Answer:
B
Step-by-step explanation:
Show that there exist a rational number a and an irrational number b such that a^b is irrational.
Answer:
In explanation below.
Step-by-step explanation:
Presumably, the proof you have in mind is to use a=b=2–√a=b=2 if 2–√2√22 is rational, and otherwise use a=2–√2√a=22 and b=2–√b=2. The non-constructivity here is that, unless you know some deeper number theory than just irrationality of 2–√2, you won't know which of the two cases in the proof actually occurs, so you won't be able to give aa explicitly, say by writing a decimal approximation.
in a multiple regression model, which of the following is correct regarding the value of the adjusted r^2?
A. It can be negative
B. It has to be positive
C. It can be larger than 1
D. It has to be larger than the coefficient of multiple determination
The correct option is option (B) .
In a Multiple regression Model , the value of adjusted r-Squared is positive.
Adjusted r-Squared :
Adjusted r-squared is a modified version of r-squared adjusted for the number of predictors in the model. The fitted r-squared increases only if the new term improves the model beyond what would be expected by chance. This is reduced if the predictor happens to not improve the model more than expected.
The formula for r-squared,
Adjusted r-squared= 1 - [ ( 1 -r²)(n-1)/(n-k-1)]
where
N --> number of points in the data sample.
K --> number of independent regressors, i. number of variables in the model excluding or constant.
r²--> Indicates how well a term (data point) fits a curve or line.
r-squared values range from 0 to 1 and are commonly stated as percentages from 0% to 100%.
100% r-squared means that all movements in the security are completely explained by movements in the index.
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(06.02)
Match the verbal expression (term) with its algebraic expression (definition).
Match
Term
A variable cubed
Quotient of some number and three
Product of an unknown value and three
Three less than a variable
Three more than some number
Definition
A) 3a
B) b + 3
C) z + 3
D) y - 3
E) x³
The values of the statements are x³, b ÷ 3, 3a, y-3, z+3.
What is an Expression?
An expression is a mathematical statement which consists of variables, constants and mathematical operators.
Hence the answer is, the statements are:
A variable cubed : x³
Quotient of some number and three: b ÷ 3
Product of an unknown value and three : 3a
Three less than a variable : y-3
Three more than some number : z+3
Hence the answer is, the values of the statements are x³, b ÷ 3, 3a, y-3, z+3.
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A certain brand of coffee comes in two sizes. An 11.5-ounce package costs 3.19. A 30.6-ounce package costs 7.98. Find the unit price for each size. Then state which size is the better buy based on the unit price. Round your answers to the nearest cent.
The size that is the better one is 30.6-ounce package costs 7.98.
How to calculate the cost?The 11.5-ounce package costs 3.19. The price per package will be:
= 3.19 / 11.5
= 0.27
A 30.6-ounce package costs 7.98. The cost per package will be:
= 7.98 / 30.6
= 0.26
In this case, it should be noted that the cheaper one.is the better buy. This was illustrated as the 30.6-ounce package costs 7.98.
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In just two days it will be seven days after three days before Halloween. What is the date today ?
Answer:
November 2nd
Step-by-step explanation:
Halloween = Oct. 31
3 days before Halloween (Oct. 31) is Oct. 28
7 days after that it is Nov. 4
2 days before is November 2nd
Evaluate 1/2x^4 – 3/4x² for x = 2.
Answer:
[tex]-\frac{5}{32}[/tex]
Step-by-step explanation:
[tex]\frac{1}{2(2)^4}-\frac{3}{4(2)^2} \\\frac{1}{32} - \frac{3}{16} = -\frac{5}{32}[/tex]
Fall Math Benchmark
1. For the scenario given, explain in words your process for solving the problem.
Two rectangular walls need to be painted. They are each 12 feet high and 23 feet
wide. It costs $1.50 per square foot for paint. How much will it cost to paint the
walls?
The amount that it will cost to paint the walls, given the cost per square foot and the dimensions of the rectangular walls is $828
How to find the cost?First, find the area of the rectangular walls by the formula for the area of a rectangle which is:
= Length x Width
The area of the rectangles is therefore:
= 12 x 23
= 276 feet ²
The area of the two rectangular walls is:
= 276 + 276
= 552 feet ²
The cost to paint the walls is:
= Area of walls x cost per square feet to paint
= 552 x 1.50
= $828
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Davis digs a hole at a rate of 3/4 feet every 10 minutes. After digging for 40 minutes, Davis places a bush in the hole that fills exactly 7/8 feet of the hole.
