Assume that on a standardized test of 100 questions, a person has a probability of 80% of answering any particular question correctly. Find the probability of answering between 74 and 84 questions

Step-by-step explanation:

thus is basically all I could get I hope that this helps a little bit :)

Answer: 0.965

Step-by-step explanation:

Given : Water use in the summer is normally distributed with

[tex]\mu=311.4\text{ million gallons per day}[/tex]

[tex]\sigma=40 \text{ million gallons per day}[/tex]

Let X be the random variable that represents the quantity of water required on a particular day.

Z-score : [tex]\dfrac{x-\mu}{\sigma}[/tex]

[tex]\dfrac{350-311.4}{40}=0.965[/tex]

Now, the probability that a day requires more water than is stored in city reservoirs is given by:-

[tex]P(x>350)=P(z>0.965)=1-P(z<0.965)[/tex]

We can see that on comparing the above value to the given P(X > 350)= 1 - P(Z < b) , we get the value of b is 0.965.

Answer: 2

Step-by-step explanation:

Given : The number of granola bars = 6

The number of pieces of dried fruit = 10

If the snack bags should be identical without any food left over, then the greatest number of snack bags Emily can make is the greatest common factor (GCF) of 6 and 10.

Since , factors of 6 = 1, 2, 3, 6

Factors of 10 = 1, 2, 5, 10

Hence, the greatest common factor of 6 and 10 = 2

Thus, the greatest number of snack bags Emily can make = 2.

Answer:

The answer is (3/2, 7/2)

Step-by-step explanation:

1+2 = 3

3/2 = 1.5

3+4 = 7

7/2 = 3.5

Answer: last option.

Step-by-step explanation:

Given two points:

 [tex](x_1,y_1)[/tex] and  [tex](x_2,y_2)[/tex]

You can find the midpoint between them by using the following formula:

[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

Then, given the point  (1, 4) and the point (2, 3), you can identify that:

[tex]x_1=1\\x_2=2\\y_1=4\\y_2=3[/tex]

Therefore, the final step is to substitute values into the formula:

 [tex]M=(\frac{1+2}{2},\frac{4+3}{2})\\\\M=(\frac{3}{2},\frac{7}{2})[/tex]

Answer:

 The candle has a height of 21.4 cm after burning for 22 hours.

Step-by-step explanation:

let x=hours, m=rate of change,  and  y= candle height

First you have to find the slope or, rate of change using the slope formula.  y2-y1 divided by x2-x1   .        

Here is our points    (9,     17.5)   and   (24,    22)

                                    x1       y1                 x2     y2

Now we put these into the equation and solve

[tex]\frac{22-17.5}{24-9}[/tex]   =[tex]\frac{3}{10}[/tex]

Now that we have the slope of 3/10 we can use this to find the y-intercept using the point-slope equation.

[tex]y-y_{1} =m(x-x_{1} )[/tex]                 y-17.5= .3(x-9) Solve

y-17.5=.3x-2.7                                        y  -14.8=      .3x

 +2.7         +2.7                                         +14.8               +14.8

y=.3x+14.8                     the y-intercept is 14.8

Now we use this equation to  plug in the 22 hours.

y=.3(22) +14.8

y=6.6+14.8

y= 21.4    The candle has a height of 21.4 cm after burning for 22 hours.

Answer:

total 900 pass codes can be made.

Step-by-step explanation:

Given situation is 3 digit pass codes are required made from the digits 0 to 9.

But the first number is not allowed to be a 0.

So for the third place we have 10 choices ( 0,1,2,3,4,5,6,7,8,9 )

For the second place we have 10 choices ( 0,1,2,3,4,5,6,7,8,9 )

But for the first place we have 9 choices ( 1,2,3,4,5,6,7,8,9 )

( 9 × 10 × 10 ) = 900

Therefore, total 900 pass codes can be made from the digits 0 to 9.

Step-by-step explanation:

o - odd number

e - even number

n + e =o, if n is odd...rule 1

n + e = e, if n is even...rule 2

n × o = o, if n is odd...rule 3

n × o = e, if n is even...rule 4

thus if 3n +6 = o,

then 3n must be odd, following rule 1

=> 3n = o, then n is an odd number, following rule 3

Answer: The weaknesses of content analysis include:   if you make a coding error you must recode all of your data.

Explanation:

Content analysis is a method for analyse documents,communication artifacts, which might be of various formats such as pictures, audio or video. Content analysis can provide valuable or cultural insights over time through analysis .

But it is more time consuming and subject to increased error . There is no theoretical base in order to create relationship between text. So in case if we make coding error then we must recode all data .

Hence option (B) is correct

Content analysis weaknesses include potential influence on subject under study, the need to recode all data if a coding error occurs, limitation to studying social artifacts, requirement of special equipment, and misconception that it can't study change over time.

The weaknesses of content analysis include:

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[tex]f(s)\Longrightarrow L^{-1}=\{\frac{-4s-9}{s^2+25-8}\}[/tex]

First dismantle,

[tex]L^{-1}=\{-\frac{4s}{s^2+25-8}-\frac{9}{s^2+25-8}\}[/tex]

Now use the linearity property of Inverse Laplace Transform which states,

For functions [tex]f(s),g(s)[/tex] and constants [tex]a, b[/tex] rule applies,

[tex]L^{-1}=\{a\cdot f(s)+b\cdot g(s)\}=aL^{-1}\{f(s)\}+bL^{-1}\{f(s)\}[/tex]

Hence,

[tex]-4L^{-1}\{\frac{s}{s^2+25-8}\}-9L^{-1}\{\frac{1}{s^2+25-8}\}[/tex]

The first part simplifies to,

[tex]

L^{-1}\{\frac{s}{s^2+25-8}\} \\

\frac{d}{dt}(\frac{1}{\sqrt{17}}\sin(t\sqrt{17})) \\

\cos(t\sqrt{17})

[/tex]

The second part simplifies to,

[tex]

L^{-1}\{\frac{1}{s^2+25-8}\} \\

\frac{1}{\sqrt{17}}\sin(t\sqrt{17})

[/tex]

And we result with,

[tex]\boxed{-4\cos(t\sqrt{17})-\frac{9}{\sqrt{17}}\sin(t\sqrt{17})}[/tex]

Hope this helps.

If you have any additional questions please ask. I made process of solving as quick as possible therefore you might be left over with some uncertainty.

Hope this helps.

r3t40

Answer:

This is a binomial experiment

Step-by-step explanation:

Binomial experiment is an experiment in which for each trial there are only two outcomes.

In case of the given experiment, it is being asked either the applicants were admitted to the Park university or not, it has only two outcomes, Yes and no. So having only two options as outcomes this experiment is a binomial experiment ..

Answer: 0.9932

Step-by-step explanation:

Given : Mean : [tex]\mu=\$2.837\text{ per gallon }[/tex]

Standard deviation : [tex]\sigma = \$0.009\text{ per gallon}[/tex]

a) The formula for z -score :

[tex]z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

Sample size = 55

For x= $2.834​ ,

[tex]z=\dfrac{2.834-2.837}{\dfrac{0.009}{\sqrt{55}}}\approx2.47[/tex]

The p-value = [tex]P(z<2.47)=[/tex]

[tex]0.9932443\approx0.9932[/tex]

Thus, the probability that the mean price per gallon is less than ​$2.834 is approximately 0.9932 .

The question asks about finding the probability that the mean price per gallon of gas is less than $2.834. This is a statistics question and requires calculation of Z-score and the finite correction factor should be considered due to our sample size being more than 5% of the population.

The question asks about the probability of a certain mean price per gallon for a sub-sample drawn from a larger population. In statistics, we often use Z-scores to calculate the probability of a score occurring within a standard distribution, but the entire population parameters should be known. Hence, we should use the finite correction factor (a.k.a the population correction factor) due to our sample size being more than 5% of the population.

In this case, the Z-score is calculated as follows:

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Answer:

c > -7

Step-by-step explanation:

Isolate the variable c. What you do to one side, you do to the other. Subtract 6 from both sides:

c + 6 (-6) > -1 (-6)

c > -1 - 6

Simplify.

c > (-1 - 6)

c > - 7

c > -7 is your answer.

