In a New York State daily lottery game, a sequence of five digits (not necessarily different) in the range 0-9 are selected at random. Find the probability that four of the five digits are the same.

Construction is a process in which required steps are considered to draw a given shape by the use of construction instruments and materials. Thus to correct the error in the given question, the third arc should be drawn centered at point F. Answer is option A.

Majorly, the use of a straight edge and a pair of compasses to draw the image of a given object is referred to as construction. Which required adhering to some steps.

The construction of a parallel line through a given point to a given line involves following the appropriate procedure. If not, an error would be committed which would result in an inappropriate shape or figure.

Therefore, to fix the error in the given question, it is important that the third arc should be drawn centered at point F. Thus, the correct answer is option A.

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The equation which determines the painted area is (x+15)(x+10)-5.

Given that there is a rectangle with a length of x plus 15 and width of x plus 10 with a rectangle in the bottom right corner labeled bench that has a given length of 5 and width of 1.

A rectangle is a two-dimensional (2D) form in which the four angles are all right angles and the opposite sides are parallel and equal to one another. The region that the rectangle's perimeter encloses is known as its area, which is equal to the product of its length and width.

Let the length of the patio be L=x+15.

The width of the patio be W=x+10.

So, the Area of the patio will be painted is, A₁=L×W

A₁=(x+15)(x+10)

Let the Length of the bench be L₁=5

The width of the bench be W₁=1

So, the Area of the bench will be painted is, A=L₁×W₁

A₂=5×1

A₂=5

The net area of the patio that will be painted is

A=A₁-A₂

A=(x+15)(x+10)-5

Hence, the equation which is used determines the area, A, of the patio that will be painted is (x+15)(x+10)-5.

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The value of x is 2wy + y - 1.

Given: (2x + 2)/y = 4w + 2

To find: the value of x

the following steps will be used.

First, Multiply both sides by y

y * (2x + 2)/y = (4w + 2) * y

2x + 2 = 4wy + 2y

Subtract 2 from both sides

2x + 2 - 2 = 4wy + 2y - 2

2x = 4wy + 2y - 2

Multiply both sides by ½

½ * 2x = ½(4wy + 2y - 2)

x = ½(4wy + 2y - 2)

Open bracket

x = ½ * 4wy + ½ * 2y - ½ * 2

x = 2wy + y - 1

Hence, the value of x is 2wy + y - 1.

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Answer:

18.54

Step-by-step explanation:

sine is opposite/hypotenuse, and you have opposite (b=15), so use that

sin(54) = 15/c

c = 15/sin54

then use calculator

c = 18.54

The expansion of the given expressions are; 4x² - 5x - 5;  2x² - 13x + 15; -2x² - 5x + 3; 3x² + 6x - 1

A) x(x - 5) + 3x² - 5

Expanding this gives us;

x² - 5x + 3x² - 5

⇒ 4x² - 5x - 5

B) (2x - 3)(x - 5)

Expanding the function gives;

⇒ (2x² - 3x - 10x + 15)

⇒ 2x² - 13x + 15

C) -2x(x + 3) + x + 3

⇒ -2x² - 6x + x + 3

⇒ -2x² - 5x + 3

D) 3(x + 1)² - 4

⇒ 3(x² + 2x + 1) - 4

⇒ 3x² + 6x + 3 - 4

⇒ 3x² + 6x - 1

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Answer:

y = - x + 10

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (6, 4 ) and (x₂, y₂ ) = (8, 2 )

m = [tex]\frac{2-4}{8-6}[/tex] = [tex]\frac{-2}{2}[/tex] = - 1 , then

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (6, 4 ) , then

4 = - 6 + c ⇒ c = 4 + 6 = 10

y = - x + 10 ← equation of line

The values of the trigonometric functions are

7. [tex]sin\theta = \frac{12}{13}[/tex]

[tex]cos\theta = \frac{5}{13}[/tex]

[tex]tan\theta = \frac{12}{5}[/tex]

[tex]csc\theta =\frac{13}{12}[/tex]

[tex]sec\theta =\frac{13}{5}[/tex]

[tex]cot\theta =\frac{5}{12}[/tex]

8. [tex]sin\theta = \frac{\sqrt{7} }{4}[/tex]

[tex]cos\theta = \frac{12}{16}[/tex]

[tex]tan\theta =\frac{\sqrt{7} }{3}[/tex]

[tex]csc\theta = \frac{4}{\sqrt{7} } \ OR \ \frac{4\sqrt{7}}{7}[/tex]

[tex]sec\theta =\frac{16}{12}[/tex]

[tex]cot\theta = \frac{3}{\sqrt{7}} \ OR \ \frac{3\sqrt{7}}{7}[/tex]

From the question, we are to determine the values of the given trigonometric functions

7.

