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3 years ago

Writing two column proofs

Mathematics

1 answer:

luda_lava [24]3 years ago

7 0

You have the right idea so far.

Use the fact that x = y and z = y to get x = z. We can use the transitive property or the substitution property (they are effectively the same idea).

Then you'll use the fact that w = x and w = t to get x = t. The same property is used here as well.

Lastly, connect x = z and x = t which will end up with t = z.

You might be interested in

If x\3-2=5x-2 then x=

nikdorinn [45]

X/3 -2 = 5x-2 (multiply by 3)

x-6=15x-6

x=15x

14x=0

x=0

6 0

3 years ago

Jason is a very good bowler and has proven over the

Nonamiya [84]

Answer:

The probability that Jason will get exactly 7 strikes out of 10 attempts is 0.117.

Step-by-step explanation:

We are given that Jason is a very good bowler and has proven over the course of a season of league play that he gets a STRIKE 50% of the time.

Also, Jason has been given 10 attempts.

The above situation can be represented through binomial distribution;

$P(X = r) = \binom{n}{r} \times p^{r} \times (1-p)^{n-r};x=0,1,2,3,.......$

where, n = number trials (samples) taken = 10 attempts

r = number of success = 7 strikes

p = probability of success which in our question is % of the time

he gets a strike, i.e; p = 50%

Let X = Number of strikes Jason get

So, X ~ Binom(n = 10, p = 0.50)

Now, probability that Jason will get exactly 7 strikes out of 10 attempts is given by = P(X = 7)

P(X = 7) = $\binom{10}{7} \times 0.50^{7} \times (1-0.50)^{10-7}$

= $120 \times 0.50^{7} \times 0.50^{3}$

= $120 \times 0.50^{10}$

= 0.117

Therefore, the probability that Jason will get exactly 7 strikes out of 10 attempts is 0.117.

6 0

4 years ago

Roni and Allie are mowing the grass at the soccer field. Roni has a riding lawn mower and can mow the field in 30 minutes. Allie

Aloiza [94]

Roni would mow about 0.71 of the field.

3 0

3 years ago

Read 2 more answers

What is the simplest form for 4/10

larisa86 [58]

4/10 in simplest form:

First, we need to find the greatest common factor (GCF) of the numerator (4) and denominator (10). To do this, we'll list the factors of each number, find the common factors, and then the greatest.

Factors of 4: 1, 2, 4
Factors of 10: 1, 2, 5, 10

The common factors are 1 and 2, so the greatest common factor is 2.

Second, our next step is to divide the numerator and denominator by the GCF we recently found which is 2.

$4 \div 2 = 2 \\ 10 \div 2 = 5$

Third, our last step is to rewrite our fraction in its simplest form. Above, we collected our brand new numerator and denominator.
$\frac{2}{5}$

Answer in fraction form: $\fbox { 2/5 }$
Answer in decimal form: $\fbox { 0.4 }$

6 0

3 years ago

Read 2 more answers

The safety inspector in a large city wants to estimate the proportion of buildings in the city that are in violation of fire cod

Drupady [299]

Answer:

Proportion of buildings in the city that have fire code violations: 10%

Uncertainty 0.3 = 30%

Step-by-step explanation:

This situation complies with a binomial model where p is the probability of finding a building having fire code violations and q=1-p

Since in random sample of 40 buildings chosen for inspection 4 of them are found to have fire code violations, the proportion is 4/40 = 0.1 or 10% and p=0.1 as well.

In a binomial model the standard deviation s is:

$\large s=\sqrt{npq}$

where n is the sample size. So

$\large s=\sqrt{40*0.1*0.9}=1.8974$

and the uncertainty is the standard error SE

$\large SE=\frac{s}{\sqrt{n}}=\frac{1.8974}{\sqrt{40}}=0.3=30\%$

7 0

4 years ago