Are the following functions exponential growth or decay?
Graphing Exponentials

a) f(x)=10(2)x

is this exponential growth? or exponential decay?

b) f(x)=2(0.5)x

is this a exponential growth? or exponential decay?

Answer:

not 100% sure but i think is 39

Step-by-step explanation:

The minimum coefficient of friction required to maintain pure rolling motion for the disk is 1.

Any coefficient of friction greater than 1 would also suffice. However, it is important to note that this assumes that the disk is not slipping at all. In reality, there will likely be some small amount of slipping, and the coefficient of friction required to maintain the motion will be slightly less than 1.

To maintain pure rolling motion, the tangential speed of the disk at the point of contact with the ground must be equal to the linear speed of the center of mass. This condition can be expressed as:

v = ωr

where v is the linear speed of the center of mass, ω is the angular speed of the disk, and r is the radius of the disk.

If the disk is rolling without slipping, the speed of the point of contact with the ground is zero. Therefore, the minimum coefficient of friction required to maintain pure rolling motion can be found by equating the magnitudes of the gravitational force and the frictional force:

mg = f

where m is the mass of the disk, g is the acceleration due to gravity, and f is the frictional force.

The frictional force can be expressed as:

f = μN

where μ is the coefficient of friction and N is the normal force.

The normal force can be found from the equation of motion in the vertical direction:

N - mg = 0

Therefore, N = mg.

Substituting these expressions for f and N, we get:

μmg = mg

Simplifying, we get:

μ = 1

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all the three terms on the right-hand side are positive and hence dy/dx is negative. Thus, this satisfies all the properties given. Therefore, the required autonomous differential equation is:dy/dx = a (y - 3) (y) (y - b).

We can obtain the autonomous differential equation having all of the given properties as shown below:First of all, let's determine the equilibrium solutions:dy/dx = 0 at y = 0 and y = 3y' > 0 for 0 < y < 3For -∞ < y < 0 and 3 < y < ∞, dy/dx < 0This means y = 0 and y = 3 are stable equilibrium solutions. Let's take two constants a and b.a > 0, b > 0 (these are constants)An autonomous differential equation should have the following form:dy/dx = f(y)To get the desired properties, we can write the differential equation as shown below:dy/dx = a (y - 3) (y) (y - b)If y < 0, y - 3 < 0, y - b < 0, and y > b. Therefore, all the three terms on the right-hand side are negative and hence dy/dx is positive.If 0 < y < 3, y - 3 < 0, y - b < 0, and y > b. Therefore, all the three terms on the right-hand side are negative and hence dy/dx is positive.If y > 3, y - 3 > 0, y - b > 0, and y > b. Therefore, all the three terms on the right-hand side are positive and hence dy/dx is negative. Thus, this satisfies all the properties given. Therefore, the required autonomous differential equation is:dy/dx = a (y - 3) (y) (y - b).

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The table below gives the dimensions of the statue and a scale drawing of the statue. The scale factor of the drawing to the real statue is 1:7.

If two figures are similar, we can use the scale factor to relate different characteristics of the figures.  The scale factor is a proportional measure to the original figure.

Using a scale factor, only similar figures can be compared.  We know that similar figures are proportionate, and the scale factor is the constant of proportionality of distinct dimensions in linear form such as length, height, width, perimeter, and so on.

To find the scale factor, we will divide the height in drawing to statute.

Height in drawing = 9 in

Height in statute = 63 in

Scale factor = 9 : 63

Converting it into lowest fraction, it will be 1: 7.

We can check the same for length

Length in drawing = 6 in

Length in statute = 42 in

Scale factor = 6 : 42

= 1 :7

Hence, the scale factor is 1:7.

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Step-by-step explanation:

3³⁸ - 3³⁷

= 3³⁷(3 - 1)

= 2 * 3³⁷

= 2 / [3^(-37)].

Hence x = -37.

A person having Tetrachronacy or the Fourth type of cone will be able to see more colors outside the conventional visible spectrum.

Recently, it has been found that some individuals possess a fourth form of the cone in addition to the three that the majority of people with normal color vision do.

When a person has tetrachromacy, their retina has four cone types instead of the typical three that most people do. It is caused by a hereditary mutation and only affects women.

In the retina, cones are a particular kind of photoreceptor cell. They enable us to see in color. We can see fine details because of the macula, the area of our retina where cones are concentrated. The retina has about 6 million cones and 120 million rods. A photopigment in the fourth type of cone found in tetrachromats enables them to perceive more colors outside of the conventional visible spectrum. ROY G. BIV is a better-known name for the spectrum (Red, Orange, Yellow, Green, Blue, Indigo, and Violet).

Cone cells come in three different subtypes:

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Answer:

45

Step-by-step explanation:

x + x + 2x = 180      {Sum of angles of a triangle}

            4x = 180 {Divide both sides by 4}

              x = 180/4

x = 45

Answer:

57 degrees

Step-by-step explanation:

The sum of any triangle is 180 degrees, so you can add the two angles given and subtract from 180 degrees:

1. 82 + 41 = 123 degrees

2. 180- 123 = 57 degrees

Answer:

\(57 \degree\)

Step-by-step explanation:

The sum of the interior angles in a triangle is added up to 180°

\(82 + 41 + x = 180 \\ 123 + x = 180 \\ x = 180 - 123 \\ x = 57 \degree\)

Hope this helps you.

