Answer:
To obtain the fraction first we need to obtained the number. The number can be identified by using algebraic expression.
The fraction is .
Given:
The given fraction is .
Let the numerator is .
The numerator is 18 less than denominator is , the fraction is .
Write the algebraic expression as per question to find the number.
Calculate the fraction.
Thus, the fraction is .
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Step-by-step explanation:
Answer:
see below
Step-by-step explanation:
assume top a, bottom b
so a/b =2/5
so a=2/5b
b=a+18 = 2/5b+18
so 3/5b = 18
b = 30
a=12
fill in the blank. because it is typically too expensive and too time consuming, researchers often select a/n___, a group of people that are representative of the larger population.
Because it is typically too expensive and too time consuming, researchers often select a sample, a group of people that are representative of the larger population.
A sample is a smaller group of individuals selected from a larger population for the purpose of studying and making inferences about the population. Sampling is used when studying the entire population is not feasible due to limitations in time, resources, or practicality. The goal is to select a sample that accurately represents the population in terms of key characteristics such as age, gender, education level, etc. The sample must be representative of the population, meaning that it should accurately reflect the characteristics of the population. This is important because any biases or inaccuracies in the sample can lead to incorrect inferences about the population. A well-selected sample should also have a large enough size to provide meaningful results, yet not be so large that it becomes difficult to manage or too expensive to study.
In conclusion, sampling is a crucial step in research because it enables researchers to study a portion of the population, rather than the entire population, in order to make inferences about the larger group.
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i need help with percentage homework
The percentage values are as follows: 75, 135, 60, 50, 245, 105, 175, 315, 450, 60, 125, 140, 280, 150, 320, 150.
What is percent?A % is a relative figure that represents the hundredth part of any amount. One percent (symbolized 1%) is one hundredth part; consequently, 100 percent denotes the complete amount and 200 percent defines twice the supplied amount. percentage. Mathematics percentile is a related topic. A percentage is a fraction of a whole represented as a number between 0 and 100. Nothing is zero percent, everything is 100 percent, half of everything is fifty percent, and nothing is zero percent. To calculate a percentage, divide the share of the total by the total and multiply by 100.
Here,
1a. 150% of 50
=1.5*50
=75
1b. 150% of 90
=1.5*90
=135
2a. 100% of 60
=1*60
=60
2b. 50% of 100
=0.5*100
=50
3a. 350% of 70
=3.5*70
=245
3b. 150% of 70
=1.5*70
=105
4a. 350% of 50
=3.5*50
=175
4b. 350% of 90
=3.5*90
=315
5a. 450% of 100
=4.5*100
=450
5b. 200% of 30
=2*30
=60
6a. 250% of 50
=2.5*50
=125
6b. 350% of 40
=3.5*40
=140
7a. 350% of 80
=3.5*80
=280
7b. 150% of 100
=1.5*100
=150
8a. 400% of 80
=4*80
=320
8b. 300% of 50
=3*50
=150
The value of percent are: 75, 135, 60, 50, 245, 105, 175, 315, 450, 60, 125, 140, 280, 150, 320, 150.
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if x = 3 when y = 6, what is y when x = -2
Answer:
If y=6 when x=3 find y when x =-33.
Step-by-step explanation:
Superior Segway Tours gives sightseeing tours around Chicago, Illinois. It charges a one-time fee of $40, plus $35 per hour. What is the slope of this situation?
80
65
40
35
Answer:
d. 35
Step-by-step explanation:
y = 35x + 40
The slope is 35 as 'm' is the slope of the equation
LMK IF IT WAS RIGHT!!
Answer:
D (35)
Step-by-step explanation:
What is the value today of $5,100 per year, at a discount rate of 7.9%, if the first payment is received 6 years from today and the last payment is received 20 years from today?
The present value of the cash flows is $30,030.78.
What is the present value?In order to determine the value today of the series of payments, the present value has to be determined. Present value is the sum of the discounted cash flows.
Present value = 5,100 / (1.079)^6 + 5,100 / (1.079)^7 + 5,100 / (1.079)^8 + 5,100 / (1.079)^9 + 5,100 / (1.079)^10 + 5,100 / (1.079)^11 + 5,100 / (1.079)^12 + 5,100 / (1.079)^13 + 5,100 / (1.079)^14 + 5,100 / (1.079)^15 + 5,100 / (1.079)^16+ 5,100 / (1.079)^17 + 5,100 / (1.079)^18 + + 5,100 / (1.079)^19 + + 5,100 / (1.079)^20 = $30,030.78
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Solve the problem below. Be sure to show all calculations. Explanations given to justify your solutions must be given in complete sentences.
