Answer:
They must mix 70 kilograms of the 10% chocolate and 30 kilograms of the 60% chocolate.
Step-by-step explanation:
Given that a candy distributor needs to mix a 10% fat-content chocolate with a 60% fat-content chocolate to create 100 kilograms of a 25% fat-content chocolate, to determine how many kilograms of each kind of chocolate must they use, the following calculations must be performed:
10 x 0.5 + 60 x 0.5 = 35
10 x 0.6 + 60 x 0.4 = 30
10 x 0.7 + 60 x 0.3 = 25
100 x 0.7 = 70
Thus, they must mix 70 kilograms of the 10% chocolate and 30 kilograms of the 60% chocolate.
A lab currently has 70 mg of radioactive material that decays at 3.5% per year. Federal regulation for the substance says that the material must be safely stored until it reaches its half-life, at which time the material can be disposed.
How many years will the lab have to safely
store the material before disposal?
Answer:
The lab will have to wait 19.45 yers to safely store the material before disposal.
Step-by-step explanation:
Exponential equation for substance decay:
A exponential equation for the amount of a substance after t years is given by:
[tex]A(t) = A(0)(1-r)^{t}[/tex]
In which A(0) is the initial amount and r is the decay rate, as a decimal.
Decays at 3.5% per year.
This means that [tex]r = 0.035[/tex]
So
[tex]A(t) = A(0)(1-r)^{t}[/tex]
[tex]A(t) = A(0)(0.965)^{t}[/tex]
How many years will the lab have to safely store the material before disposal?
It needs to reach half-life, that is, t for which A(t) = 0.5A(0). So
[tex]A(t) = A(0)(0.965)^{t}[/tex]
[tex]0.5A(0) = A(0)(0.965)^{t}[/tex]
[tex](0.965)^t = 0.5[/tex]
[tex]\log{(0.965)^t} = \log{0.5}[/tex]
[tex]t\log{0.965} = \log{0.5}[/tex]
[tex]t = \frac{\log{0.5}}{\log{0.965}}[/tex]
[tex]t = 19.45[/tex]
The lab will have to wait 19.45 yers to safely store the material before disposal.
Make t the subject of the formula p = 4t+1/2-t
Answer:
t = (p - 1/2)/3
Step-by-step explanation:
p = 4t + 1/2 - t
combine like terms:
p = 3t + 1/2
subtract 1/2 from each side of the equation:
3t = p - 1/2
divide both sides by 3:
t = (p - 1/2)/3
Information collected from runner 3# is in the table below
The constant proportionality for runner 3 is..?
Answer:
the constant of proportionality would be 9
Is 12+5(2+y) and 5y+22 equivalent
Answer:
22 + 5y
Step-by-step explanation:
Yes they are
5 x 2 = 10 + 5 x y = 5y, 10 + 12 = 22, therefore you get 22 + 5y.
x – 1/4=1/2 what is x?
Answer:
x= 3/4
Step-by-step explanation:
x-1/4=1/2
+1/4 +1/4
x=3/4
Write the absolute value equation if it has the following solutions. x = 2.5 and x = -3.5
Answer:
where's the equation? your question is missing some parts.
Step-by-step explanation:
Four friends share 2 sandwhiches equally. How much sandwhich will each friend get?
Answer:
Each friend will get a half of a sandwich
Step-by-step explanation:
1 friend 1 friend
1 friend 1 friend
(split the two sandwiches in half)
Now you have 4 halfs to give to your 4 friends
50 × {9 − [(35 − 8) ÷ (1 + 2)]} =
Answer:
look at the picture i sent
Answer:
0
Step-by-step explanation:
use mathaway :D
a recipe calls for 3/4 of a cup of flour to make 5/8 of a pond of bread dough . how many cups of flour are needed to make 1 pound of douugh
Help fast please.....
Answer:
nos etu mdei
Step-by-step explanation:
Answer:
33in squared, so B
Step-by-step explanation:
the area of a triangle is (Base x height)/2
The area of a square is just length x width
Now solve
since each triangle is the same and there a 4 triangles do
4(3x4) which is 4(12)
4 x 12= 48
48/2= 24
3 x 3 for the square
24+9=33
Hope this helps!
One year, the population of a city was 330,000. Several years later
it was 270,600. Find the percent decrease.
Answer:
18% Decrease.
Step-by-step explanation:
You can use this formula for % decrease questions. :)
Decrease= Starting value (original) - Final Value (the smaller number) / starting value x 100.
Hope this helps,
Azumayay
What principle will amount to $6000 if invested at 5.5% compounded monthly for 10 years?
Answer:In 10 years, you will have $10,386.46
Step-by-step explanation:
QUICK I NEED THIS ANSWER QUICKLY
Which of the following functions has the same solution set of g(x) = x3 + x2 - 2x?
Answer:
yes
Step-by-step explanation:
y
∝
1
√
x
If
y
=
7
when
x
=
64
find,
x
when
y
=
8
Answer:
x = 49
Step-by-step explanation:
This is an inverse relationship and it implies that, an increase in the value of one variable results in a subsequent decrease in the value of another variable.
Given the mathematical expression and data;
y = 1/√x
y = 7 and x = 64
First of all, we would find the constant of proportionality, k;
y = k/√x
7 = k/√64
7 = k/8
k = 7 * 8
Constant, k = 56
Now, to find the value of x when y = 8
y = k/√x
Substituting the values, we have;
8 = 56/√x
Cross-multiplying, we have;
8 * √x = 56
√x = 56/8
√x = 7
Taking the square of both sides, we have;
(√x)² = 7²
x = 49
1.
Identify the values of a, b and c in this expression: x2 + 8x - 3
A. a = 0, b = 8, c = -3
B. a = 1, b = 8, c = 3
C. a = 1, b = 8, C = -3
D. a = 0, b = 8, c = 3
What is the correct answer
Answer:
C. a = 1, b = 8, c = -3
Step-by-step explanation:
.........
Write the expanded form in the condensed form.
9z+9z
Answer:
nine z plus nine z.
lol tell me.if.its wrong
what is 3x+7x-9x+4x+10+12x if x=2
Answer: 44
Step-by-step explanation:
Answer:
3(2)+7(2)-9(2)+4(2)+10+12(2)
6+14-18+6+10+24
60-18
42
SOrry again but pleaaaase help
Answer:
4(10+9) - 40 + 36
9(5+2) - 45 + 18
3(12+7) - 36 + 21
8. Calculate.
a) -114 x 15
Answer:
[tex] - 1710[/tex]
Step-by-step explanation:
[tex] - 114 \times 15 \\ = - 1710[/tex]
Use the information in the table to choose the correct equation.
Answer:
y = 10x + 3
Step-by-step explanation:
Two functions are shown below.
f(x) = 2x
g(x) = x2 + 3x - 3
For what values of x is f(x) > g(x)?
Answer:
q
hey g(x) = x2 + 3x - 3
Step-by-step explanation:
es la respuesta
hello i hope you are having a nice day can somebody help me with this question thanks
Answer:
12.25 un
Step-by-step explanation:
-the formula for the area of a triangle is A=(1/2)bh or Area=(1/2)×Base×Height
to find the base you need to take 7.5 and subtract 2.5 the divide in half for each base of the triangles to get 2.5 for the bases.
then take your formula and multiply:
0.5×2.5×2.5=3.125×2=6.25 and you get the area of the triangles.
then do the area of the center square which is:
2.5×2.5=6 for the center
then add:
A=6.25+6=12.25
The graph of the function y=f(x)+35 can be obtained from the graph of y=f(x) by one of the following actions:
lin is 5 inches taller than her cousin mai. together their heights total 113. how tall is each girl
Answer:
the answer is mai is 54 and lin is 59
what is 5m-4-m+2 simplify
Step-by-step explanation:
5m-4-m+2
Simplifying
4m - 2
Hope it helps :)❤
What is the length of the dotted line in the diagram below? Round to the nearest
tenth.
50 points question to answer
Answer:
Hope it helps
Step-by-step explanation:
3/4(7/7)=21/28
1/2(8/8)=8/16
4/9(2/2)=8/18
2/5(9/9)=18/45
6/3(6/6)=36/18
3/2(7/7)=21/14
PLS RATE AS BRAINLIEST
2. For what value of p would the statement 5p = 30 be true?
Op=7
O p = 5
O p = 4
Op=6
is the following statement true false or open: 60 - g = 25
true
false
open
none of the above
which of the following an an open statement
2x + 5x = 7x
14 ÷ 2 = 7
3 + 10 = 13
3x = 12
PLEASE REAL ANSWERS I RLLY NEED HELP!!!!
Answer:
1. p=6
2. open
3. 3x = 12
PLEASE HELP! WILL MARK BRAINLIEST!!
How did advancements in the steam engine affect industrialization? (5 points)
By eliminating the need for transportation of goods by ship
By decreasing the production time for textiles
By eliminating the need for a water source to power mills
By polluting crowded urban areas
Answer:
By decreasing the production time for textiles
Step-by-step explanation: