The mathematics faculty at a college consists of 7​professors, 9 associate​ professors, 9 assistant​ professors, and 9 instructors. If one faculty member is randomly​ selected, find the probability of choosing a professor or an instructor.

Answer:

B) [tex]\frac{5}{12}[/tex]

Step-by-step explanation:

Tan= Opposite/Adjacent

HJK = RST

Tan H = Tan R

Tan H = 5 (Opposite) / 12 (Adjacent)

So...

Tan R= 5/12

The surface area of the figures are;

Rectangle = 36.2 yd^2

Cuboid = 200 ft^2

Parallelogram = 27.8 cm^2

Cylinder = 138 yd^2

We can be able to obtain the surface area of various figures by the use of formulas.

For the rectangle, the surface area is = 7.1 yd * 5.1 yd = 36.2 yd^2

For the cuboid, the surface area = 2[(8 ft * 14 ft) + (4 ft * 8ft) + (14ft * 4 ft)] = 200 ft^2

For the parallelogram, the surface area = 5.4 cm * 5.14 cm = 27.8 cm^2

For the cylinder, the surface area is; (2 * 3.14 * 4^2) + (2 * 3.14 * 4 * 6) = 138 yd^2

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Answer:

-2.5

Step-by-step explanation:

7g - 6 = -20

Add 6 to both sides

7g = -14

Divide both sides by 7
g = -2

answer: g = -2

Answer:

-2

Step-by-step explanation:

7 negative 2's equals negative 14, minus 6 equals negative 20.

Answer:

GCF(2y²z ​, 8yz²) = 2yz

Step-by-step explanation:

2y²z = (2yz) × y

8yz² = (2yz) × 4z

then

GCF(2y²z ​, 8yz²) = 2yz

Answer:

b) f(x) = x² - 256

Step-by-step explanation:

Since we have been given the zeros of a function, -16 and 16. We are asked to find which function truly has those zeros.

To find this, we can substitute the zeros for x in the functions to find the one that is true/correct.

A) f(x) = x² - 16

 ⇒  0 = 16² - 16          and          ⇒  0 = (-16)² - 16

 ⇒  0 = 256 - 16        and          ⇒  0 = 256 - 16

 ⇒  0 = 240 ✘          and          ⇒  0 = 240 ✘

B) f(x) = x² - 256

 ⇒  0 = 16² - 256          and          ⇒  0 = (-16)² - 256

 ⇒  0 = 256 - 256        and          ⇒  0 = 256 - 256

 ⇒  0 = 0 ✔                  and          ⇒  0 = 0 ✔

C) f(x) = x² - 32x + 256

 ⇒  0 = 16² - 32(16) + 256         and        ⇒  0 = (-16)² - 32(-16) + 256

 ⇒  0 = 256 - 512 + 256           and        ⇒  0 = 256 + 512 + 256

 ⇒  0 = 512 - 512                       and        ⇒  0 = 512 + 512

 ⇒  0 = 0 ✔                               and        ⇒  0 = 1,024 ✘

D) f(x) = x² + 32x + 256

  ⇒  0 = 16² + 32(16) + 256         and        ⇒  0 = (-16)² + 32(-16) + 256

  ⇒  0 = 256 + 512 + 256           and         ⇒  0 = 256 - 512 + 256

  ⇒  0 = 512 + 512                       and         ⇒  0 = 512 - 512

  ⇒  0 = 1,024 ✘                          and        ⇒  0 = 0 ✔

Therefore, Function B has the zeros of x = -16 and x = 16.

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Answer:

[tex] - 8x + 6y = - 22 \\ - 4x + 4y = - 4 \\ .............................................. \\ - 12x + 10y = - 26 \\ - 2(6x - 5y) = - 26 \\ 6x - 5y = 13[/tex]

Answer:

199 text messages (i think lol)

Step-by-step explanation:

First, you need to see how much it costs to send one text message. In this scenario, it's 5 cents each text. So then you need to calculate how many texts she sent if she spent 9.95 with the equation 9.95/0.05

Answer:

V= 400

Step-by-step explanation:

1/3×(area of the base)×(h)

10*10= 100

1/3(100)(12)

=400

about Answer: The correct answer would be d) 5x - 1

Step-by-step explanation:

Simplify or Evaluate the expression and Combine like terms

3(-5x + 2) + 20x - 7

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Answer:

Simplify (0%)

.

