Find two consecutive whole numbers that square root of 63 lies between
Answers
Given:
The number \(\sqrt{63}\) lies between two whole numbers.
To find:
The two consecutive whole numbers.
Solution:
The perfect squares of natural numbers are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, ... .
The number 63 lies between 49 and 64.
\(49<63<64\)
Taking square root on each side, we get
\(\sqrt{49}<\sqrt{63}<\sqrt{64}\)
\(7<\sqrt{63}<8\)
Therefore, the number \(\sqrt{63}\) lies between two whole numbers 7 and 8.
Related Questions
F(x)=(x+7)^3 expand the function
Answers
Step-by-step explanation:
F(x) = (x + 7)³
= 3C0 * x³ + 3C1 * x² * 7 + 3C2 * x * 7² + 3C3 * 7³
= x³ + 21x² + 147x + 343.
Answer:
f(x)=x^3+21x^2+147x+343
Step-by-step explanation:
f(x)=(x+7)(x+7)(x+7)
= f(x)=(x^2+14x+49)(x+7)
= f(x)=(x^3+14x^2+49x+7x^2+98x+343)
= f(x)=x^3+21x^2+147x+343
When two lines intersect, they intersect at a...
A) Ray
B
Point
Line
Plane
Answers
Answer:
point
Step-by-step explanation:
Is this no solution?
Answers
Answer: 0=0
Step-by-step explanation:
4(2x-15) = 2(4x-30)
Simplify
8x-60=8x-60
Add 60 to both sides
8x=8x
Answer: 0=0
So the answer is infinite. Theres an infinite about of answers for x.
Answer:
The result of your question would equal: 0 = 0
Step-by-step explanation:
First lets distribute them!
4(2x - 15) = 2(4x - 30)
8x - 60 = 2(4x - 30)
8x - 60 = 2(4x - 30)
8x - 60 = 8x - 60. :
4(2x - 15 = (4x - 30)
8x - 60 = 8x - 60.
Add:
8x - 60 = 8x - 60
8x - 60 + 60 = 8x - 60 + 60
Simplifying:
8x - 60 + 60 = 8x - 60 + 60
8x = 8x - 60 + 60
Again:
8x = 8x - 60 + 60
8x = 8x =
8x - 60 + 60 = 8x - 60 + 60
8x = 86
Subtracting:
8x = 8x
8x - 8x = 8x - 8x
Simplifying again...
Combining like terms
8x - 8x = 8x - 8x
0 = 8x - 8x
0 = 8x - 8x
0 = 0
The answer equals:
0 = 0
You have been answered by one of many helper robots.
Naomi's electricity costs depend on the number of kilowatt hours she uses, as shown in the graph below. According to this graph, which expression can be used to calculate her electricity cost after using x kilowatt hours?
A. 0.06x + 40
B. 0.08x + 20
C. 0.1x + 10
D. 0.12x
Answers
Answer:
b. 0.08x + 20
Step-by-step explanation:
its B because the price goes up $40 every 500 KW's so
40 divided by 500 = 0.08
The expression used to calculate Naomi's electricity cost after using x kilowatt hours is 0.08x+20. Therefore, option B is the correct answer.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
From the graph we have, (500, 60), (1000, 100), (1500, 140) and (2000, 180).
We know that, slope of a line is Slope=(y2-y1)/(x2-x1)
= (100-60)/500
= 40/500
= 0.08
Substitute m=0.08 and (x, y)=(500, 60) in y=mx+c, we get
60=0.08(500)+c
60=40+c
c=20
Substitute m=0.08 and c=20 in y=mx+c, we get
y=0.08x+20
The expression used to calculate Naomi's electricity cost after using x kilowatt hours is 0.08x+20. Therefore, option B is the correct answer.
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A function of the form f(x) = ab is modified so that the b value remains the same but the a value is increased by 2
How do the domain and range of the new function compare to the domain and range of the original function?
