1/2(5-2h)=h/2
solve the following linear equation

Answer:

You are multiplying the whole number with the reciprocal of the fraction.

Step-by-step explanation:

To divide a whole number by fraction.

You are taking X which is a whole number over the fraction.

its the same as taking x and multiplying it by the reciprocal of the fraction

So if you have 5 divided by 1/2, it's the same as saying 5 times 2/1.

To solve the 1-D wave equation using the method of characteristics, we first need to find the characteristic curves. For the wave equation utt = 9uxx, the characteristic equations are given by:

\(\frac{dx}{dt} = \frac{\partial u}{\partial t} + 3 \frac{\partial u}{\partial x}\\\frac{dy}{dt} = \frac{\partial u}{\partial t} - 3 \frac{\partial u}{\partial x}\)

Simplifying these equations, we have:

\(\frac{dx}{dt} = \frac{\partial u}{\partial t} + 3 \frac{\partial u}{\partial x}\\\frac{dy}{dt} = \frac{\partial u}{\partial t} - 3 \frac{\partial u}{\partial x}\)

Next, we can solve these characteristic equations. Integrating the first equation with respect to t, we get:

x - t = F(y)

where F(y) is an arbitrary function of y. Similarly, integrating the second equation with respect to t, we obtain:

x + t = G(y)

where G(y) is another arbitrary function of y.

Now, we can solve for x and t in terms of y using these characteristic equations. Adding the two equations, we have:

2x = F(y) + G(y)

\(x = \frac{F(y) + G(y)}{2}\)

Subtracting the two equations, we get:

2t = G(y) - F(y)

\(t = \frac{G(y) - F(y)}{2}\)

Now, let's consider the initial condition u(x, 0) = 0. At t = 0, the characteristic curves intersect the x-axis. Therefore, we can set t = 0 in the characteristic equations to find the relationship between x and y:

x - 0 = F(y) (1)

x + 0 = G(y) (2)

From equation (1), we have:

x = F(y)

From equation (2), we have:

x = G(y)

Since the string is fixed at x = L, we can set x = L in equation (2) to find G(y):

L = G(y)

Therefore, we have:

x = F(y)

x = L

Since \(x = \frac{F(y) + G(y)}{2}\), we can substitute x = L to find F(y):

L = F(y) + L

F(y) = 0

Hence, we have F(y) = 0, which means x = 0 along the characteristic curves.

Now, we can solve for t in terms of y using the relationship

\(t = \frac{G(y) - F(y)}{2}\)

t = (L - 0)/2

t = \(\frac{L}{2}\)

Therefore, along the characteristic curves, we have x = 0 and t = \(\frac{L}{2}\).

Now, we can express u(x, t) in terms of x and t using the initial condition u(x, 0) = 0. Along the characteristic curves, x = 0 and t =\(\frac{L}{2}\), so we have:

u(0, \(\frac{L}{2}\)) = 0

Therefore, the solution to the 1-D wave equation for a semi-infinite string fixed at x = L using the method of characteristics is u(x, t) = 0 for x = 0 and t = \(\frac{L}{2}\).

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Answer:

p=−8

Step-by-step explanation:

Regroup terms.

p /2 −9=−13

Add 9 to both sides.

p/2  =−13+9

Simplify  -13+9 to −4.

p/2=−4

Multiply both sides by 2.

p=−4×2

Simplify  4×2  to  8

.

If there are 30 skaters competing at the olympic games, then the required number of ways = 24360

The term permutation refers to a mathematical calculation of the number of ways a particular set can be arranged. Put simply, a permutation is a word that describes the number of ways things can be ordered or arranged. With permutations, the order of the arrangement matters.

Given that,

There are 30 skaters competing in the competition.

To find,

The number of ways in which they can win gold, silver, and bronze medal.

So,

We can write,

In distribution of medals(gold, silver, and bronze) we require 3 winners in a particular order, so for this we use Permutations.

