Select all pairs that are solutions

Mathematics

1 answer:

Mashcka [7]3 years ago

4 0

Answer:

the first one and the third and the fourth

Step-by-step explanation:

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Randall Racer runs the 100 meter dash in an average time of 10.4 seconds with a standard deviation of 0.1 seconds. If Randall's

Naddik [55]

Answer:

The answer is 0.68 seconds.

Step-by-step explanation:

Distance -100 meter

Average time - 1 0.4 seconds

Standard deviation - 0.1 seconds.

If Randall's times are normally distributed, we have a 99.7% expectation that his finishing time for his next race will be greater than 0.68 seconds.

Learn more about distance:brainly.com/question/15172156

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4 0

2 years ago

The sum of two consecutive odd integers is at most 123. find the pair with the greatest sum

Monica [59]

The sum of two consecutive odd integers is at most 123. find the pair with the greatest sum

two consecutive odd integers
2x+1,2x+3

The sum of two consecutive odd integers is at most 123
2x+1+2x+3≤123

Solve for x
2x+1+2x+3≤123
4x+4≤123
4x+4-4≤123-4
4x≤119
4/4x≤119/4
x≤119/4
x≤29.25

Substitute any numbers into x that are equal to 29 or less that are consecutive odd integers.
2x+1,2x+3
2 (29)+1,2 (29)+3
58+1,58+3
59,61

Check: 59+61=120

The pair of consecutive odd integers that have a sum of at most 123 are 59 and 61.

3 0

3 years ago

Select the correct answer.

DedPeter [7]

Answer: The correct option is (D) (4, -6).

Step-by-step explanation: Given that the areas of the triangles ADC and DCB are in the ratio 3 : 4.

We are to find the co-ordinates of point C.

From the diagram, we note that

the co-ordinates of point A and B are A(1, -9) and B(8,-2).

So, the length of the line segment AB, calculated by distance formula, is

$AB=\sqrt{(1-8)^2+(-9+2)^2}=\sqrt{49+49}=7\sqrt2.$

Now, area of ΔADC is

$A_{ABC}=\dfrac{1}{2}\times AC\times CD,$

and area of ΔDCB is

$A_{DCE}=\dfrac{1}{2}\times BC\times CD.$

According to the given information, we have

$A_{ADC}:A_{DCB}=3:4\\\\\\\Rightarrow \dfrac{A_{ADC}}{A_{DCE}}=\dfrac{3}{4}\\\\\\\Rightarrow \dfrac{\frac{1}{2}\times AC\times CD}{\frac{1}{2}\times BC\times CD}=\dfrac{3}{4}\\\\\\\Rightarrow \dfrac{AC}{BC}=3:4.$

So, the point C divides the line segment AB internally in the ratio 3 : 4.

We know that

if a point divides a line segment with end-points (a, b) and (c, d) internally in the ration m : n, then its co-ordinates are

$\left(\dfrac{mc+na}{m+n},\dfrac{md+nb}{m+n}\right).$

Since point C divides the line segment AB with end-points A(1, -9) and B(8, -2) internally, so the co-ordinates of point C will be

$\left(\dfrac{3\times 8+4\times 1}{3+4},\dfrac{3\times (-2)+4\times (-9)}{3+4}\right)\\\\\\=\left(\dfrac{28}{7},\dfrac{-42}{7}\right)\\\\\\=(4, -6).$