Given the velocity v = ds/dt and the initial position of a body moving along a coordinate line, find the body's position at time t. v = 9.8t + 9, s(0) = 17

Answer:

Step-by-step explanation:

Let T stand for the number of 2 point questions and F for the number of 4 point questions.

We are told that:

2T + 4F = 100 {The total score is the sum of 2 and 4 point questions times their point values]

and that

T + F = 35  [the total number of questions is 35]

Rearrange the last equation to solve for either T or F, and substitute that into the first equation:

T = 35 - F

--

2T + 4F = 100

2(35-F) + 4F = 100

70 - 2F +4F = 100

2F = 30

F = 15

Since T + F = 35, T = 20

Check:

2-Point Questions: 20*2 = 40

4-Point Questions:  15*4 = 60

Total test is 100 points

Answer:

x = 3.96

Step-by-step explanation:

apply the pitagoras theorem

x =

\( \sqrt{ {2.8}^{2} + {2.8 }^{2} } \)

In the Histogram the horizontal line (dimension) represents the value of the selected collection plan element. The vertical line (dimension) represents the count or sum of occurrences of the primary collection element on the horizontal line.

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Redundant bits are additional bits added to the data bits to achieve this purpose.

The number of redundant bits necessary for a code is related to the number of data bits to ensure error detection and correction in transmitted data. In general, redundant bits are additional bits added to the data bits to achieve this purpose.

To determine the number of redundant bits (r) needed for a specific number of data bits (k), you can use the following inequality:

\(2^r ≥ k + r + 1\)

Here, r is the number of redundant bits, and k is the number of data bits.

Step-by-step explanation:

1. Identify the number of data bits (k) in the code.
2. Use the inequality\(2^r ≥ k + r + 1\)to find the minimum value of r (redundant bits) that satisfies the inequality.
3. The value of r obtained will be the number of redundant bits necessary for the code.

By adding redundant bits to the data, it helps in detecting and correcting errors during data transmission, thereby ensuring the accuracy and reliability of the information being communicated.

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Answer:

forth one

Step-by-step explanation:

8 students selected both .then only 24 of students selected only country music and only 6 students selected jazz music.

Answer:

10.5

Step-by-step explanation:

Unit test on edge 2021

The value of x from the figure is 10.5cm

Find the diagram attached

From the given diagram

tan 55 = 15/b

Given that tan 55 = 1.4281, hence;

1.4281 = 15/b

b = 15/1.4281

b  = 10.5cm

Hence the value of x from the figure is 10.5cm

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I can still provide you with an explanation of how to approach showing that a function f(n) is θ(g(n)) using the definitions from class and providing a value for k to justify the statement is true for all n ≥ k.

To show that f(n) is θ(g(n)), we need to prove two conditions: f(n) = O(g(n)) and f(n) = Ω(g(n)).

1. Proving f(n) = O(g(n)):

To prove that f(n) = O(g(n)), we need to find a constant c and a value k such that for all n ≥ k, |f(n)| ≤ c * |g(n)|.

2. Proving f(n) = Ω(g(n)):

To prove that f(n) = Ω(g(n)), we need to find a constant c and a value k such that for all n ≥ k, |f(n)| ≥ c * |g(n)|.

By satisfying both conditions, we can conclude that f(n) is θ(g(n)).

When providing an explicit value for k, we need to find a specific point at which the inequality holds true for all subsequent values of n. This value of k will vary depending on the specific functions f(n) and g(n) being analyzed.

To perform the proof, we can start by analyzing the growth rates or behaviors of f(n) and g(n). If we can establish that the growth rates or behaviors are similar, we can proceed with finding appropriate constants c and k to satisfy the conditions.

I apologize for not being able to directly reference external sources. However, I hope this explanation gives you a general understanding of how to approach proving that a function f(n) is θ(g(n)) using the definitions from class and providing an explicit value for k to justify the statement is true for all n ≥ k.

