archeologists continue to debate the arrival of the first humans in the western hemisphere. radiocarbon dating of charcoal from a cave in chile was used to establish the earliest date of human habitation in south america as 8700 years ago. this procedure involves comparing the 14c present in a sample of charcoal to the 14c present in a living tree of the same age. 1st attempt see hint what fraction of the 14c initially present remained in the charcoal after 8700 years? the half-life of 14c is 5730 years. (write the answer as a number with a decimal.)

Diameter = 12 inch so, radius will be 6 inch

Volume of circle = 4/3πr³

= 4/3 × (6)³ π

= 4 × 2 × 36 π

= 8 × 36

= 288π in³

Answer:

A quadrilateral.

Step-by-step explanation:

The shape has 4 sides, so it is a quadrilateral.

Answer:

dart

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the series solution for the differential equation y'' + 2xy' + 2y = 0, we can assume a power series solution of the form:

Now, substitute y(x), y'(x), and y''(x) into the differential equation:

∑(n=0 to ∞) aₙn(n-1) xⁿ⁻² + 2x ∑(n=0 to ∞) aₙn xⁿ⁻¹ + 2 ∑(n=0 to ∞) aₙxⁿ = 0

We can simplify this equation by combining the terms with the same powers of x. Let's manipulate the equation step by step:

We can combine the three summations into a single summation:

∑(n=0 to ∞) (aₙ₊₂(n+1)n + 2aₙ₊₁ + 2aₙ) xⁿ = 0

Since this equation holds for all values of x, the coefficients of the terms must be zero. Therefore, we have:

This is the recurrence relation that determines the coefficients of the power series solution To find the series solution, we can start with initial conditions. Let's assume that y(0) = y₀ and y'(0) = y'₀. This gives us the following initial terms:

To know more about a series solution:- https://brainly.com/question/31522450

#SPJ11

Answer:

(2x-5)feet

Step-by-step explanation:

The area of the rectangular garden A = Length × Width

Given the area A(x) = 2x² - 21x + 40

And the width =x-8 feet

To get the length, we will simply factorise the area function as shown;

You will just factorise the area

Factorizing 2x² - 21x+40

2x² − 21x + 40

2x² -16x - 5x + 40

2x(x - 8) -5(x - 8)

=(2x−5)(x−8)

Hence the length of the garden is

(2x-5)feet

Answer:

3 7/9

Step-by-step explanation:

For the month of November, there has been a depreciation of almost $1,089.60.

By deducting the expected residual value from the cost of the tractor and dividing the result by the total projected operational life in hours, let's first get the depreciation per hour:

A tractor's depreciation per hour is calculated by deducting the residual value from the purchase price, and multiplying the result by the number of hours the tractor will be in use.

\(\rm D = \dfrac {136,700 - 14,500} { 18,800}\\D = \$6.81\)

Multiplying the depreciation per hour by the number of hours the tractor was used to get the depreciation for the month of November

\(D_m = 6.81 \times 160\\D_m = \$1,089.60\)

Therefore, for the month of November, there has been a depreciation of almost $1,089.60.

To know more about depreciation cost follow

https://brainly.com/question/19866247

#SPJ12

Answer:

55%

Step-by-step explanation:

1/4 - Micah will only have a 25% chance of selecting a blue pencil.

1/5 - Micah will only have a 20% chance of selecting a red pencil.

So, to conclude this, Micah only has a 55% chance of selecting a yellow pencil.

Answer:

14

Step-by-step explanation:

As a result, an experiment entails randomly selecting one of two urns and then drawing a marble from that urn. The probability that a green marble was picked is 0.524.

We are informed from the question that

Urn 1 has the following number of green marbles \(Ng=14\)

Urn 1 has the following number of yellow marbles \(Ny=15\)

Urn 2 has the following number of green marbles: \(n_{g} =11\)

Urn 2 has the following number of yellow marbles:\(n_{y}=8\)

The likelihood of selecting Urn 1 is \(P(U1) = 0.57\)

The likelihood of selecting Urn 2 is \(P (U2)= 1-0.57\)

                                                           \(P(U2)= 0.43\)

Let \(Nt\) be the total number of marbles in urn 1. Then,

Typically, Urn 1's total marble is \(Nt=Ng+Ny\)

                                                   \(Nt=14+15\)

                                                   \(Nt=29\)

Let \(nt\) be the total number of marbles in urn 1

Typically, Urn 2's total marble is n \(n_{t} = n_{g} +n_{y}\)

                                                     \(n_{t} =11+8\)

                                                     \(n_{t}=19\)

The likelihood of selecting green marble is typically

\(P(Ng)=P(U1)* \frac{Ng}{Nt} + [P(U2)*\frac{n_{g} }{n_{t} }]\)

\(P(Ng)=0.57*\frac{14}{29} + [0.43*\frac{11}{19} ]\)

\(P(Ng)=0.57*0.483+[0.43*0.579]\)

\(P(Ng)= 0.275+0.249\)

\(P(Ng)= 0.524\)

The probability that a green marble was picked is 0.524.

To learn more about probability, refer:-

https://brainly.com/question/9793303

#SPJ4

In Smithville, the gas station is located at Point Zero and the laundromat is 2/5 of a mile south of the gas station. The sandwich shop is 2/5 of a mile south of the convenience store and the day care is 3/5 of a mile south of the sandwich shop.

All of these locations are easily accessible and provide convenience services to the local Smithville community. The gas station offers fuel and other automotive services, while the laundromat provides laundry and dry cleaning services. The sandwich shop provides quick food and snacks, while the day care offers a safe and nurturing environment for children.

All of these locations are within a close proximity to one another and provide a convenient way for the Smithville community to access essential services.

Learn more about gas station:

https://brainly.com/question/28628930

#SPJ4

Answer:

282

Step-by-step explanation:

100⋅x=300⋅94

Cross multiply

100

100x

​

Divide both sides by 100

282

The number 1473 represents the slope, indicating that the cost per class at Michigan State University is $1473.

The number 5495 represents the y-intercept, representing the base cost for room and board regardless of the number of classes.

In the equation T = 1473c + 5495, the coefficient 1473 represents the slope.

Interpretation of the slope: The slope indicates the rate of change or cost per class. In this case, it suggests that for every additional class (c) taken at Michigan State University, the total cost (T) for the semester increases by $1473. The slope represents the linear relationship between the number of classes and the total cost.

The number 5495 represents the y-intercept in the equation.

Interpretation of the y-intercept: The y-intercept indicates the starting point or the total cost (T) when the number of classes (c) is zero. In this situation, the y-intercept of 5495 suggests that even if a student takes no classes, they would still have to pay a one-time fee for room and board amounting to $5495 for the semester.

Therefore, the slope provides insight into how the total cost changes with the number of classes taken, while the y-intercept represents the baseline cost that includes the one-time fee for room and board, regardless of the number of classes.

Know more about slope here:

https://brainly.com/question/29044610

#SPJ8

The  required answer is the angle between vectors a and b is 44.8 degrees.

To find the angle θ between two vectors a and b, we use the dot product formula:
a · b = |a| |b| cos θ

where |a| and |b| are the magnitudes of vectors a and b, respectively.
First, let's calculate the dot product of a and b:
a · b = (9)(2) + (-1)(0) + (-5)(-8) = 18 + 40 = 58
Variable  were explicit numbers solve a range of problems in a single computation. The quadratic formula solves any quadratic equation by substituting the numeric values of the coefficients of that equation for the variables that represent them in the quadratic formula. A variable is either a symbol representing an unspecified term of the theory , or a basic object of the theory that is manipulated ,without referring to its possible intuitive interpretation.
Next, let's calculate the magnitudes of vectors a and b:
|a| = sqrt(9^2 + (-1)^2 + (-5)^2) = sqrt(107)
|b| = sqrt(2^2 + 1^2 + (-8)^2) = sqrt(69)
the angle θ by taking the inverse cosine of the cosine value: θ = (57 / (√107 * √69)
Now we can substitute these values into the dot product formula to solve for θ:
58 = sqrt(107) sqrt(69) cos θ
cos θ = 58 / (sqrt(107) sqrt(69))
θ = cos^-1(58 / (sqrt(107) sqrt(69)))
Now you have the angle θ between the two vectors a and b.
Using a calculator, we find that θ is approximately 44.8 degrees.

Therefore, the angle between vectors a and b is 44.8 degrees.

To know more about the variable. Click on the link.

https://brainly.com/question/15078630

#SPJ11

The rate of change means that the designer hourly charge is $55 per hour

Linear equation

A linear equation is in the form:

y = mx + b

Where y, x are variables, m is the rate of change and b is the initial value of y.

Let y represent the total cost of hiring the designer after x hours.

From the table, using the point (0, 125) and (15, 950):

The rate of change means that the designer hourly charge is $55 per hour

To know more about linear equations.

visit-:https://brainly.com/question/11897796

#SPJ9

Answer:

-34.2

Step-by-step explanation:

when u multiply those 2 numbers, it makes -34.2

Answer: G = 35.2

Step-by-step explanation: G - 6 x 5.7 = 1

G - 34.2 = 1

G = 1 + 34.2

G = 35.2

G = 176/5 , G = 35 1/5

The diameter d(c d) of the opening 20cm from the vertex is approximately 16.33cm.


To find the diameter of the opening 20cm from the vertex, we can use the fact that the cross-section of a cone is a circle. We can also use the formula for the slant height of a cone, which is given by the equation:
s = sqrt(r^2 + h^2)
where s is the slant height, r is the radius of the circular base, and h is the height of the cone.

In this case, we know that the height of the cone is 20cm from the vertex. We also know that the radius of the circular base is d/2, where d is the diameter we are trying to find.
So, using the formula for the slant height, we can write:
s = sqrt((d/2)^2 + 20^2)
We also know that the slant height of the cone is equal to the distance from the vertex to any point on the circumference of the base. Therefore, we can write:
s = r
where r is the radius of the circle formed by the cross-section of the cone at a height of 20cm from the vertex.
Now, equating the expressions for s and r, we get:
sqrt((d/2)^2 + 20^2) = d/2
Squaring both sides and simplifying, we get:
d^2 - 4d - 800 = 0
Using the quadratic formula, we can solve for d and get:
d = (4 + sqrt(4^2 + 4*800))/2
d = 4 + sqrt(3204))/2
d ≈ 16.33
Therefore, the long answer to your question is that the diameter of the opening 20cm from the vertex is approximately 16.33cm.

To know more about diameter  visit:
https://brainly.com/question/5501950

#SPJ11

The derivative of F(x) matches the original function f(x), confirming that (9/7) * t^(7/2) + C is the correct antiderivative.To find the most general antiderivative of the function f(x) = 9t * t^2 * √t, we integrate each term separately.

∫9t * t^2 * √t dt

Using the properties of exponents and the power rule of integration, we can simplify the integral step by step.

∫9t^(5/2) dt

Applying the power rule of integration, we add 1 to the exponent and divide by the new exponent:

= (9/(5/2 + 1)) * t^(5/2 + 1) + C

Simplifying:

= (9/7) * t^(7/2) + C

Therefore, the most general antiderivative of f(x) = 9t * t^2 * √t is F(x) = (9/7) * t^(7/2) + C, where C is the constant of integration.

To verify this result, we can differentiate F(x) and check if it matches the original function f(x):

d/dt[(9/7) * t^(7/2) + C] = (9/7) * (7/2) * t^(7/2 - 1) = 9t * t^2 * √t

As we can see, the derivative the derivative of F(x) matches the original function f(x), confirming that (9/7) * t^(7/2) + C is the correct antiderivative

To learn more about derivative click here:

brainly.com/question/28170666

#SPJ11.

Step-by-step explanation:

you can draw a venn diagram in this way.

By using the Venn diagram, the LCM is 90 and HCF is 6.

The full form of LCM is Least Common Multiple. The LCM defines the least number which is exactly divisible by two or more numbers. When we have to find a number larger than given numbers, then we find LCM.

The full form of HCF is the Highest Common Factor. The HCF defines the greatest factor present in between given two or more numbers. If we have to find smaller number, then we find HCF.

For the given situation,

The numbers are 30 and 18.

The factors of \(30=2,3,5\)

The factors of \(18 = 2,3,3\)

The venn diagram below shows the LCM and HCF of the two numbers.

In venn diagram, the intersection of two numbers gives the HCF and the union of two numbers gives the LCM.

Thus, LCM = \((2,3,5)\) ∪ \((2,3,3)\)  

⇒ LCM = \(90\)

and

HCF = \((2,3,5)\) ∩ \((2,3,3)\)

⇒ HCF = \(6\)

Hence we can conclude that by using the Venn diagram, the LCM is 90 and HCF is 6.

Learn more about LCM and HCF here

https://brainly.com/question/17437347

#SPJ2

Insufficient information to determine answer.

The dot plot only shows the number of goals scored by the Springlane High School soccer team per game, not the total number of games played. Based on the dot plot, we can see that the team scored between 1 and 6 goals in a single game, but we cannot determine the exact number of games played or the total number of goals scored during the season.

To determine the total number of games played, we would need additional information, such as the length of the season and the number of games scheduled. Alternatively, we could ask someone with knowledge of the team's schedule to provide us with the total number of games played.

It is important to note that while the dot plot provides valuable information about the team's performance in individual games, it is limited in its ability to provide a complete picture of the team's performance over the course of the season.

Learn more about dot plot

brainly.com/question/27087347

#SPJ11

Answer:

B

Step-by-step explanation:

more points fall on the line. a close second is D but you can see that B is more accurate

The  probability of drawing a queen, placing it back in the deck, and drawing any face card is approximately 1.78%, rounded to the nearest whole number.

Since Phil replaces the first queen back into the deck and shuffles, each draw is independent of the other. The probability of drawing a queen on the first draw is 4/52 = 1/13, and the probability of drawing a face card (other than a queen) on the second draw is 12/52 = 3/13.

The probability of both events occurring is the product of their individual probabilities:

P(drawing a queen and then a face card) = P(drawing a queen) × P(drawing a face card) = (1/13) × (3/13) = 3/169.

To express this probability as a percentage, we can multiply by 100 and round to the nearest whole number:

P(drawing a queen and then a face card) ≈ 1.78%.

Therefore, the probability of drawing a queen, placing it back in the deck, and drawing any face card is approximately 1.78%, rounded to the nearest whole number.

Visit to know more about Probability:-

brainly.com/question/13604758

#SPJ11

The rate of change, in square inches per second, of the area of the region at the instant when R is 44 inches and r is 33 inches is

8363 square inches

The rate of change is the derivative, the rate of change is calculated by differentiation the area

formula for area of concentric circle is given by

Area A = π(R^2 - r^2) =

R = radius of the inner circle

r = radius of the outer circle

δA/δt = δA/δRδr * δRδr/δt

δA/δt = π * (2RδR/δt - 2rδr/δt)

δA/δt = π * 2(R * δR/δt - r * δr/δt)

where R = 44 and δR/δt = 22

r = 33 and δr/δt = -11

= 2π(44 * 22 - 33 * -11)

= 2π (968 - -363)

=  2π (1331)

= 2662π

= 8362.9196 square inches

Learn more about rate of change here:

https://brainly.com/question/8728504

#SPJ1

Malik's utility from his expected income is 793.0, and his expected utility of income is 818.5. The correct option is B.

To calculate Malik's utility from his expected income, we can use the weighted average of his utility from each possible income, with the probabilities as the weights:
Utility from expected income = (0.20 x 387.3) + (0.80 x 894.4) = 793.0
Finally, we can calculate Malik's expected utility of income by applying his utility function to his expected income:
Expected utility of income = √$710,000 = 818.5

First, we need to calculate Malik's expected income. We can do this using the probabilities and the given amounts of income for each outcome:
Expected income = (0.20 x $150,000) + (0.80 x $800,000) = $710,000
Next, we can use Malik's utility function to calculate his utility from each possible income:
Utility from $150,000 = √$150,000 = 387.3
Utility from $800,000 = √$800,000 = 894.4

To know more about income visit:-

https://brainly.com/question/29099506

#SPJ11

Answer: False

Step-by-step explanation:

7 is not an even number, and it never will be.

Even though january has 31 days, 7 is an odd number.

False. 7 is an odd number. This is because an even number is a number which can be divided by 2 without a remainder. 7 cannot be divided by 2 without a remainder, so it is an odd number.

To calculate this, we can use the remainder operator. This operator is represented by the percentage sign (%). When using this operator, the result is the remainder of a division operation. For example, if we divide 7 by 2, the result is 3 with a remainder of 1. If we write this as an equation, it will be 7 % 2 = 1. This means that 7 is not evenly divisible by 2, and is thus an odd number.

Therefore, even though january has 31 days, 7 is an odd number.

Learn more about odd number here:

https://brainly.com/question/240064

#SPJ4

Answer:

y= -2x -7

Step-by-step explanation:

y=mx+b

y= -2x+b

1 = -2(-4) +b

1 = 8+b

b= -7

y= -2x -7

The probability of getting all 4 cards from different suits is 0.267 or approximately 26.7%.

There are 4 suits in a standard deck of cards, and there are 13 cards in each suit. There are C(52,4) ways to choose 4 cards from a deck of 52 cards.

To calculate the probability of getting 4 cards from different suits, we can break it down into steps:

Choose 1 card from any suit (there are 52 possible cards to choose from).

Choose the next card from one of the 39 remaining cards of a different suit (there are 39 cards remaining after taking out the 13 cards from the first suit).

Choose the third card from one of the 26 remaining cards of a different suit (there are 26 cards remaining after taking out the 13 cards from the first and second suits).

Choose the fourth card from one of the 13 remaining cards of a different suit (there are 13 cards remaining after taking out the 13 cards from the first, second, and third suits).

The probability of getting all 4 cards from different suits can be calculated as:

P = (52/52) x (39/51) x (26/50) x (13/49) = 0.267

Therefore, the probability of getting all 4 cards from different suits is 0.267 or approximately 26.7%.

Learn more about probability here: brainly.com/question/30034780

#SPJ4

Answer:

1: y intercept = 5

2: y interpcept = -2

3: y intercept = -3

Step-by-step explanation:

So for the 1st and 3rd ones (the graphs), all you have to do is find which y matches the x value of 0

The 2nd one is a bit harder. I’ll explain it the best I can

So in the y section, you see that -4 goes to -3 when the x is raised by 1. There for everytime the x raises by 1, so does the y. That means when x = 0, the y = -2

Answer:

first is (0,5), second is (0,-2) third is (0, -3)

Step-by-step explanation:

The y-intercept is wherever x=0

Answer:

30.33

Step-by-step explanation:

33.70 x .10= 3.37 (discount)

33.70 - 3.37= 30.33