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Use the compound interest formulas A = P 1 + r n nt and A = Pe rt to solve. 2) Suppose that you have $8000 to invest. Which investment yields the greater return over 6 years: 6.25% compounded continuously or 6.3% compounded semiannually? 2) A) $8000 invested at 6.3% compounded semiannually over 6 years yields the greater return. B) $8000 invested at 6.25% compounded continuously over 6 years yields the greater return. C) Both investment plans yield the same return.

Answers

Answer 1

Answer:

Answer: A

Compound interest simply defined as the interest added at regular interval. Compound interested can be calculated using

Compound interest = P (1+) ^nt and Pe ^rt

P = Initial balance

r = Annual interest rate

n = Number of times the interest is compounded per year

t =Number of year money is invested

Using

Compound interest = P (1+ ) ^nt

Continuous

P= $ 8000

t = 6

r = 6.25%

= 0.0625

n = 1

Compound interest = 8000 (1+) ^1×6

= 8000 (1 + 0.0625) ^6

= 8000 (1.0625) ^ 6

= 8000× 1.4387

= $11,509.6

Semi- annually

P= $ 8000

t = 6

r = 6.3%

= 0.063

n = 2

Compound interest = 8000 (1+) ^2×6

= 8000 (1 + 0.063) ^12

= 8000 (1.063) ^12

= 8000× 1.4509

= $11,607.0

Investing $ 8000 semi-annually at 6.3% for 6 years yields greater return

Therefore the answer is (A)

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(a) Count the number of ways to select a sample of 3 people to serve on a board of directors from a population of 6 people. answer: (b) If a simple random sampling procedure is to be employed, the chances that any particular sample will be the one selected are
If you’re good at Geometry, can you help me with some math equations?

Simplify \sqrt{25a^2}

Answers

Final Answer: 5a

Explanation:

Sure! Let's simplify this step by step.

Given \sqrt{25a^2}

Step 1: Recognize that the given expression \sqrt{25a^2} represents the square root of 25 times the square of 'a'.

Step 2: Break down the expression into two parts. We have a perfect square (25) and a square term (a^2). We can separate these inside the root as follows:

\sqrt{25} * \sqrt{a^2}

Step 3: Simplify \sqrt{25}. Since 25 is a perfect square, its square root is 5. Also, simplify \sqrt{a^2}. The square root of a^2 is 'a'. Now, we have:

5 * a

Therefore, the simplified form of \sqrt{25a^2} is 5a.

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Answer:

Step-by-step explanation:

Sqrt(25a^2)

Sqrt((5a)^2)

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If ZY = 2x + 3 and WX = x+4, find WX.

Your answer will be so appreciated.

Answers

i need more info on this ? to answer.

Two - way frequency tables

Answers

Answer: Two-way frequency tables are especially important because they are often used to analyze survey results. Two-way frequency tables are also called contingency tables. Two-way frequency tables are a visual representation of the possible relationships between two sets of categorical data.

Step-by-step explanation:

Graph the following function and then find the specified limits. When necessary, state that the limit does not exist.f(x)equals=left brace Start 3 By 2 Matrix 1st Row 1st Column x minus 3 2nd Column if x less than 5 2nd Row 1st Column 2 2nd Column if 5 less than or equals x less than or equals 6 3rd Row 1st Column x plus 4 2nd Column if x greater than 6 EndMatrixx−3 if x<52 if 5≤x≤6x+4 if x>6;findModifyingBelow lim With x right arrow 5limx→5 f(x)andModifyingBelow lim With x right arrow 6limx→6 f(x)

Answers

If I'm reading the question right, you have

$f(x)=\begin{cases}x-3&\text{for }x<5\n2&\text{for }5\le x\le6\nx+4&\text{for }x>6\end{cases}$

and you have to find

$\displaystyle\lim_(x\to5)f(x)\text{ and }\lim_(x\to6)f(x)$

The limits exist if the limits from either side exist. We have

$\displaystyle\lim_(x\to5^-)f(x)=\lim_(x\to5)(x-3)=2$

$\displaystyle\lim_(x\to5^+)f(x)=\lim_(x\to5)2=2$

$\implies\displaystyle\lim_(x\to5)f(x)=2$

and

$\displaystyle\lim_(x\to6^-)f(x)=\lim_(x\to6)2=2$

$\displaystyle\lim_(x\to6^+)f(x)=\lim_(x\to6)(x+4)=10$

$\implies\displaystyle\lim_(x\to6)f(x)\text{ does not exist}$

Final answer:

The function f(x) is a piecewise function. The limit as x approaches 5 equals 2 and the limit as x approaches 6 does not exist as the values from both sides are not the same.

