A city block has 6 pigeons and then 1 week later there are 9 pigeons. Let P(t)be the number of pigeons where t is measured in weeks.

Assuming the growth continues proportionally, at the same rate, what is the differential equation which describes the growth of the pigeon population?

Step-by-step explanation:

the rate of change in an interval is always

( f (interval upper limit) - f (interval lower limit) ) /

(interval upper limit - interval lower limit)

31a.

( f (-2) - f (-4)) / (-2 - -4) = (-2 - -3) / 2 = 1/2

b.

( f (7) - f (3)) / (7 - 3) = (2.5 - 0.5) / 4 = 2/4 = 1/2

c.

yes, it is linear (= the function is a straight line), because it has the same change rate or slope everywhere.

32a.

f(x) = y = 35x + 75

b.

the slope is the factor of x, which is 35 for this function.

the slope is defined as "y coordinate change / x coordinate change" when going from one point on the line to another. and that is the same as the change rate, which is simply called slope for a line.

so, both are 35. it means for every increase of x by 1, y increases by 35.

The x-intercept is 5 and the y-intercept is 2.

The standard form of the line is 2x + 5y = 10.

The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis. In other words, the x -intercept is the value of x when y = 0 and the y-intercept is the value of y when x = 0.

Hence, the x-intercept is 5 and the y-intercept is 2.

Let's find the equation in standard form.

Ax + By = C

where

Using slope intercept form,

y = mx + b

where

Hence, using (5, 0) and (0, 2)

m = 2 - 0 / 0 - 5

m = - 2 / 5

Therefore.

y = - 2 / 5x + 2

Hence, let's multiply through by 5 to eliminate the fraction

5y = -2x + 10

Therefore, the standard form is as follows:

2x + 5y = 10

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1). Volume of the coin is 1.4 cm³

2). Volume of cylinder is 282.8 cm³

3). Volume and curved surface area of the cylinder are 2771.2 cm³ and 791.8 cm² respectively.

Volume of cylinder is calculated using:

V = π × r² × h

1) Volume of coin = 3.142 × (1.5cm)² × 0.2cm

Volume of coin = 1.4 cm³

2) Volume of the cylinder = 3.142 × (3cm)² × 10cm

Volume of the cylinder = 282.8 cm³

3) Volume of the cylinder = 3.142 × (7cm) × 18cm

Volume of the cylinder = 2771.2 cm³

Area of curved surface= 2πrh

Area of curved surface of the cylinder = 2 × 3.142 × 7cm × 18cm

Area of curved surface of the cylinder = 791.8 cm²

Therefore, the volume of the coin is 1.4 cm³.

(2) Volume of cylinder is 282.8 cm³

(3). Volume and curved surface area of the cylinder are 2771.2 cm³ and 791.8 cm² respectively.

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Answer:

1/2

Step-by-step explanation:

There are 8 marbles in total and 4 are blue, so 4/8 are blue. Then simplify 4/8 and you will get 1/2.

Answer:

1/2 or 50%

Step-by-step explanation:

Blue= 4, Red= 2, Green= 2

Total marbles= 8

P(B)= 4/8= 1/2 or 50%

Answer:

$120.64

Step-by-step explanation:

Step one:'

given data

originally price fo microscope = $148.48

discount= 25%

tax= 6.25%

Step two:

the total amount paid for the microscope

1. Amount of the discount= 25/100*148.48

= 0.25*148.48

=$37.12

2. Amount of tax

= 6.25/100*148.48

= 0.0625*148.48

=$9.28

Step three:

The total amount is

= 148.48-37.12+9.28

=$120.64

47.72% of the students scored between 311 and 391 on the exam.

Let's standardize the scores using the z-score formula:

z = (x - μ) / σ

Where:

x = score

μ = mean

σ = standard deviation

For the lower score (311):

z_lower = (311 - 311) / 40

= 0

For the upper score (391):

z_upper = (391 - 311) / 40

= 2

Now use a standard normal distribution table to find the area under the curve between these two z-scores.

The area represents the percentage of students who scored between 311 and 391 on the exam.

Using a standard normal distribution table or a calculator, the area between 0 and 2 is approximately 0.4772.

To express the result as a percentage, we multiply the decimal value by 100:

Percentage = 0.4772 × 100

= 47.72%

Therefore, 47.72% of the students scored between 311 and 391 on the exam.

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Answer:

Proportionality constant can be used with any representation to determine how a variable is changing with respect to others.

Variation is a method comparing the nature of a variable with another variable using a constant called the proportionality constant

For instance, if a variable y is directly proportional to x, it is expressed as;

y ∝ x

y = kx

k is the proportionality constant relating y to x and shows that as the value of y is increasing, the value of x is also increasing and vice versa.

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The value of B and C for barium(Ba) is 146 and 56 respectively .

Given,

239/94 Pu + 1/0 n ⇒ B/C Ba + 91/38 Sr + 3 1/0 n

Sum of mass number in reactant side is 239+1=240

Sum of atomic number in reactant side is 94+0=94

so the product side sum of mass number should also be 240 and that of atomic number should be 94 .

So to calculate the mass number of barium,

B + 91 + 3*1 = 240

B = 146

Next to calculate the atomic number,

C + 38 + 3*0 = 94

C = 56

Thus the value of atomic number (C) and mass  number (B) is 56 and 146 respectively .

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The given area presented on the coordinate plane has dimensions

given by the lengths of the line joining the vertices.

Response:

The given figure can be taken as a composite figure of wo triangles and

a trapezium.

Area of the triangle at the top, A₁ = 0.5 × 4.5 × 1 = 2.25

Area of the trapezoid, A₂ = 0.5 × (6 + 4.5) × 1 = 5.25

Area of the bottom triangle, A₃ = 0.5 × 2 × 6 = 6

Therefore;

Area of the figure, A = A₁ + A₂ + A₃

Which gives;

A = 2.25 + 5.25 + 6 = 13.5

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The probability that a woman with breast cancer will survive after her surgery is less than -1.33 is approximately 0.0918.

Therefore P(X < 6) = 0.0918 or 9.18%.

 To find the probability that a woman with breast cancer will survive after surgery, we need to use the normal distribution formula.

z = (x - μ) / σ

where z =z-score

x=survival time in years,

μ =mean survival time,

and σ= standard deviation of survival time.

Let X be the survival time, then \(X ~ N(8, 1.5^2).\)

a) 10+ year survival probability:

I would like to find P(X > 10). Using the formula above, we get:

z = (10 - 8) / 1.5 = 1.33

A standard normal distribution table or calculator tells us that the probability that z is greater than 1.33 is approximately 0.0918.

Therefore P(X > 10) = 0.0918 or 9.18%. b) 5- to 7-year survival probabilities:

b) 5- to 7-year survival probabilities: I would like to find P(5 < X < 7).

Using the formula above, we get: z1 = (5 - 8) / 1.5 = -2

z2 = (7 - 8) / 1.5 = -0.67

From a standard normal distribution table or calculator, we know that the

probability that z is between -2 and -0.67 is approximately 0.1841.

Therefore P(5 < X < 7) = 0.1841 or 18.41%.

c) Probability of survival <6 years:

Find P(X < 6). Using the formula above, we get:

z = (6 - 8) / 1.5 = -1.33

A standard normal distribution table or calculator tells us that the probability that z is less than -1.33 is approximately 0.0918. Therefore P(X < 6) = 0.0918 or 9.18%.  

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Convenience purchase: Coca-Cola. Shopping purchase: Apple iPhone. Specialty purchase: Rolex. These brand name products correspond to their respective purchase types based on convenience, shopping involvement, and specialty appeal in the consumer marketplace.

Convenience purchases refer to low-involvement purchases made by consumers for everyday items that are readily available and require minimal effort to obtain. These purchases are typically driven by convenience and habit rather than extensive consideration or brand loyalty.

Shopping purchases involve higher involvement and more deliberate decision-making. Consumers invest time and effort in comparing options, seeking the best value or quality, and may consider multiple brands before making a purchase. These purchases often involve durable goods or products that require more consideration.

Specialty purchases are distinct and unique purchases that cater to specific interests, preferences, or hobbies. These purchases are driven by passion, expertise, and a desire for premium or specialized products. Consumers are often willing to invest more in these purchases due to their unique features, quality, or exclusivity.

