Answer:
531.441
Step-by-step explanation:
8.1*8.1*8.1 = Volume of a cube
What is the surface area of the right cone below?
O A. 126x units
O B. 54 units
OC. 63x units
D. 998 units
O
Answer:
[tex]SA=54\pi\ units^2[/tex]
Step-by-step explanation:
we know that
The surface area of the cone is given by the formula
[tex]SA=\pi r^{2}+\pi rl[/tex]
where
r is the radius of the base
l is the slant height
we have
[tex]r=3\ units\\l=15\ units[/tex]
substitute
[tex]SA=\pi (3)^{2}+\pi (3)(15)[/tex]
[tex]SA=54\pi\ units^2[/tex]
Convert the angle 0= 9pi/5 radians to degrees
[tex]\frac{9\pi }{5}[/tex] radians is equal to [tex]324[/tex]° .
Step-by-step explanation:
Degrees are a unit of angle measure. A full circle is divided into 360 degrees. For example, a right angle is 90 degrees. A degree has the symbol ° and so ninety degrees would written 90°. Another unit of angle measure is the radian.
The radian is the SI unit for measuring angles, and is the standard unit of angular measure used in many areas of mathematics. The length of an arc of a unit circle is numerically equal to the measurement in radians of the angle that it subtends; one radian is just under 57.3 degrees.
We know that 1 radian = 180°/[tex]\pi[/tex] . So [tex]\frac{9\pi }{5}[/tex] radians is equal to :
⇒ [tex]\frac{9\pi }{5}(\frac{180}{\pi } )[/tex]
⇒ [tex]\frac{9(180) }{5}[/tex]
⇒ [tex]9(36)[/tex]
⇒ [tex]324[/tex]°
Therefore , [tex]\frac{9\pi }{5}[/tex] radians is equal to [tex]324[/tex]° .
To convert 9pi/5 radians to degrees, multiply by the conversion factor of 180°/π, resulting in 324 degrees.
Explanation:To convert the angle 0 = 9pi/5 radians to degrees, we need to use the relationship between radians and degrees. Recall that 360° = 2π radians. Consequently, to convert radians to degrees, we can multiply by a conversion factor of 180°/π. Using this conversion factor, the computed angle in degrees is:
9π/5 radians × (180°/π) = 9/5 × 180° = 9 × 36° = 324°
Therefore, the angle of 9π/5 radians is equivalent to 324 degrees.
a ball has a radius of 18cm. what is the approximate volume of the ball? use 3.14 for pi. round to the cone nearest hundredth if necessary.
___cm3
The volume of the ball is 24,400 cm³
Step-by-step explanation:
Step 1: Given the radius of the ball = 18cm. Use the formula for volume of a sphere to find the volume of the ball.Volume of the ball = 4/3 πr³
= 4/3 × 3.14 × (18)³
= 24,416.64 cm³ ≈ 24,400 cm³ (nearest hundredth)
A table has a square top. The area of the table top measures 18 square feet. Find
the length of one side of the table top
Answer:
the answer is about 4.243
Step-by-step explanation:
Squares mean all sides would have the same length. So you just need to find the square root of the area (18) which is about 4.243 and just to check multiply 4.243 by itself and you would get 18.
Final answer:
The length of one side of the table top with an area of 18 square feet is approximately 4.24 feet, as calculated by taking the square root of the area.
Explanation:
To find the length of one side of a table top with an area of 18 square feet, we should understand that a square has all sides of equal length. Therefore, to find the side length of a square, we take the square root of the area. In this case, we have an area of 18 square feet, so the calculation would be √18, which is approximately 4.24 feet. Thus, the length of one side of the table top is approximately 4.24 feet.
HELP PLEASE QUICKLY I CAN'T FAIL MY CLASS.: The distance of Mercury from the Sun is about 3.6×10^7 miles, while the distance of Pluto from the Sun is about 3.7×10^9 miles. About how many times farther from the Sun is Pluto than Mercury?
Answer: approximately 102.8 times farther
Step-by-step explanation: If you divide the distance of Mercury to the Sun (3.6E7) from the distance of Pluto to the Sun (3.7E9) you get 102.777777. That is the approximate distance. Rounded you get 102.8
This is the question that i need help with
Answer:
a) 8x
b)2+12y
Step-by-step explanation:
Answer:
5X+3X & 8X For the first one
and 2+12y for the second one i believe those are correct let me know in the comments below
Step-by-step explanation:
hope this helps have a great day
What is the solution of x2-1/x2+5x+4 less than or equal to 0?
Answer:
Fourth answer choice.
