A legal document contains pages numbered 1 through 50. What is the probability that the lawyer will flip to a page number that is not a multiple of 4

Answer:

P(draw 4) = 1/6

Step-by-step explanation:

Six cards means: n(s) = 6

Since the value of the discriminant (-19) < 0, no real solution(s)/root(s) exist for the equation. Thus, we can choose the first option:

"Zero, because the discriminant is negative".

A quadratic equation is a polynomial of degree 2, in a single variable x.

The standard form of a quadratic equation is ax² + bx + c = 0.

The quadratic formula is used to find the solution(s)/root(s) of this equation.

The quadratic formula is:

[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]

In this formula, [tex]b^2-4ac[/tex] is called the discriminant (D).

The solution(s)/root(s) of the equation, depends on this discriminant value as follows:

In the question, we are given that the simplest form of Quincy's equation in the radical form was,

[tex]x = \frac{-3 \pm \sqrt{-19} }{2}[/tex].

Comparing this to the quadratic formula,

[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]

we get the discriminant (D) = -19.

Since the value of the discriminant (-19) < 0, no real solution(s)/root(s) exist for the equation. Thus, we can choose the first option:

"Zero, because the discriminant is negative".

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For complete question, refer to the attachment.

Answer:

He can type 90 words in 3 minutes.

Step-by-step explanation:

We know how many words he can type per minute already. So now, to find how many words he can type in 30 minutes, simply multiply 3 by 30.

[tex]3 \times 30=90[/tex]

So 90 is our answer.

Answer:

8

Step-by-step explanation:

51 + 4x + 7 = 90 - combine like terms

58 + 4x = 90 - subtract 58 from each side

4x = 32 - divide both sides by 4

x = 8

Answer:

x = 8

Step-by-step explanation:

The red square indicates that there is a right triangle. All right triangles have angles equal to 90°. Therefore, we can find the value of "x" by setting the sum of both the interior angles to 90°.

(4x + 7) + 51° = 90°                                  <----- Sum of both angles is 90°

4x + 58 = 90°                                          <----- Combine 58 and 7

4x = 32                                                    <----- Subtract 58 from both sides

x = 8                                                        <----- Divide both sides by 4

Using the given property, we conclude that:

f(4) = 8

We know that our function has the property:

5*f(x) = f(5*x)

Now, we also know that:

f(20) = 40

Notice that we can rewrite:

f(20) = f(5*4)

Using the above property, we know that:

f(20) = f(5*4) = 5*f(4) = 40

Using the last part:

5*f(4) = 40

f(4) = 40/5 = 8

f(4) = 8

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Discriminant for the quadratic equation  [tex]2x^2+x-3=0[/tex] is [tex]d=25[/tex]

How to find the d Discriminant of the quadratic equation ?

We know that the standard quadratic equation

[tex]ax^2+bx+c=0[/tex]

Discriminant of the equation is [tex]d=b^2-4ac[/tex]

Equation given in the question is

[tex]2x^2+x-3=0[/tex]

So we can find the values of [tex]a,b,c[/tex]

[tex]a=2\\b=1\\c=-3[/tex]

Substitute the values

[tex]d=1^2-4*2*(-3)\\d=1+24\\d=25[/tex]

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Due to length restrictions, we cannot summarize the results of the three parts about the quadratic equations of the form x² + b · x + c = 0. We kindly invite to check the explanation for further details.

In this question we have several exercises with quadratic equations of the form x² + b · x + c = 0 and, to be more exactly, quadratic equations with the following characteristics:

x² - (r₁ + r₂) · x + r₁ · r₂ = 0      (1)

Please notice that the first grade coefficient is equal to the inverse of the sum of the two roots and the zero grade coefficient is the product of the two coefficients.

Now we proceed to resolve all the points:

Part I

a) (x + 17) · (x + 1) = x² + 18 · x + 18, r₁ = - 17, r₂ = - 1

b) (x + 5) · (x + 4) = x² + 9 · x + 20, r₁ = - 5, r₂ = - 4

c) (x - 11) · (x - 1) = x² - 12 · x + 11, r₁ = 11, r₂ = 1

d) (x - 18) · (x - 2) = x² - 20 · x + 36, r₁ = 18, r₂ = 2

Part II

a) x² - 12 · x + 27

b) (x + 4) · (x + 8)

c) (x - 5) · (x - 7)

d) (x - 4) · (x - 5)

Part III

a) (x - 18) · (x + 3) = x² - 15 · x - 54

b) (x + 18) · (x + 3) = x² + 21 · x + 54

c) (x + 18) · (x - 3) = x² + 15 · x - 54

d) (x - 18) · (x - 3) = x² - 21 · x + 54

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The end behavior of the given function (range) is x< 4 or x > 4. So, f(x) < 4 or f(x) > 4. The solution in interval notation is [tex]\mathbf{(-\infty, 4) \cup (4, \infty)}[/tex].

The last option is correct.

The end behavior of the given function f(x) = (8x+1)/2x-9 wants us to identify the range of the given function.

The range is the set of values of the dependent variable for which a function is defined. The function range is the combined domain of the inverse function.

From the information given:

[tex]\mathbf{f(x) = \dfrac{8x +1}{2x -9 }}[/tex]

Inverse of [tex]\mathbf{\dfrac{8x +1}{2x -9 }}[/tex] becomes [tex]\mathbf{f(x) = \dfrac{1+9x}{2(-4+x) }}[/tex]

The domain of the inverse is x< 4 or x > 4. So, f(x) < 4 or f(x) > 4. Now, representing the solution in interval notation, we have:

[tex]\mathbf{(-\infty, 4) \cup (4, \infty)}[/tex]

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Answer:

A

Step-by-step explanation:

[tex]\cos \theta=\frac{3}{8} \\ \\ \theta=\cos^{-1} \left(\frac{3}{8} \right) \\ \\ \theta \approx 68^{\circ}[/tex]

Answer:

x = -0.01685

(Is the equation written correctly?  This feels like a very unfortunate number)

Step-by-step explanation:

(2x+5/60-95x-3/30=3/2

2x+(5/60)-95x-(3/30)=3/2

2*(2x+(5/60)-95x-(3/30))=3     [Multiply both sides by 2]

4x+(10/60)-190x-(6/30))=3      

(2/30)-186x-(6/30))=3              [Simplify]

-186x-(4/30)=3

-186x=3+(4/30)

-186x=(90/30)+(4/30)

x = (94/30)/(-186)

x = -0.01685

Answer:

y < x

y < 4

Step-by-step explanation:

Dotted line means < or >, and since the shaded region is below the lines y = 4 and y = x, the answer is A.

Answer:

Greetings !

check the attachment above☝️ but i haven't done the second question wait a moment. thx

Answer: Circle lines

Step-by-step explanation:

Hopefully the attached image helps, it is a diagram of all the labeled lines on a circle excluding the radius (BG or GE)

3 is the square root of nine.

The square root of a number is the factor that we can multiply by itself to get that number. The symbol for square root is \sqrt{ } ​square root of, end square root . Finding the square root of a number is the opposite of squaring a number.

To find the fraction square root, first, find the square root of the numerator and then find the square root of denominator. After finding the square root values, simplify the fraction. For example, √(4/16), can be written as √4/√16.

(3)^2 = 9

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Answer:

31.

Step-by-step explanation:

We have the equation:

(2x - 17) / 3 = 15     where x is the number to be found.

Multiply both sides by 3:

2x - 17 = 45

2x = 45 + 17 = 62

x = 31.

The fill up of the missing points are:

Using the image attached, one can see that m<1 and m<2 creates a kind of  linear pair hence one can say they are both supplementary using the law of LINEAR POSTULATE THEOREM.

Based on the fact that the supplementary angles add up to 180 degrees, therefore:

m<1 + m<2 = 180   - will be equation 1

Since the interior angles m<2 and m<3 are known to be equal based on the CONGRUENCE POSTULATE THEOREM. Therefore

m<2 = m<3 ---  will be equation 2

Then place eqn. 2 into eqn. 2

m <1 + m <3 = 180

This connote that m<1 and m<3 are supplementary.

Hence, The fill up of the missing points are:

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The equation that represents the relation is y = 8 - 0.5x

The given parameters are:

Start = 8m

Rate = 1/2 m/s

The linear equation that represents the submarine movement is:

y = Start - Rate * x

This gives

y = 8 - 1/2 * x

Evaluate

y = 8 - 0.5x

Hence, the equation that represents the relation is y = 8 - 0.5x

See attachment for the graph

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The justification used is multiplicative property of equality because both sides are multiplied by the same value

Given the expression below

-1/3(4x^2 - 3) - 3 = 5x^2 - 2

We are to determine the justification by Anne to get the step 2 as shown

(4x^2 - 3) - 3 = -3(5x^2 - 2)

Expand

(4x^2 - 3) - 3 = -15x^2 + 6

Hence the justification used is multiplicative property of equality because both sides are multiplied by the same value

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Answer:

Step-by-step explanation:

(7x-3)(12x-7)

we are solving for x and we are multiplying.

we start with the x's 7x*12x=  84x

-3*-7=21

so now we have

84x+21=0

the 0 is a placer for answering the question

we minus 21 to both sides

84x=-21

now we divide

84/-21= -4

x=-4

The linear regression equation that models the cost of a flight in function of the distance traveled is given as follows:

C(m) = 0.08316m + 31.36331

To find the equation, we need to insert the points (x,y) in the calculator.

For this problem, the points (x,y) are given as follows:

(225, 50.3), (1100, 111), (1375, 143), (1675, 187), (1950, 214), (2250, 196).

Hence, inserting these points in the calculator, the linear regression equation that models the cost of a flight in function of the distance traveled is given as follows:

C(m) = 0.08316m + 31.36331

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Answer:

answer is 6^2 × 6^2 = squate root 72

distance equals 8.485

Answer:

6[tex]\sqrt{2}[/tex] ≈ 8.49 units

Step-by-step explanation:

calculate the distance d using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (2, - 3 ) and (x₂, y₂ ) = ( 8, - 9 )

d = [tex]\sqrt{(8-2)^2+(-9-(-3))^2}[/tex]

   = [tex]\sqrt{6^2+(-9+3)^2}[/tex]

   = [tex]\sqrt{36+(-6)^2}[/tex]

   = [tex]\sqrt{36+36}[/tex]

    = [tex]\sqrt{72}[/tex]

    = [tex]\sqrt{36(2)}[/tex]

     = [tex]\sqrt{36}[/tex] × [tex]\sqrt{2}[/tex]

     = 6[tex]\sqrt{2}[/tex] units ← exact length

     ≈ 8.49 units ( to 2 dec. places )

The explicit formula for the sequence is an = 14-6(n-1)

This are sequence that has. a common difference that is the difference between the preceding and sthe explicit formula for the sequence is an = 14-6(n-1) is equal.

Given the following

a1 = 14

an = an-1 - 6

The nth term of the sequence is expressed as:

An = a+(n-1)d

an = 14+(n-1)(-6)

an = 14 -6n + 6

an = 14-6(n-1)

Hence the explicit formula for the sequence is an = 14-6(n-1)

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Answer:

Step-by-step explanation:

[tex]52 = - 5x - 3i...given \: expression \\ - 5x - 3i = 52...switch \: sides \\ - 5x - 3i + 3i = 52 + 3i...add \: 3i \: to \: both \: sides \\ - 5x = 52 + 3i...simplify \\ \frac{ - 5x}{ - 5} = \frac{52}{ - 5} + \frac{3i}{ - 5} ...divide \: both \: sides \: by \: - 5 \\ x = \frac{ - 52}{5} - i \frac{3}{5} ...simplified[/tex]

The function that models the independent variable, x, in terms of y, is:

[tex]x = ln(\frac{y}{2.56})/ln(1.04)[/tex]

Here we have the relation:

[tex]y = 2.56*(1.04)^x[/tex]

We want to write x in terms of y, so we just need to isolate x.

We have:

[tex]\frac{y}{2.56} = (1.04)^x[/tex]

Now we can apply the natural logarithm in both sides, so we get:

[tex]ln(\frac{y}{2.56}) = ln((1.04)^x)\\\\ln(\frac{y}{2.56}) = ln((1.04))*x[/tex]

Now we can just isolate x.

[tex]x = ln(\frac{y}{2.56})/ln(1.04)[/tex]

That is the function that models the independent variable, x, in terms of y.

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Answer:171x+8

Step-by-step explanation:

3x^3+12x^2x+8

=27x+144x+8

=171x+8

Taking into account definition of probability, the probability of those who like both is 0.07 or 7%.

Probability is the greater or lesser possibility that a certain event will occur.

In other words, the probability is the possibility that a phenomenon or an event will happen, given certain circumstances. It is expressed as a percentage.

The union of events, AUB, is the event formed by all the elements of A and B. That is, the event AUB is verified when one of the two, A or B, or both occurs. AUB is read as "A or B".

The probability of the union of two compatible events is calculated as the sum of their probabilities subtracting the probability of their intersection:

P(A∪B)= P(A) + P(B) -P(A∩B)

where the intersection of events, A∩B, is the event formed by all the elements that are, at the same time, from A and B. That is, the event A∩B is verified when A and B occur simultaneously.

A complementary event, also called an opposite event, is made up of the inverse of the results of another event. That is, That is, given an event A, a complementary event is verified as long as the event A is not verified.

The probability of occurrence of the complementary event A' will be 1 minus the probability of occurrence of A:

P(A´)= 1- P(A)

In first place, let's define the following events:

Then you know:

In this case, considering the definition of union of events, the probability that a chef likes carrots and broccoli is calculated from:

P(C∪B)= P(C) + P(B) -P(C∩B)

Then, the probability that a chef likes carrots and broccoli is calculated as:

P(C∩B)= P(C) + P(B) -P(C∪B)

In this case, considering the definition of the complementary event and its probability, the probability that a chef likes NEITHER of carrots and broccoli is calculated as:

P [(C∪B)']= 1- P(C∪B)

In this case, the probability of those who like neither is 0.22

0.22= 1 - P(C∪B)

Solving

0.22 - 1= - P(C∪B)

-0.78= - P(C∪B)

- (-0.78)= P(C∪B)

0.78= P(C∪B)

Now, remembering that P(C∩B)= P(C) + P(B) -P(C∪B), you get:

P(C∩B)= 0.13 + 0.72 -0.78

Solving:

P(C∩B)= 0.07=  7%

Finally, the probability of those who like both is 0.07 or 7%.

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The trigonometric values are:

[tex]cos(\frac{3\pi}{4})=\frac{1}{\sqrt{2} } \\\\sin(\frac{3\pi}{4})=\frac{1}{\sqrt{2} }[/tex]

The given trigonometric identities are:

[tex]cos(\frac{3\pi}{4} )\\\\sin(\frac{3\pi}{4})[/tex]

Note that:

[tex]\pi=180^o\\\\\frac{3\pi}{4}=135^0[/tex]

Therefore, using the calculator for the given expressions:

[tex]cos(\frac{3\pi}{4})=cos135^0=\frac{1}{\sqrt{2} } \\\\sin(\frac{3\pi}{4})=sin135^0=\frac{1}{\sqrt{2} }[/tex]

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Answers:

i) [tex]\sf (x + 2)(x+ 3)[/tex]

ii) [tex]\sf \left(3x+1\right)\left(3x+2\right)\left(9x^2+9x-16\right)[/tex]

Factorize expression's:

i.

[tex]\sf (x + 1)^2 + 3(x + 1) + 2[/tex]

apply perfect square and distributive method

[tex]\sf (x^2 + 2(x)(1) + 1^2) + 3x + 3 + 2[/tex]

expand

[tex]\sf x^2 + 2x + 1 + 3x + 3 + 2[/tex]

collect like terms

[tex]\sf x^2 + 2x + 3x + 3 + 2 + 1[/tex]

add/subtract like terms

[tex]\sf x^2 + 5x + 6[/tex]

breakdown

[tex]\sf x^2 + 3x + 2x+ 6[/tex]

factor common term

[tex]\sf x(x + 3) + 2(x+ 3)[/tex]

collect into groups

[tex]\sf (x + 2)(x+ 3)[/tex]

ii.

[tex]\sf (9x^2 + 9x - 4)(9x^2 + 9x - 10) - 72[/tex]

breakdown

[tex]\sf (9x^2 + 12x - 3x - 4)(9x^2 + 15x - 6x - 10) - 72[/tex]

factor common term

[tex]\sf (3x(3x + 4) -1( 3x + 4)) ( (3x(3x + 5)- 2(3x +5) )- 72[/tex]

collect like terms

[tex]\sf (3x -1)( 3x + 4) (3x- 2)(3x +5) - 72[/tex]

expand

[tex]\sf 81x^4+162x^3-45x^2-126x-32[/tex]

factor

[tex]\sf \left(3x+1\right)\left(3x+2\right)\left(9x^2+9x-16\right)[/tex]

Answer:

[tex]\textsf{1.} \quad (x+3)(x+2)[/tex]

[tex]\textsf{2.} \quad (3x+1)(3x+2)(9x^2+9x-16)[/tex]

Step-by-step explanation:

Question 1

[tex]\textsf{Given expression}: \quad(x+1)^2+3(x+1)+2[/tex]

[tex]\textsf{Let }u=(x+1) \implies u^2+3u+2[/tex]

[tex]\textsf{To factor }\:\:u^2+3u+2:[/tex]

Rewrite the middle term as u + 2u:

[tex]\implies u^2+u+2u+2[/tex]

Factorize the first two terms and the last two terms separately:

[tex]\implies u(u+1)+2(u+1)[/tex]

Factor out the common term (u+1):

[tex]\implies (u+2)(u+1)[/tex]

Replace [tex]u[/tex] with [tex](x+1)[/tex] :

[tex]\implies (x+1+2)(x+1+1)[/tex]

Simplify:

[tex]\implies (x+3)(x+2)[/tex]

Question 2

[tex]\textsf{Given expression}: \quad (9x^2+9x-4)(9x^2+9x-10)-72[/tex]

Expand:

[tex]\implies 9x^2(9x^2+9x-10)+9x(9x^2+9x-10)-4(9x^2+9x-10)-72[/tex]

[tex]\implies 81x^4+81x^3-90x^2+81x^3+81x^2-90x-36x^2-36x+40-72[/tex]

Collect like terms:

[tex]\implies 81x^4+81x^3+81x^3-90x^2+81x^2-36x^2-90x-36x+40-72[/tex]

Combine like terms:

[tex]\implies 81x^4+162x^3-45x^2-126x-32[/tex]

Use the Factor Theorem:

If f(x) is a polynomial, and f(a) = 0, then (x – a)  is a factor of f(x).

[tex]\begin{aligned}\implies f \left(-\dfrac{1}{3}\right) & =81\left(-\dfrac{1}{3}\right)^4+162\left(-\dfrac{1}{3}\right)^3-45\left(-\dfrac{1}{3}\right)^2-126\left(-\dfrac{1}{3}\right)-32\\ & = 1-6-5+42-32\\ & = 0\end{alilgned}[/tex]

Therefore (3x + 1) is a factor.

[tex]\begin{aligned}\implies f \left(-\dfrac{2}{3}\right) & =81\left(-\dfrac{2}{3}\right)^4+162\left(-\dfrac{2}{3}\right)^3-45\left(-\dfrac{2}{3}\right)^2-126\left(-\dfrac{2}{3}\right)-32\\ & = 16-48-20+84-32\\ & = 0\end{alilgned}[/tex]

Therefore (3x + 2) is a factor.

Therefore:

[tex]\implies f(x)=(3x+1)(3x+2)(ax^2+bx+c)[/tex]

Compare the coefficient of x⁴ and the constant to find a and c:

[tex]\implies 3 \cdot 3 \cdot a=81 \implies a=9[/tex]

[tex]\implies 2c=-32 \implies c=-16[/tex]

Therefore:

[tex]\implies f(x)=(3x+1)(3x+2)(9x^2+bx-16)[/tex]

Expand:

[tex]\implies f(x)=81x^4+(81+9b)x^3-(126-9b)x^2-(144-2b)x-32[/tex]

Compare the coefficient of x³ to find b:

[tex]\implies 81+9b=162 \implies b=9[/tex]

Therefore, the fully factorized expression is:

[tex]\implies (3x+1)(3x+2)(9x^2+9x-16)[/tex]

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Answer:

v =L× b×h

=5× 4×3

=60 cubic centimeter

Answer:

No real roots

[tex]x = -2 + 4i, x = -2 - 4i[/tex]

Step-by-step explanation:

Hello!

We can solve the quadratic by using the Quadratic Formula.

Standard form of a Quadratic: [tex]ax^2 + bx + c = 0[/tex]

Quadratic Equation: [tex]x = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}[/tex]

Given our Equation: [tex]f(x) = x^2 + 4x + 20[/tex]

Set the equation to 0 and solve using the formula.

There are no real roots to the quadratic.