Consider a post office with two clerks. Three people, A, B, and C, enter si- multaneously. A and B go directly to the clerks, and C waits until either A or B leaves before he begins service. What is the probability that A is still in the post office after the other two have left when

Answer:

A) x = -1

Step-by-step explanation:

[tex]f(-1)=3^{-1}=\dfrac13\\\\g(-1)=2(-1)+5=3\\\\\implies f(x) < g(x)[/tex]

[tex]f(2)=3^{2}=9\\\\g(2)=2(2)+5=9\\\\\implies f(x)=g(x)[/tex]

[tex]f(-3)=3^{-3}=\dfrac{1}{27}\\\\g(-3)=2(-3)+5=-1\\\\\implies f(x) > g(x)[/tex]

[tex]f(-4)=3^{-4}=\dfrac{1}{81}\\\\g(-4)=2(-4)+5=-3\\\\\implies f(x) > g(x)[/tex]

Answer:

B

Step-by-step explanation:

Because you are multiplying the 20 by the 10 and 5 to get the percentage that wheat increased. all the other options are either just adding number together of multiplying the wrong numbers.

Answer:. Then either A = C and B = D, or A = D and B = C.

Step-by-step explanation:

Answer:

Today: Monday, 12 October 2020

Hour: 20.25 WIB (in Indonesian)

________________________

18 + (-22.45) = -4,45

-22.45

18

_____+

-4.45

Applying the definition of a parallelogram, the value of x in the length of the sides of the given parallelogram is: x = 3.

A parallelogram is a quadrilateral that has two pairs of opposite sides that are congruent to each other.

Given the following:

Find x by creating an equation:

PQ = RS (congruent sides)

Substitute

9x + 1 = 13x - 11

Combine like terms

9x - 13x = -1 - 11

-4x = - 12

x = 3

Therefore, applying the definition of a parallelogram, the value of x in the length of the sides of the given parallelogram is: x = 3.

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Answer:

330

Step-by-step explanation:

heart = 110, and the problem is asking the value of 3 hearts. 3 x 110 = 330

Answer:

d: 330

Step-by-step explanation:

spade  = heart*2

spade-heart = 110

substitute spade into spade:

2*heart-heart = 110

heart = 110

So,

heart = 110

and,

spade = 2*heart = 2*110 = 220

so spade+heart = 220 + 110 = 330

also, please mark me as brainliest.

Step-by-step explanation:

(y2-y1)/(x2-x1)=(y-y1)/(x-x1)

(-21-15)/(-2-4)=( y-15)/(x-4)

6(x-4)=y-15

6x-y-9=0

Step-by-step explanation:

Since you added 12 to the x coordinate and subtracted 7 from the y coordinate, to undo that translation, you need to subtract 12 from the x coordinate of the image and add 7 to the y coordinate of the image.

This gives you that C=(-2-12, 1+7)=(-14, 8)

Answer:

C. Natural Numbers

Step-by-step explanation:

Before we determine what groups [tex]\sqrt{100}[/tex] fits into, we must simplify it.  We get the number 10, which is much easier to categorize.  Out of the four options, the natural numbers are the smallest group, containing only the numbers we use to count (i.e. 1, 2, 3, 4 ...).  We know that 10 fits into this category because 10 is a non-zero whole number.  Since the natural numbers contain 10 and are the smallest subset, the answer is C.

As a note: 10 will also fit into the whole numbers and rational numbers since all natural numbers are parts of these two groups as well.  These groups contain more numbers, however, making them larger than the natural number set so we can eliminate them.  10 is also not an irrational number since we can accurately define it with a fraction.

Answer:

y = 6x - 2

Step-by-step explanation:

y = mx + b

y = 6x + (-2)

Answer:

4,500

Step-by-step explanation:

Area:-

Answer:

[tex]A=\boxed{10.5}\; \;\rm sq. \; un.[/tex]

Step-by-step explanation:

Area of a Trapezoid

[tex]\boxed{A=\dfrac{1}{2}(a+b)h}[/tex]

where:

From inspection of the given diagram:

Substitute the found values into the formula and solve for A:

[tex]\implies A=\dfrac{1}{2}(2+5)(3)[/tex]

[tex]\implies A=\dfrac{1}{2}(7)(3)[/tex]

[tex]\implies A=\dfrac{7}{2}(3)[/tex]

[tex]\implies A=\dfrac{21}{2}[/tex]

[tex]\implies A=10.5\; \;\rm sq. \; un.[/tex]

Answer:

It would be 6

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

5x + 2 - 7x = -10

Combine the two x's:

-2x + 2 = -10

Subtract 2 from both sides:

-2x = -12

Divide both sides by -2:

x = 6

Answer:

See attached

Step-by-step explanation:

Refer to attachment

ΔA'B'C' is the image of ΔABC

(a) ∠ORP and ∠ORN are a linear pair .

