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rusak2 [61]
3 years ago
6

Convert the decimal 0.6333… to a fraction and classify it as either rational or irrational.

Mathematics
2 answers:
Cerrena [4.2K]3 years ago
4 0

answer B

We assume        x=  0.6333

100x = 63.3333

  10x=  6.333  33               (subtract it )

----------------------------

 90x = 57 ( divide by 90 on both sides)

So x= \frac{57}{90}

Answer : \frac{57}{90}

When we can write a number in fraction form then it is a rational number.

We converted the  decimal number into a fraction so it is rational


daser333 [38]3 years ago
4 0

The answer is B. 57/90, rational.

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A short-wave radio antenna is supported by two guy wires, 150 ft and 180 ft long. Each wire is attached to the top of the antenn
Dafna1 [17]

The distance between the anchor points of the two guy wires holding radio antenna is 181 feet (to the nearest foot)

<h3>How to determine the distance between the two anchor points of the guy wire</h3>

The problem will be solved using SOH CAH TOA

let the distance between the 150 ft long guy wire and the radio antenna be x

let the distance between the 180 ft long guy wire and the radio antenna be y

cos 65° = x / 150

x = cos 65° * 150

x = 63.39 ft

The height of the antenna

sin 65° = height of antenna / 150

height of antenna = sin 65 * 150

height of antenna = 135.95

using Pythagoras theorem

(length of guy wire)² = (height of the antenna)² + (anchor distance)²

(anchor distance)² = 180² - 135.95²

anchor distance = √(180² - 135.95²)

anchor distance = 117.97

The anchor points distance apart

= 63.39 + 117.97

= 181 (to the nearest foot)

Learn more on Pythagoras theorem here:

brainly.com/question/29241066

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4 0
1 year ago
A sample of 114 mortgages approved during the current year showed that 36 were issued to a single-earner family or individual. T
kodGreya [7K]

Answer:

a-1) Reject H0 if zcalc > 1.645

a-2) z=\frac{0.316 -0.28}{\sqrt{\frac{0.28(1-0.28)}{114}}}=0.8561  

a-3) ii. False

b) ii. No

c) iii. n π > 10 and n(1 − π ) > 10

Step-by-step explanation:

1) Data given and notation

n=114 represent the random sample taken

X=36 represent the people that were issued to a single-earner family or individual

\hat p=\frac{36}{114}=0.316 estimated proportion of people that were issued to a single-earner family or individual

p_o=0.28 is the value that we want to test

\alpha=0.05 represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

p_v represent the p value (variable of interest)  

(a-1) H0: π ≤ .28 versus H1: π > .28. Choose the right option. Reject H0 if zcalc > 1.645 Reject H0 if zcalc < 1.645 a b

We need to conduct a hypothesis in order to test the claim that the true proportion is less than 0.28.:  

Null hypothesis:p\geq 0.28  

Alternative hypothesis:p < 0.28  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

The One-Sample Proportion Test is used to assess whether a population proportion \hat p is significantly different from a hypothesized value p_o.

The rejection zone would be on this case :

Reject H0 if zcalc > 1.645

Since is a right tailed test

(a-2) Calculate the test statistic. (Round intermediate calculations to 2 decimal places. Round your answer to 4 decimal places.) Test statistic

Since we have all the info requires we can replace in formula (1) like this:  

z=\frac{0.316 -0.28}{\sqrt{\frac{0.28(1-0.28)}{114}}}=0.8561  

(a-3) The null hypothesis should be rejected.

False, since our calculated value is less than our critical value we Fails to reject the null hypothesis

(b) Is this a close decision?

False the calculated value is significantly less than the critical value so we FAIL to reject the null hypothesis with enough confidence.

(c) State any assumptions that are required.

In order to satisfy the conditions we need the following two requirements:

iii. n π > 10 and n(1 − π ) > 10

And are satisfied:

114*0.28=31.92>10

114(1-0.28)=82,08>10

7 0
3 years ago
Solve the equation 0.35(x+4)=0.25(x-6)
creativ13 [48]
x = -29

because
0.35x +1.4=0.25x-1.5
-0.25x            -0.25x
_____________________
0.1x + 1.4 =  -1.5
         -1.4      -1.4
_________________________
0.1x          =-2.9
____        _____
0.1               0.1
     x =  -29


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3 years ago
Please help me on this
Eddi Din [679]

Answer:

The correct answer is True.

Step-by-step explanation:

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Answer:

By using pythagoras formula

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