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3 years ago

Write the next three terms in the pattern. What is each pattern rule?-64, +32, -16, ...

Mathematics

1 answer:

Mashcka [7]3 years ago

7 0

Answer:

+8, -4, +2

Step-by-step explanation:

The pattern rule is every other number is negative and it alternates. It would be plus, minus, plus, minus, and keep that going. The second part to the pattern rule is the next number is half of the previous. So 32 was half of 64, 16 was half of 32 so now 8 is half of 16, 4 is half of 8, and 2 is half of 4. Keep the + - + - + - pattern too.

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Tom throws a ball into the air. The ball travels on a parabolic path represented by the equation , where represents the height o

tigry1 [53]

Answer:

2.5 second

Step-by-step explanation:

The equation is missing in the question.

The equation is, $h=-8t^2+40t$ , where 'h' is the height and 't' is time measured in second.

Now we know to reach its maximum height, h in t seconds, the derivative of h with respect to time t is given by :

$\frac{dh}{dt} =0$

Now the differentiating the equation with respect to time t, we get

$\frac{dh}{dt}=\frac{d}{dt}(-8t^2+40t)$

$\frac{dh}{dt}=-16t+40$

For maximum height, $\frac{dh}{dt} =0$

So, $-16t+40=0$

$\Rightarrow 16t=40$

$\Rightarrow t=\frac{40}{16}$

$\Rightarrrow t = 2.5$

Therefore, the ball takes 2.5 seconds time to reach the maximum height.

7 0

3 years ago

If we sample from a small finite population without replacement, the binomial distribution should not be used because the event

seropon [69]

Answer:

5/4324 = 0.001156337

Step-by-step explanation:

To better understand the hyper-geometric distribution consider the following example:

There are 100 senators in the US Congress, and suppose 60 of them are republicans so 100 - 60 = 40 are democrats).

We extract a random sample of 30 senators and we want to answer this question:

What is the probability that 10 senators in the sample are republicans (and of course, 30 - 10 = 20 democrats)?

The answer using the h-g distribution is:

$\large \frac{\binom{60}{10}\binom{100-60}{30-10}}{\binom{100}{30}}=\frac{\binom{60}{10}\binom{40}{20}}{\binom{100}{30}}$

Now, imagine there are 56 senators (56 lottery numbers), 6 are republicans (6 winning numbers and 50 losers), we extract a sample of 6 senators (the bettor selects 6 numbers). What is the probability that 4 senators are republicans? (What is the probability that 4 numbers are winners?).

<em>As we see, the situation is exactly the same,</em> but changing the numbers. So the answer would be

$\large \frac{\binom{6}{4}\binom{56-6}{6-4}}{\binom{56}{6}}=\frac{\binom{6}{4}\binom{50}{2}}{\binom{56}{6}}$

Now compute each combination separately:

$\large \binom{6}{4}=\frac{6!}{4!2!}=15\\\\\binom{50}{2}=\frac{50!}{2!48!}=1225\\\\\binom{50}{6}=\frac{50!}{6!44!}=15890700$

and now replace the values:

$\large \frac{\binom{6}{4}\binom{50}{2}}{\binom{56}{6}}=\frac{15*1225}{15890700}=\frac{18375}{15890700}=\frac{5}{4324}$

and that is it.

If the decimal expression is preferred then divide the fractions to get 0.001156337

6 0

3 years ago

Two competing sports equipment suppliers sell footballs at different prices. Supplier A charges $85 in shipping, and charges $2.

S_A_V [24]

Supplier A: $188.6
Supplier B: $221.6

I hope I helped but I honestly have no idea if I did. Anyway sorry if I didn't. Good luck.

7 0

3 years ago

HIGH SCHOOL MATH ....

umka21 [38]

Answer:

The value of $B (base\ area) = 27m^2$

Step-by-step explanation:

Let's recall the the formula for volume of a pyramid.

Volume of a Pyramid $= \frac{1}{3}\times B\times H}$ ....equation $(1)$

where $B=Base\ area (m^2)$ and $H=height\ (m)$

Now we have been given the values of $V$ and $H$ and have to find the value of $B$

Plugging the values of $V$ and $H$ in equation $(1)$

$B=\frac{3\times V}{H}= \frac{3 \times 81}{9} = 27\ m^2$

Now we can also check our previous results.

$V = \frac{24\times 7}{3}=8 \times 7 =56\ m^3$

So, our final answer is $27\ m^2$

7 0

3 years ago

Simplify the radical completely.

Sonja [21]

Answer:

Step-by-step explanation:

But basically, one by one you try moving the terms out of the radical.

75 is also 25 * 3 and since 25 has a perfect square root of 5 that goes out and 3 stays inside the radical.

x^3 is also x^2 * x and since x^2 has a perfect square root which is just x that goes outside while the remaining x stays inside.

y^9 is also y^8 * y and since we move variables out the radical in twos y^ goes outside the radical and y stays inside alone.

Finally, z is just z it can't be taken out so it stays inside the radical.

Hope that helps!

8 0

2 years ago