Given,
The initial balance in the checkbook is $463.18.
The deposite money is $265.
The amount of check is $198.73.
The charge paid for bank is $2.50.
The ending balance at the month end is,
[tex]\begin{gathered} \text{Ending balance=}463.18+265-198.73-2.50 \\ =526.95 \end{gathered}[/tex]Hence, option b ($526.95) is correct.
What is 2/3 ÷8? also it needs to be a proper fraction or a improper fraction
[tex]\cfrac{2}{3}\div 8\implies \cfrac{2}{3}\div \cfrac{8}{1}\implies \cfrac{2}{3}\times \cfrac{1}{8}\implies \cfrac{2}{8}\times \cfrac{1}{3}\implies \cfrac{1}{4}\cdot \cfrac{1}{3}\implies \cfrac{1}{12}[/tex]
If the number of bacteria in a colony doubles every 236 minutes and there is currently a population of 9,085 bacteria, what will the population be 708 minutes from now?
We could state an exponential model.
Number of bateria will be given by:
[tex]N=N_0e^{kt}[/tex]where k=growth constant and t=time in minutes.
We're given that N0 is the initial population, which is:
[tex]N_0=9,085[/tex]We also know that, when t=236 min, N=2(9,085) = 18,170:
[tex]18,170=9,085e^{k(236)}^{}[/tex]We're going to solve this equation to find the value of k:
[tex]\begin{gathered} \frac{18,170}{9,085}=e^{236k} \\ 2=e^{236k} \\ \ln 2=\ln e^{236k} \\ \ln 2=236k \\ k=\frac{\ln 2}{236} \end{gathered}[/tex]Then, our expression is:
[tex]N=9,085e^{\frac{\ln 2}{236}t}[/tex]To find the population of bacteria after 708 minutes, we replace t by 708:
[tex]N=9085e^{\frac{\ln2}{236}(708)}=72680[/tex]Therefore, the population of bacteria 708 minutes from now, is 72680.
Based on the pattern in the table, what is the value of a?
-64
Powers of 2
2-²
2-3
244
2-5
2-6
Value
1
2
4
1
80
1
16
1
32
a
Answer:
equation and fraction addition and subtraction
Which equation represents the same line as the points in the table?
Input (x) Output (y)
−6 0
0 −2
3 −3
y= −1/3x−2y is equal to negative 1 third x minus 2
y=−2x−1/3y is equal to negative 2 x minus 1 third
y=−1/3x−6y is equal to negative 1 third x minus 6
y=−6x−2
The equation that represents the same line as the points in the table is y = - 1 / 3 x - 2
How to find the equation of a line?The equation of a line in slope intercept form can be represented as follows:
y = mx + b
where
m = slopeb = y-interceptUsing the table let's find the slope of the line as follows:
(-6, 0)(0, -2)
slope = m = -2 - 0 / 0 + 6
slope = - 2 / 6
slope = - 1 / 3
Therefore, let's find the y-intercept of the line using (0, -2).
y = - 1 / 3x + b
-2 = - 1 / 3 (0) + b
b = -2
Therefore, the equation of the table is y = - 1 / 3 x - 2
learn more on equation of a line here: brainly.com/question/28883396
#SPJ1
Pls help fast (10 points)
Need answer fast
Answer:
1.75
Step-by-step explanation:
1/4 (5 - -2)
1/4(5 + 2)
1/4(7)
7/4
1 3/4
geometry i need help with this assignment this is only the front so make sure to watch for the back
The values of the area of the shaded region are;
1. Area = 36, perimeter = 28
2. Area = 16, perimeter = 16
3. Area = 22, perimeter = 30
4. Area = 29, perimeter = 28
6. Area = 53.9
What is the area of a figure?The area of a figure is the area bounded by the line that serves as the boundary of the figure.
The areas and perimeters of the figures are found as follows;
1. The figure consists of two rectangles
The dimension of the small rectangle at the top are;
Length = 4, Width = 3
Area = 3 × 4 = 12
Dimensions of the larger rectangle are;
Width = 4, Length = 6
Area = 4 × 6 = 12
The area of the composite figure is therefore; A = 3 × 4 + 6 × 4 = 36
The sum of the length of the sides, which is the perimeter, P = 8 + 3 + 4 + 3 + 4 + 6 = 28
2. The figure consists of a right triangle at the top rectangle;
The leg lengths of the right triangle are; 3 and 4
The area of the right triangle = 0.5 × 3 × 4 = 6
The dimension of the rectangle are; Length = 5, width = 2
Area of the rectangle = 5 × 2 = 10
Area of the composite figure is therefore, A = 0.5 × 4 × 3 + 2 × 5 = 16
The perimeter of the composite figure, P = 4 + 3 + 2 + 5 + 2 = 16
3. The figure is a composite figure that is found by subtracting the area of a rectangle from the area of a right triangle as follows;
The dimensions of the triangle are;
Leg lengths; (8 + 4) = 12 and (3 + 2) = 5
Area of the right triangle = 0.5 × (8 + 4) × (3 + 2) = 30
Dimensions of the rectangle left blank are;
Length = 4, width = 2
Area of the rectangle = 4 × 2 = 8
Therefore;
Area of the composite figure = 0.5 × (8 + 4) × (3 + 2) - 4 × 2 = 22
Length of the hypotenuse side = √((8 + 4)² + (3 + 2)²) = 13
The perimeter of the composite figure = 3 + 13 + 8 + 2 + 4 = 30
4. The figure is a composite figure that consist a large rectangle and small rectangle.
Dimensions of the large rectangle are;
Length = 2 + 2 + 3 = 7
Width = 5
Area of the large rectangle = 7 × 5 = 35
Dimensions of small rectangle are;
Length = 3, width = 2
Area of the small rectangle = 3 × 2 = 6
Area of the composite figure = 35 - 6 = 29
The perimeter = 2 × (2 × 2 + 3) + 2 × 5 + 2 × 2 = 28
6. Area of the circle = π × 14²/4
Area of the square = 10 × 10 = 100
The area of the shaded region = π × 14²/4 - 100 ≈ 53.9
Learn more about finding the area of composite figures here:
https://brainly.com/question/24229616
#SPJ1
Marc sold 500 tickets for the school play. Student tickets cost $2 and adult tickets cost $5. Marc's sales totaled $1,789.a.) Write a system of equations that can be used to determine how many of each type of ticket Marc sold.b.) Solve the system to determine how many adult tickets and how many student tickets Marc sold.
Given that:
- Marc sold 500 tickets for the school play.
- Student tickets cost $2.
- Adult tickets cost $5.
- The total amount of money from the sale was $1,789.
a.) Let be "x" the number of student tickets Marc sold for the school play, and "y" the number of adult tickets Marc sold for the school play.
You can represent the total number of tickets he sold with this equation:
[tex]x+y=500[/tex]You can represent the total amount of money from the sale with this equation:
[tex]2x+5y=1789[/tex]Now you can set up this System of Equations that can be used to determine how many of each type of ticket Marc sold:
[tex]\begin{cases}x+y={500} \\ 2x+5y={1789}\end{cases}[/tex]b.) You can solve the System of Equations using the Elimination Method:
1. Multiply the first equation by -2:
[tex]\begin{cases}(-2)(x+y)=(-2)({500)} \\ 2x+5y={1789}\end{cases}[/tex][tex]\begin{cases}-2x-2y={-1000} \\ 2x+5y={1789}\end{cases}[/tex]2. Add the equations:
[tex]\begin{gathered} \begin{cases}-2x-2y={-1000} \\ 2x+5y={1789}\end{cases} \\ ---------- \\ 0+3y=789 \\ 3y=789 \end{gathered}[/tex]3. Solve for "y":
[tex]\begin{gathered} y=\frac{789}{3} \\ \\ y=263 \end{gathered}[/tex]4. Substitute the value of "y" into the first original equation and solve for "x":
[tex]\begin{gathered} x+263=500 \\ x=500-263 \\ x=237 \end{gathered}[/tex]Hence, the answers are:
a.)
[tex]\begin{cases}x+y={500} \\ 2x+5y={1789}\end{cases}[/tex]b.)
[tex]x=237\text{ \lparen Number of student tickets Marc sold\rparen}[/tex][tex]y=263\text{ \lparen Number of adult tickets Marc sold\rparen}[/tex]The orange figure below is a scale drawing of theblack figure. What is the scale factor, rounded tothe nearest whole number?
Scale factor is given by the formula below:
[tex]\text{Scale factor =}\frac{new\text{ length}}{\text{old length}}[/tex]Using the right-hand side
new length = 1
old length= 3
substitute the values into the formular
[tex]\text{scale factors= }\frac{1}{3}=0.33333\approx0[/tex]Hello pls help!!
The half-life of carbon-14 is 5,730 years. Suppose a fossil is found with 20 percent as much of its carbon-14 as compared to a living sample. How old is the fossil?
A. 13,307 years
B. 3,235 years
C. 1,331 years
D. 32, 346 years
Please help it's very urgent!!
Answer:
13,307 years
Step-by-step explanation:
The expression for the decay of a radiactive material is:
A = B*(1/2)^(t/HL),
where A is the amount remaining, B is the initial amount, t is time (in years), and HL is the half life (in years).
We learn that A is 20% of B, so let's rewrite for that:
0.20B = B*(1/2)^(t/HL)
and we can divide both sides by B to leave us:
0.20 = (1/2)^(t/HL)
The HL is 5730 years:
0.20 = (1/2)^(t/5730)
We need to solve this expression for t, the time (in years) that is required before we have 20% of the carbon remaining.
The answer I get, by graphing, is 13,305 years, The closest to this is A) 13,307 years. An algebraic solution might result in a slightly different number.
Michelle has a math assignment with 60 problems you saw one picture of the problems of school then Michelle solve 1/4 of the problems at home how many problems does Michelle have left to solve
Step 01:
Data
total math problems = 60
problems solved = 1/4
problems
Step 02:
Find (g∘k)(1)for g(x)=11x2−4x+6and k(x)=4x−11. (g∘k)(1)=
The first step you have to follow is to find k(1) by replacing each x in k(x) for 1:
[tex]k(1)=4(1)-11=4-11=-7[/tex]Now, find g(k(1)), it means, g(-7):
[tex]g(-7)=11(-7)^2-4(-7)+6=573[/tex](g°k)(1)=573.
a coffee machine can be adjuste4d to deliver any fixed numer of ounces of coffee. if the machine has a standard deviation of 0.4 ounces, what should be the mean setting so that an 8 ounce cup will overflow only 0.5% of the time?
The mean μ=9 is the setting so that an 8 ounce cup will overflow when only 0.5% of the time.
A Z-score indicates how far a given value is from a standard deviation. A Z-score (standard value) is the number of standard deviations that a particular data point is above or below the mean. Standard deviation essentially reflects the amount of variability within a given data set.
The average is calculated as: From the Z-score formula:
z=(x-μ)/σ
Z-score associated with 0.5% is 0
(8μ)/0.4=0
Solving for x gives:
μ=9
For μ=9, an intermediate setting such that the 8 ounce cup overflows 0.5% of the time.
To know furthermore about Z-Score at
https://brainly.com/question/28096232
#SPJ4
Fancy food catering prepares 3696 fluid ounces of fruit punch foe a wedding reception. they plan to divide the punch equally among 4 different punch bowls. each serving of punch 6 ounces. how many servings of fruit punch are available at the reception?
Fruit punch is served during the reception in 154-ounce cups using division.
Describe a division.Repetitive subtraction is the process of division. It is the multiplication operation's opposite. It is described as the process of creating equitable groupings. When dividing numbers, we divide a bigger number down into smaller ones such that the larger number obtained will be equal to the multiplication of the smaller numbers.
For instance, 4 2 Equals 2. As a multiplication fact, this can be expressed as 2 + 2 = 4.
The division is represented mathematically by a symbol consisting of a tiny horizontal line with dots above and below the line. The division of two integers is represented by one of two fundamental division symbols.
Total fruit punch foe prepared = 3696 ounces
Number of punch balls = 4
Each serving has = 6 ounces of punch
So, 4 servings will have
4 × 6 = 24
The number of servings of fruit punch available at reception is given by
3696÷24
= 154
To know more about division, visit:
https://brainly.com/question/2273245
#SPJ4
Choose the point on the terminal side of 135º.
We are given the following information.
We also know that the general equation of a line is given by
[tex]y=mx+b[/tex]Where m is the slope of the line and b is the point at which it crosses the y axis.
Since the line given goes through (0,0), b=0. Now we just need to find m.
This can be done via the formula
[tex]m=\tan (\theta)[/tex]In this case
[tex]m=\tan (135)=-1[/tex]And so, the equation of the line given is
[tex]y=-x[/tex]Now we simply need to see which of the options fit this equation. We can do this easily, because x and y are equal except for their sign.
As such, the point of the terminal side of 135° is (-1,1).
Could you quickly glance over my paper and see if it looks generally right? You dont need to go in depth i just need someone to say if i did something extremely wrong.
We need to check if y=8 and x = -1 are perpendicular or parallel.
The line y=8, is a straight line for which the y-values within it are equal to 8, therefore it is parallel to the x-axis.
The line x=-1, is a straight line for which all the values have the same value of x, which is -1, therefore it is parallel to the y-axis.
The lines are, therefore, perpendicular.
The triangles in the figure below are similar.
image b125a080d0e9444e9eebf9b6644403df
Which proportion is correct?
A.
x20=96
x
20
=
9
6
B.
x20=915
x
20
=
9
15
C.
2015=x6
20
15
=
x
6
D.
x20−x=156
x
20
−
x
=
15
6
The perimeter of the triangle is 12 in.
What is perimeter of similar triangle?
The perimeter of similar triangle is equal to the ratio of the similar sides of the triangle. The ratio of two similar perimeters of two similar shapes is equal to the ratio of the lengths of their corresponding sides.
Here, perimeter of triangle PQR = sum of all the side
=12+20+16
=48
The ratio of the corresponding side = 12/3
=4/1
Hence, the perimeter of triangle xyz = ?
perimeter of triangle PQR /perimeter of triangle xyz =4/1
48/x =4/1
x = 48/4
=12
Hence, the perimeter of triangle xyz = 12
To know more about perimeter of triangle, visit:
https://brainly.com/question/28720110
#SPJ1
If 40% of 95 is 38, what is 4% of 95?
If 40% of 95 is 38, what is 4% of 95?
Answer: 3.8
a bus drives for 3hrs and 30 mins at an average speed of 56mph.
how far does the bus drive
Answer: 196 miles
Step-by-step explanation: speed = 56 = distance / time
time = 3.5 hours
distance = speed x time = 56 x 3.5 = 196 miles
Answer:
196 miles
Step-by-step explanation:
If it drove for 56 miles per hour and rod for 3 1/2 hours the if we multiply 56 by 3 we have 168 miles and 1/2 of 56 is 28.
So the bus drove 196 miles
The cost of renting a lawnmower at the Rent-a-Center is given by the formula c = 4 +4h, where c is the total cost in dollars and h is the number of hours the mower isrented. What is the cost of renting the mower for 3 hours?2:
The cost of renting the mower for 3 hours is $16.
Formula:
[tex]c=4+4h[/tex]Where:
c= total cost in dollars
h= number of hours the mower is rented.
So, we simply have to substitute h=3 ( mower rented for 3 hours) and solve:
[tex]c=4+4(3)[/tex][tex]c=4+12[/tex][tex]c=16[/tex]GRADED HW ASSIGNMENT I need help I’m stuck on this question and it’s regarding volume and scientific notation
ANSWER:
1.8176 * 10^-20 m^3
STEP-BY-STEP EXPLANATION:
Given:
Wide = 0.000000284 m
Long = 0.000000025 m
High = 0.00000256 m
Because it is rectangular in shape, the volume is the product of the three measurements, just like this:
[tex]\begin{gathered} V=0.000000284*0.000000025*0.00000256 \\ \\ V=1.8176*10^{-20}\text{ m}^3 \end{gathered}[/tex]The volume is 1.8176 * 10^-20 cubic meters
I need help on #13 please !!! Also with the (circle the vertex on the graph and draw the axis of symmetry) !
Given the quadratic equation
[tex]2x^2-16x+24=0[/tex]we want to solve for the vertex and its axis of symmetry.
To easily identify these properties of quadratic equation, we must put the equation first into its vertex form. The first step to write it in its vertex form is to move the constant on the right-hand side of the equation
[tex]\begin{gathered} 2x^2-16x=-24 \\ x^2-8x=-12 \end{gathered}[/tex]After that, we add the square of b/2 on the equation above. The value of b on the quadratic equation is -16. We have
[tex]x^2-8x+(\frac{-8}{2})^2=-12+(\frac{-8}{2})^2[/tex]Simplify the equation above
[tex]\begin{gathered} x^2-8x+16=-12+16 \\ x^2-8x+16=4 \end{gathered}[/tex]We write the expression on the left-hand side as perfect square, which is (x-4)^2.
[tex](x-4)^2=4[/tex]Transfer 4 to left-hand side to write the vertex form of the quadratic equation
[tex](x-4)^2-4=0_{}[/tex]The vertex form has the general equation
[tex]y=a(x-h)^2+k[/tex]where (h,k) is the vertex of the parabola.
