Answer:
a. 54 = 2 * 3³
b. 108 = 2² * 3³
c. 360 = 2² * 3² * 5
etc.
Step-by-step explanation:
So, you need to have a list of primes handy:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, ...
Now, take your number and try to divide it by the first prime, 2.
54 = 27 * 2
That worked. Note down the 2 and repeat with the result. You find 27 cannot be divided by 2 again, but it can be divided by 3 (the next prime in the list):
27 = 9 * 3
Note down the 3 and repeat:
9 = 3 * 3
Note down a 3 again.
So you have
54 = 2*3*3*3 = 2 * 3³
You can continue this until the result is a prime number itself. Then you are done.
How do you write 4.1 x 10^-4 in standard form?
The given value 4.1 x 10^-4 can be written in standard form as 0.00041
How can this be written in standard form?The standard form can be done by following the format of multiplying a *10^b where b is the power and a is the digit.
A number can be expressed in a fashion that adheres to specific standards by using its standard form. Standard form refers to any number that may be expressed as a decimal number between 1.0 and 10.0 when multiplied by a power of 10.
Hence 4.1 x 10^-4 = 0.00041
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3. PLEASE THIS IS URGENT
B. Bill's Bikes sells new and used bikes. Bill buys used bikes, fixes them, and marks them up by 80%. The sales-
person selling the bike receives a 25% commission on the markup.
a. Find the missing values in the table. Show your work below
Strategies include:
Using proportions
Percent bar models
Multiplying with the decimal (or fractional) equivalent
Reasoning about with benchmark percent values
Costs and Revenue for Roberto's Sales
Buying
Markup
Selling
Commission
Profit (money the
(25% of markup) shop makes on the sale)
Price (80% of buying price) Price
$100
$180
$20
$60
$10
$55
$125
PLEASE AND I NEED THE WORK SHOWN FOR BOTH CHARTS
The values that van be put in the table based on the information will be:
Buying price (dollars) 100.
Mark-up 80.
Selling price 180
Commission 20
Profit 60
Buying price (dollars) 10
Mark-up 8
Selling price 18
Commission 2
Profit 6
Buying price (dollars) 55
Mark-up 44
Selling price 99
Commission 11
Profit 33
Buying price (dollars) 125
Mark-up 100
Selling price 225
Commission 25
Profit 75
How to explain the valueIt should be noted that the markup is 80% of the buying price. For example, when the buying price is $10, the markup will be:
= 80% × $10
= $8
The selling price is that addition of buying price and markup. This will be:
= $10 + $8
= $18
The commission is 25% of markup. This will be:
= 25% × 8
= $2
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Themba lends 12 000 to his friend to buy a car he requires the loan to be repaid after five years with a payment of 22 109,22 . what was the compound interest rate that he charged
The compound interest rate charged is given as follows:
13% per year.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
P is the principal, which is the value of deposit/loan/....r is the interest rate, as a decimal value.n is the number of times that interest is compounded per year, annually n = 1, semi-annually n = 2, quarterly n = 4, monthly n = 12.The parameters for this problem are given as follows:
P = 12000, A(t) = 22109.22, n = 1, t = 5.
Hence the interest rate is obtained as follows:
22109.22 = 12000(1 + r)^5
(1 + r)^5 = 22109.22/12000
1 + r = (22109.22/12000)^(1/5)
1 + r = 1.13
r = 1.13 - 1
r = 0.13.
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Which is larger? Circle A with an area of 10562.96 cm squared, or circle B with a circumference of 357.96 cm?
Circle A is larger.
Circle A's radius is 58 cm and circle B's radius is 57 cm.
What is a circle?A circle is a two-dimensional figure with a radius and circumference of 2πr.
We have,
Area of a circle = πr²
Circumference of a circle = 2πr
Circle A:
Area of a circle = 10562.96
πr² = 10562.96
r² = 3364
r = 58 cm ____(1)
Circle B:
Circumference = 357.96
2πr = 357.96
r = 357.96/6.28
r = 57 cm ______(2)
From (1) and (2)
58 > 57
So,
Circle A is larger.
Thus,
Circle A is larger.
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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.
Look at the table of values. What is the vertex of the graph? How do you know?
The vertex of the given graph is (5, 0)
What is vertex:A vertex is a point on a polygon where two rays or line segments meet, and the sides or edges of the object come together. Vertex is the plural form of vertices.
A straight line that can be extended endlessly is known as a ray. An angle is created when two line segments or rays cross one another. A vertex is created by definition whenever two lines come together to produce an angle.