~

Answer:

[tex]\huge \boxed{c>-7}[/tex]

Step-by-step explanation:

Subtract by 6 from both sides of equation.

[tex]\displaystyle c+6-6>-1-6[/tex]

Simplify, to find the answer.

[tex]\displaystyle -1-6=-7[/tex]

[tex]\displaystyle c>-7[/tex], which is our final answer.

Answer:

A.  MN is located at M 0,0) and N (2, 0)  is half the length of M'N'.

Step-by-step explanation:

MN was dilated with a factor 2 is is half the length of M'N'.

MN is located at M(0,0) and N(2,0) as well as it's length would be half the M'N' length. A further explanation is below.

According to the question,

M'N' is a line with,

Since,

Center of dilation = N' = (2,0)

So,

→ [tex]M' = 2\times 2[/tex]

        [tex]= 4 \ units[/tex]

Since the dilation is (2, 0), then

→ [tex]M' = (2-4, 0)[/tex]

        [tex]= (-2,0)[/tex]

M'N' is twice then MN. Thus the above answer is correct.

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Answer:

A. [tex]\text{Set builder}=\{2x:x\in Z,x>0\}[/tex]

B. [tex]\text{Set builder}=\{2x-1:x\in Z,x>0\}[/tex]

Step-by-step explanation:

Set builder form is a form that defines the domain.

A.

The given arithmetic sequence is

2,4,6,8,10,.....

Here all terms are even numbers. The first term is 2 and the common difference is 2.

All the elements are multiple of 2. So, the elements are defined as 2x where x is a non zero positive integer.

The set of all 2x such that x is an integer greater than 0.

[tex]\text{Set builder}=\{2x:x\in Z,x>0\}[/tex]

Therefore the set builder form of given elements is [tex]\{2x:x\in Z,x>0\}[/tex].

B.

The given arithmetic sequence is

1,3,5,7,....

Here all terms are odd numbers. The first term is 1 and the common difference is 2.

All the elements are 1 less than twice of an integer. So, the elements are defined as 2x-1 where x is a non zero positive integer.

The set of all 2x-1 such that x is an integer greater than 0.

[tex]\text{Set builder}=\{2x-1:x\in Z,x>0\}[/tex]

Therefore the set builder form of given elements is [tex]\{2x-1:x\in Z,x>0\}[/tex].

Answer:

Option 2: m∠1 = 147°, m∠2 = 80°, m∠3 = 148°

Step-by-step explanation:

Step 1: Consider triangle ABC from the picture attached below.

Lets find angle x

x + 47 + 33 = 180 (because all angles of a triangle are equal to 180°)

x = 100°

Angle x = Angle y = 100° (because vertically opposite angles are equal)

Step 2: Find angle 2

Angle 2 = 180 - angle x (because angle on a straight line is 180°)

Angle 2 = 180 - 100

Angle 2 = 80°

Step 3: Find angle z

48 + y + z = 180° (because all angles of a triangle are equal to 180°)

z = 32°

Angle 3 = 180 - angle z (because angle on a straight line is 180°)

Angle 3 = 180 - 32

Angle 3 = 148°

Step 4: Find angle 1

Angle 1 = 180 - 33 (because angle on a straight line is 180°)

Angle 1 = 147°

Therefore m∠1 = 147°, m∠2 = 80°, m∠3 = 148°

Option 2 is correct

!!

Answer: 157 tickets

Explanation:

The people not showing up for the flight can be treated as from Binomial distribution.

The binomial distribution B(n, p) is approximately close to the normal i.e. N(np, np(1 − p))  for large 'n' and for 'p' and neither too close to 0 nor 1 .

Now, Let us assume 'n' = n

and we are given

p=0.15

So now B(n,0.15n) follows Normal distribution

u=n

[tex]\sigma^{2}[/tex] = 0.15n

We have to calculate P(X<144) with 99% accuracy

P(X<144) = P(Z<z)

where;

z= [tex](144-\bar{X})\div \sigma[/tex]

z score for 99% is 2.33

i.e.  

[tex](144-\bar{X})\div \sigma = (144-n)/\sqrt{np} = 2.33\\\ (144-n)^{2} = \ np*2.33^{2}\\\ 20736 +n^{2} - 288n = 0.15n*5.43\\\ n^{2} - 288.81n + 20736=0[/tex]

solving this we will get one root nearly equal to 157 and other root as 133

Hence the answer is 157.

Answer:  p = 0.73

Step-by-step explanation:

Given that,

73% of the audience was under 20 years old :

so, probability (p) = 0.73

n = 146

Mean of the distribution of sample proportion = ?

According to central limit theorem,

np(1-p) ≥ 10

146 × 0.73(0.27) ≥ 10

28.77 ≥ 10

∴ Central limit theorem assumes that the sample distribution of the sample proportion is normally distributed.

Hence, the mean of the distribution of sample proportion:

μ = p = 0.73

Answer:

1/91

Step-by-step explanation:

SUMMER VACATION

There are 14 letters, 2 of them are A's

P (1st letter is an A) = 2/14=1/7

Then we keep the A

SUMMER VCATION

There are 13 letters, 1 of them is an A's

P (2nd letter is an A) = 1/13

P (1st A, 2nd A) = 1/7 * 1/13 = 1/91

Answer:

1/91

Step-by-step explanation:

Step-by-step explanation:

i think the answer is 42 to be exacr

The bacterial population's growth is represented by the exponential growth function n(t) = 400 * 3^t, where 400 is the initial number of bacteria and t is the time in hours. After 3.5 hours, the population is estimated to be approximately 21236 bacteria.

The population of the bacteria can be modeled by an exponential growth function, specifically by considering its constant rate of tripling every hour. If we denote No as the initial number of bacteria, which is 400, and t as the time in hours, the number of bacteria n after time t would be represented by the function n(t) = No * 3^t. In this case, n(t) = 400 * 3^t.

Now, to estimate the rate of growth of the bacteria population after 3.5 hours, we substitute t = 3.5 into the equation which gives n(3.5) = 400 * 3^3.5. Calculating this to the nearest whole number gives approximately 21236, which represents the size of the bacteria population after 3.5 hours. This indicates a significant increase, a characteristic of exponential growth commonly observed in prokaryotes like bacteria under suitable conditions.

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To find an expression for the number of bacteria after t hours, we can use the following formula:

n(t) = 400 * [tex]3^{t}[/tex]

Now, let’s estimate the rate of growth after 3.5 hours:

n(3.5) = 400 * [tex]3^{3.5}[/tex]

Calculating this:

n(3.5) ≈ 400 × [tex]3^{3.5}[/tex]  ≈ 400 × 46.8 ≈  18,706.15

Rounded to the nearest whole number, the estimated population after 3.5 hours is 18,706 bacteria.

Answer:

d) criterion-based sample

Step-by-step explanation:

Quantitative research analyzes a given data and forms conclusions based on the analytical tools implemented in them. The most commonly used method to gather data is through questionnaires. Now, the generation of the questionnaires is important as the hypothesis you propose must be reflected after analysis of the data i.e., the criterion for each question must be selected carefully.

Answer: A) random sample

Explanation:

Random sample is the best sampling technique for the quantitative research as, random sample comes under the probability sampling and it occurred randomization when the parameters of the sampling frame has the equal opportunity for sampling. When we want to draw the random sample, the research started with the list of elements and members and this list sometimes contain the sampling frame.

Answer:

(-1,1).

Step-by-step explanation:

We need to calculate [tex]\lim_{n \to \infty}\frac{| a_{n+1}|}{| a_{n}|} = \frac{1}{R}[/tex] where R is the radius of convergence.

[tex]\lim_{n \to \infty}\frac{\frac{|(-1)^{n+1}|}{|n+1|}}{\frac{|(-1)^{n}|}{|n|}}[/tex]

[tex]\lim_{n \to \infty}\frac{\frac{1}{|n+1|}}{\frac{1}{|n|}}[/tex]

[tex]\lim_{n \to \infty}\frac{|n|}{|n+1|}[/tex]

Applying LHopital rule we obtaing that the limit is 1. So [tex]1=\frac{1}{R}[/tex] then R = 1.

As the serie is the form [tex](x+0)^{n}[/tex] we center the interval in 0. So the interval is (0-1,0+1) = (-1,1). We don't include the extrem values -1 and 1 because in those values the serie diverges.

Answer:

x-intercept: (6,0)

y-intercept:  (0,4)

Step-by-step explanation:

The x-intercepts lay on the x-axis and therefore their y-coordinate is 0.

To find the x-intercept, you set y to 0 and solve for x.

2x+3y=12

Set y=0.

2x+3(0)=12

2x+0    =12

2x         =12

Divide both sides by 2:

 x          =12/2

 x          =6

The x-intercept is (x,y)=(6,0).

The y-intercepts lay on the y-axis and therefore their x-coordinate is 0.

To find the y-intercept, you set x to 0 solve for y.

2x+3y=12

2(0)+3y=12

0+3y    =12

3y         =12

Divide both sides by 3:

 y          =12/3

 y           =4

The y-intercept is (0,4).

The x-intercept of the equation 2x + 3y = 12 is (6,0) and y-intercept is (0,4).

To find the x-intercept of the equation 2x + 3y = 12, we set y to 0 and solve for x:

2x + 3(0) = 12
2x = 12
x = 6

So, the x-intercept is (6,0).

To find the y-intercept, we set x to 0 and solve for y:

2(0) + 3y = 12
3y = 12
y = 4

The y-intercept is (0,4).

Answer:

(a, b) see the input matrices in the calculator image below

(c) see the output matrix in the calculator image below

Laura should use Supermarket II.

Step-by-step explanation:

(a) Your data is not clearly identified, so we have assumed that the item costs are listed for one supermarket before they are listed for the next. Then your matrix A will be ...

[tex]A=\left[\begin{array}{cccc}3.15&3.79&2.99&3.49\\2.99&2.89&2.79&3.29\\3.74&2.98&2.89&2.99\end{array}\right][/tex]

__

(b) The column matrix of purchase amounts will be ...

[tex]B=\left[\begin{array}{c}2&3&2&3\end{array}\right][/tex]

__

(c) It is somewhat tedious to do matrix multiplication by hand, so we have let a calculator do it. Some calculators offer easier data entry than others, and some insist that data be entered into tables before any calculation can be done. We have chosen this one (attached), not because its use is easiest, but because we can post a picture of the entry and the result.

[tex]C=\left[\begin{array}{c}34.12&30.10&31.17\end{array}\right][/tex]

Laura's total bill is least at Supermarket II.

_____

As you know, the row-column result of matrix multiplication is the element-by-element product of the 'row' of the left matrix by the 'column' of the right matrix. Here, that means the 2nd row 1st column of the output is computed from the 2nd row of A and the 1st (only) column of B:

  2.99·2 +2.89·3 +2.79·2 +3.29·3 = 5.98 +8.67 +5.58 +9.87

  = 30.10

Answer:

D) No, the hypotenuse should be 12.

Step-by-step explanation:

Hypotenuse is the side opposite to the 90 degrees angle.

'6' is the opposite side to the given angle i.e. it is opposite from angle 30 degrees.

Step 1: Use the sin formula to find the hypotenuse.

Sin (angle) = opposite/hypotenuse

Step 2: Substitute the values in the formula

Sin (30) = 6/hypotenuse

1/2 = 6/hypotenuse

hypotenuse = 6x2

hypotenuse = 12

Therefore, the answer is option D; No, the hypotenuse should be 12.

!!

Answer:  0.4083

Step-by-step explanation:

Let D be the event of receiving a defective television.

Given : The probability that the television is defective :-

[tex]P(D)=\dfrac{3}{13}[/tex]

The formula for binomial distribution :-

[tex]P(X=x)=^nC_xp^x(1-p)^{n-x}[/tex]

If two televisions are randomly​ selected, compute the probability that both televisions work, then  the probability at least one of the two televisions does not​ work is given by :_

[tex]P(X\geq1)=P(1)+P(2)\\\\=^2C_1(\frac{3}{13})^1(1-\frac{3}{13})^{2-1}+^2C_2(\frac{3}{13})^2(1-\frac{3}{13})^{2-2}\\\\=0.408284023669\approx0.4083[/tex]

Hence , the required probability = 0.4083

We know that the binomial theorem for finding the probability of x success out of a total of n experiments is given  by:

[tex]b(x;n;p)=n_C_x\cdot p^x\cdot (1-p)^{n-x}[/tex]

(a)

b(5; 8, 0.25)

is given by:

[tex]8_C_5\cdot (0.25)^5\cdot (1-0.25)^{8-5}\\\\=8_C_5\cdot (0.25)^5\cdot (0.75)^3\\\\=56\cdot (0.25)^5\cdot (0.75)^3\\\\=0.023[/tex]

                    Hence, the answer is:  0.023

(b)

b(6; 8, 0.65)

i.e. it is calculated by:

[tex]=8_C_6\cdot (0.65)^6\cdot (1-0.65)^{8-6}\\\\=8_C_6\cdot (0.65)^6\cdot (0.35)^2\\\\=0.259[/tex]

              Hence, the answer is: 0.259

(c)

P(3 ≤ X ≤ 5) when n = 7 and p = 0.55

[tex]P(3\leq x\leq 5)=P(X=3)+P(X=4)+P(X=5)[/tex]

Now,

[tex]P(X=3)=7_C_3\cdot (0.55)^3\cdot (1-0.55)^{7-3}\\\\P(X=3)=7_C_3\cdot (0.55)^3\cdot (0.45)^{4}\\\\P(X=3)=0.239[/tex]

[tex]P(X=4)=7_C_4\cdot (0.55)^4\cdot (1-0.55)^{7-4}\\\\P(X=4)=7_C_4\cdot (0.55)^4\cdot (0.45)^{3}\\\\P(X=4)=0.292[/tex]

[tex]P(X=5)=7_C_5\cdot (0.55)^5\cdot (1-0.55)^{7-5}\\\\P(X=3)=7_C_5\cdot (0.55)^5\cdot (0.45)^{2}\\\\P(X=3)=0.214[/tex]

                                    Hence,

                  [tex]P(3\leq x\leq 5)=0.745[/tex]

(d)

P(1 ≤ X) when n = 9 and p = 0.1 .613

[tex]P(1\leq X)=1-P(X=0)[/tex]

Also,

[tex]P(X=0)=9_C_0\cdot (0.1)^{0}\cdot (1-0.1)^{9-0}\\\\i.e.\\\\P(X=0)=1\cdot 1\cdot (0.9)^9\\\\P(X=0)=0.387[/tex]

i.e.

[tex]P(1\leq X)=1-0.387[/tex]

                     Hence, we get:

                  [tex]P(1\leq X)=0.613[/tex]

To compute binomial probabilities using the formula b(x; n, p), you can substitute the values of x, n, and p into the formula and solve for the probability. For example, b(5; 8, 0.25) represents the probability of getting exactly 5 successes in 8 trials with a success probability of 0.25. (a) b(5; 8, 0.25) = 0.023. (b) b(6; 8, 0.65) = 0.259. (c) P(3 ≤ X ≤ 5) when n = 7 and p = 0.55 is approximately 0.745. (d) P(1 ≤ X) when n = 9 and p = 0.1 is approximately 0.613.

Binomial probabilities can be calculated using the formula for b(x; n, p). For example, to calculate b(5; 8, 0.25), you can use the formula:

[tex]b(5; 8, 0.25) = C(8, 5) * (0.25)^5 * (0.75)^3[/tex]

where C(8, 5) represents the number of combinations of 8 items taken 5 at a time. Solving this equation will give you the probability of getting exactly 5 successes in 8 trials with a success probability of 0.25.

Similarly, for b(6; 8, 0.65), you can use the formula:

[tex]b(6; 8, 0.65) = C(8, 6) * (0.65)^6 * (0.35)^2[/tex]

where C(8, 6) represents the number of combinations of 8 items taken 6 at a time. Solving this equation will give you the probability of getting exactly 6 successes in 8 trials with a success probability of 0.65.

(c) To calculate the probability of 3 ≤ X ≤ 5 when n = 7 and p = 0.55, you need to calculate the probabilities of 3, 4, and 5 successes individually and then sum them up.

(d) To calculate P(1 ≤ X) when n = 9 and p = 0.1, you need to calculate the probabilities of 1, 2, 3, ..., 9 successes individually and then sum them up.

Answer:

The remainder is: 3x+3

The quotient is: 1

Step-by-step explanation:

We need to divide

(3x^2 + 9x + 7) by (x+2)

The remainder is: 3x+3

The quotient is: 1

The solution is attached in the figure below.

Answer:

[tex]3x+3+\frac{1}{x+2}[/tex]

Step-by-step explanation:

We are to divide the polynomial [tex]3x^2 + 9x + 7[/tex] by [tex]x+2[/tex].

For that, we will first divide the leading coefficient of the numerator [tex]\frac{3x^2}{x}[/tex] by the divisor.

So we get the quotient: [tex]3x[/tex] and will multiply the divisor [tex]x+2[/tex] by [tex]3x[/tex] to get [tex]3x^2+6x[/tex].

Next, we will subtract [tex]3x^2+6x[/tex] from [tex]3x^2 + 9x + 7[/tex] to get the remainder [tex]3x+7[/tex].

Therefore, we get [tex]3x+\frac{3x+7}{x+2}[/tex].

Now again, dividing the leading coefficient of the numerator by the divisor [tex]\frac{3x}{x}[/tex] to get quotient [tex]3[/tex].

Then we will multiply [tex]x+2[/tex] by [tex]3[/tex] to get [tex]3x+6[/tex].

Then, we will subtract [tex]3x+6[/tex] from [tex]3x+7[/tex] to get the new remainder [tex]1[/tex].

Therefore, [tex]\frac{3x^2 + 9x + 7}{x+2}=3x+3+\frac{1}{x+2}[/tex]

Answer: 8

Step-by-step explanation:

The formula to calculate the simple interest is given by :-

[tex]S.I. =Prt[/tex], where P is the principal amount , r is rate of interest and t is time.

Given: The principal amount : P = $225

The rate of interest : r = 3.5% =0.035

Simple Interest : SI = $63

Put these value in the above formula , we get

[tex] 63=225\times0.035t\\\\\Rightarrow\ t=\dfrac{63}{225\times0.035}\\\\\Rightarrow\ t=8[/tex]

Hence, the term of loan = 8

Answer: 1537

Step-by-step explanation:

Given : Margin of error : [tex]E=0.025[/tex]

Significance level : [tex]\alpha=1-0.95=0.05[/tex]

Critical value : [tex]z_{\alpha/2}=z_{0.025}=1.96[/tex]

The formula to calculate the sample size if prior estimate pf population proportion does not exist :-

[tex]n=0.25(\dfrac{z_{\alpha/2}}{E})^2\\\\\Rightarrow\ n=0.25(\dfrac{1.96}{0.025})^2\\\\\Rightarrow\ n=1536.64\approx1537[/tex]

Hence, she should take a sample with minimum size of 1537 .

Final answer:

To estimate the proportion of students repeating a class with a 95% confidence level and a margin of error of 0.025, the instructor would need a sample size of at least 1537 students.

Explanation:

To calculate the sample size needed for constructing a 95% confidence interval for the proportion of students who are repeating a class with a specified margin of error, we can use the formula for sample size in a proportion:

n = (Z² × p × (1-p)) / E²

Where:

Substituting the values, we get:

Thus, the calculation is:

n = (1.96² × 0.5 × (1 - 0.5)) / 0.025²

n = (3.8416 × 0.25) / 0.000625

n = 0.9604 / 0.000625

n = 1536.64

As we cannot have a fraction of a person, we would round up to the next whole number.

Therefore, the instructor would need to sample at least 1537 students.