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2 years ago

(3x) (4x) = A. – x B. 7x C. 12x D. 12x² E. none of these

Mathematics

1 answer:

Mice21 [21]2 years ago

8 0

$\huge\text{Hey there!}$

$\large\textbf{Equation: }$

$\large\textsf{(3x)(4x)}$

$\large\textbf{Solving:}$

$\large\textsf{(3x)(4x)}$

$\large\textsf{= 3x} * \large\textsf{4x}$

$\large\textbf{Combine the like terms:}$

$\large\textsf{(3x * 4x)}$

$\large\textsf{= 3x * 4x}$

$\large\textsf{= 12x}^2$

$\large\textbf{Therefore, your answer should be: }$

$\huge\boxed{\frak{Option\ D. 12\mathsf{x}^2}}\huge\checkmark$

$\huge\text{Good luck on your assignment \& enjoy your day!}$

~ $\frak{Amphitrite1040:)}$

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Answer:

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(a) This means 0.9 * 1000 = 900 intervals will capture u

(b) Here we treat CI as binomial random variable, having probability 0.9 for success

n = 1000

p = 0.9

For this case, applying normal approximation to binomial, we get:

mean = n*p= 900

variance = n*p*(1-p) = 90

std dev = 9.4868

We want to Find : P(890 <= X <= 910) = P( 889.5 < X < 910.5) (integer continuity correction)

We convert to standard normal form, Z ~ N(0,1) by z1 = (x1 - u )/s

so z1 = (889.5 - 900 )/9.4868 = -1.11

so z2 = (910.5 - 900 )/9.4868 = 1.11

P( 889.5 < X < 910.5) = P(z1 < Z < z2) = P( Z < 1.11) - P(Z < -1.11)

= 0.8665 - 0.1335

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3 years ago

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Step-by-step explanation:

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3 years ago

Select the correct answer.

FromTheMoon [43]

The approximate area in square feet of the sides panel is 146.4 feet.

where

b = base

h = height

Therefore, let's find the height and the base using trigonometric ratios.

sin 30 = opposite / hypotenuse

sin 30° = h / 26

cross multiply

h = 26 × 1 / 2

h = 13 ft.

Let's find the base using Pythagoras theorem.

b² = 26² - 13²

b² = 676 - 169

b = √507

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2 years ago

Use the graph to determine

gtnhenbr [62]

Answer:

a) Domain: x≥0

b) Range: y≤-2

c) x-intercepts: None

d) y-intercepts: (0,-2)

e) f(4)= -4

Step-by-step explanation:

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5 0

3 years ago

Initially 100 milligrams of a radioactive substance was present. After 6 hours the mass had decreased by 3%. If the rate of deca

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Answer:

The half-life of the radioactive substance is 135.9 hours.

Step-by-step explanation:

The rate of decay is proportional to the amount of the substance present at time t

This means that the amount of the substance can be modeled by the following differential equation:

$\frac{dQ}{dt} = -rt$

Which has the following solution:

$Q(t) = Q(0)e^{-rt}$

In which Q(t) is the amount after t hours, Q(0) is the initial amount and r is the decay rate.

After 6 hours the mass had decreased by 3%.

This means that $Q(6) = (1-0.03)Q(0) = 0.97Q(0)$ . We use this to find r.

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$0.97Q(0) = Q(0)e^{-6r}$

$e^{-6r} = 0.97$

$\ln{e^{-6r}} = \ln{0.97}$

$-6r = \ln{0.97}$

$r = -\frac{\ln{0.97}}{6}$

$r = 0.0051$

$Q(t) = Q(0)e^{-0.0051t}$

Determine the half-life of the radioactive substance.

This is t for which Q(t) = 0.5Q(0). So

$Q(t) = Q(0)e^{-0.0051t}$

$0.5Q(0) = Q(0)e^{-0.0051t}$

$e^{-0.0051t} = 0.5$

$\ln{e^{-0.0051t}} = \ln{0.5}$

$-0.0051t = \ln{0.5}$

$t = -\frac{\ln{0.5}}{0.0051}$

$t = 135.9$

The half-life of the radioactive substance is 135.9 hours.

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3 years ago