Find the general solution of each equation. (a) y^(4) – 6y^m + 13y^n = 0(b) y^m + 2y^n + 4y' + 8y = 0 (c) y^(5) – y^(4) = 0

Given that AC is a diameter of the circle, we can conclude that triangle ABC is a right triangle, with AC being the hypotenuse. The area of the circle is not directly related to finding the lengths of BC or AB, so we will focus on the given information: AB = 16 units.

Using the Pythagorean theorem, we can find BC. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (AC) is equal to the sum of the squares of the other two sides (AB and BC):

AC² = AB² + BC²

Substituting the given values, we have:

(AC)² = (AB)² + (BC)²

(AC)² = 16² + (BC)²

(AC)² = 256 + (BC)²

Now, we need to find the length of AC. Since AC is a diameter of the circle, the length of AC is equal to twice the radius of the circle.

AC = 2 * radius

To find the radius, we can use the formula for the area of a circle:

Area = π * radius²

Given that the area of the circle is 2897 units², we can solve for the radius:

2897 = π * radius²

radius² = 2897 / π

radius = √(2897 / π)

Now we have the length of AC, which is equal to twice the radius. We can substitute this value into the equation:

(2 * radius)² = 256 + (BC)²

4 * radius² = 256 + (BC)²

Substituting the value of radius, we have:

4 * (√(2897 / π))² = 256 + (BC)²

4 * (2897 / π) = 256 + (BC)²

Simplifying the equation gives:

(4 * 2897) / π = 256 + (BC)²

BC² = (4 * 2897) / π - 256

Now we can solve for BC by taking the square root of both sides:

BC = √((4 * 2897) / π - 256)

To find the measure of angle BC (mBC), we know that triangle ABC is a right triangle, so angle B will be 90 degrees.

In summary:

BC = √((4 * 2897) / π - 256)

mBC = 90 degrees

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Answer:

truck is 100mph

Step-by-step explanation:

Answer:18.6 is the answer

Step-by-step explanation:

The duration of a nuclear reactor output power 145 MW would take to produce 10 kgPu−239 ;145 MW of nuclear reactor output power would take approximately 6.1×10 5 months to produce 10 kg of Pu−239.

Advantages of building a nuclear power plant: As a source of electricity, nuclear power is both efficient and effective. Nuclear power plants, in comparison to traditional energy sources, can generate a lot of energy with a single unit of fuel. Nuclear power plants are also capable of running for extended periods of time before requiring additional fuel. It also helps to reduce the country's carbon emissions. Disadvantages of building a nuclear power plant:

Despite the benefits, nuclear power is not without its drawbacks. Nuclear power, for example, necessitates the use of nuclear reactors, which are difficult to build and maintain. O

ne of the greatest concerns about nuclear power plants is the risk of a catastrophic nuclear meltdown, which can result in the release of radioactive materials that can have long-term consequences on the environment and human health. It is also one of the most expensive methods of producing energy.Calculation:We're given that: Energy liberated per fission of an atom of U-235 = 9×10 11
J. Given the mass of\(Pu−239 = 10 kg.\)

Number of atoms of Pu− \(239 in 10 kg= 10×1000 / 239×6×10 23\)

1.84×10 24 fissions required to produce 1.84×10 24atoms of

Pu−239

\(1.84×10 24/2= 0.92×10 24\)Energy liberated by 1 fission = 9×10 11 J. Therefore, energy liberated by 0.92×10 24

fissions= 0.92×10 24×9×10 11

8.28×10 35 J. Output power of nuclear reactor

\(145 MW= 145×10 6\)

\(145×10 6×3600= 5.22×10 11 J/s.\)

So, duration required to produce 10 kg of Pu−239

\(8.28×10 35 / 5.22×10 11= 1.59×10 24 s\)

\(1.59×10 24 / (2.6×10 6)= 611540.9 months\)

6.1×10 5 months (Approximately)Therefore, 145 MW of nuclear reactor output power would take approximately 6.1×10 5 months to produce 10 kg of Pu−239.

Given the numerous benefits and drawbacks of nuclear power, the decision to construct a nuclear power plant in Malaysia is dependent on the government's discretion. To ensure public safety, it is critical to keep the facility up to code, which necessitates additional time, effort, and expense. Additionally, Malaysia should assess its long-term energy needs and consider other energy alternatives. It is, however, advisable for the Malaysian government to build a nuclear power plant under proper safety measures, if the energy requirements increase. Safety is the top priority when it comes to nuclear power.

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Answer:

128 grains.

I think so..

Step-by-step explanation:

SEE the image for solution.

HOPE it helps

Have a great day

Answer:

Step-by-step explanation:

\(u_1=1=2^0\\u_2=2=2^1\\u_3=4=2^2\\u_4=8=2^3\\\\...\\u_{64}=2^{63}\\\\we\ must\ calculate\\\\u_1+u_2+u_3+u_4+...+u_{64}\\\\=1+2^1+2^2+2^3+2^4+....+2^{63}\\\\=\dfrac{2^{64}-1}{2-1} \\\\=2^{64}-1\\\\=18446744073709551615\\\\=1.8446744073709551615*10^{19}\)

According to the question, the homeroom class wants to get a present for a student. From \(32\)students, \(10\) choose cards, \(12\) choose t-shirts, \(6\) choose a video and the remaining choose a bracelet.

Now, calculate the probability that the exchange students should get a card or a bracelet.

Let us assume, ‘C’ represents the card and ‘B’ represents the bracelet.

Using standard probability formula:

P (C or B) = P(C)+P(B) = \(\frac{10}{32} + \frac{4}{32} = \frac{14}{32} = \frac{7}{16} = 43.8%\)

Therefore, the probability to get a card or a bracelet is \(43.8\) percent.

What is Probability?

The term probability means the study of the occurrence or the outcomes of the event. It is the measurement of the events that occurred during events. And many uncertain events cannot be measured.

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according to question the answer is (E) 35.

First, let's simplify the expression for x:

x = (21)(3^7) - (112)

x = 3^3(3^4)(7) - 2^4(7)

x = (7)(3^4)(3^3 - 2^4)

x = (7)(3^4)(65)

Now, we need to check which of the given integers does not divide x. We can use the divisibility rules for each one:

A. 7: x is divisible by 7 since it has a factor of 7.

B. 11: We can use the alternating sum of digits rule for divisibility by 11. Adding the digits of x, we get:

1 + 4 + 8 + 5 = 18

Then, 1 - 8 + 5 = -2, which is not divisible by 11. Therefore, 11 does not divide x.

C. 15: We can use the divisibility rule for 3 and 5 to check if 15 divides x. Adding the digits of x, we get:

1 + 4 + 8 + 5 = 18

Since 18 is divisible by 3, x is also divisible by 3. However, x does not end in 0 or 5, so it is not divisible by 5. Therefore, 15 does not divide x.

D. 17: We can use the divisibility rule for 17, which states that we need to subtract 5 times the units digit from the remaining digits, and the result should be divisible by 17. The units digit of x is 5, so we have:

3^4(6) - 2^4 = 96

Then, 9 - 5(6) = -21, which is divisible by 17. Therefore, 17 divides x.

E. 35: We can use the divisibility rule for 5 and the fact that x is not divisible by 7 (since it has a factor of 7). Since x ends in 5, it is divisible by 5 if and only if it is not divisible by 7. Therefore, 35 does not divide x.

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Answer:

Step-by-step explanation:

y = mx + b

Take any two points and set up 2 equations with 2 unknowns.

I'll start with the first two

y = 4x + b

410 = 4x + b                    (1)

440 = 6x + b                   (2)

Subtract (1) from (2)

440 = 6x + b

410 = 4x + b            Subtract

30  = 2x                  Divide by 2

30/2 = 2x/2

x = 15

440 = 6(x) + b

440 = 6*15 + b

440 = 90   + b

b = 350

Now here is what you found.

