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3 years ago

Alex rolls a six-sided number cube 570 times. Approximately how many times can he expect to roll a 5?

Mathematics

2 answers:

Annette [7]3 years ago

8 0

1)First determine the probability of rolling a 5

2)Since you can only roll a 5 once in a 6-sided cube the probability is ⅙ or about 0.1667

3)Multiply the probability and the total number of rolls

.1667 * 570= 95

Answer : 95 times

madreJ [45]3 years ago

5 0

Answer:

95 times

Step-by-step explanation:

Probability of rolling a 5 =1/6

So no. of times 5 is expected when the number cube is rolled out 570 times = 570*1/6 = 95 times

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A ball is thrown into the air. The path it takes is modeled by the equation: -3t+24t = h, where t is the time in seconds and h i

astra-53 [7]

Given:

The given equation is:

$-3t^2+24t=h$

Where, t is the time in seconds and h is the height of the ball above the ground, measured in feet.

To find:

The inequality to model when the height of the ball is at least 36 feet above the ground. Then find time taken by ball to reach at or above 36 feet.

Solution:

We have,

$-3t^2+24t=h$

The height of the ball is at least 36 feet above the ground. It means $h\geq 36$ .

$-3t^2+24t\geq 36$

$-3t^2+24t-36\geq 0$

$-3(t^2-8t+12)\geq 0$

Splitting the middle term, we get

$-3(t^2-6t-2t+12)\geq 0$

$-3(t(t-6)-2(t-6))\geq 0$

$-3(t-2)(t-6)\geq 0$

The critical points are:

$-3(t-2)(t-6)=0$

$t=2,6$

These two points divide the number line in 3 intervals $(-\infty,2),(2,6),(6,\infty)$ .

Intervals Check point $-3(t-2)(t-6)\geq 0$ Result

$(-\infty,2)$ 0 $(-)(-)(-)=(-)$ False

$(2,6)$ 4 $(-)(+)(-)=+>0$ True

$(6,\infty)$ 8 $(-)(+)(+)=(-)$ False

The inequality is true for (2,6) and the sign of inequality is $\geq$ . So, the ball is above 36 feet between 2 to 6 seconds.

$6-2=4$

Therefore, the required inequality is $-3t^2+24t\geq 36$ and the ball is 36 feet above for 4 seconds.

3 0

3 years ago

choose the equation of a line that is perpendicular to the y axis and passes through the point (5,-2)

kondaur [170]

Answer:

y = -2

Step-by-step explanation:

The line that is perpendicular to y-axis will be a horizontal line so it's slope is 0 => y = 0x + b or y = b

Using (5,-2) => -2 = b => b = -2

then y = -2

3 0

2 years ago

How many distinguishable a arrangements are there of the letters in "REPRESENTATION"?

Anika [276]

Answer: There are 1,816,214,400 ways for arrangements.

Step-by-step explanation:

Since we have given that

"REPRESENTATION"

Here, number of letters = 14

There are 2 R's, 3 E's, 2 T's, 2 N's

So, number of permutations would be

$\dfrac{14!}{2!\times 3!\times 2!\times 2!}\\\\=1,816,214,400$

Hence, there are 1,816,214,400 ways for arrangements.

5 0

3 years ago

You are at an pear picking farm and they allow you to pick up to 50 pears a day. Today, you have already picked 14 pears. Which

Liono4ka [1.6K]

step 1

Subtract 14 from 50

50-14=36

$p+14\leq50$

If you solve for p

$p\leq36$

the answer is the second option

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9 months ago

Find the difference. express your answer in simplest form. (2s/s^2-4s+4) - (4/s^2-4s+4)

LUCKY_DIMON [66]

To find the difference, we are going to destroy the parenthesis first, and then, we are going to perform the operations. Remember that to destroy a parenthesis preceded by a negative sign (-), you should change the signs of the factors inside the parenthesis:
$\frac{2s}{s^2-4s+4} -( \frac{4}{s^2-4s+4} )$
$\frac{2s}{s^2-4s+4} -\frac{4}{s^2-4s+4}= \frac{2s-4}{s^2-4s+4}$

Now we can factor both numerator and denominator and simplify:
$\frac{2s-4}{s^2-4s+4} = \frac{2(s-2)}{(s-2)^2} = \frac{2}{s-2}$

We can conclude that the difference in simplest form is: $\frac{2}{s-2}$

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3 years ago

Read 2 more answers