[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{2}{h}~~,~~\underset{-3}{k})}\qquad \stackrel{radius}{\underset{4}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - 2 ~~ )^2 ~~ + ~~ ( ~~ y-(-3) ~~ )^2~~ = ~~4^2\implies {\large \begin{array}{llll} (x-2)^2+(y+3)^2=16 \end{array}}[/tex]
A 6 -sided die with the numbers 1 to 6 on its faces is rolled and a ticket is drawn from a bag of 7 tickets labelled 1 to 7 . How many different ways can you roll a 1 on the die and draw a 7 from the bag of tickets?
The no. ways roll a 1 on the die and draw a 7 from the bag of tickets is 1 And the probaility is [tex]\frac{1}{42}[/tex]
What is Probability?Probability is the ratio of favorable outcomes to all other potential outcomes of an event. The symbol x can be used to signify how many positive findings there are in an experiment with 'n' results. The following formula can be used to determine the likelihood of an event:
Probability (event) equals a favorable result/the total of outcomes divided by n.
The no. ways roll a 1 on the die and draw a 7 from the bag of tickets is 1
And the probaility is -
[tex]\frac{1}{6} X \frac{1}{7}[/tex]
[tex]= \frac{1}{42}[/tex]
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How many four-letter words can be formed by using the letters in facetious? There are nine letters
available, and each one can be used at most once per word.
Answer:
Step-by-step explanation:
To find the number of four-letter words that can be formed using the letters in facetious, you can use the combination formula:
nCr = n! / (r! (n - r)!)
In this case, n is the total number of letters available (9) and r is the number of letters per word (4). Therefore, the number of four-letter words that can be formed is:
nCr = 9! / (4! (9 - 4)!) = 9! / (4! 5!) = (9 x 8 x 7 x 6) / (4 x 3 x 2 x 1) = 126
Therefore, there are 126 four-letter words that can be formed using the letters in facetious.
What is the correct answer ???????? only the answer
Answer: Open
Step-by-step explanation: the dot is only filled in when the inequallity is "greater than or equal to" or "less than or equal to"
Australia is approximately 2441 miles in width.
How many kilometers wide is Australia?
Use 1 km = 0.6214 mi
km
Answer:
3928.4087
Step-by-step explanation:
2441/0.6214
The width of Australia in kilometres will be equal to 3928.4087 km.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Australia is approximately 2441 miles in width. The width of Australia in kilometres will be calculated as,
1 km = 0.6214 miles
1 mile = 1 /0.624 kilometres
Width = 2441/0.6214
Width = 3928.4087 kilometres
Hence, the width of Australia in kilometres is 3928.4087.
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A ramp goes from a doorway of a building to the ground. The end of the ramp connected to the doorway is 1 foot above the ground. The horizontal distance from the bottom of the ramp to the building is 10 feet. What is the angle of elevation of the ramp to the nearest degree?
The angle of elevation of the ramp to the nearest degree will be 5.71°.
What is trigonometry?The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry. The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.
Given that a ramp goes from a doorway of a building to the ground. The end of the ramp connected to the doorway is 1 foot above the ground. The horizontal distance from the bottom of the ramp to the building is 10 feet.
The angle of elevation will be calculated as,
tanθ = ( 1 / 10)
θ = tan⁻¹(1/10)
θ = 5.7°
Therefore, the angle of elevation of the ramp to the nearest degree will be 5.71°.
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Mrs. magil asks her students to draw a right triangle with one angle measuring 63 degrees. Which equation can be used to determine a, the measure of the third angle in their triangle?
Answer: a = 180 - 63 - 90
Step-by-step explanation:
180 degrees in a triangle
90 degrees in a right triangle
180 = 63 + 90 + a
move 63 and 90 to the other side
a = 180 - 63 - 90
Solve 15x - 10y = -30 and 5x - 9y = 7 using elimination. Show Steps. Put answer in coordination form (x,y)
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The coordinates are (0, 3) or (34/5, 3)
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
15x - 10y = -30 _____(1)
5x - 9y = 7 ______(2)
Multiply 3 on (2)
15x - 27y = 21 _____(3)
Using the elimination method we get,
From (1) and (3) we get,
15x - 10y = -30
15x - 27y = 21
(-) (+) (-)
17y = 51
This means,
y = 51/17
y = 3
Now,
Put y = 3 in (1) we get,
15x - 10y = -30
15x- 10 x 3 = -30
15x - 30 = -30
15x = 0
x = 0
Put y = 3 in (2) we get,
5x - 9y = 7
5x - 9 x 3 = 7
5x - 27 = 7
5x = 7 + 27
5x = 34
x = 34/5
Thus,
The coordinates are (0, 3) or (34/5, 3)
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Two years ago, you purchased a $1,000 par value corporate bond with a coupon interest rate of 6.5 percent. Today, comparable bonds are paying 5.75 percent. What is the approximate dollar price for which you could sell your bond? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Answer:
you could sell is for $10,000
Step-by-step explanation:
because it increased in value you could sell it for more
A park has two sprinklers that are used to fill a fountain. One sprinkler can fill the
fountain in 3 h, whereas the second sprinkler can fill the fountain in 6 h. How long will
it take to fill the fountain with both sprinklers operating?
