Answer:
24 cm
Step-by-step explanation:
The volume of a sphere is given by
V = 4/3 pi r^3
2304 pi = 4/3 pi r^3
Divide each side by pi
2304 = 4/3 r^3
Multiply each side 3/4
2304 * 3/4 = 4/3 r^3 * 3/4
1728 = r^3
Take the cube root of each side
1728 ^ 1/3 = r^3 ^ 1/3
12 = r
We want the diameter
d = 2*r
d = 2*12
d = 24
Answer:
24 centimeters
Step-by-step explanation:
A basketball is a sphere. The volume of a sphere can be found using the following formula:
V= 4/3 π r^3
We know that the volume is 2304 π cm^3, therefore we can substitute 2304π in for V.
2304π = 4/3 π r^3
We want to find out what r is. Therefore, we must get r by itself. First, divide both sides by pi.
2304π/π=4/3πr^3/π
2304π/π=4/3r^3
2304=4/3r^3
Next, divide both sides by 4/3, or multiply by the reciprocal of 4/3. The reciprocal of 4/3 is 3/4 (flip the numerator and denominator).
2304*3/4=4/3r^3*3/4
2304*3/4=r^3
1728=r^3
Now, take the cube root of both sides.
∛1728=∛r^3
∛1728=r
12=r
r= 12 cm
The radius is 12 centimeters, but the question asks us to find the diameter. The diameter is twice the radius.
d= 2r
d= 2* 12 cm
d= 24 cm
The diameter of the basketball is 24 centimeters.
Solve the equation below for the variable (x):
2y + x = 10 + 2 x
A. x = 8y
B. x = 10 - 2y
C. x = 2y - 10
D. x = -8y
Answer:
Hope this helps. If not let me know and I'll explain it better
Which expression is equivalent to
-21/4over -2/3
Answer:
[tex]\frac{9}{4}/\frac{3}{2}[/tex]
Step-by-step explanation:
[tex]-2\frac{1}{4}[/tex] is equilavalent to [tex]-\frac{9}{4\\}[/tex].
[tex]-\frac{2}{3}[/tex] can stay put.
The equation is division so neither answers #2 and #3 are the correct ones because when dividing fractions the second fraction has to be flipped in order to continue multiplying instead.
In addition, when two negatives are put together the answer must always be positive.
Hence the answer is [tex]\frac{9}{4}/\frac{3}{2}[/tex].
On a coordinate plane, a graph shows Street on the x-axis and Avenue on the y-axis. A line is drawn from Tia to Lei. Tia is at (4, 8) and Lei is at (12, 20). Tia lives at the corner of 4th Street and 8th Avenue. Lei lives at the corner of 12th Street and 20th Avenue. The fruit market is Three-fourths the distance from Tia’s home to Lei's home.
Answer:
(10, 17)
Step-by-step explanation:
It might be easier to explain with a picture or drawing, but I am new to this, so I would try using words.
Assuming the fruit market is on that straight line from Tia's home to Lei's, So we look at both address (coordinates)
From Tia to Lei, x coordinate is from 4 to 12, that's increased by 8, divide by 4, one step is 2.
y coordinate is from 8 to 20, an increase of 12, divide by 4 again, one step is 3.
The fruit market is at 3/4 distance, so 3 steps, on both x and y coordinates.
x: 4+6 = 10
y: 8+9=17
The fruit market is at point (10,17)
What is graph?
A graph can be defined as a pictorial representation or a diagram that represents data or values.
The point (x,y) which divides the segment AB with endpoints at A(x₁,y₁) and B(x₂,y₂) in ratio m:n has cordinates
[tex]x= \dfrac{nx_1+nx_2}{m+n}[/tex]
[tex]y= \dfrac{ny_1+ny_2}{m+n}[/tex]
Tia is at P(4, 8) and Lei is at Q(12, 20).
The fruit market (F) is three-fourths the distance from Tia’s home to Lei's home, then PM : PQ = 3:4 or PM : MQ = 3:1
So,
[tex]x= \dfrac{1.4+3.12}{3+1} = \dfrac{4+36}{4} = \dfrac{40}{4} = 10 \\y= \dfrac{1.8+3.20}{3+1} = \dfrac{8+60}{4} = \dfrac{68}{4} = 17[/tex]
Hence, the fruit market is at point (10,17) which means it is placed at the corner of 10th Street and 17th Avenue.
