The diagram below shows the partial construction of which shape?
a circle inscribed in a circle
an equilateral triangle inscribed in a circle
a regular hexagon inscribed in a circle
a square inscribed in a circle
Answers
Answer:
The correct option is 2.
Step-by-step explanation:
Steps for construction of a circle inscribed in a circle:
1. Draw a circle using compass.
2. Draw a diameter of that circle, using the scale.
3. Place the compass on a end point of diameter and draw a full circle, without changing the span on compass.
4. Mark the points of intersection of the two circle.
5. Using scale connect both points of intersection.
6. Using the scale connect each in intersection point with the second end point of diameter.
The diagram below shows the partial construction of a circle inscribed in a circle. Therefore the correct option is 2.
Related Questions
On Monday, a local hamburger shop sold a combined total of 556 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold. How many hamburgers were sold on Monday?
Answers
c = number of cheeseburgers sold.
we know that "c" is three times the number of "h", thus c = 3h
we also know, the total amount sold for both is 556, h + c = 556
h + c = 556
c = 3h
thus
h + (3h) = 556 <---- solve for "h" to see how many hamburgers were sold.
what about "c"? well, c = 3h
c=3h
The total number sold is:
c+h=556, using c found earlier in this equation gives you:
(3h)+h=556
4h=556 divide both sides by 4
h=139
So 139 hamburgers were sold on Monday.
Hans's vegetable garden has an area of 400 ft2. It is the shape of a rectangle with a length of 40 ft and a width of 10 ft. He has decided to expand the garden to make room for several new varieties of lettuce. The new garden will be a larger rectangle. He plans on making the new length 3 times the current length and the new width 3 times the current width.
Answers
To calculate the new area of Hans's expanded garden, multiply the new length by the new width. The new garden will have an area of 3600 ft^2.
The original garden area is 400 ft2, with a length of 40 ft and a width of 10 ft.
To find the new garden's area after expansion:
Calculate the new length: 40 ft * 3 = 120 ft.Calculate the new width: 10 ft * 3 = 30 ft.Multiply the new length by the new width: 120 ft * 30 ft = 3600 ft2.2. Wandabaked168cookies,packagedtheminboxesof12,andsoldeachboxfor $1.20. How many boxes of 12 can be packaged if there are 168 cookies? What was the total amount of money that Wanda made for all of the boxes sold?
Answers
------------------------------------------------------
This question is solved using proportions.
In each box, there are 12 cookies.She baked 168 cookies.Thus, to find the number of boxes, we use a rule of three.
1 box - 12 cookies.
x boxes - 168 cookies.
Applying cross multiplication:
[tex]12x = 168[/tex]
[tex]x = \frac{168}{12}[/tex]
[tex]x = 14[/tex]
Thus, 14 boxes can be packaged.
------------------------------------------------------
Now, we find the amount of money she made.
She sold 14 boxes.Each box for $1.20.Thus:
[tex]T = 14 \times 1.2 = 16.8[/tex]
She made $16.8.
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When a crew rows with the current, it travels 18 miles in 3 hours. Against the current, the crew rows 6 miles in 3 hours. Let x=the crew's rowing rate in still water and let y = the rate of the current. Find the rate of rowing in still water and the rate of the current.
Answers
3(x+y)=18 and 3(x-y)=6 divide both equations by three
x+y=6 and x-y=2 now add the two equations together...
x+x+y-y=6+2
2x=8 divide both sides by 2
x=4 mph, and since x+y=6
4+y=6
y=2 mph
So the speed of the boat in still water is 4mph and the speed of the current is 2mph.
The speed of the boat in still water is 4mph and the speed of the current is 2mph.
Using the distance formula expressed as:
Distance = speed * time
d = st
Let x be the crew's rowing rate in still water and;
let y be the rate of the current
If a crew rows with the current and it travels 18 miles in 3 hours, the
3(x+y)=18
If they row against the current, the crew rows 6 miles in 3 hours then;
3(x-y)=6
The equations becomes
x + y = 6
x - y = 2
Add both equations
2x = 6 + 2
2x = 8
x = 4
Recall that x + y = 6
4 + y = 6
y = 2
Hence the speed of the boat in still water is 4mph and the speed of the current is 2mph.
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Three tables are placed side by side. One table is 2 feet 9 inches wide, another is 4
feet 8 inches wide, and the third is 6 feet 11 inches wide. How wide are they combined?
Write your answer in feet and inches. Use a number less than 12 for inches
Answers
Final answer:
The combined width of the three tables is 14 feet 4 inches, calculated by first converting each table's width to inches, adding them together, and then converting the total back to feet and inches.
Explanation:
To find the combined width of the three tables placed side by side, you need to add the widths together. First, convert all measurements to inches, add them, and then convert back to feet and inches.
Table 1: 2 feet 9 inches = (2 × 12) + 9 = 24 + 9 = 33 inches
Table 2: 4 feet 8 inches = (4 × 12) + 8 = 48 + 8 = 56 inches
Table 3: 6 feet 11 inches = (6 × 12) + 11 = 72 + 11 = 83 inches
Now, add the inches: 33 + 56 + 83 = 172 inches.
To convert 172 inches back to feet and inches, divide by 12 (since there are 12 inches in a foot): 172 ÷ 12 = 14 feet 4 inches (since 172 divided by 12 is 14 with a remainder of 4).
Therefore, the combined width of the tables is 14 feet 4 inches.
To solve problems about spans of time that include B.C. and A.D. dates, you would need to use which numbers?
Answers
The correct numbers to use in solving problems about spans of time like B.C. and A.D. should be “integers”.
Integers are whole numbers (not a fractional number or not a decimal number) which can take a value of negative, zero, or positive number. Example of integers would be -1, 0 and 1.
In calculations, the time period would be on the x-axis. Since B.C. and A.D. are two different spans of time, therefore in the calculations, the date of BC should be negative (negative x-axis) while the date of AD should be positive (positive x-axis). This would place the origin as the common reference.
To solve problems about spans of time that include B.C. and A.D. dates, Integers will be used .
What is B.C. and A.D. ?
The terms A.C. and B.C. stands for anno Domini and before Christ
These are used to label years in the Gregorian calendars.
For solving a Problem that involve B.C and A.D. , Integers will be used
As the time span are neither in fraction or decimal
It can be negative , 0 and positive
B.C will be on the negative side of the x axis and A.D. will be equal to the positive side of the x axis.
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Simplify 2 square root of 10 times 3 square root of 12
answers
A.6squar rootof120
B.12squar rootof60
C.12squar rootof30
D.5squar rootof120
Answers
The simplified form of the expression [tex]2\sqrt{10} \times 3\sqrt{12}[/tex] is [tex]6\sqrt{120}[/tex] which corresponds to answer choice A.
Given: [tex]2\sqrt{10} \times 3\sqrt{12}[/tex]
To find: simplify
We can break down the expression [tex]2\sqrt{10} \times 3\sqrt{12}[/tex] and multiply the roots and whole numbers as follows:
[tex]\text{product is} = 2\sqrt{10} \times 3\sqrt{12} \\\text{product is} = 2 \times 3 \times \sqrt{10} \times \sqrt{12}\\\text{product is} = 6 \times \sqrt{120}\\\text{product is} = 6\sqrt{120}[/tex]
The simplified form of the given expression is 6√120, which corresponds to answer choice A.
If you are given a circle with center c, how do you locate the vertices of a square inscribed in circle c?
Answers
Answer:
The square is inscribed in a circle that means the square is drawn inside a circle such that it's vertices lie on the circle.
You need to remember that the vertices of the square lie on the circumference of circle and the center of circle is also the midpoint of diagonals of the square i.e. Diagonal of the square is equal to diameter of the circle.
We could also see the image of such figure.
To locate the vertices of a square inscribed in a circle, follow these steps: draw the circle, choose a point on the circumference, create a radius, find the midpoint, and connect the points to form a square.
Explanation:To locate the vertices of a square inscribed in a circle, you can follow these steps:
Draw the circle with center C.Choose any point on the circumference of the circle and label it A.Draw a line segment from C to A, creating a radius.Construct a perpendicular bisector of the radius to find the midpoint, which we'll call M.Draw a line segment from M to the circumference of the circle, which intersects at two points. Label them B and D.Connect points ABCD to form a square.Now you have located the vertices of a square inscribed in circle C.
How many integers between 100 and 300 inclusive,are divisible by 10?
Answers
10≤n≤30
So the number of multiples of 10 from 100 to 300 inclusive is:
(30-10+1)=21
The final answer is 21.
A 250 ml glass of orange juice contains 22 grams of sugar. how much sugar is in a two-liter (2,000 ml) bottle of orange juice?
Answers
cross multiply
(250)(x) = (2000)(22)
250x = 44,000
x = 44,000/250
x = 176 grams of sugar <==
Orange juice contains some amount of sugar in it. There is 176 g of sugar present in a 2000 ml bottle of orange juice.
Given:
A 250 ml glass of orange juice contains 22 grams of sugar.
It is required to calculate the amount of sugar present in the 2000 ml bottle of juice.
Now, the amount of sugar present in 1 ml of juice will be,
[tex]\dfrac{22}{250}=\dfrac{11}{125}\rm \; g[/tex]
So, the amount of sugar in 2000 ml of juice will be,
[tex]\dfrac{11}{125}\times 2000=11\times 16\\=176\rm \; g[/tex]
Therefore, there is 176 g of sugar present in a 2000 ml bottle of orange juice.
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It takes 23 minutes for 6 people to paint 6 walls. How many minutes does it take 9 people to paint 7 walls?
Answers
Once you have this rate you can find how many minutes it takes to do any number of walls with any number of people.
Lets call this unit rate 'r'. Number of people = n, Number of walls = w.
By multiplying the unit rate by 'n', you get the speed n people can paint a wall. Example, if it takes 4 min to paint 1 wall the unit rate = 1/4. The speed for 8 people is 8*(1/4) = 2 walls per minute. Time = 1/rate. So 2 walls per minute = 1/2 min per wall. Now multiply time by w. If there are 10 walls, (1/2)*10 = 5 , It takes 8 people 5 min to paint 10 walls.
The general formula is:
[tex]t = \frac{w}{n*r} \\ \\ r = \frac{w}{n*t}[/tex]
Now apply to given problem:
Time = 23 min, n = 6, w = 6
Solve for unit rate 'r'
[tex]r = \frac{6}{6*23} = \frac{1}{23} [/tex]
Find time, given
n = 9, w = 7
[tex]t = \frac{7}{9*(1/23)} = \frac{7*23}{9} = 17.89[/tex]
Answer:
it takes 17.89 min or 17 min 53 sec
Help with this math question
Answers
4/7 = 7/DG ⇒ DG = 7*7/4 = 12.25
Thus, 4/7 = 7/DG. To solve for DG, invert both sides of this equation:
7/4 = DG/7
and then multiply both sides of this last equation by 7, to eliminate 7 from the denominator of DG/7:
49/4 = DG
The length of side DG is 49/4.
How many numbers are between 0 and 1/10
Answers
what are characteristics of complex numbers
Answers
What is the ratio of 400 to 400 in fraction form
Answers
Answer: 400/400 which reduces to 1/1
Step-by-step explanation:
Susan invests
3
times as much money at
11
%
as she does at
7%
. If her total interest after
1
year is
$2000
, how much does she have invested at each rate?
Answers
now, she invested at 11% three times as much, so 3*a or "3a"
how much is 7% of a? well, (7/100)*a or 0.07a
how much is 11% of 3a? well (11/100)* 3a or 0.11(3a)
now, we know her total yield in interest is 2000 bucks, so whatever 0.07a is and 0.11(3a) are, they add up to 2000
0.07a + 0.11(3a) = 2000
solve for "a".
find the poin on the graph 0f f(x)=1-x^2 that are closest to0(0,0)
Answers
[tex] \sqrt{(x-0)^2+(1-x^2-0)^2}=\sqrt{x^2+(1-x^2)^2}=\sqrt{x^2+1-2x^2+x^4} [/tex]
To make this easier, let's minimize the SQUARE of this quantity because when the square root is minimal, its square will be minimal.
So minimize [tex]L=x^4-x^2+1[/tex]
Find the derivative of L and set it equal to zero.
[tex]\frac{d}{dx}(L)=4x^3-2x \\ 4x^3-2x=0 \\ 2x(2x^2-1)=0[/tex]
This gives you [tex]x=0[/tex] or [tex]x^2=\frac{1}{2} \\ x=\pm\sqrt{2}/2[/tex]
You can use the Second Derivative Test to figure out which value(s) produce the MINIMUM distance.
[tex]\frac{d^2}{dx}=12x^2-2[/tex]
When x = 0, the second derivative is negative, indicating a relative maximum. When [tex]x=\pm\frac{\sqrt{2}}{2}[/tex], the second derivative is positive, indicating a relative MINIMUM.
The two points on the curve closest to the origin are [tex]\left( \pm\frac{\sqrt{2}}{2},\frac{1}{2} \right)[/tex]
The sum of 5 consecutive even number is 100 the middle number is
Answers
100/5 =20
16 + 18 +20 +22 +24 = 100
middle number is 20
what is the relationship between the 3s in 9338
Answers
Answer:
The 3 in the hundreds place has 10 times the value of the 3 in the tens place.
Step-by-step explanation:
In a base-10 place-value number system such as the one we customarily use, the value of a given digit is multiplied by 10 when it is placed one position farther to the left of the decimal point.
The threes in this number are in adjacent positions—one is in the tens place, and the one to its left is in the hundreds place. The digit in the hundreds place has a value of 300, which is 10 times the value of 30 that the digit in the tens place has.
A standard deck of cards contains 52 cards. one card is selected from the deck. ?(a) compute the probability of randomly selecting aa heartheart or spadespade. ?(b) compute the probability of randomly selecting aa heartheart or spadespade or clubclub. ?(c) compute the probability of randomly selecting aa twotwo or diamonddiamond.
Answers
The probability of randomly selecting a heart or a spade is 1/2. The probability of randomly selecting a heart or a spade or a club is 3/4. The probability of randomly selecting a two or a diamond is 17/52.
Explanation:(a) There are 13 hearts and 13 spades in a standard deck of cards. The probability of randomly selecting a heart or a spade can be calculated as:
P(Heart or Spade) = P(Heart) + P(Spade) = 13/52 + 13/52 = 26/52 = 1/2
(b) To find the probability of randomly selecting a heart or a spade or a club, we add the probability of selecting a club to the previous result:
P(Heart or Spade or Club) = P(Heart or Spade) + P(Club) = 1/2 + 13/52 = 39/52 = 3/4
(c) There are 4 twos and 13 diamonds in a standard deck of cards. The probability of randomly selecting a two or a diamond can be calculated as:
P(Two or Diamond) = P(Two) + P(Diamond) = 4/52 + 13/52 = 17/52
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Solve the equation for a. 55a – 44a = 11
Answers
11a=11 divide both sides by 11
a=1
11a = 11
a = 1
Use the percent of change to find the new amount 120 pounds decreased by 30%
Answers
In 2006,111.7 million household owned at least
Answers
In 2006, 112.8 million households owned at least one TV set. About 5.8 million households owned 3 or more TV sets in 2006. What percentage of those owning atleast one TV set was this? Round to the nearest integer
5.8 / 112.8 = 0.051418 which is 5.1418 percent, rounds down to 5%.
What is the solution set of x 2 + 5x - 5 = 0?
Answers
Answer:
a=1 b=5 c=-5
We solve by using the quadratic formula.
x = -5 +- sq root (5² - 4*1*-5) / (2 * 1)
x = [-5 +- sq root (25 + 20)]/ 2
Step-by-step explanation:
Evaluate the expression 3c – d for the given variable. d = -c + 7
Answers
3c-(-c+7)
3c+c-7
4c-7
Final answer: 4c-7
When a measurement in inches is converted to centimeters,will the number of centimeters be greater or less than the number of inches
Answers
what is the value of -2 x^2 +4y if x = -2 and y =3
Answers
-2(-2)^2+4(3)
First evaluate the exponent.
-2(4)+4(3)
Then evaluate multiplication.
-8+4(3)
-8+12
Then add.
Final answer:4
One 16-ounce bottle of an energy drink has an average of 500 mg of caffeine with a standard deviation of 25 mg. In a carton containing 30 bottles, what is the standard deviation of the average amount of caffeine?
Answers
Final answer:
The standard deviation of the average amount of caffeine in a carton containing 30 bottles of an energy drink is approximately 4.564 mg.
Explanation:
To calculate the standard deviation of the average amount of caffeine in a carton containing 30 bottles of an energy drink, we can use the concept of the sampling distribution of the sample mean.
When independent random samples of a fixed size are taken from a population, the standard deviation of the sample means (σx-bar) is equal to the population standard deviation (σ) divided by the square root of the sample size (n), which is also known as the standard error of the mean.
The formula to find the standard deviation of the sample means is:
σx-bar = σ / √n
In this case, the population standard deviation is given as 25 mg of caffeine, and the sample size is 30 bottles.
So, we calculate the standard deviation of the average amount of caffeine as follows:
σx-bar = 25 mg / √30
σx-bar ≈ 25 mg / 5.477
σx-bar ≈ 4.564 mg (rounded to three decimal places)
Thus, the standard deviation of the average amount of caffeine in a carton containing 30 bottles is approximately 4.564 mg.
You put $100 in an account. The account earns $2 simple interest in 6 months. What is the annual interest rate?
Answers
Lowell bought 4 1/4 pounds of apples and 3 3/5 pounds of oranges. How many pounds of fruit did lo buy?
Answers
Answer:
7.85 pounds (or 7 17/20 pounds)
Step-by-step explanation:
In decimal, the total is ...
4.25 + 3.60 = 7.85 . . . pounds
As mixed numbers, the total is ...
(4 +1/4) + (3 +3/5) = (4 +3) + (1/4 +3/5) = 7 +(5/20 +12/20) = 7 17/20 . . . pounds
Lowell bought 7 17/20 pounds of fruit.
_____
Comment on the math
Any calculator can add these numbers for you. You may have to enter them as (4+1/4) and (3+3/5) if your calculator does not support mixed number entry. Depending on the calculator, you may be able to get it to show you the mixed number result. If you want a mixed number and you get a decimal number, you may have to reduce the fraction yourself:
7 85/100 = 7 17/20 . . . . . . a factor of 5/5 can be removed from the fraction
___
Any two fractions can always be added using the formula ...
a/b + c/d = (ad +bc)/(bd)
Here, that means the sum of 1/4 and 3/5 is ...
1/4 + 3/5 = (1·5 +4·3)/(4·5) = (5+12)/20 = 17/20 . . . . . the result above
In some cases, you may have to reduce the resulting fraction.
Lowell bought [tex]4 \frac{1}{4}[/tex] pounds of fruit.
Explanation:To find the total weight of fruit Lowell bought, we need to add the weights of the apples and oranges together.
Lowell bought [tex]4 \frac{1}{4}[/tex] pounds of apples and [tex]3 \frac{3}{}[/tex] pounds of oranges. To add these fractions, we need to find a common denominator, which in this case is 20.
Converting both fractions to twentieths, we have [tex]\frac{17}{20}[/tex] pounds of apples and [tex]\frac{68}{20}[/tex] pounds of oranges. Adding these together, we get a total of [tex]\frac{85}{20}[/tex] pounds. Simplifying the fraction, we find that Lowell bought [tex]4 \frac{1}{4}[/tex] pounds of fruit.
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