Find the optimized volume of a rectangular prism with a surface area of 864 m^2

(a) How many integers in the range 1 through 120 are integer multiples of 2, 3, or 5? keyboard_arrow_down Solution (b) How many

Umnica [9.8K]

Answer:

(a) 88 integers

(b) 92 integers

Step-by-step explanation:

(a) integers whose last digits are divisible by 2 are multiples of two or numbers whose digits ends with zero. So for number 1-120 , all the even numbers which are sixty in number are are multiples of two.

For 3, numbers whose digits sum is divisible by three are multiples of three. 3,6,9,12,15,18,21,24,27,30 are multiples of three from numbers 1-30. we have four 30s in 120. which means numbers of integers will be 10*4 = 40integers. However out of these numbers , half are also integers of 2 which reduces the number added to 20integers.

For 5, numbers whose digits ends with 5 or 0 are multiples of 5. this gives us 24 integers for 1-120. but out of these 24integers, 16 are common integers of 2 and 3 which reduces the number added to 8integers.

Thus from 1-120 the intergers of 2,3 or 5 = 60+20+8 = 88integers.

(b) if we are considering from numbers 1-140;

for 2 we wil have 70 integers,

for 5 we will have 28 integers, but those integers that end with 0 are also integers of 2 which reduces the number added to 14.

For 7, numbers 7,14,21,28,35,42,49,56,63,70 are multiples of three from 1-70. This pattern is repeated from number 71-140. hence we have 20 integers in all. However 12 of the multiples are also multiples of either 2 or 5 which reduces the number to 8 integers.

Thus from 1-140, the integers of 2, 5, or 7 = 70+14+8 = 92integers

3 0

3 years ago

The equation y=20646 x 0.86^x estimates the value of a brand of car x years after it was purchased new. milo purchased this bran

torisob [31]

20646(.86^11) = 3929

5 0

3 years ago

Read 2 more answers

Integrate t sec^2 (2t) dt

Neporo4naja [7]

F = t ⇨ df = dt
dg = sec² 2t dt ⇨ g = (1/2) tan 2t
⇔
integral of t sec² 2t dt = (1/2) t tan 2t - (1/2) integral of tan 2t dt
u = 2t ⇨ du = 2 dt

As integral of tan u = - ln (cos (u)), you get :

integral of t sec² 2t dt = (1/4) ln (cos (u)) + (1/2) t tan 2t + constant
integral of t sec² 2t dt = (1/2) t tan 2t + (1/4) ln (cos (2t)) + constant
integral of t sec² 2t dt = (1/4) (2t tan 2t + ln (cos (2t))) + constant ⇦ answer

8 0

4 years ago

Read 2 more answers

A digital camcorder repair service has set a goal not to exceed an average of 5 working days from the time the unit is brought i

garri49 [273]

Answer:

The degrees of freedom first given by:

$df=n-1=12-1=11$

Then we can find the critical value taking in count the degrees of freedom and the alternative hypothesis and then we need to find a critical value who accumulates 0.05 of the area in the right tail and we got:

$t_{\alpha}= 1.796$

And for this case the rejection region would be:

b) Reject H0 if tcalc >1.7960

Step-by-step explanation:

Information given

5, 7, 4, 6, 7, 5, 5, 6, 4, 4, 7, 5.

System of hypothesis

We want to test if the true mean is higher than 5, the system of hypothesis are :

Null hypothesis: $\mu \leq 5$

Alternative hypothesis: $\mu > 5$

The statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

The degrees of freedom first given by:

$df=n-1=12-1=11$

Then we can find the critical value taking in count the degrees of freedom and the alternative hypothesis and then we need to find a critical value who accumulates 0.05 of the area in the right tail and we got:

$t_{\alpha}= 1.796$

And for this case the rejection region would be:

b) Reject H0 if tcalc >1.7960

6 0

3 years ago

This is for anyone who has ever been cheated on before...

Evgen [1.6K]

Answer:

thank you

Step-by-step explanation:

4 0

3 years ago

Find the optimized volume of a rectangular prism with a surface area of 864 m^￼2

Find the optimized volume of a rectangular prism with a surface area of 864 m^2