The mass of an atom or molecule is measured in atomic mass units. Which is greater, a carat or a milligram?
Answers
Notice that:
[tex]\begin{gathered} -23<-21, \\ 8.3<10. \end{gathered}[/tex]Therefore:
[tex]8.3\times10^{-24}<10\times10^{-24}=10^{-23}<10^{-21}<1.66\times10^{-21}\text{.}[/tex]Then a carat is greater.
Now, since:
[tex]1atomic\text{ mass unit=8.3}\times10^{-24}carat.[/tex]Then:
[tex]\frac{1}{8.3}\times10^{24}\text{atomic mass unit=1carat.}[/tex]Simplifying the above result we get:
[tex]1\text{carat}=1.20\times10^{23}\text{atomic mass units.}[/tex]Also, since:
[tex]1\text{atomic mass unit=1.66}\times10^{-21}milligram[/tex]then:
[tex]\frac{1}{1.66}\times10^{21}\text{atomic mass unit=1 milligram.}[/tex]Simplifying the above result we get:
[tex]1\text{ milligram=6.02}\times10^{20}atomic\text{ mass units.}[/tex]Answer:
A carat is greater.
[tex]1\text{carat}=1.20\times10^{23}\text{atomic mass units.}[/tex]and
[tex]1\text{ milligram=6.02}\times10^{20}atomic\text{ mass units.}[/tex]and
Related Questions
You are cycling around Europe with your friends.You want to frame a photo from your trip to send home. Select a frame that is suitable for a photo with a perimeter of 70 cm. Is this frame suitable?YesNoIs this frame suitable?YesNoIs this frame suitable?YesNo
Answers
The perimeter of frame is given 70 cm.
There are two frames given.
For first frame , calculating the perimeter .
[tex]P=2(15+20)=2\times35=70\operatorname{cm}[/tex]For second frame, calculating the perimeter.
[tex]P=2(30+40)=2\times70=140\operatorname{cm}[/tex]Hence the first frame is suitable for for a photo with a perimeter of 70 cm.
This is the frame which is suitable.
Joshua earned $646 for 40 hours. Find the unit rate.
Answers
To find the unit rate (amount per hour) you divide the given amount into the given number of hours:
[tex]\frac{646}{40h}=16.15/h[/tex]Then, the unit rate is $16.15/hour
Find the perimeter.A rectangle measuring 4 1/3 mm by 4 1/2 mm
Answers
Answer:
[tex]17\text{ }\frac{2}{3}\text{ mm}[/tex]Explanation:
Here, we want to find the perimeter of the rectangle
Mathematically, the formula for the perimeter of a rectangle is:
[tex]P\text{ = 2\lparen L + B\rparen}[/tex]Substituting the values, we have it that:
[tex]\begin{gathered} P\text{ = 2\lparen4}\frac{1}{3}\text{ + 4}\frac{1}{2}) \\ \\ P\text{ = 2\lparen}\frac{13}{3}+\text{ }\frac{9}{2}) \\ \\ P\text{ = 2\lparen}\frac{26\text{ + 27}}{6}) \\ \\ P\text{ = }\frac{53}{3}\text{ = 17 }\frac{2}{3}\text{ mm} \end{gathered}[/tex]Translate to an equation, then solve.The product of 2, and a number increased by 7, is – 36.
Answers
Let the number be r then
2r is the product of 2 and the number
2r + 7 is when the product is increased by 7
2r + 7 = -36
2r = -36 - 7
2r = -41
r = -41/2
= -20 1/2
ERROR ANALYSIS: Student A says there is no solution to the graphed system of equations. Student B says there is one solution. Which student is correct? Why?
Answers
Then, to solve the exercise, we need to know the slope of each line. The slope of a line is the measure of the steepness of a line.
The graph shows that the red line has a greater steepness than the blue line. Thus, the lines have different slopes. Also, two lines are parallel if they have the same slope. Since these lines have different slopes, they are not parallel.
