A time of 40.7 minutes is taken for 170 grams of element X to decay to 5 grams.
How to analyze a radioactive decay caseLet suppose that element X experiments a simple radioactive decay, that is, that the element X becomes gradually into another less radioactive stable element in time.
We know that decay behaves exponentially and follows this model:
[tex]m(t) = m_{o}\cdot e^{-\frac{t}{\tau} }[/tex] (1)
Where:
[tex]m_{o}[/tex] - Initial mass, in gramst - Time, in minutesτ - Time constant, in minutesm(t) - Current mass, in gramsThe time constant can be described in terms of half-life ([tex]t_{1/2}[/tex]), in minutes, through the following expression:
[tex]\tau = \frac{t_{1/2}}{\ln 2}[/tex] (2)
If we know that [tex]t_{1/2} = 8\,min[/tex], [tex]m_{o} = 170\,g[/tex] and [tex]m(t) = 5\,g[/tex], then the time needed for the decay is:
τ ≈ 11.541 min
[tex]t = -\tau \cdot \ln \frac{m(t)}{m_{o}}[/tex]
t ≈ 40.698 min
A time of 40.7 minutes is taken for 170 grams of element X to decay to 5 grams. [tex]\blacksquare[/tex]
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Find the smallest number by which 6615 is to be multiplied by to get a perfect square
Answer:
3x 5
Step-by-step explanation:
An angle of measure [tex]\frac{4\pi }{3}[/tex] intersects the unit circle at point ([tex]-1/2,- \frac{\sqrt{3} }{2}[/tex]). What is the exact value of tan([tex]\frac{4\pi }{3}[/tex])?
a. -1/2
b. [tex]\sqrt{3[/tex]
c. [tex]\frac{\sqrt{3} }{3}[/tex]
d. [tex]-\frac{\sqrt{3} }{2}[/tex]
Answer:
b. √3
Step-by-step explanation:
Given a point on the unit circle that represents the position of the terminal ray of an angle, the tangent of that angle is the ratio of the y-coordinate to the x-coordinate.
tan(4π/3) = y/x = (-√3/2)/(-1/2) = √3/1
tan(4π/3) = √3
_____
Additional comment
A calculator can confirm this for you.
What is the standard form of the equation of a parabola that opens left or right? A. Y = ax2 + bx + c B. X = ay2 + by + c C. X = a(y - v)2 + h D. Y = a(x - h)2 + v
Answer:
The equation of the parabola which opens left or right is (B) x= ay^2 + by + c
:)
What is the value of c
Answer:
x = 49º
Step-by-step explanation:
This is right angle, and right angle's are always a 90º angle. 90º - 41º is 49.
So the basic answer is 49, but it's properly written as "49º".
Hope this helps!!
The value of x: 49 degrees
Note: All the angles in a triangle add up to 180 degrees
What we're given:
41 degrees, A right angle, and x.
A right angle is 90 degrees.
Equation:
41 + 90 + x = 180
131 + x = 180
x = 49 degrees
The function P(x) is mapped to I(x) by a dilation in the following graph.
Which answer gives the correct transformation of P(x) to get to I(x)?
The correct transformation of P(x) to get I(x) is I(x) = 2P(x)
What is transformation?
Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.
From the graph of I(x) and P(x), we can see that:
I(x) = 2P(x)
The correct transformation of P(x) to get I(x) is I(x) = 2P(x)
Find out more on transformation at: https://brainly.com/question/1548871
A figure is made up of three triangles. Each triangle has a base of 5 feet and a height of 4.5 feet. What is the total area of the figure?
Group of answer choices
33.75 ft²
43.75 ft²
67.5 ft²
22.5 ft²
Answer:
Step-by-step explanation:
3 * 1/2 * 5 * 4.5
= 33.75 fT^2.
someone please help me find the value of x
Answer:
x = 102.5°
Step-by-step explanation:
these two angles are adjacent and supplementary which means their sum must be equal to 180 degrees
create this equation to find 'x':
x + x-25 = 180
combine 'like' terms:
2x - 25 = 180
add 25 to each side:
2x = 205
x = 205/2 or 102.5°
Elaine sold twice as many T-shirts as Kim
How many did each girl sell if the total
number of T-shirts sold was 27?
(no links no files) I need equation
Pllllssss answer!! i only have a few more minutess!! (i'll give brainilest) tyler wants to buy some cherries at the farmer's market. he has $ 10 and cherries cost $4 per pound. 1. if c is the number of pounds of cherries that tyler can buy, write one or more inequalities or equations describing c. 2. can 2 be a value of c? can 3 be a value of c? what about -1? explain your reasoning. 3. if m is the amount of money, in dollars. tyler can spend, write one or more inequalities or equations describing m. 4. can 8 be a value of m? can 2 be a value of m? what about 10.5? explain your reasoning. did you answer all 4 parts?
answer:
step by step explanation:
10-4 = c
6 = c
he can buy 2 pounds of cherries
2. 2 can be the value of c
c = 2
10- 4c
10- 4(2)
10 - 8 = 2
c = 3
10 - 4c
10- 4(3)
10 - 12 = -2
c = -1
10 - 4(-1)
10 - (-4)
10 + 4
= 14
manage this
mark me brainliest
how do you do thissss???
The solid above is a triangular prism. Therefore, the surface area of the triangular prism is 157.2 cm².
How to calculate surface areaThe figure above is a triangular prism. The surface area of a triangular prism can be calculated as follows:
Surface area = bh + l(p)
where
p = perimeter of the triangular basel = height of prismb = base of the triangular baseh = height of the triangular baseTherefore,
p = 6 + 6 + 6 = 18 cm
l = 7 cm
b = 6 cm
h = 5.2 cm
Therefore,
Surface area = (6 × 5.2) + 7(18)
Surface area = 31.2 + 126
Surface area = 157.2 cm²
learn more on surface area here: https://brainly.com/question/2835293
1. Janelle began the work below to find 368 ÷ 16. Complete the work.
Answer:
23
Step-by-step explanation:
[tex]368/16=23[/tex]
What is the correct answer for this?
Volume:-
side³a³5³125cm³Subway creates a paid promotion featuring a different 6-inch sub of the day each day of the week. The sub of the day is only $3. 50. Subway utilizes the radio to spread the word. Which promotion method is subway using?.
Based on the information provided, the promotion method subway is using is sales promotion.
What is promotion?It is a marketing tool that involves letting know potential customers about a product that a company wants to sell.
What are the promotion methods?Most common methods include:
Direct selling.Public relations.Sales promotion.What is sales promotion?This involves promoting or advertising products through sales, which means customers are offered special discounts or lower prices. This is the method used by the subway because the sub of the day is a sales.
Learn more about sales in: https://brainly.com/question/15375944
Whoever answers first gets 30 points plus brainliest
how many months are there in 7 years???
good luck ;)
Answer:
84
Step-by-step explanation:
1 year= 12 months
7 years × 12 months each= 84 months in total for 4 years
Find S.P. in the following cases. a) M.P. = Rs 540, discount = 5 %
Step-by-step explanation:
Given:-
MP = Rs 540. Discount = 5 %To Find:-
Sell priceSolution:-
SP = MP - Discount.
MP = Marked Price ( Also called List Price) SP = Selling Price.Discount = (Discount %) of MP
Discount = (5/100) 54p
Discount = 27 Rs
Subtract discount from MP to get SP
SP = MP - Discount
SP = 540 - 27 Rs
SP = 513 Rs
Answer;
soln;
MP= Rs 540
discount = 5%
now,
SP = MP - D% of MP
= 540 - 5/100 * 540
=Rs 513
Y^2+8y+2 y=-5 evaluate the expression
Answer:
the correct answer is shown below
Step-by-step explanation:
hope this helps
have an awesome day -TJ
pls mark brainliest if this helps :)
I need the green box with question mark I can’t get the second part
Answer:
-14
Step-by-step explanation:
-8 = 3/2 x 4 + ?
-8 = 6 + ?
-8 - 6 = -14
Your answer will be -14.
Have an amaizng day!!
Please rate and mark brainliest!!
Trigonometry, how would I find the area of this triangle?
Answer:
Step-by-step explanation:
Area of triangle = 1/2 * base * height
Use the side of length 5.6cm as base, the height will be a perpendicular line from the base to the tip of the triangle.
From the right-angle triangle formed by the height and the side of length 3.9cm,
sin(56°45') = height / 3.9
height = 3.9*sin(56°45')
Substituting back into the area equation:
Area = 1/2*5.6*3.9*sin(56°45')
= 9.0cm^2
= 9cm^2
Use sine rule for Area
[tex]\\ \rm\rightarrowtail Area=\dfrac{1}{2}absinC[/tex]
[tex]\\ \rm\rightarrowtail Area=\dfrac{1}{2}(3.9)(5.6)sin56°45'[/tex]
[tex]\\ \rm\rightarrowtail Area=10.92(0.836)[/tex]
[tex]\\ \rm\rightarrowtail Area=10.22cm^2[/tex]
2/5 g+3h -6 when g=10 h=6
let's evaluate this expression
[tex]\pmb{\displaystyle\frac{2}{5}g+3h-6 }[/tex]
[tex]\pmb{\displaystyle\frac{2}{5} *10+3(6)-6}[/tex]
[tex]\pmb{\displaystyle\frac{2}{5} *10+18-6}[/tex]
[tex]\pmb{\displaystyle\frac{2}{5} *10+12}[/tex]
Multiply:
[tex]\pmb{\displaystyle\frac{2}{5} *\frac{10}{1} =\frac{20}{5} =4}[/tex]
Final Step:-
[tex]\pmb{4+12}[/tex]
[tex]\pmb{16}[/tex]
======================================================
note:-Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I'll comment and/or edit my answer :)
Solve the system of equations at right. 2^(x+y)=16 2^(2x+y)= 1/8
Answer:
(x, y) = (-7, 11)
Step-by-step explanation:
The system of exponential equations can be solved by the use of logarithms. Equivalently, the equations can be written so that exponents can be equated. This system is equivalent to two linear equations.
First equation:
2^(x+y) = 16
2^(x +y) = 2^4 . . . . use the same base to write the constant
x +y = 4 . . . . . . . . equate exponents of 2 (take log₂ of both sides)
Second equation:
2^(2x +y) = 1/8
2^(2x +y) = 2^(-3) . . . . use the same base to write the constant
2x +y = -3 . . . . . . equate exponents of 2
Solve the linear equations:
We can subtract the first equation from the second to get ...
(2x +y) -(x +y) = (-3) -(4)
x = -7
y = 4 -x = 4 -(-7) = 4 +7 = 11 . . . . use the first equation to find y
The solution to the system is (x, y) = (-7, 11).
Natalie can hop 24 times in 8 minutes at a constant rate. How many times can she hop in 7 minutes?
Answer:
in 7 mins she can hop 21 times
Step-by-step explanation:
24 divided by 8 = 3
24-3=21
Answer:
Natalie can hop 21 times in 7 minutes
Step-by-step explanation:
To figure out how many times she can hop in 7 minutes you need to find the average hop each minute.
First, you write 24/8. You simply that to 3/1.
So Natalie can jump 3 times in 1 minute.
If you want 7 minutes, you multiply 1 by 7, and 3 by 7, which gets you 21 hops for 7 minutes.
-I hope this helps!
ASAPPPP!! Please!
The histogram shows the number of days in the past week that 30 surveyed people exercised.
Number of Days per person.
And days
How many people who were surveyed exercised fewer than 4 days last week?
12
14
16
18
Answer:
16
Step-by-step explanation:
2 from 3 days
another 2 on 2 days
5 for 1 day
7 for 0 days
2+2+5+7= 16
Determine which polynomial is a perfect square trinomial. 4x2 − 12x 9 16x2 24x − 9 4a2 − 10a 25 36b2 − 24b − 16.
This [tex]4x^2 - 12x + 9[/tex] factors into [tex](2x - 3)^2[/tex], and is thus a perfect square trinomial.
What is a perfect square?A perfect square is a number system that can be expressed as the
square of a given number from the same system.
Trinomial [tex]Ax^2 + Bx + C[/tex] is a perfect square if
A > 0
C > 0
B = ±2√A√C
1. [tex]36b^2 - 24b - 16[/tex]
C < 0
2. [tex]4a^2 - 10a + 25[/tex]
2√A√C = 2×2×5
= 20,
B = −10
3. [tex]16x^2 + 24x - 9[/tex]
not a perfect square,
C < 0
4. [tex]4x^2- 12x + 9[/tex]
perfect square
A>0,
C>0,
2√A√C = 2×2×3
-B = 12
= [tex](2x - 3)^2[/tex]
Thus, [tex]4x^2- 12x + 9[/tex] the polynomial is a perfect square trinomial.
Learn more about perfect square;
https://brainly.com/question/1832550
Thank you to who ever answers this
Answer:
The answer is G.
Step-by-step explanation:
Trust me.
Answer:
J is the answer
Step-by-step explanation:
I had given the explanation but brainly deleted it for having a link.
Just use this:
"What is a box and whisker plot?
A box and whisker plot—also called a box plot—displays the five-number summary of a set of data. The five-number summary is the minimum, first quartile, median, third quartile, and maximum.
In a box plot, we draw a box from the first quartile to the third quartile. A vertical line goes through the box at the median. The whiskers go from each quartile to the minimum or maximum.
Example: Finding the five-number summary
A sample of 101010 boxes of raisins has these weights (in grams):
252525, 282828, 292929, 292929, 303030, 343434, 353535, 353535, 373737, 383838
Make a box plot of the data.
Step 1: Order the data from smallest to largest.
Our data is already in order.
252525, 282828, 292929, 292929, 303030, 343434, 353535, 353535, 373737, 383838
Step 2: Find the median.
The median is the mean of the middle two numbers:
252525, 282828, 292929, 292929, \large{30}3030, \large{34}3434, 353535, 353535, 373737, 383838
\dfrac{30+34}{2}=32
2
30+34
=32start fraction, 30, plus, 34, divided by, 2, end fraction, equals, 32
The median is 323232.
Step 3: Find the quartiles.
The first quartile is the median of the data points to the left of the median.
252525, 282828, \large{29}2929, 292929, 303030
Q_1=29Q
1
=29Q, start subscript, 1, end subscript, equals, 29
The third quartile is the median of the data points to the right of the median.
343434, 353535, \large{35}3535, 373737, 383838
Q_3=35Q
3
=35Q, start subscript, 3, end subscript, equals, 35
Step 4: Complete the five-number summary by finding the min and the max.
The min is the smallest data point, which is 252525.
The max is the largest data point, which is 383838.
The five-number summary is 252525, 292929, 323232, 353535, 383838.
Example (continued): Making a box plot
Let's make a box plot for the same dataset from above.
Step 1: Scale and label an axis that fits the five-number summary.
Step 2: Draw a box from Q_1Q
1
Q, start subscript, 1, end subscript to Q_3Q
3
Q, start subscript, 3, end subscript with a vertical line through the median.
Recall that Q_1=29Q
1
=29Q, start subscript, 1, end subscript, equals, 29, the median is 323232, and Q_3=35.Q
3
=35.Q, start subscript, 3, end subscript, equals, 35, point
Step 3: Draw a whisker from Q_1Q
1
Q, start subscript, 1, end subscript to the min and from Q_3Q
3
Q, start subscript, 3, end subscript to the max.
Recall that the min is 252525 and the max is 383838.
We don't need the labels on the final product:
Want to learn more about making box and whisker plots? Check out this video.
Want to practice making box plots? Check out this exercise."
please check picture and answer correctly please.
Answer:
27
Step-by-step explanation:
multiply 9 x 6 and you get 54. Since it's a triangle divide by 2 and you get 27
Can someone help me out with this?
What is the value of x?
Enter your answer in the box.
Answer:
x = 4Step-by-step explanation:
x has the same value as RT since they are equal sides of the isosceles triangle.
RT is also the hypotenuse of ΔRST - 30°×60°×90° right triangle.
Acoording to the property of such triangles, the ratio of sides is:
a : b : c = 1 : √3 : 2We have:
b = 2√3 and c = RTUse the ratio to find the lenght of RT
2√3 : RT = √3 : 2RT = 2*2√3/√3RT = 4So the value of x is 4 units
Find RT
sin60=2√3/RT√3/2=2√3/RTRT=4√3/√3RT=4Now
tan45=x/4x=4please help me with the question in the picture
Answer:
(x - 5) / (x - 6) (don't put them in brackets, i'm doing this to signify that all of x - 5 is being divided by all of x - 6).
Step-by-step explanation:
x² + 2x - 35:
what multiplies into -35 and adds into 2?
7 and -5
so the top is now (x + 7)(x - 5)
x² + x - 42
what multiplies into -42 and adds into 1?
-6 and 7
so the bottom is now (x + 7)(x - 6)
the 2 lots of (x + 7) cancel and you are left with (x - 5) / (x - 6)
Answer:
[tex]\frac{x-5}{x-6}[/tex]
Step-by-step explanation:
Let's start with the numerator to factor it.
We need two numbers adding up to 2 and multiplying to -35. Easy to see the number are +7 and -5. You can then factor as [tex]x^2+2x-35=(x+7)(x-5)[/tex]
Denominator then. Same story, Two number adding to 1 and multiplying to -42. Numbers are +7 again and -6. Factors as before:
[tex]x^2+x-42=(x+7)(x-6)[/tex].
Now you can simplify
[tex]\frac{x^2+2x-35}{x^2+x-42} = \frac{(x+7)(x-5)}{(x+7)(x-6)}= \frac{x-5}{x-6}[/tex]
Question 7 (1 point)
Which polynomial is equivalent to x2 + 3x ?
O a
-
-
Ob
-
-3 (22 – 2x) + 4x (x + 3) - 12x
3 (22 + 2x) - 4x (x - 3) + 3x
-3 (x2 + 2x) + 4x (x + 3) - 3x
3(x2 - 2x - 4x (x - 3) + 12x
ос
Od
-
-
-
Answer:
c
Step-by-step explanation:
Angle 1 and Angle _____________ are supplementary angles.
Answer: number 2
Step-by-step explanation: so a supplementary Angle adds up to a 180 angle so it would be number 2 I think.
please help i am confused
Answer:
Step-by-step explanation:
If 70% passed both, then that means 30% passed either one test, or neither test.
Since 80% passed the first test, we know that 20% of the students failed the first test.
This means that the other 10% of the students came from the 80% that already passed the first test.
These make up 10/80 = 12.5% of the people that passed the first test, meaning your answer is 100-12.5=87.5%