According to permutation , number of ways of selecting r things out of ,

n = \(\frac{n!}{(n-r)!}\)

Then, The number of ways in which 18 skaters can win 3 medals,

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

= \(\frac{30!}{27!}\)

= \(\frac{30*29*28*27!}{27!}\)

= \(30*29*28\)

= 24360

Therefore,

If there are 30 skaters competing at the olympic games, then the required number of ways = 24360

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Answer: 7.5

Step-by-step explanation:

\(-15=\frac{x}{-0.5}\\\\-15=-2x\\\\x=\boxed{7.5}\)

The values of theta that make the equation tan(theta) = 0 true when 0 <= theta <= 4 pi are 0, pi, 2 pi, and 3 pi.

To determine these values, we need to remember that the tangent function is defined as the ratio of the opposite side to the adjacent side in a right triangle. This means that when tan(theta) = 0, the opposite side must be equal to 0. This occurs when theta is equal to 0, pi, 2 pi, and 3 pi radians.

We can also use the fact that the tangent function has a period of pi radians. This means that the function repeats itself every pi radians. So, if tan(theta) = 0 at theta = 0, then it will also be equal to 0 at theta = 0 + pi, theta = 0 + 2 pi, and theta = 0 + 3 pi.

Therefore, the values of theta for tan(theta) = 0 true when 0 <= theta <= 4 pi are 0, pi, 2 pi, and 3 pi.

These values can be written as 0, pi, 2 pi, 3 pi and separated by a comma.

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Answer:

A- 200+25x

B- 200+25×4=300

Continued for question B: The input of 4 into "x" indicates how many cans of paint you have bought

Step-by-step explanation:

Answer:

A box and whisker plot—also called a box plot—displays the five-number summary of a set of data. The five-number summary is the minimum, first quartile, median, third quartile, and maximum. In a box plot, we draw a box from the first quartile to the third quartile. A vertical line goes through the box at the median.

Step-by-step explanation:

hope you get it right    :)

The probability of randomly selecting the number 0.13 from a uniform distribution between 0 and 1 can be calculated by considering the range of values that satisfy the condition.

Since the distribution is uniform, all numbers within the range have an equal probability of being selected. The range between 0 and 1 is of unit length, and any specific number within that range represents a single point. Therefore, the probability of selecting any particular point, such as 0.13, is infinitesimally small since it represents a single value within an infinite set of possible values. The probability of randomly selecting the number 0.13 from a uniform distribution between 0 and 1 is extremely low, approaching zero. This is because the range of possible values within the distribution is continuous, and the probability of selecting any specific point is infinitesimal.

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the solution to the system of equations is:
x = 5/6
y = 1/3
z = -2/3

To solve the given system of equations using the Gaussian-Jordan algorithm, we can perform row operations to reduce the augmented matrix to reduced row-echelon form (rref).

The given system of equations:
-2x + 3y + z = -2
-3x + y + 3z = -4
2y - z = 0

We can represent this system in the augmented matrix form:
| -2  3  1  | -2 |
| -3  1  3  | -4 |
|  0  2 -1  |  0 |

Performing row operations:
1. R2 = R2 + (3/2)R1
| -2  3   1  | -2 |
|  0  7/2  7/2  | -7/2 |
|  0  2  -1  |  0 |

2. R2 = (2/7)R2
| -2  3   1  | -2 |
|  0  1  1  | -1 |
|  0  2  -1  |  0 |

3. R1 = R1 + 3R2
| -2  6   4  | -5 |
|  0  1   1  | -1 |
|  0  2  -1  |  0 |

4. R1 = (-1/2)R1
|  1 -3/2 -1  | 5/2 |
|  0   1   1  | -1 |
|  0   2  -1  |  0 |

5. R3 = R3 - 2R2
|  1 -3/2 -1  | 5/2 |
|  0   1   1  | -1 |
|  0   0  -3  |  2 |

6. R3 = (-1/3)R3
|  1 -3/2 -1  | 5/2 |
|  0   1   1  | -1 |
|  0   0   1  | -2/3 |

7. R2 = R2 - R3
|  1 -3/2 -1  | 5/2 |
|  0   1   0  | 1/3 |
|  0   0   1  | -2/3 |

8. R1 = R1 + R3
|  1 -3/2  0  | 7/6 |
|  0   1   0  | 1/3 |
|  0   0   1  | -2/3 |

9. R1 = R1 + (3/2)R2
|  1   0   0  | 5/6 |
|  0   1   0  | 1/3 |
|  0   0   1  | -2/3 |

The resulting matrix is in reduced row-echelon form. Thus, the solution to the system of equations is:
x = 5/6
y = 1/3
z = -2/3

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Answer:

slope:12

Step-by-step explanation:

I HOPE IT HELP YOU

0_<

Answer:

12

Step-by-step explanation

To convert 4.42 kg into pounds, the starting place in the conversion process is to understand the conversion factor between kilograms and pounds.

