A. 0.2794; The probability of at least 2 apples being bruised in a bushel of 50 apples is approximately 0.8466
To compute the probability that at least 2 apples are bruised in a bushel of 50 apples, we can use the binomial probability formula. The formula is:
P(X ≥ k) = 1 - P(X < k)
Where P(X ≥ k) is the probability of having at least k successes, P(X < k) is the probability of having less than k successes, and k is the number of bruised apples.
In this case, k = 0 (no bruised apples) and k = 1 (1 bruised apple) are not of interest, so we'll calculate the complement of those probabilities.
Step 1: Calculate the probability of no bruised apples (k = 0):
P(X = 0) = (0.05)^0 * (0.95)^50 = 0.95^50 ≈ 0.0765
Step 2: Calculate the probability of 1 bruised apple (k = 1):
P(X = 1) = (0.05)^1 * (0.95)^49 * (50 choose 1) = 0.05 * 0.95^49 * 50 ≈ 0.0769
Step 3: Calculate the probability of at least 2 bruised apples:
P(X ≥ 2) = 1 - (P(X = 0) + P(X = 1)) = 1 - (0.0765 + 0.0769) = 1 - 0.1534 ≈ 0.8466
Therefore, the probability that at least 2 apples are bruised in a bushel of 50 apples is approximately 0.8466, which corresponds to option A.
The probability of at least 2 apples being bruised in a bushel of 50 apples is approximately 0.8466, which can be calculated using the binomial probability formula.
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What is the y-intercept (b) of the line that passes through (1,1)(2,5) You must solve for slope (m) first.
b=
Answer:
slope (m) is 4, y-intercept (m) is -3
Step-by-step explanation:
y=4x-3
use y¹-y² over x¹-x² to find slope, then use one of the points to fill in for x and y to find y-intercept
State the slope and y-intercept of the line with equation y = 9 + 7x
Answer:
The Y intercept is 9, and The Slope is 7x
Answer:
slope: 7 (or 7/1)
y int: 9
Step-by-step explanation:
Slope intercept formula is y=mx+b
(m) is slope
(b) is y intercept
so in
y=9+7x
we can flip the numbers around
y=7x+9
so 7 is our slope and 9 is the y intercept
Hope this helps! If you have any questions on how I got my answer feel free to ask. Stay safe!
Triangle ABC is dilated. The image is A'B'C'
Find the value of x.
Answer:
x = 2
Step-by-step explanation:
6 : 4 = 3 : x
x = 4 * 3 / 6
x = 4/2
x = 2
The value of x in the given figure is 2
What is dilation?Dilation is a transformation, which is used to resize the object. Dilation is used to make the objects larger or smaller. This transformation produces an image that is the same as the original shape. But there is a difference in the size of the shape.
Given that, Triangle ABC is dilated into A'B'C'
We know that dilated triangles are similar
Hence, their corresponding sides are in equal ratio,
BC : B'C' = AC : A'C'
6 : 4 = 3 : x
x = 4 × 3 / 6
x = 4/2
x = 2
Hence, The value of x in the given figure is 2
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can someone help me please
I will give you brainliest if you answer the question!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
How many ounces of a 4% acid solution and how many ounces of a 10% acid solution must be mixed to make 24oz of a 6% acid solution
a = acid solution 4%
b = acid solution 10%
a + b = 24
0.04*a+0.1*b=0.06*24
a=24-b
0.04*(24-b) + 0.1*b = 1.44
0.96 - 0.04b + 0.1*b = 1.44
0.06*b = 0.48
b = 8 oz
a=24-b
a = 24 - 8
the mathematical answer of 1+1
Answer:
two
Step-by-step explanation:
one and add another one
7x - 5 = 2x - 15
5x + 2 = 4x - 1
3 - X = 4x + 13
16 - 2x = 5x + 9
3X + 5 = 2x + 7
Answer:
5x- 10
20x=5
3= 17x
25-10x
6x=12
Step-by-step explanation:
If Denise were to paint her living room alone, it would take 55 hours. Her sister Rachel could do the job in 77 hours. How many hours would it take them working together
Total time taken by Denise and Rachel to paint the room together us around 32.10 hours.
To determine how many hours it would take Denise and Rachel to paint the living room together:
Denise can complete the job within 55 hours, so her work rate is 1/55 of the job per hour.
Rachel can complete her job in 77 hours, so her work rate is 1/77 of the job per hour.
When they work together to paint, their work rates are also combined. Therefore, the combined work rate of Denise and Rachel is the sum of their individual work rates:
= 1/55 + 1/77
= 0.01818 + 0.01299
= 0.03117
To find the time taken by them for working together, we take the reciprocal of the combined work rate obtained:
1 / 0.03117 = 32.10 hours
Therefore, it would take Denise and Rachel approximately around 32.10 hours to paint the living room together.
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Sven investigates the amount of damage to the head gaskets on the trucks in his fleet and find that the damage index depends on the ambient temperature. He develops the equation y = −23x + 14 to model the relationship. What does 14 mean?
The y-intercept of 14 may serve as a reference point for the amount of damage to the head gaskets when the temperature is relatively low.
What is an equation?
An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides separated by an equals sign (=).
In the equation y = -23x + 14, y represents the amount of damage to the head gaskets on the trucks in Sven's fleet, and x represents the ambient temperature.
The constant term, 14, is the y-intercept of the equation. It represents the value of y when x is equal to zero.
In this context, the y-intercept of 14 means that when the ambient temperature is zero (which is unlikely in most cases), the amount of damage to the head gaskets on the trucks in Sven's fleet is equal to 14. However, this value may not be meaningful in practical terms since it is unlikely that the ambient temperature will ever be exactly zero.
Therefore, in practical terms, the y-intercept of 14 may serve as a reference point for the amount of damage to the head gaskets when the temperature is relatively low.
It is important to note that the value of y will decrease by 23 for every increase of one unit in the ambient temperature (x).
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order the measurements from greatest to least 45 inches, 6 yards, and 2 and1/4 feet
Answer:
2.25 feet, 45 inches, and 6 yards
Step-by-step explanation:
first, convert all to the same unit of measurement
I will use inches
45 inches = 45 inches
6 yards, 1 yard = 3 feet so 6 yards are equal to 18 feet and 1 foot is equal to 12 inches so 12*18 is 216 inches so 6 yards = 216 inches
Next 1 foot equals 12 inches so 2.25 * 12 = 27 so 2.25 feet = 27 inches.
Now let's look at the complete conversion
45 inches
6 yards = 216 inches
2.25 feet = 27 inches
looking at the inches we can see that 27 is the least then 45 then 216 therefore
2.25 feet < 45 inches < 6 yards so the order is
2.25 feet, 45 inches, and 6 yards
Identify the domain, range, and codomain in each graph. Then use the codomain and range to determine whether the
function is onto.
Answer:
Step-by-step explanation:
Domain : Set of all possible input values (x-values) on a graph
Codomain : Set of all possible out values for the input values (y-values) on the graph
Range : Actual output values for the input values (x-values) given on the graph.
Therefore, for the given graph,
Domain : (-∞, ∞)
Codomain : (-∞, 2]
Range : (-∞, 2]
From the given graph every input value there is a image or output value.
Therefore, the given function is onto.
What is the image of (-1,-1) after a dilation by a scale factor of 5 centered at the origin
Answer:
If the plot point was dilated by a scale factor, it would be multiplying the scale factor with each X and Y. Therefore it would be (-5,-5)
The image of (-1, -1) after the dilation by a scale factor of 5 centered at the origin is (-5, -5).
To find the image of (-1, -1) after a dilation by a scale factor of 5 centered at the origin, we can apply the formula for dilation in the coordinate plane.
