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2 years ago

6

A jet flies at a rate of 1.3 * 10^6 feet per hour. Written in scientific notation, which is the best estimate of how many feet t

he jet will travel in 2.8 *10^3 hours?

2 answers:

kow [346]2 years ago

8 0

Answer:

C. 3x10^9

Step-by-step explanation:

FromTheMoon [43]2 years ago

3 0

To determine the distance covered by the jet in a given time, we simply multiply the rate or velocity of the jet to the time elapsed. It is important to take note of the units. It should be homogeneous. We calculate as follows:

1.3x10^6 x 2.8x10^3 = 3.64x10^9 ft

Hope this answers the question. Have a nice day.

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Evelyn has $524.96 in her checking account. She must maintain a $500 balance to avoid a fee. She wrote a check for $32.50 today.

barxatty [35]

Answer:

524.96 − 32.50 + x ≥ 500

Amount need to deposit = $7.54

Step-by-step explanation:

Given:

Amount in checking account = $524.96

Maintain amount = $500

Amount of check = $32.50

Find:

Amount need to deposit

Computation:

Assume, amount need to deposit = x

So,

For avoiding fee

524.96 − 32.50 + x ≥ 500

x = 7.54

Amount need to deposit = $7.54

4 0

2 years ago

Which sequence could be partially defined by the recursive formula f (n + 1) = f(n) + 2.5 for n ≥ 1?

horrorfan [7]

Option C: –10, –7.5, –5, –2.5, … is the sequence that could be partially defined by the recursive formula $f(n+1)=f(n)+2.5$

Explanation:

The given recursive formula is $f(n+1)=f(n)+2.5$ for $n\geq 1$ and $f(1)=-10$

We need to determine the sequence.

The sequence can be determined by substituting n = 1, 2, 3, 4,....

<u>2nd term of the sequence:</u>

Substituting n = 1 in the formula $f(n+1)=f(n)+2.5$ , we get,

$f(1+1)=f(1)+2.5$

Simplifying, we have,

$f(2)=-10+2.5=-7.5$

Thus, the 2nd term of the sequence is -7.5

<u>3rd term of the sequence:</u>

Substituting n = 2 in the formula $f(n+1)=f(n)+2.5$ , we get,

$f(2+1)=f(2)+2.5$

Simplifying, we have,

$f(3)=-7.5+2.5=-5$

Thus, the 3rd term of the sequence is -5

<u>4th term of the sequence:</u>

Substituting n = 3 in the formula $f(n+1)=f(n)+2.5$ , we get,

$f(3+1)=f(3)+2.5$

Simplifying, we have,

$f(4)=-5+2.5=-2.5$

Thus, the 4th term of the sequence is -2.5

Therefore, the sequence is –10, –7.5, –5, –2.5, …

Hence, Option C is the correct answer.

3 0

1 year ago

Kate packs snow into 5 identical jars. Each jar represents a different depth of snow. Kate then lets the snow in each jar comple

Xelga [282]

Answer:

A, C, E

Step-by-step explanation:

From the table you can see that the water depth cahnges

$0.8-0.4=1.2-0.8=1.6-1.2=2.0-1.6=0.4\ in$

for every

$4-2=6-4=8-6=10-8=2\ in$ of snow (option B is false).

This means that the function modelling this situation is linear function (option A is true and option D is false). Let the equation of this function be $y=ax+b.$ Then

$0.4=2a+b,\\ \\0.8=4a+b.$

Subtract these two equations:

$2a=0.8-0.4,\\ \\2a=0.4,\\ \\a=0.2.$

Hence,

$b=0.4-2\cdot 0.2=0.$

The equation of the straight line (the graph of linear function) is $y=0.2x.$ (option E is true) This line passes through the point (0,0), because its coordinates satisfy the equation (option C is true).

9 0

2 years ago

Read 2 more answers

According to a Wired magazine article, of e-mails that are received are tracked using software that can tell the e-mail sender w

VladimirAG [237]

Answer:

a. 12

b. 7.200 and 2.683

Step-by-step explanation:

The computation is shown below:

Given that

P = 0.40 and n = 30

a)

The expected value of received e-mails is

= n × p

= 30 × 0.4

= 12

b)

The variance of emails received is

= n × p × (1 - p)

= 30 × 0.4 × 0.6

= 7.200

Now

The standard deviation of emails received is

= sqrt(variance)

= 2.683

We simply applied the above formula

8 0

1 year ago

A box contains 5 red and 5 blue marbles. Two marbles are withdrawn randomly. If they are the same color, then you win $1.10; if

topjm [15]

Answer:

a) The expected value is $\frac{-1}{15}$

b) The variance is $\frac{49}{45}$

Step-by-step explanation:

We can assume that both marbles are withdrawn at the same time. We will define the probability as follows

#events of interest/total number of events.

We have 10 marbles in total. The number of different ways in which we can withdrawn 2 marbles out of 10 is $\binom{10}{2}$ .

Consider the case in which we choose two of the same color. That is, out of 5, we pick 2. The different ways of choosing 2 out of 5 is $\binom{5}{2}$ . Since we have 2 colors, we can either choose 2 of them blue or 2 of the red, so the total number of ways of choosing is just the double.

Consider the case in which we choose one of each color. Then, out of 5 we pick 1. So, the total number of ways in which we pick 1 of each color is $\binom{5}{1}\cdot \binom{5}{1}$ . So, we define the following probabilities.

Probability of winning: $\frac{2\binom{5}{2}}{\binom{10}{2}}= \frac{4}{9}$

Probability of losing $\frac{(\binom{5}{1})^2}{\binom{10}{2}}\frac{5}{9}$

Let X be the expected value of the amount you can win. Then,

E(X) = 1.10*probability of winning - 1 probability of losing = $1.10\cdot \frac{4}{9}-\frac{5}{9}=\frac{-1}{15}$

Consider the expected value of the square of the amount you can win, Then

E(X^2) = (1.10^2)*probability of winning + probability of losing = $1.10^2\cdot \frac{4}{9}+\frac{5}{9}=\frac{82}{75}$

We will use the following formula

$Var(X) = E(X^2)-E(X)^2$

Thus

Var(X) = $\frac{82}{75}-(\frac{-1}{15})^2 = \frac{49}{45}$

7 0

2 years ago