you gave your friend a short term 2 year loan of 43.000 at 3% compounded annually. what will be your total return?

The average cost per item over the interval (1,000,1,010] is (C(1010) - C(1000)) / (1010 - 1000) = (10,000 + 5(1010) - 10,000 - 5(1000)) / 10 = $5.50.

The average cost per item over the interval [999.5, 1000] is (C(1000) - C(999.5)) / (1000 - 999.5) = (10,000 + 5(1000) - 10,000 - 5(999.5)) / 0.5 = $5.00.

The given function C(x) represents the cost in dollars to manufacture x items. To find the average cost per item over a given interval, we use the formula: (C(b) - C(a)) / (b - a), where a and b are the endpoints of the interval.

For the interval (1,000,1,010], we substitute a = 1000 and b = 1010 into the formula to obtain (C(1010) - C(1000)) / (1010 - 1000). Simplifying the expression using the given function C(x) yields ($10,000 + $5(1010) - $10,000 - $5(1000)) / 10 = $5.50 per item.

For the interval [999.5, 1000], we substitute a = 999.5 and b = 1000 into the formula to obtain (C(1000) - C(999.5)) / (1000 - 999.5). Simplifying the expression using the given function C(x) yields ($10,000 + $5(1000) - $10,000 - $5(999.5)) / 0.5 = $5.00 per item.

To find C'(1000), we differentiate the function C(x) with respect to x, which gives C'(x) = 5. The value of C'(1000) is therefore 5, rounded to 1 decimal place.

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The answer inequality of the given line will be -4<n<5.

A number line is an image of numbers plotted on a straight line, either horizontally or vertically. We can compare numbers and execute simple arithmetic operations on them easily by writing the numbers down on a number line. The starting point of a number line is often regarded as zero (0).

These numbers to the left of zero are all negative while the numbers just on right of zero are all positive. As a result, we can argue that on a number line, the value of numbers grows as we approach the right. The numbers on the right are therefore larger than the ones on the left, according to this statement.

The endpoints of the given line are -4 and +5.

So the value of inequality should lie between these two lines only.

The inequality can be written as n< 5 and n>-4

or -4<n<5

Hence the answer inequality of the given line will be -4<n<5.

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The explicit formula for the sequence is aₙ=(-4).(-4)ⁿ⁻¹ and the 8th term is 65536

The given sequence is -4, 16, -64, 256,...

If we observe the sequence it is a geometric sequence

aₙ=a.rⁿ⁻¹

a is the first term and r is the common ratio

From the sequence the first term is -4 and common ratio is -4

aₙ=(-4).(-4)ⁿ⁻¹

Plug in the value n as 8

a₈=(-4).(-4)⁷

The value of minus four power seven is minus sixteen thousand three hundred eighty four

a₈=(-4)(-16384)

When four is multiplied with sixteen thousand three hundred eighty four we get sixty five thousand five hundred thirty six

a₈= 65536

Hence, the explicit formula for the sequence is aₙ=(-4).(-4)ⁿ⁻¹ and the 8th term is 65536

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Answer: 3/4

Step-by-step explanation:

Slope=rise/run

In this case we rise up 3

And we run 4 to the right

Which makes the slope 3/4

Hi ! The answer would be 3/4.

To get this answer, the red line represents the RISE, and the blue line represents the RUN.

Your slope will always have RISE/RUN.

Now, you count how many squares there are in your rise, in this case, 3.

Then, you do the same for your run, which would be 4.

Rise/Run becomes 3/4.

What would determine it to be a negative? Well, if you see charts like these: You'll see that the red is going up, it is a positive slope, while the blue, which is going down, is a negative slope.

For example, if sales at your store increased, your slope would go up (positive), while if the opposite it'd go down (negative).

In this case, it is a positive slope.

The expectation value of the position squared when the particle in the box is in its third excited state is equal to \(\frac{9l^2}{8}\), where l is the length of the box. This is equal to nine-eighths of the length of the box squared.

