For these traditional cooking measurements, there are no specific definitions. The majority of sources, however, claim that a dash is roughly 1/8 of a teaspoon, a pinch is 1/16 of a teaspoon, and a smidgen is 1/32 of a teaspoon.
How many teaspoons is two dashes?For these traditional cooking measurements, there are no specific definitions. The majority of sources, however, claim that a dash is roughly 1/8 of a teaspoon, a pinch is 1/16 of a teaspoon, and a smidgen is 1/32 of a teaspoon.One tablespoon or less of a soft food, like whipped cream or sour cream, is typically referred to as a "dollop."Because of the action of adding an ingredient, such bitters, a dash frequently refers to liquid substances, especially when creating cocktails.Furthermore, a pinch is, as its name suggests, the quantity of an ingredient (such as salt or a dry herb) that you can hold between your thumb and fingers. Additionally, there is a "healthier-sized" pinch that involves your thumb, forefinger, and middle finger, known as a "three-finger pinch." It probably equals between a quarter and an eighth of a teaspoon in terms of volume.The Complete Question.
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Shawn is 23 years old, and Yu Yan is 15 years old. How many years ago was Shawn 3 times as old as Yu Yan was?
Answer:
11
Step-by-step explanation:
Now:
Shawn: 23
Yu Yan: 15
x years ago:
Shawn: 23 - x
Yu Yan: 15 - x
x years ago, Shawn was 3 times as old as Yu Yan.
23 - x = 3(15 - x)
23 - x = 45 - 3x
2x = 22
x = 11
Check:
11 years ago Shaw was 23 - 11 = 12, and Yu Yan was 15 - 11 = 4.
12 is indded 3 times 4.
Answer: 11
6=7/w-3 solve for w??????
Answer:
w=7/9
Step-by-step explanation:
6=7/w-3
Move the terms
6=7/w-3, w [tex]\neq[/tex] 0
Calculate
-7/w=-3-6
Multiply both sides
-7/w=-9
Swap the sides
7=9w
Divide both sides
9w=7
w=7/9, w [tex]\neq[/tex] 0
w=7/9
motorola used the normal distribution to determine the probability of defects and the number of defects expected in a production process. assume a production process produces items with a mean weight of 8 ounces.
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Solve the equation
1
4
(4x − 24) + x = 14.
The solution to an equation is 10.Solving an equation refers to the process of determining its solution.
Which one provides an answer to the problem?A variable's value that, when substituted into the equation, results in a true assertion is known as the solution. Solving an equation refers to the process of determining its solution. Finding the value of the variable that causes an equation to hold true is referred to as finding the solution to an equation.Solving an equation refers to the process of determining its solution. Finding the value of the variable that causes an equation to hold true is referred to as finding the solution to an equation.Make the available
14to obtain the desired amount:
x – 6 + x = 14
Put similar phrases together to get:
2x – 6 = 14
Adding 6 to both sides yields:
2x = 20
x = 10.
The complete question is,
1 4 (4x 24) + x = 14 must be solved.
By dividing the 1 by 4, you can obtain:
Put similar phrases together to get:
Adding 6 to both sides yields:
x =
Consequently, is the necessary response.
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Find the midpoint between (-1, -5) and (-5, 9) by using the Midpoint Formula.
Answer: Midpoints (-3/2)
Step-by-step explanation:
Midpoint formula is (x1+x2)/2 , (y1+y2)/2
Plugin x values and solve
(-1 +-5)/2 = -3
Plugin y values and solve
(-5+9)/2 = 2
The midpoint is -3/2
I hope this helped you :D
during a severe storm, electrical transformers that function independently are expected to operate 85 percent of the time. suppose 20 electrical transformers are randomly selected from the population. let the random variable t represent the number of electrical transformers operating during a severe storm. which of the following is the best interpretation of the random variable t ?
The binomial variable with mean 17 transformers and standard deviation √2.55 transformers.
