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Trapezoid PQRS
4650
be inscribed in a circle because the
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65°

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

Answer:

2.45 units

5 units

5.99 units

5.10 units

20 girls and 30 boys

A branch of mathematics that deals usually with the nonnegative real numbers including sometimes the transfinite cardinals and with the application of the operations of addition, subtraction, multiplication, and division to them

To make the new situation:

Suppose A classroom has 50 people.

The ratio of girls to boys is 2:3, so in other words, we need to find out how many boys and girls there are, and there are 2 girls for every three boys, So ,how many boys and girls are there?

The answer would be :

Let the two parts in which we divide 50 be 2x and 3x respectively

2x+3x=50

5x=50

x= [tex]\frac{50}{5}[/tex]

x=10

Here,

2x= 2×10=20

3x =3*10=30

20 girls and 30 boys.

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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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For this problem, I will be using the equal sign instead of the congruent sign for segments.

1) AC = AB, CD = DE, m∠ABC = 70°, m∠ECB = 35° (given)

2) ∠ACB is congruent to ∠ABC (base angles theorem)

3) m∠ACB = 70° (congruent angles have equal measure)

4) m∠DCE = 35° (angle subtraction postulate)

5) ∠DCE and ∠DEC are congruent (base angles theorem)

6) m∠DEC = 35° (congruent angles have equal measure)

7) ∠DEC is congruent to ∠ECB (angles with the same measure are congruent)

8) DE is parallel to BC (if two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel)

Answer:

353.9 + 3.8 = 357.7 million barrels of oil

Answer:

x = 2

Step-by-step explanation:

AB is given as 3(3x-1) multiply inside the parenthesis with 3

AB = 9x - 3

AC is given as 5(2x+2) multiply inside the parenthesis with 5

AC = 10x + 10

if B is midpoint of AC then AB = BC and AC = AB + BC if we write this equation using the given values

9x - 3 + 9x - 3 = 10x + 10 add like terms

18x - 6 = 10x + 10 transfer like terms to the same side of the equation

18x - 10x = 10 + 6

8x = 16 divide both sides by 8

x = 2 replace x with 2 in given expressions to find the value of each component

Answer:   x = 2; AB = 15; BC = 15; AC = 30

Step-by-step explanation:

AB = BC = 3(3x - 1) = 9x - 3

AC = 5(2x + 2) = 10x + 10

AB + BC = AC

(9x - 3) + (9x - 3) = 10x + 10

   9x - 3 + 9x - 3 = 10x + 10

               18x - 6 = 10x + 10

                8x - 6 = 10

                      8x = 16

                        x = 2

Plug x = 2 to find AB, BC, and AC.

AC = BC = 3(3x - 1) = 9x - 3 = 9(2) - 3 = 18 - 3 = 15

AC = 5(2x + 2) = 10x + 10 = 10(2) + 10 = 20 + 10 = 30

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

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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The following logarithmic expression can be used to approximate the given expression,

[tex]\frac{log_{b} x}{log_{b} a}[/tex]

Finding the Logarithmic Expression

It is given that for all positive numbers a, b, and x on the condition that a≠1 and b≠1.

Now, for positive values of m and n, we have the following logarithmic expression,

[tex]\frac{log_{m} x}{log_{n} a}[/tex]

Here, m, n and x are all positive numbers.

The logarithmic property imposes that m and n are not equal to 1.

So, by substituting the values m and n by a and b respectively, we get the following logarithmic expression,

[tex]\frac{log_{b} x}{log_{b} a}[/tex]

Therefore, [tex]\frac{log_{b} x}{log_{b} a}[/tex] is the required expression.

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Answer:

n(AnB)= {4, 29}

n(BnC)= {9,29}

n(AnC)= {29}

Answer:

Step-by-step explanation: The answer is 5/11.



Hello!

Fraction of boys = Number of boys / Total kids

Fraction of boys = [tex]\boxed {\frac{5}{11}}[/tex]

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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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 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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The graph that has been drag into the box in the image attached are the options that shows the results of that transformation.

Note that there are 4 types of function transformations which are are:

Therefore, The function above is known to have passed through the following points

(1,1) and (0,-1)

The graphs of the functions

(a) Function g(x)

The equation of the function is given as: g (x) = 2 + f (x)

This implies that f(x) is said to be translated up by 2 units.

The graph that shows this is graph (b)

(b) Function h(x) = f (x + 2)

This implies that f(x) is translated left by 2 units.

The graph that shows this is graph (e)

(c) Function k(x)  = f (x) -2

This implies that f(x) is translated down by 2 units.

The graph that shows this is graph (c)

(d) Function m(x) =  f (x - 2)

This implies that f(x) is translated right by 2 units.

The graph that depicts this is graph (f)

Therefore,  The graph that has been drag into the box in the image attached are the options that shows the results of that transformation.

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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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What is initial value?

It is given that,

The height of the palm tree at the time Myles bought it was 62 inches.

He is tracking the growth of the tree and he has observed that it has grown 6 inches per year.  

So, the initial value of the tree, here, is representing the height of the palm tree when it was bought.

As can be seen clearly, there is no input for the initial value. And, the output for the initial value is given to be 62 inches.

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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 = -2x+2

Step-by-step explanation:

See attached image

To find Y-intercept, the x-value must be 0.

In the table you can see x = 0 and y = -4

so, the y-intercept of this line is (0 -4)

Hope it helps!

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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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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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 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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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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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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