Therefore, student B is correct because the lines are not parallel, so they will intersect.
Could you help me with these problems ? I don't really know how to put the equation together and the steps I should take to solve it, it would be amazing if you could show me how, and I'd be very thankful if you could also add a picture showing the steps if possible. Thank you so much.
Answers
Since it is a right triangle, you can use the trigonometric ratio sin(θ) to solve the exercise:
[tex]\sin (\theta)=\frac{\text{opposite side}}{\text{hypotenuse}}[/tex]Graphically,
So, in this case, you have
[tex]\begin{gathered} \theta=54\text{\degree} \\ \text{ Opposite side }=72 \\ \text{ Hypotenuse }=x \\ \sin (54\text{\degree})=\frac{72}{x} \\ \text{ Multiply by x from both sides of the equation} \\ \sin (54\text{\degree})\cdot x=\frac{72}{x}\cdot x \\ \sin (54\text{\degree})\cdot x=72 \\ \text{ Divide by }\sin (54\text{\degree})\text{ from both sides of the equation} \\ \frac{\sin(54\text{\degree})\cdot x}{\sin(54\text{\degree})}=\frac{72}{\sin(54\text{\degree})} \\ x=\frac{72}{\sin(54\text{\degree})} \\ x=\frac{72}{0.8090} \\ x=88.99 \\ \text{ Rounding to the nearest tenth} \\ x=89.0 \end{gathered}[/tex]Therefore, the measure of the missing side is 89.
Martin orders a pasta dish that is priced at $11.99. He also orders a drink. The total cost for the pasta and drink is $14.48. What is the cost of the drink?
Answers
Explanation
Let the cost of the drink be x.
Therefore;
[tex]\begin{gathered} cost\text{ of dish+cost of drinks =total cost} \\ 11.99+x=14.48 \\ x=14.48-11.99 \\ x=2.49 \end{gathered}[/tex]Answer: 2.49 dollars
Steve Conway wants his team to win more than 57 games this year. His team has already won 2 games this season and there are 5 more months to play. Based on his goal, how many games must his team win per month?
Answers
Using a linear function, it is found that:
The inequality is: 5m + 2 > 57.The solution is: m > 11.They team needs to win more than 11 games per month.Linear functionThe linear function that models this situation is defined as follows:
y = mx + b.
In which the parameters are as follows:
m is the slope, which is the number of games that he wants to win per month.b = 2 is the intercept, which is the number of games that he has already won.They want to win more than 57 games, and there are 5 months to play, hence the inequality is given as follows:
5m + 2 > 57.
It is solved similarly to an equality, isolating the variable m and finding the range of values, as follows:
5m > 55
m > 55/5
m > 11.
Hence the team needs to win more than 11 games a month, and the solutions is illustrated by the image given at the end of the answer.
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Iman is playing a game. On one turn she earns 2 points and on the next turn she loses 5 points.
Graph her points on the number line.
Answers
Iman will be on - 3 on the number line after the game.
A number line is a representation of a graduated straight line that is used to represent real numbers visually. It is assumed that every point on a number line corresponds to a real number and that every real number corresponds to a point.
When laying a game, Iman earns 2 points on one turn and losses 5 points on the next turn.
Now, let's say Iman started from zero on the number line,
Then, on the first turn, she earns 2 points.
So, the number of points Iman has will be:
x = 0 + 2 = 2
After the next turn she losses 5 points.
x = 2 - 5 = - 3
Then Iman will be on - 3 on the number line.
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Given g(k) = 2k² - 4, find g(-5).