In math standard deviation is defined as a measure of how dispersed the data is in relation to the mean.
Here we have know that the good electrical transformers operate at approximate 85% of the total time and 20 electrical transformers are chosen at random.
Here let us assuming the variable is a binomial variable.
Then we have written it as in the following form,
=> Mean = number of samples * probability
And the value of standard deviation is calculated as
=> Standard Deviation = √mean (1 − probability)
Here we know that the value of mean is calculated as,
=> 85% * 20 = 0.85*20 = 17 transformers
Then the value of Standard deviation is calculated as,
=> √mean * (1 − 0.85)
Apply the values on the formula, then we get,
=> √17 * 0.15 =√2.55 transformers.
Hence the random variable is a binomial variable.
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Identifying Linear Equations Let x1, x2, ..., In be variables. Determine whether the following equations are linear or non-linear and explain why: (a) (x1 – 1)(x2 + 1) = 0 (b) 5x1 = 2x2 – 3x3 +4 (c) x1 + xż + x3 + ... + x n = 0 (d) sin(x3)x1 + x2 = 4 – cos^2(x3)21 (e) exı + e-x2 + ... +e" In = ln(5)
The following systems are :
a) Non-linear
b) Linear
c) Linear
d) Non-linear
e) Linear
a) Non-linear: The equation is non-linear because it contains a product of two variables (x1 - 1) and (x2 + 1). A linear equation only contains variables and their coefficients, not products of variables.
b) Linear: The equation is linear because it only contains variables and their coefficients.
c) Linear: The equation is linear because it only contains variables and their coefficients and the sum of variables.
d) Non-linear: The equation is non-linear because it contains the sine and cosine functions, which are non-linear.
e) Linear: The equation is linear because it only contains variables raised to a constant power (e raised to a constant power) and their coefficients.
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In a closed bottle, the product of the pressure and volume is constant. By what percent mist the volume be decreased to increse the pressure by 25%?
Answer: This is known as Gay-Lussac's Law.
The relationship states that the pressure and volume of a gas are directly proportional at constant temperature. Therefore, if the pressure is increased by 25%, the volume must be decreased by 25% to maintain the constant product of pressure and volume.
You measure the mass of a ring three times using the same balance and get slightly different values: 17.46 g, 17.42 g, 17.44 g
The variation in the values is due to random error. Hence, it can be reduced by taking more observations to estimate the measure of the mass of the ring.
One way to minimize experimental error in this situation is to take multiple measurements and use the average of those measurements as the final value. This helps to account for any small fluctuations or inaccuracies in the individual measurements.
Also, it is important to ensure that the balance is properly calibrated and that the ring is placed on the balance in the same way each time.
Other ways to minimize experimental error include using a more precise measuring instrument, such as a digital scale, and ensuring that the lab environment is controlled and stable (i.e. no drafts or vibrations that could affect the measurements).
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The complete question is -
You measure the mass of a ring to be used in your experiment three times using the same balance and get slightly different values: 17.46 g, 17.42 g, and 17.44 g. How can you minimize experimental error?
What is the sum
of the rational expressions below?
Answer:
D. 4x² - x / x² - x - 2
Step-by-step explanation:
First cross multiply then sum the results:
cross:
x(x + 2) = x² + 2x
3x(x - 1) = 3x² - 3x
sum the results of the cross:
x² + 2x + 3x² - 3x
4x² - x (this goes at the top)
Then multiply the bottom:
(x - 1 )(x + 2)
x² + 2x - x - 2
x² - x - 2 (this stays at the bottom)
Fraction ends up like:
4x² - x / x² - x - 2
Two planes travel at a constant speed. Plane A travels 2,800 miles in 5 hours. Plane B travels 3,885 miles in 7 hours. Which plane is faster. Explain your answer.
Answer:
Plane B
Step-by-step explanation:
Plane A: 2800/5 = 560 m/h
Plane B: 3885/7 = 555 m/h
His total bill, with tax, was $7.95. He paid 6 percent sales tax. How much did he pay for the cooler alone without the tax?
The amount that he pays for the cooler alone without the tax will be $7.37.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
His total bill, with tax, was $7.95. He paid 6 percent sales tax.
Let 'x' be the total bill without the sales tax. Then the equation is given as,
107.95% of x = $7.95
1.0795x = $7.95
x = $7.37
The amount that he pays for the cooler alone without the tax will be $7.37.
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Several years ago, the average earnings for male workers between the uges of 25 and 34 with a high school diploma was $31,560. Comparing this
value in constant dollars to the average earnings 13 yr later showed that the average earnings have decreased to $28,700. Find the average rate of
change in dollars per year for this time period.
[ Hint: Use the ordered pairs (0, 31,560) and (13, 28,700).]
Using slope of the graph, The average rate of change in dollars per year for this time period is -220.
How is a slope determined?You may determine the slope of the line by determining the rise and the run using two of the line's points. The rise and the run are terms used to describe changes in height between two points. Rise divided by Run gives you the slope. Rise/run on a slope Rise or run is a slope.
We have coordinates that represent the given information,
Let x = number of year,
Y = Change in income,
So, Our coordinates become = (0, 31560) and (13, 28700)
The average rate of change is defined as slope of the graph
Slope of graph = y2 - y1 / x2 - x1
⇒ 28700 - 31560 / 13 - 0
⇒ -2860 / 13
⇒ - 220
The value of slope is negative, which indicates depreciation.
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help me please asap!!!
The scale factor for the dilation in this problem is given as follows:
2.
What is a dilation?A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.
The equivalent side lengths in this problem are given as follows:
AD, with length 8 - 0 = 8.DE, with length 8 - 4 = 4.The dilated triangle is triangle DAB, hence the scale factor is obtained as follows:
k = 8/4 = 2.
(that is, the side lengths of triangle DEF were multiplied by 2 to generate triangle DAB).
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find exact value of sin -7pi/6??
Climbing Mt. Everest is not an easy task! Not only is it a difficult hike, but the Earth's atmosphere
decreases exponentially as you climb above the Earth's surface, and this makes it harder to breathe. The air
pressure at the Earth's surface (sea level) is approximately 14.7 pounds per square inch (or 14.7 psi). In
Denver, Colorado, elevation 5280 feet, the air pressure is approximately 12.15 psi.
a.) write an exponential equation
b.) what is the air press at the top of mount everest, elevation 29,000 feet?
The exponential equation that represents the relationship between the air pressure and the elevation above the Earth's surface is
y = 14.7 x 0.827^x
The air pressure at the top of Mount Everest, elevation 29,000 feet is approximately 1.931 psi
Finding exponential equation and calculating air pressureTo write an exponential equation for the relationship between the air pressure and the elevation above the Earth's surface, we can use the form y = a x b^x,
where y is the air pressure,
x is the elevation,
and a and b are constants.
We can use the data given in the problem to find the values of a and b.
Let y = air pressure (psi)
x = elevation (feet)
We know that at sea level (x = 0), y = 14.7 psi
At Denver, Colorado, elevation 5280 feet, y = 12.15 psi
We can use these two points to find the values of a and b in the equation y = a x b^x
12.15 = 14.7 x b^5280
b = (12.15/14.7)^(1/5280)
b = 0.827
a = 14.7
The exponential equation that represents the relationship between the air pressure and the elevation above the Earth's surface is
y = 14.7 x 0.827^x
b.) To find the air pressure at the top of Mount Everest, elevation 29,000 feet, we can substitute that value for x into the exponential equation.
y = 14.7 x 0.827^29000
y = 1.931 psi
The air pressure at the top of Mount Everest, elevation 29,000 feet is approximately 1.931 psi. It's worth noting that this is a very low air pressure and the human body is not able to survive with such low pressure without proper equipment.
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What is the Puzzle code for puzzle 2.
