 9degrees Celsius.

Answer:

$54

Step-by-step explanation:

45 increase 20% =

45 × (1 + 20%) = 45 × (1 + 0.2) = 54

Answer:

7 cubes (having 2 m sides) can be completely covered with 7500 ml of paint, assuming the "2m" refers to side length in the question.

Step-by-step explanation:

No definition of a "cube" is provided.  The area in a cube must be known to determine the number of cubes that the paint will cover.  The entry "2 m" is confusing.  Is this supposed to be 2m^2, a unit of area for each cube?  2m is a length.  If 2 m is the side of a cube, then the following calculation will work:

====

1.  Calculate the area of a cube:

 A cube has 6 faces, all having the same lengths (2 m).  The are of one face is the quare of the length, or 4 m^2.  6 faces make the total area 24 m^2 per cube.

This can be made into a conversion factor:  (24 m^2/cube)

2.  Calculate the area that 7500 ml of paint will cover:

Since 40ml of paint covers 1 m^2, we can write a conversion factor:  (1 m^2)/(40 ml).

3.  Calculate the number of cubes covered by 7500 ml of paint:

Use the conversion factors.  Focus on arrange the factors so that the units cancel to just cubes, the desired answer.

 a) Start with the 7500 ml and use a conversion factor to eliminate ml and leave on m^2.  This will tell us how many square meters of surface the 7500 ml of paint will cover.  The first conversion factior has both ml and m^2, so lets use it.  The factor, as written, can be multiplied by the 7500ml to leave only m^2, since the ml units will cancel:

  (7500 ml)*[(1 m^2)/(40 ml)] = 187.5 m^2

 b)  The desired final unit is simply cubes.  The second coversion factor has both m^2 and cubes, so we can use it to convert m^2 into cubes.  But note that if the conversion facotr is multiplied, we'll wind up with unit of m^4/cube:

    (187.5 m^2)*[(24 m^2/cube)    [The resulting unit of m^4/cube makes no sense]

      In this situation, we may divide instead:

  (187.5 m^2)/[(24 m^2/cube) = 7.81 cubes  

[This step can be written as:  

  (187.5 m^2)/[(24 m^2/cube) is the same as [(187.5m^2/24)] (cube/m^2)

---

II don't enjoy division, so my preferred step is o invert the conversion factor:

   Original: (24 m^2/cube)

  Inverted:  (1 cube/24 m^2)    This is allowed since in a conversion factor, both the top and bottom are equal.  [So we can write (1 foot/12 inches), or (12 inches/1 foot), for example.  Both are correct.]

Using this approach:

  (187.5 m^2)*(1 cube/24 m^2) = 7.81 cubes  The m^2 units cancel leaving only (187.5/24) cubes (or 7.81 cubes).

Since the question stipulates that the cubes must be "completely" covered, we need to round down.  That make 7 cubes (having 2 m sides) can be completely covered with 7500 ml of paint.

1) The statement "content loaded bjects are me uishable" appears to contain a typo. It is unclear what is meant by "me uishable." P(n) = p(n,1) + p(n,2) + ... + p(n,n) .We can use the recurrence relation for p(n,k) to compute P(n).

2) Let's consider the given problem statement. We need to find a formula for f(m,n), the number of m x n matrices whose entries are 0 or 1 and with at least one 1 in each row and each column.

Suppose we have an m x n matrix with at least one 1 in each row and column. Let's focus on a specific row, say the first row. There must be at least one 1 in the first row, so we can assume that the first entry is a 1.

Now let's consider the rest of the matrix, which is an (m-1) x (n-1) matrix. This matrix must also have at least one 1 in each row and column. We can repeat the same argument for the first column, leaving us with an (m-1) x (n-1) matrix that satisfies the condition.

So we have the following recursive formula:
f(m,n) = f(m-1,n) + f(m,n-1) - f(m-1,n-1)

The first two terms count the number of matrices that have a 1 in the first row and in the first column, respectively. But we have double-counted the (m-1) x (n-1) matrix, so we subtract it once. The base cases are f(1,n) = f(m,1) = 1, since a 1 x n or m x 1 matrix with at least one 1 in each row and column has to have all entries equal to 1.

3) Now let's move on to part 3. We need to find a formula for P(n), the number of partitions of the positive integer n. Let p(n,k) be the number of partitions of n into k parts. We can write a recurrence relation for p(n,k) as follows:

p(n,k) = p(n-k,k) + p(n-1,k-1)
The first term counts the number of partitions of n into k parts, where each part is at least 1. We can subtract 1 from each part to get a partition of n-k into k parts. The second term counts the number of partitions of n into k parts, where the largest part is k. We can remove the largest part and get a partition of n-1 into k-1 parts.

The base cases are p(n,1) = 1, since there is only one partition of n into 1 part, and p(n,n) = 1, since there is only one partition of n into n parts (namely, n).
Now we can express P(n) in terms of p(n,k):
P(n) = p(n,1) + p(n,2) + ... + p(n,n)
We can use the recurrence relation for p(n,k) to compute P(n).

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Answer:

Step-by-step explanation:

\(cos\alpha =\sqrt{1-sin^{2} \alpha } =\sqrt{1-(\frac{5}{13})^{2} } =\sqrt{\frac{144}{169} }\)

=\(\frac{12}{13}\)

\(tan\alpha =\frac{sin\alpha }{cos\alpha } =\frac{\frac{5}{13} }{\frac{12}{13} } = \frac{5}{12}\)

Answer:

1= 8

3= 12

5= 16

7= 20

9= 24

Step-by-step explanation:

1+3=4x2=8

3+3=6x2=12

5+3=8x2=16

9+3=12x2=24

ANSWER:1=8

3=12

5=16

7=20

9=24

step -by - step explanation: 1+3=4×2=8

3+3=6×2=12

5+3=8×2=16

9+3=12×2=24

Answer:

21.45

Step-by-step explanation:

Answer:

20.9

Step-by-step explanation:

9514 1404 393

Answer:

Step-by-step explanation:

The third line of the solution is incorrect. It should be ...

  5x +2 = -5x +2

Then the one solution can be found:

  10x = 0 . . . . . . . . . add 5x-2 to both sides

  x = 0

Answer:

Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean. In graph form, normal distribution will appear as a bell curve.

Answer: 196.5 lbs

Step-by-step explanation:

\(237-9(4.5)=196.5\)

Answer:

The y intercept is always (0,y) so in this case it is (0,8)

Step-by-step explanation:

Answer:

so on a graph you have two axis's: the x (horizontal) and y (vertical). The y intercept is the point at which your line touches the y axis which is also when x=0. So your y intercept will always be (0,y) in this case when x is t and when t is 0, C (or y) is 8. x is your input (independent) and y is your output (dependent). The y intercept in the above model can be written as (0,8) or m=8

Step-by-step explanation:

Answer:

The equation is = I = \(e^{4.8}\)

Step-by-step explanation:

As given ,

M - magnitude of an earthquake

I - intensity of earthquake

I₀ - intensity of a reference earthquake

The relation between the three is as follows :

M = log(\(\frac{I}{I0}\) )

As given -

M = 4.8,  I₀ = 1

⇒ 4.8 = log(\(\frac{I}{1}\)) = log(I)

⇒ 4.8 = log(I)

⇒I = \(e^{4.8}\)

So, the equation becomes I = \(e^{4.8}\)

The thickness of the clay layer, which drains only from the upper surface, can be determined based on the consolidation settlement observations. With 50% of consolidation settlement occurring in 1 hour for a 25 mm thick specimen, and a total primary consolidation settlement of 35 mm occurring over many years, the thickness of the clay layer is approximately 87.5 mm.

