Answer:
Let s be the length of a side of the cube, then its surface area is given by 6s^2. We know that the surface area of the cube is 486 in^2, so we can set up the equation:
6s^2 = 486
Solving for s, we get:
s^2 = 81
s = 9
Therefore, the length of a side of the cube is 9 in. The radius of the inscribed sphere is half the length of a side, so it is r = 4.5 in. The volume inside the cube but outside of the sphere is equal to the volume of the cube minus the volume of the sphere:
V = s^3 - (4/3)πr^3
V = 9^3 - (4/3)π(4.5)^3
V ≈ 328.8 in^3
Rounding to the nearest tenth, the volume inside the cube but outside of the inscribed sphere is approximately 328.8 in^3.
an elephant skeleton has about
345 bones. at Birth a human skeleton has about 3/5 x 345 bones which has more bones an elephant or a human? explain.
Answer: elephant
Step-by-step explanation:
3/5 x 345 = 207
345 > 207
Which components are a possible representation of vector u if ||-4u|| ≈ 14.42?
Answer: <3, -2>
One possible representation of such a vector is u = (3, 2), which has a magnitude of approximately 3.605 and makes an angle of about 33.69 degrees with the positive x-axis in the standard Cartesian coordinate system.
Firstly, it is important to understand the meaning of the double vertical bars (|| ||), which denote the magnitude or length of a vector. For instance, if we have a vector
=> v = (2, 3),
then its magnitude can be computed as
=> ||v|| = √(2² + 3²) = √13.
Similarly, if we have a vector u = (u₁, u₂), then its magnitude can be expressed as
=> ||u|| = √(u₁² + u₂²).
The given condition
=> ||-4u|| ≈ 14.42
can be rewritten as
=> 4||u|| ≈ 14.42
=> ||u|| ≈ 3.605.
This means that the magnitude of vector u is approximately equal to 3.605.
Therefore, to obtain a possible representation of vector u with a magnitude of approximately 3.605, we can solve the following system of equations:
||u|| = √(u₁² + u₂²) ≈ 3.605
θ = tan⁻¹(u₂/u₁)
Note that there are infinitely many solutions to this system, since the direction of u is not uniquely determined.
However, one possible solution is u = (3, 2), which has a magnitude of
=> ||u|| = √(3² + 2²) = √13 ≈ 3.605
and makes an angle of
=> θ = tan⁻¹(2/3) ≈ 33.69 degrees
with the positive x-axis.
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Find the value of x if log6 36 = x
Answer:
The answer for x is 2
Step-by-step explanation:
write the equation
log6(36)= x
rewrite the equation as, x = log6(36) [ formula used; logb x=y; x=y^b]
so, x^6=36
x^6=2^6[ 36=2^6=2*2*2*2*2*2]
thus, x=2
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what is the probability that either event will occur?
Answer:
0.75
Step-by-step explanation:
P(A) = 9+9 = 18
P(B) = 9+9 = 18
P(A and B) = 9
P ( A or B) = 18+18-9 = 27
Probability = ans / total = 27/36 = 0.75
The probability that either event will occur is given as follows:
P(A or B) = 0.75.
We have,
The figure about the possible outcomes are shown in image.
Now, The formula used to calculate the probability is given as follows:
P(A or B) = P(A) + P(B) - P(A and B).
The total number of events from the Venn's diagram is given as follows:
4 x 9 = 36.
Hence the probability of each outcome is given as follows:
P(A) = (9 + 9)/36 = 0.5.
P(B) = (9 + 9)/36 = 0.5.
P(A and B) = 9/36 = 0.25.
Hence the or probability is given as follows:
P(A or B) = P(A) + P(B) - P(A and B).
P(A or B) = 0.5 + 0.5 - 0.25
P(A or B) = 0.75.
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Let r be a primitive root of the odd prime p.
Prove: if p ≡ 1 (mod 4), then -r is also a primitive root of p
As we have proved that if p ≡ 1 (mod 4), then -r is also a primitive root of p.
Since r is a primitive root of p, we know that every non-zero integer modulo p can be written as a power of r. That is, for any integer a with gcd(a, p) = 1, there exists an integer k such that a ≡ rˣ (mod p). This follows from the fact that the order of the element r modulo p is φ(p) = p-1, where φ denotes the Euler totient function.
Now, let us consider the case where p ≡ 1 (mod 4). This means that there exists an integer x such that p = 4x + 1. We want to show that -r is also a primitive root of p.
