This is for mathematics!p

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.

the total annual costs associated with Sam's current ordering policy amount to $1,215.

The student has provided the necessary information to calculate the total annual costs associated with Sam's current ordering policy at his auto shop. Sam orders 650 oil filters at a time and the shop uses 150 filters per week. The key components involved in this calculation are the order cost, annual demand, holding cost, and the size of each order.

The total annual demand (D) is the weekly demand (d) multiplied by the number of weeks per year:

D = d × 52
D = 150 filters/week × 52 weeks/year
D = 7,800 filters/year

The order cost (S) is given as $20 per order and the annual holding cost per unit (H) is $3 per filter. The size of each order (Q) is 650 filters.

The total annual ordering cost (AOC) can be calculated as the annual demand divided by the order size, multiplied by the order cost:

AOC = (D/Q)  × S
AOC = (7,800/650) × $20
AOC = 12 × $20
AOC = $240

The total annual holding cost (AHC) can be calculated as the average inventory level (which is Q/2 for consistent orders) multiplied by the holding cost per unit:

AHC = (Q/2) × H
AHC = (650/2) × $3
AHC = 325 × $3
AHC = $975

The total annual costs (TAC) are the sum of the total annual ordering cost and the total annual holding cost:

TAC = AOC + AHC
TAC = $240 + $975
TAC = $1,215

Therefore, the total annual costs associated with Sam's current ordering policy amount to $1,215.

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.

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.

Check the picture below.

Answer:

2

Step-by-step explanation:

If the first card drawn is a diamond, the total number of cards reduces to 51 for the second draw. Out of these, 25 are red (13 hearts + 12 diamonds). So, the probability of drawing a red card on the second draw, if the first drawn card was a diamond, is 25/51 approximated to 0.4902.

The subject of this question is probability in mathematics, specifically related to a scenario that involves sampling without replacement from a deck of playing cards. Firstly, let us familiarize ourselves with the composition of a standard deck of cards. It consists of 52 cards divided into four suits: clubs, diamonds, hearts, and spades. Clubs and spades are black cards, while diamonds and hearts are red cards. Each suit has 13 cards.

If the first card drawn is a diamond, the total count of cards in the deck reduces to 51 (because we are drawing without replacement), and, since a diamond card has been withdrawn, the count of remaining red cards is 25 (13 hearts and 12 remaining diamonds). Thus, to find the probability of drawing a red card on the second draw, we simply count the remaining red cards and divide by the remaining total cards, giving us a probability of 25/51 or approximately 0.4902 when rounded to four decimal places.

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The probability of choosing a red card for the second card drawn, if the first card was a diamond, is 0.4902.

So, the calculated probabilities are:

- The probability of drawing a diamond first: 0.25
- The probability of drawing a red card second, given that the first card drawn was a diamond: 0.4902

Therefore, the probability of choosing a red card for the second card drawn, if the first card was a diamond, is approximately 0.4902.

Step-by-step explanation:

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

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:

(-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 with explanation:

⇒ A point k is said to be fixed point of function, f(x) if

        f(k)=k.

The given function is

           f(x)=2 x - x³

To determine the fixed point

f(k)=2 k - k³=k

→2 k -k -k³=0

→k -k³=0

→k×(1-k²)=0

→k(k+1)(k-1)=0

→k=0 ∧ k+1=0∧k-1=0

→k=0∧ k= -1 ∧ k=1

So, the three fixed points are=0,1 and -1.

To Check Stability of fixed point

1.⇒  f'(x)=2-3 x²

|f'(0)|=|2×0-0³|=0

⇒x=0, is Superstable point.

2.⇒|f'(-1)|=2 -3×(-1)²

 =2 -3

= -1

|f'(-1)| <1

⇒x= -1, is stable point.

3.⇒|f'(1)|=2 -3×(1)²

=2 -3

= -1

|f'(1)| <1

⇒x= 1, is also a stable point.

