Given the following piecewise function, determine the value of g(4) - 3g(3).10%ifx<-3g(x) = {x+ + x2 + x^3* if x 2 3

Answer:

Probability of Four of a Kind

The probability of being dealt four of a kind is 0.0002400960384. On average, four of a kind is dealt one time in every 4,165 deals.

Probability of Two Pair

On average, players get two pair about one time in every 21 deals.

Step-by-step explanation:

Probability of Four of a Kind

Let's execute the analytical plan described above to find the probability of four of a kind.

First, we count the number of five-card hands that can be dealt from a standard deck of 52 cards. This is a combination problem. The number of combinations is n! / r!(n - r)!. We have 52 cards in the deck so n = 52. And we want to arrange them in unordered groups of 5, so r = 5. Thus, the number of combinations is:

52C5 = 52! / 5!(52 - 5)! = 52! / 5!47! = 2,598,960

Hence, there are 2,598,960 distinct poker hands.

We count the number of ways that five cards can be dealt to produce four of a kind. It requires three independent choices to produce four of a kind:

Choose the rank of the card that appears four times in the hand. A playing card can have a rank of 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king, or ace. For four of a kind, we choose 1 rank from a set of 13 ranks. The number of ways to do this is 13C1.

Choose one rank for the fifth card. There are 12 remaining ranks, from which we choose one. The number of ways to do this is 12C1.

Choose a suit for the fifth card. There are four suits, from which we choose one. The number of ways to do this is 4C1.

The number of ways to produce four of a kind (Num4) is equal to the product of the number of ways to make each independent choice. Therefore,

Num4 = 13C1 * 12C1 * 4C1 = 13 * 12 * 4 = 624

Conclusion: There are 624 different ways to deal a poker hand that can be classified as four of a kind.

Finally, we compute the probability. There are 2,598,960 unique poker hands. Of those, 624 are four of a kind. Therefore, the probability of being dealt four of a kind (P4) is:

P4 = 624 / 2,598,960 = 0.0002400960384

The probability of being dealt four of a kind is 0.0002400960384. On average, four of a kind is dealt one time in every 4,165 deals.

Probability of Two Pair

To find the probability for two pair, we execute the same analytical plan that we've used to compute the other probabilities.

There are 2,598,960 distinct poker hands.

Next, count the number of ways that five cards can be dealt to produce two pair. It requires five independent choices to produce two pair:

Choose the rank for cards of matching rank. A playing card can have a rank of 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king, or ace. For two pair, we choose 2 ranks from a set of 13 ranks. The number of ways to do this is 13C2.

Choose the rank of the remaining non-matching card. There are 11 remaining ranks, from which we choose one. The number of ways to do this is 11C1.

Choose suits for the first two-card combination. There are four suits, from which we choose two. The number of ways to do this is 4C2.

Choose suits for the second two-card combination. There are four suits, from which we choose two. The number of ways to do this is 4C2.

Choose a suit for the non-matching card. There are four suits, from which we choose one. The number of ways to do this is 4C1.

The number of ways to produce two pair (Numtp) is equal to the product of the number of ways to make each independent choice. Therefore,

Numtp = 13C2 * 11C1 * 4C2 * 4C2 * 4C1

Numtp = 78 * 11 * 6 * 6 * 4 = 123,552

Finally, compute the probability. There are 2,598,960 unique poker hands. Of those, 123,552 are two pair. Therefore, the probability of being dealt two pair (Ptp) is:

Ptp = 123,552 / 2,598,960 = 0.04753901561

On average, players get two pair about one time in every 21 deals.

Given:

Triangle ABC is similar to triangle XYZ.

In triangle ABC AB=2, BC=4, CA=3.

In triangle XYZ, XY=7, YZ=14, ZX=N.

To find:

The length of ZX.

Solution:

If two triangles are similar, then their corresponding sides are proportional.

