a magician designed an unfair coin so that the probability of getting a head on a flip is $60\%$. if he flips the coin three times, what is the probability that he flips more heads than tails? express your answer as a common fraction.
Probability of getting a head is 60%
More heads than tails means these possibilities are
2 Heads - 1 Tail
3 Heads - 0 Tails
Probability of 2 Heads and 1 Tail = C (3,2) (.60) ^2 (.40)
=3 * (.36) (.40)
=3 * .144
=3 (144/1000)
=3 (18/125)
=54/125
Probability of 3 Heads = (.60) ^3
= .6 (.36)
= .216 = 216 / 1000
= 27 / 125
Hence, total probability = 54 / 125 + 27 / 125
= 81 / 125
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lindsay bedford works at the baseball cap shop. she is paid $6.50 per hour plus $0.45 for each cap she embroiders. how many caps must she embroider to earn at least $85 in an 8-hour day?
15 caps are needed so that she can earn $85 in an [tex]8[/tex]hour day.
How is the direct equation calculated?The direct variation equation has the form y = kx, where k is the constant proportionality. It is a linear equation with two variables. In a coordinate plane, the direct variation graph is a straight line. A constant is the ratio of two quantities that vary directly. Relationship between two variables that can be described mathematically by an equation where one variable equals a constant multiplied by the other.
For each hour she is compensated $6.50 with $0.45.
For an 8 hour day =6.50 *8 + 0.45x
Let x be the caps and earning is $85
6.50*8+0.45*x=85
=> 52+0.45x=85
=> 0.45x=33
=> x=15 (approx.)
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doug entered a canoe race. He rowed 3 1/3 miles in 1/3 hour. What is his average speed in miles per hour?
Answer:
10 MPH
Step-by-step explanation:
Doug entered a canoe race. He rowed 3 1/3 miles in 1/3 hour. What is his average speed in miles per hour?
If Doug rowed 3 1/3 miles in 1/3 hour the equation is:
3 1/3x = 1/3
multiply both sides by 3:
3(3 1/3x) = 3(1/3)
10x = 1 hour
Doug rowed 10 MPH
Answer:
10 mile per hour
Step-by-step explanation:
3 1/3 mile = 3.3333333333333333333333333333333 mile
1/3 hour = 0.3333333333333333333333333333333333 hour
divide 3.33333333333333333333333 by 0.3333333333333333333333333
= 3.333333333333333333333333333333333 * 1/.33333333333333333333
= 3.3333333333333333333333333 * 3
= 9.99999999999999999999999
= 10
at 111111:55\text{ p.m.}55 p.m.55, start text, space, p, point, m, point, end text, thomas ties a weight to the minute hand of a clock. the clockwise torque applied by the weight (i.e. the force it applies on the clock's hand to move clockwise) varies in a periodic way that can be modeled by a trigonometric function. the torque peaks 151515 minutes after each whole hour, when the minute hand is pointing directly to the right, at 3\text{ nm}3 nm3, start text, space, n, m, end text (newton metre, the si unit for torque). the minimum torque of -3\text{ nm}−3 nmminus, 3, start text, space, n, m, end text occurs 151515 minutes before each whole hour, when the minute hand is pointing directly to the left. find the formula of the trigonometric function that models the torque \tauτtau applied by the weight ttt minutes after thomas attached the weight. define the function using radians.
The trigonometric function's formula, which simulates the torque (tau) that the weight applied t minutes after Thomas attached it is
[tex]3 Sin (\frac{2\frac{22}{7} }{60} (t-51))[/tex]
The angular speed of the minutes hand is
[tex]w = \frac{2 (\frac{22}{7}) }{60}[/tex] rad/min
Following the application of weight, the torque as a function of time t is,
[tex]t= t_{0} sin (w (t-5) min)\\ = (3 Nm) sin ((\frac{2 (\frac{22}{7} }{60} ) rad/min (t-5) min)[/tex]
[tex]= (3 Nm) sin ( \frac{2 (\frac{22}{7} }{60} (t-5) rad ) \\= 3 sin (\frac{2 \frac{22}{7} }{60} (t-5)[/tex]
What is torque ?Torque, which is also known as the moment of a force, is the propensity of a force to rotate the body to which it is applied. Force (F) x Distance (r) = Torque is how torque is calculated. The distance (r) between the pivot point and the force's action point. A vector quantity is a torque. As a vector quantity, torque always has a direction that is perpendicular to the plane that contains the vectors of force and displacement.
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why does the inequality sign have to be flipped when dividing by a negative number?
The inequality sign have to be flipped when dividing by a negative number.
What is inequality?
The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than’, or < ‘less than’.
Given:
The given statement is the inequality sign have to be flipped when dividing by a negative number.
According to given question we have
A number that is larger when positive becomes "more negative," and thus smaller when negative, and vice versa.
Dividing by a negative number is the same as dividing by a positive number and then multiplying by −1. Dividing an inequality by a positive number retains the same inequality. But, multiplying by −1 is the same as switching the signs of the numbers on both sides of the inequality, which reverses the inequality:
a<b⟺−a>−b.
Ex:
when dividing both sides by a negative number, we reverse the inequality sign.
Take −3x<9
To solve for x, we divide both sides by −3 and get
x>−3.
Therefore, the inequality sign have to be flipped when dividing by a negative number.
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Maggie owes the clerk $85 dollars. Each of 5 friends will help pay the debt. How much will each friend pay? Find the solution and what it means in the context of the problem.
shane is standing at the base of a truck-mounted stairway to board an aircraft. the stairway begins at the ground. the length of the stairway is 18 feet, and the elevation of the top of the stairway from the ground is 13 feet. what is the approximate angle made by the stairway with the ground? a. 46.24° b. 54.16° c. 43.76° d. 35.84°
The approximate angle will be made by the stairway with the ground is 46.24°.
As we are been given that, the length of the stairway from the ground is 18 feet, under the right angle triangle, that will be the length of the hypotenuse. Next, since the elevation of the top of the stairway from, the ground is 13 feet, which is considered to be the length of the perpendicular of the assumed right angled triangle.
Now, we are asked to find the angle x,
Since, we know that
sin θ = perpendicular/ hypotenuse
So, substituting the required values the desired angle we get is :
sin θ = 13/18
sin θ = 0.7222
θ = sin ⁻¹ (0.7222)
= 46.2364
x = 46.24
the angle θ or x is 46. 24°.
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'
Can someone please help mee (20 points
brainliest!!!)
Answers:
16.50 for the first box
10 for the second box
======================================
Explanation:
Part (a)
Plug in x = 20 and solve for p.
0.2x+4p = 70
0.2*20+4p = 70
4 + 4p = 70
4p = 70-4
4p = 66
p = 66/4
p = 16.50
They should charge $16.50 per gallon if the demand is 20 million gallons.
------------------------
Part (b)
Let's say the price is initially $10 per gallon. The starting price could be anything you want.
Plug p = 10 into the equation and solve for x.
0.2x+4p = 70
0.2x+4*10 = 70
0.2x + 40 = 70
0.2x = 70-40
0.2x = 30
x = 30/(0.2)
x = 150
The demand is 150 million gallons if the price were $10 per gallon.
Now let's increase the price by $0.50 to get to p = 10.50
Let's solve for x based on this larger value of p.
0.2x+4p = 70
0.2x+4*10.50 = 70
0.2x+42 = 70
0.2x = 70-42
0.2x = 28
x = 28/(0.2)
x = 140
The demand is now 140 million gallons if the price were $10.50 per gallon.
The demand has gone down by 10 million gallons (since 150-140 = 10).
Find the distance between each pair of points. Round to one decimal place. A(-4, 6) and B(3, -7), and E(-6, -5) and F(2, 0).
AB=(
EF=
To one decimal place, round. points A(-4, 6), B(3, -7), E(-6, -5) and F (2, 0).
The distance between AB is [tex]\sqrt{185}[/tex]=13.601 and EF is [tex]\sqrt{89}[/tex]=9.433.
Given that,
To one decimal place, round.
A(-4, 6), B(3, -7), E(-6, -5) and F (2, 0).
We have to find the distance between two points that are AB and EF.
1. The distance between 2 points A and B.
A(-4, 6) and B(3, -7).
Distance formula is [tex]\sqrt{(x_{2} -x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]
Here, x₁=-1,x₂=3 and y₁=6,y₂=-7
After substituting we get,
[tex]\sqrt{{(3 -(-1)} )^{2} +(-7 -6 )^{2} }\\[/tex]
[tex]\sqrt{{(3 +1} )^{2} +(-7 -6 )^{2} }\\[/tex]
[tex]\sqrt{{(4} )^{2} +(-13 )^{2} }\\[/tex]
[tex]\sqrt{16 +163}\\[/tex]
[tex]\sqrt{185}[/tex]
13.601
Therefore, the distance between AB is [tex]\sqrt{185}[/tex]=13.601.
2.The distance between 2 points E and F.
E(-6, -5) and F (2, 0).
Distance formula is [tex]\sqrt{(x_{2} -x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]
Here, x₁=-6,x₂=2 and y₁=-5,y₂=0
After substituting we get,
[tex]\sqrt{{(2 -(-6)} )^{2} +(0 -(-5) )^{2} }\\[/tex]
[tex]\sqrt{{(2 +6} )^{2} +(0 +5 )^{2} }\\[/tex]
[tex]\sqrt{{(8} )^{2} +(5 )^{2} }\\[/tex]
[tex]\sqrt{64 +25}\\[/tex]
[tex]\sqrt{89}[/tex]
9.433
Therefore, the distance between EF is [tex]\sqrt{89}[/tex]=9.433.
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Suppose xy > 0. Describe the points whose coordinates are solutions to the inequality.
The solutions fo the inequality are all the points (x, y) that meet these 3 conditions.
x ≠ 0y ≠ 0Sign(x) =sign(y)Which points are solutions of the inequality?
We want to find points of the form (x, y) that are solutions of the inequality:
x*y > 0
Clearly x and y must be different than zero.
So, for example if x = -1, y can be any negative number, for example y= -3
x*y > 0
(-1)*(-3) > 0
3 > 0
This is true.
Now if x = 1, y must be positive. LEt's take y = 103, then:
x*y > 0
1*103 > 0
103 > 0
Then we have 3 conditions:
x ≠ 0y ≠ 0Sign(x) =sign(y)The solutions fo the inequality are all the points (x, y) that meet these 3 conditions.
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Lesson 1.10: Daniel works at least 30 hours a week. He works as a math tutor
and as a teacher. The number of hours Daniel works as a tutor (y) is at most
twice the number he works as a teacher (x).
• Write the set of inequalities that represents the constraints of the situation
and state a point (x, y) that is the feasible region.
The set of inequalities that represents the constraints of the situation is y ≤ 2x, x + y ≥ 30 and a point (x, y) that is the feasible region is (10, 20)
How to write the set of inequalities that represents the constraints of the situation and state a point (x, y) that is the feasible region.The given parameters are:
Number of hours = at least 30 hours a week
This means that
x + y ≥ 30
Also, we have:
The number of hours Daniel works as a tutor (y) is at most twice the number he works as a teacher (x).
This means that
y ≤ 2x
Substitute y ≤ 2x in x + y ≥ 30
x + 2x ≥ 30
This gives
3x ≥ 30
Divide
x ≥ 10
Substitute x ≥ 10 in y ≤ 2x
y ≤ 2 x 10
Evaluate
y ≤ 20
Hence, the set of inequalities that represents the constraints of the situation is y ≤ 2x, x + y ≥ 30 and a point (x, y) that is the feasible region is (10, 20)
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if the federal debt is $24 trillion, and if this debt were divided equally among 300 million people, then how much would each person owe? describe how to estimate mentally the answer to the federal debt problem, and explain briefly why your strategy makes sense.
Using the concept of division we can find the amount of money each person owes.
Why should we use Division?Division is one of the fundamental operations used in mathematics which involves breaking a bigger value into smaller groups with the same number of components.
The federal debt =$24 trillion=$24000000
(one trillion=1000000 million)
The value in trillion is converted to million by multiplying by 1000000.
The number of people the amount to be equally distributed= 300 million
Amount of money equally distributed among each person
=[tex]\frac{Total debt amount}{number of people}[/tex]
=[tex]\frac{24000000}{300}[/tex]
=80000
The amount each person owes is $80000
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Could someone help explain this asap
x-7/8=-3/4
Answer: x=1/8
Step-by-step explanation:
[tex]\displaystyle\\x-\frac{7}{8}=-\frac{3}{4} \\\\ x-\frac{7}{8}+\frac{7}{8}=-\frac{3}{4}+\frac{7}{8}\\\\x=-\frac{3}{4} +\frac{7}{8} \\\\ x=\frac{7}{8}-\frac{3*2}{4*2}\\\\ x=\frac{7}{8} -\frac{6}{8} \\\\x=\frac{7-6}{8} \\\\x=\frac{1}{8}[/tex]
Draw an area model that demonstrates that the quotient of 2080 and 40 is 52 explain how the model relates to the calculation
We can see in the picture an area model that demonstrates that the quotient of 2080 and 40 is 52.
Given that,
52 is the quotient of 2080 and 40.
The expression can be represented by
2080/40=52
We divide 2080 as 1200+800+80
(1200+800+80)/40=1200/40+800/40+80/40
(1200+800+80)/40=30+20+2
(1200+800+80)/40=52
An area model is a rectangular diagram or model used in mathematics for problems involving multiplication and division, where the length and breadth of the rectangle are determined by the factors, quotient, and divisor. Using number bonds, we may divide the rectangle's enormous area into a number of smaller boxes to simplify the calculation. The product or quotient is then obtained by adding to obtain the area of the entire.
We can see in the picture an area model that demonstrates that the quotient of 2080 and 40 is 52.
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I need help with these!
The results of the three cases are listed below:
g ° f (x) = 8 · x + 5 h ° g (- 3 · x) = - 36 · x - 9 f ° g (- 3) = - 14How to evaluate the composition between two functionsIn this problem we find three cases of composition between two functions, each of which has to be evaluated. The definition of the composition between the two functions f and g is presented below:
f ° g (x) = f( g(x) ) (1)
Where x is the input variable of the composite function.
In other words, the input of the function f is the output of the function g.
Now we proceed to find the expressions of the each of the two cases:
Case 1
g ° f (x) = g( f(x) )
g ° f (x) = 4 · (2 · x + 2) - 3
g ° f (x) = 8 · x + 8 - 3
g ° f (x) = 8 · x + 5
Case 2
h ° g (- 3 · x) = h [g (- 3 · x)]
h ° g (- 3 · x) = 3 · [4 · (- 3 · x) - 3]
h ° g (- 3 · x) = 3 · (- 12 · x - 3)
h ° g (- 3 · x) = - 36 · x - 9
Case 3
f ° g (- 3) = f( g(- 3) )
f ° g (- 3) = 3 · [2 · (- 3) + 1] + 1
f ° g (- 3) = 3 · (- 5) + 1
f ° g (- 3) = - 15 + 1
f ° g (- 3) = - 14
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PLEASE HELP ILL GIVE BRAINLEST
A. divide 2x by 2
B. add 5 to both sides of the equation
C. divide both sides of the equation by 26
D. subtract 5 from the left side of the equation
what is the term for tying individual events together to provide meaningful alerts? event correlation
The correct answer is event correlation.
Event correlation is a technique for making sense of a large number of events and pinpointing the few events that are really important in that mass of information. This is accomplished by looking for and analyzing relationships between events.
Event can be defined as a set of outcomes of an experiment. In other words, an event in probability is the subset of the respective sample space. So, what is sample space? The entire possible set of outcomes of a random experiment is the sample space or the individual space of that experiment
One example of event correlation can occur with intrusion detection. Perhaps there is an employee account that hasn't been accessed for years, and suddenly a large number of login attempts are noticed. That account may start executing suspicious commands.
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HELP ASAP DU TODAY...... WILL GIVE BRAINILIS.
Short Answer
Note: Your teacher will grade your responses to questions 6–7 to ensure that you receive proper credit for your answers.
1. Explain why (4, 1) is not a solution to the equation y = 3x +
2. Pizza costs $1.50 per slice. Use a table and an equation to represent the relationship between the number of slices of pizza bought and the total cost.
Answer: y = 3x+1
Step-by-step explanation: If (4,1) is a solution of y = 3x+1, that means if we plugin the respective values of (4,1), we should have an EQUALITY:
1 = 3(4) + 1
1 = 13 , which is wrong, then the point (4,1) is NOT a solution of y = 3x+1.
corporation uses trucks to transport bottles from the warehouse to different retail outlets. gasoline costs are per mile driven. insurance costs are per year. calculate the total costs and the cost per mile for gasoline and insurance if the truck is driven (a) miles per year or (b) miles per year. (round the cost per mile to the nearest cent, $x.xx.)
The total cost = $5000 (Option A) and $9400 (Option B)
Cost per mile = $0.33 (option A) and $0.25 (Option B)
What is unitary method?A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method.
Given:
Cost of gasoline for each mile driven = $0.20Cost of insurance for each year = $2000To find: Total costs and cost per mile, when the truck is driven (A) 15000 miles per year (B) 37000 miles per year.
Finding:
(A) By unitary method,
When the truck is driven 1 mile, cost of gasoline = $0.20
When the truck is driven 15000 miles, cost of gasoline = $ 0.20(15000) = $3000 in an year
Cost of insurance in an year = $2000
Thus, total cost = $ 3000 + $2000 = $5000
Now, for per mile cost:
Cost of gasoline = $0.20
Cost of insurance = $0.13
Thus, Cost per mile = $0.20 + $0.13 = $0.33
(B) Again, by unitary method,
When the truck is driven 1 mile, cost of gasoline = $0.20
When the truck is driven 37000 miles, cost of gasoline = $ 0.20(37000) = $7400 in an year
Cost of insurance in an year = $2000
Thus, total cost = $ 7400 + $2000 = $9400
Now, for per mile cost:
Cost of gasoline = $0.20
Cost of insurance = $0.5
Thus, Cost per mile = $0.20 + $0.5 = $0.25
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The equation 7(v-5)=-21 is solved in several steps below. For each step, choose the reason that best justifies it.
The solution to the equation is, v = 2.
See the steps explained below.
How to Solve an Equation?Given an equation, 7(v - 5) = -21, the following steps would be taken as shown below:
7(v - 5) = -21 ---> Given
7v - 35 = -21 ----> distribution property
7v - 35 + 35 = -21 + 35 -----> addition property of equality
7v = 14
Divide both sides by 7
7v/7 = 14/7 -----> division property of equality
v = 2
Thus, the solution to the equation as solved above is: v = 2.
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Square root of 81/9 - 7 Times Square root of 4
Answer: -125
Step-by-step explanation:
√81/9 = 9/3 =3
√4 = 2∧7 = 128
3-128 = -125
Which is larger?
3/5 or 4/7
Answer:
3/5 is bigger
Step-by-step explanation:
if the numerator is the same then the one with the smaller denominator is bigger
Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. (Hint: Let (×,y) be the unknown endpoint. Apply the midpoint formula, and solve the
two equations for x and y.)
midpoint (=4,5), endpoint (0, - 4)
Answer:
See below
Step-by-step explanation:
For x : from end point to midpoint 0====> 4 is 4 units ...add 4 more to get x = 8 for other endpoint
For y 5====> -4 is - 9 add -9 more to midpoint to get y = -13
7 gallons = how many pints
Answer:
56 pints hope this helps Brainliest please
Step-by-step explanation:
Answer:
7 gallons = 56 liquid pints!
Explanation= 1 gallon = 8 pints
Your friend says that the line with the equation 2x + 3y = 7 has a slope of 2. explain to them the error in their thinking.
Answer:
The error of their thinking is that they did not convert the equation to slope intercept form, so they assumed that the 2x was the slope. They got the standard form mixed up with slope intercept.
I hope this helps you!
Can someone please help mee (20 points + brainliest!!!)
Answer:
A) x = 225 - 7.5p
B) x = 180 millions of gallons
Step-by-step explanation:
A) Make "x" the subject:
[tex]\sf \rightarrow 0.4x + 3p = 90[/tex]
[tex]\sf \rightarrow 0.4x = 90-3p[/tex]
[tex]\sf \rightarrow x = \dfrac{90-3p}{ 0.4}[/tex]
[tex]\sf \rightarrow x = 225-7.5p[/tex]
B) Demand when the price per gallon is $6:
substitute p = 6
[tex]\sf \rightarrow x = 225-7.5(6)[/tex]
[tex]\sf \rightarrow x = 225-45[/tex]
[tex]\sf \rightarrow x =180[/tex]
a car valued at $28,000 depreciates at a rate of 20% per year. what will the car be worth after 6 years?
The value of the car after 6 years will be $7340 .
The Depreciation can be calculated using the formula
A = P( 1 - r/100)ⁿ
where , A = amount , P = principal , r = rate of deprecation , n = time period
In the question ,
it is given that
the value of the car (P) = $28000
rate of deprecation (r) = 20% per year
time period (t) = 6 years
Substituting the values in the Depreciation formula we get ,
Amount = 28000*( 1 - 20/100 )⁶
= 28000*(80/100)⁶
= 28000*(0.80)⁶
= 28000*0.26214
= 7339.92
≅ 7340
Therefore , the value of the car after 6 years will be $7340 .
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4(-15).
Which problem would give the same result? Select two options.
15 + 15 + 15 + 15
4 + 4 + 4 + 4
(–1)(15 + 15 + 15 + 15)
(–15) + (–15) + (–15) + (–15)
Answer:
the last two because it needs to be negative
Answer:
The last 2 options
Step-by-step explanation:
4(-15) = -60.
(–1)(15 + 15 + 15 + 15) = -60.
(–15) + (–15) + (–15) + (–15) = -60.
Do the circles having the equations (x - 2)2 + y2 = 4 and (x + 2)2 + y2 = 4 intersect on the Cartesian plane? If so, where do they intersect?
Answer: (0,0)
Step-by-step explanation:
[tex]\displaystyle\\\left \{ {{(x-2)^2+y^2=4} \atop {(x+2)^2+y^2=4}} \right. \\Hence,\\(x-2)^2+y^2=(x+2)^2+y^2\\(x-2)^2=(x+2)^2\\x^2-2*x*2+2^2=x^2+2*x*2+2^2\\-4x=4x\\-4x+4x=4x+4x\\0=8x\\[/tex]
Divide both parts of the equation by 8:
[tex]0=x[/tex]
Hence,
[tex](0+2)^2+y^2=4\\2^2+y^2=4\\4+y^2=4\\y^2=0\\y=0\\Thus,\ (0,0)[/tex]
Answer:
The two circles intersect at one and only point A(0 , 0)
Step-by-step explanation:
Let ς₁ be the circle of equation :
ς₁ : (x - 2)² + y² = 4
and ς₂ be the circle of equation :
ς₂ : (x + 2)² + y² = 4
Consider the point M (x , y) ∈ ς₁∩ς₂
M ∈ ς₁ ⇔ (x - 2)² + y² = 4
M ∈ ς₂ ⇔ (x + 2)² + y² = 4
M (x , y) ∈ ς₁∩ς₂ ⇒ (x - 2)² + y² = (x + 2)² + y²
⇒ (x - 2)² = (x + 2)²
⇒ x² - 4x + 4 = x²+ 4x + 4
⇒ - 4x = 4x
⇒ 8x = 0
⇒ x = 0
Substitute x by 0 in the first equation:
(0 - 2)² + y² = 4
⇔ 4 + y² = 4
⇔ y² = 0
⇔ y = 0
Conclusion:
The two circles intersect at one and only point A(0 , 0).
Clara knows she is 450 yards from the local swimming pool on the map on her phone the pool is 2/3 inch from her current location if her current locations is 4 inches from home on the same map how far is she from home
Clara is 2700 yards far from the home.
How to Calculate Yard and inches?In mathematics, yard and inches are two different units of length. we can say that yard is the one of the measurement of length. Conversion of yard in various quantities is as below:
In inches :1 yard = 36 inches
In feet :1 yard = 3 feet
In meters :1 yard = 0.914 meters
How to solve statement based questions ?For the statement based question first of all try to find out that what is given in the statement and what we have to find out. Now, try to form the statements in the mathematical notation and then solve the equations by performing certain mathematical and algebra operations according to need.
Now, for the given question :
as, Clara is 450 yards from the local swimming pool on the map on her phone and the pool is 2/3 inch from her current location.
Therefore, the pool distance is 450 / (2/3) = 675 yards
Now, distance of current location = 4 inches
Thus, Distance from the home = 675 × 4 = 2700 yards
Hence, Clara is 2700 yards far from the home.
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