The half-life of this radioactive element is approximately 2 years.
We have,
The decay of a radioactive element follows an exponential decay model of the form:
[tex]N = N_0 e^{-kt}[/tex]
where:
N0 is the initial concentration of the radioactive element
N is the concentration after time t
k is the decay constant
We are given that the element has decayed to 1/32 of its original concentration, which means that its current concentration is 1/32 times its initial concentration:
N/N0 = 1/32
Taking the natural logarithm of both sides and rearranging, we get:
ln(N/N0) = ln(1/32) = -3.465
Now we can use the formula for half-life, which relates the decay constant to the half-life t1/2:
t1/2 = ln(2) / k
We can solve for the decay constant k by using the information that the element has decayed to 1/32 of its original concentration in 10 years:
ln(N/N0) = -kt
-3.465 = -k x 10
k = 0.3465
Substituting this value of k into the formula for half-life, we get:
t1/2 = ln(2) / k = ln(2) / 0.3465 = 2.0 x 10^0 years = 2 years.
Therefore,
The half-life of this radioactive element is approximately 2 years.
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Muriel translated the phrase below into an algebraic expression and then evaluated it for n = 4.
the product of a number and 8
Which of the following contains the correct expression and value?
Answer:
[tex]8n=32[/tex]
Step-by-step explanation:
Muriel's algebraic expression for the phrase "the product of a number and 8" would be 8n, where n represents the number. When n = 4, the value of 8n would be 8 times 4, which is 32. Therefore, the correct expression and value is 8n = 32 when n = 4.
Answer:
8n=32
Step-by-step explanation:
got it right on homework
what is the value of sin B?
8/17
17/15
15/17
8/15
The sine of angle B is obtained dividing the length of the opposite side to angle B by the length of the hypotenuse.
What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined on the bullet points below:
Sine of angle = length of opposite side to the angle divided by the length of the hypotenuse of the triangle.Cosine of angle = length of adjacent side to the angle divided by the length of the hypotenuse of the triangle.Tangent of angle = length of opposite side to the angle divided by the length of the adjacent side to the angle of the triangle.Missing InformationThe problem is incomplete, hence the general procedure to obtain the sine of angle B is presented.
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Convert 135° from degrees to radians.
Answer: 2.35619
Step-by-step explanation: Hope this helps! :)
Evaluate the algebraic expression t + s - r when r=13, s=10, t = 7 and u=15,
A) 2
B) 4
C) 16
D) 30
Accounting 125000 loan for 5 years to start business
Owner paid 250 to the county for a business license
Answer:
p
Step-by-step explanation:
ok so first u take away the underlined letter and give and carry sorry the first one
Question content area top
Part 1
The length of a rectangular park is six times its width. The park is surrounded by a 3-foot-wide path. Let x denote the width of the park. Write a quadratic function to represent the total area of the park and the path.
The quadratic function to represent the total area of the park and the path will be 6(x² + 7x + 6).
Given that:
Width, W = x
Length, L = 6x
Path width, d = 3
The rectangle's area will be given as,
Area of the rectangle = L × W square units
The quadratic function to represent the total area of the park and the path will be given as,
A = (x + 2 · 3) (6x + 2 · 3)
A = (x + 6)(6x + 6)
A = 6(x + 6)(x + 1)
A = 6(x² + 7x + 6)
The quadratic function to represent the total area of the park and the path will be 6(x² + 7x + 6).
