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2 years ago

T ✓ Х Find the sum of (x2 – 7x + 5) and (-3x2 - x + 10) [

Mathematics

1 answer:

Zanzabum2 years ago

8 0

Answer:

-2x² - 8x + 15 = 0

Step-by-step explanation:

Given the following algebraic expression;

x² – 7x + 5

-3x² - x + 10

To add the equation together;

x² – 7x + 5 + (-3x² - x + 10) = 0

x² – 7x + 5 - 3x² - x + 10 = 0

Collecting like terms, we have;

(x² - 3x²) - (7x + x) + (5 + 10) = 0

-2x² - 8x + 15 = 0

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6.Suppose the Gallup Organization wants to estimate the population proportion of those who think there should be a law that woul

drek231 [11]

Answer:

A sample of $n = (\frac{1.96\sqrt{0.3696*0.6304}}{E})^2$ is needed, in which E is the desired margin of error, as a proportion. If we find a decimal value, we round up to the next whole number.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is of:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

In a previous study of 1012 randomly chosen respondents, 374 said that there should be such a law.

This means that $n = 1012, \pi = \frac{374}{1012} = 0.3696$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

How large a sample size is needed to be 95% confident with a margin of error of E?

A sample size of n is needed, and n is found when M = E.

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$E = 1.96\sqrt{\frac{0.3696*0.6304}{n}}$

$E\sqrt{n} = 1.96\sqrt{0.3696*0.6304}$

$\sqrt{n} = \frac{1.96\sqrt{0.3696*0.6304}}{E}$

$(\sqrt{n})^2 = (\frac{1.96\sqrt{0.3696*0.6304}}{E})^2$

$n = (\frac{1.96\sqrt{0.3696*0.6304}}{E})^2$

A sample of $n = (\frac{1.96\sqrt{0.3696*0.6304}}{E})^2$ is needed, in which E is the desired margin of error, as a proportion. If we find a decimal value, we round up to the next whole number.

4 0

3 years ago

A closed box with a square base is to have a volume of 13 comma 500 cm cubed. The material for the top and bottom of the box cos

andrezito [222]

Answer:

x = 1,5 cm

h = 6 cm

C(min) = 135 $

Step-by-step explanation:

Volume of the box is :

V(b) = 13,5 cm³

Aea of the top is equal to area of the base,

Let call " x " side of the base then as it is square area is A₁ = x²

Sides areas are 4 each one equal to x * h (where h is the high of the box)

And volume of the box is 13,5 cm³ = x²*h

Then h = 13,5/x²

Side area is : A₂ = x* 13,5/x²

A(b) = A₁ + A₂

Total area of the box as functon of x is:

A(x) = 2*x² + 4* 13,5 / x

And finally cost of the box is

C(x) = 10*2*x² + 2.50*4*13.5/x

C(x) = 20*x² + 135/x

Taking derivatives on both sides of the equation:

C´(x) = 40*x - 135*/x²

C´(x) = 0 ⇒ 40*x - 135*/x² = 0 ⇒ 40*x³ = 135

x³ = 3.375

x = 1,5 cm

And h = 13,5/x² ⇒ h = 13,5/ (1,5)²

h = 6 cm

C(min) = 20*x² + 135/x

C(min) = 45 + 90

C(min) = 135 $

8 0

3 years ago

The forth term of an arithmetic seaquence is 19 and the fifth term is 13 . what is the third term

Vaselesa [24]

The third term was likely to be 25. You can see a pattern -6 when it goes up a term.

5 0

2 years ago

“Use the graph or table to write a linear function that relates y to x”

Igoryamba

Answer:

8)y=2x-3

9)y= -1/2+4

Step-by-step explanation:

5 0

2 years ago

Please answer all questions thank you.

Ad libitum [116K]

1) 78.5/pi = 25
radius = 5
The one 5 digits away from that coordinate is (2,-1)

2) This question is area, not perimeter. The width and length has to be added by 4 because of 2 feet on both sides.
9*10 = 90 - 30 = 60

3) 25pi according to pythagorean theorem.

4 0

2 years ago