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2 years ago

Question 4.

Mathematics

1 answer:

Ludmilka [50]2 years ago

5 0

Answer:

9.80 m

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to remind you of the relationship between sides of a right triangle and its angles.

<h3>setup</h3>

The geometry of this problem can be modeled by a right triangle, so these relations apply. We are given an angle and adjacent side, and asked for the opposite side, so the relation of interest is ...

Tan = Opposite/Adjacent

Using the given values, we have ...

tan(24°) = AC/AB = (tree height)/(distance from tree)

tan(24°) = AC/(22 m)

<h3>solution</h3>

Multiplying by 22 m gives ...

tree height = AC = (22 m)·tan(24°) ≈ 9.79503 m

The height of the tree is about 9.80 meters.

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Step-by-step explanation:

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3 years ago

In a college parking lot, the number of ordinary cars is larger than the number of sport utility vehicles by 42.9%. the differen

fenix001 [56]

Let
x = number of common cars
y = number of suvs
we can write the following system of equations
x-y = 12
x = 1.429y
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x-y = 12
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and (1,429-1) = 12
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answer
The number of suvs in the parking lot is 28

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3 years ago

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noname [10]

Answer:

Translation

Step-by-step explanation:

Vertical and horizontal translation

4 0

2 years ago

Solve for m<br><br><br> m<br><br> m<br><br><br><br><br><br><br><br><br><br><br><br> Please help!!!

jarptica [38.1K]

Answer:

m∠ TRS = 60° , m∠ SRW = 120°

Step-by-step explanation:

First, find x

∠TRS = ∠VRW (vertically opposite angles are equal)

x + 40° = 3x

x - 3x = -40

-2x = -40

x = -40/-2

x = 20

m∠ TRS = 60° [x + 40 = 20+40 = 60]

m∠ SRW + m∠ TRS = 180° (linear pair)

m∠ SRW + 60° = 180°

m∠ SRW = 180° - 60°

m∠ SRW = 120°

hope this helps you

6 0

3 years ago

USA Today reports that about 25% of all prison parolees become repeat offenders. Alice is a social worker whose job is to counse

pychu [463]

Answer:

a) $P(X=0)=(4C0)(0.75)^0 (1-0.75)^{4-0}=0.0039$

$P(X=1)=(4C1)(0.75)^1 (1-0.75)^{4-1}=0.0469$

$P(X=2)=(4C2)(0.75)^2 (1-0.75)^{4-2}=0.211$

$P(X=3)=(4C3)(0.75)^2 (1-0.75)^{4-3}=0.422$

$P(X=4)=(4C4)(0.75)^2 (1-0.75)^{4-4}=0.316$

b) $E(X) = np = 4*0.75=3$

c) $Sd(X) =\sqrt{np(1-p)}=\sqrt{4*0.75*(1-0.75)}=0.866$

d) $P(X \geq 3) \geq 0.98$

And the dsitribution that satisfy this is $X\sim Binom(n=9,p=0.75$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=4, p=1-0.25=0.75)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

Part a

$P(X=0)=(4C0)(0.75)^0 (1-0.75)^{4-0}=0.0039$

$P(X=1)=(4C1)(0.75)^1 (1-0.75)^{4-1}=0.0469$

$P(X=2)=(4C2)(0.75)^2 (1-0.75)^{4-2}=0.211$

$P(X=3)=(4C3)(0.75)^2 (1-0.75)^{4-3}=0.422$

$P(X=4)=(4C4)(0.75)^2 (1-0.75)^{4-4}=0.316$

Part b

The expected value is givn by:

$E(X) = np = 4*0.75=3$

Part c

For the standard deviation we have this:

$Sd(X) =\sqrt{np(1-p)}=\sqrt{4*0.75*(1-0.75)}=0.866$

Part d

For this case the sample size needs to be higher or equal to 9. Since we need a value such that:

$P(X \geq 3) \geq 0.98$

And the dsitribution that satisfy this is $X\sim Binom(n=9,p=0.75$

We can verify this using the following code:

"=1-BINOM.DIST(3,9,0.75,TRUE)" and we got 0.99 and the condition is satisfied.

4 0

3 years ago