Polya's 4 step method is a process designed to help problem solvers become better at tackling difficult problems.
It was developed by the mathematician George Polya in 1945 and consists of four basic steps:
1. Understand the problem: The first step is to read and understand the problem. This means understanding the problem and identifying what information is given and what is required.
2. Devise a plan: The second step is to identify a strategy or plan of attack. This involves breaking the problem down into smaller parts, identifying the key elements, and using logical reasoning to identify a solution.
3. Carry out the plan: The third step is to execute the plan. This involves following the steps of the plan in order to solve the problem.
4. Look back: The fourth and final step is to take a look back at the solution and evaluate it. This involves checking to make sure the solution is correct and making any necessary adjustments.
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Ok can someone help me with this?
Answer:
1. 14
2. 2.83
3. 6.71
4. 8.77
5. 9.22
6. 5.20
7. 2.45
8. 19
9. I would love to help you with this but I don't know what it means by "circled problems"
Step-by-step explanation:
Answer:
Circle questions 2, 3, 4, 5, 6, 7
Simplified square root:
1. 14
2. 2.8
3. 6.7
4. 8.8
5. 9.2
6. 5.2
7. 2.4
8. 19
Step-by-step explanation:
I'm sure you can do the line plot. It's pretty mandatory.
Question #9:
If a number can be written or can be converted to p/q form, where p and q are integers and q is a non-zero number, then it is said to be rational and if not then it is irrational.
If you don't understand how to draw a line graph then check the two photos as a guide. Hope it helped :)
According to the linear regression model, the men’s world record mile run time in 1940 would have been how many seconds?
The men’s world record mile run time in 1940 would have been 10.454 seconds
Here, the equation of the linear function that best fits the data (the line of best fit) is Finishing time = 10.878 - 0.0106(Year after 1900)
Let k be the finishing time in seconds and t be the number of years after 1900
So, the equation of regression line becomes,
k = 10.878 - (0.0106) t
To find the the men’s world record mile run time in 1940 first we find the the number of years (t)
t = 1940 - 1900
t = 40 years
So, the finishig time (k) would be,
k = 10.878 - (0.0106) × 40
k = 10.454 seconds
Therefore, the finishing time was 10.454 seconds
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Forming Equations with a given variable
1. The ages of three cats are and. Their total age is
21. Determine.
The value of {a} in the given modelled statement equation is 5.
What are equations?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign "=".
Given is that the ages of three cats are (a) , (a + 4) and (2a - 3). Their total age is 21.
We can model the given equation is -
(a) + (a + 4) + (2a - 3) = 21
a + a + 4 + 2a - 3 = 21
4a + 1 = 21
4a = 20
a = 5
Therefore, the value of {a} in the given modelled statement equation is 5.
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{
Complete question is given below -
The ages of three cats are a, a+4 and 2a-3. Their total age is 21. Determine a.
}
help help help help help help help
The required point-slope form of the equation of the line is y - 20= -5(x + 1).
Given that, To determine an equation in point-slope form for the line that passes through the point with the given slope. point: (-2,-20) and m=-5.
What is the slope of the line?The slope of a line is the measure of the steepness and the direction of the line. Finding the slope of lines in a coordinate plane can help in predicting whether the lines are parallel, perpendicular, or none without actually using a compass.The slope of any line can be calculated using any two distinct points lying on the line. The slope of a line formula calculates the ratio of the "vertical change" to the "horizontal change" between two distinct points on a line. In this article, we will understand the method to find the slope and its applications.To learn more about point-slope refer to:
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I need help with my final!
Answer:
it is c
Step-by-step explanation:
What is 5c−3d−12c+d−6 written in simplest form?
To simplify the expression 5c−3d−12c+d−6, we can combine like terms:
5c − 12c + d − d − 6 = (-12c + d) + (-6)
Therefore, the expression 5c−3d−12c+d−6 can be simplified to -12c + d - 6.
How many cups are in 7 liters of water? (round to 3 decimal points only, use c for
cups) *
Answer:
29.587 Happy Learning :)
The data below shows the survey result of 75 randomly selected students.
The school has 1,138 students total. Based on the results of the poll, how many of the school's students should be expected to travel by car? Round your answer to the nearest whole number.
Show your work using the sketch board OR you may insert an image of your work on the following slide.
Chart relating to the question is attached below.
Answer:
349 students
Step-by-step explanation:
Based on the chart given, we can obtain the experimental probability or proportion for the travel plan of 75 students :
Proportion who would be traveling by car :
Number traveling By car / number of samples
p(car) = 23 / 75 = 0.30666
If total number of students = 1138
Using the proportion obtained from the sample, the number of students who would be traveling by car from the population would be :
= 0.30666 * 1138
= 348.98 students
= 349 students
If the figure is translated 4 units left what are the coordinates
Answer: (-4,0)
Step-by-step explanation:
Answer: A
Step-by-step explanation:
- Left and right translations affect the x-coordinate
- subtract 4 from the x-coordinate
What is an intractable problem?
Answer: A problem is said to be intractable if there is no efficient algorithm to solve it.
Intractable problems are common. We need to discuss how we approach it when we actually encounter it.
Step-by-step explanation:
How many colours do you need to colour a graph such that no adjacent vertices are of the same colour showed in the image below?
Conclusion : Provided the graph with a large number of vertices, we see that we are again faced with resorting to a systematic tracing of all paths, comparison of the neighbour's colours, backtracking, etc resulting in exponential time complexity once again.
elsa received a $80 dollar gift card for a coffee store. she used it in buying some coffee that cost $7.52 per pound. after buying the coffee, she had $34.88 left on her card. how many pounds of coffee did she buy?
Elsa purchased 6 pounds of coffee.
What is product pricing?The process of figuring out a product's quantitative worth based on both internal and external elements is called product pricing. Product price directly affects your company's entire success, including cash flow, profit margins, and client demand.
Here is an easy example of value-based pricing. When you bring a young child to a petting zoo, she expresses a desire to feed the goats. The goat food dispenser is topped off with a quarter. From a financial standpoint, there is the price of the goat food, which is around two cents.
Calculate the total cost of all the items you bought. To calculate the cost price, divide the total cost by the quantity of units purchased. To determine the ultimate price, use the selling price formula: Cost price plus profit margin equals selling price.
Since she started with $80 and ended with with $34,88, we can find the total amount she spent by subtracting these amounts:
$80 - $34.88 = $45.12
This means that she spent $45.12 on coffee. If each pound cost $7.52, we can divide $45.12 by $752 to see how many pounds she bought (ignoring tax):
45.12 / 7.52 = 6 pounds of coffee purchased
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A, B & C form the vertices of a triangle.
∠ CAB = 90°, ∠ ABC = 73° and AB = 9.4
Answer:
cos37= 9.4/BC,cos37=0.8
BC= 9.4/0.8
bc = 11.75
Answer:
BC ≈ 32.2
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos73° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AB}{BC}[/tex] = [tex]\frac{9.4}{BC}[/tex] ( multiply both sides by BC )
BC × cos73° = 9.4 ( divide both sides by cos73° )
BC = [tex]\frac{9.4}{cos73}[/tex] ≈ 32.2 ( to 3 sf )
Solve for the variable using cross products.
3/5 = x/6
Solve for x as a decimal
Answer:
x = 3.6
Step-by-step explanation:
3/5 = x/6
multiply both sides by 6
18/5 = x
as a decimal
x = 3.6
Answer:
x = 3.6
Step-by-step explanation:
3/5 = x/6
multiply both sides by 6
18/5 = x
as a decimal
x = 3.6
Which statement correctly identifies an asymptote of f (x) = StartFraction 16 x squared minus 35 Over x squared minus 5 EndFraction using limits?
Because Limit of f (x) as x approaches plus-or-minus infinity = 7, the function has a vertical asymptote at x = 7.
Because Limit of f (x) as x approaches plus-or-minus infinity = 7, the function has a horizontal asymptote at y = 7.
Because Limit of f (x) as x approaches plus-or-minus infinity = 16, the function has a vertical asymptote at x = 16.
Because Limit of f (x) as x approaches plus-or-minus infinity = 16, the function has a horizontal asymptote at y = 16.
Answer:
D
Step-by-step explanation:
Edge
The limit of x approaching infinite of a function gives it's horizontal assymptote. We use this to solve the question, getting the following answer:
Because Limit of f (x) as x approaches plus-or-minus infinity = 16, the function has a horizontal asymptote at y = 16.
Horizontal asymptote:
An horizontal asymptote is the value of y given by:
[tex]y = \lim_{x \rightarrow \infty} f(x)[/tex]
In this question:
[tex]f(x) = \frac{16x^2 - 35}{x^2 - 5}[/tex]
The horizontal asymptote is:
[tex]y = \lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} \frac{16x^2 - 35}{x^2 - 5}[/tex]
Considering it is a limit of x going to infinite, we just consider the terms with the highest exponents both in the numerator and in the denominator, so:
[tex]y = \lim_{x \rightarrow \infty} \frac{16x^2 - 35}{x^2 - 5} = \lim_{x \rightarrow \infty} \frac{16x^2}{x^2} = \lim_{x \rightarrow \infty} 16 = 16[/tex]
Thus, the correct answer is:
Because Limit of f (x) as x approaches plus-or-minus infinity = 16, the function has a horizontal asymptote at y = 16.
From the graph of the function, given at the end of this answer, you can check that as x goes to infinity, y(green line) approches 16(blue line).
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What is the surface area of the following prism
Answer:
588 ft^2
Step-by-step explanation:
Lets start by making either a mental or physical list of the different sized sides on the prism. Check that the number of sides you assign to the dimensions has an overall total of six. I've made that mistake before lol it was a bit depressing.
16x6, two sides16x9, two sides6x9, two sidesthats 96 ft^2, and two sides makes it 192 ft^2thats 144 ft^2, and two sides makes it 288 ft^2thats 54 ft^2, and two sides makes it 108 ft^2We can now add all of our values up:
192 + 288 + 108 = 588 ft^2
24 less than z is less than 12.
Answer:
36
Step-by-step explanation:
24+12=36
Working together, two pumps can drain a certain pool in 3 hours. If it takes the older pump 9 hours to drain the pool by itself, how
long will it take the newer pump to drain the pool on its own?
Do not do any rounding.
Plz help me with this worksheet, I will give brainliest
Answer:
Step-by-step explanation:
You don't seriously want someone to answer all those problems, do you?
I will tell you that you need to use the Pythagorean theorem, the side relationship in a 30-60-90 and a 45-45-90 triangle. Get off your rear and go for it!!!
8. Given : triangle PQR and triangle TSR are right triangles , R is the midpoint of overline PT , overline PQ cong overline TS Prove : Delta PQR cong Delta TSR
By using the ASA Congruence Theorem, Delta PQR is congruent to Delta TSR.
We can prove this by using the fact that triangle PQR and triangle TSR are both right triangles and that R is the midpoint of overline PT and overline PQ is congruent to overline TS. Since R is the midpoint of overline PT, it follows that overline PR is congruent to overline TR (by the midpoint theorem).
Since PQR is a right triangle, and R is the right angle, it follows that angle PQR is congruent to angle TSR (by the definition of a right angle). Since overline PQ is congruent to overline TS, it follows that angle PQS is congruent to angle TSR (by the definition of congruence). Together, these congruences imply that triangle PQR is congruent to triangle TSR by the ASA congruence theorem.
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How do you find the domain of a function with two variables?
The domain of a function with two variables is the set of all possible inputs (x-values and y-values) that make the function defined. To find the domain, first identify all of the restrictions on the x-values and y-values, then combine them into a single set of restrictions.
The domain of a function with two variables is the set of all possible inputs (x-values and y-values) that make the function defined. To find the domain, first identify all of the restrictions on the x-values and y-values. These restrictions may come from the function itself, such as any values that would make the function undefined, or from outside sources, such as boundaries placed on the function’s input. Once all of the restrictions are identified, they must be combined into a single set of restrictions. This set of restrictions defines the domain. For example, if the function is defined for all x-values between 1 and 5 and all y-values between -3 and 7, then the domain is all x-values between 1 and 5 and all y-values between -3 and 7. The domain of a function with two variables is an important part of understanding how the function behaves, as it defines the range of inputs for which the function is valid.
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Two friends went to a carnival. They rode carnival rides, played arcade games and bought
candy and snacks at several different concessions. Here is what the friends spent:
Jim spent the following on rides: $4, $3, $1, $1, $5, $2, $3, $1
Sara spent the following on rides: $1, $3, $1, $3, $2, $3, $5, $5, $1
Which person has a larger average?
Answer:
Sarah has a larger average
Step-by-step explanation:
to find the average of each person, you add how much they spent then divide by the total number of values in the set of each person.
Jada earns $7 dollars per hour mowing her neighbors’ lawns. Name the two quantities in Jada’s situation that are in a functional relationship. Which did you choose to be the independent variable? What is the variable
The two quantities in Jada’s situation that are in a functional relationship are the number of hours she works (independent variable) and the amount of money she earns (dependent variable).
The two quantities in Jada’s situation that are in a functional relationship are the number of hours she works and the amount of money she earns. The number of hours worked is the independent variable because it is the variable that affects the amount of money earned. The amount of money earned is the dependent variable because this is the variable that is dependent on the number of hours worked.If she works 8 hours, she would earn $56.Jada earns $7 per hour, so if she works 3 hours, she would earn
$21 (3 x 7 = 21).
If she works 5 hours, she would earn
$35 (5 x 7 = 35).
If she works 8 hours, she would earn
$56 (8 x 7 = 56).
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What is the mole of H2?
One mole of H2 contains 6.022 x 10^23 H2 molecules. This can be used to calculate the number of H2 molecules in a given volume or mass of hydrogen gas.
What is mole?A mole is a unit of measurement in chemistry that expresses the amount of a substance. It is defined as the number of entities (such as atoms, ions, or molecules) in a sample of the substance. The number of entities in one mole of a substance is known as Avogadro's number.
What is Avogadro's number?Avogadro's number is a fundamental constant of physics and chemistry, defined as the number of atoms, ions or molecules in one mole of substance. It is approximately 6.022 x 10^23 and is used in many calculations in chemistry and physics, such as the number of atoms in a sample of an element, the number of ions in a salt, or the number of molecules in a gas sample. The constant is named after Amedeo Avogadro, an Italian scientist who first proposed the concept in 1811.
One mole of a substance is equal to Avogadro's number, which is approximately 6.022 x 10^23.
The mole of H2 (hydrogen gas) is the number of H2 molecules in a sample of hydrogen gas. One mole of H2 contains 6.022 x 10^23 H2 molecules. This can be used to calculate the number of H2 molecules in a given volume or mass of hydrogen gas.
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please help me!! i would really appreciate it
m = ___ feet
Answer:
Step-by-step explanation:
Since it's a 45-45-90 degree triangle, the base and the leg will be the same length. So from there, you just use the Pythagorean theorem and do [tex]5^{2} +5^{2} =m^{2} \\[/tex]
[tex]50=m^{2}[/tex]
and m is [tex]5\sqrt 2[/tex]
Read the passage. Bee Stings: The Aftermath You don't have to have a life-threatening allergy to have a negative response to bee stings. Many people experience uncomfortable itching and swelling when stung. But are such reactions merely an annoyance, or might they serve a purpose? Several years ago, researchers who study the immune system wanted to find out. To do this, they injected a group of mice with bee venom. Some of the mice had allergic reactions (such as swelling) to the venom, and others did not. Three weeks later, the researchers injected the same mice with venom for a second time—this time with a dose so large it could be deadly. They found that the mice who had previously had allergic reactions to the venom were much more likely to survive the potentially lethal dose. What is the main idea of the passage?
Researchers found that allergic reactions to bee venom can be as mild as swelling or as severe as death.
Researchers found that mild allergic reactions may help prevent severe reactions to the same allergin in the future.
Researchers found that bee venom courses allergic reaction in some mice but not others.
Answer:
Researchers found that mild allergic reactions may help prevent severe reactions to the same allergin n the future.
Step-by-step explanation:
I currently have this on IXL & I got it correct.
Simplifying algebraic expression
4-6 = -2
x/7-6
Substitute
28/7-6
PEMDAS
28/7 = 4
4-6 = -2
(If you're looking for the expression, it's 4-6. But if straight answer, -2)
Answer:
[tex] \sf \: \frac{x}{7} - 6 = - 2[/tex]
Step-by-step explanation:
Given information,
[tex] \sf \rightarrow \: \frac{x}{7} - 6[/tex]
[tex] \sf \rightarrow \: x = 28[/tex]
Now the value of expression is,
[tex] \sf \rightarrow \: \frac{x}{7} - 6[/tex]
[tex] \sf \rightarrow \: \frac{28}{7} - 6[/tex]
[tex] \sf \rightarrow \: 4 - 6[/tex]
[tex] \sf \rightarrow \: - 2 = > final \: value[/tex]
Therefore, the answer is -2.
when you multiply or divide a negative and a negative integer the product will be ? positive or negative?
Answer: The product of a positive integer and a negative integer is negative. RULE 2: The product of two positive integers is positive. RULE 3: The product of two negative integers is positive.
When you multiply a negative number by a positive number then the product is always negative
HOPE THIS HELPS
SUKHMANJOT
Guided Practice
Write an equation of a line with the given slope and y-intercept.
m = –1, b = –6
A.
y = x + 6
B.
y = –6x – 1
C.
y = –x – 6
Answer:
C.
y = –x – 6
Step-by-step explanation:
Use the slope-intercept form
y
=
m
x
+
b
to find the slope
m
and y-intercept
b
.
Slope:
5
3
y-intercept:
( 0 , − 2 )
Write in slope-intercept form,
y = m x + b . y = 5 /3 x − 2
Graph the line using the slope and y-intercept, or two points.
Slope:
5
3
y-intercept:
(
0
,
−
2
)
x
y
0
−
2
3
3
Use the slope-intercept form
y
=
m
x
+
b
to find the slope
m
.
m
=
5
3
Use the slope-intercept form to find the slope and y-intercept.
Slope:
1
y-intercept:
( 0 , 6 )
Use the slope-intercept form to find the slope and y-intercept.
Slope:
−
6
y-intercept:
( 0 , − 1 )
Use the slope-intercept form to find the slope and y-intercept.
Slope:
−
1
y-intercept:
( 0 , − 6 )
Betsy and her sister have $15 to
spend on lunch. They buy several
mini-hamburgers, which cost $1. 80
cach. If they received change after
buying their food, which inequality
could be used to find h, the number
of mini-hamburgers Betsy and her
sister bought?
A 1. 89 s 15
B 1. 8 > 15
C 1. 82 > 15
D 1. 85 < 15
Therefore, the inequality 1.85 < 15 can be used to find h.
What is inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance. For instance, let's say you have 225 and want to purchase a new bicycle that costs $250.
Define expressions or values.When the expression's variables and constants are given values, the calculation it describes yields the expression's value. In an algebraic expression, numbers can be represented by letters.
The inequality 1.85 < 15 can be used to find h, the number of mini-hamburgers Betsy and her sister bought. This inequality represents the constraint that the total cost of the mini-hamburgers (1.85h) must be less than the amount of money they have to spend (15). To solve for h, you would divide both sides of the inequality by 1.85, giving you h < 8.1, so h can be any number less than 8.1.
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Type the correct answer in the box.
C
square units.
m
AADC is formed by reflecting AABC across line segment AC, as shown in the figure.
If the length of AC is 4 units, the area of AADC is
The area of ΔADC is equal to 6 unit².
What is the triangular area formula?The total area that is bounded by a triangle's three sides is referred to as the triangle's area. In essence, it is equal to 1/2 of the height times the base, or A = 1/2 b h.
A abc = A adc because the areas of the initial and reflected triangles are equal.
Using the formula area=1/2 base height, determine the area of triangle ABC.
ABC in a triangle:
base = 4 units + AC
height = 3 units + BE
AΔ= abc = 1/2×4×3 =6 unnit²
Hence,
ΔADC = 6 unit²
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