A pair of shoes you want to purchase is on sale for 40% off the original price. If you paid $36 for the shoes, what was the original price?

Answer:

y = 2x³ +x² -3x +6

Step-by-step explanation:

The polynomial correlation function of a graphing calculator can work with the table of function values to give you the equation. (See attached)

_____

If you want to solve this by hand, you can write the equations for the unknown coefficients in the polynomial function, then solve those. First of all, notice that you are given the y-intercept, (0, 6), so you know one of the coefficients already. That leaves a system of 3 equations in 3 unknowns that need to be solved.

___

Writing the equations

... ax³ +bx² +cx +6 = y . . . . the generic linear equation in a, b, c that you're writing

For x = -1:

... -a +b -c +6 = 8

For x = 1

... a + b + c + 6 = 6

For x = 2

... 8a +4b +2c +6 = 20

In augmented matrix terms, this set of linear equations looks like ...

[tex]\left[\begin{array}{ccc|c}-1&1&-1&2\\1&1&1&0\\8&4&2&14\end{array}\right][/tex]

___

Solving the equations

There are a number of ways to solve these. Again, a graphing calculator often has solution functions, such as reducing a matrix to row-echelon form, that will solve this in a keystroke or two.

If you add the first two equations, you get ...

... 2b = 2 ⇒ b = 1

Substituting that into the first equation allows you to simplify it to ...

... -a -c = 1

Dividing the third equation by 2 (and substituting for b) makes it ...

... 4a +c = 5

Adding these equations gives ...

... 3a = 6 ⇒ a = 2

Then ...

... c = -a -1 = -2 -1 = -3

And our polynomial function is ...

... y = 2x³ +x² -3x +6

Answer: (x, y - 8)

Step-by-step explanation:

Start with the innermost parentheses (reflection over the y-axis), which changes the sign of the y-coordinate:

Now perform the next inner parenthesis (rotation 180°), which changes the signs of both the x- and y-coordinates:

Now perform the last set of parenthesis (reflection over y=4), which has the rule of (x, y) → (x, y + 2(4 - y))  = (x, y + 8 - 2y)  =  (x, 8 - y):

Answer:

(a) 8√3

Step-by-step explanation:

All of the triangles are similar, so the ratio of hypotenuse to long side is the same for all. Comparing the middle-size triangle to the largest, we have ...

... x/12 = 16/x

... x² = 192 . . . . . . . . . . . . . multiply by 12x; next take the square root

... x = √192 = 8√3 . . . . . . seems to match answer choice (a)

Answer: Option 'A' is correct.

Step-by-step explanation:

Since we have given that

30% chance that the company will lose $30000.

40% chance of a break even that there is no loss and no profit.

30% chance that the company will profit $ 60000.

As we know the formula for "Expectation":

So, Expected value will be

[tex]\frac{30}{100}\times (-30000)+\frac{40}{100}\times 0+\frac{30}{100}\times 60000\\\\=03\times (-30000)+0.4\times 0+0.3\times 60000\\\\=-9000+18000\\\\=\$9000[/tex]

Expected value is $9000. So, the company should proceed with the project.

Hence, Option 'A' is correct.

Answer:

24 munchkins.

Step-by-step explanation:  

Let C be the number of chocolate and D be number of glazed donut holes in the original box.

We are told if Jacob ate 2 chocolate  munchkins, then 1/11 of the remaining Munchkins would be chocolate. We can represent this information as:

[tex]C-2=\frac{1}{11}*(C+D-2)...(1)[/tex]

We are also told if he instead added 4  glazed Munchkins to the original box, 1/7 of the Munchkins would be chocolate. We can represent this information as:

[tex]C=\frac{1}{7}*(C+D+4)...(2)[/tex]

Upon substituting C's value from equation (2) in equation (1) we will get,

[tex]\frac{1}{7}*(C+D+4)-2=\frac{1}{11}*(C+D-2)[/tex]

Let us have a common denominator on right side of equation.

[tex]\frac{1}{7}*(C+D+4)-\frac{7*2}{7}=\frac{1}{11}*(C+D-2)[/tex]

[tex]\frac{C+D+4-14}{7}=\frac{1}{11}*(C+D-2)[/tex]

Multiplying both sides of our equation by 7, we will get,

[tex]7*\frac{C+D-10}{7}=7*\frac{1}{11}*(C+D-2)[/tex]

[tex]C+D-10=\frac{7}{11}*(C+D-2)[/tex]  

Multiplying both sides of our equation by 11, we will get,

[tex]11*(C+D-10)=11*\frac{7}{11}*(C+D-2)[/tex]  

[tex]11*(C+D-10)=7*(C+D-2)[/tex]

[tex]11C+11D-110=7C+7D-14[/tex]

[tex]11C-7C+11D-7D=-14+110[/tex]  

[tex]4C+4D=96[/tex]

[tex]4(C+D)=96[/tex]  

[tex](C+D)=\frac{96}{4}[/tex]

[tex](C+D)=24[/tex]

Therefore, the total number of Munchkins in original box is 24.

Answer:

B on edg

Step-by-step explanation:

You got this chief.

Answer:

The answer is 5.

Step-by-step explanation:

5+(-9) or

5-9=-4

Answer:

[tex]11:45\ am[/tex]

Step-by-step explanation:

Total distance between Kiran and Clare is 24 miles. They started walking at 8.00 am.

Speed of Kiran is 3 miles/hr and speed of Clare is 3.4 miles/hr.

So the relative speed of them is,

[tex]=3+3.4=6.4[/tex] miles/hr

Both the speed are added as they moving in opposite direction.

We know that,

[tex]\text{Relative speed}=\dfrac{\text{Relative distance}}{\text{Time}}[/tex]

i.e [tex]\text{Time}=\dfrac{\text{Relative distance}}{\text{Relative speed}}[/tex]

Putting the values,

[tex]t=\dfrac{24}{6.4}=3.75\ hr=3\ hr\ 45\ min[/tex]

As they started at 8.00 am, so the time at which will meet will be,

[tex]=8+3\ hr\ 45\ min=11:45[/tex]

Answer:

11:45PM

Step-by-step explanation:

The empirical rule states that at 95% the measurements would be within 2 standard deviations of the mean.

You are given a mean of 68 inches and a standard deviation of 4.

2 times the standard deviation = 2 x 4 = 8

So 95% of the heights would be between 68-8 = 60 inches and 68+8 = 76 inches.

Answer:

60 -76 is the range

Step-by-step explanation:

As the graph shows, if we are in 2 standard deviations of the mean, we are in (34.1 + 13.6) *2 = 47.7*2 = 95.4 %

Our mean is 68

2  standard deviations is 2 * 4 = 8

68-8 = 60

68 * 8 = 76

We need to be between 60 and 76 to have at 95% confidence interval

Answer:

The equation should read c = 61m + 75

Step-by-step explanation:

We can find this because we know that the 61 dollars is a dependent cost on the number of months. Therefore they have to be multiplied together.

The 75 is a constant, which means it gets added to the end.

Answer:

D. [tex]\frac{3}{7}[/tex]

Step-by-step explanation:

We have been given that the probability of an event is 3/10.  

To find the odds of the same event we will use formula:

[tex]\text{Odds of an event}=\frac{\text{Probability of the event}}{\text{1-Probability of the event}}[/tex]

[tex]\text{Odds of the event}=\frac{\frac{3}{10}}{1-\frac{3}{10}}[/tex]

[tex]\text{Odds of the event}=\frac{\frac{3}{10}}{\frac{1*10}{10}-\frac{3}{10}}[/tex]

[tex]\text{Odds of the event}=\frac{\frac{3}{10}}{\frac{10-3}{10}}[/tex]

[tex]\text{Odds of the event}=\frac{\frac{3}{10}}{\frac{7}{10}}[/tex]

Dividing a fraction with another fraction is same as multiplying the 1st fraction by the reciprocal of second fraction.

[tex]\text{Odds of the event}=\frac{3}{10}\times \frac{10}{7}[/tex]

[tex]\text{Odds of the event}=\frac{3}{7}[/tex]

Therefore, the odds of the same event is [tex]\frac{3}{7}[/tex] and option D is the correct choice.

Answer:

See below

Step-by-step explanation:

m < 1 = 180 - m<4 (supplementary angles)

= 180 - 143

= 37 degrees

m <2 = m< 4 ( opposite angles)

= 143 degrees

M< 3 = m < 1  = 37 degrees  (opposite angle)

Angle 1 measures 143 degrees, while angles 2 and 3 both measure 37 degrees.

To find the measure of angle 2, we can use the fact that adjacent angles on a straight line are supplementary. This means that angle 2 and angle 4 add up to 180 degrees. Since angle 4 is 143 degrees, angle 2 is 180 - 143 = 37 degrees.

To find the measure of angle 3, we can use the fact that corresponding angles of parallel lines cut by a transversal are congruent. This means that angle 3 and angle 2 have the same measure. Since angle 2 is 37 degrees, angle 3 is also 37 degrees.

Therefore, the measures of angle 1, 2, and 3 are 143 degrees, 37 degrees, and 37 degrees, respectively.

To learn more about angles

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Answer:

The answer is x = 7

Step-by-step explanation:

√2x − 5 + 4 = x

= √2x − 5 + 4 + − 4 = x + −4  (add -4 to both sides)

=√2x − 5 = x − 4

=√2x−5=x−4

2x−5=(x−4)2 (Square both sides)

2x−5=x2−8x+16

2x−5−(x2−8x+16)=x2−8x+16−(x2−8x+16)(Subtract x^2-8x+16 from both sides)

−x2+10x−21=0

(−x+3)(x−7)=0 (Factor left side of equation)

−x+3=0 or x−7=0 (Set factors equal to 0)

x=3 or x=7

Answer: 7

Step-by-step explanation:

[tex]\sqrt{2x-5}+4 = x[/tex]

Restriction: x ≥ 4  why? because [tex]\sqrt{2x-5}\geq0[/tex]

[tex]\sqrt{2x-5}+4 = x[/tex]

            -4     -4  

[tex]\sqrt{2x-5} = x - 4[/tex]

[tex](\sqrt{2x-5})^2 = (x - 4)^2[/tex]

2x - 5 = x² - 8x + 16

-2x +5        -2x   +5  

       0 = x² - 10x + 21

       0 = (x - 3) (x - 7)

0 = x - 3        0 = x - 7

3 = x              [tex]\big{\boxed{7=x}}[/tex]

  ↓

not valid

Answer:

Area shaded part = 116 to three sig digs.

Step-by-step explanation:

I don't know if your answer is correct or not, but the number of sig digs is not. The way the question has been posed is not to 3 sig digs either.

The answer should be 116 if they want it to three sig digs.

Let's see if the answer is correct

Area of the whole circle.

Area of unshaded smaller circle

Area of the shaded part

Answer:

116 cm^2  to 3 significant figures.

Step-by-step explanation:

Your calculations are correct. You just haven't corrected the answer to 3 significant figures.

Answer:

The correct answer is B) y – 2 = (x – 3)

Step-by-step explanation:

In order to find this, look at the base form of point-slope form.

y - y1 = m(x - x1)

Seeing as there is subtraction symbols after x and y, we know that we would be subtracting the x and y values. Since 2 is the y value, it would go in for y1 and 3 being the x value puts it in for x1. Once you do that, you'll get the equation above.

Answer:

-1/2

Step-by-step explanation:

The critical path in a project schedule is the longest sequence of tasks from start to finish and determines the minimum total duration for the project. Without the diagram, the correct duration from your multiple-choice options cannot be determined accurately. The correct answer represents the duration of the longest path from the given options.

Without the graphic showing the schedule network diagram for assembling a toy train set, providing an accurate answer would be difficult. Normally, in project management, a Critical Path represents the longest sequence of tasks (or activities) in a project schedule from start to finish. It determines the minimum total duration required to complete the project. You identify the critical path by adding the times for the activities in each sequence and determining the longest path in the project.

In this case, assuming that you have the diagram in front of you and you've calculated the total duration for all paths, one of the multiple choice options (A) 38 minutes, (B) 41 minutes, (C) 49 minutes, or (D) 51 minutes would represent the duration of the critical path in the network diagram.

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Answer: 33

Step-by-step explanation:

           Today                3 years ago

Ben:   x + 20                  (x + 20) - 3    

Dan:     x                          x - 3

  3 years ago, Ben was 3 times as old as Daniel

⇒  (x + 20) - 3  = 3(x - 3)

       x + 17        = 3x - 9

             17        = 2x - 9

             26       = 2x

             13        = x

Today, Ben = x + 20

                   = 13 + 20

                   = 33

Answer:

Ben is 33 years old

Step-by-step explanation:

Let Ben’s age = B

Let Daniel’s age = x

B = x + 20  (20 years older than Daniel)

Their ages 3 years ago:

B = 3x  (also given in problem)

B = x + 20  (given in problem)

x + 20 = 3x  (Since both equations are equal to B, set them equal to each other)

20 = 2x (simplify)

x = 10

B = 10 + 20 = 30

Their ages now:

Add 3 to their "ages three years ago"

New x = Daniel’s age = old age + 3 = 10 + 3 = 13 years old

B = Ben’s age = old age + 3 = 30 + 3  = 33 years old

Answer:

The denominators of fractions are : 2 and 10

Step-by-step explanation:

[tex]\text{Let the two fractions be : }\frac{1}{x}\thinspace and\thinspace \frac{1}{y}\\\\\implies \frac{1}{x}+\frac{1}{y}=\frac{3}{5}\\\\\implies 5\cdot x +5\cdot y-3\cdot x\cdot y=0[/tex]

By hit and trial method, if we put x = 2 and y = 10 then the resulting equation (1) is satisfied and all the conditions hold.

So, the denominators are 2 and 10

Through the hit and trial method, the value of the denominator 'a' is 2 and the value of denominator 'b' is 10 and there is also the use of arithmetic operations.

Given :

To determine the denominator of the two fractions whose sum is 3/5, first, let that numbers be 1/a and 1/b.

[tex]\dfrac{1}{a}+\dfrac{1}{b}= \dfrac{3}{5}[/tex]

[tex]5a + 5b = 3ab[/tex]

Now, put a = 2 then b becomes:

[tex]10 + 5b = 6b[/tex]

b = 10

So, through the hit and trial method, the value of a is 2 and the value of b is 10.

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Answer: The Answer is B

Step-by-step explanation:

FIrst we see post 7 and -5 we need to cancel out seven sooooo we make sevena a neg and do -5 and -7 and we get -12 we divide this by -2 and we get post 6

x=6

-2x+7=-5

-2(-7)+7=-5(-7)

-2(-2)x=-12(-2)

x=6

Answer:

b  6

Step-by-step explanation:

-2x+7 = -5

Subtract 7 from each side

-2x +7-7 = -5 -7

-2x = -12

Divide by -2

-2x/2 = -12/-2

x=6

The formula of a volume of a rectangle prism:

[tex]V=lwh[/tex]

l - length

w - width

h - height

The larger rectangle prism:

[tex]l = 10cm,\ w=7cm,\ h=4cm[/tex]

Substitute:

[tex]V_1=(10)(7)(4)=280\ cm^3[/tex]

The smaller rectangle prism:

[tex]l=3cm,\ w=7cm,\ h=5cm[/tex]

Substitute:

[tex]V_2=(3)(7)(5)=105\ cm^3[/tex]

Total volume:

[tex]V=V_1+V_2\to V=280\ cm^3+105\ cm^3=385\ cm^3[/tex]

The combined volume is 385 cm³

For the lower box, the volume will be = (7 x 10 x 4) cm³ = 280 cm³

For the upper box, the volume will be = (7 x 5 x 3) cm³ = 105 cm³

∴  Combined volume will be equal to = ( 280 + 105) cm³ = 385 cm³

Option C is correct.

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Answer:

[tex]y= 51(1.5)^x[/tex]

Step-by-step explanation:

The ordered pairs model an exponential growth function. {(−1,34), (0,51), (1,76.5), (2,114.75)}

Exponential function equation is y=ab^x

Lets plug in the ordered pairs and find our 'a'  and 'b'

(0,51)

[tex]51= ab^0[/tex]

a= 51

(−1,34)

[tex]34= 51b^{-1}[/tex]

Divide both sides by 51

[tex]\frac{34}{51} = b^{-1}[/tex]

So b = 51/34

b= 1.5

Plug in the values of 'a'  and 'b'

Equation becomes [tex]y= 51(1.5)^x[/tex]

Answer:  a) Independent

b) Independent

c) Dependent

Step-by-step explanation:

Since, If a coin is tossed three times,

Then, total number of outcomes, n(S) = 8

a)  [tex]E_1[/tex] : tails comes up with the coin is tossed the first time;

[tex]E_1[/tex] = { TTT, THH, THT, TTH }

[tex]E_2[/tex] :  heads comes up when the coin is tossed the second time.

[tex]E_2[/tex] = { THT, HHH, THH, HHT }

Thus, [tex]n(E_1)=4[/tex]

⇒  [tex]P(E_1)=\frac{n(E_1)}{n(S)}=\frac{4}{8}=\frac{1}{2} [/tex]

Similarly,  [tex]P(E_2)=\frac{1}{2}[/tex]

⇒  [tex]P(E_1)\times P(E_2)=\frac{1}{2}\times \frac{1}{2}=\frac{1}{4} [/tex]

Since,   [tex]E_1\cap E_2 [/tex] = { THH, THT }

[tex]n(E_1\cap E_2) = 2 [/tex]

⇒ [tex]P(E_1\cap E_2) = \frac{n(E_1\cap E_2)}{n(S)}= \frac{2}{8}=\frac{1}{4}[/tex]

Thus,  [tex]P(E_1\cap E_2)=P(E_1)\timesP(E_2)[/tex]

Therefore,  [tex]E_1[/tex] and [tex]E_2[/tex] are independent events.

B)  [tex]E_1[/tex] :  the first coin comes up tails

[tex]E_1[/tex] = { TTT, THH, THT, TTH }

[tex]E_2[/tex] :   two, and not three, heads come up in a row

[tex]E_2[/tex] = { HHT, THH }

Thus, [tex]n(E_1)=4[/tex]

⇒  [tex]P(E_1)=\frac{n(E_1)}{n(S)}=\frac{4}{8}=\frac{1}{2} [/tex]

Similarly,  [tex]P(E_2)=\frac{1}{4}[/tex]

⇒  [tex]P(E_1)\times P(E_2)=\frac{1}{2}\times \frac{1}{4}=\frac{1}{8} [/tex]

Since,   [tex]E_1\cap E_2 [/tex] = { THH }

[tex]n(E_1\cap E_2) = 1 [/tex]

⇒ [tex]P(E_1\cap E_2) = \frac{n(E_1\cap E_2)}{n(S)}= \frac{1}{8}[/tex]

Thus,  [tex]P(E_1\cap E_2)=P(E_1)\timesP(E_2)[/tex]

Therefore,  [tex]E_1[/tex] and [tex]E_2[/tex] are independent events.

C)  [tex]E_1[/tex] :  the second coin comes up tails;

[tex]E_1[/tex] = { HTH, HTT, TTT, TTH }

[tex]E_2[/tex] :   two, and not three, heads come up in a row

[tex]E_2[/tex] = { HHT, THH }

Thus, [tex]n(E_1)=4[/tex]

⇒  [tex]P(E_1)=\frac{n(E_1)}{n(S)}=\frac{4}{8}=\frac{1}{2} [/tex]

Similarly,  [tex]P(E_2)=\frac{1}{4}[/tex]

⇒  [tex]P(E_1)\times P(E_2)=\frac{1}{2}\times \frac{1}{4}=\frac{1}{8} [/tex]

Since,   [tex]E_1\cap E_2 [/tex] = [tex]\phi[/tex]

[tex]n(E_1\cap E_2) = 0 [/tex]

⇒ [tex]P(E_1\cap E_2) = 0[/tex]

Thus,  [tex]P(E_1\cap E_2)\neq P(E_1)\timesP(E_2)[/tex]

Therefore,  [tex]E_1[/tex] and [tex]E_2[/tex] are dependent events.

Answer:

P (E1) = 18 / 38

P (E2) = 18 / 38

P (E1 and E2) = 10 / 38

Step-by-step explanation:

Answer:

Eric is not correct.

Step-by-step explanation:

We have been given that Eric estimated [tex]28\times 48[/tex] by finding [tex]30\times 50[/tex]. His estimate was 1500, but he says the actual product will be greater than that amount.

To find if Eric is correct or not, let us see how to estimate an answer.

While estimating our given numbers we will round to nearest tenth and change the digit to the right of the rounding place to 0.

As 8 is greater than 5, so we will round 28 to 30 and 48 to 50.

Since we are rounding up, so our estimated answer will be greater than actual answer, therefore, Eric is not correct.  

Answer:

A function describes this way is y = 4x + 2

Step-by-step explanation:

In order to find this, we have to start with slope-intercept form.

y = mx + b

Knowing this, we can then input the slope in for m and the intercept in for b. This will give us the equation.

y = 4x + 2

Lisa spends 4 minutes per call, so to spend a total of 12 minutes on the phone, she needs to route 3 calls.

Lisa spent 8 minutes on the phone routing 2 phone calls, which means she spends 4 minutes per call. This is calculated using the unit rate which is the time spent per phone call. To find out how many phone calls Lisa would have to route to spend a total of 12 minutes, we can set up a proportion where 4 minutes corresponds to 1 phone call (the unit rate), and 12 minutes corresponds to the number of phone calls we want to find (let's call it x calls).

The proportion is as follows:

4 minutes/1 call = 12 minutes/x calls

Cross-multiplying to solve for x gives us:

4 * x = 12 * 1

4x = 12

x = 12 / 4

x = 3 calls

Therefore, Lisa needs to route a total of 3 calls to spend 12 minutes on the phone.

[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ C(\stackrel{x_1}{x}~,~\stackrel{y_1}{y})\qquad E(\stackrel{x_2}{-8}~,~\stackrel{y_2}{-3}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{-8+x}{2}~~,~~\cfrac{-3+y}{2} \right)=\stackrel{\stackrel{midpoint}{D}}{(2,3)}\implies \begin{cases} \cfrac{-8+x}{2}=2\\[1em] -8+x=4\\ \boxed{x=12}\\[-0.5em] \hrulefill\\ \cfrac{-3+y}{2}=3\\[1em] -3+y=6\\ \boxed{y=9} \end{cases}[/tex]

Answer:

Cubic

Step-by-step explanation:

A cubic function is a function whose degree is 3 (the highest exponent or power on the variable). It has a distinctive sideways S shape that can either start down and end up or start up and end down. It also crosses through the x-axis an odd number of times. It will have up to three x-intercepts or roots.

Answer:

Robbie pay in twelve months $1080 .

$92.47 more Robbie pay and 9.36 %(Approx) Robbie pay.

Step-by-step explanation:

As given

Robbie Morse has a $47,500 insurance policy.

The annual premium is $987.53.

Robbie pays $90.00 monthly.

First find out the Robbie pay in twelve months .

Robbie pay in twelve months = 12 × 90

                                                  = $ 1080

Second find out how much more does Robbie pay .

Robbie pay extra = Robbie pay in twelve months -  annual premium

                             = $ 1080 - $987.53

                             = $92.47

Therefore the $92.47 more Robbie pay .

Third find out the what percentage does Robbie pay .

 Formula

[tex]Percentage = \frac{Robbies\ pay\ more\times 100}{annual\ premium}[/tex]

Robbies pay more = $92.47

Annual premium = $987.53

Put in the above

[tex]Percentage = \frac{92.47\times 100}{987.53}[/tex]

[tex]Percentage = \frac{9247}{987.53}[/tex]

Percentage = 9.36 % (Approx)

9.36 %(Approx) Robbie pay.

Robbie pays a total of $1,080.00 over twelve months, which is $92.47 more than the annual premium. This amount is approximately 9% more than the original annual premium.

To determine how much Robbie pays for his monthly premium over twelve months, we need to perform the following calculations:

First, calculate the total amount Robbie pays monthly. He pays $90.00 monthly, so over twelve months:

$90.00  times 12 = $1,080.00

Next, we need to find out how much more Robbie pays compared to the annual premium of $987.53:

$1,080.00 - $987.53 = $92.47

Percentage Calculation:

To find the percentage Robbie pays compared to the original annual premium, use the formula:

(difference / original amount) times 100

($92.47 / $987.53) times 100 ≈ 9%

Thus, Robbie pays approximately 9% more than the annual premium.