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Math Problems
Grade 6
Estimate decimal quotients
Find the perimeter of the isosceles trapezoid below.
\newline
A.
66
66
66
units
\newline
B.
42
42
42
units
\newline
C.
7
2
7 \sqrt{2}
7
2
units
\newline
D.
42
+
14
2
42+14 \sqrt{2}
42
+
14
2
units
\newline
E.
42
+
7
2
42+7 \sqrt{2}
42
+
7
2
units
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Select all of the true statements.
\newline
Multi-select Choices:
\newline
(A)
8
×
1
0
−
3
8 \times 10^{-3}
8
×
1
0
−
3
is
200
200
200
times as much as
4
×
1
0
−
5
4 \times 10^{-5}
4
×
1
0
−
5
.
\newline
(B)
2
×
1
0
6
2 \times 10^{6}
2
×
1
0
6
is
50
50
50
times as much as
4
×
1
0
4
4 \times 10^{4}
4
×
1
0
4
.
\newline
(C)
3
×
1
0
−
2
3 \times 10^{-2}
3
×
1
0
−
2
is
0.1
0.1
0.1
times as much as
3
×
1
0
−
3
3 \times 10^{-3}
3
×
1
0
−
3
.
\newline
(D)
6
×
1
0
4
6 \times 10^{4}
6
×
1
0
4
is
200
200
200
0
0
0
times as much as
200
200
200
1
1
1
.
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Which sample has particles with the lowest average kinetic energy?
\newline
(
1
1
1
)
1.0
g
1.0 \mathrm{~g}
1.0
g
of
I
2
\mathrm{I}_{2}
I
2
at
50
.
∘
C
50 .^{\circ} \mathrm{C}
50
.
∘
C
\newline
(
3
3
3
)
7.0
g
7.0 \mathrm{~g}
7.0
g
of
I
2
\mathrm{I}_{2}
I
2
at
40.
∘
C
40 .{ }^{\circ} \mathrm{C}
40.
∘
C
\newline
(
2
2
2
)
2.0
g
2.0 \mathrm{~g}
2.0
g
of
I
2
\mathrm{I}_{2}
I
2
at
30.
∘
C
30 .{ }^{\circ} \mathrm{C}
30.
∘
C
\newline
(
4
4
4
)
9.0
g
9.0 \mathrm{~g}
9.0
g
of
I
2
\mathrm{I}_{2}
I
2
at
I
2
\mathrm{I}_{2}
I
2
1
1
1
\newline
1
1
1
\newline
2
2
2
\newline
3
3
3
\newline
4
4
4
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Algebra
2
2
2
\newline
Name
\qquad
Elizabeth
\newline
Torres
\newline
Right Triangles
\newline
Date
\qquad
P
e
\mathrm{Pe}
Pe
\newline
Find the measure of each side indicated. Round to the nearest tenth.
\newline
1
1
1
)
\newline
sin
52
=
13
x
x
⋅
7881
13
x
⋅
x
7881
7881
=
13
7881
x
=
16.49
\begin{array}{l} \sin 52=\frac{13}{x} \\ x \cdot 7881 \frac{13}{x} \cdot x \\ \frac{7881}{7881}=\frac{13}{7881} \\ x=16.49 \end{array}
sin
52
=
x
13
x
⋅
7881
x
13
⋅
x
7881
7881
=
7881
13
x
=
16.49
\newline
3
3
3
)
\newline
5
5
5
)
\newline
7
7
7
)
\newline
9
9
9
)
\newline
2
2
2
)
\newline
4
4
4
)
\newline
6
6
6
)
\newline
8
8
8
)
\newline
10
10
10
)
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5
5
5
\newline
8
8
8
Here are parts of two train timetables.
\newline
One shows journeys from Manchester to Leeds and the other shows journeys from Leeds to Manchester.
