-4x - 15y = -10
x + 3y = 1

The balance in the account after 1 year due to continuous compounding is approximately $1030.45 and AYP is 3.04%.

What is meant by continuous compounding?

If compound interest is calculated and reinvested into the balance of an account across an essentially unlimited number of periods, continuous compounding is the mathematical limit that compound interest can reach. Continuous compounding determines interest by assuming constant compounding across an infinite number of periods, as opposed to computing interest on a finite number of periods, such as annually or monthly.

Given,

rate per period  = 3%

Principal amount = $1000

Compounding is done after 1,5 and 20 years.

But we are asked to find the amount after continuous compounding after 1 year.

The formula of the amount after continuous compounding is:

[tex]A = Pe^{rt}[/tex]

where A = amount after continuous compounding

        r = rate of period

     t = time period

    P  = principal amount

[tex]A = Pe^{rt} = 1000e^{0.03*1}[/tex] = $1030.45

Annual yield formula (AYP) = [tex](1+\frac{r}{n} )^n-1[/tex]

n = times it compounds per year = 365

r = 0.03

AYP = [tex](1+\frac{0.03}{365} )^{365}-1 = 0.0304[/tex]

                                  = 3.04%

Therefore The balance in the account after 1 year due to continuous compounding is approximately $1030.45 and AYP is 3.04%.

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According to the information in the graph, the cheapest route to travel through all cities would be: Atlanta - Dallas - San Francisco - Los Angeles - New York - Detroit - Atlanta.

To calculate the cheapest option to travel to all cities, we must identify our starting point in the city of Atlanta and analyze which is the cheapest option to travel. In this case, it would be the Detroit or Dallas option (at this point we can choose either one).

Once we choose Dallas, we must apply a location strategy so that the next move leaves us in a suitable position to go to the cities of the east coast. Therefore, the best option would be San Francisco and then Los Angeles.

After this, the best (cheaper) option would be to take transportation to New York, Detroit, and finally to Atlanta. Finally, we must add the values of the displacements to know what the total value is:

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The required, area of the triangle to the nearest 10th of a square inch is 34.1 square inches.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should equal to 180°

Here,
Calculating unknown angle v,
Since the sum of the angles in the triangle is equal to 180,
u + w+ v = 180
5 + 19 + v = 180
v = 180 - 24
v = 156°

Now,
Calculating the unknown side w,
U/sinu = W/sinw
6.7/sin5° = W/sin19°

W =25.0277

Now,
Area of the triangle is given as
= 1/2 UW sinv

= 1/2× (25.027)×(6.7)×(sin156°)

= 34.1 square inch

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The linear equation for the parallel line will be y=6x-3.

What exactly is a linear equation?

The equation is referred to as linear when a variable's maximum power is 1. A one-degree equation is another name for it. A linear equation in one variable has the conventional form Ax + B = 0. This equation has three variables: x, A, and B. A is a coefficient. A linear equation in which there are only two variables typically takes the form Ax + By = C. In addition to the constant C, there are three other constants: the variables x and y, the coefficients A and B, and the variables.

Now,

Line parallel to line y=6x-7 will have same slope which will be m=6

as general equation is y=mx+c where m=slope and c=constant.

For parallel line c will be as it is passing through (2,9)

9=6*2+c

c=9-12

c=-3

then the equation will be y=6x-3

Hence,

           The equation for the parallel line will be y=6x-3.

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x= 19, y=19

There is a theorem with 45 degrees 45 degrees 90 degrees triangles, it is that the two legs are equal to a and the hypotenuse is equal to a√2

So, since we know the hypotenuse is 19√2, a=19

so x = 19and y = 19

The value of the exterior angle x of the quadrilateral is equal to

The sum of the exterior angles of any convex quadrilateral is 360 degrees so we have that:

65 + 106 + 78 + x = 360

simply the left hand side of the equation

249 + x = 360

subtract 249 from both sides of the equation

249 - 249 + x = 360 - 249

x = 111°

In conclusion, since the sum of the exterior angles of a quadrilateral is s 360°, we have got the measure of one the the exterior angle x to be equal to 111°

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Distance of the house from the base of the cliff is 282.27 m.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

From the figure attached,

AB = Height of the cliff = 60 m

Let the distance between the base of the cliff and the house 'C' = x m

If the angle of depression = 12°

Then angle of elevation of the top of the cliff from the house = 12°

Now from right triangle ABC,

tan12=60/x

x=60/tan 12

x=60/0.21256

x = 282.27 m

Therefore, distance of the house from the base of the cliff is 282.27 m.

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Answer:

The answer is thirty (30)

Answer:

-1/2

Step-by-step explanation:

cos(-360+60)=-1/2

[tex]\cos(\alpha - \beta)= \cos(\alpha)\cos(\beta) + \sin(\alpha)\sin(\beta) \\\\[-0.35em] ~\dotfill\\\\ -300\implies 30-330\hspace{5em}\cos(-300^o)\implies \cos(30^o-330^o) \\\\\\ \cos(30^o-330^o)\implies \cos(30^o)\cos(330^o)+\sin(30^o)\sin(330^o) \\\\\\ \cfrac{\sqrt{3}}{2}\cdot \cfrac{\sqrt{3}}{2}~~ + ~~\cfrac{1}{2}\cdot \cfrac{-1}{2}\implies \cfrac{3}{4}~~ + ~~\cfrac{-1}{4}\implies \cfrac{3}{4}-\cfrac{1}{4}\implies \cfrac{2}{4}\implies \boxed{\cfrac{1}{2}}[/tex]

The demand function of the question is expressed as;

D(q) = -²/₅₀₀₀q + 14.6

The formula to find the slope between two coordinates is;

m = (y2 - y1)/(x2 - x1)

The coordinates we are given are;

(28000, 9) and (33000, 7)

Thus;

Slope; m = (7 - 9)/(33000 - 28000)

m = -2/5000

Now, the equation of a line in point slope form is;

y - y1 = m(x - x1)

Where (x1, y1) is (28000, 9)

y - 9 = (-2/5000)(x - 28000)

y - 9 = -²/₅₀₀₀x + 5.6

y = -²/₅₀₀₀x + 14.6

This can be rewritten as a demand function; D(q) = -²/₅₀₀₀q + 14.6

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Answer:x^3+x^2-8x-32

Step-by-step explanation:

Answer:

28

Step-by-step explanation:

IF 20 GALLONS IS EQUIVALENT TO 5 SECONDS WHAT ABOUT 7 SECONDS

CROSS MULTIPLY

Answer:

20 gallons / 5 seconds = 4 gallons / second

Therefore, In 7 seconds you get (7 x 4 ) or 28 gallons.

Step-by-step explanation:

The number of inches Sami is taller to his younger sister as per their respective given heights is equal to 9 inches.

Height of Sami in feet and inches is equal to 5 feet 8 inches

Height of Sami's younger sister is equal to 4 feet 11 inches

Convert all height into inches we get,

1 feet = 12inches

5 feet = 5 × 12 inches

          = 60 inches

4 feet = 4 × 12 inches

          = 48 inches

Number of inches Sami's is taller than his younger sister is equal to

= ( 5 feet 8 inches ) - ( 4 feet 11 inches )

= ( 60 + 8 ) inches - ( 48 + 11 ) inches

= 68 inches - 59 inches

= 9 inches

Therefore, the number of inches Sami is taller than his younger sister is equal to 9 inches.

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The graph of the quadratic function can be seen on the image at the end.

The only way to graph or sketch a function by hand, is by finding some points on the graph and then connecting them.

To find the points we need to evaluate the quadratic equation.

if x = 0

y = 5*0^2 + 2 = 2

So we have the point (0, 2)

if x = 1

y = 5*1^2 + 2 = 7

So we have the point (1, 7)

if x = -1

y = 5*(-1)^2 + 2 = 7

So we have the point (-1, 7)

And so on, once you have enough points, you can graph them on the coordinate axis and then connect them. The graph of the quadratic equation can be seen on the image at the end.

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Step-by-step explanation:

you have to find your five number summary

The solutions to the quadratic equation 25 = (x + 9)² are x = -4 and x = -14.

What is quadratic equation?

A quadratic equation is a polynomial equation of degree 2, which means that the highest power of the variable in the equation is 2. The general form of a quadratic equation is:

ax^2 + bx + c = 0

where x is the variable, and a, b, and c are constants, with a not equal to 0. The quadratic equation can have two solutions, one solution, or no real solutions, depending on the values of a, b, and c.

Starting with the given equation:

25 = (x + 9)²

We can start by taking the square root of both sides of the equation, which gives us:

±5 = x + 9

Next, we can isolate x by subtracting 9 from both sides of the equation:

x = -9 ± 5

This gives us two solutions:

x = -9 + 5 = -4

or

x = -9 - 5 = -14

Therefore, the solutions to the quadratic equation 25 = (x + 9)² are x = -4 and x = -14.

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The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the following formula:

m = (y2 - y1) / (x2 - x1)

Plugging in the points (-11, 12) and (5, 4), we get:

m = (4 - 12) / (5 - (-11)) = -8 / 16 = -1/2

So the slope of the line passing through (-11, 12) and (5, 4) is -1/2.

Answer:

Step-by-step explanation:

Let's call the present value of the loan P. The payments of $1,550 in 1 year and $2,400 in 4 years can be expressed as an ordinary annuity with semi-annual payments. We can calculate the present value of this annuity using the formula:

PV = A * (1 - (1 + r)^-n) / r

where

A = $1,550 / 2 = $775 (semi-annual payment)

n = (4 x 2) + 2 = 10 (number of semi-annual periods)

r = 0.045 / 2 = 0.0225 (semi-annual interest rate)

So,

PV = $775 * (1 - (1 + 0.0225)^-10) / 0.0225 = $8,100.40

Thus, the present value of the loan is P = $8,100.40.

Next, we can calculate the present value of the payment of $1,050 in 24 months and the balance in 30 months.

The payment of $1,050 in 24 months can be expressed as a single amount due in 24 months. The present value of this payment can be calculated as:

PV = $1,050 / (1 + 0.0225)^(24/2) = $1,000.54

So, the balance of the loan after this payment would be P - $1,000.54 = $8,099.86.

The balance in 30 months can be expressed as an ordinary annuity due with semi-annual payments. We can calculate the present value of this annuity using the formula:

PV = A * (1 - (1 + r)^-n) / r

where

A = ($8,099.86) / 6 = $1,349.98 (semi-annual payment)

n = 6 (number of semi-annual periods)

r = 0.0225 (semi-annual interest rate)

So,

PV = $1,349.98 * (1 - (1 + 0.0225)^-6) / 0.0225 = $7,999.86

Therefore, the payment required in 30 months for the rescheduled option to settle the loan is $1,349.98 per semi-annual period.

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Answer:

(C) 29

Step-by-step explanation:

Answer:

the least possible number of marbles in the bag is 12.

Step-by-step explanation:

As for the question about the marbles, let's call the number of red marbles "x". Then the number of white marbles is 4x, the number of blue marbles is 5x, and the number of green marbles is (1/2) * 5x = 2.5x.

The total number of marbles in the bag is x + 4x + 5x + 2.5x = 12.5x.

To find the least possible number of marbles, we need to find the smallest possible value of x, which will give us the smallest total number of marbles. Since x represents the number of red marbles, it must be a positive integer. The smallest positive integer value of x is 1.

So, if there is one red marble, there are 4 white marbles, 5 blue marbles, and 2.5 green marbles. The total number of marbles in the bag is 1 + 4 + 5 + 2.5 = 12.5.

Therefore, the least possible number of marbles in the bag is 12.

45 and 27.6 degrees are the two complementary angles.

The various angles or measurements include:

Angles that are complementary are those whose sum is 90 degrees. If the smaller angle has a measure of x, then the complementary angle's measure is 90 - x.

The issue shows that the greater angle (x + 17.4) is 17.4 degrees larger than the corresponding angle's measurement (90 - x). To find x, we can construct the following equation:

x + 17.4 = 90 - x + 17.4

When we simplify and find x, we obtain:

2x = 55.2

x = 27.6

The greater angle's measure is x + 17.4 = 45 degrees, while the smaller angle's measure is x = 27.6 degrees.

The two complementary angles are 27.6 and 45 degrees as a result.

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In the vertex form the equation can be rewritten as x = 1×(y - 2)² + 5

The equation is given in the standard form y²-4y-x+9 = 0 and we have to convert it into vertex form

So basically, the general vertex form of any equation is x = a(y - k)² + h

⇒ y²-4y-x+9 = 0

Shifting the x to RHS,

⇒ x = y²- 4y + 9

Writing y²- 4y in the form of (a-b)²,

⇒ x = y²- 4y + 4 + 5

⇒ x = 1×(y - 2)² + 5,

Hence the equation is now converted to vertex form

⇒ where a = 1, k = 2 and h = 5

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Answer:

3,641 cups drank

Step-by-step explanation:

A quart is 4 cups

At the start of the party, there were 912 quarts, multiply that by 4 to get 3,648 cups

At the end of the party, only 7 cups remained

3648 - 7 = 3,641 cups drank

Percentages are:

Middle school

Spring = 75%    Winter = 25%

High school

Spring = 40%     Winter = 60%

What is the percentage?

A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Frequently, it is indicated with the per cent sign, "%".  A percentage is a number without dimensions and without a standard measurement.

Given,

Middle school

Number of students preferring spring = 93

Number of students preferring winter = 31

High school

Number of students preferring spring = 36

Number of students preferring winter = 54

Total  number of middle school students =  93 + 31 = 124

Percentage of middle school students who prefer spring =  [tex]\frac{93}{124} * 100[/tex]

                                                                                     = 75%

Percentage of middle school students who prefer winter = [tex]\frac{31}{124} * 100[/tex] = 25%

Total number of high school students = 36+54 = 90

Percentage of high school students who prefer spring = [tex]\frac{36}{90} * 100[/tex]

                                                                                             =  40%

Percentage of high school students who prefer winter = [tex]\frac{54}{90} *100[/tex]

                                                                                            = 60%

Therefore the above is the percentage of students who prefer spring and winter.

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Answer:-50/7 or -7.143

Step-by-step explanation:

you have to turn the 3 4/7 into an improper fraction by this:

3x7=21

21+4=25

which makes it 25/7

(25/7)x(-2) = -50/7 or -7.143

The transformation of triangle XYZ vertices at X(0, 5), Y(10, 3), and Z(4, -1), indicates that the coordinate of the point Z'' following a composite transformation of a translation of (x, y) → (x + 2, y + 3), and a reflection across the x-axis, is located at the point (6, -2). The correct option is therefore;

A reflection transformation is a transformation that produces a mirror image of a geometric figure across a line of reflection.

The coordinates of the vertices of the triangle are;

X(0, 5), Y(10, 3), Z(4, -1)

The transformation rule that is used to translate the triangle ΔXYZ (to get ΔX'Y'Z'), can be presented as follows;

The reflection of the translated figure of the triangle (ΔX'Y'Z'), to get ΔX''Y''Z'', is a reflection across the x-axis, therefore, we get;

Therefore, we get the coordinate of the point (x, y) following the composite transformation is the point (x + 2, -(y + 3))

The coordinates of the point Y(4, -1) following the composite transformation is therefore;

Y(4, -1) → (4 + 2, -(-1 + 3)) = (6, -2)

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Answer:

6-oz bottle is a better deal

Step-by-step explanation:

To find which is a better value, find the unit rates for both types of bottles

The bottle with the lower unit rate is the better deal

6-ounce bottle costs $4.19
Unit rate = 4.19/6 oz = $0.70 per oz

14-ounce bottle costs $10.89
Unit rate = 10.89/14 = $0.78 per oz

Hence the 6-oz bottle is a better deal

Answer:

3 and 1/12 left

Step-by-step explanation:

The numbers can be arranged as follows

The math question is solved using the idea of PEMDAS which is an acronym for order of arrangement of mathematical operations as

the full meaning include

P - parenthesis

E  - exponents

M - multiplication

D - division

A - addition

S - subtraction

Applying the sequence the to make the expression 1 2 3 4 5 6 7 8 9 equal to 30 using addition and subtraction signs:

(1 - 1) + 2 - (3 + 4) + (5 + 6 + 7 + 8 + 9) = 30

You can use parentheses to group the numbers and then add or subtract the groups to get the desired result.

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There are 16% of the Green were Planes.

The percentage is defined as a ratio expressed as a fraction of 100.

Total number of green planes = 250

The total number of all planes = 1550

The percent of green planes = (number of green planes/number of total planes ) x 100

The percent of green planes = (250/1550) x 100

The percent of green planes = 0.1612 x 100

The percent of green planes = 16.129

Round to the nearest percent, and we get

The percent of green planes = 16%

Thus, 16% of the Green were Planes.

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