The age of the radioactive artifact is approximately 19029.6 years old
RadioactivityRadioactivity is the phenomenon of the spontaneous disintegration of unstable atomic nuclei to atomic nuclei to form more energetically stable atomic nuclei. Radioactive decay is a highly exoergic, statistically random, first-order process that occurs with a small amount of mass being converted to energy.
To solve this problem, we have to find the disintegration constant and we can use the formula of half-life of the sample to do that.
The half-life of a sample is given as;
[tex]T_\frac{1}{2}=\frac{ln}{\lambda}\\T_\frac{1}{2} =\frac{ln}{5715} \\ T_\frac{1}{2} = 0.000121\\[/tex]
The formula of radioactivity is given as
[tex]N = N_oe^(^-^\lambda ^t)[/tex]
Substituting the values into the equation
[tex]N = N_oe^(^-^\lambda ^t)\\\frac{N}{N_o} = e^-^(^\lambda ^t)\\0.1 = e^-^(^0^.^0^0^0^1^2^1^*^t^)\\t = 19029.6 years[/tex]
The artifact is approximately 19029.6 years.
Learn more on radioactivity here;
https://brainly.com/question/26626062
#SPJ1
Hi Can someone help this is hard?
The domain is the set of all real numbers and the range is the set of all real numbers larger than -4, so the correct option is the third one.
How to get the domain and the range?For a function y = f(x) we define the domain as the set of the x-values (horizontal axis) and the range as the set of the y-values (vertical axis).
Here we have a parabola, in this case the domain is always the set of all real numbers, and the range is all the values above or equal to the vertex (in cases like this, where the parabola opens up).
We can see that the vertex is at y = -4
So the range is.
[-4, ∞]
So the correct option is 3.
Learn more about domain and range:
https://brainly.com/question/10197594
#SPJ1
you are driving a 30 foot bus on a highway at 45 mph. the road is dry and visibility is good. a safe distance between you and the vehicle ahead of you should be at least:
PLEASE HELP
Which transformation represents a reflection over the x-axis?
Answer: E
Step-by-step explanation:
Option A is a reflection over the y-axis.
Option B is a rotation of 180 degrees about the origin followed by a dilation.
Option C is a reflection over the line y=x.
Option D is a reflection over the y-axis.
Option E is a reflection over the x-axis.
In *triangle* HIJ, i = 890 inches, h = 740 inches and H=127°. Find all possible values of angle I, to the nearest degree.
The given conditions cannot form a triangle. A triangle cannot be formed if the sum of three angle measurements does not equal 180°.
How to calculate angle of Triangle ?A triangle is a three-sided polygon with three edges and three vertices in geometry. The sum of a triangle's internal angles equals 180 degrees, which is its most important property. This is known as the angle sum property of a triangle.
A triangle's interior angles always add up to 180°, whereas its exterior angles are equal to the sum of the two interior angles that are not adjacent to it. Another method for calculating a triangle's exterior angle is to subtract the angle of the vertex of interest from 180°.
A protractor is the most convenient tool for measuring angles. If you don't have a protractor, you can use the basic geometric principles of triangles to determine the size of an angle. To solve the equations, you'll need a scientific calculator.
To learn more about Triangle refer ?
https://brainly.com/question/1058720
#SPJ1
A student performed the following steps to find the solution to the equation
x² + 4x-12-0. Where did the student go wrong?
Step 1. Factor the polynomial into (x + 6) and (x-2)
Step 2. x-6= 0 and x + 2 = 0
Step 3. x = 6 and x = -2
O A. in Step 3
B. The student did not make any mistakes, the solution is correct
O C. in Step 1
OD. in Step 2
The student got the solution to the quadratic equation wrong at step 2
What are quadratic equations?A quadratic equation is a mathematical equation in which it's higher power of unknown is 2.
A quadratic equation can be solved by using 4 different method of choice which are formula method, factorization method , completing the square and graphical method.
x^2+4x-12=0 is an example of quadratic equation.
using factorization method to solve the value of x
x^2+6x-2x-12=0
grouping the equation
(x^2+6x)(-2x-12)=0
x(x+6)-2(x+6)=0
(x+6)(x-2)=0
for the equation to be satisfied
(x+6)=0
or
(x-2)=0
Therefore x= -6 or+2
learn more about quadratic equations from
https://brainly.com/question/28038123
#SPJ1
Multiply. [−3⋅914]⋅[(−0.1)⋅(−28)]
The solution to the given expression is 7,677.6.
This is a question of multiplication.
