unit 11: volume & surface area homework 8
The volumes of the pyramids are listed below:
V = 1437.333 cm³V = 75,398 km³V = 59.2 ft³V = 393.3 yd³V = 1134.116 m³V = 403.333 mm³V = 405.6 in³V = 886.808 ft³How to determine the volume of a pyramidVolume is the space occuppied by an object. In this question we must determine the volumes of pyramids of circular base and polygonal base (V). All the formulas needed are described below:
Volume of the pyramidV = (π/3) · B · h (1)
Base of the pyramid - CircleB = (π/4) · R² (2)
Base of the pyramid - Regular polygon
B = (n · L²)/(4 · tan 0.5α) (3)
Base of the pyramid - Right triangleB = (1/2) · b · z (4)
Base of the pyramid - RectangleB = b · z
Where:
R - Radiusn - Number of sides of the polygon.l - Side lengthα - Internal angle, in degree.h - Height of the pyramidb - Base of the right triangle/rectangle.z - Length of the right triangle/rectangle.Now we proceed to solve each pyramid:
1) Square, n = 4, α = 90°, L = 14 cm, h = 22 cm
B = 196 cm², V = 1437.333 cm³
2) Circle, R = 3 km, h = 8 km
B ≈ 28.274 km², V = 75,398 km³
3) Right triangle, b = 12 ft, z = 3.7 ft, h = 8 ft
B = 22.2 ft², V = 59.2 ft³
4) Rectangle, b = 23 yd, z = 9 yd, h = 5.7 yd
B = 207 yd², V = 393.3 yd³
5) Circle, R = 9.5 m, h = 12 m
B ≈ 283.529 m², V = 1134.116 m³
6) Regular pentagon, B = 110 mm², h = 11 mm
V = 403.333 mm³
7) Square,n = 4, α = 90°, L = 13 in, h = 7.2 in
B = 169 in², V = 405.6 in³
8) Regular triangle, n = 3, α = 120°, L = 16 ft, h = 24 ft
B ≈ 110.851 ft², V = 886.808 ft³
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1/6 of a wall painted in 3/10 of an hour, how much did he paint in 1 hour
what is the value of x?
Answer:
If you mean the angle at X... 70°
Step-by-step explanation:
Angles on a straight line sum up to 180°115° + Y = 180°Y = 180° - 115° = 65°Angles in a triangle sum up to 180°X + Y + Z = 180°(4k + 5)° + (6k + 10)° + 65° = 180°We turn everything into degrees4k° + 5° + 6k° + 10° + 65° = 180°We then sum up the "like" terms (as in, we put all the k together, and put all the normal numbers together)10k° + 80° = 180°10k° = 180° - 80° = 100°k° = 100° ÷ 10 = 10°At X:6k° + 10° = 6 × 10° + 10° = 60° + 10° = 70°what plus 23 equals 180
Answer:
157
Step-by-step explanation:
To find this, we just have to reverse the problem and subtract 23 from 180:
[tex]180-23=157[/tex]
So your answer is 157.
Hope this helps! Have a good day! :)
157
Step-by-step explanation:
180-23= 157
The answer is 157
solve for x
[tex] \binom{1}{2} ^{3x + 1} = 32[/tex]
how do i solve for x
Answer:
Yes diciembre Eqsakdulien
Help a fella out:)))))))))
Answer:
See below
Step-by-step explanation:
the x + 4 will shift the graph 4 units LEFT
the - 8 part will shift the graph 8 units DOWN
You have $300. Your sister has at most $50 less than you. Write an inequality that matches the situation. Give an amount of money your sister could have.
HELP!!!!
Find the inverse of f(x)=5x-4.
The inverse of f is g(x)= ?
If g(x) is the inverse of f(x), then by definition of inverse function,
f(g(x)) = g(f(x)) = x
Given that f(x) = 5x - 4, we have
f(g(x)) = 5 g(x) - 4 = x
Solve for g(x) :
5 g(x) - 4 = x
5 g(x) = x + 4
g(x) = (x + 4)/5
What does the red arrow represent in the dot plot?
