The distance between R and S on the coordinate grid is units. (Input whole numbers only) Numerical Answers Expected! Answer for Blank 1​

Answer:

a) 0.0013 = 0.13% probability that by 7:30 a.m. Mary receives exactly four messages – two of her best friend and two of her mother.

b) [tex]1.6 \times 10^{-9}[/tex] probability that there are no typos in the text messages Matilda receives between 2 p.m. and 5 p.m.

Step-by-step explanation:

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

A) Find the probability that by 7:30 a.m. Mary receives exactly four messages – two of her best friend and two of her mother.

Two from the best friend:

Her best friend sends a message once every 10 minutes.

From 6 to 7:30, there is an hour and a half, that is, 90 minutes, so the mean for her best friend is [tex]\mu = \frac{90}{10} = 9[/tex]

Two messages is P(X = 2). So

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 2) = \frac{e^{-9}*9^{2}}{(2)!} = 0.0050[/tex]

Two from the mother:

Message every hour = 60 minutes. So [tex]\mu = \frac{90}{60} = 1.5[/tex]. This is P(X = 2).

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 2) = \frac{e^{-1.5}*1.5^{2}}{(2)!} = 0.2510[/tex]

Two of her best friend and two of her mother:

Independent events, so the probability of both happening is the multiplication of their separate probabilities.

[tex]p = 0.005*0.251 = 0.0013[/tex]

0.0013 = 0.13% probability that by 7:30 a.m. Mary receives exactly four messages – two of her best friend and two of her mother.

B) With a chance of 75% a text message contains a typo independent of the sender. Find the probability that there are no typos in the text messages Matilda receives between 2 p.m. and 5 p.m.

In 3 hours, she is expected to receive:

3*60/10 = 18 messages from her best friend.

3*60/60 = 3 messages from her mother.

3*60/30 = 6 messages from her brother.

In total, 27 messages.

75% probability of a typo, so [tex]\mu = 0.75*27 = 20.25[/tex]

This is P(X = 0).

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-20.25}*20.25^{0}}{(0)!} = 1.6 \times 10^{-9}[/tex]

[tex]1.6 \times 10^{-9}[/tex] probability that there are no typos in the text messages Matilda receives between 2 p.m. and 5 p.m.

Answer:

the 1st one

Step-by-step explanation:

thank u and have a nice day and i hope this helped

Answer:

A+A+B+B+B+C+C+D

Step-by-step explanation:

it's just the letter wrote the amount of times the number says

Answer:

(0,-7)

(4, -4)

(8, -1)

Step-by-step explanation:

(0,-7)

(4, -4)

(8, -1)

Hope I helped!

Answer:

6

Step-by-step explanation:

The product of four and nine is 36.

If you make 1/6 into a decimal, then multiply it by 36 you get 6!

I hope this helps, and have a great day! :)

Answer:

6

Step-by-step explanation:

4*9=36

6/6=36

36*1/1*6

36/6

6

Answer:

-9(2y+3) Tip: Download photo math lol : )

Answer:

D:

Null: Pf = Ps

Alternative: Pf > Ps

Step-by-step explanation:

Hypothesis test is the test which uses the random sample data to evaluate that whether the null hypothesis to reject or accept.The null and alternate hypothesis for the given question is,

[tex]H_0:P_f=P_s[/tex]

[tex]H_a:P_f>P_s[/tex]

Hence the option D is the correct option.

[tex]P_p[/tex] represent the proportion of all Friday night calls.

[tex]P_s[/tex] represent the proportion of all Sunday night calls.

Hypothesis test is the test which uses the random sample data to evaluate that whether the null hypothesis to reject or accept.

As part of investigation the police taken the random sample of the Friday night and the Saturday night phone calls.

Null hypothesis [tex](H_0)[/tex] states that the parameter of two proportion are are equal to the hypothesis value.  If the proportion of all Friday night calls and proportion of all Sunday night calls is equal. Then the Null hypothesis for the investigation is,

[tex]H_0:P_f=P_s[/tex]

The alternate hypothesis states that the population parameter is smaller greater or must be different than the hypothesis value.The alternate hypothesis for the given question,

[tex]H_a:P_f>P_s[/tex]

Thus the null and alternate hypothesis for the given quyestion is,

[tex]H_0:P_f=P_s[/tex]

[tex]H_a:P_f>P_s[/tex]

Hence the option D is the correct option.

