The half-life of bismuth-210 is given as follows:
5 days.
How to model an exponential function?A decaying exponential function is modeled as follows:
y = a(1 - r)^t.
In which the parameters are given as follows:
a represents the initial value.r represents the decay rate, as a decimal.For this problem, we have that:
a = 122.y(21) = 6.64.Hence the decay rate is obtained as follows:
[tex]6.64 = 122(1 - r)^{21}[/tex]
[tex](1 - r)^{21} = \frac{6.64}{122}[/tex]
[tex]((1 - r)^{21})^{\frac{1}{21}} = \left(\frac{6.64}{122}\right)^{\frac{1}{21}}[/tex]
1 - r = 0.8706
r = 1 - 0.8706
r = 0.1294.
Hence the function is given as follows:
y = a(0.8706)^t.
The half-life is the value of t for which:
y = 0.5a.
Hence:
0.5a = (0.8706)^t.
(0.8706)^t = 0.5
log((0.8706)^t) = log(0.5)
tlog(0.8706) = log(0.5)
t = log(0.5)/log(0.8706)
t = 5 days.
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Which of the following triangles is congruent to triangle PQR?
Third triangle is congruent to triangle PQR.
Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved.
For triangles, there are five primary congruency rules:
Side-Side-Side is an SSS criterion.
The side-angle-side SAS criterion.
Angle, Side, Angle is an ASA criterion.
Angle-Angle-Side is an AAS criterion.
Right Angle Hypotenuse Side (RHS) Criteria
As Height of the triangle PQ is similar to triangle third
Angle 90° ≈ Angle 90° of third triangle
Angle 67° ≈ Angle 67° of third degree
So, By ASA, both the triangles are congruent.
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need help with this can you help me
When two lines are parallel, they do not intersect, so there will be no angle formed between them. Therefore, the number of 90° angles formed by the intersection of EF and the two parallel lines AB and CD is zero.
Identify the initial amount a and the rate of decay r (as a percent) of the exponential function h(t)=1250(0.865)^t. Evaluate the function when t=3 . Round your answer to the nearest tenth.
When t = 3, the exponential function has a value of 809.0.
What is exponential function?The exponential function is a mathematical function denoted by f(x)=\exp or e^{x}. Unless otherwise indicated, the word refers to a positive-valued function of a real variable, however it can be extended to complex numbers or applied to other mathematical objects such as matrices or Lie algebras. A mathematical function of the following type is an exponential function: f (x) = an x, where x is a variable and an is a constant known as the function's basis. The transcendental number e, which is about 2.71828, is the most often encountered exponential-function base.
Here,
Given the exponential function h (t) = 1250(0.865)^t
When t = 3
h(3) = 1250(0.865)^3
h(3) = 1250 (0.6472)
h(3) = 809.0
The exponential function when the value of t is 3 is 809.0.
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What is the equation of this table?
Answer:
y = 1/4x +1/8
Step-by-step explanation:
You want to know the equation of the table showing a linear function and points (0, 1/8), (1, 3/8).
Y-interceptThe y-intercept of the line described by this table is the y-value when x=0. That value is 1/8.
SlopeThe slope of the line described by the table is the difference in y-values for a difference in x-values of 1. The difference between x=1 and x=0 is ...
∆y = 3/8 -1/8 = 2/8 = 1/4
Slope-intercept equationThe slope-intercept equation for the table is then ...
y = mx +b . . . . . . . line with slope m and y-intercept b
y = 1/4x +1/8 . . . . . line with slope 1/4 and y-intercept 1/8
The equation of the table is ...
y = 1/4x +1/8
Which statement is true of table A and table B shown below?
Table A represents a function because there is only one output for
each input value.
Table B represents a function because there is only one output for
each input value.
Table A represents a function because there is only one input for each
output value.
Table B represents a function because there is only one input for each
output value.
Table A represents a function, but Table B does not represent a function.
What is a function?
A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.
A function or mapping is described as a collection of pairs of x and y that are ordered such that given different values of x, there will also be different values of y, or vice versa. For instance, the function x=y+2 yields a different x for every different value of y, while yielding the same x value for every single different value of y. We obtain two distinct x for two distinct ys, thus we can refer to this as a function at that point.
As, each element of X is associated with unique element of Y, so this is a function.
Table A
X Y
3 1
2 0
1 0
As, each element of X is associated with a unique element of Y, so this is a function.
