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3 years ago

Which point represents −238 on the number line?

Mathematics

1 answer:

Hunter-Best [27]3 years ago

5 0

Answer:

Step-by-step explanation:

Draw a line and take a point O(zero) in the middle.Divide both sides in equal distances.

Every positive integer lies to the right of O and every negative integer lies to the left of O.

-238 is 238 units away from 0(to the left) = -283

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Stells [14]

Answer:

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3 years ago

First-order linear differential equations

kkurt [141]

Answer:

$(1)\ logy\ =\ -sint\ +\ c$

$(2)\ log(y+\dfrac{1}{2})\ =\ t^2\ +\ c$

Step-by-step explanation:

1. Given differential equation is

$\dfrac{dy}{dt}+ycost = 0$

$=>\ \dfrac{dy}{dt}\ =\ -ycost$

$=>\ \dfrac{dy}{y}\ =\ -cost dt$

On integrating both sides, we will have

$\int{\dfrac{dy}{y}}\ =\ \int{-cost\ dt}$

$=>\ logy\ =\ -sint\ +\ c$

Hence, the solution of given differential equation can be given by

$logy\ =\ -sint\ +\ c.$

2. Given differential equation,

$\dfrac{dy}{dt}\ -\ 2ty\ =\ t$

$=>\ \dfrac{dy}{dt}\ =\ t\ +\ 2ty$

$=>\ \dfrac{dy}{dt}\ =\ 2t(y+\dfrac{1}{2})$

$=>\ \dfrac{dy}{(y+\dfrac{1}{2})}\ =\ 2t dt$

On integrating both sides, we will have

$\int{\dfrac{dy}{(y+\dfrac{1}{2})}}\ =\ \int{2t dt}$

$=>\ log(y+\dfrac{1}{2})\ =\ 2.\dfrac{t^2}{2}\ + c$

$=>\ log(y+\dfrac{1}{2})\ =\ t^2\ +\ c$

Hence, the solution of given differential equation is

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4 years ago

In the length of each leg of an isosceles triangle is 13 and the base is 24, the length of the altitude to the base is

Likurg_2 [28]

Answer:

<h2>altitude = 5</h2>

Step-by-step explanation:

Look at the picture.

Use the Pythagorean theorem:

$a^2+12^2=13^2$

$a^2+144=169$ <em>subtract 144 from both sides</em>

$a^2=25\to a=\sqrt{25}\\\\a=5$

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3 years ago

(20 points) A statistics practitioner calculated the mean and the standard deviation from a sample of 400. They are x = 98 and s

Nimfa-mama [501]

Answer:

The P-value is 0.0234.

Step-by-step explanation:

We are given that a statistics practitioner calculated the mean and the standard deviation from a sample of 400. They are x = 98 and s = 20.

Let = population mean.

So, Null Hypothesis, : = 100 {means that the population mean is equal to 100}

Alternate Hypothesis, : > 100 {means that the population mean is more than 100}

The test statistics that will be used here is One-sample t-test statistics because we're yet to know about the population standard deviation;

T.S. = ~

where, = sample mean = 98

s = sample standard deviation = 20

n = sample size = 400

So, the test statistics = ~

= -2

The value of t-test statistics is -2.

Now, the P-value of the test statistics is given by;

P( < -2) = 0.0234 {using the t-table}

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Answer:

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