Answer:
Option: c is correct.
Step-by-step explanation:
We are given that paco needs at least 3/8 yard of twine to build a model ship.
that is we require twine of amount greater than 3/8 yards.
<em>now we need to check among the given options which quantity is greater than 3/8 yards.</em>
a)
3/10 yard.
As we know that for two rational numbers with the same numerator but with different denominator the number whose denominator is smaller is a greater quantity.
Hence 3/10 < 3/8
Hence option a is incorrect.
b)
1/4 yard
As to compare to rational numbers we have to either make the numerator equal or their denominator equal. Hence here we multiply and divide 1/4 by 2 to get 8 in the denominator.
as 2/8 < 3/8
since the denominator is same and the number with the same denominator but with different numerator are compared as whose numerator is greater is a greater quantity.
Hence option b is incorrect.
c)
3/4 yard
Clearly both the numbers have the same numerator but different denominator and we know that for two rational numbers with the same numerator but with different denominator the number whose denominator is smaller is a greater quantity.
Hence 3/8 < 3/4
Hence, option c is correct.
d)
1/8 yard
clearly both the numbers have the same denominator and we know that for two rational numbers withe same denominator but with different numerator the number whose numerator is smaller is a smaller quantity.
Hence, 1/8 < 3/8
Hence, option d is incorrect.
Answer:
Step-by-step explanation:
Let the base camp is point A and boats' locations after two hours are points B and C.
By connecting the three points together we get a triangle ABC with sides:
- AB = 50*2 = 100 km
- AC = 70*2 = 140 km
The angle between AB and AC is:
- 60 + 50 = 110 degrees (opposite directions from south)
We are looking for the distance BC, which can be found by using the law of cosines:
- BC² = AB² + AC² - 2AB*AC*cos ∠BAC
- BC² = 100² + 140² - 2*100*140*cos 110°
- BC² = 39176.56 (rounded)
- BC = √39176.56 = 197.93 km (rounded)
The distance between the boats is 197.93 km.
Answer:
Step-by-step explanation:
Hello!
Your study variable is X: "number of ColorSmart-5000 that didn't need repairs after 5 years of use, in a sample of 390"
X~Bi (n;ρ)
ρ: population proportion of ColorSmart-5000 that didn't need repairs after 5 years of use. ρ = 0.95
n= 390
x= 303
sample proportion ^ρ: x/n = 303/390 = 0.776 ≅ 0.78
Applying the Central Limit Theorem you approximate the distribution of the sample proportion to normal to obtain the statistic to use.
You are asked to estimate the population proportion of televisions that didn't require repairs with a confidence interval, the formula is:
^ρ±
* √[(^ρ(1-^ρ))/n]
= 
= 2.58
0.78±2.58* √[(0.78(1-0.78))/390]
0.0541
[0.726;0.834]
With a confidence level of 99% you'd expect that the interval [0.726;0.834] contains the true value of the proportion of ColorSmart-5000 that didn't need repairs after 5 years of use.
I hope it helps!
Answer:
Step-by-step explanation:
Choose a random fraction less than 1. I will choose 1/4.
1/6 ÷ 1/4 = 1/6 × 4/1 = 4/6 = 2/3
2/3 > 1/6 so this example supports his claim.
Now chose a fraction greater than 1. I will choose 4/3
1/6 ÷ 4/3 = 1/6 * 3/4 = 3/24
3/24 < 1/6 so this contradicts his claim
Total no. of buttons = 300 + 700 + 1000
+ 500 = 2500
Possibility for a person to pick a pink button = 300/2500 = (3/25)%
Amount of pink buttons she can expect her friends to pick = 50(3/25) = 6
She can expect to make 6 pink barrettes.
