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Minchanka [31]
2 years ago
13

Antonio runs 5 3/4 miles a day hes halfway through his run

Mathematics
2 answers:
nataly862011 [7]2 years ago
5 0
1/2 of 5 3/4 is 2.875 
Vikentia [17]2 years ago
4 0
2.875 is the answer
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What is the completely factored form of f(x)=x3+5x2+4x−6?
Gre4nikov [31]
f(x)=x^3+5x^2+4x-6
f(-3)=(-3)^3+5(-3)^2+4(-3)-6=0\implies x+3\text{ is a factor of }f(x)

Synthetic division yields

-3  |  1   5   4   -6
.    |      -3  -6    6
- - - - - - - - - - - - -
.    |  1   2  -2    0

which translates to

\dfrac{x^3+5x^2+4x-6}{x+3}=x^2+2x-2

with remainder 0. Now by the quadratic formula,

x^2+2x-2=0\implies x=\dfrac{-2\pm\sqrt{2^2-4(1)(-2)}}2=-1\pm\sqrt3

and so

f(x)=x^3+5x^2+4x-6=(x+3)(x-(-1+\sqrt3))(x-(-1-\sqrt3))
3 0
2 years ago
Repair calls are handled by one repairman at a photocopy shop. Repair time, including travel time, is exponentially distributed,
seropon [69]

Answer and Step-by-step explanation:

Data provided in the question

Mean = 1.1 hours per call =

R = Mean rate = 1.6 per eight hour day

\mu = \frac{8}{1.6} = 5 per day

Based on the above information

a. The average number of customers is

= \frac{R^2}{\mu(\mu- R)}

= \frac{1.6^2}{5(5- 1.6)}

= 151

b. The system utilization is

= \frac{R}{\mu}

= \frac{1.6}{5}

= 0.32

c. The amount of time required is

= 1 - system utilization

= 1 - 0.32

= 0.68

And, there is 8 hours per day

So, it would be

= 0.68 \times 8

= 5.44 hours

d. Now the probability of two or more customers is

= 1 - (0.68 + 0.68 \times 0.32)

= 0.1024

Therefore we simply applied the above formulas

4 0
2 years ago
A building has an entry the shape of a parabolic arch 74 ft high and 28 ft wide at the base as shown below.
sergiy2304 [10]
The equation of a parabola with vertex at (h,k) is 
y=a(x-h)²+k

vertex isi at (0,0)

y=a(x-0)²+0
y=a(x)²
y=ax²
find a

we see that one point is (14,-74)
x=14 and y=-74

-74=a(14²)
-74=196a
divide both sides by 196
-37/98=a

the equation is 

y= \frac{-37}{98} x^2




6 0
2 years ago
Read 2 more answers
Arthur took out a 20 year loan for $60,000 at an APR of 4.4% compounded monthly. Approximately how munch would save if he paid i
Eduardwww [97]
Monthly payments, P = {R/12*A}/{1- (1+R/12)^-12n}

Where R = APR = 4.4% = 0.044, A = Amount borrowed = $60,000, n = Time the loan will be repaid

For 20 years, n = 20 years
P1 = {0.044/12*60000}/{1- (1+0.044/12)^-12*20} = $376.36

Total amount to be paid in 20 years, A1 = 376.36*20*12 = $90,326.30

For 3 years early, n = 17 year
P2 = {0.044/12*60,000}/{1-(1+0.044/12)^-12*17} = $418.22

Total amount to be paid in 17 years, A2 = 418.22*17*12 = $85,316.98

The saving when the loan is paid off 3 year early = A1-A2 = 90,326.30 - 85,316.98 = $5,009.32

Therefore, the approximate amount of savings is A. $4,516.32. This value is lower than the one calculated since the time of repaying the loan does not change. After 17 years, the borrower only clears the remaining amount of the principle amount.
8 0
2 years ago
Read 2 more answers
On some days,Melvin commutes 3.5 hours per day to the city for business meetings.Last week he commuted for a total of 14 hours.H
DanielleElmas [232]
Formula:

Total hours ÷ hour per day

14 ÷ 3.5 = 4.

The answer is 4.

He commuted 4 days for the city.


3 0
2 years ago
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