Find the following cardinalities: a. |A| when A= {2,3,4,5,..., 38). } = b. A when A= {re Z:-1

The monthly payment for a salary loan of 70,000 pesos at a 10% annual interest rate compounded monthly for 18 months is approximately 4,530.79 pesos.

To calculate the monthly payment for the salary loan, we can use the formula for the equal payment amount in an amortizing loan:

Payment = (Principal * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-n))

Where:

Principal = 70,000 pesos (loan amount)

Monthly Interest Rate = Annual Interest Rate / 12 = 10% / 12 = 0.0083333

n = number of payments (18 months)

Let's calculate the payment amount:

Payment = (70,000 * 0.0083333) / (1 - (1 + 0.0083333)^(-18))

Payment = 4,530.79 pesos

Therefore, the monthly payment for the salary loan is approximately 4,530.79 pesos.

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The point that satisfies the equation  y+6=x is :

A (−5,1)

The line represented by the equation y+6 = x can be rewritten as x - y = -6. The equation is in the standard form:

Ax + By = C.

The x-intercept and y-intercept can be found using the standard form. Then, plot these points on the graph and draw a straight line between them to complete the graph of the equation.

Using the equation x - y = -6 to find the x-intercept, set y = 0 and solve for x.

Thus, x - 0 = -6x = -6

The x-intercept of the line is (-6, 0).

Using the equation x - y = -6 to find the y-intercept, set x = 0 and solve for y.

Thus, 0 - y = -6y = 6

The y-intercept of the line is (0, 6).

Plot the x-intercept (-6,0) and the y-intercept (0,6) on the coordinate plane. Then, draw the line through these points.

Now, we need to find which point is found on the line represented by the equation y+6 = x.

We can now plug in the values of the points to the equation:

y + 6 = x

x - y = -6(-5) - 1 = -6

The point A (-5,1) satisfies the equation since x - y = -6.

So, the answer is A (−5,1).

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Let's denote the length of the table as "x" feet. According to the problem, the width is 2 feet less than the length, so the width can be represented as "x - 2" feet. The area of the table is given as 20 square feet.

The formula for the area of a rectangle is length times width. Therefore, we can set up the equation:

Length × Width = Area

x(x - 2) = 20

Expanding the equation, we get:

x^2 - 2x = 20

Rearranging the equation in quadratic form:

x^2 - 2x - 20 = 0

To solve this quadratic equation, we can factor it or use the quadratic formula. Let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 1, b = -2, and c = -20. Plugging these values into the quadratic formula, we get:

x = (-(-2) ± √((-2)^2 - 4(1)(-20))) / (2(1))

Simplifying further:

x = (2 ± √(4 + 80)) / 2

x = (2 ± √84) / 2

x = (2 ± 2√21) / 2

Simplifying the expression inside the square root:

x = (1 ± √21)

So the possible values for x are 1 + √21 and 1 - √21.

Since the length cannot be negative, we take the positive value:

x = 1 + √21

Now we can find the width by substituting this value of x into the expression for width:

Width = x - 2

Width = (1 + √21) - 2

Width = -1 + √21

Therefore, the dimensions of the table are approximately 1 + √21 feet for the length and -1 + √21 feet for the width.

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Answer:

8

Step-by-step explanation:

Because i wanted extra points.

Answer:

6

Step-by-step explanation:

No. of people going to beach = 46 .

Using Unitary Method ,

9 people can go in one van .

1 person can go in 1/9

46 people can go in 1/9 * 46 = 5.1

Since vans can't be in fraction , 1 extra van for 1 person is need that is for 46th person .

So total number of vans = 5 + 1 = 6

Answer:

{48, 64, 81}

Step-by-step explanation:

Answer:

hope this helpss

Step-by-step explanation:

Answer:

Step-by-step explanation:

if you have to simplify it then distribute -2

x²-2(x+5)=x²-2x-10

if problem is as mentioned by other answerer,then

[tex]\frac{d}{dx} (x^2-2(x+5))=-2\\x^2-2x-10= \int (-2dx)+c\\x^2-2x-10=-2x+c\\x^2=c+10\\x=\pm \sqrt{c+10}[/tex]

Step-by-step explanation:

f(3)= -2*3^2 +3 -5

= -2*9 +3 -5

= 16

Answer: the answer is A !!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Step-by-step explanation:

After paying off the mortgage, Frank will have accrued interest costs of $111,000 in total. $111,000 is the correct response.

