Solve each equation.
1.) 12b+9=12b+11
2.) 6y-8=2(3y-4)
3.) -3k+4=-2-6k

The probability of getting exactly 3 successes (p(x)) in 5 independent trials, each with a probability of success (p) of 0.3, is approximately 0.1323, or 13.23%.

To find the probability of getting exactly x successes (p(x)) in n independent trials, each with a probability of success (p) using the binomial probability formula, we can follow these steps:

Step 1: Identify the values:

n = 5 (number of trials)

x = 3 (number of successes)

p = 0.3 (probability of success on a given trial)

Step 2: Apply the binomial probability formula:

The binomial probability formula is given by:

p(x) = (nCx) * (p^x) * ((1 - p)^(n - x))

Step 3: Calculate the values:

nCx represents the number of ways to choose x successes from n trials and can be calculated using the combination formula:

nCx = n! / (x! * (n - x)!)

In our case, n = 5 and x = 3, so:

nC3 = 5! / (3! * (5 - 3)!)

= 5! / (3! * 2!)

= (5 * 4 * 3!) / (3! * 2 * 1)

= (5 * 4) / (2 * 1)

= 10

Now we can substitute the values into the binomial probability formula:

p(3) = (10) * (0.3^3) * ((1 - 0.3)^(5 - 3))

= 10 * (0.3^3) * (0.7^2)

= 10 * (0.027) * (0.49)

= 0.1323

Step 4: Final Answer:

Therefore, the probability of getting exactly 3 successes (p(x)) in 5 independent trials, each with a probability of success of 0.3, is 0.1323, or approximately 13.23%.

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The value of a = -2 and b = 3.

What is a system of equations?

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.

Here, we have

Given: 3a - 5b = -26, a + 2b = 6

We have to solve this equation.

3a - 5b = -26...(1)

a + 2b = 6...(2)

Now we multiply equation (1) by 2 and equation (2) by 5 and we get

6a - 10b = -52....(3)

5a + 10b = 30....(4)

After solving equations (3) and (4), we get

11a = -22

a = -2

Now we put the value of 'a' in equation(3) and we get

6(-2) - 10b = -52

-10b = -52 + 12

-10b =  -30

b = 3

Hence, the value of a = -2 and b = 3.

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Every quadratic nonresidue of p is a primitive root of p, when p = 2^k + 1 is primeIf p = 2^k + 1 is a prime number, we want to show that every quadratic nonresidue of p is a primitive root of p.

In other words, we aim to prove that if an element x is a quadratic nonresidue modulo p, then it is also a primitive root of p.

Let's assume p = 2^k + 1 is a prime number. To prove that every quadratic nonresidue of p is a primitive root of p, we can use the properties of quadratic residues and quadratic nonresidues.

A quadratic residue modulo p is an element y such that y^((p-1)/2) ≡ 1 (mod p), while a quadratic nonresidue is an element x such that x^((p-1)/2) ≡ -1 (mod p).

Now, let's consider an element x that is a quadratic nonresidue modulo p. We want to show that x is a primitive root of p.

Since x is a quadratic nonresidue, we know that x^((p-1)/2) ≡ -1 (mod p). By Euler's criterion, this implies that x^((p-1)/2) ≡ -1^((p-1)/2) ≡ -1^2 ≡ 1 (mod p).

Since x^((p-1)/2) ≡ 1 (mod p), we can conclude that the order of x modulo p is at least (p-1)/2. However, since p = 2^k + 1 is a prime, the order of x modulo p must be equal to (p-1)/2.

By definition, a primitive root of p has an order of (p-1). Since the order of x modulo p is (p-1)/2, it follows that x is a primitive root of p.

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Answer:

Step-by-step explanation:

(x,y)→(11.2x,11.2y)

Answer:

2,6 and 10 respectfully for the out put 1,3 and 5.

Step-by-step explanation:

•2/2=1

•6/2=3

•10/2=5

Answer:

x=4 i did math

Step-by-step explanation:

Using the given average cost, standard deviation, and assuming a normal distribution, we can determine the probability that the cost for a randomly selected college is more than a certain value.

