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2 years ago

Use substitution method & show your work.y = x^2 + 3x - 14x + 1 = y

1 answer:

7 0

4x + 1 = x^2 + 3x - 1
4x = x^2 + 3x - 2
0 = x^2 -x - 2
0 = x^2 -x + 1 - 3
0 = (x - 1)^2 - 3
3 = (x - 1)^2
sqrt 3=(x-1) and (-(x-1))
x = 1+sqrt 3 and 1-sqrt 3
sqrt means square root

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A high school principal wishes to estimate how well his students are doing in math. Using 40 randomly chosen tests, he finds tha

ollegr [7]

Answer:

99% confidence interval for the population proportion of passing test scores is [0.5986 , 0.9414].

Step-by-step explanation:

We are given that a high school principal wishes to estimate how well his students are doing in math.

Using 40 randomly chosen tests, he finds that 77% of them received a passing grade.

Firstly, the pivotal quantity for 99% confidence interval for the population proportion is given by;

P.Q. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of students received a passing grade = 77%

n = sample of tests = 40

p = population proportion

<em>Here for constructing 99% confidence interval we have used One-sample z proportion test statistics.</em>

So, 99% confidence interval for the population proportion, p is ;

P(-2.5758 < N(0,1) < 2.5758) = 0.99 {As the critical value of z at 0.5%

level of significance are -2.5758 & 2.5758}

P(-2.5758 < $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < 2.5758) = 0.99

P( $-2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < ${\hat p-p}$ < $2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.99

P( $\hat p-2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < p < $\hat p+2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.99

<u>99% confidence interval for p</u> = [ $\hat p-2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ , $\hat p+2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ]

= [ $0.77-2.5758 \times {\sqrt{\frac{0.77(1-0.77)}{40} } }$ , $0.77+2.5758 \times {\sqrt{\frac{0.77(1-0.77)}{40} } }$ ]

= [0.5986 , 0.9414]

Therefore, 99% confidence interval for the population proportion of passing test scores is [0.5986 , 0.9414].

Lower bound of interval = 0.5986

Upper bound of interval = 0.9414

6 0

2 years ago

How to find area of parallelogram with coordinates of verticles?

ExtremeBDS [4]

You find a parallelogram area by this formula:
$A=b\cdot h$
Where b is its base and h, its height.
You get b's value applying distance between two points formula.
If A and B points form the base:
$A(x_1,y_1)\;\;\;\;B(x_2,y_2) \\ \\ 
d_{AB}= \sqrt{(x_1-x_2)^2+(y_1-y_2)^2} =b$

And h is the perpendicular distance between both bases.
You can visit next link to know further about it:
https://www.ck12.org/geometry/Distance-Between-Parallel-Lines/lesson/Distance-Between-Parallel-Lines
-GEOM/

And in attached picture you can find an example in progress you may want to finish.

5 0

3 years ago

Select the correct answer. Which point is a solution of x + 2y ≤ 4? A. (2, 4) B. (1, 1) C. (3, 5) D. (-1, 5)

stira [4]

Answer:

Step-by-step explanation:

Of you put the values of c and y from B in the equation, then the result is,

$1 + 2 \times 1 \leqslant 4 \\ 1 + 2 \leqslant 4 \\ 3 \leqslant 4$

here, 3 is less than 4, which is true.

But the result will come out as greater than 4 if you put other points in the equation, which is not true for the given condition.

6 0

2 years ago

Find mike average monthly income based on these weekly incomes

7nadin3 [17]

Answer:

Mike's average monthly salary is $ 1,814.

Step-by-step explanation:

To determine Mike's average monthly salary, taking into account that he earns $ 284, $ 292, $ 418, $ 350, and $ 470 weekly, these amounts must be added for the 5-week duration of the month through the following calculation:

284 + 292 + 418 + 350 + 470 = X

1814 = X

Thus, given that this sum totals $ 1,814, Mike's average monthly salary is $ 1,814.

5 0

2 years ago

Calculate the area of the circle. round your answer to the nearest hundredth

Artemon [7]

52 is the answer I believe

8 0

3 years ago