O outlier
O mean
O spread
O median
NO LINKS!!!
The red arrow represents an outlier in the given dot plot. which the correct answer would be an option (A).
What is the dot plot?A dot plot, sometimes known as a dot chart, is a sort of basic histogram-like graphic used in statistics for very small data sets with discrete values.
An outlier is a value in a random sampling from a population that is significantly different from the other values. In some ways, this definition leaves it up to the analyst (or a consensus process) to determine what is abnormal. Normal observations must first be characterized before anomalous observations may be identified.
The dot plot is given in the question,
According to the given dot plot,
Most data are clustered around [12, 14], while 24 is distant from this interval.
Thus, the red arrow represents an outlier in the given dot plot.
Hence, the correct answer would be option (A).
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help me please need help
Answer:
Step-by-step explanation:
Hypotenuse: The longest side in the triangle and it is opposite to 90°
Opposite Side: The side oppoiste to the angle.
Adjacent side: The side next to the angle.
First find 'c' using Pythagorean theorem,
c² = 9² + 12²
= 81 + 144
= 225
c =√225
c = 15
[tex]\sf \ Sin \ \theta = \dfrac{opposite \ side \ of \ \theta}{hypotenuse}= \dfrac{12}{15}[/tex]
[tex]\sf \ Cos \ \theta = \dfrac{adjacent \side \ of \ \theta}{hypotenuse}= \dfrac{9}{15}\\\\ Tan \ \theta= \dfrac{opposite \ side \ of \ \theta}{adjacent \ side \ of \ \ theta}= \dfrac{12}{9}[/tex]
[tex]\sf \ Csc \ \theta= \dfrac{hypotenuse}{opposite \ side \ of \ \ theta}= \dfrac{15}{12}\\\\\ Sec \ \theta = \dfrac{hypotenuse}{adjacent \ side \ of \ \theta}= \dfrac{15}{9}\\\\Cot \ \theta= \dfrac{adjacent \ side \ of \ \theta}{opposite \ side \ of \ \theta}= \dfrac{9}{12}[/tex]
[tex]\sf \ Sin \ \alpha = \dfrac{opposite \ side \ of \ \alpha \theta}{hypotenuse}= \dfrac{9}{15}[/tex]
[tex]\sf \ Cos \ \alpha = \dfrac{adjacent \side \ of \ \alpha }{hypotenuse}= \dfrac{12}{15}\\\\ Tan \ \alpha = \dfrac{opposite \ side \ of \ \alpha }{adjacent \ side \ of \ \ theta}= \dfrac{9}{12}[/tex]
[tex]\sf \ Csc \ \alpha = \dfrac{hypotenuse}{opposite \ side \ of \ \alpha }= \dfrac{15}{9}\\\\\ Sec \ \alpha \theta = \dfrac{hypotenuse}{adjacent \ side \ of \ \alpha }= \dfrac{15}{12}\\\\Cot \ \alpha = \dfrac{adjacent \ side \ of \ \alpha }{opposite \ side \ of \ \alpha }= \dfrac{12}{9}[/tex]
PLEASE HELP!!! I have no idea how to solve for this
m1=
Answer:
mAngle 1 = 40°
Step-by-step explanation:
You can use Corresponding Angles to directly state Angle1 is 40°. If you have to prove it you can show that the horizontal lines are parallel bc they are both perpendicular to the same line (the vertical line in the middle)
OR...
Use vertical angles and supplementary angles to find all the six pack of angles right in the middle of the diagram. 40°, 50°, 90°, 40°, 50° 90° And the use the idea that a triangle's three angles must add up to 180°.
90+50+Angle1=180
140 + Angle1 = 180
Angle1 = 40°
Katie went to a craft store to purchase the supplies she needed to make two types of jewelry. The table shows the cost of supplies Katie needed. Katie purchase the exact amount of supplies to make 1 bracelet and 2 necklaces.
Part A Write an expression to determine the cost of supplies to make 1 bracelet.
