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3 years ago

Solve 12x - z = y for x.

Mathematics

1 answer:

Tresset [83]3 years ago

7 0

Answer:

$x=\frac{y+z}{12}$

Step-by-step explanation:

Step 1: Add z to both sides

12x - z + z = y + z

12x = y + z

Step 2: Divide both sides by 12

$\frac{12x}{12} = \frac{y+z}{12}$

$x=\frac{y+z}{12}$

Answer: $x=\frac{y+z}{12}$

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If it costs $90 to feed a family of 3 for one week. (3 points) Unit 8 lesson 4

liubo4ka [24]

X = number of weeks
1 week =
3x = $90
Divide by 3
3x/3 = x
$90/3 = $30
1 person = $30 per week
x 5
5 people = $150 per week

x6
6 people = $180 per week

3 0

2 years ago

Write an equation of the line containing the given point and parallel to the given line.

Dafna11 [192]

Answer:

y = 5/9x - 37/3

Step-by-step explanation:

5x - 9y = 8

-9y = -5x + 8

y = 5/9x - 8/9

When a line is parallel, the slope remains the same.

y = 5/9x + b

-9 = 5/9(6) + b

-9 = 10/3 + b

-37/3 = b

6 0

2 years ago

Is the domain {1.8,3.4,9,9.8}

Effectus [21]

You need to find the values of x that correspond to the given values of f(x). That is, you need to solve for x:
.. y = 7x -2.7
.. y +2.7 = 7x
.. x = (y +2.7)/7

You are given y values of {14.1, 30.9, 41.4, 58.9, 68}. The corresponding x values are {2.4, 4.8, 6.3, 8.8, 10.1}, corresponding to selection C.

_____
Since the first number in each choice is different, you only need to evaluate f(x) for those numbers to see which gives the correct result. Only the 3rd one (2.4) give f(2.4) = 14.1, the correct answer.

4 0

2 years ago

A and b are positive integers and a–b = 3. Evaluate the following: 27/1/3 b/9/ 1/2 a

DaniilM [7]

Answer:

$\dfrac{1}{27}$

Step-by-step explanation:

Given that,

a-b = 3

We need to find the value of $\dfrac{27^{\dfrac{1}{3}b}}{9^{\dfrac{1}{2}a}}$ .

We know that,

$27=3^3\\\\9=3^2$

So,

$\dfrac{27^{\dfrac{1}{3}b}}{9^{\dfrac{1}{2}a}}=\dfrac{3^3^({\dfrac{1}{3}b})}{3^2^{\dfrac{1}{2}a}}\\\\=\dfrac{3^b}{3^a}$

We know that : $\dfrac{x^p}{x^q}=x^{p-q}$

So,

$\dfrac{3^b}{3^a}=3^{b-a}$

Since, b-a = -3. So,

$3^{b-a}=3^{-3}\\\\=\dfrac{1}{3^3}\\\\=\dfrac{1}{27}$

So, the value of the given expression is equal to $\dfrac{1}{27}$ .

7 0

2 years ago

A major hurricane is a hurricane with wind speeds of 111 miles per hour or greater. During the 20th century the mean number of t

Bas_tet [7]

Answer:

a) 0.3293 = 32.93% probability that the number of major hurricane to strike U.S mainland in any any give year is exactly one.

b) 0.878 = 87.8% probability that the number of major hurricane to strike U.S mainland in any any give year is at most one.

c) 0.122 = 12.2% probability that the number of major hurricane to strike U.S mainland in any any give year is more than one.

Step-by-step explanation:

We have the mean during an interval, which means that the Poisson distribution is used to solve this question.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given interval.

During the 20th century the mean number of the major hurricanes to strike U.S mainland per year was 0.6.

This means that $\mu = 0.6$

Find the probability that the number of major hurricane to strike U.S mainland in any any give year is:

a) Exactly one

This is P(X = 1). So

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 1) = \frac{e^{-0.6}*0.6^{1}}{(1)!} = 0.3293$

0.3293 = 32.93% probability that the number of major hurricane to strike U.S mainland in any any give year is exactly one.

b) At most one

This is:

$P(X \leq 1) = P(X = 0) + P(X = 1)$

Then

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 0) = \frac{e^{-0.6}*0.6^{0}}{(0)!} = 0.5488$

$P(X = 1) = \frac{e^{-0.6}*0.6^{1}}{(1)!} = 0.3293$

$P(X \leq 1) = P(X = 0) + P(X = 1) = 0.5488 + 0.3292 = 0.878$

0.878 = 87.8% probability that the number of major hurricane to strike U.S mainland in any any give year is at most one.

c) More than one

This is:

$P(X > 1) = 1 - P(X \leq 1) = 1 - 0.878 = 0.122$

0.122 = 12.2% probability that the number of major hurricane to strike U.S mainland in any any give year is more than one.

6 0

2 years ago