Learn more about graph here:
brainly.com/question/16608196
#SPJ5
Arrange the systems of equations in order from least to greatest based on the number of solutions for each system.
Answer:
work is shown and pictured
Answer:
case 1
3x-7y=9
-4x+5y=1
using a graph tool
the solution is the point (-4,-3)------------------> one solution
case 2
y=6x-2
y=6x-4
two parallel lines
the system has no solution---------------> zero solution
case 3
-5x+y=10
-25x+5y=50
is the same line----------------> infinite solutions
HELP PLEASE Solve the equation for x. the square root of the quantity x plus 4 end quantity minus 7 equals 1 x = 4 x = 12 x = 60 x = 68
Answer:
679=49
Step-by-step explanation:
3838 is the one for 928 cause 666
U
Which statements are true about x? Select three
options
B
XEBUC
Oxenc
OXEAUC
Oxeanc
ΕχεΑ
с
Answer:
A, B, C
Step-by-step explanation:
x is in the intersection of sets B and C, in set B, in set C, in the union of sets B and C, in the union of sets A and C
Answer: A, B, C
Answer:
[tex]\huge\boxed{x\in\bigg(A\cup C\bigg)}[/tex]
[tex]\huge\boxed{x\in\bigg(B\cup C\bigg)}\\\\\boxed{x\in\bigg(B\cap C\bigg)}[/tex]
Step-by-step explanation:
Look at the picture
the scale on the map of a park is 5 in. : 3 mi.
Answer:
If the scale on a map is 5in : 3 miles, it means every 3 inches is 5 miles. 6 inches is 10 miles and so on.
Please answer it now in two minutes
Answer:
4.5
Step-by-step explanation:
Use sin64=x/5 and simplify to
5sin64 and plug it into a calculator to get 4.49 which is 4.5
George spent $40.80 on 3 identical files and 2 identical pencil cases. Each file cost $5.40 less than a pencil case. How much did George pay for each file?
Answer:
He spent $6 on each file
Step-by-step explanation:
Hello,
To solve this question, we need to bring out our variables from the equation.
He spent $40.80 for 3 files and 2 pencil cases
Let x represent the file
Let y represent the pencil case
But the file is $5.40 less than each pencil case
x = y - 5.40.....equation (i)
40.80 = 3x + 2y .......equation (ii)
Substitute equation (i) into equation (ii)
40.80 = 3(y - 5.40) + 2y
40.80 = 3y - 16.20 + 2y
Collect like terms
40.80 + 16.20 = 3y + 2y
57 = 5y
Solve for y
y = 57 / 5
y = 11.4
The pencil case costs $11.4 each.
Put y = 11.4 into equation (i)
x = 11.4 - 5.40
x = 6.0
The file costs $6 each
How do I know the following equation is true:
Answer:
The equation is true
Step-by-step explanation:
The best way to check if this equate is true is to convert the pi in radians to degree and actually evaluate the trigonometric terms.
Mathematically we know that pi = 180 degrees
So pi/8 = 22.5
and pi/4 = 180/4 = 45
So let’s make our check.
Insert pi = 22.5 and pi = 45
So we have;
tan 22/5 = √(1-cos45)/(1+cos45)
Now let’s evaluate this using a calculator.
tan 22/5 = 0.414213562373
The term in the root; 0.171572875254
The square root of this number is 0.414213562373
This is exactly as what is obtained with the tan 22.5
So we conclude that what we have is true
PLEASE ANSWER I WILL GIVE BRAINLIEST AND THANKS DESCRIBE FULLY THE SINGLE TRANSFORMATION THAT MAPS A ONTO C
Step-by-step explanation:
Shape A is flipped horizontally onto the x-axis
The new shape is mirroring Shape A
Solve the inequality for y.
y - 9x > 6
please help!!!!!!!
