1. The total must be at least $1975: 
2. Dog walks is no more than 4 times lawns:
3. At least 50 dog walks:
2. Dog walks is no more than 4 times lawns:
3. At least 50 dog walks:
What percent of 40m is 16m
2 answers:
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Answer:
Step-by-step explanation:
Hello!
You have the variable
X: Area that can be painted with a can of spray paint (feet²)
The variable has a normal distribution with mean μ= 25 feet² and standard deviation δ= 3 feet²
since the variable has a normal distribution, you have to convert it to standard normal distribution to be able to use the tabulated accumulated probabilities.
a.
P(X>27)
First step is to standardize the value of X using Z= (X-μ)/ δ ~N(0;1)
P(Z>(27-25)/3)
P(Z>0.67)
Now that you have the corresponding Z value you can look for it in the table, but since tha table has probabilities of , you have to do the following conervertion:
P(Z>0.67)= 1 - P(Z≤0.67)= 1 - 0.74857= 0.25143
b.
There was a sample of 20 cans taken and you need to calculate the probability of painting on average an area of 540 feet².
The sample mean has the same distribution as the variable it is ariginated from, but it's variability is affected by the sample size, so it has a normal distribution with parameners:
X[bar]~N(μ;δ²/n)
So the Z you have to use to standardize the value of the sample mean is Z=(X[bar]-μ)/(δ/√n)~N(0;1)
To paint 540 feet² using 20 cans you have to paint around 540/20= 27 feet² per can.
c.
P(X≤27) = P(Z≤(27-25)/(3/√20))= P(Z≤2.98)= 0.999
d.
No. If the distribution is skewed and not normal, you cannot use the normal distribution to calculate the probabilities. You could use the central limit theorem to approximate the sampling distribution to normal if the sample size was 30 or grater but this is not the case.
I hope it helps!
Answer:
46 cm
Step-by-step explanation:
It is given that the angle bisector AC divides the trapezoid ABCD into two similar triangles Δ ABC and Δ ACD.
Let us first find the corresponding sides of triangles Δ ABC and Δ ACD.
Since AC is the angle bisector of ∠A,
∠DAC = ∠CAB --- (1)
Also, since ∠DAC and ∠ACB are alternate interior angles,
∠DAC = ∠ACB --- (2)
From (1) and (2),
∠CAB = ∠ACB
Therefore, in Δ ABC,
BC = AB (sides opposite to equal angles are equal)
So, BC = 9 cm.
Now, since ∠DAC = ∠ACB and ∠DAC = ∠CAB, we can take either ∠ACB or ∠CAB as the angle corresponding to ∠DAC. Let us take ∠ACB as the corresponding angle of ∠DAC.
So, the side opposite to ∠DAC in Δ ACD is the corresponding side to the side opposite to ∠ACB in Δ ABC.
That is, the side CD in Δ ACD is the corresponding side to the side AB in Δ ABC.
Now, suppose if the side BC in Δ ABC corresponds to side AD of Δ ACD, then the remaining side AC of Δ ABC should correspond to side AC of Δ ACD which is not possible since they are congruent.
So, the side BC in Δ ABC should correspond to side AC of Δ ACD and the remaining side AC of Δ ABC should correspond to side AD of Δ ACD.
Therefore, we have,
But,
Therefore,
AC = 12 cm
Also,
AD = 16 cm
Now, the perimeter of the trapezoid = AB + BC + CD + AD
= 9 + 9 + 12 + 16
= 46 cm
