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Math
Expression
Problem 4501
What is 5 tens + 1 one + 4 tenths + 39 hundredths in standard form? Options: (A) 51.439 (B) 51.1439 (C) 51.79 (D) 52.79
See Solution
Problem 4502
Select all correct representations of 73.218. Options: 1) 73 ones + 218 thousandths 2) 7 tens + 3 ones + 218 thousandths 3) 73 tens + 218 thousandths 4) 7 tens + 3 ones + 2 tenths + 18 hundredths 5) 7 tens + 3 ones + 2 tenths + 18 thousandths
See Solution
Problem 4503
Write 2.075 in words and identify the place and value of the digit 5.
See Solution
Problem 4504
Calculate the sum of 18 nnes, 20 hundredths, and 5 thousandths.
See Solution
Problem 4505
Find the height change per second as the elevator descends 420 meters in 60 seconds. What is the integer value?
See Solution
Problem 4506
Arrange these fractions in decreasing order:
5
6
,
1
3
,
7
3
,
5
2
,
5
4
\frac{5}{6}, \frac{1}{3}, \frac{7}{3}, \frac{5}{2}, \frac{5}{4}
6
5
,
3
1
,
3
7
,
2
5
,
4
5
.
See Solution
Problem 4507
Find the altitude change per minute for a balloon that descended 2,700 feet in 135 minutes. What is the value?
See Solution
Problem 4508
Evaluate
x
+
y
x+y
x
+
y
where
x
=
5
+
3
x=\sqrt{5}+\sqrt{3}
x
=
5
+
3
and
y
=
5
−
3
y=\sqrt{5}-\sqrt{3}
y
=
5
−
3
.
See Solution
Problem 4509
Evaluate the integral
∫
0
a
x
a
2
−
x
2
d
x
\int_{0}^{a} x \sqrt{a^{2}-x^{2}} \, dx
∫
0
a
x
a
2
−
x
2
d
x
.
See Solution
Problem 4510
Convert the unit fraction
1
4
\frac{1}{4}
4
1
to a percentage. What is it?
See Solution
Problem 4511
Convert
80
%
80\%
80%
to its simplest fraction form. Options:
1
8
\frac{1}{8}
8
1
,
4
5
\frac{4}{5}
5
4
,
8
10
\frac{8}{10}
10
8
,
40
50
\frac{40}{50}
50
40
.
See Solution
Problem 4512
Convert
49
%
49\%
49%
to a decimal. How many places does the decimal point move? What is the decimal form?
See Solution
Problem 4513
Find the actual distance from town A to town B at a scale of 1 cm: 100 km. Choose A-D. 400 cm, 400 km, 25 km, 0.04 cm.
See Solution
Problem 4514
Find the probability of the letter
O
O
O
in "BOOK". What is the distance from town
A
A
A
to town
B
B
B
at a scale of
1
c
m
:
100
k
m
1 \mathrm{~cm}: 100 \mathrm{~km}
1
cm
:
100
km
? Round 55.89934 to three decimals.
See Solution
Problem 4515
Convert
12
4
6
124_{6}
12
4
6
to base ten to find the total number of pens in the box.
See Solution
Problem 4516
Evaluate the expression
6
2
−
(
3
2
+
1
)
6^{2} - (3^{2} + 1)
6
2
−
(
3
2
+
1
)
.
See Solution
Problem 4517
Calculate
6
2
−
(
3
2
+
1
)
6^{2} - (3^{2} + 1)
6
2
−
(
3
2
+
1
)
.
See Solution
Problem 4518
Calculate
2
3
÷
4
3
+
(
8
5
−
1
2
5
)
2
\frac{2}{3} \div \frac{4}{3} + \left(\frac{8}{5} - 1 \frac{2}{5}\right)^{2}
3
2
÷
3
4
+
(
5
8
−
1
5
2
)
2
.
See Solution
Problem 4519
Find
sin
θ
\sin \theta
sin
θ
given
csc
θ
=
44
5
\csc \theta = \frac{\sqrt{44}}{5}
csc
θ
=
5
44
. Rationalize denominators if needed.
See Solution
Problem 4520
Calculate
64500
⋅
1
0
3
64500 \cdot 10^{3}
64500
⋅
1
0
3
.
See Solution
Problem 4521
Find the exact values of
sin
θ
\sin \theta
sin
θ
and
cos
θ
\cos \theta
cos
θ
if
tan
θ
=
−
3
4
\tan \theta = -\frac{3}{4}
tan
θ
=
−
4
3
in quadrant II.
See Solution
Problem 4522
Show
5
3
×
3
4
\frac{5}{3} \times \frac{3}{4}
3
5
×
4
3
on a number line. Is it less than, greater than, or equal to
3
4
\frac{3}{4}
4
3
?
See Solution
Problem 4523
Simplify:
18
3
=
\frac{18}{3}=
3
18
=
See Solution
Problem 4524
What is the probability of guessing a 5-digit code from 5 unique numbers? A.
1
12
\frac{1}{12}
12
1
B.
1
120
\frac{1}{120}
120
1
C.
1
40
\frac{1}{40}
40
1
D.
1
60
\frac{1}{60}
60
1
See Solution
Problem 4525
Find
sin
θ
\sin \theta
sin
θ
given
csc
θ
=
117
6
\csc \theta = \frac{\sqrt{117}}{6}
csc
θ
=
6
117
. Simplify your answer.
See Solution
Problem 4526
Find
sin
θ
\sin \theta
sin
θ
given
csc
θ
=
44
2
\csc \theta = \frac{\sqrt{44}}{2}
csc
θ
=
2
44
. Simplify your answer.
See Solution
Problem 4527
Find (a) the complement and (b) the supplement of an angle measuring
1
7
∘
1
5
′
17^{\circ} 15^{\prime}
1
7
∘
1
5
′
.
See Solution
Problem 4528
Calculate
2
3
8
+
(
−
4
1
4
)
2 \frac{3}{8} + \left(-4 \frac{1}{4}\right)
2
8
3
+
(
−
4
4
1
)
. Choose from:
−
2
1
3
-2 \frac{1}{3}
−
2
3
1
,
−
1
7
8
-1 \frac{7}{8}
−
1
8
7
,
1
7
8
1 \frac{7}{8}
1
8
7
,
2
1
2
2 \frac{1}{2}
2
2
1
.
See Solution
Problem 4529
Find (a) the complement and (b) the supplement of an angle measuring
1
7
∘
1
5
′
17^{\circ} 15^{\prime}
1
7
∘
1
5
′
.
See Solution
Problem 4530
Find the complement and supplement of an angle measuring
2
2
∘
1
3
′
22^{\circ} 13^{\prime}
2
2
∘
1
3
′
.
See Solution
Problem 4531
Calculate the sum of the points on a number line from -2 to 2. Possible answers: (A) -4, (B) 0, (C) 2, (D) 4.
See Solution
Problem 4532
Round
6.24159
6.24159
6.24159
to two decimal places.
See Solution
Problem 4533
Find the distance between points
A
A
A
at 14 and
D
D
D
at 50 on a number line.
See Solution
Problem 4534
Find the integral
∫
x
2
x
3
+
9
d
x
\int \frac{x^{2}}{x^{3}+9} d x
∫
x
3
+
9
x
2
d
x
and provide the result in terms of
c
c
c
.
See Solution
Problem 4535
Calculate the distance between points A(4,9) and B(2,-3) using the formula
d
=
(
x
2
−
x
1
)
2
+
(
y
2
−
y
1
)
2
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
d
=
(
x
2
−
x
1
)
2
+
(
y
2
−
y
1
)
2
.
See Solution
Problem 4536
Calculate the distance between points A(4,9) and C(9,0) using the formula
d
=
(
x
2
−
x
1
)
2
+
(
y
2
−
y
1
)
2
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
d
=
(
x
2
−
x
1
)
2
+
(
y
2
−
y
1
)
2
.
See Solution
Problem 4537
Calculate the distance between points B(2,-3) and C(9,0) using the formula:
d
=
(
x
2
−
x
1
)
2
+
(
y
2
−
y
1
)
2
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
d
=
(
x
2
−
x
1
)
2
+
(
y
2
−
y
1
)
2
.
See Solution
Problem 4538
Find the distances between points A(4,9), B(-2,-3), and C(0,0). Round to the nearest tenth.
See Solution
Problem 4539
Calvin sells large paintings for \$ 56.25 and small ones for \$ 34.89. How much does he make selling one of each?
See Solution
Problem 4540
Write the expression
x
1
2
f
(
x
1
)
+
x
2
2
f
(
x
2
)
+
x
3
2
f
(
x
3
)
+
x
4
2
f
(
x
4
)
+
x
5
2
f
(
x
5
)
x_{1}^{2} f\left(x_{1}\right)+x_{2}^{2} f\left(x_{2}\right)+x_{3}^{2} f\left(x_{3}\right)+x_{4}^{2} f\left(x_{4}\right)+x_{5}^{2} f\left(x_{5}\right)
x
1
2
f
(
x
1
)
+
x
2
2
f
(
x
2
)
+
x
3
2
f
(
x
3
)
+
x
4
2
f
(
x
4
)
+
x
5
2
f
(
x
5
)
in summation notation. Choose the correct option.
See Solution
Problem 4541
Rewrite the expression (60 - (2 + 3 × 8) + 16 ÷ 2 × 4) - (49 ÷ 7 + 7). Which option is correct?
See Solution
Problem 4542
Find how many men are needed to move
x
x
x
boxes and how many of 680 bulbs are non-defective. Choose the correct option.
See Solution
Problem 4543
Evaluate
(
4
a
+
c
)
÷
b
−
(
b
d
)
÷
(
a
c
)
(4a+c) \div b - (bd) \div(ac)
(
4
a
+
c
)
÷
b
−
(
b
d
)
÷
(
a
c
)
for
a
=
−
2
a=-2
a
=
−
2
,
b
=
3
b=3
b
=
3
,
c
=
−
1
c=-1
c
=
−
1
,
d
=
1
d=1
d
=
1
. What is the result?
See Solution
Problem 4544
Simplify the expression
6
y
−
2
4
y
2
−
2
3
y
+
1
y
2
\frac{6 y-2}{4 y^{2}}-\frac{2}{3 y}+\frac{1}{y^{2}}
4
y
2
6
y
−
2
−
3
y
2
+
y
2
1
and choose the correct result. Options: a.
y
+
3
3
y
2
\frac{y+3}{3 y^{2}}
3
y
2
y
+
3
, b.
10
y
+
6
10 y+6
10
y
+
6
, c.
10
y
−
5
12
y
2
\frac{10 y-5}{12 y^{2}}
12
y
2
10
y
−
5
, d.
5
y
+
3
6
y
2
\frac{5 y+3}{6 y^{2}}
6
y
2
5
y
+
3
.
See Solution
Problem 4545
Find the value of
c
c
c
for which
x
2
+
10
x
+
c
x^{2}+10x+c
x
2
+
10
x
+
c
is a perfect square. Options: A. 100 B. 20 C. 5 D. 25
See Solution
Problem 4546
Write 26,832 as an expanded form using place values.
See Solution
Problem 4547
Add the numbers 42 and 29. What is the result?
See Solution
Problem 4548
Write 563235 in numerical form.
See Solution
Problem 4549
How many total crayons and markers did Elsa put in the bucket if she has 27 crayons and 23 markers?
27
+
23
27 + 23
27
+
23
See Solution
Problem 4550
Calculate
15
+
(
16
−
6
)
×
1
15+(16-6) \times 1
15
+
(
16
−
6
)
×
1
.
See Solution
Problem 4551
Calculate the value of
(
18
+
23
+
22
)
÷
9
(18+23+22) \div 9
(
18
+
23
+
22
)
÷
9
.
See Solution
Problem 4552
Calculate the expression:
15
+
(
16
−
6
)
×
1
15 + (16 - 6) \times 1
15
+
(
16
−
6
)
×
1
See Solution
Problem 4553
Calculate
(
1
2
+
1
2
)
×
5
\left(\frac{1}{2}+\frac{1}{2}\right) \times 5
(
2
1
+
2
1
)
×
5
.
