Situation:
A geologist in South America discovers a
bird skeleton that contains 61% of its
original amount of C-14.
N = Noe-kt
No = inital amount of C-14 (at time
t = 0)
N = amount of C-14 at time t
k = 0.0001
t = time, in years

From the given information provided, 20% off 250000 is 50000, and the discounted price is 200000.

The formula for calculating percentage is:

percentage = (part/whole) x 100

Here's an example:

Let's say you got 35 out of 50 questions correct on a test. To calculate the percentage of questions you answered correctly, you would use the formula as follows:

percentage = (35/50) x 100

percentage = 0.7 x 100

percentage = 70%

To calculate 20% off 250000, you can multiply 250000 by 20% (which is 0.20 in decimal form) and then subtract the result from 250000:

250000 - (0.20 x 250000) = 250000 - 50000 = 200000

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The distance between the student and the mirror is apprοximately 29.41 feet.

Distance is a numerical measurement of hοw far apart or how far away objects or lοcations are from each other. It is a physical quantity that is usually expressed in units such as meters, kilοmeters, miles, οr feet. Distance is a scalar quantity, meaning it οnly has magnitude and nο direction.

To sοlve the problem, we can use the similar triangles prοperty of geometry. Let's denοte the distance between the student and the mirrοr as d. Then, we can set up the follοwing proportion:

(student height + height of mirrοr) / distance frοm student to mirror = height of schοol / distance from mirrοr to school

Plugging in the given values, we get:

(5.1 + 0) / d = 30 / (50 + d)

Simplifying and sοlving for d, we get:

5.1d + 0 = 150

d = 29.41

Therefοre, the distance between the student and the mirrοr is apprοximately 29.41 feet.

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The measure of angle A is 52 degree.

Vertical angles are angles that are opposite of each other when two lines crosses, they are congruent.

Given that;

Since vertical angles are congruent,

Angle A = Angle B

Plug in the given values

( 7x - 18 ) = ( 6x - 8)

Solve for x

7x - 18 = 6x - 8

7x - 6x = -8 + 18

x = -8 + 18

x = 10

Hence, angle A will be;

Angle A = 7x - 18

Plug in x = 10

Angle A = 7( 10 ) - 18

Angle A = 70 - 18

Angle A = 52°

Therefore, angle A is 52 degree.

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The length of the base is approximately 8.71 units.

What is triangle ?

Triangle can be defined in which it consists of three sides, three angles and sum of three angles is always 180 degrees.

Let's call the two legs of the right triangle a and b, and the hypotenuse c. The hypotenuse is the side opposite the right angle, so in this case, we have c = 29. We also know that one of the acute angles is 71 degrees.

Using trigonometry, we can use the tangent function to find the length of the base:

tan(71) = a/b

We can solve for b by multiplying both sides by b:

b tan(71) = a

Now we can substitute c = 29 and solve for b:

b = c / tan(71)

b = 29 / tan(71)

b ≈ 8.71

Hence, The length of the base is approximately 8.71 units.

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By using synthetic division, we can find all the roots of the function f(x) = x³ + 3x² - x - 3 and determine that the roots are 1, -1, and -3.

A root of a function is a value for x that makes the function equal to zero.

In this case, we have a function f(x) = x³ + 3x² - x - 3 and we know that f(1) = 0. To find all the roots of this function, we can use the remainder theorem.

The remainder theorem states that if we divide a polynomial by a linear expression (such as x - a), the remainder will be equal to the value of the polynomial at that value of x (a). In other words, if we write f(x) = (x - a)q(x) + r, where r is the remainder, then f(a) = r.

So, if we divide our function f(x) by x - 1, the remainder will be equal to f(1), which we know is zero. Therefore, (x - 1) is a factor of f(x), and the function has a root at x = 1.

Next, we can divide f(x) by (x - 1) to get a quotient, q(x), and a new remainder, r. We can repeat this process, dividing q(x) by another linear expression until we have no more remainders.

The roots of f(x) will be the values of x that we used as factors in each step of the division process.

This process of dividing a polynomial by a linear expression to find its roots is called synthetic division.

Complete Question

If f(1) = 0, what are all the roots of the function f(x) = x³ + 3x² - x - 3. Use the remainder theorem.

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According to the information in the table, the graph would look like the one in the attached image.

