Rupert is copying some files from his computer to a compact disc, like the one shown above.


If the diameter of the compact disc is 120 millimeters, what is the approximate area ignoring the center hole? (Use 3.14 for pi.)

A.

376.8 mm2

B.

11,304 mm2

C.

753.6 mm2

D.

45,216 mm2

Answer:

Option C. 11

Step-by-step explanation:

If a point P lies on an ellipse, The sum of distances between the point p and the foci will be equal the major axes.

So, applying the previous rule to the problem

The red line + the blue line = major axis

6 + the blue line = 17

So, the blue line = 17 - 6 = 11

The answer is option C. 11

After the second day of their road trip, the Murphy family has

9/20 or 45% of the total distance left to travel.

To solve this problem, let's denote the total distance of the trip as $D$.

On the first day, the Murphy family travelled 30% of the total distance, which can be written as:

[tex]\[ 0.30 \times D = \frac{30}{100} \times D = \frac{3}{10} \times D \][/tex]

On the second day, they travelled another 1/4 of the total distance, which is: [tex]\[ \frac{1}{4} \times D \][/tex]

The total distance travelled after two days is the sum of the distances travelled on the first and second days: [tex]\[ \frac{3}{10} \times D + \frac{1}{4} \times D \][/tex]

To add these fractions, we find a common denominator, which is 20:

[tex]\ total \ distance \ travelled =6/20D+5/20D[/tex]

[tex]\ total \ distance \ travelled =11/20D[/tex]

The remaining distance after the second day is:

Distance left=D−Total distance travelled

[tex]Distance \ left=D-11/20D[/tex]

[tex]Distance \ left=20/20 D-11/20D[/tex]

[tex]Distance \ left=9/20D[/tex]

Express the fraction and percentage of the distance left:

Fraction of the total distance left:

Fraction= Distance left/D

[tex]Fraction=9/20D/D=9/20[/tex]

After the second day, the Murphy family has 9/20 of the total distance left.​

Percentage of the total distance left:

Percentage= Distance left/D×100%

[tex]Percentage= 9/20D/D*100%[/tex]

[tex]Percentage=9/20*100%[/tex]

[tex]Percentage=45[/tex]

Therefore, after the second day of their road trip, the Murphy family has

9/20 or 45% of the total distance left to travel.

Step-by-step explanation:

We know that

[tex]tan\theta =\frac{altitude}{base}[/tex]

Using this for the triangles

For the small triangle

[tex]tan \theta =\frac{6\frac{1}{2} }{9}[/tex]

[tex]\Leftrightarrow tan \theta =\frac{\frac{13}{2} }{9}[/tex]

[tex]\Leftrightarrow tan \theta =\frac{13} {18}[/tex]

Again for the bigger triangle

[tex]tan \theta =\frac{h}{31\frac{1}{2} }[/tex]

[tex]\Leftrightarrow tan \theta =\frac{h}{\frac{63}{2} }[/tex]

[tex]\Leftrightarrow tan \theta =\frac{2h}{63}[/tex]

Therefore

[tex]\frac{2h}{63} =\frac{13}{18}[/tex]

[tex]\Leftrightarrow h=\frac{13 \times 63}{18 \times 2}[/tex]

[tex]\Leftrightarrow h=\frac{819}{36}[/tex]

[tex]\Leftrightarrow h = 22.75[/tex] ft

Therefore h = 22.75 ft

Answer:

Step-by-step explanation:

Subtract  

6 u  from  2 u .

− 4 u + 9 = 19

Move all terms not containing  u  to the right side of the equation.

− 4 u = 10

Divide each term by  − 4  and simplify.

u = −  [tex]\frac{5}{2}[/tex]

The result can be shown in multiple forms.

