7.23. A freight train travels 1 mile in 1 minute 30 seconds. At this rate, how many miles will the train travel in 1 hour?
Answer:
40 miles in 60 minutes
Step-by-step explanation:
1 hour has 60 minutes, and since the freight train travels 1 mile in 1.5 minutes, it can be said that the train travels 2 miles in 3 minutes (assuming a constant rate). This becomes a problem of equal ratios:
[tex]\frac{2}{3}=\frac{x}{60}[/tex] , where the numerator refers to distance, and the denominator refers to the time
After cross multiplication, we find that 3x = 120, or x = 40.
Therefore, it takes 1 hour for the train to travel 40 miles
Answer:
The number of miles will the train travel in 1 hour is 40 miles.
Step-by-step explanation:
Given:
A freight train travels 1 mile in 1 minute 30 seconds.
Find:
The number of miles that the train will travel in 1 hour
Step 1 of 1
One minute 30 seconds is [tex]$\frac{3}{2}$[/tex] minutes, so the train's speed is
[tex]$$\begin{aligned}\text { spced } &=\frac{1 \text { miles }}{\frac{3}{2} \text { minutes }} \\&=\frac{2}{3} \frac{\text { miles }}{\text { minute }}\end{aligned}$$[/tex]
There are 60 minutes in an hour, so the distance traveled in 60 minutes is distance [tex]=(60$ minutes $) \cdot\left(\frac{2}{3} \frac{\text { miles }}{\text { minute }}\right)$[/tex]
=40 miles.
8.28 Katie wants a fancy new music player that costs $300. Katie can buy it in her home state and pay 8% sales tax, or she can drive to a neighboring state and pay only 5% sales tax. How much does Katie save on the player if she drives to the neighboring state?
Answer:
Explanation
Given:- Katie wants a fancy new music player that costs $300
. Katie can buy it in her home state and pay 8% sales tax, or she can drive to a neighboring state and pay only 5% sales tax
To Find:- To determine the cost Katie saves on the player if she drives to the neighboring state
The difference between the sales tax of the home state and the neighboring state provides the percentage of sales tax . Then, multiplying the determined percentage of sales tax on the new music player would be the cost Katie saves on the player if she drives to the neighboring state.
Step-by-step explanation:
The sales tax in the home state is 8% and the sales tax in the neighboring state is 5%The percentage of sales tax saved when travelling from home state to neighboring state will be=8%-5%
=3%
Therefore, the cost Katie saves on the new music player which costs $300 if she drives to the neighboring state will be=300*3%
=300*(3/100)
=3*3
=$9
The amount Katie saves on the new music player if she drives to the neighboring state is $9
Answer:
Katie saves $9.
Step-by-step explanation:
Buy it in her home:
8% of $300 = $24
Buy it in neighbouring state:
5% of $300 = $15
How much she save's (Answer):
She saves $9 because 24 - 15 = 9.
How many arrangements of all eight letters in TRESPASS do not have S as the final letter?
Answer:
i think its 16
Step-by-step explanation:
Compare the expressions using >, < or =
-5 + (-3) and -5- (-3)
Answer:
-5 + (-3) < -5 - (-3)
Step-by-step explanation:
so -5 + (-3) evaluates to -5 - 3 which then evaluates to -8, because you're "going back" on the number line by 3.
-5 - (-3) evaluates to -5 + 3 since the negatives cancel out. this further evaluates to -2. this is greater than the previous value so we use the < (if you put this equation on the right side, since you can technically use > if you put the equation on the left side, just depends on what side you put it on)
-5 + (-3) < -5 - (-3)
Please Help!
What is 3,198.7 as a fraction
Answer:
31987/10 or 3198 7/10
Step-by-step explanation:
Hi!! Here's how to solve your problem!!
Step 1: Convert decimal to fraction.
3198.7 = 31987 over 10 (31987/10)
(You add a 1 under the decimal point and there is a 7 next to the decimal point so you add one 0 since there aren't any numbers after 7.)
Step 2: Change the fraction (if you want)
31987/10 = 3198 and 7 over 10
31987 ÷ 10 = 3198 remainder 7 so it will be 3198 7/10.
I hope this helps!!!
The lengths of the sides of triangle ABC are consecutive whole numbers. The median from angle A is perpendicular to the angle bisector of ∠B. Find the lengths of the sides of the triangle.
16. During a choir rehearsal, 25 students were standing in a line at equal distances. The distance between the first and the fourth student was 2.7 m. What was the distance between the first and the last student?
Answer:
Step-by-step explanation:
25 - 4 = 21
2.7*21=56.7m
There are 3 times as many females as males on the maths course at university. What fraction of the course are male?
Give your answer in its simplest form.
Answer:
1/4
Step-by-step explanation:
3*1 "female" parts and 1 "male" part
3+1=4
Males : 1/4
Answer:
1/4
Step-by-step explanation:
(x + 3x = 4x)
x = male
3x = female
Therefore add both and get 4x.
So male is 1 out of 4 or 1/4
What is the volume of a rectangular prism with side lengths 15.8 m, 24.5 m, and 4.2 m? Round to the nearest cubic meter.
Answer: 1,626 cubic meters
Step-by-step explanation:
V= lwh
V= length x with x height
Each number isn't specified (i dont know which numbers represent the width, length, and height since it isn't said) but that doesn't matter because according to the commutative property , you can multiply in any order and still get the same result.
So V= 15.8 x 24.5 x 4.2
V= 1,625.82
Rounded to the nearest cubic meter: 1,626 because 1625.82 becomes 1625.8, which, to the nearest whole number, is 1,626.
7.63. Kim was elected class president. She received 3 votes for every 2 that Amy got. No one else ran. However, if 8 of the people who voted for Kim had voted for Amy instead, Kim would have received only 1 vote for every 2 that Amy would have gotten. How many people voted?
Hint: Assign a variable so you can write expressions and set up equations. What's often a useful way to assign a variable in a ratio problem?
Answer:
The number of people who voted is 30 people.
Step-by-step explanation:
Given:
Kim was elected class president. She received 3 votes for every 2 that Amy got.
No one else ran.
However, if 8 of the people who voted for Kim had voted for Amy instead, Kim would have received only 1 vote for every 2 that Amy would have gotten
Find:
the number of people voted
Step 1 of 1
The ratio of Kim's votes to Amy's votes is 3:2, so Kim received 3x votes and Amy received 2x votes for some value of x. If 8 of the people had voted for Amy instead of Kim, then Kim would have 3x-8 votes and Amy would have 2x+8 votes. If this had happened, then Amy would have twice as many votes as Kim, so 2x+8=2(3 x-8).
Expanding the right-hand side gives 2x+8=6x-16.
Subtracting $2 x$ from both sides and adding 16 to both sides gives 24=4x, so x=6.
Since 3x+2x=5x people voted, the number of voters is [tex]$5 \cdot 6=30$[/tex].
Answer:
30 people
Step-by-step explanation:
The ratio of Kim's votes to Amy's votes is 3:2, so Kim received 3x votes and Amy received 2x votes for some value of x. If 8 of the people had voted for Amy instead of Kim, then Kim would have 3x-8 votes and Amy would have 2x+8 votes. If this had happened, then Amy would have twice as many votes as Kim, so 2x+8=2(3 x-8).
Expanding the right-hand side gives 2x+8=6x-16.
Subtracting $2 x$ from both sides and adding 16 to both sides gives 24=4x, so x=6.
Since 3x+2x=5x people voted, the number of voters is .
PLS ANSWER THIS QUESTION- this is 8th grade math
7.59. Five workers together can build a road in 20 days. Suppose every worker works at the same rate. If three workers work on the road for 10 days before eleven more workers join them, then how long total will it take to build the road?
Hint: Problems involving rates and work can often be solved by thinking about how much work is done per unit of time.
Hint: How long would it take one worker to build the whole road? What fraction of the road does one worker complete in one day?
Answer:
The number of days it takes to complete the work is 15 days.
Step-by-step explanation:
Given:
Five workers together can build a road in 20 days. Suppose every worker works at the same rate. If three workers work on the road for 10 days before eleven more workers join them
Find:
the numbers of days it takes to complete the work
Step 1 of 1
Because 5 workers can build a road in 20 days, each worker can build [tex]$\frac{1}{5}$[/tex] of a road in 20 days.
Therefore, each worker can build 1 road working alone in [tex]$20 \cdot 5=100$[/tex] days.
So, each worker builds [tex]$\frac{1}{100}$[/tex] road each day.
Therefore, three workers together build [tex]$\frac{3}{100}$[/tex] of a road each day, so in 10 days they build $10.
[tex]$\frac{3}{100}=\frac{3}{10}$[/tex] of a road.
At this point, they have [tex]$1-\frac{3}{10}=\frac{7}{10}$[/tex] of the road to the finish.
After the 11 extra workers join in, the 14 workers build [tex]$\frac{14}{100}$[/tex] of the road each day.
