Roger Ratkin, the owner of Roger’s Subs, has three employees who earn $500, $550, and $700, respectively. How much does Roger owe for the first 12 weeks for SUTA and FUTA? Assume a SUTA rate of 5.3% and a FUTA rate of .8%.

Answer:

Option A is the correct choice.

Step-by-step explanation:  

We have been given the system of linear equations written by Draco. We are asked to find Draco's error.

Let us form a system of equations using our given information.

Let m represent the price of one muffin and b represent the cost of one bagel.

We are told that in one hour a bakery sold five muffins and nine bagels for a total of $25.50. We can represent this information in an equation as:

[tex]5m+9b=25.50...(1)[/tex]

The next hour the bakery sold three muffins and 12 bagels for a total of $28.50. We can represent this information in an equation as:

[tex]3m+12b=28.50...(2)[/tex]

Now let us see system of equations written by Draco.

[tex]5m+9b=28.50[/tex]

[tex]3m+12b=25.50[/tex]

We can see that Draco has set the price of 5 muffins and 9 bagels equal to $28.50, which is the price of 3 muffins and 12 bagels.

Therefore, Draco should have set the first equation equal to 25.50 and the second equation equal to 28.50. The correct choice is option A.

Answer:

You must have all A's for Honor roll.

Step-by-step explanation:

My sister is in it and she has all A's

A 3.4 unweighted GPA is generally considered good and may qualify for the honor roll, depending on your school's criteria.

Based on your grades, you have a 3.4 unweighted GPA.

To determine if this qualifies you for the honor roll, it would be best to check your school's specific requirements, as they can vary.

Typically, a 3.4 GPA is considered solid and may be sufficient for honor roll status in many high schools.

Here is a breakdown of your grades:

While you have mostly As and Bs, the C in Spanish 2 may affect your honor roll eligibility depending on your school's criteria.

Answer:

26/3 or if you want it simplified its 8 2/3 im not sure if you need it in decimals so i thought id write it anyway   8.666667

Step-by-step explanation:

1) Conversion a mixed number to a improper fraction

2) Conversion the other mixed number to a improper fraction      

3)  Multiply both numerators and denominators. Result fraction keep to lowest possible denominator

The value of [tex]2 \frac{3}{5} * 3 \frac{1}{3}[/tex] = 263 = 8 23 ≅ 8.6666667.

Given:

[tex]2 \frac{3}{5} * 3 \frac{1}{3}[/tex]

1) Conversion of a mixed number to an improper fraction.

2) Conversion of the other mixed number to an improper fraction.    

3)  Multiply both numerators and denominators. The result fraction keeps to the lowest possible denominator.

Therefore, the value of [tex]2 \frac{3}{5} * 3 \frac{1}{3}[/tex] is 8.6666667.

To learn more about improper fraction

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Answer:

Hello from MrBillDoesMath!

Answer:

Choice A.   (1/25 )

Discussion:

The caret symbol, "^", denotes "exponentiation".  So

5 ^-2  = (1/5)^2 = (1/5)* (1/5) = 1/25

Regards,  

MrB

f  ( x ) =  3 x −  1

Hope that helps

Answer:

C.  [tex]\sqrt{\frac{25}{36} }[/tex]

Step-by-step explanation:

This comes from the property of exponents which says for any numbers [tex]a[/tex], [tex]b[/tex], and  [tex]c[/tex],

[tex](a*b)^c=a^c*b^c[/tex]

Since square roots are just exponents of [tex]\frac{1}{2}[/tex] power ([tex]\sqrt{x} =x^\frac{1}{2}[/tex]), and [tex]\frac{1}{x} =x^{-1}[/tex], we have

[tex]\frac{\sqrt{25}}{\sqrt{36} }=25^{\frac{1}{2} }*36^{-\frac{1}{2} }=25^{\frac{1}{2} }*(36^{-1})^{\frac{1}{2} }=(25*(36^{-1})})^{\frac{1}{2}[/tex]

[tex]=\sqrt{25*36^{-1}} =\sqrt{\frac{25}{36} }[/tex]

Which is choice C.

Answer:

the guy is correct

Step-by-step explanation:

i got it right on apex

Answer:

thousands place?

