Situation:
An archaelogist in Turkey discovers a
spear head that contains 55% of its
original amount of C-14.

PLS HELP AHHHHH

After evaluating the given integral by changing to polar coordinates we get [tex]7 e^8-31[/tex]

As per the details shared in the above question it is given that,

[tex]$x^2+y^2=64$[/tex]

[tex](x, y)=r(\cos \theta, \sin \theta)[/tex]

[tex]d A=r d r d \theta.[/tex]

Further solving above we get,

[tex]r^2=64 \\\Rightarrow & r=8 . \\0 \leq r \leq 8 ; & 0 \leq \theta \leq \pi / 2[/tex]

The polar coordinate,

[tex]\iint_{R} y e^x d A=\int_0^{\frac{\pi}{2}} \int_0^8 r^2 \sin \theta e^{r \cos \theta} d r d \theta[/tex]

[tex]& =\int_0^8 \int_0^{\frac{\pi}{2}} r^2 \sin \theta e^{r \cos \theta} d \theta ; \\& =\int_0^8\left[-r e^{r \cos \theta}\right]_0^{\pi / 2} d r[/tex]

[tex]=\int_0^8 r\left[-e^{r \cos \left(\frac{\pi}{2}\right)}+e^\alpha\right] d r .[/tex]

[tex]=\int_0^8 r e^r d r-\left.\frac{r^2}{2}\right|_0 ^8[/tex]

Now substituting the value we get,

[tex]7 e^8-31[/tex]

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Note the correct question should be ,

Evaluate the given integral by changing to polar coordinates.

[tex]\iint_R y e^x d A[/tex] , where R is the region in the first quadrant enclosed by the circle  [tex]x^2+y^2=64[/tex].

Answer:

Step-by-step explanation:

The value of c in the equation A is 7 and the value of d in the equation B is 5

The first equation is

[tex]\sqrt{448x^c}=8x^3\sqrt{7x}[/tex]

Move the term 8x^3 inside the square root

[tex]\sqrt{448x^c}=\sqrt{7x(8x^3)^2}[/tex]

Multiply the terms in the equation

[tex]\sqrt{448x^c} = \sqrt{448x^7}[/tex]

Here the both terms are equal. Therefore the value of x^c and the x^7 will be equal.

Then the value of c = 7

Part 2

The second equation is

[tex]\sqrt[3]{576x^d}=4x \sqrt[3]{9x^2}[/tex]

Move the term 4x inside the square root

[tex]\sqrt[3]{576x^d}=\sqrt[3]{9x^2(4x)^3}[/tex]

Multiply the terms in the equation

[tex]\sqrt[3]{576x^d}=\sqrt[3]{576x^3}[/tex]

Here the both terms are equal. Therefore the value of x^d and the x^5 will be equal

Then the value of d = 5

Therefore, the value of c = 7 and the value of d = 5

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Answer:

yes it is function.........

The triangle ΔRCD is similar to the triangle ΔRAP. Then the value of the variable 'x' is 28 units.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

The triangle ΔRCD is similar to the triangle ΔRAP. Then the equation is given as,

RC / CA = RD / DP

x / 10 = 42 / 15

x / 2 = 14

x = 2 (14)

x = 28

The triangle ΔRCD is similar to the triangle ΔRAP. Then the value of the variable 'x' is 28 units.

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Answer:

x = 28 units

Step-by-step explanation:

As AP is parallel to CD (indicated by the arrows on the line segment), triangle APR is similar to triangle CDR.

In similar triangles, corresponding sides are always in the same ratio.

[tex]\implies \sf AP:CD=PR:DR=AR:CR[/tex]

Given

Therefore:

[tex]\implies \sf PR:DR=AR:CR[/tex]

[tex]\implies \sf 57:42=10+x:x[/tex]

[tex]\implies \sf \dfrac{57}{42}=\dfrac{10+x}{x}[/tex]

[tex]\implies \sf 57x=42(10+x)[/tex]

[tex]\implies \sf 57x=420+42x[/tex]

[tex]\implies \sf 15x=420[/tex]

[tex]\implies \sf x=28[/tex]

The type of function is it is C . Exponential growth .

Given :

For the x-values 1,2,3, and so on, the y-values of a function form a geometric sequence that increases in value .

If  for values of x values of y increases and forms a geometric sequence then it would be an exponential growth function because geometric sequence is an exponential function and since, it is increasing hence, an exponential growth.

Option B is incorrect because  because y is not decreasing

Option C and D are incorrect because geometric sequence can never be linear since, it gives common ratio.

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The amount after 20 years is $662.04.

The interest does she earn is $240.

What is compound interest?

Compound interest, also known as interest on principal and interest, is the addition of interest to the loan or deposit principal.

One plus the annual interest rate raised to the number of compound periods minus one is multiplied by the initial loan amount, or principal, to determine compound interest.

Given:

Jessica puts away $200 a month for 20 years.

P = $200

t = 20 years

r = 6% = 0.06

n = 12 (compounded monthly)

Consider the compound interest formula,

[tex]A = P(1+\frac{r}{n})^n^t[/tex]

Plug the values of P, r, n and t in the above equation.

⇒

[tex]A = 200(1+\frac{0.06}{12})^1^2^*^2^0\\ A = 200(1+0.005)^2^4^0\\A = 200(1.005)^2^4^0\\A = 662.04089\\A = 662.04[/tex]

Hence, the amount after 20 years is $662.04.

Now to find the interest does she earn.

Interest = Principle x time x rate

             = 200 x 20 x 0.06

Interest = $240

Hence, the interest does she earn is $240.

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Step-by-step explanation:

the mean score is the sum of all scores divided by the number of scores.

64 = (s1+s2+s3+...+s26+s27)/27

64×27 = (s1+s2+s3+...+s26+s27)

1728 = (s1+s2+s3+...+s26+s27)

now, one of the scores changes from 47 to 74. that means the sum of all scores is increased by 74-47 = 27.

so, we get

1728 + 27 = (s1+s2+s3+...+s26+s27+27)

1755 = (s1+s2+s3+...+s26+s27+ 27)

we still have 27 scores, so for the updated mean we have to divide both sides by 27 again :

1755/27 = (s1+s2+s3+...+s26+s27+27)/27

65 = (s1+s2+s3+...+s26+s27+27)/27

the correct mean is therefore 65%.

Answer:

you multiply to find common denominators. in the example below you multiply the denominators by themselves, and then individually. 1/2 and 1/3 are the fractions your working with. (2x3)=6 and then (1x3)=3 and (1x2)=2 (2+3)=5 and so (5/6)

Step-by-step explanation:

example: 1½+1⅓=2⅚

Answer: You have to find a common denominator.

Step-by-step explanation: Look at this attachment to understand: (Directions included)

I hoped this helped! If you can, may you PLEASE mark me brainliest?

To find the Fourier cosine series of the function f(x), we first need to find the Fourier coefficients of f(x).

The Fourier coefficients of f(x) are given by:

a0 = (2/L) * integral of f(x) from x=0 to x=L

an = (2/L) * integral of f(x) * cos(npix/L) from x=0 to x=L

bn = (2/L) * integral of f(x) * sin(npix/L) from x=0 to x=L

Using the result from part a) and the fact that the series can be integrated term by term, we can find the Fourier cosine series of f(x) as follows:

F(x) = a0/2 + sum from n=1 to infinity of an * cos(npix/L)

Therefore, the Fourier cosine series of the function f(x) is:

F(x) = (1/L) * integral of f(x) from x=0 to x=L + sum from n=1 to infinity of (2/L) * integral of f(x) * cos(npix/L) from x=0 to x=L

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To find the probability that Y1 = 71 and Y2 = y2, we can write G(y1, y2) = P(Y1 = 71, Y2 = y2).

To find the probability that Y1 = 71 and Y2 = y2, we need to consider the possible values of X1 and X2 that could lead to these values of Y1 and Y2. The probability density functions (PDFs) of an exponential distribution with mean 1000 is f(x) = 1/1000 * e^(-x/1000). Therefore, the probability of this event is

Another possibility is that X1 = y2 and X2 = 71. The probability of this event is

Since these two events are mutually exclusive and exhaust all possible ways that Y1 can equal 71 and Y2 can equal y2, the probability of these events occurring is the sum of these probabilities. Therefore,

Note that this expression is only valid when 0 < 71 < y2 < ∞ since these are the conditions under which Y1 can equal 71 and Y2 can equal y2.

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The leftmost value on the 3rd level of the binary tree with given elements 47, 38, 66, 57, 19, 31, 45, 88 is 19

To build a binary tree first we have to insert 47 into the tree as the root of the tree. The read the next element if it is smaller than the root node, insert it as the left subtree and if it is larger than the root node, insert it as the subtree.