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Answer:

y=35

Step-by-step explanation:

y in (-oo:+oo)

14 = (2*y)/5 // - (2*y)/5

14-((2*y)/5) = 0

(-2/5)*y+14 = 0

14-2/5*y = 0 // - 14

-2/5*y = -14 // : -2/5

y = -14/(-2/5)

y = 35

y = 35

Betty now has 5 times as many sweets as Gemma.

5x - 120 = x + 245x -x = 24 + 1204x = 144x = 362x = 72

Because both Gemma and Betty have x sweets each and we are finding the total number of sweets.

Have a luvely day!

Betty and Gemma have 72 sweets in total.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them. Variables are the name given to these symbols because they lack set values. We frequently observe constant change in specific variables in our day-to-day situations. But the need to depict these shifting values is ongoing. These values are frequently represented in algebra by symbols such as x, y, z, p, or q, and these symbols are known as variables. In order to determine the values, these symbols are also subjected to different addition, subtraction, multiplication, and division arithmetic operations.

let the number of sweets be x

Gemma gives 24 of her sweets to Betty

Betty have = x+ 24

Now, Betty now has 5 times as many sweets as Gemma.

5(x - 24) = x + 24

5x - 120 = x+ 24

5x -x = 24 + 120

4x = 144

x = 72

Hence, Betty and Gemma have 72 sweets in total.

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Answer:

I think the answer is -7

because : 3(-5) + 4(2)

-15 + 8

= -7

The compound inequality for the given situation is $2.75x + $4.25y ≥ $65 and $2.75x + $4.25y ≤ $75, where x represents the number of daylight cameras and y represents the number of flash cameras.

To solve this compound inequality, we need to find the values of x and y that satisfy both conditions. The inequality $2.75x + $4.25y ≥ $65 represents the lower bound, ensuring that the total cost of the cameras is at least $65. The inequality $2.75x + $4.25y ≤ $75 represents the upper bound, making sure that the total cost does not exceed $75.

To list the solutions involving whole numbers of cameras, we need to consider integer values for x and y. We can start by finding the values of x and y that satisfy the lower bound inequality and then check if they also satisfy the upper bound inequality. By trying different combinations, we can determine the possible solutions that meet these criteria.

After solving the compound inequality, we find that the solutions involving whole numbers of cameras are as follows:

(x, y) = (10, 10), (11, 8), (12, 6), (13, 4), (14, 2), (15, 0), (16, 0), (17, 0), (18, 0), (19, 0), (20, 0).

These solutions represent the combinations of daylight and flash cameras that fulfill the requirements of buying exactly 20 cameras and spending between $65 and $75.

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Aunque el álgebra no está directamente relacionado con el desarrollo personal espiritual, puede ayudar a desarrollar habilidades mentales y cognitivas.

El conocimiento algebraico no está directamente relacionado con el desarrollo personal espiritual, pero el proceso de aprendizaje de la álgebra puede ser beneficioso para el desarrollo de habilidades mentales y cognitivas que pueden ser útiles para el desarrollo personal y espiritual en general.

continuación se presentan algunas formas en que el conocimiento algebraico puede ser útil para su desarrollo personal:

Pensamiento lógico: El álgebra implica la resolución de problemas y el uso de la lógica para llegar a una solución. Al practicar el álgebra, puede mejorar su capacidad para analizar situaciones, identificar patrones y llegar a conclusiones lógicas.

Resolución de problemas: El álgebra también puede ayudar a desarrollar habilidades para resolver problemas complejos y abstractos. Al practicar la resolución de problemas algebraicos, puede aprender a dividir un problema en partes más pequeñas y abordarlo de manera más efectiva.

Flexibilidad mental: La resolución de problemas algebraicos requiere que se piense de manera abstracta y se trabaje con conceptos abstractos. Al aprender a pensar de esta manera, puede mejorar su flexibilidad mental y capacidad para adaptarse a situaciones nuevas y complejas.

Autoconfianza: Aprender y dominar un tema como el álgebra puede aumentar su autoconfianza y autoestima. Al superar desafíos y resolver problemas, puede sentirse más capaz de enfrentar desafíos en otras áreas de su vida.

