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soldier1979 [14.2K]

3 years ago

15

Julio works at an electronics store where he earns $11 an hour. Last week, he received a $120 bonus. How many hours did he work

if he earned $505 total last week

1 answer:

love history [14]3 years ago

7 0

He worked for 35 hours.

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Enter your answer and show all the steps that you use to solve this problem in the space provided.

NARA [144]

Answer:

19y - 9

Step-by-step explanation:

- 3(- 4y + 3) + 7y ← multiply each term in the parenthesis by - 3

= 12y - 9 + 7y ← collect like terms

= 19y - 9

3 0

3 years ago

What is considered the most famous impossible problem from Greek antiquity?

zaharov [31]

The most famous impossible problem from Greek Antiquity is doubling the cube. The problem is to construct a cube whose volume is double that of a given one. It is often denoted to as the Delian problem due to a myth that the Delians had look up Plato on the subject. In another form, the story proclaims that the Athenians in 430 B.C. consulted the oracle at Delos in the hope to break the plague devastating their country. They were advised by Apollo to double his altar that had the form of a cube. As an effect of several failed attempts to satisfy the god, the plague only got worse and at the end they turned to Plato for advice. (According to Rouse Ball and Coxeter, p 340, an Arab variant asserts that the plague had wrecked between the children of Israel but the name of Apollo had been discreetly gone astray.) According to a message from the mathematician Eratosthenes to King Ptolemy of Egypt, Euripides mentioned the Delian problem in one of his (now lost) tragedies. The other three antiquity are: angle trisection, squaring a circle, and constructing a regular heptagon.

7 0

3 years ago

Read 2 more answers

A news item is spreading by word of mouth through a population of size 12,000 people. After t days, the number of people (in tho

Lilit [14]

Answer:

a) 2.303

b) $f'(t)=\frac{432e^{-0.48t}}{(1+75e^{-0.48t})^{2}}$

c) 1.3609

e) $\frac{dy}{dx}=0.04y(12-y)$

f) 4.5 thousand people(smaller)

7.5 thousand people (larger)

e) t=7.93 days (smaller)

t=10.06 days (larger)

g) 1.44

Step-by-step explanation:

The given function is $y=f(t)=\frac{12}{1+75e^{-0.48t}}$

To find how many thousand people have heard the news after 6 days, we substitute to get:

$f(6)=\frac{12}{1+75e^{-0.48*6}}=2.303$ thousands.

b) We rewrite to get: $f(t)=12(1+75e^{-0.48t})^{-1}$

We differentiate using the chain rule to obtain:

$f'(t)=-12(1+75e^{-0.48t})^{-2}\cdot 75e^{-0.48t}\cdot -0.48$

This simplifies to:

$f'(t)=432e^{-0.48t}(1+75e^{-0.48t})^{-2}$

We rewrite as positive index to get:

$f'(t)=\frac{432e^{-0.48t}}{(1+75e^{-0.48t})^{2}}$

c) To find the rate at which the news is spreading after 8 days, we substitute t=8 into $f'(t)=\frac{432e^{-0.48t}}{(1+75e^{-0.48t})^{2}}$ to get:

$f'(8)=\frac{432e^{-0.48\cdot 8}}{(1+75e^{-0.48\cdot 8})^{2}}=1.3609$

d) The solution to the logistic differential equation:

$\frac{dy}{dt}=ky(M-y)$

is

$y=\frac{M}{1+be^{-Mkt}}$

By comparison, M=12, and $Mk=0.48$

$12k=0.48\\k=0.04$

The differential equation is:

$\frac{dy}{dx}=0.04y(12-y)$

e) To how many people have heard the news when its rate of spread is 1.35 thousand per day, we equate the differential equation to 1.35 and so for t first.

$\frac{432e^{-0.48t}}{(1+75e^{-0.48t})^{2}}=1.35$

This gives us: t=10.06 ot t=7.93

We substitute the times into the function to get:

$f(7.93)=\frac{12}{1+75e^{-0.48\cdot7.93}}$ =4.5 thousand: smaller value

$f(10.06)=\frac{12}{1+75e^{-0.48\cdot10.06}}=7.5$ thousand: Larger value

f) The two times that the news is spreading at rate 1.35 thousand people per day are:

$t=7.93$ days: Smaller value

$t=10.06$ : Larger value

g) To find the fastest rate at which the news spread we take the second derivative and equate it to zero.

$f''(t)=0$

This corresponds to where the horizontal line is tangent to

$f'(t)=\frac{432e^{-0.48t}}{(1+75e^{-0.48t})^{2}}$

From the graph the point of tangency is:

(8.99,1.44)

Therefore the fastest rate at which the news spread is 1.44

7 0

3 years ago

Write an equivalent expression by distributing the "_" sign outside the parentheses-(6p-7.2)

kramer

What’s the 6p-7.2 is that suppose to be like an example or page number

8 0

3 years ago

5n +20n = 5(n+20) find N

likoan [24]

Answer:

n = 5

Step-by-step explanation:

Given

5n + 20n = 5(n + 20), that is

25n = 5(n + 20) ← divide both sides by 5

5n = n + 20 ( subtract n from both sides )

4n = 20 ( divide both sides by 4 )

n = 5

6 0

3 years ago

Read 2 more answers