So, to finish the remaining [tex]$\frac{7}{10}$[/tex] of a road, the workers must work for
[tex]$$\begin{aligned}\frac{\frac{7}{10} \text { road }}{\frac{14}{100} \frac{\text { ruad }}{\text { day }}} &=\frac{7}{10} \cdot \frac{100}{14} \text { days } \\&=5 \text { days. }\end{aligned}$$[/tex]
Therefore, the road is built in 10+5=15 days
It will take 15 days to finish the road.
What is Proportion?Proportion is defined as where two or more ratios are set to be equal to each other.
If two quantities are directly proportional, if one increases or decreases, other also increases or decreases simultaneously.
If two quantities are inversely proportional, if one increases, other decreases and vice versa.
Here,
Number of days and number of workers are directly proportional to the road built.
Number of workers to build the road is inversely proportional to number of days to build the road.
Let R be the total road need to be built.
Five workers together can build a road in 20 days.
Road built by 5 workers in 20 days = R
Road built by 1 worker in 20 days = R/5
Road built by 1 worker in 1 day = (R/5) / 20
= R/100
Now, three workers work on the road for 10 days.
We have,
Road built by 1 worker in 1 day = R/100
Road built by 3 workers in 1 day = 3R/100
Road built by 3 workers in 10 days = (3R/100) × 10
= 30R/100
Remaining road to complete = R - (30R/100)
= 70R/100
= 7R/10
This is the time when eleven more workers joined.
That is, total number of workers = 3 + 11 = 14
We have,
Number of days taken by 5 workers to complete R = 20 days
Number of days taken by 1 worker to complete R = 20 × 5 = 100 days
Number of days taken by 1 worker to complete 7/10 of R = 100 × [tex]\frac{7}{10}[/tex]
= 70 days
Number of days taken by 14 workers to complete 7/10 of R = 70/14
= 5 days
Total number of days taken = 10 + 5 = 15 days
Hence if three workers work on the road for 10 days before eleven more workers join them, then it will take a total of 15 days to build the road.
Learn more about Proportion here :
https://brainly.com/question/29774220
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please answer correctly.
Answer:
The answer is the second option down.
I REALLY NEED HELP: A cook is planning a banquet dinner a recipe that serves 8 people calls for 2 cups of milk. How many cups of milk will be needed for 36 servings?
The cook will need 9 cups of milk for the banquet dinner.
How many cups of milk will be needed for 36 servings?Since the recipe calls for 2 cups of milk per 8 servings. We can say:
cups of milk / servings = 2 / 8 = 1/4
We can solve for the cups of milk by multiplying both sides of the proportion by 36.
cups of milk for 36 servings = (cups of milk / servings) * 36
= (1 / 4) * 36
= 9
Therefore, 9 cups of milk will be needed for the banquet dinner.
Learn more about proportion on:
https://brainly.com/question/1781657
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PLEASE ANSWER: 3 1/2 + (-7) x (2 2/3 + 1 1/2) = ?
Answer:
[tex]-\frac{77}{3}[/tex]
Step-by-step explanation:
So we have the equation: [tex]3\frac{1}{2} + (-7) * (2\frac{2}{3} + 1\frac{1}{2})[/tex]. and I'm assuming you meant to do mixed fractions and not actually multiplying. 2 * 2/3. So the first thing to do is follow PEMDAS which essentially says Parenthesis first, Exponents next, Multiplication or Division, and then Addition or Subtract. So let's start by evaluating the 2 2/3 and 1 1/2. The first step is to combine 2 into the 2/3 and the 1 into 1/2. This is done by multiplying the 2 by the denominator of 3, and adding it to the numerator so: [tex]2\frac{2}{3} = > \frac{(2*3)+2}{3} = > \frac{8}{3}[/tex]. And you do this for the 1/2 as well: [tex]1\frac{1}{2} = > \frac{(2*1)+1}{2}= > \frac{3}{2}[/tex].
Now when adding fractions, you can only add them when they have the same denominator, so we have the get 3/2 and 8/3 to have the same denominator. You can list the multiplies of 2 and 3 to try to find a LCM, but in this case, I'll just multiply 2 and 3, since they're really small numbers, also because 6 is the LCM. [tex]\frac{8}{3} * \frac{2}{2} = \frac{16}{6}[/tex]. And now do this to the 3/2 you get: [tex]\frac{3}{2} * \frac{3}{3} = \frac{9}{6}[/tex]. Now the inside of the parenthesis is: [tex]\frac{9}{6} + \frac{16}{6} = \frac{25}{6}[/tex]. So now we have the equation: [tex]3\frac{1}{2} -7 * \frac{25}{6}[/tex] . Also notice how I got ride of the plus sign and made it negative? Think of it as having a 1 in front and simply distributing that to the -7, 1*(-7) becomes -7.
Now to multiply the fraction by a whole number you simply multiply the denominator and numerator, and you can think of the denominator of a whole number as a 1. So this gives you: [tex]\frac{-7}{1} * \frac{25}{6} = \frac{-7 * 25}{1 * 6} = -\frac{175}{6}[/tex]. Now we have the equation: [tex]3\frac{1}{2} - \frac{175}{6}[/tex]. And to subtract these two numbers I'll make the 3 1/2 a fraction by multiplying the 3 by the denominator and adding it to the 1 which should become 7/2. And after that multiply both sides by 3/3 to get 21/6 so they have the same denominator. This gives you the equation: [tex]\frac{21}{6} - \frac{175}{6} = \frac{21-175}{6} = -\frac{154}{6}[/tex]. Which can simplify by dividing both sides by 2 to get: [tex]-\frac{77}{3}[/tex]
PLEASE ANSWER ASAP: Last year, Springfield Middle School had 526 students. This year, it has 496 students. To the NEAREST TENTH, what is the percent of decrease.
Answer:
5.7 is the answer good sir your welcome
Answer:
The percentage decrease is
[tex]5.7\%[/tex]
Step-by-step explanation:
The solution is in the image
help i dont know how to find the surface area. a step by step explanation would help me better.
Answer:
256
Step-by-step explanation:
so there is 4 rectangles, 1 square, and 4 triangles within the composite figure in the question.
so basically you find the area of each of those shapes and add them together and that's your answer.
the rectangles width is 4 and length is 12, to find the area of a rectangle you do length times width so 4 times 12 which is 48, you have 4 rectangles so 48 times 4, which is 192.
the squares sides are 4 so you multiple two of the sides so 4 times 4 which is 16.
now we have the triangles, the formula for the area of a triangle is A=[tex]\frac{hx_{b}b }{2}[/tex], so b is base, the base is 4, h is height, the height is 6, so you plug in those numbers in the formula and you get 12. you have 4 triangles so 12 times 4 which is 48.
so now you add them all together 192 + 16 + 48 = 256
Can someone help me these 2 questions? PLS and ty!
I’ll give Brainliest if you explain how you solved this
25 points?
Answer:
y=60° b=60°
Step-by-step explanation:
the sum of all degrees of interior triangle is 180
in the first one, 30° and 90° have been given.(that small square represent 90°)
so 180°-90°-30°=60°
in the second one, the 120° is on the other side of a line, a line has a degree of 180, therefore the interior angle is 60°, the same rule 180°-2*60°=60°
Let's take this problem step-by-step:
Both problems involve triangles:
⇒ let's find out the sum of the interior angle w/ formula 180(n-2)
Total Interior Angle Sum of Triangle = 180(3-2) = 180
Let's solve the first problem (A)
⇒ we know the total interior angle sum is 180 degrees
⇒ we know that two of the angles are 30 degrees and 90 degrees
* any angle with a square on them is 90 degrees
⇒ therefore:
30 + 90 + y = 180
120 + y= 180
y = 60
Let's solve the second problem:
⇒ the angle opposite the exterior angle, 120 degrees, is on a flat line
with it
⇒ therefore it is 60 degrees
⇒ two angles on a flat line equal 180 degrees
⇒ two angles are therefore 60 degrees
⇒ therefore:
60 + 60 + y = 180
120 + y = 180
y = 60
Answer:
(A) y= 60(B) y =60
18. The mass of a box with 20 similar bottles of cooking oil is 18.6 kg. The mass of the empty box is 1.4 kg. What is the mass of each bottle of oil in kilograms?
Step-by-step explanation:
Total mass = 18.6kgMass of empty box = 1.4kgno. of bottles = 20subtract the mass of the empty box from the total mass to get the mass of only the bottles: 18.6 - 1.4 = 17.2kgMass of the 20 bottles = 17.2kg To get the mass of each bottle, we divide the mass of the bottles by the number of bottles.therefore: 17.2 ÷ 20 = 0.86 kgTherefore the mass of each bottle = 0.86kg.Hope this helps.
Good luck ✅.
THIS QUESTION IS GOING TO SAVE MY LIFE:
Write each ratio as a fraction in lowest terms:
Q1 - 24.8 to 13.4
Q2 - 1.5 to 4.5
Answer:
Step-by-step explanation:
(1) The ratio 24.8 to 13.4 can be rewritten as 24 8/10 or 248/10 to 13 4/10, or, after simplification, 248/10 to 134/10. This version of the given ratio reduces to 248/134, or 124/67. This last version cannot be reduced further.
(2) The ratio 1.5 to 4.5 is equivalent to 3(.5) / 3(1.5), or 1/3.
Find the amount of discount using the following numbers.
Original price: $60; Rate of discount: 20%
PLEASE HELP ME
I GOT STUCK
THANK YOU!!
Answer:
Discount = 20%
Original price = $60
Discounted price = $48
Step-by-step explanation:
To find the amount of the discount, we take the original price and multiply it by the rate of the discount. In this case, we would take $60 and multiply it by 0.20 to get $12. This is the amount of the discount.
Which of the following expressions are equivalent to -1/2 x (4x5)
Choose all that apply.
A. -4 x (1/2 x 5)
B. 1/2 x (-4 x 5)
C. None of the above
please help!!!
Answer:
I might be wrong but I think the answer is that A and B are equivalent to -1/2 x (4x5)
Step-by-step explanation:
math
7.24. If you walk for 45 minutes at a rate of 4 \mathrm{mph}$ and then run for 30 minutes at a rate of 10 mph, then how many miles have you gone at the end of one hour and 15 minutes? What was your average speed for the journey?
Answer:
The average speed for the journey is 6.4 mph.
Step-by-step explanation:
Given:
If you walk for 45 minutes at a rate of [tex]$4 \mathrm{mph}$[/tex] and then run for 30 minutes at a rate of [tex]$10 \mathrm{mph}$[/tex], then how many miles have you gone at the end of one hour and 15 minutes Find the average speed for the journey
Step 1 of 1
We can compute the walking distance and running distances separately, then add them.
You walk for 45 minutes, which is [tex]\frac{3}{4}$[/tex] hours, at a rate of [tex]$4 \mathrm{mph}$[/tex], so the walking distance is [tex](4 \mathrm{mph})\left(\frac{3}{4}\right.$ hours $)=3$[/tex] miles. You run for 30 minutes, which is [tex]\frac{1}{2}$ hour, at a rate of $10 \mathrm{mph}$[/tex], so the running distance is [tex]$(10 \mathrm{mph})\left(\frac{1}{2} h o u r\right)=5$[/tex] miles.
So the total distance you cover is 3+5=8 miles.
Now we can also compute the average speed for the journey.
You covered 8 miles in [tex]$\frac{5}{4}$[/tex] hours, so your average speed was
[tex]$$\begin{aligned}&\frac{8 \text { miles }}{\frac{5}{4} \text { hours }}=\frac{8}{\frac{5}{4}} \mathrm{mph} \\&\frac{32}{5} \mathrm{mph}=6.4 \mathrm{mph}\end{aligned}$$[/tex]
Tell which number is greater.
11. 0.12, 1.2%
Answer: 11
Step-by-step explanation:
Out of the 3 choices, the last two both give decimals less than one, so we know they won't be greater than 11.
Find the degree of 3m^2·n^4
Hello!
The degree of the term will be the highest power to which a variable in the term is raised.
Hence, the degree of 3m²n⁴ is [tex]\fbox {4}[/tex]
PLEASE HELP!!!
Due in 10 minutes!
Answer:
41ft²
Step-by-step explanation :
8ft - 2ft = 6ft
6ft - 2ft = 4ft
4ft - 1ft = 3ft
3ft * (8ft + 2ft) / 2 = 15ft²
1ft * (8ft + 2ft) = 10ft²
8ft * 2ft = 16ft²
Total : 16 + 15 + 10 = 41ft²
The difference of two odd numbers is a multiple of ______ 11. | -56 | = ____
Answer:
1. The difference of two odd numbers is a multiple of 2
2. | -56 | = 56
Step-by-step explanation:
1. Since the difference between two odd numbers is always even, this means the difference of two odd numbers is a multiple by 2. This is because all even numbers are divisible by 2.
2. The absolute value of | -56 | would be 56
2. WHAT IF? A random sample of 8 speeding tickets issued in State C has a median of $120. Can you conclude that a speeding ticket in State C costs more than in States A and B? Explain.
no you cannot conclude that state c costs more than a and b because you do not know the value of state a and b
Answer:
no
Step-by-step explanation:
how many two-digit positive numbers are divisible by 3 or 5?
Answer:
it is one ez l ez ez ez ez bozo
which ratio is greater than 5/8
Answer:
4/5 is greater thwn 5/8
Step-by-step explanation:
because ot just is
Answer:
Possible answers are 5/6, 3/4, etc.
Step-by-step explanation:
Many different ratios are greater than 5/8. If I wrote them all it would take FOREVER...
5/8 is greater than 1/2, therefore, ratios: 3/6, 2/4, etc. would not work.
I think you wrote the question wrong and forgot to type the options.
Sorry.