6. suppose that a brand of aa batteries reaches a significant milestone to their death on average after 7.36 hours, with standard deviation of 0.29 hours. assume that when this milestone occurs follows a normal distribution (a) calculate the probability that a battery does not reach this milestone in its first 8 hours of usage. (b) suppose that the company wants to sell a pack of n batteries of which (at least) 10 will last until after 7.5 hours of usage. if n12, what is the probability of this goal being met? (c) How many batteries n should be in the package in order for the probability to exceed 1%? Give the smallest number n which works.

Answer:

x=12

Step-by-step explanation:

4x+6y=60                    y=2

4x+6(2)=60

4x+12=60

4x=60-12

4x=48

x=\(\frac{48}{4}\)

x=12

Answer: X= 12

Y= 2

Step-by-step explanation:

He can invite 7 friends.Because he had $40. He will spent for each person $5.25.

In mathematics, a relationship between two expression that are not equal to each other is called inequality.The word inequality mean not being equal ,especially in status, rights and opportunities.

A statement is a declarative statement that is true or false but both not.A statement is also called proposition.It may contain symbols and  words.

he has total money = $40

 cost of burger        =$4.50

 cost of soda           =$0.75

 Let, he will spend for each person

 4.50+0.75=$5.25

so, he can invite=40/5.25

                          =7.619

he can invite 7 friends.

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The equation that represents this parabola in standard form is y = x²

From the question, we have the following parameters that can be used in our computation:

(0,0) , (1,1) and (-1, 1)

A parabola in standard form is represented as

y = ax² + bx + c

Using the points, we have

(0)²a + (0)b + c = 0

c = 0

Next, we have

(1)²a + (1)b + 0 = 1

a + b = 1

(-1)²a + (-1)b + 0 = 1

a - b = 1

Add the equations

2a = 2

a = 1

So, we have

1 + b = 1

b = 0

This means that the equation is y = x²

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Question

Given three points that lie on the parabola, find the equation that represents this parabola in standard form

(0,0) , (1,1) and (-1, 1)

9514 1404 393

Answer:

  B.  91

Step-by-step explanation:

14C12 = 14!/(12!(14-12)!) = 14·13/(2·1) = 7·13 = 91

Answer:

Either -8b - 24 or b = 3

Step-by-step explanation:

Answer: - 8b - 24

Distributive property

Aksa is correct, that each layer has 24 cubes in it, as each layer is composed of four lines, and each line is composed by six cubes.

The number of cubes in each layer is obtained applying the proportions in the context of the problem.

For each layer, we have that:

Then the number of cubes in each layer is given as follows:

6 x 4 = 24 cubes.

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The probability of having an "ideal" family of one boy and one girl when planning to have two children is 1/4 or 0.25. This is because there are four equally likely possibilities for the gender of the two children, and only one of those possibilities results in having one boy and one girl.

Assuming that the probability of having a boy or a girl is equal and independent of previous outcomes, the probability of having a boy and a girl in a family of two children is 1/4 or 0.25.

This is because there are four equally likely possibilities for the gender of the two children: boy-boy, boy-girl, girl-boy, and girl-girl. Only one of these outcomes, boy-girl, results in the couple having their "ideal" family of one boy and one girl.

Therefore, the probability of having their ideal family is 1/4 or 0.25.

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Answer:

4x + 10

Step-by-step explanation:

1/2 x 4x =2x

2x + 2x =4x

1/2 x 4 = 2

2 + 8 = 10 Answer: 4x + 10

Answer:

66(2/3) %

Step-by-step explanation:

There are 30 possible outcomes because there are 30 cold drinks.

 The Probability of orange flavored  20/30   = 2/3 = 0.6666....

66.6666....%= 66(2/3) %

The two found rational expressions with the difference that completes the equation is  (x + 2)/(x² - 36) and 1/(x² + 6x).

Consider the two rational expressions.

(x + 2)/(x² - 36)    ...eq 1

and 1/(x² + 6x)   ....eq 2

Subtract the second from the first.

=  [(x + 2)/(x² - 36)] - [1/(x² + 6)]

Factorise the denominator of the first equation-

= [(x + 2)/(x + 6)(x - 6)] - [1/(x(x + 6)]

Taking the LCM

= [x(x + 2) - (x - 6)]/[x(x + 6)(x - 6)]

Further simplifying,

= [x² + x + 6]/[x(x-6)(x + 6)]

Thus, the two found rational expressions with the difference that completes the equation is  (x + 2)/(x² - 36) and 1/(x² + 6x).

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The complete question is-

Drag each expression to the correct location in the equation. Not all expressions will be used.

Determine the two rational expressions whose difference completes this equation.

x² + x + 6

x(x-6)(x + 6)

To compute the values for X* and X**, we need to use the standard normal distribution and the cumulative distribution function (CDF).

Since X follows a normal distribution with mean 100 and standard deviation 20, we can standardize the values using the formula:

Z = (X - μ) / σ

where Z is the standardized value, X is the given value, μ is the mean, and σ is the standard deviation.

a. P(X < X*) = 80%

To find the value X* for which P(X < X*) = 80%, we need to find the z-score corresponding to this probability. Using Excel, we can use the NORM.INV function.

Excel Command: NORM.INV(0.8, 100, 20)

This command calculates the inverse of the cumulative distribution function (CDF) for the standard normal distribution with a probability of 0.8. The mean is set to 100, and the standard deviation is set to 20. The result will give us the value of X*.

b. P(X > X**) = 60%

To find the value X** for which P(X > X**) = 60%, we need to find the z-score corresponding to this probability and then use the formula to calculate X. Since we want the probability of X being greater than X**, we can use the complementary probability (1 - 0.6 = 0.4) to find the z-score.

Excel Command: NORM.INV (0.4, 100, 20)

This command calculates the inverse of the cumulative distribution function (CDF) for the standard normal distribution with a probability of 0.4. The mean is set to 100, and the standard deviation is set to 20. The result will give us the value of X**.

Using these Excel commands, you can input the formulas into Excel and obtain the values for X* and X**.

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Answer:

96

Step-by-step explanation:

576/6

96

Answer:

$96 for each ticket

Step-by-step explanation:

$576 / 6 = $96

Answer:

There are 315 salmon and 135 fish that aren't salmon.

Step-by-step explanation:

The number of salmon in the aquarium would be 70% of the 450 fish, so to find the number you multiply .7 by 450:

450 × .7 = 315

So, there are 315 salmon. To find how many fish are not salmon, you would subtract 315 from 450:

450 - 315 = 135

So, 135 of the fish are not salmon.

Answer:

\(2a^2-5a+3\)

Step-by-step explanation:

2a(a-3)-1(a-3)=

2a^2-6a-a+3=

2a^2-5a+3

Answer:

Step-by-step explanation:

The rate of speed of the slower bus is 68 km/h the faster bus travels 7 km/h faster when they meet in 2 hours, and the total distance traveled by each bus is 136 km.

Let's assume the rate of the slower bus is x km/h.

The rate of the faster bus is then (x + 7) km/h, as it is traveling 7 km/h faster.

When they travel toward each other, the total distance covered is the sum of their individual distances, which is 286 km.

We know that distance = rate × time.

For the slower bus, the distance it travels in 2 hours is 2x km.

For the faster bus, the distance it travels in 2 hours is 2(x + 7) km.

Since they meet, the sum of their distances should be equal to the total distance: 2x + 2(x + 7) = 286.

Simplifying the equation: 2x + 2x + 14 = 286.

Combining like terms: 4x + 14 = 286.

Subtracting 14 from both sides: 4x = 272.

Dividing both sides by 4: x = 68.

Therefore, the rate of the slower bus is 68 km/h.

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Answer:

Equation: 3(x+5)=60

Solution: 15 inches

Step-by-step explanation:

Let x represent the original side length of the equilateral triangle. Then, the new length of each side is x+5. Because a triangle has three sides, the new perimeter is 3(x+5), which is 60 inches. Dividing both sides by 3, we get that x+5=20, so x=15.

If circle has "r" radius and "c" circumference, then the formula which expresses the "c" in terms of "r" and "π" is "c = 2πr".

The "Circumference" of a circle is defined as the distance around the edge or boundary of a circle, and it is equal to the product of the circle's diameter and the mathematical constant π (pi). In other words, it can be called as the perimeter of a circle.

The formula that expresses the value of the circumference (c) of a circle in terms of its radius (r) and π is: c = 2×π×r,

This formula states that the circumference of a circle is equal to twice the product of its radius and the mathematical constant π (pi).

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The given question is incomplete, the complete question is

A circle has a radius of r cm and circumference of c cm. Write a formula that expresses the value of c in terms of r and π.

When the thief is 15 meters from the building, the rate of change of the length of his shadow on the building is 19.63 m/s.

Let AB be the height of the building, and TC be the length of the shadow cast by the thief when he is 15 meters from the building. Also, let BD be the length of the thief's shadow at the given instant.Since the distance between the building and the floodlight is 45 meters, we have AC = 45 meters.

At a given instant, let x be the distance from the thief to the floodlight.

Then, we have TC = 1/2 * BD ...........(1) (By AA similarity)

Thus, we need to find dB/dt when x = 15 meters.

Differentiating equation (1) with respect to time t, we get:(dT_C)/(dt) = 1/2 * (dB)/(dt)

Since the thief is moving towards the building, we have x = 45 - 15 = 30 meters.

So, using Pythagoras theorem, we have:

AB² = AC²+ BC²=> AB² = 45²+ BD²=> AB² = 2025 + BD²

Differentiating with respect to time, we get:

2AB(dAB)/(dt) = 2BD(dBD)/(dt)=> (dBD)/(dt) = (AB/(BD)) * (dAB)/(dt)...........(2)

Putting AB² = 2025 + BD², we get:

AB = √(2025 + BD²)

Putting AB = 47.53 m and BD = 8.66 m (using x = 15 m), we get:

d(BD)/(dt) = (47.53/(8.66)) * (dAB)/(dt)

d(BD)/(dt) = 5.487(dAB)/(dt)

Using the similar triangles ABD and ACT, we get:

AB/BD = AC/TC=> (AB/BD) = (AC/TC) => AB = (AC/TC) * BD

Substituting the value of AB = 47.53 m, AC = 45 m and TC = BD/2, we get:

(BD/2) = (45/47.53) * BD=> BD = 17.94 meters

Substituting BD = 17.94 m in equation (2), we get:

d(BD)/(dt) = (47.53/(8.66)) * (dAB)/(dt)

d(17.94)/(dt) = 5.487(dAB)/(dt)

AB= 19.63

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Answer and Step-by-step explanation:

\(\frac{9}{10}\) ÷ \(\frac{4}{10}\)

(\(\frac{2}{5}\) × \(\frac{2}{2} = \frac{4}{10}\))

\(\frac{9}{10}\) ÷ \(\frac{4}{10}\) = \(\frac{90}{40} = \frac{9}{4} = 2.25\) - This is the answer.

#teamtrees #PAW (Plant And Water)

Answer:

i believe QuickMAth or CalculatorSOup can help with this if nobody answers, sorry ik im taking points but its not letting me comment :/

Step-by-step explanation:

The given second-order linear nonhomogeneous differential equation can be rewritten to include the effect of a sudden rapid heat release. The equation can then be solved using the Laplace transform technique.

c. To include the effect of a sudden rapid heat release amounting to 10¹⁰ Joule at t = m microseconds, we can rewrite the second-order differential equation as follows:

7 d²x/dt² + 6x + 10¹⁰ δ(t - m) = e^(2t) sinh(t),

where δ(t - m) represents the Dirac delta function centered at t = m microseconds.

d. To solve the equation using the Laplace transform technique, we can take the Laplace transform of both sides of the equation, considering the initial conditions. The Laplace transform of the Dirac delta function is 1, and using the initial conditions, we can obtain the Laplace transform of the solution.

After solving the resulting algebraic equation in the Laplace domain, we can then take the inverse Laplace transform to obtain the solution in the time domain. This will give us the analytical solution for the heat released by the radioactive substance, taking into account the sudden rapid heat release and the given differential equation.

Note: Due to the complexity of the equation and the specific initial conditions, the detailed solution steps and calculations are beyond the scope of this text-based format. However, with the rewritten equation and the Laplace transform technique, it is possible to obtain an analytical solution for the given problem.

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As per the rules of the Australian Taxation Office, when an individual wins from gambling, it is not taxable unless it becomes part of their business activity. Since Jane’s online gambling is only a hobby, the $50,000 gain would not be considered as ordinary income.

a. Calculation of Jane's taxable income:

Given information as at 1 July 2018;

Stock on hand of hair-related products was valued at $300,000 (at cost).

Given information for the year;

Additional stock purchased = $250,000

Sales = $600,000

Given information as at 30 June 2019;

Stock on hand of hair-related products valued at $400,000 (at cost), $450,000 (at replacement value), and $500,000 (at market selling value).

To calculate taxable income from trading activities for the year, we can use either the opening stock method or the closing stock method. Here we are using the closing stock method.

Closing stock at cost = $400,000

Opening stock at cost = $300,000

Purchases made during the year = $250,000

Cost of goods available for sale (opening stock + purchases) = $300,000 + $250,000

Cost of goods sold = Cost of goods available for sale - closing stock at cost= $300,000 + $250,000 - $400,000= $150,000

Gross profit on sales = $600,000 - $150,000= $450,000

Therefore, Jane's taxable income from her trading activities for 2018/19 is $450,000.

b. As per the rules of the Australian Taxation Office, when an individual wins from gambling, it is not taxable unless it becomes part of their business activity. Since Jane’s online gambling is only a hobby, the $50,000 gain would not be considered as ordinary income.

c. Jane liquidated two assets: a parcel of shares in ATC Ltd and a block of land. The effect of each on her taxable income is discussed below: Parcel of Shares in ATC Ltd:

Gain made from the sale of the shares:

$100,000 - $40,000 = $60,000.

The $60,000 gain will form part of Jane’s assessable income.

Block of land: If the land is considered as a capital asset, there would be no impact on Jane’s taxable income unless there was a capital gain or loss on disposal.

However, if the land was held for the purpose of producing assessable income, it would form part of Jane’s business assets and would be considered as trading stock. If Jane could not prove that the land was held as a capital asset, she would have to pay tax on the proceeds received from the sale of the land.

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Answer: The other point is (17, -6).

Step-by-step explanation:

Midpoint (x,y) of the line segment joining (a,b) and (c,d) is given by :-

\((x,y) =(\dfrac{a+c}{2}, \dfrac{b+d}{2})\)

Here, we need to find the other endpoint of a segment with one endpoint at(-3, 8) and the midpoint at (7, 1).

Let other point be (a,b), then

\((7,1)=(\dfrac{-3+a}{2},\dfrac{8+b}{2})\\\\\Rightarrow\ \dfrac{-3+a}{2}=7\ \text{ and }\dfrac{8+b}{2}=1\\\\\Rightarrow\ -3+a = 7\times2 \text{ and } 8+b=1\times2\\\\\Rightarrow\ -3+a=14\text{ and }8+b=2\\\\\Rightarrow\ a=14+3, \ \ \ b= 2-8\\\\\Rightarrow\ a=17, b= -6\)

hence, the other point is (17, -6).

4 + 2x = 16. First, we must subtract 4 from both sides.

2x = 12. Now, divide both sides by 2

x = 6.

Answer choice "a" is correct. You need to use subtraction and division to solve this equation.

Answer:

the answer is 50

Step-by-step explanation:

each day it is adding 4 so by the 7th day it will be 50

The percentage of the downhill grade required for the combination to roll downhill at a constant speed without the application of any rim pull from the engine is equal to 11.5%.

Given data, Weight of tractor (Wt) = 24,500 lb

Weight of trailer (Wt) = 12,300 lb

Rolling resistance of tractor (rrt) = 80 lb/ton

Rolling resistance of trailer (rrt) = 220 lb/ton

Let us assume that the vehicle is traveling down the hill with velocity 'v'.

Therefore, the total weight of the combination is W = Wt + Wt = 24,500 + 12,300 = 36,800 lb

Now, force due to gravity = Weight * Sinθ

where, θ is the angle of inclination of the hill

Therefore, the force due to gravity = 36,800 * Sinθ

Now, force resisting the motion = rolling resistance * Weight * Cosθwhere, rolling resistance is given in lb/ton

So, rolling resistance of tractor = 80 * 24,500 / 2000 * Cosθ = 9800 / Cosθ

Rolling resistance of trailer = 220 * 12,300 / 2000 * Cosθ = 13530 / Cosθ

Now, the vehicle is moving down the hill with a constant velocity. So, there is no application of rim pull from the engine.

Therefore, the net force acting on the vehicle will be zero.

The force due to gravity = force resisting motion or the force due to gravity = rolling resistance of tractor + rolling resistance of trailer

i.e. 36,800 * Sinθ = 9800 / Cosθ + 13530 / Cosθ

Or, 36,800 * Sinθ * Cosθ = 9800 + 13530

Or, 18,400 * Sin2θ = 23330

Or, Sin2θ = 23330 / 18,400

Or, 2 * Sinθ * Cosθ = 23330 / 18,400

Or, 2 * Sinθ * √(1 - Sin2θ) = 23330 / 18,400

Or, 2 * Sinθ * √(1 - 23330² / 18,400²) = 23330 / 18,400

Or, Sinθ = 23330 / 18,400 * 2 * √(1 - 23330² / 18,400²)

Or, Sinθ = 0.2

Or, θ = 11.5°

Therefore, the percentage of the downhill grade required for the combination to roll downhill at a constant speed without the application of any rim pull from the engine is equal to 11.5%.

