Answer:
Population: 21 million; parameter: 57%; sample: 85,349; statistic: 72%.
Explanation:
The population is the entire group being studied, which in this case is all the residents of Florida, with a total population of 21 million.
The parameter is a numerical summary of the population, which in this case is the proportion of residents who visit a doctor annually and is stated as 57% in the problem.
The sample is a subset of the population that is selected for study, which in this case is the 85,349 adults surveyed by the surveyor.
The statistic is a numerical summary of the sample, which in this case is the proportion of adults in the sample who stated that they have visited a doctor within the past year and is stated as 72% in the problem.
at ignus school there are 425 students. of these students 351 study mathematics, 71 study latin, and 203 study chemistry. there are 199 students who study more than one of these subjects, and 8 students who do not study any of these subjects. find the number of students who study all three of these subjects.
Answer: 9 study all three subjects
Step-by-step explanation:
Discuss the similarities and the differences between the Empirical Rule and Chebychev's Theorem What is a similarity between the Empirical Rule and Chebychev's Theorem? 0 A. O B. ° C. Both apply only to symmetric and bell-shaped distributions. Both do not require the data to have a sample standard deviation. Both calculate the variance and standard deviation of a sample. D. Both estimate proportions of the data contained within k standard deviations of the mean What is a difference between the Empirical Rule and Chebychev's Theorem? A. The Empirical Rule assumes the distribution is aproximately symmetric and bell-shaped and Chebychev's Theorem makes no assumptions O B. Chebychev's Theorem estimates proportions of data contained within infinite standard deviations and the Empirical Rule has a limit of 5 standard deviations ° C. The Empirical Rule assumes a small data set (less than 50 values) where Chebychev's Theorem has no limit on data size. O D. Chebychev's Theorem applies only to distributions which are approximately symmetric or bell-shaped and the Empirical Theorem has no restrictions
A. The correct option for similarity is option D - Both estimate proportions of the data contained within k standard deviations of the mean.
Both the Empirical Rule and Chebyshev's Theorem are used to estimate the proportion of data contained within a certain number of standard deviations from the mean.
Therefore, option 'D' is the correct answer: Both estimate proportions of the data contained within k standard deviations of the mean.
B. The correct option for difference is option A - The Empirical Rule assumes the distribution is aproximately symmetric and bell-shaped and Chebychev's Theorem makes no assumptions.
The Empirical Rule assumes that the distribution is approximately symmetric and bell-shaped, while Chebyshev's Theorem makes no assumptions about the shape of the distribution.
Another difference is that the Empirical Rule is only applicable for normal distributions, while Chebyshev's Theorem can be applied to any distribution.
Therefore, option 'A' is the correct answer: The Empirical Rule assumes the distribution is approximately symmetric and bell-shaped and Chebychev's Theorem makes no assumptions.
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(h² − h) + (5h + 6)-(3h² +4h - 9)
Answer in expanded form
The expanded form of the given expression (h² − h) + (5h + 6)-(3h² +4h - 9) is -2h² + 15.
What is the expanded form of the given expression?Given the expression in the question;
(h² − h) + (5h + 6) - (3h² + 4h - 9)
Expanding an algebraic expression means to remove any parentheses and simplify the expression as much as possible.
In the given expression, we have three sets of parentheses:
(h² − h)
(5h + 6)
(3h² +4h - 9)
To expand the expression, we will remove the parentheses and simplify the resulting terms.
(h² − h) becomes h² - h
(5h + 6) remains the same
(3h² +4h - 9) becomes 3h² + 4h - 9
Putting all the terms together, we get:
h² - h + 5h + 6 - (3h² + 4h - 9)
Now, we will distribute the negative sign to all the terms inside the parentheses:
h² - h + 5h + 6 - 3h² - 4h + 9
Simplifying further by combining like terms, we get:
h² - 3h² - h + 5h - 4h + 6 + 9
-2h² + 15
Therefore, the expanded form is -2h² + 15.
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Enrique has 1 gallon of milk and 1 pint of orange juice in his refrigerator how many cups of milk and orange juice does Enrique have in all
The total cups of milk orange juice Enrique has in refrigerator is equal to 18 cups.
Gallons of milk Enrique has in his refrigerator = 1 gallon
Pint of orange juice Enrique has in his refrigerator = 1 pint
Convert gallons to cups and pint to cups .
There are ,
16 cups = 1 gallon of milk
And 2 cups = 1 pint of orange juice
Enrique has 16 cups of milk
and 2 cups of orange juice.
Total cups of milk and orange juice in refrigerator
=16 cups of milk + 2 cups of orange juice
= 18 cups of milk and orange juice
Therefore, in total Enrique has 18 cups of liquid in his refrigerator.
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Find the value of x in the following equation
3.6(2x+5)=7.2x+18
At LaGuardia Airport for a certain nightly flight, the probability that it will rain is 0.07 and the probability that the flight will be delayed is 0.17. The probability that it will rain and the flight will be delayed is 0.02. What is the probability that the flight would leave on time when it is not raining? Round your answer to the nearest thousandth.
The probability that the flight will leave on time when it is not raining is approximately 0.83.
What is probability?
Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 represents impossibility (the event will not occur) and 1 represents certainty (the event will definitely occur).
According to the given information:
To find the probability that the flight will leave on time when it is not raining, we need to subtract the probability of the flight being delayed due to rain from 1 (since the sum of all probabilities in a given event space is equal to 1).
Let:
P(rain) = 0.07 (probability of rain)
P(delayed) = 0.17 (probability of delay)
P(rain and delayed) = 0.02 (probability of rain and delay)
We can use the formula for conditional probability:
P(A|B) = P(A and B) / P(B)
In this case, we want to find P(on time | not raining), which can be expressed as:
P(on time | not raining) = P(on time and not raining) / P(not raining)
Since rain and not raining are mutually exclusive events (i.e., they cannot occur simultaneously), we have:
P(on time | not raining) = P(on time) / (1 - P(rain))
We can now substitute the given probabilities to calculate the required probability:
P(on time | not raining) = P(on time) / (1 - P(rain))
P(on time | not raining) = (1 - P(delayed)) / (1 - P(rain))
P(on time | not raining) = (1 - 0.17) / (1 - 0.07)
P(on time | not raining) = 0.83
So, the probability that the flight will leave on time when it is not raining is approximately 0.83 (rounded to the nearest thousandth).
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Question 2
Find the area of the composite figure.
143 ft
10 ft
0
square feet
I
X
+
*/*
18 ft
0|0
00
2|5
ft
do yo
12 ft
= = < > < ≥ (0)
TT
216.25 square feet
……….
Find the closing cost, to the nearest cent: house value of $89,548, two points, attorney's fees $324, title fees $105.
a 4,439. 92
b 2,219. 96
c 2,114. 96
d 1324. 48
If the house value of $89,548 and two points, attorney's fees $324, title fees $105, then closing cost is option (b) $2,219.96
Closing costs are fees associated with the purchase or refinance of a property that are paid at the closing of the transaction.
To calculate the closing cost, we need to add up all the fees associated with the purchase of the house.
First, we need to calculate the cost of the points. Two points on a house value of $89,548 would be
2 x $89,548 x 0.01 = $1,790.96
Next, we need to add the attorney's fees and title fees
$1,790.96 + $324 + $105 = $2,219.96
Therefore, the correct option is (b) $2,219.96
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State the most specific name for each figure
PLS HELP
1.) parallelogram
2.) trapezoid
3.) kite
4.) parallelogram
What are the qualities of a parallelogram?The parallelogram is a type of quadrilateral that has the following unique properties such as:
The opposite sides are parallel and equal.The opposite angles are equal.The consecutive or adjacent angles are supplementary.If any one of the angles is a right angle, then all the other angles will be at right angle.The two diagonals bisect each other.The kite is also a type of quadrilateral that has two pairs of adjacent equal sides with a pair of opposite angles that are equal.
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21. shipping crates a square-based, box-shaped shipping crate is designed to have a volume of 16 ft3. the material used to make the base costs twice as much (per square foot) as the material in the sides, and the material used to make the top costs half as much (per square foot) as the material in the sides. what are the dimen- sions of the crate that minimize the cost of materials?
Therefore, the dimensions of the crate that minimize the cost of materials are approximately:
l = 1.587 ft
w = 2.519 ft
h = 3.159 ft
To minimize the cost of materials, we need to find the dimensions of the crate that will minimize the surface area of the crate. Let's call the height, width, and length of the crate "h", "w", and "l", respectively.
We know that the volume of the crate is 16 ft3, so we can write:
lwh = 16
We want to minimize the cost of materials, which is determined by the surface area of the crate. The surface area consists of the top, bottom, front, back, left, and right sides of the crate. The cost of the materials for the base is twice the cost of the materials for the sides, and the cost of the materials for the top is half the cost of the materials for the sides. Let's call the cost of the materials for the sides "c".
The surface area of the crate can be written as:
2lw + 2lh + 2wh
We can use the volume equation to solve for one of the variables, say "h":
[tex]h = \frac{16}{(lw)}[/tex]
Now we can substitute this expression for "h" into the surface area equation:
[tex]2lw + 2l(\frac{16}{(lw))} + 2wh[/tex]
Simplifying this expression gives:
[tex]2lw + 32/l + 2wh[/tex]
To find the dimensions that minimize this expression, we need to take the partial derivatives with respect to "l" and "w" and set them equal to zero:
[tex]\frac{d}{dl} (2lw + 32/l + 2wh) = 2w - \frac{32}{l^2} = 0\\[/tex]
[tex]\frac{d}{dw} (2lw + 32/l + 2wh) = 2l + 2h = 2l + 2(16/(lw)) = 2l + 32/(lw) = 0[/tex]
Solving these equations for "l" and "w" gives:
[tex]l = 2^{(1/3)}\\w = 2^{(2/3)}[/tex]
Substituting these values into the equation for "h" gives:
[tex]h = 8/(2^{(2/3)})[/tex]
Therefore, the dimensions of the crate that minimize the cost of materials are approximately:
l = 1.587 ft
w = 2.519 ft
h = 3.159 ft
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The dimensions of the box that minimize the cost of materials are approximate:
x ≈ 2.52 ft
y ≈ 3.55 ft
z ≈ 2.52 ft
Let's denote the length, width, and height of the box as x, y, and z,
respectively. We are given the volume of the box is [tex]16 ft^3[/tex], so we
have:
x × y × z = 16
We are also given that the material used to make the base costs twice as
much (per square foot) as the material in the sides.
Let's denote the cost of the material for the sides as c, so the cost of the
material for the base is 2c.
The area of the base is xy, so the cost of the material for the base is
2cxy.
Similarly, the material used to make the top costs half as much (per
square foot) as the material in the sides.
Let's denote the cost of the material for the top as 0.5c.
The area of the top is also xy, so the cost of the material for the top is 0.5cxy.
The cost of the material for the four sides is simply 4cz.
Therefore, the total cost of materials is:
C(x, y, z) = 2cxy + 4cz + 0.5cxy
Simplifying, we have:
C(x, y, z) = (2.5c)xy + 4cz
We want to minimize this function subject to the constraint that the volume of the box is [tex]16 ft^3[/tex]:
x × y × z = 16
We can use the method of Lagrange multipliers to solve this constrained optimization problem:
L(x, y, z, λ) = (2.5c)xy + 4cz - λ(xyz - 16)
Taking partial derivatives with respect to x, y, z, and λ, we get:
dL/dx = 2.5cy - λyz = 0
dL/dy = 2.5cx - λxz = 0
dL/dz = 4c - λxy = 0
dL/dλ = xyz - 16 = 0
From the first two equations, we can solve for λ:
λ = 2.5cy/yz = 2.5cx/xz
Setting these two expressions equal to each other and simplifying, we get:
y/x = z/y
This implies that x:y:z = 1:√2:1, since we know that the dimensions of the box must be in proportion to each other.
Substituting this into the constraint x × y × z = 16, we get:
x = 2∛2
y = 2∛4
z = 2∛2
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The Golf King Driving Range is installing a huge net to catch long golf drives. The poles to hold the net up are 50 feet high. The contractor needs to run a wire from the top of the pole to the ground to keep the poles and the net secure. This wire is called a guy wire. a. If the guy wire runs from the top of the pole to a point on the ground 22 feet from the base of the pole, how long must the guy wire be? Round up to the next highest foot. b. What is the slope of the guy wire, expressed as a fraction?
The guy wire must be about 55 feet long and the slope of the guy wire, expressed as a fraction is 25/11.
We can use the Pythagorean Theorem to find the length of the guy wire. Let's call the length of the guy wire "g".
g^2 = 50^2 + 22^2
g^2 = 2500 + 484
g^2 = 2984
g ≈ 54.65
So the guy wire must be about 55 feet long.
The slope of the guy wire is the ratio of the vertical distance it covers to the horizontal distance it covers. In this case, the vertical distance is 50 feet (the height of the pole) and the horizontal distance is 22 feet. So the slope is
50/22 = 25/11
Therefore, the slope of the guy wire is 25/11.
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An engineer has a 50:1 scale drawing of a bridge. The dimensions of the scaled bridge deck are 24 inches by four and one fifth inches. What is the area of the actual bridge deck in square feet?
120 square feet
875 square feet
1,750 square feet
3,500 square feet
Thus, the area of the actual bridge deck is found as 1750 square feet.
Explain about the scale factor:A scale factor refers to the amount by which an object is multiplied to produce a second object of different size but with the same appearance. Just a larger or smaller version of the original is created, not an exact copy.
Given dimension-
Length l = 24 inches
width w = 4 1/5 = 21/5 inches
Convert inches to feet:
1 foot = 12 inches.
Scaled length = 24 inches ÷ 12 inches/foot = 2 feet
Scaled width =21/5 inches ÷ 12 inches/foot = 21 / 5*12 = 0.35 feet
Now, scale factor = 50.: 1
Actual length = Scaled length × Scale factor
Actual length = 2 feet × 50 = 100 feet
Actual width = Scaled width × Scale factor
Actual width = 0.35 feet × 50 = 17.5 feet
Area of actual bridge deck:
Area = Actual length × Actual width
Area = 100 feet × 17.5 feet
Area = 1750 square feet
Thus, the area of the actual bridge deck is found as 1750 square feet.
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John and Mary are young professionals who both have good jobs with
possibilities for advancement. They are trying to decide whether to rent or to buy
their housing. They are relocating to a large urban area with the availability of
public transportation. They have a dog that needs to be exercised. They need a
home office because they will be working from home part of the time.
List AT LEAST three reasons John and Mary should buy AND AT LEAST three
reasons John and Mary should rent.
Some reasons why John and Mary should buy a house could be investment, control and stability. The reasons why they should rent could be flexibility, maintenance costs and lower upfront.
What would be the best decision for them?When considering whether to rent or buy a home, there are many factors to take into account, including financial considerations, lifestyle preferences, and personal circumstances.
Therefore, the decision to rent or buy a home is a complex one that involves many factors. By carefully considering these factors and weighing the pros and cons of each option, John and Mary can make an informed decision that is best for their needs and goals.
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state the most specific name of these quadrilateral...50 points
Answer:
parallelogram kite kite trapazoid
a pharmaceutical company receives large shipments of ibuprofen tablets and uses an acceptance sampling plan. this plan randomly selects and tests 27 tablets, then accepts the whole batch if there is at most one that doesn't meet the required specifications. what is the probability that this whole shipment will be accepted if a particular shipment of thousands of ibuprofen tablets actually has a 11% rate of defects?
The probability of accepting the whole shipment is 0.384, or about 38.4%.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
This is a binomial probability problem, where the probability of a defect (or non-conformance) is p=0.11 and the sample size is n=27. We want to find the probability of having at most one defect in a sample of 27 tablets.
Let X be the number of defects in the sample. Then X follows a binomial distribution with parameters n=27 and p=0.11. We want to find P(X ≤ 1), which is the probability of having 0 or 1 defects in the sample.
Using the binomial distribution formula, we have:
P(X ≤ 1) = P(X = 0) + P(X = 1)
= (27 choose 0) * [tex](0.11)^{0}[/tex] * [tex](0.89)^{27}[/tex] + (27 choose 1) * [tex](0.11)^{1}[/tex] * [tex](0.89)^{26}[/tex]
= (1) * (1) * [tex](0.89)^{27}[/tex] + (27) * (0.11) * [tex](0.89)^{26}[/tex]
= 0.384
Therefore, the probability of accepting the whole shipment is 0.384, or about 38.4%.
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What is the first step to solve this equation? (4)/(x)+(1)/(2)=(5)/(x) The first step in solving the equation is to multiply both sides by
The first step in solving the equation is to multiply both sides by the least common multiple (LCM) of the denominators.
To solve the equation (4)/(x) + (1)/(2) = (5)/(x):
Find a common denominator for the fractions on both sides of the equation. In this case, the common denominator is 2x.
Multiply the left side of the equation by 2/2 to get:
(8)/(2x) + (1)/(2) = (5)/(x)
Combine the two fractions on the left side of the equation:
(8+1)/(2x) = (9)/(2x)
Set the left side of the equation equal to the right side:
(9)/(2x) = (5)/(x)
Cross-multiply:
9x = 10x
Simplify:
x = 0
Therefore, the solution to the equation is x = 0.
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Does the image below prove ABC = DEF? Explain your answer.
Step-by-step explanation:
yes,because of SAS side angle side are equal.
The area of a semicircle is 1. 2717 square meters. What is the semicircles diameter
The diameter of the semicircle for the given area of the semicircle 1. 2717 square meters is equal to 1.8 meters.
Area of a semicircle = 1. 2717 square meters
The area of a semicircle is given by the formula,
A = πr^2 / 2
where A is the area
And r is the radius of the semicircle.
Rearrange the formula to solve for r,
r = √(2A/π)
Substituting the given value of A = 1.2717 square meters into this formula, we get,
⇒ r = √(2 × 1.2717 / π)
⇒ r = 0.9 meters
Since the diameter of a semicircle is twice the radius,
The diameter of this semicircle is equal to,
d = 2r
= 2 × 0.9
= 1.8 meters
Therefore, the diameter of the semicircle is equal to 1.8meters.
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Find all numbers c that satisfy the conclusion of Rolle's Theorem for the following function and interval. Enter the values in increasing order and enter N in any blanks you don't need to use. 7sin(2pix)
The value of c in increasing order which satisfy the Rolle's theorem for a given function is equal to c = 1/4 and c = 3/4.
Function f(x) = 7sin(2πx) ,
Interval = [0, 1]
To apply Rolle's Theorem, check the following conditions,
f(x) must be continuous on the closed interval [a, b].
Here, the interval is [0,1].
f(x) must be differentiable on the open interval (a, b).
f(a) = f(b)
Function f(x) = 7sin(2πx).
f(x) is continuous on the interval [0, 1].
f(x) is differentiable on the interval (0, 1), and its derivative is,
f'(x) = 14π cos(2πx)
The derivative is continuous on the interval (0, 1).
f(0) = 7sin(0)
= 0
f(1) = 7sin(2π)
= 0
Since f(0) = f(1) = 0,
⇒ As per Rolle's Theorem there exists at least one number c in the interval (0, 1) .
Such that f'(c) = 0.
Values of c that satisfy this conclusion,
Solve the equation
f'(c) = 14π cos(2πc)
⇒14π cos(2πc) = 0
⇒ cos(2πc) = 0
This equation has solutions at c = 1/4 and c = 3/4,
As
cos(2π(1/4))
= cos(π/2)
= 0
and
cos(2π(3/4))
= cos(3π/2)
= 0.
Therefore, the values of c that satisfy the conclusion of Rolle's Theorem for the given function are c = 1/4 and c = 3/4, and they are already in increasing order.
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The above question is incomplete, the complete question is:
Find all numbers c that satisfy the conclusion of Rolle's Theorem for the following function 7sin(2pix) and interval [0, 1 ]. Enter the values in increasing order and enter N in any blanks you don't need to use.
A rectangular pen is to be constructed with three equal sections. One side of the pen will be enclosed with the side of the barn. All other sides need to be fenced. If the total amount of fencing available is 510 feet, calculate the dimensions of each rectangular pen that would maximize the fenced area. State the maximum area as well. Show all work.
Answer:
Let x be width and y = length of barn wall y + 2x =20Area = xy= x(20 - 2x)=20x -2x^2dA/dx = 20 - 4xmax at dA/dx =0 so 20 - 4x = 0x=5 y=10 max area is 50 sq ft
PLEASEE HELPPPP
(Solving Two-Step Equations MC)
Solve the equation for x.
−0.18x − 13.7 = 2.41
1: x = −89.5
2: x = −62.7
3: x = 62.7
4: x = 89.5
The equation is solved as x = −89.5. The correct option is 1.
