The probability that there are 3 people between x and y is 1/659470.
The total number of ways in which x and y can stand in a line with 10 other people is (12C2) = 66.
To find the number of ways in which there are exactly 3 people between x and y, we can treat x and y as a single entity and arrange them along with the 10 other people in 8 available spots in the line. This can be done in (8C1) = 8 ways.
Within this arrangement, there are 3 spots where x and y can be placed with 3 people between them,
Once x and y have been placed in one of these 3 spots, the remaining people can be arranged in the remaining spots in
10!/(10-8)! = 1814400 ways.
So the number of ways in which there are exactly 3 people between x and y is,
8 * 3 * 1814400 = 43545600.
Therefore, the probability that there are 3 people between x and y is,
43545600/66 = 659469.69 (rounded to 2 decimal places)
So, the probability is approximately 1 in 659470 or 1/659470.
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carrie and diana ate lunch at a restaurant. they ordered 1 pizza that cost $13.02. dianna ordered chicken wings for $12.99 and a drink for $3.25. carrie ordered a salad for $6.25 and a drink for $3.25. they left a $10.00 tip. diana paid for her food, plus half the cost of the pizza and half the tip. what was the total amount diana paid? show your work on the sketchpad or explain in the text box.
To find out how much Diana paid, we need to first calculate the total cost of the pizza, the chicken wings, the salad, the drinks, and the tip, and then divide that total by 2, since Diana is paying for half.
The total cost of the pizza, chicken wings, salad, and drinks is:
$13.02 (pizza) + $12.99 (chicken wings) + $6.25 (salad) + $3.25 (Diana's drink) + $3.25 (Carrie's drink) = $38.76
Adding the tip of $10.00 to this total gives:
$38.76 + $10.00 = $48.76
Half of this total is:
$48.76 / 2 = $24.38
Therefore, Diana paid $24.38 for her food, half the cost of the pizza, and half the tip.
Diana paid $19.65, which includes $9.02 for her share of the pizza, $5.00 for her share of the tip, $12.99 for chicken wings and $3.25 for a drink. Below is the working on the sketchpad.What is shown on the sketchpad?It is shown on the sketchpad below how Diana paid for her lunch at the restaurant.
The items that she paid for are indicated in the table below the sketchpad.What is the calculation for the amount Diana paid for lunch?Diana's share of the pizza is half of $13.02, which is $6.51. Adding $6.51 to the cost of the chicken wings and a drink gives a total of $22.75 for the cost of the lunch.
After adding the tip to the total cost of the lunch, we have $32.75 ($22.75 + $10.00 tip). To find the amount Diana paid, we need to find half of the total cost of the lunch and half of the tip.The following calculation shows the amount Diana paid:Her share of the cost of the lunch was $11.37 (($6.51 + $12.99 + $3.25)/2).Her share of the tip was $5.00/2, which is $2.50.The amount Diana paid for her food, plus her share of the cost of the pizza and tip is therefore $13.87 ($11.37 + $2.50).
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Find the area and perimeter
Answer:
A=240 P=64
Step-by-step explanation:
A=240 because you take lxw and that gives you the answer
P=64 because you just add 12+12+10+10
Answer: The area is 240 and the perimeter is 64
Step-by-step explanation:
To get the area you need to do 20 x 12 = 240
And to get the perimeter you need to add up all the sides;
20 + 20 + 12 + 12 = 64
The equation for the line of fit shown is y = 8.2x + 25, where x
represents the number of minutes the water has been heated and y represents the temperature of the water.
Based on the equation for the line of fit, what will be the estimated temperature of the water, to the tenth of a degree, when it has been heated for 8 min?
Answer:
90.6°
Step-by-step explanation:
It is given that x represents the number of minutes. You are solving for 8 minutes. Therefore, plug in 8 for x in the given equation, and simplify:
[tex]y = 8.2x + 25\\y = 8.2(8) + 25[/tex]
Simplify. Remember to follow PEMDAS. PEMDAS is the order of operations and stands for:
Parenthesis
Exponent (& Root)
Multiplication
Division
Addition
Subtraction
~
First, multiply 8.2 with 8:
[tex]y = (8.2 * 8) + 25\\y = (65.6) + 25\\[/tex]
Next, add:
[tex]y = 65.6 + 25\\y = 90.6[/tex]
90.6 is your answer.
~
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All of the quadrilaterals in the shape below are squares. Find the area of the shaded
region.
To find the area of the shaded region subtract the unshaded region from the total area, so we got 87.
What are the square area formulae?Square Area equals Side x Side. The square's size is therefore equal to side square units. and a square's circumference equals four side units.
To find the area of the shaded region first we need to find the sum of the area of all quadrilaterals and then subtract the area of the unshaded region.
Area of first quadrilateral A1 = [tex]16^{2}[/tex] = 256
Area of first quadrilateral A2 = [tex]3^{2}[/tex] = 9
Area of first quadrilateral A3 = [tex]3^{2}[/tex] = 9
Area of first quadrilateral A4 = [tex]19^{2}[/tex] = 361
To find the area of the shaded region subtract the unshaded region from the total area = Area of first quadrilateral A4 - (Area of first quadrilateral A1 + Area of first quadrilateral A2 + Area of first quadrilateral A3)
= 361 - (9 + 9 + 256)
=87
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in a hypothesis test, what does it mean to say that the null hypothesis was rejected? rejecting the null hypothesis means that the sample data provide convincing evidence against the ---select--- hypothesis and in favor of the ---select--- hypothesis.
When it is said that the null hypothesis was rejected in a hypothesis test, it means that the sample data has given strong evidence against the null hypothesis and in favor of the alternative hypothesis.
What is a hypothesis?
A hypothesis is a statement that proposes a potential relationship between two variables. It's a conjecture about the nature of the relationship between the two variables that a researcher might test.In hypothesis testing, the null hypothesis is always the hypothesis being tested. A null hypothesis is a statement that assumes there is no relationship between the variables being studied. It is denoted by H0.The alternative hypothesis is a statement that negates the null hypothesis. It suggests that there is a relationship between the variables being studied. It is denoted by Ha.When it is said that the null hypothesis was rejected in a hypothesis test, it means that the sample data has given strong evidence against the null hypothesis and in favor of the alternative hypothesis. As a result, the researcher may conclude that the alternative hypothesis is true with a certain level of confidence.If the null hypothesis is not rejected in a hypothesis test, it means that there is insufficient evidence to support the alternative hypothesis. As a result, the researcher cannot conclude that the alternative hypothesis is true with a certain level of confidence.
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Can someone please help
The total possible outcomes are 36 and the probability of rolling a 5 and a 6 is 2.78 approximately.
What is dice?
Dice are small objects with different numbers of dots or pips on each side used in games of chance or strategy. Most commonly, dice are cubes with each of the six faces marked with a different number of pips from one to six. When rolled, the number that appears on the top face of the die is used to determine the outcome of the game or the action of the player.
Dice are used in a wide variety of games, including board games, tabletop games, role-playing games, and gambling games. They can also be used for randomization in decision-making or statistical analysis. Some games use dice with more or less than six sides, with various shapes and markings, or even electronic versions that simulate rolling.
When rolling two six-sided dice, the total number of possible outcomes is 6 x 6 = 36, as there are 6 possible outcomes for each die.
To determine the probability of rolling a 5 and a 6, we first need to determine the number of ways this outcome can occur. There is only one way to roll a 5 and a 6, which is to have one die show a 5 and the other die show a 6.
So, the probability of rolling a 5 and a 6 is
P(rolling a 5 and a 6) = number of ways to roll a 5 and a 6 / total number of possible outcomes
= 1 / 36
Therefore, the probability of rolling a 5 and a 6 is 1/36, or approximately 0.0278, or about 2.78%.
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If the length breadth and height of 3x+y cm 2x+2y cm and 3y cm respectively and find its volume
Answer: The length, breadth, and height of the rectangular prism are:
Length = 3x + y cm
Breadth = 2x + 2y cm
Height = 3y cm
The volume of the rectangular prism is given by the formula:
Volume = Length x Breadth x Height
Substituting the values, we get:
Volume = (3x + y) x (2x + 2y) x (3y)
Simplifying the expression, we get:
Volume = 18x^2 y + 15xy^2 + 6x^2 y^2 + 6y^3
Therefore, the volume of the rectangular prism is 18x^2 y + 15xy^2 + 6x^2 y^2 + 6y^3 cubic cm.
Step-by-step explanation:
an urn contains 1 green ball, 1 red ball, 1 yellow ball and 1 white ball. i draw 3 balls with replacement. what is the probability that exactly two balls are of the same color?
The probability that exactly two balls are of the same color when drawing 3 balls with replacement from an urn containing 1 green ball, 1 red ball, 1 yellow ball and 1 white ball is 4/16 or 1/4.
There are three ways to draw two balls of the same color: two green balls and one of any other color, two red balls and one of any other color, or two yellow balls and one of any other color. Each of these ways can occur in 4 different orders (e.g. GGR, GRG, RGG, etc.) for a total of 12 possible outcomes. The probability of each of these outcomes is (1/4)^3 = 1/64. Therefore, the probability of exactly two balls being of the same color is 12/64 or simplified to 3/16, which is equivalent to 1/4.
Therefore, the probability of exactly two balls being of the same color when drawing 3 balls with replacement from an urn containing 1 green ball, 1 red ball, 1 yellow ball and 1 white ball is 1/4.
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Nikki used the calculations shown to determine whether a carton of 12 eggs or a carton of 18 eggs was the better buy.
A carton of 12 eggs cost $2.39 , and a carton of 18 eggs cost $3.39 .
Unit price of the 12 -egg carton = ($2.39)(12 eggs) = $28.68 per egg
Unit price of the 18 -egg carton = ($3.39)(18 eggs) = $61.02 per egg
The 12 -egg carton has the lower unit cost, so it is the better buy.
What was her first error?
Answer:
She was supposed to DIVIDE the amount of money by the amount of eggs in the carton.
Step-by-step explanation:
12 egg carton = $2.40, 1 egg = $2.40 ÷ 12 = 0.2c
18 egg carton = $3.40, 1 egg = $3.40 ÷ 18 = 0.188 (1.9)
The 18 egg carton was more affordable by about 1.22 cents. Nikki was supposed to divide the amount of money it was worth by the quantity in it.
suppose that, of women who undergo routine screening, 1/101 have breast cancer. of the women who undergo screening and do have breast cancer, 80% will have a positive test. of the women who undergo screening but don't have breast cancer, only 5% have a positive test. a woman of this age undergoes routine screening and has a positive test. what is the probability that she has breast cancer? give your answer as a numerical value between 0 and 1, to three decimal places. (do not give it as odds, a fraction, or a percentage!)
Answer:
The probability that she has breast cancer if she gives a positive test result is P=0.16
Step-by-step explanation:
And according to the Bayes theorem I got 0.16
The probability that the woman who underwent routine screening and has a positive test has breast cancer is 0.017.
Let A denote the event that the woman has breast cancer, and let B denote the event that she has a positive test result. Then we need to find P(A|B), the probability that A occurs given that B has occurred. By Bayes' theorem, we have:
P(A|B) = P(B|A)P(A) / [P(B|A)P(A) + P(B|not A)P(not A)]
where P(not A) = 1 - P(A) is the probability that the woman does not have breast cancer.
From the problem statement, we have:
P(A) = 1/101, P(B|A) = 0.8, and P(B|not A) = 0.05.
Therefore,
P(not A) = 100/101,
and
P(A|B) = (0.8 x 1/101) / [(0.8 x 1/101) + (0.05 x 100/101)] = 0.017 (to three decimal places).
Therefore, the probability that the woman who underwent routine screening and has a positive test has breast cancer is 0.017.