The expectation value of the position squared when the particle in the box is in its third excited state can be calculated using the formula\(\langle x^2 \rangle = \frac{l^2}{8} \left( 2n^2 + 6n + 3 \right)\),

where n is the quantum number of the state and l is the length of the box. Here, n is 3, so the expectation value is equal to

\(\frac{l^2}{8} \left( 2 \times 3^2 + 6 \times 3 + 3 \right) = \frac{9l^2}{8}\).

This can be written as nine-eighths of the length of the box squared.

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a) The value of z corresponding to an area of 0.1210 can be found using statistical tables or a statistical calculator.

b) Similarly, the value of z corresponding to an area of 0.9898 can be obtained using statistical tables or a statistical calculator.

c) To find the value of z at the 45th percentile, we can use the standard normal distribution table or a statistical calculator.

a) To find the value of z corresponding to an area of 0.1210, you can use a standard normal distribution table or a statistical calculator. By looking up the area of 0.1210 in the table, you can determine the corresponding z-value. For example, if you find that the z-value for an area of 0.1210 is -1.15, then -1.15 is the value of z corresponding to the given area.

b) Similarly, to find the value of z corresponding to an area of 0.9898, you can refer to a standard normal distribution table or use a statistical calculator. Find the z-value that corresponds to the area of 0.9898. For instance, if the z-value for an area of 0.9898 is 2.32, then 2.32 is the value of z corresponding to the given area.

c) To find the value of z at the 45th percentile, you can use a standard normal distribution table or a statistical calculator. The 45th percentile corresponds to an area of 0.4500. By finding the z-value for an area of 0.4500, you can determine the value of z at the 45th percentile. For example, if the z-value for an area of 0.4500 is 0.125, then 0.125 is the value of z at the 45th percentile.

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Answer:

Step-by-step explanation: it is x=x

Answer:

x=x

Step-by-step explanation:

Answer:

sorry, but there is nothing to answer here :(

Step-by-step explanation:

Answer:

in abc, M???

Step-by-step explanation:

From the figure, angle ACB anf angle BCD are complementary, that is,

∠ACB + ∠BCD = 90°

Replacing with data

61° + ∠BCD = 90°

∠BCD = 90° - 61°

∠BCD = 29°

From the picture, angle BCD and angle FCE are vertical angles, then they are congruent, which means that:

∠FCE = ∠BCD = 29°

Angle FCA is a right angle, that is, ∠FCA = 90°. Therefore:

∠FCE + ∠FCA = ∠ACE

29° + 90° = ∠ACE

119° = ∠ACE

Answer:

(-3) x (-3) x (-3) x (-3)

(-3)²

Pregnancy is a physiological state where a woman carries a developing embryo or fetus within her uterus. It is an important stage in a woman's life that comes with various physical, emotional, and psychological changes. One of the earliest indicators of pregnancy is a missed menstrual period. However, there are other signs and symptoms that can confirm the presence of pregnancy. The correct answer is C) palpable fetal movement.

In the given options, all of the choices are potential signs of pregnancy, but only one of them can confirm the pregnancy. The correct answer is C) palpable fetal movement. This is because fetal movements are usually first felt by the mother between 16-25 weeks of pregnancy, indicating the presence of a growing fetus. This is a definitive sign of pregnancy that is not present in any other condition.

A missed menstrual period (option A) can be a strong indication of pregnancy, especially if the woman has regular menstrual cycles. However, it is not definitive as menstrual irregularities can be caused by various factors, such as stress or hormonal imbalances.

Abdominal enlargement (option B) can also be a sign of pregnancy, but it is not definitive as it can be caused by other factors, such as weight gain or bloating.

Morning sickness (option D) is a common symptom of pregnancy, but it is not definitive as it can also be caused by other factors, such as gastrointestinal disorders or food poisoning.

It is important to note that there are various other signs and symptoms of pregnancy, such as breast tenderness, fatigue, frequent urination, and food cravings or aversions. However, none of these symptoms are definitive on their own, and a confirmatory diagnosis of pregnancy can only be made through medical tests such as a urine or blood pregnancy test, or an ultrasound.

