What is the probability of rolling a “7" on a fair 6-sided die and flipping a tails on a
fair coin?

Answer:

[tex](-\frac{3}{22},\frac{185}{22} )[/tex]

Step-by-step explanation:

Step 1: Find out what the question is asking

Because we want the point to be equidistant to all the vertices of the triangle formed we want the circumcenter of the triangle as it is equidistant from all of the vertices, a circumcenter is made from the perpendicular bisectors of the triangle

Step 2: Give the vertices variables

A = (-4,8)

B = (-1,-1)

C = (3,7)

Step 2: Find the Circumcenter

Find the mid point of side AB

MAB

[tex]=(\frac{-4+(-1)}{2} ,\frac{8+(-1)}{2} )\\=(\frac{3}{2},\frac{7}{2} )[/tex]

Find the slope of side AB

mAB

[tex]=\frac{y2-y1}{x2-x1} \\=\frac{8-(-1)}{-4-(-1)} \\=\frac{9}{-3}\\ =-3[/tex]

Solve for 'b'

[tex](\frac{7}{2})=(-3)(\frac{3}{2} ) +b\\\frac{7}{2}=-\frac{9}{2}+b\\\frac{7}{2}+ \frac{9}{2}=b\\b = 8[/tex]

Therefore the equation for line AB is:

y = -3x + 8

Find the midpoint of side AC

MAC

[tex]=(\frac{-4+(3)}{2} ,\frac{8+(7)}{2} )\\=(-\frac{1}{2},\frac{15}{2} )[/tex]

Find slope of AC

mAC

[tex]=\frac{y2-y1}{x2-x1} \\=\frac{8-7}{-4-3} \\=\frac{1}{-7}\\ =-\frac{1}{7}[/tex]

Solve for 'b'

[tex]y=mx+b\\\frac{15}{2} =-\frac{1}{7} (-\frac{1}{2} )+b\\\frac{15}{2} =-\frac{1}{14} +b\\\frac{1}{14}+\frac{15}{2} = b\\b=\frac{53}{7}[/tex]

Therefore the equation for line AC is:

y = [tex]-\frac{1}{7}[/tex]x+[tex]\frac{53}{7}[/tex]

Step 3: Find the P.O.I of the 2 lines

Set both of the equation equal to each other

[tex]3x + 8=-\frac{1}{7} x+\frac{53}{7} \\3x +\frac{1}{7} x=\frac{53}{7}-8\\\frac{22}{7} x=-\frac{3}{7} \\x=-\frac{3}{22}[/tex]

We now know 'x' and we substitute x into any equation to find 'y'

[tex]y = -3(-\frac{3}{22} ) + 8\\y = \frac{9}{22} + 8\\y = \frac{185}{22}[/tex]

Therefore the new firehouse should be built at [tex](-\frac{3}{22},\frac{185}{22} )[/tex]

Answer:

The difference between the area of the original triangle and the area of the new triangle is 5(3x + 7)(5x - 1)/2

Step-by-step explanation:

We know that the area of a triangle A = 1/2bh where b = base and h = height.

Let A be the area of triangle 1 with base (3x + 7) and height (5x - 1).

So its area A = (3x + 7)(5x - 1)/2.

Now for the second triangle, the base is tripled, so its base is 3(3x + 7) and its height is doubled, so its height is 2(5x - 1)

So its area is A' = 3(3x + 7) × 2(5x - 1)/2 = 3(3x + 7)(5x - 1)

So the difference between the area of the original triangle and the new triangle is

A' - A = 3(3x + 7)(5x - 1) - (3x + 7)(5x - 1)/2

= (3x + 7)(5x - 1)(3 - 1/2)

= 5(3x + 7)(5x - 1)/2

So the difference between the area of the original triangle and the area of the new triangle is 5(3x + 7)(5x - 1)/2

Answer:

  y +2 = 4(x -3)

Step-by-step explanation:

Point-slope form of the equation of a line with slope m through point (h, k) is ...

  y -k = m(x -h)

For m = 4 and (h, k) = (3, -2), the equation is ...

  y +2 = 4(x -3) . . . . . matches the first choice

Answer:

B

Step-by-step explanation:

It is B because every number, x, you plug in 5x-3, it is y.

Answer:

B

Step-by-step explanation:

If we plug in x = 5 because every chart has x = 5 as a different answer into the equation you will find it equals 22 and only B has 22 as the answer

Answer:

Elena has 6 and fran has 8

Step-by-step explanation:

Step-by-step explanation:

so the answer must be 2025 km.

The distance of the plane travel from 11:15 a.m. to 1:30 p.m. on the same day will be 2025 km.

The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.

We know that the speed formula

Speed = Distance/Time

A plane is flying at a cruising speed of 900 km/h.

The distance of the plane travel from 11:15 a.m. to 1:30 p.m. on the same day will be

From 11:15 a.m. to 1:30 p.m., there are 2.25 hours.

Then the distance will be

D = 900 x 2.25

D = 2025 km

More about the speed link is given below.

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Answer:

280-17=273

Step-by-step explanation:

because 80-17 equals 73 sooooooo add 200

Answer:

3 meters

Step-by-step explanation:

Step 1: State what is known

Volume of cube is 27 cubic meters

Important formula: Volume of cube = [tex]l^{3}[/tex]

Step 2: Input value into formula and solve for "l"

[tex]27=t^{3} \\\sqrt[3]27}=\sqrt[3]{t^{3} } \\3 = t[/tex]

Therefore the length of 1 edge of the cube is  meters

Length of each edge of cube is 3 metres.

What is the volume of cube?

The volume of a cube defines the number of cubic units, occupied by the cube completely. The volume of cube is found by multiplying the value of the edge with itself three times that is a³.

It is given that volume of cube is 27 cubic metres.

a³ = 27

a = ∛27

a = 3

Hence, length of each side of cube is 3 metres.

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In the equation 40+70+?=360, they are trying to find the last angle.

First they would add 40 and 70, which is 110.

So 110+?=360

360-110=?

360-110=250

Well this is wrong, because every angle in a triangle adds up to 180 degrees.

If you are adding up the angles in a quadrilateral, only then it adds up to 360 degrees.

So they did everything right, but they didn't use the right "total degrees"

This is what it was supposed to look like.

40+70+?=180

110+?=180

180-110=?

180-110=70

?=70

♡ Hope this helped! ♡

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❀ 0ranges ❀

Answer:

Sets, in mathematics, are an organized collection of objects and can be represented in set-builder form or roster form. Usually, sets are represented in curly braces {},

For example, A = {1,2,3,4} is a set.

Answer:

[tex]-\frac{16.7}{13.3}[/tex]

Step-by-step explanation:

Step 1: Collect the like terms

8.8 + 7.9 = -5.5x - 7.8x

Step 2: Simplify

16.7 = -13.3x

Step 3: Divide both sides by -13.3

[tex]\frac{16.7}{-13.3} =\frac{-13.3}{-13.3}x[/tex]

[tex]x =- \frac{16.7}{13.3}[/tex]

Therefore the answer is [tex]-\frac{16.7}{13.3}[/tex]

Answer:

  x = -1 34/133

Step-by-step explanation:

Given

  8.8 +7.8x = -7.9 -5.5x

  13.3x = -16.7 . . . . . . . . . . . add 5.5x -8.8

  x = -16.7/13.3 = -167/133 . . . . divide by 13.3 and simplify

  x = -1 34/133 ≈ -1.25564

Answer:

0

Step-by-step explanation:

0 · |-6|

Absolute value means take the non negative number

0* 6

0

The value of the given absolute value equation 0 · |-6| is 0.

Given that an absolute value equation 0 · |-6|, we need to evaluate this.

To evaluate the expression 0 · |-6|, let's break it down step by step:

First, calculate the absolute value of -6:

|-6| = 6

Now, multiply the result from step 1 by 0:

0 · 6 = 0

When you multiply any number by 0, the result is always 0.

In this case, even though |-6| equals 6, multiplying it by 0 will make the overall result 0.

This is a fundamental property of multiplication with zero.