Let us prove that option a , is the correct option by finding the value of x .

Angle ORP and angle ORN are a linear , which means their sum will be equal to 180° .

So :-

[tex]80 + 3x + 10 = 180[/tex]

[tex]3x + 80 + 10 = 180[/tex]

[tex]3x + 90 = 180[/tex]

[tex]3x = 180 - 90[/tex]

[tex]3x = 90[/tex]

[tex]x = \frac{90}{3} [/tex]

[tex]x = 30°[/tex]

As we were able to find put the value of x only after we cam to know that ∠ORP and ∠ORN are a linear pair , we say that option a is the correct statement .

Therefore , the correct answer is :-

(a) ∠ORP and ∠ORN are a linear pair .

The value of x is equal to 30°. Hence, proved.

Angles on a straight line relate to the sum of angles that can be arranged together so that they form a straight line. Angles on a straight line add to 180°.

Given that, m∠ORP=80° and m∠ORN=(3x+10)°.

Here, m∠ORP+m∠ORN=180° (Angles on straight line adds upto 180°)

80°+(3x+10)°=180°

90°+3x=180°

3x=90°

x=90°/3

x=30°

Hence, proved.

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Answer:

Step-by-step explanation:

the least value is negative 9 x 10-³

the greatest value is positive 7 x 10-⁵

Answer:

2,4,1,3

Step-by-step explanation:

So, I labeled each one, 1,2,3, and 4 respectively.

1, when expanded is 0.000005

2 is equal to -0.009

3 is simple 0.00007

and 4 is -0.0000002

Obviously the one of the negative numbers is the smallest. The bigger number with the negative sign is more negative because it is farther away from one on the number line. Therefore 2 is the smallest. That makes 4 the second smallest. 3 is larger than 1 because there are less zeros to the first non-zero digit. That places the order from least to greatest as:

2,4,1,3

Answer:

2.6x

Step-by-step explanation:

Answer:

2.6

Step-by-step explanation:

Answer:

b. {(2, 1), (3, 1) (4, 3), (5, 3)}

Answer:

Step-by-step explanation:

The 3 equivalent pairs are:

Remember that two numbers A and B are equivalent if:

A = B

The first pair given is:

-0.5 and (-1/2).

We know that 1/2 = 0.5, then (-1/2) = -0.5

So we conclude that

-0.5 and (-1/2) are equivalent.

Another equivalent pair is:

11/20 and 0.55

To check this, you can just solve the fraction in your calculator, you will see that:

11/20 = 0.55

Then 11/20 and 0.55 are equivalent.

The final equivalent pair is:

-1/50 and -0.02

Because:

-(1/50) = -(0.02) = -0.02

Then -1/50 and -0.02 are equivalent.

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Answer:

A B

Step-by-step explanation:

Answer:

Step-by-step explanation:

m∠ACB = m∠CBD = 90° ⇒ m∠CAB = 90° - 50° = 40° = m∠ABD ( Alternate interior angles )

m∠CBD = 90°

m∠CDB = 50 °

Check the picture below, notice the tickmarks, both sides are equal and they make twin angles on the "base" side of the isosceles triangle.

Answer:

40 points

Step-by-step explanation:

The score for the first four rounds of the game is 13, 17, 19, and 21 points.

Let [tex]S_5[/tex] and [tex]S_6[/tex] be the scores of the fifth and sixth games respectively in order to achieve an average score of 20 points per round for all six rounds.

[tex]\text{Average score} = \frac{\text{Sum of the scores of all the rounds}}{\text{Total number of the rounds}}[/tex]

[tex]\Rightarrow 20=\frac{13+17+19+21+S_5+S_6}{6}[/tex]

[tex]\Rightarrow 20\times6=80+S_5+S_6[/tex]

[tex]\Rightarrow S_5+S_6=120-80=40.[/tex]

Hence, the combined score of the fifth and sixth rounds are 40 points.

