The diameter of a circle is 5 cm. Find its area to the nearest whole number.
Answers
Therefore, the area of the circle is approximately 20 square centimeters.
What is diameter?Diameter is a term used in geometry to describe the distance between two points on the circumference of a circle or sphere, passing through the center. In other words, it is the longest straight-line segment that can be drawn from one point on the circle or sphere to another, passing through the center.
Given by the question.
The diameter of a circle is the distance across it passing through its center. Given the diameter of 5 cm, we can find the radius (half the diameter) by dividing 5 by 2, which gives us:
radius = 5/2 = 2.5 cm
The area of a circle is given by the formula:
area = π\(r^{2}\)
where π (pi) is a mathematical constant approximately equal to 3.14159.
Plugging in the value of the radius, we get:
\(area= π (2.5)^{2}\)
area ≈ 19.63
Rounding this to the nearest whole number, we get:
area ≈ 20
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Related Questions
2.Ainsley thought there were 25 students in her math class, but there were actually 27 students. What is
her percent error?
Answers
Next, we need to find the absolute value of this difference. Since the difference is 2 students, the absolute value of the difference is simply 2.
Finally, we need to divide the absolute value of the difference by the actual value and multiply the result by 100 to find the percent error. In this case, the percent error is (2 / 27) * 100 = 7.4%. Therefore, Ainsley's percent error is 7.4%
Find the equation of the line through the points (7,2) and (−5,−10)
Answers
7 = X1
2 = Y1
-5 = X2
-10 = Y2
-10-2 = -12
-5 - 7 = -12
M (slope) is 1
Use the coordinate (7, 2)
2 = 1(7) + b
2 = 7 + B
Subtract 7 from both sides to keep your equation even
B equals -5
Y = X -5
A real-estate agent conducted an experiment to test the effect of selling a staged home vs. selling an empty home. To do so, the agent obtained a list of 10 comparable homes just listed for sale that were currently empty. He randomly assigned 5 of the homes to be "staged,” meaning filled with nice furniture and decorated. The owners of the 5 homes all agreed to have their homes staged by professional decorators. The other 5 homes remained empty. The hypothesis is that empty homes are not as appealing to buyers as staged homes and, therefore, sell for lower prices than staged homes. The mean selling price of the 5 empty homes was $150,000 with a standard deviation of $22,000. The mean selling price of the five staged homes was $175,000 with a standard deviation of 35,000. A dotplot of each sample shows no strong skewness and no outliers.
The agent tests H0: μ1 – μ2 = 0, Ha: μ1 – μ2 < 0, where μ1 = the true mean selling price of all comparable empty homes and μ2 = the true mean selling price of all comparable staged homes. Are the conditions for inference met for carrying out a t-test for a difference in means?
No, the random condition is not met.
No, the 10% condition is not met.
No, the Normal/large sample condition is not met.
Yes, all of the conditions for inference have been met.
Answers
Yes, all of the conditions for inference have been met to carry out a t-test for a difference in means.
Three main conditions need to be satisfied: the random condition, the 10% condition, and the Normal/large sample condition.
The random condition is met because the real-estate agent randomly assigned the homes to be staged or empty. This ensures that the sample is representative of the population of comparable homes.
The 10% condition is met because the agent selected 10 comparable homes, and the sample of 5 staged and 5 empty homes represents less than 10% of the population of comparable homes.
The Normal/large sample condition is met because the dot plot of each sample shows no strong skewness and no outliers. Additionally, with a sample size of 5 for each group, the t-test can still be valid even if the population distributions are not exactly normal.
Therefore, all the conditions for inference have been met, allowing the real-estate agent to carry out a t-test for a difference in means and test the hypothesis regarding the selling prices of staged and empty homes.
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3t= -8.16 what does t equal?? help me, please!!!!
Answers
Answer:
2.72
Step-by-step explanation:
you divide 8.16 by 3
to double check you multiply 3 by 2.72
Answer:
t=-2.72
Step-by-step explanation:
3t=-8.16
3 = 3
t=-2.72
choose the equation of the graphed function
Answers
Answer:
Its option j.
Step-by-step explanation:
The graph is the graph of y = |x| moved 1 unit to the right,
Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms.
Second-degree, with zeros of −2 and 4, and goes to −∞ as x→−∞.
Answers
The possible polynomial function with the given properties is:
f(x) = -1/5(x2 - 10x + 16)
Now, Based on the given properties, a possible polynomial function would be:
⇒ f (x) = a(x + 2)(x - 4)
To satisfy the second-degree requirement, we need to have an x² term in the function.
By factoring the function above as shown, we can see that it has two roots: x = -2 and x = 4.
Therefore, we can say that this function has zeros at x = -2 and x = 4.
To determine the value of the coefficient "a", we can use the information that the function goes to -∞ as x → -∞.
This means that the leading coefficient of the function must be negative.
Since, we have a(x + 2)(x - 4), and the x² term has a coefficient of a, we can see that a must be negative.
To further simplify the function and reduce all fractions to lowest terms, we can distribute the negative sign and multiply out the factors:
f(x) = a(x + 2)(x - 4)
= a(x² - 2x - 8x + 16)
= a(x² - 10x + 16)
Therefore, The possible polynomial function with the given properties is:
f(x) = -1/5(x2 - 10x + 16)
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Solve this system using the substitution method.
-2x – y = -7
x + 7y = 10
Solve using the substitution method and be sure to show all of your work.
Answers
Using the substitution method equation form is x is 3 and y is1
What is substitution method?The algebraic approach to solving simultaneous linear equations is known as substitution method. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies.Finding the value of any variable from one equation in terms of another variable is the first step in the substitution method. For instance, if there are two equations,-2x – y = -7 and x + 7y = 10, Applying the replacement approach begins with this.One of the equations' initial variable should be solved for, and the answer should be inserted into the other equation.Form of Point: (3 , 1 )
Equation Form: x = 3 and y =1
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Right triangle EFG has its right angle at F, EG = 6 , and FG = 4 What is the value of the trigonometric ratio of an angle of the triangle? Drag a value to each box to match the trigonometric ratio with its value .
Answers
Answer:
\(\cos G=\dfrac{2}{3}\)
\(\csc E=\dfrac{3}{2}\)
\(\cot G=\dfrac{2}{\sqrt{5}}\)
Step-by-step explanation:
If the right angle of right triangle EFG is ∠F, then EG is the hypotenuse, and EF and FG are the legs of the triangle. (Refer to attached diagram).
Given ΔEFG is a right triangle, and EG = 6 and FG = 4, we can use Pythagoras Theorem to calculate the length of EF.
\(\begin{aligned}EF^2+FG^2&=EG^2\\EF^2+4^2&=6^2\\EF^2+16&=36\\EF^2&=20\\\sqrt{EF^2}&=\sqrt{20}\\EF&=2\sqrt{5}\end{aligned}\)
Therefore:
EF = 2√5FG = 4EG = 6\(\hrulefill\)
To find cos G, use the cosine trigonometric ratio:
\(\boxed{\begin{minipage}{9 cm}\underline{Cosine trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)
For angle G, the adjacent side is FG and the hypotenuse is EG.
Therefore:
\(\cos G=\dfrac{FG}{EG}=\dfrac{4}{6}=\dfrac{2}{3}\)
\(\hrulefill\)
To find csc E, use the cosecant trigonometric ratio:
\(\boxed{\begin{minipage}{9 cm}\underline{Cosecant trigonometric ratio} \\\\$\sf \csc(\theta)=\dfrac{H}{O}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)
For angle E, the hypotenuse is EG and the opposite side is FG.
Therefore:
\(\csc E=\dfrac{EG}{FG}=\dfrac{6}{4}=\dfrac{3}{2}\)
\(\hrulefill\)
To find cot G, use the cotangent trigonometric ratio:
\(\boxed{\begin{minipage}{9 cm}\underline{Cotangent trigonometric ratio} \\\\$\sf \cot(\theta)=\dfrac{A}{O}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)
For angle G, the adjacent side is FG and the opposite side is EF.
Therefore:
\(\cot G=\dfrac{FG}{EF}=\dfrac{4}{2\sqrt{5}}=\dfrac{2}{\sqrt{5}}\)
Please help me nowww
I need this right away!!
Answers
there is not enough information to complete the answer
Find x when () = 2. Please explain step by step
Answers
Answer: Ans is 990. First such a number is 5×0 +2=2, then 5×1 +2=7, like that in all 20 numbers are there from 2 to 97 in A.P.with common difference of 5.
Step-by-step explanation:
4x-8=12
4×-8=12+8
4×=20
4/4×=20/4
×=
Answers
Answer:
\(x = \frac{20}{4} \\ x = 5\)
Answer:
x=5
Step-by-step explanation:
Picture is it............
Answers
In this triangle the three interior angles are = ∠82° , ∠54° and ∠x .
Then ;
∠82° + ∠54° + ∠x = 180° ( under angle sum property which says that the sum of the three interior angles of a triangle is equal to 180° )
= 136 ° + x = 180
= x = 180 - 136
= x = 44°∠x and ∠y will sum up to 180° as they are a linear pair .
= 44° + y = 180
= y = 180 - 44
= y = 136°Since ∠y and ∠z are vertically opposite angles their angle measure will be equal . Which means ;
= ∠y = ∠z
= 136° = ∠z
= ∠z = 136°Therefore :-
The value of x = 44°Which expression is equival 81 1/3?
Answers
Answer: 3^3 Square root 3
Step-by-step explanation:
Write a function that sums all the numbers of the major diagonal in an matrix of integers using the following header:def sumMajorDiagonal(m):The major diagonal is the diagonal that runs from the top left corner to the bottomright corner in the square matrix. Write a test program that reads a matrix anddisplays the sum of all its elements on the major diagonal. Here is a sample run
Answers
The sum of the diagonal is 34.
A function that sums all the numbers of the major diagonal in a matrix of integers using the following header: def sumMajorDiagonal(m): The major diagonal is the diagonal that runs from the top left corner to the bottom right corner in the square matrix.
A test program that reads a 4-by-4 matrix and displays the sum of all its elements on the major diagonal.
import java.util.Scanner;
public class twoDimentionalArrays
{
public static int sumMajorDiagonal(int[][] m)
{
int sum =0;
for(int i =0;i<m.length;i++)
sum += m[i][i];
return sum;
}
public static void main (String[] args)
{
Scanner scan = new Scanner (System.in);
System.out.println("Fill in this 4x4 matix");
int[][] nums = new int[4][4];
for (int i =0;i<nums.length;i++)
{
for (int j =0;j<nums[i].length;j++)
{
nums[i][j] = scan.nextInt();
}
}
System.out.println("Diagonal sum is " + sumMajorDiagonal(nums));
}
}
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Help meeeeeeeeeeeeeeeeeeee
Answers
Answer:
I believe it is y=1x or y=x
Answer:
14
Step-by-step explanation:
The constant of proportionality is the y number when x is 1. Look on the bottom of the graph. Find 1, so up to the line and then across left to the y axis. you will be at 14. This means that every time the x increases by 1, the increases by 14
T
55
R
45
Find Q.
A. 40°
B. 80°
C. 130°
D. 260°
Answers
Answer:
B. 80°
Step-by-step explanation:
55+45=100
180-100=80
Q=80°
10. Prime numbers from 1 to 100 are running a restaurant - PRIME SPOT, near a tourist point. On a winter holiday, 1 and the composite numbers up to 100 enter the restaurant for dinner after their picnic at the same point. The dining hall has tables with seating capacity 15 for each. If they occupy tables without leaving any chair free, how many tables are required? If each prime number attender has to serve equal number of customers, how many customers should each one get to serve?
Answers
6 tables are required. Each prime number attender should serve 3 customers each.
The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
All the numbers other than prime numbers are composite numbers.
The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.
Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.
Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables
Therefore, 6 tables are required.
Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.
Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.
Thus, each prime number attender should serve 3 customers each.
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Two regular 6-sided dice are tossed. Compute the probability that the sum of the pips on the upward faces of the 2 dice is the following. (See the figure below for the sample space of this experiment. Enter your probability as a fraction.)
At least 11
Answers
The probability that the sum of the pips selected that is at least 11 would be = 1/12.
How to determine the probability of the selected events?To determine the probability of the selected events, the formula for problem should be used which is given below;
Probability = possible outcome/sample space
Possible outcome = at least 11 = (5,6),(6,5),(6,6)
= 3
Sample space = 36
Probability = 3/36 = 1/12
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he diameter of the circle is 18 m. Eugene incorrectly says that the circumference of the circle is about 113.04 m. What is the circumference of the circle? What mistake did Eugene make? Use 3.14 for pi.
Answers
Answer:
The circumference of the circle is \(C=56.55 \:m\).
Eugene confused the radius with the diameter to find the circumference of the circle.
Step-by-step explanation:
The circumference of a circle is the distance around the outside of the circle.
The circumference of a circle is found using this formula:
\(\begin{matrix} C=\pi \cdot d\\or\\ \, C=2\pi \cdot r \end{matrix}\)
From the information given the diameter of the circle is 18 m. Therefore, the circumference of the circle is
\(C=\pi \cdot d\\\\C=3.14 \cdot 18 \approx 56.55 \:m\)
Eugene used the wrong formula to find the circumference of a circle.
\(C=2\cdot(3.14)\cdot 18=113.04 \:m\)
He confused the radius with the diameter.
Answer:
Eugene used the wrong formula to find the circumference of a circle.
He confused the radius with the diameter.
Step-by-step explanation:
ways to select the 7 math help websites
Answers
Answer:
Step-by-step explanation:
If the order you select them is important
nmber of ways = 9! / (9-7)!
= (9*8*7*6*5*4*3*2*1) / (2*1)
= 9*8*7*6*5*4*3
= 181,440.
If the order does not matter:
nmber of ways = 9! / ((9-7)! * 7!)
= 9*8 / 2*1
= 36.
Which choice is equivalent to the expression below?
28.24
O A. 28 + 22/10 + 24/100
O B. 28+ 2/10 + 4/10
O C. 28. 22/10. 24/100
O D. 28. 224/10
Answers
Answer:
C
Step-by-step explanation:
sin(60-theta)sin(60+theta)
Answers
Step-by-step explanation:
\( \sin(60 - \theta) \sin(60 + \theta) \\ = \{ \sin(60) \cos( \theta) - \sin( \theta) \cos(60) \} \{ \sin(60) \cos( \theta) + \cos(60) \sin( \theta) \} \\ = \{ \frac{ \sqrt{3} }{2} \cos( \theta) - \frac{1}{2} \sin( \theta) \} \{ \frac{ \sqrt{3} }{2} \cos( \theta) + \frac{1}{2} \sin( \theta) \} \\ \\ \)
from difference of two squares:
\({ \boxed{(a - b)(a + b) = ( {a}^{2} - {b}^{2} ) }}\)
therefore:
\( = \{ {( \frac{ \sqrt{3} }{2}) }^{2} { \cos }^{2} \theta \} - \{ {( \frac{ \sqrt{3} }{2} )}^{2} { \sin }^{2} \theta \} \\ \\ = \frac{3}{4} { \cos }^{2} \theta - \frac{3}{4} { \sin}^{2} \theta\)
factorise out ¾ :
\( = \frac{3}{4} ( { \cos }^{2} \theta - { \sin}^{2} \theta) \\ \\ = { \boxed{ \frac{3}{4} \cos(2 \theta) }}\)
Jeffrey earned $65 doing yard work. He bought a pair of jeans
for $31.25 and a sweatshirt for $16.50. He set aside the
money left from his shopping trip to buy a gift for his cousin.
How much money did he set aside for the gift?
1. What do you need to find before you can solve the
problem?
2. Write equations to represent the problem. Then solve
the problem.
How do I write the equations to solve #2?
Answers
Answer:
65 - (31.25 + 16.50) = x
Step-by-step explanation:
Please help me asap
Answers
Answer:
To find the inverse interchange the variables and solve for y.
Step-by-step explanation:
f−1(x)=6x−53(1+x)
For the equation y=5x, identify the:
slope
y-intercept
Answers
Answer:
slope = 5; y-intercept = (0,0)
Step-by-step explanation:
Answer:
slope= 5/1
y-intercept=0
Step-by-step explanation:
I hope this helps... if it does, may I be brainliest???
Is there anyone here who does Calvert or Odessy?
I was quite behind on my assignments, and, somehow, I go to catch up and they've been completed or something. It says I'm 100% on pace, and I know for a fact that I wasn't. What happened?
Answers
what happen is there is a glitch probably
yes this is what happened to me. if u get too far behind they will change the due dates to your "pace" and make it easier for you.
The capacity of a water tank is 10000 litres and there is 4800 litres of water. A water tap can fill 40 litres of water per minute and another tap can empty 25 litres of water per minute. If both the taps are opened together for 10 minutes, then how much water will be in the tank after 10 minutes?
Answers
The amount of water tank with water after 10 minutes will be 4950 liters.
To solve this problem, we need to keep track of the net flow of water into the tank over the course of 10 minutes. The tap filling water adds water to the tank, while the tap emptying water removes water from the tank.
Let's calculate the net flow rate of water per minute:
Flow rate = (filling tap flow rate) - (emptying tap flow rate)
Flow rate = 40 L/min - 25 L/min
Flow rate = 15 L/min
Now, we can calculate the net flow of water over 10 minutes:
Net flow of water = (flow rate) * (time)
Net flow of water = 15 L/min * 10 min
Net flow of water = 150 L
Therefore, over the course of 10 minutes, the net flow of water into the tank is 150 liters.
Initially, the tank had 4800 liters of water. Adding the net flow of water, we can determine the final amount of water in the tank:
Final amount of water = (initial amount of water) + (net flow of water)
Final amount of water = 4800 L + 150 L
Final amount of water = 4950 L
After 10 minutes, there will be 4950 liters of water in the tank.
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What is the unit price of the cereal box?
Answers
Answer:
h f
Step-by-step explanation:
hf hf
Music students and art students at a middle school were surveyed to choose a cardiovascular activity: playing sports or dancing.
Do you prefer dancing or playing sports?
Playing sports Dancing Row totals
Music students 32 15 47
Art students 31 22 53
Column totals 63 37 100
What is the marginal frequency of students who chose dancing?
15
22
37
53
Answers
The marginal frequency of students who chose dancing is 37.
The correct answer to the given question is option 3.
The marginal frequency of students who chose dancing can be calculated by adding up the number of students who chose dancing in each row or column. In this case, we need to add up the number of art students who chose dancing (22) and the number of music students who chose dancing (15), which gives us a total of 37. This is the marginal frequency of students who chose dancing.
Based on the survey results, it appears that a slightly higher percentage of art students prefer dancing (41.5%) compared to music students (31.9%). However, both groups of students seem to be fairly evenly split between dancing and playing sports, with a slight preference for playing sports overall.
It's worth noting that cardiovascular activity is important for overall health and well-being, and both dancing and playing sports can provide great opportunities for exercise and physical activity. Additionally, both activities can also be enjoyable and provide a sense of community and social connection, which is important for middle school students who are still developing their social skills and relationships. Ultimately, the choice between dancing and playing sports will depend on individual interests, preferences, and abilities.
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Jeanette purchased a concert ticket on a web site. The original price of the
ticket was $75. She used a coupon code to receive a 20% discount. The
web site applied a 10% service fee to the discounted price. Jeanette's ticket
was less than the original price by what percent?
0 7%
O 10%
O 12%
0 28%
Question 4
Answers