It takes 2 hrs to fill the fountain with both sprinklers operating
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
A park has two sprinklers that are used to fill a fountain
One sprinkler can fill the fountain in 3 h
second sprinkler can fill the fountain in 6 h
We need to find the time required to fill the fountain by two sprinklers.
Let t = time required with both sprinklers working
t/3+t/6=1
2t+t/6=1
3t/6=1
Apply cross multiplication
3t=6
Divide both sides by 3
t=2
Hence, it takes 2 hrs to fill the fountain with both sprinklers operating
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Alex can earn $15 an hour mowing neighborhood lawns on weekends. If Alex decides to spend an hour mowing rather than watching a football game, his opportunity cost of mowinf lawns is:
a. The $15 he earns
b. The enjoyment he would have received from watching the football game during that time.
c. The $15 he earns minus the enjoyment he would have received from watching the football game during that time.
d. The $15 he earns plus the enjoyment he would have received from watching the football game during that time.
e. Nothing because he would have received $15 worth of enjoyment from watching the football game during that time
The opportunity cost of mowing the lawn is The $15 he earns minus the enjoyment he would have received from watching the football game during that time.
Opportunity costs are the possible advantages that a person, investor, or company forgoes while deciding between two options. Opportunity costs are by definition invisible, making it simple to ignore them. Making smarter decisions requires an understanding of the possible opportunities lost when a company or person selects one investment over another.
Opportunity Cost =FO−CO where:
FO=Return on best-forgone option
CO=Return on the chosen option
The formula for calculating an opportunity cost is simply the difference between the expected returns of each option.
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x/4 -6 = -8 pls help i really dont understand this one
Answer:
x = -8
Step-by-step explanation:
Given equation,
→ (x/4) - 6 = -8
Now the value of x will be,
→ (x/4) - 6 = -8
→ x/4 = -8 + 6
→ x/4 = -2
→ x = -2 × 4
→ [ x = -8 ]
Hence, the value of x is -8.
Dividing power algebra two
By power algebra method,
a) [tex]\frac{16}{81}[/tex]
b) [tex]\frac{2xy}{3}[/tex]
c) [tex]\frac{16x^4}{y^8}[/tex]
d) [tex]\frac{3y^2}{x^3}[/tex]
What is dividing power property?According to the Quotient of Powers Property, you can maintain the base and subtract the exponents when dividing two exponents by the same base. Since you cannot divide by zero, this characteristic will always hold true as long as the base is not zero. For more information on this property, use the interactive below.
The Exponents Power Rule: am*n = (am)n. Multiply the exponent by the power to increase a number with an exponent to that power.
You divide them by the highest exponent in the numerator (the numerator) and the lowest exponent in the denominator (the bottom exponent).
a) [tex](\frac{2}{3})^4[/tex] = [tex]\frac{2*2*2*2}{3*3*3*3}[/tex] = [tex]\frac{16}{81}[/tex]
b) [tex]\frac{2x^2y}{3x}[/tex] = [tex]\frac{2*x*x*y}{3*x}[/tex] = [tex]\frac{2xy}{3}[/tex]
c) [tex](\frac{2x}{y^2})^4[/tex] = [tex]\frac{2x*2x*2x*2x}{y^2*y^2*y^2*y^2}[/tex] = [tex]\frac{16x^4}{y^8}[/tex]
d) [tex]\frac{3xy^4}{x^3}[/tex][tex].\frac{y}{xy^3}[/tex] = [tex]\frac{3x*y*y*y*y}{x*x*x} . \frac{y}{x*y*y*y}[/tex] = [tex]\frac{3y^2}{x^3}[/tex]
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anybody want to answer this? give the right answer tho
Length of rectangle Width of rectangle Area of rectangle
A. a + 5 3 3(a + 5) = 3a + 15
B. 6 + x 1/3 1/3(6 + x) = 2 + 1/3x
C. 3 r r(1+1+1) = 3r
What is a rectangle?
An example of a quadrilateral with equal and parallel opposite sides is a rectangle. It is a polygon with four sides and four angles that are each 90 degrees. A rectangle is a shape with only two dimensions.
A.
There are 2 rectangles with side a and 5.
Therefore the length of the rectangle is (a + 5).
The width the rectangle is 3.
The area of rectangle is product of length and width.
The area of the rectangle is 3(a + 5)
Applying distributive property:
= 3a + 15
B.
There are 2 rectangles with side 6 and x.
Therefore the length of the rectangle is (6 + x).
The width the rectangle is 1/3.
The area of rectangle is product of length and width.
The area of the rectangle is 1/3(6 + x)
Applying distributive property:
= 2 + 1/3 x
C.
There are 3 rectangles with side 1, 1, and 1.
Therefore the length of the rectangle is (1 + 1 + 1).
The width the rectangle is r.
The area of rectangle is product of length and width.
The area of the rectangle is r(1 + 1 + 1)
Applying distributive property:
= r + r + r
= 3r
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Given: A AED and A BEC are isosceles, with congruent bases AD and BC Prove: ABCD is a rectangle
We have proved that ABCD is a rectangle.
What is the isosceles triangle?
An isosceles triangle in geometry is a triangle with two equal-length sides. It can be specified as having exactly two equal-length sides or at least two equal-length sides, with the latter definition including the equilateral triangle as an exception.
<EAD=<EDA ------------------∆AED is isosceles triangle.
<EBC=<ECB ------------------ ∆EBC is isosceles triangle.
AD= BC -------------------------Given
<AED=<BEC ------------------- Vertically opposite angle
<EAD=<ECB
2<EAD=180°- <AED
= 180°-<BEC
=2<ECB.
∆AED congruent to ∆BEC --------- By A-S-A Congruency.
AE=EC, DE=EB ----------Corresponding sides
ABCD is a parallelogram ----------- Diagonals bisect to each other.
AC=BD
AE+EC=DE+EB.
ABCD is a rectangle. ------------- Diagonals are equal.
Hence, we have proved that ABCD is a rectangle.
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If a= (-9 9), find |a|, giving your answer as a surd in its simplest form.
Answer:
The absolute value of a is equal to 3 * √(2), which is the simplest form of the surd.
Step-by-step explanation:
The absolute value of a number is the distance of the number from zero on the number line. To find the absolute value of a complex number, we take the square root of the sum of the squares of the real and imaginary parts.
In this case, the absolute value of a is given by:
|a| = √((-9)^2 + 9^2) = √(81 + 81) = √(162) = √(9 * 18) = 3 * √(2)
Therefore, the absolute value of a is equal to 3 * √(2), which is the simplest form of the surd.
Diego has 48 chocolate chip cookies, 64 vanilla cookies and 100raisin cookies for a bake sale. He wants to make bags that have all three cookie flavors and the same number of each flavor per bag.
A. How many bags can he make without having any cookies left over?
B. Find another solution to this problem
Answer:
Step-by-step explanation:
The number of bags he can make without having any cookies left over is 4 bags.
Number of chocolate chips = 48
Number of vanilla cookies = 64
Number of raisin cookies = 100
Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4
The equation which have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p is 230p – 1010 = 650p – 400 –p
What is an expression?Expression in mathematics is combination of variables with the use of operations and given rules. It can be in the form of equation, numbers etc.
Given that an expression;
2.3p – 10.1 = 6.5p – 4 – 0.01p
Firstly we will simplify the above expression by removing decimals.
For that,
(23 / 10)p – (101 / 10) = (65 / 10)p – 4 – (1 / 100)p
Now we will take LCM,
{ (23 - 101) / (10) }p = {650p - 400 - p} / 100
230p – 1010 = 650p – 400 –p
Therefore The equation which have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p is 230p – 1010 = 650p – 400 –p.
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-2 = y - 9 solve for y
this is ur answer
[tex]2y = - 9 \\ y = ( - 9) - 2 \\ y = - 11[/tex]
Type the correct answer in the box. In a relay race, the probability of the Galaxy team winning is 22%. In another unrelated relay race, the probability of the Komets team winning is 47%. If the possibility of a tie is not an option, the probability of the Komets losing their race and the Galaxy winning theirs is %. Reset Next
The probability of the Komets losing their race and the Galaxy winning theirs is
What is mean by Probability?
The term probability refers to the likelihood of an event occurring.
Given that;
The probability of the Galaxy team winning is 22%.
And, The probability of the Komets team winning is 47%.
Now,
Since, The probability of the Galaxy team winning is 22%.
And, The probability of the Komets team winning is 47%.
Hence, The probability of the Komets team losing = 100% - 47%
= 53%
= 0.53
Then, The probability of the Komets losing their race and the Galaxy winning theirs is = 0.53 × 0.22
= 0.1166
Thus, probability of the Komets losing their race and the Galaxy winning theirs is 0.1166.
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Answer:
11.66%
Explanation:
I put 12% as my answer, but I got it wrong. So I talked to my teacher and she said the CORRECT ANSWER WAS 11.66%!!
solve by completing the square
Answer:
Attached
Step-by-step explanation:
what is the shortest side of a triangle when the numbers are 63,47,70
The shortest side of a triangle is just opposite of the angle 47°.
What is mean by Triangle?
A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
All the angle of a triangle are,
⇒ 63°, 47°, 70°
Now,
Since, All the angle of a triangle are,
⇒ 63°, 47°, 70°
We know that;
The smallest side of a triangle is just opposite of the smallest angle.
Thus, The shortest side of a triangle is just opposite of the angle 47°.
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In 1992, there were 285 alligators in Orange County, Florida. The number of alligators increased by 75% per year after 1992. How many alligators were there in Orange County, Florida in 2001?
The number of alligators was there in Orange country, Florida in 2001 is equal to 43872.
What is the Percentage?The Latin term "per centum," which signifies "by the hundredth," was the source of the English word "percentage." Segments with a denominator of 100 are considered percentages. In other words, it is a relationship where the worth of the entire is always considered 100.
As per the given information provided in the question,
Total number of alligators 1992 = 285
Percent increase of alligators every year = 75%
Total number of years from 1992 to 2001,
2001 - 1992 = 9 years
The population of alligators in 2001,
= 285 × (175/100)⁹
= 285 × (7/4)⁹
= 43871.98 or,
= 43872 alligators.
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The area of a circle is 0.2826 square inches. What is the circle's diameter?
Use 3.14 for .
Submit
inches
Answer:
0.6 inches
Step-by-step explanation:
The equation to find the area of a circle is:
[tex]{a} = \pi {r}^{2} [/tex]
however the problem requires you replace π with 3.14.
Using inverse operations you can find the variable r.
Step 1:
Plug in variables.
[tex]0.2826 = 3.14{r}^{2} [/tex]
Step 2:
Solve for r.
[tex]0.2826 \div 3.14 = 3.14 \div 3.14 \times {r}^{2} \\ \sqrt{0.09} = \sqrt{ {r}^{2} } \\ r = 0.3[/tex]
Step 3:
Find diameter from radius.
[tex]0.3 \times 2 = 0.6[/tex]
The diameter of the circle is 0.6 inches.
It is given § = {x: 1 ≤ x ≤ 10, x is an integer); P= {odd numbers); Q= {prime numbers) and R= {1,2,3,4,5} List the elements of each of the following sets. (a) (PNQ)UR (b) (RNP)'UQ (c) Q'N(PUR) (d) (PUQUR)' (POR)
The elements of the required sets would be:
(a) (P∩Q)∪R = {1, 2, 3, 4, 5, 7}
(b) (R∩P)'∪R = {2, 3, 4, 5, 6, 7, 8, 9, 10}
(c) Q'∩(P∪R) = {2, 3, 5, 7}
(d) (P∪Q∪R)'∩(P∩R) = ∅
What are sets?A set, denoted by the curly brackets , is a grouping of items, numbers, elements or objects.
A set of numbers, for instance, is 1, 2, 3, 4.
Solution:
P' = {2, 4, 6, 8, 10}
Q' = {1, 4, 6, 8, 9, 10}
R' = {6, 7, 8, 9, 10}
P∩Q = {3, 5, 7}
R'∪P' = {2, 4, 6, 7, 8, 9, 10}
P∪R = {1, 2, 3, 4, 5, 7, 9}
P∩R = {1, 3, 5}
P∪Q∪R = {1, 2, 3, 4, 5, 7, 9}
P'∩Q'∩R' = S - P∪Q∪R
= {6, 8, 10}
Now we can find the elements of the required sets:
(a) (P∩Q)∪R = {1, 2, 3, 4, 5, 7}
(b) (R∩P)'∪R = {2, 3, 4, 5, 6, 7, 8, 9, 10}
(c) Q'∩(P∪R) = {2, 3, 5, 7}
(d) (P∪Q∪R)'∩(P∩R) = ∅
Hence, the elements of the required sets would be
(a) (P∩Q)∪R = {1, 2, 3, 4, 5, 7}
(b) (R∩P)'∪R = {2, 3, 4, 5, 6, 7, 8, 9, 10}
(c) Q'∩(P∪R) = {2, 3, 5, 7}
(d) (P∪Q∪R)'∩(P∩R) = ∅
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Kim ran a 26-mile marathon.
She ran 1/7 of the marathon during
the first hour. How many miles did
Kim run during the first hour?
Answer:
3.714
Step-by-step explanation:
26 x ⅐ = 26 / 7
= 3.714 or [tex] 3 \frac{5}{7} [/tex]
use these grids and, in each case, find the number of paths from a to b, traveling along grid lines. at any given intersection, you may proceed only to the right (r) or down (d). (hint: a path is a sequence of r's and d's.)
Use the multinomial rule, the possible number of paths from A to B is m! n1! ×n2!
How do you find the number of paths on a grid?
To generalize our formula for any NxN grid, we can write: Incidentally, there is an easier way to write this: the number D = N! / (K! * (N-K)!) is also called the binomial coefficient and we can write (N choose K).
You may create a table by combining several question kinds using the grid question type. This implies that you could, for instance, create a grid that included both a multiple-choice question and a free-text inquiry.
A map's grid is a pattern made up of both horizontal and vertical straight lines. They cross one another to create a group of squares. On a map, grids aid in location finding. At the top, there are numbered gaps between the horizontal (side-to-side) lines.
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I need help with this Question
Step-by-step explanation:
Just Substitute in place of X
A certain statistic will be used as an unbiased estimator of a parameter. Let J represent the sampling distribution of the estimator for samples of size 40, and let K represent the sampling distribution of the estimator for samples of size 100.
e. The expected values of J and K will be equal, and the variability of J will be greater than the variability of K.
The true statement about J and K is - The expected values of J and K will be equal, and the variability of J will be greater than the variability of K.
The correct answer is option (c)
In this question, we have been given that a certain statistic will be used as an unbiased estimator of a parameter.
The sample size of J = 40.
and the sample size of K = 100.
We need to find the true statement about J and K.
By central limit theorem, both J and K will have same means.
An expression for standard deviation is:
s = σ/√n
From the above expression standard deviation is inversely proportional to the sample size n. This means, as the sample size increases, the standard deviation decreases.
Thus, the correct statement is - The expected values of J and K will be equal, and the variability of J will be greater than the variability of K.
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The complete question is:
A certain statistic will be used as an unbiased estimator of a parameter. Let J represent the sampling distribution of the estimator for samples of size 40, and let K represent the sampling distribution of the estimator for samples of size 100.
Which of the following must be true about J and K ?
a. The expected values of J and K will be equal, and the variability of J will be less than the variability of K.
b. The expected values of J and K will be equal, and the variability of J will be equal to the variability of K.
c. The expected values of J and K will be equal, and the variability of J will be greater than the variability of K.
d. The expected value of J will be greater than the expected value of K, and the variability of R will be greater than the variability of K.
e. The expected value of J will be greater than the expected value of K, and the variability of R will be less than the variability of K.
PLEASE HELP NOW!!!!!
The percentage for blue balls will be 56% and the percentage for red balls will be 44%.
What is the percentage for the colors of the gumball?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred.
In this situation, there are 4000 balls and 2240 of then are blue while 1760 area red.
The percentage for blue balls will be:
= Number of blue balls / Total balls × 100
= 2240 / 4000 × 100
= 56%
The percentage for red balls will be:
= Number of red balls / Total balls × 100
= 1760 / 4000 × 100
= 44%
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NO LINKS!! Find the missing length indicated. The triangle is similar.
Answer:
143
Step-by-step explanation:
35/55 = 91/x
7/11 = 91/x so 143
Answer:
DB = 143 units
Step-by-step explanation:
In similar triangles, corresponding sides are always in the same ratio.
If ΔDCB ~ ΔDRS then:
[tex]\implies \sf DC : DR = CB : RS = DB : DS[/tex]
From inspection of the given diagram:
DC = 91DR = 35DS = 55Therefore:
[tex]\implies \sf 91 : 35 =DB : 55[/tex]
[tex]\implies \sf \dfrac{91}{35} =\dfrac{DB}{55}[/tex]
[tex]\implies \sf 55 \cdot \dfrac{91}{35} =55 \cdot \dfrac{DB}{55}[/tex]
[tex]\implies \sf 143=DB[/tex]