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2 years ago

What is the solution to 9x−6<21?

Mathematics

1 answer:

Alisiya [41]2 years ago

7 0

Answer:

$x > 3$

Step-by-step explanation:

1) Add 6 to both sides.

$9x > 21 + 6$

2) Simplify 21 + 6 to 27.

$9x > 27$

3) Divide both sides by 9.

$x > \frac{27}{9}$

4) Simplify 27/9 to 3.

$x > 3$

Therefor, the answer is option B. x > 3.

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3 years ago

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Explain how to add 678 + 303 using mental math

zloy xaker [14]

Answer:

You add it in your mind.

Step-by-step explanation:

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3 years ago

Suppose the number of radios in a household has a binomial distribution with parameters n=11 and p=40%. Find the probability of

Ivenika [448]

Answer:

Step-by-step explanation:

The formula for binomial distribution is expressed as

P(x=r) = nCr × q^(n-r) × p^r

From the information given,

n = 11

p = 40% = 40/100 = 0.4

q = 1 - 0.4 = 0.6

x represent the number of radios

a) P( x = 1) or P(x = 9)

P(x = 1) = 11C1 × 0.6^(11-1) × 0.4^1

P(x = 1) = 0.027

P(x = 9) = 11C9 × 0.6^(11-9) × 0.4^9

P(x = 9) = 0.0052

P( x = 1) or P(x = 9) = 0.027 + 0.0052 = 0.0322

b) P(x lesser than or equal to 7) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3) + P(x = 4) + P(x = 5) + P(x = 6)

P(x = 0) = 11C0 × 0.6^(11-0) × 0.4^0 = 0.004

P(x = 1) = 0.027

P(x = 2) = 11C2 × 0.6^(11-2) × 0.4^2 = 0.089

P(x = 3) = 11C3 × 0.6^(11-3) × 0.4^3 = 0.177

P(x = 4) = 11C4 × 0.6^(11-4) × 0.4^4 = 0.24

P(x = 5) = 11C5 × 0.6^(11-5) × 0.4^5 = 0.22

P(x = 6) = 11C6 × 0.6^(11-6) × 0.4^6 = 0.15

P(x = 7) = 11C7 × 0.6^(11-7) × 0.4^7 = 0.15

P(x lesser than or equal to 7) = 0.004 + 0.027 + 0.089 + 0.177 + 0.24 + 0.22 + 0.15 + 0.07 = 0.977

c) P(x greater than or equal to 5) = 1 - P(x lesser than or equal to 4) = 1 - (0.004 + 0.027 + 0.089 + 0.177 + 0.24) = 1 - 0.537 = 0.463

d) P(x lesser than 9) = P(x lesser than or equal to 7) + P(x = 8)

P(x = 8) = 11C8 × 0.6^(11-8) × 0.4^8 = 0.02

P(x lesser than 9) = 0.977 + 0.02 = 0.997

e. P(x greater than 7) = 1 - P(x lesser than or equal to 7) = 1 - 0.977 = 0.023

5 0

3 years ago

What is the slope of (8,3) and (-4,-6)?

Nonamiya [84]

Answer: The slope of the line formed by these two points is $\frac{3}{4}$

Step-by-step explanation:

To calculate the slope, we use the formula:

$Slope=\frac{y_2-y_1}{x_2-x_1}$

For the coordinates given:

$x_1=8\\y_1=3\\x_2=-4\\y_2=-6$

Putting values in above equation, we get:

$Slope=\frac{(-6-3)}{(-4-8)}\\\\Slope=\frac{-9}{-12}\\\\Slope=\frac{3}{4}$

Hence, the slope of the line formed from these two coordinates is $\frac{3}{4}$

8 0

3 years ago

The ratio of water to punch mix is 8 parts to 1 part. If you use 6 gallons of water predict the amount of punch mix to use

Valentin [98]

Answer:

The amount of punch mix to use is 3/4 gallons

Step-by-step explanation:

Let

x ----> parts of water

y ---> parts of punch mix

we know that

$\frac{x}{y} =\frac{8}{1}$

$x=8y$ ----> equation A

That means ---> The parts of water is 8 times the parts of punch mix

If we have 6 gal of water

then

$x=6\ gal$

substitute in the equation A

$6=8y$

solve for y

$y=\frac{6}{8}\ gal$

Simplify

$y=\frac{3}{4}\ gal$

therefore

The amount of punch mix to use is 3/4 gallons

6 0

2 years ago