To do this, we first observe that (-1)² ≡ 1 (mod p) since p is an odd prime. Therefore, (-1)^(4x) ≡ 1 (mod p), which implies that (-1)²ˣ ≡ 1 (mod p).
Now, if we can show that (-1)ˣ = -1, then we will have (-1)²ˣ = (-1)ˣ*(-1)ˣ = (-1)*(-1) = 1 (mod p), which will allow us to prove that -r is also a primitive root of p.
To see that (-1)ˣ = -1, we use the fact that p ≡ 1 (mod 4) and the properties of quadratic residues. Specifically, we know that -1 is a quadratic non-residue modulo p, since if -1 ≡ a² (mod p) for some integer a, then we would have
=> [tex](-1)^{((p-1)/2) }[/tex] ≡ [tex]a^{(p-1) }[/tex]≡ 1 (mod p),
which contradicts the fact that
=> [tex](-1)^{((p-1)/2) }[/tex]= -1.
Therefore, there exists an integer b such that b² ≡ -1 (mod p).
Now, consider the product brˣ. We claim that brˣ is a primitive root of p. To see this, note that for any integer a with gcd(a, p) = 1, we can write a ≡ rˣ (mod p) for some integer k. Then, we have:
(a*brˣ)² = a² * b² * r²ˣ ≡ r²ˣ * (-1) ≡ -r²ˣ (mod p)
Since r is a primitive root of p, we know that rˣ and r²ˣ cover all the non-zero residue classes modulo p. Therefore, we can choose k such that r²ˣ ≡ -1 (mod p), which implies that (a*brˣ)² ≡ -1 (mod p).
Since a was arbitrary, this shows that brˣ is a quadratic non-residue modulo p, and therefore a primitive root of p.
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Can someone help me
Answer:
Y = -½x + 3/2
Y = -3x + 5
Y = 1/4x - 3¼
Step-by-step explanation:
Parallel implies they have the same gradient
Perpendicular implies the gradient is a negative reciprocal of the other.
Select the true statement. A. 5 tons> 10, 500 pounds B. ton + ton > 3,800 pounds C. 2 tons = 64, 000 ounces D. 1 tons-ton < 24,000 ounces
I think it is C.
C. 2 tons = 64, 000 ounces
The net below shows a square pyramid. What is the lateral surface area?
The lateral surface area of the pyramid is 112 sq. in.
The correct answer is an option (B)
From the attached figure of the net of a square pyramid, we can observe that the side length of the square base is 8 in and height of the lateral triangular face is 7 in.
The lateral surface area of the pyramid is equal to the area of the four triangular faces of the pyramid.
Using the formula of the area of triangle, the lateral surface area would be,
A = 4 × (1/2 × base × height)
A = 4 × (1/2 × 8 × 7)
A = 4 × (4 × 7)
A = 4 × 28
A = 112 sq. in.
This is the required lateral surface area.
The correct answer is an option (B) 112 in²
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Find the complete question below.
The net below shows a square pyramid. What is the lateral surface area? A. 176 in^2
B. 112 in^2
C. 64 in^2
D. 210 in^2
what is another name for line Q R
Answer:
line RQ
Step-by-step explanation:
The points on a line can be flipped when naming. For example, line AB is the same as line BA.
HELP PLEASE! Which reason is the justification for the statement that angle A ≅ angle B?
A) Vertical angles are congruent.
B) Linear angles are equal.
C) Intersecting lines form opposing angles.
D) Lines intersect at one point.
Please help 20 points !!!!!!
Based on the information, the regular polygon has 35 sides.
How to calculate the number of sidesIn order to determine the number of sides that a regular polygon has if the sum of the interior angles is given, you can use the formula:
sum of interior angles = (n - 2) x 180°
solve for n, you can rearrange the formula as:
n = (sum of interior angles ÷ 180°) + 2
Then, plug in the given sum of interior angles and solve for n.
b. Using the formula above, we can find the number of sides of the regular polygon with a sum of interior angles of 6,300°:
n = (6300° ÷ 180°) + 2
n = 35
The regular polygon has 35 sides.
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What type of graph would have the title, "Monthly Company Profit for the Year?"
line graph
pictograph
bar graph
line plot
The type of graph would have the title, "Monthly Company Profit for the Year?" is line graph (option a).
Using a line graph to display monthly company profits allows for the visualization of the overall trend and any fluctuations or changes in the profits over the year. It also allows for easy comparison of the profits from one month to another, as well as identifying which months were particularly profitable or unprofitable.
In mathematical terms, a line graph can be defined as a graph in which the data points are plotted as individual points, and a line is drawn to connect the points.
