prove that for every positive rational number r satisfying the condition r2<2 one can always find a larger rational number r h (h>0 ) for which (r h)2<2 .
Answer: Suppose there exists a positive rational number r such that r^2 < 2. Then we have 2 - r^2 > 0. Let h = (2 - r^2)/4. Then h > 0 because r^2 < 2.
Consider the number rh = r + h. We have:
(rh)^2 = (r + h)^2 = r^2 + 2rh + h^2 = r^2 + 2(2 - r^2)/2 + (2 - r^2)/16
= r^2 + 2 + (2 - r^2)/16
< 2 + 2 + (2 - 2)/16 = 2.
Thus, for any positive rational number r such that r^2 < 2, there exists a larger positive rational number rh = r + h such that (rh)^2 < 2.
Step-by-step explanation:
1/5 x 10 multiply fractions: parts of a group
Grade level and gender Describing the sampling distribution of ħi - Pz PROBLEM: In a very large high school, the junior class has 800 students, 54% of whom are female. The senior class has 700 students, 49% of whom are female. The student council selects a random sample of 40 juniors and a separate random sample of 35 seniors. Let P, - ., be the difference in the sample proportions of females. (a) What is the shape of the sampling distribution of p,, - P..? Why? (b) Find the mean of the sampling distribution. (c) Calculate and interpret the standard deviation of the sampling distribution.
The size of sample are both large enough 40 and 35. The mean and standard deviation of given data is 0.05 and 0.105 respectively.
The shape of the sampling distribution of [tex]\hat{p}_j - \hat{p}_s[/tex]is approximately normal, according to the Central Limit Theorem. This is because the sample sizes are both large enough (40 and 35, respectively) and the population proportions are unknown but assumed to be independent.
The mean of the sampling distribution is the difference in the population proportions of females, which is 0.54 - 0.49 = 0.05.
The standard deviation of the sampling distribution can be calculated as:
[tex]$\sqrt{\frac{\hat{p}_j(1 - \hat{p}_j)}{n_j} + \frac{\hat{p}_s(1 - \hat{p}_s)}{n_s}}$[/tex]
where [tex]\hat{p}_j = 0.54$, $n_j = 40$, $\hat{p}_s = 0.49$, and $n_s = 35$.[/tex]Plugging in these values, we get:
[tex]$\sqrt{\frac{0.54(1 - 0.54)}{40} + \frac{0.49(1 - 0.49)}{35}} \approx 0.105$[/tex]
Interpretation: The standard deviation of the sampling distribution tells us how much we can expect the sample proportion difference to vary across different random samples. In this case, we can expect the difference between the sample proportions of females in the junior and senior classes to vary by about 0.105 on average across different samples.
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Sonia takes a 45
-mile walk every day.
What part of her walk has she completed once she has walked 35
mile?
She has completed 3/4 of her walk, she has walked 3/5 miles.
We are given that Sonia takes 4/5 mile walk everyday.
What is a proportion?A proportion is a fraction of a total amount, the relations between variables, could be direct or inverse proportional, can be built to find the desired measures in the problem.
Consider 4/5 represent the 100 percent.
Using the proportion we can find which part of her walk she completed once she has walked 3/5 miles.
Find out what percentage represent 3/5
Let x be the percentage that represent 3/5
Then convert to fraction number
4/500 = 3/5x
x = 75
Therefore, the value of x in percentage is 75 percent.
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The complete question is
Sonia takes a 4/5 mile walk every day. What part of her walk has she completed once she has walked 3/5 miles
An amount of $100 is invested at 9% compounded semi-annually. What is the balance after 6 years?
O $150.00
O $169.58
O $112.00
O $189.90
The balance (future value) after 6 years of investing $100 at 9% compounded semi-annually is B. $169.58.
What is the future value?The future value represents the present value or investment compounded at an interest rate for a period.
Compounding involves computing interest on accumulated interest, not only on the principal like simple interest.
