Solve the following exponential equation. Express your answer as both an exact expression and a decimal approximation rounded to two decimal places. Use P=2.71828182845905.e^2x-1= 12^x/2

The answer from part A tells us that the trout population was 10 in the first month after it was introduced.

A. P(0) = 740 / (1 + 73e^-0) = 740 / (1 + 73) = 740 / 74 = 10, so the answer is 10.

B. The answer from part A tells us that the trout population was 10 in the first month after it was introduced.

C. To find the number of trout in the lake after 1 year, we need to find P(12): P(12) = 740 / (1 + 73e^-0.07*12) = 740 / (1 + 73e^-0.84) ≈ 490, so the answer is 490.

D. To find the number of trout in the lake after 10 years, we need to find P(120): P(120) = 740 / (1 + 73e^-0.07*120) = 740 / (1 + 73e^-8.4) ≈ 740, so the answer is 740.

E. lim t→∞ P(t) = 740, so the answer is 740.

F. The answer from part E tells us that as the number of months t approaches infinity, the trout population will approach 740. This means that the trout population will eventually stabilize at 740 if no other factors such as predators, disease, or lack of food affect the population.

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Answer:

10 centimeters

Step-by-step explanation:

For the height:

40 ft / 20 cm = 2 ft / cm

With this ratio, we find the length as follows:

2 ft / cm = 20 ft / x cm

\(2 = \frac{20}{x} \)

\(2x = 20\)

\(x = 10\)

Answer:

10 cm

Step-by-step explanation:

Look at the answer

The equation of a circle that is congruent to circle C and is centered at point P is (x - 5)² + (y - 1)² = 5².

In Geometry, the standard form of the equation of a circle is modeled by this mathematical equation;

(x - h)² + (y - k)² = r²

Where:

Based on the information provided, we have the following parameters for the equation of this circle:

By substituting the given parameters, we have:

(x - h)² + (y - k)² = r²

(x - 5)² + (y - 1)² = 5²

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Answer: Velocity is a vector, so it has a magnitude and direction.

Speed is its magnitude, which is obtained from

|〈-3, 4〉 m/s| = √((-3 m/s)² + (4 m/s)²) = √(25 m²/s²) = 5 m/s

Its direction is an angle θ made with the positive horizontal axis, satisfying

tan(θ) = (4 m/s) / (-3 m/s) = -4/3   →   θ = arctan(-4/3) + 180°n

where n is any integer. Now you have to consider that the x coordinate is negative and the y coordinate is positive, so 〈-3, 4〉 points into the second quadrant, and we get an angle there for n = 1 of about

θ ≈ 126.87°

Alternatively, you can use the vector 〈1, 0〉 in place of the axis, then compute the angle by relating it to the dot product, so θ is such that

〈-3, 4〉 • 〈1, 0〉 = |〈-3, 4〉| |〈1, 0〉| cos(θ)

(-3)•1 + 4•0 = √((-3)² + 4²) • √(1² + 0²) cos(θ)

-3/5 = cos(θ)   →   θ = arccos(-3/5) + 360°n

where again, n is any integer, and we get the same solution θ ≈ 126.87° in the second quadrant when n = 0.

Step-by-step explanation:

Answer:

there is no mode

Step-by-step explanation:

None of the numbers repeat more than once

Answer:

42

Step-by-step explanation:

p - 13 = 29

Add 13 to both sides.

p - 13 + 13 = 29 + 13

p = 42

Answer:

p= 42

Step-by-step explanation:

29 plus 13 equals 42 which leaves p alone so p equals 42

Answer:

Step-by-step explanation:

310 is the answer.

When viewed through the magnifying glass, the termite appears to be approximately 1.58 mm in length.

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The percent of the original price you end up paying is 42%.

Let's assume that the original price of an item is $100

The first discount of 25% off would reduce the price by:

25% of $100 = $25

So the sale price after the first discount is:

$100 - $25 = $75

Then, the store is offering an additional discount of 45% off on the clearance items.

The discount is removed from the sale price after the first discount:

45% of $75 = $33

So the final sale price after both discounts is:

$75 - $33 = $42

Therefore, you end up paying $42 for an item that originally cost $100. This is equivalent to paying:

($42 / $100) x 100% = 42% of the original price.

Hence, the percent of the original price you end up paying is 42%.

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That both a and b are equally likely, is also not true since the Probability of option b is higher than that of option a.

Option b is more likely to be true. This is because the given information states that the showerhead heights were designed to be 72 inches, which is well above the mean height of 69.5 inches. Therefore, it is reasonable to assume that the majority of the players' heights are below 72 inches. Since the heights of the athletes are normally distributed, the probability of selecting a player at random with a height above 72 inches is relatively low. On the other hand, option a suggests that the mean height of a sample of 20 players is more than 72 inches, which is less likely than option b. Option c, which suggests that both a and b are equally likely, is also not true since the probability of option b is higher than that of option a.

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A. The equation that relates these variables is:

d = s * t. B. The biker would travel 10 miles in 20 minutes. C. The biker would bike for 96 minutes to travel 48 miles. Rounded to the nearest tenth, this is 96.0 minutes.

a. Let's define the variables:

t = time in minutes

d = distance traveled by the biker in miles

s = speed of the biker in miles per minute

The equation that relates these variables is:

d = s * t

b. If the biker travels for 20 minutes, we can use the equation above to find the distance traveled:

d = s * t

d = s * 20 (since t = 20 minutes)

We need to know the speed of the biker to calculate the distance traveled. Let's assume that the biker's speed is 0.5 miles per minute (which is equivalent to 30 miles per hour):

d = 0.5 * 20

d = 10

Therefore, the biker would travel 10 miles in 20 minutes.

c. If the biker traveled 48 miles, we can rearrange the equation above to find the time:

d = s * t

t = d / s

We need to know the speed of the biker to calculate the time. Let's assume that the biker's speed is still 0.5 miles per minute:

t = 48 / 0.5

t = 96

Therefore, the biker would bike for 96 minutes to travel 48 miles. Rounded to the nearest tenth, this is 96.0 minutes.

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The error is:

∠M and ∠N are supplementary.

m∠M + m∠N = 180

∠N and ∠0 are supplementary.

m∠N + m∠0 = 180

We have,

In a parallelogram, consecutive angles are supplementary.

A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length.

Since opposite sides are parallel, opposite angles in a parallelogram are congruent (equal in measure).

Consecutive angles are the pair of angles that share a side in the parallelogram.

The sum of the measures of these consecutive angles is always 180 degrees, making them supplementary.

Thus,

The error is:

∠M and ∠N are supplementary.

m∠M + m∠N = 180

∠N and ∠0 are supplementary.

m∠N + m∠0 = 180

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Answer:

5.86666666667

Step-by-step explanation:

Answer:

Answer is 5 13/15

Answer:

104.0 °F

Step-by-step explanation:

Divide Celsius by 5, then multiply by 9, then add 32 = Fahrenheit

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The boxplots 1 and 2 represent the distribution of data using a five number summary for the male and the female attendance.

(a) The IQR of the male's data

The first box plot represents the male's boxplot.

So, we have:

Upper quartile (Q3) = 14

Lower quartile (Q1) = 2

The IQR is the difference between the above values

IQR = Q3 - Q1

So, we have:

IQR = 14 - 2 = 12

So: the IQR for the males' data is 12

(b) The difference in the median values

From the first and second boxplots, we have:

Median male = 10

Median female = 18

The difference (d) between these values is

d = 18 - 10

d = 8

So: the difference between the median values of each data set is 8

(c) The distribution of data

This is dependent on whether the dataset has an outlier or not.

From the figure, we have:

Male's data: presence of an outlier - use median

Female's data: absence of an outlier - use mean

So: the male dataset is measured by median, while the mean is a better measure of center for the female's data

(d) Reason for outliers

A possible reason for outliers is sampling problems

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Answer:

-2<x<35

hope this helps

Answer:18

Step-by-step explanation:

The 17.55 rounded to nearest pound is 18.

Answer:

36°

Step-by-step explanation:

Measure of an exterior angle of n-sided polygon = 360/n

Therefore,

Exterior angle of a 10-sided polygon = 360/10 = 36°

hope this helps!!!

Answer:

2.02955

Step-by-step explanation:

Given that:

Susan invests $Z as each year ends for seven years.

So we assume that Z = 1

Susan's accrued value comprises $7 invested each year at a 6 percent annual effective rate.

The cashflow interest:

The cashflow of Susan interest payments are:

Payments   Time

0                     1

0.05               2

2(0.05)           3

3(0.05)           4

4(0.05)            5

5(0.05)            6

6(0.05)            7

The accumulated value of this cash flow is:

\((0.05)I_{6\%} = (0.05) \dfrac{((1+0.06)_{6\%} - 6)}{0.06} \\ \\ \implies 1.1653\)

So Susan accumulated values is:

X = 7 + 1.1653

X = 8.1653

Lori's accumulated value is $14, which she has set aside to plan her cash flow for interest.

The cashflow of Lori interest payments are;

Payments    0     0.025     2(0.025)       3(0.025)    .........   13(0.025)

Time             1        2              3                    4            ..........  14

The accumulated value of cash flow is:

\((0.025 )(I)_{3\%} =(0.025) \dfrac{(1+0.03)_{3\%}-13}{0.03}\\ \\= 2.5719\)

Now, Lori's accumulated value is:

Y = 14 + 2.5719

Y = 16.5719

Since; Susan value X = 8.1653

Lori's value Y = 16.5719

∴

\(\dfrac{Y}{X}= \dfrac{16.5719}{8.1653}\)

= 2.02955

Answer: It would be 7.5.

Answer:

the answer would be 7 1/2

Step-by-step explanation:

convert the mixed number into fractions so it would become :

3/1 ÷ 2/5

multiply :

3/1 × 2/5 which equals 15/2

simplify and get : 7 1/2

Answer:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

y-2*x-(6)=0

STEP

1

:

Equation of a Straight Line

1.1 Solve y-2x-6 = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

Answer: It's 2.) 4 is the answer

Using an algebraic equation to represent the word problem, the smallest integer is 1

This is a way of representing mathematical problems with words. To solve this, we have to use algebraic equations or expressions.

Let the integers be represented as

We can write an equation from the word problem given as

7 × (x + 2) = 15 + [x + (x + 4)]

7x + 14 = 15 + x + x + 4

7x + 14 = 15 + 2x + 4

collect like terms

7x - 2x = 15 - 14 + 4

5x = 5

Divide both sides by coefficient of x

5x / 5  = 5 / 5

x = 1

The smallest integer is 1

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Translation:

Find the smallest of three consecutive odd integers such that 7 times the middle integer is 15 more than the sum of the first and third integers

Answer:

value of r is 6

Step-by-step explanation:

Given that the slope is 1/2

So we can set up the linear equation like this:

y= 1/2x + b

Since it also goes through (-5, 2)

plug in:

\(2 = \dfrac12*-5 + b\\b=2 +2.5 = 4.5\\y = \dfrac12x +4.5\)

Then we plug in x=3 to find out the value of r

\(r = \dfrac12*3+4.5=1.5+4.5=6\)

Answer:

x=3

Step-by-step explanation:

5x - 2 = 3x +4

=> 5x - 3x = 4 + 2

=> 2x = 6

=> x = 6/2 = 3

Answer:

the answer is D. F(x) = 1/x(x-3)

Step-by-step explanation:

The answers are as follow

1. ∠a and ∠b are supplementary angles, ∠b and ∠c are supplementary angles: given

2. m∠a + m∠b = 180, m∠b + m∠c = 180 : definition of supplementary angles

3. m∠a + m∠b = m∠b + m∠c : substitution property of equality

4. m∠a = m∠c: subtraction property of equality

5. ∠a ≅ ∠c: if two angles have the same measure, then they are congruent.

The proof is shown below:

Congruence in two or more triangles depends on the measurements of their sides and angles. The three sides of a triangle determine its size and the three angles of a triangle determine its shape. Two triangles are said to be congruent if pairs of their corresponding sides and their corresponding angles are equal. They are of the same shape and size.

Two triangles are said to be congruent if they are of the same size and same shape. Necessarily, not all the six corresponding elements of both the triangles must be found to determine that they are congruent. Based on studies and experiments, there are 5 conditions for two triangles to be congruent. They are SSS, SAS, ASA, AAS, and RHS congruence properties.

Given that:

∠A and ∠B are supplementary angles, ∠B and ∠C are supplementary angles

So,  ∠A + ∠B = 180,

∠B + ∠ C= 180 b  (supplementary angles)

∠A + ∠B = ∠B + ∠C

∠A = ∠C

Hence,  ∠A ≅ ∠C (if two angles have the same measure, then they are congruent).

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