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2 years ago

What is the value of x in the equation 4(2x − 1) = 2x + 35?

Mathematics

1 answer:

Grace [21]2 years ago

5 0

Answer:

x = 6.5 or 13/2

Step-by-step explanation:

4(2x − 1) = 2x + 35

distribute the 4 to 2x - 1

8x - 4 = 2x + 35

subtract 2x

6x - 4 = 35

add 4

6x = 39

divide by 6

x = 6.5 or 13/2

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What is the probability that a hand of five cards contain a queen of hearts,?

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2 years ago

What is 1/10 of 1,700,000 square feet

Dima020 [189]

1/10 of 1,700,000 of anything =

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2 years ago

Read 2 more answers

Suppose that Y has density function

zvonat [6]

I'm assuming

$f(y)=\begin{cases}ky(1-y)&\text{for }0\le y\le1\\0&\text{otherwise}\end{cases}$

(a) f(x) is a valid probability density function if its integral over the support is 1:

$\displaystyle\int_{-\infty}^\infty f(x)\,\mathrm dx=k\int_0^1 y(1-y)\,\mathrm dy=k\int_0^1(y-y^2)\,\mathrm dy=1$

Compute the integral:

$\displaystyle\int_0^1(y-y^2)\,\mathrm dy=\left(\frac{y^2}2-\frac{y^3}3\right)\bigg|_0^1=\frac12-\frac13=\frac16$

So we have

k / 6 = 1 → k = 6

(b) By definition of conditional probability,

P(Y ≤ 0.4 | Y ≤ 0.8) = P(Y ≤ 0.4 and Y ≤ 0.8) / P(Y ≤ 0.8)

P(Y ≤ 0.4 | Y ≤ 0.8) = P(Y ≤ 0.4) / P(Y ≤ 0.8)

It makes sense to derive the cumulative distribution function (CDF) for the rest of the problem, since F(y) = P(Y ≤ y).

We have

$\displaystyle F(y)=\int_{-\infty}^y f(t)\,\mathrm dt=\int_0^y6t(1-t)\,\mathrm dt=\begin{cases}0&\text{for }y$

Then

P(Y ≤ 0.4) = F (0.4) = 0.352

P(Y ≤ 0.8) = F (0.8) = 0.896

and so

P(Y ≤ 0.4 | Y ≤ 0.8) = 0.352 / 0.896 ≈ 0.393

(c) The 0.95 quantile is the value φ such that

P(Y ≤ φ) = 0.95

In terms of the integral definition of the CDF, we have solve for φ such that

$\displaystyle\int_{-\infty}^\varphi f(y)\,\mathrm dy=0.95$

We have

$\displaystyle\int_{-\infty}^\varphi f(y)\,\mathrm dy=\int_0^\varphi 6y(1-y)\,\mathrm dy=(3y^2-2y^3)\bigg|_0^\varphi = 0.95$

which reduces to the cubic

3φ² - 2φ³ = 0.95

Use a calculator to solve this and find that φ ≈ 0.865.

8 0

3 years ago

The specifications for the diameter of a molded part are 10 mm ± 0.5 mm. The actual average and standard deviation from 250 part

ad-work [718]

Answer: Capable

Step-by-step explanation: The capability of a process could be exaplained as a measure of the ability of a process to produce part within specified limits by making use of statistical measurement. In determining if a certain process is capable or not, the value of process capability (Cp) is measured, in most cases, a process is deemed capable by having a Cp value of 1.33 or higher.

Cp formula :

(Upper specification limit(USL) - Lower specification limit(LSL) ) / 6* standard deviations

Diameter = 10 mm ± 0.5 mm

Standard deviation = 0.1mm

USL = 10 + 0.5 = 10.5

LSL = 10 - 0.5 =. 9.5

Cp = (10.5 - 9.5) / 6*0.1

Cp = 1/0.6

Cp = 1.6666

Cp = 1.67

Hence, the process is capable

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3 years ago

Please help me with this homework

RUDIKE [14]

Answer:

Step-by-step explanation:

C=49

A=37

Therefore to get the difference of C and A you need to subtract A from C

=C- A

=49-37

=12

7 0

2 years ago