Her base salary is 350 dollars

Each television she sells brings her an addition 15.

Answer:

multiply opposite side and the answer is ready now because check your soulation

The engineer measuring the western rod with a sample size of 20 is expected to have a more precise (narrower) confidence interval compared to the engineer measuring the eastern rod with a sample size of 25.

The engineer who measures the length of the western rod 20 times and calculates the average is expected to have a more precise (narrower) confidence interval compared to the engineer who measures the length of the eastern rod 25 times.

In statistical terms, the precision of a confidence interval is influenced by the sample size. The larger the sample size, the more precise the estimate tends to be. In this case, the engineer measuring the western rod has a sample size of 20, while the engineer measuring the eastern rod has a sample size of 25. Since the sample size of the western rod is smaller, it is expected to have a narrower confidence interval and therefore a more precise estimate of the true length of the rod.

A larger sample size provides more information and reduces the variability in the estimates. It allows for a more accurate estimation of the population parameter. Therefore, the engineer with a larger sample size is likely to have a more precise interval.

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Aggregate Demand (AD) is a macroeconomic concept that represents the total demand for goods and services in an economy. The X factor in the AD equation represents exports, which are an important part of the economy.

AD is calculated by adding up the individual components of demand, which include consumer spending (C), investment spending (I), government spending (G), and net exports (X-M). The X-M component represents the difference between exports (X) and imports (M).

The X component in the equation represents exports, which are the goods and services produced domestically and sold to foreign countries. Exports are an important part of the economy as they generate income and create jobs. The M component in the equation represents imports, which are the goods and services purchased from foreign countries and consumed domestically. Imports can have a negative impact on the economy as they represent a drain on resources and can lead to a trade deficit. The X factor in the equation is used to represent exports because it is a variable that can change over time. Factors that can affect exports include exchange rates, tariffs, and global demand for certain products. If the exchange rate between two currencies changes, it can make exports more or less expensive for foreign buyers, which can affect the level of exports. Tariffs are taxes on imports, which can make domestic products more competitive in foreign markets.

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Answer:

the expression is equal to 31

Step-by-step explanation:

Answer:

31

Step-by-step explanation:

Substitute x and y into the equation to get..

(3×7)-(-5×2)

21- -10

31

Hope this helps :)

a. The tree diagram that summarizes the given probabilities is attached.

b.  The probability that the individual does not participate in sports, given that he graduate sis  0.2 =  20%.

We apply Bayes' theorem to calculate:

Probability (Does not participate in sports if graduates)  = (P(Does not participate in sports) * P(Graduates | Does not participate in sports)) / P(Graduates)

The given data include: probability of not participating in sports = 0.02 probability of graduating given no participation in sports = 0.82 probability of graduating  = 0.18

Probability (Does not participate in sports if graduates)  = (0.02 * 0.82) / 0.18 = 0.036 / 0.18=  0.2

| Sports | No Sports |

                          |-------|--------|

Student participates | 0.18  | 0.62  |

                          |-------|--------|

Student does not participate | 0.02  | 0.78  |

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Answer:

The question is not clearly stated, but I can correctly infer that you wanted to ask the question below:

Out of 150 members, 120 took part, what is the percentage of the total that took part:

Answer:

80%

Step-by-step explanation:

The question is asking us to find what percentage of 150 is 120

Let the percentage of 150 that is 120 be x

x % of 150 = 120

x/100 × 150 = 120

0.01x × 150 = 120

0.01x = 120 ÷ 150 = 0.8

x = 0.8 ÷ 0.01 = 80

∴ 120 = 80% of 150

So to find any last digit of 3^2011 divide 2011 by 4 which comes to have 3 as remainder. Hence the number in units place is same as digit in units place of number 3^3. Hence answer is 7.

Each individual result of a probability experiment is called an "outcome" (d).

An outcome refers to a specific result or occurrence that can happen when conducting a probability experiment. It represents the different possibilities or potential results of an experiment.

For example, when flipping a fair coin, the possible outcomes are "heads" or "tails." In this case, "heads" and "tails" are the two distinct outcomes of the experiment.

Similarly, when rolling a fair six-sided die, the possible outcomes are the numbers 1, 2, 3, 4, 5, or 6. Each number represents a different outcome that can occur when rolling the die.

In summary, an outcome is a specific result or occurrence that can happen during a probability experiment. It is essential to understand outcomes as they form the basis for calculating probabilities and analyzing the likelihood of different events occurring.

Thus, each individual result of a probability experiment is called an "outcome" (d).

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If Ridgewood Savings Bank charges a $27 per check overdraft protection fee. The amount she will owe the bank after July 12 is: $1,071.42.

Total obligation can be defined as the amount a person owe another person or the debt amount a borrower  is expected to payback to a lender.

Balance $1,400

July 9 check ($1,380.15)

Balance $19.85

July 10 check ($765.67)

($670 + $95.67)

Balance -$745.82 (Overdraft)

Now let find the amount she owe

Balance -$745.82

July 11 check $130

Balance -$875.82

July 12 check $87.60

Ending balance -$963.42

Overdraft fee $108

($27 ×4)

Total obligation -$1,071.42

Therefore her total obligation is $1,071.42.

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Answer:

56$

Step-by-step explanation:

35$ + 60% = 56$

Answer:

280/3

Step-by-step explanation:

multiply the number by 10x

subtract it by the original number on both sides

it should give u 9x to whatever answer u got multiply by 10 then divide by 90

Answer:

$1,754,31

Step-by-step explanation:

Furniture = $213 + $812.50 + $499.99 = $1,525.49

15% * $1,525.49 = $228.82

Total = $1,525.49 + $228.82 = $1,754,31

Candace should have gone to Wayfair

If there were 132 crayons in John's backpack, the number of blue crayons is equal to blue crayons.

In Mathematics, a proportion simply refers to an equation which is typically used to represent the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.

By applying direct proportion to the given information, we have the following mathematical expression:

3 crayons = 8 blue crayons

132 crayons = X blue crayons

By cross-multiplying, we have the following:

3x = 132 × 8

3x = 1,056

x = 1,056/3

x = 352 blue crayons.

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Answer:

???????????????????????

Step-by-step explanation:

sorry di ko po alam yung sagot pasensiya na po

Given :

Parallel lines are

x – 2y = 3 and 2x – 4y = 12

Step-by-step explanation:

Lets write the given lines in slope intercept form y=mx+b

\(x -2y = 3 \\-2y=-x+3\\Divide \; both \; sides \; by -2\\y=\frac{x}{2} -\frac{3}{2}\)

From the above equation , y intercept of first line is \(\frac{-3}{2}\)

Solve the second equation for y and find out y intercept

\(2x-4y=12\\-4y=-2x+12\\Divide \; by \; -4\\y=\frac{1}{2} x-3\)

y intercept of second line is -3

To find the distance between parallel lines, we subtract the y intercepts

\(\frac{-3}{2} -(-3)=\frac{-3}{2} +\frac{6}{2} =\frac{3}{2} =1.5\)

Answer:

The distance between the parallel lines = 1.5

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Answer:

\(9\)

Step-by-step explanation:

Answer:

6 2/3 cups

Step-by-step explanation:

10- 1 2/3- 1 2/3= 8 1/3- 1 2/3= 6 2/3

Answer:

\(6 \frac{2}{3}\) cups of crispy cereal.

Step-by-step explanation:

\(10- 1 \frac{2}{3} - 1 \frac{2}{3} =\)

\(\frac{30}{3} -\frac{5}{3} -\frac{5}{3} =\)

\(\frac{20}{3} =\)

\(6 \frac{2}{3}\) cups of crispy cereal.

Answer:

x = 4

Step-by-step explanation:

3(2x + 1) = 18 + 4x - 7

First distribute 3 by multiplying it by 2x and 1.

= 6x + 3 = 18 + 4x - 7

Then, add any like terms.

= 6x + 3 = 11 + 4x

 -4x                -4x

= 2x + 3 = 11

         -3    -3

= 2x = 8

 /2     /2

x = 4

Carson Kelly is expected to hit approximately 31 home runs in 2024.

To find how many home runs Carson Kelly is expected to hit in 2024, we can use the formula for compound interest, where the initial amount is the number of home runs he hit in 2019, and the interest rate is the expected growth rate of his home run hitting ability, which is 12 percent or 0.12 as a decimal.

Let H be the number of home runs hit in 2019, and H(n) be the number of home runs hit in year n, then we can write:

H(n) = H * (1 + r)^n

Where r is the growth rate, and n is the number of years into the future.

If we plug in the given values, we can find the number of home runs Carson Kelly is expected to hit in 2024, which is 5 years after 2019.

H = 18 (number of home runs in 2019)

r = 0.12 (growth rate)

n = 5 (number of years into the future)

H(5) = 18 * (1 + 0.12)^5

H(5) = 18 * 1.7623

H(5) = 31.9214

It's important to note that this is simply an estimate based on the given growth rate, and the actual number of home runs he hits in 2024 may vary based on many factors, including injuries, team support, and the skill of opposing pitchers, among others.

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Using a system of equations, Christine's investments in account one were $4,000 and in account two $16,000.

A system of equations refers to simultaneous equations.

Simultaneous equations are two or more equations solved concurrently.

Total investment in two accounts = $20,000

The simple interest rate for account one, x = 8%

The simple interest rate for account two, y = 10%

Total interest for a year = $1,920

Let account one = x and account two = y

x + y = 20,000 ... Equation 1

0.08x + 0.1y = 1,920 ... Equation 2

Multiply Equation 1 by 0.08

0.08x + 0.08y = 1,600 ... Equation 3

Subtract Equation 3 from Equation 2:

0.08x + 0.1y = 1,920

-

0.08x + 0.08y = 1,600

0.02y = 320

y = 16,000

= $16,000

In Equation 1, x + y = 20,000, Substitute y = 16,000:

x + 16,000 = 20,000

x = 4,000

= $4,000

Check:

From Equation 2:

0.08x + 0.1y = 1,920

0.08(4,000) + 0.1(16,000) = 1,920

320 + 1,600 = 1,920

Thus, using simultaneous equations, we can conclude that Christine invested $4,000 in the first account and $16,000 in the second account.

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Last year, Christine had $20,000 to invest. She invested some of it in an account that paid 8% simple interest per year, and she invested the rest in an account that paid 10% simple interest per year. After one year, she received a total of $1920 in interest. How much did she invest in each account?

First account:

Second account:

Answer:

38%

Step-by-step explanation:

Answer:

the answer is 38%

Step-by-step explanation:

multiply 19 by 2 because 50 is half of 100

The statement that accurately describes the form of the sampling distribution is:The inspecting dissemination is regularly circulated with a mean of 37 and standard deviation 1.41.

According to the central limit theorem, regardless of how the population distribution is shaped, the sampling distribution of the sample mean will be approximately normally distributed for a sufficiently large sample size.

For this situation, irregular examples of 32 are drawn from Meredith's patient populace, which fulfills the state of a sufficiently huge example size. The central limit theorem can be used to determine the sampling distribution's mean and standard error.

In this instance, the population mean, which is 37, is equal to the mean of the sampling distribution.

The population standard deviation divided by the square root of the sample size is the sampling distribution's standard error. For this situation, the standard mistake is 8 partitioned by the square foundation of 32, which is around 1.41.

Therefore, the statement that accurately describes the form of the sampling distribution is:

The inspecting dissemination is regularly circulated with a mean of 37 and standard deviation 1.41.

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