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3 years ago

The scatter plot shows the time spent watching TV, x, and the time spent doing homework, y, by each of 24 students last week.

Mathematics

1 answer:

evablogger [386]3 years ago

8 0

Answer:

y = - 0.833 + 29.5

y = 17

Step-by-step explanation:

Drawing a best fit line through the data points:

The approximate regression model would have an intercept of about 29.5

The slope = Rise / Run = (y2 - y1) / (x2 - x1)

The slope = (5 - 25) / (27 - 3) = 20 / 24 = -0.8333

The regression equation is thus :

y = mx + c

m = slope ; c = intercept

y = - 0.833 + 29.5

x = 15

y = - 0.833(15) + 29.5

y = -12.5 + 29.5

y = 17

Approximately 17 hours watching TV

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Expand (2 + a)9 using Pascal’s triangle.

Natalija [7]

Answer:

Step-by-step explanation:

The Pascal triangle is used to determine the coefficients of the terms when we expand the expression.

1 $(A + B) ^ 0$ = 1

1 1 $(A +B ) ^ 1 = 1A + 1B$

1 2 1 $(A+ B) ^ 2 = 1A^2 + 2 AB + 1B^2$

By extending the triangle, you will get the 9th row, which is your expression, of the coefficients. that is

1 9 36 84 126 126 84 36 9 1

Now, fill in AB in the gaps.

1AB + 9 AB + 36AB + 84AB + 126AB + 126AB +84AB + 36AB + 9AB + 1AB

Next, you need to go from the left to fill out the exponent of A and it will go down from 9 (the exponent of the whole thing) . That is

$1A^9B+9A^8B+36A^7B+84A^6B+126A^5B+126A^4B+84A^3B+36A^2B+9A^1B+1A^0B$

Next will be the exponent of B. this time, you go from the right and do the same with A. You can go from the left also, but go up from 0 to 9 for the exponent of B

$1A^9B^0+9A^8B^1+36A^7B^2+84A^6B^3+126A^5B^4+126A^4B^5+84A^3B^6+36A^2B^7+9A^1B^8+1A^0B^9$

The last step is just to simplify the A^0=1 and B^0 =1 at the first and the last terms.

$A^9+9A^8B^1+36A^7B^2+84A^6B^3+126A^5B^4+126A^4B^5+84A^3B^6+36A^2B^7+9A^1B^8+B^9$

Hope you can learn the method

5 0

3 years ago

Graph by using the slope and the y intercept.

Mashutka [201]

1. a) equation of the line :

$y = \dfrac{2}{5}x - 7$

y - intercept = -7

so, it will pass through point (0, -7)

and if we plug the value of x as 5, we get

$y = (\dfrac{2}{5} \times 5) - 7$

$y = 2 - 7$

$= - 5$

so, it will pass through point (5, -5) too

now, just plot the points (0 , -7) and (5 , -5) and join them.

2. b) equation of line is :

$y = - 3x + 5$

here, y - intercept = 5

so the line passes through point (0 , 5)

now, Plugging the value of x = 1 we get :

$y =( - 3 \times 1) + 5$

$y = - 3 + 5$

$y = 2$

so, the given line passes through point (1 , 2)

plotting the points, we can get our required line.

6 0

3 years ago

Write x^2 − 8x + 13 = 0 in the form (x −

padilas [110]

If you would like to write the equation in the above form, you can calculate this using the following steps:

x^2 - 8x + 13 = 0
(x - 4)^2 = x^2 - 8x + 16
(x - 4)^2 - 3 = 0
(x - 4<span>)^2 = 3
</span>
The correct result would be (x - 4<span>)^2 = 3.</span>

4 0

3 years ago

What is 9/20 and 6/11 in decimal form

Rama09 [41]

Answer:

$\frac{9}{20}$ = 0.45

$\frac{6}{11}$ = 0.54 repeating

Step-by-step explanation:

You can solve these easily with a calculator.

$\frac{9}{20}$ = 0.45

$\frac{6}{11}$ = 0.54 repeating

8 0

3 years ago

What is the y-coordinate of the solution for the system of equations?

8_murik_8 [283]

First equation is: x - y = 12
x = 12 + y

Now, substitute this in 2nd equation,
2x - 3y = 27
2(12+y) - 3y = 27
24 + 2y - 3y = 27
-y = 27 - 24
y = -3

In short, Your Answer would be -3

Hope this helps!

5 0

3 years ago