the lifetime of a certain electronic component is a random variable with an expectation of 6000 hours and a standard deviation of 120 hours. what is the probability that the average lifetime of 500 randomly selected components is between 5990 hours and 6010 hours? answer the following questions before computing the probability.

Aaron's taxable income is negative (-$10,100), it means that he does not have any taxable income.

To determine the amount of taxable income for Aaron Rentz in 2020, we need to consider his wages, interest income, and any deductions or credits he may be eligible for.

From the given information, Aaron has $900 of wages and $1,400 of interest income.

In 2020, the standard deduction for a single individual was $12,400. Since Aaron is a qualifying child of his parents, he may not be able to claim his own personal exemption.

To calculate Aaron's taxable income, we subtract the standard deduction from his total income:

Taxable Income = Total Income - Standard Deduction

Taxable Income = $900 + $1,400 - $12,400

Taxable Income = $2,300 - $12,400

Taxable Income = -$10,100

Since Aaron's taxable income is negative (-$10,100), it means that he does not have any taxable income.

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Answer:

-3 and 7

Step-by-step explanation:

EDGE2021

The x-intercepts are (0, 0), (1, 0) and (-1, 0), the y-intercept is (0, 0), the stationary points are (1, 0), (-1, 0), (1/√5, 16/25√5) and (-1/√5, -16/25√5) and the inflection points are (0, 0), (√(3/5), 4/25√(3/5)) and (-√(3/5), -4/25√(3/5)).

Given that a function p(x) = x (x² - 1)², we need to find the coordinates of the intercepts, stationary points, and the inflection point,

x-intercept =

0 = x (x² - 1)²

x = 0,

x² - 1 = 0

x = ± 1

Thus, the x-intercepts are (0, 0), (1, 0) and (-1, 0)

y-intercept =

y = x (x² - 1)²

y = 0(0-1)²

y = 0

Thus, y-intercept is (0, 0)

Differentiate the function,

dy/dx = d/dx[x (x² - 1)²]

= (x² - 1)² + 4x²(x²-1)]

= (x²-1)(5x²-1)

Put dy/dx = 0

(x²-1)(5x²-1) = 0

x²-1 = 0

x = ±1

5x²-1 = 0

x = ±1/√5,

When, x = ±1 then y = 0

When x = 1/√5, then,
y = 1/√5((1/√5)²-1)²

= 16/25√5

Similarly, for x = -1/√5,

y = -1/√5((1/√5)²-1)²

= -16/25√5

Thus, the stationary points are (1, 0), (-1, 0), (1/√5, 16/25√5) and (-1/√5, -16/25√5)

Now, differentiate the function y = (x²-1)(5x²-1)

d²y/dx² = (5x²-1)2x + (x²-1)10x

= 20x³ - 12x

Put d²y/dx² = 0,

20x³ - 12x = 0

4x(5x²-3) = 0

4x = 0, x = 0

5x²-3 = 0

x = ±√(3/5)

When x = 0, y = 0,

When x = √(3/5)

y = √(3/5)((√(3/5))²-1)²

= 4/25(√(3/5))

When x = -√(3/5)

y = -√(3/5)((√(3/5))²-1)²

Thus, the inflection points are (0, 0), (√(3/5), 4/25√(3/5)) and (-√(3/5), -4/25√(3/5)).

Hence the x-intercepts are (0, 0), (1, 0) and (-1, 0), the y-intercept is (0, 0), the stationary points are (1, 0), (-1, 0), (1/√5, 16/25√5) and (-1/√5, -16/25√5) and the inflection points are (0, 0), (√(3/5), 4/25√(3/5)) and (-√(3/5), -4/25√(3/5)).

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The quadratic equation is \(x^2+x-12\)

What is quadratic equation?

Quadratics can be defined as a polynomial equation of a second degree, which implies that it comprises a minimum of one term that is squared. It is also called quadratic equations. The general form of the quadratic equation is:

ax² + bx + c = 0

where x is an unknown variable and a, b, c are numerical coefficients.

Given, the roots of quadratic equation as (3,-4).

The formula to find the quadratic equation, as

x2 – (Sum of the roots)x + Product of the roots = 0

Sum of roots = 3-4

=-1

Product of roots = 3(-4) = -12

The quadratic equation is

x²+x-12

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0.65 is the correct one if not up there try 0.45 other possible one

Step-by-step explanation:

A rational number is defined as any number which can be expressed in fractional p/q of two integers, where 'p' is the numerator and 'q' is the denominator. 'q' can never be zero. A rational number can also be expressed as a terminating decimal. So, when 0.25 is added in 0.45 it becomes 0.65 which is rational.

Answer:

y = x^58/5

Step-by-step explanation:

Nothing further can be done with this topic. just remove the parentheses and it becomes x^58 and u cannot dive because they’re like terms

Answer:

\(x + \frac{5}{3}-x - \frac{3}{2} = \frac{1}{6}\)

Step-by-step explanation:

Given

\(x + \frac{5}{3}-x - \frac{3}{2}\)

Required

Solve

\(x + \frac{5}{3}-x - \frac{3}{2}\)

Collect like terms

\(x + \frac{5}{3}-x - \frac{3}{2} = x -x+ \frac{5}{3} - \frac{3}{2}\)

\(x + \frac{5}{3}-x - \frac{3}{2} = \frac{5}{3} - \frac{3}{2}\)

Take LCM

\(x + \frac{5}{3}-x - \frac{3}{2} = \frac{10 -9}{6}\)

\(x + \frac{5}{3}-x - \frac{3}{2} = \frac{1}{6}\)

Answer:

$5 ( sorry if it is incorrect)

Step-by-step explanation:

The astronaut swings the hammer in one direction, an equal and opposite force acts on the astronaut in the opposite direction.    

The astronaut swings the hammer to hammer the loose rivet back in place outside the spaceship, they will experience an equal and opposite force known as "reaction force" as described by Newton's Third Law of Motion.

This means that for every action (force) in one direction, there is an equal and opposite reaction (force) in the opposite direction.

The astronaut swings the hammer, they will experience a small amount of recoil or pushback in the opposite direction.

The magnitude of the reaction force will be equal to the force exerted by the hammer on the rivet, but in the opposite direction.

The effect of this recoil on the astronaut will depend on the mass of the astronaut and the force exerted by the hammer.

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Answer:

1.15%

Step-by-step explanation:

Given that :

Total charge = 5892.17

Charge = 67.71

The percentage charge, of charge is 67.71 is obtained thus :

(Charge / total charge) * 100%

(67.71 / 5892.17) * 100%

0.0114915 * 100%

= 1.1491521%

= 1.15%

a) The area of the square is 1, so the result is ∮c F · T ds = 3.

b)  Using Green's theorem,  the answer is $cFinds∮c F · ds = 28/3.

To apply Green's theorem, we need to find the curl of F:

curl F = (∂Q/∂x - ∂P/∂y)k

where P = x^2 + 4y and Q = x + y^2.

So, ∂Q/∂x = 1 and ∂P/∂y = 4. Therefore, curl F = (4 - 1)k = 3k.

(a) By Green's theorem,

∮c F · T ds = ∬R (curl F) · k dA,

where R is the region enclosed by the square C and T is the unit tangent vector to C oriented counterclockwise.

Since curl F = 3k, the double integral reduces to

∬R 3 dA = 3(area of R).

The area of the square is 1, so the result is ∮c F · T ds = 3.

(b) By Green's theorem,

∮c F · ds = ∬R (curl F) · n dA,

where n is the unit outward normal vector to C.

Since curl F = 3k, the double integral reduces to

∬R 3z dA,

where z is the z-coordinate of the point (x,y,z) on the surface z = 10 - x^2 - y^2 above the square C.

The region R is a square in the xy-plane, so we can integrate over x and y from 0 to 1:

∬R 3z dA = 3∫0^1∫0^1 (10 - x^2 - y^2) dxdy

= 3(10 - 2/3) = 28/3.

Therefore, ∮c F · ds = 28/3.

