Sketch the graph to show the relationship between tand mfor t≥ 0 days.Show that the value of A is 120.Show that the value of k is 0.02877, given to 4 significant figures.Using the value of k as 0.02877, find the mass of the substance after 16 days,giving the answer to 3 significant figures,Using the value of k as 0.02877, find the day during which the mass of thesubstance first reaches 50 milligrams.
Answers
Given the mass of a radioactive substance after time t days is given by
\(m(t)=Ae^{-kt}\)The initial mass of the substance is 120 milligrams, which means m(0)=120. So,
\(\begin{gathered} m(0)=120 \\ \Rightarrow Ae^0=120 \\ \Rightarrow A=120 \end{gathered}\)The mass of the substance is 90 milligrams after 10 days, which means m(10)=90. So,
\(\begin{gathered} m(10)=90 \\ \Rightarrow120e^{-10k}=90 \\ \Rightarrow e^{-10k}=\frac{3}{4} \end{gathered}\)Now, take natural logarithm on both the side and use the property
\(\ln (e^n)=n\)So, the above equation will become
\(\begin{gathered} \ln (e^{-10k})=\ln (\frac{3}{4}) \\ \Rightarrow-10k=-0.2877 \\ \Rightarrow k=\frac{-0.2877}{-10} \\ \Rightarrow k=0.02877 \end{gathered}\)Therefore, the relation between the mass of the substance at time t days is given by t
\(m(t)=120e^{-0.02877t}\)The mass of the substance after 16 days will be
\(m(16)=120e^{-0.02877(16)}=120(0.631)=75.729\text{ milligrams}\)The day during which the mass of the substance reaches 50 milligrams can be obtained as follows:
\(\begin{gathered} m(t)=50 \\ 120e^{\mleft\{-0.02877t\mright\}}=50 \\ \Rightarrow e^{-0.02877t}=\frac{50}{120} \\ \Rightarrow-0.02877t=\ln (\frac{50}{120}) \\ \Rightarrow t=\frac{-0.8754}{-0.02877} \\ \Rightarrow t=30.43\text{ days} \end{gathered}\)The graph that shows the relationship between m and t is given below:
Related Questions
what is the measure of SR?
Answers
Answer:
RS = 8
Step-by-step explanation:
Given:
Secant QU = internal secant segment PU + external secant segment PQ = 7 + 9 = 16
Secant QS = internal secant segment RS + external secant segment RQ = (3x - 5) + 8
To find the measure of RS, we need to find the value of x.
Thus, recall the "Two Secant Theorem"
According to the theorem,
(RS + RQ)*RQ = (PU + PQ)*PQ
Thus,
\( (3x - 5 + 8)*8 = (7 + 9)*9 \)
\( (3x + 3)*8 = (16)*9 \)
\( 24x + 24 = 144 \)
Subtract 24 from both sides
\( 24x + 24 - 24 = 144 - 24 \)
\( 24x = 120 \)
Divide both sides by 24
\( \frac{24x}{24} = \frac{120}{24} \)
\( x = 5 \)
Plug in the value of x into (3x - 5) to find the measure of RS
RS = 3(5) - 5 = 15 - 7
RS = 8
15 = -3(2c + d) (Solve for c)
Answers
Answer:
(15+3d)/6 = c
2 1/2 + 1/2d = c (more simplified)
Step-by-step explanation:
15 = -3(2c +d)
15 = -6c -3d
+3d +3d
15 +3d = -6c
/-6 /-6
(15+3d)/6 = c
2 1/2 + 1/2d = c
let f(x)= 1/x+(1/y-2)+7 what i the domain of difinition of f(x)
Answers
Step-by-step explanation:
(x)=1/x+(1/y-2)+7
(x-1/x)=1/2y+7
3x/2=8/2Y
3x×8=2×2y
24x:4y
where happened if you have sex
Answers
Answer:
you have a chance of having a baby...
Answer:
chance of relief stress and having a baby
Step-by-step explanation:
hope it helps you
the sum for 3 times x and eleven
Answers
Answer:
3x +11 = 32
Step-by-step explanation:
hope this is correct! <3
Answer:
3x +11 = 32
3x = 32-11
3x = 21
x = 21/3
x = 7
check answer:
3(7)+11 = 32
21 + 11 = 32
32 = 32
LHS = RHS
Hence, verified
What is the answer please help no links no links
Answers
30/45 = 2/3 = about 0.67 and 70% (0.70) is the closest
Simplify to a single trig function or constant with no fractions.
Answers
We can simplify cosec(t)tant(t) to sec(t). A trigonometric function is a mathematical function that relates the angles of a triangle to the ratios of its sides.
The most common trigonometric functions are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).
To simplify the expression cosec(t)tant(t), we need to use the trigonometric identity:
cosec(t) = 1/sin(t)
tant(t) = sin(t)/cos(t)
Substituting these expressions into the original expression, we get:
cosec(t)tant(t) = (1/sin(t))(sin(t)/cos(t))
The sin(t) term in the numerator and denominator cancel out, leaving:
cosec(t)tant(t) = 1/cos(t)
Recalling the definition of secant, sec(t) = 1/cos(t), we can express the simplified expression as:
cosec(t)tant(t) = 1/sec(t)
Therefore, we can simplify cosec(t)tant(t) to sec(t).
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The mass of the part of a metal rod that lies between its left end and a point x meters to the right is 4x2 kg. (See this example.) (a) Find the linear density when x is 4 m. kg/m (b) Find the linear density when x is 6 m. kg/m (c) Find the linear density when x is 9 m. kg/m
Answers
Answer:
A) 32 kg/m
B) 48 kg/m
C) 72 kg/m
Step-by-step explanation:
We are given mass is; m = 4x²
Linear density is the derivative of mass with respect to the position x. So linear density is;
ρ = dm/dx
Differentiating 4x²,we have; ρ = 8x
A)at x = 4; ρ = 8(4) = 32 kg/m
B) at x = 6; ρ = 8(6) = 48 kg/m
C) at x = 9; ρ = 8(9) = 72 kg/m
Please help.
Is it no solution, one solution or infinitely many
Solution.
Answers
f(x)= a(x+p)² +q and g(x)= 0 3 3.1 x + p 1. The turning point of f is (1;4) and the asymptotes of g intersect at the turning point of f. Both graphs cut the y-axic at 3. 3.2 3.3 3.4 a 10 g +94 (1:4) Determine the equation of f Determine the equation of g Determine the coordinates of the x-intercept of g For which values of x will f(x) ≥ g(x)? [9]
Answers
Step-by-step explanation:
Let's solve the given questions step by step:
1. Determine the equation of f:
From the given information, we know that the turning point of f is (1, 4). The general form of a quadratic function is f(x) = ax^2 + bx + c. We are given that f(x) = a(x + p)^2 + q, so let's substitute the values:
f(x) = a(x + p)^2 + q
Since the turning point is (1, 4), we can substitute x = 1 and f(x) = 4 into the equation:
4 = a(1 + p)^2 + q
This gives us one equation involving a, p, and q.
2. Determine the equation of g:
The equation of g is given as g(x) = 0.3x + p1.
3. Determine the coordinates of the x-intercept of g:
The x-intercept is the point where the graph of g intersects the x-axis. At this point, the y-coordinate is 0.
Setting g(x) = 0, we can solve for x:
0 = 0.3x + p1
-0.3x = p1
x = -p1/0.3
Therefore, the x-intercept of g is (-p1/0.3, 0).
4. For which values of x will f(x) ≥ g(x)?
To determine the values of x where f(x) is greater than or equal to g(x), we need to compare their expressions.
f(x) = a(x + p)^2 + q
g(x) = 0.3x + p1
We need to find the values of x for which f(x) ≥ g(x):
a(x + p)^2 + q ≥ 0.3x + p1
Simplifying the equation will involve expanding the square and rearranging terms, but since the equation involves variables a, p, and q, we cannot determine the exact values without further information or constraints.
To summarize:
We have determined the equation of f in terms of a, p, and q, and the equation of g in terms of p1. We have also found the coordinates of the x-intercept of g. However, without additional information or constraints, we cannot determine the exact values of a, p, q, or p1, or the values of x for which f(x) ≥ g(x).
Please help for brainliest :(
Given the figure below, find the values of x and z.
Answers
Answer:
Below in bold.
Step-by-step explanation:
z = 87 degrees ( vertical angles)
9x - 87 = 180 - z ( adjacent angles are supplementary)
9x - 87 = 180 - 87
9x = 180
x = 20 degrees.
Which of the expressions are equivalent to the one below check all the apply (12 + 3) ÷ 5
Answers
The expression is equivalent to the expression (12 + 3) ÷ 5 is (3 + 12) ÷ 5
Which of the expressions are equivalent to the expressionFrom the question, we have the following parameters that can be used in our computation:
(12 + 3) ÷ 5
The above expression is a quotient expression
However, we can apply some algebraic properties
Take for instance;
12 + 3 can be expressed as 3 + 12
So, we have
(12 + 3) ÷ 5 = (3 + 12) ÷ 5
Hence, the expression is equivalent to the expression is (3 + 12) ÷ 5
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What is an equation of the line that passes through the points (-5, -8)(−5,−8) and (-4, -6)(−4,−6)?
Answers
Answer:
Step-by-step explanation:
General equation of a line is y= mx+b,
where m is the slope and b is the y- intercept
For points (-5, -8) and (-4, -6) the slope is
m= difference in y / difference in x
m = [-6 - (-8)] / [-4 - (- 5)] = (-6+8)/(-4+5) = 2/1 =2
Now we know that y= 2x+b , to find b substitute the coordinate (x, y) with coordinate (-4, -6) -you could pick the other point if you want will work because both points are on the line.
-6 = 2(-4) +b , multiply
-6 = -8 + b, add 8 to both sides
-6+8 =b , add
2 =b
The equation of the line that passes through the points (-5, -8) and (-4, -6) is
y= 2x+2
First of all, you will find the gradient. The formula for finding the gradient is y2-y1 /x2-x1. - 6--8/-4--5.If two negatives meet they change to positive. - 6+8/-4+5=2/1,therefore the gradient is 2,after that then you will find the equation of the line. The formula for finding the equation of the line is y-y1=m(x-x1). y-(-8)=m(x--5),y+8=2(x+5),y+8=2x+10,y=2x+2.
A train travels 25 miles in 20 minutes. What is the train’s speed in miles perhour?
Answers
Answer:
So,
The rate of the train is 25mi/20mins. We need (x)mi/hr. We can do that by multiplying by 3.
25(3) = 75
The train's speed in mph is 75 mph.
Step-by-step explanation:
Suppose that 45% of students in a college have a smart phone. If you select three students at random, what is the probability that all three have a smart phone? Give your answer as a decimal (to at least 3 places) or fraction
Answers
Answer:
\( P(X=3)\)
And we can use the probability mass function and we got:
\(P(X=3)=(3C3)(0.45)^3 (1-0.45)^{3-3}=0.091\)
Then the probability that all three have a smart phone is 0.091
Step-by-step explanation:
Let X the random variable of interest "number of students with smartphone", on this case we now that:
\(X \sim Binom(n=3, p=0452)\)
The probability mass function for the Binomial distribution is given as:
\(P(X)=(nCx)(p)^x (1-p)^{n-x}\)
Where (nCx) means combinatory and it's given by this formula:
\(nCx=\frac{n!}{(n-x)! x!}\)
And we want to find this probability:
\( P(X=3)\)
And we can use the probability mass function and we got:
\(P(X=3)=(3C3)(0.45)^3 (1-0.45)^{3-3}=0.091\)
Then the probability that all three have a smart phone is 0.091
There is plot behind Best Buy and Academy
Answers
Answer:
What is the question???
 Hey guys, I would really appreciate if one of you help me with this question
Answers
Answer: 28.25%
Step-by-step explanation:
113/400=0.2825=28.25%
A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 65% salt and Solution B is 90% salt. She wants to obtain 150 ounces of a mixture that is 80% salt. How many ounces of each solution should she use?
Answers
The amount of solution A and B required are 60 and 90 ounces respectively.
Creating simultaneous equations for the problem:
Mass of solution A = a
Mass of solution B = b
a + b = 150 _____(1)
0.65a + 0.90b = 150×0.80
0.65a + 0.90b = 120 __(2)
From (1)
a = 150-b ____(3)
substitute (3) into (2)
0.65(150-b) + 0.90b = 120
97.5 - 0.65b + 0.90b = 120
0.25b = 120-97.5
0.25b = 22.5
b = 22.5/0.25
b = 90
a = 150 - b
a = 150 - 90
a = 60
Therefore , 60 ounces of solution A and 90 ounces of solution B is required.
