Answer:
The artifact was made approximately 13,306 years ago
Step-by-step explanation:
The half-life of Carbon-14 = 5730 years
The formula for radioactive decay is given by the equation:
[tex]N=N_0 e^{- \lambda t}\\where:\\N = Number\ of\ particles\ at\ time\ t\\N_0= Number\ of\ particles\ at\ time\ t_0\\\lambda = decay\ constant = \frac{In}{t_{1/2}} ; t_{1/2} = half-life\\t = time\ in\ years[/tex]
The amount of Carbon-14 left = 20% = 20/100 = 0.2
[tex]\therefore \frac{N}{N_0} = 20 \% = 0.2[/tex]
[tex]N=N_0 e^{- \lambda t}\\\\dividing\ both\ sides\ by\ N_0\\\frac{N}{N_0} = e^{- \lambda t}\\0.2 = e^{- \lambda t}\\taking\ natural\ logarithm\ of\ both\ sides\\In 0.2 = Ine^{- \lambda t}\\In0.2 = -\lambda \times t\\but\ \lambda = \frac{In2}{t_{1/2}} \\\therefore In0.2 = -\lambda \times t\\\\= In0.2 = - \frac{In2}{t_{1/2}} \times t\\where\ t_{1/2} = 5730\ years\\-1.6094 = - \frac{0.6931}{5730} \times t\\-1.6094 = - 0.00012095 \times t\\t = \frac{-1.6094}{-0.00012095} \\t = 13,306.32[/tex]
t ≈ 13,306 years
1. The diagram represents a cone.
The height of the cone is 12 cm.
The diameter of the base of the cone is 10 cm.
Calculate the curved surface area of the cone.
2. A sphere has a volume of 500 m3.
(b) Calculate the radius of the sphere. Give your answer correct to 3
significant figures.
Answer:
1. The curved surface area of the cone is 282.74 cm²
2. Radius of sphere r = 4.924 m
Step-by-step explanation:
1. Height of cone = 12 cm
Diameter of base of cone = 10 cm
Surface Area of cone = ?
The formula used is: [tex]A=\pi r(r+\sqrt{h^2+r^2})\\[/tex]
h= 12 cm
r = diameter/2 r = 10/2 = 5 cm
Putting values and finding surface area
[tex]A=\pi r(r+\sqrt{h^2+r^2})\\A=3.14*5 (5+\sqrt{(12)^2+(5)^2})\\A=15.7 (5+\sqrt{144+25})\\A=15.7 (5+\sqrt{169})\\A=15.7 (5+13)\\A=15.7(18)\\A=282.74 \ cm^2[/tex]
So, the curved surface area of the cone is 282.74 cm²
2. Sphere of Volume = 500 m³
We need to find radius of sphere
The formula used is: [tex]Volume=\frac{4}{3}\pi r^3[/tex]
Putting values and finding radius of sphere
[tex]Volume=\frac{4}{3}\pi r^3\\500=\frac{4}{3}*3.14* r^3\\500=4.186*r^3\\=> r^3=\frac{500}{4.186}\\r^3=119.446\\Taking \ cube \ root \ on \ both \ sides.\\\sqrt[3]{r^3}=\sqrt[3]{119.446}\\r= 4.924 \ m\\[/tex]
So, Radius of sphere r = 4.924 m
Sketch the graph of the function by (a) applying the Leading Coefficient Test, (b) finding the zeros of the polynomial, (c) plotting sufficient solution points, and (d) drawing a continuous curve through the points. 65.) f(x)=x^3-9x 66.) g(x)=x^4-4x^2
Answer:
C
Step-by-step explanation:
If its C I'm sorry That seems correct but I don't know for sure, just my advice!
Help fast
Ian and his friends are renting a cabin that charges an initial fee plus a rate per night. The relationship between the cost and the number of nights is shown in the graph.
What is the initial fee to rent the cabin?
$50, this is the y-intercept
What is the cost per night?
$75, this is the slope
Write an equation to represent the situation.
y = 75x + 50
The library has 27 chairs and 5 tables. If the same nur chairs can be placed at each table? Will there be any
Answer:
no
Step-by-step explanation:
27 divided by 5 = 5.4 so there would not be enouph
Answer:
Each table will have 5 chairs, with 2 chairs leftover.
Step-by-step explanation:
27 divided by 5 equals 5 with a remainder of 2.
8.9 x 7 can u solve it with work shown
Answer:
62.3
Step-by-step explanation:
6
8.9
*7
____
62. 3
I tried to show how to do it but carry the 6 at the top
Answer:
64 (I rounded btw)
Step-by-step explanation:
8.9 × 7 = ??
1. Round 8.9
2. 8.9 can be rounded to 9
3. change equation
4. 9×7= 63
Thus, your answer is 63
(If your supposed to do the math differently tell me and I'll correct it)
Susie is paying $538.66 every month for her $150,000 mortgage. If this is a 30 year mortgage, how much interest will she pay over the 30 years of payments?
Answer:
Step-by-step explanation:
So First we know she pays (538.66) every month (12months in a year ) for (30) years
So 538.66*12*30 = 193,917.60
Then, we take his total payment minus the what he originally owed.
193,917.60 - 150,000 = $43,917.60
Susie's monthly mortgage payment on her $150,000 home is $538.66. If the loan has a 30-year term, the total interest she will have to pay throughout that time will be $43,917.60.
What is a mortgage?
A mortgage is, to put it simply, a contract that a person forms after borrowing money from a lender (in this case, a bank) and giving the lender a guarantee (in the form of a real estate property) that the money will be paid back in full.
So first one must know as she pays 538.66 every month as there are 12 months in a year and for 30 years, the payment calculation is:
538.66 × 12 × 30 = 193,917.60
Then, deduct the amount he originally owed from his total payment.
193,917.60 - 150,000 = $43,917.60
Therefore, the total interest she will have to pay throughout that time will be $43,917.60.
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If 8 is added to five times a number, the result is equal to three times the number. Find the number.
Answer:
8+5x=3x 8= -2x x = -4
Step-by-step explanation:
May I have brainliest please? :)
Answer:
-4
Step-by-step explanation:
5x + 8 = 3x
Jacob bought 10 liters of milk at the supermarket. How many gallons of milk did he buy?
Answer:
2 ,but exact is 2.64172
Step-by-step explanation:
Answer:
2.64 gallons
Step-by-step explanation:
10/3.785= 2.64
Tom has a solid, wooden block that is a rectangular prism with non-square bases. He saws the prism parallel to the base. What shape is the cross section?
rectangle not square
triangle
diamond
square
Answer:
A) Rectangle
Step-by-step explanation:
Hope this helps :D
y'all helpppp on this question ASAP please!!!!
Heather wrote her bike at a rate of 15 per second which graph best represents the relationship between this time in seconds Heather rode her bike, x, and the distance in feet she rode, y?
The graph will be linear with a positive slope if distance is increasing with time.
Relationship between distance and timeThe question is incomplete but I will try to help you the much I can. The speed of a body is the ratio of distance covered to the time taken. The shape of the distance time graph depends on the nature of the relationship.
Even though the graph is not shown, the graph will be linear with a positive slope if distance is increasing with time.
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The following is a special trapezoid. Given WX is parallel to ZY. Which of the following is also true about trapezoid WXYZ?
∠W ≅ ∠Z
∠Z and ∠W are supplementary
∠W ≅ ∠X
∠X and ∠Y are complementary
Answer:
∠Z and ∠W are supplementary
Step-by-step explanation:
In the diagram given showing a special trapezoid, WX and ZY are two opposite sides that are parallel to each other.
Thus, consecutive angles would be supplementary.
Therefore, the only correct option that is true is:
∠Z and ∠W are supplementary.
The test options are incorrect as consecutive angles are not complementary and they are not in themselves congruent to each other.
They ARE supplementary so it WOULD be B <z and <w are supplementary
Monica makes tomato sauce with the plants she grows in her garden. she uses 3 basil leaves in her sauce for every 8 tomatoes. she is making a big batch of sauce with 32 tomatoes from her garden. how many basil leaves should monica use in her sauce?
The number of basil leaves required will be 12.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that Monica makes tomato sauce with the plants she grows in her garden. she uses 3 basil leaves in her sauce for every 8 tomatoes. she is making a big batch of sauce with 32 tomatoes from her garden.
The number of basil leaves will be calculated as:-
3 basil leaves = 8 tomatoes
1 tomato = 3 / 8 basil leaves
32 tomatoes = ( 32 x 3) / 8 = 4 x 3 = 12
Therefore, the number of basil leaves required will be 12.
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A hockey puck with a mass of 0.18 kg is at rest on the horizontal frictionless surface of the rink. A player applies a horizontal force of 0.5 N to the puck. Find the speed and the traveled distance 5 s later.
Answer:
1) The speed after 5 seconds is 13.[tex]\bar 8[/tex] m/s
2) The distance traveled after 5 seconds is 34.7[tex]\bar 2[/tex] meters
Step-by-step explanation:
1) The given parameters are;
The mass of the hockey puck, m = 0.18 kg
The horizontal force applied by the player, m = 0.5 N
The time at which the speed is calculated, t = 5 seconds after the force is applied
Therefore;
From the equation for the applied force, F = m × a. where a represents the acceleration, by substituting the known values get;
0.5 = 0.18 × a
∴ a = 0.5/0.18 = 50/18 = 25/9 = 2.[tex]\bar 7[/tex]
a = 2.[tex]\bar 7[/tex] m/s²
The speed after 5 seconds is given from the kinematic equation, v = u + a·t
Where;
v = The final velocity
u = The initial velocity = 0 m/s
t = The time = 5 seconds
By substitution of the known values, we get;
v = 0 + 2.[tex]\bar 7[/tex] × 5 = 13.[tex]\bar 8[/tex]
The speed after 5 seconds = 13.[tex]\bar 8[/tex] m/s
2) The distance traveled, s, after 5 seconds is given by the equation, s = u·t + 1/2·a·t²
From which we have;
s = 0 × 5 + 1/2 × 2.[tex]\bar 7[/tex] × 5² = 34.7[tex]\bar 2[/tex]
The distance traveled after 5 seconds = 34.7[tex]\bar 2[/tex] meters
paying 20$ cashapp if you get this correct
Answer:
148⁰
Step-by-step explanation:
M< EDF = M< DFE (because the two angles are equal because the triangle has two equal sides)
2x + 8 = 3x + 4
8 – 4 = 3x - 2x
4=x or x=4
So M< EDF= 2x4+8 = 16⁰
So M< EDF + M< DFE= 32⁰
180⁰- 32⁰ = 148⁰
The rectangle shown as a perimeter of 70 cm and the given area. It’s length is 8 more than twice it’s width. Write and solve a system of equations to find the dimensions of the rectangle.
The length of the rectangle is ___cm and the width of the rectangle is ___cm.
width of the rectangle = b = x
length of the rectangle = l = 8 + 2x
Perimeter of the rectangle = 70cm
Also, perimeter of the rectangle = 2(l + b)
70 = 2[x + (8 + 2x)]
70 = 2(x + 8 + 2x)
70 = 2(3x + 8)
70 = 6x + 16
70 - 16 = 6x
54 = 6x
54/6 = x
9 = x
Therefore, b = x
b = 9cm
l = 8 + 2x
I = 8 + 2×9
I = 8 + 18
I = 26cm
eleanor was curious if triangles DEF and GHI were similiar so she tried to map one figure onto the other using rigid transformations
Answer:
Eleanor was curious if triangles DEF and GHI were similar, so he tried to map one figure onto the other using rigid transformations Eleanor concluded "It's not possible to map triangle DEF on GHI using a sequence of rigid transformations, so the triangles are not similar. ... So the triangles are similar.
Step-by-step explanation:
Answer:
It is B. One more transformation — a dilation — would map \triangle DEF△DEFtriangle, D, E, F onto \triangle GHI△GHItriangle, G, H, I. So the triangles are similar.
Step-by-step explanation:
Mr. Brown’s bank account is overdrawn $110.55 and he deposits $18 a week. His wife has a separate account and her account is also overdrawn $63.12 and she deposits $22.50 a week. How many weeks will it be before Mr. Brown’s wife has more in her account than her husband?
Answer:
y=mx+b sdi c xc xx cx cx cxc xc 87
Step-by-step explanation:
A manufacturer knows that their items have a normally distributed lifespan, with a mean of 12.3 years, and standard deviation of 0.7 years. If you randomly purchase 14 items, what is the probability that their mean life will be longer than 12 years?
Answer:
The probability is [tex]P(\= X > 12 ) = 0.72688[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 12.3 \ years[/tex]
The standard deviation is [tex]\sigma = 0.7 \ years[/tex]
The sample size is n = 14
Generally the standard error of the mean is mathematically represented as
[tex]\sigma _{x} = \frac{\sigma}{\sqrt{n} }[/tex]
=> [tex]\sigma _{x} = \frac{0.7}{\sqrt{14} }[/tex]
=> [tex]\sigma _{x} = 0.1871[/tex]
Generally the probability that their mean life will be longer than 12 years is mathematically represented as
[tex]P(\= X > 12 ) = P(\frac{\= X - \mu }{\sigma} > \frac{12 - 12.3}{ 0.1871 } )[/tex]
[tex]\frac{\= X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ \= X )[/tex]
[tex]P(\= X > 12 ) = P(Z > -0.6034 )[/tex]
From the z table the area under the normal curve to the left corresponding to -0.6034 is
=> [tex]P(Z > -0.6034 ) = 0.72688[/tex]
=> [tex]P(\= X > 12 ) = 0.72688[/tex]
What is the length of CD?
Answer:
5
Step-by-step explanation:
Use formula or count the steps since it's on the same line
When performing a translation you _____________ the movements to your x and y values of the coordinates. Select all that apply.
Multiply
Divide
Subtract
Add
a refrigerator was originally sold for $360 and has been markdowned to $270. what is the percentage of the discount for the refrigerator? ____%
Step-by-step explanation:
percentage discount = (360 - 270)/360 x 100% = 25%
Topic: Percentage
You can check out my insta (learntionary) for the formula for these types of questions or look for other cool math tips!
Which of the following is NOT true about cluster sampling?
A.
B.
C.
D.
Answer:
c
Step-by-step explanation:
Answer:
The correct answer is A
Step-by-step explanation:
Write a function to describe the following scenario.
After sprinting, Emilie has a heart rate of 160. As
she cools down, her heart rate falls by 12 beats
per minute. What will her heart rate be after a
certain number of minutes?
y = [?] - [ ]2
Answer:
[tex]r=160-12m[/tex]
Step-by-step explanation:
Heart rate will be represented by [tex]r[/tex], minutes will be represented by [tex]m[/tex].
Here's the equation I came up with:
[tex]r=160-12m[/tex]
We can also rearrange it to look like a point-slope equation. Either way works, it's the same equation.
[tex]r=-12m+160[/tex]
This works because her heart rate is decreasing by a constant value. The initial heart rate is like the y-intercept, while the amount that it decreases by is the slope.
I hope this helps!
The equation is y=160-12t where t is the time in minutes.
What is a linear equation?The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.
Given here, After sprinting, Emilie has a heart rate of 160. As
she cools down, her heart rate falls by 12 beats therefore, we can form the equation as if the time is t minutes of cooling down then we can the heartbeat at a given time as y=160-12t
Hence, the equation is y=160-12t where t is the time in minutes.
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How do the expressions 72 divided and -72divided by (-9) and compare when they are evaluated?
Complete question is;
How do the expressions 72 divided by 9 and -72 divided by (-9) compare when they are evaluated?
A. They have different values and are different signs.
B. They have different values but are the same sign.
C. They have the same value but are different signs.
D. They have the same value and the same sign
Answer:
D. They have the same value and the same sign
Step-by-step explanation:
For 72 divided by 9,it is;
72/9 = 8
Usually when we don't have any sign in front of a number, it is said to be positive.
Thus, the answer can be expressed as; +8
Also, when -72 is divided by (-9), it is;
-72/-9
The negative signs will cancel out to give; 8
Similar to the first division, since no sign is attached to 8,it is said to be positive as +8.
This means both divisions yield same values and same signs
Which statement is true about points located in quadrant I in the coordinate
plane?
A. The x-coordinate is negative, and the y-coordinate is negative.
B. The x-coordinate is positive, and the y-coordinate is positive.
C. The x-coordinate is positive, and the y-coordinate is negative.
O D. The x-coordinate is negative, and the y-coordinate is positive.
Please hurry
Answer:
B
Step-by-step explanation:
In Quadrant I, both the x– and y-coordinates are positive; in Quadrant II, the x-coordinate is negative, but the y-coordinate is positive; in Quadrant III both are negative; and in Quadrant IV, x is positive but y is negative.
Answer: its actually A
Step-by-step explanation:
Its not b it is A The x-coordinate is negative, and the y-coordinate is negative
The unit rate of video games is ?
How much would you pay for 10 video games?
Answer:
you will pay $75
Step-by-step explanation:
A poster is to have a total area of 500 square centimeters. There is a margin around the edges of 4 cm at the top and 8 cm on the bottom and sides where nothing is printed. Express the printed area A in terms of the width w (in centimeters) of the bottom.
Answer:
A(w) = 692 - 12w - (8000/w)
Step-by-step explanation:
Since it has a total area of 500 cm², it means that;
A = hw
Where;
A is area
h is height
w is width
Thus;
500 = hw
h = 500/w
We are told that There is a margin around the edges of 4 cm at the top and 8 cm on the bottom and sides where nothing is printed.
Thus;
We have height as; (h - 4 - 8) and width as; (w - 8 - 8)
Thus;
Area = (h - 4 - 8) × (w - 8 - 8)
Area = (h - 12) × (w - 16)
We know that h = 500/w
And we want to find the printed area in terms of the width(w)
Thus;
A(w) = ((500/w) - 12) × (w - 16)
A(w) = 500 - 12w - 8000/w + 192
A(w) = 692 - 12w - (8000/w)
Using the area formula, the appropriate expression for the area of the poster is A(w) = - 8000/w - 12w + 692
Total Area = 500 cm²
Area = Length × width
Entire area can be expressed thus :
500 = l × w l = 500 / wArea with print can be expressed thus :
Length with print = (l - 8 - 4) = (l - 12) cm
Height with print = (w - 2(8)) = (w - 16) cm
Area = (l - 12)(w - 16)
Area = (500/w - 12)(w - 16)
Expressing in terms of width :
A(w) = 500 - 8000/w - 12w + 192
A(w) = - 8000/w - 12w + 692
Hence, the required expression is : A(w) = - 8000/w - 12w + 692
Look at this set of ordered pairs: (14, 19) (14, 5) (4, 18) Is this relation a function? yes no
Answer:
This is a relationship, and NOT a function
Step-by-step explanation:
Notice that from the pairs listed, we find that the number 14 in the Domain is connected via the relationship with TWO different numerical values in the Range (with 19 and with 5).Therefore, this cannot be a function, since in such case, each element of the Domain must connect with no more than one element of the Range.
pleasseee helllp meeee
Answer:
The third one
Step-by-step explanation:
Answer:
Y=3x
Step-by-step explanation:
I'm pretty sure it would be y=3x because you have to multiply the cost of the tickets by the number of tickets