All categories

2 years ago

Prove that the square of an odd number is always 1 more than a multiple of 4

Mathematics

1 answer:

loris [4]2 years ago

5 0

Answer:

By these examples you are able to see that the square of an odd number is always 1 more than a multiple of 4.

Step-by-step explanation:

For examples,

Let's consider squares of 3, 11, 25, 37 and 131.

${3}^{2} = 9$

8 is a multiple of 4, and 9 is more than 8.

${11}^{2} = 121$

120 is a multiple of 4 and 121 is one more than it.

${25}^{2} = 625$

624 is a multiple of 4 and 625 is one more than it.

${37}^{2} = 1369$

1368 is a multiple of 4 and 1369 is one more than 1368.

${131}^{2} = 17161$

17160 is a multiple of 4.

You might be interested in

A mother explains to her child that the price on the sign is not the total price for an oil painting, because the price does not

dlinn [17]

Answer:

Or u cld simply just say 945 - 875 = 70

3 0

2 years ago

Rebecca collected data from a random sample of 1200 homeowners in her state asking whether or not they use electric heat. Based

larisa [96]

Hi,

The answer is c. The sample is biased.

This is because the sample is taken on a single state, an Rebecca reports a statistic about the nation. Her data contains information only of her state. If she lives in a very cold state, there is probably more homeowners using electric heat than in a hot state.

6 0

3 years ago

Calcula la aceleración que debe tener un auto para alcanzar una velocidad de 108 km/h en 10 s si parte del reposo. ¿Qué distanci

sashaice [31]

sen bu me bu set an sus ye babe smnsnssnnsnsnsnsnsnsnsns

6 0

2 years ago

Rosetta wants to estimate the percentage of people who rent their home. She surveys 250 individuals and finds that 48 rent their

Andreas93 [3]

Answer:

$0.192 - 1.645\sqrt{\frac{0.192(1-0.192)}{250}}=0.151$

$0.192 + 1.645\sqrt{\frac{0.192(1-0.192)}{250}}=0.233$

Step-by-step explanation:

Information given

$X= 48$ number of people who rent their home

$n= 250$ represent the sample size

$\hat p =\frac{48}{250}= 0.192$ represent the proportion of people who rent their home

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by $\alpha=1-0.90=0.1$ and $\alpha/2 =0.05$ . And the critical value would be given by: