A marble is selected at random from a jar containing 4 red marbles, 5 yellow
marbles,and 3 green marbles. What is the probability that the marble is red?

The solution to the differential equation 0 a. + dt = 8(t), subject to the constraint that a(0) = 0, is: a(t) = 0

To write the ordinary differential equation +2.-a0 as a system of first-order equations, we can introduce a new variable y(t) such that y(t) = a'(t). Then, we have the system of equations:

a'(t) = y(t)
y'(t) = -2a(t)

To solve the differential equation 0 a. + dt = 8(t), subject to the constraint that a(0) = 0, we can use the method of integrating factors. First, we rewrite the equation as:

a'(t) + 8(t) = 0

Then, we multiply both sides by the integrating factor e^(∫8(t)dt):

e^(∫8(t)dt) a'(t) + e^(∫8(t)dt) 8(t) = 0

Using the product rule for derivatives, we can rewrite the left-hand side as:

(e^(∫8(t)dt) a(t))' = 0

Integrating both sides with respect to t, we get:

e^(∫8(t)dt) a(t) = C

where C is a constant of integration. Solving for a(t), we get:

a(t) = C e^(-∫8(t)dt)

To satisfy the initial condition a(0) = 0, we can substitute t = 0 into the above expression and solve for C:

0 = C e^(-∫8(0)dt)
0 = C

Therefore, the solution to the differential equation 0 a. + dt = 8(t) is a(t) = 0

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Answer:

A

Step-by-step explanation:

According to the given question.

Total number of shirts, n = 12

Number of shirts to be selected, r = 3

As we know, the total number of ways of selection of r objects from n objects at a time without replacement is given by

C(n, r) = n!/r!(n - r)!

Determine the steady-state current in the RLC circuit to be 0.68 A.

The equation for Lq′′ + Rq′ + 1/C q = E is used to find the steady-state current in each RLC circuit. The circuit parameters are L = 0.1 H, C = 0.01 F, R = 3 Ω, and E(t) = 5cos10t - 5sin10t.Lq′′ + Rq′ + 1/C q = E can be written as Ld²q/dt² + Rdq/dt + 1/C q = E(t)The current flowing through the circuit can be determined using this formula. To calculate the current, we can use E(t) = 5cos10t - 5sin10t.The current can be found using the equation q(t) = Q cos(wt - φ), where Q = I/Z, Z = √(R² + (wL - 1/wC)²), w = 2πf, and φ = tan⁻¹((wL - 1/wC)/R). Z, w, and φ can be calculated from the parameters of the circuit.Using the above formulas, the following is obtained.I = 5/√(3² + (10π x 0.1 - 1/(10π x 0.01))²) = 0.68 ADetermine the steady-state current in the RLC circuit to be 0.68 A.

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Answer:

67

Step-by-step explanation:

Tell me if it works if it is not right then try 113.

9514 1404 393

Answer:

  100°

Step-by-step explanation:

Angle AKC is a vertical angle with angle BKD, so has the same measure. Since K is the center of the circle, arc AC has the same measure as angle AKC: 100°.

__

A diagram may help.

Answer:

14800 sq yd

Step-by-step explanation:

area of a trapeziod

Answer:

Step-by-step explanation:

4.5+173=177.5.

122.5 does not equal 0.

Answer:

932

Step-by-step explanation:

If they have 4 every hour, and there's 233 hours, you multiply 233 by 4.

