The equation of the volume of the sphere is 4/3 × 27π
The volume of a cylinder is expressed as
V = πr²h
Since the cylinder has thesame height and radius, therefore, the volume of the cylinder will now be
V = πr² × r
V = πr³
The volume of a sphere is expressed as
V = 4/3(πr³)
Therefore we can say
the volume of sphere = 4/3 × volume of the cylinder
Volume of cylinder = 27π
volume of sphere = 4/3 × 27π
= 4 × 9
= 36πft³
suppose that a biologist is watching a trail known for wildebeest migration. During the first minute, 24 wildebeests migrated past the biologist on the trail. Was hoping minute, the number increased by 3. How many wildebeests migrated past the biologist during the first 20 mins
Answer:
=1050 wildebeests
Step-by-step explanation:
We can form an arithmetic series for the wildebeest migration.
Sₙ=n/2(2a+(n-1)d) where n is the number of terms, d is the common difference and a is the first term.
a=24
n=20
d=3
Sₙ=(20/2)(2(24)+(20-1)3)
Sₙ=10(48+57)
=1050 wildebeests
Five men can install 200 yards of pipeline in an eight hour day three men are added to the job assuming the individuals rates remain the same how many days will it take the entire crew to install 2240 yards of pipeline
Answer:
7 days
Step-by-step explanation:
Five men do 200 yards in one day
One man does 200/5 = 40 yards in 1 day.
=============
Now you want to know something about 8 men
8 men can do 40 * 8 = 320 yards in 1 day
=============
2240 yards / 320 yards = 7 days
Write an expression for the area of a square with side s = 2x + 5
Answer:
[tex]4x^2+20x+25[/tex] square units
Step-by-step explanation:
We are given that side of a square has the dimension [tex]s = 2x + 5[/tex] and using this, we are to write an expression for the area of this square.
We know that the formula of area of a square is given by:
Area of square = [tex]s^2[/tex]
So substituting the given value in the above formula to get:
Area of square = [tex](2x+5)^2 = (2x+5)(2x+5) = 2x(2x)+2x\times5+5(2x)+5\times5 = 4x^2+20x+25[/tex] square units
Answer:
[tex]A = 4x ^ 2 + 20x +25[/tex]
Step-by-step explanation:
Remember that all sides of a square have the same length. Therefore, the Area of a square is defined as:
[tex]A = s ^ 2[/tex]
Where s is the length of the sides of the squares.
In this case we know that the length of the sides is:
[tex]s = 2x + 5[/tex]
So the area is:
[tex]A = (2x +5) ^ 2[/tex]
We develop the expression and we have left that the area is:
[tex]A = 4x ^ 2 + 20x +25[/tex]
The set of possible values of n is {-2, 1; 4).
What is the set of possible values of m if
3m = n-7?
How do I solve it
Replace n in the equation with each given value and solve for m.
You are given n = {-2, 1, 4}
When n = -2:
3m = -2-7
3m = -9
m = -9/3
m = -3
When n = 1:
3m = 1-7
3m = -6
m = -6 /3
m=-2
When n = 4:
3m = 4-7
3m = -3
m = -3/3
m = -1
m = {-3, -2, -1}
A discrete randem variable is a variable that is randomly chosen and can only take on certain values.
A. True
B. False
Answer:
A. True.
Step-by-step explanation:
For example, the results of throwing a fair dice. The variable can only be 1,2,3,4,5,6.
Answer: True
A P E X
A discrete randem variable is a variable that is randomly chosen and can only take on certain values.
Which of the following solids has a triangular cross section when the cross section is taken perpendicular to the base?
A.
square pyramid
B.
cube
C.
hexagonal prism
D.
rectangular prism
Answer:
A. square pyramid
Step-by-step explanation:
A square pyramid has a triangular cross section when the cross section is taken perpendicular to the base.
The solid that has a triangular cross section when the cross section is taken perpendicular to the base is a square pyramid. A cross section through the sloping triangular faces of the square pyramid will reveal a triangular shape.
To answer this, consider the properties of each option:
A square pyramid has a square base and triangular faces that meet at a common point above the base, resembling a series of tetrahedra joined together. When a cross section is taken perpendicular to its square base, it would indeed reveal a triangle shape as it would pass through these sloping triangular faces.
A cube would not result in a triangular cross section since it has all square faces.
A hexagonal prism has a hexagon as its base, and taking a cross section perpendicular to this base would yield a hexagon, not a triangle.
Similarly, a rectangular prism would result in a rectangle or square from such a cross section.
Therefore, the correct answer is a square pyramid.
Find the equation of a line passing through the points (2,6) and (-2,-10)
[tex]\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{-10}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-10-6}{-2-2}\implies \cfrac{-16}{-4}\implies 4 \\\\\\ \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-6=4(x-2) \\\\\\ y-6=4x-8\implies y=4x-2[/tex]
Answer:
y = 4x - 2.
Step-by-step explanation:
The slope is difference in y values / difference in x values
= (6 - -10) / (2 - -2)
= 16 / 4
= 4.
Using the point-slope form of a line
y - y1 = m(x - x1) where m = slope and (x1, y1) is a point on the line, we have:
y - 6 = 4(x - 2)
y = 4x - 8 + 6
y = 4x - 2.
The data represents the semester exam scores of 8 students in a math course.
{51, 91, 46, 30, 36, 50, 73, 80}
What is the five-number summary?
Answer:
C
Step-by-step explanation:
if u try and find the median you get 50.5 because it is the middle of 50 (fourth term) and 51 (fifth term) and only c has the correct median
What polynomial has roots of −6, 1, and 4?
x3 − 9x2 − 22x + 24
x3 − x2 − 26x − 24
x3 + x2 − 26x + 24
x3 + 9x2 + 14x − 24
Answer:
The correct option is C
Step-by-step explanation:
We have given the roots -6, 1 and 4.
Write down the roots:
x= -6 , x=1 , x=4
Rewrite the roots as an expression:
x+6=0
x-1=0
x-4=0
Now we have the following expressions:
=(x+6)(x-1)(x-4)
Now Multiply the terms:
=(x²-x+6x-6)(x-4)
=(x²+5x-6)(x-4)
=x(x²+5x-6) -4(x²+5x-6)
=x³+5x²-6x-4x²-20x+24
Solve the like terms:
=x³+x²-26x+24
Thus the correct option is C....
Answer:
aaaaaaaa top one wrong
Step-by-step explanation:
Suppose Q and R are independent events. Find P(Q and R) if P(Q) = 7/15 and P(R) = 4/7
Answer:
4/15.
Step-by-step explanation:
In probability, there are two types of events: the ones that are not related to each other and the ones that are related to each other. The former types of events are called independent events. In such cases, since the occurrence of one event is not related to and does not affect the other event, therefore, the probabilities of both events can be multiplied if they occur together. It is given that:
P(Q) = 7/15.
P(R) = 4/7.
P(Q and R) = P(Q)*P(R) = 7/15 * 4/7 = 4/15.
Therefore, the probability is 4/15!!!
(x-2)(-5x^2+x)=(x)(-5x^2)+(x)(x)+(-2)(-5x^2)+(-2)(x)
Answer:
Step-by-step explanation:
First we will solve the Left Hand Side:
(x-2)(-5x²+x)
Multiply the terms:
= -5x³+x²+10x²-2x
Solve the like terms
= -5x³+11x²-2x
Now we will solve the Right Hand Side:
(x)(-5x²)+(x)(x)+(-2)(-5x²)+(-2)(x)
Multiply the terms:
-5x³+x²+10x²-2x
Solve the like terms:
-5x³+11x²-2x
Hence it is proved that L.H.S = R.H.S....
Complete: 45° C = ___° F
A. 81 B. 77 C. 25 D. 13
Answer:
113ºF
Step-by-step explanation:
Remember that exist a conversion rule that states:
[tex]F=\frac{9*C}{5} +32[/tex]
using it we have the following expression:
[tex]1.8*(45)+32=113[/tex]
What is the standard form for the quadratic function? g(x)=(x+1)^2−2
g(x)=x^2−2x−4
g(x)=x^2−1
g(x)=x^2+2x−1
g(x)=x^2−3
the standard form is g(x)=x^2+2x-1
Which of the following are remote interior angles of _1? Check all that apply.
Answer:
B and E
Step-by-step explanation:
The remote interior angles to ∠1 are the 2 opposite interior angles, that is
∠5 and ∠6
a ladder is 40 ft and an 80 degree decline its an isosceles right triangle what so my sides equal
Answer:
The sides are equal to
x=6.9 ft and y=39.4 ft
Step-by-step explanation:
step 1
Find the adjacent side to the angle of 80 degrees
Let
x ----> the adjacent side to the angle of 80 degrees
we know that
The function cosine of angle of 80 degrees is equal to divide the adjacent side to the angle of 80 degrees by the hypotenuse (40 ft)
cos(80°)=x/40
x=(40)cos(80°)
x=6.9 ft
step 2
Find the opposite side to the angle of 80 degrees
Let
y ----> the opposite side to the angle of 80 degrees
we know that
The function sine of angle of 80 degrees is equal to divide the opposite side to the angle of 80 degrees by the hypotenuse (40 ft)
sin(80°)=y/40
y=(40)sin(80°)
y=39.4 ft
URGENT,PLEASE HELP ME !!!!!!!!!!!!!!!
Answer: The last one
Step-by-step explanation:
I think this because the graph starts from H the number of hours studied and when u add the numbers and divide them up which gives you the equation 65 + 50 . Any questions please text me. Have a nice day.
A species of extremely rare, deep water fish rarely have children. if there are 821 of this type of fish and their growth rate is 2% each month, how many will there be in half of a years, in 2 years, and in 10 years?
Answer:
There are 925 in half of a year
There are 1321 in 2 years
There are 8838 in 10 years
Step-by-step explanation:
* Lets revise the exponential function
- The original exponential formula was y = ab^x, where a is the initial
amount and b is the growth factor
- The new growth and decay functions is y = a(1 ± r)^x. , the b value
(growth factor) has been replaced either by (1 + r) or by (1 - r).
- The growth rate r is determined as b = 1 + r
* Lets solve the problem
∵ The number of fish is growth every month
∴ We will use the growth equation y = a(1 + r)^x, where a is the initial
amount of the fish, r is the rate of growth every month and x is the
number of months
- There are 821 of a type of fish
∴ The initial amount is 821 fish
∴ a = 821
- Their growth rate is 2% each month
∴ The rate of growth is 2% per month
∴ r = 2/100 = 0.02
- We want to find how many of them be in half year
∵ There are 6 months in half year
∴ y = 821(1 + 0.02)^6
∴ y = 821(1.02)^6 = 924.58 ≅ 925
* There are 925 in half of a year
∵ There are 24 months in 2 years
∴ y = 821(1 + 0.02)^24
∴ y = 821(1.02)^24 = 1320.53 ≅ 1321
* There are 1321 in 2 years
∵ There are 120 months in 10 years
∴ y = 821(1 + 0.02)^120
∴ y = 821(1.02)^120 = 8838.20 ≅ 8838
* There are 8838 in 10 years
(11z2+4z-6)+(4z-7+12z2)+(-8+13z2+4z)
Answer: [tex]36z^2+12z-21[/tex]
Step-by-step explanation:
You need to remember the multiplication of signs:
[tex](+)(+)=+\\(+)(-)=-\\(-)(-)=+[/tex]
In order to simplify the given the expression:
[tex](11z^2+4z-6)+(4z-7+12z^2)+(-8+13z^2+4z)[/tex]
You must distribute signs:
[tex]=11z^2+4z-6+4z-7+12z^2-8+13z^2+4z[/tex]
And finally, you must add the like terms:
[tex]=36z^2+12z-21[/tex]
Answer:
huifytyjctrxrtfygvjhk
Step-by-step explanation:
yeah he is right
Patrick travels from A to B at an average speed of 8km/h and then he travels from B to C at an average speed of 6 km/h.It is given that Patrick travels 26.4 km in 234 minutes for the whole journey.Find the distance that Patrick travels from A to B.
Answer:
12 km
Step-by-step explanation:
So the situation is:
8 km/h for X hours
6 km/h for y hours
X * 8 + y * 6 = 26.4
and X + Y = 3.9 hours
Since 234/60 = 3.9 hours
You could write that X = 3.9 - Y
(3.9-Y) * 8 + y * 6 = 26.4
31.2 -8Y +6Y = 26.4
-2Y = -4.8
Y = 2.4 hours
X = 3.9-2.4 = 1.5 hours
So 1.5 * 8 = 12 km
Answer:
AB = 12km
Step-by-step explanation:
From the question we can get the following information,
The whole trip is 26.4 km and 3.9 hours ([tex]\frac{234}{60}[/tex]), and we can form the following two equations.
[tex]x + y = 3.9[/tex] and [tex](x*8km/h) + (y*6km/h) = 26.4km[/tex]
Where X is distance between A and B, and Y is distance between B and C. We can solve the first equation for X and plug X into the second equation.
[tex]x = 3.9 - y[/tex] ........ and we can plug it into the the second equation and solve for y
[tex]((3.9-y)*8)+(6y) = 26.4[/tex]
[tex](31.2-8y)+6y = 26.4[/tex]
[tex]31.2-2y = 26.4[/tex]
[tex]-2y = -4.8[/tex]
[tex]y = 2.4[/tex]
Now we can plug in y to the first equation to solve for x
[tex]x = 3.9-2.4[/tex]
[tex]x = 1.5[/tex]
Finally, we can multiplay 8km/h by 1.5 hours to find the distance from A to B
[tex]AB = 8km/h * 1.5h[/tex]
[tex]AB = 12km[/tex]
Find the value of z.
A. 6
B. 3
C. 4
D. 2
The two chords on top of each other are the same length as the single vertical chord.
The vertical chord is 2 + 4 +2 = 8 units long.
Z = 8-2 = 6
The answer is A.
Length of chord z is 6.
What is chord length?It is defined as the line segment joining any two points on the circumference of the circle, not passing through its center. Therefore, the diameter is the longest chord of a given circle, as it passes through the center of the circle.
From the figure we can write,
[tex]z+2=2+4+2[/tex]
[tex]z+2=8[/tex]
[tex]z=8-2=6[/tex]
Length of chord z is 6.
Find out more information about chord length here
https://brainly.com/question/9857445
#SPJ2
(3x-5)+(15-x)+(2x-3)
The perimeter is 35 ft.
Answer:
17x
Step-by-step explanation:
combine like terms,you would end up with 20x because if you combine 3x and 2x=5 then 5x+15x is 20x.then 20x-3 is 17x.
Find the geometric means in the following sequence.
47,
?
,
?
,
?
,
?, - 789, 929
R
Select one:
a. -6,580, -9,870, -13,160, -16,450
b. 329, 2,303, 16,121, 112,847
C. 2,303, -16,121, 112,847, -789,944
d. -329, 2,303, -16,121, 112,847
Answer:
d (last choice)
Step-by-step explanation:
The explicit form of a geometric sequence is [tex]a_n=a_1 \cdot r^{n-1}[/tex] where [tex]a_1[/tex] is the first term while [tex]r[/tex] is the common ratio.
We are given the first term [tex]a_1=47[/tex].
We are given the sixth term [tex]a_6=-789929[/tex].
If we divide 6th term by 1st term this is the result:
[tex]\frac{a_1 \cdot r^5}{a_1 }=\frac{-789929}{47}[/tex]
Simplify both sides:
[tex]r^5=-16807[/tex]
Take the fifth root of both sides:
[tex]r=-7[/tex]
The common ratio is -7.
So all we have to do is start with the first term and keep multiplying by -7 to get the other terms.
[tex]a_1=47[/tex]
[tex]a_2=47(-7)=-329[/tex]
[tex]a_3=47(-7)^2=2303[/tex]
[tex]a_4=47(-7)^3=-16121[/tex]
[tex]a_5=47(-7)^4=112847[/tex]
[tex]a_6=47(-7)^5=-789929[/tex]
The terms -329,2303,-16121,112847 are what we are looking for in our choices.
That's the last choice.
Which exponential function is represented by the values in the table? A.f(x) = 1/2(4)x B.f(x) = 4(4)x C.f(x) = 4(1/2) D.f(x) = 1/2(1/2)^x
Answer:
The Answer is D
Step-by-step explanation:
If the Exponent is 1 or just x then it is linear.
If the Exponent is 2 or x^2 then it is quadratic* If the Exponent has and x, then this graph is exponential because anything to the power of X is exponential.
1/2(1/2)=0.25^x
Answer:
The Answer is C
Step-by-step explanation:
Just took ed2020 test
Find the x value do that the line through the points (x,-9) and (0,1) has a slope of -4 PLEASE ANSWER
[tex]\bf (\stackrel{x_1}{x}~,~\stackrel{y_1}{-9})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-(-9)}{0-x}=\stackrel{\stackrel{slope}{\downarrow }}{-4}\implies \cfrac{1+9}{-x}=-4 \\\\\\ \cfrac{10}{-x}=-4\implies 10=4x\implies \cfrac{10}{4}=x\implies \cfrac{5}{2}=x[/tex]
PLEASE HELP ME!!! what are the roots of x in -10x^2+12x-9=0
Answer:
Option B.
Step-by-step explanation:
We have the following polynomial: -10x^2+12x-9=0
Multiplying by -1:
10x^2-12x+9=0
Using the quadratic formula, we find that the roots are:
0.6 ± 3√(6)/10i
Therefore, the correct answer is B.
