Value of composite functions (g-f)(x) and (f/g)(x) are x² - 2x - 8 and
(x+1)/(2x - 3) respectively.both of these functions don't have the same
domain and range.
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given functions,
f(x) = x² - 3x - 4
g(x) = 2x² - 5x - 12
1. (g - f)(x)
= g(x) - f(x)
= 2x² - 5x - 12 - (x² - 3x - 4)
= 2x² - 5x - 12 - x² + 3x + 4)
= x² - 2x - 8
x is defined for all real numbers
Domain = (-∞, ∞)
let y = x² - 2x - 8
x = √y + 2(x) - 8
Function is defined for y ≥ 9
Range is {y∈R , y ≥ 9}
2. (f/g)(x)
= f(x)/g(x)
= (x² - 3x - 4)/(2x² - 5x - 12)
= (x² - 4x + x - 4)/(2x² - 8x + 3x - 12)
= (x(x - 4) + 1(x - 4))/(2x(x - 4) + 3 (x - 4))
= (x+1)(x-4)/(2x+3)(x-4)
= (x+1)/(2x - 3)
function is defined for x ≠ 3/2, Domain is {x ∈ R : x ≠ 3/2}
Let y = (x+1)/(2x - 3)
y.2x - 3y = x + 1
-3y - 1 = x - 2xy
x = (-1 - 3y)/(1 - 2y)
function is defined for y ≠ 1/2, Range is {y ∈ R : y ≠ 1/2}
Domain and range are not same for both functions.
Hence, Value of composite functions (g-f)(x) = x² - 2x - 8 and
(f/g)(x) = (x+1)/(2x - 3), Domain and range is not same for both functions.
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A procedure for using sample data to find the estimated regression equation isa. point estimation. b. interval estimation.c. the least squares method. d. extrapolation..
A procedure for using sample data to find the estimated regression equation is (c) the least squares method.
The least squares method is a commonly used statistical procedure for finding the estimated regression equation by minimizing the sum of the squared differences between the observed and predicted values.
The goal of this method is to find the line of best fit that closely represents the relationship between the independent and dependent variables in the sample data. The regression equation obtained from the least squares method can be used to make predictions about the dependent variable based on the values of the independent variable.
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Martín did the following work and found his surfing increased 50% from the first week to the second.
Percent of change= amount of change/Original amount = 9-6/6 = 3/6 =0.5.
0.5—->50%. Describe Martin’s method for finding percent change in your own words.
The surfing increased by 50% from the first week to the second. His method is correct.
What is the percentage change?The amount of any product is given as if it were a percentage of a hundred. The ratio is one-quarter of one hundred. % is an abbreviation for one hundred percent. It is represented by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
The Surfing 6 seconds to reach 9 seconds. Then the percentage is given as,
P = [(9 - 6) / 6] x 100
P = (3 / 6) x 100
P = 0.50 x 100
P = 50%
The surfing increased by 50% from the first week to the second. His method is correct.
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A group of marine biologists tags 45 great white sharks off the coast of Mexico
to study migratory patterns. All of the tag numbers are unique. Weeks later, the
marine biologists travel to Hawaii. While there, they randomly capture and release
20 great white sharks per day, for three consecutive days. On the first day, 3 of the
sharks have the original tags. On the second day, 2 of the sharks have the original
tags. On the third day, 4 of the sharks have the original tags. Based on the data,
what is the estimated population of great white sharks that have migrated from
Mexico to Hawaii?
Yall are some cheaters. Quit looking it up on this website like, dang....
5/18 + 11/12
fractions
adding fractions with unlike denominators
Answer:
= 43.
Step-by-step explanation:
[tex] \frac{5}{18} + \frac{11}{12} \\ = 36 \times \frac{5}{18} + 36 \times \frac{11}{12} \\ = 2(5) + 3(11) \\ = 10 + 33 \\ = 43[/tex]
Note// the LCM for 18 and 12 is 36.
Naomi has taken six science tests so far this year. The tests are out of 100 points, and she has gotten the following scores.
64, 88, 92, 86, 81, 92
What must Naomi score on her seventh test in order to raise her mean to an 85?
88
92
85
95
Answer:92
Step-by-step explanation:
[tex]\frac{64+88+92+89+81+92+x}{7} =85[/tex]
85 x 7 = 595
595 - 64 - 88 - 92 - 89 - 81 - 92 = 92
Answer:
Naomi needs to score a 92 on her seventh test to raise her mean to an 85.
Step-by-step explanation:
Let's call the score Naomi needs to get on her seventh test "x".
To find out what score she needs to raise her mean to 85, we can set up an equation:
(64 + 88 + 92 + 86 + 81 + 92 + x) / 7 = 85
We add up all her scores so far (64 + 88 + 92 + 86 + 81 + 92) and add the score she needs to get on her seventh test (x). We divide the sum by the total number of tests (7) to get the mean score of 85.
Simplifying the equation, we get:
503 + x = 595
Subtracting 503 from both sides, we get:
x = 92
A deli is trying out new labels for their cylindrical-shaped wheels of cheese. The label covers the entire wheel except the circular top and bottom.
If the wheel has a radius of 22 centimeters and a height of 16 centimeters, how many square centimeters of the wheel does the label cover? (Approximate using pi equals 22 over 7)
15,488 over 7 square centimeters
36,784 over 7 square centimeters
1,936 over 7 square centimeters
340,736 over 7 square centimeters
The true response would be 15,488/7 square centimeters based on the information provided.
What is Square used for?Square offers businesses a range of goods and services to help them complete sales transactions, use marketing strategies, and control their finances, inventory, and workforce.
The lateral surface (the curved portion of the cylinder) is added to the areas of a round top and bottom to figure out the surface surface of the cylindrical cheese wheel. The perimeter of the base (2πr, where r is the radius) as well as the height can be used to compute the lateral surface area. Each round top and bottom's surface area is πr².
Hence, the cheese wheel's overall surface area is:
(2πr × h) + (2πr²)
Inputting the values provided yields:
(2 × 22/7 × 22 × 16) + (2 × 22/7 × 22 × 22)
When we simplify and find the total area of the surface, we obtain:
15,488/7 square centimeters
As a result, 15,488/7 square centimeter of the cheese wheel are covered by the label.
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I will give you a Brainliest
Answer:
192
Step-by-step explanation:
2x9=18
18x12=192
in what time will the simple interest on Rs7560 be Rs1102.50 at 25/4% per annum
The amount of time in which the simple interest on Rs7560 be Rs1102.50 at 25/4% per annum, 5 years
What is simple interest?Simple interest is an amount which is calculated for a certain period of time and for a certain rate, in simple interest calculation there are three factors which we consider: principal amount(P), rate(R) and time(T).
Every time we calculate simple interest the principal values will be the same unlike compound interest.
Formula; Simple Interest(I) = P × R × T/100
To find the time it takes for the simple interest on Rs. 7560 to be Rs. 1102.50 at 25/4% per annum, we can use the formula for simple interest:
We are given I = 1102.50 and P = 7560, and the interest rate is 25/4% per annum, which we can convert to a decimal:
r = 25/4% ÷ 100
= 0.25/4
= 0.0625
Now, we can substitute the known values into the formula and solve for t:
1102.50 = 7560 x r x t
1102.50 / 7560 = r x t
t = 1102.50 / (7560 x 0.0625)
t = 5 years
So, it will take 5 years for the simple interest on Rs. 7560 to be Rs. 1102.50 at 25/4% per annum.
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3. Xavier has $43 in his savings account and plans to save $15 each week. Write an alger
expression to represent how much Xavier will have in his savings account after w weeks.
An algebraic expression to represent how much Xavier will have in his savings account after w weeks is; y = 15w + 43
How to solve Linear Equation Word problems?The general form of the equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
We are given that Xavier has $43 in his savings account. Thus;
y-intercept = $43
He plans to save $15 each week. Thus;
Slope = $15
Now, after w weeks, the total savings is expressed as;
y = 15w + 43
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a person is standing exactly 36 ft from a telephone pole there is a 30 degree angle of elevation from the ground to the top of the pole. what is the height of the pole
Answer:
Therefore, the height of the pole is approximately 20.79 feet.
