Rewrite the sum of 96+80 using the distributive property as a multiple of a sum of two whole numbers with no common factor
which of the following is equal to 5 4/9 5.49 5.25 7.25 5.4
Answer:
5.4
Step-by-step explanation:
We are given that
[tex]5\frac{4}{9}[/tex]
We have to find the value which is equivalent to given fraction number.
[tex]5\frac{4}{9}=\frac{45+4}{9}[/tex]
[tex]5\frac{4}{9}=\frac{49}{9}[/tex]
When we divide 49 by 9 then we get
[tex]\frac{49}{9}=5.4444[/tex]
It can write as 5.4
Hence, [tex]5\frac{4}{9}=5.4[/tex]
Answer:5.4
The mass of a an atom of helium is 6.65 x 10^−24. Use scientific notation to express the mass of 250 helium atoms.
A) 1.6625 x 10−21
B) 1.6625 x 10−22
C) 1.6625 x 10−24
D) 1.6625 x 10−26
Scientific notation is the way of writing a large number between 1 to 10 with a power of 10.
The mass of one atom is 6.65 x [tex]10^{-24}[/tex]
The mass of 250 helium atoms is 1662.5 x [tex]10^{-24}[/tex].
The scientific notation to express the mass of 250 helium atoms is
1.6625 x [tex]10^{-21}[/tex].
What is scientific notation?It is the way of writing a large number between 1 to 10 with a power of 10.
Example:
1.2 x 10² is in scientific notation.
9.1 x 10³ is in scientific notation.
We have,
Mass of one atom of helium = 6.65 x [tex]10^{-24}[/tex]
Mass of 250 atoms of helium:
= 250 x 6.65 x [tex]10^{-24}[/tex]
= 1662.5 x [tex]10^{-24}[/tex]
Now,
We will make 1662.5 into a number between 1 and 10.
1662.5
= (1662.5/1000) x 1000
= 1.6625 x 10³
Now,
= 1.6625 x 10³ x [tex]10^{-24}[/tex]
= 1.6625 x [tex]10^{3 - 24}[/tex]
= 1.6625 x [tex]10^{-21}[/tex]
Thus,
The mass of one atom is 6.65 x [tex]10^{-24}[/tex]
The mass of 250 helium atoms is 1662.5 x [tex]10^{-24}[/tex].
The scientific notation to express the mass of 250 helium atoms is
1.6625 x [tex]10^{-21}[/tex].
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six is greater than or equal to the quotient of a number y and 2.5
The statement 'six is greater than or equal to the quotient of a number y and 2.5,' can be converted into the inequality 6 >= y/2.5. Solving for y by multiplying both sides by 2.5 gives y <= 15. Therefore, any number y that is 15 or less will satisfy this inequality.
Explanation:The question provided, 'six is greater than or equal to the quotient of a number y and 2.5,' requires manipulation of an inequality in mathematics to find the potential values of y. To represent this in mathematical terms, one could write the inequality as 6 ≥ y/2.5. From here, it is a simple matter of isolating y by multiplying both sides of the inequality by 2.5, which results in y ≤ 15. Therefore, any number y that is less than or equal to 15 satisfies the inequality.
Inequality, Isolating variables and Mathematical terms are vital concepts for understanding and solving problems in algebra.
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Which ordered pairs lie on the graph of the exponential function f(x)=4(5)2xf(x)=4(5)2x ?
Select each correct answer.
(−1,425)(−1,425)
(0,0)
(1,4)
(2,2500)
The ordered pairs lie on the graph of the exponential function [tex]\rm f(x) = 4(5)^{2x}[/tex] is (2,2500) and this can be determined by using the arithmetic operations.
Given :
Exponential Function --- [tex]\rm f(x) = 4(5)^{2x}[/tex]
The following steps can be used in order to determine the ordered pairs lie on the graph of the exponential function:
Step 1 - Write the exponential function.
[tex]\rm f(x) = 4(5)^{2x}[/tex]
Step 2 - Substitute the value of (x = -1425) in the above exponential function.
[tex]\rm f(x) = 4(5)^{2\times -1425}[/tex]
[tex]\rm f(x) = 4(5)^{-2850}[/tex]
By simplifying the above function it does not give the value of f(x) = -1425, therefore, option (A) is incorrect.
Step 3 - Substitute the value of (x = 0) in the above exponential function.
[tex]\rm f(x) = 4(5)^{2\times 0}[/tex]
f(x) = 4
Therefore, option (B) is also incorrect.
Step 4 - Substitute the value of (x = 1) in the above exponential function.
[tex]\rm f(x) = 4(5)^{2\times 1}[/tex]
f(x) = 100
Therefore, option (C) is also incorrect.
Step 5 - Substitute the value of (x = 2) in the above exponential function.
[tex]\rm f(x) = 4(5)^{2\times2}[/tex]
f(x) = 2500
Therefore, option (D) is correct.
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Henry is building a fence in his backyard for his new puppy he has 36 ft of fencing and wants to fence in a rectangular area what is one set of whole number dimensions of the fenced-in area
Let f(x)=2(3)^x+1 +4. The graph of f(x) is stretched vertically by a factor of 2 to form the graph of g(x). What is the equation of g(x)?
the equation of g(x) after stretching the graph of f(x) vertically by a factor of 2. Therefore, the equation of g(x) is g(x) = 4(3)^x+1 + 8.
To stretch the graph of (f(x)) vertically by a factor of 2 to form the graph of ( g(x)), we need to multiply the entire function (f(x)) by 2.
Given:
[tex]\[ f(x) = 2(3)^{x+1} + 4 \][/tex]
To stretch the graph vertically by a factor of 2, we multiply the function by 2:
[tex]\[ g(x) = 2 \cdot f(x) \][/tex]
Substitute the expression for [tex]\( f(x) \):[/tex]
[tex]\[ g(x) = 2 \cdot [2(3)^{x+1} + 4] \][/tex]
Now, distribute the 2 inside the brackets:
[tex]\[ g(x) = 4(3)^{x+1} + 8 \][/tex]
This is the equation of [tex]\( g(x) \)[/tex] after stretching the graph of [tex]\( f(x) \)[/tex] vertically by a factor of 2.
Therefore, the equation of [tex]\( g(x) \) is \( g(x) = 4(3)^{x+1} + 8 \).[/tex]
is the expression 3x + 2x - 4 in simplest form?Explain.
round 98984 to one significant figure
The number 98984 rounded to one significant figure is 100000
What is rounding up numbers?
There are basically two rules while rounding up numbers
If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down and if the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.
Non-zero digits are always significant
Zeros between non-zero digits are always significant
Leading zeros are never significant
Trailing zeros are only significant if the number contains a decimal point
Given data ,
Let the number be N
The value of N = 98984
Now , the number N has 5 significant numbers
So , the next higher number where N can be rounded is
Now , the number N can be rounded to one significant figure by
The nearest number which the number N can be rounded of to is 100000
So , Let the number 100000 = M
Now , the number M has only 1 significant number and is close to 98984
Therefore , the value of M is 100000
Hence , The number 98984 rounded to one significant figure is 100000
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Yi and Sue play a game. They start with the number $42000$. Yi divides by a prime number, then passes the quotient to Sue. Then Sue divides this quotient by a prime number and passes the result back to Yi, and they continue taking turns in this way.
For example, Yi could start by dividing $42000$ by $3$. In this case, he would pass Sue the number $14000$. Then Sue could divide by $7$ and pass Yi the number $2000$, and so on.
The players are not allowed to produce a quotient that isn't an integer. Eventually, someone is forced to produce a quotient of $1$, and that player loses. For example, if a player receives the number $3$, then the only prime number (s)he can possibly divide by is $3$, and this forces that player to lose.
Who must win this game, and why?
Answer:
The first person starting will always lose.
Step-by-step explanation:
First, I will the prime factorization of 42000. After finding the prime factorization of 42000, I will count the number of primes in the prime factorization. After that, we will find which round the person will lose.
Prime Factorization of 42000: 2*2*2*2*3*5*5*5*7
Number of Primes in List: 9
The person losing: The person on the 9th turn will lose.
The person on the 9th turn is Yi. Therefore, no matter how Yi or Sue keeps mixing the order of the numbers, Yi will always lose.
I hope this helps!
Karen runs a print shop that makes posters for large companies. It is a very competitive business. The market price is currently $1.00 per poster. She has fixed costs of $250.00. Her variable costs are $1,500 for the first thousand posters, $1,200 for the second thousand, and then $800 for each additional thousand posters.What is her AFC per poster if she prints 1,000 posters? What is her AVC and ATC?
which of the following is the correct graph of the compound inequality 4p+1>-7 or 6p+3 <33?
Answer:
set of all real numbers (-∞,∞)
Step-by-step explanation:
Solve each inequality
[tex]4p+1>-7[/tex]
Subtract 1 from both sides
[tex]4p>-8[/tex]
Divide by 4 on both sides
[tex]p>-2[/tex]
[tex]6p+3 <33[/tex]
Subtract 3 from both sides
[tex]6p<30[/tex]
Divide both sides by 6
[tex]p<5[/tex]
[tex]p>-2[/tex] or [tex]p<5[/tex]
The graph is attached below
The sum of five consecutive numbers is -75. Which number is the least of these five numbers?
Simplify.
43 · 44 / 49
A) 4^16
B) 4^2
C) 1/4^2
D) 1/4
Answer: The correct option is C.
Explanation:
The given expression is,
[tex]\frac{4^3.4^4}{4^9}[/tex]
Using the exponent rule [tex]a^m.a^n=a^{m+n}[/tex] , we get,
[tex]\frac{4^{3+4}}{4^9}[/tex]
[tex]\frac{4^{7}}{4^9}[/tex]
Using the exponent rule [tex]\frac{a^m}{a^n}=a^{m-n}[/tex] , we get,
[tex]{4^{7-9}}[/tex]
[tex]4^{-2}[/tex]
Using the exponent rule [tex]\frac{1}{a^n}=a^{-n}[/tex] , we get,
[tex]4^{-2}}=\frac{1}{4^2}[/tex]
Therefore, the option C is correct.
At the beginning of the year, Adrian's savings account balance was $28. Each week, he deposits another $15 into that account, and he doesn't spend any of his savings.
Is his savings account balance proportional to the number of weeks since the start of the year?
Answer:
The given condition is not proportional.
Step-by-step explanation:
At the beginning of the year, Adrian's savings account balance was $28.
Let Adrian invests for 'x' weeks.
So, total amount will becomes :
[tex]28+15x[/tex]
Since 4 weeks = 1 month, it will represent a linear equation only.
Linear functions have a constant rate of change and describe a straight line on a graph. So, this is not proportional.
The given equation is in the form y = mx + b, so its linear. For the equation to be proportional, it should be in the form of y = kx.
In a competition where the teams have five members, the rule is that the members of each team must have birthdays in the same months. How many persons are needed in order to guarantee that they can raise a team? But two teams?
To guarantee a team, you would need 13 persons, and to guarantee two teams, you would need 24 persons.
Explanation:The number of persons needed to guarantee that they can raise a team is one more than the number of months in a year. This is because there are 12 months in a year, and to ensure that all team members have birthdays in the same month, you would need at least one person for each month. Therefore, you would need 13 persons to guarantee a team.
To guarantee that there are two teams, you would need a total of 24 persons. This is because each team needs at least one person for each month, and there are 12 months in a year. So, for the first team, you would need 13 persons, and then you would need an additional person for each month to form the second team. This would give you a total of 24 persons to guarantee two teams.
Final answer:
To guarantee that a team can be formed, there needs to be at least one person born in each month of the year. To guarantee that two teams can be formed, you would need at least two people born in each month of the year.
Explanation:
To guarantee that a team can be formed, there needs to be at least one person born in each month of the year. Since there are 12 months, you would need a minimum of 12 people to ensure that a team can be formed.
To guarantee that two teams can be formed, you would need at least two people born in each month of the year, as each team needs five members. So, you would need a minimum of 24 people to ensure that two teams can be formed.
I am asking the same question again in the hope of finding a more detailed answer. Explain why the two figures below are not similar.
Stan's steak house has the server to cook ratio of 5 to 2 the total number of servers and Cooks is 42 how many servers does Stan Steakhouse in employ
What is the measure of angle x?
2(b+3c) equivalent expressions
Options:
3(b+2c)
(b+3c) +(b+3c)
None of the above
The correct answer to the given expression 2(b+3c) is 'None of the above' as none of the provided options represent an equivalent expression after the application of distributive property.
Explanation:The expression 2(b+3c) cannot be transformed into any of the given options directly. If we use distributive property, we expand 2(b+3c) to get 2b + 6c, which is equivalent to the original expression.
The options provided, such as 3(b+2c), (b+3c) +(b+3c), or 'None of the above', do not simplify or represent an equivalent expression to 2(b+3c). The correct answer is 'None of the above'. It's important to note that the commutative property of addition, A+B = B+A, and the associative property, (A+B) + C = A +(B+C), suggest that we can regroup or reorder terms in an addition expression without changing its value. However, none of these properties help in finding an equivalent expression among the given options for 2(b+3c).
If the side of a square is doubled and then increased by 7, the new perimeter is 8 more then 3 times the old perimeter. What is the side of the original square?
To find the side of the original square, we can set up an equation and solve for x.
Explanation:To solve this problem, let's assume that the side length of the original square is 'x'. If we double it, the new side length would be '2x'. Adding 7 to it gives us '2x + 7'.
The new perimeter of the square is 8 more than 3 times the old perimeter, so we can set up the equation: 2(2x + 7) = 3(4x).
Simplifying this equation, we get 4x + 14 = 12x. By rearranging the equation, we find that 8x = 14, which leads to x = 1.75.
Therefore, the side length of the original square is 1.75 units.
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Which equation shows y=34x−52 in standard form? 4x−3y=−10 3x−4y=10 3x−4y=−10 4x−3y=10
Answer: The equation that shows y=(3/4)x-5/2 is standard form is:
Second option: 3x-4y=10
Solution:
y=(3/4)x-5/2
Standard form of the equation Ax+By=C, with A, B, and C integer numbers
The coefficient of "x" and the independent term are fractions. To simplify them, let's multiply both sides of the equation by 4:
4y=4 [ (3/4)x-5/2]
4y=4(3/4)x-4(5/2)
4y=(4/1)(3/4)x-(4/1)(5/2)
4y=[(4*3)/(1*4)]x-(4*5)/(1*2)
4y=(12/4)x-20/2
4y=3x-10
The two variables must be in the same side of the equation and the independent term in the other side, but the coefficient of "x" must be positive, then subtracting 4y and adding 10 both sides of the equation:
4y-4y+10=3x-10-4y+10
10=3x-4y
3x-4y=10
Answer:
its B i took the test explanation:
How do you find the X and Y values and what theorems must I use?
Can you please help me?
marlis has 765 cards in her baseball collection. she sells 153 of cards. What is the percent of decrease in the number of cards in the collection?
Answer:
20%
Step-by-step explanation:
(765 - 153)/765*100
(612)/765*100
0.8*100
80% of original
100% - 80% = 20% reduction
Please Help me I would beg you and 20 points!
What is 0.27% as a decimal
Which figure does not appear to be congruent to this one?
Answer:
Choice C is the correct one.Step-by-step explanation:
In the image you can observe that the third choice doesn't appear to be congruent to the given one, beacuse it's smaller.
On the other hand, choice A, B and D, have figures that apparently are the same size and shape to the given one, they were just rotated, which is a rigid transformtion, that is, they just move, their size or shape doesn't shape.
Therefore, the right answer is C figure.
Kevin is 3 times as old as Daniel, 4 years ago, Kevin was 5 times as old as Daniel. How old is Kevin
By using equations to represent the relationship between Kevin and Daniel's ages, we can determine that Kevin is 24 years old.
Kevin is 3 times as old as Daniel. Let's denote Kevin's age as K and Daniel's age as D. From the information given, we can form two equations:
K = 3D
K - 4 = 5(D - 4)
3D - 4= 5D -20
16 = 2D
D = 8
K = 24
Solving these equations simultaneously gives the age of Kevin, therefore, Kevin is 24 years old.
What is the value of x?
x = ?
x^2 +6^2 = 10^2
x^2 + 36 =100
x^2 = 64
x = sqrt(64)
x = 8