Answer:
6.38548 years
Step-by-step explanation:
1 = 2 [tex]e^{42k}[/tex]
1/2 = [tex]e^{42k}[/tex]
ln(1/2) = 42k ln(e)
ln(1/2)/42 = k
k = -0.01650
~~~~~~~~~~~~~~
45 = 50 [tex]e^{-0.01650t}[/tex]
45/50 = [tex]e^{-0.01650t}[/tex]
ln(45/50) = -0.01650 t ln(e)
ln(45/50)/ -0.01650 = t
t = 6.38548 years
The number of years for the radioactive element to reach a mass of 45 grams is given by t = 6.384129 years
What is half-life of an element?The half-life of a radioactive isotope is the amount of time it takes for one-half of the radioactive isotope to decay. The half-life of a specific radioactive isotope is constant; it is unaffected by conditions and is independent of the initial amount of that isotope.
Half-life (symbol t½) is the time required for a quantity (of substance) to reduce to half of its initial value
The decay constant λ is = 0.693/t½
where t½ is the half-life of the element
Given data ,
Let the number of years be t
Let the initial mass of the element be a = 50 grams
The final mass of the element be ( a - x ) = 45 grams
Now , Element X is a radioactive isotope such that every 42 years, its mass decreases by half
And , half life t½ = 42 years
So , the decay constant k = 0.693/t½
k = 0.693 / ( 42 )
k = 0.0165
And , k= 2.303/t {log (a/a-x)}
So , t = 2.303 / ( 0.0165 ) log ( 50/45 )
On simplifying , we get
t = 6.384129 years
Hence , the number of years for the radioactive element to reach 45 grams is 6.384129 years
To learn more about half-life of an element click :
https://brainly.com/question/16387602
#SPJ2
What is the solution to the system of equations graphed below? PLSSS HELP
Answer:
C (-2,0)
Step-by-step explanation:
Find the point where they intersect. It's (-2,0) on the graph
Answer:
C
Step-by-step explanation:
Looking at the graph, the solution is (-2, 0).
This is because on the x axis, the point is 2 units to left (negative number) and does not move on the y axis (leaving it at 0).
Another way to see this is by plugging in these coordinates into the system of equations:
0 = -2(-2) - 4
0 = 4 - 4
0 = 0
0 = -2 + 2
0 = 0
These are both correct, once again proving the solution is (-2, 0).
4. (03.05)
The graph shows the production of cars per day at a factory during a certain period of time. What is the domain of this function during this period? (1 point)
The domain is all real numbers o through 9.
The domain is all integers o through 9.
The domain is positive real numbers.
The domain is all positive integers.
Answer:
B. domain is all integers 0 through 9
Step-by-step explanation:
Domain values area usually plotted along the horizontal axis. In this case, the number of days is the domain of the of the function.
The domain of the function that is plotted on the graph ranges from 0, 1, 2 to 9.
1, 2, 3 to 9 are all integers. Therefore, we can conclude that the "domain is all integers 0 through 9."
14. The following solution contains errors. Identify the errors and explain why they are incorrect.
Explain what should have been done to answer the question properly.
Find AB, given that line AD is the perpendicular bisector of BC
Answer:
11
Step-by-step explanation:
because line AD divided the triangle ABC into two equal halves
This trapezium is drawn on a centimetre grid.
Find the area of the trapezium.
Answer:
20 unit²
Step-by-step explanation:
A trapezium is given to us on the grid and we need to find out the area of the trapezium . In order to find the area , we need to find the measure of the parallel sides and the distance between the parallel sides.
