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Tems11 [23]
2 years ago
14

A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than ex

amine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. If the dean wanted to estimate the proportion of all students receiving financial aid to within 3% with 99% reliability, how many students would need to be sampled?
Mathematics
1 answer:
quester [9]2 years ago
4 0

Answer:1866

Step-by-step explanation:

Given

n=200

x=118

Population proportion P=\frac{118}{200}=0.59

\alpha=0.005

Realiability =99%

Z_{\frac{\alpha }{2}}=2.576

Margin of erroe is given by \sqrt{\frac{p\left ( 1-p \right )}{N}}

0.03= \sqrt{\frac{0.59\left ( 1-0.59 \right )}{N}}

85.667=\sqrt{\frac{N}{0.6519}}[tex]N=1865.88[tex]\approx 1866 Students

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(Hehe...Please ignore the markings)
inysia [295]

Answer:

See below:

Step-by-step explanation:

Problem 1:

Multiply Equation 1 by 4, keep Equation 2 the same.

x+y=8, multiply each term by 4:

4*x=4x, 4*y=4y, 8*4=32

so, the equivalent system is: 4x+4y=32 and x-y=2

Solve the system of equations:

x-y=2 becomes x=y+2

plug into 4x+4y=32 to solve for y

4(y+2)+4y=32---> 4y+8+4y=32--->8y=24---> y=3

Plug into x-y=2---> x-3=2---> x=5

Problem 1 Answer:

Equivalent system: 4x+4y=32, x-y=2; solution: x=5, y=3

Problem 2:

Keep Equation 1 the same. Add 1 and 2.

To add an equation, add the left sides together, and then the rights.

so: x+y=8 + x-y=2 gives us: 2x=10

solve for x ---> 2x/2=10/2--->x=5

plug x into x+y=8--->5+y=8--->y=3

Problem 2 answer:

Equivalent system: x+y=8, 2x=10; solution:x=5, y=3

Problem 3:

Subtract Equation 2 from 1, and keep 2 the same.

To subtract an equation, subtract the left sides, then the rights. We are subtracting 1<em> from </em>2, so its 2-1.

x-y=2 - x+y=8 gives us: -2y=-6

Solve for y by dividing by -2-->-2y/-2=-6/-2---> y=3

Plug into x-y=2---> x-3=2---> x=5

Problem 3 answer:

Equivalent system: -2y=-6, x-y=2; solution: x=5, y=3

Problem 4:

Multiply the sum of Equation 1 and 2 by a factor of 3. Keep equation 2 the same.

First we add 1 and 2: (we did this earlier) ---> 2x=10 ---> now we multiply it all by 3---> 2x*(3)=10*(3)---> this gives us: 6x=30---> now divide by 6 to solve for x: 6x/6=30/6 gives us: x=5

Now, solve for y by plugging x into equation 2: x-y=2---> 5-y=2--->y=3

Problem 4 answer:

Equivalent system: 6x=30, x-y=2; solution: x=5, y=3

______

Quick Tip: One thing inherent of Equivalent systems is that they have the same set of solutions. Thus, we know the systems are equivalent when they have the same set of solutions for x and y. Moreover, you don't need to solve every time after you attempt to find an equivalent system, instead, just plug in the values found in problem 1 to each new set of equations to test if they are equivalent.

If we find x=5 and y=3 for x+y=8 and x-y=2, then all we have to do is plug them in to 6x=30 and -2y=-6 to see if they are equivalent.

6(5)=30 ---> true

-2(3)=-6 ---> true

3 0
2 years ago
7-9: Practice Buddy: Independent Practice; Problem Solving please help!
strojnjashka [21]

Answer:

4/3/8

Step-by-step explanation:

12/1/2-8/8/1

=25/2-65/8

=100-65/8

=35/8

=4/3/8

3 0
2 years ago
Read 2 more answers
If MO = 7x - 4, and NO = 6x, what is the length of line MN?
Gennadij [26K]

Answer:

13x-4

Step-by-step explanation:

8 0
3 years ago
Need help vrtfv fvvfgsf
maksim [4K]

Answer:

b = 8

Step-by-step explanation:

Use the Pythagorean theorem

c^2 = a^2 + b^2  

c = 10

a = 6

b = ?

Substitute into the formula

10^2 = 6^2 + b^2      

100 = 36 + b^2            Subtract 36 from both sides

100 - 36 = b^2             Combine

64 = b^2                      Take the square root of both sides.

√64 = √b^2

b = 8

7 0
2 years ago
Landon used a semicirce, a rectangle, and a right triangle to form the figure shown.
ankoles [38]
Area of rectangle= base x height
6x4=24

Area of triangle= 0.5 base x height
We have the height but we don’t have the base, to calculate the base we subtract 10-6 which equals to 4
0.5 x 4 x4 =8

Area of a semicircle= o.5 x pi x r^2
We have the diameter and to find the radius we divide it by 2
4/2 = 2
0.5 x pi(or 3.14) x 2^2
=6.28
Total area = 24 + 8+ 6.28 =38.28cm^2


8 0
3 years ago
Read 2 more answers
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