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3 years ago

Solve. 3/2x – 4 = 16

2 answers:

5 0

$\dfrac{3}{2x}-4=16\ \ \ |add\ 4\ to\ both\ sides\\\\\dfrac{3}{2x}=20\\\\\dfrac{3}{2x}=\dfrac{20}{1}\ \ \ |cross\ multiply\\\\20\cdot2x=3\cdot1\\\\40x=3\ \ \ |divide\ both\ sides\ by\ 40\\\\\boxed{x=\frac{3}{40}}$

poizon [28]3 years ago

5 0

Answer: The required solution of the given equation is $x=\dfrac{40}{3}.$

Step-by-step explanation: We are given to solve the following equation :

$\dfrac{3}{2}x-4=16~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

To solve the given equation, we must find the value of the unknown variable x.

The solution of equation (i) is as follows :

$\dfrac{3}{2}x-4=16\\\\\\\Rightarrow \dfrac{3}{2}x=16+4\\\\\\\Rightarrow \dfrac{3}{2}x=20\\\\\Rightarrow 3x=40\\\\\Rightarrow x=\dfrac{40}{3}.$

Thus, the required solution of the given equation is $x=\dfrac{40}{3}.$

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Please help me on number 4

Mariulka [41]

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Angle 6 = 63° because it is vertical to angle 7.
Angle 1 = 117° because it is corresponding to angle 5.
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3 0

3 years ago

Calculate the length of the altitude (h) of the rhombus

allochka39001 [22]

Answer:

h = 15

Step-by-step explanation:

Use Pythagorean Theorem to solve for h.

a² + b² = c²

8² + h² = 17²

64 + h² = 289

h² = 225

h = 15

7 0

2 years ago

An article in The Engineer (Redesign for Suspect Wiring," June 1990) reported the results of an investigation into wiring errors

GarryVolchara [31]

Answer:

a) The 99% confidence interval on the proportion of aircraft that have such wiring errors is (0.0005, 0.0095).

b) A sample of 408 is required.

c) A sample of 20465 is required.

Step-by-step explanation:

Question a:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

Of 1600 randomly selected aircraft, eight were found to have wiring errors that could display incorrect information to the flight crew.

This means that $n = 1600, \pi = \frac{8}{1600} = 0.005$

99% confidence level

So $\alpha = 0.01$ , z is the value of Z that has a pvalue of $1 - \frac{0.01}{2} = 0.995$ , so $Z = 2.575$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.005 - 2.575\sqrt{\frac{0.005*0.995}{1600}} = 0.0005$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.005 + 2.575\sqrt{\frac{0.005*0.995}{1600}} = 0.0095$

The 99% confidence interval on the proportion of aircraft that have such wiring errors is (0.0005, 0.0095).

b. Suppose we use the information in this example to provide a preliminary estimate of p. How large a sample would be required to produce an estimate of p that we are 99% confident differs from the true value by at most 0.009?

The margin of error is of:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

A sample of n is required, and n is found for M = 0.009. So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.009 = 2.575\sqrt{\frac{0.005*0.995}{n}}$

$0.009\sqrt{n} = 2.575\sqrt{0.005*0.995}$

$\sqrt{n} = \frac{2.575\sqrt{0.005*0.995}}{0.009}$

$(\sqrt{n})^2 = (\frac{2.575\sqrt{0.005*0.995}}{0.009})^2$

$n = 407.3$

Rounding up:

A sample of 408 is required.

c. Suppose we did not have a preliminary estimate of p. How large a sample would be required if we wanted to be at least 99% confident that the sample proportion differs from the true proportion by at most 0.009 regardless of the true value of p?

Since we have no estimate, we use $\pi = 0.5$

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.009 = 2.575\sqrt{\frac{0.5*0.5}{n}}$

$0.009\sqrt{n} = 2.575*0.5$

$\sqrt{n} = \frac{2.575*0.5}{0.009}$

$(\sqrt{n})^2 = (\frac{2.575*0.5}{0.009})^2$

$n = 20464.9$

Rounding up:

A sample of 20465 is required.

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2 years ago

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Vanyuwa [196]

Answer:

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Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

The 190° arc measures 25 mm. What is the diameter of the entire circle?

Ilia_Sergeevich [38]

You can start by converting from degrees to radians and using the relation

$L=r\theta=\dfrac12d\theta$

Or just set up the proportion equation,

$\dfrac{\text{arc length}}{\text{circumference}}=\dfrac{25\text{ mm}}{180^\circ d}=\dfrac{190^\circ}{360^\circ}=\dfrac{\text{angle subtended by arc}}{\text{one revolution}}\implies d=\dfrac5{19}$

5 0

3 years ago