linear equation that has a slope of 5/6 and y-intercept of 14

A. Using the given information, y expressed in terms of x is y = x + 50

B. The table that shows the relationship between y and x is

x               y

10             60

20            70

30             80

40             90

50             100

From the question, we are to express y in terms of x

From the given information,

There are x sparrows in a tree and 50 sparrows on the ground beneath the tree

If y represent the total number of sparrows in the tree and on the ground,

Then,

We can write that

y = x + 50

B.

We are to make a table to show the relationship between y and x

Using the equation above

y = x + 50

When x = 10

y = 10 + 50

y = 60

When x = 20

y = 20 + 50

y = 70

When x = 30

y = 30 + 50

y = 80

When x = 40

y = 40 + 50

y = 90

When x = 50

y = 50 + 50

y = 100

Thus,

The table is:

x               y

10             60

20            70

30             80

40             90

50             100

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Answer:

Hey mate....

Step-by-step explanation:

This is ur answer....

Hope it helps!

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Answer:

1)False

2)True

3)True

4)False

Step-by-step explanation:

Answer:

C. 4x²

Step-by-step explanation:

8x^4 = 2 × 2 × 2 × x × x × x × x

12x³ = 2 × 2 × 3 × x × x × x

20x² = 2 × 2 × x × x

Look at the factors. Which factors do both numbers have?

They are in bold below.

8x^4 = 2 × 2 × 2 × x × x × x × x

12x³ = 2 × 2 × 3 × x × x × x

20x² = 2 × 2 × 5 × x × x

The common factors are 2, 2, x, x.

The GCF = 2 × 2 × x × x = 4x²

Answer: C. 4x²

The following statements make a false statement.

Given that,

A function argument  a exists until the function's end is reached.

A local variable 

can only share a name with another variable inside the function and exists only until the function's end.

Answer C : Can not share a name with variable outside a function.

Because the function is considered as a single line of code.

Answer True

They have same presidence but they are evaluated from left to right

Answer D : The calculation totals both positive (Profits) and negative (loss) earnings

Code doesn't check if the number of positive or not before adding

Answer D.

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The present value of A = $35,000, r = 7% compounded monthly, t = 6 years is $24,036.89.

The present value is the amount of money that is needed today in order to produce a specified future value at a specified interest rate and time period. It is calculated using the formula: PV = A / (1 + r/n)^(n*t), where A is the future value, r is the interest rate, n is the number of compounding periods per year, and t is the time period in years.

Given that A = $35,000, r = 7%, n = 12 (since the interest is compounded monthly), and t = 6 years, we can plug these values into the formula to calculate the present value:

PV = $35,000 / (1 + 0.07/12)⁷²
PV = $35,000 / (1.00583)⁷²
PV = $35,000 / 1.45558
PV = $24,036.89

Therefore, the present value is $24,036.89.

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Answer:

-7 degrees

Step-by-step explanation:

Answer:

/ 3=/ 5 { alternate anglea}

/ 5+/6 =180° {straight angle}

/ 6=180-26

/ 6=154°

hope it helps

One-twelfth interest every month on an initial one pound will give (1 + (1/12))¹² pounds at the end of the year due to the compounding effect of interest.

The interest rate of investment of one-twelfth per month means that for every pound invested, one-twelfth of that amount will be added as interest at the end of the month. Therefore, at the end of the first month, the initial investment of one pound will earn an additional interest of (1/12) pound, making the total amount of money to be 1+(1/12) pounds.

At the end of the second month, the new amount of money will earn another one-twelfth of interest, which will be added to the previous total. Therefore, the new total amount of money will be (1+(1/12))+(1/12) = (1+(2/12)) pounds, which can be simplified to (1+(1/6)) pounds.

By the end of the twelfth month, the initial one pound investment will have earned twelve one-twelfth interests, which can be calculated as (1+(1/12)\()^12\) pounds, using the formula for compound interest. This simplifies to (1+1/12\()^12\) pounds or (1.0833\()^12\) pounds, which is approximately equal to 2.613 pounds.

Therefore, an initial investment of one pound with a one-twelfth interest rate per month will earn a total of (1+(1/12)\()^12\) pounds or approximately 2.613 pounds by the end of the year.

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The solution to the inequality is: n < -9.

