As the sample size increases, the variability among the sample means decreases, option A.
The number of observations used to calculate estimates for a certain population is known as the sample size. The sample size was determined by drawing from the population. Sampling is the practise of choosing a portion of the population from which to draw conclusions about the characteristics of the entire population. A subset of a population is chosen for study based on the number of entities in it.
Population data is a sizable collection of information that covers the whole population under investigation. All the components that are investigated for the research make up a population.
Yet, sample data is a component of the population. Generally, computing the entire population is rather cumbersome and challenging. In this instance, a representative sample of the population is chosen. Sample data refers to this sample.
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assume you have a coin that for each flip, there is a 50% chance of coming up heads, and a 50% chance of coming up tails. what is the probability of getting exactly 3 heads out of 5 flips?
The required probability of getting exactly 3 heads after flipping a coin 5 times is equal to 0.3125 or 31.25%.
Using the binomial distribution,
probability of getting heads represents the success = p
Number of time coin flips = n
The probability of getting exactly x successes (heads in this case) in n independent Bernoulli trials ,
P(x) = (ⁿCₓ) × p^x × (1-p)^(n-x)
where (ⁿCₓ) represents the number of ways to choose k successes out of n trials.
The probability of getting exactly 3 heads out of 5 flips,
with a probability of 0.5 for each flip.
n = 5 (5 coin flips)
k = 3 (getting 3 heads)
p = 0.5 (probability of getting heads on each flip)
Using the formula above, we get,
P(3) = (⁵C₃) × 0.5^3 ×0.5^(5-3)
= 10 × 0.125 × 0.25
= 0.3125
Therefore, the probability of getting exactly 3 heads out of 5 flips is 0.3125 or 31.25%.
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based on the pictures, how many hours should the student record on the nighttime picture to complete a day-night cycle?
The number of hours the student should record on the nighttime picture to complete a day-night cycle = 13 hours
The correct answer is an option (c)
We need to find the number of hours the student should record on the nighttime picture to complete a day-night cycle.
From the following pictures we can observe that, the sunrise time is 7:10 A.M. and the sunset timing is 6:10 P.M.
This means that thet daytime is of 11 hours (from 7:10 A.M. to 6:10 P.M.)
We know that the number hours in a day = 24
Let us assume that x represents the nighttime hours.
From this situation we get an equation,
x = 24 - 11
x = 13 hours
And the nighttime cycle would be:
from 6:10 P.M. to 7:10 A.M.
Therefore, the required number of hours = 13 hours
The correct answer is an option (c)
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Find the complete question below.
- Add and subtract rational numbers: word problems ZAL
4) Khalil and Sophia weighed their pet cats. Khalil's cat weighed 18 5/6 pounds and
Sophia's cat weighed 10 1/3 pounds. How much more did Khalil's cat weigh than Sophia's
cat?
Write your answer as a fraction or as a whole or mixed number.
Khalil's cat weighed 8 1/2 pounds more than Sophia's cat.
What is rational number?In mathematics, any integer that can be written as p/q where q 0 is considered a rational number. Additionally, any fraction that has an integer denominator and numerator and a denominator that is not zero falls into the group of rational numbers.
To find out how much more Khalil's cat weighed than Sophia's cat, we need to subtract the weight of Sophia's cat from the weight of Khalil's cat.
Khalil's cat weighed 18 5/6 pounds.
Sophia's cat weighed 10 1/3 pounds.
Subtracting the weights:
18 5/6 - 10 1/3
To subtract mixed numbers, we need to find a common denominator. In this case, the least common multiple of 6 and 3 is 6. So, we can convert the fractions to have a denominator of 6:
18 5/6 - 10 1/3 = 18 5/6 - 10 2/6
Now, we can subtract the whole numbers and the fractions separately:
18 - 10 = 8
5/6 - 2/6 = 3/6
Putting it back together:
8 3/6
We can simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which is 3 in this case:
8 3/6 = 8 1/2
So, Khalil's cat weighed 8 1/2 pounds more than Sophia's cat.
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a bicycle odometer is designed for 27 wheels. what happens if you use it on a bicycle with 24 wheels?
The second wheel has a smaller circumference compared to the first wheel. The second wheel completes a revolution when the wheel turns 75.40 inches, but the odometer reads 84.82 inches.
There are two types of odometers
one mechanical and the other digital.In the case of a mechanical odometer, the worm gear is used to make the gear train, and the overall gear ratio is 1690:1, which means that when the vehicle travels a distance of 1 mile, the mechanical odometer input shaft makes 1690 revolutions during this time. In the case of a digital odometer, a magnetic sensor is used to receive pulses, each of which counts as one revolution. We now have a bicycle odometer designed for 27 wheels. Thus, d₁ = 27 inches is the diameter of the first wheel
d₂= 24 inches is the diameter of the second wheel
The odometer is the distance traveled by the vehicle, given as the number of revolutions of the wheel multiplied by the circumference of the wheel. So for the first wheel, Therefore, in case of first
wheel, [tex]C_1 = πd_1 [/tex]
= π × 27
= 84.82 inches
In case of second wheel,
[tex]C_2 = π × d_2[/tex]
= π × 24 inches
= 75.40 inches
So, [tex]C_1 - C_2 = [/tex] 84.82 inches - 75.40 inches
= 9.42 inches
So we can see that the second wheel has circumference is less as compared to the first wheel.
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Complete question:
bicycle odometer is designed for 27 wheels. what happens if you use it on a bicycle with 24 wheels?
Need help ASAP with homework
Answer:
A
Step-by-step explanation:
Since this is a rectilinear angle, we can find x:
x = 180° - 98° = 82°
Can someone help meee?
Therefore, the equation of the line is 5x - 3y = -15 and the equation of the line passing through E(4,-3) can be expressed using the point-slope form as y = (5/7)x - (20/7).
How are coordinates determined?a) We can rewrite the provided line in the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept, to determine the slope.
y + 1 = (5/7)(x - 4) (x - 4)
y = (5/7)x - (20/7) - 1
y = (5/7)x - (27/7)
This line and the one we're looking for are parallel, thus their slopes are the same (5/7). Hence, the equation of the line passing through E(4,-3) can be expressed using the point-slope form:
y - (-3) = (5/7)(x - 4) (x - 4)
y = (5/7)x - (20/7)
How are equations determined?b) The intercept form of the equation of a line with an x-intercept of 3 and a y-intercept of 5 is:
x/(-3) + y/5 = 1
The result of multiplying both sides by -15 (the least frequent multiple of -3 and 5) is as follows:
5x - 3y = -15
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Write an equation for the nth term of the geometric sequence 896,-448, 224,.... Find the eighth term of this sequence.
896 (-1);
Oa. an
Ob. 9, -224 (-:-1.
a
896(1)
Oc. an-896
;-7
7-1
;7
Od. a=-448 (-1):
; 3.5
The eighth term of the sequence is -14
What is common ratio?
The common ratio between consecutive terms in a geometric sequence is constant. Let's denote this common ratio by 'r'. To find 'r', we can divide any term by the preceding term,
r = -448/896 = -1/2
Now we can use the formula for the nth term of a geometric sequence,
[tex]a_n = a_1 \times p^{n - 1}[/tex]
where '
[tex]a_1[/tex] is the first term and 'n' is the index of the term we want to find.
Substituting the values we have,
[tex]a_8 = 896 (-1/2)^{8-1} \\ = 896 \times (-1/2)^{7} = -14[/tex]
Therefore, the eighth term of the sequence is -14.
So, option A is the correct answer.
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Correct question is "Write an equation for the nth term of the geometric sequence 896,-448, 224,.... Find the eighth term of this sequence.
A) -14
B) -18
C) -19
D) 18"
One of the angles of a parallelogram is 36° greater than another one. Find the angles
of the parallelogram.
The angles are_,_,_,_
Answer:
Step-by-step explanation:
Opposite angles of a parallelogram are congruent.
Adjacent angles equal 180°.
If one angle is 36 ° more than the other than they are supplementary or equal to 180°.
x + x + 36 = 180
2x + 36 = 180
2x + 36 - 36 = 180 -36
2x = 144
2x/2 = 144/2
x = 72
2 angles = 72°
2 angles = 108°
All the angles = 360°.
72 × 2 = 144
108 x 2 = 216
144 + 216 = 360°
So this is correct.
Does anyone know the answer to this?
Answer:
[tex] \frac{a - 3}{a + 2} [/tex]
Step-by-step explanation:
[tex] \frac{ {a}^{2} - 7a + 12 }{ {a}^{2} - 2a - 8} = \frac{(a - 3)(a - 4)}{(a + 2)(a - 4)} = \frac{a - 3}{a + 2} [/tex]
In three to four sentences, describe why CEOs (that is, the chief executive officers or the leaders of large companies) make very high salaries, while their administrative assistants make much less.
Well, CEOs are on the top of the food chain. It takes a lot of work and ambition to become one, and once they are one, CEOs accept a huge amount of responsibility - that means having to take blame if things go wrong and having more tasks to complete such as having to attend numerous meetings, make decisions. They are also on the board of directors.
Assistants do not have to do as much, they likely won't have that much responsibility or experience, their tasks revolve around ensuring meetings are scheduled and performing other ad-hoc duties.
(Not Mine)
What is the following product?
3√5-√2
06/10
O 6/200
O 6/500
O 6/100000
To find the product of this expression, we can use the distributive property:
3√5 - √2 = 3√5 * 1 - √2 * 1
= 3√5 * (√2/√2) - √2 * (3√5/3√5)
= (3√10/√2) - (3√10/5)
= 15√10/5√2 - 3√10/5
= (15 - 3√2)√10/5√2
So the product is (15 - 3√2)√10 / 5√2.
Simplifying this expression by rationalizing the denominator, we get:
= (15 - 3√2)√10 / 5√2 * √2 / √2
= (15√2 - 3 * 2)√10 / 10
= (15√2 - 6)√10 / 10
= (3√2(5 - 2√10)) / 10
Hence, the product is (3√2(5 - 2√10)) / 10.
The product of expression 3√5-√2 is ( 15√2 - 2)√10 / 10
What is Expression?An expression is combination of variables, numbers and operators.
To find the product of this expression
Apply the distributive property:
3√5 - √2 = 3√5 × 1 - √2 × 1
= 3√5 × (√2/√2) - √2 × (3√5/3√5)
= (3√10/√2) - (√10/5)
= 15√10/5√2 - √10/5
= (15 - √2)√10/5√2
So the product is (15 - √2)√10 / 5√2.
Simplifying this expression by rationalizing the denominator, we get:
= (15 - √2)√10 / 5√2 × √2 / √2
= (15√2 - 2)√10 / 10
Hence, the product of expression 3√5-√2 is ( 15√2 - 2)√10 / 10
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how do you graph 2y=-3x
helpppp
Answer:
please see the attached I put the answer.
Step-by-step explanation:
I put the steps I did, to graph it.
PLEASE CHECK GEOMETRY WILL GIVE BRAINLIEST
Answer:
YES!!!
Step-by-step explanation:
An altitude is drawn from the vertex of an isosceles triangle, forming a right angle and two congruent triangles. As a result, the altitude cuts the base into two equal segments. The length of the altitude is 18 inches, and the length of the base is 15 inches. Find the triangle’s perimeter. Round to the nearest tenth of an inch.
Answer: 54 in
Step-by-step explanation:
Since the altitude drawn from the vertex of the isosceles triangle forms two congruent right triangles and divides the base into two equal segments, we can work with one of the right triangles to find the length of the other side of the isosceles triangle.
Let's denote the length of the altitude as a, the length of half the base as b, and the length of the other side of the isosceles triangle as c. From the problem, we know that a = 18 inches and b = 15 inches / 2 = 7.5 inches.
We can use the Pythagorean theorem to find the length of c:
a² + b² = c²
Substitute the known values:
18² + 7.5² = c²
324 + 56.25 = c²
380.25 = c²
Now, take the square root of both sides to find the length of c:
c = √380.25
c ≈ 19.5 inches
Since the isosceles triangle has two sides with equal length, the perimeter is:
Perimeter = base + 2 * c
Perimeter = 15 + 2 * 19.5
Perimeter = 15 + 39
Perimeter = 54 inches
Thus, the perimeter of the isosceles triangle is approximately 54 inches.
A set of wooden blocks includes a triangular prism like the one shown below. Find the volume of the block
A triangular prism whose length is l units, and whose right triangular cross section has base b units and height h units, the volume(V) of the triangular prism 31.5 cubic inches.
Since this figure represents the triangular Prism, it is given in the figure:
Length of triangular prism is 4.5 in.
In the right triangular cross-section,
Base (b) = 2 in and the height (h) = 7 in.
Volume of triangular prism formula: - A triangular prism whose length is l units, and whose right triangular cross section has base b units and height h units, then:
Volume(V) of the right triangular prism is given by V = 1/2xbhl cubic unit
Using the above values; solve for V;
V = Axl, where A is the area of right triangle, or we can write it as:
V = 1/2bhl
⇒ V = 1/2 x 2 x 7 x 4.5 cubic inches.
On simplifying we get, V = 31.5 inches³
Hence, the volume of the triangular Prism is, 31.5 cubic inches.
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are the measured mean values of vcom,1 and vcom,2 the same or different (i.e. within the experimental uncertainty)?
Based on this information, we can conclude that the measured mean values of vcom,1 and vcom,2 are not significantly different from each other and fall within the range of experimental error.
Assuming that the mean value of vcom,1 is 5.2 m/s with an experimental uncertainty of 0.1 m/s, and the mean value of vcom,2 is 5.5 m/s with an experimental uncertainty of 0.2 m/s, we can calculate the difference between the two mean values and compare it with the combined experimental uncertainty.
The difference between the two mean values is 0.3 m/s, which is greater than the combined experimental uncertainty of 0.22 m/s (calculated as the square root of (0.1² + 0.2²)). Therefore, we can conclude that the two mean values are different and outside the range of experimental error.
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The complete question is :
What is the experimental uncertainty of the mean values of vcom,1 and vcom,2, and is the difference between them significant? Can we conclude that the two mean values are the same, or are they within the range of experimental error?
Which equation is represented in the graph? parabola going down from the left and passing through the point negative 3 comma 0 then going to a minimum and then going up to the right through the points 0 comma negative 6 and 2 comma 0 Group of answer choices y = x2 − x − 6
The equation represented by the graph is: y = x² - x - 6. We can solve it in the following manner.
The vertex of the parabola is at (0, -6). We can calculate it in the following manner.
Yes, the equation represented by the graph is: y = x² - x - 6
This is a quadratic equation in standard form, where the coefficient of the x² term is positive, which means that the parabola opens downwards. The equation has a y-intercept of -6 and crosses the x-axis at x = -1 and x = 3. The vertex of the parabola is at (0, -6).
A parabola is a symmetrical plane curve that results from the intersection of a cone with a plane parallel to its side. It is a type of conic section, along with circles, ellipses, and hyperbolas.
A parabola can also be defined as the graph of a quadratic equation, which is a second-degree polynomial. The general form of a quadratic equation in one variable is:
ax² + bx + c = 0
Where a, b, and c are constants and x is the variable. When graphed, a quadratic equation in one variable produces a parabolic curve. The direction and shape of the parabola depend on the sign and value of the coefficient a.
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An ice machine produces ice cubes that are 3/4 inch on each side. What is the volume, in cubic inches, of one ice cube produced by this ice machine? A. 37/4 B. 9/4 C. 9/16 D. 27/64
oh and explain it pls
The volume of one ice cube produced by this ice machine is 27/64 cubic inches.
What do you mean by volume of cube?The volume of a cube refers to the amount of space that is contained within the cube.A cube is a three-dimensional geometric shape that has six equal square faces and all its edges have equal length. The volume of a cube can be found by multiplying the length of its sides together, using the formula:Volume of cube = (length of side)³
The volume of a cube is given by the formula V = S³ where s is the length of one side of the cube.
In this case, the length of one side of the ice cube is 3/4 inch. Therefore, the volume of one ice cube is:
V = (3/4)³ = 27/64 cubic inches.
So, the volume of one ice cube produced by this ice machine is 27/64 cubic inches.
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The volume of one ice cube produced by this ice machine is 27/64 cubic inches. The correct option is D. 27/64.
In cubic inches, of one ice cube produced by an ice machine with each side measuring 3/4 inch.
Volume’ is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a
closed surface. The unit of volume is in cubic units such as m3, cm3, in3 etc. Volume is also termed as capacity,
sometimes.
To find the volume, use the formula for the volume of a cube:
[tex]V = side^3.[/tex]
Determine the side length, which is given as 3/4 inches.
Apply the formula for the volume of a cube:
[tex]V = (3/4)^3[/tex]
Calculate the volume by cubing the side length:
V = (3/4) × (3/4) × (3/4) = 27/64 cubic inches
The volume of one ice cube produced by this ice machine is 27/64 cubic inches.
The correct option is D. 27/64.
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Solve the following system of equations.
Answer:
D
Step-by-step explanation:
y = x² - 4x - 5 → (1)
y = x - 9 → (2)
substitute y = x² - 4x - 5 into (2)
x² - 4x - 5 = x - 9 ( subtract x - 9 from both sides )
x² - 5x + 4 = 0 ← in standard form
(x - 1)(x - 4) = 0 ← in factored form
equate each factor to zero and solve for x
x - 1 = 0 ⇒ x = 1
x - 4 = 0 ⇒ x = 4
substitute these values into (2) for corresponding values of y
x = 1 : y = 1 - 9 = - 8 ⇒ (1, - 8 )
x = 4 : y = 4 - 9 = - 5 ⇒ (4, - 5 )
Which fraction is equivalent to 6/18
Please help asap.
The sample space for tossing a fair coin 4 times is {HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT}.
Determine P(at least 2 tails).
32.25%
37.50%
43.75%
68.75%
From the given sample space the probability of P(at least 2 tails) is 68.75%.
What is probability?Probability is a way to gauge how likely something is to happen. It is a number between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty for the occurrence. Probability is a key idea in mathematics, statistics, and many other disciplines. It is used to describe uncertain events. Many techniques, such as counting techniques, probability distributions, and simulations, can be used to determine probability. Many uses for it include risk analysis, making decisions, and statistical inference.
From the given sample space the outcomes with at least 2 tails are:
{TTTT, TTT H, TT HT, T H TT, H TTT, H HTT, HT HT, HTTH, THHT, THTH, THH H}
Now,
P(at least 2 tails) = 11/16 = 0.6875 ≈ 68.75%
Hence, from the given sample space the probability of P(at least 2 tails) is 68.75%.
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HELPP PLS this is due today. Look at the picture I attatched.
Step-by-step explanation:
Because a cube has 6 sides ...and a cube has equal side lengths so the area of each side is s x s = s^2
then the total is 6 s^2
A girl bought a total of 12 fiction and non-fiction books. The fiction books cost $12 each and the non-fiction books cost $25 each. If she paid $248 altogether, how many of each kind of book did she buy? How do I write that as an expression?
can someone solve this for me
3√2 sin π/3 (x − 2) + 4 = 7
The solution to the trigonometric equation with sine function is x = 2.5.
EquationsStarting with 3√2 sin π/3 (x − 2) + 4 = 7:
First, we can simplify 3√2 sin π/3 to 3, since sin π/3 = √3/2 and 3√2 = 3 x √2 x √2 = 3 x 2 = 6.
6(x - 2) + 4 = 7
6x - 12 + 4 = 7
6x - 8 = 7
6x = 15
x = 2.5
What is general and particular solution?A particular solution to a trigonometric equation is one that is valid for a particular value or range of values of the variable, as opposed to a general solution, which is valid for all conceivable values of the variable.
Finding the general solution, which entails locating all feasible solutions to the equation within a specific range or domain, is frequently necessary while solving trigonometric equations. In order to simplify the problem and describe the answers in a compact form that can be applied to every value of the variable, one often applies a variety of trigonometric identities and algebraic operations to get the general solution.
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A ulangle whose vertices ore P. and A is mapped on a triangle whose vertices P. 04.0 sof ation PU"#" by a ma M en mapped onto triang ch would map /
1. Write an equation (y = a/x) that shows this relationship. Use y as your number of tacos and x as the price 2. How many tacos would you buy if they were $2.40 each ? 3. What would the price of a taco be if you bought 16 tacos? Your answer
Answer:
The equation that shows the relationship between the number of tacos (y) and the price (x) is: y = a/x If we use y as the number of tacos and x as the price of one taco, we can substitute the given values to find a. Let's assume that you would buy 5 tacos when the price is $1.20 each. Then we have: 5 = a/(1.20) Multiplying both sides by 1.20, we get: a = 6 So the equation becomes: y = 6/x Now we can answer the other questions: 2. If the price of a taco is $2.40 each, we can substitute x = 2.40 into the equation to find y: y = 6/2.40 = 2.5 So you would buy 2.5 tacos, whicha man has 32 coins in his pocket, all of which are dimes and quarters. if the total value of his change is 515 cents, how many dimes and how many quarters does he have?your answer is
Answer:
19 dimes and 13 quarters
Step-by-step explanation:
Let's start by defining some variables:Let's call the number of dimes the man has "d".
Let's call the number of quarters the man has "q".We know that the man has 32 coins in total, so we can write:
d + q = 32We also know that the total value of the change is 515 cents. Since dimes are worth 10 cents and quarters are worth 25 cents, we can write an equation for the total value in cents:
10d + 25q = 515
We now have two equations with two variables, which we can solve simultaneously. Let's rearrange the first equation to solve for one of the variables:
d = 32 - q
We can substitute this expression for "d" into the second equation:
10(32 - q) + 25q = 515Simplifying and solving for "q", we get:
320 - 10q + 25q = 515
15q = 195
q = 13
So the man has 13 quarters. We can substitute this value into the first equation to find the number of dimes:
d + 13 = 32
d = 19
Therefore, the man has 19 dimes and 13 quarters.
There are 19 dimes and 13 quarters.
Let x represent the number of dimes and y represent the number of quarters.
There are a total of 32 coins, so:
x + y = 32
We know that the total value of the change is 515 cents
. The value of x dimes is 10x cents and the value of y quarters is 25y cents. So:
10x + 25y = 515
We can simplify the first equation by solving for one variable in terms of the other:
x + y = 32x = 32 - y
Now we can substitute this expression for x into the second equation:
10(32 - y) + 25y = 515
Simplify and solve for y:
320 - 10y + 25y = 515
15y = 195y
y = 13
So there are 13 quarters. We can find the number of dimes by substituting y = 13 into x + y = 32:x + 13 = 32x = 19So there are 19 dimes.
So, There are 19 dimes and 13 quarters.
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Max’s first test score was a 73. His second test score was a 96. What was his percent change? Round to the nearest whole percent of necessary.
To find the percent change, we need to use the formula:
percent change = (new value - old value) / old value * 100%
In this case, Max's old value is 73 and his new value is 96. So:
percent change = (96 - 73) / 73 * 100%
percent change = 23 / 73 * 100%
percent change = 0.3151 * 100%
percent change = 31.51%
Therefore, Max's percent change is 31.51%, rounded to the nearest whole percent, it is 32%.
Quadrilateral ABCD is a parallelogram. Complete the statements to prove that AB = CD and BC = AD.
Given that ABCD is a parallelogram:
Opposite sides of a parallelogram are parallel and congruent. Therefore, AB = DC.
Diagonals of a parallelogram bisect each other. Therefore, the midpoint of AC is the same as the midpoint of BD. Let M be the midpoint of AC, and N be the midpoint of BD.
By the midpoint theorem, BM = DM and BN = AN.
Since BM = DM and BN = AN, we can conclude that quadrilateral ABCD is a parallelogram in which BC || AD and CD || AB.
Therefore, we have shown that AB = CD and BC = AD in parallelogram ABCD.
Six different names were put into a hat. A name is chosen 116 times and the name Grace is chosen 15 times. What is the experimental probability of the name Grace being chosen? What is the theoretical probability of the name Grace being chosen? Use pencil and paper. Explain how each probability would change if the number of names in the hat were different.
Answer:
Try this!!!
Step-by-step explanation:
Experimental Probability:
The experimental probability of an event is found by dividing the number of times the event occurs by the total number of trials. In this case, the name Grace was chosen 15 times out of 116 trials, so the experimental probability of choosing Grace is:
Experimental Probability = Number of times Grace was chosen / Total number of trials
Experimental Probability = 15 / 116
Experimental Probability = 0.1293 or approximately 12.93%
Theoretical Probability:
The theoretical probability of an event is found by dividing the number of favorable outcomes by the total number of possible outcomes. In this case, there are six names in the hat, so the probability of choosing Grace is:
Theoretical Probability = Number of favorable outcomes / Total number of possible outcomes
Theoretical Probability = 1 / 6
Theoretical Probability = 0.1667 or approximately 16.67%
If the number of names in the hat were different, both the experimental and theoretical probabilities would change. For example, if there were only three names in the hat, the theoretical probability of choosing Grace would be 1/3 or approximately 33.33%. The experimental probability would also change based on the number of times Grace was chosen out of the total number of trials. As the number of names in the hat increases, the theoretical probability of choosing Grace decreases, and the experimental probability becomes more accurate as the number of trials increases.