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3 years ago

Find an equation for the line perpendicular to 4x+12y=72 and goes through the point (-9,6)

Mathematics

1 answer:

il63 [147K]3 years ago

7 0

Answer:

Step-by-step explanation:

Given the equation

4x+12y=72

The equation of a line can written as

y=mx+c

Where m is the slope

And c is the intercept on y axis

Then, we need to write the equation given in the form of equation of a line (y=mx+c), by making y subject of the formula

4x+12y=72

12y=-4x+72

Divide through by 12

y=-4x/12 + 72/12

y=-⅓x+6

Then, comparing with equation of a line shows that

m=-⅓ and c=6

So we need to get another linen that is perpendicular to this line and passes through the point (-9,6)

The slope of the line perpendicular to another line is given as

m1=-1/m2

Then, m1=-1÷-⅓

Then, the slope of the perpendicular line is 3

Then, m=3

So apply this to equation of the line

y=mx+c

Then, y=3x+c

So to know c, we will insert the point given(-9,6), x=-9 and y=6

y=3x+c

6=3(-9)+c

6=-27+c

Then, c=6+27

c=33

Then, the equation of line becomes

y=3x+33

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Nata [24]

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2 years ago

Set up and solve the following using dimensional analysis.

Softa [21]

1). Multiply (5400 inches) by (1 foot / 12 inch) then by (1 mile / 5280 foot).

(See explanation at the bottom)

= (5400 inch) x (1 foot / 12 inch) x (1 mile / 5280 foot)

= (5400 x 1 x 1 / 12 x 5280) (inch - foot - mile / inch - foot)

= 0.0852 mile

2). Multiply (16 week) by (7 day/week) then by (24 hour/day)
then by (60 minute/hour) then by (60 sec/minute).

3). Multiply (54 yards) by (3 foot/yard) then by (1 meter/3.28 foot)
and then by (1000 mm/meter)

4). Multiply (36 cm/second) by (3600 second/hour) then by (1 meter/100 cm)
then by (1 mile/1609.3 meter).

5). Look up how many grams in a pound ('P')
Look up how many mL in a gallon ('G')

Multiply (1.09 g/mL) by ( 1 pound/ P gram) then by (1 gallon/ G mL)

6). Multiply (32 foot/sec) by (1 meter / 3.28 foot) then by (60 sec/minute).

Each time I told you to multiply by something, it was always a fraction
where the numerator and denominator are equal, like (60 seconds/minute)
or (1 foot / 12 inch). Since the top and bottom of the fraction are equal, the
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it only changes the units ... that's what this whole exercise is about.
When you multiply, KEEP the units in the product, and then, after you multiply, you can 'cancel' units out of the top and bottom of the product.
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4 0

3 years ago

A sanitation department is interested in estimating the mean amount of garbage per bin for all bins in the city. In a random sam

soldi70 [24.7K]

Answer:

a) $52.8-2.02\frac{3.9}{\sqrt{40}}=51.554$

b) $52.8+2.02\frac{3.9}{\sqrt{40}}=54.046$

c) $52.8-2.71\frac{3.9}{\sqrt{40}}=51.129$

d) $52.8+2.71\frac{3.9}{\sqrt{40}}=54.471$

e) Yes, depends of the confidence level.

At 95 % of confidence the value 54.1985 pounds is not included on the interval. At 5% of significance the statement is FALSE.

At 99 % of confidence the value 54.1985 pounds is included on the interval. So at 1% of significance the statement is TRUE.

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X =52.8$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=3.9 represent the sample standard deviation

n=40 represent the sample size

a) What is the lower limit of the 95% interval? Give your answer to three decimal places

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the mean and the sample deviation we can use the following formulas:

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=40-1=39$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,39)".And we see that $t_{\alpha/2}=2.02$

Now we have everything in order to replace into formula (1):

$52.8-2.02\frac{3.9}{\sqrt{40}}=51.554$

b) What is the upper limit of the 95% interval? Give your answer to three decimal places

$52.8+2.02\frac{3.9}{\sqrt{40}}=54.046$

So on this case the 95% confidence interval would be given by (51.554;54.046)

c) What is the lower limit of the 99% interval? Give your answer to three decimal places

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,39)".And we see that $t_{\alpha/2}=2.71$

Now we have everything in order to replace into formula (1):

$52.8-2.71\frac{3.9}{\sqrt{40}}=51.129$

d) What is the upper limit of the 99% interval? Give your answer to three decimal places

$52.8+2.71\frac{3.9}{\sqrt{40}}=54.471$

So on this case the 99% confidence interval would be given by (51.129;54.471)

e) Consider the claim that the mean amount of garbage per bin is 54.1985 pounds. Is the following statement true or false? The decision about the claim would depend on whether we use a 95% or 99% confidence interval: True/False

Yes, depends of the confidence level.

At 95 % of confidence the value 54.1985 pounds is not included on the interval. At 5% of significance the statement is FALSE.

At 99 % of confidence the value 54.1985 pounds is included on the interval. So at 1% of significance the statement is TRUE.

3 0

4 years ago

Britney read a total of 10 books over 2 months. After belonging to the book club for 3 months, how many books will Britney have

agasfer [191]

Answer:

she will have read 15 books in all

Step-by-step explanation:

if she has read 10 books in 2 months that means she has read 5 books each month, because 10 ÷ 2 = 5.

so if another month passes by that means she reads another 5 books.

10 + 5 = 15

so in total britney has read 15 books in total

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3 years ago

I need help with this thank you

kari74 [83]

1= 5/4

2= -103/40

1st explanation

-12/15 + 4/5 + 7/12

-8 + 48 + 35/60

75/60

5/4

2nd explanation

-1 3/5 + 5 1/8 - 6 1/10

-8/5 + 41/8 + 61/10

- 64 + 205 + 244 / 40

-103/140

-103 / 40

8 0

3 years ago