The quantities X and Y are proportional

Using the combination formula, the committee can be selected in 1,211,760 ways.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

Combination formula is the number of different combinations of x objects from a set of n elements.

In this problem:

There are 10 sophomore, 8 junior, and 9 senior members in student council.

They are independent, so we can just multiply them, thus;

T = 18!/ 2! 16! x 12!/ 2! 10! x 10!/ 3! 7!

T  = 1,211,760

Hence, The committee can be selected in 1,211,760 ways.

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The equation and the solution are 2 = -8 * -x and x = 1/4, respectively

On the model, we have the following representations

[1][1]          [-1][-1][-1][-1][-1][-1][-1][-1][-x]

When represented as an equation, we have the following equation

So, we have

2 = -8 * -x

Evaluate the product in the above equation

So, we have

2 = 8x

Divide both sides of the above equation by 8

So, we have

1/4 = x

Rewrite the above expression as

x = 1/4

Hence, the equation and the solution are 2 = -8 * -x and x = 1/4, respectively

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18/ 3x+1 is  18x²-2/ 3x²-5x - 2}  in simplest terms.

What are examples of linear equations?

18 x² - 2 / 3x² - 5x - 2

3x² - 5x - 2 = 3x² - ( 6- 1 ) x - 2 = 0

                    ⇒  3x² - 6x + x - 2 = 0

                     ⇒  3x( x - 2 ) + 1 ( x - 2) = 0

                      ⇒ ( 3x + 1 ) ( x - 2 ) = 0

put in equation -

= 18 x² - 2 /  ( 3x + 1 ) ( x - 2 )

= 18/ 3x+1

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The given equations have in one, (1/5) is the coefficient of x, in the second equation, (1/5) is the coefficient of (x + 2), while both equations equals 6. Therefore, the value of x is different in both equations which do not represent the same situation.

The given equations are presented as follows;

[tex]\frac{1}{5} \cdot x + 2 = 6...(1)[/tex]

[tex] \frac{1}{5} \cdot (x + 2) = 6...(2)[/tex]

Solving each equation for x gives;

For equation (1), x = 5×(6 - 2) = 20

x = 20

For equation (2), we have;

x = 6 × 5 - 2 = 28

x = 28

Given that the value of x in the given equations are different, the situations are different.

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the equation for y will be y = 4ˣ / 16 when the function y is defined as y = f ( g ( x ) ).

We are given the functions:

f ( x ) = 4ˣ

g ( x ) = x - 2

Now, we have a function y defined as:

y = f ( g ( x ) )

Now, we need to find the equation for y.

We know that:

f ( g ( x ) ) = 4⁽ ˣ⁻ ² ⁾

f ( g ( x ) ) = 4ˣ / 4²

f ( g ( x ) ) = 4ˣ / 16

Therefore, we get that, the equation for y will be y = 4ˣ / 16 when the function y is defined as y = f ( g ( x ) ).

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The 9th term of the geometric sequence can be determined by using the nth term of geometric sequence formula: an=arn-1

Geometric sequence is the series of number in which each term is determined by multiplying the common ratio with the preceding term.

In the formula, an=arn-1, a is the first term, n is the number of terms, and r is the common ratio.

The geometric sequence from the part b is 2,4,8,…

The first term a = 2

The common ratio r = 2

The number of term n = 9

Hence, to find the 9th term,

a9=2(2)9-1

a9=2(2)8

a9=512

The 9th term of the geometric sequence 2,4,8,… is 512

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The average interest rate does he pay on the total $32,000 he owes is 9. 5%

From the information given, we have that;

Given the total pay he owes as;

= $22, 000 +$ 10, 000

= $32, 000

The average interest rate is expressed as;

= sum of interest rate for college loan and car/ number of interest rate

Substitute the values

= 8 + 11/ 2

= 19/ 2

Find the quotient

= 9. 5%

Thus, the average interest rate does he pay on the total $32,000 he owes is 9. 5%

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Answer:

2b + 9

Hope this helps :)

Step-by-step explanation:

This equation shows the statement, "Ava's sister is 9 years less than twice Ava's age b."

4)

The measures of the angles m∠1 and m∠2  are: m∠1 = 109 and m∠2 = 71

Linear pair angles are two angles which are adjacents and supplementary.

Given that: m∠2 and m∠1 form a linear pair

we know that the angles   and   are supplementary, which means that they add up to 180 degrees.

In order to solve for "x," we can write the following expression:

180 = (5x + 9) + (3x + 11)

8x = 180 - 20

x = [tex]\frac{160}{8}[/tex]

x = 20

Therefore, substituting, we get that the measures of the angles   and   are

m∠1 = 5(20) +9 = 109

m∠2 = 3(20) + 11 = 71

5)

the angle m∠2 = 86°

Given that m∠1 and m∠2 are vertical angles and m∠1 = (17x + 1) and m∠2 =  (20x - 14)

Vertical angles are always congruent

m∠1 = 17x + 1

m∠2 = 20x - 14

Since ∠1 and ∠2 are vertical:

m∠1 = m∠2

17x + 1  = 20x - 14

Collect like terms

20x - 17x = 1 + 14

3x = 15

Divide both sides by 3

3x / 3 = 15/3

x = 5

m∠2 =  20x  -  14

m∠2 =  20(5)  -  14

m∠2 =  100    -   14

m∠2 =   86°

6)

The value of each angle that is p=119 and q=61

In light of this, the measure of an angle is P, which is three less than the measure of angle q.