Answer:  see proof below

Step-by-step explanation:

Given: A + B + C = π                →      A + B = π - C

                                                         A + C = π - B

                                                         B + C = π - A

Cofunction Identities:       sin [(π/2) - A] = cos A

                                          cos [(π/2) - A] = sin A

Sum to Product Identity:   sin A - sin B = 2 cos [(A + B)/2] · sin [(A - B)/2]

Pythagorean Identity:       cos²A + sin²A = 1    →   cos²A = 1 - sin²A

Even/Odd Identity:           cos (-A) = -cos(A)

Double Angle Identity:     cos (2A) = 2 cos²A - 1

Proof LHS → RHS:

LHS:                      cos [(B + C) - A] - cos [(A + C) - B] + cos [(A + B) + C]

Given:                   cos [(π - A) - A] - cos [(π - B) - B]  + cos [(π - C) - C]

                         =  cos (π -2A) - cos (π -2B) + cos (π -2C)

Cofunction:          cos (-2A)  - cos (-2B) + cos (-2C)

Even/Odd:            -cos (2A) + cos (2B) - cos (2C)

Double Angle:     -(2cos²A - 1) + cos (2B) - cos (2C)

                           = 1 - 2cos²A + cos (2B) - cos (2C)

Sum to Product:    1 - 2cos²A - 2sin(B+C) · sin (B-C)

Given:                     1 - 2cos²A - 2sin (π - A) · sin (B - C)

Cofunction:             1 - 2cos²A - 2sin A · sin (B - C)

Pythagorean:         1 - 2(1 - sin²A) - 2sin A · sin (B - C)

                            = 1 - 2 + 2sin²A - 2sin A · sin (B - C)

                            =     -1 + 2sin²A - 2sin A · sin (B - C)

Factor:                        -1 + 2sin A (sin A - sin (B - C))

Given:                     -1 + 2sin A [sin (π - (B + C)) - sin (B - C)]    

Cofunction:             -1 + 2sin A [sin (B + C) - sin (B - C)]  

Sum to Product:      -1 + 2sin A [2 cos B · sin C]  

                               = -1 + 4sin A · cos B · sin C

LHS = RHS  [tex]\checkmark[/tex]

the radius is approximately 6 meters,

height is approximately 11 meters

The radius of cylinder = 6 meter.

The height of cylinder = 11 meter.

A cylinder is a "three-dimensional object with two round flat bases and one curved side. It has a curved surface in the middle. The base and the top surface are identical".

According to the question,

Surface area of the cylinder = 640.56 m²

Let the height of the cylinder = x meters

Let the radius of the cylinder = (x-5)meters

Formula for surface area of cylinder = 2πrh ( where 'r' is the radius of the cylinder and 'h' height of the cylinder)

640.56 = 2(3.14)(x-5)(x)

640.56/(6.28) = x² - 5x

x² - 5x =102

x² - 5x - 102 =0

using quadratic equation, [-b±√(b² - 4ac)]/2a.

b = -5; a=1; c=102

x =[-(-5) ±√(-5)² - 4(1)(102)]/2

 = [5 ± √433]/2

x = 11 and -7

since x=-7 neglect negative value, we get x=11.

The height of the cylinder is 11 meters

The radius of the cylinder is  (11 - 5) = 6 meters.

Hence, The radius of cylinder = 6 meter.

The height of cylinder = 11 meter.

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Answer:

y = [tex]\frac{10-2v}{3}[/tex]

Step-by-step explanation:

Given

2v + 3y = 10 ( subtract 2v from both sides )

3y = 10 - 2v ( divide both sides by 3 )

y = [tex]\frac{10-2v}{3}[/tex]

The volume of the resulting cone is equal to 50 [tex]m^3[/tex].

Given the following data:

Mathematically, the volume of a cone is given by this formula:

[tex]V = \frac{1}{3} \pi r^2h[/tex]

Where:

Applying the dilation factor, we have:

[tex]V =(\frac{1}{3} )^3 \times 1350\\\\V=0.037037037 \times 1350[/tex]

V = 50 [tex]m^3[/tex].

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