Express the given product as a sum or difference containing only sines or cosines.
sin (4x) sin (2x)
sin(4x) sin (2x) =________ (Simplify your answer.)

Answer:

The  revenue is [tex]R(9) = \$ 876.9[/tex]

Step-by-step explanation:

From the question we are told that

  The  rate of change  in revenue for Under Armour from 2004 through 2009 is  

   [tex]\frac{d R }{dt } = 13.897t + \frac{284.653}{t}[/tex]

Now  

     [tex]dR = (13.897t + \frac{284.653}{t})dt[/tex]

Integrating both sides to obtain R(t)

     [tex]\int\limits dR = \int\limits (13.897t + \frac{284.653}{t})dt[/tex]

    [tex]\int\limits dR = \int\limits (13.897\frac{t^2}{2} + 284.653(ln (t)) ) + C[/tex]

=>   [tex]R(t) = 6.9485t^2 + 284.653(ln (t) ) + C[/tex]

From the question we have that at  t  = 8  [tex]R(8)= \$ 725.2 \ million[/tex]

   [tex]725.2 = 6.9485(8)^2 + 284.653(ln (8) ) + C[/tex]

=>   [tex]C = -311.4[/tex]

So  

    [tex]R(t) = 6.9485t^2 + 284.653(ln (t) ) -311.4[/tex]

At  t = 9  

   [tex]R(9) = 6.9485*(9)^2 + 284.653(ln (9) ) -311.4[/tex]

     [tex]R(9) = \$ 876.9[/tex]

Answer:

(-3/4)x^2 + 6x = 3

Step-by-step explanation:

It takes 8 seconds for the ball to reach its maximum height and then return to ground level; thus, the highest point (vertex) the ball will reach is reached after 4 seconds.  The graph showing this motion is a parabola that opens down.  Thus, the coefficient 'a' must be negative.

Returning to a * x ^ 2 + bx + c, we write out two instances of this formula, one for x = 0 and the other for x = 8.  This is because {0, 8} are the x-intercepts.

Then, for x = 0, a * x ^ 2 + bx + c   becomes  a * 0 ^ 2 + b*0 = 0,

and for x = 8,  a * x ^ 2 + bx + c  becomes  a(8)^2 + b(8) + c = 0

The first equation tells us that 'c' must be 0.  The second equation tells us that  64a + 8b = 0, which is equivalent to 8a = -b, or a = -b/8.

We then have the quadratic function  (-b/8)x^2 + bx + 0.  All we have to do now is to find the value of b.  The vertex of this parabola is (4, 12), and so the quadratic becomes

(-b/8)(4)^2 + b(4) = 12.  To solve this for b, multiply all terms by 8:

-b(16) + 32b = 96, or

16b = 96, or b = 6.  Since a = -b/8 (see above), a = -6/8 or a = -3/4.

Then the equation of motion is

height of ball = (-3/4)x^2 + 6x

We want to know when the ball is at a height of 3 m.  Thus, set this equation of motion = to 3 and solve for x (the times at which height = 3 m):

(-3/4)x^2 + 6x = 3            This is the desired quadratic equation.

Answer:

-3

Step-by-step explanation:

Slope = [tex]\frac{y_{2} -y_{1}}{x_{2} - x_{1} }[/tex]

slope  = 6 - -9/ -4 - 1

slope = 15 / -5

slope = -3

Answer:

discrete probability distribution

Step-by-step explanation:

A discrete probability distribution is a term that describes a form of a probability distribution that is used in a situation where the set of possible outcomes is discrete.

While it also has a tendency to take on a countable number of values, it is a probability distribution where a sample is drawn from a larger population, this sample points possess an empirical distribution that is considered to be discrete, which resulted in information about the population distribution.

Hence, given that Bob is dealing with discrete data and the samples are drawn without replacement, the likely probability distribution is DISCRETE PROBABILITY DISTRIBUTION

Answer:-1

Step-by-step explanation:

Do Rise-over-run which is -1/1 (y over x)

Answer:

-1

Step-by-step explanation:

Pick two points on the line

(-2,0)  and ( 0,-2)

Using the slope formula

m = (y2-y1)/(x2-x1)

    = (-2-0)/(0 - -2)

    ( -2-0)/(0+2)

   -2/2

   -1

Answer:

C) P(x)=1.10x+25

Step-by-step explanation:

The algebraic expression for the amount Ana will pay for furniture with a pretax price of x dollars = 1.1x + 25

An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations.

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Answer:

15 days

Step-by-step explanation:

It seems that the fines are 10x cents for every x days overdue. Therefore, 10x = 150 (150 because $1.50 is 150 cents) so x = 15 days.

Answer:

D.) MC≅MC

Step-by-step explanation:

We already know that the hypotenuses are the same (because of that tiny line), so we need the legs (HL: hypotenuse-leg). As we can see in the picture, MC is a shared side of both triangles, and this is also the leg. Option D is correct.

:Done

Answer:

Reject H0 as the critical region for alpha = 0.07 is  z ≤ -1.82  and z≥ 1.82

Step-by-step explanation:

For the significance level ∝ = 0.07

For a two tailed test we divide it with 2 and get 0.035

When we subtract 0.035 from 1 we get 0.965

And when we look at the z- table and corresponding to 0.965 we find the value of z to be 1.82

Now the calculated value of z=  -1.94 which is less than ±1.82.

Hence reject H0 if z ≤ -1.82  and z≥ 1.82

Therefore reject H0.

While ∝ =0.07

p- value = 0.06 should be examined

the p- value is the smallest value of ∝ where we reject H0.

Hence at ∝= 0.06  critical region is  z ≤ -1.88  and z≥ 1.88

At ∝= 0.05  critical region is  z ≤ -1.96  and z≥ 1.96

So p- value is near 0.06

The total number of children who attended play is 10 and this can be determined by forming the linear equation in two variables.

Given :

The following steps can be used in order to determine the total number of children attending play:

Step 1 - Let the total number of adults attending play be 'x' and the total number of children attending play be 'y'.

Step 2 - The linear equation that represents the total number of people attending the play is:

x + y = 40

x = 40 - y    --- (1)

Step 3 - The linear equation that represents the price of all the tickets is:

12x + 8y = 440    --- (2)

Step 4 - Now, substitute the value of 'x' in the above expression.

12(40 - y) + 8y = 440

Step 5 - Simplify the above expression.

480 - 12y + 8y = 440

40 = 4y

y = 10

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Answer:

55mph

None of the option is correct

Step-by-step explanation:

Let v be the speed and t as the time taken. If speed varies inversely as the time it takes to drive, then v ∝ 1/t.

v = k/t where k is the constant of proportionality.

IF it takes Kris 5 hours when driving at 55 mph, then v = 55mph when t = 5 hours.

Substituting this values into the formula above;

55 = k/5

k = 55*5

k = 275mp/hr²

To calculate the speed it will Martin to  drive for 5 hours, we will substitute k = 275 and t = 5 into the original equation v = k/t

v = 275/5

v = 55 mph

Hence, martin will also need to drive at 55mph to take 5 hours

Answer:

Rectangles

Step-by-step explanation:

Answer:

[tex]\Large \boxed{\mathrm{Rectangles}}[/tex]

Step-by-step explanation:

Figure A and figure B are rectangles.

Rectangles have opposite sides equal and parallel.

Rectangles have 4 right angles and 4 pairs of perpendicular sides.

Answer:

D) X′ (0, 6), Y′ (0, 0), Z′ (15, 0)

Step-by-step explanation:

From the image attached, given that the location of the triangle is at:

X(0, 2). Y(0, 0), Z(5, 0)

Transformation is the movement of a point from its initial position to a new position. A shape is transformed by transforming all the points in the shape. Types of transformations are reflection, rotation, dilation and translation.

A dilation produces the same shape but different size. If the dilation < 1, then it is a reduction but if dilation > 0 then it is an enlargement.

A point A(x, y) which is dilated by a factor of c at the origin has new coordinates at A'(cx, cy).

Since triangle XYZ is dilated by a factor of 3 with the center of dilation at the origin, this represents an enlargement and the new coordinates of the triangle are:

X'(3*0, 3*2) = X'(0, 6)

Y'(3*0, 3*0) = Y'(0, 0)

Z'(3*5, 3*0) = X'(15, 0)

Answer:

D

Step-by-step explanation:

Answer:

4^-2=1/16

Step-by-step explanation:

When we are multiplying exponents and the bases are the same, we add the exponents

4^6 * 4^-8

4^(6+-8)

4^-2

1/16

Answer:

11

Step-by-step explanation:

f(x) = 3x + 2

Let x = 3

f(3) = 3*3 +2

f(3) = 9+2

      = 11

Answer:

Step-by-step explanation:

f(x) = 3x + 2

In order to find f(3) substitute the value of x that's 3 into f (x) that's replace every x in f (x) by 3

That's

f(3) = 3(3) + 2

= 9 + 2

We have the final answer as

Hope this helps you

Answer:

15

Step-by-step explanation:

Because I said so

The distance from point F to point H is 15 units. Option C is correct.

In order to get the distance from point F to point H, we will use the distance formula as shown:

[tex]D =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Given the coordinate points F(0,0) and H(9, 12)

[tex]FH=\sqrt{(12-0)^2+(9-0)^2}\\FH =\sqrt{12^2+9^2}\\FH=\sqrt{144+81}\\FH=\sqrt{225}\\FH = 15units[/tex]

Hence the distance from point F to point H is 15 units. Option C is correct.

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Answer:

0

Step-by-step explanation:

Natural numbers or the counting numbers is all the positive, non-decimal numbers. They are 1, 2, 3... and so on. Natural numbers does not include 0.

Whole numbers are all the natural numbers with the addition of 0. In other words, whole numbers are: 0, 1, 2, 3... and so on.

Therefore, the only number that is a whole number and that's not a natural number is 0.

Answer: 0

Step-by-step explanation: The set of counting numbers, {1, 2, 3, 4, ...}

is called the set of natural numbers.

When we include 0 in the set of natural numbers,

the new set, {0, 1, 2, 3, ...} is called the set of whole numbers.

Notice that all natural numbers are

included within the set of whole numbers.

We can represent the relationship between these two

sets of numbers using the diagram shown below.

In fact, 0 is the only whole number that's not a natural number.

Answer:

0.1^5=0.00001

Step-by-step explanation:

[tex]0.1^5\\0.1^5=0.00001[/tex]

The answer is

A : x=-5

Answer:

A) Cross-sectional

Step-by-step explanation:

A cross-sectional study is a type of study that involves the data i.e. taken from a population for a specific time period.

Here study shows the peoples interest in variables that are be chosen

In the given situation, since a town obtains a data of the current employment for 10,000 of its total citizens

So this represents the cross-sectional

hence, the correct option is A.   Cross-sectional

Answer:

x=-1

Step-by-step explanation:

w-2=-8-5w

-2=-8-6w

+8 +8

6=-6w

divide 6 in both side

x=-1

hope this help.

Answer:

0

Step-by-step explanation:

In the roll of a pair of fair dice, The sample space is as follows:

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

If x,y represent  the  possible outcome of rolling the two die

Then the total number of possibilities for  the sample space = (x,y)

= (6 × 6) = 36

Now, the probability of getting a sum of 1 does not exist in the roll of a pair of  fair dice.

Therefore, Probability(1) = 0

Answer:

x=4

Step-by-step explanation:

Building an equation and solving it, it is found that the number is 4.

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

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

The equality is:

[tex]x^2 = 8x - 16[/tex]

[tex]x^2 - 8x + 16 = 0[/tex]

Applying the perfect square binomial:

[tex](x - 4)^2 = 0[/tex]

[tex]\sqrt{(x - 4)^2} = \sqrt{0}[/tex]

[tex]x - 4 = 0[/tex]

[tex]x = 4[/tex]

The number is 4.

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Answer:

Step-by-step explanation:

P= (l+w)

56 = 2(l+8)

56=2l+8

56-8= 2l

48=2l

Length=24

Area = ?

A = l×w

A=24×8

Area= 192inches²

Answer: c. 42%.

Step-by-step explanation:

P(ship A reaches target) : P(A) = 0.30

P(ship B reaches target) : P(B) = 0.60

P( Ship B not reaching target ) : P(B^c) = 1 - p(B) = 1 - 0.60 = 0.40

P( Ship A not reaching target ) : P(A^c) = 1 - p(B) = 1 - 0.30 = 0.70

NOW

define A for A wins

define A^c for A loss

define B for B wins

define B^c for B loss

A ⇒ P(A) = 0.30

A^c B^c A ⇒P(A^c B^c A) = 0.70 × 0.40 × 0.30

A^c B^c A^c B^c A ⇒ P(A^c B^c A^c B^c A) = ( 0.70 × 0.40)² × 0.30

↓↓↓

∴P(A survives) = sum of all probabilities

⇒ 0.30 + ( 0.70 × 0.40 × 0.30 ) + ( 0.70 ×0.40 )² × 0.30 +...........................

⇒ 0.30 [ 1 + ( 0.28) + (0.28)² +..........................]

Now sum of geometric series S∞ = a / 1-β = 1 / 1 - 0.28

∴ 0.30 × 1/1-0.28 = 0.42

now converting to percentage

0.42 × 100 = 42%

Ship A's survival probability is 42%

Answer:

B. VOLUNTARY RESPONSE

Step-by-step explanation:

The sampling method here is voluntary response.

Sampling methods are used to choose members from the population to be a part of a study.

There are different kinds of sampling methods used in different scenarios like simple random sample, stratified random sample, systematic random sample and cluster random sample.

There are also methods like voluntary response and convenience sample which are not that effective.

Voluntary response sample is a method of sampling by which researcher requests to members of a population to take part in the sample and the member decides to whether join or not to join in the sample.

Given study is an internet poll where the researches asks people to indicate whether or not they have a cable subscription. 1974 people responded to the poll fully on their consent.

Researcher has not selected or did any systematic method in selecting these members.

Hence the sampling study given here worked through voluntary response sampling.

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Answer:

g,h,m

Step-by-step explanation:

All three of these line segments are perpendicular on n (which acts as the base).

Therefore , g,h,m are corresponding heights

Answer:

the distance from Fresno to San Francisco on the second map is 75cm

Step-by-step explanation:

The scale on the first map is 1 cm to 20 km

The distance from Fresno to SanFrancisco is 15 cm

1cm/20km = 15cm

The scale on the second map is 1 cm to 100 km.

1cm/100km = x

X= 15cm*100km/20km *1cm/1cm

X=15cm *5

X= 75 cm

the distance from Fresno to San Francisco on the second map is 75cm