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3 months ago

If (a^3+27)=(a+3)(a^2+ma+9) then m equals

Mathematics

1 answer:

Inessa [12.5K]3 months ago

7 0

Answer:

m = - 3

Step-by-step explanation:

a³ + 27 can be recognized as a sum of cubes, which factors generally as

a³ + b³ = (a + b)(a² - ab + b²). Therefore:

a³ + 27

= a³ + 3³

= (a + 3)(a² - 3a + 9).

By comparing a² - 3a + 9 to a² + ma + 9, we find that

m = - 3.

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Students have organized

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Answer:

Part A. At least 6 hours

Part B. In less than 2.5 hours, Elijah will fall behind Mercedes

Part C. In over 2.5 hours, Elijah will lead Aubrey

Step-by-step explanation:

D = distance

v = speed

t = time

Formula connecting D, v, and t:

$D=v\cdot t$

Part A.

Steve's speed: $v=3.5\ mph$

Distance: a minimum of 21 miles

Time: unknown, so

$3.5\cdot t\ge 21\\ \\35t\ge 210\ [\text{Multiplied by 10}]\\ \\t\ge \dfrac{210}{35}\\ \\t\ge \dfrac{30}{5}\\ \\t\ge 6$

It would require Steve a minimum of 6 hours to traverse at least 21 miles on Day 1.

Part B.

Mercedes's speed: $v_M=2.4\ mph$

Elijah's speed: $v_E=3.2\ mph$

Elijah's Distance walked: $D_E$ miles

Mercedes's Distance walked: $D_M$ miles

Time: x hours

Mercedes is 2 miles ahead, therefore

$D_E=3.2x\\ \\D_M=2.4x+2$

Elijah will trail behind until

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In 2.5 hours, Elijah will close the gap on Mercedes, and in less than 2.5 hours, Elijah will trail behind her.

Part C.

Aubrey's speed: $v_M=3\ mph$

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Elijah's Distance walked: $D_E$ miles

Aubrey's Distance walked: $D_A$ miles

Time: x hours

At the beginning of Day 3, Elijah starts from Mile 42, while Aubrey begins at Mile 42.5.

$D_E=42+3.2x\\ \\D_A=42.5+3x$

Elijah will be ahead of Aubrey when

$D_E>D_A\\ \\42+3.2x> 42.5+3x\\ \\3.2x-3x>42.5-42\\ \\0.2x>0.5\\ \\2x>5\ [\text{Multiplied by 10}]\\ \\x>\dfrac{5}{2}\\ \\x>2.5\ hours$

In 2.5 hours, Elijah will surpass Aubrey, and after more than 2.5 hours, Elijah will outpace Aubrey.

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3 months ago

Energy drink consumption has continued to gain in popularity since the 1997 debut of Red Bull, the current leader in the energy

tester [12383]

Answer:

1. 3.767

2. 0.145

Step-by-step explanation:

Define X as the exam scores and Y as the number of drinks.

X Y X-Xbar Y-Ybar (X-Xbar)(Y-Ybar) (X-Xbar)² (Y-Ybar)²

75 5 -2.3 2.3 -5.29 5.29 5.29

92 3 14.7 0.3 4.41 216.09 0.09

84 2 6.7 -0.7 -4.69 44.89 0.49

64 4 -13.3 1.3 -17.29 176.89 1.69

64 2 -13.3 -0.7 9.31 176.89 0.49

86 7 8.7 4.3 37.41 75.69 18.49

81 3 3.7 0.3 1.11 13.69 0.09

61 0 -16.3 -2.7 44.01 265.69 7.29

73 1 -4.3 -1.7 7.31 18.49 2.89

93 0 15.7 -2.7 -42.39 246.49 7.29

sumx=773, sumy=27, sum(x-xbar)(y-ybar)= 33.9, sum(X-Xbar)²= 1240.1,sum(Y-Ybar)²= 44.1

Xbar=sumx/n=773/10=77.3

Ybar=sumy/n=27/10=2.7

$Cov(x,y)=sxy=\frac{Sum(X-Xbar)(Y-Ybar)}{n-1}$

Cov(x,y)=33.9/9

Cov(x,y)=3.76667

Thus, the sample covariance of exam scores and energy drink consumption is 3.767

$Cor(x,y)=r=\frac{Sum(X-Xbar)(Y-Ybar)}{\sqrt{Sum(X-Xbar)^2sum(Y-Ybar)^2} }$

$Cor(x,y)=r=\frac{33.9}{\sqrt{(1240.1)(44.1)} }$

Cor(x,y)=r=33.9/233.85553

Cor(x,y)=r=0.14496

The sample correlation coefficient for the relationship between exam scores and energy drink consumption is 0.145.

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