Answer: 2500 years
Step-by-step explanation:
I'm not quite sure if I'm doing this right myself but I'll give it a shot.
We use this formula to find half-life but we can just plug in the numbers we know to find t.
[tex]A(t)=A_{0}(1/2)^t^/^h[/tex]
We know half-life is 5730 years and that the parchment has retained 74% of its Carbon-14. For [tex]A_{0[/tex] let's just assume that there are 100 original atoms of Carbon-14 and for A(t) let's assume there are 74 Carbon-14 atoms AFTER the amount of time has passed. That way, 74% of the C-14 still remains as 74/100 is 74%. Not quite sure how to explain it but I hope you get it. h is the last variable we need to know and it's just the half-life, which has been given to us already, 5730 years, so now we have this.
[tex]74=100(1/2)^t^/^5^7^3^0[/tex]
Now, solve. First, divide by 100.
[tex]0.74=(0.5)^t^/^5^7^3^0[/tex]
Take the log of everything
[tex]log(0.74)=\frac{t}{5730} log(0.5)[/tex]
Divide the entire equation by log (0.5) and multiply the entire equation by 5730 to isolate the t and get
[tex]5730\frac{log(0.74)}{log(0.5)} =t[/tex]
Use your calculator to solve that giant mess for t and you'll get that t is roughly 2489.128182 years. Round that to the nearest hundred years, and you'll find the hopefully correct answer is 2500 years.
Really hope that all the equations that I wrote came out good and that that's right, this is definitely the longest answer I've ever written.
Big Smiles Toy Company needs to pack marbles into a box. The company has two boxes they can use. Box A is 9 inches wide, 13 inches long, and 11.5 inches high. Box B is 14 inches wide, 8.5 inches long, and 12 inches high. Big Smiles Toy Company wants to use the larger box. Which box should the company choose and how much larger is it?
Answer:
The answer is Box B by 82.5 inches, let me know if it helped.
Step-by-step explanation
The company should choose Box B as it is larger than Box A. The volume of Box A is 1,497.75 cubic inches and the volume of Box B is 1,428 cubic inches, making Box A 69.75 cubic inches larger than Box B.
Explanation:The company should choose Box B as it is larger than Box A. To calculate the size difference, we need to find the volume of each box, which is calculated by multiplying the length, width, and height of the box. For Box A, the volume is 9 inches * 13 inches * 11.5 inches = 1,497.75 cubic inches. For Box B, the volume is 14 inches * 8.5 inches * 12 inches = 1,428 cubic inches. Therefore, Box A is 69.75 cubic inches larger than Box B.
Which of the tables would show inverse variation?
Answer:
C
Step-by-step explanation:
An inverse variation is where the product of inputs and outputs is constant. This means x*y is always the same number.
A is not a solution since it has 3*-4 = -12 and -2*4 = -8. It's not the same.
B is not a solution since it has 2*8 = 16 and 3*12 = 36. It's not the same.
C is a solution since 12*4 = 48 and 8*6 = 48 and 4*12 = 48 and 3*16 = 48. It's the same.
D is not a solution since it has 1*6 = 6 and 2*4 = 8. It's not the same.
PLEASE HELP!!!! WILL MARK BRAINLIEST!!!
A science museum has a spherical model of the earth with a diameter of 8.5 m. What is the volume of the
model? Use 3.14 for
and round your answer to the nearest whole number. Show your work.
Answer:
The volume of the model is [tex]321\ m^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the sphere (model of the earth) is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
In this problem we have
[tex]r=8.5/2=4.25\ m[/tex] ----> the radius is half the diameter
substitute the values
[tex]V=\frac{4}{3}(3.14)(4.25)^{3}=321\ m^{3}[/tex]
An engineering professor acquires a new computer once every 2 years. the professor can choose from three models: m1, m1, and m3. if the present model is m1, the next model can be m2 with probability .2, or m3 with probability .15. if the present model is m2, the probabilities of switching to m1 and m3 are .6 and .25, respectively. and, if the present model is m3, then the probabilities of purchasing m1 and m2 are .5 and .1, respectively. represent the situation as a markov chain.
Final answer:
The engineering professor's choice of new computer models over time can be modeled using a Markov chain, with specific transition probabilities for moving between models M1, M2, and M3. These probabilities are used to construct a transition matrix that allows us to analyze the selection pattern.
Explanation:
The scenario described can be represented as a Markov chain, which is a mathematical system that undergoes transitions from one state to another, with probabilities that are dependent on the current state only. Here, we have three models, M1, M2, and M3, which represent the states of the Markov chain. The transition probabilities define how likely it is to move from one state to another.
