Find the value of [-3/7] raised to the power -2 and (3) raised to the power -4

Phoenix [80]

probability that a randomly selected person is on the swim team = 28/67
probability as a percent rounded to the nearest tenth of a percent = 41.8%

8 0

3 years ago

Read 2 more answers

How many different 4 color code stripes can be made on a sports car if each code consists of the colors green, red, blue, and wh

Akimi4 [234]

From the list of colors: green, red, blue, and white, there are four colors. The concept that should be used in order to determine the number of 4-color code stripes that can be drawn in the sports car is the concept of BASIC PRINCIPLE OF COUNTING.

The equations that would best help us in answering the question is,
n = 4! (that is, four factorial)
For the first pick, there are four choices. When one is already used then, there are only 3 choices for the second color, and so on until the last color.
n = 4 x 3 x 2 x 1 = 24
Thus, there are 24 types of 4-color codes.

5 0

3 years ago

Write a complete two-column proof for the following information given

rosijanka [135]

Statement Reason

1. AB = x + 16 1. Given

BC = 4x + 11

AC = 77

2. AB + BC = AC 2. Segment Addition Postulate

3. x + 16 + 4x + 11 = 77 3. Substitution Property

4. 5x + 27 = 77 4. Simplification (added like terms)

5. 5x = 50 5. Subtraction Property of Equality

6. x = 10 6. Division Property of Equality

7. AB = 10 + 16 7. Substitution Property

8. AB = 26 8. Simplification (added like terms)

5 0

4 years ago

What is the slope of this equation? y = 3x - 4

Rainbow [258]

Answer:

m=3 is the slope of this equation y=3x-4

6 0

3 years ago

How many solutions does the system of equations below have?

soldier1979 [14.2K]

Answer:

One solution

Step-by-step explanation:

5x + y = 8

15x + 15y = 14

Lets solve using substitution, first we need to turn "5x + = 8" into "y = mx + b" or slope - intercept form

So we solve for "y" in the equation "5x + y = 8"

5x + y = 8

Step 1: Subtract 5x from both sides.

5x + y − 5x = 8 − 5x

Step 2: 5x subtracted by 5x cancel out and "8 - 5x" are flipped

y = −5x + 8

Now we can solve using substitution:

We substitute "-5x + 8" into the equation "15x + 15y = 14" for y

So it would look like this:

15x + 15(-5x + 8) = 14

Now we just solve for x

15x + (15)(−5x) + (15)(8) = 14(Distribute)

15x − 75x + 120 = 14

(15x − 75x) + (120) = 14(Combine Like Terms)

−60x + 120 = 14

Step 2: Subtract 120 from both sides.

−60x + 120 − 120 = 14 − 120

−60x = −106

Divide both sides by -60

$\dfrac{ -60x }{ -60 } = \dfrac{ -106 }{ -60 }$

Simplify

$x = \dfrac{ 53 }{ 30 }$

Now that we know the value of x, we can solve for y in any of the equations, but let's use the equation "y = −5x + 8"

$\mathrm{So\:it\:would\:look\:like\:this:\ y = -5 \left( \dfrac{ 53 }{ 30 } \right) +8}$

$\mathrm{Now\:lets\:solve\:for\:"y"\:then}$

$y = -5 \left( \dfrac{ 53 }{ 30 } \right) +8}$

$\mathrm{Express\: -5 \times \dfrac{ 53 }{ 30 }\:as\:a\:single\:fraction}$

$y = \dfrac{ -5 \times 53 }{ 30 } +8$

$\mathrm{Multiply\:-5 \:and\:53\:to\:get\:-265 }$

$y = \dfrac{ -265 }{ 30 } +8$

$\mathrm{Simplify\: \dfrac{ -265 }{ 30 } \:,by\:dividing\:both\:-265\:and\:30\:by\:5} }$

$y = \dfrac{ -265 \div 5 }{ 30 \div 5 } +8$

$\mathrm{Simplify}$

$y = - \dfrac{ 53 }{ 6 } +8$

$\mathrm{Turn\:8\:into\:a\:fraction\:that\:has\:the\:same\:denominator\:as\: - \dfrac{ 53 }{ 6 }}$

$\mathrm{Multiples\:of\:1: \:1,2,3,4,5,6}$

$\mathrm{Multiples\:of\:6: \:6,12,18,24,30,36,42,48}$

$\mathrm{Convert\:8\:to\:fraction\:\dfrac{ 48 }{ 6 }}$

$y = - \dfrac{ 53 }{ 6 } + \dfrac{ 48 }{ 6 }$

$\mathrm{Since\: - \dfrac{ 53 }{ 6 }\:have\:the\:same\:denominator\:,\:add\:them\:by\:adding\:their\:numerators}$

$y = \dfrac{ -53+48 }{ 6 }$

$\mathrm{Add\: -53 \: and\: 48\: to\: get\: -5}$

$y = - \dfrac{ 5 }{ 6 }$

$\mathrm{The\:solution\:is\:the\:ordered\:pair\:(\dfrac{ 53 }{ 30 }, - \dfrac{ 5 }{ 6 })}$

So there is only one solution to the equation.

5 0

2 years ago