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3 months ago

Given: PFST is a rectangle m∠SOT = 60°, OS = R=4 Find: ST and PT

Mathematics

2 answers:

babunello [11.8K]3 months ago

7 0

The full question is depicted in the attached image.

Given that

the circle's radius r is 4 units,

in triangle OST,
each side OT and OS measures 4 units,
with m∠OST = 60°. Therefore, cos 60°=(ST/2)/r leads to ST=2*r*cos 60° which equals 2*4*(1/2) resulting in ST = 4 units.
Thus,
triangle OST is an equilateral triangle.

Part a) results in
ST = 4 units

Part b)
To determine PT,
in triangle POT,
m∠POT = (180°-60°) equals 120°.
Furthermore, m∠OTP = 30°. The relationship cos 30°=(PT/2)/r gives us PT=2*r*cos 30°, leading to PT=2*4*(√3/2), resulting in PT=4√3 units.

Part b) results in
PT=4√3 units

AnnZ [12.3K]3 months ago

5 0

Answer:

pt= $8\sqrt{3$

st=4

Step-by-step explanation:

Half of PT is 4√3.

ST is equivalent to r, which is 4.

Use the 30-60-90 triangle to find PT.

I hope this is useful to you

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8 0

3 months ago

Read 2 more answers

A study1 conducted in July 2015 examines smartphone ownership by US adults. A random sample of 2001 people were surveyed, and th

Inessa [12570]

Answer:

a) Null hypothesis: $p_{1} = p_{2}$

Alternative hypothesis: $p_{1} \neq p_{2}$

b) $z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}$ (1)

Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{688+671}{989+1012}=0.679$

c) $z=\frac{0.696-0.663}{\sqrt{0.679(1-0.679)(\frac{1}{989}+\frac{1}{1012})}}=1.58$

d) In this scenario, we notice that $\hat p_1 > \hat p_2$ thus the conclusion for this case would indicate

Step-by-step explanation:

Information provided

$X_{1}=688$ denote the number of men possessing smartphones

$X_{2}=671$ signify the number of women possessing smartphones

$n_{1}=989$ group of men sampled

$n_{2}=1012$ group of women sampled

$p_{1}=\frac{688}{989}=0.696$ symbolize the proportion of men with smartphones

$p_{2}=\frac{671}{1012}=0.663$ symbolize the proportion of women with smartphones

$\hat p$ denote the pooled estimate of p

z would denote the test statistic

$p_v$ signify the value

Part a

The objective is to evaluate if there is a disparity in smartphone ownership between men and women; the hypothesis statements would be:

Null hypothesis: $p_{1} = p_{2}$

Alternative hypothesis: $p_{1} \neq p_{2}$

Part b

The statistic relevant to this case is expressed as:

$z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}$ (1)

Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{688+671}{989+1012}=0.679$

Part c

By substituting the provided information, we find:

$z=\frac{0.696-0.663}{\sqrt{0.679(1-0.679)(\frac{1}{989}+\frac{1}{1012})}}=1.58$

Part d

In this instance, it is evident that $\hat p_1 > \hat p_2$ thus the conclusion for this case would seem

4 0

2 months ago

2 intersecting lines are shown. A line with points T, R, W intersects a line with points S, R, V at point R. Angle T R V is 95 d

tester [12383]

Answer:

$95^\circ$

Step-by-step explanation:

Consider the two lines TRW and SRV intersecting at point R, as illustrated in the diagram below and:

$\angle TRV=95^\circ$

$m\angle TRV=m\angle SRW$ (Vertically Opposite Angles)\\Therefore:\\m\angle SRW=95^\circ$

6 0

3 months ago

Read 2 more answers

Five teachers were hired at Oakdale Middle School at the beginning of the 2005 school year. The performance of each teacher was

babunello [11817]

I believe the answer is Jill.

3 0

3 months ago

Leonora is factoring a trinomial. The factors of the trinomial are shown on the model. An algebra tile configuration. 7 tiles ar

AnnZ [12381]

Leanora is factoring in Amacher the factors of the thermometer are shown in the elevator 3+3 = 7 4+4 equalsTake away 100 and then +3 that gives you 6 billion in 2/3+6+4+3+8+9 that gives you a BCDEFGHIJK jelly jelly jelly diaper

6 0

2 months ago