In 2008, the number of digital cameras shipped totaled 186 million. There were 24 million shipped in 2013. Find and
interpret the average rate of change in the number of digital cameras shipped per year.

Step-by-step explanation:

\(4\sin{x} + 3\cos{x} = 4\)

Move the sine term to the right hand side so it becomes

\(3\cos{x} = 4 - 4\sin{x}\)

Now take the square of the equation to get

\(9\cos^2{x} = 16 - 32\sin{x} + 16\sin^2{x}\)

Use the relation \(\cos^2{x} = 1 - \sin^2{x}\) to get

\(9 - 9\sin^2{x} = 16 - 32\sin{x} + 16\sin^2{x}\)

Collect all similar terms and we will get

\(25\sin^2{x} - 32\sin{x} + 7 = 0\)

Let \(y = \sin{x}\) so the above equation becomes

\(25y^2 - 32y + 7 = 0\)

Using the quadratic equation, the roots of the above equation are

\(y = 1, \frac{7}{25}\)

This means that

\( y = \sin{x} = 1 \Rightarrow x = 90°\)

and

\(y = \sin{x} = \frac{7}{25} \Rightarrow x = 16.26°\)

Answer:

The growth model that represents the population of this city is not linear--it is exponential:

\(f(t) = 10000( {1.025}^{t} )\)

\(t = 0 \: represents \: 2010\)

Answer:

Let random variable "x" be a count of player gain.

X-values are: 4, -1

P(x=4) = 1/6; P(x= -1) = 5/6

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

E(x) = (1/6)(4) + (5/6)(-1)

E(x) = [4-5]/6

E(x) = -1/6 = -17 cents

=============================

Cheers,

Stan H.

Answer:

should be 1305 yd^2

Step-by-step explanation:

to get the surface area of one of the 3 recanglular sides take 24 x 15 to get 360 then muliply by 3 to get 1080 since all the recanglular sides are the same then do 15 x 15 to get both of the triangle sides to get 225 since the equation is 1/2 B x H then add them together

Answer:

x >>>>>>>> f(x)

–9 >>>>>> 10

–7 >>>>>>> 0

0 >>>>>>>> –35

5 >>>>>>>> –60

Step-by-step explanation:

f(x) = –5(x + 7)

1. x = –9, f(x) =?

f(x) = –5(x + 7)

f(x) = –5(–9 + 7)

f(x) = –5(–2)

f(x) = 10

2. f(x) = 0, x =?

f(x) = –5(x + 7)

0 = –5(x + 7)

Divide both side by –5

0 / –5 = x + 7

0 = x + 7

Collect like terms

x = 0 – 7

x = –7

3. x = 0, f(x) =?

f(x) = –5(0 + 7)

f(x) = –5(7)

f(x) = –35

4. f(x) = –60, x =?

f(x) = –5(x + 7)

–60 = –5(x + 7)

Divide both side by –5

–60 / –5 = x + 7

12 = x + 7

Collect like terms

x = 12 – 7

x = 5

SUMMARY:

x >>>>>>>> f(x)

–9 >>>>>> 10

–7 >>>>>>> 0

0 >>>>>>>> –35

5 >>>>>>>> –60

P=160-70*cos(2π*(1/12)*t)

• Pressure in mathematics or physics is defined as force per unit area. The pressure exerted by a solid object which is resting on top of a solid surface is the weight divided by the area of the object . SI unit of force is Newton (N).

First, we find the amplitude by taking the difference between the peak values and dividing by two:

Amplitude=(230+90)/2=70

We can find the center value by either adding 70 to the minimum or subtracting 70 from the maximum:

90+70=160

230-70=160

This tells us that the Center Value=160

The frequency that we are operating at is given as:

f = 5/hour

so in minutes

f=5*(1/60)/minute=5/60=1/12 per minute

So, combining everything we get

P=160-70*cos(2π*(1/12)*t)

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The tree is approximately 12 feet tall to the nearest tenth of a foot.

We have,

To find the height of the tree, we can set up a proportion using the measurements of the shadow.

Since we know that Tyler is 6 feet tall and his shadow is 10 ½ feet long, we can set up the following expression:

Tyler's height / Tyler's shadow length = Tree's height / Tree's shadow length

6 feet / 10.5 feet = Tree's height / 21 feet

To find the tree's height, we can cross-multiply and solve for it:

6 feet x 21 feet = 10.5 feet x Tree's height

126 feet = 10.5 feet x Tree's height

Dividing both sides of the expression by 10.5 feet:

126 feet / 10.5 feet = Tree's height

12 feet = Tree's height

Therefore,

The tree is approximately 12 feet tall to the nearest tenth of a foot.

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The phrase can be expressed as 3x-6, 3(x-2), x+2x-2-4, 4x-x+4-10 and x+x+x-2-2-2 and so on

It consists of several mathematical symbols organized in such a way that it can express mathematical concept.

Mathematical  phrase can be written in one or more different pattern to show the same expression.

As per question given, the phrase is expressed by

3x-6, where x is used to represent a number

the phrase can be written in 3(x-2)

other variable expressions of same phrase are x+2x-2-4

or 4x-x+4-10 or x+x+x-2-2-2

hence, a phrase can be written in one or more pattern to show same expression.

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Answer:

5(6x-1)

Step-by-step explanation:

Step 1 Subtract the numbers:

6x[3+(4-2)]-10+5

6x[3+(2))]-10+5

Step 2 Add the Numbers:

6x[3+2]-10+5

6x[5]-10+5

Step 3 Multiply the Numbers:

6x*5-10+5

30x-10+5

So the answer is 5(6x-1).

Hope You understand.

9514 1404 393

Answer:

  A. 3 packs

  B. $78.84

Step-by-step explanation:

A. Two bottles for each of 26 guests is a total of 2×26 = 52 bottles.

That many bottles will be found in 52/18 = 2 16/18 packs of bottles. Since Eliana cannot purchase partial packs, she will need to buy 3 packs of bottles.

__

B. Each pack costs $26.28, so the cost of 3 packs is 3×$26.28 = $78.84. Eliana will spend $78.84 on water for her guests.

Step-by-step explanation:

x-intercept= -4

yintercept= -7

Answer:

T =54 degrees

since x=10

6x-6 =54

are you clear, if yes give me brainliest and if no draw my attention by hitting the comment section

Answer:

D

Step-by-step explanation:

1 + 4x and 57° are corresponding angles and are congruent , so

1 + 4x = 57 ( subtract 1 from both sides )

4x = 56 ( divide both sides by 4 )

x = 14

Answer:

\(\frac{2}{3}\)(-\(\frac{3}{5}\)) ÷ \(\frac{1}{4}\) = -\(\frac{2}{5}\) × \(\frac{4}{1}\)

            = -\(\frac{8}{5}\)

-\(\frac{3}{4}\)(-\(\frac{1}{7}\)) ÷ \(\frac{1}{2}\) = \(\frac{3}{28}\) × \(\frac{2}{1}\)

             = \(\frac{6}{28}\)

             = \(\frac{3}{14}\)

The effective tax rate for a taxable income of $115,500 is A) 18.71%

The introductory $10,275 is subjected to a 10% tax burden, with the converted dollar amount representing $1,027.50 in taxes. The additional taxable sum of $30,900 ($41,175 - $10,275) is accessed at a 12% charge and aggregates to $3,708 worth of duties. An extra levy of 22% is imposed on the total $47,900 that lies between the two stipulated ranges ($89,075 - $41,175). The final evaluation stands at 24%, which provides an identical tax rate for the remaining $25,350 ($115,500 - $89,075). ).

Effective Tax Rate = (Total Tax Paid / Taxable Income) x 100%; which further articulates to ($21,357.50 / $115,500) x 100%,

= 18%

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Answer:

−0.250

If this helps please mark brainliest.

The amount of Duane's first payment that goes to interest is approximately $26.47.

To determine the amount of Duane's first payment that goes to interest, we need to use the amortization formula for a loan.

The formula to calculate the interest portion of a loan payment is:

Interest = Remaining Balance * Monthly Interest Rate.

Let's calculate the interest for the first payment using the given information:

Loan Amount = $5,000.00

Monthly Payment = $118.57

First, we need to calculate the monthly interest rate:

Monthly Interest Rate = Annual Interest Rate / 12

= 6.5% / 12

= 0.00542

Next, we need to calculate the remaining balance after the first payment:

Remaining Balance = Loan Amount - Principal Paid

= $5,000.00 - $118.57

= $4,881.43

Finally, we can calculate the interest portion of the first payment:

Interest = Remaining Balance * Monthly Interest Rate

= $4,881.43 * 0.00542

= $26.47

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Answer:

Step-by-step explanation:

Starting from the right, put this into groups of three so you can see for sure where a million is.

254 212 610

A million is right where the 4 is. So use the hundred thousands (the second 2) to round to the nearest million. Since 2 is less than 5, it rounds like this.

254 000 000

The solution for y in the triangle by virtue of similar triangles is 3√7

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

The triangle

Using the theorem of similar triangles, we have the following equation

y/9 = 7/y

Cross multiply the above equation

so, we have the following representation

y^2 = 9 * 7

Evaluate

y^2 = 63

Take the square root of both sides

y = 3√7

Hence, the solution for y is 3√7

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Answer: 2x5x1, 1x10x1 (in any order) and any 3 multiples that make 10

Step-by-step explanation:

Answer:

There are multiple possible sets of dimensions for a rectangular prism with a volume of 10 cubic feet. Here are some possible solutions:

A rectangular prism with dimensions of 1 ft x 2 ft x 5 ft (length x width x height) would have a volume of 10 cubic feet, since 1 x 2 x 5 = 10.

A rectangular prism with dimensions of 2 ft x 1 ft x 5 ft (length x width x height) would also have a volume of 10 cubic feet, since 2 x 1 x 5 = 10.

A rectangular prism with dimensions of 0.5 ft x 1 ft x 20 ft (length x width x height) would also have a volume of 10 cubic feet, since 0.5 x 1 x 20 = 10.

A rectangular prism with dimensions of 5 ft x 1 ft x 2 ft (length x width x height) would have a volume of 10 cubic feet, since 5 x 1 x 2 = 10.

There are infinitely many other possible sets of dimensions for a rectangular prism with a volume of 10 cubic feet.

The intersection of sets M and F contains the elements "c" and "d".

To find the intersection of sets M and F, we need to identify the elements that are common to both sets.

M = {a, b, c, d}

F = {c, d, e, f}

The intersection of M

and F is denoted by M ∩ F, which represents the set containing elements that are present in both M and F.

Looking at the elements in M and F, we can see that the common elements between the two sets are "c" and "d".

Therefore, the intersection of M and F can be expressed as:

M ∩ F = {c, d}

So, the intersection of sets M and F contains the elements "c" and "d".

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Step-by-step explanation:

p union ( Q union R)

let solve for d elements inside d bracket

p = 1,6,10,14 Q = 1,5,11

R = 3,5,10,11

union means joining elements that is p with R.if there is occurrence just pick one.

(Q u R ) = ( 1,3,5,10,11)

so p u ( Q u R ) = ( 1,3,5,6,10,11,14)

Given data:

The first equation of the line is y= 2/3 x -9.

The second equation of the line is y= 2/3 x +3.

The standard equation of the line is,

Compare the given equation with the standard equation of the line.

As the slope of both the lines are equal, it means above lines are parallel.

Thus, the given lines are parallel, so there is no solution option (A) is correct.

Answer:

The constant of proportionality(Unit rate) is 0.23

Step-by-step explanation:

Given equation is:

\(P = 0.23n\)

Here

P is the price and n is the number of apples

The price is usually directly proportional to quantity so the relationship can be written as:

P ∝ n

Removing the proportionality symbol, we get

P = kn

Comparing the given equation with this equation we get

k = 0.23

Hence,

The constant of proportionality(Unit rate) is 0.23

The length of Marisa's garden is 10

The given parameters are:

Perimeter = 32 feet

Width = 6 feet

The perimeter is calculated as:'

Perimeter = 2 * (Length + width)

So, we have

2 * (Length + 6) = 32

Divide by 2

Length + 6 = 16

Subtract

Length = 10

Hence, the length of Marisa's garden is 10

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Answer:

I'm not sure if this is a real problem and I don't think it is but the answer is 6.5

Step-by-step explanation:

first you have to add -2 and 2, then plus 3 and 2 and subtract 2 from it and then and 2+4 and subtract -5 and divide 2 and add 3 and add the answer to al of that to 2 + 3 and subtract - 10 and you get your answer of 6.5