A dilation is a rigid transformation.<br><br> True or False

If arc XV = 80° and arc YX = 120°, what is the measure of ?YUV?

kramer

Answer:

The measure of angle YUV is 40°

Step-by-step explanation:

Consider the diagram of this question is attached below,

Where, Tangent line UV and secant XY intersect outside the circle at U,

Since,

$\widehat{XV}+\widehat{XY}+\widehat{VY}=360^{\circ}$

We have,

$\widehat{XV}=80^{\circ}, \widehat{XY}=120^{\circ}$

$\implies 80^{\circ}+120^{\circ}+\widehat{VY}=360^{\circ}$

$200^{\circ}+\widehat{VY}=360^{\circ}$

$\widehat{VY}=360^{\circ}-200^{\circ}=160^{\circ}$

Since, the measure of intercepted angle outside the circle is half of the difference of measure of intercepted arcs,

$\implies m\angle YUV = \frac{\widehat{VY}-\widehat{XV}}{2}$

$=\frac{160^{\circ}-80^{\circ}}{2}$

$=\frac{80^{\circ}}{2}$

$=40^{\circ}$

6 0

4 years ago

Choose an SRS of 1000 men from this population. Now what is the probability that x falls within ±2 mg/dL of μ? The larger sample

anyanavicka [17]

Answer:

(a) 0.5398

(b) 0.06376

Step-by-step explanation:

Given u=118, SD = 25, n = 10

Since we are dealing with a stratified random sampling (SRS)

We use,

Z = X - U/(Sd/√n).

The required probability =

Pr(112 < Z < 114)

Pr(112< Z< 114)=Pr( Z<114) - Pr(Z<112)

=Pr [Z<(114-118)/(25/√100)] - Pr[Z<(112-118)/(25/√100)]

= Pr(Z<-1.6) - PR(Z<-2.4)

= 0.5498 - 0.00820

= 0.5398

(b) Now since we are considering the whole population of 1000 men we use

Z = (X - U)/Sd

Now we the Probability of Pr(118±2)= Pr(120, 116)

= Pr(116 < X <120)

Pr(118±2) = Pr(Z<120-118/25) - Pr(Z<116-118/25)

Pr(118±2) = Pr(Z<0.08) - Pr(Z< -0.08)

= 0.53188 - 0.46812

Pr(118±2)= 0.06376

Please note the complete form of this question was gotten through Google.

A government sample survey plans to measure the LDL (bad) cholesterol level of an SRS of 100 men aged 20 to 34. Suppose that in fact the LDL cholesterol level of all men aged 20 to 34 follows the Normal distribution with mean μ = 118 milligrams per deciliter (mg/dL) and standard deviation σ = 25 mg/dL.

(a) What is the probability that

¯¯¯

x

x takes a value between 114 and 122 mg/dL? This is the probability that

¯¯¯

x

x estimates μ within ±4 mg/dL.

(b) Choose an SRS of 1000 men from this population. Now what is the probability that

¯¯¯

x

x falls within ±4 mg/dL of μ? The larger sample is much more likely to give an accurate estimate of μ.

8 0