Relative to ground level, what is the elevation of the hole after placing the bush in the hole?
Enter your answer as a simplified fraction. NOT MIXED NUMBER
The elevation of the hole after placing the bush in the hole is 17/8 feet
How calculate the elevation of the hole after placing the bush in the hole?
Given: Davis digs a hole at a rate of 3/4 feet every 10 minutes
After digging for 40 minutes, Davis places a bush in the hole that fills exactly 7/8 feet of the hole
This involves subtraction and multiplication of fractions
Since the rate of digging = 3/4 feet every 10 minutes
Thus, after digging for 40 minutes, the depth will be:
3/4 × 4 = 3 feet
If Davis places a bush in the hole that fills exactly 7/8 feet of the hole, the remaining depth or elevation will be:
3 feet - 7/8 feet = 17/8 feet
Therefore, after placing the bush in the hole, the elevation of the hole is 17/8 feet
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What is the slope of the line represented by the equation 2x-5y=9
The slope of the line represented by the equation 2x - 5y = 9 is 2/5 .
In the question ,
it is given that ,
the equation of the line is 2x - 5y = 9 .
we know that the equation of the line is represented as y = mx + c ,
where slope of the equation is "m" .
So , rewriting 2x - 5y = 9 in the form of y = mx + c ,
w get ,
2x - 5y = 9
5y = 2x - 9
dividing both sides of the equation 5y = 2x - 9 by 5 ,we get
y = 2/5x - 9/5
y = (2/5)x - 9/5
the slope is = 2/5 .
Therefore , The slope of the line represented by the equation 2x - 5y = 9 is 2/5 .
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Dora is paid a salary of $50,000per year. How much would she be paid if she's weekly
Answer:
about 958 dollars
Step-by-step explanation:
50,000÷52.1429 is about 958 dollars weekly
1-8: MathXL for School: Practice & Problem Solving
0 Assignment is past due (10/27/22 11:59pm)
Question Help
The populations of Cities A and B are 3.7 x 105 and 2,115,000, respectively. The population of City C is twice the population
of City B.
The population of City C is how many times the population of City A?
1.8.PS-15
The population of City C is times the population of City A.
(Round the final answer to the nearest whole number as needed. Round all intermediate values to the nearest tenth as needed.)
Answer:
11
Step-by-step explanation:
You want the ratio of the populations of city C and city A, given city C is 2 times the 2,115,000 population of city B, and city A's population is 3.7×10⁵.
EvaluationThe ratio of interest is ...
2B/A = 2(2115000)/(3.7×10⁵)
A calculator provides an easy answer to the value of this expression. (See attached.)
City C is about 11 times the population of City A.
__
Additional comment
If you want to work this out "by hand", you will need to find the quotient of ...
4230000/370000 = 423/37 = 11 17/37 ≈ 11
because 17/37 < 1/2.
princeton pretzels picks a package box A 6in 7in 6in box B 3in 8in 9in calculate the volume of each box answer
Answer:
box a - 252 inches squared (6 x 7 x 6)
box b - 216 inches squared (3 x 8 x 9)
Step-by-step explanation:
18 POINTS AND WILL MARK BRAINLIEST PLS HELP ME IT WAS DUE LAST WEEK
Answer:
B
Step-by-step explanation:
y intercept is 500 so that is how much was in the tank when it started
And slope is -9 which is the steady decline in water
Hopes this helps
Answer: i'm writeing this so you can mark the other person brainliest
Step-by-step explanation:
Henry drinks 1/2 of a bottle of soda. Sasha then drinks 1/3 of the soda that is left in the bottle. There is now 6 ounces of soda in the bottle. How many ounces of soda were there in the full bottle?
Answer: There were 18 oz. in the full bottle.
Step-by-step explanation:
If there are 6 oz. left, and Sasha drank 1/3 of half the bottle, then that means she drank 3 oz, since 6 is 2/3 of 9, which means that half of the bottle was 9 oz. 9 oz. is half of 18 oz, which means that there were 18 ounces in the full bottle.
g if you randomly select 850 credit card users, what interval will contain the sample proportion for 95% of samples of that size?
