in how many ways can first, second, and third prizes be awarded in a contestant with 375 contestants? assume there are no ties

If Ram gets 3 correct and 4 incorrect out of 7 questions he attempted then Ram's score in the test is 7.

To find Ram's score, we will use the given formula:S = 5c - 2w

where S is the score, c is the number of correct answers and w is the number of wrong answers.

Ram attempted 7 questions and answered 3 of them correctly and 4 of them incorrectly.

So:

c = 3 (number of correct answers)w = 4 (number of wrong answers)

We can now substitute these values in the formula to get Ram's score:

S = 5c - 2w

S = (5 x 3) - (2 x 4)

S = 15 - 8

S = 7

Therefore, Ram's score is 7.

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Answer:

3.65

Step-by-step explanation:

Answer:

approx answer should be 25

Step-by-step explanation:

you should have given naming to figure

but let it be

so coming to the answer

length of base of the triangel will be half the length of base of rectangle by symmetry so base length of triangle = 7/2

to find perimeter we have to do sum of lengths of all sides

so by pythagoras theorem we can find side length of triangle

(7/2)^2 + 2^2 = side^2

side = 4.04 approx so let take side = 4 for easy calculation

now triangel is equilateral so other side is also same now we have to just do just sum of all sides

= 5+5+7+4+4 = 25 approx answer should be 25

if you take side length of triangle as 4.04 you will get accurate answer

hope this answer help

According to the information we can infer that the two squares would need to be coloured in to give a shape with two lines of symmetry are 6f and 5g.

To identify the two squares that would be coloured we have to analyze the graph and its shape. In this case two sides have 3 squares coloured (diagonal). So, we have to colour two squares to complete four sides with 3 squares coloured (diagonal).

In this case we can infer that the two squares would need to be coloured in to give a shape with two lines of symmetry are 6f and 5g.

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Answer:

Vivek has Rs. 150

Step-by-step explanation:

Amount of Money Vivek has = x

Irfan = 7x

Irfan = 900 + x

Set Irfan's equations equal to one another:

7x = 900 + x

=> 6x + x = 900 + x (Now you can subtract x from both sides)

=> 6x = 900

=> x = 900/6 (Divide both sides by 6 to isolate x)

=> x = 150

Irfan has Rs. 1050 (7 x 150 = 1050)

Since Vivek's money is x, Vivek has Rs. 150

After purchasing the bike with the discount and sales tax, you will have approximately $105.331 left over.

In order to determine how much will be left, we can do this;

1. The discounted price of the bike is;

Discounted price = Original price - (Discount percentage * Original price)

Discounted price = $625 - (0.25 * $625)

Discounted price = $625 - $156.25

Discounted price = $468.75

2. Calculate the sales tax:

Sales tax is added to the price of the bike, so we need to calculate 5.53% of the discounted price.

  Sales tax = Sales tax percentage * Discounted price

  Sales tax = 0.0553 * $468.75

  Sales tax = $25.912

3. Calculate the total amount to be paid:

  Total amount to be paid = Discounted price + Sales tax

  Total amount to be paid = $468.75 + $25.919

  Total amount to be paid ≈ $494.669 (rounded to three decimal places)

4. Calculate the money left over:

  Money left over = Total amount saved - Total amount to be paid

  Money left over = $600 - $494.669

  Money left over = $105.331

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Answer: X is an exponent, and the correct answer is x ≈ 0.884228217

Step-by-step explanation:

To solve for x in the equation 12^x = 9, you need to use logarithms. A logarithm is the inverse of an exponent. It tells you what power you need to raise a base to get a certain number. For example, log2(8) means “what power do you need to raise 2 to get 8?” and the answer is 3.

So, to solve 12^x = 9, you can take the logarithm of both sides with any base, such as 10 or e. For example, using base 10, you get:

log10(12^x) = log10(9)

Then, you can use the property of logarithms that says logb(a^c) = c * logb(a). This means you can bring down the x as a coefficient of the logarithm on the left side:

x * log10(12) = log10(9)

Then, you can divide both sides by log10(12) to isolate x:

x = log10(9) / log10(12)

Using a calculator, you can find that log10(9) is about 0.954242509 and log10(12) is about 1.079181246. So,

x = 0.954242509 / 1.079181246

x ≈ 0.884228217

Answer x = log 12(9)= 0.8765

Step-by-step explanation:

The couple should withdraw approximately $1,120.28 each month for a period of 10 years in order to deplete the account balance to zero by the end of the term.

To calculate the monthly withdrawal amount for the couple, we can use the concept of an annuity.

Principal amount (P) = $200,000

Interest rate (r) = 8.4% per year = 8.4/100 = 0.084

Number of compounding periods per year (n) = 12 (monthly compounding)

Number of years (t) = 10

The formula for calculating the monthly withdrawal amount from an annuity is:

Withdrawal Amount [tex]= P \times (r/n) / (1 - (1 + r/n)^{(-n\times t)})[/tex]

Plugging in the given values, we get:

Withdrawal Amount [tex]= $200,000 \times (0.084/12) / (1 - (1 + 0.084/12)^{(-12\times 10)})[/tex]

Now, let's calculate it step by step:

Calculate the value inside the parentheses:[tex](1 + 0.084/12)^{(-1210)}[/tex]

(1 + 0.084/12) = 1.007

(-1210) = -120

[tex](1.007)^{(-120)[/tex] ≈ 0.433

Substitute the value into the formula:

Withdrawal Amount [tex]= $200,000 \times (0.084/12) / (1 - 0.433)[/tex]

Simplify the denominator:

Withdrawal Amount [tex]= $200,000 \times (0.084/12) / 0.567[/tex]

Perform the division:

Withdrawal Amount ≈ $1,120.28

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[tex]\textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &6\\ t=years\dotfill &10000\\ h=\textit{half-life}\dotfill &5730 \end{cases} \\\\\\ A = 6\left( \frac{1}{2} \right)^{\frac{10000}{5730}}\implies A = 6\left( \frac{1}{2} \right)^{\frac{1000}{573}}\implies A \approx 1.8[/tex]

The solution to the inequality |x + 3| > 2 is (b) x < -5 and x > -1

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

|x + 3| > 2

Remove the absolute bracket

So, we have

-2 > x + 3 > 2

Add -3 to all sides of the inequality

This gives

-5 > x > -1

This means that

x < -5 and x > -1

The number line that represents the inequality x < -5 and x > -1 is (b)

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a. The rock's velocity at time t is v = 24 - 1.6t m/s. Its acceleration is constant at a = -1.6 m/s².

b. It takes 15 seconds for the rock to reach its highest point.

c. The rock reaches a height of 180 meters.

d. It takes approximately 4.74 seconds and 19.26 seconds for the rock to reach half its maximum height.

e. The rock is aloft for a total of 15 seconds.

a. To find the velocity and acceleration at time t, we need to differentiate the height equation with respect to time.

Given: s = 24t - 0.8t^2

Taking the derivative of s with respect to t:

ds/dt = 24 - 1.6t

This is the expression for velocity (v) at time t. So, the velocity of the rock at time t is given by v = 24 - 1.6t.

To find the acceleration (a), we differentiate the velocity equation with respect to time:

dv/dt = -1.6

This gives us the constant acceleration of the rock, which is -1.6 m/s^2.

b. The rock reaches its highest point when its velocity becomes zero. Setting the velocity equation equal to zero:

24 - 1.6t = 0

Solving for t:

1.6t = 24

t = 24 / 1.6

t = 15 seconds

Therefore, it takes 15 seconds for the rock to reach its highest point.

c. To find the maximum height the rock reaches, we substitute the value of t = 15 into the height equation:

s = 24t - 0.8t^2

s = 24(15) - 0.8(15)^2

s = 360 - 0.8(225)

s = 360 - 180

s = 180 meters

Thus, the rock reaches a height of 180 meters.

d. To find the time it takes for the rock to reach half its maximum height, we need to set the height equation equal to half of the maximum height and solve for t.

s = 24t - 0.8t^2

0.5(180) = 24t - 0.8t^2

90 = 24t - 0.8t^2

0.8t^2 - 24t + 90 = 0

Solving this quadratic equation will give us the time when the rock reaches half its maximum height.

Using the quadratic formula, t = (-b ± √(b^2 - 4ac)) / (2a), where a = 0.8, b = -24, and c = 90.

Calculating the roots, we get:

t ≈ 4.74 seconds or t ≈ 19.26 seconds

Therefore, it takes approximately 4.74 seconds and 19.26 seconds for the rock to reach half its maximum height.

e. The total time the rock is aloft is equal to the time it takes for the rock to reach its highest point and then return to the surface. Since the rock reaches its highest point at t = 15 seconds, it will take the same amount of time to return to the surface.

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The probability of making a Type I error using the decision rule above is 0.00045 or 0.045%.

The hypothesis for this testing situation are given below:H0: μ = 10.13HA: μ > 10.13μ denotes the actual population mean amount of mercury in tuna per ounce.

Therefore, the company has set a limit of 12 micrograms of mercury per ounce of albacore tuna. If the sample mean amount of mercury in tuna exceeds this amount, the production line will be stopped to find the source of contamination.

To calculate the chance of making a Type I error using the decision rule above, we will use the mean for the normal distribution in the graphing calculator, which is 10.13. The standard deviation is 2.03 and the sample size is 10 cans of tuna. We need to find the z-value that corresponds to a sample mean of 12 or greater.

The formula for calculating the z-value is shown below z = (x - μ) / (σ / sqrt(n))where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Using the given information, we can calculate the z-value as follows:z = (12 - 10.13) / (2.03 / sqrt(10))z = 3.32Therefore, the probability of making a Type I error using the decision rule above is the area to the right of the z-value of 3.32. To calculate this probability, we can use a standard normal distribution table or a graphing calculator.

Using a graphing calculator, we can find the probability by graphing a standard normal distribution with a mean of 0 and a standard deviation of 1 and shading the area to the right of the z-value of 3.32.

The graphing calculator gives the probability of 0.00045.

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The three true statements of the function g(x) = x² are

g(0) = 0, g(-1) = 1, and g(-1) = 1.

Options B, D, and E are the correct answer.

We have,

Function:

g(x) = x²

Substitute x = 0, 1, -1, 4 in the function.

So,

g(0) = x² = 0² = 0

This is true.

g(1) = x²= 1² = 1

This is true.

g(-1) = x² = (-1)² = 1

This is true.

g(4) = x² = 4² = 16

This s not true.

Thus,

The three true statements of the function g(x) = x² are

B. g(0) = 0

D. g(-01) = 1

E. g(-1) = 1

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The complete question:

The function g(x) = x²  is graphed. Which statements about the function are true?

g(1) = -1

g(0) = 0

g(4) = -2

g(1) = 1

g(-1) = 1

The probabilities obtained from z-scores found from the specified mean and standard deviation (approximate values) are;

a. Normal distribution

X ~ N(16, 2.5)

b. 0.19089

c. 15.04 and 16.96

The z-score is a measure of the number of standard deviation a data point or raw score is from the mean.

a. The distribution of X with a mean and standard deviation of 16 and 2.5 years is a normal distribution, therefore; X ~ N(16, 2.5)

b. The probability that an indoor cat dies when it is between 16.9 and 18.5 can be found as follows;

The z-scores for the two ages are;

z-score for 16.9 years z = (16.9 - 16)/2.5 = 0.36

z-score for 18.4 years z = (18.4 - 16)/2.5 = 0.96

The standard normal table can be used to find the area under the standard normal curve as follows;

P(z < 0.36) = 0.64058

P(z < 0.96) = 0.83147

Therefore; P(0.36 < z < 0.96) = 0.83147 - 0.64058 = 0.19089

The probability that the age at which an indoor cat dies is between 16.9 and 18.4 years is about 0.19089

c. The z-score that corresponds to the lower and upper bounds of the middle 30% of the standard normal distribution, can be found as follows;

The middle 30% is symmetrical about the mean, we get;

The lower bound is the z-score for which 35% of the distribution are located, and 35% are upper bound is the z-score for which 35% of the distribution are located to the right. Using an online calculator, we get;

The lower bound z-score = -0.385

The upper bound z-score = 0.385

The raw score values are therefore;

z = (x - μ)/σ

x = zσ + μ

The lower bound value for X = 16 + 2.5 × -0.385 = 15.0375 ≈ 15.04

The upper bound value for X = 16 + 2.5 × 0.385 = 16.9625 ≈ 16.96

The ages between which the middle 30% of indoor cats dies are therefore about 15.04 and 16.96 years

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Answer:

-8,4

Step-by-step explanation:

because the slope is slightly 0n 5 and 4

The rent for The new monthly lease amount is $858.

To find out the new monthly lease amount, we need to take into account that there is one month free, which we need to apply to all the months of the lease period.

A one-year lease is for 12 months.

The total rent amount for 12 months = Regular rent for 12 months - One-month free rent= $936 × 12 - $936 = $11232 - $936= $10296

The free rent is distributed equally across the 12 months:$936 ÷ 12 = $78

The new monthly rent amount is the total rent amount for 12 months divided by the number of months:

Total rent amount for 12 months = $10296

New monthly lease amount = Total rent amount for 12 months ÷ 12

New monthly lease amount = $10296 ÷ 12

New monthly lease amount = $858

Therefore, the new monthly lease amount is $858.

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Answer:

Step-by-step explanation:

its b

the answer is b.8

In the picture. both 51 degrees and 4x+7 are connecting to form a 90 degree angle.

So, we need to set an expression where you add 51 and 4x+7 and equal it to 90.

4x+7+51=90

now solve:

4x+58=90.

4x=90-58

4x=32

x=32/4

x=8 answer.

Answer:

B. 8

Step-by-step explanation:

The angle measure given as 51° and the angle measure represented with (4x + 7)° are complementary angles which means their sum is equal to 90°.

We can write the following equation to find the value of x based on above mentioned information:

51° + (4x + 7)° = 90°

58° + 4x = 90°

4x = 32

x = 8

The expression to find the number of cups of water Katrina drinks in a week is 0.5 gallons/day x 16 cups/gallon x 7 days/week = 56 cups/week.

To find the number of cups of water Katrina drinks in a week, we need to convert the given information from gallons to cups and then multiply it by the number of days in a week.

Given that Katrina drinks 0.5 gallons of water per day, we know that there are 16 cups in a gallon. Therefore, Katrina drinks 0.5 x 16 = 8 cups of water per day.

To calculate the number of cups of water she drinks in a week, we multiply the daily consumption by the number of days in a week, which is 7.

Therefore, the expression to find the number of cups of water Katrina drinks in a week is: 8 cups/day x 7 days/week = 56 cups/week.

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The perimeter of this square with an area x is four times the square root of x i.e P = 4√x.

The intercept of this function is (0, 0).

The domain and range of this function are [0, ∞].

The function is increasing.

In Mathematics and Geometry, the perimeter of a square can be calculated by using the following formula;

P = 4s

Where:

For the area of a square, we have:

x = s²

s = √x

By substituting the given parameters into the formula for the perimeter of a square, we have the following;

Perimeter of a square, P = 4s

Perimeter of a square, P = 4 × √x

Perimeter of a square, P = 4√x

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The equations of the rows are

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

The augmented matrix given as

[tex]\left[\begin{array}{ccc|c}1&3&-1&4\\4&-2&7&20\\-3&1&5&8\end{array}\right][/tex]

From the above, we set the columns as follows:

x = first row

y = second row

z = third row

constant = fourth row

Using the above as a guide, we have the following:

x + 3y - z = 4

4x - 2y + 7 = 20

-3x + y + 5 = 8

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The monthly payment for the annuity would be $18 (rounded to the nearest whole number) in order to save $1,269 over a period of 6 years with a 5% interest rate per year.

To calculate the monthly payment for the annuity, we need to use the formula for the present value of an annuity.

The formula is:

[tex]PMT = PV / [(1 - (1 + r)^(-n)) / r][/tex]

Where:

PMT = Monthly payment

PV = Present value of the annuity

r = Interest rate per period

n = Number of periods

In this case, the present value (PV) of the annuity is $1,269, the interest rate (r) is 5% per year, and the number of periods (n) is 6 years.

We need to convert the interest rate to a monthly rate by dividing it by 12 (since there are 12 months in a year).

So the monthly interest rate (r) would be 5% / 12 = 0.4167%.

Now we can substitute the values into the formula:

[tex]PMT = $1,269 / [(1 - (1 + 0.4167%)^(-6)) / 0.4167%][/tex]]

Evaluating the formula, we find that the monthly payment (PMT) rounds to the nearest whole number is approximately $18.

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The solution to the equation 1/sqrt(8) = 4(m - 2) is m = (sqrt(2) + 32)/4.

To find the solution to the equation, let's solve it step by step:

The given equation is:

1/sqrt(8) = 4(m - 2)

First, let's simplify the left side of the equation by rationalizing the denominator. We can do this by multiplying the numerator and denominator by sqrt(8):

(1/sqrt(8)) * (sqrt(8)/sqrt(8)) = 4(m - 2)

Simplifying further:

sqrt(8)/8 = 4(m - 2)

Now, let's simplify the left side of the equation:

sqrt(8)/8 = (2 * sqrt(2))/8

Next, let's simplify the right side of the equation by distributing the 4:

(2 * sqrt(2))/8 = 4m - 8

Simplifying further:

sqrt(2)/4 = 4m - 8

To isolate the variable m, we can add 8 to both sides of the equation:

sqrt(2)/4 + 8 = 4m

Now, let's simplify the left side:

sqrt(2)/4 + 8 = (sqrt(2) + 32)/4

Finally, we can divide both sides by 4 to solve for m:

(sqrt(2) + 32)/4 = m

Therefore, the solution to the equation 1/sqrt(8) = 4(m - 2) is m = (sqrt(2) + 32)/4.

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a) Michelle wants to invest £2900 in one of these accounts for 19 years. Compound interest at a rate of 5% per year in Account 2 will pay Michelle more interest after 19 years.

b) The interest paid by Account 2 is £2202.55 which is £331.87 more than the interest paid by Account 1.

Account 2 will pay Michelle £331.87 more interest than Account 1 after 19 years.
Account 1 pays simple interest at a rate of 8% per year. The formula for simple interest is given as follows:

I = P * r * t

Where, I = Interest earned

P = Principal (initial amount invested)

r = Rate of interest per year (in decimals

)t = Time period for which money is invested A

ccount 2 pays compound interest at a rate of 5% per year.

The formula for compound interest is given as follows:

A = P * (1 + r/n)^(n*t)  

Where, A = Amount earned

P = Principal (initial amount invested)

r = Rate of interest per year (in decimals)

n = Number of times interest is compounded per year (in this case, n = 1 as interest is compounded annually)

t = Time period for which money is investedIn this case, Michelle invests £2900 in both accounts for 19 years.

Account 1: I = P * r * tI = 2900 * 0.08 * 19I = £4396.00

Account 2: A = P * (1 + r/n)^(n*t)A = 2900 * (1 + 0.05/1)^(1*19)A = £5102.55

The interest earned in Account 2 is A - P = £5102.55 - £2900 = £2202.55.

The difference in interest earned between Account 2 and Account 1 is £2202.55 - £4396.00 = £-2193.45.

Therefore, Account 2 pays Michelle £2193.45 more interest than Account 1.

However, the question asks for the amount in pounds to the nearest 1p.

Rounding off the values of interest earned to 2 decimal places gives the interest earned by Account 1 as £4396.00 and the interest earned by Account 2 as £2202.55.

The difference in interest earned is £2202.55 - £4396.00 = £-2193.45 ≈ £-2193.44.

Rounding this value to the nearest 1p gives the difference in interest earned as £-2193.44 ≈ £-2193.44 ≈ -£2193.44.

The value is negative because Account 2 pays Michelle less interest than Account 1.

Therefore, Account 1 pays £2193.44 more interest than Account 2.

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The volume of the solid generated when R is revolved around the x-axis is 20π/3 cubic units.

To find the volume of the solid generated when the region R is revolved around the x-axis, we can use the method of disks or washers.

First, let's find the points of intersection of the curves.