What is a mathematical equation?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
To solve the equation −0.18x − 13.7 = 2.41 for x, we need to isolate x on one side of the equation by adding 13.7 to both sides and then dividing by −0.18:
−0.18x − 13.7 = 2.41
−0.18x = 2.41 + 13.7
−0.18x = 16.11
x = 16.11 / (−0.18)
x = −89.5
Therefore, the solution to the equation is x = −89.5. the correct option is 1.
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Find the length of the rectangular prism.
The length of the rectangular prism given the volume, width and height is 19 yd.
What is the length of the rectangular prism?Volume of a rectangular prism = length × width × height
Volume of the prism = 2,280 yd³
Width of the prism = 20 yd
Height of the prism = 6 yd
Length of the prism = x
So,
Volume of a rectangular prism = length × width × height
2,280 = x × 20 × 6
2,280 = 120x
divide both sides by 120
x = 2,280 / 120
x = 19 yd
Therefore, the length is 19 yd
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Jenny has some tiles in a bag. The tiles are of three different colors: purple, pink, and orange. Jenny randomly pulls a tile out of the bag, records the color, and replaces the tile in the bag. She does this 50 times. The results are recorded in the given table:
Color of Tile Purple Pink Orange
Number of times the tile is drawn 6 18 26
What is the experimental probability that Jenny will pull out an orange tile? (5 points)
a
fraction 18 over 26
b
fraction 24 over 26
c
fraction 24 over 50
d
fraction 26 over 50
The experimental probability that Jenny will pull out an orange tile is option d.) fraction 26 over 50 or [tex]\frac{26}{50}[/tex].
What is an Experimental Probability?Based on the results of an experiment or a real-world scenario, the experimental probability is a measurement of the chance that an event will take place. By dividing the number of positive outcomes (or the frequency of an event) by the entire number of possibilities that may occur, it is determined (or the total number of trials).
Given:
[tex]Color of Tile\quad\qquad | Purple | \; Pink | \; Orange\\Number of times drawn 6 | 18 | 26[/tex]
Given data indicates that an orange tile gets drawn [tex]26 \,times[/tex] total. Jenny goes through the procedure [tex]50\, times[/tex], thus there are [tex]50[/tex] drawings in all.
We divide the experimental chance of drawing an orange tile (26 times) by the total number of draws (50), to get Experimental Probability as:
The experimental Probability of drawing an orange tile =[tex]Number \,of times \,orange\, tile\, is \,drawn \,/ \,Total\, number \,of \,draws[/tex]= 26/50
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What else would need to be congruent to show that APQR = ASTU by ASA? T Given: P OA.
The thing that would be needed to be congruent to show that APQR = ASTU by ASA is A. <Q ≡ <T
How to prove congruenceTo prove the congruence of triangles ΔPQR and ΔSTQ, we need to establish that the angle Q in ΔPQR is congruent to the angle T in ΔSTQ, in addition to the given conditions that PQ = ST and ∠P = ∠S.
This is because the ASA (angle-side-angle) congruence postulate states that if two triangles have two pairs of corresponding angles and a corresponding side between them equal, then the triangles are congruent.
Therefore, establishing the congruence of the angles Q and T, along with the given conditions, satisfies the requirements of the ASA postulate, and proves the congruence of ΔPQR and ΔSTQ.
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Type the correct answer in each box. Use numerals instead of words for numbers.
Soccer ball specifications require a diameter of 8.65 inches with an allowable margin of error of 0.05 inch.
Use this information to complete these statements.
The equation that can be used to find d, the diameter of a new soccer ball, is |
| =
.
The minimum possible diameter of a soccer ball is
, and the maximum possible diameter is
.
Reset
The minimum possible diameter of a soccer ball is 8.60 inches, and the maximum possible diameter is 8.70 inches.
What is equations?
Equivalent equations are algebraic equations that are having identical roots or solutions.
The soccer ball specifications require a diameter of 8.65 inches, with an allowable margin of error of 0.05 inch.
This means that the actual diameter of any new soccer ball should be within the range of 8.60 inches to 8.70 inches. The equation that can be used to find the diameter of a new soccer ball is d = 8.65 ± 0.05, where d represents the diameter. The symbol "±" indicates that the diameter can be either 0.05 inches larger or smaller than the specified diameter of 8.65 inches.