Linear equation Digital Escape!!!
Please need the puzzle code for PUZZLE 2. WILL GIVE BRAINLIST.
All the equations are matched with the line graph are given below.
And the letter code is AEBG.
What is graph?In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.
The relationships between two or more items are frequently represented by the points on a graph.
Given:
All the equations are matched with the line graph:
A: y = 3x + 1 → Line 1
B: y = -2x + 2 → Line 3
G: y = -1/2x + 2 → Line 4
E : y = x+ 4 → Line 2
The letter code is AEBG.
Therefore, the letter code is AEBG.
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5. Over the last 35 years, the average price of computers has dropped 76%. People now spend an average of $1,456 less for a computer today. How much did the average computer cost 35 years ago? Round to the nearest cent O$1,899.79 O $2,262.79 O $459.79 O$1,915.79
The average of cost computers was $1,915.79 35 years ago. The correct answer would be an option (D).
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
Let the average computer cost was x 35 years ago.
As per the question, we have
76% of x = $1,456
76% is expressed as 0.76 in decimal form
0.76x = 1,456
x = 1,456/0.76
x = 1,915.7947
Rounded to the nearest cent, and we get
x = 1,915.79
Thus, the average of cost computers was $1,915.79.
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Rectangular pool is 7 m wide and 12 m long if you swim diagonally from one corner to the other how many meters are you swim approximately the answer to the nearest 10th
The measure of diagonal in a rectangular pool is 13.9 meters. Therefore, option A is the correct answer.
Given that, a rectangular pool is 7 meters wide and 12 meters long.
What is the Pythagoras theorem?
The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.
We know that, measure of each angle in a rectangle is 90°.
Let the length of diagonal of rectangular pool be x
So using Pythagoras theorem, we get
x²=12²+7²
⇒ x²=144+49
⇒ x²=193
⇒ x=√193
⇒ x=13.89
≈13.9 meters
The measure of diagonal in a rectangular pool is 13.9 meters. Therefore, option A is the correct answer.
males in the netherlands are the tallest, on average, in the world with an average height of centimeters (cm) (bbc news website). assume that the height of men in the netherlands is normally distributed with a mean of cm and standard deviation of cm.
The probability that a Dutch male is taller than 195 cm is 0.2525
Out of a random sample of 1000 Dutch men, people taller than 190 cm are 253 in number using statistics.
Mean = 183 cm
SD = 10.5 cm
Z score = ( Value - Mean ) /SD
Dutch male is shorter than 175 cm
Z score = ( 175 - 183)/10.5 = -0.762
from z score table probability is 0.223
Dutch male is taller than 195 cm
Z score = ( 195 - 183)/10.5 = 1.143
from z score table probability is 0.8735 for shorter than 195 cm
Hence probability that a Dutch male is taller than 195 cm = 1 - 0.8735
= 0.1265
Dutch male is between 173 and 193 cm
Z score = ( 173 - 183)/10.5 = -0.952 => 0.1705Z score = ( 193 - 183)/10.5 = 0.952 => 0.8295
0.8295 - 0.1705 =0.659
taller than 190 cm
Z score = ( 190 - 183)/10.5 = 0.6667
taller than 190 cm = 1 - 0.7475 = 0.2525
Hence in 1000 = 252.5 = 253
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The complete question is :
Height of Dutch Men. Males in the Netherlands are the tallest, on average, in the world with an average height of 183 centimeters (cm) (BBC News website). Assume that the height of men in the Netherlands is normally distributed with a mean of 183 cm and standard deviation of 10.5 cm.a.What is the probability that a Dutch male is shorter than 175 cm?b.What is the probability that a Dutch male is taller than 195 cm?c.What is the probability that a Dutch male is between 173 and 193 cm?d.Out of a random sample of 1000 Dutch men, how many would we expect to be taller than 190 cm?
delta airlines quotes a flight time of hours, minutes for its flights from cincinnati to tampa. suppose we believe that actual flight times are uniformly distributed between hours and hours, minutes.
