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Ulleksa [173]

2 years ago

2}" alt="24x^{2}+bx^{2} =25x^{2}" align="absmiddle" class="latex-formula">

Mathematics

1 answer:

Liula [17]2 years ago

8 0

Answer:

x = 0

Step-by-step explanation:

Subtract 25x^2 from both sides

24x^2 + bx^2 - 25x^2 - 25x^2

Simplify

bx^2 - x^2 = 0

Factor bx^2 - x^2: x^2(b - 1)

bx^2 - x^2

Factor out common term x^2

= x^2 (b - 1)

x^2(b - 1) = 0

Using the Zero Factor Principle: If ab = 0 then a = 0 or b = 0

x^2 = 0

Apply rule x^n = 0 x = 0

x = 0

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An estimated regression equation that was fit to estimate ductility in steel using its carbon content was found to be significan

AnnZ [28]

Answer:

At a level of 95%, it is expected that the interval [0.45; 11.59] contains the value of the ductility in steel when its carbon content is 0.5%.

Step-by-step explanation:

Hello!

Considering the dependent variable:

Y: Ductility in steel.

And the independent variable:

X: Carbon content of the steel.

The linear regression was estimated and a prediction interval was calculated.

The prediction interval is calculated to predict a value that the variable Y (response variable) can take for a given value of the variable X (predictor variable) in the definition range of the linear regression line. Symbolically [Y/X= $x_{0}$ ]

In this case 95% prediction interval for Y/X=0.5

At a level of 95%, it is expected that the interval [0.45; 11.59] contains the value of the ductility in steel when its carbon content is 0.5%.

I hope it helps!

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2 years ago

Can somebody please answer this asap

erastovalidia [21]

Answer:

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1 year ago

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he number of surface flaws in plastic panels used in the interior of automobiles has a Poisson distribution with a mean of 0.02

Yakvenalex [24]

Answer:

a) 98.01%

b) 13.53\%

c) 27.06%

Step-by-step explanation:

Since a car has 10 square feet of plastic panel, the expected value (mean) for a car to have one flaw is 10*0.02 = 0.2

If we call P(k) the probability that a car has k flaws then, as P follows a Poisson distribution with mean 0.2,

$P(k)= \frac{0.2^ke^{-0.2}}{k!}$

In this case, we are looking for P(0)

$P(0)= \frac{0.2^0e^{-0.2}}{0!}=e^{-0.2}=0.9801=98.01\%$

So, the probability that a car has no flaws is 98.01%

Ten cars have 100 square feet of plastic panel, so now the mean is 100*0.02 = 2 flaws every ten cars.

Now P(k) is the probability that 10 cars have k flaws and

$P(k)= \frac{2^ke^{-2}}{k!}$

and

$P(0)= \frac{2^0e^{-2}}{0!}=0.1353=13.53\%$

And the probability that 10 cars have no flaws is 13.53%

Here, we are looking for P(1) with P defined as in b)

$P(1)= \frac{2^1e^{-2}}{1!}=2e^{-2}=0.2706=27.06\%$

Hence, the probability that at most one car has no flaws is 27.06%

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2 years ago

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From 1984 to 1995 the winning scores for a golf tournament were 275,279,279,276,278,277,280,282,284and 270 Find the mean of the

andreyandreev [35.5K]

Answer: The mean of the data is 278.

Step-by-step explanation:

To the the mean of the data, we’ll have to add all the numbers up and divide it by the amount of data.

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What is the area of the given figure?

kirza4 [7]

$\huge\boxed{192\ \text{in}^2}$

There are three parts to this figure: a rectangle and two triangles that are congruent.

We'll add together the area for each to get the total area.

We'll start by finding the area of the rectangle. We don't know its length, so we need to find the bases of the triangles and add them together.

We know that $a^2+b^2=c^2$ . Substitute and solve for $a$ :

$\begin{aligned}a^2+6^2&=10^2\\a^2+36&=100\\a^2+36-36&=100-36\\a^2&=64\\\sqrt{a^2}&=\sqrt{64}\\a&=8\end{aligned}$

Now, double this to get the total length of the rectangle, which is $16$ inches.

The area of the rectangle is equal to its length times its height:

$16\cdot9=\underline{144}$

Now, we'll find the area of one of the triangles and double it since they're congruent.

The area of a triangle is one-half of its base times its height, which we then double.

$2\left(\frac{1}{2}\cdot b\cdot h\right)$

The $2$ and the $\frac{1}{2}$ cancel each other out.

$b\cdot h$

Substitute and solve:

$8\cdot6=\underline{48}$

Finally, add the rectangle's area to the two triangles' area.

$144+48=\boxed{192}$

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