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3 years ago

Solve for y. 7y - 14 = 35

Mathematics

2 answers:

Radda [10]3 years ago

8 0

Answer:

it's 7

Step-by-step explanation:

this needs to be 20 characters long

Andreyy893 years ago

5 0

Answer:

switch the -14 to positive and the add 35+14 and then divide the number you get by 7

Step-by-step explanation:

y=7

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Joes apple weighs 4/5 martas apple weighs 0.5 how much more does joes weigh than martas

FromTheMoon [43]

Answer:

0.3

Step-by-step explanation:

4/5=0.8

0.8-0.5=0.3

6 0

4 years ago

Read 2 more answers

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taurus [48]

Answer:

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7 0

3 years ago

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:

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

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

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

The area of one fabric is 4.85 square what is the area of a quilt made with 10.2 fabric squares

Sindrei [870]

10 x 10 = $2_{10}$

since 1 square equals 4.85 sq inches we can multiply 4.85 with 100

4.85 x 100 = 485

so, your answer is <u>485 </u>

hope this helps!

5 0

4 years ago

6. Let E, F, G be three events. Find expressions for the events that of E, F, G a. only E occurs; b. both E and G but not F occu

marta [7]

Answer:

a.) only E occurs :

E((FUG)')

b.) both E and G but not F

EG(F')

C.) Atleast one of the events :

(E U G U F)

d.) Atleast two of the events

(EG U EF U GF)

E.) all three occurs

(EGF)

F.) none of the events occur :

(E U G U F)'

G.) At most one of the events occur

(EG U EF U GF)'

H.) at most two of them occur

(E' U G' U F')

I.) exactly two of them occur;

(EG U EF U GF) * (EGF)'

j. at most three of them occur.

EFG U (EFG)'

Step-by-step explanation:

Events = {E, F, G}

a.) only E occurs :

E((FUG)') ; E and not F or G

b.) both E and G but not F

EG(F') ; both E and G and not F

C.) Atleast one of the events :

(E U G U F) ; Either E or F or G

d.) Atleast two of the events

(EG U EF U GF) ; Either EG or EF or GF occurs

E.) all three occurs

(EGF) ; All three events, E, G and F occurs

F.) none of the events occur :

(E U G U F)' ; Neither E, G nor F occurs

G.) At most one of the events occur

(EG U EF U GF)' ; complement of atleast two) at most one

H.) at most two of them occur

(E' U G' U F') ; Either E , F or G does not occur

I.) exactly two of them occur;

(EG U EF U GF) * (EGF)' ; Exactly two events occurs and all three events Do not occur

j. at most three of them occur.

EFG U (EFG)' ; All three events occur union all three events do not occur

6 0

3 years ago