To graph the information in the table we must carefully observe the information. In this case, the relationship is decreasing because the number of infected is decreasing as time increases. In accordance with the above, the curve that shows this relationship is a decreasing curve.

In this case, we must locate the time on the x axis and the infected on the y axis and mark a point in the areas where the data coincide. Later we must graph a line that joins the points and our graph would be finished.

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Answer: Increases by 16 students per year

Step-by-step explanation:

100% = 800

2% = x

So between 100% and 2%, the scale factor would be 50 since 100 / 2 = 50

Then 800 / 50 would be 16

So..

1 Year = 816 students

2 Years = 832 students

3 Years = 848 students

4 Years = 864

And so on..

The magnitude of given operations of vectors are found.

Quantities with the independent characteristics of magnitude and direction are called vectors.

Given:

u = (-3, 8) and v = (-14, 6)

So, 3u = (-9, 24) and 2v = (-28, 12)

3u - 2v = (-9+28, 24-12)

3u - 2v = (19, 12)

Magnitude of 3u - 2v = √19² + 12²  = √505 units

2u = (-6, 16) and 3v = (-42, 18)

2u - 3v = (36, -2)

Magnitude = √36² + (-2)²  = √1300 units

u = (-3, 8) and 4v = (-56, 24)

u + 4v = (-59, 32)

Magnitude = √(-59)² + 32²  = √4505  units

5u = (-15, 40) and v = (-14, 6)

5u - v = (-1, 34)

Magnitude = √1157  units

7u = (-21, 56) and 2v = (-28, 12)

7u - 2v = (7, 44)

Magnitude = √1985 units.

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Answer:

8.31, 8.3, 8.296, 8.06

Step-by-step explanation:

8.31, 8.296, 8.06, 8.3

The order of decimals from greatest to least is

8.31, 8.3, 8.296, 8.06

The area of the logo is given as 139 cm

In order to get the area of the shape, i would have to get the area of the triangles first

area of a triangle = 1/2 b * h

base = 9 / 2 = 4.5

h = 6

area = 1/2 * 9 * 6

= 27

Area of 2 triangle = 2 x 27

= 58

The are aof the square = a * a

= 9 * 9

= 81

The total area of the logo is given as 81 + 58

= 139 cm

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To convert 200 micrograms (mcg) to milligrams (mg), we need to use the conversion factor that 1 milligram is equal to 1000 micrograms, 200 micrograms (mcg) is equal to 0.2 milligrams (mg).

When we want to convert a unit of measurement to another unit of measurement, we use conversion factors to make the conversion. In the case of converting micrograms (mcg) to milligrams (mg), we need to know that 1 milligram is equal to 1000 micrograms. This means that to convert any value from micrograms to milligrams, we need to divide by 1000.

To convert 200 micrograms (mcg) to milligrams (mg), we need to use the conversion factor that 1 milligram is equal to 1000 micrograms.

So, to convert 200 mcg to mg, we divide 200 by 1000:

200 mcg ÷ 1000 = 0.2 mg

Therefore, 200 micrograms (mcg) is equal to 0.2 milligrams (mg)

It is important to understand the concept of unit conversions because it is a crucial aspect of many scientific and engineering calculations. Knowing how to convert units of measurement allows us to work with data that is expressed in different units and compare results from different experiments. In addition, being able to convert units is a valuable skill for everyday life, such as when reading nutrition labels or measuring medication dosages.

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Answer:

Step-by-step explanation:

y= -2x + 5

The distance d between the student and the mirror is given by the similar triangles are d = 10.5 feet

If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.

Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides

Given data ,

Let the triangles be represented as ΔABC and ΔCDE

Now , they are similar triangles

The measure of AB = height of the school = 30 feet

The measure of BC = distance from the school to the mirror = 50 feet

And ,

The measure of DE = height of the student = 6.3 feet

The measure of CD = distance d between the student and the mirror

So , the corresponding sides of similar triangles are in the same ratio

On simplifying the equation , we get

BC / AB = CD / DE

And , 50 / 30 = d / 6.3

Multiply by 6.3 on both sides , we get

d = ( 5/3 ) x 6.3

d = 31.5 / 3

d = 10.5 feet

Hence , the distance d between the student and the mirror is 10.5 feet

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An equation of the line that passes through the points (4, -3) and (8,5) is y + 3 = 2(x - 4).

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

At data points (4, -3), a linear equation of this line can be calculated by using the point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - (-3) = (5 - (-3))/(8 - 4)(x - 4)

y + 3 = 8/4(x - 4)

y + 3 = 2(x - 4)

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Answer:

To complete the first set of data so that it has six values and a mean of 21, you can add the following values: 20, 20.5, 20.5, 21.5, 21.5, 21.

The mean of this set is calculated as follows: (20 + 20.5 + 20.5 + 21.5 + 21.5 + 21) / 6 = 21.

To complete the second set of data so that it has six values and a mean of 21, you can add the following values: 20, 21, 21, 21, 21, 22.

The mean of this set is calculated as follows: (20 + 21 + 21 + 21 + 21 + 22) / 6 = 21.

The simplified expression is given as follows:

-27j/10 - 1/8.

The expression for this problem is defined as follows:

-j/5 + 3/4 - (5j/2 + 7/8).

The negative sign means that every term in the parenthesis has the signal exchanged, hence:

-j/5 + 3/4 - 5j/2 - 7/8.

Then the expression is simplified combining the like terms, as follows:

Meaning that the expression is of:

-27j/10 - 1/8.

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The number of liters of water that can be conserved will be 11.76 liters. The initiative by the company is beneficial for water conservation.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

The number of liters of water that can be conserved is given as,

⇒ 28% of 42

⇒ 0.28 x 42

⇒ 11.76 liters

The number of liters of water that can be conserved will be 11.76 liters. The initiative by the company is beneficial for water conservation.

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Figure ABCD is a square. If AC+BD=56, the length of AX is 28.

Since ABCD is a square, all sides have the same length, let's call it "x".

We know that the sum of the diagonals of a square is equal to twice the length of a side, so AC + BD = 2x.

Therefore, 56 = 2x, and x = 28.

So the length of AX (or any side of the square) is 28 units

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The inverse of function is  f(x) = (x - 4)³/8 + 3

A function that reverses the results of another function is known as an inverse function. If y = f(x), then x = g(y), then a function g is the opposite of a function f. To put it another way, applying f and then g is equivalent to doing nothing. This can be expressed as g(f(x)) = x in terms of how f and g are made up.

Given g(x) = 2(∛x-3)+4

let g(x) = y

y = 2(∛x-3)+4

change the variables since options are in form of x

x =  2(∛y-3)+4

simplify for y

subtract 4 from both side

x - 4 = 2(∛y-3)+4 - 4

x - 4 = 2(∛y-3)

divide both side by 2

(x - 4)/2 = (2(∛y-3))/2

(x - 4)/2 = (∛y-3)

cube both side

((x - 4)/2)³ = ((∛y-3))³

(x - 4)³/8 = y - 3

(x - 4)³/8 + 3 = y

Hence  the value f(x) =  (x - 4)³/8 + 3 .

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If a 2020 study showed that the presence of male pattern baldness and a severe reaction to COVID-19 had a strong association: A. Age is the most likely lurking variable in this scenario.

In this case, the relationship between male pattern baldness and severe COVID-19 reactions may be influenced by age, as older individuals are more likely to experience both male pattern baldness and severe COVID-19 symptoms.

Age could also affect other factors such as overall health and immune system function, which may contribute to the severity of COVID-19 symptoms.

Diet, height, and weight may also be related to overall health and immune system function, but they are less likely to be related specifically to male pattern baldness

Therefore, age is the most likely lurking variable in this scenario.

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Answer:

The graph in the attached figure

we have

----> inequality A

The solution of the inequality A is the shaded area below the dashed line

The slope of the dashed line A is  positive m=2

The y-intercept of the dashed line A is (0,-5)

The x-intercept of the dashed line A is (2.5,0)

----> inequality B

The solution of the inequality B is the shaded area above the dashed line

The slope of the dashed line B is  negative m=-3

The y-intercept of the dashed line B is (0,1)

The x-intercept of the dashed line B is (1/3,0)

The solution of the system of inequalities is the shaded area between the two dashed lines

using a graphing tool

The graph in the attached figure

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The diameter of the Ferris wheel will be the difference between two consecutive maximum height and minimum height of the ferris wheel.

Diameter is the line jwhich passes through the center of a circle and joins two points on the circumference of the circle.

