The number of carbon atoms in a fossil is given by the function y = 51000(0.85), where t represents the number of
years since being discovered. What is the percent of change each year? Explain how you arrived at your answer.

The value of x=0.301 at the x the graph of the function have a horizontal tangent.

Given that,

The function is f(x)=eˣ-2x

We have to find the value of x does the graph of the function have a horizontal tangent.

Where the derivative of a function is zero, a graph's horizontal tangent line is a mathematical feature. This is so that the derivative, by definition, can provide the slope of the tangent line. The slope of horizontal lines is zero. As a result, when the derivative is zero, the tangent line is horizontal.

For horizontal tangent line,

f'(x)=0

The differentiation of the function is

eˣ-2=0

eˣ=2

Taking logarithm on both sides.

logeˣ=log2

We know that loge=1

So,

x loge=log2

x(1)=log2

x=log2

x=0.301

Therefore, the value of x=0.301 at the x the graph of the function have a horizontal tangent.

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The solving linear equation states that the temperature of the oven is 119 after an minute.

A linear equation is just an algebraic equation of something like the form y=mx+b that only contains a constant and a first-order (linear) component, where m represents the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where y and x are now the variables.

Given:

y = 40x+79

X = number of minutes using it to bare:

When X = 1

y = 40(1)+79

y = 119

It means that the temperature of the oven is 119 after an minute.

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The exponential model of the given data is f(t) = 30.18 × 1.06^t.

Some of the rules of exponents are as follows,

The product of two exponents having the same power is equal to the power of their base multiplied.

The product of two exponents having the same base is equal to the sum of the powers of different exponents to the same base.

Given that,

The average price for office space in 2004 is $30.18.

The average price for office space in 2015 is $66.85.

Suppose the average price in 2004 is taken as y₀.

The given situation can be represented in the form of exponential function f(t) = y₀b^t as,

Take t = 0 for 2004

Then,  f(0) = y₀b^0

⇒ f(0) = y₀ = $30.18.

Then, at 2015, t = 12. Substitute the respective values to get,

f(12) = 30.18 × b^12

⇒ 66.85 = 30.18 × b^12

⇒ b^12 = 66.85 / 30.18

⇒ b = 1.06

Thus in exponential form the given situation can be written as,

f(t) =30.18 × 1.06^t

Hence, the given data can be modeled in exponential function as  f(t) =30.18 × 1.06^t.

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Answer:

x° = 34°

Step-by-step explanation:

First, find the interior angle supplementary to the given exterior angle 124°.

I will label it y.

124° + y° = 180°

y° = 180° - 124°

y° = 56°

Next, solve for x° by equating the sum of the interior angles of the triangle to 180° and plugging in the y-value that we just solved for.

x° + y° + 90° = 180°

x° + y° = 90°

x° + 56° = 90°

x° = 90° - 56°

x° = 34°

Answer:

---------------------------

9/16 must be added to this expression [tex]x^{2} -3x/2[/tex] to make it a perfect square.

According to the question,

We have the following expression:

[tex]x^{2}[/tex] -3x/2

Now, in the given four options, we only have two perfect squares which 9/16 and 16/9.

Now, 9/16 is the square of 3/4.

So, we will first solve it using 9/16:

[tex]x^{2}[/tex]-3x/2+9/16

Now, this formula is of identity [tex](a-b)^{2}[/tex] where we have a = x and b = 3/4.

The formula of the identity [tex](a-b)^{2} = a^{2} + b^{2} -2ab[/tex].

Now, adding 9/16 make it a perfect whole square.

(More to know: we can add or subtract a number or a term from an expression to make it a perfect square or perfect cube.)

Hence, the correct option is C.

