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Archive
/
Math
Numbers & Operations
Problem 3101
How many unique 4-letter passwords can be formed from the 26-letter English alphabet without repeating letters? [?] ways
See Solution
Problem 3102
Determine the center and radius of the circle given by
(
x
−
2
)
2
+
(
y
+
3
)
2
=
36
(x-2)^{2}+(y+3)^{2}=36
(
x
−
2
)
2
+
(
y
+
3
)
2
=
36
.
See Solution
Problem 3103
How many ways can you choose 3 books from 11? Use the formula for combinations:
(
11
3
)
\binom{11}{3}
(
3
11
)
.
See Solution
Problem 3104
Find
x
x
x
such that
f
(
x
)
=
0
f(x)=0
f
(
x
)
=
0
for
f
(
x
)
=
x
3
−
3
x
+
1
f(x)=x^{3}-3x+1
f
(
x
)
=
x
3
−
3
x
+
1
using the Intermediate Value Theorem.
See Solution
Problem 3105
Megan has 55 prizes and fills 12 bags equally. After filling 6 bags, what fraction of the prizes remains?
See Solution
Problem 3106
Find the limit:
lim
x
→
0
f
(
x
)
\lim_{x \rightarrow 0} f(x)
lim
x
→
0
f
(
x
)
where
f
(
x
)
=
2
x
cos
(
1
x
2
)
f(x)=2 x \cos \left(\frac{1}{x^{2}}\right)
f
(
x
)
=
2
x
cos
(
x
2
1
)
.
See Solution
Problem 3107
Calculate:
−
9
+
(
−
15
)
-9 + (-15)
−
9
+
(
−
15
)
See Solution
Problem 3108
Calculate
3
×
9
3 \times 9
3
×
9
.
See Solution
Problem 3109
Find
m
∠
A
B
C
m \angle A B C
m
∠
A
BC
if
m
∠
A
B
D
=
7
6
∘
m \angle A B D=76^{\circ}
m
∠
A
B
D
=
7
6
∘
and
m
∠
D
B
C
=
6
8
∘
m \angle D B C=68^{\circ}
m
∠
D
BC
=
6
8
∘
.
See Solution
Problem 3110
Convert
15
l
b
15 \mathrm{lb}
15
lb
to ounces.
See Solution
Problem 3111
Calculate the distance
d
d
d
between points
A
(
11
,
−
5
)
A(11,-5)
A
(
11
,
−
5
)
and
B
(
1
,
7
)
B(1,7)
B
(
1
,
7
)
.
See Solution
Problem 3112
What is the converse of "If I studied for it, then I did well on the exam"?
See Solution
Problem 3113
How many computers were delivered to the third store if 28,500 were assembled and 9,300 and 6,860 went to the first two stores?
See Solution
Problem 3114
Calculate the expected value of winnings with payouts
2
,
3
,
4
,
5
,
6
2, 3, 4, 5, 6
2
,
3
,
4
,
5
,
6
and probabilities
0.40
,
0.20
,
0.17
,
0.13
,
0.10
0.40, 0.20, 0.17, 0.13, 0.10
0.40
,
0.20
,
0.17
,
0.13
,
0.10
. Round to the nearest hundredth.
See Solution
Problem 3115
Simplify the expression:
4
x
2
x
2
y
3
⋅
4
x
y
2
3
4
x
y
2
3
\frac{4 x}{\sqrt[3]{2 x^{2} y}} \cdot \frac{\sqrt[3]{4 x y^{2}}}{\sqrt[3]{4 x y^{2}}}
3
2
x
2
y
4
x
⋅
3
4
x
y
2
3
4
x
y
2
.
See Solution
Problem 3116
Is the Garamycin dose of
35
m
g
35 \mathrm{mg}
35
mg
every
6
h
6 \mathrm{h}
6
h
safe for a
42
l
b
42 \mathrm{lb}
42
lb
child? Justify your answer.
See Solution
Problem 3117
A child weighing 32 lb needs acetaminophen. Calculate mg in 1/2 tsp and check if it's safe based on 25-35 mg/kg/day.
See Solution
Problem 3118
Is a daily dose of
175
m
c
g
175 \mathrm{mcg}
175
mcg
of Levothyroxin safe for an 8-year-old weighing
29.5
k
g
29.5 \mathrm{~kg}
29.5
kg
? Explain.
See Solution
Problem 3119
Calculate the mg per dose of Augmentin for a 66 lbs child, given the dosage is
50
m
g
/
k
g
/
50 \mathrm{mg} / \mathrm{kg} /
50
mg
/
kg
/
day, divided q
6
h
6 \mathrm{~h}
6
h
.
See Solution
Problem 3120
Find the ratio of men to total persons in a company with 112 men out of 288 total. Options: 0.3042, 0.2625, 0.3875, 7:8.
See Solution
Problem 3121
A child weighing 80 lbs needs Phenytoin
60
m
g
60 \mathrm{mg}
60
mg
every 8 hours. Find the safe dose range in
m
g
\mathrm{mg}
mg
per day.
See Solution
Problem 3122
A child weighing 80 lbs needs Phenytoin elixir
60
m
g
60 \mathrm{mg}
60
mg
every 8 hours. How many mls per dose? (Round to 1 decimal place)
See Solution
Problem 3123
Is a
600
m
g
600 \mathrm{mg}
600
mg
dose of Amoxicillin every 6 hours safe for a child weighing 35 pounds, given the
150
−
350
m
g
150-350 \mathrm{mg}
150
−
350
mg
daily range?
See Solution
Problem 3124
A child weighs 72 pounds. Gentamicin is prescribed at
8
m
g
/
k
g
/
8 \mathrm{mg} / \mathrm{kg} /
8
mg
/
kg
/
day every 6 hours. How many
m
l
s
\mathrm{mls}
mls
per dose?
See Solution
Problem 3125
Calculate the dose of Ceclor in mg for a 12 lb infant, and find the mL needed per dose. Ceclor is
20
m
g
/
k
g
/
d
a
y
20 \mathrm{mg} / \mathrm{kg} / \mathrm{day}
20
mg
/
kg
/
day
and
100
m
g
/
2
m
L
100 \mathrm{mg} / 2 \mathrm{mL}
100
mg
/2
mL
.
See Solution
Problem 3126
Is a dose of Eryped drops
120
m
g
120 \mathrm{mg}
120
mg
every 6 hours safe for a 27-pound child given the safe range of
30
−
50
m
g
/
k
g
/
d
a
y
30-50 \mathrm{mg} / \mathrm{kg} / \mathrm{day}
30
−
50
mg
/
kg
/
day
?
See Solution
Problem 3127
A child weighing 35 pounds needs Amoxicillin. How many
200
m
g
200 \mathrm{mg}
200
mg
tablets for a
600
m
g
600 \mathrm{mg}
600
mg
dose every 6 hours?
See Solution
Problem 3128
A child weighing 58 pounds needs Tetracycline elixir at
40
m
g
/
k
g
/
40 \mathrm{mg} / \mathrm{kg} /
40
mg
/
kg
/
day every 6 hours. How many mls per dose?
See Solution
Problem 3129
A child weighing 58 pounds needs Tetracycline elixir at
40
m
g
/
k
g
/
40 \mathrm{mg} / \mathrm{kg} /
40
mg
/
kg
/
day every 6 hours. How many
m
g
s
\mathrm{mgs}
mgs
per dose?
See Solution
Problem 3130
Find the safe dose range for a 35-pound child taking Amoxicillin, with a daily dose of
150
m
g
−
350
m
g
150 \mathrm{mg}-350 \mathrm{mg}
150
mg
−
350
mg
.
See Solution
Problem 3131
A child weighing 80 pounds needs Phenytoin
60
m
g
60 \mathrm{mg}
60
mg
every 8 hours. How many mls per dose? (Round to 1 decimal place)
See Solution
Problem 3132
A child weighs 29 pounds. Find the safe Digoxin dose range in mg/day for a weight under 15 kg:
11.3
−
18.8
m
g
/
k
g
11.3-18.8 \mathrm{mg} / \mathrm{kg}
11.3
−
18.8
mg
/
kg
.
See Solution
Problem 3133
See Solution
Problem 3134
A child weighing
19.5
k
g
s
19.5 \mathrm{kgs}
19.5
kgs
needs Prednisolone
200
m
c
g
/
k
g
200 \mathrm{mcg} / \mathrm{kg}
200
mcg
/
kg
. How many mls will the nurse prepare?
See Solution
Problem 3135
Calculate the safe dose range for a 27-pound child given Eryped drops of
30
−
50
m
g
/
k
g
/
d
a
y
30-50 \mathrm{mg} / \mathrm{kg} / \mathrm{day}
30
−
50
mg
/
kg
/
day
.
See Solution
Problem 3136
A child weighing 72 pounds needs Gentamicin
8
m
g
/
k
g
/
8 \mathrm{mg} / \mathrm{kg} /
8
mg
/
kg
/
day every 6 hours. How many mls per dose?
See Solution
Problem 3137
Solve the system of equations:
x
+
y
=
5
x + y = 5
x
+
y
=
5
and
x
−
y
=
−
1
x - y = -1
x
−
y
=
−
1
.
See Solution
Problem 3138
A child weighs 29 pounds. Is a dose of
0.125
m
g
0.125 \mathrm{mg}
0.125
mg
every 12 hours safe, given the range
11.3
−
18.8
m
g
/
k
g
/
d
a
y
11.3-18.8 \mathrm{mg} / \mathrm{kg} / \mathrm{day}
11.3
−
18.8
mg
/
kg
/
day
?
See Solution
Problem 3139
Calculate:
−
12
−
(
−
10
)
-12 - (-10)
−
12
−
(
−
10
)
See Solution
Problem 3140
Calculate
−
30
÷
(
−
6
)
-30 \div (-6)
−
30
÷
(
−
6
)
.
See Solution
Problem 3141
Calculate
−
8
⋅
2
-8 \cdot 2
−
8
⋅
2
.
See Solution
Problem 3142
Solve for
x
x
x
in the equation
7
4
×
7
x
7
11
=
1
\frac{7^{4} \times 7^{x}}{7^{11}}=1
7
11
7
4
×
7
x
=
1
. Find
x
=
x=
x
=
See Solution
Problem 3143
Calculate the product of
−
1
-1
−
1
and
−
7
-7
−
7
.
See Solution
Problem 3144
Tasha's drawing shows piers
12
c
m
12 \mathrm{~cm}
12
cm
apart. If
2
c
m
2 \mathrm{~cm}
2
cm
=
0.5
m
i
0.5 \mathrm{mi}
0.5
mi
, find the actual distance between the piers.
See Solution
Problem 3145
Find the perimeter of a rectangle with length 6 feet and width 3 feet. Use the formula
P
=
2
(
l
+
w
)
P = 2(l + w)
P
=
2
(
l
+
w
)
.
See Solution
Problem 3146
Circle the digit in the hundredths place of 8,656.175.
See Solution
Problem 3147
Emily's barn drawing is 15 in. wide and 18 in. long. If the actual width is 10 ft, find the actual length.
See Solution
Problem 3148
Convert 24 kg to grams. Recall that 1 kg = 1,000 g.
See Solution
Problem 3149
Write 814,496 in words.
See Solution
Problem 3150
If a wire creates a
10
T
10 \mathrm{~T}
10
T
field at distance
r
r
r
, what is the net field at
r
r
r
with another wire at
2
r
2r
2
r
?
See Solution
Problem 3151
Rosa took 15.6 min to the store and 18.5 min to return. How much longer was her return trip?
See Solution
Problem 3152
Hannah baked
n
n
n
brownies, gave away 12, and ate 6. Write an expression for the remaining brownies.
See Solution
Problem 3153
Mrs. Miller uses
4
/
8
4/8
4/8
cup for cake and
3
/
8
3/8
3/8
cup for frosting. Total honey used?
See Solution
Problem 3154
Find the dimensions of a rectangle scaled by
2
3
\frac{2}{3}
3
2
if the original is 12 inches long and 8 inches wide.
See Solution
Problem 3155
Is 729 divisible by 7? Circle:
729
729
729
is divisible by
7
7
7
or
729
729
729
is NOT divisible by
7
7
7
.
See Solution
Problem 3156
Circle the digit in the hundredths place of
3
,
656.175
3,656.175
3
,
656.175
.
See Solution
Problem 3157
Prove that
sin
3
θ
+
sin
θ
=
4
sin
θ
−
4
sin
3
θ
\sin 3\theta + \sin \theta = 4 \sin \theta - 4 \sin^3 \theta
sin
3
θ
+
sin
θ
=
4
sin
θ
−
4
sin
3
θ
.
See Solution
Problem 3158
What time is it 14 hours after 5:00 p.m.?
See Solution
Problem 3159
Circle the smallest number: 5,211,528,706, 6,078,934, 340,987,126, 349,726,390,418.
See Solution
Problem 3160
Giá trị của
a
a
a
,
b
b
b
sau khi chạy code:
a
=
1
a=1
a
=
1
,
a
+
=
a
a+=a
a
+
=
a
,
b
=
a
+
1
∗
2
+
16
/
a
+
3
b=a+1*2+16/a+3
b
=
a
+
1
∗
2
+
16/
a
+
3
,
b
∗
=
4
+
5
b^*=4+5
b
∗
=
4
+
5
. Tính
a
a
a
,
b
b
b
.
See Solution
Problem 3161
Find
d
d
x
f
−
1
(
0
)
\frac{d}{d x} f^{-1}(0)
d
x
d
f
−
1
(
0
)
for
f
(
x
)
=
x
+
sin
x
f(x)=x+\sin x
f
(
x
)
=
x
+
sin
x
. At
x
=
0
x=0
x
=
0
,
f
f
f
has slope 2, so
f
−
1
f^{-1}
f
−
1
slope is
1
2
\frac{1}{2}
2
1
.
See Solution
Problem 3162
Find the derivative of
f
(
x
)
=
x
2
f(x) = x^2
f
(
x
)
=
x
2
using the limit definition:
f
′
(
x
)
=
lim
h
→
0
f
(
x
+
h
)
−
f
(
x
)
h
f'(x) = \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}
f
′
(
x
)
=
lim
h
→
0
h
f
(
x
+
h
)
−
f
(
x
)
.
See Solution
Problem 3163
Find the value of
69
\sqrt{69}
69
.
See Solution
Problem 3164
Find the annual interest rate for an investment of \$3500 that doubles in 5 years. Options: 40\%, 50\%, 30\%, 20\%.
See Solution
Problem 3165
Solve for
x
x
x
in the equation:
2
x
+
5
=
10
2 x + 5 = 10
2
x
+
5
=
10
.
See Solution
Problem 3166
What is the concentration in
g
/
f
l
.
o
z
\mathrm{g}/\mathrm{fl.oz}
g
/
fl.oz
for
90
o
z
7
g
r
/
g
a
l
90 \mathrm{oz} 7 \mathrm{gr}/\mathrm{gal}
90
oz
7
gr
/
gal
?
See Solution
Problem 3167
Find the debt-equity ratio given a cost of equity of 14.9%, cost of debt of 7.3%, and return on assets of 12.6%.
See Solution
Problem 3168
Malkin Corp. has no debt, WACC 9.6%, borrowing at 5.9%. Find cost of equity with 0%, 30%, and 60% debt. What are WACCs?