Given the inequality statement, 4n - 6 (n + 1) > 12, to solve for the value of n, we would isolate the n to one side of the inequality as shown below:

4n - 6 (n + 1) > 12

Distribute

4n - 6n - 6 > 12

Combine like terms

-2n - 6 > 12

-2n - 6 + 6 > 12 + 6

-2n > 18

Divide both sides by -2

-2n/-2 < 18/-2

n < -9

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Answer:

y = - 7

Step-by-step explanation:

we have successfully verified the trigonometric identity:

sin^4(x) + cos^4(x) = 1 - 2cos^2(x) + 2cos^4(x)

To verify the trigonometric identity:

sin^4(x) + cos^4(x) = 1 - 2cos^2(x) + 2cos^4(x)

To verify this identity, we will manipulate one side of the equation until it resembles the other side. Let's start with the left side:

sin^4(x) + cos^4(x)

Recall the Pythagorean identity: sin^2(x) + cos^2(x) = 1. We can square this identity to get:

(sin^2(x) + cos^2(x))^2 = 1^2

Expanding the left side:

sin^4(x) + 2sin^2(x)cos^2(x) + cos^4(x) = 1

Now, we want to isolate sin^4(x) + cos^4(x). To do this, subtract 2sin^2(x)cos^2(x) from both sides:

sin^4(x) + cos^4(x) = 1 - 2sin^2(x)cos^2(x)

Next, we can use the Pythagorean identity again to replace sin^2(x) with 1 - cos^2(x):

1 - 2(1 - cos^2(x))cos^2(x)

Now, distribute -2cos^2(x) to the terms inside the parentheses:

1 - 2cos^2(x) + 2cos^4(x)

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Answer:

Step-by-step explanation:

Rob has (1/2) * x - $25.75 of his earnings left from this week. This is obtained by subtracting the amount spent on bills and the cost of the video game from his total earnings.

To find out how much of his earnings Rob has left, we need to calculate the portion he spent and subtract it from his total earnings.

Given that Rob spends 1/2 of his earnings on bills, he has 1 - 1/2 = 1/2 of his earnings remaining.

If Rob buys a video game for $25.75, we can subtract this amount from his remaining earnings.

Let's say Rob's total earnings for the week were x dollars.

Amount spent on bills: (1/2) * x

Amount spent on the video game: $25.75

Remaining earnings: x - [(1/2) * x + $25.75]

Simplifying the expression, we have:

Remaining earnings: x - (1/2) * x - $25.75

Remaining earnings: (1/2) * x - $25.75

So, Rob has (1/2) * x - $25.75 of his earnings left from this week.

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Answer:

3.6

Step-by-step explanation:

4.25 x 6 = 25.5 25.5 divided by 7 = 3.6

4.25 x 7 =29.7 29.7 divided by 6 = 4.9

The first student if correct.

Wayne's Actual ACT score is 19.2 where mean is 21, standard deviation is 5 and the Z - score is -0.6.

Standard Deviation:

Standard deviation is  a measure of the dispersion of a set of numerical values from their mean.

The general form of the standard deviation is,

\(SD=\sqrt{\frac{\sum (x_i-\bar{x})}{n} }\)

where

xi is each value in the data set,

x-bar is the mean, and

n is the number of values in the data set.

Given,

Mean = 21.

Standard deviation = 5

Wayne's standardized score on the act = −0.6 .

Here we need to find the Wayne's Actual ACT score.

Let x be the Wayne's Actual ACT score.

So,
=> z-score = (x - mean)/SD

Apply the values on it,

=> -0.6 = (x - 21) / 3

=> -1.8 = x - 21

=> x = 21 - 1.8

=> x = 19.2

Therefore, Wayne's Actual ACT score is 19.2

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Two marbles are selected at random with replacement.

the probability that both marbles are red in colour is 1/4..

Probability:

Probability multiply helps in visualize the multiple trials involved in a probability situation. The joint and conditional probabilities are easier to see and calculate with the use of the tree.

We have given that,

Number of Red marbles = 5

Number of Green marbles = 3

Number of blue marbles = 2

Total number of marbles = 10

i.e, total possible outcomes for selecting marbles = 10

Two marbles are selected at random with replacement.

we have to calculate probability that both marbles are red.

firstly, we consider that first selected marble is red.

Probability that the first selected marble is red

= 5/10

Then it put again with other marbles i.e with replacement.

second marble is selected from random.

Probability that both marbles are red in colour

= 5/10 ×5/10 = 25/100 = 1/4

Hence, the required probability is 1/4 .

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When you write your measurement as the mean ± standard deviation, it means that you are displaying how far the data is spread out from the mean value. A normal distribution is one that is symmetrical and bell-shaped, where most of the data lies near the mean value.

When you write your measurement as the mean ± standard deviation, it means that you are displaying how far the data is spread out from the mean value. In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. When you add the standard deviation to the mean and also subtract the standard deviation from the mean, you get the upper and lower bounds of the range that contains about 68% of the data. This range is called one standard deviation.The value of the standard deviation indicates how much the data varies around the mean. If the standard deviation is high, then the data is widely spread out and vice versa. Additionally, when you write a measurement as the mean ± standard deviation, it is assumed that the data is normally distributed. A normal distribution is one that is symmetrical and bell-shaped, where most of the data lies near the mean value.

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Interior Angle is 180n = 375 - x in given question.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360 °.

To determine the number of sides in a convex polygon given the sum of all but one of its interior angles, we can use the formula:

Sum of interior angles = (n - 2) * 180 degrees,

where n represents the number of sides in the polygon.

In this case, the sum of all but one of the interior angles is missing, so we need to subtract one interior angle from the total sum before applying the formula.

Let's denote the missing interior angle as x. Therefore, the sum of all but one of the interior angles would be the total sum minus x.

Given that the stamina is 15, we can express the equation as:

(15 - x) = (n - 2) * 180

Simplifying the equation, we have:

15 - x = 180n - 360

Rearranging the terms:

180n = 15 - x + 360

180n = 375 - x

Now, we need more information or an equation to solve for the number of sides (n) or the missing interior angle (x).

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Answer:

the answer would be 86

\(25.00 + 4.50 + 56.50\)

86

The probability that their coin flips will successfully divide them into two teams on the first try is 3/8.

To calculate this probability, we need to consider the possible outcomes of the four coin flips. Each coin flip has two possible outcomes: heads (H) or tails (T). Since there are four coin flips, there are a total of 2^4 = 16 possible outcomes.

Out of these 16 outcomes, we are interested in the ones where two coins show heads and the other two coins show tails. Let's denote H as heads and T as tails. The possible successful outcomes are HH TT, HT TH, and TT HH. There are three successful outcomes out of the 16 possible outcomes.

Therefore, the probability of successfully dividing into two teams on the first try is 3/16.

It's important to note that the order of the outcomes doesn't matter in this case. For example, HH TT and TT HH are considered the same outcome since both represent a successful division into a heads team and a tails team.

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The assumption that should not be met before conducting an independent groups t-test is that the samples should have the same number of participants.

An independent groups t-test is a statistical test used to compare the means of two independent groups of data. Before conducting this test, there are several assumptions that should be met to ensure the validity of the results. The first assumption is that the dependent variable should be measured on at least an interval level scale.

This means that the values of the dependent variable should be meaningful and can be compared using mathematical operations such as addition and subtraction. The second assumption is that the dependent variable scores should be normally distributed in their parent populations. This means that the distribution of scores should resemble a bell-shaped curve, with most scores clustering around the mean and fewer scores at the tails.

The third assumption is that the samples should be randomly selected to ensure that the sample is representative of the population from which it was drawn. The fourth assumption is that the samples should have approximately equal variances to ensure that the test is not biased towards one sample over the other. If any of these assumptions are violated, the results of the t-test may not be reliable.

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The dual linear program is as follows:

y1 + 4y2 - w1 = 1

2y1 + 3y2 + w2 = -2

-y1 + 4y2 + 2y3 >= 1

y1 - 2y3 <= 0

y2, y3 >= 0

The primal linear program is:

x1 + 2x2 - x3 + x4 >= 0

4x1 + 3x2 + 4x3 - 2x4 <= 3

-x1 - x2 + 2x3 + x4 = 1

x2, x3 >= 0

To find the dual, we introduce dual variables y1, y2, and y3 for the primal's three constraints, and w1 and w2 for the primal's two non-negativity constraints on x2 and x3, respectively.

