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liq [111]
2 years ago
8

Kayla wants to find the width, AB, of a river. She walks along the edge of the river 65 ft and marks point C. Then she walks 25

ft further and marks point D. She turns 90° and walks until her location, point A, and point C are collinear. She marks point E at this location, as shown.
(a) Can Kayla conclude that Δ and Δ are similar? Why or why not?

(b) Suppose DE = 15 ft. What can Kayla conclude about the width of the river?

Mathematics
1 answer:
AlladinOne [14]2 years ago
8 0

Answer:

Part A) The triangles ABC and EDC are similar by AAA, because the three internal angles are equal in both triangles

Part B) The width of the river is about 39\ ft

Step-by-step explanation:

we know that

If two triangles are similar, then the ratio of its corresponding sides is equal and its corresponding angles are congruent

Part A) we know that

In this problem , triangles ABC and CDE are similar by AAA, because its corresponding angles are congruent

so

m<DCE=m<ACB -----> by vertical angles  

m<EDC=m<ABC -----> is a right angle

m<DEC=m<CAB -----> the sum of the internal angles must be equal to 180 degrees

Part B) we know that

The triangles ABC and EDC are similar -------> see Part A

therefore

\frac{BC}{DC}=\frac{AB}{DE}

substitute the values and solve for AB

\frac{65}{25}=\frac{AB}{15}

AB=15*(\frac{65}{25})=39\ ft

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Given the following triangle, if b = 9 and B = 15°, find a.
NeX [460]
The picture in the attached figure

we know that
Applying the law of sines
b/sin B=a/sin A------> a=b*sin A/sin B
b=9
B=15°
A=180-(90+15)-----> A=75°
a=?
a=b*sin A/sin B-----> a=9*sin 75/sin 15----> a=33.59 units

the answer is
33.59 units


6 0
3 years ago
The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 46 o
meriva

Answer:

(a) 68% of the widget weights lie between <u>43 ounces</u> and <u>49 ounces</u>.

(b) The percentage of the widget weights lie between 43 and 87 ounces is 15.87%.

(c) The percentage of the widget weights lie below 76 is 100%.

Step-by-step explanation:

Let <em>X</em> = weight of widgets manufactured by Acme Company.

The distribution of the random variable <em>X</em> is, N (<em>μ </em>= 46, <em>σ</em>²<em> </em>=<em> </em>3²).

According to the Empirical Rule in a normal distribution with mean <em>µ</em> and standard deviation <em>σ</em>, nearly all the data will fall within 3 standard deviations of the mean. The empirical rule can be broken into three parts:

  • 68% data falls within 1 standard deviation of the mean.                       That is P (µ - σ ≤ X ≤ µ + σ) = 0.68.
  • 95% data falls within 2 standard deviations of the mean.                   That is P (µ - 2σ ≤ X ≤ µ + 2σ) = 0.95.
  • 99.7% data falls within 3 standard deviations of the mean.                   That is P (µ - 3σ ≤ X ≤ µ + 3σ) = 0.997.

(a)

According to the Empirical rule, 68% data falls within 1 standard deviation of the mean.

P (µ - σ ≤ X ≤ µ + σ) = 0.68.

Compute the upper and lower values as follows:

<em>µ</em> - <em>σ</em> = 46 - 3 = 43 ounces

<em>µ</em> + <em>σ</em> = 46 + 3 = 49 ounces

Thus, 68% of the widget weights lie between <u>43 ounces</u> and <u>49 ounces</u>.

(b)

Compute the probability of the widget weights lie between 43 and 87 ounces as follows:

P(43

                          =P(-1

*Use a <em>z</em>-table.

The percentage is, 0.1587 × 100 = 15.87%.

Thus, the percentage of the widget weights lie between 43 and 87 ounces is 15.87%.

(c)

Compute the probability of the widget weights lie below 76 as follows:

P(X

                  =P(Z

*Use a <em>z</em>-table.

The percentage is, 1 × 100 = 100%.

Thus, the percentage of the widget weights lie below 76 is 100%.

8 0
3 years ago
Which account earns more intrest
8090 [49]

Answer:

the answer is the account with 1.5% interest

hope this helps

6 0
2 years ago
A pizzeria sells two types of pizza for lunch: pepperoni and cheese. The pepperoni pizza costs $8.50 and the cheese pizza costs
Usimov [2.4K]

Answer:

Let the no. Of cheese pizzas be x

Let the no. Of pepperoni pizzas be y

x + y = 45 (No. Of pizzas)

x = 45 - y

6x + 8.5y = 365 (cost of pizzas)

6(45-y) + 8.5y = 365

270 - 6y + 8.5y = 365

2.5y = 365 - 270

2.5y = 95

y = 95/2.5

y = 38

x = 7

Therefore 7 cheese pizzas were sold and 38 pepperoni pizzas were sold

Hope this helps!

7 0
2 years ago
Cicero and Themistocles run for the same political office. Cicero received w votes in the election, and
Serhud [2]

Answer:

Step-by-step explanation:

Cicero and Themistocles run for the same political office. Cicero received w votes in the election, and

Themistocles received v votes.

Which of the following expressions always represents how many more votes the winner received than the

loser?

The answer is B trust me

5 0
3 years ago
Read 2 more answers
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