The average cost of tuition and fees at private nonprofit four-year colleges is $26,640 per year, with a standard deviation of $6,617. Assuming a normal distribution, let x represent the cost for a randomly selected college.
To find the probability that x is more than a certain value, we can use the Z-score formula: Z = (x - mean) / standard deviation.
To find the probability that x is more than a certain value, we can use the Z-score formula: Z = (x - mean) / standard deviation.
Let's say we want to find the probability that x is more than $30,000.
Z = (30000 - 26640) / 6617
Z = 0.051
Using a Z-table or calculator, we can find the corresponding probability to be approximately 0.4801. This means that there is a 48.01% chance that the cost for a randomly selected college is more than $30,000.
In conclusion, using the given average cost, standard deviation, and assuming a normal distribution, we can determine the probability that the cost for a randomly selected college is more than a certain value.

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Given the expression: (3.2+0.2)2+12​

To get the value of the expression, do the following:

1. add 3.2 and 0.2

2. multiply 3.4 by 2

3. add 6.8 and 12

So, the value of the expression = 18.8

Answer:

Its in my explanation

Step-by-step explanation:

The math is simple and it will only take a few seconds to figure out. Just take your desired millionaire age (when you want to have saved $1 million) and subtract your current age. So, if you want to reach $1 million at age 65 and you're currently 30, you have 35 years to save.

Answer:

2*12x-5

Step-by-step explanation:

In geometry, a vertex form is a point where two or more curves, lines, or edges meet. As a consequence of this definition, the point where two lines meet to form an angle and the corners of polygons and polyhedra are vertices. For example, a square has four corners, each is called a vertex.

1. I beleive it would be 187,5$, 75.00 + 150% = 187,5.

2. if rounding it would be 9.1$ she had to pay for one times 3 would be 27.3 for three boxes.

3. Not sure what this question is asking but I'll try my best so here: 27.3 +9% × 3 = 89.271 rounded would be 90$

4. 90$ if I did that correctly

5. 1.38 - 1.25 = 0.13 which I beleive would be 13%

0.13 as a percent woudl be 13%

The total area filled by a flat (2-D) surface or an object's form is referred to as the area and the required area of the metal frame is 93.76x² unit square.

The area is the total area occupied by a flat (2-D) surface or the form of an object.

Create a square on paper by using a pencil.

Two dimensions make it up.

A form's area on paper is the space it takes up.

So, given, a square metal frame encircles a circular mirror.

The mirror has a 4x radius.

The metal frame's side length is 12x.

According to the basic formula for the area of a circle and a square:

area of a circle = pi * radius * radius

Square Area = Side * Side

In the given situation:

Mirror's Area = pi * 4x * 4x = pi * 16x² = 50.24x

Squared mirror's Area = 12x * 12x = 144x²

The area of the metal frame is the sum of the areas of the squared and round mirrors.

Metal frame area =   144x² -  50.24x²

Metal frame size = 93.76x²

Therefore, the total area filled by a flat (2-D) surface or an object's form is referred to as the area and the required area of the metal frame is 93.76x² unit square.

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Correct question:

A circular mirror is surrounded by a square metal frame. The radius of the mirror is 4x. The side length of the metal frame is 12x. What is the area of the metal​ frame?

Answer:

Subtract 4, addition property of equality

Step-by-step explanation:

Answer:

1) Subtract 4

2) Subtraction

3) Equality

Answer:

My friend didn't factorise the x in 4xy out.

Step-by-step explanation:

15x-20xy= 5x(3-4y)

The magnetic potential U at a point on the axis of a circular coil is U = A / r (2/3).

