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Elden [556K]
3 years ago
14

Given that is a standard normal random variable, compute the following probabilities. Round your answers to 4 decimal places. a.

P(0 ≤ z ≤ 0.70) b. P(-1.57 ≤ z ≤ 0) c. P (z > 0.39) d. P(z ≥ -0.33) e. P(z< 2.10) f. P (z≤ -0.63)
Mathematics
1 answer:
Lyrx [107]3 years ago
3 0

Answer:

a)0 .7580     b) 0.4406     c) 0.6554      d) 0.3745     e) 0.9817     f)0.2611

Step-by-step explanation:

All values where obtain from  normal distribution table for Z

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irakobra [83]

<h3><u>Answer:</u></h3>

  • B) 22.32 feet

\quad\rule{300pt}{1pt}

<h3><u>Solution</u><u>:</u></h3>

we are given that , a ladder is placed against a side of building , which forms a right angled triangle . We wre given one side of a right angled triangle ( hypotenuse ) as 23 feet and the angle of elevation as 76 ° . We can find the Perpendicular distance from the top of the ladder go to the ground by using the trigonometric identity:

\qquad\quad\bull ~{\boxed{\bf{ Sin\theta =\dfrac{Perpendicular}{Hypotenuse}}} }~\bull

Here,

  • hypotenuse = 23 feet
  • \theta = 76°
  • Value of Sin\theta = 0.97
  • Perpendicular = ?

\quad\dashrightarrow\quad \sf { sin\theta =\dfrac{P}{H}}

\quad\dashrightarrow\quad \sf { sin76° =\dfrac{P}{23}}

\quad\dashrightarrow\quad \sf { 0.97=\dfrac{P}{23}}

\quad\dashrightarrow\quad \sf {P = 0.97 \times 23 }

\quad\dashrightarrow\quad \sf { P = 22.32}

‎ㅤ‎ㅤ‎ㅤ~<u>H</u><u>e</u><u>n</u><u>c</u><u>e</u><u>,</u><u> </u><u>the </u><u>distance </u><u>from </u><u>the </u><u>top </u><u>of </u><u>the </u><u>ladder </u><u>to </u><u>the </u><u>ground </u><u>is </u><u>2</u><u>2</u><u>.</u><u>3</u><u>2</u><u> </u><u>feet </u><u>!</u>

\rule{300pt}{2pt}

4 0
3 years ago
Which algebraic rule describes the transformation of rectangle RSTU to R'S'T'U'?
kondaur [170]

Did this question come with a photo?

3 0
3 years ago
Derivative of these questions<br>​
shtirl [24]

Answer:  \bold{y'=\dfrac{1}{2(a-b)^2}\bigg(\dfrac{1}{\sqrt{x+a}}+\dfrac{1}{\sqrt{x+b}}\bigg)}

<u>Step-by-step explanation:</u>

y=\dfrac{1}{\sqrt{x+a}-\sqrt{x+b}}\\\\\\\text{Rationalize the denominator:}\\y=\dfrac{1}{\sqrt{x+a}-\sqrt{x+b}}\bigg(\dfrac{\sqrt{x+a}+\sqrt{x+b}}{\sqrt{x+a}+\sqrt{x+b}}\bigg)\\\\\\y=\dfrac{\sqrt{x+a}+\sqrt{x+b}}{x+a-x-b}\\\\\\y=\dfrac{\sqrt{x+a}+\sqrt{x+b}}{a-b}\\\\\\\text{Apply the derivative (derivative of the numerator (top) divided by the}\\\text{denominator (bottom) squared).}

\text{Derivative of }\sqrt{x+a}\quad \rightarrow \quad (x+a)^{\frac{1}{2}}\quad = \quad \dfrac{1}{2}(x + a)^{-\frac{1}{2}}\\\\\text{Derivative of }\sqrt{x+b}\quad \rightarrow \quad (x+b)^{\frac{1}{2}}\quad = \quad \dfrac{1}{2}(x + b)^{-\frac{1}{2}}\\\\\\\text{Derivative of}\ \dfrac{\sqrt{x+a}+\sqrt{x+b}}{a-b}:\\\\= \dfrac{\dfrac{1}{2}(x + a)^{-\frac{1}{2}}+\dfrac{1}{2}(x + b)^{-\frac{1}{2}}}{(a-b)^2}

\text{Factor out }\dfrac{1}{2}\ \text{from the numerator:}\\\\\dfrac{(x+a)^{-\frac{1}{2}}+(x+b)^{-\frac{1}{2}}}{2(a-b)^2}\\\\\\\text{Move the terms with negative exponents to the denominator:}\\\\=\dfrac{1}{2(a-b)^2}\bigg(\dfrac{1}{\sqrt{x+a}}+\dfrac{1}{\sqrt{x+b}}\bigg)

3 0
4 years ago
X^3 + 2x^2 – 24x<br><br> ^ <br> write the polynomial in factored form
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Answer:

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Step-by-step explanation:

They all have x in it, which means we can factor out x first.

x(x^2 + 2x -24)

Now we can factor out the inside doing algebra.

Since 6 multiplied by -4 gives us -24 and adding them gives us 2, 6 and -4 works. This means that we can factor out (x+6) and (x-4).

We still have to multiply the x from the beginning, giving us a final equation of

x(x+6)(x-4).

8 0
3 years ago
Dylan opened a credit card account with $600.00 of available credit. Now that he has made some purchases, Dylan's account only h
Dahasolnce [82]

Answer:

26% decrease of the amount

Step-by-step explanation:

8 0
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