P + q = 180  ( By definition of supplementary)

p = 2q -3

Substitute the value

Then ,we get

2q - 3 + q =180

3q = 180 + 3

3q = 183

q= [tex]\frac{183}{3}[/tex]

= 61

then, if you substitute q's value, you get

p= 2(61) - 3 = 122 - 3 = 11.9

Hence, p= 119 and q= 61

7)

The value of x is 19°

Given that : ∠DBE =2x - 1

∠CBE =5x – 42  and BD is perpendicular to AC.

A right angle is formed when two lines are perpendicular.

∠DBE + ∠CBE = 90

90 = (2x - 1) + (5x - 42)

7x = 133

x = 19°

8)

The value of x and y are : x= 26° and y= 9°.

As a linear pair, (5x - 17)° + (3x - 11)° = 180°.

or, 8x - 28°= 180°

8x = 180° + 28°

Therefore, the value of x is 26°.

Now,

3x - 11°= 3×26°-11° = 67°

Again,

67°+90°+(2y+5)° = 180° { being linear pair}.

157°+2y+5° = 180°

or, 2y + 162° = 180°

or, 2y = 180° - 162°

y = [tex]\frac{18}{2}[/tex]

Therefore, the value of y is 9°.

The value of x is 26° and y is 9°.

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The Slope-intercept form of the given equation is y = -3x + 18 .

An equation in Slope-intercept form is of the form

[tex]y = mx + b[/tex]

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

Now, the given equation is (y/9) + (x/3) = 2

Taking LCM on the left hand side of the equation, we get

⇒ [tex](3y+9x)/(2y) = 2[/tex]

⇒ 3y + 9x = 54

⇒ 3y = 54 - 9x

Dividing both side of the equation by 3, we get

⇒ y = [tex](54 - 9x)/3[/tex]

⇒ y = 18 - 3x

⇒ y = -3x + 18

∴ The equation y = -3x + 18 is in Slope-intercept form.

In the equation the slope is -3 and the y-intercept is 18.

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The naive forecast for day 6 is 94.

The naive forecast for the nth period is calculated as follows.

Forecast period Yn=Yn−1​

Period Sales Naive Forecasts

1         90                   -

2         97                  90

3         92                  97

4         90                  92

5         94                  90

6                            94

Hence, the naive forecast for day 6 is 94.

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Answer:

[tex]{ \tt{change = \frac{y_{b} - y _{a} }{x _{b} - x _{a} } }} \\ \\[/tex]

[tex]{ \tt{ change = \frac{16 - 2}{4 - 1} }} \\ \\ = { \tt{ \frac{14}{3} }} \\ \\ = 4 \frac{2}{3} [/tex]

Answer: Two planes intersecting in a line

Explanation:

The wall and floor are two different planes. They meet up to form a line which is the crease between them.

A plane is a flat surface without any bends or curves to it. In theoretical terms, planes go on forever in all directions. Realistically there are limits of course. The wall or floor cannot go on forever.

Another example of two planes would be found in a book. Each page is a plane. Two adjacent pages meet up to form a line (i.e. the spine of the book is a line).

Answer:

no solution

Step-by-step explanation:

5n + 1 = 5n - 1 ( subtract 1 from both sides )

5n = 5n - 2 ( subtract 5n from both sides )

0 = - 2 ← not possible

this indicates that the equation has no solution

Answer:

5 gg

Step-by-step explanation:

Let us treat the number of gigabytes of data she can use (at max) per month as x.

We can say that [tex]54.5 + 5x = 74[/tex] will always be deducted from her and $5x per month for the extra data she uses.

    [tex]54.5 + 5x = 74[/tex]

⇒  [tex]5x = 74 - 54.5[/tex]

⇒  [tex]5x = 25.5[/tex]

⇒  [tex]x = 25.5 / 5[/tex]

⇒ [tex]x = 5.1[/tex]

As she can only buy a fixed number of data, which cannot be a decimal, let us take the number directly below 5.1 - which is 5 - as the answer.

Caroline can use up to 5gg of data

The Gary's score after getting stuck in the dust storm will be -35 points.

It is given in the problem that,

The points gained by Gary by jumping over a crater = 20 points

And then,

The points lost by Gary for getting stuck in a dust storm = 45 points

We need to find,

The Gary's score after getting stuck in the dust storm

As in the beginning of the game, Gary's account had 20 points but as he then stuck in the dust storm he lost 45 points, which means he has lost points more than he had. So, now Gary would have negative points left in his account in the game

= 10 - 45

= - 35

Hence, the Gary's score after getting stuck in the dust storm will be -35 points.

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Answer: jane has 1.5 meters of ribbon

Step-by-step explanation:

Answer:

D. 52 45

Step-by-step explanation:

The arithmetic mean of two terms in an arithmetic sequence is 42 .

One term is 30 then other term is

42 = (x+30)/2

x=54

An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.

Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.

An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.

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Answer: $244.55

A = $250  ;  r=0.002   t= 11   [From 2007 to 2018 , t=2018-2007]

By elimination, the solution of the system of equations, 6x - 3y = 3 and 5x - 5y = 10, is (-1 , -3).

A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.

There are three methods that can be used to solve system of equations.

1. Elimination

2. Substitution

3. Graphing

First, simplify both equations by dividing the first equation by 3 and the second equation by 5.

6x - 3y = 3 ⇒ 2x - y = 1     (equation 1)

5x - 5y = 10 ⇒ x - y = 2     (equation 2)

Use the elimination method since subtracting the two equations will eliminate the variable y.

2x - y = 1     (equation 1)

 x - y = 2     (equation 2)

x        = -1

x = -1

Substitute the value of x to any of the two equation and solve for y.

6x - 3y = 3     (equation 1)

6(-1) - 3y = 3

-3y = 3 + 6

-3y = 9

y = -3

Hence, the solution of the system of equations is (-1 , -3).

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A circle is a curve sketched out by a point moving in a plane. The radius and the diameter of the circle are 19.73 ft and 39.46 ft, respectively.

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the center.

Given that circumference of the circle as 124 ft. Therefore, the radius and the diameter of the circle can be written as,

Circumference of circle = 2 × π × (Radius of the circle)

124 ft = 2 × π × (Radius of the circle)

(Radius of the circle) = 124 ft/ (2 × π)

The radius of the circle = 19.73 ft

Diameter of circle = 2 × (Radius of the circle)

                              = 2 × 19.73 ft

                              = 39.46 ft

Hence, the radius and the diameter of the circle are 19.73 ft and 39.46 ft, respectively.

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The two numbers which are 5 units away from zero on the number line as required in the task content are; -5 and 5.

It follows from the task content that the numbers which are 5 units away from zero on the number line be identified and plotted.

Hence, given that the numbers in discuss are represented by; x; we have;

| x - 0 | = 5

| x | = 5

Ultimately, x = ±5. where +5 is to the right and -5 is to the left of zero respectively.

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Answer: f(-1) = -12

Step-by-step explanation:

        To solve, we will substitute t for -1 into the function.

Given:

    h(t) = (t + 7)(t - 1)

Substitute:

    h(-1) = (-1 + 7)(-1 - 1)

Add and subtract:

    h(-1) = (6)(-2)

Multiply:

    f(-1) = -12

Answer:

if the peak level is 14949 above sea level , so the difference in elevation is 14949 + 39 =14988 feet

Answer:

n = 1

Step-by-step explanation:

[tex]\frac{8}{3}[/tex] = [tex]\frac{19}{6}[/tex] n - [tex]\frac{1}{2}[/tex] n

multiply through by 6 ( the LCM of 3, 6 and 2 ) to clear the fractions

16 = 19n - 3n

16 = 16n ( divide both sides by 16 )

1 = n

Answer:

where is the equal to sign????

The definite integral that represents the area of the region under the given curves is:  [tex]\int\limits^3_{-3} {x^2-9} \, dx[/tex]

Given:

The points where the two intersect will be given by:

y₁ = y₂

=> x² + 2x + 3 = 2x + 12

=> x² + 3 = 12

=> x² = 9

=> x = ± 3

For x₁ = 3, y₁ = 2(3) + 12 = 18 => (x₁, y₁) = (3, 18)

For x₂ = -3, y₂ = 2(-3) + 12 = 6 => (x₂, y₂) = (-3, 6)

Now, for the area of the region under first curve [tex]y_1=x^2+2x+3[/tex]:

A₁ =  [tex]\int\limits^3_{-3} {x^2+2x+12} \, dx[/tex]

For the area of the region under the second curve [tex]y_2=2x+12[/tex]:

A₂ = [tex]\int\limits^3_{-3} {2x+12} \, dx[/tex]

For the required area of the region bounded by the two curves will be given by:

A = A₂ - A₁ = [tex]\int\limits^3_{-3} {x^2+2x+3 - (2x +12)} \, dx[/tex]

A = [tex]\int\limits^3_{-3} {x^2-9} \, dx[/tex]

Refer to the image for the area so bounded by the curves.

Hence, The definite integral that represents the area of the region under the given curves is:  [tex]\int\limits^3_{-3} {x^2-9} \, dx[/tex].

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By using collinearity assumptions and addition and subtraction of line segments, the length of the line segment AB is 26 units.

Let A, B, D, F be points lying on the same line such that A(x) ≤ B(x) ≤ D(x) ≤ F(x), where x is the position of each point on a number line. Then, the value of the length of the line segment AB is:

AB = AD + DF - BF

AB = 26 + 8 - 8

AB = 26

Please notice that B(x) = D(x) as AB = AD.

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