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2 years ago

Find the value of the length a x rounded to 1 DP. The diagram is not drawn accurately

Mathematics

1 answer:

son4ous [18]2 years ago

8 0

Answer:

x ≈ 3.7 m

Step-by-step explanation:

Use the right triangle on the left to find the height h , using the sine ratio

sin39° = $\frac{opposite}{hypotenuse}$ = $\frac{h}{7}$ ( multiply both sides by 7 )

7 × sin39° = h , then

h = 4.4

Using the tangent ration on the right side right triangle, then

tan50° = $\frac{opposite}{adjacent}$ = $\frac{h}{x}$ = $\frac{4.4}{x}$ ( multiply both sides by x )

x × tan50° = 4.4 ( divide both sides by tan50° )

x = $\frac{4.4}{tan50}$ ≈ 3.7 m ( to 1 dec. place )

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Suppose that your business is operating at the 4.5-Sigma quality level. If projects have an average improvement rate of 50% annu

Luda [366]

Answer:

11.75 years

Step-by-step explanation:

If we ignore the fact that "6-sigma" quality means the error rate corresponds to about -4.5σ (3.4 ppm) and simply go with ...

P(z ≤ -6) ≈ 9.86588×10^-10

and

P(z ≤ -4.5) ≈ 3.39767×10^-6

the ratio of these error rates is about 0.000290372. We're multiplying the error rate by 0.5 each year, so we want to find the power of 0.50 that gives this value:

0.50^t = 0.000290372

t·log(0.50) = log(0.00290372) . . . . take logarithms

t = log(0.000290372)/log(0.50) ≈ -3.537045/-0.301030

t ≈ 11.75

It will take about 11.75 years to achieve Six Sigma quality (0.99 ppb error rate).

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<em>Comment on Six Sigma</em>

A 3.4 ppm error rate is customarily associated with "Six Sigma" quality. It assumes that the process may have an offset from the mean of up to 1.5 sigma, so the "six sigma" error rate is P(z ≤ (1.5 -6)) = P(z ≤ -4.5) ≈ 3.4·10^-6.

Using that same criteria for the "4.5-Sigma" quality level, we find that error rate to be P(z ≤ (1.5 -4.5)) = P(z ≤ -3) ≈ 1.35·10^-3.

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t ≈ log(0.00251699)/log(0.5) ≈ 8.6 . . . . years

5 0

3 years ago

A researcher is interested in determining if the more than two thirds of students would support making the Tuesday before Thanks

Yakvenalex [24]

Answer:

The null hypothesis is, {H₀}: p = 0.66, H₀: p = 0.66 .

The alternative hypothesis is, {Hₐ}: p > 0.66, Hₐ: p > 0.66

Step-by-step explanation:

Let p represent the proportion of students who are supportive of making the day before Thanksgiving a holiday.

Since two populations are considered, the alternative hypothesis for the difference of the means of the two populations has to be stated.

The proportion of two-third students are supportive of making the day before Thanksgiving a holiday is p = 0.66 obtained as shown below:

The null hypothesis is,

{H₀}:p = 0.66, H₀: p = 0.66

The alternative hypothesis is,

{Hₐ:p > 0.66, Ha: p > 0.66

The null hypothesis is, {H₀}: p = 0.66, H₀: p=0.66 .

The alternative hypothesis is, {Hₐ}: p > 0.66, Hₐ: p > 0.66

3 0

3 years ago

Find the length of the other two side of the isosceles right triangle

Valentin [98]

Answer:

The other two sides are 7 units each.

Step-by-step explanation:

The triangle is isosceles.

The sides are in the ratio of

$x : x : x \sqrt{2}$

The hypotenuse is

$7\sqrt{2}=x \sqrt{2}\\\\x = 7$

So, the other two sides are 7 units each.

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3 years ago

Two friends, Hailey and Jenna bought two tickets to see a play at a local theater . Each ticket cost $17.25. Each friend donated

Sliva [168]

Per ticket cost $17.25

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Percent increase in the cost of per ticket

17.39%

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3 years ago

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OLga [1]

The tips were $115.50

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3 years ago

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