Answer:

Step-by-step explanation:
We have the cone and the half-sphere.
The formula of a volume of a cone:

r - radius
H - height
We have r = 7cm and H = (22-7)cm=15cm. Substitute:

The formula of a volume of a sphere:

R - radius
Therefore the formula of a volume of a half-sphere:

We have R = 7cm. Substitute:

The volume of the given shape:

Substitute:

Answer:
The slope is 2/3
Step-by-step explanation:
-1/2x+3/4y=0
To find the slope, we need to get the equation in the form y= mx+b
Add 1/2x to each side
-1/2x+ 1/2 x+3/4y=0+1/2x
3/4 y = 1/2x
Multiply by 4/3 to isolate y
4/3 * 3/4 y = 4/3 * 1/2 x
y = 2/3 x
The slope is 2/3 and the y intercept is 0
Answer:
x=5 and x=6
Step-by-step explanation:
Answer:
0.6154 = 61.54% probability that the student is an undergraduate
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is

In which
P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Foreign
Event B: Undergraduate.
There are four times as many undergraduates as graduate students
So 4/5 = 80% are undergraduate students and 1/5 = 20% are graduate students.
Probability the student is foreign:
10% of 80%
25% of 20%. So

Probability that a student is foreign and undergraduate:
10% of 80%. So

What is the probability that the student is an undergraduate?

0.6154 = 61.54% probability that the student is an undergraduate
Answer and Step-by-step explanation: Scaterplot is a type of graphic which shows the relationship between to variables. In this question, you want to determine if there is a linear relationship between overhead widths of seals and the weights. So, the hypothesis are:
H₀: no linear correlation;
H₁: there is linear correlation;
In this hypothesis test, to reject H₀, the correlation coefficient r of the data set has to be bigger than the critical value from the table.
With α = 0.05 and n = 6, the critical value is 0.811.
The linear correlation is calculated as:
r = n∑xy - ∑x.∑y / √[n∑x² - (∑x)²] [n∑y² - (∑y)²]
r = 
r = 0.9485
Since r is bigger than the critical value, H₀ is rejected, which means there is enough evidence to conclude that there is linear correlation between overhead widths and the weights.
In the attachments is the scaterplot of the measurements, also showing the relationship.