Suppose you draw a card, put it back in the deck, and draw another one. What is the probability that the first card is a two and the second is a three? (Enter your probability as a fraction.) P =

Answer:

If the cost X is higher or equal than 35, then no one wants to buy the any mouse pads.

Step-by-step explanation:

When N is 0 or lower then it means that no one buys it.

N=35x-[tex]x^{2}[/tex], if N=0 then

0=35x-[tex]x^{2}[/tex] or

35x=[tex]x^{2}[/tex] dividing each side by x we get:

35=x

This is the cost which nobody will buy the mouse pad anymore.

Answer:

oooooooooo yea

Step-by-step explanation:

Answer:

Option A) It is a constant.

Step-by-step explanation:

We are given the following information in the question:

The general form of regression equation is:

[tex]Y = a + bX[/tex]

[tex]Y-bX = a[/tex]

where Y is the dependent variable and we want to predict the value of Y and X is the independent variable and the predictor.

If we compare the above equation with the point slope form:

[tex]y = mx + c[/tex]

where m is the slope of the line and c is the y-intercept.

We get,

Slope, m  = b

Y-intercept = a

Thus, a is the y-intercept that is the value of Y when X is 0.

It is a constant.

It can also be interpreted as the difference of Y and X when slope is 1.

The constant 'a' in the regression equation represents the y-intercept, which is the value of Y when X is equal to 0.

The constant a in the regression equation Y = a + bX is called the y-intercept. It represents the value of Y when X is equal to 0. In other words, it is the point where the regression line crosses the y-axis.

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Answer:

D

Step-by-step explanation:

16*12 is 192. Plus the 6 for the bride and groom, and you get a total of 198.

Amy will need between 16 to 22 round tables for her wedding reception, accounting for a total guest range of 198 to 270, and considering that the head table seats 8 people. We calculate the number of tables by dividing the remaining guests by 12 and rounding up.

Let's solve the problem of determining the number of round tables Amy will need for her wedding reception. First, we know that the head table can sit the bride, groom, and their 6 attendants, totaling 8 people. Next, we calculate the number of guests that can be seated at the round tables, by subtracting the 8 people at the head table from the total number of guests:

Each round table can sit 12 guests, so we divide the numbers of remaining guests by 12 to find the range of tables needed:

Since we can't have a fraction of a table, we round up because each table can only seat whole numbers of guests. Therefore, Amy will need at least 16 tables for the minimum number of guests and at most 22 tables for the maximum number of guests.

The range for the number of round tables Amy will need for her reception, therefore, is 16 to 22 tables.

After reviewing the options, we can see that Option D matches our calculated range and is the correct choice for Amy’s wedding reception planning.

You can use variables to model the situation and convert the description to mathematical expression.

The time that the fountain will take to get drained completely with both valves open is approximately 2.27 hours.

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on  methods can be used to convert description to mathematical expressions.

Let the fountain contains V amount of water

Let the first valve emits x liter of water per hour

Let the second valve emits y liter of water per hour

Then, from the given description, we have:

With only the first valve open, the fountain completely drains in 4 hours

or

[tex]x \times 4 = V\\\\x = \dfrac{V}{4}[/tex] (it is since V volume of water is drained when we let x liter of water drained for 4 hours, thus adding x 4 times which is equivalent of x times 4)

Similarly,

With only the second valve open, the fountain completely drains in 5.25 hours
or

[tex]y \times 5.25 = V\\y = \dfrac{V}{5.25}[/tex]

Let after h hours, the fountain gets drained, then,

[tex]x \times h + y \times h = V\\\\\dfrac{V}{4}h + \dfrac{V}{5.25}\times h = V\\\\\text{Multiplying both the sides with} \: \dfrac{4 \times 5.25}{V}\\\\5.25 \timses h + 4 h = 4 \times 5.25\\9.25h = 21\\\\h = \dfrac{21}{9.25} \approx 2.27[/tex]

Thus,

The time that the fountain will take to get drained completely with both valves open is approximately 2.27 hours.

