Abe purchased a candle at the candle store. The candle is nine inches long and the packaging states the candle burns down at the rate of 1/2 an inch per hour. Write a function to determine the length of the candle, y, after burning for x number of hours.

Answer:

6.324555320336759

Step-by-step explanation:

To find a missing leg in a right triangle use Pythagorean Theorem.

a^2 + b^2 = c^2                        Substitution

6^2 + 2^2 = c^2                         Simplify

36 + 4 = c^2                               Simplify

40 = c^2                                     Simplify
6.324555320336759 = c

Answer:

P((1 + r)^4) = 1,300

P((1 + r)^7) = 1,525

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

(1 + r)^3 = 61/52, so r = .0547 = 5.47%

P(1.0547^4) = 1,300, so P = $1,050.78

The measure of angle C is given as follows:

m < C = 44º.

To obtain the measures of the angles in this problem, we must consider that the sum of the measures of the internal angles of a triangle is of 180º.

Considering that the sum of the measures of the internal angles of a triangle is of 180º, and angles C, D and E, the value of x is obtained as follows:

4x - 16 + 6x - 1 + 4x - 13 = 180

14x - 30 = 180

14x = 210

x = 210/14

x = 15.

Hence the measure of angle C is obtained as follows:

m < C = 4 x 15 - 16 = 44º.

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The probability that a random point on the AK line will be on the BE line is 0.5 or 50%, since the length of the BE line is 10 units and the length of the AK line is 20 units.

To find the probability that a random point on the AK line will be on the BE line, we need to determine the length of the BE line and the length of the AK line.

The BE line extends from point -5 to point 5, a distance of 5 - (-5) = 10 units.

The AK line extends from point -10 to point 10, a distance of 10 - (-10) = 20 units.

Therefore, the probability that a random point on the AK line will be on the BE line is

Length of BE line / Length of AK line = 10 / 20 = 0.5

So, the probability that a random point on the AK line will be on the BE line is 0.5 or 50%.

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a: $145,912,000,000

b: 4.6 bn shares

c: $31.72/per share (divide in half)

Answer:

False. The product of two negative integers is a positive integer.

Answer:

16

Step-by-step explanation:

2×2×2×2=16

So, the answer is 16.

The new drug appears to reduce epileptic seizures since the rerandomized mean differences are close to the mean difference found between the two groups studied.

The rerandomized mean differences are:

1.2, 2.4, 1.8, 1.3, 2.1, 0.9, 1.5, 0.7, 2.1, and 2.3.

Several of these values are close to the observed mean difference of 1.8, which suggests that the observed difference could be due to chance alone.

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The total investment done by Lydia when her total annual interest is $420 at 11% dividend and 14% interest is equal to $3360.

Total annual interest = $420

Half of the investment in stock paying = 11% dividend

Half of the investment in stock paying = 14% interest

Let x be the amount Lydia has invested in each stock.

Since she has half of her investments in each stock,

The following system of equations to represent the situation,

Total annual interest is $420.

This implies ,

0.11x + 0.14x = 420

And  total investment is,

x + x = 2x

Simplifying the first equation, we get,

⇒ 0.25x = 420

Dividing both sides by 0.25, we get,

⇒ x = 1680

So, Lydia has invested $1680 in each stock, for a total investment of,

⇒ 2x = 2(1680)

        = 3360

Therefore, Lydia has a total investment of $3360.

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The quantity of candy that Eric ate would be = 14/15

The quantity of Candy Kim had = 2⅓ pounds.

The quantity of Kims candy that Eric ate = 2/5

That is 2/5 of 2⅓.

The actual quantity of candy that Eric ate = 2/5× 7/3 = 14/15

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Answer: 3.1

Step-by-step explanation: they are giving you the diameter so you halve it then you multiply it my 3.14 (pi) then you round it to the nearest tenth which is the 1 so you look to the left and it's not bigger than 5 so you round down so it stays as a 1

Answer:

Given equations are,

5x+2y=−2        (1)

3x−5y=17.4      (2)

Multiply equation (1) by 5 and equation (2) by 2, we get,

5(5x+2y)=5×−2

∴25x+10y=−10          (3)

2(3x−5y)=2×17.4

∴6x−10y=34.8          (4)

Adding equations (3) and (4), we get,

31x=24.8

∴x=

31

24.8

​

Put this value in equation (1), we get,

5(

31

24.8

​

)+2y=−2

∴

31

124

​

+2y=−2

∴2y=−2−

31

124

​

∴2y=

31

−186

​

∴y=

31

−93

​

Step-by-step explanation:

The lateral surface area of the cylinder is approximately 175.84 square meters.

We have,

The lateral surface area of a cylinder.

= 2πrh

where r is the radius of the base, h is the height of the cylinder, and π is approximately 3.14.

