10. A statue casts a shadow 30 feet long. At the same time, a person who is 5 feet tall casts a
shadow that is 6 ft long. How tall is the statue?
A. 30 ft
B. 25 ft
C. 18 ft
D.12.5 ft

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

To learn more about division, please check: https://brainly.com/question/13281206

#SPJ1

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

Read more about simple interest at

https://brainly.com/question/20690803

#SPJ1

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

Read more about  algebraic expressions at; https://brainly.com/question/4344214

#SPJ1

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 .

Learn more about Algebra here

https://brainly.com/question/26957806

#SPJ4

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.

To know more about compound interest visit: brainly.com/question/14295570

#SPJ4

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

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.

Know more about quadratic equations here:

https://brainly.com/question/1214333

#SPJ4

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 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.

Read more about distance - time graph at; https://brainly.com/question/13877898

#SPJ1

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.

⭐if this response helped you, please mark it the "brainliest"!⭐

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

Learn more about exterior angles here:

https://brainly.com/question/7620723

#SPJ1

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.

Learn more about Linear Equations at

https://brainly.com/question/11897796

#SPJ1

The required coordinate pair for W" is (2,-3)

When a point is reflected over axes, its position changes and sign of coordinates also change.

Given that, Point W is located at (-2, 3) on a coordinate plane. Point W is reflected over the x-axis to create point W'. Point W' is then reflected over the y-axis to create point W".

When a point is reflected over the x-axis, then we know,

(x, y) = (x,-y)

W(-2,3) = W (−2,−3)

And,

When a point is reflected over the y-axis, then we know,

(x, y) = (-x, y)

Therefore, W'(-2,-3) = W" (2,-3)

Hence, the coordinates of the point W" are (2,-3)

For more references on reflection of points, click;

https://brainly.com/question/1548989

#SPJ1

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

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.

To Learn more About percentages refer to:

https://brainly.com/question/24877689

#SPJ4

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

To Learn more About  Probability, Check out: https://brainly.com/question/11234923

#SPJ4

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.

Learn more about rate here

https://brainly.com/question/13481529

#SPJ4

Answer:

Slope:  - 4/3

Point (4,1)

Step-by-step explanation:

hope this helps

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 )

Therefore, Gracie will earn $61600 if she waits until December 21. However, she will earn bank discount $61132.87 on November 12.

A bank discount is interest that the bank deducts beforehand in the basic discount note. The maturity value less the bank discount equals the amount owed. The total of the principle and interest due at the conclusion of the time period is the maturity value.

Date of note = 14th July

Face value = $60000

Length of note = 160 days,

Interest rate = 6%

Calculating the interest and maturity value:

Interest  = Principal × interest × time

= 60000 × 0.06 × 160/360

= 1600

So the maturity value MV = Face value + interest

= 60000 + 1600

= 61600

2. Calculating discount period:

Note discounted on 12th November

Time till 12th November = 315 days

Time till 14th July = 194 days

So days before note is discount = 315 - 194= 121 days

Length of note = 160 days,

So the discount period = 160 - 121 = 39 days

3 - Bank discount:

Bank discount = MV × Bank discount rate × number of days bank waits till due date

= 61600 × 0.07 × 39/360

= 467.133

4 - Proceeds from bank: Proceeds = MV - Bank discount

= 61600 - 467.133

= 61132.87

To learn more about bank discount

https://brainly.com/question/4533136

#SPJ4

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.

To know more about stock, go to link

https://brainly.com/question/25818989

#SPJ1

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

To learn more about mean:

https://brainly.com/question/20747890

#SPJ4

Aggregates is distorts the effectiveness of charting data points. So the option d is correct.

In the given question, we have to select which of the following, when included, distorts the effectiveness of charting data points.

Charts are a quick and efficient way to communicate information to your audience. If the charts are properly created, that is.

A lot goes into creating the ideal visual material, and it's simple to let some components slip. Charts that are hurriedly created are frequently more detrimental than beneficial.

We've compiled a list of useful do's and don'ts to bear in mind while building your own data representations, whether they take the shape of straightforward bar charts and graphs or more intricate interactive visualizations, in order to help you prevent this.

To learn more about interactive visualizations link is here

brainly.com/question/28110252

#SPJ4

Step-by-step explanation:

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

Answer:

20

Step-by-step explanation:

h=hypotenuse. s1=side 1. s2=side 2

h^2 = (s1)^2 + (s2)^2  ==> hypotenuse formula

h^2 = 12^2 + 16^2  => plug in known values

h^2 = 144 + 256  

h^2 = 400  ==> simplify

[tex]\sqrt{h^2 = 400}[/tex]  ==> take the square root on both sides to remove the power

[tex]\sqrt{h^2}[/tex] = [tex]\sqrt{400}[/tex]

h = 20

To learn more about hypotenuse, click here:

https://brainly.com/question/11356906

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.

To know more about the expression:

https://brainly.com/question/13947055

#SPJ1

Answer:

1.1 hectares

Step-by-step explanation:

6.93/6.3 = 1.1

He can plant 1.1 hectares of land.

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

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

Learn more about Pythagoras theorem from

https://brainly.com/question/231802

#SPJ1