The equation of a line perpendicular to y=2x-5 that passes through the point (2,-5) is y = -1/2x - 4.
What is point slope form?The point slope form is given as y - y1 = m(x - x1). When a line's slope and a point on the line are known, the equation may be used to get the equation of the line. Just enter the specified point and slope into the equation and simplify as necessary to utilise the point-slope form.
A line graph can also be drawn using the point-slope form. Plot the provided point on the coordinate plane first before using this form to graph a line. As you move up or down and to the right or left from the starting point, depending on whether the slope is positive or negative, you may utilise the slope to identify more places along the line.
The given equation of the line is y = 2x - 5.
Here the slope is 2.
For a perpendicular line the slope is negative and reciprocal thus.
slope = - 1/2.
Now using the point slope form:
y - y1 = m(x - x1)
y + 5 = -1/2(x - 2)
y + 5 = (-1/2)x + 1
y = (-1/2)x - 4
Hence, the equation of a line perpendicular to y=2x-5 that passes through the point (2,-5) is y = -1/2x - 4.
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[tex]\sqrt{2x} + 3 = 8[/tex]2 x + 3 = 8
Answer: x= 6241/2
Step-by-step explanation:
how far is sam from the top of a temple?
The distance between Sam from the top of the temple is 56. 6 feet
How to determine the distanceTo determine the distance, we need to know that trigonometric identities are mathematical identities that is mostly used to prove that all the values of the functions of trigonometry are true.
The types of trigonometric identities are;
tangentsinecosinecotangentcosecantsecantFrom the information given, we can deduce that;
The angle of elevation, θ = 62 degrees
The opposite side of the angle that is the height of the temple is 50 feet
The distance is the hypotenuse side
Then, using sine identity, we have;
sin 62 = 50/d
d = 50/0. 8829
d = 56. 6 feet
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An industrial plant claims to discharge no more than 1000 gallons of wastewater per hour, on the average, into a neighboring lake. An environmental action group decides to monitor the plant, in case this limit is being exceeded. A random sample of 42 hours is selected over a period of a month. The data are unimodal and roughly symmetric.
= 1138, s= 605, and Standard Error = 93.354
(a) Using StatCrunch, the p-value = (3 decimal places)
(b) Are the conditions met to conduct this test?
Yes, the population is approximately normal because n > 30.
Yes, np and n(1-p) are both > 15.
No, np and n(1-p) are not both > 15.
Yes, because the data are approximately normal.
(c) At alpha = 0.05, which of the following is the correct conclusion?
Reject the null hypothesis. There is sufficient evidence that the wastewater discharged by the industrial plant exceeds 1000 gallons per hour.
Do not reject the null hypothesis. There is evidence that the wastewater discharged by the industrial plant exceeds 1000 gallons per hour.
Reject the null hypothesis. There is insufficient evidence that the wastewater discharged by the industrial plant exceeds 1000 gallons per hour.
Do not reject the null hypothesis. There is insufficient evidence that the wastewater discharged by the industrial plant exceeds 1000 gallons per hour.
(a) The p-value = 0.017 (b) the conditions are met to conduct the test. (c) the correct conclusion is: Reject the null hypothesis
How to find the The p-value and if the conditions met to conduct this test(a) Using the given data, we can calculate the test statistic z-score as:
z = (xbar - μ) / (σ / sqrt(n))
= (1138 - 1000) / (605 / sqrt(42))
= 2.378
Using StatCrunch, the p-value for a two-tailed test with a test statistic of 2.378 and degrees of freedom of 41 (n - 1) is 0.017.
Therefore, the p-value = 0.017 (to 3 decimal places).
(b) To conduct a hypothesis test for a population mean, we need to check if the following conditions are met:
The population is approximately normal or the sample size is large (n ≥ 30).
The population standard deviation (σ) is unknown.
Here, n = 42 which is greater than 30, so we can assume that the population is approximately normal. The standard deviation of the population is unknown.
Therefore, the conditions are met to conduct the test.
(c) The null and alternative hypotheses are:
Null hypothesis (H0): The mean wastewater discharged by the industrial plant is 1000 gallons per hour (μ = 1000).
Alternative hypothesis (Ha): The mean wastewater discharged by the industrial plant exceeds 1000 gallons per hour (μ > 1000).
At alpha = 0.05 (5% level of significance), the critical z-value for a one-tailed test is 1.645.
Since the calculated z-score (2.378) is greater than the critical value (1.645), we reject the null hypothesis.
Therefore, the correct conclusion is: Reject the null hypothesis. There is sufficient evidence that the wastewater discharged by the industrial plant exceeds 1000 gallons per hour.
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maria scored 92 points in 4 games at the same rate, how many points would she scored in 17 games
Explanation:
She scored 92 points in 4 games. The unit rate is 92/4 = 23 points per game.
Over the course of 17 games, Maria would have a total of 17*23 = 391 points assuming her scoring rate is kept the same.
9. Which statement about the diagonals of a non-square rectangle is true?
The diagonals are parallel.
The diagonals are congruent.
The diagonals are perpendicular.
The diagonals bisect a pair of opposite angles.
The correct statement about the diagonals of a non-square rectangle is "The diagonals bisect a pair of opposite angles"
What is a non-square rectangle?A rectangle is a four-sided flat shape with opposite sides of equal length and opposite sides that are parallel.
A non-square rectangle is simply a rectangle whose opposite sides are not equal in length. In other words, a non-square rectangle is a rectangle that has two pairs of sides, each of which has a different length.
If a rectangle has sides that are equal in length, it is called a square. However, if the sides are not equal, then it is a non-square rectangle. Non-square rectangles are commonly encountered in everyday life, such as in the shape of paper, books, windows, doors, and many other objects.
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Watch help video
Given circle E with diameter CD and radius EA. AB is tangent to E at A. If
EC = 3 and EA = 3, solve for AC. Round your answer to the nearest tenth if
necessary. If the answer cannot be determined, click "Cannot be determined."
C
A
B
The circle E with diameter CD and radius EA having the length of AC is approximately 4.2 units.
What is Pythagoras' Theorem?
In a right-angled triangle, the square of the hypotenuse side equals the sum of the squares of the other two sides.
Since EA is a radius of circle E, and AB is tangent to E at A, we know that AB is perpendicular to EA. Thus, triangle EAB is a right triangle.
Let x be the length of AC. Then, by the Pythagorean Theorem in triangle EAC, we have:
[tex]AC^{2} = EA^{2} +EC^{2}[/tex]
[tex]AC^{2} = 3^{2} + 3^{2}[/tex]
[tex]AC^{2} = 18[/tex]
AC ≈ 4.2 (rounded to the nearest tenth)
Therefore, the length of AC is approximately 4.2 units.
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pls help me with this
Therefore , the solution of the given problem of unitary method comes out to be rectangle's size is 7/12 square inches.
An unitary method is what ?The objective can be accomplished by using what was variable previously clearly discovered, by utilizing this universal convenience, or by incorporating all essential components from previous flexible study that used a specific strategy. If the anticipated claim outcome actually occurs, it will be feasible to get in touch with the entity once more; if it isn't, both crucial systems will undoubtedly miss the statement.
Here,
=> A = L x W,
where A is the area, L is the length, and W is the breadth, is the formula for calculating the area of a rectangle.
Inputting the numbers provided yields:
=> A = (7/4) x (1/3)
These fractions can be made simpler by eliminating any shared variables in the numerator and denominator before being multiplied. Since 7 and 3 are both prime integers in this instance, there are no shared factors to cancel.
The new numerator and denominator can then be obtained by multiplying the numerators and denominators, respectively. Thus, we get:
=> A = (7 x 1) / (4 x 3)
When we multiply the numerator by the remainder, we obtain:
=> A = 7/12
The rectangle's size is 7/12 square inches as a result.
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Anyone know the diameter?
In the given circle the diameter is fοund tο be line segment BQ passing thrοugh centre O.
What is a circle?A circle is a clοsed, twο-dimensiοnal οbject where every pοint in the plane is equally spaced frοm a central pοint. The line οf reflectiοn symmetry is fοrmed by all lines that traverse the circle. Additiοnally, every angle has rοtatiοnal symmetry arοund the centre.
A circle is given with centre marked as O.
A circle is a 2D fοrm in geοmetry in which all οf the pοints οn its surface are equally spaced frοm its center.
The radius is the length frοm any pοint οn the surface tο the center.
A diameter is a chοrd that is equidistance frοm centre οf the circle.
