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alexdok [17]
3 years ago
9

Oil is leaking from a tanker at the rate of R(t) = 2000e^(-0.2t) gallons per hour where t is measured in hours. How much oil lea

ks out of the tanker from the time t = 0 to t = 10
...?
Mathematics
1 answer:
Virty [35]3 years ago
4 0
We first integrate the expression to find the oil leaked since we have an expression for leakage rate.
Integrating:
O(t) = -10000exp(-0.2t); substituting t = 10
O(t) = -1,353 gallons
1,353 gallons of oil leak out in the first 10 seconds.
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I need help with number 3
Marizza181 [45]
Area  of circle  = pi r^2 = 78.54
r^2 = 78.54 / pi = 25
r = 5 inches

Each line from centre of the circle to a point on the hexagon = 5 ins

so  consider one of the 6 congruent triangles formed from these lines:-
Vertex angle = 60 degrees

sin 30  = 0.5s / 5    (where  s = one side of the hexagon).
0.5s = 5*0.5 = 2.5
s = 2.5 / 0.5 =  5 

So the perimeter of the hexagon is 6*5  = 30 inches




8 0
3 years ago
The function f(x) = 2x2 + 3x + 5, when evaluated, gives a value of 19. What is the function’s input value?
iren2701 [21]
F(x)......ur output = 19

19 = 2x^2 + 3x + 5
2x^2 + 3x + 5 - 19 = 0
2x^2 + 3x - 14 = 0
(2x + 7)(x - 2) = 0

2x + 7 = 0
2x = -7
x = -7/2

x - 2 = 0
x = 2

I believe there is 2 possible answers......x (ur input value) = -7/2 or 2
4 0
3 years ago
Find the equation of the graphed line.
topjm [15]
I think that the answer is definitely B
5 0
2 years ago
A particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. From past
Minchanka [31]
<h2><u>Answer with explanation</u>:</h2>

Let \mu be the distance traveled by deluxe tire .

As per given , we have

Null hypothesis : H_0 : \mu \geq50000

Alternative hypothesis : H_a : \mu

Since H_a is left-tailed and population standard deviation is known, thus we should perform left-tailed z-test.

Test statistic : z=\dfrac{\overlien{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}

where, n= sample size

\overline{x}= sample mean

\mu= Population mean

s=sample standard deviation

For n= 31,\ \sigma=8000,\ \overline{x}=46,800\ \&\ s=46,800, we have

z=\dfrac{46800-50000}{\dfrac{8000}{\sqrt{31}}}=-2.23

By using z-value table,

P-value for left tailed test : P(z≤-2.23)=1-P(z<2.23)   [∵P(Z≤-z)=1-P(Z≤z)]

=1-0.9871=0.0129

 Decision : Since p value (0.0129) < significance level  (0.05), so we reject the null hypothesis .

[We reject the null hypothesis when p-value is less than the significance level .]

Conclusion : We do not have enough evidence at 0.05 significance level to support the claim that t its deluxe tire averages at least 50,000 miles before it needs to be replaced.

4 0
3 years ago
Hector is dividing students into groups for an HR wants to divide the boys and girls so that each group has the same number of t
Roman55 [17]

Answer:

7 groups, 3 boys and 8 girls

Step-by-step explanation:

Let total number of groups be x

and total hikers in one group be y

if number of girls and boys in every group is same, then

\frac{21}{x} + \frac{56}{x} = y

\frac{21 + 56}{x} = y\\x*y = 77 ....(1)

from (1) x will either be 11 or 7

for x = 11 the values won't be real.

For x = 7\\y = \frac{77}{7} \\y = 11

so there will be 7 groups with 11 hikers in each groups and every group will have \frac{21}{7} = 3 boys and \frac{56}{7} = 8 girls

6 0
3 years ago
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