Answers
Answer:
Step-by-step explanation:
Notice that f(x) = ab would be a constant function, as 'x' does not appear on the right side. If 'a' were increased by 2, the magnitude of f(x) would be increased by a factor of 2. The domain of f(x) would not change; the range would be [a·(b+2)) (a single numeric value).
FLUENCY
A function is a rule that for every input it assigns
(1) exactly one output
(2) at least one output
(3) two or more outputs
(4) an infinite number of outputs
Answers
A function is a rule that for every input it assigns exactly one output. The Option 1 is correct.
What does a function mean?A function is a rule that assigns each input exactly one output. We call the output the image of the input. The set of all inputs for a function is called the domain. The set of all allowable outputs is called the codomain.
To be able to define the function, we must describe the rule. This is often done by giving a formula to compute the output for any input (although this is certainly not the only way to describe the rule). The key thing that makes rule actually a function is there is exactly one output for each input. That is, it is important that the rule be a good rule.
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Three machines turn out all the products in a factory, with the first machine producing 30% of the products, the second machine 20%, and the third machine 50%. The first machine produces defective products 13% of the time, the second machine 9% of the time and the third machine 9% of the time. What is the probability that a non-defective product came from the second machine
Answers
Answer:
0.2027 = 20.27% probability that a non-defective product came from the second machine
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)
In which
P(B|A) is the probability of event B happening, given that A happened.
\(P(A \cap B)\) is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Non-defective product.
Event B: From the second machine.
Probability of a non-defective product:
100-13 = 87% of 30%(first machine)
100-9 = 91% of 20%(second machine)
100-9 = 91% of 50%(third machine).
So
\(P(A) = 0.87*0.3 + 0.91*0.2 + 0.91*0.5 = 0.898\)
Non-defective and from the second machine:
91% of 20%. So
\(P(A \cap B) = 0.91*0.2 = 0.182\)
What is the probability that a non-defective product came from the second machine
\(P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.182}{0.898} = 0.2027\)
0.2027 = 20.27% probability that a non-defective product came from the second machine
what would be your first step in completely factoring 6a^2-15a+6
Answers
The completely factoring form of 6a^2 - 15a + 6 is 3(2a - 1)(a - 2).
To completely factor the expression 6a^2 - 15a + 6, the first step is to check if there is a common factor among the coefficients (6, -15, and 6) and the terms (a^2, a, and 1).
In this case, we can see that the common factor among the coefficients is 3, so we can factor out 3:
3(2a^2 - 5a + 2)
Now we need to factor the quadratic expression inside the parentheses further. We are looking for two binomials that, when multiplied, give us 2a^2 - 5a + 2. The factors of 2a^2 are 2a and a, and the factors of 2 are 2 and 1. We need to find two numbers that multiply to give 2 and add up to -5.
The numbers -2 and -1 fit this criteria, so we can rewrite the expression as:
3(2a - 1)(a - 2)
Therefore, the completely factored form of 6a^2 - 15a + 6 is 3(2a - 1)(a - 2).
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FILL IN THE BLANK. you transfer $100 from your savings account to your checking account. as a result, m1 will and m2 will .
Answers
You transfer $100 from your savings account to your checking account as a result, m1 will Remains unchanged and m2 will increase by $100.
Checking and savings accounts are also a part of M2. Thus, moving $100 from a savings account to a checking account won't have an impact on M2. Savings accounts are not included in M1, whereas checking accounts are. Therefore, a $100 transfer from savings to checking accounts will result in a $100 rise in M1.The ability to write checks from and access your bank account in a variety of other ways makes a checking account your default daily transaction bank account. You store money in a savings account that you aren't ready to use quite yet, frequently with the intention of building up more.Hence, You transfer $100 from your savings account to your checking account as a result, m1 will Remains unchanged and m2 will increase by $100.
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Y=x^3-4x^2-20x+48 use the rational zero theorem
Answers
The roots of the given polynomial using the rational zero theorem are; 2, -4 and 6.
How to use the rational zero theorem?We are given the polynomial;
y = x³ - 4x² - 20x + 48
Since all coefficients are integers, we can apply the rational zeros theorem.
The trailing coefficient (the coefficient of the constant term) is 48
Find its factors (with the plus sign and the minus sign): ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±16, ±24, ±48.
These are the possible values for p.
The leading coefficient (the coefficient of the term with the highest degree) is 1.
These are the possible rational roots:
±1, ±2, ±3, ±4, ±6, ±8, ±12, ±16, ±24, ±48.
Checking the possible roots: if a is a root of the polynomial P(x), the remainder from the division of P(x) by x - a should equal 0 (according to the remainder theorem, this means that P(a)=0
Plugging in those values, the only ones that yield P(a) = 0 are; 2, -4 and 6.
Thus, these are the roots of the given polynomial.
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2. Increasing the minimum wage has not traditionally caused massive unemployment though traditional economists have argued that it should. Why have changes to minimum wage not affected unemployment too much?
3. The US has one of the lowest federal minimum wages compared to other developed nations. Can you think of reasons why this might be?
4. The real minimum wage has fallen over time with the rise of inflation. This represents less purchasing power for minimum wage workers. Are you ok with that? Why or why not? How many people actually earn at or near minimum wage?
Answers
Despite traditional economic theory suggesting that an increase in the minimum wage should lead to unemployment, the actual impact on employment has been more nuanced. Empirical evidence suggests that moderate increases in the minimum wage have not led to massive job losses, but rather have resulted in small increases in labor costs that are offset by increased productivity and reduced employee turnover. Additionally, higher wages can increase consumer spending, leading to an increase in demand for goods and services, which can ultimately create more jobs.
There are several reasons why the federal minimum wage in the US is lower than in other developed countries. One reason is the political climate in the US, where there is often resistance to government intervention in the labor market. Additionally, many US states have their own minimum wage laws, which can be higher than the federal minimum wage. Finally, the US has a large low-skilled immigrant workforce, which can put downward pressure on wages.
I am not okay with the real minimum wage falling over time with the rise of inflation. Inflation erodes the purchasing power of workers, making it difficult for them to make ends meet. This can lead to increased financial hardship, which can have negative effects on individuals and families. Furthermore, the minimum wage was originally designed to ensure that workers earn a living wage, which is a basic necessity for a decent standard of living. As such, it is important that the minimum wage keep pace with inflation.
According to the Bureau of Labor Statistics, in 2021, about 1.9 million workers in the US earned at or below the federal minimum wage of $7.25 per hour. However, many more workers earn slightly above the minimum wage, and an increase in the minimum wage could potentially raise wages for those workers as well. Additionally, many states have higher minimum wage rates than the federal minimum wage, which means that the number of workers affected by changes to the minimum wage will vary depending on the state.
~~~Harsha~~~
3. One reason why the US has one of the lowest federal minimum wages compared to other developed nations is because of the country's historical emphasis on individualism and free-market capitalism. Many Americans believe that the government should not interfere too much in the economy and that wages should be determined by market forces rather than government regulations. Additionally, some argue that a higher minimum wage would lead to higher prices and inflation, which could hurt the economy as a whole.
4. it could be argued that a falling real minimum wage represents a failure of the system to provide for the basic needs of its citizens. Minimum wage workers may struggle to make ends meet, which can lead to a host of social and economic problems. In terms of the number of people who earn at or near minimum wage, this varies by location and industry, but it is estimated that around 2.3% of US workers earn the federal minimum wage or less.
pls help me hurry-
Graph y=-1/4x+6
Answers
Answer:
Step-by-step explanation:
Answer:
Desmos graphing tool online
Step-by-step explanation:
Y-intercept= 6
X-intercept= 24
Rise. 1
-------- = negative -------
Run. 4
What is the measure of ∠r?
Answers
Write 3,408,000 in expanded form.
Answers
Answer:
3.408 × 10 ^6
Step-by-step explanation:
one card is drawn from a pack of 52cards each of the 52 cards being equally likely to be drawn. what is the probability that the card drawn is a king?
Answers
The probability of drawing a king from a standard deck of 52 cards is 1/13.
In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.
To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).
The total number of possible outcomes is 52 because there are 52 cards in the deck.
The favorable outcomes, in this case, are the four kings.
Therefore, the probability of drawing a king is given by:
Probability = (Number of favorable outcomes) / (Number of possible outcomes)
= 4 / 52
= 1 / 13
Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.
This means that out of every 13 cards drawn, on average, one of them will be a king.
It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.
Each draw is independent, and the probability of drawing a king is constant.
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Given f(-8) = 0 (-8 is a root) and f(5) = 0 (5 is a root), which of these expressions could
possibly be the factored form of the polynomial?
Answers
Given f(-8) = 0 (-8 is a root) and f(5) = 0 (5 is a root), then option d (x+8)(x-5) is the factor form.
What is Polynomial?Polynomials are sums of terms of the form k⋅xⁿ, where k is any number and n is a positive integer.
Given that f(-8) = 0 (-8 is a root) and f(5) = 0 (5 is a root),
Minus eight and plus five are two roots of which expression we have to find.
Among the given options
(x+8)(x-5) is the expression
When we solve this
x+8=0
x=-8
Which is one of the required root
x-5=0
x=5 which is other root.
Hence (x+8)(x-5) is the required factored form of the polynomial
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Find the value of x
Answers
Answer:
x = 13
Step-by-step explanation:
We know that 5x, x+12, and 90 makes a straight line, which is 180 degrees
5x + x+12 + 90 = 180
Combine like terms.
6x+102=180
Subtract 102 from each side.
6x+102-102=180-102
6x = 78
Divide each side by 6
6x/6 = 78/6
x = 13
Answer:
x = 13
Step-by-step explanation:
Now we have to,
→ Find the required value of x.
We know that,
→ The angle of right angle is 90°.
Forming the equation,
→ (x + 12)° + (5x)° = 90°
Then the value of x will be,
→ (x + 12)° + (5x)° = 90°
→ x + 12 + 5x = 90
→ (x + 5x) + 12 = 90
→ 6x + 12 = 90
→ 6x = 90 - 12
→ 6x = 78
→ x = 78 ÷ 6
→ [ x = 13 ]
Hence, the value of x is 13.
finding arc ABC if lines ab, bc, and ac are equal.
Answers
Answer:
60
Step-by-step explanation:
If all lines are equal, all angles will also be the same in this equilateral triangle.
Therefore, divide 180/3 to get Angle ABC
Simplify the polynomial, then evaluate for x = 2.
x+3x²+2x-3-4x²+6
x² + 3x + 9; 19
x² + 3x + 3; 5
-x² + 3x + 9; 11
O
O
-x² + 3x + 3; 13
Answers
Answer:
x^2 + 3x + 9 = (x + 3)(x + 3)
When x = 2, we have:
(2 + 3) * (2 + 3)
5 * 5
25
The sum of three integers is 12. The sum of the first and second integers exceeds the third by 32. The third integer is 15 less than the first. Find the three integers.
Answers
Step-by-step explanation:
So we know the sum of three integers is 12
x+y+z=12
Next we know that the sum of the first and second integer is more than the third by 32
x+y=z+32
Finnaly, we can see that the third is 15 less than the first.
x-15=z
Now time to put it all together.
x+(x-15+32-x)+(x-15)=12
2x-15-15+32=12
2x-30+32=12
2x+2=12
2x=14
x=7
Now time to plug it all in
7 also known as x minus 15 = z
7-15=-8
z=-8
Next we can plug it in the first equation.
7+y-8=12
-1+y=12
y=11
Now time to check if I am correct(spoiler, if it's posted it means I am correct :D)
x=7,y=11,z=-8
7+11-8=12
Yay there is ur answer.
Answer: First Integer Is 7, 2nd is 11, third is -8
P.S. Sorry if it is correct, my first answer.
A farmer plans to plant wheat and rye. However, he has only $1200 to spend. Each acre of wheat costs $200 to plant and each acre of rye costs $100 to plant. Moreover, the farmer has to get the planting done in 12 days before it's too late. It takes one day to plant an acre of wheat and 2 days to plant an acre of rye. If the profit is $500 per acre of wheat and $300 per acre of rye. How many acres of each should be planted to maximize profits
Answers
9514 1404 393
Answer:
4 acres each of wheat and rye
Step-by-step explanation:
Let x and y represent acres of wheat and rye, respectively. Then the constraints of the problem are ...
200x +100y ≤ 1200 . . . . . . cost constraint
x + 2y ≤ 12 . . . . . . . . . . . time constraint
The objective is to maximize profit (p):
p = 500x +300y
The constraints can be graphed (see attached). The profit function will be maximized at one of the vertices of the "feasible region," the portion of the graph that satisfies the constraints. The vertices are (x, y) = (0, 6), (4, 4), and (6, 0). The associated profit values are $1800, $3200, and $3000.
Maximum profit is obtained when 4 acres of wheat and 4 acres of rye are planted.
PROBLEM
A theater is selling tickets to a
"preview night" of their new
musical. The tickets cost $12 per
adult and $7.50 per child. Due to
limits on seating, they can sell no
more than 150 tickets. However,
they would like to make at least
$675 from ticket sales.
How do I graph this
Answers
We know that the theater can sell no more than 150 tickets, so the graph should be limited to the region where the sum of the x and y values is less than or equal to 150. This creates a triangular region in the coordinate plane.
Next, we need to find the equation of the line that represents the minimum revenue of $675. Let's call the number of adult tickets sold "x" and the number of child tickets sold "y". Then, the revenue can be expressed as:
Revenue = 12x + 7.5y
We want to find the equation of the line where Revenue = $675. This can be written as:
12x + 7.5y = 675
Solving for y, we get:
y = (-4/5)x + 90
This is the equation of a line with a y-intercept of 90 and a slope of -4/5.
To graph this line, we can plot the y-intercept (0, 90) and then use the slope to find additional points. For example, if we increase the number of adult tickets by 5, the number of child tickets must decrease by 4 to maintain the same revenue. So, we can plot the point (5, 86) on the line.
Finally, we can shade the region of the graph that satisfies both the revenue requirement and the ticket limit. This is the intersection of the triangular region and the region above the revenue line. The shaded region represents all the possible combinations of adult and child tickets that satisfy the constraints of the problem.
I would like a cobweb graph of Newton's Method in python using MatPlotLib please! Something similar to the graph attached please
Answers
The steps to visualize Newton's Method by using Matplotlib and PIL is mentioned below.
Describe Derivative?In calculus, the derivative is a fundamental concept that describes how a function changes with respect to its input variable. More specifically, the derivative of a function represents the instantaneous rate of change of the function at a particular point.
Geometrically, the derivative can be interpreted as the slope of the tangent line to the graph of the function at a specific point. If the derivative is positive, the function is increasing at that point; if it is negative, the function is decreasing. A derivative of zero indicates that the function has a stationary point at that location.
To create visualizations of Newton's Method, you will need to use a programming language like Python and some libraries such as Matplotlib, PIL, and NumPy.
Here are some steps you can follow:
Define the function f(x) you want to find the roots of, and its derivative f'(x).Write a function that implements Newton's Method using the formula X_n+1 = Xn-(f(x_n))/ f'(x_n).Choose a starting point x_0 and apply the Newton's Method function to it.Plot the convergence of Newton's Method using Matplotlib. You can plot the function f(x) and the iterations of the Newton's Method on the same plot to see how it converges to the root. You can also plot the convergence rate of the method for different starting points.Use PIL to create a visualization of the basins of attraction for a given function. You can use NumPy to generate a mesh grid of complex numbers in the complex plane and apply Newton's Method to each point to determine which root it converges to. You can then color each point according to which root it converges to and display the resulting image using PIL.By following these steps, you can create interesting visualizations of Newton's Method and explore the properties of this powerful numerical method.
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What does the point (12,4) represent in this situation?
Answers
Answer:
what is the situation?
Step-by-step explanation:
Venessa bought 80 apples for 4$.out of these apples 25 precent were rotten and had to be thrown away Vanessa sold the remaining apples at 6 cents per apple. What is the profit or loss percentage
Answers
The loss percentage is 91%.Given that Venessa bought 80 apples for 4$, out of these apples, 25% were rotten and had to be thrown away. Venessa sold the remaining apples at 6 cents per apple.To calculate the profit or loss percentage, we need to determine the cost price, selling price, and the number of apples sold.
Cost price (CP) = 4 $.Selling price (SP) = 80 × 0.75 × 6 cents= 36 cents = 0.36 $.Now, let's calculate the profit.Profit = SP – CP= 0.36 $ – 4 $= – 3.64 $Loss = CP – SP= 4 $ – 0.36 $= 3.64 $.
Therefore, Venessa incurred a loss of $3.64 when she sold 80 apples at 6 cents per apple.Now let's calculate the loss percentage Loss Percentage = (Loss / CP) × 100= (3.64 / 4) × 100= 91%.
Therefore, the loss percentage is 91%.Note: If the result obtained after the subtraction of SP from CP is negative, it means there is a loss, and the percentage of loss can be calculated by (loss/CP) × 100.
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Eighteen less than 9 times a number is the same as 22 more than the number. what's the number ? Please 20 points!
Answers
Answer:
5
Step-by-step explanation:
let "a number" be y
Set up equation
9y-18=y+22
solve
8y=40
y=5
Pls help it's due tonight!!!
:((((((
Answers
i hope i’m right good luck ,:D
Answer:
∆EDA~∆ECB (AAA)
3÷ (15+3) = AB ÷ (12+AB)
AB = 2.4
Jo has a 10 GB monthly cell phone plan. Jo has used 8 GB in the first 10 days of the month. At that rate, how many GB will Jo use after a month of 30 days?
Answers
Answer:
Step-by-step explanation:
1st 10 days - 8 GB
2nd 10 days - 8 GB
3rd 10 days - 8 GB
________________
30 days - 24 GB
I will give 20 points for this question please help because this is hard
Answers
Area of triangle A = 7.5 square units.
Area of triangle B = 15 square units.
Area of the whole figure = 22.5 square units.
How to Find the Area of a Triangle?To find the area of a triangle, the formula used is expressed as: A = 1/2 × length of the base of the triangle × height of the triangle.
Calculate the area of triangle A:
Height of triangle A = 3 units
Length of the base of triangle A = 5 units
Area of triangle A = 1/2 × 5 × 3
Area of triangle A = 7.5 square units.
Calculate the area of triangle B:
Height of triangle B = 3 units
Length of the base of triangle B = 10 units
Area of triangle B = 1/2 × 10 × 3
Area of triangle B = 15 square units.
Calculate the area of the whole figure:
Area of the whole figure = area of A + area of B
Area of the whole figure = 7.5 + 15
Area of the whole figure = 22.5 square units.
In summary, we have:
Area of triangle A = 7.5 square units.
Area of triangle B = 15 square units.
Area of the whole figure = 22.5 square units.
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4
What is the value of the expression (81
(804)
?
O A 3
OB. 12
O c. 27
OD. 81
Answers
1/4 x 4 = 1
81^1 = 81