Part A
Given:
Volume of square pyramid = 73.5 cubic inches
height of square pyramid = 4.5 inches
To find:
1)Side length of square pyramid.
2)if side length of square pyramid is rational or irrational
Steps:
1) Side length = [tex]\sqrt{\frac{3v}{h} }[/tex]
Side length = [tex]\sqrt{\frac{3*73.5}{4.5} }[/tex]
Side length = [tex]\sqrt{\frac{3*73.5*10}{4.5*10} }[/tex] (multiplying both sides to make it a whole number)
Side length = [tex]\sqrt{\frac{3*735}{45} }[/tex]
Side length = [tex]\sqrt{\frac{735}{15} }[/tex] (3 gets canceled out)
Side length = [tex]\sqrt{49}[/tex]
Side length = 7 inches
Therefore, the side length of the square pyramid is 7 inches long
2) 7 is a rational number, so the side length of the square pyramid is a rational number.
It is a rational number because,
it can be written in the form p/q, where
1) q [tex]\neq[/tex]0
2) p and q are co-prime
3) p and q are integers
Part B
Given:
Volume of Khafre's pyramid = 9/10 of Khufu's pyramid's volume
Volume of Kristina's first pyramid = 73.5 cubic inches
To find:
Volume of Kristina's second pyramid
Steps:
Volume of Kristina's second pyramid = 9/10 the volume of Kristina first pyramid
Volume of second pyramid = [tex]\frac{9}{10}*73.5[/tex]
Volume of second pyramid = 9 [tex]*[/tex] 7.35
Volume of second pyramid = 66.15 cubic inches
The volume of the second pyramid should be 66.15 cubic inches
Part C
Given:
Height of pyramid = 4.41 inches
Volume of pyramid = 66.15 cubic inches
To find:
1) Side length of pyramid
2) if the side length is rational or irrational
Steps:
1) Side length = [tex]\sqrt{\frac{3v}{h} }[/tex]
Side length = [tex]\sqrt{\frac{3*66.15}{4.41} }[/tex]
Side length = [tex]\sqrt{\frac{3*66.15*100}{4.41*100} }[/tex] (multiplying both sides to make it a whole number)
Side length = [tex]\sqrt{\frac{3*6615}{441} }[/tex]
Side length = [tex]\sqrt{\frac{6615}{147} }[/tex] (3 gets canceled)
Side length = [tex]\sqrt{45}[/tex]
Side length of pyramid is [tex]\sqrt{45}[/tex] inches
2) [tex]\sqrt{45}[/tex] cant be written in the form of a fraction, so it is an irrational number
(if u want i can explain this more)
Part D
Given
Height of model pyramid = 4.5 inches
Height of Khufu's pyramid = 755.75 feet (had to search the internet for the answer, so I am not sure if it is correct)
Side length of model pyramid = 7 inches
Side length of Khufu's pyramid = 481.4 feet (had to search the internet for the answer)
To find:
1)If the model is to scale with Khufu's pyramid
2) If the model is close to scale with Khufu's pyramid
Steps:
1) First lets find the ratio of the height to the side length of the model
Ratio = 4.5 in : 7 in
= 45 : 70
= 9 : 14
= 0.6428
Now lets find the ratio of the height to the side length of Khufu's pyramid
Ratio = 481.4 feet : 755.75 feet
= 5776.8 in : 9069 in
= 0.6369
Therefore the model is not to scale with Khufu's pyramid
2) Yes the scale is close
Part E
Given:
Height of model pyramid = 4.41 inches
Height of Khafre's pyramid = 448 feet
Side length of model pyramid = [tex]\sqrt{45}[/tex] inches
Side length of Khafre's pyramid = 706 feet
To find:
1) If the model is to scale with Khafre's pyramid
2) If the model is close to scale with Khafre's pyramid
Steps:
1) First lets find the ratio of the height to the side length of the model pyramid,
Ratio = 4.41 in : [tex]\sqrt{45}[/tex] in
= 4.41 : 6.7082
= 0.6574
Now lets find the ratio of the height to the side length of Khafre's pyramid
Ratio = 448 ft : 706 ft
= 5376 in : 8472 in
= 0.6345
Therefore the model is not to scale with Khafre's pyramid
2) No, the model is not close to scale, (it depends by what is meant by close, for me its 0.01)
Happy to help, and I hope you learnt something from this answer that will help you in the future
If you didn't understand any topic pls ask
5. For the final touches, John wanted to paint the house using 3 colors. If he has 5
gallons of paint for each color, write an equation for the total number of gallons of
paint he has?
