Step-by-step explanation:
[tex]algenbraic[/tex]
Given: Circle X with Radius r and circle Y with radius s
Prove: Circle X is similar to Circle Y
It can be proved that Circles X and Y are similar.
How can we prove that the circles are similar?We were told that circle Y have a radius of s
And X have the Radius r
Going with the theorem that Similar shapes are proportional, we can find the scale factor from circle X to circle Y by making a division on the radii of both circles.
Then the scale factor is [tex]\frac{s}{r}[/tex] which implies that circle Y will gotten by dilation of circle Y.
Therefore, both circles are similar
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Consider a regular hexagon inscribed in circle C with radius r. Regular hexagons have six congruent sides and six congruent angles. In the figure, angle CAB measures 60°.
What is m∠ACB?
°
What is the length of segment AB?
What is the perimeter of the hexagon?
The perimeter of the hexagon is
the circumference of the circle.
The circumference of the circle is
.
The solution to the questions are:
The value of [tex]< ACB\ is\ 60\textdegree[/tex]. As a consequence, the radius of the circle is equal to the length of the segment AB.AB = BC =CA = R. As a consequence, the radius of the circle is equal to the length of the segment AB. The perimeter of the hexagon is equal to r times 6. As a result, the number 6r represents the hexagon's perimeter.P=6.28r. As a result, the diameter of the circle is a fraction of a unit bigger than.P=6.28r. As a result, the diameter of the circle is a fraction of a unit bigger than.What is the length of segment AB?1) Generally, the equation for m∠ACB is mathematically given as
CA= CB
CA = radius of the circle
Therefore,
∠CAB =
[tex]\angle CBA = 60 \textdegree[/tex]
the sum of all the angles of a triangle
the sum of all the angles of a triangle is 180°
[tex]< CAB + < CBA + < ACB = 180 \textdegree[/tex]
[tex]60\textdegree + 60\textdegree + < ACB = 180\textdegree[/tex]
[tex]120\tetxtdegree + < ACB = 180\tetxtdegree[/tex]
[tex]< ACB = 60\textdegree[/tex]
The value of [tex]< ACB\ is\ 60\textdegree[/tex].
2. What is the length of segment AB?
In the same manner, as in ACB, all of the angles are the same. As a result, we may say that the triangle has equal sides.
In a triangle with equilateral sides, each of the triangle's three sides has the same length.
AB = BC =CA = R
As a consequence, the radius of the circle is equal to the length of the segment AB.
3. What is the perimeter of the hexagon?The formula for calculating the hexagon's perimeter is 6a, where an is the number of sides in the hexagon.
The circumference of the hexagon is equal to 6 times a.
The circumference of the hexagon is equal to six times each side (AB)
The perimeter of the hexagon is equal to r times 6.
As a result, the number 6r represents the hexagon's perimeter.
4. The perimeter of the hexagon is 6r the circumference of the circle.
the perimeter of the hexagon = 6rthe perimeter of the circle = [tex]2 \pi[/tex][tex]P=2*\pi*r[/tex]
P=2*3.14*r
P=6.28r
As a consequence of this, the hexagon's perimeter is less than the diameter of the circle.
5. The circumference of the circle is 6.28r.
the perimeter of the circle = [tex]2 \pi r[/tex]
[tex]P=2*\pi*r[/tex]
P=2*3.14*r
P=6.28r
As a result, the diameter of the circle is a fraction of a unit bigger than.
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Answer:
1. 60 degrees
2. r
3. 6r
4. slightly less than
5. slightly greater than 6r
Step-by-step explanation: I just did it on edge 2023. Hope this helps!
Which geometric shape could be used to model the building?
cylinder
pyramid
cone
rectangular prism
Answer:
Rectangular Prism
Step-by-step explanation:
We usually see building shaped as a 3D rectangle. If this is the type of building you are talking about, we use a rectangular prism in order to build the building with correct measurements.
