Answers
A function is an equation with one solution to every value of x for the variable y. A input of a specific type is paired with exactly 1 output by a function.
What do functions mean?Quantities and their modifications, equations and surrounding structures, locations of forms and forms themselves are all included in the field of mathematics. The term "function" describes the connection between a group of inputs, of which each has a corresponding output. A function is an association between inputs and outcomes in which each input results in a single, unique output. Functions are typically denoted by the letter f. (x). The input is just a variable x. There are four primary categories of functionality available. depending on the following elements: on.
Given:
A function is an equation with one solution to every value of x for the variable y.
Each argument of a specific type is paired with absolutely one output by a function. Typically, functions are named f(x) or g instead of y. (x). When x equals 2, as directed by f(2), we should choose the value of given function.
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Related Questions
Solve the following equation: x = 6.0% X 99.5% X 1.3 X 1.6
Answers
Answer:
0.124176
Step-by-step explanation:
.06 x .995 x 1.3 x 1.6= 0.124176
You change a percent into a decimal by dividing it by 100%
PLSSSS HELP TYYYYYT !!!!!
Answers
Answer:
Total people =107
Women =57
Men =50
Men who don't like tea =20
Men who like tea= 30
Women who like tea = (total people who like tea)-(men who like tea)
Women who like tea= 30
Women who don't like tea =27
a=50
b=30
c=20
d=57
e=30
f=27
Which overlapping triangles are congruent by ASA?
Answers
The overlapping triangles which are congruent by ASA are ΔEBC and ΔADC which is therefore denoted as option C.
What is a Congruent triangle?This is a scenario in which all three corresponding sides are equal and all the three corresponding angles are equal in measure.
Taking ΔEBC and ΔADC, we have the following below:
∠B=∠D (90°)
CB= CD (Given)
∠BCE=∠ACD( Common)
Therefore, by ASA we can deduce that,
Δ EBC ≅ΔADC.
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$2750 is invested at an interest rate of 3.5% APR compounded quarterly. Determine the amount after 7 years. Round your answer to the nearest hundredth.
Answers
Work Shown:
A = P*(1+r/n)^(n*t)
A = 2750*(1+0.035/4)^(4*7)
A = 2750*(1+0.00875)^(28)
A = 2750*(1.00875)^(28)
A = 2750*1.27626052446017
A = 3509.71644226547
A = 3509.72
(5v-w)(5v−w) centimeters, and its length measures (6v+8w)(6v+8w) centimeters.
Answers
Answer:
If you want an answer I would suggest you to put the whole question up ty
Step-by-step explanation:
Please help me solve this 9th grade math equation
Answers
Number of pounds of banana sold is, 14
And, Number of pounds of grapes sold is, 36
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Each pound of banana sell for $2.
And, Each pound of grapes sell for $1.
Now, Let number of pounds of sell banana = x
And, Number of pounds of sell grapes = y
Since, There are 50 pounds of fruits are sell.
So, We can formulate;
⇒ x + y = 50 .. (i)
And, Each pound of banana sell for $2.
And, Each pound of grapes sell for $1.
Hence, We get;
⇒ $2x + $1y = $64
⇒ 2x + y = 64 .. (ii)
Substitute value of y from (i) in (ii), we get;
⇒ 2x + y = 64
⇒ 2x + (50 - x) = 64
⇒ 2x + 50 - x = 64
⇒ x = 64 - 50
⇒ x = 14
And, From (i);
⇒ x + y = 50
⇒ 14 + y = 50
⇒ y = 50 - 14
⇒ y = 36
So, Number of pounds of sell banana = 14 pounds
And, Number of pounds of sell grapes = 36 pounds
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Assume you are given the set B where B = {2,4,6,8,10}. Consider this statement.
Answers
Answer:false
Step-by-step explanation:
Please show work on a paper and upload it need it ASAPPP
Answers
The value of the summation expression given in the task content is; 16.
What is the value of the summation expression given?It follows from the task content that the value of the summation expression given is to be determined.
