A rod of length L is placed along the X-axis between X=0 and x=L. The linear density (mass/length) rho of the rod varies with the distance x from the origin as rho=a+bx. (a) Find the SI units of a and b. (b) Find the mass of the rod in terms of a,b and L.

(a) (i) If the yearly interest rate is 5%, the amount in the account in the year 2012 would be approximately $1,012,469.71.

(a) (ii) If the yearly interest rate is 7%, the amount in the account in the year 2012 would be approximately $23,127,812.13.

To calculate the amount in the account in the year 2012, we can use the continuous compounding formula: A = \(pe^{rt}\), where A is the final amount, P is the initial principal (the sale price of $24), e is Euler's number approximately equal to 2.71828, r is the interest rate, and t is the time in years.

(a) (i) For a 5% yearly interest rate: r = 0.05 and t = 2012 - 1626 = 386 years. Plugging these values into the formula, we have A = 24\(e^{ 0.05 * 386}\)

(a) (ii) For a 7% yearly interest rate: r = 0.07 and t = 386. Plugging these values into the formula, we have A = \(24e^{0.07 * 386 }\)

Calculating these expressions will give us the amount in the account in the year 2012 for the respective interest rates of 5% and 7%.

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Answer:

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

When the cannonball lands the height h is zero.

Set the value of the function as zero and solve for t:

The greater value of t represents the time we need.

The equation of the polynomial function is f(x) = 2(x + 4)(x + 4) (x + 4)(x -10)

The given parameters are:

The polynomial function is represented as:

f(x) = n * (x - root)^multiplicity

So, we have:

f(x) = 2 *(x + 4)^3 * (x -10)^1

This gives

f(x) = 2(x + 4)(x + 4) (x + 4)(x -10)

Hence, the equation of the polynomial function is f(x) = 2(x + 4)(x + 4) (x + 4)(x -10)

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Answer:

C f(x) = 2(x + 4)(x + 4) (x + 4)(x -10)

Step-by-step explanation:

TRUS. HAVE A GOOD TEST

Answer:

Step-by-step explanation:

2.00/5= 0.40 an orange

12*.40= $4.80

Answer:

where is the number line at?

Answer:

jhgvghj

Step-by-step explanation:

ihuvubij

the matches are

-2(2x+5) ≤ -7(x+4)         x<=-6

4x-3x-1                          x<=-1

5(x-3)9(x+1)                   x>=-6

3(x-4)+5 2x-9                x>=-2

Generally, Inequality is a mathematical statement that compares two values or expressions and indicates whether they are equal or not equal, or which one is greater or smaller. Inequalities are expressed using symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to).

For example, 5 < 8 is an inequality that indicates that 5 is less than 8, and x + 3 ≥ 7 is an inequality that indicates that the value of x plus 3 is greater than or equal to 7.

Inequalities are commonly used in algebra and other branches of mathematics to represent relationships between quantities.

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The correct matching of the inequalities can be shown from the calculations below

Inequalities are an important tool in mathematical modeling and optimization problems, where they are used to express constraints and objective functions.

Using the principle of inequalities we have;

1) -2(2x + 5) ≤ - 7(x + 4)

-4x -10 ≤ -7x -28

-4x +7x ≤ -28 + 10

3x ≤ -18

x ≤ -6

2) 4x - 6/2 ≥ 3x - 1

4x - 6 ≥ 6x - 2

4x - 6x ≥ -2 + 6

-2x ≥ 4

x  ≤ -2

3) 5(x - 3) ≤ 9(x + 1)

5x - 15  ≤ 9x + 9

5x - 9x  ≤ 9 + 15

-4x  ≤ 24

x ≥ -6

4) 3(x - 4) + 5 ≥ 2x - 9

3x - 12 + 5≥ 2x - 9

3x - 2x ≥ -9 + 12 -5

x ≥ -2

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Answer:

x = -8

Step-by-step explanation:

Step 1: Write out the equation

-4(2x + 3) = 2x + 6 - (8x + 2)

Step 2: Distribute

-8x - 12 = 2x + 6 - 8x - 2

Step 3: Combine like terms

-8x - 12 = -6x + 4

Step 4: Isolate x's

-2x -12 = 4

-2x = 16

Step 5: Divide both sides by -2

x = -8

Answer:

b) x = -8

Step-by-step explanation:

Now we have to,

→ find the required value of x.

Forming the equation,

→ -4(2x + 3) = (2x + 6) - (8x + 2)

Then the value of x will be,

→ -4(2x + 3) = (2x + 6) - (8x + 2)

→ -4(2x + 3) = 2x + 6 - 8x - 2

→ -8x - 12 = (2x - 8x) + (6 - 2)

→ -8x - 12 = -6x + 4

→ -8x + 6x = 4 + 12

→ -2x = 16

→ x = 16/-2

→ [ x = -8 ]

Hence, the value of x is -8.

The number of oranges that are expected to weigh more than 4 oz is:

1400 - (1400 × 0.0228)≈ 1368.

The mean weight of the oranges growing in an orchard is 8 oz and standard deviation is 2 oz, the distribution of the weight of oranges can be represented as normal distribution.

From the batch of 1400 oranges, the number of oranges is expected to weigh more than 4 oz can be found using the formula for the Z-score of a given data point.

\(z = (x - μ) / σ\)

Wherez is the Z-score of the given data point x is the data point

μ is the mean weight of the oranges

σ is the standard deviation

Now, let's plug in the given values.

\(z = (4 - 8) / 2= -2\)

The area under the standard normal distribution curve to the left of a Z-score of -2 can be found using the standard normal distribution table. It is 0.0228. This means that 0.0228 of the oranges in the batch are expected to weigh less than 4 oz.

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The enjoyment of movies and concerts is not independent, as the conditional probabilities are not equal to the marginal probabilities.

Hence, statement A is correct.

According to the given table:

The probability of enjoying movies (p(movies)) is 0.6, which means that 60% of the total group enjoy going to movies.

The probability of not enjoying movies (p(don't enjoy movies)) is 0.4, which means that 40% of the total group do not enjoy going to movies.

The probability of enjoying concerts (p(concerts)) is 0.55, indicating that 55% of the total group enjoy going to concerts.

The probability of not enjoying concerts (p(don't enjoy concerts)) is 0.45, suggesting that 45% of the total group do not enjoy going to concerts.

To analyze the conditional probabilities:

The probability of enjoying movies given that someone enjoys concerts (p(movies|concerts)) is 0.25, meaning that 25% of the people who enjoy concerts also enjoy movies.

The probability of enjoying concerts given that someone enjoys movies (p(concerts|movies)) is 0.35, which implies that 35% of the people who enjoy movies also enjoy concerts.

Based on these probabilities, we can conclude that the enjoyment of movies and concerts are not independent, as the conditional probabilities are not equal to the marginal probabilities.

Hence,

The statement A is correct.

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The complete question is:

a group of people were asked if they enjoy going to concerts or movies. the table shows the probabilities of the results.

                       enoyed         don't enjoyed      total

Enjoy movie     0.25                 0.35                  0.6

don't enjoy       0.3                   0.1                     0.1

total                   0.55                0.45                   1

Which statement is true?  

A: Enjoying the movie concert is not independence since p(movies| concerts) is not equal to p(movies) and  p(concerts|movies) not equal p(concerts),  

B: Enjoying the movie concert is independence since p(movies| concerts) is not equal to p(movies) and  p(concerts|movies) not equal p(concerts,

C:  Enjoying the movie concert is not independence since p(movies| concerts)= p(movies),

D:  Enjoying the movie concert is independence since p(movies| concerts)= p(movies)

its 12.0

Step-by-step explanation:

1.) Side LM is congruent to side QR

2.) Angle MNO is congruent to angle QRS.

Given that LMNO ≅ QRST, we can complete the statements as follows:

1.) Side LM is congruent to side QR.

Since the two triangles are congruent, their corresponding sides are also congruent. Therefore, side LM is congruent to side QR.

2.) Angle MNO is congruent to angle QRS.

When two triangles are congruent, their corresponding angles are also congruent. Thus, angle MNO is congruent to angle QRS.

Now, let's explore angle MNO in detail.

Angle MNO is an angle in triangle LMNO. Due to the congruence between LMNO and QRST, we can infer that angle QRS in triangle QRST is also congruent to angle MNO.

The congruence of angle MNO and angle QRS indicates that they have the same measure. Therefore, any property or characteristic applicable to angle MNO can also be applied to angle QRS.

For instance, if we know that angle MNO is a right angle, we can conclude that angle QRS is also a right angle. This is because congruent angles have equal measures, and if angle MNO has a measure of 90 degrees (which characterizes a right angle), angle QRS must also have a measure of 90 degrees.

In summary, the congruence between triangles LMNO and QRST implies that angle MNO and angle QRS are congruent, allowing us to apply the same properties and measurements to both angles.

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Answer:

A. This scatter plot has no association, no form, weak strength, and no apparent outliers.

Step-by-step explanation:

The scatter shows several data points plotted on the graph, of which show no particular trend.

Every data point on the plot are far apart from each other and do not follow any trend or have any shape, and as such show very weak strength.

We can hardly pick out which data point is an outlier.

There's also no form of association or whatsoever since no trend can be observed.

Therefore, we can conclude that:

"This scatter plot has no association, no form, weak strength, and no apparent outliers."

Answer:

maybe A

Step-by-step explanation:

Answer:

The correct answer is the second choice.

Answer:

2nd Is correct i literally had to study this in college I watched the history channel 24/7 to solve this. Pls brainliest!

Answer:

Step-by-step explanation:

\(\frac{1}{5}\) ∠ 7x

\(\frac{1/5}{7}\) ∠ x

1/35 ∠x

x ≥ \(\frac{1}{35}\)

Answer:

Step-by-step explanation:

Set the following equations based on the question:

Solve the system by elimination, multiply the first equation by 23 and subtract the second one:

Find the value of c:

Answer:

Chaperones = 8 and Student = 117

Step-by-step explanation:

Let,

Chaperones = x

Student = y

x + y = 125

=> x = 125 - y (1)

23x + 16y = 2056

=> 23(125 - y) + 16y = 2056

=> 2875 - 23y + 16y = 2056

=> 2875 - 7y = 2056

=> 2875 - 2056 = 7y

=> 819 = 7y

=> 819/7 = y

=> 117 = y

From 1

=> x = 125 - 117

=> x = 8

p-9/3 = 2

p-9 = 2×3

p-9 = 6

p = 6+9

... Hope this will help...

the rate of change of the radius at the instant the volume equals 36π cm³ is 7 / (36π) cm/sec.

The volume V of a sphere with radius r is given by the formula V = (4/3)πr³. We are given that the rate of change of the volume is 7 cm³/sec. Differentiating the volume formula with respect to time, we get dV/dt =(4/3)π(3r²)(dr/dt), where dr/dt represents the rate of change of the radius with respect to time.

We are looking for the rate of change of the radius, dr/dt, when the volume equals 36π cm³. Substituting the values into the equation, we have: 7 = (4/3)π(3r²)(dr/dt)

7 = 4πr²(dr/dt) To find dr/dt, we rearrange the equation: (dr/dt) = 7 / (4πr²) Now, we can substitute the volume V = 36π cm³ and solve for the radius r: 36π = (4/3)πr³

36 = (4/3)r³

27 = r³

r = 3  Substituting r = 3 into the equation for dr/dt, we get: (dr/dt) = 7 / (4π(3)²)

(dr/dt) = 7 / (4π(9))

(dr/dt) = 7 / (36π)

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A term that describes a numerical value measuring the likelihood of an uncertain event is - a probability.

A probability is a numerical value that measures the likelihood of an uncertain event occurring.

It ranges from 0 (impossible event) to 1 (certain event), with values in between representing the varying degrees of likelihood.

To calculate the probability of an event, you can divide the number of favorable outcomes by the total number of possible outcomes in a given scenario.

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Step 1: Suppose, for the sake of contradiction, that there are integers A and B such that A2 = 3B2 + 2015. Let N = A2. Then, N ≡ 1 (mod 3).

Step 2: By the Legendre symbol, since (2015/5) = (5/2015) = -1 and (2015/67) = (67/2015) = -1, we know that there is no integer k such that k2 ≡ 2015 (mod 335).

Step 3: Let's consider A2 = 3B2 + 2015 (mod 335). This can be written as A2 ≡ 195 (mod 335), which can be further simplified to N ≡ 1 (mod 5) and N ≡ 3 (mod 67).

Step 4: However, since (2015/5) = -1, it follows that N ≡ 4 (mod 5) is a contradiction.

Therefore, there are no integers A, B such that A2 = 3B2 + 2015.

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Answer:

Let P(h,k) be the point which is equidistant from the point (2,4) and the y-axis. The distance of point P(h,k) from the y-axis is h. ∴h=√(h−2)2+(k−4)2⇒h2−4h−4+k2−8k+16=h2⇒k2−4h−8k+20=0.

Hence,the locus of (h,k)is y2−4x−8y+20=0.

Step-by-step explanation:

The solutions to the equation 4x^2 - 20x + 25 = 10 are x = 5/2 and x = 3/2.

The equation 4x^2 - 20x + 25 = 10 can be rewritten as 4x^2 - 20x + 15 = 0. To find the solutions to this equation, we can factor it or use the quadratic formula.

The equation factors as (2x - 5)(2x - 3) = 0. Setting each factor equal to zero, we get 2x - 5 = 0 and 2x - 3 = 0. Solving these equations, we find x = 5/2 and x = 3/2.

Using the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions are given by x = (-b ± sqrt(b^2 - 4ac)) / 2a, we can determine the solutions.

