4. Rephrase the following statements in standard "if.. then" form:

Mathematics

1 answer:

Firdavs [7]3 years ago

8 0

Answer:

See step-by-step explanation.

Step-by-step explanation:

a) If the old TV breaks down then we are buying a new TV.

b) If you have a good credit score in the United States, then you obtain a loan.

c) If you don't make me a better offer then I will keep my current job.

d) If we observe faster than light travel then we would question relativity theory.

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How many positive integers $n$ from 1 to 5000 satisfy the congruence $n \equiv 5 \pmod{12}$?

irga5000 [103]

The equivalence $n \equiv 5 \pmod{12}$

means that n-5 is a multiple of 12.

that is

n-5=12k, for some integer k

and so

n=12k+5

for k=-1, n=-12+5=-7

for k= 0, n=0+5=5 (the first positive integer n, is for k=0)

we solve 5000=12k+5 to find the last k

12k=5000-5=4995

k=4995/12=416.25

so check k = 415, 416, 417 to be sure we have the right k:

n=12k+5=12*415+5=4985

n=12k+5=12*416+5=4997

n=12k+5=12*417+5=5009

The last k which produces n<5000 is 416

For all k∈{0, 1, 2, 3, ....416}, n is a positive integer from 1 to 5000,

thus there are 417 integers n satisfying the congruence.

Answer: 417

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3 years ago

Tanya is training a turtle for a turtle race. For every 1/6 of an hour that the turtle crawling he can travel 2/23 mile. at what

zavuch27 [327]

So first I hope this helps! But from what I’ve learned in school is that a unit rate pretty much just mean *1... so in words the answers would be 1/6 and hour for every 2/23 miles

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3 years ago

A rectangular piece of poster board measures 60 centimeters by 80 centimeters. Linn draws the net of a box on the poster board a

Ksju [112]

60*80-10*16 if it's regular area and not surface area

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2 years ago

a fair coin is flipped 10 times. what is the probability of getting the same number of heads and tails

Dafna11 [192]

If you flip a coin one time, the probability to get a Head is

p = 1/2

The probability of not getting a head in a single toss is :

q = 1 - 1/2 = 1/2

Thus there is only one unique situation to get the same number of heads and tails : in 10 toss you need to get exactly five heads, it will means that the rest is the tails.

Now using Binomial theorem of probability, the probability of getting exactly x = 5 heads in a total of n = 10 tosses is :

P(X = 5) = $\frac{10!}{5!*5!} *(\frac{1}{2})^{5} *(\frac{1}{2})^{5}$ ≈ 0.246

So the probability of that is 24,6 %

Good Luck

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2 years ago

3/7 = /12<br> How do I find the answer

guajiro [1.7K]

Cross multiply the denominators by the numerators. In other words, 12 times 3 and 7 times x (x, being our missing number).
We end up with 36 and 7x.
Divide both sides by 7.
36/7x = 5.14
x = 5.14
Hope this helps!

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2 years ago