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Answer:

27/35

Step-by-step explanation:

We use combination to solve for this

C(n, r), =nCr = n!/r!(n - r)!

From the question, we are told that:

Four couples are at a party. Four of the eight people are randomly selected to win a prize.

Four couples = 8 people.

= 8C4 = 8!/4! (8 - 4)!

= 70

No person can win more than one prize. ( No person can win more than one prize of the 4 people selected)

This can happen in 4 ways

[4C1 × 3C2 ] × 4=

[4!/1! ×( 4 - 1)!] × [3!/2! ×(3-2)!] × 4 ways

= 4 × 3 × 4 ways

= 48

The probability that both of the members of at least one couple win prizes

48 + 4C2/ 8C4

4C2 = 4!/2!(4 - 2) !

= 6

8C4 = 8C4 = 8!/4! (8 - 4)!

= 70

48 + 6/ 70

= 54/70

= 27/35

Therefore, the probability that both of the members of at least one couple win prizes is 27/35.

The probability that both of the members of at least one couple win prizes is 27/35 and this can be determined by using the given data.

Given :

The following steps can be used in order to determine the probability that both of the members of at least one couple win prizes:

Step 1 - The concept of probability is used in order to determine the probability that both of the members of at least one couple win prizes.

Step 2 - According to the given data, the total number of people is 8.

Step 3 - So, the probability that both of the members of at least one couple win prizes is:

[tex]\rm P =\dfrac{ \;^4C_1\times \;^3C_2\times 4 + \;^4C_2}{\;^8C_4}[/tex]

Step 4 - Simplify the above expression.

[tex]\rm P =\dfrac{48+ 6}{70}[/tex]

[tex]\rm P = \dfrac{27}{35}[/tex]

So, the probability that both of the members of at least one couple win prizes is 27/35.

For more information, refer to the link given below:

https://brainly.com/question/795909

Answer:

7/6

Step-by-step explanation:

The LCD of these three fractions is 6; the denominators 3, 3 and 6 divide evenly into 6.

Therefore we have:

4/6 + 2/6 + 1/6 = 7/6

Answer:

[tex]\large \boxed{\mathrm{34.2}}[/tex]

Step-by-step explanation:

[tex]\sf B= arcsin (\frac{b \times sin(A)}{a} )[/tex]

[tex]\sf B= arcsin (\frac{7 \times sin(40\°)}{8} )[/tex]

[tex]\sf B = 0.59733 \ rad = 34.225\°[/tex]

Answer:

  linear with a common first difference of 2

Step-by-step explanation:

On the face of it, you can reject answers that ascribe a common ratio to a linear or quadratic function. (A common ratio is characteristic of an exponential function.)

You can also reject the answer that ascribes a common first difference to a quadratic function. (A quadratic function has a common second difference.)

After you reject the nonsense answers, there is only one remaining choice. It is also the correct one:

  linear with a common first difference of 2

_____

The ratio of change in y to change in x is ...

  (0 -(-2))/(-2 -(-3)) = 2

  (4 -0)/(0 -(-2)) = 2

  (12 -4)/(4 -0) = 2

That is, y increases by 2 when x increases by 1. The common first difference is 2.

Answer:

Step-by-step explanation:

This is an example of a frequency distribution for a class interval. In order to complete the frequency distribution, we will count the number of data occurring in each group, and write that number as the frequency for that group. This is done as shown below:

 Age                Frequency          ages in class

20-29                       4                  22, 26, 27, 27                

30-39                       3                  31, 34, 36

40-49                       5                  42, 43, 44, 48, 49

50-59                       5                  52, 53, 55, 56, 57

60-69                       6                  60, 56, 65, 66, 67, 69

70-79                        6                  72, 75, 77, 78, 78, 79

80-89                       1                   87

Total                        30

Answer:

5/7

Step-by-step explanation:

There are a couple ways to solve this.  One would be by finding the least common denominator for each one with 2/3, subtracting, and seeing what is left over.  Another way is converting to decimals.

2/3=0.666666

————————-

7/8=0.875

8/9=0.88888

4/5=0.8

5/7=0.7143

They are all greater than 2/3 (0.6666666), but 5/7 is the closest, so would have the least waste.

Answer:

40

Step-by-step explanation:

In the question only lies the answer:

"and a total of forty students plan to participate in cross country."

Answer:

2

Step-by-step explanation:

2

Answer:

The probability  is  [tex]P(x < 13) = 0.8732[/tex]

Step-by-step explanation:

From the question we are told that

    The  probability of success is    p = 0.70

     The  sample size is  [tex]n = 15[/tex]

Generally the distribution of U.S. households have vcrs follow a binomial distribution given that there are only two outcome (household having vcrs or household not having vcrs )

The probability of failure is mathematically evaluated as

       [tex]q = 1- p[/tex]

substituting values

      [tex]q = 1- 0.70[/tex]

      [tex]q = 0.30[/tex]

The probability that fewer than 13 have vcrs is mathematically represented as

          [tex]P(x < 13) = 1- [P(13) + P(14) + P(15)][/tex]

=>     [tex]P(x < 13) = 1-[( \left 15 } \atop {}} \right. C_{13} *p^{13}* q^{15-13})+ (\left 15 } \atop {}} \right. C_{14} *p^{14}* q^{15-14}) +( \left 15 } \atop {}} \right. C_{15} *p^{15}* q^{15-15}) ][/tex]

 Here  [tex]\left 15 } \atop {}} \right. C_{13}[/tex] means  15 combination 13 and the value is  105 (obtained from calculator)

 Here  [tex]\left 15 } \atop {}} \right. C_{14}[/tex] means  15 combination 14 and the value is  15 (obtained from calculator)

 Here  [tex]\left 15 } \atop {}} \right. C_{15}[/tex] means  15 combination 15 and the value is  1 (obtained from calculator)

So

 [tex]P(x < 13) = 1-[(105 *p^{13}* q^{2})+ (15 *p^{14}* q^{1}) +(1*p^{15}* q^{0}) ][/tex]

substituting values      

 [tex]P(x < 13) = 1-[(105 *(0.70)^{13}* (0.30)^{2})+ (15 *(0.70)^{14}* (0.30)^{1}) +(1*(0.70)^{15}* (0.30)^{0}) ][/tex]

 [tex]P(x < 13) = 0.8732[/tex]

Answer:

Step-by-step explanation:

Lets, turn this into words and use order of operations, First, we look for multiplication and division.

the sum of one fourth of 5 times of 8 and 10 gets you 1/4(5*8) + 10 = 20

what is the number if 4 is subtracted from the sum

20 - 4 = 16

Answer:

Student t-distribution.

Step-by-step explanation:

In this scenario, a test is being conducted to test the difference between two population "means" using data that are gathered from a matched pairs experiment. If the paired differences are normal, then the distribution used for testing is the student t-distribution.

In Statistics and probability, a student t-distribution can be defined as the probability distribution which can be used to estimate population parameters when the population variance is not known (unknown) and the sample population is relatively small. The student t-distribution is a statistical distribution which was published in 1908 by William Sealy Gosset.

A student t-distribution has a similar curve with the normal distribution curve, except that it is fatter and a little bit shorter.

Answer:

D. the coefficient of determination is .81.

Step-by-step explanation:

SST = SSE + SSR

where

SST is the summation of square total

SSE is the summation of squared error estimate = 608

SSR is the summation of square of residual = 2593

with these in mind we put the values into the formula

= 2592 + 608

=3200

Coefficient of determination = SSR/SST

= 2592/3200

= 0.81

Therefore option D is the correct answer to the question.

Answer:

Following are the correct code to this question:

import re#import package for regular expression

def check_time(text):#defining a method check_time that accepts string value  

   p = r'(1[012]|[1-9]):[0-5][0-9][ ]{0,1}?(am|pm|AM|PM)'#defining string variable p that stores values

   val = re.search(p, text)#defining val variable that check serachs p and text variable values

   return val!= None#use return keyword to return val value

print(check_time("12:45pm"))#defining print method that calls method by input value  

print(check_time("9:59 AM")) #defining print method that calls method by input value

print(check_time("6:60 am")) #defining print method that calls method by input value

print(check_time("five o'clock"))#defining print method that calls method by input value

Output:

True

True

False

False

Step-by-step explanation:

In the above-given program, some data is missing that is code file so, the correct code can be defined as follows:

In the above-given method, that is "check time" it uses 12-hour time format validation, that is tested by coding the regex and  all the value validates in the "val" variables, that can be defined as  follows:  

Answer:

the log to the base 3 of 14 is 2.402

Step-by-step explanation:

You must find a way to indicate that 3 is the base; you cannot run this '3' together with 2, 7 or 14.

Example:  

log to the base 3 of 2 = 0.631

log to the base 3 of 7 = 1.771

Note that 2 times 7 is 14.  Thus, to obtain the log to the base 3 of 14, we must ADD the two logs shown above:

0.631

+1.771

----------

2.402

Thus, the log to the base 3 of 14 is 2.402.

Check:  Does 3^2.402 = 14?  YES

Answer:

38.911≤p≤41.089

Step-by-step explanation:

The formula for calculating confidence interval for a population mean us as shown below;

CI = xbar ± Z×S/√N where;

xbar is the sample mean = 40

Z is the z score at 95% confidence interval = 1.96

S is the standard deviation = 5

N is the sample size = 81

Substituting this parameters in the formula we have;

CI = 40±1.96×5/√81

CI = 40±(1.96×5/9)

CI = 40±(1.96×0.556)

CI = 40±1.089

CI = (40-1.089, 40+1.089)

CI = (38.911, 41.089)

The 95% confidence interval for the population mean is 38.911≤p≤41.089

Answer:

38.9 ≤ U ≤ 41.1

Step-by-step explanation:

Mean, m = 40; standard deviation, α = 5; Confidence limit, U = 95% or 0.95

N = 81

The standard error, α(m) = α/√(N) = 5/√81 =5/9

Using table: 0.95 = 0.0379

Z(0.95) = 2 - 0.0379 = 1.9621 or 1.96

Hence, confidence interval = { m - 1.96(α/√N) ≤ U ≤ m +1.96(α/√N)}

But, 1.96(α/√N) = 1.96 X 5/9 = 1.96 X 0.56 = 1.1

(40 - 1.1 ≤ U ≤ 40 + 1.1)

∴ the confidence interval = 38.9 ≤ U ≤ 41.1

Answer:

The number of ways is  [tex]\left n} \atop {}} \right. P_r = 336[/tex]

Step-by-step explanation:

From the question we are told that

   The number of tickets are   [tex]n = 8[/tex]

    The number of finalist are [tex]r =3[/tex]

Generally the number of way by which this winners can be drawn and arrange in the order of   [tex]1^{st} , \ 2nd , \ 3rd[/tex]    is mathematically represented as

             [tex]\left n} \atop {}} \right. P_r = \frac{n\ !}{(n-r) !}[/tex]

substituting values

             [tex]\left n} \atop {}} \right. P_r = \frac{ 8!}{(8-3) !}[/tex]

           [tex]\left n} \atop {}} \right. P_r = \frac{ 8* 7*6*5*4*3*2*1}{ 5*4*3*2*1}[/tex]

           [tex]\left n} \atop {}} \right. P_r = 336[/tex]

Answer:

50hours

Step-by-step explanation:

Given that there are 400 pages in Sheila's favorite book.

The average number of words per page in the book is 300

She types an average rate of 40words per minute.

So to type 400pages of the book

Total number of words in the pages = 400×300 = 120000 words

Typing rate : 40words ------- 1minute

120000 words ----------- x minutes

Hence we have 40 × X mins = 120000 × 1min

Make X the subject

40X = 120000minutes

X = 120000/40

X = 3000minutes

Since 60minutes = 1hour

3000minutes = 3000minutes/60

= 50hours

Hence it took her 50hours to type 400pages

Solution:

The total number of words in the book is 400 x 300. Sheila types at a rate of 40 words per minute, or 40 x 60 words per hour. The number of hours it takes her is equal to the number of words divided by her rate of typing, or 400x300/40x60 = 50 hours.

Answer:

7

Step-by-step explanation:

10+4 = 14

14/2  = 7

x = 7

Answer:

Linear

Step-by-step explanation:

Given

Height of a tree grows by 2.5 feet

Required

Determine the type of relationship

Take for instance, the height of the tree at year 1 is x

At year 2, it will be x + 2 * 1

At year 3, it will be x + 2 * 2

At year 4, it will be x + 2 * 3

Following same pattern

At year n, it will be x + 2 *(n - 1)

Hence, growth rate = x + 2(n -1)

From the list of given options, the correct answer is Linear because the derived formula above is an example of a linear equation

Answer:

  see the attachment

Step-by-step explanation:

When you have a number of function evaluations to do, it is convenient to let a graphing calculator or spreadsheet do them. That avoids the tedium and the mistakes in arithmetic.

Here's your completed table.

Answer:

Nine thousandths = 0.009

Step-by-step explanation:

thousandths =  1/1000 = 0.001

nine thousandths = 9/1000 = 0.009

Answer:

.009

Step-by-step explanation:

9 thousandths as a decimal is 9/1000.  Which is the same 0.009

Answer:

x = 6

Step-by-step explanation:

In the third line of the solution on right side of the equal sign, middle term should be 8x instead of 4x.

The final value of x will be 6.

[tex] PQ^2 + QO^2 = PO^2 \\

x^2 + 8^2 = (4+x)^2 \\

x^2 + 64 = 16 + 8x + x^2 \\

64 = 16 + 8x \\

64 - 16 = 8x \\

48 = 8x \\

6 = x\\[/tex]

Answer:

It sold 14 cans boxes of food and 12 cans of food.

Step-by-step explanation:

The factor for the food cans depend upon every seven food boxes .So, the same no. of sets of food cans will be sold.

Let the no. of sets of food boxes be x.

According to the question,

6x+7x=26

13x=26

x=26/13

x=2

No. of food cans =6x=6×2=12 cans

No. of food boxes=7x=7×2=14 boxes

Please mark brainliest ,if it is truly the best ! Thank you!

Answer:

a) 40 dollars

b) 480 dollars

Step-by-step explanation:

Given the average property tax on a three bedroom home in a certain community modelled by the equation T(x) =20x²+40x+600, the rate at which the property tax is increasing with respect to time in 2008 can be derived by solving for the function T'(x) at x=0

T'(x) = 2(20)x¹ + 40x° + 0

T'(x) = 40x+40

At x = 0,

T'(0) = 40(0)+40

T'(0) = 40

Hence the property tax was increasing at a rate of 40dollars with respect to the initial year (2008).

b) There are 4 years between 2008 and 2012. To know how much that the tax change between the years 2008 and 2012, we will find T(4) - T(0)

Given T(x) =20x²+40x+600

T(4) =20(4)²+40(4)+600

T(4) = 320+160+600

T(4) = 1080 dollars

Also T(0) =20(0)²+40(0)+600

T(0) = 0+0+600

T(0)= 600 dollars

T(4) - T(0) = 1080 - 600

T(4) - T(0) = 480 dollars

Hence, the tax has changed by $480 between 2008 and 2012

Answer:

A)0.126775 B)0.000004325376 C) 0.07548

Step-by-step explanation:

Given the following :

A.) a. n = 15, p = 0.4, find P(4 successes)

a = number of trials p=probability of success

P(4 successes) = P(x = 4)

USING:

nCx * p^x * (1-p)^(n-x)

15C4 * 0.4^4 * (1-0.4)^(15-4)

1365 * 0.0256 * 0.00362797056

= 0.126775

B)

b. n = 12, p = 0.2, find P(2 failures),

P(2 failures) = P(12 - 2) = p(10 success)

USING:

nCx * p^x * (1-p)^(n-x)

12C10 * 0.2^10 * (1-0.2)^(12-10)

66 * 0.0000001024 * 0.64

= 0.000004325376

C) n = 20, p = 0.05, find P(at least 3 successes)

P(X≥ 3) = p(3) + p(4) + p(5) +.... p(20)

To avoid complicated calculations, we can use the online binomial probability distribution calculator :

P(X≥ 3) = 0.07548

Answer:

  3x +4 = -2x -1

Step-by-step explanation:

The line that goes up to the right has a y-intercept of +4. This is where it crosses the y-axis. It's slope (rise/run) is 3/1 = 3, so its equation in slope-intercept form is ...

  y = mx +b . . . . where m is the slope, b is the y-intercept

  y = 3x +4

The other line has a negative slope and a y-intercept of -1. The slope of that line is rise/run = -2/1 = -2, so its equation is ...

  y = -2x -1

__

The solution point will have the x-coordinate that is the solution of the equation ...

  y = y

  3x +4 = -2x -1 . . . . . . substituting the above expressions for y.

Answer:

x = -5/2

Step-by-step explanation:

1+2x=6x+11

Subtract 2x from each side

1+2x-2x=6x-2x+11

1 = 4x+11

Subtract 11 from each side

1-11 = 4x

-10 =4x

Divide by 4

-10/4 = 4x/4

-5/2 =x

Answer:

[tex]\boxed{x=-\frac{5}{2}}\\[/tex]

Step-by-step explanation:

To begin, get the variable on one side of the equation - preferably the left for standard solution notation (for this equation, it is easier to place it on the right side to avoid negative values). Do this by subtracting 2x from both sides of the equation. Then, subtract 11. Finally, divide by 4 and get the answer in terms of x.

1 + 2x = 6x + 11

1 = 4x + 11

-10 = 4x

[tex]\boxed{x=-\frac{5}{2}}[/tex]

Answer:

hello your question is incomplete below is the complete question

Find the minimum sample size n needed to estimate μ For the given values of​ c, σ​, and E. c=0.98​, σ=6.5​, and E=22 Assume that a preliminary sample has at least 30 members.

Answer : 48

Step-by-step explanation:

Given data:

E = 2.2,

std ( σ ) = 6.5

c ( level of confidence ) = 0.98

To find the minimum sample size

we have to first obtain the value of  [tex]Z_{a/2}[/tex]  

note : a can be found using this relation :

( 1 - a ) = 0.98 ----- equation 1

a = 1 - 0.98 = 0.02

hence:  a/2 = 0.01

This means that P( Z ≤ z ) = 0.99  the value of z can be found using the table of standard normal distribution. from the table the value of z = 2.33

P( Z ≤ 2.33 ) = 0.99

To obtain the sample size n

[tex]n = (\frac{std*z}{E} )^{2}[/tex]

n = [tex](\frac{6.5*2.33}{2.2} )^2[/tex] =  (6.88409)^2

Therefore n ≈ 48

Answer:

The answer is option D

Step-by-step explanation:

Volume of a sphere is given by

[tex]V = \frac{4}{3} \pi {r}^{3} [/tex]

where r is the radius

From the question to calculate the radius we use the formula

radius = diameter / 2

diameter =70mm

radius = 70/2 = 35 mm

So the volume of the sphere is

[tex]V = \frac{4}{3} \pi \times {35}^{3} [/tex]

[tex]V = \frac{171500\pi}{3} [/tex]

We have the final answer as

Hope this helps you

Answer:

Solution : 5.244 - 16.140i

Step-by-step explanation:

If we want to express the two as a product, we would have the following expression.

[tex]-6\left[\cos \left(\frac{2\pi }{5}\right)+i\sin \left(\frac{2\pi }{5}\right)\right]\cdot 2\sqrt{2}\left[\cos \left(\frac{-\pi }{2}\right)+i\sin \left(\frac{-\pi \:}{2}\right)\right][/tex]

Now we have two trivial identities that we can apply here,

( 1 ) cos(- π / 2) = 0,

( 2 ) sin(- π / 2) = - 1

Substituting them,

= [tex]-6\cdot \:2\sqrt{2}\left(0-i\right)\left(\cos \left(\frac{2\pi }{5}\right)+i\sin \left(\frac{2\pi }{5}\right)\right)[/tex]

= [tex]-12\sqrt{2}\sin \left(\frac{2\pi }{5}\right)+12\sqrt{2}\cos \left(\frac{2\pi }{5}\right)i[/tex]

Again we have another two identities we can apply,

( 1 ) sin(x) = cos(π / 2 - x )

( 2 ) cos(x) = sin(π / 2 - x )

[tex]\sin \left(\frac{2\pi }{5}\right)=\cos \left(\frac{\pi }{2}-\frac{2\pi }{5}\right) = \frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}[/tex]

[tex]\cos \left(\frac{2\pi }{5}\right)=\sin \left(\frac{\pi }{2}-\frac{2\pi }{5}\right) = \frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}[/tex]

Substitute,

[tex]-12\sqrt{2}(\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}) + 12\sqrt{2}(\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4})[/tex]

= [tex]-6\sqrt{5+\sqrt{5}}+6\sqrt{3-\sqrt{5}} i[/tex]

= [tex]-16.13996 + 5.24419i[/tex]

= [tex]5.24419i - 16.13996[/tex]

As you can see option d is the correct answer. 5.24419 is rounded to 5.244, and 16.13996 is rounded to 16.14.