Here οnly the straight line is equidistance frοm centre οf the circle.
That line is BQ.
Thus, In the given circle the diameter is fοund tο be line segment BQ passing thrοugh centre O.
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You deposit $5,000.00 in an account earning 8% interest compounded annually. How much will you have in the account in 5 years?
Answer:
Answer:
50313.28
Step-by-step explanation:
A = total amount
P = principal or amount of money deposited,
r = annual interest rate
n = number of times compounded per year
t = time in years
For the formula:
A=P(1+r/n)n⋅t
P=$5000 , r=8% , n=1 and t=30 years
Solution:
A= 5000(1+0.08/1) to the power 1.30
= 5000*1.08 to the power 30
= 5000*10.062657
= 50313.28
20 points!! please help!!
To find the area of the total figure, we need to first find the areas of the rectangle and triangle, and then add them together.Therefore, the area of the total figure is 200 square feet.
What is area?Area is the measurement of the size of a two-dimensional surface enclosed by a closed figure
Area of rectangle = length x width
= 20 ft x 8 ft
= 160 sq. ft
Area of triangle = 1/2 xbase xheight
= 1/2 x 8 ft x 10 ft
= 40 sq. ft
To find the base of the triangle, we can use the Pythagorean theorem, which states that the square of the hypotenuse (slope) of a right triangle is equal to the sum of the squares of its two sides. In this case, the hypotenuse is 12 ft, one of the other sides is the height of the triangle (10 ft), and the other side is the base of the triangle (b).
Using the Pythagorean theorem, we have:
12² = 10² + b²
144 = 100 + b²
44 = b²
b = √44
b ≈ 6.63 ft
Now that we know the base of the triangle, we can find the area of the total figure by adding the area of the rectangle and the area of the triangle:
Area of total figure = area of rectangle + area of triangle
= 160 sq. ft + 40 sq. ft
= 200 sq. ft
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Please help meee don’t understand
In the diagram, point B is a point of tangency. Find
the radius r of OC.
The radius r for the circle C is equal to 39 using the Pythagoras rule for the right triangle ABC
How to evaluate for the radius using Pythagoras ruleSince the line AB is tangent to the circle at point B, then the triangle ABC is a right triangle and the Pythagoras rule can be applied as follows:
(50 + r)² = r² + 80²
r² = (50 + r)² - 80²
r² = (50 + r - 80)(50 + r + 80) {difference of two square}
r² = (r - 30)(r + 130)
r² = r² + 130r - 30r - 3900 {expansion of brackets}
r² - r² + 130r - 30r = 3900 {collect like terms}
100r = 3900
r = 3900/100 {divide through by 100}
r = 39
Therefore, the radius r for the circle C is equal to 39 using the Pythagoras rule for the right triangle ABC.
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Solve 6x+14x+5=5(4x+1) and write a word problem to the equation or any relevant forms of it represents.
After solving the given expression, the value of x is 5.
What exactly are expressions?
An expression in mathematics is a set of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division) that may be evaluated to generate a value. Expressions can be simple or complicated, with one or more variables involved.
Now,
To solve the equation 6x+14x+5=5(4x+1), we first need to simplify both sides of the equation using the distributive property of multiplication:
6x + 14x + 5 = 20x + 5
Now we can simplify further by subtracting 20x and 5 from both sides of the equation:
6x + 14x - 20x = 0 - 5
Simplifying again:
x = -5
Finally, we can solve for x by multiplying both sides by -1:
x = 5
Therefore, the solution to the equation 6x+14x+5=5(4x+1) is x=5.
Word problem:
A clothing store sells two types of shirts: T-shirts and polo shirts. The store makes a profit of $6 on each T-shirt sold and a profit of $14 on each polo shirt sold. Last week, the store sold a total of 5 shirts and made a total profit of $25. If x represents the number of T-shirts sold, write an equation to represent the situation.
Solution:
Let x be the number of T-shirts sold, then the number of polo shirts sold is 5 - x (since a total of 5 shirts were sold). The total profit from selling x T-shirts and (5-x) polo shirts can be calculated as:
Profit = (profit per T-shirt x number of T-shirts) + (profit per polo shirt x number of polo shirts)
Profit = (6x) + (14(5-x))
Profit = 6x + 70 - 14x
Profit = -8x + 70
Since the total profit is given as $25, we can write the equation:
-8x + 70 = 25
Simplifying:
-8x = -45
x = 5.625
Since we can't sell a fraction of a shirt, we need to round down to the nearest integer. Therefore, the store sold 5 T-shirts.
