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3 years ago

Trey needs to find the zero of the equation 9x + 2y = 18. Which describes the steps he should take?

Mathematics

1 answer:

Fudgin [204]3 years ago

3 0

Answer:

a. Substitute 0 for x and solve for y

b. Substitute 0 for y and solve for x

Step-by-step explanation:

Getting the zeros of the given equation is similar to finding the x-intercept and y-intercept of the equation

The x intercept occurs where y = 0

Substituting y = 0 into the expression and getting x we have;

9x + 2y = 18

9x +2(0)= 18

9x = 18

x = 18/9

x=2

Hence the x intercept is 2

Similarly, to get the y intercept, we will substitute x = 0 and get the value of x a shown:

When x =0.

9(0)+2y = 18

0+2y = 18

2y= 18

y = 18/2

y = 9

Hence the zeros of the equations occurs at (2, 9)

The correct options are

-Substitute 0 for x and solve for y

-Substitute 0 for y and solve for x

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In a population of 10,000, there are 5000 nonsmokers, 2500 smokers of one pack or less per day, and 2500 smokers of more than on

Kazeer [188]

Answer:

In one month, we will have 4,950 non-smokers, 2,650 smokers of one pack and 2,400 smokers of more than one pack.

In two months, we will have 4,912 non-smokers, 2,756 smokers of one pack and 2,332 smokers of more than one pack.

In a year, we will have 4,793 non-smokers, 3,005 smokers of one pack and 2,202 smokers of more than one pack.

Step-by-step explanation:

We have to write the transition matrix M for the population.

We have three states (nonsmokers, smokers of one pack and smokers of more than one pack), so we will have a 3x3 transition matrix.

We can write the transition matrix, in which the rows are the actual state and the columns are the future state.

- There is an 8% probability that a nonsmoker will begin smoking a pack or less per day, and a 2% probability that a nonsmoker will begin smoking more than a pack per day. <em>Then, the probability of staying in the same state is 90%.</em>

- For smokers who smoke a pack or less per day, there is a 10% probability of quitting and a 10% probability of increasing to more than a pack per day. <em>Then, the probability of staying in the same state is 80%.</em>

- For smokers who smoke more than a pack per day, there is an 8% probability of quitting and a 10% probability of dropping to a pack or less per day. <em>Then, the probability of staying in the same state is 82%.</em>

<em />

The transition matrix becomes:

$\begin{vmatrix} &NS&P1&PM\\NS& 0.90&0.08&0.02 \\ P1&0.10&0.80 &0.10 \\ PM& 0.08 &0.10&0.82 \end{vmatrix}$

The actual state matrix is

$\left[\begin{array}{ccc}5,000&2,500&2,500\end{array}\right]$

We can calculate the next month state by multupling the actual state matrix and the transition matrix:

$\left[\begin{array}{ccc}5000&2500&2500\end{array}\right] * \left[\begin{array}{ccc}0.90&0.08&0.02\\0.10&0.80 &0.10\\0.08 &0.10&0.82\end{array}\right] =\left[\begin{array}{ccc}4950&2650&2400\end{array}\right]$

In one month, we will have 4,950 non-smokers, 2,650 smokers of one pack and 2,400 smokers of more than one pack.

To calculate the the state for the second month, we us the state of the first of the month and multiply it one time by the transition matrix:

$\left[\begin{array}{ccc}4950&2650&2400\end{array}\right] * \left[\begin{array}{ccc}0.90&0.08&0.02\\0.10&0.80 &0.10\\0.08 &0.10&0.82\end{array}\right] =\left[\begin{array}{ccc}4912&2756&2332\end{array}\right]$

In two months, we will have 4,912 non-smokers, 2,756 smokers of one pack and 2,332 smokers of more than one pack.