The required probability for the given delta airlines is given by :
a. Probability of flight late no more than 5 minutes is 0.25.
b. Probability of flight late more than 10 minutes is 0.5
c. Expected flight time is equal to 130 minutes.
Flight time from Cincinnati to Tampa = 2 hours 5 minutes
Actual time distributed between 2 hours and 2 hours 20 minutes
2 hours = 120 minutes
2 hours 20 minutes = 140 minutes
f(x) = [tex]\left \{ {{\frac{1}{( 140 - 120)} , 120 \leq x\leq 140\atop {0 , x = 0 }} \right.[/tex]
a. Probability of flight no more than 5 minutes late
[tex]\int_{130}^{125} \frac{1}{20} dx[/tex]
= 1 / 4
= 0.25
b. Probability of flight more than 10 minutes late
[tex]\int_{135}^{125} \frac{1}{20} dx[/tex]
= 1/2
= 0.5
c. Expected flight time in minutes
= [tex]\int_{140}^{120} \frac{x}{20} dx[/tex]
= 130 minutes
Therefore, the required probability are given by :
a. Probability of flight late no more than 5 minutes is 0.25.
b. Probability of flight late more than 10 minutes is 0.5
c. Expected flight time is equal to 130 minutes.
The above question is incomplete , the complete question is :
Delta Airlines quotes a flight time of 2 hours, 5 minutes for its flights from Cincinnati to Tampa. Suppose we believe that actual flight times are uniformly distributed between 2 hours and 2 hours, 20 minutes. What is the probability that the flight will be no more than 5 minutes late (to 2 decimals)? What is the probability that the flight will be more than 10 minutes late (to 2 decimals)? What is the expected flight time, in minutes?
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help me with 6th grade math
The value of x that solves the equation is x = 28.10, and there are 4 eggs per batch.
Which value satisfies the equation?Particularly x is not in that equation, but we can write:
5x = 140.50
To solve for x, we need to divide both sides by 5, then we will get:
5x/5 = 140.50/5
x = 140.50/5
x = 28.10
How many eggs are needed per batch?To find this, we need to take the quotient between the number of eggs and the number of batches, so we will get:
12 eggs.
3 batches.
12/3 = 4
This means that you need 4 eggs per batch.
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Samantha bought an equal number of $11.00,$9.00 and $8.00 tickets for a concert. she spent $196 for all of the tickets. how many of each did she
Answer: Samantha bought 7 tickets for a concert
Step-by-step explanation:
$11.00 + $9.00 + $8.00 = 28
$196 / 28 = 7
Imagine a study that looks at nutrition and memory. Each subject is randomly assigned to one of three groups: high-protein diet; high-fiber diet; standard diet (control). After a month on this diet, each subject undergoes a memory test. The initial statistical analysis of this study would be conducted using __________ because __________.
A. Analysis of variance (ANOVA) / there are more than two levels of the independent variable
B. Analysis of variance (ANOVA) / there are more than two levels of the dependent variable
C. A t test / there are only two experimental conditions (plus a control condition)
D. A t test / the goal would be to compare high-protein with control and high-fiber with control
Options
I can’t fit the whole question but if anybody knows this it would be great
The glide reflection that maps triangle ABC into triangle A'B'C' is given as follows:
Shift right of 7 units and reflection over the x-axis.
What is a glide reflection?The glide reflection is a combination of a reflection with a translation.
The vertices of the original triangle are given as follows:
A(-3,-2), B(-6,-5) and C(-1,-4).
The vertices of the reflected triangle are given as follows:
A'(4,2), B'(1,5) and C'(6,4).
Hence the composite rule is given as follows:
(x,y) -> (x + 7, -y).
Meaning that the glide reflection is defined as follows:
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NO LINKS!!!