Answer: 25($0.05)+4($0.45)
Cost of bead +cost of charm needed for 1bracelet
Step-by-step explanation: If you need to break it down further,
$1.25+$1.8=$3.03.05
x is an integer.
The Lowest Common Multiple (LCM) of x and 12 is 120
The Highest Common Factor (HCF) of x and 12 is 4
Work out the value of x
Since 120 = 12 • 10 and LCM(x, 12) = 120, these suggest x is some multiple of 10.
HCF(x, 12) = 4 tells us that x is a multiple of 4.
If x is a both a multiple of 4 and 10, then the smallest x that fits both conditions is 4 • 10 = 40. (-40 also satisfies the criteria.)
The value of x for which the LCM and HCF of x and 12 are 120 and 4 respectively is 40.
What do we mean by Lowest Common Multiple (LCM) and Highest Common Factor (HCF)?
The Lowest Common Multiple (LCM) of the numbers is the smallest common multiple of the given numbers.
The Highest Common Factor (HCF) of the numbers is the greatest factor of the given numbers.
In the case of two numbers, the product of LCM and HCF is equal to the product of the numbers.
How do we solve the given question?We are given two numbers, x and 12.
Their LCM and HCF are 120 and 4 respectively.
We are asked to find the number x.
For two numbers, we know that the product of two numbers is equal to the product of their HCF and LCM.
∴ x*12 = 120*4
or, 12x = 480
or, x = 480/12
or, x = 40.
∴ The value of x for which the LCM and HCF of x and 12 are 120 and 4 respectively is 40.
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Can someone help me with this
Answer:
3^14
Step-by-step explanation:
Taking a look at the question, try to break it down into these general steps:
1. Identify the base number. Are they the same? In this case, the base number is 3 so they are the same.
2. Recall the rules when multiplying exponents. In this case, multiplying exponents across will end up being 9+5.
3. Rewrite the equation as 3^(9+5). This should give you 3^14
Please help? This is complicated
Select the correct answer from each drop-down menu. Consider functions h and k.
h(t) = 5x^2 - 1
k(u) = √5x+1
For I > 0, the value of h(k(x)) is ____the value of k(h(x))
options-
equal to
not equal to
For I > 0, functions h and k ____ inverse functions
options-
are
are not
Answer:
(a) Not equal to
(b) Are not
Step-by-step explanation:
Plot G(8,-6) , H(2,-6) , J(7,4) , and K(7,10) in a coordinate plane. Are GH and JK congruent?
Answer:
Yes GH ≅JK
Step-by-step explanation:
The line GH and JK are congruent because they measures are equal.
JK line is vertical so the x-coordinate is constant and the difference in y is 10-4 = 6 and
GH line is horizontal so the y-coordinate is constant and the difference in x is 8-2 = 6
a , b , c , d ???????????
Answer:
c
Step-by-step explanation:
if this is wrong im sorry...
Elaine drives her car 70 miles and has an average of a certain speed. If the average speed had been 3mph more, she could have traveled 77 miles in the same length of time. What was her average speed
Answer:
30 miles/hr
Step-by-step explanation:
d / r = time distance divided by rate = time
70 / r = time and 77/(r+3 ) = time r = her original average speed
'time' is the same for both so we can equate the equations
70/r = 77/(r+3) cross multiply
70r + 210 = 77r
7r = 210
r = 30 m/hr
Jaylen bought j crackers and combined them with Marvin m crackers they then split the crackers equally among 7. Type an algebraic expression that represent the verbal expression
Answer:
Gimme brainliest
Step-by-step explanation:
ip grabber goated
If you borrow $700 for 5 years at
an annual interest rate of 7%, how
much will you pay altogether?
The amount you would pay altogether if you borrow $500 for 5 years at
an annual interest rate of 7% is $945.
How much would you pay altogether?The amount you would pay altogether is the sum of the amount borrowed and the interest.
Total value of the debt = interest + amount borrowed
Interest = $700 x 7% x 5 = $245
Total value of the debt = $245 + $700 = $945
Hey there! Can anyone help me out with this? I need help with both of these. Will give brainliest! :D
[tex]area = length \times width[/tex]
____________________________________________
c .