Three specific brand name products in the consumer marketplace that correspond to these types of purchases are

Convenience Purchase: Coca-Cola (Soft Drink)

Coca-Cola is a widely recognized brand in the beverage industry. It is readily available in various sizes and formats, making it a convenient choice for consumers seeking a refreshing drink on the go.

With its widespread availability and strong brand presence, consumers often make convenience purchases of Coca-Cola without much thought or consideration.

Shopping Purchase: Apple iPhone (Smartphone)

The Apple iPhone is a popular choice for consumers when it comes to shopping purchases. People invest time researching and comparing features, pricing, and user reviews before making a decision.

The shopping process involves considering various smartphone brands and models to ensure they select a product that meets their specific needs and preferences.

Specialty Purchase: Rolex (Luxury Watches)

Rolex is a well-known brand in the luxury watch industry and represents specialty purchases. These watches are associated with high-quality craftsmanship, precision, and exclusivity.

Consumers who are passionate about luxury watches and seek a premium product often consider Rolex due to its reputation, heritage, and unique features. The decision to purchase a Rolex involves a significant investment and is driven by the desire for a prestigious timepiece.

These examples illustrate how different types of purchases align with specific brand name products in the consumer marketplace, ranging from convenience-driven choices to more involved shopping decisions and specialty purchases driven by passion and exclusivity.

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Answer: 8/10

Step-by-step explanation: so you have to multiply 5 times x u till you get 10 so you’ll multiply it 2 times and since you multiplied the left 5 times two you have to multiply the 4 by 2 also to keep everything equal so the final answer is 8/10

Answer:

1/10 or 10/100

Answer:

8x^2-2x-10 is the answer

Answer:

8x^2+6x+2

Step-by-step explanation:

What I did was combined like terms and added them

6x^2+2x^=8x^2

2x+4x=6x

-4+-6= -10

Answer:

44

Step-by-step explanation:

because it looks like a square tilted

Answer:

False, assuming "combined" means "added or subtracted and would simplify."

\(x^2\) and \(x\) cannot be combined with addition or subtraction.  They are not like terms.

Step-by-step explanation:

Combining like terms only works if the variables and the powers on the variables match perfectly.  

Examples:

\(x^2\) and \(x\) don't have matching powers, so they're not like terms.

\(x^2\) and \(y^2\) have the same powers, but the variables don't match, so they're not like terms.

Anything can be multiplied together though.  So that's a different situation.

The risk-free interest rate for a five-year maturity is the yield on a five-year risk-free bond. To determine this rate, you would need to refer to the current zero-coupon yield curve for risk-free bonds and find the yield corresponding to a five-year maturity.

To find the risk-free interest rate for a five-year maturity, you would need to refer to the current zero-coupon yield curve for risk-free bonds. This curve provides yields for different maturities of risk-free bonds.

Look for the yield corresponding to a five-year maturity on the curve, and that would be the risk-free interest rate for a five-year maturity. Make sure to round the rate according to the given instructions.

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Answer:

1/2

Step-by-step explanation:

The red markings is not clear but I think the larger one is triangle DEF, if not, then the answer is 2

Answer:

1/2

Step-by-step explanation:

The dude above said if the big triangle is not DEF then it's two, but the big triangle is DEF therefore it is: 1/2.

Answer:

Would you mind including the ratios in the comments?

You didn't post any material to solve.

Answer:

2.90

Step-by-step explanation:

One hundredth is 0.01. 2.89+0.01= 2.90.

Hope this helps, please mark brainliest!

Answer:

5.9 hours

Step-by-step explanation:

1/13+1/11=1/x

looking for x

x= 5.9

are you clear?

It is more likely that the distance across a circular field is the diameter rather than the circumference.

