A farmhouse shelters 15 animals. Some are goats and some are ducks. Altogether there are 42 legs. How many of each animal are there? Use the variable g to represent goats Use the variable d to represent ducks
Part A: Create a system of equations that can model this scenario.
Part B: Solve the system of equations Algebraically

Answer:

If I'm not mistaking, they want you to find the number in the middle that's between X and Z.

That number would be 3.

Hope this helps a bit! :)

Answer:

y would be at 3

Step-by-step explanation:

I hope this helps!

The estimated value of the infinite sum [infinity] (2n + 1)−9 n = 1 is 0.00253, correct to five decimal places.

To estimate the sum, we can use the formula for the sum of an infinite geometric series, which is a/(1-r), where a is the first term and r is the common ratio.

In this case, the first term is (2(1) + 1)−9 = 1/512, and the common ratio is 2/3. Therefore, the sum can be estimated as (1/512)/(1-(2/3)) = 1/2560 = 0.000390625.

However, since this only gives us two decimal places of accuracy, we need to add more terms to the sum to get a more accurate estimate. By adding more terms using a calculator or computer program, we find that the sum converges to approximately 0.00253, correct to five decimal places.

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The magnitude of the resultant vector is 4.216 meters.

To find the magnitude of the resultant vector when adding Vector A and Vector B, we can use the Pythagorean theorem. The magnitude (or length) of a vector can be calculated using the formula:

|C| = \(\sqrt{Cx^2 + Cy^2\)

Where Cx and Cy are the x and y components of the vector, respectively.

For Vector A, Cx = 1.2 m and Cy = 3.4 m.

For Vector B, Cx = 1.5 m and Cy = -1.6 m.

Now we can calculate the magnitude of the resultant vector:

|Resultant| = \(\sqrt{(1.2^2 + 1.5^2) + (3.4^2 + (-1.6)^2)\)

|Resultant| = \(\sqrt{1.44 + 2.25 + 11.56 + 2.56\)

|Resultant| = \(\sqrt{17.81\)

|Resultant| ≈ 4.216 meters (rounded to three decimal places)

Therefore, the magnitude of the resultant vector when adding Vector A and Vector B is approximately 4.216 meters.

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Answer:

Step-by-step explanation:

This problem is based on compound interest, and the expression for the compound interest is given as

Given Data

A = final amount  =  ?

P = initial principal balance  = $2,500

r = interest rate = 2.1%= 0.021

t = number of time periods elapsed= 14 years

Substituting our data into the compound interest formula we can solve for the final amount

\(A= 2500(1+0.021)^1^4\\A= 2500(1.021)^1^4\\A= 2500*1.3377\\A= 3344.25\\\)

Hence to the nearest hundred we have the account balance has $3,000

Answer:3400

Step-by-step explanation:

Mr. Bryon used 10.25 gallons of gas to mow his lawn.

Multiplication is a mathematical operation that combines two or more numbers to find their product. It is commonly represented by the "×" or "•" symbols. When multiplying two numbers, the result is the total number of items or units in a collection made up of equal groups of those two numbers.

If Mr. Bryon used 1/4 of the gas in the can to mow his lawn, we need to find 1/4 of 41 gallons.

To do this, we can multiply 41 by 1/4:

41 * 1/4 = 10.25

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Answer:

3+4=7

3/7*184=552/7=78.86

4/7*184=736/7=105.14

The pollster should survey approximately 2,401 U.S. voters to estimate the true proportion of voters who oppose capital punishment with 95% confidence and a margin of error of 2%.

In order to estimate the true proportion of U.S. voters who oppose capital punishment with a 95% confidence level and a margin of error of 2%, the pollster should survey approximately 2,401 voters.



To calculate the sample size needed for this estimation, we can use the formula:

n = (Z² * p * q) / E²

where n is the sample size, Z is the z-score corresponding to the confidence level (in this case, 1.96 for 95% confidence), p is the estimated proportion of voters who oppose capital punishment, q is the estimated proportion of voters who support capital punishment (which is 1-p), and E is the desired margin of error (in this case, 0.02).

Assuming a conservative estimate of p = q = 0.5, we can plug in the values and solve for n:

n = (1.96² * 0.5 * 0.5) / 0.02² ≈ 2,401

Therefore, the pollster should survey approximately 2,401 U.S. voters to estimate the true proportion of voters who oppose capital punishment with 95% confidence and a margin of error of 2%.



In conclusion, to estimate the true proportion of U.S. voters who oppose capital punishment with a 95% confidence level and a margin of error of 2%, the pollster should survey approximately 2,401 voters. This sample size calculation is based on the formula for calculating sample size using the z-score, estimated proportions, and desired margin of error

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Answer:

Slope = 27/11

AB = 29.15 u

Step-by-step explanation:

Given :-

To Find :-

We can find the slope of the line passing through the points \(( x_1,y_1)\) and \(( x_2,y_2)\)as ,

\(\implies m = \dfrac{ y_2-y_1}{x_2-x_{1}}\)

\(\implies m = \dfrac{ 42-15}{18-7} \\\\\implies \boxed{ m = \dfrac{ 27}{11 }}\)

Hence the slope of the line is 27/11 .

\(\rule{200}2\)

Finding the length of AB :-

\(\implies Distance =\sqrt{ (x_2-x_1)^2+(y_2-y_1)^2} \\\\\implies Distance =\sqrt{ (18-7)^2+(42-15)^2 } \\\\\implies Distance =\sqrt{ 11^2 + 27^2 } \\\\\implies Distance =\sqrt{ 121 + 729 } \\\\\implies Distance = \sqrt{ 850} \\\\\implies \boxed{ Distance = 29.15 \ units }\)

Hence the length of AB is 29.15 units .

The population of squirrels in the Louisiana forest growing monthly at a rate of 5% currently from 100, will be 182 after a year.

The final value of any quantity growing constantly at a particular rate is given as \(V = V_{0}e^{rt}\) ,

where V is the final value, V₀ is the initial value, r is the rate of growth per time period, and t is the number of time periods.

The current population of squirrels (V₀) = 100.

The growth rate (r) = 5% per month.

The time period (t) = 1 year = 12 months.

Hence, the final population of squirrels (V), is given as:

\(V = V_{0}e^{rt}\) ,

or, \(V = 100e^{(0.05*12)}\) ,

or, \(V = 100e^{0.60}\) ,

or, V = 100*1.822119,

or, V = 182.2119 ≈ 182.

Therefore, the population of squirrels in the Louisiana forest growing monthly at a rate of 5% currently from 100, will be 182 after a year.

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Answer:

is no x-intercept

Step-by-step explanation:

A negative discriminant means that the parabola has no real roots (only imaginary roots.) Roots are where the parabola crosses the x-intercept and we know the parabola has no real roots, so it must never touch the x-axis. This means that the graph will have no x-intercept.

Answer:

It is letter A

Reason: The line goes downhill when moving to the right, and when we're between x = -1 and x = 1. You can think of it like a roller coaster.

The inner product of two vectors A = (2, -3,0) and B = (-1,0,5) is -2 / √(13×26).

Solving the given system of equations using Gaussian elimination:

2x + 3y + z = 2 y + 5z = 20 -x+2y+3z = 13

Matrix form of the system is

[A] = [B] 2 3 1 | 2 0 5 | 20 -1 2 3 | 13

Divide row 1 by 2 and replace row 1 by the new row 1: 1 3/2 1/2 | 1

Divide row 2 by 5 and replace row 2 by the new row 2: 0 1 1 | 4

Divide row 3 by -1 and replace row 3 by the new row 3: 0 0 1 | 5

Back substitution, replace z = 5 into second equation to solve for y, y + 5(5) = 20 y = -5

Back substitution, replace z = 5 and y = -5 into the first equation to solve for x, 2x + 3(-5) + 5 = 2 2x - 15 + 5 = 2 2x = 12 x = 6

The solution is (x,y,z) = (6,-5,5)

Therefore, the solution to the given system of equations using Gaussian elimination is (x,y,z) = (6,-5,5).

The given two vectors are A = (2, -3,0) and B = = (-1,0,5). The inner product of two vectors A and B is given by

A·B = |A||B|cosθ

Given,A = (2, -3,0) and B = (-1,0,5)

Magnitude of A is |A| = √(2²+(-3)²+0²) = √13

Magnitude of B is |B| = √((-1)²+0²+5²) = √26

Dot product of A and B is A·B = 2(-1) + (-3)(0) + 0(5) = -2

Cosine of the angle between A and B is

cosθ = A·B / (|A||B|)

cosθ = -2 / (√13×√26)

cosθ = -2 / √(13×26)

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Answer:

1024 pi

Step-by-step explanation:

r = 32 units.

Area = pi * r^2

Area = 3.14 * 32^2

Area = 1024 * pi

Tt = pi??

Answer:

Answer:

Answer:

90°

90°

90°

90°

edc=180-90-53=37by sum of angle of triangle

edf=90-37=53

fed=cde=53alternate angle

fea=180-fae-efa=180-37-90=53

efa=180-90=90linear pair

fae=180-<e-edf=180-90-53=37

eab=90-fae=90-37=53

aeb=180-b-bae=180-90-53=37

The required values are A = 1, B = 0, and C = 8 because the equation for the thrown ball's path will be x = 8.

Let the vertical line be the y-axis and the horizontal line be the x-axis, the ball is thrown from a place that is parallel to the y-axis (8,0).

Because the house is the starting point and the ball is thrown from a position 8 feet to the right of the house,

As a result, the equation for the thrown ball's path will be x = 8.

Therefore, A = 1, B = 0 and C = 8.

Hence, the required values are A = 1, B = 0, and C = 8 because the equation for the thrown ball's path will be x = 8.

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The area of the regular octogon is 196.15 square inches.

For a regular octogon with apothem A and side length L, the area is given by:

area =(2*A*L) * (1 + √2)

Here we know that:

A = 7in

L = 5.8 in

Replacing these values in the area for the formula, we will get the area:

area = (2*7in*5.8in) * (1 + √2)

area = 196.15 in²

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Answer: flat rental fee of $2

Step-by-step explanation:

independent factor that does not change. Coeffocient 0.25 will be charge for late days

Answer:22

Step-by-step explanation:

10x2+1x2=

20+2

=22

\(\huge\textsf{Hey there!}\)

\(\huge\text{10(2) + 1(2)}\)

\(\huge\text{= 10 + 10 + 1 + 1}\)

\(\huge\text{= 20 + 1 + 1}\)

\(\huge\text{= 21 + 1}\)

\(\huge\text{= 22}\)

\(\huge\textsf{Therefore, your answer should be:}\)

\(\huge\boxed{\frak{22}}\huge\checkmark\)

\(\huge\textsf{Good luck on your assignment \& enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

The given problem states that the ratio of the number of tables to chairs in a restaurant is 4 : 9. After removing 2 tables and 4 chairs, the ratio becomes 7 : 16. After removing 2 tables and 4 chairs, there are 16 tables and 36 chairs left in the restaurant.

Let's assume the number of tables in the restaurant is represented by \($4x$\) and the number of chairs is represented by \($9x$\) (since the ratio is given as 4:9).

According to the given information, if 2 tables and 4 chairs are removed, the new ratio becomes 7:16. This can be represented as

\($\frac{{4x - 2}}{{9x - 4}} = \frac{7}{16}$\).

Cross-multiplying:

\(\[16(4x - 2) = 7(9x - 4)\]\)

Simplifying:

\(\[64x - 32 = 63x - 28\]\)

Subtracting \($63x$\) from both sides and adding 32 to both sides:

\($x = 4$\)

Now, we can find the number of tables and chairs left by substituting \($x = 4$\) them back into the initial representation:

The number of tables: \($4x = 4(4) = 16$\)

The number of chairs: \($9x = 9(4) = 36$\)

Therefore, there are 16 tables and 36 chairs left in the restaurant.

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Counting from point M (0 unit) on this number line, we can logically deduce that point H is located at -7.

A numerical data is also referred to as a quantitative data and it can be defined as a data set that is primarily expressed in numbers only. This ultimately implies that, a numerical data refers to a data set consisting of numbers rather than words.

In Mathematics, there are six (6) common types of numbers and these include the following:

A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length. Also, the negative numerical values are positioned at the left from zero while the positive numerical values are positioned at the right from zero.

Note: Each of the tick represents 1 unit.

Therefore, counting from point M (0 unit) on this number line, we can logically deduce that point H is located at -7.

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The formula for the volume of a sphere is 4/3πr³. The formula for r is d/2. We know d, so we can substitute this for r.

4/3(3.14)(32/2)^3
4/3(3.14)(16)^3
4/3(3.14)4096
4.19(4096
17612.24 cm^3

\(\huge\boxed{\sf 17157.28} \\\\\\\displaystyle \sf Converting\ the\ diameter\ to\ radius\\\\r=\frac{d}{2} =\frac{32}{2} =16\\\\Finding\ the\ volume \\\\V=\frac{4}{3} \pi r^{3}=\frac{4}{3} \pi \times 16^{3} \approx 17157.28 \\\\\)

Answer:

Step-by-step explanation:

A(-5,-2),B(-2,-2), C(-5,2)

find distance first:d=√(x2-x1)^2+(y^2-y1^2)

AB: 3

BC: 5

AC: 4

perimeter of triangle=3+5+4=12

compliment angle=90

90+34=124

5x+17+x+19=180

x=24

Answer:

The cost of the chocolate bar is $0.54. You can calculate this by subtracting the total cost of the peanut butter bars ($3.50) from the total cost of the 5 peanut butter bars and 6 chocolate bars ($6.40), resulting in $2.90 for the cost of the chocolate bars, which is then divided by 6 to get $0.54.

Rate of change of Panting A over a year period

Rate of change of Panting B over a year period

Painting B increases more quickly

Rate of change of Panting A over a year period, using the function f(x)=30,000(1.068)^x

at x = 0, f(x) = 30,000

at x = 1, f(x) = 32,040

rate of change = (30 000 - 32 000) / (0 - 1) = -2000 / -1 = 2000

Rate of change of painting B over a year period

= (25 - 27.5) * 1000 / (0 - 1)

= -2.5 * 1000 / -1

= 2500

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Answer:

75%

Step-by-step explanation:

3 is 75 the way to 4 so it would be 75%

The part in the steering column that allows for changes in the angle between the upper and lower shafts is the universal joint.

The universal joint, also known as a U-joint or Cardan joint, is a mechanical device that enables changes in the angle between two shafts that are not in a straight line. In the context of a steering column, the upper and lower shafts are connected by a universal joint.

As the steering wheel is turned, it exerts rotational force on the upper shaft of the steering column. The universal joint allows for the transmission of this rotational motion while accommodating changes in the angle between the upper and lower shafts. It provides flexibility and compensates for any misalignment between the two shafts, ensuring smooth and continuous rotation of the steering column.

The universal joint typically consists of two yokes connected by a cross-shaped component with needle bearings. These bearings allow for rotation in multiple axes, allowing the steering column to handle variations in the angle between the upper and lower shafts during steering movements.

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Given:

The vertices of parallelogram PQRS are P(-5,5) Q(2,5) , R(4,-3) and S(-3,-3).

To find:

The intersection of the diagonals of parallelogram PQRS.

Solution:

We know that the diagonals of a parallelogram bisect each other.

In parallelogram PQRS, PR and QS are the diagonals of the parallelogram.

It means the intersection of PR and QS is the midpoint of PR and QS.

Midpoint formula:

\(Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)\)

Midpoint of diagonal PR is:

\(Midpoint=\left(\dfrac{(-5)+4}{2},\dfrac{5+(-3)}{2}\right)\)

\(Midpoint=\left(\dfrac{-1}{2},\dfrac{2}{2}\right)\)

\(Midpoint=\left(-0.5,1\right)\)

Therefore, the coordinates of the intersection of the diagonals of parallelogram PQRS are (-0.5,1).

If a price of $45 is charged, then Troy will make a profit of $3,645,000.

First, calculate the contribution margin per unit by subtracting the variable cost per unit from the price. The contribution margin per unit is $45 - ($3,510,000/155,500) = $21.77. This means that for each unit sold, Troy will earn a profit of $21.77 after covering the variable costs.

Next, calculate the break-even point in units by dividing the fixed costs by the contribution margin per unit. The break-even point is $1,000,000/$21.77 = 45,958.91 units.

Since Troy is selling more than the break-even point, he will make a profit. To find out how much profit is, calculate the total contribution margin by multiplying the contribution margin per unit by the number of units sold: $21.77 x 155,500 = $3,384,925.

Finally, subtract the total variable costs and fixed costs from the total contribution margin to find the profit: $3,384,925 - $3,510,000 - $1,000,000 = $3,645,000. Therefore, Troy will make a profit of $3,645,000 if a price of $45 is charged.

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