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lord [1]
3 years ago
5

Sam is an apprentice carpenter whose boss asked him to construct a perfectly rectangular frame with a diagonal brace. When Sam h

ad finished his boss measured the width of the frame to be 50 cm, the length to be 90 cm and the diagonal brace to be 100 cm. was Sam's boss happy with his work? Use mathematics to explain how you determined your answer
Mathematics
1 answer:
zalisa [80]3 years ago
3 0
If it's a perfectly rectangle frame with W = 50 cm & L= 90 cm

So the right diagonal should be √(50² +90²) = √10600 =102.96 cm

as per the calculation the diagonal should have a length of 102.96 cm, but the boss found 100 cm, that means their should be a frame which diagonal equal to 100 cm, short by 2.96 cm, that means short by 2.96/2 = 1.48 cm from the bottom & 1.48 cm from the top (same as well as for the 2nd diagonal)
In this case the boss should be happy

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Help - i'll give brainliest
Serggg [28]

Answer:

W=91.2

Step-by-step explanation:

8 0
3 years ago
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For what values of p does the equation px = 10 have a solution −5; 1; 20?
shutvik [7]

The values of p for which the equation px = 10 have a solution −5; 1; 20 is -2, 10, \frac{1}{2}

<u>Solution:</u>

Given, equation is px = 10.

We have to find the values of p for which solutions of given equations becomes -5, 1, 20.

We just need to substitute -5, 1, 20 in given equation as x, to values of p.

Now, For -5 ⇒ p(-5) = 10 ⇒ -5p = 10 ⇒ p = -2

For 1 ⇒ p(1) = 10 ⇒ p = 10

For 20 ⇒ p(20) = 10 ⇒ 20p = 10 ⇒ p = \frac{1}{2}

Hence, the values of p are -2, 10, \frac{1}{2} for the solutions -5, 1, 20 respectively.

3 0
4 years ago
The ability of lizards to recognize their predators via tongue flicks can often mean life or death for lizards. Seventeen juveni
Sloan [31]

Answer:

Confidence level is (380.7133, 533.2867)

Step-by-step explanation:

Responses in number of tongue flicks per 20 minutes of lizards, are: 727,217, 268, 438, 625, 319, 200, 591, 574, 727, 693, 336, 302, 761, 268, 353, 370

n = 17

Mean (μ) is:

\mu=\frac{{\Sigma}x}{n} = \frac{727+217+ 268+ 438+ 625+ 319+ 200+ 591+ 574+ 727+ 693+ 336+ 302+ 761+ 268+ 353+ 370}{17} = 439.3529

Standard deviation (σ) is:

\sigma=\sqrt{\frac{\Sigma(x-\mu^2)}{n} } =\sqrt{\frac{(727-457)^2+(217-457)^2+...+(370-457)^2}{17} } =191.2

The confidence interval (c) = 90% = 0.9

\alpha=1-0.9=0.1\\\frac{\alpha }{2} = 0.05\\Z_{\frac{\alpha }{2} }=1.64

Margin of error (e) = =Z_{\frac{\alpha}{2} }*\frac{\sigma}{\sqrt{n} }=1.64*\frac{191.2}{\sqrt{17} }=76.2867

Confidence level = μ ± e = 457 ± 76.2867 = (380.7133, 533.2867)

8 0
4 years ago
It is claimed that the proportion of people who favor the use of oxygenated fuels year around to reduce air pollution is 60%. A
attashe74 [19]

Answer:

Conclusion is that there is sufficient evidence to reject the claim that the proportion of people who favor the use of oxygenated fuels year around to reduce air pollution is 60%.

Step-by-step explanation:

We are given;

Population proportion; p = 60% = 0.6

Sample mean: x¯ = 315

Sample size; n = 500

Significance level = 0.09

Defining the hypothesis, we have;

Null Hypothesis; H0: p = 0.6

Alternative hypothesis; Ha: p > 0.6

z-score formula in this case is;

z = (x¯ - np)/√(np(1 - p))

Plugging in the relevant values;

z = (315 - (500 × 0.6))/√(500 × 0.6(1 - 0.6))

z = 1.72

From z-distribution table, the p-value at z = 1.72 is;

1 - P(Z ≤ z-score)

This gives:

p-value = 1 - 0.95728 = 0.04272

Thus p-value is less than the significance level of 0.09, thus we will reject the null hypothesis and conclude that there is sufficient evidence to reject the claim that the proportion of people who favor the use of oxygenated fuels year around to reduce air pollution is 60%.

6 0
3 years ago
Calcule as potências a seguir e veja se a diferenças entre elas:<br>a)2⁴<br>b)(-2)⁴<br>c)-2⁴​
Volgvan
2^4 = 16
(-2)^4 =16
-2^4 =-16
4 0
3 years ago
Read 2 more answers
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