Step-by-step walkthrough:
a.
Well a standard half-life equation looks like this.
[tex]N = N_0 * (\frac{1}{2})^{t/p[/tex]
[tex]N_0[/tex] is the starting amount of parent element.
[tex]N[/tex] is the end amount of parent element
[tex]t[/tex] is the time elapsed
[tex]p[/tex] is a half-life decay period
We know that the starting amount is 74g, and the period for a half-life is 2.8 days.
Therefore you can create a function based off of the original equation, just sub in the values you already know.
[tex]N(t) = 74g * (\frac{1}{2})^{t/2.8days[/tex]
b.
This is easy now that we have already made the function. Here we just reuse it, but plug in 2.8 days.
[tex]N(t) = 74g * (\frac{1}{2})^{t/2.8days} = N(2.8days) = 74g * (\frac{1}{2})^{2.8days/2.8days}\\= 74g * \frac{1}{2} = 37g[/tex]
c.
Now we just gotta do some algebra. Use the original function but this time, replace [tex]N(t)[/tex] with 10g and solve algebraically.
[tex]10g = 74g * (\frac{1}{2})^{t/2.8days}\\\\\frac{10g}{74g} = (\frac{1}{2})^{t/2.8days}[/tex]
Take the log of both sides.
[tex]log(\frac{5}{37}) = log((\frac{1}{2})^{t/2.8days})[/tex]
Use the exponent rule for log laws that, [tex]log(b^x) = x*log(b)[/tex]
[tex]log(\frac{5}{37}) = \frac{t}{2.8days} * log(\frac{1}{2})[/tex]
[tex]\frac{log(\frac{5}{37})}{log(\frac{1}{2})} = \frac{t}{2.8days}[/tex]
[tex]2.8 * \frac{log(\frac{5}{37})}{log(\frac{1}{2})} = t[/tex]
slap that in your calculator and you get
[tex]t = 8.1 days[/tex]
Please help me with this question , we are now just learning it .
Answer:
angle 3 and angle 4 are adjacent angle
The regular admission price to an amusement park is $28. You have a
coupon for 25% off the regular admission. Find the total cost of admission
to the park when the sales tax is 6% of the reduced price.
Answer:
$22.26
Step-by-step explanation:
To solve, all we need to do is 28(1-.25) to get 21, then we set up the equation 21(1+.03) and we get our total for the price.
we subtract in the first place, because it is a discount, and we add in the second one because it is a sales tax.
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if raymond had 50 dogs and gets 80 how many does he have?
Answer:
50+80 = 130
Step-by-step explanation:
Answer:
50+80=130
Step-by-step explanation:
please mark me the brainiest
Marcy charges $3 to walk a small dog and $5 to walk a big dog. If Marcy walks 15 small dogs and 6 big dogs, how much money will she make?
Answer:
hee-hee!
Step-by-step explanation:
Marcy charges $3 to walk a small dog and $5 for a big dog.
She walks 15 small dogs and 6 big dogs.
We can use an expression that would show the problem:
3s + 5b
(s = small dogs & b = big dogs)
s = 15 | b = 6
3(15) + 5(6)
45 + 30 = 75
Marcy earns $75 of profit.
What are the coordinates of the vertex of the function f(x)=x2 10x−3?
Answer:
A. (-5, -28)
Step-by-step explanation:
The coordinates of the vertex of the function [tex]\rm f(x) = x^2+10x-3[/tex] is
(-5, -28).
It is given that the function [tex]\rm f(x) = x^2+10x-3[/tex]
It is required to find the coordinates of the vertex.
What is a parabola?It is defined as the graph of a quadratic function that has something bowl-shaped.
We have a function:
[tex]\rm f(x) = x^2+10x-3[/tex]
This function represents a parabola.
