In this type of calculations, we decompose 13 by checking the lowest powers of the base, that is 40. for example we check 40^2, or 40^3 and compare it to 85
Notice
40*40*40=64,000
so we check how many time does 85 fit into 64,000:
64,000/85=752.94
85*753=64,005; 64000-64,005=-5
this means that
thus
Answer: 10 (mod85)
Remark, the set of all solutions is:
{......-75, 10, 95, .....}, that is 85k +10
Answer:
4 t - 7 = 2 t+ 13 is the required equation.
The number of race medals Tara has is t = 20 medals.
Step-by-step explanation:
Let the number of medals Tara has = t medals
So, the number of medal Anita has = 4( Medals of Tara) - 7
= 4t - 7
And the number of medals Gary has = 2 times (Medals of Tara) + 13
= 2(t) + 13 = 2t + 13
Now, Annita and Gary has same number of medals.
⇒ 4t - 7 = 2t+ 13
or, 4t - 2t = 7 + 13
⇒ 2t = 20
⇒ t = 20/2 = 10
or t = 10
Hence, the number of race medals Tara has is t = 20 medals
Answer:
1.375 or 1/38
Step-by-step explanation:
(3/8+2/3)+1/3
(1.04166666667)+1/3
1.375 or 1 3/8
Answer:
0.36878
Step-by-step explanation:
Given that:
Mean number of miles (m) = 2135 miles
Variance = 145924
Sample size (n) = 40
Standard deviation (s) = √variance = √145924 = 382
probability that the mean of a sample of 40 cars would differ from the population mean by less than 29 miles
P( 2135 - 29 < z < 2135 + 29)
Z = (x - m) / s /√n
Z = [(2106 - 2135) / 382 / √40] < z < [(2164 - 2135) / 382 / √40]
Z = (- 29 / 60.399503) < z < (29 / 60.399503)
Z = - 0.4801364 < z < 0.4801364
P(Z < - 0.48) = 0.31561
P(Z < - 0.48) = 0.68439
P(- 0.480 < z < 0.480) = 0.68439 - 0.31561 = 0.36878
= 0.36878
0.9x = 450
x = 450/0.9
x = 500
Answer = 500
