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3 years ago

Select the correct product. (y + z)3 y3 + z3 y3 + 3y2z + 3yz2 + z3 3y + 3z y3z3

1 answer:

8 0

(y + z)³

in expanded form: (y + z) (y + z) (y + z)

y(y + z) + z(y + z) 1st and 2nd set
y² + yz + yz + z² product of 1st and 2nd set
(y² + 2yz + z²)(y + z) multiply with 3rd set
y(y² + 2yz + z²) + z(y² + 2yz + z²)
y³ + 2y²z + yz² + y²z + 2yz² + z³
y³ + 2y²z + y²z + yz² + 2yz² + z³ Group like terms.

y³ + 3y²z + 3yz² + z³ Product of 1st, 2nd, and 3rd set ...2nd CHOICE

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Larry claims that (14 + 12) × (8 + 12) and (14 × 12) + (8 × 12) are equivalent because they have the same digits and the same op

DochEvi [55]

Answer:

Larry is wrong

Step-by-step explanation:

Multiplying big numbers will give significantly bigger results then multiplying smaller numbers then adding them. 14 + 12 = 26 & 8 + 12 = 20. 14 x 12 = 68 & 8 x 12 = 96. 96 + 168 is alot less then 26 * 20 so that is why larry is wrong

4 0

2 years ago

A researcher wants to construct a 90% confidence interval for the proportion of elementary school students in Seward County who

dezoksy [38]

Answer:

The sample size is $n =68$

Step-by-step explanation:

The population proportion is $\^ p = 0.50$

The margin of error is $E = 0.1$

From the question we are told the confidence level is 90% , hence the level of significance is

$\alpha = (100 - 90 ) \%$

=> $\alpha = 0.10$

Generally from the normal distribution table the critical value of $\frac{\alpha }{2}$ is

$Z_{\frac{\alpha }{2} } = 1.645$

Generally the sample size is mathematically represented as

$n = [\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \^ p (1 - \^ p )$

=> $n = [\frac{1.645 }{0.1} ]^2 * 0.50 (1 - 0.50 )$

=> $n =68$

6 0

3 years ago

The formula s = StartRoot StartFraction S A Over 6 EndFraction EndRoot gives the length of the side, s, of a cube with a surface

never [62]

Answer:

$2\sqrt{2}\ ft\ longer$

Step-by-step explanation:

Suppose a cube with side length s, the area of one side is

$A_s=s^2$

Since the cube has 6 sides, the total area is

$A=6A_s=6s^2$

But if we have the area, we can solve the above formula for s to get

$A=6s^2$

$\displaystyle s=\sqrt{\frac{A}{6}}$

We have two different cubes with areas 1,200 square inches and 768 square inches. Let's compute their side lengths

$\displaystyle s_1=\sqrt{\frac{1,200}{6}}=\sqrt{200}$

$\displaystyle s_1=10\sqrt{2}\ ft$

$\displaystyle s_2=\sqrt{\frac{768}{6}}=\sqrt{128}$

$\displaystyle s_2=8\sqrt{2} ft$

The difference between them is

$10\sqrt{2}\ ft-8\sqrt{2}\ ft=2\sqrt{2}\ ft\approx 2.83\ ft$

The side of the cube with area 1,200 square inches is $2\sqrt{2}\ ft$ longer then the side of the cube with area 768 square inches

7 0

3 years ago

Read 2 more answers

Add fraction 6 4/5 + 3 7/10 how do i add this fraction

Dafna1 [17]

The answer is 10 1/2.

First you need to convert 4/5 and 7/10 so the denominator is the same. 4/5=8/10, 7/10 stays the same.

Now we add= 6 8/10 +3 7/10 =9 15/10.
9 15/10=10 5/10=10 1/2.

Hope this helps and hope you have a great day and please make brainiest

7 0

3 years ago

Read 2 more answers

Veronica is self employed. In one year, Veronica generates a gross income of $65,500. When calculating her taxes, Veronica is al

butalik [34]

Answer:

$44,850

Step-by-step explanation:

Gross income is $65,500

Allowable deductions are $2,500

Operating income is $65,500-$2,500=$63,000

From the given tax structure, Veronia will pay 15% for the first $25,000 then 30% for $63,000-$25,000=$38,000

Tax will be (0.15*$25,000)+(0.3*$38,000)=$15,150

Remaining expenses will be $5,500-$2,500=$3,000

Income after tax will be $63,000-$15,150=$47,850

Net income=$47,850-$3,000=$44,850

7 0

3 years ago