See Solution
Problem 4554
Calculate
80
−
6
×
5
×
2
80 - 6 \times 5 \times 2
80
−
6
×
5
×
2
.
See Solution
Problem 4555
Evaluate
9
×
(
40
+
5
)
9 \times(40+5)
9
×
(
40
+
5
)
in two different methods.
See Solution
Problem 4556
Find the result of dividing 0.03 by 10:
0.03
÷
10
=
0.03 \div 10 =
0.03
÷
10
=
See Solution
Problem 4557
Simplify the expression:
(
2
x
−
1
)
2
−
(
x
+
2
)
2
(2 x-1)^{2}-(x+2)^{2}
(
2
x
−
1
)
2
−
(
x
+
2
)
2
.
See Solution
Problem 4558
Calculate
0.008
×
100
0.008 \times 100
0.008
×
100
.
See Solution
Problem 4559
Calculate
0.03
×
1
,
000
0.03 \times 1,000
0.03
×
1
,
000
.
See Solution
Problem 4560
Beregn rabatpriser: a)
70
%
70\%
70%
af
680
680
680
, b)
70
%
70\%
70%
af
870
870
870
, c)
25
%
25\%
25%
af
392
392
392
, d)
30
%
30\%
30%
af
350
350
350
, e)
20
%
20\%
20%
af
260
260
260
, f)
22
%
22\%
22%
af
550
550
550
, g)
20
%
20\%
20%
af
195
195
195
, h)
92
%
92\%
92%
af
150
150
150
.
See Solution
Problem 4561
Beregn rabatten: a)
75
%
75\%
75%
af
352
352
352
; b)
25
%
25\%
25%
af
176
176
176
; c)
16
%
16\%
16%
af
650
650
650
; d)
72
%
72\%
72%
af
175
175
175
; e)
25
%
25\%
25%
af
476
476
476
; f)
12
%
12\%
12%
af
750
750
750
; g)
65
%
65\%
65%
af
260
260
260
; h)
15
%
15\%
15%
af
620
620
620
.
See Solution
Problem 4562
Find the discount on these amounts without a calculator: a)
10
%
10\%
10%
of
110
k
r
=
110 \mathrm{kr}=
110
kr
=
b)
50
%
50\%
50%
of
250
k
r
=
250 \mathrm{kr}=
250
kr
=
c)
20
%
20\%
20%
of
220
k
r
=
220 \mathrm{kr}=
220
kr
=
d)
10
%
10\%
10%
of
350
k
r
=
350 \mathrm{kr}=
350
kr
=
e)
40
%
40\%
40%
of
460
k
r
=
460 \mathrm{kr}=
460
kr
=
f)
80
%
80\%
80%
of
510
k
r
=
510 \mathrm{kr}=
510
kr
=
See Solution
Problem 4563
Find the limit:
lim
x
→
π
cos
x
+
sin
(
2
x
)
+
1
x
2
−
π
2
\lim _{x \rightarrow \pi} \frac{\cos x+\sin (2 x)+1}{x^{2}-\pi^{2}}
lim
x
→
π
x
2
−
π
2
c
o
s
x
+
s
i
n
(
2
x
)
+
1
. Options: (A)
1
2
π
\frac{1}{2 \pi}
2
π
1
(B)
1
π
\frac{1}{\pi}
π
1
(C) 1 (D) nonexistent.
See Solution
Problem 4564
Beregn rabatpriser: a)
75
%
75\%
75%
af
352
352
352
, b)
25
%
25\%
25%
af
176
176
176
, c)
16
%
16\%
16%
af
650
650
650
, d)
72
%
72\%
72%
af
175
175
175
, e)
25
%
25\%
25%
af
476
476
476
, f)
12
%
12\%
12%
af
750
750
750
, g)
65
%
65\%
65%
af
260
260
260
, h)
15
%
15\%
15%
af
620
620
620
.
See Solution
Problem 4565
Beregn rabatten uden lommeregner: a)
30
%
30\%
30%
af
100
k
r
=
100 \mathrm{kr}=
100
kr
=
, b)
20
%
20\%
20%
af
200
k
r
=
200 \mathrm{kr}=
200
kr
=
, c)
5
%
5\%
5%
af
400
k
r
=
400 \mathrm{kr}=
400
kr
=
, d)
8
%
8\%
8%
af
700
k
r
=
700 \mathrm{kr}=
700
kr
=
, e)
40
%
40\%
40%
af
600
k
r
=
600 \mathrm{kr}=
600
kr
=
.
See Solution
Problem 4566
Divide 142 by 5 using long division.
See Solution
Problem 4567
Beregn vækstprocenten for følgende: a) stigning 45, startværdi 240 b) stigning 47, startværdi 160 c) stigning 36, startværdi 375 d) stigning 76, startværdi 250 e) stigning 81, startværdi 144 Vækstprocent
=
stigning
startværdi
×
100
%
= \frac{\text{stigning}}{\text{startværdi}} \times 100 \%
=
startværdi
stigning
×
100%
See Solution
Problem 4568
When multiplying by a power of 10, how do digit shifts relate to zeros in the power? Give an example.
See Solution
Problem 4569
Find the altitude difference between Mount Everest (29,028 ft) and Mauna Kea (13,796 ft) above sea level.
See Solution
Problem 4570
Estimate the difference in Internet users between English (
478
,
582
,
273
478,582,273
478
,
582
,
273
) and Chinese (
383
,
212
,
617
383,212,617
383
,
212
,
617
) languages.
See Solution
Problem 4571
Calculate the product:
8.9
×
0.068
=
8.9 \times 0.068=
8.9
×
0.068
=
See Solution
Problem 4572
Find the numbers one-tenth less and more for 3 and 4: (3.)
2.8
≡
2.8 \equiv
2.8
≡
(4.)
2.1
≡
2.1 \equiv
2.1
≡
See Solution
Problem 4573
Find the numbers that are 0.01 less and 0.01 more for 2.33 and 2.10.
See Solution
Problem 4574
Find the values for: 1)
3.59
−
0.01
3.59 - 0.01
3.59
−
0.01
and 2)
5.64
+
0.1
5.64 + 0.1
5.64
+
0.1
.
See Solution
Problem 4575
Calculate the sum:
−
7
+
(
−
7
)
-7 + (-7)
−
7
+
(
−
7
)
.
See Solution
Problem 4576
Calculate the sum:
−
3
+
(
−
8
)
-3 + (-8)
−
3
+
(
−
8
)
.
See Solution
Problem 4577
Calculate
−
3
+
3
-3 + 3
−
3
+
3
.
See Solution
Problem 4578
The Dolphins gained 16 yards and lost 11 yards. Write the expression
16
+
(
−
11
)
16 + (-11)
16
+
(
−
11
)
, find the sum, and explain its meaning.
See Solution
Problem 4579
Calculate
15
−
(
−
7
)
15 - (-7)
15
−
(
−
7
)
.
See Solution
Problem 4580
Lupe has 7.2L and 0.92L of water in two fishbowls. How to compare their amounts? Marta freezes
3
4
\frac{3}{4}
4
3
of 24 cups of grapes. How many cups?
See Solution
Problem 4581
Estimate
391
×
22
391 \times 22
391
×
22
and explain your method. Also, calculate total costs for items: \$3.47, \$1.99, \$0.25, \$5.
See Solution
Problem 4582
Classify the probability: Is picking a blue marble from 2 blue and 5 yellow marbles
2
5
\frac{2}{5}
5
2
theoretical or experimental?
See Solution
Problem 4583
Estimate the total cost of items priced at \$3.47, \$1.99, \$0.25, \$5.69, \$3.04, and \$12.49 without calculating exactly.
See Solution
Problem 4584
Simplify
−
(
x
3
)
4
(
−
2
y
)
3
-\left(\frac{x}{3}\right)^{4}(-2 y)^{3}
−
(
3
x
)
4
(
−
2
y
)
3
.
See Solution
Problem 4585
Calculate the product of 28.4 and 7.7:
28.4
×
7.7
28.4 \times 7.7
28.4
×
7.7
.
See Solution
Problem 4586
Simplify
(
p
−
q
)
1
3
(
p
−
q
)
−
8
3
\frac{(p-q)^{\frac{1}{3}}}{(p-q)^{-\frac{8}{3}}}
(
p
−
q
)
−
3
8
(
p
−
q
)
3
1
.
See Solution
Problem 4587
Calculate the value of
40
×
638
40 \times 638
40
×
638
. Select the correct answer: A. 24,520 B. 24,220 C. 2,552 D. 25,520
See Solution
Problem 4588
Calculate
1
3
+
2
5
+
1
30
23
30
\frac{\frac{1}{3}+\frac{2}{5}+\frac{1}{30}}{\frac{23}{30}}
30
23
3
1
+
5
2
+
30
1
.
See Solution
Problem 4589
Solve: 4 tens + 6 tens, 8 hundreds + 2 hundreds, 5 thousands + 7 thousands. Write answers in standard form.
See Solution
Problem 4590
Model
4
+
(
−
9
)
4 + (-9)
4
+
(
−
9
)
on the number line.
See Solution
Problem 4591
Estimate if
22.8
×
4.7
=
107.16
22.8 \times 4.7 = 107.16
22.8
×
4.7
=
107.16
is reasonable. Respond with yes or no, and give a better estimate if no.
See Solution
Problem 4592
Estimate if the answers are reasonable. Write "yes" or "no" with a reasonable estimate.
21.
22.8
×
4.7
=
107.16
22.8 \times 4.7=107.16
22.8
×
4.7
=
107.16
22.
2.1
×
4.9
2.1 \times 4.9
2.1
×
4.9
23.
7.8
×
1.1
×
4.2
=
50
7.8 \times 1.1 \times 4.2=50
7.8
×
1.1
×
4.2
=
50
See Solution
Problem 4593
Estimate if
2.1
×
4.9
×
7.2
≈
105.84
2.1 \times 4.9 \times 7.2 \approx 105.84
2.1
×
4.9
×
7.2
≈
105.84
is reasonable. Answer yes or no, with a better estimate if no.
See Solution
Problem 4594
Estimate if the following products are reasonable:
22.8
×
4.7
22.8 \times 4.7
22.8
×
4.7
and
2.1
×
4.9
×
7.2
2.1 \times 4.9 \times 7.2
2.1
×
4.9
×
7.2
. Write yes or no with an estimate.
See Solution
Problem 4595
Estimate if these answers are reasonable:
7.8
×
1.1
×
4.2
=
50
7.8 \times 1.1 \times 4.2=50
7.8
×
1.1
×
4.2
=
50
and
43.8
×
2.8
×
3.1
=
371.8
43.8 \times 2.8 \times 3.1=371.8
43.8
×
2.8
×
3.1
=
371.8
.
See Solution
Problem 4596
Estimate if the answer is reasonable:
0.8
×
1.1
×
4.2
=
50
0.8 \times 1.1 \times 4.2 = 50
0.8
×
1.1
×
4.2
=
50
. Write yes or no with a better estimate if no.
See Solution
Problem 4597
Miguel thinks
$
47.25
\$ 47.25
$47.25
is less than
$
50
\$ 50
$50
. Estimate
43.8
×
2.8
×
3.1
43.8 \times 2.8 \times 3.1
43.8
×
2.8
×
3.1
and say if
371.8
371.8
371.8
is reasonable.
See Solution
Problem 4598
Find the converse of: If it's snowing, then Malika wears a coat out. Options include statements about snowing and wearing a coat.
See Solution
Problem 4599
Identify the contrapositive: If two figures are similar, then all corresponding angles are equal.
See Solution
Problem 4600
Multiply
−
1
7
8
-1 \frac{7}{8}
−
1
8
7
by
2
9
10
2 \frac{9}{10}
2
10
9
.
See Solution
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