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3 years ago

Slope= 1/5, y-intercept=1

Mathematics

1 answer:

const2013 [10]3 years ago

6 0

Y = mx + b
y = 1/5x + 1

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A jacket with an original price of $67.80 is discounted 10%. What is the sale price?

Advocard [28]

I’m pretty sure it is $61.02

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3 years ago

A ball is thrown into the air by a baby alien on a planet in the system of Alpha Centauri with a velocity of 30 ft/s. Its height

Crank

Answer:

a) h = 0.1: $\bar v = -11\,\frac{ft}{s}$ , h = 0.01: $\bar v = -10.1\,\frac{ft}{s}$ , h = 0.001: $\bar v = -10\,\frac{ft}{s}$ , b) The instantaneous velocity of the ball when $t = 2\,s$ is $-10$ feet per second.

Step-by-step explanation:

a) We know that $y = 30\cdot t -10\cdot t^{2}$ describes the position of the ball, measured in feet, in time, measured in seconds, and the average velocity ( $\bar v$ ), measured in feet per second, can be done by means of the following definition:

$\bar v = \frac{y(2+h)-y(2)}{h}$

Where:

$y(2)$ - Position of the ball evaluated at $t = 2\,s$ , measured in feet.

$y(2+h)$ - Position of the ball evaluated at $t =(2+h)\,s$ , measured in feet.

$h$ - Change interval, measured in seconds.

Now, we obtained different average velocities by means of different change intervals:

$h = 0.1\,s$

$y(2) = 30\cdot (2) - 10\cdot (2)^{2}$

$y (2) = 20\,ft$

$y(2.1) = 30\cdot (2.1)-10\cdot (2.1)^{2}$

$y(2.1) = 18.9\,ft$

$\bar v = \frac{18.9\,ft-20\,ft}{0.1\,s}$

$\bar v = -11\,\frac{ft}{s}$

$h = 0.01\,s$

$y(2) = 30\cdot (2) - 10\cdot (2)^{2}$

$y (2) = 20\,ft$

$y(2.01) = 30\cdot (2.01)-10\cdot (2.01)^{2}$

$y(2.01) = 19.899\,ft$

$\bar v = \frac{19.899\,ft-20\,ft}{0.01\,s}$

$\bar v = -10.1\,\frac{ft}{s}$

$h = 0.001\,s$

$y(2) = 30\cdot (2) - 10\cdot (2)^{2}$

$y (2) = 20\,ft$

$y(2.001) = 30\cdot (2.001)-10\cdot (2.001)^{2}$

$y(2.001) = 19.99\,ft$

$\bar v = \frac{19.99\,ft-20\,ft}{0.001\,s}$

$\bar v = -10\,\frac{ft}{s}$

b) The instantaneous velocity when $t = 2\,s$ can be obtained by using the following limit:

$v(t) = \lim_{h \to 0} \frac{x(t+h)-x(t)}{h}$

$v(t) = \lim_{h \to 0} \frac{30\cdot (t+h)-10\cdot (t+h)^{2}-30\cdot t +10\cdot t^{2}}{h}$

$v(t) = \lim_{h \to 0} \frac{30\cdot t +30\cdot h -10\cdot (t^{2}+2\cdot t\cdot h +h^{2})-30\cdot t +10\cdot t^{2}}{h}$

$v(t) = \lim_{h \to 0} \frac{30\cdot t +30\cdot h-10\cdot t^{2}-20\cdot t \cdot h-10\cdot h^{2}-30\cdot t +10\cdot t^{2}}{h}$

$v(t) = \lim_{h \to 0} \frac{30\cdot h-20\cdot t\cdot h-10\cdot h^{2}}{h}$

$v(t) = \lim_{h \to 0} 30-20\cdot t-10\cdot h$

$v(t) = 30\cdot \lim_{h \to 0} 1 - 20\cdot t \cdot \lim_{h \to 0} 1 - 10\cdot \lim_{h \to 0} h$

$v(t) = 30-20\cdot t$

And we finally evaluate the instantaneous velocity at $t = 2\,s$ :

$v(2) = 30-20\cdot (2)$

$v(2) = -10\,\frac{ft}{s}$

The instantaneous velocity of the ball when $t = 2\,s$ is $-10$ feet per second.

8 0

3 years ago

Which of the following events are dependent?

cestrela7 [59]

Answer:

A. Archie and Harris take turns picking yellow- or purple-colored chips from a dish.

C. Lily draws a marble from a bag filled with red and blue marbles, places her selection in a separate bag, and draws from the original bag of marbles again.

Step-by-step explanation:

Two events will be dependent if the first event influences the probability of the second event. If the first event takes something and doesn't put it back, that means the second event can't pull the same roll and the total pool of items changed.

A. Beth and Corrie take turns picking a card at random and recording each outcome. They replace the selected card at the bottom of the pile after each turn.

This option put replace the card, so it is independent

B. Archie and Harris take turns picking yellow- or purple-colored chips from a dish.

No replacement, the event should be dependent.

C. Jared pulls out a sock from the laundry basket containing white and black socks, puts it back, and then draws another sock at random.

This option put back the pulls, so it is independent

D. Lily draws a marble from a bag filled with red and blue marbles, places her selection in a separate bag, and draws from the original bag of marbles again.

No replacement for the marble taken, each draws probability should depend on the earlier draw result.

8 0

3 years ago

I need help on the first question please will mark brainiest

Whitepunk [10]

Answer:

D. $2^{18}$

Step-by-step explanation:

The expression is: $(2^{6}) ^{3}$ * $2^{0}$

For the first term: When a term with an exponent is inside parentheses with another exponent on the outside, the two exponents are multiplied by each other:

6 * 3 = 18

Now the expression looks like this: $2^{18}$ * $2^{0}$

Any number to the power of zero is 1.

So the equation now looks like this: $2^{18}$ * 1

After you multiply the two terms, you end up with $2^{18}$ .

4 0

3 years ago

Read 2 more answers

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ch4aika [34]

Answer:

57120

Step-by-step explanation:

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2 years ago