Explanation:

The function f(x) given is a piecewise function which is defined differently on different intervals of x.

First let's graph these three conditions:

For x < 5, f(x) = x - 3. It is a straight line that crosses the Y-axis at -3.
For 5 ≤ x ≤ 6, f(x) = 2. It is a horizontal line along the height of 2 from x=5 to x=6.
For x > 6, f(x) = x + 4. It is a straight line that crosses the Y-axis at 4.

Next, we'll find the specified limits:

limx→5 f(x): As x approaches 5, we will look at values from both sides. From the left (x < 5), it would be 5 - 3 = 2. From the right (5 ≤ x ≤ 6), f(x) = 2. The value is the same from both sides, so the limit as x approaches 5 equals 2.
limx→6 f(x): As x approaches 6, from the left (5 ≤ x ≤ 6), f(x) = 2. From the right (x > 6), it would be 6 + 4 = 10. The values are not the same from both sides, so the limit as x approaches 6 does not exist.

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An advertisement claims that Fasto Stomach Calm will provide relief from indigestion in less than 10 minutes. For a test of the claim, 35 randomly selected individuals were given the product; the average time until relief was 9.25 minutes. From past studies, the standard deviation of the population is known to be 2 minutes. Can you conclude that the claim is justified? Find the P-value and let a = 0.05.

Answers

Answer:

$z=(9.25-10)/((2)/(√(35)))=-2.219$

$p_v =P(z<-2.219)=0.0132$

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v<\alpha$ so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is significantly lower than 10 minutes.

Step-by-step explanation:

Data given and notation

$\bar X=9.25$ represent the sample mean

$\sigma=2$ represent the population standard deviation

$n=35$ sample size

$\mu_o =10$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is less than 10 minutes, the system of hypothesis would be:

Null hypothesis: $\mu \geq 10$

Alternative hypothesis: $\mu < 10$

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=(\bar X-\mu_o)/((\sigma)/(√(n)))$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$z=(9.25-10)/((2)/(√(35)))=-2.219$

P-value

Since is a left tailed test the p value would be:

$p_v =P(z<-2.219)=0.0132$

Conclusion

Interpret the slope in terms of the situation. Does it make sense?Interpret the y-intercept in terms of the situation. Does it make sense?

Determine the equation of the line of best fit. Write your answer in slope-intercept form. Any non-integers in this problem should be entered as decimal numbers. Round to three decimal places when necessary.

Answers

a) Yes the slope makes sense, as the players foot length gets larger, their overall height also increases signifying that there is a correlation between foot size and height.

b) The y-intercept occurs when the line "intercepts" the y-axis. It also makes sense because a player that has 25 cm in distance from heel to toe may very likely be 1.55 meters in height. This is probable.

c) The equation of any line is:

y=mx+b (m= slope, b= y-intercept)

The slope of this line can be found by locating two points where the line intersects. I will use points (25.5,1.6) and (26.25,1.7).

The formula to find the slope is (y(2)-y(1)) / (x(2)-x(1)) = m

1.7 - 1.6 / 26.25 - 25.5 = .1/.75 = .13333

This line crosses the y-intercept at about 1.55m

The equation of this line is:

y = .1333 x + 1.55

Answer:

y = 0.133x - 1.791

Step-by-step explanation:

The points (27, 1.8) and (27.75, 1.9) lie on the line of best fit. Use these points to find the slope:

m = y2 - y1 1.9 - 1.8 0.1

------------- = ----------------- = -------- = 0.133

x2 - x1 27.75 - 27 0.75

Plug the value of the slope into the equation of the line y = mx +b to get .

y = 0.133x + b

Substitute the point (27, 1.8) into the equation and solve for b:

1.8 = 0.133(27) + b

b = -1.791

Plug the value of b into the equation of the line of best fit to get:

y = 0.133x - 1.791

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This answer came straight from the sample answer on Edmentum.com.

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