Quadrilateral A'B'C'D' is the result of rotating quadrilateral ABCD by 60 about
the origin
y
0
Select all of the correct statements about the unchanged properties of quadrilateral
ABCD and quadrilateral A'B'C'D.
Choose all answers that apply.
O
B
3 4/5 6
BC and BC are both parallel to the y-axis
2B and B' have the same measures.
D and D' have the same coordinates.
None of the above
Activate
Answer: B
Step-by-step explanation:
A) False. Rotations do not preserve parallelism.
B) True. Rotations are rigid motions and thus preserve angle measure.
C) False. A rotation that changes the location of every point except for the center of rotation.
A set of twins, Andrea and Courtney, are initially 10 years old. While Courtney remains on Earth, Andrea rides on a spaceship that travels away from Earth at a speed of 0.60c for 10 years (as measured by Courtney). At the end of the trip, Courtney is 20 years old. How old is Andrea
The initial age of 10 years and the spaceship speed of 0.60•c, gives the Andrea's age at the end of the trip as 18 years.
How can Andrea's new age be calculated?The time dilation using the Lorentz transformation formula is presented as follows;
[tex]t' = \frac{t}{ \sqrt{1 - \frac{ {v}^{2} }{ {c}^{2} } } } [/tex]
From the question, we have;
The spaceship's speed, v = 0.6•c
∆t = Rest frame, Courtney's time, change = 10 years
Therefore;
[tex]\delta t' =\delta t \times \sqrt{1 - \frac{ {(0.6 \cdot c)}^{2} }{ {c}^{2} } } = 8[/tex]
The time that elapses as measured by Andrea = 8 years
Andrea's age, A, at the end of the trip is therefore;
A = 10 years + 8 years = 18 years
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given that the midpoints of pq is (-3,1) and q (7,5), obtain the co-ordinates of p
The coordinates of P are (-13, -3), given the coordinates of Q as (7, 5) and the coordinates of the midpoint of PQ as (-3, 1).
The midpoint of AB, given any points A (x₁, y₁) and B(x₂, y₂) is given as point M = ({(x₁ + x₂)/2},{(y₁ + y₂)/2}).
In the question, we are given that the midpoint of PQ is (-3, 1) and point Q is (7, 5).
We are asked to find the coordinates of point P.
We assume the coordinates of point P as (x, y).
Thus, the midpoint of PQ = ({(x + 7)/2}, {(y + 5)/2}),
that is, (-3, 1) = ({(x + 7)/2}, {(y + 5)/2}).
Thus, we can show that:
(x + 7)/2 = -3,
or, x + 7 = -6,
or, x = -6 - 7 = -13.
(y + 5)/2 = 1,
or, y + 5 = 2,
or, y = 2 - 5 = -3.
Thus, the coordinates of P are (-13, -3), given the coordinates of Q as (7, 5) and the coordinates of the midpoint of PQ as (-3, 1).
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Can you construct an example of a discrete random variable which does not have a finite expectation?
Throwing a coin until it lands tails is an example of a discrete random variable which does not have a finite expectation.
For the given question,
A discrete random variable is a type of variable whose value depends upon the numerical outcomes of a certain random phenomenon. Discrete random variables are always whole numbers, which are easily countable.
It is a variable that can take on a finite number of distinct values and takes numerous values. It is also known as a stochastic variable. When you consider probabilistic experiments with infinite outcomes, it is easy to find random variables with an infinite expected value.
Let X be a random variable that is equal to 2ⁿ with probability 2⁻ⁿ (for positive integer n). Then,
[tex]E(X)=\sum_{n:1}^{\infty} |2^{-n}2^{n}|[/tex]
⇒ [tex]E(X)=\sum_{n:1}^{\infty} (1)[/tex]
⇒ [tex]E(X)=\infty[/tex]
Consider the following example,
You throw a coin until it lands tails.
