How much principal must be deposited to earn $744 simple interest in 3 years at an rate of 5.4%?

If a sum of $500 were shared among a group of people in the following ratios,

a) 6:4 then, 6x = 300 and 4x = 200.

b) 1:4:5 then, x = 50 , 4x = 200 and 5x = 250.

c) 1 : 8 : 1 then, x =50 , 8x = 400 and x = 50

d) 10 : 5: 4: 1 then, 10x = 250 , 5x = 125, 4x = 100, x = 25.

What is ratio?

a) 6:4

Let it be 6x , 4x

6x + 4x = 500

10x = 500

x = 50

Then, 6x = 300 and 4x = 200.

b) 1:4:5

Let be x, 4x, 5x

x + 4x + 5x = 500

10x = 500

x = 50.

Then x = 50 , 4x = 200 and 5x = 250.

c) 1 : 8 : 1

x + 8x + x =500

10x = 500

x = 50

Then, x =50 , 8x = 400 and x = 50

d) 10 : 5: 4: 1

10x + 5x + 4x + x = 500

20x = 500

x = 25

Then, 10x = 250 , 5x = 125, 4x = 100, x = 25.

Hence, If a sum of $500 were shared among a group of people in the following ratios,

a) 6:4 then, 6x = 300 and 4x = 200.

b) 1:4:5 then, x = 50 , 4x = 200 and 5x = 250.

c) 1 : 8 : 1 then, x =50 , 8x = 400 and x = 50

d) 10 : 5: 4: 1 then, 10x = 250 , 5x = 125, 4x = 100, x = 25.

To know more about ratio check the below link:

https://brainly.com/question/2914376

#SPJ4

The perimeter of the rhombus in this problem is given as follows:

19.8 units.

The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.

The diagonal length can be obtained as follows:

RU + UT = 7.

Applying the Pythagorean Theorem, the side length is obtained as follows:

x² + x² = 7²

2x² = 49

\(x = \sqrt{\frac{49}{2}}\)

x = 4.95.

Then the perimeter is given as follows:

P = 4 x 4.95

P = 19.8 units.

More can be learned about the perimeter of a polygon at https://brainly.com/question/3310006

#SPJ1

Answer:

A scale is just another way of saying what we want to count by on our graph.

Step-by-step explanation:

A "scale" is just another way of saying what we want to count by on our graph. The scale is the range of values that are shown on the axis of a graph. It helps to determine the size and spacing of the intervals or ticks on the axis. The scale can be in different units, such as time, distance, weight, or any other measurable quantity depending on the type of data being represented in the graph.

Answer:

(4 - 5y)(2 + 3x)

Step-by-step explanation:

Given

8 - 10y + 12x - 15xy ( factor the first/second and third/fourth terms )

= 2(4 - 5y) + 3x(4 - 5y) ← factor out (4 - 5y) from each term

= (4 - 5y)(2 + 3x) ← in factored form

Answer:

the answer is 24192

Answer: 24192

Step-by-step explanation:

Express the mixed number as a fraction:

Now, let's use the following formula to divide fractions:

So:

Answer:

x = 43

Step-by-step explanation:

Answer:

120 degrees

Step-by-step explanation:

55+ 185/2 = 120

So,

Using the z-table:

Answer:

a. 0.996

a) Comparing the two functions, Scooter's business has a lower slope of 15 compared to Karissa's business with a slope of 35. b) Both Scooter and Karissa earned a total of $500 in that month. Therefore, they had an equal month in terms of total money earned.

a) In the context of Scooter's business, the slope of the function f(x) = 200 + 15x represents the rate at which the total money earned increases with each additional sale. Each unit increase in x (number of sales) results in an increase of $15 in total money earned. The y-intercept of 200 represents the initial amount of money Scooter already had before making any sales.

In the context of Karissa's business, the slope of the function f(x) = 80 + 35x represents the rate at which the total money earned increases with each additional repair job. Each unit increase in x (number of repairs) results in an increase of $35 in total money earned. The y-intercept of 80 represents the initial amount of money Karissa already had before doing any repair jobs.

Comparing the two functions, Scooter's business has a lower slope of 15 compared to Karissa's business with a slope of 35. This means that Karissa's business earns more money per repair job compared to Scooter's business per t-shirt sale.

b) To determine who had the better month, we need to calculate the total money earned by each individual based on the given sales/repairs.

For Scooter, with x = 20 (number of shirts sold):

f(x) = 200 + 15x

f(20) = 200 + 15 * 20

f(20) = 200 + 300

f(20) = 500

For Karissa, with x = 12 (number of repairs):

f(x) = 80 + 35x

f(12) = 80 + 35 * 12

f(12) = 80 + 420

f(12) = 500

Both Scooter and Karissa earned a total of $500 in that month. Therefore, they had an equal month in terms of total money earned.

learn more about functions at https://brainly.com/question/11624077

#SPJ1

Answer:

34/3, -2/3

Step-by-step explanation:

See image below:)

Step-by-step explanation:

2x + 3y = 34

3y = 34 - 2x

y = 3x - 2x/3

Answer:

$54.87

Step-by-step explanation:

The area of the triangular garden is (1/2) x base x height = (1/2) x 6 x 5 = 15 square feet.

The area of the rectangular mulch area is base x height = 12 x 9 = 108 square feet.

The total area to be covered with mulch is 108 - 15 = 93 square feet.

The cost of the mulch is $0.59 per square foot, so the total cost is 93 x $0.59 = $54.87.

Therefore, the total cost of the mulch will be $54.87.

The completed list of numbers would be: 1, 1, 1, 2, 1, 4, 1, 2

By examining the given list of numbers 1, 1, 1, 2, 1, 4, 1, we can observe a pattern emerging.

The pattern seems to involve alternating sequences. The first sequence is the number 1 repeated three times (1, 1, 1). The second sequence is a number that follows the pattern of increasing by 1 each time (2). The third sequence is the number 1 repeated once (1). The fourth sequence is a number that follows the pattern of doubling each time (4). This pattern of alternating sequences continues.

Based on this pattern, we can predict that the next number in the sequence will follow the alternating sequence pattern. Since the last number in the sequence is 1, the next sequence will involve a number that follows the pattern of increasing by 1. Therefore, the next number in the sequence would be:

1 + 1 = 2

Hence, based on the observed pattern, the next number in the sequence is 2.

Therefore, the completed list of numbers would be:

1, 1, 1, 2, 1, 4, 1, 2

For more such questions on numbers visit:

https://brainly.com/question/24644930

#SPJ8

Answer:

Each person would get 1/6 of the pizza

Step-by-step explanation:

1/3 divided by 2 is 1/6. Do that again and you will get four of 1/6.

Answer:

-5<x<7.

Step-by-step explanation:

let the number be represented by 'x'

3x + 5 > -10 < 26

-10<3x+5<26

-10 < 3x +5

-10 -5 < 3x

-15< 3x

-15÷3 < x

-5 < x

and

3x+5 < 26

3x<26-5

3x < 21

x < 21÷3

x< 7

answer is -5<x<7

Answer:

[⁵/3,7[

Step-by-step explanation:

10 ≤ 3x + 5 < 26

10-5 ≤ 3x < 26-5

⁵/3 ≤ X <7

[ 5/3 , 7 [

Therefore, the domain is (-∞, ∞) and the range is (-∞, ∞) for the given function.

In mathematics, a function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range) with the property that each input is associated with exactly one output. In other words, a function is a rule that assigns a unique output value to each input value.

Here,

To find the domain and range of the function f(x) = -1/4(x³ + 6x² + 5x - 4), we need to consider the restrictions on x and the possible values of f(x).

Domain:

Since the function involves a cubic expression in the numerator, there are no restrictions on x, and the domain of the function is all real numbers, or (-∞, ∞).

Range:

To find the range of the function, we need to consider the behavior of the cubic expression as x goes to positive infinity or negative infinity. As x becomes very large or very small, the dominant term in the expression becomes x³, and the other terms become negligible. The coefficient of x³ is negative, which means that the cubic expression approaches negative infinity as x goes to negative infinity and approaches positive infinity as x goes to positive infinity.

Therefore, as x approaches negative infinity, f(x) approaches positive infinity, and as x approaches positive infinity, f(x) approaches negative infinity. Hence, the range of the function is all real numbers, or (-∞, ∞).

To know more about function,

https://brainly.com/question/28193995

#SPJ1

If Leila makes a dot plot of the heights of the girls in her class to the nearest ¹/₂ inch, the number of different heights that will include on the number line is 5.

A dot plot is a data visualization tool that consists of data points plotted as dots on a graph with an x- and y-axis.

The number of dots plotted on each number line shows the frequency of the data group.

Height    Frequency   Cumulative Frequency

56¹/₂             2                               2

57                 2                               4

57¹/₂             2                               6

58                2                               8

58¹/₂             1                               9

Thus, arranging the heights according to groups, the different heights on the number line can be classified into 5.

Learn more about the dot plot at https://brainly.com/question/15853311.

#SPJ1

Total number of people surveyed = 118

Number of people who own dogs = 78

Number of people who own cat = 44

Number of people who own both cats and dogs = 26

Number of people who only own dogs = 78 - 26 = 52

Number of people who own only cats = 44 - 26 = 18

Only dog owners + Only cat owners + Both + Neither = Total people surveyed

52 + 18 + 26 + Neither = 118

Neither = 22(answer)

The algebraic expression is x + y = -17

Given,

The sum of two numbers = -17

One number = x

We have to write an algebraic expression for the above condition:

Algebraic expression

In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.).

You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression. If we are aware of the values of our variables, we can substitute those values for the original variables before evaluating the expression.

So, let’s find the algebraic expression:

Given that one number is x. We can take other number as y.

So, the expression will be like:

x + y = -17

Learn more about algebraic expressions here:

https://brainly.com/question/2278920

#SPJ1

Answer:

Below.

Step-by-step explanation:

11 feet=132 Inches.

12(Number of inches in a foot)

12x11=132.

135>132.

Answer:

three

Step-by-step explanation:

stem. is the tens place and the leaf is the. ones place

so you want to find 68 so you look in the stem column and look for six

in the row there are 6 numbers which mean:

60, 61, 67, 68, 68, 68

as you can see there is three 68 there for the answer ths 3

Answer:

The equation is 5x - 9 = 2x + 23.

The answer is option A.

Step-by-step explanation:

We're given:

If the shop sold " \(9\dfrac{9}{10}\)  times as much milk chocolate as white chocolate", we must multiply \(9\dfrac{9}{10}\) by the amount of white chocolate sold to find the amount of milk chocolate sold.

Multiply \(9\dfrac{9}{10}\) by 9 ounces:

\(9\dfrac{9}{10}\times9\)

Convert the fraction into an improper fraction:

\(=\dfrac{99}{10}\times9\)

Multiply:

\(=\dfrac{891}{10}\)

The shop sold \(\dfrac{891}{10}\) ounces of milk chocolate.

\(\text{Given that,}\\\\~~~~~~~~\cos \theta = \dfrac 35\\\\\implies \cos^2 \theta = \dfrac 9{25}\\\\\implies 1-\sin^2 \theta = \dfrac{9}{25}\\\\\implies \sin^2 \theta = 1-\dfrac{9}{25}\\\\\implies \sin^2 \theta = \dfrac{16}{25}\\\\\implies \sin \theta = \pm\sqrt{\dfrac{16}{25}}\\\\\implies \sin \theta = \pm\dfrac 45\\\\\text{Given that,}~ 270^{\circ} \leq \theta \leq 360^{\circ}, \text{So}~ \theta ~ \text{lies in fourth quadrant.}\\\\\)

\(\text{Which means that}~ \sin \theta ~ \text{will be negative.}\\\\\text{Hence,}~ \sin \theta = -\dfrac 45\)

Answer:

B. 10x -40

Step-by-step explanation:

To rewrite the expression 5(2x-8) using the distributive property, we need to separate the expression inside the parentheses and then multiply the two expressions by 5. The answer is: 10x-40.

Complete Question

Professor Jin wants to travel from place A to place B without a map. There are four ways lead away from place A. If road I is selected, the probability of arriving place B is 1/8; if road II is selected, the probability of arriving place B is 1/6; if road III is selected, the probability of arriving place B is 1/4; and if road IV is selected,the probability of arriving place B is 9/10.

(a) What is the probability that professor will arrive at place B?

(b) If Professor Jin arrives at place B, what is the probability that she chooses road IV?

Answer:

a

  \(P(B) = 0.36\)

b

  \(P(4 /B) = 0.62\)

Step-by-step explanation:

From the question we are told that

  The number of ways from A to B is  n =  4

   The  probability if road 1 is selected is  \(P(1) = \frac{1}{8}\)

   The  probability if road 2 is selected is  \(P(2) = \frac{1}{6}\)

    The  probability if road 3 is selected is \(P(3) = \frac{1}{4}\)

    he  probability if road 4 is selected is \(P(4) = \frac{9}{10}\)

The probability that professor will arrive at place B is mathematically represented as

      \(P(B) = \frac{1}{n} * P(1) + \frac{1}{n} * P(2) + \frac{1}{n} * P(3)+ \frac{1}{n} * P(4)\)

      \(P(B) = \frac{1}{4} * \frac{1}{8} + \frac{1}{4} * \frac{1}{6} + \frac{1}{4} * \frac{1}{4} + \frac{1}{4} * \frac{9}{10}\)

      \(P(B) = 0.36\)

If Professor Jin arrives at place B, what is the probability that she chooses road IV is mathematically represented as

      \(P(4 /B) = \frac{ \frac{1}{n} * P(4)}{P(B)}\)

=>     \(P(4 /B) = \frac{ \frac{1}{4} * \frac{9}{10} }{0.36}\)

=>      \(P(4 /B) = 0.62\)