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3 years ago

If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 =

1 answer:

5 0

$x\ \diamond\ y=(x+y)^2-(x-y)^2=x^2+2xy+y^2-(x^2-2xy+y^2)\\\\=x^2+2xy+y^2-x^2+2xy-y^2=4xy\\\\\sqrt5\ \diamond\ \sqrt5=4\cdot\sqrt5\cdot\sqrt5=4\cdot5=20$

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Simplify -2(3x-5)+5x

Sauron [17]

-1x+10 is the answer

8 0

3 years ago

Two friends are collecting cards. Frank has 7 more than half the number of cards as his friend. Together they have 42 cards. How

Naddika [18.5K]

Answer:

The number of cards Frank has is 18 and the number of cards his friend has is 24.

Step-by-step explanation:

The correct question is

Two friends are collecting cards. Frank has 6 more than half the number of cards as his friend. Together they have 42 cards. How many cards does each friend have?

Let

x ----> the number of cards that Frank has

y ----> the number of cards that his friend has

we know that

Together they have 42 cards

$x+y=42$ ----> equation A

Frank has 6 more than half the number of cards as his friend

$x=\frac{y}{2} +6$ ---> equation B

Solve the system by substitution

Substitute equation B in equation A

$\frac{y}{2} +6+y=42$

solve for y

$\frac{3}{2}y=42-6\\\\\frac{3}{2}y=36\\\\y=36(2)/3=24$

Find the value of x

$x=\frac{24}{2} +6=18$

therefore

The number of cards Frank has is 18 and the number of cards his friend has is 24.

7 0

3 years ago

Can someone help me pls

Wittaler [7]

Answer:

3 cm

Step-by-step explanation:

$V_{cylinder} = 189\pi \: cm^3$ (Given)

$h_{cylinder} = 21\: cm$ (Given)

Formula for $V_{cylinder}$ is given as:

$V_{cylinder} = \pi r^2h$

$\implies 189\pi = \pi r^2(21)$

$\implies \frac{ 189\pi}{21\pi} = r^2$

$\implies 9 = r^2$

$\implies \pm\sqrt 9 = r$

$\implies \pm 3 = r$

Length of radius can not negative

$\implies r = 3 \: cm$

Hope it helps you in your learning process.

8 0

2 years ago

Read 2 more answers

Fill in the blanks below to make a true statement. In a binomial experiment with n trials and probability of success p, if np (1

Sergeu [11.5K]

Answer:

$\mu_{x}=np$

$\sigma^2_{X}=np(1-p)$

Step-by-step explanation:

∵ When x is a random variable having distribution B(n, p), then for sufficiently large value of n, the following random variable has a standard normal distribution,

$\frac{x-\mu}{\sigma}\sim N(0,1)$

Where,

$\mu=np$

$\sigma^2=np(1-p)$

Here the variable X has a binomial distribution,

Such that, np (1 - p) ≥ 10 ⇒ n is sufficiently large.

Where, n is the total numbers of trials, p is success in each trials,

So, the mean of variable X is,

$\mu_{X} = np$

And, variance of variable X is,

$\sigma^2{X}=np(1-p)$

3 0

3 years ago

Write each Percent as a decimal and as a mixed number or fraction in simplest form

sveticcg [70]

$p\%=\dfrac{p}{100}\\\\225\%=\dfrac{225}{100}=2\dfrac{25}{100}=2.25=2\dfrac{1}{4}\\\\550\%=\dfrac{550}{100}=\dfrac{55}{10}=5\dfrac{5}{10}=5.5=5\dfrac{1}{2}\\\\0.8\%=\dfrac{0.8}{100}=\dfrac{0.8\cdot10}{100\cdot10}=\dfrac{8}{1,000}=0.008=\dfrac{1}{125}\\\\0.06\%=\dfrac{0.06}{100}=\dfrac{0.06\cdot100}{100\cdot100}=\dfrac{6}{10,000}=0.0006=\dfrac{3}{5,000}$

6 0

3 years ago