Please help me #49 and 50
Answer:
49. a) A - C - 1
49. b) 1 - 2R
49. c) 2Q - P
50. x = 103
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{5cm}\underline{Log laws}\\\\$\log_axy=\log_ax + \log_ay$\\\\$\log_a \left(\dfrac{x}{y}\right)=\log_ax - \log_ay$\\\\$\log_ax^n=n\log_ax$\\\\$\log_ab=c \iff b=a^c$\\\\&\log_aa=1$\\ \end{minipage}}[/tex]
Question 49Part a
Given:
[tex]\log_5 9=A[/tex]
[tex]\log_5 6=B[/tex]
[tex]\log_5 11=C[/tex]
[tex]\begin{aligned}\log_5 \dfrac{9}{55}&=\log_5 9 - \log_5 55\\&=\log_5 9 - \log_5 (11 \cdot 5)\\&=\log_5 9 - (\log_5 11 + \log_5 5)\\&=\log_5 9 - \log_5 11 - \log_5 5\\&=A-C-1\\\end{aligned}[/tex]
Part b
Given:
[tex]\log_3 10=R[/tex]
[tex]\log_3 4=S[/tex]
[tex]\log_3 11=T[/tex]
[tex]\begin{aligned}\log_3 \dfrac{3}{100}&=\log_3 3 - \log_3 100\\&=\log_3 3 - \log_3 (10 \cdot 10)\\&=\log_3 3 - \log_3 10^2\\&=\log_3 3 - 2\log_3 10\\&=1-2R\\\end{aligned}[/tex]
Part c
Given:
[tex]\log_3 4=P[/tex]
[tex]\log_3 10=Q[/tex]
[tex]\log_3 7=R[/tex]
[tex]\begin{aligned}\log_3 25&=\log_3 \dfrac{100}{4}\\&=\log_3 100 - \log_3 4\\&=\log_3 (10 \cdot 10) - \log_3 4\\&=\log_3 10^2 - \log_3 4\\&=2 \log_3 10 - \log_3 4\\&=2Q-P\end{aligned}[/tex]
Question 50The error was in line 4 of the calculation. The log law
[tex]\log_ab=c \iff b=a^c[/tex]was not applied correctly.
The correct solution is:
[tex]\begin{aligned}3 \log (x-3) + 1 & = 7\\3 \log (x-3) & = 6\\\log (x-3) & = 2\\x-3&=10^2\\x&=3+10^2\\x&=103\end{aligned}[/tex]
Describe the y-intercept and end behavior of the following graph: The graph starts on the top left and curves down to the right, crosses the x axis at negative 2, then crosses the y axis at negative 4 and continues decreasing to the bottom right. a (−2, 0); The graph approaches y = −6 to the right. b (0, −5); The graph approaches y = −6 to the right. c (−2, 0); The graph decreases to the left. d (0, −5); The graph decreases to the left.
The correct alternative is -
The graph starts on the top left and curves down to the right, crosses the {x} axis at -2, then crosses the {y} axis at -4 and continues decreasing to the bottom right to (−2, 0).What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the graph of the function.
The correct alternatives are -
The graph starts on the top left and curves down to the right, crosses the {x} axis at -2, then crosses the {y} axis at -4 and continues decreasing to the bottom right to (−2, 0).Therefore, the correct alternative is -
The graph starts on the top left and curves down to the right, crosses the {x} axis at -2, then crosses the {y} axis at -4 and continues decreasing to the bottom right to (−2, 0).To solve more questions on graphs, visit the link below-
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Find the following for the given functions.
f(x): =
X/X + 9 ,
g(x) = x³
The results of operations between functions:
Case A: (f + g) (x) = x / (x + 9) + x³
Case B: (f - g) (x) = x / (x + 9) - x³
Case C: (f · g) (x) = x⁴ / (x + 9)
Case D: (f / g) (x) = 1 / [x² · (x + 9)]
Function (f / g) (x) has the following domain: x ∈ R - {- 9, 0}.