O A. 6

O B.

01

6

O C. 64

O D. 616

Step-by-step explanation:

It will take 0.556 seconds for an echo to reach one's ears

From the question, we are to determine how long it would take an echo to reach one's ears

From the formula,

[tex]Speed = \frac{2 \times distance \ travelled\ by \ sound}{Time}[/tex]

NOTE: To hear an echo, the sound will travel to and fro, hence, it will cover twice the distance

From the given information,

Distance = 92.0 m

NOTE: Speed of sound in air at 0 °C ≅ 331 m/s

Putting the parameters into the formula, we get

[tex]331 = \frac{2 \times 92.0}{Time}[/tex]

[tex]Time = \frac{2 \times 92.0}{331}[/tex]

Time = 0.556 secs

Hence, it will take 0.556 seconds for an echo to reach one's ears.

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2 teachers for 29 students

hope it helps...!!!

Answer:

29 students

Step-by-step explanation:

Hello!

When expressed that the ratio of Teachers to Students is 2:29, the ratio is in the format Teachers: Students.

That means, for every 2 teachers, there are 29 students.

Ratio:

2(teachers): 29(students)

There are 29 students for 2 teachers.

We can also find the number of students for 4 teachers by simply multiplying both sides by 2

A ratio can be expressed as a fraction : [tex]x:y = \frac xy[/tex]

Answer:

$16

Step-by-step explanation:

You would just multuply the amount of time and the amount of money it costs.

Answer:

$1

Step-by-step explanation:

4 divided by 4 is 1 like the other person said. You can give them brainliest.

Hope It Helps

Answer:

c

Step-by-step explanation:

Answer:

The right answer is 15t times 2.

The garden club earns 15 dollars per hour

t is the hours

A generous donor doubles their earnings

Double means times 2

Step-by-step explanation:

Step-by-step explanation:

a.

x = number of matching questions

y = number of essay questions

x >= 3

x <= 12

y >= 4

y <= 15

x + y <= 20

the delimiter lines are therefore

x = 3

x = 12

y = 4

y = 15

y = 20 - x

when you graph these lines, the corners (intersection points) of the inner shaded area are

(3, 4)

(12, 4)

(3, 15)

(12, 8)

(5, 15)

the other intersection points

(12, 15)

(3, 17)

(16, 4)

are outside the inner shaded area.

b.

10x + 25y = score

and this we want to maximize.

we have to try the 5 corners from a. and see, which one gives the maximum score.

(3, 4) gives

10×3 + 25×4 = 30 + 100 = 130

(12, 4) gives

10×12 + 25×4 = 120 + 100 = 240

(3, 15) gives

10×3 + 25×15 = 30 + 375 = 405

(12, 8) gives

10×12 + 25×8 = 120 + 200 = 320

(5, 15) gives

10×5 + 25×15 = 50 + 375 = 425

that is the most.

so, Phil should do 5 matching questions and 15 essay questions for maximum score.

Answer: 637 m²

Step-by-step explanation:

   We need to find the area of four triangles and one square.

   The square: 169 m²

A = L²

A = (13 m)²

A = 169 m²

   The triangles: 468 m²

-> We have four congruent triangles. I will find the area of two (skipping the "divide by two" part of the formula) and multiply by two to find all four at once.

A = B * H

A = (13 m) * (18 m)

A = 234 m²

-

234 m² * 2 = 468 m²

   Total surface area:

169 m² + 468 m² = 637 m²

The vertical asymptote is x = 1 and the horizontal asymptote is y = -1 if the equation of the hyperbola is f(x)=−3/x−1 −1

It's a two-dimensional geometry curve with two components that are both symmetric. In other words, the number of points in two-dimensional geometry that have a constant difference between them and two fixed points in the plane can be defined.

We have the equation of the hyperbola:

[tex]\rm f(x)=\dfrac{-3}{x-1} -1[/tex]

The asymptotes will be

Vertical asymptote:        x -1 = 0 ⇒ x = 1

Horizontal asymptote:   y + 1= 0 ⇒ y = -1

Thus, the vertical asymptote is x = 1 and the horizontal asymptote is y = -1 if the equation of the hyperbola is f(x)=−3/x−1 −1

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Answer:

Move all terms that don't contain y to the right side and solve.y=4−6x/5

Step-by-step explanation:

Answer:

[tex]0.09375[/tex]

Step-by-step explanation:

the total number of balls = 3 + 3 + 2 = 8

Let p be the probability of choosing a green ball, replacing it, and then choosing a yellow ball.

[tex]p=p\left( \text{choosing a green ball} \right) +p\left( \text{choosing a yellow ball} \right)[/tex]

  [tex]=\frac{2}{8} \times \frac{3}{8}[/tex]

  [tex]=\frac{6}{64}[/tex]

  [tex]= 0.09375[/tex]

Answer:

∠A≅∠Y        AB≅YZ

∠B≅∠Z          AC≅YX

∠C≅∠X         BC≅ZX

ΔABC ≅ ΔYZX

Step-by-step explanation:

congruent is identical in form so if the angle has one dash than look for the identical version on the other triangle

Answer:

A. x = 5 and x = 6

Step-by-step explanation:

What are zeroes?

Zeroes are simply the x intercepts of a function or the coordinates where the function crosses the x axis

Finding the zeroes.

By looking at the graph, we can say that the function crosses the x axis at (5,0) and (6,0).

This means the x intercepts / zeroes are at x = 5 and x = 6 so the answer is A

Answer:

27 cubic millimeters

Step-by-step explanation:

Remember that a cube's surface area is [tex]SA=6s^2[/tex] where [tex]s[/tex] is any side length of the cube.

Hence, by solving [tex]54=6s^2[/tex], we find that the side length of a cube is 3 millimeters.

This means that the volume of the cube is [tex]V=s^3=3^3=27mm^3[/tex]

[tex]\text{Apply Pythagorean theorem,}\\\\~~~~x^2 = 6^2 +8^2\\\\\implies x = \sqrt{6^2 +8^2}\\\\\implies x = \sqrt{36 +64}\\\\\implies x =\sqrt{100}\\\\\implies x = 10~~ \text{units.}[/tex]

Step-by-step explanation:

x² - 12x + 32 = 0

the goal is the vertex form : a form like

(x - h)² + k = r²

with (h, k) being the vertex or center and r the radius.

doing all the multiplications we get

x² - 2hx + h² + k - r² = 0

and we compare this with our original equation. we see

x² = x²

-12x = -2hx

-12 = -2h

6 = h

32 = h² + k - r²

32 = 36 + k - r²

-4 = k - r²

possible solution : k = 0 and then r = 2

but also e.h. k = 12, r = 4

so, without the information about e.h. the radius we cannot identify one solution.

so, "A" vertex form (one of many possible ones) is

(x - 6)² = 4

Answer:

[tex]y = -\frac{3}{4} sin(\frac{2}{3}x)[/tex]

Step-by-step explanation:

First determine whether it is a sine function or a cosine function. Since

sin(x) = 0 at x = 0 and we see indeed that the value of the function is 0 at x = 0 it must be a sine function

The general equation of a sine function is [tex]a sinbx[/tex]

where a is the amplitude. The amplitude is one-half the difference between the lowest and highest values in the graph.From the graph we can see that the highest value is 3/4 and lowest is -3/4 so the amplitude = 1/2 (3/4 + 3/4) = 3/4

If the amplitude were positive, the function would be increasing at (0,0) and going up to its amplitude value. However we can see that the function is decreasing at (0,0 ) and goes down to -3/4. Therefore the amplitude a has a negative sign so a = -3/4

To compute b, note that the period of the function ie where it finishes a full cycle is 3π since the function at that x value repeats itself. The relationship between b and the period is 2π/b = 3π in this particular case

This gives b = 2/3

So a = -3/4, b = 2/3 and the equation is [tex]y = -\frac{3}{4} sin(\frac{2}{3}x)[/tex]

Answer:

y = 1.8x, where time is the independent variable, x, and distance is the dependent variable.

Step-by-step explanation:

The independent variable is along the x-axis.

The dependent variable is along the y-axis.

Therefore,

Equation of the line

To find the equation of the line, define two points on the line:

Use the slope formula to find the slope (m) of the line:

[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{9-0}{5-0}=1.8[/tex]

From inspection of the graph, the y-intercept is at (0, 0).

Point-slope form of a linear equation:  [tex]y = mx + b[/tex]

Substitute the found slope and y-intercept into the formula to create the equation of the line:

[tex]\implies y=1.8x+0[/tex]

[tex]\implies y=1.8x[/tex]

Conclusion

y = 1.8x, where time is the independent variable, x, and distance is the dependent variable.