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Final answer:

By adding the work rates of the two valves and then calculating the reciprocal of the combined rate, it is estimated that it will take approximately 2.27 hours for the fountain to drain with both valves open.

Explanation:

To find out how long it will take for the fountain to drain with both valves open, you can use the rate of work formula, which states that work is the product of rate and time. When dealing with two independent work rates that contribute to completing a single job, we can add their work rates together to find the combined work rate.

Valve 1's rate of work is draining the fountain in 4 hours, which means its rate is 1/4 fountain per hour. Valve 2's rate of work is draining the fountain in 5.25 hours, which means its rate is 1/5.25 fountain per hour.

To find the combined rate, we add these two rates together:

1/4 + 1/5.25 = 0.25 + 0.19 = 0.44 (approximately)

This combined rate is 0.44 fountain per hour. Now, to find the total time to drain the fountain with both valves open, we take the reciprocal of the combined rate:

1 / 0.44 = 2.27 hours (approximately)

Therefore, it will take approximately 2.27 hours for the fountain to drain with both valves open.

Answer: $66

Step-by-step explanation:

Area of a rectangular =length*breadth

= 3.2 km * 3.0 km = 9.6km(squared)

Note, 1.6km = 1 mile

Cost of a hiking trail = $11 per mile

Converting kilometer to kill = 9.6km/1.6km = 6 miles

Hence, cost of a hiking trail to surround the rectangular shaped wilderness = $11 * 6 = $66

In case the cost is $11,000 per mile; total cost of hiking trails to surround the wilderness equals $66,000

You can find the cost of the trail by first calculating the perimeter of the rectangular wilderness area in kilometers, converting this into miles, and then multiplying by the given cost per mile. The total cost to install the trail would be approximately $85,250.

To calculate the cost of installing the hiking trail, we first need to find the perimeter of the rectangular forest, which will represent the length of the trail. In a rectangle, the perimeter is calculated as 2*(length + width).

Thus, the perimeter of the forest is 2*(3 km + 3.2 km) = 2*6.2 km = 12.4 km.

Next, we need to convert this into miles, as the cost is given in dollars per mile. We know that 1 mile is approximately equivalent to 1.6 km, so to convert km to miles, we can divide the distance in kilometers by 1.6.

The length in miles is therefore 12.4 km / 1.6 = 7.75 miles.

Finally, to find the total cost, we multiply the length of the trail in miles by the cost per mile: $11,000*7.75 miles = $85,250.

So, the cost to install the trail surrounding the wilderness area would be approximately $85,250.

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Answer:

The answer to your question is the last option

Step-by-step explanation:

Here there is a rational function so, we need to find the values where the denominator equals zero.

                         [tex]f(x) = \frac{x^{2} + 6x + 5}{x^{2}- 25 }[/tex]

                                [tex]x^{2} - 25 = 0[/tex]

Factor                      (x - 5)(x + 5) = 0

                               x₁ - 5 = 0               x₂ + 5 = 0

The function does not exist in -5 and 5

                              x₁ = 5                    x₂ = -5

Domain

                      (  -∞ , -5) U (-5, 5) U (5, ∞)

Answer:

the answer is d in edge

Step-by-step explanation:

(–∞, –5) U (–5, 5) U (5, ∞)

Answer: it’s easy your teacher should’ve taught this in 9th

Step-by-step explanation:

Answer:

The answer to your question is  2 x 10¹⁴

Step-by-step explanation:

Process

1.- Divide the whole numbers

                                                [tex]\frac{4}{2}  = 2[/tex]

2.- Apply rule of exponents

                                              8 - (-6) = 8 + 6 = 14

3.- Write the answer

                                              2 x 10¹⁴

Answer: a) Labor force participation rate = 72.46%, b) Unemployment rate = 1.8%.

Step-by-step explanation:

Since we have given that

Number of people who have at least a bachelor's degree = 71.9 millions

Number of people who were employed = 52.1 millions

Number of people who were unemployed = 1.3 millions

So, Labor- force participation rate would be

[tex]\dfrac{Employed}{Total}\times 100\\\\=\dfrac{52.1}{71.9}\times 100\\\\=72.46\%[/tex]

Unemployment rate for this group would be

[tex]\dfrac{Unemployed}{total}\times 100\\\\=\dfrac{1.3}{71.9}\times 100\\\\=1.8\%[/tex]

Hence, a) 72.46%, b) 1.8%.

Answer:

i) There is insufficient evidence to support the claim that the standard deviation of the instruments is less than 0.00002 millimeters.

ii) [tex] p_v= P(\chi^2_{7} <1.75)=0.0276[/tex]

Step-by-step explanation:

[tex]s=0.00001[/tex] represent the sample standard deviation

[tex]\alpha =0.01[/tex] represent the significance level for the test

[tex]\sigma_o =0.00002[/tex] represent the value that we want to test

n=8 represent the sample size

A chi-square test can be used to test "if the standard deviation of a population is equal to a specified value. This test can be either a two-sided test or a one-sided test".

Null and alternatve hypothesis

The system of hypothesis on this case would be given by:

Null Hypothesis: [tex]\sigma \geq 0.00002[/tex]

Alternative Hypothesis: [tex]\sigma <0.00002[/tex]

The statistic to test this is given by:

[tex]T=(n-1)(\frac{s}{\sigma_0})^2 [/tex]   (1)

Part i) Calculate the statistic

If we replace into formula (1) we got this:

[tex]T=(8-1)(\frac{0.00001}{0.00002})^2 =1.75 [/tex]   (1)

The critical region for a for a lower one-tailed alternative is given by

[tex]T< \chi^2_{1-\alpha/2,N-1}[/tex]

The degrees of freedom are given by

[tex] df=n-1=8-1=7[/tex]

And if we use the Chi Square distribution with 7 degrees of freedom we see that [tex] \chi^2_{1-0.01/2,7}=1.239[/tex]

And our critical region would be [tex]T< 1.239[/tex] so on this case we can conclude that we fail to reject the null hypothesis. So it's not enough evidence to conclude that the population standard deviation is less than 0.00002 mm.

Part ii) Calculate the p value

In order to calculate the p value we can do this:

[tex] p_v= P(\chi^2_{7} <1.75)=0.0276[/tex]

If we compare this value with the significance level (0.01) we see that [tex]p_v>\alpha[/tex]

This agrees with the conclusion since when the p values is greater than the significance level we FAIL to reject the null hypothesis, same conclusion as part i).

Answer:

c

Step-by-step explanation:

Answer:

Ashley and her 4 friends would required 5.33 hours to repair 1575 bags of sample.

Step-by-step explanation:

75% is written as 0.75 as a decimal or 3/4 as a fraction.

Her friends take 75% longer, so multiply the time it takes Ashley by 1 + the percentage: 1.75 as a decimal or [tex]1 \frac{3}{4} \ \ or \ \ \frac{7}{4}[/tex] as a fraction.

[tex]\frac{2}{3} \times \frac{7}{4} =\frac{14}{12} = 1 \frac{2}{12} = 1 \frac{1}{6} minutes[/tex].

1 hour = 60 minutes.

Divide minutes in an hour by minutes per pack:

Ashley can pack: [tex]\frac{60}{\frac{2}{3}} = 90 \ bags\ per \ hour[/tex]

1 friend can pack: [tex]\frac{60}{1\frac{1}{6}}=\frac{360}{7} = 51 \frac{3}{7} \ bags \ per \ hour.[/tex]

multiply the amount 1 friend can pack by 4 friends: [tex]51 \frac{3}{7} \times 4 = \frac {1440}{7} = 205 \frac{5}{7} \ bags \ per \ hour[/tex]

Ashley and her friends can pack [tex]90 + 205 \frac{5}{7} = 295 \times \frac{5}{7} \ bags \ per \ hour.[/tex]

Now divide the total bags by bags per hour:

[tex]\frac{1575}{295 \frac{5}{7}} = 5.33 \ hours[/tex] ( Round answer as needed.)

