The expected gain after 16 tosses of the coin is $400.
State the term equally likely events?Equally likely denotes the probability that each experiment's result will occur. For instance, if you throw a fair, six-sided die, any of the faces (1, 2, 3, 4, 5, or 6) has the same chance of coming up. A fair coin has an equal chance of landing on its head (H) or tail (T).Let x stand in for your entire savings.
There is a 0.5 likelihood of heads and a 0.5 possibility of tails. (equally likely events).
The value of accepting this offer is 1.5. The formula is as follows:
2 heads.
0.5 = P(Heads)
Value anticipated if the coin came out heads: 2x*0.5 = x
Plus
(1 - 0.5)x = 0.5x for tails.
0.5 = P(Tails)
Value anticipated if the coin came up tails: 0.5x*0.5 = 0.25x
Total projected value is equal to 1.25x.
For x = $20
Thus,
Amount = 1.25(20) = $25.
Thus, for the 16 tosses = $25 x 16 = $400.
Therefore, the expected gain after 16 tosses of the coin is $400.
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The data represent the number of mines traveled by 10 delivery drivers in a community for one day.
218,223,211,299,231,245,261,278,212,233
What is the first quartile of miles driven?
A. 218
B. 261
C. 215
D. 232
The first quartile of miles driven is 218 miles.
What are quartiles in a data set?Quartiles are three values that divide the sorted data into four parts, each of which has the same observation value.
First quartile: Also known as Q1 or lower quartile. Second Quartile: Also called Q2 or median. Third Quartile: Also known as Q3 or upper quartile.The four quarters that divide the dataset into quartiles are:
At least 25% of the number.The next lowest 25% of the numbers (up to the median).25% of the second highest number (above the median).Up to 25% of the number.Let's arrange the data in an order:
211,212,218,223,231,233,245,261,278,299
Since the data has 10 observation, for which the median will be simply the average of two middle terms i.e.5th and 6th term dividing the data in two halves.
Median: 232
First half: 211,212,218,223,231
Second half: 233,245,261,278,299
As, quartiles are the medians of each half,
First quartile: 218
Third quartile: 261
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Use factoring to prove that 16⁵+16⁴ is divisible by 17.
Answer:
To prove that 16^5+16^4 is divisible by 17 using factoring, first rewrite the expression 16^5+16^4 using the distributive law as 16^4*(16+1). Then, note that 16+1 is divisible by 17. Since 16^4 is also divisible by 17, the expression 16^4*(16+1) is also divisible by 17. Therefore, 16^5+16^4 is divisible by 17.
A deck of cards contains red, yellow, and blue cards. The probability of selecting a red card out of a deck is 1 9 . The probability of selecting a yellow card is 3 times the probability of selecting a blue card. What is the probability of randomly selecting a blue card on your first try?
We are given that the probability of selecting a yellow card is 3 times the probability of selecting a blue card, so we can write the following equation:
yellow = 3 * blue
We also know that the sum of the probabilities of selecting a red, yellow, or blue card must be equal to 1, so we can write the following equation:
red + yellow + blue = 1
Substituting the expression for yellow from the first equation into the second equation, we get:
red + 3 * blue + blue = 1
Combining like terms, we get:
red + 4 * blue = 1
We are given that the probability of selecting a red card is 1/9, so we can substitute this value into the equation:
1/9 + 4 * blue = 1
Solving for blue, we get:
blue = (1 - 1/9) / 4
blue = (8/9) / 4
blue = 2/9
Therefore, the probability of selecting a blue card on the first try is 2/9.
find the centroid of the region in the first quadrant bounded by the given curves. y = x8, x = y8
The centroid of the region in the first quadrant bounded by the given curves is (81/170, 81/170).
In the given question, we have to find the centroid of the region in the first quadrant bounded by the given curves.
The given curves are:
y = x^8, x = y^8
We can write the curves as
y = x^8...........................(1)
y = x^{1/8}.......................(2)
Now putting the value of y from equation 1 in equation 2, we get
x^8 = x^{1/8}
Now simplifying,
x^{64} = x
x^{64}-x = 0
x(x^{63} - 1) = 0
After equating equal to zero,
x = 0, x = 1
My = [tex]\int_{a\rightarrow b}x[f(x)-g(x)]dx[/tex]
My = [tex]\int_{0}^{1}x[x^{1/8} - x^{8}]dx[/tex]
My = [tex]\int_{0}^{1}[x^{9/8} - x^{9}]dx[/tex]
My = [tex][(8/17)x^{17/8} - (1/10)x^{10}]_{0}^{1}[/tex]
My = (8/17)-(1/10)
My = 63/170
Mx = 1/2[tex]\int_{a\rightarrow b}[(f(x))^2-(g(x))^2]dx[/tex]
Mx = 1/2[tex]\int^{1}_{0}[x^{1/4} - x^{16}]dx[/tex]
Mx = 1/2 [tex][(4/5)x^{5/4} - (1/17)x^{17}]^{1}_{0}[/tex]
Mx = (1/2)[(4/5)- (1/17)]
Mx = 63/170
M = [tex]\int_{a\rightarrow b}[f(x)-g(x)]dx[/tex]
M = [tex]\int^{1}_{0}[x^{1/8} - x^{8}] dx[/tex]
M = [tex][(8/9)x^{9/8} - (1/9)x^{9}]^{1}_{0}[/tex]
M = [(8/9) - (1/9)]
M =7/9
Center of mass(x',y') = (My/M, Mx/M)
Center of mass(x',y') = ((63/170)/(7/9), (63/170)/(7/9))
Center of mass(x',y') = (81/170, 81/170)
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John spread 45 minutes after school reviewing his notes before taking a 15 minute break for a snack. After that snack, he continues reading his notes for the other 30 minutes. What would you add to find the total time that John studied?
Answer:
its A
Step-by-step explanation:
Ben
please answer I have limited time!!!!
Answer:
First second and third
Step-by-step explanation:
A function can only have one output for every input
Answer:
2, 3, 4
Step-by-step explanation:
an input can only have 1 output
Solve the equation.
9( x− 2)²-4=14
Your answer would be x = 2 ± √2
Step-By-Step Solution:
Step one:
9x² - 36x + 32 = 14
Step two:
9x² - 36x + 32 - 14 = 14 - 14
9x² - 36x + 18 = 0
Now we use the quadratic formula.
Step three:
Plug the numbers into the quadratic formula.
x = [tex]\frac{-b±\sqrt{b^{2} - 4ac } }{2a}[/tex]
x = [tex]\frac{-(-36 ± \sqrt{(-36^{2})-4(9)(18 } )}{2(9)}[/tex]
x = [tex]\frac{36 ± \sqrt{648} }{18}[/tex]
x = 2 + √2 or x = 2 - √2
Answer:
(2 + √2; 2 - √2)--------------------------------
Given equation:
9(x - 2)² - 4 = 14Solve it in below steps:
9(x - 2)² - 4 = 14 Add 4 to both sides9(x - 2)² = 18 Divide both sides by 9(x - 2)² = 2 Square root both sidesx - 2 = ± √2 Add 2 to both sidesx = 2 ± √2 AnswerCaroline drinks 2 cups of milk per day. She buys 4 quarts of milk. How many days will her 4 quarts of milk last?
Answer:
4 quarts of milk will last her 8 days.
We can solve this by finding how many cups are in a quart.
1 quart=4 cups
4 quarts= 16 cups
Since Caroline drinks 2 cups a day, divide 16 by 2.
16/2=8
4 quarts will last her 8 days.
Hope this helps! :D
Step-by-step explanation:
helloo pls help me!!
Answer:
l = 2.55 meters
Step-by-step explanation:
Tunnels are usually in cylinder shape
Surface Area of Cylinder:
l = s/(2πr)
l = 48/(2π(3)) ==> plug in known values
l = 48/(6π)
l = 8/π
l = 2.546 meters
l = 2.546 meters
l = 2.55 meters
Jordan and Raj each bake 7 batches of muffins. Jordan makes 18 muffins per batch, and Raj makes 15 muffins per batch. They combine their muffins and put all of them into boxes. They fill as many boxes as possible with 6 muffins each. They place the remaining muffins in the last box. How many full boxes do they make, and how many muffins will be in the last box?
Answer:
38 full batch with a remainder of 3
Step-by-step explanation:
18*7 + 15*7 = 231
231/6 = 38 r3
Write the following as an algebraic expression. Then
simplify.
The perimeter of a triangle whose sides are of
lengths 6x, 6x + 6, and x.
Answer:
[tex]6x + 6x + 6 + x = 13x + 6[/tex]
Explain three of seven phases of the impulse purchase cycle
Three of the seven phases of the impulse purchase cycle. The other phases include antecedent, search, and selection.
The impulse purchase cycle is a model that describes the process of making an impulsive purchase. It is typically divided into seven phases:
Antecedent: This phase is characterized by a need or desire for something. It can be triggered by a variety of factors, such as boredom, hunger, or a sudden craving for a particular product.
Search: In this phase, the consumer begins to actively search for a product that will satisfy their need or desire. They may search online or in physical stores, and they may consider various options before deciding on a product.
Selection: In this phase, the consumer narrows down their options and selects a specific product that they want to purchase. They may consider factors such as price, quality, and convenience when making their decision.
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evaluate the integral. (use c for the constant of integration.) x2 15 + 6x − 9x2 3/2 dx
On integrating the function f(x), we get - (x³/45) + (3x²) - (2x³) + C.
What is integration?An integral is a function, of which a given function is the derivative. Integration is basically used to find the areas of the two-dimensional region and computing volumes of three-dimensional objects. Mathematically, we can write -[tex]$\int_a^b \! f(x) \, \mathrm{d}x.[/tex]
Given is the function, as follows -
f(x) = (x²/15 + 6x - 9x²/{3/2})
The given function is -
f(x) = (x²/15 + 6x - 9x²/{3/2})
∫f(x) = ∫(x²/15 + 6x - 9x²/{3/2}) dx
∫f(x) = ∫(x²/15)dx + ∫(6x)dx - ∫(6x²)dx
∫f(x) = (1/15)(x³/3) + C₁ + (6)(x²/2) + C₂ - (6)(x³/3) + C₃
∫f(x) = (x³/45) + (3x²) - (2x³) + {C₁ + C₂ + C₃}
∫f(x) = x³/45) + (3x²) - (2x³) + C (C = C₁ + C₂ + C₃)
Therefore, on integrating the function f(x), we get (x³/45) + (3x²) - (2x³) + C.
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pls help i’ll give brainlist to right answer
Answer:
i believe its 5+n ≤ -7
Step-by-step explanation:
the sum of 5 and a number(n) would be 5+n, and no more woukd be the ≤ sign, which would lead to -7
Use the image below to answer the identify the following: One pair of vertical angles: One pair of adjacent angles: One pair of supplementary angles:
A pair of vertical angles is; Angle 1 and Angle 4
A pair of supplementary angles are; Angle 2 and angle 1
How to identify angle properties?Vertical Angles are defined as the angles that are opposite each other when two lines cross each other.
Two angles are defined as adjacent angles when they share the common vertex and side.
Two angles are defined as supplementary angles if they sum up to 180 degrees.
By those definitions above, we can say that;
Angle 1 & 2 as well as angle 3 & 4 are pairs of supplementary angles.
We can also say that;
Angle 4 and 1 are vertical angles while angle 2 and 3 are vertical angles as well.
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Find the area and the circumference of a circle with radius 7 m.
Use the value 3.14 for 7, and do not round your answers. Be sure to include the correct units in your answers.
Answer:
Area :153.86 m
Circumference: 43.96 m
Step-by-step explanation:
Area: 3.14 x r^2
or, A= 3.14 x 7^2
Therefore, A= 153.86m
Circumference: 2 x 3.14 x r
or, C= 2 x 3.14 x 7
Therefore, C= 43.96 m
Hope this helps:)
(btw I put so much time and effort in this answer as it is hard to type mathematical problems in mobile, so I hope I can get marked as brainliest, I have written all the answer that needs to be written in an exam. Anyone can copy it and their work is done.)
Given that the measurement is in inches find the circumference of the circle to the nearest tenth use 3.14 for
The circumference of the circle is 25.12 inches
How to determine the circumference?From the question, we have the following parameters that can be used in our computation:
Radius = 4 inches
The circumference of a circle can be calculated using
C = 2πr
Substitute the known values in the above equation, so, we have the following representation
C = 2 * 3.14 * 4
Evaluate
C = 25.12
Hence, the circumference is 25.12 inches
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Ticket to a baketball game can be ordered online for a et price per ticket plu a $5. 50 ervice fee. The total cot in dollar for ordering 5 ticket i $108. 0. Which linear function repreent c, the total cot, when x ticket are ordered? (A ervice fee i a ingle fee applied to the total, no matter the number of ticket purchaed). C(x) = 5. 50 20. 50x
c(x) = 5. 50x 20. 50
c(x) = 5. 50 21. 60x
c(x) = 5. 50x 21. 60
The function is: c(x) = 5.50 + 21.60x. This means that for each ticket purchased, an additional $21.60 will be added to the service fee of $5.50.
The total cost for ordering 5 tickets is $108.00. This means that each ticket costs $20.50 plus a service fee of $5.50.
Therefore, we can create a linear function that represents the total cost when x tickets are ordered. The function is: c(x) = 5.50 + 21.60x. This means that for each ticket purchased, an additional $21.60 will be added to the service fee of $5.50.
When x = 5, then c(x) = 5.50 + 21.60x = 5.50 + 21.60(5) = 108.00, which matches the given total cost.
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PLSSS HELPP ASAPPP
On the diagram below, a boat, represented by point A, is 450 feet away from a buoy, represented by point B. Another buoy is located at point C. The three points form a right triangle with the measure of <
A equal to 21.3°
The distance between two buoys by the trigonometric function will be 175.48 feet.
What is a trigonometric function?The fundamental 6 functions of trigonometry have a range of numbers as their result and a domain input value that is the angle of a right triangle.
The trigonometric function is very good and useful in real-life problems related to the right-angle triangle.
As per the given situation is making a right angle triangle.
By tan trigonometric function,
tan21.3° = BC/450
BC = 175.48 feet
Hence "According to the trigonometric function, there will be 175.48 feet between two buoys.".
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3x + 5 < 2x - 8 is:
all values more than -13.
all values less than -13. all values less than 3. all values less than -3.
Answer:
all values less than -13
Step-by-step explanation:
3x + 5 < 2x - 8
3x + 5 - 5 = 2x - 8 - 5 ==> isolate x by subtracting 5 on both sides
3x < 2x - 13 ==> simplify
3x - 2x < 2x - 2x - 13 ==> subtract 2x from both sides to move x to the left
side of the inequality
x < -13 ==> simplify
Hence, the answer is all values less than -13.
Hassan buys an apartment for $78 000.
After one year the value decreases by 5%.
Work out the new value of Hassan’s apartment.
Answer:
3900 is decreased.$74100 is new value
Step-by-step explanation:
5% of 78000 subtracted by 78000...
The Valdez family left at noon for a 4-hour trip to viit relative. They topped 1 hour for lunch and 2 hour to viit an amuement park. What time did they get to their relative' houe?
The Valdez family left at noon for a 4-hour trip to visit relative. They topped 1 hour time for lunch and 2 hour to visit an amusement park.The Valdez family would have arrived at their relative's house at 5 pm.
1. The Valdez family left at noon, so they had 12 hours to get to their relative's house.
2. They stopped for 1 hour for lunch, so they had 11 hours left.
3. They then stopped for 2 hours at the amusement park, so they had 9 hours left.
4. 9 hours later would be 9 pm.
5. However, since it is summer, the clocks are set to daylight savings time and it is currently one hour ahead, so the time is actually 5 pm.
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what kind of sampling technique is this? a) random sampling. b) stratified random sampling. c) cluster random sampling. d) systemic random sampling. e) a combination of random, stratified and cluster sampling.
The resulting sampling technique is Stratified sampling.
As in the concept of statistical study, sampling methods refer to how we select members from the population to be in the study and if a sample isn't randomly selected, it will probably be biased in some way and the data may not be representative of the population.
Here we need to find the type of sampling method.
Here the Stratified random sampling involves classifying the units of the population into different strata.
And the give units in each stratum should possess similar characteristics which then allows the researcher to pick a sample from each.
Then the stratified sampling approach can be divided into proportionate stratified sampling and disproportionate stratified sampling
Therefore, these method is employed in cases where the population is heterogeneous.
So, option (b) is correct.
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4
The volume of a spherical balloon (V=4/3pir^3) is increasing at a constant rate of 0.78 inches per minute. At the instant when the radius is 3.20 inches, the radius is
increasing at a rate of…
The rate at which the radius is increasing is; 0.006 in/min
How to find the rate of increase of radius?We are given that the formula for the volume of a spherical balloon is;
V = ⁴/₃πr³
where r is the radius
The volume is increasing at the constant rate of 0.78 inches per minute. Thus;
dV/dt = 0.78
Now, differentiating with respect to t gives;
dV/dt = ⁴/₃(3πr²)(dr/dt)
At radius of 3.2 inches, we have;
0.78 = 4π * 3.2² * dr/dt
dr/dt = 0.78/(4π * 3.2²)
dr/dt = 0.006 in/min
This is therefore the rate at which the radius is increasing.
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when the angle of an incline with a block resting on it increases the normal support force? A) decreases B) increases C) stays the same
Answer:
normal force decreases
Step-by-step explanation:
N=mgcosθ, and cosine decreases as theta increases
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Answer:
A) decreases
Step-by-step explanation:
As the angle of the incline increases, the normal force decreases, which decreases the frictional force. The incline can be raised until the object just begins to slide.
Kayla works at a trampoline gym that hosts birthday parties. Parties are priced at $75 plus $12.50 per guest. Kayla rang up a customer who paid $200 for a party. How many guests were at the party?
Write and solve an equation to find the answer
Answer:
10 Guests
Step-by-step explanation:
200 - 75 = 125 (We need to find a number that will spend 125 dollars)
125 / 12.50 = 10
12.50 x 10 = 125
So the answer is 10
A line passes through the point (9,
- 4) and has a slope of 3/4
Write an equation in slope-intercept form for this line.
The scale below is balancedwhch meas they are equal
The addentical ball and small box weigh the same amount as the big box
How much does each ball weigh?
Answer:
x weigh of ball
2x+40=160
2x=120
x=60g
The solution is 60 grams
The size of each of the balls is given by the equation x = 60 grams
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the size of the balls be represented as = x
The number of balls = 2
So , the total size of the balls = 2x
Now , the equation will be
The weight of all the elements = 160 grams equation (1)
The weight is balanced by = 40 grams + 2x equation (2)
Now , equation (1) = equation (2)
Substituting the values in the equation , we get
160 = 2x + 40
On simplifying the equation , we get
Subtracting 40 on both sides of the equation , we get
2x = 120
Divide by 2 on both sides of the equation , we get
x = 60 grams
Therefore , the value of x is 60 grams
Hence , the size of the ball is 60 grams
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Select the correct systems of equations. Identify the systems of equations that have a as their point of intersection.
We can identify a correct system of equations after draw the graph of the system. The point of intersection indicates the correct solution of the system.
What is the system of equation?Two or more equations which have the same variables, and we can use these all together. The equations are called a set of equations. We get the solution from the system while plotting in the XY coordinate system.
Such as we have two or more linear equations, and we solve each equation and draw a graph for each. We will notice a point of intersection of the straight lines and that refers the solution of the system of equation.
How can we identify a system of equation that have a point of intersection in the graph?There are many sets or system of equation. Some systems have infinity many solutions and graph of the equations never intersect each other. In the next, there are system of equations such as a set of linear function from where we get a point of intersection after plotting the graphs together. The line of intersection is the correct solution of the system.
On the other hand, there are some sets which have no solution, and they are called inconsistent.
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Write a system of equations and then solve by the method of your choice: substitution or elimination
There are 30 questions for 2 points and 10 questions for 4 point.
What is elimination method?
The elimination approach involves taking one variable out of the system of linear equations by utilizing addition or subtraction together with multiplication or division of the variable coefficients.
Given that, the total number of equations is 40. Total point on the paper is 100 points.
There are two types questions, one type question contains 2 points and other type question contains 4 points.
Assume that, there are x questions for 2 points and y questions for 4 points.
The total number of questions is x + y.
The total point is 2x + 4y.
Therefore,
x + y = 40 ......(i)
2x + 4y = 100 .....(ii)
Multiply 2 with equation (i)
2x + 2y = 80
2x + 4y = 100
___________
-2y = -20
Divide both sides by -2:
y = 10
Putting y = 10 in equation (i)
x + 10 = 40
x = 30
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