Answer:
The weight of the yard waste = 1650 pounds
Step-by-step explanation:
* Lets revise the rule of the volume of the prism
- The rectangular prism has 6 rectangular faces
- Its base shaped a rectangle of dimensions length and width
- The volume of the rectangular prism = Area of its base × its height
∵ Area of the rectangle = length × width
∴ The volume of the prism = length × width × height
* Now lets solve the problem
∵ The length of the rectangular prism = 10 feet
∵ The width of it = 5.5 feet
∵ The height of it = 4 feet
∴ Its volume = 10 × 5.5 × 4 = 220 feet³
- The prism is completely full of yard waste
∴ The volume of the yard waste = the volume of the prism
∴ The volume of the yard waste = 220 feet³
- The average weighs of it is 7.5 pounds/cubic foot
∴ The weight of the yard waste = the average of weight × the volume
∴ The weight of the yard waste = 7.5 × 220 = 1650 pounds
A farmer wants to build a new grain silo. The shape of the silo is to be a cylinder with a hemisphere on top, where the radius of the hemisphere is to be the same length as the radius of the base of the cylinder. The farmer would like the height of the silo’s cylinder portion to be 3 times the diameter of the base of the cylinder. What should the radius of the silo be if the silo is to hold 22,500 cubic feet of grain?
Answer:
about 10.24 ft
Step-by-step explanation:
The formula for the volume of a cylinder is ...
V = πr²h . . . . where h is the height and r is the radius
The formula for the volume of a sphere is ...
V = (4/3)πr³ = πr²·(4/3r) . . . . equivalent to a cylinder of height 4/3r
__
We have a cylinder of height 3d = 3(2r) = 6r. It has half a sphere on top, so the equivalent height of that is (1/2)·(4/3r) = 2/3r.
Then our total volume is equivalent to a cylinder with radius r and height (6 2/3)r = (20/3)r. That is, ...
22,500 ft³ = πr²·(20/3)r = (20π/3)r³
Multiplying by the inverse of the coefficient of r³, then taking the cube root, we have ...
r = ∛(22,500·3/(20π)) ft ≈ 10.24 ft
The radius of the silo should be about 10.24 feet.
Answer:
10.24 ft
Step-by-step explanation:
RST and XYZ are equilateral triangles. The ratio of the perimeter of RST to the perimeter of XYZ is 1 to 2. the area of RST is 10.825 square inches. what is the area of XYZ
Answer:
The CORRECT answer is 97.4 in ^2
Step-by-step explanation:
Usatestprep , the other answer is wrong trust me.
This image shows a square pyramid. What is the surface area of this square pyramid?
25 ft²
100 ft²
125 ft²
200 ft²
Note: Image not drawn to scale. The figure shows a square pyramid. The slant height is shown as a dashed line perpendicular to the base edge. The length of the base edge is 10 feet. The lateral edge makes a 45 degree angle with the base edge.
Answer:
200 ft²
Step-by-step explanation:
Each face is an isosceles right triangle with a hypotenuse of length 10 ft. The area of each of those triangles is
A = 1/4·h² . . . . where the h in this formula is the hypotenuse length
So, the area of the four faces (the lateral area of the pyramid is 4 times this, or ...
A = 4·1/4·(10 ft)² = 100 ft²
Of course, the base area is simply the area of the square base, the square of its side length:
A = (10 ft)² = 100 ft²
So, the total area is the sum of the lateral area and the base area:
total area = 100 ft² +100 ft² = 200 ft²
_____
If you think about this for a little bit, you will realize the pyramid must have zero height. That is, the slant height of a face is exactly the same as the distance from the center of an edge to the center of the base. "Not drawn to scale" is a good description.
Answer:
200 [tex]ft^{2}[/tex]
Step-by-step explanation:
The function f(x) = x2 - 6x + 9 is shifted 5 units to the left to create g(x). What is
g(x)?
Answer:
g(x) = x^2 + 4x + 4
Step-by-step explanation:
In translation of functions, adding a constant to the domain values (x) of a function will move the graph to the left, while subtracting from the input of the function will move the graph to the right.
Given the function;
f(x) = x2 - 6x + 9
a shift 5 units to the left implies that we shall be adding the constant 5 to the x values of the function;
g(x) = f(x+5)
g(x) = (x+5)^2 - 6(x+5) + 9
g(x) = x^2 + 10x + 25 - 6x -30 + 9
g(x) = x^2 + 4x + 4
Choose the equation and the inequality needed to answer this question.
Trevor tutors French for $15 and hour and scoops ice cream for $10 an hour. He is going to work 15 hours this week. At least how many hours does he need to tutor to make more than $180? Let x equal the number of hours he tutors and y be the number of hours he scoops ice cream.
Options (you can pick more than one):
x + y = 15
x + y > 15
x + y < 15
15x + 10y = 180
15x + 10y > 180
15x + 10y < 180
So far all I have it the fourth option (15x + 10y = 180).
Answer:
Actually, what you said you have so far is not correct. The 2 correct answers are the 1st one (x + y = 15) and the 5th one (15x + 10y > 180)
Step-by-step explanation:
If tutoring French is x hours and scooping ice cream is y hours and he is going to work 15 hours for sure doing both, then we can add them together to get that x hours + y hours = 15 hours, or put simply: x + y = 15.
Now we are going to throw in the added fun of the money he makes doing each. The thing to realize here is that we can only add like terms. So looking at the equation above, we have x hours of tutoring and y hours of scooping, so if we want to add them, we will add those number of hours together to get the total number of hours he worked, which we know to be 15. The same goes for money. If we add money earned from tutoring to money earned from scooping, we need that to be greater than the money he wants to earn which is 180 at least. Because he wants to earn MORE than $180. we use the ">" sign. Since he earns $15 an hour tutoring, that expression is $15x; since he earns $10 an hour scooping, that expression is $10y. Now add them together (and you CAN because they are both expressions relating dollars to dollars) and set the sum > $180:
$15x + $10y > $180. That's why your answer is not correct. Use mine (with the understanding that you care about why yours is wrong and mine is correct) and you'll be fine.
what is an equation of the line containing the points (-1,5) and (3,9)
Answer:
y = x+6
Step-by-step explanation:
You can find an equation by using the 2-point form of the equation for a line:
y = (y2 -y1)/(x2 -x1)·(x -x1) +y1
Filling in the given values, we have ...
y = (9 -5)/(3 -(-1))·(x -(-1)) +5
y = (4/4)(x +1) +5 . . . . simplifying a bit
y = x +6
3) Solve each equation using the quadratic formula. Show
a. x2 – 3x – 10 = 0
Answer:
x = -2 or x = 5Step-by-step explanation:
The quadratic formula of a quadratic equation
[tex]ax^2+bx+c=0\\\\\text{If}\ b^2-4ac>0\ \text{then the equation has two solutions}\ x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]\text{If}\ b^2-4ac=0\ \text{then the equation has one solution}\ x=\dfrac{-b}{2a}[/tex]
[tex]\text{If}\ b^2-4ac<0\ \text{then the equation has no solution}[/tex]
We have:
[tex]x^2-3x-10=0\to a=1,\ b=-3,\ c=-10\\\\b^2-4ac=(-3)^2-4(1)(-10)=9+40=49>0\\\\x=\dfrac{-(-3)\pm\sqrt{49}}{2(1)}=\dfrac{3\pm7}{2}\\\\x=\dfrac{3-7}{2}=\dfrac{-4}{2}=-2\\or\\x=\dfrac{3+7}{2}=\dfrac{10}{2}=5[/tex]
A marketing firm tracks data on grocery store visits. In one study, it finds that the probability that a shopper buys bread during a visit to the grocery store is 0.70, and the probability that a shopper buys cheese is 0.20.Event A = A shopper buys bread.Event B = A shopper buys cheese.A and B are independent events if _____.
Answer:
Option B.
Step-by-step explanation:
Two events are said to be independent of each other, if the probability of one event ocurrin in not way affects the probability of the other event occurring.
The interception of two independent events P(A ∩ B) = P(A) × P(B), where:
P(A) = 0.70
P(B) = 0.20
P(A ∩ B) = P(A) × P(B) = 0.70x0.20 = 0.14
The two events are independent if the probability of buying Bread AND cheese equals: 0.14, which is Option B.
Answer:
B
Step-by-step explanation:
find the area of a regular hexagon inscribed in a circle of radius 6 cm
Answer:
C
Step-by-step explanation:
If the hexagon is regular, that means that all of its sides are the same length, all of its interior angles are equal, as are the central angles formed by the triangles within in it. It is one of these triangles that we are concerned about.
If the regular hexagon is inscribed in a circle with a radius of 6, that means that the radius of the hexagon is also 6. The radii of the regular hexagon start at its center and go to each one of the 6 pointy ends (vertices). There are 6 sides so that means that there are 6 radii. That also means that each pair of radii create a triangle. There are 6 triangles inside this hexagon, and all of them are congruent. Because there are 6 central angles and because the degree measure around the outside of a circle is 360 degrees, we can find the vertex angle of each one of these 6 triangles by dividing 360 by 6 to get 60 degrees. The Isosceles Triangle Theorem tells us that if two sides of a triangle are congruent, then the angles opposite those congruent sides are also congruent. So 180 - 60 (the vertex angle) = 120, and 120 divided in half is 60. So this is an equilateral/equiangular triangle. Since all the angles measure 60, that means that all the sides measure the same, as well. So they all measure 6 cm. That gives us that one side of the hexagon measures 6 cm and we will need that for the formula for the area of said hexagon. The altitude of one of those equilateral triangles serves as the apothem that we also need for the area of the hexagon. If we split one of those triangles in half at the altitude, the base will measure 3 and the vertex angle will measure 30 degrees. In the Pythagorean triple for a 30-60-90, the side across from the 30 angle measures x, the side across from the 60 angle measure x times the square root of 3, and the hypotenuse measure 2x. That means that the apothem (which is the altitude of this triangle) is the length across from the 60 angle. So if x measures 3, then the side across from the 60 measures [tex]3\sqrt{3}[/tex]
The formula for the area of a regular polygon is
[tex]A=\frac{1}{2}ap[/tex]
where a is the apothem and p is the perimeter around the hexagon. We found one side to be 6 cm, so 6 times the 6 sides of the hexagon is 36 cm. The apothem is [tex]3\sqrt{3}[/tex]
so putting it all together in our formula looks like this:
[tex]A=\frac{1}{2}(3\sqrt{3})(36)[/tex]
Do the math on that and you will get
[tex]A=54\sqrt{3} cm^2[/tex]
93.53 cm².
The area of a regular hexagon inscribed in a circle of radius 6 cm can be calculated using the formula for the area of a regular hexagon.
Calculate the area of one of the equilateral triangles formed by the hexagon inscribed in the circle.
Multiply the area of one triangle by 6 to find the total area of the regular hexagon.
In this case, the area of the regular hexagon is approximately 93.53 cm².
Does the midpoint BC lie on line AG? Why or why not?
Answer:
see below
Step-by-step explanation:
Put the (x, y) values of point F into the equation for line AG and see if they work:
y = (b/(a+c))x
For (x, y) = (a+c, b), this is ...
b = (b/(a+c))(a+c) = b·(a+c)/(a+c) = b·1 = b . . . . . a true statement
Yes, F lies on line AG.
Answer:
D
Step-by-step explanation:
The coordinates of point A on a coordinate grid are (−2, −3). Point A is reflected across the y-axis to obtain point B and across the x-axis to obtain point C. What are the coordinates of points B and C?
A) B(2, 3) and, C(−2, −3)
B) B(−2, −3) and C(2, 3)
C)B(2, −3) and C(−2, 3)
D) B(−2, 3) and C(2, −3)
Answer:
B) B(2,-3) and C(-2,3)
Step-by-step explanation:
The given point A, has coordinates (-2,-3).
When point A(-2,-3) is reflected over the y-axis to obtain point B, then the coordinates of B is obtained by negating the x-coordinate of A.
Therefore B will have coordinates (2,-3).
When point A(-2,-3) is reflected over the x-axis to obtain point C, then the coordinates of C is obtained by negating the y-coordinate of A.
Hence the coordinates of C are (-2,3)
A mining company has two mines. One day's operation at mine #1 produces ore that contains 30 metric tons of copper and 600 kilograms of silver, while one day's operation at mine #2 produces ore that contains 40 metric tons of copper and 380 kilograms of silver. Let v1 = (30, 600) [vector] and v2 = (40, 380) [vector]. Then v1 and v2 represent the "output per day" of mine #1 and mine #2, respectively.a) What physical interpretation can be given to the vector 5v1?b) Suppose the company operates mine #1 for x1 days and mine #2 for x2 days. Write a vector equation whose solution gives the number of days each mine should operate in order to produce 240 tons of copper and 2824 kilograms of silver. Do not solve the equation.c) [M] Solve the equation in (b).