Hence, Ashley and her 4 friends would required 5.33 hours to repair 1575 bags of sample.

Final answer:

The major difference between a calculator and a computer in performing calculations is that a calculator requires more human interaction for input and verification, whereas a computer can process complex tasks with less human assistance and is generally faster. Therefore, option A is the correct answer.

Explanation:

The primary difference between a calculator and a computer when performing calculations is that calculators typically require more human interaction to input and verify data, while computers can process complex tasks with less human assistance. A calculator is designed for straightforward numerical computations and requires accurate input from the user. Meanwhile, a computer can carry out a wide range of tasks, including calculations, with greater speed and autonomy, thanks to its ability to run complex software programs. However, even though computers are powerful, solving certain mathematical problems, such as differential equations, can be challenging since they cannot make infinitely fine time steps and must approximate using small ones. Moreover, calculators, being simpler devices, require very little energy to operate and often rely on solar cells or small batteries, unlike computers, which have a greater energy demand. Therefore, option A is the correct answer.

Answer:

Step-by-step explanation:

An ellipse is of the form:

[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex] if it is horizontally stretched, or

[tex]\frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}=1[/tex] if it is vertically stretched.

To begin writing the equation of the ellipse, we will group together all the x-terms and then all the y-terms, moving the constant to the other side of the equals sign in order to make completing the square on these 2 terms a bit easier.

[tex](36x^2+360x)+(25y^2+100y)=-100[/tex]

The first rule for completing the square is that the leading coefficients on the squared terms HAVE to be a 1.  Neither of ours is, so we factor those out, getting:

[tex]36(x^2+10x)+25(y^2+4y)=-100[/tex]

Now we can complete the squares.  We will start with the x-term.  The rule is to take half the linear term, square it, then add it to both sides.  Our linear x-term is a 10.  Half of 10 is 5, and 5 squared is 25.  So we add 25 inside the parenthesis with the x stuff, BUT we cannot forget about that 36 hanging around out front refusing to be ignored.  It is a multiplier.  That means that we didn't just add in 25, we added in 25 * 36 which is 900.  So what we have right now is

[tex]36(x^2+10x+25)+25(y^2+4y)=-100+900[/tex]

Now we will do the same with the y-term.  Take half the linear term, square it, and add it (along with its multiplier) to both sides.  Our linear y-term is 4.  Half of 4 is 2, and 2 squared is 4, so now we have:

[tex]36(x^2+10x+25)+25(y^2+4y+4)=-100+900+100[/tex]

Now we will do 2 things simultaneously.  We will simplify the right side which is easy, and then create the perfect square binomials on the left that was the whole point of doing all that.  It now looks like this:

[tex]36(x+5)^2+25(y+2)^2=900[/tex]

Almost there.  Last thing we do is divide everything by 900 so we get a 1 on the right:

[tex]\frac{36(x+5)^2}{900}+\frac{25(y+2)^2}{900}=1[/tex]

Simplifying by division in both the rational terms:

[tex]\frac{(x+5)^2}{25}+\frac{(y+2)^2}{36}=1[/tex]

That means that this is a vertically stretched ellipse with a = 6 and b = 5.  In an ellipse, the a value is always the bigger one.  So if the bigger value in the denominator is under the x fraction, then it is a horizontal ellipse.  If the bigger value in the denominator is under the y fraction, like ours, then it is a vertical ellipse.

Answer:

Meningitis

Step-by-step explanation:

Meningitis is a inflammation of the membrane surrounding your brain and spinal cord.

In most cases it is caused by viral infection.

Some cases it improve without treatment in few days

Symptoms include:

As 17 year old had some symptoms such as headache,stiff neck, chills and vomiting o might be he have been suffered from Meningitis.

Answer:a is the correct option

Step-by-step explanation:

The table is divided into columns for month, sales and expense

Total number of sales for four months is determined by adding up the sales for each month. It becomes

35.75+65.34+12.15+49.68= $162.92

Total number of sales for four months is determined by adding up the expenses for each month. It becomes

43.18+52.24+41.09+59.50=196.01

Profit or loss = total sales - total expenses

Therefore 162.92-196.01 = - $33.09

It's a loss because it is negative

The computed value of the test statistic is 4.06 when using a sample size of 25 observations and a correlation coefficient of 0.60. Since this value is greater than 2.045 (the critical value for a two-tailed test at an alpha level of 0.05), we conclude that the population correlation is significantly different from zero.

In the context of this question, the student is conducting a hypothesis test to examine whether the population correlation is significantly different from zero. Given that the student has a sample size of 25 observations with a correlation coefficient of 0.6, we can calculate the test statistic. Our first step is to find the t value using the formula: t = r*sqrt[(n-2)/(1-r²)], where n is the sample size and r is the correlation coefficient.

Substituting the given values, t=0.6*sqrt[(25-2)/(1-0.6²)].

Solving this gives a t-value that can be rounded to 4.06. Since this value is greater than the critical value of 2.045 for a two-tailed test at an alpha level of 0.05, we reject the null hypothesis and conclude that the sample correlation coefficient is statistically significant, meaning it is unlikely that the correlation in the population is zero.

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Answer:

5/7 > 1/13. Hence Greater than Symbol will be used to compare the fractions.

Step-by-step explanation:

Given:

Two fractions given are 5/7 and 1/13

We will first calculate each of the fraction and then we will decide which one is greater and which one is smaller accordingly we will assign the symbol for the same.

First we will find the answer for 5/7.

Now dividing the number 5 from 7 we get;

[tex]5/7= 0.714[/tex]

Now we will find the answer for 1/13

Now dividing the number 1 from 13 we get;

[tex]\frac{1}{13}= 0.076[/tex]

From above we can see that 0.714 is greater than 0.076.

Hence we can say that 5/7 is greater than 1/13.

So the symbol used will be greater than > where number 5/7 is greater than 1/13

5/7 > 1/13

5/7>1/13 is the answer because 5/7 is closer to its whole when a number is closer to its whole its bigger for example 4/5>7/10 hope it helps

Answer:

Step-by-step explanation:

the formular for distance between two points is: [tex]\sqrt{(x2-x1)^2+(y2-y1)^2} \\\\\sqrt{4^{2}+1^{2} } \\\sqrt{17}\\ = 4.12[/tex]

Answer: Distance = 4.123

Step-by-step explanation:

The given coordinates are P(-1,5) and Q (3,4)

- 1 = x1 = the horizontal coordinate(along the x axis) at P

3 = x2 = the horizontal coordinate (along the x axis) at Q

5 = y1 = vertical coordinate( along the y axis) at P

4 = y2 = vertical coordinate(along the y axis) at Q

The distance between points P and Q is expressed as square root of the sum of the square of the horizontal distance and the square of the vertical distance. It becomes

Distance = √(x2 - x1)^2 + (y2 - y1)^2

Distance = √(3 - - 1)^2 + (4 - 5)^2

Distance = √ 4^2 + (-1)^2

Distance = √16+1 = √17

Distance = 4.123

Answer:

The total number of men is 32. Of these men, 25 wore a watch. So, the number of men who didn’t wear a watch is 7, because 32 − 25 = 7.

Step-by-step explanation:

Answer:

Internal users refer to management members of a company and other people who use financial information to run and manage the business

Explanation:

They work within the business and make business decisions. Accounting information is important for all management levels. In order to make decisions about the company's future, the top managers need information about the past performance of the company.

To determine the results of their past decisions, they need data. The financial statements will determine the company's performance and its financial position and guide them in making future decisions.

Answer: A. To make business decisions and compare business performance with previous years

Explanation:

Management uses accounting information for evaluating and analyzing an organization's financial performance and position, to take important decisions and appropriate actions to improve the business performance in terms of profitability, financial position, and cash flows.

Internal users refer to the members of a company's management and other individuals who use financial information in running and managing the business. They work within the company and make decisions for the business.

Answer:

  16

Step-by-step explanation:

Let "a" represent the measure of the angle. Then ...

  5a -30 = 2a +18

  3a = 48 . . . . . . . add 30-2a

  a = 16 . . . . . . . . . divide by 3

An angel is beyond measure, but this angle has measure 16.

Answer:

The answer is 1.5

Step-by-step explanation:

You have to find the pattern and work your way down to the 11th term.

Answer:

1.5

Step-by-step explanation:

The sequence given is a geometric progression (G.P). For a G.P where the first term is a, the common ratio (which is the ratio between successive terms), the nth term of the GP is given as

Tn = ar^n-1

From the sequence given  

a = 1536

r = 768/1536

= 1/2

= 0.5

Hence the 11th term of the sequence

T11 = 1536 (1/2)^11-1

= 1536 (1/2)^10

= 1536/1024

= 1.5

Answer: 0.0142

Step-by-step explanation:

Given : The mean height of women in a country​ (ages 20 - ​29) is 64.2 inches.

i.e. [tex]\mu=64.2[/tex]

Also, [tex]\sigma=2.58[/tex]

Sample size : n= 50

Let x denotes the height of women.

Then, the probability that the mean height for the sample is greater than 65​ inches :-

[tex]P(x>65)=1-P(x\leq 65)\\\\=1-P(\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}\leq\dfrac{65-64.2}{\dfrac{2.58}{\sqrt{50}}})\\\\=1-P(z\leq2.193)\ \ [\because z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=1-0.9858463\ \ [\text{By using z-value table or calculator}]\\\\=0.0141537\approx0.0142[/tex]

Hence, the the probability that the mean height for the sample is greater than 65​ inches = 0.0142

Answer:

  2485

Step-by-step explanation:

The number of seats in row n is given by the explicit formula for an arithmetic sequence:

  an = a1 +d(n -1)

  an = 20 +3(n -1)

The middle row is row 18, so has ...

  a18 = 20 + 3(18 -1) = 71 . . . . seats

The total number of seats is the product of the number of rows and the number of seats in the middle row:

  capacity = (71)(35) = 2485

The seating capacity is 2485.

Answer: The speed of the motorboat in still water is 45mph

The current rate is 9mph.

Step-by-step explanation:

Let u be the motorboat speed in still water and v be the current rate.

The effective speed going upstream is

Distance÷Time = 108÷3 = 36mph

It is the DIFFERENCE of the motorboat speed in still water and the rate of the current. It gives you your first equation

u - v = 36. (1)

The effective speed going downstream is

Distance÷Time = 108÷2 = 54mph

It is the SUM of the motorboat speed in still water and the rate of the current. It gives you your second equation

u + v = 54. (2)

Thus you have this system of two equations in 2 unknowns

u - v = 36, (1) and

u + v = 54. (2)

Add the two equations. You will get

2u = 36 + 54 = 90 ====> u = 90÷2 = 45mph

So, you just found the speed of the motorboat in still water. It is 45mph

Then from the equation (2) you get v = 54 = 45 = 9mph is the current rate.

Answer. The speed of the motorboat in still water is 45mph

The current rate is 9mph

Answer:

H₀: µ ≤ $8,500; H₁: µ > $8,500

z= +1.645

Step-by-step explanation:

From the given problem  As average cost of tuition and room and board at a small private liberal is less than the financial administrator As hypothesis is true.

As standard deviation is $ 1,200

α = 0.05

H₀: µ ≤ $8,500

if the null hypothesis is true then value for critical z is +1.645.

The critical z-value for a one-tailed test at a significance level (α) of 0.05 is approximately 1.645. This statistic is used in hypothesis testing to make informed financial decisions about tuition costs.

We are asked to find the critical z-value for a one-tailed test at a significance level (α) of 0.05. In this case, the financial administrator believes the average cost is higher, thus the test is one-tailed to the right. Looking up the z-table, we know that for a one-tailed test with a significance level of 0.05, the critical z-value is 1.645 (approximate).

The information about rising tuition costs and student loan debt demonstrates the real-world importance of using statistical analysis to understand trends and make informed financial decisions.

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Each rope was 84.64 meters long.

Step-by-step explanation:

Given,

No. of ropes bought = 66

Total length = 5586.5 meters

Length of one rope = [tex]\frac{Total\ length}{No.\ of\ ropes\ bought}\\[/tex]

[tex]Length\ of\ one\ rope=\frac{5586.5}{66}\\Length\ of\ one\ rope=84.64\ meters[/tex]

Hence,

Each rope was 84.64 meters long.

Keywords: Division.

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Final answer:

The value of the CD when it matures is $8480, calculated using simple interest. Bill received $8366.02 from his friend, who extended a loan expecting a 10% annual simple interest return.

Explanation:

To calculate the value of the CD when it matures, we use the formula for simple interest: Interest = Principal × Rate × Time. In this case, the Principal is $8000, the Rate is 8% per annum, and since the CD is for 9 months, the Time is ⅓ year. The simple interest earned on the CD is calculated as:
Interest = $8000 × 0.08 × ⅓ = $8000 × 0.08 × ⅔ = $480.
So, the mature value of the CD is the principal plus the interest, which is $8000 + $480 = $8480.

To determine how much Bill received from his friend with a 10% annual simple interest rate, the friend would expect to get the mature value of the CD in 3 months, which is one-quarter of a year. The agreement suggests that the friend treats the loan to Bill as an investment, thus expecting the same return as the interest he could have earned elsewhere at his desired 10% rate for the time frame. So, the calculation would be:
8480 = Principal × (1 + (10% × ⅔)), solving for Principal gives Bill:
Principal = 8480 ÷ (1 + (0.10 × ⅔)) = $8366.02 (rounded to the nearest cent).

The equation for the situation is [tex]y=200(\frac{2}{3})^{x}[/tex]

It will take around 9 years for her to have around 5 sheep

Step-by-step explanation:

The exponential decay growth/decay equation is [tex]y=a(b)^{x}[/tex] , where

Erica is a sheep farmer. She is having a problem with wolves attacking the flock. She starts with an initial 200 sheep and notices that the population is two-thirds of the previous year

∵ The population is decreased

∴ The equation is decay

∵ The population is two-thirds of the previous year

∴ The decay factor is [tex]\frac{2}{3}[/tex]

∵ She starts with an initial 200 sheep

∴ the initial value is 200

∵ The decay equation is [tex]y=a(b)^{x}[/tex] , where y represent the

   population in x years

∵ a = 200

∵ b = [tex]\frac{2}{3}[/tex]

∴ [tex]y=200(\frac{2}{3})^{x}[/tex]

The equation for the situation is [tex]y=200(\frac{2}{3})^{x}[/tex]

∵ The population after x years is around 5 sheep

- Substitute y by 5 to find x

∵ [tex]5=200(\frac{2}{3})^{x}[/tex]

- Divide both sides by 200

∴ [tex]0.025=(\frac{2}{3})^{x}[/tex]

- Insert ㏒ for both sides

∴ [tex]log(0.025)=log(\frac{2}{3})^{x}[/tex]

∴ [tex]log(0.025)=xlog(\frac{2}{3})[/tex]

- Divide both sides by [tex]log(\frac{2}{3})[/tex]

∴ 9.098 = x

∴ x is around 9 years

It will take around 9 years for her to have around 5 sheep

Learn more:

You can learn more about the equation  in brainly.com/question/10666510

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Answer:

[tex] log_{4}(2) = log_{ {2}^{2} }(2) = \frac{ log_{2}(2) }{2} = \frac{1}{2} [/tex]

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