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lions [1.4K]
2 years ago
6

The expression 8x2 − 144x 864 is used to approximate a small town's population in thousands from 1998 to 2018, where x represent

s the number of years since 1998. choose the equivalent expression that is most useful for finding the year where the population was at a minimum. 8(x2 − 18x 108) 8(x2 − 18x) 108 8(x − 9)2 − 216 8(x − 9)2 216
Mathematics
1 answer:
Rzqust [24]2 years ago
8 0

The expression that is most useful for finding the year where the population was at a minimum would be 8(x − 9)² + 216.

Given expression 8x² − 144x + 864 is used to approximate a small town's population in thousands from 1998 to 2018, where x represents the number of years since 1998.

<h3>What is a quadratic equation?</h3>

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

Given expression is 8x² − 144x + 864

Let y = 8x² − 144x + 864

also,  y - 864 = 8x² - 144x

by Extracting common factor 8 on the right side

y - 864 = 8(x² - 18x)

Add (18/2)² on both sides, we get

y - 864 + 8(18/2)² = 8 (x² - 18x + 81²)

y - 864 + 648 = 8 (x² - 8x + 9)

on simplification

y - 216 = 8 (x - 9)²

y = 8(x - 9)² + 216

therefore, y = 8 (x - 9)² + 216

The expression that is most useful for finding the year where the population was at a minimum would be 8(x − 9)² + 216.

Learn more about a quadratic equation here:

brainly.com/question/2263981

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antiseptic1488 [7]

Answer:

the numbers who's difference is 16 and the product is 720 is

36 &20

Explanation:

to finding numbers you have to express the equation in a quadratic equation then Factor it.

since the two numbers have a difference of 16 you can say that the first number is x and the second number is x -16 then their product is 720.

x(x-16)=720

x²-16x=720

x²-16x-720=0

(x-36)(x+20)

there are two possible value of x but since you are looking for the positive value of x, choose the positive value of x the first number is 20.

To find the second number

x-16=20

x=20+16

x=36

the second number is 36

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8 0
3 years ago
What is the base five representation of The number 219
ICE Princess25 [194]

assuming 219_{10}

Then the column values for base five here are

5³  5²  5^{1}  5^{0}

We can get 1 × 5³ = 125 → 219 - 125 = 94

We can get 3 × 5² = 75 → 94 - 75 = 19

We can get 3 x 5^{1} → 19 - 15 = 4

and 4 = 4 × 5^{0}

Thus 219_{10} = 1334_{5}

As a check

(1 × 125 ) + (3 × 25 ) + (3 × 5 ) + 4 = 219


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3 years ago
Since an instant replay system for tennis was introduced at a major​ tournament, men challenged 1406 referee​ calls, with the re
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Answer:

Step-by-step explanation:

This is a test of 2 population proportions. Let 1 and 2 be the subscript for men and women players. The population proportions of men and women challenges for calls would be p1 and p2

P1 - P2 = difference in the proportion of men and women challenges for calls.

The null hypothesis is

H0 : p1 = p2

p1 - p2 = 0

The alternative hypothesis is

Ha : p1 ≠ p2

p1 - p2 ≠ 0

it is a two tailed test

Sample proportion = x/n

Where

x represents number of success(number of complaints)

n represents number of samples

For old dough

x1 = 416

n1 = 1406

P1 = 416/1406 = 0.3

For new dough,

x2 = 217

n2 = 778

P2 = 217/778 = 0.28

The pooled proportion, pc is

pc = (x1 + x2)/(n1 + n2)

pc = (416 + 217)/(1406 + 778) = 0.29

1 - pc = 1 - 0.29 = 0.71

z = (P1 - P2)/√pc(1 - pc)(1/n1 + 1/n2)

z = (0.3 - 0.28)/√(0.29)(0.71)(1/1406 + 1/778) = 0.02/√0.00553857907

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Since it is a two tailed test, the curve is symmetrical. We will look at the area in both tails. Since it is showing in one tail only, we would double the area

From the normal distribution table, the area below the test z score to the left of 0.99 is 1 - 0.84 = 0.16

We would double this area to include the area in the left tail of z = - 0.99 Thus

p = 0.16 × 2 = 0.32

Since 0.1 < 0.5, we would accept the null hypothesis.

p value = 0.337

Since 0.05 < 0.32, we would accept the null hypothesis

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How May I Draw My number Line And Where Would My Numbers Go?
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