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Given:

Hyperbola with directrices at y = ±2 and foci at (0, 6) and (0, −6).

To find:

The equation of hyperbola.

Solution:

We have, directrices at y = ±2 so this hyparabola is along the y-axis.

The standard form of hyperbola is

\(\dfrac{(y-k)^2}{a^2}-\dfrac{(x-h)^2}{b^2}=1\)      ...(i)

where, (h,k) is center, foci are \((h,k\pm c)\) and directrix are \(y=k\pm \dfrac{a^2}{c}\).

On comparing foci, we get

\((h,k\pm c)=(0,\pm 6)\)

\(h=0,k=0,c=6\)

On comparing directrix we get

\(k\pm \dfrac{a^2}{c}=\pm 2\)

\(\dfrac{a^2}{c}=2\)

\(\dfrac{a^2}{6}=2\)

\(a^2=12\)

Now,

\(a^2+b^2=c^2\)

\(12+b^2=(6)^2\)

\(b^2=36-12\)

\(b^2=24\)

Putting \(h=0,k=0,a^2=12,b^2=24\), we get

\(\dfrac{(y-0)^2}{12}-\dfrac{(x-0)^2}{24}=1\)

\(\dfrac{y^2}{12}-\dfrac{x^2}{24}=1\)

Therefore, the equation of hyperbola is \(\dfrac{y^2}{12}-\dfrac{x^2}{24}=1\).

Answer:

the person above has the right answer. I took the test.

Step-by-step explanation:

The person above is correct.

We are given a rectangle with one of its sides ( length ) equal to ( x - 7 ) Meters.

We have to find the expression for another side of the rectangle i.e it's width

We will use the formula of area of rectangle to find the expression :

Therefore,

‎ㅤ‎ㅤ➝ A = l × w

‎ㅤ‎ㅤ➝ x² - 15x + 56 = ( x - 7 ) × w

‎ㅤ‎ㅤ➝ x² - 8x -7x + 56 = ( x - 7 ) × w

‎ㅤ‎ㅤ➝ (x² - 8x )( - 7x + 56 ) = ( x-7 ) w

‎ㅤ‎ㅤ➝ x( x - 8 )-7( x - 8 ) = ( x - 7 )w

‎ㅤ‎ㅤ➝ ( x - 8 )( x - 7 ) = ( x - 7 )

‎ㅤ‎ㅤ➝ ( x - 8 )w = ( x - 8 )( x - 7 )

‎ㅤ‎ㅤ➝ w = ( x - 8 )( x - 7 ) / ( x - 7 )

‎ㅤ‎ㅤ➝ w = ( x - 8 )

The null hypothesis for the data will be 21.62 and the alternate hypothesis is 2.02 for the p-value for the data is 0.2253 .

The charge at which anything happens is referred to as the velocity at which it happens.

The required details for mean rate :

(a) H0: µ = 21.62

Ha: µ ≠ 21.62

(b) t = -1.231

p-value = 0.2253

(c) Stop rejecting H0 right now. No longer significantly different from the domestic water tariff in Tulsa, the suggested household water charge per five CCF for the entire USA.

(d) H0: µ = 21.62

Ha: µ ≠ 21.62

t = -1.231

check statistic ≥ 2.020

Don't dismiss H0 any longer. The suggested five CCF residential water charge for the entirety of the USA is no longer significantly different from the five CCF residential water tariff in Tulsa.

The P-value is higher at 0.05, the level of significance. The impact in this instance is negligible. The attempt to reject the null hypothesis failed.

The conclusion is that there is insufficient statistical support to determine whether other American cities have a different mortality rate than Tulsa.

The crucial values for t at this level of significance are t=2.019.

Given that the statistic t = -1.15 is inside the acceptance range in this case, the null hypothesis is not disproved.

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The measure of angle A in the triangle is 18°

The angles in the triangle are given as:

m∠A = (2x − 24)°, m∠B = (x + 8)°, m∠C = (4x + 49)°

The sum of angles in a triangle is 180

So, we have

m∠A + m∠B + m∠C = 180

Substitute the known values in the above equation

So, we have:

2x − 24 + x + 8 + 4x + 49 = 180

Evaluate the like terms

7x = 147

Divide both sides by 7

x = 21

Substitute x = 21 in m∠A = (2x − 24)°

m∠A = (2 * 21 − 24)°

Evaluate

m∠A = 18°

Hence, the measure of angle A in the triangle is 18°

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