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2 years ago

If a lineman can install 12 insulators in 183/4 hours, how many insulators should he be able to install in 281/8 hours?

Mathematics

1 answer:

katrin2010 [14]2 years ago

3 0

Answer: 9

Step-by-step explanation:

12 insulators = 183/4 hours

x = 281/8

x × 183/4 = 12 ×281/ 8

183x/4 = 6 × 281/4

183x / 4 = 1686 / 4

4 cancel out 4

183x = 1686

Divide bothside by 183

x = 1686/183

x= 9.21311

x = 9 approximately.

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First, she needs to find her resting heart rate by counting her pulse for one minute immediately after she wakes up for 5 days i

andreyandreev [35.5K]

Answer:

Step-by-step explanation:

She finds her average resting heart rate to be 62 after 5 days.

That means, average of the 5 heart rate pulse=62

If the last day was 58 and all the other days were the same.

Let x be her pulse on the other days,

Then,

$Average, 62=\dfrac{58+4x}{5}\\\text{Cross Multiply}\\58+4x=62 X 5\\\text{Suntract 58 from both sides}\\4x=(62X5)-58\\4x=310-58\\4x=252\\\text{Divide both sides by 4}\\x=63$

Her pulse on all the other days is 63.

4 0

2 years ago

Almonds cost $5.20 per pound Raisins cost $2.75 per pound Priya spent $11.70 of buying almonds & raisins Equation: 5.20+2.75

murzikaleks [220]

Answer:

If she bought 2lbs of almonds, she bought 0.4lbs of raisins. If she bought 1lb of almonds, she can buy up to 2.36lbs of raisins. If she bought 0.64lbs of almonds, she can buy up to 1.9lbs of almonds.

Step-by-step explanation:

6 0

2 years ago

What are the factors of the polynomial function? Use the rational root theorem to determine the factors. f(x) = 2x³ + x² - 8x -

fredd [130]

Answer:

( x + 2 ) ( x - 2 ) ( 2x + 1)

Step-by-step explanation:

coefficient of x³ is 2 and denote it with q and denote -4 as p

the set of possible rational roots through rational theorem will be within ± (p/q)

now factors of -4 are ±(1,2,4) and factors of 2 are ± (1,2) the possible rational roots are ± ( 1/1, 1/2, 2/1, 2/2, 4/1, 4/2) which reduces to ± (1, 1/2, 2, 4)

substitute each of the value into the equation

f(x) = 2x³ + x² - 8x - 4 to the root ( that gives f(x) = 0)

the equation can be made easy writing it in reduced form

2x³ + x² - 8x - 4

(2x³ + x²) - (8x + 4)

x² (2x + 1) - 4 (2x + 1)

(x² - 4) (2x + 1)

( x + 2 ) ( x - 2) ( 2x + 1) are the factors which correspond to 2, -2, -1/2 roots

4 0

2 years ago

5 equally sized boxes of cake mix fell off the back of Jake's truck. Together they weigh 925.98 pounds. How much does each ball

uysha [10]

we are given

5 equally sized boxes of cake mix fell off the back of Jake's truck

it means that

total number of balls =5

Together they weigh 925.98 pounds

total weighs =925.98 pounds

each ball weighs = (total weights)/(total number of balls)

now, we can plug values

each ball weighs = $\frac{925.98}{5}$

each ball weighs is 185.196 pounds..................Answer

4 0

2 years ago

The time intervals between successive barges passing a certain point on a busy waterway have an exponential distribution with me

lisov135 [29]

Answer:

a) 0.4647

b) 24.6 secs

Step-by-step explanation:

Let T be interval between two successive barges

t(t) = λe^λt where t > 0

The mean of the exponential

E(T) = 1/λ

E(T) = 8

1/λ = 8

λ = 1/8

∴ t(t) = 1/8×e^-t/8 [ t > 0]

Now the probability we need

p[T<5] = ₀∫⁵ t(t) dt

=₀∫⁵ 1/8×e^-t/8 dt

= 1/8 ₀∫⁵ e^-t/8 dt

= 1/8 [ (e^-t/8) / -1/8 ]₀⁵

= - [ e^-t/8]₀⁵

= - [ e^-5/8 - 1 ]

= 1 - e^-5/8 = 0.4647

Therefore the probability that the time interval between two successive barges is less than 5 minutes is 0.4647

Now we find t such that;

p[T>t] = 0.95

t_∫¹⁰ t(x) dx = 0.95

t_∫¹⁰ 1/8×e^-x/8 = 0.95

1/8 t_∫¹⁰ e^-x/8 dx = 0.95

1/8 [( e^-x/8 ) / - 1/8 ]¹⁰_t = 0.95

- [ e^-x/8]¹⁰_t = 0.96

- [ 0 - e^-t/8 ] = 0.95

e^-t/8 = 0.95

take log of both sides

log (e^-t/8) = log (0.95)

-t/8 = In(0.95)

-t/8 = -0.0513

t = 8 × 0.0513

t = 0.4104 (min)

so we convert to seconds

t = 0.4104 × 60

t = 24.6 secs

Therefore the time interval t such that we can be 95% sure that the time interval between two successive barges will be greater than t is 24.6 secs

6 0

2 years ago