Holly opened a savings account at a local bank. She deposited $1,300.00 into the account 6 years ago. If the account earns an annual simple interest rate of 6.8%, how much interest has she earned?

Answer:

[tex]d^{2}[/tex] - 16.

Step-by-step explanation:

To solve for the product of (d + 4) and (d - 4), we can use the FOIL method.

This means we multiply the first terms, then the outer, then the inner, and finally the last terms, then we add all the products together.

So, (d + 4) (d - 4) can be expanded like this:

Adding all of them together, we get: [tex]d^{2}[/tex] - 4d + 4d - 16, which simplifies to [tex]d^{2}[/tex] - 16.

Therefore, (d + 4)(d - 4) = [tex]d^{2}[/tex] - 16.

The ordered pair (2,6) means that 2 plain rings and 6 initial rings were purchased, and the total cost would be 23 + 64 = 24 dollars.

In mathematics, an ordered pair is a collection of two objects, which are arranged in a specific order. The order of the objects in the pair is important, as the ordered pair (a, b) is different from the ordered pair (b, a) if a and b are not equal.

The two objects in an ordered pair can be anything, such as numbers, variables, or other mathematical entities. The ordered pair (x, y), for example, can represent a point on a two-dimensional coordinate plane, where x represents the horizontal coordinate and y represents the vertical coordinate.

The ordered pair notation is commonly used in set theory and other branches of mathematics to represent relationships between two objects. Ordered pairs can also be used to define functions, where the first object in the pair represents an input to the function, and the second object represents the output.

Here's the completed table and ordered pairs:

Cost of plain rings (x) Cost of initial rings (y) (Ordered Pairs (x,y))

              0                                 4                              (0,4)

               1                                 5                              (1,5)

               2                                 6                              (2,6)

               3                                 7                              (3,7)

               4                                 8                              (4,8)

In each ordered pair, the first number represents the number of plain rings purchased (x) and the second number represents the number of initial rings purchased (y). For example, the ordered pair (2,6) means that 2 plain rings and 6 initial rings were purchased, and the total cost would be 23 + 64 = 24 dollars.

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Heather's account balance will be approximately $1,340.55 after 7 years if the interest is compounded 6 times each year.

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

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

Where:

A is the account balance after a certain amount of time

P is the principal or initial amount invested

r is the annual interest rate (as a decimal)

n is the number of times the interest is compounded per year

t is the time period in years

Given tha data in the question;

First, convert R as a percent to r as a decimal

r = R/100

r = 3.5/100

r = 0.035 rate per year.

Substituting these values into the formula solve for accrued amount, we get:

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

A = 1,050(1 + 0.035/6)^(6 × 7)

A = 1,050(1 + 0.005833333333333)⁴²

A = 1,050(1.005833333333333333)⁴²

A = $1,340.55

Therefore, the accrued amount is $1,340.55.

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To calculate the total amount paid over two years, we first need to determine the annual premium increase percentage. Let's assume the insurer increases the premium by 5% per year to keep up with inflation.

After the first year, the new premium would be:

R450 + (5% of R450) = R472.50 per month

After the second year, the new premium would be:

R472.50 + (5% of R472.50) = R496.13 per month

To calculate the total amount paid over two years, we can use the following formula:

Total amount paid = (monthly premium x 12 months x number of years)

= (R450 x 12 x 2) + (R472.50 x 12 x 1) + (R496.13 x 12 x 1)

= R10,800 + R5,670 + R5,953.56

= R22,423.56

Therefore, you would have paid a total of R22,423.56 over two years.

Answer:

Step-by-step explanation:

(y^2)/1600-(x^2)/81=1. y21600−x281=1 y 2 1600 - x 2

Answer: y21600x281=1 y 2 1600 - x 2

Step-by-step explanation: for sure chfjjgffjfj ;)

Answer:

-3/2

Step-by-step explanation:

cubed roots of -27 is -3

cubed root of 8 is 2

The standard equation of a conic section with its center or vertex at the origin is x² = 4ay.

The graph of this conic section is a parabola that opens upward with with its vertex at the origin (0, 0).

