A regular six sided die and an eight equal segment spinner, numbered 1 to 8, are rolled/spun simultaneously. What are the odds in favor of spinning a prime number on the spinner and rolling a number less or equal to 4 on the die?

Step-by-step explanation:

a) k = 1

b) geometric progression formula:

Tn = ar^(n-1)

first term, a = 3/2

Answer:

B 720

Step-by-step explanation:

same process as the previous image I sent ya

Answer:

B) 720.

Step-by-step explanation:

We can use the Binomial Expansion Theorem:

[tex]\displaystyle (a+b)^n=\sum_{k=0}^{n}\binom{n}{k}a^kb^{n-k}[/tex]

We have the expression:

[tex]\displaystyle (2x-3)^5[/tex]

Therefore, a = 2x, b = -3, and n = 5.

We want to find the coefficient of x³. To get x³, we can cube a. Therefore, we can find our coefficient by letting k = 3. Hence:

[tex]\displaystyle \binom{5}{3}(2x)^3(-3)^{5-3}[/tex]

Evaluate:

[tex]\displaystyle =10(8x^3)(9)=720x^3[/tex]

Our answer is B.

Answer:

About Points

S = (x,y)        searched point (it will be in the third quadrant )

M = (-2,0)      Midpoint | SP |

P = (3,5)        one end of the segment | SP |

You have to draw Cartesian.

we set in a point M and P. We both points by a simple and we extend it for the third quarter of the system. Compass measure the distance from the point M to the point P. From the point M we set a compass point S. Figure attached. Received point S = ( -7 , -5 ) . It sought a point that calculate .

We use the information that | SM | = | MP |

Answer : S = (-7,-5)

Step-by-step explanation:

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ P(\stackrel{x_1}{3}~,~\stackrel{y_1}{5})\qquad \underline{Q}(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{x+3}{2}~~,~~\cfrac{y+3}{2} \right)=\stackrel{M}{(-2,0)}\implies \begin{cases} \cfrac{x+3}{2}=-2\\[1em] x+3=-4\\ \boxed{x = -7}\\[-0.5em] \hrulefill\\ \cfrac{y+3}{2}=0\\[1em] y+3=0\\ \boxed{y=-3} \end{cases}[/tex]

Answer:

17.9375 square yards

Step-by-step explanation:

Let us have a common unit

What we have here is the case of inches and ft

10 ft 3 inches

1 ft = 12 inches

so 3 inches is 3/12 = 0.25 ft

= 10+0.25 = 10.25 ft

15 ft 9 in

= 15 + 9/12 = 0.75 + 15 = 15.75 ft

So let us convert to yards ;

Mathematically, 3 ft = 1 yard

so 10.25 ft = 10.25/3 = 3.4167 yards

15.75 ft = 15.75/3 =5.25 yards

So the square yards would be the product of this two;

which is;

(10.25/3) * (15.75/3) = 17.9375 square yards

Answer:

3 x + 2 y + z/ x + y + z ,  x = 2 ,  y = 3 ,  z = 1

tan ( x ) ,  x = − π

cot ( 3 x ) ,  x = 2 π /3

Step-by-step explanation:

Answer:

C=20

Step-by-step explanation:

Given:

Axis of symmetry of a parabola is [tex]x=4[/tex].

A point on the parabola is (0,2).

To find:

The another point on the parabola.

Solution:

The point (0,2) lies on the parabola and the axis of symmetry of a parabola is [tex]x=4[/tex].

It means, the another point on the parabola is the mirror image of (0,2) across the line [tex]x=4[/tex] because the parabola is symmetric about the axis of symmetry.

If the point is reflected across the line [tex]x=4[/tex], then

[tex](x,y)\to (-(x-4)+4,y)[/tex]

[tex](x,y)\to (-x+4+4,y)[/tex]

[tex](x,y)\to (-x+8,y)[/tex]

Using this rule, we get

[tex](0,2)\to (-0+8,2)[/tex]

[tex](0,2)\to (8,2)[/tex]

Therefore, the other point on the parabola is (8,2).

Answer:

x^2 + 3x + 5

Step-by-step explanation:

sum of the two given side = 2x^3 + 3x^2 + 3x -2

missing side = 2x^3 + 4x^2 + 6x + 3 - 2x^3 - 3x^2 - 3x + 2 = x^2 + 3x + 5

Answer:

Step-by-step explanation:

The absolute value of a number is defined as the positive of either a positive or a negative number. By that I mean that

| 1 | = 1 and | -1 | = 1.  Right?

We use that idea here. Either:

6x + 3 = 27     OR      6x + 3 = -27 and solve both equations.

6x = 24 so x = 4 OR

6x = -30 so x = -5

Choice D is the one you want.

Answer:

The removed number is 16

Step-by-step explanation:

Five numbers have a mean of 12.

Now;

Mean = Σx/x

Thus; Σx = 12 × 5 = 60

Now,we are told that if one number is removed, the mean is 11.

Thus;

(60 - x)/4 = 11

60 - x = (11 × 4)

60 - x = 44

x = 60 - 44

x = 16

Thus,the removed number is 16

[tex]\huge\boxed{\boxed{\underline{\textsf{\textbf{Answer}}}}}[/tex]

Given,

ΔABC ≅ ΔXYZ

If these 2 triangles are congruent with each other then,

∠ A = ∠ X [tex]\boxed{\bf{Corresponding \ parts \ of \ congruent \ triangles}}[/tex]

∠ B = ∠ Y [tex]\boxed{\bf{Corresponding \ parts \ of \ congruent \ triangles}}[/tex]

∠ C = ∠ Z [tex]\boxed{\bf{Corresponding \ parts \ of \ congruent \ triangles}}[/tex]

Now,

We saw that ∠ C = ∠ Z.

⟹ So, if ∠ C = 32°, then even ∠ Z will be equal to 32°. [tex]\boxed{\sf{Equal \ angles \ have \ equal \ measurements}}[/tex]

ᶛɲƧཡэʀ ↦ C. m ∠X = 32°

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐

The equation of the line is y + 1 = 3(x - 2).

The correct option is (3).

Equation: A statement that two variable or integer expressions are equal. In essence, equations are questions, and the motivation for the development of mathematics has been the systematic search for the answers to these questions.

As per the given data:

The line passes through the point (2, -1)

slope of the given line is 3

By using the slope intercept form of line:

y = mx + c

where m is the slope

c is the y intercept

The line passes through the point (2, -1) so substituting the point in the equation also m = 3

y = 3x + c

-1 = 3(2) + c

c = -7

The equation of the line now can be written as:

y = 3x - 7

y + 1 = 3x - 7 + 1

y + 1 = 3(x - 2)

Hence, the equation of the line is y + 1 = 3(x - 2).

To learn more about equation, click:

brainly.com/question/10413253

#SPJ5

Answer:

16,500

Step-by-step explanation:

Just use a calculator-simple

What do you mean "let me y"?

Answer:

the answer is 16500 or sixteen thousand five hundred

Step-by-step explanation:

:)

Answer:

(D) 27 - C

Step-by-step explanation:

The "less than" means we are subtracting C from 27, so 27 - C.

Hope it helps (●'◡'●)

Answer:

could you show the ine?

Step-by-step explanation:

If “the notation arcsin x represents the inverse function to sine” is true when the sine function is to the interval [ -pi/2, pi/2 ].

The sine function is one of the three primary functions in trigonometry, the others being cosine, and tan functions.

The confusion is compounded by the fact that we use the notation sin⁻¹(x) interchangeably with arcsin(x), and we call it the inverse sine.

Here is a counterexample disproving your given statement:

Let x = π.

The value π is in the domain of sin(x).

arcsin[sin(π)] = arcsin(0) = 0

arcsin[sin(π)] ≠ π

Therefore arcsin(x) is not the inverse of sin(x).

If you restrict the sine function to the interval [ -pi/2, pi/2 ]. Otherwise, arcsin will not be a function.

Hence, If “the notation arcsin x represents the inverse function to sine” is true when the sine function is to the interval [ -pi/2, pi/2 ].

Learn more about sin function here;

https://brainly.com/question/14397255

#SPJ2

Answer:

H

Step-by-step explanation:

lets say the first big square has side s, so the area will be s²

then the side of the small square is s/3, and the area is (s/3)²= s²/3² =s²/9

the area of the smaller square is 1/9 smaller than the area of the big square

Answer:

x = -3

Step-by-step explanation:

Here, this is a vertical line

What this mean here is that the x-value remains constant irrespective of the y value

For all the y values, we have a single x-value

so what this mean is to simply locate the x-axis. value and equate it to x

We have this as;

x = -3

Answer:

[tex]{ \bf{f(x) = {x}^{3} + {ax}^{2} - 1 }} \\ { \tt{f( - 1) : {( - 1)}^{3} + a {( - 1)}^{2} - 1 = 0}} \\ { \tt{f( - 1) : a - 2 = 0}} \\ a = 2[/tex]

The polynomial function [tex]$x^3 + ax^2 -1[/tex] will have -1 as a root at the value of

a = 2.

A polynomial function exists as a function that applies only non-negative integer powers or only positive integer exponents of a variable in an equation like the quadratic equation, cubic equation, etc.

Given: A root exists at a value of x such that the polynomial exists equivalent to zero.

