To get at least a 50% probability of getting at least three heads, you must flip a fair coin at least four times.
Explanation:To calculate the minimum number of times a fair coin must be flipped before there is at least a 50% probability of getting at least three heads, we can use the concept of probability. Let's assume that flipping a coin is a binary event with two possible outcomes: heads (H) or tails (T).
The probability of getting three or more heads in one flip is zero, since we can only get a maximum of two heads in one flip. However, we can calculate the probability of getting three or more heads in a series of flips.
The probability of getting at least three heads in one flip is zero, but we can calculate the probability of getting at least three heads in two flips, three flips, four flips, and so on. We continue calculating the probability until we find the number of flips that gives us a probability of at least 50%.
Using this method, we find that we need to flip the coin at least 4 times to have a probability of at least 50% of getting at least three heads. This means that after flipping the coin four times (or more), there is a better than 50% chance of getting at least three heads.
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Can someone explain 2.2
Answer:
C. 2
Step-by-step explanation:
Point B is 6-(-4) = 10 units up from point A. A point (F) that partitions that distance in the ratio 3:2 will be 3/(3+2) = 3/5 of the distance from A to B. That is, it will be ...
3/5 · 10 units = 6 units
above A. The y-coordinate of F will be 6 units added to the y-coordinate of point A, -4 +6 = 2.
A phone company wants to know if its customers are satisfied with their service. 100 people are surveyed. The results show that 40 people are satisfied. There are 1,200 people the company services. About how many people are satisfied with their service?
100:40
=2.5
1200 : 2.5
=480
About 480 people out of the 1,200 customers are likely satisfied with their service.
To determine how many of the company's customers are likely satisfied with their service based on the survey results, we can use the concept of proportions. This involves simple multiplication and understanding ratios in percentages.
Find the proportion of satisfied customers in the survey:
Number of satisfied customers in the survey: 40
Total number of people surveyed: 100
Proportion of satisfied customers = (Number of satisfied customers) / (Total number of people surveyed)
Proportion of satisfied customers = 40 / 100 = 0.4 or 40%
Apply this proportion to the entire customer base:
Total number of the company's customers: 1,200
Estimate of satisfied customers = Proportion of satisfied customers × Total customers
Estimate of satisfied customers = 0.4 × 1,200 = 480
The 5th picture with the question I need help with.
Answer:
Step-by-step explanation:
27
Which ratio correctly compares 2 feet to 48 inches, when the lengths are written using the same units?
Note: 12 inches = 1 foot
A. 2 : 1
B. 24 : 1
C. 1 : 24
D.1 : 2
Answer: OPTION D
Step-by-step explanation:
To solve this problem you must apply the proccedure shown below:
- Convert from 48 inches to foot. You know that 12 inches=1 foot. Then you have:
[tex](48inches)(\frac{1foot}{12inches})=4feet[/tex]
- Therefore, keeping on mind that 48 inches is 4 feet, and you must find the ratio that correctly compares 2 feet to 48 inches, you can write:
[tex]ratio=\frac{2feet}{4feet}[/tex]
- Reduce the fraction, then:
[tex]ratio=\frac{1}{2}[/tex]
- You can rewrite it as following:
[tex]ratio=1:2[/tex]
Answer:
D
Step-by-step explanation:
Consider the equation log5(x + 5) = x2.
What are the approximate solutions of the equation? Check all that apply.
Answer:
x ≈ -0.93, x ≈ 1.06
Step-by-step explanation:
A graphing calculator can show you the approximate solutions. (It is also capable of refining those solutions to full calculator precision, if you need.)
_____
Comment on the graphical solution
I prefer to have the calculator show me the zeros of a function, where the zeros correspond to solutions of the original equation. For the purpose, it is sufficient to define the function as the difference between the sides of the original equation.
__
The definition of g(x) in the attachment corresponds to the iterator of Newton's Iteration method for finding zeros of a function. When the input and output values of that iteration function match, the value of x is a zero of the function f(x).
Please help
problem 4 I took picture of
problem 13
the perimeter of a rectangle is 336 inches. the ratio of the length to the width is 9:5. Find the length of the rectangle.
problem 16
a blueprint for a house states that 2 inches on the blueprint represent 8 feet. If the width of a window is 2.5 inches on the blueprint, what is the actual windows with?
Answer:
Since 2 inches represent 8 feet then 2.5 would represent x feet so
2/8 = 2.5/x
By doing cross multiplication :
2 x = 20 --> x = 10 feet
Step-by-step explanation:
what is the multiplicative inverse of 2/5
Answer:
5/2
Step-by-step explanation:
The multiplicative inverse is what me need to multiply by to get 1
2/5 * what = 1
Multiply by the reciprocal
5/2 *2/5 * what = 1 *5/2
what = 5/2
The multiplicative inverse is 5/2
5/2 is the multiplicative inverse
select the rigid transformation
Answer:
(x, y) ⇒ (-x, y)
Step-by-step explanation:
Any transformation that multiplies a variable by something other than ±1 is not a rigid transformation — it involves some sort of dilation. Constants can be added or subtracted to effect translation, but none of the transformations shown here do any translation.
The first transformation is a reflection across the y-axis, hence the rigid transformation you're looking for.
_____
Comment on rotations
A rotation about the origin can be written in the form ...
(x, y) ⇒ (ax -by, bx +ay)
where a^2 +b^2 = 1 and b/a = tan(angle of rotation)
This rigid transformation is an exception to the statement above about multiplication by something other than ±1.
in a right circular cylinder of height 2 meters, if the volume is increasing at 10 m^3/min how fast is the radius of the cylinder increasing when the radius is 4in?
Given dimensions:
Height of the cylinder = 2 m
Volume is increasing at a rate of = 10 m³/min
Radius = 4 inches
Converting radius in meters.
1 inch = 0.0254 meters
4 inches = [tex]4\times0.0254=0.1016[/tex] meters
[tex]\frac{dv}{dt}=10[/tex]
we have to find, [tex]\frac{dr}{dt}=?[/tex]
Volume of the cylinder is given by [tex]\pi r^{2} h[/tex]
= [tex]\pi r^{2} *2 = 2\pi r^{2}[/tex]
Now differentiating with respect to 't'
[tex]\frac{dv}{dt} = \frac{d}{dt} (2\pi r^{2})[/tex]
[tex]\frac{dv}{dt} = 2\pi (2r)(\frac{dr}{dt})[/tex]
[tex]10=2\pi (2*0.1016)\frac{dr}{dt}[/tex]
[tex]10=2*3.14(0.2032)\frac{dr}{dt}[/tex]
[tex]\frac{dr}{dt}=\frac{10}{1.276}[/tex]
= 7.83 meter per minute.
In the equation y=(x-2)^2, the minimum value occurs when x is....
And explenation.
Answer:
x = 2
Step-by-step explanation:
The minimum occurs where the value being squared is zero. x-2 = 0 when x=2.
Which statement about the rates of changes of Functions A and B as shown is true?
Answer: function b has a greater rate of change
in this right triangle the length of the hypotenuse, BC, is
Answer:
√13 units
Step-by-step explanation:
Find points B and C on the figure and locate the line between those points. The number next to the line is its length. Read the length from the diagram.
In a right triangle, the hypotenuse is the side across from the 90 degree angle. Without more information, we can't determine the length of the hypotenuse (BC), but if the lengths of the other two sides or the measurements of the other angles are known, the Pythagorean theorem or trigonometry can be used. It is expressed as BC^2 = AB^2 + AC^2.
Explanation:In a right triangle, the hypotenuse is the side that is opposite to the 90 degrees angle. In your right triangle, as you mentioned the sides as BC, I assume you have a triangle ABC where B and C are the two base angles and A is the right angle (90 degrees).
Without additional information such as the lengths of the other two sides (AB, AC), or the measurements of angles B or C, it is impossible to determine the length of the hypotenuse (BC). However, if you do have this information, you can use the Pythagorean theorem or trigonometric ratios to find the length. Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (BC) is equal to the sum of the squares of the lengths of the other two sides. It is expressed as BC^2 = AB^2 + AC^2.
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what is the volume?
Answer:
1282.82ft³
Step-by-step explanation:
To find the volume of the entire shape, we first need to find the volume of the cone and the cylinder separately.
Let's begin by getting the volume of the cylinder.
The formula to find the volume of a cylinder is:
[tex]V=\pi r^{2}h[/tex]
r = 7 ft
h = 6 ft
Let's plug in our values into the formula.
[tex]V=\pi (7)^{2}6[/tex]
[tex]V=\pi (49)6[/tex]
[tex]V=\pi (294)[/tex]
[tex]V=923.63[/tex]ft³
Now that we have the volume of our cylinder we need to find the volume of the cone.
The volume of the cone can be found by using the formula:
[tex]V=\dfrac{1}{3}\pi r^{2}h[/tex]
Our variables for the cone are:
r = 7 ft
h = 7 ft
[tex]V=\dfrac{1}{3}\pi (7)^{2}(7)[/tex]
[tex]V=\dfrac{1}{3}\pi (49)(7)[/tex]
[tex]V=\dfrac{1}{3}\pi (343)[/tex]
[tex]V=\dfrac{1}{3}1077.57[/tex]
[tex]V=359.19[/tex]ft³
Now that we found both of the volumes of the two shapes, we can then simply get the sum of both volumes to get the total volume of the shape.
Total Volume = 923.63ft³ + 359.19ft³
Total Volume = 1282.82ft³
I have a stat class review and what would be the letter choice for this scatter plot?
A Scatterplot with the least squares regression line is shown.
estimate the value to the nearest half unit
what is the observed value for X=3
A 1.5
B -1.5
C 4.5
D 6
Please any explanation helps im offering 25 pts:)
The observed value when x = 3, estimated to the nearest half unit is y = 4.5.
What is known as observed value?The observed value is the actual value of the variable. The points on the regression line are called predicted values.
From the given image, we can observe that the value of y for which x is 3 is shown as somewhere between 4 and 5. The only value of y which lies between 4 and 5 in the given options is 4.5. It is the observed value.1.5, -1.5, and 6 do not lie between 4 and 5. Therefore, they are not the correct answers.Therefore, the observed value of y when x = 3, estimated to the nearest half unit is y = 4.5. The correct answer is option C.
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Lines AB and AC tangent to circle k(O) at B and C respectively. Find BC, if m∠OAB=30°, and AB=5 cm.
Answer:
5 cm
Step-by-step explanation:
ΔABC is equilateral, so BC = AB = 5 cm.
____
AO is the perpendicular bisector of BC and the angle bisector of angle A, so ∠OAC = ∠OAB = 30°. Then vertex angle BAC of isosceles triangle ABC is 60°, which means all angles in the triangle are 60° and the triangle is equilateral.
The length of BC is 5cm
Given that line AB is tangent to circle K at point B, and line AC is tangent to circle K at point C, we know that the radius of the circle at the point of tangency is perpendicular to the tangent line. Therefore, OB is perpendicular to AB, and OC is perpendicular to AC. This forms two right triangles,[tex]$\triangle OAB$ and $\triangle OAC$.[/tex]
Let's denote OB as the side opposite the 30° angle and OA as the hypotenuse. Then we have:
[tex]OB = $\frac{1}{2}$AB = $\frac{1}{2} \times 5$ cm = 2.5 cm[/tex]
OA = AB = 5 cm (since AB is the hypotenuse of the right triangle)
Now, since the circle is the same, OA is also the radius of the circle, and thus OB = OC = 2.5 cm.
Therefore [tex], $\triangle OBC$[/tex] is an equilateral triangle because all angles are 60° and the sides opposite these angles are equal. Hence, BC = OB = OC = 2.5 cm.
Thus, BC = OB + OC' = 2.5 cm + 2.5 cm = 5 cm.
But this is not the final answer. We have to consider that the length of the chord BC is equal to the diameter of the circle because the tangents from a common external point to a circle are equal in length. Therefore, the diameter of the circle is twice the length of the radius OB (or OC').
Diameter = 2 * OB = 2 * 2.5 cm = 5 cm
BC = 5cm
Any Help would be appreciated!!
Multiply.
(5 − 1)(6^2 + 3 + 7)
Answer:
184
Step-by-step explanation:
1st step
we simplify (5-1) which is just 4 and (3+7) which is 10
and we also simply 6^2 which is 36
now we plug the simplified terms back in
(4)(36+10)
(4)(46)
184
Answer:
184
Step-by-step explanation:
Subtract: 5 - 1 = 4
Power: 6 ^ 2 = 36
Add: 36 + 3 = 39
Add: 39 + 7 = 46
Multiple: 4 * 46 = 184
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Which of the following ordered pairs represents a solution to the linear inequality y>2x-3
Answer:
D. (2, 5)
Step-by-step explanation:
On a graph, (2, 5) is the only point in the solution space.
___
You can evaluate the inequality for each of the points to see which works.
A. 4 > 2·4 -3 . . . . false
B. 12 > 2·9 -3 . . . . false
C. 2 > 2·3 -3 . . . . false
D. 5 > 2·2 -3 . . . . TRUE
Two cyclists, Alan and Brian, are racing around oval track of length 450m on the same direction simultaneously from the same point. Alan races around the track in 45 seconds before Brian does and overtakes him every 9 minutes. What are their rates, in meters per minute?
Answer:
Alan: 200 m/minBrian: 150 m/minStep-by-step explanation:
Let n represent the number of laps that Alan completes in 9 minutes. Then n-1 is the number of laps Brian completes, and the difference in their lap times in minutes per lap is ...
9/(n -1) - 9/n = 3/4 . . . . . minutes
Multiplying by (4/3)n(n -1), we get
12n -12(n -1) = n(n -1)
12 = n(n -1)
Solutions to this are n=4 and n=-3. We are only interested in the positive solution, n = 4. Then Alan's speed in m/min is ...
(4·450 m)/(9 min) = 200 m/min
Brian completes 3 laps in that 9-minute time, so his rate is ...
(3·450 m)/(9 min) = 150 m/min
a similar figure compared to the original figure is ___ a translation. A.) sometimes B.) never C.) always D.) none of these choices will make a true statement
Answer:
A). Sometimes.
Step-by-step explanation:
Sometimes a translation because it might be a rotation or a reflection.
Translation in geometry always results in a similar figure. Hence, the correct answer is C.
A similar figure compared to the original figure is **always** a translation.
Translation in geometry involves moving a figure without rotating or flipping it. When a figure is translated, all the points move in the same direction by the same distance. This means that a translation produces a figure that is congruent to the original figure.
(8q+5)^2=64q^2+[]q+25
What is the missing value? []
Answer:
80
Step-by-step explanation:
The square of a binomial is ...
(a +b)^2 = a^2 + 2ab + b^2
You have a=8q, b=5, so the square is ...
(8q)^2 + 2(8q)(5) + (5)^2
= 64q^2 +80q +25
The coefficient missing from your given expression is 80.
what is the sum of measurements of the interior angles of a 12-gon?
Answer:
1800
Step-by-step explanation:
Given in the question a polygon of 12 sides
Formula to calculate sum of interior angles of 12-gon is
(n – 2)180where n is the number of sides
which in this case = 12
plug values in the formula above
(12 - 2)180
12*180 - 180(2)
2160 - 360
1800
Sum of measurements of the interior angles of a 12sided polygon is 1800
Answer:
=1800°
Step-by-step explanation:
A 12 sided figure is called a do-decagon or a 12-gon. The general formula for calculating the sum of all interior angles of a regular polygon is=180(n-2)
n represents the number of sides of the polygon.
Therefore, the sum of all angles= 180(12-2)
=1800°
Hi there!
Can I get some help with this calculus homework. #6a and 8b. Don't forget to show your work! Thank you!
Answer:
6a. -8
8b. 1/125
Step-by-step explanation:
If you know powers of 2 and the squares and cubes of small integers, you can work these in your head. There is no "work" to show. Of course, a calculator can evaluate these easily. (see attached)
___
6a. (-128)^(3/7) = ((-2)^7)^(3/7) = (-2)^3 = -8
___
8b. (27^(2/3) +8^(4/3))^(-3/2) = ((3^3)^(2/3) +(2^3)^(4/3))^(-3/2)
= (3^2 +2^4)^(-3/2) = (9+16)^(-3/2) = 25^(-3/2)
= (5^2)^(-3/2) = 5^(-3) = 1/5^3
= 1/125
tomas and emilio are twins. they want to invite their friends to celebarte their shared birthday at the movie theater. they have a budget of $200 to plan their party. the party room at the theater costs $45.99 to rent and include a free cake. movie tickets cost $12.50 each and a small bag of popcorn cost $ 4.50. Tomas write an equation to represent the cost of their party. emilio writes an inequality. both use p to represent the number of people who can attend. wtrite tomas possible equation and emilio possible inequality.
Answer:
1) 17p + 45.99 = 200
2) 200 > 45.99 + 17p
Step-by-step explanation:
Total Budget = $200
Cost of Party Room = $45.99
Cost of movie ticket for one person = $12.50
Cost of one small bag of popcorn = $4.50
Part 1: Possible Equation by Tomas
The possible equation that can be set up will have the total budget equal to total expenses.
So,
200 = Total Cost of party
200 = Cost of Party Room + Cost of Movie Tickets + Cost of popcorns
If p people attend the party, the cost of movie tickets will be $12.50p and cost of popcorns will be $4.50p, assuming that each person get a small popcorn bag.
So, now the equation will be:
200 = 45.99 + 12.50p + 4.50p
200 = 45.99 + 17p
or
17p + 45.99 = 200
This is a possible equation that Tomas might have used to represent the cost of the party.
Part 2: Possible Inequality by Emilio
Emilio might want to keep the cost below $200 of the entire party. So the possible inequality will be of the form:
200 > Total Cost of party
200 > Cost of Party Room + Cost of Movie Tickets + Cost of popcorns
200 > 45.99 + 12.50p + 4.50p
200 > 45.99 + 17p
This is a possible inequality that Emilio might have used to represent the cost of the party.
what is the sum of the geometric series sigma 15,x=0, 2(1/3)x
Answer:
[tex]\sum_{x=0}^{15}2(\frac{1}{3})^x=3.0[/tex]
Step-by-step explanation:
We want to evaluate:
[tex]\sum_{x=0}^{15}2(\frac{1}{3})^x[/tex]
When x=0, we obtain the first term of the geometric series as
[tex]a_0=2(\frac{1}{3})^0[/tex]
The common ratio of this geometric series is [tex]r=\frac{1}{3}[/tex]
The sum of the first n-terms of a geometric series is
[tex]S_n=\frac{a(1-r^n)}{1-r}[/tex]
From x=0 to x=15, we have 16 terms.
The sum of the first 16 terms of the geometric series is
[tex]S_{16}=\frac{a(1-(\frac{1}{3})^{16})}{1-\frac{1}{3}}=2.99999993031[/tex]
[tex]\sum_{x=0}^{15}2(\frac{1}{3})^x=3.0[/tex] to the nearest tenth.
The sum of two numbers is 69. The larger number is three less than twice the smaller number. Find the numbers.
Answer:
x = 45, y = 24.
Step-by-step explanation:
If the 2 numbers are x and y:
x + y = 69...........(1)
x = 2y - 3
x - 2y = -3...........(2)
Subtract: (1) - (2):
x - x + y - (-2y) = 69 - (-3)
y + 2y = 72
3y = 72
y = 24.
From equation 1:-
x + 24 = 69
x = 45.
The numbers are x = 24 and y = 45 respectively.
What is algebraic expression?An algebraic expression in mathematics is a combination of terms both constant and variable. For example, we can write the expressions as -
2x + 3y + 5
2z + y
x + 3y
Given is that the sum of two numbers is 69. The larger number is three less than twice the smaller number.
Assume that the numbers are {x} and {y}. So, we can write the equations as -
x + y = 69
y = 2x - 3
Rewriting equation {1}, we get -
x + y = 69
x + 2x - 3 = 69
3x = 72
x = 24
and
y = 2 x 24 - 3
y = 45
Therefore, the numbers are x = 24 and y = 45 respectively.
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a movie rental club charges a one time fee of $25 to join and $2 for every movie rented which equation could represent how much you would spend to join the club and rent movies for a year?
A c=12+25m
B c=25+2m
C c=12m+2
D c=25m+24
Answer:
The correct answer option is B. c = 25 + 2m.
Step-by-step explanation:
We are given that a movie rental club charges a one time fee of $25 to join and $2 for every movie rented.
We are to determine whether which of the given equations in the answer options represent how much you would spend to join the club and rent movies for a year.
The correct answer option is B. c = 25 + 2m.
One time charges = 25 plus $2 multiplied by the number of movies rented.
Find the sum of the first 12 terms of the arithmetic series 32+27+22+...
Answer:77
32+27+22+17+12+7+2-3-8-13-15-18=77
Answer:
54
Step-by-step explanation:
The first twelve terms would be, in decreasing order, 32, 27, 22, 17, 12, 7,2, -3, -8,-13,-18,-23.
1. -23+22 = -1
2. -13+12 = -1
3. -18+17 = -1
4. -8+7 = -1
5. -3+2 = -1
Using these five facts, we can simplify this to 32+27 -5(1) = 32+27-5 = 54
Write the expression as a polynomial, using the corresponding formula for special product: (−a+b)(b–a)
Answer:
b² -2ab +a²
Step-by-step explanation:
The first factor can be rearranged to put the minus sign in the middle. Then you have
(b -a)(b -a) = (b -a)² = b² -2ab +a²
___
If you like, you can also write this as ...
a² -2ab + b² . . . . . . terms in lexicographical order
_____
The "special product" of interest here is the square of a binomial:
(p +q)² = p² +2pq +q²
You have p=b, q=-a, so the result is as shown above.
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Answer:
Vel_jet_r = (464.645 mph) North + (35.35 mph) East
||Vel_jet_r|| = 465.993 mph
Step-by-step explanation:
We need to decompose the velocity of the wind into a component that can be added (or subtracted from the velocity of the jet)
The velocity of the jet
500 mph North
Velocity of the wind
50 mph SouthEast = 50 cos(45) East + 50 sin (45) South
South = - North
Vel_ wind = 50 cos(45) mph East - 50 sin (45) mph North
Vel _wind = 35.35 mph East - 35.35 mph North
This means that the resulting velocity of the jet is equal to
Vel_jet_r = (500 mph - 35.35 mph) North + 35.35 mph East
Vel_jet_r = (464.645 mph) North + (35.35 mph) East
An the jet has a magnitude velocity of
||Vel_jet_r|| = sqrt ((464.645 mph)^2 + (35.35 mph)^2)
||Vel_jet_r|| = 465.993 mph
The price of an apple is one third that of an orange. Robert paid $10.80 for 5 oranges and 12 apples.
(a) How many apples could he buy for $10.80?
(b) How much does one apple cost?
Answer:
a: 27 apples
b: $0.40 apples
Step-by-step explanation:
a: another way of saying that the price of an apple one-third that of an orange is that you can get 3 apples for the price of 1 orange. If he bought 5 oranges, he could have gotten 15 apples, so 27 apples total.
b: $10.80/27 = $0.40 per apple