The length of the triangle ΔABC will be √7 inches.
What is a Pythagoras theorem?The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The Pythagoras theorem formula is given as
H² = P² + B²
In triangle ΔABC, AC = BC, the CD is perpendicular to AB with D belonging to AB, AB = 4 inches, and CD = √(3) inches.
The CD is half of the length AB. Then we have
CD = AB / 2
CD = 4 / 2
CD = 2 inches
Then the length of AC is calculated as,
h² = (√3)² + (2)²
h² = 3 + 4
h= √7 inches
The length of the triangle ΔABC will be √7 inches.
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Salma's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Salma $5.60 per pound, and type B coffee costs $4.40 per pound. This month's blend used three times as many pounds of type B coffee as type A, for a total cost of $451.20. How many pounds of type A coffee were used?
Answer: hi
11,28 pound / usd
Step-by-step explanation:
What would the approximate amperage setting be if a welder were set to the high range (150 to 350 amps) and the fine adjustment knob were painting at 5 on a 10 point scale
On solving the provided question, we can say that the approximate amperage setting be if a welder were set to the high range would be 350 amps.
What is range?The variable's range is obtained by finding its largest observed value (maximum) and subtracting its smallest observed value (minimum). Variational bounds or possible range: various steel prices; various styles; The extent or magnitude of a procedure or action: insight. the maximum or expected range of a weapon's projectile. The range of a list or set is the number between the minimum and maximum. Prior to identifying the region, align all the numbers. Remove (remove) the lowest number from the highest number next. The list's range is provided in the solution.The solution provides the list's range.
here,
the approximate amperage setting be if a welder were set to the high range would be 350 amps
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An item is regularly priced at $90. It is now priced at a discount of 40% off the regular price. What is the price now?
Answer:
Price after discount is $54
You save $36
Step-by-step explanation:
Dollhouse furnishing comes in different sizes depending on the size of the dollhouse. Write a ratio of the size of the dollhouse item to the size of the larger item.
dollhouse sofa: 1 1/2 in. Long
real sofa: 6 ft long
The ratio of the size of the dollhouse item to the doll house is 14 : 9.
What are ratios?
When b does not equal 0, an ordered pair of numbers a and b, represented as a / b, is said to be a ratio.
A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as 1: 3 (for every one boy, there are three girls), which means that 14 of the population is made up of boys and 34 of the population is made up of girls.
The ratio is a mathematical expression that can be used to represent one item as a percentage of another.
First convert feet to inches
1 feet = 12 inches
12 x 6 = 72 inches
dollhouse item : doll house
112 : 72
14 : 9
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What is called composite function?
A composite function is a type of function that is made up of two or more other functions. It is created by combining two or more functions together. The resulting function can be written as a single expression, or as a composition of multiple functions.
A composite function is a type of function that is formed by combining two or more other functions. It is created by combining two or more functions together using the mathematical operations of addition, subtraction, multiplication, division, or composition. The resulting function can be written as a single expression, or as a composition of multiple functions. A composite function is often used to simplify a complex problem, or to manipulate and analyze data. For example, if a data set contains two sets of data, a composite function could be used to combine the two sets of data into a single expression. Additionally, composite functions can be used to solve problems that involve multiple variables, as the resulting function can be used to represent the relationship between the variables. Furthermore, composite functions can be used to create graphs, which can be used to further analyze the data.
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write days in May to days in a year as a ratio.
Answer:
Step-by-step explanation:
Days in may = 31
Days in a year = 365
therefore, expected ratio = 31/365
What is the opposite reciprocal of 0/6
Answer: The reciprocal of a number is defined as 1 divided by that number. The opposite of a number is the number with the opposite sign. Therefore, the opposite reciprocal of a number is equal to the reciprocal of the opposite of that number.
In this case, the opposite reciprocal of 0/6 is the reciprocal of the opposite of 0/6. The opposite of 0/6 is 0/-6, which is equal to -0/6. The reciprocal of -0/6 is 1/(-0/6) = -6/0.
However, division by 0 is not defined, so it is not possible to find the reciprocal of -0/6. Therefore, the opposite reciprocal of 0/6 is undefined.
Step-by-step explanation:
Answer:
there is no reciprocal for 0/6
Step-by-step explanation:
PLEASE HELPPPP! Round to the nearest tenth, then find the sum. 0.92 + 5.37 2. Round to the nearest whole number, then find the difference. 6.3 − 2.8 3.Round to the nearest tenth, then find the difference. 13.56 − 10.02 4.Oliver did the high jump three times. His scores were 7.032 feet, 2.485 feet, and 4.59 feet. How many feet did he jump in total? 5.Clark ran the hurdles in 57.403 seconds. Grant ran the hurdles in 55.78 seconds. What is the difference between the two times? 6.Round to the nearest tenth, then find the sum. 13.46 + 7.84 + 2.59 7.Round to the nearest whole number, then find the difference. 1,472.63 − 975.28 8.Round to the nearest whole number, then find the sum. 38.24 + 14.53 + 8.93 9.Round to the nearest whole number, then find the sum. 16.4 + 12.8
Answer:
6.3
3
3.6
14
1.6
23.9
498
62
29
Step-by-step explanation:
0.9+5.4=6.3
6-3=3
13.6-10=3.6
7.032+2.485+4.59=14.107
57.403−55.78=1.623
13.5+7.8+2.6=23.
1,473−975=498
38+15+9=62
16+13=
Answer:
1. 0.92 rounds to 0.90 and 5.37 rounds to 5.40 (0.9 + 5.4 = 6.3)
2. 6.3 rounds to 6 and 2.8 rounds to 3 (6 - 3 = 3)
3. 13.56 rounds to 13.60 and 10.02 rounds to 10 (13.6 - 10 = 3.6)
4. 7.032 + 2.485 + 4.59 = 14.107
5. 57.403 - 55.78 = 1.623
6. 13.46 rounds to 13.50, 7.84 rounds to 7.80 and 2.59 rounds to 2.60 (13.5 + 7.8 + 2.6 = 23.9)
7. 1,472.63 rounds to 1,473 and 975.28 rounds to 975(1,473 - 975 = 498)
8. 38.24 rounds to 38, 14.53 rounds to 15 and 8.93 rounds to 9(38 + 15 + 9 = 62)
9. 16.4 rounds to 16 and 12.8 rounds to 13(16 + 13 = 29)
(some may be wrong but i did my best)
Evaluate the expression 4xy-yz
The expression 4xy-yz is an algebraic equation.
What is expression?Expression is defined as a way of conveying one's thoughts and feelings through spoken or written words, behavior, or art. It is a form of communication, which can be both verbal and non-verbal. Expression can also be used to show an emotion, opinion, or reaction. Expression is a way of expressing oneself, and it can be used to share ideas, feelings, and experiences with others.
To evaluate it, one must first substitute numerical values for the variables. For example, if x=2, y=3, and z=1, then the equation can be solved as follows: 4(2)(3) - (3)(1) = 12 - 3 = 9. Therefore, the expression 4xy-yz evaluates to 9.
The expression 4xy-yz can also be evaluated using the Order of Operations. This is the rule that states that multiplication and division should be done before addition and subtraction. In the equation 4xy-yz, the multiplication (4xy) should be done first, followed by the subtraction (-yz). This would yield an answer of 4x-z. Again, numerical values must be assigned to the variables in order to find the answer.
In conclusion, the expression 4xy-yz can be evaluated by either substituting numerical values for the variables or following the Order of Operations. The answer will depend on the values that are assigned to the variables.
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The expression 4xy-yz is an algebraic equation.
What is expression?Expression is defined as a way of conveying one's thoughts and feelings through spoken or written words, behavior, or art. It is a form of communication, which can be both verbal and non-verbal. Expression can also be used to show an emotion, opinion, or reaction. Expression is a way of expressing oneself, and it can be used to share ideas, feelings, and experiences with others.
To evaluate it, one must first substitute numerical values for the variables. For example, if x=2, y=3, and z=1, then the equation can be solved as follows: 4(2)(3) - (3)(1) = 12 - 3 = 9. Therefore, the expression 4xy-yz evaluates to 9.
The expression 4xy-yz can also be evaluated using the Order of Operations. This is the rule that states that multiplication and division should be done before addition and subtraction. In the equation 4xy-yz, the multiplication (4xy) should be done first, followed by the subtraction (-yz). This would yield an answer of 4x-z. Again, numerical values must be assigned to the variables in order to find the answer.
In conclusion, the expression 4xy-yz can be evaluated by either substituting numerical values for the variables or following the Order of Operations. The answer will depend on the values that are assigned to the variables.
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Match each power of a power expression with its simplified expression.
(4-3)-3
(46)-3
(49)-9
(-49)²
↑
↑
1
418
49
(-4)18
40
need to know which one goes to which
Answer:
(4^6)^-3 = 1/4^18(4^0)^-9 = 4^0(4^-3)^-3 = 4^9(-4^9)^2= (-4)^18Step-by-step explanation:(4^6)^-3 = 1/4^18(4^6)^-3= 4^(6*-3)(4^6)^-3= 1/4^18(4^0)^-9 = 4^0(4^0)^-9 = 4^(0*-9)(4^0)^-9= 4^0(4^-3)^-3 = 4^9(4^-3)^-3= 4 ^ (-3*-3)(4^-3)^-3 = 4^(9)(-4^9)^2= (-4)^18(-4^9)^2= -4^(9*2)(-4^9)^2=(-4)^18
Step-by-step explanation:
Answer:
[tex](4^{-3})^{-3}=4^9[/tex]
[tex](4^6)^{-3}=\dfrac{1}{4^{18}}[/tex]
[tex](4^0)^{-9}=4^0[/tex]
[tex](-4^9)^2=(-4)^{18}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{3 cm}\underline{Exponent Rules}\\\\$(a^b)^c=a^{bc}$\\\\$a^{-n}=\dfrac{1}{a^n}$\\\end{minipage}}[/tex]
Apply the above exponent rules to simplify each expression.
[tex]\begin{aligned}\implies (4^{-3})^{-3}&=4^{-3 \times -3}\\&=4^9\end{aligned}[/tex]
[tex]\begin{aligned}\implies (4^6)^{-3}&=4^{6 \times -3}\\&=4^{-18}\\&=\dfrac{1}{4^{18}}\end{aligned}[/tex]
[tex]\begin{aligned}\implies (4^0)^{-9}&=4^{0 \times -9}\\&=4^0\end{aligned}[/tex]
[tex]\begin{aligned}\implies (-4^9)^2&=(-4)^{9 \times 2}\\&=(-4)^{18}\end{aligned}[/tex]
A 140 meter rope is cut into two pieces. One piece is four time as long as the other. How long is each piece? Solve using substitution or elimination.
Answer:
28 m, 112 m
Step-by-step explanation:
x = length of short piece
4x = length of long piece
x + 4x = 140
5x = 140
x = 140/5 = 28
4x = 4(28) = 112
Select all the expressions that are equivalent to 16x - 12- 24x+ 4 16 x − 12 − 24 x + 4. Explain or show your reasoning.
1. 4+16x-12(1+2x)4 + 16 x − 12 ( 1 + 2 x )
2. 40x-1640 x − 16
3. 16x-24x-4+1216 x − 24 x − 4 + 12
4. -8x-8- 8 x − 8
5. 10 (1. 6x - 1. 2 - 2. 4x + 4)
1) 16x - 12(1 + 2x) + 4 is the expression that are equivalent to 16x-12-24x+4.
what is expression?An expression is a mathematical phrase that can contain numbers, variables, and operators. It can be a combination of these elements and can be evaluated to a specific value or a mathematical function.
An expression can be a simple mathematical statement such as 2x+3, or a more complex one involving multiple operations such as
(3x^2 - 4x + 5) / (2x +1). Expressions are used to represent mathematical operations, equations and relations between variables.
so we need to evaluate option 1 :
16x - 12 -24x +4
=> 16x - 12 -24x +4
the above expression is same as the expression mentioned in the question so option 1 is correct.
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Complete question :
Select all expressions that are equivalent to 16x−12−24x+4. Show or explain your reasoning.
1. 16x - 12(1 + 2x) + 4
2. 40x - 16
3. 4 - 12 + (2x - 3x)
4. -8(x+1)
two cards are drawn from a shuffled deck of 52 cards. what is the probability that the first card is a king and the second is a heart
On solving the provided question, we can say that the required probability is = 13/204.
What is probability?Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.
probability of 1st card = 1/4
since the card is not replaced
total number remaining cards = 51
second card 13/51
the required probability is = 13/204
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A school administrator asks each student if they participate in a sport and if they participate in a club. The results are shown below.
Participates in a Sport
Yes No Total
Participates in a Club Yes 620 450 1070
No 325 535 860
Total 945 985 1930
What percentage of students do not participate in a sport?
27.7%
44.6%
51.0%
62.2%.
answer is 51.1
The percentage of students who do not participate in a sport is C. 51.0%.
How to calculate the percentage?To find the percentage of students who do not participate in a sport, we can use the following formula:
(Number of students who do not participate in a sport) / (Total number of students) * 100%
From the table, we can see that the number of students who do not participate in a sport is 985, and the total number of students is 1930. So, plugging these values into the formula gives us:
= 985 / 1930 * 100%
= 51.03%
So, about 51.03% of students do not participate in a sport.
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2.6.2 Test (CST): Functions and Relations
Question 7 of 25
The function h(x) = -x] is a transformation of the absolute value parent
function, f(x) = [x]. Which graph shows h(x)?
Answer:
b
Step-by-step explanation:
The graph that shows the function h(x) = -x] which is a transformation of the absolute value parent function, f(x) = [x] is Option C.
The graph of the function h(x) = -x] is the reflection of the graph of f(x) = [x] about the x-axis. The graph of f(x) is piecewise defined as follows:
f(x) = x, when x ≥ 0f(x) = -x, when x < 0The graph of h(x) will have the same shape as f(x), but with all the y-values negated, so:
h(x) = -x, when x ≥ 0h(x) = x, when x < 0The graph of h(x) will thus be a downward-facing step function, with steps at x = 0, moving from -x to x as x moves from negative to non-negative values. Thus, Option C is correct.
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Which word or phrase describes the value of the function over the interval [ -6, 0]
Answer:
decreasing is the answer
The ratio of cassettes tapes to compact discs is 5 to 2, and the number of cassette tapes is 10 less than 5 times the number of compact discs. How many cassette tapes are there
There are 4 cassette tapes.
Given that,
Let x be the number of compact discs
Then 5 times the number of CD's= 5x and 10 less than 5 times the number of CDs is 5x-10
Therefore the number of cassettes is 5x-10
Now we are told that the ratio of cassettes to CDs which is
((5x-10)/x) equals 5/2 so our equation to solve is:
(5x-10)/x=5/2 multiply both sides by 2x to get rid of the fractions and we get:
2(5x-10)=5x
Further solving this equation, we get:
10x-20=5x
5x=20
x= 4 (number of compact discs)
Thus, there are in total 4 cassette tapes.
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Show the correct relationship between altitude and boiling point.
Altitude
Boiling Point Temp.
The relationship between altitude and boiling point is given below.
What is altitude?
Altitude is the height above sea level. It is usually measured with a barometer or GPS satellite. Altitude can be used to describe the height of an airplane, a mountain, or even the position of a satellite in space. Altitude can also be used to measure how high a person is standing on Earth. Altitude can also be used to compare the relative heights of two different points on Earth. Altitude is an important factor when flying, as it can determine air pressure, air temperature, and wind speed.
Sea Level 212°F
1,000 ft. 211°F
2,000 ft. 210°F
3,000 ft. 209°F
4,000 ft. 208°F
5,000 ft. 207°F
6,000 ft. 206°F
7,000 ft. 205°F
8,000 ft. 204°F
9,000 ft. 203°F
10,000 ft. 202°F
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Which milk product will have approximately 15.36 grams of milk fat in an 80-gram serving?(Heavy Cream: 36.7%, Light Cream 19.2%, Whole Milk 3.5%, Low-Fat Milk 1.5%, Skim Milk 0.05%)
The Light cream with 19.2% content will have 15.36g of milk.
What are percentages?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”
Given here Light cream as 19.2% of 80g
∴ 0.192×80=15.36g
Hence, The Light cream with 19.2% content will have 15.36g of milk.
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i need hlep with this q
The slope of the line is 40 if the points are joined.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
given:
Take two points from the graph as (2, 80) and (4, 160)
Then, the slope of line is
slope, m = ( 160- 80) / ( 4- 2)
slope, m = 80 /2
slope , m = 40
Hence, the slope is 40.