Since \(\Delta ABC\sim \Delta XYZ\), therefore

\(\dfrac{AB}{XY}=\dfrac{BC}{YZ}=\dfrac{CA}{ZX}\)

\(\dfrac{2}{7}=\dfrac{4}{14}=\dfrac{3}{N}\)

\(\dfrac{2}{7}=\dfrac{2}{7}=\dfrac{3}{N}\)

\(\dfrac{2}{7}=\dfrac{3}{N}\)

On cross multiplication, we get

\(2\times N=3\times 7\)

\(2N=21\)

Divide both sides by 2.

\(N=\dfrac{21}{2}\)

\(N=10.5\)

Therefore, the length of side ZX is 10.5 units.

Answer:

a

Step-by-step explanation:

the perimeter (P) of a square is the sum of the 4 congruent sides.

the area of a square is calculated as

area = s² ( s is the length of a side )

here area is 36 , then

s² = 36 ( take square root of both sides )

s = \(\sqrt{36}\) = 6

then

P = 4s = 4 × 6 = 24 cm

Answer:

2412

Step-by-step explanation:

(36 x 3) - (-48²)

For the transformations of the triangle, we have that:

1. The translation of triangle ABC preserves side lengths and angles.

2. The dilation of triangle ABC preserves angles but not side lengths.

Hence the correct options are, respectively, C and B.

A translation involves shift left, shift right, shift down, or shift up, meaning that just the coordinates of the figure change, not the angles or the side lengths,

1. The translation of triangle ABC preserves side lengths and angles.

For a dilation, the coordinates of the vertices are multiplied by a constant, hence the side lengths change while the angles remain constant, thus:

2. The dilation of triangle ABC preserves angles but not side lengths.

Hence the correct options are, respectively, C and B.

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Answer:

The value of x is 117.

Step-by-step explanation:

\(180 \\ \frac{ - 63}{117} \)

Answer:

x = 5

Step-by-step explanation:

x + 1 = 6. subtract the given numbers

(5) + 1 = 6. find the solution (x)

x = 5

Answer:

x=5

Step-by-step explanation:

hope this helps

The quadrilateral can bet be classified to be a : Trapezium

A trapezium can be defined as a quadrilateral that has four side. It has a pair of parallel sides which are mostly the top and the bottom.

A trapezium is a shape that is made up of a square and two right angled triangle.

So from the vertices given we could see that the top is smaller than the bottom, which will lead to a trapezium when all four points are joined together.

In conclusion, The quadrilateral can bet be classified to be a Trapezium

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Answer:

32 red cars.

Step-by-step explanation:

Let the red cars be denoted by R

Let the green cars be denoted by G

Translating the word expression into an algebraic equation;

\( R + G = 36\) ...........equation 1

\( R = 8G\) ...........equation 2

Substituting equation 2 into equation 1;

\( 8G + G = 36\)

\( 9G = 36\)

\( G = \frac{36}{9}\)

G = 4

The number of green cars are 4.

From, \( R = 8G\)

\( R = 8*4\)

R = 32

Therefore, the number of red cars that Susan counted are 32.

The coefficient of variation or CV of the given numbers is 45.64%.

Given numbers are,

5, 8, 9, 2, 6

We have to find Coefficient of variation.

CV = (Standard deviation / sample mean ) × 100

Sample mean = Sum of the values / total number of values

                       = (5 + 8 + 9 + 2 + 6) / 5

                       = 6

Standard deviation = √[(Σ(x - mean)² / (n - 1)]

Σ(x - mean)² = (5 - 6)² + (8 - 6)² + (9 - 6)² + (2 - 6)² + (6 - 6)²

                    = 30

Standard deviation = √(30 / (5 - 1) = 2.7386

CV = (2.7386 / 6) × 100

     = 45.64%

Hence CV is 45.64%.

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Answer:

z = 66

Step-by-step explanation:

QT is a midsegment. Thus, applying the midsegment theorem:

RS = 2(QT)

QT = z - 33,

RS = z

Plug in the values into the equation

z = 2(z - 33)

z = 2z - 66

Subtract 2z from each side

z - 2z = -66

-z = -66

Divide both sides by -1

z = 66

Answer:

Basically it just means that you are trying to spend money that you don't have on things you don't need.

Step-by-step explanation:

Taken literally, you can live in a pretty small house and be content. You don;t need to spend tons of money to be happy. This can be a bad thing to do because you don't want to be in debt to anyone, especially when that could have been avoided.

Answer:  The correct answer is b=5g/(n^3−t)

Step-by-step explanation:

Solve for b in the following equation

n³b - tb = 5g

First factor out variable b

b(n^3−t)=5g

Divide both sides by n^3-t

b(n^3−t)/n3−t=5g/n^3−t

b=5g/(n^3−t)

20 × 23 + 20 - 23 can be simplified to 460 + 20 - 23, which can be simplified further to 480 - 23, or 457.

Answer:

1.646%

Step-by-step explanation:

Sample size (n) = 2000

Sample Proportion p = 17% = 0.17

α = 0.95

Margin of Error :

Z(1-α)/2 * √((p*(1 - p)) /n)

Z(1 - 0.95/2) * √((0.17 * (1 - 0.17) / 2000)

Zscore = 1.96

1.96 * √(0.1411/2000)

1.96 * √0.00007055

1.96 * 0.0083994

Hence,

1.96 * 0.0083994

= 0.0164628

= 0.0164628 * 100%

= 1.646%

The margin of error for the random sample 2,000 driver's license applications is 1.646%.

The probability or the chances of error while choosing or calculating a sample in a survey is called the margin of error.

It can be found out using the following formula.

\(MOE=Z_{\frac{\alpha}{2}}\times\left(\sqrt{p\times\dfrac{1-p}{n}}\right)\)

Here, α is the level of significance, n is the sample size and p is the sample proportion.

A random sample of 2,000 driver's license applications found that 17% reported their eye color as blue.

Let level of significance is 0.05. At this level of significance the critical value of Z is 1.96. Put the values in the above formula as,

\(MOE=(1.96)\times\left(\sqrt{0.17\times\dfrac{1-0.17}{2000}}\right)\\MOE=0.01646\\MOE=1.646\%\)

Thus, the margin of error for the random sample 2,000 driver's license applications is 1.646%.

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The coordinates of the vertices for the image is A′(−3, 6), B′(0, 10), C′(−3, 3).

The vertices of the preimage triangle ABC are given as A(-3,3), B(0,7), and C(-3,0). To translate the preimage 3 units up, we need to add 3 to the y-coordinate of each vertex. Therefore, the vertices of the image triangle A'B'C' will be A'(-3,6), B'(0,10), and C'(-3,3). Thus, option B, A′(−3, 6), B′(0, 10), C′(−3, 3), is the correct answer.

To check the answer, we can plot the points on a coordinate plane and observe that the image triangle is obtained by moving the preimage triangle 3 units up. Translation is a type of transformation in which the position of a figure is changed without changing its shape or orientation.

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Here we have a dilation of scale factor 2.

We can see that bot figures we have the same slope, so we just have a dilation of scale factor K to go from figure A to figure B.

To find the value of K, notice that for some side length L in figure A, the correspondent length L' in figure B must be:

L' = K*L

Here if we use the left sides, we will get:

for figure A; L= 2

for figure B: L = 4

4 = K*2

4/2 = K

2 = K

So this is a dilation of scale factor k = 2.

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Answer:

The National Woman Suffrage Association advocated for a range of reforms to make women equal members of society, such as the right to own property, etc. The American Woman Suffrage Association lobbied state governments to enact laws granting or expanding women's right to vote in the United States.

Answer:

C: The NWSA wanted to address the voting rights of both women and formerly enslaved people.

Step-by-step explanation:

The NWSA wanted to address and justify the rights of both former slaves and women, while the AWSA only wanted to either help women or former slaves, not simultaneously.

Answer:

Step-by-step explanation:

-4(3)² - 1/5(-5) + 1/7(-21)

-4(9) + 1 - 3

-36 + 1 - 3

-35 - 3 = -38

The increase in height (rise) of the balloon is \(35.53 feet\)

What is Pythagorean Theorem?

Pythagoras' theorem states that "the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides."

The angle of elevation is generated by the intersection of the horizontal line and the line of sight. If the line of sight is directed upward from the horizontal line, the resulting angle is an angle of elevation.

According to the given information:

Given that,

Initial angle of elevation = \(19.3^{0}\).

Final angle of elevation = \(32.3^{0}\).

Distance = \(126 feet\).

How to calculate the height (rise).

In order to determine the increase in height (rise) of the balloon, we would apply Pythagorean Theorem. Mathematically, this is given by this formula:

tan∅ = \(\frac{height}{adj}\)

height = adjacent \(*\) tan∅

At an initial angle of elevation:

height \(=126* tan 19.3^{0} \\= 126 * 0.3501\\= 44.11 feet\)

At a final angle of elevation:

height \(=126* tan 32.3^{0} \\= 126* 0.6321\\= 79.64 feet\)

For the change in height:

Δh \(= 79.64-44.11\\=35.53 feet\)

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Answer: a= 16 a=8

              b=4 b=2

because, 2 when multiplied by 4 gives 8

4 when multiplied gives 16

The cuboid has the following dimensions (A = 11 in, B = 4 in, C = 8 in, D = 4 in) and the following surface areas: Lateral: S = 264 in², Total: S' = 328 in².

In this problem we find a cuboid, whose lateral and total surface area must be found. The lateral surface area is the sum is the sum of the areas of all faces except bases and the total surface area is the sum of the areas of the six faces. The area formula needed for the surface area is the rectangle:

S = w · h

Where:

Sides

A = 11 in, B = 4 in, C = 8 in, D = 4 in

Lateral surface area

S = 2 · (11 in) · (4 in) + 2 · (11 in) · (8 in)

S = 88 in² + 176 in²

S = 264 in²

Total surface area

S' = 2 · (4 in) · (8 in) + 264 in²

S' = 328 in²

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Among the mean, mode, and median, the unique one is the b. mode.

The mode is the data value that occurs many times more than other data values.

Unlike the mean that shows the average value of all the data values, the mode occurs more.  While we compute the mean by dividing the total data value by the number of data items, the mode is not computed but found as the most frequent data value.

Similarly, the median can be computed when two values occur as the middle values.

Thus, among the three measures of central tendency, the mean, the median, and the mode, the mode is the most unique since it is not computed.

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If the value of sin x = 0.2, then the values for sin(π - x) is 0.2.

Given that,

the value of sin x = 0.2

We have to find the value of sin(π - x).

We know the trigonometric rule that,

sin(π - x) = sin (x)

for any value of x.

So here whatever the value of x, the value of  sin(π - x) is sin (x) itself.

So here sin x = 0.2.

So, by the rule,

sin(π - x) = sin (x) = 0.2

Hence the value is 0.2.

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Initially she had 70 pounds in her gift card.

After buying her coffee she was left with 36.04 pounds.

Amount she spent on coffee is 70-36.04=34.96

One pound of coffee costs 8.49

To calculate how many pounds of coffee Lisa bought ->

34.96/8.49= 4

So in total she bought 4 pounds of coffee.

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Answer:

1191 cm²

Step-by-step explanation:

Area of parallelogram = base X vertical height.

Call the vertical line h.

h/ sin 80  =  7/ sin 10

h = (7 sin 80) / sin 10

= 39.7.

Area of parallelogram = 30 X 39.7

= 1191 cm²

The Area of Parallelogram whose side length is 30 cm is 1,190.952 square cm.

Given:

Side length = 30 cm

Using Trigonometry

tan 80 = P / Base

5.6712 = P / 7

P = 39.6984 cm

Using the formula for Area of parallelogram

= Base x height

= 30 x 39.6984

= 1,190.952 square cm.

Therefore, the area is 1,190.952 square cm.

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Answer:

Step-by-step explanation:

A

Answer:

Step-by-step explanation:

1)  DE = 6/sin63 = 6.7

DF = 6/tan63 = 3.1

m∠E = 180 - 90 - 63 = 27°

2)  tan30 = 1/√3 = UV / (27√10)

UV = (27√10) / √3 · (√3/√3) = (27√30) / 3 = 9√30

3)  cosV = 3/8

cos⁻¹(3/8) = 68

m∠V = 68°