We know the standard form of parabola in quadratic style:
[tex]\rm f(x)=ax^2+bx+c[/tex]
By comparing the given function to the standard form of parabola, we get
a = 1, b = 10, and c = -3
The vertex of the parabola is given by:
[tex]\rm x = -\frac{b}{2a}[/tex]
Putting the values in the above equation, we get:
[tex]\rm x = -\frac{10}{2\times1} \Rightarrow -5[/tex]
x = -5 put this value in the given parabola function, we get:
[tex]\rm f(-5) = (-5)^2+10(-5)-3\\\rm f(-5) = 25-50-3\\\rm f(-5) = -28[/tex]
or y = -28
The coordintes = (x, y) : (-5 , -28) which is shown in the graph.
Thus, the coordinates of the vertex of the function [tex]\rm f(x) = x^2+10x-3[/tex] is (-5, -28).
Know more about the parabola here:
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(
−
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,
−
6
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∪
(
−
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,
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-
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,
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on a number line
Answer:
I think your adopted and nobody loves you
Step-by-step explanation:
Answer this question for points
Answer:
102 or the 12th number considering 38 is the 4th
Jasmine got a prepaid debit card with $25 on it. For her first purchase with the card, she bought some bulk ribbon at a craft store. The price of the ribbon was 23 cents per yard. If after that purchase there was 19.71 left on the card, how many yards of ribbon did jasmine buy?
Answer:
23 Yards
Step-by-step explanation:
So for this question, we would have to start off with writing an equation: 19.71+0.23x=25 once we subtract 19.71 on both sides, the left over sum of money will be 5.29. Since we are dealing with BOTH Dollars and Cents, it should be remembered to use 23 CENTS instead of Dollars. [tex]\frac{5.29}{0.23}[/tex]= 23 so the finals answer is 23 yards.
Answer:
23 Yards
Step-by-step explanation:
So for this question, we would have to start off with writing an equation: 19.71+0.23x=25 once we subtract 19.71 on both sides, the left over sum of money will be 5.29. Since we are dealing with BOTH Dollars and Cents, it should be remembered to use 23 CENTS instead of Dollars. = 23 so the finals answer is 23 yards.
Find the 12th term of the geometric sequence 1, -4, 16,
Answer:
a₁₂ = - 4194304
Step-by-step explanation:
the nth term of a geometric sequence is
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
here a₁ = 1 and r = [tex]\frac{-4}{1}[/tex] = - 4 , then
a₁₂ = 1 × [tex](-4)^{11}[/tex] = - 4194304
is this correct or no if not what the answer
Answer:
A.
While D is partially correct, A is the way to go, because samples are easier to collect than whole populations. The internet quotes, "It is a much quicker process and is more time efficient." This proves the theory why A is the correct answer.
Solve these equation
4(3-x)=(1-2x)
To attempt this algebraic equation we will be multiplying 4 to (3 - x) bracket so as to form the term on L.H.S.
[tex]:\implies\tt{4(3 - x) = (1 - 2x)}[/tex]
[tex]:\implies\tt{(12 - 4x) = (1 - 2x)}[/tex]
[tex]:\implies\tt{12 - 4x = 1 - 2x}[/tex]
Combining like terms, we get,
[tex]:\implies\tt{12 - 1 = - 2x + 4x}[/tex]
[tex]:\implies\tt{11 = 2x}[/tex]
[tex]:\implies\tt{2x = 11}[/tex]
[tex]:\implies\tt{x = \frac{11}{2} }[/tex]
[tex]:\implies\tt{x = 5.5}[/tex]
The value of x is 5.5Hey there!
4(3 - x) = (1 - 2x)
4(3) + 4(-x) = 1 - 2x
12 - 4x = 1 - 2x
-4x + 12 = -2x + 1
ADD 2x to BOTH SIDES
-4x + 12 + 2x = -2x + 1 + 2x
SIMPLIFY IT!
-2x + 12 = 1
SUBTRACT 12 to BOTH SIDES
-2x + 12 - 12 = 1 - 12
SIMPLIFY IT!
-2x = -11
DIVIDE -2 to BOTH SIDES
-2x/-2 = -11/-2
SIMPLIFY IT!
x = 11/2
Therefore, your answer should be:
x = 11/2
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Solve the System of Equations x = -2 ; y = 3 .(Choose from a,b, or c. Show your work step by step).
a) x+y=1
2x+y=5
b) x+2y = 4
x +y = 1
c) x-y=-5
x+y= 11
Pls show your work as I want to understand how to solve this type of equation.
Answer:
b no. is the correct answer
Lowes is having a Customer Appreciation Day Sale. Everything in the store is 25% off. The final purchase for the consumer is $2021.63. What is the cost to the consumer? Sales tax is 5%.
Answer:
$1592.03
Look at image above...
One box measures 2 feet by 1 foot by 1 foot a larger box measures 2feet by 2 1/2 feet by 2 how many times larger is the volume of the larger box then the smaller box
The number of times the larger box is bigger than the smaller box is 5.
How many times larger is the larger box?The first step is to determine the volume of both boxes.
Volume = length x width x height
Volume of the larger box = 2 x 2 1/2 x 2 = 10ft³
Volume of the smaller box = 2 x 1 x 1 = 2 ft³
Now divide the Volume of the larger box by the volume of the smaller box : 10 / 2 = 5
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Find the distance between (1, 1) and (3, 4).
Answer:
√13
Step-by-step explanation:
Let,
( x1, y1 ) = ( 1, 1 )
Here,
x1 = y1 = 1
( x2, y2 ) = ( 3, 4 )
Here,
x2 = 3
y2 = 4
Formula : -
( Distance )² = ( x2 - x1 )² + ( y2 - y1 )²
( Distance )² = ( 3 - 1 )² + ( 4 - 1 )²
= 2² + 3²
= 4 + 9
( Distance )² = 13
Distance = √13
Answer:
3.61
Step-by-step explanation:
length=[tex]\sqrt{(x_{2}-x_{1} )^{2}+(y_{2}-y_{1} )^{2} )}[/tex]
=[tex]\sqrt{(3_{}-1_{} )^{2}+(4_{}-1_{} )^{2} )}[/tex]
= 3.61
Sonia has only dimes and nickels in her coin jar; they are in a ratio of 3 to 5. IF she had 120 coins in the jar, how many are dimes? PLEASE HELP
Answer:
45 dimes and 75 nickels
Step-by-step explanation:
3 ÷ 8 × 120 = 45
you divide the three by both ratios summed up (8) and then you multiply that by the coins
doing so will you can get 45
and to get the amount of nickels you just subtract 45 from 120 and you get 75
Need some help with trinomial
Answer:
(x - 6)(x + 2)
Step-by-step explanation:
assuming you require the trinomial to be factorised.
x² - 4x - 12
consider the factors of the constant term (- 12) which sum to give the coefficient of the x- term (- 4)
the factors are - 6 and + 2 , since
- 6 × 2 = - 12 and - 6 + 2 = - 4 , then
x² - 4x - 12 = (x - 6)(x + 2)
Without solving the addition problems, tell whether the answers are going to be odd or even. Model 39 +42 odd 1. 64 + 82 2. 129 + 377 3. 468 +599 4. 1,987 + 9,888 Activity 4 Without solving the multiplication problems, tell whether the answers are going to be odd or even. Model 39x42 even 2. 137 x 141 1. 78 X 44 4. 5,111 x 8,222 3. 528 X 603.
SOS HOMEWORK
Answer:
3. 1067
4. 11875
5. 1638
6. 19317
7. 3432
8. 42022642
9. 318384
students were grouped into 4 classrooms with an average of 33.5 students per classroom. if the students were regrouped into 5 classrooms, what would be the average number of students in each room?
Answer:
26.8
Step-by-step explanation:
Because 33.5 was the average of how many students were in a classroom (if there were 4 classrooms), then 33.5 is can somewhat be the average of how many students were in one classroom; 1/4 of the classrooms can hold an average of 33.5.
Total students that were divided into 4 classrooms :
33.5 × 4 = 134
So if there is 134 students that will be grouped into 5 different classrooms, divide 134 by 5 to find the average amount of students that will be grouped.
134 ÷ 5 = 26.8
So, the average amount of students that will be grouped if they were divided into 5 classrooms would be 26.8 .
Hope this helped !
Write the expression t = 8 + 2h to represent the
temperature change for that day. Circle all of the expressions below that are equivalent to T
t=8+2h
a. t = h + 8 + 2h
c. t = 4h + 6 - 2h + 2
b. t= 8 + h + h
d. t = 8 - 2h
arah walks 3.1 kilometers on Monday and 1.35 kilometers on Tuesday. On Wednesday she walks 2.4 times as far as she walked on the previous two days combined.
How far does Sarah walk on Wednesday?
Answer:
10.68
Step-by-step explanation:
3.1+1.35=4.45 4.45×2.4=10.68
For a project in her Geometry class, Naomi uses a mirror on the ground to measure
the height of her school building. She walks a distance of 12.25 meters from the
school, then places a mirror on flat on the ground, marked with an X at the center.
She then steps 1.7 meters to the other side of the mirror, until she can see the top of
the school clearly marked in the X. Her partner measures the distance from her eyes
to the ground to be 1.15 meters. How tall is the school? Round your answer to the
nearest hundredth of a meter.
Answer:
8.28
Step-by-step explanation:
we can express this question as
12.25/1.7=x/1.15
this can be simplified to
x=8.28
The height of Naomi's school building is 8.29 meters
Concept of similar triangles:
Two triangles are similar if their corresponding angles are equal and their corresponding sides are within the same ratio (or proportion). Similar triangles will have the same shape, but not necessarily the same size.
In the given question and attached figure we have,
BC = 12.25 metersCD = 1.7 metersDE = 1.15 metersNow we have to find the height(AB) of the building,
By the properties of similar triangles, we can write,
AB / BC = DE / CD
Putting all the values we get,
AB / 12.25 = 1.15 / 1.7
Simplifying we get,
AB = (1.15 / 1.7) × 12.25
By further simplifying,
AB = 8.29 meters
Therefore, the height of Naomi's school building is 8.29 meters.
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what
arithmetic sequence with a_{4}=18 and a_{10}=48
Answer:
[tex]a_{n}[/tex] = 5n - 2
Step-by-step explanation:
the nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
given a₄ = 18 and a₁₀ = 48 , then
a₁ + 3d = 18 → (1)
a₁ + 9d = 48 → (2)
subtract (1) from (2) term by term to eliminate a₁
6d = 30 ( divide both sides by 6 )
d = 5
substitute d = 5 into (1) and solve for a₁
a₁ + 3(5) = 18
a₁ + 15 = 18 ( subtract 15 from both sides )
a₁ = 3
Then
[tex]a_{n}[/tex] = 3 + 5(n - 1) = 3 + 5n - 5 = 5n - 2
The amount of a radioactive substance remaining after t years is given by the function , where m is the initial mass and h is the half-life in years. cobalt-60 has a half-life of about 5.3 years. which equation gives the mass of a 50 mg cobalt-60 sample remaining after 10 years, and approximately how many milligrams remain? ; 13.5 mg ; 34.6 mg ; 0.2 mg ; 4.6 mg
The required equation f(10) = 13.52 mg remains.
We have given that ,
m is the initial mass and h is the half-life in years. cobalt-60 has a half-life of about 5.3 years. which equation gives the mass of a 50 mg cobalt-60
What is the fromula for he amount of a radioactive substance remaining after t years?The amount of a radioactive substance remaining after t years is given by the function
[tex]f(t)=m(0.5)^{t/h}[/tex]............ (1),
where m = initial mass and h= half-life in years.
Now, for Cobalt-60, h = 5.3 years, m = 50 mg and t = 10 years,
then from equation (1) we get,
[tex]f(10)=50(0.5)^{10/5.3}[/tex]
Therefore the required equation f(10) = 13.52 mg .
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Answer:
The required equation f(10) = 13.52 mg remains.
We have given that ,
m is the initial mass and h is the half-life in years. cobalt-60 has a half-life of about 5.3 years. which equation gives the mass of a 50 mg cobalt-60
What is the fromula for he amount of a radioactive substance remaining after t years?
The amount of a radioactive substance remaining after t years is given by the function
............ (1),
where m = initial mass and h= half-life in years.
Now, for Cobalt-60, h = 5.3 years, m = 50 mg and t = 10 years,
then from equation (1) we get,
Therefore the required equation f(10) = 13.52 mg .
To learn more about the mass of radioactive substance visit:
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Please answer these questions:
a) What are the 2 features that make this shape a square?
b) A quadrilateral has no pairs of parallel sides. What 2 shapes could this be?
c) A triangle has one pair of equal sides and one pair of equal angles. What is it called?
Answer:
A. 1. The sum of all interior angles is equal.
2. All sides are equal in length.
B. Trapezium.
C. isosceles triangle.
help please, can you figure it out?
Answer:
4,333$
Step-by-step explanation:
There are 12 months in a year so we divide 52,000 by 12 and it equals 4,333 if you rounded it.
PLEASE HELP!!!!!!!!!!!!!!
Answer:
[tex]\frac{4}{5}[/tex] (4/5)
just fill out 4 in the blank
Step-by-step explanation:
1. Equal the denominator for 1/4
End result=[tex]\frac{11}{20}[/tex]
So all the other ones have to be made according to this
20/4=5
1x5=5
[tex]\frac{1}{4}[/tex] will now be [tex]\frac{5}{20}[/tex]
2. Figure out what ?/5 will be
If this number is getting subtracted by [tex]\frac{5}{20}[/tex] then, we have to add [tex]\frac{11}{20}[/tex] by [tex]\frac{5}{20}[/tex] to get our answer.
[tex]\frac{11}{20} +\frac{5}{20} =\frac{16}{20}[/tex]
this means that when [tex]\frac{16}{20}[/tex] gets subtracted by [tex]\frac{5}{20}[/tex] it will equal [tex]\frac{11}{20}[/tex]
3. Simplify 16/20 to it's lowest terms
5x4=20
20/5=4
so, each part ([tex]\frac{1}{5}[/tex]) worth's 4
20-4=16
So that means, that the simplest for for this is [tex]\frac{4}{5}[/tex]
So hence, your answer is 4/5just fill out 4 in the blank
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:D
Answer:
4
Step-by-step explanation:
Let the blank = x
Thus,
[tex]\frac{x}{5}-\frac{1}{4}=\frac{11}{20}[/tex]
[tex]\mathrm{Add\:}\frac{1}{4}\mathrm{\:to\:both\:sides}[/tex]
[tex]\frac{x}{5}-\frac{1}{4}+\frac{1}{4}=\frac{11}{20}+\frac{1}{4}[/tex]
[tex]\mathrm{simplify}[/tex]
[tex]\frac{x}{5}=\frac{4}{5}[/tex]
[tex]\mathrm{Multiply\:both\:sides\:by\:}5[/tex]
[tex]\frac{5x}{5}=\frac{4\cdot \:5}{5}[/tex]
[tex]\mathrm{simplify}[/tex]
x = 4
Hence, the blank = 4
Equation = [tex]\frac{4}{5}-\frac{1}{5}=\frac{11}{20}[/tex]
[RevyBreeze]
10 people each wants 3 slices but a box has 8 slices
Answer:
you need 30 slices
a minimum of 4 boxes of pizza
Step-by-step explanation:
Will give brainly if right
Answer:
60.61
Step-by-step explanation:
the missing angle is 51 degrees
we can say sin74/x = sin51 / 49
now we just solve for x.
x = 60.61
for every 1/2 cup portion of baby cereal you will need 4 oz of milk. how many ounces of milk will you need to prepare 20 portions
Answer:
80 oz
Step-by-step explanation:
20 portions times 4 oz is 80 oz