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2 years ago

The leg of an isosceles triangle has a length 2x+4 and the base has length 3x. The

Mathematics

1 answer:

ikadub [295]2 years ago

4 0

Answer:

$Base = 57$

Step-by-step explanation:

Given

$Length = 2x + 4$

$Base = 3x$

$Perimeter = 141$

Required

Determine the length of the base

The perimeter of an isosceles triangle is:

$Perimeter = 2*Length + Base$

$141 = 2 (2x + 4) + 3x$

$141 = 4x + 8 + 3x$

Collect Like Terms

$4x + 3x = 141 - 8$

$7x = 133$

Divide both sides by 7

$x = 19$

To get the base, we substitute 19 for x in $Base = 3x$

$Base = 3 * 19$

$Base = 57$

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A confidence interval (CI) is desired for the true average stray-load loss u (watts) for a certain type of induction motor when

Genrish500 [490]

Answer:

A) CI = (57.12 , 59.48)

B) CI = (57.71 , 58.89)

C) CI = (57.53 , 59.07)

D) n = 239.63

Step-by-step explanation:

given data:

mean, $\bar X = 58.3$

standard deviation, σ = 3

sample size, n = 25Given CI level is 95%, hence α = 1 - 0.95 = 0.05

α/2 = 0.05/2 = 0.025,

Zc = Z(α/2) = 1.96

$ME = Zc * σ \sqrt{n}$

$ME = 1.96 * 3 \sqrt{25}$

ME = 1.18

$CI = (\bar X - Zc * s\sqrt{n} , \barX + Zc * s\sqrt{n})$

$CI = (58.3 - 1.96 * 3\sqrt{25} , 58.3 + 1.96 * 3\sqrt{25})$

CI = (57.12 , 59.48)

Given data:

mean, $\bar X = 58.3$

standard deviation, σ = 3

sample size, n = 100

Given CI level is 95%, hence α = 1 - 0.95 = 0.05

α/2 = 0.05/2 = 0.025, Zc = Z(α/2) = 1.96

$ME = zc * σ \sqrt{n}$

$ME = 1.96 * 3\sqrt{100}$

ME = 0.59

$CI = (\bar X - Zc * s\sqrt{n} , \barX + Zc * s\sqrt{n})$

$CI = (58.3 - 1.96 * 3\sqrt{100} , 58.3 + 1.96 * 3\sqrt{100})$

CI = (57.71 , 58.89)

sample mean, $\bar X = 58.3$

sample standard deviation, σ = 3

sample size, n = 100

Given CI level is 99%, hence α = 1 - 0.99 = 0.01

α/2 = 0.01/2 = 0.005, Zc = Z(α/2) = 2.58

$ME = Zc * σ \sqrt{n}$

$ME = 2.58 * 3\sqrt{100}$

ME = 0.77

$CI = (\bar X - Zc * s\sqrt{n} , \barX + Zc * s\sqrt{n})$

$CI = (58.3 - 2.58 * 3\sqrt{100} , 58.3 + 2.58 * 3/\sqrt{100}$

CI = (57.53 , 59.07)

Given data:

Significance Level, α = 0.01,

Margin or Error, E = 0.5,

σ = 3

The critical value for α = 0.01 is 2.58.

for calculating population mean we used

$n \geq (zc *σ/E)^2$

$n = (2.58 * 3/0.5)^2$

n = 239.63

7 0

3 years ago

Please help and explain these two problesm -2a + 4 (a - b ) + 5b x + 3 + 5 (x - 3)

Alenkinab [10]

Just use the distributing property and combine like terms. There isn’t a definite answer since it is an expression.

4 0

2 years ago

True or false

valina [46]

False because a number is rational if we can write it as a fraction where the top number of and bottom number are both whole numbers but irrational numbers is any number that is not rational. It is a number that cannot be written as a ratio of two integers(or cannot be expressed as a fraction)

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3 years ago

Write an algebraic expression to represent each scenario. Part A: “the sum of 6 and y”

Nostrana [21]

Answer:

6 + y

Step-by-step explanation:

Here, we want to write an algebraic expression to represent the situation

Mathematically, we want to add 6 and y

The algebraic expression will be;

6 + y

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3 years ago

What is 7 1/2 - 3 4/41

Radda [10]

The LCD of 2 and 41 is 82 so we write 1/2 as 41/82:-

7 41/82 - 3 8/82

= 4 33/82 Answer

7 0

3 years ago

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