Step-by-step explanation:
Start by factoring the numerator and the denominator:
(x - 1)(x + 1)
-----------------
(x + 1)(x + 4)
Note that x can be neither -1 nor -4, since either results in an undefined quotient. These two x-values are critical values because of this. If we cancel the (x + 1) terms, we obtain the result
(x - 1)
--------- for x ≠ -1 and x ≠ - 4
(x + 4)
The next step is to evaluate the given quotient on the three intervals defined by {-4, -1}: (-∞, -4), (-4, -1), (-1, ∞ ). We choose an x-value from within each interval and evaluate the given function at each. Suitable test values include {-10, -3, 0}:
At x = -10, the reduced given quotient (x - 1) / (x + 4) takes on the value (-10 - 1) / (-10 + 4) = -11/(-6), which is positive. Reject this interval, as we want and expect the quotient value to be 0 or less.
At x = -3, we get (-3 - 1) / (-3 + 4), which is negative. The given inequality is true on the interval (-4, -1) (or -4 < x < -1).
At x = 0, we get (0 - 1) / (0 + 4), which is negative, so the inequality is true on (-1, ∞ ).
So the fourth answer choice is the correct one.
Answer:
Answer D
Step-by-step explanation:
Write the linear equation given two points (-6, 8) and (3, -7). *
[tex]\bf (\stackrel{x_1}{-6}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-7}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-7}-\stackrel{y1}{8}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-6)}}}\implies \cfrac{-15}{3+6}\implies \cfrac{-15}{9}\implies -\cfrac{5}{3}[/tex]
[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{8}=\stackrel{m}{-\cfrac{5}{3}}[x-\stackrel{x_1}{(-6)}]\implies y-8=-\cfrac{5}{3}(x+6) \\\\\\ y-8=-\cfrac{5}{3}x-10\implies y = -\cfrac{5}{3}x-2[/tex]
Answer:
[tex]m=\frac{-5}{3}[/tex]
Step-by-step explanation:
Step 1: Let's find the slope between your two points.
[tex](-6,8); (3,-7)\\\\(x_{1} ,y_{1} )=(-6,8)\\\\(x_{2} ,y_{2} )=(3,-7)[/tex]
Step 2: Use the slope formula
[tex]m = \frac{y_{2} - y_{1} }{x_{2} - x_{1} }\\\\=\frac{(-7) - 8}{3- (-6)} \\\\=\frac{-15}{9}\\\\= \frac{-5}{3}[/tex]
Therefore, the equation is [tex]\frac{-5}{3}[/tex]
The box plots show the average gas mileage, in miles per gallon, of the cars sold at a dealership in June and in December.
Gas Mileage of Cars Sold in June
2 box plots. The number line goes from 14 to 34. For cars sold in June, the whiskers range from 21 to 33, and the box ranges from 22 to 29. A line divides the box at 24. For Cars sold in December, the whiskers range from 14 to 26, and the box ranges from 18 to 21. A line divides the box at 19.
Gas Mileage of Cars Sold in December
Which inference can be made about the cars?
The type of cars sold in June typically gets better gas mileage.
The type of cars sold in December typically gets better gas mileage.
The types of cars sold in the two months typically get about the same gas mileage.
The types of cars sold in the two months typically get better gas mileage than those sold in other months.
PLS HELP! THANKS
Since both have the same interquartile range, the inference made would be: types of cars sold in the two months typically get about the same gas mileage.
What is the Interquartile Range?The interquartile range is a measure of variability, which can be used in comparing two data distribution.
Interquartile range = Q3 - Q1.
Interquartile range for gas mileage of cars sold in June = 33 - 21 = 12.
Interquartile range for gas mileage of cars sold in December = 26 - 14 = 12.
Therefore, since both have the same interquartile range, the inference made would be: types of cars sold in the two months typically get about the same gas mileage.
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Answer: Its C.
