Carbon-14 Dating Skeletal remains had lost 70% of the C-34 they only contained. Determine the approximate apen years of the bones. (Assume the art of carbon 10 is 5730 years Round your answer to the nearest whole number

Answer:

When your graph is a horizontal line the slope will be zero.

Step-by-step explanation:

The slope is the rise over the run.  If you have a horizonal line, the rise is zero.

Answer:

find common denominator

1/5

2/3

common denominator is 15

convert 2/3 into a fraction with a denominator of 15

1/5 —> 3/15

2/3 —> multipky numerator and denominator by 5 —> 10/15 (toddlers)

infants = total - toddlers - preschoolers

infants = 15/15 - 10/15 - 3/15 = 2/15

multipky the fractions by 60 (the total number of students) to find for the number in each age group

(10/15)*60 = 40

(3/15)*60 = 12

(2/15)*60 = 8

The quadratic functions can be identified as being in general form, factored form, vertex form, or none of these forms.

To identify the form of a quadratic function, we need to examine its equation.

1. General Form: The general form of a quadratic function is written as \(ax^2 + bx + c\), where a, b, and c are constants. If the given equation is in this form, we can identify it as being in general form.

2. Factored Form: The factored form of a quadratic function is expressed as a product of binomial factors. It can be written as a(x - p)(x - q), where a, p, and q are constants. If the given equation can be factored in this way, we can identify it as being in factored form.

3. Vertex Form: The vertex form of a quadratic function is written as a\((x - h)^2 + k\), where a, h, and k are constants representing the vertex coordinates (h, k). If the given equation can be rearranged to match this form, we can identify it as being in vertex form.

If the equation does not match any of these forms, it can be concluded that the quadratic function is in none of these forms. It may be written in a different form or require further manipulation to determine its specific representation.

By examining the structure and arrangement of the terms in the equation, we can easily identify the form of a quadratic function.

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Answer:

Option 1

Step-by-step explanation:

The given equation equals 3072, so find the other equation that equals 3072.

Option 1 = 3072 - correct

Option 2 = 432 - wrong

Option 3 = 2883 - wrong

Option 4 = 432 - wrong

I hope this helps!

Answer:

580 +70 which is 650

Step-by-step explanation:

add

The storm rainfall flux is 0.00127 m2/hr, 1.27 kg liquid water/m2hr, 2.8 lb liquid water/m2hr, 1.27 liters liquid water/m2hr, and 0.335 gallons liquid water/m2hr. The amount of liquid water fell on the garden is 80.6 L, 21.3 gallons.

Dimensions of outdoor vegetable garden = 2 m × 2 m

Storm rainfall = 0.8 inches of rain

Time of storm = 1 hr(

a) The rainfall flux is the amount of rainfall per unit area and unit time. It is given as:

Rainfall flux = (Amount of rainfall) / (Area × Time)

Given the area of the garden is 2 m × 2 m, and the time is 1 hr, the rainfall flux is:

Rainfall flux = (0.8 inches of rain) / (2 m × 2 m × 1 hr)

Converting inches to meters, we get:

1 inch = 0.0254 m

Therefore,

Rainfall flux = (0.8 × 0.0254 m) / (2 m × 2 m × 1 hr) = 0.00127 m/hr

Converting the rainfall flux to other units:

In kg/hr:

1 kg of water = 1000 g of water

Density of water = 1000 kg/m3

So, 1 m3 of water = 1000 kg of water

So, 1 m2 of water of depth 1 m = 1000 kg of water

Therefore, 1 m2 of water of depth 1 mm = 1 kg of water

Therefore, the rainfall flux in kg/hr = (0.00127 m/hr) × (1000 kg/m3) = 1.27 kg/m2hr

In lbs/hr:

1 lb of water = 453.592 g of water

So, the rainfall flux in lbs/hr = (0.00127 m/hr) × (1000 kg/m3) × (2.20462 lb/kg) = 2.8 lbs/m2hr

In liters/hr:

1 m3 of water = 1000 L of water

So, 1 m2 of water of depth 1 mm = 1 L of water

Therefore, the rainfall flux in L/hr = (0.00127 m/hr) × (1000 L/m3) = 1.27 L/m2hr

In gallons/hr:

1 gallon = 3.78541 L

So, the rainfall flux in gallons/hr = (0.00127 m/hr) × (1000 L/m3) × (1 gallon/3.78541 L) = 0.335 gallons/m2hr

(b) To calculate the amount of water that fell on the garden, we need to calculate the volume of water.

Volume = Area × Depth.

The area of the garden is 2 m × 2 m.

We need to convert the rainfall amount to meters.

1 inch = 0.0254 m

Therefore, 0.8 inches of rain = 0.8 × 0.0254 m = 0.02032 m

Volume of water = Area × Depth = (2 m × 2 m) × 0.02032 m = 0.0806 m3

Converting the volume to other units:

In liters:

1 m3 of water = 1000 L of water

Therefore, the volume of water in liters = 0.0806 m3 × 1000 L/m3 = 80.6 L

In gallons:

1 gallon = 3.78541 L

Therefore, the volume of water in gallons = 80.6 L / 3.78541 L/gallon = 21.3 gallons.

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According to the Centers for Disease Control and Prevention (CDC), about 73.6 percent of adults in the United States are overweight or obese. So, the correct answer is D).

This means that a majority of adults in the U.S. have a body mass index (BMI) above the healthy range, which is defined as a BMI of 18.5-24.9, which puts them at increased risk for a range of health issues, including heart disease, diabetes, and some types of cancer.

The prevalence of overweight and obesity has been increasing in the United States in recent decades, and it is a significant public health concern. Obesity is a complex issue with many causes, including genetics, environment, and lifestyle factors such as diet and physical activity levels. So, the correct answer is D).

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--The given question is incomplete, the complete question is given

"  According to the Centers for Disease Control and Prevention (CDC), approximately what percentage of u.s. adults is overweight? select one: a. 24 percent b. 44 percent c. 64 percent d. 73.6 percent "--

To determine whether Melissa can apply two coats of paint to the entire sculpture with a can of spray paint that covers 6,500 square centimeters need to consider the surface area of the sculpture and the amount of paint required for two coats.

Let's assume the sculpture has a total surface area of S square centimeters.

To apply one coat of paint to the entire sculpture, Melissa would need approximately S square centimeters of paint.

The can of spray paint covers 6,500 square centimeters, it would be sufficient to cover the sculpture with one coat.

A second coat of paint, Melissa would need an additional S square centimeter of paint.

The first coat has already covered the sculpture, the second coat would only require coverage of any missed spots or areas that need additional touch-up.

The amount of paint required for the second coat would generally be less than the amount required for the first coat.

Considering these factors, it is likely that Melissa can apply two coats of paint to the entire sculpture with a can of spray paint that covers 6,500 square centimeters.

The actual feasibility would depend on the size and complexity of the sculpture, as well as the efficiency of Melissa's painting technique.

If the sculpture has a significantly larger surface area than 6,500 square centimeters, or if it has intricate details that require a substantial amount of touch-up, Melissa may require additional cans of spray paint to achieve two coats.

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Answer:

-14

Step-by-step explanation:

I did the math

The roots of the function f(x) = 5x³ + 5x² - 170x + 280 are 2, 4 and -7

The function is given as:

f(x) = 5x³ + 5x² - 170x + 280

Factor out 5 in the function

f(x) = 5(x³ + x² - 34x + 56)

One of the roots is x + 7.

So, we have:

f(x)/(x + 7) = 5(x³ + x² - 34x + 56)/(x + 7)

Factor the expression on the right-hand side

f(x)/(x + 7) = 5((x - 2)(x - 4)(x + 7))/(x + 7)

Cancel out the common factors

f(x) = 5((x - 2)(x - 4)(x + 7)

Set the function to 0

5((x - 2)(x - 4)(x + 7) = 0

Divide through by 5

(x - 2)(x - 4)(x + 7) = 0

Expand

x - 2 = 0 or x - 4 = 0 or x + 7 = 0

Solve for x

x = 2, or x = 4 or x = -7

Hence, the roots of the function f(x) are 2, 4 and -7

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Polynomials are algebraic expressions that contain more than two terms. AN example would be: f(x) = x^3 + x^2 + x +1. This equation contains three terms, with the 3rd degree as its highest term. It also means that the graph passed three x-intercepts. This depends in the highest degree. So, the first thing you do is plot the intercepts because for sure, the graph will pass there.

Hope this helps :)

Answer:

B

Step-by-step explanation:

11x - 6x + 20

combine like terms:

5x + 20

The direction in which the maximum rate of change of f occurs at the point (5, 6, -1) is approximately (-0.17, -0.11, -0.98).

To find the maximum rate of change of the function f at the given point (5, 6, -1) and the direction in which it occurs, we can calculate the gradient of f at that point.

The gradient vector represents the direction of maximum increase of the function, and its magnitude represents the rate of change in that direction.

