A
D
Consider these two claims:
•
ABC is similar to both AACD and ACBD.
• (ACI2 + IBC12 = (ABI2
Explain why these claims are correct or incorrect. Provide valid
mathematical reasoning to support your responses.
Answers
As the corresponding angles are same in each of the right triangles, they are similar to each other (AAA rule).
AC² + BC² = AB² is true according to the Pythagorean theorem.
What is Pythagorean theorem?One of the earliest known theorems to ancient civilizations was the Pythagorean Theorem. Pythagoras, a Greek mathematician and philosopher, inspired the name of this famous theorem. He is credited with numerous mathematical contributions, some of which may have been the work of his students.
They were adamant that any two lengths had to be integral multiples of some unit length. There have been numerous attempts to conceal the fact that the square root of 2 is irrational. According to legend, the man who revealed the secret drowned at sea.
The Pythagorean Theorem describes triangles with a right angle. According to Pythagorean Theorem:
"The area of the square constructed on the hypotenuse of a right triangle equals the sum of the areas of the squares constructed on the remaining sides."
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Related Questions
What are the 4 types of computer system components?
Answers
The 4 types of computer system components are Input devices, Output devices, Memory and Central Processing Unit (CPU).
To give input and instructions to the computer for processing, input devices are employed. These items, which also go by the name of peripheral devices, include the mouse, keyboard, microphone, scanner, etc.
Monitors and printers are examples of output devices that are used to display the outcomes of the instructions that the computer has processed.
The main part of a computer that processes data is called a CPU (Central Processing Unit). The mother board, registers, buses, and other subcomponents of the CPU are used to carry out processing operations. Memory, another crucial computer component, is used by the CPU to temporarily or permanently store the instructions.
Then, there are further types of memory, including RAM, ROM, and supplementary storage devices. Together, these parts carry out the numerous instructions provided by the user.
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A bicycle wheel has a radius of 225 mm and has 25 equally spaced spokes. What is the approximate arc length, rounded to the nearest hundredth, between each spoke? Use 3.14 for . Show your work.
Answers
The approximate arc length is 56.52mm.
What is arc length in a circle?The central angle that creates the intercepted arc's central angle, or the arc measure, is expressed in degrees. Arc length can be estimated as a percentage of the circle's circumference by multiplying the circle's diameter by the arc length, divided by 360.
The distance between two places along a segment of a curve is known as the arc length.
Given that, the bicycle wheel has a radius (r) = 225 mm
And number of equally spaced spokes (n) = 25
π = 3.14
Perimeter of the bicycle wheel (P) = 2*π*r
Perimeter of the bicycle wheel = 2 * 3.14 * 225 mm
Perimeter of the bicycle wheel = 1413 mm
The arc length = Perimeter of the bicycle wheel (P) / number of spokes (n)
The arc length = 1413 / 25 mm
The arc length = 56.52 mm
The approximate arc length is 56.52mm.
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A right triangle is shown below.
ہو
60%
X
What is the sine of t?
1
Answers
The functions sin and cosine, sometimes known as sin() and cos(), show how a right triangle is shaped. Answer is 8.212°.
What does sin t mean in math?The functions sin and cosine, sometimes known as sin() and cos(), show how a right triangle is shaped.
The ratio of the opposite side to the hypotenuse is called sin(), and the ratio of the adjacent side to the hypotenuse is called cos(), when viewed from a vertex with angle.
So, the Pythagorean identity-based formula for sin is sin²x = 1 - cos²x.
Hypotenuse²=base²+perp²
(8)²=(7)²+(perp)²
64=49+(perp)²
64/49=perp²
1.306=perp²
Now taking square root on both sides
Perp=√1.306
Perp=1.142
Sin C=opposite/hypotenuse
Sin =1.142/8
Sin C=0.14285
C=Sin^-1 0.14285
C=8.212°
Answer is 8.212°.
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Which statement is true of table A and table B shown below?
Table A represents a function because there is only one output for
each input value.
Table B represents a function because there is only one output for
each input value.
Table A represents a function because there is only one input for each
output value.
Table B represents a function because there is only one input for each
output value.
Answers
Table A represents a function, but Table B does not represent a function.
What is a function?
A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.
A function or mapping is described as a collection of pairs of x and y that are ordered such that given different values of x, there will also be different values of y, or vice versa. For instance, the function x=y+2 yields a different x for every different value of y, while yielding the same x value for every single different value of y. We obtain two distinct x for two distinct ys, thus we can refer to this as a function at that point.
As, each element of X is associated with unique element of Y, so this is a function.
Table A
X Y
3 1
2 0
1 0
As, each element of X is associated with a unique element of Y, so this is a function.
Table B
X Y
3 -2
5 1
5 2
Hence, Table A represents a function, but Table B does not represent a function.
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Flu is spreading exponentially at a school. The number of new flu patients can be modeled using the
equation F=10e^0. 12d, where d represents the number of days since 10 students had the flu.
(a) How many days will it take for the number of new flu patients to equal 50? Determine your answer
algebraically using the natural logarithm. Round your answer to the nearest day
Answers
If the number of flu patients at the school is modelled by the equation [tex]F=10e^{0. 12d}[/tex] , then the number of days that it will take for the number of patients to reach 50 is 13 days .
The Exponential Growth equation is given as : [tex]F=10e^{0. 12d}[/tex] ;
We have to find How many days will it take for the number of new flu patients to equal 50 .
So , we substitute the value [tex]F=50[/tex] in the model equation ;
we get ;
⇒ [tex]50 = 10e^{0. 12d}[/tex] ;
dividing both side by 10 ,
we have ;
⇒ [tex]5=e^{0. 12d}[/tex] ;
taking [tex]\ln[/tex] on both sides ,
⇒ [tex]\ln 5 = 0.12d(\ln e)[/tex] ,....we know that [tex]\ln e = 1[/tex] ;
⇒[tex]d= \frac{\ln 5}{0.12}[/tex] ⇒ 13.41198 ;
≈ 13 days .
Therefore , it will take 13 days for the number of patients to reach 50 .
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coco flips a penny, a nickel, and a quarter. each coin is fair. what is the probability that at least one of the coins comes up heads/
Answers
When four coins are flipped at once, there is probability a 1/4 chance that the penny and nickel will both come up heads.
As per the data given in the above question are as bellow,
The data provided are as ,
As stated in the query,
Four coins are flipped simultaneously.
Flipping a coin might result in either a head or a tail.
Total results equal 2
For each coin, there is a one-in-two chance of obtaining a head.
likelihood of finding heads on both penny and nickel coins
= ( 1 / 2 ) × ( 1 / 2 )
= ( 1 / 4 )
As a result, 1 / 4 represents the likelihood of finding heads on both the penny and nickel.
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ange the following polynomial in column and then add 1.(9x+3y)+(5x-4y)
)????????????????????????????????????????????????
Answers
Answer:
14x - y
Steps:
(9x + 3y) + (5x - 4y)
Determine the sign:
9x + 3y + 5x - 4y
Combine as terms:
14x - y
I hope it helps you :)
Please Help me out!!
Answers
The solution to f(g(h(x))) = [tex]x^{2} - 12x^{3/2} + 54x -108\sqrt{x} + 87[/tex]
f(x) = [tex]x^{4} + 6[/tex]
g(x) = [tex]x-3[/tex]
h(x) = [tex]\sqrt{x}[/tex]
Therefore to find f(g(h(x))),
fogoh(x) = f(g(h(x)))
We first substitute the value of h(x) as above,
f(g([tex]\sqrt{x}[/tex] )) ....... as h(x) = [tex]\sqrt{x}[/tex]
Now, we substitute the value of g(x) where x is [tex]\sqrt{x}[/tex]
f([tex]\sqrt{x} -3[/tex]) ....... as g(x) = [tex]x-3[/tex]
Then we substitute the value of x in f(x) with [tex]\sqrt{x} -3[/tex]
[tex](\sqrt{x} -3)^{4} + 6[/tex]
Now we further solve to find a simpler form of the equation,
[tex](\sqrt{x} -3)^{4} + 6[/tex]
= [tex](x^{2} -12x^{3/2} +54x- 108\sqrt{x} +81) + 6[/tex]
= [tex]x^{2} - 12x^{3/2} + 54x -108\sqrt{x} + 87[/tex]
Therefore, fogoh(x) = f(g(h(x))= [tex]x^{2} - 12x^{3/2} + 54x -108\sqrt{x} + 87[/tex]
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Wyatt has $780 to spend at a bicycle store for some new gear and biking outfits. assume all prices listed include tax.
he buys a new bicycle for $398.35.
he buys 2 bicycle reflectors for $19.41 each and a pair of bike gloves for $35.27.
he plans to spend some or all of the money he has left to buy new biking outfits for $46.60 each.
write and solve an inequality which can be used to determine oo, the number of outfits wyatt can purchase while staying within his budget.
Answers
The inequality which can be used to determine too, the number of outfits Wyatt can purchase while staying within his budget is:
780 ≥ 472.44 + 46.60x
Inequality:
In mathematics, equations are not always balanced on both sides using equal signs. It can also be about "not equal" relationships, such as one being greater than the other or less than the other. In mathematics, an inequality refers to a relationship in which two numbers or other mathematical expressions do not compare equally. These formulas belong to algebra and are called inequalities.
An inequality means that two things are not the same. One of them may be less than, greater than, less than or equal to, greater than or equal to the other.
p ≠ q means p is not equal to qp < q means p is less than qp > q means p is greater than qp ≤ q means p is less than or equal to qp ≥ q means p is greater than or equal to qAccording to the question:
As based on the information,
he can't spent more than $780.
Four cycle reflector cost = 2 × $19.41
= $38.82
Let maximum number of outfit = x
and Cost = 46.60x
and the the pair of glove is for $35.27.
Therefore,
New bicycle + Bicycle reflectors + Biker gloves + Biking Outfit ≤ 780
⇒ $398.35 + $ 38.82 + $ 35.27 + $46.60 x ≤ 780
⇒ 472.44 + $ 46.60x ≤ 780
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suppose car gas mileage is normally distributed with a mean of 25 miles per gallon. if 67% of cars get at least 23 miles per gallon, what percentage of cars get less than 30 miles per gallon? a
Answers
So, on solving the provided question, we can say that percentage = 1/15 X 100 = 15%
What is percentage?A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.
car gas mileage is normally distributed with a mean of = 25 miles per gallon
67% of cars get at least 23 miles per gallon
percentage of cars get less than 30 miles per gallon
25-23/30
2/30
1/15
percentage = 1/15 X 100 = 15%
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The label on a \frac{1}{3}
3
1
-pound bag of seeds states that it will cover an area of 56 square feet. How many square feet do the seeds cover per pound?
On the double number line below, fill in the given values, then use multiplication to find the missing value. Enter your answers as fractions, mixed numbers, or whole numbers.
Answers
The number of square feet that the seed cover per pound is given as follows:
168 square feet per pound.
How to obtain the number of square feet that the seed covers per pound?The number of square feet that the seed covers per pound is obtained applying the proportions in the context of this problem.
The term proportion is used because the number of square feet that the seed covers per pound is given by the division of the total area by the number of pounds in the bag.
The parameters for this problem are given as follows:
Weight: 1/3 pound.Area: 56 square feet.Hence the number of square feet that the seed cover per pound is calculated as follows:
56/(1/3) = 56 x 3 = 168 square feet per pound.
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a lawn sprinkler located at the corner of a yard rotates through 80 degrees and sprays water of 20 ft. what is the length of the arc of the sector watered?
Answers
The length of the arc of the sector watered is 0.89π.
In the given question, a lawn sprinkler located at the corner of a yard rotates through 80 degrees and sprays water of 20 ft.
We have to find the length of the arc of the sector watered.
From the given question,
r = 20 ft, θ = 80 degree
A sector is referred to as a component of a circle made up of the circle's arc and its two radii. It is a section of the circle made up of the arc's circumference and the radii of the circle at its ends.
The formula for the length of the arc of the sector watered is
L = [tex]\frac{\theta}{360^{o}}\times 2\pi r[/tex]
Now putting the value
L = [tex]\frac{80^{o}}{360^{o}}\times 2\times\pi \times20[/tex]
Now simplifying the length
L = [tex]\frac{320^{o}}{360^{o}}\pi[/tex]
L = 0.89π
Hence, the length of the arc of the sector watered is 0.89π.
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a jit system uses kanban cards to authorize movement of incoming parts. in one portion of the system, a work center uses an average of 99 parts per hour while running. the manager has assigned an inefficiency factor of .31 to the center. standard containers are designed to hold 5 dozen parts each. the cycle time for parts containers is about 105 minutes. how many containers are needed? (
Answers
The required number of containers are two.
How to solve the problem to number of container?105 minutes per process cycle.
We must first determine the utilization rate of the process in order to determine the number of containers required for the parts. Usage rate is the typical unit utilised each hour.
The scenario specifies that the procedure uses 88 components every hour.
The net cycle time per part per hour is determined as follows: (99/60) x 105 = 173.25
0.31 is the efficiency factor.
We can determine the total number of things Kanban can maintain using the information provided:
= 173.25/(1 - 0.31)
= 119.54
We may calculate the total number of containers required by dividing the container capacity by the entire number of parts after we know how many total pieces will be stored.
Each container can hold 8 dozens, or 96 pieces.
= 119.54
Consequently, two containers are required.
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10. Your little brother borrows
$5.50 from you. You now have
$20. Which equation shows how
much money you had before you
let your brother borrow money?
Answers
Answer:x-5.50=20
Step-by-step explanation:
4
Complete each congruency statement, and name the rule used.
If you cannot show the triangles are congruent from the given information, leave the triangle's name blank and write CNBD for "CanNot Be Determined" in place of the rule.
Chapter Reference
b
M is the midpoint of
CI
△CAM ≅ △____ by ____
A
M
I
C
Answer:
△C AM ≅△
By rule
Answers
△TAN ≅ △LEF, by the SSS congruence theorem.
What is the SSS congruence theorem?The SSS (Side - Side - Side) congruence theorem states that if two triangles have three sides that are congruent to each other, then the two triangles are congruent by the SSS theorem.
From the triangles given by the image presented at the end of the answer, the congruent sides are given as follows:
NT and LE.TA and EF.AN and FL.(the congruence of each side is represented by the |, || and ||| notations).
As the three sides are congruent, we have that triangles TAN and LEF are congruent by the Side - Side - Side congruence theorem.
Missing InformationThe two triangles are given by the image presented at the end of the answer.
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what is the maximum of the sinusoidal function? enter your answer in the box.
Answers
Answer:
Step-by-step explanation:
B
what are the four calculator operations that a student is expected to be able to perform on the ap test?
Answers
While some College Board math sections permit all students to use a calculator, other math portion do not. Students can prayer the use of a four-function calculator for use on Non calculator sections.
Four-function calculators are basic calculators that have functions limited to subtraction, addition, multiplication, square roots, division, and percentage.
Four-function calculators can only be used on test portion that need math calculations.
They must be put away during non-mathematical part.
Board policy on use of a calculator may vary by exam. Check by reading calculator rules for the PSAT/NMSQT and PSAT 10 and the SAT or visiting AP Students to read calculator policies for specific AP exams.
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Zell invested $80,000 in two different types of stocks. The first type earned 9% and the second type earned 12%. If the profit on the 12% stocks was $150 more than the profit on the 9% stocks, how much did Zell invest in the 9% stock?
Answers
Zell invested $80,000 in two different types of stocks. Solving for x gives us the amount invested in the 9% stock:
x = $45000
What is stock?Generally, Let x be the amount invested in the 9% stock.
Then (80,000 - x) is the amount invested in the 12% stock.
The profit on the 9% stock is 0.09 * x and the profit on the 12% stock is
0.12 * (80,000 - x).
We know that the profit on the 12% stock is $150 more than the profit on the 9% stock.
So we can set up the following equation:
0.12 * (80,000 - x)
= 0.09 * x + 150
x=45000
Therefore, Zell invested $80,000 in two different types of stocks. the amount invested in the 9% stock is $45000
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Answer:
$45,000
Step-by-step explanation:
Convert 17 cm to decimeters
Answers
Answer: 1.7
Step-by-step explanation: First, let's see how many decimeters are in 1 cm. To find it, we must divide the cm by 10. So, we can do 17 / 10 or move the decimal one spot left. They should both = 1.7. I hope this helped!
give the equation of the line in slope intercept form of the line with a slope of -4/3 and that passes through the point (3,-3)
Answers
[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{-3})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{4}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{- \cfrac{4}{3}}(x-\stackrel{x_1}{3}) \implies y +3= -\cfrac{4}{3} (x -3) \\\\\\ y+3=-\cfrac{4}{3}x+4\implies {\Large \begin{array}{llll} y=-\cfrac{4}{3}x+1 \end{array}}[/tex]
Juanita makes $30 an hour at work. She has to take time off work to purchase her dress, so each hour away from work costs her $30 in lost income. Assume that returning to work takes Juanita the same amount of time as getting to a store and that it takes her 30 minutes to shop. As you answer the following questions, ignore the cost of gasoline and depreciation of her car when traveling.
Answers
On solving the provided question, we can say that bye equation, The total cost will be: [tex]= $75 + $60 = $135[/tex]
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
from the data provided
opportunity cost of time will be $144.
opportunity cost oftown will be -
[tex]= 1.5 × 30 = $45.[/tex]
The total cost will be:
= $45 + $86 = $131
[tex]= 2.5 × 30 = $75[/tex]
The total cost will be:
[tex]= $75 + $60 = $135[/tex]
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In manufacturing, systematic sampling could be used to determine if the machines are operating correctly. Which of the following best describes this type of sampling
Answers
According to the given information Every 10th product in the line is selected.
How does systematic sampling work?Systematic sampling is a probabilistic strategy that includes selecting people from the general population at predetermined intervals, such as each 15th people on a list of the population. If the community is set up in a random order, this can replicate the benefits of simple random sampling.
Why is sampling a systematic process?Biased sample sizes and subpar survey results are reduced by systematic sampling. If there is a low chance that data will be manipulated: Data validity may be compromised if researchers rearrange a data set. The best strategy for surveys when there is little likelihood of data manipulation is systematic sampling.
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Jessica is measuring two line segments. The first line segment is 30 cm long while the second line segment is 500 mm long. How long are the two line segments together?A. 80 cmB. 25 cmC. 47 cmD. 49 cm
Answers
The length of the two line segments together is 80 cm
Step 1: Convert 500mm into cm.
We know that the value of 1mm is equal to 0.1 cm.
Then, 500mm will be 500mm*0.1 = 50 cm.
Therefore, the second line segment is 50 cm long.
Step 2: Calculate total length.
Let the first line segment be L1= 30 cm long and the second line segment be L2= 50 cm long.
Now, the total length is
L = L1 + L2
Substitute the values L1= 30 cm and L2= 50 cm in L = L1 + L2.
Hence, the length of the two line segments together is 80 cm
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In the diagram, if PW = 12 and PT = 9, find PX.
Answers
The length of segment PX in this problem is given as follows:
PX = 9.
How to obtain the length of segment PX?The theorem used to solve this problem is given as follows:
A line parallel to one side of a triangle divides the other two proportionately.
In this problem, all the horizontal lines are parallel, hence the side is divided proportionality, as the resulting triangles in the context of this problem are all similar.
PX is three-fourths of the length of the segment PW = 12, hence it's length is given as follows:
PX = 3 x 12/4
PX = 3 x 3
PX = 9 units.
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question 6 a data analyst at an e-commerce company is working with a spreadsheet containing last month's sales. the most expensive product their company sells costs $49.99, so they want to quickly confirm that all of the data in the sales column is $49.99 or less. what function can they use?
Answers
The required function,which best describe the problem is split function.
What is Split function?By designating one of the given string's sub-strings as the delimiter, the split() method can be used to divide a given string or line. The output is the string that comes before and comes after the substring that was supplied as a delimiter.
According to question:a data analyst at an e-commerce company is working with a spreadsheet containing last month's sales.
the most expensive product their company sells costs $49.99, so they want to quickly confirm that all of the data in the sales column is $49.99 or less.
This situation is defined for split function, which is best describe it.
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lanie has decided to add strength training to her exercise program. her trainer suggests that she add weight lifting for 5 minutes during her routine for the first week. each week thereafter, she is to increase the weight lifting time by 2 minutes. a) which formula represents this sequential increase in weight lifting time?
Answers
23 minutes she will be devoting to weightlifting in week 10.
function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
A technical definition of a function is: a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Formula represent the sequential increase in weight lifting time is :
f (n) = 2n + 5
f (n) = 2n + 5
f (10-1) = 2(10-1) + 5
f(9) = 2(9)
f(9) = 18
f(9) = 23
Therefore,23 minutes she will be devoting to weightlifting in week 10.
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It takes Logan 3/10 of an hour to complete 1 lap.
How many laps will he complete 2/3 of an hour.
Answers
Answer:
20/9 laps
Step-by-step explanation:
convert everything to minutes to make things a little easier
3/10 of an hour = 1/10 of an hour (6 minutes) * 3 = 18 minutes
2/3 of an hour = 1/3 of an hour (20 minutes) * 2 = 40 minutes
18 minutes = 1 lap
40 minutes = ? laps
multiply the first equation by 40/18 to get 40 minutes on the left sides
40 minutes = 40/18 laps = 20/9 laps
___ units of measure.
Answers
Of all the total units of measurements, the seven base units are given above.
What are the units of measurement?A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.
Given are the units of measurements.
The seven SI base units, which are comprised of:
Length - meter (m)Time - second (s)Amount of substance - mole (mole)Electric current - ampere (A)Temperature - kelvin (K)Luminous intensity - candela (cd)Mass - kilogram (kg)Therefore, of all the total units of measurements, the seven base units are given above.
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Simplify to 5c + 3p,
The variable and the number come in one team.
We call that a(n)
Answers
Answer:
3(5/3c+p)
Step-by-step explanation:
5c+3p=3(5/3c+p)
Can anyone help me answer this question?
In a geometric progression, the first term is 7, the last term 448 and the sum 889. Find
the common ratio.
Answers
Answer:
Step-by-step explanation:
Given : In a GP the first term is 7
the last term is 448
and the sum 889
To find : Common ratio ? The number of terms is 7.
The common ratio is 2
Answer:
common ratio (r) = 2
Step-by-step explanation:
solution in picture