Answers
Answer:
g(-5)=46
Step-by-step explanation:
given that function is,
g(k) = 2k² - 4,
and we find the value of g(-5)
so,
g(-5)=2(5)^2-4
simpley put -5 in place of k
g(-5)=2×25-4
g(-5)=46
Answer:
g(-5) = 46
Step-by-step explanation:
Given function:
[tex]g(k)=2k^2-4[/tex]
To find g(-5), substitute k = -5 into the given function:
[tex]\begin{aligned}\implies g(-5)&=2(-5)^2-4\\&=2(25)-4\\&=50-4\\&=46\end{aligned}[/tex]
f(x) = 4
this line is
vertical
O horizontal
O diagonal
O impossible to graph
Answers
f(x) = 4
this line is
O vertical
O horizontal
O diagonal
O impossible to graph
A model rocket is launched with an initial upward velocity of 113 ft/s. The rocket’s height h (in feet) after t seconds is giving by the following. h=113t-16t^2 Find all values of t for which the rockets height is 39 feet. Round your answer(s) to the nearest hundredth.
Answers
Your friend just purchased a new sports car for $32,000. He received $6,000 for his trade in and he used that money as a down payment for the new sports car. He financed the vehicle at 6.76% APR over 48 months. Determine the amount financed from the given information.
a.
$38,000
c.
$29746.15
b.
$32,000
d.
$26,000
Answers
Answer: C. $29,746.08
Step-by-step explanation:
community gym charges a $50 membership fee and a $60 monthly fee. Workout gym charges a $225 fee and a $5 monthly fee. After how many months will the total amount paid to both gyms be the same?
Answers
Step 1 : Let's review the information given to us to answer the problem correctly:
Community Gym = $50 (Membership fee) + $ 60 (Monthly fee)
Workout Gym = $ 225 (Membership fee) + $ 5 (Monthly fee)
Step 2: Let's write the equation to answer the question, as follows:
Let x to represent the number of months that the total amount paid to both gyms will be the same
Community Gym = Workout Gym
Therefore,
50 + 60x = 225 + 5x
Like terms:
60x - 5x = 225 - 50
55x = 175
Dividing by 55 at both sides:
55x/55 = 175/55
x = 3.18 months
0.18 * 30 = 5.4 days
Step 3: Interpretation of the answer
Approximately after 3 months and 5 days and a half the total amount paid to both gyms will be the same
What is the smallest 3 digit number that is divisable by 2, 3, 4 , 5 and 6
Answers
The smallest 3 digit number that is divisible by 2, 3, 4 , 5 and 6 is 720.
How can the digit number that is divisible be caculated?Let us find the factors of the given numbers which are Factors of 2 are 1 and 2. then the factors of 3 are 1 and 3, the Factors of 4 are 1, 2 and 2, then the Factors of 5 are 12 and 5, then the Factors of 6 are 12, 2 and 3.
Then we can find the Lowest Common Factor of them as (1*2*3*2*2*5*2*3) which will give us 720.
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Factor completely 12m^2-3
Answers
Answer:
3 ( 2m-1)(2m+1)
Step-by-step explanation:
12m^2-3
Factor out the 3
3( 4m^2 -1)
3 ( ( 2m)^2 - 1^2)
Using the difference of squares ( a^2 - b^2) = ( a-b) (a+b)
3 ( 2m-1)(2m+1)
12m^2 - 3 = 3(4m^2 - 1)
but the bracket contains the difference between two squares
= 3(2m - 1)(2m + 1)
At a school concert the total value of tickets sold was $3990. Student tickets sold for $8 and adult tickets sold for $11. The number of adult tickets sold was 6 less than 4 times the number of student tickets. Find the number of student tickets sold.
Answers
The number of student tickets sold is 78.
Given,
The number of student tickets sold = x
The number of adult tickets sold = 4x - 6
Total value of tickets sold = $3990
Value of one student ticket = $8
Value of one adult ticket = $11
Now, we have to find the number of student tickets sold:
Here,
The expression :8x + 11(4x - 6) = 3990
Solve the expression:
8x + 44x - 66 = 3990
52x - 66 = 3990
Add 66 to both sides
52x - 66 + 66 = 3990 + 66
We get,
52x = 4056
Divide 52 on both sides
52x / 52 = 4056/52
That is,
x = 78
Therefore,
The number of student tickets sold is 78.
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a casting weighted 148 lb out of the mold. it weighed 141 lb after finishing. what percent of the weight was lost in the finishing?
Answers
The amount of weight lost will be equal to 4.72%.
Percentage may be defined as a form of expressing a number as a fraction of hundred. To find the percentage of a number we divide the number by the total amount and then multiply the answer with hundred. The initial weight of the casting was 148 lb and the final weight is 141 lb. To find the percentage we use the formula
Percentage lost = [(Final weight - Initial weight)/Initial weight] × 100
Percentage lost = [(141 - 148)/148] × 100
Percentage lost = ( -7/148) × 100
Percentage lost = -0.0472 × 100
Percentage lost = -4.72% and since we write the absolute value therefore, Percentage lost = 4.72%.
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Simplify using order of
operations.
3 • 10 (9 + 1)²
Answers
Answer:
3000
Step-by-step explanation:
Parentheses - (9 + 1) = 10
Exponents - 10 x 10 = 100
Multiplication - 10 x 100 = 1000 then 1000 x 3 = 3000
D
A
S
5 Jamila sells honey. She posts this sign for her customers.Then she makes a graph that shows the price of each size jar.Is Jamila's price the same per ounce for any size jar? Explain.HONE201612Price ($)4Х004 81216Jar Capacity (oz)
Answers
it is given that, the relation between the price of honey and jar capacity is in the given graph.
so, we have three points on the graph,
A(4,5), B(10,12.5) and C (15,19)
so, price of 4 oz = 5 $
price of 1 oz = 5/4 = 1.25 $
price of 10 oz = 12.5
price of 1 oz = 1.25 $
price of 15 oz is 19 $
price of 1 oz is 19/15 = 1.26 $
so, the approx price for 1 oz of honey is 1.25 that is approx same per ounce for any size of the jar.
thus, yes Jamila's price is the same per ounce for any size jar
Write an expression that is the product of two factors and is equivalent to - 3x - 15.Which expression is the product of two factors and is equivalent to - 3x - 15?A. - 3x-2-13B.-3(x - 5)C. (7x-2)-(10x - 13)D. -3(x+5)
Answers
Amon the choices given, letter D is equivalent to - 3x - 15.
-3 ( x + 5 )
if we distribute -3 , we will have
-3 (x ) = -3x , and
-3 ( +5) = -15
-3 ( x + 5) = -3x - 15
Answer: D. -3 (X + 5)
what is8.546 rounded to nearest tenth
Answers
If we round to the nearest tenth, it would be 8.5 because the hundredth digit is less than 5.
Hence, the answer is 8.5.←
Determine whether the statement makes sense or does not make sense, and explain your reasoning.
.I read that a certain star is 10^5 light-years from Earth, which is 100,000 light-years.
Choose the correct answer below.
OA. The statement makes sense. The value of 10^5 is not 100,000.
OB. The statement makes sense. The value of 10^5 is 100,000.
OC. The statement does not make sense. The value of 10^5 is not 100,000.
OD. The statement does not make sense. The value of 10^5 is 100,000.
Answers
OB. The statement makes sense. The value of 10^5 is 100,000 is the correct answer.
How to expand exponential expressions?10^5 = 10*10*10*10*10 = 100,000
Repeated multiplication is expressed using exponential notation.
For instance, 10*10*10 can be expressed more briefly as 10^3.
The base is the number 10 in 10^3.
Exponent refers to the 3 in 10^3.
The exponential expression is known as the number 10^3.
You can learn how to conduct mathematical operations on an exponential expression or term by being familiar with its constituent parts' names.
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A company is conducting a survey to determine how prepared people are for a long-term power outage, natural disaster, or terrorist attack. The frequency distribution on the right shows the resultsUse the table to answer the following question. What is the probability that the next person surveyed is very prepared?
Answers
The probability the next person surveyed is very prepared is 0.119.
What actually does probability mean?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number ranging from zero and 1, where, roughly, 0 denotes the event's impossibility and 1 represents certainty.Formula of total frequency is,
Total = f₁ + f₂ + f₃ + f₄ +...............n∑fi
The total frequency is,
total = n∑i=2 fi ⇒ 262 + 992 + 587 + 313 + 52
The total number of people prepared for a long-term power outage, natural disaster, or terrorist attack is obtained by taking the sum of the all frequencies.
probability = N(E)/N(S)
the information given, there are 262 people are very prepared.
That is, N(A) = 262
The required probability is,
P(A) = 262/2206
= 0.119
The probability the next person surveyed is very prepared is 0.119.
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David watches Maria and Alma race electric trains around a track. Maria's train goes around the track in 10 seconds. Alma's train goes around the track in 12 seconds.
How long will it take for both trains to cross the finish line together the first time?
Answers
Answer:
60 seconds
Step-by-step explanation:
The LCM of 10 and 12 is
10 = 2 × 5
12 = 2² × 3
LCM = 2² × 3 × 5 = 60
Answer: 60 seconds
the anwser is 60 seconds
Does the point (1, 0) satisfy the equation y = 7x + 1? yes no
Answers
To find out if the point (1,0) satisfy the equation we plug x=1 and y=0 into the equation:
[tex]\begin{gathered} 0=7\cdot1+1 \\ 0=8 \end{gathered}[/tex]since this is not true we conclude that th
Enter the ratio as a fraction in lowest terms
2ft to 40 in.
Answers
Answer:
[tex]\frac{3}{5}[/tex]
Step-by-step explanation:
2 feet is equivalent to 24 inches. (12 inches make a foot 2 x 12 = 24)
[tex]\frac{24}{40}[/tex] = [tex]\frac{3}{5}[/tex] Divide the top (numerator) and the bottom (denominator) by 8 to simplify.
to convert a decimal to do a fraction for the decimal over ______and multiply the numerator and denominator by _______and tell there is no longer a decimal in the numerator then___ your fraction
Answers
1) Let's proceed the steps
To convert a decimal to do a fraction for the decimal over one
Ex
0.5/1
And multiply the numerator and denominator by ten
Ex
5/10
(..) *until there is no longer a decimal in the numerator then simplify your fraction
Ex
1/2
Solve: 12/40 = 30/×
Answers
Given:
[tex]\frac{12}{40}=\frac{30}{x}[/tex][tex]\begin{gathered} x=30\times\frac{40}{12} \\ x=\frac{1200}{12} \\ x=100 \end{gathered}[/tex]Answer:
100Step-by-step explanation:
Solve:
12/40 = 30/×
it's a simple equation12 : 40 = 30 : x
x = 30 * 40 : 12
x = 1200 : 12
x = 100
In the diagram, .
Triangles G E F and J H I are shown. The length of side G F is 20 and the length of side I J is 10. Th elength of side F E is 40 and the length of side I H is 20.
To prove that the triangles are similar by the SAS similarity theorem, it needs to be proven that
Answers
In order prove that the triangles are similar by the SAS similarity theorem, it needs to be proven that A. J measures 60°.
What is SAS Similarity Theorem?The SAS Similarity Theorem states that two triangles are similar if their included angles are congruent and their two sides are proportionate to one other. Triangle congruence and resemblance are both criteria for SAS.
The triangles are congruent if two sides and the included angle of one triangle are equivalent to two sides and the included angle of another triangle.
In this case, the length of side FE is 40 and the length of side IH is 20. This gives a value of 60. Therefore, J should measure 60°.
In conclusion, the correct option is A.
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Triangles G E F and J H I are shown. The length of side G F is 20 and the length of side I J is 10. Th elength of side F E is 40 and the length of side I H is 20. To prove that the triangles are similar by the SAS similarity theorem, it needs to be proven that
J measures 60°.
J measures 30°.
I measures 60°.
I measures 30°.