Let, the polynomial equation be [tex]$x^3 + ax^2 -1[/tex]

then [tex]$\mathbf{f}(\mathbf{x})=\mathbf{x}^{3}+a \mathbf{x}^{2}-\mathbf{1}$[/tex]

Put, x = -1, then we get

[tex]$\mathbf{f}(-1)=(-1)^{3}+\mathrm{a}(-1)^{2}-1=0$[/tex]

f(-1) = a - 2 = 0

a = 2

Therefore, the value of a = 2.

To learn more about polynomial function

https://brainly.com/question/26240147

#SPJ2

Answer:

Sue candy = 13 - x

Tony candy = 9 + 1/2x

Step-by-step explanation:

Sue candy = 18

Tony candy = 18

Let x = some candy gives to tony

Sue candy = 18 - x

Tony candy = 18 + x

sue then eats five of hers

Sue candy = 18 - x - 5

= 13 - x

tony eats half of his

Tony candy = 1/2(18 + x)

= 18/2 + x/2

= 9 + 1/2x

Expressions for the number of pieces candy sue and tony now have:

Sue candy = 13 - x

Tony candy = 9 + 1/2x

Answer:

T(x) = 21 + 4.5x

Step-by-step explanation:

Given :

Original temperature = 21°C

Final temperature = 75°C

Time, x = 12 minutes

The temperature, T as a function of x, heating time in minutes :

We need to obtain the constant heating rate per minute :

Final temperature = initial temperature + (constant rate change,△t * time)

75 = 21 + 12△t

75 - 21 = 12 △t

54 = 12 △t

△t = 54 / 12

△t = 4.5°C

Hence, temperature change is 4.5°C per minute.

Hence,

T(x) = 21 + 4.5x

Answer:

T= 21+4.5x

Step-by-step explanation:

I got it right on Khan Academy

PLEASE MARK BRAINLIEST

Answer:

Slope-intercept

y = 3/4(x) - 7

Point slope

y -5= 3/4(x - 16)

Step-by-step explanation:

In slope-intercept

We have the general slope intercept as;

y = mx + b

where m is the slope and b is the y-intercept

in this case, m = 3/4 and b = -7

So we have;

y = 3/4(x) - 7

In point-slope

we have the general form as;

y-y1 = m(x-x1)

So what we have is as follows;

y -5= 3/4(x - 16)

Where we have (x1,y1) = (16,5)

Given:

[tex]Domain\neq -1[/tex]

[tex]Range\neq 2[/tex]

To find:

The function for the given domain and range.

Solution:

A function is not defined for some values that makes the denominator equals to 0.

The denominator of functions in option A and C is [tex](x-1)[/tex].

[tex]x-1=0[/tex]

[tex]x=1[/tex]

So, the functions in option A and C are not defined for [tex]x=1[/tex] but defined for [tex]x=-1[/tex]. Therefore, the options A and C are incorrect.

In option B, the denominator is equal to [tex]x+1[/tex].

[tex]x+1=0[/tex]

[tex]x=-1[/tex]

So, the function is not defined for [tex]x=-1[/tex]. Thus, [tex]Domain\neq -1[/tex].

If degree of numerator and denominator are equal then the horizontal asymptote is [tex]y=\dfrac{a}{b}[/tex], where a is the leading coefficient of numerator and b is the leading coefficient of denominator.

In option B, the leading coefficient of numerator is 2 and the leading coefficient of denominator is 1. So, the horizontal asymptote is:

[tex]y=\dfrac{2}{1}[/tex]

[tex]y=2[/tex]

It means, the value of the function cannot be 2 at any point. So, [tex]Range\neq 2[/tex].

Hence, option B is correct.

To find a probability you take the specific parameters divided by the entire set of possibilities.

For example, the specific parameter here is that the drink must be a medium, (no matter the temperature). So, we would add 48 and 12 to get 60.

And we know that the total number of orders is 100.

So, we should divide 60 by 100, and we get 60%.

Answer:

slope= difference in y ÷difference in x

=y-y1÷x-x1

=-3-(-1)÷-3-1

=-3+1÷-3-1

=-2÷-4

=1/2

Step-by-step explanation:

hope this is helpful

Y2 -Y1 ÷ X2-X1

-1 - 1 ÷ -3 - -3= 0.5 or 1/2

Answer:

5.28

Step-by-step explanation:

we use the formula

H²=B²+P²

and we will get the answer

branliest if it is helpful

Answer:

Angle BXY

using pythogoras theory which is

hyp*2= opp*2 +adj*2

hypothenus being the longest part of the angle BX=?

Step-by-step explanation:

hyp= 4.2*2+ 3.2*2

hyp*2 =17.64 + 10.24

hyp*2 = 27.88

hyp =√27.88

hyp=5.28...Ans

note *2...square