Perform each of the following computations using the measured quantities below. a. 917.2 + 45.63 = ___
b. 3.423 x 10^-4 - 6.42 x 10^-3 =_

Answers

Answer 1

Answer:

Question

Perform each of the following computations using the measured quantities below.

Write your final answer with the correct number of significant figures in proper scientific notation (one non-zero number to the left of the decimal point).

a. 917.2 + 45.63 = ___________

b. 3.423 x 10^-4 - 6.42 x 10^-3 =_________

Answer:

(a) 9.6 x 10²

(b) -6.1 x 10⁻³

Step-by-step explanation:

(a) 917.2 + 45.63

First add the two numbers as follows (ensure that the decimal numbers are well aligned);

9 1 7 . 2

+ 4 5 . 6 3

9 6 2 . 8 3

To write the result in a proper scientific notation (one non-zero number to the left of the decimal point),

i. Express the number is standard form

962.83 = 9.6283 x 10²

Note that;

From the result in (i)

9.6283 = mantissa

10 = base

² = power or exponent.

ii. Express the mantissa of the number in 1 decimal place.

9.6 x 10²

Therefore, the result in the proper scientific notation is 9.6 x 10².

(b) 3.423 x 10⁻⁴ - 6.42 x 10⁻³

Find the difference between the two numbers as follows;

i. Re-write the numbers so that they both have the same exponents:

0.3423 x 10⁻³ - 6.42 x 10⁻³

ii. Factor out 10⁻³

10⁻³(0.3423 - 6.42)

iii. Solve the bracket

10⁻³(-6.0777)

iv. Rewrite the result in (iii)

-6.0777 x 10⁻³

To write the result in a proper scientific notation (one non-zero number to the left of the decimal point),

i. Express the number is standard form

-6.0777 x 10⁻³ [already in standard form]

Note that;

From the result in (i)

-6.0777 = mantissa

10 = base

⁻³ = power or exponent.

ii. Express the mantissa of the number in 1 decimal place.

-6.1 x 10⁻³

Therefore, the result in the proper scientific notation is -6.1 x 10⁻³.

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Answer:

See below.

Step-by-step explanation:

Rule:

$a^m * a^n = a^(m + n)$

Explanation:

When multiplying monomials with the same base, write the same base and add the exponents.

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The route used by a certain motorist in commuting to work contains two intersections with traffic signals. The probability that he must stop at the first signal is 0.45, the analogous probability for the second signal is 0.5, and the probability that he must stop at at least one of the two signals is 0.9.Required:
a. What is the probability that he must stop at both signals?
b. What is the probability that he must stop at the first signal but not at the second one?
c. What is the probability that he must stop at exactly one signal?

Answers

Answer: a. 0.05

b. 0.40

c. 0.85

Step-by-step explanation:

Let F= Event that a certain motorist must stop at the first signal.

S = Event that a certain motorist must stop at the second signal.

As per given,

P(F) = 0.45 , P(S) = 0.5 and P(F or S) = 0.9

a. Using general probability formula:

P(F and S) =P(F) + P(S)- P(F or S)

= 0.45+0.5-0.9

= 0.05

∴ the probability that he must stop at both signals = 0.05

b. Required probability = P(F but (not s)) = P(F) - P(F and S)

= 0.45-0.05= 0.40

∴ the probability that he must stop at the first signal but not at the second one =0.40

c. Required probability = P(exactly one)= P(F or S) - P(F and S)

= 0.9-0.05

= 0.85

∴ the probability that he must stop at exactly one signal = 0.85

Final answer:

The probability of stopping at both signals is 0.225, the probability of stopping at the first one but not the second one is 0.225. The probability of stopping at exactly one signal is 0.675.

Explanation:

The probability theory can be used to answer these questions. The probabilities of stopping at various traffic signals can be calculated using some assumptions about the independence of the events.

The probability of the motorist having to stop at both signals can be found by multiplying the individual probabilities, assuming that these are independent events. So, P(stop at both signals) = P(stop at first signal) * P(stop at second signal) = 0.45 * 0.5 = 0.225.
The probability of him stopping at the first signal but not at the second one is again found by multiplying the probability of stopping at the first by the probability of not having to stop at the second. Therefore, P(stop at first, not at second) = 0.45 * (1 - 0.5) = 0.225.
To find the probability that the driver must stop at exactly one signal, we can subtract the probability of stopping at both signals from the probability of stopping at least one signal. So, P(stop at one signal) = P(stop at at least one signal) - P(stop at both signals) = 0.9 - 0.225 = 0.675.

Learn more about Probability here:

brainly.com/question/22962752

#SPJ3

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Answers

$\large\begin{array}{I} \mathtt{ ( √(9x^2))/( √(18y^2))= (3x)/( 3√(2)y)= (x)/( √(2)y)}= ( √(2)x)/(2y) \end{array}$

Answer is A

A. 3x /3ysqrtof2. Multiply numerator and denominator by sqrt of 2
Then you have 3xsqrt of 2 /. 6y reduce by 3 both numerator and denominator
You have x sqrt of 2 / 2y

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Answers

P(Larger or blue) = 7/10. In a bag we have blue and red marbels, which are large and small as in the table shown in the image, the probability of taking a large or blue marble is 7/10.

The key to solve this problem is find the probability of the union events using the equation P(A∪B) = P(A) + P(B) - P(A∩B).

For this problem we have P(Large or Blue) = P(Large) + P(Blue) - P(Large and Blue). The total of the large ones is 25 and the small ones is 15, meaning that the sum of both is 40. P(large) = 25/40, P(Blue) 20/40, and P(Large and Blue) = 17/40

P(Large or Blue) = 25/40 + 20/40 - 17/40 = 28/40 dividing by 4 both terms of the fraction.

P(large or Blue) = 7/10

A boat propeller spins 1044 times in 3 MINUTES. Find the rate in revolutions per SECOND.

Answers

Answer:

The answer is 5.8 times a second

Step-by-step explanation:

Divide 1044 by 180 (The number of seconds in 3 minutes)

Final answer:

To calculate the rate in revolutions per second, we first convert the 3 minutes into seconds, which is 180 seconds. We then divide the total number of revolutions, 1044, by 180. This gives us a rate of 5.8 revolutions per second.

Explanation:

To solve this problem, we need to convert minutes into seconds because the rate is asked in revolutions per second.

Let's start by figuring out how many seconds are in those 3 minutes. We know that in 1 minute, there are 60 seconds. So, 3 minutes would be 3 times 60, which is 180 seconds.

Next, we will calculate the rate by dividing the total number of revolutions, which is 1044, by the total number of seconds, which is 180. So, 1044 ÷ 180 = 5.8.

This means that the propeller spins at a rate of 5.8 revolutions per second.