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A 12 ft ladder is leaning against a building. The top of the ladder is 7 ft above the ground.
How far from the building is the ladder?
Answer:
The ladder is approximately 9.75ft from the building
Step-by-step explanation:
We can use Pythagoras theorem:
[tex]c^2=a^2+b^2[/tex]
where:
[tex]c =[/tex] it's the size of the ladder, 12ft
[tex]b=[/tex] it's the top of the ladder above the ground, 7ft
so:
[tex]c^2-b^2=a^2\\\implies a=\sqrt{c^2-b^2}\\ a=\sqrt{(12)^2-(7)^2}\\a=\sqrt{95}\\ a\approx 9.75ft[/tex]
[tex]\text{-B$\mathfrak{randon}$VN}[/tex]
solve the inequality 4x - 9 > 23
A pizzeria charges $3.50 for a slice of pizza and $1.75 for a bottle of soda. Write an equation that models the number of slices of pizza(p) and bottles that can be purchased for $35.00.
WILL GIVE BRAINLIEST
Answer:
A
Step-by-step explanation:
If bottles of soda are marked S, and one bottle costs $1,75
And slices of pizza - P, and one slice costs $3,5
Then the equation would be:
3,50p + 1,75s = 35,00
how many different samples of size 4 (without replacement) can be taken from a finite population of size 10? a. 10,000 b. 210 c. 40 d. 5,040
Answer:
Step-by-step explanation:(10,4)=10.9.8.7/4.3.2.1=210
The number of different samples of size 4 that can be taken from a finite population of size 10, without replacement, is 210.
The formula for calculating the number of different samples of size r that can be taken from a finite population of size n without replacement is given by the combination formula: nCr = n! / (r! * (n-r)!), where n! denotes n factorial (n × (n-1) × (n-2) × … × 1).
In this case, we want to find the number of different samples of size 4 that can be taken from a population of size 10, so we use the combination formula with n=10 and r=4:
10C4 = 10! / (4! × (10-4)!) = (10987) / (4321) = 210
Therefore, there are 210 different samples of size 4 that can be taken from a population of size 10 without replacement.
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Can someone please help thank you, I will give brainliest to the first person that answers
The following are answers to the probability questions;
1. 2/3 or 0.67 or 0.7 chances
2. 2/3 or 0.67 or 0.7 chances
3. No probability is greater than the other. They are both 2/3.
4. There are 36 possible outcomes
5. 3/36 or 1/12
What is probability?
Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain.
To calculate the probability of choosing a password with no Y's and With no O's we need to consider all the combinations that do not have Y and O. There are 20 combinations with no Y's and 20 combinations with no O.
Therefore, the probability of choosing a password with no Y's or O's are 20 each. When then calculate by sating
20/30, which simplifies to 2/3 or 0.67.
The number of possible outcomes for a single number cube is as follows;
1 2 3 4 5 6
1 1,1 1,2 1,3 1,4 1,5 1,6
2 2,1 2,2 2,3 2,4 2,5 2,6
3 3,1 3,2 3,3 3,4 3,5 3,6
4 4,1 4,2 4,3 4,4 4,5 4,6
5 5,1 5,2 5,3 5,4 5,5 5,6
6 6,1 6,2 6,3 6,4 6,5 6,6
In total, there are 36 combinations.
! There are three ways to obtain a sum of 10: rolling a 4 and a 6, rolling a 6 and a 4, or rolling two 5's. Since there are 36 possible outcomes in total (as we determined earlier), the probability of rolling two numbers that have a sum equal to 10 is:
P(sum of 10) = number of outcomes that add up to 10 / total number of possible outcomes
P(sum of 10) = 3 / 36
P(sum of 10) = 1/12
So the probability of rolling two numbers that add up to 10 is 1/12.
The answers provided is based on the full questions below as seen in the picture;
12. Higher Order Thinking The table shows the sample space of picking a 2-character password using the letters Y, B, R, O, G, and P. If double letters are not allowed, what is the probability of choosing a password with no Y's? With no O's? Is one probability greater than the other? Explain.
Possible Combinations
Y, B B, R R, O O, G G, P P. Y
Y, R B, O R, G O, P G, Y P, B
Y, O B, G R, P O, Y G, B P, R
Y, G B, P R, Y O, B G, R P, O
Y, P B, Y R, B O, R G, O P,G
13. A single number cube is rolled twice.
PART A
Determine the number of possible outcomes. Explain how you know you have found all the possible outcomes.
PART B
Find the probability of rolling two numbers that have a sum equal to 10.
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Two observers are 500 ft apart on opposite sides of a
flagpole. The angles of elevation from the observers to
the top of the pole are 16° and 19° Find the height of the
flagpole.
graph f(x) = x^2 and g(x) = 2^x for x
Answer:
Step-by-step explanation:
Identify the combination of angle measures that could form a triangle. (1 point)
O 40,55", and 95°
O 25°, 65°, and 90°
O 30,75°, and 85°
O 45,65", and 75"
Please help I am so confused
Answer:
25°, 65°, and 90°
Step-by-step explanation:
To form a triangle the 3 angles must sum to 180 degrees.
The
dimensions
(in inches)
of a rectangular
tile can be
modeled by A(x)=x² + 5
and B(x) = 2x - 1.
a. Find (A + B)(x) and
(AB)(x).
The composite functions are (A + B)(x) = x² + 2x + 4. and (AB)(x) = 2x³ - x² + 10x - 5.
Evaluating the composite functionsTo find (A + B)(x), we add the two functions A(x) and B(x):
(A + B)(x) = A(x) + B(x)
So, we have
= x² + 5 + 2x - 1 (substituting the given expressions for A(x) and B(x))
= x² + 2x + 4
Therefore, (A + B)(x) = x² + 2x + 4.
To find (AB)(x), we multiply the two functions A(x) and B(x):
(AB)(x) = A(x)B(x)
= (x² + 5)(2x - 1) (substituting the given expressions for A(x) and B(x))
= 2x³ - x² + 10x - 5
Therefore, (AB)(x) = 2x³ - x² + 10x - 5.
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The points N
(
6
,
−
3
)
(6,−3), O
(
0
,
−
1
)
(0,−1), and P
(
2
,
5
)
(2,5) form a triangle. Plot the points then click the "Graph Triangle" button.
Answer:
Step-by-step explanation:
The first number within the the x axis.
The second number is the y axis.
the point you're looking is where they both intersect,
Do that for the 3 points, and you get 3 dots.
Make a line connecting each other in order.
And you made a shape.
Happy Solving
Find x when one arc measure is 59 and another arc is 2x and one anhle is 15
This value of x doesn't satisfy the Equation we set up earlier (59 + 2x = 360). So, we must conclude that this value of x is incorrect, and the value we found earlier (x = 150.5) is the correct one.
Let's start with the given information: we have two arc measures and an angle measure. We know that the sum of the arc measures is equal to the total circumference of the circle, which is 360 degrees. So, we can set up an equation:
59 + 2x = 360
Solving for x, we get:
2x = 301
x = 150.5
So, the value of x that makes one arc measure 2x and the other arc measure 59, and the angle measure 15, is 150.5.
Now, let's think about why this makes sense. The sum of the arc measures is equal to the total circumference of the circle, which means that the angle formed by those two arcs must be half of the central angle that intercepts them. In other words, the angle formed by the 59-degree arc and the 2x-degree arc is (59 + 2x)/2. We also know that the angle formed by the 15-degree angle and the same arc is equal to half of the angle formed by the two arcs. So:
(59 + 2x)/2 = (180 - 15)/2
59 + 2x = 165
2x = 106
x = 53
However, this value of x doesn't satisfy the equation we set up earlier (59 + 2x = 360). So, we must conclude that this value of x is incorrect, and the value we found earlier (x = 150.5) is the correct one.
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the earths diameter is approzimentley 13000km find the distance around the equator
The distance around the equator is 40,820 km, when the Earth's diameter is approximately 13000km. The distance around the Earth is the circumference.
Why are Earth's distances significant to astronomers?The Earth is nearly a perfect sphere, but not quite. Astronomers utilized the diameter of the Earth as their primary measuring tool to gauge the extent of the solar system during the 18th and 19th centuries. Today's astronomers typically don't need to be aware of the Earth's size for their regular research tasks.
Nonetheless, the Earth's diameter continues to be the starting point for us, the inhabitants of this planet, in our quest to comprehend the cosmic distance scale. Eratosthenes measured the polar radius, and the number he obtained using the conversion of 0.15 km/stadium sits halfway between the polar and equatorial values.
Given:
Diameter = 13,000 km
Circumference = pi x diameter
Circumference = 3.14 x 13,000 = 40,820 km
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the ability to find a job after graduation is very important to gsu students as it is to the students at most colleges and universities. suppose we take a poll (random sample) of 3700 students classified as juniors and find that 2926 of them believe that they will find a job immediately after graduation. what is the 99 % confidence interval for the proportion of gsu juniors who believe that they will, immediately, be employed after graduation.
The 99% confidence interval for the proportion of GSU Juniors who believe that they will, immediately, be employed after graduation is (0.835, 0.866), option B.
In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts. So, it may be concluded that there is a 95% likelihood that the real value falls within that range if a point estimate of 10.00 is produced using a statistical model with a 95% confidence interval of 9.50 - 10.50.
Confidence intervals are used by statisticians and other analysts to comprehend the statistical significance of their estimates, conclusions, or forecasts. One cannot reasonably assert that a result from data produced by testing or experimentation is to be ascribed if a confidence interval involves the value of zero.
Confidence interval for Population Proportion is given as below:
Confidence Interval = [tex]p \pm Z\sqrt{\frac{p(1-p)}{n} }[/tex]
Where, p is the sample proportion, Z is critical value, and n is sample size.
We are given
x = number of items/observations of interest = 3010
n = sample size = 3539
Best Point Estimate = p = x/n
= 3010/ 3539
= 0.850522747
Confidence level = 99%
Critical Z value = 2.5758
(We can find this z-value by using R, excel, z-table, Ti-83/84 calculator, software, etc.)
[Excel command: =NORMSINV(1 - (1 - 0.99)/2)]
Confidence Interval = [tex]p \pm Z\sqrt{\frac{p(1-p)}{n} }[/tex]
Confidence Interval = [tex]0.850522747 \pm 2.5758 \sqrt{\frac{0.850522747(1-0.850522747)}{3539} }[/tex]
Confidence Interval = 0.850522747 ± 2.5758 x 0.0060
Confidence Interval = 0.850522747 ± 0.015
Lower limit = 0.850522747 - 0.015 = 0.835
Upper limit = 0.850522747 + 0.015 = 0.866
Confidence interval = (0.835, 0.866)
B. (0.835, 0.866).
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Complete question:
The ability to find a job after graduation is very important to GSU students as it is to the students at most colleges and universities. Select one answer 10 points Suppose we take a poll (random sample) of 3539 students classified as Juniors and find that 3010 of them believe that they will find a job immediately after graduation What is the 99% confidence interval for the proportion of GSU Juniors who believe that they will, immediately, be employed after graduation A. (0.839, 0.862) B.O(0.835, 0.866) C. (0.845, 0.857) D.O(0.841, 0.86)
Help pls due tmrw!!!!
Answer: a. x ≤7 b. x<6
Step-by-step explanation:
a. 6x-3≤4x+11
6x-4x≤11+3
2x≤14
x≤7
b. x<-x+12
x+x<12
2x<12
x<6
Answer:
Step-by-step explanation:
6x+3-3= 4x + 11-36x = 4x + 8Answer x=4Determine the equation of the circle with radius 8 and center (-2,9).
According to the solution we have come to find that, The equation of the circle with radius 8 and center (-2,9) is [tex](x + 2)^2 + (y - 9)^2 = 64.[/tex]
What is radius?
Radius is a straight line segment that joins the center of a circle to any point on its circumference. It is half of the diameter of the circle. The length of the radius is denoted by the letter "r".
The equation of a circle with center (a,b) and radius r is given by:
[tex](x - a)^2 + (y - b)^2 = r^2[/tex]
Substituting the given values, we have:
[tex](x - (-2))^2 + (y - 9)^2 = 8^2[/tex]
Simplifying, we get:
[tex](x + 2)^2 + (y - 9)^2 = 64[/tex]
Therefore, the equation of the circle with radius 8 and center (-2,9) is [tex](x + 2)^2 + (y - 9)^2 = 64.[/tex]
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The teacher said that both equations were correct. Explain why?
Answer:
Both are correct as we can transform one from the other.
Step-by-step explanation:
The equations describe the relation between the distance(m) speed (9) and time (h),
distance = speed * time
m = 9h
Divide both sides by 9:
m/9 = h
h = (1/9) m
how many ways are there to write a 3 digit positive number integer using the digits 1,3,5,7, and 9 if no digit is used more than once
Answer: 60
Step-by-step explanation:
To form a 3-digit positive integer using the digits 1, 3, 5, 7, and 9 without repeating any digit, we can use the counting principle.
There are 5 choices for the first digit (hundreds place) since any of the 5 digits (1, 3, 5, 7, or 9) can be placed there.
5 (choices for the first digit) × 4 (choices for the second digit) × 3 (choices for the third digit) = 60
There are 60 ways to write a 3-digit positive integer using the digits 1, 3, 5, 7, and 9 without using any digit more than once.
Rua and Liz have a bag of 24 cherries. Liz keeps most for herself, but gives some to Rua. He complained, so she gave him five more. She then had one Cherry fewer than 1.5 times the number of cherries that Rua had. Write an equation and solve it to find how many cherries she gave to Rua at the start.
Answer:
8 cherries
Step-by-step explanation:
Let r represent the number of cherries Rua was given
24 - r - 5 = 1.5r - 1
Simplify and solve for r.
19 - r = 1.5r - 1
-2.5r = -20
r = 8
So Liz gave Rua 8 cherries at the start.
guy makes a drink by mixing apple juice and water in the ratio 1:4 kim makes a drink by mixing apple juice and water in the ratio 2:7 who has the drink with the higher proportion of apple juice?
if club members charge $3 admission to a classic car show, 1000 people will attend, and for each $1 increase in price, 100 fewer people will attend. what price will give the maximum revenue for the show? $ per ticket find the maximum revenue. $
the price per ticket that will give maximum revenue is $6.5, and the maximum revenue in dollars per ticket is $2.925.
As given,If club members charge $3 admission to a classic car show, 1000 people will attend, and for each $1 increase in price, 100 fewer people will attend.
We need to determine the price that will give the maximum revenue for the show and the maximum revenue in dollars per ticket.
Let the number of $1 increases in price be x. Then the number of people attending will be (1000 - 100x), and the price per ticket will be $(3 + x).The total revenue will be:
Revenue = Price × Quantity= $(3 + x) × (1000 - 100x)= $3000 - $100(x^2 + 7x)
The revenue function is quadratic, with the coefficient of the x^2 term being negative. Hence the graph of the function is a parabola which opens downwards, with a maximum at the vertex of the parabola.To find the value of x that will give maximum revenue, we first find the x-coordinate of the vertex.
For a quadratic function of the form f(x) = ax^2 + bx + c, the x-coordinate of the vertex is given by x = -b / (2a).In this case, a = -100, and b = -100(7) = -700. Therefore, the x-coordinate of the vertex is:x = -b / (2a)= 7/2= 3.5
Therefore, the value of x that will give maximum revenue is 3.5. Substituting this value of x in the revenue function, we get:Revenue = $3000 - $100(x^2 + 7x)= $3000 - $100(3.5^2 + 7(3.5))= $2925
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