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The final answer is 8arcsin(x/4) - 4sin(2arcsin(x/4)) + C, where C represents the constant of integration. The expression is given in terms of x only.

To evaluate the given integral, we can use trigonometric substitution. Let's substitute x = 4sinθ, which allows us to rewrite the integrand in terms of θ. The differential becomes dx = 4cosθ dθ.

Using this substitution, the integral transforms into ∫(4sinθ)²√(16-(4sinθ)²)(4cosθ) dθ. Simplifying this expression yields 16∫sin²θ√(1-cos²θ)cosθ dθ.

We can apply the double-angle identity sin²θ = (1-cos2θ)/2 to simplify further. This results in 8∫(1-cos2θ)√(1-cos²θ)cosθ dθ.

Next, we can apply the trigonometric identity sin(2θ) = 2sinθcosθ to obtain 8∫(sinθ-sin³θ) dθ.

Finally, integrating term by term and substituting back x = 4sinθ, we arrive at the final answer of 8arcsin(x/4) - 4sin(2arcsin(x/4)) + C. This expression represents the antiderivative of the given function in terms of x only, where C represents the constant of integration.

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Answer: the percent is 112.01. please mark brainliest

Step-by-step explanation:

Answer:

6000+300+70+4

Step-by-step explanation:

6000 plus 300 =  6300

70 plus 4= 74

6300+74=6374

Answer:

6,000

+  300

+     70

+       4

-------------

6, 3 7 4

Step-by-step explanation:

Answer:

36

because 2x3= 6

6x6 is 36

1) El vehículo tardará 14 minutos en recorrer la misma distancia a una rapidez de 50 kilómetros por hora.

2) La rapidez registrada equivale al 55.556 % de la velocidad máxima de la zona.

1) En este problema tenemos el caso de un vehículo que se desplaza a rapidez constante. Aquí tenemos que la rapidez (v), en kilómetros por hora, es inversamente proporcional al tiempo invertido (t), en minutos.

[(40 km /h) / (50 km / h)] = t / 20 min

4 / 5 = t / 20

t = 80 / 5

t = 14 min

El vehículo tardará 14 minutos en recorrer la misma distancia a una rapidez de 50 kilómetros por hora.

2) El porcentaje correspondiente a la rapidez reportada se calcula mediante porcentajes:

r = [(50 km / h) / (90 km / h)] × 100 %

r = 55.556 %

La rapidez registrada equivale al 55.556 % de la velocidad máxima de la zona.

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The correct answer is option C: Yes, because 12-9<6

A triangle can be formed with side lengths 6, 9, and 12. This is because the Triangle Inequality states that the sum of any two side lengths of a triangle must be greater than the third side length. In this case, 6+9=15 and 12+9=21, both of which are greater than 12, so a triangle can be formed. The correct answer is therefore option C, "yes, because 12 − 9 < 6."

Therefore, as per Triangle Inequality, a triangle can be formed with side lengths 6, 9, and 12, Correct answer option C (Yes, because 12-9<6)

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(a) The plot of y versus t for several values of y₀ between 1/2 and 1 shows oscillations with higher y₀ resulting in larger oscillations.

(b) The critical initial population \(y_c\) below which the population becomes extinct is \(y_c\) = 2.5k.

(c) For different values of k, the corresponding critical initial populations \(y_c\) are found

(d) The relationship between the critical initial population \(y_c\) and the predation rate k can be summarized as \(y_c\) = 2.5k.

(a) Plotting y versus t for several values of y₀ between 1/2 and 1:

To solve the initial value problem dy/dt = r(t) * y - k, y(0) = y₀, we need to integrate the differential equation numerically.

Given:

- r(t) = (1 + sin t) / 5

- k = 1/5

We can observe the following:

For each value of y₀ between 1/2 and 1, the population y will exhibit a fluctuating behavior over time. The sine function in r(t) causes the growth rate to oscillate, leading to oscillations in the population as well. The magnitude of the oscillations depends on the initial population y₀.

Higher values of y₀ will result in larger oscillations, while lower values will lead to smaller oscillations. As time progresses, the population may increase or decrease depending on the interplay between the growth rate and the predation rate.

(b) Estimating the critical initial population \(y_c\) below which the population will become extinct:

To estimate the critical initial population \(y_c\), we need to find the value of y₀ for which the population becomes extinct. This occurs when the population y drops to zero or a very small positive value.

For the given differential equation dy/dt = r(t) * y - k, we can see that when y is very close to zero, the rate of decrease (k) dominates over the growth rate (r(t) * y). Therefore, we can set up the following equation:

0 = r(t) * y - k

Solving this equation for y, we find:

y = k / r(t)

Substituting r(t) = (1 + sin t) / 5, we have:

y = 5k / (1 + sin t)

To find the critical initial population \(y_c\), we need to determine the smallest value of y for all t. Since the minimum value of sin t is -1, the smallest value of y is obtained when sin t = -1, yielding:

\(y_c\) = 5k / (1 - (-1))

   = 5k / 2

   = 2.5k

Therefore, the critical initial population \(y_c\) is 2.5 times the predation rate k.

(c) Choosing other values of k and finding the corresponding \(y_c\) for each one:

Let's consider different values of k and calculate the corresponding critical initial population \(y_c\) using the formula derived in part (b):

For k = 1/10:

\(y_c\) = 2.5 * (1/10) = 1/4 = 0.25

For k = 1/4:

\(y_c\) = 2.5 * (1/4) = 5/8 = 0.625

For k = 1/2:

\(y_c\) = 2.5 * (1/2) = 5/4 = 1.25

For k = 1:

\(y_c\) = 2.5 * 1 = 2.5

For k = 2:

\(y_c\) = 2.5 * 2 = 5

For k = 5:

\(y_c\) = 2.5 * 5 = 12.5

These are the corresponding critical initial populations \(y_c\) for different values of k.

(d) Plotting \(y_c\) versus k:

Using the values of \(y_c\) and k calculated in part (c), we can plot \(y_c\) versus k:

k       |   \(y_c\)

-------------------

1/10   |  0.25

1/4    |  0.625

1/2    |  1.25

1       |  2.5

2      |  5

5      |  12.5

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The left side of the equation is equal to the right side, which confirms that a = 11/10 is the correct solution.

To solve the equation, we need to isolate the variable "a". The equation is given as a - 1/2 = 3/5.
To eliminate the fraction, we can multiply both sides of the equation by the least common denominator (LCD), which is 10. This will clear the fractions and make the equation easier to solve.
Multiplying the left side of the equation by 10, we get:
10(a - 1/2) = 10(3/5)
10a - 5 = 6
Next, we can simplify the equation by adding 5 to both sides:
10a - 5 + 5 = 6 + 5
10a = 11
Finally, we can solve for "a" by dividing both sides of the equation by 10:
(10a)/10 = 11/10
a = 11/10
Therefore, the solution to the equation is a = 11/10 or a = 1 1/10.
To check the solution, substitute a = 11/10 back into the original equation:
11/10 - 1/2 = 3/5
(11/10) - (5/10) = 3/5
6/10 = 3/5
In summary, the solution to the equation a - 1/2 = 3/5 is a = 11/10 or a = 1 1/10. This solution has been checked and is correct.

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The proportional relationship connecting the circumference of the circle and the length of its radius is:

\(C = kr\)

\(y = kx\)

In this problem:

Hence, the formula is:

\(C = kr\)

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The probability that the drink Salma chooses is in a can or is a soda is 0.75.

To calculate the probability, we need to determine the number of favorable outcomes (drinks in a can or sodas) and the total number of possible outcomes (all types of drinks in the cooler).

Let's assume there are 5 bottles of soda, 3 cans of soda, 4 bottles of juice, and 2 cans of juice. The total number of possible outcomes is 14 (5 + 3 + 4 + 2). The number of favorable outcomes (drinks in a can or sodas) is 10 (3 cans of soda + 2 cans of juice + 5 bottles of soda).

Therefore, the probability is 10/14 = 0.714. Rounded to the nearest hundredth, the probability is approximately 0.75.

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a. The probability that a student scores higher than 85 on the exam can be calculated using the standard normal distribution and the given mean and standard deviation.

b. The probability that 4 or more students score 85 or higher on the exam can be calculated using the binomial distribution, assuming independence of the exam scores and using the probability calculated in part (a).

a. To find the probability that a student scores higher than 85 on the exam, we need to calculate the area under the normal distribution curve to the right of the score 85.

By standardizing the score using the z-score formula, we can use a standard normal distribution table or a statistical calculator to find the corresponding probability.

The z-score is calculated as (85 - mean) / standard deviation, which gives (85 - 80) / 5 = 1. The probability of scoring higher than 85 can be found as P(Z > 1), where Z is a standard normal random variable.

This probability can be looked up in a standard normal distribution table or calculated using a statistical calculator.

b. To calculate the probability that 4 or more students score 85 or higher on the exam, we can use the binomial distribution. The probability of a single student scoring 85 or higher is the probability calculated in part (a).

Assuming independence among the students' scores, we can use the binomial probability formula: P(X ≥ k) = 1 - P(X < k-1), where X is a binomial random variable representing the number of students scoring 85 or higher, and k is the number of students (4 in this case). We can then plug in the values into the formula and calculate the probability using a statistical calculator or software.

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Answer:

Gym A is growing faster

Gym A gained 13 members between months 2 and 4

Gym B gained 10 members between months 2 and 4

Step-by-step explanation:

Gym A:  (2,20) (4,46)

rate of change = (46-20)/(4-2)  =  26/2 or 13

Gym B:  (2,40) (4,60)

rate of change = (60-40)/(4-2)  =  20/2 or 10

The probability that the product of the numbers on the top faces of four standard six-sided dice will be prime is approximately 0.09%.

To calculate this probability, a table can be created that outlines the 36 possible combinations of numbers on the top faces of four dice. From this table, the number of prime products can be determined. As there are only three primes (2, 3, and 5) in the 36 possible products, the probability of rolling a prime product is 3/36, which is approximately 0.09%. This means that the probability of rolling a prime product on four standard six-sided dice is very low, approximately 0.09%.

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Answer:

The correct answer is B

Step-by-step explanation:

#Carry On Learning

Answer:

Cube both sides tham solve the resulting quadratic

The correct statement is:

Cube both sides and then solve the resulting quadratic equation.

The cube root of a number is the factor that we multiply by itself three times to get that number.

Given:

∛(x² - 6) = ∛(2x + 2)

For solving the above equation we have to take cube on both side

x² - 6 = 2x +2

x² - 2x -8 = 0

Then we get the quadratic equation.

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Answer:

30

Step-by-step explanation:

12×5=60 60÷1/2=30

srry if I was wrong

12×5=60 60÷1/2=30 i hope it's right!! :)

Answer:

(2a+b)^3

Step-by-step explanation:

8a^3+b^3+12a^2b+6ab^2​

(2a)^3 + 3. (2a)^2 b + 3 (2a) b^2 + b^3

the above equation compare to (a+b)^3 = a^3 + 3a^2b+3ab^2 +b^3

when we compare both the equations

our a= 2a and b=b

so, our answer is (2a + b)^3

Answer:

SAS

Step-by-step explanation:

If two sides and the included and the included angle of one triangle are congruent to two sides and the included angle of another triangle , then the triangles are congruent. The included angle is the angle formed by the two sides.

EF = BC

∠ F = ∠ C

DF = AC

then the two triangles are congruent by the SAS postulate.

Answer:

SAS

Step-by-step explanation:

On triangle one and two, they both start by having a congruent side, then a congruent angle, then another congruent side, thus making these triangles congruent by Side Angle Side.

It can't be AAS because there is only one angle, we know is congruent.

It can't be SSS because there are only two sides, we know are congruent.

It can't be HL because there is no right angle, meaning these aren't right triangles.

Answer: $512.20

Step-by-step explanation: