15. A board game has 5 different pieces. Players can choose a boat, a car, a top
hat, a shoe, and a dog. Ayers randomly selects one of the pieces, and then Nolan
randomly selects one of the remaining pieces. State how many combinations are
possible and list each possible combination that Ayers and Nolan could choose.

39 * (1-15/100) = 39*0.85 = 33.15 (dollars)

Answer:

2x-2

Step-by-step explanation:

ln(e2x/x³)

as ln ex = x

thus, ln(e2x/x³) = 2x / x³

= 2x1-3 = 2x-2

The point D is called Incenter of ΔABC, because AD, BD and CD are the angle bisector.

Given is a triangle ABC and there are angle bisectors AD, BD and CD which are meeting at point D, we need to identify the name of the point D,

So,

The incenter of a triangle is the point where the three angle bisectors of the triangle intersect.

It is the center of the incircle, which is the largest circle that can be inscribed inside the triangle.

The incenter is equidistant from all three sides of the triangle.

Hence the point D is called Incenter of ΔABC, because AD, BD and CD are the angle bisector.

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The order of G is 24, and the only Subgroups of order 12 are isomorphic to A4 or S3 x Z2, neither of which contain N.

Let us first understand the definitions of subgroups and maximal subgroups.A subgroup is a set of elements in a group that are themselves a group under the group operation.

In other words, a subgroup is a subset of a group that contains the identity element, and is closed under group multiplication and taking inverses.

A maximal subgroup of a finite group G is a proper subgroup M of G, which is not equal to G itself, and such that there are no proper subgroups of G that contain M. In other words, M is as large as possible among all proper subgroups of G.

This means that M is not a subset of any larger proper subgroup of G.Example: Let G be the symmetric group S4 and let H be the subgroup of G generated by (1 2 3) and (1 2).

Then H is not a maximal subgroup of G because it is contained in the larger subgroup K generated by (1 2 3) and (1 2) and (1 3) and (2 4).

On the other hand, if we consider the subgroup N generated by (1 2) and (3 4), then N is a maximal subgroup of G because there are no proper subgroups of G that contain N. This can be seen by noting that any proper subgroup of G must have order 12,

since the order of G is 24, and the only subgroups of order 12 are isomorphic to A4 or S3 x Z2, neither of which contain N.

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Step-by-step explanation:

Using the laws of logorithms, this equals

2 ln (x-1) = 3      

ln(x-1) = 3/2             now   e^x both sides

e^( ln (x-1) =  e^(3/2)  

(x-1)  = e^(3/2)

x = 5.4817

x = 180-73 = 107

6z-103 = x = 107

6x = 107+103 = 210

z = 35

Answer:

  C.  no solution

Step-by-step explanation:

You want to know the solution to the system of equations ...

Equations are best examined for the possible number of solutions when they are written in the same form. Here, we can put both equations into slope-intercept (y=) form by multiplying the second equation by -1.

  -y = -x + 11 . . . . . . . .second equation

  y = x - 11 . . . . . . . . equivalent equation; multiplied by -1

Now, you see that these slope-intercept equations have the same slope (x-coefficient = 1), but different intercepts (11, -11).

Lines with the same slope and different intercepts are parallel lines. They never meet, so never have any points in common. There are no values of x and y that satisfy both equations at the same time.

There are no solutions.

<95141404393>

Answer: x=9

Step-by-step explanation:

Combine like terms

Add 7 to both sides

Simplify the expression

Subtract 4x from both sides

Simplify the expression

Based on the given options, the closest choice to the value of the upper quartile is "O. 54 056."

To find the value of the upper quartile, we first need to arrange the given run times in ascending order:

40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59

Next, we calculate the position of the upper quartile. Since the upper quartile represents the 75th percentile, we divide the data into four equal parts. The upper quartile is located at the position (3/4) * (n + 1), where n is the total number of data points.

In this case, n = 20, so the position of the upper quartile is (3/4) * (20 + 1) = (3/4) * 21 = 15.75. Since the position is not an integer, we can take the average of the values at positions 15 and 16 to find the upper quartile.

The values at positions 15 and 16 are 55 and 56, respectively. Taking the average, we get (55 + 56) / 2 = 111 / 2 = 55.5.

Therefore, the value of the upper quartile is 55.5 seconds.

