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dybincka [34]
3 years ago
13

Which expressions have a value of 16/81? Check all that apply.

Mathematics
1 answer:
lana [24]3 years ago
6 0

Which expression have a value of 16/81? check all that apply. (2/3)^4, (16/3)^4, (4/81)^2, and (4/9)^2

Answer:

First and last option is correct.

(\frac{2}{3})^{4}=\frac{16}{81}

(\frac{4}{9})^{2}=\frac{16}{81}

Step-by-step explanation:

Given:

There are four options.

(2/3)^4, (16/3)^4, (4/81)^2, and (4/9)^2

We need to check all given options for value of 16/81.

Solution:

Using rule.

(\frac{a}{b})^{n}=\frac{a^{n}}{b^{n}}

Solve for option (\frac{2}{3})^4.

(\frac{2}{3})^{4}=\frac{2^4}{3^4}=\frac{2\times 2\times 2\times 2}{3\times 3\times 3\times 3}=\frac{16}{81}

Solve for option (\frac{16}{3})^4.

(\frac{16}{3})^{4}=\frac{16^4}{3^4}=\frac{16\times 16\times 16\times 16}{3\times 3\times 3\times 3}=\frac{65536}{81}

Solve for option (\frac{4}{81})^2.

(\frac{4}{81})^{2}=\frac{4^2}{81^2}=\frac{4\times 4}{81\times 81}=\frac{16}{6561}

Solve for option (\frac{4}{9})^2.

(\frac{4}{9})^{2}=\frac{4^2}{9^2}=\frac{4\times 4}{9\times 9}=\frac{16}{81}

Therefore, expression (\frac{2}{3})^4 and (\frac{4}{9})^2 have a value of  \frac{16}{81}.

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Answer:

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if x = 0  thus e^{-kx} = 1

so at 0 the function value would be A

f(x)=2e^{-kx}

Step-by-step explanation:

6 0
3 years ago
A school has an equal amount of boys and girls. You use a coin to simulate the first three students to arrive at school each day
Nimfa-mama [501]

Answer:3/20

Step-by-step explanation:

Heads=Boy

Tails=Girl

If the first 3 students are boys, all 3 coins must be heads.

Because in 3 of these experiments, the coins all land on heads, and there are 20 experiments completed, 3 out of the 20 experiments are 3 boys; 3/20.

3 0
2 years ago
If a certain cannon is fired from a height of 8.8 meters above the​ ground, at a certain​ angle, the height of the cannonball ab
Dennis_Churaev [7]

Answer:

It would take approximately 6.50 second for the cannonball to strike the ground.

Step-by-step explanation:

Consider the provided function.

h(t)=-4.9t^2+30.5t+8.8

We need to find the time takes for the cannonball to strike the ground.

Substitute h(t) = 0 in above function.

-4.9t^2+30.5t+8.8=0

Multiply both sides by 10.

-49t^2+305t+88=0

For a quadratic equation of the form ax^2+bx+c=0 the solutions are: x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}

Substitute a = -49, b = 305 and c=88

t=\frac{-305+\sqrt{305^2-4\left(-49\right)88}}{2\left(-49\right)}=-\frac{-305+\sqrt{110273}}{98}\\t = \frac{-305-\sqrt{305^2-4\left(-49\right)88}}{2\left(-49\right)}= \frac{305+\sqrt{110273}}{98}

Ignore the negative value of t as time can't be a negative number.

Thus,

t=\frac{305+\sqrt{110273}}{98}\approx6.50

Hence, it would take approximately 6.50 second for the cannonball to strike the ground.

6 0
3 years ago
HelP me plz i'll give brainliest or whatever
aivan3 [116]
The answer is d

explanation: its right in between 50 and 60 making it 55, and the picture is showing it as an angle.
3 0
3 years ago
Solve. <br> 1/2x + 3 &lt; 4x - 7<br><br> A) x &gt; 8/7<br> B) x &lt; -8/7<br> C) x &gt; 20/7
anyanavicka [17]
C would be your answer and here is how you would solve the problem.

5 0
3 years ago
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