15 When you have two or more
linear equations is called a____
of equations

Function: P = 25,000(1+0.0095)^(t/365)

Daily Growth Rate: 0.003%

Answer:

AD crosses the scale marked on the vertical line at the value 10. This means that there is 10 feet of available space left between the top of the debris pile and ground level.

Step-by-step explanation:

PLATO

AD crosses the scale marked on the vertical line at the value 10. This means that there is 10 feet of available space left between the top of the debris pile and ground level.

If the expected number of inches of rain on saturday is 2 and the expected number of inches on sunday is 1, the expected number of inches of rainfall over the weekend is 7/3.

To solve the problem, we need to use the concept of conditional probability. Let's denote the total rainfall over the weekend by X, and the rainfall on Sunday by Y. We know that E(Y) = 1 and that if there is no rain on Saturday, Y = 0. Therefore, we need to calculate the conditional expectation of X given that there is no rain on Saturday.

If there is rain on Saturday, the expected value of X is 2+1 = 3. If there is no rain on Saturday, the expected value of X is just E(Y) = 1. We can write this as:

E(X | no rain on Saturday) = E(X | rain on Saturday) * P(rain on Saturday) + E(Y | no rain on Saturday) * P(no rain on Saturday)

We know that P(no rain on Saturday) = 1/3 (since the probability of rain on Saturday is not given). Therefore:

E(X | no rain on Saturday) = (3 * P(rain on Saturday)) + (1 * (1 - P(rain on Saturday)))

E(X | no rain on Saturday) = 2P(rain on Saturday) + 1

To find the expected value of X over the weekend, we need to take the average of the expected values with and without rain on Saturday:

E(X) = E(X | rain on Saturday) * P(rain on Saturday) + E(X | no rain on Saturday) * P(no rain on Saturday)

E(X) = (3 * P(rain on Saturday)) + ((2P(rain on Saturday) + 1) * (1 - P(rain on Saturday)))

E(X) = 2P(rain on Saturday) + 1

E(X) = 2 * 2/3 +1 = 7/3

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The concentration of lycopene solution in the spectrophotomer cell before isomerization, given that the molar absorptivity of lycopene at 471 nm is 0.00001 M.

To calculate the concentration of lycopene solution in the spectrophotometer cell before isomerization, we will use the Beer-Lambert Law. The Beer-Lambert Law states that the absorbance (A) of a solution is directly proportional to its concentration (c) and path length (l), and is expressed as:

A = ε × c × l

where A is the absorbance, ε is the molar absorptivity (given at 471 nm), c is the concentration, and l is the path length of the spectrophotometer cell (usually in cm).

Follow these steps to calculate the concentration:

1. Measure the absorbance (A) of the lycopene solution at 471 nm using a spectrophotometer.

2. Determine the path length (l) of the spectrophotometer cell. This is typically given by the manufacturer or can be measured manually (usually 1 cm).

3. Use the given molar absorptivity (ε) of lycopene at 471 nm.

4. Rearrange the Beer-Lambert Law equation to solve for the concentration (c):

c = A / (ε × l)

5. Plug in the measured absorbance (A), given molar absorptivity (ε), and path length (l) into the equation to calculate the concentration of the lycopene solution before isomerization.

Let's assume that the path length of the cell is 1 cm. Therefore, we can rearrange the Beer-Lambert Law to solve for the concentration, which gives us c = A/εl. Let's say that the absorbance of the lycopene solution before isomerization is 0.5. Then, the concentration of the lycopene solution would be: c = 0.5/(50,000 M^-1cm^-1 x 1 cm) = 0.00001 M. Therefore, the concentration of lycopene solution in the spectrophotometer cell before isomerization is 0.00001 M.

By using the Beer-Lambert Law and following these steps, you can accurately determine the concentration of lycopene in the spectrophotometer cell before the isomerization process occurs.

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The probability that the student is a junior is 0.5.

