Answers
Answer:
a. Since the half-life of the isotope is 8 hours, we know that the decay rate is exponential and we can use the formula:
A(t) = A0 * (1/2)^(t/8)
where A0 is the initial amount of the substance, t is the time elapsed, and A(t) is the amount of substance remaining after t hours.
Substituting the given values, we get:
A(t) = 7 * (1/2)^(t/8)
b. To find the rate at which the substance is decaying, we need to take the derivative of A(t) with respect to t:
A'(t) = -7/8 * (1/2)^(t/8) * ln(1/2)
Simplifying, we get:
A'(t) = -ln(2) * (7/8) * (1/2)^(t/8)
c. To find the rate of decay at 14 hours, we can plug in t=14 into the equation we found in part b:
A'(14) = -ln(2) * (7/8) * (1/2)^(14/8) ≈ -0.4346 grams per hour (rounded to four decimal places)
Related Questions
A hiker hikes at a steady rate throughout the day on a mountain. Which student wrotr a correct equation to represent the linear relationship shown on the table between X, the number of hours hiked and y, the current altitude of the climber?
Answers
There is no table provided to reference, but the equation that represents a linear relationship between X and Y is:
y = mx + b
where m is the slope of the line and b is the y-intercept. The equation can also be written as:
y = b + mx
where b is the y-intercept and m is the slope. The equation represents a straight line on a graph, where the slope determines the steepness of the line, and the y-intercept is the point where the line crosses the y-axis. To write the equation for the table of X and Y values, we need to determine the slope and y-intercept from the given data.
10. Point A is located at (4, 3). Point A is reflected
across the line y = -2, then rotated 90 degrees
clockwise about the origin. What is the final
location of A after both transformations?
Answers
If Point A is located at (4, 3). Point A is reflected. the final location of A after both transformations is (-4, -7).
What is the final location of A after both transformations?To reflect point A across the line y = -2, we need to find the point that is the same distance from the line but on the other side. The line y = -2 is a horizontal line that is 5 units above the point A (since the y-coordinate of A is 3). Therefore, the reflected point will be 5 units below the line, which gives us:
A' = (4, -7)
To rotate point A' 90 degrees clockwise about the origin, we can use the following rotation matrix:
| 0 1 |
| -1 0 |
Multiplying this matrix by the coordinates of A', we get:
| 0 1 | | 4 | | -7 |
| -1 0 | * | -7 | = | -4 |
So the final location of A after both transformations is (-4, -7).
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On the bottom shelf there are 20 shirts . Three-fourths of them are red. Draw a picture to show the shirts.
Answers
Answer:
Step-by-step explanation:
Find the Volume of the triangular prism
Answers
For the given triangular prism, the volume value is obtained as Option B: 31.5 in³.
What is a triangular prism?
The pentahedron Triangular Prism contains nine different nets. The bases' vertices and edges are connected by means of their three rectangular sides. The rectangular sides of the triangular prism are joined to one another side by side. Every cross-section that is perpendicular to the base faces is a triangle.
The height of the triangular prism is given as 2 inches.
The base of the triangular prism is given as 7 inches.
The length of the triangular prism is given as 4.5 inches.
The volume of a triangular prism is given by the formula -
V = (1/2) × b × h × l
where b is the base of the triangle, h is the height of the triangle, and l is the length of the prism.
Substituting these values into the equation, we get -
V = (1/2) × 7 inches × 2 inches × 4.5 inches
V = 7 inches × 1 inch × 4.5 inches
V = 31.5 cubic inches
Therefore, the volume of the triangular prism is 31.5 cubic inches.
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The ships kitchen stocks 1 3/5 quarts of ice cream for every 1/4 cake. There are 10 cakes in the kitchen. How many quarts of ice cream are there?
Please explain if you really really know the answer
Answers
Therefore , the solution of the given problem of unitary method comes out to be the pantry has 16 quarts of ice cream.
What is an unitary method?The goal can be achieved by making use of what has expression learned to date, utilizing this global access, and incorporating all crucial elements from previous changeable study that employed a specific technique. It is going to be equation possible to get in touch with the entity again if the expected claim result actually happens, or both crucial processes will surely miss the statement. A Rs ($1.21) redeemable fee may be needed for fifty pens.
Here,
Finding the overall quantity of cake in the kitchen is a good place to start. If there are 10 pastries, each measuring 1/4 inch, then there will be:
=> 10 desserts divided by 1/4 each equals the total cake.
=> Cake total equals 10/4 cakes.
=> 2.5 pastries altogether
=> 1 3/5 pints of ice cream for every 1/4 cake.
=> 8 and a half pints of ice cream per 1/4 cake
To determine the total amount of ice cream, we can multiply the ice cream per cake by the total number of cakes:
=> Total ice cream equals the sum of the cakes' ice cream.