Answer:
3 x 5 = 15
Step-by-step explanation:
To explain this in short, John has 5 gallons of 3 colors, meaning that 3 x 5 = 15 would be the appropriate equation to finish this question. I hope this helps!
A rectangle measures 3 1/4 inches by 3 3/4 inches. What is the area
Answer:
12.1875 or 195/16 or 12 3/16
Step-by-step explanation:
All you must do is multiply them by each other
hope this helps
Answer:
12.19 inches
Step-by-step explanation:
please mark brainliest
Write an equivalent expression using the Distributive Property.35 + 21 = 7( + )
Answer:
$2200/month
$2200/month
Answer:43.1
Explanation
C = 2pi r
C = 2 x 3.14 x 6.87
C = 43.1 ft
This sounds like an answer....
what is 8x5 please help
Answer:
8x5 equals 40.
Step-by-step explanation:
Answer:
8x5 is 40, hope that helped :)
We wish to modify the cellular telephone coding system in order to reduce the number of errors. In particular, if there are two or three zeroes in the received sequence of 5 bits, we will say that a deletion (event D) occurs. Otherwise, if at least 4 zeroes are received, then the receiver decides a zero was sent. Similarly, if at least 4 ones are received, then the receiver decides a one was sent. We say that an error occurs if either a one was sent and the receiver decides zero was sent or if a zero was sent and the receiver decides a one was sent. For this modified protocol, what is the probability P[E] of an error? What is the probability P[D] of a deletion?
Solution :
Here, we have 5 trails that corresponds to the 5 times the binary symbol is sent. On each trail, success is said to occur when the binary symbol is received correctly. The probability of a success is p = 1 - q = 0.9 and q = 0.1
Now if the 0 is being transmitted, then the 0 is sent 5 number of times and then we call the decoding a 0 success. Let the repeated transmission are independent. In this case, we have 5 trails. Let each repeated bit the receiver decodes as 1 a success, using the binomial probabilities. We using the [tex]$S_{k,5}$[/tex] to denote an event of [tex]$k$[/tex] successes in the 5 trails, then the probability k are decoded at the receiver is:
[tex]$P[S_{k,5}]=\binom{5}{k}p^k(1-p)^{5-k}$[/tex]
[tex]$=\binom{5}{k}(0.9)^k(1-0.9)^{5-k}$[/tex]
[tex]$=\binom{5}{k}(0.9)^k(0.1)^{5-k}$[/tex]
Here, k = 1, 2, 3, 4, 5
The probability of the transmitted bit to be decoded correctly is:
[tex]$P[C]=P[S_{5,5}]+P[S_{2,5}]$[/tex]
[tex]$=\binom{5}{3}(0.9)^5(0.1)^{0}+\binom{5}{4}(0.9)^4(0.1)^1$[/tex]
[tex]$=(0.9)^5+5(0.9)^4(0.1)^1$[/tex]
= 0.91854
The probability that the deletion occurs is
[tex]$P[D]=P[S_{3,5}]+P[S_{2,5}]$[/tex]
[tex]$=\binom{5}{3}(0.9)^3(0.1)^{2}+\binom{5}{2}(0.9)^2(0.1)^3$[/tex]
[tex]$=10(0.9)^3(0.1)^2+10(0.9)^2(0.1)^3$[/tex]
= 0.081
The probability of an error is
[tex]$P[E]=P[S_{1,5}]+P[S_{0,5}]$[/tex]
[tex]$=\binom{5}{1}(0.9)^1(0.1)^{4}+\binom{5}{0}(0.9)^0(0.1)^5$[/tex]
[tex]$=5(0.9)^1(0.1)^4+(0.1)^5$[/tex]
= 0.00046
find the measurement of the question mark. please help image included.
9514 1404 393
Answer:
45°
Step-by-step explanation:
The base angles in any isosceles triangle are congruent.
? = 45°
__
The acute angles in any right triangle are complementary.
? = 90° -45° = 45°
__
However you decide to think about it, you get ? = 45°.
How does the size of the product change from problem to problem?
2
It takes Nathan 4 minutes to solve 3 math problems. Choose a ratio tool to determine how long will it take Nathan to solve 12 math problems.
Answer: since 4mins->3math prob.
then 12/3=4 and 4x4=16
It will take him 16 minutes to solve 12 math problems
Step-by-step explanation:
A cone has a volume of 350 cubic meters. The area of the baseis
70 square meters. What is the height of the cone?
Answer:
The height is 15
Nora made 15 gallons of lemonade for a community picnic. She served 100 pints to the people. How many pints are leftover? Please help!
Answer:
There are 8 pints to a gallon so she makes 120 gallons, and since she served 100 pints then there are 20 pints left over.
Brainliest please?
is 0.23 or 2.3% greater?
Answer:
0.23
Step-by-step explanation:
If you convert 0.23 into a percent, it becomes 23%, which is more than 2.3%.
Hope that helps!
-Sabrina
Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form. 2,5,8,... ?
Answer:
Arithmetic sequence with common difference of 3.
Step-by-step explanation:
Arithmetic sequence:
The difference between consecutive terms is always the same, and this difference is called common difference.
Geometric sequence:
The quotient between consecutive terms is always the same, and this quotient is called common ratio.
In this question:
5 - 2 = 8 - 5 = 3
5/2 = 2.5 different of 8/5 = 1.6
This means that it is an arithmetic sequence with common difference of 3.
The distance in feet karina swims in a race is represented by 6d-6, where d is the distance for each lap what is an expression equivalent to 6d-6
Answer:
its c
Step-by-step explanation:
Which of the following options have the same value as 96% of 25?
Choose 2 answers:
96
100
• 25
Pro
B
0.96 - 25
Tea
0.96 . 0.25
96 25
100 100
96 - 25
Answer:
A
Step-by-step explanation:
yyjvgyujjjjuyrcjkoiffffgy
Write the equation of a line in slope-intercept form if m=2 and b=8.
Answer:
y=2x+8
Step-by-step explanation:
The slope intercept form is:
y=mx+b
with m and b already given, just plug in m and b and you will get your answer.
help!!!!!!!!!!!!!!!!
how could i find the value of this expression?
Answer:
you plug in the numbers
Step-by-step explanation:
Please mark brainliest!!
Answer:
√x⁴-y²
x²-y²
(x+y)(x-y)
when
x=3
y=-6
√x⁴-y²=(3-6)(3+6)=-3×9=-27 is your answer
Anyone know this please I really need help
what is the measure of angle 1?
a. 36
b. 86
c. 89
d. 94
Answer:
D, 94
Step-by-step explanation:
Angles of a triangle add up to 180 degrees. 180 - 29 - 65 = 86 Angles 1 and 2 add up to 180 degrees. 86 = 2 180 - 86 = 94 94 = 1
Hope this helps! If it did, please mark it as brainliest! It would help me out a lot! :D
WHO EVER ANSWERS FIRST WILL GET BRAINLY
3a = 42
Answer:
a=14
Step-by-step explanation:
Plz help it’s due tomorrow
Answer:
x=121 degrees
Step-by-step explanation:
Sorry if my work is a bit messy. If you need me to rewrite it i can
What is four plus eight
Answer:
12
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
you take the number 8 and then you add 4. and you find yourself with the answer 12
The ratio of cats to dogs is 5:4 in Riverside. If there are 20 dogs, how many cats live in Riverside?
Select one:
25
20
30
16
Answer:
25
Step-by-step explanation:
c to d is 5 to 4
5x5=25
fffff
Answer:
25
Step-by-step explanation:
We need to divide 20 by 4 to see how much 1 equals in this problem.
20÷4=5
5 equals 1
Now we add 5 to 20 because the ratio is 5:4.
20+5=25
Our answer is 25.
If US $1.00 is equivalent to EC $ 2.70, how much in US would one get from EC 297.00?
The circumference of the smaller circle is 20% of the circumference of the larger circle. Find the circumference of the larger circle. Round your answer to the nearest tenth.
Answer:
92.5
Step-by-step explanation:
Corey records the temperature in degrees Celsius each morning. At 8am the temperature was 3 degrees below zero. It rose 3 degrees by 10am. Which equation shows the change in temperature from 8am to 10am?
A 3+3=6
B-3+3=0
C-3+3= -6
D-3-3= -6
200 is between what two consecutive whole
numbers?
A.
14 and 15
B.
15 and 16
C.
19 and 20
D.
39 and 40
E.
99 and 100
Evaluate the expression.
3×2⁴
Tom is 10 years younger than Becky. In two years, Becky will be twice as old as Tom. How old is Tom now?
Answer:
20
Step-by-step explanation:
Answer:
tom is 8 and becky is 18 now
Step-by-step explanation:
in two years becky would be 20 and tom will be 10
hope this helps