The formula for dilation with a scale factor of k centered at the origin is (k * x, k * y), where (x, y) is the original point.
In this case, the original point is (-1, -1), and the scale factor is 5. Applying the dilation formula, we have:
Image = (5 * (-1), 5 * (-1))
= (-5, -5)
This means that the point (-1, -1) is dilated by a factor of 5, and its position is shifted five times farther from the origin in both the x and y directions.
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Find x
Please show your work
Answer:
I think it would be
A= 3/5
B= 7/6
please answer my question in the image
The value of this simplification is - 20. 72.
What is simplification?
The act of simplifying something that is simpler to carry out or understand, or the thing that is the product of this simplifying process: The group offers suggestions for streamlining business processes. This grossly oversimplifies what actually transpired.
Here, we have
Given the equation, we solve this through simplification
We get,
= {(1.88 + 2.12) × 0.1875}/{(0.625 - 0.722)÷2.888} + {(1.44 + 0.56)÷0.5}/{(7.7÷24.75 + 0.133)× 4.5}
= 0.75/(-0.033) + 4/1.988
= -22.72 + 2.00
= - 20.72
Hence, the value of this simplification is - 20. 72.
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Where is the midline of this function?
Answer:
the midline is the line:
y = 0.
Step-by-step explanation:
The midline of a function is a horizontal line that divides evenly the graph of the function in two parts.
Particularly, for trigonometric functions, we usually have:
f(x) = A*sin(k*x + p) + M
Where:
A is the amplitude.
x is the variable
k is a constant related to the frequency of the function.
p is a phase shift
M is the midline of the function, which means that the line that divides evenly the graph is y = M.
For our case, we have:
y = f(x) = 3*sin(2*x - π)
Then:
A = 3
k = 2
p = -π
And we do not have a constant term in that equation, this means that:
M = 0
This means that the line that divides evenly the graph is the line y = 0.
prove that the area of triangle is "half of base times height. i.e.(A=1/2×b×h).
please give the explanation and do it ASAP please!
Answer:
Step-by-step explanation:
any triangle is half of a polygon of 4 sides
the area of a rectangle is height * base or length*width
and since the triangle is half a rectangle then Area=1/2 *b*h
Estimate ΔyΔy using differentials.
y=cos(5x),=/30,x=0.055
(Give your answer to three decimal places.)
The estimated change in yy using differentials is -0.00679. This means that if xx is increased by 0.005, then yy is estimated to decrease by 0.00679. The differential of yy is dy=-5sin(5x)dxdy=−5sin(5x)dx. We are given that y=cos(5x)=π/30y=cos(5x)=π/30 and x=0.055x=0.055.
We want to estimate ΔyΔy, which is the change in yy when xx is increased by 0.005. We can use the differential to estimate ΔyΔy as follows:
Δy≈dy≈dy=-5sin(5x)dx
Plugging in the values of y, x, and dxdx, we get:
Δy≈-5sin(5(0.055))(0.005)≈-0.00679
Therefore, the estimated change in yy using differentials is -0.00679.
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2 ( 3x - 1) = -6x -2
Answer:
6x -2 is the solved answer for the bracketed question.
Step-by-step explanation:
6x- 2 is not = to -6x -2
Answer: x=0
Step-by-step explanation:
if you are sloving fo x
2(3x-1) = -6x-2 cancel equal terms
6x-2=-6x-2 move the variable to the left
6x=-6x collect like terms
12x=0 divide both sides
x=0
Aaron has a collection of American coins. He has 3 times as many 10 cent coins as 25 cent coins, and he has some 5 cent coins as well. If he has 8 coins with total value $11.40. how many of each type does he have?
Step-by-step explanation:
SEE THE IMAGE FOR SOLUTION
HOPE IT HELPS
HAVE A GREAT DAY
What is the slope????
