the probability that a randomly selected student attends full-time and does not receive financial aid is ( 0.1376 ), or ( 13.76% ).
To find the probability that a student attends full-time and does not receive financial aid, we can use the multiplication rule for independent events.
Given:
- Probability of attending full-time: [tex]\( P(\text{full-time}) = 0.320 \)[/tex]
- Probability of not receiving financial aid:[tex]\( P(\text{no financial aid}) = 0.430 \)[/tex]
By the multiplication rule, the probability of both events occurring is the product of their individual probabilities:
[tex]\[ P(\text{full-time and no financial aid}) = P(\text{full-time}) \times P(\text{no financial aid}) \][/tex]
[tex]\[ = 0.320 \times 0.430 \][/tex]
[tex]\[ = 0.1376 \][/tex]
Therefore, the probability that a randomly selected student attends full-time and does not receive financial aid is ( 0.1376 ), or ( 13.76% ).
In the game of blackjack played with one deck, a player is initially dealt 2 different cards from the 52 different cards in the deck. a winning "blackjack" hand is won by getting 1 of the 4 aces and 1 of 16 other cards worth 10 points. the two cards can be in any order. find the probability of being dealt a blackjack hand. what approximate percentage of hands are winning blackjack hands?
We are given here that a blackjack hand consists of:
1 of the 4 aces = 4 / 52
1 of the 16 cards worth 10 points (10, jack, queen, king) = 16 / 52
So assuming that cards are dealt without replacement, therefore the probability of getting a blackjack hand is:
P = 1st is ace * 2nd is 10 pt card + 1st is 10 pt card * 2nd is ace
P = (4 / 52) * (16 / 51) + (16 / 52) * (4 / 51)
P = 0.04827 = 4.83%
Therefore there is a 4.83% probability to get a blackjack hand.
Final answer:
The probability of being dealt a blackjack hand with a single deck is approximately 0.0483, which translates to about 4.83% of the hands.
Explanation:
To find the probability of being dealt a blackjack hand in a single-deck game, we need to calculate the chances of drawing an ace and a 10-point card (10, Jack, Queen, or King) in any order. There are 4 aces and 16 cards worth 10 points in a deck of 52 cards. The probability of drawing an ace first is 4/52, and then drawing a 10-point card is 16/51, giving us (4/52)*(16/51). Conversely, if a 10-point card is drawn first (16/52) followed by an ace (4/51), the probability is (16/52)*(4/51). Adding the two probabilities gives us the chance of a blackjack in either order:
P(Blackjack) = (4/52)*(16/51) + (16/52)*(4/51) = (64/2652) + (64/2652) = 128/2652 ≈ 0.0483
The approximate percentage of hands that are winning blackjack hands is about 4.83%.
A heap of rubbish in the shape of a cube is being compacted into a smaller cube. given that the volume decreases at a rate of 4 cubic meters per minute, find the rate of change of an edge, in meters per minute, of the cube when the volume is exactly 125 cubic meters.
Using implicit differentiation, it is found that the rate of change of an edge is of -0.0533 meters per minute.
---------------------
The volume of a cube of edge e is given by:
[tex]V = e^3[/tex]
In this problem, the volume is of 125 m³, thus, we solve the above equation to find the length of an edge, in metres.
[tex]V = e^3[/tex]
[tex]125 = e^3[/tex]
[tex]e = \sqrt[3]{125}[/tex]
[tex]e = 5[/tex]
Now, for the rate of change, we need to apply the implicit differentiation, thus:
[tex]V = e^3[/tex]
[tex]\frac{dV}{dt} = 3e^2\frac{de}{dt}[/tex]
[tex]\frac{dV}{dt} = 3(5)^2\frac{de}{dt}[/tex]
[tex]\frac{dV}{dt} = 75\frac{de}{dt}[/tex]
Volume decreases at a rate of 4 cubic meters per minute, thus:
[tex]\frac{dV}{dt} = -4[/tex]
The rate of change of an edge is [tex]\frac{de}{dt}[/tex]. Then:
[tex]-4 = 75\frac{de}{dt}[/tex]
[tex]\frac{de}{dt} = -\frac{4}{75}[/tex]
[tex]\frac{de}{dt} = -0.0533[/tex]
The rate of change is of -0.0533 cubic meters per minute.
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Every week, Mr. Kirkson uses 316 gallon of water to water every 13 square foot of his garden. How many gallons of water does Mr. Kirkson use per square foot to water his garden each week? Enter your answer in the box as a fraction in simplest form.
Is It A Fraction If So Then The Answer Is [tex]\frac{9}{16}[/tex]
If Not Then The Other Guy Is Right
HoPe It HeLpS PlEaSe MaRk Me ThE BRAINlYEST!!!!!!!!!!!!
