2. Find the volume to the nearest cubic millimeter of the 3-D object in the diagram.
200 mm
300 mm
Answers
Volume of a pyramid is calculated using the same basic formula as that of a cone: volume = (1/3) × base area × height, where height is the distance between the base and the apex. Then the height is 6 feet.
What is the volume of the square pyramid?Using the equation volume = base area height / 3, one may calculate the volume of a regular square pyramid. Keep in mind that the base area is equal to the base edge length squared.
A polygonal base and an apex come together to form a polyhedron known as a pyramid. Volume of a pyramid is calculated using the same basic formula as that of a cone: volume = (1/3) × base area × height, where height is the distance between the base and the apex.
The volume of a square pyramid exists found by multiplying the area of the base by the height divided by 3.
32 = 4² × h/3
32 = 16 × h/3
Multiply both sides by 3
96 = 16 × h
Divide both sides by 16
H = 96/16
H = 6
Therefore, the height is 6 feet.
The complete question is:
Find the height of a square pyramid that has a volume of 32 cubic feet and a base length of 4 feet.
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Related Questions
A bag contains ten tlles labeled B, C, D, E, F, G, H, I, J, and K. One tile will be randomly picked.What is the probability of picking a letter that is not a vowel?Write your answer as a fraction in simplest form.
Answers
The number of vowels is:
[tex]2[/tex]The total number of tiles is:
[tex]10[/tex]Therefore, the total number of letters not vowels is given by:
[tex]10-2=8[/tex]Hence, the probability of picking a letter that is not a vowel:
[tex]\frac{8}{10}=\frac{4}{5}[/tex]Therefore the required probability is 4/5
Match the ratio of side lengths to its corresponding anglemeasure.
Answers
Consider the formulae from Inverse Trigonometry,
[tex]\begin{gathered} \theta=\sin ^{-1}(\frac{\text{ Opposite Leg}}{\text{ Hypotenuse}}) \\ \theta=\tan ^{-1}(\frac{\text{ Opposite Leg}}{\text{ Adjacent Leg}}) \\ \theta=\cos ^{-1}(\frac{\text{ Adjacent Leg}}{\text{ Hypotenuse}}) \end{gathered}[/tex]Solve for the first angle as,
[tex]\begin{gathered} \theta=\cos ^{-1}(0.139) \\ \theta\approx82^{\circ} \end{gathered}[/tex]Thus, the required angle measure is 82 degrees approximately.
Solve for the second angle as,
[tex]\begin{gathered} \theta=\tan ^{-1}(0.249) \\ \theta\approx14^{\circ} \end{gathered}[/tex]Thus, the required angle measure is 14 degrees approximately.
Solve for the third angle as,
[tex]\begin{gathered} \theta=\sin ^{-1}(0.469) \\ \theta\approx28^{\circ} \end{gathered}[/tex]Thus, the required angle measure is 28degrees approximately.
Solve for the fourth angle as,
[tex]\begin{gathered} \theta=\cos ^{-1}(0.682) \\ \theta\approx47^{\circ} \end{gathered}[/tex]Thus, the required angle measure is 47 degrees approximately.
Solve for the fifth angle as,
[tex]\begin{gathered} \theta=\sin ^{-1}(0.848) \\ \theta\approx58^{\circ} \end{gathered}[/tex]Thus, the required angle measure is 58 degrees approximately.
What is the slope of the line?
Answers
Answer:
-7/4 seeing how the line touches -3,4 and 1, -3 only it goes down 7 and 3 to the right
Step-by-step explanation:
sub to imagine fn
Using the SSS congruence criterion, what additional information is needed to show that ARST AUTS?
Answers
if you’re going by the SSS congruence therom you can see that side RS and UT are congruent. that’s given and TS and ST are also congruent because of the reflexive property. therefore all you need left is RT and US to prove SSS congruence therom
the diagram shows triangle ABC. D is on the point AB such that CD is perpendicular to AB. AC=9.4cm, AD=5.2cm and BD=7.8cm. Work out the size of angle ABC.
