A book sold
34,900
copies in its first month of release. Suppose this represents
9.1%
of the number of copies sold to date. How many copies have been sold to date?
Round your answer to the nearest whole number.
Let X be the number of copies sold to date.
0.091 * X = 34900
X = 34900 / 0.091
X ≈ 384615.38
The number of copies sold to date is approximately 384,615.
Light travels
×310^5
kilometers in one second. How far does it travel in
47
seconds?
Write your answer in scientific notation.
To find the distance travelled in 47 seconds, we need to multiply the speed of light by the number of seconds.
×310^5 * 47 = 310^5 * 47
Since both numbers are in scientific notation, we can simply multiply the coefficients and add the exponents.
310 * 47 = 14570
The exponent remains the same.
Therefore, the distance light travels in 47 seconds is 1.4570 × 10^5 kilometers.
6.6632495807 to the nearest hundredth
6.66
There are
9
roses in a vase of
13
flowers. The rest are daisies.
(a) What is the ratio of daisies to all flowers in the vase?
(b) What is the ratio of daisies to roses?
(a) The ratio of daisies to all flowers in the vase is (13 - 9):13 or 4:13.
(b) The ratio of daisies to roses is 4:9.
Lucy drove
13
laps on a race track. Each lap was the same length. If she drove a total of
57.2mi
what was the length of each lap? Write your answer in yards.
Use the table of conversion facts as necessary, and do not round your answer.
1760 yd = 1mi
To find the length of each lap in yards, we need to convert the total distance (57.2 miles) to yards and then divide by the number of laps (13).
1 mile = 1760 yards
57.2 miles = 57.2 * 1760 yards = 100672 yards
Length of each lap = 100672 yards / 13 laps = 7759.38 yards (rounded to two decimal places)
Therefore, the length of each lap is 7759.38 yards.
A-1 Chemical Supply pays Scott Simmons a
$2960
monthly salary plus a
13
% commission on merchandise he sells each month. Assume Scott's sales were
$69,000
for last month.
Calculate the following amounts:
1. Amount of Commission: $
2. Gross Pay:
1. To calculate the amount of commission, we multiply Scott's sales ($69,000) by the commission rate (13% or 0.13):
Amount of Commission = $69,000 * 0.13 = $8,970
Therefore, the amount of commission Scott earned is $8,970.
2. To calculate the gross pay, we add Scott's monthly salary ($2,960) to the amount of commission ($8,970):
Gross Pay = $2,960 + $8,970 = $11,930
Therefore, Scott's gross pay is $11,930.
A watermelon seed is
0.4cm
long. How far would a line of
120
watermelon seeds stretch?
Write your answer in meters.
Conversion facts for length
1000millimeters
mm
=1meter
m
100centimeters
cm
=1meter
m
10decimeters
dm
=1meter
m
1decameter
dam
=10meters
m
1hectometer
hm
=100meters
m
1kilometer
km
=1000meters
To find the distance the line of 120 watermelon seeds would stretch, we need to multiply the length of each seed (0.4 cm) by the number of seeds (120).
Distance = 0.4 cm * 120
Since we want the answer in meters, we need to convert centimeters to meters using the conversion factor of 100 centimeters = 1 meter.
Distance = (0.4 cm * 120) / 100
Distance = (48 cm) / 100
Distance = 0.48 meters
Therefore, the line of 120 watermelon seeds would stretch 0.48 meters.
Fill in the blanks below with the correct units.
(a) The mass of the baseball was about
145
.
________________________________________
(b) Tom drank about
200
of juice with lunch.
________________________________________
(c) The opening of the drinking straw was about
6
wide.
(a) The mass of the baseball was about 145 grams.
(b) Tom drank about 200 milliliters of juice with lunch.
(c) The opening of the drinking straw was about 6 millimeters wide.
Write the following ratio using two other notations.
7
:
9
Use only the numbers above (not any others).
Notation one:
Notation two:
Notation one: 7/9
Notation two: 7 to 9
Kareem received a
$1300
bonus. He decided to invest it in a
2
-year certificate of deposit (CD) with an annual interest rate of
1.16%
compounded daily.
Answer the questions below. Do not round any intermediate computations, and round your final answers to the nearest cent. If necessary, refer to the
list of financial formulas
. Assume there are
365
days in each year.
(a) Assuming no withdrawals are made, how much money is in Kareem's account after
2
years?
$
(b) How much interest is earned on Kareem's investment after
2
years?
$
(a) To calculate the amount of money in Kareem's account after 2 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the amount of money in the account after t years
P = the principal amount (initial investment)
r = annual interest rate (in decimal form)
n = number of times the interest is compounded per year
t = number of years
Given:
Principal amount (P) = $1300
Annual interest rate (r) = 1.16% or 0.0116
Number of times compounded per year (n) = 365 (compounded daily)
Number of years (t) = 2
Substituting these values into the formula:
A = $1300 * (1 + 0.0116/365)^(365 * 2)
Using a calculator, we find that A ≈ $1335.51.
Therefore, after 2 years, there would be approximately $1335.51 in Kareem's account.
(b) To calculate the interest earned on Kareem's investment after 2 years, we can subtract the principal amount from the total amount in the account:
Interest = A - P
= $1335.51 - $1300
= $35.51
Therefore, after 2 years, Kareem would earn approximately $35.51 in interest.
For the first week of June, Frank Green worked
55
hours. Frank earns
$19.80
an hour. His employer pays overtime for all hours worked in excess of
40
hours per week and pays
1.5
times the hourly rate for overtime hours.
Calculate the following for the first week of June (round your responses to the nearest cent if necessary):
1. Regular pay amount: $
2. Overtime pay: $
3. Gross pay: $
To calculate the pay for the first week of June, we need to consider both regular hours and overtime hours.
1. Regular pay amount:
Frank worked 40 regular hours, so the regular pay amount is:
Regular pay amount = 40 hours * $19.80/hour = $792.
2. Overtime pay:
Frank worked 55 hours in total, which means 15 hours were overtime hours. Overtime pay is calculated at 1.5 times the regular hourly rate:
Overtime pay = 15 hours * $19.80/hour * 1.5 = $445.50.
3. Gross pay:
The gross pay is the sum of the regular pay amount and the overtime pay:
Gross pay = Regular pay amount + Overtime pay = $792 + $445.50 = $1237.50.
Therefore, the regular pay amount is $792, the overtime pay is $445.50, and the gross pay is $1237.50 for the first week of June.
0.000876 Scientific notation
0.000876 can be expressed in scientific notation as 8.76 x 10^(-4).
Write this ratio as a fraction in simplest form without any units.
27
feet to
8
yards
You can use the table below to help convert the units.
Length 1
foot
=12
inches
1
yard
=3
feet
Weight 1
pound
=16
ounces
Capacity (Volume) 1
pint
=2
cups
1
quart
=2
pints
1
gallon
=4
quarts
To convert the units, we know that 1 yard is equal to 3 feet. Therefore, we can convert the first quantity to yards by dividing it by 3:
27 feet ÷ 3 = 9 yards
Now we have the ratio of 9 yards to 8 yards. As we're looking for the ratio without any units, we can write it simply as:
9/8
Therefore, the ratio of 27 feet to 8 yards in simplest form without any units is 9/8.
7^5/7 Answer must have an exponent
Recall that when you have a fraction with the same base raised to different exponents, you can subtract the exponents when dividing. Therefore,
7^5/7 = 7^(5-1) = 7^4
1/1679616 Answer must have a single exponent
To express 1/1679616 with a single exponent, we can rewrite the denominator as a power of the base. Since the base is 1, we can write it as 1^6:
1/1679616 = 1/(1^6 * 6^6) = 6^(-6)
exponent has to be positive
Apologies for the mistake. To express 1/1679616 with a positive exponent, we need to find the reciprocal of the number.
1/1679616 = (1/1679616)^-1 = (1679616)^-1
Therefore, 1/1679616 can be expressed as (1679616)^-1.
Answer must have a single positive exponent
To express 1/1679616 with a single positive exponent, we can rewrite it as a power of the base. Since 1679616 is a large number, it can be expressed as 2^24:
1/1679616 = 1/(2^24)
Therefore, 1/1679616 can be expressed as (2^24)^-1.
At the city museum, child admission is
$5.90
and adult admission is
$9.30
. On Sunday,
154
tickets were sold for a total sales of
$1190.80
. How many adult tickets were sold that day?
Number of adult tickets:
Let's assume the number of child tickets sold is C and the number of adult tickets sold is A.
According to the given information, the total number of tickets sold is 154, so we have:
C + A = 154
The total sales is $1190.80, which means the sum of the sales from child tickets and adult tickets is $1190.80:
5.90C + 9.30A = 1190.80
We have a system of two equations:
C + A = 154
5.90C + 9.30A = 1190.80
To solve this system, we can use either substitution or elimination. Let's use the substitution method.
From the first equation, we have C = 154 - A. We can substitute this value into the second equation:
5.90(154 - A) + 9.30A = 1190.80
Expanding and rearranging the equation, we get:
905.60 - 5.90A + 9.30A = 1190.80
3.40A = 285.20
A = 285.20 / 3.40
A ≈ 84
Therefore, the number of adult tickets sold that day was approximately 84.
A coffee pot holds
512
quarts of coffee. How much is this in cups?
Write your answer as a whole number or a mixed number in simplest form. Conversion facts for volume
1
cup
c = 8
fluid ounces
fl oz
1
pint
pt = 2
cups
c
1
quart
qt = 2
pints
pt
1
gallon
gal = 4
quarts
qt
c
To convert quarts to cups, we can use the conversion factor that 1 quart is equal to 2 cups.
Therefore, for 512 quarts:
512 quarts * 2 cups/quart = 1024 cups
Thus, 512 quarts is equal to 1024 cups.
The ratio of union members to nonunion members working for a company is
3
to
2
. If there are
50
nonunion members working for the company, what is the total number of employees?
Let's assume the number of union members is U.
According to the given information, the ratio of union members to nonunion members is 3 to 2. This means that for every 3 union members, there are 2 nonunion members. We also know that there are 50 nonunion members.
We can set up a proportion to find the number of union members:
3/2 = U/50
Cross-multiplying, we get:
2U = 3 * 50
2U = 150
Dividing both sides by 2, we find:
U = 150 / 2
U = 75
Therefore, the number of union members is 75.
To find the total number of employees, we add the number of union members and nonunion members:
Total number of employees = Union members + Nonunion members
Total number of employees = 75 + 50
Total number of employees = 125
Therefore, the total number of employees is 125.