The line represents a mathematical function that can be used to model the relationship between the variables being plotted. In the case of the monthly company profits, the function would model the relationship between time and profit.
Hence the correct option (a).
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How many commutes are exactly 68 minutes
Answer:
three
Step-by-step explanation:
stem. is the tens place and the leaf is the. ones place
so you want to find 68 so you look in the stem column and look for six
in the row there are 6 numbers which mean:
60, 61, 67, 68, 68, 68
as you can see there is three 68 there for the answer ths 3
Suppose the length of a certain rectangle is 6 meters less than four times its width. The perimeter of the rectangle is 78 meters. Find the length and width of the rectangle.
Answer:
Let's start by using the formula for the perimeter of a rectangle, which is:
P = 2L + 2W
where P is the perimeter, L is the length, and W is the width.
We're given that the perimeter is 78 meters, so we can write:
78 = 2L + 2W
Simplifying this equation, we get:
39 = L + W
We're also given that the length is 6 meters less than four times the width, so we can write:
L = 4W - 6
Now we can substitute this expression for L into the equation we got earlier:
39 = (4W - 6) + W
Simplifying this equation, we get:
39 = 5W - 6
Adding 6 to both sides, we get:
45 = 5W
Dividing both sides by 5, we get:
W = 9
So the width of the rectangle is 9 meters. We can use this value to find the length:
L = 4W - 6 = 4(9) - 6 = 30
So the length of the rectangle is 30 meters.
Hi school basketball team is selling donuts to raise money for their new uniforms. The team makes a goal to sell at least $1000 in donuts. They are selling half a dozen box of donuts for eight dollars and a full dozen box of donuts for $12. They write the inequality 8x+12y>_ 1000 to determine how many boxes they need to sell, where X is the number of half dozen boxes, and why is the number for dozen boxes they sell. Which of the following solutions are viable in terms of the given context? Select all that apply A. (0,83) B. (32,70) C. (60,50) D. (14,74) E. (6,100) F.(-50,150)
The team can sell 50 half dozen boxes and 50 full dozen boxes to raise at least $1000.
We can derive an inequality from the problem statement which is:
8X + 12Y ≥ 1000
This inequality represents the amount of money the basketball team needs to raise by selling donuts.
X is the number of half dozen boxes sold
Y is the number of full dozen boxes sold.
To find a solution in terms of the given context, we can plug in different values for X and Y that satisfy the inequality. For example:
If the team sells 50 half dozen boxes and 50 full dozen boxes, they will make:
8(50) + 12(50) = $400 + $600 = $1000
So this is a valid solution that meets the fundraising goal.
If the team sells 100 half dozen boxes and 0 full dozen boxes, they will make:
8(100) + 12(0) = $800
This is not enough to meet the fundraising goal, so it is not a valid solution.
If the team sells 0 half dozen boxes and 100 full dozen boxes, they will make:
8(0) + 12(100) = $1200
This is more than the fundraising goal, so it is a valid solution, but the team may not want to sell so many full dozen boxes.
Therefore, one solution in terms of the given context is that the team can sell 50 half dozen boxes and 50 full dozen boxes to raise at least $1000.
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Helen is building a rectangular garden in her backyard and she wants to have a fence around it.The perimeter of her garden is 20 yards. She is buying wood fence panels that cost $2 per foot. How many feet of fence panels does she need
Based on the calculations, Helen needs to buy 60 feet of fence panels for her rectangular garden in the backyard
How many feet of fence panels does she needFrom the question, we have the following parameters that can be used in our computation:
The perimeter of her garden is 20 yards. She is buying wood fence panels that cost $2 per footThis means that
Perimeter = 20 yards
By metrric unit of conversion, we have
1 yard = 3 feet
So, we have
Perimeter = 20 * 3 feet
Evaluate
Perimeter = 60 feet
Hence, she needs to buy 60 feet of fence panels
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A dilation is a transformation in which the _____, but not the shape, of a geometric figure is changed.
what is 1,908,890,556 times 1,092,847
Answer: 2.1468 times 10^15
Step-by-step explanation: you times them together
The perimeter of the pentagon below is 64 units. Find the length of side AB
Step-by-step explanation:
If this is a regular pentagon , it has FIVE sides of equal length
64 ÷ 5 = 12.8 units = AB
find the area of a regular pentagon with radius 22
PLEASE HELP! ITS NOT HARD I JUST CANT COPY PASTE IT
The inequality that can be used to find the number of sales she needs to make is D. 100 + 15x ≥ 500.
