Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.
A TV station executive is planning the new lineup for next season's shows. On Monday nights, there will be 6 sitcoms and 1 drama, for a total of 179 minutes of programming, not counting commercials. On Tuesday nights, she has scheduled 6 sitcoms and 4 dramas, for a total of 302 minutes of non-commercial programming. All sitcoms have the same length and all dramas have the same length. How long is each type of show?

Answer:

  B.  y -6 = 2(x -2)

Step-by-step explanation:

You want the point-slope equation of the line with slope 2 through point (2, 6).

The point-slope equation for a line with slope m through point (h, k) is ...

  y -k = m(x -h)

Then the equation for the line with slope 2 through point (2, 6) is ...

  y -6 = 2(x -2) . . . . . choice B

__

Additional comment

If any function goes through the point (0, 0), it can be translated so that it goes through the point (h, k) by the replacements ...

A line with slope 2 through the origin is y = 2x. When that is translated so it goes through (2, 6), the equation becomes ...

  y -6 = 2(x -2)

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Out of total 508 tickets, the adult tickets sold were 127 in number.

Let the number adult ticket be x. So the number of students tickets is 3x. Also, we know the sum of these tickets will be total number of tickets, which is already mentioned as 508. Thus, the expression that will form is -

Number of student tickets + number of adult tickets = total number of tickets

3x + x = 508

Performing addition on Left Hand Side of the equation

4x = 508

x = 508/4

Performing division on Right Hand Side of the equation

x = 127

Number of adult ticket = 127

Number of student ticket = 3x

Number of student ticket = 3×127

Number of student ticket = 381

Thus, 127 adult tickets were sold.

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The common difference of ap = 41/4 and the sum of 200 terms = 204575.

The difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same amount. It also goes by the name Arithmetic Sequence. For instance, the natural number sequence 1, 2, 3, 4, 5, 6,... is an example of an arithmetic progression. It has a common difference of 1 between two succeeding terms (let's say 1 and 2). (2 -1). We can see that the common difference between two subsequent words will be equal to 2 in both the case of odd and even numbers.

We have a3= 5 and a11=87 we have to find the value of d,

n th term of ap= An= a+(n-1)d

A3=5

5=a+2d

87=a+10d

d=41/4 and a=-31/2

the sum of 200 terms when a=3

[tex]S_n=\frac{n}{2}{(2a+(n-1)d)\\S_{200}=100(6+199*41/4)\\\\S_{200}=204575.[/tex]

The complete question is :-

suppose {an} is arithmetic and a3 = 5, a11 = 87. what is the common difference

And find [tex]\sum_{3}^{200}ak[/tex],

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The complete equation is 3 lb/sec ≈ 4897.0806 kg/h.

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

3 Ib/sec ≈ ? kg/h

To convert pounds per second (lb/sec) to kilograms per hour (kg/h), we can use the conversion factor: 1 lb = 0.45359237 kg.

So, 3 lb/sec = 3 * 0.45359237 kg/sec = 1.361 kg/sec

To convert from per second to per hour, we multiply by the number of seconds per hour:

1.3607771 kg/sec * 3600 sec/hour = 4897.0806 kg/h

Therefore, 3 lb/sec ≈ 4897.0806 kg/h.

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Answer:

Answer is 382.5 square inch

Step-by-step explanation:

calculate all the area of the surface

Answer is 382.5 square inch

The surface area of the prism is given by the equation A = 382.5 inches²

The surface area of the prism is calculated as

The formula for the surface area of a prism is SA=2B+ph, where B, is the area of the base, p represents the perimeter of the base, and h stands for the height of the prism

Surface Area of the prism = 2B + ph

The area of the triangular prism is A = ph + ( 1/2 ) bh

Given data ,

Let the surface area of the prism be represented as A

Now , the prism consists of 2 right angled triangles and 3 faces of rectangles

So , the base of the triangle b = 9 inches

The height of the triangle h = 10 inches

So , the area of the 2 triangles = 2 ( bh ) / 2

On simplifying the equation , we get

The area of 2 triangles = 9 x 10 = 90 inches²

The area of first rectangle = 9 x 10 = 90 inches²

The area of second rectangle = 9 x 9 = 81 inches²

The area of third rectangle = 13.5 x 9 = 121.5 inches²

So , the area of the prism = area of 2 triangles + area of first rectangle + area of second rectangle + area of third rectangle

Substituting the values in the equation , we get

The area of the prism A = 90 + 90 + 81 + 121.5

The area of the prism A = 382.5 inches²

Hence , the surface area of prism is 382.5 inches²

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Answer:

I think I'm wrong but I Think its C and D

Step-by-step explanation: Tell me if I'm wrong that way other people know

The standard notation of the given term is 70,000.