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For question number 5
Answer: A' will be at (-2,0)
Step-by-step explanation:
Reflecting things over a line can be done in several different ways, I will try to explain the one I use and the easiest one. What I use is to look at it and find the shortest distance between the line and A, in this case, the shortest distance is at (-.5,1.5), since A is at (1,3) the distance between them is (-1.5,-1.5) If you double this change you will find how far away the new point A is from the Old point, so its a change of (-3,-3). (1,3)+(-3,-3) gets you to the final points of (-2,0)
Another, probably easier, method is to go down from point A until you hit the line, and then go over that many points. In this case, you go down 3 from A to hit the line, and then go 3 to the left which reflects it over the line. Either way you do it, you get (-2,0)
Please help with this question I’m stuck brainiest and points will be rewarded
Matching of the statements with their respective linear equations are:
1) The line contains (0, -8) and a slope of 3/2: y = ³/₂x - 8
2) A line that contains the point (0, -2) and (4, 0): 2y - x = -4
3) y-intercept is (0, -2) and slope is -3/4: y = -³/₄x - 2
4) A line that has a slope of 5/3 and a y-intercept of -4: 5x + 3y = -12
How to Identify the linear equation?The formula for the equation of a line in slope intercept form is:
y = mx + c
where:
m is slope
c is y-intercept
1) The line contains (0, -8) and a slope of 3/2
The only option that even has a slope of 3/2 is option B with the equation: y = ³/₂x - 8
2) A line that contains the point (0, -2) and (4, 0)
The only one that fits this is option C with the equation:
2y - x = -4
3) y-intercept is (0, -2) and slope is -3/4.
This means the only equation that matches it is:
y = -³/₄x - 2
4) A line that has a slope of 5/3 and a y-intercept of -4.
This means the only equation that matches it is:
5x + 3y = -12
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I can prove that 2=1, where is the error?
X = 1
X+X = 1+X
2x = 1+X
2x = X+1
2X-2 = X+1-2
2x-2 = X-1
2 (x-1)/(x-1) = X-1/X-1
2 times 1 = 1 1-1 / 1-1
2 = 1
I subtracted -2
because thats the # I chose to subtract with.
The mistake is when you try to divide by X - 1, because you can't divide by zero.
Where is the problem in this procedure?Here we start by defining:
X = 1
The second step makes sense, we are adding the same value in both sides:
X + X = X + 1
2X = X + 1
Now subtract 2 in both sides:
2X - 2 = X + 1 - 2
2X - 2 = X - 1
Here is the mistake, you divide both sides by X - 1
But we already defined that X = 1
Then you are trying to divide by zero, and that opeartion is not defined, that is why you reach a false equation.
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Que tipo de corriente circula por el océano glaciar ártico ??
Answer:Transpolar Drift Stream y el anticiclónico Beaufort Gyre
Step-by-step explanation:
What is the nature of the roots of each quadratic equation?
1. [tex]x^{2}[/tex] + 5x + 3 = 0
2. [tex]2x^{2}[/tex] - 2x + 1 = 0
x² + 5x + 3 = 0, the quadratic equation has two distinct real roots
2x² - 2x + 1 = 0, no real roots. Instead, it has two complex conjugate roots.
x² + 5x + 3 = 0
To determine the nature of the roots of this quadratic equation, we need to calculate the discriminant using the formula:
Discriminant = b² - 4ac
where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c = 0.
In this case, a = 1, b = 5, and c = 3.
Discriminant = (5)² - 4(1)(3)
= 25 - 12
= 13
Since the discriminant is positive and not a perfect square, the quadratic equation has two distinct real roots
Now 2x² - 2x + 1 = 0
a = 2, b = -2, and c = 1
Plugging these values into the discriminant formula, we get:
b² - 4ac = (-2)² - 4(2)(1) = 4 - 8 = -4
Since the discriminant is negative, the quadratic equation 2x² -2x+1=0 has no real roots.
Instead, it has two complex conjugate roots.
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The phone case you want to buy is marked down 30%, and you have a 25% off coupon. You pay $42.00. Can this equation be used to find the original price of the phone case? If so, what is the original price of the item? Explain
Answer:
meaning that you're answer would be $7.34 please make brainliest
Step-by-step explanation:
can u please help me with number 3 the graph
This prompt has to do with the analysis of random outcomes. See the attached tables and graphs accordingly.
What are random outcomes?An exhaustive depiction of all possible marble combinations that may arise out of a chance experiment involving two random selections has been depicted in this table.
The table enlists five different-colored marbles available in a bag and elaborates its varying conclusions based on two distinct selections.
The columns indicate colors, whereas each result depicts two correlated choices made during an experiment's progression to illustrate randomness accurately.
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determine the volume of a sphere with a radius of 4.75 inches round your answer to the nearest hundredth use 3.14 for pie.