The dual linear program is:

maximize 0y1 + 3y2 + y3

subject to:

y1 + 4y2 - w1 = 1

2y1 + 3y2 + w2 = -2

-y1 + 4y2 + 2y3 >= 1

y1 - 2y3 <= 0

y2, y3 >= 0

The objective function of the dual is the sum of the products of the primal's objective coefficients and the dual variables, which gives 0y1 + 3y2 + y3. The new objective is to maximize this expression subject to the dual constraints.

Note that the dual program is also written in standard form, with all inequality constraints replaced by equality constraints and non-negativity constraints.

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Inverse trigonometric integrals involve inverse trigonometric functions and are used to evaluate integrals containing trigonometric functions and their derivatives

Inverse trigonometric integrals are a group of integrals that include inverse trigonometric functions like arcsine, arccosine, and arctangent. These functions are utilized to assess integrals that include expressions containing trigonometric functions and their derivatives.

Inverse trigonometric functions are the Inverse of their respective trigonometric functions and can be utilized to find the point that compares to a given ratio of sides in a right triangle. Inverse trigonometric integrals are generally experienced in analytics and are helpful in different fields like physics, engineering, and statistics. They are ordinarily assessed utilizing algebraic manipulation, substitution, and integration by parts

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To plot the function f(x) = -4x^2 + sin(5x) and its derivative, and to save the results in a file named "results.txt" with 2 decimal places.

You can use the following MATLAB code:

```matlab

x = -10:0.5:10; % Generate x values

f = -4*x.^2 + sin(5*x); % Calculate f(x)

df_dx = -8*x + 5*pi*cos(5*x); % Calculate the derivative

% Saving results to file

output = [x', f', df_dx'];

dlmwrite('results.txt', output, 'delimiter', '\t', 'precision', '%.2f');

1. First, we define the range of x values using the vector `-10:0.5:10` to cover the desired interval with a step size of 0.5.

2. Next, we calculate the values of f(x) and its derivative using the defined mathematical expressions.

3. We then plot the function and its derivative using the `plot` function. The red dashed line represents f(x), and the blue solid line represents its derivative.

4. To save the results, we create a matrix `output` that concatenates the x values, f(x), and the derivative column-wise.

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Answer:

1. 1/120

2. 7/24

Step-by-step explanation:

n = 10

Number of defective = 3

1. Probability of all defective =

(Number of defective/n) x (number of defective -1/n -1)...(number of defective -n/n-1)

=3/10 x 2/9 X 1/8

= 6/720

= 1/120

2. probability of none defective

Since 3 are defective, those that are not defective = 7

The probability is therefore:

7/10 x 6/9 x 5/8

= 210/720

= 7/24.

Answer:2.25 m/s^2

Step-by-step explanation:

a = (v-u)/t = 27/12 = 2.25 m/s^2

Different logs measure different physical properties of the formation that are related to porosity, and the relationship between the log measurement and porosity can be expressed through equations.

The different logs used to obtain porosity and their principles of measurement, quantities measured, and relation to porosity.
There are three main types of logs used to obtain porosity: neutron logs, density logs, and sonic logs.
Neutron logs: These logs measure the hydrogen content in a formation, which is directly related to porosity. The tool emits neutrons that interact with hydrogen atoms, and the resulting gamma rays are measured. The count rate decreases with increasing porosity. The neutron log can be expressed as:
Porosity = (neutron log reading - matrix reading) / (fluid reading - matrix reading)
Density logs: Density logs measure the bulk density of a formation, which can be related to porosity. The tool emits gamma rays that interact with the formation, and the scattered gamma rays are measured. The bulk density decreases with increasing porosity. The density log can be expressed as:
Porosity = (matrix density - bulk density) / (matrix density - fluid density)
Sonic logs: Sonic logs measure the travel time of sound waves through a formation, which can be related to porosity. The tool sends an acoustic wave and measures the time it takes to travel a specific distance. The travel time increases with increasing porosity. The sonic log can be expressed using Wyllie's time-average equation:
Porosity = (sonic log reading - matrix reading) / (fluid reading - matrix reading)
In summary, neutron logs measure hydrogen content, density logs measure bulk density, and sonic logs measure travel time of sound waves. These measurements can be used to calculate porosity using the respective equations provided.

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Answer:

The average monthly payment would be most affected by Mark's observation of one significantly lower payment. The reason is that the average is calculated by summing all the payments and dividing by the total number of payments, so any extreme values (such as the significantly lower payment) can have a substantial impact on the average value.

Step-by-step explanation: