A company can sell 2000 magazine subscriptions at $40 each. For each $5 increase in the price, it will sell 200 fewer subscriptions. What subscription price will provide the maximum revenue for the company?

$55

$40

$45

$50

The equation is y = 2x - 12

Equation in slope intercept form is

[tex]y = mx + b[/tex]

Where,

m = slope

b = y-intercept

Putting the value of slope in this equation:

[tex]y = 2x + b[/tex]

From this we can solve the equation for b

[tex]b = y - 2x[/tex]

[tex]b = -2 - 2(5)[/tex]

[tex]b = -12[/tex]

Now, the equation of y-intercept becomes

[tex]y = 2x - 12[/tex]

Answer:

0,1 and 2 on edg

Step-by-step explanation:

The function that models the total cost of the repair service as a function of the number of hours, [tex]\( h \),[/tex] is given by:  [tex]\[ C(h) = 75 + 55h \][/tex]

  In this situation, the appliance repair service charges a fixed amount of  [tex]75[/tex] for making a service call, regardless of how long the repair takes. This is the flat fee component of the cost. Additionally, the service charges [tex]55[/tex] for each hour of work performed by the technician. This is the hourly rate component of the cost.

 To model the total cost as a function of the number of hours [tex]h[/tex] that the repair takes, we start with the flat fee of [tex]75[/tex]. We then add the product of the hourly rate [tex]55\\[/tex] and the number of hours [tex]\( h \)[/tex]. This gives us the total cost function:

[tex]\[ C(h) = \text{Flat Fee} + (\text{Hourly Rate} \times h) \][/tex]

[tex]\[ C(h) = 75 + 55h \][/tex]

 Here, [tex]\( C(h) \)[/tex] represents the total cost in dollars as a function of the number of hours [tex]\( h \)[/tex] spent on the repair. The term [tex]\( 75 \)[/tex] is the fixed cost, and [tex]\( 55h \)[/tex] represents the variable cost that depends on the number of hours worked.

 This linear function correctly models the total cost of the repair service based on the given rates and the time spent on the repair.

The 6th number is in the pattern 0.08, 0.4, 2, 10 is 250 because the sequence represents a geometric sequence option (B) is correct.

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

Divergent sequences are those in which the terms never stabilize; instead, they constantly increase or decrease as n approaches infinity, approaching either infinity or -infinity.

It is given that:

The first four numbers of the pattern are shown below:

0.08, 0.4, 2, 10

The above sequence represents the geometric sequence.

The common ratio = second term/first term

The common ratio = 0.4/0.08

The common ratio = 5

The nth term of the geometric sequence:

a(n) = a(r)ⁿ⁻¹

a(n) = 0.08(5)ⁿ⁻¹

Plug n = 6 in the above expression:

a(6) = 0.08(5)⁶⁻¹

After calculating:

a(6) = 250

Thus, the 6th number is in the pattern 0.08, 0.4, 2, 10 is 250 because the sequence represents a geometric sequence.

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Answer:

D) Column: In a Band, Not in a Band; Row: Play a Sport, Do Not Play a Sport

Answer: Option 'D' is correct.

Step-by-step explanation:

Since we have given that

Number of students in the band = 48

Number of students both play in the band and play a sport = 24

Number of students who are not in band and do not play a sport = 22

Total number of students = 80

so, we will make a table:

                                 In a band          Not in a band

Play a sport                  24                         10    

Don't play a sport         24                         22

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

Total                               48                  (80-48) = 32

So, Column: In a Band, Not in a Band; Row: Play a Sport, Do Not Play a Sport.

Hence, Option 'D' is correct.

There would be 4 groups of 8 coins. 32/8=4 Hope I could help!!!

The correct answer is u/v+9/v= 9u/v

A and A

the equation of a parabola in vertex form is

y = a(x - h)² + k

where ( h, k ) are the coordinates of the vertex and a is a multiplier

y = - 2(x + 3)² + 2  is in this form

with vertex = ( - 3, 2)

To find the y-intercept let x = 0

y = - 2(3)² + 2 = - 18 + 2 = - 16

Similarly

y = - 2(x + 2)² + 2 is in vertex form

vertex = ( - 2 , 2)

x = 0 : y = - 2(2)² + 2 = - 8 + 2 = - 6 ← y- intercept

The formula for the correlation coefficient is quite messy. I suggest checking some websites discussing this and am also attaching the formula how to calculate it by hand (the ∑'s mean summation over all the elements listed.

But unless your teacher does not allow using online calculators, you can use them. I used python's function to process the data in the table and the result is approximately -0.81. So that's your answer.

Negative value like -0.81 means that the variables x and y are quite "anit-correlated" meaning the value behave like opposites: when x is small, y tends to be large, and vice versa.  

Answer:

-0.81

Step-by-step explanation:

x y xy

12 6 72

13 21 273

14 14 196

6 28 168

25 2 50

31 1 31

1 67 67

Total   857

Mean 14.57142857 19.85714286 214.25

Std dev 10.37396007 23.06099572  

Cov (x,y) -75.09693878  

Correlation coefficient is obtained by the formula

r = {E(xy)-E(x)E(y)}/(std dev x )(std dev y)

From the data we find x bar=14.57 and y bar = 19.86

STd dev of x = 10.37 and y = 23.06

E(xy) = average of product x and y = 214.25

Hence substitute to get r = -0.81

The ____ is used to determine the left-hand and right-hand behavior of the graph of a polynomial function.

When largest exponent of the polynomial is even and leading coefficient is positive , then left hand and right hand ends of the graph goes up

When largest exponent of the polynomial is even and leading coefficient is negative , then left hand and right hand ends of the graph goes down

When largest exponent of the polynomial is odd and leading coefficient is positive , then left hand graph goes down and right hand ends of the graph goes up

When largest exponent of the polynomial is odd and leading coefficient is negative , then left hand graph goes up and right hand ends of the graph goes down

Hence, Leading coefficient test is used to determine the left-hand and right-hand behavior of the graph of a polynomial function.

The leading coefficient test is used to determine the left-hand and right-hand behavior of the graph of a polynomial function.

The correct choice to fill in the blank is Leading coefficient test.

The leading coefficient, which is the coefficient of the highest power term in a polynomial function, helps determine the behavior of the graph. If the leading coefficient is positive, the graph will have an upward (right-hand) behavior, while if the leading coefficient is negative, the graph will have a downward (left-hand) behavior.

For example, in the polynomial function f(x) = 3x^3 - 2x^2 + 5x - 1, the leading coefficient is 3. Therefore, the graph of this function will have an upward (right-hand) behavior.

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Remark

The diameter of the circle is AC. The hypotenuse of the right triangle is also AC. This assumes that A,B and C all lie on the circumference of the circle.

Answers

One

The center of the circle is on the diameter of the circle. In fact, the center bisects the diameter. So the center lies on AC and if the center is labeled O then AO = BO.

Answer 1: AC

Two

The answer is the single word diameter.

answer=3.20/16=0.20 is cost per ounce

Remark

How does this poor soul survive?

Solution

Let the number of faults he has in his teens = x

1/7 of (of means multiply) those faults were there at birth.

1/7 x = 326     Solve for x by multiplying by 7

7* (1/7 x) = 326 * 7

x = 2282 is the number of faults Patrick has. Answer

Answer: sin2y =240/289 where 0<y <π/2

Step-by-step explanation:

Given  sin(x) = 1/3 and sec(y) = 17/15 , where x and y lie between 0 and π/2.

We now that

[tex]cosy = \frac{1}{secy} =\frac{15}{17} \\and\\\text{using identity } sin^2y+cos^2y=1\\\text{we have}\\siny=\sqrt{1-cos^2y}=\sqrt{1-(\frac{15}{17} )^2}=\sqrt{1-\frac{225}{289} }=\sqrt{\frac{64}{289} }=\frac{8}{17} \\\Rightarrow\ siny=\frac{8}{17} \\\text{Now we are using identity sin2A=2sinAcosA we have}\\sin2y=2\cdot\ siny\cdot\ cosy=2\cdot\ \frac{8}{17} \cdot\ \frac{15}{17} =\frac{240}{289}[/tex]

To solve the question, we firstly find cos(y) from 'sec(y) = 17/15' because secant is the reciprocal of cosine. Then, we use the Pythagorean identity to find sin(y). Finally, we substitute these values into the double angle identity 'sin(2y) = 2sin(y)cos(y)' to find the final answer.

In this high school level mathematics problem, 'sin(x) = 1/3' and 'sec(y) = 17/15' are given. From 'sec(y) = 17/15', we can calculate cos(y) because secant is the reciprocal of cosine. Hence, 'cos(y) = 15/17'. The question asks for the evaluation of the expression 'sin(2y)'. Here, we can use a trigonometric identity for double angles, which states 'sin(2y) = 2sin(y)cos(y)'.

However, we are only given secant of y, not sine. To find sin(y), we can use the Pythagorean identity. According to this identity, 'sin^2(y) = 1 - cos^2(y)'. So, 'sin(y) = sqrt[1 - (15/17)^2]'.

So, the final answer becomes 'sin(2y) = 2 * √[1 - (15/17)²] * 15/17'. It's useful to note that you should always check that your angle lies within the given range when using a square root in trigonometry, to ensure your answer is correct.

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Answer: Option C. 8,064 pounds

Solution:

Unit weight: U=63 pounds/foot^3

Total Weight: W=?

W=U*V

Volume: V

Length: l=8 feet

Width: w=4 feet

Height: h=4 feet

V=l*w*h

Replacing the knwon values in the formula above:

V=(8 feet)*(4 feet)*(4 feet)

V=128 feet^3

Replacing in the formula of total Weight:

W=U*V

W=(63 pounds/foot^3)*(128 feet^3)

W=8,064 pounds

Final answer:

To calculate the weight of one cord of red oak, multiply the cord's volume (128 cubic feet) by the density of red oak (63 pounds/cubic foot), which results in 8,064 pounds.

Explanation:

To answer this question, we will calculate the weight of one cord of red oak by multiplying the volume of a cord by the weight per cubic foot.

Therefore, one cord of red oak weighs 8,064 pounds, which matches option C.

area = 98 cm²

the area of a rectangle = length × width

here length = 14 and width = 7

area = 14 × 7 = 98 cm²

Answer:  b. $3,374.65

Step-by-step explanation:

The exponential equation of growth (continuously) is given by :-

[tex]y=Ae^{rx}[/tex], where A is the initial amount, r is the rate of growth ( in decimal) and x is the time period.

Given : You invest $2,500 in an account that grows 5% each year.

i.e.  A= $2,500  and r= 5%=0.05

Then, the equation model this situation will be :-

[tex]y=2500e^{0.05x}=2500(1.05)^x[/tex]

Now, At x= 6

[tex]y=2500e^{0.05\times6}\\\\\Rightarrow\ y=2500e^{0.3}=3374.64701894\approx3374.65[/tex]

Hence, the investment amount after 6 years will be $3,374.65.

The amount of the investment after 6 years is $3,374.65

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

Inital value, a = $2500

Rate of increase, r = 5%

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

The function of the situation is

f(x) = a * (1 + r)ˣ

Substitute the known values in the above equation, so, we have the following representation

f(x) = 2500 * (1 + 5%)ˣ

So, we have

f(6) = 2500 * (1 + 5%)⁶

Evaluate

f(6) = $3,374.65

Hence, the amount is $3,374.65

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So,

1400 people in total. Though, subtract 200 for the amount of extra adults. This makes 1200. Divide that by two. You get 600

You need to add 200 to the 600 to get the amount of adults. The amount of adults on board is 800.

The amount of children on board is 600.

600 plus 800 equals 1400, it makes sense. :P

To find the number of children on the ship, we can set up an equation based on the given information and solve for x. The number of children can be represented as x, and the number of adults can be represented as x + 200.

Let's use x to represent the number of children on the ship. Since there are 200 more adults than children, the number of adults can be represented as x + 200. We know that the total number of people on board is 1400, so we can set up the equation: x + (x + 200) = 1400.

Combining like terms, we get 2x + 200 = 1400. Subtracting 200 from both sides gives us 2x = 1200. Dividing both sides by 2, we find x = 600.

Therefore, there are 600 children on the ship.

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Answer:

Step-by-step explanation:

A vertical stretch by a factor of k means that the point (x, y) on the graph of f (x) is transformed to the point (x, ky) on the graph of g(x), where k <1.

If k =1, then same graph we obtain and if k>1 we get a vertically shrink graph.

In our question, there is a vertical stretch of 3. This means new graph would have points as (x,y/3)

i.e. instead of f(x) = y, we have now f(x) = y/3

So transformation is g(x) = 3f(x)

Option A is correct.

2) Here f(x) = 3x+8 is transformed to g(x) =3x+6

i.e. y intercept is reduced by 2 units.  Hence there is a translation of 2 units down.

I did not have the answer to the second question but here is the first.

Answer:

Option A is right.

Step-by-step explanation:

For answering this question we must understand what is a function.

A function is different from mapping.

Mapping is just a subset of AxB where A and B are two sets.

But function is constrained to the point that elements of I set will have unique image in second set.

We find From the options

in option A, each of 2,-2, 5 and 7 have unique images.  Hence it is a function.

But in option B,, we find that 3 has two images 5 and 2.  i.e. 3 does not have unique image. Hence not a function.

Similarly  in option C,, we find that -3 has two images 4 and 1.  i.e. -3 does not have unique image. Hence not a function

and  in option D,, we find that 5 has two images 1 and -4.  i.e. 5 does not have unique image. Hence not a function.

Only first option is a function.

answer is

f (x) = 108. (2/3)x

Answer:

The correct graph is graph C

Step-by-step explanation:

Given that a sequence defined by the function f(x + 1) =[tex]\frac{2}{3}[/tex] f(x)

Also given that initial value is 108

i.e. f(0) = 108

Applying the recurrence formula given we get

f(0+1) = 2/3 f(0) = 2/3 (108) = 72

Hence (1,72) should be next point

Now we have

f(2) = f(1+1) = 2/3 f(1) = 2/3 (72) =48

(2,48) is next point

f(3) = f(2+1) = 2/3 f(2) = 2/3 (48) = 32

(3,32) is the next point

The graph covering all these points is the graph C

Hence answer is graph C

[tex]\text{The formula of a perimeter of a rectangle:}\\\\P=2(w+l)\\\\\text{we have}\\w:l=3:2\to w=\dfrac{3}{2}l,\ P=55\ cm\\\\\text{substitute}\\\\55=2\left(\dfrac{3}{2}l+l\right)\\\\55=2\cdot\left(\dfrac{3}{2}l+\dfrac{2}{2}l\right)\\\\55=2\cdot\dfrac{5}{2}l\\\\55=5l\ \ \ \ \ |:5\\\\l=11\ cm\\\\w=\dfrac{3}{2}\cdot11=\dfrac{33}{2}=16.5\ cm\\\\Answer:\ b.\ 11\ cm,\ 11\ cm,\ 16.5\ cm,\ 16.5\ cm[/tex]

The answer is B hope this helped

Answer:b

Step-by-step explanation:

Answer:

Option 3 (7,2) is right answer.

Step-by-step explanation:

Given two equations

3x-2y=17    ... i

x-3y=1         ... ii

We can solve this by elimination.

coefficients of x are 3 and 1 with LCD = 3

Hence multiply ii equation by 3

3x-9y = 3  ... iv

3x-2y = 17  ... i

Subtract i from iv

-7y = -14

Divide by -7

y =2

Substitute in ii

x-3(2) = 1

x=7

Hence solution is (7,2)

Verify:

We can verify our solution by substituting in i and ii.

3(7)-2(2) = 17 and 7-6 =1

Verified

Answer:

Angelica's bouquet has 7/12 pink roses.

Step-by-step explanation:

A dozen is defined to be a set of 12 in number or group pf anything. Here, in this case we have roses so a dozen of roses means '12 roses'.

5 of the roses in the bouquet are white roses, so the fraction of white roses will be 5 divided by the total number of roses i.e. 12:

White roses =  [tex]\frac{5}{12}[/tex]

Rest of the roses are pink, so we can simply subtract 5 from 12 to get the number of roses which will be 12 - 5 = 7

Or

we can subtract the fraction of white roses from 1 to get the fraction of pink roses in the bouquet:

Pink roses = [tex]1 - \frac{5}{12}[/tex] = [tex]\frac{7}{12}[/tex]

In △BAH and △CAK

AB = AC   (Given congruent sides of triangle)

m∠BAK = m∠CAH ( Given congruent angles)

AH = AK   (Given congruent sides of triangle)

Therefore, triangle △BAH congruent to triangle △CAK.

△BAH ≅ △CAK by (Side Angle Sngle or SAS triangle congruency postulate).

Therefore, m∠K = m∠H  (Congurent parts of the congruent triangles are congruent).

36

area of square = s²

given s = 6 , then

area = 6² = 36

Length of a side is considered to calculate area of a square. The area of a square can be defined as the number of square units needed to fill a square.  

The formula to calculate Area of square is:

                                     [tex]\rm Area\: of\:square = \rm side^2[/tex]

We need to calculate area of a square with sides [tex]\rm\\6 \:centimetres[/tex].

As per above stated formula:

Area of square is square of length of its sides.

[tex]\begin{aligned}\rm Area\:of\: square &= \rm side^2\\&= 6^2\\&= 36\end[/tex]

Therefore, the area of square with side 6 is 36.

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