Step-by-step explanation:
Edge 2022
What is the slope of (4,12) and (-8,2)
Answer:
Slope = [tex]\frac{5}{6}[/tex]
Step-by-step explanation:
Slope = [tex]\frac{y2 - y1}{x2 - x1}[/tex]
Slope = [tex]\frac{2 - 12}{-8 - 4}[/tex]
Slope = [tex]\frac{-10}{-12}[/tex]
Slope = [tex]\frac{5}{6}[/tex]
Answer: Slope = [tex]\frac{5}{6}[/tex]
y=3x+5 that passes through (4,-1)
Answer:
No, not a solution
Step-by-step explanation:
Step 1: Check if solution
y = 3x + 5
-1 = 3(4) + 5
-1 = 12 + 5
-1 = 17
DOES NOT EQUAL
Answer: No, not a solution
5x + 2y=7
- 2x + 6y=9
Answer:
x = [tex]\frac{12}{17}[/tex] or 0.706
[tex]y = \frac{59}{34}[/tex] or 1.735
Step-by-step explanation:
5x + 2y=7 ----->(eq 1)
- 2x + 6y=9 ----->(eq 2)
Multiply (eq 1) with 3
3×(5x + 2y) = 3×7
15x + 6y = 21 ----->(eq 3)
substract (eq 3) from (eq 2)
- 2x + 6y - (15x + 6y) = 9-21
- 2x + 6y - 15x - 6y = 9-21
- 2x - 15x + 6y - 6y = 9-21
-17x = -12
x = -12 ÷ -17
x = [tex]\frac{12}{17}[/tex]
put x = [tex]\frac{12}{17}[/tex] in (eq 1)
[tex]5*\frac{12}{17} + 2y = 7[/tex]
[tex]2y = 7- 5*\frac{12}{17}[/tex]
[tex]2y = \frac{7*17 - 60}{17}[/tex]
[tex]2y = \frac{119- 60}{17}[/tex]
[tex]2y = \frac{59}{17}[/tex]
[tex]y = \frac{59}{17*2}[/tex]
[tex]y = \frac{59}{34}[/tex]
Simplify 20 radical 16
Answer:
80
Step-by-step explanation:
Simply radical 16 which will give you 4, then multiply 4 by 20 which equals 80
Please hurry it’s urgent
Answer:5
Step-by-step explanation:
A credit card customer owes $523.85 they are only able to make a payment of $184.50 how much money does the customer still owe?
Answer:
339.35
Step-by-step explanation:
The amount of money the credit card customer still owes to pay is $339.35.
We are given that,
The amount the credit card customer owes = $523.85.
The amount the credit card customer paid = $184.50.
We have to find the amount of money the credit card customer still owes to pay.
The amount of money the credit card customer still owes to pay :
= The amount the credit card customer owes - The amount the credit card customer paid
= $523.85 - $184.50
= $339.35
Thus, the amount of money the credit card customer still owes to pay after paying $184.50 is $339.35.
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What is the length of EF in the triangle? Show your work. HELP!
The length of EF in the given triangle is 8.80 m.
Step-by-step explanation:
Step 1:
In the given triangle, the opposite side's length is 16.2 m, the adjacent side's length is x m while the triangle's hypotenuse measures 16.2 m units.
The angle given is 90°, this makes the triangle a right-angled triangle.
So first we calculate the angle of E and use that to find x.
Step 2:
As we have the values of the length of the opposite side and the hypotenuse, we can calculate the sine of the angle to determine the value of the angle of E.
[tex]sinE = \frac{oppositeside}{hypotenuse} =\frac{13.6}{16.2} = 0.8395.[/tex]
[tex]E = sin^{-1} (0.8395), E = 57.087.[/tex]
So the angle E of the triangle DEF is 57.087°.
Step 3:
As we have the values of the angle and the hypotenuse, we can calculate the cos of the angle to determine x.
[tex]cos E = \frac{adjacentside}{hypotenuse} = \frac{x}{16.2} .[/tex]
[tex]cos(57.087) = 0.5433, x = 16.2 (0.5433) = 8.8014.[/tex]
Rounding this off to the nearest hundredth, we get x = 8.80 m.
To find the height of the Eiffel Tower, Antoine placed a mirror of 500 meters away from the tower. He then positions himself so the top of the tower is visible in the mirror. He is standing 2.75 meters from the mirror and his eyes are 1.8 meters off the ground. How y’all is the tower?
984′, 1,063′ to tip.
the ' is feet
The required height of the Eiffel Tower is given as 327.27 meters.
What is the Ratio?The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Let the height of the Eiffel tower be x,
According to the question,
The ratio of the height to the base of the Eiffel tower is equal to the ratio of height to the
base of men,
x / 500 = 1.8 / 2.75
x = 327.27 meters
Thus, the required height of the Eiffel Tower is given as 327.27 meters.
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find the value of b
b-12=46
Answer:
b=58
Step-by-step explanation:
b-12=46
b=46+12
b=58
9: Part A The diameter of a circle is 63 centimeters. Find its circumference. Use π=3.14. A 31.5 centimeters B 98.91 centimeters C 197.82 centimeters D 3,115.67 centimeters Part B Find the area of the circle. ( use π=3.14 ) Round your answer to the nearest hundredth. Answer: square centimeters.
