A windowpane is 63 inches tall and the diagonal distance from one corner to the other is 65 inches. How wide is the windowpane?

Answer:

The selling price of the bag is $22.5

Step-by-step explanation:

Buying Price = $25,

Selling Price = ?

Since they sold it at a loss of 10%,

So, they sold it for a price 10% less than the buying price,

or at 90% or 0.9 of the buying price,

so,

Selling Price = (0.9)(25) = $22.5

Answer:

The function form is:

f(x) = 2x - 8

The second transformation which is (x+0, y-4), 180° rotation, reflection over the x-axis would carry the rectangle onto itself.

What is transformation?

Forms on a coordinate plane can be rotated, reflected, or translated using transformations. Each vector can be translated, any line can be reflected, and any point can be rotated.

We are given a graph on which a rectangle is drawn. This has to be transformed in such a way that it lands onto itself.

Of the given options only the second option is through which it will land on itself.

As when we reflect over x - axis, the rectangle will come in the 3rd quadrant and after rotating it 180°, there will be no change.

Now, to bring it back to its original position, we will have to reduce the y - coordinate by 4 due to which it will shift upwards.

Hence, the second option is the correct option.

Learn more about transformation from the given link

https://brainly.com/question/29788009

#SPJ1

To start off, we can use the fact that the total area under the probability density function (PDF) must equal 1. This is because the PDF represents the probability of X taking on any particular value, and the total probability of all possible values of X must add up to 1.

So, we can set up an integral to solve for the constant c:

integral from 0 to 1 of c(1-x) dx = 1

Integrating c(1-x) with respect to x gives:

cx - (c/2)x^2 evaluated from 0 to 1

Plugging in the limits of integration and setting the integral equal to 1, we get:

c - (c/2) = 1

Solving for c, we get:

c = 2

Now that we have the value of c, we can use the PDF to find probabilities of X taking on certain values or falling within certain intervals. For example:

- The probability that X is exactly 0.5 is:

PDF(0.5) = 2(1-0.5) = 1

- The probability that X is less than 0.3 is:

integral from 0 to 0.3 of 2(1-x) dx = 2(0.3-0.3^2) = 0.36

- The probability that X is between 0.2 and 0.6 is: integral from 0.2 to 0.6 of 2(1-x) dx = 2[(0.6-0.6^2)-(0.2-0.2^2)] = 0.56

Visit here to learn more about  probability : https://brainly.com/question/30034780
#SPJ11

We can see that since the values that multiply each component (x & y) are less than an unit, the transformation rule would be a reduction.

Answer:

128 square units

Step-by-step explanation:

At first I thought it would be as simple as 150% of 32 = 48.

Then I thought about increasing the sides of the rectangle 150% and that would make it 4 times larger.

Answer:

30ft

Step-by-step explanation:

Given data

Volume= 360 ft^3

Area= 12 ft^2

We know that the expression for volume is

Volume= Area*Height

Substitute

360= 12*h

h= 360/12

h= 30 ft

Hence the height of the prism is 30ft

Answer: 9 hours

Step-by-step explanation: divide 450 total miles by how many miles you drive per hour (50).

Answer:

Horizontal asymptote: y=2

Reflect over the y-axis because of the negative raise power of x.

Domain: (-∞,∞)

Range: (2, ∞)

Decreasing all through the function.

Step-by-step explanation:

To approach this problem, we need to remember some of the transformation rules for functions:

*f(x)+d vertical translation up d units

*af(x) vertical stretch when a>1

Therefore, for the following function:

Since the function h(x) is shifted 2 units up, then the asymptote of the original Euler function would translate 2 units up.

Horizontal asymptote: y=2

Reflect over the y-axis because of the negative raise power of x.

Domain: (-∞,∞)

Range: (2, ∞)

Decreasing all through the function.

Required value of angle R is 21°.

What is the relationship between the angle of circumference and angle of centre of circles?

Following is the relationship between angle of an arc on that circle and the angle of the center of a circle,

1)We can say that the angle of an arc is half the angle at the center that it deleted.

2) Or we can say oppositely the angle at the center of a circle is twice the angle of the arc that it subtends.

The measure of an arc is proportional to the measure of the angle it subtends and that the angle at the center of a circle is always twice the angle formed by any two points on the circumference of the circle that are connected to the center This relationship is based on the fact that.

Here, angle of circumference is angle R and angle of centre is angle P.

According to their relationship,

angle P = 2 × angle R

15x+3 = 2 × ( 10x-3)

We are Simplifying,

15x+3 = 20x-6

20x-15x = 3+6

5x = 9

x = 9/5

So, required angle R = 10x + 3 = 10×(9/5)+3 = 21

Learn more about circle here,

https://brainly.com/question/28162977

#SPJ1

Answer:

512, -512

Step-by-step explanation:

Cube root(512) =8

Cube root (-512) = -8

Absolute of - 8 is 8 ( |-8|=8 )

The system of equations that represent this situation is x + y = 52 and x + 2.25y = 72

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.