[tex]area = \frac{3}{8} \times \frac{4}{5} \\ [/tex]
[tex]area = \frac{4 \times 3}{4 \times 2 \times 5} \\ [/tex]
[tex]area = \frac{3}{2 \times 5} \\ [/tex]
[tex]area = \frac{3}{10} \: \: {cm}^{2} \\ [/tex]
_____________________________________________
d.
[tex]area = \frac{1}{4} \times \frac{3}{7} \\ [/tex]
[tex]area = \frac{3}{28} \: \: {m}^{2} \\ [/tex]
The graph of a linear equation has a slope of 4 and an x-intercept at (2, 0). What is the y-intercept of the graph?
Answer:
y-intercept = -8
Step-by-step explanation:
Slope-intercept form of a linear equation: y = mx + b
(where m is the slope and b is the y-intercept)
Given:
slope (m) = 4point (x₁, y₁) = (2, 0)Substituting the given values into the slope-point form of a linear equation:
[tex]\sf y-y_1=m(x-x_1)[/tex]
[tex]\implies \sf y-0=4(x-2)[/tex]
[tex]\implies \sf y=4x-8[/tex]
Comparing the final equation with the Slope-intercept form of a linear equation, we can see that the y-intercept is -8
(will mark brainlist )
a=&b=-6.C=13
a=-6.5=-8. C=13
a=-6.5=-S.C=-13
a=-&b=-6.C=-13
Answer:
A) 8, -6, 13
Step-by-step explanation:
See attached image.
1. If x: 5 = 12:21 find the value of x.
Answer:
x = 2.85 = 20/7
Step-by-step explanation:
x : 5 = 12 : 21
=》x/5 = 12/21
Cross multiply,
21 *x = 5*12
21x = 60
x = 60/21
x = 2.85 = 20/7
________
Hope it helps ⚜
Answer:
[tex]\huge\boxed{\sf x = 2.86}[/tex]
Step-by-step explanation:
Given proportionality:
x : 5 = 12 : 21
We know that:
Product of means = product of extremes
Means : 5,12
Extremes : x,21
5 × 12 = x × 21
60 = 21 x
Divide both sides by 21
60/21 = x
2.86 = x
x = 2.86
[tex]\rule[225]{225}{2}[/tex]
Joan must save at least $500 to open a savings account. She saves $80 each month toward her goal. What is the fewest number of months before Joan can open the account?
A. 5 months
B. 6 months
C. 7 months
D. 8 months
500 divided by 8 is 6.25 ( 6 months and 25 days) so he answer round to the nearest digit is 6 so the answer is B (6 months)
Laura has a set of 16 books. Each book in the set weighs the same. One book has a weight of 0.8 kilograms (kg). Laura wants to find the total weight, w, of the set of books. What is the equation and solution shows the total weight(w) of the set of books?
Answer:
12.8kg
Step-by-step explanation:
1 book =0.8kg
16 books=16*0.8kg
which is equal to 12.8kg
Write the decimal in standard form.
seventy-three thousandths
7300
7×10³+3×10²+0×10¹+0×10⁰
please give me brainliest
A car dealership offers two types of discounts.
Discount 1: Take 5% off the original price of a care built last year and then receive a $3,500 rebate.
Discount 2: Take 10% off the original price of a car built this year and then receive a $1,250 rebate.
A customer is deciding between two cars.
Car R was built last year and has an original price of $25,340.
Car S was built this year and has an original price of $22,860.
Based on this information, which statement is true?
Question 10 options:
The customer would pay $24,073 for Car R.
The customer would pay $19,324 for Car S.
The customer would pay $23,107 for Car R.
The customer would pay $21,824 for Car S.
Answer:
3.55,11.25,48.20,49.413,42.184
Step-by-step explanation:
$3,500 + 0.05% = $3.55
$1,250 + 0.010% = $11.25
$25,340 + $22,860 = $ 48.20
$25,340 + $ 24,073 = $ 49.413
$22,860 + $ 19,324 = $42.184
please help i don’t understand
Answer:5
Step-by-step explanation: