Answers
The length of OP in the given circle figure is 2.
We know that the area of a sector which obtain 'A' degree at center in a circle with radius 'r' is given by,
A = (A/360)*πr²
Here length of OP represents the radius of the circle with center O.
Let OP = R.
The area of the whole circle will be = πR²
Given that the sector which intends an angle of 72 degrees in center has area 4π/5.
According to the condition,
(72/360)* πR² = 4π/5
R²/5 = 4/5
R² = 4
R = 2 [since length cannot be negative so the negative value of square root is ignored.]
Hence the length of OP is 2.
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Related Questions
Which relation is a function?
Answers
Answer:
Step-by-step explanation:
The relation that is a function is the relation (b)
Checking the relations that are functionsFrom the question, we have the following parameters that can be used in our computation:
The relations (1) to (4) represent the given parameter
Next, we test the options
Relation (a)
This relation is not a function
This is because it the vertical line test i.e. some output values all point to the same input value,
Relation (b)
This relation is a function
This is because the inputs all point to different output values
Relation (c)
This relation is not a function
This is because it fails the vertical line test i.e. some output values all point to the same input value,
Relation (d)
This relation is not a function
This is because it fails the vertical line test i.e. some output values all point to the same input value,
Hence, the relation that represents a function is option (b)
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a. How much warmer is 82 than 40?
b. How much warmer is 82 than -40?
Answers
a>82 is 42 degrees warmer than 40.
Please help asap need this answer fast.
Answers
Answer:
D
Step-by-step explanation:
Because 2×2 is 12 and 12×5 is 60
Use a calculator to solve the following equation for θ on the interval (−π/2,π/2).
tan(θ)=3.804
Round to three decimal places.
θ=? Radians
Answers
the solution for \(\theta\) on the interval \((-\pi/2,\pi/2)\) is approximately \(1.305\)radians.
What is interval?An interval is a set of real numbers that includes all the numbers between two endpoints. The endpoints can be included or excluded from the interval, depending on whether square brackets or parentheses are used to define the interval.
The equation is:
\(tan(\theta) = 3.804\)
To solve for θ, we can use the inverse tangent function (also known as arctan or tan^-1) on both sides of the equation:
\(\theta = tan^-1(3.804)\)
Using a calculator, we can evaluate this expression and get:
\(\theta \approx 1.305\) radians (rounded to three decimal places)
Therefore, the solution for \(\theta\) on the interval \((-\pi/2,\pi/2)\) is approximately \(1.305\)radians.
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3. Mr. Gregory is a math teacher. He found that 27, or 15%, of his students are
athletes. How many students does Mr. Gregory have?
Answers
Answer:
180 students
Step-by-step explanation:
We Know
He found that 27, or 15%, of his students are athletes.
How many students does Mr. Gregory have?
First, we find 1% by taking
27 ÷ 15 = 1.8
Then we find 100% by taking
1.8 x 100 = 180 students
So, Mr.Gregory has 180 students.
Learning Task 3 Answer the questions that follow. Put a check mark (/) on the space provided. Copy and answer in your math notebook. 1. The units for Volume are always ______squared _____cubed 2. Volume is the amount of space an object takes up. ___True ___False Calculate for the volume of solid. 3. Chona is selling Pringle Chips to raise money for a field trip. The container has a diameter of 9 inches and a height of 32 inches. 4. A 3-tier cake with the same height of 10 in and radius of 12 in, 8 in, 5 in respectively is to be delivered to a birthday party. How much space does this cake take up? Use 3.14 for π. 5. A Styrofoam model of a volcano is in the shape of a cone. The model has a circular base with a diameter of 48 centimeters and a height of 12 centimeters. Find the volume of foam in the model to the nearest tenth. Use 3.14 for π.
Answers
3. The volume of the Pringle Chips container is approximately 2034.72 cubic inches.
4. The cake takes up approximately 7317 cubic inches of space.
5. The volume of foam in the model of the volcano is approximately 7234.08 cubic centimeters.
1. The units for Volume are always cubed.
2. Volume is the amount of space an object takes up. True.
3. To calculate the volume of the Pringle Chips container, we need to find the volume of a cylinder. The formula for the volume of a cylinder is V = πr^2h, where π is a constant (approximately 3.14), r is the radius, and h is the height. Given that the diameter is 9 inches, the radius would be half of that, which is 4.5 inches. Substituting the values into the formula, we have:
V = 3.14 * (4.5)^2 * 32
V = 3.14 * 20.25 * 32
V ≈ 2034.72 cubic inches
4. To find the volume of the 3-tier cake, we need to find the volume of each tier separately and then add them together. Since all the tiers are cylinders, we can use the formula V = πr^2h.
Tier 1:
V1 = 3.14 * (12)^2 * 10 = 4521.6 cubic inches
Tier 2:
V2 = 3.14 * (8)^2 * 10 = 2010.4 cubic inches
Tier 3:
V3 = 3.14 * (5)^2 * 10 = 785 cubic inches
Total volume:
Total V = V1 + V2 + V3
Total V = 4521.6 + 2010.4 + 785
Total V ≈ 7317 cubic inches
5. To find the volume of the Styrofoam model of the volcano, we can use the formula for the volume of a cone, V = (1/3)πr^2h. Given that the diameter is 48 centimeters, the radius would be half of that, which is 24 centimeters. Substituting the values into the formula, we have:
V = (1/3) * 3.14 * (24)^2 * 12
V = (1/3) * 3.14 * 576 * 12
V ≈ 7234.08 cubic centimeters
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Rewrite in simplest terms: 4(-69 – 10h) + 3h = 4(-3h – 10g) Answer: Submit Answer
Answers
We are given a mathematical expression that needs to be simplified in the most meaningful form as follows:
\(4\cdot(-6g\text{ - 10h ) + 3h -4}\cdot(-3h\text{ -10g )}\)Whenever we are dealing with either an equation that needs to be solved or an expression that needs to be simplified we always refer to the rule of PEMDAS. The rule gives us the order in which mathematical operators are to be applied in decreasing order as follows:
\(\begin{gathered} P\colon\text{ Parenthesis} \\ E\colon\text{exponents} \\ M\colon\text{ Multiplication} \\ D\colon\text{Division} \\ A-S\colon\text{Addition-Subtraction } \end{gathered}\)We will use the above rule and work through with the given expression for the process of simplification.
We will first solve the parenthesis for the entire expression as follows:
\(4\cdot(-6g\text{ ) -4}\cdot(-10h\text{ ) + 3h -4}\cdot(-3h)\text{ -4}\cdot(-10g)\)Then we apply the mathematical operation of M: Multiplication as follows:
\(-24g\text{ + 40h + 3h + 12h + 40g}\)Now we will group the like terms i.e defined by a particular variable ( h or g ) and apply the A-S: Addition-Subtraction operator as follows:
\(\begin{gathered} (40g-24g\text{ ) + ( 3h + 12h + 40h ) } \\ 16g\text{ + 55h} \end{gathered}\)The form expressed can not be further simplified as the variables ( h and g ) are expressed in the most simplified form i.e there is only one term for each variable. Hence, the algebraic expression is simplified to:
\(\textcolor{#FF7968}{16g}\text{\textcolor{#FF7968}{ + 55h}}\)
why is angle 3 congruent to angle 7?
Answers
Answer:
they are congruent because they are corresponding angles
Step-by-step explanation:
help with this please
Answers
y=-2*0+12 —> y=0+12 —> y=12
so you would put that 12 in the first box. that gives you the points (0,12) on the graph and that’s where you would put your first dot…
you repeat this process for all the other x values
Find the x- and y-intercepts of the graph of the equation y = x2 + 3x – 40.
Answers
The quadratic equation given is,
\(y=x^2+3x-40\)To find the x-intercept (s), we set y = 0. So,
\(\begin{gathered} y=x^2+3x-40 \\ 0=x^2+3x-40 \\ (x+8)(x-5)=0 \\ x=-8,5 \end{gathered}\)To find the y-intercept, we set x = 0. So,
\(\begin{gathered} y=x^2+3x-40 \\ y=0^2+3(0)-40 \\ y=-40 \end{gathered}\)Answersx-intercepts --- x = - 8, x = 5y-intercept --- y = - 40
For each value of w, determine whether it is a solution to 6w +9=33.
Is it a solution?
Answers
Answer:
Hello!!! Princess Sakura here ^^
Step-by-step explanation:
3 (no)
9 (no)
-7 (no)
-1 (no)
The solution to the equation 6w + 9 = 33 is 4.
The values of 2 = 3, 9, -7, and -1 are not solutions to 6w + 9 = 33.
What is a solution?Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.
We have,
6w + 9 = 33
6w = 24
w = 4
For w = 3
6 x 3 + 9 = 33
18 + 9 = 33
27 = 33
This is not true so it is not a solution.
For w = 9
6 x 9 + 9 = 33
54 + 9 = 33
63 = 33
This is not true so it is not a solution.
For = - 7
6 x (-7) + 9 = 33
-42 + 9 = 33
-33 = 33
This is not true so it is not a solution.
For w = -1
6 + (-1) + 9 = 33
-6 + 9 = 33
3 = 33
This is not true so it is not a solution.
Thus,
None of the values of w are solutions to 6w + 9 = 33.
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Please see the attached
Answers
Using the ratios, 1 yd/3 feet, 1 mi/5,280 feet, and 200 yards/1 feet, the number of flags required to mark the racecourse with a flag every 200 yards is 22.
What are the ratios?Ratios are relative sizes of one quantity or value compared to another.
Ratios are depicted as fractional values using decimals, percentages, or fractions, including the standard ratio form (:).
The total distance of the racecourse = 2.5 miles
The common distance between each flag = 200 yards
1 mile = 1,760 yards
2.5 miles = 4,400 yards
1 yard = 3 feel
The number of flags required to cover the distance = 22 (4,400 ÷ 200)
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what is the answer to x/3+8=-2
Answers
Answer:
x = - 30
Step-by-step explanation:
x/3 + 8 = - 2 subtract 8 from both sides of the equation
x/3 = -2 - 8 = -10 now multiply both sides by 3
x = -30
Convert the following repeating decimal into a fraction. *
___
2.111
Answers
Answer: i think that the only fraction that we can convert this into is 2111/1000
Answer:
\(\frac{2111}{1000}\)
Step by step:
2.111 = \(\frac{2.111}{1}\)
then, get rid of the decimal sign in 2.111 by multiplying it by 1000 since there are 3 numbers after the decimal point.
your new fraction is \(\frac{2111}{1000}\)
PLEASE HELP ME PLEASE I NEED IT RN
Answers
Answer:
A. -9/2
Step-by-step explanation:
Rate of change of y in respect to x = change in y/change in x
Using two pairs of values, say (-6, 33) and (-2, 15),
Rate of change = (15 - 33)/(-2 - (-6))
Rate of Change = -18/4
Simplify
Rate of change = -9/2
Really need help thank you!
Answers
Answer:
x=28
Step-by-step explanation:
when the angles are supplementary add them together and set them to 180 after doing so you'll have
4x+2x+12=180
now you combine like terms and then solve for x
Frank is going to plant b vegetable seeds in one garden and 5b + 6 vegetable seeds in another . How many seeds is frank going to plant ?
Answers
The total number of seeds Frank is going to plant is 6b + 6 seeds.
How many seeds is frank going to plant ?From the question, we have the following parameters that can be used in our computation:
Graden 1 = b
Graden 2 = 5b + 6
Frank is going to plant b seeds in one garden and 5b + 6 seeds in another garden.
The total number of seeds Frank is going to plant is:
b + (5b + 6) = 6b + 6
So Frank is going to plant 6b + 6 seeds.
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please solve need help ASAP :)
Answers
Answer:
p^m+n
Rember than please
<3
Red
QRS is similar to XYZ.of QR=5,QS=7,and XY=30 find the value of XZ
Answers
Let f(t)=4-3t^2. Evaluate f(t+1).
Answers
Answer:
f=4-3t^2/t+1
Step-by-step explanation:
You might need:
Calculator
A store has a 40% off sale on headphones. With this discount, the price of one pair of headphones is $36.
What is the original price of the pair of headphones?
$
Show Calculator
Stuck? Watch a video or use a hint.
Report a problem
Answers
Answer:
90
Step-by-step explanation:
Given the following sets, find the set (A U B) n (AUC).
U= {1, 2, 3, ..., 10}
A=(2, 5, 7, 10}
B = {1, 2, 3)
C={1, 2, 3, 4, 5}
Answers
The set (A U B) n (A U C) is {2, 5, 7, 10}. A.
To find the set (A U B) n (A U C), we first need to calculate the union of sets A and B, and then calculate the union of that result with set C. Finally, we find the intersection of these two sets.
Set A U B:
The union of sets A and B, denoted as A U B, is the combination of all elements from both sets without any repetitions.