Answers
Answer:
45°
Step-by-step explanation:
Triangles ADC and BDC are right triangles, since CD⊥AB.
Use Pythagorean to find the length of CD:
CD² + AD² = AC²CD² + 5.2² = 9.4²CD² = 9.4² - 5.2²CD² = 61.32CD = √61.32CD = 7.83Use trigonometry to find the angle ABC:
tan (∠ABC) = CD/BDtan (∠ABC) = 7.83/7.8tan (∠ABC) = 1.0 (rounded)m∠ABC = arctan 1m∠ABC = 45°Evaluate. Write your answer as a whole number or as a simplified fraction.
Answers
36.
When you divide powers with the same base (in this case, 6), you subtract the exponents.
See details:
[tex]\frac{6^{8} }{6^{6} } \\8-6=2\\6^{2}=36[/tex]
2w - 15w - 18 = -83 solve for w simplify as much as possible
Answers
Answer:
w = 5
Step-by-step explanation:
2w - 15w - 18 = -83
combine w on left side:
-13w - 18 = -83
add 18 to both sides:
-13w - 18 + 18 = -83 + 18
-13w = -65
divide both sides by -13:
-13w/-13 = -65/-13
w = 5
The accurate scale drawing shows a car and a lamp post.
The car has a real width of 1.5 metres.
Find an estimate for the real height, in metres of the lamp post.
Answers
An estimate of the real height of the lamp post is 9m.
What is the estimate of the real height?The first step is to determine the scale of the drawing. The scale can be determined by dividing the height of the lamp post by the height of the car. The height of the lamp post when measured with a ruler is 10.8 cm and the height of the car is 1.8cm
Scale = length of the lamp post / height of the car
10.8 / 1.8 = 6
Now, multiply the scale by the width of the car.
The real height of the lamp post = 6 x 1.5 = 9m
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what two numbers make a product of 50 and a sum of -15?
Answers
-10 x -5 = 50
is it right? but there isn't a square root for 3. And also I need an answer for the other one.. I need a great explanation quickly help!
Answers
Answer:
[tex]x=0, \quad x=3[/tex]
Step-by-step explanation:
Given equation:
[tex]9x^2-27x=0[/tex]
Factor out the common term 9x:
[tex]\implies 9x(x-3)=0[/tex]
Zero Product Property: If a⋅b = 0 then either a = 0 or b = 0 (or both).
Using the Zero Product Property, set each factor equal to zero and solve for x:
[tex]\begin{aligned}\underline{\sf Case\; 1} & & \underline{\sf Case \;2}\\9x&=0 & x-3&=0\\\dfrac{9x}{9} & =\dfrac{0}{9} & \quad \quad x-3+3 & =0+3\\x&=0 & x&=3\end{aligned}[/tex]
Therefore, the solutions to the given equation are:
[tex]x=0, \quad x=3[/tex]
Donnie writes an absolute value equation to determine the values that are 0.8 units from 3.5.
What equation does Donnie write and what values does he find?
Enter your answer in decimal form by filling in the boxes.
Absolute value equation |x- ___ | = ___
The values that are 0.8 units from 3.5 are ___ and ___
Answers
The absolute value equation which correctly represents the situation as described is; | x- 3.5 | = 0.8.
The values which are 0.8 units from 3.5 as given are therefore; 4.3 and 2.7.
What values are 0.8 units from 3.5 as described in the task content?It follows from the task content that the numbers which are 0.8 units away from 3.5 on the number line be determined.
On this note, the correct representation of the situation above involves an absolute value equation such that;
| x- 3.5 | = 0.8
Hence, to solve the equation; (x- 3.5) = 0.8 OR (x- 3.5) = -0.8.
x = 0.8 + 3.5. OR. x = -0.8 + 3.5
x = 4.3 OR x = 2.7.
