the life of light bulbs is distributed normally. the variance of the lifetime is 900 and the mean lifetime of a bulb is 580 hours. find the probability of a bulb lasting for at most 610 hours. round your answer to four decimal places.

The two equations that are true for x = –2 and x = 2 are:

x2 – 4 = 0 (true for x = –2) and 4x2 = 16 (true for x = –2 and x = 2)

Quadratic equation can be defined as equation in which it is in the form of[tex]ax^2+bx+c = 0[/tex]

The options are:

x2 – 4 = 0

x2 = –4

3x2 + 12 = 0

4x2 = 16

2(x – 2)2 = 0

To check which equations are true for x = –2 and x = 2, we can substitute these values into each equation and see if it results in a true statement or not.

Substituting x = –2:

(-2)2 – 4 = 0 --> True

(-2)2 = –4 --> False

3(-2)2 + 12 = 0 --> True

4(-2)2 = 16 --> True

2((-2) – 2)2 = 0 --> False

Substituting x = 2:

22 – 4 = 0 --> False

22 = –4 --> False

3(2)2 + 12 = 0 --> False

4(2)2 = 16 --> True

2((2) – 2)2 = 0 --> True

Therefore, the two equations that are true for x = –2 and x = 2 are:

x2 – 4 = 0 (true for x = –2) and 4x2 = 16 (true for x = –2 and x = 2)

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We need to add approximately 14.86 mL of water to 14 mL of 14% alcohol solution to reduce the concentration to 7%.

First, let's figure out how much alcohol is in the first 14 mL of the 14% alcohol solution.

Alcohol is equal to 0.14 x 14 (14%) times 14%, or 1.96 mL.

We need to add water so that the amount of alcohol stays the same while the overall volume grows in order to lower the concentration to 7%.

Assume that x mL of water needs to be added.

The volume of the solution will be (14 + x) mL with the addition of x mL of water, while the amount of alcohol will remain at 1.96 mL.

The equation for the ultimate concentration can be written as follows:

1.96 mL / (14 + x) mL = 0.07

When we find x and simplify, we get:

x = (1.96 mL / 0.07) - 14 mL

x ≈ 14.86mL

In order to lower the concentration to 7%, we must therefore add around 14.86 mL of water to 14 mL of 14% alcohol solution.

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The value of 135 kg into lbs can be converted by multiplying kilogram by 2.204622  so the answer is 297.624 pounds.

Unit conversion is the process of converting the measurement of a given amount between various units, often by multiplicative conversion factors that alter the value of the measured quantity without altering its effects.

The SI unit of mass is the kilogramme (kg). It has the same mass as the international kilogramme prototype. The International Bureau of Weights and Measures maintains a platinum-iridium international prototype similar to this one. A kilogramme is about equivalent to 2.20462262184878 pounds.

The legal definition of a pound, or the international avoirdupois pound, is 0.45359237 kilogrammes.

Pounds = kilograms × 2.20462262184878

= 135 x 2.20462262184878

= 297.624 pounds or lbs.

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Answer:

yeah sure, what you need?

Answer:

110

Step-by-step explanation:

Answer: You only need to write the formula then rewrite it then multiply then add and then you divive by 2

Step-by-step explanation: it is the top of the shape which is 10cm2

Answer:

$18.27 an hour

Step-by-step explanation:

To figure out how much $38,000 a year is as an hourly wage, divide $38,000 by 40 hours and 52 weeks. So if you were to work full-time, 40 hours a week, making $38,000 a year, you would earn $18.27 an hour.

Anaiah is currently spending $150 on eggplants and kiwis.

Anaiah is behaving irrationally, because

1) He is not spending his entire income

2) He is spending too much on kiwis

3) He is not balancing what he spends on each good

4) His marginal utility per dollar spent is not the same for both goods.

Currently, Anaiah is spending:

On eggplants: 20 x $3 = $60

On kiwis: 30 x $3 = $90

Total spending: $60 + $90 = $150

Therefore, Anaiah is currently spending $150 on these goods.

The reasons that Anaiah is behaving irrationally are:

He is not spending his entire income: Anaiah has $180 to spend but he is only spending $150, which means he is not maximizing his utility by fully utilizing his budget.

He is spending too much on kiwis: Anaiah's marginal utility per dollar spent on kiwis is lower than his marginal utility per dollar spent on eggplants. Therefore, he should be spending more on eggplants and less on kiwis to maximize his utility.

He is not balancing what he spends on each good: Anaiah is consuming 20 eggplants and 30 kiwis, which means he is not allocating his budget efficiently to maximize his total utility. He should be consuming a combination of eggplants and kiwis that gives him the highest total utility within his budget constraint.

His marginal utility per dollar spent is not the same for both goods: Anaiah's marginal utility per dollar spent on eggplants is 160 utils while his marginal utility per dollar spent on kiwis is 190 utils. Therefore, he should be consuming more eggplants and fewer kiwis to maximize his total utility within his budget constraint.

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The solution is, Loan origination fee = $696

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

Given:

Home value = $58,000

Loan-to-value loan = 80%

Loan origination fee = 1.5 points = 1.5%

Find:

Loan origination fee = ?

Computation:

Total loan amount = Home value × Loan-to-value loan

Total loan amount = $58,000 × 80%

Total loan amount = $46,400

Loan origination fee = Total loan amount × 1.5%

Loan origination fee = $46,400 × 1.5%

Loan origination fee = $696

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Answer:

Step-by-step explanation:

Find the sum: 9/10 9/100

A: 18/100

B: 90/100

C: 18/10

D; 99/100

9/10 = 90/100

so

90/100 + 9/100 = 99/100

Answer: D 99/100 I hope this helps

Step-by-step explanation:

9/10+9/100

Write all numerators above the least common denominator 100

90+9/100

Add the numbers 90+9 which would will give you your answer

99/100

Yes, 0.5 - 3(-2x - 1 over 3 + 4 + 8x) and -1.5(12x + 7) are equivalent expressions.


To prove this, we can use the distributive property:

0.5 - 3(-2x - 1 over 3 + 4 + 8x)

= 0.5 - 3(-2x/3 - 1/3 + 4/3 + 8x/3)

= 0.5 - (-6x - 1 + 4 + 24x)/3

= (0.5*3 + 6x + 1 - 4 - 24x)/3

= (-1.5*12x - 1.5*7)/3

= -1.5(12x + 7)
No, 0.5 - 3(-2x -1 over 3 +4 + 8x) and -1.5(12x +7) are not equivalent expressions.

To determine if two expressions are equivalent, we can simplify both expressions and compare them.

For the first expression, 0.5 - 3(-2x -1 over 3 +4 + 8x), we can distribute the -3 and combine like terms:

0.5 - 3(-2x) - 3(-1) - 3(3) - 3(4) - 3(8x)
= 0.5 + 6x + 3 - 9 - 12 - 24x
= -18x - 7.5

For the second expression, -1.5(12x +7), we can distribute the -1.5:

-1.5(12x) - 1.5(7)
= -18x - 10.5

As we can see, the simplified expressions are not the same, so they are not equivalent expressions.

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The two smaller positive integers are:

m = 675

n = 45

And the sum is 675

We know that we have two positive integers, m and n.

And we know that:

3*m³ = 5*n⁵

One way of finding the numbers is evaluating one of the two in positive integers, until we get that the other one is also an integer.

For example,we can solve this for m to get:

m³ = (5/3)*n⁵

m = ∛((5/3)*n⁵)

Now just evaluate in different integer values of n.

if n = 3 we will get:

m = ∛((5/3)*3⁵) =  ∛(405) = 7.39

So this is not a solution.

Now I will use n = 45 = 5*3*3 (so all the exponents inside the cubic root are multiples of 3)

m = ∛((5/3)*(5*3²)⁵)

m = ∛(5⁶*3⁹) = 5²*3³ = 25*27 = 675

Then the sum is:

45 + 675 = 720

These is the smaller sum.

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8)

The indicated 3th root of 125 is 5.

9)

The indicated 4th root of 81 is 3.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

8)

∛125

5 x 5 x 5 = 125

And,

5³ = 125

So,

= ∛5³

= 5

9)

[tex]\sqrt[4]{81}[/tex]

3 x 3 x 3 x 3 = 81

And,

[tex]3^4[/tex] = 81

So,

= [tex]\sqrt[4]{3^4}[/tex]

= 3

Thus,

8)

∛125 is 5.

9)

[tex]\sqrt[4]{81}[/tex] is 3.

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It has to be smaller than $7800

I am not sure if this answer is right.

Answer:

7800-936=6864

Step-by-step explanation:

x/12 7800/100

100x=93600

936

The cone’s radius r in terms of x is x + 7

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

Volume, V = 3πx^2 + 42πx + 147π

Height, h = 9

The volume of a cone is

V = 1/3πr^2h

Substitute the known values in the above equation, so, we have the following representation

1/3πr^2 * 9 = 3πx^2 + 42πx + 147π

So, we have

3πr^2 = 3πx^2 + 42πx + 147π

Divide by 3π

r^2 = x^2 + 14x + 49

So, we have

r = √(x² + 14x + 49)

Take the square roots of both sides

r = x + 7

Hence, the value of r is x + 7

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Answer:

Step-by-step explanation:

The function to represent the population of bacteria after t days can be written as:

P(t) = P0 * (1 + r)^t

where P0 is the initial population (7500), r is the daily growth rate (14% = 0.14), and t is the number of days.

Substituting the values, we get:

P(t) = 7500 * (1 + 0.14)^t

Simplifying, we get:

P(t) = 7500 * 1.14^t

To find the percentage rate of change per hour, we need to convert the daily growth rate to an hourly growth rate. Since there are 24 hours in a day, the hourly growth rate, denoted by h, is given by:

h = (1 + r)^(1/24) - 1

Substituting the value of r, we get:

h = (1 + 0.14)^(1/24) - 1

= 0.005521

So, the percentage rate of change per hour is:

h * 100% = 0.5521%

Rounding to the nearest hundredth of a percent, we get:

h * 100% ≈ 0.55%

Recursive form of sequence is given by f(n)  = f(n-1) - 3

What is function?

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

The explicit form of sequence is  given as

      f(n) = −3n + 2

So nth term is given by

           f(n) = −3n + 2

(n-1)th term is given by    

           f(n-1) = −3(n-1) + 2

We have

         f(n) -  f(n-1) = −3n + 2 - (−3(n-1) + 2)

          f(n) -  f(n-1) = −3n + 2 +3(n-1) - 2

          f(n) -  f(n-1) = −3n + 2 +3n -3 - 2

          f(n) -  f(n-1) = -3

          f(n)  = f(n-1) - 3

Recursive form of sequence is given by f(n)  = f(n-1) - 3

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In observational studies, the variable of interest The correct answer is (a) is not controlled.

The variables are measured as they occur naturally, without any manipulation or intervention by the researcher. Therefore, the variable of interest is not controlled in observational studies.

Observational studies are used in situations where it is not feasible or ethical to conduct controlled experiments, such as in studies of the effects of environmental exposures or lifestyle factors on health outcomes. In these studies, the researcher cannot control the exposure or intervention and must rely on observational data to draw conclusions about the relationship between the exposure and the outcome.

The other options are not correct because:

b. If the variable of interest is controlled, then the study is a controlled experiment, not an observational study.

c. The variable of interest can be numerical or categorical in observational studies.

d. The variable of interest does not have to be numerical in observational studies, as it can also be a categorical variable

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The sum of the measures of the interior angles of a polygon with n sides can be found using the formula (n-2) * 180 degrees.

For a 10-sided figure, we have (10-2) * 180 = 8 * 180 = 1,440 degrees.

Therefore, the sum of the measures of the interior angles of a 10-sided figure is 1,440°.

The answer is A.

Answer:

u < 11

Step-by-step explanation:

u + 7 < 18

u < 11

To solve the inequality:

u + 7 < 18

We need to isolate the variable u on one side of the inequality symbol.

Subtracting 7 from both sides, we get:

u < 18 - 7

Simplifying the right-hand side, we get:

u < 11

Therefore, the solution to the inequality is:

u < 11

In interval notation, the solution is:

(-∞, 11)

The volume of the solid generated when the region bounded by y = 9x and y = 27x/x is revolved around the x-axis is given by V = 27lnx - 9x + c

To calculate this volume, we need to calculate the area of the cross-section of a shell at x.

The cross-section is found by taking the difference of the two curves, y = 9x and y = 27x/x, at that particular x in the form of a rectangle.

The height of the rectangle is y₂ - y₁ and the width is the interval dx. Therefore, the area of the cross-section is given by

A(x) = (y₂ - y₁)dx = [(27x/x - 9x)dx].

The volume of the solid is then given by the formula

=> V = ∫A(x)dx.

Substituting in the expression for A(x), we have

=>  V = ∫(27x/x - 9x)dx.

Integrating this expression, we get V = 27lnx - 9x + c, where c is an arbitrary constant.

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Trigonometric functions derivative is a method for calculating how quickly trigonometric functions change in relation to a variable angle.

Differentiation of trigonometric functions refers to the process of determining a trigonometric function's derivatives. In other words, finding the rate of change of the function with respect to the variable is what is meant by the differentiation of trigonometric functions. There are differentiation formulas for the six trigonometric functions that can be applied to a variety of derivative application issues.

The sine (sin x), cosine (cos x), tangent (tan x), cotangent (cot x), secant (sec x), and cosecant are the six fundamental trigonometric functions (cosec x).

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The least common denominator is [tex](x^2-3x-4)/(x-4)(x+1) + (x^2-6x+8)/(x-4)(x-2) = 2/(x-4)(x+1)(x-2)[/tex]

Simply put, a rational expression is the product of two polynomials. Or to put it another way, it is a fraction using polynomials as the numerator and denominator.

Reasonable expressions resemble fractions with variable denominators (and often numerators too).

For rational expressions, any value can be entered with the exception of those that set the denominator to 0 (because division by 0 is an undefinable operation).

In other words, all real numbers other than those that make a rational expression's denominator zero are included in the domain of a rational expression.

[tex]x^2-3x-4 = (x-4)(x+1)\\x^2-6x+8 = (x-4)(x-2)[/tex]

The least common denominator is: [tex](x-4)(x+1)(x-2)[/tex]

To add these two rational expressions, we need to rewrite each of them with the LCD as the denominator:

[tex](x^2-3x-4)/(x-4)(x+1) = [(x-4)(x+1)]/(x-4)(x+1)(x-2) = 1/(x-2)\\(x^2-6x+8)/(x-4)(x-2) = [(x-4)(x-2)]/(x-4)(x+1)(x-2) = 1/(x+1)[/tex]

So the sum of the numerators is 1 + 1 = 2.

Therefore,[tex](x^2-3x-4)/(x-4)(x+1) + (x^2-6x+8)/(x-4)(x-2) = 2/(x-4)(x+1)(x-2)[/tex]

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(a) To find the probability that a randomly selected adult who visited a therapist during the past year also used antidepressants, we use the formula:

P(A|B) = P(A and B) / P(B)

where A is the event that an adult used antidepressants, and B is the event that an adult visited a therapist. We are given:

P(A) = 0.43

P(B) = 0.27

P(A and B) = 0.20

Plugging these values into the formula, we get:

P(A|B) = 0.20 / 0.27 ≈ 0.74

Therefore, the probability that a randomly selected adult who visited a therapist during the past year also used antidepressants is approximately 0.74.

(b) To find the probability that an adult visited a therapist during the past year, given that he or she used antidepressants, we use Bayes' theorem:

P(B|A) = P(A|B) * P(B) / P(A)

where A and B are defined as before. We have already calculated P(A|B) and P(B), and we know:

P(A) = 0.43

Plugging these values into Bayes' theorem, we get:

P(B|A) = (0.74 * 0.27) / 0.43 ≈ 0.47

Therefore, the probability that an adult visited a therapist during the past year, given that he or she used antidepressants, is approximately 0.47.

Anil borrowed the sum of money $12,300 on rate of 10% per annum, for a period of 5 years.

We can use the simple interest formula to solve this problem:

Simple Interest = (Principal x Rate x Time) / 100

Where,

Principal = 12,300

Rate = 10% per annum

Simple Interest = 18,450 - 12,300 = 6,150

Substituting the given values in the formula, we get:

6,150 = (12,300 x 10 x Time) / 100

Simplifying the equation, we get:

Time = (6,150 x 100) / (12,300 x 10)

Time = 5 years

Therefore, Anil borrowed the money for a period of 5 years. Simple interest is a type of interest calculation where the interest is calculated only on the principal amount borrowed or invested. It is calculated as a percentage of the principal amount, multiplied by the time period of the loan or investment. Simple interest does not take into account any interest earned on interest, unlike compound interest. It is a straightforward method used to determine the total amount to be repaid on a loan or the interest earned on an investment. Simple interest is commonly used in personal loans, small business loans, and short-term investments.

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Using integration by substitution, the value of ∫31xf(x^2-1)dx is 6.

To solve this problem, we can use integral by substitution.

Let's set u = x^2 - 1, then du/dx = 2x, or dx = du / (2x).

Using this substitution, we can rewrite the integral as:

∫(3^2-1)^(8^2-1) f(u) * (du / 2)

Next, we can use the fact that f is continuous and the integral of f from 8 to 0 is 6. We can split the integral into two parts:

∫(3^2-1)^(8^2-1) f(u) * (du / 2) = ∫0^(8^2-1) f(u) * (du / 2) - ∫0^(3^2-1) f(u) * (du / 2)

The first integral on the right-hand side is the integral we're given:

∫0^(8^2-1) f(u) * (du / 2) = 6

The second integral can be rewritten using our substitution:

∫0^(3^2-1) f(u) * (du / 2) = ∫(3^2-1)^(0) f(u) * (du / 2)

Notice that we've switched the limits of integration, which means we need to negate the integral:

∫(3^2-1)^(0) f(u) * (du / 2) = -∫0^(3^2-1) f(u) * (du / 2)

Substituting back into our original integral and using these results, we get:

∫(3^2-1)^(8^2-1) f(u) * (du / 2) = 6 - (-∫0^(3^2-1) f(u) * (du / 2)) = 6 + ∫0^(3^2-1) f(u) * (du / 2)

Finally, we can substitute back in for x and simplify to get our answer:

∫31xf(x^2-1)dx = (1/2) * ∫(3^2-1)^(8^2-1) f(u) * du = (1/2) * (6 + ∫0^(3^2-1) f(u) * du) = (1/2) * (6 + ∫0^8 f(u) * du) = (1/2) * (6 + 6) = 6

∫31xf(x^2-1)dx  = 6.

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The total of a hexagon's internal angles is 720 degrees.

The internal angles of a hexagon may be calculated using the formula "180 - (360/n)," where n is the number of sides. When you enter 6 for a hexagon, the response is 120 degrees.

We might begin by imagining a hexagon to better comprehend the notion. It is a basic design made up of six distinct straight lines that join to form a closed shape. The internal angles are the angles on the inside of the form.

The above-mentioned formula may be used to compute the internal angles of a hexagon. For each inner angle of a hexagon, the computation yields a value of 120 degrees. Hence the total of a hexagon's internal angles is 720 degrees.

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The line of the best fit of the scatter plot is added as an attachment

The missing graph is added as an attachment

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

The graph

A good line of best fit would have equal number of points on either sides

To plot the graph, we draw a line that divides the points on the graph evenly

This line when drawn on the scattered points divided the points approximately evenly

The line is not a proportional relationship because it does not go through the origin

Hence, the line of the best fit is attached

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