Let me know if you have any other questions :-):-)

Answer:

58

Step-by-step explanation:

We are given the arithmetic sequence:-

-12,-7,-2,3,...

First, find the common difference which we can obtain by:-

\( \displaystyle \large{d = a_{n + 1} - a_n}\)

Check:-

-7-(-12) = -7+12 = 5

-2+7 = 5

3+2 = 5

Therefore, our common difference is 5.

General Arithmetic Term

\( \displaystyle \large{a_n = a_1 + (n - 1)d}\)

Since we want to find the 15th term, substitute a1 = -12, n = 15 and d = 5.

\( \displaystyle \large{a_{15}= - 12 + (15 - 1)5} \\ \displaystyle \large{a_{15}= - 12 + (14)5} \\ \displaystyle \large{a_{15}= - 12 + 70} \\ \displaystyle \large{a_{15}= 58} \\ \)

Answer:

x = 9

m∠1 = m∠2 = 54°

Step-by-step explanation:

Two lines r and s are the parallel lines and a transversal line is intersecting these lines at two distinct points.

a). ∠1 ≅ ∠2 [Corresponding angles]

    Therefore, m∠1 = m∠2

    (63 - x)° = (72 - 2x)°

    2x - x = 72 - 63

    x = 9

b). m∠1 = (63 - x)°

            = 63 - 9

            = 54°

    m∠2 = (72 - 2x)°

             = 72 - 18

             = 54°

The lifetime of light bulbs that are advertised to last for 5900 hours are normally distributed with a mean of 6165.5 hours and a standard deviation of 150 hours.

To find the probability that a bulb lasts longer than the advertised figure, we need to calculate the z-score of 5900. Then, we will use the z-score table to find the probability of the bulb lasting longer than 5900 hours.

z-score formula is given by: Z = (X - μ) / σ, where, X = 5900 hours μ = 6165.5 hours σ = 150 hours

Plugging these values in the formula, we get :Z = (5900 - 6165.5) / 150

Z = -0.177

Let us check the z-table to find the probability for z = -0.177 from the standard normal distribution table, the area to the left of the z-score -0.177 is 0.4306.

Since we want to find the probability that a bulb lasts longer than 5900 hours, we need to subtract the value obtained from 1. Thus, the probability that a bulb lasts longer than the advertised figure is: 1 - 0.4306 = 0.5694, which is approximately equal to 0.57 or 57%.

Therefore, the probability that a bulb lasts longer than the advertised figure is 0.57 or 57%.

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The point estimate of the population proportion defective will be 0.0945

The formula for calculating the point estimate is expressed as;

p = x/n,

where p is the proportion of successes in the sample

n is the total sample

Given the following

n = 550 items

x = 52

Substitute

p = 52/550

p = 0.0945

Hence the point estimate of the population proportion defective will be 0.0945

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Answer:

at least 80%

Step-by-step explanation:

The equation can be used to solve for b is b = 5 / tan30°

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, a triangle, ∠ BCA = 90°, ∠ CAB = 30°, we need to find the equation for AC,

The equation for AC(b) =

tan30° = 5/b

b = 5 / tan30°

Hence, the equation can be used to solve for b is b = 5 / tan30°

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Answer:

it 5.5⋅10−^8m

Step-by-step explanation:

Unless I'm missing something important here, you can find the difference between the two wavelengths by subtracting one from the other. Since you're interested in finding how much longer the wavelength associated with the orange light is, subtract the wavelength of the green light from the wavelength of the orange light. You know that the two measured wavelengths are 6.15 ⋅ 10 − 7 m → orange light 5.6 ⋅ 10 − 7 m → green light Therefore, the difference between the two wavelengths will be Δ wavelength = 6.15 ⋅ 10 − 7 m − 5.6 ⋅ 10 − 7 m = 5.5 ⋅ 10 − 8 m

The 95% confidence interval for the weights of the special type of rock is given as (2.62, 6.80). The margin of error can be calculated by finding the difference between the upper and lower bounds of the interval, then dividing by 2.
Margin of error = (6.80 - 2.62) / 2 = 4.18 / 2 = 2.09 pounds

The margin of error for this 95% confidence interval can be calculated as half of the width of the interval.

Width of interval = upper limit - lower limit = 6.80 - 2.62 = 4.18

Therefore, the margin of error will be half of the width of the interval, which is 4.18/2 = 2.09.

So, the margin of error for this 95% confidence interval is 2.09 pounds. This means that if we were to take multiple samples of this special type of rock and construct 95% confidence intervals for each sample, about 95% of the intervals would contain the true population weight of the rock, with a margin of error of 2.09 pounds.

