1. The expression that represents the area of the shaded region is π (R² - r²). 2. Yes, the expression is a polynomial with degree 2. 3. The difference is given by the (R - r). It is a polynomial with degree 1.
What is a polynomial?When variables and coefficients are joined using addition, subtraction, and multiplication operations, the result is a polynomial. The coefficients of a polynomial can be any real number, and the variables can only have non-negative integer exponents. Polynomials can have one or more terms, and they can be categorised according to the degree of the variable in the expression with the largest power. For instance, the aforementioned polynomial is of fourth degree since the maximum power of the variable x is 4.
The area of the circle is given as:
A = πr²
For the outer circle the area is:
A1 = πR²
The area of inner circle is:
A2 = πr²
Now, the area of the shaded portion is:
A = A1 - A2
A = πR² - πr²
A = π (R² - r²)
Hence, the expression that represents the area of the shaded region is π (R² - r²).
2. Yes, the expression is a polynomial with degree 2.
3. The difference between the two radii is given by the expression R - r. It is a polynomial with degree 1.
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Determine the numbers of solutions for 4x + 8 = 12x
Answer:
x= 1
Step-by-step explanation:
Step 1- Subtract 4x to both sides(Move the x to one side).
4x+8= 12x
-4x -4x
8= 8x
Step 2- Divide both sides by 8(Isolate the variable).
8 = 8x
8 8
x= 1
how much volume in one grain of rice
A grain of rice contains about 0.029 milliliters of volume.
A grain of rice is a tiny, ingestible seed that comes from either Oryza sativa (Asian rice) or Oryza glaberrima, two types of grass (African rice). A single grain of rice is round or oval in shape and measures about 3–4 millimeters in length. A grain of rice has a volume of 0.029 milliliters and a mass of approximately 0.05 grams. The type of rice and the method of processing affect the size and form of a single grain of rice. Over half of the world's population relies heavily on rice as a source of nutrition and as a staple food in many different cultures. Sushi, risotto, rice pudding, and many more recipes all use rice as an ingredient.
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sin² x + cos²x = 1
Which Trigonometric Identity is given above?
- Pythagorean Identity
- Lagrange's Trigonometric Identity
- Angle Sum and Difference Identity
- Tangent Identity
The Trigonometric Identity sin² x + cos²x = 1 is: A. Pythagorean Identity.
What is Pythagorean Identity?The Pythagorean Identity which tend to asserts that for every angle x, the sum of the squares of the sine and cosine of x is equal to one is known as or called a trigonometric identity.
The Pythagorean identity can be expressed as:
sin² x + cos² x = 1
This identity is crucial to understanding trigonometry and tend to have several uses in numerous branches of science and engineering.
Therefore the correct option is A.
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Suppose a population consists of 850,000 people which of the following numbers of members of the population being surveyed could result in a parameter but not a sample statistic
The number of members of the population that could result in a parameter but not a statistic is given as follows:
A. 850
What is a parameter and what is a statistic?A parameter is used to describe the whole population, while a statistic is used to describe the sample.
For this problem, we have that:
The population size is of 850,000.The sample size is of 850.Meaning that 850,000 describes the population, and thus the correct option is option C.
Missing Information
The options are given as follows:
A. 850
B. Both 850 and 850,000
C. 850,000
D. Neither 850 nor 850,000
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if i roll standard -sided dice and multiply the number on the face of each die, what is the probability that the result is a composite number?
The probability that the result is a composite number is calculated as 0.99 using the given data.
What in mathematics is a probability?In everyday speech, the term "probability" refers to the likelihood that a specific event (or set of events) will take place, expressed as a number between 0 and 100% or as a linear scale from 0 (impossibility) to 1 (certainty).
Let,
A - the result is a composite number
A' - the result is not a composite number
Number of possible numbers appearing on dice = 6⁵ = 7776
A' = {11111, 21111, 12111, 11211, 11121, 11112}
Total number of results that are not composite numbers = 6
Total number of results that are composite numbers = 7776-6
= 7770
Probability that the result is a composite number = 7770/7776
= 0.99
Therefore, the probability that the result is a composite number is calculated as 0.99.
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prove that if a symmetric matrix is invertible, then its inverse is symmetric also.
Let A be a symmetric matrix that is invertible. This means that there exists a matrix B such that AB = BA = I, where I is the identity matrix. We want to show that B is also symmetric, that is, \(B = B^{T}\)
To prove this, we can use the definition of matrix inversion. We know that AB = I, so we can take the transpose of both sides:
\(AB^{T} = I^{T}\)
Using the transpose rules, we can rewrite this as:
\(B^{T} * A^{T}\) = I
Now, we can multiply both sides of this equation by A:
\(B^{T} * A^{T}\)* A = A
Since A is invertible, we can multiply both sides by A⁻¹ to get:
\(B^{T}\) = A⁻¹
Therefore, we have shown that the inverse of a symmetric matrix A, which we denote as A⁻¹, is also symmetric, since A⁻¹ = \(B^{T}\), which is the transpose of the matrix B.
Hence, we have proved that if a symmetric matrix is invertible, then its inverse is symmetric as well.
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nine eighteenths plus one third
Answer:
5/6
Step-by-step explanation:
Step 1: Rewrite 9/18
9/18 = 1/2
Step 2: Rewrite problem
1/2 + 1/3
Step 3: Find GCD (Greatest common denominator)
6
Step 4: Rewrite fractions
3/6 + 2/6
Step 5: Add
5/6
Step-by-step explanation: That's your answer 5/6
Hope this helps lol!
vă rog am nevoie de ajutor la ex 6 dacă il faceți dau corana ex este de clasa a 6
Answer:
sry but i can't help you with it bcz i don't understand spanish can u write it in clear english
Sry
Sarah tosses a coin and spins a spinner
Answer:
Good for her ig
Step-by-step explanation:
Which equations are true equations? Select all correct answers. Responses 15052=30−42−12 150 over 5 squared equals 30 minus 4 squared minus 12 48 ÷ 8 + 2³ = 5 + 3² 48 ÷ 8 + 2³ = 5 + 3² 92−72=20÷(7−2) 9 squared minus 7 squared equals 20 divided by open parenthesis 7 minus 2 close parenthesis 8⋅72−12=22−2⋅3
All the correct answers of the equations using order of operations are;
B. 8⋅7 ÷ 2 − 12 = 22 − 2⋅3
C. 48 ÷ 8 + 2³ = 5 + 3²
How to use order of operations?The rule used for order of operations is PEMDAS and it states that the order of operation starts with the calculation enclosed in brackets or the parentheses first. Exponents (degrees or square roots) are then operated on, followed by multiplication and division operations, and then addition and subtraction.
Using the PEMDAS rule, the solutions would be as follows:
A. 9² − 7² = 20 ÷ (7 − 2)
81 - 49 = 20 ÷ 5
32 = 4
Thus, this is not true.
B. 8⋅7 ÷ 2 − 12 = 22 − 2⋅3
56 ÷ 2 − 12 = 22 - 6
28 - 12 = 16
16 = 16
Thus, this is true.
C. 48 ÷ 8 + 2³ = 5 + 3²
6 + 2³ = 5 + 9
6 + 8 = 14
14 = 14
Thus, this is true.
D. 150 ÷ 5² = 30 − 4² − 12
150 ÷ 25 = 30 − 16 − 12
6 = 30 - 28
6 = 2
Thus, this is not true.
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Complete question is;
Which equations are true equations? Select all correct answers.
A. 9² − 7² = 20 ÷ (7 − 2)
B. 8⋅7 ÷ 2 − 12 = 22 − 2⋅3
C. 48 ÷ 8 + 2³ = 5 + 3²
D. 150 ÷ 5² = 30 − 4² − 12
Could someone please help. please help asap I need it. see picture...
find the x- and y-intercepts
and write The equation in standard form with integer coefficients
The x-intercept is 5 and the y-intercept is 2.
The standard form of the line is 2x + 5y = 10.
How to find the x-intercept, y-intercept and equation in standard form?The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis. In other words, the x -intercept is the value of x when y = 0 and the y-intercept is the value of y when x = 0.
Hence, the x-intercept is 5 and the y-intercept is 2.
Let's find the equation in standard form.
Ax + By = C
where
A, B and C are constantUsing slope intercept form,
y = mx + b
where
m = slopeb = y-interceptHence, using (5, 0) and (0, 2)
m = 2 - 0 / 0 - 5
m = - 2 / 5
Therefore.
y = - 2 / 5x + 2
Hence, let's multiply through by 5 to eliminate the fraction
5y = -2x + 10
Therefore, the standard form is as follows:
2x + 5y = 10
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A campary hat \( \$ 100,000 \) in cash and annual sales of \( \$ 720,000 \) Using a 360 day year, how many days' sales in cash is the comigany curfenty holdeg? 50 days 100 days 25 days 75 days
The company currently holds approximately 50 days' sales in cash for the comigany curfenty holdeg
To determine the number of days' sales in cash that the company currently holds, we need to divide the cash amount by the daily sales amount. With annual sales of $720,000 and a 360-day year, the company holds approximately 100 days' sales in cash.
To calculate the number of days' sales in cash, we divide the cash amount by the daily sales amount.
Given that the company has $100,000 in cash and annual sales of $720,000, we can determine the daily sales amount by dividing the annual sales by the number of days in a year. Since the year is assumed to have 360 days, the daily sales amount is $720,000 / 360 = $2,000.
Next, we divide the cash amount by the daily sales amount to find the number of days' sales in cash:
$100,000 / $2,000 = 50.
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4 red bricks have a mean weight of 5 kg.
5 blue bricks have a mean weight of 9 kg.
1 green brick has a weight of 6 kg.
Donna says,
"The mean weight of the 10 bricks is less than 7 kg. "
Is Donna correct?
You must show how you get your answer.
Donna is not correct, as the mean is of 7.1 kg, which is greater than 7 kg.
How to obtain the mean of a data-set?The mean of a data-set is obtained as the sum of all observations in the data-set divided by the number of observations.
The sum of the data-set in this problem is given as follows:
4 x 5 + 5 x 9 + 1 x 6 = 71 kg.
The number of observations is given as follows:
10.
Hence the mean is given as follows:
71/10 = 7.1 kg > 7 kg.
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Since the cost of cheese went up, the cost of small pizza went from $5.45 to $6.50. calculate the percent increase.
I will give Brainliest is, but I also will report you if you don't give a reasonable answer.
Answer:
19.3%
Step-by-step explanation:
6.50-5.45 = 1.05
1.05/5.45 = 0.192605505
* 100 = 19.27% = 19.3% increase
ONE SHARE OF BEEPCO PREFERRED STOCK PAYS AN
ANNUAL DIVIDEND OF $1. 20. TODAY BEEPCO CLOSED AT
$34. 50 WITH A NET CHANGE OF -$0. 50. WHAT WAS THE
STOCK'S YIELD AT YESTERDAY'S CLOSING PRICE?
O
The yield of stock at yesterday's closing price is 3.43%.
What is Annual Dividend?Annual dividend is the profit of the stock which is divided among the shareholders, both common and preferred shareholders annually.
Given,
Annual dividend = $1.20
Today's closing price = $34.50
Net change = -$0.50
Let x be yesterday's closing price.
Net change = Today's closing price - yesterday's closing price
⇒ -0.50 = 34.50 - x
⇒ x = 34.50 + 0.50
⇒ x = 35
Yield = \(\frac{Annual dividend}{Price}\) × 100
= \(\frac{1.2}{35}\) × 100
= 3.4286 % ≈ 3.43 %
Hence the stock's yield at yesterday's closing price of preferred stock is 3.43 %.
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Can some body please help me whit this question?
8 - (7/10)t = 6 - (1/5)t Thx
Answer:
8-(7/10)t=6-(1/5)t - Get Easy Solution
Simple and best practice solution for 8-(7/10)t= 6-(1/5)t equation. Check how easy it is, and learn it for the future. Our solution is simple,
Step-by-step explanation:
make me as brain liest
5. Solve for x.
10x + 44
8x - 23
what’s the equation to solve this?
Answer:
equation is 10x+44= 8x-23
X= -10.5
Step-by-step explanation:
Answer:
for the first one is 4.4 and the second one is 2.875
Step-by-step explanation:
when your solving the first one you got to get x by itself so u divide 10/10 then that cancels and you got x once you do that to one side you gotta do it to the other so you do 44/10 then you get your value of x
which expression represents the difference of (5x-3y) and (8x+8y)?
Given:
The expressions are:
\((5x-3y)\) and \((8x+8y)\)
To find:
The difference of \((5x-3y)\) and \((8x+8y)\).
Solution:
Difference of \((5x-3y)\) and \((8x+8y)\) is written as:
\(Difference=(5x-3y)-(8x+8y)\)
On simplification, we get
\(Difference=5x-3y-8x-8y\)
\(Difference=(5x-8x)+(-3y-8y)\)
\(Difference=-3x-11y\)
Therefore, the difference of \((5x-3y)\) and \((8x+8y)\) is \(-3x-11y\).
The expression 15n + 2(3p) represents the amount Isaiah spent buying gasoline and snacks, where n represents the price of each gallon of gasoline and p represents the cost of each snack that he bought. Which statement is true about the amount Isaiah spent?
· He spent 6p dollars on gasoline.
· He spent n + p dollars in all.
· He bought 15 gallons of gasoline.
· He bought 6 dollars worth of snacks.
Answer:
He bought 15 gallons of gasoline
Step-by-step explanation:
Where, "n" represents the amount in dollars each gallon costs, 15n would represent Isaiah spending 15 times that initial amount of "n." Considering the fact that n represents the cost of a single gallon, you can conclude that he had bought 15 gallons of gasoline.
He bought 15 gallons of gasoline.
We have given that,
The expression 15n + 2(3p) represents the amount Isaiah spent buying gasoline and snacks, where n represents the price of each gallon of gasoline and p represents the cost of each snack that he bought.
Where n represents the amount in dollars each gallon costs, 15n would represent Isaiah spending 15 times that initial amount of n.
What is the initial amount?The first value in your equation is the initial amount. This is the number you would get if you plugged x=0 into your equation. The number that is NOT raised to the x power in your equation is your initial amount.
What is considering the fact that n represents the cost of a single gallon, you can conclude that he had bought 15 gallons of gasoline.
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What is the common difference between successive terms in the sequence? 0.36, 0.26, 0.16, 0.06, -0.04, -0.14, ... a) -0.1 b) -0.1, 0.1 c) -0.1, 0.2 d) 0.1
The common difference between successive terms in this sequence is -0.1.
The common difference between successive terms in a sequence is the constant value that is added or subtracted to each term to obtain the next term in the sequence. To find the common difference in the given sequence, we need to subtract each term from the term that follows it.
Subtract the first term (0.36) from the second term (0.26): 0.26 - 0.36 = -0.1
Subtract the second term (0.26) from the third term (0.16): 0.16 - 0.26 = -0.1
Subtract the third term (0.16) from the fourth term (0.06): 0.06 - 0.16 = -0.1
Based on the calculations, the common difference between successive terms in this sequence is -0.1. Therefore, the correct answer is a) -0.1.
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Side AB is opposite which angle in triangle ABC?
Answer:
Angle C is the opposite angle of AB
Side AB is opposite to angle ∠ACB in triangle ABC
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
In the given rectangle, AC is the diagonal
ABC and ADC are two right triangles.
We have to find the angle which is opposite to the side AB.
The angle opposite to side AB is angle C.
In the option we have angle ∠ACB.
Hence, Side AB is opposite to angle ∠ACB in triangle ABC
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Real GDP in 2018 was 500 million and in 2019 it was 520 million. What is the real growth rate?
Expenditure is divided by total GDP at market price multiplied by 100.
How do you determine the rate of real GDP growth?Real GDP is computed by subtracting the most recent year’s real GDP from the previous year’s real GDP. The difference is then divided by the previous year’s actual GDP. Real GDP may also be calculated if nominal GDP and the current inflation rate are known.
GDP at market value is the total of all expenditures. The GDP market price percentage rate is computed by dividing spending by total GDP at market price and multiplying by 100. GDP may be calculated in three ways: the value added technique, the income approach (how much money is made as revenue from resources utilized to manufacture things), and the expenditures approach (how much is spent on stuff).
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The amunt of money that college students spend on rent each month is usually between $300 and $600. However, there are a few students who spend $1,300. What measure of spread would be most appropriate to measure the amount of money that college student spend on rent per month? Explain in detail why or why not one of the below measures would be used.
A. Median
B. Range
C. Standard Deviation
D. Inquartile Range
The range would be the most appropriate measure of spread in this case because it takes into account the extreme values of $300 and $1,300 and provides a clear measure of the difference between them.
To measure the amount of money college students spend on rent per month, the most appropriate measure of spread would be the range. The range is the simplest measure of spread and is calculated by subtracting the lowest value from the highest value in a data set. In this case, the range would be $1,300 - $300 = $1,000.
The median would not be the best choice in this scenario because it only represents the middle value in a data set. It does not take into account extreme values like the $1,300 rent expense.
Standard deviation would not be the most appropriate measure of spread in this case because it calculates the average deviation of each data point from the mean. However, it may not accurately represent the spread when extreme values like the $1,300 rent expense are present.
The interquartile range (IQR) would not be the best choice either because it measures the spread of the middle 50% of the data set. It does not consider extreme values and would not accurately represent the range of rent expenses in this scenario.
In summary, the range would be the most appropriate measure of spread in this case because it takes into account the extreme values of $300 and $1,300 and provides a clear measure of the difference between them.
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If you are standing 75 ft away from a tree and looking up at the top at a 40° angle, what is the height of the tree?
Answer:
Step-by-step explanation:
Solve for x. Round to the nearest tenth, if necessary. PLEASE HELP!
Answer:
15.6
Step-by-step explanation:
SOH -CHA-TOA
Tan = opp / adj
Tan(60) = 27/x
x = 27/tan(60)
Answer:
x ≈ 5.4
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan60° = \(\frac{opposite}{adjacent}\) = \(\frac{MN}{LM}\) = \(\frac{9.3}{x}\) ( multiply both sides by x )
x × tan60° = 9.3 ( divide both sides by tan60° )
x = \(\frac{9.3}{tan60}\) ≈ 5.4 ( to the nearest tenth )
1. What is the perimeter of the figure below. Simplify.
4x^3-5x 2x^3+6x 6x^3+x
Answer:
\(12x^3+2x\)
Step-by-step explanation:
The perimeter of a polygon is equal to the sum of its sides.
The sides in the triangle shown have lengths \(2x^3+6x\), \(4x^3-5x\), and \(6x^3+x\) in no specific order.
Since its perimeter is given by the sum of its sides, the perimeter is equal to:
\(2x^3+6x+4x^3-5x+6x^3+x\)
Combine like terms:
\(\boxed{12x^3+2x}\)
Solve the following equation to find the value of x
\(45 + x = 50\)
Answer:
x=5
Step-by-step explanation:
Sorry if wrong :> Hope i helped! Have a awesome day!!! You're a great hooman ^_^ Please mark brainliest !!
Answer:
45 plus 5 equal 50
Step-by-step explanation:
Write an equation for the line parallel to the given line that contains C.
5
C(1,7); y=x+4
The equation of the line parallel to the given line that contains C is obtained as y = x + 6.
What is termed as the parallel lines?Parallel lines are two or more lines which lie within the same plane but never intersect. They are equal in distance and have the same slope. Parallel lines have been straight lines which never meet, no matter how far they are extended. Numerous pairs of angles are formed when two parallel lines have been intersected by another line known as a transversal.For the given question;
The equation of the line is given as;
y = x + 4
The standard form of the equation of line in slope intercept form is;
y = m x + c
where, m is the slope and c is the y intercept.
On comparing;
m₁ = 1
Now, the other lien is parallel to the given line.
Thus, slopes of both lines will be equal.
m₁ = m₂ = 1
The passing points of the line are;
(x₁, y₁) = C(1, 7)
Now, the equation of lien will be;
y - y₁ = m₂(x - x₁)
Put the values;
y - 7 = 1(x - 1)
Simplifying.
y = x + 6
Thus, the equation of the line parallel to the given line that contains C is obtained as y = x + 6.
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A triangular prism is 12 meters long and has a triangular face with a base of 8 meters and a height of 9 meters. What is the volume of the triangular prism?
The volume of the triangular prism is 216 cubic meters.
To find the volume of a triangular prism, we need to multiply the area of the triangular base by the length of the prism.
Calculate the area of the triangular base.
The base of the triangular face is given as 8 meters, and the height is 9 meters. We can use the formula for the area of a triangle: area = (1/2) * base * height.
Plugging in the values, we get:
Area = (1/2) * 8 meters * 9 meters = 36 square meters.
Multiply the area of the base by the length of the prism.
The length of the prism is given as 12 meters.
Volume = area of base * length of prism = 36 square meters * 12 meters = 432 cubic meters.
Adjust for the shape of the prism.
Since the prism is a triangular prism, we need to divide the volume by 2.
Adjusted Volume = (1/2) * 432 cubic meters = 216 cubic meters.
Therefore, the volume of the triangular prism is 216 cubic meters.
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Find the area of hexagon DEFGHI.
Step-by-step explanation:
Break it up into two trapezoids as shown
area = trap1 + trap2
= 2 * (7+3) / 2 + 3 * ( 7 + 3) / 2 = 10 + 15 = 25 units^2