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Answer:

101.8 unit sqaure

Step-by-step explanation:

Solution Given:

no of side(n)=8

radius(r)=6

Area =?

we have

[tex]\boxed{\bold{Area\: of \:regular\: polygon =nr^2sin(\frac{180}{n})Cos(\frac{180}{n})}}[/tex]

where

r is the radius and n is no of the side.

Now

Substituting Value:

[tex]Area\: of \:regular\: polygon =8*6^2sin(\frac{180}{8})Cos(\frac{180}{8})\\=8*36*0.38268*0.923879\\=101.823[/tex]

in nearest tenth 101.8 unit square

Answer:

101.8 square units

Step-by-step explanation:

The given diagram shows a regular octagon with a radius of 6 units.

The radius of a regular polygon is the distance from the center of the polygon to one of its vertices.

Therefore:

To find the area of a regular polygon given its radius and number of sides, we can use the following formula:

[tex]\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=nr^2\sin \left(\dfrac{180^{\circ}}{n}\right)\cos\left(\dfrac{180^{\circ}}{n}\right)$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]

Substitute n = 8 and r = 6 into the formula and solve for A:

[tex]A=8\cdot 6^2\sin \left(\dfrac{180^{\circ}}{8}\right)\cos\left(\dfrac{180^{\circ}}{8}\right)[/tex]

[tex]A=288\sin \left(22.5^{\circ}\right)\cos\left(22.5^{\circ}\right)[/tex]

[tex]A=101.823376...[/tex]

[tex]A=101.8\; \sf square\;units\;(nearest\;tenth)[/tex]

Therefore, the area of a regular octagon with a radius of 6 units is 101.8 square units, to the nearest tenth.

The calculated measure of the angle ABC is 57.5 degrees

From the question, we have the following parameters that can be used in our computation:

Arc AC = 115 degrees

The angle ABC subtends the arc AC

using the above as a guide, we have the following:

Angle ABC = 1/2 * Arc AC

substitute the known values in the above equation, so, we have the following representation

Angle ABC = 1/2 * 115 degrees

Evaluate the equation

Angle ABC = 57.5 degrees

Hence, the measure of angle ABC is 57.5 degrees

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After gaining 2.3 ounces, the weights of the kittens are 5.9 ounces, 6.5 ounces, and 5.6 ounces, respectively.

To determine the weights of the kittens after gaining 2.3 ounces, we need to add this amount to their initial weights.

The initial weights of the kittens were 3.6 ounces, 4.2 ounces, and 3.3 ounces. Adding 2.3 ounces to each of these weights, we have:

Kitten 1: 3.6 + 2.3 = 5.9 ounces

Kitten 2: 4.2 + 2.3 = 6.5 ounces

Kitten 3: 3.3 + 2.3 = 5.6 ounces

It's worth noting that these calculations assume that all kittens gained the same amount of weight. In reality, weight gain can vary between individuals, and other factors such as health and nutrition can also influence weight. The given information provides a simplified scenario for calculating the weight changes based on a uniform weight gain of 2.3 ounces.

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Answer:

diameter = 2(radius)

Step-by-step explanation:

not sure what your question is but the diameter of a circle is equal to 2 times the length of its radius

The solution sets are  {√5, -√5}, {√61, -√61}, {5√2, -5√2}, {5√2, -5√2},  {3√3, -3√3}, {2√2, -2√2}, {7√3, -7√3}, {2√7, -2√7},  {√2, -√2}, {2√21, -2√21}

Let's solve each quadratic equation one by one:

1. 3x^2 + 4x^2 = 35

Combine like terms:

7x^2 = 35

Divide by 7:

x^2 = 5

Take the square root of both sides:

x = ±√5

Solution set: {√5, -√5}

2. 3x^2 – 28 = 2x^2 + 33

Combine like terms:

x^2 = 61

Take the square root of both sides:

x = ±√61

Solution set: {√61, -√61}

3. x^2 – 25 = 25

Move 25 to the other side:

x^2 = 50

Take the square root of both sides:

x = ±√50

Simplify the square root:

x = ±5√2

Solution set: {5√2, -5√2}

4. 2x^2 – 30 = 70

Move 30 to the other side:

2x^2 = 100

Divide by 2:

x^2 = 50

Take the square root of both sides:

x = ±√50

Simplify the square root:

x = ±5√2

Solution set: {5√2, -5√2}

5. 8x^2 – 6x^2 = 54

Combine like terms:

