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3 years ago

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In a video game, each rocket has an 80% chance of hitting a target. Three rockets are now fired at a target. What is the probabi

lity that exactly two of the rockets will hit the target? Express your answer as a decimal to the nearest thousandth.

1 answer:

vitfil [10]3 years ago

7 0

See https://web2.0calc.com/questions/help_69037.

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Sarah cannot completely remember her four-digit ATM pin number. She does remember the first two digits, and she knows that each

OLga [1]

Answer:

3/16 or 0.1875

Step-by-step explanation:

Since she remembers the first two digits, she only has to guess the last two digits. If both digits are greater than 5, there are 4 possible alternatives for each digit (6, 7, 8 or 9).

In three tries, the probability that she will get it right is:

$P=\frac{3}{4*4}\\P=\frac{3}{16}=0.1875$

The probability she will get access to her account is 3/16 or 0.1875.

4 0

3 years ago

Help me plz ._. i beg u

Fynjy0 [20]

The answer is D because a gas is like carbon dioxide and stuff like that a liquid is something that can take shape of whatever you put it in and a solid Is it stays the shape it was originally put in

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2 years ago

How many terms of the arithmetic sequence {1,22,43,64,85,…} will give a sum of 2332? Show all steps including the formulas used

MA_775_DIABLO [31]

There's a slight problem with your question, but we'll get to that...

Consecutive terms of the sequence are separated by a fixed difference of 21 (22 = 1 + 21, 43 = 22 + 21, 64 = 43 + 21, and so on), so the <em>n</em>-th term of the sequence, <em>a</em> (<em>n</em>), is given recursively by

• <em>a</em> (1) = 1

• <em>a</em> (<em>n</em>) = <em>a</em> (<em>n</em> - 1) + 21 … … … for <em>n</em> > 1

We can find the explicit rule for the sequence by iterative substitution:

<em>a</em> (2) = <em>a</em> (1) + 21

<em>a</em> (3) = <em>a</em> (2) + 21 = (<em>a</em> (1) + 21) + 21 = <em>a</em> (1) + 2×21

<em>a</em> (4) = <em>a</em> (3) + 21 = (<em>a</em> (1) + 2×21) + 21 = <em>a</em> (1) + 3×21

and so on, with the general pattern

<em>a</em> (<em>n</em>) = <em>a</em> (1) + 21 (<em>n</em> - 1) = 21<em>n</em> - 20

Now, we're told that the sum of some number <em>N</em> of terms in this sequence is 2332. In other words, the <em>N</em>-th partial sum of the sequence is

<em>a</em> (1) + <em>a</em> (2) + <em>a</em> (3) + … + <em>a</em> (<em>N</em> - 1) + <em>a</em> (<em>N</em>) = 2332

or more compactly,

$\displaystyle\sum_{n=1}^N a(n) = 2332$

It's important to note that <em>N</em> must be some positive integer.

Replace <em>a</em> (<em>n</em>) by the explicit rule:

$\displaystyle\sum_{n=1}^N (21n-20) = 2332$

Expand the sum on the left as

$\displaystyle 21 \sum_{n=1}^N n-20\sum_{n=1}^N1 = 2332$

and recall the formulas,

$\displaystyle\sum_{k=1}^n1=\underbrace{1+1+\cdots+1}_{n\text{ times}}=n$

$\displaystyle\sum_{k=1}^nk=1+2+3+\cdots+n=\frac{n(n+1)}2$

So the sum of the first <em>N</em> terms of <em>a</em> (<em>n</em>) is such that

21 × <em>N</em> (<em>N</em> + 1)/2 - 20<em>N</em> = 2332

Solve for <em>N</em> :

21 (<em>N</em> ² + <em>N</em>) - 40<em>N</em> = 4664

21 <em>N</em> ² - 19 <em>N</em> - 4664 = 0

Now for the problem I mentioned at the start: this polynomial has no rational roots, and instead

<em>N</em> = (19 ± √392,137)/42 ≈ -14.45 or 15.36

so there is no positive integer <em>N</em> for which the first <em>N</em> terms of the sum add up to 2332.

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2 years ago

Using number 3,7,3, and 5 make the greatest 4 digit number and the least 4 digit number..use each digit once

zalisa [80]

Solving equations simple
9n + 12 = 30

7 0

2 years ago

Is an angle that is greater than 90 degrees is acute True or False

Brilliant_brown [7]

Hey there!

The answer is false. A 90 degree angle is called a right triangle. Any angle less than 90 degree is called an acute angle. Any angle more than 90 degree is called an obtuse angle

7 0

3 years ago

Read 2 more answers