The area of a regular hexagon inscribed in a circle is equal to two-thirds of the area of the circle. [tex]$324\pi\div 2\div 3[/tex]= [tex]108\pi$ $108\pi \approx 339.292$[/tex] square units The answer in simplest radical form is[tex]$\sqrt{339.292}$[/tex] square units.
it is important to first understand the concept of a regular hexagon inscribed in a circle. A regular hexagon inscribed in a circle is a six-sided polygon whose interior angles are all equal and whose sides are all of equal lengths. This means that the hexagon will have six equal-length sides and six equal-sized angles.
The area of such a hexagon is equal to two-thirds of the area of the circle in which it is inscribed. In this problem, the area of the circle is given as [tex]$324\pi$[/tex] square units. To determine the area of the regular hexagon inscribed in the circle, the area of the circle needs to be divided by two and then by three.
This yields a result of [tex]$108\pi$[/tex] square units, which is approximately equal to 339.292 square units. This result can be written in the simplest radical form as [tex]$\sqrt{339.292}$[/tex] square units, which is the answer to the problem.
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A local ice-cream shop sells ice-cream cones for $2.00, and customers can choose from the following options.Ice-cream flavorType of cone: sugar or waffleChocolate dipped for an additional $0.50Sprinkles for an additional $0.50Which of the following is a quantitative variable?answer choicesIce-cream flavorType of coneChocolate dipped or notSprinkles or notThe total cost of the cone
4, 5 and 6 are quantitative variable
given that
Quantitative variablesWhen you collect quantitative data, the numbers you record represent real amounts that can be added, subtracted, divided, etc. There are two types of quantitative variables: discrete and continuous.
When you graph or plot statistical data, make sure you have quantitative data of known units. If you don’t have known units, then you won’t be able to graph it.
Variables whose values result from counting or measuring something.
Examples: height, weight, time in the 100 yard dash, number of items sold to a shopper
answer choices
1. Type of cone
2.Chocolate dipped: yes / no
3.Sprinkles: yes / no
4.Cost of chocolate dip
5.Cost of sprinkles
6.Cost of one cone
4, 5 and 6 are quantitative variable
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What is the product? help
Answer:
C. 14x^7-56x^6-126x^5+35x^4-140x^3-315x^2
I'm only providing an answer but if you need an explanation you can ask me because I did it in my journal.
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Which graph shows the solution to the system of linear equations? y equals one half times x x + 2y = 8 coordinate plane with one line that passes through the points 0 comma 4 and 2 comma 5 and another line that passes through the points 0 comma 0 and 2 comma 1 coordinate plane with one line that passes through the points 0 comma 4 and 2 comma 3 and another line that passes through the points 0 comma 0 and 2 comma 1 coordinate plane with one line that passes through the points negative 1 comma 2 and 0 comma 4 and another line that passes through the points 0 comma 0 and 1 comma 2 coordinate plane with one line that passes through the points 0 comma 4 and 2 comma 0 and another line that passes through the points 0 comma 0 and 1 comma 2
Answer:
a line
Step-by-step explanation:
y equals one half times x x + 2y = 8 coordinate plane with one line that passes through the points 0 comma 4 and 2 comma 5 and another line that passes through the points 0 comma 0 and 2 comma 1 coordinate plane with one line that passes through the points 0 comma 4 and 2 comma 3 and another line that passes through the points 0 comma 0 and 2 comma 1 coordinate plane with one line that passes through the points negative 1 comma 2 and 0 comma 4 and another line that passes through the points 0 comma 0 and 1 comma 2 coordinate plane with one line that passes through the points 0 comma 4 and 2 comma 0 and another line that passes through the points 0 comma 0 and 1 comma 2
Answer:
B) A coordinate plane with one line that passes through the points (0, 4) and (2, 3) and another line that passes through the points (0, 0) and (2, 1)
Step-by-step explanation:
Given system of linear equations:
[tex]\begin{cases}y=\frac{1}{2}x\\x+2y=8\end{cases}[/tex]
Substitute the first equation into the second equation and solve for x:
[tex]\implies x+2\left(\dfrac{1}{2}x\right)=8[/tex]
[tex]\implies x+x=8[/tex]
[tex]\implies 2x=8[/tex]
[tex]\implies x=4[/tex]
Substitute the found value of x into the first equation and solve for y:
[tex]\implies y=\dfrac{1}{2}(4)[/tex]
[tex]\implies y=2[/tex]
Therefore, the solution to the given system of linear equations is:
(4, 2)The point of intersection is the solution to a graphed system of linear equations.