=> Total ice cream = (8/5 quarts per 1/4 cake) * (10/4 cakes)
=> Total ice cream = 16 quarts
Consequently, the pantry has 16 quarts of ice cream.
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What is the center and radius of a circle with the following equation
Answers
Answer:
Center: (1, -3); radius: 2
Step-by-step explanation:
(x - h)² + (y - k)² = r²
(x - 1)² + (y + 3)² = 4
(x - 1)² + (y - (-3))² = 2²
Center: (1, -3); radius: 2
Matt increased his typing speed from 32 to 38 words per minute. What is the percent of increase
Answers
Answer:
Matt's typing speed increased by 18.75%.
Step-by-step explanation:
To find the percent increase, we can use the following formula:
percent increase = (new value - old value) / old value x 100%
Using this formula, we can calculate the percent increase in Matt's typing speed as follows:
percent increase = (38 - 32) / 32 x 100%
percent increase = 6 / 32 x 100%
percent increase = 0.1875 x 100%
percent increase = 18.75%
PLEAS HELP!!!
Find the volume of the pyramid. Write your answer as a fraction or mixed number.
Answers
The volume of the triangular pyramid is 26 2/3 yd³
How to determine the volumeThe formula for calculating the volume of a triangular pyramid is expressed with the equation
A = 1/3bh
Such that the parameters in the equation are;
A is the area of the triangular pyramid.b is the base area of the triangular pyramid.h is the height of the pyramid.The base area of the pyramid is;
Area = 1/2 × 4 × 5
Multiply the values
Base area =20/2
Base area = 10 yd
Substitute the value
Volume = 1/3 × 10 × 8
Multiply the values
Volume = 80/3
Divide the values
Volume = 26 2/3 yd³
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there are 3 containers of chocolate ice cream for every 2 containers of vanilla ice cream. What is the constant of proportionality in terms of vanilla to chocolate.
Answers
Answer: 2:3
Step-by-step explanation:
If you need $25,000 eight years from now, what is the minimum amount of money you need to deposit into a bank account that pays an annual percentage rate (APR) of 5% that is compounded--
i need an answer ASAP because i need to bring up my grade thanks also its due today
Answers
The minimum amount of money to be deposited in the bank account is $16,921. The solution has been obtained by using compound interest.
What is compound interest?
Compound interest is the type of interest that is calculated using both the principal and the interest that has accumulated over the preceding period. In contrast to simple interest, compound interest does not factor in the principal when calculating the interest for a subsequent period. In mathematics, compound interest is frequently referred to as C.I.
We are given that we need $25,000 eight years from now and the account pays an annual percentage rate (APR) of 5% which is compounded annually.
So, using the compound interest formula, we get the principal as
⇒ P = [tex]\frac{A}{(1 + \frac{r}{n} )^{nt} }[/tex]
⇒ P = [tex]\frac{25000}{(1 + \frac{0.05}{1} )^{8} }[/tex]
⇒ P = $16,920.98
Hence, the minimum amount of money to be deposited in the bank account is $16,921.
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Solve the following quadratic-like equation.
[tex]y^\frac{1}{2} -6y^\frac{1}{4} +8=0[/tex]
Answers
Step-by-step explanation:
given quadratic equation is
simplification,
by using,
[tex]y^\frac{1}{2} -6y^\frac{1}{4} +8=0
\\ y^\frac{1}{2} -6y^\frac{1}{4} = - 8 \\
[/tex]
[tex]square[/tex]
[tex] \\ {(y^\frac{1}{2} -6y^\frac{1}{4})}^{2} = {(- 8)}^{2}[/tex]
[tex]y + 36 {y}^{ \frac{1}{2}} \: [/tex]
-5 + x-2 = 3x + 10 - x Which of the following statements correctly describe the solution(s) of the equation above? Select all that apply. • The equation has only one solution. • The equation has no solutions. F The equation has infinitely many solutions. ) The equation's only solution is x = - 17. • The equation is solved by all numbers less than 17.
Answers
The equation's only solution is x = -17.
Simplifying the left-hand side of the equation:
-5 + x - 2 = -7 + x
Simplifying the right-hand side of the equation:
3x + 10 - x = 2x + 10
Substituting into the original equation, we get:
-7 + x = 2x + 10
Subtracting x from both sides, we get:
-7 = x + 10
Subtracting 10 from both sides, we get:
-17 = x
So the only solution to the equation is x = -17. Therefore, the correct statement about the solution(s) of the equation is:
• The equation's only solution is x = -17.
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Gianna is going to throw a ball from the top floor of her middle school. When she throws the ball from 48feet above the ground, the function h(t)=-16t^2+32t +48 models the height,h, of the ball above the ground as a function of time, t. Find the zero of this function that tells us when the ball will hit the ground.
Answers
Substitute h(t) = 0 in the given equation:
-16t^2 + 32t + 48 = 0
Dividing both sides by -16:
t^2 - 2t - 3 = 0
Factorizing the equation:
(t - 3)(t + 1) = 0
So, the solutions are t = 3 or t = -1.
Since time can't be negative, the only solution that makes sense in this context is t = 3.
Therefore, the ball will hit the ground after 3 seconds.
how you can find the most common and least common on a line plot
giving away 100 points whoever gets it right, if your not trying to help and just get the points leave.
Answers
Answer:
siuuuuuuuuuuuuuuuuuuuuuuuuuu
A square wrestling mat has a perimeter of (12x−32)
feet. Write an expression in simplest form that represents the side length (in feet) of the mat.
Answers
Answer:
The perimeter of a square is given by the formula P = 4s, where s is the side length. In this case, we are given that the perimeter is (12x - 32) feet, so we can set up an equation:
P = 4s
(12x - 32) = 4s
To solve for s, we can divide both sides by 4:
(12x - 32)/4 = s
Simplifying the expression on the left:
3x - 8 = s
Therefore, the expression in simplest form that represents the side length of the square wrestling mat is 3x - 8 feet.
Answer:
Step-by-step explanation:
the answer would be 3 x − 8 3x-8 3x−8 ft
Set up and solve a proportion for the following application problem. If 5 pounds of grass seed cover 355 square feet, how many pounds are needed for 6035 square feet?
Answers
Let x be the number of pounds needed for 6035 square feet.
We can set up a proportion between the pounds of grass seed and the square feet covered:
5 pounds / 355 square feet = x pounds / 6035 square feet
To solve for x, we can cross-multiply and simplify:
5 pounds * 6035 square feet = 355 square feet * x pounds
30175 = 355x
x = 30175 / 355
x ≈ 85.07
Therefore, approximately 85.07 pounds of grass seed are needed for 6035 square feet
What’s 4559.886 rounded to the nearest inch
Answers
Answer:
Step-by-step explanation:
Assuming that the original measurement is in millimeters, since they are commonly used in precision applications, we know that 1 millimeter is equal to 0.03937 inches. Therefore, we can convert 4559.886 millimeters to inches by multiplying by 0.03937:
4559.886 mm * 0.03937 in/mm = 179.72467632 in (rounded to 8 decimal places)
To round this to the nearest inch, we need to look at the first decimal place after the decimal point. In this case, the digit in the first decimal place is 7, which is greater than or equal to 5. Therefore, we round up to the nearest inch, which gives us:
179.72467632 in rounded to the nearest inch is 180 in.
Therefore, 4559.886 rounded to the nearest inch is 180.
circumference is 1884, what is the diameter
Answers
Answer: how many places are you looking for? because it would be around 599.696332...(and more decimal numbers)
you get this from dividing 1884 by 3.14159 (pi)
PLS HELP!!! DUE TOMORROW!! 50 POINTS!! show work pls!!
Answers
The right triangle BCD have the following solution:
a). The opposite side to the angle D is BC and the adjacent side is DC
b). sin D = 0.55
c). D = 33°
d). B = 57°
How to evaluate for the solutions of the right triangle BCD.Considering the angle D for right triangle BCD, the side opposite the angle D is BD which is also equal to 11 cm, and the side adjacent to the angle D is DC.
sin D = 11/20 {opposite/hypotenuse}
sin D = 0.55 to the nearest tenth
D = sin⁻¹(0.55)
D = 33.3670
D = 33 to the nearest degree
angle B = 180 - (90 + 33) {sum of interior angles of a triangle}
angle B = 57°.
Therefore, the right triangle BCD have the following solution:
a). The opposite side to the angle D is BC and the adjacent side is DC
b). sin D = 0.55
c). D = 33°
d). B = 57°
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Who knows this? I need help
#16
Answers
Answer:
Step-by-step explanation:
adjacent: [tex]\angle BOC, \angle EOD[/tex] (both are adjacent)
complementary: [tex]\angle BOC[/tex]
supplementary: [tex]\angle EOD[/tex]
vertical angles: [tex]\angle AOE[/tex]
Mr. Jonas's aquarium holds 8 gallons
of water. If he buys another that
holds 1½ times as many gallons,
how many gallons of water does
Mr. Jonas's new tank hold?
Answers
20) Calculate the average rate of change of f(x) = −x² + 3x - 6 on the interval [1, 3].
Answers
Answer:
asdf
Step-by-step explanation:
How many total blocks does Ben need to walk north and east to get from his home to the playground and home again?