A form of writing a certain number, an equation, or an expression in a way that adheres to set norms is known as a standard notation.

Given a phrase

7 times 10 four square

so 10 four square is 10 to the power 4

10 four square = 10⁴

and 7 times 10⁴ = 7 x 10⁴

the standard form of 7 x 10⁴ is

10⁴ = 10,000

7 x 10⁴ = 7 x 10,000

7 x 10⁴ = 70,000

Hence standard form is 70,000.

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Answer:

I'm sorry I don't know

Step-by-step explanation:

but I think that you do need to multiply it by 1pp just asyou multiply the amp by 100 from Ma to A

The pearson correlation coefficient is equal to 4.6/1.25, or 3.68. This is approximately equal The closest answer is e. 0.98.

Coefficient is a numerical or statistical value used to measure the strength or magnitude of a relationship between two or more variables. It is commonly used in mathematics, physics, engineering, and economics to quantify the strength of a linear relationship between two variables. In mathematics, coefficients are used to measure the degree of influence of a certain variable on the relationship between two variables.

The correlation between x and y can be found by calculating the Pearson correlation coefficient. This can be done by first calculating the covariance of x and y, which is equal to 4.6, and then dividing it by the standard deviation of x multiplied by the standard deviation of y, which is equal to 1.25.

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The total cost of Stun Arun's driving from Indianapolis to Albuquerque, a distance of 1,285 miles, is $244.10.

The total cost means the sum of different expenses.

In this situation, the driving cost per mile for the first 350 miles is different from the rest of the distance.

Therefore, we find the different costs and sum them up to get the total cost incurred by Stun Arun, who is driving from Indianapolis to Albuquerque.

The total distance from Indianapolis to Albuquerque = 1,285 miles

The driving cost per mile for the first 350 miles = $0.27

The total cost for the first 350 miles = $94.50 (350 x $0.27)

The difference between 1,285 and 350 miles = 935 miles

The driving cost per mile for 935 miles = $0.16

The total cost for 935 miles = $149.60 (935 x $0.16)

The total driving cost from Indianapolis to Albuquerque = $244.10 ($94.50 + $149.60)

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The probability that you will walk at least 2 dogs this week is 0.74

The probability that you will walk at most 2 dogs this week is 0.41

The probability that you will walk 3 dogs this week is 0.23

The probability that the number of dogs you will walk this week is not less than 5 is 0.18

The expected number of dogs you will walk this week is 2.83

The expected value of x is 11.29

The variance of dogs you will walk this week is 3.2811

The standard deviation of dogs you will walk this week is 1.8113

X: Random variable denoting how many dogs you walk this week.

Table attached at the end of solution

a) Probability that you will walk at least 2 dogs this week

[tex]P(x \geqslant 2) & =1-P(x < 2) \\[/tex]

= 1 - [P(x = 0) + P(x = 1)]

= 1 - [0.14 + 0.12]

= 1 - 0.26

[tex]P(x \geqslant 2) &[/tex] = 0.74

b) What is the probability that you will walk at most 2 dogs this week

P(x < 2) = P(x = 0) + P(x = 1) + P(x = 2)

= 0.14 + 0.12 + 0.15

P(x < 2) = 0.41

c) Probability that you will walk 3 dogs this week

P(x = 3) = 0.23

d) Probability that the number of dogs you will walk this week is not less than 5

[tex]P(x \geqslant 5) &[/tex] = P(x = 6) + P(x = 7) + P(x = 5)

= 0.08 + 0.01 + 0.09

= 0.09 + 0.09

= 0.18

e) Expected number of dogs you will want this week

F(x) = [tex]\sum_i p_i x_i[/tex]

E(x) = 0 × 0.14 + 1 × 0.12 + 2 × 0.15 + 3 × 0.23 + 4 × 0.18 + 5 × 0.09 + 6 × 0.08 + 7 × 0.01

E(x) = 2.83

f) Expected value of [tex]$x^2$[/tex]

[tex]E\left(x^2\right) & =\sum_1 p_i x_i^2 \\[/tex]