The probability that the selected student takes calculus is given by:

P(C) = probability that the selected student takes calculus= probability of seniors taking calculus + probability of juniors taking calculus= 0.4 x 1/2 + 0.2 x 1/2= 0.2

Now,Let's find the probability that a calculus student selected is a junior.i.e., we need to find P(J|C).We know that,

P(J|C) = probability that the selected student is a junior given that the student takes calculus= P(C|J) × P(J) / P(C)

We already know,P(C) = 0.2

Also,P(C|J) = probability that a junior student takes calculus= 0.2

So,P(J|C) = probability that the selected student is a junior given that the student takes calculus= P(C|J) × P(J) / P(C)= 0.2 × 1/2 / 0.2= 1/2= 0.5

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Answer:

3(3/7)

Step-by-step explanation:

Just by doing the math.

Answer:

1. = 63

2.= 77 miles

Step-by-step explanation:

Answer:

hope this helps

Step-by-step explanation:

1. 6(22-17)+(33)

=132-102+33

=30+33

=63

2. The answer is 77 miles

The actual length of the truck is 15.6 meters and the actual width is 3.24 meters.

The actual length of the truck can be calculated by multiplying the length of the model by the scale factor:

Similarly, the actual width of the truck can be calculated as:

Therefore, the actual length of the truck is 15.6 meters and the actual width is 3.24 meters.

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Answer:

Option C

Step-by-step explanation:

Given the following question:

Total cost is $725
15% Marcus makes in commission.

In order to find the answer, we have to find 15% of $725 and that number will be the total in commissions he earned that week.

\(\frac{15\times725}{100} =15\times725=10875\div100=108.75\)

Marcus makes "$108.75" or option C in commissions last week.

Hope this helps.

The ratio shows how many times one value is contained in another value.

Calories:  25  50  75  200

servings:  1/3  2/3  1    4/3

The ratio shows how many times one value is contained in another value.

Example:

There are 3 apples and 2 oranges in a basket.

The ratio of apples to oranges is 3:2 or 3/2.

We have,

Calories:  25

servings:  1/3

This means,

25 calories can serve 1 out of 3.

25 calories = 1/3 servings ______(1)

Multiply 2 on both sides of (1).

50 calories = 2/3 servings

Multiply 3 on both sides (1).

75 calories = 1 serving.

Multiply 4 on both sides of (1).

200 calories = 4/3 servings.

Thus,

Calories: 25  50  75  200

servings:  1/3  2/3  1    4/3

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The quantity of salt in grams needed to complete the experiment is 180 grams.

Ratio expresses the relationship between two or more numbers. It shows the frequency of the number of times that one value is contained within other value(s).

Quantity of salt needed = (grams of baking soda x ratio of salt) / ratio of baking soda

(3 x 420) / 7 = 180 grams

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The value of the correlation coefficient is 0.34. Thus, the option (B) 0.34 is the correct answer.

Given that a researcher measures the relationship between two variables, X and Y.

If SS(XY) = 340 and SS(X)SS(Y) = 320,000, then we need to calculate the value of the correlation coefficient.

Correlation coefficient:

The correlation coefficient is a statistical measure that determines the degree of association between two variables.

It is denoted by the symbol ‘r’.

The value of the correlation coefficient lies between -1 and +1, where -1 indicates a negative correlation, +1 indicates a positive correlation, and 0 indicates no correlation.

How to calculate correlation coefficient?

The formula to calculate the correlation coefficient is as follows:

r = SS(XY)/√[SS(X)SS(Y)]

Now, substitute the given values, we get:

r = 340/√[320000]r = 0.34

Therefore, the value of the correlation coefficient is 0.34. Thus, the option (B) 0.34 is the correct answer.

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Answer:

$17,800

Step-by-step explanation:

Base salary = $400

Commission = 2%

Total = $756

Find the amount of money you get as commission:

This amount is 2% of total sales, thus

$356 - 2%

$x - 100%

Answer:

P = 37.4 m

Step-by-step explanation:

let the third side of the triangle be x

using Pythagoras' identity in the right triangle.

x² + 7² = 16²

x² + 49 = 256 ( subtract 49 from both sides )

x² = 207 ( take square root of both sides )

x = \(\sqrt{207}\) ≈ 14.4 m ( to 1 decimal place )

the perimeter (P) is then the sum of the 3 sides

P = 7 + 16 + 14.4 = 37.4 m

The pieces of cloth are beyond the standard at 0.05 level of significance.

