Factorize: x²+2+1/x² ​

On solving the provided question we can say that As a result, the probability of a student P(x < 75) = 75 + (-75 ) =  0 .

Probability is a measure of how likely an event is to occur. It is represented by a number between 0 and 1, with 0 representing a rare event and 1 representing an inescapable event. Switching a fair coin and coin flips has a chance of 0.5 or 50% since there are two equally likely outcomes. (Heads or tails). Probabilistic theory is an area of mathematics that studies random events rather than their attributes. It is applied in many disciplines, including statistics, economics, science, and engineering.

z = (x - μ) / σ

z = (75 - 75) / 10 = 0

That is, a raw score of 75 equates to a z-score of 0.

P(z < 0) = 0.5

As a result, the likelihood of a student scoring less than 75% is 0 or 0%.

So, P(x < 75) = 75 + (-75 ) = 0

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Answer:

1.25b when b < 12 , 1b & then 0.75 b when b > 12

Step-by-step explanation:

* Less than 12 bagels bought, cost $1.25 per bagel

So, price for b bagels, when (b < 12) = 1.25b

* 12 or more than 12 bagels bought, cost $1 upto first 12 bagels & 0.75b on each additional bagel

So, price for b bagels, when (b = 12) = b

So, price for b bagels, when (b > 12) = b + 0.75b' , where b' denotes extra b beyond 12

The inequality used to represent this constraints is:

Price = 1.25b  when b < 12

Price = 0.75b + 3 when b ≥ 12

Inequalities is an expression used to show the non equal comparison of numbers and variables.

Let b represent the number of bagels bought.

When a customer buys fewer than 12 bagels, each one costs $1.25. Hence:

Price = 1.25b  when b < 12

When a customer buys 12 or more bagels, the first 12 bagels cost $1 each and each additional bagel costs $0.75. Hence:

Price = 12 + (b - 12)0.75 = 0.75b + 3 when b ≥ 12

The inequality used to represent this constraints is:

Price = 1.25b  when b < 12

Price = 0.75b + 3 when b ≥ 12

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Answer:

Step-by-step explanation:

a(c + b) = d

c + b = d/a

c = d/a - b

Answer:

97.65

Step-by-step explanation:

97.65

Step-by-step explanation

The probability of rolling a die and getting a 2, then a 5, is 1/36.

To determine the probability of rolling a die and getting a 2, then a 5, we need to multiply the probabilities of each event happening.

First, let's consider the probability of rolling a die and getting a 2. Since there are six equally likely outcomes when rolling a fair six-sided die (numbers 1 to 6), the probability of rolling a 2 is 1/6.

Now, let's consider the probability of rolling a die and getting a 5. Again, there are six equally likely outcomes, so the probability of rolling a 5 is also 1/6.

To find the probability of both events happening, we multiply the probabilities:

Probability of rolling a 2 and then a 5 = (1/6) * (1/6) = 1/36.

Therefore, the probability of rolling a die and getting a 2, then a 5, is 1/36.

It's important to note that each roll of the die is an independent event, meaning that the outcome of one roll does not affect the outcome of the next roll. Therefore, the probability of rolling a 2 and then a 5 remains constant at 1/36 regardless of previous rolls or the order in which they occur.

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Answer:

-4.51500

Step-by-step explanation:

Answer:

-4.515

Step-by-step explanation:

Assuming the "x" is multiplication, 5.8-7.09=-1.29, then 3.5*(-1.29)=-4.515

An inequality to represent the cost of Jason’s food for the party is

An inequality to represent this situation "Jason knows that he will be buying at least 5 packages of hot dogs" is

The two options for buying wings and hot dogs include the following:

In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of packages of hot dogs and number of packages of wings respectively, and then translate the word problem into algebraic equation as follows:

Since one package of wings costs $7 and Hot dogs cost $5 per package, and he must spend no more than $40, a linear inequality which represents this situation is given by;

7x + 5y ≤ 40

Additionally, since Jason knew he would buy at least 5 packages of hot dogs, a linear inequality which represents this situation is given by;

y ≥ 5

Next, we would use an online graphing calculator to plot the above system of linear inequalities as shown in the graph attached below.

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Two stockpots are similar cylinders. The smaller stockpot has a height of 10 inches and a radius of 2.5 inches, the volume of larger one is 628.32 cubic inches.

We know that, to find volume:

Volume = π * \(r^2\) * h

For the smaller stockpot:

Radius (r) = 2.5 inches

Height (h) = 10 inches

Volume = π * (2.5)² * 10 ≈ 196.35 cubic inches

For the larger stockpot:

Radius (r) = 2.5 inches

Height (h) = 16 inches

Volume = π * (2.5)² * 16

             ≈ 628.32 cubic inches

Thus, the volume of larger one is 628.32 cubic inches.

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The total volume of the air space of spherical ball is A = 12.265625 inches³

Given data ,

Since each tennis ball has a diameter of 2.5 inches, the radius of each ball is 1.25 inches.

The air space around the balls can be thought of as a cylinder with a height equal to the diameter of one ball and a radius equal to the radius of one ball.

The height of the cylinder is 2.5 inches, and the radius is 1.25 inches.

The formula for the volume of a cylinder is:

V = πr²h

V = ( 3.14 ) ( 1.25 )² ( 7.5 )

V = 36.796875 inches³

where V is the volume, r is the radius, and h is the height.

So, the volume of the one ball is:

V₁ = ( 4/3 )π(1.25)³

V₁ = 8.177083 inches³

The total volume of three balls is = volume of 3 spherical balls

V₂ = 3V₁ = 3(8.177083) ≈ 24.53125 cubic inches

Therefore, the total volume of the air space around the three tennis balls is approximately A = 36.796875 inches³ - 24.53125 inches³

A = 12.265625 inches³

Hence , the volume of air space is A = 12.265625 inches³

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\(\\ \rm\Rrightarrow \dfrac{2}{x+3}-\dfrac{1}{x-3}=\dfrac{-7}{x^2-9}\)

\(\\ \rm\Rrightarrow \dfrac{2(x-3)-1(x+3)}{(x+3)(x-3)}=\dfrac{-7}{x^2-9}\)

\(\\ \rm\Rrightarrow \dfrac{2x-6-x-3}{x^2-9}=\dfrac{-7}{x^2-9}\)

\(\\ \rm\Rrightarrow \dfrac{x-9}{x^2-9}=\dfrac{-7}{x^2-9}\)

\(\\ \rm\Rrightarrow x-9=-7\)

\(\\ \rm\Rrightarrow x=9-7\)

\(\\ \rm\Rrightarrow x=2\)

Answer:

x = 2

Step-by-step explanation:

\(\large \begin{aligned}\dfrac{2}{x+3}-\dfrac{1}{x-3} & = \dfrac{-7}{x^2-9}\\\\\dfrac{2(x-3)}{(x+3)(x-3)}-\dfrac{1(x+3)}{(x+3)(x-3)} & = \dfrac{-7}{(x+3)(x-3)}\\\\\dfrac{2(x-3)-(x+3)}{(x+3)(x-3)} & = \dfrac{-7}{(x+3)(x-3)}\\\\\dfrac{x-9}{(x+3)(x-3)} & = \dfrac{-7}{(x+3)(x-3)}\\\\x-9 & = -7\\\\x&=-7+9\\\\x & = 2\end{aligned}\)

Answer:

20

Step-by-step explanation:

70% of x = 14
0.7x = 14
x = 14/0.7
x = 20

Answer:

\((\frac{1}{2}+\frac{\sqrt{3}}{2}i)^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

Step-by-step explanation:

Convert 1/2 + i√3/2 to rectangular form

\(\displaystyle z=a+bi=\frac{1}{2}+\frac{\sqrt{3}}{2}i\\\\r=\sqrt{a^2+b^2}=\sqrt{\biggr(\frac{1}{2}\biggr)^2+\biggr(\frac{\sqrt{3}}{2}\biggr)^2}=\sqrt{\frac{1}{4}+\frac{3}{4}}=\sqrt{1}=1\\\\\theta=\tan^{-1}\biggr(\frac{b}{a}\biggr)=\tan^{-1}\biggr(\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}\biggr)=\tan^{-1}(\sqrt{3})=\frac{\pi}{3}\\\\z=\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}\)