The interest earned on savings that are computed using both the original principal and the interest accrued over time is known as compound interest. [tex]A = P(1 + r/n)^{nt[/tex], where P is the principal balance, r is the interest rate, n is the number of times interest is compounded annually, and t is the number of years, which is the formula for compound interest.

The total amount paid by Frank over 30 years will be the product of the monthly payment and the number of months in 30 years:

The total amount paid = Monthly payment × Number of months

Total amount paid = $700/month × 12 months/year × 30 years

Total amount paid = $252,000

However, this total amount includes both the principal (the original loan amount of $141,000) and the interest. To find the amount of interest paid, we need to subtract the principal from the total amount:

Interest paid = Total amount paid - Principal

Interest paid = $252,000 - $141,000

Interest paid = $111,000

Therefore, Frank will have paid $111,000 in interest once he has paid off the mortgage. The answer is A. $111,000.

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Answer:

90

Step-by-step explanation:

Answer:

90 degrees

Step-by-step explanation:

Step One: In order to solve this problem, you need to know that all angles in a triangle add up to 180 degrees.

Step Two: Now that we know that information, we need to add the angles we do know together: 34+56= 90 degrees.

Step Three: We subtract 90 from 180 to figure out the missing angles: 180-90= 90 degrees.

Answer:

hmmm I think u need to talk to ur teacher

Answer:

3861.75

Step-by-step explanation:

i hope its the good answer

Answer:

The minimize size that can be taken is - 31.28 or 31 .

Step-by-step explanation:

Lets calculate -

    Population standard deviation, [tex]\sigma=3.4 inches[/tex]

    Margin of error, E = 1

    Critical value , [tex]z_0_._0_5 =1.645[/tex]

Now , the size of the sample , [tex]n=(\frac{z\times \sigma}{E} )^2[/tex]

   Putting the given values ,

                    [tex]=(\frac{1.645\times 3.4}{1})^2[/tex]

                  = 31.28 or 31 .

The given table of the question has been attached here .

Hence , the answer is 31.

Answer:

x = 20

y = 7.2

Step-by-step explanation:

12/x = 9/15

9x = 180

x = 20

12/x= y/12

12/20 = y/12

144 = 20y

y = 7.2

y = 20

Answer:

x = 76°

Step-by-step explanation:

76° and x are alternative interior angles, so they are congruent when lines a and b are parallel

Answer:

18 is 3 more than 9- false

18 is 3 times as much as 6 - true

9 is 3 times as much as 27- false

9 is 3 more than 6 - true

Answer:

1)

Triangle formula:

A = 1/2bh

A = 1/2(3)(5.9)

A = 8.85

2)

Parallelogram Area:

A = bh

A = (8.9)(6)

A = 53.4

The profit function is; P(x) = -0.01·x² + 3.2·x + 150

What is a profit?

Profit is the amount gained following a business transaction, which is the difference between the amount received as payment for doing a business transaction, within a specified period, known as the revenue and the amount amount spent or invested in doing the business, including the fixed and variable expenses, which is the cost of the business.

The cost and the revenue functions, obtained from a similar question on the internet are;

The cost function is; C(x) = 150 + 5.8·x

The profit function is; R(x) = 9·x - 0.01·x²

The profit function, P(x), is therefore; P(x) = 9·x - 0.01·x² - (150 + 5.8·x) = -0.01·x² + 3.2·x + 150

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(a)  The equation of the regression line Percent Body Fat = -42.734 + 1.70 * Waist Size

(b) The higher the R-squared value, the better the regression line fits the data and the stronger the relationship between the variables.

(c) It means that as waist size increases, the percentage of body fat also tends to increase, and vice versa.

(d) The residual associated with this point is approximately -6.766

(a) The equation of the regression line can be written as:

Percent Body Fat = -42.734 + 1.70 * Waist Size

In this equation, Percent Body Fat represents the dependent variable, Waist Size represents the independent variable, -42.734 is the intercept (constant), and 1.70 is the coefficient for the Waist Size variable.

(b) R-squared is a measure of how well the regression line fits the data. In this context, R-squared of 67.8% indicates that 67.8% of the variation in the percent body fat can be explained by the linear relationship with waist size. The higher the R-squared value, the better the regression line fits the data and the stronger the relationship between the variables.

(c) To calculate the correlation coefficient (r), we can take the square root of the R-squared value. In this case, the correlation coefficient would be approximately √(0.678) ≈ 0.823.

Interpretation: The correlation coefficient (r) of 0.823 indicates a strong positive linear relationship between waist size and percent body fat. It means that as waist size increases, the percentage of body fat also tends to increase, and vice versa.

(d) To calculate the residual associated with the point for an individual with a waist size of 35 inches and 10% body fat, we need to substitute the waist size value into the regression equation and calculate the difference between the actual percent body fat and the predicted percent body fat.

Using the regression equation: Percent Body Fat = -42.734 + 1.70 * Waist Size

Substituting Waist Size = 35:

Percent Body Fat = -42.734 + 1.70 * 35 = -42.734 + 59.5 ≈ 16.766

The actual percent body fat for this individual is 10%. Therefore, the residual can be calculated as:

Residual = Actual Percent Body Fat - Predicted Percent Body Fat

Residual = 10 - 16.766 ≈ -6.766

The residual associated with this point is approximately -6.766. This indicates that the actual percent body fat is about 6.766 units lower than the predicted value based on the regression equation.

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The regression model estimates the portfolio return closest to 13.79% when the benchmark return is 14%.

The analyst performed a regression analysis using the benchmark returns as the explanatory variable and the portfolio returns as the dependent variable. The y-intercept of the regression line is 0.013, indicating that when the benchmark return is zero, the estimated portfolio return is 0.013%. The slope coefficient of the benchmark returns is 0.892, meaning that for every 1% increase in the benchmark return, the estimated portfolio return increases by 0.892%.

To estimate the portfolio return when the benchmark return is 14%, we plug the value of 14 into the regression model. The estimated portfolio return is calculated as follows: 0.013 + 0.892 * 14 = 13.79%.

Therefore, based on the regression analysis, the model estimates that the portfolio return would be closest to 13.79% when the benchmark return is 14%.

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The probability that Astronaut Joe, who is currently on Zorgon, will be affected by the impact is 0.667%.

To determine the probability that Astronaut Joe will be affected by the impact of the asteroid on planet Zorgon, we need to consider the area of the blast zone in relation to the total area of the planet.

An asteroid is heading for the planet Zorgon with a diameter of 2600 miles. When it hits, it will create a blast zone that extends 150 miles in all directions from the point of impact.

What is the probability that Astronaut Joe, who is currently on Zorgon, will be affected by this impact?

The total surface area of Zorgon is given by:2 * 3.14 * (1,300 miles)2 = 10.6 million sq Miles

The blast zone covers an area of:3.14 * (150 miles)2 = 70,685 sq Miles

To calculate the probability that Astronaut Joe will be affected by the impact, we divide the area of the blast zone by the total surface area of the planet.

That is,70,685 / 10.6 million = 0.00667 = 0.667%.

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Answer:

3500 dandelions

Step-by-step explanation:

To start you must multiply the number of dandelions by the growth rate to find the number of dandelions grown each day:

2,000 * 0.025 = 50

Then you multiply the number of dandelions by 30 for each day:

50 * 30= 1500

Lastly, you add the dandelions grown in 30 days to the original for your answer.

To find the slope of the line, we need to put the equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

Step 1: Divide both sides of the equation by 3 to get y by itself on one side of the equation.