Thus, we can state that a vertex is formed when two line segments or rays intersect.
Here we have a graph
The equation of the graph is y = |x - 5| + 1
As we can see that two lines are intersected at a point (5, 0)
Therefore,
The vertex of the given graph is (5, 0)
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Ed is on a road trip. He has already traveled 239 miles and is driving at a rate of 64 miles per hour. Which equation could be used to find how many hours, x, Ed has left in his road trip if he is traveling 642 total miles?
The equation to represent the given scenario is 642=239+64x.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, Ed is on a road trip. He has already traveled 239 miles and is driving at a rate of 64 miles per hour.
Let x be the number of hours.
We know that, Distance =Speed×Time
Now, total distance = 239+64×x
642=239+64x
Therefore, the equation to represent the given scenario is 642=239+64x.
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a bucket that weights 70lb when filled with water is lifted at a constant rate, by a mechanical winch, from the bottom of a well that is 60 feet deep. a) compute the work required to lift the bucket from the bottom of the well to the top. (5pts) b) oops, we forgot to tell you! the chain that is being used to lift the bucket weighs 0.55 lbs per foot. now find the correct amount of work required to lift the bucket from the bottom of the well all the way to the top. (5pts) c) oh no! where is our head at today? we completely forgot to mention that the bucket has a hole in the bottom. it only weighs 35lb when it reaches the top, due to the water leaking out at a constant rate. now compute the real work required to lift the bucket from the bottom of the well to the top of the well. (recall that the bucket is being lifted at a constant rate, as well.) (5pts)
If the weight of the bucket is 70 lb , then the work required to lift the bucket from bottom is 135240 foot-pounds .
We use the formula : Work = Force × Distance to calculate the work done
where "Force" is weight of bucket filled with water and "Distance" is height it is lifted.
The weight of bucket filled with water is = 70 pounds.
We convert this to a force in pounds force, by using g = 32.2 feet per second squared ;
So , Force = Weight × Gravity
⇒ 70 lb × 32.2 ft/s² = 2254 lb-ft/s²
The distance that the bucket is lifted is = 60 feet ;
So , work required to lift bucket from bottom of well to top is :
⇒ Work = Force × Distance = 2254 lb-ft/s² × 60 ft
⇒ 135240 foot-pounds
Therefore , it will require 135240 foot-pounds of work to lift the bucket filled with water from the bottom of the well to the top.
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The given question is incomplete , the complete question is
A bucket that weights 70lb when filled with water is lifted at a constant rate, by a mechanical winch, from the bottom of a well that is 60 feet deep.
Compute the work required to lift the bucket from the bottom of the well to the top .
Solve 2 ―8―33 = 0 by factoring.
Answer:
the equation 2 - 8 + 33 = 0 can be factored as 27 = 0, which is a verified answer
Step-by-step explanation:
To factor the equation 2 - 8 + 33 = 0, we start by collecting all the terms on one side of the equation:
2 - 8 + 33 = 0
becomes
33 - 8 + 2 = 0
Next, we can rewrite this as:
33 - 6 = 0
Finally, we factor the left-hand side of the equation to get:
33 - 6 = (33 - 3) - 3 = 30 - 3 = 27 - 0
So the factored form of the equation 2 - 8 + 33 = 0 is 27 = 0.
Verification: We can verify that the factored form of the equation is correct by substituting 0 for 27 and checking that the equation holds. So, if we replace 0 for 27 in equation 27 = 0, we get:
27 = 0, which is true.
Therefore, the equation 2 - 8 + 33 = 0 can be factored as 27 = 0, which is a verified answer.
Points: 0 of 1
A student wants to simulate 28 birthdays, but she does not have a calculator or software program available, so she makes up 28 numbers between 1 and 365
it okay to conduct the simulation this way? Why or why not?
Choose the correct answer below.
OA. Yes. People are capable of randomly making up numbers between two values.
OB. No. People generally favor some numbers over others so that they don't select numbers with a process that is truly random.
OC. No. Simulations must be performed with either a calculator or a statistical program.
OD. Yes. People are better at picking birth dates than computers, since they can base the numbers on the birth dates of people they know.
Save
From the given choices, we get:
No. People generally favor some numbers over others so that they don't select numbers with a process that is truly random.
The correct option is D.
What is simulation?A computer experiment in which you can select a random sample from the given probability distributions is called a simulation.
Given:
A student wants to simulate 28 birthdays,
but she does not have a calculator or software program available,
so she makes up 28 numbers between 1 and 365.
By comparing with the definition:
From the given choices, we get,
D. No. People generally favor some numbers over others so that they don't select numbers with a process that is truly random.
