The length of the original piece of fabric, given the proportion cut by Yu Yan and the amount cut in total, is 75 .75 inches
How to find the original length of fabric ?Assume that the original length of fabric was denoted as x, this means that the first cutting by Yu Yan took out :
= 1 / 3 x
The equation would then be :
x - 1 / 3 x - 10 - 5 = 35 + 1 / 2
x - 1 / 3 x - 10 - 5 = 35 . 5
The length of the original fabric is:
2 / 3x = 35. 5 + 10 + 5
x = 50. 5 ÷ 2 / 3
x = 50. 5 x 3 / 2
x = 75 .75 inches
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Kathy is organizing her desktop, which measures 22 inches by 4 feet. What is the area of Kathy’s desktop?
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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15. Find the perimeter.
11.8
13.3
7.5
11.9
Answer: 47.20cm
Step-by-step explanation:
Please find the missing side length using trig
Answer:
13.0898597466511 or 13.09
Step-by-step explanation:
If Jimmy drove 300 miles at a rate of 50 miles per hour, find the number of hours Jimmy traveled.
Answer:
He drove 6 hours.
Step-by-step explanation:
distance = rate times time
300 = 50t Divide both sides by 50
t = 6
U={ positive integer between 9 and 21} P={odd numbers} Given that P and Q are subsets of U a. List all the members of P, Q and U b. Illustrate the information on a Venn diagram c. Find P1 and Q1
The set of the numbers are all integers from 9 to 21 inclusive
What is a set?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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During its first month of business, Dig the Dogs, Inc. purchased $900 of hotdogs of which it paid $300 and owes the rest. During the month, it sold 3/4 of its inventory for $1,000 on account. What is the amount of Cost of Goods Sold for the month ended?
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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Which statements are true about the angles in the figure? Select two options.
Angle x and angle y are supplementary angles.
Angle W and angle Z are a linear pair.
Angle W and angle Y are adjacent angles.
Angle X and Angle Z are vertical angles.
Angle Z and angle Y are complementary angles angles.
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
Blake purchased a new car in 1990 for \$15,200$15,200. The value of the car has been depreciating exponentially at a constant rate. If the value of the car was \$10,000$10,000 in the year 1992, then what would be the predicted value of the car in the year 2001, to the nearest dollar?
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$.
Which of the following sequences are geometric?
Check all that apply.
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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How long will it take someone to knit a scarf that is 160 cm long?
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?
3. Meenakshi bought 12 books, each costing 250.75, if she gave the shopkeeper ₹ 4000. How much money will returned?
ans
4. One crayon set costs 25. How many crayon sets can be bought for rupees 2750
ans
5. Manu goes to buy a new bicycle in an exchange offer. The price of the new bicycle is bike on exchange is he pays for his new bike?
ans
pls put the questin number and give the answer
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.
What are the mathematical operations?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.
Books: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)
Crayon: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).
Bicycle: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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Question Completion: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?
which set or sets the number below belongs to: natural numbers, whole numbers, integers, rational numbers, irrational numbers, or real numbers.
19
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.
Are a set of natural numbers and a set of integers the same thing?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.
What are a few examples in groups?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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Write the exponential function that describes the situation.
The initial amount of the function is 12, and then it decreases by a factor of 7/9
with each unit increase in x.
Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the high temperature of 80 degrees occurs at 5 PM and the average temperature for the day is 60 degrees. Find the temperature, to the nearest degree, at 3 AM.
The temperature at 3 AM is about 53 degrees Fahrenheit.
How would you define temperature?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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which expression is equivalent to 2(a-3)+4a
The expression is equivalent to 2(a -3) + 4a will be 6a - 6. Then the correct option is A.
What is an equivalent?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
1. The volume of the cone is 27pi what is the volume of the cylinder
with the same radius and height
The height is 9 units
V = 763.407015 m
draw an angle of 65° and draw an angle equal to this angle, using ruler and compass
The Construction of angle equal to 65 degree is shown below with attached figure.
What is Construction?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 table shows the monthly revenue of a business rising exponentially since it opened an online store.
b. Write an equation to represent the revenue, R, as a function of months, m, since the online store opened.
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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A rectangle is divided up into four smaller rectangles/ The length of each segment is a whole number of cm. The areas of three rectangles is given in the diagram. Find the number of sq. cm in the total area of rectangle ACEG
The solution is, The value of N is 12 sq cm.
What is area of a rectangle?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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What is the measure of the smallest angle?
(Image)
67°
69°
52°
61°
The measure of the smallest angle is 52 degrees
How to determine the measure of the smallest angle?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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In this figure, lines a and b intersect a transversal, c. What is the relationship between ∠1 and ∠5?
m∠1 = m∠5, because alternate exterior angles are congruent.
What are angles of parallel lines?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.
A survey was done that asked employees to indicate whether they ride a bicycle or drive to work, and whether they live up to 5 miles or more than 5 miles from work. What is the probability that a randomly selected worker lives more than 5 miles from work and rides their bicycle? Enter your answer, rounded to the nearest whole percent, in the box
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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if the mean is 9,8,10,x,14 is 11 then find the value of x
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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What is the answer to 52+6y-22
pls help i dont know how to do it i've been out sick
a plane contains 40 lines, no 2 of which are parallel. suppose that there are 3 points where exactly 3 lines intersect, 4 points where exactly 4 lines intersect, 5 points where exactly 5 lines intersect, 6 points where exactly 6 lines intersect, and no points where more than 6 lines intersect. find the number of points where exactly 2 lines intersect.
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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A submarine starts at the depth of -15 meters and then dives down 0.5 meter every second
The linear function representing the depth of the submarine after t seconds is given as follows:
d(t) = -15 - 0.5t.
How to obtain a linear function?
The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change.The intercept b represents the value of y when x = 0.The parameters for this problem are given as follows:
b = -15 -> initial depth of the submarine.m = -0.5 -> each second, the height decays by 0.5.Hence the function is given as follows:
d(t) = -15 - 0.5t.
Missing InformationThe problem asks for the linear function representing the depth of the submarine after t seconds.
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Please help thank you
The tension forces are 1895 N and 2542 N.
What is the tension in the ropes?
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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15 pts pls help me TvT
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
What is Circle?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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Ata school
number of boys : number of girls = 11: 9
There are 124 more boys than girls.
Work out the total number of students at the school.
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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