Using the Fundamental Counting Theorem, the number of possible sequences of eight coin faces is of 256.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
In this problem, there are 8 events, each with 2 possible outcomes, hence:
[tex]n_1 = n_2 = \cdots = n_8 = 2[/tex]
Hence, the total number of sequences is given by:
[tex]N = 2^8 = 256[/tex].
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Answer:
C) 256
Step-by-step explanation:
Essentially, each coin flip is a decision, and heads or tails is the choice offered. Therefore, we calculate that there are 28 possible sequences, or 256.
Took the quiz ;)
A simple random sample from an infinite population is a sample selected such that.
A simple random sample from an infinite population is a sample selected such that each element is selected independently and from the same population.
What is Simple Random Sampling?Simple random sampling is known to be a types of sampling where there are no laws, rules etc., on how to select the samples.
Note that it is seen easiest way of sampling and as such, A simple random sample from an infinite population is a sample selected such that each element is selected independently and from the same population.
See full question below
A simple random sample from an infinite population is a sample selected such that:
a. each element is selected independently and from the same population
b. each element has a 0.5 probability of being selected
c. each element has a probability of at least 0.5 of being selected
d. the probability of being selected changes
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Which choice could represent the surface area of a pyramid? 75.6 feet superscript 4 75.6 feet cubed 75.6 feet squared 75.6 feet
The choice that could represent the surface area of a pyramid is 75.6 feet squared
Surface area of a pyramid.The surface area of an object is the total sum of the area of its net. The surface area of any object is expressed in square units.
For instance, a pyramid with 4 triangles and a base area with al the units in feet can be expressed as:
TSA = area of 4 triangles + area of the base
Hence the choice that could represent the surface area of a pyramid is 75.6 feet squared
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Answer:
C/3
Step-by-step explanation:
In your opinion, what components of a free market are the most important
A free market is one where voluntary exchange and the laws of supply and demand provide the sole basis for the economic system, without government intervention. A key feature of free markets is the absence of coerced (forced) transactions or conditions on transactions.
x² + y² = 8
x - y = 0
Select all of the following that are solutions to the system shown.
O (2, 2)
O (2,-2)
O (-2,2)
0 (-2,-2)
Answer:
[tex](2,2)~ \text{and}~ (-2,-2)[/tex]
Step by step explanation:
[tex]x^2 +y^2 =8~~~~~~...(i)\\\\x-y=0~~~~~~~~~...(ii)\\\\\text{From (ii):}\\\\x-y = 0 \implies x = y\\\\\text{Substitute x = y in eq (i):}\\\\~~~~~~y^2 +y^2 =8\\\\\implies 2y^2 = 8\\ \\\implies y^2 = \dfrac 82\\\\\implies y^2 = 4\\\\\implies y = \pm\sqrt 4\\\\\implies y = \pm 2\\\\\text{Substitute y = x in equation (i):}\\ \\~~~~~~x^2 +x^2 = 8\\ \\\implies 2x^2 = 8\\\\\implies x^2 = \dfrac 82\\\\\implies x^2 = 4\\\\\implies x = \pm\sqrt 4\\\\\implies x = \pm2\\\\[/tex]
[tex]\text{Hence,}~ (x,y) = (\pm2, \pm 2)[/tex]
William needs to translate ΔLMN by the rule (x,y)→(x−4,y+7). Which of the following graphs represents that translation?
Answer:
B
Step-by-step explanation:
let me know if you need an explanation, I'll add one :D
what is the anwer to 81 = 27x-4
Answer: x= [tex]\frac{85}{27}[/tex]=x
Step-by-step explanation:
1. Add 44 to both sides.
81+4=27x
2. Simplify 81+4 to 85.
85=27x
3. Divide both sides by 27.
[tex]\frac{85}{27}[/tex]=x
4. Switch sides.
X= [tex]\frac{85}{27}[/tex]
Decimal form: 3.148148
An open box is to be made out of a 6-inch by 18-inch piece of cardboard by cutting out squares of equal size from the four corners and bending up the sides. find the dimensions of the resulting box that has the largest volume.
dimensions of the bottom of the box:
height of the box:
An open box is to be made out of a 6-inch by 14-inch piece of cardboard by cutting out squares of equal size from the four corners and bending up the sides. Find the dimensions of the resulting box that has the largest volume.
Dimensions of the bottom of the box: L x W
Height of the box:
SOLUTION
Diagram
Cardboard with x2 area cutouts...
··················14 - 2x
···x··¦¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¦···x··
¦——¦·······························¦——¦
¦·············································¦
¦·············································¦ 6 - 2x
¦·············································¦
¦——¦·······························¦——¦
···x··¦___________________¦··x···
Volume = l·w·h
After cutouts:
l = 14 - 2x
w = 6 - 2x
h = x
V = (14 - 2x)(6 - 2x)(x) in3
V = 4x3 - 40x2 + 84x in3
To maximize the volume, take the derivative of V with respect to x, set it equal to zero, and solve for x:
dV/dx = 0 = 12x2 - 80x + 24
x2 - (20/3)x + 7 = 0
x = (10 ± √37)/3 in
Since (6 - 2x) yields a negative number for x = (10 + √37)/3 we use only x = (10 - √37)/3
Thus, the dimensions are:
l = 14 - 2x = 11.39 in
w = 6 - 2x = 3.39 in
h = x = 1.31 in
Base = l·w = 38.59 in2
Volume = 50.39 in3
Segment AB has point A located at (6, 5). If the distance from A to B is 5 units, which of the following could be used to calculate the coordinates for point B? (1 point)
The equation that can be determined by the coordinates for point B will be 25 = (x - 6)² + (y - 5)².
What is coordinate geometry?The study of geometry using points in space is known as coordinate geometry. This may be used to discover the length between the endpoints, the dividing line's m:n ratio, the line's mid-point, and so on.
Segment AB has point A located at (6, 5). If the distance from A to B is 5 units.
Then the equation that can be determined by the coordinates for point B will be
[tex]\rm 5 = \sqrt{(x-6)^2 +(y-5)^2}[/tex]
This can be written as
25 = (x - 6)² + (y - 5)²
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find the total surface area of this cuboid.
6cm
5cm
4cm
Answer:
148cm^2
Step-by-step explanation:
The formula for surface area of a rectangular prism is 2(hl)+2(hw)+2(wl).
we just plug in the values.
2(6 x 5) + 2(6 x 4) + 2(4 x 5)
= 2(30) + 2(24) + 2(20) then simplify
= 60 + 48 + 40
= 148
What is the perimeter of ΔWXY?
11.57 cm
12.22 cm
12.46 cm
14.50 cm
The perimeter of the triangle ΔWXY is P = 14.50 cm
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the triangle be represented as ΔXYZ
Now , the measure of sides of the inscribed triangle ΔQRS is
QR = 2.93 cm
RS = 2.04 cm
QS = 2.28 cm
where the points Q , R and S are the midpoints of the sides of the triangle ΔXYZ
So , the measure of sides of the triangle are twice the lengths of the sides of triangle ΔQRS
And , the perimeter P = 2 ( 2.93 + 2.04 + 2.28 )
On simplifying , we get
P = 2 ( 7.25 )
P = 14.50 cm
Hence , the perimeter is P = 14.50 cm
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The complete question is attached below :
What is the perimeter of ΔWXY?
a) 11.57 cm
b) 12.22 cm
c) 12.46 cm
d) 14.50 cm
In a group of 60 workers, the average salary is $80 a day per worker. if some of the workers earn $75 a day and all the rest earn $100 a day how many workers earn $75 a day?
The total number of workers that earn $75 per day is 48
What is average salary?The average salary is calculated based on reported salaries of respondents. The average salary definition is to add the salaries in the sample together, then divide by the number of respondents.
Given that:
In a group of 60 workers, the average salary is $80 a day per worker.
If some of the workers earn $75 a day and all the rest earn $100 a day.
Let 'x' be the total number of workers that earn $75 per day.
So, the total number of workers that earn $100 per day is (60 - x).
As the average salary of 60 workers is $80.
Then,
[tex]\frac{75x + 100(60-x)}{60} =80[/tex]
or, 75 x + 6000- 100x = 80*68
or, -25x= -1200
x= 48
So, the total number of workers earn $75 per day is 48.
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What is the arc length of ACB?
Answer:
C. 82.43
Step-by-step explanation:
acb's angle is 315 degrees because
360 - 45 = 315
arc length is in radians
arc length is radius times (angle times (pi÷180))
arc length is 15 times (315 times (pi÷180))
arc length is 82.43
cuemathcomgeometry
pls my test is tomorrow and its 11:30pm lol:(. so the question, a person at the top of a 25 yard tall hill looks down at a tree that is 100 yards diagonally away from the person. what is the angle of depression from the person to the tree
Answer:
76°
Step-by-step explanation:
Taking the cosine ratio of the angle of depression :
cos θ = height of hill / distance from person diagonallycos θ = 25/100cos θ = 1/4θ = cos⁻¹ (0.25)θ = 76° (nearest whole degree)PLEASE PLEASE HELP ME OUT
26.4
Answer:
S8nce N is inthe center NL is one half of KM
The base of a solid is bounded by the curve y = sqrt (x+1) the x-axis and the line x = 1. the cross sections, taken perpendicular to the x-axis, are squares. find the volume of the solid.
a. 1
b. 2
c. 2.333
d. none of these
(will vote brainlest, like and rate)
See attached for a sketch of some of the cross sections.
Each cross section has area equal to the square of the side length, which in turn is the vertical distance between the curve y = √(x + 1) and the x-axis (i.e. the distance between them that is parallel to the y-axis). This distance will be √(x + 1).
If the thickness of each cross section is ∆x, then the volume of each cross section is
∆V = (√(x + 1))² ∆x = (x + 1) ∆x
As we let ∆x approach 0 and take infinitely many such cross sections, the total volume of the solid is given by the definite integral,
[tex]\displaystyle \int_{-1}^1 (x+1) \, dx = \left(\frac{x^2}2 + x\right) \bigg|_{-1}^1 = \boxed{2} ~~~~ (B)[/tex]
7
——
math
math geniuses pls help!!!
——
pls check other questions as well thanks,!
Answer:
The time spent by a physician with a patient
Step-by-step explanation:
Option C is the answer
Find pi using circumference of 78.5 and the radius is 5. Explain how you found pi.
Answer:
Pi is normally 3.14 but in this case it is 15.7
Step-by-step explanation:
78.5 divided by 5 = 15.7
5 x 3.14 = 15.7
Please help me answer the question to the picture attached!!! I need help REALLY BAD!!!!
Answer:
Step-by-step explanation:
it might be like this but im not sure
HELP <3333333333333333333333333333333333333333
Answer:
$30
Step-by-step explanation:
since 7 = 28
and 1 = 4
divide 1 in half to find the half hour amount
1/2 hr = 2
28 + 2 = 30
your answer is $30
hope this helps:)
Jayne stacked 2 cubes on top of each other as shown. The edge length of the smaller cube is half the edge length of the cube below it. What is the surface area of the new figure?
Considering the surface area of a cube, and that the figure has two cubes, the total surface area is of 1470 m².
What is the surface area of a cube?The surface area of a cube of edge length a is given by:
S(a) = 6a².
In this problem, we have two cubes, one with a = 14 m and the other with a = 7 m. Hence, the total surface area, in m², is given by:
S(a) = 6 x 14² + 6 x 7² = 1470.
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Find the value of x.
11.4
12.6
18.9
15.3
Helloppp i need hwlp with this plllss
If there are about 5 × 10^6 hair follicles on the human body and about 7 × 10^9 people on the planet, approximately how many total human follicles are there? Give your answer in scientific notation.
There are about 3.5 * 10¹⁶ human hair follicles.
What are mathematical operations?The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
given, If there are about 5 × 10^6 hair follicles on the human body and about 7 × 10^9 people on the plane.
=35×10⁹⁺⁶
=35x10¹⁵
=3.5×10¹⁶
So the answer is "There are about 3.5 x 10¹⁶ human hair follicles"
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GUYS HELP ME IM FAILING GEOMETRY AND I NEED HELP pleaseee I need help with both please I’m begging
Step-by-step explanation:
Here is the solution hope it helps:)
Option 1: use the applet to construct circles for problems 1 & 2 or 3 & 4.
take a screenshot and insert them into your student companion.
1. circle a, with a diameter of
6 cm.
2. circle c, with a radius that is
equal to circle a's diameter.
3. circle b, with a radius of 5
cm.
4. circle d, with a diameter
that is equal to circle b's
radius.
Answer:
9
Step-by-step explanation:
Option 1: use the applet to construct circles for problems 1 & 2 or 3 & 4.
take a screenshot and insert them into your student companion.
1. circle a, with a diameter of
6 cm.
2. circle c, with a radius that is
equal to circle a's diameter.
3. circle b, with a radius of 5
cm.
4. circle d, with a diameter
that is equal to circle b's
radius.
List one algebraic equation with a distributive property
Answer:
3(4x+6)=24
Step-by-step explanation:
The distribute property is when you distribute the what is inside of the parentheses.
Answer:
an example would be -5(x+9)=-5
now distribute -5 to x and -5 to9
= -5x-45= -5
A box with square base and a height of 8cm has a volume of 1 332 cm3. find the length of the side base
Answer:
12.9 cm
Explanation:
Volume of rectangular box = Length × Width × Height
Given following:
Height = 8 cmConsider one of the base side as xSolve for volume:
L × W × H = Vx × x × 8 = 1332x² = 1332/8x = √166.5 ≈ 12.9 cmwhat is the lowest common multiple of 8,12,9
Answer:
LCM of 8, 9, and 12 is 72.
Step-by-step explanation:
The LCM of three non-zero integers, a(8), b(9), and c(12), is the smallest positive integer m(72) that is divisible by a(8), b(9), and c(12) without any remainder.
appreciate it if someone will follow me.
Answer:
72
Step-by-step explanation:
To find the Lowest Common Multiple (LCM), prime factorize the included terms, and multiply the factors of each number of the highest power together.
Prime factorizing
8 = 2³12 = 2² x 39 = 3²LCM (8, 12, 9)
= 2³ x 3²
= 8 x 9
= 72
Using the image above, what is the measure of Angle J? Round to the nearest hundredth
Answer:
∠J = 31.06°
Step-by-step explanation:
Taking the inverse sin function :
sin ∠J = 1.6/3.1J = sin⁻¹ (0.516)∠J = 31.06°
What transformation will prove that these two triangles are CONGRUENT.
Answer:
Reflection across the x axis
Step-by-step explanation:
When the triangle reflects across the x axis it will directly map over the other triangle and will appear to be congruent
Answer:
A reflection over the x - axis.
Step-by-step explanation:
The new position of a point, a line, a line segment, or a figure after a transformation is called its image. line y=x. A reflection is a type of transformation known as a flip. The figure will not change size or shape. Mathematical reflections are shown using lines or figures on a coordinate plane. The reason these two triangles are congruent is they reflect each other meaning that they are complete opposites reflecting. When mapped, they are completely reflecting.