Now,

r = 2 m, h = 14 m

Substituting these values in the formula, we get:

Lateral surface area = 2πrh

= 2 x 3.14 x 2 x 14

= 175.84 m² (rounded to the nearest tenth)

Therefore,

The lateral surface area of the cylinder is approximately 175.84 square meters.

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Answer:

Step-by-step explanation:

Tom traveled for 4 hours by train and 4 hours by plane, for a total trip time of 8 hours.

We have,

Let's call the number of hours Tom traveled by train t.

Since he traveled the same number of hours by plane, he also traveled for t hours at 275 mph.

The total distance he traveled is given by the sum of the distances traveled by train and by plane:

Distance by train = 50t

Distance by plane = 275t

Total distance = 1300

So we can set up the equation:

50t + 275t = 1300

Simplifying and solving for t, we get:

325t = 1300

t = 4

Therefore,

Tom traveled for 4 hours by train and 4 hours by plane, for a total trip time of 8 hours.

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The length of the secant line JK is 32.

The secant-tangent power theorem states that if a tangent and a secant are drawn from a common external point to a circle, then the product of the length of the secant segment and its external part is equal to the square of the length of the tangent segment.

It is expressed as:

( tangent segment )² = External part of the secant segment × Secant segment.

From the diagram:

Tangent line JI = 24

External part of the secant segment LJ = 18

Secant segment JK = x + 18

Plug these values into the above formula and solve for b.

( tangent segment )² = External part of the secant segment × Secant segment.

24² = 18 × ( x + 18 )

576 = 18x + 324

18x = 576 - 324

18x = 252

x = 252/18

x = 14

Hence, secant line JK will be:

x + 18 = 14 + 18 = 32

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3. The factored polynomial is p(x) = (x - 1)(x - 5)

4. The factored polynomial is p(x) = (x + 3)²

A polynomial is a mathematical expression in which the power of the unknown is greater than or equal to 2.

3. To factorize the polynomial using the graph, we see that the polynomial cuts the x - axis at x = 1 and x = 5.

This implies that its factors are (x - 1) and (x - 5)

So, the factored polynomial is p(x) = (x - 1)(x - 5)

4. To factorize the polynomial using the graph, we see that the polynomial touches the x - axis at only one point x = -3. So,it has repeated roots

This implies that its factors are (x - (-3)) = (x + 3) twice

So, the factored polynomial is p(x) = (x + 3)²

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-63.63 m/s is the rate of change of the distance between the plane and the car when both are maximum speed and the plane is ahead by 70m?

Let's use the Pythagorean theorem to relate the distance between the car and the plane to their individual distances traveled. Let d be the distance traveled by the car, then the distance traveled by the plane is d + 70 (since the plane is ahead by 70m). Then, the distance between them is given by:

distance = [tex]\sqrt{d^{2}+500^{2} }[/tex] (using Pythagorean theorem)

Now, let's differentiate both sides with respect to time (t) to find the rate of change of the distance between the car and the plane:

d(distance)/dt = (1/2)[tex](d^{2} +500^{2} )^{(-1/2)}[/tex] * (2d/dd)(dd/dt)

where the first term on the right side is the derivative of the square root expression and the second term is the derivative of d with respect to time.

Now we need to find d in terms of t, given the maximum speeds of the car and the plane. Let's assume that they both start at time t = 0 and are racing for a time of T. Then, we can write:

d = 200T (distance traveled by the car)

d + 70 = 300T (distance traveled by the plane)

Solving for T, we get:

T = 70/100 = 0.7 hours = 42 minutes

Substituting T back into the expressions for d, we get:

d = 200(0.7) = 140 km

d + 70 = 300(0.7) = 210 km

Now we can substitute these values into the expression for the rate of change of the distance between the car and the plane:

d(distance)/dt = (1/2)[tex](d^{2} +500^{2} )^{(-1/2)}[/tex]  * (2d/dd)(dd/dt)

d(distance)/dt = (1/2)[tex](140^{2} +500^{2} )^{(-1/2)}[/tex] * (2*140/60)(300 - 200)

d(distance)/dt = -63.63 m/s

Therefore, the rate of change of the distance between the car and the plane when both are at maximum speed and the plane is ahead by 70m is approximately -63.63 m/s. Note that the negative sign indicates that the distance between them is decreasing, since the plane is ahead of the car.

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According to the information, It's important to acknowledge both of their perspectives and try to find a way to resolve the situation and move forward positively.

The situation is: two friends are having an argument because one of them forgot to invite the other to a party.

I can imagine that it must be really difficult for both of your friends right now. One of them might be feeling hurt and left out because they didn't get an invitation to the party, while the other might be feeling guilty and regretful for forgetting to invite them. It's important to acknowledge both of their perspectives and try to find a way to resolve the situation and move forward positively.

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The final amount in the retirement account in which the rate or return and the regular contributions change over time is $33,844.51.

