What is the quotient and remainder of 27÷2

The volume of an oblique pyramid with a square base is V units3 and the height is h units.Which expression represents the area o

melamori03 [73]

Answer: a) $\dfrac{3V}{h}\ units^2$

Step-by-step explanation:

We know that the volume of an oblique pyramid is given by :-

$\text{Volume}=\dfrac{1}{3}\text{(Base Area x height) }$

If the volume of an oblique pyramid with a square base is V units³ and the height is h units.

Then, we have

$V=\dfrac{1}{3}\text{(Base Area x h) }$

Multiply 3 on both sides , we get

$3V=\text{(Base Area x h) }$

Divide both sides by h , we get

$\dfrac{3V}{h}=\text{Base Area }$

i.e. $\text{Base Area }=\dfrac{3V}{h}\ units^2$

Hence, the expression represents the area of the base of the pyramid = $\dfrac{3V}{h}\ units^2$

Hence, the correct answer is a) 3 v/h units^2

7 0

3 years ago

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I need help solving number 11 please.

Mnenie [13.5K]

set up the triangle with the information given. then just solve for x.

3 0

3 years ago

A printing company charges a fixed rate to set up the printing press, plus a cost of $3.50 for every 100 copies. If 800 copies c

pychu [463]

The answer is $12,052.5. youd divide 800 into 1500 then you multiply the answer you get by 6400 then add (1500/100) x 3.5 to get your answer.

6 0

3 years ago

Of the entering class at a college, % attended public high school, % attended private high school, and % were home schoole

Veronika [31]

Answer:

(a) The probability that the student made the Dean's list is 0.1655.

(b) The probability that the student came from a private high school, given that the student made the Dean's list is 0.2411.

(c) The probability that the student was not home schooled, given that the student did not make the Dean's list is 0.9185.

Step-by-step explanation:

The complete question is:

Of the entering class at a college, 71% attended public high school, 21% attended private high school, and 8% were home schooled. Of those who attended public high school, 16% made the Dean's list, 19% of those who attended private high school made the Dean's list, and 15% of those who were home schooled made the Dean's list.

a) Find the probability that the student made the Dean's list.

b) Find the probability that the student came from a private high school, given that the student made the Dean's list.

c) Find the probability that the student was not home schooled, given that the student did not make the Dean's list.

Solution:

Denote the events as follows:

A = a student attended public high school

B = a student attended private high school

C = a student was home schooled

D = a student made the Dean's list

The provided information is as follows:

P (A) = 0.71

P (B) = 0.21

P (C) = 0.08

P (D|A) = 0.16

P (D|B) = 0.19

P (D|C) = 0.15

(a)

The law of total probability states that:

$P(X)=\sum\limits_{i} P(X|Y_{i})\cdot P(Y_{i})$

Compute the probability that the student made the Dean's list as follows:

$P(D)=P(D|A)P(A)+P(D|B)P(B)+P(D|C)P(C)$

$=(0.16\times 0.71)+(0.19\times 0.21)+(0.15\times 0.08)\\=0.1136+0.0399+0.012\\=0.1655$

Thus, the probability that the student made the Dean's list is 0.1655.

(b)

Compute the probability that the student came from a private high school, given that the student made the Dean's list as follows:

$P(B|D)=\frac{P(D|B)P(B)}{P(D)}$

$=\frac{0.21\times 0.19}{0.1655}\\\\=0.2410876\\\\\approx 0.2411$

Thus, the probability that the student came from a private high school, given that the student made the Dean's list is 0.2411.

(c)

Compute the probability that the student was not home schooled, given that the student did not make the Dean's list as follows:

$P(C^{c}|D^{c})=1-P(C|D^{c})$

$=1-\frac{P(D^{c}|C)P(C)}{P(D^{c})}\\\\=1-\frac{(1-P(D|C))\times P(C)}{1-P(D)}\\\\=1-\frac{(1-0.15)\times 0.08}{(1-0.1655)}\\\\=1-0.0815\\\\=0.9185$

Thus, the probability that the student was not home schooled, given that the student did not make the Dean's list is 0.9185.

3 0

3 years ago

What is the median of the following salary list $32,019, $21,971, $27,512, $43,702, $38,860, $25,997

mylen [45]

Answer:

$29765.50

Step-by-step explanation:

Median is the middlemost value (or the average of the 2 middlemost value if there are even number of values) in an ascending order.

First, arrange the salary list in an ascending order.

$21,971 , $25,997 , $27,512 , $32,019 , $38,860 , $43,702

As we can see here, there are even number of values (6), so the median will be the average of the 2 middlemost value, which will be:

Median = $\frac{27512 + 32019}{2}$

= $\frac{59531}{2}$

= $29765.50

3 0

2 years ago

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