Answer:
y>9x+6
Step-by-step explanation:
y-9x+(9x)>6+(9x)
y>9x+6
TRUE OF FALSE : -2 > 6
Answer: False for sure
Answer:
[tex]\boxed{\mathrm{False}}[/tex]
Step-by-step explanation:
[tex]-2<6[/tex]
-2 is less than 6.
6 is a greater value than -2.
Use the elimination method to solve the ststem of equations.choose the correct ordered pair 10x+2y=22 3x-4y=-21
Answer:
x=1 and y=6
Step-by-step explanation:
10x+2y=22
3x-4y=-21
First at all, you have to multiply both sides of this equation of 10x+2y=22, like this,
2(10x+2y)=2*22
*Put the 2 for the both sides.
Then, expand them.
20x+4y=44
When we have 20x+4y=44, we can eliminate with another equation.
20x+4y=44
3x-4y=-21
So, the first equation has +4y and the second equation has -4y, so we can use elimination method to eliminate one variable.
This time we can sum these equation to get one variable to get the answer easily. Like this...
20x+4y=44
3x-4y=-21
to become...
23x=23
x=23/23
x=1
When we get the equation like this, we can divide 23 by 23, so we can get the value of x. So, the value of x is 1.
When we know x is equal to 1, we can do the last part substitute x=1 into the second equation which is 3x-4y=-21.
The following steps is like this:
Substitute x=1 into 3x-4y=-21,
3(1)-4y= -21
3-4y= -21
Move the 3 to the another side, like this;
-4y= -21-3
-4y= -24
y= -24/ -4
y=6
*Be careful! When you calculate -24/-4 , you have to know how to eliminate the negative sign. (-) / (-) = +
Negative number divided by negative number is equal to positive number.
So, here we go! the value of x is 1 and the value of y is 6.
That is my solution and explanation from me. I hope you can understand. Bye!
A bin has 5 white balls and k black balls in it, where k is an unknown positive integer. A ball is drawn at random from the bin. If a white ball is drawn, the player wins 1 dollar, but if a black ball is drawn, the player loses 1 dollar. If the expected loss for playing the game is 50 cents, then what is k?
Answer:
Step-by-step explanation: The expected loss is 50 cents, we know that it is more likely to lose than win. It is therefore difficult to get-50, so the overall difference between the two possibilities is 2, 50/200=1/4, and the probability to win is 1/4, and the probability to lose is 3/4. Since (1/4)*3=3/4, the number of black balls is 3 times the number of white balls, so k=15.
Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the rectangle: A ( 2, -6) B ( 5, -6) C (5,-2) D (2.-2) What is the perimeter of rectangle ABCD? PLEASE ANSWER QUICK!!!
Answer:
The answer is 14
Step-by-step explanation:
Point A to Point B is 3
Point C to Point D is 3
Point B to Point c is 4
Point D to point A is 4.
Add all those together to get 14
Answer:
the answer is 14
hope you like this
keep rocking
stay at home stay safe
To prove that the triangles are similar by the SAS similarity theorem, it needs to be shown that
Answer:
The triangle has two sides that are equivalent and the angle where the two meet are also equivalent.
In other words, two sides and the angle between them are congruent.
Hope this helps, if it does please give me brainliest, it will help me a lot :)
Have a good day
Answer:
A on edge
Step-by-step explanation:
I need helpppppppppppppppppp
Answer:
A:
9×1=9
9×2=18
9×3=27
9×4=36
9×5=45
9×6=54
9×7=63
9×8=72
9×9=81
9×10=90
B:
It goes down by 1 after multiplying a bigger number.
C:
It goes up by 1 after multiplying a bigger number.
Step-by-step explanation:
hope this helps you and have a great day
Which description best describes the solution to the following system of equations? y = −2x + 3 y = −x + 6
Answer:
Step-by-step explanation:
-2x + 3 = -x + 6
-x + 3 = 6
-x = 3
x = -3
y = 3 + 6
y = 9
(-3, 9)
(sec A + tan A) (1 - sin A) = cos A prove
Answer:
(identity has been verified)
Step-by-step explanation:
Verify the following identity:
(sec(A) + tan(A)) (1 - sin(A)) = cos(A)
Write secant as 1/cosine and tangent as sine/cosine:
(1 - sin(A)) (1/cos(A) + sin(A)/cos(A)) = ^?cos(A)
Put 1/cos(A) + sin(A)/cos(A) over the common denominator cos(A): 1/cos(A) + sin(A)/cos(A) = (sin(A) + 1)/cos(A):
(sin(A) + 1)/cos(A) (1 - sin(A)) = ^?cos(A)
Multiply both sides by cos(A):
(1 - sin(A)) (sin(A) + 1) = ^?cos(A)^2
(1 - sin(A)) (sin(A) + 1) = 1 - sin(A)^2:
1 - sin(A)^2 = ^?cos(A)^2
cos(A)^2 = 1 - sin(A)^2:
1 - sin(A)^2 = ^?1 - sin(A)^2
The left hand side and right hand side are identical:
Answer: (identity has been verified)
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
Let's do this step by step.
Prove that sec A ( 1 - sin A) ( sec A + tan A) = 1
Solving L.H.S
sec A ( 1 - sin A) ( sec A + tan A)
[tex]= \frac{1}{cos A} ( 1 - sin A ) ( \frac{1}{cos A} + \frac{sin A }{cos A})[/tex]
[tex]= \frac{(1 - sin A)}{cos A} ( \frac{1 + sin A }{cos A })[/tex][tex]= \frac{( 1 - sin A)( 1 + sin A)}{cos A X cos A}[/tex]
We know that [tex]( a - b) ( a + b) = a^2 - b^2[/tex]
[tex]= \frac{( 1^2 - sin^2 A)}{cos^2 A}[/tex]
[tex]= \frac{( 1 - sin^2 A)}{cos^2 A}[/tex]
[tex]= \frac{cos^2 A}{cos^2 A}[/tex] [tex]| cos^2 A + sin^2 A = 1 | cos^2 A = 1 - sin^2 A |[/tex][tex]1 - sin^2 A = cos^2 A[/tex]
[tex]= 1[/tex]
[tex]= R . H. S[/tex]
Thus, L.H.S = R.H.S
Hence proved.
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hope this helped you.
Could you maybe give brainliest..?
❀*May*❀
BRAINLIEST, THANKS AND 5 STARS IF ANSWERED CORRECTLY. Find the 15th term: 3, 1, -1, -3, -5... Find the 14th term: 3, 1, -1, -3, -5...
Answer:
-25 and -23
Step-by-step explanation:
The arithmetic sequences are the same so we will have the same formula for each of them. The first term (a₁) is 3 and the common difference (d) is -2.
Explicit formula: aₙ = a₁ + (n - 1) * d
Our formula is aₙ = 3 + (n - 1) * (-2) = -2n + 5
a₁₅ = -2 * 15 + 5 = -25
a₁₄ = -2 * 14 + 5 = -23
Answer: -25 and -23
Step-by-step explanation:
12.
Find the values in the interval [-n/2, n] that satisfy the equation.
arctan (V3/3) = x
с
a. since tan (n/6) = 13/3, X = n/6
b. since sin (-1/4)= -V2/2, x = -1/4
c. since cos (3n/2) = -1/2, X = 3n/2
d. since cos 0 = 1, x = 0
e. since cos (1/4) = V2/2, X = n/4
13
Answer:
Step-by-step explanation:
[tex]tan^{-1} (\frac{\sqrt{3} }{3} )=x\\tan x=\frac{\sqrt{3} }{3} =tan (\frac{\pi}{6} )\\x=\frac{\pi}{6}[/tex]
Please answer this question now
Answer:
d = 8.5
Step-by-step explanation:
The following data were obtained from the question:
Angle D = 100°
Opposite D = d
Opposite E = e = 6
Opposite F = f = 5
Thus, we can obtain the value of d by using the cosine rule as shown below:
d² = e² + f² – 2ef Cos D
d² = 6² + 5² – 2 × 6 × 5 × Cos 100°
d² = 36 + 25 – 60 × Cos 100°
d² = 61 – – 10.419
d² = 61 + 10.419
d² = 71.419
Take the square root of both side.
d = √71.419
d = 8.5
Therefore, the value of d is 8.5
The cylinder shown has a lateral surface area of about 400 square inches. Which answer is closest to the measure of the cylinder's radius? Use 3.14 to approximate pi.
Answer:
r = 1.59inch
the radius of the cylinder is
1.59inch
Step by step Explanation
lateral surface of a cylinder can be calculated using the below formula
Surface Area= 2 πr h
We were given area as 400inch^2 and height as 40inch then substitute we have
400 = 2 ×π × r ×40
400= 2×22/7×40
Then do the calculation, where, π
=22/7
400 = r × 251.2
Make r subject of formula we have
r = 400 / 251.2
r = 1.59inch
Therefore, the radius of the cylinder is
1.59inch
CHECK THE ATTACHMENT FOR THE FIGURE
Solve for x: (-1/2) x = 6
Answer: x = -12
Step-by-step explanation:
-1/2x=6
Divide by -1/2
x = -12
Hope it helps <3
a rectangular fish tank is 50 cm long, 40 cm wide, and 30 cm high.
a) how many cubic centimeters of water will the tank hold?
b) how many milliliters of water will the tank hold?
c) how many liters of water will the tank hold?
Answer:
a) 60,000 cubic cm
b)600,000 cubic mm
c)60 L
Step-by-step explanation
To find the volume, you would have to multiply the height length and width.
50*40*30 and that equals to 60,000 cm. 10 mm=1cm.
So 60,000*10=b, b=600,000, 1,000 cm=1 L
60,000/1,000=L, L=60
Hope this helps. If it does, please rate 5 stars!
In a survey of 2957 adults, 1455 say hey have started paying bills online in the least year construct a 99% confidence interval for the population proportion
Answer: 0.49 ± 0.0237
Step-by-step explanation: A interval of a 99% confidence interval for the population proportion can be found by:
[tex]p_{hat}[/tex] ± z.[tex]\sqrt{\frac{p_{hat}(1-p_{hat})}{n} }[/tex]
[tex]p_{hat}[/tex] is the proportion:
[tex]p_{hat}[/tex] = [tex]\frac{1455}{2957}[/tex]
[tex]p_{hat}[/tex] = 0.49
For a 99% confidence interval, z = 2.576:
0.49 ± 2.576.[tex]\sqrt{\frac{0.49(1-0.49)}{2957} }[/tex]
0.49 ± 2.576.[tex]\sqrt{\frac{0.49*0.51}{2957} }[/tex]
0.49 ± 2.576.(0.0092)
0.49 ± 0.0237
For a 99% confidence interval, the proportion will be between 0.4663 and 0.5137 or 0.49 ± 0.0237
4/5 (x − 20) = 8 solve it
Answer:
30
Step-by-step explanation:
4/5 (x-20)=8
4/5x-4/5*20=8
4/5x-16=8
4/5x=24
x=(24*5)/4
x=30
hope it helps..
Simplify: |x−y| if x is less than y
Answer:
y-x
Step-by-step explanation:
I assumed you meant that you wanted me to rewrite the expression without the absolute value signs. Since the absolute value of a number will be the same whichever way you place the numbers, you can rewrite |x-y| as y-x, as x is less than y.
URGENT!! Please help me with this as soon as possible!!
The statement is valid because the measure of the vertices located in the center of the pentagon is the quotient of 360 and 5, and the sum of two base angles in the given isosceles triangle is 108.
==========================================================
Explanation:
Check out the diagram below. I have added x and y such that
x = base angle
y = vertex angle (located adjacent to center of polygon)
The pentagon is sliced up like a cake into 5 equal portions. Each vertex angle is y = 360/5 = 72 degrees.
The two base angles x must add with the vertex angle y to get 180
(angle1)+(angle2)+(angle3) = 180
x+x+y = 180
2x+y = 180
2x+72 = 180
2x = 180-72
2x = 108
This is true for any one of the five triangles. Notice that for angle LMN, we can divide it into LMQ and QMN where Q is the center of the polygon. Both of these angles are x. Since we've shown 2x = 108, we can see that LMN must also be 108 as well.
Choice A is close, but we wouldn't use the exterior angle theorem. Choice B is the better answer.