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2 years ago

10

a fast food chain surveyed a random sample of students to determine what pizza they prefer. Based on the results, how many of th

e 340 students can be expected to prefer cheese pizza?

1 answer:

Elza [17]2 years ago

8 0

50% (170) since there’s only 2 opinion and that’s the only info it gives us

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Problems 2.21, 2.22, 2.23

RoseWind [281]

Statements can be proved by contrapositive, contradiction or by induction.

<em>2.21 and 2.23 are proved by contrapositive</em>
<em>2.22 is proved by induction</em>

<u />

<u />

<u>2.21: If </u> $n^3$ <u> is even, then n is even (By contrapositive)</u>

The contrapositive of the above statement is that:

<em>If n is odd, then </em> $n^3$ <em> is odd</em>

Represent the value of n as:

$n = 2k + 1$ , where $k \ge 0$

Take the cube of both sides

$n^3 = (2k + 1)^3$

Expand

$n^3 = 8k^3 + 6k^2 + 6k + 1$

Group

$n^3 =[ 8k^3 + 6k^2 + 6k] + 1$

Factor out 2

$n^3 =2[4k^3 + 3k^2 + 3k] + 1$

Assume w is an integer; where:

$w =4k^3 + 3k^2 + 3k$

So, we have:

$n^3 =2w + 1$

The constant term (i.e. 1) means that $n^3$ is odd.

Hence, the statement has been proved by contrapositive.

<em>i.e. If n is odd, then </em> $n^3$ <em> is odd</em>

<u />

<u>2.22 </u> $3n + 4$ <u> is even, if and only if n is even</u>

We have: $3n + 4$ <u />

<u />

Assume that: $n = 2k + 2$ for $k \ge 0$

So, we have:

$3n + 4 = 3(2k + 2) + 4$

Open bracket

$3n + 4 = 6k + 6 + 4$

$3n + 4 = 6k + 10$

Factorize

$3n + 4 = 2(3k + 5)$

The factor of 2 means that $3n + 4$ is even.

<em>Hence, </em> $3n + 4$ <em> is even, if and only if n is even </em>

<em />

<u />

<u>2.22: </u> $s \ne -1$ <u> and </u> $t \ne -1$ <u>, then </u> $s + t + st \ne -1$ <u />

To do this, we prove by contrapositive.

The contrapositive of the above statement is:

If $s = -1$ and $t=-1$ , then $s + t + st = -1$

We have:

$s + t + st = -1$

Substitute the values of s and t in: $s + t + st = -1$

$-1 -1 -1 \times -1 = -1$

$-1 -1 + 1 = -1$

$-1 = -1$

Hence, by contrapositive:

If $s = -1$ and $t=-1$ , then $s + t + st = -1$

Read more about proofs at:

brainly.com/question/19643658

7 0

3 years ago

Write the following question expression in simplest binomial form 4(3x-2)-2(4x+5)

Oduvanchick [21]

$4(3x-2)-2(4x+5)$

$12x-8-8x-10
$

$(12x-8x)+(-8-10)
$

$4x-18
$

4 0

3 years ago

(PLEASE HELP ME ASAP‼️)

tia_tia [17]

Answer:

1

Step-by-step explanation:

I really can't give you a step-by-step

7 0

3 years ago

Which polynomial expression represents the area of the outer most square tile, shown below?

Andrew [12]

ANSWER

${x}^{2} - 6x + 9$

EXPLANATION

The outermost square tile has side length,

$l = x - 3$

The area of a square is given by;

$Area= {l}^{2}$

We substitite the given expression for the side length into the formula to obtain,

$Area= {(x - 3)}^{2}$

$Area= {(x - 3)}(x - 3)$

We expand using the distributive property to obtain;

$Area=x {(x - 3)} - 3(x - 3)$

This gives us:

$Area= {x}^{2} - 3x - 3x + 9$

$Area= {x}^{2} - 6x + 9$

The last choice is correct.

7 0

3 years ago

Read 2 more answers

1. What is greater? 6 pounds and 11 ounces OR 117 ounces? 2. 3/4 tons = how many pounds? (Answer the ones u know!) pls help due

lesya [120]

Answer:

1. Equal. 2. 1500

Step-by-step explanation:

6 x 16 = 96 + 11= 117

3/4 x 2000 = 1500

4 0

3 years ago