Suppose that you wish to cross a river that is 3900 feet wide and flowing at a rate of 5 mph from north to south. Starting on the eastern bank, you wish to go directly across the river to a point on the western bank opposite your current position. You have a boat that travels at a constant rate of 11 mph.

a) In what direction, measured clockwise from north, should you aim your boat? Include appropriate units in your answer.

b) How long will it take you to make the trip? Include appropriate units in your answer.\

Please show your work so I may understand. Thank you so much!

Answer:

The value of det (3A) is -108.

Step-by-step explanation:

If M is square matrix of order n x n, then

[tex]|kA|=k^n|A|[/tex]

Let as consider a matrix A or order 3 x 3. Using the above mentioned property of determinant we get

[tex]|kA|=k^3|A|[/tex]

We need to find the value of det(3A).

[tex]|3A|=3^3|A|[/tex]

[tex]|3A|=27|A|[/tex]

It is given that the det(A)= -4. Substitute |A|=-4 in the above equation.

[tex]|3A|=27(-4)[/tex]

[tex]|3A|=-108[/tex]

Therefore the value of det (3A) is -108.

Answer:

$100 * (1 + 6.8%/12)^216 + $100*(1+6.8%/12)^215 + ... + $100*(1+6.8%/12)^1  

Now note that  

x + x^2 + x^3 + ... + x^N = x ( 1 + x + ... + x^(N-1) )  

= x ( (x^N -1)/(x-1) )  

Here, x = 1+6.8%1 = 1.00566666 and N = 216, so  

$100 * ( 1.00566666 ( 1.00566666^216 -1) / 0.00566666 )  

= $ 42398.33  

The total interest earned is $42,398 - $21,600 = $20,798

Step-by-step explanation:

The generic formula used in this compound interest calculator is V = P(1+r/n)^(nt)

V = the future value of the investment

P = the principal investment amount

r = the annual interest rate

n = the number of times that interest is compounded per year

t = the number of years the money is invested for

Answer:

The amount of water released during the​ week-long flood was 15,180,400,000 cubic feet per second.

Step-by-step explanation:

How many seconds are there in a week?

Each minute has 60 seconds

Each hour has 60 minutes

Each day has 24 hours

Each week has 7 days. So

60*60*24*7 = 604,800

A week has 604,800 seconds.

Water was released at a rate of 25,100 cubic feet per second.

In a week(604,800 seconds)

604,800*25,100 = 15,180,400,000

The amount of water released during the​ week-long flood was 15,180,400,000 cubic feet per second.

Answer: 0.0336

Step-by-step explanation:

Given : The distribution of cholesterol levels in teenage boys is approximately normal with mean :[tex]\mu= 170[/tex]

Standard deviation : [tex]\sigma= 30[/tex]

The formula for z-score is given by :-

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

For x=225

[tex]z=\dfrac{225-170}{30}=1.83[/tex]

The p-value =[tex]P(z>1.83)=1-P(z<1.83)[/tex]

[tex]=1-0.966375=0.033625\approx0.0336[/tex]

The probability that a teenage boy has a cholesterol level greater than 225 =0.0336

Answer:

B. price

Step-by-step explanation:

The equation is linear and looks like this:

C(x) = 5.99x

where C(x) is the cost of x number of movies.  The cost is the dependent variable, since it is dependent upon how many movies you rent at 5.99 each.

Answer:

[tex]6.1\frac{\text{ g}}{\text{ cm}^3}[/tex]

Step-by-step explanation:

We have been given that mass of an irregular object is 1220 g and it displaces 200 cubic cm of water when placed in a large overflow container. We are asked to find density of the object.

We will use density formula to solve our given problem.

[tex]\text{Density}=\frac{\text{Mass}}{\text{Volume}}[/tex]

Since the object displaces 200 cubic cm of water, so the volume of irregular object will be equal to 200 cubic cm.