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92920625 rounded to the nearest million
Answer:
93 million
Step-by-step explanation:
93 Million
The quadrilateral on the graph below is rotated about the point (0, 0). What are the new coordinates of Point B and Point C after a 90 degree clockwise rotation?
A 90 degree clockwise rotation about the point (0,0), the new coordinates of Point B are (3, -1) and the new coordinates of Point C are (1, -2).
How do you check if a quadrilateral is a rectangle on a graph?A quadrilateral can be proven to be a rectangle in a number different ways. Here are the three simplest methods: 1. Establish that all angles are 90 degrees; 2. Establish that two opposed angles are 90 degrees; and 3. Establish that the diagonals are equally long and intersect one another.
The following transformation matrix can be used to rotate a point (x,y) 90 degrees clockwise with respect to the origin (0,0):
|0 1|\s|-1 0|
This transformation matrix can be applied to each point to determine its new coordinates upon rotation.
Point B is the first point, and its initial coordinates are (-1, 3). The transformation matrix in use:
|0 1| |-1| |3|
|-1 0| x |3| = |-1|
After rotating Point B 90 degrees clockwise, the new coordinates are: (3, -1).
The transformation matrix is then applied to Point C, whose initial coordinates are (2, 1):
|0 1| |2| |1|
|-1 0| x |1| = |-2|
After rotating in a clockwise direction by 90 degrees, Point C's new coordinates are (1, -2).
As a result, after rotating 90 degrees in a clockwise direction around Point 0, Point B's new coordinates are (3, -1), while Point C's new coordinates are (1, -2).
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Patrick biked 27 miles last week. He biked 9 miles more than Ibrain. The equation m + 9 = 27 gives the number of miles m that Ibrain biked last week. Which is the solution of the equation?
Answer:
Step-by-step explanation:
We can solve the equation m + 9 = 27 by subtracting 9 from both sides to isolate m:
m + 9 - 9 = 27 - 9
m = 18
Therefore, Ibrain biked 18 miles last week.
What is the fourth term of the sequence:
Write the number in the blank only.
a_1 = 5
a_n = 2a_n-1 + 3
The fourth term of the sequence with the definition of functions a₁ = 5 and aₙ = 2aₙ₋₁ + 3 is 61.
Calculating the fourth term of the sequenceGiven the following definition of functions
a₁ = 5
aₙ = 2aₙ₋₁ + 3
To find the fourth term of the sequence defined by a₁ = 5aₙ = 2aₙ₋₁ + 3, we can use the recursive formula to generate each term one by one:
a₂ = 2a₁ + 3 = 2(5) + 3 = 13
a₃ = 2a₂ + 3 = 2(13) + 3 = 29
a₄ = 2a₃ + 3 = 2(29) + 3 = 61
Therefore, the fourth term of the sequence is 61.
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Jane made $143 for 11 hours of work. At the same rate, how many hours would she have to work to make $169 ?
13
First, we divide to figure out how much Jane makes an hour
143 ÷ 11 = 13
Second, we multiply multiply by 13 until we get 169
13 × 13 = 169
So Jane will make 169 dollars in 13 hours
Answer:
13 Hours
Step-by-step explanation:
$143 ÷ 11hrs = $13/hr that Jane is paid, so to find how many hours she will need to work to make $169
$169 ÷ $13 = 13 hours
Anyone help??? It’s geometryyy
hi :) i sense that it's the rhombus again, but please let me know if i'm wrong.
assuming this is about the rhombus, which i've attached below, here is your answer:
the diagonals of a rhombus bisect each other at right angles. this means that the angles created by the intersection of AC and BD are all equal to 90 degrees, including CEB.
hope this helps!
The graph shows the velocity versus time for 4 different cars on a race track. If all four cars have the same mass, which one experiences the largest net force?
Answer:
Step-by-step explanation: 1
question included below
Therefore , the solution of the given problem of unitary method comes out to be P = 1/72.
An unitary method is what?The objective can be accomplished by utilizing what has been expression learned thus far, making use of this global availability, and incorporating all essential components from earlier changeable study that utilized a particular method. If the anticipated claim result actually occurs, it will be feasible to contact the entity once more; otherwise, both important processes will undoubtedly miss the statement.
Here,
There are two situations to take into consideration because there are seven courses in Group A and six courses in Group B:
The student in Case 1 selects two classes from Group A. The student has seven choices for the first course in this situation, and six options for the second course.
Case 2: The student has a total of 5 choices for courses, as follows:
=>2 × (42 + 30) = 144
As a result, the student has 144 choices for 5-course sequences.
b. There are two choices for the fifth course because the student can select one more course from either Group A or Group B.
There are a total of three methods to select this set of courses:
=> 1 × 1 × 1 × 1 × 2 = 2
the likelihood of selecting Introduction
=> P = 2/144 = 1/72
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Select the correct answer. Which function has an average rate of change of -4 over the interval [-2,2]?
A. x | -2 | -1 | 0 | 1 | 2
m(x) | -12 | -5 | -4 | -3 | 4
B.
C.
D.
Answer:
The correct answer is option B.
To find the function with an average rate of change of -4 over the interval [-2,2], we need to calculate the slope of the function between the two points -2 and 2.
Average rate of change = (f(2) - f(-2))/(2 - (-2)) = (-4)
Option B has the function qx with values {-4, 0, 0, -4, -12} at x values {-2, -1, 0, 1, 2}. The average rate of change of this function over the interval [-2,2] is indeed -4.
b. Rewrite 4 x 63 as the product of a unit fraction and a whole number.
Solve.
Rewriting 4 x 3/6 as the product of a unit fraction and a whole number is: 12 * 1/6
How to multiply fractions?The parameters are given as:
Number - 4
Fraction - 3/6
The following steps can be used to determine the product as the product of a whole number and a unit fraction:
Step 1 - Remember the whole number are those numbers that involve all positive integers and zero.
Step 2 - Also remember that the unit fraction is nothing but a fraction whose numerator is 1.
Step 3 - Write the given expression.
4 * 3/6
Step 4 - Convert the given fraction into a unit fraction by multiplying 4 by 3 in the above expression.
4 * 3 * 1/6
Step 5 - Simplify the above expression.
12 * 1/6
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2. Suppose a consumer has $30 available to be divided between commodities A and B and the unit price of B is fixed at $3. What will be his demand equation for A if his utility function is U = 4XgXb?
The demand equation for commodity A is Xa = (4/10)Xb.
What is demand equation?A demand equation is a mathematical representation of the relationship between the quantity of a good or service that consumers are willing to buy and the various factors that influence that demand, such as price, income, and preferences.
In the given question,
To find the consumer's demand equation for A, we need to use the utility maximization rule, which states that a consumer will allocate their budget in such a way as to maximize their total utility subject to their budget constraint.
Let Xa be the quantity of commodity A and Xb be the quantity of commodity B. We know that the consumer has $30 to spend, so the budget constraint is:
3Xb + pXa = 30
where p is the price of commodity A. We also know the utility function:
U = 4XgXb
To maximize U subject to the budget constraint, we can use the Lagrangian method:
L = 4XgXb + λ(30 - 3Xb - pXa)
where λ is the Lagrange multiplier.
To find the demand equation for A, we need to take the partial derivative of L with respect to Xa and set it equal to zero:
∂L/∂Xa = -λp = 0
This gives us λ = 0, which we can substitute back into the Lagrangian equation to get:
L = 4XgXb + 0(30 - 3Xb - pXa)
L = 4XgXb
To find the demand equation for A, we need to take the partial derivative of L with respect to p and solve for Xa:
∂L/∂p = -4XgXb/Xa = -30/3
Xa = (4/10)Xb
So the demand equation for commodity A is Xa = (4/10)Xb.
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The demand equation for commodity A is Xa = (4/10)Xb.
What is demand equation?
A demand equation is a mathematical formula that expresses the relationship between the quantity of a good or service that consumers are willing and able to purchase and various factors that affect that quantity, such as price, income, and the prices of other goods.
According to given information:To find the consumer's demand equation for A, we need to use the utility maximization rule, which states that a consumer will allocate their budget in such a way as to maximize their total utility subject to their budget constraint.
