QUESTION 1
A credit card has a balance of $1,400. The APR is 25% and the minimum payment is 3% of the balance. You will pay the minimum balance this month. If you do not use the card again then how much
should the balance be next month?
QUESTION 2
A credit card with an APR of 18% has a balance of $2500 on it. You make a $1400 payment that posts on the 11th day of a 31-day month. How much interest will you be charged for the month?
QUESTION 3
Suppose we have a card with an APR of 25%. The minimum payment is 7% of the balance Suppose we have a balance of $350 on the credit card. We decide to stop charging and to pay it off by making
the minimum payment each month.
Calculate the new balance after the first minimum payment is made.
Calculate the minimum payment that is due the next month.
QUESTION 4
Your credit card has a balance of $2500 and an interest rate of 21%. The credit card requires a minimum payment of 3%
Lennors

The correct interpretation of the slope and y-intercept of the equation y = mx + b in this context is:

A. The slope predicts a temperature increase of about 50° for every increase of 1 chirp per minute. The y-intercept shows that when the crickets are not chirping (x=0), the temperature is 0.

In other words, according to the given equation, for each additional chirp per minute, the temperature is expected to increase by approximately 50 degrees Fahrenheit. Additionally, when there are no chirps (x=0), the equation suggests that the temperature is 0 degrees Fahrenheit.

~~~Harsha~~~

Answer:

C

Step-by-step explanation:

I am pretty certain the math is incorrect on the other posted answer

The slope is   rise/run   means every degree produces 6 chirps more ....or conversely , 1/6 degree produces one more chirp.  

  when the temperature is 50 F there are ZERO chirps

The confidence interval using a margin of error of 0.07 is (0.85,0.99)

Sample proportion = 0.92

Margin of error = 0.07

Lower bound of the confidence interval = Sample proportion - Margin of error

Lower bound = 0.92 - 0.07 = 0.85

Upper bound of the confidence interval = Sample proportion + Margin of error

Upper bound = 0.92 + 0.07 = 0.99

Confidence interval = [Lower bound, Upper bound]

Confidence interval = [0.85, 0.99]

Therefore, the confidence interval for the proportion of math majors who found the curriculum challenging is approximately 0.85 to 0.99.

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The reason of discontinuity of the given function is described below.

Since we know that,

A continuous function, as the name implies, is one whose graph is continuous with no breaks or jumps. In other words, if we can draw the curve (graph) of a function without ever raising a pencil, we may claim that the function is continuous. The study of a function's continuity is critical in calculus because a function cannot be differentiable unless it is continuous.

A function is considered continuous if its graph is an uninterrupted curve with no holes, gaps, or breaks.

Now by mathematical definition of continuity

Left hand limit of a function at any point = right hand limit of function at that point = value of function at that point

Now from the graph we can see that,

At point point 3

The left hand limit and right hand limit are not equal and also the curve is discontinuous.

Hence, the given function is discontinuous function.

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Answer:

The length of a side of the base of the box is 13 cm.

Step-by-step explanation:

To find the length of a side of the base of the box, we need to use the formula for the volume of a box.

The volume of a box is given by the formula:

V = l^2 * h

Where:

V is the volume,

l is the length of a side of the base, and

h is the height of the box.

Substituting the given values:

V = 1352 cm^3

h = 8 cm

1352 = l^2 * 8

Dividing both sides by 8:

l^2 = 169

Taking the square root of both sides:

l = √169

Calculating the length of a side of the base:

l = 13 cm

Therefore, the length of a side of the base of the box is 13 cm.

a. Shape 1 = 24cm²

Shape 2 = 14.1cm²]

Total area = 38.1cm²

b. Shape 1 = 50ft²

Shape 2 = 24ft²

Total area =  74ft²

The formula for calculating area of a triangle is;

A = 1/2bh

Substitute the values

A = 1/2 × 8 × 6

Multiply the values

A = 24cm²

Area of a semicircle =3. 14 × 3²/2 = 14.1cm²

Total area = 38.1cm²

2. Area of the trapezoid is;

A = a +b/2h

A = 20/2(5) = 50ft²

Area of the triangle;

A = 1/2 × 6 × 8

A = 24ft²

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The length of segment TU for the intersecting chords is determined as 28.

The length of segment TU is calculated by applying intersecting chord theorem for two chords in a circle as shown below.

From the given diagram we will have the following equation;

UV (UV + TU) = WV (WV + XW)

We know that TU is 3 more than XW;

TU = XW + 3

So our new equation becomes;

26( ( 26 + XW + 3) = 27( 27 + XW)

26(29 + XW) = 27 (27 + XW)

Simplify further as follows;

754 + 26XW = 729 + 27XW

754 - 729 = XW

25 = XW

The length of segment TU is calculated as;

TU = 3 + 25

TU = 28

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Based on the LCM, Jaziel, Elisa, and Sofía will coincide again after 60 days.

From the information, in the family business, the siblings Jaziel Elisa and Sofía must help take care of it, so he comes every four days, Elisa every five days and Sofía that at six o'clock.

In order to determine when Jaziel, Elisa, and Sofía will coincide again, we need to find the least common multiple (LCM) of their visit intervals.

The intervals for Jaziel, Elisa, and Sofía are 4 days, 5 days, and 6 days, respectively. We need to find the smallest number that is divisible by all three of these intervals.

The LCM of 4, 5, and 6 is 60. Therefore, Jaziel, Elisa, and Sofía will coincide again after 60 days.

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In the family business, the siblings Jaziel Elisa and Sofía must help take care of it, so he comes every four days, Elisa every five days and Sofía that at six o'clock if the three have coincided on March 4 after how many days will they coincide again

Answer:

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

The y-intercept of (0, 4) means the function has a value of 4 when x = 0.

Verify it with given functions:

A) y = 3x + 1

B) y = 4ˣ

C) y = 1ˣ

D) y = 2ˣ + 3

Answer:

View explanation

Step-by-step explanation:

The highlighted arc from D to O

The linear program shows that there are different attainable arrangements that accomplish the same ideal objective function value..

Based on the given data, since the objective function values at the five corner points are diverse, able to conclude that there's no one-of-a-kind ideal arrangement for this linear program.

The reality that there are numerous distinctive objective function values at the corner points suggests that there are numerous ideal arrangements or that the objective work isn't maximized or minimized at any of the corner points.

In this case, the linear program may have numerous ideal arrangements, showing that there are different attainable arrangements that accomplish the same ideal objective function value.

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The own price elasticity of good X is -0.60, so we can conclude that good X is price inelastic.

The own price elasticity of good X is calculated using the formula:

Given the demand function for good X: Qxd = 6 - 2Px + 5Py, we can calculate the initial quantity demanded at a price of $3 per unit:

Qxd1 = 6 - 2(3) + 5(2)

= 6 - 6 + 10

= 10

The new quantity demanded when the price changes to $2.90 per unit:

[tex]Qxd_2[/tex] = 6 - 2(2.90) + 5(2)

[tex]Qxd_2[/tex] = 6 - 5.80 + 10

[tex]Qxd_2[/tex] = 10.20

Now, we can calculate the percentage change in quantity demanded:

% Change in Quantity Demanded = (Qxd2 - Qxd1) / Qxd1 * 100

% Change in Quantity Demanded = (10.20 - 10) / 10 * 100

% Change in Quantity Demanded = 0.20 / 10 * 100

% Change in Quantity Demanded = 2%

Next, we calculate the percentage change in price:

% Change in Price = (New Price - Old Price) / Old Price * 100

% Change in Price = (2.90 - 3) / 3 * 100

% Change in Price = -0.10 / 3 * 100

% Change in Price = -3.33%

The own price elasticity will be:

Elasticity = (% Change in Quantity Demanded) / (% Change in Price)

Elasticity = 2% / -3.33%

Elasticity ≈ -0.60

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It means that the domain of the relation [tex]R[/tex] is the set of such elements [tex]u[/tex] for which there exists such an element [tex]v[/tex] that [tex]u[/tex] and [tex]v[/tex] are related.

Answer:

2/13

Step-by-step explanation:

To find the probability of drawing a 6 or a king from a standard deck of cards, we need to determine the number of favorable outcomes (cards that are either a 6 or a king) and the total number of possible outcomes (total number of cards in the deck).

There are 4 kings in a standard deck (one king in each suit: hearts, diamonds, clubs, and spades) and 4 6s (one 6 in each suit).

Total number of favorable outcomes = 4 (4 kings) + 4 (4 6s) = 8

Total number of possible outcomes = 52 (total number of cards in the deck)

Therefore, the probability of drawing a 6 or a king is:

Probability = Number of favorable outcomes / Total number of possible outcomes

= 8 / 52

= 2 / 13

So, the probability of drawing a 6 or a king from a standard deck of cards is 2/13.

Answer:

0.5ml/hr

Step-by-step explanation:

Given:

Infusion rate: 0.002 units/min

To convert the infusion rate from units/min to ml/hr, we need to know the flow rate conversion factor specific to the medication and solution being administered.

In this case, we have the information that the patient is receiving 10 units of oxytocin (Pictocin) in 250 ml of D5W solution.

To calculate the ml/hr rate, we can use the following formula:

ml/hr = (Infusion rate in units/min * Volume in ml) / Time in min

ml/hr = (0.002 units/min * 250 ml) / 1 min

ml/hr = 0.5 ml/min

Therefore, the infusion rate of 0.002 units/min is equivalent to 0.5 ml/hr.

The step in which the subtraction property of equality was applied to solve the equation is given as follows:

D. The subtraction property of equality was not applied to solve this equation.

The subtraction property of equality states that subtracting the same number from both sides of an equation does not affect the equality, and hence it is used to isolate a variable that is adding on a side of the expression.

For this problem, to remove the term -7, we add 7 to both sides of the expression, hence the addition property of equality was applied.

In the other step, the multiplication property was applied, hence option D is the correct option for this problem.

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The measure of the ∠d is 65 degrees.

The measure of the ∠c is 89 degrees.

The measure of the arc a is 131 degrees.

The measure of arc b is 47 degrees.

The value of each variable. For the circle, the dot represents the center.

1. The measure of ∠d is;

∠d+ 115°= 180°

∠d= 180°-115°= 65°

The measure of the ∠d is 65 degrees.

2. The measure of ∠c is,

∠c+ 91°= 180°

∠c =180°-91° =89°

The measure of the ∠c is 89 degrees.

3. The measure of arc a is,

The inscribed angle measures half that of the arc comprising;

arc a = 230 - 90

arc a = 131 degrees

4. The measure of arc b is,

The inscribed angle measures half that of the arc comprising;

arc b = 178 - 131

arc b = 47 degrees

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Answer:

The area bounded by the two functions f(x) and g(x) on the interval [0, 2π] is 6π.

Step-by-step explanation:

The range of y = sin(2x) is [-1, 1].

As function f(x) = sin(2x) + 1 has been translated 1 unit up, the range of f(x) is [0, 2].

The range of y = cos(x) is [-1, 1].

As function g(x) = cos(x) - 2 has been translated 2 units down, the range of g(x) is [-3, -1].

As ranges of the functions do not overlap, the two functions do not intersect.

As the curve of f(x) is above the x-axis, and the curve of g(x) is below the x-axis, we can integrate to find the area between the curve and the x-axis for each function in the given interval, then add them together.

Note: As g(x) is below the x-axis, the evaluation of the integral will return a negative area. Therefore, we need to negate the integral so we have a positive area (since area cannot be negative).

[tex]\begin{aligned}A_1=\displaystyle \int^{2\pi}_{0} (\sin(2x)+1)\; \text{d}x&=\left[-\dfrac{1}{2}\cos(2x)+x \right]^{2\pi}_{0}\\\\&=\left(-\dfrac{1}{2}\cos(2(2\pi))+2\pi\right)-\left(-\dfrac{1}{2}\cos(2(0))+0\right)\\\\&=\left(-\dfrac{1}{2}+2\pi\right)-\left(-\dfrac{1}{2}\right)\\\\&=2\pi\end{aligned}[/tex]

As the curve is below the x-axis, remember that we need to negate the integral to find the area.

[tex]\begin{aligned}A_2=-\displaystyle \int^{2\pi}_{0} (\cos(x)-2)\; \text{d}x&=-\left[\vphantom{\dfrac12}\sin(x)-2x \right]^{2\pi}_{0}\\\\&=-\left[(\sin(2\pi)-2(2\pi))-(\sin(0)-2(0))\right]\\\\&=-\left[(0-4\pi)-(0-0)\right]\\\\&=-\left[-4\pi\right]\\\\&=4\pi\end{aligned}[/tex]

[tex]\begin{aligned}A_1+A_2&=2\pi+4\pi\\&=6\pi\end{aligned}[/tex]

Therefore, the area bounded by the two functions f(x) and g(x) on the interval [0, 2π] is 6π.

Which is the standard equation for a circle centered at the origin with radius r be,

⇒   x² + y²  = r²

Hence option D is correct.

We have to find the standard equation of circle,

Given that,

Center of circle is at (0, 0)

And radius is r

Let a point (x, y) on the circle.

We know that,

The distance between the point (x, y) and origin is also known as radius of the circle,

Since we know that,

The distance between two points (x₁ , y₁) and (x₂, y₂) is,

⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²

Therefore distance between (0, 0) and (x, y),

⇒   √[ (x - 0)² + (y - 0)²] = r

Squaring both sides we get,

⇒   (x - 0)² + (y - 0)²  = r²

⇒   x² + y²  = r²

This  is the standard equation of circle.

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The statement about the graph of y = tan x that is true is A The period is 2pi.

In the graph of y = tan x, the function has vertical asymptotes at x = (2n + 1)π/2, where n is an integer. At these points, the value of cos x becomes zero, causing the tangent function to approach positive or negative infinity.

The period of a function is the smallest positive number such that the graph of the function repeats itself after being shifted that number of units to the right or left. In the case of y=tanx, the graph repeats itself after being shifted π units to the right.

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Which statement about the graph of y = tan x is true?

A The period is 2pi.

B The function has horizontal asymptotes whenever cos x = 0.

C The function has zeros whenever csc x = 0.

D The function is increasing everywhere in its domain

The angles supplementary to ∠EOF are ∠FOB and ∠COE.

Supplementary angles are those angles that sum up to 180 degrees. In

other words, two angles are called supplementary when their measures

add up to 180 degrees.

Therefore, let's find the angles that are supplementary angles to ∠EOF.

Therefore, let's use the angle relationships in the line intersection to find

the angles that are supplementary to ∠EOF.

Hence, the angles supplementary to  ∠EOF are ∠FOB and ∠COE

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The value of angle x is determined as 40 degrees.

The value of angle y is determined as 180 degrees.

The value of the missing angles is calculated by applying intersecting chord theorem which states that the angle at tangent is half of the arc angle of the two intersecting chords.

The value of angle x is calculated as follows;

50 = ¹/₂ (140 - x ) (exterior angle of intersecting secants)

2(50) = 140 - x

100 = 140 - x

x = 140 - 100

x = 40

The value of angle y is calculated as follows;

The value of angle y is equal to the value of the remaining arc.

y = 360 - (40 + 140 ) ( sum of angles in a circle)

Simplify further as follows;

y = 360 - 180

y = 180⁰

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Answer:

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

The segment GI contains both GH and HI.

Using the segment addition postulate we set up an equation:

Substitute to get:

So the value of x is 9.

Answer:

$81.18

Step-by-step explanation:

Sale Price = Original Price - (Original Price * Discount Percentage)

Given:

Original Price = $82

Discount Percentage = 10%

Let's calculate the sale price:

Sale Price = $82 - ($82 * 10%)

Sale Price = $82 - ($82 * 0.1)

To simplify the calculation, we can convert 10% to its decimal form by dividing by 100:

Sale Price = $82 - ($82 * 0.1)

Sale Price = $82 - ($82 * 0.01)

Sale Price = $82 - $0.82

Using a calculator, we can find the value:

Sale Price = $81.18

Therefore, the sale price after a 10% discount would be $81.18.

Answer: $73.80 is sale price

Step-by-step explanation:

Original: $82

10% of 82

=.1(82)

=8.2       >this is your discount

Subtract

82-8.2

$73.80 is sale price

[tex]|\Omega|=8\\|\text{odd}|=4\\\\P(\text{odd})=\dfrac{4}{8}=\dfrac{1}{2}[/tex]

Answer:

4/8

or, 1/2

Step-by-step explanation:

odd numbers (O) = (1,3,5,7) = 4

total numbers (T) = 8

P(odd) = n(O)/n(T)

           = 4/8

To find the length of the third side of a right triangle when two sides are given, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Let's assume the two given sides are 'a' and 'b', and the unknown third side is 'c' (the hypotenuse).

Using the Pythagorean theorem:

c² = a² + b²

Substituting the given values:

c² = 4² + 5²

c² = 16 + 25

c² = 41

To find the length of 'c', we need to take the square root of both sides:

c = √41

So, the length of the third side is √41 (approximately 6.40) when rounded to two decimal places.

Therefore, the possible length of the third side of the right triangle is √41.

Step-by-step explanation:

We will use a phayragoras theorem

a^2 +b^2= c^2

let side1=4 be a

let side2=5 be b

let the 3rd side be the hypotnuous=c

therfore 4^2+5^2=c^2

=16+25=c^2

=41=c^2.

therfore c=√41

Answer:

  tan(2x) = 2√2

Step-by-step explanation:

You want tan(2x) when tan(x) is -2/√2 and x is a 4th-quadrant angle.

The tangent double-angle identity is ...

  tan(2x) = 2tan(x)/(1 -tan(x)²)

For tan(x) = -2/√2, this gives ...

  tan(2x) = 2(-2/√2)/(1 -(-2/√2)²) = -2√2/(1 -2)

  tan(2x) = 2√2

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Answer:

fraction of circle = [tex]\frac{3}{10}[/tex]

Step-by-step explanation:

a complete circle has central angle of 360° , then

fraction of circle = [tex]\frac{108}{360}[/tex] ← divide numerator/ denominator by 36

fraction of circle = [tex]\frac{3}{10}[/tex] ← in simplest form

The values of m and n are 15 and 19, respectively in the given data.

From the given values:

x: 1, 2, 7, 4, 9

y: 3, 5, 11, m, n

Looking at the x-values, we can observe that they are increasing by 1 each time.

Looking at the y-values, we can observe that they are increasing by 2 each time except for the last two values (m and n) which are unknown.

Based on this pattern, we can establish the following equation:

y = 2x + 1

Now, let's calculate the values of m and n using this equation:

For x = 7:

y = 2(7) + 1

y = 14 + 1

y = 15

Therefore, m = 15.

For x = 9:

y = 2(9) + 1

y = 18 + 1

y = 19

Therefore, n = 19.

Hence, the values of m and n are 15 and 19, respectively.

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