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6 days ago

What information can you obtain about the scores in a regular frequency distribution table that is not available from a grouped

table.
A. The number and width of the class intervals

B. The exact frequency for each category on the scale of measurement

C. The overall frequency for each class interval

Mathematics

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Given: KL ║ NM , LM = 45, m∠M = 50° KN ⊥ NM , NL ⊥ LM Find: KN and KL

Leona [12618]

Answer:

$KL=45\tan 50^{\circ}\sin 50^{\circ}\approx 41.08\\ \\KN=45\sin 50^{\circ}\approx 34.47$

Step-by-step explanation:

Given:

KL ║ NM,

LM = 45

m∠M = 50°

KN ⊥ NM

NL ⊥ LM

To determine: KN and KL

1. Analyzing triangle NLM, we see it is a right triangle due to NL ⊥ LM. In this context,

LM = 45

m∠M = 50°

Consequently,

$\tan \angle M=\dfrac{\text{opposite leg}}{\text{adjacent leg}}=\dfrac{NL}{LM}=\dfrac{NL}{45}\\ \\NL=45\tan 50^{\circ}$

It is also true that

(angles LNM and M are complementary). $m\angle LNM=90^{\circ}-50^{\circ}=40^{\circ}$

2. Now considering triangle NKL, it also forms a right triangle as KN ⊥ NM. Within this triangle,

$NL=45\tan 50^{\circ}$

$m\angle KLN=m\angle LNM=40^{\circ}$ (alternate interior angles)

$m\angle KNL=90^{\circ}-40^{\circ}=50^{\circ}$ (angles KNL and KLN are complementary).

Thus,

$\sin \angle KNL=\dfrac{\text{opposite leg}}{\text{hypotenuse}}=\dfrac{KL}{LN}=\dfrac{KL}{45\tan 50^{\circ}}\\ \\KL=45\tan 50^{\circ}\sin 50^{\circ}\approx 41.08$

and

$\cos \angle KNL=\dfrac{\text{adjacent leg}}{\text{hypotenuse}}=\dfrac{KN}{LN}=\dfrac{KN}{45\tan 50^{\circ}}\\ \\KN=45\tan 50^{\circ}\cos 50^{\circ}=45\sin 50^{\circ}\approx 34.47$

3 0

2 months ago

Read 2 more answers

When jumping, a flea rapidly extends its legs, reaching a takeoff speed of 1.0 m/s over a distance of 0.50 mm . part a what is t

zzz [12365]

The flea experiences an acceleration of 1,000 m/s².

Detailed explanation

This scenario involves motion with constant acceleration.

The relevant variables include the following.

$\boxed{u \ or \ v_i = initial \ velocity}$

$\boxed{u \ or \ v_t \ or \ v_i = terminal \ or \ final \ velocity}$

$\boxed{a = acceleration \ (constant)}$

$\boxed{d = distance \ travelled}$

We know the flea attains a takeoff velocity of 1.0 m/s over a distance of 0.50 mm.

The flea starts from rest, so the initial velocity is zero. The question asks for the flea's acceleration during leg extension.

The equation we apply is:

$\boxed{ \ v^2 = u^2 + 2ad \ }$

a = acceleration (m/s²)
u = initial speed = 0 m/s
v = takeoff velocity = 1.0 m/s
d = displacement = 0.50 mm

First, convert 0.50 mm to meters: $\boxed{0.50 \ mm = 0.50 \times 10^{-3} \ m = 5.0 \times 10^{-4} \ m}$

Solution steps:

Rearrange the formula to isolate acceleration (a).

$\boxed{ \ v^2 = u^2 + 2ad \ }$

$\boxed{ \ v^2 - u^2 = 2ad \ }$

$\boxed{ \ 2ad = v^2 - u^2 \ }$

$\boxed{ \ a = \frac{v^2 - u^2}{2d} \ }$

Insert the given values into the rearranged equation.

$\boxed{ \ a = \frac{(1.0)^2 - (0)^2}{2(5.0 \times 10^{-4})} \ }$

$\boxed{ \ a = \frac{1}{10 \times 10^{-4}} \ }$

$\boxed{ \ a = \frac{1}{1 \times 10^{-3}} \ }$

$\boxed{ \ a = 1 \times 10^{3}\ = 1,000 \ m/s^2 \ }$

This yields the flea's acceleration as 1,000 m/s².

Additional resources

Scientific notation: brainly.com/question/7263463
Determining substance mass: brainly.com/question/4053884
Conversion into cubic units: brainly.com/question/1446243

Keywords: flea, jumping, leg extension, takeoff velocity, initial speed, displacement, acceleration, constant acceleration, unit conversion

5 0

3 months ago

Read 2 more answers

Patty has a flower box in the shape of a rectangular prism with interior dimensions that are 15 inches in length, 8 inches in wi

Inessa [12570]

Respuesta:

Explicación paso a paso:

V=1/2lbh

V=1/2×15×8×6

V=360pulgadas

7 0

2 months ago

Marc mows lawns for $25 each lawn, plus $5 for every hour he spends mowing. The equation for his total earnings per lawn is y =

tester [12383]

Answer:

The constant pay of $25 signifies the intercept

Step-by-step explanation:

To address this query, we first need to comprehend and relate it to the formula for a straight line.

i.e $y= mx+c$ this represents the line's equation

where m= slope

y= dependent variable

x= independent variable

c= intercept

Given

$y= 25+5h$

by comparing the two expressions, we can observe that

25 is equivalent to c, which denotes the intercept

6 0

3 months ago

Bob Nale is the owner of Nale's Texaco GasTown. Bob would like to estimate the mean number of litres (L) of gasoline sold to his

AnnZ [12381]

a. The point estimate for the population mean is b. The confidence interval at 80% is c. This means there is an 80% probability that the true mean of the population lies within the given confidence interval.

3 0

1 month ago