We can use a one-sample t-test to determine if the mean length of the 35 pieces of cloth is significantly different from the standard length of 3.25 meters.

The null hypothesis is that the mean length of the cloth pieces is equal to the standard length:

H0: μ = 3.25

The alternative hypothesis is that the mean length of the cloth pieces is greater than the standard length:

Ha: μ > 3.25

We can calculate the test statistic as:

t = (x - μ) / (s / √n)

where x is the sample mean length, μ is the population mean length (3.25 meters), s is the sample standard deviation (0.52 meters), and n is the sample size (35).

Plugging in the values, we get:

t = (3.52 - 3.25) / (0.52 / √35) = 3.81

Using a t-table with 34 degrees of freedom (n-1), and a significance level of 0.05 (one-tailed test), the critical t-value is 1.690.

Since our calculated t-value (3.81) is greater than the critical t-value (1.690), we reject the null hypothesis and conclude that the mean length of the 35 pieces of cloth is significantly greater than the standard length at the 0.05 level of significance.

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To calculate the radiative heat transfer coefficient and the heat lost due to radiation for a cylinder, we can use the Stefan-Boltzmann Law and the view factor.

The radiative heat transfer coefficient (h_rad) can be calculated using the following formula:

h_rad = εσ(T_s^4 - T_sur^4)

where ε is the emissivity of the surface, σ is the Stefan-Boltzmann constant (5.67 × 10^(-8) W/m²K⁴), T_s is the surface temperature, and T_sur is the surrounding temperature.

Plugging in the given values:

ε = 0.95

σ = 5.67 × 10^(-8) W/m²K⁴

T_s = 100 °C = 373 K

T_sur = 25 °C = 298 K

h_rad = 0.95 * 5.67 × 10^(-8) * (373^4 - 298^4)

h_rad ≈ 11.31 W/m²K

The heat lost due to radiation (Q_rad) can be calculated using the formula:

Q_rad = h_rad * A * (T_s - T_sur)

where A is the surface area of the cylinder.

The surface area of a cylinder can be calculated using the formula:

A = 2πrh + πr^2

where r is the radius and h is the height (or length) of the cylinder.

Given:

diameter = 0.02 m

radius (r) = 0.02/2 = 0.01 m

length (h) = 0.12 m

A = 2π(0.01)(0.12) + π(0.01)^2

A ≈ 0.0754 m²

Plugging in the values:

Q_rad = 11.31 * 0.0754 * (373 - 298)

Q_rad ≈ 303.95 W

Therefore, the radiative heat transfer coefficient is approximately 11.31 W/m²K, and the heat lost due to radiation is approximately 303.95 W.

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To calculate the radiative heat transfer coefficient and the heat lost due to radiation for a cylinder, we can use the Stefan-Boltzmann Law and the view factor.

The radiative heat transfer coefficient (h_rad) can be calculated using the following formula:

h_rad = εσ(T_s^4 - T_sur^4)

where ε is the emissivity of the surface, σ is the Stefan-Boltzmann constant (5.67 × 10^(-8) W/m²K⁴), T_s is the surface temperature, and T_sur is the surrounding temperature.

Plugging in the given values:

ε = 0.95

σ = 5.67 × 10^(-8) W/m²K⁴

T_s = 100 °C = 373 K

T_sur = 25 °C = 298 K

h_rad = 0.95 * 5.67 × 10^(-8) * (373^4 - 298^4)

h_rad ≈ 11.31 W/m²K

The heat lost due to radiation (Q_rad) can be calculated using the formula:

Q_rad = h_rad * A * (T_s - T_sur)

where A is the surface area of the cylinder.

The surface area of a cylinder can be calculated using the formula:

A = 2πrh + πr^2

where r is the radius and h is the height (or length) of the cylinder.

Given:

diameter = 0.02 m

radius (r) = 0.02/2 = 0.01 m

length (h) = 0.12 m

A = 2π(0.01)(0.12) + π(0.01)^2

A ≈ 0.0754 m²

Plugging in the values:

Q_rad = 11.31 * 0.0754 * (373 - 298)

Q_rad ≈ 303.95 W

Therefore, the radiative heat transfer coefficient is approximately 11.31 W/m²K, and the heat lost due to radiation is approximately 303.95 W.

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Answer:

The correct answer would be 25

Step-by-step explanation:

32+(−3)(4)−(−5)

=32+−12−(−5)

=20−(−5)

=25

Hope this helps have an amazing day!!

Answer:

121

Step-by-step explanation:

32+(-3)×4-(-5)

29×4-(-5)

116-(-5)

116+(+5)

121

Answer:

14

Step-by-step explanation:

16H = 208

H = 208 / 16

H = 14

Answer:

13

Step-by-step explanation:

To get the answer, you have to divide 16 on both sides:

16H ÷ 16 = 208 ÷ 16

H = 13

Answer:

The market equilibrium price is approximately $36.43 per barrel.

Step-by-step explanation:

To find the market equilibrium price, we need to set the quantity supplied (QS) equal to the quantity demanded (QD) and solve for the price (P).

Given:

QS = -250 + 7P

QD = 260 - 7P

Setting QS equal to QD:

-250 + 7P = 260 - 7P

Now, let's solve for P:

Add 7P to both sides:

-250 + 7P + 7P = 260 - 7P + 7P

Combine like terms:

14P - 250 = 260

Add 250 to both sides:

14P - 250 + 250 = 260 + 250

Simplify:

14P = 510

Divide both sides by 14:

14P/14 = 510/14

Simplify:

P = 36.43

The market equilibrium price can be found by setting the quantity supplied (QS) equal to the quantity demanded (QD) and solving for the price (P) that satisfies this condition.

In the given scenario, the supply function is QS = -250 + 7P, and the demand function is QD = 260 - 7P. To find the equilibrium price, we set QS equal to QD:

-250 + 7P = 260 - 7P

Simplifying the equation, we get:

14P = 510

Dividing both sides by 14, we find:

P = 36.43

Therefore, the market equilibrium price is approximately $36.43 per barrel. At this price, the quantity supplied and quantity demanded will be equal, resulting in a state of equilibrium in the perfectly competitive domestic crude oil market.

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In linear equation, Using the confidence interval for a proportion, it is found that 3458 students should be sampled.

What in mathematics is a linear equation?

In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.

       π ± z√π( 1 - π)/n

In which

z is the z-score that has a p-value of 1 + α/2

The margin of error is of

               M =   z√π( 1 - π)/n

In this problem:

    M =   z√π( 1 - π)/n

0.01 = 1.96√0.1(0.9)/n

0.01√n =  1.96√0.1(0.9)

√n = 1.96 √0.1(0.9)/0.01

(√n)² = ( 1.96 √0.1(0.9)/0.01)²

 n = 3457.4

3458 students should be sampled.

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The factorized expressions is 3(x-4)(x-5).

We are given that;

The expression 3x² - 27x+60​

Now,

1.1.1 After simplification

-3(2x - 4y)² = -12(x-y)²

1.1.2 x+2/3*5x+1

= (3x+5)/(3x+3)

1.2.1 ny + 4z + 4y + nz

= (n+4)(y+z)

1.2.2 3x² - 27x+60

= 3(x-4)(x-5)

Therefore, by the expression the answer will be 3(x-4)(x-5).

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The total amount of money earned by Nora salary over the 21 years is approximately $1,848,000.

To find the total amount of money earned by Nora over 21 years, we need to calculate the salary for each year and then sum them up.

In the first year, Nora's salary is $40,000.

In the second year, her salary will be increased by 3%, so it will be:

$40,000 + 3% of $40,000 = $40,000 + $1,200 = $41,200.

In the third year, her salary will again increase by 3%, so it will be:

$41,200 + 3% of $41,200 = $41,200 + $1,236 = $42,436.

We can continue this process for each year, adding 3% of the previous year's salary to calculate the next year's salary.

To calculate the total amount of money earned over the 21 years, we need to sum up the salaries for each year. Here's the calculation:

Total = $40,000 + $41,200 + $42,436 + ... (21 terms)

To simplify the calculation, we can use the formula for the sum of an arithmetic series:

Total = (n/2) * (2a + (n - 1)d)

where:

n = number of terms (21 in this case)

a = first term ($40,000)

d = common difference (3% of the previous year's salary)

Plugging in the values:

Total = (21/2) * [2(40,000) + (21 - 1)(0.03)(40,000)]

Simplifying further:

Total = (21/2) * [80,000 + 20(0.03)(40,000)]

= (21/2) * [80,000 + 2,400(40,000)]

= (21/2) * [80,000 + 96,000]

= (21/2) * 176,000

= 21 * 88,000

= 1,848,000

Therefore, the total amount of money earned by Nora salary over the 21 years is approximately $1,848,000.

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There is a 0.2428 percent chance that the sample comprises exactly three graduate students.

Given That,

15% of the students at a big western university are graduate students. If five students are chosen at random as a sample

What is Binomial Distribution ?

The binomial distribution is the discrete probability distribution used in probability theory and statistics that only allows for Success or Failure as the possible outcomes of an experiment. For instance, if we flip a coin, there are only two conceivable results: heads or tails, and if we take a test, there are only two possible outcomes: pass or fail. A binomial probability distribution is another name for this distribution.

This is a binomial distribution, the probability distribution function is

P(X =x) = C^320 (0.15)^3(1-0.15)^20-3

           = [(20x19x18)/2x3](0.15)^3(1-0.15)^20-3

           = 0.2428

As a result, 0.2428 is the likelihood that the sample contains exactly three graduate students.

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Answer: A

Step-by-step explanation:

L correspods to itself, and the only option which satisfies this is A.

Gradual, long-term movement in time-series values is called temporal variation. Therefore, the correct option is (a) temporal variation.

Temporal variation is one of the components of a time series, along with seasonal variation, cyclical movement, and irregular or random variation. Temporal variation refers to the long-term trend or pattern of movement in the time series, which can be increasing, decreasing, or remaining constant over time. It is often caused by underlying factors such as population growth, economic changes, or technological advancements.

Cyclical movement refers to the regular, repeating up and down patterns in the time series, which are usually longer than a year and can be caused by factors such as business cycles or political cycles. Exponential smoothing and linear regression are statistical methods used to forecast or model time series data, but they do not describe the components of the time series themselves.

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An equation that best fits the data above is y = 3 - 0.5x.

There is no correlation between the data.​

In this exercise, we would plot the x-values on the x-axis (x-coordinates) of a scatter plot while the y-values would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.

On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display a linear equation for the line of best fit (trend line) on the scatter plot.

Based on the scatter plot shown below, which models the relationship between the x-values and y-values, an equation for the line of best fit is modeled as follows:

y = 3 - 0.5x

Correlation coefficient, r = -1

In conclusion, there is no correlation between the data because the correlation coefficient (r) is less than 0;

0＜|r| ≤ 0.2  (no correlation)

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The value of the sample statistic is used to estimate the value of the population parameter.

The sample statistic is the value that is calculated from the sample data, which is used to make inferences about the population parameter. Sample statistics are used to estimate population parameters. A sample statistic is an estimate of a population parameter that is obtained from a sample, whereas a population statistic is a value that is computed from a population.

Therefore, the correct answer is a. sample statistic.

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Answer: (-13, -3), (-1, 0), and (7, 2).

Step-by-step explanation:

First, we have a function f(x) and we know that 3 points (x, y) of this function are:

(-3, -13), (0, -1), and (2, 7).

Now, if we have a function g(x) and we know that g(x) is the inverse of f(x), we have that:

g(f(x)) = x.

this means that if f(x) = y then g(y) = x.

then if (-3, -13) is a point in the f(x) graph, (-13, -3) must be a point in the g(x) graph.

Then 3 points in on the inverse of the function f(x) are:

(-13, -3), (-1, 0), and (7, 2).