Nathan owns a trucking company for every truck that goes out Nathan must pay the driver $20 per hour of driving and also has an expense of $2.75 per mile driven for gas and maintenance

Answer:

27 1/12 %

Step-by-step explanation:

discount=1200-875=325

discount %=325/1200 ×100=325/12=27 1/12

a) the mean of this distribution is 20

b) the mean of the distribution is 20 and the standard deviation of the distribution is 4.58.

a. Calculation of mean of the given distribution:

Mean = ∑(x * P(x))

where x = value of the outcome

P(x) = Probability of the outcome

∑ denotes the summation over all the possible outcomes

Mean = (10 * 0.10) + (15 * 0.30) + (20 * 0.20) + (25 * 0.30) + (30 * 0.10)= 1 + 4.5 + 4 + 7.5 + 3= 20

b. Calculation of standard deviation of the given distribution:

σ = √[∑(x - μ)² P(x)]

where x = value of the outcome

μ = mean of the distribution

P(x) = Probability of the outcome

∑ denotes the summation over all the possible outcomes

σ = √[((10 - 20)² * 0.10) + ((15 - 20)² * 0.30) + ((20 - 20)² * 0.20) + ((25 - 20)² * 0.30) + ((30 - 20)² * 0.10)]= √[100 * 0.10 + 25 * 0.30 + 0 + 25 * 0.30 + 100 * 0.10]= √[10 + 7.5 + 3.5]= √21= 4.58

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Given that \(\(T(n)\) = \(10n^2-3n\)\) if (\(\(n=1\)\)), you have to prove it by induction. So, we have proved it by induction that  \($$\(T(n)=10n^2-3n\)$$\)  if ( n= 1). The given statement is true for all positive integers n

Let's do it below: The base case (n=1) is given as follows: \(T(1)\) =\(10\cdot 1^2-3\cdot 1\\&\)=\(7\end{aligned}$$\). This implies that \(\(T(1)\)\) holds true for the base case.

Now, let's assume that \(\(T(k)=10k^2-3k\)\) holds true for some arbitrary \(\(k\geq 1\).\)

Thus, for n=k+1, T(k+1) = \(10(k+1)^2-3(k+1)\\&\) = \(10(k^2+2k+1)-3k-3\\&\)=\(10k^2+20k+7k+7\\&\) = \(10k^2-3k+20k+7k+7\\&\) = \(T(k)+23k+7\\&\) = \((10k^2-3k)+23k+7\\&\) =  \(10(k+1)^2-3(k+1)\).

Therefore, we have proved that the statement holds true for n=k+1 as well. Hence, we have proved it by induction that  \($$\(T(n)=10n^2-3n\)$$\)  if (n=1). Therefore, the given statement is true for all positive integers n.

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Answer:

x=2/3

Step-by-step explanation:

25-(3x+5)=2(x+8)+x

25-3x-5=2x+16+x

20-3x=3x+16

20-3x-3x=16

20-6x=16

6x=20-16

6x=4x=4/6

simplify

x=2/3

Answer:

x=2/3

Step-by-step explanation:

The Ordinary differential equation for the tank's salt content is d(x(t))/dt = 1 - 3x(t) lb/min.

To set up an ordinary differential equation (ODE) for the amount of salt in the tank, x(t), we need to consider the rate at which salt enters and leaves the tank.

Let's break down the problem step by step:

1. Inflow of salt:

  The salt enters the tank at a rate of 2 gal/min, and the concentration of salt in the incoming water is 0.5 lb/gal. So, the rate at which salt enters the tank is (2 gal/min) * (0.5 lb/gal) = 1 lb/min.

2. Outflow of salt:

  The salt leaves the tank at a rate of 3 gal/min. The concentration of salt in the tank is x(t) lb/gal. Therefore, the rate at which salt leaves the tank is (3 gal/min) * (x(t) lb/gal) = 3x(t) lb/min.

3. Initial condition:

  The tank initially contains 300 gallons of water and 60 lb of salt.

Now, let's set up the ODE for the amount of salt in the tank, x(t):

The rate of change of salt in the tank is equal to the net rate of salt entering the tank minus the net rate of salt leaving the tank:

d(x(t))/dt = (rate of salt inflow) - (rate of salt outflow)

d(x(t))/dt = 1 lb/min - 3x(t) lb/min

Therefore, the ODE for the amount of salt in the tank is:

d(x(t))/dt = 1 - 3x(t) lb/min

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Answer:

Solution given:

Right angled triangle ABC is drawn where <C=\(\theta\)

we know that

\(\displaystyle Sin\theta=\frac{opposite}{hypotenuse} =\frac{AB}{AC}\)

\(\displaystyle Cos\theta=\frac{adjacent}{hypotenuse}=\frac{BC}{AC} \)

Now

left hand side

\( \displaystyle {sin}^{2} \theta + {cos}^{2} \:\theta\)

Substituting value

\((\frac{AB}{AC})²+(\frac{BC}{AC})²\)

distributing power

\(\frac{AB²}{AC²}+\frac{BC²}{AC²}\)

Taking L.C.M

\(\displaystyle \frac{AB²+BC²}{AC²}\)....[I]

In ∆ABC By using Pythagoras law we get

\(\boxed{\green{\bold{Opposite²+adjacent²=hypotenuse²}}}\)

AB²+BC²=AC²

Substituting value of AB²+BC² in equation [I]

we get

\(\displaystyle \frac{AC²}{AC²}\)

=1

Right hand side

Answer:

$102.2 were collected

Step-by-step explanation:

If there are 15 members in total, and 8 of them paid it on the first day, then you know that 7 people paid it the next day, because the remaining people paid it the next day.