Hence, D is the correct option.
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question 9
help me asap
The length of major arc CBD is given as follows:
C = 40.39 m.
What is the measure of the circumference of a circle?The circumference of a circle of radius r is given by the multiplication of 2 by the number π = 3.14 and the radius r, as follows, hence the equation is given as follows:
C = 6.28r.
For this problem, the parameters are given as follows:
Radius of 9 m -> distance of the center to any point on the circumference of the circle.Fraction of the circumference of (10π/7)/2π = 5/7 of the circumference, as the entire circumference has an angle of 2π.Hence the arc length is given as follows:
C = 5/7 x 6.28 x 9
C = 40.39 m.
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A coin is flipped 14 times and lands on heads 8 times. The theoretical probability that the next coin flip will be heads is 50%.
The statement, coin is flipped 14 times and lands on heads 8 times. The theoretical probability that the next coin flip will be heads is 50% is True.
What is probability?The probability of an occurrence is a figure that represents how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place. A definite occurrence has a chance of 1 while an impossible event has a probability of 0.
When a coin is flipped the probability of getting a heads and a tail is 50%.
Hence, without the consideration of the flips and the result the theoretical probability that the next coin flip will be heads is 50%.
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the probability of the union of two events occurring can never be more than the probability of the intersection of two events occurring.
False. The probability of the union of two events occurring can be greater than the probability of the intersection of two events occurring.
The probability of the union of two events A and B, written as P(A union B), is the sum of the individual probabilities of the two events minus the probability of their intersection.
P(A union B) = P(A) + P(B) - P(A intersection B)
If the two events are not mutually exclusive, meaning that they have a non-empty intersection, then P(A union B) will be greater than P(A intersection B).
In other words, the union of two events gives you the combined probability of both events happening, while the intersection gives you the probability of both events happening simultaneously, which is always smaller or equal to the probability of either event happening.
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The probability of the union of two events occurring can never be more than the probability of the intersection of two events occurring? TRUE/ FALSE.
Explain how to determine the reduction identities from the double-angle identity cos(2x)=cos2x−sin2x
The double-angle identity for cosine is cos(2x) = cos²(x) - sin²(x).
To derive the reduction identities, we can use this double-angle identity and manipulate it to express cosine or sine of x in terms of cosine or sine of a smaller angle. Here are the steps for deriving the reduction identity for cosine: Start with the double-angle identity: cos(2x) = cos²(x) - sin²(x).
Divide both sides by cos²(x): cos(2x) / cos²(x) = (cos²(x) - sin²(x)) / cos²(x).
Use the identity sin²(x) + cos²(x) = 1 to replace cos²(x) in the denominator: cos(2x) / cos²(x) = (1 - sin²(x)) / cos²(x).
Rearrange the right-hand side: cos(2x) / cos²(x) = 1/cos²(x) - sin²(x) / cos²(x).
Recognize that 1/cos²(x) is equal to sec²(x), and use the identity tan²(x) + 1 = sec²(x) to replace it: cos(2x) / cos²(x) = sec²(x) - tan²(x).
Simplify using the identity cos(x)/sin(x) = cot(x): cos(2x) / cos²(x) = cosec²(x) - cot²(x).
Simplify the left-hand side using the identity cos(2x) = 2cos²(x) - 1: (2cos²(x) - 1) / cos²(x) = cosec²(x) - cot²(x).
Rearrange and simplify: 2 - (1/cos²(x)) = cosec²(x) - cot²(x).
Recognize that 1/cos²(x) is equal to sec²(x) and cosec(x) is equal to 1/sin(x): 2 - sec²(x) = 1/sin²(x) - cot²(x).
Simplify the left-hand side using the identity 1 - sin²(x) = cos²(x): cos²(x) - sec²(x) = 1/sin²(x) - cot²(x).
Recognize that sec(x) is equal to 1/cos(x) and cot(x) is equal to cos(x)/sin(x): cos²(x) - 1/cos²(x) = sin²(x)/cos²²(x) - cos²x)/sin²(x).
Simplify: cos⁴(x) - 1 = sin²(x) - cos⁴(x).
Rearrange: 2cos⁴(x) = sin²(x) + 1.
Finally, recognize that sin²(x) + cos²(x) = 1, and use it to replace sin²(x): 2cos⁴(x) = cos²(x). This is the reduction identity for cosine: cos²(x/2) = (1 + cos(x))/2.
To derive the reduction identity for sine, we can use the same double-angle identity for cosine and manipulate it to express sine of x in terms of sine or cosine of a smaller angle. The steps are similar but may require using different.
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Shape ABCD is a rectangle.
C is the point with coordinates (0,-8)
The equation of the straight line through A and B is 2y + x = 4. Find the equations of the lines
DC, AD and BC.
Equation of line DC is y = -1/2 x - 8
Equation of line AD is y = 2x + 2
Equation of line BC is y = 2x - 8
How to find the equation of the linesThe equation of the line 2y + x = 4 is arranged in slope intercept form to have
y = -x/2 + 2
The slope is -1/2
with a slope of -/2 and points (0, -8) line DC is written as
y - -8 = -1/2 (x - 0)
y + 8 = -1/2 x
y = -1/2 x - 8
Equation of line AD
line AD is a perpendicular line to line DC hence the slope is negative reciprocal of the slope of line DC
slope = 2
point A(0, 2) line AD is written as
y - 2 = 2 (x - 0)
y - 2 = 2x
y = 2x + 2
Equation of line BC
line BC is a parallel to line AD hence the slopes are equal
slope = 2
point C (0, -8) line AD is written as
y - - 8 = 2 (x - 0)
y + 8 = 2x
y = 2x - 8
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what is the value of the y-intercept of the graph of f(x)= 57(3.2)x
The y-intercept of the graph of a function is the point at which the graph intersects the y-axis. In other words, it's the value of the function when x=0.
So to find the y-intercept of f(x) = 57(3.2)x, we can substitute x=0 into the function:
f(0) = 57(3.2)(0)
f(0) = 0
So the y-intercept of this function is (0,0).
a number less than or equal to 52
Answer:
x[tex]\leq[/tex]52
Step-by-step explanation:
x[tex]\leq[/tex]52
1.Which quadrant will the terminal ray falls for an angle of rotation equal to 1.2 radians.
A.) QIV
B.)QII
C.)QI
D.)QIII
Answer:
D.) QIII
Step-by-step explanation:
Because 1.2 radians is in between 7π/6 and 5π/4
3.162 corrected to a 2 significant figure
Explanation:
The left-most digits are more significant than digits on the right.
For example, in the very large number 1,234,567 the "1" and "2" are more important than the "6" and "7". We focus on the more important digits when rounding. This would mean 1,234,567 rounds to 1,200,000 = 1.2 million = 1.2*10^6
Going back to 3.162, we have "3" and "1" as the left-most digits. We'll bump 3.1 up to 3.2 because of the digit 6 fits the criteria of "5 or larger".
Put another way: 3.162 is closer to 3.2 than it is to 3.1
This is why 3.2 is the final answer.
what distance does the tip of the minute hand on a clock travel in 11 minutes if the minute hand is 23 cm long?
The tip of the minute hand on a clock travels approximately 26.4 cm in 11 minutes if the minute hand is 23 cm long.
What is Circle?
A circle is a two-dimensional geometric shape that is defined as the set of all points in a plane that are a fixed distance away from a given point, called the center of the circle. This distance is known as the radius of the circle.
A circle can also be defined as the locus of a point that moves in a plane in such a way that its distance from a fixed point is constant. The constant distance is the radius of the circle.
The minute hand on a clock makes a full rotation in 60 minutes, which means it travels the circumference of a circle with a radius of 23 cm in 60 minutes. The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle, and π is a mathematical constant approximately equal to 3.14.
Therefore, the circumference of the circle traced by the tip of the minute hand is:
C = 2πr = 2 × 3.14 × 23 cm ≈ 144.44 cm
To find out how far the minute hand travels in 11 minutes, we need to calculate what fraction of the circumference it covers in that time. Since 11 minutes is about 18.3% of an hour (60 minutes), the minute hand travels 18.3% of the circumference of the circle in that time:
Distance traveled = 0.183 × 144.44 cm ≈ 26.4 cm
Therefore, the tip of the minute hand on a clock travels approximately 26.4 cm in 11 minutes if the minute hand is 23 cm long.
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Tanya went to the store and bought a box of spaghetti noodles for $4. She also bought x pounds of ground beef for $3.52 per pound. The total amount of money Tanya spent can be represented by the equation 18 = 3.52x + 4. How many pounds of ground beef did Tanya buy?
Answer:
Answer is in the attached photo.
Step-by-step explanation:
SolutionThe solution is in the attached photo, do take note for this question, we will have to make x the subject and solve for x.
This morning, Brendan tock a history test. There were 20 multiple-choice problems on the
test and Brendan answered 85% of them correctly. How many problems did Brendan get
right?
the probability that a product will operate properly within an expected time frame is the dimension of quality known as
The probability that a product will operate properly within an expected time frame is the dimension of quality known as reliability
The probability is the ratio of the number of favorable outcomes to the total number of outcomes. The value of the probability is varies from zero to one
Here, the product will operate properly within an expected time frame is the dimension of quality
Reliability is expressed as the probability that a given item will perform its intended function with no failures for a given period of time under a given set of conditions that means the reliability is the complementary to the failure of probability
Therefore, the given statement is know as the reliability
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y=3x+2
-4x+2y=8
elimination method
The solution of the equations y = 3x + 2 and - 4x + 2y = 8 by elimination method will be (2, 8).
What is the solution to the equation?An answer to a formula is any variable value that fulfills the equal outcomes, that is, it tends to make the Left Hand Side (LHS) and Right Hand Side (RHS) of the formula equal. To solve an equation, you must locate the feasible solution) to that formula.
The equations are given below.
y = 3x + 2
2y = 6x + 4
6x - 2y = - 4 ...1
- 4x + 2y = 8 ...2
Add both equations, then we have
6x - 4x = - 4 + 8
2x = 4
x = 2
Then the value of 'y' is given as,
y = 3(2) + 2
y = 6 + 2
y = 8
The solution of the equations y = 3x + 2 and - 4x + 2y = 8 by elimination method will be (2, 8).
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What is the area of the figure?
(NEED THE ANSWER ASAP. PLEASE DONT PUT ANYTHING NONSENSE OR I'LL REPORT U. THANK U FOR UR HELP)
The area of the given figure is 12 square meters
The given figure is a parallelogram
Parallelogram is a geometric figure that has both pair of opposites parallel sides and opposite sides are equal . Number of vertices and edges are four
The height of the parallelogram = 2 meters
The base length of the parallelogram = 6 meters
The area of the parallelogram = The height of the parallelogram × The base length of the parallelogram
Substitute the values in the equation
The area of the parallelogram = 2 × 6
Multiply the numbers
= 12 square meters
Therefore, the area is 12 square meters
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I have solved the question in general , as the given question is incomplete
The complete question is :
What is the area of the figure ?
if 3 is subtracted to a number and the sum is multiplied by 5 the number thus obtained is 575 find the original number
Answer:
118
Step-by-step explanation:
Let the original number be x.
After subtracting 3, the result is x - 3.
When this result is multiplied by 5, we get (x - 3) * 5 = 575.
Expanding and solving for x, we have:
5x - 15 = 575
5x = 590
x = 118
So the original number was 118.
If the maximum payment of $5,000 is made into a Individual Retirement Account (IRA) for 25 years at an annual interest rate of 3.2%, determine the amount in the account. Round to the nearest cent.
now, we're assuming the deposits of $5000 are made at the beginning of the year.
[tex]~~~~~~~~~~~~\stackrel{\textit{payments at the beginning of the period}}{\textit{Future Value of an annuity due}} \\\\ A=pmt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right]\left(1+\frac{r}{n}\right)[/tex]
[tex]\begin{cases} A=\textit{accumulated amount} \\ pmt=\textit{periodic payments}\dotfill & 5000\\ r=rate\to 3.2\%\to \frac{3.2}{100}\dotfill &0.032\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &25 \end{cases}[/tex]
[tex]A=5000\left[ \cfrac{\left( 1+\frac{0.032}{1} \right)^{1 \cdot 25}-1}{\frac{0.032}{1}} \right]\left(1+\frac{0.032}{1}\right) \\\\\\ A=5000\left[ \cfrac{\left( 1.032 \right)^{ 25}-1}{0.032} \right]\left(1.032\right) \implies A \approx 193148.73[/tex]
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?
word problem using division where the answer is 64
Answer:
Step-by-step explanation:
There are 256 people in a room. If they are divided into groups of 4, how many groups are there?
Answer: 64
Can someone please help me with this aleks
The measure of <E= 60, <F= 95 and <G= 25 degree.
What is similarity?In geometry, two similar forms are those whose dimensions are identical or have a same ratio but the size or length of their sides differ. Examples include similar triangles, similar rectangles, and similar squares. The scale factor is another name for the common ratio. Additionally, the equivalent angles have the same magnitude.
Given:
The two triangles are similar.
In triangle JKL using Angle Sum Property
<J + <K + <L = 180
95 + 60 + <K = 180
155 + <K = 180
<K = 180- 155
<K = 25 degree
Thus, the measure <E= 60
and, the measure <F= 95
and, the measure of <G= 25.
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