The distribution of the sample means will have a smaller standard deviation
Identifying which will have a smaller standard deviationFrom the question, we have the following parameters that can be used in our computation:
Observations = 9
The population is not given
However by the theorem of the central limit; we understand that
The distribution of the sample means will always have a smaller standard deviation
This is because the sample mean selected from the population might not totally represent the whole population, but would have smaller standard deviation
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Brian is decorating a rectangular bulletin board. He wants to add trim along both diagonals. If MN = 4x - 0.1 meters and NK = 2x + 0.4 meters, then how many meters of trim will Brian need?
The measure of the diagonal of given rectangular bulletin board is 6x+0.3 meters.
Given that, MN=4x-0.1 meters and NK=2x+0.4 meters.
Here, diagonal = MK=MN+NK
= 4x-0.1+2x+0.4
= 6x+0.3
Therefore, the measure of the diagonal of given rectangular bulletin board is 6x+0.3 meters.
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A Father is three times as old as his son. Five years later he will be only 2 ½ times older than his son: Find their present age
Answer: the present age of son is 15 years, and the present age of father is 45 years.
Step-by-step explanation:
Let the age of son be 'x' and that of his father be 'y'.
So according to the question, the 1st equation that can be formed will be:
y = 3(x) ->(1)
[as father's age is 3 times the age of son]
Now after 5 years:
Age of son = (x+5)
Age of father = (y+5)
So according to the question, the 2nd equation that can be formed will be:
(y+5) = 2.5×(x+5) ->(2)
[as father is now two and half times old as his son]
Substituting the value of equation (1) in (2), we get:
(3x+5) = 2.5×(x+5)
=> 3x + 5 = 2.5x + 12.5
=> 3x - 2.5x = 12.5 - 5
=> 0.5x = 7.5
=> x = 7.5/0.5 = 15
Thus, the present age of son is 15 years.
Note : we can calculate the age of father by putting the value of x in equation (1) or (2):
y = 3(x) = 3 × 15 = 45 (putting x in equation 1)
Thus, the present age of father is 45 years.
Aaron flips a penny 100 times. HEADS comes up 58 times. Based on Aaron's experiment, what is the probability that TAILS turns up when a penny is flipped 100 times? Compare the theoretical probability of HEADS coming up to Aaron's experimental probability.
A. 21/50 ; 1/2 < 29/50
B. 29/50 ; 1/2 < 29/50
C. 21/50 ; 1/2 = 1/2
D. 21/50 ; 21/50 <29/50
Answer:
Number of TAILS outcomes = 100 - 58 = 42
Experimental probability of TAILS = Number of TAILS outcomes / Total number of outcomes = 42/100 = 0.42
The theoretical probability of getting HEADS or TAILS is 0.5 each, assuming the penny is fair.
The experimental probability of HEADS is 58/100 = 0.58, which is close to the theoretical probability of 0.5. This suggests that Aaron's experiment is consistent with the theoretical probability. Similarly, the experimental probability of TAILS is 0.42, which is also close to the theoretical probability of 0.5. This further supports the idea that the penny is fair.
I need help please!!!
Siama and Wills used different methods to find the differences between (5x + 6x) and (2x - 1) but they both arrived at the same answer.
I prefer Wills method because it is easier and less complicated.
How to solve differences?Wills method:
(5x + 6x) - (2x - 1)
Subtract both 2x and -1
5x + 6x - 2x - - 1
5x + 4x + 1
In conclusion, Wills method is preferred when both methods are compared.
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Need help with this question
The height d as shown in the right angled triangle is 4.95.
What is height?Height is the vertical distance between two points.
To calculate the height d as shown in the right angled triangle, we use the formula below
Formula:
d = hcos∅.............. Equation 1From the diagram in the question,
Given:
h = 7∅ = 45°Substitute these values into equation 1
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In art class students are mixing blue and red paint to make purple paint. Cameron mixes 5 cups of blue paint and 8 cups of red paint. Dianelys mixes 7 cups of blue paint and 10 cups of red paint. Use Cameron and Dianelys’s percent of red paint to determine whose purple paint will be redder.
What is the answer???
Answer:
2ab(b + 4 - 3a)
Step-by-step explanation:
a^2b + 2ab^2 + 8ab - 7a^2b
= 2ab^2 + 8ab + a^2b - 7a^2b
= 2ab^2 + 8ab - 6a^2b
= 2(ab^2 + 4ab - 3a^2b)
= 2a(b^2 + 4b - 3ab)
= 2ab(b + 4 - 3a)
Haley try to solve the equation log⇩4 2x=5. She got the wrong answer. What was her mistake? What should the correct answer be?
Help DUE! ASAP HELP ASAP
Answer:
Step-by-step explanation:
[tex]log_{4}2x = 5 \\2x = 4^5\\2x = 2^{10}\\x = \frac{2^{10}}{2}\\ x = 2^9\\x = 512[/tex]
Mistake is in step - 3 .
1. Explain and illustrate the difference between and (4) 2. Explain and illustrate the difference between ratio and proportional reasoning. Do not copy definitions from any source but use your own understanding. (4) 3. Illustrate with a drawing or diagram what "fifth" means in each of the following instances: ordinal number unit fraction 4. Show with a diagram 3, using the following: 1.1 the area model 1.2 set mode 1.3 the length model (3) 2. A rectangular piece of paper has a perimeter of 54 cm. Its length is 1 of its width. Find its dimensions. (3) 3. If the given regular hexagon represents one whole: 3.1 Show three sixths. 3.2 Write the equivalence 6.1 above. Represent in the figure given to prove that a set of two halves 3 3 + 6 6 make a whole. 6.3.1 Draw a number line showing a whole made of six equal parts. Show the sum of two halves on the same number line. 6.3.2 Show how you would teach equivalence to grade 4 learners using the number line provided. Your focus should be on the Preparatory MTE1502/102/0/2023 strategy in 5.2 in your study guide. Follow the steps and show how you would unpack the process to solve the problem given. 3 10 of her birthday cake and ㅈ the cake was bought for the birthday? 7.2What fraction is missing to make the cake whole? 7.1 Mavis ate ate of it. What fraction of (4) (1) (1) (2) (3) (3) (2) (2) 3 3/6
The difference between 1/5 and 2/10 is that they are different representations of the same value.
The ratio is a comparison of two quantities while proportional reasoning involves finding an equivalent ratio.
"Fifth" can refer to the ordinal number of a position or the unit fraction 1/5.
The diagram can be used to illustrate fraction concepts.
How to solve1/5 is simple, but 2/10 can be reduced to 1/5 by dividing both numbers by 2. They are both 0.2 or 20%. 1/5 and 2/10 are different fractions with different purposes.
Use 1/5 for 5 parts and 1/5 (simplified from 2/10) for 10 parts. 1/5 and 2/10 = 0.2, ratio reasoning emphasizes ratios between quantities. A 2:3 boys-to-girls ratio compares the constant ratio between changing quantities.
Proportional reasoning maintains constant ratios between quantities, while ratio reasoning uses fractions or ratios to compare relationships. For instance, if distance doubles, so does speed.
Step 3/5: "Fifth" is the ordinal number for the object five places away in a sequence. See diagram. The fifth circle is 1/5 of a whole in unit fraction sequence. Imagine a rectangle divided into five equal parts, each shaded to show 1/5. Shaded part = 1/5 of whole.
To show 25/7 with area model, make 7x25 rectangle and split into 7 equal parts. 25/7 per part.
1.2 The set model:
To represent 25/7, divide 25 objects into 7 equal sets, resulting in 3 objects per set with 1 left over. This represents the fraction of 25/7.
1.3 The length model:
To show 25/7 on a length model, draw a line of 25 units and divide it into seven equal parts. Each part represents 1/7 or 25/7.
Step 5/5
Let's assume the width of the rectangular piece of paper as x cm. Then the length of the paper would be:
Now we know that the perimeter of the rectangle is given by the formula:
So, for this rectangle:
54 = 2(5x + x)
Simplifying and solving for x, we get:
54 = 2(6x)
27 = 6x
x = 4.5 cm
Therefore, the width of the paper is 4.5 cm and the length is 5 times the width which is 22.5 cm.
The difference between 1/5 and 2/10 is that they are different representations of the same value.
The ratio is a comparison of two quantities while proportional reasoning involves finding an equivalent ratio.
"Fifth" can refer to the ordinal number of a position or the unit fraction 1/5.
The diagram can be used to illustrate fraction concepts.
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Boris is playing a role playing game with his friends. He will roll dice to determine if his character casts a spell. The odds in favor of his character casting a spell are 8/7. Find the probability of his character casting a spell.
The Probability of Boris' character casting a spell is 8/15, based on the given odds in favor of 8/7.
The probability of Boris' character casting a spell, we can use the odds in favor of casting a spell. The odds in favor are given as 8/7.
Odds in favor of an event are calculated as the ratio of the number of favorable outcomes to the number of unfavorable outcomes. In this case, the favorable outcomes are the instances where Boris' character casts a spell, and the unfavorable outcomes are the instances where his character does not cast a spell.