Given the figure to the right and the fact that m∠ABD= 133°, find the measurements of the angles below.
m∠ABC=___ m∠BCD=___ m∠ACB=___
The angle measures for this problem are given as follows:
m∠ABC = 112º.m∠BCD = 34º.m∠ACB = 34º.How to obtain the angle measures?ADC is an isosceles triangle, with an angle of 44º, hence the base angles have the measure given as follows:
2x + 44 = 180. (sum of the internal angles of a triangle).
2x = 136
x = 136/2
x = 68º.
Hence the measure of angles ACB and BCD is of 34º, as the bisection divides the angle into two angles of equal length.
Considering the two base angles of 34º, the measure of angle ABC is given as follows:
m < ABC + 2 x 34 = 180
m < ABC = 112º.
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Consider the following balls-and-bin game. We start with one black ball and one white ball in a bin. We repeatedly do the following: choose one ball from the bin uniformly at random, and then put the ball back in the bin with another ball of the same color. We repeat until there are n balls in the bin. Show that the number of white balls is equally likely to be any number between 1 and n − 1.
The number of white balls is equally likely to be any number between 1 and n−1.
Let W be the number of white balls in the bin after the nth iteration. W can be any number between 1 and n−1. We can calculate the probability of obtaining a specific number of white balls in the bin by considering the number of possible sequences of choices. There are 2^n possible sequences of choices as each choice is either a white ball or a black ball. The number of sequences in which W white balls are selected is (W choose 1)*(n−W choose 1), which is equal to W*(n−W). Therefore, the probability of W white balls in the bin after the nth iteration is P(W) = (W*(n−W))/(2^n).
Since P(W) is equal for all values of W between 1 and n−1, it follows that the number of white balls is equally likely to be any number between 1 and n−1.
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Find the measure of each angle please help
(picture included) show work please
1,3
Step-by-step explanation:
if you invest $550.00 and your annual interest is 4%, what will be the interest
The annual interest is $22.
What is simple interest?Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time period.
Simple Interest = (Principal × Rate × Time) / 100
Given;
Amount invested= $550
Annual interest= 4%
SI= 550*4*1/100
=5.5*4
=22
Therefore, the simple interest will be $22.
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Determine whether the mean, median, or mode would be the best choice to describe the center of the following set of data.
An elementary school has 92 first graders. They take a vocabulary test that estimates the number of vocabulary words they know. Most of the first-graders had a good start on language acquisition and knew between about 15,000 and 20,000 words. However, there were a few first-graders who were a little behind in language acquisition and only knew about 7,000 words.
Would it be best to use the mean, median, or mode to describe the number of vocabulary words that are understood by the first-graders?
To describe the number of vocabulary words that are understood by the first-graders is better to use the mode.
What is the difference between the mean, the mode, and the median?Mean= This refers to the average, which is obtained y adding all the data and dividing by the number of numerical values.Median= This is obtained by organizing the data and choosing the value that is right in the middle.Mode= This refers to the most common value or the value that is the most frequent.Based on this, the factor to be considered to know the number of words first-graders know is the mode because this is the most common number of words and the most accurate information.
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Becky was told that based on the price of her home, her approximate closing costs would range from $4,000 to $12,000. How much was the price of her home?
Answer: $200,000
Step-by-step explanation:
The price of her home is $200,000.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
The closing costs run from 2% to 7% of the purchase price.
Approximate closing costs would range from $4,000 to $12,000.
Price of her home = x
This means,
2% of x = 4000
(2/100)x = 4000
(1/50)x = 4000
x = 4000 x 50
x = 200,000 ____(1)
7% of x = 12,000
(7/100)x = 12,000
x = (12,000 x 100)/7
x = 171428.57
x = 171429 _____(2)
Now,
From (1) and (2) we can say that,
x = $200,000
Thus,
$200,000 is the price of her home.
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The complete question:
The closing costs run from 2% to 7% of the purchase price.
Becky was told that based on the price of her home, her approximate closing costs would range from $4,000 to $12,000. How much was the price of her home?