So, the final answer is 0.

Learn more about absolute value click;

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Answer:

An action performed without any concious thoughts

The simple definition of reflex is the sudden movement that occurs when it responds to a stimulus in the body. This movement is without any conscious thought beforehand.

For example, you are facing one way and a ball gets thrown toward you from behind. If you have fast enough reflexes, you will sense the ball coming from behind and turn around to catch it.

Best of Luck!

Answer:

(1.5,0)

Step-by-step explanation:

midpoint coordinate (x+x1/2  , y+y1/2)

x+x1=7-4/2=3/2=1.5

y+y1/2 = 2-2/2=0

Answer:

b = sqrt(39)

Step-by-step explanation:

Since this is a  right triangle, we can use the Pythagorean theorem

a^2+b^2 = c^2

5^2 + b^2 = 8^2

25+b^2 =64

b^2 =64-25

b^2 =39

Take the square root of each side

b = sqrt(39)

Answer:

[tex]\sqrt{39}[/tex]

Step-by-step explanation:

Step 1: Find the unknown wide using Pythagorean Theorem

[tex]a^{2}+ b^{2} = c^{2}[/tex]

[tex]a^{2}+ 5^{2} = 8^{2}[/tex]

[tex]a^{2}+ 25 = 64[/tex]

[tex]a^{2}= 64-25[/tex]

[tex]a^{2=39[/tex]

[tex]\sqrt{a^{2}} = \sqrt{39}[/tex]

[tex]a=\sqrt{39}[/tex]

[tex]\sqrt{39}[/tex] cannot be simplified and more

Therefore the unknown side is [tex]\sqrt{39}[/tex]

Answer:

4

Step-by-step explanation:

First, solve in the brackets,

-3+(-1)

-3-1

-4

Since it is absolute value, take the minus sign away,

therefore the answer is 4

Answer:

Step-by-step explanation:

[tex]f(x)=-x-11\\\\\frac{f(9)}{f(-6)}\\\\ f(9)= -9-11\\- 20\\\\f(-6) = -(-6)-11\\= 6-11 = -5\\\\\\\frac{f(9)}{f(-6)}\\ \\= \frac{-20}{-5}\\ \\= 4[/tex]

Answer:

4

Step-by-step explanation:

This means that where ever you see x in the function; f(x)= -x-11, you replace it with 9 for the numerator and -6 for the Denominator

=-(9)-11/-(-6)-11

=-9-11÷6-11

=-20÷-5

=4

Answer:

8

Step-by-step explanation:

3 - (-5)

This can be rewitten to

3 + 5

Why?

2 negatives cancel each other out to make a positive, therefore:

3 + 5 = 8 or 3 - (-5) = 8

Answer:

8

3-(-5)=8 because two negatives make a positive so it is like adding 3 and 5 together to get the answer of 8.

Answer:

1320

Step-by-step explanation:

as

SI=(P×T×R)/100

SI=(2000×12×11/2)/100

SI=132000/100

:.SI=1320

Answer:1320

Step-by-step explanation:2000×12×11/2/100

Two divide by twelve=6

2000÷100=20

20×6×11=1320

Answer:

y + 6 = - 2(x - 4)

Step-by-step explanation:

The equation of a line in point- slope form is

y + b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = - 2 and (a, b) = (4, - 6) , thus

y - (- 6) = - 2(x - 4) , that is

y + 6 = - 2(x - 4)

Answer: A.  [tex]h(x)=16x^2-50x+38[/tex]

Step-by-step explanation:

Given: Francesca graphs the function  [tex]f(x) =2x - 3[/tex], George graphs the function [tex]g(x) = 4x^2 -x - 1[/tex].

Harold graphs the function [tex]h(x) = g(f(x))[/tex].

i.e. [tex]h(x)=g(2x - 3)[/tex]  [put value of f(x)]

[tex]=4(2x-3)^2-(2x-3)-1\\\\= 4((2x)^2-2(2x)(3)+3^2)-2x+3-1\ \ [(a-b)^2=a^2-2ab+b^2]\\\\= 4(4x^2-12x+9)-2x+2\\\\=16x^2-48x+36-2x+2\\\\=16x^2-50x+38[/tex]

So, Harold graph [tex]h(x)=16x^2-50x+38[/tex]

Hence, the correct option is A.  [tex]h(x)=16x^2-50x+38[/tex]

Answer: He run 7 high-speed intervals and 8 low-speed intervals.

Step-by-step explanation:

Let x = Number of high-speed intervals.

y= Number of low-speed intervals .

He runs high-speed intervals in 16 seconds, and low-speed intervals in 23 seconds, and he runs a combined total of 15 intervals in 4 minutes and 56 seconds.

4 min 56 sec = (4(60)+56) sec = 296  sec   [ 1 minute = 60 seconds]

According to the question , we have the following linear equations :

[tex]x+y=15\ ...(i)\\\\ 16x+23y=296\ ...(ii)[/tex]

Multiply (i)by 16 , we get

[tex]16x+16y=240\ ...(iii)[/tex]

Subtract (iii) from (ii)

[tex]7y=56\\\\\Rightarrow\ y=8[/tex]

Put value of y in (i) , we get

[tex]x+8=15\Rightarrow\ x=7[/tex]

Hence, he run 7 high-speed intervals and 8 low-speed intervals.

Answer:

D. 13.

Step-by-step explanation:

f(x)=2x+1/x-4

let y = 2x + 1 / x - 4

xy - 4y = 2x + 1

xy - 2x = 4y + 1

x(y - 2) = 4y + 1

x = (4y + 1)/(y - 2)

So f^-1(x) = (4x + 1)/(x - 2)

and f^-1(3) = (4(3) + 1) / (3 - 2)

= 13/1

= 13.

Explanation:

There are n = 8 sides in a regular octagon. The smallest angle of rotational symmetry is 360/n = 360/8 = 45 degrees. Rotating this amount will not change the regular octagon. The before and after will look identical.

ANSWER:

Your answer is 45 Degrees

Answer:

Flour need for 1 cup of water = [tex]1\frac{7}{8}[/tex] cups

Step-by-step explanation:

Given:

Cups of water = [tex]1\frac{1}{3}[/tex] = 4/3

Cups of flour = [tex]2\frac{1}{2}[/tex] = 5/2

Find:

Flour need for 1 cup of water

Computation:

Flour need for 1 cup of water = Cups of flour / Cups of water

Flour need for 1 cup of water = (5/2) / (4/3)

Flour need for 1 cup of water = 15/8

Flour need for 1 cup of water = [tex]1\frac{7}{8}[/tex]

Answer:

Least: 1 hour

Maximum: 5 hours

Step-by-step explanation:

Given

Boat hourly rate = $8.00

Paddle daily rate = $5.00

Required

Determine the least hour, David could use the boat

First, we need to represent this as an inequality.

Since David has $45, then

[tex]\$8.00 * x + \$5.00 \leq \$45.00[/tex]

Where x represents the number of hours

Collect Like Terms

[tex]\$8.00 * x \leq \$45.00 - \$5.00[/tex]

[tex]\$8.00 * x \leq \$40.00[/tex]

Divide both sides by $8.00

[tex]x \leq \frac{\$40.00}{\$8.00}[/tex]

[tex]x \leq 5[/tex]

Hence, the least number of hour is 1 hour while the maximum is 5 hours

Answer:

B. 1995

Step-by-step explanation:

As per the graph the lowest production was in 1995, the production figure was around 203 billion dollars

So the answer choice is B. 1995

Answer:

abscissa of origin is 0.

Step-by-step explanation:

The abscissa of a point is the signed measure of its projection on the primary axis, whose absolute value is the distance between the projection and the origin of the axis, and whose sign is given by the location on the projection relative to the origin (before negative; after: positive).

Your answer would be D, the equation is a function because it is a polynomial and all polynomials are functions.

Step-by-step explanation: I like to remember that polynomials have no negative , fraction exponents and no division. In this case everything is positive so I knew it was a polynomial , and like the answer says all polynomials are functions ! Hope this helped