Use the distributive property to write an equivalent expression. (6+8)x 2

Ty is eight inches shorter than his brother Reece. If Ty is 42 inches tall, how tall is Reece.

sammy [17]

Answer: reece is 50 inches tall

Step-by-step explanation:

42+8=50

4 0

3 years ago

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Consider the following equation. f(x, y) = y3/x, P(1, 2), u = 1 3 2i + 5 j (a) Find the gradient of f. ∇f(x, y) = Correct: Your

BaLLatris [955]

$f(x,y)=\dfrac{y^3}x$

a. The gradient is

$\nabla f(x,y)=\dfrac{\partial f}{\partial x}\,\vec\imath+\dfrac{\partial f}{\partial y}\,\vec\jmath$

$\boxed{\nabla f(x,y)=-\dfrac{y^3}{x^2}\,\vec\imath+\dfrac{3y^2}x\,\vec\jmath}$

b. The gradient at point P(1, 2) is

$\boxed{\nabla f(1,2)=-8\,\vec\imath+12\,\vec\jmath}$

c. The derivative of $f$ at P in the direction of $\vec u$ is

$D_{\vec u}f(1,2)=\nabla f(1,2)\cdot\dfrac{\vec u}{\|\vec u\|}$

It looks like

$\vec u=\dfrac{13}2\,\vec\imath+5\,\vec\jmath$

so that

$\|\vec u\|=\sqrt{\left(\dfrac{13}2\right)^2+5^2}=\dfrac{\sqrt{269}}2$

Then

$D_{\vec u}f(1,2)=\dfrac{\left(-8\,\vec\imath+12\,\vec\jmath\right)\cdot\left(\frac{13}2\,\vec\imath+5\,\vec\jmath\right)}{\frac{\sqrt{269}}2}$

$\boxed{D_{\vec u}f(1,2)=\dfrac{16}{\sqrt{269}}}$

7 0

3 years ago

Simplify the product using the distributive property. (-4h +2)(3h +7)

Alekssandra [29.7K]

Answer:

A. -12h² - 22h + 14

Step-by-step explanation:

(-4h +2)(3h +7) = -4h(3h +7) +2(3h +7) . . . . . . . (a +b)c = ac +bc

= (-4h)(3h) + (-4h)(7) + (2)(3h) + (2)(7) . . . . . . . a(b +c) = ab +ac . . . (twice)

= -12h² -28h +6h +14

= -12h² -22h +14 . . . . . . . . collect terms

3 0

3 years ago

The mean preparation fee H&R Block charged retail customers in 2012 was $183 (The Wall Street Journal, March 7, 2012). Use t

astraxan [27]

Answer:

a)0.6192

b)0.7422

c)0.8904

d)at least 151 sample is needed for 95% probability that sample mean falls within 8$ of the population mean.

Step-by-step explanation:

Let z(p) be the z-statistic of the probability that the mean price for a sample is within the margin of error. Then

z(p)= $\frac{ME*\sqrt{N}}{s }$ where

Me is the margin of error from the mean

s is the standard deviation of the population

N is the sample size

a.

z(p)= $\frac{8*\sqrt{30}}{50 }$ ≈ 0.8764

by looking z-table corresponding p value is 1-0.3808=0.6192

b.

z(p)= $\frac{8*\sqrt{50}}{50 }$ ≈ 1.1314

by looking z-table corresponding p value is 1-0.2578=0.7422

c.

z(p)= $\frac{8*\sqrt{100}}{50 }$ ≈ 1.6

by looking z-table corresponding p value is 1-0.1096=0.8904

d.

Minimum required sample size for 0.95 probability is

N≥ $(\frac{z*s}{ME} )^2$ where

N is the sample size

z is the corresponding z-score in 95% probability (1.96)

s is the standard deviation (50)

ME is the margin of error (8)

then N≥ $(\frac{1.96*50}{8} )^2$ ≈150.6

Thus at least 151 sample is needed for 95% probability that sample mean falls within 8$ of the population mean.

7 0

3 years ago

Select the solution(s) of the original equation. 3+ √21/2+4 3+ √21/2-4 3- √21/2+4 3-√21/2-4

jarptica [38.1K]

Answer:

2nd and 4th on edg

Step-by-step explanation:

3+21pi / 2 +4

3-21pi / 2 -4

4 0

2 years ago

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Use the distributive property to write an equivalent expression. (6+8)x 2​

Use the distributive property to write an equivalent expression. (6+8)x 2