Let n be the number of heads
Then number of heads can be found by, 2ⁿ
Now, the expected value function is
[tex]E(X)=\frac{1}{2}(2^{0} )+ \frac{1}{4}(2^{1} )+....[/tex]
⇒ [tex]E(X)=\sum_{n:1}^{\infty} |2^{-n}2^{n-1}|[/tex]
⇒ [tex]E(X)=\sum_{n:1}^{\infty} \frac{1}{2}[/tex]
⇒ [tex]E(X)=\infty[/tex]
Since the number of outcomes is infinite. The probability of each outcome decreases exponentially.
Hence we can conclude that throwing a coin until it lands tails is an example of a discrete random variable which does not have a finite expectation.
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pls answer fast , pls
Answer:
x is 14
1st is 14
2nd is 20
Step-by-step explanation:
4/7 (x ) = (34 - x )(2/5)
4x/7 + 2x/5 = 34 x 2/5 = 68/5
34x/35 = 68/5
x = 14
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pls help ILL MARK BRAINLIEST
Answer:
a) Height of the ledge is 1.6 m.
b) roots of the equation are: [tex]\bf d = 2[/tex] , [tex]\bf d = -1[/tex]
c) Maximum height reached = 1.8 m.
Step-by-step explanation:
a) The height of the ledge is the same as the height at which Jake is when he hasn't moved any horizontal distance from the ledge yet, that is, when d = 0:
[tex]h = -0.8(0)^2 + 0.8(0) + 1.6[/tex]
⇒ [tex]\bf h = 1.6 \space\ m[/tex]
∴ Height of the ledge is 1.6 m.
b) The x-intercepts occur where y = 0, that is when h = 0:
[tex]-0.8d^2 + 0.8d + 1.6 = 0[/tex]
Divide both sides of the equation by -0.8:
[tex]d^2 - d -2 = 0[/tex]
Factorizing:
⇒ [tex]d^2 -2d + d - 2 = 0[/tex]
⇒ [tex]d(d-2) +1 (d-2) = 0[/tex]
⇒ [tex](d-2)(d+1) = 0[/tex]
⇒ [tex]d - 2 = 0[/tex] or [tex]d + 1 = 0[/tex]
∴ roots are : [tex]\bf d = 2[/tex] , [tex]\bf d = -1[/tex]
c) To find the maximum value of a quadratic equation in the form
y = ax² + bx + c , use the formula:
max = c - (b² / 4a).
Using the formula for [tex]h = -0.8x^2 + 0.8x + 1.6[/tex] :
max h = [tex]1.6 - ( \frac{0.8^2}{4(-0.8)} )[/tex]
= 1.8
∴ Maximum height reached = 1.8 m.
Answer:
a) 1.6 m
b) -1, 2 meters
c) 1.8 m
Step-by-step explanation:
Apparently, technology tools are allowed when solving this problem. They readily show you the x- and y-intercepts and the vertex of the graph.
a) ledge heightThe height of the ledge is the value of h when d=0. It is the constant in the given equation, and the y-intercept of the graph.
The height of the ledge is 1.6 meters.
b) rootsThe x-intercepts are the values of d that make h equal to zero. The graph shows them to be ...
d = -1
d = 2 . . . . meters
c) maximum heightThe maximum height is the "h" coordinate of the vertex (d, h).
The maximum height is 1.8 meters.
__
Additional comment
"x" is the generic independent variable. The horizontal axis of a graph is often called the "x-axis" and places where the graph crosses that axis are called "x-intercepts" even when the independent variable is named something else. Here, the independent variable is "d", not "x".
Similarly, "y" is the generic dependent variable, and the vertical axis of a graph is often called the "y-axis" even when the dependent variable is something else. This is why we refer to h when d=0 as the "y-intercept". It is the point where the graph crosses the vertical axis.
mAFD=90 mAFB=31 Find mCFE
The value of angle CFE in the diagram attached is 51 degrees.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
From the diagram:
∠AFB = ∠CFD; ∠BFC = ∠DFE
Hence:
∠AFC = ∠CFE
∠AFD = ∠AFC + ∠CFD = ∠AFC + ∠AFB
90 = ∠AFC + 31
∠AFC = 51° = ∠CFE
The value of angle CFE in the diagram attached is 51 degrees.
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the cost of 4 ice cream cones from the snack bar was $10.40. if each ice cream costs the same amount, which model correctly illustrates the relationship? check all that apply
Write the equation of the circle whose center is at the origin and whose diameter is 12.5
The equation of the circle whose center is at the origin and whose diameter is 12.5 is x²+y²=39.0625
Equation of a circleThe formula for finding the equation of a circle is expressed as:
(x-a)² + (y - b)² = r²
where
(a, b) is the centre
r is the radius
Given the following
(a, b) = (0, 0)
r = 12.5/2 = 6.25
Substitute
(x-0)² + (y - 0)² = 6.25²
x²+y²=39.0625
Hence the equation of the circle whose center is at the origin and whose diameter is 12.5 is x²+y²=39.0625
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Diagram 1 shows a tangent to a circle, centre O. Find x and y; 40° y Diagram 1
Answer:
x = 80 , y = 50
Step-by-step explanation:
the angle between the tangent and the radius at the point of contact is 90°
given the angle between the tangent and the chord is 40° , then
angle inside triangle = 90° - 40° = 50°
the triangle has 2 equal radii forming 2 sides thus is isosceles with 2 base angles being congruent, then
y = 50°
the sum of the 3 angles in the triangle = 180° , then
x = 180° - 50° - 50° = 180° - 100° = 80°
Answer:
x = 80°
y = 50°
Step-by-step explanation:
the legs of the inner triangle (tangent to O, and O to point with y angle) are equal because both are the radius of the circle.
that makes the inner triangle an isoceles triangle with both angles on the baseline (tangent to point with y angle) being equal.
the angle of the tangent to the leg "tangent to O" is per definition a right angle (90°). otherwise it would not be a tangent.
one post of the right angle is 40°, so the other part (the triangle inner angle at the tangent point) is then 90-40 = 50°.
since both leg angles must be equal (as described above), y = 50° too.
and as the sum of all angles in a triangle must be 180°, that gives us for x
180 = 50 + 50 + x
x = 180 - 50 - 50 = 80°
The vehicle preference of police officers and firefighters is given in the table.
Police Officers Firefighters
Cars 12 3
Trucks 9 4
SUVs 15 2
Based on the information in the table, which of the following is an example of independent events.
Based on the information in the table, an example of independent events is the: P(policer officer and chooses car).
What is an independent event?An independent event can be defined as an event that isn't dependent on other events. Thus, it isn't affected by any previous event.
Based on the information provided, we can infer and logically deduce that an example of independent events is the probability of being a policer officer and chooses a car because they aren't overlapping probabilities.
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Word Problem
Beau Thai has a rectangular mirror with a length of 6 inches and a width of 10 inches.
a) How much ribbon could Beau wrap around the outside of the mirror?
b) What is the area of Beau Thai's mirror?
10in
Beau can wrap 32 inches of ribbon outside the mirror.
Area of Beau Thai's mirror is 60 sq. inches.
An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.
The word "area" refers to a free space. A shape's length and width are used to compute its area.
Given information:
Length of mirror = 6 inches
Width of mirror = 10 inches
To Find:
The amount of ribbon Beau could wrap around the outside of the mirror.
Perimeter of the mirror = 2(6+10)
= 2(16)
= 32 inches
The area of Beau Thai's mirror.
Area of the mirror = 6*10
= 60 sq. inches
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There are Z fish in a aquarium. 1/4 of the fish are angelfish. How may are angelfish?
Step-by-step explanation:
since there are z fishes
the number of angelfish = 1 × z
4
= 1 z
4
help me please.bnt8349rf8
Answer: No solutions
Step-by-step explanation: there would be no solutions, because these equations have the same slope and different y-intercepts, so they would end up being parallel from each other, and would never intersect or be equivalent.
Answer:
No solution.
Explanation:
Given equations:
(1) y - 4x = -3
(2) y = 4x + 7
Substitute equation 2 into 1
y - 4x = -3
4x + 7 - 4x = -3
7 = -3
As L.H.S ≠ R.H.S, There are no solution.
The lines are parallel and do not intersect each other. Their slope is same.
I cant figure this out
Answer:
x = 2 or x = -1/4
Step-by-step explanation:
Let's solve your equation step-by-step.
4x2−7x−2=0
For this equation: a=4, b=-7, c=-2
4x^2+−7x+−2=0
Step 1: Use quadratic formula with a=4, b=-7, c=-2.
[tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
[tex]x=\frac{-(-7)\pm\sqrt{(-7)^2-4(4)(-2)} }{2(4)}[/tex]
[tex]x=\frac{7\pm\sqrt{81} }{8}[/tex]
x = 2 or x = -1/4
Answer:
x = 2 or x = -1/4
She needs to know the length of each side so she can buy fencing. What is the length of line segment FJ
Using the Pythagorean theorem, the length of line segment FJ is: 42 ft.
How to Apply the Pythagorean Theorem?To find the length of line segment FJ, we need to apply the Pythagorean theorem to find the length of the segment from F to the point, say point O, on FJ where a right triangle FOG will be gotten.
Thus, we have:
FO = √(GF² - GO²)
FO = √(30² - 24²)
FO = 18 ft.
FJ = FO + GH
Plug in the values
FJ = 18 + 24
FJ = 42 ft.
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Find the number of units in the length of diagonal $DA$ of the regular hexagon shown. Express your answer in simplest radical form.
17.32 the number of units in the length of diagonal $DA$ of the regular hexagon.
How do you find the length of the diagonal of a regular hexagon?Six equilateral triangles can be formed from the hexagon. The equilateral triangle has an equal length on each side. The diagonal of the hexagon is formed by joining two of the sum of the lengths of the equilateral triangles. As a result, the hexagon's diagonal is twice as long as its sides.
For a polygon, the SUM of the internal angles is:
(n-2) * 180 (n=6 for hexagon)
(6-2)*180 = 720 Thus EACH angle is : 720/6 = 120 degrees
Therefore, the triangle's main angle is 120 degrees, and its other two angles are equal.
There are 180 degrees in any triangle:
(180-120) / 2 = 30 degrees for each of the smaller angles.
Now use the law of sines:
10/sin30 = x/(sin120)
10/(.5) × (sqrt3 )/ 2 = x
10 sqrt 3
10/sin30 × sin 120 = 17.32
17.32 is the number of units in the length of diagonal $DA$ of the regular hexagon.
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Find a polynomial function of degree 7 with a leading coefficient of 1 and with - 3 as a zero of multiplicity 3,0 as a zero of multiplicity 3, and 3 as a zero of multiplicity 1.
The least polynomial in standard form is defined by the function f(x) = x⁷ + 6 · x⁶ - 54 · x⁴ - 81 · x³.
How to determine the least polynomial given a set of roots and a leading coefficient
Polynomials can be expressed as a product of binomials of the form (x - r) multiplied by a leading coefficient. The least polynomial contain the number of roots presented in statement, whose factor form is shown below:
f(x) = 1 · (x + 3)³ · x³ · (x - 3)
f(x) = (x + 3)³ · (x⁴ - 3 · x³)
f(x) = (x³ + 9 · x² + 27 · x + 27) · (x⁴ - 3 · x³)
f(x) = x⁷ + 9 · x⁶ + 27 · x⁵ + 27 · x⁴ - 3 · x⁶ - 27 · x⁵ - 81 · x⁴ - 81 · x³
f(x) = x⁷ + 6 · x⁶ - 54 · x⁴ - 81 · x³
The least polynomial in standard form is defined by the function f(x) = x⁷ + 6 · x⁶ - 54 · x⁴ - 81 · x³.
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If the range for a set of number is 8 and the maximum number is 2 what is the answer/
The range is -6.
What is a range?The range of a collection of data in statistics is the difference between the largest and lowest values. The difference here is that the range of a collection of data is determined by subtracting the sample maximum and minimum. In descriptive statistics, however, the concept of the range has a more nuanced meaning.To find the answer, calculate as follows:
Range = Maximum - Minimum
Range = 8 and Maximum = 2
Let, the minimum be x.
Now, substitute values in the formula.
8 = 2 - x
x = 2 - 8
x = -6
Therefore, the answer is -6.
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what are the domain and range of the graph below.
O domain: [0,00)
range: (-00,00)
O domain: [0,00)
range: (-0,4]
domain: (0,4)
range:
(-00,00)
domain: (-∞,4]
range: [0,00)
Answer:
Domain: [0,∞)
Range: (-∞, 4]
Step-by-step explanation:
The required domain and range of the function shown in the graph are,
Domain = (0, ∞)
Range = (-∞, 4)
To calculate the domain and range of a function from its graph, you can follow these steps:
Identify the x-coordinates of all the points on the graph. The set of all possible x-coordinates is the domain of the function.Write the domain as an interval or as a set of values, depending on the format of the original problem. For example, if the graph is defined for all real numbers, the domain would be written as (-∞, ∞).Identify the y-coordinates of all the points on the graph. The set of all possible y-coordinates is the range of the function.Write the range as an interval or as a set of values, depending on the format of the original problem.So, from the above definition, from the graph we have,
Domain = (0, ∞)
Range = (-∞, 4)
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Given the following vectors in component form:
r = ⟨2, 3⟩
s = ⟨5, –3⟩
t = ⟨–8, 6⟩
Check all expressions whose sum represents the same vector as (r + s) + t.
LeftAngleBracket 0, 7 RightAngleBracket + LeftAngleBracket negative 8, 6
RightAngleBracket LeftAngleBracket 7, 0 RightAngleBracket + LeftAngleBracket negative 8, 6 RightAngleBracket LeftAngleBracket 2, 3 RightAngleBracket + LeftAngleBracket negative 3, 3 RightAngleBracket LeftAngleBracket 2, 3 RightAngleBracket + LeftAngleBracket 3, negative 3 RightAngleBracket LeftAngleBracket negative 6, 9 RightAngleBracket + LeftAngleBracket 5, negative 3 RightAngleBracket
All expressions whose sum represents the same vector as (r + s) + t. is Option b,c,e
What are the expressions that equals (r + s) + t. ?Where
r= (2,3)
s= (5,-3)
t= (-8,6)
Generally, the equation for statement is mathematically given as
(7,0)+(-8,6) ,(2,3)+(-3,3) and (-6,9)+(5,-3) are equal to (r+s)+t
Therefore
x=(2,3)+(5,-3)
x=(7,0)
Now we can calculate (r+s)+t as
(7,0)+(-8,6)
(7-8,0+6)
(-1,6)
For (b)
x=(7,0)+(-8,6)
x=(-1,6)
in this scenario x expressions is equal to (r+s)+t
For (c)
x=(2,3)+(-3,3,)
x=(-1,6)
in this scenario x expressions is equal to (r+s)+t
For (e)
[tex]x=(-6,9)+(5,-3)[/tex]
x=(-1,6)
in this scenario x expressions is equal to (r+s)+t
In conclusion, all expressions whose sum represents the same vector as (r + s) + t. is b,c,e
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At a restaurant, Lana gets a bill that is $40 for the food plus a 5% sales tax. Lana decides to tip 20% on the total bill. How much will Lana pay in total?
Answer:
$50.40
Step-by-step explanation:
To find how much Lana will pay in total follow these steps.
First, multiply 40 by 1.05.
40×1.05=42.
This is how much she will pay for the food plus tax.
Now, multiply 42 by 1.2.
42×1.2=50.40
This is how much she will pay for the food, tax, and tip.
Lana will pay a total of $50.40.
Hope this helps!
The median for the samples from the 30 mile race of cars and SUVs are:
The median of Sample 1 for cars is 132.
The median of Sample 2 for SUVs is 115.
What conclusions can you derive from the random samples?
The sample size was too small to derive a valid conclusion.
SUVs can perform well under testing conditions.
Cars and SUVs performed equally well.
Cars are slower than SUVs.
Cars are faster than SUVs.
A conclusion which can be derived from these random samples is that: E. Cars are faster than SUVs.
What is a median?A median can be defined as the middle number (center) of a sorted data set, which is typically when the data set is arranged in from the least to greatest or the greatest to least.
In Mathematics, the median of a data set is generally considered to be a better measure of center than the mean when there's an outlier in the data set.
Based on the information provided for these random samples from the race, we can infer and logically conclude that Cars are faster than SUVs because a median speed of 132 is greater than a median speed of 115.
In conclusion, it is important to note that the Cars used in this survey (research) are faster than SUVs because the median for the SUVs in Sample 2 is equal to 115 while the median for the Cars in Sample 1 is equal to 132.
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Rita is making a beaded bracelet. She has a collection of 160 blue beads, 80 gray beads, and 240 pink beads. What is the estimated probability that Rita will need to pick at least five beads before she picks a gray bead from her collection
The probability that Rita will need to pick at least five beads before she picks a gray bead from her collection is approximately (C) 0.45.
What is probability?
Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.To find the probability that Rita will need to pick at least five beads before she picks a gray bead from her collection:
Given that Rita is making a beaded bracelet. She has a collection of 160 blue beads, 80 gray beads, and 240 pink beads. We are to calculate the probability that Rita will need to pick at least 5 beads before she picks a grey bead from her collection.Prob for drawing at least 5 beads before she picks a grey bead from her collection= 1-Prob for drawing at least one grey beed in the first 5 draws.(Because these two are complementary events)number of grey beads drawn in the first 5 trials is[tex](5, \frac{80}{80+160+240} ) = (5,\frac{1}{6} )[/tex]Prob for drawing at least one grey beed in the first 5 draws.=1-Prob of no greyHence required prob=P(X=0 in the first 5 draws)[tex](1-\frac{1}{6})^{5}\\0.4018[/tex]The 6th beeds onwards can be grey also.The nearest answer is (C) 0.45Therefore, the probability that Rita will need to pick at least five beads before she picks a gray bead from her collection is approximately (C) 0.45.
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The question you are looking for is given below.
Rita is making a beaded bracelet. She has a collection of 160 blue beads, 80 gray beads, and 240 pink beads. What is the estimated probability that Rita will need to pick at least five beads before she picks a gray bead from her collection?
(A) 0.05
(B) 0.10
(C) 0.45
(D) 0.55
Which expression is equivalent to (2 Superscript one-half Baseline times 2 Superscript three-fourths Baseline) squared?
RootIndex 4 StartRoot 2 cubed EndRoot
StartRoot 2 Superscript 5 EndRoot
RootIndex 4 StartRoot 4 cubed EndRoot
StartRoot 4 Superscript 5 EndRoot
Answer:
D
Step-by-step explanation:
If a family has 6 children, in how many ways could the parents have 3 boys and 3 girls?
The parents could have 3 boys and 3 girls in 400 ways
How to determine the number of ways?The given parameters are
Children, n = 6
Boys, r = 3
Girls, r =3
The number of combination is:
[tex]Ways = ^nC_{r1} *^nC_{r2}[/tex]
So, we have:
[tex]Ways = ^6C_3 *^6C_3[/tex]
Apply the combination formula
[tex]Ways = \frac{6!}{3!3!} *\frac{6!}{3!3!}[/tex]
This gives
Ways = 400
Hence, the parents could have 3 boys and 3 girls in 400 ways
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Ummm can y’all solve these problems I’ll give extra points for this
Pls solve step by step and label which is which