HELPPP PLSSSSSSSSSS
Decide the type or transformation and state the rule

1. Required profit function is P(x)= -0.5x² + 60x + 6850

2. The domain of P(x) is 20 - 4√205 ≤ x ≤ 170.

3. P(70) = 2650 and P(80) = 2600.

The company should choose to produce 70 items as it results in a higher profit.

4. The leads to a decrease in profit, which is why the company makes less profit when producing 10 more units.

What is profit function?

A profit function is a mathematical formula that describes the relationship between the level of production or sales and the resulting profit of a business. The profit function takes into account the costs of production, including fixed costs and variable costs, and the revenue generated by the sale of goods or services.

1. The profit function P(x) is given by subtracting the cost function C(x) from the revenue function R(x):

P(x) = R(x) - C(x)

= [−0.5(x−120)²+7,200] - [50x+250]

= -0.5x² + 60x + 6850

2. The domain of P(x) is the set of all possible values of x for which the profit function P(x) makes sense. Since P(x) involves subtracting the cost function from the revenue function, it only makes sense to calculate P(x) when the revenue generated from selling x items is greater than or equal to the cost of producing x items. Therefore, the domain of P(x) is the set of all x such that R(x) ≥ C(x),

R(x) ≥ C(x)

-0.5(x−120)²+7,200 ≥ 50x+250

-0.5x²+60x+6850 ≥ 50x+250

-0.5x²+10x+6600 ≥ 0

Solving for x, we get:

x ≤ 20 - 4√205 or x ≥ 20 + 4√205

Since the maximum capacity of the company is 170 items, the domain of P(x) is the intersection of the above solution and the maximum capacity, i.e. x ≤ 170. Therefore, the domain of P(x) is 20 - 4√205 ≤ x ≤ 170.

3. To find the profit when producing 70 items, substitute x = 70 into the profit function P(70) = -0.5(70)² + 60(70) + 6850

= 2650

To find the profit when producing 80 items, substitute x = 80 into the profit function P(80) = -0.5(80)² + 60(80) + 6850

= 2600

Therefore, the company should choose to produce 70 items as it results in a higher profit.

4. The profit function P(x) is a quadratic function with a negative leading coefficient (-0.5), which means that it opens downwards. This implies that the profit function reaches its maximum value at the vertex of the parabola, which occurs at x = -b/2a, where a = -0.5 and b = 60. Therefore, the vertex occurs at x = -60/-1 = 60. This means that the maximum profit occurs at x = 60.

When the company produces 10 more units (i.e. x increases by 10), it moves away from the optimal production level of 60 and closer to the maximum capacity of 170. As a result, the cost of production increases while the revenue generated from selling those extra units decreases due to diminishing returns. This leads to a decrease in profit, which is why the company makes less profit when producing 10 more units.

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The discrepancy between the column spaces of a matrix's echelon form U and its original form A, C(U) and C(A) respectively, originates from how column space is defined.

Column space is purported as the set of all linear combinations of the columns in the matrix. Nonetheless, despite elementary row operations modifying the linear independence of the matrix, it does not alter its column space.

Subsequently, therby resulting to C(U) being a subspace of C(A). This concept can be exemplified via an example: When we employ 3x3 matrix with linearly independent columns, then its echelon form U may only display two linearly independent columns; thus increasingly shrinking the dimension of the transformed matrix's column space.

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Answer:

The items arranged from least steep to steepest rate of change are:

Michele's spending: $125 to $75 over time, spending $10 per week.

Elisa's puppy's weight: Started at 4 pounds, gained 5 pounds per month until it was 9 months old.

f(t): -6.2x + 2.9, a linear function with a rate of change of -6.2.

g(x): 8.1x + 45.64, a linear function with a rate of change of 8.1.

So the correct order is:

Michele's spending

Elisa's puppy's weight

f(t)

g(x)

Step-by-step explanation:

The time it took Milan longer to clean the bathroom is 3 1/8 hours

Time taken for Milan to clean the bathroom = 3 1/4 hours

Time taken for Milan to clean the kitchen = 1/8 hours

Time taken longer for Milan to clean the bathroom = 3 1/4 hours - 1/8 hours

= 13/4 - 1/8

= (26-1) / 8

= 25/8

= 3 1/8 hours

In conclusion, it took Milan 3 1/8 hours longer to clean the bathroom.

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Answer: 5 5/8 more feet of snow in December.

Step-by-step explanation: 5 7/8 also equals 47/8, and we need convert 1/4 to something over 8 so we can subtract the two. 1/4, but multiply both sides by 2 is 2/8. 47/8-2/8=45/8. 45/8 as a mixed fraction is 5 5/8.

The better statistics to use to compare the distributions includes mean and standard deviation. The Option C is correct.

Mean represents the central tendency of the distribution, while standard deviation reflects the spread of the data around the mean. Comparing mean & standard deviation of 2 or more distributions can provide insights into similarities and differences.

If the means of two distributions are similar, it suggests the data points in each distribution are centered around similar value. But if standard deviations are also similar, it indicates that the spread of the data points around the mean is also similar.

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A loan of $595 borrowed on June 15 and repaid on Dec 17 at an exact interest rate of 6%. The exact time between the two dates is 170 days, and the maturity value is $611.69 rounded to the nearest cent.

Using the Days in a year table, we can find the exact time between June 15 and December 17 as follows

June has 30 days in the table and July through November have 31 days each. December has 17 days until the loan is repaid. Therefore, the exact time is

30 + 31 + 31 + 30 + 31 + 17 = 170 days

Next, we can calculate the interest using the formula

interest = principal x rate x time / 365

where the principal is $595, the rate is 6%, and the time is 170 days.

Substituting these values, we get

interest = 595 x 0.06 x 170 / 365

interest = $16.69

Therefore, the exact interest is $16.69.

Finally, we can calculate the maturity value by adding the principal and the interest

maturity value = principal + interest

maturity value = $595 + $16.69

maturity value = $611.69

Therefore, the maturity value is $611.69 rounded to the nearest cent.

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It is a right triangle so f² =  g² + h² not f² + g² = h²

What is the Pythagoras theorem?

A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Here, we have

Given: Lindsay sketches a right triangle with lengths f, g, and h has shown. She uses the Pythagorean Theorem to write the equation f² + g² = h² to represent the triangle.

It is a right triangle.

∴ f² =  g² + h² not f² + g² = h²

Hence, It is a right triangle. f² =  g² + h² not f² + g² = h²

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Answer:

radius = 72.00 units

Step-by-step explanation:

The general formula for circumference (C) of a circle is C = πd, where d is the diameter.  The formula using 3.14 for π is C = 3.14d   The diameter (d) is simply twice the radius (r) as d = 2r

Thus, we can rewrite the formula for circumference in terms of radius as C = 3.14(2r)

To solve for r, we can divide the circumference we're given by the product of 3.14 and 2 to find r:

[tex]C/(2*3.14)=r\\452.16(2*3.14)=r\\452.16/6.28=r\\72=r[/tex]

Answer:

The interest earned in $210.00

Step-by-step explanation:

i = prt

i = 3000(.07)(1)

i = 210.00

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Answer:

s = 10√3

Step-by-step explanation:

This is a 30°-60°-90° right triangle, so s, the length of the longer leg, is √3 times the length of the shorter leg. Since the length of the shorter leg is 10, s = 10√3.

This expression [tex]r_{i-j}[/tex] describes the distance between two points i and j in a geometric object

In the context of symmetry and rotations, [tex]r_{i-j}[/tex] typically refers to the distance between two points i and j in a geometric object, such as a crystal lattice or a molecule.

It is a vector that points from point i to point j, and its magnitude is the distance between the two points.

The distance vector [tex]r_{i-j}[/tex] is also used to describe the position of a point in the crystal lattice relative to the rotation axis.

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In this case, renting the huge van would be a more cost-effective option because it would run you $289 as opposed to $354.65 for the minivan.

To compare the costs of renting the minivan and the large van, we need to calculate the total cost for each option.

For the minivan, the cost per day is $24.95 and the cost per mile is $0.15. So, for 7 days and 1,200 miles, the total cost would be:

Total cost = 7($24.95) + 1,200($0.15)

= $354.65

For the large van, the cost is a flat rate of $289 per week with no additional charge for mileage. So, for 7 days and 1,200 miles, the total cost would be:

Total cost = $289

Therefore, renting the large van would be a better buy in this scenario, as it would cost $289 compared to $354.65 for the minivan.

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When Joann turns 18, she will have approximately $41,551.20 in her investment account.

FV = P * [(1 + r)^n - 1] / r

FV = future value

P = periodic payment ($300)

r = interest rate per period (0.04 / 2 = 0.02)

n = total number of periods (18 years * 2 = 36)

FV = 300 * [(1 + 0.02)^36 - 1] / 0.02

FV ≈ 300 * [2.3084] / 0.02

FV ≈ 34,626.00

Solve for inotial investment

FV_initial = PV * (1 + r)^n

FV_initial = 3000 * (1 + 0.02)^36

FV_initial ≈ 3000 * 2.3084

FV_initial ≈ 6,925.20

we have to add both future values

Total_FV = 6,925.20 + 34,626.00

Total_FV ≈ 41,551.20

When Joann turns 18, she will have approximately $41,551.20 in her investment account.

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Answer:

43

Step-by-step explanation:

The distance formula is

[tex] \sqrt{{(x2 - x1)}^{2} + (y2 - y1)^{2} } [/tex]

So

[tex] \sqrt{(25 + 18) ^{2} + ( - 7 + 7)^{2} } \\ = \sqrt{ {43}^{2} + 0 {}^{2} } = 43[/tex]

Answer:

Step-by-step explanation:

The distance between the two given points can be found using the formula for the distance between two points in a coordinate plane,

which is d = √((x₂ - x₁)² + (y₂ - y₁)²). In this case, the x-coordinates of both points are the same (-7), so we only need to calculate the difference between their y-coordinates: d = √((0)² + (25 - (-18))²) = √(43²) = 43 units. Therefore, the distance between the two points located at (-7, -18) and (-7, 25) is 43 units

Answer:

70

Step-by-step explanation:

The non-labeled side (next to 130) has to be supplementary to the angle outside, hence it has to be 50. Since all the sides of an angle must add up to 180, we can subtract 60+50 to get 70. Hope this helps!

Answer:

70°

Step-by-step explanation:

Theorem:

The measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles.

130 = x + 60

x = 70

Answer: 70°

The table describes the relationship between membership status and attendance of classes under the principle of independence.

Option A is the correct answer.

We have,

This table describes the relationship between membership status and attendance of classes.

To determine if there is a relationship, we need to apply the principle of independence.

If the principle of independence holds, then the events "having a membership" and "attending one or more classes" are independent of each other, and similarly, the events "not having a membership" and "attending none of the classes" are independent of each other.

To check for independence, we can calculate the expected values for each cell assuming independence holds, and compare them to the observed values.

The expected value for "Have a membership" and "Attend one or more classes".

= (40/70) x (31/70) x 70

= 17.86

The expected value for "Have a membership" and "Attend none of the classes".

= (40/70) x (39/70) x 70

= 22.14

The expected value for "Do not have a membership" and "Attend one or more classes".

= (30/70) x (31/70) x 70

= 13.14

The expected value for "Do not have a membership" and "Attend none of the classes".

= (30/70) x (39/70) x 70

= 16.86

Comparing these expected values with the observed values, we see that they are reasonably close, indicating that the principle of independence holds.

