Yu Yan makes a wall hanging from a piece of fabric. For the first part, she cuts off 1/3 of the length of the original piece of fabric. For the next two parts, she cuts off 10 inches and 5 inches from the length of the remaining fabric. In total, she cuts 35 1/2 inches from the length of the original piece of fabric. How long was the original piece of fabric? Write and solve an equation. Check your solution.

Answer:

$3,000

Step-by-step explanation:

To find the predicted value of the car in 2001, we need to use the exponential decay formula:

V(t) = V0 * e^(-kt)

where V0 is the initial value of the car ($15,200), t is the time in years since 1990, and k is the exponential decay constant. We can find k using the value of the car in 1992:

V(2) = $10,000 = $15,200 * e^(-2k)

Solving for k, we get:

k = -ln(0.654) / 2

Now that we have k, we can find the value of the car in 2001:

V(11) = $15,200 * e^(-11k)

To the nearest dollar, the predicted value of the car in 2001 is $$3,000$.

Answer: A and C

Step-by-step explanation:

- Geometric sequences are sequences where there is a constant number being multiplied or divided.

- In A, we are dividing by 2 each time. In C, we are multiplying by 3

each time.

- B is not multiplication or division. Neither is D.

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The height is 9 units

V = 763.407015 m

The solution is, The value of N is 12 sq cm.

Area of a rectangle (A) is the product of its length (l) and width (w).

A= l. w

here, we have,

1. Find the greatest common factor of 35 and 42 to find the length (horizontal). The GCF is 7.

2. The horizontal length of the 35 and 42 sq cm is 7, and the heights are 5 and 6 respectively.

3. Moving on tot he 10 sq cm rectangle,

since the height of just that one rectangle is  and 10/5 is 2, the horizontal length is 2.

4. For n, the horizontal length is 2 and the height is 6.

2 X 6 is 12 sq cm.

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If Pat can knit 2cm in 35 minutes, then would take Pat approximately 2800 minutes to knit a scarf that is 160cm long.

If Pat can knit 2cm in 35 minutes time

then she can knit 1cm in (35/2) minutes, or 17.5 minutes.

To determine the total time to knit a 160cm scarf

Pat would need to work a total of

160cm x 17.5 minutes/cm = 2800 minutes.

Hence,

It would take Pat approximately 2800 minutes to knit a scarf that is 160cm long. This is equivalent to about 46.7 hours or 1.94 days of work

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Pat is knitting a scarf . On average she can knit 2cm in 35mins. How long will take her to knit a scarf that is 160cm long?​

The probability that a randomly selected worker lives more than 5 miles from work and rides their bicycle is 57%.

To calculate the probability that a randomly selected worker lives more than 5 miles from work and rides their bicycle, we need to use the data from the survey. Let's assume that the survey results are summarized in the following table (attached) :

From this table, we can see that the probability of a worker living more than 5 miles from work is 35%. We can also see that the probability of a worker riding their bicycle is 50%, and the probability of a worker living more than 5 miles from work and riding their bicycle is 20%.

To calculate the probability that a randomly selected worker lives more than 5 miles from work and rides their bicycle, we can multiply the probabilities of these two events:

P(Lives > 5 miles and Rides Bicycle) = P(Lives > 5 miles) x P(Rides Bicycle | Lives > 5 miles)

= 35% x (20%/35%)

= 0.5714 or 57% (rounded to the nearest whole percent)

Therefore, the probability that a randomly selected worker lives more than 5 miles from work and rides their bicycle is 57%.

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The tension forces are  1895 N and  2542 N.

Tension force is a type of force that results from the stretching or pulling of an object, such as a rope, cable, or string. When an object is under tension, it experiences a force that acts along its length, pulling it apart

We know that the third angle in the triangle that is formed is;

180 - [35 + 48]

= 97 degrees

We then have the tension in the ropes as T1 and T2

Using the sine rule;

T1/sin 35 = 3275/sin97

sin97T1 = 3275 sin 35

T1 = 3275 sin 35/sin97

T1 = 1895 N

For T2

T2/sin48 = 3275/sin97

sin97T1 = 3275 sin 48

T1 = 3275 sin 48/sin97

T1 = 2542 N

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The temperature at 3 AM is about 53 degrees Fahrenheit.

The average kinetic energy of the particles in a medium, such as a gas, liquid, or solid, is measured by its temperature. It is a basic physical characteristic that governs the rate and amount of heat transmission between two bodies that are in thermal contact.

A thermometer is commonly used to measure temperature. It does this by detecting changes in a substance's physical characteristics that change with temperature, such as the expansion or contraction of a liquid or the resistance of a wire.

We are aware that a sinusoidal function models temperature, and the following information is crucial:

A high of 80 degrees is reached at 5 PM, or 17:00 in a 24-hour period.

The day's average temperature is 60 degrees.

We're looking for the temperature at three in the morning, or three in 24-hour time.

We can utilize the fact that the temperature moves through one full cycle in a 24-hour day to determine the frequency. As the time frame is 24 hours, the frequency is:

B = 2π/24 = π/12

To find the phase shift, we can use the fact that the high temperature occurs at 5 PM, which is 8 hours after noon (when the temperature starts to rise). So the phase shift is:

C = (8/24) * 2π = (1/3)π

To find the amplitude, we can use the fact that the temperature swings 10 degrees above and below the average. So the amplitude is:

A = 10

Finally, we can use the formula to find the temperature at 3 AM:

f(x) = A sin(B(x - C)) + D

f(3) = 10 sin(π/12(3 - (1/3)π)) + 60

f(3) ≈ 53.4

So the temperature at 3 AM is about 53 degrees Fahrenheit.

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Natural numbers are sometimes known as counting numbers. Numbers that can be counted but not zero. Whole numbers are a modest extension of natural numbers and include Zero.

A subset of the natural numbers are the positive integers, often known as non-negative integers. Here are a few instances: 1, 2, 3, 4, 5, 6,... In other words, the "natural numbers" are the collection of all whole numbers that do not include 0.

There are just a limited amount of parts to it. Example: A = 1, 2, 3, and 4. An infinite set has unlimited items. All entire numbers are in a set called  whole numbers.

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The value of x is 14

In statistics, in addition to the mode and median, the mean is one of the measures of central tendency. Simply put, the mean is the average of the values in the given set. It indicates that values in a particular data set are distributed equally. The three most frequently employed measures of central tendency are the mean, median, and mode. The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to determine the mean. When all of the values are organised in ascending order, the Median is the median value of the given data. While the number in the list that is repeated a maximum of times is the mode.

To find the mean, add up all the numbers and then divide by the number of numbers

(9+ 8+10+ x+14)/5 = 11

Multiply each side by 5

9+ 8+10+ x+14 = 55

Combine like terms

41 +x = 55

Subtract 41 from each side

x =14

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Answer:

13.0898597466511 or 13.09

Step-by-step explanation:

Answer: 47.20cm

Step-by-step explanation:

Cost of goods sold (COGS) is an important accounting calculation that measures the costs associated with selling a company’s goods or services. Therefore, the cost of goods sold for the month ended is $600.

Cost of Goods Sold (COGS) is a measure of the cost of goods sold during the accounting period. It is calculated by subtracting the beginning inventory from the cost of goods purchased during the accounting period and then adding the ending inventory. For Dig the Dogs, Inc., the cost of goods sold for the month ended is calculated as follows: Beginning Inventory = 0 Cost of Goods Purchased = $900 Ending Inventory = $300 .COGS = Beginning Inventory + Cost of Goods Purchased - Ending Inventory  = 0 + 900 - 300   = $600 Therefore, the cost of goods sold for the month ended is $600.

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3. The amount that should be returned to Meenaski for buying 12 books worth R250.75 each and giving the shopkeeper R4,000, using mathematical operations, is R991.

4. The number of crayon sets that can be bought for R2,750 if one set costs R25, using division operation, is 110.

5. Manu will pay R1,700, exchanging his old bike for a new bike.

The four basic mathematical operations include addition, subtraction, division, and multiplication.

These mathematical operations are performed to solve algebraic problems using the relevant mathematical operands and rules.

The number of books bought = 12

The unit cost of each book = R250.75

The total cost of the 12 books = R3,009 (R250.75 x 12)

The amount advanced to the cashier = R4,000

The balance to be returned = R991 (R4,000 - R3,009)

The cost of a set of crayon = R25

The amount of money for the purchase = R2,750

The number of crayon sets that can be bought with R2,750 = 110 (R2,750/R25).

The price of the new bicycle = R2,500

The value of the old bike for exchange = R800

The amount to be paid = R1,700 (R2,500 - R800)

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The price of the new bicycle is R2,500. The bike on exchange is worth R800.  How much does he pay for his new bike?

