Answer: [tex]25.5 m^{3}[/tex]
Step-by-step explanation:
If the volume of a sphere is
[tex]V=\frac{4}{3} \pi r^{3}[/tex]
Where [tex]r=2.3 m[/tex] is the radius
The volume of a hemisphere is half the volume of the total sphere:
[tex]V_{hemisphere}=\frac{V}{2}=\frac{\frac{4}{3} \pi r^{3}}{2}[/tex]
[tex]V_{hemisphere}=\frac{2}{3} \pi r^{3}[/tex]
Solving this equation:
[tex]V_{hemisphere}=\frac{2}{3} \pi (2.3 m)^{3}[/tex]
Finally:
[tex]V_{hemisphere}=25.48m^{3} \approx 25.5 m^{3}[/tex]
The volume is approximately 12.8 cubic meters.
To find the volume of a hemisphere, we can use the formula for the volume of a sphere and then take half of that volume.
The formula for the volume of a sphere is:
V = (4/3)πr³
Since we only need the volume of a hemisphere, we'll divide by 2:
V = (1/2) * (4/3)πr³
Given the radius (r) is 2.3 meters, we substitute the value into the formula:
V = (1/2) * (4/3)π (2.3)³
First, calculate the cube of the radius:
2.33 = 2.3 * 2.3 * 2.3 = 12.167
Next, plug this back into the formula:
V = (1/2) * (4/3)π * 12.167
Then, calculate the constant part of this equation:
(4/3)π ≈ 4.18879
So:
V = (1/2) * 4.18879 * 12.167 = 25.5288
Finally, divide by 2:
V ≈ 12.7644
Rounding to the nearest tenth, the volume of the hemisphere is 12.8 cubic meters.
simplify ( 1/2 x− 3/8 )÷ 1/3 + 4/7 (5− 1/4 x)
Answer:
19x/14 + 97/56
Step-by-step explanation:
The following diagram shows that the state of Nevada is shaped somewhat like a trapezoid. Which measurement is the approximate area of the state of Nevada 320 miles, 200 miles, and 480 miles?
The area of Nevada, based on map measurements converted to actual miles using the map's scale, is calculated to be approximately 156,800 square miles.
Explanation:The question relates to finding the area of the state of Nevada using its scaled measurements from a map. Given that the scale on the map is 1/2" to 20 miles, and the physical distances measured on the map are 8" wide and 12.25" long, we need to convert these measurements into actual miles before calculating the area. To do this conversion, we set up a proportion based on the scale given:
0.5 inch/20 miles = 12.25 inches/x milesBy cross-multiplying, we find that x, the actual length in miles, is approximately 490 miles. Having converted both the width (8" which is equivalent to 320 miles) and the length, we can now calculate the area of the trapezoid that represents Nevada. Assuming the shape is close to rectangular for simplicity, the area would be width × length, or:
Area = 320 miles × 490 miles = 156,800 square miles.
5. Ms. Steinle can grade 30 tests in 75 minutes. How many tests can she get done during her 50-minute prep
period?
Answer: 20 tests
Step-by-step explanation: She does every test in 2 1/2 mins. So she can do 20 in 50 mins.
The length of a rectangle is 2 feet more than the width. If it’s perimeter is 40 feet, find the length and width
Answer:
w=9 feet
l=11 feet
Step-by-step explanation:
Let the length of the rectangle be l and width be w
Condition 1:
l=2+w --------(I)
Condition 2:
2l+2w=40--------(2)
Putting eq (1) in (2)
2(2+w)+2w=40
4+2w+2w=40
4+4w=40
4w=40-4
4w=36
Dividing both sides by 4
w=9
Now
Putting w=9 in eq (1)
l=2+9
l=11
1/6 / 1 2/3 divide fraction to simplest form
Answer:
1/10
Step-by-step explanation:
1/6 / 1 2/3
Convert 1 2/3 to 5/3.
1/6 / 5/3
1/6 x 3/5
3/30 or 1/10
The result of the division of 1/6 by 1 2/3 can be found by first converting 1 2/3 to an improper fraction, then taking the reciprocal of this fraction and multiplying it by 1/6. This gives the result as 1/10.
Explanation:To solve this fraction division problem, we first need to convert the mixed number 1 2/3 to an improper fraction. A mixed number like 1 2/3 means one plus 2/3, and it can be converted to an improper fraction by multiplying the whole number by the denominator and adding the numerator. For 1 2/3, this means: (1*3 + 2)/3 = 5/3.
Now, we have the problem 1/6 / 5/3. In fraction division, we can replace the division with multiplication by the reciprocal of the second fraction. The reciprocal of a fraction is created by switching the numerator and the denominator. So, the reciprocal of 5/3 is 3/5.
Our equation 1/6 / 5/3 then becomes 1/6 * 3/5 = 3/30 = 1/10 when simplified. Hence, the result of 1/6 divided by 1 2/3 in its simplest form is 1/10.
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Yesterday 5/7 of the 49 students in a contest gave their speeches. How many students gave their speeches? Write your Answer in simplest form.
Answer:
35
Step-by-step explanation:
given total number of students = 49
fraction of students that gave speeches = 5/7
number of students that gave speeches
= (5/7) x 49
= (5 x 49) / 7
= 245/7
= 35
Answer:35 students have their speeches
Step-by-step explanation:
1/7 of 49 is 7, so if it is 5/7 of the students multiply 5x7
Answer the question below. Type your response in the space provided.
What is the answer?
12 X 4 [1 over 2]
Answer:54
Step-by-step explanation:
(12 x 4) = 48
(12 x .5) = 6
48 + 6 = 54
What is the value of the expression 22 + 62 ÷ 22? 10 13 16 36
Answer:10, hope it helps!! :)
Step-by-step explanation:
22 + 62 ÷ 22=
4 + 36 ÷ 4=10
whats the answer for
2×(9×4-35)+27=
Answer:
Step-by-step explanation: 2× (9×4-35) +27
Using BODMAS
= 2× (36-35)+27
=2×(1) + 27
=2 + 27
=29
I do not get how to do this problem
Answer:
Cross multiply
Step-by-step explanation:
[tex]\frac{2x+1}{3}\geq 5\\\\ 2x+1\geq 15\\2x\geq 15-1\\2x\geq 14\\\frac{2x}{2}\geq \frac{14}{2}\\ x\geq \frac{(2)(7)}{2}\\ x\geq 7[/tex]
a sequence starts 1 4 9 16
the nth term is n squared
use this fact to find the nth term of the following sequences
2 5 10 17
2 8 18 32
Answer:
See the attached image for the answers and the working out.
Step-by-step explanation:
The nth term of the sequences 2, 5, 10, 17... and 2, 8, 18, 32... are n² + 1 and 2n² respectively.
What are sequences?Sequences are a group of numbers written in a specific order such that the nth term of the sequence can be determined using some logic or formula.
We can find the nth term of the given sequences as follows:It is given that the nth term of the sequence 1, 4, 9, 16... is n squared.
We can find the nth term of the sequences 2, 5, 10, 17... as shown below:2, 5, 10, 17...
1² + 1, 2² + 1, 3² + 1, 4² + 1...
This is of the form n² + 1. The nth term can be found using the formula n² + 1.
We can find the nth term of the sequences 2, 8, 18, 32... as shown below:2, 8, 18, 32...
2×1², 2×2², 2×3², 2×4²...
This is of the form 2n². The nth term can be found using the formula 2n².
Therefore, we have found that the nth term of the sequences 2, 5, 10, 17... and 2, 8, 18, 32... are n² + 1 and 2n² respectively.
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Given: x is an integer. Conjecture: -x is negative. Counterexample:
Using zero as a counterexample, it disproves the conjecture '-x is negative', because when x=0, -x (which becomes -0) equals 0, not negative.
Explanation:A counterexample is an example that disproves a statement or proposition. In this case, we are given the conjecture '-x is negative'. If x is an integer, it can be positive, negative, or zero. To counter this statement, we can use zero as a counterexample. When x=0, -x (which becomes -0) is not negative but equals to 0. This proves that the original conjecture is not always correct, as it can have exceptions.
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The sum of the least and greatest of 3
consecutive integers is 60. What are the
values of the 3 integers?
Answer:
Step-by-step explanation:
The the 3 consecutive numbers be
X, X + 1, X + 2
: X + X + 2 = 60
2X = 60 - 2
2X = 58
X = 58/2
X = 29
THE NUMBERS ARE 29, 30 AND 31
You roll a six-sided die. How likely is it that you roll a number less than 6?
A) certain
B) likely
C) unlikely
D) impossible
Answer:
b
Step-by-step explanation:
Which option gives f(x) = x² - 4x - 12 rewritten in vertex form as well as the function's correct axis of symmetry?
f(x) = (x -2)² - 16, x = -16
f(x) = (x + 2)(x - 6), x = 6
f(x) = (x + 2)(x - 6), x = -2
f(x) = (x - 2)² - 16, x = 2
Answer:
Part 1) [tex]f(x)=(x-2)^{2}-16[/tex]
Part 2) The function's correct axis of symmetry is x=2
Option f(x) = (x - 2)² - 16, x = 2
Step-by-step explanation:
we have
[tex]f(x)=x^{2} -4x-12[/tex]
This is a vertical parabola open upward
The vertex is the minimum
Part 1) Convert to vertex form
Complete the square. Remember to balance the equation by adding the same constants to each side.
[tex]f(x)=(x^{2} -4x+2^2)-12-2^2[/tex]
[tex]f(x)=(x^{2} -4x+4)-16[/tex]
Rewrite as perfect squares
[tex]f(x)=(x-2)^{2}-16[/tex] ----> function in vertex form
Te vertex is the point (2,-16)
Part 2) Find the axis of symmetry
we know that
The equation of the axis of symmetry of a vertical parabola is equal to the x-coordinate of the vertex
The vertex is the point (2,-16)
therefore
The function's correct axis of symmetry is x=2
Final answer:
The function f(x) = x² - 4x - 12 rewritten in vertex form is f(x) = (x - 2)² - 16, and the axis of symmetry for this function is x = 2.
Explanation:
To rewrite the function f(x) = x² - 4x - 12 in vertex form, we need to complete the square. This involves the following steps:
Factor out the coefficient of the x² term, if it is not 1 (which it is in this case).Rearrange the equation to isolate the x-terms: x² - 4x.Find the number that completes the square for x² - 4x, which is the square of half of the coefficient of x. This number is (-4/2)² = 4.Add and subtract the determined number inside the brackets: (x² - 4x + 4) - 4.Rewrite the function in vertex form: f(x) = (x - 2)² - 16.The axis of symmetry for a parabola in the form (x - h)² is always x = h, which in this case is x = 2.
Therefore, the correct answer is f(x) = (x - 2)² - 16, x = 2.
PLZ answer this question correctly
What combination equals 12345
There are 120 combination in 12345.
What is Combination?A combination is a technique to determines the number of possible arrangements in a collection of items where the order of the selection does not matter.
Given that;
To find number of combination in 12345.
Since, There 5 digits in the given number.
Hence, Possible combinations are,
⇒ 5!
⇒ 5 × 4 × 3 × 2 × 1
⇒ 120
Thus, There are 120 possible combination in 12345.
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Complete question is,
How many combinations with 12345 without repeating the numbers?
What is the slope of a line that is parallel to the line shown on the graph?
−4
4
Answer:
C (1/4)
Step-by-step explanation:
Answer:
C 1/4
Step-by-step explanation:
If 3 (x+6)= 39, Then x =
The value of x = 7
What are linear equalities in one variable?
The linear equation in one variable is an equation that is expressed within the form of ax+b = zero, where a and b are integers, and x is a variable and has only one answer.
Conclusion: For example, 2x+3=8 is a linear equation having a single variable in it. therefore, this equation has only one solution, which is x = 5/2.
3 (x+6)= 39
3x + 18 = 39
3x = 39 - 18
3x = 21
x = 21/3
x = 7
The above question is an example of linear equalities in one variable.
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Simplify the expressions and evaluate for (i) y = -2, (ii) y = 3.
3y (2y-7) - 3 (y - 4) - 63
Simplified expression is 6y² - 24y - 51. Value for y=-2 is 21 and value for y=3 is -69.
Step-by-step explanation:
Step 1: Given expression is 3y(2y-7) - 3(y - 4) - 63. Simplify it.⇒ 6y² - 21y - 3y + 12 - 63
⇒ 6y² - 24y - 51
Step 2: Find value of the expression for y = -2⇒ 6y² - 24y - 51 = 6(-2)² - 24(-2) - 51 = 24 + 48 - 51 = 21
Step 3: Find value of the expression for y = 3⇒ ⇒ 6y² - 24y - 51 = 6(3)² - 24(3) - 51 = 54 - 72 - 51 = -69
Refer to the rectangle below. The length of the rectangle is x + 12. The width of the rectangle is x + 3.
Please determine the area of the rectangle.
Answer:x^2 +15x +36
Step-by-step explanation:
Iris's Botanical Garden produced flowers throughout the year. A graph demonstrating how many flowers she produced over a 11-month period is shown:
A: The domain represents a 180-month period of flower production.
B: The domain represents a 11-month period of flower production.
C: The domain represents the total number of flowers produced each month.
D: The domain represents the total number of flowers produced in 11 months.
Answer:
B: The domain represents a 11-month period of flower production.
Step-by-step explanation:
The domain of a Function
It's the set of all the values a function can take in its independent variable. The independent variable (usually x) is represented as the horizontal axis of a graph, where we can know the interval of values considered for values of the function.
In the provided graph, we can see the horizontal axis is labeled 'Months' and its values range from 1 to 11. The vertical axis is labeled "Number of flowers produced" which will be the Range of the function.
From the options presented, we can discard the C and D because they are related to the number of flowers produced, which is not the domain of the function. The option A talks about the months of production but the months range up to 180. Option B is the correct choice.
B: The domain represents a 11-month period of flower production.
Which three statements about the expression x² + 7x + 6 are true? Can you choose which are correct please?
x is a variable in the expression.
2 is the coefficient of one term of the expression.
The expression has three terms.
6 is a factor of the expression.
7 is the coefficient of one term of the expression.
Answer:
A, C, and E are correct
Step-by-step explanation:
B can't be right because 2 is an exponent, not a coefficient
D can't be right because 6 doesn't go into 7
Hope this helped!
-8-w/9 + 4s use w=36 and s equal 5
Answer:
ight man that answer is 43 your welocome smart aint i
Step-by-step explanation:
Answer:
answers: 8
Step-by-step explanation:
PLEASE HELP QUICK I CANT FAIL THIS TEST
Simplify: 2x2(4x3 - 3x2 + 6x).
A) 6x5 - 5x4 + 8x3
B) 6x6 - 5x4 + 8x2
C) 8x5 - 3x4 + 12x2
D) 8x5 - 6x4 + 12x3
Answer:
24+24x I believe is the answer. Good luck on your test :)
Answer:
D
Step-by-step explanation:
2x2(4x3 - 3x2 + 6x)
= 2x²(4x³ - 3x² + 6x)
= 8x^5 - 6x⁴+ 12x³
Can someone please help me find x
Answer:
x = 17
Step-by-step explanation:
Vertical angles are congruent, so ...
5x° = 85°
x = 85°/5° . . . . . . divide by the coefficient of x
x = 17
(0.3x + 64) degrees (0.1 + 32) degrees find the value of x
Answer:
[tex]x=-15[/tex]
Step-by-step explanation:
Complete question : In a right triangle other two angles are [tex](0.3x+64)\textdegree\ and\ (0.1x+32)\textdegree[/tex] find the value of [tex]x[/tex].
In a right angle the third angle is [tex]90\textdegree[/tex]
we know that
Sum of angle in a triangle [tex]=180\textdegree[/tex]
[tex](0.3x+64)+(0.1x+32)+90=180\\\\0.3x+64+0.1x+32+90=180\\\\0.4x+96+90=180\\\\0.4x+186=180\\\\0.4x=-6\\\\[/tex]
Dividing [tex]0.4[/tex] both sides
[tex]\frac{0.4x}{0.4}=\frac{-6}{0.4}\\\\x=\frac{-60}{4}\\\\x=-15[/tex]
1/4(10-7y)=15
Solve for y
Answer:
1/3 (39.09)=17 thats all thanks
Let’s consider all possible rectangles with the same area of 30 square inches.
Please note: the length of the sides are whole numbers.
Let the base of such a rectangle be x and the height be y. How would y depend on x?
Answer:
Given:
Area of the rectangle = 30 square inches.
length of the sides are whole numbers.
Solution:
The base of the rectangle is x and the height is y
We know that Area of the rectangle = [tex]length \times breadth[/tex]
That is
30 = [tex]x \times y[/tex]
The possible values of length and breadth
length x : 1 2 3 5 6 10 15 30
breath y: 30 15 10 6 5 3 2 1
Now
30 = xy
[tex]y = \frac{30}{x}[/tex]
when y increases x decreases and vice versa
One leg of a right triangle has a length of 3. The other sides have lengths that are consecutive integers. Find these lengths.
Answer:
Therefore other two sides of the triangle are 4 and 5.
Step-by-step explanation:
Given one leg of a right triangle has a length of 3
Let other sides of the triangle be x and x+1 [ since they are consecutive]
According to the problem,
3²+x²=(x+1)²
⇔9 + x²=x²+2x+1
⇔2x+1=9
⇔2x=9-1
⇔2x=8
⇔x=4
Therefore other two sides of the triangle are 4 and 5.
To find the lengths of the other two sides of the right triangle with one leg of length 3, we can use the Pythagorean theorem. The lengths of the other two sides are 4 and 5.
Explanation:To find the lengths of the other two sides of the right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Since one leg has a length of 3, let's call the lengths of the other two sides x and x+1. We can set up the equation:
3^2 + x^2 = (x+1)^2
Simplifying the equation:
9 + x^2 = x^2 + 2x + 1
Subtracting x^2 from both sides:
9 = 2x + 1
Subtracting 1 from both sides:
8 = 2x
Dividing both sides by 2:
4 = x
So, the lengths of the other two sides are 4 and 5.
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