Therefore,

We can conclude that this table describes the relationship between membership status and attendance of classes under the principle of independence.

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Answer:

--------------------

The range of the given function has one restriction, its denominator can't be zero, hence:

Therefore the function can get any value but zero:

The matching answer choice is D.

Linear function is f(x) = mx + b.

Reciprocal of a function f(x)  is 1/f(x).

So the reciprocal of linear function has a form of f(x) = 1 / (mx + b).

The only answer choice in same form is D.

Substitute x = - 5/3 into function to get:

This is undefined value, therefore it represents the vertical asymptote.

The function gets close to - ∞ when x → - 5/3 from left and gets close to +∞ when x → - 5/3 from right (see attached graph).

Therefore the correct choice is B.

The measure of the arc angle is as follows:

m∠BAC = 228°

The central angle of an arc is the central angle subtended by the arc.  

The measure of an arc is the measure of its central angle.

The Central Angle theorem states that the central angle subtended by

two points on a circle is  twice the inscribed angle subtended by those

points.

Therefore, let's find m∠BAC

Hence,

m∠BC = Central angle

m∠BAC = 360 - 132

m∠BAC = 228 degrees

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The recursive equation for this table is given as follows:

f(n) = 3f(n - 1) + 1.

To obtain the recursive equation, we must obtain a pattern between a term and the previous term.

For this problem, we have that each term is the previous term multiplied by 3 and added by one.

Hence the recursive equation for this table is given as follows:

f(n) = 3f(n - 1) + 1.

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We can see here that the equation that best models the situation is: B.  13 - (60h/23) = 10.

Speed is a scalar quantity that describes how fast an object is moving, or the rate at which it covers distance. It is typically measured in units of distance per unit of time, such as miles per hour or meters per second.

Speed only tells us how fast an object is moving, without any information about the direction of motion or changes in direction.

We can see that if we find the time, h in hours, we will have:

h = (3 x 23)/60

Simplifying this expression gives us:

h = 69/60

Therefore, the equation is:

h = 1.15

(Note: 3 is gotten from 13 gallons - 10 gallons = 3 gallons that was used at that particular time and speed).

If we substitute h = 1.15 into our model equation, we will get the correct answer.

Thus, 13 - (60 × 1.15)/23 = 10.

∴ Option B is the correct answer.

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Answer:

Plot the points on the graphing calculator, and then determine the linear regression function: y = -1.16786x + 8.82857

You may obtain a slightly different linear regression equation.

1) -1 (g)

2) 8 (not one of the choices)

3) graph (i)

4) approximately -1/strong negative trend (not one of the choices)

5) y = -x + 8 (h)

Answer:

f(x) =

0 if -1 < x < 0,

1 if 0 < x < 3,

2 otherwise

Hence, the value of CosФ + Cos (2π+Ф) + Cos (4π+Ф) is 0.6 .

The cosine function One of the fundamental trigonometry functions is cos x as the others being the co-secant, cotangent, secant, sine, and tangent. Let theta represent the angle that can be calculated by rotating the unit circle's arc anticlockwise from the x-axis. Cos theta is the arc endpoint of  horizontal coordinate after that.

trigonometric functions are used in an expression or equation, trigonometric Identities are helpful. For every value of a variable appearing on both sides of an equation, a trigonometric identity is true. Certain trigonometric functions such as sine, cosine, and tangent of one or more angles are involved geometrically in these identities.Three main are  trigonometry functions are sine, cosine, and tangent, while the other three are cotangent, secant, and co-secant. All six trigonometric functions serve as the foundation for the trigonometric identities.

Given, CosФ = 0.2,

thus we can use the trigonometric identity:

cos(2 n π+Ф) = cosФ

where any integer n is used. Therefore:

Cos(2 π+ Ф) = CosФ

cos (4π+Ф) = cosФ

These values, put into the given expression

than we get,

cos Ф+ cos (2π+Ф) + cos (4π+Ф) = cos Ф+ cosФ + cosФ.

= 3 cosФ

= 3×0.2

= 0.6

So,CosФ + Cos (2π+Ф) + Cos (4π+Ф) = 0.6

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the speed of the train in km/h is 40.32 whereas the speed of the train in m/s is 11.2.

(i) To find the speed of the train in km/h, we can use the formula:

speed = distance/time

Here, the distance travelled by the train is 16.8 km, and the time taken is 25 minutes, which is equivalent to 0.4167 hours (since 1 hour = 60 minutes). Substituting these values in the formula, we get:

speed = 16.8 km/0.4167 hours

speed = 40.32 km/h (rounded to two decimal places)

Therefore, the speed of the train in km/h is 40.32.

(ii) To find the speed of the train in m/s, we can convert the speed in km/h to m/s by multiplying by 1000/3600 (since 1 km/h = 1000 m/3600 s). Using the speed of 40.32 km/h from part (i), we get:

speed = 40.32 km/h * 1000 m/km / 3600 s/h

speed = 11.2 m/s (rounded to one decimal place)

Therefore, the speed of the train in m/s is 11.2.

If the speed limit is 55 km/h, we cannot directly determine the distance travelled by the train without additional information. The distance travelled by the train would depend on the time it took to travel at the given speed limit.

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Answer: x=5

Step-by-step explanation:

Not much calculations needed, but since we have two points where x=5, a vertical line that is equal to x=5 will hit both points. I attached it visually below!

Step-by-step explanation:

6 or 7.

that means either exactly 6 or exactly 7 out of the 10 board the flight.

these are non-depending (or non-overlapping) scenarios. so, for this "or" remained we can simply add the 2 individual probabilities P(6) and P(7).

P(6) is the probability of exactly 6 passengers out of 10 will board the flight.

because of the 75% certainty overall we can conclude that the probabilty for each booked passenger to board is 0.75 (75% means 75 out of 100 = 0.75).

and the probabilty to not board is

1 - 0.75 = 0.25

so, for a specific group of exactly 6 booked passengers out of 10 their probabilty to board is

0.75⁶ × 0.25⁴ = 0.000695229...

6 passengers board, 4 do not board.

but this is for only one possible grouping of 6 passengers out of 10.

since the sequence does not matter, and we have no repetitions (every passenger counts as 1), we have combinations :

C(10, 6) = 10! / (6! × (10-6)!) = 10!/(6!×4!) = 10×9×8×7/4! =

= 5×3×2×7 = 210

therefore,

P(6) = 210 × 0.75⁶ × 0.25⁴ = 0.145998001...

and for a specific group of exactly 7 booked passengers out of 10 their probabilty to board is

0.75⁷ × 0.25³ = 0.002085686...

7 passengers board, 3 do not board.

but this is for only one possible grouping of 7 passengers out of 10.

since the sequence does not matter, and we have no repetitions (every passenger counts as 1), we have combinations :

C(10, 7) = 10! / (7! × (10-7)!) = 10!/(7!×3!) = 10×9×8/3! =

= 5×3×8 = 120

therefore,

P(7) = 120 × 0.75⁷ × 0.25³ = 0.250282288...

so, the probability that either 6 or 7 booked passengers are actually boarding is

P(6) + P(7) = 0.396280289... ≈ 0.396

Answer:

y = -5/3 x - 13

Step-by-step explanation:

Parallel lines have the same slope.  The slope will be -5/3

y = mx + b

We will substitute -3 for y (-6,-3).

We will substitute -5/3 for m.

We will substitute -6 for x (-6,-3)

-3 = -5/3(-6) + b

-3 = [tex]\frac{30}{3}[/tex] + b

-3 = 10 + b  Subtract 10 from both sides

-3 - 10 = 10 - 10 + b

-13 = b

To write the equation, use -5/3 for m (the slope) and -13 for b (the y-intercept)

y = mx + b

y = -5/3 x - 13

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