Answer:
Step-by-step explanation:
V≈448.92in³
r Radius = 4.75
V=4/3πr3=4/3·π·4.753≈448.9205in³
URGENT STATISTICS AND PROBABILITIES
Answer:
the expected point value is -1/5, so it is not advantageous to guess.
Step-by-step explanation:
1(1/5)+(-1/2)(4/5)
1/5-2/5
-1/5
A rectangular prism has a volume of 2288 cubic meters a height of 13 meters and a length of 22 meters. What is the measure of the missing dimension?
The measure of the missing dimension is 8 meters.
We are given that;
Volume= 2288 cubic meters
Height= 13meter
Length= 22meter
Now,
To find the width.
You can rearrange the formula to solve for width by dividing both sides by length and height:
Width = Volume / (length × height)
Plug in the given values:
Width = 2288 / (22 × 13)
Simplify:
Width = 2288 / 286
Width = 8
Therefore, by the given rectangular prism the answer will be 8 meters.
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dillon has a bank account that pays 3.2% simple interest. his balance is $1,766. how long will it take for the amount in the account to grow to $2,000? round to the nearest year.
It will take approximately 4 years for the amount in Dillon's bank account to grow to $2,000.
We use the formula for simple interest to solve this problem;
I = P × r × t
where;
I = the interest earned
P = the initial principal (balance) = $1,766
r = the interest rate (as a decimal) = 3.2% = 0.032
t = the time (in years) we need to find
We know that the interest earned is the difference between the final amount (balance + interest) and the initial principal (balance), so we can write;
Interest = Final Amount - Initial Principal
Plugging in the values, we get;
I = $2,000 - $1,766
I = $234
Now we can substitute the values of I, P, and r into the simple interest formula and solve for t;
234 = 1766 × 0.032 × t
Dividing both sides of the equation by (1766 * 0.032) to isolate t:
t = 234 / (1766 × 0.032)
t ≈ 4.19
So, it will take approximately 4.19 years for the amount in Dillon's bank account to grow to $2,000. Since time cannot be in decimal years, we round to the nearest whole year:
t ≈ 4
Therefore, it will take 4 years for the amount in Dillon's bank account to grow to $2,000.
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What is the equation of the line in the slope-intercept form?
Answer:
5y= -3x +15
Step-by-step explanation:
y=mx+c is slope Intercept form where M is slope and c is Intercept
Consider the parabola given by the equation:
f
(
x
)
=
−
2
x
2
−
8
x
+
14
Find the following for this parabola:
A) The value of
f
(
−
5
)
:
B) The vertex = (
,
)
C) The
y
intercept is the point (0,
)
D) Find the two values of
x
that make
f
(
x
)
=
0
. Round your answers to two decimal places. Write the values as a list, separated by commas:
x
=
Answer:
Sure, here are the answers to your questions:
**A) The value of $f(-5)$ is $-2$.**
To find the value of $f(-5)$, we can simply substitute $x=-5$ into the equation $f(x)=-2x^2-8x+14$. This gives us:
$$f(-5)=-2(-5)^2-8(-5)+14=-2(25)+40+14=-50+54=4$$
**B) The vertex of the parabola is $(2,6)$.**
To find the vertex of the parabola, we can complete the square. This involves adding and subtracting $\left(\dfrac{{b}}{2}\right)^2$ to both sides of the equation, where $b$ is the coefficient of the $x$ term. In this case, $b=-8$, so we have:
$$\begin{aligned}f(x)&=-2x^2-8x+14\\\\ f(x)+20&=-2x^2-8x+14+20\\\\ f(x)+20&=-2(x^2+4x)\\\\ f(x)+20&=-2(x^2+4x+4)\\\\ f(x)+20&=-2(x+2)^2\end{aligned}$$
Now, if we subtract 20 from both sides, we get the equation of the parabola in vertex form:
$$f(x)=-2(x+2)^2-20$$
The vertex of a parabola in vertex form is always the point $(h,k)$, where $h$ is the coefficient of the $x$ term and $k$ is the constant term. In this case, $h=-2$ and $k=-20$, so the vertex of the parabola is $(-2,-20)$. We can also see this by graphing the parabola.