The rectangular sandbox at the local community park has a width of 24.5 meters and its length is 31.7 meters. What is the perimeter, in meters, of the rectangular sandbox?
To calculate the perimeter of the rectangular sandbox, use the formula P = 2l + 2w, where l is the length and w is the width. For the given dimensions, 31.7 meters in length and 24.5 meters in width, the perimeter is 112.4 meters.
Explanation:The question asks us to calculate the perimeter of a rectangular sandbox. The formula to calculate the perimeter of a rectangle is 2 times the length plus 2 times the width, often written as P = 2l + 2w.
Given the dimensions of the sandbox, the length (l) is 31.7 meters, and the width (w) is 24.5 meters.
We calculate the perimeter as follows:
Perimeter = 2 × Length + 2 × WidthPerimeter = 2 × 31.7 m + 2 × 24.5 mPerimeter = 63.4 m + 49.0 mPerimeter = 112.4 metersTherefore, the perimeter of the rectangular sandbox is 112.4 meters.
Doors for a small cabinets are 11.5 inches long. Doors for the large cabinets are 2.3 times as long as the doors for the small cabinets. How many large doors can be cut from a board that is 10.5 feet long?
A manufacturing company has developed a cost model, C(X)= 0.15x^3 + 0.01x^2 +2x +120, where X is the number of item sold thousand. The sales price can be modeled by S(x) + 30- 0.01x. Therefore revenues are modeled by R(x)= x*S(x).
The company's profit, P(x) = R(x)-C(x) could be modeled by
1. 0.15x^3+ 0.02x^2- 28x+120
2. -0.15x^3-0.02x^2+28x-120
3. -0.15x^3+0.01x^2-2.01x-120
4. -0.15x^3+32x+120
Suppose Georgette buys 400 shares of Google at $250 a share. She sells them at $350 a share. What is her capital gain?
a. 400 times $100
b. 400 times $250
c. 400 times $350
d. 400 times $600
Answer: A
Step-by-step explanation:
Simplify. 1/4 (-12+4/3)
The simplification of 1/4 (-12+4/3) first involves simplifying the operation in the parentheses which gives -10.67. Multiplying this by 1/4 we get -2.67.
Explanation:To simplify the expression 1/4 (-12+4/3), first simplify the operation in the parentheses.
-12 + 4/3 equals -12 + 1.33 (approx.), which simplifies to -10.67.
Then, multiply this result by 1/4. So, 1/4 of -10.67 equals -2.67 (approx.).
So, 1/4 (-12+4/3) simplifies to -2.67.
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What is the gcf for 84
What is 2 3/4 - 1/2? A. -2 1/4 B. 1 1/4 C. 2 1/4 D. 3
Round 10,386.145 to the nearest tenth
Isaac drinks 8 glasses of water each day. He says he will drink 2,920 glasses of water in a year that has 365 days. Is the exact answer reasonable
multiply 365 by 8
365 * 8 = 2920
so yes it is reasonable
Jack has 702 acres of land which requires 1.2 acre-feet of water to grow crops successfully. Currently it cost 12.95 per acre-foot to purchase water. How much will it cost to water all his crops
A) 9,090.90
B) 10,909.08
C) 15,540.00
D) none
Julian is 10 years younger the Thomas. The sum of their ages is 74. What is Thomas’s age?
Thomas = x
Julian = x-10
x +x-10 = 74
2x-10 = 74
2x = 84
x = 84/2 = 42
Thomas is 42
Julian is 32
A family has five children. the probability of having a girl is 1/2. what is the probability of having at least 4 girls?
What is the solution of the equation f(x) = g(x) ?
A. x = -4
B. x = -2
C. x = 2
D. x = 4
solve the system of linear equations. separate the x- and y- with a coma.
6x=-14-8y
-12x=20+8y
Answer:
-16 81 19
Step-by-step explanation:
A square with an area of 49 in2 is rotated to form a cylinder. What is the volume of the cylinder
A wheel turns 1,800 revolutions per minute. How fast does it turn in radians per second?
A wheel turn 60π radians per second.
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
A wheel turns 1,800 revolutions per minute.
Now,
Since, A wheel turns 1,800 revolutions per minute.
Hence, Number of revolution in one seconds = 1800 / 60
= 30
We know that;
⇒ 1 revolution = 2π radian
So, Number of revolution in radian per second = 30 × 2π
= 60π
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Karen is riding her bike at 4 miles per hour she wants to show this on a graph what should she draw
20 randomly selected statistics students were given 15 multiple-choice questions and 15 open-ended questions - all on the same material. the professor was interested in determining which type of questions the students scored higher. this experiment is an example of a one sample test of means. a two sample test of means. a paired t-test. a test of proportions.
What is the matter with this number: .000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
Is it real?
The department store where you work is having a sale. Every item is to be marked down 15% What will the sale price of a $152 coat be
multiply 152 by 15%
152 * 0.15 = 22.80 ( amount of discount
152 - 22.80 = 129.20 ( sale price)
Can someone help me with this?
What is the cytoplasm? A. a fluid in which organelles are suspended B. a type of organelle that assembles proteins C. the exterior envelope surrounding the nucleus D. the inner surface of the cell's wall
Which are zeros of the following polynomial?
6x 2 - 11x - 10 = 0
A x = 6, x = 10
B x = ; x =
C x = -2; x = 5
D x = ; x =
Answer:
x = -2/3; x = 5/2.
Step-by-step explanation:
6x 2 - 11x - 10 = 0
Use the 'ac' method:
6 * -10 = -60. We need 2 numbers whose product is -60 and whose sum is -11.
That would be -15 and +4. So we write:
6x^2 - 15x + 4x - 10 = 0 Factor by grouping:
3x(2x - 5) + 2(2x - 5) = 0
(3x + 2)(2x - 5) = 0
x = -2/3; x = 5/2.
A person standing 20 feet from a street light casts a 10 foot shadow. How many times taller is the streetlight than the person? Assume the triangles are similar.
If 5x=3x-8, evaluate 4x+2
tiffany and Adele sold cookies and brownies to raise money for their school. They sold a total of 25 sweets. If each cookie costs 1$ and the brownies cost a 1.50 each and they made a total of 32$, how many did each sell?
By setting up a system of equations based on the total number of sweets sold and the total amount of money made, we find that Tiffany and Adele sold 11 cookies and 14 brownies.
To determine how many cookies and brownies Tiffany and Adele sold, we can set up a system of equations. Let's define the number of cookies sold as x and the number of brownies sold as y.
The first equation comes from the total number of sweets sold: x + y = 25. The second equation is based on the total amount of money made: 1*x + 1.50*y = 32.
Solving this system of equations will give us the number of each type of sweet sold.
To solve the system of equations, we can use substitution or elimination. I'll use substitution:
From the first equation, we can express y as y = 25 - x.Next, we substitute y in the second equation: 1*x + 1.50*(25 - x) = 32.Simplify and solve for x: X + 37.50 - 1.50x = 32, which simplifies further to 0.50x = 5.50. Divide both sides by 0.50 to find x = 11.Now that we have the value for x, substitute it back into the equation for y: y = 25 - 11 = 14.Tiffany and Adele sold 11 cookies and 14 brownies.
A solid lies above the cone z = x2 + y2 and below the sphere x2 + y2 + z2 = z. write a description of the solid in terms of inequalities involving spherical coordinates
The solid lying above the cone z = x^2 + y^2 and below the sphere x^2 + y^2 + z^2 = z, in spherical coordinates, is described by the inequalities 0 ≤ ρ ≤ 2 cos φ (W.r.t the sphere) and φ ≥ π/4 (W.r.t the cone), with 0 ≤ θ ≤ 2π (full revolution for θ).
Explanation:In spherical coordinates, we represent a point in space using three values: ρ (the distance from the origin), φ (the angle measured from the positive z-axis down to the line connecting the origin and the point), and θ (the angle measured in the x-y plane from the positive x-axis to the projection of the line segment from the origin to the point).
The given cone z = x2 + y2 in spherical coordinates becomes ρ cos φ = ρ2 sin2 φ, which simplifies to tan φ = 1/ρ or φ = π/4. This is because for a cone with vertex at the origin, φ is constant. So, our first inequality is φ ≥ π/4.
The sphere's equation x2 + y2 + z2 = z becomes ρ2 = ρ cos φ, which further simplifies to ρ = 2 cos φ. So, the second inequality is ρ ≤ 2 cos φ, which bounds ρ from above by the sphere.
In summary, the solid is described by the inequalities 0 ≤ ρ ≤ 2 cos φ and φ ≥ π/4, with 0 ≤ θ ≤ 2π (since θ revolves full circle in spherical coordinates).
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The solid can be described using the inequalities: 0 ≤ r ≤ cos(θ), 0 ≤ θ ≤ 2π, and 0 ≤ ϕ ≤ π. These inequalities define the limits for the radius, polar angle, and azimuthal angle in spherical coordinates.
Explanation:To describe the solid in terms of inequalities involving spherical coordinates, we need to find the limits for the radius, polar angle, and azimuthal angle.
Considering the given information, the solid lies above the cone z = x2 + y2, which implies that the z-coordinate ranges from 0 to r2.
As for the sphere x2 + y2 + z2 = z, we can rewrite it in spherical coordinates as r2 = r cos(θ) or r = cos(θ).
Therefore, the solid can be described using the following inequalities in spherical coordinates:
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