Based on the vertex form of the quadratic formula, the vertex exists at (4,-4). Also, the axis of symmetry is equal to h, which is in this case, equal to 4.
The representation of a vertex and axis of symmetry in a quadratic plot will be
Answer: Vertex = (4,-4)
Axis of symmetry = 4
PLEASE EXPLAIN THE GOT THESE NUMBERS QUICK
The line y = 2x + 6 shown in the data is the line of best fit of the data
What is line of best fit?
There are many points of the data and by plotting the points on the graph, a single line cannot pass through all the points.
Line of best fit minimize the distance between the line and the points of the data
The points which are plotted on the graph in red are the points of the data and y = 2x + 6 is the line of best fit of the data.
To learn more about line of best fit, refer to the link-
https://brainly.com/question/17013321
#SPJ1
i really really need help on this qustion
The coordinates of R are (7, -3).
What is meant by ordered pair?An ordered pair is a composition of the x coordinate (abscissa) and the y coordinate (ordinate), with two values written within parentheses in a fixed order. It aids visual comprehension by locating a point on the Cartesian plane.An ordered pair's numeric values can be integers or fractions. An ordered pair is a pair of two numbers (or variables) separated by a comma and written inside brackets. (1, 2) is an ordered pair, for example.It represents a point in coordinate geometry and an element of a relation/cartesian product in set theory.Ordered pairs are also known as 2-tuples or sequences (or lists in a computer science context).Therefore,
R are (7, -3)
P are (4,-3)
Q are (4,4)
To learn more about ordered pair, refer to:
brainly.com/question/11139505
#SPJ1
In parallelogram PQRS, QP is entended to pointT and ST is drawn
Answer
Angle PST = 80°
Explanation
Opposite angles of a parallelogram are equal.
Angle R = 130° = Angle QPS
The sum of angles on a straight line is 180°.
Angle QPS + Angle SPT = 180°
130° + Angle SPT = 180°
Angle SPT = 180° - 130° = 50°
Then, we were told that ST = SP, so, the the base angles of triangle PST are equal.
Angle SPT = Angle STP = 50°
Sum of angles in a triangle = 180°
Angle SPT + Angle STP + Angle PST = 180°
50° + 50° + Angle PST = 180°
100° + Angle PST = 180°
Angle PST = 180° - 100°
Angle PST = 80°
Hope this Helps!!!
For what value of x must ABCD be a parallelogram? 14-7=12x+1
Answer:
Step-by-step explanation:
14-7=7
7-1=6
6=12x
x=0.5
Indigo has $700 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
She buys a new bicycle for $296.71.
She buys 3 bicycle reflectors for $12.34 each and a pair of bike gloves for $33.66.
She plans to spend some or all of the money she has left to buy new biking outfits for $68.49 each.
Which inequality can be used to determine
o
o, the maximum number of outfits Indigo can purchase while staying within her budget?
68.49
o
+
367.39
≤
700
68.49o+367.39≤700
68.49
+
367.39
o
≥
700
68.49+367.39o≥700
68.49
o
+
367.39
≥
700
68.49o+367.39≥700
68.49
+
367.39
o
≤
700
68.49+367.39o≤70
The inequality that can be used to determine x, the number of outfits Indigo can purchase will be; 367.39 + 68.49x ≤ 700
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions.
The given parameters are:
Budget = $700
New bicycle = $296.71
Three bicycle reflectors = $12.34 each
Pair of a bike gloves = $33.66.
New biking outfits = $68.49 each.
Let the number of new biking outfits be x
So, we have the inequality;
New bicycle + 3 times price of bicycle reflectors + Pair of a bike gloves + New biking outfits ≤ Budget
This gives;
296.71 + 3( 12.34) + 33.66+ 68.49x ≤ 700
296.71 + 68.49x ≤ 700
Solve the inequality
367.39 + 68.49x ≤ 700
Hence, the inequality that can be used to determine x, the number of outfits Indigo can purchase will be; 367.39 + 68.49x ≤ 700
Read more about inequality at
brainly.com/question/24372553
#SPJ1
The total cost of three shirts and two sweatshirts is $203.75. If the sales tax rate on clothing is 6%, how much money will be owed to the cashier?
The money owed by the cashier after selling three shirts and two sweatshirts for $203.75 and 6% clothing tax is $215.975.
The percentage tax is the tax amount charged for the item. The tax amount is given by dividing the per cent by 100 and multiplying it by the total amount of the item.
The total cost of three shirts and two sweatshirts is $203.75 and the tax is 6%.
The tax amount will be,
Tax amount = [tex]\frac{6}{100}\times203.75[/tex]
[tex]=12.225[/tex]
So, the total money owed by the cashier will be,
Total money owed by cashier [tex]=203.75+12.225[/tex]
= $215.975
Therefore, the money owed by the cashier after selling three shirts and two sweatshirts is $215.975.
To learn more about Cost and Tax visit here:
https://brainly.com/question/9437038
#SPJ9
find the total surface area of a solid cube given that its volume is 343 m square.
find the volume of a solid cube given that its total surface area is 216.
Step-by-step explanation:
what is the basic unit of length ? m or meter ?
a cube is like a 3-dimensional square : all side lengths are equal.
the volume of a cube =
side³
side³ = 343 m³
side = cubic root(343) = 7 m
a cube has 6 sides (look at dice). the surface of a cube is therefore 6 times the area of a side² square.
so, for side = 7 the surface area of the cube is
6 × 7² = 6 × 49 = 294 m²
and in the other direction, when we have the surface area (216 m²) :
216 m² = 6 × side²
36 = side²
side = sqrt(36) = 6 m
the volume of that cube is then
6³ = 216 m³
Suppose at 21 inches of wire cost $.84 at the same rate how much incense for 14 inches of wire cost
Step 1:
Concept:
The cost of wire varies directly to the length in inches
Step 2:
[tex]\begin{gathered} \text{If 21 inches cot \$0.84} \\ \text{Then 1 inches will cost = }\frac{0.84}{21}\text{ = 0.04 \$/inch} \end{gathered}[/tex]Final answer
14 inches will cost = 14 x 0.04 = $0.56 = 56 cents
56 cents
where Ais the initial amount present and A is the amount presenteStrontium-90 is a radioactive material that decays according to the function A(t) = Age-0.02441at time t (in years). Assume that a scientist has a sample of 800 grams of strontium-90.ce(a) What is the decay rate of strontium-90?(b) How much strontium-90 is left after 30 years?(c) When will only 200 grams of strontium-90 be left?(d) What is the half-life of strontium-90?-stilCOREcio (a) The decay rate of strontium-90 is %.(Type an integer or a decimal. Include the negative sign for the decay rate.)LiolewMat
The given information is:
- The function of decay is:
[tex]A(t)=A_0e^{-0.0244}[/tex]Where A0 is the initial amount of strontium-90, A is the amount present at time t (in years).
- The initial amount is 800 grams.
a. What is the decay rate of strontium-90?
The given formula is written in the form:
[tex]A(t)=A_0e^{rt}[/tex]Where r is the decay rate in decimal form, so:
[tex]r=-0.0244*100\%=-2.44\%[/tex]The decay rate is -2.44%.
b. How much strontium-90 is left after 30 years?
Replace t=30 and solve:
[tex]\begin{gathered} A(30)=800g*e^{-0.0244*30} \\ A(30)=800g*e^{-0.732} \\ A(30)=800g*0.481 \\ A(30)=384.8g \end{gathered}[/tex]There is 384.8 grams after 30 years.
c. When will only 200 g of strontium-90 be left?
A(t)=200g, then replace it and solve for t:
[tex]\begin{gathered} 200g=800g*e^{-0.0244t} \\ \frac{200g}{800g}=e^{-0.0244t} \\ \ln(\frac{200g}{800g})=\ln e^{-0.0244t} \\ -1.386=-0.0244t \\ t=\frac{-1.386}{-0.0244} \\ t=56.8 \end{gathered}[/tex]There will be 200 g left after 56.8 years.
d. What is the half-life of strontium-90?
The half-life is when A(t)=A0/2, then if we replace this into the decay formula we obtain:
[tex]\begin{gathered} \frac{A_0}{2}=A_0*e^{-0.0244t} \\ Simplify\text{ A0 on both sides} \\ \frac{1}{2}=e^{-0.0244t} \\ \ln(0.5)=\ln e^{-0.0244t} \\ -0.693=-0.0244t \\ t=\frac{-0.693}{-0.0244} \\ t=28.4 \end{gathered}[/tex]The half-life of strontium-90 is 28.4 years.