⇒⇒There are two points of Stability,which are, x=1 and , x=-1.

The equation of the cone should be [tex]z=\sqrt{x^2+y^2}[/tex]. Parameterize [tex]S[/tex] by

[tex]\vec s(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec\jmath+u\,\vec k[/tex]

with [tex]1\le u\le2[/tex] and [tex]0\le v\le2\pi[/tex]. Take the normal vector to [tex]S[/tex] to be

[tex]\vec s_v\times\vec s_u=u\cos v\,\vec\imath+u\sin v\,\vec\jmath-u\,\vec k[/tex]

Then the integral of [tex]\vec F[/tex] across [tex]S[/tex] is

[tex]\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\int_0^{2\pi}\int_1^2(-u\cos v\,\vec\imath-u\sin v\,\vec\jmath+u^3\,\vec k)\cdot(u\cos v\,\vec\imath+u\sin v\,\vec\jmath-u\,\vec k)\,\mathrm du\,\mathrm dv[/tex]

[tex]=\displaystyle\int_0^{2\pi}\int_1^2(-u^2-u^4)\,\mathrm du\,\mathrm dv[/tex]

[tex]=\displaystyle-2\pi\int_1^2(u^2+u^4)\,\mathrm du\,\mathrm dv=\boxed{-\frac{256\pi}{15}}[/tex]

To evaluate the surface integral, we need to find the flux of the vector field F across the oriented surface S. Given that F(x, y, z) = −xi − yj + z3k, and S is the part of the cone z = x2 + y2 between the planes z = 1 and z = 2 with downward orientation, we can proceed as follows: First, find the unit normal vector to the surface. Next, calculate the dot product between the vector field F and the unit normal vector. Finally, integrate the dot product over the surface S using the downward orientation.

To evaluate the surface integral, we need to find the flux of the vector field F across the oriented surface S. Given that F(x, y, z) = −xi − yj + z3k, and S is the part of the cone z = x2 + y2 between the planes z = 1 and z = 2 with downward orientation, we can proceed as follows:

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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:

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: 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 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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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:

  35, 66

Step-by-step explanation:

The perimeter is twice the sum of length and width:

  2(5.50 m + 12.0 m) = 2(17.50 m) = 35.00 m

__

The area is the product of the length and width:

  (5.50 m)(12.0 m) = 66.000 m^2

The perimeter of the rectangle is 35.0 m, and the area is 66.0 m², both calculated using standard geometry formulas and reported with three significant figures.

To calculate the perimeter and area of a rectangle, we use the formulas: Perimeter = 2(length + width) and Area = length × width. In this case, the rectangle has a length of 5.50 m and a width of 12.0 m. Therefore, the perimeter is 2(5.50 m + 12.0 m) = 2(17.5 m) = 35.0 m. The area is 5.50 m × 12.0 m = 66.0 m².

It's important to express your answers with the correct number of significant figures and proper units. The length of 5.50 m has three significant figures, and the width of 12.0 m has three significant figures as well. Thus, our final answers for both perimeter and area should also be reported to three significant figures: 35.0 m for the perimeter and 66.0 m² for the area.

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:

Horizontal axis

Step-by-step explanation:

By convention, the independent variables is arrayed along the Horizontal axis (abscissa) in a scattergram.

The stcattergram has two dimensions

Answer:

​(a) State the appropriate null and alternative hypotheses to assess whether women are taller today.

Solution:

Definition of null hypothesis : The null hypothesis attempts to show that no variation exists between variables or that a single variable is no different than its mean. it is denoted

Alternative Hypothesis: In statistical hypothesis testing, the alternative hypothesis is a position that states something is happening, a new theory is true instead of an old one (null hypothesis).

We are given that The mean height of women 20 years of age or older was 63.7 inches.

So, null hypothesis : [tex]H_0: \mu=63.7[/tex]

Alternative Hypothesis : [tex]H_1: \mu>63.7[/tex]

b)The​ P-value for this test is 0.16.

