The measure of the central angle in degrees subtended by an arc of length 5 meter is 71.61 degrees
The radius of the circle = 4 meters
The circumference of the circle = 2πr
Where r is the radius of the circle
The value of π = 3.14
The circumference of the circle = 2π × 4
= 8π
The arc length = 5 meters
Consider the x as the central angle
The proportion of central angle and circumference will be
5/8π = x radiance / 2π
Cross multiply the terms
x × 8π = 5 × 2π
x = 10π / 8π
x = 5/4 radiance
Convert radiance to degrees
We know
1 radiance = 180/π degrees
5/4 radiance = 5/4 × 180/π degrees
= 71.61 degrees
Therefore, the central angle is 71.61 degrees
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Find the equation of a line that contains the points (−7,2) and (2,−2). Write the equation in slope-intercept form using fraction if necessary.
The required equation of the line which contains the points (−7,2) and (2,−2) is y = -4/9x - 8/9.
What is the equation of the line?A straight line's general equation is y = MX + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept.
The equation of the line's general form is:
y = MX + c
Where, m = slope, c = y-intercept and slope = ( y₂ - y₁ ) / ( x₂ - x₁ ).
Determine the line's slope:
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope = ( -2-2) / (2+7 )
Slope= -4/9
The y-intercept is determined as follows:
y = MX + c
2 = -4/9x 2+c
c = -8/9
The lines' equation:
y = MX + c
y = -4/9x - 8/9
Therefore, the required equation of the line which contains the points (−7,2) and (2,−2) is y = -4/9x - 8/9.
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Which number is a solution of the inequality?
x(7-x) > 8
x(7 - x) > 8
Steps for calculationFirst solve x(7 - x) = 8
x^2 - 7x + 8 = 0
x = 5.56, 1.44
If we plug in these values into the original equation we can see that solution is
1.44 < x < 5.56
Meaning and definition of systems of inequality:The value of the variable(s) that transforms the inequality into a true statement is the solution. Think about the example (x+3>5). If we provide any real value bigger than (2) for this inequality, it will be true (x). (therefore) This inequality's answer is (x>2)A collection of two or more inequalities in one or more variables is referred to as a system of inequalities. Systems of inequalities are utilized when a scenario calls for several solutions but also places multiple restrictions on those answers.The best answer is often found by solving a set of linear inequalities. This response could be as simple as calculating the number of products that need be produced in order to maximize profit or as complex as selecting the ideal medication regimen for a patient. The different kinds of inequalities and how to solve them will be covered in this article.To learn more about Systems of inequalities refer https://brainly.com/question/26119697
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Evaluate the expression below for s=3 and t=6.
3st² - s²
For s = 3 and t = 6, 3st² - s² =
The value of the expression is 3st² - s² is 315.
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)
Given expression is 3st² - s².
For s = 3 and t = 6, find the value of the expression 3st² - s².
To find the value of the expression, replace s by 3 and t by 6:
3st² - s²
= 3×3×6² - 3²
= (9 × 36) - 9
= 324 - 9
= 315
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Given a binomial experiment with the probability of success on a single trial p = 0.80, find the probability that the first success occurs on trial number n = 3. (Round your answer to three decimal places.)
The probability that the first success occurs on trial number n = 3 is 0.032
How to find the probability that the first success occurs on trial number n = 3?Given:
probability of success on a single trial p = 0.80
trial number, n = 3
Recall the formula for the Geometric Probability Distribution
P(n) = p(1 - p)ⁿ⁻¹
where n is the number of the binomial trial on which the first success occurs and p is the probability of success on each trial
P(n) = p(1 - p)ⁿ⁻¹
P(3) = 0.8(1-0.8)³⁻¹
P(3) = 0.8(0.2)²
P(3) = 0.032
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Find the x and y intercepts of the line: 3x - 4y = -24
Answer:
x- intercept = - 8 , y- intercept = 6
Step-by-step explanation:
to find the x- intercept let y = 0 in the equation and solve for x
3x - 4(0) = - 24
3x = - 24 ( divide both sides by 3 )
x = - 8 ← x- intercept
to find the y- intercept let x = 0 in the equation and solve for y
3(0) - 4y = - 24
- 4y = - 24 ( divide both sides by - 4 )
y = 6 ← y- intercept
- At a bake sale, the Math Club raised $225 by selling 300 baked goods. If the amount
raised varies directly with the baked goods sold, how much money will be raised for
selling 450 baked goods?
Record your answer on the answer document.
5x3
The amount of money for selling 450 baked goods will be
What is Proportional?Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
At a bake sale, the Math Club raised $225 by selling 300 baked goods.
And, The amount raised varies directly with the baked goods sold.
Now,
Let the amount of money for selling 450 baked goods = x
Since, At a bake sale, the Math Club raised $225 by selling 300 baked goods.
And, The amount raised varies directly with the baked goods sold.
Hence, By definition of proportion we get;
⇒ $225/300 = x / 450
⇒ x = 225 × 450 / 300
⇒ x = $337.5
Thus, The amount of money for selling 450 baked goods = $337.5
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which of the following is not a valid property of circles? a rotateangle b none of these c left d width
There is no property named 'left' for the circle. So the answer is 'c'.
What is Circle?Circle is a two dimensional figure which has a round shape. It is formed by joining all the points which are at an equal distance from a fixed point called the center of the circle.
The line formed by joining the center to any point on the boundary of the circle is called radius. Diameter is double of the radius.
Rotate angle is the term defining the angle of rotation of the circle. Angle of rotation of a complete circle is 2π.
Width is another term for diameter of the circle, although it is not commonly used.
Left is the only term which does not have any role in the properties of circles.
Hence, the term 'left' is not a valid property of circles.
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PLEASE HELP WILL GIVE BRAINLIEST IF HELPFUL.
log base (2) of (x^2 +5) = (3)
Answer:
Step-by-step explanation:
log base (2) of (x^2 +5) = (3) can also be described as 2^3 = x^2 + 5
simplify: 8 = x^2+5
Subtract 5 from each side: 3 = x^2
square root: x = sqrt(3)
Answer:
Step-by-step explanation:
[tex]log(2)^{(x^2+5)}=3\\[/tex]
[tex]2^3 =x^2+5\\8-5=x^2\\x^2=3\\x=\pm\sqrt{3}[/tex]
Find f(x) where f'(x)=4x+7
Answer:
[tex]2x^2+7x+C[/tex]
Step-by-step explanation:
Find the antiderivative of f'(x)=4x+7
[tex]\frac{4x^{1+1} }{1+1}+7x+C\\\frac{4x^2}{2}+7x+C\\ 2x^2+7x+C\\[/tex]
The area of ground A is given by 12x^2y sq. units and the area of ground B is given by 6xy^2sq Units
where x>0 and y> 0. Tiles of the same size need to be installed on both the grounds. What should
be the maximum tile area so that it can be used for both the grounds?
The maximum area of the tile to contain both grounds is 12x²y²
How to determine the maximum area of the tile?From the question, we have the following parameters that can be used in our computation:
Area of ground A = 12x^2y sq. units
Area of ground B = 6xy^2sq units
Rewrite these areas properly
So, we have the following representation
Area of ground A = 12x²y sq. units
Area of ground B = 6xy² sq units
Express the areas as the products of their prime factors
This gives
Area of ground A = 2 * 2 * 3 * x * x * y
Area of ground B = 2 * 3 * x * y * y
From the above products, we have
Least common multiple = 2 * 2 * 3 * x * x *y * y
Evaluate the products
Least common multiple = 12x²y²
This represents the greatest area
Hence, the greatest area is 12x²y²
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An air traffic controller is tracking two planes. To start, plane A is at an altitude of 3500 feet and plane B is at an altitude of 2609 feet. Plane A is gaining altitude at 45.5 feet per second and plane B is gaining 65.75 feet per second. How many seconds will pass before the planes are at the same altitude? What will their altitudes be when they’re at the same altitude?
44 seconds will pass before the planes are at the same altitude.
What do you mean by algebraic expression?
An algebraic expression in mathematics is an expression that consists of variables and constants and algebraic operations (addition, subtraction, etc.). Expressions are made up of concepts.
There are three main types of algebraic expressions:
Monomial Expression
Binomial Expression
Polynomial Expression
An algebraic expression with only one term is called a monomial.
It is given that plane A is at an altitude of 3500 feet and plane B is at an altitude of 2609 feet. Plane A is gaining altitude at 45.5 feet per second and plane B is gaining 65.75 feet per second.
Let x seconds will pass before the planes are at the same altitude.
Plane A, 3500 + 45.5x
Plane B, 2609 + 65.75x
x is number of seconds of time
When altitudes equal
3500 + 45.5x = 2609 + 65.75x
3500 - 2609 = 65.75x - 45.5x
891 = 20.25x
891/20.25 = x
44 = x
Therefore, 44 seconds will pass before the planes are at the same altitude.
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Find the dimensions of the rectangular box with largest volume if the total surface area is given as 100 cm2. (Let x, y, and z be the dimensions of the rectangular box.)(x, y, z) =
The dimensions of the rectangular box with largest volume if the total surface area is given as 100 cm2: x = y = z = 2.449 cm.
Given that:
Total surface area of the rectangular box or cuboid = 100 cm²
A rectangular box with largest volume is a cube.
The total surface area of a cube = 6 times square of one edge length.
Let the edge length = given dimensions; x, y, z
So,
x = y = z
6x^2 = 100
x^2 = 100 / 6
x = √ 100 / 6
x = 10 / √ 6 cm
x = 2.449 cm
Hence, dimensions of the rectangular box with largest volume if the total surface area is given as 100 cm2: x = y = z = 2.449 cm.
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Find the angle round to the nearest degree. please help.
63 degrees is the angle.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
The given triangle is a right angle triangle.
The opposite side length is 85 and the adjacent side is 38.
Opposite side=85
Adjacent side=38.
Calculate Opposite/Adjacent
= 85/38= 2.236
Which is tanθ=2.236
Now tan inverse on both the sides
θ=tan⁻¹2.236
θ=tan⁻¹2
θ=63 degrees.
Hence, the angle is 63 degrees.
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Allie receives a $20 gift card for the local coffee shop, where she only buys lattes and muffins. If the price of a latte is $4 and the price of a muffin is $2, then we can conclude that Julia:
If the price of a latte is $4 and the price of a muffin is $2, then we can conclude that Julia can buy 5 lattes or 10 muffins ($20) if she chooses to buy only one of the two goods.
How to illustrate the price?A price is the sum of money that one party pays or receives in exchange for another's goods or services. The cost of production may go by another name in certain circumstances. If the item is a "good" in a commercial transaction, the cost of the item will probably be referred to as its "price."
In this case, Allie receives a $20 gift card for the local coffee shop, where she only buys lattes and muffins. Here, we can conclude that Julia can buy 5 lattes. This will be 5 × $4 = $20 or 10 muffins which will be:
= 10 × $2
= $20
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emily surveyed all the students at her school to find out if they plan to attend college. the results are shown in the two-way frequency table. emily knows that the student body at her high school is distributed as follows: freshmen: 28% sophomores: 26% juniors: 24% seniors: 22% according to the information emily has gathered, which of the following statements are true? choose all that are correct. responses more than 40% of the students at the school are freshmen or sophomores who plan to attend college. more than 40% of the students at the school are freshmen or sophomores who plan to attend college. more than 10% of the students at the school are juniors or seniors who do not plan to attend college. more than 10% of the students at the school are juniors or seniors who do not plan to attend college. if a student who plans to attend college is selected at random, the probability that he or she is a senior is 0.1804. if a student who plans to attend college is selected at random, the probability that he or she is a senior is 0.1804. if a student at the high school is selected at random, the probability that he or she is a freshman who does not plan to attend college is 0.15. if a student at the high school is selected at random, the probability that he or she is a freshman who does not plan to attend college is 0.15.
The following statements are true are more than 40% of the students at the school are freshmen or sophomores who plan to attend college.
Given :
emily surveyed all the students at her school to find out if they plan to attend college. the results are shown in the two-way frequency table. emily knows that the student body at her high school is distributed as follows: freshmen: 28 % sophomores: 26 % juniors: 24 % seniors: 22 % .
Freshmen = 0.85
sophomores = 0.80
it is clearly visible that the freshmen or sophomores is greater than the 40 % .
Hence , more than 40% of the students at the school are freshmen or sophomores who plan to attend college.
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City A is located in a valley 15 meters below sea level, and City B is located *
43 meters above sea level. What is the difference, in meters, between the
elevations of these two cities? Remember, difference means subtract (and
you will need to SCO).
Answer:
To find the difference between the elevations of City A and City B, we need to subtract the elevation of City A from the elevation of City B. Since City A is located 15 meters below sea level, and City B is located 43 meters above sea level, the difference between their elevations is $43 - (-15) = 43 + 15 = 58 meters. Therefore, the difference between the elevations of City A and City B is 58 meters.
8w-16 how do i answer this
The factor of the expression 8w - 16 will be 8 and (w - 2).
What is factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
A frequency table displays a sequence of scores in either increasing or decreasing order together with their occurrences as a way to compactly organize raw data.
The expression is given below.
⇒ 8w - 16
The factor of each term in the expression, then we have
8w = 8 x w
16 = 8 x 2
Then the expression is written as,
⇒ 8w - 16
⇒ 8 × w - 8 × 2
⇒ 8 × (w - 2)
⇒ 8(w - 2)
The component of the articulation 8w - 16 will be 8 and (w - 2).
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At a football game, a vender sold a combined total of 244 sodas and hot dogs. The number of hot dogs sold was 42 less than the number of sodas sold. Find the number of sodas sold and the number of hot dogs sold.
Answer:
143 sodas101 hot dogsStep-by-step explanation:
Given a total of 244 sodas and hot dogs sold, with sodas numbering 42 more than hot dogs, you want to know the number of each that were sold.
SetupLet s represent the number of sodas sold. Then s-42 is the number of hot dogs sold, and the total sold is ...
s +(s -42) = 244
SolutionAdd 42 and simplify
2s = 286
s = 143 . . . . . divide by 2
hot dogs = 143 -42 = 101 . . . . . figure the number of hot dogs
143 sodas and 101 hot dogs were sold.
A _______ is a set of input data in a relationship
The complete answer: A domain is a set of input data in a relationship.
What is domain?The collection of all conceivable independent values that a function or relation may take is known as its domain.
An input value and an output value are matched in a relation.
A relation is a function where each input value yields one and only one output value.
Graphs, tables, and ordered pairs can all be used to represent functions. The domain is the set of input values,
while the range is the set of output values.
The domain of a function or relation is the set of all possible independent values that it can have.
Therefore, a domain is a set of input data in a relationship.
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The area of a rectangle is given by the function A(x) = 2x3 + 6x2 + 5x + 15. If the length is defined by x + 3, what is the width of the rectangle?
Answer:
2x² +5
Step-by-step explanation:
You want the width of a rectangle with a length of x+3 and an area of A(x) = 2x³ +6x² +5x +15.
AreaThe area is the product of length and width, so the width will be ...
A = LW
W = A/L = (2x³ +6x² +5x +15)/(x +3)
The cubic expression can be factored by grouping, so we have ...
Area = (2x³ +6x²) +(5x +15)
= 2x²(x +3) +5(x +3)
= (2x² +5)(x +3)
Then the width is ...
[tex]\text{width}=\dfrac{(x+3)(2x^2+5)}{x+3}=\boxed{2x^2+5}[/tex]
The width of the rectangle is 2x² +5.
<95141404393>
You are given the figure below well as the following information.
Answer:
A. 110°
Step-by-step explanation:
according to the theorems,
m∠1=m∠6=m∠9=m∠14=110°;
m∠2=m∠5=m∠10=m∠13=70°;
m∠3=m∠8=m∠11=m∠16=70°;
m∠4=m∠7=m∠12=m∠15=110°.
all the details are in the attachment.
Can anyone help me ASAP?
a number has the same digit in its hundreds place and in its hundreds place. how many times greater is the value of the digit in the hundreds place than the value of the digit in the hundreds place
A number has the same digit in its hundreds place and in its hundreds place. 10,000
What is the value of the digit?Generally, Given that a number's hundreds place and its hundredths place both have the same digit, we may assume that the number is perfect.
Let's say that the digit is a 1.
Therefore, the value of the hundreds position in a number is equal to 100.
The value of the hundredth position in a number is equal to 0.01%.
The following formula may be used to determine the number of instances in which the value of the digit in the hundreds place is higher than the value of the digit in the hundredths place:
As a result, the difference between the value of the digit in the hundreds place and the value of the digit in the hundredth place is 10,000 times bigger.
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CQ
A number has the same digit in its hundreds place and its hundredths place. How many times greater is is the value of the digit in the hundreds place than the value of the digit in the hundredths place?
A. 100,00
B. 100
C. 1,000
D. 10,000
Kim decided that she wanted to go bowling. The bowling alley charges $2.75 per game and $10 for shoes. If Kim has $30, how many complete games can she bowl?
Write an equation and solve it.
Answer: 2 complete games
Step-by-step explanation:
add shoes and game charge
$10.00 + 2.75 = 12.75 <— that’s 1 complete game
subtract it from $30.00
$30.00 - 12.75 = 17.25.
A complete game costs 12.75. so, Kim had enough money for one more game.
17.25 - 12.75 = $4.50 remaining after 2 complete games
Answer: 7 games
Step-by-step explanation: if it charges 10 for shoes, then you already subtract 10 from 30. 30-10=20. then, to find out how many games she can play, divide 2.75 from 20. 20/2.75=7.272727.... Since you can't pay for half of a game, it would be 7 games.
which are prime polynomials
-12f+21
f-36
-3f-23
5f+10
Answer:
f - 36
-3f - 23
are your prime polynomials.
What is an equation of the parabola
Answer:
(c) x = -1/11(y -3)²
Step-by-step explanation:
You want an equation of the parabola with directrix x = 11/4 and vertex (0, 3).
EquationThe directrix is a vertical line to the right of the vertex. This means the parabola opens to the left.
The vertex form of the equation is ...
x = 1/(4p)(y -k)² +h . . . . . . . . where (h, k) is the vertex, and p is the distance from the directrix to the vertex (also, the distance from the vertex to the focus)
ApplicationHere, we have ...
p = 0 -11/4 = -11/4 . . . . negative because the vertex is left of the directrix
and
(h, k) = (0, 3)
so the equation is ...
x = 1/(4(-11/4))(y -3)² +0
x = -1/11(y -3)²
MP MODELING REAL LIFE You sell instruments at a
Caribbean music festival. You earn $326 by selling 12 sets
of maracas, 6 sets of claves, and x djembe drums. Find the
number of djembe drums you sold.
The number of djembe drums you sold is 8
How to determine the number of djembe drums you sold.From the question, we have the following parameters that can be used in our computation:
Total = 12 sets of maracas, 6 sets of claves, and x djembe drums.
Earning = $326
Also, we have:
The maracas costs $14 per set, the claves costs $5 per set, and the drum cost $16.
So, we have
12 * 14 + 6 * 5 + x * 16 = 326
Evaluate the products
198 + 16x = 326
Evaluate the iike terms
16x = 128
So, we have
x = 8
Hence, the number of djembe drums is 8
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Complete question
You sell instruments at a Caribbean music festival. You earn $326 by selling 12 sets of maracas, 6 sets of claves, and x djembe drums.
The maracas costs $14 per set, the claves costs $5 per set, and the drum cost $16.
Find the number of djembe drums you sold.
You install 538 feet of fencing along the perimeter of a rectangular yard. The width of the yard is 127 feet. What is the length of the yard?
What values of x make the two expressions below equal?
(x-1)(x-6)_
4(x-1)
x-6
4
A. All real numbers except 1
B. All real numbers except 6
C. All real numbers
D. All real numbers except 1 and 6
All the real numbers except 1 make the two expressions equal. Then the correct option is A.
What is an equivalent expression?The equivalent is the expression that is in different forms but is equal to the same value.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The expressions are given below.
[(x - 1)(x - 6)] / [4(x - 1)] and (x - 6) / 4
Simplify the expression [(x - 1)(x - 6)] / [4(x - 1)], then we have
⇒ [(x - 1)(x - 6)] / [4(x - 1)]
⇒ (x - 6) / 4
But at x = 1, the expression [(x - 1)(x - 6)] / [4(x - 1)] is not defined.
All the real numbers except 1 make the two expressions equal. Then the correct option is A.
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A scientist began measuring the temperature of a solution when it was 100 °F. The temperature of the solution
decreased at a constant rate of 1.5 °F per hour.
Which function can be used to find y, the temperature of the solution in degrees Fahrenheit after x hours?
Ay 1.5x - 100
By 1.5x + 100
y 100x1.5
Oy - 100x + 1.5
Conditional problems are problems that involve one or more conditions that must be met in order for a certain action to be taken or a certain result to be obtained. The temperature of the solution in degrees Fahrenheit after x hours, is y = 1.5x - 100.
The required details for Conditional problems in given paragraph
This function models the temperature of the solution as it decreases at a constant rate of 1.5 °F per hour. The initial temperature of the solution is 100 °F, and the temperature decreases by 1.5 °F for each hour that passes. Therefore, the temperature of the solution after x hours can be found by subtracting 1.5x degrees from the initial temperature of 100 degrees.
For example, if we plug in x = 2 into the function, we get y = 1.5 * 2 - 100 = 3 - 100 = -97, which means that the temperature of the solution after 2 hours is -97 °F.
The other options listed are not correct because they do not correctly model the temperature of the solution as it decreases at a constant rate of 1.5 °F per hour. Option A is incorrect because it adds 1.5x degrees to the initial temperature, rather than subtracting it. Option B is incorrect because it adds 100 degrees to the temperature, rather than subtracting it. Option C is incorrect because it multiplies the initial temperature by 1.5x, rather than subtracting 1.5x degrees from it. Option D is incorrect because it adds 1.5 to the temperature, rather than subtracting 1.5x degrees from it.
what are conditional problems?
Conditional problems are often expressed using words like "if," "then," or "when." For example, a conditional problem might involve finding the value of a variable x if it satisfies a certain condition, such as "If x is greater than 5, then x is even." In this case, the problem specifies that x must be greater than 5 in order for it to be even.
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