The expected amount of money in the bag if 90 coins are in the bag is [tex]\(\$5.78\)[/tex].
We need to determine the total value of the coins in the bag based on the given handful and then extrapolate that to the total number of coins in the bag.
First, let's calculate the value of the coins in the handful:
The value of five nickels is [tex]\(5 \times 5\)[/tex] cents = 25 cents.
The value of three quarters is [tex]\(3 \times 25\)[/tex] cents = 75 cents.
The value of nine pennies is [tex]\(9 \times 1\)[/tex] cent = 9 cents.
Adding these values together gives us the total value of the handful:
[tex]\[25 + 75 + 9 = 109 \text{ cents}\][/tex]
Next, we need to find out the ratio of each type of coin in the handful. We have a total of [tex]\(5 + 3 + 9 = 17\)[/tex] coins in the handful.
The ratios for each type of coin are as follows:
Nickels: [tex]\(\frac{5}{17}\)[/tex]
Quarters: [tex]\(\frac{3}{17}\)[/tex]
Pennies: [tex]\(\frac{9}{17}\)[/tex]
Now, let's calculate the expected number of each type of coin in the bag, given that there are 90 coins in total:
Expected nickels: [tex]\(90 \times \frac{5}{17}\)[/tex]
Expected quarters: [tex]\(90 \times \frac{3}{17}\)[/tex]
Expected pennies: [tex]\(90 \times \frac{9}{17}\)[/tex]
Using these ratios, we can calculate the expected number of each coin type:
Expected nickels: [tex]\(90 \times \frac{5}{17} \approx 26.47\)[/tex], but since we can't have a fraction of a coin, we'll consider 26 nickels.
Expected quarters: [tex]\(90 \times \frac{3}{17} \approx 15.88\)[/tex], rounding to 16 quarters.
Expected pennies: [tex]\(90 \times \frac{9}{17} \approx 47.65\)[/tex], rounding to 48 pennies.
Finally calculate the total expected value in the bag by multiplying the number of each type of coin by its value:
Value of expected nickels: [tex]\(26 \times 5\)[/tex] cents = 130 cents
Value of expected quarters: [tex]\(16 \times 25\)[/tex] cents = 400 cents
Value of expected pennies: [tex]\(48 \times 1\)[/tex] cent = 48 cents
Adding these values together gives us the total expected value in the bag:
[tex]\[130 + 400 + 48 = 578 \text{ cents}\][/tex]
To convert the total value from cents to dollars, we divide by 100:
[tex]\[578 \text{ cents} \div 100 = \$5.78\][/tex]
From a group of 7 candidates, a committee of 6 people is selected. In how many different ways can the committee be selected?
C(n,r)=C(7,6)
=7!(6!(7−6)!)Final answer:
There are 7 different ways to select a committee of 6 people from a group of 7 candidates, calculated using the combinations formula C(7, 6) = 7! / (6! * (7 - 6)!) = 7.
Explanation:
The question is asking to determine the number of different ways a committee can be selected from a group of candidates, which is a common problem in combinatorics, a branch of mathematics. To find the number of different ways a committee of 6 people can be selected from a group of 7 candidates, you can use combinations. Since the order in which the committee is chosen does not matter, you calculate combinations and not permutations. The formula for combinations is:
C(n, k) = n! / (k! * (n - k)!)
Applying the formula:
C(7, 6) = 7! / (6! * (7 - 6)!) = 7 / 1 = 7
Therefore, there are 7 different ways to select a committee of 6 people from a group of 7 candidates.
A ball is thrown vertically upward from the top of a 100-foot tower, with an initial velocity of 20 ft/sec. Its position function is s(t) = –16t2 + 20t + 100. What is its velocity in ft/sec when t = 1 second? (This is Calculus, involving limits, please help and explain, because I mostly just need to know how to do this. :) )
Final answer:
The velocity of the ball at t = 1 second is found by taking the derivative of the position function s(t) and evaluating it at t = 1. The derived velocity function is v(t) = -32t + 20, and the velocity at t = 1 second is 8 ft/sec.
Explanation:
The student wants to find the velocity of a ball at t = 1 second when thrown vertically upward from the top of a 100-foot tower with an initial velocity of 20 ft/sec. The position function given is [tex]s(t) = -16t^2 + 20t + 100[/tex]. To find velocity, we need to take the derivative of the position function with respect to time, which represents the velocity function v(t).
The derivative of the position function is:
v(t) = −32t + 20.
To find the velocity at t = 1 second, substitute 1 for t:
v(1) = −32×1 + 20 = −12 + 20 = 8 ft/sec.
Therefore, the velocity of the ball at t = 1 second is 8 ft/sec.
The given measurements may or may not determine a triangle. If not, then state that no triangle is formed. If a triangle is formed, then use the Law of Sines to solve the triangle, if it is possible, or state that the Law of Sines cannot be used.
B = 137°, c = 9, b = 14
An image point after a 180° rotation is Z'(3, 7). What were the coordinates of the pre-image point?
Z(-3, -7)
Z(7, 3)
Z(-7, -3)
Z(7, -3)
Hector drove 185 miles to a business meeting. His business partner drove 5/4 of this distance to get to the same
meeting. How many miles did the business partner drive?
If 3 3/4 pounds of candy cost $20.25 how much would 1 pound of candy cost
Find the area of the circle with the given radius or diameter. Use = 3.14.
r = 4
A =
50.24 sq. units
100.48 sq. units
25.12 sq. units
Answer:
50.24 square units
Step-by-step explanation:
Hope this helps.
Zoe is making a quilt using 15 red squares and 30 green squares. Which combination shows the same ratio of red squares to green squares
Please help, an explanation would be really helpful too
Two classes have a total of 50 students. One of the classes has 6 more students than the other. How many students are in the larger class.
To find the number of students in the larger class, set up a system of equations using the given information. Solve the system to find the value of x, which represents the number of students in the larger class. The larger class has 28 students.
To find the number of students in the larger class, we can set up a system of equations. Let's call the number of students in the larger class x, and the number of students in the smaller class y. The problem states that one class has 6 more students than the other, so we can write the equation x = y + 6.
We also know that the two classes have a total of 50 students, so x + y = 50. We can solve this system of equations to find the value of x, which represents the number of students in the larger class.
Using the second equation, we can substitute the value of x from the first equation into the second equation: (y + 6) + y = 50. Simplifying this equation, we get 2y + 6 = 50. Next, subtract 6 from both sides to isolate the variable: 2y = 44. Finally, divide both sides by 2 to solve for y: y = 22. Now, we can substitute this value of y back into the first equation to find x: x = 22 + 6 = 28. Therefore, there are 28 students in the larger class.
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Two rockets, A and B, are shot from two different launch pads. The path of rocket A can be represented by the quadratic function A(t) = −(t − 8)2 + 535, where height, A(t), is in meters, and time, t, is in seconds. The path of rocket B is shown below.
This question deals with the physics of projectile motion and rocket trajectories. By analyzing the given equations for acceleration and position over time, we can determine the units of constants and describe the motion of the rockets, emphasizing their parabolic paths.
Explanation:The question at hand involves understanding the motion of two rockets using principles of physics and applying mathematical functions to describe their trajectories. For rocket A, the given quadratic function A(t) = −(t − 8)2 + 535, describes its height as a function of time, indicating a parabolic trajectory, which is typical for projectiles under gravity's influence.
In rocket motion, the acceleration can sometimes be described by an equation of the form a(t) = A - Bt1/2. Here, A and B are constants that determine the rocket's changing acceleration over time. The units of A would be meters per second squared (m/s2), since it represents acceleration, and the units of B would have to be meters per second to the power of five halves (m/s5/2) to ensure the units of time (t) cancel out correctly. When a rocket starts from rest, its velocity changes over time, initially increasing but then possibly decreasing if the acceleration is negative due to the subtraction of the term involving Bt1/2.
If the initial position is set to zero, the rocket's position as a function of time can be found by integrating the velocity function, which is the integral of the acceleration function with respect to time. This integration process accounts for the initial conditions and gives a complete description of the rocket's motion.
In the context of projectile motion, the trajectory is indeed parabolic, represented by the equation y = ax + bx2. To prove this, we use the kinematic equations that separately describe the horizontal and vertical motions (x = Voxt for horizontal and y = Voyt - (1/2)gt2 for vertical motion) and eliminate the time variable to find y as a function of x.
What is the standard form of the number shown in this calculator display? The calculator shows three point eight two e positive seven. HURRY ANSWER IMMA FAIL!!! IMMA GIVE 30 POINTS BRUH PLZ AND IF YOU JUST ANSWER IMMA REPORT YOU!!
Answer:38200000 Is the correct answer
Step-by-step explanation:
For how many positive integer values of x is the sum x^2+4x+4 less than 20?
Answer:
2 times
Step-by-step explanation:
Note that since we can only use positive integers for , the minimum will be x = 1. Testing x = 2, we get . Since , we know that only will work, thus, there are positive integer values of such that this function is less than 20.
Find the height of a triangle whose base is 2 square root 2 inches and area is 8 square root 6 square inches.
When 100 is added to a number, the result is 60 more than 5 times the number
What is the mean of 82 64 73 91 85
A student earned 23 out of 30 points on a quiz. What percent of the points did the student earn?
Name two fractions that are less than 0.7 ? Plz help
given that the two triangles are similar, solve x if AU=20x+108, UB= 273, BC= 703, UV= 444, AV= 372 and AC=589.
Solve y over negative 6 + 5 = 9. 24 −24 78 −78
[tex] \dfrac{y}{-6}+5=9\ \ \ \ |-5\\\\\dfrac{y}{-6}=4\ \ \ \ |\cdot(-6)\\\\y=-24 [/tex]
Mike deposited $6500 into two saving accounts bearing simple interest. One of the accounts has an interest rate of 3% while the other rate is 6%. If the total interest earned after one year is $225, find the amount deposited into each of the accounts.
Which is not used to reach a conclusion in a formal proof?
In mathematics especially in verifying certain statements regarding geometry, two column proofs are used. A two-column proof contains a table with a logical series of statements and reasons that reach a conclusion. It is commonly present in geometry. Two column proofs always have two columns: statements and reasons. The other choices don’t fit in the definition of two column proof.
In science, the four ways to incorporate proof into the research paper are:
1. If the research you are investigating has been with other research paper before.
2. There is an experimental proof that the evidence is true.
3. The research published belongs to a reliable source.
4. There are citations of the evidence that you are investigating
1.2, 3, 7.5, 18.75, ...
Which formula can be used to describe the sequence?
f(x) = 1.2(2.5)x – 1
f(x) = 2.5(1.2)x – 1
f(x) = 1.2(2.5)x
f(x) = 2.5(1.2)x
It's geometric sequence:
[tex]a_1=1.2,\ a_2=3,\ a_3=7.5,\ a_4=18.75,\ ....[/tex]
Calculate the common ratio:
[tex]r=\dfrac{a_{n+1}}{a_n}\to r=\dfrac{3}{1.2}=2.5[/tex]
The explicit formula of geometric sequence:
[tex]a_n=a_1r^{n-1}\to f(x)=a_1r^{x-1}[/tex]
Substitute:
[tex]a_1=1.2,\ r=2.5\\\\f(x)=1.2\left(2.5)^{x-1}[/tex]
Answer: "f(x) = 1.2(2.5)x-1"
Answer:
AStep-by-step explanation:
100% righttt
The oven tray is 600mm by 500mm. A cake tin is 25cm in diameter. How many cake tins can jenny fit on the oven tray at one time?
Three cube-shaped boxes are stacked one above the other. The volumes of two of the boxes are 1,331 cubic meters each, and the volume of the third box is 729 cubic meters. What is the height of the stacked boxes in meters?
Answer: The height of the stacked boxes is 31 meters.
Step-by-step explanation:
Since, the Volume of a cube = (side)³
The volume of first box = 1331 cubic meters,
⇒ (side)³ = 1331
⇒
Similarly, the side of second box = 11 meters ( Because, both boxes have the same volume )
Now, the volume of third box = 729 cubic meters
⇒ ⇒ (side)³ = 729
⇒
Thus, the height of the stacked boxes = Side of first box + side of second box + side of third box
= 11 + 11 + 9
= 31 meters.
At the fall festival the tennis team is selling hamburgers for $2.00, hotdogs for $1.50, and drinks for $1.00. Half of the money raised will go towards the purchase of team uniforms. If they sell 21 hamburgers, 34 hotdogs, and 65 drinks, how much money will they have to put towards the purchase of uniforms?
write a description of the rule (x,y) (x-2,y-7)
The mathematical rule (x,y) to (x-2, y-7) signifies a transformation in the coordinate plane shifting points 2 units to the left and 7 units down. To apply this rule to any point, subtract 2 from the x-coordinate and 7 from the y-coordinate.
Explanation:The rule (x,y) to (x-2,y-7) in Mathematics signifies a specific transformation in a coordinate plane. This is essentially a rule used in graph transformations to shift a point in the coordinate plane. In this specific rule, every point (x, y) is shifted 2 units to the left and 7 units down to get the new point (x-2, y-7). For example, if we take a point, (5,10), applying this rule means we subtract 2 from the x-coordinate and 7 from the y-coordinate resulting in a new point (3,3). Therefore, simplifying this process, to apply the rule (x,y) to (x-2,y-7) to any point, all you need to do is subtract 2 from the x-coordinate and 7 from the y-coordinate of the point.
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what are all the exact solutions of 2sec^2x-tan^4x=-1 ?
Answer:
A
Step-by-step explanation:
on Edge
To find the exact solutions of the given equation 2sec^2x-tan^4x=-1, we can simplify the equation using trigonometric identities and solve for tanx. The solutions are x = pi/3 + n*pi for tanx = sqrt(3), and x = -pi/4 + n*pi for tanx = -1.
Explanation:The given equation is 2sec^2x-tan^4x=-1. To solve this equation, we need to simplify the trigonometric terms using known identities. The identity sec^2x = 1 + tan^2x can be used here. Substituting this identity into the equation gives us 2(1 + tan^2x) - tan^4x = -1. Simplifying further, we have 2 + 2tan^2x - tan^4x = -1. Rearranging the terms, we get tan^4x - 2tan^2x - 3 = 0.
Now, let's substitute tan^2x with u, giving us the equation u^2 - 2u - 3 = 0. This is a quadratic equation that can be factored as (u - 3)(u + 1) = 0. Solving for u, we have u = 3 or u = -1. Substituting back tan^2x for u, we get tan^2x = 3 or tan^2x = -1. Taking the square root of both sides, we have tanx = sqrt(3) or tanx = -1.
Finally, to find the exact solutions of x, we need to consider the periodic nature of trigonometric functions. Since tanx repeats every pi radians, the solutions are x = pi/3 + n*pi, where n is an integer, for tanx = sqrt(3), and x = -pi/4 + n*pi, for tanx = -1.
Janise Smithson invested $4,000 for one year in a CD that earns interest at a rate of 4% compounded monthly. What is the interest earned during the year?
Answer:
$162.97 is the exact answer.
Step-by-step explanation:
what must be subtracted from 4x4 - 2x3 - 6x2 + x - 5 so that the answer is exactly divisible by x + x - 2
To solve this problem, what we have to do is to divide the whole equation 4 x^4 – 2 x^3 – 6 x^2 + x – 5 with the equation 2 x^2 + x – 1. Whatever remainder we get must be the value that we have to subtract from the main equation 4 x^4 – 2 x^3 – 6 x^2 + x – 5 for it to be exactly divisible by 2 x^2 + x – 1.
By using any method, I used long division we get a remainder of -6.
Therefore we have to subtract -6 from the main equation which results in:
4 x^4 – 2 x^3 – 6 x^2 + x – 5 – (-6) = 4 x^4 – 2 x^3 – 6 x^2 + x + 1