In preparation for the upcoming school year, a teacher looks at raw test scores on the statewide standardized test for the students in her class. Instead of looking at the scores relative to the norms in the state, the teacher wants to understand the scores relative to the students who will be in the class. To do so, she decides to convert the test scores into z-scores relative to the mean and standard deviation of the students in the class. The mean test score in her upcoming class is 202, and the standard deviation is 38.2. The following are the scores for some (not all) of her students. Complete the table using the dropdown menus. The teacher wants to identify those students who may need extra challenge or extra help. As a first cut, she decides to look at students who have z-scores above z = 2.00 or below z = -2.00. Identify the test score corresponding to each of the following z-scores. Round to the nearest whole number. For z = 2.00, test score = .For z - -2.00, test score = .
Z-scores are used to standardize a raw score by converting it into the number of standard deviations it is above or below the mean.
The formula to convert a raw score into a z-score is:
z = (X - Mean) / Standard Deviation
Where X is the raw score, Mean is the mean of the population, and Standard Deviation is the standard deviation of the population.
For z = 2.00:
z = (X - Mean) / Standard Deviation
X = (z * Standard Deviation) + Mean
X = (2.00 * 38.2) + 202 = 238.4 + 202 = 440.4 (rounded to nearest whole number = 440)
For z = -2.00:
z = (X - Mean) / Standard Deviation
X = (z * Standard Deviation) + Mean
X = (-2.00 * 38.2) + 202 = -76.4 + 202 = 125.6 (rounded to nearest whole number = 126)
So for z = 2.00, the corresponding test score is 440, and for z = -2.00, the corresponding test score is 126.
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What is the value today of $6,500 that is due in 414
years if the interest rate is 3.96% compounded semi-annually?
Answer:
approximately $4,609,968.67
Step-by-step explanation:
To calculate the future value of a lump sum after compounding over a certain number of years with a specific interest rate, you can use the formula:
FV = PV * (1 + r/n)^(nt)
Where:
FV is the future value
PV is the present value (6500)
r is the annual interest rate (3.96%)
n is the number of times compounded per year (semi-annually, so 2)
t is the number of years (414)
Plugging in the values, you get:
FV = 6500 * (1 + 0.0396 / 2)^(2 * 414)
The future value of $6,500 in 414 years at an interest rate of 3.96% compounded semi-annually is approximately $4,609,968.67.
suppose x has a geometric distribution with probability 0.3 of success and 0.7 of failure on each observation. the probability that x is 4 is
the probability that x is 4 is given by the formula P(x) = [tex](1 - p)^(x-1) * p[/tex]
The formula for the probability of a geometric distribution is [tex]P(x) = (1 - p)^(x-1) * p[/tex]
Given the probability of success (p) is 0.3, the probability of x being 4 would be:[tex]P(x) = (1 - 0.3)^(4-1) * 0.3[/tex]
P(x) = 0.0729 or 7.29%
The geometric distribution is a probability distribution for the number of failures before the first success in a series of independent trials.
In this problem, the probability of success (p) is 0.3 and the probability of failure (1-p) is 0.7.
Therefore, the probability that x is 4 is given by the formula [tex]P(x) = (1 - p)^(x-1) * p[/tex]
Plugging in the values of p and x, we get:
[tex]P(x) = (1 - 0.3)^(4-1) * 0.3[/tex]
This simplifies to
P(x) = 0.0729 or 7.29%
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Determine a the domain and range
The domain and range of a function is discussed above.
What is a function?An function in mathematics defines a relationship between one variable (the independent variable {x}) and another variable (the dependent variable {y}). Example → y = f{x} = ax + b.
Given is the graph of the function as shown in the image.
Domain represents the set of values along the {x} - axis or the possible values of {x} for which f{x} exists.
Range represents the set of values along the {y} - axis or the possible existing values of f{x} for a specific value of {x}.
Therefore, the domain and range of a function is discussed above.
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Three students are working to find solution set of this system of equations
y=2x+6
2y=4x-2
Use the drop down menus to complete the statements about each of their methods
The system of equation has no solution.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The system of solution is
y=2x+6...(1)
2y=4x-2...(2)
Multiply equation 1 with 2
2y=4x+12...(3)
Subtract equation 2 and 3
2y-2y=4x-2-4x-12
0=-14
Hence, the system of equation has no solution.
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Is their a linear relationship between the height and volume of a cylinder
A car leaves a city at the rate of 60 mi/h and goes 80 miles before a second car follows at a rate of 70 mi/h. In this situation, let x= the number of hours, and y= the distance the car travels. The distance the first car travels can be represented by the equation y=60x+80.