In Euclidean geometry, a conic section can be defined as a curve that is generated as the intersection of the surface of a right circular cone with a plane.

In Mathematics, the standard equation of a conic section is represented or modeled by the following mathematical equation:

(x - h)²/a² - (y - k)²/b² = 1

Where:

Based on the information provided about the vertex at (0, 0), the foci would be at (0, a) and the directrix would be represented by a horizontal line at y = -a. Therefore, the required equation of a conic section in standard form is given by:

x² = 4ay.

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Answer:

0.7

Step-by-step explanation:

Answer: 0.7

Step-by-step explanation: The tenths place in decimals is the number directly to the right of the decimal. the 5 next to the six is greater than or equal to 5 meaning you can round up the 6 to a 7.

By answering the presented question, we may conclude that As a result, fraction the answer is nine thirty-fifths.

A whole can be represented by any number of equal sections or fractions. In standard English, fractions represent the number of units of a specific size. 8, 3/4. A whole contains fractions. In mathematics, numbers are stated as the ratio of the numerator to the denominator. Each of these is an integer in simple fractions. A fraction exists in the numerator or denominator of a complex fraction. True fractions have numerators that are smaller than their denominators. A fraction is a sum that represents a piece of a total. You may assess it by dividing it up into smaller chunks. Half of a whole number or object, for example, is represented as 12.

We can simplify both fractions to have a common denominator of 12 for the first problem:

Four-sixths = Eighteenths

Three-twelfths + three-twelfths = three-twelfths

As a result, the phrase becomes: 8/12 - 3/12 = 5/12

As a result, the answer is five-twelfths.

For the second case, we may reduce both fractions again such that they have a common denominator of 16:

Seventy-eighths = fourteenteenths

Nineteenths + nineteenths = nineteenths

As a result, the equation becomes: 14/16 - 9/16 = 5/16.

As a result, the answer is five-sixteenths.

We can simplify both fractions to obtain a common denominator of 35 for the third problem:

Two-fifths = 14-thirty-fifths

One-seventh Equals thirty-fifths

As a result, the phrase becomes: 14/35 - 5/35 = 9/35

As a result, the answer is nine thirty-fifths.

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a. The probability that it is not a 10-peso coin is  [tex]\frac{12}{17}[/tex].

b. The probability that it is a 5-peso coin is [tex]\frac{3}{17}[/tex] .

What is probability?

The mathematical notion of probability is used to determine the likelihood of an event. It is only helpful for estimating the likelihood that an event will happen. A scale from 0 to 1, where 0 denotes impossibility and 1 denotes a specific occurrence.

We are given that a purse contains five 10-peso coins, three 5-peso coins, and nine 1-peso coins.

Total coins = 5 + 3 + 9 = 17

a. Probability of getting a 10 peso coin is

P (A) = [tex]\frac{5}{17}[/tex]

Probability of not getting a 10 peso coin is

⇒Probability = 1 - P (A)

⇒Probability = 1 - [tex]\frac{5}{17}[/tex]

⇒Probability = [tex]\frac{12}{17}[/tex]

b. Probability of getting a 5 peso coin is [tex]\frac{3}{17}[/tex] .

Hence, the required probabilities have been obtained.

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Answer:

Step-by-step explanation:

Use SAS congruency; AD=DC, and they both share side BD. Also, BD is the perpendicular bisector to AC, so it also forms 2 right angles. Proof using SAS.

Or, if you don’t know SAS congruency, you may use SSS congruency;

Use the Pythagorean theorem. Side length AB^2 = AD^2 + BD^2
BC^2 = DC^2 + BD^2.

AD=DC, so therefore AB = BC. Use SSS congruency, and there you go.

The value of the perimeter:

1. 97. 3 units

2. 27. 8 units

The formula for the perimeter of a triangle is expressed as;

P = a + b + c

Given that;

From the diagram shown, we have that;

Using the tangent identity;

tan 44 = BC/29

find the value and cross multiply

BC = 28. 00

Also, AC ²= 29² + 28²

AC = √1625 = 40. 3

Then, the perimeter = 29 + 28. 00 + 40. 3 = 97. 3 units

For the second diagram;

Note that the perimeter of a rectangle is expressed as 2(length + width)

Substitute the values

Perimeter =2 ( 4 + 3) = 14 units

For triangle;

sin 45 = 4/t

cross multiply

t = 5. 7 units

To determine the adjacent side;

5.7² - 4² = x²

32. 5 - 16 = a²

a = √16. 49

a = 4. 1

Then, the perimeter = perimeter of rectangle + perimeter of triangle

= 14 + 13. 8

= 27. 8 units

Note that no specific unit was given as thus, we used 'units' as the measuring scale.

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Answer: Based on the data displayed, Mrs. Cheng's class lost fewer pencils overall as it has a smaller spread in the data compared to Mr. Johnson's class. The box plot of Mrs. Cheng's class has a smaller spread, with a larger interquartile range and smaller range compared to Mr. Johnson's class, indicating that the data is more concentrated and consistent. Additionally, the median value of Mrs. Cheng's class is higher than Mr. Johnson's class, indicating that half of the students in Mrs. Cheng's class lost fewer pencils than half of the students in Mr. Johnson's class. Therefore, the correct answer is "Mrs. Cheng's class; it has a narrow spread in the data".

Step-by-step explanation:

The number 3 in the equation h(t) = -16t² + 6t+ 3 represents option 2 - the height from which the ball is thrown.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The equation h(t) = -16t² + 6t+ 3 gives the height of the ball as a function of time.

The constant term in this equation is 3, which represents the initial height of the ball when it is thrown.

Therefore, the correct answer is (2) the height from which the ball is thrown.

Option (1) cannot be correct, because the maximum height of the ball occurs when the derivative of h(t) is zero, which is not necessarily equal to the constant term in the equation.

Option (3) cannot be correct, because the ball reaches the ground when h(t) = 0, which requires solving a quadratic equation.

Option (4) cannot be correct, because the time it takes for the ball to reach its maximum height is given by the formula t = -b/2a, where a and b are the coefficients of the quadratic equation, and it does not depend on the constant term.

Therefore, option 2 is the correct answer.

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Joel cannot buy 2 games and 6 puzzles and satisfy the constraints was solved by using inequality.

The total cost of x puzzles and y games must be less than or equal to $96, which gives us the first inequality: 8x + 12y ≤ 96

The second inequality: x + y ≥ 9.

An inequality is a mathematical statement that compares two quantities or expressions and shows the relationship between them using one of the following symbols: <, >, ≤, or ≥. For example, "x > 5" is an inequality that states that x is greater than 5.

In the given question,

Part A:

Let x be the number of puzzles Joel can buy and y be the number of games Joel can buy.

The total cost of x puzzles and y games must be less than or equal to $96, which gives us the first inequality: 8x + 12y ≤ 96

Joel needs to buy at least 9 gifts, which means that the total number of gifts must be greater than or equal to 9. Since x represents the number of puzzles and y represents the number of games, the total number of gifts is x + y. This gives us the second inequality: x + y ≥ 9

We also know that Joel can only buy puzzles or games, not both. Therefore, x and y must be either both integers or both half-integers (such as 1.5 or 2.5), but they cannot be mixed. This gives us the third inequality:

x, y are both integers or both half-integers

Part B:

To see if Joel can buy 2 games and 6 puzzles and satisfy the constraints, we can substitute x = 6 and y = 2 into the inequalities:

8x + 12y ≤ 96

8(6) + 12(2) ≤ 96

72 ≤ 96

This inequality is true, so the first constraint is satisfied.

x + y ≥ 9

6 + 2 ≥ 9

8 ≥ 9

This inequality is not true, so the second constraint is not satisfied. Therefore, Joel cannot buy 2 games and 6 puzzles and satisfy the constraints.

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The five-number summary of the class, determined by the results of the final test, is:

Minimum = 60

Lower quartile = 71.5.

Median = 85.

Upper Quartile = 94.

Maximum = 98

The median, a measure of the center of gravity, reflects the center of value in the collection when values are sorted in either ascending or descending order. The value that distinguishes the lower 50% of the information from the upper 50% of the data is, in other words, the value.

The lowest score is 60, which is the minimum. The highest score, 98, will serve as the maximum.

The formula: can be used to determine the lower quartile.

= (Second score + Third score) / 2

= (65 + 78) / 2

= 71.5.

The upper quartile is:

= (Third to last score + Second to last score) / 2

= (93 + 95) / 2

= 94

The median is:

= (5th score + 6th score) / 2

= (82 + 88) / 2

= 85

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Step-by-step explanation:

Interchange just means to switch really. The first 3 will stay the same be cause they are the same numbers.

The last one will be (2,8) because that's (8,2) but with the numbers switched

On solving the provided question, we can say that Hence, the solution to the system of equations is x = 19/8 and y = 5/8.

A math equation is a technique that links two statements and utilises the equals sign (=) to express equivalence. In algebra, an equation is a mathematical statement that proves the equivalence of two mathematical expressions. For example, in the computation 3x + 5 = 14, the equal sign inserts a gap between the numbers 3x + 5 and 14. A mathematical formula may be used to explain the link between the two phrases written on either side of a letter. The logo and the programme are usually the same. For example, 2x - 4 equals 2.

4x + 4y = 12 is obtained by multiplying the first equation by four.

To remove y, combine the first and second equations: (4x + 4y) + (4x - y) = 12 + 7, which simplifies to 8x = 19.

Divide both sides of the equation by 8 to find x: x = 19/8.

To find y, plug the value of x into either equation: y = 3 - x = 3 - 19/8 = 5/8.

Hence, the solution to the system of equations is x = 19/8 and y = 5/8.

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The volume of Eli's trophy case is 64.4 cubic feet.

Eli's trophy case's length, breadth, and height must be multiplied to determine its volume. The case has the following measurements:

Length = 4 3/5 feet

Width = 2 feet

Height = 3 1/2 feet

We can sum the improper fractions after converting the mixed integers to fractions to arrive at:

Length = 4 3/5 feet = (5*4 + 3)/5 = 23/5 feet

Height = 3 1/2 feet = (2*3 + 1)/2 = 7/2 feet

Now that we have the volume, we can multiply the length, width, and height:

Volume equals length, width, and height

= (23/5) feet x 2 feet x (7/2) feet

= (23 x 2 x 7)/(5 x 2) cubic feet

= (644/10) cubic feet

= 64.4 cubic feet

Eli's trophy case therefore has a 64.4 cubic foot volume.

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Answer:

Therefore, 3 bakers can make 30 loaves of bread in 2 hours.

Therefore, 5 bakers can make 30 loaves of bread in 2 hours.

Therefore, 6 bakers can make 30 loaves of bread in 1.25 hours.

Therefore, 15 bakers can make 30 loaves of bread in 2 hours.

Step-by-step explanation:

In the number of bakers, it would take 2 hours to make 30 loaves of bread.

A proportion is an equation in which two ratios are set equal to each other.

Let h be the number of hours needed for a given number of bakers to make 30 loaves. Then we have:

2 bakers can make 30 loaves in 1 hour, so 1 baker can make 15 loaves in 1 hour.

Therefore:

3 bakers can make 45 loaves in h hours, so 45/3 = 15 loaves can be made in 1 hour. Thus, 3 bakers can make 30 loaves in 2 hours.

5 bakers can make 75 loaves in h hours, so 75/5 = 15 loaves can be made in 1 hour. Thus, 5 bakers can make 30 loaves in 2 hours.

6 bakers can make 90 loaves in h hours, so 90/6 = 15 loaves can be made in 1 hour. Thus, 6 bakers can make 30 loaves in 2 hours.

15 bakers can make 225 loaves in h hours, so 225/15 = 15 loaves can be made in 1 hour. Thus, 15 bakers can make 30 loaves in 2 hours.

Therefore, regardless of the number of bakers, it would take 2 hours to make 30 loaves of bread.

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The area of the regular polygon which is given above would be = 64.5 cm². That is option D.

To calculate the area of the given regular polygon will require the use of this formula such as:

Area = 1/2(a×p)

where;

a = length of an apothem = 4.3 cm

p = perimeter = 6×5 = 30cm

Area = 1/2 ( 4.3×30)

= 129/2

= 64.5 cm²

Therefore, in conclusion the area of the regular polygon which is a hexagon with 6 sides would be = 64.5 cm².

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a) The speed at which the car gets maximum gas mileage is given as follows: 48 miles per hour.

b) The max gas mileage is given as follows: 29.5 miles per gallon.

The gas mileage is modeled as a function of the velocity x according to the quadratic function presented as follows:

m(x) = -0.028x² + 2.688x - 35.012.

The coefficients are given as follows:

a = -0.028, b = 2.688, c = -35.012.

The leading coefficient a is negative, hence the vertex represents the point at which the maximum mileage is obtained.

The velocity is given as follows:

x = -b/2a

x = -2.688/[2(-0.028)]

x = 48 miles per hour.

The max gas mileage is obtained as follows:

m(48) = -0.028(48)² + 2.688(48) - 35.012.

m(48) = 29.5 miles per gallon.

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Answer: 5

Step-by-step explanation:

A = Lw (area of rectangle is length times width)

A = 15 (Area is 15)

L = 2x + 5 (length is 2 times a number plus another 5)

w = x - 4 (width is 4 less than that number

Plug in the values:

15 = (2x + 5)(x - 4)

FOIL

15 = 2x2 - 8x + 5x - 20

simplify:

15 = 2x2 - 3x - 20

Subtract 15

0 = 2x2 - 3x - 35

Factor out the quadratic. We know that one number has to be 7 and the other 5 so that they multiply together to make 35, and that one of them has to be negative so that it's actually -35.

That means we have m * n = -35

We also need it set up so that so that 2m + n = -3:

2 * -5 + 7 = -3

0 = (2x + 7)(x - 5)

So:

0 = 2x + 7, or 0 = x - 5

x = -7/2 or 5

We cannot have a negative length, so x = 5

Check:

15 = (2 * 5 + 5) (5 - 4)

15 = 15 * 1

15 = 15

Answer:its b 6,12

Step-by-step explanation:

The length of AC to the nearest tenth of a cm, in the given kite, is: 8.7 cm.

Applying the Pythagorean Theorem, the length of AC to the nearest tenth of a cm, in the given kite, is: 8.7 cm.

From the information given, we know the following:

Triangles AED and CED are right-angled triangles

Thus:

AC = AE + CE

Find AE and CE using the Pythagorean Theorem , where c if the hypotenuse of the right triangle.

Length of AE:

AE = [tex]\sqrt{5^2 -4^2}[/tex]

AE= [tex]\sqrt{9}[/tex]

AE= 3

Length of CE:

CE = [tex]\sqrt{7^2 -4^2}[/tex]

CE= [tex]\sqrt{33}[/tex]

CE= 5.7

Length of AC:

AC = AE + CE

Put the values together:

AC = 3 + 5.7

= 8.7cm

Therefore, the length of AC to the nearest tenth of a cm, in the given kite, is: 8.7 cm.

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We estimate that Jordan will drive a distance of approximately 4668.3 miles during the entire 7-day road trip.

Distance and displacement are two key words in mechanics that, although having similar sounds, have distinct definitions and meanings. How much of an object's path is covered by a moving object is measured in terms of distance. Whereas "How much route is covered by the item in a specific direction" is measured by displacement, The main distinction between distance and displacement is therefore that the former is a scalar quantity while the latter is a vector quantity.

Given that, the distance travelled is  666.9 miles.

The same distance is travelled for 7 days thus,

distance = Distance per day x Number of days

distance = 666.9 miles/day x 7 days

distance = 4668.3 miles

Hence, we estimate that Jordan will drive approximately 4668.3 miles during the entire 7-day road trip.

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Answer:

Option B

3&5, 4&6

Step-by-step explanation:

An interior angle is an angle inside a shape