The future value can be determined using an online finance calculator as follows:
N (# of periods) = 12 semi-annual periods (6 x 12)
I/Y (Interest per year) = 9%
PV (Present Value) = $100
PMT (Periodic Payment) = $0
Results:
Future Value (FV) = $169.58
Total Interest = $69.58
Thus, the investment is expected to be worth B. $169.58 in 6 years.
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Mr.Aba builds a circular patio with a diameter of 12 feet.He covers the patio with paving stones.The cost of the paving stones is $10.50 per square foot.To the nearest dollar,how much do the paving stones cost?
The total cost of the paving stones for building a circular patio with a diameter of 12 feet is C. $1,187.
How is the total cost determined?The area of the circular patio using its diameter and pi (22/7) is determined with the formula below.
The unit cost per square foot is multiplied by the area to determine the total cost.
A = π (d/2)^2
The diameter of a circular patio = 12 feet
The area, A = π (d/2)^2
= 22/7(12/2)^2
= 113.14 ft²
The cost per square foot of paving stones = $10.50
The total cost = $1,187.97 ($10.50 x 113.14)
= $1,188
Thus, using the mathematical operation of multiplication, we can conclude that Mr. Aba's project will cost Option C.
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suppose the mean height in inches of all 9th grade students at one high school is estimated. the population standard deviation is 5 inches. the heights of 7y randomly selected students are 68, 63, 70, 69, 75, 63 and 72.x¯ = Margin of error at 90% confidence level = 90% confidence interval = [
,
]
[smaller value, larger value]
The 90% confidence interval is [64.21, 73.79].
To find the margin of error and confidence interval,
we can use the following formula:
Margin of error [tex]= z* (sigma / \sqrt{(n))[/tex]
where z* is the z-score corresponding to the desired confidence level, sigma is the population standard deviation, n is the sample size, and sqrt represents the square root.
Since we want a 90% confidence interval, the corresponding z-score can be found using a standard normal distribution table or calculator.
The z-score for a 90% confidence level is 1.645.
Plugging in the values we have:
Margin of error = 1.645 * (5 / sqrt(7))
≈ 4.05
So the margin of error is approximately 4.05 inches.
To find the confidence interval, we need to add and subtract the margin of error from the sample mean:
Lower bound = x¯ - margin of error
= (68+63+70+69+75+63+72) / 7 - 4.05
≈ 64.21
Upper bound = x¯ + margin of error
= (68+63+70+69+75+63+72) / 7 + 4.05
≈ 73.79
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what three numbers can be multiplied to get 100000
Answer: 10*100*100
10 times 100 times 100 = 100,000
hope this helped =)
The graphs below show the sales of touchless thermostats, y, for the first 8 months last year. Both graphs show the same information.
Touchless Thermostat
Touchless Thermostat
Sales ($)
80,000
60,000
40,000
20,000
0
Sales
2
4
6
Months since
Start of the Year
Graph A
8
Sales ($)
40,000
30,000
20,000
10,000
0
Sales
To emphasize the slow increase in sales, it would be best for Samantha to use
Samantha should use this graph for her presentation because the sales
2
4 6 8
Months since
Start of the Year
Graph B
Samantha is preparing a presentation and wants to emphasize that the sales increased slowly over the first 8 months last year.
Complete the following sentences.
for her presentation.
Y
on this graph.
To me, Benjamin should use graph A to show the decrease in temperature. It would be best for Benjamin to use this graph for his presentation because the temperature decrease in this graph
What is graph?In mathematics, the graph of a function f is the set of ordered pairs, where {\displaystyle f(x)=y.} In the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.
here, we have,
How to determine the appropriate graph?
The graphs that complete the question are added as an attachment
From the attached graph, we have the following highlights:
The data points on the y-axis of graph A are in an arithmetic sequence i.e. 30, 60, 90, 120....
The data points on the y-axis of graph B are not in an arithmetic sequence i.e. 60, 20, 40, 80....
The above means that graph B is a misleading graph
Hence, Benjamin should use graph A for his report
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According to the U.S. Mint, the number of quarters minted in 2018 was about 2 x 10°. The mass of a quarter is about 6 X 10-3 kg. Write the number of quarters and the mass of a quarter in standard form.
The number of quarters is 2 and mass of quarter is 0.006 Kg.
What is Scientific Notation?With scientific notation, one can express extremely big or extremely small values. If a number between 1 and 10 is multiplied by a power of 10, the result is written in scientific notation.
Given:
The number of quarters minted in 2018 was about 2 x 10°
and, The mass of a quarter is about 6 X [tex]10^{-3[/tex] kg.
As, in standard form the decimal is place after one significant and the rest raised to 10 to the powers and if the number are in power then it can be written in form of decimal.
Here, number of quarters minted is already in standard form 2 x 10° or 2 x 1
and, mass of a quarter can be written as
= 6 X [tex]10^{-3[/tex] k
= 6/ 10³
= 6/ 1000
= 0.006
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WHAT IS THE DOMAIN? PLEASE HELP
The domain of the given relation is:
D: {-3, -2, -1, 0, 1, 3}
What is the domain?For any relation that maps elements from one set into elements of another set, the domain is just the set of the inputs, and usually the domain is the se of the values "x"
Here the domain is the listof numbers in the left,the domain is:
D: {-3, -2, -1, 0, 1, 3}
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Which relationship represents an example of mutualism? A a lynx hunting a snowshoe hare B an owl and a snake feeding on rats C a tapeworm absorbing nutrition from the intestines of a host organism D an ant colony living on an acacia tree and not allowing vines to grow on the bark
The scenerio that represents an example of mutualism would be an ant colony living on an acacia tree and not allowing vines to grow on the bark. That is option D.
What is mutualism?Mutualism is defined as the feeding relationship where by the both organisms which are involved work together to benefit from each other.
A typical example of mutualism is the relationship that exists between the ant and the acacia tree.Here, the ant colony living on an acacia tree and not allowing vines to grow on the bark shows that both organisms benefits from each other.
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_______ the term applies to an ordered set of observations from smallest to largest. the cumulative relative frequency is the sum of the relative frequencies for all values that are less than or equal to the given value
Ascending order is a term that applies to an ordered set of observations from smallest to largest.
This means that the values are arranged in order of increasing magnitude, starting from the lowest value. The cumulative relative frequency is the sum of the relative frequencies for all values that are less than or equal to the given value. This is calculated by adding the relative frequencies of each value from the lowest value up to the given value, and then dividing the sum by the total number of observations. This helps us to determine the percentage of observations that lie below or equal to the given value. For example, given a set of five values, the cumulative relative frequency of the third value would be calculated by adding the relative frequencies of the first two values and then dividing by 5.
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Required Information NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Show that if n is an integer and m+ 5 is odd, then n is even using a proof of contraposition. Rank the options below. We can write n = 2k +1 for some integer k. As n + 5 Is two times an integer, it is even. Assume that n is odd. Thus, if n is odd, then 3 + 5 is even. Then, 13 + 5 = (2K+993 +5=863 +1242 +66+6 = 2(4x3 +672 + 3k + 3).
If n is an integer and m + 5 is odd, then n must be even.
To prove this statement using contraposition, we need to show that if n is odd, then m + 5 must be even. Assume that n is odd, which means we can write n = 2k + 1 for some integer k.
Then, we can rewrite m + 5 as (2k + 1) + 5 = 2k + 6 = 2(k + 3), which is even.
Therefore, we have shown that if n is odd, then m + 5 is even.
By contraposition, we can conclude that if m + 5 is odd, then n must be even. Overall, the proof uses the fact that odd + odd = even and even + odd = odd, along with the definition of even and odd integers.
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what is the probability that delay time is within one standard deviation of its mean value? (round your answer to four decimal places.)
The probability that a data point falls within one standard deviation of its mean value is 0.6827 or 68.27%.
The normal distribution is a continuous probability distribution that describes the distribution of a set of data around its mean. It is often represented by a bell-shaped curve, where the mean is located at the center and the standard deviation determines the width of the curve.
To find the probability that a data point falls within one standard deviation of the mean, we need to calculate the area under the normal distribution curve between the mean minus one standard deviation and the mean plus one standard deviation. This area represents the proportion of the data that falls within one standard deviation of the mean.
The probability of a data point falling within one standard deviation of the mean can be calculated using the following formula:
P(x - s < X < x + s) = 0.6827
Where P represents the probability, X represents the variable we are measuring, x represents the mean value, and s represents the standard deviation.
The value 0.6827 represents the proportion of the data that falls within one standard deviation of the mean in a normal distribution.
This means that if we have a data set with a mean value of 50 and a standard deviation of 5, then there is a 68.27% chance that a randomly chosen data point will fall between 45 and 55.
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What is the value of log4^16
Answer:
Step-by-step explanation:
Using properties of logs:
= 16 log 4
= 9.63
The distance d an object falls after t seconds is given by d = 16t² (ignoring air resistance). To find
the height of an object launched upward from ground level at a rate of 32 feet per second, use
the expression 32t - 16t^2, where t is the time in seconds. Factor the expression.
The object will hit the ground in 2 seconds.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The distance d an object falls after t seconds is given by d = 16t²
To detemine the height of an object launched upward from ground level at a rate of 32 feet per second, use the expression 32t - 16t^2, where t is the time in seconds.
Therefore, put h = 0 in the equation;
0 = 32t - 16t²
16t² = 32t
16t = 32
t = 2
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find mGHJ in degrees inscribed angles
If the measure of the intercepted arc GHJ is 180°, the measure of the inscribed angle GHJ will be mGHJ = 360° - 180° = 180°.
What is angle?Angel is a geometric figure that can be described as the amount of rotation between two straight line or planes and angles is measured in degree with the full circle being 360°.
The measure of an inscribed angle in a circle is always equal to the measure of its intercepted arc. The measure of the arc intercepted by a central angle is determined by the formula, mGHJ = 360° - mJKH. Therefore, the measure of an inscribed angle in a circle with intercepted arc GHJ is equal to mGHJ = 360° - mJKH. This means that the measure of an inscribed angle in a circle can vary depending on the measure of its intercepted arc. For example, if the measure of the intercepted arc GHJ is 180°, the measure of the inscribed angle GHJ will be mGHJ = 360° - 180° = 180°.
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When simplifying an expression like (x2yz4)5 , what should you do with the little 5 on the outside is the parentheses?
Question 3 options:
Distribute it to all variables by dividing their exponents
Distribute it to all variables by multiplying their exponents
Distribute it to all variables by adding their exponents
Distribute it to all variables by subtracting their exponents
Answer:
B
Step-by-step explanation:
Answer:
B: Distribute it to all variables by multiplying their exponents
Step-by-step explanation:
GDP has many known biases that make it a poor absolute measure of the welfare of a society. Why might GDP still be a good measure of changes in welfare?
Select one:
a.
The underground economy bias is rapidly changing.
b.
The biases may be relatively constant over time.
c.
This question is silly; GDP can’t be used to measure change in welfare.
d.
The biases are mainly political and they can change with different election results.
As research have shown that GDP has many known biases that make it a poor absolute measure of the welfare of a society. A reason why GDP will still be a good measure of changes in welfare will likely be because biases may be relatively constant over time. The Option B is correct.
Why do GDP produce poor measure of welfare?GDP is a poor indicator of a society's standard of living because it does not directly account for leisure, environmental quality, levels of health and education, activities conducted outside the market, changes in income inequality, increases in variety, increases in technology, and so on.
So, GDP does not directly measure the things that make life worthwhile, but it does measure our ability to obtain many of the inputs that make life worthwhile. GDP, however, is not a perfect measure of happiness. Some factors that contribute to a happy life are excluded from GDP.
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Nico, Aditi, Erick, Raj, and Sandra are solving the equation. Two-fifths (5 + x) = 8 Each student begins to solve the problem as shown. Nico Aditi Erick Two-fifths (5 + x) = 8. (Five-halves) two-fifths (5 + x) = 8 (five-halves) Two-fifths (5 + x) = 8. Five-halves (5) + five-halves x = (five-halves) 8 Two-fifths (5 + x) = 8. Two-fifths (5 + x) minus 5 = 8 minus 5 Raj Sandra Two-fifths (5 + x) = 8. (one-half) two-fifths (5 + x) = 8 (one-half) Two-fifths (5 + x) = 8. two-fifths (5) + two-fifths x = 8 Which students are correct in their approach to solving the problem? Select three options. Nico Aditi Erick Raj Sandra
The correct students in their approach to solving the problem are Aditi, Erick, and Raj. Nico and Sandra's approaches are incorrect.
The following are the correct approaches to solving the equation:
Aditi: two-fifths (5 + x) = eight. five-hundredths (5) + five-hundredths x = (five-halves) 8
Erick: two-fifths (5 + x) equals eight. two-fifths (5 + x) minus 5 equals eight minus five.
Raj: two-fifths (5 + x) = eight. two-fifths (5) + two-fifths x = eight.
As a result, Aditi, Erick, and Raj are the correct students in their approach to solving the problem. The approaches of Nico and Sandra are incorrect.
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Market Foods sells 24 cans of soda for $6.79, a 128-ounce bottle of detergent for $2.89, a 13.8-ounce can of peanuts for $2.59, and a cooked 1.75-pound chicken half for $2.65
According to the information, the unit price of the products is: $0.28 for each can of soft drink, $0.022 for each ounce of detergent, $0.18 for each ounce of peanuts, $0.0033 for each gram of cooked chicken.
How to calculate the unit price of products?To calculate the unit price of the products we must perform the following procedure:
We must divide the value of each product into the amount of product as shown below:
$6.79 / 24 cans = $0.022$2.89 / 128oz = $0.022$2.59 / 13.8oz = $0.18$2.65 / 793.7g (1.75 lbs) = $0.0033Accordingly, the unit price of these products is the result of these divisions.
Note: This question is incomplete. Here is the complete information:
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Which statement is missing from step 4 above? Part a
part b which of the following reasons complete step 4?
The missing statement from step 4 is that the angles OAKRV, OASVT, OARQP, and OAPQR are congruent.
What is congruent?Congruent is a term used in mathematics to describe two figures or objects that have the same shape and size. This means that the two objects have identical angles and sides, so they can be perfectly superimposed on each other.
This can be concluded using the Angle-Angle-Side (AAS) Theorem, which states that if two triangles have two angles and a side in common, the triangles are similar. Since the angles OAKRV, OASVT, OARQP, and OAPQR are the corresponding angles of the similar triangles AVKR and APQR, the reason that completes step 4 is the converse of the Isosceles Triangle Theorem, which states if two sides of a triangle are congruent, then the angles opposite those sides are congruent.
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Find the measure of an
exterior angle of a regular
polygon with 36 sides.
[?]°
Enter
Answer:
The measure of an exterior angle of a regular polygon with n sides is given by the formula:
360°/n
For a regular polygon with 36 sides, the measure of each exterior angle is:
360°/36 = 10°
Therefore, the measure of an exterior angle of a regular polygon with 36 sides is 10°.
Step-by-step explanation:
There are 52 cards in a deck with 13 cards of each of the four suits. Marlin draws one card, put its back and draws another one. What is the probability that she draws a hearts card and then a 6? Enter your answer as a fraction or a decimal rounded to the nearest hundredth.
Answer: 1/52
Step-by-step explanation:
There is a 13/52 chance of drawing a hearts card and then there is a 4/52 chance of drawing a 6
(13/52)(4/52)=1/52
There is a 1/52 chance of Marlin drawing a hearts card and then a 6
Maggie is making 30 sundaes with mint, chocolate, and vanilla ice cream.
1
3
of the sundaes are mint ice cream and
1
2
of the remaining sundaes are chocolate. The rest will be vanilla. How many sundaes will be vanilla? 1 unit = 10 sundaes help!!!!!!!!!!!!!!!!!!!!! Please
Its due BY TOMORROW!
There are how much total chocolate and vanilla sundaes.
Proportionately, the number of sundaes that will be vanilla is 10 sundaes.
What is proportion?Proportion refers to the part or portion of a whole.
Proportions show the relative size (ratio) of a value compared to another.
The difference between proportion and ratio is that proportions are two ratios equated to each other.
The total number of sundaes Maggie is making = 30
The types of sundaes = mint, chocolate, and vanilla ice cream.
Proportions:Mint ice cream = 1/3 = 10 sundaes (1/3 x 30)
The remaining sundaes = 2/3 (1 - 1/3)
= 20 (30 - 10) or (30 x 2/3)
Chocolate ice cream = 1/2 of 20 = 10 sundaes
Vanilla sundaes = 10 (30 - 10 - 10) or (1/2 of 20)
Thus, using the proportional or fractional relationships among the different sundaes, the number of vanilla sundaes that Maggie will make is 10.
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ASAV ANSWER PLAZ HELP
Answer:
man female women man women male female measurement measurement master mysteries milkman milkmaid monk non Mr Mrs nephew nice papa
Solve the system of equations using subtraction. 3x−2y =−1
3x+ y =14 QUICK PLEASEE
The required values are,
x = 3
y = 5.
Linear Equation in two variables:An equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero
Now in the given question,
we have two equations,
3x - 2y = -1 ......(1)
3x + y = 14 .......(2)
subtract (2) from (1), we get
-3y = -15
divide both sides by -3, we get
y = 5
now put this value of y in (2),
3x + 5 = 14
subtarct both sides by 5, we get
3x = 9
divide both sides by 3, we get
x = 3
Hence, the required values are,
x = 3
y = 5
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4-Omertopen
CLIOCOMANIA.COM
what is a solution to a system?
what does a solution look like?
Determine if (10, 2) is a solution to the system
(x-2y = 8
(x + 2y = 14
The solution of the given system of equation is (11, 3/2) and (10, 2) is not a solution of the equations,
What is an equation?A mathematical statement connecting two expressions by equal sign is called an equation.
Given is a system of equations, x-2y = 8 and x + 2y = 14, we are to find the solution and determine if (10, 2) is a solution to the system,
x-2y = 8
x+2y = 14
Adding both the equations,
2x = 22
x = 11
Put x = 11 in any equation to find the value of y,
11 - 2y = 8
2y = 3
y = 3/2
Now, to determine whether (10, 2) is a solution to the system or not, put x = 10 and y = 2 and see if the value is satisfying the equation or not,
10 - 4 = 6
6≠8
Therefore, (10, 2) is not a solution of the equations,
Hence, the solution of the given system of equation is (11, 3/2) and (10, 2) is not a solution of the equations,
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The question is solved for :
Determine if (10, 2) is a solution to the system and what is a solution to a system?
x-2y = 8
x + 2y = 14
A phone sells for $230. It is now on sale for 30% off. How much money will April save if she
buys the phone on sale?
A
B
C
D
$69
$25
$49
$68
Answer:
I believe the answer would be A- $69. I just do 230-30% and I got the answer of 69.
I hope this helped!
Answer:
Option 1. A
Step-by-step explanation:
= (30/100)*230
= (30*230)/100
= 6900/100 = 69.
Thus, your answer is, A.
( There is nothing else I could explain to you! )