# Which of the following numbers can be expressed as a decimal that terminates? a) 7 over 4 and 3 over 8 b) 5 over 9 and 2 (2023)

17.05.2023the following question

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17.05.2023, solved by verified expert

The easiest way to make a fraction into a decimal is to divide the numerator by the deniminator. Since terminating is a decimal that ends, and doesn't repeat, the answer would have to be A. To eliminate, 5/9 is 0.555.. so it's not the answer.7/4 is 1.75, but 5/9 is 0.55... 3/8 is 0.375, but 2/3 is 0.666

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Mathematics

Which of the following numbers can be expressed as a decimal that terminates? a) 7 over 4 and 3 over 8 b) 5 over 9 and 2 over 3 c) 7 over 4 and 5 over 9 d) 3 over 8 and 2 over 3 if possible, provide details of how you got your answer.

The easiest way to make a fraction into a decimal is to divide the numerator by the deniminator. Since terminating is a decimal that ends, and doesn't repeat, the answer would have to be A. To eliminate, 5/9 is 0.555.. so it's not the answer.7/4 is 1.75, but 5/9 is 0.55... 3/8 is 0.375, but 2/3 is 0.666

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A graphing calculator is recommended. A crystal growth furnace is used in research to determine how best to manufacture crystals used in electric components for the space shuttle. For proper growth of the crystal, the temperature must be controlled accurately by adjusting the input power. Suppose the relationship is given by T(w) = 0.1w2 + 2.159w + 20 where T is the temperature in degrees Celsius and w is the power input in watts. (a) How much power is needed to maintain the temperature at 198°C? (Round your answer to two decimal places.) watts

Step-by-step explanation:

For this case we have the following function

Where T represent the temperature in Celsius and w the power input in watts.

Part a

For this case we need to find the value of w that makes the temperature 203C, so we can set the following equation:

And we can rewrite the expression like this:

And we can solve this using the quadratic formula given by:

Where a =0.1, b =2.156 and c=-183. If we replace we got:

And since the power can't be negative then the solution would be w = 33.34 watts.

Part b

For this case we can find the values of w for the temperatures 203-1= 202C and 203+1 = 204 C. And we got this:

So then the range of voltage would be between 33.22 W and 33.45 W.

Part c

For this case since that's the tolerance 1C

For this case we can do this:

So then we select the smallest value on this case

For this case if we assume a tolerance of for the temperature and a tolerance for the power input we see that:

Where a = 33.34 W, f(x) represent the temperature, x represent the input power and L = 203C

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The answer is in the image

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A scientist created a scatterplot to display the height of a plant over a 12-day period. Plant Height A graph has days on the x-axis and height (inches) on the y-axis. A trend line goes through points (5, 3) and (12, 7). Which is the equation of the trend line that is shown?

A. y=1/7×+4/7;
B. y=1/7×+16/7;
C. y=4/7×-1/7;
D. y=4/7×+1/7​.

Explanation:
The two-point form for the equation of straight line is:
(y-y1)=y2-y1/x2-x1*(x-x1).
The two points provided are:
A = (5, 3);
B = (12, 7).
Compute the equation of the trend line as follows:
(y-y1)=y2-y1/x2-x1*(x-x1);
(y-3)=7-3/12-5*(x-5);
(y-3)=4/7*(x-5);
y-3=4/7x-20/7;
y=4/7x-20/7+3;
y=4/7x+(-20+21)/7;
y=4/7x+1/7.
Thus, the equation of the trend line is y=4/7x+1/7.
The correct option is (D).

Mathematics

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Correct question:
The dance committee of Pine Bluff Middle School earns \$72 from a bake sale and will earn \$4 for each ticket they sell to the Spring Fling dance. The dance will cost \$400 . Write an inequality to determine the number, t , of tickets the committee could sell to have money left over after they pay for this year's dance.

Explanation:
Given:
The dance committee of Pine Bluff Middle School earns \$72 from a bake sale and will earn \$4 for each ticket they sell to the Spring Fling dance.
The dance will cost \$400.
Let x number of tickets the committee could sell.
Total money earned is 72 + 4 × x.
The committee should have some left over money also after spending for the dance which costs \$400.
Thus the inequality to determine the number of tickets the committee could sell to have money left over after they pay for this year's dance is given by,
72+4*x>=400.

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