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3 years ago

Lines k and n are perpendicular. If the slope of line k is -6, what is the slope of line n?

Mathematics

1 answer:

CaHeK987 [17]3 years ago

8 0

Lines k and n are perpendicular

The slope of line k is -6

Fact: The product of slopes of two perpendicular lines = -1

So the slope of line n = -1 ÷ -6 = 1/6

The correct choice is 'D.'

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Events X and Y are independent. The probability of X occurring is 1/3 . The probability of Y occurring is 1/2 . What is P(X and

Step2247 [10]

For independent events $X,Y$ , $\mathbb P(X\cap Y)=\mathbb P(X)\times\mathbb P(Y)$ .

So

$\mathbb P(X\cap Y)=\dfrac13\times\dfrac12=\dfrac16$

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120 students voted for Jennifer and 180 students voted for Kevin. 60 students voted more for Kevin than for Jennifer.

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3 years ago

What is 3 tenths more than 8.154 ? What is 2 and 2 tenths more than 1.425? Explain please !

Anna11 [10]

8.454 is 3 tenths more than 8.154
3.625 is 2 and 2 tenths more than 1.425

Place values after the decimal point are tenths, hundredths, thousandths, ten thousandths...so on.

So 3 tenths looks like this 0.30 ⇒ 3 is in the tenths place. When you say 3 tenths more, it is a clue that the operation to be done is addition. thus,

8.154
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2 and 2 tenths is like this 2.20 ⇒ 1st 2 is in the ones or units place and the 2nd 2 is in the tenths place. Again it states more than so addition must be done.

1.425
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There are nickels, dimes, quarters in a large piggy bank, for every 2 nickels there are 3 dimes, for every 2 dimes there are 5 q

Alex

There are 80 nickels and 120 dimes and 300 quarters in piggy bank

Solution:

Given that,

For every 2 nickels there are 3 dimes ,

So, ratio of nickel to dime will be 2 : 3

Also for every 2 dimes there are 5 quarters

So, ratio of dime to quarters is 2 : 5

Let us first find the ratio of nickles to dimes to quarters

nickel : dime = 2 : 3

dime : quarters = 2 : 5

$\frac{nickel}{dime} = \frac{2}{3}$

$nickel = \frac{2}{3} dime$

$\frac{dime}{quarter} = \frac{2}{5}$

$quarter = \frac{5}{2}dime$

So,

$nickel : dime : quarter = \frac{2}{3}dime : dime : \frac{5}{2}dime\\\\nickel : dime : quarter = \frac{2}{3} : 1 : \frac{5}{2}\\\\nickel : dime : quarter = 4 : 6 : 15$

Thus nickel : dime : quarters = 4 : 6 : 15

Now, let the number of nickel be 4x

Let the number of dimes be 6x

Let the number of quarters be 15x

From given question,

There are 500 coins in all.

number of nickel + number of dimes + number of quarters = 500

4x + 6x + 15x = 500

25x = 500

x = 20

Thus,

number of nickel = 4x = 4(20) = 80

number of dimes = 6x = 6(20) = 120

number of quarters = 15x = 15(20) = 300

Thus there are 80 nickels and 120 dimes and 300 quarters in piggy bank

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