En resumen, aunque el álgebra no está directamente relacionado con el desarrollo personal espiritual, puede ayudar a desarrollar habilidades mentales y cognitivas que pueden ser beneficiosas para su desarrollo personal en general.

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The probability of household views between 5 and 11 hours will be 0.7653. Number of hours needed in order to be in top 3% will be 13.03 hours. Probability of views more than 3 hours will be 0.9838.

a) The probability of television views between than 5 and 11 hours.

 P( 5≤X≤11) = P[ (5-μ)/σ ≤ (X-μ)/σ ≤ (11-μ)/σ]

                   = P [ (5-8.35)/2.5 ≤ z ≤ (11-8.35)/2.5)

                    = P ( -1.34 ≤ z ≤ 1.06)

                    = P ( z≤ 1.06) - P(z ≤ -1.34)

Substituting values from the z-table

   P ( 5≤X≤11) = 0.85543 - 0.09012 = 0.76531

Probability that household views between 5 and 11 hours is  0.7653.

b) Hours needed to be in top 3% of all households.

 P( X> h) = 0.03

 P[ (X-μ)/σ > (h-μ)/σ] = 0.03

P ( z >h-8.35/2.5) = 0.03

P ( z ≤ h-8.35/2.5) = 0.97

From the table

  (h - 8.35)/ 2.5 = 1.87

   h = (1.87× 2.5) + 8.35

      = 13.025 = 13.03 hours

So if the viewing time is more than 13.03, the household will be in the top 3%.

c) Probability of viewing more than 3 hours

 P(X> 3) = P[ (X-μ)/σ > (3-μ)/σ]

               = P( z < -2.14) = 0.9838

So probability the household will have views more than 3 hours will be 0.9838.

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The volume of the connector given the base area and the height is 84.70cm³.

A hexagonal prism is a three dimensional object that is made up of a hexagonal base. It has 8 faces, 18 edges, and 12 vertices.

Volume = \(\frac{3\sqrt{3} }{2} a^{2}h\)

Where:

2.598076 x 8.15 x 4 = 84.70cm³

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Answer:

32.6 cm³ for K12

Answer:

f(1) = 93

f(n) = f(n - 1) + 4

Step-by-step explanation:

The recursive formula for an arithmetic sequence is given as:

f(1) = a

f(n) = f(n - 1) + d

where a = first term and d = common difference

An arithmetic sequence is in the form:

f(n) = a + d(n - 1)

where a = first term and d = common difference

The common difference in f(n) = 93 + 4(n-1) is 4.

The first term is 93.

The recursive formula is therefore:

f(1) = 93

f(n) = f(n - 1) + 4

Answer:

f(1)=93

f(n)=f(n-1)+4

Step-by-step explanation:

As you can see in the picture, the initial value is 93, which is why it's the first part of the equation. The 4 is multiplying the (n-1) part in the equation and as we complete the recursive formula of N, you have to put the numbers in the correct order.

Answer: 6\(a^{2}\)+a-12

Step-by-step explanation:

First, you want to distribute (2a+3)(3a-4) ---> 2a(3a-4) + 3a(3a-4)

That will get you 6\(a^{2}\)-8a+9a-12

Next, you will want to combine like terms to get 6\(a^{2}\)+a-12

Since you cannot simplify that any further, 6\(a^{2}\)+a-12 is your answer.

Answer:

36.9

Step-by-step explanation:

sinJ=\(\frac{21}{35}\)

    J= \(sin^{-1}\)\(\frac{21}{35}\)

    J= 36.9

Answer:

x = 1   ,or   x = -7

Obviously, the true answer is not in the options given.

Step-by-step explanation:

x² + 6x - 6 = 10

The above equation can not be factorized, hence the use of Almighty Formula.

x = [-b +- √b² - 4ac] / 2a

Where a = 1, b = 6, c = -6

x = [-6 +- √6² - (4*1*-6)] / 2*1

x = [-6 +- √36 - (-24)] / 2

x = [-6 +- √36 + 24] / 2

x = [-6 +- √60] / 2

x = [-6 +- 7.75] / 2

x = [-6 + 7.75] / 2   ,or   x = [-6 - 7.75] / 2

x = 1.75/2   ,or   x = -13.75/2

x = 0.875   ,or   x = -6.875

Approximately

x = 1   ,or   x = -7

Answer:

x=In2+1

Step-by-step explanation:

3+4ex+1-3=11-3

0+4ex+1=8

4ex+1=8

during a six-mile trip, each tire of the giant earthmover makes approximately 878 revolutions.

