There are 5,245,786 possible winning number combinations in a 6/42 lottery, and for every ticket purchased, there is a 1 in 5,245,786 chance of winning the jackpot prize.
What is the combinations?
Combinations refer to the different ways of selecting a subset of items from a larger set without regard to the order in which the items are selected. In other words, combinations are the different ways of choosing a group of items without taking into account their arrangement or order.
In a 6/42 lottery, there are 6 numbers drawn from a pool of 42 numbers. To determine the number of possible winning number combinations, we can use the formula for combinations:
C(n,r) = n! / (r! * (n-r)!)
where n is the total number of items in the set and r is the number of items being chosen.
In this case, we have 42 numbers in the pool and we need to choose 6 numbers, so the formula becomes:
C(42,6) = 42! / (6! * (42-6)!)
which simplifies to:
C(42,6) = 5,245,786
Therefore, there are 5,245,786 possible winning number combinations in a 6/42 lottery.
To calculate the probability of winning the jackpot prize, we need to divide the number of ways to win by the total number of possible outcomes. Since there is only one winning combination, the probability of winning the jackpot is:
1 / 5,245,786
which simplifies to approximately:
0.000019% or 1 in 5,245,786.
This means that for every ticket purchased, there is a 1 in 5,245,786 chance of winning the jackpot prize.
hence, there are 5,245,786 possible winning number combinations in a 6/42 lottery, and for every ticket purchased, there is a 1 in 5,245,786 chance of winning the jackpot prize.
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You design a tree house using
a coordinate plane in which
the coordinates are measured
in meters (m ). The vertices of
the rectangular floor are
(6, 7), (-3, 7), (-3,2),
and (6,2).
What is the perimeter of the tree house?
What is the area of the tree house floor?
Perimeter = 28 yards
Area 49 square yards.
Activity 3
A
Write in increasing order according to their capacity:
In increasing order according to their capacity:
C, A, B A, B, CB, C, A B, C, AA, B, C C, A, BB, C, A A, C, BWhat is capacity?The capacity of a container, such as a cup, bottle, or tank, is the amount of fluid or material it can hold. It is usually stated in volume quantities such as liters, milliliters, gallons, or ounces.
Capacity is a necessary concept in engineering, manufacturing, and transportation, where it is used to design and run systems involving the storage, movement, and processing of fluids or materials.
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Determine if each of the following relationships represents a proportional relationship or not.
SELECT ALL situations that represent a proportional relationship.
A). Natalia is selling fresh eggs at the local farmer's market. She sells 6 eggs for $3.12, a dozen eggs for $6.24, and eighteen eggs for $9.36.
B). Joey is training for a bicycle race and has been completing his longer training rides on Saturdays. Over the past month, Joey has ridden his bicycle 36 miles in 3 hours, 46 miles in 4 hours, and 22 miles in 2 hours.
C). graph 1 provided in the pictures
D). graph 2 provided in the pictures
E). Azul bought several different packages of 8-inch by 10-inch art canvases for craft project at her family reunion. The number of canvases in a package and the cost of the package is shown in the table. (TABLE PROVIDED IN PICTURES)
F). Kareem is comparing the cost of regular unleaded gasoline at three different gas stations near his home. Instead of filling up his car's gas tank at one station, he puts a few gallons in at each of the three different stations. The number of gallons of gasoline and the cost of the gasoline is shown in the table. (TABLE PROVIDED IN PICTURES)
The situations that represent a proportional relationship are:
A). Natalia is selling fresh eggs at the local farmer's market. She sells 6 eggs for $3.12, a dozen eggs for $6.24, and eighteen eggs for $9.36.
C). Graph 1 provided in the pictures. This graph shows a straight line passing through the origin, which indicates a proportional relationship.
D). Graph 2 provided in the pictures. This graph also shows a straight line passing through the origin, which indicates a proportional relationship.
E). Azul bought several different packages of 8-inch by 10-inch art canvases for a craft project at her family reunion. The number of canvases in a package and the cost of the package is shown in the table.
Therefore, the situations A, C, D, and E represent proportional relationships.
What is Proportional Relationship?A proportional relationship is a relationship between two quantities where one quantity is a constant multiple of the other quantity. In other words, if one quantity increases or decreases by a certain factor, then the other quantity will increase or decrease by the same factor. This relationship can be represented by a straight line passing through the origin on a graph.
For example, if the price of gasoline is proportional to the number of gallons purchased, then buying twice as many gallons would cost twice as much money. Similarly, if the distance traveled is proportional to the time taken, then traveling twice as long would cover twice the distance.
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Two points on a circle of radius 1 are chosen at random. Find the probability that the distance between the two points is at most 1.5.
The probability that the distance between two points on a circle of radius 1 is at most 1.5 is approximately 0.477 or 47.7%, which corresponds to the range of central angles less than or equal to 3 radians out of the total central angle of 2π radians.
Let's consider two points on a circle of radius 1, labeled A and B. The distance between A and B is given by the length of the arc AB on the circle, which is a fraction of the circumference of the circle. The circumference of a circle of radius 1 is 2π, so the length of the arc AB is given by
d = θ/2π * 2πr = θ
where d is the distance between A and B, θ is the central angle between A and B (in radians), and r is the radius of the circle (which is 1 in this case).
To find the probability that the distance between A and B is at most 1.5, we need to find the range of central angles that correspond to arc lengths less than or equal to 1.5. Let's call this range of angles θ₁. We have
θ₁ = 2d/r = 2(1.5)/1 = 3
This means that the central angle between A and B must be less than or equal to 3 radians for the distance between A and B to be at most 1.5. Since the total central angle of the circle is 2π radians, the probability of selecting two points with a central angle less than or equal to 3 radians is
P(θ ≤ 3) = θ/2π = 3/2π ≈ 0.477
Therefore, the probability that the distance between two points on a circle of radius 1 is at most 1.5 is approximately 0.477 or 47.7%.
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Find the y intercept of the equation 5x-2y=28
Answer:
y- intercept = - 14
Step-by-step explanation:
the y- intercept is the point on the y- axis where the line crosses.
at any point on the y- axis, the x- coordinate is zero.
let x = 0 in the equation and solve for y , the y- intercept
5(0) - 2y = 28
0 - 2y = 28
- 2y = 28 ( divide both sides by - 2 )
y = - 14 ← y- intercept
In Bridget's class, 35% of the students chose pizza as their favorite food. If 14 of the students chose pizza as their favorite food, how many students are in the class?
Answer:
40 students are in the class :)
Step-by-step explanation:
35%=14
1%=14/35=0.4
0.4*100=40=100%
Joseph bought a T-shirt for $10.30 and another T-shirt for $18.90. what is the total amount spent
Answer:
29.2
Step-by-step explanation:
10.30+18.90=29.2
Answer:
$29.20
Step-by-step explanation:
$10.30
+$18.90
=$29.20
Lily has a storage box shaped like a rectangular prism with a length of 4 feet, a width of 3 feet, and a height of 2 feet. She has a fishing pole that is 6 feet long. Can she store the fishing pole in the box?
Answer:
Volume L× W × H
Volume 4 × 3 × 2
4 × 3 × 2 =24
If the fish poke is 6 feet long and she has a rectangular prism of 24 since 4 × 3 ×2 equals 24 then yes she can store the fishing pole in the box
24
what is an equation of the line that passes through the points (0,8) and (-6,-2)?
Points are (0,-8) and (-6,-3) Slope m = rise/run = Δy/Δx. [(-3 - (-8)]/[-6 - 0] = 5/-6 = -5/6
y = mx + b Using the (0,-8) point: -8 = 0x + b, so b = -8
The line is y = -5x/6 - 8 or (-5/6)x - 8. You can check via the Desmos Graphing Calculator site
I used the slope-intercept form, but you could also use the point-slope form (y2 - y1) = m(x2 - x1)
Three pipes in a school building are
leaking. After 30 minutes, pipe A has leaked 3/4 gallon of water. After 45 minutes, pipe B has leaked 1 1/4 gallons of water. After 20 minutes, pipe C has leaked 1/2 gallon of water.
Which sentence is true?
A. Pipe A is leaking at the fastest rate
B. Pipe C is leaking at the slowest rate.
C. Pipe A and C are leaking at the same rate.
D. Pipes A and B are leaking at a faster rate than Pipe C.
Answer: Option C
Step-by-step explanation: To compare the rates at which the pipes are leaking, we can find the amount of water each pipe leaks per minute.
For Pipe A:
3/4 gallon ÷ 30 minutes = 1/40 gallon per minute
For Pipe B:
1 1/4 gallon ÷ 45 minutes = 5/36 gallon per minute
For Pipe C:
1/2 gallon ÷ 20 minutes = 1/40 gallon per minute
Therefore, Pipes A and C are leaking at the same rate, which means option C is true. Option A and D are false, as Pipe B has the fastest leak rate. Option B is false, as both Pipe A and Pipe C are leaking at the same rate.
According to Thomson Financial, last year the majority of companies reporting profits had beaten estimates. A sample of 162 companies showed that 94 beat estimates, 29 matched estimates, and 39 fell short.
(a) What is the point estimate of the proportion that fell short of estimates? If required, round your answer to four decimal places.
pshort = .2407
(b) Determine the margin of error and provide a 95% confidence interval for the proportion that beat estimates. If required, round your answer to four decimal places.
ME =
(c) How large a sample is needed if the desired margin of error is 0.05? If required, round your answer to the next integer.
n* =
a)0.2407 is the point estimate of the proportion.
b) The 95% confidence interval for the proportion that beat estimates is (0.4858, 0.6746).
c) A sample size of 754 is needed to achieve a desired margin of error of 0.05.
(a) What is the point estimate of the proportion?
The point estimate of the proportion that fell short of estimates is 39/162 = 0.2407. Rounded to four decimal places, this is pshort = 0.2407.
(b) How to determine the margin of error and provide a 95% confidence interval for the proportion that beat estimates?
To determine the margin of error and provide a 95% confidence interval for the proportion that beat estimates, we need to first find the point estimate and standard error of the proportion that beat estimates.
The point estimate of the proportion that beat estimates is 94/162 = 0.5802.
The standard error can be calculated as:
SE = √(p×(1-p)/n)
where p is the point estimate of the proportion that beat estimates and n is the sample size. Substituting the values we get:
SE = √(0.5802×(1-0.5802)/162) = 0.0482
To calculate the margin of error, we use the formula:
ME = zSE
where z is the z-score corresponding to the desired confidence level. For a 95% confidence level, z* = 1.96 (from the standard normal distribution table).
Substituting the values we get:
ME = 1.96×0.0482 = 0.0944
Therefore, the margin of error is 0.0944. To find the 95% confidence interval, we add and subtract the margin of error from the point estimate of the proportion that beat estimates:
CI = 0.5802 ± 0.0944
CI = (0.4858, 0.6746)
Therefore, the 95% confidence interval for the proportion that beat estimates is (0.4858, 0.6746).
(c) How large a sample is needed if the desired margin of error is 0.05?
To find the sample size needed for a desired margin of error of 0.05, we use the formula:
n* = (z*/ME)² × p×(1-p)
where z* is the z-score corresponding to the desired confidence level (we use 1.96 for a 95% confidence level), ME is the desired margin of error (0.05), and p is an estimate of the proportion (we use the point estimate of 0.5802 for the proportion that beat estimates).
Substituting the values we get:
n* = (1.96/0.05)² × 0.5802×(1-0.5802) = 753.16
Rounding up to the next integer, we get n* = 754. Therefore, a sample size of 754 is needed to achieve a desired margin of error of 0.05.
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i need help with this one, thank you
Answer: 288.62
Step-by-step explanation:
10.4^2 + 15.3^2 = 342.25,
c^2 = 342.25
c (hypotenuse of the right triangle & length of rectangle) = 18.5
7(8) + 10.4(15.3) = 288.62
A construction worker throws a water bottle out of the basement to his friend, who did not catch it. The equation below can be used to determine h, the height of the bottle in feet, base on t, the time in seconds since the bottle was thrown. h=-16t^2+56t-24
When is the height of the thrown bottle equal to 0?
The height of the thrown bottle becomes zero at the t = 1/2 that is half a second and at t = 3 seconds
How do you form an equation?An equation is formed by expressing the relationship between two or more mathematical expressions. It can be formed by using mathematical symbols, operations, and variables. Typically, equations are used to solve problems or find unknown quantities by setting up an equation that represents the problem and then manipulating the equation using algebraic operations until the solution is obtained. For example, to solve the equation 2x + 3 = 7, you would use algebraic operations to isolate the variable x on one side of the equation, giving you the solution x = 2.
To find when the height of the thrown bottle is equal to 0, we need to solve the given equation:
h = -16t² + 56t - 24 = 0
Takin -8 common out we get,
-8(2t² - 7t + 3) = 0
Now we can use the zero product property, which states that if the product of two factors is equal to zero, then at least one of the factors must be zero:
-8 = 0 or 2t² - 7t + 3 = 0
But -8 ≠ 0, so we only possible one is,
2t² - 7t + 3 = 0
(2t - 1)(t - 3) = 0
Using the zero product property, we get,
2t - 1 = 0 or t - 3 = 0
Solving for t we get,
t = 1/2 or t = 3
Therefore, the height of the thrown bottle is equal to 0 at t = 1/2 seconds and t = 3 seconds.
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The height of the thrown bottle becomes zero at the t = 1/2 that is half a second and at t = 3 seconds
How do you form an equation?An equation is formed by expressing the relationship between two or more mathematical expressions. It can be formed by using mathematical symbols, operations, and variables. Typically, equations are used to solve problems or find unknown quantities by setting up an equation that represents the problem and then manipulating the equation using algebraic operations until the solution is obtained. For example, to solve the equation 2x + 3 = 7, you would use algebraic operations to isolate the variable x on one side of the equation, giving you the solution x = 2.
To find when the height of the thrown bottle is equal to 0, we need to solve the given equation:
h = -16t² + 56t - 24 = 0
Takin -8 common out we get,
-8(2t² - 7t + 3) = 0
Now we can use the zero product property, which states that if the product of two factors is equal to zero, then at least one of the factors must be zero:
-8 = 0 or 2t² - 7t + 3 = 0
But -8 ≠ 0, so we only possible one is,
2t² - 7t + 3 = 0
(2t - 1)(t - 3) = 0
Using the zero product property, we get,
2t - 1 = 0 or t - 3 = 0
Solving for t we get,
t = 1/2 or t = 3
Therefore, the height of the thrown bottle is equal to 0 at t = 1/2 seconds and t = 3 seconds.
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A single letter from the word SLEEPLESS is chosen. What is the probability of choosing a P or an S? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
If a single letter from the word SLEEPLESS is chosen, the probability of choosing a P or an S as a fraction in lowest terms is 5/8.
To find the probability of choosing a P or an S from the word SLEEPLESS, we need to first determine the total number of letters in the word and then count how many of those letters are P's or S's.
There are 8 letters in the word SLEEPLESS, so there are 8 possible outcomes when selecting a single letter at random. Of these 8 letters, 2 are P's and 3 are S's.
Therefore, the probability of choosing a P or an S is the sum of the probabilities of choosing a P and choosing an S:
P(P or S) = P(P) + P(S)
P(P) = 2/8 = 1/4, since there are 2 P's out of 8 total letters.
P(S) = 3/8, since there are 3 S's out of 8 total letters.
P(P or S) = 1/4 + 3/8
P(P or S) = 5/8, which is the final probability expressed as a fraction in lowest terms.
Alternatively, we can convert the fraction to a decimal and round to the nearest millionth:
P(P or S) = 0.625
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The image of a trapezoid is shown. What is the area of a trapezoid?
