Which sentence means Jack ate 2 ⁄ 4 of a pizza?

marshall27 [118]

Answer:

300

Step-by-step explanation:

The red portion is marked with a small square; that means it is a 90° section. It is 1/4 of the whole circle. They also said 75 kids chose red. If 1/4 of the circle represents 75 kids, then the whole entire circle would represent 75+75+75+75 kids or 4(75) kids, which is 300 kids.

7 0

2 years ago

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Ryan rolls two fair number cubes labeled 1 through 6. What is the probability that the sum of the two number cubes is 5 or more?

Aleksandr [31]

Answer:

1/3.

Step-by-step explanation:

2 x 6 = 12

1 2 3 4 5 6

4/12 = 1/3

4 0

2 years ago

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Which ratio is equivalent to 12 over 14

Alecsey [184]

12/14=6/7

Because you divide by 2.

5 0

3 years ago

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In a recent survey in a Statistics class, it was determined that only 74% of the students attend class on Fridays. From past dat

Anna007 [38]

Answer:

a) 83%

b) 0.892

Step-by-step explanation:

percentage that attends class on friday = 74%

percentage that pass because they attend class on friday = 88%

percentage that pass but did not go to school on friday = 20%

a) percentage of students expected to pass the course

= (74% x 88%) +(88% x 20%)

= 0.6512 + 0.176

= 0.8272

= 83%

b) If a person passes the course, what is the probability that he/she attended classes on Fridays

= 74% divided by 83%

= 0.892

7 0

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 n-th term of the sequence, a (n), is given recursively by

• a (1) = 1

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

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

a (2) = a (1) + 21

a (3) = a (2) + 21 = (a (1) + 21) + 21 = a (1) + 2×21

a (4) = a (3) + 21 = (a (1) + 2×21) + 21 = a (1) + 3×21

and so on, with the general pattern

a (n) = a (1) + 21 (n - 1) = 21n - 20

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

a (1) + a (2) + a (3) + … + a (N - 1) + a (N) = 2332

or more compactly,

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

It's important to note that N must be some positive integer.

Replace a (n) 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 N terms of a (n) is such that

21 × N (N + 1)/2 - 20N = 2332

Solve for N :

21 (N ² + N) - 40N = 4664

21 N ² - 19 N - 4664 = 0

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

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

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

4 0

2 years ago