) A company has determined that its profit for a product can be described by a linear function.
The profit from the production and sale of 150 units is $455, and the profit from
250 units is $895.
(i) What is the average rate of change of the profit for this product when
between 150 and 250 units are sold?
(ii) Write the equation of the profit function for this product.
(iii) How many units give break-even for this product?
(b) You are the CEO for a lightweight compasses manufacturer. The demand
function for the lightweight compasses is given by p = 40 − 4q
2where q
is the number of lightweight compasses produced in millions.It costs the company $15
to make a lightweight compass.
(i) Write an equation giving profit as a function of the number of lightweight compasses
produced.
(ii) At the moment the company produces 2 million lightweight compasses and makes a profit
of $18,000,000, but you would like to reduce production. What smaller number of
lightweight compasses could the company produce to yield the same profit?

There is no change in its slope as initial and final slope is 1.

What is slope?

In arithmetic, the slope or gradient of a line may be a variety that describes each the direction and therefore the abruptness of the line.

Main body:

formula for slope with two points form is =

y -y₁ =( y₂-y₁ /x₂-x₁ )(x - x₁)

according to question ,

points are (0,0) and (3,3)

y - 0 = (3-0/3-0)(x -0)

y = 3/3 *x

y = x

hence slope of line is 1.

Now points are (0,0) and (-3,-3).

y - 0 = (-3-0/-3-0)(x -0)

y =- 3/-3 *x

y = x

hence slope of line is 1.

So there is no change in its slope.

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She made sales of =$61,200.00

acc to our  question-

Step-by-step explanation:

1.5% = 0.015 , 4% = 0.04 , 5% = 0.05

16,000 × 0.015 = $240.00

$25,000 × 0.04 = $1,000.00

$2,250.00 - ($240.00 + $1,000.00) = $1,010.00

$1,010.00 ÷ 0.05 = $20,200.00

$20,200.00 + $25,000.00 + $16,000.00 = $61,200.00

hence,She made sales of =$61,200.00

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Answer:

44

Step-by-step explanation:

vertical angles

Answer:

n = p - m - k

Step-by-step explanation:

p = n + m + k ( isolate n by subtracting m and k from both sides )

p - m - k = n

Answer:

The height of the tree is 35 meters.

Step-by-step explanation:

Let the height of the tree be x meters, then the length  of the wire is

x+2 meters.

The distance from the tree to the anchor is  x-23 meters.

So using the pythagoras theorem:

(x + 2)^2 = x^2 +(x -23) ^2

x^2 + 4x + 4 = x^2 + x^2 - 46x + 529

x^2 - 50x + 525 = 0

( x - 15)(x - 35) = 0

x = 15, 35

x cannot be 15   as this would make the distance 15-23 which is negative so x mustr be 35 meters,

The parallel lines are r and s.

Parallel lines are those lines that are equidistance from each other and never intersect each other.

Given that;

There are 4 lines ae shown in figure.

Now,

Since, There are 4 lines ae shown in figure.

We know that,

Parallel lines are those lines that are equidistance from each other and never intersect each other.

And, Here p and s are intersect at a point.

Lines q and r are intersect at a point.

Lines p and r are intersect at a point.

And, Lines r and s are not intersect at any point and equidistance from each other.

Thus, The lines r and s are parallel lines.

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Answer:

1025/4

Step-by-step explanation:

x^6 - x

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

4y

Let x =-4 and y = 4

(-4)^6 - (-4)

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

4*4

4096 +4

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

16

4100/16

1025/4

The answer is C. 1025/4

For a set of seven numbers , {1, 2, 3, 4, 5, 6, 7} the probability of finding a number less than 327 is 0.329..

Three numbers are drawn from set

S = {1, 2, 3, 4, 5, 6, 7}

(a) for three digit number less than 327 without replacement,

case -1 : If the number starts with three then the 2nd place can be filled with 2 choices either 1 or 2. So, there are 4 choices and 5 choices for the 3rd place if 2nd place is filled up by 2 and 1 numbers respectively. So,total number of ways are 9 .

case -2 : If number starts with Two then the remaining two digits can be choosen in 6x5 ways.

Case-3 : If the number starts with One then the remaining two digits can be choosen 6× 5 ways.

The Required probability two digits can be less than 327 is ( 9+ 6x5 + 6 x 5)/ 7× 6x5

= 69/210 = 23/70 = 0.3285

Hence, the probability of finding a number less than 327 is 0. 3285 ~ 0.329 .

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Answer:

D point

hope this helps you

Answer:

See step by step.

Step-by-step explanation:

lets define the events:
A: cuban festival        C: tropical Garden
B: street art show      D: african festival

a) theoretically the probability is

\(P(A)=P(B)=P(C)=P(D)= \frac{1}{4} = 0.25 \\\)
This is 25% (for each one, equally)

b) The experimental probability is given by:

\(P(A)= \frac{32}{150} =0.2133\)

\(P(B)= \frac{38}{150} =0.2533\)

\(P(C)= \frac{35}{150} =0.2333\)
\(P(D)= \frac{45}{150} =0.3000\)

c) The theoretically probabilities are all equally, the experimental probabilities are close to 25% each one, but differ lightly each one, since is an experiment and the result is random.  

Answer:240 square feet

Step-by-step explanation:length of rectangle DMLG

= DM = LG = (25 + 5) = 30 feet

width of rectangle DMLG

= ML = 8 feet

area of rectangle DMLG

= length × width

= 30 × 8

= 240 square feet

Answer: length of rectangle DMLG

= DM = LG = (25 + 5) = 30 feet

width of rectangle DMLG

= ML = 8 feet

area of rectangle DMLG

= length × width

= 30 × 8

= 240 square feet

wish that helped :)

Step-by-step explanation:

Answer:

THIS IS FALSE.

Step-by-step explanation:

MARK BRAINLIESSSTTTTT I NEED 2 MORE SO I CAN RANKUPP

\(d^2=(x_2-d_1)^2+(y_2-y_1)^2\\ \\ d^2=(9-1)^2+(18-12)^2\\ \\ d^2=64+36\\ \\ d=\sqrt{100}\\ \\ d=10\)

Answer:

simple interest=$97.50.

compound interest= $100.668

Step-by-step explanation:

Given:

Principal (P) = $750

Rate (R) = 6.5% (in decimal form, 0.065)

Time (T) = 2 years

Simple Interest = Principal*Rate*Time

Using the formula, the simple interest is calculated as follows:

Simple Interest = $750*0.065*2 = $97.50

Therefore, the simple interest for $750 with a 6.5% interest rate over 2 years is $97.50.

Again:

Compound Interest = Principal*(1 + Rate)^(Time)-Principal

Using the same values as above, the compound interest can be calculated as follows:

Compound Interest = $750*(1+0.065)^(2)-$750

= $750*1.065^2 -$750

= $750 × 1.134225 - $750

= $850.66875-$750

= $100.668

Therefore, the compound interest for $750 with a 6.5% interest rate over 2 years is $100.668

Answer:

Step-by-step explanation:

To solve the homogeneous differential equation:

dy/dx = (y^2 + x^2)/x^2

We first need to rewrite it in a homogeneous form by dividing both sides by y^2:

dy/dx = (1 + x^2/y^2)/(x^2/y^2)

Let u = y/x, then we can substitute y = ux and dy/dx = u + x(du/dx) into the differential equation to get:

u + x(du/dx) = (1 + u^2)/x^2

Rearranging and separating variables:

x(du/dx) = (1 + u^2 - u)/x

dx/x = (1 - u + u^2)/x * du

Integrating both sides:

ln|x| = ∫(1 - u + u^2)/u du + C

ln|x| = u - 0.5ln|u^2 - u + 1| + C

Substituting back u = y/x:

ln|x| = y/x - 0.5ln|(y/x)^2 - y/x + 1| + C

Simplifying:

ln|x| = y/x - 0.5ln|y^2 - xy + x^2| + C

Exponentiating both sides:

|x| * e^(y/x) = Ce^(-0.5ln|y^2 - xy + x^2|)

|x| * e^(y/x) = C|y^2 - xy + x^2|^-0.5

Squaring both sides and simplifying:

(x^2 + y^2)e^(2y/x) = D

where D = C^2. This is the general solution to the homogeneous differential equation.

The median of the distances is M = 6.5 kilometers

Given data ,

To find the median of a set of numbers, we arrange the numbers in ascending order and then locate the middle value. If there is an odd number of values, the median is the middle number. If there is an even number of values, the median is the average of the two middle numbers.

Arranging the given set of numbers in ascending order: {4, 5, 8, 11}

Since the set has an even number of values, the median is the average of the two middle numbers. In this case, the two middle numbers are 5 and 8. To find the average, we add these two numbers and divide by 2:

(5 + 8) / 2 = 13 / 2 = 6.5

Hence , the median of the given set {4, 5, 8, 11} is 6.5

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You would expect to find the middle 98% of most averages for the lengths of pregnancies in the sample between approximately 264.0 days and 274.1 days.

To find the range in which you would expect to find the middle 98% of most pregnancies, you can use the concept of z-scores and the standard normal distribution.

For the given data:

Mean (μ) = 269 days

Standard deviation (σ) = 17 days

To find the range, we need to find the z-scores corresponding to the 1% and 99% percentiles. Since the normal distribution is symmetric, we can find the z-scores by subtracting and adding the respective values from the mean.

To find the z-score for the 1% percentile (lower bound):

z1 = Φ^(-1)(0.01)

Similarly, to find the z-score for the 99% percentile (upper bound):

z2 = Φ^(-1)(0.99)

Now, we can calculate the z-scores:

z1 = Φ^(-1)(0.01) ≈ -2.33

z2 = Φ^(-1)(0.99) ≈ 2.33

To find the corresponding values in terms of days, we multiply the z-scores by the standard deviation and add/subtract them from the mean:

lower bound = μ + (z1 * σ) = 269 + (-2.33 * 17) ≈ 229.4 days

upper bound = μ + (z2 * σ) = 269 + (2.33 * 17) ≈ 308.6 days

Therefore, you would expect to find the middle 98% of most pregnancies between approximately 229.4 days and 308.6 days.

Now, let's consider drawing samples of size 58 from this population. The mean and standard deviation of the sample means can be calculated as follows:

Mean of sample means (μ') = μ = 269 days

Standard deviation of sample means (σ') = σ / sqrt(n) = 17 / sqrt(58) ≈ 2.229

To find the range in which you would expect to find the middle 98% of most averages for the lengths of pregnancies in the sample, we repeat the previous steps using the mean of the sample means (μ') and the standard deviation of the sample means (σ').

Now, calculate the z-scores:

z1 = Φ^(-1)(0.01) ≈ -2.33

z2 = Φ^(-1)(0.99) ≈ 2.33

Multiply the z-scores by the standard deviation of the sample means and add/subtract them from the mean of the sample means:

lower bound = μ' + (z1 * σ') = 269 + (-2.33 * 2.229) ≈ 264.0 days

upper bound = μ' + (z2 * σ') = 269 + (2.33 * 2.229) ≈ 274.1 days

Therefore, you would expect to find the middle 98% of most averages for the lengths of pregnancies in the sample between approximately 264.0 days and 274.1 days.

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Slope of regression is 0.8710 and at 4 tons top speed of boat is 111.064 mph.

Linear regression is a data analysis technique that predicts the value of unknown data by using another related and known data value. It mathematically models the unknown or dependent variable and the known or independent variable as a linear equation.

Given, In a study of the performance of a new engine design, the weight of 12 speed boats (in tons) and the top speed (in mph) were recorded.

Solution(a)

Given in the question

Dependent variable is top speed of a boat (in mph) Independent variable is weight of boat (in tons)

from the coefficient table of Enova summary we can write least square regression line as follows

Top speed = 107.58 +0.8710* Weight of boat

Here intercept of regression line = 107.58

Slope of regression line = 0.8710

Solution(b)

if X = 4 tons

than predictive value of the top speed of a boat can be calculated as

Top speed = 107.58 +0.8710 * 4 = 107.58 +3.484 = 111.064 mph predictive value of the top speed of a boat = 111.064 mph if its weigh It is 4 tons.

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Complete question:

Matching of the functions domain and range are as follows:

f(x)   = 4-4x ;

Domain:{0,1,3,5,6}

Range;{-20,-16,-8,0,4}

f(x) = 5x - 3

Domain:{-2,-1,0,3,4}

Range:{-13,-8,-3,12,4}

f(x) = -10x

Domain:{-4,-2,0,2,4}

Range:{-40,-20,0,20,40}

f(x) = (3/x) + 1.5

Domain:{-3,-2,-1,2,6}

Range:{0.5,0,-1.5,3,2}.

1) The function f(x) = 4 - 4x

Take Domain:{0,1,3,5,6}

If, we take x=0 and put in the function then we get

f(x)=4-0

f(x)=4

put x=1

f(x) = 4 - 4 =0

put x=3 then we get

f(x)=4-12=--8

put x=5 them we get

f(x)=4-20=-16

put x=6 then we get

f(x)=4-24=-20

Therefore ,range:[-20,-16,-8,0,4}

2) The function f(x)=5x-3

Take domain{-2,-1,0,3,4}

Now, put x=-2 in the function then we get

f(x) = -13

now put x=-1 then we get

f(x)=-5-3=-8

Put x=0 then we get

f(x)=0-3=-3

Put x=3 then we get

f(x)=15-3=12

Put x=4 then we get

f(x)=20-3=17

Therefore , range:{-13,-8,-3,12,17}

3) The function f(x)=-10x

Take domain:{-4,-2,0,2,4}

Put x=-4 in the function then we get

f(x)=40

Put x= -2 then we get

f(x)=20

Put x=0 then we get

f(x)=0

Put x=2 then we get

f(x)=-20

Put x=4 then we get

f(x)=-40

Therefore , range :{-40,-20,0,20,40}

4) The function f(x)= (3/x) + 1.5

Take domain:{-3,-2,-1,2,6}

Put x= -3 in the taken function then we get

f(x)=-1+1.5=0.5

put x=-2 then  we get

f(x)= -1.5+1.5=0

Put x=-1 then we get

f(x)=-3+1.5=-1.5

Put x= 2 then we get

f(x)=1.5+1.5=3

Put x= 6 then we get

f(x)=0.5+1.5=2

Therefore, range : {0.5,0,-1.5,3,2}.

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Answer:

The triangles are similar.

Explanation:

Similar triangles have 3 pairs of congruent angles. In this diagram, we can see that the triangles WXP and WYZ share angle W, which is congruent to itself; therefore, they have at least 1 pair of congruent angles. We are given that angle X is congruent to angle Y, so that is a second pair of congruent angles. Finally, we know that angle P is congruent to angle Z because if two pairs of corresponding angles are congruent, then the third pair must also be congruent because the measures of the interior angles of both triangles have to add to 180°.

Answer: -6, not 60

Step-by-step explanation:

Negative+Positive=Negative  

Positive+Positive=Negative

Negative+Negative=Positive

Question 6

Given:

QR = RS

QR = x + 6

RS = 4x

To find:

Length of line segment QS

Steps:

We know QR = RS, so substituting we get,

x + 6 = 4x

     6 = 4x - x

     6 = 3x

  6/3 = x

     2 = x

      x = 2

Now,

QS = QR + RS

QS = x + 6 + 4x

QS = 2 + 6 + 4(2)

QS = 2 + 6 + 8

QS = 8 + 8

QS = 16 units

Therefore, the length of QS is 16 units

Question 7

Given:

QR = RS

QR = 2x - 2

RS = 2x

To find:

Length of line segment QS

Steps:

We know that QR = RS, so substituting the values we get,

          QR = RS

      3x - 2 = 2x

3x - 2 - 2x = 0

     3x - 2x = 2

               x =2

Now,

QS = QR + RS

QS = 3x - 2 + 2x

QS = 3(2) - 2 + 2(2)

QS = 6 - 2 + 2(2)

QS = 6 - 2 + 4

QS = 4 + 4

QS = 8 units

Therefore, the length of QS is 8 units

Happy to help :)

If u need any help feel free to ask

Answer:

6.) QS = 16

7.) QS = 8

Step-by-step explanation:

The midpoint splits the segment into 2 equal segments. Therefore, set both expressions equal to each other and solve for x.

6.)

\(QR=RS\\\\x+6=4x\\\\x+6-x=4x-x\\\\6=3x\\\\\frac{6}{3}=\frac{3x}{3}\\\\2=x\\\\\\QR+RS=QS\\\\(2)+6+4(2)=QS\\\\16=QS\)

7.)

\(QR=RS\\\\3x-2=2x\\\\3x-2-3x=2x-3x\\\\-2=-x\\\\\frac{-2}{-1}=\frac{-x}{-1}\\\\2=x\\\\\\QR+RS=QS\\\\3(2)-2+2(2)=QS\\\\8=QS\)

The function f(x) = 4x⁵ - 3x + 2x³ has it's end behavior as f(x) ⇒ -∞ as x ⇒- ∞ and f(x) ⇒ ∞ as x ⇒∞

Since the leading term of the polynomial (the term in the polynomial which contains the highest power of the variable) is 4x⁵ and the highest degree is 5 which is odd and the leading coefficient is 4 which is positive.

as f(x) ⇒ -∞ as x ⇒- ∞ and f(x) ⇒ ∞ as x ⇒∞

The function f(x) = 4x⁵ - 3x + 2x³ increases or decreases uniformly till infinity.

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Answer:

the first two answers you put are correct but the last one you selected is incoorect, but the one that says segment AB is congruent to segment CB is correct

Step-by-step explanation:

so the correct answers are

A. segment AD is congruent to segment DC

C. angle ADE is congruent to angle CDE

D. segment AB is congruent to segment CB

HOPE THIS HELPS!

Answer:

d .

x=11

Step-by-step explanation:

ML and JK are chords of the circle

MN*LN=JN*KN

(x-7)*(x+21)=(x+5)*(x-3)

x^2+21x-7x-7*21=x^2-3x+5x-5*3

x^2+14x-147=x^2+2x-15

x^2-x^2+14x-2x=147-15

12x=132

x=132/12=11

Answer:

my answer is c

Step-by-step explanation:

The option A is correct

In other words, the amount of heat entering the system must be greater than the amount of mechanical effort leaving the system.

Recall the first law of thermodynamics' ideas in order to comprehend this.

dQ = dU + dW

Assuming perfect conditions. There is no heat loss outside. No matter how much heat we give the gas dQ , some of it will be utilised to boost the gas's internal energy while the rest will be used to produce work. This must be less than dQ in turn.

Because of this extremely fundamental characteristic of all engines, none of them can operate at 100% efficiency. Even the "Carnot engine," the most ideal engine, is not entirely efficient.

The option A is correct

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