The remainder when f(x)=-6x^23+x^11-x^6+2x is divided by x+1 is -7.
Explanation: In this question, we can solve the problem by using the Remainder Theorem. The remainder theorem states that when we divide a polynomial f(x) by x−a then we get a remainder equal to f(a). So, here we can take a=−1 and find the remainder of f(x).
Here is the given polynomial,
()=−6^23+^11−^6+2
We are asked to find the remainder when f(x) is divided by x+1. Using the remainder theorem, we can find the remainder of f(x) by evaluating f(−1).
(−1)=−6(−1)^23+(−1)^11−(−1)^6+2(−1)=6+1+1−2=6
Now, we have the remainder as 6. However, we need the remainder when f(x) is divided by x+1. The relationship between the remainder and the divisor of a polynomial is that when we divide a polynomial f(x) by x−a, we get a remainder of r(x) such that:
()=(−)()+()
where q(x) is the quotient of the division.
So, the question asks us to divide the polynomial f(x) by x+1 and get the remainder. Here is the long division of f(x) by x+1:
The remainder is −7. Therefore, the remainder when f(x) is divided by x+1 is -7.
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If you go up to your attic on a summer day, which best explains why you may feel very hot?
A Conduction caused hot air to rise to the top of your house.
B Convection caused hot air to rise to the top of your house.
C The attic is insulated from the cooler temperatures below.
D None of the above
Answer:
Step-by-step explanatB Convection caused hot air to rise to the top of your house is the best explanation for why you may feel very hot when you go up to your attic on a summer day.
Convection is the transfer of heat by the movement of a fluid, such as air. On a hot summer day, the air inside your attic can become very hot, and because hot air rises, it will accumulate at the top of your house. When you go up to your attic, you will feel the heat from this accumulated hot air.
Conduction, on the other hand, is the transfer of heat through a material, such as the roof or walls of your house. While some heat may be conducted through the roof, it is unlikely to be the primary cause of the heat in your attic.
Insulation (option C) can help to keep the heat from the attic from escaping into the cooler temperatures below, but it is not the primary cause of the heat in the attic.
ion:
3 pts Suppose a college apparel clothing manufacturer would like to estimate the population mean height for college students. Assume the population standard deviation of student height is 9.48 centimeters. Find the sample size needed to obtain a 95% confidence interval with a 1.2 centimeters margin of error. We cannot find the an appropriate critical value to use since we do not know the degrees of freedom 239,75 239 240
We need a sample size of 239 to estimate the population mean height for college students with 95% confidence interval and 1.2 cm margin of error.
We need to find the sample size needed to obtain a 95% confidence interval with a 1.2 centimeters margin of error.Given that population standard deviation of student height is 9.48 centimeters.Using the formula of margin of error, we getME = z* σ/√nHere, σ = 9.48, ME = 1.2, and confidence interval = 95%.Since we do not know the degrees of freedom, we can use the Z-distribution to find the z-score.For 95% confidence interval, α/2 = 0.025The z-score for the 0.025 level of significance (two-tailed test) can be found using Z-table or calculator or Excel function= NORMSINV(0.025) = -1.96ME = z* σ/√n1.2 = -1.96 * 9.48 /√n√n = 1.96 * 9.48 /1.2= 15.42n = (15.42)^2= 238.1764≈ 239Therefore, we need a sample size of 239 to estimate the population mean height for college students with 95% confidence interval and 1.2 cm margin of error.
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the international average salary income database provides a comparison of average salaries for various professions. the data are gathered from publications and reports obtained directly from government agencies (such as the us bureau of labor statistics) or from the international labour organization. suppose an industrial/organizational psychologist is interested in the relationships between job satisfaction, job performance, and job compensation. she has data from five different countries on the average monthly salaries paid to accountants. she begins her analysis by converting all of the salary data into us dollars:
To convert the salary data from different countries into US dollars, the industrial/organizational psychologist would need to use the exchange rates between each country's currency and the US dollar. Exchange rates are the value of one currency in terms of another currency.
For example, if the exchange rate between the US dollar and the British pound is 1.38, this means that one US dollar is worth 1.38 British pounds. So, to convert the average monthly salary of an accountant in the UK into US dollars, the psychologist would divide the salary in pounds by the exchange rate.
Once the psychologist has converted all of the salary data into US dollars, she can then compare the average monthly salaries of accountants across the five different countries and analyze the relationships between job satisfaction, job performance, and job compensation.
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Part I: Draw a line connecting each sphere to its volume in terms of me and rounded to the nearest tenth. (Not all of the values will be used. ) Pls help
Answer:
Step-by-step explanation:
A store began selling its line of fall sweaters. On the first day, 6 cotton, 4 orlon, and 5 wool sweaters were sold. On the second day, 3 cotton, 5 orlon, and 8 wool sweaters were sold. On the third day, 4 cotton, 1 orlon and 4 wool sweaters were sold. Total sales for the three days were $395, $505, and $260, respectively. What was the sale price for each sweater?
The given data in this problem allows for the creation of a system with three variables, that represent the earnings from the sales in the three days, by solving this system we can obtain these following sale prices:
Cotton: $15.Orlon: $20.Wool: $45.How to obtain the sale price for each sweater?The sale price for each sweater is obtained solving a system of equations.
The variables of the system of equations are given as follows:
Variable x: cost of a cotton sweater.Variable y: cost of an orlon sweater.Variable z: cost of a wool sweater.Considering the profits for each day, along with the amounts of each sweater sold, the equations that compose the system are given as follows:
6x + 4y + 5z = 395.3x + 5y + 8z = 505.4x + y + 4z = 260.Inserting these three equations into a calculator, the solution to the system of equations is given as follows:
x = 15, y = 20, z = 45.
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the data are a random sample from the population of interest. the sample size is less than 10% of the population size. the population distribution is approximately normal. np > 10 and n(1 - p) > 10 more than one condition is violated.
From the given data, we can see that only one condition is violated, which is the sample size being less than 10% of the population size. The other conditions, such as the population distribution being approximately normal, np > 10, and n(1-p) > 10, are all satisfied. Therefore, the statement "more than one condition is violated" is incorrect.
Only one condition is violated in the given data, which is the sample size being less than 10% of the population size. The other conditions are all satisfied and do not violate any of the conditions for a representative sample.
It is important to note that in order for a sample to be representative of the population, the sample size should be at least 10% of the population size. If the sample size is less than 10% of the population size, the sample may not accurately represent the population and the results may be biased.
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Chucky grabbed 12 items in the grocery store that each had a different price and had a mean cost of about $7. 41 $7. 41dollar sign, 7, point, 41. One of the items was an entire wheel of cheese that cost $39. 99\$39. 99 $39. 99 dollar sign, 39, point, 99
B. Both the mean and median will decrease, but the mean will decrease by more than the median.
Since the wheel of cheese has a much higher cost than the other 11 items, removing it will decrease the overall mean cost of the items purchased. However, the median, which is the middle value when the items are arranged in order, will also decrease but not by as much as the mean since it is not as affected by outliers like the wheel of cheese.
The mean is calculated by taking the sum of all the prices and dividing it by the number of items, so removing the most expensive item (the wheel of cheese) will decrease the sum of prices and thus decrease the mean.
The median is the middle value when all the prices are arranged in order. Since the wheel of cheese is the most expensive item, it will be the last item on the ordered list. Removing it will not change the position of any other items, so the median will simply be the middle value of the remaining 11 items. The value of the median is not affected by the price of the wheel of cheese, so the median will also decrease but only by a small amount. T
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The correct question should be:
Chucky grabbed 12 items in the grocery store that each had a different price and had a mean cost of about $7.41. One of the items was an entire wheel of cheese that cost $39.99. Chucky then decided to put the wheel of cheese back and only buy the other 11 items. How will removing the wheel of cheese affect the mean and median?
A. Both the mean and median will decrease, but the median will decrease by more than the mean.
B. Both the mean and median will decrease, but the mean will decrease by more than the median.
C. Both the mean and median will increase, but the median will increase by more than the mean.
D. Both the mean and median will increase, but the mean will increase by more than the median.
The function is defined by the following rule..
f(x)=-3x-3
Complete the function table.
X
-5
0
2
X
Explanation
0
0
0
0
0
5
Check
The value for f(-5), f(-1), f(0), f(2), f(4) are 12, 0, -3, -9, -15.
What is a function?
In mathematics, a function is a relation between a set of inputs (called the domain) and a set of outputs (called the range) with the property that each input is related to exactly one output. A function is usually denoted by a symbol such as f(x), where x is the input variable and f(x) is the output variable. The value of the output variable depends on the value of the input variable and the rule that defines the function.
Given function:
f(x) = -3x -3
Now, we will substitute values of x in f(x) as follows:
when x =-5,
f(-5) = -3 (-5) - 3
= 15 -3 = 12.
when x =-1,
f(-5) = -3 (-1) - 3
= 3 -3 = 0.
when x = 0,
f(-5) = -3 (0) - 3
= 0 -3 = -3.
when x = 2,
f(-5) = -3 (2) - 3
= -6 -3 = -9.
when x = 4,
f(-5) = -3 (4) - 3
= -12 -3 = -15.
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When we find the area of a 3D figure, we label our answer as "units 2 (squared)".
When we find the volume of a 3D figure, what do we label our answers as? "units
Need help with this one thanks
By answering the presented question, we may conclude that For slope example, if a figure's measures are in metros, the volume will be in cubic metros (m3).
what is slope?The slope of a line determines how steep it is. The gradient is expressed mathematically as gradient overflow. The slope is computed by dividing the vertical difference (run) between two locations by the height difference (rise). The curve form of an expression is used to describe the straight line equation, which is written as y = mx + b. The y-intercept of the line is located where the inclination is m, b is b, and (0, b). For example, consider the slope and y-intercept of the equation y = 3x - 7. (0, 7). The y-intercept is placed where the slope of the path is m, b is b, and (0, b).
When we calculate the volume of a 3D figure, we call our solution "units 3 (cubed)".
The term "cubed" is used since volume is calculated by multiplying three dimensions (length, breadth, and height), resulting in a unit raised to the power of three. For example, if a figure's measures are in metres, the volume will be in cubic metros (m3).
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A homeowner is building a patio with concrete blocks. The blocks are 11" x 10" x 6". The blocks are in a stack at the store that is 60" x 55" x 54". How many blocks are in a stack?
According to the question, if the blocks are 11" x 10" x 6" and the blocks are in a stack at the store that is 60" x 55" x 54" then there are 270 blocks in the store.
Given that dimensions of the blocks and the store :-
Block :- 11" x 10" x 6"
Store :- 60" x 55" x 54"
To find the number of blocks in a stack we need to first calculate the volume of the block as well as the store.
This, Volume of block = 11 x 10 x 6 = 660
and, Volume of the store = 60 x 55 x 54 = 178200
Therefore, the number of blocks would be = Volume of the store / Volume of block
No. of block = 178200/660
No. of block = 270
Hence Number of blocks stored in the stack at the storeroom is 270 blocks.
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Can someone please explain how to solve this step by step really stuck
Answer:
[tex]x=\frac{b-a}{ab}[/tex]
Step-by-step explanation:
[tex]\frac{1}{ax} -\frac{1}{bx} =1\\\frac{1}{ax} *\frac{b}{b} -\frac{1}{bx} *\frac{a}{a} =1\\\frac{b}{abx} -\frac{a}{abx}=1\\\frac{b-a}{abx}=1\\b-a=abx\\x=\frac{b-a}{ab}[/tex]
how do i find the center and radius of the given circle
There are multiple ways to find the center and radius of a circle, depending on what information your provided.
Method 1: Reading the standard equation of a circle
Equation of a circle: [tex](x-h)^{2} +(y-k)^{2} =r^{2}[/tex]
where h is the center's x-coordinate, k is the center's y-coordinate, and r is the radius. Here's an example:
[tex](x-5)^{2} +(y+2)^{2} =25[/tex]
In this case, the center would be (5,-2) and the radius is 5
Method 2: Reading a graph
In the attached graph, there is a circle with a labeled center point. The radius can be found by finding the distance from the center to a different point on the circle.
Distance Formula:
[tex]D = \sqrt{ (x_{2}-x_{1}) ^{2} + (y_{2}-y_{1}) ^{2}}\\[/tex]
The first point we use will be the center ( 5 , -2 ), and the second point will be a point on the circle, (10,-2).
[tex]r = D = \sqrt{ ((10)-(5)) ^{2} + ((-2)-(-2) )^{2}}\\r = D = \sqrt{ (5 ^{2} + 0)^{2}}\\r = D = \sqrt{25}\\r = 5[/tex]
Next, plug in the values into the standard equation of a circle formula
[tex](x-5)^{2} +(y+2)^{2} =5^2[/tex]
Simplify
[tex](x-5)^{2} +(y+2)^{2} =25[/tex]
20 Points
...................................
Answer:
Its the 3rd one
Step-by-step explanation:
I had this question twice
Answer:
number 3 i did this 2 days ago
Step-by-step explanation:
Graph the linear equation find three points that solve the equation then plot on the graph -x-3y=-6
The quotient of 30 and the sum of five and seven
Answer:
sum of 5 and 7
Step-by-step explanation:
5+7
sum means an adding equetion
Answer:
The answer is 2.5
Step-by-step explanation:
° The sum of 5 and 7 is 5 + 7 = 12
° The quotient of means "the result got from dividing one variable by another", so, 30/12 = 2.5
I NEED THIS DONE ASAP!!
Simplify a^-4/4a^6
Hence, in answering the stated question, we may say that Therefore, the simplified expression is [tex]1/(4a^6).[/tex]
what is expression ?In mathematics, you can multiply, divide, add, or subtract. An expression is formed as follows: Expression, number, and math operator Numbers, parameters, and functions make up a mathematical expression. It is possible to contrast phrases and expressions. Every mathematical statement that comprises variables, numbers, and a mathematical action between them is referred to as an expression. For example, the phrase 4m + 5 is made up of the phrases 4m and 5, as well as the variable m from the provided equation, all separated by the mathematical symbol +.
To simplify this expression, we can use the laws of exponents:
[tex]a^-4/4a^6 = 1/(4a^4 * a^2) = 1/(4a^6)[/tex]
Therefore, the simplified expression is [tex]1/(4a^6).[/tex]
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PLEASE HELPPPP FAST In the picture below, find the value of a.
Answer:
A should be 180 - 68 which is 112 degrees
Step-by-step explanation:
Answer:a=108
Step-by-step explanation:
140+(180-60)+(180-84)+(180-68)=140+120+96+112=260+208=468
sum of angles are 540, so,
540-468=180-a
72=180-a
a=108
Eman is planning to sell wind chimes at the craft fair. The cost of her tools for selling wind chimes is 130$. The costs of materials 10$ per wind chime. What is the total cost to make 100 wind chimes?
Therefore, the total cost to make 100 wind chimes is 14,000$.
What is equation?In mathematics, an equation is a statement that two expressions are equal. It typically contains one or more variables (unknowns) and specifies a relationship between those variables. Equations are used to model real-world phenomena, solve problems, and make predictions. There are many types of equations in mathematics, including linear equations, quadratic equations, polynomial equations, exponential equations, trigonometric equations, and many more. Each type of equation has its own set of methods and techniques for solving it.
Here,
The cost of making one wind chime is 10 + 130 = 140$.
To make 100 wind chimes, the total cost would be:
100 x 140 = 14,000$.
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Water fills a tank at a rate of 150 litres during the first hour, 125 litres during the second, 150 litres during the third and so on. Find the number of hours necessary to fill a rectangular tank 16m x 6m x 5m
Water fills a tank at a rate of 150 liters during the first hour, 125 liters during the second, 150 liters during the third, and so on. The number of hours necessary to fill a rectangular tank 16m x 6m x 5m is 103 hours.
The volume of the rectangular tank can be found by multiplying its length, width, and height:
The volume of the tank = Length x Width x Height
Volume of tank = 16m x 6m x 5m
The volume of the tank = 480 cubic meters
We need to convert this volume to liters in order to compare it to the flow rate of water. Since 1 cubic meter is equal to 1,000 liters, we have:
Volume of tank = 480 x 1,000 = 480,000 liters
Now we can add up the flow rate of water over time until it exceeds the volume of the tank. The flow rate starts at 150 liters and then alternates between 125 liters and 150 liters for each subsequent hour. We can express this pattern as:
[tex]150 + 125 + 150 + 125 + 150 + ...[/tex]
This is an arithmetic sequence with a first term of 150, a common difference of -25 (since each subsequent term is 25 less than the previous one), and an unknown number of terms. We can use the formula for the sum of an arithmetic sequence to find the number of terms:
Sum = (n/2)(first term + last term)
where n is the number of terms.
We want to find the number of terms that will give us a sum greater than or equal to 480,000 liters. We can set up an inequality:
(n/2)(150 + (150 + (n-1)(-25))) ≥ 480,000
Simplifying and solving for n, we get:
n ≥ 102.4
Since we need a whole number of terms, we can round up to 103 terms. This means it will take 103 hours to fill the tank.
Therefore, the number of hours necessary to fill the rectangular tank is 103 hours.
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(x+2)(2x-3)=5(x+2)...
Answer:
Step-by-step explanation:
x = 4 or x = -2
Solve 3x − 2 = 37. Group of answer choices 2 5 7 9
Answer:
x = 13
Step-by-step explanation:
To find the value of x we need to isolate it! To do this we have to get rid of any other value around it...
Firstly we need to get rid of the ' -2 '. We have to add 2 to both sides!
3x -2 + 2 = 3x37 + 2 = 39Now we are left with 3x = 39 so we have to get rid of the 3. We have to divide 3 from both sides!
3x ÷ 3 = x39 ÷ 3 = 13x = 13!
Hope this helps, have a lovely day! :)
y
8
X
Solve for y.
Start by finding the side
lengths of the smallest triangle.
Fill in the green blank.
2
[?] X
Enter
The equation given is an instance of a linear equation in two variables, which can be solved by using the process of substitution to find the value of one of the variables.Therefore, the solution to the given equation is y = 4√(3).
What is equation?Equation is a mathematical statement that states the equality of two expressions. It is usually expressed as a numerical equation with an equal sign (=) between the two expressions. Equations are used to express relationships between various quantities and can be used to solve problems in many areas of mathematics, science, and engineering. In addition, equations are often used to describe physical laws and chemical reactions.
In this case, the equation is y = 8/x, and we want to solve for y.
To do this, we need to first find the value of x. We can do this by using the side lengths of the triangle given, which are 2 and x. We can use the Pythagorean theorem to calculate the value of x. The Pythagorean theorem states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the longest side. So, we can use this equation to find the value of x: 2²+ x²= (8/x)². Solving for x, we get x = 2√(3).
Now that we have the value of x, we can substitute it into the original equation and solve for y. So, y = 8/2√(3), which simplifies to y = 4√(3). Therefore, the solution to the given equation is y = 4√(3).
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A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
The three options of exterior angles are m∠5 + m∠6 =180°,
m∠2 + m∠3 = m∠6
m∠2 + m∠3 + m∠5 = 180°
What is an exteriοr angle?The angles that are created οutside οf a triangle are its exteriοr angles. In οther wοrds, the angle fοrmed between οne οf a triangle's sides and its adjacent extended side is the triangle's exteriοr angle.
Given that the exteriοr angles are m∠1, m∠4, and m∠6.
The interiοr angles οf the triangle are angles m∠2, m∠3, and m∠5.
The sum οf all angles οf a triangle is 180°.
Thus m∠2 + m∠3 + m∠5 = 180°
The interiοr angle and the cοrrespοnding exteriοr angle in a triangle make up a linear pair. Exteriοr Angle plus Interiοr Angle equals 180°, sο.
The exteriοr angle at angle 5 is angle 6.
Thus m∠5 + m∠6 =180°
The interiοr and exteriοr angles that make up a triangle are always added tοgether tο fοrm the exteriοr angle. The term "exteriοr angle prοperty" refers tο this feature. If twο triangles' cοrrespοnding angles tend tο be cοngruent and their side lengths are prοpοrtiοnal, any twο triangles will be similar tο οne anοther.
The οppοsite interiοr angles οf m∠6 are m∠2, m∠3.
Thus m∠2 + m∠3 = m∠6
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Does the table below describe a linear or an exponential function?
a.The x-values are equally spaced, and the y-values change by equal differences, so the function is linear.
b.The x-values are equally spaced, and the y-values change by equal differences, so the function is exponential.
c. The x-values are equally spaced, and the y-values change by equal factors, so the function is exponential.
d. The x-values are equally spaced, and the y-values change by equal factors, so the function is linear.
Answer:
a. The x-values are equally spaced, and the y-values change by equal differences, so the function is linear.
Step-by-step explanation:
A linear function is categorized by a function which has a constant factor separating all coordinates. In this table, each x-value increases by 1 while each y-value increases by 2. So, it is linear.
averaged 462 raindrops over an area of 55 square meters. A nearby picnic table has an area of 1 square meter. Use the Poisson distribution to find the probability that exactly 11 raindrops fall on the picnic table the next time it sprinkles. Do not round intermediate computations, and round your answer to three decimal places.
The probability that exactly 11 raindrops fall on the picnic table the next time it sprinkles is 0.066, rounded to three decimal places.
We can model the number of raindrops that fall on the picnic table as a Poisson distribution with parameter a, where a is the expected number of raindrops that fall on a 1 square meter area during a rainstorm. Since 462 raindrops fell over an area of 55 square meters, the average number of raindrops per square meter is:
a = 462/55 ≈ 8.4
Therefore, the probability that exactly 11 raindrops fall on the picnic table during a rainstorm is:
P(X = 11) = (eᵃ * a¹¹) / 11!
= (e⁻⁸ ⁴ * 8.4¹¹) / 11!
≈ 0.066
Rounding to three decimal places, we get the probability that exactly 11 raindrops fall on the picnic table as 0.066.
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A father's age is four times the age of his daughter. After 5 years his age would be three times his daughters age. After 5 more years , how many times of his daughter age his age would be
If a father's age is four times the age of his daughter.. After 5 more years , his age would be 5 times his daughter's age at that time.
Let's use D to represent the daughter's current age and F to represent the father's current age.
We know that the father's age is four times the age of his daughter, so we can write an equation to represent this relationship:
F = 4D
We also know that after 5 years, the father's age would be three times his daughter's age, so we can write another equation to represent this:
F + 5 = 3(D + 5)
Now we can substitute the first equation into the second equation to get an equation with only one variable:
4D + 5 = 3(D + 5)
Simplifying the equation, we get:
4D + 5 = 3D + 15
Subtracting 3D and 5 from both sides, we get:
D = 10
Therefore, the daughter's current age is 10 years old. We can use the first equation to find out the father's current age:
F = 4D = 4(10) = 40
After 5 more years, the father's age would be:
F + 5 + 5 = 40 + 10 = 50
In summary, after 5 more years, the father's age would be 50 and his daughter's age would be 10, which is 5 times younger than the father.
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A wooden beam is (7y^2+7y+1) meters long. If a piece of length (y^2-10) meters is cut off, express the length of the remaining piece of beam as a polynomial in y.
The length of the remaining piece of beam as polynomial is 6y²⁺⁷⁺¹¹
Describe a polynomial.An algebraic expression with two or more algebraic terms is known as a polynomial.It has exponents, operators, coefficients, coefficients, variables, and constants. A polynomial is a mathematical expression that solely uses the operations addition, subtraction, multiplication, and non-negative integer powers of variables. It is made up of indeterminates (also known as variables) and coefficients.
The length of the wooden beam is (7y²⁺⁷⁺¹) meters long and a piece of length (y²⁻¹⁰) meters is cut off ¹.
Therefore, the length of the remaining piece of beam can be expressed as follows:
(7y²⁺⁷⁺¹)-(y²⁻¹⁰) = 6y²⁺⁷⁺¹¹
So, the length of the remaining piece of beam is 6y²⁺⁷⁺¹¹
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Andy is a restaurant owner. He believes 72% of his customers are satisfied with the food quality of his restaurant. From a random sample of 78 customers, what are the following probabilities? (Round to 2 decimal places for all z-values and round all other answers to 4 decimal places, if needed.)
(a) What is the probability that less than 57 customers are satisfied with the food quality?
(b) What is the probability that at least 57 customers are satisfied with the food quality?
(c) What is the probability that the sample proportion of customers who are satisfied with the food quality is between 70% and 77%?
The probability that the sample proportion of customers who are happy with the food quality is between 70% and 77% is 0.693
Andy is a restaurant owner who believes that 72% of his customers are happy with the food quality of his restaurant. What are the probabilities for the following questions, given a random sample of 78 customers? Probability that less than 57 customers are satisfied with the food quality:To find the probability that less than 57 customers are happy with the food quality, we'll first compute the z-score.Z = (x - µ) / σZ = (56.5 - 72.84) / 4.392 Z = -3.7 Using the table, we can find that the probability of a z-score less than -3.7 is 0.0001. Thus, the probability that less than 57 customers are happy with the food quality is 0.0001.
Probability that at least 57 customers are satisfied with the food quality:The probability that at least 57 customers are satisfied with the food quality is the complement of the probability that less than 57 customers are satisfied with the food quality. Hence, the answer is: 1 - 0.0001 = 0.9999 Probability that the sample proportion of customers who are satisfied with the food quality is between 70% and 77%:To calculate the probability that the sample proportion of customers who are happy with the food quality is between 70% and 77%, we'll need to compute the z-scores for both values.
The z-score is given by Z = (p - P) / sqrt(PQ/n), where P is the true proportion (0.72), Q is 1 - P (0.28), and n is the sample size (78).Z1 = (0.70 - 0.72) / sqrt(0.72*0.28/78) = -0.85Z2 = (0.77 - 0.72) / sqrt(0.72*0.28/78) = 1.24The probability is the difference between the two probabilities of the standard normal distribution, which is 0.8907 - 0.1977 = 0.693. Hence, the probability that the sample proportion of customers who are happy with the food quality is between 70% and 77% is 0.693.
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Raymond’s class measures the masses of the books in their library. The mass of the dictionary is 2,702 grams. The dictionary’s mass is 1,429 grams greater than the mass of Raymond’s favorite book. What is the mass, in grams, of Raymond’s favorite book?
The mass of Raymond's favorite book is 1273 grams.
What is the linear function?
A linear function is defined as a function that has either one or two variables without exponents. It is a function that graphs to a straight line.
Let x be the mass of Raymond's favorite book in grams. According to the problem, we have:
2702 = x + 1429
To solve for x, we can isolate it on one side of the equation by subtracting 1429 from both sides:
x = 2702 - 1429
x = 1273
Therefore, the mass of Raymond's favorite book is 1273 grams.
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