George says to subtract fractions with different denominators, you always have to multiply the denominators to find the common denominator; for example: 3/8 - 1/6 = 18/48 - 8/48
Is George correct? Why or why not?
George is not correct because we can find the least common multiple of 8 and 6 which is 24. This allows us to solve the problem with simple numbers and ease our calculations to get the answer in the simplest form.
The equation solved by George is 3/8 - 1/6 = 18/48 - 8/48
To solve the given fractions in the simplest form, we will find the common denominator which would be the least common multiple of both denominators.
we can see that the numbers in the denominator are 8 and 6.
Multiples of 8: 8, 16, 24, 32, 40,...
Multiples of 6: 6, 12, 18, 24, 30,...
Hence, LCM of 8 and 6 is 24.
thus we can solve the equation as follows -
3/8 - 1/6
= 3*3/8*3 - 1*4/6*4
= 9/24 - 4/24
= 5/24
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a statistics professor asked students in a class their ages. based on this information, the professor states that the average age of students in the university is 21 years. this is an example of .
The problem where the professor states that the average age of students in the university is 21 years is an example of statistical inference.
Statistical inference is the process of using data from a sample to make inferences or conclusions about a population. It allows us to draw conclusions about a larger group of individuals or objects based on information from a smaller sample. It is a fundamental part of statistical analysis and is used in many fields, including research, business, and government.
Statistical inference includes two main types: estimation and hypothesis testing.
Estimation: This involves using sample data to make estimates about population parameters. For example, using the sample mean to estimate the population mean or the sample proportion to estimate the population proportion.
Hypothesis testing: This involves using sample data to test a claim or hypothesis about a population parameter. For example, testing the claim that a coin is fair, based on the proportion of heads in a sample of coin flips.
The goal of statistical inference is to use the information from a sample to make informed decisions or predictions about a population. It allows us to draw general conclusions from a specific set of data, and it is an essential tool for making sense of data in many fields.
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if the slope of a line in the xy plane that passes through the points (1/2/, -1) and (2, b) is 8/3, what is the value of b?
The slope of a line in the xy plane b = 13/3
The slope of a line in the xy plane can be calculated by using the equation m = (y2-y1)/(x2-x1). In this equation, m is the slope, x1 and y1 are the coordinates of the first point, and x2 and y2 are the coordinates of the second point.
Using this formula, we can solve for b.
m = (y2 - y1) / (x2 - x1)
8/3 = (b - (-1)) / (2 - (1/2))
24/3 = (b + 1) / (5/2)
24/3 * (5/2) = (b + 1)
40/3 = b + 1
40/3 - 1 = b
b = 13/3
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Given the function defined in the table below, find the average rate of change, in
simplest form, of the function over the interval 16 ≤ x ≤ 22.
x f(x)
4 10
10 19
16 28
22 37
28 46
Answer:
Step-by-step explanation:
2/5 meter= how many centimeters
Answer: 40 cm
Step-by-step explanation: 2/5 x 100 =
200/5 = 40
URGENT!!
Which of the 3 graphs to the left best models the path
of a firework given it didn't explode?
Note: The path may be going in a different direction,
perhaps reflected or translated vertically or horizontally
while maintaining the same shape.
Linear
Quadratic
Exponential
Explain your thinking.
Answer:
Quadratic
Step-by-step explanation:
The path of a firework is modeled by a quadratic function. The firework ascends from point of launch with decreasing speed (negative acceleration due to gravity) until it reaches it maximum height and then starts dropping back to ground at increasing speeds due to positive acceleration exerted by the force of gravity.
The flight path of the parabola can thus be modeled by height as a function of elapsed time
h = f(t) where f(t) is a quadratic equation in t with the general form being
a · t² +b · t + c
We can easily eliminate the linear model since that implies the firework will ascend at a constant speed forever
The exponential model indicates that at the moment of launch the speed of the firework is constant and then it suddenly accelerates. However we know from observation that the firework has the highest speed at the moment of launch
Do not be confused by the shape of the graph - it seems to indicate the firework shoots down and up.