In this case, a = 4, b = -20, and c = 15. Substituting these values into the quadratic formula, we get x = (-(-20) ± sqrt((-20)^2 - 4 * 4 * 15)) / (2 * 4), which simplifies to x = (20 ± sqrt(400 - 240)) / 8.

Simplifying further, we have x = (20 ± sqrt(160)) / 8, which becomes x = (20 ± 4sqrt(10)) / 8. Finally, simplifying again, we obtain x = 5/2 ± sqrt(10)/2, which gives us the same solutions as before: x = 5/2 and x = 3/2.

Therefore, the solutions to the equation 4x^2 - 20x + 25 = 10 are x = 5/2 and x = 3/2.

To find the solutions to the equation, we can either factor it or use the quadratic formula. In this case, factoring and using the quadratic formula both yield the same solutions: x = 5/2 and x = 3/2. These values of x satisfy the equation 4x^2 - 20x + 25 = 10 when substituted back into the equation.

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Answer:

A group of five people are at a restaurant, the bill comes and is $50, the bill is split evenly amongst the five people, each person pays $10 which is the same as gaining -$10 which is the answer to the expression

Answer:

you should of not said exam you will prob get banned now

Step-by-step explanation:

Answer:

We can determine from their equations whether two lines are parallel by comparing their slopes. If the slopes are the same and the y-intercepts are different, the lines are parallel. If the slopes are different, the lines are not parallel. Unlike parallel lines, perpendicular lines do intersect.

Step-by-step explanation:

Answer:

x = 4

Step-by-step explanation:

8x = 180  - 148                           [ corresponding angles are equal ]

8x = 32

x = 4

Answer:

Step-by-step explanation:

4x-17+3x+8+x+13=180

8x+4 =180

8x=176

X=22

Answer:

x = 22

Step-by-step explanation:

<A + <B + <C = 180

<A = 4x - 17

<B = 3x + 8

<C = x + 13

4x - 17 +  3x + 8 +  x + 13 = 180           Collect the like terms

8x + 4 = 180                                        Subtract 4 from both sides

8x = 180 - 4

8x = 176                                               Divide by 8

x = 176/8

x = 22

The exact solution of the given equation is 2x² - 2x + 5y² + 18y = C.

What is exact solution of differential equation?

Exact equations are certain differential equations that meet requirements, making it easier to find the solutions to them.

As per question given that,

Gerneral differential equation is,

(2x - 1) dx + (5y + 9) dy = 0

By comparing equation,

Mdx +Ndy = 0

Here,

M = 2x - 1

N = 5y + 9

Now finding the partial derivatives are,

dM / dy = d (2x -1) / dy

From derivative formula: [d (constant) / dy = 0]

Apply formula,

dM / dy = 0          ...... (1)

Similarly,

dN / dx = d (5y + 9) / dx

Differentiate partially with respect to x. keeping y is constant.

dN / dx = 0          ......(2)

Equate both equations (1) and (2),

dM / dy = dN / dx

The given differential equation is exact.

Then the general solution is,

∫ M dx + ∫ N dy = C

Substitute values respectively,

∫ (2x - 1) dx + ∫ (5y + 9) dy = C

∫ (2x) dx - ∫ dx + ∫ (5y) dy + ∫ 9 dy = C

2· x² / 2 - x + 5· y² / 2 + 9y = C

x² - x + 5· y² / 2 + 9y = C

Simplify terms,

2x² - 2x + 5y² + 18y = C.

Which is required solution.

Hence, the exact solution of the given equation is 2x² - 2x + 5y² + 18y = C.

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Answer:

2.

the distance from E to D,D toF and F to E are equal.

Answer:

yes the distance between E to D and D to F, F to E are equal hope it's helps you

have a good day ☺

Answer:

Troy is either 16 or 32.

Step-by-step explanation:

Sorry for not giving the exact answer the question is worded badly..

Answer: 32

Step-by-step explanation:

16 + 16. if you break it down, you can get 8 x 4. so if you count 8, 16, 24, (32) is your answer.

To prove that HIK = HJK when K is the midpoint of IJ, we can use the c. HL theorem. Using the HL theorem, we can prove that two right triangles are congruent if the hypotenuse and one leg of one triangle are equal to the corresponding parts of the other triangle.

In this case, we can consider triangles HIK and HJK.
First, we know that HI = HJ since they are both radii of the same circle.
Next, we know that IK = JK because K is the midpoint of IJ.
Lastly, we need to prove that angle HIK = angle HJK.
We know that HI = HJ and IK = JK. Additionally, both triangles share a common side, HK. Therefore, the two triangles satisfy the HL criterion for congruence, which means that HIK = HJK.
In conclusion, we used the HL theorem to prove that HIK = HJK when K is the midpoint of IJ.

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