Exact Form:

u = −  [tex]\frac{5}{2}[/tex]

Decimal Form:

u =− 2.5

Mixed Number Form:

u = −  2 [tex]\frac{1}{2}[/tex]

Answer:

$2,225.54

Step-by-step explanation:

Principal, p = $1000

interest rate r = 16% 0r 0.16

years of deposit, t = 5

Finding ending balance below

Since interest compounded continuously,

Substitute the following values

p = $1000, e = exponent, r = 0.16 and t = 5

B = 1000e^((0.16)(5))

=1000e^(0.8)

=1000 X 2.2255409284924676

=2,225.5409284924676

Which B is approximately $2,225.54

Ending balance =$2,225.54

Assuming the amount of  $1,000 was invested at an interest rate of 16%, compounded continuously, for a period of five years, what the ending balance will be is: $2,225.54

p represent Principal = $1000

r represent Interest rate= 16% or 0.16

t represent=5 years  

Now let determine the ending balance

Ending balance= $1000e^(0.16)(5)

Ending balance=$1000e^(0.8)

Ending balance=$1000 X 2.2255409284924

Ending balance=$2,225.5409284924

Ending balance=$2,225.54 (Approximately)

Inconclusion if  the amount of  $1,000 was invested at an interest rate of 16%, compounded continuously, for a period of five years, what the ending balance will be is: $2,225.54

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Answer: 18/40 and 27/60

Step-by-step explanation:

Multiply the numerator and denominator by whatever number it needs to be multiplied by

9*2 to get 18

20*2 to get 40

9*3 to get 27

20*3 to get 60

The answer to your question is 4x^2 - 16

Hope this helped

Answer:

Step-by-step explanation: (2x + 4) x (2x - 4)

2x + 4 = 6x

2x - 4 = 4 - 2x = 2x

6x X 2x = 12x

Answer:

0.45

Step-by-step explanation:

No explanation calculators rule

The length of the rug is 4 ft.

The width of the rug is 2.5 ft.

Explanation:

The area of the rug is 10 ft.

The length of the rug be l.

Let us convert the inches to feet.

Thus, [tex]18 inches = 1.5 ft[/tex]

Thus, the length of the rug is [tex]l=1.5+w[/tex]

Let the width of the rug be w.

Substituting these values in the formula of area of the rectangle, we get,

[tex]A=length\times width[/tex]

[tex]10=(1.5+w)(w)\\10=1.5w+w^2\\w^2+1.5w-10=0[/tex]

Solving the expression using the quadratic formula,

[tex]$w=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$[/tex]

Substituting the values, we have,

[tex]$w=\frac{-15 \pm \sqrt{15^{2}-4 \cdot 10(-100)}}{2 \cdot 10}\\[/tex]

[tex]$w=\frac{-15 \pm \sqrt{4225}}{20}$[/tex]

[tex]$w=\frac{-15 \pm 65}{2 0}$[/tex]

Thus,

[tex]w=\frac{-15 + 65}{2 0}\\w=\frac{50}{20} \\w=2.5[/tex]  and   [tex]w=\frac{-15 - 65}{2 0}\\w=\frac{-80}{20} \\w=-4[/tex]

Since, the value of w cannot be negative, the value of w is 2.5ft

Thus, the width of the rug is 2.5ft

Substituting [tex]w=2.5[/tex] in [tex]l=1.5+w[/tex], we get,

[tex]l=1.5+2.5\\l=4[/tex]

Thus, the length of the rug is 4 ft.

It's A

length 4 and width 2.5

Answer:

18 dimes and 9 nickels

Step-by-step explanation:

I assume you mean twice as many dimes "then" nickels which would make it 18 dimes = 1.80$ 9 nickels=0.45$

Answer: A. Subtract 6 from 18

43,604

Subtract 5398 from 49002

Answer:

Step-by-step explanation:

49,002 is greater than -5,398

Answer:

12.28

Step-by-step explanation:

[tex]\sqrt{14}-\sqrt{3} )(\sqrt{12}+\sqrt{7})[/tex]

Multiplying [tex]\sqrt{14} and\sqrt{3}[/tex] individually to the values inside the brackets to find the product of the equation.