How to find the inequality ?In this scenario, Aaliyah wants to earn at least $500. The fixed amount she earns is $100, and she earns $15 for each sale.
Therefore, the total amount she earns can be represented as 100 + 15x, where x is the number of sales she makes. To ensure that she earns at least $500, we can set up the inequality 100 + 15 x ≥ 500.
With this inequality, we can see that the sum of the $ 100 base salary and the $ 15 per sale would add up to a sum that is either $ 500 or above.
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if 1 cm is 20 km then how many km equals 9 cm
Simplify the expression using properties of operations.
7 1/3t−(10 2/3t−6)
Answer:
Step-by-step explanation:
Given expression is 7 1/3t-(10 2/3t-6)
Now, convert the proper fraction present in the question to improper fractions.
proper fractions are 7 1/3 and 10 2/3
so, 7 1/3 =(7*3+1)/3 = 22/3
10 2/3 = (10*3+2)/3=32/3
= >22t/3 - (32t/3 -6)
= >22t/3 - 32t/3 +6
= >6 - 10t/3
This is the final solution.
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Solve for x.
10 cm
X
8 cm
X = = [?]°
Round to the nearest hundredth.
The value of the variable x is 51.340 degrees
How to determine the valueNote that their are six different trigonometric identities in mathematics.
These identities are;
sinecosinetangentcotangentsecantcosecantAlso, these identities have their different ratios, they are;
sin θ= opposite/hypotenuse
tan θ = opposite/adjacent
cos θ = adjacent/hypotenuse
From the information given, we have that;
Opposite = 10cm
Adjacent = 8cm
Substitute the values
tan x = 10/8
Divide the value, we have;
tan x = 1.25
Find the tangent inverse, we get;
x = 51. 340 degrees
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What measurement is equivalent to 1 2 3 1 2 3 yards?
Which of these statements is true for the Cartesian coordinate system?
A.
the values below the X-axis are negative values of x
B.
the values below the X-axis are negative values of y
C.
the values above the X-axis are negative values of x
D.
the values above the X-axis are negative values of y
E.
the values on the X-axis are positive v
The statement that is true for the Cartesian coordinate system is A. the values below the X-axis are negative values of x.
What is the Cartesian coordinate system?The Cartesian coordinate system, also called rectangular coordinate system, helps plot coordinates in a two-dimensional plane. This model contains two axes -- the x-axis (horizontal) and y-axis (vertical) -- that meet at the origin. The values beneath the x-axis represent negative y-values, not x-values as some assume.
Likewise, above the x-axis represents positive y-values, not x-values. Meanwhile, points along the x-axis aren't considered either positive or negative but rather labeled based on their distance away from the origin as per this structure's guidelines.
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Which of the following is equivalent to 2.76?
The expression that is equivalent to 2.76 is two and nineteen twenty fifths
Which of the expressions is equivalent to 2.76?The number in the question is given as 2.76
This means that we have
Number = 2.76
We can rewrite this as a mixed number.
2 + a/b
Such that:
a/b = 0.76
From the list of options, we have
two and nineteen twenty fifths = 2 + 19/25 = 2.76
This means that the correct expression is two and nineteen twenty fifths
Hence, the expression that is equivalent to 2.76 is two and nineteen twenty fifths
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Complete question
Which of the following is equivalent to 2.76?
2.76%
27.6%
two and nineteen twenty fifths
twenty five over nineteen
please help with this question
Answer:
Step-by-step explanation: Here if we put [tex]x=0[/tex] then we will get initial temperature. That is [tex]T_0=70+20=90[/tex].
The temperature will cools down [tex]70(0.8)^{10}+20=27.52(approx)[/tex].
So the final temperature after 10 minutes will be :[tex]90-27.52=62.48(approx)[/tex].
Final Answer: The temperature is 62.48 degree Celsius.
Analyze the diagram below and complete the instructions that follow.
Find cos 45°.
A 1
NI-
2
45°
B. √√√2
2
Answer:
cos(45°) = √2/2
B is correct.
Amy is going on a roadtrip with her friends and needs to save $160. If she starts saving 18% of her weekly earnings at the pool, how many whole weeks will it take her to save $160?
There are 6 whole weeks will it take her to save $160.
We have to given that;
Amy is going on a road trip with her friends and needs to save $160.
And, she starts saving 18% of her weekly earnings at the pool,
Now, Let number of weeks it take her to save $160 is, x
Hence, We get;
160 = 160 x 0.18 x t
t = 1/0.18
t = 5.55 weeks
Thus, There are 6 whole weeks will it take her to save $160.
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