Table B
X Y
3 -2
5 1
5 2
Hence, Table A represents a function, but Table B does not represent a function.
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What is the value of y in the triangle? a 30-60-90 triangle with long leg length y and hypotenuse length 6 a. B. C. D.
The value of y in the right triangle is found to be 3√3 units.
Explain the term trigonometric ratios?Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six common uses for an angle in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their names, respectively, as well as their abbreviations.Given data:
Right triangle with angles:30-60-90.Long length = y.Hypotenuse length = 6So, apply trigonometric ratios:
cos 30 = y / 6
y = cos 30 * 6
y = √3 / 2 * 6
y = 3√3
Thus, the value of y in the triangle is found to be 3√3 units.
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42
1. Solve for the missing angle measures.
1)
a = 75⁰
d
b
2)
a
b
d=1040
The angle created by the two rays or arms at a shared vertex is known as the angle measure in geometry.
How do you find an angle measure?With a protractor, you can determine how large an angle is. Alternatively, the congruent angles could be indicated on the figure by an arc. Supplementary angles are two angles whose combined measurements are 180°, such as two right angles since 90° + 90° Equals 180°. the measurement of an angle wherein 1 degree equals 1/360 of a circle.
An angle (created by perpendicular lines) that is exactly 90 degrees is called a right angle. Less than 90 degrees is considered an acute angle. Revolutions, degrees, and radians are the three types of angles that can be measured. Degrees serve as a more widely used measurement unit. In order for a right angle to be 90 degrees, a circle must be divided into 360 equal degrees.
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What is the scale factor of the dilation in the similarity transformation?
The scale factor of a similarity transformation is the ratio of the lengths of the corresponding sides of the two similar figures.
What is scale factor?The scale factor is a ratio between two corresponding lengths, areas, or volumes of two similar figures. It is used to compare the size of one figure to another, as well as to enlarge or reduce the size of a figure. The scale factor is expressed as a ratio, such as 1:2, where the first number is the original size and the second is the new size.
It is usually represented as a decimal or fraction, and can be calculated by dividing the length of one of the sides of one figure by the length of the corresponding side of the other figure. For example, if we have two triangles with corresponding sides that measure 3 units and 6 units, then the scale factor of the dilation is 0.5 (3/6). This means that the second triangle is half the size of the first.
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What is the result of dilating a figure using a scale factor of 1?
When a figure is dilated using a scale factor of 1, the resulting figure is the same as the original figure.
This is because a scale factor of 1 means that the dimensions of the original figure are not changed in any way.
Mathematically, this is represented by the equation:
Original Length x Scale Factor = Resulting Length
For a scale factor of 1, the equation simplifies to:
Original Length x 1 = Resulting Length
Therefore, the resulting length is equal to the original length.
For example, if a line had a length of 5 units before dilating, the resulting length would be 5 units after dilating.
5 units x 1 = 5 units
This is because the scale factor of 1 does not change the length of the line in any way.
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Given f(x) = -4x² + 4x - 1, find f(-6)
Please!!!
Answer:
Step-by-step explanation:
To find f(-6), we need to substitute -6 for x in the function f(x) = -4x² + 4x - 1.
f(-6) = -4(-6)² + 4(-6) - 1
f(-6) = -4(36) + (-24) - 1
f(-6) = -144 + (-24) - 1
f(-6) = -167
Therefore, f(-6) = -167
There are x sparrows in a tree. There are 50 sparrows on the ground beneath the tree. Let y represent the total number of sparrows in the tree and on the ground.
A. Express y in terms of x
B. Make a table to show the relationship between y and x. Use values of x=10,20,30,40, and 50 in your table
We can write the linear equation:
y = x + 50
And evaluating it on the given values of x, we will get the table:
x y
10 60
20 70
30 80
40 90
50 100
How to express y in terms of x?We know that there are x sparrows in a tree, and there are 50 sparrows on the ground beneath the tree.
y represents the total number of sparrows, then y is equal to the number of sparrows on the tree (x) plus the ones beneath (50) then we will get:
y = x + 50
B) Now we want to make a table. To make that table, we need to evaluate the linear equation in different values of x.
if x = 10
y = 10 + 50 = 60
if x = 20
y = 20 + 50 = 70
if x = 30
y = 30 + 50 = 80
if x = 40
y = 40 + 50 = 90
if x = 50
y = 50 + 50 = 100
Then the table will be:
x y
10 60
20 70
30 80
40 90
50 100
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I need help asap! Please and thank you
Amanda bought a dektop computer and a laptop computer. Before finance charge, the laptop cot more than the dektop. She paid for the computer uing two different financing plan. For the dektop the interet rate wa per year, and for the laptop it wa per year. The total finance charge for one year were. How much did each computer cot before finance charge?
The desktop computer cost $1750 before the finance charge, and the laptop cost $1900 before the finance charge.
The discipline of finance is the study of money, money systems, and capital assets. It is associated with economics, which is the study of the production, distribution, and consumption of money, assets, products, and services, but is not the same thing
Let x be the cost of the desktop computer before finance charges.
We know that the laptop cost 150 more than the desktop, so the cost of the laptop is x+150
We also know that the total finance charge for one year is $303 and the interest rate of the desktop is 7% and the interest rate of the laptop is 9.5%
So we can set up the following equations using the information provided:
(x*0.07) + ((x+150)*0.095) = 303
Simplifying and solving for x:
0.07x + 0.095x + 14.25 = 303
0.165x = 288.75
x = $1750
Therefore, the desktop computer cost $1750 before the finance charge, and the laptop cost $1900 before the finance charge.
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Kathy has a job on the farm she earns $3.20 every 15 minutes she picks green peppers.
she earns $3.00 every 20 minutes she picks carrots.she picked green peppers for 45 minutes and then spent an hour picking carrots. how much money did Kathy earn?
The total money earned after working the given number of hours is $18.60.
What is cross-multiplication?When using the cross-multiplication approach, the denominator of the first term is multiplied by the numerator of the second term, and vice versa.
Given that to pick green peppers:
15 minutes = $3.20
45 minutes = x
Using cross multiplication solve the above equation:
[tex]x = \frac{(3.20)(45)}{15} \\\\x = 9.60\\[/tex]
For picking carrots:
20 minutes = $3. 00
1 hour = 60 minutes = x
Using cross multiplication solve the above equation:
[tex]x = \frac{(3)(60)}{20}\\ \\x=9[/tex]
The total amount made after all the work is:
A = 9.60 + 9
A = 18.60.
Hence, the total amount of money she earned after all the work is $18.60.
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Please help, the "Pagemarker/Pencil and Paper" thing at the top of the page just means to digitally write the answer where needed. Thank you sm.
-3x=4y+8 is a continuous and linear equation and it can be written as y=-3/4x-2
What is slope intercept form of line?The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The given equation is -3x=4y+8
This equation can written in y=mx+b form
-3x=4y+8
Add 3x on both sides
0=4y+3x+8
Subtract 4y on both sides
-4y=3x+8
Multiply with minus
4y=-3x-8
y=-3/4x-2
The line is continuous and linear
Hence, -3x=4y+8 is a continuous and linear equation and it can be written as y=-3/4x-2
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Assume the two triangles shown are similar then the missing length
On solving the provided question, we can say that - Since the two triangle are similar and each sides are 3 times the others, so x= 3 X 4 = 12 cm
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
Since the two triangle are similar
\and each sides are 3 times the other,
so x= 3 X 4 = 12 cm
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help is needed please
Answer:
A = 72 units²
Step-by-step explanation:
the area (A) of a trapezoid is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )
where h is the perpendicular height between the bases b₁ and b₂
note that the middle section of the lower base = upper base = 6
here h = 8 , b₁ = 3 + 6 + 3 = 12 , b₂ = 6 , then
A = [tex]\frac{1}{2}[/tex] × 8 × (12 + 6) = 4 × 18 = 72 units²
nine divide by 60?? and nine divided by 390
When nine is divided by 60 , the quotient would be 0. 15 .
The quotient when nine is divided by 390 is 0. 023 or 3 / 130 .
How to find the quotient ?The quotient refers to the result when a number is divided by another number as is the case with nine being divided by 60 .
The quotient is therefore :
= 9 ÷ 60
= 9 / 60
= 0. 15
The quotient for the division of nine by 390 is :
= 9 ÷ 390
= 9 / 390
= 0. 023
Another way to do this is to find the greatest common factor of nine and 390 which is 3 . Then use it to take the numbers to their simplest form. The quotient would then be :
= ( 9 / 3 ) / ( 390 / 3 )
= 3 / 130
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The future amount due on a compound interest loan of $12,000 at 7% compounded semiannually for four years is approximately ____. If the compounding period is increased to monthly, the amount due on the loan would be approximately ____
Part a: Future amount due on a compound interest loan is $12271.78.
Part b: The amount due on the loan would be $12033.64, if the compounding period is increased to monthly.
Explain the term compounding?Compounding is the method through which interest is added to both the principle balance already in place and the interest that has already been paid. Thus, compounding can be thought of as interest on interest, with the result that returns on interest are magnified over time, or the so-called "magic of compounding."The formula for compounding is:
A = P(1 + r/100n)∧nt
P = $12,000
r = 0.07
Part a: compounded semiannually.
t = 4 years.
n = 2
A = 12000(1 + 0.07/100*2)∧2*4
A = 12000*1.00280
A = 12271.78
Thus, future amount due on a compound interest loan is $12271.78.
Part b:
t = 4 years.
n = 12
A = 12000(1 + 0.07/100*12)∧12*4
A = 12000*1.0028038
A = 12033.64
Thus, if the compounding period is increased to monthly, the amount due on the loan would be $12033.64.
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Answer: $15,802
$15,865
Step-by-step explanation:
What is the law of exponential change?
The law of exponential change states that when a quantity grows or decays at a rate proportional to its size, then the quantity changes exponentially over time. In other words, it follows an exponential function as opposed to a linear function.
The law of exponential changeThe law of exponential change describes the phenomenon of a quantity changing exponentially over time. This means that the rate of change is proportional to the quantity itself. For example, if a quantity increases by 10% each minute, then the quantity will double every 7.2 minutes. This is because each time the quantity increases by 10%, it is multiplying by 1.1. This process is ongoing and the rate of growth or decay will continue to increase exponentially.
The law of exponential change is used in many areas of science and mathematics, such as population growth and radioactive decay. It is also an important concept in economics, as it can be used to measure the growth of money over time.
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V/-15=20 what does V equal?
Answer:
-300
just do inverse operation, and multiply both sides of the equation by -15 to cancel out the -15 from the denominator and you get V=20(-15)
solve for 20(-15) and you get -300
Suppose that 60% of the people who inquire about investments at a certain brokerage firm end up investing in stocks, 50% end up investing in bonds, and 44% end up investing in both stocks and bonds. What is the probability that a person who inquires about investments at this firm will invest in stocks or bonds (or both)?
Suppose that 60% of the people who inquire about investments at a certain brokerage firm end up investing in stocks. The probability that a person who inquires about investments at this firm will invest in stocks or bonds (or both) is 66%.
How to find the probability?60% invest in stocks
50% invest in bonds
44% invest in both bonds and stocks
Percent (only stock) = 60% -44%
Percent (only stock) = 16%
Percent (only bond) = 50% - 44%
Percent (only bond) = 6%
Percent (both) = 44%
Total = 16% + 6% + 44%
Total = 66%
Therefore the probability is 66%.
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Help with geometry similar triangles. Solve for x if ABC ~ JKL.
A line passes through the point (1, -9) and has a slope of 5.
Write an equation in slope-intercept form for this line.
Answer:
y = 5x - 14
Step-by-step explanation:
The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line crosses the y-axis).
Given that the line passes through the point (1, -9) and has a slope of 5, we can use the point-slope form of a line, which is y - y1 = m(x - x1)
Substituting the point and slope we have:
y - (-9) = 5(x - 1)
y + 9 = 5x - 5
Now we can solve for y by adding 9 to both sides of the equation:
y = 5x - 14
So the equation in slope-intercept form for the line that passes through the point (1, -9) and has a slope of 5 is:
y = 5x - 14
Answer:
y = 5x - 14
Step-by-step explanation:
The equation of a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line crosses the y-axis).
Given that the line passes through the point (1, -9) and has a slope of 5, we can use point-slope form to write the equation of the line. Point-slope form is written as: y - y1 = m(x - x1)
Where (x1, y1) is a point on the line, and m is the slope of the line.
We know that the line passes through the point (1, -9) and has a slope of 5, so we can substitute these values into the point-slope form:
y - (-9) = 5(x - 1)
Simplifying, we get:
y + 9 = 5x - 5
Now we can add 9 to both sides to get:
y = 5x - 14
So the equation of the line in slope-intercept form is y = 5x - 14
We can confirm that the point (1,-9) belongs to the line by substitute the values x =1 and y = -9 into the equation y = 5x - 14, if the equation holds true then the point belongs to the line.
PLEASE HELP I WILL GIVE BRAINLIST!
What is the length of the square’s side?
Answer:
x = 6 / sqrt(2)
Step-by-step explanation:
We are given the diagonal of a square
The side length is x
Using the Pythagorean theorem
x^2 + x^2 = h^2 where h is the length of the hypotenuse which is 6
x^2+x^2 = 6^2
2x^2 = 36
x^2 = 18
Taking the square root of each side
sqrt(x^2) = sqrt(18)
x = 3 sqrt(2)
This can be rewritten as
x = 3 sqrt(2) * sqrt(2)
------------------------
sqrt(2)
x = 3*2
-------
sqrt(2)
x = 6 / sqrt(2)
6. Find the coordinates of the orthocenter of AABC with vertices A (2,6), B (8,6), and C(6,2). (1 point)
O (5,4)
O (1,2)
O (6,4)
O (6,8)
The coordinates of the orthocenter of ABC are (6,4).
The correct option is C) (6,4).
What is an orthocenter of a triangle?
In geometry, an orthocenter is a point in a triangle that is the intersection of the three lines containing the altitudes of the triangle. An altitude of a triangle is a line segment from a vertex of the triangle to the line containing the opposite side, and is perpendicular to that side. The orthocenter of a triangle is the point where all the altitudes of a triangle meet.
To find the orthocenter of a triangle, the first step is to find the equation of the altitudes from each vertex. Then, we can find the point of intersection of these three lines.
Given the triangle ABC with vertices A (2,6), B (8,6), and C(6,2),
The equation of altitude from vertex A is (x-2) = -2(y-6)
The equation of altitude from vertex B is (x-8) = -2(y-6)
The equation of altitude from vertex C is (x-6) = 2(y-2)
By solving the system of these three equations, we can find the coordinates of the orthocenter.
Hence, The coordinates of the orthocenter of ABC are (6,4).
The correct option is C) (6,4)
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Find an expression to present the area of the trapezoid below
Area of a trapezoid is found with the formula, A=(a+b)/2 x h. so the answer is 9(w-3) / (w + 7) (w + 2).
What is meant by trapezoid ?
An open, flat object with four straight sides and one pair of parallel sides is referred to as a trapezoid or trapezium.A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases. The legs of a trapezium can also be parallel.The trapezoid belongs to the category of shapes that only has one set of parallel sides. The isosceles trapezoid, which has two non-parallel sides of the same length, falls under a specific category. Although they are both quadrilaterals, a rhombus and a trapezoid are not the same thing.An isosceles trapezoid has equal base angles and diagonals. The midpoints of the two opposing sides are parallel to the place where the diagonals intersect.To learn more about trapezoid refer to
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Lahon bought a reel of thread for ewing the=at i 5 meter long and he ue 300cm of it how many cm of thread doe he have left?
The total length of the reel of thread is 5 meters, which is equal to 500 centimeters. Since Lahon used 300 centimeters of thread, he has 200 centimeters of thread left.
Lahon recently purchased a reel of thread that was 5 meters long. This is equivalent to 500 centimeters. He then used 300 centimeters of the thread for sewing. This leaves him with 200 centimeters of thread remaining. This can be expressed as 2 meters. Thus, Lahon has 2 meters of thread left from the reel of thread that he originally bought. This leftover thread can be used for other sewing projects or kept for future use. It is important to keep track of how much thread has been used and how much is left to ensure that an adequate amount of thread is available for future projects. The total length of the reel of thread is 5 meters, which is equal to 500 centimeters. Since Lahon used 300 centimeters of thread, he has 200 centimeters of thread left.
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which is larger 7/12 or 2/3 with explanation
Answer:
2/3
Step-by-step explanation:
First divide the numerator by the denominator.
You then get the percentage and then you can judge from there.
Answer:
2/3
Step-by-step explanation:
first we have to equalise the denominators
we know 3 × 4 = 12 so we multiply both the denominator and the nominator by 4 which would give us 8/12
so the answer would be 2/3 since 8/12>7/12
A fruit shop bought 500 kg of apples for R900 and sold them for R2,80 per kg. a) What is the profit per kilogram?
Profit per kilogram = R1.90
The profit per kilogram is the difference between the selling price and the cost price per kilogram.
a) To find the profit per kilogram, we can use the following formula:
Profit per kilogram = Selling price per kilogram - Cost price per kilogram
Therefore,
Profit per kilogram = R2.80 - R0.90
Profit per kilogram = R1.90
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