Use DeMoivre's Theorem

\(\displaystyle z^n=r^n(\cos(n\theta)+i\sin(n\theta))\\\\z^5=1^5\biggr(\cos\biggr(\frac{5\pi}{3}\biggr)+i\sin\biggr(\frac{5\pi}{3}\biggr)\biggr)\\\\z^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

Answer:

V = 1130.4 cm³

Step-by-step explanation:

Given that V varies jointly with r² and h then the equation relating them is

V = kr²h ← k is the constant of variation

To find k use the condition when r = 3 and h = 5 then V = 141.3 , then

141.3 = k × 3² × 5 = 45k ( divide both sides by 45 )

k = 3.14 ← note approximation for π

V = 3.14r²h ← equation of variation

When r = 6 and h = 10, then

V = 3.14 × 6² × 10 = 3.14 × 36 × 10 = 1130.4 cm³

The only equivalent expression is option (a) \(7^x\).

What is expression ?

An expression in mathematics is a group of symbols that represent a statistical correlation or quantity, such as integers, variables, and operators. It may contain exponents, logarithms, and trigonometric functions in addition to mathematical operations like addition, multiplication, multiplication, and division. It may also contain constants, variables, and functions. Expressions can be used in a variety of subjects, including mathematics, calculus, geometry, and statistics, to represent mathematical models, resolve equations, and carry out calculations.

To find equivalent expressions for\(21^x/3^x\), we can try to simplify the expression using exponent rules.

21 can be factored as 7*3, so we can write:

\(21^x/3^x = (7 × 3)^x/3^x = 7^x × 3^x/3^x = 7^x\)

Therefore, we can see that option (a) 7^x is equivalent to the given expression.

To check the other options:

b) \((7/3)^x\) = \((7^x)/(3^x)\) which is not equivalent to the given expression.

c) \(3^(2x+1)\) can be written as \(3^(2x)\) × \(3^1\) = \((3^2)^x\) × 3 = \(9^x\) × 3 which is not equivalent to the given expression.

d) \(7^(x-1)\) can be written as \(7^x/7\) which is not equivalent to the given expression.

e) \((3/7)^x\) is not equivalent to the given expression.

Therefore, the only equivalent expression is option (a) \(7^x\).

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The complete question is:

Which expressions are equivalent to \(21^x/3^x\)? Check all that apply.

a) \(7^x\)

b) \((7/3)^x\)

c) \(3^(2x+1)\)

d) \(7^(x-1)\)

e) \((3/7)^x\)

We have two functions f and g, defined as:

f(x) = √(5x + 25) - 1

g(x) = x² - 2x - 3

We need to find the points of intersection. These are defined as the values taken by x that make the two functions equal:

f(x) = g(x)

From the definition above:

√(5x + 25) - 1 = x² - 2x - 3

√(5x + 25) = x² - 2x - 2

Now, we take the square on both sides:

5x + 25 = ( x² - 2x - 2 )²

But:

( x² - 2x - 2 )² = x⁴ + 4x² + 4 - 4x³ - 2x² - 2x² + 4x + 4x = x⁴ - 4x³ + 8x + 4

Replacing this:

5x + 25 = x⁴ - 4x³ + 8x + 4

0 = x⁴ - 4x³ + 3x - 21

If we solve the equation, we obtain only two real results:

x1 = -1.6618

x2 = 4.1231

To the nearest tenth:

x1 = -1.7

x2 = 4.1

the counting number just before C5F16 is 3,072.

We will have that it is a function, but not one-to-one. That given that when we operate for x = 0 we will obtain y = 1 and when we operate x = 8 we will also obtain x = 1.

The statement 'A vector b is a linear combination of the columns of a matrix A is and only if the equation Ax = b has at least one solution.' is True.

We first thought of a matrix as a rectangular array of numbers. When the number of rows is m and columns is n, we say that the dimensions of the matrix are m×n.

A vector is most simply thought of as a matrix with a single column. There are two operations we can perform with vectors: scalar multiplication and vector addition. Both of these operations have geometric meaning.

Given a set of vectors and a set of scalars we call weights, we can create a linear combination using scalar multiplication and vector addition.

The product of two matrices can be seen as the result of taking linear combinations of their rows and columns. This way of interpreting matrix multiplication often helps to understand important results in matrix algebra.

The statement 'A vector b is a linear combination of the columns of a matrix A is and only if the equation Ax = b has at least one solution.' is True.

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Answer:

The mean of the sampling distribution of sample means is equal to the population mean, which is 5.3 years.

give thanks for more! your welcome!

Step-by-step explanation:

Answer:

$20.52

Step-by-step explanation:

19 × 8% = 1.52

1.52 + 19 = $20.52

Answer:

We conclude that an equation in the point-slope form will be:

y+5 = -2/5 (x+3)

Hence, option A is true.

Step-by-step explanation:

We know that the point-slope form of the line equation is

\(y-y_1=m\left(x-x_1\right)\)

where m is the slope of the line and (x₁, y₁) is the point

Given

substituting the values m = -2/5 and the point (-3, -5) in the point-slope form of the line equation

\(y-y_1=m\left(x-x_1\right)\)

y - (-5) = -2/5 (x-(-3))

y+5 = -2/5 (x+3)

Therefore, we conclude that an equation in the point-slope form will be:

y+5 = -2/5 (x+3)

Hence, option A is true.

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

Work Shown:

Before we can use derivatives, we need to find the value of s when (x,y) = (15,20)

s^2 = x^2+y^2

s^2 = 15^2+20^2

s^2 = 225+400

s^2 = 625

s = sqrt(625)

s = 25

-----------

Now we can apply the derivative to both sides to get the following.  Don't forget to use the chain rule.

s^2 = x^2 + y^2

d/dt[s^2] = d/dt[x^2 + y^2]

d/dt[s^2] = d/dt[x^2] + d/dt[y^2]

2s*ds/dt = 2x*dx/dt + 2y*dy/dt

2(25)*ds/dt = 2(15)*5 + 2(20)*(10)

50*ds/dt = 150 + 400

50*ds/dt = 550

ds/dt = 550/50

ds/dt = 11

-----------

Side note: The information t = 40 is never used. It's just extra info.

If Natalie puts 4 pears in each bag, she will be able to sell a total of 12 bags of pears at the Saturday market.

To represent the number of bags of pears, b, that Natalie sells at the Saturday market, we can use the following equation:

b = total_number_of_pears / pears_per_bag

In this equation, "total_number_of_pears" represents the total quantity of pears Natalie has, and "pears_per_bag" represents the number of pears she puts in each bag.

Given that Natalie has a total of 48 pears, we can substitute the value into the equation:

b = 48 / pears_per_bag

Now, we need to determine the number of pears she puts in each bag. The information provided states that Natalie sells bags of pears, and each bag is sold for $5. However, the specific number of pears per bag is not given. To proceed, we need this information.

Let's assume that Natalie puts 4 pears in each bag. We can substitute this value into the equation:

b = 48 / 4

Simplifying the equation gives:

b = 12

So, if Natalie puts 4 pears in each bag, she will be able to sell a total of 12 bags of pears at the Saturday market.

It's important to note that the specific value of "pears_per_bag" will affect the final result. If Natalie puts a different number of pears in each bag, the equation will yield a different number of bags sold.

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Answer:

its C

Step-by-step explanation:

i just did it on edge and plus its really not cool to post answers when you dont actually know the answer bc people that actually want to help cant bc there only two answers allowed per question. so please dont answer if your not trying to help.  

The geometric series \(\sum_{n=1}^{\infty} 5(-1)^{n-1}\) converges to zero.

A mathematical term denoting an endless series of the form

a + ar + ar² + ar³ + ⋯, where r is referred to as the common ratio. The geometric series for a = 1 and r = 1/2, or 1 + 1/2 + 1/4 + 1/8 +, is a straightforward example.

A series is considered to be convergent if the partial sums gravitate to a certain value, also known as a limit.

In contrast, a divergent series is one whose partial sums do not reach a limit. The Divergent series usually approaches infinity.

From the given options let us try with \(\sum_{n=1}^{\infty} 5(-1)^{n-1}\).

\(= 5\sum_{n=1}^{\infty} (-1)^{n-1}.\)

\(= 5\sum_{n=1}^{\infty} (-1)^{n}.\frac{1}{-1}\).

\(= -5\sum_{n=1}^{\infty} (-1)^{n}.\)

= - 5[- 1 + 1 - 1 + 1 ...+ 1].

= - 5[0].

= 0.

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Answer:

\(x=\frac{z-y}{2y}\)

Step-by-step explanation: