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3 years ago

Solve 6x + 3) = 21.

Mathematics

1 answer:

LiRa [457]3 years ago

8 0

Answer:

18x^2 - 9

Step-by-step explanation:

y = f(x)= 6x^3 - 9x + 4

dy/dx = d/dx(6x^3) - d/dx(9x) + d/dx (4)

=6.d/dx(x^3) - 9.d/dx (x) + d/dx. (4)

=6.3x^2 - 9.1 + 0 =18x^2 - 9

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The ratio of the measures of the three sides of a triangle is 1/4:1/3:1/6 and its perimeter is 31.4 centimetres find the length

lina2011 [118]

Given:

The ratio of the measures of the three sides of a triangle is $\dfrac{1}{4}:\dfrac{1}{3}:\dfrac{1}{6}$ .

Its perimeter is 31.4 centimeters

To find:

The shortest side of the triangle.

Solution:

Let the measures of the three sides of a triangle are $\dfrac{1}{4}x,\dfrac{1}{3}x,\dfrac{1}{6}x$ respectively (in cm).

Its perimeter is 31.4 centimeters.

$\dfrac{1}{4}x+\dfrac{1}{3}x+\dfrac{1}{6}x=31.4$

$\dfrac{3x+4x+2x}{12}=31.4$

$\dfrac{9x}{12}=31.4$

$\dfrac{3x}{4}=31.4$

On further simplification, we get

$3x=4\times 31.4$

$3x=125.6$

Divide both sides by 3.

$x=\dfrac{125.6}{3}$

$x=41.867$

Now, the sides of triangle are

$\dfrac{1}{4}(41.867)=10.467$

$\dfrac{1}{3}(41.867)=13.956$

$\dfrac{1}{6}(41.867)=6.978$

Therefore, the length of the shortest side is 6.978 cm.

5 0

3 years ago

Pls help soon:)!! I'll give brainliest

Roman55 [17]

Decay every two years over a period of t years:
Fourth option: f(t)=(0.75)^(t/2)

decay 2 times a year over a period of t years:
Second option: f(t)=(0.9306)^(2t)
Sixth option: f(t)=(0.8660)^(2t)

decay once per year over a period of t years:
First option: f(t)=(0.9306)^t
Third option: f(t)=(0.8660)^t

7 0

3 years ago

If you have 2a-15=-1 what is the answer

wlad13 [49]

Answer:

Step-by-step explanation:

4 0

4 years ago

Read 2 more answers

Parallel and perpendicular lines

pentagon [3]

Answer:

Parallel lines are lines in a plane that are always the same distance apart. Parallel lines never intersect. Perpendicular lines are lines that intersect at a right (90 degrees) angle.

Step-by-step explanation:

4 0

3 years ago

Barron's reported that the average number of weeks an individual is unemployed is 18.5 weeks. Assume that for the population of

Ket [755]

Answer:

A) The sampling distribution for a sample size n=50 has a mean of 18.5 weeks and a standard deviation of 0.849.

B) P = 0.7616

C) P = 0.4441

Step-by-step explanation:

We assume that for the population of all unemployed individuals the population mean length of unemployment is 18.5 weeks and that the population standard deviation is 6 weeks.

A) We take a sample of size n=50.

The mean of the sampling distribution is equal to the population mean:

$\mu_s=\mu=18.5$

The standard deviation of the sampling distribution is:

$\sigma_s=\dfrac{\sigma}{\sqrt{n}}=\dfrac{6}{\sqrt{50}}=0.849$

B) We have to calculate the probability that the sampling distribution gives a value between one week from the mean. That is between 17.5 and 19.5 weeks.

We can calculate this with the z-scores:

$z_1=\dfrac{X_1-\mu}{\sigma/\sqrt{n}}=\dfrac{17.5-18.5}{6/\sqrt{50}}=\dfrac{-1}{0.8485}=-1.179\\\\\\z_2=\dfrac{X_2-\mu}{\sigma/\sqrt{n}}=\dfrac{19.5-18.5}{6/\sqrt{50}}=\dfrac{1}{0.8485}=1.179$

The probability it then:

$P(|X_s-\mu_s|$

C) For half a week (between 18 and 19 weeks), we recalculate the z-scores and the probabilities:

$z=\dfrac{X-\mu}{\sigma/\sqrt{n}}=\dfrac{18-18.5}{6/\sqrt{50}}=\dfrac{-0.5}{0.8485}=-0.589$

$P(|X_s-\mu_s|$

5 0

3 years ago