The gradient vector (∇f) of f(x, y, z) = (8x + 5y)/z can be found by taking the partial derivatives with respect to each variable:

∂f/∂x = 8/z

∂f/∂y = 5/z

∂f/∂z = -(8x + 5y)/z^2

Evaluated at the point (5, 6, -1), we have:

∂f/∂x = 8/(-1) = -8

∂f/∂y = 5/(-1) = -5

∂f/∂z = -((8(5) + 5(6))/(-1)^2) = -46

So, the gradient vector (∇f) at the point (5, 6, -1) is (-8, -5, -46).

The maximum rate of change of f at this point is given by the magnitude of the gradient vector:

|∇f| = √((-8)^2 + (-5)^2 + (-46)^2) = √(64 + 25 + 2116) = √2205 = 47.

Therefore, the maximum rate of change of f at the point (5, 6, -1) is 47.

To determine the direction in which this maximum rate of change occurs, we normalize the gradient vector by dividing it by its magnitude:

Direction vector = (∇f) / |∇f| = (-8/47, -5/47, -46/47).

Hence, the direction in which the maximum rate of change of f occurs at the point (5, 6, -1) is approximately (-0.17, -0.11, -0.98).

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Unit rate is the quantity of an amount of something at a rate of one of another quantity.

The fewest number of hours he would need to work to reach his goal of $280 is 28 hours working in the library.

It is the quantity of an amount of something at a rate of one of another quantity.

In 2 hours, a man can walk for 6 miles

In 1 hour, a man will walk for 3 miles.

We have,

Amount to earn = $280

Grocery store:

Earnings per hour = $8

1 hour = $8

Multiply 280/8 on both sides.

280/8 x 1 hour = $280

35 hours = $280

Library:

Earnings per hour = $10

1 hour = $10

Multiply 280/10 on both sides.

28 hours = $280

We see that,

Working in the Library would make $280 in fewer hours than working in the grocery store.

Thus,

The fewest number of hours he would need to work to reach his goal of $280 is 28 hours working in the library.

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The dimensions that maximize the enclosed area are L = 41.665 feet and W = 41.665 feet for each corral and the maximum area is 10868.09 square feet.

To find the dimensions that maximize the enclosed area, we need to use optimization techniques. Let's denote the length of each rectangular corral by L and the width by W. We can write the total enclosed area as A = 6LW.

The perimeter of each corral is given by P = 2L + 2W, and we have a total of 6 corrals, so the total length of fencing required is 6P = 12L + 12W.

We are given that we have 1,000 feet of fencing, so we can write 12L + 12W = 1000, or equivalently, L + W = 83.33 (rounded to two decimal places).

We can now use this equation to express one of the variables (say, W) in terms of the other: W = 83.33 - L.

Substituting this expression for W into the formula for the enclosed area, we get A = 6L(83.33 - L) = 499.98L - 6L^2.

To find the value of L that maximizes the area, we need to take the derivative of A with respect to L and set it equal to zero: dA/dL = 499.98 - 12L = 0. Solving for L, we get L = 41.665 (rounded to three decimal places).

Substituting this value back into the expression for W, we get W = 83.33 - L = 41.665.

The maximum area is A = 6LW = 10868.09 square feet (rounded to two decimal places).

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The constant term does not have the same sign as the second expression, the two expressions are not equivalent. Also, if you substitute a value for x and evaluate each expression, the values will not be equal.

Expression 1: \(-0.5(3x+5)\)

Using the distributive property to expand the first expression, we get

\(-0.5(3x+5) = -1.5x-2.5\\\)

Expression 2: \(-1.5x + 2.5\)

Since the constant term does not have the same sign as the second expression, the two expressions are not equivalent.

Also, if you substitute a value for x and evaluate each expression, the values will not be equal.

Q. Are the expressions –0.5(3x + 5) and –1.5x + 2.5 equivalent? Explain why or why not.

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Answer:Using the distributive property to expand the first expression, you would get -1.5x - 2.5. Since the constant term does not have the same sign as the second expression, the two expressions are not equivalent. Also, if you substitute in a value for x and evaluate each expression, the values will not be equal.

Step-by-step explanation: sample explanation

\( \frac{k}{5} - 1 = - 4\)

\( \frac{k}{5} = - 4 + 1\)

\( \frac{k}{5} = - 3\)

\(k = - 3(5)\)

\(k = - 15\)

Answer:

(2, -4).

Step-by-step explanation:

x^2 - 4x

= (x - 2)^2 - 4.

So the vertex is at

(2, -4).

Answer:

(2,-4)

Step-by-step explanation:

x²-4x

First, we need to complete the square of this quadratic.

1) Half the coefficient of x and subtract it (depends on the sign) from x. Then, square the whole expression.

