How many solutions does 1/3(6w - 12) = 2w + 2 have?

Answer:94

Step-by-step explanation:

English is not my first language, so I don't know if you understand what I meant in the explanation.

Answer: The hypotenuse are both 13 cm

Step-by-step explanation:

The length of the hypotenuse of a right triangle can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

So, in this case:

c^2 = a^2 + b^2

c^2 = 5^2 + 12^2

c^2 = 25 + 144

c^2 = 169

c = √169

c = 13

So the length of the hypotenuse is 13 cm.

Next, we can use the Pythagorean theorem to find the length of the segments into which the bisector of the right angle divides the hypotenuse. Let's call the length of the segments x. Then, the segments form two right triangles with legs of length x and (13-x)/2.

Using the Pythagorean theorem on each triangle, we have:

x^2 + ((13-x)/2)^2 = 13^2

x^2 + (13-x)^2/4 = 169

x^2 + (13^2 - 2x(13) + x^2)/4 = 169

x^2 + (13^2 - 2x(13))/4 = 169

x^2 + (169 - 26x)/4 = 169

x^2 + 169 - 26x = 676

x^2 - 26x + 507 = 0

Now, we can use the quadratic formula to find x:

x = (-b ± √(b^2 - 4ac)) / 2a

a = 1, b = -26, c = 507

x = (26 ± √(26^2 - 4 * 1 * 507)) / 2 * 1

x = (26 ± √(676)) / 2

x = (26 ± 26) / 2

x = 26 / 2

x = 13

So, the lengths of the segments into which the bisector of the right angle divides the hypotenuse are both 13 cm, to the nearest tenth.

Let p be the number of pounds of candy Joe will buy, since he will spend at most $72 on candy, and each pound has a cors of $6 we get:

Dividing by 6 the above inequality we get:

Answer:

Answer:

1.9 years

Step-by-step explanation:

There are 365 days in a year

694.44 / 365 = 1.9

Hope this helps!

Answer:  1.9013

Step-by-step explanation:

Answer:

not positive or negative

Step-by-step explanation:

It is 0 but i would say it is positive nor negative :)

0, It not really postive or negative

37 + -37 = 0 =

Neither negative nor positive

:/

The number in the solution set is 20

From the question, we have the following parameters that can be used in our computation:

x + 30 = 50

To find the solution to the equation x + 30 = 50, we can start by isolating x on one side of the equation:

x + 30 = 50

Subtracting 30 from both sides, we get:

x = 50 - 30

Simplifying, we get:

x = 20

Hence, the only number that belongs to the solution set of the equation x + 30 = 50 is 20.

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Answer:

Attached to this answer are some of the ways you could rewrite \(4*10^{-3}\)

Answer:

(A,1) (A,2) (A,3) (A,4) (B,1) (B,2) (B,3) (B,4)

Hope that helped?

Since the angles given by the equation are alternate interior angles the are the same, that is

9x + 41 = 13x - 15

Using this equation, we can find x value

Rearraging the equation so the terms with the unkown variable x are on the right side and the other ones on the left side:

9x + 41 = 13x - 15

↓ substracting 9x both sides

41 = -9x + 13x - 15

41 = 4x - 15

↓ adding 15 both sides

41 + 15= 4x

56 = 4x

Solving the equation for x

56 = 4x

↓ dividing by 4 both sides

56/4 = x

14 = x

Answer A: x = 14

Now we want to find angle 4. Since it makes a straight line with the angle given by the expression 13x - 15, then their addition should be equal to 180°:

∡4 + 13x - 15 = 180

We want to find ∡4, and we do know the value for x, so, using the expression we can find it.

Replacing x by 14:

∡4 + 13x - 15 = 180

↓replacing x = 14

∡4 + 13 · 14 - 15 = 180

∡4 + 182 - 15 = 180

∡4 + 167 = 180

We follow the same previous steps to find ∡4

Rearraging the equation so the terms with the unkown variable ∡4 are on the left side and the other ones on the right side:

∡4 + 167 = 180

↓ substracting 167 both sides

∡4 = - 167 + 180

∡4 = 13°

Step 2:We already found it using step 1 so step 2 is not neccesary to be followed

Answer B: ∡4 = 13°

Answer:

The answer should be $30.

Answer:

30 * t

Step-by-step explanation:

The garden club earned $15 per hour by weeding neighborhood gardens for t hours.

A generous donor has agreed to double their earnings.

Double their earnings means we multiply by 2

So earning 15 per hour becomes 2*15 = 30 per hour

Given the number of hours is t

Earnings = $30 times number of hours

Earnings = 30 * t

Answer:  L isn't the midpoint of segment MN.

Step-by-step explanation:

NL+LM=NM

6x-5+2x+3=4x+9

8x-2=4x+9

8x-2+2=4x+9+2

8x=4x+11

8x-4x=4x+11-4x

4x=11

Divide both parts of the equation by 2:

2x=5.5

NL=6x-5

NL=(2x)(3)-5

NL=(5,5)(3)-5

NL=16.5-5

NL=11.5

LM=2x+3

LM=5.5+3

LM=8.5

NL≠LM

Hence, L isn't the midpoint of segment MN.

In summary, based on the given lengths and mathematical reasoning, we have determined that point L is the midpoint of segment MN because the lengths of NL and LM are equal when x = 2.

We must compare the lengths of the two segments NL and LM and see if they are identical in order to establish whether point L is the midpoint of segment MN.

NL = 6x - 5

LM = 2x + 3

The lengths of NL and LM ought to be equal if L is the middle of segment MN. To put it another way, NL and LM ought to be equal.

Constructing the equation

6x - 5 = 2x + 3

Now, solve for x:

6x - 2x = 3 + 5

4x = 8

x = 2

As soon as we know the value of x, we can put it back into the NL and LM formulas to get their lengths at x = 2:

NL = 6x - 5 = 6 * 2 - 5 = 12 - 5 = 7

LM = 2x + 3 = 2 * 2 + 3 = 4 + 3 = 7

The lengths of NL and LM are both 7 units.

Point L is in fact the middle of segment MN because both segments NL and LM have similar lengths.

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At this rate of growth, it would take approximately 17.7 years for the population to double.

Predicted population in 2030: Assuming exponential growth, we can use the formula for exponential growth:

P(t) = \(P_0\) * \(e^r^t\)

where P(t) is the population at time t, \(P_0\) is the initial population, r is the growth rate, and e is the base of the natural logarithm.

Given that the population was 850,000 in 2008 and 980,000 in 2012, we can calculate the growth rate as follows:

r = ln(P2/P1) / (t2 - t1) = ln(980,000/850,000) / (2012-2008) ≈ 0.069

Using this growth rate, we can predict the population in 2030 (22 years later):

P(2030) = 850,000 * \(e^0^.^0^6^9 ^* ^2^2\)≈ 1,738,487

Therefore, the predicted population in 2030 is approximately 1,738,487

Year when the population reaches 1.5 million: To find the year when the population reaches 1.5 million, we can solve the exponential growth equation for time (t):

1,500,000 = 40,000 * \(e^r ^* ^t\)

Dividing both sides by 40,000 and taking the natural logarithm:

ln(1,500,000/40,000) = r * t

Simplifying:

ln(37.5) = r * t

To solve for t, we need to know the value of r. However, the value of r is not provided in the question, so we cannot determine the exact year when the population will reach 1.5 million without that information.

Time for the population to double: To find the time it takes for the population to double, we can use the exponential growth equation and solve for time (t):

2P0 = P0 * e^(r * t)

Dividing both sides by P0 and taking the natural logarithm:

ln(2) = r * t

Simplifying:

t = ln(2) / r

Using the given growth rate, we can substitute the value of r into the equation:

t = ln(2) / 0.039

Calculating:

t ≈ 17.7 years

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A set of reflections that would carry hexagon ABCDEF onto itself would be "x-axis, y=x, x-axis" or "y=x, x-axis, y-axis".

What is a combination of reflections?

Combination of Two Reflections. A point or object once reflected can further be reflected to form a new image. The axes of these reflections may be parallel to each other or they intersect each other at a point.

Given the coordinates of hexagon ABCDEF, it can be determined that a set of reflections that would carry the hexagon onto itself would be a combination of reflections over the x-axis and y-axis.

One possibility would be to reflect over the x-axis, then reflect over the y=x line, and finally reflect over the x-axis again.

This would take the hexagon from its original position to itself.

Another possibility would be to reflect over the y = x line, then reflect over the x-axis, and finally reflect over the y-axis.

This would also take the hexagon from its original position to itself.

Hence, a set of reflections that would carry hexagon ABCDEF onto itself would be "x-axis, y=x, x-axis" or "y=x, x-axis, y-axis".

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The equation of the surface of revolution generated by revolving x = (1/z)^z about the z-axis is x = e^(-y).

To find the equation of the surface of revolution, we start with the parametric equation x = (1/z)^z, y = t, z = t. We eliminate the parameter t by substituting z for t in the equation x = (1/z)^z. Simplifying further, we obtain x = e^(-y).

This equation represents the surface of revolution generated by revolving the curve x = (1/z)^z about the z-axis. The exponentiation by e^(-y) signifies that the x-coordinate changes exponentially as the y-coordinate varies.

Therefore, as we revolve the curve around the z-axis, it forms a surface with an exponential decay in the x-direction. Hence, the equation x = e^(-y) describes the surface of revolution.

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By the Mean Value Theorem, there exist at least two values c in (1, 5) such that f'(c) = 37/2.

The Mean Value Theorem (MVT) is an important theorem in calculus.

The theorem states that given a continuous function f(x) over an interval [a, b], there exists a value c in (a, b) such that the derivative of f(x) at c is equal to the average rate of change of f(x) over the interval [a, b]. That is, f'(c) = (f(b) - f(a))/(b - a).The function f(x) satisfies the hypothesis of the Mean Value Theorem, which states that the function must be continuous over the interval [a, b] and differentiable over the open interval (a, b).

This means that f(x) is continuous over the interval [1, 5] and differentiable over the open interval (1, 5).Thus, the Mean Value Theorem applies to the function f(x) on the interval [1, 5]. We are to find or approximate the point(s) that are guaranteed to exist by the Mean Value Theorem.

We can do this by finding the derivative of f(x) and setting it equal to the average rate of change of f(x) over the interval [1, 5].f'(x) = 3x^2 - 4xf'(c) = (f(5) - f(1))/(5 - 1) = (75 - 1)/(5 - 1) = 74/4 = 37/2.

Setting these two equations equal to each other, we get:3c^2 - 4c = 37/2

Multiplying both sides by 2 gives:6c^2 - 8c = 37

Simplifying:6c^2 - 8c - 37 = 0

Using the quadratic formula, we get:c = (8 ± sqrt(8^2 - 4(6)(-37)))/(2(6)) = (8 ± sqrt(880))/12 ≈ 2.207 and 1.424.

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Answer:

5:2

6

Step-by-step explanation:

I simplest form it is 5:2

You need 6 more triangles

Answer: 7

Step-by-step explanation:

A function composed with its inverse results in an output equal to the original input.

No, a trapezoid.

14) Let's plot those points for a visual conclusion

Note that B = B'

So the answer is:

No, as we can see the image defines a Trapezoid as another quadrilateral. without four right angles, and without four congruent sides.

We can also be sure by the fact that if we subtract the corresponding x values of each point of ABCD we'll have 4 units.

The actual distance between the two cities is 288 miles.

A scale drawing is a smaller version of a larger image / city. The scale drawing is reduced by a constant ratio.  This means that the scale drawing of the two cities would be smaller than the actual cities.

The scale is used to keep the proportion of the dimensions between the scale drawing and the original diagram similar. This means that the scale drawing of the two cities would be smaller than the actual cities.

The actual distance between the two cities = (3 x 24) ÷ 1/4

= 3 x 24 x 4 = 288 miles

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Answer:

81.6

Step-by-step explanation:

divide 136 by 5 when you get the answer to that you multiply by 3 and that's your answer

Answer:

81.6

Step-by-step explanation:

Divide than multiply

Answer:

Condition:

If a series converges, then the terms of the series approach 0.

Converse:

If the terms of a series approach 0, then the series converges.

The forward stepwise regression would have advantages as a screening procedure over the all-possible-regressions procedure in this case.

The best subset of predictor variables for predicting patient satisfaction according to each of the following criteria are:

R^2a,p: The subset consisting of X1 and X2.

AICp: The subset consisting of X1 and X2.

Cp: The subset consisting of X1, X2, and X3.

PRESSp: The subset consisting of X1 and X2.

The four criteria do not identify the same best subset.

Forward stepwise regression may have advantages over the all-possible-regressions procedure as a screening procedure since it is computationally more efficient and may reduce the risk of overfitting. However, it is still prone to overfitting and may miss important predictor variables.

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To determine which payment plan the real estate investor would prefer, we need to compare the present value of each payment option. Assuming a discount rate of 0%, meaning no time value of money is considered, we can directly compare the payment amounts.

1. Payment of $2,000 at the first of each month: This results in a total payment of $24,000 over the 12-month lease.

2. Upfront payment of $24,000: This option requires paying the full amount at the beginning of the lease.

3. Payment of $2,000 at the end of each month: Similar to option 1, this results in a total payment of $24,000 over the 12-month lease.

4. Upfront payment of $12,000 and $12,000 half-way through the lease: This option requires paying $12,000 at the beginning of the lease and another $12,000 halfway through the lease.

Since all the payment options have a total cost of $24,000, the real estate investor would likely prefer the payment plan that offers more flexibility or matches their cash flow preferences. Options 1 and 3 provide the investor with the option to pay monthly, while options 2 and 4 require a larger upfront payment. The choice would depend on the investor's financial situation and preferences.

Answer:

Step-by-step explanation:

There are 3 mangoes left behind after making 39 trays of 9 mangoes each

To find out how many trays can be made from 354 mangoes, we divide the total number of mangoes by the number of mangoes per tray.

Number of mangoes per tray = 9

Number of trays = 354 mangoes / 9 mangoes per tray

Number of trays = 39 trays

So, 39 trays can be made from 354 mangoes.

To determine how many mangoes are left behind, we subtract the number of mangoes used for the trays from the total number of mangoes.

Number of mangoes left behind = Total number of mangoes - Number of mangoes used for trays

Number of mangoes left behind = 354 mangoes - (39 trays * 9 mangoes per tray)

Number of mangoes left behind = 354 mangoes - 351 mangoes

Number of mangoes left behind = 3 mangoes

Therefore, there are 3 mangoes left behind after making 39 trays of 9 mangoes each

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A) The measure of central tendency that best describes the data for time spent on the internet (min/day) is the median.

The median is the middle value in a set of data when the data is arranged in numerical order. In this case, the data arranged in numerical order is 38, 43, 48, 52, 65, 75, 120. The median value is 52, which is the middle value in the data set.

B) The measure of central tendency that best describes the data for the weight of books (oz) is the mode. The mode is the value that occurs most frequently in a data set. In this case, the data is 12, 10, 9, 15, 16, 10. The mode is 10, as it occurs twice in the data set and is the most frequent value.

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a) The average rate of change over the interval [−2,2] is 4.

b) The instantaneous rates of change at the endpoints of the interval are the same (12), but they are not equal to the average rate of change over the interval (4).

A) To find the average rate of change of g(x) over the interval [-2,2], we need to calculate the slope of the line passing through the points (-2,g(-2)) and (2,g(2)).

g(-2) = (-2)³ - 6 = -8 - 6 = -14

g(2) = (2)³ - 6 = 8 - 6 = 2

Therefore, the slope of the line passing through these two points is:

(g(2) - g(-2))/(2 - (-2)) = (2 - (-14))/(2 - (-2)) = 16/4 = 4

B) To compare this rate with the instantaneous rates of change at the endpoints of the interval, we need to find the derivative of g(x):

g'(x) = 3x²

At x=-2, the instantaneous rate of change of g(x) is:

g'(-2) = 3(-2)² = 12

At x=2, the instantaneous rate of change of g(x) is:

g'(2) = 3(2)² = 12

We can see that the instantaneous rates of change at the endpoints of the interval are the same (12), but they are not equal to the average rate of change over the interval (4). This is because the function g(x) is not a straight line and its rate of change varies across the interval.

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Answer:

0 makes the statement true.

explanation:

5+(3×n)=5

5 + 3n = 5

3n = 5 - 5

3n = 0

n = 0

check:

5+(3×0) = 5

5 + 0 = 5

5 = 5

Both sides equal, therefore statement true.

¬ (p ↔ q) and p ↔¬q are proved to be logically equivalent.

The given statement are-

¬ (p ↔ q) and p ↔¬q

To prove these are logically equivalent, use contrapositive law

¬(p↔q) = ¬[(p∧q) ∨ (¬p∧¬q)]

¬(p↔q) = (p∧¬q) ∨ (¬p∧q)

And,

p↔¬q = (p∧¬q) ∨(¬p∧¬(¬q))

p↔¬q = (p∧¬q) ∨(¬p∧ q)

Thus,  ¬ (p ↔ q) and p ↔¬q are proved to be logically equivalent.

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