Answer:
2. a. The volume of the pyramid is approximately 363.62 cm³
b. The depth of the solution in the dish is approximately 0.15046 cm
Step-by-step explanation:
2. a. A right square pyramid is a pyramid with the vertex at the top directly above the center of the base
The area of the base of the right square pyramid = 100 cm²
The area of one of the face = 60 cm²
∴ The length of the side of the base, s = √(100 cm²) = 10 cm
The area of the face = 1/2 × s × l
Where;
l = The slant height
∴ 1/2 × 10 cm × l = 60 cm²
l = 60 cm²/(5 cm) = 12 cm
l = 12 cm
The height of the pyramid, h = √(l² - (s/2)²)
∴ h = √(12² - 5²) = √(119)
The volume of the pyramid = 1/3 × Base Area × Height
∴ The volume of the pyramid, V = 1/3 × 100 cm² × √(119) cm ≈ 363.62 cm³
The volume of the pyramid, V ≈ 363.62 cm³
b. The initial level of the solution in the pyramid = The pyramid was filled with the solution
∴ The initial level of the solution in the pyramid = The height of the pyramid
The radius of the cylindrical dish into which the solution is poured, r = 4 cm
The level by which the liquid drops in the pyramid after pouring = 3 cm
Therefore, by proportion of volume, we have;
Let V₁ and 'V' represent the volume that was drained out the vertex into the cylindrical dish and the volume of the whole pyramid respectively
Therefore;
V₁/V = (3/(√119))³
V₁ = V × (3/(√119))³
V = 1/3 × 100 cm² × √(119) cm
∴ V₁ = 1/3 × 100 cm² × √(119) cm × (3/(√119))³ = 100 cm² × 1 cm × 3²/(119) = 900/119 cm³
The volume that was drained out the vertex, V₁ = 900/119 cm³
The volume of the cylindrical dish, [tex]V_d[/tex] = π·r²·h
Where h = The depth of the solution in the dish
∴ When [tex]V_d[/tex] = V₁, and r = 4 cm, we have;
π × 4² × h = 900/119
h = (900/119)/(π × 4²) ≈ 0.15046
The depth of the solution in the dish, h ≈ 0.15046 cm.
Sunny can read 60 pages in 5 hours how many pages can he read in 7 hours
Answer:
i will help
Step-by-step explanation:
the answer is 91 do the math bro
you welcome
1\2 x 12 x 14 plz I need help
Answer:
84
Step-by-step explanation:
x12
Simplify ———
x14
Dividing exponential expressions :
1.1 x12 divided by x14 = x(12 - 14) = x(-2) = 1/x2
Final result :
1
——
x2
Find the distance between the points (-8, -3) and (-2, 5). Hint: Use the Pythagorean theorem.
Answer:
1/5
Step-by-step explanation:
Use Pythagoras theorem
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!
Answer:
1. 48ft
2. 28 inches
Step-by-step explanation:
1. 6x8=48
2. 4x7=28
help please in this question?
Answer:
see explanation
Step-by-step explanation:
∠ 1 and ∠ 2 are adjacent angles and are supplementary, sum to 180° , so
5x + x + 54 = 180 ← equation to solve to find x
6x + 54 = 180 ( subtract 54 from both sides )
6x = 126 ( divide both sides by 6 )
x = 21
Then
∠ 1 = 5x = 5 × 21 = 105°
∠ 2 = x + 54 = 21 + 54 = 75°
list some values that would make this inequality -2x>10
Answer:
-6,-9,-20,-25.
Step-by-step explanation:
You need to multiply a negative to make it positive as a negative multiplied by a negative equals a positive. But anything besides -1,-2,-3,-4,-5 and all positves can be placed.
the number that makes the ratio equivalent to 1:9.
7:
Answer:
63. so it'll be 7:63
Step-by-step explanation:
1:9
7:x
(we multiplied 1 by 7 to get 7 so multiply 9 by 7)
9*7= 63
find the measure of each interior angle of a regular polygon with the following number of sides 10
Answer:
a regular polygon has all angles measure sum up to 360 degrees so each interior angle = sum of alll angles/no.of sides so it is 360/10= 36 degrees hope its clear now
Step-by-step explanation:
Carol has had a $145,000 fixed mortgage for 5 years at 5.5% and is
considering refinancing. She can now get an 80/20 mortgage with 4.5% and
9.5% interest, respectively. Based only on this information, should she
refinance?