[Image of a parabola with vertex at (-2, -20)]
**C) The $y$-intercept is the point $(0,14)$.**
The $y$-intercept of a parabola is the point where the parabola crosses the $y$-axis. This happens when $x=0$, so we can simply substitute $x=0$ into the equation $f(x)=-2x^2-8x+14$ to find the $y$-intercept:
$$f(0)=-2(0)^2-8(0)+14=14$$
Therefore, the $y$-intercept is the point $(0,14)$.
**D) The two values of $x$ that make $f(x)=0$ are $2.5$ and $-3.5$.**
To find the values of $x$ that make $f(x)=0$, we can set the equation $f(x)=-2x^2-8x+14$ equal to zero and solve for $x$. This gives us:
$$-2x^2-8x+14=0$$
We can factor the left-hand side of the equation as follows:
$$-2(x-2)(x-3)=0$$
This means that either $x-2=0$ or $x-3=0$. Solving for $x$ in each case gives us the following values:
$$x=2\text{ or }x=3$$
However, we need to round our answers to two decimal places. To do this, we can use the calculator. Rounding $x=2$ and $x=3$ to two decimal places gives us the following values:
$$x=2.5\text{ and }x=-3.5$$
Therefore, the two values of $x$ that make $f(x)=0$ are $2.5$ and $-3.5$.
I need help with solving and graph each of the following inequalities
The solution and graph of each of the inequalities is shown below:
k ≥ 4v < 17x ≤ 6y > 8g > 3.9w > -7What is an inequality?In Mathematics and Geometry, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;
Greater than (>).Less than (<).Greater than or equal to (≥).Less than or equal to (≤).Next, we would determine the solution for each of the inequalities as follows;
k + 7 ≥ 11
k ≥ 11 - 7
k ≥ 4
5 > v - 12
5 + 12 > v
17 > v
v < 17 (flip).
-5x ≤ -30
x ≤ 6
y/4 > 2
y > 2(4)
y > 8
10g + 19 > 49
10g > 49 - 19
10g > 39
g > 3.9
-w - 7 > 0
-w > 7
w > -7
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Jerry had 35 big stickers and 20 small stickers at first. He exchanged 10 small stickers for 5 big stickers. What percentage of his sticker are big stickers in the end?
(1) 10% (2) 20% (3) 40% (4) 80%
Answer:
80%
Step-by-step explanation:
After all the trade he got 50 stickers
40 Big
10 small
50 stickers is 100%
40B stickers is ??
WE multiply 40 by 100 then divide by 50
so 80%
Solve for θ if −10sinθ−8=5√3−8 and 0≤θ<2π.
The value of variable θ would be,
⇒ θ = 5π/3 and θ = 4π/3
We have to given that;
Expression is,
⇒ - 10sin θ - 8 = 5√3 - 8
Now, We can simplify as;
⇒ - 10sin θ - 8 = 5√3 - 8
⇒ - 10sin θ = 5√3
⇒ sin θ = - 5√3/10
⇒ sin θ = - √3/2
We know that sinθ = -√3/2 when θ = 4π/3 and θ = 5π/3 (among other angles).
However, since 0 ≤ θ < 2π, only the angles in the second and third quadrants are valid solutions for sinθ = -√3/2.
Therefore, the solutions are θ = 5π/3 and θ = 4π/3, option D is correct.
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Find the missing angle
Answer:
none
Step-by-step explanation:
None, 106 is from the numbers being added and it is a right angle
What function does this table make
Answer:
f(n) = 3^(n -1)
Step-by-step explanation:
You want a function that describes the relation shown in the table.
AnalysisThe values under Steps are sequential, which makes determining the function a lot easier.
The values listed under Black Triangles don't have a common difference, but they do have a common ratio:
r = 3/1 = 9/3 = 27/9 = 3
Exponential functionFor this function, we'll use 'n' as the independent variable (the number of steps), and we'll call the function 'f'.
For common ratio r and a pair of table values (n, f(n)) = (a, b), the exponential function can be written as ...
f(n) = b·r^(n -a)
With r=3 and (a, b) = (1, 1), this becomes ...
f(n) = 1·3^(n -1)
The multiplier 1 isn't really needed, so we can use ...
f(n) = 3^(n -1)
Classify the triangle described below.
A triangle with measures of x°, 4x°, and 4x° is a(n) triangle.
We can see that the triangle has two equal angles, then it is an isosceles triangle.
How to classify the triangle?Here we have a triangle where we know that the interior angles are:
x°, 4x°, and 4x°
remember that the sum of the interior angles of any triangle is 180°, then we can write the linear equation:
x + 4x + 4x = 180
Solving that for x we will get:
9x = 180
x = 180/9
x = 30
Then the angles are:
x° = 20°
4x° = 80°
4x° = 80°
We can see that we have two equal angles, then the triangle is an isosceles triangle.
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La empresa clarisse dedicada al rubro de telefónica, está ampliando su cobertura, debido a esto está colocando postes, donde la séptima parte de un poste está enterrada, y sobresale del suelo 25 metros. Calcular la altura del poste aproximado a los centímetros.
The approximate height of the pole in centimeters is 17,500 centimeters.
We have,
Let's start by calculating the total length of the pole, which is buried plus the part that protrudes from the ground.
We know that the part that protrudes is 25 meters and that it represents one-seventh of the total length.
25 = L/7
where L is the total length of the pole.
We can solve for L by multiplying both sides of the equation by 7:
L = 7 x 25
= 175 meters
Now we need to convert this length to centimeters.
Since 1 meter is equal to 100 centimeters,
175 meters x 100
= 17,500 centimeters
Therefore,
The approximate height of the pole in centimeters is 17,500 centimeters.
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The complete question.
The Clarisse company, dedicated to the telephone business, is expanding its coverage, due to this, it is placing poles, where the seventh part of a pole is buried, and protrudes 25 meters from the ground. Calculate the approximate height of the pole in centimeters.
HELP 15 POINTS
Solve for x.
X
12 cm
x = [?] cm
Round to the nearest hundredth.
620
The opposite side of the right triangle is determined as 10.6 cm.
What is the value of x?The value of x is calculated by applying trigonometry ratio as shown below;
we will use the short form; SOH CAH TOA
SOH = sin θ = opposite /hypothenuse side
TOA = tan θ = opposite side / adjacent side
CAH = cos θ = adjacent side / hypothenuse side
The hypotenuse side of the right triangle is given, and we are required to find the opposite side of the right triangle.
sin (62) = x/12
x = 12 sin (62)
x = 10.6 cm
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a. A train is traveling in a circular track of 53 km radius at 44 km per hour. Find in degrees the angle through which it turns in 1 minute.
Answer:
0.38 degrees.
Step-by-step explanation:
C = 2π(53) = 106π km
The train is traveling at a speed of 44 km/h, which is equivalent to (44/60) km/min since there are 60 minutes in an hour.
d = (44/60) km/min
θ = (d / C) x 360°
θ = [(44/60) / (106π)] x 360°
θ ≈ 0.38°
Therefore, the angle through which the train turns in 1 minute is approximately 0.38 degrees.
prove the identity tan3x-tanx =2sinxsec3x
PLEASE HELP ITS URGENT ILL GIVE YOU BRAINLIEST.
The following are daily high temperatures (°F) in Auckland, New Zealand: 75 67 83 90 79 74 70 71 72 78 76 67 66 80 77 77 84 74
Using the data above, make a box-and-whisker plot. If the set has outliers, use an * to show them.
if you answer as a troll I will report
Answer: The box goes from Q1 to Q3, with the middle spoken to by a line interior the box at Q2. The bristles expand from the box to the least and most extreme values. There's one exception, spoken to by an bullet (*), at the esteem of 90.
Step-by-step explanation: box and whisker plot:
|
90 ---| *
84 ---|
83 ---|
80 ---|_____
79 ---| |_____
| | |
76 ---| | |
| | |
72 ---|_____| |
71 ---| |
70 ---|___________|
66 75