The area of a trapezoid =1/2× (sum of the parallel sides)×h
=1/2×(a + b)×h=1/2×(3+6)×4=9×2= 18 square units.
What is a trapezoid?A trapezoid is a geometric shape with four sides, where two of the sides are parallel and the other two sides are not parallel. The parallel sides are called bases, and the non-parallel sides are called legs. The height or altitude of the trapezoid is the distance separating the two bases.
There are two main types of trapezoids: isosceles and non-isosceles. In an isosceles trapezoid, the legs are congruent, and the base angles (the angles formed between each base and a leg) are also congruent. In a non-isosceles trapezoid, the legs and base angles are not congruent.
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When Jace runs the 400 meter dash, his finishing times are normally distributed with a mean of 87 seconds and a standard deviation of 2.5 seconds. Using the empirical rule, determine the interval of times that represents the middle 95% of his finishing times in the 400 meter race.
The middle 95% of Jace's finishing times in the 400 meter race is between 82 and 92 seconds.
Approximately 68% of the data falls within 1 standard deviation of the mean (i.e., between μ - σ and μ + σ).
Approximately 95% of the data falls within 2 standard deviations of the mean (i.e., between μ - 2σ and μ + 2σ).
Approximately 99.7% of the data falls within 3 standard deviations of the mean (i.e., between μ - 3σ and μ + 3σ).
We want to find the interval of times that represents the middle 95% of Jace's finishing times, which means we want to find the interval that falls between μ - 2σ and μ + 2σ.
Substituting the given values, we get:
μ - 2σ = 87 - 2(2.5) = 82
μ + 2σ = 87 + 2(2.5) = 92
Therefore, the middle 95% of Jace's finishing times in the 400 meter race is between 82 and 92 seconds.
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A party company is designing a new line of individualized bubbles for various celebrations such as birthday parties, weddings, and anniversaries. The bubbles will be sold in various-sized packs. The individual container of bubbles will be a plastic cylindrical tube with a diameter 2 cm and a height of 8 cm.
How many square centimeters of plastic are needed for one tube of bubbles?
Round your answer to the nearest whole number.
A. 50 cm^2
B. 57 cm^2
C. 63 cm^2
D. 53 cm^2
Answer:
The formula for the surface area of a cylinder is:
SA = 2πr^2 + 2πrh
where r is the radius and h is the height.
Since the diameter of the tube is 2 cm, the radius is 1 cm.
Substituting the given values, we get:
SA = 2π(1^2) + 2π(1)(8)
SA = 2π + 16π
SA = 18π
To find the surface area in square centimeters, we need to multiply by the conversion factor (1 cm)^2/(1 π) = 1 cm^2/3.14.
SA = 18π × (1 cm^2/3.14)
SA ≈ 18 × 0.3185
SA ≈ 5.73 cm^2
Rounding to the nearest whole number, we get:
SA ≈ 6 cm^2
Therefore, the answer is B. 57 cm^2.
Step-by-step explanation:
Choose a correct name for the line shown. C B A overleftrightarrow BB overleftrightarrow AB AC BC
Note that the best name for the line segment indicated is [tex]\overleftrightarrow {AB}[/tex]
What is a line segment?A line segment is a section of a straight line that is bounded by two different end points and contains every point on the line between them. The Euclidean distance between the ends of a line segment determines its length.
Other types of lines are:
Lines that are parallel. Two lines in the same plane, either intersecting or not.
Lines that cross. Intersecting lines are two or more lines that cross in a plane.
Lines that are concurrent. Concurrent lines are defined as numerous lines that cross through each other at the same place.
Points that are curved.
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Full Question:
See attached image.
Mrs Smith oatmeal cookie recipe calls for 2/5 of a cup of sugar how much sugar which she need to make 1/2 of a batch of cookies
If Mrs. Smith's oatmeal cookie recipe calls for 2/5 of a cup of sugar to make a full batch of cookies, then to make half a batch of cookies, she will need half the amount of sugar.
So, to find out how much sugar Mrs. Smith needs to make half a batch of cookies, we can use the following calculation:
Sugar needed for half a batch = (2/5 cup sugar) x (1/2 batch)
Simplifying this expression, we get:
Sugar needed for half a batch = 2/10 cup sugar
Which can be further simplified to:
Sugar needed for half a batch = 1/5 cup sugar
Therefore, Mrs. Smith will need 1/5 cup of sugar to make half a batch of oatmeal cookies.
HELP URGENT PLEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEZE
350 is the answer
Step-by-step explanation:
I hope it helps
What is the critical value t* for constructing a 95% confidence interval for a mean from a sample size of n=20 observations?
The critical value t* for a two-tailed 95% confidence interval with 19 degrees of freedom is approximately 2.093.
How to determine the critical value tThe critical value t* depends on the degrees of freedom (df) and the desired level of confidence. For a 95% confidence interval and a sample size of n=20, the degrees of freedom would be df = n-1 = 19.
Using a t-distribution table with 19 degrees of freedom (since n-1=20-1=19), we can find the value of t* that corresponds to a 95% confidence level. For a two-tailed test (which is typically used for a confidence interval), the area in each tail is 0.025 (since 1 - 0.95 = 0.05, and we need to split this evenly between the two tails).
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How many radians are in a full circle?
Answer: 2 Radians
Step-by-step explanation:
A full circle is 2 full radians, also known as 2π. Half of a circle is equal to 180 degrees, which is equal to one radian, π.
I have attached a picture of the unit circle below, this picture comes form www.remind.com, but you can find many online.
Need help asap please!
Answer:
[tex]2 \dfrac{1}{2}[/tex] OR [tex]\dfrac{5}{2}[/tex]
Step-by-step explanation:
We can see that there are 2 whole shaded circles, and there is 1 half shaded circle.
Therefore, we can represent the shaded area as [tex]\bold{2 \dfrac{1}{2}}[/tex] circles.
We can convert this mixed number to an improper fraction by multiplying the whole number by the denominator and adding the resulting value to the numerator.
[tex]2 \dfrac{1}{2}[/tex]
[tex]= \dfrac{(2 \times 2) + 1}{2}[/tex]
[tex]= \dfrac{5}{2}[/tex]
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The profit for one small cake is £1.31.
How to calculate the profitLet's first determine the overall count of parts demonstrated in the ratio 5:7:12, which is equal to 24. Subsequently, each part would hence correspond to a quantity of nine cakes as per the equation below:
216 cakes / 24 = 9 cakes
5 parts x 9 cakes/part = 45 cakes
Likewise, similarly calculating the number of medium cakes leads us to 63 cakes, while that of large cakes sums up to 108 cakes:
7 parts x 9 cakes/part = 63 cakes
12 parts x 9 cakes/part = 108 cakes
Considering what the profit for one small cake is denoted by "x", and similarly, the profit for one medium cake is "2x" and the profit for one large cake is "3x", we can express the total gain as follows:
45x + 63(2x) + 108(3x) = 648.45
After similifying and solving for "x", we obtain an answer of £1.31 after rounding it off to two decimal places:
495x = 648.45
x = 1.31 (rounded to two decimal places)
Thus, the income earned from selling one single small cake is estimated at £1.31.
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Janelys has a bag of candy full of 15 strawberry chews and 5 cherry chews that
she eats one at a time. Which word or phrase describes the probability that
she reaches in without looking and pulls out a strawberry chew?
The word that describes the probability that Janelys reaches in without looking and pulls out a strawberry chew is "the probability of selecting a strawberry chew randomly from the bag".
Calculating the phrase of the probabilityThe word or phrase that describes the probability of pulling out a strawberry chew without looking is "the probability of selecting a strawberry chew at random" or "the probability of picking a strawberry chew by chance".
This probability is calculated by dividing the number of strawberry chews in the bag by the total number of chews in the bag, since each chew is equally likely to be selected.
In this case, there are 15 strawberry chews and 5 cherry chews, so the probability of selecting a strawberry chew at random is 15/(15+5) or 3/4, which is approximately 0.75 or 75%.
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61) If an ellipse has vertices at (-7.0). (7.0), (0.4), and (0-4), what is its domain? What is its range?
The domain of the ellipse is [-7, 7].
The range of the ellipse is [-4, 4].
What is a domain?In mathematics, the domain of a function is the set of all possible input values for which the function is defined. In other words, it is the set of all values of the independent variable (usually denoted by x) for which the function produces a valid output (usually denoted by y).
What is the range?In mathematics, the range of a function is the set of all possible output values that the function can produce for a given set of input values. In other words, it is the set of all values of the dependent variable (usually denoted by y) that can be obtained from the function.
According to the given informationTo find the domain and range of an ellipse, we need to identify the minimum and maximum x-coordinates and y-coordinates of the points on the ellipse.
The center of the ellipse is the midpoint of its major axis, which is the line segment connecting its vertices (-7,0) and (7,0). The midpoint is ((-7+7)/2, (0+0)/2), or (0,0). This means the center of the ellipse is at (0,0).
The semi-major axis is the distance from the center of the ellipse to one of its vertices, which is 7. The semi-minor axis is the distance from the center of the ellipse to one of its co-vertices, which is 4.
So, the equation of the ellipse can be written in standard form as:
(x - 0)²/7² + (y - 0)²/4² = 1
Simplifying, we get:
x²/49 + y²/16 = 1
To find the domain and range, we need to consider the x-coordinates and y-coordinates separately.
For the x-coordinates, we can rearrange the equation as:
x² = 49 - 49y²/16
This tells us that the minimum and maximum values of x occur when y is at its extremes, which are -4 and 4. Substituting these values, we get:
x² = 0 and x² = 49
Taking the square root, we get:
x = 0 and x = ±7
So, the domain of the ellipse is [-7, 7].
For the y-coordinates, we can rearrange the equation as:
y² = 16 - 16x²/49
This tells us that the minimum and maximum values of y occur when x is at its extremes, which are -7 and 7. Substituting these values, we get:
y² = 0 and y² = 16
Taking the square root, we get:
y = 0 and y = ±4
So, the range of the ellipse is [-4, 4].
Therefore, the domain of the ellipse is [-7, 7], and the range of the ellipse is [-4, 4].
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The figure below shows the transformation A to become rectangle B.
Which steps describe the transformation shown in figure?
A. a dilation with a factor of 1 1/2 followed by a translation to the left
B. a dilation with a factor of 2/3 followed by a translation to the left
C. a translation with a factor of 1 1/2 followed by a dilation to the left
D. a translation with a factor of 2/3 followed by a dilation to the left
Answer:
Step-by-step explanation:
A is correct
-3+8n=-5 for 7th grade math equation algebra
Answer: -0.25
Step-by-step explanation:
Start by undoing with PEMDAS (order of operations, P-parenthesis, E-exponents, etc)
+3 on both sides of equal sign, which gives you
8n=-2
then divide by 8 on both sides (undo the times 8)
n=-0.25
Answer: -0.25
Step-by-step explanation:
Start by undoing with PEMDAS (order of operations, P-parenthesis, E-exponents, etc)
+3 on both sides of equal sign, which gives you
8n=-2
then divide by 8 on both sides (undo the times 8)
n=-0.25
Clinton and Stacy decided to travel from their home near Austin, Texas, to Yellowstone National Park in their RV.
- The distance from their home to Yellowstone National Park is 1,701 miles.
- On average the RV gets 10.5 miles per gallon.
- On average the cost of a gallon of gasoline is $3.60.
Based on the average gas mileage of their RV and the average cost of gasoline, how much will Clinton and Stacy spend on gasoline for the round trip to Yellowstone National Park and back home?
A. $1,166.40
B. $2,480.63
C. $583.20
D. $64,297.80
Answer:
The answer is A. $1,166.40
Step-by-step explanation:
Find the area of the triangle. The area is yd² (Simplify your answer.) 17.5 yd 42 yd 45.5 yd