abet level 4 Life orientation 2023 final​

As a result, the rectangular prism has a volume of 1 cubic centimeter.

The volume of an object is the area enclosed inside its three-dimensional boundaries. It is referred to as an object's capability on occasion.

We must multiply the rectangular prism's length, width, and height to determine its volume. Although we don't directly know these values, we can use the regions of the faces to locate them.

Let's use the letters l, w, and h to denote the prism's length, breadth, and height, respectively. The area of a top and bottom sides is thus determined to be lw = 10 cm², the front and rear faces are lh = 15 cm², and the left and right sides are wh = 6 cm².

These equations can be used to solve for every variable using the following descriptions of the other variables:

l = 10/w

h = 15/l

w = 6/h

When we add these expressions to the volume formula, we obtain:

V = lwh = (10/w)(6/h)(15/l) = 900/whl = 900/(6×10×15) = 1 cm³

As a result, the rectangular prism has a volume of 1 cubic centimeter.

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The nth term of the given sequence is 1/n².

An arithmetic progression (AP) is a sequence of numbers in which each term, starting from the second term, is obtained by adding a fixed constant value to the previous term. This constant value is called the common difference, and it remains the same throughout the sequence.

A geometric progression (GP) is a sequence of numbers in which each term, starting from the second term, is obtained by multiplying the previous term by a fixed constant value. This constant value is called the common ratio, and it remains the same throughout the sequence.

In the given question,

The given sequence is of the form:

1, 1/2², 1/3², 1/4², ...

So, the nth term can be written as:

1/n²

Therefore, the nth term of the given sequence is 1/n².

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Answer:

Step-by-step explanation:

The corresponding equal angles must be written in the same order. So the first one is the correct answer.

Answer: To find the proportions of each type of juice in the 6 quarts of fruit punch, we need to use ratios:

For every 2.5 quarts of apple juice, we need (6/8) x 2.5 = 1.875 quarts of apple juice.

For every 1.5 quarts of cranberry juice, we need (6/8) x 1.5 = 1.125 quarts of cranberry juice.

For every 3 quarts of grape juice, we need (6/8) x 3 = 2.25 quarts of grape juice.

So the proportions of apple, cranberry, and grape juice in the 6 quarts of fruit punch are approximately:

1.875 quarts of apple juice

1.125 quarts of cranberry juice

2.25 quarts of grape juice

Note that these proportions are approximate because we rounded the amounts of each juice to two decimal places.

Step-by-step explanation:

Answer:

Therefore, the maturity value of the loan is $2568.75.

Step-by-step explanation:

To calculate the maturity value of the loan, we need to add the interest to the principal.

First, we need to find out how much interest Ricardo will owe for the 180-day period.

The formula for calculating ordinary interest is:

Interest = Principal x Rate x Time

where:

Principal = $2500

Rate = 7.8% = 0.078 (expressed as a decimal)

Time = 180/360 (since the interest is for a 180-day period and the rate is an annual rate)

Time is expressed as a fraction of a year because the rate is an annual rate. In this case, the time is 180/360 because the loan is for 180 days, which is half of a year.

Using the formula above, we can calculate the interest as follows:

Interest = $2500 x 0.078 x 180/360 = $68.75

Therefore, Ricardo will owe $68.75 in interest for the 180-day period.

To find the maturity value of the loan, we add the interest to the principal:

Maturity Value = Principal + Interest = $2500 + $68.75 = $2568.75

Therefore, the maturity value of the loan is $2568.75.

The minimum amount of money to be deposited in the bank account is $16,921. The solution has been obtained by using compound interest.

What is compound interest?

Compound interest is the type of interest that is calculated using both the principal and the interest that has accumulated over the preceding period. In contrast to simple interest, compound interest does not factor in the principal when calculating the interest for a subsequent period. In mathematics, compound interest is frequently referred to as C.I.

We are given that we need $25,000 eight years from now and the account pays an annual percentage rate (APR) of 5% which is compounded annually.

So, using the compound interest formula, we get the principal as

⇒ P = [tex]\frac{A}{(1 + \frac{r}{n} )^{nt} }[/tex]

⇒ P = [tex]\frac{25000}{(1 + \frac{0.05}{1} )^{8} }[/tex]

⇒ P = $16,920.98

Hence, the minimum amount of money to be deposited in the bank account is $16,921.

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Expression equivalent to 5x - 4 are 5(x - 4/5), 5x - 20/5, 10x/2 - 8/2 and 3(5x/3) - 4

To create an expression equivalent to 5x - 4, we need to use arithmetic operations such as addition, subtraction, multiplication, and division, along with numbers and variables. The goal is to manipulate the numbers and variables in a way that results in the same value as 5x - 4.

Here are some examples of how we can do this:

5(x - 4/5)

In this expression, we start with x and subtract 4/5 from it. Then we multiply the result by 5. This is equivalent to distributing the 5 to x and -4/5, which gives us 5x - 4.

5x - 20/5

Here, we simply subtract 20/5 (which simplifies to 4) from 5x. This gives us 5x - 4.

(25x - 20)/5

In this expression, we start with 25x and subtract 20 from it. Then we divide the result by 5. This is equivalent to simplifying the expression to 5x - 4.

10x/2 - 8/2

This expression might look a bit different, but it's still equivalent to 5x - 4. Here, we start with 10x and divide it by 2, which gives us 5x. Then we subtract 8/2 (which simplifies to 4) from it, giving us 5x - 4.

3(5x/3) - 4

In this expression, we start with 5x and divide it by 3. Then we multiply the result by 3, which gives us 5x. Finally, we subtract 4 from it, giving us 5x - 4.

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Answer:

Step-by-step explanation:

To convert the mixed angle measure 96° 29' 1" to decimal degrees, we can use the following formula:

decimal degrees = degrees + (minutes / 60) + (seconds / 3600)

Using this formula, we have:

decimal degrees = 96 + (29 / 60) + (1 / 3600)

decimal degrees = 96.4836111

Therefore, mHJ = 96.4836111 degrees (rounded to seven decimal places).

Answer:

x = 20.4

Step-by-step explanation:

cos(32) = adjacent/ hypotenuse

24 cos (32) = x

x = 20.4

Answer: I'm not really sure what the question is but the volume is 224

Step-by-step explanation:

The range of the function for one day of work is 75 ≤ y ≤ 425. So, correct  option is B.

In mathematics, a function is a mathematical object that takes an input (or several inputs) and produces a unique output. It is a relationship between a set of inputs, called the domain, and a set of outputs, called the range.

Formally, a function f is defined by a set of ordered pairs (x, y) where x is an element of the domain, and y is an element of the range, and each element x in the domain is paired with a unique element y in the range. We write this as f(x) = y.

The linear function that models the daily cost of hiring an electrician can be written as:

y = 50x + 75

where x is the number of hours worked by the electrician and y is the cost in dollars.

Since the electrician works a maximum of 7 hours per day, the domain of the function is 0 ≤ x ≤ 7.

To find the range of the function, we can substitute the maximum and minimum values of x into the function and see what values of y we get:

When x = 0 (no hours worked), y = 50(0) + 75 = 75.

When x = 7 (maximum hours worked), y = 50(7) + 75 = 425.

Therefore, the range of the function for one day of work is:

75 ≤ y ≤ 425

So the answer is (B) 75 ≤ y ≤ 425.

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The set of numbers 36 and 96 has a greatest common factor of 12.

The greatest common factor (GCF) of a set of numbers is the largest number that can evenly divide all the numbers in the set. To find the GCF, we can list all the factors of each number and find the largest one they have in common.

For set A, the factors of 3 are 1 and 3, and the factors of 4 are 1, 2, and 4. There is no common factor greater than 1.

For set B, the factors of 6 are 1, 2, 3, and 6, and the factors of 18 are 1, 2, 3, 6, 9, and 18. The largest factor they have in common is 6.

For set C, the factors of 32 are 1, 2, 4, 8, 16, and 32, and the factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48. The largest factor they have in common is 16.

For set D, the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36, and the factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96. The largest factor they have in common is 12.

Therefore, set D, consisting of the numbers 36 and 96, has a greatest common factor of 12.

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Answer:

x-5=0

10=2x

(1/2)x=10

x>2=25

Step-by-step explanation:

all of these are x=5

the ones that are wrong are 11-x=3 and 1+x=5

Answer:

0.375

Step-by-step explanation:

3/2 equals 1 and a half, and 1 and a half divided by 4 will get you 0.325

Answer:

4x - 2 = 3x + 1. Solution We substitute the value 3 for x in the equation and see if the left-hand member equals the right-hand member. 4(3) - 2 = 3(3) + 1.

Answer:

Step-by-step explanation:

Fractions are parts or pieces of a complete thing.

In this problem, the fractions start out with varying denominators, and then end with the same denominator.  In order to go from different denominators to the same denominator, we must find a common denominator.

A common denominator is a number that denominators of fractions can equal when multiplied by something else.  Ex:  1/3 + 2/ 7  Multiples of 3:  3, 6, 9, 12, 15, 18, 21   Multiples of 7:  7, 14, 21.  Both 3 and 7 have 21 in common, so this would be the common denominator.

A common denominator is needed so fractions with different denominators can be combined.  To get from 6, 3, and 7 to 42, the multiples of 2, 3, and 7 must be listed.

Multiples of 6:  6, 12, 18, 24, 30, 36, 42

Multiples of 3:  3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 29, 42

Multiples of 7:  7, 14, 21, 28, 35, 42

All three numbers have 42 in common, so that is their common denominator.  Whatever was done to the denominator, must be done to the numerator.  Now, we must take the number that can be multiplied by the denominator to reach 42 and multiply it by the numerator.

[tex]\frac{1*7}{6*7}}[/tex]

[tex]=\frac{7}{42}[/tex]

[tex]\frac{2*14}{3*14}[/tex]

[tex]=\frac{28}{42}[/tex]

[tex]\frac{3*6}{7*6}[/tex]

[tex]=\frac{18}{42}[/tex]

So, to sum it up, when trying to add fractions with different denominators, find a common denominator by listing multiples of the denominators and multiply the numerator by the number the denominator was multiplied by to get the common denominator.

The logic in this fraction addition problem is to find a common denominator for all the fractions and then add the numerators. In this case, the common denominator is the least common multiple of the denominators, which is 42.

Now that all the fractions have a common denominator of 42, we can add the numerators to get the final answer:

[tex]\begin{aligned} \sf \dfrac{1}{6} + \dfrac{2}{3} + \dfrac{3}{7} = \dfrac{7}{42} + \dfrac{28}{42} + \dfrac{18}{42} = \bold{\dfrac{53}{42}} \end{aligned}[/tex]

Therefore, the sum of the fractions is 53/42.

I hope this helps!

Finally, express the solution as an interval of real numbers or as a set of values that make the inequality. x<10.4, x>3.3, x≥32 and x≤-15.

To solve an inequality, you need to find the set of values that make the inequality true. The process for solving an inequality depends on the type of inequality and the variables involved. Here are the general steps:

Finally, express the solution as an interval of real numbers or as a set of values that make the inequality true. If the inequality is strict (> or <), use an open interval (e.g., (a, b)). If the inequality includes equality (≥ or ≤), use a closed interval (e.g., [a, b]).

by the question.

a. x-3.5>6.9

x>6.9+3.5

x>10.4

b. 6.4>x+3.1

x[tex]\geq 32[/tex]

c. x/4≤8

x≤32

d. 2/3x≤-10

x≤-15

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The statement that is true, given that ΔCBX ≅ ΔSML, would be G. XC ≅ ML.

Given that ΔCBX ≅ ΔSML, we can use the properties of congruent triangles to determine which statement is true. The correspondence between the vertices of the two triangles is as follows:

C ↔ S

B ↔ M

X ↔ L

XC ≅ ML is true because XC corresponds to the side connecting vertices X and C in ΔCBX, and ML corresponds to the side connecting vertices M and L in ΔSML. Since the triangles are congruent, their corresponding sides are congruent.

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The amount Elsa earns per week, which is $150 more than Anna per week and Elsa had saved $2400 more than Anna when Anna had saved $2880, found by solving the simultaneous equations obtained is $650.

Simultaneous equations are equations that share the same variables.

Let x represent the amount Elsa earn per week, we get;

The amount Anna earns per week + 150 = The amount Elsa earns per week

Therefore; The amount Anna earns per week = x - 150

The amount each girl spent per week = $320

The amount saved per week = The rest of their weekly earning

The mount more Elsa add saved when Anna saved $2880 = $2400

Let n represent the number of weeks after which Anna had saved $2,880, we get the following equations;

n × (x - 150 - 320) = 2800

n × (x - 470) = 2800...(1)

n × (x - 320) = 2880 + 2400 = 5280

n × (x - 320) = 5280...(2)

The above simultaneous equations (1) and (2) indicates;

n × (x - 470) = 2800

x - 470 = 2880/n

x = 2880/n + 470

n × (x - 320) = 5280

x - 320 = 5280/n

x = 5280/n + 320

2800/n + 470 = 5280/n + 320

5280/n - 2880/n = 470 - 320 = 150

(5280 - 2880)/n = 150

n = (5280 - 2880)/150 = 16

n = 16

x = 5280/n + 320

Therefore;

x = 5280/16 + 320 = 650

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Answer:

y

Step-by-step explanation:

Answer:

Step-by-step explanation:

The radius of the Earth's orbit around the sun is approximately 93 million miles.

To calculate the circumference of the Earth's orbit, we can use the formula:

C = 2πr

where C is the circumference and r is the radius. Plugging in the value for the radius, we get:

C = 2π(93,000,000) = 584,336,000 miles

So the Earth travels approximately 584,336,000 miles in one orbit around the sun.

The speed of the Earth in its orbit around the sun can be calculated using the formula:

v = 2πr/T

where v is the velocity, r is the radius, and T is the period (the time it takes for the Earth to complete one orbit). The period of the Earth's orbit is approximately 365.25 days, or 31,557,600 seconds.

Plugging in the values, we get:

v = 2π(93,000,000)/(31,557,600) = 29,784 miles per hour

So the Earth travels at approximately 29,784 miles per hour in its orbit around the sun.

Answer: Supplementary   x=2

Step-by-step explanation:

supplementary adds up to 180

complementary adds up to 90

Answer:

130

Step-by-step explanation:

Answer: y=130  x=130

Step-by-step explanation:

The sum of the given fractions is (2x + 10)/x.

What is fraction ?

A fraction is a way of representing a part of a whole or a ratio between two quantities. It is written in the form of a numerator and a denominator separated by a horizontal line. The numerator represents the number of equal parts under consideration, while the denominator represents the total number of equal parts that make up the whole. For example, the fraction 3/4 represents three equal parts out of a total of four equal parts. Fractions can be added, subtracted, multiplied, and divided to perform various mathematical operations.

According to the question:
The given fractions can be added if they have a common denominator. In this case, the common denominator is 9x.

So, we need to write the fractions with 9x as the denominator:

2/1 * (9x/9x) = 18x/9x

10/1 * (9/9x) = 90/9x

Now, we can add these two fractions:

18x/9x + 90/9x = (18x + 90)/9x = 9(2x + 10)/9x = 2x + 10/ x

Therefore, the sum of the given fractions is (2x + 10)/x.

Q: Find K by Adding the fractions and simplify if possible k=(2*(9x))+(10*(9x))

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Answer: 160

Step-by-step explanation: The straight line or line X is 180 degrees. So subtracted 20. This is because X is intersected by another line which makes the upper notch 20 degrees.

Answer: 2.45 m/s.  

acceleration due to gravity 9.8 m/s

Miles is going to spend less than the hours that were spent last week since 2/3 is a fraction.

A fraction represents a part of a whole, and is therefore always less than the whole. For example, 2/3 represents two out of three equal parts of a whole.

The implication of this is that the time that Miles would have to spend on biking in the coming week would be wo out of three equal parts of a whole time that was spent in the last week and this would be less than the time spent last week.

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Answer:

  C.  396

Step-by-step explanation:

You want the LCM of 4, 18, and 44.

You can find the least common multiple by considering the unique factors to their highest powers.

  4 = 2^2

  18 = 2·3^2

  44 = 2^2·11

The unique factors are 2, 3, 11, and their highest powers are 2, 2, and 1, respectively. The LCM is ...

  2² × 3² × 11 = 396

__

Check

  396 = 4·99 = 18·22 = 44·9 . . . . . 99, 22, and 9 have no common factors

Answer:

19.2 ft

Step-by-step explanation: