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Answer:

3 pennies, 9 nickels, and 6 dimes

Step-by-step explanation:

We have three conditions:

(1)         p +        n +        d = 18

(2) 0.01p + 0.05n + 0.10d = 1.08

(3)                                   d = 2p

Multiply (2) by 100 and rearrange (3) to get a standard array.

(4)      p +   n +     d =   18

(5)      p + 5n + 10d = 108

(6)  -2p          +     d =    0

Subtract (4) from (5). This gives

(4)      p +   n +   d =  18

(7)            4n + 9d = 90

(6)  -2p          +   d =   0

Multiply (4) by 2 and add to (6). This gives

(4) p +   n +    d =  18

(7)        4n + 9d = 90

(8)        2n + 3d = 36

Double (8) and subtract from (7). This gives

(4)      p +   n +   d = 18

(7)            4n + 9d = 90

(9)                    3d = 18

Divide (9) by 3. This gives

(10) d = 6

Substitute (10) into (7). This gives

4n + 9(6) = 90

4n +   54 = 90

4n           = 36

(11) n       =    9

Substitute (10) and (11) into (4). This gives

p + 9 + 6 = 18

p +      15 = 18

p              =  3

Sasha has 3 pennies, 9 nickels, and 6 dimes.

Answer:

Exoected age is 15.49 years

Step-by-step explanation:

Expected age

= E(x)

= sum (p(i)*i)

= 13*0.01+14*0.23+15*0.26+16*0.28+17*0.20+18*0.02

= 15.49

Answer:

See Attachment for graph

Charges = $200 when number of she works for 3 hours

Step-by-step explanation:

Given

Charges = $25 per hour + $125 (c = 25n + 125)

Required

Graph the equation.

From the graph, determine c when n = 3

To plot the graph; first, we have to determine the points to use;

When n = 1

[tex]c = 25 * 1 + 125[/tex]

[tex]c = 25 + 125[/tex]

[tex]c = 150[/tex]

When n = 2

[tex]c = 25 * 2 + 125[/tex]

[tex]c = 50 + 125[/tex]

[tex]c = 175[/tex]

When n = 3

[tex]c = 25 * 3 + 125[/tex]

[tex]c = 75 + 125[/tex]

[tex]c = 200[/tex]

When n = 4

[tex]c = 25 * 4 + 125[/tex]

[tex]c = 100 + 125[/tex]

[tex]c = 225[/tex]

Plotting n on the x axis and c on the y axis; we have

c   ||   n

1    ||   150

2   ||   175

3   ||    200

4   ||    225

(See attachment)

From the attachment;

When she works for 3 hour; This implies that n = 3

And c = $200 when n = 3

See Proof

[tex]c = 25n + 125[/tex]

Substitute 3 for n

[tex]c = 25 * 3 + 125[/tex]

[tex]c = 75 + 125[/tex]

[tex]c = 200[/tex]

Answer:

La pendiente de la recta L es [tex]\frac{3}{2}[/tex].

Step-by-step explanation:

La recta está presentada en su forma implícita, es decir, que está bajo la forma:

[tex]f(x,y) = 0[/tex]

Para determinar la pendiente de la recta, se debe transformarla a su forma explícita, cuya fórmula es:

[tex]y = m \cdot x + b[/tex]

Donde:

[tex]x[/tex] - Variable independiente, adimensional.

[tex]y[/tex] - Variable dependiente, adimensional.

[tex]m[/tex] - Pendiente, adimensional.

[tex]b[/tex] - Intercepto, adimensional.

Entonces:

[tex]3\cdot x - 2\cdot y + 1 = 0[/tex]

[tex]2\cdot y = 3\cdot x +1[/tex]

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

Por simple inspección, se determina que la pendiente de la recta L es [tex]\frac{3}{2}[/tex].

Answer:

3

Step-by-step explanation:

[tex]f(-1)g(-1) \text{ is the same thing as } f(-1)\cdot g(-1). \\\text{Therefore, find f(-1) and g(-1)}[/tex]

[tex]f(-1)=(-1)^2-4\\f(-1)=1-4\\f(-1)=-3[/tex]

[tex]g(-1)=3(-1)+2\\g(-1)=-3+2\\g(-1)=-1[/tex]

Therefore:

[tex]f(-1)\cdot g(-1)\\=(-3)(-1)=3[/tex]

Answer:

100°

Step-by-step explanation:

We know that angles EFD and AEF are the same as they are alternate interior angles.

We also can note that BEF and AEF are supplementary, meaning their angle lengths will add up to 180°.

So we can create an equation:

(2x + 60) + (3x + 20) = 180

Combine like terms:

5x + 80 = 180

Subtract 80 from both sides

5x = 100

Divide both sides by 5

x = 20.

Now we can use this to find the measure of BEF.

[tex]2\cdot20 + 60[/tex]

[tex]40 + 60 = 100[/tex]

Hope this helped!

Answer:

BEF = 100

Step-by-step explanation:

The angles are same side interior angles and same side interior angles add to 180 degrees

2x+60 + 3x+20 = 180

Combine like terms

5x+80 = 180

Subtract 80

5x = 100

Divide by 5

5x/5 = 100/5

x = 20

We want BEF

BEF = 2x+60

      = 2x+60

      = 2*20 +60

     = 40+60

     = 100

Hector outperformed the challenge rate as he exercised 2.88 hours a week.

It is best to convert the mixed fraction to decimals for easier calculation.

The students are encouraged to exercise 2¹/₂ hours per week. In decimals this is:

= 2 + ¹/₂

= 2 + 0.5

= 2.5 hours per week

In the 4 week period, Hector exercised 11¹/₂ hours which is:

= 11 + ¹/₂

= 11 + 0.5

= 11.5 hours

The number of hours he exercised per week is:

= Number of hours in total / Number of weeks

= 11.5 / 4

= 2.88 hours per week

When compared to the fitness challenge rate, we can conclude that Hector outperformed the challenge rate

Find out more at https://brainly.com/question/17951676.

Answer:

The answer is 2 7/8

Answer:

W = 9 * g

Step-by-step explanation:

W/9 = g

W = 9 * g

The expression W/9 = g can be written as W = 9g after cross multiplication.

It is defined as the combination of constants and variables with mathematical operators.

We have an expression:

W/9 = g

To solve for W

Make subject as W:

W = 9g

By cross multiplication.

Thus, the expression W/9 = g can be written as W = 9g after cross multiplication.

Learn more about the expression here:

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Answer:

Step-by-step explanation:

[tex] \frac{2}{5} + p = \frac{4}{5} + \frac{3}{5} p[/tex]

Multiply through by the LCM

The LCM for the equation is 5

That's

[tex]5 \times \frac{2}{5} + 5p = 5 \times \frac{4}{5} + \frac{3}{5}p \times 5[/tex]

We have

2 + 5p = 4 + 3p

Group like terms

5p - 3p = 4 - 2

2p = 2

Divide both sides by 2

We have the final answer as

Hope this helps you

Answer:

Step-by-step explanation:

Since the figure above is a right angled triangle we can use trigonometric ratios to find GV

To find GV we use cosine

cos∅ = adjacent / hypotenuse

From the question

GV is the adjacent

GC is the hypotenuse

So we have

GC = 55°

GV = 55 cos 37

GV = 43.92495

We have the final answer as

Hope this helps you

Answer:

  C)  549 km²

Step-by-step explanation:

The area of the regular pentagon is given by ...

  A = (1/2)Pa

where P represents the perimeter, and 'a' represents the apothem (6.2 km). Of course, the perimeter is 5 times the side length.