Step-by-step explanation:
the person is standing at point A, which is 36 ft away from the base of the telephone pole. The angle of elevation from the ground to the top of the pole is 30 degrees. We want to find the height of the pole, which is represented by "h" in the diagram.
To solve for "h", we can use the tangent function, which relates the opposite side (height) to the adjacent side (distance from the pole to the person) of a right triangle:
tan(30°) = h / 36
We can solve for "h" by multiplying both sides by 36 and taking the tangent of 30 degrees:
h = 36 * tan(30°)
h = 36 * 0.5774 (rounded to four decimal places)
h ≈ 20.79
Therefore, the height of the pole is approximately 20.79 feet.
Answer:
20.78460969082652752232935609807
Step-by-step explanation:
;)
please help me on this
Answer:
[tex]\frac{4}{90}[/tex]
Step-by-step explanation:
[tex]\frac{4}{9}[/tex] - [tex]\frac{4}{10}[/tex]
to subtract the fractions we require them to have a common denominator
the LCM of 9 and 10 is 90
= = [tex]\frac{4(10)}{9(10)}[/tex] - [tex]\frac{4(9)}{10(9)}[/tex]
= [tex]\frac{40}{90}[/tex] - [tex]\frac{36}{90}[/tex]
= [tex]\frac{40-36}{90}[/tex]
= [tex]\frac{4}{90}[/tex]
Anita uses one sheet of paper to make a calendar showing each month of the year. Draw Anita’s calendar. Show how she can divide her calendar so that each month is given the same space. What fraction of the calendar does each month receive
The requried, each month receives 1/12 of the calendar or about 8.33% of the total space.
What is the fraction?A fraction is a mathematical concept that can be used to express a portion of a whole or a number that can be written as the ratio of two integers.
Here,
Anita can start by drawing a large rectangle on the paper to represent the entire year. Then, she can divide the rectangle into 12 equal parts, each representing a month. One way to do this is to draw four vertical lines to divide the rectangle into five equal columns, and then draw three horizontal lines to divide each column into four equal rows.
Each of the 12 parts represents 1/12 or one-twelfth of the calendar. Therefore, each month receives 1/12 of the calendar, or about 8.33% of the total space.
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it is possible to make a ratio between 2 kg and 3m? write with reason
It is not possible to make a ratio between 2kg and 3m, as the measures have different units of measurement.
How to obtain the ratio between two amounts?The ratio between two amounts a and b is obtained applying a proportion, dividing the amount a by the amount b.
The division can only be calculated if the two amounts have the same unit of measurement, for example, if both are kg or if both are m.
As 2 kg and 3 m have different units of measurement, a ratio cannot be calculated between these two units.
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1. draw the graphs of:
a. g(x) = -4x - 5
b. h(x) = - 4x - 12
c. j(x)= -4x -15
2. Write an equation for the linear function with a gradient of - 4 and an
unknown y-intercept of k.
1. a. The graph for the g(x) = -4x - 5 is mentioned in the image below.
1. b. The graph for the h(x) = - 4x - 12 is mentioned in the image below.
1. c. The graph for the j(x)= -4x -15 is mentioned in the image below.
2. The equation for the linear function with a gradient of - 4 and an unknown y-intercept of k is y = -4x + k.
What is slope intercept form?A slope-intercept form is an equation that represents a straight line and is written as y = mx + c, where m is the gradient and c is the y-intercept. If c becomes zero, it passes through the origin.
1. a.
The function g(x) = -4x - 5 represents a straight line that has a slope of -4 and a y-intercept of -5.
When x = 0, g(x) = -5. The point is (0,-5).
When x = 1, g(x) = -9. The point is (1,-9).
When x = -1, g(x) = -1. The point is (-1,-1).
The graph of the function is given below.
1. b.
The function h(x) = -4x - 12 represents a straight line that has a slope of -4 and a y-intercept of -12.
When x = 0, h(x) = -12. The point is (0,-12).
When x = 1, h(x) = -16. The point is (1,-16).
When x = -1, h(x) = -8. The point is (-1,-8).
The graph of the function is given below.
1. c.
The function j(x) = -4x - 15 represents a straight line that has a slope of -4 and a y-intercept of -15.
When x = 0, j(x) = -15. The point is (0,-15).
When x = 1, j(x) = -15. The point is (1,-19).
When x = -1, j(x) = -11. The point is (-1,-1).
The graph of the function is given below.
2.
The slope-intercept form of a line is y = mx + c. On substituting m = -4 and c = k into the equation, it gets reduced to y = -4x + k.
Therefore, the obtained answer is y = -4x +k.
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100 POINTS!
Select the true statement that describes a right circular cone.
A right circular cone does not have a base.
A right circular cone has a rectangular face.
A right circular cone has one apex.
A right circular cone has 7 edges.
Answer:
C
Step-by-step explanation:
It makes the most sense.
Determine the point ths of the way from point A: (3, 2) to point B: (4, -3) shown on the coordinate plane below.
The point 3/4th of the way from point A to point B is (3.25, -1.25).
What is the coordinate geometry?
In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements
To determine the point 3/4th of the way from point A to point B, we can use the midpoint formula to find the coordinates of the midpoint M of the line segment AB, and then use those coordinates to find the point 3/4th of the way from point A to point B.
The midpoint M of the line segment AB can be found using the midpoint formula:
M = ((x1 + x2)/2, (y1 + y2)/2)
where (x1, y1) and (x2, y2) are the coordinates of points A and B, respectively.
Substituting the given coordinates, we get:
M = ((3 + 4)/2, (2 - 3)/2) = (3.5, -0.5)
Now we can find the point 3/4th of the way from point A to point B by starting at point A and moving 3/4th of the way towards point B. To do this, we can use the following formula:
P = ((1 - 3/4)*x1 + (3/4)*x2, (1 - 3/4)*y1 + (3/4)*y2)
Substituting the coordinates of points A and B, we get:
P = ((1 - 3/4)*3 + (3/4)*4, (1 - 3/4)2 + (3/4)(-3)) = (3.25, -1.25)
Hence, the point 3/4th of the way from point A to point B is (3.25, -1.25).
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A ramp 22 ft long rises to a platform. The bottom of the platform is 12 ft from the foot of the ramp. Find x, the angle of elevation of the ramp. Round the answer to the nearest tenth of a degree.
The angle of elevation is 61.34°.
What is angle of elevation?An angle of elevation is defined as an angle between the horizontal plane and line of sight from the observer's eye to some object above.
here, we have,
Given here, ramp 18 ft long rises to a platform.
The bottom of the platform is 13 ft from the foot of the ramp.
Let the angle be x then angle of elevation is
tanx =22/12
x = tan⁻¹(22/12)
x =61.34°
Hence, the angle of elevation is 61.34°
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1 and 2 form a linear pair. The
measure
measure
of 2 is six more than twice the
of 1. Find m2
Answer:
Step-by-step explanation:
a + 2a + 6 = 180
3a = 174
a = 58
2(58) + 6 = 122
Tickets for a game cost a dollars for adults and c dollars for children the expression 3a+5c represents the cost in dollars for a family for the game what is the cost for the family when an adult ticket is 13 and a child ticket costs 8$ Relatively simple but my brain is just farting thanks !
Since an adult ticket costs $13, a child ticket is $8, and expression 3a+5c indicates the price in dollars for a family to attend the game, the total cost is $79 for the event.
what is expression ?Increasing, partitioning, adding, or reducing are all doable in mathematics. As an example, take this expression: Function is defined, equation, and number The components that compose an algebraic equations are numbers, variables, but rather functions (such as addition, subtraction, multiplication or division etc.) One can differentiate two terms or sentences. The terms "expression" or "algorithmic expression" refer to any detailed estimate that suitable parameter, numbers, or an arithmetic action among both them. For instance, the phrase 4m + 5 consists of the terms 4m but also 5, as well as the number m from the given expression, which are all separated by that of the arithmetic symbol +.
given
expression 3a+5c represents the cost
3a + 5c
= 5 * 8 + 3 * 13
= 39 + 40
= 79
Since an adult ticket costs $13, a child ticket is $8, and expression 3a+5c indicates the price in dollars for a family to attend the game, the total cost is $79 for the event.
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what is the value of 5g in mg?
The value of 5g in mg is 5000mg. This is because 1g is equal to 1000mg, and 5g is equal to 5 times that amount, or 5000mg.
When converting between different metric units of mass, the prefixes are used to denote the multiple of the base unit. In this case, the base unit is the gram, and the prefix we are using is 'milli', which is equal to one thousandth of the base unit. Therefore, in order to convert 5g to mg, the prefix 'milli' is multiplied by the base unit of grams, resulting in a value of 5000mg.When converting between metric units, it is important to remember that the decimal point moves right by a number of places equal to the number of zeroes in the prefix. For example, if we were converting 5g to kg, the prefix 'kilo' has three zeroes, so the decimal point would move three places to the right, resulting in a value of 0.005kg.When converting from a larger unit to a smaller unit, the numerical value will increase, and when converting from a smaller unit to a larger unit, the numerical value will decrease. In this case, we are converting 5g to mg, which is a smaller unit, so the numerical value of 5g increases to 5000mg.
Overall, the value of 5g in mg is 5000mg. This is because 1g is equal to 1000mg, and the prefix 'milli' is multiplied by the base unit of grams, resulting in a value of 5000mg.
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1. A slide is 15 ft. high. If the slides makes a 50° angle with theground, how long is the slide?
The approximate measure of the slide is 20 feet.
What are heights and distances?Heights and Distances is a study about the applications of Trigonometry. It has many real-life applications, such as measuring the object’s height, depth of the object, the distance between two celestial objects etc. The formulas and the ratios of trigonometry are helpful in the study of heights and distances.
Given that, a slide is 15 feet high and the slides makes a 50° angle with the ground.
Let the length of the slide be x.
Now, sin50° =15/x
0.766=15/x
x=15/0.766
x=19.58
≈ 20 feet
Therefore, the approximate measure of the slide is 20 feet.
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What is the value of 1 gallon in kg?
Answer:
kg = gal × 3.7854 × density.
Step-by-step explanation:
Determine whether each number is an integer, a rational number that is not an integer, or an irrational number. pls help very urgent
Integer: 12
Irrational numbers: -2√10 and √20
Rational numbers: 17/4, 0.25, and -77/11.
What are integers?Any positive or negative number without fractions or decimal places is known as an integer, often known as a "round number" or "whole number."
Given:
There are rational and irrational numbers in the image.
The numbers can be written in the form of p/q, where q is never zero is rational numbers.
And rest of the numbers are irrational numbers.
So, the solutions are given in the image below.
√144 = 12
0.25 = 25/100 = 1/4
Therefore, the solutions are given in the image below.
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Which one of the following best defines the notion of the significance level of a hypothesis test?
a. The probability of rejecting H_o, whether it's true or not
b. The probability of observing a sample statistic more extreme than the one actually obtained, assuming the null hypothesis is true
c. The probability of the type I error
d. The probability of the type II error
C. The probability of the type I error best defines the notion of the significance position of a thesis test.
The significance position, denoted by alpha( α), is the probability of rejecting the null thesis(H_o) when it's actually true. This is also known as a type I error, which occurs when we inaptly reject a true null thesis.
Option a isn't correct because the probability of rejecting H_o, whether it's true or not, isn't fixed and depends on the sample and the chosen significance position.
Option b isn't correct because it describes the p- value, which is a affiliated conception but not the significance position. The p- value is the probability of observing a sample statistic as extreme or more extreme than the one actually attained, assuming the null thesis is true.
Option d is also not correct because it describes the probability of a type II error, which occurs when we fail to reject a false null thesis. The probability of a type II error is denoted by beta( β) and is told by factors similar as sample size and effect size.
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What does t-test assuming equal variances mean?
The t-test assuming equal variances means Pooled t-test in which variances of the two sample populations are equal.
The pooled t-test is the statistical procedure that assumes that population variances are equal. Finding a weighted average of the two independent sample variances is referred to as pooling. By combining data from samples from populations 1 and 2, we may estimate the common variance when there is solid evidence that population 1's variance is equal to population 2's variance.
Compare the ratio of the two sample standard deviations as a quick way to verify this. The ratio would be compared as: S1/S2. The ratio would be 1, or, in the event that the two are equal.
However, we cannot anticipate the ratio to be exactly 1, as they are samples and as a result, there will be some errors. Thus, the pooled t-test implies whether the null-hypothesis should be accepted or rejected.
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HJK and RST are supplementary angles. If HJK is 56 , what is the measure of RST?
Answer: The measure of RST is 124 degrees.
Step-by-step explanation:
If HJK and RST are supplementary angles, it means that their sum is equal to 180 degrees. So we can use this information to find the measure of RST.
HJK + RST = 180
Substituting HJK = 56, we get:
56 + RST = 180
Subtracting 56 from both sides, we get:
RST = 180 - 56
RST = 124
Therefore, the measure of RST is 124 degrees.
In the Diagram segment ad bisects angle bac
Since segment AD bisects angle BAC, the value of x is equal to 14.6.
What is an angle bisector?In Mathematics, an angle bisector can be defined as a type of line, ray, or segment, that bisects or divides a line segment exactly into two (2) equal angles.
By applying the angle bisector theorem to this triangle (ΔABC), we have:
AB/BD = AC/DC
19/x = 17/(20 - x)
17x = 19(20 - x)
17x = 380 - 19x
19x + 17x = 380
26x = 380
x = 380/26
x = 14.6.
In conclusion, we can reasonably infer and logically deduce that the value of x in triangle ABC is 14.6.
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In the U.S., shoe sizes are defined differently for men and women, but in Europe, both genders use the same shoe size scale. The accompanying histograrn shows the European shoe sizes of 269 male and female college students, converted from their reported U.S. shoe sizes. a) Describe the shape. b) How many modes does the histogram have? What might explain that?
the shape is bimodal and symmetric and histogram have 38 to 40 and 44 to 46.
If the two peaks are mirror reflections of one another, the bimodal distribution may be symmetrical. symmetrical Cauchy distributions exist. These are not likely to be found in basic statistics. These distributions belong to a family where the anticipated value is hypothetical. the long tails of the logistic distribution. If the data is symmetric but contains more extreme values than one would anticipate from a normal distribution, the logistic and Cauchy distributions are utilized. these different distribution types. It is symmetric for the uniform distribution. Since the odds are same at every location, the distribution is essentially a straight line. The distribution is bimodal and nearly symmetric. There are two modes in the distribution, from 38 to 40 and 44 to 46. The existence of data for both men and women may account for this. Women may prefer the lower mode, whereas males may prefer the upper.
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Look at pic for info
40) Given the information in the figure shown, what is the measure of "angle m" in triangle PQR?
P
68
R
111
Oa.) 45 degrees
Ob.) 179 degrees
Oc.) 44 degrees
Od.) 43 degrees
The measure of angle m is,
⇒ m = 43°
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The triangle PQR is shown in figure.
Now, We know that;
An exterior angle of a triangle is sum of two opposite angle of that triangle.
⇒ m + 68° = 111°
Solve for m;
⇒ m = 111° - 68°
⇒ m = 43°
Thus, The measure of angle m is,
⇒ m = 43°
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What are examples of continuous variable?
Answer:
Step-by-step explanation:
Continuous variables are variables that can take on any value within a specified range. Some common examples of continuous variables include:
Height: Height can be measured in inches, centimeters, or any other unit of length and can take on any value within the range of human heights.
Weight: Weight can be measured in pounds, kilograms, or any other unit of weight and can take on any value within the range of human weights.
Age: Age can be measured in years, months, or days and can take on any value within the range of human ages.
Time: Time can be measured in seconds, minutes, or hours and can take on any value within the range of time that can be measured.
Temperature: Temperature can be measured in degrees Celsius, Fahrenheit, or any other unit of temperature and can take on any value within the range of temperatures that can be measured.
Income: Income can be measured in dollars, euros, or any other currency and can take on any value within the range of human incomes.
These are just a few examples of continuous variables. In general, any variable that can take on an infinite number of values within a specified range can be considered a continuous variable.