Twelve people apply for a teaching position in mathematics at a local college. Six have a PhD and six have a master’s degree. If the department chairperson selects three applicants at random for an interview, find the probability that all three have a PhD

Answer:

(1+b/60) minutes

Step-by-step explanation:

A minute = 1minute

b seconds = b/60minutes =b/60 minutes

sum of a minute and b seconds= (1+ b/60) minutes

[tex]===================================[/tex]

let's find the value of h(2)

we know that

h(r)=5r-5

which means

h of r is 5 times r minus 5

hence

h of 2 is 5 times 2 minus 5

simplify:

h(2)=5(2)-5

h(2)=10-5

h(2)=5

[tex]==================================[/tex]

Answer:

5

Step-by-step explanation:

h(2)=5r-5

=5×2-5

=10-5

=5

[tex]y = ab^x \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x}{0}~~,~~\stackrel{y}{9})\qquad \implies 9=ab^0\implies 9=a(1)\implies 9=a~\hfill \underline{y=9b^x} \\\\\\ (\stackrel{x}{10}~~,~~\stackrel{y}{9216})\qquad \implies 9216 = 9b^{10}\implies \cfrac{9216}{9}=b^{10}\implies 1024=b^{10} \\\\\\ \sqrt[10]{1024}=b\implies 2=b~\hfill \underline{y=9(2)^x}[/tex]

The Exponential function is [tex]y = 9(2^{x} )[/tex]

The mathematical expression for an exponential function is f (x) = aˣ where “x” denotes a variable and “a” denotes a constant that is the base of the function and ought to be greater than 0. The most regularly utilized remarkable capability base is the supernatural number e, which is roughly equivalent to 2.71828.

Given function

y = abˣ

and coordinates (0, 9) and (10, 9216)

when x = 0,  y = 9

[tex]y = ab^{x}[/tex]

substitute values

9 = ab⁰

9 = a

and [tex]y = ab^{x}[/tex]

when x= 10 and y = 9216

9216 = 9(b)¹⁰

1024 = b¹⁰

[tex]\sqrt[10]{1024}[/tex] = b

b = 2

[tex]y = 9(2^{x} )[/tex]

Hence equation is [tex]y = 9(2^{x} )[/tex].

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Answer:

[tex]9 \times 3 = 27 \\ 15 \times 6 = 90 \\ = 30.255 \\ 49 \times 3.14 = 153.86 \\ 153.86 + 30.255 + 27 = 211.115[/tex]

Step-by-step explanation:

=[tex] =(3x + 2)(x + 1) \\ = 3x(x + 1) + 2(x + 1) \\ = {3x}^{2} + 3x + 2x + 2 \\ = {3x}^{2} + 5x + 2[/tex]

Answer:

Bro really?? Anyway it's

[tex]anyway \: its \: 3x { }^{2} + 3x + 2x + 2[/tex]

Answer:

x = 9

Step-by-step explanation:

Simplifying

2 + -6(1 + -1x) = 6 + -4(-1x + -2)

2 + (1 * -6 + -1x * -6) = 6 + -4(-1x + -2)

2 + (-6 + 6x) = 6 + -4(-1x + -2)

Combine like terms: 2 + -6 = -4

-4 + 6x = 6 + -4(-1x + -2)

Reorder the terms:

-4 + 6x = 6 + -4(-2 + -1x)

-4 + 6x = 6 + (-2 * -4 + -1x * -4)

-4 + 6x = 6 + (8 + 4x)

Combine like terms: 6 + 8 = 14

-4 + 6x = 14 + 4x

Solving

-4 + 6x = 14 + 4x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-4x' to each side of the equation.

-4 + 6x + -4x = 14 + 4x + -4x

Combine like terms: 6x + -4x = 2x

-4 + 2x = 14 + 4x + -4x

Combine like terms: 4x + -4x = 0

-4 + 2x = 14 + 0

-4 + 2x = 14

Add '4' to each side of the equation.

-4 + 4 + 2x = 14 + 4

Combine like terms: -4 + 4 = 0

0 + 2x = 14 + 4

2x = 14 + 4

Combine like terms: 14 + 4 = 18

2x = 18

Divide each side by '2'.

x = 9

Simplifying

x = 9

Answer:

3x + 5y = 15

Find gradient:

coordinates taken: (5, 0), (0, 3)

[tex]\rightarrow \sf \dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\rightarrow \sf \dfrac{3-0}{0-5}[/tex]

[tex]\rightarrow \sf -\dfrac{3}{5}[/tex]

equation:

[tex]\sf \bold{ y = m(x) + b}[/tex]

[tex]\rightarrow \sf y = -\dfrac{3}{5} x + 3[/tex]

[tex]\rightarrow \sf y = -\dfrac{3}{5} x + \dfrac{15}{5}[/tex]

[tex]\rightarrow \sf 5y =-3x+15[/tex]

[tex]\rightarrow \sf 3x+5y =15[/tex]

Take two points

So

equation of line in intercept form

[tex]\\ \rm\rightarrowtail \dfrac{x}{a}+\dfrac{y}{b}=1[/tex]

[tex]\\ \rm\rightarrowtail \dfrac{x}{5}+\dfrac{y}{3}=1[/tex]

[tex]\\ \rm\rightarrowtail 3x+5y=15[/tex]

Answer: a third

Step-by-step explanation: im simply a genius

The expression that best represents the value of pi is 53/d.

Pi can be described as the ratio of the circumference of a circle to its diameter. The circumference of the patio is the distance round the patio. The formula that can be used to represent the circumference of the patio is πD

53 = πD

π = 53/d

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Answer: 166 feet^2

Step-by-step explanation:

The equation for surface area is 2(wl+hl+hw). So that would be:
Surface Area = 2×(5×7 + 5×4 + 7×4) = 166 feet^2

Answer:16 square cm

Step-by-step explanation: Surface area = base, height (Side 1 + Side 2+ Side 3) H = Side 1 = 5 cm

Side 2 = 7cm

Side 3 = 4cm (add all these numbers ) = 16 Square cm

Answer:

$1920.00

Step-by-step explanation:

You want to calculate the interest on $6000 at 4% interest per year after 8

year(s).

The formula we'll use for this is the simple interest formula, or:

I= P * r * t

Where:

• P is the principal amount, $6000.00.

• r is the interest rate, 4% per year, or in decimal form, 4/100=0.04.

• t is the time involved, 8.…..year(s) time periods

So, t is 8...year time periods.

To find the simple interest, we multiply 6000 x 0.04 x 8 to get that:

The interest is: $1920.00

Answer:

-2

Step-by-step explanation:

25°-27°= -2°

At noon, the temperature outside was 25 degrees. By 8:00pm, the temperature had dropped 27 degrees. What was the temperature outside at 8:00pm, in degrees?

= 25 - 27

= - 2°

Step-by-step explanation:

a + 2 = 2

a = 2 - 2

a = 0

a² - b² = 8

0 - b² = 8

b² = -8

This question is impossible.

Answer:

i think 20 times bigger  

Step-by-step explanation:

Answer:

times 20

Step-by-step explanation:

2 quart to 10 gallon

4 quarts= 1 gallon

So 2quarts x 20 quarts= 40 quarts= 10 gallons

Answer:

8

Step-by-step explanation:

For the smallest possible length, this has to be one of the shorter sides. Let the length of this side be x.

So, by the triangle inequality theorem, 1+x>8, which means x>7.

So, the smallest possible whole number length is 8.

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Cavalier's Principle tells you that the slant figures with the same base area and height have the same volume, regardless of the amount of offset.

__

The volume of the oblique cylinder is the same as the volume of the right cylinder: 700 cubic centimeters.

__

Disagree. Both the volume formula for the pyramid and Cavalier's Principle tell you that the volume is not a function of the slant height.

The percentage 68% is converted into a fraction number as 17/25.

A fraction number is a number that represents the part of the whole, where the whole can be any number. It is in the form of a numerator and a denominator.

The amount of any product is presented as though it were a percentage of a hundred. The ratio is one-quarter of one hundred.

The faction number is given in the form of a percentage. Then the percentage is converted into a decimal number by dividing 100.

⇒ 68%

⇒ 0.68 x 100 / 100

⇒ 68 / 100

⇒ 17 / 25

The percentage 68% is converted into a fraction number as 17/25.

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Answer:

a= 50

b=50

c=110

d=20

Answer:

Step-by-step explanation:

This is a kite. So the two triangles formed by the longest diagonal being drawn in form 2 congruent triangles.

Therefore c = 110 degrees.

d = 20 degrees.

a and b are found by noting that every triangle has 180 degrees.

110 + 20 + a = 180           Combine the left.

130 + a = 180                   Subtract 130 from both sides

a = 180 - 130

a = 50 degrees

b also equals 50 degrees.  Congruent triangles

Answer

Answer: 21

Step-by-step explanation:

Answer:

1,040kg/m³

Step-by-step explanation:

1g/cm³ =1,000kg/m³

1.04g/cm³=?

= 1.04×1000

Density =1,040kg/m³

The similar Triangle OPN and triangle LMN are similar have the ratio LM / MN = OP / NP

Two figures are said to be similar if they have the same shape and the ratio of their corresponding sides are in the same proportion.

Triangle OPN and triangle LMN are similar, hence:

LM / MN = OP / NP

The similar Triangle OPN and triangle LMN are similar have the ratio LM / MN = OP / NP

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Answer:

33.3333333333

Step-by-step explanation:

we see that there are 6 candies in total

we also see that there is a 50% chance that someone will take out 3 candies of the same color,

50/3 = 16.66666666666667

so the chance of getting 2 marbles of the same color is 16.66666666666667 + 16.66666666666667 which is 33.3333333333

I hope I could help

Answer:

120 miles/hour

Step-by-step explanation:

6 x 10= 60 min

12 x 10= 120 miles

Answer:

Definitely 120 miles per hour.

Step-by-step explanation:

First, if she drove 50,000,000 fast, you need to do 6 minutes x 10 because 10 can go into 50,000,000. So, yes, it's 60. But that isn't right... it's too short. Try the next one.

How about we do the miles. 12 miles x 10 will get you your answer; 120.

I honestly don't know what I'm doing. It most likely isn't 120, but I did the math, and it was hard.

Bonjour,

πr² *h

3,14 * 3² *8

= 3,14 *9 *8

=>226, 08 ....²

Answer:

66π square units

Step-by-step explanation:

As we can see the value of root 6 does not terminate after 3 decimal places. It can still be extended further. Hence, this makes √6 an irrational number.

hope it will help you..

Answer:

C

Step-by-step explanation:

It's 50 cm for sure

Answer:

C

Step-by-step explanation:

It's 50 cm for sure

Answer:

0.729 cubic millimeters

Step-by-step explanation:

Here,

Length ( l ) = 0.9 mm

Base ( b ) = 0.9 mm

Height ( h ) = 0.9 mm

l = b = h = 0.9 mm = a

To find : Volume

This shape is a cube.

Formula : -

Volume of cube = a³

Volume of cube

= 0.9³

= 0.9 x 0.9 x 0.9

= 0.729 cubic milimeters

Answer:

Formula for volume of cube;

V = [tex]s^{3}[/tex]

Where 's' represents one side of a cube which is being cubed.

or

V = w · l · h

Where 'w' stands for the width, 'l' is the length, and 'h' represents the height.

For this, I'll be using the formula [tex]s^{3}[/tex].

What we know:

Use one of these sides to substitute for 's';

V = [tex]s^{3}[/tex]

V = 0.9^3 ← (The " ^ " symbol is another way of showing to the power of.)

V = (0.9 · 0.9 · 0.9)

V = 0.729 mm, the volume of this cube is 0.729 cubic millimetres.

Answer:

9x^2 - 24x + 16 is area in terms of x alternativly (3x-4)^2 is also true

Step-by-step explanation:

L * W =  area  length = width on a sqare so L * L = area too

(3x - 4) * (3x - 4)

use foil method

9x^2 - 24x + 16

Answer:

9x^2 − 24x + 16

Step-by-step explanation:

To find the area of a square, you use the formula

A = x^2

So we plug in 3x-4 for x

A = (3x-4)^2

A = 9x^2 − 24x + 16