The lateral area is the product of the perimeter and the height:

  LA = Ph

Using these formulas, and recognizing the total area includes two (2) pentagons, we have ...

  total area = (LA) +2(A) = Ph +2(1/2)Pa = P(h +a)

  = (45 km)(6 km +6.2 km) = 549 km^2

Answer:

-36

Step-by-step explanation:

3*12=36

she is going down (negative) so, it is -36

not sure if this is what you are asking for, if not try this

0-12-12-12=-36

One way to write this polar coordinate is to say (2.5, pi/2) meaning we move 2.5 units away from the origin toward the pi/2 direction

pi/2 radians = 90 degrees

An alternative is to write (-2.5, 3pi/2) which is where we aim at the 3pi/2 direction (270 degrees) and walk backward while still facing directly south, and we'll arrive at the same location.

Answer:

the line of best fit can be approximated to:

y = -1.560 x + 22.105

Step-by-step explanation:

You are most likely expected to use a graphing tool are statistical program to calculate this. So enter the list of x-values separate from the list of y values and run the tool in linear regression mode.

Look at the attached image with the actual results including the line of best fit.

The equation can be written (rounding slope and y-intercept to 3 decimals) as:

y = -1.560 x + 22.105

Answer:

Step-by-step explanation:

vertical stretching / shrinking has the following transformation.

f(x) -> a * f(x)

when a >  1, it is stretching

when 0< a < 1, it is shrinking.

when  -1 < a < 0, it is shringking + reflection about the x-axis

when a < -1, it is stretching + reflection about the x axis.

Here it is simple shrinking, so 0 < a < 1.

I expect the answer choice to show (1/3) f(x).

However, if the question plays with the words

"shrink by a factor of 1/3" to actually mean a "stretching by a factor of three", then B is the answer (stretch by a factor of three).

[tex] \Large{ \boxed{ \bold{ \color{lightgreen}{Solution:}}}}[/tex]

So, Let's solve this question by using cartesian plane.

Well, What is cartesian plane?

A - A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a set of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in the same unit of length. 

━━━━━━━━━━━━━━━━━━━━

Answer:

x = 17/5

y = -2/5

Step-by-step explanation:

2x + 2y = 6

3x - 2y = 11

sum both equations results

5x + 0 = 17

x = 17/5

2x + 2y = 6

2*17/5 + 2y = 6

34/5 + 2y = 6

2y = 6 - 34/5

2y = 30/5 - 34/5

2y = -4/5

y = (-4/5)/2

y = -2/5

verify:

3x - 2y = 11

3*17/5 - 2*-2/5 = 11

51/5 + 4/5 = 55/5

51 + 4 = 55

The required value of the tanФ is given as -3/4. C option is correct.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

These are the equation that contains trigonometric operators such as sin, cos.. etc. In algebraic operations.

here,
Tan(180 - Ф) = -tanФ = perpendicular / base

From figure,  perpendicular= 12 and  base = 16
-tanФ = 12 / 16
tanФ = -3/4

Thus, the required value of the tanФ is given as -3/4. C option is correct.

Learn more about trigonometry equations here:

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Answer:

y = 700x - 400

Step-by-step explanation:

A negative number represents an altitude below sea level.

Beginning: -400

y = mx + b

y = mx - 400

In 2 hours the altitude was now 1000 m.

1000 m - (400 m) = 1400 m

The altitude went up 1400 m in 2 hours. The rate of change is

1400/2 m/h = 700 m/h

The rate of change is the slope.

y = 700x - 400

Answer:

The graph answer is below :)

Step-by-step explanation:

Answer:

  (c) 1.02

Step-by-step explanation:

(c) The tangent is the ratio of Opposite to Adjacent. Its lowest value will be found where Opposite is lowest, and Adjacent is highest:

  min tan(A) = (min BC)/(max AB) = 75/73.5 ≈ 1.020408...(42-digit repeat)

Answer:

[tex]\sin \left(\theta \right)-\frac{1}{2}\cos \left(2\theta \rightt)+C[/tex]

Step-by-step explanation:

We are given the graph of r = cos( θ ) + sin( 2θ ) so that we are being asked to determine the integral. Remember that [tex]\:r=cos\left(\theta \right)+sin\left(2\theta \right)[/tex] can also be rewritten as [tex]\int \cos \left(\theta \right)+\sin \left(2\theta \right)d\theta \right[/tex].

Let's apply the functional rule [tex]\int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx[/tex],

[tex]\int \cos \left(\theta \right)+\sin \left(2\theta \right)d\theta \right[/tex] = [tex]\int \cos \left(\theta \right)d\theta \right+\int \sin \left(2\theta \right)d\theta \right[/tex]

At the same time [tex]\int \cos \left(\theta \right)d\theta \right=\sin \left(\theta \right)[/tex] = [tex]sin( \theta \right ))[/tex], and [tex]\int \sin \left(2\theta \right)d\theta \right[/tex] = [tex]-\frac{1}{2}\cos \left(2\theta \right)[/tex]. Let's substitute,

[tex]\int \cos \left(\theta \right)d\theta \right+\int \sin \left(2\theta \right)d\theta \right[/tex] = [tex]\sin \left(\theta \right)-\frac{1}{2}\cos \left(2\theta \right)[/tex]

And adding a constant C, we receive our final solution.

[tex]\sin \left(\theta \right)-\frac{1}{2}\cos \left(2\theta \rightt)+C[/tex] - this is our integral

Answer:

Step-by-step explanation:

Given the inequality [tex]|z+4|>15[/tex], we are to find the solution set of the inequality. Since the the function is an absolute value, this means that the function will be positive and negative.

For the positive value of the function;

[tex]z+4>15\\\\subtract\ 4\ from \ both \ sides\\z+4-4 > 15 -4\\\\z>11[/tex]

For the negative value of the function we have;

[tex]-(z+4) > 15\\\\-z-4> 15\\add\ 4 \ to\ both \ sides\\\\-z-4+4> 15+4\\\\-z> 19\\\\[/tex]

Multiplying both sides of the inequality by -1 will change the sense of the inequality sign;'

[tex]-(-z)< -19\\\\z<-19[/tex]

Hence the solution sets are [tex]z> 11 \ and \ z< -19 \\[/tex] OR z less-than negative 19 or z greater-than 11

Answer:

z less-than negative 19 or z greater-than 11

Step-by-step explanation:

Answer:

Prove:

Using 1

n³+2n = (1)³+2(1) = 1+2= 3 ---> 3/3= 1 ✔

Using 2

n³+2n = (2)³+2(2)= 8+4=12 --> 12/3=4✔

Using 3

n³+2n= (3)³+2(3)= 27+6= 33 --> 33/3=11✔

So it is proven that n³+2n is divisible by 3 for every positive integer.

I hope this helps

if u have question let me know in comments

Answer:

The area of the pyramid is 360 unit²

Step-by-step explanation:

Given

Base Edge, a = 10

Height, h = 12

Required

Determine the surface area

The surface area of a regular pyramid is calculated as thus;

[tex]A = a^2 + 2a\sqrt{\frac{a^2}{4} + h^2}[/tex]

Substitute values for a and h

[tex]A = 10^2 + 2 * 10 * \sqrt{\frac{10^2}{4} + 12^2}[/tex]

Evaluate all squares

[tex]A = 100 + 2 * 10 * \sqrt{\frac{100}{4} + 144}[/tex]

[tex]A = 100 + 2 * 10 * \sqrt{25 + 144}[/tex]

[tex]A = 100 + 2 * 10 * \sqrt{169}[/tex]

Take positive square root of 169

[tex]A = 100 + 2 * 10 * 13[/tex]

[tex]A = 100 + 260[/tex]

[tex]A = 360[/tex]

Hence, the area of the pyramid is 360 unit²

Answer:

B.) 360 units2

Step-by-step explanation:

I got it correct on founders education

Answer:

Given f(x)=8sin(x)+cot(x) for -pi<x<pi :

Note that:

f'(x)=8cos(x)-csc^2(x)

f''(x)=-8sin(x)+2csc^2(x)cot(x)

(1) To find the intervals where f(x) is increasing or decreasing we use the first derivative test; if the first derivative is positive on an interval the functio is increasing, negative implies the functio is decreasing.

Using technology we find the approximate zeros of f'(x) on -pi<x<pi :

x~~-1.443401

x~~-.3752857

x~~.3752857

x~~1.443401

Plugging in test values on the intervals yields:

f'(x)<0 on (-pi,-1.443401)

f'(x)>0 on (-1.443401,-.3752857)

f'(x)<0 on

Plz correct me if wrong

Answer:

87 mph

Step-by-step explanation:

Total distance needed is 120 mi + 300 mi and that is 420 mi.

Driving at 65 mph means that it would take

420 / 65 hours to reach his destination.

6.46 hours .

at the first phase, he drove at 40 mph for 120 mi, this means that it took him

120 / 40 hours to complete the journey.

3 hours.

the total time needed for the whole journey is 6.46 hours, and he already spent 3 hours in the first phase. To keep up with the 6.46 hours required, in the second phase, he has to drive at a speed of

6.46 - 3 hours = 3.46 hours.

300 mi / 3.46 hours => 86.71 mph approximately 87 mph

Therefore, he needs to drive at not more than 87 mph to keep up with the journey while not breaking his speed limit

Answer:

Yes

Step-by-step explanation:

you would do 2(5x-10) + 2(8x+4)= 26x-12

Answer:

26x - 12

Step-by-step explanation:

The perimeter is the sum of all the exterior sides of a figure.

Here, we have a parallelogram, and its sides are 5x - 10, 8x + 4, 5x - 10, and 8x + 4. Adding these, we get:

(5x - 10) + (8x + 4) + (5x - 10) + (8x + 4) = 26x - 12

Thus, the answer is 26x - 12. Note that since the problem doesn't give a value for x, this cannot be simplified further.

~ an aesthetics lover

Step-by-step explanation:

sin∠M = cos∠N

sin∠M = cos(30°)

sin∠M = √3 / 2

m∠M = 60° or 120°

If ∠M is acute, m∠M = 60°.

Answer: The measure of ∠M is 60°

Step-by-step explanation:

The complement of 30° is 60°

sin∠M =cos∠N

sin∠60°=cos∠30°

the measure of ∠M is 60°

Answer:

The value of x is 30°

Step-by-step explanation:

We are given that the outer angle of the parallelogram is 60 degrees. Therefore it's respective inner angle will be 180 - 60 = 120 degrees. And, by properties of a parallelogram, the angle opposite to this angle will be 120 degrees as well.

If we draw extend the line creating angle 2x, then we will make ( 1 ) a vertical angle to 2x, ( 2 ) a 90 degree angle, and ( 3 ) and angle that we can let be y. Therefore, 2x + y = 90, and 3x + y = 120.

[tex]\begin{bmatrix}2x+y=90\\ 3x+y=120\end{bmatrix}[/tex] ,

[tex]\begin{bmatrix}6x+3y=270\\ 6x+2y=240\end{bmatrix}[/tex] ,

[tex]6x+2y=240\\-\\\underline{6x+3y=270}\\y=30[/tex],  

[tex]2x + (30) = 90,\\2x = 60,\\x = 30[/tex]

Solution : x = 30°

Answer:

x = 30

Step-by-step explanation:

a+ 60 = 180

a = 120

3x+b = 120  because opposite angles in a parallelogram are equal

2x+90+b = 180 since it forms a line

2x+b = 90

We have 2 equations and 2 unknowns

3x+b = 120

2x+b = 90

Subtracting

3x+b = 120

-2x-b = -90

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

x = 30

Answer:

each ice coffee is $2.25

Step-by-step explanation:

13.50 - 9 = 4.50

4.50 / 2 = 2.25