= 0 × 0.14 + 1 × 0.12 + 4 × 0.15 + 9 × 0.23 + 16 × 0.18 + 25 × 0.09 + 36 × 0.08 + 49 × 0.01

[tex]E\left(x^2\right) &[/tex] = 11.29

g) Variance of dogs you will walk this week

[tex]V(x) & =E\left(x^2\right)-[E(x)]^2 \\[/tex]

[tex]& =11.29-(2.83)^2 \\[/tex]

= 3.2811

h) Standard deviation of dogs you will walk this week

SD (x) = [tex]\sqrt{3.2811} \\[/tex]

= 1.8113

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You start a dog-walking business. Define X to be a random variable denoting how many dogs you walk

this week. The probability mass function (pmf), f(x), of X is defined as follows:

Table attached at end of the solution

(a) What is the probability that you will walk at least 2 dogs this week?

(b) What is the probability that you will walk at most 2 dogs this week?

(c) What is the probability that you will walk 3 dogs this week?

(d) What is the probability that the number of dogs you will walk this week not be less than 5 ?

(e) What is the expected number of dogs you will walk this week?

(f) What is the expected value of [tex]$X^2$[/tex] ?

(g) What is the variance of dogs you will walk this week?

(h) What is the standard deviation of dogs you will walk this week?

Answer:

[tex]350%[/tex]%

Step-by-step explanation:

[tex]\frac{70}{20}[/tex] x 100% = 350%

Answer:

- 1 [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

-3.75 can be written as a fraction as -3 [tex]\frac{75}{100}[/tex] o r-3 [tex]\frac{3}{4}[/tex]  if I divide the numerator and the denominator by 25.

[tex]\frac{2}{5}[/tex] (-3 [tex]\frac{3}{4}[/tex])

We can change -3 [tex]\frac{3}{4}[/tex] into an improper fraction.  We can do that a few ways but I am going to the it the way that is most intuitive to me.

another name for 1 is [tex]\frac{4}{4}[/tex] because 4 ÷ 4 = 1.  I am going to use that knowledge to convert -3 [tex]\frac{3}{4}[/tex] into a mixed number.

-( [tex]\frac{4}{4}[/tex] + [tex]\frac{4}{4}[/tex] + [tex]\frac{4}{4}[/tex] + [tex]\frac{3}{4}[/tex]) =  - [tex]\frac{15}{4}[/tex]  The negative sign can go in the numerator, denominator or in front to the fraction to show that the number is negative.

[tex]\frac{2}{5}[/tex] x  -[tex]\frac{15}{4}[/tex]  = - [tex]\frac{30}{20}[/tex]  Divide the numerator and the denominator by 10

= [tex]\frac{3}{2}[/tex]

Which means the same thing as -( [tex]\frac{2}{2}[/tex] + [tex]\frac{1}{3}[/tex] ) which means the same thing as -(1 + [tex]\frac{1}{3}[/tex] +or -  1 [tex]\frac{1}{3}[/tex]

Answer:

0.58

Step-by-step explanation:

First, we need to find the total number of pieces of clothing in the dryer. We do this by adding up the number of black shirts, gray shirts, black sweaters, and gray sweaters: 3 + 8 + 13 + 7 = 31

Next, we need to find the number of gray pieces of clothing in the dryer. We do this by adding up the number of gray shirts and gray sweaters: 8 + 7 = 15

Now we can find the probability of Bill taking out a gray piece of clothing by dividing the number of gray pieces of clothing by the total number of pieces of clothing: 15/31

To find the probability of Bill taking out a shirt, we add the number of black shirts and gray shirts: 3 + 8 = 11

Now we can find the probability of Bill taking out a shirt by dividing the number of shirts by the total number of pieces of clothing: 11/31

To find the probability that the piece of clothing Bill takes out is gray or is a shirt, we add the probability of Bill taking out a gray piece of clothing and the probability of Bill taking out a shirt.

So the probability that the piece of clothing Bill takes out is gray or is a shirt is: (15/31)+(11/31)= 0.58 rounded to the nearest hundredth.

It is going to take 140 seconds to walk from first floor to the fifth floor.

They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

According to the data problem,

Time taken for walking up 3 floors = 84 seconds

Time taken for walking up 1 floor = 84 seconds/3 = 28 seconds/floor

Time it is going to take for walking up 5 floors =  28 second/floor* 5  floor

Time it is going to take for walking up 5 floors = 140 seconds

We can conclude, it will take 140 seconds to walk from the first floor to the fifth floor.

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Answer: the smallest number out of the four is 0.13

Step-by-step explanation:

First, let's think about the number 13. It's a whole number and it's pretty big. It's definitely larger than the other numbers we're looking at today.

Next, let's take a look at 0.13. This number is a decimal, which means it's a number that has a whole number part and a fractional part. The whole number part is 0 and the fractional part is 13. So, 0.13 is smaller than 13.

Now, let's move on to 1.03. This is also a decimal and it's a little bit bigger than 0.13, but smaller than 13.

Finally, we have 1.3. This number is a decimal with a whole number part of 1 and a fractional part of 3. It is bigger than 0.13 and 1.03 but smaller than 13.

So, we can see that the smallest number out of the four is 0.13.

Answer: There are 48 numbers of 12-ounce in 36 pounds of the dog food.

To understand more, check below explanation.

Pounds to ounce conversion:

Given that,

There are 16 ounces in 1 pound .

First , we have to convert 36 pounds of dog food into ounces.

1 pound = 16 ounces

36 pounds = 16 * 36 = 576 ounces

We have to find  how many 12-ounce servings are in 36 pounds of dog food.

So that, number of 12-ounce of dog food =

Hence, there are 48 numbers of 12-ounce in 36 pounds of the dog food.

The Pearson correlation coefficient = r =[tex]\\sqrt{0.64}\\[/tex] = [tex]\\pm0.80[/tex]

The absolute value of Pearson correlation coefficient is greater than 0.75, the relationship between two variables is very strong.

The Percentage of the variance in the relationship between these two variables accounted for is 0.64×100=64%

Correlation Coefficient value always lies between -1 to +1. If correlation coefficient value is positive, then there is a similar and identical relation between the two variables. Else it indicates the dissimilarity between the two variables.

The covariance of two variables divided by the product of their standard deviations gives Pearson’s correlation coefficient. It is usually represented by ρ (rho).

ρ (X, Y) = cov (X, Y) / σX.σY.

Given, coefficient of determination, [tex]r^2[/tex] = 0.64

a)  Pearson correlation coefficient = r =[tex]\\sqrt{0.64}\\[/tex] = [tex]\\pm0.80[/tex]

b) Since the absolute value of Pearson correlation coefficient is greater than 0.75, the relationship between two variables is very strong.

c) Percentage of the variance in the relationship between these two variables accounted for is 0.64×100=64%

Therefore, the Pearson correlation coefficient = r =[tex]\\sqrt{0.64}\\[/tex] = [tex]\\pm0.80[/tex], the absolute value of Pearson correlation coefficient is greater than 0.75, the relationship between two variables is very strong, Percentage of the variance in the relationship between these two variables accounted for is 0.64×100=64%.

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Answer:

C' - (6, -6)

D' - (8, -6)

E' - (10, -8)

F' - (8, -10)

Step-by-step explanation:

Hey there!

To solve this problem, we must first know what the rule for rotating a shape 90 degrees clockwise is:

(x, y) --> (y, -x)

Now, we can apply this rule to all of the points/vertices

C' - (6, -6)

D' - (8, -6)

E' - (10, -8)

F' - (8, -10)

These are the points and their coordinates after the rotation has been applied.

The required simplified value of the f + g(x) =  3x² + 5x + 2.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
f(x)=3x²-2x+6

g(x) = 7x - 4

f+g = f(x) + g(x)
      = 3x²-2x+6 + 7x - 4
      = 3x² + 5x + 2

Thus, the required simplified value of the f + g(x) =  3x² + 5x + 2.

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1. The slope-intercept form of the equation of each line given the slope and y-intercept are as follows:

2. The given slopes are:

3. Two slopes of the parallel lines are:

The slope of the line parallel is 2/3.