(x-2)²

2) If this was to be expanded as a double bracket, we would acquire:

x²-4x+4

In order to achieve the form above, we need to subtract 4. This can be found quickly by subtracting the square of the integer from the bracket. (Ignore the sign when squaring here.)

(x-2)²-4           ------>This is in the completing the square from.

From this, the vertex is determined by using the opposite sign of the number in the bracket for the \(x\) coordinate and the outside number is kept constant for the \(y\). Note that, in graph transformations, the number inside the brackets is the "opposite of what you expect"; the same logic is applied here.

Therefore, the vertex is (2,-4)

The cost per customer becomes $( 10+ x) and the average number of customers can be represented as (16 - 2x). Also the inequality equation is 160 - 4x -2\(x^{2}\)  \(\geq\) 130 to maintain minimum revenue of $130 after rising price by x number of times by $1 as 2 customers leave on average per hour.

Let x represents the number of $1 increases in the cost of the buffet.

Noah manages a buffet at a local restaurant and charges  $10 for the buffet.

On average, 16 customers choose the buffet as their meal every hour.

That is, the average revenue from 16 customers is = $(10*16)= $160

After surveying Noah has determined that for every $1 increase in the cost of the buffet, the average number of customers who select the buffet will decrease by 2 per hour.

That is, as cost of buffet for every hour rises by $x from $10 we get, $ (10+x) , and the average number of customers who select the buffet will decrease by 2 per hour.

The new average number of customers per hour after rise in cost of buffet by $x is (16 -2x).

This implies, the revenue earned now is = $(16- 2x)(10 + x) = $(160 + 16x - 20x -2\(x^{2}\) ) = $ (160 - 4x -2\(x^{2}\) )

The restaurant owner wants the buffet to maintain a minimum revenue of $130 per hour.

Thus, after the increase in price by $x per hour , the inequality equation that helps Noah to pick best pricing decisions will be ,

160 - 4x -2\(x^{2}\)  \(\geq\) 130

Here, cost per customer becomes $( 10+ x) and the average number of customers can be represented as (16 - 2x).

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Answer:

A rhombus is a special type of parallelogram

Step-by-step explanation:

Similarities in a rhombus and parallelogram:

A rhombus is a special type of parallelogram in that

Answer:

The circumference for circle a is \( \\ C = 131.9430\)m.

The circumference for circle b is \( \\ C = 175.9240\)m.

The relationship between the radius of a circle and the circumference (the distance around the circle) is constant and is the same for all circles and can be written as \( \\ \frac{C}{r} = 2\pi\) or, in a less familiar form, \( \\ \frac{r}{C} = \frac{1}{2\pi}\). The number \( \\ \pi\) is constant for all circles and has infinite digits, \( \\ \pi = 3.14159265358979....\).

Step-by-step explanation:

The circumference of a circle is given by:

\( \\ C = 2*\pi*r\) [1]

Where

\( \\ C\) is the circle's circumference.

\( \\ r\) is the radius of the circle.

And

\( \\ \pi = 3.141592....\) is a constant value (explained below)

We can say that the distance around the circle is the circle's circumference.

The circumferences of the two circles given are:

Circle a, with radius equals to 21 meters (\( \\ r = 21m\)).

Using [1], using four decimals for \( \\ \pi\), we have:

\( \\ C = 2*\pi*r\)

\( \\ C = 2*3.1415*21\)m

\( \\ C = 131.9430\)m

Then, the circumference for circle a is \( \\ C = 131.9430\)m.

Circle b, with radius equals to 28 meters (\( \\ r = 28m\)).

\( \\ C = 2*3.1415*28\)m

\( \\ C = 175.9240\)m

And, the circumference for circle b is \( \\ C = 175.9240\)m.

We know that

\( \\ 2r = D\)

That is, the diameter of the circle is twice its radius.

Then, if we take the distance around the circle and we divided it by \( \\ 2r\)

\( \\ \frac{C}{2r} = \frac{C}{D} = \pi\)

This ratio, that is, the relationship between the distance around the circle (circumference) and the diameter of a circle is \( \\ \pi\) and is constant for all circles. This result is called the \( \\ \pi\) number, which is, approximately, \( \\ \pi = 3.141592653589793238....\) (it has infinite number of digits).

We can observe that the relationship between the radius of a circle and the circumference is also constant:

\( \\ \frac{C}{2r} = \frac{C}{D} = \pi\)

\( \\ \frac{C}{2r} = \pi\)

\( \\ \frac{C}{r} = 2\pi\)

However, this relationship is \( \\ 2\pi\).