Answers
ABCD is a square. P and D are points on the y-axis. A is a point on the x-axis. PAB is a straight line. The equation of the line that passes through the points A and D is y=-2x+6. Find the length of PD.
Answers
The length of the segment PD obtained using the relationship between similar right triangles is; PD = 7.5 units
What is a right triangle?A right triangle is a triangle that has an interior angle of 90° (a right angle) and the side opposite the right angle (90°) interior angle is known as the hypotenuse side, while the other two sides of the triangle are the legs of the right triangle.
The possible drawing in the question, obtained from a similar online question, created with MS Word is attached.
The equation of the line that passes through the points A and D, y = -2·x + 6, indicates;
The coordinates of the y-intercept of the line of the equation, is; (0, 6)
The y-intercept indicates that OD = 6 units
The x-intercept coordinates of the graph of the equation, can therefore be obtained as follows; 0 = -2·x + 6
2·x = 6
x = 6/2 = 3
x = 3
The x-intercept is; (0, 3)
The x-intercept indicates that OA = 3 units
The length of the side of the square, s, is therefore;
s = √(s²) = √(6² + 3²) = 3·√5
OA = The length of the x-intercept of ; y = -2·x + 6
The ∠DAO ≅ ∠OPA, and m∠DOA = m∠POA = 90°
Therefore;
∠DOA ≅ ∠POA
ΔOPA is similar to ΔOAD, by Angle-Angle similarity postulate
The ratio of corresponding sides of similar triangles indicates;
OP/OA = OA/OD
Therefore;
OP/OA = OA/OD
OP/3 = 3/6
OP = 3 × 3/6 = 1.5
PD = OP + OD (Segment addition postulate)
PD = 1.5 + 6 = 7.5
The length of segment PD is 7.5 unitsPlease find attached the possible drawing in the question, created with MS Word, obtained from a similar question posted online.
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Solve for X
x^2+ y^2=25 and y=x
Answers
The solutions for x are x= +[tex]\sqrt{12.5[/tex] and -[tex]\sqrt{12.5[/tex] which has been obtained by solving the equations given in the question.
Define Equation?
An equation can be defined in numerous ways. An equation is a claim that demonstrates the equivalence of two mathematical expressions, according to algebra.
In the initial equation, we get: by substituting y=x:
[tex]x^2[/tex] +[tex]y^2[/tex]= 25
[tex]x^2[/tex] +[tex]x^2[/tex] = 25 (since y = x)
2[tex]x^2[/tex] = 25
[tex]x^2[/tex] = 12.5
When the two sides are square, we get:
x = ±[tex]\sqrt{12.5[/tex]
Therefore, the solutions for x are x = +[tex]\sqrt{12.5[/tex] and x = -[tex]\sqrt{12.5[/tex]
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Lmkkkk helppppppppppp
Answers
Answer:
1.986 x 10 to the tenth power
Step-by-step explanation:
Tashaun drove 74 miles in 2 hours. Kamari drove 153 miles in 3 hours. If the speed limit is 50 miles per hour, who was speeding?
Group of answer choices
Neither
Tashaun
Both
Kamari
Answers
Answer:
kamari
Step-by-step explanation:
Tashaun: [tex]\frac{74}{2}[/tex]= 32mph
kamari: 153/3=51mph
so we can see that kamari is speeding the speed limit is 50 and 51>50 brainliest?
Find the distance between (3,3) & (5,3)
Answers
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Using this formula, we can find the distance between the points (3, 3) and (5, 3):
Distance = sqrt((5 - 3)^2 + (3 - 3)^2)
= sqrt(2^2 + 0^2)
= sqrt(4)
= 2
Therefore, the distance between (3, 3) and (5, 3) is 2 units.
maria scored 92 points in 4 games at the same rate, how many points would she scored in 17 games
Answers
Explanation:
She scored 92 points in 4 games. The unit rate is 92/4 = 23 points per game.
Over the course of 17 games, Maria would have a total of 17*23 = 391 points assuming her scoring rate is kept the same.
Joe made
4
identical necklaces, each having beads and a pendant. The total cost of the beads and pendants for all
4
necklaces was
$
25.60
. If the beads cost
$
2.70
for each necklace, how much did each pendant cost?
Answers
Answer:
Each pendant costs $3.70.
Step-by-step explanation:
Let's assume that the cost of each pendant is x dollars.
The total cost of the beads for all 4 necklaces is 4 * $2.70 = $10.80.
The total cost of the beads and pendants for all 4 necklaces is $25.60.
So, the total cost of the pendants for all 4 necklaces is
$25.60 - $10.80 = $14.80.
Since there are 4 necklaces and each necklace has a pendant, the total cost of all the pendants is 4x dollars.
So we can write
4x = $14.80
Dividing both sides by 4, we get
x = $3.70
Therefore, each pendant costs $3.70.