How to find the result of operations between two functions
According to function theory, we can obtain a function with more complexity by operations between two functions, the most common operations are listed below:
Addition: (f + g) (x) = f (x) + g (x)Subtraction: (f - g) (x) = f (x) - g (x)Multiplication: (f · g) (x) = f(x) · g(x)Division: (f / g) (x) = f (x) / g (x)Now we proceed to determine the resulting function:
Case A:
(f + g) (x) = f(x) + g(x)
(f + g) (x) = x / (x + 9) + x³
Case B:
(f - g) (x) = f(x) - g(x)
(f - g) (x) = x / (x + 9) - x³
Case C:
(f · g) (x) = f (x) · g (x)
(f · g) (x) = [x / (x + 9)] · x³
(f · g) (x) = x⁴ / (x + 9)
Case D:
(f / g) (x) = f(x) / g(x)
(f / g) (x) = [x / (x + 9)] / x³
(f / g) (x) = 1 / [x² · (x + 9)]
The domain of (f / g) (x) is the set of all values of x-values such that the function exists. In this case, we must determine the values of the denominator of (f / g) (x) such that it is not equal to zero.
x² · (x + 9) = 0
x = 0 or x = - 9
The domain of (f / g) (x) is: x ∈ R - {- 9, 0}.
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The College Board reported that in 2014, the mean Math Level 2 SAT subject test score was 686 with a standard deviation of 96. Assuming scores follow a bell-shaped distribution; use the empirical rule to find the percent of students who scored less than 494.
Feedback: Incorrect. The z-score for this situation is (494 - 686) / 96 = -2. Recall that 95% of observations will fall within 2 standard deviations of mean. This means that 2.5% of observations will fall above 2 standard deviations and 2.5% of observations will fall below 2 standard deviations. This question asks for the percent of students who scored less than 494 (below 2 standard deviations). The correct answer is 2.5%.
Totally correct about the mentioned before is 2.5%. This is because the z-score for this situation is (494 - 686) / 96 = -2. According to the Empirical Rule, approximately 95% of observations will fall within 2 standard deviations of the mean. In this case, the question is asking for the percent of students who scored less than 494, which is below 2 standard deviations, so the answer is 2.5%.
SAT Math Level 2 ScoreThe Empirical Rule states that for a normal distribution, approximately 68% of the data will fall within one standard deviation of the mean, approximately 95% of the data will fall within two standard deviations of the mean, and approximately 99.7% of the data would get fall within 3 standard deviations of the mean. So if we know the mean and standard deviation of a normal distribution, we can use this rule to estimate the percentage of data that falls within a certain range.
In this specific question, the mean of Math Level 2 SAT subject test score was 686 with a standard deviation of 96. We were asked to find the percent of students who scored less than 494. To find this we first calculated the z-score which is (494 - 686) / 96 = -2.
Since the z-score is -2 it means that it's 2 standard deviation below the mean, and according to the Empirical rule 95% of observations will fall within 2 standard deviations of mean. This means that 2.5% of observations will fall above 2 standard deviations and 2.5% of observations will fall below 2 standard deviations. So the answer is 2.5%.
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Three vertices of a parallelogram are shown in the figure below.
Give the coordinates of the fourth vertex.
(-3, 1)
(3,-1)
(5,-5)
The coordinates of the fourth vertex of the parallelogram are (11, -7).
What is a parallelogram?
A parallelogram is a quadrilateral with opposite sides that are parallel to each other. The opposite sides of a parallelogram are also equal in length.
The fourth vertex of a parallelogram can be determined by finding the vector that connects one vertex of the parallelogram to the opposite vertex, and then adding that vector to the third vertex given in the problem.
The vector that connects the first vertex (-3, 1) to the third vertex (5, -5) is (8, -6). To find the fourth vertex, we add this vector to the second vertex (3, -1) :
(3,-1) + (8, -6) = (11, -7)
Hence, the coordinates of the fourth vertex of the parallelogram are (11, -7).
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