Write the equation that represents the distance traveled by the second car.
The equation that represents the distance traveled by the second car is 60(t + 1.33).
Let t = travel time of the 2nd car when it overtakes the 1st
:
Find the travel time of the 1st car to go 80 mi; time = dist/speed
time = 80%2F60
time = 1.33 hrs for the 1st car to go 80 mi
therefore
(t+1.33) = travel time of the 1st car when it is overtaken
:
When the 2nd overtakes the 1st, they will have traveled the same distance
Write a distance equation, dist = speed * time
:
2nd car dist = 1st car dist
70t = 60(t+1.33)
70t = 60t + 80
70t - 60t = 80
10t = 80
t = 8 hrs travel time of the 2nd car to overtake the 1st
:
;
Confirm this by finding the actual distances, should be equal
70*8 = 560 mi
60*9.33 ~ 560 mi
Hence , the equation that represents the distance traveled by the second car is 60(t + 1.33).
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Akira and Jen are competing to see who can sell the most tickets for the Winter Dance. On Monday, Akira sold 20 and then sold 30 per day after that. Jen sold 50 on Monday and then sold 20 per day after that. This situation can be represented with the system y=30x+20 and y=20x+50 , where x is the number of days after the first day, and y is the total tickets sold. After how many days did they sell the same
number of tickets?
The two equations can be set equal to each other and solved for x:
30x + 20 = 20x + 50
10x = 30
x = 3
Therefore, they sold the same number of tickets after 3 days
Given the rate per compounding period, find r, the annual rate.
0.425% per month
Answer:
Step-by-step explanation:
To find the annual rate given the rate per compounding period, we need to convert the rate from the compounding period to the annual period. In this case, the rate is given as 0.425% per month.
One way to convert the rate is to multiply it by the number of compounding periods in a year:
r = 0.425%/month * 12 months/year
r = 5.1%/year
Therefore, the annual rate, r, is 5.1%.
what is The equation of The line
Answer:
y = (2/3)x + 10
Step-by-step explanation:
To find the equation of the line in slope-intercept form, y=mx+b, we need to know the slope and the y-intercept. The slope, or m, is rise over run. To find slope, we need to look at 2 points. For this question, I will be using the points (0,10) and (30,30). The rise, or change in y value, is 20, while the run, or change in x value, is 30. This means our rise over run in 20/30, or 2/3. Now that we have established the slope, or m, let's find the y-intercept, or b. To do this, you just need to look at where the line passes through the y-axis. In the image, you can see the line passes through the y-axis as x=10, making our y-intercept, or b, 10. Using this information, we can now find the equation of the line:
y = mx + b
m = slope, 2/3
b = y-intercept, 10
y = (2/3)x + 10
So, the equation of the line is y = (2/3)x + 10
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Your current salary is $43,000 a year. You are expecting a 12% raise. What will your salary be after the raise?
Answer: 43516
Step-by-step explanation:
C =(Current Salary). C x .012( 12%)=516
C + 516 = 43516
A painting contractor determined the average amount of time needed to paint a house. When 2 painters are used, it takes 15 hours to paint • When 6 painters are used, it takes 5 hours to paint. If p represents the number of painters and h represent the number of hours required to paint the house, which statement is true about this relationship?
The statement that is true about the proportional relationship is that; The time required to paint a house varies directly with the number of painters.
How to find proportional Relationship?The parameters are;
p represents the number of painters.
h represent the number of hours required to paint the house
In this case, the number of hours will be the output variable while the number of painters will be the input variable. Thus, we will have the relationship;
h = kp
where k is the constant of proportionality
When 2 painters are used, it takes 15 hours to paint and as such;
k = 15/2
k = 7.5 hours per painter
When 6 painters are used, it takes 5 hours to paint. Thus;
k = 5/6
k = 0.833 hours per painter
Thus, we can say that the time required to paint a house varies directly with the number of painters.
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_ /12 > 11/12 what is the missing ?
Answer: 12
Step-by-step explanation:
12/12 is greater than 11/12
12/12>11/12
Click on all the values that are equivalent to
-(2/3).
A.-2/-3
B.2/-3
C.-2/3
D.-3/-2
E.-3/2
F.3/-2
Answer:
-2/-3
Step-by-step explanation: Because -2/-3=2/3.
} problem 9. (10 pts) determine which of the following subsets of r 3 are subspaces of r 3 . you should use the subspace test from the lectures to show that a given subset is a subspace, or, if it is not a subspace, exhibit one of the axioms of a vector space that fails to be satisfied. (a) a
Options C and D are subsets of R³, which are {(-5x,4x,3x)| x arbitary} and {(x,y,z)| x+y+x=0}
A) Correct. We have to check whether the potential subspace containing the zero vector is a great place to start on these sorts of problems. No zero vector so this is not a subspace.
B) This is a subspace. The set of solutions of a homogeneous linear system is always a subspace it is known as a "null space" of some corresponding linear transformation.
Let, [tex]M=\left[\begin{array}{ccc}2&9&0\\8&0&-5\\\end{array}\right][/tex] then the set in B) is just Null(M). Again, Nullspaces are always subspaces.
Alternatively, you could solve the corresponding system Mx=0 and find the elements of that set [tex]x=\left[\begin{array}{c}5/8&-5/36&1\\\\\end{array}\right][/tex] for any choice of z∈R. So this
can be a set in the span of [tex]x=\left[\begin{array}{c}5/8&-5/36&1\\\\\end{array}\right][/tex]
C) Correct. we can see a subspace because the elements are just multiples of (−5,3,4) and again spans are subspaces.
D) Correct. This can be a subspace for the same reasons as part B.
E) Correct. Not a subspace. An easier counter-example: (1,1,1) is in there. But (−1)(1,1,1)=(−1,−1,−1) is not.
F) Not a subspace. (0,0,0) is not in there.
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Which of the following is equivalent to the rational expression below, where x≠1
?
The equivalent expression is x + 3 + 4/(x - 1)
Option A is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
(x² + 2x + 1) / (x - 1)
Now,
x² + 2x + 1
= x² + (1 + 1)x + 1
= x² + x + x + 1
= x(x + 1) + 1(x + 1)
= (x + 1)(x + 1)
= (x + 1)²
Now,
(x² + 2x + 1) / (x - 1)
= (x + 1)² / (x - 1)
Now,
x + 3 + 4/(x - 1)
((x - 1)x + 3(x - 1) + 4) / (x - 1)
= (x² - x + 3x - 3 + 4) / (x - 1)
= (x² + 2x + 1) / (x - 1)
Thus,
x + 3 + 4/(x - 1) is the equivalent expression.
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find two positive numbers that satisfy the given requirements. the second number is the reciprocal of the first number and the sum is a minimum
The two positive numbers are 1 and 1, depending on the given information.
Let first number be x. So, the second number is 1/x. Now, their sum is minimum, so representing the expression for given information -
Sum (x) = x + 1/x
Rewriting the expression -
Sum (x) = x + [tex] {x}^{-1} [/tex]
Finding the derivative
Sum' (x) = 1 + (-1) [tex] {x}^{-2} [/tex]
Sum' (x) = 1 + (-1)/[tex] {x}^{-1} [/tex]
Sum' (x) = (x² - 1)/x²
Now, to find the minimum -
x² - 1/x² = 0
Multiplying x² on Right Hand Side of the equation
x² - 1 = 0
Rewriting the equation
x = ± 1
As the numbers are positive, so x will be 1.
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Simplify
6 (2x^2-5)=
x= -3
The value of the expression for x=-3 is 78.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
The given expression is 6(2x²-5).
Here, x=-3
Substitute x=-3 in the expression 6(2x²-5), we get
6(2(-3)²-5)
= 6(18-5)
= 78
Therefore, the value of the expression is 78.
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Consider the continuous random variable xx, which has a uniform distribution over the interval from 20 to 28. What is the probability that xx will take on a value between 21 and 25?
The probability that X will be between 21 and 25 is increased.
The probability that a continuous random variable with a uniform distribution takes on a value between two specific points (a, b) is given by:
P(a X b) = (b - a) / (max - min)
where X is the random variable, max and min are the distribution's upper and lower bounds, and (b - a) is the length of the interval between two specific points.
In this case, the uniform distribution of X is from 20 to 28, so:
max = 28 min = 20
And we want to know how likely it is that X will have a value between 21 and 25:
P(21 < X < 25) = (25 - 21) / (28 - 20) = 4 / 8 = 0.5
As a result, the probability that X will be between 21 and 25 is increased.
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