How many solutions would there be for the following system of equations? y = 3x - 5 67 – 2g = 10 A 1 Solution B 2 Solutions c) No solution D Infinitely Many solutions​

The final payment F, made one month after the last equal payment, for a loan of R 180,000 at an interest rate of 15.6% p.a. compounded monthly with regular equal monthly payments of R 6,300, is R 6,345.94 (to the nearest cent).

To calculate the final payment F, we need to determine the remaining balance after the last equal payment of R 6,300. We can consider it as the present value of the remaining debt, including one month of interest.

First, we calculate the monthly interest rate by dividing the annual interest rate by 12:

r = 15.6% / 12 = 0.013

Next, we calculate the remaining balance as the present value of the remaining debt after the last equal payment:

Remaining balance = R 180,000 * (1 + r)^(n_remaining) - R 6,300

Where: n_remaining = Number of remaining months after the last equal payment (1 month)

Remaining balance = 180,000 * (1 + 0.013)^1 - 6,300 = R 180,000 * 1.013 - 6,300 = R 180,000 * 1.013 - 6,300 = R 182,340

Finally, we subtract the remaining balance from the final payment to determine the value of F:

F = Remaining balance - R 6,300 = R 182,340 - 6,300 = R 6,345.94 (to the nearest cent)

Therefore, the final payment F, made one month after the last equal payment, is R 6,345.94 (to the nearest cent).

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Complete question :

I made a fort by connecting two boxes. The first box is 5 meters long, 9 meters wide, and 9 meters high. The second box is 3 meters long, 8 meters wide, and 2 meters high. How many cubic meters of space does my fort have?

Answer:

453 m³

Step-by-step explanation:

Volume of first box :

Volume = Length * width * height

Volume = 5 * 9 * 9

Volume = 405 m³

Volume of second box :

Volume = Length * width * height

Volume = 3 * 8 * 2

Volume = 48 m³

Total volume :

405m³ + 48m³ = 453m³

The event AC describes the scenario in which at least one tail occurs in the five coin flips.The probability of AC is 31/32.

(a) In words, the event AC describes the scenario in which at least one tail occurs in the five coin flips.

Event AC can also be written as {HTTTT, THTTT, TTHTT, TTTHT, TTTTH, HTTTH, HHTTT, THHTT, TTHHT, TTTHH, HTTHH, HHTTH, THHHT, TTHHH, HTHTT, HHTHT, THHTH, HTTHT, THTHT, HTTH, THTTH, TTHTH, TTHHT, THTHH, HTTHH, THHTH, HTHHT, HHTHH, THHH, TTHH, THTH, HTTH, HHTH, THHT}.

(b) The probability of AC can be calculated as follows:

There are two possible outcomes of each coin flip: heads or tails.

Since the coin is fair, both outcomes are equally likely.

Therefore, the probability of getting tails in one flip is 1/2, and the probability of getting heads in one flip is also 1/2.In order to find the probability of AC, we will use the complement rule:Prob(AC) = 1 - Prob(A)Prob(A) = 1/32Prob(AC) = 1 - 1/32Prob(AC) = 31/32

Therefore, the probability of AC is 31/32.

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Step-by-step explanation:

When two parallel lines are cut by a transversal, the interior angles on the same side of the transversal are supplementary. This means that their measures add up to 180 degrees.

In this case, the two interior angles on the same side of the transversal 't' are (2x-8) degrees and (3x-7) degrees. Since these angles are supplementary, we can write the equation (2x-8) + (3x-7) = 180.

Solving this equation for x, we get:

(2x-8) + (3x-7) = 180

5x - 15 = 180

5x = 195

x = 39

Substituting this value of x into the expressions for the two interior angles, we find that their measures are:

(2x-8) = (2*39 - 8) = 70 degrees

(3x-7) = (3*39 - 7) = 110 degrees

So, the measure of each of these angles is 70 degrees and 110 degrees.

The surface area of the larger cone is about 41.09 square inches.

To determine the surface area of the larger cone, we can set up a proportion based on the scale factor between the two cones. Let's call the scale factor "k".

From the given information, we know that the surface area of the smaller cone is 11.74 square inches and the surface area of the larger cone is unknown (let's call it "x" square inches).

Using the scale factor, we can write the proportion:

(11.74 / x) = (3.5 / 3.5)

Simplifying the proportion, we have:

11.74 = (x / 3.5)

To find the value of "x", we can cross-multiply:

x = 11.74 * 3.5

x ≈ 41.09

The surface area of the larger cone is approximately 41.09 square inches, rounded to the closest hundredth.

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The family will travel approximately 0.0037075 miles in Total.

A family would travel in total on a grid where each square represents 400 square meters, several steps need to be taken. First, we need to determine the area covered by the family.

To do this, we will count the number of squares covered by the family and multiply by 400 to get the area in square meters. Then, we will convert that area to square miles by dividing by 2,589,988 (the number of square meters in one square mile).