[tex]\sqrt{14}\sqrt{12}+\sqrt{14}\sqrt{7}-\sqrt{3}\sqrt{12} -\sqrt{3} \sqrt{7}[/tex]

[tex]\sqrt{168} +\sqrt{98} -\sqrt{36}- \sqrt{21}\\2\sqrt{42}+7\sqrt{2}-6-\sqrt{21}\\ 12.96 +9.90 -6 -4.58\\12.28[/tex]

The product of the above values is 12.28

Answer:

2√42 + 7√2 - √21 - 6

Step-by-step explanation:

(√14-√3)(√12+√7)

First let us expand the expression by doing the following:

√14(√12+√7) -√3(√12+√7)

√168 + √98 - √36 - √21

√(4x42) + √(49x2) - 6 - √21

2√42 + 7√2 - √21 - 6

Answer:

A- 170$

Step-by-step explanation:

The approximate six month premium is $170.

A linear equation is an equation in which there is one variable that is raised to the power of 1. An example is x + 2

In order to determine the six month premium, substitute for d and b in the given equation:

P = 2 x 1.02 x $500 = $1020

Monthly premium = $1020 / 6 = $170

Here is the complete question:

Jerome uses the formula, P = 2DB, to find his approximate six-month premium when his driver risk factor, D, is 1.02 and the basic six-month premium is $500.What will his monthly premium be?

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The equation to find David’s hourly wage is:

David’s hourly wage =  [tex]\frac{1}{2}[/tex] x + 1.75, where x represents Amelia’s hourly wage

Step-by-step explanation:

The given is:

Amelia’s hourly wage is $3.50 less than double David’s hourly wage

We need to find an equation to find David’s hourly wage

Assume that:

∵ Amelia’s hourly wage is $3.50 less than double David’s

   hourly wage

- That means multiply David’s hourly wage by 2, then

    subtract 3.50 from the product to get Amelia’s hourly wage

∴ x = 2y - 3.50

Now let us find y in terms of x

∵ x = 2y - 3.50

- Add 3.5 to both sides

∴ x + 3.50 = 2y

- Divide each term by 2

∴ [tex]\frac{1}{2}[/tex] x + 1.75 = y

- Switch the two sides

∴ y =  [tex]\frac{1}{2}[/tex] x + 1.75

∵ y represents David’s hourly wage

∴ David’s hourly wage =  [tex]\frac{1}{2}[/tex] x + 1.75, where x represents

   Amelia’s hourly wage

The equation to find David’s hourly wage is:

David’s hourly wage =  [tex]\frac{1}{2}[/tex] x + 1.75, where x represents Amelia’s hourly wage

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Answer:

x- intercept (- 8, 0), y- intercept (0, 8)

Step-by-step explanation:

To find the y- intercept, let x = 0 in the equation and solve for y

y = 0 + 8 = 8 ⇒ (0, 8 ) ← y- intercept

To find the x- intercept, let y = 0 in the equation and solve for x

x + 8 = 0 ( subtract 8 from both sides )

x = - 8 ⇒ (- 8, 0 ) ← x- intercept

X-intercept is (-8,0) and y-intercept is (0,8). the correct option is A.

The intersection of the graph of the function with the y-axis gives y-intercept of that function. The y-intercept is the value of y on the y-axis at which the considered function intersects it.

Assume that we've got: y = f(x)

At y-axis, we've got x = 0, so putting it will give us the y-intercept.

Thus, y-intercept of y = f(x) is y = f(0)

We are given that;

Function y=x+8

Now,

The equation of the graph is y = x + 8. To find the x-intercept, we set y = 0 and solve for x.

0 = x + 8

x = -8

Therefore, the x-intercept is (-8, 0).

To find the y-intercept, we set x = 0 and solve for y.

y = 0 + 8

y = 8

Therefore, X-intercept will be (-8,0) and y-intercept will be (0,8).

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Answer:

b)  Complement of spinning any number less than 3 is Spinning 3 or 4.

Step-by-step explanation:

COMPLIMENT of any Set A  is the set of all the elements which are in the  sample space but NOT IN SET A.

Here, Event E  = Spinning a spinner with 4 parts and getting a number less than 3.

Here, Sample Space = {1,2,3,4}

Also, as outcomes is LESS THAN 3, ⇒   E  = {1 ,2}  

Now, Compliment E  = Sample Space - { Elements in set E}

                                    = {1,2,3,4} -  {1 ,2}

or, E'  = { 3,4}

Hence,  complement of spinning any number less than 3 is Spinning 3 or 4.

Answer:

Spinning a 3 or 4

Step-by-step explanation:

The numbers that are less than 3 on the spinner, are 1 and 2. Therefore, the complement or opposite of that are all the numbers other than 1 and 2. So the answer is 3 and 4.

Answer:

When you use 2 GB

Step-by-step explanation:

Data Plan a Formula 35(12p)

P = per GB

Data Plan B 25(17p)

Set each on equal to each other

Please Check my work, but I think this is on the right track.

The costs for both the data plans A and B will be the same for 2GB of data. The cost for each plan will be $59.

This problem is essentially asking us to find the number of gigabytes (GB) at which both data plans A and B cost the same. We can form two equations representing the costs of the plans. For plan A, the cost is $35 + $12 per GB. For plan B, the cost is $25 + $17 per GB. We can express these costs mathematically as: 35+12x=25+17x (where 'x' is the number of gigabytes). By solving this equation for 'x', we subtract 25 from both sides and also subtract 12x from both sides, which gives us 10 = 5x. Dividing by 5 from both sides give us x = 2 GB. So, for 2GB of data, the costs for both the data plans will be the same and the cost for each plan is $35 + 12(2) = $59 for plan A and $25 + 17(2) = $59 for plan B.

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Answer:

B. 119.32

Step-by-step explanation:

Use C = πd as the formula, which is 3.14x38=119.32

Answer:

B) [tex]119.32[/tex] [tex]cm[/tex]

Step-by-step explanation:

Circumference of a circle is the total length of its boundaries that it makes to complete 360°

Circumference of a circle = [tex]2\pi r[/tex]

Given:

             [tex]r=19 cm\\\pi =3.14[/tex]

Putting the given values in the formula of circumference of the circle

               = [tex]2*3.14*19[/tex]

               = [tex]119.32[/tex] [tex]cm[/tex]

On putting the value of radius and [tex]\pi[/tex] in the formula the circumference of the circle is ≈[tex]119.32[/tex] [tex]cm[/tex]

I assume you mean (x^2+8)/(x-5)?

If so, we have:

(8^2+8)/(8-5)

(64+8)/3

72/3

24

So the value is 24 when x=8

Hope this helped!

When x dissapears we have a false equation:

-4 = 5, so the equation does not have solutions, which means that Evelyn is incorrect.

The equation has infinite solutions?

Let's simplify the equation:

3(x - 3) + 5 = 3x + 1 + 4

distributing the left side.

3x - 9 + 5 = 3x + 1 + 4

3x - 4 = 3x + 5

If you subtract 3x in both we will get:

3x - 4 - 3x = 3x + 5 - 3x

-4 = 5

This is false, and x disappeared, so there is no value of x that makes this equation true, meaning that the equation does not have a solution.

The product of 9.42 and 6.83 is found by direct multiplication, which is not listed in the reference provided. The correct answer, using standard multiplication, is approximately 64.355 when rounded to three decimal places.

To calculate the product of 9.42 multiplied by 6.83, we use the multiplication method that is taught in mathematics. Multiplying these two numbers together is a straightforward process:

9.42 × 6.83

This calculation is something we can easily undertake with a calculator or by using the long multiplication technique. Neither of the reference information provided lists this specific product, so to ensure accuracy, we would perform the calculation directly. The correct solution is not provided in the data set above.

The answer to 9.42 multiplied by 6.83 is approximately 64.355 when rounded to three decimal places.

Step-by-step explanation:

Given,

The height of a rectangular prism(h) =  3 in and

The perimeter of a rectangular prism =  88 in

To find, the base of a rectangular prism(b) = ?

We know that,

The perimeter of a rectangular prism = 2l + 2b or 2b + 2h or 2h + 2l

∴ 2b + 2(3) = 88

⇒ 2b = 88 - 6

⇒ 2b = 82

⇒ b = 41 in

Thus, the base of a rectangular prism(b) = 41 in.

Answer:

x = [tex]\frac{2}{5}[/tex]

Step-by-step explanation:

Given

[tex]\frac{2}{3}[/tex] + [tex]\frac{1}{3}[/tex] x = 2x

Multiply through by 3 to clear the fractions

2 + x = 6x ( subtract x from both sides )

2 = 5x ( divide both sides by 5 )

[tex]\frac{2}{5}[/tex] = x

Answer:     x=2/5

Step-by-step explanation:

Trust me

The police cruiser travels a total distance of 275.0 meters. It covers 137.5 meters during acceleration and the same distance during deceleration (in the opposite direction), summing up to 275.0 meters in total.

Calculating the distance covered during acceleration:

The equation for distance covered with constant acceleration is given by:

[tex]\[ s = ut + \frac{1}{2}at^2 \][/tex]

Where:

[tex]\( u \)[/tex] = Initial velocity

[tex]\( a \)[/tex] = Acceleration

[tex]\( t \)[/tex] = Time

Given:

Initial velocity [tex](\( u \))[/tex] = 20.0 m/s

Acceleration[tex](\( a \))[/tex] = 3.0 m/s²

Time[tex](\( t \))[/tex]= 5.0 seconds

Let's find the distance covered during acceleration using the above formula:

[tex]\[ s = ut + \frac{1}{2}at^2 \][/tex]

[tex]\[ s = (20.0 \, \text{m/s} \times 5.0 \, \text{s}) + \frac{1}{2} \times 3.0 \, \text{m/s}^2 \times (5.0 \, \text{s})^2 \][/tex]

[tex]\[ s = (100.0 \, \text{m}) + \frac{1}{2} \times 3.0 \, \text{m/s}^2 \times 25.0 \, \text{s}^2 \][/tex]

[tex]\[ s = 100.0 \, \text{m} + 37.5 \, \text{m} \][/tex]

[tex]\[ s = 137.5 \, \text{m} \][/tex]

Therefore, the distance covered during acceleration is 137.5 meters.

Calculating the distance covered during deceleration (slowing to a stop):

The cruiser starts at a speed of 20.0 m/s and decelerates uniformly until it comes to a stop. The distance covered during deceleration will be the same as the distance covered during acceleration but in the opposite direction.

So, the distance covered during deceleration = 137.5 meters (in the opposite direction).

Total distance traveled:

The total distance traveled by the cruiser during acceleration and then deceleration is the sum of these distances (taking the magnitudes):

Total distance = Distance during acceleration + Distance during deceleration

Total distance = 137.5 m + 137.5 m

Total distance = 275.0 meters

Therefore, the entire distance covered by the cruiser in the entire time is 275.0 meters.

Answer:

$12.79

Step-by-step explanation:

$45 - $18.63 = $26.37

$26.37 - ($.47 x 2) = $26.37 - $.94 = $25.43

$25.43 - $12.64 = $12.79

The answers is 2,200

Answer:

2600

Step-by-step explanation:

first you would round them to the nearest hundred. this means that if the figure in the tens column is greater than or equal to 5 you would round up. if it is less than 5 you round down

so 1400+400+800=

then you would add them up

so 1400+400+800=2600

1400+400=1800

1800+800=2600

Step-by-step explanation:

Given, the chipmunks dropped an acron from the top of a tree. The acron was 0.25 kg and had a velocity of 4 m/s when it hit ground.

Kinetic energy =[tex]\frac{1}{2} m v^2[/tex]

Here m = 0.25 kg and v =4 m/s

Kinetic energy of the acron had =[tex]\frac{1}{2}\times 0.25 \times 4^2[/tex] J

                                                    = 2 J

The kinetic energy of the Chipmunk is 2 Joules.

Kinetic energy is the energy than an object possesses due to its motion. It is given by:

Kinetic Energy(KE) = (1/2)mv²

Where m is mass, v is velocity.

Given that m = 0.25 kg, v = 4 m/s, hence:

KE = (1/2)mv²

KE = (1/2) * 0.25 * 4² = 2J

The kinetic energy of the Chipmunk is 2 Joules.

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Answer:

Step-by-step explanation: