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2 years ago

The perimeter of a triangle is 170 ft and the sides are in the ratio of 25:14:12. Find the area of the triangle

Mathematics

1 answer:

EastWind [94]2 years ago

8 0

using the ratio, the length of the sides are:

25x + 14x + 12x = 170

51x = 170

x = 170 / 51

x = 3 1/3

The lengths of the sides are: 25 * 3 1/3 = 83 1/3 feet

14 x 3 1/3 = 46 2/3 feet

12 x 3 1/3 = 40 feet

Using Heron's formula

the semi perimeter (S) = 170/2 = 85 ft.

The area of the triangle = SQRT(S*(S-83 1/3) * (S - 46 2/3) * (S-40))

= SQRT (85 * (85-83 1/3) * (85 - 46 2/3) * (85-40)

= SQRT (85 * 1 2/3 * 38 1/3 * 45)

= SQRT(244374)

= 494.34 square feet ( round answer as needed).

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Which expressions are equivalent to StartFraction 1 Over 36 EndFraction? Check all that apply. 3 Superscript negative 6 6 Supers

Elenna [48]

Answer:

6^-2

6^3/6^5

6^-9 *6^ 7

Step-by-step explanation:

We want the fractions equal to 1/36

We know that a^-b = 1/a^b

We also know that a^b / a^c = a^(b-c)

We also know that a^b * a^c = a^(b+c)

3^ -6 = 1/3^6 = 1/729

6^-2 = 1/6^2 = 1/36

6^3/6^5 = 6^(3-5) = 6^-2 = 1/6^2 = 1/36

6^2 / 6^-1 = 6^(2- -1) = 6^3 = 216

6*6^-2 = 6^(1-2) = 6^-1 = 1/6

6^-9 *6^ 7 = 6^(-9+7) = 6^ -2 = 1/6^2 = 1/36

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2 years ago

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Consider the following scenario. Bob is playing a board game where he blindly picks a tile from a container and moves some space

postnew [5]

The game is fair.

Pls. see my attachment.

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2 years ago

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The dye dilution method is used to measure cardiac output with 3 mg of dye. The dye concentrations, in mg/L, are modeled by c(t)

Lemur [1.5K]

Answer:

Cardiac output: $F=0.055 L\s$

Step-by-step explanation:

Given : The dye dilution method is used to measure cardiac output with 3 mg of dye.

To Find : Find the cardiac output.

Solution:

Formula of cardiac output: $F=\frac{A}{\int\limits^T_0 {c(t)} \, dt}$ ---1

A = 3 mg

$\int\limits^T_0 {c(t)} \, dt =\int\limits^{10}_0 {20te^{-0.06t}} \, dt$

Do, integration by parts

$[\int{20te^{-0.6t}} \, dt]^{10}_0=[20t\int{e^{-0.6t} \,dt}-\int[\frac{d[20t]}{dt}\int {e^{-0.6t} \, dt]dt]^{10}_0$

$[\int{20te^{-0.6t}} \, dt]^{10}_0=[\frac{-20te^{-0.6t}}{0.6}+\frac{20}{0.6}\int {e^{-0.6t} \,dt]^{10}_0$

$[\int{20te^{-0.6t}} \, dt]^{10}_0=[\frac{-20te^{-0.6t}}{0.6}+\frac{20e^{-0.6t}}{(0.6)^2}]^{10}_{0}$

$[\int{20te^{-0.6t}} \, dt]^{10}_0=[\frac{-200e^{-6}}{0.6}+\frac{20e^{-6}}{(0.6)^2}]+\frac{20}{(0.60^2}$

$[\int{20te^{-0.6t}} \, dt]^{10}_0=\frac{20(1-e^{-6}}{(0.6)^2}-\frac{200e^{-6}}{0.6}$

$[\int{20te^{-0.6t}} \, dt]^{10}_0\sim {54.49}$

Substitute the value in 1

Cardiac output: $F=\frac{3}{54.49}$

Cardiac output: $F=0.055 L\s$

Hence Cardiac output: $F=0.055 L\s$

4 0

2 years ago

The time between failures for an electrical appliance is exponentially distributed with a mean of 25 months. What is the probabi

katrin [286]

Answer:

The probability that the next failure will not occur before 30 months have elapsed is 0.0454

Step-by-step explanation:

Using Poisson distribution where

t= number of units of time

x= number of occurrences in t units of time

λ= average number of occurrences per unit of time

P(x;λt) = e raise to power (-λt) multiplied by λtˣ divided by x!

here λt = 25

x= 30

P(x= 30) = 25³⁰e⁻²⁵/ 30!

P (x= 30) = 8.67 E41 * 1.3887 E-11/30! (where E= exponent)

P (x=30) = 1.204 E31/30!

Solving it with a statistical calculator would give

P (x=30) = 0.0454

The probability that the next failure will not occur before 30 months have elapsed is 0.0454

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2 years ago

The volume of air inside a rubber ball with radius r can be found using the function V(r) = four-thirds pi r cubed. What does V

Nat2105 [25]

Corrected Question

The volume of air inside a rubber ball with radius r can be found using the function V(r) = four-thirds pi r cubed. What does V(5/7) represent?

Answer:

(B)the volume of the rubber ball when the radius equals five-sevenths feet

Step-by-step explanation:

The Volume of a sphere of radius r can be found using the formula:

$V(r)=\dfrac43 \pi r^3$

Therefore comparing the expression: $V(\dfrac57)$ with V(r):

$Radius, r=\dfrac57$

Thus, $V(\dfrac57)$ is the volume of a ball of radius $\dfrac57$ feet.

The correct option is B.

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2 years ago

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