The conversion factor between kilograms (kg) and pounds (lbs) is 1 kg = 2.20462 lbs. This means that 1 kilogram is equal to approximately 2.20462 pounds. To convert a given weight in kilograms to pounds, you need to multiply the weight in kilograms by the conversion factor.

In this case, you want to convert 4.42 kg into pounds. The starting place in the conversion process is to use the conversion factor:

4.42 kg * 2.20462 lbs/kg = 9.7314044 lbs

By multiplying the given weight in kilograms (4.42 kg) by the conversion factor (2.20462 lbs/kg), you find that 4.42 kg is approximately equal to 9.7314044 pounds. Therefore, when converting kilograms to pounds, the first step is to apply the appropriate conversion factor by multiplying the weight in kilograms by the conversion factor.

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Answer:

no

Step-by-step explanation:

All triangles must add up to one 180 degrees 23+49+106 does not equal 180

Answer:16(1+2)

Step-by-step explanation:

Answer: HI = 5.3 cm

Let HI = x

GH = 2cm

m< H = 68 degrees

to find HI, we will need to apply the SOH CAH TOA RULE

HI = hypotenus

GH = adjacent

Cos 68 = adjacent / hypotenus

Cos 68 = 2 / x

Cross multiply

2 = x * cos 68

cos 68 = 0.3746

2 = x * 0.3746

Isolate x

x = 2/0.3746

x = 5.3cm

Therefore, HI is 5.3cm

Answer: Choice B

The initial amount in the account.

==================================================

Reason:

x is the number of years

x = 0 is the starting point. Let's plug that in to find...

\(y = 982(1.07)^x\\\\y = 982(1.07)^0\\\\y = 982(1)\\\\y = 982\\\\\)

At the start, Sammy has $982 in the bank.

Side note: The 1.07 means the account is growing by 7% each year.

For two rectangular prisms, the difference of masses of golden rectangular prism with density 19.3 g/cm³ and lead rectangular prism with density 11.3 g/cm³ is equals to the 1728 grams.

There is jacob made two rectangular prisms one from gold and other lead.

Height of each rectangular prism h = 8 cm

length of each rectangular prism, l = 9 cm

width of each rectangular prism, w = 3 cm

The density of golden rectangular prism = 19.3 g/cm³

The density of lead rectangular prism

= 11.3 g/cm³

We have to determine the difference of masses of the rectangular prisms. Using the formula of volume, volume of golden rectangular prism, \(V = l × w × h \)

= 8 × 9 × 3 cm³ = 216 cm³

Similarly, volume of lead rectangular prism = 216 cm³

From density formula, \(d = \frac{ mass}{ volume }\)

=> Mass = density × volume

So, Mass of golden rectangular prism

= 19.3 g/cm³ × 216 cm³

= 216× 19.3 g = 4,168.8 grams

Similarly, Mass of lead rectangular prism = 11.3 g/cm³ × 216 cm³

= 216× 11.3

= 2,440.8 g

The difference between masses of rectangular prism= 4168.8 - 2440.8 = 1728 grams. Hence, required value is 1728 grams.

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Answer:

A: 120

Step-by-step explanation:

5! means 5 factorial

the factorial of a number is the number times every whole number until 1

in this case,

5 * 4 * 3 * 2 * 1

5 * 4 = 20 , 3 * 2 * 1 = 6

20 * 6 = 120 (option A)

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Answer:

a 120

Step-by-step explanation:

Answer:

5y - 2

Step-by-step explanation:

1/3 ( 15y - 6 ) = (15y - 6) / 3 = 5y - 2

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Answer:

After 8 years, the amount owed would be approximately $3959.79. Rounded to the nearest cent, the amount owed is $3959.80.

