Answer:
number of shells zoe gives to dev = 7
number of shells zoe is left with = 55-7= 48
number of shells dev has = 9+7=16
Step-by-step explanation:
let the initial number of shells that dev has be A, and initial number of shells that zoe has be B.
let the number of shells that zoe gives to dev be x.
after giiving x shells zoe is left with 3 times the number of shell as that of dev.
therefore number of shells with zoe = 3×number of shells with dev.
number of shells with zoe = initial shells - x = 55-x
number of shells with dev = initial shells + number of shells he gets
= 9+x
therefore (55-x)=3×(9+x)
55-x = 27+3x
55-27=3x+x
4x = 28
x= 7
therefore number of shells zoe gives to dev = 7
number of shells zoe is left with = 55-7= 48
number of shells dev has = 9+7=16
<span>The chance or probability that the lawn mower will hit a piece of glass that is already cracked is calculated by dividing the number of glasses that are cracked by the total number of glasses. In this item, the unknown can be calculated by 3/15. The answer is therefore, 1/5 or 0.20. </span>
Step 1
<u>Find the measure of angle x</u>
we know that
If ray NP bisects <MNQ
then
m<MNQ=m<PNM+m<PNQ ------> equation A
and
m<PNM=m<PNQ -------> equation B
we have that
m<MNQ=(8x+12)°
m<PNQ=78°
so
substitute in equation A
(8x+12)=78+78-------> 8x+12=156------> 8x=156-12
8x=144------> x=18°
Step 2
<u>Find the measure of angle y</u>
we have
m<PNM=(3y-9)°
m<PNM=78°
so
3y-9=78------> 3y=87------> y=29°
therefore
<u>the answer is</u>
the measure of x is 18° and the measure of y is 29°
Answer:
We can claim with 95% confidence that the proportion of executives that prefer trucks is between 19.2% and 32.8%.
Step-by-step explanation:
We have a sample of executives, of size n=160, and the proportion that prefer trucks is 26%.
We have to calculate a 95% confidence interval for the proportion.
The sample proportion is p=0.26.
The standard error of the proportion is:
The critical z-value for a 95% confidence interval is z=1.96.
The margin of error (MOE) can be calculated as:

Then, the lower and upper bounds of the confidence interval are:

The 95% confidence interval for the population proportion is (0.192, 0.328).
We can claim with 95% confidence that the proportion of executives that prefer trucks is between 19.2% and 32.8%.