What solid figure is shown below? triangular pyramid square pyramid rectangular prism cylinder

Suppose y=0. That means
x+z = 18 
x-z = 26/5 

x = 58/5 
z = 32/5 

So, the largest x can be is 58/5 
Now, suppose we toss in y. If we subtract y/2 from both x and z, then the difference between x and z is still 26/5, and the sum is 

(x-y/2) + y + (z-y/2) = x+z = 18 

For example, if y = 4, 

x = 48/5 
y = 20/5 
z = 22/5 

x-z is still 26/5, and the sum is still 18.

7 0

4 years ago

300 students in a high school freshman class are surveyed about what kinds of pets they have. Of the 300 students, 200 have a do

katrin2010 [14]

This Question is not complete

Complete Question:

300 students in a high school freshman class are surveyed about what kinds of pets they have. Of the 300 students, 200 have a dog, 180 have a cat, and 150 have a cat and a dog. Using this information, answer each of the following questions, Let D be the event that a randomly selected student has a dog and C be the event that a randomly selected student has a cat.

a . What is P(D), the probability that a student in the class has a dog?

b. What is P(C), the probability that a student in the class has a cat?

c. What is P(D and C), the probability that a student in the class has a dog and a cat?

d. What is P(D or C), the probability that a student in the class has a dog or a cat?

Answer:

a. 2/3

b) 3/5

c) 1/2

d) 19/ 15 = 1 4/15

Step-by-step explanation:

The formula for probability =

Number of possible outcomes ÷ Number of events.

Total number of Students = 300

Number of Students that have a dog = 200

Number of Students that have a cat = 180

Number of Students that have a dog and cat = 150

a. What is P(D), the probability that a student in the class has a dog?

In the question, the given data is interpreted as :

Number of possible outcomes = 200

Number of events = 300

P(D) = 200/300

= 2/3

Therefore, the probability that a student has a dog = 2/3

b. What is P(C), the probability that a student in the class has a cat?

In the question, the given data is interpreted as :

Number of possible outcomes = 180

Number of events = 300

P(D) = 180/300

= 3/5

Therefore, the probability that a student has a cat = 3/5

c. What is P(D and C), the probability that a student in the class has a dog and a cat?

In the question, the given data is interpreted as :

Number of possible outcomes = 150

Number of events = 300

P(D) = 150/300

= 1/2

Therefore, the probability that a student has a dog and cat = 1/2

d. What is P(D or C), the probability that a student in the class has a dog or a cat?

The is calculated as

P(D) + P(C)

In the above question,

P(D) is calculated as 2/3

P(C) is calculated as 3/5

Therfore, P(D or C), the probability that a student in the class has a dog or a cat is calculated as:

= 2/3 +3/5

= 19/15 = 1 4/15

7 0

3 years ago

Two chemical companies can supply a raw material. The concentration of a particular element in this material is important. The m

svp [43]

Answer:

As the calculated F lies in the acceptance region therefore we conclude that there is not sufficient evidence to support the claim that the variability in concentration may differ for the two companies. Hence Ha is rejected and H0 is accepted.

Step-by-step explanation:

As we suspect the variability of concentration F - test is applied.

n1=10 s1=4.7

n2=16 s2=5.8

And α = 0.05.

The null and alternate hypothesis are

H0: σ₁²=σ₂² Ha: σ₁²≠σ₂²

The null hypothesis is the variability in concentration does not differ for the two companies.

against the claim

the variability in concentration may differ for the two companies

The critical region F∝(υ1,υ2) = F(0.025)9,15= 3.12

and 1/F∝(υ1,υ2) = 1/3.77= 0.26533

where υ1= n1-1= 10-1= 9 and υ2= n2-1= 16-1= 15

Test Statistic

F = s₁²/s₂²

F= 4.7²/5.8²=0.6566

Conclusion :

As the calculated F lies in the acceptance region therefore we conclude that there is not sufficient evidence to support the claim that the variability in concentration may differ for the two companies. Hence Ha is rejected and H0 is accepted.

3 0

3 years ago