Mr.Heritage invests $6000 total into two diffent bank accounts. One account pays 8% interest annually. The second par 10% interest antally. If he earns $560 in interest after one year, how much did he put in each account?​

The length of the bottom diagram in the final tape diagram is 5.04 units.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred.

The top diagram length is 60 units.

20 % of the 60 units is carried down, the length of the new section is:

20/100 * 60 = 12units.

60% of the next 12 units are carried down, the length of the new section is:

60/100 * 12 = 7.2 units

Similarly, when 70% of the section is carried down the length of the new section is:

70/100 * 7.2 = 5.04 units.

Hence the length of the bottom diagram is 5.04 units.

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Answer:

1/70

Step-by-step explanation:

(63-40) (21-10) 23 11 23-22 1

(---------)-(--------)=------ - ------ = -------- = --

( 70 ) ( 35 ) 70 35 70 70

the plot is attached below and the slope is 4.

What is the slope of line?

Given two line-side coordinates, use the slope formula to determine the slope of the line. The slope is defined as the ratio of the change in the y values to the change in the x values using the formula m=(y2-y1)/(x2-x1). x1 and y1 are represented by the first point's coordinates. The second points are located at x2, y2, and their locations. Whichever point you choose to classify as the first and which as the second doesn't matter.

We know that formula two find the slope of the line joining two points which is

The equation y = 4x + 3 models the data below.

x 1   2  3  4   5    6   7   8

y 8 13 16 21 26 29 33 37

The plot will be using this data.

Hence the plot is attached below and the slope is 4.

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The equation which states that the population of a town is 20,000 and decreased by 2% each year is y=20000(1-0.2x)

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Different Types of Equations

Linear Equation.

Radical Equation.

Exponential Equation.

Rational Equation.

Let the population be y and the of years be x

According to the question, the equation should be

y=20000(1-0.02x)

In 2025 the population will be

y=20000(1-0.02*25)

y=100000

The population will become 10000

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Answer:

35.87

Step-by-step explanation:

First, what is 7.86 by 4.564?
It is 35.87304.

But the answer needs to be in significant figures, so how do we do that?

Well, significant figures are the numbers that comes after the decimal place. For example, 0.52, which has 2 significant figures.

So with 7.86, there are 2 significant figures and with 4.565, there are 3.

We want to use the one with the least amount of significant figures, so we would round our answer to the hundredth:

35.87

Hope this helps!

The required answer is 35.8730

The number of significant figures in a measurement represents the level of precision in that measurement. In general, the last digit in a number is considered uncertain and is rounded based on the number of significant figures.

When performing arithmetic calculations, the result should be rounded to the same number of significant figures as the least precise measurement used in the calculation.

In this case, the least precise measurement is 4.564, with four significant figures. Therefore, the final result of the calculation 7.86 x 4.564 should be reported with four significant figures.

The answer is 35.87304 and should be reported as 35.8730

(Please mark my answer Brainliest if this helped.)

Using the details given, the area of the triangle in which the angles lies between the two sides is 90.3 units²

The area of a triangle can be calculated using the formula A = 1/2bh, where b is the base of the triangle and h is the height. Area of a triangle can be calculated using the formula: Area = (base x height) / 2, where base is the length of one side and height is the length of the side that forms the angle. In order to use this formula, you must know the length of two sides and the measure of the angle between them. However, this formula is subjective to details given

The area of a triangle can be calculated by

A = a×b×sinθ

a = 15

b = 8.1

θ = 132°

Substituting the values into the formula

A = 15 × 8.1 × sin 132

A = 90.3 units²

The area of the triangle is 90.3 units²

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Answer:

Step-by-step explanation:

2-(-2)

=2+2

=4

Answer: the difference when -2 is subtracted from 2 will be 4

Step-by-step explanation: according to question

                                               2 -(-2)

                                             =2+2    ( - + - = +)

                                             = 4

Converting within measurement systems means that we are changing the unit of measurement from one to another.

It is referred to as converting units within measuring systems if we do it using the metric or conventional systems. The conventional system and the metric system are the two most widely used measurement systems. In other words, we are not converting units from customary to metric or vice versa.

Simple unit conversions can be performed mentally or with one-step multiplication or division. There are, however, more difficult conversions that call for many conversions between a wide range of units.

The Unit Factor Method, another name for the Dimensional Analysis process, is a mathematical technique that takes advantage of the fact that any number or statement may be multiplied by "one" without changing its value. By multiplying the previous measurement by one (or more) different representations of the number 1, you can convert units. Although the measurement's value is unaffected by the factor of 1, the measurement's units are.

A ratio of one is referred to as a conversion ratio or unit factor. The names of the units that will be used in the conversion are listed in this ratio. It can be used to convert values both within the English and Metric Systems and between the two. The idea of equivalent values serves as the foundation for the conversion ratio.

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Complete question:

What do you mean by converting within measurement systems?

Answer:

-34 - 24i

Step-by-step explanation:

To calculate ( – 2 – 3i)^4, we can use the property that (a + bi)^n = a^n + (n*a^(n-1)b)i + (na^(n-2)*b^2)i^2 + ...

So, ( – 2 – 3i)^4 = (-2 - 3i) * (-2 - 3i) * (-2 - 3i) * (-2 - 3i)

= -2^4 - 2^3 * 3i - 2^2 * 3^2i^2 - 2 * 3^3i^3 - 3^4i^4

= -16 - 24i + 18i^2

= -16 - 24i -18

= -34 - 24i

The amount that he will pay on March 10th is $1287 with interest rate.

The annual rate that is charged for borrowing (or made by investing), given as a single percentage number, represents the real yearly cost of money throughout the course of a loan.

Given that he is aware that he can begin loan repayment on a $7,500 loan in 4.5 years at the present interest rate of 4.29%, the following will be applicable:

4.29% of 7500 after the first year

4.29 × 7500/100

321.75

After the 4.5-year term, multiply the interest by 4.5 to determine the overall interest:

321.75 × 4

$1287.

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The solution to the expression 5 2 (3x4) divided by 3-5 is -312

Fractions are simply described as part of a whole number or variable.

There are different types of fraction which includes;

PEMDAS is a mathematical acronym used to give the order of operations to be followed in solving expressions.

It stands for;

Given the expression;

52(3×4)/3 - 5

expand the parentheses

52(12)/-2

624/-2

Divide the values

-312

Hence, the values is -312

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The required quadratic equaiton is h(x) = (x + 1)² -3. Option D is correct.

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

here,
From the data select 1 pair of values,
x = 0, when h(0) = -2

Now, put this pair in each quadratic equation, since the equation that satisfies this fair will be the required quadratic equation.

A,
h(x) = (x − 1)² + 1
h(0) = (0 − 1)² + 1
h(0) =  2

B.
h(x) = (x − 1)² + 3
h(0) = 4

C.
h(x) = (x + 1)² - 1
h(0) = 0

D.
h(x) = (x + 1)² - 3

h(0) = 1 - 3 = -2
h(0) = -2

Thus, the required quadratic equaiton is h(x) = (x + 1)² -3. Option D is correct.

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Answer:

To solve this problem, we will use the following steps:

Step 1: Let's assume that the larger number is x and the smaller number is y, we know that the difference between the two numbers is 9, so we can write the equation: x-y = 9

Step 2: We know that Four times the larger number plus one-half the smaller is 45, so we can write the equation: 4x + 0.5y = 45

Step 3: Now we have two equations with two unknowns, we can solve for one of the unknowns by isolating it in one of the equations.

x-y = 9

x = y+9

Step 4: Now we can substitute the value of x in the second equation

4(y+9) + 0.5y = 45

4y + 36 + 0.5y = 45

4.5y + 36 = 45

4.5y = 9

y=2

Step 5: We can substitute the value of y in one of the equation, to find the value of x

x-2 = 9

x = 11

Final Answer: The two numbers are 11 and 2.

Answer:

The interest earned is $92.40

The amount in the bank is 92.40 + 700 = $792.40

Step-by-step explanation:

I do not see a number line

Interest = principle x rate x time

Interest = 700 x .033 x 4

Interest = 92.40

The cyclist's average speed is

14.93

mph.

Total

distance

covered is=2+8=10

Total time =10+30=40

=40/60 min

=.0.67 hours.

Convert miles per min to miles per hour,

average speed= 10 miles/0.67 hours,

=14.93 mph.

The average speed is =4.93 mph

The total distance covered is 2 + 8 = 10 miles. The total time taken is 10 minutes + 30 minutes = 40 minutes. To convert minutes to hours, divide the time in minutes by 60. So, the total time taken in hours is 40 minutes / 60 = 0.67 hours. To convert miles per minute to miles per hour, multiply the speed in miles per minute by 60. So, the average speed in miles per hour is

10 miles / 0.67 hours = 14.93 mph

The average speed is =14.93 mph

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Answer:

To determine how much you should invest to receive $100,000 on the maturity date, you will need to calculate the present value of the cash flows at the beginning of the investment. The present value is the amount of money you would need to invest today to receive a certain amount at a future date, taking into account the time value of money and the interest rate.

You can calculate the present value by using the formula:

PV = CF / (1 + r)^t

Where:

PV = present value

CF = cash flow (the amount you will receive at the maturity date)

r = interest rate

t = time (in years)

The first 18 months, the interest rate is 8% per year, which is equivalent to 8/12 = 0.67% per month.

The next 6 months, the interest rate is 1.5% per quarter, which is equivalent to 1.5/4 = 0.375% per month.

The last 12 months, the interest rate is 2% per semi-annual, which is equivalent to 2/2 = 1% per month.

For the first 18 months, the present value of the cash flow is:

PV = 100,000 / (1 + 0.0067)^(18/12) = 95,167

For the next 6 months, the present value of the cash flow is:

PV = 95,167 / (1 + 0.00375)^(6/12) = 94,853

For the last 12 months, the present value of the cash flow is:

PV = 94,853 / (1 + 0.01)^(12/12) = 94,853

So, to receive $100,000 on the maturity date, you should invest 94,853 dollars to the nearest dollar.

Answer:

8:39 is the answer.

The rest, when simplified, change to 1:5.

The resulting image of the triangle ABC after the transformations is given by the image presented at the end of the answer.

The vertices of the original triangle ABC are given as follows:

A(0,2), B(3,2), C (2,7).

First we have the reflection across the line x = 1, which is a vertical line, meaning that:

Hence the vertices after the reflection are given as follows:

A'(2,2), B'(-1,2), C'(0,7).

For example, a coordinate of 0 is one unit left of x = 1, hence the coordinate of the image will be one unit right, at x = 2.

The dilation with a scale factor of 2 centered at the origin means that the coordinates are multiplied by 2, hence:

A''(4,4), B''(-2,4), C''(0,14).

The vertices of the original triangle ABC are given as follows:

A(0,2), B(3,2), C (2,7).

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Step-by-step explanation:

16 transactions per hour (60 minutes).

in short :

16/1

or 16/60 (for minutes instead of 1 hour)

in 20 minutes 6 transactions.

so,

6/20

hour many transactions then in 1 hour (60 minutes) ?

60 = 20×3

so, to bring the ratio to 1 hour (60 minutes) we need to multiply the denominator by 3. and to keep the ratio value, we need to to do the same thing also to the numerator.

therefore,

6/20 × 3/3 = 18/60

so, the clerk will do 18 transactions per hour.

he will meet his goal of 16 : true

he will even exceed but definitely meet his goal.

12 transactions in 1 hour : false

9 transactions every half hour : true

as he will do 18 transactions in 1 hour, he will do half of these transactions (9) in half an hour.

96 transactions in 6 hours : false

18/1

6 = 1×6

so, with the same trick as above we get

18/1 × 6/6 = 108/6

and we see, he would complete 108 transactions in a 6- hour shift.

96 would be right, if the actual ratio would be 16/1 :

16/1 × 6/6 = 96/6

Answer:

Area =312cm²

Step-by-step explanation:

since two rectangle are joined together you will find each area of the diagram and finally you add the two rectangle.

so the value for A1

A1 × Length × width.

A1 =16 ×17

A1 =272cm²

the value for A2

A2 Length × width

A2 = 14 × 3

A2 =42cm²

The area of the diagram

=A1 + A2

=272 + 42

=312cm².

The total area of the given figure is 468 cm².

Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.

From the given figure,

Larger rectangle has length=30 cm and width=14 cm.

Smaller rectangle has length=16 cm and width=3 cm.

We know that, the area of a rectangle is Length×Width

Area of Larger rectangle is

30×14 = 420 cm²

Area of Smaller rectangle is

16×3 = 48 cm²

Total area = 420+48 =468 cm²

Therefore, the total area is 468 cm².

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They intersect in the 2nd quadrant. Only one answer choice (–0.3, 2.1)

Horizontal axis represents a variable x and the vertical axis represents a variable y, a y-intercept or vertical intercept is a point where the graph of a function or relation intersects the y-axis of the coordinate system.

The graph shows you the lines all differ in their y-intercepts. This means you can identify the y-intercepts of the equations of interest, and you will know which lines to look at.

The y-intercept is found by setting x=0 and solving for y:

x +5y = 10

 0 + 5y = 10

 y = 10/5 = 2

3x +y = 1

 3·0 +y = 1

 y = 1

The two lines of interest are the ones that have y-intercepts of 2 (pink) and 1 (blue). They intersect in the 2nd quadrant. Only one answer choice can apply: (–0.3, 2.1)

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Answer:

30%.

Step-by-step explanation:

Ayo earns 50,000 monthly and he spends 35,000 altogether, so he saves the rest of his income. To find the percentage of his savings, we can divide his savings by his total income and multiply by 100.

His total income is 50,000

His total expenditure is 35,000

His savings = total income - total expenditure = 50,000-35,000 = 15,000

So the percentage of his savings = (savings / total income) x 100 = (15,000 / 50,000) x 100 = 0.3 x 100 = 30%

Therefore, Ayo's savings percentage is 30%.

Answer:

26 and 27

Step-by-step explanation:

If the smaller integer is represented using the variable n, then the next consecutive integer is n + 1

3 times the smaller => 3n

2 times the larger => 2(n + 1 = 2n + 2

We are given 3 times the larger exceeds twice the smaller by 24 which can be represented as:

3n - (2n + 2) = 24

3n - 2n - 2 = 24

n - 2 = 24

n = 24 + 2 = 26

So the integers are 26 and 27

Answer: We know that in a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Using the triangle inequality theorem, we can set up the following inequality:

BD + BC > CD

7x - 10 + 4x - 29 > 5x - 9

Simplifying, we get:

11x - 39 > 5x - 9

Subtracting 5x from both sides, we get:

6x - 39 > -9

Adding 39 to both sides, we get:

6x > 30

Dividing by 6 from both sides, we get:

x > 5

So x must be greater than 5.

To find the value of BD, we can substitute the value of x in the equation:

BD = 7x - 10

BD = 7(5) - 10 = 25 - 10 = 15

To find the value of BC, we can substitute the value of x in the equation:

BC = 4x - 29

BC = 4(5) - 29 = 20 - 29 = -9

To find the value of CD, we can substitute the value of x in the equation:

CD = 5x - 9

CD = 5(5) - 9 = 25 - 9 = 16

So, BD = 15, BC = -9, CD = 16

Step-by-step explanation:

Answer:

  6

Step-by-step explanation:

You want to know how many chairs are usually around the table if 1 chair must be added to accommodate Mr. and Mrs. DiNapoli and their two sons and three daughters.

The number present for a family dinner is ...

  1 (Mr. DiNapoli) +1 (Mrs. DiNapoli) +2 (sons) +3 (daughters) = 7

If one chair is added to make 7, then there are usually ...

   7 - 1 = 6 . . . . chairs at the table

Answer:

  369,287 in the US

  3.69287×10⁵ in the UK

Step-by-step explanation:

Given the number (8*10)+(6*10,000)+(3*100,000)+(2*100)+(9*1,000)+(7*1), you want it written in standard form.

The "standard form" of a number is different depending on your local culture.

In the US, the standard form of this number can be had by performing the indicated addition.

  (8*10)+(6*10,000)+(3*100,000)+(2*100)+(9*1,000)+(7*1)

  = 80 +60,000 +300,000 +200 +9,000 +7

  = 300,000 +60,000 +9,000 +200 +80 +7 . . . . more useful order

  = 369,287

In the UK, "standard form" of a number refers to "scientific notation". The leading digit is shown to the left of the decimal point, and the multiplier is the power of 10 corresponding to that digit's place value.

  = 3.69287×10⁵

Answer:

t = [tex]\frac{7}{3}[/tex]

Step-by-step explanation:

t - [tex]\frac{4}{3}[/tex] = 1 ( multiply through by 3 to clear the fraction )

3t - 4 = 3 ( add 4 to both sides )

3t = 7 ( divide both sides by 3 )

t = [tex]\frac{7}{3}[/tex]

Answer:

-2x^2+5y^3+

Step-by-step explanation: