Select all order pairs that satisfy the function y = -2x + 5

A politician estimates that 61% of his constituents will vote for him in the coming election. How many constituents are required

Katyanochek1 [597]

Using the z-distribution, as we are working with a proportion, it is found that 1016 constituents are required.

<h3>What is a confidence interval of proportions?</h3>

A confidence interval of proportions is given by:

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

In which:

$\pi$ is the sample proportion.

z is the critical value.

n is the sample size.

The margin of error is given by:

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

In this problem, we have a 95% confidence level, hence $\alpha = 0.95$ , z is the value of Z that has a p-value of $\frac{1+0.95}{2} = 0.975$ , so the critical value is z = 1.96.

The estimate is of $\pi = 0.61$ , while the margin of error is of M = 0.03, hence solving for n we find the minimum sample size.

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

$0.03 = 1.96\sqrt{\frac{0.61(0.39)}{n}}$

$0.03\sqrt{n} = 1.96\sqrt{0.61(0.39)}$

$\sqrt{n} = \frac{1.96\sqrt{0.61(0.39)}}{0.03}$

$(\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.61(0.39)}}{0.03}\right)^2$

$n = 1015.5$

Rounding up, 1016 constituents are required.

More can be learned about the z-distribution at brainly.com/question/25890103

8 0

1 year ago

#13) Mrs. Frye says that the following triangles are congruent. Is she correct? Why or why not?

kkurt [141]

Answer: The following triangles are congruent.

7 0

2 years ago

1. Find the cost of levelling the ground in the form of a triangle having the sides 51 m, 37 m and 20 m at the rate of ₹ 3 per m

Flauer [41]

1. Find the cost of levelling the ground in the form of a triangle having the sides 51 m, 37 m and 20 m at the rate of ₹ 3 per m².

a = 51 m, b = 37 m, c = 20 m

semiperimeter: p = (51+37+20):2 = 54 m

Area of triangle:

$A=\sqrt{p(p-a)(p-b)(p-c)}\\\\A=\sqrt{54(54-51)(54-37)(54-20)}\\\\A=\sqrt{54\cdot3\cdot17\cdot34}\\\\A=\sqrt{9\cdot2\cdot3\cdot3\cdot17\cdot17\cdot2}\\\\A=3\cdot2\cdot3\cdot17\\\\A=306\,m^2$

Rate: ₹ 3 per m².

Cost: ₹ 3•306 = ₹ 918

2. Find the area of the isosceles triangle whose perimeter is 11 cm and the base is 5 cm.

a = 5 cm

a+2b = 11 cm ⇒ 2b = 6 cm ⇒ b = 3 cm

p = 11:2 = 5.5

$A=\sqrt{5.5(5.5-3)^2(5.5-5)}\\\\ A=\sqrt{5.5\cdot(2.5)^2\cdot0.5}\\\\ A=\sqrt{11\cdot0.5\cdot(2.5)^2\cdot0.5}\\\\A=0.5\cdot2.5\cdot\sqrt{11}\\\\A=1.25\sqrt{11}\,cm^2\approx4.146\,cm^2$

3. Find the area of the equilateral triangle whose each side is 8 cm.

a = b = c = 8 cm

p = (8•3):2 = 12 cm

$A=\sqrt{12(12-8)^3}\\\\ A=\sqrt{12\cdot4^3}\\\\ A=\sqrt{3\cdot4\cdot4\cdot4^2}\\\\A=4\cdot4\cdot\sqrt{3}\\\\A=16\sqrt3\ cm^2\approx27.713\ cm^2$

4. The perimeter of an isosceles triangle is 32 cm. The ratio of the equal side to its base is 3 : 2. Find the area of the triangle.

a = 2x

b = 3x

2x + 2•3x = 32 cm ⇒ 8x = 32 cm ⇒ x = 4 cm ⇒ a = 8 cm, b = 12 cm

p = 32:2 = 16 cm

$A=\sqrt{16(16-8)(16-12)^2}\\\\ A=\sqrt{16\cdot8\cdot4^2}\\\\ A=\sqrt{2\cdot8\cdot8\cdot4^2}\\\\ A=8\cdot4\cdot\sqrt2\\\\ A=32\sqrt2\ cm^2\approx45.2548\ cm^2$

8 0

2 years ago

The graph shows the height in inches, h, of a bamboo plant t months after it has been planted. Write an equation that describes

Komok [63]

Answer gonna b appl if wrong sorry

3 0

2 years ago

Drag each real-world situation to the correct column to show whether it can be modeled by combining additive inverses to get 0.

Flauer [41]

Answer:

. An investment account earns 2.8% simple interest.

Since investment amount increases every year linearly, therefore, the modeled situation represents a LINEAR FUNCTION.

B). The price of a stock varies by 2.8% each week.

Since price of the stock may increase or decrease every week, therefore, this situation can't be modeled by any function.

Therefore, the answer is NEITHER.

C). An investment account earns 2.8% compound interest, compounded monthly.

Formula to get the value of the final amount in the account is,

Final value = Initial value ×

Here 't' = Duration of investment

It's an EXPONENTIAL FUNCTION.

Step-by-step explanation:

3 0

2 years ago