Let x represent the number of pounds of bananas sold and y represent the grapes sold, hence:

x + y = 52   (1)

Also:

x + 2.25y = 72    (2)

The system of equations that represent this situation is x + y = 52 and x + 2.25y = 72

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Answer:

20 ft

Step-by-step explanation:

It is 20 ft because you use pathagoren therom.

a^2 + b^2 = c^2

Answer:

The question cut off but I'm assuming this is basically just a find the area of the shaded region type of question. First thing you need to do is calculate the areas of the right triangle and the rectangle. Subtract the area of the triangle from the area of the rectangle.

Area of rectangle: 8 x 7 = 56ft^2

Area of the triangle: (6 x 2)/2 = 6ft^2

Subtract 6ft^2 from 56ft^2 and you get:

56 - 6 = 50ft^2

Area of shaded region is 50ft^2

The reason why the boy's choice is a mistake is that the amount given by  Plan A in a year is $180, while the amount given by Plan B, which is a geometric progression (exponential function) in a year is over $4.5 × 10¹³ which is over 45 trillion Dollars

A geometric sequence or progression consists of a set of numbers which are nonzero, and in which the ratio of consecutive numbers is a constant.

The given parameters are;

Plan A; $15 per month for one year

Plan B: $0.01 on the first week, $0.02 the second, $.04, the third, ...

The plan chosen by the boy is Plan A

The total allowance the boy receives when he chooses plan A = $15 × 12 = $180

The amount received each week on Plan B is 0.01, 0.02, 0.04, ...

The common ratio of the amount received each week is a constant and given by the equation;

\(r = \dfrac{0.02}{0.01} =2\)

The amount received on the nth week is therefore a geometric progression given by the equation; aₙ = a·r⁽ⁿ⁻¹⁾

The sum of n terms of a geometric progression is given by the formula;

\(S_n = \dfrac{a\cdot \left(r^n-1\left)}{r-1}\)

Where;

a = The first term = 0.01

The number of weeks in a year, n = 52 weeks, which gives;

\(S_n = \dfrac{0.01\times \left(2^{52}-1\left)}{2-1} \approx 4.5\times 10^{13}\)

Therefore, the amount Plan B gives in one year is approximately $4.5 × 10¹³, which is over 45 trillion Dollars in a year

Learn more about geometric progression or sequence here:

https://brainly.com/question/22762639

#SPJ1

Answer:

5 x 12 = 60

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

13 / 17 = y / 10

13 x 10 = y x 17

130 = 17y

y = 130 / 17

y = 7.12

7.12 in nearest tenth is approximately 7.

The value of y, rounded to the nearest tenth, is approximately 7.6.

To solve the proportion (13/17) = (y/10) for y, we can cross-multiply and then solve for y.

Cross-multiplying:

13 * 10 = 17 * y

130 = 17y

To isolate y, we divide both sides of the equation by 17:

y = 130/17

Calculating the value:

y ≈ 7.6 (rounded to the nearest tenth)

Therefore, y is approximately 7.6 when solving the given proportion.

To know more about nearest tenth, refer here:

https://brainly.com/question/11454706

#SPJ2

The labor cost percentage for next Friday at Fawlty Towers would be approximately 0.63%, which is closest to the option a. 0.05%.

To calculate the labor cost percentage for next Friday at the Fawlty Towers, we need to consider the number of rooms, the time required to clean each room, the number of working hours, the labor rate, and the occupancy rate. Here are the steps to determine the labor cost percentage:

Calculate the number of rooms to be cleaned. If the hotel has 1000 rooms and the occupancy rate for next Friday is 80%, then the number of occupied rooms would be 1000 * 0.8 = 800 rooms.

Calculate the total time required to clean the rooms. Since each room attendant is allocated 30 minutes per room, the total time required would be 800 rooms * 30 minutes = 24,000 minutes.

Convert the total cleaning time to hours. Since there are 60 minutes in an hour, the total cleaning time would be 24,000 minutes / 60 = 400 hours.

Calculate the total labor cost. Each room attendant works 8 hours per day, so for 400 hours, the hotel would require 400 hours / 8 hours = 50 room attendants. Considering their hourly rate of $15, the total labor cost would be 50 room attendants * $15/hour = $750.

Calculate the total revenue. The Average Daily Rate (ADR) is expected to be $150, and with an occupancy rate of 80%, the total revenue would be 800 rooms * $150/room = $120,000.

Calculate the labor cost percentage. Divide the total labor cost ($750) by the total revenue ($120,000) and multiply by 100 to get the percentage: ($750 / $120,000) * 100 = 0.625%.

Therefore, the labor cost percentage for next Friday at Fawlty Towers would be approximately 0.63%, which is closest to the option 0.05%.

Learn more About labor cost from the given link

https://brainly.com/question/26527325

#SPJ11

The Fawlty Towers is a Nuxury 1000 room hotel catering to business executives. The occupancy for nad Friday is expected to be 80% Room attendants are allocated 30 minutes to clean each room Room attendants work 8 hours per day at a rate of $15/hour. ADR is expected to be $150 What would the labour cost percentage be for next Friday assuming everything stays the same?

a. 0.05%

b. 5.00%

c. 20.00%

d. 0.20%

Answer:

36km/h

speed =distance/time

= 90/2.5

=36km/h

Therefore, the rate of the boat in still water is 70 mph, and the rate of the current is 30 mph.

Let's denote the rate of the boat in still water as "b" and the rate of the current as "c."

When the boat is traveling upstream, it is going against the current, so the effective speed is reduced. The speed of the boat relative to the ground can be calculated as (b - c).

Given that it takes 5 hours to travel 200 miles upstream, we can set up the equation:

Distance = Speed * Time

200 = (b - c) * 5

Dividing both sides by 5, we get:

40 = b - c (Equation 1)

When the boat is traveling downstream, it is aided by the current, so the effective speed is increased. The speed of the boat relative to the ground can be calculated as (b + c).

Given that it takes 2 hours to travel 200 miles downstream, we can set up the equation:

200 = (b + c) * 2

Dividing both sides by 2, we get:

100 = b + c (Equation 2)

Now we have a system of equations consisting of Equation 1 and Equation 2:

40 = b - c

100 = b + c

We can solve this system of equations using any method of solving simultaneous equations, such as substitution or elimination.

Adding Equation 1 and Equation 2:

40 + 100 = (b - c) + (b + c)

140 = 2b

Dividing both sides by 2, we get:

b = 70

Substituting the value of b back into Equation 1 or Equation 2:

40 = 70 - c

Subtracting 70 from both sides:

-30 = -c

Multiplying both sides by -1, we get:

30 = c

To know more about rate,

https://brainly.com/question/29270113

#SPJ11

(a) The student repays $6200 ($5000 principal + $1200 interest) over 4 years. (b) Varies; paying interest is generally ethical, compensating the lender. Loan amount and duration impact interest and commitment.

(a) To calculate the amount repaid, we need to add the principal amount ($5000) to the interest accrued over the 4 years. The simple interest is calculated as I = P * R * T, where P is the principal amount, R is the interest rate (6% or 0.06), and T is the time period (4 years).

Interest accrued = 5000 * 0.06 * 4 = $1200

Amount repaid = Principal amount + Interest accrued = $5000 + $1200 = $6200

The student repays $6200 in total.

(b) Personal experiences and financial arrangements may vary for individuals. Regarding the ethical aspect, it is generally considered fair and ethical to pay interest when borrowing money, as the lender is sacrificing the opportunity cost of utilizing that money elsewhere. The amount and duration of the loan matter as they determine the interest accrued and the level of financial commitment.

Disclosure: As an AI, I don't have personal experiences or engage in financial transactions with family and friends.

To learn more about interest , click here:

brainly.com/question/8100492

#SPJ11

The probability that exactly one of the coins is a 10p piece is 1/2.

To find the probability that exactly one of the coins is a 10p piece, we can consider the possible outcomes.

There are two coins, and each coin can be either a 10p piece or a non-10p piece. Let's consider the four possible outcomes:

1. Erin's coin is a 10p piece, and Jack's coin is a non-10p piece.

2. Erin's coin is a non-10p piece, and Jack's coin is a 10p piece.

3. Both Erin's and Jack's coins are 10p pieces.

4. Both Erin's and Jack's coins are non-10p pieces.

Since the total amount of the two coins is less than 50p, we can eliminate the third possibility (both coins being 10p pieces).

Now, let's calculate the probability for each of the remaining possibilities:

1. Erin's coin is a 10p piece, and Jack's coin is a non-10p piece:

The probability of Erin having a 10p piece is 1/2, and the probability of Jack having a non-10p piece is also 1/2. Therefore, the probability of this outcome is (1/2) * (1/2) = 1/4.

2. Erin's coin is a non-10p piece, and Jack's coin is a 10p piece:

This is the same as the previous case, so the probability is also 1/4.

3. Both Erin's and Jack's coins are non-10p pieces:

The probability of Erin having a non-10p piece is 1/2, and the probability of Jack having a non-10p piece is also 1/2. Therefore, the probability of this outcome is (1/2) * (1/2) = 1/4.

Now, we sum up the probabilities of the two cases where exactly one of the coins is a 10p piece:

1/4 + 1/4 = 2/4 = 1/2.

Learn more on probability here;

https://brainly.com/question/24756209

#SPJ1

The $1314^\text{th}$ digit past the decimal point is 2.

To find the $1314^\text{th}$ digit past the decimal point in the decimal expansion of $\frac{5}{14}$, we can use long division to compute the decimal expansion of the fraction.

The long division of $\frac{5}{14}$ is as follows:

```

0.35    <-- Quotient

-----

14 | 5.00

   4.2    <-- Subtract: 5 - (14 * 0.3)

   -----

     80   <-- Bring down the 0

     70    <-- Subtract: 80 - (14 * 5)

     -----

     100   <-- Bring down the 0

      98    <-- Subtract: 100 - (14 * 7)

      -----

       20   <-- Bring down the 0

       14    <-- Subtract: 20 - (14 * 1)

       -----

        60   <-- Bring down the 0

        56    <-- Subtract: 60 - (14 * 4)

        -----

         40   <-- Bring down the 0

         28    <-- Subtract: 40 - (14 * 2)

         -----

         120   <-- Bring down the 0

         112    <-- Subtract: 120 - (14 * 8)

         -----

           80   <-- Bring down the 0

           70    <-- Subtract: 80 - (14 * 5)

           -----

           ...

```

We can see that the decimal expansion of $\frac{5}{14}$ is a repeating decimal pattern with a repeating block of digits 285714. Therefore, the $1314^\text{th}$ digit past the decimal point is the same as the $1314 \mod 6 = 0^\text{th}$ digit in the repeating block.

Since $1314 \mod 6 = 0$, the $1314^\text{th}$ digit past the decimal point in the decimal expansion of $\frac{5}{14}$ is the first digit of the repeating block, which is 2.

So, the $1314^\text{th}$ digit past the decimal point is 2.

To know more about Decimal Point related question visit:

https://brainly.com/question/28338004

#SPJ11

The Process Capability Index (Cpk) is 0.24

The process capability index (Cpk) for the organic yogurt processing plant can be calculated as follows:

Cpk = min[(USL - μ) / (3σ), (μ - LSL) / (3σ)]

Where:

- USL is the upper specification limit (16.9 ounces)

- LSL is the lower specification limit (15.1 ounces)

- μ is the process mean (16.0 ounces)

- σ is the process standard deviation (1.25 ounces)

To calculate Cpk, we need to consider the specifications and the process performance. The formula compares the process variation to the specification limits. The numerator represents the distance between the process mean and the nearest specification limit, while the denominator represents three times the process standard deviation.

In this case, the process mean (μ) is 16.0 ounces, the upper specification limit (USL) is 16.9 ounces, and the lower specification limit (LSL) is 15.1 ounces. The process standard deviation (σ) is 1.25 ounces.

By plugging these values into the Cpk formula, we can determine the smaller value between the two ratios, representing the capability of the process to meet the specifications. This Cpk value indicates how well the process fits within the specification limits, with higher values indicating better capability.

Learn more about Standard Deviation here:

brainly.com/question/29115611

#SPJ11

The coordinates of point D in the parallelogram ABCD are (15, 10).

To find the coordinates of point D, we can use the properties of a parallelogram. In a parallelogram, opposite sides are parallel and congruent. Therefore, we can use this information to determine the coordinates of point D.

Let's consider the given points:

A(-3, 5)

B(7, 12)

C(5, 3)

Since opposite sides of a parallelogram are parallel, the vector connecting points A and B should be equal to the vector connecting points C and D. We can express this as:

AB = CD

To find the vector AB, we subtract the coordinates of point A from the coordinates of point B:

AB = (7 - (-3), 12 - 5)

= (10, 7)

Now, we can express the vector CD using the coordinates of point C and the vector AB:

CD = (5, 3) + (10, 7)

= (15, 10)

Therefore, the coordinates of point D are (15, 10).

for such more question on coordinates

https://brainly.com/question/30107320

#SPJ8

your answer will be 0.

Answer:

45km i think

Step-by-step explanation:

Answer:

\( {3}^{2} x - 9 = 0 \\ 9x = 9 \\ x = 1\)

Answer: x: 1,2,3,4 y: 2,4,8,16

Step-by-step explanation:

Exponential growth means that the rate of the line of a graph or chart is rapidly growing in size or number.

1 | 2

2 | 4

3 | 8

4 | 16

5 | 32

6 | 64

etc.

Answer:

option B edg 2021

Step-by-step explanation:

im too lazy to explain but its option B