To construct this Markov chain, we set up a probability matrix P where the rows represent the current state, and the columns represent the next state. For the given model:
If the current model is M1, we have transition probabilities of 0.2 to M2 and 0.15 to M3.
If the current model is M2, we have transition probabilities of 0.6 to M1 and 0.25 to M3.
If the current model is M3, we have transition probabilities of 0.5 to M1 and 0.1 to M2.
Since the probabilities must add up to 1, the probability of remaining in the same state is 1 minus the sum of transition probabilities to other states. With these probabilities, we can fill in the transition matrix P:
P(M2|M1) = 0.2, P(M3|M1) = 0.15, P(M1|M1) = 0.65.
P(M1|M2) = 0.6, P(M3|M2) = 0.25, P(M2|M2) = 0.15.
P(M1|M3) = 0.5, P(M2|M3) = 0.1, P(M3|M3) = 0.4.
By using this transition matrix, we can analyze the professor's behavior in selecting new computer models over time.
Write the equation of a line in slope intercept form that has a slope of 4/5 and has a y- intercept of 0
Answer: y = 4\5*x
We can get this through slope intercept form.
Slope intercept form is y=mx +b where m is the slope and b is the y intercept.
We plug in 4.5 for the slope and 0 for the y-intercept.
Katie works as a waitress and records her monthly tips in the table shown below. If Katie decided not to work the month of November, how would her five month average compare to her six month average for monthly tips? June July August Septemper October November $133.45 $235.31 $239.45 $258.87 $298.45 $115.67 a. Her monthly average would have decreased by $19.57. b. Her monthly average would have increased by $19.57. c. Her monthly average would have increased by $2.07. d. Her monthly average would have decreased by $2.07.
Answer:
Correct answer is B.) Her monthly average would have increased by $19.57.
Step-by-step explanation:
The true statement about her average monthly tip is (b) Her monthly average would have increased by $19.57.
What is average?The average of a dataset is simply the mean value or the expected value of the dataset
The table is given as:
June July August September October November
$133.45 $235.31 $239.45 $258.87 $298.45 $115.67
For the 6 months, the average is:
Average = (133.45+235.31+239.45+258.87+298.45+115.67)/6
Average = 213.53
For the 5 months (i.e. exclusive of December), the average is:
Average = (133.45+235.31+239.45+258.87+298.45)/5
Average = 233.10
The 5 months average is greater than the 6 months average.
And the difference (d) is:
d = 233.10 - 213.53
Evaluate
d = 19.57
Hence, Her monthly average would have increased by $19.57.
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I will give brainliest to whoever is right and provides an explanation
Answer:
1024π
Step-by-step explanation:
The formula for the surface area of a sphere is 4πr².
Since the radius is 16 cm, the surface area is:
SA = 4×π×16²= 1024π.
A=4πr^2
A = 4π(16)^2
A = 3216.99
which is the same as 1024π cm^2
Explain the difference between an absolute minimum and a local minimum. a function f has an absolute minimum at x = c if f(c) is the smallest function value on the entire domain of f, whereas f has a local minimum at c if f(c) is the smallest function value when x is near
c.
Answer:
Step-by-step explanation:
Absolute minimum is where, in the infinite domain of f(x), the least value the function is the absolute minimum.
However, the local minimum is only a specific interval on the domain of f(x) where the lowest value is, but only in that interval.
So, usually, this comes up when you're dealing with 1st and 2nd derivatives. The first derivative tells you where local max and mins are, where the 2nd derivative tells you if the concavity is up or down.
An absolute minimum is the lowest point on the entire domain of a function, while a local minimum is the lowest point in a specific interval or neighborhood around a point on the graph.
Explanation:
An absolute minimum and a local minimum are both points on a graph where the function reaches its lowest value, but there are key differences between them.
An absolute minimum is the lowest point on the entire domain of the function. In other words, it is the smallest function value among all the points.
On the other hand, a local minimum is the lowest point in a specific interval or neighborhood around a particular point on the graph. It is possible for a function to have multiple local minima.
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Identify the domain of the function shown in the graph.
Answer:
B
Step-by-step explanation:
Domain of a function (Graph) is the set of ALLOWED x-values. Or, the x-values for which the function is defined.
Now, looking at the graph, we can see the line is defined in the region from x = 1 till x = 4, so the domain would be 1 ≤ x ≤ 4.
Answer choice B is right.