Since the given expression is; 2x - 3,
On this note;
When x = 2; 2(2) - 3 = 1When x = 3; 2(3) - 3 = 3When x = 4; 2(4) - 3 = 5When x = 5; 2(5) - 3 = 7On this note, the sum of all of the results above is the correct Evaluation of the given expression; 1 + 3 + 5 + 7 = 16.
On this note, the result of the evaluation is; 16.
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Select the correct answer.
Stephanie is exploring the key features of the functions ƒ (z) = and g(z) = 4=+5
She says that the graphs of the two functions will have the same vertical asymptote but different horizontal asymptotes because she ca
define function g as a transformation of function f and g(x) = f(x) + 4. Which statement is true?
O A. Stephanie correctly rewrote g(x) as a transformation of f(x), and she described the asymptotes of the two functions
correctly.
OB. Stephanie correctly rewrote g(x) as a transformation of f(x), but she described the asymptotes of the two functions
incorrectly.
OC. Stephanie rewrote g(x) as a transformation of f(x) incorrectly, but she described the asymptotes of the two functions
correctly.
O D. Stephanie rewrote g(x) as a transformation of f(x) incorrectly, and she described the asymptotes of the two functions
incorrectly.
Answers
Answer:
A. Stephanie correctly rewrote g(x) as a transformation of f(x), and she described the asymptotes of the two functions correctly.
Step-by-step explanation:
The statement is true because, g(x) = f(x) + 4 is indeed a transformation of f(x) by shifting the graph 4 units up, and because the horizontal asymptote is determined by the highest degree term in the function, which in this case is the same for both functions, so the two functions will have the same vertical asymptote, but the horizontal asymptote is determined by the leading coefficient which is different for both functions, so the two functions will have different horizontal asymptotes.
At a local hospital, 75% of nurses have diploma qualifications and the rest are working towards diplomas. There are 160 nurses in this hospital. How many nurses do not have a nursing diploma yet?
Answers
A total of 40 nurses do not have a nursing diploma yet
How many nurses do not have a nursing diploma yet?From the question, we have the following parameters that can be used in our computation:
Nurses = 160 nurses
Diploma qualitifications = 75%
The above parameters mean that
No diploma qualification = (1 - Diploma qualitifications) * Nurses
Substitute the known values in the above equation, so, we have the following representation
No diploma qualification = (1 - 75%) * 160
Evaluate
No diploma qualification = 40
Hence, the nurses are 40
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William Sealy Gosset worked at the Guinness Brewery in Dublin and made substantial contributions to the practice of statistics. In his work at the brewery, he collected and analyzed a great deal of data. Archives with Gosset’s handwritten tables, graphs, and notes have been preserved at the Guinness Storehouse in Dublin. In one study, Gosset examined the change in the double stout market before and after World War I (1914‑1918). For various regions in England and Scotland, he calculated the ratio of sales in 1925, after the war, as a percent of sales in 1913, before the war. Here are the data:
Region Ratio
Bristol 94
Cardiff 112
English Agents 78
English O 68
English P 46
English R 111
Glasgow 66
Liverpool 140
London 428
Manchester 190
Newcastle‑on‑Tyne 118
Scottish 24
(a) Compute the mean for these data. Give your answer to two decimal places.
⎯⎯⎯=
(b) Compute the median for these data. Give your answer to two decimal places.
=
(c) Which measure describes the center of this distribution the most accurately? Explain your answer.
The mean represents the center of the data most accurately because the mean incorporates all of the individual values, whereas the median depends more on the order of the values than their actual amounts.
The mean and the median should both be used. By comparing the mean and median, you can tell if the data are skewed.
The median represents the center of the data most accurately because the mean is more affected by extreme values.
The mean and the median are equally as accurate because the distribution of the data is approximately symmetical.
Region RelativeTo1913 RelativeToPast4
Bristol 94 82
Cardiff 112 80
English Agents 78 83
English O 68 88
English P 46 99
English R 111 99
Glasgow 66 78
Liverpool 140 106
London 428 105
Manchester 190 107
Newcastle-on-Tyne 118 115
Scottish 24 78
Answers
Answer: a) To compute the mean of these data, we need to add up all of the ratios and divide by the total number of ratios.
(94+112+78+68+46+111+66+140+428+190+118)/11 = 101.36
The mean is 101.36
b) To compute the median of these data, we need to arrange the data in increasing order and find the middle value.
46, 66, 68, 78, 94, 111, 112, 118, 140, 190, 428
The median is 111
c) The measure that describes the center of this distribution the most accurately is the mean, because it takes into account all of the values in the data set and provides an overall measure of central tendency. The median is also a measure of central tendency but it is affected by the outliers present in the dataset and doesn't provide a good representation of the central value.
Step-by-step explanation:
Exercise 4.1 Identify critical numbers and find the absolute maximum value and absolute minimum value for each of the given functions on the given interval. 1 f(x) = x³; [-2, 1] 2 f(x)=x²- 2x² + 3; [−1, 2] 3 5 (5 - 2x); [-1,2] f(x) = f(x)=x²-3x²; [-1, 3] 4 6 f(x)=2cosx+x; [0,2 ] f(x) = 3x³ - 20x³; [-2, 2]
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F(x) = x³ on the interval [-2, 1], x = -2 and x = 1, the absolute maximum value is 1 and the absolute minimum value is -8.
What are the critical numbers?A function's critical numbers are the independent variable values at which the function is not continuous, or when the derivatives are equal to 0 or undefined.
1. For the function f(x) = x³ on the interval [-2, 1], the critical numbers are x = -2 and x = 1. The absolute maximum value is 1 and the absolute minimum value is -8.
2. For the function f(x) = x² - 2x² + 3 on the interval [-1, 2], the critical numbers are x = -1 and x = 2. The absolute maximum value is 5 and the absolute minimum value is -2.
3. For the function f(x) = 5 - 2x on the interval [-1,2], the critical numbers are x = -1 and x = 2. The absolute maximum value is 5 and the absolute minimum value is -3.
4. For the function f(x) = x² - 3x² on the interval [-1, 3], the critical numbers are x = -1, x = 0, and x = 3. The absolute maximum value is 0 and the absolute minimum value is -3.
5. For the function f(x) = 2cosx + x on the interval [0,2], the critical numbers are x = 0 and x = 2. The absolute maximum value is 3 and the absolute minimum value is -1.
6. For the function f(x) = 3x³ - 20x³ on the interval [-2, 2], the critical numbers are x = -2 and x = 2. The absolute maximum value is -4 and the absolute minimum value is -32.
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In the diagram below, D is a point on segment CE such that segments AD and BE are parellel and point A is not on segment BC. Line segments AD and BC intersect at point P.
If angle CAD = 67 degrees, then what is angle CBE?
Answers
Answer:
Step-by-step explanation:
Since segment AD and BE are parallel, we can use the Alternate Interior Angles Theorem to solve this. According to this theorem, if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are equal. Since angle CAD = 67 degrees, angle DBE is also equal to 67 degrees.
Now, if we look at the diagram, angle DBE is supplementary to angle CBE, meaning that the two angles add up to 180 degrees. Therefore, angle CBE = 180 degrees - 67 degrees = 113 degrees.
i need help pleaseeee!!!
Answers
Answer:
-4 < 2 - a < -8
Step-by-step explanation:
Casandras fish bowl holds 9/10 gallon of water. It is now 2/3 full. How much water is in the bowl?
Answers
The amount of water in Casandra's bowl, given the gallons of water it can hold and the fraction full it is, is 0.6 gallons
How to find the quantity of water ?Casandra' s fish bowl is able to hold a total of 9 / 10 gallons of water which is also 0.9 gallons of water. This means that you can find out how much water is in the bowl if told the fraction of the bowl that is currently full up to.
This time, the bowl is said to be 2 / 3 full which means that out of the capacity of 9 / 10 gallons or 0 . 9 gallons, the bowl is two - thirds full.
The amount of water in the bowl is therefore:
= Capacity of fish bowl x Proportion of water in the bowl
= 9 / 10 x 2 / 3
= 0. 9 x 2 / 3
= 0 . 6 gallons
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log10 2=P,then the value of log10 5 is
Answers
The value of log10 5 as required to be determined using the given information is; 0.3979 + P..
What is the value of log10 5 as required?It follows from the task content that; the value of log10 5 is to be determined based on the given information.
Since the given expression is; log10 2 = P;
The expression which can be inferred from the equation above is;
10^P = 2..............(i)
However, let; log10 5 = x
Therefore; 10^x = 5..........(ii)
By dividing the equation (ii) by (i); we have that;
10^(x - P) = 2.5
Therefore, from the converse of logarithmic law;
x - P = log10 2.5
x = P + log10 2.5
where, log10 2.5 = 0.3979
x = 0.3979 + P
Ultimately, the value of log10 5 as required is; 0.3979 + P.
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You want to buy a 11-year bond with a maturity value of $12,000, and you wish to get a return of 7.25% annually. How much will you pay? (Round your answer to the nearest cent.)
Answers
Answer:The price of a bond can be calculated using the formula:
Price = Maturity Value / (1 + r)^n
Where:
Maturity Value = $12,000
r = the annual interest rate as a decimal (7.25% / 100 = 0.0725)
n = the number of years to maturity (11 years)
So the price of the bond is:
Price = $12,000 / (1 + 0.0725)^11
By solving this equation we get the price of bond is $7,065.87 approximately.
Note: The bond price is the amount you pay to buy the bond and receive the maturity value at the end of the bond term.
Step-by-step explanation:
Eva has a points card for a movie theater. She receives 85 rewards points just for signing up. She earns 2.5 points for each visit to the movie theater. She needs at least 310 points for a free movie ticket.
Answers
Answer: 90
Step-by-step explanation:
If you're looking for the number of times she has to visit the movie theater in order to have 310 points for the free movie ticket then;
310-85 = 225
225/2.5 = 90
Eva needs 90 visits before she can get a free movie ticket.
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
Answers
The equations which represent circles whose diameters are 12 units and a center line lies on the y-axis are:
x² + (y – 3)² = 36 x² + (y – 5)² Equation of a circle.It is noteworthy to know that a center line on the y-axis can be interpreted as a coordinating pair in which case the pair looks like;
( 0, y )
Recall the equation of a circle which takes the form;
(x - h)² + (y - k)² = r²
Hence, since the center that lies on the y-axis, it automatically means that h = 0.
Also, if the diameter of the circle is 12 units
r = 12 / 2 = 6.
On this note, the required equation is;
x² + (y - k) = 6²
where k could be any real number.
Ultimately, the equations which are correct are;
x² + (y – 3)² = 36
x² + (y – 5)²
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Christian recorded the grade-level and instrument of everyone in the middle school School of Rock below.
Seventh Grade Students
Instrument # of Students
Guitar 6
Bass 4
Drums 7
Keyboard 2
Eighth Grade Students
Instrument # of Students
Guitar 4
Bass 15
Drums 13
Keyboard 6
Based on these results, express the probability that a student chosen at random will play the bass as a fraction in simplest form.
Answers
Answer: the probability that a student chosen at random plays the bass is 1/3 in simplest form.
Step-by-step explanation:
The probability of an event can be found by taking the number of favorable outcomes and dividing it by the total number of outcomes. In this case, we are looking for the probability that a student chosen at random plays the bass.
We know that there are a total of 6 + 4 + 7 + 2 = 19 seventh grade students and 4 + 15 + 13 + 6 = 38 eighth grade students. So there are a total of 19 + 38 = 57 students.
We also know that there are 4 seventh grade bass players and 15 eighth grade bass players, for a total of 4 + 15 = 19 bass players.
So, the probability that a student chosen at random plays the bass is 19/57. This fraction can be simplified by dividing both the numerator and denominator by their greatest common factor which is 19/57 = 1/3.
So, the probability that a student chosen at random plays the bass is 1/3 in simplest form.
In an absolute value graph, the slope of one side of the graph is the ______________ of the other side.
Then give an example...If the slope of one side of an absolute value function is _________, then the other side of the equation has a slope of ________.