Solution: The p-value represents the probability of getting a sample mean height of 65.1 inches.

c) Write a conclusion for this hypothesis test assuming an alpha equals 0.10 level of significance.

Solution:

[tex]\alpha = 0.10[/tex]

p- value = 0.16

[tex]p-value> \apha[/tex]

Since the p - value is high .

So, we will accept the null hypothesis

So,  [tex]H_0: \mu=63.7[/tex]

Hence The mean height is 63.7 inches

The null hypothesis states that the mean height of women today is equal to the mean height several years ago. The P-value represents the probability of obtaining the observed sample mean if the null hypothesis is true. With an alpha level of 0.10, we fail to reject the null hypothesis, indicating no significant evidence to suggest that women today are taller.

(a) Null hypothesis: The mean height of women 20 years of age or older today is equal to 63.7 inches. Alternative hypothesis: The mean height of women 20 years of age or older today is greater than 63.7 inches.

(b) The P-value represents the probability of obtaining a sample mean height of 65.1 inches or higher, given that the true mean height is 63.7 inches. A P-value of 0.16 indicates that there is a 16% chance of observing such a sample mean height even if the true mean height is 63.7 inches.

(c) Conclusion: Assuming an alpha level of 0.10, we fail to reject the null hypothesis. There is not enough evidence to conclude that women today are taller than before.

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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

Answer:

amount pull out each month is $4518.44

Step-by-step explanation:

principal (p) = $500000

rate (r) = 4% = 0.04 = 0.04/12 per month

time period = 25 years = 25 × 12 = 300 months

to find out

how much amount pull out each month

solution

we will calculate the amount by given formula i.e.

principal = amount  ( 1 - [tex](1+r)^{t}[/tex] ) / r     ....................1

now put the value amount rate time in equation 1

we get amount

500000 = amount ( 1 - [tex](1+0.04/12)^{300}[/tex] ) / 0.04/12

500000 = amount (2.711062 ) / 0.00333

amount = 1666.6666 * 2.711062

amount =  4518.44

amount pull out each month is $4518.44

Final answer:

To determine how much you can pull out each month, you can use the formula for the future value of an ordinary annuity. Plugging in the given values, you will be able to pull out approximately $1,408.19 each month if you want to be able to take withdrawals for 25 years.

Explanation:

To determine how much you can pull out each month, you can use the formula for the future value of an ordinary annuity. The formula is:

FV = P * [(1 + r)^n - 1] / r

Where:

FV is the future value of the annuity

P is the monthly withdrawal amount

r is the monthly interest rate (4% divided by 12)

n is the number of months (25 years multiplied by 12)

Plugging in the values, we get:

FV = P * [(1 + 0.04/12)^(25*12) - 1] / (0.04/12)

To find the monthly withdrawal amount (P), we need to solve for P. Rearranging the formula:

P = FV * (0.04/12) / [(1 + 0.04/12)^(25*12) - 1]

Now substitute the values back in and calculate P:

P = $500,000 * (0.04/12) / [(1 + 0.04/12)^(25*12) - 1]

Simplifying the equation gives us:

P ≈ $1,408.19

Therefore, you will be able to pull out approximately $1,408.19 each month if you want to be able to take withdrawals for 25 years.

Answer:

Predetermined overhead rate of the year = $12.3

Option 2 is correct.

Step-by-step explanation:

Let P = Predetermined overhead

Actual direct labor hours = 17,500

So, applied overhead = (17,500 *P)

Actual overhead = 227,750

Under applied overhead = 12,500

Applied Overhead = Actual overhead - Under applied overhead

Applied Overhead = 227,750 - 12500

Applied Overhead = 215,250

Using Formula:

215250 = (17,500 *P)

=> P = 215250/17500

P = 12.3

So, Predetermined overhead rate of the year = $12.3

Option 2 is correct.

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:

27.The angle between two given curves is [tex]0^{\circ}[/tex].

28.[tex]\theta=tan^{-1}(2\sqrt2)[/tex]

Step-by-step explanation:

27.We are given that two curves

y=x,y=x

We have to find the angle between the two curves

The angle between two curves is the angle between their tangent lines at the point of intersection

We know that the values of both curves at the point of intersection are equal

Let two given curves intersect at point [tex](x_1,y_1)[/tex]

Then [tex]y_1=x_1[/tex] because both curves are same

[tex]\frac{dy}{dx}=1[/tex]

[tex]m_1=1,m_2=1[/tex]

[tex]m_1(x_1)=1,m_2(x_1)=1[/tex]

Using formula of angle between two curves

[tex]tan\theta=\frac{m_1(x_0)-m_2(x_0)}{1+m_1(x_0)m_2(x_0)}[/tex]

[tex]tan\theta=\frac{1-1}{1+1}=\frac{0}{2}=0[/tex]

[tex]tan\theta=tan 0^{\circ}[/tex]

[tex]\theta=0^{\circ}[/tex]

Hence,the angle between two given curves is [tex]0^{\circ}[/tex].

28.y=sin x

y= cos x

By similar method we solve these two curves

Let two given curves intersect at point (x,y) then the values of both curves at the point are equal

Therefore,  sin x = cos x

[tex]\frac{sin x}{cos x}=1[/tex]

[tex]tan x=1[/tex]

[tex]tan x=\frac{sin x}{cos x}[/tex]

[tex]tan x= tan \frac{\pi}{4}[/tex]

[tex]x=\frac{\pi}{4}[/tex]

Now, substitute the value of x then we get y

[tex]y= sin \frac{\pi}{4}=\frac{1}{\sqrt2}[/tex]

[tex] sin \frac{\pi}{4}=cos \frac{\pi}{4}=\frac{1}{\sqrt2}[/tex]

The values of both curves are same therefore, the point [tex](\frac{\pi}{4},\frac{1}{\sqrt2})[/tex] is the intersection point of two curves .

[tex]m_1=cos x[/tex]

At [tex] x=\frac{\pi}{4}[/tex]

[tex]m_1=\frac{1}{\sqrt2}[/tex]

and

[tex]m_2=-sin x=-\frac{1}{\sqrt2}[/tex]

Substitute the values in the above given formula

Then we get [tex]tan\theta =\frac{\frac{1}{\sqrt2}+\frac{1}{\sqrt2}}{1-\frac{1}{2}}[/tex]

[tex]tan\theta=\frac{\frac{2}{\sqrt 2}}{\frac{1}{2}}[/tex]

[tex]tan\theta=\frac{2}{\sqrt 2}\times 2[/tex]

[tex] tan\theta=\frac{4}{\sqrt2}=\frac{4}{\sqrt 2}\times\frac{\sqrt2}{\sqrt2}[/tex]

[tex]tan\theta=2\sqrt2[/tex]

[tex]\theta=tan^{-1}(2\sqrt2)[/tex]

Hence, the angle between two curves is [tex]tan^{-1}(2\sqrt2)[/tex].

Answer:

Maximum is 8 while the minimum is -8.

Step-by-step explanation:

If we consider y=cos(x), the maximum is 1 and the minimum is -1.

This is the parent function of y=8cos(x) which has been vertically stretched by a factor of 8.  So now the maximum of y=8cos(x) is 8 while the minimum of y=8cos(x) is -8.

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: Cost of member = $15 and Cost of non member = $45

Step-by-step explanation:

a) Define variables.

Let x be the cost of member.

Let y be the cost of non member.

b) Write a system of equations:

According to question, we get that

x+3y=$150--------------(1)

2x+y=$75---------------(2)

Now, we need to calculate the cost for a member and a non member.

Using graphing method, we get that (15,45) is the solution set.

Hence, cost of member = $15 and Cost of non member = $45

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.

[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