A contains the elements 2, 5, 7, and 10, while B contains the elements 1, 2, and 3.
A U B consists of the elements {1, 2, 3, 5, 7, 10}.
Set (A U B) U C:
Next, we calculate the union of the set (A U B) with set C, denoted as (A U B) U C. A U B contains the elements {1, 2, 3, 5, 7, 10} and C contains the elements {1, 2, 3, 4, 5}.
Taking the union of these two sets results in {1, 2, 3, 4, 5, 7, 10}.
Finding the intersection:
Finally, we find the intersection of (A U B) U C with A U C. A U C consists of the elements {2, 5, 7, 10}.
The intersection of these two sets is the combination of common elements.
The common elements are {2, 5, 7, 10}.
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prepare to analyze the data (step 1): identify and classify the variable(s) you will use. here is the list of variables in the data set. use the menu to the right of each variable to: O indicate whether the variable is relevant to the questions we are investigating, and O identify the variable as either categorical or quantitative.
Answers
The Variables (a) Gender is Categorical , (b) Alcohol can be either Categorical or Quantitative and (c) Height is Quantitative .
We can identify the type of each variable as categorical or quantitative.
(a) Gender: This variable is categorical, as it describes a characteristic that can only take on a limited number of values (e.g., male or female).
(b) Alcohol: Without additional information , it is not clear whether this variable is categorical or quantitative.
If the data set only includes information about whether an individual drinks alcohol or not, then this variable is categorical. If the data set includes information about how much alcohol an individual consumes, then this variable would be quantitative.
(c) Height: This variable is quantitative, as it represents a numerical measurement of a continuous variable.
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The given question is incomplete , the complete question is
Identify and classify the variable(s) you will use. here is the list of variables in the data set.
(i) identify the variable as either categorical or quantitative.
the variables are (a) Gender , (b) Alcohol , (c) Height .
pasagot nmn po thanks
Answers
Answer:
wag Po lagi umasa sa brainl.
some adults and children are watching a musical there are n children there are 25 fewer adults
Answers
According to the concept of algebraic expression and arithmetic, the correct answers are A) Number of adults = N - 25. B) Number of adults when N = 124: 124 - 25 = 99
A) Let's denote the number of children as N. Since there are 25 fewer adults than children, the number of adults can be expressed as N - 25.
B) If there are 124 children, we substitute N with 124 in the expression from part A. Thus, the number of adults would be 124 - 25 = 99.
To arrive at these answers, we used the given information that there are "N" children and 25 fewer adults than children. By substituting the value of N, we determined the number of adults in terms of N and then calculated the specific number of adults when N is equal to 124.
Note: The given question is incomplete. The complete question is:
Some adults and children are watching a musical. there are 'N' number of children. There are 25 fewer adults than children.
A) find the number of adults in terms of 'N'.
B) if there are 124 children how many adults are there?
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What is the area of
the segment? Express
the answer in terms
of pi.
Answers
The area of the segment is 9( π-2) units²
What is area of segment?The area of a figure is the number of unit squares that cover the surface of a closed figure.
A segment is the area occupied by a chord and an arc. A segment can be a major segment or minor segment.
Area of segment = area of sector - area of triangle
area of sector = 90/360 × πr²
= 1/4 × π × 36
= 9π
area of triangle = 1/2bh
= 1/2 × 6²
= 18
area of segment = 9π -18
= 9( π -2) units²
therefore the area of the segment is 9(π-2) units²
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1 and 1 half times 3 and 1 fourth
Answers
Answer:
1 1/2 x 3 1/4
make them improper fractions
3/2 x 13/4 = 4 7/8
HELP PLEASE
Which combination of integers can be used to generate the Pythagorean
triple 5,12,13)?
A. X = 1, y = 3
B. X = 3.y = 2
C. X = 3.y = 4
D. X = 2 y = 2
Answers
step by step explanation
HELP ASAP PLS! The ratio of bows to headbands of Monique’s hair accessories is 8:4. Select all true statements.
A. For every 8 hair accessories, 4 are bows.
B. For every 8 bows, there are 4 headbands.
C. For every 8 headbands, there are 4 bows.
D. For every 8 hair accessories, 4 are headbands.
E. For every 12 hair accessories, 4 are headbands.
Answers
I need help!!!! Please!!!!
Answers
Answer:
I need help!!!! Please!!!!