See Solution
Problem 3169
Nyatakan sama ada semua segi empat tepat adalah segi empat sama: benar atau palsu?
See Solution
Problem 3170
Tentukan tinggi tiang silinder dengan isi padu
404
c
m
3
404 \mathrm{~cm}^{3}
404
cm
3
dan jejari
2
c
m
2 \mathrm{~cm}
2
cm
.
See Solution
Problem 3171
Buat kesimpulan umum secara induksi untuk urutan nombor
−
1
2
,
3
2
,
25
6
,
…
-\frac{1}{2}, \frac{3}{2}, \frac{25}{6}, \ldots
−
2
1
,
2
3
,
6
25
,
…
mengikut pola yang diberikan.
See Solution
Problem 3172
Dalam Rajah 5, cari (a) titik tengah garis
P
Q
P Q
PQ
, (b) panjang
Q
R
Q R
QR
untuk trapezium PQRS dengan P(-2,4), Q(4,6), R(9,1).
See Solution
Problem 3173
Demuestra la ley de Boyle:
p
V
=
p V=
p
V
=
const, la ley de Charles:
V
/
T
=
V / T=
V
/
T
=
const, y la ley de Gay-Lussac:
p
/
T
=
p / T=
p
/
T
=
const.
See Solution
Problem 3174
A particle with mass
m
1
m_{1}
m
1
and momentum
p
1
p_{1}
p
1
collides elastically with mass
m
2
m_{2}
m
2
at rest. Show
E
3
E_{3}
E
3
and
p
3
p_{3}
p
3
formulas.
See Solution
Problem 3175
Find the parametrization of the circle centered at
1
−
i
1-i
1
−
i
with radius 3:
z
(
t
)
=
z(t)=
z
(
t
)
=
.
See Solution
Problem 3176
Expand the expression
(
4
+
3
x
)
5
(4+3 x)^{5}
(
4
+
3
x
)
5
.
See Solution
Problem 3177
Simplify the expression:
1
x
+
2
1
x
+
1
2
\frac{\frac{1}{x+2}}{\frac{1}{x}+\frac{1}{2}}
x
1
+
2
1
x
+
2
1
.
See Solution
Problem 3178
Find the limit: If
f
(
z
)
=
z
+
z
ˉ
z
f(z)=\frac{z+\bar{z}}{z}
f
(
z
)
=
z
z
+
z
ˉ
, then
lim
x
→
0
f
(
x
+
0
i
)
=
\lim _{x \rightarrow 0} f(x+0 i)=
lim
x
→
0
f
(
x
+
0
i
)
=
.
See Solution
Problem 3179
Solve the equation by factoring:
x
3
+
5
x
2
−
4
x
−
20
=
0
x^{3}+5 x^{2}-4 x-20=0
x
3
+
5
x
2
−
4
x
−
20
=
0
.
See Solution
Problem 3180
Solve the equation:
3
x
−
5
x
2
+
1
=
x
−
7
3x - 5x^{2} + 1 = x - 7
3
x
−
5
x
2
+
1
=
x
−
7
.
See Solution
Problem 3181
How many trucks does a factory produce in 8 days at 18 trucks per day? Calculate
8
×
18
8 \times 18
8
×
18
.
See Solution
Problem 3182
See Solution
Problem 3183
How many liters of alcohol are needed to make 500,000 patches if each contains
0.3
m
L
0.3 \mathrm{~mL}
0.3
mL
of alcohol?
See Solution
Problem 3184
Find the real and imaginary parts of
f
(
z
)
=
z
2
+
i
z
ˉ
f(z)=z^{2}+i \bar{z}
f
(
z
)
=
z
2
+
i
z
ˉ
:
u
(
x
,
y
)
=
u(x, y)=
u
(
x
,
y
)
=
and
v
(
x
,
y
)
=
v(x, y)=
v
(
x
,
y
)
=
.
See Solution
Problem 3185
How many kg of aluminium hydroxide gel are needed for 250,000 bottles with 100 tablets each, if each tablet has
80
m
g
80 \mathrm{mg}
80
mg
?
See Solution
Problem 3186
Find side
B
C
BC
BC
of triangle
A
B
C
ABC
A
BC
with
A
B
=
8
AB=8
A
B
=
8
,
A
C
=
8
2
AC=8\sqrt{2}
A
C
=
8
2
,
∠
A
B
C
=
4
5
∘
\angle ABC=45^{\circ}
∠
A
BC
=
4
5
∘
,
∠
A
C
B
=
3
0
∘
\angle ACB=30^{\circ}
∠
A
CB
=
3
0
∘
.
See Solution
Problem 3187
A 15-ml nasal spray has 20 sprays/ml, each with
1.5
m
g
1.5 \mathrm{mg}
1.5
mg
. (a) Total sprays? (b) Total mg of drug in the package?
See Solution
Problem 3188
Determine if a perfect hedge exists using the matrix
A
A
A
and vector
b
b
b
. Solve for
x
^
\hat{x}
x
^
using
x
^
=
(
A
∗
A
)
−
1
A
∗
b
\hat{x}=(A^{*} A)^{-1} A^{*} b
x
^
=
(
A
∗
A
)
−
1
A
∗
b
.
See Solution
Problem 3189
Find
lim
x
→
0
f
(
x
+
0
i
)
\lim _{x \rightarrow 0} f(x+0 i)
lim
x
→
0
f
(
x
+
0
i
)
and
lim
y
→
0
f
(
0
+
i
y
)
\lim _{y \rightarrow 0} f(0+i y)
lim
y
→
0
f
(
0
+
i
y
)
for
f
(
z
)
=
z
+
z
ˉ
z
f(z)=\frac{z+\bar{z}}{z}
f
(
z
)
=
z
z
+
z
ˉ
.
See Solution
Problem 3190
Evaluate the limit as
x
x
x
approaches 0:
lim
x
→
0
x
2
−
25
x
2
−
4
x
−
5
\lim _{x \rightarrow 0} \frac{x^{2}-25}{x^{2}-4 x-5}
lim
x
→
0
x
2
−
4
x
−
5
x
2
−
25
.
See Solution
Problem 3191
Calculate
12
/
20
12 / 20
12/20
and find the missing number in the sequence: 100, 93, 84, 73.
See Solution
Problem 3192
Find the next number in the sequence: 7, 11, 16, 22, 29, ?
See Solution
Problem 3193
Find the next number in the sequence:
6
,
3
,
12
,
9
,
36
,
33
6, 3, 12, 9, 36, 33
6
,
3
,
12
,
9
,
36
,
33
.
See Solution
Problem 3194
Find the algebraic expression for "a number plus 17 equals 30".
See Solution
Problem 3195
True or false: For a population proportion confidence interval, we use
z
\mathrm{z}
z
-distribution, not
t
\mathrm{t}
t
-distribution.
See Solution
Problem 3196
Identify which statements about confidence intervals and distributions are true or false: 1) z vs t for population proportion, 2) degrees of freedom, 3) known
σ
\sigma
σ
and Z, 4) unknown
σ
\sigma
σ
and S, 5) t vs z for population proportion.
See Solution
Problem 3197
Find the test statistic
z
z
z
for a sample mean of 84, size 49, standard deviation 14, testing if mean > 80 at
α
=
0.05
\alpha = 0.05
α
=
0.05
.
See Solution
Problem 3198
Identify which statements are true or false regarding confidence intervals and distributions.
See Solution
Problem 3199
Identify the number that doesn't fit the pattern:
2
,
20
,
4
,
8
,
300
2, 20, 4, 8, 300
2
,
20
,
4
,
8
,
300
.
See Solution
Problem 3200
How much will you pay in total if you borrow \$400 for 2 years at an annual interest rate of 15%?
See Solution
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