\newline
\begin{tabular}{|l|l|l|l|l|l|l|}
\newline
\hline Manchester &
07
:
40
07: 40
07
:
40
&
08
:
11
08: 11
08
:
11
&
08
:
41
08: 41
08
:
41
&
09
:
11
09: 11
09
:
11
&
09
:
41
09: 41
09
:
41
&
10
:
10
10: 10
10
:
10
\\
\newline
\hline Stalybridge &
07
:
53
07: 53
07
:
53
&
08
:
25
08: 25
08
:
25
&
08
:
54
08: 54
08
:
54
&
09
:
25
09: 25
09
:
25
&
08
:
11
08: 11
08
:
11
0
0
0
&
08
:
11
08: 11
08
:
11
1
1
1
\\
\newline
\hline Huddersfield &
08
:
11
08: 11
08
:
11
2
2
2
&
08
:
11
08: 11
08
:
11
3
3
3
&
08
:
11
08: 11
08
:
11
4
4
4
&
08
:
11
08: 11
08
:
11
5
5
5
&
08
:
11
08: 11
08
:
11
6
6
6
&
08
:
11
08: 11
08
:
11
7
7
7
\\
\newline
\hline Dewsbury &
08
:
11
08: 11
08
:
11
8
8
8
&
08
:
11
08: 11
08
:
11
9
9
9
&
08
:
41
08: 41
08
:
41
0
0
0
&
08
:
41
08: 41
08
:
41
1
1
1
&
08
:
41
08: 41
08
:
41
2
2
2
&
08
:
41
08: 41
08
:
41
3
3
3
\\
\newline
\hline Leeds &
08
:
41
08: 41
08
:
41
4
4
4
&
08
:
41
08: 41
08
:
41
5
5
5
&
08
:
41
08: 41
08
:
41
6
6
6
&
08
:
41
08: 41
08
:
41
7
7
7
&
08
:
41
08: 41
08
:
41
8
8
8
&
08
:
41
08: 41
08
:
41
9
9
9
\\
\newline
\hline
\newline
\end{tabular}
\newline
\begin{tabular}{|l|c|c|c|c|c|c|}
\newline
\hline Leeds &
09
:
11
09: 11
09
:
11
0
0
0
&
08
:
11
08: 11
08
:
11
4
4
4
&
09
:
41
09: 41
09
:
41
&
09
:
11
09: 11
09
:
11
3
3
3
&
09
:
11
09: 11
09
:
11
4
4
4
&
09
:
11
09: 11
09
:
11
5
5
5
\\
\newline
\hline Dewsbury &
09
:
11
09: 11
09
:
11
6
6
6
&
09
:
11
09: 11
09
:
11
7
7
7
&
09
:
11
09: 11
09
:
11
8
8
8
&
09
:
11
09: 11
09
:
11
9
9
9
&
09
:
41
09: 41
09
:
41
0
0
0
&
09
:
41
09: 41
09
:
41
1
1
1
\\
\newline
\hline Huddersfield &
09
:
41
09: 41
09
:
41
2
2
2
&
09
:
41
09: 41
09
:
41
3
3
3
&
09
:
41
09: 41
09
:
41
4
4
4
&
09
:
41
09: 41
09
:
41
5
5
5
&
09
:
41
09: 41
09
:
41
6
6
6
&
09
:
41
09: 41
09
:
41
7
7
7
\\
\newline
\hline Stalybridge &
09
:
41
09: 41
09
:
41
8
8
8
&
08
:
11
08: 11
08
:
11
0
0
0
&
10
:
10
10: 10
10
:
10
0
0
0
&
08
:
41
08: 41
08
:
41
3
3
3
&
10
:
10
10: 10
10
:
10
2
2
2
&
10
:
10
10: 10
10
:
10
3
3
3
\\
\newline
\hline Manchester &
10
:
10
10: 10
10
:
10
4
4
4
&
10
:
10
10: 10
10
:
10
5
5
5
&
10
:
10
10: 10
10
:
10
6
6
6
&
10
:
10
10: 10
10
:
10
7
7
7
&
10
:
10
10: 10
10
:
10
8
8
8
&
10
:
10
10: 10
10
:
10
9
9
9
\\
\newline
\hline
\newline
\end{tabular}
\newline
(a) Carlos is travelling from Stalybridge to Leeds on the
08
08
08
:
54
54
54
train.
\newline
Find how long his journey takes.
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Without dividing, determine if
79
79
79
,
644
644
644
is divisible by
3
3
3
and explain how you know.
\newline
79
,
644
□
79,644 \square
79
,
644
□
divisible by
3
3
3
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Without dividing, determine if
91
91
91
,
626
626
626
is divisible by
6
6
6
and explain how you know.
\newline
91
,
626
□
divisible by
6
91,626 \square \text { divisible by } 6
91
,
626
□
divisible by
6
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Without dividing, determine if
23
23
23
,
688
688
688
is divisible by
6
6
6
and explain how you know.
\newline
23
,
688
□
divisible by
6
23,688 \square \text { divisible by } 6
23
,
688
□
divisible by
6
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6
6
6
.) A life insurance company insures policyholders of all ages. An actuary compiled the below table on the company's insured policyholders:
\newline
\newline
Age Group
\newline
Probability of Death in the Next Year
\newline
Portion of Company's Policyholders
\newline
\newline
0
−
20
0-20
0
−
20
\newline
0.001
0.001
0.001
\newline
0.10
0.10
0.10
\newline
\newline
21
−
40
21-40
21
−
40
\newline
0.01
0.01
0.01
\newline
0.20
0.20
0.20
\newline
\newline
41
−
60
41-60
41
−
60
\newline
0.05
0.05
0.05
\newline
0.60
0.60
0.60
\newline
\newline
61
−
80
61-80
61
−
80
\newline
0.001
0.001
0.001
0
0
0
\newline
0.05
0.05
0.05
\newline
\newline
0.001
0.001
0.001
2
2
2
\newline
0.001
0.001
0.001
3
3
3
\newline
0.05
0.05
0.05
\newline
\newline
A randomly selected policyholder dies in the next year. Calculate the probability that the driver was over
0.001
0.001
0.001
5
5
5
years old.
\newline
(A)
0.001
0.001
0.001
6
6
6
\newline
(B)
0.001
0.001
0.001
7
7
7
\newline
(C)
0.001
0.001
0.001
8
8
8
\newline
(D)
0.001
0.001
0.001
9
9
9
\newline
(E)
0.10
0.10
0.10
0
0
0
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