To determine the final amount in the retirement account, we first compute the future value of the periodic deposits of $213 for 4 years, using an online finance calculator.

The future value of $213 deposited for 48 months is used as the present value of the investment for the next 4 years or 48 months.

Then, with the present value and the periodic deposits, the final amount (future value) of the retirement account is determined as follows:

N (# of periods) = 48 months (4 years x 12)

I/Y (Interest per year) = 4%

PV (Present Value) = $0

PMT (Periodic Payment) = $213

Results:

FV = $11,067.40

Sum of all periodic payments = $10,224.00

Total Interest $843.40

N (# of periods) = 48 months (4 years x 12)

I/Y (Interest per year) = 7%

PV (Present Value) = $11,067.40

PMT (Periodic Payment) = $348

Results:

Final Value (FV) = $33,844.51

Sum of all periodic payments = $16,704.00

Total Interest = $6,073.11

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Answer:

Concave up on the intervals (-π/2, π/2), and concave down on the intervals (-π,-π/2) and (π/2,π).

Step-by-step explanation:

To find the intervals where the function y = -cot(x) is concave up and concave down, we need to find the second derivative of the function and then determine its sign for different intervals.

First, we find the first derivative of y = -cot(x):

dy/dx = csc^2(x)

Then, we find the second derivative by differentiating the first derivative:

d^2y/dx^2 = -2csc^2(x) * cot(x)

We know that the function is concave up when the second derivative is positive, and concave down when the second derivative is negative.

Now, we need to determine the intervals where the second derivative is positive and negative.

d^2y/dx^2 > 0 when:

-2csc^2(x) * cot(x) > 0

csc^2(x) < 0 and cot(x) < 0 or csc^2(x) > 0 and cot(x) > 0

Since csc^2(x) is always positive, we can ignore the first inequality. Therefore, the second derivative is positive when cot(x) > 0.

d^2y/dx^2 < 0 when:

-2csc^2(x) * cot(x) < 0

csc^2(x) > 0 and cot(x) < 0 or csc^2(x) < 0 and cot(x) > 0

Since csc^2(x) is always positive, we can ignore the first inequality. Therefore, the second derivative is negative when cot(x) < 0.

Recall that cot(x) = cos(x)/sin(x), which changes signs at x = kπ, where k is an integer.

So, we can now use this information to determine the intervals of concavity:

   For x in (-π/2,0) and (0,π/2), cot(x) is positive and therefore, the function is concave up.

   For x in (-π,-π/2) and (π/2,π), cot(x) is negative and therefore, the function is concave down.

Therefore, the function y = -cot(x) is concave up on the intervals (-π/2, π/2), and concave down on the intervals (-π,-π/2) and (π/2,π).

The surface area of the larger pyramid in discuss would be 25 times the surface area of the smaller pyramid.

It follows from the task content that the surface area of the larger pyramid and the smaller pyramid are to be compared.

By observation; the differing dimensions are such that the ratio of the larger pyramid to the smaller pyramid is; 10 / 2 = 5.

On this note, the ratio of the area of the pyramids are such that the larger pyramid is 5² = 25 times larger than that of the smaller pyramid.

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Answer:

Fred doesn't run

Step-by-step explanation:

Fred doesn't run, Fred likes to walk, you obviously don't know Fred enough to answer this question, so tell your teacher how you can get in touch with Fred for a better relationship

let's firstly convert the mixed fractions to improper fractions, then sum them up.

[tex]\stackrel{mixed}{1\frac{1}{4}}\implies \cfrac{1\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{5}{4}}~\hfill \stackrel{mixed}{1\frac{3}{8}} \implies \cfrac{1\cdot 8+3}{8} \implies \stackrel{improper}{\cfrac{11}{8}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{5}{4}+\cfrac{11}{8}\implies \cfrac{(2)5~~ + ~~(1)11}{\underset{\textit{using this LCD}}{8}}\implies \cfrac{10+11}{8}\implies \cfrac{21}{8}\implies 2\frac{5}{8}~miles[/tex]

Answer:

Step-by-step explanation:

January, June, and July

are 3 months out of 12, which equals 1/4 (12 : 3 = 4),

1/4 equals 25% (100 : 4 = 25%)

Answer: r=2sinθ.

Step-by-step explanation:To convert to polar coordinates, we use the relationships

xy=rcosθ=rsinθ.

Substituting these into the given equation, we find

x2+y2(rcosθ)2+(rsinθ)2r2cos2θ+r2sin2θ=2y=2(rsinθ)=2rsinθ

Factoring and applying the Pythagorean identity, we obtain

r2(cos2θ+sin2θ)r2(1)r2=2rsinθ=2rsinθ=2rsinθ

Dividing both sides by r yields

r2rr=2rsinθr=2sinθ

Thus, a polar equation representing the given function is r=2sinθ.