a rational number between
1
3
and
5
3

When we calculate probabilities involving one event AND another event occurring, we multiply their probabilities.

According to me , independent is the word which is associated with multiplication when computing probabilities . Because when the events are independent then we multiply the probabilities .

According to the multiplication rule of probability, the probability of occurrence of both the events A and B is equal to the product of the probability of B occurring and the conditional probability that event A occurring given that event B occurs.

The probability of the union of two events is equal to the sum of individual probabilities. The union of two set contains all the elements of previous sets. The union is denoted by ∪. The equation for the students earnings will be expressed as P(A∪B). The occurrence of event A changes the probability of B then the events are dependent. If the probability of two events happening together is zero then the events are mutually exclusive.

Therefore,

When we calculate probabilities involving one event AND another event occurring, we multiply their probabilities.

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The term is called an identity element. In multiplication, the identity element is one because any number multiplied by one results in the same number. In addition, the identity element is zero because any number added to zero results in the same number.

The term in mathematics for the operation or number that leaves others unchanged when combined with them is called the identity element.

It is also known by the name of neutral element.

In multiplication, the identity element is one (1) because when you multiply a number by one the result remains the same as the original number. For any number a,

a1=1a=a.

While in addition, the identity element is zero (0) because when you add zero to a number, the result remains the same as the original number. For any number a,

a+0=0+a=a.

There is no identity element for subtraction, and division only has an identity element for certain sets.

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Answer:

A = 6

Step-by-step explanation:

4(3A - 4) = 56 (Distribute/multiply the 4 to everything inside the parentheses)

12A - 16 = 56 (Add 16 to both sides to get A on one side)

12A = 72 (Divide both sides by 12 to get A by itself)

A = 6

Answer:

A = 6.

Step-by-step explanation:

4(3a-4)=56

distribute

12a-16=56

add 16

12a = 72

divide by 12

a = 6

An interval on the graph above that is increasing include the following: B. -2 < x < 2.

For any given function, y = f(x), if the output value (range) is increasing when the input value (domain) is increased, then, the function is generally referred to as an increasing function.

On the other hand (conversely), if the output value (range) is decreasing when the input value (domain) is increased, then, the function is generally referred to as a decreasing function.

By critically observing the graph above, we can reasonably infer and logically deduce that it is increasing over the interval -2 < x < 2.

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Answer:

72yd2

Step-by-step explanation:

making figure into 2

1st figure

= 6×5

= 30yd^2

2nd figure

= 14×3

= 42yd^2

Area of the full figure

= (30+42)yd^2

= 72yd^2

PLZZZ MARK ME AS BRAINLIEST:)

The absolute value function for this problem is given as follows:

g(x) = |x - 1| - 2.

An absolute value function of vertex (h,k) is defined as follows:

y = a|x - h| + k.

In which a is the leading coefficient.

The coordinates of the vertex for this problem are given as follows:

(1, -2).

As the slope of the line is of 1, the leading coefficient is given as follows:

a = 1.

Hence the absolute value function for this problem is given as follows:

g(x) = |x - 1| - 2.

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Step-by-step explanation:

this is the hardest I think

Answer:

1) 1/10

2)2/10

3)8/10

Step-by-step explanation:

the numbers 1 and 10 both have 1 in them

Answer:

4

Step-by-step explanation:

10% of 20 is

20÷10=2

20% = 10% × 2

20% = 2×2

20%= 4

Answer:

The answer to your question is 4

Step-by-step explanation:

20% of 20

20/100 ×20(zeroes of 100 will cut off with zeroes of 20's)

2×2= 4

I hope this helps and have a good day!

The null and alternative hypothesis for this test would be:

Symbolically,

H0: p ≥ 0.9

Ha: p < 0.9

where p represents the true population proportion of people who own cats.

To test this hypothesis, we would need to collect a random sample of people and determine the proportion in the sample who own cats. We would then use a one-tailed z-test to determine if the sample proportion is significantly different from the hypothesized proportion of 0.9 at the 0.1 significance level.

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It will take 7 years to double the invested amount if the invested amount is compounded at 10% continuously.

Therefore, it will take 7 years to double the invested amount if the invested amount is compounded at 10% continuously.

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Answer:

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

Each coordinate of the midpoint is the average of endpoints:

Therefore M is (13, 14).

The general solution to the given system of differential equations is:

x₁ = (C₂)\(e^{-3t}\)

x₂ = (C₂)\(e^{-3t}\) - (1/2)(C₂²)\(e^{-6t}\)+ C₁

where C₁ and C₂ are arbitrary constants.

We have the following system of differential equations:

x₁' = x₁ + x₂'

x₂' = 4x₁ + x₂

To decouple this system, we'll aim to isolate one variable in each equation. Let's start by isolating x₂' in the first equation:

x₁' - x₂' = x₁

x₂' = x₁' - x₁

Now, let's substitute this expression for x₂' into the second equation:

x₁' - x₁ = 4x₁ + x₁'

0 = 3x₁ + x₁'

Next, we can rewrite this equation by swapping the positions of the derivatives:

x₁' + 3x₁ = 0

Now we have decoupled the system into two separate equations:

x₂' = x₁' - x₁

x₁' + 3x₁ = 0

To solve the first equation, we can integrate both sides with respect to the independent variable, let's say t:

∫x₂' dt = ∫(x₁' - x₁) dt

x₂ = x₁ - ∫x₁ dt

x₂ = x₁ - ∫x₁ dt = x₁ - ∫x₁ dx₁/dt dt

Now, we integrate with respect to x₁:

x₂ = x₁ - ∫x₁ dx₁

Integrating x₁ with respect to itself yields:

x₂ = x₁ - (1/2)x₁² + C₁

where C₁ is the constant of integration.

Moving on to the second equation, we have a first-order linear homogeneous differential equation:

x₁' + 3x₁ = 0

The general solution to this type of equation can be obtained by integrating factor method. The integrating factor is \(e^{3t}\). Multiplying both sides of the equation by this integrating factor, we get:

\(e^{3t}\)x₁' + 3\(e^{3t}\)x₁ = 0

Now, we can rewrite the left-hand side as the derivative of the product:

(\(e^{3t}\)x₁)' = 0

Integrating both sides with respect to t, we have:

∫(\(e^{3t}\)x₁)' dt = ∫0 dt

\(e^{3t}\)x₁ = C₂

where C₂ is another constant of integration.

Finally, we can solve for x₁:

x₁ = (C₂)\(e^{-3t}\)

Substituting this back into the expression for x₂, we have:

x₂ = (C₂)\(e^{-3t}\)- (1/2)(C₂²)\(e^{-6t}\)+ C₁

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Answer: -2. Bc if you look on the graph of the y axis you'll see its located at -2.

Hope this helps :)

Step-by-step explanation:

Answer:

45 dimes and 75 nickels

Step-by-step explanation:

3 ÷ 8 × 120 = 45

you divide the three by both ratios summed up (8) and then you multiply that by the coins

doing so will you can get 45

and to get the amount of nickels you just subtract 45 from 120 and you get 75

A. 7658.8 hr/year

B. 4.082 hr/year

C. 99206 kwh

Moreover, The annual average wind speed was calculated directly at 4.56 m/s. Using the Weibull distribution, the annual wind speed is 4.55 m/s, while using the Rayleigh distribution it is 4.523 m/s. The annual wind power density was directly calculated to be 114.54 W/m2.

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Answer:

144 in^2

Step-by-step explanation:

Using the A = s^2 and the text says that s= 12in

 the answer is 12 in * 12 in = 144 in^2

A = 10x = 10(12) = 120
Thus, the angle of 10x is 120 degrees.

Suppose you're given a triangle with interior angles A, B, and C. In this case, angle A is 10x, angle B is 2x, and angle C is 3x. According to the Triangle Sum Theorem, the sum of the interior angles in a triangle always adds up to 180 degrees.

Using this theorem, we can create the following equation:

10x + 2x + 3x = 180

Combine the terms on the left side of the equation:

15x = 180

Now, to find the value of x, you'll need to divide both sides of the equation by 15:

x = 12

Now that you have the value of x, you can determine the angle of 10x (angle A) by substituting x into the equation:

A = 10x = 10(12) = 120

Thus, the angle of 10x is 120 degrees.

Remember, this is just an example scenario. To find the angle of 10x in your specific situation, you will need to know more about the problem you're working with, such as the angles of other figures or additional equations.

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Both a square and a rhombus have diagonals that are always perpendicular to each other.

In a square, all sides are equal in length, and all angles are right angles. Since the diagonals of a square bisect each other and each angle is a right angle, the diagonals are perpendicular.

In a rhombus, all sides are equal in length, but the angles are not necessarily right angles. However, the diagonals of a rhombus bisect each other at right angles, making them perpendicular.

So, both a square and a rhombus have diagonals that are always perpendicular to each other.

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The given statement exists true. A matrix is broken down into orthogonal (Q) and upper triangular (R) matrices in a process known as QR decomposition (factorization).

A matrix can be expressed as the union of two distinct matrices, Q and R, using the QR matrix decomposition. R is a square upper/right triangular matrix and Q is an orthogonal matrix. R is also invertible because it is square and doesn't have zeros in its diagonal entries.

A matrix is broken down into orthogonal (Q) and upper triangular (R) matrices in a process known as QR decomposition (factorization). Finding eigenvalues and solving linear least squares problems both use QR factorization.

A = QR. Be aware that the QR-factorization of a rectangular matrix A is sometimes understood with Q square and R rectangular rather than Q rectangular and R square, as with the MATLAB command qr.

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Answer:

60

Step-by-step explanation:

210÷3.5=60

3.5x60=210

Hope this helps!

: )

we find that the numerical approximation using Euler's method gives y(2) ≈ 1.865, while the analytical solution gives y(2) = 2.5.

Using the formula y(n+1) = y(n) + Δx * f(x(n), y(n)), where f(x, y) = x² √y, we can calculate the values of y at each step. Here's the step-by-step calculation:

Step 1: For x = 0, y = 1 (initial condition).

