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2 years ago

Find ST if S(-3,10) and T(-2,3)

Mathematics

2 answers:

Aleonysh [2.5K]2 years ago

6 0

Answer:

ST = 7.07 units

Step-by-step explanation:

* Lets explain how to find the length of a segment

- The length of a segment whose endpoints are $(x_{1},y_{1})$

and $(x_{2},y_{2})$ can be founded by the rule of the distance

$d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$

* Lets solve the problem

∵ The line segment is ST

∵ S is (-3 , 10)

∵ T is (-2 , 3)

- Assume that S is $(x_{1},y_{1})$ and T is $(x_{2},y_{2})$

∴ $x_{1}=-3$ and $x_{2}=-2$

∴ $y_{1}=10$ and $y_{2}=3$

- By using the rule above

∴ $ST=\sqrt{(-2--3)^{2}+(3-10)^{2}}$

∴ $ST=\sqrt{(1)^{2}+(-7)^{2}}$

∴ $ST=\sqrt{1+49}$

∴ $ST=\sqrt{50}$

∴ ST = 7.07 units

Oksana_A [137]2 years ago

5 0

Answer:

7.07 units

Step-by-step explanation:

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VladimirAG [237]

Answer:

$n=\frac{0.4(1-0.4)}{(\frac{0.05}{1.96})^2}=368.79$

n=369

Step-by-step explanation:

1) Notation and definitions

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

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The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

2) Solution tot he problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

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The margin of error for the proportion interval is given by this formula:

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And on this case we have that $ME =\pm 0.05$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

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And replacing into equation (b) the values from part a we got:

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8 0

1 year ago

Sometimes a change of variable can be used to convert a differential equation y′=f(t,y) into a separable equation. One common ch

enot [183]

Answer:

$y=\frac{-7t^2+22t-7}{7t-22}$

Step-by-step explanation:

We are given that

Initial value problem

$y'=(t+y)^2-1$ , y(3)=4

Substitute the value $z=t+y$

When t=3 and y=4 then

z=3+4=7

$y'=z^2-1$

Differentiate z w.r.t t

Then, we get

$\frac{dz}{dt}=1+y'$

$z'=1+z^2-1=z^2$

$z^{-2}dz=dt$

Integrate on both sides

$-\frac{1}{z}dz=t+C$

$z=-\frac{1}{t+C}$

Substitute t=3 and z=7

Then, we get

$7=-\frac{1}{3+C}$

$21+7C=-1$

$7C=-1-21=-22$

$C=-\frac{22}{7}$

Substitute the value of C then we get

$z=-\frac{1}{t-\frac{22}{7}}$

$z=\frac{-7}{7t-22}$

$y=z-t$

$y=\frac{-7}{7t-22}-t$

$y=\frac{-7-7t^2+22t}{7t-22}$

$y=\frac{-7t^2+22t-7}{7t-22}$

8 0

2 years ago

A trapezoid has a base of 4.5 inches, a height of 6 inches, and an area of 21 square inches. The equation below can be used to d

Troyanec [42]

Answer:

$b_2 = -2.5$

Step-by-step explanation:

Given

$\frac{1}{2}(4.5 + b_2) * 6 = 21$

Required

Determine the value of T

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Multiply both sides by 2

$2 * \frac{1}{2}(4.5 + b_2) * 6 = 21 * 2$

$(4.5 + b_2) * 6 = 42$

Divide through by 6

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$4.5 + b_2 = 7$

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2 years ago

Alannah has two lengths of ribbon.

ankoles [38]

Answer:

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Step-by-step explanation:

Alannah has two ribbons one length is 36cm and other is 45cm.

It asked to find shorter length of ribbons that each cut into equal pieces with out no ribbon left over.

So, let's find greatest common factor for both 36 and 45.

Let's prime factor each number

36= 2*2*3*3

45= 3*3*5

So, GCF is product of common factors for both numbers.

GCF= 3*3 =9

So, longest possible length for each of the shorter lengths of ribbon is 9 cm.

Learn more about GCF in brainly.com/question/21612147.

7 0

1 year ago

Interpret the meaning of the point (9, 378).

lions [1.4K]

Answer:

it means the the line falls on 9 on the x-axis

and intersects at 378 on the y-axis

Step-by-step explanation:

hope that helped

7 0

2 years ago