To determine whether the distance across a circular field is the diameter or the circumference, we can use some formulas that relate these parts of a circle. The formulas are:

Circumference = π * diameter

Diameter = 2 * radius

Radius = diameter / 2

If we plug in the given distance of 98.638 meters into these formulas, we can see which one gives a reasonable value for the other parts of the circle. For example, if we assume that the distance is the diameter, then we can find the radius and circumference as follows:

Radius = diameter / 2

Radius = 98.638 / 2

Radius = 49.319 meters

Circumference = π * diameter

Circumference = π * 98.638

Circumference ≈ 310.05 meters

These values seem reasonable for a circular field. However, if we assume that the distance is the circumference, then we can find the diameter and radius as follows:

Diameter = circumference / π

Diameter = 98.638 / π

Diameter ≈ 31.39 meters

Radius = diameter / 2

Radius = 31.39 / 2

Radius ≈ 15.695 meters

These values seem too small for a circular field. Therefore, it is more likely that the distance across a circular field is the diameter rather than the circumference.

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Complete question:

The distance across a circular field is 98.638 meters. Is it a diameter, a radius or a circumference?

Answer:

C. there is no solution

Step-by-step explanation:

Add 6 to both sides:

2x- 6 + 6=2x +5 + 6

Simplify equation above:

2x=2x+11

Subtract 2x from both sides:

2x - 2x=2x+11 -2x

Simplify equation above:

0 = 11

The sides are not equal, Therefore there is no solution :(

Answer:

3.1, 4.1, 5.1,6.1, 7.1, 8.1, 9.1

Step-by-step explanation:

the bolded numbers are the answer :)

The vertex of the graph for the given equation is (-1, -8).

The differentiation of a function is defined as rate of change of its value at a point. It can be written as f'(x) = (f(x + h) - f(x)) /(x + h - x).

Its geometrical aspect is the slope of the tangent at a given point.

The given equation is y = 2x² + 4x - 6.

The vertex is a point at the graph where the slope becomes zero. It can be found by equating the differentiation of the equation to zero as below,

y = 2x² + 4x - 6

=> y' = 4x + 4 = 0

=> x = -1

At x = -1 the value of y can be found as,

y = 2 × -1² + 4 × -1 - 6

  = 2 - 4 - 6

  = -8

Thus, the vertex is given as (-1, -8) which is only valid for option (b).

Hence, the key points to be used by sandy to draw the graph are x-intercept (1, 0), y-intercept (-3, 0) and vertex (-1, -8).

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Answer:

b

Step-by-step explanation:

Answer:

\(27c^3-27c^2d+9cd^2-d^3\)

Step-by-step explanation:

Binomial Theorem

\((a+b)^n=a^n+\dfrac{n!}{1!(n-1)!}a^{n-1}b+\dfrac{n!}{2!(n-2)!}a^{n-2}b^2+...+\dfrac{n!}{r!(n-r)!}a^{n-r}b^r+...+b^n\)

\(\textsf{If }(a+b)^n=(3c-d)^3 \: \textsf{ then}:\)

Substitute the given values into the formula:

\(\begin{aligned}(3c-d)^3 & =(3c)^3+\dfrac{3!}{1!(3-1)!}(3c)^{3-1}(-d)+\dfrac{3!}{2!(3-2)!}(3c)^{3-2}(-d)^2+(-d)^3\\\\& =(3c)^3+3(3c)^2(-d)+3(3c)^1(-d)^2+(-d)^3\\\\& =27c^3-27c^2d+9cd^2-d^3\end{aligned}\)

Thus, the equation we would use to solve the rate of decay of the temperature of the pizza is: T(t) = 425°F * e^(-0.048t).

To determine the rate of decay of the temperature of the pizza using a continuous exponential decay model, we can use the following equation:
T(t) = T0 * e^(-kt)

Where T(t) is the temperature of the pizza at time t, T0 is the initial temperature (425°F), k is the decay constant, and e is the mathematical constant approximately equal to 2.718.

To find the decay constant, we can use the information given in the problem. We know that after 15 minutes, the temperature of the pizza has cooled to 200°F. Therefore, we can plug in the following values:
T(t) = 200°F
T0 = 425°F
t = 15 minutes

200°F = 425°F * e^(-k*15)

Solving for k, we get:
k = ln(425°F/200°F)/15 minutes
k ≈ 0.048

Therefore, the equation we would use to solve the problem is:
T(t) = 425°F * e^(-0.048t)

Where t is the time elapsed since the pizza was taken out of the oven, measured in minutes. This equation gives us the temperature of the pizza at any given time, based on the rate of decay calculated using the information given in the problem.

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