PLS HELP, I'm not very good at math so I need the answer to this
Answer:
A BT = CT
Step-by-step explanation:
BAT ≅ CAT
That means
The angles are the same and the sides are the same by CPCTC
AB = AC
CT = BT
AT=AT
and
< BAT = <CAT
< ATB = <ATC
< TBA = <TCA
Given the choices on the left
A BT = CT is one of them
Samantha’s rectangular gift is 10 inches. by 12 inches and is framed with a ribbon. She wants to use the same length of ribbon to frame a circular clock. What is the maximum radius of the circular clock? Round to the nearest whole number.
(JUSTIFY)
Answer:
7 inches
Step-by-step explanation:
The dimension of the rectangular gift is 10 by 12 inches so let us find the perimeter of this rectangle.
Perimeter of rectangular gift = 2 (L+ W) = 2 (10 +12) = 44 inches
Since we are to use the same length of ribbon to wrap a circular clock so the perimeter or circumference should be 44 inches.
[tex]2\pi r=44[/tex]
[tex]r=\frac{44}{2\pi }[/tex]
[tex]r=7.003[/tex]
Therefore, the maximum radius of the circular clock would be 7 inches.
Answer:
The maximum radius of the circular clock is 7 in
Step-by-step explanation:
We must calculate the perimeter of the rectangle
We know that the rectangle is 10 in x 12 in
If we call L the rectangle length and we call W the width of the rectangle then the perimeter P is:
[tex]P = 2L + 2W[/tex]
Where
[tex]L = 10[/tex]
[tex]W = 12[/tex]
[tex]P = 2 * 10 + 2 * 12\\\\P = 20 + 24[/tex]
[tex]P = 44\ in[/tex]
Now we know that the perimeter of a circle is:
[tex]P = 2\pi r[/tex]
In order for the perimeter of the circumference to be equal to that of the rectangle, it must be fulfilled that:
[tex]2\pi r = 44\\\\r=\frac{44}{2\pi}\\\\r=7\ in[/tex]
We solve the equation for r
what is the gcf of 42 and 60
Answer:
The GCF of 42 and 60 is 6
Step-by-step explanation:
42: 1,2,3,6,7,14,21,42
60: 1,2,3,4,5,6,10,12,15,20,30,60
Answer:
6
Step-by-step explanation:
Factors of 42 = 1, 2, 3, 6, 7, 14, 21 and 42
Factors of 60 = 1 , 2 , 3 , 4 , 5 , 6 , 10 , 12 , 15 , 20 , 30 and 60
The highest factor which comes in both 42 and 60 is 6
Help please!!!
What is the distance between the two endpoints in the graph below? If necessary, round your answer to two decimal places.
Answer:
A) 7.07
Step-by-step explanation:
[tex]The \: distance \: formula = \sqrt{(x_2 - x_1) ^{2} + (y_2 - y_1) ^{2} } [/tex]
[tex]P_1(-3, -2) \: \: \: \: \: \: \: \: \: \: \: P_2(2, 3)[/tex]
[tex]d = \sqrt{ {(2 - ( - 3))}^{2} + {(3 - ( - 2))}^{2} } \\ d = \sqrt{ {(2 + 3)}^{2} + {(3 + 2)}^{2} } \\ d = \sqrt{ {5}^{2} + {5}^{2} } \\ d = \sqrt{25 + 25} \\ d = \sqrt{25(1 + 1)} \\ d = \sqrt{25(2)} \\ d = \sqrt{25} \times \sqrt{2} \\ d = 5 \sqrt{2} \\d = 7.07106781187 \\ d = 7.07[/tex]
Answer: A. 7.07 units
Step-by-step explanation:
The distance between any two points (a,b) and (c,d) is given by :-
[tex]D=\sqrt{(d-b)^2+(c-a)^2}[/tex]
From the given picture , we can see that the line is passing through (2,3) and (-3,-2).
The distance between (2,3) and (-3,-2) is given by :-
[tex]D=\sqrt{(-2-3)^2+(-3-2)^2}\\\\\Rightarrow\ D=\sqrt{(-5)^2+(-5)^2}\\\\\Rightarrow\ D=\sqrt{25+25}=\sqrt{50}\\\\\Rightarrow\ D=7.07106781187\approx7.07[/tex]
Hence, the distance between the two endpoints = 7.07 units
(X+3)(x^2-6x+5). Please help multiply polynomials
Answer:
s is neding some more in fo
Step-by-step explanation:
Answer:
x³ - 3x² - 13x + 15
Step-by-step explanation:
Each term in the second factor is multiplied by each term in the first factor, that is
x(x² - 6x + 5) + 3(x² - 6x + 5) ← distribute both parenthesis
= x³ - 6x² + 5x + 3x² - 18x + 15 ← collect like terms
= x³ - 3x² - 13x + 15