Multiplication
In mathematics, multiplication is used as a method of finding the product of two or more numbers. It is one of the arithmetic operations, like addition, subtraction and division that we use in everyday life. The major application we can see in multiplication tables.
In arithmetic, the multiplication of two numbers is represented by the repeated addition of one number with respect to another.
Given expression:-
[−3*914]*[(−0.1)*(−28)]
We have to find the solution of the given expression.
We have,
-3*914 = -2742
(-0.1)*(-28) = 2.8
Hence, we can write,
[−3*914]*[(−0.1)*(−28)] = (-2742)*(2.8)
(-2742)*(2.8) = 7,677.6
To learn more about multiplication, here:-
https://brainly.com/question/24327297
#SPJ1
PLSSSSSSSSS HELP DUE SOON!!!
Answer:
option 4
Step-by-step explanation:
let c represent the old amount , then twice the old amount is 2c.
1.5 less than twice the old amount is 2c - 1.5 , so
2c - 5 = 6
if the flow rate in an artery has been reduced to 8.5% of its normal value by a blood clot and the average pressure difference has increased by 20.5%, what percent of the original is the radius of the reduced artery?
Percent of the original is the radius of the reduced artery is 0.070 times the original radius.
Given that,
A blood clot has lowered the flow rate in an artery to 8.5% of its usual value, and the average pressure difference has increased by 20.5%.
p1 = 8.5 % ,
p2 = 20.5 %
The equation is using here is From Poiseuille's equation
Q = \Delta p \pi r4 / 8 \eta L
now
Q1 = \Delta p1\pi r14 / 8 \eta L
and
Q2 = \Delta p2\pi r24 / 8 \eta L
Q1 = \Delta p1\pi r14 / 8 \eta L / Q2 = \Delta p2\pi r24 / 8 \eta L
Q1 / Q2 = \Delta p1 ro4 / \Delta p2 r24
r24 = ( 0.085 Q1 / Q1 ) ( \Delta p1 / \Delta p1 + 0.20 \Delta p1 ) ro4
r24 = 0.085 X ( 1 / ( 1 + 0.20 ) ro4
r2 = 0.070 ro
As a result, the shortened artery's radius is 0.070 times its original radius, or percent of the original.
To learn more about radius click here:
brainly.com/question/13986226
#SPJ4
What is two divided by three I’ve two
Answer:
2 divided by 3 is 0.6 or 2/3
Step-by-step explanation:
Answer:
2/3 or 0.66666666667...
this sentence is false
Answer: what sentence ?
Step-by-step explanation:
Answer:
True
Step-by-step explanation:
The sentence is true because if it is true, then the sentence is false.
You are asking if the sentence is false, and it is false, so the question you asked is true.
This is so confusing though...
Elias has a collection of 1,200 baseball trading cards. Of these cards, 35% are from the American League, 45% are from the National League, the rest are international players. How many trading cards are of international players?
Answer:
240 trading cards
Step-by-step explanation:
20% of 1200 = .2 × 1200 = 240
Question 3 (5 points)
Find the equation of a parabola with a focus at (-2,-3) and a directrix at y = -5
The equation of a parabola with a focus at (-2,-3) and a directrix at y = -5 is y = 1/7(x + 2)^2 - 8/7 vertex is (2, -8/7)
What is Parabola?
A parabola is the location of a moving point whose distance from a given focus point and directrix line, respectively, is always constant.
let's keep it simple: (x, y). Focus is on (7,5)
When the separation from focus is
[tex]\sqrt{(x - (-2)^{2}) + (y - (-3)^{2} ) }[/tex] . Its distance from directrix y = -5 i.e.
y + 5 = |y + 5|^2
Hence, equation of parabola:
(x - (-2))^2 + (y - (-3))^2 = |y + 5|^2
or, (x + 2)^2 + (y + 3)^2 = |y + 5|^2
x^2 + 4x + 4 + y^2 + 3y + 9 = y^2 + 10y + 25
or, x^2 + 4x + 13 + y^2 + 3y = y^2 + 10y + 25
x^2 + 4x - 12 = 7y
y = (x^2 + 4x - 12)/7
y = 1/7(x^2 + 4x +4 - 4) - 12/7
y = 1/7(x + 2)^2 - 12-4/7
y = 1/7(x + 2)^2 - 8/7
Hence, parabola's equation is y = 1/7(x + 2)^2 - 8/7 vertex is (2, -8/7)
To learn more about Parabola click on the link
https://brainly.com/question/4061870
#SPJ13
I also need help with this question
Answer: (-3, 3)
Step-by-step explanation:
See the attached image for my work. First, you need to know the quadrants. In order from the top right counter-clockwise, it goes I (1), II (2), III (3), and IV (4).
Next, we will count up five units since Quadrant II is above the point, in Quadrant III.
Find the zeros of f(x)=x(x+2)^3
List them in order of least to greatest, separated by commas. If the multiplicity is more than one, only list the zero once.
All the x-values that bring a polynomial, p(x), to zero are referred to as its zeros. They are intriguing to us for a variety of reasons, one of which is that they provide information on the graph's x-intercepts for the polynomial.
We will also observe that they have a direct connection to the polynomial's factors.
What are polynomial zeros with an example?
Real number k is referred to as the zero of a polynomial P(x) if P(k) = 0. As a result, the polynomial x2 - 3x + 2 has a zero at 1 and a zero at 2.
The equation p(x)=(x-1) (x-3)
Although it is a polynomial of third degree, 2, only has two different zeros. This is due to the zero x=3 having a connection to the factor.
To learn more about Zero of a polynomial refer to:
https://brainly.com/question/352871
#SPJ13
Simplify the following expressions by combining like terms, if possible.
20 + xy - 3 + 4y^2 + 10 - 2y^2
(20 - 3 + 10) + (4y^2 - 2y^2) + xy
27 + 2y^2 + xy
Oct 24, 6:34:22 PM
Write two numbers that multiply to the value on top and add to the value on botton
42
-17
14 and 3 are two numbers for multiplication and addition.
What is multiplication ?
The four fundamental operations in mathematics are addition, subtraction, division, and multiplication. In mathematics, multiply refers to the repetitive addition of sets of identical size. Let's use the ice creams as a multiplication example to help us comprehend. There are two groups of this nature, and each group has ice cream.Multiplying in math is equivalent to adding like groups. The number of items in the group grows as we multiply. An example of a multiplication problem would be the product and the two factors. The factors and the product in the multiplication problem 6 x 9 = 54 are the numbers 6 and 9, respectively.The two numbers are 14 and 3.
14 + 3 = 17
14 * 3 = 42
Learn more about multiplication
brainly.com/question/5992872
#SPJ13
Funds are distributed to five families affected by floods in the ratio 5:12:2:15:29. The total amount that the five families received was $630.
a) The first family received _____
b) The difference between the amount of money the first and last family received was _____
c) A sixth family joins. They receive n amount of money and the average amount of money donated to all six families becomes 140. How much money does the sixth family receive?
Step-by-step explanation:
We must first add up the ratios:5+12+2+15+29 = 63, this will be the total ratio the money was shared Then we pick out the ratio for each family accordingly:For the first family, 5 out of the total ratio = 5/63
For the second family, 12 out of the total ratio = 12/63
For the third family, 2 out of the total ratio = 15/63
For the fifth family, 29 out of the total ratio = 29/63
a) The first family = 5/63 of the money, $630
we can therefore say the money they received is
= 5/63 ×630
= $50
b) The last family = fifth family = 29/63 of the money, 630
= 29/63 × 630
= $290
recall that the first family received $50 , the positive difference between the money received by both the first and last family
= $290 - $50
= $240
c) Since another family joins in, the total number of families become 6
the money the received is nwe can't find the average without knowing what the second, third, and fourth family received out of that money
we apply the same stepthe second family = 12/63 ×630
= $120
the third family = 2/63 × 630
= $20
the fourth family = 15/63 × 630
= $150
Average generally is = total sum/ frequency or number of occurrences or peoplein this case, we were told the average became $140
which means that
sum of money received by the families/ the number of families involved in the sharing = $140
( $50+$120+$20+$150+$290+n)/6 = $140($630+n)/6= $140
now the plan would be to make n subject of formula
multiply both sides of the equation by 6, the equation will become$630+n = $840
take $630 to the other side, it becomes -$630
n = $840-$630
n = $210
therefore the newly added family received $210
I honestly hope I explained it properly...thank you
Find the surface area of the triangular prism Formula: SA= p * h + 2 * b
ANSWER:
139 square yards
STEP-BY-STEP EXPLANATION:
We have that the formula for the surface area of a triangular prism is the following:
[tex]A=p\cdot h+2b[/tex]Where p, is the perimeter is the base and h is the height, while b is the area of the base, we replace and calculate the area like this:
[tex]\begin{gathered} p=4+4+5=13 \\ A=13\cdot9.5+2\cdot7.75 \\ A=123.5+15.5 \\ A=139 \end{gathered}[/tex]The area is 139 square yards
ASAP PLEASEEE HELPPP PLEASEEEE
1.If the parent function f(x) = |x| is transformed to h(x) = |x| - 3, what transformation occurs from f(x) to h(x)?
A.Shift left 3 units
B.Shift right 3 units
C.Shift up 3 units
D.Shift down 3 units
2. If the parent function f(x) = |x| is transformed to h(x) = |x| - 3, how is the vertex affected? Select all that apply.
A.The vertex will not change.
B.The vertex will shift right 3 units.
C.The vertex will shift left 3 units.
D.The vertex will shift up 3 units.
E.The vertex will shift down 3 units.
F.The vertex will not move up or down.
G.The vertex will not move right or left.
3. If the parent function f(x) = |x| is transformed to h(x) = |x| - 3, how is the range affected?
A.The range will not change.
B.The range will be all real numbers.
C.The range will change from y ≥ 0 to y ≥ -3.
D.The range will change from x ≥ 0 to x ≥ -3.
1) A translation of 3 units down, option D.
2) The vertex moves 3 units down.
3) The new range is y ≥ -3, correct option is C.
Which transformation is applied?For a function f(x) a vertical shift of N units is written as:
g(x) = f(x) + N
In this case, we have:
f(x) = |x|
h(x) = |x| - 3
Then h(x) = f(x) - 3
This is a shift of 3 units down, the correct option is D.
How is the vertex affected?
The vertex is translated 3 units down, like the whole graph of the function.
How is the range affected?
The vertex defines the minimum of the range, so if the vertex goes 3 units down, then the range also does, the new range will be:
y ≥ -3.
So the correct option is C.
Learn more about translations:
https://brainly.com/question/24850937
#SPJ1
Would you use circumference
or area to solve the following problem?
Your math teacher bakes a round pizza with a 4 foot
diameter to share with the class. You need to tell your teacher how many square feet?
are available to enjoy the Pizza Pi.
Answer: You always use circumference if you are talking about a round object.
Five boxes of crackers cost 9 at this rate how much do 20 boxes cost
Answer:
36
Step-by-step explanation:
Unit price: 9 / 5 = 1.8
20 box price: 1.8 * 20 = 36
When Felix started his paper route, he had 25 customers. Every second week he gained 2 new customers. Every third week he lost a customer. How many customers did he have in the seventh week? pls help
The number of customers he would have in the seventh week is 37.
How many customers would there by in the seventh week?The customers of Felix grow at a linear rate. A linear growth rate is when a value increases a constant rate. The customers would increase by 2 each week.
The linear equation that represents the number of customers in the seventh week:
Initial number of customers + [ rate of increase x (number of weeks - 1)]
25 + [2 x (7 - 1)]
25 + (2 x 6)
25 + 12 = 37
To learn more about linear functions, please check: https://brainly.com/question/26434260
#SPJ1
A rectangular garden has a length that is 3 feet longer than its width. Let represent the width of the garden, in feet. The entire garden is surrounded by a 2-foot wide cement walkway. What does the algebraic expression ( w + 4) (w + 7) represent in this context?
HIghschool Alegbra 1
Expression ( w+4)(w + 7) represent the total area of the garden and walkway.
What is Area of Rectangle?The area of Rectangle is length times of width.
Given that the width of the garden, in feet be w.
The length is 3 feet longer than its width, hence: w + 3
The entire garden is surrounded by a 2-foot-wide cement walkway. Therefore:
garden and walkaway length= (w + 3) + 2 + 2 = w + 7
garden and walkaway width = w + 2 + 2 = w + 4
The area of garden and walkaway
= length times of width
=Length × Width
= (w + 7)(w + 4)
Hence expression ( w+4)(w + 7) represent the total area of the garden and walkway
To learn more on Area of Rectangle click:
https://brainly.com/question/20693059
#SPJ1
Determine which integer in the solution set will make the equation true.
6x − 6 = 2(2x + 5)
S: {−2, 0, 8, 11}
Answer:
8
Step-by-step explanation:
[tex]6x-6=2(2x+5) \\ \\ 6x-6=4x+10 \\ \\ 2x-6=10 \\ \\ 2x=16 \\ \\ x=8[/tex]
Please help ASAP, I am in a super big hurry and have no idea what I’m doing! Please help!
Given the function:
h(x)=-6/7x+8/9
Find the following values.
a) h(1)
h(1)=
b) h(2)
h(2)=
c) h (-1/2)
h(-1/2)=
Answer: [tex]2/63, -52/63, 83/63[/tex]
Step-by-step explanation:
[tex]h(1)=-\frac{6}{7}(1)+\frac{8}{9}=\frac{2}{63}\\\\h(2)=-\frac{6}{7}(2)+\frac{8}{9}=-\frac{52}{63}\\\\h(-1/2)=-\frac{6}{7}(-1/2)+\frac{8}{9}=\frac{83}{63}[/tex]
Jill earns $264.50 a week. She is married and claims 3 allowances. What amount is withheld weekly for federal income tax?
As Jill claims 3 allowances then the amount which is withheld weekly for federal income tax is $11.
Given, Jill earns $264.50 a week.
She is married and claims 3 allowances.
From the table if the wage of a married person is at least $260 but less than $270 and has 3 allowances then weekly income tax is $11.
Individual federal income tax rates in the US are progressive, which means that they rise in proportion to taxable income. Federal income tax rates range from 10% to 37%, and they become effective at a certain level of income. Tax brackets are the ranges of income that the rates apply to. Each tax bracket has a different rate of taxation that applies to certain types of income.
Hence the amount is $11 for federal tax.
Learn more about Federal tax here:
brainly.com/question/1775528
#SPJ1
The length of a car is 4.2m,correct to 1 decimal place. Write down the upper bond and the lower bond of the length of this car.
Answer:
The upper pound is 4.25 m and the lower bound is 4.15 m
4.15 m ≤ 4.2 m < 4.25 m
Step-by-step explanation:
Let us solve the question
∵ The length of the car corrected to 1 decimal place
→ 1 decimal place means tenth
∴ It corrected to the tenths place which is 0.1
→ Divide it by 2
∵ 0.1 ÷ 2 = 0.05
∴ The limit is 0.05 m
→ To get the lower bound subtract 0.05 from the length of the car
∵ The length of the care is 4.2 m
∴ The lower bound = 4.2 - 0.05
∴ The lower bound = 4.15 m
→ To get the upper bound add 0.05 to the length of the car
∵ The length of the care is 4.2 m
∴ The upper bound = 4.2 + 0.05
∴ The upper bound = 4.25 m
∴ 4.15 m ≤ 4.2 m < 4.25 m
∴ The upper pound is 4.25 m and the lower bound is 4.15 m
P.s hopes this helps
The quantities xxx and yyy are proportional.
xxx yyy
222 222222
777 777777
999 999999
The value of y when x is 9 for the proportional relationship between is 31.5.
What is constant of proportionality?The constant of proportionality is used to show the proportional relationship between the numbers given.
In this case, when x is 2, y is 7. This will be illustrated thus:
y = kx
7 = 2k
Divide
k = 7/2
k = 3.5
Therefore, when x is 9, the value of y will be:
y = kx
y = 3.5 × 9
y = 31.5
Therefore, y is 31.5.
Learn more about constant of proportionality on:
brainly.com/question/28413384
#SPJ1
one student from the school will be selected at random. what is the probability that the student is in the age-group of 6 to 8 years given that the selected student responded joy?
Given that the chosen kid gave a joy response, the probability that the student belongs to the age range of 6 to 8 years is 28/89.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.So, the likelihood that a pupil is between the ages of 6 and 8 can be calculated using the techniques below:
Step 1: 89 pupils out of a possible 200 answered with joy, as shown in the table.Step 2 - It is also stated that there were a total of 28 students in the age range of 6 to 8 years who answered positively.Step 3 - Accordingly, the likelihood that the pupil belongs to the 6 to 8-year-old age range is:P = 28/89
Therefore, given that the chosen kid gave a joy response, the probability that the student belongs to the age range of 6 to 8 years is 28/89.
Know more about probability here:
https://brainly.com/question/28924396
#SPJ13
The complete question is given below:
Students at a local elementary school were shown a painting and asked which emotion—joy, happiness, love, or anger—they felt by looking at the painting. The students were classified by their age. The following table summarizes the responses of the students by age group. One student from the school will be selected at random. What is the probability that the student is in the age group of 6 to 8 years given that the selected student responded with joy?
kayla has a deck that measures 4 feet by 21 feet. she wants to increase each dimension by equal lengths so that the area is doubled. how much should she increase each dimension?
Answer:
Increase by 3.
Step-by-step explanation:
4 x 21 = 84
84 x 2 = 168
Begin to try numbers.
5 x 22 = 110
6 x 23 = 138
7 x 24 = 168
7 - 4 = 3
24 - 21 = 3
Increase each side by 3 ft. for a total dimension of 7 ft. x 24 ft.