Use the volume formula to find the volume of the prism.
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NI
2
N
O A. 2, cubic units
B. 5 cubic units
C. 9 cubic units
D. 4 cubic units

The binomial distribution is applicable when only two outcomes are possible. The probability that the newspaper staff receives quotes from exactly 3 athletes is 0.1238.

A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. It is given by the formula,

[tex]P(x) = ^nC_x p^xq^{(n-x)}[/tex]

Where,

x is the number of successes needed,

n is the number of trials or sample size,

p is the probability of a single success, and

q is the probability of a single failure.

Given that 18 of the senior DLT members are athletes, therefore, the probability of a DLT member being an athlete is,

[tex]P = \dfrac{18}{30} = \dfrac{6}{10} = 0.6[/tex]

Also, 12 of the senior DLT members are non-athletes, therefore, therefore, the probability of a DLT member being a non-athlete is,

[tex]q = \dfrac{12}{30} = \dfrac{4}{10} = 0.4[/tex]

Now, using the binomial distribution the probability that the newspaper staff receives quotes from exactly 3 athletes can be written as,

[tex]P(x) = ^nC_x p^xq^{(n-x)}\\\\P(x=3) = ^8C_3\cdot (0.6)^3\cdot (0.4)^{(8-3)}\\\\P(x=3) = ^8C_3\cdot (0.6)^3\cdot (0.4)^{(5)}\\\\P(x=3) = 0.1238[/tex]

Hence, the probability that the newspaper staff receives quotes from exactly 3 athletes is 0.1238.

Learn more about Binomial Distribution:

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Answer:

1st option

Step-by-step explanation:

given a quadratic function in standard form

f(x) = ax² + bx + c ( a ≠ 0 ) , then

• if a > 0 , the function opens up and has a minimum

• if a < 0 , the function opens down and has a maximum

here a = [tex]\frac{1}{2}[/tex] > 0

then f(x) opens up and has a minimum

Answer:

Option A, open up and have a minimum

Step-by-step explanation:

Step 1:  Determine if it opens up or down

Since the value of a is 1/2 which means that it's positive which also means that it opens up.  When a parabola opens up, that means that it has a minimum.  

The picture attached to this answer shows an example of how a graph would look when using this equation.  If a was -1/2 then the parabola would be facing down and would have a maximum.

Answer:  Option A, open up and have a minimum

25 76

Step-by-step explanation:

Answer: C ( x ≥ -1 )

Step-by-step explanation:

Answer:

x=6 y=2

Step-by-step explanation:

y=2

so 6x+9(2)=-24

6x+18=-24

6x=42

x=6

Answer:

Because the cost price of 30 pens = Rs. 150

So, the cost price of 1 pen = 150/30 =5

so, the cost price of 20 pens =

Rs. 5 x 20 = 100

Cp is Rs. 100

Sp is Rs. 140

So, profit = 140-100 = Rs. 40

Profit % = (Profit x 100)xCp

=(40 x 100)/100

= 4000/100

= 40% profit

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

is the situation could the expression model.

The equation of the trend line is ŷ = 0.15x - 23.21

The points are given as:

hr =>808, 768, 655, 684, 637, 619, 613, 609, 563

w =>  93, 94, 66, 81, 86, 75, 61, 69, 55.

Using a graphing calculator, we have the following calculation summary:

The regression equation is represented as:

ŷ = bX + a

Where:

b = SP/SSX

b = 7547.11/50569.56

b = 0.14924

a = MY - bMX

a = 75.56 - (0.15*661.78)

a  = -23.20961

This gives

ŷ = 0.14924X - 23.20961

Approximate

ŷ = 0.15x - 23.21

Hence, the equation of the trend line is ŷ = 0.15x - 23.21

Read more about trend lines at:

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Answer:

D.) y = 0.15 - 23.21

Step-by-step explanation:

I took the assignment

Step-by-step explanation:

10.4feet by 7.4feet11.1 feet by 8.1 feet

Answer:

84, do 252/3

7.5, do 180/24

0.45, do 9/20

1.4, do 11.2/8

AS BASICALLY IF I TELL U THE CORRECT ANSWER OF ORANGE RECTANGLE IS16ML2

Answer:

16 mi squared

Step-by-step explanation:

Gray perimeter :16 (5,5,3,3)

Orange perimeter :16 (4,4,4,4)

Area of Gray :15 (5x3)

Area of Orange :16(4x4)

Answer:

the median is 3 for your question

Answer:

the answer is C

Step-by-step explanation:

Step-by-step explanation:

11/6 !!

Please make me brainliest if this was helpful

Answer:

it equals =204 y=12

Answer:

Option. C

Step-by-step explanation:

A and C are the two points of tangencies on sphere

There are two tangents to the sphere in the figure. Option C. is the correct option

A and C are the two points of tangencies of respective tangents that makes a perpendicular to the centre of the sphere of 'O' point ( lined on a plane circle of sphere ).

Answer:

-5, 22, 292

Step-by-step explanation:

Subbsittutoin mehtod

(i) n = 1 , 3n - 8

       = 3 x 1 - 8

                 = -5

(ii) n = 10 , 3n - 8

        = 3 x 10 - 8

                    =22

(iii) n = 100 , 3n - 8

         = 3 x 100 - 8

               = 300 - 8

                     = 292

Answer:

There are 12 possible outcomes.

Step-by-step explanation:

For each of the three sizes of beverages, there are four flavors. So there are 3 * 4, or 12, possible outcomes.

Answer:

A. 7.93 x 104

Step-by-step explanation:

[tex] \: [/tex]

Explanation :

So, here we are to factor the polynomial :

[tex]\\ \longrightarrow \sf \qquad10m^2n+30mn^2+5mn\\ \\[/tex]

[tex] \longrightarrow \sf \qquad5mn(2m+6n + 1)\\ \\[/tex]

Some points to know :

Answer:

[tex]\boxed{5\left(6mn^{2}+mn+2\left(m^{n}\right)^{2}\right)}[/tex]

Step-by-step explanation:

[tex]10m ^ { 2n } +30mn ^ { 2 } +5mn[/tex]

Factor out the common factor: 5

[tex]=5\left(2m^{2n}+6mn^{2}+mn\right) [/tex]

[tex]=5\left(6mn^{2}+mn+2\left(m^{n}\right)^{2}\right)[/tex]

=》This expression cannot be further simplified.

___________

Hope it helps ⚜

Answer:

       a = 3

        b = 4

Step-by-step explanation:

Simultaneous equation

              3a = 2b + 1

         3a - 2b = 1  ------------------(I)

               3b  = 5a - 3

       -5a + 3b = -3 --------------(II)

Multiply equation (I) by 3  & equation (II) by  2 and then add. So, now 'b' will be eliminated and we can find the value of 'a'.

(I)*3       9a - 6b = 3

(II)*2    -10a + 6b = -6  {Now add}

            -a            = -3

                       a = -3/(-1)

        [tex]\sf \boxed{a = 3}[/tex]

Plugin a = 3 in equation (I)

              3*3 - 2b = 1

                  9 - 2b = 1

                     -2b  = 1 - 9   {Subtracting 9 from both sides}

                      -2b = - 8        

                         b = (-8)/(-2)         {Dividing both sides by (-2_}

          [tex]\sf \boxed{b = 4}[/tex]                      

Answer:

  (a, b) = (3, 4)

Step-by-step explanation:

In order to eliminate one of the variables in this system of equations, both equations need to be multiplied by different numbers before they are added or subtracted. We can eliminate the 'b' variable by subtracting 3 times the first equation from 2 times the second. (Putting the 'b' terms on the same side of the equal sign makes this easier.)

__

  2(3b) -3(2b +1) = 2(5a -3) -3(3a)

  6b -6b -3 = 10a -6 -9a

  3 = a . . . . . . . add 6 and collect terms

  3b = 5(3) -3 . . . . use the second equation to find b from a

  b = 4 . . . . . . . divide by 3

The solution is (a, b) = (3, 4).

_____

The multiplier used in each case is the coefficient of the variable in the other equation. The two equations have 'b' coefficients of 2 and 3, so we multiplied the equations by 3 and 2 before subtracting. That makes the 6b terms cancel, leaving only terms with the 'a' variable.

By swapping sides of the equation the way we did, the 'a' terms end up on the same side of the equal sign, which is where we want them. Likewise, the 'b' terms end up on the same side of the equal sign, so their cancellation is easier to see.

Answer:

$1.62

Step-by-step explanation:

Penny = 1 cent

Dime = 10 cents

10 x 15 = 150 + 12 = 162

$68.15

P=Original price=145

D=Discount=53%

Sales=S

S=P-PD

S=145-(145×53%)

Answer:

I like turtlesion:



Step-by-step explanation:

the answer is easy you take 2 + 2 + 2 + 2 + 2 + 2 + 2 and then you got8 twos so you kind of want to do that and add another number to the 8th and then got 82 there's a step-by-step explanation and this is not actually not the answer I just want to fool around with some people

Answer:

Maddie has 6 cookies

Step-by-step explanation:

Let a symbolise the sugar cookies

so, Jacob has 3a

And Mary has double of Jacob's cookies

Hence,

3a * 2

= 6 cookies

Answer:

The answer is B.

Step-by-step explanation:

There isn't much to explain.

3/6 people like chocolate ice cream and x/600 where x is the number of people who like chocolate ice cream.

[tex]\frac{3}{6}=\frac{x}{600} \\[/tex]

Cross multiply to solve for x.

6*x = 3*600

6*x = 1800

x = 300

300 people like chocolate ice cream so about half of people like chocolate ice cream compare to 3/6 the same.

Answer:

p = 34d * k - 6000d

Step-by-step explanation:

profit equals to the number of skates sold that number - the rent for the building

Answer:

D. Keep track of the number of heads flipped in 50 flips. These represent the number of females born today. Repeat this 200 times.

Step-by-step explanation:

Step-by-step explanation:

Let the numbers be a, b, c in ascending order.

Mean is 7, i.e. (a+b+c)/3 = 7 or a+b+c=21

Median(middle number) is 5, i.e. b=5

Range is 8, i.e. c-a=8 or c=8+a

Solving the above three equations simultaneously, we have

a+5+8+a=21

a=4, hence c=12

Therefore the three numbers are 4, 5 and 12

The equation could be used to calculate the sum of the geometric series is [tex]S_n=\dfrac{\frac{1}{3} (1-(\frac{2}{3} )^n)}{1-\frac{2}{3} }[/tex]

Geometric sequence are sequence that increase expoentially. The formula for calculating the sum of an exponential sequence is expressed as:

[tex]S_n=\frac{a(1-r^n)}{1-r}[/tex]

where

From the given sequence

a= 1/3

r = 2/9 * 3 = 2/3

Substitute into the formula

[tex]S_n=\dfrac{\frac{1}{3} (1-(\frac{2}{3} )^n)}{1-\frac{2}{3} }[/tex]

Hence the equation could be used to calculate the sum of the geometric series is [tex]S_n=\dfrac{\frac{1}{3} (1-(\frac{2}{3} )^n)}{1-\frac{2}{3} }[/tex]

Learn more on geometric series here; https://brainly.com/question/24643676

Answer:

A

Step-by-step explanation:

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