Answer: no the two blended interest rates are the same
Step-by-step explanation:
Answer:
no, the new blended rate is higher than the old interest rate
Step-by-step explanation:
bc i said so
Enter 4/5 and 1/3 as a pair of equivalent fractions with the least common denominator between the two fractions.
What is the initial value?
A. -8
B. -5
C. 0
D. 7
Answer:
A. -8
Step-by-step explanation:
Given the values of the function in a table, to determine the initial value of the function, you need to determine where x = 0.
Since the function is linear, the rate of change will be constant/the same.
To find the rate of change, you need to divide the change in the y value by the change in the x value.
X Y
+2↓ -5 | 7 ↓ -6
+2↓ -3 | 1 ↓ -6
+2↓ -1 | -5 ↓ -6
1 | -11
_____________
Since y changes by -6 and x changes by +2 every time, ∆Y/∆X = -6/+2 [Reduce] = -3/+1.
Slope = -3.
This means that y will decrease by 3 units every increase of 1 unit in x.
If (-1, -5) is a point which means that -1 is x when -5 is y.
We can apply the rate of change to see where x = 0.
So -5 + 1(-3/+1) → -5 + -3 = -8
ABCD is an isosceles trapezoid.
measure of angle B=
measure of angle C=
measure of angle D=
Answer:
Angle b= angle c =83degree
Angle d =97degree
Step-by-step explanation:
Since isosceles:
Angle b =angle c
Angle a= angle d
Angle d =a=97
Sum of quadrilateral inner degrees:360
(360-2x97)/2=b=c=83
Answer:
Answer:
Angle b= angle c =83degree
Angle d =97degree
Step-by-step explanation:
Since isosceles:
Angle b =angle c
Angle a= angle d
Angle d =a=97
Sum of quadrilateral inner degrees:360
(360-2x97)/2=b=c=83
Step-by-step explanation:
pls help me!!!!!!!!!
Answer:
y = 5 - ×
Step-by-step explanation:
I guessed but the numbers work
Can someone help me?
Find the quotient. Write your answer in scientific notation, (3.6 x 10 to the power of 7) divided by (7.2 times 10 to the 7)
Given:
The given expression is:
[tex]\dfrac{3.6\times 10^7}{7.2\times 10^7}[/tex]
To find:
The value of the quotient.
Solution:
We have,
[tex]\dfrac{3.6\times 10^7}{7.2\times 10^7}[/tex]
It can written as:
[tex]=\dfrac{3.6}{7.2}\times \dfrac{10^7}{10^7}[/tex]
[tex]=\dfrac{1}{2}\times 1[/tex]
[tex]=0.5[/tex]
It can be rewritten as:
[tex]=5\times \dfrac{1}{10}[/tex]
[tex]=5\times 10^{-1}[/tex]
Therefore, the value of the quotient is [tex]5\times 10^{-1}[/tex].
drawing a vowel from letter tiles that spell out MATHEMATICS
chance
Blank 1:
Blank 2:
Given:
Drawing a vowel from letter tiles that spell out MATHEMATICS.
Chances = [tex]\dfrac{?}{?}[/tex]
To find:
The correct values for the blanks.
Solution:
Vowels are a, e, i, o, u.
In MATHEMATICS, the vowels are A, E, A, I.
Number of vowels = 4
We know that,
[tex]Probability=\dfrac{\text{Number of selected vowels}}{\text{Total number of vowels}}[/tex]
[tex]Probability=\dfrac{1}{4}[/tex]
So, the chance of drawing a vowel from letter tiles that spell out MATHEMATICS is [tex]\dfrac{1}{4}[/tex].
Blank 1: 1
Blank 2: 4
Therefore, the value for blank 1 is 1 and the value for blank 2 is 4.
2)
A line passes through the points (0.5) and (-6,3). A second line passes through
(-15, 0) and (-21, -2).
A) Do the lines intersect? Show work to prove it! Grcle YES or
NO
Answer:
Step-by-step explanation:
Find the slope of each line. If the slopes are the same, the lines are parallel. Otherwise, the lines intersect.