Step 2: For x = 0.2, y = 1 + 0.2 * (0.2)² * √1 = 1.008.

Step 3: For x = 0.4, y = 1.008 + 0.2 * (0.4)² * √1.008 = 1.024.

Step 4: For x = 0.6, y = 1.024 + 0.2 * (0.6)² * √1.024 = 1.052.

Step 5: For x = 0.8, y = 1.052 + 0.2 * (0.8)² * √1.052 = 1.094.

Step 6: For x = 1.0, y = 1.094 + 0.2 * (1.0)² * √1.094 = 1.155.

Step 7: For x = 1.2, y = 1.155 + 0.2 * (1.2)² * √1.155 = 1.238.

Step 8: For x = 1.4, y = 1.238 + 0.2 * (1.4)² * √1.238 = 1.346.

Step 9: For x = 1.6, y = 1.346 + 0.2 * (1.6)² * √1.346 = 1.483.

Step 10: For x = 1.8, y = 1.483 + 0.2 * (1.8)² * √1.483 = 1.654.

Step 11: For x = 2.0, y = 1.654 + 0.2 * (2.0)² * √1.654 = 1.865.

Therefore, using Euler's method with a step size of Δx = 0.2, we approximate y(2) to be 1.865.

To obtain the analytical solution to the ODE, we can separate variables and integrate both sides:

∫(1/√y) dy = ∫x² dx

Integrating both sides gives:

2√y = (1/3)x³ + C

Solving for y:

y = (1/4)(x³ + C)²

Using the initial condition y(0) = 1, we can substitute x = 0 and y = 1 to find the value of C:

1 = (1/4)(0³ + C)²

1 = (1/4)C²

4 = C²

C = ±2

Since C can be either 2 or -2, the general solution to the ODE is:

y = (1/4)(x³ + 2)² or y = (1/4)(x³ - 2)²

Now, let's evaluate y(2) using the analytical solution:

y(2) = (1/4)(2³ + 2)² = (1/4)(8 + 2)² = (1/4)(10)² = 2.5

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Work Shown:

d = 3 = diameter

r = d/2 = 3/2 = 1.5 = radius

h = 12 = height or length of the pipe

pi = 3.14 approximately

V = volume of the cylinder pipe

V = pi*r^2*h

V = 3.14*(1.5)^2*12

V = 84.78

V = 85

The cylindrical pipe's volume is about 85 cubic feet.

The length of the apothem of the regular octagon will be equal to 1.75 cm

The regular octagon is the shape made up of the 8 sides or also the combination of the 8 isosceles triangles connected together side by side.

Here it is given:

Area of the Octagon = \(10.15\ cm^2\)

The side of the octagon=1.45 cm

As we know that the octagon consists of the 8 isosceles triangles so the area of one triangle will be

\(= \dfrac{10.15}{8} =1.27\ cm^2\)

Now the area of the isosceles triangle is given as:

\(A=\dfrac{1}{2} \times h\times b\)

\(1.27=\dfrac{1}{2} \times h\times 1.45\)

\(h=1.75\ cm\)

Thus the length of the apothem of the regular octagon will be equal to 1.75 cm

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Answer:

the answer is b

Step-by-step explanation:

Answer:

3,1 or 1,3

Step-by-step explanation:

see it for figure

Answer:

y= -0.5x + 5.5

Step-by-step explanation: mark this as solved because this is correct

slope = -0.5

intercept = 5.5

Answer:

x=-1

Step-by-step explanation:

the points are both on the line x=-1.

For future reference, use demos graphing calculator and type in the points, you can drag your line through.

Answer:

Diameter Length: ( About ) 5.4 km; Option B

Step-by-step explanation:

~ Let us apply the Area of the Circle formula πr^2, where r ⇒ radius of the circle ~

1. We are given that the area of the circle is 22.9 km^2, so let us substitute that value into the area of the circle formula, solving for r ( radius ) ⇒ 22.9 = π * r^2 ⇒ r^2 = 22.9/π ⇒ r^2 = 7.28929639361.... ⇒

radius = ( About ) 2.7

2. The diameter would thus be 2 times that of the radius by definition, and thus is: 2.7 * 2 ⇒ ( About ) 5.4 km

Diameter Length: ( About ) 5.4 km

The explicit equation of the sequence is an = 3 + (n-1)*6

First term = 3

Second term = 9

A series of numbers in mathematics whose each term is always expressed as a, a+d, a+2d, or a+3d. An arithmetic progression is defined as a + (n-1)d, where a is the first term,d is the common difference of the series and n is the number of terms in the sequence

Any two continuous terms in the arithmetic sequence differ by the same number.

Arithmetic sequence is given by an = a + (n-1)d

So, the common difference = 9-3 = 6

a = 3

Substituting the values in the formula we get:

For nth term: an = 3 + (n-1)*6

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Answer:

19,584

Step-by-step explanation:

36% of 30,600 is 11,016.

30,600 - 11,016 = 19,584