True
5^2 = 25
12^2 = 144
25+144=169
13^2=169
Answer:
1. m∠B=110°
2. 560 cm3
3. Numerical data
4. 2000 cm3
5. 50%
Step-by-step explanation:
1. The explanation of part 1 is given in the attachment.
2. Given dimensions : 10 cm, 8 cm, and 7 cm.
Let Length of cuboid =10 cm
breadth/width of cuboid =8 cm
height of cuboid = 7cm
Volume of cuboid = length *width* height
=( 10 *8*7) cm3
=(560) cm3
3. Age, Birth date and weight are the types/examples of "<u>Numerical Data"</u> because these all are describe in terms of numeric values.
4. 1 liter = 1000 cm3 or 1 cm3 = 0.001 liter
1.5 liters =(1.5*1000) cm3 = (15*100) =1500 cm3
1 dm3 =1000 cm3
0.35 dm3 = (0.35*1000) cm3 = (35*10) cm3 =350 cm3
Given expression: 1.5 litre + 0.35 dm3 + 150 cm3 = <u> </u> cm3
1500 cm3 + 350 cm3 +150 cm3 = <u>2000</u> cm3
5. If A=(1/2)B, then B : A = <u>50</u> %
Ratio: B : A
B : (1/2) B
1: (1/2)
50 % (The value of A is half of the value of B)
Let the total be x
1/6x=3
x/6=3
x=18
therefore Ramal's stamp has 18 pages
<span>1,
During a 1-hr television program, there were 22 commercials, Some
commercials were 15 sec and some were 30 sec long. Find the number of
15- sec commercials and the number of 30 sec commercial if the total
playing time for commercial was 9.5 minutes.
</span>a) <span>show how to formulate your system of equations for your problem,
Answer:
- state the variables: x number of 15 sec commercials, y number of 30 sec commercials
- translate the word statement into algebraic language
b) state the two equations:
- translate the word statement into algebraic equations:
</span><span>* there were 22 commercials => x + y = 22
* the total playing
time for commercial was 9.5 minutes => 15x + 30y = 9.5*60 </span><span>
Answer:
Equation (1) x + y = 22
Equation (2) 15x + 30y = 570
c) state which method you will use to solve either addition or substitution
Answer:
adition: multiply the first equation times - 15 and add the two equations.
d) solve your system showing and explaining each step of the process
Answer:
- muliply eq (1) times - 15
-15x - 15y = - 330
- add that to the eq (2):
-15x + 15x - 15y + 30y = -330 + 570
- add like terms: 15y = 240
- divide both members by 15: 15y/15 = 240 / 15 => y = 16
- replace y = 16 in eq I(1) => x + 16 = 22 => x = 22 - 16 = 6
Solution: x = 6, y = 16
e) Be sure to check your solution!
x + y = 22
6 + 16 = 22
22 = 22 --> check
15x + 30y = 9.5*60
15(6) + 30(16) = 570
90 + 480 = 570
570 = 570 ---> check
f) Once a solution is found explain what this solution means in the context
of the problem, write the answer to the word problem in words</span><span>
The solution means that d</span><span>uring a 1-hr television program, there were</span><span> 6 commercials of 15 sec and 16 commercials of 30 sec.
2, How many quarts of water should be mixed with a 30% vinegar solution
to obtain 12 qt of a 25% vinegar solution. (Hint: water is 0% vinegar).</span>
a) variables:
- state the variables
x: number of quarters of water
y: number of quarters of vinegar
- translate the words into mathematical language
12 qt 25% vinegar solution
=> total number of quarts = 12 = x + y
balance in vinegar:
vinegar from water + vinegar from 30% vinegar solution = vinegar in the 25% vinegar solution
0 + 0.3y = 0.25 (x + y)
c) Equations
Eq (1) x + y = 12
Eq (2): 0.3y = 0.25x + 0.25y
=> 0.25x - 0.05y = 0
d) solve
- multiply eq (1) times 0.05 and add to eq (2)
0.05x + 0.05y = 0.6
0.25x - 0.05y = 0
------------------------
0.30x = 0.6
x = 0.6 / 0.3 = 2
x + y = 12 => y = 12 - y = 12 - 2 = 10
Solution: x = 2, y = 10
e) check:
x + y = 12
2 qt + 10qt = 12 qt
12 qt = 12 qt ---> check
vinegar:
10*0.3 = 12*0.25
3 = 3 -> check
f) Explanation of the solution
The solution means that you have to mix 2 qts of water with 10 qts of 30% vinegar solution to obtain 12 qt of 25% vinegar solution.
Leo's balance after 9 months will be: $1757.49
Step-by-step explanation:
It is given that the balances follow a geometric sequence
First of all, we have to find the common ratio
Here
Common ratio is:
So r = 1.02
The general form for geometric sequence is:
Putting the first term and r
To find the 9th month's balance
Putting n=9
Rounding off to nearest hundredth
$1757.49
Hence,
Leo's balance after 9 months will be: $1757.49
Keywords: Geometric sequence, balance
Learn more about geometric sequence at:
#LearnwithBrainly
