The notation f:S→T denotes that f is a function, also called a map , defined on all of a set S and whose outputs lie in a set T . A function f:S→T is injective if for all x,y∈S , f(x)=f(y) implies that x=y . Alternatively: a function is injective if we can uniquely recover some input x based on an output f(x) . What functions are injective?
Answers
Answer:
There are many. Two examples are
\(f(x) = x, \\f(x) = x^3\)
Step-by-step explanation:
There are many examples. The simplest is
1 -
\(f(x) = x\)
It is trivial that
\(\text{if \,\,\,\,} f(x) = f(y) \,\,\,\,\,\text{then} \,\,\,\,\, x=y\)
2 -
\(f(x) = x^3\)
That function is injective as well.
\(\text{if \,\,\,\,} x^3 = y^3 \,\,\,\,\,\text{then} \,\,\,\,\, x=y\)
An example of a function that is NOT injective is
\(f(x) = x^2\)
Notice that
\(f(-2) = (-2)^2 = 2^2 = 4\)
Related Questions
Evaluate (–1)8 + (–1)7 – 16 – 14 – (–1)2. Pay attention to the placement of the parentheses and negative signs. Question 1 options: A) 5 B) –3 C) –4 D) –23
Answers
Original Expression: (-1)8+(-1)7-16-14-(-1)2.
Evaluating: -8-7-16-14+2
-8-7=-15-16=-31-14=-45+2=-43.
The answer is -43 according to PEMDAS.
helpppppophsbajjakska
Answers
solve 4 + 1.8x = 8 (1 + 0.1x)
Answers
Answer: x=4
Distribute
4+1.8x=8+0.8x
Move terms
4+1.8x-0.8x=8
Collect liketerms
x=8-4
x=4
Answer: x = 4
Step-by-step explanation:
Given:
4 + 1.8x = 8 (1 + 0.1x)
Distribute:
4 + 1.8x = 8 + 0.8x
Subtract 0.8x and 4 from both sides of the equation:
1x = 4
Divide both sides of the equation by 1:
x = 4
Feb 17 A zoo feeds its monkeys a mixture of fruits and biscuits. The diagram shows the ratio of fruit n mass to biscuit mass. Ratios with tape diagrams The table shows the mass, in grams, of fruit and biscuits that the zoo fed two of the monkeys. Monkey A Fruit mass Based on the ratio, complete the missing values in the table. B Biscuit mass Fruit mass (g) Biscuit mass (g) 28 45
help fast
Answers
Answer:
Fruit mass = 63.2 g
Biscuit mass = 94.8 g
Step-by-step explanation:
Since the ratio of fruit mass to biscuit mass is 2:3, the fraction of fruit mass to the total of fruit and biscuit mass is 2/5 and the fraction of biscuit mass to the total of fruit and biscuit mass is 3/5.
For Monkey A, the total of fruit and biscuit mass is 73 g, which means that the fraction of fruit mass is 2/5 × 73 g = 29.2 g and the fraction of biscuit mass is 3/5 × 73 g = 43.8 g. Therefore, the values for fruit mass and biscuit mass are:
Fruit mass = 29.2 g
Biscuit mass = 43.8 g
For Monkey B, the total of fruit and biscuit mass is 73 + 85 = 158 g, which means that the fraction of fruit mass is 2/5 × 158 g = 63.2 g and the fraction of biscuit mass is 3/5 × 158 g = 94.8 g. Therefore, the values for fruit mass and biscuit mass are:
Fruit mass = 63.2 g
Biscuit mass = 94.8 g
factor 20mn-15m
solve (5/6z + 5)+(-1/3z-4)
Show work
Answers
Factorisation:
\(\rightarrow \sf 20mn-15m\)
take 5m as common term
\(\rightarrow \sf 5m\left(4n-3\right)\)
solving/simplifying:
\(\rightarrow \sf \left(\dfrac{5}{6}z\:+\:5\right)+\left(-\dfrac{1}{3}z-4\right)\)
\(\rightarrow \sf \dfrac{5}{6}z+5-\dfrac{1}{3}z-4\)
\(\rightarrow \sf \dfrac{5}{6}z-\dfrac{1}{3}z+5-4\)
\(\rightarrow \sf \dfrac{5}{6}z-\dfrac{1(2)}{6}z+1\)
\(\rightarrow \sf \dfrac{5-2}{6}z+1\)
\(\rightarrow \sf \dfrac{3}{6}z+1\)
\(\rightarrow \sf \dfrac{1}{2}z+1\)
Answer:
\(5m(4n - 3)\)
\(\dfrac12z+1\)
Step-by-step explanation:
Given expression:
\(20mn-15m\)
Rewrite 20 as \(4\cdot 5\)
Rewrite 15 at \(3 \cdot 5\)
Therefore,
\(20mn-15m=4\cdot 5m\cdot n-3 \cdot 5m\)
Factor out common term \(5m\) :
\(\implie 5m(4n-3)\)
-------------------------------------------------------------------------------------
Given expression:
\(\left(\dfrac56z + 5\right)+\left(-\dfrac13z-4\right)\)
Simplify:
\(\dfrac56z+5-\dfrac13z-4\)
Group like terms:
\(\dfrac56z-\dfrac13z+5-4\)
Combine like terms:
\(\dfrac12z+1\)
For how many books produced will the costs from the two methods be the same
Answers
Answer:
\(4780\text{ books}\)Explanation:
Here, we want to get the number of books for which the cost of the two methods will be the same
What we have to do here is to get the cost of each method, then equate to find the number of books
Let the number of books be b
For the first method, we have it that:
\(\begin{gathered} 70976\text{ + }9.75(b) \\ =\text{ 70976 + 9.75b} \end{gathered}\)For the second method, we have it that:
\(\begin{gathered} 16006\text{ + }21.25(b) \\ =\text{ 16006 + 21.25b} \end{gathered}\)To get the number of books, we have to equate both
Mathematically, that would be:
\(\begin{gathered} 70976\text{ + 9.75b = 16006 + 21.25b} \\ 70976-16006\text{ = 21.25b-9.75b} \\ 54970\text{ = 11.5b} \\ b\text{ = }\frac{54970}{11.5} \\ b\text{ = 4,780} \end{gathered}\)I GIVE BRAINLILEST
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Answers
Answer:
answer is c makes sense because you just add 1.25 x 20
find the ratio of 81 to 108
Answers
Answer: 3:4
Step-by-step explanation:
Answer:
hope it becomes helpful to you ☺️☺️
good luck
The physician orders Keflex (cephalexin monohydrate) 0.5 g per NG tube q6h. Read the label and calculate the correct dosage.
Label reads : 250 mg per 5 mL
Answers
Answer:
100 mL
Step-by-step explanation:
0.5 x 1000 =500mg
250mg/5ml= 5mg per 1ml
500mg/x mL = 5mg/1ml
cross multiply
500=5mg XmL
=100mL
Tyler used 27.05 gallons of gas Marie used 6.2 times as many gallons of gas as Taylor how many gallons of gas did Marie use ?
Answers
167.71 = Marie
27.05 = Tyler
Answer:
167.71
Step-by-step explanation:
Multiply 27.05 and 6.2.
6 + 4|2x + 6| = 14
Solve for x
Answers
Answer:
x = -1
Step-by-step explanation:
6+4 = 10
14-10 = 4
2x + 6 = 4
2x (-2) = -2
-2 + 6 = 4
What to numbers multiply to -38 and add to 17
Answers
Answer:
-2 and 19
Step-by-step explanation:
Answer:
19 and -2
Step-by-step explanation:
19 * -2 = -38
19 + -2 = 17
Hope this helps
6 divided-3 minus 15-7 divided by -2
Answers
Step-by-step explanation:
6−3−15−7−2=−13.5−13.5=−13.5
SO THE ANSWER IS 13.5ShhshshahahsshahahBaj
The measure of an angle is 89 times the measure of its supplementary angle. What is the measure of each angle
Answers
Answer:
2 and 178
Step-by-step explanation:
If we take an instance of a number 'x', according to the question we find that x+x*89=180(Because they are complementary)
We get, = 89x+x=180
=> 90x=180
=> x=180/90
=> x =2
So, we found that x=2 , hence the other angle is going to be 2*89=178
This is correct as 2+178=180(as they are supplementary to each other)
Hope this answer helps, Please mark me as brainliest, Thank you!
transformation of the graph of f(x)=x^3 for the graph of g(x)=-x^3
Answers
The transformation was a reflection over the x-axis. This is because \(g(x)=-f(x)\).
labor-hours and its standard cost card per unit is as follows:
Direct material: $ pounds at $11.00 per pound
Direct labor: 3 hours at $12 per hour
Variable overhead: 3 hours at $7 per hour
Total standard variable cost per unit
The company also established the following cost formulas for its selling expenses:
sales salaries and commissions
shipping expenses
Fixed Cost per
Month
$ 280,000
$ 260,000
$ 55.00
36.00
$112.00
Variable
Cost per
Unit Sold
$ 20.00
$ 11.00
The planning budget for March was based on producing and selling 21,000 units. However, during March the company
actually produced and sold 26.600 units and incurred the following costs:
a Purchased 154.000 pounds of raw materials at a cost of $9.50 per pound. All of this material was used in production.
b. Direct laborers worked 63,000 hours at a rate of $13.00 per hour
e Total variable manufacturing overhead for the month was $510,930
d Total advertising sales salaries and commissions, and shipping expenses were $286,000, $495,000, and $195,000,
respectively
6 What direct labor cost would be included in the company's flexible budget for March?
Answers
The direct labor cost included in the Preble Company's flexible budget for March is $819,000.
