The area of the major sector is 2807. 1 cm²
How to calculate the area of the major sector?
The perimeter of a sector given by the formula:
P = θ/360 × 2πr
where r is the radius and θ is the angle subtended at the centre
Since the perimeter of a major sector is 168cm and the angle subtended by the minor arc is 72 degrees. We can say:
angle subtended by the major arc = 360 -72 = 288 degrees
P = θ/360 × 2πr
168 = 288/360 × 2πr
210 = 2πr
r = 210/2π
r = 33.42 cm
Thus, the radius of the major arc is 33.42 cm
The area of a sector given by the formula:
A = θ/360 × πr²
A = (288/360) × π × 33.42²
A = 2807. 1 cm²
Thus, the area of the major sector is 2807. 1 cm²
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Can someone help me fast need help on it for grade tomorrow
Answer:
x = 5
Step-by-step explanation:
Angles on a straight line add up to 180, so add up the angles and equate to 180:
9x + 85 + 10x = 180
Now we can solve for x by simplifying further:
19x + 85 = 180
Subtract 85 on both sides:
19x + 85 - 85 = 180 - 85
19x = 95
Divide 19 on both sides which cancels out the 19 on the left:
x = 95/19 = 5
A cla contain b boy and g girl if the number of way of electing 3 boy and 2 girl i 168
Since b and g are the numbers of boys and girls in class b + 3g is equal to [tex]b^3 - 3b^2 + 5g^2 - 3g + 2b[/tex]
We can use the concept of combination to determine the value of b + 3g.
The number of ways to choose 3 boys from b boys and 2 girls from g girls is:
(b choose 3) x (g choose 2) = (b! / (3!(b-3)!) ) x (g! / (2!(g-2)!) ) = (b x (b-1)(b-2))/(321) x (g(g-1))/(2 x 1)
We know that this is equal to 168, so we can set up the equation:
(b x (b-1)(b-2))/(321) x (g(g-1))/(2 x 1) = 168
We can solve this equation to find the value of b + 3g. Since b and g are the numbers of boys and girls in the class, we know that b + g is the total number of students in the class.
So we can simplify the equation as:
(b x (b-1)(b-2)) x (g(g-1)) = 32121 x 168
and rearrange it to:
[tex](b^3 - 3b^2 + 2b) * (g^2 - g) = 1008[/tex]
[tex]= b^3 - 3b^2 + 2b = 1008 / (g^2 - g)b + 3g \\= (b^3 - 3b^2 + 2b) + 3(g^2 - g) \\= b^3 - 3b^2 + 2b + 3g^2 - 3g \\= b^3 - 3b^2 + 5g^2 - 3g + 2b[/tex]
So we can see that b + 3g is equal to b^3 - 3b^2 + 5g^2 - 3g + 2b. However, the exact value cannot be determined without the specific values of b and g.
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How do you determine if a function is convex or concave?.
An intuitive definition: a function ݂f is said to be convex at an interval I if, for all pairs of points on the ݂f(x) graph, the line segment that connects these two points passes above the ݂f(x) curve.
A function ݂ is said to be concave at an interval I if, for all pairs of points on the graph f(x), the line segment that joins these two points passes below the ݂f(x) curve.
A convex function has a regularly increasing first derivative, making it appear to bend upwards.
Contrarily, a concave function has a regular decreasing first derivative making it bend downwards. It is very important to know the distinction between the first derivative, that tells us of the slope of the tangent of a function, and the second derivative, which shows us how it is curved.
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How do you divide two digit numbers without a calculator?.
The process of dividing the two digit numbers without a calculator is solved by using the dividend, divisor, quotient and remainder.
Division in math is defined as the process to distribute the whole thing to a group in equal parts or make equal parts.
Here we need to find he way to divide two digit numbers without a calculator.
As per the definition of division, here we have to divide the first number of the dividend or the two first numbers if the previous step took another digit by the first digit of the divisor.
And then we have to write the result of this division in the space of the quotient.
Finally we have to multiply the digit of the quotient by the divisor, then write the result beneath the dividend and subtract it.
This process is repeated until we get zero as remainder.
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look at this graph...
last year, Reuben biked 496 miles. This year, he biked m miles. Using m, write an expression for the total number of miles he biked.
The total number of miles Reuben biked last year and this year is the sum of the miles he biked last year and this year.
You can represent the total number of miles he biked as:
Total miles = 496 + m
Where 496 is the number of miles biked last year and m represents the number of miles biked this year.
So the expression for the total number of miles he biked is 496 + m
What is the slope of the line that passes through the points (9, 5)(9,5) and (21, -5)(21,−5)? Write your answer in simplest form.
The slope of a line is determined by the formula:
(y2 - y1) / (x2 - x1)
So for the points (9, 5) and (21, -5), the slope would be:
(-5 - 5) / (21 - 9) = -10 / 12 = -5/6
So the slope of the line that passes through the points (9, 5) and (21, -5) is -5/6 in simplest form.
are the inhabitants of a certain village on the Nigerian border speaker the French or English if 64% speak French and 58% speak English what percentage speak
both languages? Two set problems
Answer: We can use the formulas for conditional probability to calculate the percentage of people in the village who speak both French and English.
P(French and English) = P(French) x P(English|French)
We know that P(French) = 64% and P(English|French) is the probability of someone speaking English given that they already speak French, which is 58%. So we can plug these values into the formula:
P(French and English) = 64% x 58% = 37.12%
Therefore, 37.12% of the inhabitants of the village on the Nigerian border speak both French and English.
Note that this is an estimation since this formula assumes independence and the real probabilities might be different.
Step-by-step explanation:
How do you find the range of a function?.
The range is the spread of the values of the output of a function.
To Find : The Range of a Function ,Consider a function y = f(x)
The spread of all the y values from minimum to maximum is the range of the function. In the given expression of y, substitute all the values of x to check whether it is positive, negative or equal to other values. Find the minimum and maximum values for y. Then draw a graph for the same.
The range of a function is a set of all its possible outputs.
Example: Let’s consider a function ƒ: A⇢A, where A = {1,2,3,4}.
The elements of the set Domain, are called pre-images, and elements of the set Co-Domain which are mapped to pre-images are called images. The range of a function is a set of all the images of elements in the domain. In this example, the range of the function is {2,3}.
The range is the spread of the values of the output of a function. If we are able to calculate the maximum and the minimum values of the function, we can get an idea of the range of the function.
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What is the distance between the points with coordinates 3/4 and 0 0 )?.
The distance between the pair of points with the coordinates ( 3, 4 ) and (0, 0) is given by 5 units.
As given in the question,
Given pair of points with the coordinates are as follow :
( x₁ , y₁ ) = ( 3,4 )
( x₂ , y₂ ) = ( 0, 0 )
General formula to determine the distance between two pair of points with the coordinates is :
= √( y₂ - y₁ )² + (x₂ - x₁ )²
Now, substitute the values of the coordinates to find the distance between two pair of points :
= √ ( 0 - 4 )² + ( 0 - 3 )²
= √4² + 3²
= √16 + 9
= √25
= 5 units.
Therefore, the distance between the given pair of points with the coordinates is equal to 5 units.
The above question is incomplete , the complete question is:
What is the distance between the pair of points (3, 4) and (0, 0) ?
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Which equation has roots of 3+i and 3-I
Answer:
The equation x2+6x+9 = 0 has roots of 3+i and 3-i. By the fundamental theorem of algebra, this equation has three roots, two of which may be equal. The standard quadratic equation using the given set of solutions {3+i,3-i} is y=x2+6x+9.
How many solutions are there to the inequality x1 x2 x3 <= 11?.
There are 364 solutions to the given inequality: x1 + x2 + x3 <= 11.
To get the solution of the inequality x1 + x2 + x3 <= 11, we first need to include an additional variable in the inequation to write in as an equation.
Therefore, let the additional variable be x4.
Thus, equation is x1 + x2 + x3 + x4 = 11
The number of solutions of an equation can be calculated by the formula,
[tex]( \left \ {{n+ r - 1} \atop {n}} \right.)[/tex], where n is the constant value of the equation and r is the number of variables in the equation.
