Answer:
?
Step-by-step explanation:
How many solutions (m, n) exist for the equation n = √(100 - m²) where both m and
n are integers?
(A) 4
(C) 7
(D) 8
(B) 6
(E) 10
Answer:
A) 4
Step-by-step explanation:
First note that m cannot exceed 10 otherwise 100-m² will be negative and √(100-m²) will not be a real number much less an integer
Enumerate all values of m from 0 through 10, find the square, subtract from 100 and see if the result is a perfect square.- we take the square root and see if it is an integer value. The table below details everything. m and n are integers on in 4 cases m = 0, 6, 8 or 10.
Hence the answer is 4 solutions
m m² 100-m² √(100-m²)
0 0 100 10
1 1 99
2 4 96 9.797958971
3 9 91 9.539392014
4 16 84 9.16515139
5 25 75 8.660254038
6 36 64 8
7 49 51 7.141428429
8 64 36 6
9 81 19 4.358898944
10 100 0 0
What is the simplified form of the quantity x over 4 plus y over 3 all over the quantity x over 3 minus y over 4?
The simplified form of a given phrase x over 4 plus y over 3 all over the quantity x over 3 minus y over 4 is (3x + 4y) / (4x - 3y).
What is an expression?An expression is a combination of some mathematical symbol such that arithmetic operator and variable such that all are constrained and create an equation.
For example 3x +5y
Given the phrase,
x over 4 = x/4
y over 3 = y/3
Combine x/4 + y/3
x over 3 minus y over 4 = x/3 - y/4
Therefore ;
(x/4 + y/3) ÷ (x/3 - y/4)
⇒ (3x + 4y)/12 ÷ (4x - 3y)/12
The second fraction will inverse in multiplication
⇒ (3x + 4y)/12 × 12/(4x - 3y)
⇒ (3x + 4y) / (4x - 3y).
Hence "The simplified form of a given phrase x over 4 plus y over 3 all over the quantity x over 3 minus y over 4 is (3x + 4y) / (4x - 3y)".
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The length of a rectangle is 6 inches longer than its width. What are the possible widths if the area of the rectangle is at least 667 square inches?
Answer:
D, [tex]w\geq 23[/tex]
Step-by-step explanation:
The length is 6 inches longer than it's width, therefore:
[tex]l=w+6[/tex]
The area of the rectangle is AT LEAST 667 square inches, so:
[tex]lw\geq 667[/tex]
Now, we have a system of two equations:
[tex]\left \{ {{l=w+6} \atop {lw\geq 667}} \right.[/tex]
We want to isolate the width, so substitute the first equation into the second to eliminate the length.
[tex](w+6)w\geq 667[/tex]
Simplify:
[tex]w^2+6w\geq 667[/tex]
Since we now have a polynomial equation that needs to be factored, set the value of one side to 0.
[tex]w^2+6w-667\geq 0[/tex]
Now factor the equation:
[tex](w-23)(w+29)\geq 0[/tex]
Taking each factor individually, we find the following:
[tex]w\geq 23\\w\geq -29[/tex]
Since a negative width doesn't make any sense, we can eliminate that solution, and we are left with the correct answer!
[tex]w\geq 23[/tex]
suppose that $a$ and $b$ are digits, not both nine and not both zero, and the repeating decimal $0.\overline{ab}$ is expressed as a fraction in lowest terms. how many different denominators are possible?
The possible denominators are {3, 9, 11, 33, 99}.
What is the Quotient?A quotient is defined as the outcome of dividing an integer by any divisor that can be said to be a quotient. The dividend contains the divisor a specific number of times.
We have been given that a and b are digits, not both nine and not both zero, and the repeating decimal.
⇒ 100x = ab⋅abababab
⇒ x = 0.abababab
Subtract the above equation from 100x = ab⋅abababab,
So 99x = ab
The denominator of this fraction will always be a divisor of 99 when represented in the lowest term = 3⋅3⋅11
According to this, we have the options in the set. {1, 3, 9, 11, 33, 99}.
Since a and b both are not both 9 and not both zero the denominator 1 cannot be possible.
Hence, the possible denominators are {3, 9, 11, 33, 99}.
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f(x)= 3x - 2 and g(x) = 2x+1
Answer:
What do I solve for with these functions?