Let's represent the probability of casting a spell as P(casting spell). We can use the formula for odds in favor to find the probability:
Odds in favor = Favorable outcomes / Unfavorable outcomes
8/7 = Favorable outcomes / Unfavorable outcomes
To solve for the probability, we need to convert the odds into a fraction. We can do this by considering the odds as a ratio of favorable outcomes to the total number of outcomes.
The odds can be written as:
8/(8+7) = Favorable outcomes / (Favorable outcomes + Unfavorable outcomes)
8/(8+7) = Favorable outcomes / Total outcomes
8/15 = Favorable outcomes / Total outcomes
Since the total outcomes represent all possible outcomes, the denominator represents the total number of outcomes, which includes both the favorable and unfavorable outcomes.
Therefore, the probability of Boris' character casting a spell is 8/15.
In summary, the probability of Boris' character casting a spell is 8/15, based on the given odds in favor of 8/7.
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Precalc question below.
The number of additional copies you could ship by ordering 128 instead of 127 copies is 0 copies.
We have,
To determine the number of additional copies you could ship if you ordered 128 copies instead of 127 copies, we need to compare the costs of ordering each quantity using the given function C(n).
For n = 127:
C(127) = $6.91 x 127 = $878.57
For n = 128:
C(128) = $5.16 x 128 = $660.48
By subtracting the cost of ordering 127 copies from the cost of ordering 128 copies, we can determine the cost difference:
Cost difference = C(128) - C(127)
= $660.48 - $878.57
= -$218.09
Since the cost difference is negative, it means that ordering 128 copies is cheaper than ordering 127 copies.
However, the question asks for the number of additional copies, so we need to consider the whole number of copies.
Rounding down to the nearest whole copy, the number of additional copies you could ship by ordering 128 instead of 127 copies is 0 copies.
Thus,
The number of additional copies you could ship by ordering 128 instead of 127 copies is 0 copies.
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An investment of $2000 is put in account that earns 4% interest, compounded quarterly. Find the amount of money, rounded to the nearest dollar, in the account after
8 years.
Use the formula A = P(1+r/n)^nt to help you find the answer.
Answer: $275
Step-by-step explanation:
A traditional test for extrasensory perception (ESP) involves a set of playing cards, each of which shows a different symbol (circle, square, cross, star, or wavy lines). If C represents a correct guess and I an incorrect guess, what is the probability of
C?
CI (in that order) for two guesses?
CCC for three guesses?
III for three guesses?
The solutions are,
a) the statistical procedure you should use to answer this question is normal approximation.
b) p = 0.1034 is the probability of correctly predicting exactly 20 cards in a series of 100 trials.
c) 0.1238 is the probability of correctly predicting more than 16 cards in a series of 64 trials.
Here, we have,
a)
X - the number of success
following the binomial distribution with p = 1/5
or when np > 5 ,nq > 5
we can use normal approximation
mean = np
sd =sqrt(npq)
b)
here n = 100
P(X = k) = 100Ck * (1/5)^k *(1-1/5)^(100-k)
P(X = 20) = 100C20 (1/5)^20* (4/5)^80
by normal approximation
μ = 20 and σ = 4 For X = 20,
P(19.5 < X< 20.5)
P ( −0.13<Z<0.13 )=0.1034
and p = 0.1034.
c)
P(X > 16)
mean = np = 64/5 = 12.8
sd = sqrt(npq) = sqrt(12.8*.8)= 3.2
P(X > 16)
=P(Z > (16.5 - 12.8)/3.2)
= P(Z> 1.1562)
= 0.1238
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This question is incomplete, here is the complete question:
A test developed to measure ESP involves using Zener cards. Each card shows one of five equally likely symbols (square, circle, star, cross, wavy lines) and the person being tested has to predict the shape on each card before it is selected. Answer questions a-c below to find each of the probabilities requested for a person who has no ESP and is just guessing. a. Determine the statistical procedure you should use to answer this question and explain why. b. What is the probability of correctly predicting exactly 20 cards in a series of 100 trials? c. What is the probability of correctly predicting more than 16 cards in a series of 64 trials?
the value of eva's car is $9000 this value decreased by 15% work out the new value of evs car
Answer:
Step-by-step explanation:express the 15% as a fraction divided by 100.Multiply the result by $9000.
The result is $ 1350
Subtract the result from new price of the car.$9000-$1350
=$7650
Please help and thank you so much
Answer:
SSS∆KLM ~ ∆UTSStep-by-step explanation:
You want to know the postulate used to declare the triangles similar, and the corresponding similarity statement.
Side ratiosThe side length ratios of the larger triangle are ...
45 : 63 : 90 = 5 : 7 : 10 . . . . . divide by 9
For the smaller triangle, they are ...
25 : 35 : 50 = 5 : 7 : 10 . . . . . divide by 5
The ratios of the three side lengths are the same, so the triangles are similar by the SSS postulate.
Similarity statementOne triangle is designated as ∆KLM. In terms of (reduced) ratio units, the sides in order are ...
KL = 10, LM = 7, MK = 5
The corresponding sides in the smaller triangle are ...
UT = 10, TS = 7, SU = 5
This means the similarity statement must be written as ...
∆KLM ~ ∆UTS . . . . . . matches the last choice
__
Additional comment
It is generally helpful to list the sides in some recognizable order (here, longest to shortest) so that the correspondence is clear.
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How many fewer people in the 18-25 year age group have
some form of technology career compared to all other
age groups combined?
Technology Career types for
different age groups (as a number)
41+ yrs
36-40 yrs
26-35 yrs
18.25
690
782
1.784
1673
24312
3.215
2.709
3.567
4.673
14326
15,822
Please select the correct answer from the options
shown.
a. 26,191
b. 28,345
c. 30,139
d. 33,469
Given statement solution:- The fewer people in the 18-25 year age group result is negative, it indicates that the 18-25 year age group has more people with some form of technology career than all other age groups combined. None of the options provided (a, b, c, d) are correct.
To find the number of fewer people in the 18-25 year age group with some form of technology career compared to all other age groups combined, we need to sum up the technology career numbers for all age groups except the 18-25 year age group and then subtract it from the number for the 18-25 year age group.
Sum of technology career numbers for age groups other than 18-25 years:
(41+ yrs) + (36-40 yrs) + (26-35 yrs) = 24312 + 3.215 + 2.709 = 24318.924
Number of fewer people in the 18-25 year age group compared to all other age groups combined:
1673 - 24318.924 = -22645.924
Since the fewer people in the 18-25 year age group result is negative, it indicates that the 18-25 year age group has more people with some form of technology career than all other age groups combined. Therefore, none of the options provided (a, b, c, d) are correct.
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find the expected value of the winnings from a game that has the following payout I cannot proceed without your help :)
The expected value of the winnings from the game is $3.24.
To find the expected value of the winnings, we multiply each possible payout by its corresponding probability and sum them up.
Expected Value = (2 x 0.64) + (4 x 0.18) + (6 x 0.12) + (8 x 0.04) + (10 x 0.02)
Expected Value = 1.28 + 0.72 + 0.72 + 0.32 + 0.20
Expected Value = 3.24
Therefore, the expected value of the winnings from the game is $3.24.
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Find a and b such that f(x) can be written as f(x) = (x +a) (5) 3 −b
The value of variables a and b are,
a = - 4,
b = - 2
WE have to given that;
Function is,
⇒ f (x) = x³ - 12x² + 48x - 62
Now, We can simplify for change the function in the form of
f (x) = (x + a)³ + b as;
⇒ f (x) = x³ - 12x² + 48x - 62
⇒ f (x) = x³ - 12x² + 48x - 62 - 2 + 2
⇒ f (x) = (x - 4)³ + 2
Hence, We get;
By comparing we get;
a = - 4,
b = - 2
Thus, The value of variables a and b are,
a = - 4,
b = - 2
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Can somebody please help me please
The correct solution is,
D. Mean = 50.4,
Variance = 27.2,
Standard deviation = 5.2.
Now, Formula for the mean, variance, and standard deviation of the given values,
Mean (μ) = (Σx) / n
Variance (σ) = (Σ(x-μ)) / n
Standard deviation (σ) = sqrt(σ)
where: Σx = sum of the values
Σ(x-μ)² = sum of the squared differences between each value and the mean
n = number of values
Substituting the given values into these formulas, we get:
Mean (μ) = (50 + 46 + 53 + 51 + 52) / 5
Mean (μ) ≈ 50.4
Variance (σ) = [(14 - 50.4)² + (50 - 50.4)² + (-0.4 - 50.4)² + ... + (2.6 - 50.4)] / 13
Variance (σ) ≈ 27.2
Standard deviation (σ) = √(27.2)
Standard deviation (σ) ≈ 5.2
Therefore, the correct answer is,
D. Mean = 50.4,
Variance = 27.2,
Standard deviation = 5.2.
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The diagram shows a circle inside a square.
Work out the area of the circle.
16 cm
Optional working
The area of the escribed circle is: 201.06 cm²
What is the area of the circle?The formula for the area of a circle is:
A = πr²
where:
A is area
r is radius
From the given diagram, we see that, the side length of the square is 16 cm. Now, we also see that the side length of the square serves as the diameter of the circle and as such:
Radius of circle: r = 16/2 = 8 cm
Thus:
A = π(8²)
A = 201.06 cm²
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Matthew examines the relation shown in the below.
{(4,-11), (3,1), (0,1), (2,6), (3, -1)}
Is the relation a function? Why or why not?
No. There are x values which map to more than 1 y-value.
Yes. Every y-value maps to exactly 1 x-value.
No. There are y-values which map to more than 1 x-value.
Yes. Every x-value maps to exactly 1 y-value.
No, there are x values which map to more than 1 y-value.
Given that Matthew examines the relation as shown in the below.
{(4, -11), (3,1), (0,1), (2,6), (3, -1)}
We need to check whether the relation is a function or not,
So, we know that,
A relation can map inputs to multiple outputs. It is a function when it maps each input to exactly one output. The set of all functions is a subset of the set of all relations.
If any x values are repeated, and the corresponding y values are different, then we have a relation and not a function.
Here we can see that the y values are repeated, so it is not a function.
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Help please!! Thank youuuuu!!!
I’ll give brainliest if you show work as well.
The value of x from given parallel lines is 2.
In the given figure, three lines are parallel and two lines are passing through.
When three or more parallel lines are cut by two transversals, the line segments formed are proportional.
That is, 2x/x = (x+4)/(4x-5)
2/1 = (x+4)/(4x-5)
2(4x-5)=1(x+4)
8x-10=x+4
8x-x=4+10
7x=14
x=2
Therefore, the value of x from given parallel lines is 2.
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please help! thank uu ~ :)
Answer:
certain
Step-by-step explanation:
The question says "strawberry OR cherry chew", which means if you have only 17 strawberry and 3 cherry chews, the answer is certain, as you will always pull out one of those options.
What is the slope below
Answer: -5/4
Step-by-step explanation:
Solve the system of equations using elimination. 6x + 6y = 36 5x + y = 10 (1, 5) (2, 0) (3, 3) (4, 2)
Answer:
begin equation begin cases x = 1y = 5 end cases end equation. Rearrange like terms to the same side of the equation
Step-by-step explanation:
begin equation begin cases x = 1y = 5 end cases end equation. Rearrange like terms to the same side of the equation
What does a positive scatter plot represents y= 2x+0.9
Answer:
Pretty sure the answer is A
Step-by-step explanation:
Which expression is equal to 3√5/√11
A.√33/5
B.3√55/11
C.3√55/√11
D.O√55/11
Answer:
B
Step-by-step explanation:
3√5/√11 = 2.02
3√55/11 = 2.02
so,
3√5/√11 = 3√55/11
A certain airline requires that carry-on luggage is designed to fit within a rectangular prism with a length of 22 inches, a height of 14 inches, and a width of 9 inches. What is the maximum possible volume of a piece of carry-on luggage?
The maximum possible volume for a piece of carry-on luggage is given as follows:
2772 cubic inches.
How to obtain the volume of a rectangular prism?The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:
Volume = length x width x height.
The dimensions for this problem are given as follows:
22 inches, 14 inches and 9 inches.
Hence the volume is given as follows:
22 x 14 x 9 = 2772 cubic inches.
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In the figure below, . Find .
Answer:
x = 93
Step-by-step explanation:
the adjacent angle to x ( on the right side) and 48° are alternate angles and are congruent.
the 3 angles lying on line m sum to 180° , that is
39 + x + 48 = 180
x + 87 = 180 ( subtract 87 from both sides )
x = 93
Choose the words to finish the explanation of how to plan a coordinate proof to show that all isosceles right triangles are similar.
The words that has to be kept in the blank space to prove the similarity are (a, 0), (0, a) and scale factor.
Here we have to choose the words to finish the explanation of how to plan a coordinate proof to show that all isosceles right triangles are similar.
Isosceles right triangles are the right triangles which has the two legs of same length.
For that first consider an isosceles right triangle with legs having length "a".
Then if we place the triangle with one of the vertices at origin, then since the length of the legs is "a", the other vertices will be at (a, 0) and (0, a).
If we place another triangle similarly with length of legs "b", then we have to prove that they are similar.
For them to be similar, there must exist a scale factor that maps one triangle on to the other.
Hence the spaces are (a, 0), (0, a) and scale factor.
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