In this case, n = 11 and r = 4
Therefore,
[tex]( \left \ {{n+ r - 1} \atop {n}} \right.)[/tex] = [tex]( \left \ {{11+ 4 - 1} \atop {11}} \right.)[/tex] = [tex]( \left \ {{14} \atop {3}} \right.)[/tex]
= 14 * 13 * 12 * 11!/(3 * 2 * 1 * 11!)
=2184/6 = 364
Therefore, there are 364 possible solutions of the inequality.
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Yeterday King Kog Bike old 9 road bike and 3 tationary bike out of a total of 60 bike. Baed on thi data, what i the probability that the next cutomer purchae a tationary bike?
Anwer in the form of a fraction reduced to the lowet term
If the historical data says that the number of road bikes sold is 9 and the number of stationary bikes sold is 3, out of a total of 60 bikes, then the probability that the next customer purchase a stationary bike is 1/20.
A probability based on historical data is referred to as empirical probability or experimental probability. In other words, empirical probability depicts the probability of an occurrence occurring based on past data.
Empirical probability is also known as the relative frequency.
Formula for the empirical probability is:
Empirical probability = times of event A occurs / total number of trials
In the problem, there are two kinds of bike: road bike and stationary bike.
The historical data:
sales of road bike = 9
sales of stationary bike = 3
total bikes = 60
Hence, the probability that the next customer will buy a stationary bike is:
P(stationary) = sales of stationary bike / total bikes
P(stationary) = 3/ 60 = 1/20
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Amelia cut a 168 inch long ribbon into 6 equal part. Patrick cut a 14 foot long ribbon into 7 equal piece
Amelia cut a 168 inch long ribbon into 6 equal part. Patrick cut a 14 foot long ribbon into 7 equal piece.
Amelia's ribbon pieces were 28 inches long each. Patrick's ribbon pieces were 2 feet long each.
Amelia's ribbon:
To calculate how long each piece of ribbon is, we need to divide 168 inches (the total length of the ribbon) by 6 (the number of pieces).
168 ÷ 6 = 28
Therefore, Amelia's ribbon pieces were 28 inches long each.
Patrick's ribbon:
To calculate how long each piece of ribbon is, we need to divide 14 feet (the total length of the ribbon) by 7 (the number of pieces).
14 ÷ 7 = 2
Since 1 foot is equal to 12 inches, we can convert 2 feet to 24 inches.
Therefore, Patrick's ribbon pieces were 2 feet (or 24 inches) long each.
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Find an equivalent expression using the Distributive Property.
4xy−16x
First, determine the range of the data without the outlier.
Then, determine the range of the data with the outlier.
Finally, make a conclusion about the effect of an outlier on range
Number of Purple Cars
Seen on the Way to School
A number line labeled number of cars ranges from 0 to 10 in increments of 1. It is titled number of purple cars seen on the way to school. Data are: 0, 3; 1, 3; 2, 2; 3, 1; 8, 1.
Number of Cars
The range of the data with the outlier is 7 and without is 2
How to determine the rangeFrom the question, we have the following parameters that can be used in our computation:
0, 3; 1, 3; 2, 2; 3, 1; 8, 1.
The range without the outlier
The range is calculated as
Range = Highest - Least
Without the outlier, we have
Range = 3 - 1
Range = 2
The range with the outlier
The range is calculated as
Range = Highest - Least
With the outlier, we have
Range = 8 - 1
Range = 7
Hence, the range are 2 and 7
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Solve equation by using the quadratic formula. 6 x squared minus 2 x = 8 a. X = three-fourths, negative 1 c. X = three-fourths, 0 b. X = three-fourths, 1 d. X = four-thirds, negative 1.
The roots of the quadratic equation 6x²-2x=8 are x=4/3 and x=-1.
Given that,
The equation is 6x²-2x=8
To find : The roots of the quadratic equation 6x²-2x=8
Any equation that can be rearranged in standard form as where x represents an unknown value, and a, b, and c represent known values, where a 0, is referred to as a quadratic equation in algebra (from Latin quadratus, "square"). The equation is linear, not quadratic, if a = 0 and b 0. The coefficients of the equation are the numbers a, b, and c, which can be separated by naming them, respectively, the quadratic coefficient, the linear coefficient, and the constant coefficient or free term.
We know that,
The solutions are x1 and x2 = -b±√b²-4ac/2a
Here b = -2 ,a = 6 and c= -8
No substitute those values in the formula,
= -b±√b²-4ac/2a
= -(-2) ± √(-2²)-4(6)(-8) / 2(6)
x = 4/3 and x =-1
So, The roots of the quadratic equation 6x²-2x=8 are 4/3 and -1
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8. If the system has no
solution, what number
does the value of h need
to be? Show your work to
justify your answer.
− 6(hx + 2) = 3(x − 3) + 2(x + 2) +13x
The system has no solution when h is not equal to ( 18x+7 )/( -6x)
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
− 6(hx + 2) = 3(x − 3) + 2(x + 2) +13x
-6hx-12=3x-9+2x+4+13x
=> -6hx-12= 18x-5
=> -6hx = 18x-5 +12
=> -6hx = 18x+7
=> h = ( 18x+7 )/( -6x)
The system has no solution when h is not equal to ( 18x+7 )/( -6x)
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Are the following triangles congruent? Why or
why not?
Yes, SSS
Yes, ASA
Yes, AAS
No, there is not enough information
The following triangles are congruent.
Yes AAA
Find the first four terms of the sequence defined below, where n represents the position of a term in the sequence.
Start with n = 1.
an = -74 - 7
In the given arithmetic sequence, the First term is -74, 2nd term is -81 3rd term is -88 and 4th term is -95.
What is arithmetic sequence?There are two ways to define an arithmetic sequence. It is a "sequence where the differences between every two successive terms are the same" (or) In an arithmetic sequence, "each term is obtained by adding a fixed number (positive or negative or zero) to its preceding term." The following is an arithmetic sequence where each term is obtained by adding 4 to the term before it.
We know that arithmetic sequence is:
[tex]a_{n}=a_{1}+(n-1)d[/tex]
Given
a = -74, d = -7
[tex]a_{1} = -74 + (1 - 1)(-7)[/tex]
[tex]a_{1} = -74 + (0)(-7)[/tex]
[tex]a_{1} = -74[/tex] (First term)
[tex]a_{2} = -74 + (2 - 1)(-7)[/tex]
[tex]a_{2} = -74 + (1)(-7)[/tex]
[tex]a_{2} = -81[/tex] (2nd term)
[tex]a_{3} = -74 + (3- 1)(-7)[/tex]
[tex]a_{3} = -74 + (2)(-7)[/tex]
[tex]a_3 = -88[/tex] (3rd term)
[tex]a_{4} = -74 + (4- 1)(-7)[/tex]
[tex]a_{4} = -74 + (3)(-7)[/tex]
[tex]a_3 =-95[/tex] (4th term)
Thus, In the given arithmetic sequence, the First term is -74, 2nd term is -81 3rd term is -88 and 4th term is -95.
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number 5 math heellppp
The value of x as shown in the straight line is 32
What is an equation?An equation is an expression showing the relationship between numbers and variables.
An angle is formed when two lines intersect at a point. The sum of angles in a straight line is 180 degrees.
From the diagram:
(3x - 4) + (3x - 8) = 180° (sum of angle in a straight line)
3x + 3x - 4 - 8 = 180
6x - 12 = 180
6x = 192
x = 32
The value of x is 32
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Gina buys a television priced at $70. If the sales tax is 5%, how much tax will Gina pay?
Step-by-step explanation:
The answer is gotten by 5% of 70
5/100 × 70/1
= 35/10
= 3.5
Answer: $73.50
Step-by-step explanation:
First, we need to find what is 5% worth of 70 bucks. We would divide 5 by 100 since percents are based on 100 which gets us 0.05. Next do 0.05 * 70 = 3.5. Means that she'll pay $3.50 on top of the 70 bucks, so add the two together, common sense: $73.50. Have a good day ;)
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The double number line shows how many bananas are needed to make 1 loaf of banana bread.
0
Loaves ++
Bananas H
1
+
+
2
Complete the table to show the same information as the double number line.
Number of loaves Number of bananas
5
The complete table would look like this:
Number of loaves Number of Bananas
1 2 1/2
2 5
4 10
What is a number line?
A number line is a visual representation of a continuous range of numbers, usually represented as a straight line. Numbers are represented by points along the line, and the distance between two numbers corresponds to the difference between their numerical values. The numbers are usually represented by evenly spaced marks or tick marks on the line, and they can be positive or negative numbers, integers or fractions, or real numbers. The number line is used to represent various mathematical concepts such as inequalities, absolute values, and intervals. It is also used to help students understand concepts such as addition, subtraction, and ordering of numbers.
So the first one was easy because it already said it in the number line.
For the second one you simply multiply 2x 2 1/2
For the third one, you multiply 4x 2 1/2.
Hence, The complete table would look like this:
Number of loaves Number of Bananas
1 2 1/2
2 5
4 10
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Use the number line to solve -2+4
Answer:
-2+4=2
Step-by-step explanation:
All you need to do is count 4 spaces from -2 on the number line. See in image.
-Hope this helped
1.036
+_____
= 4
What is 1.036+ blank that equals 4.
Answer:
2.964
Step-by-step explanation:
4-1.036=2.964
Answer:
2.964
Step-by-step explanation:
4 - 1.036 = 2.964
AC= 4√11
4√22
CB=
if my AC is 4√11 then how do i get CB??
x/sin 45 = 4√22/sin 90
CB = 4√22/sin 90 × sin 45
CB = 4√11
or
CB = √(4√22)²-(4√11)²
= 4√11
Answer:
CB = AC = 4√11
Step-by-step explanation:
We know that the sum of the angles of a triangle is 180°. If angle A = 45° and C = 90°, then angle B = 180° - 90° - 45° = 45°. This shows us that the triangle is isosceles and the leg AC is equal to the leg CB.
Consequently: CB = AC = 4√11
If we didn't know the length of AC, then it can be calculated from the hypotenuse:
AC² + CB² = AB²
2 * CB² = (4√22)²
CB² = (4√22)² / 2
CB² = 16 * 22 / 2
CB = √(16 * 11)
CB = 4√11
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A rental car company charges $40.50 per day to rent a car and $0.12 for every mile driven. Sebastian wants to rent a car, knowing that: He plans to drive 400 miles. He has at most $210 to spend. Write and solve an inequality which can be used to determine dd, the number of days Sebastian can afford to rent while staying within his budget. Inequality: dd
Answer:
88.50
Step-by-step explanation:
0.12x400=48 dollars +the 40.50 dollars answer 88.50
What is the distance between points 2 3 and 5 7?.
The distance between two points (2, 3) and (5, 7) is 5 units.
Therefore the answer is 5.
To find the distance between the points (2, 3) and (5, 7), we can use the distance formula:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
where (x₁, y₁) = (2, 3) and (x₂, y₂) = (5, 7)
Substituting the coordinates of the two points into the formula:
d = √((5 - 2)² + (7 - 3)²)
d = √((3)² + (4)²)
d = √(9 + 16)
d = √(25)
d = 5
So the distance between the points (2, 3) as well as (5, 7) will be 5 units by solving the above expression.
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How does the process of solving an inequality with variables on both sides compare to solving an equation with variables on both sides?
Answer: It's the same process to get the variable by itself. But once found depending on how you are required to represent the solution, the final answer may vary. You need to also keep in mind that with negatives when multiplying and dividing you have to flip the inequality sign.
Step-by-step explanation:
Ex. 2x>4
x>2
but if
-2x>4
x<-2
5x(h+3) for h = 7 PLEASE HELP ME PLEASE IF YOU DO THANK YOU SO MUCH
This problem may be simplified by substituting the number seven into the original equation. The result will then be obtained by solving the given expression.
Put the supplied value of h, which is seven, in the given phrase to begin solving this problem. Then, using the BODMAS rule, the bracket will be solved first, followed by the addition, from which this can be solved yielding a result of 50.
This may be resolved as follows:
For h=7, in 5 x ( h + 3 )
= 5 x ( 7 + 3 )
= 5 x ( 10 )
= 50
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