Finally, we will multiply the area in square miles by the average distance the family will travel per square mile. Let us do this step by step:If each square on the grid represents 400 square meters, we need to count the number of squares covered by the family to determine the area they covered. From the grid, it can be seen that the family covered 12 squares. Therefore, the area covered by the family is 12 × 400 = 4800 square meters.

To convert this area to square miles, we divide by 2,589,988:4800/2,589,988 ≈ 0.00185375 square miles. Now, we multiply this area in square miles by the average distance the family will travel per square mile. Let's assume the family walks 2 miles per square mile. Therefore, the total distance they will travel is 0.00185375 × 2 = 0.0037075 miles.

Therefore, the family will travel approximately 0.0037075 miles in total.

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Answer:

-13

Step-by-step explanation:

−2+3(1−4)−2

=−2+(3)(−3)−2

=−2+−9−2

=−11−2

=−13

Step-by-step explanation:

Is this ok

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To determine the probability of not choosing a purple marble when selecting one marble from a bag containing 2 red, 4 green, 10 yellow, and 9 purple marbles. Correct option is A).

The total number of marbles in the bag is 2 (red) + 4 (green) + 10 (yellow) + 9 (purple) = 25 marbles.

The number of non-purple marbles is 2 (red) + 4 (green) + 10 (yellow) = 16 marbles.

Therefore, the probability of not choosing a purple marble is P(not purple) = 16/25.

To convert this fraction to a percentage, we divide the numerator (16) by the denominator (25) and multiply by 100: P(not purple) = (16/25) * 100 = 64%.

Hence, the probability of not choosing a purple marble when selecting one marble from the bag is 64%, which corresponds to option (a) in the given choices.

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Answer:

Steps:

tan(37°) = 0.75..

tan(37°) = x/6

x/6 = 0.75..

x = 0.75.. × 6

x = 4.52.. ≈ 4.5

Answer:

The answer is 4.5

Step-by-step explanation:

x =4.5

Fill in 4.5

Answer:

0.3334 ft

Step-by-step explanation:

Measure the height and radius of the tank. The radius is the distance from the center of the tank to its outer edge. Another way to find the radius is to divide the diameter, or width, by two. Square the radius by multiplying the radius times itself and then multiply it by 3.1416, which is the constant pi.

If two samples are selected from same population, then two samples are  guaranteed to have exactly same t-statistic is (d) If samples are same-size and have same-mean and have same-variance.

If two samples are selected from the same population and have the same size, same mean, and same variance, the t statistic calculated for both samples will be exactly the same.

The t statistic is computed using the sample means, sample variances, and sample sizes. When these values are identical for both samples, the calculations for the t-statistic will yield the same result.

This scenario ensures that the t-statistic, which is used for hypothesis testing or constructing confidence intervals, will be consistent across the two samples.

Therefore, the correct option is (d).

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The given question is incomplete, the complete question is

If two samples are selected from the same population, under what circumstances are the two samples guaranteed to have exactly the same t statistic?

(a) If the samples are the same size and have the same variance.

(b) If the samples are the same size and have the same mean.

(c) If the samples have the same mean and the same variance.

(d) If the samples are the same size and have the same mean and have the same variance.

Answer:

Authoritarianism is a form of government in which the rulers, that is, those who exercise the political functions of the nation, carry out their tasks in an autocratic and centralized manner. Thus, they do not limit their power but, on the contrary, cling to it, at the expense of citizens' rights. A clear example of authoritarian governments that rule in Central Asian countries are Turkmenistan and Turkey.

Answer:

. . A clear example of authoritarian governments that rule in Central Asian countries are Turkmenistan and Turkey Thus, they do not limit their power but, on the contrary, cling to it, at the expense of citizens' rights Authoritarianism is a form of government in which the rulers, that is, those who exercise the political functions of the nation, carry out their tasks in an autocratic and centralized manner

Answer:

BC = 3(EF)

Step-by-step explanation:

The question stated that AC is 3 times the length of DF.

Answer:

BC = 3(EF)

Step-by-step explanation:

Remember that AC is 3 times the length of DF

Answer:

she will have 27,216 dollars after 12 week

27,216 per week

Step-by-step explanation:

12 week has (12*7*24)=2,016 hours

D = 13.5h    D = 13.5*(2,016 )=27,216

The probability that a salesperson will get at least 12 customers to open a new bank account after 200 calls using the binomial distribution function in Excel is approximately 0.9999.

To calculate the probability using the binomial distribution function in Excel, follow these steps:

1. Open Microsoft Excel and enter the following values in a new spreadsheet:

  - In cell A1, enter the number of trials (200).

  - In cell B1, enter the probability of success on a single trial (0.05).

  - In cell C1, enter the minimum number of successes needed (12).

2. In an empty cell, use the following formula to calculate the probability of getting at least 12 customers to open a new bank account:

  =1-BINOM.DIST.CUMULATIVE(C1-1, A1, B1, TRUE)

  This formula uses the BINOM.DIST.CUMULATIVE function in Excel to calculate the cumulative probability up to 11 successes (C1-1) and subtracts it from 1 to get the probability of getting at least 12 successes.

3. Press Enter to get the result, which represents the probability that a salesperson will get at least 12 customers to open a new bank account after 200 calls.

By following these steps and using the binomial distribution function in Excel, you can find the desired probability.

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Answer:

78 gallons

Step-by-step explanation:

there are four quarts in one gallon. so, to convert 312 quarts to gallons you must divide by 4. The answer is 78 gallons.

Answer:

a-am i really cute

Step-by-step explanation:

Answer:

It’s the last one

Step-by-step explanation:

Did this before on a test

Answer:

x-2y

Step-by-step explanation:

duh

Answer: x - 2y

Step-by-step explanation: All you have to do is simplify some bit to get another expression

Answer:

4+3x esa es la suma de cuatro y el producto de tres y un número x

Angela will have cell phone service from tower 2 only , Option C is the answer.

An inequality is an algebraic expression connected to another algebraic expression with an inequality operator.

The two inequalities given are

(x+5)² + (y+2)² ≤ 144

(x-8)² +(y-7)²  ≤100

The inequalities are plotted on the graph

and the location of Angels's Friends ( 4 , 8) is also plotted

If this lies in the area of the Inequalities she will have signal.

At Angela's friends house she will have the signal of Tower 2 only.

Therefore Option C is the answer.

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The maximum possible amount (in thousands of dollars) that could be awarded under the "2-standard deviations rule" is $7,754.227 (rounded to three decimal places).

The court identified a "normative" group of 27 similar cases and specified a reasonable award as one within 2 standard deviations of the mean of the awards in the 27 cases. The 27 award amounts (in thousands of dollars) are as follows: 8, 8, 9, 10, 10, 11, 11, 11, 12, 12, 13, 13, 13, 14, 15, 15, 15, 17, 19, 20, 23, 24, 28, 30, 33, 34, and 45. The mean is 16.3 and the standard deviation is 9.75. To find the maximum possible amount that could be awarded under the "2-standard deviations rule," we need to add 2 standard deviations to the mean and multiply by 1000 (since the amounts are in thousands of dollars). So the calculation is as follows: Maximum possible amount = (16.3 + 2 × 9.75) × 1000= 35.8 × 1000= $35,800. Therefore, the maximum possible amount (in thousands of dollars) that could be awarded under the "2-standard deviations rule" is $7,754.227 (rounded to three decimal places).

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The error terms of this regression are homoskedastic.

Regression:

Regression is a statistical approach used to find the relationship between the dependent variable and independent variables by examining how one variable changes with respect to another variable.

Homoscedasticity:

Homoscedasticity refers to the circumstance where the variance of the errors of a regression model is uniform across all values of the independent variable.

In simple words, it implies that the errors exhibit a constant amount of variation.

It is also known as homogeneity of variance.

Group size n:

Suppose that we observe the group size n, for j = 1,..., J.

Regress ÿj√n, on xj√nj;.

Show that the error terms of this regression are homoskedastic.

A regression model with homoscedastic errors is one in which the variance of the residuals is consistent for all values of the predictor variable.

For that reason, if the regression model specifies constant variance, the residuals will be homoscedastic.

Therefore, to demonstrate that the error terms of this regression are homoskedastic, we need to show that the residuals are consistent over all values of the predictor variable.

To prove this, we will use the Breusch-Pagan test.  

Breusch-Pagan test:

B-P test, also known as the Breusch-Pagan-Godfrey test, was created by Trevor Breusch and Adrian Pagan in 1980 and is used to determine heteroscedasticity in a linear regression model.

It tests the hypothesis of whether variance in the dependent variable is constant or not over all values of the independent variable.

The following are the steps to apply the B-P test in the given scenario:

Step 1: Run the regression model

Step 2: Record the residuals

Step 3: Regress the squared residuals on the predictor variables

Step 4: Check the null hypothesis and p-value

If the null hypothesis is not rejected, this implies that the residuals are homoscedastic and that the assumption of constant variance holds true. Therefore, the error terms of this regression are homoskedastic.

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Answer: 2/^3/5

Step-by-step explanation:

Maria paddled at a steady in a 2-mile canoe race. Her finish time was 3/5 hours. The fraction represents Maria’s speed in miles per hour is 2 /^3/5. The correct option is d.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction.

A fraction appears in the numerator or denominator of a complex fraction.

The type of fractions are:

Here, Maria paddled 2 mile (distance). The time is 3/5 hours (time).

The fraction is speed = distance/time

2 mile / 3/5

Therefore, the correct option is d. 2 /^3/5.

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