Answer:
-6
Step-by-step explanation:
is that quizzes join lol
could you please help solve this math question
Q.5) (10 p.) Solve the differential equation given as d'y dy dy +2- dr² da dr Y
The general solution to the given differential equation is y = -2r + Cy + D, where C and D are constants.
The given differential equation is d²y/dy² + 2d²r/da dr = 0. In order to solve this equation, we will need to find the general solution that satisfies the equation.
To solve the given differential equation d²y/dy² + 2d²r/da dr = 0, we can start by rearranging the terms. Let's separate the variables and rewrite the equation as d²y/dy² = -2d²r/da dr.
Next, we integrate both sides of the equation with respect to the corresponding variables. Integrating d²y/dy² with respect to y gives us y', and integrating -2d²r/da dr with respect to r gives us -2r'.
Now we have the equation y' = -2r' + C, where C is the constant of integration.
To further simplify the equation, we can rearrange it as dy/dy = -2dr/da + C.
Integrating both sides with respect to y, we obtain y = -2r + Cy + D, where D is another constant of integration.
Therefore, the general solution to the given differential equation is y = -2r + Cy + D, where C and D are constants.
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6. Solve each of the following recurrence relations. a. an = : -3an-1 with a₁ = -1 b. an = an-1 + an-2 with ao = 0 and a₁ = 1 = c. an = -6an-1-9an-2 with a -1 and a₁ = -3
a) The recurrence relation an = -3an-1 with a₁ = -1 can be solved as an = (-3)ⁿ⁻¹.
b) The recurrence relation an = an-1 + an-2 with a₀ = 0 and a₁ = 1 can be solved using the Fibonacci sequence formula, an = Fₙ₊₁, where Fₙ is the nth Fibonacci number.
c) The recurrence relation an = -6an-1 - 9an-2 with a₀ = -1 and a₁ = -3 can be solved as an = 3ⁿ - 2ⁿ.
a) For the recurrence relation an = -3an-1 with a₁ = -1, we notice that the ratio between consecutive terms is a constant (-3). This means that each term can be expressed as a power of -3 raised to a certain exponent. In this case, we have an = (-3)ⁿ⁻¹.
b) The recurrence relation an = an-1 + an-2 with a₀ = 0 and a₁ = 1 is a well-known relation that corresponds to the Fibonacci sequence. The Fibonacci sequence is defined by the recurrence relation Fn = Fn-1 + Fn-2 with F₀ = 0 and F₁ = 1. By comparing the given relation with the Fibonacci relation, we can conclude that an = Fₙ₊₁, where Fₙ is the nth Fibonacci number.
c) For the recurrence relation an = -6an-1 - 9an-2 with a₀ = -1 and a₁ = -3, we can rewrite it as a quadratic equation in terms of aₙ. By solving the quadratic equation, we find that the characteristic equation is x² + 6x + 9 = 0, which factors as (x + 3)² = 0. This means that the roots of the characteristic equation are both -3. Consequently, the solution to the recurrence relation is an = A(-3)ⁿ + Bn(-3)ⁿ, where A and B are constants determined by the initial conditions a₀ and a₁. By substituting the given initial conditions, we can solve for the values of A and B, leading to the final solution an = 3ⁿ - 2ⁿ.
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2. Consider the system defined by the impulse response h(n)=28(n+3)+28(n)+28(n-3). a) b) c) d) z Represent h(n). (1 v.) Characterize the system in terms of causality and stability. Justify. (1 v.) Determine the frequency response of the system H(ew). (1 v.) Represent module and phase of the system. (1 v.)
The system defined by the impulse response h(n) = 28(n+3) + 28n + 28(n-3) can be represented as h(n) = 28δ(n+3) + 28δ(n) + 28δ(n-3), where δ(n) denotes the unit impulse function.
In terms of causality, we can determine whether the system is causal by examining the impulse response. If the impulse response h(n) is non-zero only for n ≥ 0, then the system is causal. In this case, since the impulse response h(n) is non-zero for n = -3, 0, and 3, the system is not causal.
To determine the stability of the system, we need to examine the summation of the absolute values of the impulse response. If the summation is finite, the system is stable. In this case, we can calculate the summation as ∑|h(n)| = 28 + 28 + 28 = 84, which is finite. Therefore, the system is stable.
However, since the impulse response is given in the time domain and not in a closed-form expression, it is not possible to directly determine the frequency response without further manipulation or additional information.
Given the absence of specific frequency domain information or a closed-form expression for the frequency response, it is not possible to accurately represent the module and phase of the system H(e^ω) without further calculations or additional details about the system.
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A ski jump is designed to follow the path given by the parametric equations: x = 3.50t² y = 20.0 +0.120t⁴ - 3.00√t⁴+1 (0≤ t ≤ 4.00 s) where distances are in meters Find the resultant velocity and the acceleration of a skier when t = 4.00 sec.
The resultant velocity and acceleration of the skier at t=4.00 sec on the ski jump path are 12.8 m/s and 45.9 m/s², respectively.
To find the resultant velocity, first find the velocity vector components using the parametric equations:
vx = 7.00t, vy = 0.48t³ - 6.00t²/√(t⁴+1)
At t=4.00 s, vx = 28.0 m/s and vy = 10.50 m/s. The resultant velocity is the magnitude of the velocity vector, given by:
|v| = √(vx² + vy²) = 12.8 m/s
To find the acceleration vector components, differentiate the velocity vector components with respect to time:
ax = 7.00 m/s², ay = 1.44t² - 12.00t/√(t⁴+1) - 6.00t³(t⁴+1)^(-3/2)
At t=4.00 s, ax = 7.00 m/s² and ay = 45.9 m/s². The acceleration vector magnitude is:
|a| = √(ax² + ay²) = 46.1 m/s².
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The total cost c(x), in dollars, for renting a car for a day and driving it x miles is shown: c(x) = 75 + 0.55x What does c(20) represent?
*
The number of dollars it costs to drive the car 20 miles.
The number of miles driven for a cost of $20.
The number of miles driven on the car in 20 days.
The number of dollars spent to rent the car for 20 days.
Answer: The number of dollars it costs to drive the car 20 miles.
Step-by-step explanation:
The function c(x) models the cost for renting a car for driving it ‘x’ miles.
c(20) would represent the cost of driving a car 20 miles since c represents cost and x represents the miles driven
At the movie theatre, child admission is $5.20 and adult admission is $9.00. On Friday, twice as many adult tickets as child tickets were sold, for a total sales of $696.00. How many child tickets were sold that day?
Answer:
30
Step-by-step explanation:
Let the number of child tickets sold be \(x\), then the number of adult tickets sold will be \(2x\).
Then the amount made from child tickets will be \(5.2x\), and \((9*2x)=18x\) for adults.
So we have
\(5.2x+18x=696\\23.2x=696\\x=30\)
So 30 child tickets were sold that day.
Because of a shortage of workers, a radiologic technologist is working
overtime. She gets overtime pay for any hours over 8 hours per day. How
many hours of overtime did she work in 1 week?
Answer:
8
Step-by-step explanation:
Find the value of x…
Answer:
x = 12
Step-by-step explanation:
You want the measure of x, given inscribed angle (5x+1)° subtends an arc of measure (14x-46)°.
Inscribed angleAn inscribed angle has half the measure of the arc it subtends. This tells us the arc measure is twice the angle measure:
2(5x +1)° = (14x -46)°
10x +2 = 14x -46 . . . . . divide by °, eliminate parentheses
48 = 4x . . . . . . . . add 46-10x
12 = x . . . . . . divide by 4
The value of x is 12.
__
Additional comment
The angle is 61°; the arc is 122°.
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What's 1.48 repeating as a
Answer:
147/99
Step-by-step explanation:
(1.48 x 100) - 1 99