Ellen has a $19,750 balance on a credit card with an APR of 18%. If she makes minimum monthly payments of $300, how much will it cost Ellen to repay the total amount on the credit card? $

Answer with explanation:

The Vertices of quadrilateral A B CD, are A(1, a - 3), B(10, a), C(9, a + 3) and D(0, a).

Mid point of AC= (5,1)

Mid point of B D= (5,1)

Mid point formula of two points having coordinates , (a,b) and (c,d) is , if (x,y), then

    [tex]x=\frac{a+b}{2},y=\frac{c+d}{2}[/tex]

 [tex]So,\rightarrow \frac{a-3+a+3}{2}=1\\\\\rightarrow \frac{2a}{2}=1\\\\\rightarrow a=1[/tex]

So, the coordinates of vertices of quadrilateral A B CD, are A(1, -2), B(10, 1), C(9, 4) and D(0, 1).

Distance formula of two points having coordinates, (a,b) and (c,d) is,

       [tex]=\sqrt{(a-c)^2+(b-d)^2}[/tex]

   [tex]AB=\sqrt{(10-1)^2+(1+2)^2}=\sqrt{81+9}=\sqrt{90}=3\sqrt{10}\\\\BC=\sqrt{(10-9)^2+(1-4)^2}\\\\=\sqrt{1+9}\\\\=\sqrt{10}\\\\CD=\sqrt{(9-0)^2+(3-0)^2}=\sqrt{90}=3\sqrt{10}\\\\DA=\sqrt{(1-0)^2+(1+2)^2}=\sqrt{10}\\\\AC=\sqrt{(9-1)^2+(4+2)^2}=\sqrt{64+36}\\\\AC=\sqrt{100}\\\\AC=10\\\\BD=\sqrt{(10-0)^2+(1-1)^2}\\\\BD=10[/tex]

Opposite sides  AB and CD are equal to 3√10 unit and , BC and AD are equal to √10 unit.

Also,length of Diagonals , AC=B D=10 unit.

∴ The Quadrilateral, AB CD is a Rectangle.

An algebraic expression is a mathematical phrase that contains numbers, variables (like x or y) and operators (like add,subtract,multiply, and divide).

We have to form the algebraic expression for the phrase

" The product of 86 and the depth of the river"

Let the depth of the river be 'd'

Therefore, the algebraic expression = Product of '86' and 'd'

= [tex] 86 \times d [/tex]

= 86d.

Therefore, the algebraic expression for the given phrase is "86d".

Final answer:

Emma takes 4 hours to knit a hat and 10 hours to knit a pair of mittens, which was determined by solving two linear equations based on the time she spent knitting during two different falls.

Explanation:

Emma likes to knit hats and mittens, and we need to find out how long it takes her to knit a hat and a pair of mittens individually. Given that last fall she knitted 4 hats and 3 pairs of mittens in 46 hours, and this fall she knitted 2 hats and 1 pair of mittens in 18 hours, we can set up two equations to solve for the time it takes to knit each item.

Let's define H as the number of hours it takes to knit one hat and M as the number of hours it takes to knit one pair of mittens. The equations based on the given information are:

4H + 3M = 46 (Last fall's knitting)

2H + 1M = 18 (This fall's knitting)

To solve these equations, multiply the second equation by 2 to align the hats:

2(2H + 1M) = 2(18)

4H + 2M = 36

Now subtract this equation from the first equation to find M:

4H + 3M - (4H + 2M) = 46 - 36

M = 10

Substituting M back into the second original equation:

2H + 1(10) = 18

2H = 8

H = 4

Emma takes 4 hours to knit a hat and 10 hours to knit a pair of mittens.

Answer: Option 'B' is correct.

Step-by-step explanation:

Your anniversary is usually when you are given a job review and possible increase in pay.

As in a job, job review is given at the time of anniversary, then on the basis of their performance there may be increase in pay.

So, Meaning of anniversary in a official way is when work performance of an individual is discussed and if there is good record , there is an increment.

Hence, Option 'B' is correct.

Answer:

B-5.49

Step-by-step explanation:

Final answer:

Angela's total restaurant bill, after adding a 15% tip to her $30.00 original charge, will be $34.50.

Explanation:

To find out how much Angela's total bill will be after leaving a 15% tip at a restaurant, you first need to calculate the tip amount and then add it to the original bill. You calculate the tip by converting the percentage to a decimal and then multiplying by the cost of the meal. In this case, 15% of $30.00 is found by multiplying $30.00 by 0.15 which gives you $4.50. After calculating the tip amount, add it to the original bill to get the total amount Angela will pay.

Tip: $30.00 * 0.15 = $4.50.

Total bill: $30.00 + $4.50 = $34.50.

Therefore, Angela's total bill, including the 15% tip, will be $34.50.

Answer: [tex]\dfrac{2}{5}[/tex]

Step-by-step explanation:

From the given table, The number of times arrow stops over Section 3  = 32

The total number of times spinner spins = 80

Now, the experimental probability of the arrow stopping over Section 3 is given by :-

[tex]P(S-3)=\frac{32}{80}\\\\\Rightarrow P(S-3)=\dfrac{2}{5}[/tex]

Hence, the experimental probability of the arrow stopping over Section 3  is [tex]\dfrac{2}{5}[/tex]

Let H be the event that head occurs and let T be the event that tail.

Then the complete Sample Space,S for the experiment given in the question is:

S={ HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}

As we can see the total number of elements in the sample space is 8. Let us represent this by the letter N.

Therefore, N=8

Now, the event of interest to us is TTT and it's occurrence is once. Let represent this by the letter E.

Therefore, E=1

Thus, the probability of the event E occurring is given as:

[tex] P(E)=\frac{E}{N}=\frac{1}{8} [/tex]

[tex] \frac{1}{8} [/tex] is the required answer. This can be represented in percentage too as:

[tex] \frac{1}{8}\times 100=12.5 [/tex]%

Answer:

The function has

2 real roots and

2 imaginary roots.

Answer:

3(8+3)

Step-by-step explanation:

The correct unit price for the work gloves is $1.13 per pair, and the error in the reported unit price is $12.43 per pair, as the contractor incorrectly reported it as $13.56 per pair.

The question is asking to calculate the correct unit price for the padded work gloves purchased by the contractor and to identify the error in the calculation provided in the expense report.

Firstly, let's determine the total number of pairs of gloves. Since 1 dozen represents 12 items, 7 dozen pairs of gloves will be [tex]7 \times 12 = 84[/tex] pairs of gloves.

Now, to find the correct unit price, we divide the total cost by the total number of pairs:

Unit Price = Total Cost / Total Number of Pairs

Unit Price = $94.92 / 84 pairs

Unit Price = $1.13 per pair

The incorrect unit price was calculated as $13.56 per pair. Therefore, the error in the calculation is:

Error = Incorrect Unit Price - Correct Unit Price

Error = $13.56 - $1.13

Error = $12.43 per pair

The contractor overestimated the unit price by $12.43 per pair.