To calculate the number of revolutions the giant earthmover's tire makes during a six-mile trip, we'll need to find the distance covered by one tire revolution and then divide the total distance by that value.
The diameter of the tire is 11.5 feet. To find the circumference (distance covered in one revolution), use the formula: Circumfrence = π × Diameter, where π (pi) is approximately 3.14. So, the circumference is:
Circumference ≈ 3.14 × 11.5 ≈ 36.11 feet
Next, convert the six-mile trip to feet. Since there are 5,280 feet in a mile, the trip is:
6 miles × 5,280 feet/mile = 31,680 feet
Now, divide the total distance (31,680 feet) by the distance covered in one revolution (36.11 feet):
Revolutions ≈ 31,680 feet ÷ 36.11 feet ≈ 877.57
Round this number to the nearest whole number:
Revolutions ≈ 878

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All solutions to the given problem regarding matrices have been explained and answered below.

We have been given the equations,

x + y - z = 2

x + 2y + z = 3

x + y + (k²-5) z = k

the augmented matrix for the given equations will be,

\(\left[\begin{array}{ccc|c}1&1&-1&2\\1&2&1&3\\1&1&(k^{2}-5)&k\end{array}\right]\)

After applying row operations we get the row-reduced form of the matrix, i.e.

\(\left[\begin{array}{ccc|c}1&0&0&\frac{5+k}{2+k} \\0&1&0&\frac{k}{2+k} \\0&0&1&\frac{1}{2+k}\end{array}\right]\)

For a matrix to be no solutions the rank of the matrix has to be lesser than the rank of the augmented matrix,

If we put k = -2, we get

\(\left[\begin{array}{ccc|c}1&0&-3&0\\0&1&2&0 \\0&0&0&1\end{array}\right]\)

∴ for k = -2, we get no solutions for the equations.

For a matrix to be having infinitely many solutions, the rank of the matrix has to be lesser than the no. of variables,

but for no values of k this condition is satisfied for the given equations,

∴ for no values of k, we get infinitely many solutions for the equations.

And for any other of k, the solutions will be unique.

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hzhdhzhehzgxfshzjfhegxg

Answer:

10

Step-by-step explanation:

We solve using Pythagoras Theorem. Pythagoras Theorem is used to solve for the missing side of a right angled triangle.

The formula for Pythagoras Theorem =

c² = a² + b²

c = √a² + b²

Where c is the longest side

From the above diagram, we are looking for c

c = ?

a = 6

b = 8

Hence,

c = √6² + 8²

c = √36 + 64

c = √100

c = 10

Therefore, side c = 10

Answer:

1/5

Step-by-step explanation:

sqrt(40)/sqrt(1000)

2sqrt(10)/10sqrt(10)

1/5

Answer:

\(x > \frac{5}{2} > 2\frac{1}{2}\)

Step-by-step explanation:

group

\(4x-7 > 3\\4x-7+7 > 3+7\\4x > 3+7\\4x > 10\)

isolate "x"

\(4x > 10\\=\frac{4x}{4} > \frac{10}{4}\\x > \frac{10}{4}\\x > \left(\frac{5\cdot 2}{2\cdot 2}\right)\\x > \frac{5}{2}\)

Answer:

x > 2.5 or in fraction form x > 2 1/2

Step-by-step explanation:

4x - 7 > 3

     +7  +7         Add seven to both sides.

4x > 10

÷4     ÷4            Divide both sides by 4.

x > 2.5

Hope this helps!

The speed of train B is 60 miles per hour, and the speed of train A is 90 miles per hour.

To determine the speeds of trains A and B, we can set up a proportion based on the given information. Let's assume the speed of train B is x miles per hour. According to the problem, train A's speed is 30 miles per hour greater than that of train B, so train A's speed can be represented as (x + 30) miles per hour.

Now, we can set up a proportion based on the distances traveled by the two trains. The distance traveled by train A is 210 miles, and the distance traveled by train B is 120 miles. The proportion can be written as:

x/120 = (x + 30)/210

To solve this proportion, we can cross-multiply and solve for x:

210x = 120(x + 30)

210x = 120x + 3600

90x = 3600

x = 40

Therefore, the speed of train B is 40 miles per hour. Since train A's speed is 30 miles per hour greater, train A's speed is 40 + 30 = 70 miles per hour.

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Answer:

time required = 26 min

Step-by-step explanation:

To solve this, let's first list all the given information, and change the units to millimeters (mm) if required (because the discharge rate is given in mm/s):

○ diameter of pipe = 64 mm ⇒ radius = 32 mm

○ water discharge rate = 2.05 mm/s

○ diameter of tank = 7.6 cm = 76 mm ⇒ radius = 38 mm

○ height of tank = 2.3 m = 2300 mm.

Now, let's calculate the cross-sectional area of the pipe:

Area = πr²

       ⇒ π × (32 mm)²

       ⇒ 1024π mm²

Next, we have to calculate the volume of water transferred from the pipe to the tank per second. To do that, we have to multiply the pipe's cross-sectional area and the discharge rate of the water:

Volume transferred = 1024π mm² × 2.05 mm/s

                                ⇒ 6594.83 mm³/s

Now. let's find the volume of the cylindrical tank using the formula:
Volume = π × r² × h

            ⇒ π × (38)² × 2300

            ⇒ 10433857 mm³

We know that 6594.83 mm³ of water is transferred to the tank every second, so to fill up 10433857 mm³ with water,

time required =  \(\frac{10433857 \space\ mm^3}{6594.83\space\ mm^3/s}\)  

                     ⇒ 1582.12 s

                     ⇒ 1582.13 ÷ 60

                     ≅ 26 min

Answer:

  26 minutes

Step-by-step explanation:

The rate of filling the tank matches the rate of discharge from the pipe. Each rate is the ratio of volume to time. Volume is jointly proportional to the square of the diameter and the height.

For some constant of proportionality k, the volume of discharge in 60 seconds from the pipe is ...

  V = k·d²·h . . . . d = diameter; h = rate×time

  V = k(0.64 dm)²(0.0205 dm/s × 60 s) = k·0.503808 dm³

For the tank, the height (h) is the actual height of the tank. The volume of the tank is ...

  V = k(0.76 dm)²(23 dm) = k·13.2848 dm³

Then the proportion involving (inverse) rates is ...

  time/volume = (fill time)/(k·13.2848 dm³) = (1 min)/(k·0.503808 dm³)

  fill time = 13.2848/0.503808 min ≈ 26.369

__

Additional comments

1 dm = 100 mm = 10 cm = 0.1 m

1 dm³ = 1 liter, though we don't actually need to know that here.

We have used 1 decimeter (dm) as the length unit to keep the numbers in a reasonable range. We have worked out the rate numbers, but that isn't really necessary (see attached).

__

The value of k is π/4 ≈ 0.785398. We don't need to know that because the values of k cancel when we solve the proportion.

Yes, irrational numbers such as π are included in the domain of the function f(x) = 7.

The domain of a function is the set of all possible input values (x) for which the function is defined. In the case of the function f(x) = 7, the output value (y) is always equal to 7, regardless of the input value.

Since every real number, including irrational numbers like π, can be an input value for f(x) = 7, the domain of this function is the set of all real numbers, which includes both rational and irrational numbers. Therefore, π is included in the domain of the function f(x) = 7.

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Answer:

2x-9=0

2x-9+9=0+9.add the inverse of subtraction /addition/ (+9)

2x=9....then divide by 2

x=9/2

x=4.5. will the final answer

Answer:

X=-3

Step-by-step explanation:

3x-5x+4=10

-2x=6

x=-3

note:  I wasn’t sure if the equation ended in 10 or 10x. I think it ends at 10 so that is how I solved.