Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
You have a credit card with a balance of $1,367.90 at a 9.5% APR. You pay $400.00 each month on the
due date until the card is paid off. How many months does it take to pay off the card, and what is the total
amount paid including interest?
Be sure to include in your response: answer and steps

The measure of the side AE would be 70 units.

We know that the triangle midpoint theorem says that the line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is congruent to one half of the third side.

In the given triangle B, D, F are the midpoints of the triangle.

AC=50, CE=60,

BD=35

Then, in the given triangle if BD is connecting the midpoints of AC and CE then it must be parallel to AE and equal to FE ( half of AE).

⇒ BD ≅ FE= 1/2 AE

AE = 70 units

Then, the length of line segment AE = 70 units

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The time it takes the bicycle to travel along the road is 20 seconds.

The rate of change of position of an object in any direction is called as Speed.

The formula for speed is Distance divided by Time.

So Time = distance / speed

we need to know the distance the bicycle travels to use this formula.

If we have this distance, we can divide it by the speed of 5 m/s to find the time.

Let the distance is 100 meters, then the time taken is:

time = distance / speed = 100 / 5 = 20 seconds

Hence, the time it takes the bicycle to travel along the road is 20 seconds.

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The complete question is given below:

A bicycle travels along with the road at an average speed of 5 m/s work out the time it takes the bicycle to travel along the road of distance 100 meters.

Give your answer in seconds

Answer:

[tex] \frac{1}{2} \times 25 \times 10 = 125 [/tex]

[tex] \frac{1}{2} \times breath \times perpedicular \: hight[/tex]

The difference between the median rating for each company is approximately 0.3 times the interquartile range.

Generally speaking, the median for 20 observations is the average of the 10th and 11th number:

Median rating of Company A = (4 + 4)/2

Median rating of Company A = 8/2

Median rating of Company A = 4.

Median rating of Company B = (3 + 3)/2

Median rating of Company B = 6/2

Median rating of Company B = 3.

Difference in median = 4 - 3

Difference in median = 1

For the required expression that models the difference between the median rating for each company and the interquartile range, we have the following:

1 = 3x

x = 1/3.

x = 0.3

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Answer:

  b = 30

Step-by-step explanation:

You want the value of b given line y = 20x +b passes through the points (6, 150) and (11, 250).

The equation y = 20x +b can be solved for b:

  b = y -20x . . . . . . . . subtract 20x

Using the given point (x, y) = (6, 150), you have ...

  b = 150 -20(6) = 150 -120

  b = 30

The magnitude of the vector is 25.5 metres.

The magnitude of a vector is the length of the vector. Therefore, the magnitude of a vector can be found using Pythagoras's theorem as follows:

Hence,

c² = a² + b²

where

Therefore,

| N | = √22.2² + 12.6²

| N | =  √492.84 + 158.76

| N | =  √651.6

| N | = 25.5264568634

| N | = 25.5 metres

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The points M(0, -1), and T(4, 6), on the diagonal [tex]\overline{MT}[/tex] of the rhombus MATH, indicates that the equation of the line containing the diagonal [tex]\overline{AH}[/tex], in slope and intercept form is; [tex]y = 3\frac{9}{14} - 4\cdot \frac{x}{7}[/tex]

A rhombus is a quadrilateral that has four congruent sides.

The specified shape of the quadrilateral MATH = A rhombus

The coordinates of the endpoints of the diagonal [tex]\overline{MT}[/tex] of the rhombus are;

The equation of the line that contains the diagonal [tex]\overline{AH}[/tex] of the rhombus can be found as follows;

The diagonals of a rhombus are perpendicular, therefore, the slope of the diagonal, [tex]\overline{AH}[/tex]is -1 divided by the slope of the diagonal [tex]\overline{MT}[/tex]

The slope of [tex]\overline{MT}[/tex] = (6 - (-1))/(4 - 0) = 7/4

The slope of [tex]\overline{AH}[/tex] = -1/(7/4) = -4/7

The diagonals of a rhombus bisect each other, therefore, the diagonals [tex]\overline{MT}[/tex] and [tex]\overline{AH}[/tex] intersect at the midpoint of point [tex]\overline{MT}[/tex]

Therefore, the midpoint of [tex]\overline{MT}[/tex] is a point on the diagonal line that contains the diagonal [tex]\overline{AH}[/tex]

The midpoint of [tex]\overline{MT}[/tex] = ((0 + 4)/2, (-1 + 6)/2) = (2, 2.5)

The equation of the line containing the diagonal [tex]\overline{AH}[/tex] is therefore;

y - 2.5 = (-4/7)·(x - 2)

y = -4·x/7 + 8/7 + 2.5 = -4·x/7 + 51/14

y = -4·x/7 + 51/14 = -4·x/7 + 3 9/14

y = [tex]3\frac{9}{14}[/tex] - 4·x/7

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On solving the provided question, we can say that in the equation,Often, there is only one variable, which also serves as the symbol. An illustration would be , [tex]D = 4(82-D)+2[/tex]

The equal sign (=), which denotes equality, is used to unite two statements in a mathematical equation. In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions.

For instance, the equal sign separates the variables 3x + 5 and 14 in the equation 3x + 5 = 14.The two sentences on either side of a letter are connected by a mathematical formula.

Each equation has a formula. Not every equation has a formula. Equations are created with the intention of being solved for a variable. If an equation meets the requirements for a function, it is a function. But not every equation is a function.

M+D = 82 marbles

[tex]M= 82- D[/tex]

[tex]D= 4M+2[/tex]

[tex]D= 4(82-D) +2[/tex]

[tex]D= 328 - 4D+2[/tex]

[tex]5D = 330[/tex]

[tex]D= 66[/tex]

Therefore, Don has 66 and Mark has 82-66 = 16

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The inequality is written as 15x + 70y ≤ 920. Then the region below the line is the solution to inequality.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

Serenity is assembling beaded jewelry with no more than 920 beads she presently has in inventory. Bracelets use 15 beads and necklaces use 70 beads.

Let 'x' be the number of bracelets and 'y' be the number of necklaces. Then the inequality is given as,

15x + 70y ≤ 920

The region below the line is the solution to inequality.

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The amount of money that is invested in the first and second accounts will be 40,000 and 60,000, respectively.

The possible value of the variables that satisfy the equation which is known as the solution of the equation.

The interest is given as,

I = PRT / 100

Let 'x' be the amount invested in the first bank. Then the amount of investment in the second bank is (100,000 - x). Then the equation is given as,

x · 0.06 · 1 + (100,000 - x) · 0.08 · 1 = 7,200

0.06x + 8,000 - 0.08x = 7,200

-0.02x = -800

x = 40,000

The amount in the second bank is given as,

⇒ 100,000 - 40,000

⇒ 60,000

The amount of money that is invested in the first and second accounts will be 40,000 and 60,000, respectively.

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The x-intercepts of the graph of the given polynomial function as described is; 2, 3 and -5.

The x-intercepts of a polynomial function are otherwise termed, roots, solutions or zeroes of the polynomial function.

On this note, the x-intercepts of the polynomial function which is as described in this scenario are;

x - 2 = 0; x = 2.

x - 3 = 0; x = 3.

x + 5 = 0; x = -5.

Ultimately, the x-intercepts of the polynomial function in discuss are; 2, 3 and -5.

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Answer:

5/6

Step-by-step explanation:

The number of ways 3 man and 3 woman line up at the counter in a store is 720 ways.

Factorials is defined as the mathematical expression that is the product of the given number down to 1. It is denoted with the symbol n! which means that is n is given as 4, then it's factorial would be = 4×3×2×1 = 24.

Given that, three men and three women line up at a checkout counter in a store.

a) Number of ways = 6!

= 6×5×4×3×2×1

= 720 ways

b) The first person in line is a woman, and then the line alternates by gender that is a woman, a man, a woman, a man, a woman, a man, and so on

There are 3 number of ways for woman standing in the odd position and for men standing in the even position.

So, number of ways = 3!×3!

= 3×2×1×3×2×1

= 36 ways

c) There are 3 men and 3 women.

Probability first is a woman is 3/6

Probability second is a man is 3/5

Probability third is a woman is 2/4

Probability fourth is a man is 2/3

Probability fifth is a woman is 1/2

Probability sixth is a man is 1/1

Multiply all these probabilities together and you get:

3/6 × 3/5 × 2/4 × 2/3 × 1/2 × 1/1 = 0.05

Therefore, the number of ways 3 man and 3 woman line up if the first person in line is a woman, and then the line alternates by gender that is a woman is 36 ways.

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Answer:

The complement of a set A, denoted A', is the set of all elements that are not in A. The complement of B, denoted B', is the set of all elements that are not in B.

Step-by-step explanation:

(a) A' = {b, d}

(b) B' = {a, c, d}

(c) A' U B = {a, b, c, d, e} (the union of A' and B contains all elements in both sets)

(d) A U B' = {a, b, c, e} (the union of A and B' contains all elements in both sets)

(e) A' n B = {} (the intersection of A' and B is an empty set)

(f) A n B' = {c} (the intersection of A and B' contains all elements that are in A but not in B)

(g) A' U A = {a, b, c, d, e} (the union of A' and A is the universal set, containing all elements)

(h) B' n B = {} (the intersection of B' and B is an empty set)

(i) A U B = {a, b, c, e} (the union of A and B contains all elements in both sets)

(j) A' U B' = {a, b, c, d, e} (the union of A' and B' is the universal set, containing all elements)

(k) [A n B]' = {b, d} (the complement of the intersection of A and B is the union of the complements of A and B)

(l) A' n B' = {} (the intersection of A' and B' is an empty set).

Aɳʂɯҽɾҽԃ Ⴆყ ɠσԃKEY ꦿ

Answer:

A = 0.50x+20

B= 0.75x+22

4 games

$19

Step-by-step explanation:

For abbey, the 20 dollars she starts with is the initial value. the 50 cents per game would be the constant rate of change/slope. So, the equation(y=mx+b) would be A = 0.50x + 20. For Bianca, the 22 dollars she starts with is her initial value. the 75 centers per game would be the constant rate of change/slope. So, the equation(y=mx+b) would be B = 0.75x + 22.

We can find out when they will have the same amount of money left by making two small tables -> one for abbey and one for Bianca.

Abbey: (the number is the number of games and the corresponding value next to it is the amount of money left ---- its kind of hard to make a table on BRAINLY)

Bianca: (the number is the number of games and the corresponding value next to it is the amount of money left ---- its kind of hard to make a table on BRAINLY)

For both girls after four games, they have the same amount of money- $19.

Step-by-step explanation:

7.

the probability of picking a defective missile with the first pull is

5/22

the probability of picking a working missile with the first pull is

17/22 = ((22-5)/22)

I have to assume that the picked missiles are not put back into the main pile after the check.

and I have to assume that the sequence of the pulled missiles don't matter.

a.

all are defective.

since there are only 5 defective missiles, there is only one possibility out of all the possibilities to pull 5 out of 22 to get 5 defective missiles.

the possible combinations to pull 5 out of 22 :

C(22, 5) = 22! / ((22 - 5)! × 5!) =

= 22×21×20×19×18×17/(5×4×3×2) =

= 22×21×19×3×17 = 447,678

and we have one desired situation (all 5 are defective).

so, the probability is

1/447678 = 0.000002233748364... = 2.233748364e-006

b.

all 5 are functional.

the total possible cases to pull 5 out of 22 are still

447,678.

the desired cases are all cases to pull 5 out of the 17 (22 - 5) functional missiles.

that is

C(17, 5) = 17! / ((17 - 5)! × 5!) =

= 17×16×15×14×13 / (5×4×3×2) =

= 17×2×14×13 = 6,188

so, the probability to get one of these cases is

6188 / 447678 = 0.013822435...

The probability of picking a defective missile with the first pull is 5/22

The probability of picking a working missile with the first pull is 17/22

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

If we assume that the picked missiles are without replacements and the sequence of the pulled missiles don't matter,

Therefore, the probability that:

a. all are defective is 2.233748364e-006

Since there are only 5 defective missiles, there is only one way to get 5 defective missiles out of 22 possible outcomes.

The possible combinations to pull 5 out of 22 :

C(22, 5) = 22! / ((22 - 5)! × 5!) =

= 22×21×20×19×18×17/(5×4×3×2) =

= 22×21×19×3×17 = 447,678

and we have one desired situation (all 5 are defective).

so, the probability is 1/447678 = 0.000002233748364... = 2.233748364e-006

b. all 5 are functional is 0.013822435

the total possible cases to pull 5 out of 22 are still 447,678.

The ideal scenario is for all incidents to result in the removal of 5 of the 17 (22 - 5) operational missiles.

that is

C(17, 5) = 17! / ((17 - 5)! × 5!) =

= 17×16×15×14×13 / (5×4×3×2) =

= 17×2×14×13 = 6,188

so, the probability to get one of these cases is

6188 / 447678 = 0.013822435

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The number of gallons of paint that the painter should buy is; 4 gallons

The parameters given are;

Side length of cube = 20 ft

Area that a gallon of paint can cover = 400 square feet

Since the room is shaped like a cube, then it will have 4 equal wall areas.

Area of one wall = 20 * 20 = 400 square feet

Area of 4 walls = 4 * 400 = 1600 square feet

Since 400 sq.ft  is covered by 1 gallon, then;

1600 sq.ft = (1600 * 1)/400

= 4 gallons

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Answer: The correct system of linear inequalities that represents Leslie's situation is:

4x + 10y ≥ 120 (to represent the requirement to raise at least $120)

x + y ≥ 18 (to represent the requirement to sell at least 18 items in total)

x ≥ 0, y ≥ 0 (to represent that Leslie must sell a non-negative number of keychains and t-shirts)

Where x represents the number of keychains sold and y represents the number of t-shirts sold. The first inequality represents the minimum amount of money Leslie needs to raise, and the second inequality represents the minimum number of items she needs to sell. The last two inequalities represent that Leslie can only sell a non-negative number of items.

Step-by-step explanation:

Answer: 10.7 or 10.8

Step-by-step explanation:

so, first  [tex]a^{2} +b^{2} =c^{2}[/tex]

while [tex]a = 3.75[/tex] and [tex]b=10[/tex] and [tex]c=?[/tex]

so, it will be written as,

[tex]3.75^{2} +10^{2} =c^{2} \\[/tex]

[tex]14.0625+100=c^2[/tex]

[tex]114.0625=c^2[/tex] then square root both sides to have an answer of:

[tex]10.7=c[/tex]

That's if you are going to use the [tex]a=3.75[/tex]. as written in the question...

while if you're going to use [tex]a=4[/tex] (as shown in the figure) then only change the 3.75 with 4.

which will equal to...

[tex]4^2+10^2=c^2[/tex]

[tex]16+100=c^2[/tex]

[tex]116=c^2[/tex] then square root both sides to have an answer of:

[tex]10.77=c[/tex]

[tex]10.8[/tex] ≈ [tex]c[/tex]

hope you've understanded.!

Answer:

1 this is the answer because 1 is more than other number

Answer: 2: 56 degrees

4: 56 degrees

(Number 6 is not in the image)

Step-by-step explanation:

So for #2 we know the whole angle is 90 degrees, so all we have to do is 90-34 = 56

And for #4, we know the angle is 180 so all we have to do is 180-124=56

The equation of line is y = 1.5x + 5.5.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

We have the reference point as (-2, 2.5) and (-1, 4)

so, slope

= (4- 2.5)/ (-1 + 2)

= 1.5

and, the equation of line is

y- 2.5 = 1.5 (x+ 2)

y- 2.5 = 1.5x + 3

y = 1.5x + 5.5

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7200+80x = 3200+120x

Reason:

Canton starts off with 7200 people. Add on 80x to represent the fact the town grows 80 people per year. That's how we end up with the expression of 7200+80x

Similarly, the expression 3200+120x represents the idea Holly Springs started off with 3200 people and grows at 120 people per year.

The requried teacher needs $59.5 more to buy cups and napkins, as of the given condition.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
To find out how much more money the teachers will need to buy cups and napkins, we can first calculate the cost of each item and then add those costs together.

Each package of cups costs $3.50

The teachers need to buy 12 cups

So the total cost of cups is = 12 cups × ($3.50 per package) = $42

Now let's do the same thing for the napkins:

Each package of napkins costs $4.25

The teachers need to buy 10 napkins

So the total cost of napkins is = 10 napkins × ($4.25 per package) = $42.50

To find out how much more money the teachers will need to buy cups and napkins,

= $42 + $42.50 - $25
= $59.50 - $25 = $59.5

Therefore, the teachers will need $59.5 more to buy cups and napkins.

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Answer:a

Step-by-step explanation:

Answer: a

Step-by-step explanation: it's increasing and it's a line

The expression represents a quintic polynomial with 4 terms. The constant term is -6, the leading term is x⁵/2, and the leading coefficient is 1/2.

A polynomial expression is a mathematical equation in which the polynomial is set to zero. The equation is made up of variables, non-negative integer exponents, coefficients, arithmetic operations, and an equal sign.

From the polynomial expression given:

[tex]\dfrac{1}{2}x^5 - 6 - x^4 -5x^2[/tex]

The degree of a polynomial is the highest degree of its terms which helps us to determine the type of polynomial (quintic polynomial). The constant term is -6.

The leading term in a polynomial is the term with the highest degree = x⁵/2. The leading coefficient of a polynomial is the coefficient of the leading term is 1/2.

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Answer:

quadrinomial, 4, -6, 1/2x^5, 1/2

Step-by-step explanation:

quadrinomials are polynomials with 4 terms

constant is the number with no variable

leading term is the term at the beginning

leading coefficient is the number at the beginning

The radius, diameter, area and circumference of circle 1, 2, 3 and 4 are; (2, 4, 4π, 4π), (4, 8, 16π, 8π), (1, 2, 1π, 2π) and ( 8, 16, 64π, 16π) respectively.

The diameter of a circle is 2 times the radius of the circle.

The area of a circle is expressed as: A = πr²

The circumference of a circle is expressed as: 2πr

For question 1)

Radius r = 2

Diameter = 2 × radius = 2 × 2 = 4

Area = πr² = π( 2 )² = 4π

Circumference = 2πr = 2 × π × 2 = 4π

For question 2)

Radius r = 4

Diameter = 2 × radius = 2 × 4 = 8

Area = πr² = π( 4 )² = 16π

Circumference = 2πr = 2 × π × 4 = 8π

For question 3)

Diameter d = 2

Radius = diameter / 2 = 2/2 = 1

Area = πr² = π( 1 )² = 1π

Circumference = 2πr = 2 × π × 1 = 2π

For question 4)

Diameter d = 16

Radius = diameter / 2 = 16/2 = 8

Area = πr² = π( 8 )² = 64π

Circumference = 2πr = 2 × π × 8 = 16π

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Answer: A = 15 units²

Step-by-step explanation:

The figure has 1 pair of parallel sides and is therefore a trapezium.

The area (A) of a trapezium is calculated as

A =  h (b₁ + b₂ )

where h is the perpendicular height between bases and b₁, b₂ are bases

here h = 3, b₁ = 3 , b₂ = 7 , then

A =  × 3 × (3 + 7) = 1.5 × 10 = 15 units²