How to compute Preble Company's direct labor cost?To find the direct labor cost included in the company's flexible budget for March, we shall estimate the actual direct labor cost incurred during the period.
Given:
Actual production and sales =n26,600 units
Actual direct labor rate = $13.00 per hour
Actual direct labor hours worked = 63,000 hours
Direct labor cost = Actual direct labor rate × Actual direct labor hours worked
Direct labor cost = $13.00/hour × 63,000 hours
Direct labor cost = $819,000
Hence, the direct labor cost included in the company's flexible budget for March would be $819,000.
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Jimmy ran 20 meters west from home and then turned north to jog 25 meters. Jimmy ran 45 meters, but could have arrived at the same point by jogging in a straight line. How many meters could he have jogged using a straight line distance?
Responses
3.5 meters
3.5 meters
45meters
7 meters
Answers
The distance he would've covered is 32.02m if he ran through a straight line.
What is Pythagoras's Theorem?In mathematics, the Pythagorean theorem, or Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
We can proceed to use this to find the distance from point a to point b assuming he ran through a straight line.
Mathematically, the theorem can be expressed as
\(x^2 = y^2 + z^2\\\)
Let's substitute the values into the equation and solve.
\(x^2 = 20^2 + 25^2\\x = 32.02m\)
Jimmy would've jogged 32.02m if he ran through a straight line.
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Using the textbook example of 420 California school districts and the regression of testscores on the student-teacher ratio, you find that the standard error on the slope coefficient is 0.51 when using the heteroskedasticity robust formula, while it is 0.48 when employing the homoskedasticity only formula. When calculating the t-statistic, the recommended procedure is to A. use the homoskedasticity only formula because the t-statistic becomes larger B. first test for homoskedasticity of the errors and then make a decision C. use the heteroskedasticity robust formula D. make a decision depending on how much different the estimate of the slope is under the two procedures
Answers
Answer:
The answer is "Option C".
Step-by-step explanation:
Robust standard errors or generic White-Huber mistakes depending on this procedure. This is also recognized as the Variance Sandwich Stimator because of the appearance of the formula. Therefore, which is under homoskedasticity, robust error terms were appropriate, in which the standard deviations of its predictor variables are non-constant and are tracked across different values or linked to pre-time periods of an exponential function.
Find the x intercepts. Show all possible solutions.
Answers
For the function f(x) = 7/8x² - 14, the x-intercepts are x = -4 and x = 4.
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
To find the x-intercepts of the function f(x), we need to solve the equation f(x) = 0.
f(x) = 7/8x² - 14
Substitute f(x) with 0 -
0 = 7/8x² - 14
Add 14 to both sides -
7/8x² = 14
Multiply both sides by 8/7 -
x² = 16
Take the square root of both sides -
x = ±4
Therefore, the x-intercepts of the function f(x) are x = -4 and x = 4.
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HELPPP PLEASE YOU’LL GET 10 POINTS
Answers
Answer:
angle y and angle x
Step-by-step explanation:
2x+10= 5x-17 hurry is for a test
Answers
Explanation
Answer:
X is 9
Step-by-step explanation:
Order cube root of eighty-eight, twenty-eight ninths, square root of nineteen from greatest to least.
cube root of eighty-eight, twenty-eight ninths, square root of nineteen
twenty-eight ninths, square root of nineteen, cube root of eighty-eight
twenty-eight ninths, cube root of eighty-eight, square root of nineteen
cube root of eighty-eight, square root of nineteen, twenty-eight ninths
Answers
Answer:
(a) twenty-eight ninths, square root of nineteen, cube root of eighty-eight
Step-by-step explanation:
When ordering a list of numbers by hand, it is convenient to convert them to the same form. Decimal equivalents are easily found using a calculator.
OrderThe attachment shows the ordering, least to greatest, to be ...
\(\dfrac{28}{9}.\ \sqrt{19},\ \sqrt[3]{88}\)
__
Additional comment
We know that √19 > √16 = 4, and ∛88 > ∛64 = 4, so the fraction 28/9 will be the smallest. That leaves us to compare √19 and ∛88, both of which are near the same value between 4 and 5.
One way to do the comparison is to convert these to values that need to have the same root:
√19 = 19^(1/2) = 19^(3/6) = sixthroot(19³)
∛88 = 88^(1/3) = 88^(2/6) = sixthroot(88²)
The roots will have the same ordering as 19³ and 88².
Of course, these values can be found easily using a calculator, as can the original roots. By hand, we might compute them as ...
19³ = (20 -1)³ = 20³ -3(20²) +3(20) -1 = 8000 -1200 +60 -1 = 6859
88² = (90 -2)² = 90² -2(2)(90) +2² = 8100 -360 +4 = 7744
Then the ordering is ...
28/9 < 19³ < 88² ⇒ 28/9 < √19 < ∛88
Answer:
the ordering is
28/9 < 19³ < 88² ⇒ 28/9 < √19 < ∛88
Step-by-step explanation:
Brainlyist!!!! Simplify
Answers
hi can you use Indonesian? because I can't speak English
Express (x+8)squared as a trinomial in standard form
Answers
Step-by-step explanation:
(x + 8)²
= (x + 8)(x + 8)
= x² + 2(x)(8) + 8²
= x² + 16x + 64.
The binomial expression (x + 8)² is converted into trinomial in standard form x² + 16x + 64.
What is a polynomial?A polynomial expression is an algebraic expression with variables and coefficients. Unknown variables are what they're termed. We can use addition, subtraction, and other mathematical operations. However, a variable is not divisible.
The expression is given below.
⇒ (x + 8)²
Simplify the expression, then we have
⇒ (x + 8)²
⇒ x² + 8² + 2·8·x
⇒ x² + 16x + 64
The binomial expression (x + 8)² is converted into trinomial in standard form x² + 16x + 64.
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A Broadway theater has 510 seats, divided into orchestra, main, and balcony seating. Orchestra seats sell for $140, main seats for $135, and balcony seats for $100. If all the seats are sold, the gross revenue to the theater is $62,700. If all the main and balcony seats are sold, but only half the orchestra seats are sold, the gross revenue is $55,700. How many of each kind of seat are there?
Answers
The Broadway theater had 100 Orchestra, 220 main seat and 190 balcony seats.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the number of Orchestra, y represent the main seat and z represent the balcony seat.
A Broadway theater has 510 seats, Hence:
x + y + z = 510 (1)
Also:
140x + 135y + 100z = 62700 (2)
And:
135y + 100z + (1/2)(140)x = 55700 (3)
From the three equations:
x = 100, y = 220, z = 190
The Broadway theater had 100 Orchestra, 220 main seat and 190 balcony seats.
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Solve this question as soon as possible!
Answers
Answer:
B, C, and E
Step-by-step explanation:
Jeremiah is traveling 70 mph. If Jeremiah keeps driving that speed, how far will Jeremiah be
able to travel in 5 hours?
Answers
Mph means miles per hour.
So in five hours, it’d be 70 times 5.
This means in 5 hours, Jeremiah can travel up to 350 miles.
Answer:
350mph
Step-by-step explanation:
70mph × 5hours
=350mph
that is the total mph Jeremiah covers
Which best describes the composition of tranformations that maps ∆LMN to ∆L'M'N'. 0,0 is the center of the dilation in each choice.
A. a reflection over the line y=3 followed by a dilation of scale factor 2
B. a dilation of scale factor 2 followed by a dilation of scale factor 12
C. a dilation of scale factor 12 followed by a translation left 1 down 3
D. a dilation of scale factor 2 followed by a translation right 1 up 3
Answers
Triangle LMN was dilated by a scale factor of 2 followed by a translation 1 unit right and 3 unit up to form triangle L'M'N'
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, translation, rotation and dilation.
Rigid transformation preserves the shape and size of the figure. Reflection, translation, rotation are rigid transformations.
Triangle LMN was dilated by a scale factor of 2 followed by a translation 1 unit right and 3 unit up to form triangle L'M'N'
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Complete the statement using always, sometimes, or never.
A rectangle is_______. a square
a,) always
b.) sometimes
c.) never
Answers
Answer:
B
Step-by-step explanation:
10. Find the values of x and y that make these triangles congruent by the HLTTheorem2x - 1y-3x+3y - 1
Answers
So,
We want to find the values of x and y such that these triangles:
Be congruent.
For this, we could state the following equations:
What we're going to do is to solve this system so we could find the values for x and y:
By elimination's method:
Now, replacing x=2:
2-y+4=0
y=6
Therefore, x=2 and y=6.
