A lake is to be stocked with smallmouth and largemouth bass. Let represent the number of smallmouth bass and let represent the number of largemouth bass. The weight of each fish is dependent on the population densities. After a six-month period, the weight of a single smallmouth bass is given by and the weight of a single largemouth bass is given by Assuming that no fish die during the six-month period, how many smallmouth and largemouth bass should be stocked in the lake so that the total weight of bass in the lake is a maximum

The study is investigating the relationship between the exposure to the suspected drug during pregnancy and the risk

of delivering a malformed infant. This study design is a case-control study design.

The resultant data are: forty mothers have taken the suspected drug during their pregnancies. Of these mothers, 35

have delivered malformed infants. In addition, 10 other infants are born with malfunctions," then the answer would be

as follows:

The type of study design that is described in this scenario is a case-control study design.

A case-control study design is a type of observational study design that compares people with a particular condition

(cases) to people without that condition (controls) to determine whether there is a relationship between the exposure

to a suspected risk factor and the development of the condition.

In this scenario, the cases are the 35 mothers who delivered malformed infants, and the controls are the 5 mothers

who did not deliver malformed infants. The study is investigating the relationship between the exposure to the

suspected drug during pregnancy and the risk of delivering a malformed infant. Therefore, this study design is a case

control study design.

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35% more than 78?

35% of 78;

78 x .35 = 27.3

78 + 27.3 = 105.3

Answer:

AA criterion

a/x = c/a

a² = cx

b/(c - x) =c/b

b² = c(c - x)

a² + b² =cx + c(c - x) = c²

a² + b² = c²

Step-by-step explanation:

The answer is Y=3x-2. I used desmos.

Answer:

Sugar = 0.8 lb

milk = 0.6 lb

Flour = 2.6 lb

Step-by-step explanation:

Firstly, we add the ratios = 3 + 4 + 13 = 20

For milk, we have 3/20 * 4 = 12/20 = 0.6 lb

For sugar l, we have 4/20 * 4 = 16/20 = 0.8 lb

For flour = 13/20 * 4 = 52/20 = 2.6

You will need:

\(Milk = 0.6 $ lb\\Sugar = 0.8 $ lb\\Flour = 2.6 $ lb\)

Given:

Milk : Sugar : Flour = 3 : 4 : 13

To find the number of pounds of each ingredient required to produce 4 lb of baking mix, solve as follows:

Amount of each ingredient needed = ratio of each ingredient / total ratio value x 4 lb

Thus:

Total ratio value = \(3 + 4 + 13 = 20\)

Amount of milk needed = \(\frac{3}{20} \times 4 = 0.6 $ lb\)

Amount of Sugar needed = \(\frac{4}{20} \times 4 = 0.8 $ lb\)

Amount of Flour needed = \(\frac{13}{20} \times 4 = 2.6 $ lb\)

Therefore, you will need the follow amounts to make 4 lb of baking mix:

\(Milk = 0.6 $ lb\\Sugar = 0.8 $ lb\\Flour = 2.6 $ lb\)

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Answer: the answer to that problem is

X=2

After 3 hours, the boat is approximately 16.43 miles from the marina, and the bearing from the boat back to the marina is approximately 209.9°

We have,

To solve this problem, we can break down the boat's motion into two components: north-south displacement and east-west displacement.

Given:

The boat travels due south for 1 hour at a constant speed of 15 mph.

The boat then changes course to a bearing of S47°E and travels for 2 hours at the same constant speed of 15 mph.

a.

To find how far the boat is from the marina after 3 hours, we need to calculate the total displacement using the Pythagorean theorem.

First, let's find the north-south displacement:

Distance = Speed x Time = 15 mph x 1 hour = 15 miles

Next, let's find the east-west displacement using the given bearing:

Angle of S47°E = 180° - 47° = 133°

Using trigonometry, we can find the east-west displacement:

East-West Displacement = Distance x cos(Angle) = 15 miles x cos(133°)

Now, let's calculate the total displacement:

Total Displacement = √(North-South Displacement² + East-West Displacement²)

b.

To find the bearing from the boat back to the marina, we can use trigonometry to calculate the angle between the displacement vector and the north direction.

Let's calculate the values:

a. North-South Displacement = 15 miles

b. East-West Displacement = 15 miles x cos(133°)

c. Total Displacement = sqrt(North-South Displacement² + East-West Displacement²)

b. Bearing = atan(East-West Displacement / North-South Displacement) + 180°

Now, let's perform the calculations:

a. North-South Displacement = 15 miles

b. East-West Displacement = 15 miles x cos(133°) ≈ -6.83 miles (rounded to two decimal places)

c. Total Displacement = √(15² + (-6.83)²) ≈ 16.43 miles (rounded to two decimal places)

b.

Bearing = atan(-6.83 / 15) + 180° ≈ 209.9° (rounded to one decimal place)

Therefore,

After 3 hours, the boat is approximately 16.43 miles from the marina, and the bearing from the boat back to the marina is approximately 209.9°

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Answer:

x =6

Explanation:

To solve the system for x, substitute the value of y from the second equation into the first to get

adding 7 to both sides gives

Subtracting 2x from both sides gives

dividing both sides by 2 gives

which is our answer!

The constant of proportionality is 0.5.

From the information, Rocko paid $12.50 for 25 game tickets and Louisa paid $17.50 for 35 game tickets.

The constant of proportionality can be illustrated as k.

Therefore, 12.50 = 25 × k

12.50 = 25k

Divide

k = 12.50/25

k = 0.5

The constant of proportionality is 0.5.

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Answer:

The answer is 36.

Step-by-step explanation:

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First, divide 108 by 12.

The result is 9.

Now square root 9.

The result is 3.

Now, multiply 12 by 3.

The result is 36.

To check that this is the pattern, we multiply 36 by 3, and we indeed see that 3 times 36 is equal to 108.

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#teamtrees #WAP (Water And Plant)

Answer:

32,800

Step-by-step explanation:

The fourth vertex's coordinates are as follows: ( 2.1, -3.6)

A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.

So, let the missing coordinates be (a,b).

Let's now utilize the midpoint formula to locate the erroneous coordinate.

Let the reference point be (-2.3, 3.6) A.

Let point B be (2.3, 2.2).

(2.1, 2.2) Let C be the point.

The center of AC should be at BD.

Step 1: Locating the AC's midpoint

Middle pint of AC:

(-2.3 + 2.1/2), (-3.6 + 2.2/2)

(0.2/2), (1.4/2)

(-0.1, -0.7)

Let's equate the midpoints in step two.

The BD mid-point:

(a + -2.3/2), (b + 2.2/2) =  (-0.1, -0.7)

(a + -2.3/2) = -0.1

(a -2.3/2) = -0.1*2

a = -0.2+2.3

a = 2.1

(b + 2.2/2) = -0.7

b + 2.2 = -0.7*2

b + 2.2 = -1.4

b = -1.4 -2.2

b = -3.6

Therefore, the fourth vertex's coordinates are as follows: ( 2.1, -3.6)

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Complete question:

Freddy drew a plan for a rectangular piece of material that hehe will use for a blanket. Three of the vertices are ​( -2.3 and −3.6​), ​(−2.3​, and 2.2​), and ​(2.1​, and 2.2​). What are the coordinates of the fourth​ vertex?

Lets do

\(\\ \Large\sf\longmapsto 150:450:750\)

\( \\ \Large\sf\longmapsto \frac{150}{ \dfrac{450}{750} } \\ \\ \Large\sf\longmapsto \frac{15}{ \dfrac{45}{75} } \\ \\ \Large\sf\longmapsto \frac{3}{ \dfrac{9}{15} } \\ \)

Simplified ratio is

\(\boxed{\LARGE{\sf \$1:\$3:\$5}}\)

Answer:

1        : 3     : 5

Step-by-step explanation:

$150 : $450 : $750

Divide each by 150

$150/150 : $450/150 : $750/150

1        : 3     : 5

The solution is TRUE

What is union and intersection of sets?
The union of two sets A and B is the set of all those elements which are either in A or in B, i.e. A ∪ B, whereas the intersection of two sets A and B is the set of all elements which are common. The intersection of these two sets is denoted by A ∩ B

The union of two sets is a new set that contains all of the elements that are in at least one of the two sets

The intersection of two sets is a new set that contains all of the elements that are in both sets

Given data ,

Let the equation be x

x = A ∩ ( B' ∪ C' )

Now , from Distributive law of set

A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

And , ( A ∩ B' ) = A - B

So , substituting the formulas in the equation , we get

x = A ∩ ( B' ∪ C' )

x = ( A ∩ B' ) ∪ ( A ∩ C' )

x = ( A - B ) ∪ ( A - C )

Hence , the solution is TRUE

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Answer:

a 75% chance the weather will stay dry

Step-by-step explanation:

3/4

Answer:

400

Step-by-step explanation:

There is not enough evidence to conclude that more than 1.9% of Lipitor users experience flulike symptoms.

1. Null Hypothesis (H0):

The proportion of Lipitor users experiencing flulike symptoms is equal to 1.9%.

Alternative Hypothesis (Ha):

The proportion of Lipitor users experiencing flulike symptoms is greater than 1.9%.

2. Test Statistic: We will use the z-test statistic for proportions, which is calculated as:

  z = (P - p0) / √((p0 (1 - p0)) / n)

Here, P = 19/863 and p0 = 0.019 or 1.9%

n = 863

So, z = (0.0030162224797219) / 0.0000215979

z  = 139.65

3. Critical Value and p-value:

The critical value is 2.326.

4. Decision Rule:

  - If the calculated z-value is greater than the critical value, we reject the null hypothesis.

  - If the calculated p-value is less than α, we reject the null hypothesis.

5. Calculation:

z = (19/863 - 0.019) / √((0.019  (1 - 0.019)) / 863)

z  = 0.64902

For z = 139.65, the p value 0.257

6. Confidence Interval:

CI = P ± z√(P  (1 - P)) / n)

= 19/863 ± 0.64902(19/836 (1-19/863) / 863)

= 0.022 ± 0.64902(0.022 (1-0.022)/ 863)

= 0.022 ± 0.00001618

So, Lower bound: 0.02198382

Upper bound:0.02201618

Since, z-value is less than the critical value or the p-value is greater than α (0.01), we fail to reject the null hypothesis, and there is not enough evidence to conclude that more than 1.9% of Lipitor users experience flulike symptoms.

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1) the fuction is:

and the derivate will be:

2) The function is:

and the derivate:

3) the function is:

and the derivate will be:

4) the function is:

and the derivation will be:

5) the equation is:

first we rewrite the equation so:

and now we derivate so:

Answer:

16%

Step-by-step explanation:

Equation: \(\frac{new value-old value}{old value}\) * 100

\(\frac{3.70-3.20}{3.20}\)* 100= \(\frac{0.50}{3.20}\)* 100

0.15625 (round to .16)

16%

To determine the value of β, we need to analyze the rolling motion of the cylindrical object and apply the principles of conservation of energy and rotational motion.

Conservation of energy:

Initially, the object has gravitational potential energy due to its height, which is converted into kinetic energy as it rolls down the ramp and onto the floor. The equation for conservation of energy is:

M * g * H = (1/2) * M * v^2 + (1/2) * I * ω^2

where:

M is the mass of the object

g is the acceleration due to gravity

H is the initial height

v is the linear velocity of the object

I is the rotational inertia of the object

ω is the angular velocity of the object

Rolling motion:

For a rolling object, the linear velocity and angular velocity are related by:

v = R * ω

where R is the radius of the object.

Expression for rotational inertia:

The rotational inertia (I) of the object is given by:

I = β * M * R^2

where β is a constant that depends on the object's mass distribution.

Now, let's proceed with the calculations:

From the given information, we have:

H = 0.95 m

h = 0.12 m

d = 0.475 m

Using conservation of energy, we can equate the initial potential energy to the final kinetic energy:

M * g * H = (1/2) * M * v^2 + (1/2) * I * ω^2

Substituting the expressions for v and I from the rolling motion and rotational inertia equations:

M * g * H = (1/2) * M * (R * ω)^2 + (1/2) * (β * M * R^2) * ω^2

Simplifying the equation:

g * H = (1/2) * R^2 * ω^2 * (1 + β)

Rearranging the equation to isolate β:

β = (2 * g * H) / (R^2 * ω^2) - 1

Now, we need to determine the values of g, H, R, and ω in order to calculate β.

Please provide the values for the acceleration due to gravity (g), the initial height (H), the radius of the object (R), and the angular velocity (ω), so we can continue with the calculation.

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A- The scale factor from Polygon A to Polygon B is 2.

B- The missing length of each side marked with ? in Polygon B is 3, 5

C- The measure of each angle marked with ? in Polygon A is 53°, 82°

Given that,

A- scale factor = side A/ side B = 5 / 2.5 = 2

B- Length of each missing sides= 1.5*2 = 3 and 2.5* 2 = 5

C- Since the scale factor does not change the measure of the angles, the missing angles remain the same that is 53° and 82°

Thus,

The scale factor from Polygon A to Polygon B is 2.

The missing length of each side marked with ? in Polygon B is 3, 5

The measure of each angle marked with ? in Polygon A is 53°, 82°

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To determine the sum of money Jeff should invest on January 21, 2020, in order to reach $80000 on August 8, 2020, at an annual interest rate of 5%, we need to calculate the present value of the future amount using the time value of money concepts.

We can use the formula for the present value of a future amount to calculate the initial investment required. The formula is:

Present Value = Future Value / (1 + interest rate)^time

In this case, the future value is $80000, the interest rate is 5% per year, and the time period is from January 21, 2020, to August 8, 2020. The time period is approximately 6.5 months or 0.542 years.

Plugging these values into the formula, we have:

Present Value = $80000 / (1 + 0.05)^0.542

Evaluating the expression, we find that the present value is approximately $75609. Therefore, Jeff should invest approximately $75609 on January 21, 2020, to amount to $80000 on August 8, 2020, at a 5% annual interest rate.

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Accoding to the calculations , the correct answer is:

A) Depreciation charge 16,000; revaluation surplus £20,000

According to IAS 16 Property, Plant and Equipment, the depreciation charge for an asset should be based on its carrying amount, useful life, and residual value.

In this case, the buildings were purchased for £400,000 (£480,000 - £80,000) and had a useful life of 25 years. Since there is no residual value, the depreciable amount is equal to the initial cost of the buildings (£400,000).

To calculate the annual depreciation charge, we divide the depreciable amount by the useful life:

£400,000 / 25 = £16,000

Therefore, the depreciation charge for the year ended 30 September 2021 is £16,000.

Now, let's calculate the balance on the revaluation surplus as at that date.

The revaluation surplus is the difference between the fair value of the property and its carrying amount. On 1 October 2020, the property was revalued to £500,000, and the carrying amount was £480,000 (£400,000 for buildings + £80,000 for land).

Revaluation surplus = Fair value - Carrying amount

Revaluation surplus = £500,000 - £480,000

Revaluation surplus = £20,000

Therefore, the balance on the revaluation surplus as at 30 September 2021 is £20,000.

Based on the calculations above, the correct answer is:

A) Depreciation charge £16,000; revaluation surplus £20,000

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Answer:

4d + 16 = 36

or 16 + 4n = 36

it depends on what type of question you have. the second one is best to use, but you can pick.

Answer:

Step-by-step explanation:

4.5 miles

Answer:

1/2

Step-by-step explanation:

2/3 x 3/4 = 6/12 =1/2

The amount of inches of trim that Maria would need is equal to 22 inches.

In Mathematics and Geometry, the perimeter of a triangle can be calculated by using this mathematical equation:

P = a + b + c

Where:

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

Perimeter of a triangle, P = 8 + 6 + 8

Perimeter of a triangle, P = 22 inches.

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