From the grid :-
[tex]\rm\implies Side_1 = 7 \ units [/tex]
[tex]\rm\implies Side_2 = 3 \ units [/tex]
[tex]\rm\implies \perp \ Distance =4 \ units [/tex]
Now here we got the two parallel sides of the trapezium and the distance between the two parallel sides. Now we can find the area as ,
[tex]\rm\implies Area_{Trapezium}= \dfrac{1}{2}\times ( s_1 + s_2) \times \perp \ Distance \\\\\rm\implies Area = \dfrac{1}{2} \times ( 7 + 3 ) \times 4 \ unit^2 \\\\\rm\implies Area = \dfrac{1}{2} \times ( 10) \times 4 \ unit^2 \\\\\rm\implies\boxed{\rm Area = 20 \ unit^2}[/tex]
What is value of x if 20x-10*110=50
Answer:
57.5
Step-by-step explanation:
20x - (10 x 110) = 50
=> 20x - 1100 = 50
=> 20x = 1150
=> x = 1150/20
=> x = 115/2
=> x = 57.5
A line segment has one endpoint of A (2,5) and a slope of (2/3). Find coordinates for B
Answer:
B could be (4,8), (6,11), (8,14), (10,17), (12,20), etc.
Step-by-step explanation:
quick mafhs
What is the probability that a random sample of 12 second grade students from the city in a mean reading rate of more than 96 words per minute?
Complete Question
The reading speed of second grade students in a large city is approximately normal, with a mean of 90 words per minute (wpm) and a standard deviation of 10 wpm.
What is the probability that a random sample of 12 second grade students from the city in a mean reading rate of more than 96 words per minute?
Answer:
[tex]P(\=x >96 )=0.01884[/tex]
Step-by-step explanation:
From the question we are told that:
Sample size [tex]n=12[/tex]
Sample mean [tex]\=x =90[/tex]
Standard Deviation [tex]\sigma=10[/tex]
Generally
[tex]\sigma_x=\frac{\sigma}{\sqrt{10}}[/tex]
[tex]\sigma_x=\frac{10}{\sqrt{12}}[/tex]
[tex]\sigma_x=2.887[/tex]
Generally the equation for P(\=x >96 ) is mathematically given by
[tex]P(\=x >96 )=P(Z>\frac{\=x-\mu_x}{\sigma_x})[/tex]
[tex]P(\=x >96 )=P*(Z>\frac{90-96}{2.887})[/tex]
[tex]P(\=x >96 )=1-P(Z<2.08)[/tex]
[tex]P(\=x >96 )=1-0.98116[/tex]
[tex]P(\=x >96 )=0.01884[/tex]
Solve the formula A = lw for /
Answer:
A/w = l
Step-by-step explanation:
A = lw
Divide each side by w
A/w = lw/w
A/w = l
In the function, g(x) = -2x , the independent variable has a value of 6. Find the value of the dependent variable.
Answer:
-12
Step-by-step explanation:
x=6
g(6)=-2*6=-12. Answered by Gauthmath
HELP I WILL GIVE BRAINLIEST
Answer:
A.) 6.4 units
Step-by-step explanation:
We can use the Pythagorean theorem to find the length of AB.
If we find the horizontal and vertical distance of A and B, we form a triangle, with leg lengths of 5 and 4.
Now, we just solve using the Pythagorean theorem.
5^2 = 25
4^2 = 16
25 + 16 = 41
sqrt 41 ≈ 6.4 units.
Hope this helps!
If there is something wrong, just let me know.
Can someone help me with this math homework please!
Answer:
C
Step-by-step explanation:
Find EH , given that line HF is the perpendicular bisector of EG
Answer:
EH = 5
Step-by-step explanation:
HF is the perpendicular bisector of EG , then
EH = HG = 5
as part of a weight loss plan, Levi's average calories consumed per day, denoted by c, subject to a maximum of 15 calories, is measured to calculate the amount of weight he will lose. if he is losing weight consistently, what is the domain of the function
Answer:
The domain is;
0 < c ≤ 15
Step-by-step explanation:
We are told that Levi's average calories consumed per day is denoted by c.
Now, we are told it is subject to a maximum of 15 calories.
Thus; c ≤ 15
Now,if he is losing weight consistently, then c must be greater than 0.
Thus,the domain is;
0 < c ≤ 15
A grocery store recently sold 12 cans of soup, 6 of which were black bean soup. Based on experimental probability, how many of the next 20 cans sold should you expect to be black bean soup?
Answer:
10
Step-by-step explanation:
P(black bean soup) = cans of black bean / total = 6/12 =1/2
out of the next 20
20 *P(black bean)
20 * 1/2 = 10
The functions f and g are defined as follows.
Answer:
f(4) = -14
g(-2) = 22
Step-by-step explanation:
f(x) = -4x+2
Let x = 4
f(4) = -4*4 +2
= -16+2
= -14
g(x) = -3x^3 -2
Let x = -2
g(-2)= -3(-2)^3-2
= -3(-8)-2
= 24-2
=22
[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}[/tex]
Here,
f(x)=-4x+2
we have to find the value of f(4)
[tex]\sf{f(4)=-4(4)+2=-16+2=-14 }[/tex]g(x)=[tex]{-3x^3-2 }[/tex]
we have to find the value of g(-2)
[tex]\sf{g(-2)=-3(-2)^3-2 }[/tex] [tex]\sf{ g(-2)=-3(-8)-2 }[/tex] [tex]\sf{g(-2)=24-2=22 }[/tex] More information:-[tex]\begin{gathered} \: \: \: \footnotesize{\boxed{\begin{array}{c|c} \\\\{\bf {f(4)}} & {\bf {-14}} \\ \\\\ \text{g(-2)} & \sf{22} \end {array}}}\end{gathered}[/tex]
Jamar has 90 cents in his pocket. One coin is a quarter, and the others are
nickels. How many nickels does he have?
A. 23
B. 65
C. 13
D. 15
Answer:
C. 13
Step-by-step explanation:
Quarters are worth 25 cents each
Nickels are worth 5 cents each
Let n be the number of nickels that Jamar as in his pocket.
We already know that he only has 1 quarter in his pocket which is worth 25 cents, so we can form this equation:
5n + 25 = 90
5 meaning that each nickel is worth 5 cents, 25 meaning that he has only 1 quarter in his pocket (25 cents) and 90 meaning that he has a total of 25 cents in his pocket.
We have to isolate the n so we can subtract 25 from both sides to get:
5n = 65
After that we can get n by dividing 5 from both sides:
n = 13
Therefore there are 13 nickels in his pocket.
Let me know if I did anything incorrectly.
The number of nickels he has is 13. The correct option is C.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that quarters are worth 25 cents each and nickels are worth 5 cents each.
Let n be the number of nickels that Jamar has in his pocket.
We already know that he only has 1 quarter in his pocket which is worth 25 cents, so we can form this equation:
5n + 25 = 90
5 meaning that each nickel is worth 5 cents, 25 meaning that he has only 1 quarter in his pocket (25 cents), and 90 meaning that he has a total of 25 cents in his pocket.
We have to isolate the n so we can subtract 25 from both sides to get:
5n = 65
After that we can get n by dividing 5 from both sides:
n = 13
Therefore, the number of nickels he has is 13. The correct option is C.
To know more about expression follow
brainly.com/question/723406
#SPJ2
Find the surface area of the composite figure. Round to the nearest square centimeter
Answer:
Surface area = 726 cm²
None of the options is correct.
Step-by-step explanation:
Surface area of the composite figure = surface area of cone + surface area of cylinder - 2(area of base of cone)
✔️Surface area of cone = πr(r + l)
Where,
Radius (r) = 5 cm
Slant height (l) = √(10² + 5²) (Pythagorean theorem)
Slant height (l) = 11.2 cm
Plug in the values
= π*5(5 + 11.2)
= 254.5 cm²
✔️Surface area of the cylinder = 2πr(h + r)
r = 5 cm
h = 15 cm
Plug in the values into the formula
S.A = 2*π*5(15 + 5)
S.A = 628.3 cm²
✔️area of base of cone = πr²
r = 5 cm
Area = π*5² = 78.5 cm²
✅Surface area of the composite figure = 254.5 + 628.3 - 2(78.5)
= 882.8 - 157
= 726 cm² (nearest square meter)
None of the options is correct.
On a coordinate plane, a triangle has points A (negative 2, negative 2), B (1, negative 5), and C (negative 5, negative 5).
If a translation of T2, –7(x, y) is applied to ΔABC, what are the coordinates of B'?
Answer:
The answer is number 2. hope that helps
Answer:
(3,-12)
Step-by-step explanation:
the triangle has points A(-2,-2) B(1,-5) and C(-5,-5) the translation of (2 horizontally,-7 vertically) will cause B to translate to coordinates (3, -12)
The dimensions of a garden are 300' by 200'. If a model garden with the
scale of 10' = 1" is to be made, find the dimensions of the model.
A.) 3" by 1"
B.) 30" by 20"
C.) 45" by 10"
D.) 60" by 20"
Answer:
B
Step-by-step explanation:
We know that 10' = 1". We want to find a x and y for 300' = x" and 200' = y". We can do this by figuring out ratios between similar values. For the numbers ending in ', we can say that 300/10 = 30 and 200/10 = 20. Therefore, to get x and y, we can multiply
10' = 1" by 30 on both sides to get
300' = 30"
and multiply by 20 on both sides to get
200' = 20"
Therefore, we can say that 300' by 200' = 30" by 20"
asap please help! and explain how you got the answer!
A dilation maps (8, 12) to (2, 3). What are the coordinates of the image of (9, 3) under
the same dilation?
Answer:
(9/4,3/4) or (2.25, 0.75)
Step-by-step explanation:
The dilation is 1/4. We can tell this by looking at (8,12) and (2,3). 8*1/4=2 and 12*1/4=3. So therefore we just need to times 9 and 3 by 1/4. 9*1/4=2.25 or 9/4 and 3*1/4=0.75 or 3/4. so the dilation (9/4, 3/4). I believe this is correct but if I am not please tell me.
A house has increased in value by 28% since it was purchased. If the current value is $288,000, what was the value when it
was purchased?
Answer:
$368,640
Step-by-step explanation:
288,000 * .28 = 80640
288,000 + 80640 = 368640
5x + 4 < X-5, when X belongs to Z
Answer:
Step-by-step explanation:
5x+4<x-5
5x-x<-5-4
4x<-9
x<-9/4
x=(-∞,...,-4,-3]
Answer:
Step-by-step explanation:
5X + 4 < X - 5
5x - x < -5-4
4x<-1
4x/4 > -1/4
x>-1/4
Please help, I will give brainliest if you explain.
Answer:
A.
Step-by-step explanation:
Basically.. when you draw a line from the vertex of a right triangle's 90 degree angle to its hypotenuse, it'll make two triangles with the same angles. Then you can use ratios to discern the size of said rectangles. I hope that helps.
rút gọn √(6-3(√(2+√3)-√(2+√(2+√3)
Answer:
10
Step-by-step explanation:
not sure please verify
Find the value or JM in the image below
Las dimensiones de un paquete de galletas son 2 cm x 0.75 cm x 25 cm. Cuántos paquetes de galletas caben en una caja cuyas dimensiones son 2 cm de ancho, 75 cm de largo y 2.5 cm de alto?
Least common factor how to do in 121,99
Answer:
Step-by-step explanation:
Prime factorize 121 and 99
121 = 11 * 11
99 = 11 * 3 * 3
Common factor = 11
Type the equation used and answer for credit:
1) You bought a car that was $25500 and the value depreciates by 4.5% each year.
The general Population equation is modeled by: V(x) =
***
a. How much would the car be worth after 5 years?
the Evaluated equation I used to get the following answer is
and
the answer after 5 years the car is worth
dollars.
b. How much would the car be worth after 8 years?
the Evaluated equation I used to get the following answer is
and
After eight years the car is worth
dollars.