The slope of the line parallel is 9/5

4. The slopes of all perpendicular lines are:

The slope-intercept form of the equation of a line given is given below:

where;

m is the slope

c is the intercept

a. Slope-10, y-intercept = -5

The equation will be: y = -10x - 5

b. Slope 7, y-intercept = 5

The equation will be: y = 7x + 5

c. Slope = -9/5, y-intercept =- 4

The equation will be: y = -9/5x - 4

d. Slope = -5/4, y-intercept - 5

The equation will be: y = -5/4x - 5

2. Slope = y₂ - y₁ / x₂ - x₁

a. (17,-6), (-11,7)

slope = 7 - (-6) / -11 - 17

slope = -13/28

b. (3,4), (-4,-5)

slope = -5 - 4 / -4 - 3

slope = -9/7

c. (-20, 14),(17, 15)

slope = 15 - 14 / 17 - (-20)

slope = 1/37

d. (11,-18), (-1,-7)

slope = -7 - (-18) / -1 - 11

slope = -11/12

3. Two lines are parallel if the slopes are equal.

a. y = 2/3x - 4

The slope of its line is 2/3

The slope of the line parallel is 2/3.

b. y = 9/5x - 5

The slope of its line is 9/5

The slope of the line parallel is 9/5

4. The slope of all perpendicular lines is the negative reciprocal, that is, (-1/m).

a. y = -1/2x -2

slope, m = -1/2

The slope of a perpendicular line = -1/(-1/2)

The slope of a perpendicular line = 2

b.  y = -x -1

slope, m = -1

The slope of a perpendicular line = -1/(-1)

The slope of a perpendicular line = 1

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Grace enjoys salads a lot. If she can select one from each of the aforementioned vegetables and dressings, she can create 56 salads.

Grace has two options for lettuce, four options for vegetables, and seven options for dressing. To determine the total number of salads she can make, we multiply the number of options for each ingredient. In this case, we have 2 options for lettuce, 4 options for vegetables, and 7 options for dressing. Multiplying these numbers, we get:

The result, 56, represents the total number of different salads Grace can make by choosing one option from each category.

This question should be written as:

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The top 25 percent, a data point would need to have a z score greater than 0.67.

A z score is a measure of how many standard deviations a data point is from the mean of a data set.

To determine the minimum z score, we first need to find the mean and standard deviation of the data set. The mean represents the center of the data and the standard deviation tells us how spread out the data is.

If a data point has a z score greater than 0, it is above the mean and considered in the top half of the data set.

To be in the top 25 percent, the data point would need to have a z score greater than the value that separates the top 75 percent from the bottom 25 percent.

This value can be found using a table of standard normal distributions or using software that calculates z scores.

In a standard normal distribution, the value that separates the top 75 percent from the bottom 25 percent is about 0.67.

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On U.S. converting to Metric System , the Advantages are Standardization , Improved Science and Technology and the Disadvantages are Cost , Resistance to change .

The Advantages of the U.S. converting to the metric system:

(i) Standardization: The metric system is used by the majority of countries in the world, making international trade and communication easier and more efficient.

(ii) Improved Science and Technology: The metric system is the standard system used in science and technology, making it easier for the U.S. to collaborate with other countries and to participate in international research.

The Disadvantages of the U.S. converting to the metric system:

(i) Cost: The conversion to the metric system would be a costly and time-consuming process, involving changes to products, labeling, and infrastructure.

(ii) Resistance to change: There may be resistance from people who are used to the imperial system and are comfortable with it.

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Now that we have added up all three alternatives ("or" = sum), we have the general option of choosing two different colors. = 0.7316

There must be some mistakes in this. But I make an effort to address the appropriate topics.

Nothing is underneath (a). I have nothing to say in response.

(a) Her purse contains 20 candies. If all 20 are yellow, then 9.

As a result, the probability is the proportion of desirable possibilities to all possible outcomes.

Hence, ta da! 9/20

That is the likelihood that Samira will choose a yellow candy.

Again, 20 candies are the starting point [1](i).

Six are green.

When she chooses the first option, her likelihood of selecting a green option is 6/20 = 3/10 = 0.3.

She chooses another candy now, assuming that her prediction came true.

Only 19 were left this time, and 5 of them are green.

Therefore, the likelihood is 5/19.

For the situation we are describing, both occurrences are now required. No overlapping, no ifs, ands, or buts exist. It is simply the sum of the two probabilities.

3/10 × 5/19 = 15/190 = 3/38

That's what I believe the description calls for.

(ii) The likelihood is that the first choice is red and the second is not, plus the first choice is green and the second is not, plus the first choice is yellow and the second is not.

so,

red and not red

5/20 = 1/4 red

15/19 not red (there are still 15 sweets of other colors in the bag, but again now only 19 total).

red and not red = 1/4 × 15/19 = 15/76 = 0.1974

green and not green

6/20 = 3/10 = green

14/19 = not green

green and not green = 3/10 × 14/19 = 52/190 = 26/95 =

= 0.2737

yellow and not yellow

9/20 = yellow

11/19 = not yellow

yellow and not yellow = 9/20 × 11/19 = 99/380 = 0.2606

Now that we have added up all three alternatives ("or" = sum), we have the general option of choosing two different colors.

= 0.7316

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Lisa’s average speed is: 11.4 miles/hours

It is a physical quantity that indicates the displacement of a mobile per unit of time, it is expressed in units of distance per time, for example (miles/h, km/h).

The formulas and procedures we will use to solve this exercise are:

Where:

Given info:

Applying the time formula we get:

t2= 135 mi / 15 mi/h

t2= 9 h

Calculating t1 we get:

t1= 9h -1 h

t1= 8 h

Applying the average velocity formula we get:

vm= x(total)/t(total)

vm= (60 mil + 135 mil) /( 9h + 8h)

vm= 195 mil/17 h

vm= 11.4 mil/h

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The total amount Ofelia had was $ 15.

The equations are mathematical statements with two algebraic expressions flanking the equal to the sign on either side.

It can demonstrate the equality of the relationship between the expressions printed on the left and right sides.

There are some components of an equation, that are:

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign.

The "=" sign determines on both sides must always be present when writing an equation.

Given data,

Let the equation be represented as A

Now, the value of A is equal to the original amount of money

The amount Ofelia spends = $ 12

The remaining amount of money Ofelia had=(1/5)A

So, the equation will be

subtract the original amount of money A - amount Ofelia spends = remaining amount of money Ofelia had

By substituting the values in the equation, we get

A - 12 = ( 1/5 )A

Add 12 on both sides of the equation, and we get

A = (1/5)A + 12

Subtract (1/5 )A on both sides of the equation, and we get

A - ( 1/5 )A = 12

On simplifying the equation, we get

(5A - A)/5 = 12

4A/5 = 12

Multiplying by 5 on both sides of the equation, we get

4A = 60

Divide by 4 into both sides of the equation, and we get

A = $ 15

The value of A is $ 15

Hence, the original amount is $ 15

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Answer:

The man took 0.7 Hours for resting

Step-by-step explanation:

Total time taken = 6 hours

We can remove the first 2 hours as it isn't necessary in this question

so Total time taken  = 4 hours

Speed traveled  = 60kph

distance traveled = 200km

Time taken to travel  = Distance/ speed

= 200 / 60

= 3.3 Hours

Time taken for resting = Total time - Time taken for travel

= 4 hours - 3.3 hours

= 0.7 Hours

The man took 0.7 Hours for resting

If ABC is a right angled triangle and angle BAC = 90°. If AD perpendicular to BC and BD=DC then BC² = 4AD² is 4 * AD^2.

How to prove that BC² = 4AD²?​

In right triangle ABC, by Pythagorean theorem, we have:

AC^2 + BC^2 = AB^2

Since AD is perpendicular to BC, by similarity, triangle ABD is similar to triangle ADC. Therefore, we have:

BD/AD = AD/DC

BD = AD^2/DC

Substituting BD into the first equation, we get:

AC^2 + BC^2 = AB^2 = AD^2 + (AD^2/DC)^2

AC^2 + BC^2 = AD^2 + AD^4/DC^2

AC^2 + BC^2 = AD^2(1 + AD^2/DC^2)

Since BD = DC, we have:

AC^2 + BC^2 = AD^2(1 + AD^2/BD^2)

And substituting DC = BD:

AC^2 + BC^2 = AD^2(1 + AD^2/BD^2) = AD^2(1 + AD^2/BD^2) = AD^2(1 + AD^2/BD^2) = AD^2(1 + AD^2/BD^2) = AD^2(1 + AD^2/BD^2) = AD^2(1 + AD^2/BD^2) = AD^2(1 + AD^2/BD^2)

Since AB^2 = AC^2 + BC^2, we have:

BC^2/AD^2 = AB^2/AD^2 - AC^2/AD^2 = (AB^2 + AC^2)/AD^2 - AC^2/AD^2 = (BC^2 + AC^2)/AD^2 = 4

Therefore, BC^2 = 4 * AD^2.

Learn more about  right angled triangle here:https://brainly.com/question/1248322

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