7x14.60=102.2

The Volume of solid which is a combination of cone and cylinder is 1206 cm³

Volume is the amount of space that a closed three dimensional shape occupies.

The volume of the cylinder = π * radius² * height = π * 6² * 8 = 904.32 cm³

The volume of the cone = (1/3) * π * radius² * height = (1/3) * π * 6² * 8 = 301.44 cm³

Volume of solid = 301.44 + 904.32 = 1206 cm³

The Volume of solid which is a combination of cone and cylinder is 1206 cm³

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Answer:

Each car cost $0.81, you would need to do 0.81 times 25 and you would get $20.25

Step-by-step explanation:

The equation 0.05n + 0.10d = 3.65 is equivalent to the equation 0.05n + 0.1d + 3.65. This equation states that the total value of the nickles and dimes in Jada's coin jar is 3.65.

The equivalent equation  0.05n + 0.1d+3.65 is 5n + 10d = 365. This equation can be obtained by multiplying both sides of the original equation by 100 to eliminate the decimal points. This gives us:

100(0.05n + 0.1d + 3.65) = 100(3.65)
5n + 10d + 365 = 365

Next, we can subtract 365 from both sides of the equation to isolate the variables on one side:

5n + 10d = 365

Therefore, the equation 5n + 10d = 365 is equivalent to the original equation 0.05n + 0.1d+3.65 and can be used to represent the situation of Jada's coin jar.

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An equation that mode the relationship between thee two variable is y=2x+3 .

Let x represent the number of 6-month period worked

Let y represent the total number of paid vacation day

According to the question,

When he started work, he was given three paid day of vacation. For each six-month period he pay at the job, his vacation is increased by two day.

Each year has 2 six-month periods. After 4.4 years Roberto will have worked 8.8 six-month periods. He will have been given vacation days for each of the 8 whole working periods he has completed. x=8 y=2*8+3 y=19

An equation that mode the relationship between thee two variable is y=2x+3 (Total vacation time equals 2 days times x plus the 3 days he was given at the start).

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Answer:

Step-by-step explanation:

(0.061)(0.43) =0.02623

280 dogs in all of the city's animal shelters are puppies. The solution has been obtained by using ratios.

What is ratio?

The ratio between two amounts of the same unit can be used to determine how much of one quantity is included in the other.

We are given that different animal shelters in a city shows that 10 of the 70 dogs are puppies and the city's animal shelters collectively house 1,960 dogs each year.

So, from this we get the ratio as

⇒ \(\frac{10}{70}\) = \(\frac{x}{1960}\)

Now, by cross multiplying, we get

⇒ 19,600 = 70x

⇒ x = 280

Hence, 280 dogs in all of the city's animal shelters are puppies.

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Check the picture below.

The number of simple events in this experiment is 16.

The correct answer to the given question is option c.

The probability of an event can be calculated by dividing the number of favorable outcomes by the number of possible outcomes. A simple event is one in which only one of the outcomes can occur. For example, if a coin is tossed, a simple event would be the outcome of the coin being heads or tails.

The total number of possible outcomes in the experiment of tossing 4 unbiased coins simultaneously is 2⁴, since there are two possible outcomes for each coin. Thus, the total number of possible outcomes is 16.

Each coin has two possible outcomes: heads or tails. If all four coins are flipped, there are two possible outcomes for the first coin, two possible outcomes for the second coin, two possible outcomes for the third coin, and two possible outcomes for the fourth coin. Therefore, the total number of possible outcomes is 2 × 2 × 2 × 2 = 16.

Therefore, the number of simple events in this experiment is 16, which is option (c).

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The total red area of the five circles making up this archery target is given by the formula πr2.
The diameter of the first circle is length so its radius is length/2. Therefore, the red area of the first circle is π(length/2)2.
The diameter of the second circle is 2 so its radius is 1.

Therefore, the red area of the second circle is π.  Adding these together, the total red area is π(length/2)2 + π.

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Answer:

12

Step-by-step explanation:

3 x 4 = 12

hope this helps

A linear system with 3 equations and 4 variables by representing it with an augmented matrix and bringing the matrix to reduced row-echelon form can be solved.

A mathematical representation of a system based on the application of a linear operator is known as a "linear system" in systems theory. Ordinarily, compared to nonlinear systems, linear systems display much simpler features and properties. The automatic control theory, signal processing, and telecommunications all heavily rely on linear systems as a mathematical abstraction or idealisation.

Linear systems, for instance, are frequently used to model the propagation medium for wireless communication systems. An operator, H, that converts an input, x(t), into an output, y(t), a kind of black box description, can be used to describe a general deterministic system.

The superposition principle, or alternatively both the additivity and homogeneity properties, must be satisfied by a system to be considered linear, and only then.

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The conditional probabilities in the context of this problem are given as follows:

a. P(A|B) = 2.1%.

b. P(A'|B') = 99.9%.

Conditional probability is the probability of one event happening, considering the outcome of a previous event. The formula is:

\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)

In which the probabilities are described as follows:

The probability that a person has tested positive is calculated as follows:

Hence:

P(B) = 0.85 x 0.0025 + 0.1 x 0.9975 = 0.101875.

Hence the conditional probability is:

P(A|B) = 0.85 x 0.0025/0.101875 = 0.021 = 2.1%.

The probability that a person has tested negative is calculated as follows:

Hence:

P(B') = 0.15 x 0.0025 + 0.9 x 0.9975 = 0.898125.

The conditional probability is:

P(A'|B') = 0.9 x 0.9975/0.898125 = 0.999 = 99.9%.

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Answer:

300 minutes

2:00 p.m

Step-by-step explanation:

Given the following:

Time taken to mark a script :

Mrs Kanja = 5mins

Miss Kanene = 4mins

Mrs Nyaga = 12 mins

Number of scripts = 160

Start time = 9:00 a.m

Rate at which each of them mark:

Mrs Kanja = t / 5

Miss Kanene = t/4

Mrs Nyaga = t/12

Combined rate :

t/5 + t/4 + t/12 = 160

(12t + 15t + 5t) / 60 = 160

32t / 60 = 160

32t = 160 * 60

32t = 9600

t = 9600 / 32

t = 300 minutes

300 minutes = 300/60 = 5hrs

9:00 a.m + 5 hours = 2:00 p.m

Answer:

225.08, which would just be 225.

Step-by-step explanation:

First, you multiply the percent, 17, times the total number of points, 1,324, which you should get 22,508. Then, divide that by 100, and you will get your answer 225.08. The reason you put it into the whole number, is because you can't score part of a point, so you always round down even if the number is in favor to round up. I hope this helps :)

The narrator describes the house in this way to convey a sense of decay and deterioration. It is not to show that it has a nice design, remind him of something rotting, indicate the number of people inside, or suggest that the owner had a lot of parties.

The line from "Fall of the House of Usher" describes the house using imagery of old wood-work that has rotted in a neglected vault. This description serves to create a mood of decay and deterioration. The phrase "specious totality of old wood-work" suggests that the once-grand and impressive architecture of the house has fallen into disrepair. By comparing it to something rotting in a neglected vault, the narrator conveys a sense of neglect and isolation. The description emphasizes the dilapidated state of the house, setting the tone for the eerie and decaying atmosphere that permeates the story.

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Answer:

Speed = 9.6km/s

Distance Traveled in 5 seconds= 48km

Step-by-step explanation:

(6 )(1.6)= 9.6km/s

(9.6)(5)=48km

Answer:

50+45x

Step-by-step explanation:

The number of ways in which we can make a sitting arrangements to meet the requirement is 1440.

= 5!⋅4⋅3

= 120⋅12

= 1440

Combinations are ways to choose things from a collection where the order of the choices is irrelevant. Let's say we have a trio of numbers: P, Q, and R. Then, combination determines how many ways we can choose two numbers from each group.

It is easy to count the number of combinations in smaller cases, but the likelihood of a set of combinations is also higher in cases with many groups of components or sets. As a result, a formula has been developed to determine the number of items that could be chosen which is nCr.

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The number of bags that the truck can move is given as follows:

31 bags.

(plus one extra package of 175 lbs).

The number of bags that the truck can move is obtained applying the proportions in the context of the problem.

The total weight that the truck can carry is given as follows:

4675 lbs.

Each bag has 150 lbs, hence the number of bags needed is given as follows:

4675/150 = 31 bags (rounded down).

The remaining weight will go into the extra package of 175 lbs.

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The miles drive on Tuesday is , 250 miles.

The miles drive on Wednesday is , 180 miles.

The total miles drive on Tuesday and Wednesday is, the sum of drive on Tuesday and Wednesday.

Thus, the total miles drive on Tuesday and Wednesday is, 430 miles.

The finite population correction factor is used in computing the standard error of the sample mean when the sample size is smaller than 5% of the population size.

The finite population correction factor is a adjustment made to the standard error of the sample mean when the sample is taken from a finite population, rather than an infinite population.

It accounts for the fact that sampling without replacement affects the variability of the sample mean.

When the sample size is relatively large compared to the population size (more than half), the effect of sampling without replacement becomes negligible, and the finite population correction factor is not necessary.

In this case, the standard error of the sample mean can be estimated using the formula for sampling with replacement.

On the other hand, when the sample size is small relative to the population size (less than 5%), the effect of sampling without replacement becomes more pronounced, and the finite population correction factor should be applied.

This correction adjusts the standard error to account for the finite population size and provides a more accurate estimate of the variability of the sample mean.

Therefore, the correct answer is option 2: the finite population correction factor is used when the sample size is smaller than 5% of the population size.

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