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Dividing the sum of (7/8) (15/4) (1/12) by their multiplication gives _________
Answers
The Division of the sum of (7/8), (15/4), and (1/12) by their multiplication is (2712/168).
To find the division of the sum of (7/8), (15/4), and (1/12) by their multiplication, we first need to calculate the sum and multiplication of the given fractions.
The sum of the fractions is:
(7/8) + (15/4) + (1/12)
To add these fractions, we need a common denominator. The least common multiple of 8, 4, and 12 is 24. Let's convert each fraction to have a denominator of 24:
(7/8) = (21/24)
(15/4) = (90/24)
(1/12) = (2/24)
Now we can add the fractions:
(21/24) + (90/24) + (2/24) = (113/24)
The multiplication of the fractions is:
(7/8) * (15/4) * (1/12)
To multiply fractions, we multiply the numerators and denominators:
(7*15*1) / (8*4*12) = (7/96)
Now we can divide the sum of the fractions by their multiplication:
(113/24) / (7/96)
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
(113/24) * (96/7) = (2712/168)
Therefore, the division of the sum of (7/8), (15/4), and (1/12) by their multiplication is (2712/168).
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Write an integer to represent a 6 yard loss in football.
Answers
Answer: - 6.
Step-by-step explanation:
The set of integers is the set of the whole numbers. {..., -1, 0, 1, 2, ...}
We want to represent a loss by 6 yards in football.
Because this is a loss, we should use a negative number, then we can use:
-6
This represents the number of yards by which your team losts.
Notice that I did not write the units, this is because:
-6 yards is a measure, furthermore can be "an integer number of yards"
-6 is an integer.
In a study relating college grade point average to time spent in various activities, you distribute a survey to several students. The students are asked how many hours they spend each week in four activities: studying, sleeping, working, and leisure. Any activity is put into one of the four categories, so that for each student the sum of hours in the four activities must be 168. a) Consider the model GPA = β0 + β1study + β2work + β3leisure + β4sleep + u. Interpret the coefficient β1. Does it make sense to hold work, leisure, and sleep fixed, while changing study? b) Explain why this model violates Assumption MLR.3. c) How could you reformulate the model so that its parameters have a useful interpretation and it satisfies Assumption MLR.3?
Answers
Step-by-step explanation:
Given
GPA = NO + B1Study + B2work + B3leisure + B4sleep + u
1. No it makes no sense. There is an intercorellation between these explanatory variables. Changing study while holding the rest variables constant or fixed would not make sense. If study us changed then one or more of the other predictors should be changed so that they can still be equal to 168
2. Study is a perfect linear function of work, leisure and sleep. There is the problem of multicollinearity among these independent variables. One assumption of the MLR is no multicollinearity.
3. To reformulate model, you have to drop the variable that is having the issue. Let's say that leisure is dropped from the model. After this the assumption is satisfied.
GPA = b0 + B1Study + b2sleep + b3work + u
On a scale drawing of a fence, 3.75 inches represents 24 feet. What os the actual length of a fence that is 2.8 inches long in the drawing?
Answers
Therefore , the solution of the given problem of unitary method comes out to be the fence's true length is about 17.92 feet.
Definition of a unitary method.Use the tried-and-true fundamental method, the actual variables, and any relevant information gleaned from general and specific questions to complete expression the assignment. Customers may be given another chance to taste the products in response. If these adjustments don't happen, we'll lose out on significant advancements in our understanding of programmes.
Here,
We can utilise the idea of proportions to determine the fence's actual length based on the scale drawing.
Given:
24 feet are represented by 3.75 inches at the given scale.
Let's establish a ratio:
=> 24 feet x 3.75 inches = 2.8 inches
where x represents the fence's real length.
If we cross-multiply, we obtain:
=> 24 feet * 2.8 inches * 3.75 inches
If we simplify, we get:
=> 3.75x = 67.2
By multiplying both sides by 3.75, we obtain:
=> x = 67.2 / 3.75
=> × ≈ 17.92 feet
Therefore, the fence's true length is about 17.92 feet.
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Solve for a in the figure shown.
122
1499
A
58°
B
31°
U
31°
D
27°
Answers
Answer: 58 is the answer
hope this help and here my steps use a mark or a pin
and line it with the line if it's wrong sorry for the wrong
answer
Check the picture below.
Whitney's Diner sold 96 milkshakes last week. 25% of the milkshakes had whipped cream on top. How many milkshakes with whipped cream were sold?
Answers
Number of milkshake with whipped cream will be 24.
What is mean by Percentage?
A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
To Calculate the percent of a number , divide the number by whole number and multiply by 100
Given that;
Whitney's Diner sold 96 milkshakes last week.
25% of the milkshakes had whipped cream on top.
Now,
Total number of milkshake = 96
Milkshakes with whipped cream on top = 25%
Hence, Number of milkshakes with whipped cream on top is;
= 25% of 96
= 25 / 100 x 96
= 96 / 4
= 24
Thus, Number of milkshake with whipped cream will be 24.
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Sam is collecting money for an animal shelter. He collects $150.00 each day for 6 days. The shelter will use 35% of the money he collects to buy pet food. The rest of the money will be used to buy cleaning supplies.
How much of the money that Sam collects will be used to buy cleaning supplies?
Answers
According to the solving Sam will spend $585.00 of the money he collects on cleaning materials.
What do the percentages mean?%, a relative figure signifying hundredths of any amount. Since one percent (symbolised as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified. percentage. Mathematical percentile is a related topic.
According to the given information:Sam collects $150.00 each day for 6 days, so the total amount he collects is:
$150.00/day x 6 days = $900.00
The shelter will use 35% of the money he collects to buy pet food. To find out how much money will be used to buy pet food, we can multiply the total amount Sam collects by 35% (or 0.35):
$900.00 x 0.35 = $315.00
So, $315.00 of the money that Sam collects will be used to buy pet food. To find out how much money will be used to buy cleaning supplies, we can subtract the amount used to buy pet food from the total amount collected:
$900.00 - $315.00 = $585.00
$585.00 of the money that Sam collects will be used to buy cleaning supplies.
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At a spa, the cost of a manicure is $25 and a person decides to leave a 20% tip. What was the total cost of the manicure, including tip?
Answers
The cost of a manicure is $25.
We want to find the 20% of $25. We have the following equivalence
20% → ?
100% → $25
If we divide each side of the equivalence we will have the same answer
\(\begin{gathered} \frac{20}{100}=\frac{?}{25} \\ \frac{1}{5}=\frac{?}{25} \end{gathered}\)Multiplying both sides by 25 we have:
\(\begin{gathered} 25\cdot\frac{1}{5}=\text{?} \\ 5=\text{?} \end{gathered}\)Then the person decides to leave $5 (that is the 20% of $25)
Then, the total cost including the tip is $25 + $5 = $30
Answer: $30You got 84 of 100 questions on the test correct. What percent did you get correct?Answer: 84%100%16%8.4%11/100 is equal to what percent?Answer: 110%10%89%11%3 out of 4 students in your class are girls. What percent of the class are girls?Answer: 3%4%75%25%
Answers
15 PIONTS! HELP ASAP >3
What is the value of 2 - (-2)?
Answers
Answer:
4
Step-by-step explanation:
key = leave, change, opposite
leave the first value
change the minus sign to a plus sign
change the second value to its opposite, which is 2
2+2=4
therefore it is 4.
five thousand, three and
fourteen ten-thousandths.
Answers
how would i anwser this? help pls!
Answers
Answer:
Step-by-step explanation:
To get the y values all you need to do is substitute the x value in the equation y=-2/3x+7.
For example:
y=-2/3(-6)=7
-2/3x6=-4
-4+7=3
(-6,3)
You can double check your work by filling the x and y coordinates in the equation and when solved if it it true you know you were correct.
To get the x value, you need to fill in the y in the equation y=-2/3x+7
for example:
5=-2/3x+7
-2=-2/3x
3=x
(3,5)
y=-2/3x+7
y=-2/3(15)+7
y=-10+7
y=-3
(15,-3)
y=-2/3x+7
15=-2/3x+7
8=-2/3x
-12=x
(-12,15)