The monthly revenue of the business grows by 8%, monthly.

The definition of revenue?

The total income a firm receives from the sale of products or services that are connected to its core business operations is referred to as revenue.

                           Since it appears at the top of the income statement, revenue, also known as gross sales, is frequently referred to as the "top line." An organization's whole earnings or profit is known as income, or net income.

An exponential function is represented as

   y = abˣ

From the  table we have the following ordered pair

(x,y) = {(0,72000) (3,90000)}

So, we have

   90000 = 72000 * b³

     Divide both sides by 72000

      b³  = 1.25

Take the cube roots of both sides

   b = ∛1.25

    b = 1.08

Recall that

b = 1 +r

  1 + r = 1.08

  r = 0.08

  r = 8%

Hence, the monthly revenue of the business grows by 8%, monthly.

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The area of any other shape can be broken down into smaller rectangles and the area of each rectangle can be calculated and added together to get the total area.

Kathy is organizing her desktop, which measures 22 inches by 4 feet. To calculate the area of Kathy’s desktop, we can use the formula for area, which is length multiplied by width. In this case, the length is 4 feet and the width is 22 inches. To make the measurements easier to work with, we can convert the length into inches. There are 12 inches in a foot, so 4 feet is equal to 48 inches. Now, the length of Kathy’s desktop is 48 inches and the width is 22 inches. To calculate the area, we multiply the length (48 inches) by the width (22 inches). The area of Kathy’s desktop is 1,056 square inches.

To further explain the concept of area, it is the amount of two-dimensional space that a shape takes up. It is measured in square units, such as square inches, square feet, or square yards. To calculate the area of any shape, you need to know its length and width. To calculate the area of a rectangle, you multiply the length by the width. The area of any other shape can be broken down into smaller rectangles and the area of each rectangle can be calculated and added together to get the total area.

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The expression is equivalent to 2(a  -3) + 4a will be 6a - 6. Then the correct option is A.

The equivalent is the expression that is in different forms but is equal to the same value.

The expression is given below.

⇒ 2(a  -3) + 4a

Simplify the expression, then we have

⇒ 2(a  -3) + 4a

⇒ 2a - 6 + 4a

⇒ 6a - 6

The expression is equivalent to 2(a  -3) + 4a will be 6a - 6. Then the correct option is A.

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The missing options are given below.

A. 6a - 6

B. 6a - 1

C. a - 6

D. None of the above

The set of the numbers are all integers from 9 to 21 inclusive

It is the collection of items to form a group

All  the members of:

P={odd numbers}

P={9,11,13,15,17,19,21}

Q={Even numbers}

Q= {10,12,14,16,18,20}

U={ positive integer between 9 and 21}

This means that U = {9,10,11,12,13,14,15,16,17,18,19,20,21}

Therefore,  P1 and Q1​

P prime include all the elements in the universal set that are not in the subset P  = {10,12,14,16,18,20}

and Q prime include all the elements in the universal set that are not in subset Q =  P={9,11,13,15,17,19,21}

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Answer:

He drove 6 hours.

Step-by-step explanation:

distance = rate times time

300 = 50t  Divide both sides by 50

t = 6

Chords AB and CD intersect at E and AE= EB is Semi circle is drawn with diameter CD. EF perpendicular to CD meet this semi circle at F then AE= EF

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Let M be the midpoint of AB, so EM is perpendicular to AB.

Since OF is a diameter of the circle, angle EOF is a right angle.

Triangles EOF and EMA are similar, since they both have a right angle and angle EFM is congruent to angle EAM, being alternate interior angles of parallel lines.

The corresponding sides are proportional:

EF / EA = EO / EM.

EM is half the length of AB, which is the diameter of the semicircle,

EO must be equal to the radius of the semicircle.

Therefore, we have EF / EA = radius / (diameter / 2) = 2 / 2 = 1,

EF = EA.

Hence, chords AB and CD intersect at E and AE= EB is Semi circle is drawn with diameter CD. EF perpendicular to CD meet this semi circle at F then AE= EF

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The measure of the smallest angle is 52 degrees

The complete question is added as an attachment

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

The triangle

The sum of angles in a triangle is 180

So, we have

2x + 3x - 11 + 2x + 9 =  180

Evaluate the like terms

7x = 182

So, we have

x = 26

This means that

2x = 2 * 26 = 52

3x - 11 = 3 * 26 - 11 = 67

Hence, the smallest is 52 degrees

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The linear function representing the depth of the submarine after t seconds is given as follows:

d(t) = -15 - 0.5t.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The parameters for this problem are given as follows:

Hence the function is given as follows:

d(t) = -15 - 0.5t.

The problem asks for the linear function representing the depth of the submarine after t seconds.

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The Construction of angle equal to 65 degree is shown below with attached figure.

Geometric constructions are precise drawings of geometrical shapes, angles, and lines. We will need a pencil, a ruler (or other straight edge), and compasses to do this. Perpendicular bisector and angle bisector are the fundamental constructs.

The steps to draw angle 65 and copy of Angle:

(i) Draw ∠AOB = 65° with the help of protractor.

(ii) Draw a ray O’X.

(iii) With O as center and any radius, draw an arc cutting OA and OB at C and D respectively.

(iv) With O’ as center and with the same radius, draw an arc, cutting O’X at P.

(v) With P as center and radius equal to CD, cut the arc through P at Q.

(vi) Join O’Q and produce it to Y. Then ∠YO’X is the required angle equal to ∠AOB.

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The total number of students at the school is 1240.

What is Ratio ?

With the dividend or number being divided as the antecedent and the divisor or number that is dividing as the consequent, a ratio compares two quantities by division.

we know that, number of boys : number of girls = 11: 9

Let's assume the number of boys = 11x

and, the number of girls = 9x

similarly, There are 124 more boys than girls

So, number of boys = 124 +  number of girls

           11x = 124 + 9x

          2x = 124

          x = 62

So, number of boys = 11 ×62 = 682

number of girls = 9 × 62 = 558

∴ Total number of students is 1240 i.e.(682+558).

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The true statements are ∠X and ∠Y are supplementary angles, ∠W and ∠Z are a linear pair and ∠Y and ∠Z are complementary angles. The solution has been obtained by using angles and line.

What are angles and line?

Lines having little depth or width are said to be straight. Lines can be perpendicular, intersecting, transversal, and many more various forms. A figure in which two rays emanate from the same point is referred to be an angle.

We know that angles on a straight line add up to 180° and such angles are called supplementary angles.

Therefore, ∠X and ∠Y are supplementary angles.

Similarly, we know that angles on a straight line form a linear pair.

Therefore, ∠W and ∠Z are a linear pair.

Also, we know that two angles are complementary when their sum is 90°.

We can see from the figure that ∠Z and ∠Y add up to 90°.

Therefore, ∠Y and ∠Z are complementary angles.

Hence, the above provided statements are true about the angles.

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The figure of the question is attached below

m∠1 = m∠5, because alternate exterior angles are congruent.

Angles formed by intersecting two parallel lines with a transversal are known as angles in parallel lines.

Given:

lines a and b intersect a transversal, c.

The pair of angles on the outside of the two parallel lines but on the other side of the transversal are known as alternate exterior angles.

m∠1 = m∠5 (Alternate exterior angles are congruent)

m∠1 = m∠5, because alternate exterior angles are congruent.

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The Complete Question is attached below.

With a plane containing 40 lines, no 2 of which are parallel , here are 43 points where exactly 2 lines intersect.

In a plane that contains 40 lines, we are asked to find the number of points where exactly 2 lines intersect. Let's call this number "x".

Since every line intersects exactly 2 points, the total number of line intersections is equal to 2x. In other words, if we add up the number of intersections at each point, the total number should equal 2x.

The problem states that there are 3 points where exactly 3 lines intersect, 4 points where exactly 4 lines intersect, 5 points where exactly 5 lines intersect, and 6 points where exactly 6 lines intersect. At the same time, it states that there are no points where more than 6 lines intersect.

To calculate the total number of intersections, we need to multiply the number of lines that intersect at each point by the number of points, and then add them up. In mathematical terms:

2x = 3 * 3 + 4 * 4 + 5 * 5 + 6 * 6

Expanding the right side of the equation:

2x = 9 + 16 + 25 + 36

= 86

Dividing both sides of the equation by 2:

x = 43

So there are 43 points where exactly 2 lines intersect.

This is because at each point where exactly 2 lines intersect, the number of intersections is equal to the number of lines. In total, these 43 points account for 86 line intersections, which is half of the total number of line intersections in the plane.

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