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3 years ago

Suppose segment PQ has one endpoint at P (0,0). If T (6,3) is a point 3/10 of the way from P to Q, find the coordinates of Q.

Mathematics

1 answer:

mixer [17]3 years ago

3 0

Answer:

Q(20,10)

Step-by-step explanation:

If point T (6,3) is a point 3/10 of the way from P(0,0) to Q(x,y), then

$\overrightarrow {PT}=\dfrac{3}{10}\overrightarrow {PQ}.$

Find the coordinates of the vectors $\overrightarrow {PT},\ \overrightarrow {PQ}:$

$\overrightarrow {PT}=(6-0,3-0)=(6,3);\\ \\\overrightarrow {PQ}=(x-0,y-0)=(x,y).$

Thus,

$(6,3)=\dfrac{3}{10}(x,y),\\ \\(x,y)=\dfrac{10}{3}(6,3)=(20,10).$

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The pth percentile is a value such that approximately a. p percent of the observations are less than the value and (100 - p) per

kogti [31]

Answer:

p percent of the observations are less than the value and (100 - p) percent are more than this value.

Step-by-step explanation:

Given : The pth percentile is a value such that approximately

Solution :

Definition : A percentile is a measure used in statistics indicating the value below which a given percentage of observations in a group of observations falls

So, The pth percentile means p percentage of observations in a group of observations falls bellow the value

So, (100-p) percentage of observations in a group of observations falls above the value

So, Option a is true

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yanalaym [24]

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3 years ago

Select the correct answer from each drop-down menu.

vazorg [7]

Answer:

Step 1: Distribute $-2$ to $5x$ and $8$

Step 2: Subtract from both sides of the equation $6x$

Step 3: Add to both sides of the equation $16$

Step 4: Divide both sides of the equation by $-16$

Step-by-step explanation:

Step 1: Apply the Distributive Property. Then you must distribute $-2$ to $5x$ and $8$

Then:

$-2(5x+8)=14+6x\\\\-10x-16=14+6x$

Step 2: You must apply the Subtraction property of Equality and subtract $6x$ from both sides of the equation. Then:

$-10x-16-6x=14+6x-6x\\\\-16x-16=14$

Step 3: You must apply the Addition property of Equality and add $16$ to both sides of the equation. Then:

$-16x-16+16=14+16\\\\-16x=30$

Step 4: You must apply the Division property of Equality and divide both sides by $-16$ . Then:

$\frac{-16x}{-16}=\frac{30}{-16}\\\\x=\frac{30}{-16}\\\\x=-\frac{15}{8}$

6 0

3 years ago

a woman has $28,000. part is invested for one year in a certificate of deposit paying 7% interest, and the remaining amount in c

alexira [117]

Answer:

Amount invested at 7% = 16000

Amount invested at 9% = 12000

Step-by-step explanation:

Let x be the amount invested at 7% and y be the amount invested at 9%.

Since the total amount invested is $28000, therefore, we can set up the first equation as:

$x+y=28000$

Secondly, we are give that sum of two investments is $2200. Therefore, we can write the second equation as:

$0.07x+0.09y=2200$

Now we need to solve these two equations to get the values of x and y.

First of all, we multiply the second equation with 100 in order to get rid of decimal values.

$(0.07x+0.09y)*100=2200*100\\7x+9y=220000$

Let us use substitution method here. First of all we will solve for y from first equation and plug that into second equation.

$y=28000-x$

$7x+9(28000-x)=220000\\7x+252000-9x=220000\\-2x=-32000\\x=16000$

Therefore, amount invested at 7% is $16000 and amount invested at 9% is 28000-16000=$12000.

7 0

3 years ago