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Answer:

The correct answer is A. x > -3/35

Step-by-step explanation:

-3/2(x - 1/3) > 1/5 - 5x

-3/2x + 1/2 > 1/5 - 5x

-15x + 5 > 2 - 50x

-15x + 50x + 5 > 2

-15x + 50x > 2 - 5

35x > 2 - 5

35x > -3

x > -3/35

Hope this helped! :)

Answer: A. x > -3/35

Step-by-step explanation:

Answer:

The value belonging to the green box is b

Step-by-step explanation:

QP uses the points Q and P

Q is (0,-a)

P is (b,-c)

The distance between the two points can be calculated using the distance formula;

D = √(x2-x1)^2 + (y2-y1)^2

(x1,y1) = (0,-a)

(x2,y2) = (b,-c)

D = √(b-0)^2 + (-c + a)^2

D = √(b)^2 + (-c + a)^2

Answer:

7 cups = 3.5 pints

Step-by-step explanation:

Adjacent angles are two angles that lie in the same plane and have a common vertex and a common side but have no common interior points.

The terms adjacent, neighboring, contiguous, and juxtaposed all denote being close by. Although adjacent might indicate a touch or not, it is usually assumed that there is nothing of the same sort in between. a home with a garage close by. Adjoining clearly means coming together and touching at a certain location or line.

When two angles have a similar vertex and side, they are referred to as neighboring angles. The vertex of an angle is the point at which the rays that make up its sides come to a stop. When adjacent angles have the same vertex and side, they might be a complimentary angle or supplemental angle.

Thus, adjacent angles are two angles that lie in the same plane and have a common vertex and a common side but have no common interior points.

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Based on the given perimeter of the polygon and the length of each side; the length of the longest side of the polygon is 29 cm

Perimeter of the polygon = x + (x + 6) + (x + 5) + (x + 1) + (x + 8) + (x + 4)

150 = x + x + 6 + x + 5 + x + 1 + x + 8 + x + 4

150 = 6x + 24

150 - 24 = 6x

126 = 6x

x = 126/6

x = 21

The longest side of the polygon is (x + 8)

= 21 + 8

= 29 cm

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Mia will pay a total of $4.5 for the shipping and handling of the t-shirt

From the question, we have the following parameters that can be used in our computation:

Cost of the shirt = $15

shipping and handling = 30%

The amount paid for the shipping and handling of the t-shirt can be calculated using the following equation

Amount paid = original price * + shipping and handling

Substitute the known values in the above equation, so, we have the following representation

Amount paid = 15 * 30%

Evaluate the products

Amount paid = 4.5

Hence, the amount paid is $4.5

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Answer:

k=2

Step-by-step explanation:

8+2k=4k+4

Step 1: Simplify both sides of the equation.

2k+8=4k+4

Step 2: Subtract 4k from both sides.

2k+8−4k=4k+4−4k

−2k+8=4

Step 3: Subtract 8 from both sides.

−2k+8−8=4−8

−2k=−4

Step 4: Divide both sides by -2.

−2k

−2

=

−4

−2

k=2

Answer:

k = 2

Step-by-step explanation:

8 + 2k = 4k + 4

    -2k    -2k

8 = 2k + 4

-4         -4

4 = 2k

divide both sides by 2

2 = k

k = 2

Hope this Helps

Answer:

a = (w - 3b + 4)/6

Step-by-step explanation:

w = 3(2a + b) - 4

w = 6a + 3b - 4

6a + 3b - 4 = w

6a = w - 3b + 4

a = (w - 3b + 4)/6

Answer:

\( \frac{y - 18}{x - 1} = \frac{23 - 18}{1.5 - 1} = \frac{5}{0.5} = 10 \\ y - 18 = 10(x - 1) = 10x - 10 \\ y = 10x + 18 - 10 = 10x + 8 \\ \boxed{f(x) = 10x + 8}\)

hope this helps.

The item which is closest in size to one mole of gas at STP is C) A microwave

A mole is the quantity of matter contained in a body.

We know that at STP the volume of gas occupied by one mole of a gas at STP is 22.4 dm³.

Now, we have 4 items.

Let us assume that each item is a cube. Also, since 22.4 dm³ is the volume of the cube, its length is

L = ∛22.4 dm³

=  ∛(22.4 × 10³) cm³

= 28.2 cm

So, ithe item that is comparable to this length is the microwave.

So, the item is C. A microwave

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The decision that most clearly reflects a lack of understanding of the concept of sunk costs is "You study eight hours for a final exam even though there is no way now that you can pass the course".

Sunk costs refer to any costs that have already been incurred and cannot be recovered. Sunk costs are irrelevant in decision-making because they are already gone and cannot be recovered. Decision-makers must only consider future costs and benefits when making decisions.

A lack of understanding of sunk costs may result in individuals making decisions based on past costs rather than future costs and benefits. Decision-making that is influenced by sunk costs may result in inefficient resource allocation and lost opportunities.

Individuals must ignore sunk costs and instead focus on future costs and benefits to make effective decisions.

In the given options, "You study eight hours for a final exam even though there is no way now that you can pass the course" is the decision that most clearly reflects a lack of understanding of the concept of sunk costs.

Even though the student has already spent 8 hours studying, the sunk costs are irrelevant because the student cannot pass the course now. The student should focus on future costs and benefits and use the remaining time to study for other courses.

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