All categories

4 years ago

The sum of the squares of 3 consecutive positive integers is 116. What are the numbers?

1 answer:

3 0

Let's say, the first number is "n"

well, the consecutive number of "n" is "n + 1"and the consecutive number of "n+1" is "n + 1" +1 or n + 2

so, the numbers are (n), (n+1) and (n+2), whatever "n" is

now, the sum of their squares is 116

$\bf (n)^2+(n+1)^2+(n+2)^2=116$

expand the binomials by FOIL or binomial theorem, and then simplify

You might be interested in

What’s the word for this definition? “The change in the Y values divided by the change in X values”

miss Akunina [59]

Answer:

slopes is the ratio of the change in the y value over the change in the x value

6 0

3 years ago

Danny walks at an average speed of 5 m/s foe 1 minute. Work out the distance that Danny has travelled in metres.

Dahasolnce [82]

Answer:

D = 300 m

Step-by-step explanation:

Given :

Speed = 5 m/s

Time = 1 min = 60 secs

Required:

Distance = ?

Formula :

Speed = Distance/Time

Solution:

Distance = Speed × Time

D = 5 × 60

D = 300 m

4 0

3 years ago

Read 2 more answers

prove that every positive integer can be written as a finite sum of distinct integral powers of the golden ratio.

mote1985 [20]

z1 =........=zm = 0 and n=m because n0 cannot be expressed in the +ve Phi / golden ratio form.

<h3>What is golden ratio?</h3>

important is that the ratio between each succeeding pair of Fibonacci numbers approaches 1.618, or its inverse, 0.618, as the numbers get bigger. The holy proportion, the golden ratio, and the golden mean are some additional names for this proportion. Then why is this number so important? The fact that so many items in nature have dimensions characteristics that conform to the 1.618 ratio suggests that it plays a fundamental role for the components of nature. Due to its visual appeal compared to other proportions, the golden ratio is frequently used in the arts. The Great Pyramid in Giza, the Mona Lisa by Da Vinci, and the Parthenon in Athens are all.

z1 =........=zm = 0 and n=m

z1 =........=zm = 0 and n=m because n0 cannot be expressed in the +ve Phi / golden ratio form.

To know more about golden ratio visit ::-

brainly.com/question/2263789

#SPJ4

8 0

1 year ago

suppose line a is parallel to line b and line b is perpendicular to line c. what relationship between line a and line c

kykrilka [37]

Answer:

a and c would also be perpendicular

Step-by-step explanation:

because a║b and b⊥c you would use the transitive property of equality.

6 0

3 years ago

For the hypothesis test H0: μ = 10 against H1: μ >10 and variance known, calculate the Pvalue for each of the following test

Basile [38]

Answer:

a) $p_v =P(Z>2.05)=1-P(z$

b) $p_v =P(Z>-1.84)=1-P(z$

c) $p_v =P(Z>0.4)=1-P(z$

Step-by-step explanation:

Some previous concepts

The p-value is the probability of obtaining the observed results of a test, assuming that the null hypothesis is correct.

A z-test for one mean "is a hypothesis test that attempts to make a claim about the population mean(μ)".

The null hypothesis attempts "to show that no variation exists between variables or that a single variable is no different than its mean"

The alternative hypothesis "is the hypothesis used in hypothesis testing that is contrary to the null hypothesis"

Hypothesis

Null hypothesis: $\mu=10$

Alternative hypothesis: $\mu >10$

If the random variable is distributed like this: $X \sim N(\mu,\sigma)$

We assume that the variance is known so the correct test to apply here is the z test to compare means, the statistic is given by the following formula:

$z_o=\frac{\bar X -\mu}{\sigma}$

Since we have the values for the statistic already calculated we can calculate the p value using the following formulas:

Part a

$p_v =P(Z>2.05)=1-P(z$

And in order to find the answer using excel we can use the following code:

"=1-NORM.DIST(2.05,0,1,TRUE)"

Part b

$p_v =P(Z>-1.84)=1-P(z$

And in order to find the answer using excel we can use the following code:

"=1-NORM.DIST(-1.84,0,1,TRUE)"

Part c

$p_v =P(Z>0.4)=1-P(z$

And in order to find the answer using excel we can use the following code:

"=1-NORM.DIST(0.4,0,1,TRUE)"

Conclusions

If we use a reference value for the significance, let's say $\alpha=0.05$ . For part a the $p_v$ so then we can reject the null hypothesis at this significance level.

For part b the $p_v>\alpha$ so then we FAIL to reject the null hypothesis at this significance level.

For part c the $p_v>\alpha$ so again we FAIL to reject the null hypothesis at this significance level.

3 0

3 years ago