The Confidence interval is (0.85,1.05) which contain the sample proportion for 95%of samples size.
Confidence interval is an interval with a confidence level. Confidence interval is always constructed on basis of sample , p = sample statistic - margin of error to sample statistic + margin of error
Confidence interval for a proportion are calculated using the following formula:
p= ( p' - Z√p'(1-q')/n , p'+ Z √p'(1-p')/n ) ---(1)
where, p' ---> sample proportion for sucess
1-p' -----> sample proportion for failure
Z --> Z-value (statistic value)
n---> sample size
we have given that,
sample size ( n)=850 , sample proportion (p') = 0.95 and population proportion= 0.75
a) mean of sample of proportion is same as poplution proportion i.e 0.75 ..
1 -p' = q' = 0.05
Using the formula for margin of error ,
M .E = Z √ p'q'/n ---(2)
as the Z-value for given proportion is 13.46
putting all values in equation( 2) we get,
M.E = 13.45 √0.95×0.05/850 = 0.1005
Now, we shall calculate the confidence interval for given data
confidence interval (p)
= ( 0.95 - 0.100 , 0.95 + 0.100)
p= ( 0.85 , 1.05)
Hence,confidence interval(CI) is (0.85, 1.05).
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Complete Question:
75% of all credit card users carry a balance from month to month. a. If you randomly select 850 credit card users and will compute the sample proportion that carry a balance from month to month, what is the mean of the sample proportion? b. If you randomly select 850 credit card users, what interval will contain the sample proportion for 95% of samples of that size?
A rectangular dining room has a perimeter of 24 meters. Its area is 35 square meters. What are the dimensions of the dining room? IN NEED ASAP CLASS IS ABOUT TO END
The dimensions of the rectangle which form the dining room is 7 by 5 meters.
The perimeter of the rectangle is 24 meters.
The total length of a shape's boundaries is its perimeter. The total lengths of all other edges and sides are added to find a shape's perimeter.
Let the length be a and the width be b.
Hence 2(a + b) = 24
or, a+b = 12
Now the area of the rectangle is given as 35 square meters.
Therefore ab = 35
now we will use these two equations to find the dimension of the rectangle
a+b = 12
or, a = 12 - b
again:
ab = 35
or, (12 - b)b = 35
or, 12 b - b² = 35
or, - b² +12b -35 = 0
or, b² - 12b + 35 = 0
or, (b-7) (b-5) = 0
either b = 7 or b = 5 .
Therefore the value of a from the equations is 5 or 7.
Therefore the dimensions of the dining room are 7 by 5 meters.
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Given the perimeter of 225 ft. Solve for x and then find the indicated side lengths.
Answer:
X=14
Side GF: 41 ft
Side FE: 58 ft
Side DE: 98 ft
Side DG: 28 ft
Step-by-step explanation:
(13+2x)+(4x+2)+(7x)+(X+14)
6x+15+8x+14
14x+29=225
-29. -29
14x=196
/14. /14
X=14
Fill in 14 for x for each side
13+2(14)
13+28
Side GF: 41 ft
4(14)+2
56+2
Side FE: 58 ft
7(14)
Side DE:98 ft
14+14
Side DG: 28 ft
Hopes this helps please mark brainliest
Mrs. Singh is making snack packs for her class to eat on their field trip. She estimates that she will need 35 snack packs. The day of the field trip 4 students are absent and Mrs. Singh actually only needs 31 snack packs. What is Mrs. Singh's percent error?
Singh percent error is approximately 13%.
What is percent error?Percent error is the difference between estimated value and the actual value in comparison to the actual value and is expressed as a percentage.
Mrs. Singh is making snack packs for her class to eat on their field trip. She estimates that she will need 35 snack packs. The day of the field trip 4 students are absent and Mrs. Singh actually only needs 31 snack packs.
Therefore, Singh's percent error can be calculated as follows:
percent error = 35 - 31 / 31 × 100
percent error = 4 / 31 ×100
percent error = 400 / 31
percent error = 12.9032258065
percent error ≈ 13%
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Find the value of the variables in the figure. Explain your reasoning.
The value of the variables in the figure is x = 60 degrees and y = 10 degrees.
From the figure:
x + 120 = 180 (since consecutive interior angles equal to 180)
x = 180 - 120
x = 60 degrees.
3y + 40 + 3x - 70 = 180(since supplementary angles = 180)
3y + 3x - 30 = 180
3(y + x) = 180 + 30
y + x = 210/3
y + x = 70
substitute x value
y + 60 = 70
y = 70 - 60
y = 10 degrees.
Therefore the value of the variables in the figure is x = 60 degrees and y = 10 degrees.
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Find f(x) +g(x) if f(x)=10-3 and g(x)=-x+3
Answer:
10 - x
Step-by-step explanation:
Since f(x) = 10 - 3, we can replace the "f(x)" in the equation with "10 - 3". Likewise, we can replace the "g(x)" in the equation with "-x + 3" because g(x) = -x + 3:
10 - 3 - x + 3
7 - x + 3
10 - x
Boden's account has a principal of $600 and a simple interest rate of 3.5%. Complete the number line. How much money will be in the account after 4 years, assuming Boden does not add or take out any money?
Answer:$84
Step-by-step explanation:
$84 dollars because 3.5 percent of 600 is 21 so if we do 21x4=$84 well atleast that't what i think
if the point D (8. -5) is reflected over the y axis, the coordinates of D would be
If the point D (8. -5) is reflected over the y-axis, the coordinates of D' would be: (-8, -5).
What is a reflection?A reflection can be defined as a type of transformation which moves every point of the object by producing a flipped but mirror image of the geometric figure.
In Geometry, a reflection over the y-axis (y = x) is given by this transformation rule (x, y) → (-x, y).
By applying a reflection over the y-axis to point D, the coordinates of the vertices of point D' include the following:
(x, y) → (-x, y)
Point D = (8, -5) → Point D' = (-8, -5)
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What is the slope of a line perpendicular to the line whose equation is 6x + 2y = -32. Fully simplify your answer.
The slope of a line is m=−3
The slope of a line indicates its steepness. The slope is determined mathematically as "increase over run" (change in y divided by change in x).
Given that
the slope of 6x+2y=−32:
slope using the standard form:
slope m of a line of the form Ax+By=C equals –A/B
A=6, B=2
m=−6/2
simplify
m=−3
Therefore the slope of a line is m=−3
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solve the simultaneous equations
y = 2 - x
6x + 5y = 11
x + 2y = 2
2x + y = 1
Answer:
x = 2
y = 0
Step-by-step explanation:
Here are the simultaneous equations:
[tex]y=2-x\\6x+5y=11\\x+2y=2\\2x+y=1\\[/tex]
There are only two unknown values, so only two equations are needed to find the answer. I will use these:
[tex]y=2-x\\x+2y=2[/tex]
Substitute the first equation into the y in the second equation:
[tex]x+2(2-x)=2[/tex]
Simplify
[tex]x+4-2x=2\\x=2[/tex]
Use the value of x to find y in equation 1:
[tex]y=2-x\\y=2-2\\y=0[/tex]
Shawn had some nickels in a jar. He put 147 nickels in the jar. Now there are 435 nickels in the jar. How many nickels were in the jar at the start?
Responses
A 288288
B 218218
C 312312
D 398398
Answer:
A
288 nickels
Step-by-step explanation:
There are now 435 nickels, after he put in 147. To find the answer, we need to find what the amount of nickels was before Shawn put in the 147. So, we need to subtract 147 from 435.
435 - 147 = 288
So, there were 288 nickels in the jar at the start.
In Cedarburg, the library is due south of the courthouse and due west of the community
swimming pool. If the distance between the library and the courthouse is 12 kilometers and
the distance between the courthouse and the city pool is 13 kilometers, how far is the library
from the community pool?
kilometers
The library is 5 kilometres far from the community pool.
According to the Pythagoras theorem, the square of the hypotenuse of a triangle, which has a straight angle of 90 degrees, equals the sum of the squares of the other two sides. Look at the triangle ABC, where BC² = AB² + AC² is present. The base is represented by AB, the altitude by AC, and the hypotenuse by BC in this equation.