We can rewrite it as  

\( \\ \frac{r}{C} = \frac{1}{2\pi}\)

And it is also constant.

Answer:

Circle A is 42π

circle C is 56π

Answer:

......................

Answer:

I and III

Step-by-step explanation:

I.

-6 - x ≤ 7

-6 - (-13) ≤ 7

-6 + 13 ≤ 7

7 ≤ 7

True

II.

-6 - x ≤ 7

-6 - (-14) ≤ 7

-6 + 14 ≤ 7

8 ≤ 7

False

III.

-6 - x ≤ 7

-6 - (-6) ≤ 7

-6 + 6 ≤ 7

0 ≤ 7

True

I hope this helps!

To estimate the number of times the earth will rotate on its axis during a human's lifetime, we first need to determine the average length of a human's lifetime.

According to the World Health Organization, the global average life expectancy at birth in 2020 was approximately 72 years. Next, we need to calculate the number of days in 72 years. 72 years x 365 days/year = 26,280 days.

Since the earth rotates once every 24 hours, we can calculate the number of rotations by dividing the number of days by 24. 26,280 days ÷ 24 hours/day = 1,095 rotations. Therefore, we can estimate that the earth will rotate on its axis approximately 1,095 times during a human's lifetime.

I decided on using the average human's lifetime based on data from the World Health Organization to provide a general estimate. However, it's important to note that life expectancy can vary greatly depending on factors such as geography, lifestyle, and genetics.

we can use this formula: Number of rotations = Average lifespan (in years) x Rotations per year
Number of rotations = 72 years x 365 rotations/year
Number of rotations ≈ 26,280 rotations, So, we can estimate that the Earth will rotate on its axis about 26,280 times during an average human's lifetime.

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Answer:

the value of x is 2

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

Given 3 parallel lines intersected by 2 transversals then the parallel lines divide the transversals proportionally, that is

\(\frac{3x}{4}\) = \(\frac{7.5}{2.5x}\) ( cross- multiply )

7.5x² = 30 ( divide both sides by 7.5 )

x² = 4 ( take the square root of both sides )

x = \(\sqrt{4}\) = 2

Answer:

Wellll

Step-by-step explanation:

There is no Nash equilibrium in pure strategies because neither player has a strategy that maximizes their expected payoff.

(A) The modified payoff matrix for the matching pennies game with the updated losing payoffs is as follows:

         Player 2

         Heads (H)     Tails (T)

Player 1  +1, -1        -6, +6

Heads (H)

Tails (T) -10, +10      +1, -1

(B) The diagrams showing each player's pair of expected payoff lines and the other player's equilibrium decision probability are as follows:

Player 1's Expected Payoff Line:

H      T

Probability:  p1     1-p1

Expected Payoff:  p1(-6) + (1-p1)(+1)

Player 2's Expected Payoff Line:

H      T

Probability:  p2     1-p2

Expected Payoff:  p2(-10) + (1-p2)(+1)

The equilibrium decision probability for each player will be the value that maximizes their expected payoff. In this case, player 1 will choose heads (H) with probability p1* and player 2 will choose tails (T) with probability p2*.

(C) To calculate the numerical values of the Nash equilibrium probabilities (p1*, p2*), we need to find the values that maximize each player's expected payoff.

For player 1:

Expected Payoff = p1(-6) + (1-p1)(+1)

= -6p1 + 1 - p1 + p1

= -5p1 + 1

To maximize this expected payoff, we set the derivative equal to zero:

d/dp1 (-5p1 + 1) = -5 = 0

-5 = 0 (No solution)

For player 2:

Expected Payoff = p2(-10) + (1-p2)(+1)

= -10p2 + 1 + p2 - p2

= -9p2 + 1

To maximize this expected payoff, we set the derivative equal to zero:

d/dp2 (-9p2 + 1) = -9 = 0

-9 = 0 (No solution)

There is no Nash equilibrium in pure strategies because neither player has a strategy that maximizes their expected payoff.

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Thus, the measure of the value of 'x' for the given length of arc of circle is found as: x = 90.

The products of a measurements of the segments of two chords are equal if they overlap in a circle.

For the given arc length  of circle:

Let the intersection of the both chords be 'O'.

m∠KOL = 180 - x  ...eq 1 (linear pair).

By the  intercept chord theorem:

m∠KOL = (arc JM + arcKL)

Put the value of eq 1.

180 - x = 1/2(30 + 2x - 30)

180 - x = 1/2 * 2x

180 = x + x

x = 180/2 = 90

Thus, the measure of the value of 'x' for the given length of arc of circle is found as: x = 90.

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