Answer:
Part A is Answer C
C=2pi * r
D= 2r
C= 2 * 3.14 * 31.5
C= 197.82
__________________________
Part B is 3115.67 sq cm
A = 3.14 * r*r
A= 3.14 x 31.5x31.5
A=3115.665
Rounded: 3115.67
The circumference of the circle is C = 197.82 cm
The area of the circle is A = 3,115.67 cm²
What is a Circle?A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle
The circumference of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
The standard form of a circle is
( x - h )² + ( y - k )² = r²,
where r is the radius of the circle and (h,k) is the center of the circle.
The equation of circle is ( x - h )² + ( y - k )² = r²
For a unit circle , the radius r = 1
x² + y² = r² be equation (1)
Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )
Given data ,
Let the diameter of the circle be d = 63 cm
The circumference of a circle is given by the formula:
C = πd
where d is the diameter of the circle and π is the mathematical constant pi, approximately equal to 3.14159.
C = π(63)
C = 197.92 cm
The area of a circle is given by the formula
A = πr²
where r is the radius of the circle. Since we are given the diameter, we can find the radius by dividing the diameter by 2:
r = d/2
r = 63/2
r = 31.5 cm
Substituting the radius r = 31.5 cm into the formula for the area, we get:
A = 3.14159 x 31.5²
A = 3.14159 x 992.25
A = 3,117.15 cm²
Hence , the area of the circle is 3,117.15 cm²
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It takes Jill 2 hours to run 14.5 miles at this rate how far could she run in 3 hours
Answer:
21.75
Step-by-step explanation:
i hoped this helped. 14.50 divide-by 2 = 7.25 so 14.50 + 7.25= 21.75
Calculate the area of a rectangular prism that is 5 cm x 9 cm and 11 cm high
Answer: 398cm²
Step-by-step explanation:
Surface area of a Rectangular Prism: 2lw+2lh+2wh
l= 5cm
w= 9cm
h= 11cm
Area= (2x5x9)+(2x5x11)+(2x9x11)
=398cm²
Find the value of x.
Answer: 49.8 is the answer
Step-by-step explanation:
What is the median house price?
$750,000
$764,000
$880,000
$1,200,000
Submit
Skip
Help
Type here to search
OEM W
Answer: $822,000
Step-by-step explanation:
Median of even numbers is the average of two middle most numbers
From the question, median
= $764,000 + $880000 ÷ 2
= $1,644,000÷2
$822,000
Please help with this algebra!! I’m
Answer:
(-4, -1)
Step-by-step explanation:
x = 4y
-4x - y = 17
Plug in 4y for x in the second equation:
-4(4y) - y = 17
Simplify. Remember to follow PEMDAS. Isolate the variable, y. Note the equal sign, what you do to one side, you do to the other.
First, multiply 4y with -4:
-4(4y) = -16y
-16y - y = 17
Simplify. Combine like terms:
-16y - y = 17
-17y = 17
Isolate the variable, y. Divide -17 from both sides:
(-17y)/-17 = (17)/-17
y = 17/-17
y = -1
Plug in -1 for y in the first equation:
x = 4y
x = 4(-1)
x = -4
x = -4, y = -1
Answer: (-4, -1)
~
How much work is done lifting a 5 kg ball from a height of 2 m to a height of 6 m? (Use 10 m/s for the acceleration
of gravity)
19
In physics, work is defined force that causes displacement. So this can be expressed by the following equation:
[tex]W=Fs[/tex]
Where:
[tex]F:Force \\ \\ s:Displacement[/tex]
The force can be found as:
[tex]F=ma \\ \\ F=5(10)=50N[/tex]
And for the displacement:
[tex]s=6-2=4m[/tex]
The force (weight) is down and the displacement is up, then the work must be negative. So:
[tex]W=-(50)(4) \\ \\ \boxed{W=-200J}[/tex]
A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 5 large boxes and 6 small boxes has a total weight of 187 kilograms. A delivery of 3 large boxes and 2 small boxes has a total weight of 87 kilograms. How much does each type of box weigh? pls help!!!
Answer:
large: 18.5 kgsmall: 15.75 kgStep-by-step explanation:
Let b and s represent the weights of the big and small boxes, respectively. Then the two delivered weights can be summarized as ...
5b +6s = 187
3b +2s = 87
We can eliminate the "s" variable by subtracting the first equation from 3 times the second:
3(3b +2s) -(5b +6s) = 3(87) -(187)
4b = 74 . . . . . collect terms
b = 18.5 . . . . . divide by 4
Using this value in the second equation, we find ...
