How many faces does the polyhedron have? 3 5 6 9

Answer: a) 0.1095     b) 0.0095

Step-by-step explanation:

Given : The deck for a card game contains 30 cards.

10 are red, 10 yellow, 5 blue, and 1 green, and 4 are wild cards.

Each player is randomly dealt a five-card hand.

Number of ways to choose 5 cards out of 30 = [tex]C(30,5)=\dfrac{30!}{5!25!}=142506[/tex]

a)  Cards other than wild card = 30-4=26

Number of ways to choose exactly two wild cards = [tex]C(26,3)\timesC(4,2)[/tex]

[tex]=\dfrac{26!}{3!23!}\times\dfrac{4!}{2!2!}\\\\=15600[/tex]

Probability that a hand will contain exactly two wild cards = [tex]\dfrac{15600}{142506}=0.1095[/tex]

b) Number of ways to choose two wild cards, two red cards, and one blue cards = [tex]C(4,2)\times C(10,2)\times C(5,1)[/tex]

[tex]=\dfrac{4!}{2!2!}\times\dfrac{10!}{2!8!}\times5=1350[/tex]

Probability that a hand will contain two wild cards, two red cards, and one blue cards = [tex]\dfrac{1350}{142506}=0.0095[/tex]

Answer:

the value of the test statistic is calculated as "T - distribution" with the formula;

t = (x-bar - μ)/(s/√n)

Step-by-step explanation:

We are told that the standard deviation is unknown. But normally, we use a z-distribution if the standard deviation is known.

However, in a hypothesis test for a population mean where the population standard deviation is unknown is still conducted in the same way like we do when we know the population standard deviation. The only difference in this case is that we will use the t-distribution rather than the standard normal z-distribution.

The t-distribution formula used is;

t = (x-bar - μ)/(s/√n)

Answer:

16

Step-by-step explanation:

4 * sqrt( a^2 - b^2)

Let a = -5 and b =3

4 * sqrt( (-5)^2 - 3^2)

Do the squaring first

4 * sqrt( 25 - 9)

Subtract inside the square root

4 * sqrt( 16)

Take the square root

4 * 4

Multiply 16

Answer:

[tex]\Large \boxed{16}[/tex]

Step-by-step explanation:

[tex]4\sqrt{a^2-b^2 }[/tex]

[tex]\sf Plug \ in \ the \ values \ for \ a \ and \ b.[/tex]

[tex]4\sqrt{-5^2-3^2 }[/tex]

[tex]4\sqrt{25-9 }[/tex]

[tex]4\sqrt{16}[/tex]

[tex]4 \times 4=16[/tex]

Answer:

[tex]\boxed{v=300}[/tex]

Step-by-step explanation:

Hey there!

To find v we’ll set up the following,

v ÷ 5 = 60

To get v by itself we’ll do

5*60 = 300

v = 300

Hope this helps :)

Answer:

s = 8

Step-by-step explanation:

2s = s + 8

2s - s = 8

s = 8

Answer:

Coefficient of Correlation

Step-by-step explanation:

Coefficient of Correlation is a value that ranges between -1 to 1, which is used to denote the closeness or linear relationship between two variables.

The closer the value of the coefficient is to -1 or 1, the stringer the relationship that exists between two variables.

A negative value suggests a negative relationship. Which means, as one variable decreases, the other variable increases.

A positive coefficient of correlation shows a positive relationship between two variables. Which means, as one variable increases, the other also increases.

If the Correlation coefficient is 0, it means there's no relationship between the variables.

Answer:

-20

-5

-18

Step-by-step explanation:

AX = B to find x

A^-1 AX = A^-1 B

X =  1 -4  -2          2

       -2  2 5    *      7

       2  -4  -2        -3

We multiply across  and down

-1 *2 + -4 *7 -2 *-3 = -20

-2 * 2 + 2 * 7 + 5 * -3 = -5

2 * 2  -4 * 7 -2 * -3 = -18

The matrix is

-20

-5

-18

Answer:

The value of X will be the following :

[tex]\begin{bmatrix}-20\\ -5\\ -18\end{bmatrix}[/tex]

Step-by-step explanation:

So as you can tell, through substitution the equation for this problem will be as follows,

[tex]\begin{bmatrix}1&-4&-2\\ \:-2&2&5\\ \:\:\:\:\:2&-4&-2\end{bmatrix}^{^{^{^{-1}}}}\cdot \:X\:=\:\begin{bmatrix}2\\ \:\:7\\ \:-3\end{bmatrix}[/tex]

Therefore to isolate X, we have to multiply the inverse of the inverse of the co - efficient of X on either side, such that X = A [tex]*[/tex] B,

[tex]X = A * B = \begin{bmatrix}1&-4&-2\\ \:\:-2&2&5\\ \:\:\:2&-4&-2\end{bmatrix}^{\:}\begin{bmatrix}2\\ 7\\ \:-3\end{bmatrix}[/tex]

To solve for X we can multiply the rows of the first matrix by the respective columns of the second matrix,

[tex]\begin{bmatrix}1&-4&-2\\ -2&2&5\\ 2&-4&-2\end{bmatrix}\begin{bmatrix}2\\ 7\\ -3\end{bmatrix} = \begin{bmatrix}1\cdot \:2+\left(-4\right)\cdot \:7+\left(-2\right)\left(-3\right)\\ \left(-2\right)\cdot \:2+2\cdot \:7+5\left(-3\right)\\ 2\cdot \:2+\left(-4\right)\cdot \:7+\left(-2\right)\left(-3\right)\end{bmatrix} = \begin{bmatrix}-20\\ -5\\ -18\end{bmatrix}[/tex]

[tex]X = \begin{bmatrix}-20\\ -5\\ -18\end{bmatrix}[/tex] - if this matrix is matrix 1, matrix 1 will be our solution

Answer:

7.5

Step-by-step explanation:

Answer:

20sets

Step-by-step explanation:

Since we are to select 3 unordered letters from the word q, u, a, k, e, s, we will apply the combination rule.

For example if r objects are to be selected from n pool of objects, this can be done in nCr number of ways.

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

Since the total number of letter in the word q, u, a, k, e, s is 6letters and we are to form 3 letters from it unordered, this can be done in 6C3 number of ways.

6C3 = 6!/(6-3)!3!

6C3 = 6!/3!3!

6C3 = 6×5×4×3×2×1/3×2×1×3×2×1

6C3 = 6×5×4/3×2

6C3 = 120/6

6C3 = 20

Hence 20sets of selection are possible

Answer: 2.79 hours.

Step-by-step explanation:

Given that the function for the learning process is T(x) = 2 + 0.3 1 x , where T(x) is the time, in hours, required to produce the xth unit

To calculate the time for the new worker to produce 10 units, substitute 10 for x in the equation above.

T(x) = 2 + 0.31 (10)

T(x) = 2 + 3.1

T(x) = 5.1 hours

To calculate the time for the new worker to produce 19 units, substitute 19 for x in the equation above.

T(x) = 2 + 0.31(19)

T(x) = 2 + 5.89

T(x) = 7.89 hours

The time required for a new worker to produce units 10 through 19 will be

7.89 - 5.1 = 2.79 hours

Answer: 5.4

Step-by-step explanation: 27/5, so 5x5 makes 25 and 2 remaining so 5x0.4=2 so answer is 5+0.4 which equals to 5.4

Step-by-step explanation:

Just sub 4 into where n is

Complete Question

The complete question is shown on the first uploaded image

Answer:

a

    [tex]P(3) = 0.154[/tex]

b

    [tex]P(4) = 0.026[/tex]

c

   [tex]P( X \ge 3 ) = 0.18[/tex]

d

   option C is correct

Step-by-step explanation:

From the question we are told that

      The probability of success is  p =  0.4

      The sample size is n=  4

 This adults believe follow a binomial distribution is because there are only two outcome one is an adult  believes in  reincarnation and the second an adult does not believe in reincarnation

  The probability of  failure is mathematically evaluated as

              [tex]q = 1 - p[/tex]

substituting values

             [tex]q = 1 - 0.4[/tex]

             [tex]q = 0.6[/tex]

Considering a  

The  probability that exactly 3 of the selected adults believe in reincarnation is mathematically represented as

       [tex]P(3) = \left n} \atop {}} \right. C_ 3 * p^3 * q^{n-3}[/tex]

substituting values

     [tex]P(3) = \left 4} \atop {}} \right. C_ 3 * (0.40)^3 * (0.60)^{4-3}[/tex]

Here [tex]\left 4} \atop {}} \right.C_3[/tex] means  4  combination 3 . i have calculated this using a calculator and the value is  

           [tex]\left 4} \atop {}} \right.C_3 = 4[/tex]

So

         [tex]P(3) = 4* (0.4)^3 * (0.6)[/tex]

          [tex]P(3) = 0.154[/tex]

Considering b

The probability that all of the selected adults believe in reincarnation is mathematically represented as

        [tex]P(n) = \left n} \atop {}} \right. C_ n * p^n * q^{n-n}[/tex]

substituting values

         [tex]P(4) = \left 4} \atop {}} \right. C_ 4 * (0.40)^4 * (0.60)^{4-4}[/tex]

Here [tex]\left 4} \atop {}} \right.C_3[/tex] means  4  combination  . i have calculated this using a calculator and the value is  [tex]\left 4} \atop {}} \right.C_4 = 1[/tex]

so

          [tex]P(4) = 1* (0.4)^4 * 1[/tex]

=>       [tex]P(4) = 0.026[/tex]

Considering c

the probability that at least 3 of the selected adults believe in reincarnation is mathematically represented as

     [tex]P( X \ge 3 ) = P(3 ) + P(n )[/tex]

substituting values

    [tex]P( X \ge 3 ) = 0.154 + 0.026[/tex]

     [tex]P( X \ge 3 ) = 0.18[/tex]

From the calculation the probability that all the 4 randomly selected persons believe in reincarnation is  [tex]p(4) = 0.026 < 0.05[/tex]

But the the probability of 3 out of the 4 randomly selected person believing in reincarnation is [tex]P(3) = 0.154 \ which \ is \ > 0.05[/tex]

Hence 3 is not a  significantly high number of adults who believe in reincarnation because the probability that 3 or more of the selected adults believe in reincarnation is greater than 0.05.

Answer:

$139.23

Step-by-step explanation:

50% off the original price of $239.99

= $239.99-(0.5*239.99)

= 239.99-119.995

= $119.995

She purchase a pair of shoes also worth $34.70

Total cost now= $119.995 + $34.70

Total cost now= $154.695

But she has a coupon that gives her 10% off her total sales

Now she wants pay

= $154.695 - 0.1(154.695)

= $154.695-15.4695

= $139.2255

Approximately $139.23

Answer:

46.2÷m=x

Step-by-step explanation:

u divide the amount of water by the time it takes to fill up(m). Witch will equal the amount per minute (x).

16.5/min

time = m

gallons / minutes = rate

46.2  = 16.5 (m)

46.2 / 16.5 = 16.5 (m) / 16.5

2.8 = minutes

Answer:

$8.19

Step-by-step explanation:

1. Add the cost of the items together

5.3 + 1.29 + 0.53 + 0.68 = 7.8

2. Solve for 5% of the cost of the items

5% = 0.05

7.8 · 0.05 = 0.39

3. Add the sales tax to the price of the items

7.8 + 0.39 = 8.19

Explanation:

Add up the prices

5.30 + 1.29 + 0.53 + 0.68 = 7.80

This is the total amount before tax is added. To find the amount after tax, we multiply by 1.05 to get

1.05*7.80 = 8.19

Or a longer way is to find 5% of 7.80 getting 0.05*7.80 = 0.39 in the amount of tax owed, which is added on top of the previous total we got earlier. So we have 7.80 + 0.39 = 8.19

The use of the multiplier 1.05 is handy when you need to apply multiple percentage increases (it also works if you have multiple discounts as well).

Answer:

64 70 74 80 92

Answer = 74

Step-by-step explanation:

The median is when you have an order of numbers in ascending order (smallest to largest) then you find the middle number

Hope this helps :)

If anything is incorrect then please comment and I shall change the answer to the correct one

Median for the given data 70, 64, 80, 74,92 is equals to 74.

"Median is defined as the central value of the given data after arranging them into ascending or descending order."

According to the question,

Given data for pulse rates = 70, 64, 80, 74,92

Arrange the data in ascending order we get,

64, 70 , 74, 80, 92

Number of pulse rate reading is 5 , which is an odd number.

Therefore, median is the central value.

Median for the given data = 74

Hence, median for the given data 70, 64, 80, 74,92 is equals to 74.

Learn more about median here

https://brainly.com/question/21396105

#SPJ2

Answer:

[tex]t \: = 3.92 \: sec[/tex]

Step-by-step explanation:

When (t =0)

Height of cliff = 248 feet = 75.5m

Using Newton's equations of motion:

[tex]s = ut + \frac{1}{2} a {t}^{2} [/tex]

75.5 = 0 * t + 4.9 * t^2

Solving further :

[tex]t \: = 3.92 \: sec[/tex]

The larger metallic object is initially at rest, so the velocity is 0 when t = 0. The speed changes after t = 3 seconds.

Answer:

It would be the last one.

Step-by-step explanation:

It says the object is initially at rest, so you look for a table with 0 m/s and you find the last table had been at rest for 0 -2  seconds. The small rocky object initially had a speed of 90 m/s and then decreased to 36 m/s as its energy transferred to the metallic object. The metallic object's speed from time 4-6s with the small rocky object equals the small rocky initial speed.

Rocky Object initial speed = 90 m/s

Rocky Object new speed = 36 m/s

Large metallic object speed after collision = 64 m/s.

64 m/s + 36 m/s = 90 m/s

Large metallic object speed after collision + Rocky Object new speed

= Rocky Object initial speed

You can also test this for kinetic energy.

Step-by-step explanation:

Maximum = 62

Median = (34+37+39+32+48+45+53+62+58+61+60+41)/12= 47.5≈48

quartile

In increasing order

32, 34, 37, 39, 41, 45, 48, 53, 58, 60, 61, 62

Upper quartile= (58+60)/2 = 59

Lower quartile= (37+39)/2 = 38

Minimum= 32

Step-by-step explanation:

2x + 8 - 5 = 6

2x + 3 = 6

2x = 6 - 3

2x = 3

x = 3/2

Answer:

2 ( x+4) -5 = 3+3

=) 2x +8-5=6

=) 2x+3=6

=) 2x= 6-3

=)2x = 3

=) x =3/2= 1.5

Answer:

Determination of the least cost of fence enclosure:

= cost of heavy-duty one side of the length plus cost of remaining three sides of the fence

= $416 ($360 + $56)

= $416

Step-by-step explanation:

Rectangular Fence Area = 320 square yard

Since fence is rectangular, the two sides are length and width

Length of rectangular is always greater than the width

Length cannot be 20 yard with width as 16 yard

Therefore, length = 40 yard and width = 8 yard.

Proof: Area of a rectangular = 40 x 8 = 320 square yard

Since, parameter = 2 (Length + Width)

= 2 x (40 + 8)

= 96 yards

Therefore, along one side with heavy-duty material is one length side of the fence = 40 yard

Cost of the one length with heavy-duty material = 40 x $9 = $360

Remaining three sides = 96 - 40 = 56 yard

Cost of remaining three sides = 56 x $1 = $56

Total cost of fencing = $416 ($360 + $56)

Answer:

(-25)+(-12)+(-34) = -71

so when you add negative numbers you simply add them such as -2+-2 -4

so same conditions

so it will be -25+-12+-34 and it will simply be 25+12+34 so -71

Answer:

16,807

Step-by-step explanation:

Answer:

37 hours

Step-by-step explanation:

4.5 + 8.75 + 9.5 + 10 + 4.25 = 37 hours

Answer:

37 hours

Step-by-step explanation:

4.5 hours = 4 hrs and 30 mins

8.75 hrs = 8 hrs and 45 mins

9.5 hrs = 9 hrs and 30 mins

10 hrs = 10 hrs and 0 min

4.25 hrs = 4 hrs and 15 mins

(30 + 45 + 30 + 15) mins = 2 hrs

Therefore, total hours Sam worked = (4 + 8 + 9 + 10 + 4 + 2) hrs = 37 hours

Answer:

A: y= 1/4x - 7

if it is perpendicular, then it creates 4 right angles. so that new line would pass through (0,-7) and something else that isnt important. but the slope, or m, would be 1/4, and the y intercept would be -7. so the new equation is y=1/4x-7

Question

In a study of 100 new cars, 29 are white. Find p and q , where p is the proportion of new cars that are white.

Answer:

p = 0.29  and q = 0.71

Step-by-step explanation:

Given

Total new cars =  100

White new cars = 29

Required

Determine p and q

From the question;

p represents white new cars

Hence;

[tex]p = 29[/tex]

Note that;

[tex]p + q = 100[/tex]

Substitute 29 for p

[tex]29 + q = 100[/tex]

[tex]29 - 29 + q = 100 - 29[/tex]

[tex]q = 100 - 29[/tex]

[tex]q = 71[/tex]

The proportion of p is calculate by dividing p by the total number of new cars (Same process is done for q)

For proportion of p

[tex]Proportion,\ p = \frac{p}{new\ cars}[/tex]

[tex]Proportion,\ p = \frac{29}{100}[/tex]

[tex]Proportion,\ p = 0.29[/tex]

For proportion of q

[tex]Proportion,\ q = \frac{q}{new\ cars}[/tex]

[tex]Proportion,\ q = \frac{71}{100}[/tex]

[tex]Proportion,\ q = 0.71[/tex]

Answer:

50% chance

Step-by-step explanation:

4 * 50% = 2

Answer:

The cost of 5 hours of skiing would be the same ($125) after 5 hours.

Step-by-step explanation:

Black Diamond:  ChargeBD(h) = $50 + ($15/hr)h, where h is the number of hours spent skiing.

Bunny Hill:  ChargeBH(h) = $75 + ($10/hr)h

We equate these two formulas to determine when the cost of using the ski slopes is the same:

ChargeBD(h) = $50 + ($15/hr)h = ChargeBH(h) = $75 + ($10/hr)h

We must now solve for h, the number of hours spent skiing:

50 + 15h = 75 + 10h

Grouping like terms, we obtain:

5h = 25, and so h = 5 hours.

The cost of 5 hours of skiing would be the same ($125) after 5 hours.

Answer:

  1/10

Step-by-step explanation:

There are 5 numbers in the range that are multiples of 10: 10, 20, 30, 40, 50. The probability of choosing one of those at random from the set of 50 numbers is ...

  5/50 = 1/10