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3 years ago

See attachment below and find the equivalent of tan(∠QSR)

Mathematics

2 answers:

solmaris [256]3 years ago

7 0

I hope this helps you

Charra [1.4K]3 years ago

7 0

Answer:

$tan QSR = tan 30 \\=\frac{1}{\sqrt{3} }$

Step-by-step explanation:

Given in the attachment is a picture of a triangle with sides QR, RS and QS

The triangle is right angles at R

One exterior angle QST is given as 150 degrees.

Angle QSR is the linear pair of QST

Hence QSR and QST are supplementary

i.e. Angle QSR = 30 degrees

$tan QSR = tan 30 \\=\frac{1}{\sqrt{3} }$

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he weight of male babies less than months old in the United States is normally distributed with mean pounds and standard deviati

Degger [83]

Answer:

Step-by-step explanation:

Hello!

The variable of interest is

X: Weight of a male baby (pounds)

X~N(μ;σ²)

μ= 11.5 pounds

σ= 2.7 pounds

a) Find the 81st percentile of the baby weights.

This percentile is the value that separates the bottom 81% of the distribution from the top 19%

P(X≤x₁)= 0.81

For this you have to use the standard normal distribution. First you have to look the 81st percentile under the Z distribution and then "translate" it to a value of the variable X using the formula Z= (X- μ)/σ

P(Z≤z₁)= 0.81

z₁= 0.878

z₁= (x₁- μ)/σ

z₁*σ= x₁- μ

(z₁*σ) + μ= x₁

x₁= (z₁*σ) + μ

x₁= (2.7*0.878)+11.5

x₁= 13.8706 pounds

b) Find the 10th percentile of the baby weights.

P(X≤x₂)= 0.10

P(Z≤z₂)= 0.10

z₂= -1.282

z₂= (x₂- μ)/σ

z₂*σ= x₂- μ

(z₂*σ) + μ= x₂

x₂= (z₂*σ) + μ

x₂= (2.7*-1.282)+11.5

x₂= 8.0386 pounds

c) Find the first quartile of the baby weights.

P(X≤x₃)= 0.25

P(Z≤z₃)= 0.25

z₃= -0.674

z₃= (x₃- μ)/σ

z₃*σ= x₃- μ

(z₃*σ) + μ= x₃

x₃= (z₃*σ) + μ

x₃= (2.7*-0.674)+11.5

x₃= 9.6802 pounds

I hope this helps!

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3 years ago

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Answer:

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Step-by-step explanation:

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The perimeter of a basketball court is 84 meters and the length is 6 meters longer than twice the width. what are the length and

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The length is 30 meters and the width is 12 meters.

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3 years ago

The area of a parallelogram is 96 cm2. The height of the parallelogram is 4 cm less than the length of the base. What is the len

wolverine [178]

The answer is C. 12cm

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3 years ago

Read 2 more answers

Students have organized

Olenka [21]

Answer:

Part A. At least 6 hours

Part B. In less than 2.5 hours Elijah will be behind Mercedes

Part C. In more than 2.5 hours Elijah will be ahead Aubrey

Step-by-step explanation:

D = distance

v =speed

t = time

Formula connecting D, v and t:

$D=v\cdot t$

Part A.

Steve's speed: $v=3.5\ mph$

Distance: at least 21 miles

Time: unknown, so

$3.5\cdot t\ge 21\\ \\35t\ge 210\ [\text{Multiplied by 10}]\\ \\t\ge \dfrac{210}{35}\\ \\t\ge \dfrac{30}{5}\\ \\t\ge 6$

It would take Steve at least 6 hours to walk at least 21 mi on Day 1.

Part B.

Mercedes's speed: $v_M=2.4\ mph$

Elijan's speed: $v_E=3.2\ mph$

Elijan's Distance walked: $D_E$ miles

Mercedes's Distance walked: $D_M$ miles

Time: x hours

Mercedes is 2 miles ahead, so

$D_E=3.2x\\ \\D_M=2.4x+2$

Elijan will be behind when

$D_E$

In 2.5 hours Elijan will catch up Mercedes, and in less than 2.5 hours Elijah will be behind Mercedes.

Part C.

Aubrey's speed: $v_M=3\ mph$

Elijan's speed: $v_E=3.2\ mph$

Elijan's Distance walked: $D_E$ miles

Aubrey's Distance walked: $D_A$ miles

Time: x hours

At the beginning of Day 3, Elijah starts walking at the marker for Mile 42, and Aubrey starts walking at the marker for Mile 42.5.

$D_E=42+3.2x\\ \\D_A=42.5+3x$

Elijan will be ahead of Aubrey when

$D_E>D_A\\ \\42+3.2x> 42.5+3x\\ \\3.2x-3x>42.5-42\\ \\0.2x>0.5\\ \\2x>5\ [\text{Multiplied by 10}]\\ \\x>\dfrac{5}{2}\\ \\x>2.5\ hours$

In 2.5 hours Elijan will catch up Aubrey, and in more than 2.5 hours Elijah will be ahead Aubrey.

4 0

4 years ago