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trapecia [35]
3 years ago
8

Susan is attending a talk at her son's school. There are 8 rows of 10chairs where 54 parents are sitting. Susan notices that eve

ry parent is either sitting on their own or next to just one other person. What is the largest possible number of adjacent empty chairs in a single row at that talk?
Mathematics
1 answer:
kozerog [31]3 years ago
4 0

Answer:

The largest possible number of adjacent empty chairs in a single row is 3

Step-by-step explanation:

The parameters given are;

The number of chairs = 8 × 10 = 80 chairs

The number of parents = 54

Sitting arrangements of parents = Alone or to one other person

Therefore;

The maximum number of parents on a row = 1 + 1 + 0 + 1 + 1 + 0 + 1 + 1 + 0 + 1 = 7

Hence when the rows have the maximum number of parents occupying the seats we have for the 8 rows;

7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 = 56

But there are only 54 parents, therefore, up to the 7th row will have 7 parents while the 8th row will have only 5 parents to make the possible sitting arrangement to be as follows;

7 + 7 + 7 + 7 + 7 + 7 + 7 + 5 = 54

The sitting arrangement for the 8th row is therefore

1 + 1 + 0 + 1 + 1 + 0 + 1 + 0 + 0 + 0

Hence there will be three empty seats in the 8th row making the largest possible number of adjacent empty chairs in a single row = 3.

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A manufacturer of computer printers purchases plastic ink cartridges from a vendor. When a large shipment is received, a random
g100num [7]

Answer:

97.4% probability

Step-by-step explanation:

Since there is only two possible outcome of inspecting the catridge : either defective or not, we can solve the problem using the binomial probability distribution (approximated to normal).

To approximate the binomial probability to normal, we find the expected value and the standard deviation of the probability of exactly x sucesses on n repeated trials with p probability

Expected values E(X) = np

Standard deviation √V(X) = √np(1-p)

using the z-score formula (X - μ)/σ, we can solve normally distributed problem.

Where μ is the mean and σ is the standard deviation. The Z-score is is the measure of how much a sample is from the mean. The p-value associated with this z-score which is the probability that the value of the measure is smaller than X can be checked on the z-score table.

FOR THIS QUESTION,

a random sample of 200 cartridges is selected

n = 200

Therefore If there are more than 0.02 × 200 = 4 defective, the sample will be returned.

To determine the approximate probability that a shipment will be returned if the true proportion of defective cartridges in the shipment is 0.05

μ = E(X)

= 0.05 × 200 = 10

σ = √V(X) = √np(1-p)

= √200 × 0.05 × 0.95

= 3.08

This probability is 1 subtracted by the pvalue of Z when X =4

Z = (X - μ)/σ

Z= (4 - 10)/3.08

Z = -1.95

Z = -1.95 has a P-value of 0.026 (on the z-score table)

This means that there is a 1 - 0.026 = 0.974

= 97.4% probability that a shipment will be returned if the true proportion of defective cartridges in the shipment is 0.05.

6 0
3 years ago
Defining congruent triangles
seropon [69]

Answer:

E -->R

D-->K

O-->O

Step-by-step explanation:

Assuming you are asking for congruent parts, correspondence is the part which corresponds and is also equal.

Here Angle E corresponds and is congruent to Angle R in these congruent triangles.

Angle D is congruent and corresponds to Angle K for these congruent triangles.

Angle O is equal to Angle O as they are vertical angles across a vertex.

5 0
3 years ago
HELP PLEASE ILL GIVE BRAINLIEST
user100 [1]

first 1 because it saws less than or equal to 175

3 0
3 years ago
Need help pls , 20 points <br> no links or else I will report
uysha [10]

Answer:

x=72

Step-by-step explanation:

x=3/4x+18

4(x=3/4+18)

4x=3x+72

x=72

7 0
3 years ago
Read 2 more answers
How do you figure 1/8 of 50 in fraction form
Elodia [21]

Turn the 50 into a fraction (50/1) then cross multiply the fractions after that turn it into a equivalent fraction and you you get your answer

(I think)

6 0
3 years ago
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