All categories

3 years ago

What is the contrapositive of the statement? All squares are rectangles.

2 answers:

8 0

D.) If a figure is not a rectangle, then it is not a square
Contrapositive is when it switches the two sides up and makes it negative as well.

GuDViN [60]3 years ago

8 0

Answer:

Step-by-step explanation:

Ed2020

You might be interested in

How do I turn those numbers into a mixed number?

BigorU [14]

Number 2 is already a mixed number. But it says mixed number as a decimal. So -1 29/40 as a decimal is -1.725.

8 0

3 years ago

Prove or disprove (from i=0 to n) sum([2i]^4) <= (4n)^4. If true use induction, else give the smallest value of n that it doe

ddd [48]

Answer:

The statement is true for every n between 0 and 77 and it is false for $n\geq 78$

Step-by-step explanation:

First, observe that, for n=0 and n=1 the statement is true:

For n=0: $\sum^{n}_{i=0} (2i)^4=0 \leq 0=(4n)^4$

For n=1: $\sum^{n}_{i=0} (2i)^4=16 \leq 256=(4n)^4$

From this point we will assume that $n\geq 2$

As we can see, $\sum^{n}_{i=0} (2i)^4=\sum^{n}_{i=0} 16i^4=16\sum^{n}_{i=0} i^4$ and $(4n)^4=256n^4$ . Then,

$\sum^{n}_{i=0} (2i)^4 \leq(4n)^4 \iff \sum^{n}_{i=0} i^4 \leq 16n^4$

Now, we will use the formula for the sum of the first 4th powers:

$\sum^{n}_{i=0} i^4=\frac{n^5}{5} +\frac{n^4}{2} +\frac{n^3}{3}-\frac{n}{30}=\frac{6n^5+15n^4+10n^3-n}{30}$

Therefore:

$\sum^{n}_{i=0} i^4 \leq 16n^4 \iff \frac{6n^5+15n^4+10n^3-n}{30} \leq 16n^4 \\\\ \iff 6n^5+10n^3-n \leq 465n^4 \iff 465n^4-6n^5-10n^3+n\geq 0$

and, because $n \geq 0$ ,

$465n^4-6n^5-10n^3+n\geq 0 \iff n(465n^3-6n^4-10n^2+1)\geq 0 \\\iff 465n^3-6n^4-10n^2+1\geq 0 \iff 465n^3-6n^4-10n^2\geq -1\\\iff n^2(465n-6n^2-10)\geq -1$

Observe that, because $n \geq 2$ and is an integer,

$n^2(465n-6n^2-10)\geq -1 \iff 465n-6n^2-10 \geq 0 \iff n(465-6n) \geq 10\\\iff 465-6n \geq 0 \iff n \leq \frac{465}{6}=\frac{155}{2}=77.5$

In concusion, the statement is true if and only if n is a non negative integer such that $n\leq 77$

So, 78 is the smallest value of n that does not satisfy the inequality.

Note: If you compute $(4n)^4- \sum^{n}_{i=0} (2i)^4$ for 77 and 78 you will obtain:

$(4n)^4- \sum^{n}_{i=0} (2i)^4=53810064$

$(4n)^4- \sum^{n}_{i=0} (2i)^4=-61754992$

7 0

3 years ago

if two people agree to pay half of the bills each month and client a pays $488 and client b pays $294 how much is owed to client

ICE Princess25 [194]

Answer:

$ 97

Step-by-step explanation:

Total payment = A + b = 488 + 294 = 782

half of bills = 782 /2 = 391

B owe to a: 488 - 391 = 97

check: 97 + 294 = 391

3 0

3 years ago

Read 2 more answers

Y/18 = 6/9<br><br> solve for Y with explanation

Anettt [7]

The answer to your question is Y=12

3 0

3 years ago

1.What is the mean of the given distribution, and which type of skew does it exhibit? {4.5, 3, 1, 2, 4, 3, 6, 4.5, 4, 5, 2, 1, 3

marysya [2.9K]

Mean = (4.5 + 3 + 1 + 2 + 4 + 3 + 6 + 4.5 + 4 + 5 + 2 + 1 + 3 + 4 + 3 + 2)/16 = 50/16 = 3.125

The data set arranged in order is 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4.5, 4.5, 5, 6

The mean is relatively in the middle, therefore if exhibits center skewness.

4 0

3 years ago