Answer:
a) the output of mine #1 in 5 days
b) x1·v1 +x2·v2 = (240, 2824)
c) x1 = 544/315 ≈ 1.727; x2 = 1482/315 ≈ 4.705
Step-by-step explanation:
a) If v1 represents the production of mine #1 for 1 day, then 5v1 represents that mine's production for 5 days.
__
b) The production of each mine, multiplied by the number of days of production, adds together to give the total desired production:
x1·v1 + x2·v2 = (240, 2824)
__
c) Treating the vector components separately, the vector equation gives rise to two linear equations:
30x1 +40x2 = 240
600x1 + 380x2 = 2824
These can be solved by any of the usual methods. My favorite for numbers that are large or relatively prime is Cramer's rule and/or a graphing calculator. The above equations can be reduced to standard form to make the numbers slightly more manageable:
3x1 +4x2 = 24
150x1 +95x2 = 706
By Cramer's rule, ...
x1 = (4·706 -95·24)/(4·150 -95·3) = 544/315
x2 = (24·150 -706·3)/315 = 1482/315
The vector 5v1 represents the output of 5 days of operation at mine #1. The vector equation x1v1 + x2v2 = (240, 2824) gives the number of days each mine should operate to hit certain production targets. The specific solution is not given.
Explanation:a) 5v1 would represent the output of 5 days of operation at mine #1. Specifically, it would mean that in 5 days, mine #1 produces 150 metric tons of copper and 3000 kilograms of silver.
b) The vector equation we need to represent the situation could look something like this: x1v1 + x2v2 = (240, 2824). Here, x1 and x2 represent the number of days each mine should operate and v1 and v2 are the vectors that represent the daily output of each mine. The solution to this vector equation would give the number of days each mine needs to operate in order to fit these production targets.
c) Since we are not supposed to solve the equation, we will simply write it again here for reference: x1v1 + x2v2 = (240, 2824).
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find the area of the following figure
Answer:
C. 531 would be your answer.
Answer: 531
Step-by-step explanation: 21 • 18 = 378 and 17 • 9 = 153. And those together and you get 531 as yours answer!
Dan buys a car for £2700.
It depreciates at a rate of 1.4% per year.
How much will it be worth in 5 years?
Give your answer to the nearest penny where appropriate.
The car, which depreciates at an annual rate of 1.4%, will be worth approximately £2590.34 in 5 years.
Explanation:This is a problem related to depreciation, which is a concept in finance and economics. In this case, the car depreciates at a rate of 1.4% per year. This means that each year, the value of the car decreases by 1.4% of its value at the start of that year. This is an example of exponential decay.
To calculate the car's value after 5 years, we raise the depreciation rate (99.6%, or 0.996 in decimal form because the value decreases) to the power of 5, and then multiply it by the initial price of the car, £2700.
That is, Car Value = £2700 * (0.996)^5 = £2590.34
So, the car will be worth approximately £2590.34 in 5 years to the nearest penny.
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REFER TO THE PICTURE BELOW. PLEASE SHOW WORK.
Answer:
(c) 16/9·π²·r⁶
Step-by-step explanation:
The water displaced is equivalent to the volume of the sphere, given as
V = (4/3)π·r³
The product of two identical displaced volumes will be ...
V² = ((4/3)π·r³)² = (4/3)²·π²·r⁶
= 16/9·π²·r⁶ . . . . . . matches choice (c)
Please help meeeeeeee
For this case we must simplify the following expression:
[tex]3-2y-1 + 5x ^ 2-7y + 7 + 4x ^ 2[/tex]
We combine similar terms, taking into account that equal signs are added and the same sign is placed, while different signs are subtracted and the sign of the major is placed.
[tex]3-1 + 7-2y-7y + 5x ^ 2 + 4x ^ 2 =\\9-9y + 9x ^ 2[/tex]
Answer:
[tex]9-9y + 9x ^ 2[/tex]
Evaluate (2-5i)(p+q)(i) when p=2 and q=5i.
Answer:
[tex](2-5i)(p+q)(i)=29i[/tex]
Step-by-step explanation:
We have the product of 2 complex numbers
[tex](2-5i)(p+q)(i)[/tex]
We know that:
[tex]p=2\\\\q=5i[/tex]
Then we substitute these values in the expression
[tex](2-5i)((2)+(5i))(i)[/tex]
[tex](2-5i)(2+5i)(i)[/tex]
The product of a complex number [tex]a + bi[/tex] by its conjugate [tex]a-bi[/tex] is always equal to:
[tex]a ^ 2 - (bi) ^ 2[/tex]
Then
[tex](2-5i)(2+5i)(i)=(2^2-5^2i^2)(i)[/tex]
Remember that:
[tex]i=\sqrt{-1}\\\\i^2 = -1[/tex]
So
[tex](2^2-5^2i^2)(i)= (4 - 25(-1))(i)\\\\(4 - 25(-1))(i) = (4+25)i=29i[/tex]
Finally
[tex](2-5i)(p+q)(i)=29i[/tex]
Answer:
29i
Step-by-step explanation:
Edge Verified
Cole walked 2 1/2 kilometers on Monday. Isabella walked twice as many kilometers as coke. How many meters did cole and Isabella walk alotogether?
Answer:
7500 meters
Step-by-step explanation:
Isabella walked 2 × 2.5 km = 5 km. Together, they walked ...
2.5 km + 5 km = 7.5 km = 7.5×1000 m = 7500 m
Cole and Isabella walked 7500 meters altogether.
_____
"kilo-" is a prefix meaning "one thousand". So one kilometer is 1000 meters. Then 7.5 kilometers is 7.5 times 1000 meters, or 7500 meters.
State the maximum/minimum of the function H(x)=−1/2x^2+4x−5.
is noteworthy that the leading term has a negative coefficient, meaning this parabola is opening downwards like a "camel hump", so it reaches a maximum point and then goes back down, and of course the maximum point is at its vertex.
[tex]\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ H(x)=\stackrel{\stackrel{a}{\downarrow }}{-\frac{1}{2}}x^2\stackrel{\stackrel{b}{\downarrow }}{+4}x\stackrel{\stackrel{c}{\downarrow }}{-5} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{4}{2\left( -\frac{1}{2} \right)}~~,~~-5-\cfrac{4^2}{4\left( -\frac{1}{2} \right)} \right)\implies \left( 4~,~-5+\cfrac{16}{2} \right)\implies (4~~,~~3)[/tex]
Answer:
(4, -3)
Step-by-step explanation:
I'm assuming that you meant H(x) = -(1/2)x^2 + 4x - 5. Here, the coefficients of this quadratic are a = -1/2, b = 4 and c = -5.
The axis of symmetry is x = -b/(2a). This axis goes through the vertex. Here the axis of symmetry is x = -(4) / [ 2(-1/2) ], or x = 4.
Evaluating H(x) at x = 4 gives us the y value of the vertex. It is:
H(4) = (-1/2)(4)^2 + 4(4) - 5, or H(4) = -8 + 16 - 5, or 3.
We know that this function must have a max because a is - and therefore the graph opens down.
The vertex and the maximum is (4, 3).
If f(x)= 15x+7x and g(x)= x^2-5x, find (f+g)(x)
Answer:
(f+g)(x) = x^2 +10x +7
Step-by-step explanation:
(f+g)(x) = f(x) +g(x) = (15x +7) +(x^2 -5x)
= x^2 +x(15 -5) +7
= x^2 +10x +7
What is the greatest common factor of 8x and 40?
For this case we have that by definition, the Greatest Common Factor or GFC, of two or more integers is the largest integer that divides them without leaving a residue.
So:
We look for the factors of both numbers:
8: 1, 2, 4, 8
40: 1, 2, 4, 5, 8, 10, 20
It is observed that 8 is common.
So, the GFC of 8x and 40 is 8
Answer:
8
g = 15 - (m/32)If Vera stars with a full tank of gas, the number of gallons of gas g, left in the tank after driving m miles is given by the equation above. When full, how many gallons of gas does Vera's tank hold?15 gallons.17 gallons.32 gallons.480 gallons
ANSWER
15 gallons
EXPLANATION
The equation that models the situation is
[tex]g(m) = 15 - \frac{m}{32} [/tex]
When the tank was full the man did not cover any mile.
To find the the number of gallons of gases Vera's tank holds, we substitute m=0 into the equation to get,
[tex]g(0) = 15 - \frac{0}{32} = 15[/tex]
Therefore the correct answer is is option A 15 gallons
Final answer:
When Vera's tank is full, it holds 15 gallons of gas. This is found by setting the miles driven to zero in the equation g = 15 - (m/32).
Explanation:
To determine how many gallons of gas Vera's tank holds when full, we need to set m, the number of miles driven, to zero in the given equation g = 15 - (m/32). This is because we are interested in the initial amount of gas before any driving occurs.
Plugging m = 0 into the equation gives us:
g = 15 - (0/32)
g = 15
Therefore, when full, Vera's tank holds 15 gallons of gas. Among the provided options, the correct answer is 15 gallons.
Suppose ABCD is a rhombus and that the bisector of ∠ABD meets
AD
at point K. Prove that m∠AKB = 3m∠ABK.
m∠AKB = m∠KBD + m∠
by reason
Find the angle that missing angle so that angle kbd and that angle will equal angle akb.
explain
Answer:
missing angle: ∠DBCStep-by-step explanation:
Proof:
m∠ABK ≅ m∠KBD — given that BK bisects ∠ABDm∠ABD = m∠ABK + m∠KBD = 2·m∠ABKm∠ABD ≅ m∠DBC — properties of a rhombus: a diagonal bisects the anglesm∠DBC = 2·m∠ABK — transitive property (both equal to m∠ABD)m∠KBC = m∠KBD + m∠DBC — adjacent anglesm∠KBC = m∠ABK + 2·m∠ABK = 3·m∠ABK — substitute for m∠KBD and m∠DBCm∠AKB = m∠KBC — alternate interior angles of parallel lines AD, BCm∠AKB = 3·m∠ABK — substitute for m∠KBC_____
Proof is always in the eye of the beholder, and the details depend on the supporting theorems and postulates you're allowed to invoke. The basic idea is that you have cut a vertex angle in half twice, and you're trying to show that the smallest part to the rest of it has the ratio 1 : 3.
2x+4y=–3 in standard form
Standard form for linear equations is in the form ax + by = c. Thus, 2x + 4y = -3 is already in standard form.
Answer:
It is already in standard form
Step-by-step explanation:
Standard form is ax+by=c
2x=ax
4y=by
-3=c
Nothing needs to be changed
The first term of a geometric sequence is 2 and the common ratio is 4. What is the 6th term of the sequence?
Answer: 2048
Step-by-step explanation:
Tn = arⁿ⁻¹
T6 = ar⁶⁻¹
T6 = ar⁵
T6 = 2*4⁵
T6= 2048
ANSWER
[tex]a_{6} = 2048[/tex]
EXPLANATION
The general term of a geometric sequence is given by,
[tex] a_{n} = a_{1} ( {r})^{n - 1} [/tex]
The first term of the geometric sequence is 2
[tex]a_{1} =2[/tex]
The common ratio is 4. This means r=5.
The nth term of the sequence is
[tex]a_{n} = 2 ( {4})^{n - 1} [/tex]
The 6th term is
[tex]a_{6} = 2 ( {4})^{6 - 1} [/tex]
[tex]a_{6} = 2 ( {4})^{5} [/tex]
[tex]a_{6} = 2048[/tex]
A sphere has a surface area of 36π ft2. Find the volume of the sphere.
36π ft3
42π ft3
48π ft3
28π ft3
The surface area of the sphere is given by the equation
[tex]A=4\pi * r^{2}[/tex],
where A is the surface area and r is the radius.
We want to find the volume of the sphere, which is given by the equation
[tex]V = \frac{4}{3} * \pi * r^{3}[/tex],
where V is the volume and r is the radius.
Looking at these equations, we see that they both involve the sphere's radius. If we know what r is, we can calculate the volume.
We know that the sphere's surface area is [tex]36 \pi[/tex]. Plugging that in for A in the surface area equation, we get
[tex]36 \pi=4\pi * r^{2}[/tex], then divide by [tex]\pi[/tex]
[tex]36 = 4 * r^{2}[/tex], then divide by 4
[tex]r^{2} = 9[/tex], then take the square root of both sides
[tex]r = 3[/tex]
So the radius of the sphere is 3. Plugging this into the volume equation,
[tex]V = \frac{4}{3} * \pi * 3^{3}[/tex], simplify terms
[tex]V = \frac{4}{3} * \pi * 27[/tex], multiply [tex]\frac{4}{3}[/tex] by 27
[tex]V = 36 * \pi[/tex]
So the volume of the sphere is [tex]36\pi[/tex].
Answer:
36π ft^3
Step-by-step explanation:
The surface area (S) of a sphere can be defined as:
S = 4×π×r^2 = 36×π
Solve for r to get the radius of the sphere:
r = ([tex]\sqrt{36/4}[/tex] = 3
The voluem (V) of a sphere can be defined as:
V= (4/3)×π×r^3
The volume of the sphere is:
V = (4/3)×π×(3^3) = 36π ft^3
The volume of the sphere can be calculated from the surface area given.
there are 96 marbles in a box. There are 5 times as many blue marbles as red marbles. How many red marbles are there?
Answer:
16
Step-by-step explanation:
96 marbles = Box
Let's call blue marbles " 5 x " and red marbles " x "
So now an equation is setup ⇒
→ 5 x + x = 96
( Simplify )
→ 6 x = 96
( Divide by 6 from both sides to isolate x )
→ x = 16
red marbles " x " so x = 16
You would use the following equation:
96 = 5x + x
There is a total of 96 marbles. The right side of the equation represents how many blue marbles are in the box. X is red marbles in the box, since we know that red marbles is 5 times x
Add the common variables:
96 = 5x + x
96 = 6x
To solve for red marbles isolate x. To do this divide 6 to both sides. Division is the opposite of multiplication and will cancel 6 from the right side and bring it to the left
96 ÷ 6 = 6x ÷ 6
16 = x
You have 16 marbles in the box
Hope this helped!
~Just a girl in love with Shawn Mendes
13. 2 – (–8) + (–3) =
A. 1
B. 12
C. 7
D. 14
ANSWER
C. 7
EXPLANATION
We want to evaluate
[tex]2 - ( - 8) + ( - 3) [/tex]
We use the order of operations PEDMAS.
Dealing with the parenthesis first,we have
[tex]2 - - 8+- 3[/tex]
Note that:
[tex] - - = + [/tex]
and
[tex] - + = - [/tex]
Our expression now becomes:
[tex]2 + 8 - 3[/tex]
Next, we add to get:
[tex]10 - 3[/tex]
We finally subtract to get,
[tex]7[/tex]
The correct answer is C
The answer is: C. 7
Why?To solve the problem, first, we need to consider the signs out and inside of the parenthesis.
We must remember the following rule:
[tex]--=+\\+-=-[/tex]
We are given the following expression:
[tex]2-(-8)+(-3)[/tex]
Then, we can rewrite it using the rule of the signs, we have:
[tex]2--8+-3=2+8-3=2+8-3[/tex]
[tex]2+8-3=10-3=7[/tex]
Hence, the correct option is C. 7.
Have a nice day!
x-12/x-8 rational expression
It is a rational expression.
A company issues auto insurance policies. There are 900 insured individuals. Fifty-four percent of them are male. If a female is randomly selected from the 900, the probability she is over 25 years old is 0.43. There are 395 total insured individuals over 25 years old. A person under 25 years old is randomly selected. Calculate the probability that the person selected is male.
Answer:
about 0.53
Step-by-step explanation:
54% of the insured, or .54×900 = 486 individuals are males. That leaves 900-486 = 414 that are females. 43% of those, or .43×414 = 178 are over 25, so the remainder of the 395 who are over 25 are male.
Since 395 -178 = 217 of the males are over 25, there are 486 -217 = 269 who are under 25. Then the fraction of insureds who are under 25 that are male is ...
269/(900 -395) = 269/505 ≈ 0.53
_____
It can be useful to make a 2-way table from the given information.
Final answer:
Using the provided data, the probability that a person under 25 years old selected randomly is male is calculated by dividing the number of males under 25 (found by subtraction from total males and males over 25) by the total number of individuals under 25.
Explanation:
The question asks us to calculate the probability that a person under 25 years old, selected randomly from a group of insured individuals, is male. To find this, we need to use the given data:
Total insured individuals: 900
Percentage of males: 54%
Individuals over 25 years old: 395
Probability that a randomly selected female is over 25: 0.43
To calculate the number of males and females, we take 54% of 900 to get the total males, which is 486. Since there are 900 insured individuals in total, the number of females would be 900 - 486 = 414. The number of females over 25 years old is 414 * 0.43 = 178.02, which we can round to 178.
Since there are 395 individuals over 25 years old in total and 178 of them are female, 395 - 178 gives us 217 males over 25 years old. Now, we need to find the number of individuals under 25 years old. There are 900 - 395 = 505 individuals under 25.
The probability that a randomly selected person under 25 is male can be found by dividing the number of males under 25 by the total number of people under 25. The number of males under 25 is the total number of males minus males over 25, which is 486 - 217 = 269. Therefore, the probability is 269 / 505.