Therefore, the graph that shows the solution to the given system of linear equations is the graph where the point of intersection of the two lines is (4, 2).
What is a 3 regular graph?
A 3-regular graph is called a cubic graph. A strongly regular graph is a regular graph where every adjacent pair of vertices has an equal number of neighbors in common, and every non-adjacent pair of vertices has an equal number of neighbors in common.
In the mathematical field of graph postulate, a cubic graph is a graph in which all vertices have a degree of three. In other terms, a cubic graph is a 3-regular graph. Cubic graphs are also known as trivalent graphs.
A bicubic graph is called a cubic bipartite graph.
In graph theory, a regular graph is a graph where each vertex has an equal number of neighbors; i.e. every vertex has an equal degree or valency.
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3
10
3
Kathy has of a yard of fabric. She needs
of a yard to make a
4
headband. How many WHOLE headbands can she make?
Kathy can make 10 headbands from 3/4 of a yard of fabrics.
What is an equation?An equation is an expression composed of variables and numbers linked together by mathematical operations.
The unit rate is the ratio of two different units. The unit rate must always have a denominator equal to 1.
Kathy has 3/4 of a yard of fabric. She needs 3/10 of a yard to make a 4 headband.
Hence:
3/10 yards = 4 head band
For 3/4 yard:
number of headbands = 3/4 yard * 4 headband per 3/10 yard = 3/4 * 4 / (3/10) = 3/4 * 4 * 10/3 = 10
Kathy can make 10 headbands
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Select the expressions that are equivalent to 5(4u).
20u - u+20 - u+9 - 5(u+3u)
The expressions that are equivalent to 5(4u) will be 20 u and 5(u + 3u).
How to calculate the expression?It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.
Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc. The expression that is equivalent to 5(4u) will be:
= 20 u
and
5(u + 3u)
= 20u
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Construct a confidence interval of the population proportion at the given level of confidence.
x=120 n =1200 95% confidence
The upper bound of the confidence interval is ____ (round to the nearest thousandth as needed)
The lower bound of the confidence intervals is ____ (round to the nearest thousandth as needed)
The confidence interval's upper and lower bounds, respectively, are 0.117 for the higher and 0.083 for the lower.
What is proportion's subject?The interaction between two or much more quantities is the focus of the branch of mathematics known as ratio and proportion. A key component of GCSE mathematics, ratio and proportion comprehension has connections to several subjects in number, algebra, geometry, probability, and statistics. An equilibrium for two ratios is a percentage. We use proportions to construct comparable ratios and find solutions to problems involving unknown numbers.
[tex]\begin{aligned}\bar{p} & =\frac{x}{n}=\frac{120}{1200}=0.10 \\\frac{\alpha}{2} & =\frac{1-\text { Confidence } \%}{2}=\frac{1-0.95}{2}=0.025 \\z_{1-\alpha / 2} & =z_{0.975}=1.960 \Rightarrow \text { Use the Excel formula "=NORMSINV(0.975)" }\end{aligned}[/tex]
[tex]S . E .=z_{1-\alpha / 2} \sqrt{\frac{\bar{p}(1-\bar{p})}{n}}=1.960 \sqrt{\frac{0.1(1-0.1)}{1200}}=0.017[/tex]
The confidence interval's top bound: [tex]\bar{p}[/tex] + S.E = 0.10 + 0.017 = 0.117
The confidence interval's lowest bound: [tex]\bar{p}[/tex] - S.E. = 0.10 - 0.017 = 0.083
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what's the probability tgat a junior bio major who has taken statistics has also taken a computer course
The probability that a junior bio major who has taken statistics has also taken a computer course is 13.46%.
We are trying to find the probability that a junior bio major who has taken a statistics course has also taken a computer course. This is referred to as the conditional probability, denoted as P(computer | statistics).
To calculate this, we can use the formula:
P(computer | statistics) = P(computer and statistics) / P(statistics)
This formula states that the probability of a junior bio major taking a computer course given that they have taken a statistics course is equal to the probability of them taking both a computer and statistics course divided by the probability of them taking only a statistics course.
The information given in the problem is as follows:
P(statistics) = 52%
P(computer) = 23%
P(computer and statistics) = 7%
So we can plug these values into the formula to calculate the conditional probability:
P(computer | statistics) = P(computer and statistics) / P(statistics) = 7% / 52% = 0.1346153846153846 or 13.46%
Therefore, the probability that a junior bio major who has taken statistics has also taken a computer course is 13.46%.
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The complete Question is:
A university requires its biology majors to take a course called BioRe search. The prerequisite for this course is that students must have taken either a Statistics course or a computer course. By the time they are juniors, 52% of the Biology majors have taken Statistics, 23% have had a computer course , and 7% have done both. What's the probability that a junior bio major who has taken statistics has also taken a computer course?
A boy ha 35 paperback book and 20 hardback book. What fraction of the book are hardback
The fraction of the books are hardback is 4 / 11.
In Mathematics, a fraction defined as the part of the whole thing. For example, a pizza is divided into four equal pieces, then each piece is represented by ¼. Fractions help to distribute and judge the numbers easily and make the calculation faster.
from given conditions, a boy ha 35 paperback book and 20 hardback book.
so, the total books are 35 paperback book + 20 hardback book = 55 books
fraction of books which are hardback book are,
20 / 55
= 4 / 11
Therefore, the fraction of the books are hardback is 4 / 11.
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points r, s and t are vertices of an equilateral triangle, and points x, y and z are midpoints of its sides. how many noncongruent triangles can be drawn using any three of these six points as vertices?
2 congruent triangle can be drawn using any three of these six points as vertices.
What is triangle?A triangle in geometry is a three-sided polygon with three edges and three vertices.
The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic.
This characteristic is known as the triangle's angle sum property.
If ABC is a triangle, it is written as ABC, where A, B, and C represent the triangle's vertices.
In Euclidean geometry, a triangle is a two-dimensional shape represented by three non-collinear points in a single plane.
Hence, 2 congruent triangle can be drawn using any three of these six points as vertices.
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make x the subject: y=4x+3
Answer:
y equals to 4x + 3
subtract 3 on both side
4 - 3 equals to 4x + 3 - 3
divide the equation by 4 on both sides
y-3/4 = 4x/4
X = y-3/4
Find the sum of the geometric sequence if the first term is -8, the common ratio is -3 and there are 10 terms
Answer:
Step-by-step explanation:
The formula for the sum of a geometric sequence is: S = a(1 - r^n) / (1 - r)
In this case, our a = -8, r = -3, and n = 10.
S = -8(1 - (-3)^10) / (1 - (-3))
S = -8(1 - (-59049)) / 4
S = -8(59049) / 4
S = -2362196
please help me.
What is
Answer:
90
Step-by-step explanation:
The symbol represented in the angle is the right angle symbol ∟
This means that the angle would be 90
Have a lovely day :)
Answer:
There's no m so I'm assuming you meant b.
The angle of b is 121
Step-by-step explanation:
The shape here is a heptagon. The formula for calculating the sum of interior angles is ( n − 2 ) × 180. *n represents the number of sides.
(7-2) × 180 There are 7 sides so plug that in.
(5) × 180 = 900 This means the shape's interior angles add up to 900.
Now, all we have to do is add up all the sides known and set it equal to 900.
c + d + e + f + g + a = 900
148 + 90 + 142 + 130 + 139 + 130 + b = 900
779 + b = 900
now subtract 779 from both sides to isolate b.
b = 121
How do I do this step by step
Answer:
84
Step-by-step explanation:
this is an isosceles triangle so the base angles are equal meaning <BAC= <BCA =48°
48° +48° =96°
180°- 96° = 84°
<ABC = 84°
If
\[x^2 - 7x + c = (x + a)^2\]for some constants $a$ and $c,$ then find $c.$
Answer:
Step-by-step explanation:
[tex]x^{2} -7x+c=(x+a)^{2}[/tex]
[tex]x^{2} -7x+c=x^{2} +2ax+a^{2}[/tex]
[tex]-7x=2ax\\a=-7/2[/tex]
[tex]a^{2} =c\\c=(-7/2)^{2} =49/4[/tex]
PLEEEEESSSSEEEEEEEE HALPPPPPPPP
Answer:
0.75 is less than 1, so the portrait will be smaller than the actual head.
Step-by-step explanation:
The art teacher has said that the portrait will be 0.75 times as tall as the actual head.
0.75 is less than 1, so the portrait will be smaller than the actual head.
A ratio of 0.75 means that the portrait will be 3/4 the size of the actual head. So, if the actual head is 8 inches tall, the portrait will be 6 inches tall (8*0.75 = 6). Therefore, the portrait will be smaller than the actual head.
A grocery store sells a bag of 6 oranges for $5.22. What is the cost of oranges, in dollars per orange?
Convert the following degree measure to radian measure 98
98 degrees is approximately equal to 5.48 radians.
How to convert degree measure to radian measure?
To convert a degree measure to a radian measure, you can use the conversion factor of 180/π.
98 degrees is equal to (98*π)/180 radians
So, 98 degrees is approximately equal to 5.48 radians.
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which of the following is false the intermediate value theorem mean value theorem extreme value theorem
Which of the following is untrue: the extreme value theorem, mean value theorem, or intermediate value theorem? All three of the calculus-related theorems—Intermediate Value Theorem, Mean Value Theorem, and Extreme Value Theorem—are valid.
Write about the theorem.According to the intermediate value theorem, a continuous function must take on the value "c" at some point in the interval if it is defined on a closed interval and the value "c" is between the function's minimum and maximum values.
According to the Mean Value Theorem, if a function can be differentiated on an open interval, then at least one point in the interval has a derivative equal to the function's average slope.
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Complete Question is: Which of the following is false according to calculus: the extreme value theorem, mean value theorem, or intermediate value theorem?
If the age of a person and three-fourth of his áge are added, the result becomes 70 years. Find the age of the person.
I need help with the following questions please!!!!!!
Step-by-step explanation:
f(-1) = (1/8)^-1 = 1/(1/8) = 8
f(0) = (1/8)⁰ = 1 (a⁰ = 1 for any a)
f(1) = (1/8)¹ = 1/8 = 0.125
f(2) = (1/8)² = 1/64 = 0.015625
f(3) = (1/8)³ = 1/512 = 0.001953125
remember
(a/b)ⁿ = aⁿ / bⁿ
in the same way as
(a×b)ⁿ = aⁿ×bⁿ
The graph shows the depth in feet of snow after each two-hour period during a snowstorm. Find the slope of the line. Enter your answer an an integer or decimal.
Answer:
.5 or 1/2
Step-by-step explanation:
1-.5 .5
------=------- simplify= .5 slope is in fractions 1/2
2-1 1
i really need help
please and thank you
The equation 70 + 9.5x = 184 represents the situation and the number of visits is 12 if Marques has a points card for a movie theater.
We define a linear equation.Any model that meets the algebraic equation y=mx+b is said to be linear. B is the slope, and m is the y-intercept. Since both y and x are distinct factors, the preceding sentence is commonly referred as a "mathematical model with two variables." Two-variable linear equations are referred to as bivariate equations. There are several applications for linear equations, all of which end in zero.
Here,
It is given that:
Marques has a points card for a movie theater. • He receives 70 rewards points just for signing up
Let x be the number of visits.
The linear equation can be framed as follows:
70 + 9.5x = 184
9.5x = 184 - 70
After solving the above linear equation in one variable:
9.5x = 114
x = 12
Thus, the equation 70 + 9.5x = 184 represents the situation and the number of visits is 12 if Marques has a points card for a movie theater.
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four distinct fair coins are tossed. if it is known that at least one of the coins shows a head, what is the probability that all coins show heads?
Since, Four distinct fair coins are tossed. if it is known that at least one of the coins shows a head . The probability that all coins show heads is 3/4.
Probability:
Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes for an event. In an experiment with 'n' outcomes, the number of favorable outcomes can be denoted by x. The formula for calculating the probability of an event is:
Probability (Event) = Favorable Outcome / Total Outcome = x/n
The probability of an event can be calculated using the probability formula by simply dividing the number of favorable outcomes by the total number of possible outcomes. The value of the probability that an event will occur can range from 0 to 1. This is because the preferred number of outcomes can never exceed the total number of outcomes. Also, the resulting favorable number can never be negative.
Given that:
Four District fair coins are tossed.
So, possible outcomes are
HH,HT,TH,TT
We know that:
Probability= total possible outcomes / favorable outcomes
Now,
Favorable outcomes = HH,HT,TH
And,
Probability = 3/4
Therefore, the probability that all coins show heads is 3/4.
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Help me I need help on how to do this I will upload 13 questions this is number 1
The value of x is 85°
What is angle of a sector?A circular sector, also known as circle sector or disk sector is the portion of a disk enclosed by two radii and an arc, where the smaller area is known as the minor sector and the larger being the major sector
A sector is a region bounded by two radii of a circle and the intercepted arc of the circle. The angle formed by the two radii is called a central angle. A sector with a central angle less than 180° is called a minor sector. A sector with a central angle greater than 180° is called a major sector.
The sector where x is the minor sector
The angular distance is x and it is measured in degrees (°)
Therefore the value of x is 85°
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Determine the equation of the circle with center (0, -5) containing the point
(-√60,-6).
Answer:
x² + (y + 5)² = 61
Step-by-step explanation:
the equation of a circle in standard form is
(x - a)² + (y - b)² = r²
where (a, b ) are the coordinates of the centre and r is the radius
here (a, b ) = (0, - 5 ) and r has to be found
(x - 0)² + (y - (- 5) )² = r² , that is
x² + (y + 5)² = r²
the radius is the distance from the centre to a point on the circle.
using the distance formula to find r
r = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (0, - 5 ) and (x₂, y₂ ) = (- [tex]\sqrt{60}[/tex] , - 6 )
r = [tex]\sqrt{(-\sqrt{60}-0)^2+(-6-(-5))^2 }[/tex]
= [tex]\sqrt{(-\sqrt{60})^2+(-1)^2 }[/tex]
= [tex]\sqrt{60+1}[/tex]
= [tex]\sqrt{61}[/tex]
then r² = ( [tex]\sqrt{61}[/tex] )² = 61
the equation of the circle is then
x² + (y + 5)² = 61
A farmer has sixty three goats and twenty times as many sheeps. if the number of sheep he has is thirty times the number of his chickens , find the number of legs of the animals
Answer:
I would really like to help but I have no idea
addition subtraction of radicals
Step-by-step explanation:
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explain how to use arrays or area models to find factor pairs
Answer: An array is a visual representation of a multiplication problem, and an area model is a way to represent a multiplication problem using rectangles. Both arrays and area models can be used to find factor pairs of a number.
Here's an example of how to use an array to find the factor pairs of 12:
Draw a rectangle that represents 12.
Divide the rectangle into smaller rectangles by drawing rows and columns.
Fill in the rectangles with the numbers 1 through 12.
Find the factor pairs by looking for the rectangles that have the same area as the original rectangle, 12.
The factor pairs of 12 are 1 and 12, 2 and 6, and 3 and 4.
Here's an example of how to use an area model to find the factor pairs of 12:
Draw a rectangle that represents 12.
Divide the rectangle into smaller rectangles by drawing rows and columns.
Label the rectangles with the factors of 12, which are 1, 2, 3, 4, 6 and 12.
Find the factor pairs by looking for the rectangles that have the same area as the original rectangle, 12.
The factor pairs of 12 are 1 and 12, 2 and 6, and 3 and 4.
Both arrays and area models are an effective way of finding the factor pairs of a number because they help you to visualize the multiplication problem and to see the relationship between the factors and the product.
Step-by-step explanation:
How do you write an interval notation on quadratic inequality?
Solve for x values that satisfy a quadratic inequality to write interval notation. This usually involves factoring the quadratic and putting it equal to zero, then utilizing the inequality sign to select viable solutions. After finding the answers, write (a,b) to indicate the interval of x-values that make the inequality true. The interval notation for -3 and 5 is (-3,5).
What is interval notation?Generally, Before you can create an interval notation for a quadratic inequality, you must first solve for the values of x that are compatible with the inequality being satisfied. In most cases, this will require factoring the quadratic expression and fixing it so that it equals zero.
After that, the sign of inequality will be used to decide which solutions are appropriate. After you have determined the solutions, you may indicate the range of x-values that cause the inequality to hold using the notation (a,b), where a and b stand for the solutions, respectively.
As an illustration, the interval notation would look like this if the answers were -3 and 5. (-3,5).
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