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The value of TU is 21

From the question, we have

ST=3x+3 and TU=2x+9

ST = TU

3x + 3 = 2x + 9

3x - 2x = 9 - 3

x = 6

substituting the value, we get

TU = 2x + 9

= 2 (6) + 9

= 12 + 9

TU = 21

Addition:

The phrase "the addition" refers to combining two or more numbers. Adding two numbers is indicated by the plus sign (+), therefore adding three is written as three plus three. Additionally, the number of times the plus symbol (+) is used is up to you. For example, 3 + 3 + 3 + 3. Mathematical addition is a crucial component of the learning curriculum for kids. In primary school, students learn simple addition sums such as one-digit facts, Math addition sums, and double-digit Math addition sums. One of the most fundamental and interesting Math concepts for elementary school children is addition sums. Math is a fascinating subject, and children first learn basic mathematical concepts like adding numbers in their early years.

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The value of TV for the similar triangles is 25

Similar triangles are the triangles that have corresponding sides in proportion to each other and corresponding angles equal to each other. Similar triangles look the same but the sizes can be different.

Similar triangles are not the same as congruent triangles though.

triangle UXW and UTV are similar since line TV cuts lines UX and UW in the same proportion.

Let UV = p, it means also that WV = P. which means WU = 2p

so since the two triangles are similar, the ratio of their corresponding lengths are equal

meaning,

UV/UW = TV/XW

substituting their values, we have

p/2p = TV/50

by cross multiplying,

2p x TV = 50p

2TV = 50

TV = 50/2 = 25

In conclusion,  the value of TV is half the value of WX = 25

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Using the equation y = -3x - 1, the missing values are in the ordered pairs, (−3,y) and (x,2), are: x = -1 and y = 8.

An algebraic equation is an expression that has variables. The values of those variables, when plugged into the equation would make the equation true.

Given the equation, y = -3x - 1, substitute x = -3 into the equation to find y:

y = -3(-3) - 1

y = 9 - 1

y = 8

The missing value in the ordered pair is: (-3, 8).

To find the missing value of x in (x, 2), substitute y = 2 into the equation, y = -3x - 1:

2 = -3x - 1

2 + 1 = -3x

3 = -3x

3/-3 = x

x = -1

The missing value is (-1, 2).

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Proved that the triangle ABW ≅ triangle DCW

In the given question,

The length of WA = The length of WD

The measure of angle 5 = The measure of angle 7

Here we have to prove that one angle and two sides of the triangle ABW is equal to the one angle and two sides of the triangle DCW

Consider the triangle ADW,

In the triangle ADW the length of the WA is equal to the length of WD.

Therefore the measure of angle A is equal to the measure of angle D.

So in triangle ABW and the triangle DCW, one side and two angles are equal.

Therefore the triangle ABW and triangle DCW are congruent

Hence, proved that the triangle ABW ≅ triangle DCW

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Answer:

density = 1.43 × 10⁻³ g/cm³

Step-by-step explanation:

We are told that oxygen gas of mass 2.23 kg has a volume of 1.56 × 10⁶ cm³, and we are told to find its density in g/cm³.

To do this we have to first convert the mass, which is given in kg, to g:

mass = 2.23 kg = 2.23 kg × 1000 [tex]\mathrm{_\frac{g}{kg}}[/tex]

                          = 2230 g

Next, we can find the density of the gas using the following formula:

[tex]\boxed{density = \frac{mass}{volume}}[/tex]

⇒ density = [tex]\mathrm{\frac{2230 \ g}{1.56 \times 10^{6} \ cm^3}}[/tex]

                 = 1.43 × 10⁻³ g/cm³

Therefore, the density of the oxygen gas is 1.43 × 10⁻³ g/cm³.

The monthly payment is 38455 when the P for a $75,000 loan with a 20-year term (n = 240 months) and an annual interest rate of 4%.

Given that,

We have to calculate the monthly payment P for a $75,000 loan with a 20-year term (n = 240 months) and an annual interest rate of 4% (let r=.9967).

We know that,

Formula for monthly payment is P(i(1+i)ⁿ/(1+i)ⁿ-1)

Here,

P is principal amount $75,000

n is number of months 240 months

i is interest rate 4% is 0.04

=P(i(1+i)ⁿ/(1+i)ⁿ-1)

=75,000(0.04(1+0.04)²⁴⁰/(1+0.04)²⁴⁰-1)

=75,000(0.04(1.04)²⁴⁰/(1.04)²⁴⁰-1)

=75,000(0.04(12246.20236)/(12245.20236)

=75,000(0.04×1.000081665)

=38455

Therefore, The monthly payment is 38455 when the P for a $75,000 loan with a 20-year term (n = 240 months) and an annual interest rate of 4%.

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Answer:

↓ ↓ ↓

Step-by-step explanation:

7) Name of plane to piano CIJ:-

8) Name a segment parallel to BC:-

9) Which segment  is not skew to EK:-

______________________

Hope this helps!

Have a great day!

The number of ways to select 3 position out of 10 applicant is 120 ways

Combinations implies the selection of things from a given set of things. In this case, we intend to select the objects. Combination formula is illustrated as:

nCr = n! / ((n – r)! r!)

n = the number of items.

r = how many items are taken at a time.

Since there are 10 applicants applying for 3 positions. This will be:

= 10! / (10 - 3)!3!

= 10! / 7!3!

= 10 × 9 × 8 / 3 × 2

= 120

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The number of ways to form the committees, using the Fundamental Counting Theorem, are given as follows:

a) President and vice from different grades: 79,800.

b) At least one from each: 141,960.

It is a theorem that states that if there are n independent trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, the total number of outcomes is calculated by the multiplication of the factorials as presented as follows:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

For item a, there are two possible cases for the parameters, as follows:

Hence the number of ways is:

N = 7 x 15 x 20 x 19 + 15 x 7 x 20 x 19 = 79,800.

For item b, the total number of outcomes is obtained as follows:

N = 22 x 21 x 20 x 19 = 175,560.

The number of outcomes with only grade 11 students is:

N = 7 x 6 x 5 x 4 = 840.

The number of outcomes with only grade 12 students is:

N = 15 x 14 x 13 x 12 = 32760.

Hence the number of students with at least one of each is:

N = 175,560 - (840 + 32,760) = 141,960.

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The probability that a 4 is drawn from from Urn A followed by a 2 from Urn B is  1/40 .

In the question ,

it is given that

the number of balls in Urn A is 8

which are  {1,2,3,4,5,6,7,8}

the probability of getting a 4 from Urn A is (P₁) = 1/8

the number of balls in Urn B is 5 .

which are {1,2,3,4,5}

the probability of getting 2 from Urn B is (P₂) = 1/5

So ,the required probability is = P₁ × P₂

On substituting the values of P₁ and P₂ ,
we get

= 1/8 × 1/5

= 1/40

Therefore , the  required probability is 1/40 .

The given question is incomplete , the complete question is

Find the probability.

Urn A has balls numbered 1 through 8. Urn B has balls numbered 1 through 5. What is the probability that a 4 is drawn from A followed by a 2 from B?

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-353.92-(-283.56)-131.29= -20,165

The value of the x is 60 km and the value of the y is 70 km.

Given that a man travels x km at 60 km/h and y km at 40 km/h and the total time traveled is 11/4 i.e 2.75 h.

Let's suppose that the time traveled for the x km is t1, time traveled for the y km is t2 and total time is T ,so by using the speed distance formula t1 & t2 will be :

t1 = x/60 and t2 = y/40 ;

T = t1 + t2;

i.e 2.75 = x/60 + y/40 ;

Multiply both sides with 120,

330 = 2x + 3y ............i

Now given that man traveled 5x km at 40 km/h and 3y km at 50 km/h in total time of 11. 7 hours. Similarly the equation for this situation will be :

T = t1 + t2;

x/8 + 3y/50 = 11.7 ;

Multiply both sides with 200, we will get

25x + 12y = 2340 .........ii

Now by simplifying the equation i and ii we will get the value of x and y which are 60 and 70 respectively.

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The  equation of line in slope intercept form

What is equation of line in slope intercept form?

The most general form of equation of line in slope intercept form is given by y = mx + c

Where m is the slope of the line and c is the y intercept of the line.

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If [tex]\theta[/tex]  is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m = [tex]tan\theta[/tex]

The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.

The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.

Here,

Slope = [tex]\frac{1}{5}[/tex]

Point = (-2, 2)

Required equation of line =

[tex]y - 2 = \frac{1}{5}(x - (-2))\\5y - 10 = x + 2\\5y = x + 2 + 10\\5y = x + 12\\y = \frac{1}{5}x + \frac{12}{5}\\[/tex]

The graph has been attached here.

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Answer:

15.00x +5.00y = 60.00

Step-by-step explanation:

answer is to the equation is 3 because u plug in 3 to x given information provided to get 45.00 dollars. u then subtract 60 and 45 to see how much money u have left for maps. each map is 5.00 dollars and with 15.00 dollars remaining, u can get three maps and three dictionaries to equal 60.00 dollars!! Hope this helps!

Answer:

You can buy 3 maps. Equation: 15a + 5b = 60 ⇒ 15(3) + 5(3) = 60

Step-by-step explanation:

15 multiplied by 3 equals 45. Now you have $15 left. 15 divided by 5 equals 3. Therefore, you can buy 3 maps. Hope that helped! :)

The equation that represents the number of purses Paula must sell to pay for the new equipment is 5.00x = 5000.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, Paula makes purses and the materials cost $2.25 per purse.

She sells them for $5.00 each now she wants to invest $5000 in some new equipment and we are assuming the no. of purses to be x.

Here the equation 5.00x - 2.25x = 5000 represents Paula's profit.

The equation that represents the no. of purses she must sell to pay for the new equipment is 5.00x = 5000.

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Answer: 5.00x - 2.25x = 5000

Step-by-step explanation:

Answer: 2 ft.

Step-by-step explanation:
|-20| = 20, |-22| = 22
22 - 20 = 2

The paper company can produce 25 notebooks for $285

From the question, the equation of the total cost is given as

Equation = 4x + 185

Rewrite as

Cost = 4x + 185

Express the equation as a cost function

So, we have the following representations

C(x) = 4x + 185

When the total cost is $285, we have

C(x) = 285

This gives

4x + 185 = 285

Subtract 185 from both sides

4x = 100

Divide by 4

x  = 25

Hence, the number of notebooks is 25

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Answer:

The numbers in which 7 appears are. 7, 17, 27, 37, 47, 57, 67, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 87, 97, 107. So, counting all. ∴ Number of times 7 appears = 21

The result of the fractional operation in this problem is given as follows:

-21/5 = -4.20.

A fraction is represented by the division of a term x by a term y, as follows:

Fraction = x/y.

The terms that represent x and y are given as follows:

The numerator in this fraction is given as follows:

5 - (8 - 6) + 3 x 4 + 6.

The parenthesis and the multiplication have precedence, hence:

5 - (8 - 6) + 3 x 4 + 6 = 5 - 2 + 12 + 6 = 21.

The denominator in this fraction is given as follows:

5(4 - 5) = 5(-1) = -5.

The result is the division of the numerator by the denominator, hence:

21/(-5) = -21/5 = -4.20.

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Equation of the line in standard form is 6x + y + 4 = 0.

Slope-intercept form of equation -> y = mx + c

Given in question,

Slope = m = -6

y-intercept = c = -4

Putting values of m and c in Slope-intercept form of equation,

y = -6x - 4

Standard form :

6x + y + 4 = 0

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The value to make the inequality true is n > 3

Inequality, In mathematics, a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

We need to solve this problem and determine what value will solve this problem.

2(n + 2) < 5(n - 1)

2n + 4 < 5n - 5

Collect like terms

4 + 5 < 5n - 2n

9 < 3n

3n > 9

n > 3

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Answer:

$336

Step-by-step explanation:

[tex]\frac{280}{35} \times 42 \\ \\ =\frac{56}{7} \times 42 \\ \\ =8 \times 42 \\ \\ =\$336[/tex]

Answer: 324

Step-by-step explanation: 10% is the same as 1/10

360/10 is 36

360-36= 324

meaning 324 students now attend Haley elementary school <3

hope this helps <33