What is the product of 3.5 and 1.82

Use the normal approximation to the binomial distribution to answer this question. Fifteen percent of all students at a large un

Nataly_w [17]

Answer: 0.1289

Step-by-step explanation:

Given : The proportion of all students at a large university are absent on Mondays. : $p=0.15$

Sample size : $n=12$

Mean : $\mu=np=12\times0.15=1.8$

Standard deviation = $\sigma=\sqrt{np(1-p)}$

$\Rightarrow\ \sigma=\sqrt{12(0.15)(1-0.15)}=1.23693168769\approx1.2369$

Let x be a binomial variable.

Using the standard normal distribution table ,

$P(x=4)=P(x\leq4)-P(x\leq3)$ (1)

Z score fro normal distribution:-

$z=\dfrac{x-\mu}{\sigma}$

For x=4

$z=\dfrac{4-1.8}{1.2369}\approx1.78$

For x=3

$z=\dfrac{3-1.8}{1.2369}\approx0.97$

Then , from (1)

$P(x=4)=P(z\leq1.78)-P(z\leq0.97)\\\\=0.962462-0.8339768\approx0.1289$

Hence, the probability that four students are absent = $0.1289$

3 0

2 years ago

Quadrilateral WXYZ is on a coordinate plane. Segment XY is on the line x − 3y = −12, and segment WZ is on the x − 3y = −6. Which

Nostrana [21]

Answer:

Equation shown

Step-by-step explanation:

Eq(1): x-3y=-12

X=-12+3y

=-4+y

Eq(2): x-3y=-6

X=-6+3y

=-2+y

4 0

2 years ago

Read 2 more answers

Find the perimeter of $\triangle CDE$ . Round your answer to the nearest hundredth. A trapezoid A B C D is plotted on a coordina

guapka [62]

Answer:

The answer is below

Step-by-step explanation:

We are asked to find the perimeter of triangle CDE. The perimeter of a shape is simply the sum of all its sides, hence:

Perimeter of tiangle CDE = |CD| + |DE| + |CE|

Given that C(4, -1), D(4, -5), E(2, -3).

The distance between two points $X(x_1,y_1)\ and\ Y(x_2,y_2)$ is given as:

$|XY|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Therefore the lengths of the triangle are:

$|CD|=\sqrt{(4-4)^2+(-5-(-1))^2} =4\ units\\\\|DE|=\sqrt{(2-4)^2+(-3-(-5))^2} =2.83\ units\\\\|CE|=\sqrt{(2-4)^2+(-3-(-1))^2} =2.83\ units$

Perimeter of CDE = 4 + 2.83 + 2.83 = 9.66 units

8 0

2 years ago

The figure shows the layout of a symmetrical pool in a water park. What is the area of this pool rounded to the tens place? Use

k0ka [10]

Answer:

$2489ft^{2}$

Step-by-step explanation:

The pool are is divided into 4 separated shapes: 2 circular sections and 2 isosceles triangles. Basically, to calculate the whole area, we need to find the area of each section. Due to its symmetry, both triangles are equal, and both circular sections are also the same, so it would be enough to calculate 1 circular section and 1 triangle, then multiply it by 2.

<h3>Area of each triangle:</h3>

From the figure, we know that <em>b = 20ft </em>and <em>h = 25ft. </em>So, the area would be:

$A_{t}=\frac{b.h}{2}=\frac{(20ft)(25ft)}{2}=250ft^{2}$

<h3>Area of each circular section:</h3>

From the figure, we know that $\alpha =2.21 radians$ and the radius is $R=30ft$ . So, the are would be calculated with this formula:

$A_{cs}=\frac{\pi R^{2}\alpha}{360\°}$

Replacing all values:

$A_{cs}=\frac{(3.14)(30ft)^{2}(2.21radians)}{6.28radians}$

Remember that $360\°=6.28radians$

Therefore, $A_{cs}=994.5ft^{2}$

Now, the total are of the figure is:

$A_{total}=2A_{t}+2A{cs}=2(250ft^{2} )+2(994.5ft^{2})\\A_{total}=500ft^{2} + 1989ft^{2}=2489ft^{2}$

Therefore the area of the symmetrical pool is $2489ft^{2}$

3 0

2 years ago

A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is

Verdich [7]

Answer:

The solution of this system is (10,14) and it means that there are 10 three point questions and 14 five point questions.

Step-by-step explanation:

In order to find the number of questions of each kind we need to solve the given system as shown below:

$\left \{ {{x+y=24} \atop {3x + 5y=100}} \right.$

If we multiply the first equation by -3 and sum it with the second equation we can isolate the "y" variable and solve for its value:

$\left \{ {{-3x -3y=-72} \atop {3x + 5y=100}} \right.\\ \\-3y + 5y = -72 + 100\\2y = 28\\y = 14$

We can use this value to find "x":

$x + y = 24\\x + 14 = 24\\x = 24 - 14\\x = 10$

The solution of this system is (10,14) and it means that there are 10 three point questions and 14 five point questions.

6 0

2 years ago