A boat is 100 miles away from the marina, sailing directly towards it at 10 miles per hour. Write an equation for the distance of the boat from the marina after t hours.

Answer:

a. P(x=0)=0.2967

b. P(x=1)=0.4444

c. P(x=2)=0.2219

d. P(x=3)=0.0369

Step-by-step explanation:

The variable X: "number of meals that exceed $50" can be modeled as a binomial random variable, with n=3 (the total number of meals) and p=0.333 (the probability that the chosen restaurant charges mor thena $50).

The probabilty p can be calculated dividing the amount of restaurants that are expected to charge more than $50 (5 restaurants)  by the total amount of restaurants from where we can pick (15 restaurants):

[tex]p=\dfrac{5}{15}=0.333[/tex]

Then, we can model the probability that k meals cost more than $50 as:

[tex]P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{3}{k} 0.333^{k} 0.667^{3-k}\\\\\\[/tex]

a. We have to calculate P(x=0)

[tex]P(x=0) = \dbinom{3}{0} p^{0}(1-p)^{3}=1*1*0.2967=0.2967\\\\\\[/tex]

b. We have to calculate P(x=1)

[tex]P(x=1) = \dbinom{3}{1} p^{1}(1-p)^{2}=3*0.333*0.4449=0.4444\\\\\\[/tex]

c. We have to calcualte P(x=2)

[tex]P(x=2) = \dbinom{3}{2} p^{2}(1-p)^{1}=3*0.1109*0.667=0.2219\\\\\\[/tex]

d. We have to calculate P(x=3)

[tex]P(x=3) = \dbinom{3}{3} p^{3}(1-p)^{0}=1*0.0369*1=0.0369\\\\\\[/tex]

Answer:

  (2, -2)

Step-by-step explanation:

Plotting the points from the table onto the graph of the line, you see the lines intersect at (2, -2).

The solution to the system of equations is (2, -2).

Answer:

 (2, -2)

Step-by-step explanation:

The person above me explains it with a graph

Answer:

x = ± i sqrt(5/8)

Step-by-step explanation:

8x^2+4=-1

Subtract 4 from each side

8x^2+4-4=-1-4

8x^2 = -5

Divide by 8

8/8x^2=-5/8

x^2 = -5/8

Take the square root of each side

sqrt(x^2) = ±sqrt(-5/8)

x =  ±sqrt(-5/8)

x =  ±sqrt(5/8) sqrt(-1)

x = ± i sqrt(5/8)

Answer:

There are 10 teams.

Step-by-step explanation:

Given that the question wants at least 48 swimmers so any numbers above 47 are counted.

In this diagram, there are 10 teams consisting 48 swimmers and above, 48, 52, 53, 63, 76, 79, 82, 84, 85 and 86.

Answer:

10 teams have 48 or more swimmers.

Step-by-step explanation:

If we look at stem 4 there is one team with 48 members.

So counting from there we  have:

1 + 2 + 1 + 2 + 4

= 10 teams.

Answer:

c. 13.5 cm

Step-by-step explanation:

In the right triangle formed by the main sail.

Using the trigonometric function

[tex]\tan \theta =\dfrac{\text{Opposite}}{\text{Adjacent}} \\\tan 52^\circ =\dfrac{x}{9} \\x=9 \times \tan 52^\circ\\x=11.52$ cm[/tex]

Therefore:

Height of the mast = 2+11.5=13.5 cm

The height of the mast is 13.5 cm.

Answer:

100,000 ways

Step-by-step explanation:

For each note, assign a number of friends

This can be repeated among the notes.

This is a 5 digit base 10 number

thus there are 10^5 = 100,000

There are 100,000 ways to distribute the problems among his 10 friends

Answer:

9 people

Step-by-step explanation:

37, 39, 41, 46, 61, 63, 69, 77, 80

9 people waited more than 36 minutes.

Answer:

7940

Step-by-step explanation:

=> 397 * 17 + 397 * 3

=> 6749 + 1191

=> 7940

Answer:

[tex]\dfrac{15}{19}[/tex]

Step-by-step explanation:

The soccer player so far has made 15 penalty kicks in 19 attempts.

Therefore:

Total Number of trials =19

Number of Successes =15

Therefore, the relative frequency probability that she will make her next penalty​ kick is:

[tex]=\dfrac{\text{Number of Successes}}{\text{Total Number of Trials}} \\=\dfrac{15}{19}[/tex]

Answer:

CICI

Step-by-step explanation: NO cici

Christian, Iris and Morgan each get an equal share of 1/2 of the pizza and the model 1/6 represent the fraction of the ​pizza each person gets.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

Christian, Iris and Morgan each get an equal share of 1/2 of the pizza.

To find the fraction of the ​pizza each person gets:

Divide the amount of pizza by the number of people.

There are 3 people and 1/2 pizza.

The fraction of the pizza each person gets

= The amount of pizza / number of people

The fraction of the pizza each person gets

= (1/2) / 3

Simplifying into multiplication,

The fraction of the pizza each person gets = 1/2 x 1/3

The fraction of the pizza each person gets

= 1/(2x3)

= 1/6

Therefore, the model that represents the requirement is 1/6.

To learn more about the division;

https://brainly.com/question/13263114

#SPJ5

Answer:

a. 3.686 %

b. 0.41 %

c. 4.096%

Step-by-step explanation:

We make use of the binomial probability equation, which is as follows:

P = [n! / (n - r)! r!] p ^ r * q ^ (n - r)

where,

n total number samples = 6

r is the selected number, depends on each point (a, b, c)

p is the of believing in reincarnation = 0.40

q = 1 - p = 0.60

to. What is the probability that exactly 5 of the selected adults believe in reincarnation?

So we use r = 5

P = [6! / ((6 - 5)! * 5!)] * [0.40 ^ 5 * 0.60 ^ (6 - 5)]

P = 6 * 0.006144

P = 0.0368 = 3.686%

b. What is the probability that all of the selected adults believe in reincarnation?

So we use r = 6

P = [6! / ((6 - 6)! * 6!)] * [0.40 ^ 6 * 0.60 ^ (6 - 6)]

P = 1 * 0.004096

P = 0.004096 = 0.41%

c. What is the probability that at least 5 of the selected adults believe in reincarnation?

So we use r = 5 to 6

P (r = 5) = [6! / ((6 - 5)! * 5!)] * [0.40 ^ 5 * 0.60 ^ (6 - 5)]

P (r = 5) = 6 * 0.006144

P (r = 5) = 0.0368 = 3.686%

P (r = 6) = [6! / ((6 - 6)! * 6!)] * [0.40 ^ 6 * 0.60 ^ (6 - 6)]

P (r = 6) = 1 * 0.004096

P (r = 6) = 0.004096 = 0.41%

The total is the sum of all:

P (total) = 3.686% + 0.41%

P (total) = 4.096%

Answer:

f(x-2) = (x-2)²

or

f(x-2) = x² -4x + 4

Step-by-step explanation:

Simply plug in (x - 2) into f(x) to find your graph.

Edit (With Picture):

You are moving the graph right 2.

Answer:

Step-by-step explanation:

f(x) = x²

f(x - 2) = (x - 2)²

f(x - 2) = x² - 4x + 4

The grafic is below.

I hope I've helped you.

Answer:

At first it increases by 25%, then you have 1.25x the original temp. A drop of 40% gives you .6 x 1.25, or 75% of the original temperature

Step-by-step explanation:

found that on the web for yuh. I really hope it helped.

Answer:

decreased by 25%

Step-by-step explanation:

Answer:

No, because there is just as high of a possibility that the other is biased too.

Answer:

Look below

Step-by-step explanation:

Answer:

The calculated value t = 4.976 > 2.6264 at 0.01 level of significance

Null hypothesis is rejected

Alternative hypothesis is accepted

The  mean starting salary for business majors in 2013 is greater than the mean starting salary in 2012

Step-by-step explanation:

Given Mean of the population μ = $53,900

Given sample size 'n' = 100

Mean of the sample size x⁻ = 55,144

Sample standard deviation 'S' = 5200

Null hypothesis:H₀: There is no difference between the means

Alternative Hypothesis :H₁: The  mean starting salary for business majors in 2013 is greater than the mean starting salary in 2012

Test statistic

[tex]t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }[/tex]

[tex]t = \frac{55144-53900}{\frac{5200}{\sqrt{100} } }[/tex]

t = 4.976

Degrees of freedom

ν = n-1 = 100-1 =99

t₀.₀₁ = 2.6264

The calculated value t = 4.976 > 2.6264 at 0.01 level of significance

Null hypothesis is rejected

Alternative hypothesis is accepted

Final answer:-

The  mean starting salary for business majors in 2013 is greater than the mean starting salary in 2012

Answer:

We conclude that the mean starting salary for business majors in 2013 is greater than the mean starting salary in 2012.

Step-by-step explanation:

We are given that the Wall Street Journal reported that bachelor’s degree recipients with majors in business average starting salaries of $53,900 in 2012.

A sample of 100 business majors receiving a bachelor’s degree in 2013 showed a mean starting salary of $55,144 with a sample standard deviation of $5,200.

Let [tex]\mu[/tex] = mean starting salary for business majors in 2013.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\leq[/tex] $53,900     {means that the mean starting salary for business majors in 2013 is smaller than or equal to the mean starting salary in 2012}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > $53,900     {means that the mean starting salary for business majors in 2013 is greater than the mean starting salary in 2012}

The test statistics that would be used here One-sample t-test statistics because we don't know about population standard deviation;

                               T.S. =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean starting salary = $55,144

            s = sample standard deviation = $5,200

            n = sample of business majors = 100

So, the test statistics  =  [tex]\frac{55,144-53,900}{\frac{5,200}{\sqrt{100} } }[/tex]  ~ [tex]t_9_9[/tex]

                                     =  2.392

The value of t-test statistic is 2.392.

Now, at 0.01 significance level the t table gives a critical value of 2.369 at 99 degree of freedom for right-tailed test.

Since our test statistic is more than the critical value of t as 2.392 > 2.369, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the mean starting salary for business majors in 2013 is greater than the mean starting salary in 2012.

Answer:

Option B

Step-by-step explanation:

When A and B are independent events:

P(A and B) = P(A) * P(B)

OR

P(A|B) = P(A) * P(B)

Answer:

Step-by-step explanation:

Given the sample space

20 red marbles and

10 blue marbles

the sample size is

S= 20+10= 30

The probability that both are red if two marbles are pulled at once is

[tex]\frac{20}{30} *\frac{10}{30} \\\\=\frac{2}{3}*\frac{1}{3} = \frac{2}{9}[/tex]

Answer:

Option 4 is not true

Step-by-step explanation:

[tex]\frac{a}{b}=\frac{c}{d}\\\\[/tex]

1)Cross multiply,

ad = bc

So, true

2) a/ c = b/d also true

3) a+b/b = c+d/d  also true

For example:

[tex]\frac{1}{4}=\frac{2}{8}\\\\\frac{1+4}{4}=\frac{2+8}{8}\\\\\frac{5}{4}=\frac{10}{8}\\\\[/tex]

When simplifying 10/8, it is 5/4.

5) b/a = d/c is also true

EASY!

Answer: 17/16 or 1 1/16

Step-by-step explanation:

BRO IT'S ELEMANTARY FRACTIONS!!!!

Answer:

The null and alternative hypothesis are:

[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2> 0[/tex]

where μ1 is the population mean sales with compensation plan, and μ2 is the populatiojn mean sales without compensation plan.

A Type I error is made when a true null hypothesis is rejected. In this case, it would be concluded that the compensation plan increases sales, when in fact it does not (at least, not significantly).

The consequences of this error would be that the compensation plan would have evidence to be implemented in the company when in fact it will not bring the results it is expected to have.

Step-by-step explanation:

This hypothesis test will test the claim that the compensation plan increases the average sales per salesperson. This claim will be stated in the alternative hypothesis, and will state that, with the compensation plan, the sales are significantly higher than without the compensation plan.

The null hypothesis, that Steve wants to falsify, will state that the sales will not differ with or withour compensation plan.

We can write this hypothesis as:

[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2> 0[/tex]

where μ1 is the population mean sales with compensation plan, and μ2 is the populatiojn mean sales without compensation plan.

A Type I error is made when a true null hypothesis is rejected. In this case, it would be concluded that the compensation plan increases sales, when in fact it does not (at least, not significantly).

The consequences of this error would be that the compensation plan would have evidence to be implemented in the company when in fact it will not bring the results it is expected to have. The sales would be expected to increase due to this implementation, and they will not increase, at least, not for the compensation plan.

Answer: D

Step-by-step explanation:

Since we are not given the height of the trapezoid, we can split this into a triangle and a rectangle. We find the area of each and then add them together. In order to do so, we must use Pythagorean Theorem to find the missing length so that we can find the area.

a²+b²=c²

a²+4²=8²

a²+16=64

a²=48

a=√48

a=4√3

Now that we know the missing length of the triangle, we can find the area of the triangle and the rectangle.

Triangle

A=1/2bh

A=1/2(4)(4√3)

A=8√3

-----------------------------------------------------------------------------------------

Rectangle

A=lw

A=7(4√3)

A=28√3

With our areas, we can add them together.

4√3+28√3=36√3 cm²

Answer:

c.-6 = rational

e. 9= rational

h. 1/2= rational

Step-by-step explanation:

Rational numbers are numbers that can be express as a quotient of fraction.

a. -4.86= irrational

b. √5/8= irrational

c.-6 = rational

d - x/3 = rational

e. 9= rational

f.√(-4)= irrational

g-√(-4) = irrational

h. 1/2= rational

Answer: A is you answer

Answer: 8/3 and -9/4

Step-by-step explanation:

1. [tex]\frac{2^{3}}{3} = \frac{2 * 2 * 2}{3} = \frac{8}{3}[/tex]

2. In this problem, when raising a whole fraction to a power, you must both raise the numerator and denominator to that power.

[tex]-(\frac{3}{2})^2 = -(\frac{3^2}{2^2}) = -(\frac{9}{4}) = -\frac{9}{4}[/tex]

Answer:

option D is the right option.

Solution,

1 liquid pint=0.5 liquid quart

( 2 pints=1 quart)

Since,

2 pints=1 quart them,

14 pints=7 quarts

Ratio is 14 pints(7 quarts) to 45 pints.

Thus the fraction is:

[tex] \frac{14}{45} [/tex]

hope this helps...

Good luck on your assignment..

Answer:

(a)11 hours

(b)19.5 hours

(c)2.5 hours

Step-by-step explanation:

The number of hours of​ daylight, H, on day t of any given year in a particular city can be modeled by the function :

[tex]H(t)=11+8.5\sin\left(\dfrac{2\pi}{365}(t-83)\right)[/tex]

(a)When t=83

[tex]H(83)=11+8.5\sin\left(\dfrac{2\pi}{365}(83-83)\right)\\=11+8.5\sin 0\\=11$ hours[/tex]

(b)When t=175

[tex]H(175)=11+8.5\sin\left(\dfrac{2\pi}{365}(175-83)\right)\\=11+8.5\sin\left(\dfrac{2\pi}{365}\times 92 \right)\\=11+8.5\\=19.5$ hours[/tex]

(b)When t=358

[tex]H(175)=11+8.5\sin\left(\dfrac{2\pi}{365}(358-83)\right)\\=11+8.5\sin\left(\dfrac{2\pi}{365}\times 275 \right)\\=11-8.5\\=2.5$ hours[/tex]

Answer:

.8 miles further on Monday

Step-by-step explanation:

Take the miles on Monday and subtract the miles on Wednesday

3.4 - 2.6 =.8 miles

Answer:

2/7

Step-by-step explanation:

Seven employees can be arranged in 7! ways. n(S) = 7!

Two adjacent desks for married couple can be selected in 6 ways viz.,(1, 2), (2, 3), (3,4), (4, 5), (5,6),(6,7).

This couple can be arranged in the two desks in 2! ways. Other five persons can be arranged in 5! ways.

So, number of ways in which married couple occupy adjacent desks

= 6×2! x 5! =2×6!

so, the probability that the married couple will have adjacent desks

[tex]\frac{n(A)}{n(s)} =\frac{2\times6!}{7!} \\=\frac{2}{7}[/tex]

Answer:

[tex]\boxed{ \ x = 2 \ or \ x = -2 \ }[/tex]

Step-by-step explanation:

I understand that you want to solve this equation

[tex]\sqrt{x+2}\sqrt{x-2}=0[/tex]

<=>

[tex]\sqrt{(x+2)(x-2)}=0[/tex]

<=>

[tex](x+2)(x-2)=0[/tex]

<=>

x = 2 or x = -2

hope this helps

if your question is [tex](\sqrt{x}+2)(\sqrt{x}-2) = 0[/tex]

then this is [tex](\sqrt{x})^2-4 = 0\\<=> x = 4[/tex]