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statuscvo [17]
2 years ago
13

Lucy and Emily are racing with each other and Lucy is 90

Mathematics
1 answer:
Zina [86]2 years ago
8 0

Using the <em>system of equation</em> created, Emily will catch up Lucy after 30 seconds

Given the Parameters :

  • Lucy's distance = 2t
  • Emily's distance = 5t

<u>We can set up an equation to represent the required scenario thus</u> :

Emily's distance = Lucy's distance + 90

5t = 2t + 90

We solve for t

<em>Collect like terms</em> :

5t - 2t = 90

3t = 90

Divide both sides by 3 to isolate t

t = 90/3

t = 30

Therefore, Emily will catch up with Lucy after 30 seconds

Learn more :brainly.com/question/13218948

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A national survey of companies included a question that asked whether the company had at least one bilingual telephone operator.
nirvana33 [79]

Answer:

The first option is correct. Option A is correct.

LCL = 0.270, and UCL = 0.397

80% Confidence interval = (0.270, 0.397)

Step-by-step explanation:

The data for Y and N for the 90 companies is attached to this solution provided.

Y represents companies with at least 1 bilingual operator and N represents companies with no bilingual operator.

The number of Y in the data = 30

Hence, sample proportion of companies with at least one bilingual operator = (30/90) = 0.3333

Confidence Interval for the population proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample proportion) ± (Margin of error)

Sample proportion = 0.3333

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error)

Critical value at 80% confidence level for sample size of 90 is obtained from the z-tables.

Critical value = 1.280

Standard error of the mean = σₓ = √[p(1-p)/n]

p = sample proportion

n = sample size = 90

σₓ = √[0.3333×0.6667)/90] = 0.0496891568 = 0.04969

80% Confidence Interval = (Sample proportion) ± [(Critical value) × (standard Error)]

CI = 0.3333 ± (1.28 × 0.04969)

CI = 0.3333 ± 0.0636021207

80% CI = (0.2696978793, 0.3969021207)

80% Confidence interval = (0.270, 0.397)

Hope this Helps!!!

3 0
3 years ago
What is the surface area of the prism?
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234 millimeters^2 is your answer
6 0
2 years ago
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(8x + 11) - (7x - 5)?​
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Step-by-step explanation:

3 0
3 years ago
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The Kendal Company manufactures automobile engine parts. Running the manufacturing operations requires 12 watts (units of electr
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24 because when you plug in 0 for both x and y:  

0=12(0)+24  

12*0=0, leaving you with 24.

4 0
3 years ago
what are the lengths of the legs of a right triangle in which one acute angle measures 19° and the hypotensue is 15 units long?
givi [52]
Refer to the diagram shown below.

Given:
m∠A = 19°
c = 15

By definition,
sin A = a/c
Therefore
a = c*sin A = 15*sin(19°) = 4.8835

cos A = b/c
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The lengths are 4.88, 14.18, and 15.00  (nearest hundredth)  

6 0
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