Answers
Answer:
In an absolute value graph, the slope of one side of the graph is the opposite of the other side.
For example, if the slope of one side of an absolute value function is positive, then the other side of the equation has a slope of negative.
(-5x2 + 10x − 12) − (-4x2 + 8x − 15)
Answers
Answer: 1 + 2x
Step-by-step explanation:
To solve this problem, it's helpful to understand "order of operations." The order is: parentheses, exponents, multiplication, division, addition, and lastly, subtraction.
A helpful mnemonic is PEMDAS. I was taught "Parachute Expert My Dear Aunt Sally" to help remember the order.
We must work with the numbers inside the parantheses, since "parantheses" is the first operation. We'll start with the first paranthesis: (-5x2 + 10x - 12).
Since there are no exponents in this equation, we can go to the third operation: multiplication. (I like to use the "·" symbol to show that two numbers are multiplied because it's easy for me to confuse the letter X with "x" when it is used as a multiplication symbol).
-5 · 2 = -10
Two negative numbers are added, so -10 and -12 = -22
This leaves (-22 + 10x)
The -22 and 10x are not added together because numbers without a letter cannot be added to numbers with letters.
Now we'll work with the second paranthesis: (-4 · 2 + 8x - 15)
-4 · 2 = -8
-8 and -15 is added to make -23
The paranthesis now looks like:
(-23 + 8x)
Notice that there is a negative sign outside of the second paranthesis in the equation.
(-22 + 10x) − (-23 + 8x)
When a number or symbol is outside of a paranthesis, that number or symbol is multiplied across everything within the parantheses.
Now, it is:
(23 - 8x)
All of the numbers can be taken out of the parantheses now:
-22 + 10x + 23 - 8x
-22 + 23 = 1
10x - 8x = 2x
The final answer:
1 + 2x
Hope this helps!
Put the answer please!
Answers
The inequality that represents the interval shown on the number line is:
5 ≤ x ≤ 9
How to express the interval shown?We want to use inequality notation to define the interval shown on the number line.
We can see that the first point is marked with a closed circle, at x = 5.
And then we have another closed circle at x = 9
The closed circles means that these points are solutions to the inequality, so we need to use the symbols:
≤ and ≥
Then we can write the inequality:
5 ≤ x ≤ 9
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7. What is 112" in decimal feet?
a. 12.25´
b. 9.33 ´
c. 8.50 ´
d. 6.33 ´
Answers
Answer:
B 9.33
Step-by-step explanation:
Kalen and his friends are running a relay race that is 3/4 mile long.Each person will run 3/20 mile.How many runners are on Kalen’s team in total??
Answers
Answer:
5 people
Step-by-step explanation:
Relay race ---> 3/4 mile
Each runner runs 3/20 miles
3/4÷3/20
3/4×20/3=5
OR
3/4 --> 15/20
3/20 goes into 15/20 5 times
Answer:
5 runners
Step-by-step explanation:
Just multiply 3/20 by 3/4
what is the math equation what does it equal ∣7−11∣=
Answers
The solution for the absolute value equation is:
|7 - 11| = 4
How to solve the given equation?Here we want to solve an absolute value equation:
|7 - 11| = ?
First, remember how the absolute value works, it is:
|x| = x if x ≥ 0
|x| = -x if x < 0.
Now let's return to our equation:
|7 - 11|
If we simplify the left side, we will get:
|-4|
Notice that it is a negative number, so we just need to change the sign:
|-4| = 4
Then the equation is:
|7 - 11| = 4
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Answer:
[tex] \sf \: ∣7-11∣ = 4[/tex]
Step-by-step explanation:
Given problem,
→ ∣7 - 11∣
Let's solve the problem,
→ ∣7 - 11∣
→ ∣-4∣ = 4
=> Absolute value
=> It is always positive
Hence, the answer is 4.
Please look at the picture and answer the question thank you
Answers
The formula for t in terms of P, I and r is t=I/Pr.
What is the simple interest?Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.
Simple interest is calculated with the following formula: S.I. = (P × R × T)/100, where P = Principal, R = Rate of Interest in % per annum, and T = Time.
Given that, the formula form simple interest is I=Prt, where I is the interest, P is the principal, r is the interest rate and t is the number of years.
Now, I=Prt
t=I/Pr
Therefore, the formula for t is t=I/Pr.
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Choose the table or tables that represent a linear function.
Answers
Answer:
A and B
Step-by-step explanation:
You draw the points on the Cartesian plane and draw a straight line that passes through two of the drawn points, if ALL the drawn points are ON the drawn line, then it is a linear function,
If only ONE point lies outside the line, then it is NOT a linear function
5x - 2y = 10
7x - 3y = 13
Use elimination to solve for x and y
Answers
Answer:
Step-by-step explanation:
let 5x - 2y = 10 ........... (1)
and 7x - 3y = 13 ............(2)
now multiply equation (1) by 3 and equation (2) by 2, we get,
15x - 6y = 30 ............(3)
14x - 6y = 26 ............(4)
after substracting equation (3) and (4) we get,
x = 4
after putting the value of x in eq (3) we get,
15 * 4 - 6y = 30
=> 60 - 6y =30
=> y = -30/ -6
=> y = 5
so, the vale of x and y is 4 and 5 respectively.
6) Given the geometric sequence 2, 4, 8, 16,...
a) Determine the common ratio.
b) Write the explicit formula.
c) Find a10
d) Write the recursive formula.
Answers
Answer:
a) Common ratio r = [tex]\boxed{2}[/tex]
b) Formula for common ratio:
[tex]\dfrac{a_{n+1}}{a_n} , n = 1, 2, 3, 4....\\[/tex]
Formula for nth term:
[tex]a_n = a_1r^{n-1}[/tex]
(see explanation below for part b)
c) [tex]a_{10} = \boxed{1024}[/tex]
d) Recursive formula: [tex]\boxed{a_{n+1} = 2a_n}[/tex]
Step-by-step explanation:
a) The common ratio r for a geometric sequence is the ratio of any term(except the first) to the previous term. And this is a constant for that sequence
If we have a sequence [tex]a_1, a_2, a_3, a_4, a_5,....\\[/tex]
[tex]r = \dfrac{a_2}{a_1} = \dfrac{a_3}{a_2} = \dfrac{a_4}{a_3} = \dfrac{a_5}{a_4}[/tex]
Here [tex]a_1[/tex] is the first term in the sequence
The sequence we have here is
2, 4, 8, 16
So
[tex]r = \dfrac{4}{2} = \dfrac{8}{4} = \dfrac{16}{8} = 2\\[/tex]
Answer to a)
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b) This part is confusing. Are they asking for a formula for the common ratio or a formula for the nth term? You can write both or check with your teacher
The explicit formula for the common ratio is
[tex]\dfrac{a_{n+1}}{a_n} , n = 1, 2, 3, 4....\\[/tex]
The explicit formula for the nth term, [tex]a_n[/tex] of a geometric sequence is
[tex]a_n = a_1r^{n-1}[/tex]
where [tex]a_1[/tex] is the first term of the sequence and r is the common ratio
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c)
The formula for finding the nth term of a geometric sequence is
[tex]a_n = a_1r^{n-1}\\\\[/tex]
Therefore
[tex]a_{10} = a_1 r^{(10-1)} = a_1 \times r^9\\\\[/tex]
[tex]a_1 = 2, r = 2\\\\[/tex]
So
[tex]a_{10} = 2 \cdot 2^9 \\\\= 2 \cdot 512\\\\= 1024\\[/tex]ANSWER c)
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d)
A recursive formula is just an expression that denotes the relationship between one term and the next
We know that
[tex]r= \dfrac{a_{n+1}}{a_n} \\\\[/tex]
Multiplying both sides by [tex]a_n[/tex],
[tex]ra_n = a_{n+1}[/tex]
Or
[tex]a_{n+1} = ra_n\\\\[/tex]
For the specific case of r = 2 we get the recursive formula as
[tex]a_{n+1} = 2a_n[/tex]
ANSWER d)