3y = 9x + 18

y = 3x + 6

Step 2: Compare the equation to the slope-intercept form y = mx + b, and we can see that the slope is 3.

Therefore, the slope of the line is 3.

[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]

♥️ [tex]\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]

Complete question :

On their first dive, researchers explore a part of the ocean floor that is 60 feet below sea level. This depth can be represented by the integer -60. On their second dive, researchers explore a deeper depth. Write an inequality that represents the possible depth, d, of the researchers' second dive.

Answer:

d < - 60

Step-by-step explanation:

Depth explored during first dive = 60 feets below sea level = - 60 feets

The depth, d explored during second dive is deeper Than that explored during first dive

The inequality representing depth on second,

This means they the depth exceeds 60 feets below sea level. And hence. Deeper than - 60

Therefore, the depth will be values less Than - 60

Hence, d < - 60

Answer:

1/6

Step-by-step explanation:

1 out of the 6 cards is 4

Answer:

It's 3[tex]x^{2}[/tex]/86

hope this helps:)

On a 7-question multiple-choice test, with 4 answer choices for each question, we need to determine the probability of getting at least one question wrong.

To calculate the probability of getting at least one question wrong, we can consider the complementary probability, which is the probability of getting all questions correct and subtract it from 1.

The probability of getting a single question correct is 1/4, since there are 4 answer choices for each question. Therefore, the probability of getting all 7 questions correct is (1/4) * (1/4) * (1/4) * (1/4) * (1/4) * (1/4) * (1/4) = [tex](1/4)^7[/tex].

To find the probability of getting at least one question wrong, we subtract the probability of getting all questions correct from 1:

P(at least one question wrong) = 1 - P(all questions correct).

Substituting the probability of getting all questions correct, we have:

P(at least one question wrong) = 1 - [tex](1/4)^7[/tex]

Calculating this expression, the probability of getting at least one question wrong is approximately 0.99999, which is essentially equal to 1

Therefore, on a 7-question multiple-choice test with 4 answer choices for each question, the probability of getting at least one question wrong is extremely high, nearly 1. This means that it is highly likely that a test taker will get at least one question wrong on such a test.

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New Mexico is the correct option with coordinates (-2.5,-1).

To find the midpoint between two points in the Cartesian plane, you can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint between two points (x₁, y₁) and (x₂, y₂) are given by:

Midpoint = ((x₁ + x₂) / 2, (y₁ + y₂) / 2).

Here's a step-by-step process to find the midpoint:

1. Identify the coordinates of the two points you want to find the midpoint between. Let's say the coordinates are (x₁, y₁) and (x₂, y₂).

2. Add the x-coordinates of the two points together: x = x₁ + x₂.

3. Divide the sum by 2 to find the x-coordinate of the midpoint: x = x / 2.

4. Add the y-coordinates of the two points together: y = y₁ + y₂.

5. Divide the sum by 2 to find the y-coordinate of the midpoint: y = y / 2.

6. The coordinates (x, y) obtained from steps 3 and 5 represent the midpoint between the two given points.

In the given questions, we need to find the mid-point of Fairfield(-10,1) & Montgomery, Alabama(5,-3).

Let the point be N, N = ((-10 + 5) / 2, (1 + (-3)) / 2).

N = (-2.5,-1)

Therefore, From the given options ,the point where we stop is New Mexico marked at (-2.5,-1).

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Your answer for this question is B

The average rate of change of f(x) is less than average rate of change of g(x). Then the correct option is C.

A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.

The function f(x) is given in the table, then the rate of change of the function f(x) will be

Rate of change of f(x) = (-2 + 4.5) / (-2 + 3)

Rate of change of f(x) = 2.5

If function g is a quadratic function that contains the points (-3,5) and (0,14).

Then the rate of change of the function g(x) will be

Rate of change of g(x) = (14 - 5) / (0 + 3)

Rate of change of g(x) = 9/3

Rate of change of g(x) = 3

Thus, the average rate of change of f(x) is less than average rate of change of g(x).

Then the correct option is C.

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