3. the town you live in has decided to limit the amount of trash thrown out each month. your town, which has homes, has asked each household to keep track of how many pounds of trash they produce during a month. in addition, the town council has found that other sources of trash, such as local businesses, combine to create lbs of trash each month. if the town has a goal of creating less than lbs of trash, how much trash should a household be limited to? write an inequality for this situation and solve it.

The correct answer is option  A: The random variable is discrete. A decibel is a unit of measure used to quantify the loudness or intensity of sound.

From 0 dB (the quietest level of sound) to 140 dB (the loudest level of sound), it is measured on a logarithmic scale (the highest level of sound).

The decibel level of a siren is normally between 110 and 120 dB, which is regarded to be within or close to the threshold of human hearing.

The decibel level of a siren is measured on a logarithmic scale, making it a discrete variable. This indicates that it is measured in whole numbers rather than fractions of a decibel.

For instance, a siren's decibel level can be 110 dB, 111 dB, 112 dB, etc., but it cannot be 110.5 dB or 111.5 dB. Therefore, the decibel level of a siren is a discrete variable.

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Answer:

The solution to the equation 5i + 4 = 14 + 4i is i = 10.

Step-by-step explanation:

To solve for i in this equation, isolate the variable (i) on one side of the equation. To do this, we'll subtract 4 from both sides:

5i + 4 - 4 = 14 + 4i - 4

This leaves us with:

5i = 10 + 4i

Next, we'll subtract 4i from both sides:

5i - 4i = 10 + 4i - 4i

This leaves us with:

i = 10.

So the solution to the equation 5i + 4 = 14 + 4i is i = 10.

Answer:

The distance between Francesca's house and Camp  Sunshine is 214.7 units. Step-by-step explanation: Hope am right!

The exact value for each trigonometric function are -12/13, -5/13 and 12/5

To find the reference angle, we can use the properties of right triangles. We can draw a line from the point (-5, 12) to the x-axis to form a right triangle. The hypotenuse of the triangle is the distance from the point (-5, 12) to the origin, which is the square root of the sum of the squares of the x and y coordinates:

√((-5)² + 12²) = 13

The reference angle is the acute angle between the x-axis and the adjacent side of the triangle, which is the x-coordinate of the point (-5, 12) divided by the hypotenuse:

cosθ = -5/13

θ = arccos(-5/13)

θ ≈ 2.214 radians

The angle's standard form is given by the equation:

θ = n(2π) ± α

where n is an integer, and α is the angle's reference angle. Since the point (-5, 12) is in the second quadrant, the angle's terminal side intersects the unit circle at an angle of θ = π + α. Therefore, the standard form of the angle is:

θ = (2n + 1)π - arccos(-5/13)

To find the exact value of the trigonometric functions of this angle, we can use the properties of the unit circle. Since the sine function is positive in the second quadrant, we have:

sinθ = sin(π + α) = -sinα = -12/13

Similarly, since the cosine function is negative in the second quadrant, we have:

cosθ = cos(π + α) = -cosα = -5/13

Finally, since the tangent function is the ratio of the sine and cosine functions, we have:

tanθ = tan(π + α) = -tanα = 12/5

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47.5% between 38 and 52 requests for new lightbulbs have been made.

Given,

The physical plant at the main campus of a large state university receives daily requests to replace fluorescent light bulbs.

The mean of the distribution, μ = 52

Standard deviation, σ = 7

We have to find the  approximate percentage of lightbulb replacement requests numbering between 38 and 52 using empirical rule;

Here,

z score corresponding to 38 and 52

z score = (x - μ) / σ = (38 - 52) / 7 = -2

Now,

z score corresponding to 52

z score = 52 -52 / 7 = 0/7 = 0

We are aware that, in accordance with the empirical rule, 68% of the data are within one standard deviation of the mean and 95% are within two.

By comparing the z-scores of data point 38 and 52, we can observe that data point 38 is at the mean. 38 is therefore -2 standard deviations above the mean. That is -2σ to 2σ

The center of the normal distribution curve is known to be the mean. Therefore, we will divide 95% by 2 to obtain the percentage of data points 2 SD above the mean.

95/2 = 47.5%

As a result, 47.5% between 38 and 52 requests for new lightbulbs have been made.

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Answer:

602 .6

Step-by-step explanation:

∴14,400=160b

⇒b=90m

902m=45m

2πr=2π×45≈282.6m

320m+282.6m=602.6m

Answer:

Step-by-step explanation:

you find the L.C.M

18 234 270 324

 13 13 15 18

3 1 15 18

 5 1 5 6

 6 1 1

 1 1 1 ans=18×13×3×5×6=21060

We can see here that the sum of money will be: Rs. 12970.

Compound interest is the interest that is earned not only on the original amount of money that is invested or borrowed but also on any interest that has been previously earned or charged. In other words, it is interest that is calculated on both the principal amount and the accumulated interest.

By using the formula to calculate amount on which interest is compounded annually,

A = P(1+ r/100)^10

=5000(1+ r/100)^10

=5000(1.1)^10

=5000×2.594

= Rs. 12970

​

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After approximately 12.13 years, the revenue of this firm is going to drop to $1 million.

The value of shares t years after their floatation on the stock market, is modelled by V = 10e0.09t

The initial value of shares = V when t = 0. So, putting t = 0 in V = 10e0.09t,

we get

V = 10e0.09 × 0= 10e0 = 10 × 1 = 10 million dollars.

The values after 5 years, 10 years and 12 years, respectively are:

For t = 5, V = 10e0.09 × 5 ≈ 19.65 million dollarsFor t = 10, V = 10e0.09 × 10 ≈ 38.43 million dollarsFor t = 12, V = 10e0.09 × 12 ≈ 47.43 million dollars

The total revenue (TR) in t years' time is modelled as TR = 10e−0.19t (in million dollars)

The current revenue is the total revenue when t = 0.

So, putting t = 0 in TR = 10e−0.19t, we get

TR = 10e−0.19 × 0= 10e0= 10 million dollars

Revenue in 5 years' time is TR when t = 5.

So, putting t = 5 in TR = 10e−0.19t, we get

TR = 10e−0.19 × 5≈ 4.35 million dollars

To find when the revenue of this firm is going to drop to $1 million, we need to solve the equation TR = 1.

Substituting TR = 1 in TR = 10e−0.19t, we get1 = 10e−0.19t⟹ e−0.19t= 0.1

Taking natural logarithm on both sides, we get−0.19t = ln 0.1 = −2.303

Therefore, t = 2.303 ÷ 0.19 ≈ 12.13 years.

So, after approximately 12.13 years, the revenue of this firm is going to drop to $1 million.

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The number of oranges that are expected to weigh more than 4 oz is:

1400 - (1400 × 0.0228)≈ 1368.

The mean weight of the oranges growing in an orchard is 8 oz and standard deviation is 2 oz, the distribution of the weight of oranges can be represented as normal distribution.

From the batch of 1400 oranges, the number of oranges is expected to weigh more than 4 oz can be found using the formula for the Z-score of a given data point.

\(z = (x - μ) / σ\)

Wherez is the Z-score of the given data point x is the data point

μ is the mean weight of the oranges

σ is the standard deviation

Now, let's plug in the given values.

\(z = (4 - 8) / 2= -2\)

The area under the standard normal distribution curve to the left of a Z-score of -2 can be found using the standard normal distribution table. It is 0.0228. This means that 0.0228 of the oranges in the batch are expected to weigh less than 4 oz.

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The variance of the distribution is 0.964.

What is the variance?

The squared deviation from the mean of a random variable is referred to as variance in probability theory and statistics. The square of the standard deviation is another common way to express variation. Variance is a measure of dispersion, or how far apart from the mean a group of data are from one another.

Here, we have

Given:

x    P(r)

0    0.130

1      0.346

2     0.346

3      0.154

4       0.026

We have to find the variance of the distribution.

Var(X) = E(X²) - (E(X))²...(1)

E(X²) = ∑x²Pₓ(X=x)

E(X²) = 0×0.130 + 1²×0.346 + 2²×0.346 + 3²×0.154 + 4²×0.026

E(X²) = 3.532

Now,

E(X) = ∑xPₓ(X=x)

E(X) =  0×0.130 + 1×0.346 + 2×0.346 + 3×0.154 + 4×0.026

E(X) = 1.604

Now, we put the value of E(X) and E(X²) in equation (1) and we get

Var(X)  = 3.532 - (1.604)²

Var(X)  = 0.95918

Var(X)  = 0.964

Hence, the variance of the distribution is 0.964.

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Answer:

The cost of one candle is $2.

Step-by-step explanation:

First we know that 1 candle holder is $3.50 and Kayla buys 5 candle holders.  3.50 x 5= 17.50 we do this because we have to multiply the price of one candle holder by 5, we then get $17.50. We then subtract 17.50 from 27.50 and that leaves us with 10. So now we know that 5 candles cost $10.  we divide 10 by five and that leaves us with 2. So one candle cost $2.

Ka and Kb are both acid-base equilibrium constants, but they apply to different types of reactions. Ka (acid dissociation constant) is used to describe the dissociation of an acid in water, while Kb (base dissociation constant) is used to describe the dissociation of a base in water.

Specifically, Ka is a measure of the strength of an acid in terms of how easily it donates a proton (H+) to a solvent like water. A higher Ka value indicates a stronger acid, while a lower Ka value indicates a weaker acid. Kb, on the other hand, is a measure of the strength of a base in terms of how easily it accepts a proton (H+) from a solvent like water. A higher Kb value indicates a stronger base, while a lower Kb value indicates a weaker base. There is a mathematical relationship between Ka and Kb for conjugate acid-base pairs, which are molecules or ions that differ by the presence or absence of a single proton. The relationship is expressed by the equation: Ka x Kb = Kw, where Kw is the ion product constant for water, which is 1.0 x 10⁻¹⁴ at 25°C. This relationship shows that the stronger the acid, the weaker its conjugate base, and vice versa.

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Answer:

8xh h=hours

Step-by-step explanation:

8 times how ever much hour than that's all if there's tips well just add it to your answer

The probability that an individual got the flu given that they received the  vaccine is 0.739130435.

What is probability ?

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

Bayes' theorem to solve for the probability that an individual got the flu given that they received the vaccine. Bayes' theorem states that:

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

where P(A|B) is the probability of event A given that event B has occurred, P(B|A) is the probability of event B given that event A has occurred, P(A) is the prior probability of event A, and P(B) is the prior probability of event B.

The probability of event B given that event A has occurred, P(B|A), can be calculated as the general chance of both events happening, which is .27278402.

So, using Bayes' theorem:

P(A|B) = P(B|A) * P(A) / P(B) = .27278402 * .33208489 / .06803995 = .739130435

Therefore, the probability that an individual got the flu given that they received the vaccine is 0.739130435.

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The probability that an individual got the flu is approximately 1.09.

Let's call the probability of receiving a placebo "P(placebo)" and the probability of not getting the flu "P(no flu)". Then, using the information given, we have:

P(placebo) = 0.33208489

P(no flu) = 0.93196005

P(placebo and no flu) = 0.27278402

To find the probability of getting the flu given that they received the vaccine (not a placebo), we can use the formula for conditional probability:

P(flu | vaccine) = P(flu and vaccine) / P(vaccine)

Since the individual either received a placebo or a vaccine (but not both), the probability of receiving a vaccine is given by:

P(vaccine) = 1 - P(placebo) = 1 - 0.33208489 = 0.66791511

The probability of getting the flu and receiving a vaccine is equal to the complement of the probability of getting the placebo and not getting the flu, which is:

P(flu and vaccine) = 1 - P(placebo and no flu) = 1 - 0.27278402 = 0.7272159

Finally, substituting these values into the formula for conditional probability, we get:

P(flu | vaccine) = P(flu and vaccine) / P(vaccine) = 0.7272159 / 0.66791511 = 1.09103623

So, the probability of getting the flu given that an individual received the vaccine is approximately 1.09.

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Answer:

Y = 69

X = 42

Hope this helps!

Answer:

20 centimenters

Answer:

20cm

Step-by-step explanation:

Answer:

70, 130

Step-by-step explanation:

Just took the Mastery test on PLATO and this answer was correct.

The number pattern that uses the rule "add 3" is:3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ...In this pattern, each term is obtained by adding 3 to the previous term.

What is arithmetic sequence?

An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed constant number, called the common difference, to the preceding term.

A number pattern is a sequence of numbers that follows a certain rule or pattern. In this case, the rule is to "add 3" to each term to obtain the next term in the sequence.

The pattern starts with the number 3, and then we add 3 to get the next term, which is 6. Then we add 3 to 6 to get 9, and so on. Each term is found by adding 3 to the previous term.

The pattern continues indefinitely, producing an infinite sequence of numbers. The pattern is also known as an arithmetic sequence or arithmetic progression, because each term is obtained by adding a constant (in this case, 3) to the previous term.

So, the number pattern that uses the rule "add 3" is a sequence of numbers that starts with 3 and adds 3 to each term to obtain the next term in the sequence.

The number pattern that uses the rule "add 3" is:3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ...In this pattern, each term is obtained by adding 3 to the previous term.

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The main idea is using the Pythagorean formula to find the length of line segment \(DB\).

Alr so you use the formula \(A^2 + B^2 = C^2\)

\(C^2\) is already given and is \(2\sqrt{5}\)

and \(A^2\) is \(3\sqrt{2}\)

So using algebraic rules you'll get \(B\) as:

\(\sqrt{2}\)

Now using the formula: \(\frac{1}{2} b * h\), you can find the area of tri ABD and CBD which would be \(3\) and \(1\) so add them up and you get \(4\)!

Answer:

C = 2½ miles.

Step-by-step explanation:

Let the total distance be A

Let the distance covered be B.

Let the unknown distance (distance left) be C.

Given the following data;

A = 3¾ miles

B = 1¼ miles

To find the distance left to hike;

A = B + C

Substituting into the equation, we have;

3¾ = 1¼ + C

C = 3¾ - 1¼

C = (3 - 1) ¾ - ¼

C = 2 2/4

C = 2½ miles.

Method II.

We would convert the mixed fraction into a proper fraction:

A = 3¾ = (4*3 + 3)/4 = 15/4

B = 1¼ = (4*1 + 1)/4 = 5/4

C = 15/4 - 5/4

C = 10/4

C = 5/2

C = 2½ miles.

Answer:

yes!

Step-by-step explanation:

they have the same 3 angles in both

Answer:

true

Step-by-step explanation:

Answer:

sin a= 4/5 tan b=3/5

im not 100% sure but im open for suggestions

Answer:

28 miles per gallon

560/20=28

Step-by-step explanation:

Plz give me brainliest

Number of miles a car travels are 28.

The division is the process of repetitive subtraction. It is the inverse of the multiplication operation. It is defined as the act of forming equal groups. While dividing numbers, we break down a larger number into smaller numbers such that the multiplication of those smaller numbers will be equal to the larger number taken.

Number of gallons of gas = 20

A car with 20 gallons of gas can drive 560 miles

Based on the given conditions,

= \(\frac{560}{20}\)

= 28

Hence, number of miles are 28.

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Answer:

students 150

adult 550

Step-by-step explanation:

x + y = 700

5x + 2y = 3050

x = 700 - y

5(700 - y) + 2y = 3050

3500 - 5y + 2y = 3050

-3y + 3500 = 3050

-3y = 3050 - 3500

-3y = -450

y = -450 / -3

y = 150

x = 700 - y

x = 700 - 150

x = 550

The mean of T is -10 and the standard deviation of T is √425 when X1 and X2 are independent.

To find the mean of T, we can use the properties of expected values. Since T = 11X1 - 2X2, the mean of T can be calculated as follows: E(T) = E(11X1) - E(2X2) = 11E(X1) - 2E(X2) = 11(10) - 2(20) = -10. To find the standard deviation of T, we need to consider the variances and covariance of X1 and X2. Since X1 and X2 are independent, the covariance between them is zero. Therefore, Var(T) = Var(11X1) + Var(-2X2) = 11^2Var(X1) + (-2)^2Var(X2) = 121(2^2) + 4(3^2) = 484 + 36 = 520. Thus, the standard deviation of T is √520, which simplifies to approximately √425. When X1 and X2 have a correlation of -0.76, the mean and standard deviation of T remain the same as in the case of independent variables. To calculate the probability P(T > 30) when X1 and X2 are independent, normally distributed variables, we need to convert T into a standard normal distribution. We can do this by subtracting the mean of T from 30 and dividing by the standard deviation of T. This gives us (30 - (-10))/√425, which simplifies to approximately 6.16.  We can then look up the corresponding probability from the standard normal distribution table or use statistical software to find P(T > 30). The probability will be the area under the standard normal curve to the right of 6.16.

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