Step-by-step explanation:

To calculate the amount owed after 8 years with a loan of $2000 at an annual interest rate of 11.5%, compounded annually, we can use the formula for compound interest:A = P(1 + r/n)^(nt)Where:

A is the final amount owed

P is the principal amount (initial loan)

r is the annual interest rate (as a decimal)

n is the number of times the interest is compounded per year

t is the number of yearsIn this case:

P = $2000

r = 11.5% = 0.115 (as a decimal)

n = 1 (compounded annually)

t = 8 yearsSubstituting the values into the formula:A = $2000(1 + 0.115/1)^(1*8)

= $2000(1.115)^8

≈ $2000(1.979894357)

≈ $3959.79

Answer:

I needed thisssss ! Thanks for the points and you too<3

Step-by-step explanation:

Answer:

Yes! You get it, fellow human!

Step-by-step explanation:

Thank you so much! You made my day :))))) <3<3<3

The amount of fencing needed to surround the perimeter of the picnic area of the park is 107 yards. Hence, the second option is the right choice.

In the question, we are informed that the triangle KLM, represents a section of a park set aside for picnic tables. We are also informed that the picnic area will take up approximately 400 square yards of the park.

We are asked for the amount of fencing needed to surround the perimeter of the picnic area of the park.

We know the area of a triangle can be found using the trigonometric area formula, Area = (1/2)ab sin C.

Using this in the given triangle KLM, we get:

Area = (1/2)(KL)(KM)(sin K),

or, 400 = (1/2)(KL)(45)(sin 25°),

or, KL = (400*2)/(45*sin 25°) = 800/(45*0.42262) = 800/19.017822 = 42.0658 ≈ 42 yd.

Thus, we get KL = 42 yards.

Now, the perimeter of the picnic area = the perimeter of the triangle KLM = KL + LM + MK = 42 + 20 + 45 yards = 107 yards.

Thus, the amount of fencing needed to surround the perimeter of the picnic area of the park is 107 yards. Hence, the second option is the right choice.

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Answer: b

Step-by-step explanation:

In a sequence of ten ternary digits, where each digit can be 0, 1, or 2, we need to determine the number of sequences that contain a single 2 and a single 0.

To count the number of sequences that satisfy the given condition, we can break it down into two parts: placing the 2 and placing the 0.

First, we need to choose a position for the 2 in the sequence. Since there are ten positions available, we have 10 choices for placing the 2.

Next, we need to choose a position for the 0 in the remaining nine positions. After placing the 2, we are left with nine positions, and we can choose one of them for the 0.

Therefore, the total number of sequences with a single 2 and a single 0 is obtained by multiplying the number of choices for placing the 2 (10) by the number of choices for placing the 0 (9).

Hence, the total number of sequences is 10 * 9 = 90.

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We should use a sample size of at least 154 to estimate the mean fuel efficiency for the new type of motorcycle within 0.5 mpg. The confidence interval in Part A is between 60.725 and 65.555 mpg.

To construct a 95% confidence interval for the mean fuel efficiency for this vehicle, we can use the formula:

Confidence interval = sample mean ± (critical value) * (standard deviation / sqrt(sample size))

First, let's calculate the sample mean and standard deviation for the given data:

Sample mean = (57.5 + 62.3 + 67.2 + 58.1 + 59.6 + 71.9 + 55.2 + 57.6 + 71.9 + 68.8 + 69.1 + 65.3 + 62.3 + 64.7 + 59.9 + 62.1 + 63.5 + 62.9 + 66.7 + 61.3) / 20

= 63.14

Sample standard deviation = √(((57.5 - 63.14)² + (62.3 - 63.14)² + (67.2 - 63.14)² + ... + (61.3 - 63.14)²) / 19)

= 4.97

Next, we need to find the critical value for a 95% confidence level. Since the sample size is small (20), we will use a t-distribution. The degrees of freedom for this calculation is 20 - 1 = 19. Consulting a t-table or using statistical software, we find the critical value to be approximately 2.093.

Plugging the values into the formula, we get:

Confidence interval = 63.14 ± (2.093) * (4.97 / √(20)) ≈ 63.14 ± 2.415

Interpreting the confidence interval, we can say with 95% confidence that the true mean fuel efficiency for this vehicle falls between 60.725 and 65.555 mpg.

To determine if the new motorcycle has greater fuel efficiency than the previous model, we can perform a hypothesis test. The null hypothesis (H0) is that there is no difference in fuel efficiency between the two models, and the alternative hypothesis (Ha) is that the new model has greater fuel efficiency.

We can use a t-test to compare the means of two independent samples. The test statistic is calculated as:
t = (sample mean 1 - sample mean 2) / sqrt((sample variance 1 / sample size 1) + (sample variance 2 / sample size 2))

For this case, the sample mean for the new model is 65.9 mpg, and the sample standard deviation is 3.2 mpg. The sample mean and standard deviation for the previous model were calculated in Part A. We can use the same sample size of 20 for both models.

Calculating the test statistic:

t = (65.9 - 63.14) / √((4.97² / 20) + (3.2² / 20))

t ≈ 1.376

Looking up the critical value for a t-distribution with 20 - 1 = 19 degrees of freedom at a 95% confidence level, we find it to be approximately 2.093.

Since the test statistic (1.376) is less than the critical value (2.093), we do not have enough evidence to convincingly claim that the new model has greater fuel efficiency than the previous model.

To construct a 98% confidence interval for the mean fuel efficiency of the older model, we can use the same formula as in Part A. The only difference is the critical value. For a 98% confidence level, the critical value for a t-distribution with 20 - 1 = 19 degrees of freedom is approximately 2.861.

Plugging the values into the formula:

Confidence interval = 63.14 ± (2.861) * (4.97 / √(20))

≈ 63.14 ± 3.303

Interpreting the confidence interval, we can say with 98% confidence that the true mean fuel efficiency for the older model falls between 59.837 and 66.443 mpg.

The change in confidence level from 95% to 98% does not change the conclusion in Part B. The hypothesis test is based on comparing the test statistic to the critical value, and the confidence interval is based on the sample mean and standard deviation. The change in confidence level does not alter these values or the comparison between them.

To estimate the mean fuel efficiency for the new type of motorcycle within 0.5 mpg, we need to calculate the sample size required. The formula for the sample size is:

Sample size = (Z-score * standard deviation / margin of error)²

Plugging in the values:

Z-score = critical value for the desired confidence level (let's assume 95%)

Standard deviation = 3.2 mpg (from the given data)

Margin of error = 0.5 mpg

Using a Z-score of approximately 1.96 for a 95% confidence level:

Sample size = (1.96 * 3.2 / 0.5)² ≈ 153.86

We should use a sample size of at least 154 to estimate the mean fuel efficiency for the new type of motorcycle within 0.5 mpg.

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Answer:

C is the answer

Step-by-step explanation:

The domain can't be minus. That's the only stipulation. It can be equal to 0 or anything larger than 0. It just can't go into the minus numbers.

0≤x<infinity.

C

Answer:

Approximately \(0.7\; {\rm ft}\).

Step-by-step explanation:

If the current bounce is of height \(h\; {\rm ft}\), the next bounce would be of height \((78\%\, h)\; {\rm ft}\), which is equal to \((0.78\, h)\; {\rm ft}\).

It is given that the first bounce is of height \(6.5\; {\rm ft}\). Relative to this first bounce:

In general, the \(n\)th bounce would have been dampened \((n - 1)\) times. The height of that bounce would be \(((0.78)^{n - 1}\, 6.5)\; {\rm ft}\).

Thus, the \(10\)th bounce would have been dampened \((10 - 1) = 9\) times. The height of that bounce would be \(((0.78)^{10 - 1} \, 6.5)\; {\rm ft} \approx 0.7\; {\rm ft}\) (rounded to the nearest tenth, one digit after the decimal point.)

The solution to the graph of the linear inequality is the point of intersection which is (-5, 3)

A system of linear inequalities in two variables consists of at least two linear inequalities in the same variables. The solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system and the graph of the linear inequality is the graph of all solutions of the system

In this problem, to find the solution to the system of linear inequality, we have to find the point of intersection. This gives the exact solution to the graph.

Looking at this graph, the point of intersection is (-5, 3)

The solution to the graph is (-5, 3)

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