Upon substituting our given values in density formula, we will get:

[tex]\text{Density}=\frac{1220\text{ g}}{200\text{ cm}^3}[/tex]

[tex]\text{Density}=\frac{61\times 20\text{ g}}{10\times 20\text{ cm}^3}[/tex]

[tex]\text{Density}=\frac{61\text{ g}}{10\text{ cm}^3}[/tex]

[tex]\text{Density}=6.1\frac{\text{ g}}{\text{ cm}^3}[/tex]

Therefore, the density of the irregular object will be 6.1 grams per cubic centimeters.

Answer:

2100

Step-by-step explanation:

50*18=900

900+1,200=2100

To find the population in 2018, we calculate the total increase from 2000 to 2018 by multiplying the yearly increase of 50 people by 18 years, resulting in an additional 900 people. Adding this to the initial population of 1,200 people gives us a total population of 2,100 people in 2018.

If a population is recorded at 1,200 in the year 2000 and increases at a steady rate of 50 people each year, we can calculate the population in 2018 using a linear growth model. First, we need to determine the number of years between 2000 and 2018, which is 18 years. Next, we multiply the annual increase (50 people) by the number of years (18) to find the total increase over this period.

The calculation would be as follows:

We then add this total increase to the initial population to get the population in 2018:

The population in 2018 would be 2,100 people.

Answer:

Number of adults = 7

Number of children = 16

Step-by-step explanation:

Tickets for a play cost 2 pounds for a child, and 4 pounds for an adult.

Let x number of adults and y number of children.

1 child ticket cost = 2 pound

y children ticket cost = 2y pound

1 adult ticket cost = 4 pound

x adults ticket cost = 4x pound

Total number of ticket sales were 60 pounds

Therefore, 4x + 2y = 60  ------------- (1)

One adult brought 4 children with him and the remaining adults each brought 2 children with them.

Remaining number of adult whose brought 2 children = x-1

Number children = 2(x-1)

Total number of children = 2(x-1)+4

Therefore, y=2x+2 ---------------------(2)

System of equation,

 2x + y = 30

-2x + y = 2

Using augmented matrix to solve system of equation.

[tex]\begin{bmatrix}2&1&\ |30\\-2&1&|2\end{bmatrix}\\\\R_2\rightarrow R_2+R_1\\\\\begin{bmatrix}2&1& |30\\0&2&|32\end{bmatrix}\\\\R_2\rightarrow\dfrac{1}{2}R_2\\[/tex]

[tex]\begin{bmatrix}2&1&\ |30\\0&1&|16\end{bmatrix}\\\\R_1\rightarrow R_1-R_2\\\\\begin{bmatrix}2&0&\ |14\\0&1&|16\end{bmatrix}\\\\\\[/tex]

[tex]R_1\rightarrow \dfrac{1}{2}R_1\\\\\begin{bmatrix}1&0&|7\\0&1&|16\end{bmatrix}\\\\[/tex]

Now, we find the value of variable.

[tex]x=7\text{ and }y=16[/tex]

Hence, Number of adults are 7 and Number of children are 16.

Answer:

There is enough evidence to believe that the average credit card debt has changed in the past 5 years

Step-by-step explanation:

We are to compare the means of two samples. Since only sample std deviations are used, we have to use t test for this hypothesis

H0: Means are equal

Ha: Means are not equal

(Two tailed test at 5% )

Difference between means [tex]M1-M2 = -2587[/tex]

Std deviation combined = 3856

Std error for difference = 460.88

t statistic[tex]= -2587/460.88=-5.613[/tex]

p value =0

Since p <0.05 reject null hypothesis.

There is enough evidence to believe that the average credit card debt has changed in the past 5 years

Answer:    

1.  6 fives.

2.  1 ten and 4 fives.

3.  2 tens and 2 fives.

4.  3 tens.

5.  1 twenty and 2 fives.

6.  1 twenty and 1 ten.

Step-by-step explanation:

Given : A customer is owed $30.00.

To find : How many different combinations of bills,using only five, ten, and twenty dollars bills are possible to give his or her change?

Solution :

We have to split $30 in terms of only five, ten, and twenty dollars.

1) In terms of only five we required 6 fives as

[tex]6\times 5=30[/tex]

So, 6 fives.