Setting the first two equations equal to each other, we have:

√(x^2/64) = √(x/8)

Squaring both sides, we get:

x^2/64 = x/8

Multiplying both sides by 64, we have:

x^2 = 8x

Rearranging, we get:

x^2 - 8x = 0

Factoring out x, we have:

x(x - 8) = 0

So, x = 0 and x = 8 are the points of intersection.

Now, let's integrate to find the volume of the solid.

We can split the region R into two parts: the part below y = 1 and the part between the curves y = √(x^2/64) and y = √(x/8).

For the part below y = 1, the radius of each disk is given by the corresponding x-value, and the height is 1. So the volume of this part is given by:

V1 = π * ∫[0,8] (1)^2 dx

Simplifying, we get:

V1 = π * ∫[0,8] dx

Integrating from 0 to 8, we have:

V1 = π * [x] evaluated from 0 to 8

V1 = π * (8 - 0)

V1 = 8π

For the part between the curves, the radius of each washer is given by the corresponding x-value, and the height is the difference between the curves: √(x^2/64) - √(x/8). So the volume of this part is given by:

V2 = π * ∫[0,8] [(√(x^2/64))^2 - (√(x/8))^2] dx

Simplifying, we get:

V2 = π * ∫[0,8] [(x^2/64) - (x/8)] dx

Integrating from 0 to 8, we have:

V2 = π * [(x^3/192) - (x^2/16)] evaluated from 0 to 8

V2 = π * [(8^3/192) - (8^2/16) - (0^3/192) + (0^2/16)]

V2 = π * [256/192 - 64/16]

V2 = π * [4/3 - 4]

V2 = -4π/3

The total volume of the solid is the sum of V1 and V2:

V = V1 + V2

V = 8π - 4π/3

V = (24 - 4)π/3

V = 20π/3

As a result, the solid created when R is rotated about the x-axis has a volume of 20/3 cubic units.

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The standard deviation, subtract each height from the mean height, square the differences, add up all the squares, divide by the number of heights, and take the square root of the result.

The given question states that the average height of the students in a class is 155 cm.

The average height of a group of people refers to the mean height of all the people in that group, calculated by dividing the sum of all their heights by the number of people in the group.

Average height is a measure of central tendency that provides useful information when making comparisons between different groups or analyzing trends over time.

In the context of a classroom, it may be useful to know the average height of the students in order to make decisions about things like desk and chair heights, or to identify potential outliers that may need additional attention.

It is important to note that the average height is just one measure of the distribution of heights within the group.

Other measures, such as the range, standard deviation, or quartiles, may also be useful for gaining a more complete understanding of the distribution.

In order to determine the range, subtract the minimum height from the maximum height.

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The function that represents exponential growth is f(x) = 3x.

Exponential growth is a function that shows an increase within a population that occurs at the same rate over time. When populations experience doubling or tripling in numbers, you can assume the data increases exponentially. The opposite of exponential growth is exponential decay, where data shrinks rather than grows.

An example of an exponential function is the growth of bacteria. Some bacteria double every hour. If you start with 1 bacterium and it doubles every hour, you will have 2x bacteria after x hours. This can be written as f(x) = 2x.

An exponential equation is an equation with exponents where the exponent (or) a part of the exponent is a variable. For example, 3x = 81, 5x - 3 = 625, 62y - 7 = 121, etc are some examples of exponential equations.

The two types of growth curves are exponential growth curves and logarithmic growth curves. In an exponential growth curve, the slope grows greater and greater as time moves along. In a logarithmic growth curve, the slope grows sharply, and then over time the slope declines until it becomes flat.

The function that represents exponential growth is f(x) = 3x.

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Answer:

Either A or D, but the answer is f(x) = 3x.

Step-by-step explanation:

We can check for exponential growth by checking for an x in the exponent of a constant value in the function, which is this case for f(x) = 3x.

The approximate distance between station B and Fire is 29.5 miles.

The missing angle in the triangle :

180 - (30 + 50) = 100°

Let distance between fire and station B = b

Using the sine rule :

b/sin(30) = 15/sin(15)

b = (15 * sin(30)) / sin(15)

b = 7.5/sin(15)

b = 28.97

Hence, the approximate distance is 29.5 miles.

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