To compute the magnetic potential U at a point on the axis of a circular coil, we can use the given formula:

u = Ar dx/ (r²+ x²)\(^(3/2)\)

where A, r, and x are constants. To perform the integration, we can use the substitution x = r tan θ. This gives:

dx = r sec²θ dθ

r²+ x²= r² + r² tan²θ = r² sec² θ

(r²+ x²)\(^(3/2)\) = (r² sec²θ)\(^(3/2)\)= r³ sec³θ

Substituting these expressions into the formula for u, we get:

u = Ar dx/ (r² + x²)\(^(3/2)\)

= Ar r sec²θ dθ / (r²sec² θ)\(^(3/2)\)

= A / r (cos θ)³dθ

Integrating this expression with respect to θ from 0 to π/2 gives:

U = ∫u dθ from 0 to π/2

= A / r ∫cos³θ dθ from 0 to π/2

To evaluate this integral, we can use the reduction formula:

∫cos\(^n\) θ dθ = (1/n) cos\(^(n-1)\) θ sin θ + ((n-1)/n) ∫cos\(^(n-2)\) θ dθ

Applying this formula with n = 3 gives:

∫cos³θ dθ = (1/3) cos²θ sin θ + (2/3) ∫cos θ dθ

= (1/3) cos²θ sin θ + (2/3) sin θ

Substituting this back into the expression for U and evaluating it gives:

U = A / r ∫cos³θ dθ from 0 to π/2

= A / r [(1/3) cos²θ sin θ + (2/3) sin θ] from 0 to π/2

= A / r (2/3)

Therefore, the magnetic potential U at a point on the axis of a circular coil is U = A / r (2/3).

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Answer:

x= 100

Step-by-step explanation:

x/5 = 20

multiply both the sides by 5 we get

5× x/5 = 20×5

x = 100

Using the substitution method and the given information, we can evaluate ∫50f(5x)dx as 4.

We can use the substitution method to evaluate the integral ∫50f(5x)dx. Let u = 5x, then du/dx = 5 and dx = du/5. Substituting these expressions into the integral, we get:

∫50f(5x)dx = ∫10f(u) du/5

Next, we can apply the constant multiple rule for integrals, which states that ∫a kf(x)dx = k ∫a f(x)dx for any constant k. Using this rule, we can move the constant factor 1/5 outside the integral:

∫50f(5x)dx = (1/5) ∫10f(u) du

Now, we can use the given information that ∫250f(x)dx = 20 to find a relationship between ∫10f(u) du and ∫250f(x)dx. Substituting u = 5x into the bounds of integration, we get:

∫50f(5x)dx = (1/5) ∫250f(u) du, evaluated from u = 50 to u = 250

Using the Fundamental Theorem of Calculus, we can evaluate the definite integral ∫250f(u) du as follows:

∫250f(u) du = F(250) - F(50)

where F(x) is an antiderivative of f(x). Since f(x) is continuous, it has an antiderivative F(x). We are given that ∫250f(x)dx = 20, so we can write:

F(250) - F(50) = ∫250f(x)dx = 20

Simplifying, we get:

F(250) = F(50) + 20

Now we can substitute this relationship back into our expression for ∫50f(5x)dx:

∫50f(5x)dx = (1/5) ∫250f(u) du, evaluated from u = 50 to u = 250
              = (1/5) [F(250) - F(50)]
              = (1/5) [F(50) + 20 - F(50)]
              = 4

Therefore, we have found that:

∫50f(5x)dx = 4

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Answer:

30

Step-by-step explanation:

10+10+20+40+70=150

150/5=30

hope this helps!

Answer:

ok so find the average first we have to add up

10+10=20

20+40=60

70+20=90

90+60=150

then we have to divide by the number so 5 since their is 5 number in the date set

150/5=30

30

Hope This Helps!!!

The volume of the cylindrical Pringles chip can is 1508 cm³

From the question, we are to determine the volume of cylindrical can

The volume of a cylinder is given by the formula

V = πr²h

Where V is the volume of the cylinder

r is the radius

and h is the height

From the given information,

Diameter = 8 cm

But,

Radius = Diameter / 2

Therefore,  

r = 8 / 2 = 4cm

h = 30 cm

Thus,

Volume of the cylindrical can = π× 4² × 30

Volume of the cylindrical can = π× 16 × 30

Volume of the cylindrical can = 480π cm³

Volume of the cylindrical can = 1507.96447 cm³

Volume of the cylindrical can ≈ 1508 cm³

Hence,

The volume is 1508 cm³

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Answer: it would be the fourth one with the line going straight across the top

Step-by-step explanation: To use the vertical line test, take a ruler or other straight edge and draw a line parallel to the y-axis for any chosen value of x.

If the vertical line you drew intersects the graph more than once for any value of x then the graph is not the graph of a function.

The fourth graph represents a function as per the vertical line test.

To determine the function:

Simply draw a vertical line through the graph to find the number of times the function's graph is intersected by the vertical line to determine this.

The graph is said to represent a function if the vertical line only crosses it once at any given location on the graph.

A function is a relationship between a number of inputs and outputs. A function is an association of inputs where each input is coupled with exactly one output.

There is a range, co-domain, and domain for every function.

As per the given graphs,

the first three graphs do not represent a function.

only the fourth graph represents a function.

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If a jar contains 15 red marbles and 14 blue marbles. If you reach in the jar and pull out 2 marbles at random, the probability that both are red is: 2/812.

Probability

Total marbles:

Total marbles=15+14

Total marbles = 29

Chance that a red will be pulled=2/29

Chance that the second marble will be red =1/28

Hence,

Probability :

Probability = 2/29*1/28

Probability = 0.00246

Therefore  If a jar contains 15 red marbles and 14 blue marbles. If you reach in the jar and pull out 2 marbles at random, the probability that both are red is: 2/812

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Answer:

c) 15

Step-by-step explanation:

Plugging in the value of x as 15 in the equation,

15-3 which is equal to 12

Answer:

The slopes of the sides of the square ABCD are -1/3 and 3

Step-by-step explanation:

The coordinates of the vertices are;

A(-2, 5) and B(4, 3), therefore, we have;

The slope of segment AB, m, is given  as follows;

\(Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\)

Where, (x₁, y₁) = (-2, 5) and (x₂, y₂) = (4, 3), we have;

\(Slope, m \ of \ line \ AB, \ m_{AB}=\dfrac{3-5}{4-(-2)} = \dfrac{-2}{6} = -\dfrac{1}{3}\)

Therefore, given that the adjacent sides of a square are perpendicular, we have;

The slope of a line perpendicular to another line with slope, m is equal to the negative inverse of the slope of the line

Therefore, the given that the slope of a line = m, the slope of the perpendicular = -1/m

Therefore;

\(The \ slope \ of \ the \ perpendicular \ to \ the \ line \ AB = -\dfrac{1}{The \ slope \ of \ the \ line \ AB }\)

\(The \ slope \ of \ the \ perpendicular \ to \ the \ line \ AB = -\dfrac{1}{-\dfrac{1}{3} } = 3\)

Given that the one other side is parallel to the line AB, whereby the slope of parallel lines are equal, and that two sides are perpendicular to the line AB, we have, the slopes of the sides of the square ABCD are;

-1/3 and 3.

Answer:

28

Step-by-step explanation:

sry if I'm wrong although I used calculator

Call x the number of burgers in a Crave Case.

Mr. Thomas has 5x+5 burgers

Mr. Garcia has 3x + 15 burgers

We're told they're equal,

5x + 5 = 3x + 15

That's the answer to the first part:   5x + 5 = 3x + 15

2x = 10

x = 5

Answer: 5 burgers per Crave Case

Answer:

eegdujbslspm

Step-by-step explanation:

siuodby s9isbnp' udjauoeawkjshdguibdewnduewhsuidknfuk yeosjuwdi nldijs aidbskbodbshbbdpoopne f

The divergence of the gradient of a scalar function is always zero.

The gradient of a scalar function represents the rate of change of that function in different directions. The divergence of a vector field measures the spread or convergence of the vector field at a given point.

When we take the gradient of a scalar function and then calculate its divergence, we are essentially measuring how much the vector field formed by the gradient vectors is spreading or converging. However, since the gradient of a scalar function is a conservative vector field, meaning it can be expressed as the gradient of a potential function, its divergence is always zero.

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Answer: - 84/3

Step-by-step explanation: hope this helps!

Answer:

-83/4

Step-by-step explanation:

Cause

Answer: 6

Step-by-step explanation:

I need point

Answer:

3#6#8#9%8$%8&jlebsiei lebsosbe he is yes