2) In terms of only ten and five,

a) We required 1 ten and 4 fives as

[tex]1\times 10+4\times 5=10+20=30[/tex]

So, 1 ten and 4 fives.

b) We required 2 tens and 2 fives as

[tex]2\times 10+2\times 5=20+10=30[/tex]

So, 2 tens and 2 fives

3) In terms of only tens we require 3 tens as

[tex]3\times 10=30[/tex]

So, 3 tens.

4)  In terms of only twenty and five, we required 1 twenty and 2 fives as

[tex]1\times 20+2\times 5=20+10=30[/tex]

So, 1 twenty and 2 fives.

5)  In terms of only twenty and ten, we required 1 twenty and 1 ten as

[tex]1\times 20+1\times 10=20+10=30[/tex]

So, 1 twenty and 1 ten.

Therefore, There are 6 different combinations.

To write the equation 5x + 3y = 15 in slope-intercept form, solve for y to get y = (-5/3)x + 5. The slope is -5/3 and the y-intercept is 5.

To convert the equation 5x + 3y = 15 into slope-intercept form, which is y = mx + b, we need to solve for y. Here are the steps:

Answer:

The seasons would become constant. It would be equinox throughout the year.

Step-by-step explanation:

The earth would be in a state of constant equinox i.e., the length of day and night would be same in a particular place.

The season of a place would be what it is when it is normally titled at equinox.

The animal and plant life which depend on the seasons would be affected.

Snow would only occur at parts where it normally snows at equinoxes.

Answer:

Linear function is specified by the equation ⇒ answer B

Step-by-step explanation:

* Look to the attached file

Answer:

B . Linear function.

Step-by-step explanation:

3x + 4y = 1

The degree of x and y is  1 and

if we drew a graph of this function we get a straight line.

Answer with  explanation:

Let R be a communtative ring .

a and b elements in R.Let a and b are units

1.To prove that ab is also unit in R.

Proof: a and b  are units.Therefore,there exist elements u[tex]\neq0[/tex] and v [tex]\neq0[/tex] such that

au=1 and bv=1 ( by definition of unit )

Where u and v are inverse element  of a and b.

(ab)(uv)=(ba)(uv)=b(au)(v)=bv=1 ( because ring is commutative)

Because bv=1 and au=1

Hence, uv is an inverse element of ab.Therefore, ab is a unit .

Hence, proved.

2. Let a is a unit and b is a zero divisor .

a is a unit then there exist an element u [tex]\neq0[/tex]

such that au=1

By definition of unit

b is a zero divisor then there exist an element [tex]v\neq0[/tex]

such that bv=0 where [tex]b\neq0[/tex]

By definition of zero divisor

(ab)(uv)=b(au)v    ( because ring is commutative)

(ab)(uv)=b.1.v=bv=0

Hence, ab is a zero divisor.

If a is unit and b is a zero divisor then ab is a zero divisor.

[tex]u(x,y,z)=x^2+yz[/tex]

[tex]\begin{cases}x(p,r,\theta)=pr\cos\theta\\y(p,r,\theta)=pr\sin\theta\\z(p,r,\theta)=p+r\end{cases}[/tex]

At the point [tex](p,r,\theta)=(2,2,0)[/tex], we have

[tex]\begin{cases}x(2,2,0)=4\\y(2,2,0)=0\\z(2,2,0)=4\end{cases}[/tex]

Denote by [tex]f_x:=\dfrac{\partial f}{\partial x}[/tex] the partial derivative of a function [tex]f[/tex] with respect to the variable [tex]x[/tex]. We have

[tex]\begin{cases}u_x=2x\\u_y=z\\u_z=y\end{cases}[/tex]

The Jacobian is

[tex]\begin{bmatrix}x_p&x_r&x_\theta\\y_p&y_r&y_\theta\\z_p&z_r&z_\theta\end{bmatrix}=\begin{bmatrix}r\cos\theta&p\cos\theta&-pr\sin\theta\\r\sin\theta&p\sin\theta&pr\cos\theta\\1&1&0\end{bmatrix}[/tex]