Ultimately, the required values are; 4.3 and 2.7.
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what is 12 times 12 i just need to know
Answers
Answer:
144
Step-by-step explanation:
12 * 12 = 144
Answer:
It's 144.
..............
Marsha used a graphing calculator to graph an expense and a revenue function for her family’s printing business. The graph looked like the one below.
Answers
Answer:
a
Step-by-step explanation:
51 points composite functions need help soon
Answers
Answer:
(f∘g)(12) = 24
Step-by-step explanation:
Pre-SolvingWe are given the functions f(x)=4x+8 and [tex]g(x)=\sqrt{x+4}[/tex]. We want to find (f∘g)(12).
(f∘g)(12) means that we first find the value of g(12), and then plug that value into f(x).
SolvingFirst, we find g(12). To do this, substitute x as 12.
[tex]g(12) = \sqrt{12 + 4}[/tex]
Add 12 and 4 together under the radical.
[tex]g(12) = \sqrt{16}[/tex]
Take the square root of 16.
g(12) = 4
Now, substitute 4 as x in f(x) = 4x + 8.
f(4) = 4(4) + 8
Multiply.
f(4) = 16 + 8
Add 16 and 8 together.
f(4) = 24
f(4) has the same value as (f∘g)(12), since 4 is the value of (g)(12), and then the value of g(12) was plugged in as x in f(x).
Therefore, (f∘g)(12) is 24.
victor had a goal of making a 90 on each of his math tests. at the end of the year, he was within 5 points of his goal for each test. what are the maximum and minimum scores that he could have received?
Answers
Answer: he could have gotten 100 or 0
Step-by-step explanation: he could have had alot of tests and gotten 100 on all of them to even out the one zero.
1. The area of a rectangle is 45.5 square inches. The base of the rectangle is 7 inches. What is the height of the rectangle in inches?
2. A pharmacist put 4.536 ounces of vitamin pills into bottles in total. She put 0.043 ounces of vitamin pills into each bottle. How many bottles did the pharmacist use for these vitamin pills?
3. A baby weighed 7.25 lb at birth. At the end of 8 months, the baby weighed 2 3/4 times its birth weight. How many pounds did the baby weigh at the end of 8 months? Round your answer to the nearest tenth.
4. A recipe for cookies requires 2/3 cup of butter.
Rama wants to make 3/4 of the recipe. How many cups of butter should Rama use to make the cookies?
5. Ryan had a whole pizza. He ate 1/8 of the pizza for lunch and another 1/4 of the pizza for dinner. Write the fraction that represents how much of the pizza Ryan did not eat.
6. A sea turtle made 460 dives in 12 hours. At this rate, how many dives did the sea turtle make in 3 hours?
Also, can you help with the expression, solution, and work?
Answers
Using given area and base length of a rectangle we got that the height of the given rectangle is 6.5 inches.
What is the area of a rectangle?Rectangle is closed geometric figure that has four perpendicular sides with opposite sides equal.
The formula for the area of the rectangle :
Area of the rectangle = Length × Breadth
Given that the area of a rectangle is 45.5 square inches.
The base of the rectangle is given 7 inches
To find : Height of the rectangle
Let the base length is the length of the rectangle and height is the Breadth of the rectangle.
Then, Area of the rectangle = Length × Breadth
⇒ 45.5 = 7 × Height
⇒ 45.5 /7 = Height
⇒ 6.5 = Height of the rectangle
Therefore, the height of the rectangle is 6.5 inches.
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Reasonableness
Lexi subtracts 9,405 from 11,138.
Should her answer be greater than or less than 2,000?
Explain.
(Help meeee)
Answers
Answer:
I believe that it should be less than 2,000.
Step-by-step explanation:
11038 < 11405 = 9405 + 2000
11038 - 9405 < 2000
PLEASE HELP ME ON THIS
A ball is thrown in the air the function h = 30t-5t^2 can be used to find the height (h) of the ball in meters after t seconds.
how long does it take the ball to reach a height of 45 meters?
Answers
This equation represents the approximate height, h, in meters, of the ball above the ground after it falls for t seconds.
h = -5t2 + 45.
How can one determine a function's maximum height?
The vertex, which is a maximum (or minimum) in a parabola, can be located by solving the square (yuck!) or by using the formula x = -b/2a. By re-entering the original equation with this x value as the vertex's x, we can determine the appropriate maximum height.
By multiplying "D * tan (theta)," where "tan" is the tangent of angle theta, you can get the height of the item of interest. For instance, rounding up, the height is 40 tan 50 = 47.7 meters if theta is 50 degrees and D is 40 meters.
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An investor puts $800 in an account that pays 2% interest compounded annually. Find the account balance after 5 years.
Answers
The account balance is $883.264 after 5 years.
The Principal amount is $800, the time given is 5 years and the rate of interest is 2%.
We have to find the account balance after 5 years.
Formula to find the amount
Amount = Principal × [tex](1 +\frac{rate}{100}) ^{time}[/tex]
Now putting the value we get,
Amount = 800 × [tex](1 + \frac{2}{100} )^{5}[/tex]
= 800 × [tex]\frac{102}{100 } ^{5}[/tex]
= 800 ×[tex]1.02^{5}[/tex]
= 800× 1.104
= 883.264
Therefore the amount is $883.264 that is the account balance after 5 years.
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Tia rounds a number, x, to 3 sf.
The result is 7.68.
Write the error interval for x in the form a ≤
x < b.
Answers
If Tia rounds a number, x, to 3 sf and the result is 7.68. the error interval for x in the form a ≤ x < b is 7.685 ≤ x ≤ 7.684
What is error interval?The accuracy thresholds that apply when a number has been rounded or truncated are known as error intervals. In other words, they represent the range of values that a number might have taken had it not been rounded off or truncated.
To do this, we consider the smallest and largest numbers that could be rounded or truncated to a value while maintaining a certain level of accuracy.
We know that if this digit is smaller than 5, then we round down.
Then the largest number that can be rounded down to 7.68 is:
7.684
Now we want to find the smallest number that can be rounded up to 7.68
We know that if the next digit is 5 or bigger, then we round up.
Then the number 7.685 is rounded up to 7.68
Then the error interval is:
7.685 ≤ x ≤ 7.684
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simplyfy 5x-2x
How?!
Answers
Answer: 3x
Step-by-step explanation:
5x-2x=
5*x-2*x=
x(5-2)=
x*3=3x
Answer:3x
Step-by-step explanation:
combine like terms
5x-2x
2x is a negative
so 5-2=3
so in conclusion 3x
its takes 8 lemons and 18 cups of water to make lemonade. You have one lemon. How many water do you need to make lemonade?
Answers
How many cups of water do you need to make lemonade? 9/4 cups
How is the number of cups calculated?
Given:
8 lemons need =18 cups of water
1 lemon needs= x cups of water
By cross- multiplication method,
[tex]\frac{8}{1} =\frac{18}{x}[/tex]
8x = 18
x = 18/8
= 9/4 cups of water is needed to make lemonade
What is the cross- multiplication method?
In the cross multiplication method, we multiply the numerator of one fraction by its denominator and the first term's denominator by its numerator. We employ the cross multiplication approach to locate the answers to two linear equations.Cross-multiplication can be used to compare unlike fractions.To learn more about cross- multiplication method, refer:
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5(22 − 9 · 2) − 2( 3 · 2 + 4) + 7?
Answers
Answer:
Here is your answer So I did the Step for you and By the way I'm from South Africa
Answer: 7
Step-by-step explanation:
5*⁵(22-²9*¹2)-⁷2*⁶(3*³2+⁴4)+⁸7=7
1)9*2=18
2)22-18=4
3)3*2=6
4)6+4=10
5)5*4=20
6)2*10=20
7)20-20=0
8)0+7=7
please help
with answer
Answers
Answer:
-12 is the answer
Step-by-step explanation:
Substitute 1/4 for a and 6 for b in the equation
-8ab
-8(1/4)(6) Multiply
-8(1.5) Multiply
-12
prediction of the mean value of the dependent variable y for values of the independent variables x 1, x 2, . . . , x q that are outside the experimental range is called
Answers
Prediction of the mean value of the dependent variable y for values of the independent variables x 1, x 2, . . . , x q that are outside the experimental range is called extrapolation of data.
What is extrapolation of data?In statistics and mathematics, especially in the branch of data-science it is quite common to use a range of values from a parameter to predict the values of the dependent variable.
One of the most common applications of this is regression equations, when pairs of one of the independent variables with the dependent variable are used to predict the dependent variable.
In the case of this problem, we want to predict the dependent variable, but with values that are outside the experimental range, hence we extrapolate the data inside the experimental range for values that are outside the experimental range.
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urgent pls help!!!!
Answers
The number that makes the mixed fraction equation true is -1.
What number makes the equation true?The number that makes the equation true is calculated by applying the following formula as follows;
The given equation;
-7 ¹/₂ + ? = - 8 ¹/₂
The solution of the equation is calculated as follows;
Convert each mixed fraction into improper fraction;
-7 ¹/₂ = -15/2
-8 ¹/₂ = -17/2
-15/2 + ? = -17/2
Collect the similar terms together as follows;
? = -17/2 + 15/2
? = (-17 + 15) / 2
? = -2/2
? = - 1
Thus, the number that makes the equation true is -1.
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WILL GIVE BRAINLIEST
Write an equation of the parabola that passes through the points (1, – 9), (0, – 8), and (2, -8).
Answers
Answer: y = x^2 - 2x - 8
Step-by-step explanation:
Find the percent change. State whether it is an increase or decrease. Round to the nearest tenth of a percent.
From 68 to 63
Answers
The percentage increase is 7.9 %.
The given numbers are 68 and 63.
What is the percent change?Percentage change is the difference coming after subtracting the old value from the new value and then divide by the old value and the final answer will be multiplied by 100 to show it as a percentage.
Here, old value = 63 and new value = 68
Difference = 68-63 =5
Percentage increase = Difference of old value and new value ÷ old value
= 5/63 × 100
= 0.0793 × 100
= 7.93 %
≈ 7.9 %
Therefore, the percentage increase is 7.9 %.
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In the diagram below of triangle DEF, G is a midpoint of D E and H is a midpointof EF. If MZGHE = x + 52, and mZDFH = 96 – 102, what is the measureof ZDFH?
Answers
According to the given figure, angles GHE and DFH are corresponding angles, which are equal because GH and DF are parallels. So, we can express the following
[tex]m\angle GHE=m\angle DFH[/tex]Replacing the given expressions, we have
[tex]x+52=96-10x[/tex]Let's solve for x
[tex]\begin{gathered} x+10x=96-52 \\ 11x=44 \\ x=\frac{44}{11} \\ x=4 \end{gathered}[/tex]Then, we find the measure of the angle DFH
[tex]\begin{gathered} m\angle DFH=96-10x=96-10\cdot4=96-40 \\ m\angle DFH=56 \end{gathered}[/tex]Hence, the angle DFH measures 56°.How to solve? 14x(4x + y)
Answers
Answer:
| 56x² + 14xy
Step-by-step explanation:
14x(4x + y)
Apply the Distributive Property
14x x 4x + 14xy
Multiply the monomials
56x² + 14xy
Apply the distributive property on 4x + y, distributing 14x.
14x(4x + y)
(14x x 4x) + (14x x y)
56x + 14xy