name the set of 6 consecutive integers starting with -3 put the set in braces and put commas between the elements of the set

Write, in slope intercept form, the equation of the line that passes through (8, -9) and has a slope of -5/4.

dezoksy [38]

Answer:

The equation in the slope-intercept form will be:

$y=-\frac{5}{4}x+1$

Step-by-step explanation:

Given

slope = m = -5/4

point = (8, -9)

As we know that the equation of a line in point-slope form is

$y-y_1=m\left(x-x_1\right)$

substituting the values m = -5/4 and point = (8, -9)

$y-\left(-9\right)=\frac{-5}{4}\left(x-8\right)$

$y+9=\frac{-5}{4}\left(x-8\right)$

Writing the equation in slope-intercept form

$y=mx+b$

where m is the slope, and b is the y-intercept

so the equation of the line in slope-intercept form becomes

$y+9=\frac{-5}{4}\left(x-8\right)$

subtract 9 from both sides

$y+9-9=\frac{-5}{4}\left(x-8\right)-9$

$y=-\frac{5}{4}x+1$

Therefore, the equation in the slope-intercept form will be:

$y=-\frac{5}{4}x+1$

7 0

3 years ago

A business bought a lot of 2,500 lamps for 50,000 dollars and wants to sell them at 15 percent profit how much should each lamp

aev [14]

50,000 / 2500 = 20....he bought them for 20 bucks a piece. So if he wants to sell them at 15% profit, he would sell them for 20 + 0.15(20) = $ 23 bucks.

A 15% profit of 50,000 dollars is 0.15(50,000) = 7500. Plus the 50 grand spent totals 57500. So they want to make a $ 7500 profit. Selling 2500 lamps at $ 23 per lamp (2500 x 23 = 57500) makes them their profit.

I should just shut up now...answer is $ 23 per lamp

4 0

4 years ago

the mathematics Department of a college has 11 male professors 12 female professors 9 male teaching assistants and 12 female tea

Marta_Voda [28]

Answer:

P(teaching assistant or a female) = 1 - P(professor and male) = 1 - 11/44 = 1 - 0.25 = 0.75

Make a Contingency_table

7 0

3 years ago

Drag the tiles to the boxes to form correct pairs. Find the probability for the given situations, and then match the situations

frozen [14]

Answer:

3 (die)
4 (slips)
6 (spinner)
5 (ace)

Step-by-step explanation:

Josie rolls a six-sided die 18 times. What is the estimated number of times she rolls a two? 3 = (1/6)(18)

Slips of paper are numbered 1 through 10. If one slip is drawn and replaced 40 times, how many times should the slip with number 10 appear? 4 = (1/10)(40)

A spinner consists of 10 equal- sized spaces: 2 red, 3 black, and 5 white. If the spinner is spun 30 times, how many times should it land on a red space? 6 = (2/10)(30)

A card is picked from a standard deck of playing cards 65 times and replaced each time. About how many times would the card drawn be an ace? 5 = (4/52)(65)

_____

The probability of a given event is the number of ways it can occur divided by the number of possibilities. For example, a 2 is one of 6 numbers on a die, so we expect its probability of showing up to be 1/6. The expected number of times it will show up in 18 rolls of the die is (1/6)(18) = 3.

7 0

3 years ago

Consider the following.

san4es73 [151]

Answer:

Anything in the form x = pi+k*pi, for any integer k

These are not removable discontinuities.

============================================================

Explanation:

Recall that tan(x) = sin(x)/cos(x).

The discontinuities occur whenever cos(x) is equal to zero.

Solving cos(x) = 0 will yield the locations when we have discontinuities.

This all applies to tan(x), but we want to work with tan(x/2) instead.

Simply replace x with x/2 and solve for x like so

cos(x/2) = 0

x/2 = arccos(0)

x/2 = (pi/2) + 2pi*k or x/2 = (-pi/2) + 2pi*k

x = pi + 4pi*k or x = -pi + 4pi*k

Where k is any integer.

If we make a table of some example k values, then we'll find that we could get the following outputs:

x = -3pi
x = -pi
x = pi
x = 3pi
x = 5pi

and so on. These are the odd multiples of pi.

So we can effectively condense those x equations into the single equation x = pi+k*pi

That equation is the same as x = (k+1)pi

The graph is below. It shows we have jump discontinuities. These are <u>not</u> removable discontinuities (since we're not removing a single point).

3 0

3 years ago