Final answer:
The equation 100 cm = 1 m is used to create a conversion factor that allows for conversion between centimeters and meters. This conversion factor is essential when measuring lengths and is part of the metric system, which also includes units like kilometers, millimeters, micrometers, and nanometers.
Explanation:
Understanding Conversion Factors
When considering the statement that 100 cm is equivalent to 1 m, we can create a conversion factor to help us switch from one unit of measurement to another. A conversion factor is a ratio of equivalent measurements used to convert a quantity from one unit to another. In this case, 100 cm/1 m is our conversion factor, and it is equal to 1 because both numerator and denominator represent the same length but in different units.
If we were to divide both sides of the equation by 1 meter, we would get 1 m/1 m on one side and 100 cm/1 m on the other, simplifying to just 1 because any fraction with the same number in the numerator and denominator equals 1. Hence, utilizing this conversion factor allows any given number in meters to be converted into centimeters, and vice versa, without changing the measure's value.
Furthermore, knowing other unit conversions like 1 meter equals 0.001 kilometers, 1.094 yards, or 39.37 inches can be very useful in different contexts. Similarly, we can break down meters into smaller units such as centimeters, millimeters, micrometers, and nanometers, with each having its place in the metric system.
Use the formula for Interest:
P = 100
r = 7.2%
Y = 5
A = ?
An oil spill spreads 25 square meters every 16
hour. How much area does the oil spill cover after 2 hours?
△EFG≅△JKL . What is m∠K ?
The two triangles are congruent, so the corresponding angles are the same, K is the mid-late phase of JKL, so K is the same as the mid-late phase of EFG. Therefore K = F = 62°.
What is compromise?
If a geometric shape can be placed on top of another so that all its points coincide, the geometry is said to be congruent or harmonious. >
Now that K is JKL, K will be similar to EFG's mid and late game.
Middle and late phase of EFG = F
M∠F = 62°
Therefore m∠K = m∠F = 62°
So "The two triangles are congruent, so the corresponding angles will be the same. K is at the end of JKL, so K will be the same as the end of EFG. So, K = F = 62°."
The probable question maybe:
In a triangle EFG and LJK, we are given angle G = 53 degree and angle F is 62 degree. △EFG≅△JKL. find the value of m∠K ?
Parks spent 1/3 of his money on a sweater. He spent 3/5 of the remainder on a pair of jeans. If he has $36 left, how much did the sweater cost?
A boat heads south at 1,200 mph while a steamer heads east at 500 mph. If they started from the same dock and at the same time, when will the distance between them be 1,300 mi?
Answer: After t=1 hour the distance between the boat and the steamer be 1300 mi.
Step-by-step explanation:
Given the speed of boat = 1200 mph
the speed of steamer =500 mph
Distance traveled by boat in time "t"=[tex]\frac{distance}{time}=\frac{1200}{t}[/tex]
Distance traveled by steamer in time time "t"=[tex]\frac{500}{t}[/tex]
As boat head south and steamer heads east ∴ they will make a right angle triangle with hypotenuse=shortest distance between them =1300mi(given)
By Pythagoras theorem
[tex](Perpendicular)^2+(Base)^2=(Hypotenuse)^2\\\\\Rightarrow(\frac{1200}{t})^2+(\frac{500}{t})^2=(1300)^2\\\\\Rightarrow\frac{1440000}{t^2}+\frac{250000}{t^2}=1690000\\\\\Rightarrow\frac{1690000}{t^2}=1690000\\\\\Rightarrow\ t^2=\frac{1690000}{1690000}=1[/tex]
⇒t=1 hour
Thus, after t= 1 hour the distance between them be 1300 mi.
What is the maximum percentage of net spendable income that should be set aside for housing?
Answer:
The maximum percentage of net Spendable income that should be set aside for housing is given by [tex]\frac{28}{36}[/tex] rule,which states that ,if your total gross income after deduction is $ x, then you should use 28% of your income for housing finances and 36 % of your income for debt Purpose.
So, Maximum percentage of net spendable income that should be set aside for housing=28% of total gross income
The standard deviation of the sampling distribution of x overbarx, denoted sigma subscript x overbarσx, is called the
This is called as the standard error of the mean. Standard error is a numerical term that calculates the accurateness with which a sampling embodies a populace or population. In statistics, a sample mean moves away from the real mean of a population; this deviancy is the standard error.
Explain how you can use doubles when multiplying with 4 to find 4x8
Answer:
Here,
4 × 8 = 32
Now,
using the doubles when multiplying with 4
2 × (4 × 4)
= 2 × 16
= 32
Hence,
we use the doubles this way as by doubling the result obtained on multiplying the 4 with 4
Step-by-step explanation:
Here,
4 × 8 = 32
Now,
using the doubles when multiplying with 4
2 × (4 × 4)
= 2 × 16
= 32
Hence,
we use the doubles this way as by doubling the result obtained on multiplying the 4 with 4
or
double the number 4 i.e 2 × 4 = 8
then again double the result i.e 2 × 8 = 16
and, again double the result i.e 2 × 16 = 32 which the required answer.
Choose ALL that apply:
The executor of an estate does the following.
creates a will
takes an inventory of the estate's asset's
gives medical advice
gives financial advice
handles financial matters as designated in the will
How many radians are in one degree, accurate to three decimal places?
One radian is approximately 0.0175 degrees. To convert from radians to degrees, multiply the radians value by 57.3°. This conversion is commonly used in mathematics and physics.
Explanation:One radian is equal to approximately 0.0175 degrees. To convert from radians to degrees, you can use the conversion factor of 1 radian = 57.3°. So, to convert an angle from degrees to radians, you can multiply the degrees value by 0.0175. This conversion can be used when working with angular measurements in mathematics and physics.
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Sarah cut 6 yards of ribbon from a spool. How much did she cut in inches?
The length of a rectangle is 5 less than twice the width. If the perimeter of the rectangle is 146 centimeters, find the dimensions of the rectangle.
The dimension of the rectangle should be 47cm and 26 cm respectively.
Given that,
The perimeter of the rectangle is 146 cm.And, the length is 5 less than twice the width. Here we assume the length be x and the width be y.Based on the above information,
We know that
The perimeter of the rectangle = 2(l + w)
w = width
(2w - 5) = length
So,
146 = 2(2w - 5 + w)
146 = 4w - 10 + 2w
156 = 6w
w = 26 cm
And, the length is
= 2(26) - 5
= 47 cm
Therefore we can conclude that the dimension of the rectangle should be 47cm and 26 cm respectively.
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A bar of soap weighs as much as 3/4 of an identical bar plus 3/4 of a pound. How much does the bar of soap weigh?
The weight of the bar of soap can be found by setting up the equation [tex]w = \(\frac{3}{4}w + \frac{3}{4}\)[/tex] and solving for 'w', which results in the soap weighing 3 pounds.
To find the weight of the bar of soap, we can set up an equation based on the given information. Let's define the weight of the soap as 'w'. According to the problem, the weight of the soap is equal to [tex]\frac{3}{4}[/tex] of itself plus [tex]\frac{3}{4}[/tex] of a pound, which can be written as:
[tex]w = \(\frac{3}{4}w + \frac{3}{4}\)[/tex]
Now, to solve for 'w', we need to isolate it on one side of the equation. We can do this by subtracting [tex]\(\frac{3}{4}w\)[/tex] from both sides:
[tex]w - \(\frac{3}{4}w\) = \(\frac{3}{4}\)[/tex]
This simplifies to [tex]\(\frac{1}{4}w\) = \(\frac{3}{4}\)[/tex], so when we multiply both sides by 4 to solve for 'w', we get:
w = 3 pounds
Therefore, the bar of soap weighs 3 pounds.
Find the value of x so that the function has the given value.
j(x)=−4/5x+7; j(x)=−5
rounding to estimate the difference of 18.14 - 9.88
Answer:
18.14 rounds to 18 because you look at the 1 and (0, 1, 2, 3, 4) tell you to round down. That means 18.14 rounds down to 18
9.88 rounds to 10 because you look at the first 8 and (5, 6, 7, 8, 9) tell you to round up. That means 9.88 rounds up to 10.
Now it's just simple math. 18-10 = 8
Step-by-step explanation:
Answer:
18.14 rounds to 18 because you look at the 1 and (0, 1, 2, 3, 4) tell you to round down. That means 18.14 rounds down to 18
9.88 rounds to 10 because you look at the first 8 and (5, 6, 7, 8, 9) tell you to round up. That means 9.88 rounds up to 10.
18-10=8.
How are the variables on the graph related?
Answer choices:
A. As speed decreases, height stays constant.
B. As speed decreases, height increases.
C. As speed increases, height decreases.
D. As speed increases, height increases.
The graph demonstrates a uniform relationship between speed and height, indicating that as speed increases, height also increases. Therefore, the correct answer is:
D. As speed increases, height increases.
The Graph indicates a uniform relationship between speed and height. To interpret this in the context of the answer choices:
D. As speed increases, height increases.
This is the most appropriate choice based on the information provided. In a uniform relationship, as speed increases, the corresponding height also increases. Therefore, Option D accurately captures the relationship depicted on the graph.
When x = 1 then y equals
If x = 1, then the value of y in the equation [tex]\frac{4}{x}[/tex] + [tex]\frac{3}{y}[/tex] = 5 equals
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.
Given equation is,
4 / x + 3 / y = 5
We have to find the value of y, when the value of x = 1.
Substitute x = 1 in the equation.
4/1 + 3/y = 5
4 + 3/y = 5
3/y = 5 - 4
3/y = 1
y = 3/1
y = 3
Hence the value of y is 3.
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The question is incomplete. The complete question is as follows.
If x = 1, then the value of y in the equation [tex]\frac{4}{x}[/tex] + [tex]\frac{3}{y}[/tex] = 5 equals ?
Determine the number of solutions for the system y-3x=2 and 2y-6x=2
The product of two integers is 72. One number is two less than five times the other.
Which of the following equations could be used to find one of the numbers?
2x^2 - 5 = 72
2x^2 - 5x = 72
5x^2 - 2x = 72
5x^2 - 2 = 72
Answer:
[tex]5x^{2}-2x=72[/tex]
Step-by-step explanation:
Let
y------> one integer number
x----> the other integer number
we know that
[tex]xy=72[/tex] ----> equation A
[tex]y=5x-2[/tex] -----> equation B
substitute equation B in equation A
[tex]x(5x-2)=72[/tex]
[tex]5x^{2}-2x=72[/tex]
A reconnaissance airplane P, flying at 19,000 feet above a point R on the surface of the water, spots a submarine S at an angle of depression of β = 21° and a tanker T at an angle of depression of α = 33°, as shown in the figure. In addition, ∠SPT is found to be γ = 119°. Approximate the distance between the submarine and the tanker.
The solution for the problem is:
Tan 33(degrees) = opposite/adjacent
Starting off with the submarine, find how far it is from
point R.
Tan 21 = 19,000/x
or
19,000/Tan 21= x
x = 49496.69 feet the submarine is from point R.
Now, find how far the tanker is from point R.
Tan 33= 19,000/x
or
19,000/Tan 33 = x
x = 29257.43 feet the tanker is from point R.
Now subtract and the difference would be the answer
= 49496.69 - 29257.43
The tanker and sub are 20239.26 feet away from each other.
List two actions a person can take to minimize the fees paid to a bank.
ANSWER:
1. Keep good records to avoid overdraft fees.
2. Be sure to check banks carefully. Look at the services to see if the bank charges fees for those services. Compare multiple banks before settling with one.
Answer:
First, keep good records to avoid overdraft fees. Second, be sure to check banks out carefully. Look at the services you will most likely need and see whether the bank charges fees for those services. Compare several different banks before opening an account in one of them.
Step-by-step explanation:
Plato answer
Which of the following statements are equivalent to the statement "price increased by 1/2 "?
Choose all correct answers.
(A) The price doubled
(B) The price is 150% of the price before
(C) The price was reduced by a quarter
(D) The price became a half of what it was before
(E) The price is now 1.5 of what it was before
(F) The price now is 66 2 3 % of what it was before
(G) The price now is 200% of what it was before
(H) The price is 75% of what it was before
Correct answers to the statement that the price increased by 1/2 are: (B) The price is 150% of the price before and (E) The price is now 1.5 of what it was before. All other options either imply the price doubled, decreased, or was halved, which are not equivalent to an increase by half.
When it is stated that the price increased by 1/2, it means that the new price is the original price plus half of the original price. This is equivalent to multiplying the original price by 1.5. Let's evaluate the provided options:
(A) The price doubled - This would mean the new price is twice the original price, or the original price multiplied by 2, which is incorrect.(B) The price is 150% of the price before - This is correct because 150% implies the original price plus 50% of the original price, which matches our initial statement.(C) The price was reduced by a quarter - This would mean the new price is 75% of the original price, which is incorrect.(D) The price became a half of what it was before - This means the new price is half the original price, which is incorrect.(E) The price is now 1.5 of what it was before - This is correct, as it directly states that the new price is 1.5 times the original price.(F) The price now is 66 2/3% of what it was before - This would imply a decrease in price, which is incorrect.(G) The price now is 200% of what it was before - This implies the price doubled, which is not the case.(H) The price is 75% of what it was before - This would mean the price decreased, which is incorrect.Therefore, the correct answers to the statement "price increased by 1/2" are (B) The price is 150% of the price before and (E) The price is now 1.5 of what it was before.
The equivalent statements are (B) "The price is 150% of the price before" and (E) "The price is now 1.5 of what it was before".
To determine which statements are equivalent to the statement "price increased by 1/2", let's analyze each option:
(A) The price doubled:
This statement is not equivalent because doubling the price means multiplying it by 2, which is an increase of 100%.
(B) The price is 150% of the price before:
This statement is equivalent. Increasing by 1/2 is equivalent to increasing by 50%, which makes the new price 150% of the original price.
(C) The price was reduced by a quarter:
This statement is not equivalent because reducing by a quarter means subtracting 25%, not adding 50%.
(D) The price became a half of what it was before:
This statement is not equivalent because it implies a decrease to half, whereas the original statement implies an increase by half.
(E) The price is now 1.5 of what it was before:
This statement is equivalent. If the price is increased by 1/2, it becomes 1 + 1/2 = 1.5 times the original price.
(F) The price now is 66 2/3 % of what it was before:
This statement is not equivalent. 66 2/3 % represents a decrease, not an increase.
(G) The price now is 200% of what it was before:
This statement is not equivalent because 200% represents a doubling, not an increase of 1/2.
(H) The price is 75% of what it was before:
This statement is not equivalent because 75% represents a decrease, not an increase.
So, the equivalent statements are (B) and (E).
22x(4+16)-78x3 how do solve GEMDAS
Answer: 206
Step-by-step explanation:
22(4+16)-(78)(3)
(22)(20)-(78)(3)
440-(78)(3)
440-234=
206
°ω°
there are 24 students in science class. mr james will give each pair of students 3 magnets . so far ,mr James has given 9 pairs of students their magnets . how many magnets doses mr james need sp that each pair of students has exactly 3 magnes?
24/2 = 12 pairs of students
if he gave 9 pairs of students magnets there are 12-9 = 3 pairs left
3 magnets per pair
3*3 = 9 more magnets are needed
Answer:
the answer is d
Step-by-step explanation:
Which equation is an identity?
7m – 5 = 8m + 7 – m
3w + 8 – w = 4w – 2(w – 4)
9 – (2v + 3) = –2v – 6
–3y + 3 = –3y – 6
Please explain your answer.
Answer:
The correct option is 2.
Step-by-step explanation:
The equations that are true for any value of the variable, no matter what value is plugged in for the variable, then they are called Identity equations.
The first equation is
[tex]7m-5=8m+7-m[/tex]
[tex]7m-5=7m+7[/tex]
Subtract 7m from both the sides.
[tex]-5=7[/tex]
This statement is false for any value of m. Therefore this is not an Identity equation.
The second equation is
[tex]3w+8-w=4w-2(w-4)[/tex]
Using distributive property,
[tex]2w+8=4w-2w+8[/tex]
[tex]2w+8=2w+8[/tex]
[tex]0=0[/tex]
This statement is true for any value of w. Therefore this is an Identity equation.
The third equation is
[tex]9-(2v+3)=-2v-6[/tex]
[tex]9-2v-3=-2v-6[/tex]
[tex]-2v+6=-2v-6[/tex]
[tex]6=-6[/tex]
This statement is false for any value of v. Therefore this is not an Identity equation.
The fourth equation is
[tex]-3y+3=-3y-6[/tex]
Add 3y on both the sides.
[tex]3=-6[/tex]
This statement is false for any value of y. Therefore this is not an Identity equation.
Hence the correct option is 2.
How far will a cyclist travel in 1/4hour if he cycles at 18km per hour?
To do linear regression, there must be paired scores on two variables.
2 out of 10 people have an allergic reaction to a new medicine. What is the probability that exactly 4 out of 10 people given the medicine experience an allergic reaction?
The probability that exactly 4 out of 10 people given the medicine experience an allergic reaction is approximately 0.087 or 8.7%.
To find the probability that exactly 4 out of 10 people experience an allergic reaction to the new medicine, we use the binomial probability formula:
[tex]\[ P(X = k) = \binom{n}{k} \times p^k \times (1 - p)^{n - k} \][/tex]
Where:
( n ) is the number of trials (in this case, 10 people)
( k ) is the number of successes (in this case, 4 people)
( p ) is the probability of success on each trial (in this case, the probability of having an allergic reaction, which is 2 out of 10, or 0.2)
Now let's calculate:
[tex]\[ P(X = 4) = \binom{10}{4} \times 0.2^4 \times (1 - 0.2)^{10 - 4} \][/tex]
[tex]\[ P(X = 4) = \frac{10!}{4!(10-4)!} \times 0.2^4 \times 0.8^6 \][/tex]
[tex]\[ P(X = 4) = \frac{10!}{4! \times 6!} \times 0.2^4 \times 0.8^6 \][/tex]
[tex]\[ P(X = 4) = \frac{10 \times 9 \times 8 \times 7}{4 \times 3 \times 2 \times 1} \times 0.2^4 \times 0.8^6 \][/tex]
[tex]\[ P(X = 4) = 210 \times 0.2^4 \times 0.8^6 \][/tex]
[tex]\[ P(X = 4) = 210 \times 0.0016 \times 0.262144 \][/tex]
[tex]\[ P(X = 4) = 0.08704 \][/tex]
So, the probability that exactly 4 out of 10 people given the medicine experience an allergic reaction is approximately 0.087 or 8.7%.
You want to place a towel bar that is 24 1⁄4 centimeters long in the center of a door that is 70 1⁄3 centimeters wide. How far should you place the bar from each edge of the door?
Answer:
You should place it 23 1/24 centimeters from each edge.
Step-by-step explanation:
The towel bar will be in the center in the door so the space between the edge of the door and each side of the bar is equal in the left and the right of the door. So lets define:
x: distance between edge of door and the towel bar edge.
We see that x is the distance left in both sides of the towel bar from the door so:
x+24 (1/4) +x = 70 (1/3)
2x + 24 (1/4) = 70 (1/3)
2x= 70 (1/3) - 24 (1/4)
To operate the fractions , we need a common denominator that can be obtained simply by multiplying both denominators 4* 3=12
We then subtract the whole numbers and fractions
2x= 70 (4/12) - 24 (3/12) = =( 46 1/12)
x= ( 46 1/12) / 2 = 23 (1/24)
write the fraction in simplest form 8/10
The simplest form of 8/10 is 4/5.
Given,
8/10
We need to write it in the simplest form.
What is the simplest form of a given fraction?It means that there is no common factor between the numerator and the denominator other than 1.
Example:
4/8
4 = Numerator
8 = Denominator
4 = 4 x 1
8 = 4 x 2
= 4 x 1 / 4 x 2
Cancel the common factor 4.
= 1/2 is the simplest form of 4/8
Find the simplest form of 8/10.
= 8/10
Look for a common factor.
= 2 x 4 / 2 x 5
Cancel the common factor 2.
= 4 / 5
Now we do not see any common factor.
= 4/5
Thus the simplest form of 8/10 is 4/5.
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