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barxatty [35]
3 years ago
5

The grade point average at a large university is being studied, A simple random sample of 100 students is taken. What is the sha

pe of the sampling distribution of the sample mean?
Mathematics
1 answer:
S_A_V [24]3 years ago
7 0

It is always Gaussian distribution.

Hope this helps.

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What numbers make this expression undefined x^2+3/x^2-11x-12
marusya05 [52]

\frac{ {x}^{2}  + 3}{ {x}^{2}  - 11x - 12}

Because which numbers will make the expessions undefined. We will focus on the denominator only.

Factor the terms.

(x - 12)(x + 1)

Now which 2 numbers that will make these terms become 0?

12 and - 1 of course.

So these 2 numbers that will make the expressions undefined are 12 and - 1

5 0
2 years ago
Find the area of a triangle bounded by the y-axis, the line f(x)=9−4/7x, and the line perpendicular to f(x) that passes through
Setler79 [48]

<u>ANSWER:  </u>

The area of the triangle bounded by the y-axis is  \frac{7938}{4225} \sqrt{65} \text { unit }^{2}

<u>SOLUTION:</u>

Given, f(x)=9-\frac{-4}{7} x

Consider f(x) = y. Hence we get

f(x)=9-\frac{-4}{7} x --- eqn 1

y=9-\frac{4}{7} x

On rewriting the terms we get

4x + 7y – 63 = 0

As the triangle is bounded by two perpendicular lines, it is an right angle triangle with y-axis as hypotenuse.

Area of right angle triangle = \frac{1}{ab} where a, b are lengths of sides other than hypotenuse.

So, we need find length of f(x) and its perpendicular line.

First let us find perpendicular line equation.

Slope of f(x) = \frac{-x \text { coefficient }}{y \text { coefficient }}=\frac{-4}{7}

So, slope of perpendicular line = \frac{-1}{\text {slope of } f(x)}=\frac{7}{4}

Perpendicular line is passing through origin(0,0).So by using point slope formula,

y-y_{1}=m\left(x-x_{1}\right)

Where m is the slope and \left(\mathrm{x}_{1}, \mathrm{y}_{1}\right)

y-0=\frac{7}{4}(x-0)

y=\frac{7}{4} x --- eqn 2

4y = 7x

7x – 4y = 0  

now, let us find the vertices of triangle, one of them is origin, second one is point of intersection of y-axis and f(x)

for points on y-axis x will be zero, to get y value, put x =0 int f(x)

0 + 7y – 63 = 0

7y = 63

y = 9

Hence, the point of intersection is (0, 9)

Third vertex is point of intersection of f(x) and its perpendicular line.

So, solve (1) and (2)

\begin{array}{l}{9-\frac{4}{7} x=\frac{7}{4} x} \\\\ {9 \times 4-\frac{4 \times 4}{7} x=7 x} \\\\ {36 \times 7-16 x=7 \times 7 x} \\\\ {252-16 x=49 x} \\\\ {49 x+16 x=252} \\\\ {65 x=252} \\\\ {x=\frac{252}{65}}\end{array}

Put x value in (2)

\begin{array}{l}{y=\frac{7}{4} \times \frac{252}{65}} \\\\ {y=\frac{441}{65}}\end{array}

So, the point of intersection is \left(\frac{252}{65}, \frac{441}{65}\right)

Length of f(x) is distance between \left(\frac{252}{65}, \frac{441}{65}\right) and (0,9)

\begin{aligned} \text { Length } &=\sqrt{\left(0-\frac{252}{65}\right)^{2}+\left(9-\frac{441}{65}\right)^{2}} \\ &=\sqrt{\left(\frac{252}{65}\right)^{2}+0} \\ &=\frac{252}{65} \end{aligned}

Now, length of perpendicular of f(x) is distance between \left(\frac{252}{65}, \frac{441}{65}\right) \text { and }(0,0)

\begin{aligned} \text { Length } &=\sqrt{\left(0-\frac{252}{65}\right)^{2}+\left(0-\frac{441}{65}\right)^{2}} \\ &=\sqrt{\left(\frac{252}{65}\right)^{2}+\left(\frac{441}{65}\right)^{2}} \\ &=\frac{\sqrt{(12 \times 21)^{2}+(21 \times 21)^{2}}}{65} \\ &=\frac{63}{65} \sqrt{65} \end{aligned}

Now, area of right angle triangle = \frac{1}{2} \times \frac{252}{65} \times \frac{63}{65} \sqrt{65}

=\frac{7938}{4225} \sqrt{65} \text { unit }^{2}

Hence, the area of the triangle is \frac{7938}{4225} \sqrt{65} \text { unit }^{2}

8 0
3 years ago
The cost for an upcoming field trip is $30 per student. The cost of the field trip C, in dollars, is a function of the number of
kompoz [17]

Answer:options B and D are the correct answers.

Step-by-step explanation:

The cost for an upcoming field trip is $30 per student. The cost of the field trip C, in dollars, is a function of the number of students x.

The function is defined by

C(x) = 30x

The values of x must be whole numbers. Therefore, the possible outputs for the defined function would be

B. 30 which means the cost for only one student.

D. 90 which means the total cost for 3 students.

3 0
3 years ago
Plzzzz help me but dont ansewer if you dont know it. 100 points
guapka [62]
The first one is 2x-3y/2
The second one is 1/x+2
The third one is (2x-5y)/(2x+5y)
The fourth one is x^2/z^2
5 0
3 years ago
Read 2 more answers
Y=x+3over 8 proportional or nonproportional
Inessa [10]

Answer:

nonproportional

Step-by-step explanation:

x + 3

------- is definitely nonproportional.  The reason for this is that the graph (a

   8                                                      straight line) does not pass through the                          

                                                            origin; it's offset by 3/8 unit up from the          

                                                             origin.

6 0
2 years ago
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