If we repeat this multiplication 12 times from the actual state (or 10 times from the two-months state), we will get the state a year from now:

$\left( \left[\begin{array}{ccc}5000&2500&2500\end{array}\right] * \left[\begin{array}{ccc}0.90&0.08&0.02\\0.10&0.80 &0.10\\0.08 &0.10&0.82\end{array}\right] \right)^{12} =\left[\begin{array}{ccc}4792.63&3005.44&2201.93\end{array}\right]$

In a year, we will have 4,793 non-smokers, 3,005 smokers of one pack and 2,202 smokers of more than one pack.

3 0

4 years ago

I need help on dignostic

Aleksandr-060686 [28]

Answer:

1 1/2

Step-by-step explanation:

7 0

3 years ago

Fast hurry skdifhg did did do fish is

Amiraneli [1.4K]

Answer:

$-\frac{7}{10}$

Step-by-step explanation:

Given:

$\frac{1}{2}- 1 \frac{1}{5}$

Number line is from range -2 to 2 with all increment of ± $\frac{2}{10}$ on both sides.

Step 1: First we will solve the equation we will get;

$\frac{1}{2}- 1 \frac{1}{5}\\\\\frac{1}{2}- \frac{6}{5}$

Step 2: Now we will try to make the denominator common so we will get;

$\frac{1\times 5}{2\times 5}- \frac{6\times 2}{5\times 2}\\\\\frac{5}{10}- \frac{12}{10}$

Step 3: Now from the number line when we subtract $\frac{12}{10}$

from $\frac{5}{10}$ we get number of spaces left are - 7

Hence now it will become:

$\frac{5}{10}- \frac{12}{10}\\\\\frac{5 -12}{10}\\\\-\frac{7}{10}$

Hence the final Answer is $-\frac{7}{10}$

4 0

3 years ago

the angle θ is 7.2 degrees, and the circle arc s is 800 km. knowing that there are 360 degrees in a full circle what is the circ

kumpel [21]

The earth is 40000 kilometers around. There is no need to round off because the circumference already contains significant figures.

How do I calculate a circle's circumference?

A circle's diameter is multiplied by to determine its circumference (pi). You can also determine the circumference by multiplying 2radius by pi (=3.14).

Given: theta angle (central) = 7.2°; arc length S = 800 km

This indicates that an 800 km long arc is extending a circle with a 7.2° center angle ( earth in this case).

By definition, "An arc's length is a portion of a circle's diameter."

Therefore, we must first establish what percentage of the circle the specified arc length represents.

360° is a complete circle.

Thus, the fraction equals 7.2°/360°, or 1/50.

As a result, the stated arc length (800km) with a 7.2° central angle is 1/50th of the entire circle.

Thus, the whole circumference is 800 x 50, or 40000 km.

Alternately, you can calculate circumference using the formula below:

360° center angle x arc length as the circumference (theta)

Values substituted: circumference 800 = 360° 7.2°

circumference = 360°, 800°, and 7.2°, or 40000 kilometers

Therefore, the earth is 40000 kilometers around. There is no need to round off because the circumference already contains significant figures.

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4 0

1 year ago

Question content area top

Natali5045456 [20]

The circumference of the outer circle is greater than that of the inner circle by 18.86 feet.

<h3>What is Circle?</h3>

A circle is a round 2-dimensional shape. It is a closed shape with a distance from center to circumference termed as radius 'r' and distance from one point on the circumference to another point passing through center termed as diameter 'd'.

The circumference of the inner circle is 88 ft.

Circumference of a Circle = 2πr

2πr = 88

2 X 22/7 X r = 88

r = 88 X 7 / 44

r = 14 ft.

Radius of the inner circle = 14 feet

If the distance between the inner circle and the outer circle is 3 ft, the radius of the outer circle = 14+3 = 17 feet.

circumference of the outer Circle = 2πr

= 2 X 22/7 X 17

= 106.86 ft.

Difference in Circumference = 106.86 - 88 = 18.86 feet

Thus, the circumference of the outer circle is greater than that of the inner circle by 18.86 feet.

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4 0

2 years ago