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?
Determine the correct scientific notation form of the number. 60,700,000,000
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.
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]
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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Please help me on this one I’m stuck
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.
Please Help me I would beg you and 20 points!
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
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.
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.
When solving negative one over three (x − 15) = −4, what is the correct sequence of operations?
Multiply each side by negative one over three , subtract 15 from each side
Multiply each side by −3, add 15 to each side
Multiply each side by negative one over three , add 15 to each side
Multiply each side by 3, subtract 15 from each side
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!
Rewrite the sum of 96+80 using the distributive property as a multiple of a sum of two whole numbers with no common factor
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
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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What is 0.27% as a decimal
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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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
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
Simplify each of the following expressions to find the length of the tightrope.
a) 5+2+8
b) 7+3+2+(-4)
c) 4+9+3
d) 8+6+2+(-5)
How do you find the X and Y values and what theorems must I use?
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?
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).
Rewrite as a simplified fraction 1.1 3 =?
The requried 1.1 3 can be written as a simplified fraction of 44/333.
What is the fraction?A fraction is a mathematical concept that can be used to express a portion of a whole or a number that can be written as the ratio of two integers. In a fraction, the top number is referred to as the numerator, while the bottom number is referred to as the denominator.
Here,
To rewrite 1.1 3 as a simplified fraction, we can first recognize that the repeating decimal can be represented as a fraction using a geometric series.
Let x = 0.133. Then, we can multiply both sides of this equation by 1000 to obtain
1000x = 133.333...
Next, we can subtract x from 1000x to obtain
999x = 133.333... - 0.133...
Simplifying the right side gives
999x = 133.2
Finally, dividing both sides by 999 gives
x = 133.2 / 999 = 44 / 333
Therefore, 1.1 3 can be written as a simplified fraction of 44/333.
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Lena is going to cover her entire garden with topsoil. The garden is 36 feet long by 22 feet wide. A bag of topsoil costs $3 and covers 300 square feet of area. How much will the topsoil for Lena's garden cost?
Can you please help me?
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.
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