What is the probability that the roll of a six-sided die will be either even or odd? A) 1 6 B) 1 4 C) 1 2 D) 1

ANSWER

The distance is 10 units.

EXPLANATION

Let us use the distance formula to find the distance between,

[tex](x_1,y_1)=(1,4)[/tex]

and

[tex](x_2,y_2)=( - 5, - 4)[/tex]

The distance formula is given by,

[tex]d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} [/tex]

We plug in the values to get,

[tex]d = \sqrt{( - 5-1)^2 + ( - 4-4)^2} [/tex]

[tex]d = \sqrt{( -6)^2 + ( - 8)^2} [/tex]

[tex]d = \sqrt{36+ 64} [/tex]

[tex]d = \sqrt{100} [/tex]

[tex]d = 10[/tex]

Marc's son is 14 years old. We found this by creating the equation 3x + 4 = 46 based on the question, solving for x, and determining that x equals 14.

This is a problem that requires an understanding of simultaneous linear equations. Let's denote Marc's son's age as x.

Marc is 4 years older than 3 times his son's age. Therefore, we can write this as: 3x + 4 = 46.

To find the value of x, which represents the son's age, we first subtract 4 from both sides of the equation (3x + 4 - 4 = 46 - 4). Now we have 3x = 42. To get the value of x alone, we will then divide by 3 from both sides of the equation (3x/3 = 42/3). As a result, we'll find out that x equals 14, which means Marc's son is 14 years old.

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Answer:

probability is r/p+q+r

Step-by-step explanation:

to find the probability, you take the number of desired balls (blue in this case )

and divide it by the total number of balls in the problem (add them all up) to get your answer

I hope that answered your question!!

Add the two numbers in the ratio: 7 +3 = 10

Divide total capacity by 10:

70,580 / 10 = 7,058

Multiply that by the ratio of filled seats:

7,058 x 7 = 49,406

49,406 seats were filled.

Solve for r in the first equation:

3(r+300) = 6

Use the distributive property:

3r + 900 = 6

Subtract 900 from both sides:

3r = -894

Divide both sides by 3:

r = -894 / 3

r = -298

Now you have r, replace r in the second equation and solve:

r +300 -2 =

-298 + 300 - 2 = 0

The answer is 0.

Answer:

0 is the value of r+300-2

Solve for r in the first equation:

3(r+300) = 6

Use the distributive property:

3r + 900 = 6

Subtract 900 from both sides:

3r = -894

Divide both sides by 3:

r = -894 / 3

r = -298

Now you have r, replace r in the second equation and solve:

r +300 -2 =

-298 + 300 - 2 = 0

The answer is 0.

If

[tex]f(\theta)=10\cos\theta+5\sin^2\theta[/tex]

then the derivative is

[tex]f'(\theta)=-10\sin\theta+10\sin\theta\cos\theta[/tex]

Critical points occur where [tex]f'(\theta)=0[/tex]. This happens for

[tex]-10\sin\theta+10\sin\theta\cos\theta=0[/tex]

[tex]-10\sin\theta(1-\cos\theta)=0[/tex]

[tex]\implies-10\sin\theta=0\text{ or }1-\cos\theta=0[/tex]

In the first case, we find

[tex]-10\sin\theta=0\implies\sin\theta=0\implies\theta=n\pi[/tex]

In the second,

[tex]1-\cos\theta=0\implies\cos\theta=1\implies\theta=2n\pi[/tex]

So all the critical points occur at multiples of [tex]\pi[/tex], or [tex]n\pi[/tex]. (This includes all the even multiples of [tex]\pi[/tex].)

The critical numbers of the function will be at ([tex]\pi, n\pi[/tex])

Given the function

f(θ) = 10 cos(θ) + 5 sin2(θ)

At the turning point, [tex]\frac{df(\theta)}{d\theta} = 0[/tex]

[tex]\frac{df(\theta)}{d\theta} = -10sin \theta + 5(2sin\theta cos\theta)\\\frac{df(\theta)}{d\theta} = -10sin \theta + 10sin\theta cos\theta\\[/tex]

At the turning point,

[tex]-10sin \theta + 10sin \theta cos \theta=0\\-10sin \theta(1-cos\theta) =0\\-10sin\theta = 0 \ and \ 1-cos\theta =0\\sin\theta =0\\\theta=0 + n\pi\\\\For \ 1-cos\theta =0\\cos\theta = 1\\\theta = cos^{-1}1\\\theta = 0 + n\pi[/tex]

Hence critical numbers of the function will be at ([tex]\pi, n\pi[/tex])

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Answer: option c

Step-by-step explanation:

To solve this problem you must keep on mind the properties of logarithms:

[tex]log(b)-log(a)=log(\frac{b}{a})\\\\log(b)+log(a)=log(ba)\\\\a*log(b)=log(b)^a[/tex]

Therefore, knowing the properties, you can write the expression gven in the problem as shown below:

[tex]2logx-6log(x-9)\\logx^2-log(x-9)^6\\\\log\frac{x^2}{(x-9)^6}[/tex]

Answer:

c edge

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The equation is y = a(b(x-c))+d

So for it to move right three units, it would be x - 3.

For it to move up 4 unites, it would be x+4.

So the equation would be y = (x - 3)^2 + 4

The correct answer is C

First you would substitute the expression moving it to the left then you change the signs the power function with an even exponent is always a positive or 0 but there is no x intercept.

Answer:

Step-by-step explanation:

The triangle is recognizable as a 30°-60°-90° right triangle, which has side length ratios ...

  1 : √3 : 2

Side x is thus twice the length of short side 4, so x = 8.

Side y is √3 times the length of short side x-6 = 2, so y = 2√3.

_____

If you don't happen to recognize the triangle dimensions, you can find x and y using the Pythagorean theorem.

  x = √(4² +(4√3)²) = √64 = 8

  y = √(4² -2²) = √12 = 2√3

Answer:

350

Step-by-step explanation:

Set [tex]f(x)=2x^3-3x^2+2[/tex]. Find the tangent line [tex]\ell_1(x)[/tex] to [tex]f(x)[/tex] at the point when [tex]x=x_1[/tex]:

[tex]f'(x)=6x^2-6x\implies f'(x_1)=12[/tex] (slope of [tex]\ell_1[/tex])

[tex]\implies\ell_1(x)=12(x-x_1)+f(x_1)=12(x+1)-3=12x+9[/tex]

Set [tex]x_2=-\dfrac9{12}[/tex], the root of [tex]\ell_1(x)[/tex]. The tangent line [tex]\ell_2(x)[/tex] to [tex]f(x)[/tex] at [tex]x=x_2[/tex] has slope and thus equation

[tex]f'(x_2)=\dfrac{63}8\implies\ell_2(x)=\dfrac{63}8\left(x+\dfrac9{12}\right)-\dfrac{17}{32}=7x+\dfrac{151}{32}[/tex]

which has its root at [tex]x_3=-\dfrac{151}{224}\approx-0.6741[/tex].

(The actual value of this root is about -0.6777)

Lets say the number is ab. Its value is 10a + b  

When it is reversed it is 10b + a = 12a+1.2b (from the condition its value should increase 0.2 times).  

11 a = 8.8b  

a/b = 8.8/11 = 0.8/1 = 8/10 = 4/5 ( we do this because a and b should be natural numbers less than 10).  

answer is 45.

A two-digit number less than 100 that increases by one-fifth of its original value, when its digits are reversed, can be found by setting up an equation. By defining the tens digit as 'a' and the unit digit as 'b', the equation 6a = 9b is derived. Solving for the digits within their possible values, the number 12 is found.

To find a number less than 100 that increases by one-fifth of its value when its digits are reversed, we need to set up an equation. Let's call the tens digit a and the units digit b. The number can be written as 10a + b. When the digits are reversed, the number becomes 10b + a. The problem states that reversing the digits increases the number by one-fifth of its original value, which gives us the equation:

(10a + b) + \frac{1}{5}(10a + b) = 10b + a

Now solving the equation:

6a = 9b

As a and b are digits, their possible values range between 0 and 9. We find that a = 1 and b = 2 satisfy the equation. Hence, the number is:12

When we reverse the digits, we get 21, which is greater than 12 by \frac{1}{5} of 12, as required.

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Answer:

8a - 48

Step-by-step explanation:

An equivalent expression is an expression which is equal to 8(a-6). You can expand or simplify an expression to make an equivalent expression. Apply the distributive property to form a new equivalent expression by multiplying 8 into each term. 8(a-6) = 8*a - 8*6 = 8a - 48. The options listed below do not connect to this problem since they do not use the same variable as the expression.

Answer:

112

Step-by-step explanation:

so the difference is 975 - 828.75 = 146.25.

if we take 975 to be the 100%, how much is 146.25 off of it in percentage?

[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 975&100\\ 146.25&x \end{array}\implies \cfrac{975}{146.25}=\cfrac{100}{x}\implies 975x=14625 \\\\\\ x=\cfrac{14625}{975}\implies x=15[/tex]

Answer:

146.25

Step-by-step explanation:

Answer:

1.33

Step-by-step explanation:

64,781 --- 4,000

25,409 --- 400

4,000÷400=10

Answer:

C

Step-by-step explanation:

You are given that

Use the rule

[tex]\lim_{x\to x_0}(f(x)+g(x))=\lim_{x\to x_0} f(x)+\lim_{x \to x_0} g(x).[/tex]

In your case,

[tex]\lim_{x\to4}(f+g)(x)=\lim_{x\to4} (f(x)+g(x))= \lim_{x\to4} f(x)+ \lim_{x\to 4} g(x)=5+0=5.[/tex]

Answer:

Three solutions were found :

x = 5

x = 2

x = -1

Step-by-step explanation:

Answer:

d. [tex]x=-1,2,\:or\:5[/tex]

Step-by-step explanation:

The given equation is;

[tex]x^3-6x^2+3x+10=0[/tex]

To solve by the x-intercept method we need to graph the corresponding function using a graphing calculator.

The corresponding function is

[tex]f(x)=x^3-6x^2+3x+10[/tex]

The solution to [tex]x^3-6x^2+3x+10=0[/tex] is where the graph touches the x-axis.

We can see from the graph  that; the x-intercepts are;

(-1,0),(2,0) and (5,0).

Therefore the real solutions are:

[tex]x=-1,2,\:or\:5[/tex]

No way to know what reasons you're supposed to choose from...

By definition of tangent,

[tex]\tan\left(x-\dfrac\pi4\right)=\dfrac{\sin\left(x-\frac\pi4\right)}{\cos\left(x-\frac\pi4\right)}[/tex]

The angle sum identities give

[tex]\tan\left(x-\dfrac\pi4\right)=\dfrac{\sin x\cos\frac\pi4-\cos x\sin\frac\pi4}{\cos x\cos\frac\pi4+\sin x\sin\frac\pi4}[/tex]

[tex]cos\dfrac\pi4=\sin\dfrac\pi4=\dfrac1{\sqrt2}[/tex], so we can cancel those terms to get

[tex]\tan\left(x-\dfrac\pi4\right)=\dfrac{\sin x-\cos x}{\sin x+\cos x}[/tex]

as required.

Answer:

217.01

Step-by-step explanation:

Answer:

Roughly $21.70

Step-by-step explanation:

1,205.62 times 0.018 (1.8% converted into decimal, to do so, move the decimal over to the right two places) equals 21.7

Answer:

Option B. [tex]150\°[/tex]

Step-by-step explanation:

we know that

In this problem

[tex](15+15x)=(17x-3)[/tex]

solve for x

[tex]17x-15x=15+3[/tex]

[tex]2x=18[/tex]

[tex]x=9[/tex]

Find the measure of arc BC

[tex]arc\ BC=17x-3=17(9)-3=150\°[/tex]

Answer:

  y = csc(x) -1

Step-by-step explanation:

The vertical offset of -1 is your first clue. Your second clue is that the range does not include (-2, 0), typical of cosecant and secant functions (offset by -1).

_____

Comment on answer choices

Apparently the cosine choices are intended to be confused with the cosecant choice. The cosine function has a range of [-1, 1], so will not show any vertical asymptotes anywhere, regardless of scaling or translation.

the answer is B ln(0.0498)=-3

Answer:

2:3.

Step-by-step explanation:

The number of children = 2+ 4 = 6.

So the required ratio is 4:6 which simplifies to 2:3.

Answer:

2.3

is yo sex answer

Answer:

The list in order from the one with least volume to the one with the greatest volume is

case C) A square pyramid with base edges 6 cm and height 6 cm

case A) A cube with edge 5 cm

case E) A rectangular prism with a 5 cm-by-5 cm base and height 6 cm

case D) A cone with radius 4 cm and height 9 cm

case B) A cylinder with radius 4 cm and height 4 cm

Step-by-step explanation:

To solve this problem calculate the volume of each solid

case A) A cube with edge 5 cm

The volume of a cube is equal to

[tex]V=b^{3}[/tex]

where

b is the length side of the cube

substitute the value

[tex]V=5^{3}=125\ cm^{3}[/tex]

case B) A cylinder with radius 4 cm and height 4 cm

The volume of a cylinder is equal to

[tex]V=\pi r^{2} h[/tex]

substitute the value

[tex]V=(3.14)(4)^{2} (4)=200.96\ cm^{3}[/tex]

case C) A square pyramid with base edges 6 cm and height 6 cm

The volume of a pyramid is equal to

[tex]V=\frac{1}{3}Bh[/tex]

where

B is the area of the base

h is the height of the pyramid

Find the area of the base B

[tex]B=6^{2}=36\ cm^{2}[/tex] ----> is a square

substitute the values

[tex]V=\frac{1}{3}(36)(6)=72\ cm^{3}[/tex]

case D) A cone with radius 4 cm and height 9 cm

The volume of a cone is equal to

[tex]V=\frac{1}{3}Bh[/tex]

where

B is the area of the base

h is the height of the cone

Find the area of the base B

[tex]B=\pi r^{2}=(3.14)(4^{2})=50.24\ cm^{2}[/tex] ----> is a circle

substitute the values

[tex]V=\frac{1}{3}(50.24)(9)=150.72\ cm^{3}[/tex]

case E) A rectangular prism with a 5 cm-by-5 cm base and height 6 cm

The volume of a rectangular prism is equal to

[tex]V=LWH[/tex]

substitute the values

[tex]V=(5)(5)(6)=150\ cm^{3}[/tex]

therefore

The list in order from the one with least volume to the one with the greatest volume is

case C) A square pyramid with base edges 6 cm and height 6 cm

case A) A cube with edge 5 cm

case E) A rectangular prism with a 5 cm-by-5 cm base and height 6 cm

case D) A cone with radius 4 cm and height 9 cm

case B) A cylinder with radius 4 cm and height 4 cm

Answer:

[tex]0.5\frac{lb}{person}[/tex]

Step-by-step explanation:

we know that

To find out how many pounds of fries each person will receive, divide the total pounds of fries by the total number of people.

so

[tex]\frac{2}{4} \frac{lb}{persons}=0.5\frac{lb}{person}[/tex]

Each person will receive 0.5lb of fries.

To solve this problem, we need to divide the total weight of the French fries by the number of people sharing them. Carmen has prepared a 2lb bag of French fries for 4 people. To find out how much each person will get, we divide the total weight of the fries by the number of people:

[tex]\[ \text{Fries per person} = \frac{\text{Total weight of fries}}{\text{Number of people}} \][/tex]

[tex]\[ \text{Fries per person} = \frac{2 \text{lb}}{4} \] \[ \text{Fries per person} = 0.5 \text{lb} \][/tex]

So, each person will receive 0.5lb of fries.

Answer:

b. [tex]x\approx -2.426[/tex]

Step-by-step explanation:

The given equation is;

[tex]x^3+x^2+10x+15=0[/tex]

We solve by the x-intercept method. We need to graph the corresponding function using a graphing tool.

The corresponding function is

[tex]f(x)=x^3+x^2+10x+15[/tex]

The solution to [tex]x^3+x^2+10x+15=0[/tex] is where the graph touches the x-axis.

We can see from the graph  that; the x-intercept is;

(-2.426,0)

Therefore the real solution is:

[tex]x\approx -2.426[/tex]

Answer:

b. x ≈ -2.426

Step-by-step explanation:

Given that we have possible roots we can replace these values into the equation and check if it is satisfied.

option a: 2.426^3+4*2.426^2+10*2.426+15 = 77.08 ≠ 0

option b: (-2.426)^3+4*(-2.426)^2+10*(-2.426)+15 ≈ 0

option c: 5.128^3+4*5.128^2+10*5.128+15 = 306.31 ≠ 0

option d: (-5.128)^3+4*(-5.128)^2+10*(-5.128)+15 = -65.94 ≠ 0

Answer:

35 shelves

Step-by-step explanation:

If each shelf holds 36 books and there are a total of 1,260 books, divide 1,260 by 36 to get the number of shelves needed. 1,260/36 = 35 shelves. Think of it like 36 books per shelf and 35 shelves, 36*35 = 1,260.

Answer:

Yes

Step-by-step explanation: