if we repeatedly toss a balanced coin, then, in the long run, it will come up heads about half the time. but the probability that such a coin will come up heads exactly half the time in 16 tosses is 1 in 65536 (2^16).
This can be calculated using the binomial probability formula which states that the probability of getting a certain number of heads in a certain number of tosses is given by (Number of ways to get the desired number of heads) / (Total number of possible outcomes). In this case, the number of ways to get 8 heads in 16 tosses is equal to 16C8, or 120.
The total number of possible outcomes is equal to 2^16, or 65536. Thus, the probability of getting 8 heads in 16 tosses is 120/65536, which is approximately equal to 1/65536.
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Leo says that the product of n x 4/5 is greater than 4/5 because multiplication always increases a number. Which of the following values could be used for "n" that would prove that Leo is incorrect? Choose all the correct answers.a) 2b) 5/8c) 6/6d) 7/6e) 5/4
The correct answer is 5/8. Option b)
In math, to multiply means to add equal groups. When we multiply, the number of things in the group increases.
from given statements that, the product of n x 4/5 is greater than 4/5 because multiplication always increases a number.
n × 4/5 > 4/5 ⇒?
so, what are the "n" values will prove that above statement is incorrect.
so, if we put the all given options values of "n" in n × 4/5, then
⇒ n=2
8/5 > 4/5
⇒ n=5/8
20/40 < 4/5
⇒ n=6/6
1 > 4/5
⇒ n=7/6
28/30 > 4/5
⇒ n=5/4
20/4 > 4/5
Therefore, The correct answer is 5/8. Option b)
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What is the range of slope?
Birr 6,500 were divided equally among a certain number of persons. Had there
been 15 more persons, each would have got Birr 30 less. Find the original number
of persons
So, on solving the question we can say that the equation formed is - 6500 = 15x - 30y x = 433.3333333333
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
the equation formed is -
6500 = 15x - 30y
y = 0
x = 6500/15
x = 433.3333333333
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Grayson is working two summer jobs, making $18 per hour lifeguarding and making $10 per hour clearing tables. In a given week, he can work a maximum of 14 total hours and must earn no less than $180. Also, he must work no more than 10 hours lifeguarding and no less than 3 hours clearing tables. If xx represents the number of hours lifeguarding and y represents the number of hours clearing tables, write and solve a system of inequalities graphically and determine one possible solution.
The system of inequalities that models this situation is given as follows:
x ≥ 0.y ≥ 3.x + y ≤ 14.18x + 10y ≥ 180.x ≤ 10.One possible solution is given as follows:
(9,4).
Meaning that he works 9 hours lifeguarding and 4 hours clearing tables.
How to model the system of inequalities?The variables for the system of inequalities in this problem are given as follows:
Variable x: number of hours lifeguarding.Variable y: number of hours clearing tables.The number of hours cannot be negative, hence the first two restrictions are given as follows:
x ≥ 0.y ≥ 0.He can work a maximum of 14 total hours, hence:
x + y ≤ 14.
He must earn no less than $180, hence, considering the rates for each job, we have that:
18x + 10y ≥ 180.
Also, he must work no more than 10 hours lifeguarding and no less than 3 hours clearing tables, hence:
x ≤ 10.y ≥ 3.The shaded region represents all possible solutions for the system of inequalities.
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The table shows the distance why in meters that a person runs an ex seconds graph the line that passes through the points in a table then write an equation that represents the line (1,4.5),(2,9),(3,13.5).
Two APs have same common difference. If the first term is -1 and that of the other is -8. then the difference between their 4th term is?
Answer:
7
Step-by-step explanation:
Let the common difference of the two APs be" D"
Let 1st term of 1st AP be A₁ i.e = -1
And the first term of the second AP b₁ i.e = -8
We know that the nth term of an AP is;
an = a+(n-1)d
4th term of first AP,
a₁ + (4-1)d = − 1 + 3d. --Eqn. 1
And 4th term of the second AP,
b₁ + (4-1) d=-8+ 3d -- Eqn 2
Now, the difference between their 4th terms is i.e.
= (- 1+ 3d ) - (-8 + 3d )
= -1 + 3d + 8 - 3d = 7
So, the answer is 7.
A scale drawing of a rectangular park had a scale of 1 cm = 60 m
What is the actual perimeter of the park in meters?
the measure of two supplementary angles of a triangle are in the ratio 4:11. what is the measure of the larger angle?
According to the given information the supplementary angle are 132 and 48.
Are indeed the supplementary angles 90 or 180?Two angles are referred to as supplementary angles because they combine to generate a linear angle when their total is 180 degrees. When two angles add up to 90 degrees, however, they are considered to be complimentary angles and together they make a right angle.
What do complimentary and additional angles mean?If the total of two angles is 90 degrees or greater, they are complementary; if the sum is 180 degrees or greater, they are supplementary. Given that they are in the same ratio, we will call one angle 11x whilst the other is 4x.
They add up to [tex]11x+4x=15x={180}^\circ\rightarrow x=12[/tex]
So one angle is [tex]11\cdot12={132}^\circ[/tex]
And the other is [tex]4\cdot12={48}^\circ[/tex]
Check: [tex]132+48=180[/tex]
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How do you solve a 3 equation problem?
With substitution, you need to solve one of the equations for one of the unknown variables and substitute that value into one of the other equations, then solve for the remaining unknown variable.
To solve a 3 equation problem, you can use elimination or substitution. With elimination, you need to add or subtract the equations to eliminate one of the unknown variables. With substitution, you need to solve one of the equations for one of the unknown variables and then substitute that value into one of the other equations. You can then solve for the remaining unknown variable.
To solve a 3 equation problem, you can use elimination or substitution methods. With elimination, you need to add or subtract the equations to eliminate one of the unknown variables. With substitution, you need to solve one of the equations for one of the unknown variables and substitute that value into one of the other equations, then solve for the remaining unknown variable.
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what is happening when oneplus() is called? in other words, what exactly does the function receive as an argument? why isn't the value of the variable in main() altered?
Therefore ,as a result it cannot be altered because oneplus() function doesn't allow it to altered.
Describe Function.Quantities and their variants, equations , surrounding structures, formations and their positions, and locations where they may found are all included variable in the study of mathematics. The link between a collection of inputs, each of which has a corresponding output, is referred to as a "function." A function is a dynamic relationship between inputs and outputs in which each input produces a single, unique result. Each function has a designated area and only needs a tiny area, or scope.
Here,
Given :
oneplus() function
The function receives as an argument that twoplus() function is better than oneplus() .
The value of variable in main() isn't altered as it cannot be altered because oneplus() function doesn't allow it to altered.
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Minimum charge of telephone upto 175 calls is Rs. 200. The charge for each extra call is Re. 1. If a man paid Rs. 726 with 10% TSC and 10% VAT, find the total number of calls made in that month.
Given that each additional call will cost Rs. 1,
The total cost of the additional calls is Rs. 1332 calls.
How to find the calculation?Given that there is a charge for up to 175 calls, Rs 200.
And each subsequent call will cost Rs 1.
Additionally, there are 13% VAT and 10% TSC.
Taxes total 10 + 13 = 23 %.
And the full amount owed is Rs 1988.8.
Finding the monthly total of additional calls is necessary.
Therefore, the amount before tax would be
1998.8 -14% of 1988.8
- 1988.8 - 1988.8 x 14/100
=1988.8 - 457.424
=1531.376.
Additionally, the minimum telephone fee is Rs 200.
After the minimum charge, the amount is 1531.376-200.
Rs 1331.376
Given that each additional call will cost Rs. 1,
The total cost of the additional calls is Rs.
1 = 1331.376/Rs = 1332 calls.
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A tank hold 49 literof oil. If 7 liter leak what the percentage of oil ha leaed?
The percentage of oil that has leaked from the tank is 14.29%.
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100.
Given that,
The capacity of the tank = 49 litres.
Total litres of oil leaked = 7 litres.
Mathematically, the percentage for the amount of oil leakage in this tank is given by this formula:
Percentage = oil leakage/tank capacity *100
Substituting the given parameters into the formula, we have:
Percentage = 7/49 *100 = 14.29%
Thus, The percentage of oil that has leaked from the tank is 14.29%.
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in this problems you will consider paths on the integer grid that start at (0,0) in which every step increments one coordinate by 1 and leaves the other unchanged. a) (4 points) how many such paths are there from (0,0) to (85, 65)?
The number of such paths from (0,0) to (85,65) is C(150, 85).
What is co-ordinate ?
In mathematics, a coordinate is a pair of numerical values that represent a specific location on a two-dimensional surface, such as a graph, a map, or an image. The two values are usually referred to as the x-coordinate and the y-coordinate.
A path from (0,0) to (85,65) on the integer grid that starts at (0,0) and increments one coordinate by 1 and leaves the other unchanged at each step is equivalent to a sequence of 85 "right" steps and 65 "up" steps. The number of ways to arrange these steps is given by the binomial coefficient C(85+65, 85), which is the number of ways to choose 85 items (the "right" steps) from a set of 150 items (85 "right" and 65 "up" steps) without replacement and where order matters.
The general formula for the binomial coefficient is C(n, k) = n! / (k!(n-k)!), where n! is the factorial of n, i.e., the product of all integers from 1 to n, and k! is the factorial of k. Using this formula, we have:
C(150, 85) = 150! / (85!(150-85)!) = (150149148*...6665) / (858483*...1) = (150149148...6665) / (85!)
So, the number of such paths from (0,0) to (85,65) is C(150, 85).
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Pls helpppp!
What’s 4,807.50 plus 22%
Answer: 5865.15
Step-by-step explanation:
The tables show the linear relationship between a swimmers time in seconds and the number of pool laps completed use the tables to answer a-c. Please help asap I'll give brainliest answer pleaseee
a) The rate of change for swimmer A is 35.5.
b) the rate of change for swimmer B is 31.5.
c) Simmer A is swimming at faster rate than swimmer B.
What is slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
a) The rate of change for swimmer A
= (177.5- 71) / (5-2)
= 106.5/3
= 35.5
b) the rate of change for swimmer B
= (126- 94.5) / (4-3)
= 31.5
c) Simmer A is swimming at faster rate than swimmer B.
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which angles must be less than 146 degrees? please list both angles and support your answer by stating the theorem that will support your conclusion.
Any two angles whose sum is 146 degrees must both be less than 146 degrees. This can be supported by the Triangle Sum Theorem, which states that the sum of the measure of the interior angles of a triangle is 180 degrees.
The Triangle Sum TheoremThe Triangle Sum Theorem states that the sum of the measure of the interior angles of a triangle is always 180 degrees. Therefore, if two angles add up to 146 degrees, then both of those angles must be less than 146 degrees. This is because the remaining angle must make up the difference to reach the total of 180 degrees.
For example, if two angles measure 80 degrees and 66 degrees, then the third angle must measure 34 degrees in order to sum up to 180 degrees.Therefore, any two angles whose sum is 146 degrees must both be less than 146 degrees.
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a store manager wants to mix 20 lb of nuts worth $3 per pound with some nuts worth $10 per pound to make a mixture worth $5 per pound. how many pounds of $10 nuts must be used?
Find the value of 2π√l /g
when π=3⅐, l= 98 and g = 32
Answer:
Step-by-step explanation:
2π√l/g = (2*3.14*sqrt(98))/32 = 10.945
Two scuba divers are swimming below sea level. One diver is located 28 feet below sea level and the other is located 37 feet below sea level. Which expression shows how far apart the divers are?
|−37| − |−28|
|−37| + |−28|
|37| − (−|−28|)
|37| + |28|
Answer:
b. |−37| + |−28|
Step-by-step explanation:
The absolute value of a number is its distance from 0 on the number line. Since the divers are below sea level, both 37 and 28 will be negative numbers.
To find the distance between the two divers, we need to add the absolute values of their depths.
The first diver is at -37 ft and the second diver is at -28 ft, so we can calculate the distance between them as |-37| + |-28| = 37 + 28 = 65 ft
how to find the answer
x= 7; 4x + 8 ÷ 2 =
Answer: 18
unclear but appears its 18.
Step-by-step explanation:
Because x is 7; 4x+8/2 = 36.
but its not clear what is being halved: 8 or (4x+8)? so answer could be 32 as well.
Which table shows a linear function?
O
X
-5
-3
-1
1
2
X
-4
-3
-2
1
2
X
-5
-3
-1
0
2
y
-4
-3
-2
265 35.
-1
-3
-5
-2
0
9236
5
1) a man flies a kite at a height of 120 m. the wind carries the kite horizontally away from him at a rate of 6 m/sec. how fast is the distance between the man and the kite changing when the kite is 130 m away from him?
So, on solving the provided question, we can say that, here by differential equations So, 2(400)(25) = 2(500)(dy/dt) => [tex]dy/dt = 20 ft/sec[/tex]
What is differential equation?
Sequences in which the difference between succeeding terms is constant are known as arithmetic progressions. For instance, an arithmetic progression with a tolerance of 2 is the sequence 5, 7, 9, 11, 13, and so on. An arithmetic progression (A.P.) is a progression where the tolerance between two succeeding numbers is always the same.
Let x be the girl's distance from the kite at time t and y be the length of the string at that same moment.
The right triangle at time t has a hypotenuse of length y, a hypotenuse of length 300, and a hypotenuse of length x.
[tex]dx/dt = 25[/tex]
By the Pythagorean Theorem,
[tex]x2 + 3002 = y2[/tex]
[tex]2x(dx/dt) = 2y(dy/dt)[/tex]
Since [tex]x2 + 3002 = y2 and y = 500, x = 400[/tex]
So, 2(400)(25) = 2(500)(dy/dt)
[tex]dy/dt = 20 ft/sec[/tex]
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4. (20 pts) suppose four people are lining up for a photo. does this situation represent a combination or a permutation? explain. how many different ways are there for the four people to line up for the photo?
The required number of ways are 24 and the situation is permutation.
What is permutation?An arrangement of items in a specific order is referred to as a permutation. Here, the components of sets are arranged in a linear or sequential order. For instance, the set A=1,6 has a permutation of 2, which is 1,6,1.
According to question:It depicts a permutation since the order of the people in this situation matters.
According to the number of ways, the first position can be filled by four people, the second by three (because the first position has already been taken by one person), the third by two, and the fourth by one.
This results in 4321 = 4! = 24 ways as the total number of ways.
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How many faces does this polyhedron have?
HELP!!
6
12
8
10
Answer:
6
Step-by-step explanation:
you have to count the 2d faces
Answer:
6 faces
Step-by-step explanation:
DCGH
BCDA
BCGF
ADHE
BFEA
FGHE
does part 95.987 mean i can use my 10 meter radio on cb, so long as i follow the rules on frequency, and power?
No, You cannot use your 10 meter radio on CB (citizen’s band), so long as you follow the rules on frequency, and power.
What is Citizen's Band?A public, two-way personal radio service is the Citizen's Band (CB) Radio Service, usually abbreviated as CB. There are various categories for CB operating. The most popular CB method is voice communication, which rose to popularity in the 1970s. Mobile CB operating is still common, particularly in automobiles and trucks. The majority of CB operating occurs in a constrained range of frequencies around 27 MHz. This band contains 40 channels. There is excessive channel saturation.
A CB (citizen’s band) radio must be FCC type approved. Of course, I have no idea where you are, so maybe, where you are, it is ok. In the US however, CB radios are not to be “easily modified” neither to increase power out nor to allow operation outside the citizen’s band frequencies. Even as an extra class amateur radio licensee, I may not use a modified radio on the CB band. I am allowed, however to modify a CB radio to operate on amateur radio bands.
You cannot use your 10 meter radio on CB (citizen’s band), so long as you follow the rules on frequency, and power.
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A third friend, alisha, offers to drive daisa and tymar home for spring break so that they can share the cost of gas money. when asked how fast she drives, alisha reported that the distance traveled, y, for the time, x, can be expressed as y=57x.
true or false: alisha's equation, y=57x represents a proportional relationship.
Therefore , the solution of the given problem of equation comes out to be the correct equation can be = > y/x =57.
Who or what is the equation?A mathematical equation resembles a formula connecting two assertions when the equals letter (=) is employed to denote equality. An equation in algebra is a statement of fact that demonstrates the equality of numerous mathematical variables. For example, the equation obd + 6 = 12 has an equal sign separating the numbers doc d + 6 and 12. You can mathematically expression how many syllables correspond per each side of every letter. Often, a symbol's message is its exact opposite.
Here,
Given :
Equation : y =57x for the distance travelled by alisha.
Thus,
To find the equation is correct or not.
By comparing it with distance/time = speed equation we get to know
that the equation represented by alisha is wrong.
The correct equation can be => y/x =57 .
Therefore , the solution of the given problem of equation comes out to be the correct equation can be = > y/x =57.
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Q3. There are 5 red sweets, 6 blue sweets and 9 yellow sweets in a bag.
Sarah takes a sweet at random.
She replaces it back and then
Take another sweet at random.
Work out the probability the both the sweets the same colour.
Answer:
Step-by-step explanation:There are a total of 20 sweets in the bag (5 red + 6 blue + 9 yellow).
To find the probability that Sarah takes two sweets of the same color, we need to find the probability of her choosing a sweet of a specific color on her first pick and then the probability of her choosing another sweet of that same color on her second pick.
For example, if she chooses a red sweet on her first pick, the probability of that happening is 5/20, or 1/4. Then the probability of her choosing another red sweet on her second pick, given that she already picked one, is 4/20, or 2/10. Therefore the probability of her choosing two red sweets in a row is (1/4) * (2/10) = 1/20.
Similarly, the probability of her choosing two blue sweets in a row is (6/20) * (5/20) = 3/50.
The probability of her choosing two yellow sweets in a row is (9/20) * (8/20) = 9/100.
The probability of her choosing two sweets of the same color is the sum of the probability of her choosing two red sweets, two blue sweets, or two yellow sweets in a row.
P(Two same color) = 1/20 + 3/50 + 9/100 = 11/50
So, the probability of her choosing two sweets of the same color is 11/50.
How can an absolute value equation help you calculate the distance from one point to another on the coordinate plane when the points are on the same vertical or horizontal line?
The distance between the two points can be calculated from the absolute value equation if the points are on the same vertical or horizontal line
What is the distance of a line between 2 points?The distance of a line between 2 points is always positive and given by the formula
Let the first point be A ( x₁ , y₁ ) and the second point be B ( x₂ , y₂ )
The distance between A and B is D , and the distance D is
Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²
Given data ,
Let the distance be represented as D
Let the two points lie on the same vertical line
So , let the two points be P ( x , y₁ ) and Q ( x , y₂ )
The x coordinate of the two points remains the same
So , the difference between the y coordinate will give us the distance between the two points on the vertical line
So , | y₂ - y₂ | = distance D
The absolute value will always gives the result as a positive value and distance is always positive
Now , Let the two points lie on the same horizontal line
So , let the two points be R ( x₁ , y ) and S ( x₂ , y )
The y coordinate of the two points remains the same
So , the difference between the x coordinate will give us the distance between the two points on the horizontal line
And , | x₂ - x₁ | = distance D
The absolute value will always gives the result as a positive value and distance is always positive
Hence , the absolute value equation is used to calculate the distance if the two points are on the same line
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About 10000 children were asked what their favourite school subject was. The bar chart shows the results for the most popular subjects. % 30 20 10 Art History Maths Subject P.E. a) Which subject was the third most popular? b) About what percentage of the students chose Maths? Submit Answer
a) Maths was the third most popular subject, according to the chart showing the results for the most popular subjects using their percentages.
b) About 10 percent of the students chose Maths.
What is the percentage?The percentage is the ratio of one variable or value compared to another.
Percentages are proportional values. They are obtained as the quotient of one value (the numerator) divided by another value (the denominator) before being multiplied by 100.
Subject Percentage
Art 30%
History 20%
Maths 10%
Thus, based on the percentage of popular subjects, 10% chose Maths as the third most popular subject.
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The height of a kicked ball can be modeled by the quadratic function h = - 0.01x^2 + 1.18x + 2. The horizontal distance traveled by the ball in feet is represented by x, and h is the height of the ball in feet. Approximately how far does the ball travel horizontally by the time it hits the ground?
The horizontal distance travelled by the ball when it hits ground is 119.67 feet
What is an equation?An equation is an expression composed of variables and numbers linked together by mathematical operations.
Let x represent the horizontal distance traveled by the ball and h represent the height of the ball. Given that:
h = -0.01x² + 1.18x + 2
The ball hits the ground when h = 0, hence:
-0.01x² + 1.18x + 2 = 0
x = 119.67
The horizontal distance is 119.67 feet
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