Learn more about the hypothesis here;

https://brainly.com/question/2695653

Answer:

$15.06 answer C

Step-by-step explanation:

The previous day's closing price of Cisco Systems stock was $15.06. The correct option is c.

The closing price of Cisco Systems stock the previous day was $15.06.

We can see from the table that the "close" price listed in column 8 is $15.04 and the "net change" listed in column 9 is negative 0.02. This means that the stock price decreased by $0.02 from the previous day's closing price.

To find the previous day's closing price, we need to add the net change of -$0.02 to the current day's closing price of $15.04:

$15.04 + (-$0.02) = $15.02

Thus, the correct option is c.

For more details regarding closing price, visit:

https://brainly.com/question/3953674

#SPJ7

Answer:

CHOOSE  A. 48

Step-by-step explanation:

Because its easy just do it.

Answer:

1

Step-by-step explanation:

10*4=40

so 1

Answer:

Following are the solution to the given question:

Step-by-step explanation:

Let the possibility including its sale will be x

Purchases possibility for [tex]1=2x[/tex]

Purchases possibility for [tex]2=3x[/tex]

Purchases possibility for [tex]3= 4x[/tex]

Calculating the total possibility [tex]=x+2x+3x+4x=10x[/tex]

The total possibility within the framework of the sample=1

[tex]\to 10x =1\\\\\to x = \frac{1}{10}\\\\\to x = 0.1 \\\\[/tex]

[tex]Outcome \ \ \ \ \ \ \ \ \ \ Probability\\\\0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.1\\\\1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.2\\\\2 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.3\\\\3\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.4\\[/tex]

Answer:

We have been attempting to reach you about your car's extended warranty.

Step-by-step explanation:

Answer:

Step-by-step explanation:

5x + 2 = 22

Bringing like terms on one side

5x = 22 - 2

5x = 20

x = 20/5 = 4

Answer:

21507

Step-by-step explanation:

Answer:

Perimeter 182 cm, area= 2,028 cm2

Step-by-step explanation:

The perimeter of the given rectangle is

  2(6 cm + 8 cm) = 28 cm

The area of the given rectangle is

  (6 cm)*(8 cm) = 48 cm^2

The larger rectangle will have a perimeter of

  6.5*28 cm = 182 cm

The larger rectangle will have an area of

  6.5^2*48 cm^2 = 2028 cm^2 . . . . . note the scale factor is squared for area

The appropriate choice is the 3rd one, ...

  Perimeter = 182 cm, area = 2,028 cm^2

Answer: Perimeter = 182 cm, area = 2,028 cm2 3rd one

Step-by-step explanation:

Answer:

$159

Step-by-step explanation:

Answer:

$159

Step-by-step explanation:

300 decrease 50% =

300 × (1 - 50%) = 300 × (1 - 0.5) = 150

150 increase 6% =

150 × (1 + 6%) = 150 × (1 + 0.06) = 159

Answer:

0.1587 = 15.87% probability that the factory will run out of lubricant before the next replenishment arrives

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Addition of normal variables.

When we add two normal variables, the mean is the sum of the separate means, and the standard deviation is the square root of the sum of the variances. So

The first machine has a mean usage of 50.6 gallons and standard deviation of 12 gallons. The second machine has a mean usage of 64.4 gallons and standard deviation of 16 gallons.

Total consumption is of both machines, combined. So

[tex]\mu = 50.6 + 64.4 = 115[/tex]

[tex]\sigma = \sqrt{12^2 + 16^2} = 20[/tex]

What is the probability that the factory will run out of lubricant before the next replenishment arrives?

Probability of consuming more than 135 gallons, which is 1 subtracted by the pvalue of Z when X = 135. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{135 - 115}{20}[/tex]

[tex]Z = 1[/tex]

[tex]Z = 1[/tex] has a pvalue of 0.8413

1 - 0.8413 = 0.1587

0.1587 = 15.87% probability that the factory will run out of lubricant before the next replenishment arrives

Answer:

Step-by-step explanation:

2x and 50° are supplementary angles

Answer:

65

Step-by-step explanation:

2x+2x=4x

4x+50+50=360

4x+100=360

4x=260

x=65

Answer:

x=b^2+d^2/a-c

Step-by-step explanation:

Answer:

15.25

convert to ounces- 80 ounces equals 5 pounds

multiply by the unit price-5*3.05

get the answer- 15.25

Answer:

Step-by-step explanation:

(3.05/lb)(80oz)(lb/16oz)=$15.25

Answer: a = 4

Step-by-step explanation: Area of a triangle is calculated as: [tex]A_{t}=\frac{b.h}{2}[/tex].

The triangle formed by the parabola has base (b) equal to the distance between the points where the graph touches x-axis and height (h) is the point where graph touches the y-axis.

The points on the x-axis are the roots of the quadratic equation:

a(x-3)(x+2)=0

(x-3)(x+2)=0

x - 3 = 0

x = 3

or

x + 2 = 0

x = -2

So, base is the distance between (-2,0) and (3,0).

Since they are in the same coordinate, distance will be:

b = 3 - (-2)

b = 5

Area of the triangle is 10. So constant a is

[tex]10=\frac{5.a}{2}[/tex]

5a = 10.2

a = 4

The constant a of the function y = a(x-3)(x+2) is 4.

Answer: a = 2/3

Step-by-step explanation:

y-intercept: y=a(2)(-3) = -6a

x-intercepts: (-2,0) , (3,0)

height = -6a

base = 5

Area = 10 = 0.5 x 5 x -6a

10 = -15 a

a = -2/3

BUT a>0 since it opens upwards, so:

a = 2/3

Answer:

[tex]\frac{3}{11}[/tex]

Step-by-step explanation:

6/22 = 3/11

Answer:

40 books and 3 months

Step-by-step explanation:

b= books

15b=9months

1 month =15/9=5/3

24 months =24×5/3

24 months =8×5=40 books

1b=9/15

1b=3/5

5b =3/5×5

5b=3

it would take him 3 months to read 5 books

Answer:

h(-2) = -3(-2)(2)+5 = 17

Step-by-step explanation:

h(-2) = -3(-2)(2)+5 = 17

Answer:

The actual SAT score is 1260.6.

The equivalent ACT score for this student(77th percentile) is 24.7.

The equivalent ACT score to a SAT score of 1544 is 30.26.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

SAT:

[tex]\mu = 1117, \sigma = 194[/tex]

ACT:

[tex]\mu = 21.9, \sigma = 3.8[/tex]

If a student gets an SAT score that is the 77-percentile, find the actual SAT score.

This is X when Z has a pvalue of 0.77. So X when Z = 0.74.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]0.74 = \frac{X - 1117}{194}[/tex]

[tex]X - 1117 = 0.74*194[/tex]

[tex]X = 1260.6[/tex]

The actual SAT score is 1260.6.

What would be the equivalent ACT score for this student?

X when Z = 0.74, using [tex]\mu = 21.9, \sigma = 3.8[/tex]

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]0.74 = \frac{X - 21.9}{3.8}[/tex]

[tex]X - 21.9 = 0.74*3.8[/tex]

[tex]X = 24.7[/tex]

The equivalent ACT score for this student(77th percentile) is 24.7.

If a student gets an SAT score of 1544, find the equivalent ACT score.

First we find the z-score of the SAT, then we find the equivalent ACT score.

Z-score of SAT:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{1544 - 1117}{194}[/tex]

[tex]Z = 2.2[/tex]

Equivalent ACT:

X when Z = 2.2. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]2.2 = \frac{X - 21.9}{3.8}[/tex]

[tex]X - 21.9 = 2.2*3.8[/tex]

[tex]X = 30.26[/tex]

The equivalent ACT score to a SAT score of 1544 is 30.26.