Principal = 6,000, rate of interest = 10% p.a., time = 3 years
please solve​

The value of the variable I (i.e interest) is $9

From the question, we have the following parameters that can be used in our computation:

Principal, P =$400

Rate, R = 9%

Time, T = 0.25 years

The equation to calculate the interest is given as

I = PRT

Where

P, R and T are defined above

And I represents the interest

Substitute the known values in the above equation, so, we have the following representation

I = 400 * 9% * 0.25

Evaluate the products

I = 9

Hence, the interest is $9

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The solution to each of the given algebraic expressions are;

1) 2n - 2 = 10

2) 12n - 1 = 17

3) 4 * 9 = 36

4) 23 - 8 = 15

5) (3 * 7) + 1 = 22

6) ¹/₆ * 42 = 7

7) 3n - 6 = 70

8) y - 2 = 9

9) x = 5 * 12

10) -48 = -4 * 12

11) -32/-8 = 4.

12) (15 - 3)n = 2

13) (5 + 8)n = 42

14) (12 + 6)/2 = 9

15) -4 = -2(5 - 3)

16) x + (x + 1) = 25

17) (x) + (x + 1) = -3

18) 11 - x = -1

1) Two less than twice a number is equal to 10 is expressed as;

2n - 2 = 10

2) 17 is one more than twice a number;

2n - 1 = 17

3) Four times 9 is 36;

4 * 9 = 36

4) Eight less than 23 is fifteen;

23 - 8 = 15

5) One more than 3 times 7 is 22;

(3 * 7) + 1 = 22

6) One sixth of forty two is seven;

¹/₆ * 42 = 7

7) Six less than 3 times a number is equal to seventy;

3n - 6 = 70

8) Two dollars off the regular price of a calculator is $9;

y - 2 = 9

9) A number is equal to five times 12;

x = 5 * 12

10) Negative 4 is a product of the opposite of four and 12;

-48 = -4 * 12

11) Four is the quotient of -32 and -8;

-32/-8 = 4.

12) When 15 minus 3 is multiplied by a number, the product is 2;

(15 - 3)n = 2

13) A number times the sum of five and 8 is 42;

(5 + 8)n = 42

14) 9 is the quotient when 12 + 6 is divided by 2;

(12 + 6)/2 = 9

15) -4 = -2(5 - 3)

16) x + (x + 1) = 25

17) (x) + (x + 1) = -3

18) 11 - x = -1

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The equation (A) 8k-3=12 is not a quadratic equation as it is not in the form ax²+bx+c=0.

A quadratic equation is any algebraic expression that can be expressed in a standard form where x represents an unknown number, a, b, and c represent known values, and where a 0 is true.

The four methods for solving a quadratic issue are factoring, using square roots, completing the square, and the quadratic formula.

Form of a quadratic equation: ax²+bx+c=0

(A) 8k-3=12

Not in form of ax²+bx+c=0.

(B) 9r2 -25 =0

In form of ax²+bx+c=0.

(C) x2 - 5x + 3 = 0

In form of ax²+bx+c=0.

(D) (2x + 5) (x - 1) = - 6​

In form of ax²+bx+c=0.

Therefore, equation (A) 8k-3=12 is not a quadratic equation as it is not in the form ax²+bx+c=0.

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Answer:

The Pacific Ocean is approximately 4.9 times larger than Lake Superior in terms of volume. This can be shown through the following mathematical argument:

First, divide the volume of the Pacific Ocean by the volume of Lake Superior to determine the size ratio:

6 x 10^8 cubic kilometers / 1.22 x 10^4 cubic kilometers = 4.9

This shows that the Pacific Ocean is approximately 4.9 times larger than Lake Superior.

To defend this solution, we can use the concept of ratio and proportion. We know that the ratio of the volumes of the two bodies of water is equal to the ratio of their respective sizes. Therefore, by finding the ratio of the volumes, we can determine the size ratio.

In this case, the ratio of the volumes is 6 x 10^8 cubic kilometers / 1.22 x 10^4 cubic kilometers, which simplifies to 4.9. This means that the Pacific Ocean is 4.9 times larger than Lake Superior in terms of volume.

This solution can be further supported by the fact that the Pacific Ocean is the largest ocean in the world, while Lake Superior is one of the Great Lakes and is much smaller in size.

Step-by-step explanation:

SELF EXPLANATORY

Using Pythagoras theorem If sin tetha = x/4, then cos tetha = √(16-x²)/4

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.

The sides of this triangle have been named Perpendicular, adjascent and Hypotenuse. If sin (tetha) = x/4, this means

x = opposite and

4 = hypotenuse

From hypotenuse² = opposite² + adjacent²

4² = x²+y²

y² = 16-x²

y = √ ( 16-x²)

cos (tetha) = adjacent/ hypotenuse

cos (tetha) = √(16-x²)/4

Therefore the value of cos (tetha) = √(16-x²)/4

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43920  is the lowest amount that a teacher needs to make and still be one of the top 7% earners with a mean of $38,000 and a standard deviation of $4,000

According to information provided to us, the pay for elementary school teachers in a certain nation is generally distributed, with a mean of $38,000 and a standard deviation of $4,000 per year.

To resolve the issue at hand, we shall make use of the normal distribution table. Finding the z-score corresponding to the top 7% or the 93% probability from the normal distribution table (0.93).

The normal distribution table provides us with the 1.48 z-score we need.

We will now solve for the sample score using the z-score formula as follows:

z = x - μ/σ

1.48 = x - 38,000/4000

1.48 × 4000 = x - 38,000

5920 = x - 38000

x = 5920+38000

x = 43920

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Using the provided percentages, it is discovered that:

a) A randomly chosen dorm room has a 31% chance of having a TV but no refrigerator.

b) A randomly chosen dorm room has a 48% chance of having either a television or a refrigerator, but not both.

c) There is a 31% chance that a randomly chosen dorm room lacks both a refrigerator and a television.

Item a:

TVs were owned by 52% of people.

21% of them had a refrigerator as well.

52 - 21 = 31

A randomly chosen dorm room has a 31% chance of having a TV but no refrigerator.

Item b:

31% just have a TV.

Only 17% of people—38—have a refrigerator.

31 + 17 = 48

A randomly chosen dorm room has a 48% chance of having either a television or a refrigerator, but not both.

Item c:

The likelihood that at least one exists is:

P(A∪B) = P(A) + P(B) - P(A∩B)

Hence:

P(A∪B) = 0.52 + 0.38 - 21 = 0.69.

1 - 0.69 = 0.31

There is a 31% chance that a randomly chosen dorm room lacks a refrigerator or a television.

The Complete Question.

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Answer:

The probability that a randomly selected dorm room has a TV but no refrigerator is 0.31

What is Probability?

Probability is a branch of mathematics that quantifies the likelihood of an event occurring or the likelihood of a statement being true. The probability of an event is a number between 0 and 1, with approximately 0 indicating the improbability of the event and 1 indicating certainty.

According to question

The probability that a randomly selected dorm room has a TV but no refrigerator

Solution :

Suppose

A = event of having refrigerators,

B = event of having a TV,

We have,

P(A) = 34% = 0.34,

P(B) = 51% = 0.51,

P(A∩B) = 21% = 0.21

Therefore:

Probability of a TV but no refrigerator = P(A∩B')

= P(A) - P(A∩B)

= 0.34 - 0.21

= 0.31

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The number multiplied by 3 and subtracted by 2 equals 40 is 14.

The Equation that is used to find an unknown value is known as Linear Equation. To find an unknown value or quantity, first form a linear equation according to the conditions that are given the problem, here we use variables like x, y, etc. to represent the unknown value.  

Here we have

A Number is multiplied by 3 and subtracted by 2 equals 40

Let the number be x

Given that 'x' is multiplied by 3 (3x); subtracted by 2 (3x-2) equals to 40

=> 3x - 2 = 40

Add 2 on both sides

=> 3x - 2 + 2 = 40 + 2

=> 3x = 42

Divide by 3 into both sides

=> 3x/3 = 42/3

=>  x = 14

Therefore,

The number multiplied by 3 and subtracted by 2 equals 40 is 14.

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The hot air balloon travels 40 miles against the wind in the same amount of time that it travels 200 miles with the wind. Therefore, the rate of the hot air balloon against the wind is 40 miles/200 miles x 20 mph = 8 mph.

1. Calculate the ratio of the distance traveled against the wind compared to the distance traveled with the wind: 40 miles/200 miles = 0.2

2. Multiply the ratio by the speed of the wind: 0.2 x 20 mph = 4 mph

3. The speed of the hot air balloon against the wind is 8 mph.

The hot air balloon is able to travel at a speed of 20 mph when the wind is in its favor. However, when the wind is not in its favor, the hot air balloon must travel against the wind, drastically decreasing its speed. In the same amount of time, the hot air balloon was able to travel 40 miles against the wind while it was able to travel 200 miles with the wind. To calculate the speed of the hot air balloon against the wind, we can use the following formula: Speed = (Distance against the wind/Distance with the wind) x Speed of the wind. In this case, the ratio of the distance traveled against the wind compared to the distance traveled with the wind is 40 miles/200 miles = 0.2. When we multiply this ratio by the speed of the wind, which is 20 mph, we get 4 mph. Therefore, the rate of the hot air balloon against the wind is 8 mph.

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Answer:

m=-1/3

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Trust the process

Answer:

(1, - 1 )

Step-by-step explanation:

x + y = 0 → (1)

5x + y = 4 ( subtract 5x from both sides )

y = 4 - 5x → (2)

substitute y = 4 - 5x into (1)

x + 4 - 5x = 0

4 - 4x = 0 ( subtract 4 from both sides )

- 4x = - 4 ( divide both sides by - 4 )

x = 1

substitute x = 1 into (1) and solve for y

1 + y = 0 ( subtract 1 from both sides )

y = - 1

solution is (1, - 1 )

Answer:

Below

Step-by-step explanation:

Any 5 points you want

pick out 5 values of x      say     -4    -1     0      3   7  

  and calculate the value of the corresponding 'y' using the equation....then plot those points

The number of songs that he transferred per minute is 1 5/7 songs per minute (option B).

In order to determine the number of songs he can transfer in one minute, divide the number of songs transferred in 1 2/3 by the number of minutes.

Division is the process of determining the quotient of two or more numbers. It entails grouping a number into equal groups using another number. The sign that is used to represent division is ÷

Number of songs they want to transfer per minute = 2 6/7 ÷ 1 2/3

20 /7 ÷ 5/3

20/7 x 3/5 = 12/7 = 1 5/7 songs per minute

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Given that sin 30 degree = 1/2 and cos 30 degree = Squareroot 3/2the value of cot(30°) is  = Squareroot 3

Sine 30°=1/2

Cos 30° = √3/2

Sin 30 degrees has a value of 0.5. Sin 30 can also be expressed in radians as sin /6. The triangle's angles and side length are related by the trigonometric function, often known as an angle function.

The sine function, cosine function, and tangent function are the three trigonometric ratios that are the most well-known.

The ratio of the adjacent side to the hypotenuse is referred to as the cosine function. If the right triangle's angle is 30 degrees, then the cosine value at this angle, or the value of Cos 30 degrees, is expressed as 3/2.

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Answer:

3

Step-by-step explanation:

f(-7) will be equal to (-13) using given function and conditions.

What are function?

Function is an expression rule, or law that defines relationship between one variable and another variable.

An example of this would be y = x^2. If you put in anything for x, you get one output for y.

In given function,

y is represented by f(x),

f(x) = -x-6  for x ≠ 0

f(x) = 2      for x = 0

We need to find for x = -7 i.e. not equal to 0

So, we will take F(x) = -x-6

So, f(-7) = -7-6

             = -13

So, the value of f(-7) = -13.

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Answer:

Step-by-step explanation:

The surface area of solid cylinder = 231 cm²

and curved surface area = 2/3 * 231 cm² = 154 cm²

Now, 2πrh = 154 ...........(i)

2πrh+2πr² = 231

Subtracting, 2πr² =  231 - 154 = 77

⇒2 * 22/7 * r² = 77

⇒r² = 77*7/2*22 ⇒ 49/4 ⇒ (7/2)²

so, r = 7/2 cm

Now, from (i),

2 * 22/7 * 7*h/2 = 154

⇒22h = 154 ⇒ 154/22 = 7

and volume = πr²h = 22/7 * 7/2 * 7/2 * 7cm³ ⇒ 539/2 = 269.5 cm²

Answer:

-13

Step-by-step explanation:

combine the numbers and just add the - sign

hope this helps

It will take 5.625 hours for both Darryl and Valerie to paint the room if they work together .

In the question ,

it is given that ,

Darryl can paint the room in 9 hours .

So , in 1 hour Darryl can paint 1/9 of the room .

Valerie can paint the room in 15 hours .

So , in 1 hour Valerie can paint 1/15 of the room .

So , the time taken to paint the room together can be calculated using ,

1/t = 1/9 + 1/15

1/t = 5/45 + 3/45

1/t = 8/45

Simplifying further ,

we get ,

t = 45/8

t = 5.625

Therefore , the time taken will be 5.625 hours .

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Answer:

Area = 600

Step-by-step explanation:

The area formula for rectangles is length x width. In this equation, the length is 20 and the width is 30, multiplying them together gets us the area of 600.

The value of m in the triangle XYZ is 16. option D

It is important to note that the sum of angles in a triangle is 180 degrees.

From the information given, we have that;

Then we have that;

Angle MZ + Angle Z = 180

Now, substitute the values into the formula, we have;

(5m - 15) + (7m + 3) = 180°

expand the bracket

5m - 15 + 7m + 3 = 180°

collect like terms

12m - 12 = 180°

12m = 180 + 12

Add the like terms

12m = 192

Make 'm' the subject of formula by dividing both sides by 12, we get;

12m/12 = 192/12

m = 16

The value is 16.

Thus, the value is 16

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Answer:

Step-by-step explanation:

How do you solve 2x+7= −17?

2x + 7 = -17

2x = -17 - 7

2x = -24

x = -12

------------

check

2 × (-12) + 7 = -17

-24 + 7 = -17

-17 = -17

The answer is good

The arrangement is as follows;

What is stock?

A stock is a colloquial phrase for any company's ownership certificates. On the other hand, a share alludes to a certain company's stock certificate. You become a shareholder if you possess shares of a specific corporation.

The given data about stock and investment can be arranged in order  from the highest risk and return potential to the lowest risk and return potential as mentioned above in the answer.

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Analysts recommend using Alpha Aesthetics. The alpha aesthetic makes some points on the chart more transparent than others in order to draw attention to specific data points.

How can a scatterplot be explained?

A scatterplot represents a group of points displayed on both the horizontal and vertical axes. Scatter plots are very important in the field of statistics because they can show the degree of correlation that exists between the values ​​of observed quantities or events (called variables). Scatter plots are used to show the degree to which one variable is influenced by another by plotting data points on horizontal and vertical axes. This is done to show how closely related the two variables are.

The positions of the markers that symbolize each row of the data table are determined by the values ​​placed in the columns along the X and Y axes.

Refer to this complete question:

A data analyst creates a scatterplot. The analyst wants to put a text label on the plot to call out specific data points. What function does the analyst use?

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The answer is 106 since it is 26 more than twice the number and 4 less than 5 times a number.

Answer:

3 years

Step-by-step explanation:

Lawson's tree starts at 14 inches and grows 3 inches every year, so we can represent that as 3x+14

Ezra's tree starts at 8 inches and grows 5 inches every year, so we can represent that as 5x+8

x=years

So, now that we have an equation for each tree, we will now set them as equal

5x+8=3x+14

Subtract 8 from each side

5x=3x+6

Subtract 3x from each side

2x=6

Divide each side by 2

x=3

It will take 3 years for the trees to reach the same height.

The rate of change or the speed of the different sections and the distance answers are below;

1) 2 m/s

2) 0 m/s

3) 3 m/s

4) Section C

5) Section A

1) The formula for the slope is;

Slope = (y₂ - y₁)/(x₂ - x₁)

Taking two coordinates in section A, we can find the slope which gives us the speed;

Speed = (50 - 0)/(25 - 0)

Speed = 2 m/s

2) Section B shows that the speed is constant and as such the rate of change of speed 0 m/s

3) Rate of change of section C is;

Speed = (80 - 50)/(70 - 60)

Speed = 3 m/s

4) The section that the person was moving at the highest speed is 3 m/s which is section C.

5) The section that the person travelled the farthest is section A which was 50 meters.

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The symbol replaces the box to make the statement true that 16 ÷ 4 + 12 □ 4 + 24 ÷ 2 is an equal sign, so 16 ÷ 4 + 12 = 4 + 24 ÷ 2.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

Given expression:

16 ÷ 4 + 12 □ 4 + 24 ÷ 2

Here calculate the first term

16 ÷ 4 + 12 = 4 + 12 = 16

Calculate the second term

4 + 24 ÷ 2 = 4 + 12 = 16

Thus, the equal sign will replace the box,

Therefore, the symbol replaces the box to make the statement true that 16 ÷ 4 + 12 □ 4 + 24 ÷ 2 is an equal sign.

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The amount of the investment at maturity is $2443.341

Compound interest is the interest on the initial principal plus the interest which has been accumulated.

Given,

Principal amount (P)=  $1500

Rate of interest(R)= 5% = 5/100 = 0.05%

Time(T)= 10 years

The formula for annual compound interest is as follows:

FV = P (1+ r/m)^mt

Where:

FV - the future value of the investment, in our calculator it is the final balance

P - the initial balance (the value of the investment)

r - the annual interest rate (in decimal)

m - the number of times the interest is compounded per year (compounding frequency)

t - the number of years the money is invested for

FV = 1500*(1+0.05/1)^(10*1) = 2443.341

The value of the investment after 10 years will be $2443.341.

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Answer:

The answer is in the image I attached to this response. Let p = the cost of 1 pencil, and let r = the cost of 1 ruler.

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