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Sav [38]
3 years ago
8

Mike forgot to replace the cap on a bottle of room freshener. The room freshener began to evaporate at the rate of 15% per day.

If the original amount of room freshener in the bottle was 40 grams, which of the following graphs best represents the amount of room freshener f(x) that would remain in the bottle after x days?
graph of function f of x equals 30 multiplied by 0.88 to the power of x

graph of exponential function going down from left to right in quadrant 1 through the point 0, 40 and approaching the x axis

graph of function f of x equals 50 multiplied by 0.82 to the power of x

graph of exponential function going down from left to right in quadrant 1 through the point 0, 4 and approaching the x axis

Mathematics
1 answer:
Sholpan [36]3 years ago
3 0
The decay rate is 100% - 15% = 75% = 0.75

The decay equation is f(x) = 40(0.75)ˣ
Where f(x) is the mass of air freshener left after x days of use

The graph of this function is given below 

The correct description of the graph is statement 2:

<span>graph of exponential function going down from left to right in quadrant 1 through the point 0, 40 and approaching the x axis</span>

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(the dimensions are shown in the picture)
Oksanka [162]

Answer:

Total surface area of the prism =145.32 Square centimeters

Step-by-step explanation:

The given figure is a rectangular prism with the given dimensions of :

length(L)= 10.3 cm

Width(W)=2.2 cm

Height(H)=4 cm

Total surface area of the rectangular prism is:

= 2(L*W+W*H+H*L)\\\\=2((10.3*2.2)+(2.2*4)+(4*10.3))\\\\=2(22.66+8.8+41.2)\\\\=2(72.66)\\\\=145.32cm^2\\\\

Total surface area of the prism is 145.32 Square centimeters

6 0
2 years ago
Read 2 more answers
Suppose that the Celsius temperature at the point (x, y) in the xy-plane is T(x, y) = x sin 2y and that distance in the xy-plane
liraira [26]

Missing information:

How fast is the temperature experienced by the particle changing in degrees Celsius per meter at the point

P = (\frac{1}{2}, \frac{\sqrt 3}{2})

Answer:

Rate = 0.935042^\circ /cm

Step-by-step explanation:

Given

P = (\frac{1}{2}, \frac{\sqrt 3}{2})

T(x,y) =x\sin2y

r = 1m

v = 2m/s

Express the given point P as a unit tangent vector:

P = (\frac{1}{2}, \frac{\sqrt 3}{2})

u = \frac{\sqrt 3}{2}i - \frac{1}{2}j

Next, find the gradient of P and T using: \triangle T = \nabla T * u

Where

\nabla T|_{(\frac{1}{2}, \frac{\sqrt 3}{2})}  = (sin \sqrt 3)i + (cos \sqrt 3)j

So: the gradient becomes:

\triangle T = \nabla T * u

\triangle T = [(sin \sqrt 3)i + (cos \sqrt 3)j] *  [\frac{\sqrt 3}{2}i - \frac{1}{2}j]

By vector multiplication, we have:

\triangle T = (sin \sqrt 3)*  \frac{\sqrt 3}{2} - (cos \sqrt 3)  \frac{1}{2}

\triangle T = 0.9870 * 0.8660 - (-0.1606 * 0.5)

\triangle T = 0.9870 * 0.8660 +0.1606 * 0.5

\triangle T = 0.935042

Hence, the rate is:

Rate = \triangle T = 0.935042^\circ /cm

3 0
2 years ago
The table to the right shows selected ages of licensed drivers in one country and the corresponding percentiles. Find the percen
PolarNik [594]

Answer:

66%

Step-by-step explanation:

Given :

Age          Percentile

75           97

65           90

55           78

45           58

35           37

25           13

20           66

To Find :The percentage of drivers who are younger than 20 is _____%.

Solution:

Refer the given table

The percentile corresponding to age 20 is 66.

Percentile : A data item is said to be in nth percentile of distribution if n% of the distribution are less than that particular data item.

So, drivers who are younger than 20 are said to be in 66 percentile if 66%of the distribution are less than that particular data item.

Hence The percentage of drivers who are younger than 20 is 66%.

7 0
3 years ago
Read 2 more answers
Find the slope of the line. -7 , - 1/7, 7, 7/1
frutty [35]
Slope = (y₂-y₁)/(x₂-x₁)
by making (x₁,y₁) = (-2,2)   and    (x₂,y₂) = (5,3)
∴The slope = (3-2)/(5 - -2) = 1/7
5 0
2 years ago
Read 2 more answers
Solve using distributive property. (3x2-2x+7)(x2+2x) Thank you!
geniusboy [140]

Answer:

3x^4+4x^3+3x^2+14x

Step-by-step explanation:

(3x^2-2x+7)(x^2+2x)

3x^4+6x^3-2x^3-4x^2+7x^2+14x

=3x^4+4x^3+3x^2+14x

6 0
3 years ago
Read 2 more answers
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