$4,500 is invested at 10% annual interest, which is compounded continuously, what is the account balance after 3 years

The equation of the line is 2y+3x=-38

To find the equation of a line perpendicular to 3x= -20-2y that passes through the point (-6,-8), we can use the point-slope form of a line. The point-slope form of a line is[tex]y - y_1 = m(x - x_1)[/tex], where m is the slope of the line and [tex](x_1,y_1)[/tex] is an arbitrary point on the line. Since the given line has a slope of -2/3, the perpendicular line has a slope of 3/2. Therefore, the equation of the line can be written as y - (-8) = (3/2)(x - (-6)). Solving for y, we get 2y + 3x = -38. Therefore, the equation of the line is 2y + 3x = -38.

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The lateral surface area of the geometric shape formed by the given net is 3,780 sq in.

The lateral surface area is the sum of the areas of the trapezoidal faces and the rectangular faces.

The area of a trapezoid is given by the formula:

A = (1/2)h(b1 + b2)

where A is the area, h is the height, b1 and b2 are the lengths of the parallel sides.

Area of trapezoid 1 = (1/2)(30 + 18)(48) = 972 sq in

Area of trapezoid 2 = (1/2)(18 + 18)(48) = 864 sq in

The area of each rectangular face is given by the product of the length and the width.

Area of rectangular face 1 = 30 x 18 = 540 sq in

Area of rectangular face 2 = 48 x 18 = 864 sq in

Area of rectangular face 3 = 30 x 18 = 540 sq in

The total lateral surface area is the sum of the areas of all the faces:

Lateral surface area = Area of trapezoid 1 + Area of trapezoid 2 + Area of rectangular face 1 + Area of rectangular face 2 + Area of rectangular face 3

Lateral surface area = 972 + 864 + 540 + 864 + 540

Lateral surface area = 3,780 sq in

Therefore, the lateral surface area of the geometric shape formed by the given net is 3,780 sq in.

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As a result, this same current price index stands at about 481.2.

Amount offered or established as consideration again for sale of a certain item. the quantity of anything that is bought, requested, or bartered for another; also known as the price paid for something.

We may use the following formula to determine a current price index using 1975 price as reference value:

Price index: 100 multiplied by (Current market price / Reference price).

First, we must change the 56.7 cent price from 1975 to current currency:

Reference price is equal to 56.7 cents divided by $1.01 to get $0.567.

In the formula, we can then enter a current price oil $2.73 / gallon or the case the cost of $0.567 per gallon:

Price index equals ($2.73 | $0.567) x 100 ≈ 481.22

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Answer:

1) 165.7 cm²

2) 736 cm²

3) 155.5 cm²

4) 169 cm²

Step-by-step explanation:

1) To find the area of shaded region, subtract the area of circle from the area of triangle.          

r = 4 cm      

[tex]\boxed{\text{\bf Area of circle = $\pi r^2$}}[/tex]

                          [tex]= 3.14 * 4 * 4 \\\\= 50.27 \ cm^2[/tex]

Triangle :                  

base = b = 18 cm              

height  = h = 24 cm        

[tex]\boxed{\text{\bf Area of triangle = $\dfrac{1}{2}b*h$}}[/tex]

                              [tex]= \dfrac{1}{2}*18*24\\\\= 9 * 24\\\\= 216 \ cm^2[/tex]

Area of shaded part = area of triangle - area of circle                                  

                                  = 216 - 50.27                                  

                                  = 165.73                                    

                                  = 165.7 cm²

3) To find the area of shaded part, subtract the area of semicircle from the area of square.            

side = 16 cm      

[tex]\boxed{\text{\bf Area of square = side * side}}[/tex]

                            [tex]= 16 * 16\\\\= 256 cm^2[/tex]

diameter of semicircle = side of the square

d = 16 cm                                      

r = 16÷ 2                                      

r = 8 cm        

[tex]\boxed{\text{\bf area of semicircle = $\dfrac{1}{2}\pi r^2$}}[/tex]

                                 [tex]= \dfrac{1}{2}*3.14*8*8\\\\= 100.53 \ cm^2[/tex]

Area of shaded part = area of square - area of semicircle

                                 = 256 - 100.53                                  

                                 = 155.47                                  

                                 = 155.5 cm²

2)   To find the area of shaded part, add the area of rectangle I and the area of rectangle II.

Rectangle I:              

l = 32 - 8 = 24 cm              

w = 24 cm

So, it is a square.        

Area of rectangle I = 24 * 24                                        

                               = 576 cm²

Rectangle II:                

l =  8 cm              

w = 24 - 4 = 20 cm

Area of rectangle II = 8 * 20                                

                                = 160 cm²

Area of shaded part =  area of rectangle I + area of rectangle 2

                                 = 576 + 160

                                 = 736 cm²

4)      length =  l = 26 cm  

          width =  w = 13 cm

Rectangle can be divided into two congruent triangles through its diagonal. So, the area of shaded part can be found by dividing the area of rectangle by 2.      

Area of rectangle = l * w                                    

                             = 26 * 13                                    

                             = 338 cm²

Area of shaded part = area of rectangle ÷ 2                                  

                                 = 338 ÷ 2                                  

                                 = 169 cm²

Answer:

If the figure shows two rays ST and UT with a common endpoint U, then Malik's description is correct. When two rays share a common endpoint, they form an angle. The angle formed by rays ST and UT would be angle STU. So, if the figure matches this description, then Malik's statement is correct.

Answer:

 [tex]2\sqrt{21}[/tex]

Step-by-step explanation:

I'm not sure if you know how to simplify radicals or not, but the [tex]\sqrt{84}[/tex] can be further simplified to [tex]2\sqrt{21}[/tex]

To simplify a radical, you just need to divide by squares you already know

In this case, divide 84 by 4 (which is the square of 2)

This will give you 21. Leave that inside the radical. Outside the root, leave the 2 as multiplier to [tex]\sqrt{21}[/tex].

Based on this evidence and reasoning, it is reasonable to conclude that Brianna should get the credit card, as long as she uses it responsibly and pays off her balance in full every month to avoid paying interest charges.

Percent, denoted by the symbol "%", is a way of expressing a fraction or ratio as a portion of 100. It is commonly used in everyday life to express a part of a whole or to compare quantities. Percentages can be used in various contexts, such as in finance to calculate interest rates, in statistics to represent data, and in everyday life to express discounts, tax rates, and tips. It is important to understand percentages to make informed decisions and to effectively communicate information.

Here,

CER stands for Claim, Evidence, and Reasoning, which is a framework for presenting a persuasive argument. Using this framework, we can evaluate whether Brianna should get the credit card in question:

Claim: Brianna should get the credit card.

Evidence:

The credit card has an APR of 24.99%, which is high compared to other credit cards.

The credit card has a yearly fee of $150.00.

The credit card offers 1% cash back on most purchases.

Reasoning:

While the APR and yearly fee are high, Brianna can still benefit from using the credit card to build her credit.

The 1% cash back on most purchases can help offset the cost of the yearly fee and the interest charges if she pays off her balance in full every month.

By using the credit card, such as making payments on time and not carrying a high balance, Brianna can establish a positive credit history, which can help her in the future when she wants to apply for loans or other credit cards.

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Answer:

Step-by-step explanation:

To find 20 percent of 30, you can multiply 30 by 0.2 (which is the decimal equivalent of 20 percent):

20% of 30 = 0.2 x 30 = 6

So, 20 percent of 30 is 6.

To divide 6 by 100, you can simply move the decimal point two places to the left:

6 ÷ 100 = 0.06

Therefore, if you want to find what is 20% of 30 and then divide that result by 100, the answer is 0.06.

Answer:

9.6$

Step-by-step explanation:

Answer: If 8 oranges cost 1.20, we can use a proportion to find the cost of 12 oranges:

8 oranges / 1.20 = 12 oranges / x

Solving for x, we can cross-multiply and get:

8 oranges * x = 1.20 * 12 oranges

8x = 14.4

x = 1.80

Therefore, 12 oranges would cost 1.80.

Answer:

Step-by-step explanation:

1/2 x 1/8 : 1/24 =

1/16 x 24 =

24/18 =

3/2

The rates and the car value are 86.3% and 7679.66 respecyivelt

A) The annual rate

The function is represented as

y = ab^x

Where

a = 45000 i.e. value in 1991

So, we have

y = 45000b^x

In 2000, we have

45000b^9 = 12000

This gives

b^9 = 0.266

Solving for b, we have

9ln(b) = ln(0.266)

So, we have

ln(b) = ln(0.266)/9

This gives

b = e^(ln(0.266)/9)

Evaluate

b = 0.863

B) To convert the rate to a percentage, we multiply by 100 and add the percent symbol:

b = 0.863

So, we have

b = 86.3%

C) If the car value continues to drop by the same percentage, we can use the formula:

Value = 45000* (0.863)^12

Evaluate

Value = 7679.66

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The expected value of the raffle if you buy 1 ticket is -$0.56, which means, you can expect to lose $0.56 for each ticket you buy.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

To calculate the expected value of the raffle if you buy 1 ticket, we need to find the expected monetary value of the prizes you could win, and then subtract the cost of the ticket, which is $1.

The probability of winning each prize can be calculated as follows:

1 prize of $500: 1/7000 chance of winning

3 prizes of $100: 3/7000 chance of winning each prize

5 prizes of $20: 5/7000 chance of winning each prize

19 prizes of $5: 19/7000 chance of winning each prize

To calculate the expected value of each prize, we multiply the probability of winning by the amount of the prize:

$500 prize: (1/7000) x $500 = $0.07

$100 prize: (3/7000) x $100 = $0.04

$20 prize: (5/7000) x $20 = $0.01

$5 prize: (19/7000) x $5 = $0.01

To find the expected value of the raffle if you buy 1 ticket, we add up the expected values of all the possible prizes:

$0.07 + ($0.04 x 3) + ($0.01 x 5) + ($0.01 x 19) = $0.44

Therefore, the expected value of the raffle if you buy 1 ticket is $0.44 - $1 = -$0.56, which means that on average, you can expect to lose $0.56 for each ticket you buy.

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Answer: To solve the equation 1/x + 1/y = 1/19 for integer solutions, we can use a common method called "diophantine equations" which involves finding solutions to equations with integer variables.

Multiplying both sides by the least common multiple of x, y, and 19, we get:

19y + 19x = xy

Bringing all the terms to one side, we have:

xy - 19x - 19y = 0

Using Simon's Favorite Factoring Trick, we can add 361 to both sides of the equation, which gives:

xy - 19x - 19y + 361 = 361

(x - 19)(y - 19) = 361

Now, we need to find all the pairs of integers (x, y) such that (x - 19)(y - 19) = 361.

The factors of 361 are 1, 19, and 361 itself. So, we can solve the equation by setting x - 19 equal to each factor and finding the corresponding value of y:

x - 19 = 1, y - 19 = 361, then x = 20, y = 380

x - 19 = 19, y - 19 = 19, then x = 38, y = 38

x - 19 = 361, y - 19 = 1, then x = 380, y = 20

Therefore, the integer solutions to the equation 1/x + 1/y = 1/19 are (x, y) = (20, 380), (38, 38), and (380, 20).

Step-by-step explanation:

Answer: 22 miles in one day

Step-by-step explanation:

To find how far Gianna hiked, we first need to convert the mixed number for Ethan and Rylee's hike into an improper fraction, and then multiply it by 3 3/4 to find the distance Gianna hiked.

Ethan and Rylee's hike (5 13/15):

(15 * 5) + 13 = 88

So, they hiked 88/15 miles.

Now, let's convert the mixed number 3 3/4 into an improper fraction:

(4 * 3) + 3 = 15

So, 3 3/4 = 15/4.

Next, we'll multiply the two improper fractions together:

(88/15) * (15/4) = (88 * 15) / (15 * 4) = 1320 / 60

Now, simplify the fraction:

1320 ÷ 60 = 22

So, Gianna hiked 22 miles in one day.

The image of the composite figure is composed of 11 smaller cubes

The sum of the composite shape is solved by dividing the shape into two parts and courting using multiplication then adding the two parts

The first part which is the upper part is solved as follows

= length * width

= 2 * 2

= 4

The second part which is the base is solved as follows

= length * width

= 3 * 3

= 9

Sum of the counting

= 9 + 4

= 11

We can say that the composite figure is made up of 11 smaller cubes

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By answering the presented question, we may conclude that When y is 9 cuboid feet, the volume of the cube is 729 cubic feet.

A cuboid is a solid or three-dimensional form in geometry. A cuboid is a convex polyhedron with 8 vertices, 12 sides, and 6 rectangular faces. A cuboid is another name for it. A cube is a cuboid because it has six square faces. Objects found in boxes include bricks and books. The following are the primary distinctions between cubic and cubic: In contrast to a cube's rectangular faces, the faces of a cube are square and equal in size. Although the structures of the cube and cuboid are aesthetically similar, they differ significantly in terms of side length, diagonal, and area.

If you want to find the volume of a cube, the formula is:

Volume equals [tex]s^3[/tex]

where s is the length of one cube side.

If y = 9 feet and y indicates the length of one side of the cube, the volume of the cube may be determined as follows:

Volume = [tex]y^3 + 9^3 = 729 cu ft.[/tex]

When y is 9 feet, the volume of the cube is 729 cubic feet.

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Complete question -

Write and expression you can use to find the value of the cube then find the value if y=9 feet

Answer:

The best explanation for the steps to solve the pair of equations graphically is:

On a graph, find the point of intersection of two lines; the first line has y-intercept = 5 and slope = −3, and the second line has y-intercept = 2 and slope = 1.

To solve the pair of equations graphically, you need to plot the two lines on the same coordinate plane and find the point where they intersect. To do this, you can use the slope-intercept form of the equations, which gives the y-intercept and the slope of each line. The y-intercept is the value of y when x equals 0, and the slope represents how steep the line is. Once you have graphed the two lines, the point where they intersect is the solution to the system of equations. In this case, the intersection point can be found by solving the system of equations, which is (x, y) = (2, -1).

law of contraposition = if p, then q. if not q, then not p.

example: if it's snowing, then there's no school. if there is school, then it's not snowing.

The inverse transform method can be used to produce a random variate for a random variable X with p.d.f[tex]f(x) = e^{2x}[/tex].

The cumulative distribution function (CDF) of X is given by [tex]F(x) = 1 - e[/tex], and we must first determine its inverse (-2x). When x is solved for, the answer is x = -(1/2)ln(1 - u), where u is an evenly spaced random number between 0 and 1.

As a result, we can take the following actions to create a random variate for X:

Create an even, random number between 0 and 1, u.

Determine[tex]x = -(1/2)ln (1 - u)[/tex].

A random variate for X is the produced value of x.

The generated values will adhere to the specified probability distribution thanks to this procedure.

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Correct question is:

Develop a random variate generator for a random variable X with the probability density function: [tex]f(x) = e^2x x < 0 e^ -2x x > 0[/tex] Use the generator to generate two random variates using the following uniform random numbers: U1= 0.95 and U2= 0.35.

After answering the provided question, we can conclude that Therefore, derivatives the function f(x, y) = ycos(x) has no local minimum or maximum points, only two saddle points at (π/2, 0) and (3π/2, 0).

In mathematics, the derivative of a function with real variables measures how sensitively the function's value varies in reaction to changes in its parameters. Derivatives are the fundamental tools of calculus. Differentiation (the rate of change of a function with respect to a variable in mathematics) (in mathematics, the rate of change of a function with respect to a variable). The use of derivatives is essential in the solution of calculus and differential equation problems. The definition of "derivative" or "taking a derivative" in calculus is finding the "slope" of a certain function. Because it is frequently the slope of a straight line, it should be enclosed in quotation marks. Derivatives are rate of change metrics that apply to almost any function.

∂f/∂x = -ysin(x)

∂f/∂y = cos(x)

-ysin(x) = 0 (Equation 1)

cos(x) = 0 (Equation 2)

Therefore, the critical points are:

(π/2, 0) (saddle point)

(3π/2, 0) (saddle point)

∂²f/∂x² = -ycos(x)

∂²f/∂y² = 0

∂²f/∂x∂y = cos(x)

At the point (π/2, 0), ∂²f/∂x² = 0 and ∂²f/∂x∂y = 1, so it is a saddle point.

At the point (3π/2, 0), ∂²f/∂x² = 0 and ∂²f/∂x∂y = -1, so it is also a saddle point.

Therefore, the function f(x, y) = ycos(x) has no local minimum or maximum points, only two saddle points at (π/2, 0) and (3π/2, 0).

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the probability of getting red on at least one spin is 1 - 9/16 = 7/16 or 0.4375 in decimal form.

hope that helps!

It can be  estimated that 60 deliveries will be to the Forest Park neighborhood if the driver makes 200 deliveries.

We can deduct that  from  the sample of 80 deliveries, the Forest Park neighborhood received 24 deliveries.

We then  estimate how many deliveries will be to the Forest Park neighborhood if the driver makes 200 deliveries by applying  proportional reasoning:

In conclusion, the estimate is  that the driver will make 0.3 x 200 = 60 deliveries to the Forest Park neighborhood.

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Using probability, the percentage of people who test positive for the virus who actually have the virus is approximately 99.85%.

What is probability?

Probability is a measure of the likelihood or chance that an event will occur. It is a numerical value between 0 and 1, where 0 represents an impossible event (i.e., an event that will never occur) and 1 represents a certain event (i.e., an event that will always occur).

Now,

To determine the percentage of people who test positive for the virus who actually have the virus, we can use Bayes' theorem.

Let A be the event that an individual has the virus, and B be the event that an individual tests positive for the virus. Then, we want to calculate the conditional probability of A given B, denoted as P(A|B), which is the probability that an individual has the virus given that they test positive.

Using Bayes' theorem, we can write:

P(A|B) = P(B|A) * P(A) / P(B)

where P(B|A) is the probability of testing positive given that an individual has the virus, P(A) is the overall probability of having the virus, and P(B) is the overall probability of testing positive.

We are given that the test returns a positive result for 99.5% of individuals who have the virus, so P(B|A) = 0.995. We are also given that the test returns a positive result for 0.5% of those who do not have the virus, so the probability of testing positive given that an individual does not have the virus is 1 - 0.005 = 0.995.

We are given that overall, 1% of people tested positive, so:

P(B) = 0.01

We can calculate the overall probability of having the virus as:

P(A) = (number of people with the virus) / (total number of people tested)

We do not have enough information to calculate these values directly, but we can use the fact that the test returns a positive result for 99.5% of individuals who have the virus to estimate the number of true positives.

Let n be the total number of people tested. Then, we can estimate the number of true positives as:

(number of true positives) = 0.995 * (number of people with the virus)

We know that overall, 1% of people tested positive, so:

(number of true positives) / n = 0.01

Substituting the estimate for the number of true positives, we get:

0.995 * (number of people with the virus) / n = 0.01

Solving for the number of people with the virus, we get:

(number of people with the virus) = 0.01 * n / 0.995

Substituting this into the expression for P(A), we get:

P(A) = (0.01 * n / 0.995) / n = 0.01005

So the overall probability of having the virus is approximately 0.01005.

Finally, substituting all the values into the expression for P(A|B), we get:

P(A|B) = 0.995 * 0.01005 / 0.01 ≈ 0.9985

Therefore, the percentage of people who test positive for the virus who actually have the virus is approximately 99.85%.

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Answer: J=39 H=9

Step-by-step explanation:

J+H=48

J-3=6(H-3)

Use the substitution method and isolate one variable to do so.

J-3=6h-18

J=6h-15

plug J into first equation

6h+h-15=48

7h-15=48

7h=63

h=9

J+H=48

J+9=48

48-9=39

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where:

A = final amount

P = principal (initial amount)

r = annual interest rate (as a decimal)

n = number of times the interest is compounded per year

t = time (in years)

In this case:

P = $11,000

r = 2.5% = 0.025 (since it's compounded monthly, we need to divide by 12 to get the monthly rate)

n = 12 (compounded monthly)

t = 21 years

Plugging in these values, we get:

A = 11000(1 + 0.025/12)^(12*21)

A ≈ $16,180.64

Therefore, the value of the account at the child's twenty-first birthday will be approximately $16,181.

a. The relation is an equivalence relation, and its corresponding partition has blocks {1, 4}, {2}, and {3}.

b. The relation is not specified.

c. The relation is not an equivalence relation because it is not transitive.

d. The relation is not an equivalence relation because it is not reflexive.

a. The relation is an equivalence relation because it is reflexive, symmetric, and transitive. The blocks of its corresponding partition are {1, 4} and {2} and {3}.

b. The relation is not specified, so it is impossible to determine whether it is an equivalence relation or not.

c. The relation is not an equivalence relation because it is not transitive. Specifically, (3, 1) and (1, 3) are in the relation, but (3, 3) is not.

d. The relation is not an equivalence relation because it is not reflexive (i.e., 1 and 4 are not related to themselves).

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Based on the analysis it will be less expensive to get the new fridge, hence buying the new fridge is worth it.

Given that the current fridge

electricity charges= $60 monthly,

maintenance costs=$ 170

let the number of months be = x

and the total cost is y

the expression for the cost of the old fridge is

y=170+60x       ...say (1)

new fridge

electricity charges=$5

costs= $1140

let the number of months be x,

and the total cost be y'

the expression for the cost of the new fridge is

y'=1140+5x,       ... say(2)

For 10 year , there are 12*10=120 months

put x=120 in both equations,

y=170+60x  

y=170+60*120

y=170+7200

y=$7370

y'=1140+5*120

y'=1140+600

y'=$1740

Based on the analysis it will be less expensive to get the new fridge, hence buying the new fridge is worth it.

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Answer:

2

Step-by-step explanation:

The equation has 2 terms in it which means 2 is the answer.