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<image>A pharmaceutical scientist making a new medication wonders how much of the active ingredient to include in a dose. They are curious how long different amounts of the active ingredient will stay in someone's bloodstream.
The amount of time (in hours) the active ingredient remains in the bloodstream can be modeled by $f(x)=-1.25 \cdot \ln \left(\frac{1}{x}\right)$, where $x$ is the initial amount of the active ingredient (in milligrams). Here is the graph of $f$ and the graph of the line $y=4$.
Which statements represent the meaning of the intersection point of the graphs?
Choose all answers that apply:
Choices:
A:It describes the amount of time the active ingredient stays in the bloodstream if the initial amount of the active ingredient is $4 \mathrm{mg}$.
B:
C:It gives the solution to the equation $-1.25 \cdot \ln \left(\frac{1}{x}\right)=4$.
D:It describes the situation where the initial amount of the active ingredient is equal to how long it stays in the bloodstream.
E:
F:It gives the initial amount of the active ingredient such that the last of the active ingredient leaves the bloodstream after 4 hours.
|
C
|
mathverse_vi_mcq_3108
|
|
<image>In the tube shown above, the circumference of the base is 32 . If the tube is cut along $\overline{A B}$ and laid out flat to make a surface, what is the length of $\overline{A C}$ to the nearest whole number?
Choices:
A:24
B:30
C:34
D:38
|
C
|
mathverse_vi_mcq_3753
|
|
<image>The figure above shows a solid with height $\sqrt{3} x$. If the volume of the solid is $\frac{81}{4}$, what is the value of $x$ ?
Choices:
A:3
B:4
C:5
D:6
|
A
|
mathverse_vi_mcq_3758
|
|
<image>In the figure shown above, the left container has radius of 3. If all the water in the right container is poured into the left container, the water level rises from $h$ inches to $(h+x)$ inches. Which of the following is the best approximation of the value of $x$ ?
Choices:
A:3
B:3.4
C:3.8
D:4.2
|
D
|
mathverse_vi_mcq_3763
|
|
<image>In the figure above, what is the value of x?
Choices:
A.35
B.40
C.50
D.65
E.130
|
C
|
mathverse_vi_mcq_3768
|
|
<image>What is the value of x^2 + y^2?
Choices:
A.21
B.27
C.33
D.\sqrt{593} (approximately 24.35)
E.\sqrt{611} (approximately 24.72)
|
A
|
mathverse_vi_mcq_3773
|
|
<image>What is the value of a^2 + b^2?
Choices:
A.8
B.10
C.11
D.12
E.13
|
E
|
mathverse_vi_mcq_3778
|
|
<image>In the figure above. What is the value of x?
Choices:
A.90
B.120
C.144
D.156
E.168
|
C
|
mathverse_vi_mcq_3783
|
|
<image>In triangle ABC above. If AB = 6 and BD = 3, what is the measure of angle BAC?
Choices:
A.15*\degree
B.30*\degree
C.45*\degree
D.60*\degree
E.75*\degree
|
D
|
mathverse_vi_mcq_3788
|
|
<image>In the figure above. What is the value of y?
Choices:
A.65
B.70
C.75
D.80
E.85
|
A
|
mathverse_vi_mcq_3793
|
|
<image>In the figure above, the circle has radius r. What is the length, in terms of r, of segment PA?
Choices:
A.r + 1
B.2*r
C.r*\sqrt{2}
D.r*\sqrt{3}
E.r*\sqrt{5}
|
E
|
mathverse_vi_mcq_3798
|
|
<image>In the triangle above, which of the following must be true?
Choices:
A.p=r
B.p<r
C.p>r
D.p=4
E.p>4
|
C
|
mathverse_vi_mcq_3803
|
|
<image>In the figure above if the area of triangle CAF is equal to the area of CDEF, what is the length of segment AD?
Choices:
A.7/2
B.5
C.7
D.15/2
E.15
|
C
|
mathverse_vi_mcq_3808
|
|
<image>In the figure above, the radii of four circles are 1, 2, 3, and 4, respectively. What is the ratio of the area of the small shaded ring to the area of the large shaded ring?
Choices:
A.1:2
B.1:4
C.3:5
D.3:7
E.5:7
|
D
|
mathverse_vi_mcq_3813
|
|
<image>If the perimeter of the quadrilateral above is 72, what is the value of x?
Choices:
A.9
B.15
C.18
D.21
E.36
|
C
|
mathverse_vi_mcq_3818
|
|
<image>In the figure above, the area of the shaded region is given by \pi*l*w/4. If the area of the shaded region is 7*\pi, what is the total area, to the nearest whole number, of the unshaded regions of quadrilateral ABCD ?
Choices:
A.4
B.6
C.8
D.9
E.10
|
B
|
mathverse_vi_mcq_3838
|
|
<image>What fraction of the area of the figure is shaded?
Choices:
A.3/8
B.1/4
C.1/8
D.1/10
E.1/16
|
B
|
mathverse_vi_mcq_3843
|
|
<image>In the figure above, lines l and m are not parallel. Which of the following cannot be the value of x?
Choices:
A.89
B.90
C.91
D.92
E.93
|
B
|
mathverse_vi_mcq_3858
|
|
<image>In the figure above. If m = 40 and p = 25, what is the value of x?
Choices:
A.15
B.20
C.25
D.40
E.65
|
A
|
mathverse_vi_mcq_3863
|
|
<image>In the figure above, what is the value of x?
Choices:
A.72
B.70
C.68
D.66
E.64
|
A
|
mathverse_vi_mcq_3868
|
|
<image>In the figure above. If x = 80, what is the value of z?
Choices:
A.80
B.60
C.50
D.40
E.10
|
A
|
mathverse_vi_mcq_3883
|
|
<image>In the figure above. If AB = AO, what is the degree measure of angle ABO?
Choices:
A.15*\degree
B.30*\degree
C.45*\degree
D.60*\degree
E.90*\degree
|
D
|
mathverse_vi_mcq_3888
|
|
<image>In the figure above, if r = 90, s = 50, t = 60, u = 45, and w = 50, what is the value of x?
Choices:
A.45
B.50
C.65
D.75
E.It cannot be determined from the information given
|
C
|
mathverse_vi_mcq_3893
|
|
<image>In figure above, the length of AB is 3. What is the length of BC?
Choices:
A.3*\sqrt{3}
B.4*\sqrt{2}
C.4*\sqrt{3}
D.6*\sqrt{2}
E.5*\sqrt{3}
|
A
|
mathverse_vi_mcq_3898
|
|
<image>In the figure above, area of ABCE is 1. What is the perimeter of polygon ABCDE?
Choices:
A.4
B.5
C.6
D.7
E.8
|
B
|
mathverse_vi_mcq_3903
|
|
<image>In the figure above. If AE = x and ED = 4, what is length BC?
Choices:
A.6
B.8
C.2*x
D.4*x
E.4*x^2
|
B
|
mathverse_vi_mcq_3908
|
|
<image>If x = 20 and y = 30 in the figure above, what is the value of z?
Choices:
A.60
B.70
C.80
D.90
E.100
|
B
|
mathverse_vi_mcq_3913
|
|
<image>If the circumference of the large circle is 36, what is the length of the darkened arc?
Choices:
A.10
B.8
C.6
D.4
E.2
|
D
|
mathverse_vi_mcq_3918
|
|
<image>In the figure above, a shaded polygon which has equal sides is partially covered with a sheet of blank paper. If x + y = 80, how many sides does the polygon have?
Choices:
A.Ten
B.Nine
C.Eight
D.Seven
E.Six
|
B
|
mathverse_vi_mcq_3923
|
|
<image>In the figure above. If the radius of the larger circle is 4, what is the radius of the smaller circle?
Choices:
A.1
B.2
C.4
D.8
E.16
|
B
|
mathverse_vi_mcq_3928
|
|
<image>In the figure above, the smaller circles each have radius 3. What is the perimeter of the shaded region?
Choices:
A.6*\pi
B.8*\pi
C.9*\pi
D.12*\pi
E.15*\pi
|
D
|
mathverse_vi_mcq_3933
|
|
<image>If the ratio of the length of AB to the length of EB is 5:1, and the area of the triangle BED is 5*a^2 + 10, what is the area of triangle ABC?
Choices:
A.5*a^2 + 10
B.25*a^2 + 50
C.25*a^2 + 100
D.125*a^2 + 250
E.cannot be determined
|
D
|
mathverse_vi_mcq_3938
|
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