The note says:
Note: The path may be going in a different direction, perhaps reflected or translated vertically or horizontally while maintaining the same shape.
Indeed the actual path of the firework is a reflection of the graph about the x axis. so that it is a downward facing parabola. The vertex of the parabola is the highest y-value which is the maximum height the firework would reach.
The height would be the y axis and time t the x-axis
Lisa makes $30 for 4 hours of babysitting. Write an equation to represent her earnings, e, relative to the number of hours, h, that she works. Assume the relationship is proportional.
please help
The equation which represents Lisa's earnings, e, relative to the number of hours, h, that she works assume a proportional relationship is e = 7.5h
How to write equations?Amount Lisa makes for babysitting = $30
Number of hours Lisa babysit = 4 hours
Total earnings = e
Number of hours = h
If the relationship is proportional, then
k = constant of proportionality
e = k × h
30 = k × 4
30 = 4k
divide both sides by 4
k = 30/4
k = 7.5
So therefore,
e = k × h
e = 7.5 × h
e = 7.5h
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Mrs. Byrne mowed 1 4 of her lawn. Her son mowed 2 7 of it. Who mowed most of the lawn? How much of the lawn still needs to be mowed?
Mrs. Byrne mowed 1/4 of her lawn. Her son mowed 2/7 of it. Mrs. Byrne mowed most of the lawn. The lawn still needs to be mowed is 13/28.
Mrs. Byrne mowed of his lawn = 2/7
Her son mowed of his lawn = 1/4
We firstly equal the denominator of both fraction by taking the LCM of both numbers.
The LCM of 7 and 4 is 28.
So we multiply and divide by 4 in the fraction 2/7 and by 7 in fraction 1/4. Now,
Mrs. Byrne mowed of his lawn = 2/7 × 4/4 = 8/28
Her son mowed of his lawn = 1/4 × 7/7 = 7/28
Now we compare the both fraction 8/28 and 7/28. The 8/28 is greater than 7/28. So we can say that Mrs. Byrne mowed most of his lawn.
The total lawn is 28/28.
So, the remaining lawn for mowed = 28/28 - (8/28 + 7/28)
The remaining lawn for mowed = 28/28 - (8 + 7)/28
The remaining lawn for mowed = 28/28 - 15/28
The remaining lawn for mowed = (28 - 15)/28
The remaining lawn for mowed = 13/28
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The complete question is:
Mrs. Byrne mowed 2/7 of his lawn. Her son mowed 1/4 of it. Who mowed most? How much of the lawn still needs to be mowed?
what percentage of the trees have a height less than 75 feet? (round your answer to 2 decimal places.)
When using percent slope to get tree height, the tree is the rise, and the horizontal distance from the tree with the ground is the run. We can simply measure our horizontal distance from the tree, and we have instruments for gauging the percent slope to the top of a tree.
Hence, with those two measures (run and %slope) we can solve for rise.
You Total up all the trees.
let the average of number of trees are:
3+3+8+10+5+2=31
then you subtract the amount of trees under 75 feet in height.
31-8-3-3=14
divide the number of trees 14 under 75 ft in height by the total amount of trees31.
14/31=0.4516
0.4516=45.2
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The Hcf of 2 numbers O and L is the number O itself .This can be only true if
The number O is the Hcf of the two numbers L and O. This is only possible if the number O is the highest common factor of the two.
Define the term HCF of the number?The highest number among all of the common factors of something like the given numbers is known as the HCF (Highest Common Factor) for two or more numbers.
The highest integer that divides both x and y is known as that of the HCF (Highest Common Factor) for two natural numbers, x and y. Let's use the numbers 18 and 27 to further grasp this definition. 1, 3, and 9 are the common variables between 18 and 27. 9 is the greatest (biggest) number among these. An HCF of 18 with 27 is therefore 9. The formula for this is HCF (18, 27) = 9.Similarly, for the given question.
The number O is the Hcf of the two numbers L and O. This is only possible if the number O is the highest common factor of the two.
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5 POINTS UP FOR GRABS !!!
The area of the shaded part of the rectangle is 152 cm².
What is the shaded area?The area of the shaded part is the difference between the area of the larger rectangle and the smaller square.
Area of the shaded part = area of the larger rectangle - area of the square
Area of the larger rectangle = length x width
12cm x 18cm = 216 cm²
Area of the square = length²
= 8² = 64 cm²
Area of the shaded part = 216 - 64 = 152 cm²
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Hace 8 años, Maria tenía 10 años y Luis 11 años. Dentro de 7 años, Nico tendrá 27 años ¿cuanto es la suma de las edades actuales de Maria Luis y Nico?
Their ages are given below:
Maria 18, Luis 19 Nico 20The sum of their ages would be 57 years.
How to find their ages?The current age of Nico is 27 - 7 = 20 years.
Therefore, Maria and Luis's current ages would be 8 years older than when they were 10 and 11 respectively,
so Maria is currently 18 years old and Luis is currently 19 years old.
Therefore, the sum of their current ages is 18 + 19 + 20 = 57 years.
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8 years ago, Maria was 10 years old and Luis was 11 years old. In 7 years Nico will be 27 years old, what is the sum of the current ages of Maria, Luis and Nico?
Please explain and answer!
The Pythagorean identity is proved to be 1 + cot2 = cosec2, which results in sin2 + cos2 = 1.
How to verify Pythagorean identity?With the value of sine and the quadrant in which the angle is placed, we can use the Pythagorean identity to get the angle of cosine.
If we are given the cosine value and the quadrant in which the angle is placed, we may similarly compute the angle of sine.
Cosec2 = 1 + cot2
Therefore,
cosec2 = 1/sin2
Tan2 = cos2 / sin2 = cot2 = 1
Hence,
1/sin2 = 1 + cos2 / sin2.
multiplied both sides by sin2 as a result.
1(sin2 ) + (cos2 / sin2 ) = (sin2 / sin2 )
cos2 + sin2 = 1.
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by solving simultaneous equations work out the coordinates of the point where the two lines below intersect. 3x+y=11 and y=4x-3
The point where the two lines intersect each other is (2,5).
What are simultaneous equations?
Two or more algebraic equations that share variables, such as x and y, are said to be simultaneous equations. Since the equations are solved simultaneously, they are known as simultaneous equations. These equations alone could have an endless number of solutions.
When two lines intersect each other, the point of intersection is a point common to both lines.
This can be found by solving simultaneous equations.
The given equations of the two lines are
3x+y = 11
4x-y = 3
Adding the above equations, we can remove the y variable.
The result is 7x = 14
x = 2
Now we substitute this value of x in either of the above equations to get the value of y.
3 * 2 + y = 11
y = 11 -6 = 5
Therefore the point where the two lines intersect each other is (2,5).
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what are the coordinates of P?
(3,2) the eqaition would be y=3/2x+3
what is the value of k? k= …..
please help quick
180 - 115 = 65
4k + 5 + 6k + 10 + 65 = 180
10k + 80 = 180
10k = 100
k = 10
a 6 foot-tall farmer wants to determine the height of his barn. he notices that his shadow is 10 feet long and his barn casts a shadow 75 feet long. how high is the barn?
By applying the proportional relationship formula, the height of the barn is 45 ft.
In a proportional relationship, each pair of data points is related in the same way, typically by multiplying them together. A proportionate relationship can be seen in a set of numbers, an equation, or a graphical representation. In this case, we are given that :
The height of the farmer (X1) = 6 ft
The height of the farmer’s shadow (Y1) = 10 ft
The height of the barn with farmer’s shadow (Y2) = 75 ft
To calculate the actual height of the barn (X2), we can use this following formula:
X1 : Y1 = X2 : Y2
6 : 10 = X2 : 75
X2 = (6 : 10) x 75
X2 = 45
Thus, the height of the barn is 45 ft
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Rewrite the following without an exponent.
(2/3) ^-1
The expression of (²/₃)⁻¹ without an exponent is given as;
3/2
How to use Laws of exponents?The different laws of exponents are;
1) Power Law of Exponents which is expressed as; (x^m)ⁿ = x^(mn)
2) Quotient Law of Exponents is expressed as; x^m ÷ x^n = x^(m - n)
3) Product Law of Exponents is expressed as; x^(m) * x^(n) = x^(m + n)
4) Law of Reciprocal is expressed as; a⁻ⁿ = 1/aⁿ
Now, we want to rewrite the expression (²/₃)⁻¹ without using an exponent.
From the law of reciprocal of exponents we can say that;
(²/₃)⁻¹ = 1/(²/₃)
= 3/2
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Which expression is equivalent to
P
O 16/45
O√√25
02
04
4
54
4
4112
112
?
The answer is 4^2. Step-by-step explanation: This is because 4 squared is 4*4 which equals 16.
Which functions show a positive rate of change? Select all that apply
The functions that show a positive rate of change include the following:
A. y = 2x/3 - 2.
B. y = 7 - (-3x).
What is the slope-intercept form?In Mathematics, the slope-intercept form of a line can be represented or modeled by using this linear equation:
y = mx + c
Where:
m represents the slope or rate of change.c represents the y-intercept.x and y are the data points.Generally speaking, a function with a positive rate of change represents an increasing function because its numerical value is increasing over time such as in the following increasing function:
y = 2x/3 - 2.
Slope, m = 2/3 (positive slope).
y = 7 - (-3x)
y = 7 + 3x
Slope, m = 3 (positive slope).
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The functions that show a positive rate of change are y = 2/3x - 2 and y = 7 - (-3x).
What is a positive function?A positive function is a function that has the values of x that are greater or higher than zero on the graph. It means that they are always increasing on the positive y-axis i.e. f(x) > 0.
The function's outputs known as the y-values, however, must be larger than zero even though the domain values i.e. (x-values) might be negative. A positive function, then, has values that are positive for all of its domain's parameters.
To determine the positivity of the function on the graph, the slope must also be positive. Using the linear function form y = mx + b.
where;
m = slopeb = y-interceptFrom the given information, the functions that demonstrated a positive slope are:
y = 2/3x - 2 andy = 7 - (-3x)Therefore, we can conclude that the functions that show a positive rate of change are y = 2/3x - 2 and y = 7 - (-3x).
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I can’t figure this out. Which math expression means "52 more than an unknown number"?
O A. x- 52
• B. x+ 52
O C. 52 - x
• D. x = 52
Answer: B. x + 52
Step-by-step explanation:
The unknown number is represented as x.
The phrase "52 more than" means adding 52 to something
From this we can say that the expression is B. x + 52
Please answer. I've been stuck on this question for a while.
Question: A business purchased a new printer. The number of the pages, y, printed by the new printer in x minutes is represented by the equation y=37x. The number of the pages printed by the OLD printer is represented in the graph below.
Which statements about the printers are true?
Select the TWO correct statements.
Answer:
The new printer prints 100 pages about 4 minutes faster than the old printer
The new printer prints 22 move pages per minute than the old printer
Step-by-step explanation:
New printer's equation
y = 37x
Old printer's equation
y = 15x
Since the graph is proportional you can take any ordered pair (except (0,0) and put it the form y/x to find the slope. For example, The point (2,30) 30/2 = 15 or the point (4, 60) 60/4 = 15 and so on.
The difference between the rates is 22 pages a minute (37 - 15).
Substituted in 100 for y and solve for x (minutes)
New:
y = 37x
100 = 37x Divide both sides by 37
100/37 =37x/37
3 = x This is rounded
This means that it takes about 3 minutes to print 100 pages.
Old:
y = 15x
100 = 15x Divide both sides by 15
100/15 = 15x/15
7 = x This is rounded
This means that it takes about 7 minutes to print 100 pages.
The new printer can print the same amount of page (100) in 4 less minutes (7-3)
The amount of snowfall in January was 11
1/1/20
Write your answer as a mixed number in simplest form.
feet
feet. The amount of snowfall in December was 5-
5²24
feet. How much more snowfall was there in December?
0
The mixed fraction in the simplest form is 21/20, and the snowfall in December was almost 5 times more than the snowfall in January.
What are mixed fractions?A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 seems to be the quotient and 1 is the remainder. An amalgam of a whole integer and a legal fraction is a mixed fraction.
Given that the amount of snowfall in January was:
[tex]1 \frac{1}{20}[/tex]
To convert the mixed fraction to simplest form, multiply the denominator with the value and add it to the numerator:
[tex]21/20 = 1.05[/tex]
The amount of snowfall in December is:
[tex]5 \frac{2}{24} = 5 \frac{1}{12}[/tex]
To convert the mixed fraction to simplest form, multiply the denominator with the value and add it to the numerator:
[tex]\frac{61}{12} = 5.08[/tex]
Hence, the snowfall in December was almost 5 times more than the snowfall in January.
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Suppose a population consists of 4000 people. Which of the following
numbers of members of the population surveyed could result in a sample
statistic but not a parameter?
A. Both 40 and 4000
B. 40
C. 4000
D. Neither 40 nor 4000
A sample of size 40 is a valid sample size and could result in a sample statistic, as explained above, the correct answer is B.
What is the sample statistic?
A sample statistic is a measure calculated from a sample of the population, while a population parameter is a measure calculated from the entire population. Therefore, a sample statistic may differ from a population parameter due to sampling variability.
Out of the options provided, only option B (40) could result in a sample statistic but not a parameter.
This is because a sample of size 40 is a subset of the population, and a statistic calculated from this sample (such as the sample mean or sample proportion) would be a sample statistic.
Option C (4000) would result in both a sample statistic and a population parameter because a sample consisting of the entire population is a census, and any measure calculated from this sample would also be a parameter.
Option A (both 40 and 4000) and option D (neither 40 nor 4000) are not correct because 4000 is not a valid sample size, as it includes the entire population and would therefore be a census.
Hence, a sample of size 40 is a valid sample size and could result in a sample statistic, as explained above, the correct answer is B.
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Wendy solved an equation and found x to be 5. Which equation could she have solved?
O 2x + 4 = 12
O13-4x = 20
O 3x-10= 5x + 20
O 14+2x = 54 - 6x
The equation Wendy must have solve is 14+2x = 54 - 6x Option D
What is a linear equation?A linear equation is an equation whose highest power of the variable is 1.
recall that equation is a mathematical statement showing that two opposite sides are equal
the equation can be solved as follows
14+2x = 54 - 6x
Collecting the like terms from the equation we have
2x+6x = 54 -14
This implies that
8x = 40
Making x the subject of the relation
Therefore x=40/8 = 5
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a player of a video game is confronted with a series of 4 opponents and a(n) 73% probability of defeating each opponent. assume that the results from opponents are independent (and that when the player is defeated by an opponent the game ends). round your answers to 4 decimal places. (a) what is the probability that a player defeats all 4 opponents in a game? enter your answer in accordance to the item a) of the question statement (b) what is the probability that a player defeats at least 2 opponents in a game? enter your answer in accordance to the item b) of the question statement (c) if the game is played 3 times, what is the probability that the player defeats all 4 opponents at least once? enter your answer in accordance to the item c) of the question statement
The Probability that the player will win against each of the four opponents at least once is 0.7942.
The player has a P(W) = 0.80 winning chance.
The likelihood that the player will lose is hence P(L)= 1 - P(W) = 0.20.
The player is up against 4 different opponents in the video game.
It is stipulated that the game finishes when a player is defeated by an opponent.
The player can win in any of the following ways: L, WL, WWL, WWWL, and WWWW.
The results from each of the four opponents are distinct, meaning that the outcome of a game played against one opponent has no bearing on the outcome of a game against another.
P (Player defeats all 4 opponents) = 0.4096 is the probability that a player will win a game against all four opponents.
Thus, the probability that the player defeats all four opponents in a game is 0.4096.
(b) The likelihood that a player will win a game against at least two opponents is,
P = 1 (Player defeats at least 2) P = 0.64 when the player loses the first and second games.
Therefore, there is a 0.64 percent chance that the player will win at least two games against opponents.
Let X equal the number of times the player triumphs over all four opponents.
The likelihood that a player will win a game against all four opponents is,
P(WWWW) = 0.4096
The probability that a player will triumph over each of the four opponents at least once is,
P (X ≥ 1) = 1 - P (X < 1)
= 1 - P (X = 0)\s = 0.7942
Therefore, there is a 0.7942 probability that the player will win against all four opponents at least once.
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There are 150,000 households in Market City. A local phone repair shop takes a random sample of 50 households and finds that the average number of phones per household from the sample last year that needed to be repaired was 1.05 ± 0.23. Which of the following is an estimate of the total number of phones that needed repairing last year in Market City?
Between 82 and 128 phones
Between 123,000 and 192,000 phones
Between 105 and 23 phones
Between 157,500 and 34,500 phones
The correct answer is Between 157,500 and 968,187 phones.
Which of the following best describes the approximate number of phones in Market City ?The average number of phones per household from the sample from the previous year that required repair was 1.05 0.23. This suggests that the range for the genuine population mean () might be between 1.05 - 0.23 = 0.82 and 1.05 + 0.23 = 1.28 phones per home.Since the sample size was 50 households, the estimate of the total number of phones that needed repairing last year in Market City can be calculated as follows:Estimate = 50 * (1.05 + 1.05) / 2 = 52.5Estimate = 52.5 * 150,000 = 7,875,000Therefore, an estimate of the total number of phones in Market City that required repair last year ranges from 7,875,000 - 7,875,000 * 0.23 = 6,068,125 to 7,875,000 + 7,875,000 * 0.23 = 9,681,875 phones.Therefore, the correct answer is between 157,500 and 968,187 phones.To learn more about estimation refer:
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Select the values that make the inequality - v <= - 8 true. Then write an equivalent inequality, in terms of v. ( Numbers written in order from least to greatest going across .)
Answer: To find the values that make the inequality -v <= -8 true, we can first isolate v on one side of the inequality. We do this by adding v to both sides:
-v <= -8
v >= 8
This inequality states that the only values that make it true are those greater than or equal to 8.
Another equivalent inequality in terms of v would be v>=8
So, the values that make the inequality -v <= -8 true are v >= 8
Step-by-step explanation:
HELP ASAP!! GIVING 50 POINTS!!
PLEASE SHOW WORK!
for any value of n, the nth term of the equation will be:
Aₙ = -3* 2ⁿ⁻¹
What is the geometric sequence?A geometric sequence is a sequence of numbers that follows a pattern where the next term is found by multiplying by a constant called the common ratio, r.
From the general formula of the nth term of the geometric sequence:
Aₙ = A₁* rⁿ-1
Given a geometric sequence:
-3, -6, -12, 24,.....
From the general formula of the nth term of the geometric sequence:
Aₙ = A₁* rⁿ⁻¹
in our case
a₁ = -3
ratio(r) = -6/-3 = 2
Thus for any value of n, the nth term of the equation will be
Aₙ = -3* 2ⁿ⁻¹
For instance,
8th term of the given sequence:
A₈ = -3* 2⁸⁻¹
A₈ = -3* 2⁷
A₈ = -384
Therefore, for any value of n, the nth term of the equation will be
Aₙ = -3* 2ⁿ⁻¹
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Solve the system of equations x+3y=5 and -3x-2y=20 by combining the equations
On solving the linear equations x + 3y = 5 and -3x - 2y = 20, the value for x is x = -10 and the value of y is y = 5. When solved independently the value is obtained as -2x + y = 25.
What is a linear equation?
A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.
The first linear equation is - x + 3y = 5
The second linear equation is - -3x - 2y = 20
On evaluating individually the equation obtained is -
-3x - 2y + x + 3y = 20 + 5
-2x + y = 25
Multiply equation (1) with 3 -
3(x + 3y) = 5 × 3
3x + 9y = 15.....(3)
Adding equation (3) and (2) -
-3x - 2y + (3x + 9y) = 20 + 15
-3x - 2y + 3x + 9y = 35
-2y + 9y = 35
7y = 35
y = 35/7
y = 5
Substituting the value of y in equation (1) -
x + 3y = 5
x + 3(5) = 5
x + 15 = 5
x = 5 - 15
x = -10
Therefore, the value of x and y is -10 and 5 respectively.
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