The next element is 38 which is smaller than 47 so it will become the left subtree. The next element is 66 which becomes the right subtree. The next element is 57 is greater than 47 and 38 so it becomes the right subtree below 38. Similarly we go ahead and build a binary tree to find the leftmost value at 3rd level of the binary tree.

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The approximate difference between the highest and lowest oil production is 4,500,000 barrels per day

An approximation is anything that is similar, but not exactly equal, to something else. A number can be approximated by rounding.

Given is a graph of oil production between 1960 and 2010

The lowest oil production was in year 2010 = 5000,000 barrels per day

The highest oil production was in year 1970 = 9500,000 barrels per day

The difference between highest and lowest oil production = 9500,000 - 5000,000 = 4,500,000 barrels per day

Hence, The approximate difference between the highest and lowest oil production is 4,500,000 barrels per day

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Answer:

8<r

Step-by-step explanation:

5 > r – 3

+3      +3

add 3 to both sides

8>r

move variable to the left and flip the sign

8<r

Large sample significance tests for a single proportion are based on the  statistic binomial. the correct option is A

Significance test can be defined as tests for statistical significance indicate whether observed differences between assessment results occur because of sampling error. Significance tests give a formal process for using sample data to evaluate the likelihood of some claim about a population value.

Therefore a Large sample significance tests for a single proportion are based on the  statistic binomial.

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Answer:

D). 27

Step-by-step explanation:

The mass of each bag is 9 kilograms

We have 3 bags

Let's add the mass of all 3 bags to find our answer.

9 kilograms + 9 kilograms  + 9 kilograms = 27 kilograms

The solution is, D). 27  is the total mass, in kilograms, of all of the bags of pebbles.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

given that,

A worker has 3 bags of pebbles to use in a garden. The mass of each bag is 9 kilograms.

so, we have,

The mass of each bag is 9 kilograms

We have 3 bags

i.e. total mass = 9 * 3 =27

here, we have to multiply 9 by 3 we get the total mass,

i,e. 27 kg.

similarly, we have,

Let's add the mass of all 3 bags to find our answer.

9 kilograms + 9 kilograms  + 9 kilograms = 27 kilograms

Hence, The solution is, D). 27  is the total mass, in kilograms, of all of the bags of pebbles.

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Answer:

To find x and y intercept .... y = 4, and x = -2

Step-by-step explanation:

y-2x=4

y = 4

-2x=4

-2x/-2 = 4/-2

x = -2

Is this equation for solving y and x

Answer:

To find the cash flows for this project, we need to calculate the net income for each year and then subtract any investments in net working capital and capital expenditures.

In year 0, the firm will incur the following expenses:

- Research and development costs: $490,000

- Cost of the machine: $290,000

- Shipping and installation costs: $59,000

- Increase in net working capital: $145,000

Total expenses in year 0: $490,000 + $290,000 + $59,000 + $145,000 = $984,000

The net income in year 0 is equal to the revenue minus the costs: $690,000 - $340,000 = $350,000.

Therefore, the cash flow in year 0 is:

FCF0 = $350,000 - $984,000 = -$634,000

In years 1, 2, and 3, the firm will incur the following expenses:

- Cost of goods sold: $340,000

- Depreciation: (This can be calculated using the MACRS depreciation schedule. For the first year, the depreciation will be 14.29% of the cost of the machine, or 0.1429 * $290,000 = $41,461. The depreciation in subsequent years can be calculated using the same method.)

- Increase in net working capital: $145,000

Total expenses in each of years 1, 2, and 3: $340,000 + Depreciation + $145,000

The net income in each of these years is equal to the revenue minus the costs: $690,000 - (Total expenses)

The cash flow in each of these years is equal to the net income minus any investments in net working capital and capital expenditures: Net income - Increase in net working capital - Depreciation

Substituting the appropriate values, we get:

Year 1: FCF1 = $690,000 - ($340,000 + $41,461 + $145,000) = $163,539

Year 2: FCF2 = $690,000 - ($340,000 + Depreciation + $145,000)

Year 3: FCF3 = $690,000 - ($340,000 + Depreciation + $145,000)

Note that the depreciation in years 2 and 3 can be calculated using the same method as in year 1.

So, the cash flows for this project are:

Year 0 1 2 3

FCF -$634,000 $163,539

I hope this helps!

The rock will take 10.25 seconds to hit the ground, as the amount determined by the formula h=352-16t^(2).

The given equation is h=352-16t^(2). This equation can be used to calculate the time it will take for a rock to hit the ground after it has been dropped from a tower that is 352 feet high. The equation states that the rock's height (h) is equal to 352 minus 16 times the square of the time (t). To find the time it will take for the rock to hit the ground (h=0), we can rearrange the equation to solve for t. The rearranged equation is t=sqrt((352-0)/16), which simplifies to t=10.25. This means that the rock will take 10.25 seconds to hit the ground. This can also be expressed in tenths of a second as 102.5, which is the same as 10.25 seconds.

t= sqrt((352-0)/16)

t= sqrt(22)/4

t= 10.25

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false,  {b}->{a} appears to hold with respect to the given instance.

A variable created in a class that has a unique copy, or instance, for each instantiated object of the class is known as an instance variable in class-based, object-oriented programming. Although not static, an instance variable resembles a class variable.

A variable specified within a class but outside of constructors, methods, or blocks is known as an instance variable. All the constructors, methods, and blocks in the class have access to instance variables, which are created when an object is instantiated. To the instance variable, access modifiers can be applied.

false,  {b}->{a} appears to hold with respect to the given instance.

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The upper and the lower estimates (in tons) for the total quantity q(6) of erupted materials after six seconds is 224 and 166 metric tons respectively.

The volcano is erupting and readings of the rate r(t) at which solid materials are spewed into the atmosphere are given in the table

Assuming that r(t) is increasing for all t in [0,6], a lower estimate is obtained by using left endpoints and an upper estimate is achieved by using right endpoints.  

Lower estimate:  r(0)(1)+r(1)(1)+r(2)(1)+r(3)(1)+r(4)(1)+r(5)(1)

                      = 2+12+20+36+44+52 = 166 metric tons

Upper estimate:  r(1)(1)+r(2)(1)+r(3)(1)+r(4)(1)+r(5)(1)+r(6)(1)

                      = 12+20+36+44+52+60 = 224 metric tons

Midpoint estimate:  r(1)(2)+r(3)(2)+r(5)(2)

                         = 24+72+104 = 200 metric tons

Therefore, the upper and the lower estimates (in tons) for the total quantity q(6) of erupted materials after six seconds is 224 and 166 metric tons respectively.

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400 square feet of carpet area for $240 is the best deal among the given option.

The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina. Area can be interpreted as the quantity of material with a specific thickness required to create a model of the shape or as the quantity of paint required to completely cover a surface in a single coat. It is the two-dimensional equivalent of the volume of a solid or the length of a curve, both of which are one-dimensional concepts (a three-dimensional concept).

The carpets were sold for the following prices:

1) $67 for 100 square feet.

2) $130 for 200 square feet.

3) $240 for 400 square feet

4) $504 for 800 square feet.

For each of them, we would calculate the unit cost per square foot. It develops

1) The price per square foot is 67÷100 = $0.67

2) The price per square foot is 130÷200 = $0.65.

3) The price per square foot is 240÷400 = $0.6.

4) The price per square foot is 504÷800 = $0.63.

Comparing the unit costs per square foot the best deal costs $0.6 per square foot per unit, which is 400 square feet of carpet for $240.

400 square feet of carpet area for $240 is the best deal among the given option.

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We may use the instructions provided to build a finite-state machine that simulates a vintage soda machine and can carry out the specified work.

Nickels (5 cents), dimes (10 cents), and quarters are all accepted by the machine (25 cents).

The states should be s, s1, s2, s3, s4, etc.

If we add a nickel to the machine, we move from state s to state s+1 and so on, and the process is the same for a dime and a quarter.

We can build the necessary finite-state machine to simulate an antique soda machine that takes nickels, dimes, and quarters by using x as the input button for soda pop.

A mathematical model of computation is called a finite-state machine (FSM), often known as a finite automaton or just a state machine.

It is an abstract machine that has a limited number of states that it can only be in at any given time. The FSM can change from one state to another in response to some inputs; this change is known as a transition. A set of states, an initial state, and the inputs that trigger each transition comprise an FSM.

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The graph of each given piecewise function is shown below .

In the question,

a piece wise function is given ,

we have to sketch the graph of the piecewise function ,

the piecewise function f(x) is  = [tex]\left \{ {-2x-1 , {x\leq 2} \atop -x+4 , {x > 2}} \right.[/tex]

when x ≤ 2 ,

we put x =2 , we get , f(2) = -2*2-1  = -5 .

So , the point is (2,-5) .

when we put x = 0 , f(0) = -2*0 - 1 = -1

so , the second point is (0,-1) .

Now , for x>2  

we put x= 4 , we get f(4) = 0

the point will, be (4,0)

we put x = 6 , we get , f(6) = -2 .

the point will be = (6,-2) .

On plotting all the four points , we get the graph as sketched below .

Therefore , the given piecewise function's graph is shown below.

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In triangle PQR PQ equals 39 inches, PR equals 17 inches, and HTE altitude PN equals 15 inches. The correct answer is QR is, 44 in.

[tex]\boxed{\bold{= > (39)^2=(15)^2+(QN^2}}\\\boxed{= > QN=\bold{\sqrt{(39)^2-(15)^2}} }\\\boxed{= > QN=\bold{36}}[/tex]

Now we have to determine the side RN.

Now put all the values in the above expression, we get the value of side RN.

[tex]\boxed{\bold{= > (17)^2}=(15)^2+(RN)^2}\\\boxed{= > RN=\bold{\sqrt{(17)^2-(15)^2} }}\\\boxed{= > RN=\bold{8}}[/tex]

Therefore,  In triangle PQR PQ equals 39 inches, PR equals 17 inches, and HTE altitude PN equals 15 inches. The correct answer is QR is, 44 inches.

[tex]\text{The correct answer is QR is, 44 in.}[/tex]

Using Pythagoras theorem in ΔPNQ:

[tex]\boxed{(Hypotenuse)^2=(Perpendicular)^2+(Base)^2}\\\boxed{\bold{(PQ)^2=(PN)^2+(QN)^2}}[/tex]

[tex]\boxed{(39)^2=(15)^2+(QN)^2}\\\boxed{\bold{QN=\sqrt{(39)^2-(15)^2} }}\\\boxed{QN=\bold{36}}[/tex]

[tex]\boxed{(Hypotenuse)^2=(Perpendicular)^2+(Base)^2}\\\boxed{\bold{(PR)^2=(PN)^2+(QN)^2}}[/tex]

[tex]\boxed{\bold{(17)^2=(15)^2+(RN)^2}}\\\boxed{\bold{RN=\sqrt{(17)^2-(15)^2} }}\\\boxed{RN=\bold{8}}}[/tex]

Adding the numbers:

36 + 8 = 44

[tex]\text{Hence, The correct answer is QR is, 44 in.}[/tex]

Answer:

90%

Step-by-step explanation:

63 of 70 can be written as:

63/70

To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 100

63/70 × 100/100 = (63 × 100/70) × 1/100 = 90/100

Therefore, the answer is 90%

If you are using a calculator, simply enter 63÷70×100 which will give you 90 as the answer.

When "twice the sum of a number and 3 equals three times the difference of the number and 3," the value of expression is 6.

In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. A number, a variable, or a combination of numbers, variables, and operation symbols constitutes an expression. An equation consists of two expressions joined by an equal sign.

Here,

let x be the number,

2x+3=3x-3

x=6

The value of expression is 6 when "twice the sum of a number and 3 is equal to three times the difference of the number and 3."

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The volume of the composite solid that is made up of hemisphere and cylinder will be 7,121.52 cubic feet.

Volume is a measurement of three-dimensional space that is utilized. It is frequently mathematically quantified using SI-derived units or different imperial or US traditional units. The concept of length is linked to the notion of capacity.

The shape is the combination of the hemisphere and cylinder. Then the volume of the composite solid is calculated as,

V = Volume of hemisphere + Volume of cylinder

V = (2/3) πr³ + πr²h

Simplify the equation, then we have

V = (2/3) π(9)³ + π(9)²(22)

V = 486π + 1782π

V = 2268 x 3.14

V = 7,121.52 cubic feet

The volume of the composite solid will be 7,121.52 cubic feet.

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The scale factor of the geometric sequence 200, 100, 50, 25 is ½

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size.

Therefore scale factor= new dimension/ original dimension.

In the sequence 200, 100, 50, 25...., as we take 200 as the original dimension and 100 as the new dimension. From these we can discover that the object is decreasing in shape

Therefore the scale factor = new dimension/ original dimension

scale factor = 100/200

scale factor = ½

therefore the scale factor of the sequence is ½

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