A certain factory produces and sells C computers per month. It costs x dollars to produce a single computer, and the factory sells each computer for y dollars. Their monthly net profit is 10,000 dollars.

Write an equation that relates C, x and y.

If A and B are 2x2 matrices, det(A)=-1,det(B)=3 then

det(AB) = -3

det(-2A) = 8

det(A^T) = -1

det(B^-1) = 1/3

det(B^4) = 81

This can be found by :

det(AB) = det(A) * det(B) = (-1) * 3 = -3

det(-2A) = (-2)^2 * det(A) = 4 * (-1) = -4

det(A^T) = det(A) = -1

det(B^-1) = 1 / det(B) = 1/3

det(B^4) = (det(B))^4 = 3^4 = 81

For det(AB) we use the property that the determinant of a product of matrices is the product of their determinants.

For det(-2A) we use the property that the determinant of a matrix multiplied by a scalar is the determinant of the matrix multiplied by the scalar raised to the power of the matrix size.

For det(A^T) we use the property that the determinant of a matrix is the same as the determinant of its transpose.

For det(B^-1) we use the property that the determinant of the inverse of a matrix is the reciprocal of the determinant of the matrix.

For det(B^4) we use the property that the determinant of a matrix raised to a power is the determinant of the matrix raised to that power.

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Answer:

Step-by-step explanation:

all values are true

Answer:

343 cube meters of air

a. the polar coordinate r for point P, with r > 0 and 0 < θ < 180°, is approximately 5.0874. b. the Cartesian coordinates for point P are approximately (-1.4587, 4.8793). c. The curve does not pass through the origin when 0 < θ < 2π.

a) To find the polar coordinate r for point P, we substitute the given angle θ = 161.14° into the equation r = 7 + 2cosθ.

r = 7 + 2cos(161.14°)

Using a calculator, we can evaluate the cosine function:

r = 7 + 2(-0.9563)

r = 7 - 1.9126

r ≈ 5.0874

Therefore, the polar coordinate r for point P, with r > 0 and 0 < θ < 180°, is approximately 5.0874.

b) To find the Cartesian coordinates for point P, we can convert the polar coordinates (r, θ) to Cartesian coordinates (x, y) using the formulas:

x = rcosθ

y = rsinθ

Substituting r = 5.0874 and θ = 161.14° into the formulas, we have:

x = 5.0874cos(161.14°)

y = 5.0874sin(161.14°)

Evaluating the trigonometric functions:

x = 5.0874(-0.2868)

y = 5.0874(0.958)

x ≈ -1.4587

y ≈ 4.8793

Therefore, the Cartesian coordinates for point P are approximately (-1.4587, 4.8793).

c) To determine how many times the curve passes through the origin when 0 < θ < 2π, we need to examine the values of θ for which r = 0. When r = 0, it indicates that the curve passes through the origin.

Setting r = 0 in the equation r = 7 + 2cosθ:

0 = 7 + 2cosθ

Solving for θ, we have:

2cosθ = -7

cosθ = -7/2

The cosine function has values between -1 and 1. Since -7/2 is outside this range, there are no values of θ between 0 and 2π that satisfy the equation, and thus the curve does not pass through the origin.

In conclusion, for the given curve in polar coordinates with r = 7 + 2cosθ, point P has a polar coordinate r ≈ 5.0874 with θ = 161.14°, and its Cartesian coordinates are approximately (-1.4587, 4.8793). The curve does not pass through the origin when 0 < θ < 2π.

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Answer:

n = 13

Step-by-step explanation:

7n + 5 = 96

Subtract 5 from both sides to get rid of the 5 on the right side:

7n + 5 - 5 = 96 - 5

7n = 91

Divide both sides by 7 to get rid of the coefficient of n:

7n / 7 = 91 / 7

n = 13

Answer: \(n=13\)

Subtract 5 from both sides

\(7n+5-5=96-5\\7n=91\)

Divide both sides by 7

\(7n/7=91/7\\x=13\)

Answer:

122

Step-by-step explanation:

\(x^6+y^2\)

Plug in 1 for x and 11 for y

\(=1^6+11^2\)

1 to the power of any number will always equal 1

\(=1+11^2\\=1+121\\=122\)

I hope this helps!

Answer:

Q1)

GIVEN :-

TO FIND :-

FORMULAES TO KNOW BEFORE SOLVING :-

PROCEDURE :-

In the figure , the cone is mounted on a hemisphere.

⇒ Radius of cone = Radius of hemisphere = 4.5m

Total surface area of the figure = Curved surface area of both cone & hemisphere.

⇒

∴ Total surface area = 183.7 + 127.1 = 310.8m²

Q2)

GIVEN :-

TO FIND :-

FORMULAES TO KNOW BEFORE SOLVING :-

PROCEDURE :-

Volume of hemisphere = \(\frac{2}{3} \pi r^3 = \frac{2}{3} \times 3.14 \times (3)^3 = 56.52km^3\) ≈ 56.5km³

Surface area of hemisphere = \(2\pi r^2 = 2 \times 3.14 \times (3)^2 = 56.52km^2\) ≈ 56.5km²

The equation of L is L = 0.5P - W

The formula is given as:

P = 2(L + W)

Divide through by 2

0.5P = L + W

Subtract W from both sides

L = 0.5P - W

Hence, the equation of L is L = 0.5P - W

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Complete question

The formula for the perimeter of a rectangle is P=2(l+w). Solve for l.

Is the relation a function:

To determine if the relation is a function, we need to check if there is exactly one output for each input.

Looking at the given set of points, we see that there are two points with an x-coordinate of -1: (-1, 3) and (-1, -2).

This means that there are two outputs for the same input, so the relation is not a function.

Therefore, the correct answer is: "No, because for each input there is not exactly one output."

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If someone wants the product of two line segments to be represented as another line segment, they can make use of similar triangles

The correlation between the lengths of line segments can be established by creating a geometric shape comprising of two triangles that are identical and share one side.

If the legs of the triangles are used to represent the two line segments and their shared side represents the resulting line segment, it is possible for the lengths to be proportional through the similarity of the triangles.

To represent the product of the two original line segments, it is necessary to ensure that they and the resulting line segment are a collection of similar triangles. This is because the length of the resulting line segment can represent the product of the initial segments.

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Answer:

7 and 5

Step-by-step explanation:

Answer:

I think it means to take the measurements  of the bigger trash bin and turn it into the scale of 0.75

Answer:

\(m=− 32​ ≈−0.666666667\)

Step-by-step explanation:

Answer:

a) 36

b) 3.9

Step-by-step explanation:

I really hope this helps

Answer:

2 products per second.

Step-by-step explanation:

The measure of angle P formed by the tangent AP and secant PBC is 10°.

Given a circle O.

There is a tangent PA and secant PBC.

We have the theorem which states that, "Exterior angle formed by a tangent and a secant is equal to the half of the difference of the intercepted arcs".

Using the theorem,

m ∠P = (Arc AC - Arc AB) / 2

         = (80 - 60) / 2

         = 20 / 2

         = 10°

Hence the angle measure is 10°.

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The conversion 336g to m³ is impossible because they measure different units

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

Convert 336g to m³

To convert a unit to another, the units must measure the same quantity

Take for instance:

Grams can be converted to kilograms because they both measure mass

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

336g to m³  cannot be done because of the different quantities they represent

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Answer:

Hi! Based on your question, you would like to know the best measure of center to represent the data in a dot plot. Here are the options to consider:

1. Mode
2. Mean
3. Range
4. Median
5. Interquartile Range

However, without an actual dot plot to analyze, I am unable to provide specific advice on which measure(s) of center would be best for representing the data. If you can provide a dot plot or specific data points, I will gladly help you determine the best measure(s) of center for your data.

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The options that describe the best measure of center to represent the data in the dot plot are Mode and Median.

Based on the information provided, the best measure of center to represent the data in the dot plot would be:

Mode: The mode represents the value(s) that appear most frequently in the data and can be a good measure of center when there are clear peaks or modes in the distribution.

Median: The median represents the middle value in a dataset when it is arranged in ascending or descending order. It is a robust measure of center that is not affected by extreme values or outliers.

Both the mode and median are suitable measures of center for representing the data in a dot plot. However, the dot plot alone does not provide information about the mean, range, or interquartile range.

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Alrighty, so,  you know how young children often believe that a taller container will have a greater volume than a shorter container? Even after seeing that both containers hold the same amount, some children will still think the taller container holds more. It may take measuring the water a few times before they get it.

If it overflows, the first container is bigger, or is able to hold more water. If all of the water from the first container can be poured into the second container without completely filling it, then the second container holds more water.

The tallest container holds the most liquid. Identical containers can have a different capacity.

Step-by-step explanation:

x = number of years after 2007.

x = 0 for 2007.

PC(x) is a function that calculates how many pounds of chicken the average adult will eat every year (x) after 2007 (up to 2012).

PC(x) = 0.8x + 52

0 <= x <= 5

in 2007 (x = 0) the average adult ate 52 pounds.

in every year after 2007 until 2012 0.8 pounds get added to the amount of the previous year.

so, in 2012 (x = 5) the average adult will eat

PC(5) = 0.8×5 + 52 = 4 + 52 = 56 pounds of chicken.

The number of days christen’s book is overdue is 22.

The number of days christen’s book is overdue:

According to the graph, the fine levied stops rising after 20 overdue days and then stays at 10 for the remaining days.

Additionally, if Christen's fine was the same as yesterday, her late dates must be longer than 21 days (because the fine on day 20 will be the same).

22 might therefore be the number of days past due based on the options provided.

The number of days christen’s book is overdue is 22.

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Answer:

x * 5

Step-by-step explanation:

prosucts refer to multiplication

Therefore, the perimeter can be calculated by adding up all four sides: p = 2b + 2n.

To find the perimeter (p) of a parallelogram, you need to know the length of all four sides. However, in this case, you are given the ratio of the base (b) to one of the sides (a), which is n/a.
Since a parallelogram has two pairs of parallel sides, the opposite sides are equal in length. Therefore, if the base is b, then the opposite side is also b. Using the given ratio, you can find the length of the other side (n) by multiplying a by n/a, which is n.
So, the length of the other side is also n, and the perimeter can be calculated by adding up all four sides: p = 2b + 2n.
However, if given the ratio of the base to one of the sides, you can use this to find the length of the other side. For this problem, if the base is b, then the opposite side is also b, and the length of the other side is n (where n/a = b/a).

Therefore, the perimeter can be calculated by adding up all four sides: p = 2b + 2n.

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Let's call the first number in the series "x", and the last number in the series "y".

We know that the series is a consecutive series of odd numbers, and we also know that y is 6 less than the last number in the series.

Since the series is a consecutive series of odd numbers, we can say that the difference between any two consecutive numbers in the series is 2.

So, we can write an equation to represent this information:

y = x + (n-1) * 2

where n is the number of numbers in the series.

We also know that y is 6 less than the last number in the series, so we can add this information to our equation:

y = x + (n-1) * 2 - 6

To solve for n, we can rearrange the equation:

n = (y - x + 6) / 2 + 1

Now, if we know the value of x and y we can substitute them in the equation and find the number of terms in the series.

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The main answer is that the difference between the number of strikes thrown before and after the training program for the Little League pitchers is as follows: -7, -7, 2, 4, 3, 2, 0, 2, 3, 3, 0, 2, -2, -4, -1, -1, 1, -3, -2, -1.

The table provides the number of strikes each player threw before and after the training program. To calculate the difference between the number of strikes thrown before and after, we subtract the "After" value from the "Before" value for each player.

For example, for the first player, the difference is 35 (After) - 28 (Before) = -7. Similarly, for the second player, the difference is 36 - 29 = -7. We repeat this calculation for each player and obtain the following differences: -7, -7, 2, 4, 3, 2, 0, 2, 3, 3, 0, 2, -2, -4, -1, -1, 1, -3, -2, -1.

These differences represent the change in the number of strikes thrown by each player after undergoing the training program. A negative difference indicates a decrease in the number of strikes, while a positive difference indicates an improvement. The range of differences is from -7 to 4, showing that the impact of the training program varied among the players.

It's important to note that the claim made in the advertisements suggested that players would be able to throw strikes on at least 60% of their pitches after the training. However, the difference values alone do not provide information about the success rate in terms of percentage. To determine if the training program was effective in meeting this claim, further analysis is needed, such as calculating the strike percentage for each player before and after the training and comparing them to the expected 60% threshold.

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Answer:

Step-by-step explanation:

1.25=0.75+r

1.25-0.75=r

r=0.50

r=0.5

hope it helps you

The number of unique committees of 5 people that can be formed from a selection pool of 23 people is 33,649. The correct option is (B).

The number of unique committees of 5 people that can be formed from a selection pool of 23 people can be calculated using the combination formula, which is:

n C r = n! / r!(n - r)!

where n is the total number of people in the selection pool and r is the number of people needed for the committee.

In this case, we have n = 23 and r = 5, so the number of unique committees can be calculated as:

23 C 5 = 23! / 5!(23 - 5)! = 23! / 5!18! = (23 x 22 x 21 x 20 x 19) / (5 x 4 x 3 x 2 x 1) = 33,649



Therefore, the answer is option B, 33,649.

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To calculate the electric field induced both inside and outside the solenoid, we need to use Faraday's law of electromagnetic induction, which states that the electromotive force (EMF) induced in any closed circuit is equal to the negative rate of change of the magnetic flux through the circuit.

In the case of a solenoid, the magnetic flux through the solenoid is given by:

Φ = μnIπr^2

where μ is the permeability of free space, n is the number of turns per unit length, I is the current through the solenoid, and r is the radius of the solenoid.

Taking the time derivative of the flux gives:

dΦ/dt = μnπr^2(dI/dt)

This is the EMF induced in the solenoid. Using Faraday's law, we can equate this EMF to the electric field induced in the solenoid, giving:

E = -(dΦ/dt)/A

where A is the cross-sectional area of the solenoid.

Inside the solenoid, the electric field induced will be proportional to the EMF induced, so we can write:

Einside = -μnπr^2(dI/dt)/A

Outside the solenoid, the magnetic field is negligible, so the flux through any closed circuit outside the solenoid is zero. Therefore, there is no EMF induced outside the solenoid, and the electric field is zero.

In summary, the electric field induced inside the solenoid is given by Einside = -μnπr^2(dI/dt)/A, and the electric field induced outside the solenoid is zero. The value of the electric field inside the solenoid will depend on the current and the dimensions of the solenoid.

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Answer:

The initial value is 1

Step-by-step explanation:

The initial value is the value when t =0

When t=0 p =1