To find the diameter of the Ferris wheel which is a circle, we see that the grpah gives the height of a passenger on the Ferris wheel as a function of the number of complete cycles since the ride started.

Now, the diameter of the Ferris wheel will be the difference between two consecutive maximum height and minimum height of the ferris wheel.

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Answer:2

Step-by-step explanation:

59 to 1 sig. fig= 60

25 to 1 sig fig = 30

Therefore, 60/30 =2

Hope this helps :)

Answer:

2

Step-by-step explanation:

divide the numbers. then find the left furthest critical number.

count to the rifht by desired sig fig. use decimal to mark a place of significant zeros.

Answer: 35m2

Step-by-step explanation:took the test and i got it right

An isosceles trapezoid with a short base of 3 meters and a height of 5 meters then the area of the trapezoid is 35 m²

What is the area of the trapezoid?

To find the area of a trapezoid, multiply the sum of the bases (the parallel sides) by the height (the perpendicular distance between the bases), and then divide by 2.

We can start by finding the length of the long base. Since the trapezoid is isosceles, we know that the length of the portion of the large base from the left vertex to the perpendicular is equal to the length of the portion from the right vertex to the perpendicular. Let's call the length of the long base "x":

x = 4 + 7 = 11 meters

Now we can use the formula for the area of a trapezoid:

Area = (1/2) * (short base + long base) * height

Substituting the values we have:

Area = (1/2) * (3 + 11) * 5

Area = 7 * 5

Area = 35 m²

Therefore, the area of the trapezoid is 35 m².

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Answer:its 5

Step-by-step explanation: cuz

The simplest form of the given ratio 32 min : 36 min is equal to  

option a. 8 : 9.

Ratio  is equal to

32 min : 36 min

Factors of 32 are = 1, 2, 4, 8, 16, 32

Factors of 36 are = 1, 2, 3, 4, 6, 9, 12, 18, 36

Greatest common factor of 32 and 36 is equal to 4

Simplest form of the given ratio is equal to

32 min : 36 min

= ( 8 × 4 ) min : ( 9 × 4 ) min

'4' get cancelled with other we get,

= 8 min : 9 min

Therefore, the simplest form of the given ratio by taking out common factors is equal to option a. 8 : 9 .

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The true statement is (b) Function 2 has the lowest average rate

We start by calculating the average rates of each function

The interval is given as [1, 2]

For Function 1

We have

f(1) = -3

f(2) = 3

The average rate is then calculated as

Average rate = [f(2) - f(1)]/[2 - 1]

Average rate = (3 + 3)/1

Average rate = 6

For Function 2

We have

f(1) = (1/4)^1 + 4 = 4.25

f(2) = (1/4)^2 + 4 = 4.0625

The average rate is then calculated as

Average rate = [f(2) - f(1)]/[2 - 1]

Average rate = (4.0625 - 4.25)/1

Average rate =-0.1875

For Function 2

We have

f(1) = -2

f(2) = 0

The average rate is then calculated as

Average rate = [f(2) - f(1)]/[2 - 1]

Average rate = (0 + 2)/1

Average rate = 2

The lowest average rate is -0.1875 for function 2

Hence, function 2 has the least rate

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The number of small ball bags she will need is 7 small bags, the correct option is A.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given that;

Need of flour for cakes= 17 2/5 pounds

Now,

There are 4 large bags, and each one has 4 pounds.

She buys all of the large bags, she already has;

4x4=16

16 pounds. So, she only needs

17 2/5 -16= 1 2/5

=5/5+2/5

=7/5

1 2/5 pounds more, this fraction is equals to 7/5 pounds.

The small bags only contains 1/5 pounds of flour so,

7/5/1/5

=7*5/1*5

=7

Therefore, by algebra the answer will be 7 bags

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The complete question is;

Erika has a baking company and needs to purchase 17 pounds of flour for her cakes. The Baking Goods Store sells two different-sized bags of flour. The table shows the amounts of flour in the bag, the number of bags at the store, and the cost per bag of flour. Size Pounds 1 Bags for Sale 75 Cost per Bag Small $0.84 5 Large 4 4 $16.80 If Erika buys all of the large bags, how many small bags will she need? A. 7 small bags B. 12 small bags C. 28 small bags D. 71 small bags