Slope of line passing through (x₁, y₁) and (x₂, y₂) = (y₂-y₁)/(x₂-x₁)
Slope of line passing through (0, 5) and (-6, 3) = (3-5)/(-6-0) = ⅓
Slope of line passing through (-15, 0) and (-21, -2) = (-2-9)/(-21-(-2)) = 11/19
The lines intersect.
Henry painted a picture of his house on canvas. The actual width of
the driveway is 20 feet. If it is represented with a width of 4 inches on
the canvas, what was the scale factor used?
Answer:
The scale factor would be -5.
Step-by-step explanation:
If the driveway is 20 feet but 4 foot on the canvas. Then 20/4 is 5. But since the width is going from 20 to 4, the numbers are going down to it would be a negative scale factor. If it was going from 4 width to 20 width, the scale factor would be a positive 5.
You want to wrap a gift shaped like the regular triangular prism shown. How many square inches of wrapping paper do you need to completely cover the prism?
length 11 in
height 8.7 in
width 10 in
Which of the following could be a rational number
What are the options???
It cost Erica $9.75 for the ingredients to make 30 cupcakes. She sold them for $1.00 each. What was Erica’s total profit?
STEP BY STEP PLZZ PLEASE PLZZZZZ
Answer:
$30 (I think)
Step-by-step explanation:
because you have 30 cupcakes and selling 1 for a dollar but it may be $20.25 if you have to subtract the $9.75 that you used to buy the cupcakes
The question is right there please read and help I’ll give u Branliest plz
Jared made a scale drawing of his classroom for his tech project. He used a scale of 1 cm = 3.5 ft. If the length of his classroom on the drawing measured 30 cm, What is the actual length of his classroom?
Answer: 105ft
Step-by-step explanation: If 1cm is 3.5ft then you should multiply 3.5ft by 30 cm to get 105ft.
Help pleaseeeee?????
Sandra bought a pair of leather boots that were marked down by 20%. The original cost of the boots was $150. What did Sandra pay for the boots
Answer:
130 maybe
Step-by-step explanation:
Answer:
120
Step-by-step explanation:
It is 120 because if you do 20% of 150 that's 30 so subtract that with 150 leaving you 120.
does anyone get this question plss
Answer:
D) 1.0
Step-by-step explanation:
if y = 1 then x = 1
Find the perimeter of the figure at right(picture). Use 3.14 as an estimate for π
Answer:
54.88cm
Step-by-step explanation:
For shaded region perimeter, subtract the circle perimeter from the rectangle
perimeter
= (10*8) - (2 * 3.14 * 8/2)
= 80 - 25.12
= 54.88cm
Just the answer please I need you
Answer:
A = 33.6 sq units
Step-by-step explanation:
A (trapezoid) = 1/2(4)(14+2) = 2(16) = 32
A (semi-circle) = π(1)/2 = 1.57
karrie was late to work 14 times last year if she worked 250 days last year what percent of the days were she late
Emma is a professional cyclist. For the past year she has been practicing to ride as far as she can in a minute. At the beginning of the year, her personal record was 5/6 of a kilometer in one minute. After six months, she improved her record by 1/15 of a kilometer. After a year, she further improved her record by 1/12 of a kilometer. What is her best record?
Step-by-step explanation:
5/6+1/15+1/12in on minute
Emma's best record is 59/60 kilometers per minute.
Given that, Emma personal record was 5/6 of a kilometer in one minute.
What is addition of two fractions?To add fractions there are three simple steps:
Step 1: Make sure the bottom numbers (the denominators) are the same. Step 2: Add the top numbers (the numerators), put that answer over the denominator.
Step 3: Simplify the fraction (if possible)
Given, after six months, she improved her record by 1/15 of a kilometer. After a year, she further improved her record by 1/12 of a kilometer.
Now, 5/6 + 1/15 + 1/12
LCM of denominators 6, 15 and 12 is 60.
50/60 + 4/60 + 5/60
= 59/60
Therefore, Emma's best record is 59/60 kilometers per minute.
To learn more about the addition of fractions visit:
https://brainly.com/question/17544795.
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