Step-by-step explanation:

169.866666667

9 in tenths place

6 in hundredths place

1 is in the thousands place

Answer:

AB = JK = 49

Step-by-step explanation:

Since ABC = JKL

We know the length of AB has to equal the length of JK.

AB = JK

14x+7 = 5x+34

Subtract 5x from each side.

14x-5x +7 = 5x-5x+34

9x+7 = 34

Subtract 7 from each side

9x+7-7 = 34 -7

9x = 27

Divide each side by 9.

9x/9 = 27/9

x =3

AB = 14x+7

Substitute x=3

      14(3) +7

      42+7

AB =    49

Answer:

Groceries is 625 a month

Step-by-step explanation:

25 percent of 2500 is 625. To get this answer take the percent and go back 2 decimal places this will turn 25% into 0.25 then multiply 2500 by 0.25 and the answer is 625. This also is the same with the other values. 0.30 0.15 etc.

Answer:

Groceries is 625 a month.(A lot of food for a single)

Step-by-step explanation:

Answer:   88 Feet Per Second

Step-by-step explanation:  

Firstly you need to know 3 things:  

> 60 mph = 60 Miles Per Hour  

> 1 Hour = 60 mins = 60*60 = 3600 seconds  

> 1 Mile = 5280 feet  

Next you can change the miles to feet and hours to seconds.  

60 mi/ 1 hour = 60*5280/ 3600 = 316800ft/ 3600sec  

Now time to reduce that big fraction! (Or in this case just divide by 3600 sec)  

316800ft/ 3600sec  

= 88ft/1sec  

= 88 Feet Per Second  

Hope that helps!

Answer:

4.5       3.5       3           -1        -3

Step-by-step explanation

the first number of the decimal is the whole number which means 4.5 and 3.5 are the 2 largest and for negative numbers. if the number is further away from zero that number is smaller.

For example

-15 is less that -1

this is so because the 15 is further away from the zero than the one

Answer:

It is a sequence of integers cubed.

1^3 = 1

2^3 =8

3^3 = 27

4^3 =64

5^3 = 125

6^3 = 216

Step-by-step explanation:

Answer:

Emily

Step-by-step explanation:

I made all the runners times into minutes. So Adam ran 450 feet in one minute (9 × 60), Jake ran 696 feet in 1 minute (If you divide 383 by 33 you get 11.6, then you multiply 11.6 by 30 to get 348 and then 348 × 2 is 696), Ron ran 528 in a minute (1 mile = 5280 feet and 600 seconds is 10 minutes), and Emily ran 755 feet in 1 minute. So your answer is Emily because she ran the most distance in 1 minute.

Answer:

c= 12t

c is the amount of energy you burn, so it'll be the "solution" to the equation. Multiply 12 times the amount of time you spend exercising to find how much energy you'll burn.

Answer:

Step-by-step explanation:You can first divide 15 by 5, which equals 3.Then multiply that by 10.8.which gives 32.4. Then divide by 5 which would give you 2.16. Hopefully it helps?!

Also if it is right,Please make me brainliest!!!!!!!!!!!!!!!!!!!

Answer:

43.2 minutes  PLEASE GIVE BRAINLIEST

Step-by-step explanation:

10.8 ÷ 15 = .72  (72%)

Now find what 72% of an hour is:

60 x .72 = 43.2

43.2 minutes

Answer:

time upstream=24/8=3 hours

time downstream=24/12=2 hours

Step-by-step explanation:

If R*T=D, and R is speed + or - current, how can you find the rate without the time, and how can you find the time without the rate?

THE KEY WAS WHEN WE WERE TOLD THAT IT TAKES ONE HOUR LONGER TO GO UPSTREAM THAN DOWNSTREAM BECAUSE T=D/R AND WE ARE TOLD THAT:

D/R(Upstream) minus 1 equals D/R (DOWNSTREAM)

Let x=rate of current

distance(d)=rate(r) times time(t) or d=rt or t=d/r

distance upstream=distance downstream=24 mi

rate upstream=10-x

rate downstream=10+x

time upstream=(distance upstream)/(rate upstream)=24/(10-x)

time downstream=(distance downstream)/(rate downstream)=24/(10+x)

Now, we are told that time upstream minus one hour equals time downstream. So our equation to solve is:

24/(10-x)-1=24/(10+x) Multiply both sides by (10-x)(10+x)

24(10+x)(10-x)/(10-x)-1(10-x)(10+x)=24(10-x)/(10+x)/(10+x) clear fractions

24(10+x)-(10-x)(10+x)=24(10-x) clear parens

240+24x-100-10x+10x+x^2=240-24x subtract 240 from and add 24x to both sides

240-240+24x+24x-100+x^2=240-240-24x+24x collect like terms

x^2+48x-100=0 ----------------quadratic equation in standard form

This equation can be factored:

(x+50)(x-2)=0

x=-50 mph----------------discount the negative value for speed

and

x=2 mph----------------------speed of the current

CK

10-x=10-2= 8 mph -----------------------speed upstream

10+x=10+2=12 mph--------------------------speed downstream

time upstream=24/8=3 hours

time downstream=24/12=2 hours

so 3-2=1----takes 1 hour longer upstream

For this case we must find the number of marbles that Jennifer has.

Let T be the variable that determines the number of total marbles that Jennifer has.

Let x be the variable that represents the number of red marbles that Jennifer has. So, [tex]x = 7[/tex]

Let y, the variable that represents the number of marbles blues Jennifer has. So, [tex]y = 7[/tex]

To find the value of T, we must add the variables x and y.

So, [tex]T = x + y[/tex]

[tex]T = x + y[/tex]

[tex]T = 7 + 7\\T = 14[/tex]

So, Jennifer has 14 marbles.

Answer:

14 marbles

Answer:

The vertices are:

A' = (-3, -3)

B' = (3, -3)

C' = (3, 3)

D' = (-3, 3)

Step-by-step explanation:

Given:

A 2 x 2 square is centered at the origin.

So, the center of the square is (0, 0)

Since it is 2 x 2 square, the side of the square is 2 units.

So, the vertices of the 2 x 2 square are A (-1, -1),  B(1, -1), C(1. 1), D(-1, 1)

The above square is dilated by a factor of 3.

Let's name the dilated square A'B'C'D'

To find the coordinates of the vertices of dilated square, we need to multiply each vertices of ABCD by 3.

A(-1, -1) = 3(-1, -1) = A'(-3, -3)

B(1, -1) = 3(1, -1) = B'(3, -3)

C(1, 1) = 3(1, 1) = C'(3, 3)

D(-1, 1) = 3(-1, 1) = D'(-3, 3)

Answer:

Distance = 70 + 55 = 125 kilometers

Time = 4 + 3 = 7 hours

Rate = Distance / Time

Rate = 125 / 7 = 17.8571428571 kilometers per hour

Step-by-step explanation:

The average speed:

[tex]v=\dfrac{total\ distance}{total time}[/tex]

We have

total distance = 70 km + 55 km = 125 km

total time = 4 h + 3 h = 7 h

The average speed:

[tex]v=\dfrac{125\ km}{7\ km}\approx18\ \dfrac{km}{h}[/tex]

Let's read this in a more proper way.

The number of boys in Mr. Watson's class is 2/3 the number of girls. So:

[tex]18 * \frac{2}{3} = 12\\18 + 12 = 30[/tex]

There are 30 students in Mr. Watson's class.

For this ratio to be in true in the second problem (306 boys, 459 girls), 306 must be 2/3 of 459.

[tex]459 * \frac{2}{3} = 306[/tex]

The ratio holds true for the second problem.

30 students,

Yes it is possible, because 306 is 2/3 of 459.

Answer: The area is 572.5566

Step-by-step explanation:

27÷2=r=13.5

A=πr²

A=3.1416(π) · 13.5²(r)

A=572.5566

Answer:

Given:

Diameter= 27 inches

radius= d/2

        =27/2

        =13.5

Answer:

[tex]x=475[/tex] units

Step-by-step explanation:

Method 1

The given revenue function is [tex]R(x)=95x-0.1x^2[/tex].

We rewrite this function in the vertex form by completing the square.

[tex]\Rightarrow R(x)=-0.1x^2+95x[/tex].

[tex]\Rightarrow R(x)=-0.1(x^2-950x)+0[/tex].

We add and subtract half the coefficient of [tex]x[/tex] multiplied by a factor of [tex]-0.1[/tex], which is [tex]-0.1(-\frac{950}{2})^2=-0.1( -475)^2[/tex] to get,

[tex]R(x)=-0.1(x^2-950x)+-0.1(-475)^2--0.1(-475)^2 +0[/tex].

We factor [tex]-0.1[/tex] out of the first two expressions again to get,

[tex]R(x)=-0.1(x^2-950x+(-475)^2)--0.1(-475)^2 +0[/tex].

We now got a perfect square.

[tex]\Rightarrow R(x)=-0.1(x-475)^2+22562.5[/tex].

Therefore the maximum revenue occurs when [tex]x=475[/tex] units were sold.

Method 2

Use derivatives to find the x-value of the maximum point.

[tex]R(x)=-0.1x^2+95x[/tex]

[tex]R'(x)=-0.2x+95[/tex]

At maximum point,

[tex]R'(x)=0[/tex]

[tex]\Rightarrow -0.2x+95=0[/tex].

[tex]\Rightarrow -0.2x=-95[/tex].

[tex]\Rightarrow x=\frac{-95}{-0.2}[/tex].

[tex]\Rightarrow x=475[/tex].

The maximum revenue is achieved when 475 units are sold in the given function R = 95x - 0.1x^2, which was determined by taking the first and second derivatives of the revenue function.

In order to find the number of units that produce maximum revenue in the equation R = 95x - 0.1x^2, you have to differentiate the revenue function R with respect to x and set the derivative (first derivative) equal to 0 to find the critical points.

The derivative of the function R with respect to x is R' = 95 - 0.2x. Setting this equal to zero gives: 95 - 0.2x = 0. Solving for x provides x = 95/0.2 = 475. Hence, 475 units sold will maximize revenue according to the provided revenue function.

To confirm this is a maximum, you can use the second derivative test. The second derivative of R, R'' = -0.2. Since this value is negative, x = 475 indeed corresponds to a maximum point on the graph of R(x). Hence, maximum revenue is achieved when 475 units are sold.

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Answer:

There are 2,730 ways that 1st, 2nd and 3rd place can be determined in the race

Step-by-step explanation:

There are 15 (number of runners) possibilities to determine the 1st place

There are 14 possibilities (number of runners - 1) to determine the 2nd place

There are 13 possibilities (number of runners - 2) to determine the 3rd place

Number of ways that 1st, 2nd and 3rd place can be determined = 15 * 14 * 13

Number of ways that 1st, 2nd and 3rd place can be determined = 2,730

Answer:

The value of x is -0.5.

Step-by-step explanation:

The given equation is

[tex]-2(5x-6)+6x=4(x+4)[/tex]

Use distributive property to solve the above equation.

[tex]-2(5x)-2(-6)+6x=4(x)+4(4)[/tex]

[tex]-10x+12+6x=4x+16[/tex]

[tex]-4x+12=4x+16[/tex]

Add 4x both sides.

[tex]12=8x+16[/tex]

Subtract 16 from both sides.

[tex]-4=8x[/tex]

Divide both sides by 8.

[tex]\frac{-4}{8}=\frac{8x}{8}[/tex]

[tex]-0.5=x[/tex]

Therefore value of x is -0.5.

Answer:

Step-by-step explanation:

Answer:

Rounding, we get 11.5 percent

Step-by-step explanation:

To find the percent of discount, we take the original price, subtract the new price, and divide by the original price.  Then multiply by 100 for the percent.

percent discount = (original - new)/ original * 100

percent discount = (36.30-32.12) /36.30 * 100

percent discount = (4.18) /36.30 * 100

percent discount = .115151515 * 100

percent discount = 11.51515 percent

Rounding, we get 11.5 percent

Answer:

The Han dynasty last was, 215 years

Step-by-step explanation:

Given statement: The Han dynasty lasted from 206 B.C. to 9 A.D.

To find how many years did the dynasty last.

B.C. represents Before Christ

A.D. represents After Death

To find the difference between two dates,

You can see that the endings in the given 206 B.C. and 9 A.D. are B.C. and A.D. are different.

Just add these 206 and 9 we get;

[tex]206 + 9 = 215[/tex] years

Therefore, 215 years did the Han dynasty last.

Answer:

(Y × 10) + X = 30

hope it helps

Step-by-step explanation:

Y = Cost of each ticket

X = cost of entry fee

so he bought 10 tickets

so you multiply cost of each ticket ( y ) by 10

then you add the entry fee ( x ) to find the total cost ( $30 )