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Points D, B, and E are collinear. Find the value of a so that points A, B, and C
are collinear.
Answer:
Since A, O and B are collinear,
i.e.,
∠
A
O
B
=
180
∘
or,
∠
A
O
D
+
∠
D
O
C
+
∠
B
O
C
=
180
∘
(
x
−
10
)
∘
+
(
4
x
−
25
)
∘
+
(
x
+
5
)
∘
=
180
∘
Or,
x
+
4
x
+
x
−
10
∘
−
25
∘
+
5
∘
=
180
∘
Or,
6
x
−
30
∘
=
180
∘
Or,
6
x
=
180
∘
+
30
∘
=
210
∘
Or,
x
=
210
∘
6
=
35
∘
∠
B
O
C
=
x
+
5
∘
=
35
∘
+
5
∘
=
40
∘
Find the domain and range of the graph
A. D: X ≤ 5
R: y ≤ 7
B. D: X ≤ 7
R: y ≤ 5
C. D : X < 5
R: y < 7
D. D: X < 7
R: y < 5
Domain
The set of x-values that can be inputted into function f(x)Range
The set of y-values that are outputted by function f(x)Interval Notation
ApplicationStep 1: DefineLet's organize what is given to us from the problem.
We are given a graph of a function.
Step 2: SolveWe need to analyze the graph to determine the domain and range of the graph.
If we take a look at our x values, we see that our graph starts at x = 3 and continues infinitely.
∴ we can write the graph's x-values as [3, ∞), or x ≥ 3.
⇒ The domain of the graph is equal to x ≥ 3.
If we take a look at our y values, we see that our graph begins at y = 1 and also continues infinitely.
∴ we can write the graph's y-values as [1, ∞), or y ≥ 1.
⇒ The range of the graph is equal to y ≥ 1.
Answer∴ the answer to the question is equal to:
A. D: x ≥ 3
R: y ≥ 1
___
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Topic: Algebra I
Unit: Functions
you are running a marathon along a straight path. you are approaching mile marker 12 at a speed of 300 feet per minute. you are currently 1500 feet from mile marker 12. write an absolute value equation that models your distance in feet from mile marker 12 after x minutes
Therefore , the solution of the given problem of linear equation comes out to be 1200 = 400x.
What exactly is a linear equation?A linear equation is represented by the algebraic expression y=mx+b. B is the y-intercept, and m is the slope. A "simple formula with 2 factors," where both y and x are variables, is what the previous sentence was referred to as. Calculations with two variables are referred to as "bivariate linear equations." Here are a few illustrations: 2x - 3 = 0; 2y = 8; m + 1 = 0; x/2 = 3; x + y = 2; and 3x - y + z = 3 are the results. A mathematical equation is considered to be linear if its solution has the format y=mx+b, where m stands for the slope and b for the y-intercept.
Here,
Given:
300 feet per minute
where x is the number of minutes,
The Y is 1200.
Thus,
Taking account of all the above information
We get,
This will give us an equation of 1200 = 400x
Therefore , the solution of the given problem of linear equation comes out to be 1200 = 400x.
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What is the product 4y 3 )( 2y^2 3y 5?
The product for the given polynomial is [tex]8y^5 + 6y^4 + 20y^3.[/tex]
When multiplying two polynomials, it is important to keep track of the exponents of each term. The exponents will determine the degree of the resulting polynomial. To find the product, you multiply each term of the first polynomial by each term of the second polynomial, then combine like terms.
In this case, the first polynomial is 4y^3 and the second polynomial is 2y^2 3y 5. To find the product, you would multiply 4y^3 by 2y^2, 4y^3 by 3y, and 4y^3 by 5. This would give you 8y^5, 12y^4, and 20y^3. Since these are the only terms in the product, you simply add them together to get the final answer of [tex]8y^5 + 6y^4 + 20y^3.[/tex]
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!PLEASE HELP ASAP!
These two figures are similar. Find the length of side x.
the length of side x = 12.5.
What is ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
Here, we have,
From the given figure, we get.
These two figures are similar.
so, we have,
8/x=y/5 ............(1)
10/15=4/z ......(2)
8/15=y/z .....(3)
Solving we get,
x=12.5
Hence, the length of side x = 12.5.
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please i need help! anything will help
Answer:
a = 3 or -3
Step-by-step explanation:
a^2 -8 = 1
a^2 = 1 + 8
a^2 = 9
a = - [tex]\sqrt{9}[/tex] or [tex]\sqrt{9}[/tex]
a = 3 or -3
Answer: a = 3, -3
Step-by-step explanation:
Since we want to find what values of a, or x when substituted into the function, equal 1, we will set the function equal to 1 and solve for x.
Given:
f(x) = x² - 8
Set equal to 1:
1 = x² - 8
Subtract 1 from both sides of the equation:
x² - 9 = 0
Difference of squares factoring:
(x - 3)(x + 3) = 0
Answers:
x = 3, -3
So,
a = 3, -3
Why is Avogadro's number 6.02 x10 23?
The value of Avogadro's number is 6.02214076 × 10²³. The ratio of the actual mass of an element to its atomic mass is always constant which is known as Avogadro's number.
What is one mole?
One mole consists of an Avogadro number of atoms. If you are aware of the mole quantity, you can convert a mole into grams.
The mole (symbol: mol) is the unit of material quantity used by the International System of Units. The amount of a substance determines how many elementary entities of that substance are present in an object or sample. The mole must contain precisely 6.02214076×10²³ elementary entities.
The proportionality factor that connects the number of constituent particles (often molecules, atoms, or ions) in a sample with the amount of material in that sample is called the Avogadro constant, also known as NA or L. It has a precise value of 6.02214076 × 10²³ reciprocal moles and serves as a SI defining constant.
It shows how many atoms or molecules make up one gram of an element's or compound's molecular weight. The value is "6.022 × 10²³" when the atomic mass of an element is divided by the actual mass of its atom.
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Aisha bought 15 apples and oranges for $9.00. each orange costs $0.50, and each apple costs $0.65. let x represent the number of oranges and y represent the number of apples. which system can be used to find the number of apples and oranges aisha bought? x y = 15. 0.5 x 0.65 y = 9.00 x = y. 0.5 x 0.65 y = 9.00 x y = 9. 0.5 x 0.65 y = 15.00 x = y. 0.5 x 0.65 y = 15.00
Both (x + y = 15) and (0.5x + 0.65y = 9.00) make up the equation system.
What is an equation ?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
We have LHS = RHS (left hand side = right hand side) in every mathematical equation.
To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.
The statement is not an equation if there is no "equal to" sign in it
According to our question-
x is the quantity of oranges.
y is the quantity of apples.
Oranges plus apples equal 15, or x plus y equals 15, so Aisha purchased 15 pieces of fruit.
Apples cost $0.65 and oranges cost $0.50. The fruit cost Aisha $9.00.
0.5x (the total cost of the oranges) + 0.65y (the total cost of the apples) equals 9.00 (the total cost of the fruit).
x + y = 15
0.5x + 0.65y = 9.00
As a result, the system of equations is (0.5x + 0.65y = 9.00) and (x + y = 15).
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Evaluate the infinite geometric series $0.79 0.079 0.0079 0.00079 0.000079 \dotsb$. Express your answer as a fraction with integer numerator and denominator.
Sum of the infinite geometric series = 79/9
A geometric series, or the first few terms of a geometric sequence, are the sum of an infinite number of terms with a constant ratio between them in mathematics.
Given Geometric sequences,
0.79, 0.079, 0.0079, 0.00079, 0.000079
so, the geometric series is:
0.79 + 0.079 + 0.0079 + 0.00079 + 0.000079 +........
The first term of given geometric series is 0.79
The second term of given series is 0.079
Therefore, the common ration is= 0.079/0.79 = 1/10
The Sum of infinite geometric series is given by, S= a/(1-r)
a here denotes the first term of the series
r denotes the common ration
so,
S = 0.79/{1-(1/10)}
or, S = 0.79/(9/10)
0r, S = 0.79 * (10/9)
0r, S = 79/9
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a wall in marcus's bedroom is 8 2/25 feet high and 16 2/3 long. If he paints 1/2 the wall blue how many square feet will be blue
Answer: 66.70
Step-by-step explanation:
8 2/25 times 16 2/3 then divide by 2 and you get 66.70 will be blue