It is important to ensure that the diameter of a soccer ball falls within this allowable range to comply with the specifications and ensure fair play.
Therefore, The minimum possible diameter of a soccer ball is 8.60 inches, and the maximum possible diameter is 8.70 inches.
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Completely factor x^4 - 81
Answer: (x + 3) (x - 3) (x^2 + 9) (x^2 - 9)
Step-by-step explanation: We can use the difference of squares formula to factor x^4 - 81 as (x^2 + 9)(x^2 - 9).
Then, we can use the difference of squares formula again to factor x^2 - 9 as (x + 3)(x - 3).
Therefore, the complete factorization of x^4 - 81 is (x + 3)(x - 3)(x^2 + 9)(x^2 - 9).
Maxine graphs the function m(x) which has a vertex of (-3,4) and passes through the point (-1,-8). Ricardo graphs p(x) = (x+3)² +4
Maxine thinks that both functions have the same axis of symmetry equation. Do you agree or disagree?
Therefore, both functions have the same axis of symmetry equation, which is x = -3.
What is function?In mathematics, a function is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. Functions are one of the central objects of study in mathematics and have many applications in various fields such as physics, economics, engineering, and computer science. A function is typically represented using a mathematical expression or equation, and it can be analyzed and manipulated using a variety of mathematical techniques.
Here,
Both functions have a vertex of (-3,4), which means that the axis of symmetry must be a vertical line passing through x = -3.
For the function p(x) = (x+3)² +4, the axis of symmetry is indeed x = -3.
For the function m(x), since it has a vertex of (-3,4), the equation of the axis of symmetry is x = -3.
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0.4 centimeters converted into millimeters
Answer: 4 milimeters
Step-by-step explanation:
1 centimeters = 10 millimeters
0.4 centimeters= 4 miliimeters
help please. find the sum of the geometric sequence
We have confirmed that the sum of the series is 28/3. Therefore, the correct answer is option (b) 28/3.
What is geometric series?A geometric series is a series of numbers where each term is a fixed multiple of the preceding term. Specifically, a geometric series has the form:
a+ar+ar²+ar³+.....
The given series is a geometric series with first term (a) = 14 and common ratio (r) = -1/2.
Consider sum of series be S, So-
S = a/(1 - r) = 14/(1 - (-1/2)) = 28/3
To see why this is the correct answer, we can also write out the first few terms of the series:
14-7+7/2-7/4+7/8-.....
It is evident that each term is produced by multiplying the one before it by -1/2.
So, the second term is obtained by multiplying the first term by -1/2, the third term is obtained by multiplying the second term by -1/2, and so on.
We can also notice that the sum of the first two terms is 7, the sum of the first three terms is 21/2, and the sum of the first four terms is 28/3. This suggests that the sum of the first n terms of the series might be given by the formula Sn = a(1 - rⁿ)/(1 - r).
We can verify that this is true by using the formula to find the sum of the first four terms:
S4 = 14(1 - (-1/2)⁴)/(1 - (-1/2)) = 28/3
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The area of LMN is 18 ft2, and the area of FGH is 32 ft². If LMN -FGH, what is the ratio of LM to FG?
A. 3:4
B. 3√2:4
C. √3:2
D. 4:3
Please select the best answer from the choices provided
The ratio of LM to FG is 3:4, so correct option is A.
Describe Triangles?A triangle is a polygon with three sides, three vertices, and three angles. It is one of the basic shapes in geometry and has many properties that make it a useful and interesting shape to study.
The sum of the interior angles of a triangle is always 180 degrees, which is a fundamental property of triangles.
Triangles also have many interesting properties related to their sides, angles, and areas. For example, the Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. The area of a triangle can be calculated using the formula 1/2(base x height) or by using various trigonometric functions.
Triangles are important in many areas of mathematics and science, such as in geometry, trigonometry, calculus, and physics. They are also commonly used in architecture, engineering, and design.
If LMN and FGH are similar triangles, then the ratio of their areas is equal to the square of the ratio of their corresponding side lengths.
Let x be the ratio of LM to FG. Then the ratio of their areas is (x²).
So we have:
LMN / FGH = 18 / 32
(x²) = 18 / 32
x² = 9 / 16
x = (3 / 4)
Therefore, the ratio of LM to FG is 3:4, which is option A.
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