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Lena [83]
2 years ago
6

A die is thrown 300 times with frequencies for the outcome 1 2 3 4 5 6, whats the probablity of getting a prime number, given th

e frequencies are 42 60 55 53 60 and 30 respectively?
Mathematics
1 answer:
aleksklad [387]2 years ago
6 0

Answer:

58.3% to the nearest tenth.

Step-by-step explanation:

The prime numbers from 1 to 6 are 2,3 and 5.

The probability of a prime number taken from the result of the 300 throws:

=  (sum of the frequencies for 2, 3 and 5)  /  ( total throws)

= (60 + 55 + 60) / 300

=  0.5833 or 58.3%.

You might be interested in
1675 at 4.6% for 4 years What is the balance
Yuri [45]
Amount of Interest (I) = P * R * T /100
I = 1675 * 4.6 * 4 /100
I = 308.20

Balance = Initial amount + Interest amount
B = 1675 + 308.20 = 1983.20

In short, Your Answer would be $1983.20

Hope this helps!
4 0
2 years ago
Question: How long does it take an investment to quadruple in value if it earns 4% simple interest per year?
Assoli18 [71]

Answer:

It takes 75 years for the investment to quadruple in value

Step-by-step explanation:

Simple Interest

This is a simple interest problem.

The simple interest formula is given by:

E = P*I*t

In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.

After t years, the total amount of money is:

T = E + P

In this question:

4% simple interest per year, so I = 0.04.

Quadruple:

t when T = 4P.

The interest earned is:

T = E + P

4P = E + P

E = 3P

Now we find the time.

E = P*0.04*t

3P = P*0.04*t

0.04t = 3

t = \frac{3}{0.04}

t = 75

It takes 75 years for the investment to quadruple in value

7 0
2 years ago
How do you solve the equation 3x = 9 by multiplying 3 to both sides
notka56 [123]
Whenever you see <em>x </em> next to a 3, and it says that it equals 9, you know that 3•3=9.
5 0
3 years ago
Read 2 more answers
Name the set of 4 consecutive integers starting with -4
AVprozaik [17]
-4, -3, -2, -1

Consecutive integers are integers that are exactly one unit away from each other. -4 is one unit away from -3, and likewise with -3 and -2 and -2 and -1. 
7 0
3 years ago
Evaluate the triple integral ∭ExydV where E is the solid tetrahedon with vertices (0,0,0),(5,0,0),(0,9,0),(0,0,4).
Elan Coil [88]

Answer: \int\limits^a_E {\int\limits^a_E {\int\limits^a_E {xy} } \, dV = 1087.5

Step-by-step explanation: To evaluate the triple integral, first an equation of a plane is needed, since the tetrahedon is a geometric form that occupies a 3 dimensional plane. The region of the integral is in the attachment.

An equation of a plane is found with a point and a normal vector. <u>Normal</u> <u>vector</u> is a perpendicular vector on the plane.

Given the points, determine the vectors:

P = (5,0,0); Q = (0,9,0); R = (0,0,4)

vector PQ = (5,0,0) - (0,9,0) = (5,-9,0)

vector QR = (0,9,0) - (0,0,4) = (0,9,-4)

Knowing that cross product of two vectors will be perpendicular to these vectors, you can use the cross product as normal vector:

n = PQ × QR = \left[\begin{array}{ccc}i&j&k\\5&-9&0\\0&9&-4\end{array}\right]\left[\begin{array}{ccc}i&j\\5&-9\\0&9\end{array}\right]

n = 36i + 0j + 45k - (0k + 0i - 20j)

n = 36i + 20j + 45k

Equation of a plane is generally given by:

a(x-x_{0}) + b(y-y_{0}) + c(z-z_{0}) = 0

Then, replacing with point P and normal vector n:

36(x-5) + 20(y-0) + 45(z-0) = 0

The equation is: 36x + 20y + 45z - 180 = 0

Second, in evaluating the triple integral, set limits:

In terms of z:

z = \frac{180-36x-20y}{45}

When z = 0:

y = 9 + \frac{-9x}{5}

When z=0 and y=0:

x = 5

Then, triple integral is:

\int\limits^5_0 {\int\limits {\int\ {xy} \, dz } \, dy } \, dx

Calculating:

\int\limits^5_0 {\int\limits {\int\ {xyz}  \, dy } \, dx

\int\limits^5_0 {\int\limits {\int\ {xy(\frac{180-36x-20y}{45} - 0 )}  \, dy } \, dx

\frac{1}{45} \int\limits^5_0 {\int\ {180xy-36x^{2}y-20xy^{2}}  \, dy } \, dx

\frac{1}{45} \int\limits^5_0  {90xy^{2}-18x^{2}y^{2}-\frac{20}{3} xy^{3} } \, dx

\frac{1}{45} \int\limits^5_0  {2430x-1458x^{2}+\frac{94770}{125} x^{3}-\frac{23490}{375}x^{4}  } \, dx

\frac{1}{45} [30375-60750+118462.5-39150]

\int\limits^5_0 {\int\limits {\int\ {xyz}  \, dy } \, dx = 1087.5

<u>The volume of the tetrahedon is 1087.5 cubic units.</u>

3 0
3 years ago
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