In the given triangle,

Opposite = 12

Adjacent = 5

Hypotenuse = ?

Hyp² = Opp² + Adj² (Pythagorean theorem)

∴ Hyp² = 12² + 5²

Hyp² = 144 + 25

Hyp² = 169

Hyp =√169

Hyp = 13

Using SOH CAH TOA

[tex]sin\theta = \frac{12}{13}[/tex]

[tex]cos\theta = \frac{5}{13}[/tex]

[tex]tan\theta = \frac{12}{5}[/tex]

[tex]csc\theta =\frac{1}{sin\theta} =\frac{13}{12}[/tex]

[tex]sec\theta =\frac{1}{cos\theta} =\frac{13}{5}[/tex]

[tex]cot\theta =\frac{1}{tan\theta} =\frac{5}{12}[/tex]

8.

Hypotenuse = 16

Adjacent = 12

Opposite = ?

Hyp² = Opp² + Adj² (Pythagorean theorem)

Opp² = Hyp² - Adj²

∴ Opp² = 16² - 12²

Opp² = 256 - 144

Opp² = 112

Opp =√112

Opp = 4√7

Using SOH CAH TOA

[tex]sin\theta = \frac{4\sqrt{7} }{16} = \frac{\sqrt{7} }{4}[/tex]

[tex]cos\theta = \frac{12}{16}[/tex]

[tex]tan\theta = \frac{4\sqrt{7} }{12}= \frac{\sqrt{7} }{3}[/tex]

[tex]csc\theta =\frac{1}{sin\theta} =\frac{16}{4\sqrt{7} } = \frac{4}{\sqrt{7} } \ OR \ \frac{4\sqrt{7}}{7}[/tex]

[tex]sec\theta =\frac{1}{cos\theta} =\frac{16}{12}[/tex]

[tex]cot\theta =\frac{1}{tan\theta} =\frac{12}{4\sqrt{7}} = \frac{3}{\sqrt{7}} \ OR \ \frac{3\sqrt{7}}{7}[/tex]

Hence, the values of the trigonometric functions are

7. [tex]sin\theta = \frac{12}{13}[/tex]

[tex]cos\theta = \frac{5}{13}[/tex]

[tex]tan\theta = \frac{12}{5}[/tex]

[tex]csc\theta =\frac{13}{12}[/tex]

[tex]sec\theta =\frac{13}{5}[/tex]

[tex]cot\theta =\frac{5}{12}[/tex]

8. [tex]sin\theta = \frac{\sqrt{7} }{4}[/tex]

[tex]cos\theta = \frac{12}{16}[/tex]

[tex]tan\theta =\frac{\sqrt{7} }{3}[/tex]

[tex]csc\theta = \frac{4}{\sqrt{7} } \ OR \ \frac{4\sqrt{7}}{7}[/tex]

[tex]sec\theta =\frac{16}{12}[/tex]

[tex]cot\theta = \frac{3}{\sqrt{7}} \ OR \ \frac{3\sqrt{7}}{7}[/tex]

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The HCF are

This is the common factor that is the highest that a group of numbers can have in common.

1. 6 and 15

factors of 6 =  1, 2, 3, 6

factors of 15:  1, 3, 5, 15

The HCF is the number they have in common = 3

2. 12 and 18

The factors of 12:  1, 2, 3, 4, 6, 12

The factors of 18:  1, 2, 3, 6, 9, 18

The HCF = 6

3. 15 and 24

Factors of 15:  1, 3, 5, 15

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

The HCF = 3

4. 24 and 36

The factors of 24:  1, 2, 3, 4, 6, 8, 12, 24

The factors of 36:  1, 2, 3, 4, 6, 9, 12, 18, 36

The HCF :  12

5. 30 and 48

The factors of 30:  1, 2, 3, 5, 6, 10, 15, 30

The factors of 48:  1, 2, 3, 4, 6, 8, 12, 16, 24, 48

The HCF = 6

6. 36 and 54

The factors of 36:  1, 2, 3, 4, 6, 9, 12, 18, 36

The factors of 54:  1, 2, 3, 6, 9, 18, 27, 54

The hcf = 18

7. 32,40 and 56

The factors of 32:  1, 2, 4, 8, 16, 32

The factors of 40:  1, 2, 4, 5, 8, 10, 20, 40

The factors of 56:  1, 2, 4, 7, 8, 14, 28, 56

The HCF is 8

8. 28,42 and 70

The factors of 28:  1, 2, 4, 7, 14, 28

The factors of 42:  1, 2, 3, 6, 7, 14, 21, 42

The factors of 70:  1, 2, 5, 7, 10, 14, 35, 70

The HCF = 14

9. 30,75 and 90

The factors of 30:  1, 2, 3, 5, 6, 10, 15, 30

The factors of 75:  1, 3, 5, 15, 25, 75

The factors of 90:  1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

The HCF is 15

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Probability helps us to know the chances of an event occurring. The correct option is A.

Probability helps us to know the chances of an event occurring.

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

The probability of getting a heart from the first deck is 13/52. And the probability of getting a diamond from the second deck is 13/52. The probability of getting a heart from the first deck and then a diamond on the second deck is,

Probability = (13/52) × (13/52) = 0.0625 = 6.25%

Hence, the correct option is A.

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Answer:

y = -2x+2

Step-by-step explanation:

See attached image

Because you make a "half circle" when you bisect an angle, neither a ruler nor a compasses are needed. Because a bisected angle wouldn't be straight, you wouldn't need either of the two.

Teams of no more than six pupils will be formed from the total group of participating students by the teachers.

Four teachers offer an after-school chess club the table shows the number of students who joined In the box, type your response. teams Part B With 18 chess sets at its beginning, the chess club. Three cases of 15 chess sets were ordered by the professors. To provide each teacher an equal number of chess sets, they will divide the total number of chess sets. Any extra sets will then be donated to the school library.

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Answer:

R = 33.35%

Step-by-step explanation:

that is the solution above

The rigid transformations which will map the triangle ABC to triangle DEF is; Translate vertex A to vertex D, and then rotate△ABC around point A to align the sides and angles.

It follows from the task content that the two triangles given are △ABC to △DEF.

Hence, in a bid to map the triangle ABC to DEF, Vertex A is translated to point D which represents vertex D in△DEF. Afterwards, the triangle ABC is simply rotated about the translated vertex A until all sides and angles of both triangles align.

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Let [tex]S_n[/tex] be the [tex]n[/tex]-th term in this sequence, so

[tex]S_1 = 1[/tex]

[tex]S_2 = 1 + 2[/tex]

[tex]S_3 = 1 + 2 + 2^2[/tex]

and so on, with general [tex]n[/tex]-th term

[tex]S_n = 1 + 2 + 2^2 + \cdots + 2^{n-1} = \displaystyle \sum_{i=1}^n 2^{i-1}[/tex]

Observe that

[tex]2 S_n = 2 + 2^2 + 2^3 + \cdots + 2^n[/tex]

and by subtracting this from [tex]S_n[/tex], we eliminate all but the outermost terms, namely

[tex]S_n - 2S_n = 1 - 2^n[/tex]

so that

[tex]-S_n = 1 - 2^n[/tex]

[tex]S_n = 2^n - 1[/tex]

Now, the sum of the first [tex]n[/tex] terms of the sequence [tex]\{S_1,S_2,S_3,\ldots,S_n\}[/tex] is

[tex]S = S_1 + S_2 + S_3 + \cdots + S_n[/tex]

[tex]S = \displaystyle \sum_{i=1}^n S_i[/tex]

[tex]S = \displaystyle \sum_{i=1}^n (2^i - 1)[/tex]

[tex]S = \displaystyle \sum_{i=1}^n 2^i - \sum_{i=1}^n 1[/tex]

[tex]S = \displaystyle 2 \underbrace{\sum_{i=1}^n 2^{i-1}}_{S_n} - n[/tex]

[tex]S = 2(2^n - 1) - n[/tex]

[tex]S = \boxed{2^{n+1} - n - 2}[/tex]

The true equation about the functions is (d) g(2) = h(2) = 7

The graph that completes the question is added as an attachment

The function is given as:

h(x) = 2^x + 3

Calculate h(2) and h(7)

h(2) = 2^2 + 3 = 7

h(7) = 2^7 + 3 = 131

From the graph, we have:

g(2) = 7

g(7) = 610

By comparison, we have:

g(2) = h(2) = 7

Hence, the true equation is (d) g(2) = h(2) = 7

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Answer:

353.9 + 3.8 = 357.7 million barrels of oil

The geometric model to factor 3x²+4x+1 can be shown as given below in the form of geometric tiles.

A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.

The geometric model to factor 3x²+4x+1 can be shown as given below in the form of geometric tiles.

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Answer:

n(AnB)= {4, 29}

n(BnC)= {9,29}

n(AnC)= {29}

Using the normal distribution, it is found that the operating cost for the lowest 3% of the airplanes is of at most $1,630.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 2100, \sigma = 250[/tex].

The operating cost for the lowest 3% of the airplanes is of at most the 3rd percentile, hence at most X when Z = -1.88.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-1.88 = \frac{X - 2100}{250}[/tex]

X - 2100 = -1.88(250)
X = 1630.

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The probability that the person uses the gym and track but not the pool is; 1/5.

According to.the task content, it follows that 31 people use the gym and track while 4 people use all three facilities.

Hence, it follows that; 31-4 = 27 people use the gym and track but not the pool. On this note, the required probability is; 27/135 = 1/5.

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The solution to the graph is the yellow area highlighted in the graph. The point (2, 0) is a solution since it lies on the yellow area.

An equation is an expression that shows the relationship between two or more variables and numbers.

The compound inequality represented by the graph is y ≥ 2x - 4, x > -3 and y < 5.

The solution to the graph is the yellow area highlighted in the graph. The point (2, 0) is a solution since it lies on the yellow area.

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The probability that the mean of a sample of 106 randomly selected humans is lower than 98.5°F is 4.85%

An equation is an expression that shows the relationship between two or more numbers and variables.

Z score is given as:

z = (raw score - mean) ÷ (standard deviation/√sample size)

Given mean of 98.6°F,  standard deviation is 0.62°F, sample size = 106

For x < 98.5:

z = (98.5 - 98.6) ÷ (0.62÷√106) = -1.66

P(z < -1.66) = 0.0485

The probability that the mean of a sample of 106 randomly selected humans is lower than 98.5°F is 4.85%

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Answer:

To find the x-intercepts of a quadratic equation, let y = 0. Write down the new equation ax squared + bx + c = 0 and the quadratic formula that gives the solution as x = -b plus or minus the square root of (b squared - 4ac), all divided by 2a.

Step-by-step explanation:

Hope this helps.

Answer:

-3, 5

Step-by-step explanation:

The x-intercepts are the same as the zeros.

Answer:

(1+3i)(1-3i)

Step-by-step explanation:

When these terms have the same pair of numbers in them, but one set has a PLUS and one set has a MINUS, these are called CONJUGATES.

When you multiply CONJUGATES, you will eliminate the imaginary number, i.

Remember i^2=-1

see image.

Probability means Possibility. It states how likely an event is about to happen. The probability of an event can exist only between 0 and 1 where 0 indicates that event is not going to happen i.e. Impossibility and 1 indicates that it is going to happen for sure i.e. Certainty.

I'll take a stab at this one. if the number of dice showing a two-digit number  = the number of dice showing a one-digit number, then  2 must show a two-digit number and 2  must show a one-digit number

There are 3 two-digit numbers and 9 one-digit numbers on each die

So....the probability is

C(4,2) (3/12)^2 (9/12)^2    =  

C(4,2) (1/4)^2 (3/4)^2  =

27/128.

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There is a reflection at the boundary between two materials if there is a change of the speed of light in the material at the boundary.

This bending is referred to as refraction. whilst a wave traveling at an angle adjusts its velocity upon crossing a boundary among materials,. This bending is known as refraction. As a wave crosses a boundary into a new medium, its pace, and wavelength exchange simultaneously as its frequency stays equal.

While light from air hits a smooth piece of glass (n = 1. five) with the ray perpendicular to the glass floor, of the subsequent will occur while light from air hits a clean piece of glass with the ray perpendicular to the glass surface, the part of the light passing into the glass: will now not exchange its frequency.

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