The distance between the courthouse and the library is 12 kilometres and the distance between the courthouse and the city pool is 13 kilometres. Let the distance between the library and the community pool be x and it can be observed that the Courthouse, library and Community hall form a sort of right-angled triangle
So, using Pythagoras theorem, we get
[tex]13^2=x^2+12^2\\x^2=169-144\\x^2=25\\x=5 km[/tex]
So, the library is 5 kilometres far from the community pool.
Therefore, the distance between the library and the community pool is 5 kilometres.
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13) You have $80 and your sister has $160. You are saving
$7 per week and your sister is saving $5 per week. In
how many weeks you and your sister will have the same
amount of money? Write an equation and solve.
Answer: 30 weeks
Step-by-step explanation:
let w = number of weeks
you have = 60 + 7w
she has = 120 + 5w
60+7w = 120 + 5w
7w-5w = 120-60
2w = 60
w = 30 weeks
a) 6x(3x+5)-2x(9x-2)=17
b) 2x(3x -1)-3x(2x+11)-70=0
Answer:
a). 18x+30 - 18x+4=17
18x-18x 30+4 =17
34=17
[tex](a) \: { \pink{ \boxed{ \blue{ \sf{x = \frac{13}{30}}}}}}[/tex]
[tex](b) \: { \pink{ \boxed{ \blue{ \sf{x = -2}}}}}[/tex]
Step-by-step explanation:
[tex](a){ \red{ \sf{6x(3x + 5) - 2x(9x - 2) = 17}}}[/tex]
[tex]{ \red{ \sf{ { \cancel{18x}^{2} + 30x \: { \cancel { - 18x}^{2} + 4 = 17}}}}} [/tex]
[tex]{ \red{ \sf{30x + 4 = 17}}}[/tex]
[tex]{ \red{ \sf{30x = 17 - 4}}}[/tex]
[tex]{ \red{ \sf{30x = 13}}}[/tex]
Divide both the sides by 30 then,
[tex]{ \red{ \sf{ \cancel {\frac{30}{30}}}}}{ \red{ \sf{x} = \frac{13}{30}}} [/tex]
[tex]{ \red{ \boxed{ \green{ \sf{x = \frac{13}{30}}}}}} [/tex]
[tex](b) { \red{ \sf{2x(3x - 1) - 3x(2x + 11) - 70 = 0}}}[/tex]
[tex]{ \red{ \sf{ { \cancel{6x}^{2} - 2x}}}} \: \: { \red{ \sf{ \cancel { - 6x}^{2} - 33x - 70 = 0}}} [/tex]
[tex]{ \red{ \sf{ - 2x - 33x - 70 = 0}}}[/tex]
[tex]{ \red{ \sf{ - 35x - 70 = 0}}}[/tex]
[tex]{ \red{ \sf{ - 35x = 70}}}[/tex]
Divide both the sides by -35 then,
[tex]{ \red{ \sf{ \cancel {\frac{ - 35}{ - 35}}}x}}= { \red{ \sf{ { - \frac{ \cancel{70} ^{2} } { \cancel{35_{1} }}}}}}[/tex]
[tex]{ \red{ \boxed{ \green{ \sf{x = -2}}}}}[/tex]
Please answer this question, URGENT 50 POINT
Answer: Use your brain aka 12 and 7
Step-by-step explanation:isn't this urgent?
a fruit basket contains apples, oranges, and tangerines in the ratio 3:2:5, respectively. what is the total number of apples, oranges, and tangerines in the fruit basket?
The total number of apples, oranges, and tangerines in the fruit basket is in the ratio 10 or 10x
In mathematics, a ratio is a comparison of two or more numbers that indicates their sizes in relation to each other.
A ratio compares two quantities by division, with the dividend or number being divided termed the antecedent and the divisor or number that is dividing termed the consequent.
We know that : the ratio of apples : oranges : tangerines = 3 : 2 : 5.
The total number of apples, oranges, and tangerines in the fruit basket is the total number of ratio, that is 3 + 2 + 5 = 10.
Because of the question is not contain information about the number of pieces, we can describe the dividend with x (or unknown value). So, the total number of apples, oranges, and tangerines in the fruit basket with ratio, that is 10 or 10x.
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