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3 years ago

Explain how to multiply decimals by powers of 10. Use 8.653 x 10000 as an example, to show how the multiplication is done.

Mathematics

1 answer:

Lera25 [3.4K]3 years ago

4 0

Answer:

We move the decimal point to the right by a number of digit places equal to the power of 10.

Step-by-step explanation:

If we want to multiply a decimal by a power of 10, we move the decimal point to the right by a number of digit places which is the power of the number ten or the number of zeros which are present in the multiplying number 10. If we do not have a digit after the last digit, we put zeros to complete the number of digits until, we have the number of digit places added after the decimal point which are equal to the power of 10.

Using the example given above

8.653 x 10000, we have four zeros. So, in index form it is

8.653 x 10⁴

Since we have the number 10 raised to the power of four or having 4 zeros, we move the decimal point 4 places to the right.

So, 8.653 x 10000 = 8.653 x 10⁴ = 86530

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Marty's hourly rate is $20.59 per hour. He just received a

77julia77 [94]

Answer:

23.14

Step-by-step explanation:

= 20.59 x (12.4/100)

= 2.55316

= 2.55316 + 20.59

= 23.14316

= 23.14

I hope this helps.

8 0

3 years ago

Read 2 more answers

Which is one of the transformations applied to the graph of f(x)=x2 to change it into the graph of g(x) = -x2 + 16x – 44?

KatRina [158]

Answer:

Only option D is one of the transformations needed.

Step-by-step explanation:

The graph of f(x)=x^2 is a positive parabola with x=0 as the zero in ordinates and also 0 as a zero x. This is, the graph passes in (0,0) and this is the only point it crosses both axis, then for every x value we will gave a positive f(x).

Here I attach a graph that shows both, f(x)=x^2 and g(x)=-x^2+16x-44.

As you can see, for transforming f(x) in g(x) we need to reflect it over the x axis, as g is open downwards. Then, as the quadratic term is still being x^2 we do not wide it (as you see in the graph both curves are equally widened).

Then, we can also see that the graph is shifted right, so we do not shift it left 8 units (notice that we shift it right 8 units).

So, after reflecting over the x axis and shifting right we need to shift it UP, as we can see the graph is over the x axis.

So, the three transformations needed are:

1. reflect over the x axis

2. shift right 8 units

3. shift up 20 units.

So, from the options you proposed we chose only d, to which we MUST add the transformations noted above.

Sorry for the mistake!

8 0

3 years ago

Read 2 more answers

While researching the cost of school lunches per week across the state, you use a sample size of 45 weekly lunch prices. The sta

Drupady [299]

We assume the lunch prices we observe are drawn from a normal distribution with true mean $\mu$ and standard deviation 0.68 in dollars.

We average $n=45$ samples to get $\bar{x}$ .

The standard deviation of the average (an experiment where we collect 45 samples and average them) is the square root of n times smaller than than the standard deviation of the individual samples. We'll write

$\sigma = 0.68 / \sqrt{45} = 0.101$

Our goal is to come up with a confidence interval (a,b) that we can be 90% sure contains $\mu$ .

Our interval takes the form of $( \bar{x} - z \sigma, \bar{x} + z \sigma )$ as $\bar{x}$ is our best guess at the middle of the interval. We have to find the z that gives us 90% of the area of the bell in the "middle".

Since we're given the standard deviation of the true distribution we don't need a t distribution or anything like that. n=45 is big enough (more than 30 or so) that we can substitute the normal distribution for the t distribution anyway.

Usually the questioner is nice enough to ask for a 95% confidence interval, which by the 68-95-99.7 rule is plus or minus two sigma. Here it's a bit less; we have to look it up.

With the right table or computer we find z that corresponds to a probability p=.90 the integral of the unit normal from -z to z. Unfortunately these tables come in various flavors and we have to convert the probability to suit. Sometimes that's a one sided probability from zero to z. That would be an area aka probability of 0.45 from 0 to z (the "body") or a probability of 0.05 from z to infinity (the "tail"). Often the table is the integral of the bell from -infinity to positive z, so we'd have to find p=0.95 in that table. We know that the answer would be z=2 if our original p had been 95% so we expect a number a bit less than 2, a smaller number of standard deviations to include a bit less of the probability.

We find z=1.65 in the typical table has p=.95 from -infinity to z. So our 90% confidence interval is

$( \bar{x} - 1.65 (.101), \bar{x} + 1.65 (.101) )$