If 1 4 of a gallon of milk is shared equally between 6 friends, how much milk will each friend have?
1 Gallon = 4 quarts of milk
1/4 = 1 quart of milk
4 quarts of milk = 8 pints of milk
8/6 = 1.33 pints of milk
Each friend has 1.33 pints of milk
Each friend will get 1/24 of a gallon of milk.
To find out how much milk each friend will have, we need to divide 1/4 of a gallon by 6.
how much milk each friend gets,
(1/4) ÷ 6
(1/4) × (1/6)
= 1/24
Therefore, each friend gets 1/24 of a gallon of milk.
In conclusion, if 1/4 of a gallon of milk is shared equally among 6 friends, each friend will have 1/24 of a gallon of milk.
A game company makes a board game that comes with 2 dice and a card game that comes with 3 dice. Which expression shows the total number of dice in b boxes for the board game and the card game?
Answer:
5
Step-by-step explanation:
3 + 2 = 5
The expression for the total number of dice in b boxes for both a board game, which comes with 2 dice, and a card game, which comes with 3 dice, is 5b. This is calculated by adding the number of dice in each box (2b for the board game and 3b for the card game).
Explanation:The question is asking for an expression that shows the total number of dice in b boxes of the board game and the card game. The board game comes with 2 dice and the card game comes with 3 dice.
To get the total number of dice, one needs to multiply the number of dice in each type of game by the number of boxes, b, and then add the results together.
The total number of dice in the board game is 2b and the total number of dice in the card game is 3b. The sum of these two amounts gives the total number of dice. So the expression for the total number of dice in b boxes of both games is 2b + 3b, which simplifies to 5b.
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you put $634 into an investment at 6% compounded annually for six years. what will be the balance be at the end of six years?
Final answer:
The balance at the end of six years will be approximately $899.48.
Explanation:
To calculate the balance at the end of six years, we can use the formula for compound interest:
[tex]A = P(1 + r/n)^(nt)[/tex]
where A is the final amount, P is the principal amount (initial investment), r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
Plugging in the values, we have:
[tex]A = 634(1 + 0.06/1)^(1*6)[/tex]
[tex]= 634(1.06)^6[/tex]
= 634(1.418519)
= $899.48
Eric practice piano and guitar for 8 hrs. He practiced piano for 1 fourth of 8 hrs. How many hours did Eric practice the piano this week?
➷ Multiply the total value by 1/4:
1/4 x 8 = 2
He practiced it for 2 hours.
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ ʜᴀɴɴᴀʜ ♡
Answer:
2 hours.
Step-by-step explanation:
The time he practiced the piano = 1/4 * 8 = 2 hours.
Plz help meh on this
WIL GIVE BRAINLIEST
the answer is (a-4)^2
Answer:
Let's factor a2−8a+16
a2−8a+16
The middle number is -8 and the last number is 16.
Factoring means we want something like
(a+_)(a+_)
Which numbers go in the blanks?
We need two numbers that...
Add together to get -8 Multiply together to get 16 Can you think of the two numbers?
Try -4 and -4:
-4+-4 = -8
-4*-4 = 16
Fill in the blanks in
(a+_)(a+_)
with -4 and -4 to get...
(a-4)(a-4)
Answer:
(a−4)(a−4)
Maria buys a sweater at a department store. The sweater costs $40. The store is having a 35% off sale on everything in the store. Enter the amount of money, in dollars, Maria saves from the sale. Do not consider the sales tax.
Answer:
Maria gets $14 off of the original price of $40
Step-by-step explanation:
Estimate the fractional part of the shaded portions below. Explain how you decided
Answer:
do you have a picture?
I can't tell you how I decided it because there's not a picture
Can someone help me with this problem
Answer:
A = 20P = 6√10Step-by-step explanation:
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
A(-3, 0) , B(3, 2)
[tex]AB=\sqrt{(3-(-3))^2+(2-0)^2}=\sqrt{6^2+2^2}=\sqrt{36+4}=\sqrt{40}=\sqrt{4\cdot10}=\sqrt4\cdot\sqrt{10}=2\sqrt{10}[/tex]
A(-3, 0), D(-2, -3)
[tex]AD=\sqrt{(-2-(-3))^2+(-3-0)^2}=\sqrt{1^2+(-3)^2}=\sqrt{1+9}=\sqrt{10}[/tex]
AB = CD and AD = BC
The area of a rectangle:
[tex]A=(AB)(AD)[/tex]
Substitute:
[tex]A=(2\sqrt{10})(\sqrt{10})=(2)(10)=20[/tex]
The perimeter of a rectangle:
[tex]P=2(AB+AD)[/tex]
Substitute:
[tex]P=2(2\sqrt{10}+\sqrt{10})=2(3\sqrt{10})=6\sqrt{10}[/tex]
The shapes of the horizontal cross-sections of the cone below are all congruent. True or false
Answer:
the answer is false
Step-by-step explanation:
False, The shapes of the horizontal cross-sections of the cone below are not all congruent.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We are given the statement,
'The shapes of the horizontal cross-sections of the cone are all congruent'.
Now, if we cut the cone horizontally, the cross-sectional shape is a 'circle'.
Further, the radius of the circle vary depending on the position form where the cone is cut i.e.
If cut from the top, the circle is approximately equal to a point.
If cut from the middle, the radius of the circle is less than the radius of the cone.
If cut from the bottom, the radius of the circle is equal to the radius of the cone.
Now, 'two figures are congruent if they overlap each other'.
Since, the circles have different radius, they will not overlap each other.
Thus, all the cross-sections of the cone would not be congruent.
Hence, the given statement is false.
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The length of a rectangle is 3 m longer than its width.
The area of the rectangle is 154 m².
What is the width of the rectangle?
Enter your answer in the box.
Answer:
The width is 51.333
Step-by-step explanation:
l * w = area of rectangle
3 * w = 154
w= 154/3
w=51.333
Answer:
11
Step-by-step explanation:
It right
Estimate the limit
A
B
C
D
Answer:
C. [tex]\lim_{x\rightarrow f(x)=2[/tex]
Step-by-step explanation:
Given problem is [tex]\lim_{x\rightarrow \frac{\pi}{4}}\frac{tan(x)-1}{x-\frac{\pi}{4}}[/tex].
Now we need to evaluate the given limit.
If we plug [tex]\x=\frac{\pi}{4}[/tex], into given problem then we will get 0/0 form which is an indeterminate form so we can apply L Hospitals rule
take derivative of numerator and denominator
[tex]\lim_{x\rightarrow \frac{\pi}{4}}\frac{tan(x)-1}{x-\frac{\pi}{4}}[/tex]
[tex]=\lim_{x\rightarrow \frac{\pi}{4}}\frac{sec^2(x)-0}{1-0}[/tex]
[tex]=\frac{sec^2(\frac{\pi}{4})-0}{1-0}[/tex]
[tex]=\frac{(\sqrt{2})^2}{1}[/tex]
[tex]=\frac{2}{1}[/tex]
=2
Hence choice C is correct.
The circumference of a circle is 34π
find the diameter and radius
please put an explanation, I desperately need help with finding diameter/radius with circumference
The circumference of a circle is calculated like this:
[tex]c = 2 \times \pi \times r = \pi \times d[/tex]
If the circumference of the circle is 34π, its diameter is 34(cm), therefore its radius is 17(cm).
To find the diameter and radius of a circle when given the circumference, you can use the formulas C = 2πr or C = πd. In this case, the circumference is 34π. The circle's diameter is 34 units, and the radius is 17 units.
Explanation:To find the diameter and radius of a circle when given the circumference, you can use the formula C = 2πr or C = πd, where C is the circumference, r is the radius, and d is the diameter. In this case, the circumference is given as 34π. Using the formula C = πd, we can substitute the value of the circumference and solve for the diameter:
34π = πd
Dividing both sides of the equation by π, we get:
34 = d
So, the diameter of the circle is 34 units. To find the radius, we can use the formula r = d/2:
r = 34/2
r = 17
Therefore, the circle's diameter is 34 units, and the radius is 17 units.
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HELP
What is the value of x in the equation 2.5(6x-4)=10+4(1.5+0.5x) ?
A)1/3
B)1/2
C)2
D)13
Answer:
[tex]\large\boxed{C)\ 2}[/tex]
Step-by-step explanation:
[tex]2.5(6x-4)=10+4(1.5+0.5x)\qquad\text{use the distributive property}\\\\(2.5)(6x)+(2.5)(-4)=10+(4)(1.5)+(4)(0.5x)\\\\15x-10=10+6+2x\qquad\text{subtract 2x from both sides}\\\\13x-10=16\qquad\text{add 10 to both sides}\\\\13x=26\qquad\text{divide both sides by 13}\\\\x=2[/tex]
Answer:
C)2
Step-by-step explanation:
Trust me here boyzz
PLEASE HELP ME ASAAP 1 ANSWER EQUALS ONE SAVE FROM MY MOM WHOPPING MY A 2/4 + 4/6
Answer:
5/6 I think
Step-by-step explanation:
Add 2/4 + 2/6 =
2*3/4*3 + 2*2/6*2 =
6/12 + 4/12 =
6+4/12 =
10/12 =
5/6
[tex] \frac{5}{6} \\ hope \: it \: helps \: \\ :)[/tex]
Please answer this multiple choice question, will give brainliest!
Answer:
A angle V and angle Z
Step-by-step explanation:
Using the equilateral triangle's definition of all sides and angles are equal, we can determine that V, Z, and U are congruent.
Given that line EH is a median of triangle EFG find FG
Answer:
12.2
Step-by-step explanation:
We can say that FG = FH + HG
Since EH is the median, FH and HG is equal. Thus we can find x.
[tex]FH=HG\\6x-1.1=4x+1.3\\6x-4x=1.3+1.1\\2x=2.4\\x=\frac{2.4}{2}\\x=1.2[/tex]
Now we can find FH = 6x - 1.1 = 6(1.2) - 1.1 = 6.1, and
HG = 4x + 1.3 = 4(1.2) + 1.3 = 6.1
Hence, FG = 6.1 + 6.1 = 12.2
Megan' pencil is shorter than Tasha's pencil.Tasha's pencil is shorter than Kim's pencil.Is Megan's pencil shorter or longer than Kim's pencil?Draw or write to explain
Answer:
Meghan's pencil is shorter than Kim's pencil.
Step-by-step explanation:
Let's denote Meghan's pencil height with M, Tasha's with T and Kim's with K
Now, we know that
M < T
and T < K
So, by transitive property,
M < K
(5CQ) Use the comparison test to determine whether the series 25/3+125/9+625/27+... is convergent or divergent.
The terms in the sum are given by the sequence
[tex]\left\{\dfrac{5^{n+1}}{3^n}\right\}_{n\ge1}[/tex]
We have
[tex]\dfrac{5^{n+1}}{3^n}>\dfrac{5^n}{3^n}=\left(\dfrac53\right)^n>1[/tex]
for all [tex]n[/tex], and the series [tex]1+1+1+\cdots[/tex] clearly diverges, so [tex]\dfrac{25}3+\dfrac{125}9+\cdots[/tex] must also diverge.
Answer:
B. Divergent
Step-by-step explanation:
Did test
What is the slant height x of the square pyramid?
Express your answer in radical form.
Answer:
x = [tex] 4 \sqrt { 3 } [/tex]
Step-by-step explanation:
We are given a diagram of a pyramid with a right angled triangle which has [tex]30[/tex]°, [tex]60[/tex]° and [tex]90[/tex]° angles an the hypotenuse is [tex]8cm[/tex].
Since we have a right angled triangle, we can apply sin here:
We know that [tex]sin 60 = \frac{\sqrt{3} }{2}[/tex] so we can write it as
[tex]\frac{\sqrt{3} }{2} = \frac{x}{8}[/tex]
So we get the slant height of x = [tex]4\sqrt{3}[/tex].
Answer:
The slant height of square pyramid = 4√3 m
Step-by-step explanation:
From the figure we can see a square pyramid with lateral edge 8 m
Also the one angle of face triangle is 60° , therefore the face triangle is an equilateral triangle.
Therefore the base is 8 m
To find the slant height
slant height² = Lateral edge² - (base/2)²
= 8² - (8/2)² = 8² - 4²
= 64 - 16 = 48
Slant height = √48 = 4√3 m
Therefore slant height of square pyramid = 4√3 m
50 POINTS!! HURRYY
Kari, a biologist, is getting ready for a new study of tropical fish. She needs to fill the tank with precisely 5 gallons of water. She uses a quart container. Division Rules How many times will Kari have to fill the container to make 5 gallons? 10 times 15 times 20 times 25 times
Answer:
20
Step-by-step explanation:
ONE QUART IS 0.25 OF A GALLON. SORRY CAPS LOCK IS STUCK TURNED ON!
Answer:
Step-by-step explanation:
She needs to fill the quart container
20 times.
4 quarts make a gallon, so 20 quarts = 5 gallons.
Select the favorable outcomes for rolling a five on the first roll.
Please help.
A 1/6% chance because there are six sides and 5 is one of them
Answer:
(1-6) (2-5) (3-4) (4-3) (5-2) (6-1)
Step-by-step explanation:
I was just doing this lesson