Step-by-step explanation:
choose the first set in the list of natural numbers, whole numbers, integers, rational numbers, and real numbers that describes the following number.
The given number is a real number.
What are real numbers?A real number is a value of a continuous quantity that can be used to indicate a distance along a line in mathematics.
We are given the following in the question:
{natural numbers, whole numbers, integers, rational numbers, real numbers}
π / 108
We have to tell the type of number that describes the given fraction.
Evaluating the value, we have,
0.0290888208666...........
This is not a natural number or a whole number. This is not a rational number.
Since is an irrational number, thus quotient of an irrational number and a rational number is an irrational number.
Thus, it is a real number.
The complete question is given below:-
Choose the first set in the list of natural numbers, whole numbers, integers, rational numbers, and real numbers that describes the following number. StartFraction pi Over 108 EndFraction.
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I need help −1/1/5+(−3/5)=
Answer:
- 4/5 /decimal form -0.8
Step-by-step explanation:
2. Is 4x-3=19 true, false, or open? (1 point)
true
false
Open
Which graph does not represent a function?
Answer:
Choice 3
Step-by-step explanation:
The graph fails the vertical line test.
identify whether the statement describes inferential statistics or descriptive statistics. the average age of the students in a statistics class is 20 years.
The statement ''The average age of the students in a statistics class is 20 years'' describes descriptive statistics.
As they're used to represent a particular records set, metrics like average, median, mode, standard deviation, and variety are categorized underneath descriptive information.however, when a speculation check is carried out to make inferences about a population from sample records, it's miles known as inferential data.As right here we're given the average age of all 20 students in the magnificence right here, and we are not seeking to prediction from the sample records, and we're directly getting it as a population parameter. therefore descriptive statistics is the correct solution here.via creating summaries of records samples, descriptive statistics can be used to describe the characteristics of a facts set.To learn more about descriptive statistics visit:
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Simplify the following. (Do NOT evaluate!) √80y^3
After simplifying the expression √80y³, we get the answer as 4 y √5 y.
We are given that:
√80y³
We have to simplify it.
We will first make the factors of it.
Factors of 80:
80 = 2 × 2 × 2 × 2 × 5
Factors of y³:
y³ = y × y × y.
Now the expression can be re- written as:
√2 × 2 × 2 × 2 × 5 × y × y × y.
Simplifying it:
2 × 2 × y √5 y
4 y √5 y
Therefore, after simplifying the expression √80y³, we get the answer as 4 y √5 y.
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Simplify the the following
Answer:
Answer is in the picture attached
Solve the equations and check the results a. 4x+5=17-2x
an independent group of food service personnel conducted a survey on tipping practices in a large metropolitan area. they collected information on the percentage of the bill left as a tip for 2525 randomly selected bills. the average tip was 13.1.1% of the bill with a standard deviation of 2.6%2.6%. assume that the tips are approximately normally distributed. construct an interval to estimate the true average tip (as a percent of the bill) with 90% confidence. round the endpoints to two decimal places, if necessary.
90% confidence interval is 11.65 <µ< 114.566 as per standard deviation data.
What is a standard deviation?
The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. When the standard deviation is low, the data are concentrated around the mean, and when it is large, the data are widely dispersed.Sample mean (T) = 13.11%
Sample standard deviation (s) = 2.6
Sample size (h) = 25
significance level = α = 1 -0.90 = 0.1
Degrees of freedom for t- distribution (df) = 24
Critical value = ta/2
df = [tex]t_{0.1}[/tex], df=24 = ±2.80
The margin of error (E) =[tex]t_\frac{a}{2} , df\frac{s}{\sqrt{h} }[/tex]
E=2.8X [tex]\frac{2.6}{\sqrt{25} }[/tex] =1.456
Limits of 90%. Confidence Interval is.
Lowest limit = X' - E = 13.11-1.456 = 11.65
Upper limit= X' + E = 13.11+1.456 = 14.566
90% confidence interval is 11.65 <µ< 114.566 as per standard deviation data.
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midpoint of line segment with endpoints (3.2,2.5) and (1.6,-4.5)
The midpoint of the line segment with the endpoints is (2.4, -1)
How to determine the midpoint of the line segment with the endpoints?The endpoints are given as:
(3.2,2.5) and (1.6,-4.5)
The midpoint of the line segment with the endpoints is calculated as
Midpoint = 0.5 * (x1 + x2, y1 + y2)
So, we have:
Midpoint = 0.5 * (3.2 + 1.6, 2.5 - 4.5)
Evaluate the sum
So, we have:
Midpoint = 0.5 * (4.8, -2)
Evaluate the products
So, we have:
Midpoint = (2.4, -1)
Hence, the midpoint of the line segment with the endpoints is (2.4, -1)
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At a local recreation center, there were 36 people working out, 18 people swimming, and 27 were playing basketball. What percentage of people were there to swim? Round your answer to the nearest tenth.
Answer:
22.2%
Step-by-step explanation:
Total number of people at the recreation center=81
Number of people swimming=18
=18/81 x 100
=22.22222
Round of to the nearest tenth
=22.2%
Underground Floors charges $8 per square foot of wood flooring plus $150 for installation. Woody's Hardwood Flooring charges $6 per square foot plus $200 for installation. At how many square feet of flooring would the two companies charge the same amount for flooring? If you were going to put flooring on your kitchen floor that had an area of 120 square feet, which company would you choose?
AT 25 SQUARE FEET OF FLOORING
CHOOSE WOODY'S HARDWOOD FLOORING
HOW TO COMPARE RATE OF FLOORING OF TWO COMPANY ?Typically, the price of engineered hardwood flooring is $6 to $10 per square foot, plus $1.75 to $2.20 per square foot for installation. High-quality hardwood flooring typically costs between $6 and $13 per square foot from customers. Your home renovation project could be very stressful. Expectations, timeframes, budgets, and the cost of flooring contractors all need to be harmonized.
There will always be a time when you want to give up on the renovation project. For some reason, finding someone to install your flooring is usually the first step.
CALCULATION1 - 8s + 150 = 6s + 200
2s = 50
s= 25 sq.feet
2 - 120 * 8 + 150 = 1110
120 * 6 + 200 = 920
1110 > 920
so choose woody's hardwood flooring.
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What is the mean and the median of 2, 4, 6, and 8?
WILL CHOOSE BRAINLIEST!!!
Answer: 51.96m
Step-by-step explanation:
We can solve this using cosine, remember SOHCAHTOA, so cos is adjacent over hypotenuse.
hyp = 60
adj = ?
[tex]cos = \frac{adj}{hyp}\\cos 30 = \frac{x}{60} \\\\cos30 *60=x\\x=51.96m[/tex]
it takes $24$ minutes for jana to walk one mile. at that rate, how far in miles will she walk in $10$ minutes? express your answer as a decimal to the nearest tenth.
This shows that she covered 0.4 miles in 10mins
Rate of changeSpeed is defined as the rate of change of distance.
If it takes 24 minutes for jana to walk one mile, the rate of Jana is expressed as;
Rate= 24/1 mile
Rate = 24min/mile
In order to determine the distance she walk in 10 minutes, we will have;
Distance in 10min = 10/24
Distance in 10 min = 0.4 miles
This shows that she covered 0.4 miles in 10mins
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What is the difference between positive association and negative association as it pertains to the relationship between two variables?.
A positive association occurs when an increase in one variable is generally associated with the increase in the second variable and a negative association occurs when one variable tends to decrease as the other increases.
What is meant by an association relationship between two variables?An association is any relationship between two factors that produces them subordinate, i.e. knowing the value of one variable gives us some data around the possible values of the moment variable.
The objective of this variable is to utilize clear measurements and visualisations to investigate affiliations among different kinds of factors.
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the area of the rectangle is 14yd squared and the length of the rectangle is 3yds leass than twice the width
The dimensions of the rectangle are:
Length = 7/2 ydWidth = 4 ydTotal area = 14 yd²What is the area?The quantity area expresses the extent of a region on a plane or curved surface. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina.To find the dimensions of the rectangle:
Let,
Area = A = 14Width = wLength = 2w-3A = lwA = (2w-3)wExtend the area equation as follows:
A = 2w2-3wRearrange:
2w2 - 3w - A = 0Substitute known information for A:
2w2 - 3w - 14 = 0To solve quickly, factor the left side (or use the quadratic formula):
(w+2)(w - 7/2) = 0The factorial solutions for w are -2 and 7/2.
Assuming this is a genuine rectangle, the width must be positive.
As a result, the length is:
2(7/2) - 3That is,
7 - 3 = 4Therefore, the dimensions of the rectangle are:
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The complete question is given below:
The area of a rectangle is 14 yd², and the length of the rectangle is 3 yd less than double the width. find the dimensions of the rectangle.
value of x in the equation −3(3x−4)=15−8x?
Answer:x=−19
Step-by-step explanation: work in your head ppl
Answer: -3
Step-by-step explanation:
trust me
In the metric system, how many milligrams are needed to make a gram?
Answer:
In one gram, there are 1000 milligrams.
To convert g to mg, multiply the gram value by 1000.
Suppose Aji and sunshine have to pay $11 in royalties for each Beatles song and $7 for each Donovan song. How many of each type should they put on their CD to minimize their royalty costs?
To minimize their royal costs to $200, the number of Donovan songs to include is 15 and the number of Beatles songs to include is 5.
What are ratios?Ratios are numerical relationships between variables that show how much each variable is contained in another.
Ratios are stated in fractions, percentages, or decimals.
Data and Calculations:Total songs to include in the song = 20
The ratio of Donovan and Beatles = 5:1.5
The number of Donovan songs to include = 15 (20/6.5 x 5)
The number of Beatles songs to include = 5 (20/6.5 x 1.5)
Royalty cost per Donovan song = $11
Royalty cost per Beatles song = $7
Total royalty costs for Donovan and Beatles song = $200 ($11 x 15 + $7 x 5)
Thus, the number of Donovan songs to include is 15 and the number of Beatles songs to include is 5.
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Question Completion:Aji and Sunshine want to make a CD of songs from the 1960s to donate to their school library to be broadcast during school picnics. Sunshine's parents were big fans of the 60s singer Donovan, and they named her after his song "Sunshine Superman." Aji's folks were devotees of the Beatles. Aji and Sunshine want their CD to consist entirely of songs by Donovan and the Beatles. Because Sunshine is named after a Donovan song, she wants to include at least as many Donovan songs as Beatles songs. Aji agrees. In return, Sunshine agrees to include at least five Beatles songs. 5 1.5 To provide enough variety to make the mix interesting, they decide to include at least 20 songs altogether.
solve the problem. a basketball player makes approximately 69% of free throws. if she plays in a game in which she shoots 7 free throws, what is the probability the she will make all 7?
If she plays in a game in which she shoots 7 free throws, the probability that she will make all 7 = 0.0188
For given question,
a basketball player makes approximately 69% of free throws.
So, the probability of success (p) = 0.69
the probability of failure (q) = 0.31
She plays in a game in which she shoots 7 free throws.
So, n = 7
We need to find the probability that she will make all 7.
Using Binomial probability Distribution,
For x = 7,
[tex]P(x = 7) =~ ^7C_7\times (0.67)^7\times (0.31)^{7-7}\\\\P(x=7)= 1\times 0.0606\times 0.31\\\\P(x=7)=0.0188[/tex]
Therefore, if she plays in a game in which she shoots 7 free throws, the probability that she will make all 7 = 0.0188
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Evaluate.
4-6 |3-5| /3
Answer:
0
Step-by-step explanation:
I really need help on 16 and 18 I'm super confused problem because I'm tired but I really need help
Answer:
Hello,
Step-by-step explanation:
16)
Area of the square= 5²=25 (unit of square)
17)
Volume of the cube =3^3 =27 (unit of volume)
18)
side of the cube =5 (unit of lenght)
Volume of the cube = (5 (unit of lenght)) ^3
=125 * (unit of lenght)^3 =125 (unit of volume)
What
is the slope of the line that passes through the points (-4, 6) and (-4, 18)?
Write your answer in simplest form.
What is constant in the simplified form of (x - 6)²?
Answer:
36
Step-by-step explanation:
The constant is the number when complete simplified, which in this case would be only formed by squaring the 6, equaling 36.
Hope this helps! :)
Answer: +36
Step-by-step explanation:
(x - 6)² simplified: x^2 -12x + 36
The constant in this algebraic expression is 36 because it's value or number doesn't change in the expression (x^2 -12x + 36)