2x^2 = 54

Divide by 2:

x^2 = 27

Take the square root of both sides:

x = ±√27

Simplify the square root:

x = ±3√3

Solution set: {3√3, -3√3}

6. 3x^2 – 6 = 34 – 2x^2

Move all terms to one side:

5x^2 = 40

Divide by 5:

x^2 = 8

Take the square root of both sides:

x = ±√8

Simplify the square root:

x = ±2√2

Solution set: {2√2, -2√2}

7. x^2 + 49 = 196

Move 49 to the other side:

x^2 = 147

Take the square root of both sides:

x = ±√147

Simplify the square root:

x = ±7√3

Solution set: {7√3, -7√3}

8. 5x^2 – 40 = 100

Move 40 to the other side:

5x^2 = 140

Divide by 5:

x^2 = 28

Take the square root of both sides:

x = ±√28

Simplify the square root:

x = ±2√7

Solution set: {2√7, -2√7}

9. 9x^2 = 4x^2 + 10

Move 4x^2 to the other side:

5x^2 = 10

Divide by 5:

x^2 = 2

Take the square root of both sides:

x = ±√2

Solution set: {√2, -√2}

10. x^2 – 4 = 80

Move 4 to the other side:

x^2 = 84

Take the square root of both sides:

x = ±√84

Simplify the square root:

x = ±2√21

Solution set: {2√21, -2√21}

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(a): The cost, C, depends on the number of people attending, g, and the base cost is $250.

(b):    C(g) = 11g + 250

(c):  C(46) = 806.

(d):         g = 121.

(a) The given equation is,

C= 11g +250

This represents the total cost, in dollars, for a sports banquet when g people attend.

This means that the cost, C, depends on the number of people attending, g, and the base cost is $250.

b) The function can be written as follows,

⇒  C(g) = 11g + 250

c) To determine C(46),

Substitute g = 46 into the function.

So, C(46) = 11(46) + 250

                = 806.

This number represents the total cost, in dollars, for the sports banquet when 46 people attend.

d) To determine the value of g when C(g) = 1581,

Solve the equation 11g + 250 = 1581 for g.

First, we can subtract 250 from both sides to get

⇒ 11g = 1331

Then, we divide both sides by 11 to get

⇒ g = 121.

This number represents the number of people attending the sports banquet when the total cost is $1581.

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Answer:

2 + 3 + 1 + 8 + 4 = 18

3 + 1 + 8 = 12

18 - 12 = 6

6 + 5 = 11

11 + 8 + 2 + 4 = 25

25 - 7 = 18

18 + 2 + 1 + 8 + 3 = 32

32 + 6 = 38

Therefore, the length of the space rock is 38 inches.

Step-by-step explanation:

Answer:

59.3 °

Step-by-step explanation:

its trigonometry

so you have the

opposite side= 43.5

and the adjacent side = 24.8

if you use SOH CAH TOA you will find that to find y you need to use TOA as tou have the opposite and adjacent.

to find the angle (tan) you need to do tue opposite / adjacent

tan^-1 (43.5/25.8)

= 59.3 to 1 d.p.

you need to use tan^-1 as you are finding the missing angle

Answer:

one solution (- 6, 2 )

Step-by-step explanation:

- 3x + y = 20 → (1)

x + y = 4 ( subtract x from both sides )

y = - x - 4 → (2)

substitute y = - x - 4 into (1)

- 3x - x - 4 = 20

- 4x - 4 = 20 ( add 4 to both sides )

- 4x = 24 ( divide both sides by - 4 )

x = - 6

substitute x = - 6 into (2)

y = - x - 4 = - (- 6) - 4 = 6 - 4 = 2

solution is (- 6, 2 )

The value of the fifth term of the sequence is 1/256

From the question, we have the following parameters that can be used in our computation:

Third term, a(3) = 1/4

Common ratio, r = -1/8

Using the above as a guide, we have the following:

The fifth term = Third term * Common ratio * Common ratio

substitute the known values in the above equation, so, we have the following representation

The fifth term = 1/4 * -1/8 * -1/8

Evaluate

The fifth term = 1/256

Hence, the value of the fifth term is 1/256

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The value of the segment RS for the secant through R which intersect the circle at points S and T is equal to 46.4 to the nearest tenth.

Circle theorems are a set of rules that apply to circles and their constituent parts, such as chords, tangents, secants, and arcs. These rules describe the relationships between the different parts of a circle and can be used to solve problems involving circles.

For the tangent RS and the secant through R which intersect the circle at points S and T;

RQ² = RS × ST {secant tangent segments}

42² = x × 38

1764 = 38x

x = 1764/38

x = 46.4211

Therefore, the value of the segment RS for the secant through R which intersect the circle at points S and T is equal to 46.4 to the nearest tenth.

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The probability of rolling the number 3 or more when a die is thrown is 2/3.

The sample space of rolling dice = {1, 2, 3, 4, 5, 6}.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.

Probability of getting the number 3 = 1/6

Probability of getting the number more than 3 = 3/6

So, probability of getting event = 1/6 + 3/ 6

= 4/6

= 2/3

Therefore, the probability of rolling the number 3 or more when a die is thrown is 2/3.

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The equivalent decimal and mixed number for given letter C is,

⇒ C = 8.2 ; 8 2/10

We have to given that,

A number line is shown in image.

Since,

A number lines are the horizontal straight lines in which the integers are placed in equal intervals.

And, All the numbers in a sequence can be represented in a number line. This line extends indefinitely at both ends.

Now, By given number line,

Point C is two point left from point 8.

Hence, The point C is denoted as,

⇒ C = 8.2

⇒ C = 82/10

⇒ C = 8 2/10

Therefore, the equivalent decimal and mixed number for given letter C is,

⇒ C = 8.2 ; 8 2/10

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The number of cards left to be signed is 32 cards.

To determine the number of cards left to be signed, we need to calculate the number of cards signed by each person and subtract it from the total number of cards.First, Emily signed 2/5 of the cards, which is equal to (2/5) * 75 = 30 cards.

Next, we need to find the number of cards remaining after Emily signed. To do this, we subtract the cards Emily signed from the total number of cards:

75 - 30 = 45 cards.

Now, Josh signs 1/9 of the remaining cards, which is equal to (1/9) * 45 = 5 cards.

After Josh signs his portion, we need to find the number of cards still remaining. We subtract the cards Josh signed from the previous remaining cards:

45 - 5 = 40 cards.

Finally, Tatiana signs 20% of what Josh had left, which is equal to 20/100 * 40 = 8 cards.

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The exact solutions of the Quadratic equation x^2 - 3x - 5 = 0 are:

x = (3 + √29) / 2 ,x = (3 - √29) / 2. The correct answer choice is:

x = the quantity of 3 plus or minus the square root of 29 all over 2.

The exact solutions of the quadratic equation x^2 - 3x - 5 = 0 using the quadratic formula, we can identify the values of a, b, and c, and substitute them into the formula:

a = 1

b = -3

c = -5

Now, we can apply the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

Substituting the values into the formula:

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

x = (3 ± √(9 + 20)) / 2

x = (3 ± √29) / 2

Therefore, the exact solutions of the quadratic equation x^2 - 3x - 5 = 0 are:

x = (3 + √29) / 2

x = (3 - √29) / 2

The correct answer choice is:

x = the quantity of 3 plus or minus the square root of 29 all over 2.

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Answer:

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

So the answer is x^4.

Step-by-step explanation:

y-(-9) = -6(x-(-4)), y = -6x-33

The correct option is,

D. Yes, because each x-value has exactly one corresponding y-value

We have to given that,

The graph of a quadratic equation is shown in image.

Since, We know that,

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable and another variable (the dependent variable).

Now, When we apply Vertical line test on the graph.

We get;

Each x-value has exactly one corresponding y-value.

Therefore, The graph of equation is function because each x-value has exactly one corresponding y-value.

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well, let's first find out how much is the bill plus tip.

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{20\% of 100.50}}{\left( \cfrac{20}{100} \right)100.50}\implies 20.10~\hfill~\stackrel{ 100.50~~ + ~~20.10 }{\text{\LARGE 120.60}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{120.60}{\underset{\textit{divided by 2}}{2}}\implies \text{\LARGE 60.30} ~~ \textit{each person}[/tex]

The pair of factors to factor the expression are 7 and -3

From the question, we have the following parameters that can be used in our computation:

x² + 4x - 21

To determine the pair of factors to factor the expression, we find two expressions

using the above as a guide, we have the following:

The expressions are 7x and -3x

So, we have

x² + 4x - 21 = x² + 7x - 3x - 21

When factored, we have

x² + 4x - 21 = (x + 7)(x - 3)

Hence, the pair of factors to factor the expression are 7 and -3

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