By the chain rule,

[tex]u_p=u_xx_p+u_yy_p+u_zz_p=2xr\cos\theta+zr\sin\theta+y[/tex]

[tex]u_p(2,2,0)=2\cdot4\cdot2\cos0+4\cdot2\sin0+0\implies\boxed{u_p(2,2,0)=16}[/tex]

[tex]u_r=u_xx_r+u_yy_r+u_zz_r=2xp\cos\theta+zp\sin\theta+y[/tex]

[tex]u_r(2,2,0)=2\cdot4\cdot2\cos0+4\cdot2\sin0+0\implies\boxed{u_r(2,2,0)=16}[/tex]

[tex]u_\theta=u_xx_\theta+u_yy_\theta+u_zz_\theta=-2xpr\sin\theta+zpr\cos\theta[/tex]

[tex]u_\theta(2,2,0)=-2\cdot4\cdot2\cdot2\sin0+4\cdot2\cdot2\cos0\implies\boxed{u_\theta(2,2,0)=16}[/tex]

This problem is about using the Chain Rule to compute the partial derivatives of a function with respect to different variables, followed by substitution of specific values into the obtained derivatives.

The problem involves finding partial derivatives using the Chain Rule on the given equations with given parameters: p = 2, r = 2, θ = 0. By substituting the equations for x, y, z into u which gives us u = (prcosθ)² + prsinθ(p+r). The next step is to compute (partial u)/(partial p), (partial u)/(partial r), (partial u)/(partial theta) by using the Chain Rule to find each partial derivative. After computing, you just substitute the given values of p, r, θ into the obtained derivates to get the final answers.

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Answer:  0.1587

Step-by-step explanation:

Given : The amount dispensed is approximately normally distributed with Mean : [tex]\mu=\ 16[/tex]

Standard deviation : [tex]\sigma= 1[/tex]

The formula to calculate the z-score :-

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

For x= 17

[tex]z=\dfrac{17-16}{1}=1[/tex]

The p-value =[tex] P(17<x)=P(1<z)[/tex]

[tex]=1-P(z<1)=1-0.8413447\\\\=0.1586553\approx0.1587[/tex]

The proportion of bottles will have more than 17 ounces = 0.1587

Answer:

amount is $320243.25 need in your account at the beginning

Money pull in 25 years is $750000

money interest is $429756.75

Step-by-step explanation:

Given data

principal (P) = $30000

time (t) = 25 years

rate (r) = 8% = 0.08

to find out

amount need in beginning, money pull out , and interest money

solution

We know interest compounded annually so n = 1

we apply here compound annually formula i.e.

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

now put all these value principal, r , n and t in equation 1

amount = 30000 ( 1 - [tex](1+0.08/1)^{-25}[/tex] / 0.08/1

amount = 30000 × 0.853982  / 0.08

amount = $320243.25 need in your account at the beginning

Money pull in 25 years is $30000 × 25 i.e

Money pull in 25 years is $750000

money interest = total money pull out in 25 years - amount at beginning need

money interest = $750000 - $320243.25

money interest = $429756.75

The cash flow in the account are;

a. Amount in the account at the beginning is approximately $320,243.3

b. The total money pulled out is $750,000

c. Amount of in interest in money pulled out approximately $429,756.7

The reason the above values are correct are as follows;

The given parameter are;

The amount to be withdrawn each year, d = $30,000

The number of years of withdrawal, n = 25 years

The interest rate on the account = 8 %

a. The amount that should be in the account at the beginning is given by the payout annuity formula as follows;

[tex]P_0 = \dfrac{d \times \left(1 - \left(1 + \dfrac{r}{k} \right)^{-n\cdot k}\right) }{\left(\dfrac{r}{k} \right)}[/tex]

P₀ = The principal or initial balance in the account at the beginning

d = The amount to be withdrawn each year = $30,000

r =  The interest rate per annum = 8%

k = The number of periods the interest is applied in a year = 1

n = The number of years withdrawal is made = 25

We get;

[tex]P_0 = \dfrac{30,000 \times \left(1 - \left(1 + \dfrac{0.08}{1} \right)^{-25\times 1} \right) }{\left( \dfrac{0.08}{1} \right)} \approx 320,243.3[/tex]

The amount needed in the account at the beginning, P₀ ≈ $320,243.3

b. The amount of money pulled out, A = n × d

Therefore, A = 25 × $30,000 = $750,000

c. The amount of money received as interest, I = A - P₀

∴ I = $750,000 - $320,243.3 ≈ $429,756.7

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Answer:[tex]18\sqrt{3}[/tex]

Step-by-step explanation:

Given data

we haven given a parabola and a straight line

Parabola is [tex]{y^2}={-\left ( x-10\right )[/tex]

line is [tex]x=7[/tex]

Find the point of intersection of parabola and line

[tex]y=\pm \sqrt{3}[/tex] when[tex]x=7[/tex]

Area enclosed is the shaded area which is given by

[tex]Area=\int_{0}^{\sqrt{3}}\left ( 10-y^2 \right )dy[/tex]

[tex]Area=_{0}^{\sqrt{3}}10y-_{0}^{\sqrt{3}}\frac{y^3}{3}[/tex]

[tex]Area=10\sqrt{3}-\sqrt{3}[/tex]

[tex]Area=9\sqrt{3}units[/tex]

Required area will be double of calculated because it is symmetrical about x axis=[tex]18\sqrt{3}units[/tex]

To find the area of the region enclosed by the graphs of[tex]x=10-y^2[/tex]and x=7, we need to find the points of intersection between the two equations and then integrate the curve between those points.

To find the area of the region enclosed by the graphs of  [tex]x=10-y^2[/tex] and x=7, we need to find the points of intersection between the two equations. Setting x equal to each other, we have  [tex]10-y^2=7.[/tex]Solving for y, we get y=±√3.

Now we can integrate the curve between the two values of y, as y goes from -√3 to √3. So the area is given by  [tex]\int (10 - y^2 - 7) \, dy[/tex] from -√3 to √3.

Evaluating the integral, we get A=√3*10-2√3/3 ≈ 30.78.

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Answer:   [tex]\dfrac{2}{9}[/tex]

Step-by-step explanation:

Let A be the event that the sum is 7 and and B be the event that the sum is 11 .

When two pair of dices rolled the total number of outcomes = [tex]n(S)=6\times6=36[/tex]

The sample space of event A ={(1,6), (6,1), (5,2), (2,5), (4,3), (3,4)}

Thus n(A)= 6

The sample space of event B = {(5,6), (6,5)}

n(B)=2

Since , both the events are independent , then the required probability is given by :-

[tex]P(A\cup B)=P(A)+P(B)\\\\=\dfrac{n(A)}{n(S)}+\dfrac{n(B)}{n(S)}=\dfrac{6}{36}+\dfrac{2}{36}=\dfrac{8}{36}=\dfrac{2}{9}[/tex]

Hence, the required probability = [tex]\dfrac{2}{9}[/tex]

Answer:

Probability that sum of numbers is either 7 or 11 is:

0.22

Step-by-step explanation:

A pair of dice is rolled.

Sample Space:

(1,1)       (1,2)        (1,3)       (1,4)          (1,5)        (1,6)

(2,1)      (2,2)       (2,3)      (2,4)         (2,5)       (2,6)

(3,1)      (3,2)       (3,3)      (3,4)        (3,5)       (3,6)

(4,1)      (4,2)       (4,3)      (4,4)         (4,5)       (4,6)

(5,1)     (5,2)      (5,3)      (5,4)         (5,5)       (5,6)

(6,1)      (6,2)       (6,3)      (6,4)         (6,5)       (6,6)

Total outcomes= 36

Outcomes with sum of numbers either 7 or 11 are in bold letters=8

i.e. number of favorable outcomes=8

So, P(sum of numbers is either 7 or 11 )=8/36

                                                                   =0.22

With a 95% confidence level, the population mean is estimated to be between approximately 96.85 and 111.15 based on a sample size of 10, a mean of 104, and a standard deviation of 10.

With a sample size (n) of 10, a mean \bar{x}104, and a standard deviation (s) of 10, we can find the 95% confidence interval for the population mean (μ).

First, we calculate the standard error of the mean (SE). The standard error of the mean can be calculated by dividing the standard deviation by the square root of the sample size.

SE = s/√n.  
By substituting s = 10 and n = 10 into the equation, we get SE = 3.162277660168379.

Next, we need to find the critical value (t) for a 95% confidence interval based on a t-distribution. Since we're using a confidence level of 95% and the sample size is 10, which means degree of freedom is n-1=9, the critical value (t) is 2.2621571627409915 based on the t-distribution table.

To calculate the lower bound and the upper bound of the 95% confidence interval, you should subtract and add to the mean the product of the critical value and the standard error respectively.

So,
Lower Bound = \bar{x} - t * SE
Upper Bound = \bar{x} + t * SE

Substituting from our known values, we get:
Lower Bound = 104 - 2.2621571627409915 * 3.162277660168379 = 96.84643094047428
Upper Bound = 104 + 2.2621571627409915 * 3.162277660168379 = 111.15356905952572

So, with a 95% confidence level, the confidence interval estimate of the population mean is (96.84643094047428, 111.15356905952572). This means we are 95% confident that the true population mean lies somewhere between approximately 96.85 and 111.15.

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The 95% confidence interval for the population mean IQ score of professional athletes, based on a sample size of 10 with a mean of 104 and standard deviation of 10, is estimated to be between 96.83 and 111.17.

To find the 95% confidence interval estimate of the population mean [tex](\( \mu \))[/tex] given the sample data, we'll use the formula for the confidence interval for a population mean when the population standard deviation is unknown:

[tex]\[ \text{Confidence interval} = \bar{x} \pm t \left( \frac{s}{\sqrt{n}} \right) \][/tex]

Where:

-[tex]\( \bar{x} \)[/tex] is the sample mean,

-  s  is the sample standard deviation,

-  n  is the sample size, and

-  t  is the critical value from the t-distribution for the desired confidence level and degrees of freedom.

Given:

- Sample size  n  = 10

- Sample mean [tex](\( \bar{x} \))[/tex]= 104

- Sample standard deviation  s  = 10

First, we need to find the critical value t  for a 95% confidence level with 9 degrees of freedom (since n - 1 = 10 - 1 = 9 ).

Using a t-table or statistical software, [tex]\( t \approx 2.262 \)[/tex] for a 95% confidence level and 9 degrees of freedom.

Now, let's plug in the values into the formula:

[tex]\[ \text{Confidence interval} = 104 \pm 2.262 \left( \frac{10}{\sqrt{10}} \right) \][/tex]

Now, let's calculate the margin of error:

[tex]\[ \text{Margin of error} = 2.262 \left( \frac{10}{\sqrt{10}} \right) \]\[ \text{Margin of error} \approx 7.17 \][/tex]

Finally, let's calculate the confidence interval:

[tex]\[ \text{Lower bound} = 104 - 7.17 \]\[ \text{Upper bound} = 104 + 7.17 \]\[ \text{Lower bound} \approx 96.83 \]\[ \text{Upper bound} \approx 111.17 \][/tex]

So, the 95% confidence interval estimate of the population mean IQ score of professional athletes is approximately between 96.83 and 111.17.

Hey there!:

Here , we choose the 10 marbles from the box of 40 marbles without replacement  

Therefore , probability is changes for every time  

Also , the trials are dependent  

Therefore ,the assumptions of binomial distributions are not satisfied

Therefore ,  Not binomial : the trials are not independent

Hope this helps!

The given procedure does not follow the characteristics of a binomial distribution.

The procedure of choosing marbles with replacement from a box with different colored marbles does not meet the criteria for a binomial distribution.

The given procedure does not result in a binomial distribution because in a binomial distribution, the trials must be independent, there must be a fixed number of trials, and there can only be two outcomes (success and failure).

In this case, choosing marbles from a box with replacement and tracking their colors does not meet the criteria for a binomial experiment, as the trials are not independent, the number of trials is not fixed, and there are more than two possible outcomes (purple, red, green).

Therefore, the given procedure does not follow the characteristics of a binomial distribution.

Answer:

The value of P(A or B or C) is 0.382.

Step-by-step explanation:

Given,

P(A) = 0.169,

P(B) = 0.041,

P(C) = 0.172

Since, if events A, B and C are mutually events ( in which no  element is common ),

Then, P(A∪B∪C) = P(A) + P(B) + P(C)

Or  P(A or B or C) = P(A) + P(B) + P(C),

By substituting the values,

P(A or B or C) = 0.169 +  0.041 +  0.172 = 0.382

(a)

          [tex]f(x+ h)=8x+8h+3[/tex]  

(b)

            [tex]f(x+ h)-f(x)=8h[/tex]          

(c)

             [tex]\dfrac{f(x+ h)-f(x)}{h}=8[/tex]

We are given a function f(x) as :

              [tex]f(x)=8x+3[/tex]

(a)

           [tex]f(x+ h)[/tex]

We will substitute (x+h) in place of x in the function f(x) as follows:

[tex]f(x+h)=8(x+h)+3\\\\i.e.\\\\f(x+h)=8x+8h+3[/tex]

(b)

       [tex]f(x+ h)-f(x)[/tex]              

Now on subtracting the f(x+h) obtained in part (a) with the function f(x) we have:

[tex]f(x+h)-f(x)=8x+8h+3-(8x+3)\\\\i.e.\\\\f(x+h)-f(x)=8x+8h+3-8x-3\\\\i.e.\\\\f(x+h)-f(x)=8h[/tex]

(c)

           [tex]\dfrac{f(x+ h)-f(x)}{h}[/tex]            

In this part we will divide the numerator expression which is obtained in part (b) by h to get:

           [tex]\dfrac{f(x+ h)-f(x)}{h}=\dfrac{8h}{h}\\\\i.e.\\\\\dfrac{f(x+h)-f(x)}{h}=8[/tex]    

Answer: (a) 0.8641

(b) 0.1359

Step-by-step explanation:

Given : The monthly worldwide average number of airplane crashes of commercial airlines [tex]\lambda= 3.5[/tex]

We use the Poisson  distribution for the given situation.

The Poisson distribution formula for probability is given by :-

[tex]P(X=x)=\dfrac{e^{-\lambda}\lambda^x}{x!}[/tex]

a) The probability that there will be at least 2 such accidents in the next month is given by :-

[tex]P(X\geq2)=1-(P(X=1)+P(X=0))\\\\=1-(\dfrac{e^{-3.5}(3.5)^0}{0!}+\dfrac{e^{-3.5}(3.5)^1}{1!})\\\\=1-(0.1358882254)=0.8641117746\approx0.8641[/tex]

b) The probability that there will be at most 1 accident in the next month is given by :-

[tex]P(X\leq1)=(P(X=1)+P(X=0))\\\\=\dfrac{e^{-3.5}(3.5)^0}{0!}+\dfrac{e^{-3.5}(3.5)^1}{1!}\\\\=0.1358882254\approx0.1359[/tex]

Answer: Hence, our required probability is 0.001077.

Step-by-step explanation:

Since we have given that

Number of red cars = 6

Number of silver cars = 9

Number of black cars = 3

Total number of cars = 6+9+3=18

We need to find the probability that 3 cars are red and 3 are black.

So, the required probability is given by

[tex]P(3R\ and\ 3B)=\dfrac{^6C_3\times ^3C_3}{^{18}C_6}\\\\P(3R\ and\ 3B)=0.001077[/tex]

Hence, our required probability is 0.001077.

Answer:

The probability is [tex]\frac{1}{9}[/tex]

Step-by-step explanation:

There are a total of 9 die in the box after she added the "cheat" die. Since there is only 1 "cheat" die in the box and chooses a die at random then the probability of her having chosen the cheat die is [tex]\frac{1}{9}[/tex] . The fact that she rolled two sixes did not affect when she choose the die therefore the probability remains as [tex]\frac{number.of.cheat.die}{total.dice}[/tex].

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

Answer: a) 0.2   b) 0.6

c) The event of selecting red tulip is not likely to occur.

The event of selecting purple tulip is likely to occur.

Step-by-step explanation:

Given : Total number of tulips = 100

The number of red tulips = 20

The number of purple tulips =60

The probability that a randomly selected tulip bulb is​ red :-

[tex]\dfrac{\text{Number of red tulips}}{\text{Total tulips}}\\\\=\dfrac{20}{100}=0.2[/tex]

Since 0.2 is less than 0.5.

It means that the event of selecting red tulip is not likely to occur.

The probability that a randomly selected tulip bulb is​ purple :-

[tex]\dfrac{\text{Number of purple tulips}}{\text{Total tulips}}\\\\=\dfrac{60}{100}=0.6[/tex]

Since 0.6 is more than 0.5.

It means that the event of selecting purple tulip is likely to occur.

Final answer:

The probability of selecting a red tulip bulb is 20%, and the probability of selecting a purple tulip bulb is 60%. These probabilities reflect the likelihood of picking a bulb of a particular color at random from the bag.

Explanation:

The question involves calculating the probability of selecting a red or purple tulip bulb from a bag.

Probability of Selecting a Red Tulip Bulb

The probability, P(Red), is calculated by dividing the number of red bulbs by the total number of bulbs:

P(Red) = Number of Red Bulbs / Total Number of Bulbs = 20 / 100 = 0.2

Probability of Selecting a Purple Tulip Bulb

Similarly, the probability, P(Purple), is:

P(Purple) = Number of Purple Bulbs / Total Number of Bulbs = 60 / 100 = 0.6

Interpretation of Probabilities

These probabilities indicate that there is a 20% chance of selecting a red bulb and a 60% chance of selecting a purple bulb from the bag. The higher the probability, the more likely it is to select a bulb of that color at random.

Answer:

Step-by-step explanation:

Given that in the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College.

Table is prepared as follows

                            Bus coll.     Lib Arts coll      Educ. coll        Total

Observed                  90                120                 90                  300

Expected p.c.             35                 35                 30                  100

Expected number     105                105                 90                 300

Percent*300/100

Hence expected frequency for business college = 105

Answer:

720 ways to arrange

Step-by-step explanation:

Use the factorial of 6 to find this solution.  Namely, 6!

This means 6*5*4*3*2*1 which equals 720

It seems like a huge number, right?  But think of it like this:  For the first option, you have 6 collars.  After you fill the first spot with one of the 6, you have 5 left that will fill the second spot.  After the first 2 spots are filled and you used 2 of the 6 collars, there are 4 possibilities that can fill the next spot, etc.

Answer:

720 ways

Step-by-step explanation:

If you are arranging your dog's collars on a 6 hanger coat rack on the wall and if she has six collars, there are 720 ways to arrange them.

Factorial of 6 = 720

For example it could look something like,

Collar 1, Collar 2, Collar 3, Collar 4, Collar 3, Collar 2, Collar 1, and so on.

Answer:

The percent of the parts are expected to fail before the 2100 hours is 0.15.

Step-by-step explanation:

Given :Life tests on a helicopter rotor bearing give a population mean value of 2500 hours and a population standard deviation of 135 hours.

To Find : If the specification requires that the bearing lasts at least 2100 hours, what percent of the parts are expected to fail before the 2100 hours?.

Solution:

We will use z score formula

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Mean value = [tex]\mu = 2500[/tex]

Standard deviation = [tex]\sigma = 135[/tex]

We are supposed to find  If the specification requires that the bearing lasts at least 2100 hours, what percent of the parts are expected to fail before the 2100 hours?

So we are supposed to find P(z<2100)

so, x = 2100

Substitute the values in the formula

[tex]z=\frac{2100-2500}{135}[/tex]

[tex]z=−2.96[/tex]

Now to find P(z<2100) we will use z table

At z = −2.96 the value is 0.0015

So, In percent = [tex].0015 \times 100=0.15\%[/tex]

Hence The percent of the parts are expected to fail before the 2100 hours is 0.15.