The surface area of the two hemispheres combined is 100π square meters, and the volume of the two hemispheres combined is (500/3)π cubic meters.
The circumference of a great circle on a sphere is given by the formula C = 2πr, where r is the radius of the sphere.
In this case, we are given that the circumference of the great circle is 10π meters, so we can set up an equation:
10π = 2πr
Dividing both sides by 2π, we get:
r = 5
So the radius of the sphere is 5 meters.
When the sphere is cut in half, we get two equal hemispheres. The surface area of a closed hemisphere is given by the formula A = 2πr^2, where r is the radius of the hemisphere.
Since we are dealing with a radius of 5 meters, the surface area of one hemisphere is:
A = 2π(5^2) = 50π
Therefore, the surface area of the two hemispheres combined is:
2A = 2(50π) = 100π
The volume of a closed hemisphere is given by the formula V = (2/3)πr^3. Again, since we are dealing with a radius of 5 meters, the volume of one hemisphere is:
V = (2/3)π(5^3) = (2/3)π125 = (250/3)π
Therefore, the volume of the two hemispheres combined is:
2V = 2(250/3)π = (500/3)π
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Find the area of the figure.
(Sides meet at right angles.)
Answer:
22 m^2
Step-by-step explanation:
multiply the sides
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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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
What measurement is equivalent to 1 2 3 1 2 3 yards?
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.
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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find the area of a regular pentagon with radius 22
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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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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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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Use the matrices to show that matrix multiplication is associative. A=[7115], B=[14−2652], and C=⎡⎣⎢1−20⎤⎦⎥
As we have shown that matrix multiplication is associative.
Let us start by computing the products (AB) and (BC) separately. To multiply matrix A by matrix B, we need to take the dot product of each row of A with each column of B.
Simplifying the above expression, we get:
A*B = [11 -10 39] * [21 28 13]
Similarly, to multiply matrix B by matrix C, we need to take the dot product of each row of B with each column of C. Thus, the resulting matrix (B*C) will have the same number of rows as B and the same number of columns as C. Using the given matrices B and C, we have:
B*C = [1 -2 5] * [1 -2 10]
Simplifying the above expression, we get:
B*C = [39 18]
Thus, the resulting matrix (A(BC)) will have the same number of rows as A and the same number of columns as (BC). Using the given matrices A, B, and C, we have:
A*(B*C) = [7 1] * [39 18]
Simplifying the above expression, we get:
A*(B*C) = [327 489]
Now, let us compute the product ((AB)C) by multiplying the matrix (AB) with matrix C. To do this, we need to take the dot product of each row of (AB) with the only column of C. Thus, the resulting matrix ((A*B)C) will have the same number of rows as (AB) and the same number of columns as C. Using the given matrices A, B, and C, we have:
(A*B)*C = [11 -10 39] * [1 -2 10]
Simplifying the above expression, we get:
(A*B)*C = [327 489]
As we can see from the above calculations, both the products (A*(BC)) and ((AB)*C) have the same result, which is [327 489]. Therefore, we can conclude that matrix multiplication is associative.
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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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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.
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.
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 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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An expression is shown below: 3pf2 − 21p2f + 6pf − 42p2 Part A: Rewrite the expression by factoring out the greatest common factor. (4 points) Part B: Factor the entire expression completely. Show the steps of your work. (6 points)
The expression factoring out the greatest common factor is (3pf - 21p²)(f + 2).
We have the expression as
3pf² - 21p²f + 6pf - 42p²
Now, factorising the expression as
= 3pf² + 6pf - 21p²f - 42p²
= 3pf(f +2) - 21p²(f + 2)
= (3pf - 21p²)(f +2)
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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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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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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! 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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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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Simplify: x^9/11 * x^4/11Give your answer in both rational exponent form and nth root notation.
rational exponent form:
nth root notation:
The value of the index form is x¹³/11
What are index forms?Index forms are simply described as mathematical forms or expressions that are used to represent numbers or variables that are too large or too small to be written conveniently.
Some rules of index forms are;
Add the exponents of the values when multiply forms of the same basesSubtract the exponents of the values when dividing forms of same basesAdd like basesFrom the information given, we have that;
x⁹/11 × x⁴/11
Since they are of the same bases, add the exponent values
x¹³/11
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what is 1,908,890,556 times 1,092,847
Answer: 2.1468 times 10^15
Step-by-step explanation: you times them together
-
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
Find the surface area of the figure. Pentagonal prism with an apothem length of 6.9 yd, height of 4 yd and base length of 10 yd.
The required surface area of the given rectangular prism is 202 square yd.
Here, we have,
Given that,
the surface area of a rectangular prism with a base length of 9 yd, a base width of 5 yd, and a height of 4 yd is to be determined.
We have,
Surface area is defined as the measure of a region or surface is called as surface area.
Here,
The surface area of the rectangular prism is given as,
S = 2(lw + lh + wh)
S = 2 [9×5 + 5×4 + 4×9]
S = 202 square yd.
Thus, the required surface area of the given rectangular prism is 202 square yd.
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if 1 cm is 20 km then how many km equals 9 cm
Find an equation for the perpendicular bisector of the line segment whose endpoints are
(
−
5
,
−
3
)
(−5,−3) and
(
3
,
1
)
(3,1)
The solution is : equation for the perpendicular bisector of the line segment is: 7x -2y = 6
Here, we have,
The perpendicular bisector has a slope that is the opposite of the reciprocal of the slope of the segment between the two points. It must go through the midpoint of the segment.
The latter can be found by averaging the coordinates of the end points:
((-5, 6) +(9, 2))/2 = ((-5+9)/2, (6+2)/2) = (2, 4)
The difference in endpoint coordinates is ...
(Δx, Δy) = (9-(-5), 2-6) = (14, -4)
For our purpose, we're only interested in the ratio of these values, so we can divide both by the common factor of 2:
(Δx, Δy) = (7, -2)
A line perpendicular to this segment through the point (h, k) can be written as ...
Δx·x +Δy·y = Δx·h +Δy·k
7x -2y = 7(2) -2(4)
7x -2y = 6 . . . . . . . standard form equation for the perpendicular bisector
Hence, The solution is : equation for the perpendicular bisector of the line segment is: 7x -2y = 6
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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
A dilation is a transformation in which the _____, but not the shape, of a geometric figure is changed.
