Answers
so
[tex]_{100}C_{98}=_{100}C_{100-98}=_{100}C_2=4,950[/tex]
Related Questions
Suppose a laboratory has a 30 g sample of polonium-210. The half-life of polonium-210 is about 138 days. How many half-lives of polonium-210 occur in 1104 days? How much polonium is in the sample 1104 days later?
Answers
After 8 half - lives only (1 / 2^8) or (1 / 256) of the original 30 grams will remain.
(1 / 256) = 0.003906250
So, 30 * 0.003906250 = 0.1171875 grams will remain.
Answer:
8 half-lives of polonium-210 occur in 1104 days.
0.1174 g of polonium-210 will remain in the sample after 1104 days.
Step-by-step explanation:
Initial mass of the polonium-210 = 30 g
Half life of the sample, = [tex]t_{\frac{1}{2}}=138 days[/tex]
Formula used :
[tex]N=N_o\times e^{-\lambda t}\\\\\lambda =\frac{0.693}{t_{\frac{1}{2}}}[/tex]
where,
[tex]N_o[/tex] = initial mass of isotope
N = mass of the parent isotope left after the time, (t)
[tex]t_{\frac{1}{2}}[/tex] = half life of the isotope
[tex]\lambda[/tex] = rate constant
[tex]\lambda =\frac{0.693}{138 days}=0.005021 day^{-1}[/tex]
time ,t = 1104 dyas
[tex]N=N_o\times e^{-(\lambda )\times t}[/tex]
Now put all the given values in this formula, we get
[tex]N=30g\times e^{-0.005021 day^{-1}\times 1104 days}[/tex]
[tex]N=0.1174 g[/tex]
Number of half-lives:
[tex]N=\frac{N_o}{2^n}[/tex]
n = Number of half lives elapsed
[tex]0.1174 g=\frac{30 g}{2^n}[/tex]
[tex]n = 7.99\approx 8[/tex]
8 half-lives of polonium-210 occur in 1104 days.
0.1174 g of polonium-210 will remain in the sample after 1104 days.
A rectangular table top has a perimeter of 24 inches and an area of 35 square inches. find its dimensions.
Answers
let : x the lenght y : the widith
the perimeter is ; 2(x+y) and the area is : xy
so the system : 2(x+y) =24
xy = 35
x+y = 12.....(1)
xy = 35 ...(2)
by (1) : y = 12-x
subsct in (2) : (12-x)x = 35
x²-12x+35 = 0
(x-7)(x-5) = 0
x-7=0 or x-5 = 0
x=7 or x=5
if : x=7 y = 12-7 = 5
if : x=5 y = 12-5 =7
but : x > y
conclusion : one solution (7 , 5).
The dimensions are 7 and 5 inches.
The value of dimensions of rectangle are 5 and 7.
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
A rectangular table top has a perimeter of 24 inches and an area of 35 square inches.
Let the dimensions of rectangle are;
Length = L
Width = W
So, We can formulate;
⇒ 2 ( L + W ) = 24
⇒ L + W = 12 ..(i)
And,
⇒ L × W = 35
⇒ L = 35 / W ... (ii)
Substitute the value from (ii) in (i), we get;
⇒ L + W = 12
⇒ 35/W + W = 12
⇒ 35 + W² = 12W
⇒ W² - 12W + 35 = 0
⇒ W² - (7W + 5W) + 35 = 0
⇒ W² - 7W - 5W + 35 = 0
⇒ W (W - 7) - 5 (W - 7) = 0
⇒ (W - 5) (W - 7) = 0
⇒ W = 5
And, W = 7
And, We get;
⇒ L = 35 / W
Put W = 5;
⇒ L = 35 / 5
⇒ L = 7
And,
⇒ L = 35 / W
Put W = 7;
⇒ L = 35 / 7
⇒ L = 5
Thus, The possible values of dimensions are;
⇒ 5 and 7.
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Which of the following could be equal to lxl ? Select all that apply.
5
0
-2
-5
Answers
Three cards are drawn with replacement from a standard deck. what is the probability that the first card will be a diamond, the second card will be a black card, and the third card will be an ace? express your answer as a fraction or a decimal number rounded to four decimal places.
Answers
there are 13 diamonds per deck
26 black cards
4 aces
so a 13/52 chance for a diamond
a 26/52, reduced to 1/2 chance for a black card
and a 4/52 chance for an ace
13/52 x 1/2 x 4/52 = 52/5408 = 1/104 probability
A parabola is defined by the equation x = 5y2. In which direction will the parabola open? up down right left
Answers
evaluate 9 + 11g - 4h when g = 2 and h = 7
Answers
9 + 11(2) - 4(7) =
9 + 22 - 28 =
31 - 28 =
3
So, 3 is the answer.
9 + 11(2) - 4(7)
9 + 22 - 28
31 - 28
The final answer is 3.
GEOMETRY- I just need someone to check my answer!
Answers
Can someone simplify 3(2x+1)-8
Answers
3(2x)+3(1)-8
6x+3-8 combine like terms
6x+(3-8)
6x-5
first distribute the 3 through the parenthesis.
6x + 3 - 8
Combine like terms
6x - 5
How to solve this? Please help!
Answers
What is the equivalent of pi over 3 radians in degrees?
Answers
and pretty sure you know how much that is.
Answer: The equivalent expression in degrees is 60°.
Step-by-step explanation: We are given to find the equivalent of the following expression in degrees.
[tex]E=\dfrac{\pi}{3}~\textup{radians}.[/tex]
We will be using the UNITARY method the solve the given problem.
We know that
[tex]\pi~\textup{radians}=180^\circ\\\\\\\Rightarrow 1~\textup{radian}=\left(\dfrac{180}{\pi}\right)^\circ\\\\\\\Rightarrow \dfrac{\pi}{3}~\textup{radians}=\left(\dfrac{\pi}{3}\times\dfrac{180}{\pi}\right)^\circ=60^\circ.[/tex]
Thus, the equivalent expression in degrees is 60°.
Steve is buying a home worth $275,000. His closing costs will amount to 6 percent, and his down payment is 15 percent. How much is each fee?
Answers
down payment will be 275, 000 * 15 / 100 = 2, 750 * 15 = $41, 250
To do this you must convert percentages to decimals. 6% converts to .06 and 15% converts to .15. You move the decimal point to the left two places as I have just done.
Closing cost: 275,000 x .06 = 16,500.00
Down Payment: 275,000 x .15 = 41,250.00
Three children guessed the number of jelly beans in a jar.the guesses were 98,137 and 164.none of the guesses was correct.one guess was off by 12,another by 27 and the third by 39.how many jelly beans were in the jar.
Answers
If all three guesses for the number of jelly beans 98, 137, and 164 were off by 12, 27, and 39 the correct guess for the number of jelly beans is 125.
The number of jelly beans was 125.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
Example:
2x + 3 is an expression
2x - 3 = 4 is an expression
We have,
Three guesses for the number of jelly beans:
98, 137, and 164.
These three guesses were all wrong.
The three guesses were off by:
12, 27, and 39.
The correct guess is 125 because,
98 + 27 = 125
137 - 12 = 125
164 - 39 = 125
Thus,
The number of jelly beans was 125.
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How will the perimeter of the rectangle change if each side is increased by a factor of 10? the long side has 6cm and the short side is 3cm.
a.The perimeter will be 1/10 the original.
b.The perimeter will be 1/100 the original
c.The perimeter will be 10 times the original.
d.The perimeter will be 100 times the original.
Answers
p1=18
p2=2(30+60)
p2=180
p2/p1=180/18=10
c. The perimeter will be 10 times the original.
Answer: Option 'C' is correct.
The perimeter will be 10 times the original .
Step-by-step explanation:
Since we have given that
Length of the rectangle = 6 cm
Breadth of the rectangle = 3 cm
As we know the formula for "Perimeter of rectangle "
[tex]\text{Perimeter of original rectangle }=2(Length+ Breadth)\\\\\text{Preimeter of rectangle }=2(6+3)\\\\\text{Perimeter of rectangle }=18\ cm[/tex]
According to question, each side is increased by a factor of 10
so, Perimeter of new rectangle is given by
[tex]10\times 2\times (6+3)\\\\=180\ cm[/tex]
Hence, Option 'C' is correct.
So, the perimeter will be 10 times the original .
The temperature dropped 2° F every hour for 6 hours. What was the total number of degrees the temperature changed in the 6 hours
Answers
-2 x 6, -2 stands for the drop, 6 stands for the hours.
-2 x 6 = -12, meaning the temperature dropped -12 degrees.
Create a factorable polynomial with a GCF of 2y. Rewrite that polynomial in two other equivalent forms. Explain how each form was created.
I already made my polynomial, 4y^1 + 6y^3
I just don't understand how to get two equivalent forms(please explain if you can)
Answers
2y(2 + 3y^2) <== here is one form
another form would be to multiply ur equation by a multiple of ur GCF 2, such as 4
4(4y^1 + 6y^3) = 16y^1 + 24y^3 <== another form
Mentally estimate the total cost of items that have the following prices $1.85 $.98 $3.94 $9.78 and $6.18 round off the answer to the nearest half dollar
A. $22.50
B. $22.59
C. $23.00
D. $22.30
Answers
the first 4 would be rounded up tot he nearest dollar and the last one rounded down to the nearest dollar
doing that I estimate $23.00
Answer is C
If n√a=r , then which of the following are true statements? Check all that apply. A. r^n=a B. a^1/n=r C. a^r=n D. n^1/r=a
Answers
Answer:
A. r^n=a
B. a^1/n=r
Step-by-step explanation:
ape x
The true statements about the equation [tex]\sqrt[n]a = r[/tex] are (a) r^n=a and (b) a^1/n=r
How to determine the true statements?The equation is given as:
[tex]\sqrt[n]a = r[/tex]
Take the power of n on both sides of the equation
[tex](\sqrt[n]a)^n = r^n[/tex]
This gives
a = r^n
Rewrite as:
r^n = a
Also, we have:
[tex]\sqrt[n]a = r[/tex]
Apply the law of indices
a^1/n = r
Hence, the true statements about the equation [tex]\sqrt[n]a = r[/tex] are (a) r^n=a and (b) a^1/n=r
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can someone explain the diffrence between first class, second class, and third class levers?
Answers
Final answer:
Levers are classified based on the positions of the fulcrum, input force, and output force. First-class levers have the fulcrum in the middle, second-class levers have the load in the middle, and third-class levers have the effort in the middle. The Mechanical Advantage of a lever indicates how much the lever amplifies the input force.
Explanation:
The three classes of levers are differentiated by the positions of the fulcrum, input force, and output force. A first-class lever has the fulcrum placed between the input force and the output force. Examples would include a seesaw and a crowbar. A second-class lever has the output force between the input force and the fulcrum, with examples being a wheelbarrow and a nutcracker. Lastly, a third-class lever has the input force between the output force and the fulcrum, as seen in a pair of tweezers or a human arm when lifting a weight.
The Mechanical Advantage (MA) is a calculation that shows how much a lever amplifies the input force. It is given by the ratio of the distance from the fulcrum to the input force (effort arm) and the distance from the fulcrum to the output force (resistance arm). Levers are simple machines that utilize torque and the physical distances from their pivot point to achieve an output force that is greater or faster or travels a further distance than the input force.
Use the three steps to solve the problem. the length of a rectangle is 2 inches less than 3 times the number of inches in its width. if the perimeter of the rectangle is 28 inches, what is the width and length of the rectangle?
Answers
Let the length be l.
l = 3w - 2
Given,
Perimeter = 28
2*( l + w ) = 28
2*( 3w -2 + w ) = 28
4w - 2 = 14 [ Dividing both sides by 2 ]
2w - 1 = 7 [ Dividing both sides by 2 ]
2w = 8
w = 4.
Thus,
l = 3w -2 = 3*4 - 2 = 12 - 2 = 10
Therefore, the length is 10 inches and the width is 4 inches.
The lengths of the sides of a triangle are in the extended ratio 1 : 2 : 5. the perimeter of the triangle is 32 ft. the length of the longest side is:
Answers
x + 2x + 5x = 32
8x = 32
x = 32/8
x = 4
longest side = 5x = 5*4 = 20 ft
The length of longest side of the triangle is 20 ft .
What is perimeter of the triangle?The perimeter of a triangle is defined as the total length of its boundary.
The basic formula used to calculate the perimeter of a triangle is:
Perimeter = sum of the three sides
According to the question
The lengths of the sides of a triangle are in the extended ratio 1 : 2 : 5 .
Let common constant factor within ratio = x
Therefore,
Sides of triangle = x , 2x , 5x
and the perimeter of the triangle = 32 ft
i.e
according to the formula of perimeter of a triangle:
Perimeter = sum of the three sides
Now,
Substituting the value in formula
[tex]32 = x + 2x + 5x[/tex]
[tex]32 = 8x[/tex]
[tex]x = 4[/tex]
The sides of triangle is : 4 ft , 2*4 , 5*4
: 4 ft , 8 ft , 20 ft
Hence, the length of longest side of the triangle is 20 ft
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On the day their child was born, her parents deposited $25,000 in a savings account that earns 11% interest annually. How much is in the account the day the child turns 16 years old (rounded to the nearest cent)? Hint: an = a1(1 + r)n, r ≠ 1, where a1 is the initial amount deposited and r is the common ratio or interest rate.
Answer choices:
$119,614.74 $132,772.36 $128,612.52 $440,000.00
Answers
Total = 25,000 * (1.11)^16
Total = 25,000 * 5.3108943321
Total = 132,772.36
(This is the second answer)
Final answer:
After using the compound interest formula with an initial deposit of $25,000, an annual interest rate of 11%, and a time period of 16 years, the balance rounds to $120,034.10, which does not match any of the provided answer choices.
Explanation:
To find out how much is in the account when the child turns 16 years old, we can use the formula for compound interest: an = a1(1 + r)n, where a1 is the original amount deposited, r is the annual interest rate (expressed as a decimal), and n is the number of years the money is invested. In this case, a1 is $25,000, r is 0.11 (11%), and n is 16.
Using the formula, we calculate the account balance as follows:
Account Balance = 25,000(1 + 0.11)16
Account Balance = 25,000(1.11)16
Account Balance = 25,000(4.801364)
Account Balance = $119,999.10
However, this result is not in the given answer choices, so let's ensure we are rounding to the nearest cent:
Account Balance = $120,034.09 (before rounding)
Account Balance = $120,034.10 (after rounding to the nearest cent)
None of the answer choices matches this amount, so it is possible there has been a mistake in the provided choices or in our calculations. We should double-check the interest rate, time period, and the formula used.
The legs of a right triangle measure 14 and 25 what is the measure of the angle opposite to the shortest side
Answers
angle = 29.25 degrees
The measure of the angle opposite to the shortest side is, 29.25°
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The legs of a right triangle measure 14 and 25.
Now, We know that;
⇒ tan θ = Perpendicular / Base
⇒ tan θ = 14 / 25
⇒ θ = tan ⁻¹ (14/25)
⇒ θ = 29.25°
Thus, The measure of the angle opposite to the shortest side is, 29.25°
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A person's part-time job pays $5.50 per hour. Write an expression to represent the amount he earns for working n hours.
The person earns $____ for working n hours.
Answers
Solve by the linear combination method (with or without multiplication). x + y = 40 0.08x + 0.03y = 1.7
Answers
x + y = 40
.08x+.03y=1.7
We need to multiply the top equation by either a -.08 or a -.03 to eliminate one of the variables. Let's get rid of the y:
-.03(x + y) = -.03(40) which gives us
-.03x - .03y = -1.2
.08x + .03y = 1.7
When we add those together we are left with .05x = .5 and x = 10. If we sub that 10 in for x into the first equation (either would have worked but the first one is way easier to work with!) we get 10 + y = 40 and y = 30. So the solution to the system is (10, 30)
Answer:
-_- Answer is -3
Step-by-step explanation:
Doing the instruction vidio.
Describe the transformation of the graph of f into the graph of g as either a horizontal or vertical stretch. f(x)=sqrt(x) and g(x)=sqrt(0.5x)
Answers
[tex]\bf \bullet \textit{ stretches or shrinks horizontally by } {{ A}}\cdot {{ B}}\\\\ \bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if }{{ B}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the y-axis}[/tex]
[tex]\bf \bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\ \bullet \textit{ vertical shift by }{{ D}}\\ \left. \qquad \right. if\ {{ D}}\textit{ is negative, downwards}\\\\ \left. \qquad \right. if\ {{ D}}\textit{ is positive, upwards}\\\\ \bullet \textit{ period of }\frac{2\pi }{{{ B}}}[/tex]
with that template in mind, let's see [tex]\bf f(x)=\sqrt{x}\qquad \begin{array}{llll} g(x)=&\sqrt{0.5x}\\ &\quad \uparrow \\ &\quad B \end{array}[/tex]
so B went form 1 on f(x), down to 0.5 or 1/2 on g(x)
B = 1/2, thus the graph is stretched by twice as much.
The transformation of the function f(x) to g(x) is a horizontal stretch.
Step-by-step explanation:The parent function f(x) is given by:
[tex]f(x)=\sqrt{x}[/tex]
and the transformed function g(x) is given by:
[tex]g(x)=\sqrt{0.5x}[/tex]
Now we know that the transformation of the type:
f(x) → f(bx)
is a horizontal stretch if 0<b<1
and is a horizontal shrink if b>1
Here we have:
[tex]b=\dfrac{1}{2}=0.5[/tex]
i.e.
[tex]0<b<1[/tex]
This means that the transformation of the function f(x) to g(x) is a horizontal stretch by a factor of 2.
A company employs 48 people in various departments. The average annual salary of each employee is $25,000 with a maximum variance of $3,000. What is the range of the total salary that the company pays to its employees annually?
Answers
n = 48, the sample size
m = $25,000, th sample mean
σ = $3000, the maximum variance
The standard deviation is
s = √σ = √(3000) = 54.772
As a rule of thumb, the range is 4 times the standard deviation. Therefore the range is
R = 4*54.772 = 219.09
Half the range is
R/2 = 219.09/2 = 109.45
The required range is
(25000-109.45, 25000+109.45) = (24890.46, 25109.54)
Answer: ($24,890.46, $25,109.54)
Answer:
$1,056,000 ≤ x ≤ $1,344,000
Step-by-step explanation:
took test
In a rectangle ABCD, A and B are the points (4,2) and (2,8) respectively l. Given that the equation of AC is y=x-2. Find the equation of BC
Answers
A=(4,2)
B=(2,8)
(AB)≡y-2=(x-4)*(8-2)/(2-4) ==> y=-3x+14
(BC)≡y-8=(x-2)*1/3 ==> y=1/3 x+22/3
What are the real zeros of x^3 + 4x^2 − 9x − 36
Answers
[x3 + 4x2] -9 [ x+4]
take x2 common factor from first praket
x2[x+4] -9 [x+4]
= [x+4] *[x2 -9]
so the zeros of this equation are -4 , 3, -3
Answer:
x = −3, 3, −4
Step-by-step explanation:
If two sides of a triangle are 12 and 17, and the included angle is 60, what is the area of the triangle
Answers
[tex]A= \frac{1}{2}*12*17*sin(60^o) =102* \frac{ \sqrt{3} }{2}=51 \sqrt{3} \approx 88.33 \ units^2[/tex]
Determine if the function is one-to-one. A decreasing line intercepting the y axis at 0, 5.