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romanna [79]
3 years ago
13

In ΔDEF, e = 2.7 inches, ∠F=49° and ∠D=58°. Find the length of f, to the nearest 10th of an inch.

Mathematics
1 answer:
Anton [14]3 years ago
7 0

Answer:2.1

Step-by-step explanation:

\text{Draw a diagram:}

Draw a diagram:

D

E

F

e = 2.7

f = ?

49°

58°

\text{A.S.A.}\rightarrow \text{Law of Sines}

A.S.A.→Law of Sines

\frac{a}{\sin A}=\frac{b}{\sin B}

sinA

a

​

=

sinB

b

​

\text{Find other angle:}

Find other angle:

\angle E=180-49-58=73^{\circ}

∠E=180−49−58=73

∘

D

E

F

e = 2.7

f = ?

49°

58°

73°

\frac{f}{\sin 49}=\frac{2.7}{\sin 73}

sin49

f

​

=

sin73

2.7

​

f=\frac{2.7\sin 49}{\sin 73} \approx 2.131 \approx 2.1

f=

sin73

2.7sin49

​

≈2.131≈2.1

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Step-by-step explanation:

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2 years ago
Determine the value of x and y in the following systems of equations5x-2y=4 ; -2x+y=2.
V125BC [204]

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Step-by-step explanation:

Given

5x-2y=4-------1

Second Equation

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Step-by-step explanation:

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The length of a rectangular field is 4 meters less than 5 times the breadth of the hall. What is the length, if the breadth is b
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2 years ago
In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal dist
Tcecarenko [31]

Answer:

a. 0.7291

b. 0.9968

c. 0.7259

Step-by-step explanation:

a. np and n(1-p) can be calculated as:

np=23\times 0.48\\\\=11.04\\\\n(1-p)=23(1-0.52)\\\\=11.96

#Both np and np(1-p) are greater than 5, hence, normal approximation is most appropriate:

\mu_x=11.04\\\\\sigma^2=np(1-p)=0.48\times 0.52\times 23=5.7408

#Define Y:

Y~(11.04,5.7408)

P(X\leq 12)\approx P(Y\leq 12.5)\\\\P(Z\leq \frac{(12.5-11.04)}{\sqrt{5.7408}})=\\\\=1-0.2709\\\\=0.7291

Hence, the probability of 12 or fewer is 0.8291

b. The  probability that 5 or more fish were caught.

#Using normal approximation:

P(X \geq 5) \approx P(Y \geq 4.5) = P(Z \geq\frac{ (4.5-11.04)}{\sqrt{(5.7408)}})\\\\=1-0.0032\\\\=0.9968

Hence, the probability of catching 5+ is 0.9968

c. The probability of between 5 and 12 is calculated as;

-From b above P(X\geq 5)=0.9968 and a ,P(X\leq 12)=0.7291

P(5\leq X\leq 120\approx P(4.5\leq Y\leq  12.5)\\\\=0.7291-(1-0.9968)\\\\=0.7259

Hence, the probability of between 5 and 12 is 0.7259

4 0
3 years ago
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