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lilavasa [31]
3 years ago
7

determine whether y varies directly with x. if so find the constant variation and write the equation x -6, -9, -15; y 2, 3, 5

Mathematics
2 answers:
Reil [10]3 years ago
7 0

Answer:

Direct variation; k = -3; y = -3x  

Step-by-step explanation:

The formula for direct variation is

y = kx     Divide both sides by x

k = y/x

<em>For x = -6, y = 2</em>:

k = -6/2

k = -3

=====

<em>For x = -9, y = 3</em>:

k = -9/3

k = -3

=====

<em>For x = -15, y = 5: </em>

k = -15/5

k = -3

y = -3x

y and x are always in the same ratio, so y varies directly with x.

Effectus [21]3 years ago
5 0

\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}

\bf \begin{array}{|cc|ll} \cline{1-2} x&y\\ \cline{1-2} \stackrel{-3\cdot 2}{-6}&2\\ \stackrel{-3\cdot 3}{-9}&3\\ \stackrel{-3\cdot 5}{-15}&5\\ \cline{1-2} \end{array}~\hspace{5em}\textit{we know that } \begin{cases} y=3\\ x=-9 \end{cases}\implies 3=k(-9) \\\\\\ \cfrac{3}{-9}=k\implies -\cfrac{1}{3}=k\qquad therefore\qquad \blacktriangleright y=-\cfrac{1}{3}x \blacktriangleleft


as you can see above, we can see that "x" can be a product of whatever "y" happens to be, so we know each variable is just a factor away from the other.

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What is the value of x in the equation −6 + x = −1? (5 points)
Mice21 [21]

Answer:

5

Step-by-step explanation:

Add 6 to both sides. The answer is 5.

5 0
3 years ago
Read 2 more answers
Anyone please help!!!
Tanya [424]

Problem 1

Answers:

Percentage of patients that were dogs = 46%

Standard Error = 0.07048404074682

Margin of error for 90% confidence interval = 0.11594624702851

Margin of error for 95% confidence interval = 0.13814871986377

Round the decimal values however you need them

------------

To get the first answer, you add up the numbers given (7,4,5,5,2) and divide that over 50. So 7+4+5+5+2 = 23 which leads to 23/50 = 0.46 = 46%; therefore phat = 0.46 is the sample proportion of dogs.

Use the SE (standard error) formula given to you with phat = 0.46 and n = 50 to get SE = 0.07048404074682

The critical z value at 90% confidence is 1.645; this value is found in your Z table (back of your stats textbook). Multiply the SE value by 1.645 to get 0.07048404074682*1.645 = 0.11594624702851

Also found in your textbook is 1.960 which is the z critical value at 95% confidence. Multiply this with the SE value to get 0.07048404074682*1.960 = 0.13814871986377

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

Problem 2

Answer: Choice B) picking balls from a bin; the 60 randomly selected get chosen for the first bus, while the remaining 60 go to the second bus

-----------

Choice A is fairly vague on what the lower and upper boundaries are. What is the smallest number allowed? What about the largest? This isn't clear so it's possible that we could end up with more positive numbers than negative (eg: if we had an interval -10 < x < 110). So choice A is false. A similar issue shows up with choice D.

Choice B is true. Assuming the selection process is random and not biased, then each ball is equally likely for each selection. The fact that the balls are colored seems to be extra info which I'm not sure why your teacher threw that in there.

Choice C is false because choice B is true

Choice D is false for similar reasons as choice A. It's not clear where we start and where we end. If we had the interval 2 < x < 6 then x could take on the values {3, 4, 5} and we see that picking an odd number is twice as likely than picking an even. In this example, there is bias.

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

Problem 3

Answer: Choice B) Roll a die; each number corresponds to a different class

------------

Choice A is false because choice B being the answer contradicts it

Choice B is true: there are 6 sides on the die, and each side is equally likely to be landed on, so each class is equally likely

Choice C is false because 2*2*2 = 8 represents the number of combos you can have when you flip three coins (one combo being HTH for heads tail heads) but there are 6 classes, not 8

Choice D is false because while we want 6 regions on the spinner. Each region must have the same area; otherwise, one class is weighted heavier than the others making it more likely you select that particular class.


7 0
3 years ago
Read 2 more answers
NEED THIS QUICK, WILL GIVE BRAINLIEST
grin007 [14]

Answer:

The slope is 10.

Step-by-step explanation:

30/3 = 10

50/5 = 10

70/7 = 10

90/9 = 10

The common factor is 10 which is the slope.

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3 years ago
What is There are fourteen whole snack bars on a plate. There are five friends.
AleksandrR [38]

Carl is incorrect. Dave ate a higher fraction of snack bars, by 0.2 snack bars.

Carl had .5 left of a snack bar.

Dave had .3 left of a snack bar.

Tony had .5 left of a snack bar.

Gary had .0 left of a snack bar.

Tryone had .7 left of a snack bar.

If we add the above snack bars, there is a total of two remaining snack bars, meaning they only ate 12 of 14 snack bars.

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3 years ago
$150 for repair, $50 per week after repair to operate. X=#of weeks and y=total cost. Equate using slope-intercept form
Cloud [144]

Answer:

y=150+50x

Step-by-step explanation:

Given data

Repair= $150

weekly charge = $50

X=#of weeks and y=total cost.

Hence the expression in slope-intercept form is

y=150+50x

8 0
3 years ago
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