3(18.5) +2s = 87
2s = 31.5 . . . . . . . . subtract 55.5
s = 15.75 . . . . . . . . divide by 2
The large box weighs 18.5 kg; the small box weighs 15.75 kg.
Which of the following is the equation of an ellipse centered at (5,1) having a vertical minor axis of length 4 and a major axis of length 6?
Options are in image
Answer:
D
Step-by-step explanation:
Any ellipse has the following equ
ation:
[tex] \frac{ {x}^{2} }{ {a}^{2} } + \frac{ {y}^{2} }{ {b}^{2} } = 1[/tex]
where
2b = vertical axis length2a = horizontal axis length(as in the picture)
So it should be like:
[tex] \frac{ {x}^{2} }{ { (\frac{6}{2} )}^{2} } + \frac{ {y}^{2} }{ {( \frac{4}{2} )}^{2} } = 1 \\ \frac{ {x}^{2} }{ 9} + \frac{ {y}^{2} }{ 4 } = 1[/tex]
Since it should be moved to the right and up, the answer would be:
[tex]\frac{ {(x - 5)}^{2} }{ 9} + \frac{ {(y - 1)}^{2} }{ 4 } = 1[/tex]
Option D. (x - 5)²/9 + ( y - 1 )²/4 = 1
An ellipse has the following equation:
x²/a² + y²/ b² = 1
where
2b = vertical axis length
2a = horizontal axis length
So it should be like:
x²/(6÷2)² + y²/ (4÷2)² = 1
x²/9 + y²/4 = 1
Since it should be moved to the right and up, the answer would be:
(x - 5)²/9 + ( y - 1 )²/4 = 1
Please check the attached diagram for more details.
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A veterinarian collected data on the association between age and mass of Boxer puppies. A line of best fit was computed. The equation for the line is: y = 17.5x + 480. Which BEST interprets the slope of the linear model?
A) The predicted mass of a Boxer puppy at birth.
B) Every 17.5 days is associated with an additional 480 grams of mass.
C) Each additional day is associated with an additional 480 grams of mass.
D) Each additional day is associated with an additional 17.5 grams of mass.
Answer:
D) Each additional day is associated with an additional 17.5 grams of mass.
Step-by-step explanation:
Slope = 17.5
= change in mass/change in day
Which is 17.5 g increase in 1 day
Answer:
its d!
Step-by-step explanation:
Jose and Jayden go to the movie theater and purchase refreshments for their friends. Jose spends a total of $43.25 on 5 bags of popcorn and 4 drinks. Jayden spends a total of $24.25 on 3 bags of popcorn and 2 drinks. Write a system of equations that can be used to find the price of one bag of popcorn and the price of one drink. Using these equations, determine and state the price of a bag of popcorn, to the nearest cent.
Answer: The equations are as follows;
5p + 4d = 43.25 ————(1) and
3p + 2d = 24.25 ————(2)
Also a bag of popcorn costs $5.25
Step-by-step explanation: We start by assigning letters to the unknown variables. Let a bag of popcorn be p and let one drink be d. The clues given in the question include the cost of buying five bags of popcorn and four drinks which is a total of $43.25. This can be expressed as
5p + 4d = 43.25 ————(1)
Another clue is that three bags of popcorn and two drinks cost $24.25. This also can be expressed as
3p + 2d = 24.25 ————(2)
Now we have a pair of simultaneous equations as follows
5p + 4d = 43.25 ————(1)
3p + 2d = 24.25 ————(2)
We shall use the elimination method since all the unknowns have coefficients greater than 1. Multiply equation one by 3, and multiply equation two by 5 (so as to eliminate ‘p’)
5p + 4d = 43.25 ——— x3
3p + 2d = 24.25 ——— x5
15p + 12d = 129.75 ———(3)
15p + 10d = 121.25 ———(4)
Subtract equation (4) from equation (3) and we have
2d = 8.5
Divide both sides of the equation by 2
d = 4.25.
That means each drink costs $4.25
We can now substitute for the value of d into equation (2)
3p + 2d = 24.25
When d = 4.25
3p + 2(4.25) = 24.25
3p + 8.5 = 24.25
Subtract 8.5 from both sides of the equation
3p = 15.75
Divide both sides of the equation by 3
p = 5.25. This means a bag of popcorn costs $5.25
--
-
4.
The equation of the circle C is[tex] {x}^{2} + {y}^{2} - 6x + ky - 108 = 0[/tex]
where k is a constant. If the area of C is
[tex]121\pi [/tex]
find the centre of C
Answer:
(3, -2) or (3, 2)
Step-by-step explanation:
Please see the attached pictures for full solution.