Today hugo got a new credit card, and he made a purchase of $1400. The card offers an introductory apr of 0% for the first 5 months and a standard apr of 30. 8% thereafter. If the card compounds interest monthly, how much money will the introductory apr save hugo in interest over the first 5 months? (assume that hugo will make no payments or additional purchases during the first 5 months, and ignore any possible late payment fees. ).

Answer:Let the magnitude of smaller force is P, the magnitude of larger force is Q and the resultant force is R.

As the resultant force makes 90

∘

 with the smaller force P then Q forms the hypotenuse of the triangle.

Thus, it can be written as,

Q

2

−P

2

=R

2

Q

2

−P

2

=(12)

2

Q

2

−P

2

=144                                (1)

The sum of magnitudes of two forces is given as,

P+Q=18

Q=18−P                                     (2)

Substituting the value from equation (2) in equation (1), we get

(18−P)

2

−P

2

=144

P=5N

Substituting the value of P in equation (1), we get

Q=18−5

=13N

Thus, the magnitude of the forces are 5N and 13N.

Step-by-step explanation:

The angle measure of the missing angle is  630 - 11x.

Angles inside a polygon are referred to as interior angles. A triangle, for instance, has three internal angles. Interior angles are sometimes defined as "angles confined in the interior area of two parallel lines when they are crossed by a transversal."

Given:
A non-regular hexagon.

The sum of all the interior angles of the hexagon is,

= (6 - 2) 180

= 4(180)

= 720

Now, the angle measure of the missing angle,

= 720 - 2x - 3x - 2x - 4x - 90

= 630 - 11x

Therefore, 630 - 11x is the required expression.

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1) values are 15, 16 and 17

2) Drawn in the graph (2)

3)  [tex]x \geq 6[/tex] and graph (3)

Question 6)  [tex]m > 4[/tex] and graph (6)

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

1)

As per the given data:

Values are: 12, 13, 14, 15, 16, 17

Given inequality:

[tex]\frac{x}{5} \geq 3\\= x \geq 5\times3\\= x \geq 15[/tex]

The values of [tex]x[/tex] greater than or equal to 15 out of the given values are:

15, 16 and 17

15, 16, 17 are the solutions of the given equality.

2)

Given inequality:

[tex]x < 8[/tex]

For making the graph, first draw the point [tex]x=8[/tex]

The region to the left of the point [tex]x=8[/tex] will represent the graph as shown in the diagram.

3)

Given inequality:

[tex]x-5\geq 1[/tex]

= [tex]x \geq 1 + 5[/tex]

=  [tex]x \geq 6[/tex]

For making the graph, first draw the point [tex]x=6[/tex]

The region to the right and including the point  [tex]x=6[/tex] will represent the graph as shown in the diagram.

6)

Given inequality:

[tex]6m > 24[/tex]

= [tex]m > \frac{24}{6}[/tex]

= [tex]m > 4[/tex]

For making the graph, first the plot the point m = 4.

The region to the right of the point m = 4 will represent the graph as shown in the diagram.

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Answer:

See below

Step-by-step explanation:

This is a triangular prism:

h = Perpendicular height of prism

Base shape = Triangle

t = Perpendicular height of triangle

Volume of triangular prism = Base Area × h

                  = Area of triangle × h

                  = [[tex]\frac{1}{2}[/tex] × Base of triangle × t] × h

                  = [[tex]\frac{1}{2}[/tex] × 5 in × 1.7 in] × 10 in

                  = 42.5 cubic inches

Total Surface Area = [2 × Base Area] + Lateral Surface Area

             = [2 × Area of triangle] + [(Perimeter of triangle) × h]

             = {2× [[tex]\frac{1}{2}[/tex] × 5 in × 1.7 in]} + [(5 in + 3 in + 3 in) × 10 in]
             = 8.5 [tex]in^{2}[/tex]  + 110 [tex]in^{2}[/tex]

              = 118.5 square inches

The value of angle L, x and angle M is 55°, 35 and 60° respectively

An equation is an expression that shows the relationship between numbers and variables using mathematical operators like addition, subtraction, multiplication and division. Equations can be linear, quadratic.

From the triangle:

∠OLM + ∠MLN = 180° (sum of angles in a straight line)

125 + ∠MLN = 180°

∠MLN = 55°

Also:

∠MLN + ∠MNL + ∠LMN = 180 (sum of angle in a triangle)

substituting:

55 + (2x - 10) + 65 = 180

2x + 110 = 180

2x = 70

x = 35°

∠LMN = 2x - 10 = 2(35) - 10 = 60°

The value of angle M is 60°

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Possible answer: 9

Step-by-step explanation:

9 doubled is 18, and that is 9 more than the original number itself.

Unless I'm wrong.

20

Step-by-step explanation:

cause 565-65 is 500 and divide that by 25 is 20.

Answer:

20 weeks

Step-by-step explanation:

starting with an initial 65 adding money each week after 20 weeks he would've added 500

Answer:

45? I'm not 1000% sure tog

Step-by-step explanation:

Answer:

Step-by-step explanation:

1/6 ÷ 8

1/6 × 1/8

1/48

for each batch

The graph of the equation -3x+y=6 is linear and is attached with the answer below.

A linear equation is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

The given linear equation is -3x+y=6. When we plot the linear equation -3x+y=6 on the graph it will be a straight line and the x and y-intercepts are -2 and 6 respectively.

The graph of the linear equation is attached with the answer below.

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A total of 250 packets of  4g cremora will make 1kg cremora box.

A function is a elation between a dependent and independent variable.

Given are 4g cremora sachets.

We can write the total number of cremora sachets that will make 1kg cremora box as -

{n} = 1000/4

{n} = 250

Therefore, a total of 250 packets of  4g cremora will make 1kg cremora box.

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Answer:

x = 64.6 degrees

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos theta = adjacent side / hypotenuse

cos x = 3/7

Taking the inverse cos of each side

x = cos^-1 ( 3/7)

x = 64.6 degrees

Answer:operation

Step-by-step explanation:

The best explanation of how to find the experimental probability of rolling a 3:

To find the experimental probability of rolling a three, write a ratio of the number of times three occurs to the total number of trials.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

We have the Data as:

Number    Frequency     Probability

1                      4                  0.13

2                      6                  0.20

3                      5                  0.17

4                      7                  0.23

5                      3                  0.10

6                      5                  0.17

total                30                 1.00

To find the experimental probability of rolling a three, write a ratio of the number of times three occurs to the total number of trials.

= 5/30

= 1/6

= 0.166

= 16.6% or 17%.

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The ACT Math section tests a wide range of mathematical concepts and skills, so there are many formulas and concepts that you should be familiar with.

Here are some of the most important ACT math formulas that you should know:

1. Basic operations: addition, subtraction, multiplication, and division.

2. Exponents and roots: [tex]a^n[/tex] means a multiplied by itself n times; the nth root of a is the number that, when raised to the nth power, gives a.

3. Order of operations: parentheses, exponents, multiplication/division (from left to right), and addition/subtraction (from left to right).

4. Fractions: converting between fractions, decimals, and percents; adding, subtracting, multiplying, and dividing fractions.

5. Algebra: solving equations and inequalities; simplifying algebraic expressions; factoring quadratics; understanding linear and quadratic functions.

6. Geometry: properties of lines, angles, and polygons; Pythagorean theorem; trigonometric functions; volume and surface area of 3D shapes.

7. Probability and statistics: calculating probabilities; mean, median, and mode; standard deviation.

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Expression for actual length and actual width of the concrete patio are

30x inches and 30y inches respectively.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

For example, if we have a rectangle of sides 2 cm and 4 cm, we can enlarge it by multiplying each side by a number, say 2.

Given,

A blueprint of a concrete patio has a scale of 2 inches=5 feet.

2 inches = 60 inches

scale factor = 60/2 = 30

Let length of the patio on the blue print is x inches

width of the patio on the blue print is y inches

then actual length of the 30x inches

actual width of the patio = 30y inches

Hence, 30x inches is actual length and 30y inches is actual width of the concrete patio.

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The number of sunglasses that will fail the quality inspection are 7.

What is a ratio?

A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six.

We are given that, A company produced 9,800 pairs of sunglasses

in one week, and 49 of the sunglasses failed a quality inspection.

And based on this data we are asked to find the number of sunglasses which will fail the quality inspection If the company produces

1,400 pairs of sunglasses in one day

Let the number of sunglasses failing the quality inspection be x

hence the ratio becomes

9800/49 = 1400/x

x= 1400*49/9800

x= 7

The number of sunglasses that will fail the quality inspection are 7.

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The area of this figure with radius 20.8 ft include the following: D. 432.64π ft² ≈ 1358.5 ft².

Mathematically, the area of a circle can be calculated by using this mathematical expression:

Area = πr²

Where:

r represents the radius of a circle.

By substituting the radius into the formula for the area of a circle, we have the following;

Area of circle = π × 20.8²

Area of circle = 432.64π square feet.

Area of circle = 1358.5 square feet.

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Tn = 6Tn-1 is the recursive form of the sequence

A geometric sequence is determined by its common ratio. The standard recursive formula is expressed as:

Tn = rTn-1

Determine the common ratio of the sequence

r = 6/1 = 36/6

r = 6

Substitute the common ratio into the formula to have:

Tn = 6Tn-1

Hence the recursive form of the sequence above is Tn = 6Tn-1

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2.45 BTUs/ft³ is produced in 2 hours.

It is given that a human body that is performing light work generates about 700 BTUs.

Total heat generated by 3 peoples in 1 hour -

Q{heat} = 3 x 700

Q{heat} = 2100 BTUs/hr

For the two hours -

Q{T} = 2100 x 2

Q{T} = 4200 BTUs                                              ... { 1 }

Volume of the room -

V{R} = 12 x 13 x 11

V{R} = 1716 ft³                                                  ... { 2 }

So, we can write as -

BTUs per cubic foot produced in 2 hours is -

{r} = Q{T}/V{R}

{r} = 4200/1716

{r} = 2.45 ft³

Therefore, 2.45 BTUs/ft³ is produced in 2 hours.

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Answer:

Step-by-step explanation:

The ratio of a change in a quantity (dL) to the original quantity (L) is given by:

dL/L

This ratio can also be expressed as a percentage change, which is calculated by multiplying the ratio by 100:

(dL/L) * 100 = percent change

In general, the ratio of dL/L represents the fractional change in the quantity L and is used to quantify the effect of small changes in a system or process. For example, if L is the length of an object and dL is a small change in length, then dL/L represents the fractional change in length due to this change.

The system of linear inequalities (x, y) has a solution that is (-1, 2)

A system of linear inequalities is identical to a system of linear equations, but instead of equations, it is made up of inequalities. Many constraint scenarios are modeled using sets of linear inequalities.

We may determine the values of x and y in the above problem as;

x + y > 1 ...eq(i)

-x + y <= 3 ...eq(ii)

Solving both inequalities;

The solution is;

1 - x < y ≤ 3 + x

This is simple to plot on a graph, and the intersection will provide the answer;

The graph below shows the inequality's (x, y) solution, which is (-1, 2)

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Answer:

quadrilaterals

ok I only guss it

Answer:

Veronica is correct

Step-by-step explanation:

1/2 x 5/2 = 5/4

1/2 + 5/2 = 6/4

Arial's claim that the graphs of the two lines will be parallel if the coefficients are equal.

If the coefficients of the y-terms are equal and the coefficients of the x-terms are equal, the two lines represented by the equations will be parallel. Parallel lines have the same slope and do not intersect, meaning that their graphs will never cross.

To prove Arial's claim, here is an example:

y = 2x + 1 and y = 2x + 3

The coefficients of the y-terms are equal in both equations, since they both have a coefficient of 2 in front of the x-term. The coefficients of the x - terms are also equal, since they both have a coefficient of 1 in front of the constant term thereby making them parallel.

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Answer: T= 5 and s =17

Step-by-step explanation: Use the midpoint formula

Solve for T

^xm=^xC+^xD/2

15+t/2=10

15+t=20

Solve for S

^ym=^yC+^yD/2

s+3/2=10

s+3=20

The function rule that models this situation is that increase in the number of tickets would lead to an increase in the total cost charged for each individual.

A direct relationship between two values is said to exist when the increase in one value leads to the increase of the other.

The cost of 1 ticket = $.75

The cost to enter the carnival = $ 6

Therefore the total cost for each individual = 6+0.75 = $6.75

The cost for two tickets for two individuals = 2× 6.75 = $13.5.

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Answer:

(x, y) = (4, 1)

i don't have an explanation lol