Answer:

\(\frac{1}{x-1}\)

Step-by-step explanation:

(x - 1) × \(\frac{1}{x-1}\) ( cancel the factor (x - 1) on numerator and denominator

= 1

[ In the same way 2 × \(\frac{1}{2}\) = 1 ]

The required rational expression is \(\frac{1}{x-1}\)

The number of quarts of paint did mieko use in the living room is A = 3 quarts

Given data ,

Mieko bought 2 gallons of paint. she used 1/4 of the paint on her bedroom, 3 quarts on the hallway, and the rest of the paint in the living room

Now , on simplifying the equation , we get

Two gallons of paint is equal to 8 quarts (2 x 4 = 8)

Mieko used 1/4 of the paint on her bedroom, which is equal to 2 quarts (1/4 x 8 = 2)

She used 3 quarts of paint on the hallway

Thus, Mieko used a total of 2 + 3 = 5 quarts of paint on the bedroom and hallway

Therefore , she used 8 - 5 = 3 quarts of paint in the living room

Hence , the number of quarts is A = 3 quarts

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The change in air pressure when the pure tone is produced is mathematically given as

p(1/2000) =0 mP

This pressure is referred to as the atmospheric pressure, air pressure, or simply pressure. It is the force that is exerted on a surface by the air that is above it due to the gravitational pull that gravity has on the surface. A barometer is an instrument most often used to measure the pressure of the atmosphere. When the pressure in the atmosphere changes, a column of mercury contained inside a glass tube in a barometer will either rise or sink.

Generally, the equation for is pressure  mathematically given as

\(p(t) =2sin (4000\pi t)\)

Therefore

p(1/2000) =2sin (4000\pi *1/2000)

p(1/2000) = 2sin (2\pi)

p(1/2000) = 2*0

p(1/2000) =0 mP

In conclusion, the pressure

p(1/2000) =0 mP

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Answer:

132

Step-by-step explanation:

Just divide by diving 2 by 2 which is 1, then 6 divided by 2 is 3 and 4 divided by 2 is 2. Write the numbers together which is 132.

The quotient from the given division is 132 and the remainder is 0.

Given that, 264 divided by 2.

The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.

Here, 264/2

2|264|132

  2

_____

  64

  6

______

     4

     4

______

     0

Thus, quotient = 132 and remainder=0

Therefore, the quotient from the given division is 132 and the remainder is 0.

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Solutions can be divided into supersaturated, unsaturated, and saturated solutions based on how well the solute dissolves in the solvent.

A homogeneous mixture with the major ingredients solute and solvent is referred to as a solution.

Solutions can be divided into supersaturated, unsaturated, and saturated solutions based on how well the solute dissolves in the solvent.

Supersaturated solution: The excess solute will crystallize quickly in a supersaturated solution because it contains a lot of solute at a temperature where it will be decreased.

Unsaturated solution: When a solvent can dissolve any more solute at a specific temperature, the solution is said to be unsaturated.

Saturated solution: A saturated solution is one in which a solvent can no longer dissolve any more solute at a particular temperature.

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The angle of inclination of the Earth's axis with its orbital plane is approximately 23.5 degrees.

The Earth's axis of rotation is an imaginary line that runs through the North and South Poles. This axis is tilted with respect to the plane of the Earth's orbit around the Sun. The angle of inclination between the Earth's axis and its orbital plane is known as the axial tilt or obliquity of the Earth. Currently, this tilt is approximately 23.5 degrees.

The axial tilt of the Earth is responsible for the changing seasons experienced in different parts of the world throughout the year. As the Earth orbits the Sun, different parts of the planet receive varying amounts of sunlight. During the summer solstice, which occurs around June 21st in the Northern Hemisphere, the North Pole is tilted towards the Sun, resulting in longer days and warmer temperatures.

Conversely, during the winter solstice around December 21st, the North Pole is tilted away from the Sun, leading to shorter days and colder temperatures. The axial tilt also affects the distribution of sunlight, which influences climate patterns and weather conditions on Earth.

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The area of the isosceles triangle having two sides 12.5 cm and another 20cm is 75cm².

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know that an isosceles triangle has two sides having the same length and the third one is different.

We also know that the area of an isosceles triangle is (1/2)×b×√(a² - b²/4),

where b is the value of the third side and a is the value of two similar sides.

Therefore, The area of the isosceles triangle having side lengths of two similar sides is 12.5 cm and the third side is 20 cm is,

= (1/2)×20×√((12.5)²- (20)²/4) cm²,

= 10×√(156.25 - 100) cm².

= 10×√(56.25) cm².

= 10×7.5 cm².

= 75 cm².

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Answer:

150 has to be times 40

Step-by-step explanation:

150×40+25÷35=1

The number of his next 42 field goals the kicker will not make will be 35.

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

A kicker made 10 of his last 12 field goals.

Predict the number of his next 42 field goals the kicker will not make will be

Let x be the number of his next 42 field goals the kicker will not make.

Then we have

x / 10 ≠ 42 / 12

      x ≠ 35

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The required cubic polynomial is

f(x) = \(-2x^3-2x^2-28x+48\)

What is a polynomial?

An algebraic expression of the form \(a_0 + a_1x+ .... + a_nx^n\) (\(a_0 \neq 0\)) is called a polynomial of degree n.

The zeroes of the cubic polynomial are -4, 2, 3

Let the cubic polynomial is

f(x) = a(x - (-4))(x - 2)(x - 3)

f(x) = a(x + 4)(x - 2)(x - 3)

If x = -5, f(x) = 112

112 = a(-5 + 4) (-5 - 2)(-5 - 3)

112 = -56a

a = \(-\frac{112}{56}\)

a = -2

f(x) = -2(x+ 4)(x - 2)(x - 3)

\(f(x) = -2(x+ 4)(x^2 -3x -2x +6)\\f(x) = -2(x + 4)(x^2 - 5x + 6)\\f(x) = -2(x^3 - 5x^2+4x^2+6x - 20x+24)\\f(x) = -2(x^3 - x^2 - 14x +24)\\f(x) = -2x^3 -2x^2 - 28x + 48\)

(x +4)(x - 2)(x - 3)

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The technique for determining an array index using only a search key and not searching is called hashing.

Hashing is a method that maps data to a fixed-size array called a hash table. In this technique, a hash function is used to generate a unique index for each search key. The hash function takes the search key as input and performs some calculations to produce the index value.

This index is then used to access the corresponding element in the array, providing direct access to the desired data without the need for further searching.

Hashing is the technique of determining an array index using only a search key.

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Answer:

400

Step-by-step explanation:

4/5×500

=400 6s would be riled

Bonjour !

enfants = p

donc adultes = p + 3

140 enfants = 140p

130 adultes = 130(p + 3)

140p + 130(p + 3)

The possible solutions of the inequality expression given as 20y < -5 + 18y are (c) y < -5/2, y < -2.5 and (d) -2.5 > y

From the question, we have the following parameters that can be used in our computation:

20y < -5 + 18y.

To start with, we need to collect the like terms of both sides

Using the above as a guide, we have the following:

20y -18y < -5

Next, we need to evaluate the like terms of both sides

Using the above as a guide, we have the following:

2y < -5

Lastly, we divide both sides by 2

y < -5/2

Express as decimal

y < -2.5

Switch the positions

-2.5 > y

Hence, the solutions are y < -5/2, y < -2.5 and -2.5 > y

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1. x + 20

2. 0

3. 2x - 8

4. 95x + 10

5. -9x - 6

6. 4x + y - 5

7. -x + 6y + 5

8. x + y - 15

9. x + 4y + 4

• When working with variables and numbers, you have to put the variables first (in alphabetical order) and then the numbers.

• To evaluate an algebraic expression, we find the value of the expression when the variable is replaced by a given number.

• To evaluate an expression, we substitute the given number for the variable in the expression and then simplify the expression using the order of operations.

• When we are not given a number for the variable in the expression, we have to group like-terms.

1. 4x + 12 - 3x + 8

2. -8x + 1 + 2x - 1 + 6x

3. 4x - 3 - 2x - 5

4. 100x + 5 - 5x + 5

5. -4x - 4 - 2 - 5x

6. 2x - 1 + 2x - 4 + y

7. 5y - x + 2y - y + 5

8. -15 + 3y - 3x - 2y + 4x

9. 4 - 3y + 3x - 2x - y

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Answer:

Step-by-step explanation:

This is more physics than math, but since "The book of nature is written in the language of mathematics"...

Anyway, the one-dimesional motion equation you want to use here resembles the quadratic we use to model parabolic motion. It is

\(v^2=v_0^2+2a\)Δx

where v is the final velocity of the firefighter, v₀ is the initial velocity of the firefighter, a is -9.8 m/s/s (negative because the motion is in the downward direction), and Δx is -34 m. This is also negative because where the firefighter lands is below the point at which he started. This is important, because if you leave the 34 as positive, you end up with a negative radicand...and that's not gonna work. Filling in the formula:

\(v^2=(7.5)^2+2(-9.8)(-34)\)

Paying close attention to significant digits here is important (at least it is when I teach physics in school!). Since there are 2 significant digits in 7.5, we need 2 in the product. 7.5 squared is 56.25 which will round to 56. Then on the right side of the plus sign, we need 2 significant digits as well since the number 2 is part of the equation. We don't count it as significant if it is part of the equation. 2(-9.8)(-34) = 666.4 but that will round to 670. NOW, since the rules for significant digits are different in multiplication and addition, you have to round each first, then take the square root of the sum, rounding at the end. In this case we will round to the place that holds the least significance between the 2 numbers. In our case that is the tens place, since the tens place is less significant than is the 1's place. The number 7 is in the tens place. (Following that rule is super tricky, and also quite maddening!)

What we have here is

\(v^2=56+670\) and

\(v=\sqrt{56+670}\)

That leaves us with

v = 26.94438j

But don't forget we round that to the tens place which comes out in the end, finally, to

v = 30 m/s

Answer:

The profit is $100.56

Step-by-step explanation:

The total cost for the ice cream was 100 * 2.40 = 240

14 1/2 gallons were ruined so there were 100 -14 = 86 half gallons left

They sold these at 3.96 each

86 * 3.96 =340.56

The profit is the money made minus the cost

340.56-240 = 100.56

The profit is $100.56

Answer:

x^4

Step-by-step explanation:

Answer:

The given question is incomplete.

The set of numbers should be : -11, -5/6, 0, 0.75, \($\sqrt5$\), \($\pi$\), \($\sqrt{64}$\),

Step-by-step explanation:

a). Natural numbers : Natural numbers starts form 1  up to positive infinity. They are non negative integers.

The numbers are : \($\sqrt{64}$\)

b). Whole numbers : Whole numbers are numbers which starts from 0 to positive infinity.

The numbers are : 0, \($\sqrt{64}$\)

c). Integers : Integers are both positive and negative numbers including 0. But they are not fractional numbers.

The numbers are : -11, 0, \($\sqrt{64}$\)

d). Rational numbers : The rational numbers are the whole numbers or may be fractions which are represented by divisions of any two integers, in the form of m/n.

The numbers are : -11, -5/6, 0, 0.75, \($\sqrt{64}$\)

e). Irrational numbers: Irrational numbers are those numbers numbers which cannot be written in a fraction form. They are not rational numbers

The numbers are : \($\sqrt5, \pi$\)

f). Real numbers : Real numbers are those numbers which do not have any imaginary component in it.

The numbers are : -11, -5/6, 0, 0.75, \($\sqrt5$\), \($\pi$\), \($\sqrt{64}$\),

Line of best fit refers to a line through a scatter plot of data points that best expresses the relationship between those points. Statisticians typically use the least squares method to arrive at the geometric equation for the line, either though manual calculations or regression analysis software. A straight line will result from a simple linear regression analysis of two or more independent variables. A regression involving multiple related variables can produce a curved line in some cases.

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