Answer:
At 53 mph, he traveled for 1.5 hours
At 58 mph, he traveled for 2 hours
Step-by-step explanation:
Mathematically;
distance = speed * time
let the time for the first part of the trip be x hours and the second part be y hours
Total hours is 3.5
So therefore;
x + y = 3.5 ••••••••(i)
Now let’s work with the rate
53 mph for x hours = 53 * x = 53x miles
58 mph for y hours = 58 * y = 58y miles
Adding both;
53x + 58y = 195.5 miles ••••••••(ii)
We have two equations to solve simultaneously
From i, x = 3.5 - y
insert into ii
53(3.5-y) + 58y = 195.5
185.5 - 53y + 58y = 195.5
5y = 195.5-185.5
5y = 10
y = 10/5
y = 2 hours
x = 3.5 - y
x = 3.5 - 2
x = 1.5 hours
A long year-end status report for work is 81 pages long. You need to print 12 copies for a meeting next week. How much is the paper going to cost for those reports? Paper is sold in reams (500 pages) for $3.96 each.
Give your answer to the nearest cent, only for the paper you use (partial reams are OK)
Answer:
770cents
Step-by-step explanation:
If a report is 81 pages long, 12 copies will be (81 * 12)pages long
12copies = 972 pages long
If 500 pages costs $3.96 each
972 pages will cost $x
Cross multiply
500x = 972 * 3.96
500x = 3,849.12
x = 3,849.12/500
x = 7.69824
Hence the cost of the reports is $7.69824
Convert to cents;
$1 = 100cents
$7.69824 = y
y = 7.69824 * 100
y = 769.824 cents
y ≈ 770 cents (to the nearest cent.)
Hence the paper is going to cost 770cents (to the nearest cent)
A swimming pool has two pipes coming into it to fill it with water. One pipe takes 16 hours to fill it. The other takes 12 hours to fill it. How many hours will it take both pipes to fill the pool?
Answer:
8 hours
Step-by-step explanation:
8 hours because half of 16 is 8 and half of 12 is 6
If it takes 6 hours to fill one half then the other 2 hours would go to the other pipe making it 8 hours
A rectangular prism has a volume of 686 cubic units. How many unit cubes would fill the volume of the solid if they were packed without any gaps or overlaps?
Answer:
2 unit cubes of 7 units side length can fill the volume of the solid without overlap
Step-by-step explanation:
Volume of a cube is L^3
Let the number of cubes be n
Since the cubes are similar,
then;
nL^3 = 686
nL^3 = 343 * 2
By inspection
L^3 = 343 (since it is a perfect cube and the cube root is 7)
n = 2
Shelley has a 1 1/2 pound supply of Cat Treats. Each day she gives her kitten 1/8 pound of the treats. How many days will the supply of treats last
Answer:
The treats will last 12 days.
The cash price of a laptop is $1299. It can be bought at hire purchase by making a deposit of $350 and 10 monthly payments at $120 each.
(i) What is the TOTAL hire purchase
(ii) How much is saved by buying the laptop for cash
I) The TOTAL hire purchase of the laptop is; $1550
II) The amount saved by buying the laptop for cash is; $251
I) We are told that the laptop can be bought at hire purchase by making a deposit of $350 and 10 monthly payments at $120 each.
Thus;
Cost of laptop by hire purchase = 350 + 120(10)
>> 350 + 1200
>> $1550
II) Since the cash price is $1299, then amount saved = 1550 - 1299
>> $251
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A patio 44, feet wide is being constructed next to a house. To drain water off the patio and away from the house, a slope of 1/2 inch per foot is necessary. What total
difference in height is required from one edge of the patio to the other?
Answer:
the total difference in height will be 22 inches
Step-by-step explanation:
since the slope is 0.5 inch per foot, and the patio is 44 feet wide, the end of the patio will be 0.5 x 44 = 22 inches lower
the slope measures how much the height (Y axis) will change as the length (X axis) increases by 1 unit. In this case, since the height decreases as the length increases the slope is negative.
Write the slope- intercept form of the equation of the line described through (4,5) parallel to y= 1/4x-4
Answer:
y = 1/4 x + 4
Step-by-step explanation:
1. Because the new equation is parallel to y= 1/4x - 4 => the slope is still the same => New equation : y = 1/4x + b ( b is a number that we'll find now)
2. Put x = 4 and y = 5 in the new equation
=> 5 = (1/4)(4) + b
=> b = 4
3. So then we'll have the new equation that is parallel to y = 1/4x-4
Approximate the logarithm using the properties of logarithms, given
logb 2 ≈ 0.3562,
logb 3 ≈ 0.5646,
and
logb 5 ≈ 0.8271.
(Round your answer to four decimal places.)
㏒b(2b^3)
que representa Laos hombres con relacion al total
How many squares are in the 20th case
Answer:
400
Step-by-step explanation:
At least I tried!.....#DareCompleted
Answer:
Very nice Drawing. Your try is so nice
Bob paid $5.60 for 0.8 lb of fresh peaches.
How much would 3.25 lb of peaches cost?
Answer:
22.75
Step-by-step explanation:
5.6 divided by 0.8=Constant Variation=7
3.25*7=22.75
The price of the 3.25 lb peaches is $22.75.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Bob paid $5.60 for 0.8 lb of fresh peaches. The price of the 3.25 lb peaches will be calculated as,
0.8 lb of peaches ⇒ $5.60
1 lb of peach ⇒ $5.60 / 0.8
3.25 lb of peaches ⇒ (3.25 x $5.60 ) / 0.8
3.25 lb of peaches ⇒ $22.75
Therefore, the price of the 3.25 lb peaches is $22.75.
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Complete the table by finding the balance A when P dollars is invested at rate r for t years and compounded n times per year. (Round your answers to the nearest cent.)
P = $2500, r = 3%, t = 10 years
n A
1 $
2 $
4 $
12 $
365 $
Continuous $
Answer:
I had this exact question on my test yesterday! That's so crazy!
Step-by-step explanation:
I WILL GIVE BRAINLIEST PLEASE HELP
Answer:
15/19
Step-by-step explanation:
60/4 = 15
76/4 = 19
15/19
Answer:
76/60 i think
Step-by-step explanation:
Which expression represents the phrase below?
The product of 15 and the quantity 12 less than a number.
a. (15 x 12) - a
b. 15(a - 12)
c. 15+ (12-a)
d. 12a * 15
Answer:
Answer C
Step-by-step explanation:
the product of 15 and the quantity 12 less than a number
1) Fairview and Abbots Rise are 5 in apart on a map that has a scale of 1 in : 18 mi. How far apart are the real cities? 2) A particular satellite is 12 ft wide. A model of it was built with a scale of 1 in :3 ft. How wide is the model? Please help me I have 4 more questoins
Answer:
1) 90 mi
2) 4 inch
Step-by-step explanation:
1)
Given that the distance between Fairview and Abbots Rise on the map = 5 in
Scale of the map = 1 in: 18 mi
i.e. 1 inch on map is equivalent to an actual distance equal to 18 mi between the cities.
Given that the map has a distance of 5 inches.
Therefore, the actual distance between the cities = 5 [tex]\times[/tex] 18 = 90 mi
2) A particular satellite is 12 ft wide.
Model's scale = 1 in : 3 ft
i.e. 1 inch on map is equivalent to actual distance of 3 ft.
OR
3 ft of actual distance = 1 in on map
1 ft of actual distance = [tex]\frac{1}{3}[/tex] in on map
12 ft of actual distance = [tex]\frac{1}{3}\times 12 = \bold{4\ inch}[/tex]
What is the solution for y=2x+3, y=2x-3
Answer:.
Step-by-step explanation:
Gary applied the distributive property using the greatest common factor to determine the expression that is equivalent to 66+36 his work is shown below. Which statement best describes Gary's error?
A) Gary did not use correct factors for 66 in the equation
B) Gary did not use correct factors for 36 in the equation
C) Gary did not use two equivalent expressions in the equation.
D) Gary did not use the greatest common factor in the equation.
Answer:
A
Step-by-step explanation:
A because 1, 2, 3, 4, 6, 11, 22, 33, 66
(5 marks)
b) Anthony plans to take up business and purchase a shop lot near his home. He saves
RM10,000 in an account that pays 6% compounded every four months. Four years
later, he withdrew all his money to pay for the down payment of the shop lot.
D)
Find the value of the down payment.
(3 marks)
I thought this right but sorry if it is wrong
first make the 6% in amount by 6×10,000÷100=3600
then, the convert 4 year into month by (4×12)=48month. after that divide 48months by 4 month.i.e.48÷4=12.at last multiply 12 by 3600.i.e. 12×3600=43200
the weights of steers in a herd are distributed normally. the standard deviation is 200lbs and the mean steer weight is 1400lbs. find the probability that the weight of a randomly selected steer is less than 1859lbs
Answer:
The probability that the weight of a randomly selected steer is less than 1859lbs is 0.9890
Step-by-step explanation:
Given
Mean = 1400 lbs
SD = 200 lbs
In order to find the probability of a random variable x we have to find the z-score of the data point.
z-score is calculated by:
[tex]z = \frac{x-mean}{SD}[/tex]
Putting x=1859
[tex]z = \frac{1859-1400}{200}\\z = \frac{459}{200}\\z = 2.295[/tex]
The z-score for 1859 is 2.295
We have to use the z-score table to find the required probability
So,
[tex]P(z<2.295)\ or\ P(x<1859) = 0.9890[/tex]
Hence,
The probability that the weight of a randomly selected steer is less than 1859lbs is 0.9890
Four puzzles that were manufactured contained a total of 420 pieces. The next 6 puzzles contained a total of 630 pieces. If the relationship between the number of puzzles and the total number of puzzle pieces continues to be proportional, which could be the missing entries in the table?
Number of Puzzles
(x)
Number of Pieces
(y)
4
420
6
630
8 puzzles and 800 pieces
8 puzzles and 840 pieces
10 puzzles and 1,000 pieces
10 puzzles and 1,200 pieces
Answer:
ANWSER A
Step-by-step explanation:
Answer:
Answers A
Step-by-step explanation:
Just took the test
A bicycle is traveling at 21 miles per hour. How many feet will it cover in 35 second?
prove that 1/log (xy)² +1/log(xy²) + log(xy³) =1 there base are x,y and z respectively.
Answer:
[tex]1/log (xy)² +1/log(xy²) + log(xy³) =1[/tex]
Step-by-step explanation:
This is your equation, right? Just checking
3. You receive an order for 0.5 g of Tigan IM. You have a 5 mL vial labeled 100 mg/mL. What is the
volume you will need to fill the order?
a. 2 mL
c. 0.5 mL
b. 5 mL
d. 0.02 mL
Answer:
52
Step-by-step explanation:
The ratio x : y is equal to 2 : 5, and y is 80% of z. Write an equation to represent the proportional relationship between x and z.
Answer:
x : z = 8 : 25Step-by-step explanation:
Given
x : y = 2 : 5, y is 80% of zRearranging the ratios:
x/y = 2/5 ⇒ x/y = 0.4 ⇒ y = x/0.4 ⇒ y = 2.5xy is 80% of z ⇒ y = 0.8zComparing the values of y:
2.5x = 0.8zx/z = 0.8/2.5x/z = 0.32x/z = 32/100 x/z = 8/25x : z = 8 : 25Tarea resuelta de matemática semana 32 3ro de secundaria.
Answer:
Solved math homework week 32 3rd of secondary school.
Felicidades
Step-by-step explanation:
What does 2.89x0.79x1.35= equal?
Answer: 3.082185x^2
Step-by-step explanation: Find the exact value using trigonometric identities
True or false
If a prime number is greater than 2, it is odd
Answer:
true
Step-by-step explanation:
if a prime number were even, and greater than 2, they would be able to be divisible by 2 and therefore not a prime number
Answer:true
Step-by-step explanation:
A prime number is a number that can only be multiplied by 1 to get itself, an even number is a number that can be multiplied by 2. Thus it is true.
Calculate the equation of the line through the points (-1, 1), (4,0), and (24,-4).
Answer:
slope intercept form: y=-1/5x + 4/5
what is 4 divided by 0.576
4 divided by 0.576 is approximately equal to 6.9444.
To find the result of 4 divided by 0.576, we can perform the division by dividing the numerator ( 4 ) by the denominator ( 0.576 ).
When we divide 4 by 0.576, we get approximately 6.9444.
Therefore, 4 divided by 0.576 is approximately equal to 6.9444.
In decimal form, this indicates that 4 can be divided into 0.576 approximately 6.9444 times. The result is a decimal number that extends to multiple decimal places. To obtain a more precise or exact answer, additional decimal places may need to be considered in the calculation.
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I need help on my math work.
Answer:
i believe it is the suburban apartment
Step-by-step explanation:
i believe this because if the area calculation. the sides are more the other.