Overall, while the signs and symptoms of pregnancy can vary from woman to woman, it is important to seek medical advice and guidance if you suspect you are pregnant or have any concerns about your reproductive health.

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The required value of y for the unit circle is: 2/3

The circle is defined as the locus of a point whose distance from a fixed point is constant i.e center (h, k).

The equation of the circle is given by:

(x - h)² + (y - k)² = r²

where:

h, k is the coordinate of the center of the circle on coordinate plane.

r is the radius of the circle.

Here,

Equation of the unit circle is given as,

x² + y² = 1

Now substitute the given value in the equation,

5/9 + y² = 1

y² = 1 - 5/9

y² = 4/ 9

y = √(4/9)

y = 2/3

Thus, the required value of y for the unit circle is 2/3

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The 5 percentage of 1000 tests would be expected to show statistically significant results at a significance level of 0.05.

This is because when a null hypothesis is tested, the probability of rejecting it when it is true is equal to the significance level of the test, which in this case is 0.05. This means that if 1000 tests are run with a significance level of 0.05, then 5% of them or 50 tests would be expected to show statistically significant results. This is because the probability of rejecting the null hypothesis when it is true is equal to the significance level. Therefore, since the significance level is 0.05, then 5% of the tests would be expected to show significant results.

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Answer:

No, it is NOT a function.

Step-by-step explanation:

A functions' inputs are assigned to exactly one output.

We are given the points:

{(8,2) (4,-3) (6,4) (8,1)}

The input of 8 is repeating.

The given relation is not a function.  

Hope this helps!

Answer:

2 1/2 miles = 1/6 hours 2 1/2 miles * 6 = 1/6 hours * 6 12 1/2 miles = 6/6 hours 12 1/2 miles = 1 hour 12 1/2 miles/hr

Answer:

\(\frac{\frac{5}{2} * 6 }{\frac{1}{6} * 6}\) = \(\frac{\frac{30}{2} }{\frac{6}{6} }\)

Step-by-step explanation:

Answer:   \(\frac{\sqrt{55}}{8}\)

This is the same as writing sqrt(55)/8 where the 8 is not inside the square root.

=====================================================

Explanation:

Draw a right triangle in the quadrant Q1, which is in the northeast corner.

We're given \(\cos(\theta) = 3/8\). Recall that cosine is the ratio of adjacent over hypotenuse.

\(\cos(\text{angle}) = \text{adjacent/hypotenuse}\)

This right triangle will have an adjacent side of 3 and hypotenuse of 8.

Refer to the diagram below.

Use the pythagorean theorem \(a^2+b^2 = c^2\) to find the missing side is exactly \(\sqrt{55}\), which is the opposite side of angle theta.

Then as one last step, we would say:

\(\sin(\text{angle}) = \text{opposite/hypotenuse}\\\\\\\sin(\theta) = \frac{\sqrt{55}}{8}\)

--------------

A very similar approach is to use the pythagorean trig identity

\(\sin^2(\theta)+\cos^2(\theta) = 1\)

Solving for sine gets us

\(\sin(\theta)=\sqrt{1-\cos^2(\theta) }\)

Sine is positive in Q1.

Then plug in \(\cos(\theta) = 3/8\) and simplify. You should get the answer mentioned above.

D: C(25, 20) - C(13,7)  represents the number of ways a total inventory of twenty batteries be distributed among the six different types.

To find the total number of ways to distribute the twenty batteries among the six different types, we need to use the stars and bars method. Using this method, the number of ways to distribute 20 batteries among 6 different types is C(20 + 6 - 1, 6 - 1) = C(25, 5).

However, since we have only 12 A7b batteries, we need to subtract the cases where we distribute more than 12 A7b batteries. To do this, we calculate the number of ways to distribute the remaining 8 batteries among the 5 types other than A7b, which is C(8+5-1, 5-1) = C(12,4). Therefore, the total number of ways to distribute 20 batteries among the six different types while keeping at least 12 A7b batteries is C(25, 5) - C(12, 4) = C(25, 20) - C(13, 7).

The correct answer is option D.

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Answer: 1,520

Step-by-step explanation:

The time Jodie have left to match the record of Mandy is 15.11 seconds

Jodie:

= 40.25 seconds

Time spent on the rope = 12.84 seconds

Total time spent = 40.25 seconds + 12.84 seconds

= 53.09 seconds

Total time she have left to match the record = Mandy's obstacle course - Total time spent

= 68.2 seconds - 53.09 seconds

= 15.11 seconds

Therefore, the time Jodie have left to match the record of Mandy is 15.11 seconds

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Let the length of the wall be l.

The width is 4ft less than its length.

Therefore, the width is l - 4.

The wall is rectangular, therefore

Hence,

Hence, the length of the wall is 14 feet

Answer:

The tree is now 16 17/24 feet tall

Answer:

17 28/96 or simplify it to 17 7/18

Step-by-step explanation:

Since the denominators 12 and 8 share a common factor of 96 i did.

7 * 8 =56                                       7 *12 = 84

12 * 8 = 96                                     8 *12 = 96

\(25\frac{56}{96}\)            \(8\frac{84}{96}\)

Subtracted 25 -8 got 17 and did 84-56 and gotten 28.

Gotten \(17\frac{28}{96}\) then simplified and got \(17\frac{7}{18}\) since a common factor of 28 and 96 so happened to be 4

Overall, the exam scores approximately follow the 68-95-99.7% rule, suggesting that the distribution of scores is approximately normal.

The 68-95-99.7% rule, also known as the empirical rule, states that for a normal distribution, approximately:

68% of the data falls within one standard deviation of the mean

95% of the data falls within two standard deviations of the mean

99.7% of the data falls within three standard deviations of the mean.

Exam scores approximately follow this rule, we can calculate the range that includes one, two, and three standard deviations from the mean and see if the corresponding percentages of scores fall within these ranges.

The mean score is 77.7 points and the standard deviation is 8.44 points.

One standard deviation from the mean would be 77.7 ± 8.44 = [69.26, 86.14].

We can see that 16 out of the 20 scores fall within this range, which is approximately 80%, close to the 68% we would expect for a normal distribution.

Two standard deviations from the mean would be 77.7 ± 2(8.44) = [60.82, 94.58].

We can see that 19 out of the 20 scores fall within this range, which is approximately 95%, in line with the 95% we would expect for a normal distribution.

Three standard deviations from the mean would be 77.7 ± 3(8.44) = [52.38, 103.02].

All 20 scores fall within this range, which is 100%, more than the 99.7% we would expect for a normal distribution.

Could be due to the small sample size.

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The coordinates of A', B', C' and D' are obtained as follows:

A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.

Hence the coordinates of the dilated figure are obtained multiplying it's respective coordinates on the original figure by the scale factor.

The problem is incomplete, hence the answer was given in general terms.

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The future value of investment in 10 years for Steve will be $3,257.79 and for Gretta will be $5,187.48.

To find out how much money Steve and Gretta will have in 10 years, we need to calculate the future value of their investments using the compound interest formula:

FV = PV× (1 + r)ⁿ

Where:

FV is the future value of the investment

PV is the present value of the investment (i.e. the initial investment)

r is the annual interest rate (expressed as a decimal)

n is the number of years

For Steve:

PV = $2,000

r = 0.05 (5% expressed as a decimal)

n = 10

So, the future value of Steve's investment in 10 years will be:

FV = $2,000(1 + 0.05)¹⁰

FV = $3,257.79

For Gretta:

PV = $2,000

r = 0.10 (10% expressed as a decimal)

n = 10

So, the future value of Gretta's investment in 10 years will be:

FV = $2,000(1 + 0.10)¹⁰

FV = $5,187.48

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I believe it is C :)