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snow_tiger [21]

3 years ago

8

Jacob and 6 of his friends went out to eat. They decided to split the bill evenly. Each person paid $14.93. Write and solve an e

quation to find the total bill.

2 answers:

jasenka [17]3 years ago

8 0

Answer:

$89.58

Step-by-step explanation:

$14.93*6=$89.58

Sphinxa [80]3 years ago

7 0

All you would have to do is take 7 and times it by 14.93

7 • $14.93= $104.51

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M Enter the number that belongs in<br> the green box

gladu [14]

Answer:

m<C = 180 - (90+32)

= 180 - 122

= 58°

4 0

2 years ago

Find the sum of the first 20 terms of the arithmetic sequence 4, 10, 16, 22....

hammer [34]

n = 20

d = 6

a = 4

L = a + (n - 1)*d

L = 4 + (20 - 1)*6

L = 4 + 19*6

L = 118

Sum = (a + L)*n/2

Sum = (4 + 118) * 20/2

Sum = 122 * 10

Sum = 1220

3 0

3 years ago

There are 42 students in an elementary statistics class. On the basis of years of experience, the instructor knows that the time

harkovskaia [24]

Answer:

A) 0.99413

B) 0.00022

Step-by-step explanation:

A) First of all let's find the total grading time from 6:50 P.M to 11:00 P.M.:

Total grading time; X = 11:00 - 6:50 = 4hours 10minutes = 250 minutes

Now since we are given an expected value of 5 minutes, the mean grading time for the whole population would be:

μ = n*μ_s ample = 42 × 5 = 210 minutes

While the standard deviation for the population would be:

σ = √nσ_sample = √(42 × 6) = 15.8745 minutes

To find the z-score, we will use the formula;

z = (x - μ)/σ

Thus;

z = (250 - 210)/15.8745

z = 2.52

From the z-distribution table attached, we have;

P(Z < 2.52) ≈ 0.99413

B) solving this is almost the same as in A above, the only difference is an additional 10 minutes to the time.

Thus, total time is now 250 + 10 = 260 minutes

Similar to the z-formula in A above, we have;

z = (260 - 210)/15.8745

z = 3.15

P(Z > 3.15) = 0.00022

5 0

3 years ago

The contrapositive of a conditional statement is "If an item is not worth five dimes, then it is not worth two quarters.”

balandron [24]

Example of use of terms:
Statement: If it is far, we take a bus.
Inverse: If it is not far, we do not take a bus.
Converse: If we take a bus, it is far.
Contrapositive: If we do not take a bus, it is not far.

We also know that
1. The inverse of the inverse is the statement itself, and similarly for converse and contrapositive.
2. Only the contrapositive is logically equivalent to the original statement.
This means that the converse and inverse are logically different from the original statement.

Now back to the given statement.
To find the original statement, we find the contrapositive of the contrapositive.
We then find the converse from the original statement, as in the example above.

Original statement
(note that in English, if it is not worth X dollars, means if it is not worth AT LEAST X dollars")
contrapositive of
<span>
"If an item is not worth five dimes, then it is not worth two quarters.”
is the negation of the converse, which become
"If an item is worth two quarters, then it is worth (at least) five dimes."

The converse of the previous statement is therefore
"If an item is worth (at least) five dimes then it is worth two quarters"

In this particular case, we can also take advantage of the fact that the contrapositive is the negation of the converse. So all we have to do is the provide the negation of each component of the contrapositive to get the converse:
"If an item is worth (at least) five dimes, then it is worth two quarters".
as before.

Note that the converse does NOT logically mean the same as the original statement.

</span>

6 0

3 years ago

Identify whether the equation represents an exponential growth or exponential decay function.1. y = 1/4 (1/e)^-2x2. y = (1/e)^4x

zvonat [6]

The general formula for exponential growth and decays is:

$y=y_0e^{kx}$

if k>0 then then it is an exponential growth function. If k<0 then the function represents an exponential decay.

Now we need to classify each of the functions:

1.

The function

$y=\frac{1}{4}(\frac{1}{e})^{-2x}$

can be wrtten as:

$\begin{gathered} y=\frac{1}{4}(e^{-1})^{-2x}^{} \\ =\frac{1}{4}e^{2x} \end{gathered}$

comparing with the general formula we notice that k=2, therefore this is an exponential growth.

2.

The function

$y=(\frac{1}{e})^{4x}$

can be written as:

$\begin{gathered} y=(\frac{1}{e})^{4x} \\ y=(e^{-1})^{4x} \\ y=e^{-4x} \end{gathered}$

comparing with the general formula we notice that k=-4, therefore this is an exponential decay.

3.

The function

$y=2e^{-x}+1$

comparing with the general formula we notice that k=-1, therefore this is an exponential decay.

5 0

1 year ago