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3 years ago

How do you write 4540 million in standard form?

2 answers:

8 0

For this case what we should do is take into account the following conversion:
$million = 10 ^ 6
$
We then have the following number:
$4540 million
$
Applying the given conversion we have:
$4540 * 10 ^ 6
$
By doing the corresponding calculation we have that the standard form is given by:
$4540 * 10 ^ 6 = 4,540,000,000
$
Answer:
4540 million in standard form is:
$4,540,000,000$

Shalnov [3]3 years ago

7 0

$4540mln=4,540,000,000\\\\in\ scientific\ notation:4,\underbrace{540,000,000}_{\leftarrow9}=4.54\cdot10^9$

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Line JM intersects line GK at point N. Which statements are true about the figure? Check all that apply. GNJ is complementary to

Arlecino [84]

Two angles are said to be complementary when their sum is 90 degrees and are said to be supplementary when their sum is 180 degree.

From the figure, line JM intersects line GK at 90 degrees, hence

Angle GNJ is 90 degrees and angle JNK is 90 degrees. The sum of the angles GNJ and JNK is 180 degrees. Therefore, GNJ is not complemetary to JNK.

The sum of angles MNL and KNL is MNK which is 90 degrees. Therefore, MNL is complementary to GNJ.

Angle MNG is 90 degrees and angle GNJ is 90 degrees. The sum of the angles MNG and GNJ is 180 degrees. Therefore, MNG is not complemetary to GNJ.

Angle KNJ is 90 degrees and angle MNL is less than 90 degrees. The sum of the angles KNJ and MNL is less than 180 degrees. Therefore, KNJ is not supplementary to MNL.

Angle GNM is 90 degrees and angle JNK is 90 degrees. The sum of the angles GNM and JNK is 180 degrees. Therefore, GNM is supplementary to JNK.

Therefore, the true statements are:
MNL is complementary to GNJ.
and
GNM is supplementary to JNK.

7 0

3 years ago

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What is 24a-22=-4(1-6a) simplify too?

Nutka1998 [239]

24a-22=-4+24a
24a=-26+24a
a=-26

3 0

4 years ago

Let f be defined by the function f(x) = 1/(x^2+9)

riadik2000 [5.3K]

(a)

$\displaystyle\int_3^\infty \frac{\mathrm dx}{x^2+9}=\lim_{b\to\infty}\int_{x=3}^{x=b}\frac{\mathrm dx}{x^2+9}$

Substitute x = 3 tan(t ) and dx = 3 sec²(t ) dt :

$\displaystyle\lim_{b\to\infty}\int_{t=\arctan(1)}^{t=\arctan\left(\frac b3\right)}\frac{3\sec^2(t)}{(3\tan(t))^2+9}\,\mathrm dt=\frac13\lim_{b\to\infty}\int_{t=\arctan(1)}^{t=\arctan\left(\frac b3\right)}\mathrm dt$

$=\displaystyle \frac13 \lim_{b\to\infty}\left(\arctan\left(\frac b3\right)-\arctan(1)\right)=\boxed{\dfrac\pi{12}}$

(b) The series

$\displaystyle \sum_{n=3}^\infty \frac1{n^2+9}$

converges by comparison to the convergent p-series,

$\displaystyle\sum_{n=3}^\infty\frac1{n^2}$

$\displaystyle \sum_{n=1}^\infty \frac{(-1)^n (n^2+9)}{e^n}$

converges absolutely, since

$\displaystyle \sum_{n=1}^\infty \left|\frac{(-1)^n (n^2+9)}{e^n}\right|=\sum_{n=1}^\infty \frac{n^2+9}{e^n} < \sum_{n=1}^\infty \frac{n^2}{e^n} < \sum_{n=1}^\infty \frac1{e^n}=\frac1{e-1}$

That is, ∑ (-1)ⁿ (n ² + 9)/eⁿ converges absolutely because ∑ |(-1)ⁿ (n ² + 9)/eⁿ| = ∑ (n ² + 9)/eⁿ in turn converges by comparison to a geometric series.

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3 years ago

What is the probability of picking a face card given that the card is a Jack?

Kryger [21]

Answer:

1/13

Step-by-step explanation:

there are 4 jacks in a deck of 52 cards

therefore probability of picking a jack:

4/52 = 1/13

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3 years ago

What property for each step?

PolarNik [594]

For the first one it’s subtraction property of equality

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3 years ago

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