The consolidation settlement of a clay specimen can be used to estimate the thickness of a clay layer that drains only from the upper surface. In this case, the observed settlement data provides valuable information.

Firstly, we know that 50% of the consolidation settlement occurs in 1 hour for a 25 mm thick clay specimen. This is an important parameter for calculating the coefficient of consolidation (Cv) using Terzaghi's theory. From the Cv value, we can estimate the time required for full consolidation settlement.

Secondly, we are given that the same clay settles 10 mm over 10 years and eventually settles a total of 35 mm over a longer period. This long-term settlement is known as the total primary consolidation settlement. By comparing this settlement value with the settlement data from the oedometer test, we can determine the thickness of the clay layer.

To calculate the thickness, we can use the concept of the consolidation settlement ratio. The ratio of the total primary consolidation settlement to the consolidation settlement at 50% completion is equal to the ratio of the total thickness to the thickness at 50% completion. Applying this ratio, we can determine that the thickness of the clay layer, which drains only from the upper surface, is approximately 87.5 mm.

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Answer:

15

Step-by-step explanation:

The price of the bag at the pharmacy is

2/3 * 12 = 8 dollars

You have enough for 10 at the gift shop

10 * 12 = 120

Take 120 dollars and divide by 8 dollars to see how many you can get at the pharmacy

120/8 =15

Answer:

the answer is C. it was on my mid-term

Step-by-step explanation:

The integral: ∫(√x - x/3) dx = [2/3 * x^(3/2) - 1/6 * x^2] evaluated from 0 to 9. The integral represents the area between the curves.

To find the region enclosed by the given curves, we need to sketch the graphs of the equations y = √x and y = x/3.

Step 1: Sketching the Graphs

Start by plotting the points on each curve. For y = √x, you can plot points such as (0,0), (1,1), (4,2), and (16,4).

For y = x/3, plot points like (0,0), (3,1), (6,2), and (16,5.33).

Connect the points on each curve to get the shape of the graphs.

Step 2: Determining the Intersection Points

Find the points where the two curves intersect by setting √x = x/3 and solving for x. Square both sides of the equation to get rid of the square root: x = x²/9. Rearrange the equation to x² - 9x = 0, and factor it as x(x - 9) = 0. So, x = 0 or x = 9.

At x = 0, both curves intersect at the point (0,0).

At x = 9, the y-coordinate can be found by substituting x into either equation. For y = √x, y = √9 = 3. For y = x/3, y = 9/3 = 3.

Therefore, the two curves intersect at the point (9,3).

Step 3: Determining the Bounds

The region enclosed by the curves lies between the x-values of 0 and 9, as given in the problem.

Step 4: Calculating the Area

To find the area of the enclosed region, we need to calculate the integral of the difference between the curves from x = 0 to x = 9. The integral represents the area between the curves.

Set up the integral: ∫(√x - x/3) dx, with the limits of integration from 0 to 9.

Evaluate the integral: ∫(√x - x/3) dx = [2/3 * x^(3/2) - 1/6 * x^2] evaluated from 0 to 9.

Substitute the upper and lower limits into the integral expression and calculate the difference.

The calculated value will be the area of the region enclosed by the given curves.

Therefore, by following these steps, you can sketch the region enclosed by the curves and calculate its area.

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The curve xy² = 2 + xy has one horizontal tangent line at y = 0 and one vertical tangent line.

Therefore, the answer is "One horizontal and one vertical."

To determine the number of horizontal or vertical tangent lines for the curve xy² = 2 + xy, we need to find the derivative of the equation with respect to x and y and then analyze the slope.

Differentiating both sides of the equation implicitly, we get:

d/dx (xy²) = d/dx (2 + xy)

To find the derivative of xy², we apply the product rule:

d/dx (xy²) = y² + 2xy(dy/dx)

For the derivative of 2 + xy, the derivative of xy with respect to x is y(dy/dx) and the derivative of 2 with respect to x is 0.

Therefore:

0 + y² + 2xy(dy/dx) = 0 + dy/dx

Rearranging the equation, we have:

y² + 2xy(dy/dx) - dy/dx = 0

Factoring out dy/dx, we get:

(2xy - 1)(dy/dx) + y² = 0

Now, to find the slope of the tangent line, we set dy/dx = 0:

(2xy - 1)(0) + y² = 0

y² = 0

Since y² = 0 implies y = 0, we can conclude that there is only one horizontal tangent line at y = 0.

Next, we set the term 2xy - 1 equal to zero to find the vertical tangent line(s):

2xy - 1 = 0

2xy = 1

xy = 1/2

From this equation, we see that there is only one possible value for xy, which is 1/2.

Thus, there is only one vertical tangent line.

In conclusion, the curve xy² = 2 + xy has one horizontal tangent line at y = 0 and one vertical tangent line.

Therefore, the answer is "One horizontal and one vertical."

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Answer: 8 posters

Step-by-step explanation:

From the question, we are informed that Lincoln has 16 pins in one box and 17 pins in another box and that he uses 4 pins to hang each posters posted. The total number of posters he can hang with the pins goes thus:

We should first calculate the total number of pins he has.

= 16 + 17 = 33 pins

Since he uses 4 pins to hang a poster, we then divide 33 pins by 4.

= 33 ÷ 4

= 8.25

This means that he can hang 8 posters with the pin

To find the largest number of passengers in the tram, we need to calculate the maximum number of passengers who can go without a ticket.

Given that 12% of passengers go without a ticket, we can set up the following equation:

12% of x = 60

To solve for x, we can divide both sides of the equation by 0.12:

x = 60 / 0.12

x = 500

Therefore, the largest number of passengers in the tram, if it is not greater than 60, would be 500.

To find the largest number of passengers in the tram, we use the percentage given and set it equal to the number of passengers. By solving for x, we determine that the largest number of passengers in the tram is 500.

The largest number of passengers in the tram, if it is not greater than 60, is 500.

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If a rectangle has an area of A and sides b and h, then:

Solving for the base:

Basically, the sides b and h could have any value provided that b*h=A.

Nevertheless, this problem seems to want from us to factorize the expression:

So that each side is a binomial.

Part a)

To factorize that expression, find two numbers so that if they are added up, the sum is equal to -5, and if they are multiplied, the product is equal to -300.

Since the product is negative, one number must be negative. Since the sum is negative, the biggest number should be the negative one.

Consider the factors of 300:

Using those factors, we can find pairs of numbers that give 300 as a result from multiplying.

After a bit of trial and error, notice that 15*20=300. If we choose 20 as the negative number, then 15*(-20)=-300 and 15+(-20)=-5. Therefore:

So, we can choose the width and the height to be those factors. Since (x+15) is greater then (x-20), then:

Part b)

If x=45, then:

GL is equal to √25 + L2, or √5 in its simplest radical form. The Pythagorean Theorem states that the sum of the squares of the two adjacent sides of a right triangle is equal to the square of the hypotenuse.

Given:

GL = ?

m∠KLH = 90°

KH = 5

We can use the Pythagorean Theorem to solve for GL.

GL2 = K2 + L2

GL2 = 52 + L2

GL2 = 25 + L2

Therefore, GL = √25 + L2 = √5.

Given GL, m∠KLH, and KH, we can use the Pythagorean Theorem to solve for GL. The Pythagorean Theorem states that the sum of the squares of the two adjacent sides of a right triangle is equal to the square of the hypotenuse. Therefore, we can calculate the square of GL by taking the square of KH and adding it to the square of L, which is unknown. We square 5 and get 25, then we add L2 to get 25 + L2. We can then take the square root of this to get GL. Therefore, GL is equal to √25 + L2, or √5 in its simplest radical form.

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