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aleksandrvk [35]
3 years ago
11

Can someone help please

Mathematics
1 answer:
IgorLugansk [536]3 years ago
8 0

Answer:

14.5 units

Step-by-step explanation:

we need to find the length of the rectangle. To do that, we must find the hypotenuse of the right triangle below the rectangle.

Finding the hypotenuse of a right triangle uses the Pythagorean theorem, or a² + b² = c²

let a be 9 and b be 7.

9² + 7² = c²

81 + 49 = c²

130 = c²

√130 = c

c = approx. 11.4

Now, we know the length of the rectangle.

Once a rectangle is cut diagonally, it forms 2 equal right triangles. We will use the same process to find the hypotenuse of the second right triangle.

9² + 11.4² = c²

81 + 130 = c²

81 + 130 = approx. 211

c² = 211

√211 = c

c = approx. 14.5

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navik [9.2K]

Answer:

71 degrees

Step-by-step explanation:

its an isosceles triangle so those angles are equal. Draw it out if that helps you.

5 0
3 years ago
Find the value of x.
hichkok12 [17]
<h3>Angles sum up to:</h3><h3>( n - 2 ) × 180 = ( 5 - 2 ) × 180 = 3 × 180 = 540</h3>

x + 4x + 4x + 135 + 135 = 540

9x + 270 = 540

9x = 540 - 270 \\ 9x = 270

x =  \frac{270}{9}  = 30

8 0
2 years ago
Write the equation of the line in slope-intercept form. The line is parallel to y+x=3 and passes through the point (−12, 0).
nataly862011 [7]

y = -x + 3

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4 0
3 years ago
A company manufactures a brand of lightbulb with a lifetime in months that is normally distributed with mean 3 and variance 1. A
Ratling [72]

Answer:

The smallest number of bulbs to be purchased so that the succession of bulbs produces light for at least 40 months with probability at least 0.9772 is 16.

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

ax^{2} + bx + c, a\neq0.

This polynomial has roots x_{1}, x_{2} such that ax^{2} + bx + c = a(x - x_{1})*(x - x_{2}), given by the following formulas:

x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}

x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}

\Delta = b^{2} - 4ac

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

n values from a normal distribution:

The mean is \mu n and the standard deviation is s = \sigma\sqrt{n}

A company manufactures a brand of lightbulb with a lifetime in months that is normally distributed with mean 3 and variance 1.

This means that \mu = 3, \sigma = \sqrt{1} = 1

For n bulbs:

The distribution for the sum of n bulds has \mu = 3n, \sigma = \sqrt{n}

What is the smallest number of bulbs to be purchased so that the succession of bulbs produces light for at least 40 months with probability at least 0.9772?

We want that: S_{n} \geq 40 = 0.9772.

This means that when X = 40, Z has a pvalue of 1 - 0.9772 = 0.0228, that is, when X = 40, Z = -2. So

Z = \frac{X - \mu}{\sigma}

-2 = \frac{40 - 3n}{\sqrt{n}}

-2\sqrt{n} = 40 - 3n

3n - 2\sqrt{n} - 40 = 0

Using y = \sqrt{n}

3y^2 - 2y - 40 = 0

Which is a quadratic equation with a = 3, b = -2, y = -40

\Delta = b^{2} - 4ac = (-2)^2 - 4(3)(-40) = 484

y_{1} = \frac{-(-2) + \sqrt{484}}{2*3} = 4

y_{2} = \frac{-(-2) - \sqrt{484}}{2*3} = -...

Since y and n have both to be positive:

y = \sqrt{n}

\sqrt{n} = 4

(\sqrt{n})^2 = 4^2

n = 16

The smallest number of bulbs to be purchased so that the succession of bulbs produces light for at least 40 months with probability at least 0.9772 is 16.

4 0
3 years ago
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Butoxors [25]

Answer:

yes

Step-by-step explanation:

(5_3)^2+2(0)=4

substitute with the 5 to x and 0 to y

8 0
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