Let Xa be the quantity of commodity A and Xb be the quantity of commodity B. We know that the consumer has $30 to spend, so the budget constraint is:
3Xb + pXa = 30
where p is the price of commodity A. We also know the utility function:
U = 4XgXb
To maximize U subject to the budget constraint, we can use the Lagrangian method:
L = 4XgXb + λ(30 - 3Xb - pXa)
where λ is the Lagrange multiplier.
To find the demand equation for A, we need to take the partial derivative of L with respect to Xa and set it equal to zero:
∂L/∂Xa = -λp = 0
This gives us λ = 0, which we can substitute back into the Lagrangian equation to get:
L = 4XgXb + 0(30 - 3Xb - pXa)
L = 4XgXb
To find the demand equation for A, we need to take the partial derivative of L with respect to p and solve for Xa:
∂L/∂p = -4XgXb/Xa = -30/3
Xa = (4/10)Xb
So the demand equation for commodity A is Xa = (4/10)Xb.
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En un canal se necesitan diariamente 36 kg de maiz para alimentar a 480 gallinas ¿Cuantos kg se necesitan ahora si se vendieron 120 gallinas?
Resolver con reglla de 3
Answer:
Step-by-step explanation: it is -2x + 430298= -9n79000.
Sierra left $4.50 as a tip for a waiter. This was 18% of the bill before the tip. How much was her total bill before the tip?
$
Answer$81
Step-by-step explanation:
Write the next three terms of the geometric sequence where a_1 = - 8 and r = -2
a_1 = -8
a_2 =
a_3 =
a_4 =
Answer:
a_2 = 16
a_3 = -32
a_4 = 64
Step-by-step explanation:
Multiply each term by r to get the next term.
a_1 = -8
a_2 = -8 × (-2) = 16
a_3 = 16 × (-2) = -32
a_4 = -32 × (-2) = 64
[tex]65y - 147y[/tex]
Math problem.
I need help.
Answer: 82y
Step-by-step explanation:
147y - 65y = 82y
Just perform simple subtraction
The area of this trapezoid is 24.5 ft². 3 ft 4 ft What is the height of the trapezoid? Show your work.
(please hurry! i need help on this and i need to turn it in today)
The height of the trapezoid is approximately 7 feet.
What is the area of a trapezoid?
To find the height of the trapezoid, we can use the formula for the area of a trapezoid: A = ((b1 + b2) / 2) * h
where A is the area, b1 and b2 are the lengths of the two parallel bases, and h is the height.
We are given that the area is 24.5 ft², and the lengths of the bases are 3 ft and 4 ft. Substituting these values into the formula, we get:
24.5 = ((3 + 4) / 2) * h
Simplifying:
24.5 = 3.5 * h
h = 24.5 / 3.5
h ≈ 7
Therefore, the height of the trapezoid is approximately 7 feet.
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Florida Pick 3 In the Florida Pick 3 lottery, you can place a “straight” bet of $1 by selecting the exact order of three digits between 0 and 9 inclusive (with repetition allowed), so the probability of winning is 1/1000. If the same three numbers are drawn in the same order, you collect $500, so your net profit is $499.
The probability of losing is [tex]\frac{999}{1000}[/tex] (since there are 999 ways to lose and 1 way to win), so the odds against winning are [tex](\frac{\frac{999}{1000} }{\frac{1}{1000} })[/tex] = 999:1.
To understand the concept of odds against winning, we can use the analogy of flipping a coin. There are only two outcomes that can occur when we flip a fair coin: heads or tails. The probability of getting heads is 1/2 and the probability of getting tails is also [tex]\frac{1}{2}[/tex] . The odds against getting heads are the ratio of the probability of getting tails to the probability of getting heads, which is 1:1 or even odds. In the case of the Florida Pick 3 lottery, there are 1000 possible outcomes, but only one is a winning outcome. Therefore, the actual odds against winning the Florida Pick 3 lottery with a straight bet are 999 to 1.
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The complete question is:
In the Florida Pick 3 lottery, you can place a “straight” bet of $1 by selecting the exact order of three digits between 0 and 9 inclusive (with repetition allowed), so the probability of winning is 1/1000. If the same three numbers are drawn in the same order, you collect $500, so your net profit is $499.
Find the actual odds against winning