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Answer:

4210

Explanation:

A thousand =1000
Since there are 4 thousands, we multiply it by 4 to get #4000#
#4*1000 = 4000#

tens = 10
Since there are 21 tens, we multiply to get the total amount so:
#21*10=210#

Now we add it together
#4000+210=4210#

Answer:

It is the product of the two numbers.

Explanation:

The way to find the LCM is to write out both factorizations of the numbers, and then combine any factors that the two numbers share.

So, if two numbers don't share any factors greater than one, you won't combine anything, and so the LCM will just be all of the factors of the two numbers multiplied together.

Let's do an example so you can see what I mean:

Find the LCM of 7 and 15

The factorization of 7 is #7#. The factorization of 15 is #3 xx 5#.

Since none of these factors are the same, there is nothing to combine.

Therefore, the LCM is #3 xx 5 xx 7 = 105#

Answer:

See a solution process below:

Explanation:

First, let's convert hours to minutes in this problem.

There are 60 minutes per hour so we can write;

#(42"mi")/"hr" xx (1"hr")/(60"min") =>#

#(42"mi")/color(red)(cancel(color(black)("hr"))) xx (1color(red)(cancel(color(black)("hr"))))/(60"min") =>#

#(42"mi")/(60"min")#

Next, we can convert miles to inches. We know:

  • There are 5280 feet per mile
  • There are 12 inches per feet

So, we can write:

#(42"mi")/(60"min") xx (5280"ft")/"mi" xx (12"in")/"ft" =>#

#(42color(red)(cancel(color(black)("mi"))))/(60"min") xx (5280color(blue)(cancel(color(black)("ft"))))/color(red)(cancel(color(black)("mi"))) xx (12"in")/color(blue)(cancel(color(black)("ft"))) =>#

#42/(60"min") xx 5280 xx 12"in" =>#

#(2661120"in")/(60"min") =>#

#(44352"in")/"min"#

Answer:

See below.

Explanation:

The sum of the quotient of a number and 3 and 8 is 16."

One needs to translate from English to mathematics symbols. Sometimes, the words can be translated directly, piece by piece, from left-to-right, then the parts can be put together.

This one is one of those "left-to-right." translations:
"The sum of" involves adding two things, so we start with:
# ("the first thing") + ("the second thing") #

"is" translates to "=". So,
# color(blue)( ("the first thing") + ("the second thing") = 16 ) #.

Using "x" for everything can make the eyes sore, so here we use "N" for the unknown Number.

the first thing:
"the quotient of a number and 3". Since "quotient of" means divide the first thing mentioned (an unknown number, N) by the second thing mentioned (3).
# N -: 3 = N/3 #

We can fill-in part of the expression:
# color(blue)( ( N/3 ) + ("the second thing") = 16 ) #

the second thing:
The second thing being added is 8.

Now, finish the translation with a full equation:
# color(red)( N/3 + (8) = 16 ) #

To solve the math problem, subtract 8 from both sides of the equation, then multiply both sides of the result by 3.

You should get: # color(red)( N = 24 #.

Answer:

The rounded dividend would be 4.2
The rounded divisor would be 7.0
The rounded quotient would be 0.60
The exact quotient would be 0.57

Explanation:

In estimating it is helpful to round to compatible numbers.
look for a set of numbers will divide evenly.

42 is a multiple of 7 so this is a set of compatible numbers.

round 4.161 off to 4.2
round 7.3 off to 7.0
Both numbers have the same amount of significant digits.

Then divide to receive a good estimate of what the exact answer should be.
# 4.2/7.0 = 0.60 ( to two significant digits)

Use a calculator to find the exact answer.

# 4.161/7.3 = 0.57#

Answer:

-12

Explanation:

Adding and subtracting negative numbers is a pretty tricky thing to learn (trust me, I know!), but if you go through it slowly and use a couple tricks, you can figure it out.
Here's our equation:
#-16 + 9 - 5 = ?#

The first two numbers we are going to deal with are #16# and #9#. Now these aren't just normal #16# and #9#, one is positive and one is negative. I just put some parentheses around them, so that we remember that:
#(-16) + (+9)#

So the easiest way to learn how to do this type of problem is make a number line like this: enter image source here
Obviously, this number line doesn't go far enough, but you could draw it to go all the way to #-16#. Now put your finger at #-16# and count to the right 9 lines. Where is your finger at now? It should be at #-7#.

( If you need extra explanation: You moved 9 spaces to the right because that is that direction positive numbers are. Since 9 is positive, you will get closer to 0, not further away.)

Okay! So now we have:
#-7 - 5 = ?#
#(-7) + (-5) = ?# (I added parentheses again)
Put your finger back on the #-7# and move to the left 5 spaces. Because #5# is negative, we move to the left, or further away from 0.
You should now be at #-12#, which is the answer of this equation.

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