alan is saving money to buy a game. so far he has saved $30, which is 5/6 of the total cost of the game. how much does the game cost?

(a) To find the proportion of trees that are more than a certain height, we need to calculate the area under the normal distribution curve to the right of that height. To do this, we can use a standard normal distribution table or a calculator.

First, we need to standardize the height by subtracting the mean and dividing by the standard deviation. Let's assume the mean height is μ inches and the standard deviation is σ inches.

Let X be a random variable representing the height of a cherry tree. We are given that X follows a normal distribution with mean μ and standard deviation σ.
To find the proportion of trees that are more than a certain height, let's say x inches, we can calculate the z-score using the formula:
z = (x - μ) / σ

Once we have the z-score, we can use a standard normal distribution table or a calculator to find the proportion of values that are greater than that z-score. This will give us the proportion of trees that are more than x inches tall.

(b) To find the proportion of trees that are less than a certain height, we can follow a similar approach. We calculate the z-score using the formula:
z = (x - μ) / σ
Then, we can use a standard normal distribution table or a calculator to find the proportion of values that are less than that z-score. This will give us the proportion of trees that are less than x inches tall.

(c) To find the probability that a randomly chosen tree is between two heights, let's say a inches and b inches, we need to calculate the area under the normal distribution curve between those two heights. We can do this by calculating the z-scores for both heights using the formula:
z1 = (a - μ) / σ
z2 = (b - μ) / σ
Once we have the z-scores, we can use a standard normal distribution table or a calculator to find the proportion of values that are between those two z-scores. This will give us the probability that a randomly chosen tree is between a and b inches tall

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Answers:

\(\sqrt[c]{a^b}\)

\((\sqrt[c]{a})^b\)

Answer:

first 1 last 1 third 1 and forth 1

Step-by-step explanation:

- The percentage of people with blood pressure between 123 and 157 mm is approximately 60.46% (answer C).

- The percentage of people with blood pressure between 140 and 157 mm is approximately 19.77% (answer A).

- The percentage of people with blood pressure over 157 mm is approximately 19.77% (answer A).

Z = (X - μ) / o

Where:

Z is the standard score

X is the observed value

μ is the mean

o is the standard deviation

Let's calculate each percentage:

1. The percentage of people with blood pressure between 123 and 157 mm:

First, we calculate the Z-scores for 123 mm and 157 mm:

Z1 = (123 - 140) / 20

= -17/20

= -0.85

Z2 = (157 - 140) / 20

= 17/20

= 0.85

Now, we look up the probabilities associated with the Z-scores -0.85 and 0.85 in the normal table. The percentage between these two Z-scores represents the percentage of people within the range:

P(-0.85 < Z < 0.85) = P(Z < 0.85) - P(Z < -0.85)

Looking up the table, we find that P(Z < 0.85) is approximately 0.8023 and P(Z < -0.85) is approximately 0.1977.

Therefore, the percentage of people with blood pressure between 123 and 157 mm is approximately:

P(123 < X < 157) = (0.8023 - 0.1977)  100

= 0.6046  100

= 60.46%

The closest answer is C) 60.4%.

2. The percentage of people with blood pressure between 140 and 157 mm:

Since the average blood pressure is 140 mm, we only need to calculate the Z-score for 157 mm:

Z = (157 - 140) / 20

= 17/20

= 0.85

We want to find P(Z > 0.85) since we are interested in the percentage of people above the mean. Looking up the table, we find that P(Z > 0.85) is approximately 1 - 0.8023 = 0.1977.

Therefore, the percentage of people with blood pressure between 140 and 157 mm is approximately:

P(140 < X < 157) = (1 - 0.8023) 100

= 0.1977  100

= 19.77%

The closest answer is A) 19.8%.

3. The percentage of people with blood pressure over 157 mm:

  We already have the Z-score for 157 mm, which is 0.85.

We want to find P(Z > 0.85) since we are interested in the percentage of people above this value. Looking up the table, we find that P(Z > 0.85) is approximately 1 - 0.8023 = 0.1977.

Therefore, the percentage of people with blood pressure over 157 mm is approximately:

P(X > 157) = P(Z > 0.85)  100

= 0.1977 100

= 19.77%

The closest answer is A) 19.8%.

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(i) If f is an even function, then f(y) = 2 ∫[0,∞] f(x) cos(2πxy) dx.

(ii) If f is an odd function, then f(y) = -2i ∫[0,∞] f(x) sin(2πxy) dx.

The Fourier transform pair for a function f(x) is defined as follows:

F(k) = ∫[-∞,∞] f(x) \(e^{-2\pi iyx}\) dx

f(x) = (1/2π) ∫[-∞,∞] F(k) \(e^{2\pi iyx}\) dk

Now let's prove the given properties:

(i) If f is an even function, then f(y) = 2∫[0,∞] f(x) cos(2πxy) dx.

To prove this, we start with the Fourier transform pair and substitute y for k in the Fourier transform of f(x):

F(y) = ∫[-∞,∞] f(x) \(e^{-2\pi iyx}\) dx

Since f(x) is even, we can rewrite the integral as follows:

F(y) = ∫[0,∞] f(x) \(e^{-2\pi iyx}\) dx + ∫[-∞,0] f(x) \(e^{2\pi iyx}\) dx

Since f(x) is even, f(x) = f(-x), and by substituting -x for x in the second integral, we get:

F(y) = ∫[0,∞] f(x) \(e^{-2\pi iyx}\) dx + ∫[0,∞] f(-x) \(e^{2\pi iyx}\)dx

Using the property that cos(x) = (\(e^{ ix}\) + \(e^{- ix}\))/2, we can rewrite the above expression as:

F(y) = ∫[0,∞] f(x) (\(e^{-2\pi iyx}\) + \(e^{2\pi iyx}\))/2 dx

Now, using the definition of the inverse Fourier transform, we can write f(y) as follows:

f(y) = (1/2π) ∫[-∞,∞] F(y) \(e^{2\pi iyx}\) dy

Substituting F(y) with the expression derived above:

f(y) = (1/2π) ∫[-∞,∞] ∫[0,∞] f(x) \(e^{-2\pi iyx}\) + \(e^{2\pi iyx}\)/2 dx dy

Interchanging the order of integration and evaluating the integral with respect to y, we get:

f(y) = (1/2π) ∫[0,∞] f(x) ∫[-∞,∞] (\(e^{-2\pi iyx}\) + \(e^{2\pi iyx}\))/2 dy dx

Since ∫[-∞,∞] (\(e^{-2\pi iyx}\) + \(e^{2\pi iyx}\))/2 dy = 2πδ(x), where δ(x) is the Dirac delta function, we have:

f(y) = (1/2) ∫[0,∞] f(x) 2πδ(x) dx

f(y) = 2 ∫[0,∞] f(x) δ(x) dx

f(y) = 2f(0) (since the Dirac delta function evaluates to 1 at x=0)

Therefore, f(y) = 2 ∫[0,∞] f(x) cos(2πxy) dx, which proves property (i).

(ii) If f is an odd function, then f(y) = -2i ∫[0,∞] f(x) sin(2πxy) dx.

The proof for this property follows a similar approach as the one for even functions.

Starting with the Fourier transform pair and substituting y for k in the Fourier transform of f(x):

F(y) = ∫[-∞,∞] f(x) \(e^{-2\pi iyx}\) dx

Since f(x) is odd, we can rewrite the integral as follows:

F(y) = ∫[0,∞] f(x) \(e^{-2\pi iyx}\) dx - ∫[-∞,0] f(x) \(e^{-2\pi iyx}\) dx

Using the property that sin(x) = (\(e^{ ix}\) - \(e^{-ix}\))/2i, we can rewrite the above expression as:

F(y) = ∫[0,∞] f(x) \(e^{-2\pi iyx}\) - \(e^{2\pi iyx}\)/2i dx

Now, following the same steps as in the proof for even functions, we can show that

f(y) = -2i ∫[0,∞] f(x) sin(2πxy) dx

This completes the proof of property (ii).

In summary:

(i) If f is an even function, then f(y) = 2 ∫[0,∞] f(x) cos(2πxy) dx.

(ii) If f is an odd function, then f(y) = -2i ∫[0,∞] f(x) sin(2πxy) dx.

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Aya can make 14 mats of 1 foot long.

Division is one of the fundamental arithmetic operation, which is performed to get equal parts of any number given, or finding how many equal parts can be made. It is represented by the symbol "÷" or sometimes "/"

Given that, Aya has 14\(\frac{2}{5}\) feet of chain. She wants to make pieces foot long mat.

Let can make x mats out of the given chain, since each mat is 1 foot long, so,

1×x =  14\(\frac{2}{5}\)

x = 72/5

x = 14.4

x ≈ 14

Hence, She can make 14 mats out of the given chain.

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The probability P(x > 18) is equal to 1 minus the probability P(x < 18) for a normally distributed variable x with mean μ = 100 inches.

In a normal distribution, the area under the curve represents the probability of observing a certain value or a range of values. The probability P(x > 18) represents the probability of observing a value greater than 18 for the variable x. Conversely, the probability P(x < 18) represents the probability of observing a value less than 18 for the variable x.

Since the total area under the normal distribution curve is equal to 1, we can say that the sum of the probabilities of all possible events is equal to 1. Therefore, the probability of an event occurring (P(x > 18)) plus the probability of the event not occurring (P(x < 18)) is equal to 1.

Mathematically, we can express this relationship as:

P(x > 18) = 1 - P(x < 18)

So, the probability P(x > 18) is related to P(x < 18) by subtracting the latter from 1.

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The value of m + n is 12 where , m is 4 and n is 8

Vieta’s formulas are formulas that relate the coefficients of a polynomial to sums and products of its roots. It was discovered by Francois Vieta. The simplest application of Vieta’s formula is quadratics and are used specifically in algebra.

Rearranging the log

\(\frac{8}{\log n \log m}(\log x)^2 - \left(\frac{7}{\log n}+\frac{6}{\log m}\right)\log x - 2013 = 0\)

Using the Vieta's Theorem,

The sum of the possible values of log x is \(\frac{\frac{7}{\log n}+\frac{6}{\log m}}{\frac{8}{\log n \log m}} = \frac{7\log m + 6 \log n}{8} = \log \sqrt[8]{m^7n^6}\)

But the sum of the possible values of log x is the logarithm of the product of the possible values of x. Thus the product of the possible values of x is equal to \(\sqrt[8]{m^7n^6}\)

It remains to minimize the integer value of \(\sqrt[8]{m^7n^6}\).

   Since m, n>1 , we can check that m = 2² and n = 2³.

Hence , m = 4 and n = 8

m + n = 4 + 8

=> 12

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Answer:

6.21 × 10⁵

Step-by-step explanation:

move thee decimal from .21000 thats how you get 5

Answer:

so wait what are you asking about it? what’s the specific question?

Step-by-step explanation:

The equation in spherical coordinates is a) 3sin²ϕ - 2sinϕcosθ/ρ - 3cos²ϕ = 0

b) 2sinφcosθ + 4sinφsinθ + 5cosφ = 1/ρ

a) The equation in Cartesian coordinates is 3x² - 2x + 3y² - 3z² = 0. To convert to spherical coordinates, we use the following substitutions:

x = ρsinϕcosθ

y = ρsinϕsinθ

z = ρcosϕ

Substituting these values into the Cartesian equation gives:

3(ρsinϕcosθ)² - 2(ρsinϕcosθ) + 3(ρsinϕsinθ)² - 3(ρcosϕ)² = 0

3ρ²sin²ϕcos²θ - 2ρsinϕcosθ + 3ρ²sin²ϕsin²θ - 3ρ²cos²ϕ = 0

3ρ²sin²ϕ(cos²θ + sin²θ) - 2ρsinϕcosθ - 3ρ²cos²ϕ = 0

3ρ²sin²ϕ - 2ρsinϕcosθ - 3ρ²cos²ϕ = 0

Simplifying and dividing by ρ² gives:

3sin²ϕ - 2sinϕcosθ/ρ - 3cos²ϕ = 0

(b) The equation in rectangular coordinates is 2x + 4y + 5z = 1. To write it in spherical coordinates, we use the same conversion formulas as before:

2(ρsinφcosθ) + 4(ρsinφsinθ) + 5(ρcosφ) = 1

Simplifying and dividing by ρ, we get:

2sinφcosθ + 4sinφsinθ + 5cosφ = 1/ρ

This is the equation in spherical coordinates.

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The range of speeds at which a car can safely make the curve is approximately 70 km/h to 130 km/h.


When a car moves along a banked curve, the friction force plays a crucial role in preventing the car from slipping. To determine the safe range of speeds, we consider two scenarios: when the car goes too slow and when it goes too fast.
1. When the car goes too slow: If the car moves slower than the required speed, the friction force points uphill, away from the center of the curve. In this case, the static friction force needs to provide the centripetal force. Using the equation F_friction = μ_s * N, where μ_s is the coefficient of static friction and N is the normal force, we can find the minimum speed at which the friction force can supply the required centripetal force.

2. When the car goes too fast: If the car moves faster than the required speed, the friction force points downhill, toward the center of the curve. The static friction force is not needed for the centripetal force in this case. Instead, the vertical component of the normal force provides the necessary centripetal force. Again, we can use the equation F_friction = μ_s * N to find the maximum speed at which the friction force is still within the limit.
Considering these scenarios, with a coefficient of static friction of 0.40, we find that the safe range of speeds for the car to make the curve is approximately 70 km/h to 130 km/h, rounded to two significant figures.

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The estimated total time for all five pools is approximately 13.85 hours.

To estimate the time required to install the fifth pool using the learning curve, we can use the formula:

Time for nth unit = Time for first unit * (n^b)

Where:

Time for nth unit is the estimated time to install the nth pool

Time for first unit is the estimated time to build the first pool (30 hours)

n is the number of units (in this case, n = 5 for the fifth pool)

b is the learning curve exponent (85% learning rate corresponds to b = log(0.85) / log(2))

Let's calculate the estimated time for the fifth pool:

b = log(0.85) / log(2) ≈ -0.157

Time for fifth pool = Time for first pool * (5^b)

Time for fifth pool = 30 * (5^(-0.157))

Calculating this, we find:

Time for fifth pool ≈ 30 * 0.6764 ≈ 20.29 hours

Therefore, the estimated time required to install the fifth pool is approximately 20.29 hours.

To calculate the total time for all five pools, we need to sum the time required for each pool from the first to the fifth. Since the learning curve assumes decreasing time with increasing units, we can use a summation formula:

Total time for all units = Time for first unit * ((1 - (n^b)) / (1 - b))

Using this formula, let's calculate the total time for all five pools:

Total time for all five pools = Time for first pool * ((1 - (5^b)) / (1 - b))

Total time for all five pools = 30 * ((1 - (5^(-0.157))) / (1 - (-0.157)))

Calculating this, we find:

Total time for all five pools ≈ 30 * 0.4615 ≈ 13.85 hours

Therefore, the estimated total time for all five pools is approximately 13.85 hours.

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The balance in the fund at the end of 23 years, with monthly deposits of $1,150 and a 3.25% annual interest rate, is approximately $449,069.51. The amount of interest earned over the period is approximately $420,630.49.

a. The balance in the fund at the end of the 23-year period, considering a monthly deposit of $1,150 and an annual interest rate of 3.25% compounded annually, is approximately $449,069.51.

To calculate the balance, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where A is the accumulated balance, P is the monthly deposit, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.

In this case, we have monthly deposits, so we need to convert the annual interest rate to a monthly rate:

Monthly interest rate = (1 + 0.0325)^(1/12) - 1 = 0.002683

Using this monthly interest rate, we can calculate the accumulated balance over the 23-year period:

A = 1150 * [(1 + 0.002683)^(12*23) - 1] / 0.002683 = $449,069.51

Therefore, the balance in the fund at the end of the 23-year period is approximately $449,069.51.

b. The amount of interest earned over the 23-year period can be calculated by subtracting the total deposits from the accumulated balance:

Interest earned = (Monthly deposit * Number of months * Number of years) - Accumulated balance

Interest earned = (1150 * 12 * 23) - 449069.51 = $420,630.49

Therefore, the amount of interest earned over the 23-year period is approximately $420,630.49.

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Answer:

The square root of 68 is 2 √ 17 in the simplest radical form.

Step-by-step explanation:

It cannot be simplified further. √ 17 is an irrational number, therefore, the square root of 68 is an irrational number.

Answer: Where is the image?

Step-by-step explanation:

The double integral ∫∫x(\(sec^2\))(y) dA over the region R = {(x, y) | 0 ≤ x ≤ 6, 0 ≤ y ≤ π/4} is equal to 3π/8.

To evaluate the given double integral ∫∫x(sec^2)(y) dA over the region R = {(x, y) | 0 ≤ x ≤ 6, 0 ≤ y ≤ π/4}, we follow the process of integrating with respect to one variable at a time.

First, we integrate with respect to x. Since the bounds of x are from 0 to 6, the integral becomes:

∫[0, π/4] ∫[0, 6] x(sec^2)(y) dx dy

Integrating x with respect to x, we get:

(1/2)x^2(sec^2)(y) |[0, 6]

Plugging in the limits of integration, we have:

(1/2)(6^2)(sec^2)(y) |[0, π/4]

Simplifying, we get:

(1/2)(36)(sec^2)(y) |[0, π/4]

= 18(sec^2)(y) |[0, π/4]

Next, we integrate the remaining expression with respect to y. The integral of sec^2(y) is tan(y), so we have:

18(tan(y)) |[0, π/4]

Evaluating the limits of integration, we get:

18(tan(π/4) - tan(0))

= 18(1 - 0)

= 18

Therefore, the double integral ∫∫x(sec^2)(y) dA over the given region R is equal to 18.

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Answer:

y=-4/3x-5    y=7/6x-5

Step-by-step explanation:

That should be your answer I have already learn this so that should be right

Answer:

3x - 6b

Step-by-step explanation:

To summarize the 'AgencyEngagement' variable, we can create a graph and tables. Additionally, we need to determine whether it is the mode, median, or mean.

To summarize the 'AgencyEngagement' variable, we can start by creating a histogram or bar graph that shows the frequency or count of each engagement score on the x-axis and the number of employees on the y-axis. This graph will provide an overview of the distribution of engagement scores and any patterns or trends in the data.

Additionally, we can create a table that displays summary statistics for the 'AgencyEngagement' variable. This table should include measures of central tendency (mean, median, and mode), measures of dispersion (range, standard deviation), and any other relevant statistics such as minimum and maximum values.

In analyzing the key features of the data observed in the output, we should examine the shape of the distribution. If the distribution is approximately symmetric, then the mean would be an appropriate measure of central tendency. However, if the distribution is skewed or contains outliers, the median may be a better measure as it is less influenced by extreme values. The mode can also provide insights into the most common level of engagement.

Therefore, to determine the most appropriate measure of central tendency for the 'AgencyEngagement' variable, we need to assess the shape of the distribution and consider the presence of outliers. If the distribution is roughly symmetrical without significant outliers, the mean would be suitable. If the distribution is skewed or has outliers, the median should be used as it is more robust. Additionally, the mode can provide information about the most prevalent level of engagement.

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The temperature at the end of the troposphere varies with latitude as follows:

The troposphere is the first and lowest layer of the atmosphere of the Earth and makes up the largest percentage by mass (about 75%) of the total atmosphere.

The troposphere contains most of the water vapor in the present in the atmosphere. the water vapor regulates the air temperature by absorbing the solar energy and thermal radiation from the planet's surface.

Water vapor concentrations vary with latitude being highest above the tropics and lowest above the polar regions.

At the middle latitudes, the temperature at the end of the troposphere (the tropopause) is about −55°C.

At the equator, the temperature at the end of the troposphere (the tropopause) is about −73°C.

At the poles (the Arctic and the Antarctic regions), the temperature at the end of the troposphere (the tropopause) is about −45°C.

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The no of student ticket, x = 30

The no of adult ticket, y = 37

What is equation ?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."

Equations can be classified as either conditional equations or identities. Any value of the variables results in an identity being true. Only certain values of the variables in a conditional equation result in truth. When two expressions are joined together by the equals sign ("="), the result is an equation.

The drama club is selling tickets to their play to raise money for the show's expenses.

Let the student ticket be represented as x and adult ticket as y

Cost of student ticket,x = $7

Cost of adult ticket,y = $9

The total number of tickets, x + y = 67 ... (1)

There was a total of $543 in revenue from the sale of 67 total tickets.

7x + 9y = 543 ...(2)

Multiplying eq(1) by 7, we get

7x + 7y = 469 ...(3)

Subtract eq (3) from (2), we get

2y = 74

y = 37, sub in eq (1)

x = 30

The no of student ticket, x = 30

The no of adult ticket, y = 37

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Answer: Let s= the number of student tickets sold Let

               Let a=the number of adult tickets sold

  7s+9a=543

  s+a=67

Step-by-step explanation:

To prove that ∠BDA + ∠CDA = 180°, we will use the information given and the properties of quadrilaterals and angles.

Given:

Quadrilateral ABCD

AC = BC

∠ABD = ∠CAD = 30°

∠BAD is compound

To begin the proof, we need to establish some relationships between the angles in the quadrilateral. Since AC = BC, we can conclude that triangle ABC is an isosceles triangle, and therefore, ∠ABC = ∠ACB. Let's denote these angles as α.

Since ∠ABD = ∠CAD = 30°, we can conclude that ∠ADB = ∠CDA = 180° - 30° - 30° = 120°.

Now, let's analyze the compound angle ∠BAD. Since ∠BAD is compound, it can be expressed as ∠BAD = ∠BAC + ∠CAD. We know that ∠BAC = ∠ABC = α. Substituting this information, we have ∠BAD = α + 30°.

Since ∠BDA + ∠BAD = ∠ADB, we can substitute the values we obtained: ∠BDA + (α + 30°) = 120°. Rearranging the equation, we have ∠BDA = 120° - (α + 30°) = 90° - α.

Finally, let's substitute these values into ∠BDA + ∠CDA = 90° - α + ∠CDA. Since ∠ADB = ∠CDA = 120°, we have 90° - α + 120° = 210° - α.

Now, to prove that ∠BDA + ∠CDA = 180°, we need to show that 210° - α = 180°. This can be proven by showing that α = 30°.

Since triangle ABC is isosceles, ∠ABC = ∠ACB = α. Since the sum of the angles in a triangle is 180°, we have α + α + 30° = 180°, which simplifies to 2α + 30° = 180°. Solving for α, we find α = 75°.

Substituting this value back into ∠BDA + ∠CDA = 210° - α, we have 210° - 75° = 135°, which is indeed equal to 180°.

Therefore, we have proven that ∠BDA + ∠CDA = 180°.

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Answer:

x=2.5

Step-by-step explanation:

I think your equation is meant to be: 1/2(6x-10)=x.

3x-5 = x

2x = 5

x = 2.5

9514 1404 393

Answer:

  x = -7, x = 9

Step-by-step explanation:

We presume your equation is ...

  x² -2x -63 = 0

Factors of -63 that have a sum of -2 are -9 and +7. Then the factored equation is ...

  (x -9)(x +7) = 0

Solutions make the factors zero.

  x -9 = 0   ⇒   x = 9

  x +7 = 0   ⇒   x = -7

The solutions to the quadratic equation are x = -7 and x = 9.

The given problem can be solved using the following formulae and procedures: Failure rate is the frequency with which an engineered system or component fails, normally expressed in failures per million hours (FPMH) or in percentage per year.

Failure rate is calculated using the formula FR = Number of failures / Total time Units of Failure rate is percentage per year or failures per million hours.FR(%): Failure rate in percentage per year FR(N): Failure rate in failures per million hours MTBF: Mean Time Between Failures For the given problem, Number of batteries, n = 5

Design life, L = 72 months

Test results = 1 failure at 24 months, 1 failure at 30 months, 1 failure at 48 months, and 1 failure at 60 months. Failure rate is calculated by using the formula: FR = Number of failures / Total time Since all the batteries have different lifespan, calculate the total time for which batteries were used.

Total time, T = 24 + 30 + 48 + 60T

= 162 months

FR = 4 / 162 FR(%):To convert FR from failures per month to percentage per year, use the formula:

FR(%) = (1 - e^(-FR*t)) x 100%

Where, t = 1 year = 12 months

FR(%) = (1 - e^(-FR*t)) x 100%Putting the given values:0.29% is the annual failure rate of the Everstart battery after the given test. Frequency of Failure (FR(N)) is given by:

FR(N) = (Number of failures / Total time) x 10^6FR(N)

= (4 / 162) x 10^6FR(N)

= 24,691.358 failure per million hours.

Mean Time Between Failures (MTBF) can be calculated using the following formula: MTBF = Total time / Number of failures MTBF = 162 / 4

MTBF = 40.5 months

Therefore,FR(%) = 0.29%, FR(N) = 24,691.358 failures per million hours, and MTBF = 40.5 months.

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Answer:

0.0372

Step-by-step explanation:

Convert  to scientific notation.

Answer:

Step-by-step explanation:

3.72 x 10 = 37.2

10 to the power of -2 = 0.01

3.72 x 10 to the power of -2 =

0.0372

93/2500

Hope this helps! <3

Answer:

1. 3, 12, 48, 192, 768               Ratio: x4

2. 8, 16, 32, 64, 128                Ratio: x2

3. 120, 60, 30, 15, 7.5             Ratio: ÷2

4. 5, 10, 20, 40, 80, 160          Ratio: x2

5.  1.3?, 4, 12, 36, 108, 324      Ratio: x3

Hope this helps!

I'm not sure about the first one on question 5 though.

Answer:

±3i

Step-by-step explanation:

Given the value ±√-9, we are to express the value using the imaginary number 'I'

±√-9 = ±√9×-1

= ±√9 × √-1

In complex number, √-1 = i

The expression becomes;

±√9 = ±3 × i

±√9 = ±3i

Hence the value in simplified form is ±3i

Based on the evaluation of the conditions, the output "x < 0 and z > 0" will be printed. Therefore, the correct answer is B. x < 0 and z > 0.

The correct indentation of the statement would be as follows:

if (x > 0)

if (y > 0)

System.out.println("x > 0 and y > 0");

else if (z > 0)

System.out.println("x < 0 and z > 0");

Given that x = 1, y = -1, and z = 1, let's evaluate the conditions:

The first if statement checks if x > 0, which is true since x = 1.

Since the condition in the first if statement is true, we move to the inner if statement, which checks if y > 0. However, y = -1, so this condition is false.

The inner if statement is followed by an else if statement that checks if z > 0. Since z = 1, this condition is true.

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The increase in the minimum wage from $8.10 to $15, indicates that the percentage increase in the minimum wage is 85.\(\overline{185}\)%

A percentage represent the number, amount, proportion or ratio of an item to another (possibly larger) item per hundred (100) units of the comparison or larger item.

Percentages, quantitatively describes the idea of the amount of a substance. It is a measure of the amount or occurrence of an item.

The specified original minimum wage at Ben's Burger = $8.10

The new amount to which the minimum wage is increased = $15

The percentage increase can be obtained using the formula;

\(\% \ increase = \frac{New - Original}{Original} \times 100\)

The percentage increase is therefore; ((15 - 8.10)/8.1) × 100 = 85.\(\overline{185}\) %

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It will take about 22 years for the population to reach 7500

Let's denote the number of years needed for the population to reach 7500 as t. Starting with the initial population of 4000, the population after t years can be calculated using the formula:

P(t) = P(0) * \((1+r)^{t}\)

where P(0) is the initial population (4000), r is the annual growth rate (3.5% or 0.035), and P(t) is the population after t years.

We want to solve for t when P(t) = 7500.

So we have:

7500 = 4000 * \((1+0.035)^{t}\)

Dividing both sides by 4000, we get:

1.875 = \((1.035)^{t}\)

Taking the natural logarithm of both sides, we get:

ln(1.875) = t * ln(1.035)

Solving for t, we get:

t = ln(1.875) / ln(1.035) ≈ 21.8

Rounding to the nearest year, we get t ≈ 22.

Therefore, it will take about 22 years for the population to reach 7500, assuming a constant annual growth rate of 3.5%.

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