Answer:
True
Step-by-step explanation:
For one-to-one function, we have for all x₁ and x₂, where x₁ ≠ x₂, then, f(x₁) ≠ f(x₂)
Which gives;
f
Where f(x₁) = y₁, the result of the inverse of the f⁻¹(y₁) = x₁
By definition the inverse of a one-to-one function, f⁻¹ is a distinctive function whose domain is given by f⁻¹(f⁻¹(x)) = x for the values of x in f
Therefore, for one-to-one functions, f⁻¹(f⁻¹(x₁)) = x₁
Where f⁻¹(x₁) = y₁, is the inverse or reverse of a function f(x₁), therefore, we have;
f⁻¹(y₁) = x₁
Which proves the statement that y = f(x) then x= f⁻¹(y).
Melissa, of Melissa's Lawn and Landscaping Service, needs to replace her mowers.
She has ordered four new gas mowers, at $499 each, and a negotiated Trade
Discount Rate of 9%, with terms of 2/10 EOM, and FOB Shipping Point. The
seller has agreed to prepay the shipping charge of $80, which is not included in the
invoice amount. The invoice from the manufacturer is dated July 26.
Determine:
A)
By what date does Melissa have to pay in order to be able to take the cash
discount?
B)
What is the payment amount assuming that Melissa pays before the end of
the discount period?
Answer:
A) 10th of August
B) $1780.03
Step-by-step explanation:
A) From the payment terms of 2/10 EOM, Melissa is to receive a 2% discount if she pays within 10 days from the end of the month
From the date on the invoice, July 26, the date at which Melissa has to pay to take the cash discount is before the 10th of August
B) The payment amount will be 2% off the original payment amount
The total cost of the four new gas mowers less the trade discount = 499 × 4 × (100 - 9)/100 =$1816.36
The 2% discount will then be $1816.36 × (100 - 2)/100 = $1780.03
The payment amount assuming Melissa pays before the end of the discount period = $1780.03.
Let $DEF$ be an equilateral triangle with side length $3.$ At random, a point $G$ is chosen inside the triangle. Compute the probability that the length $DG$ is less than or equal to $1.$
[tex]|\Omega|=(\text{the area of the triangle})=\dfrac{a^2\sqrt3}{4}=\dfrac{3^2\sqrt3}{4}=\dfrac{9\sqrt3}{4}\\|A|=(\text{the area of the sector})=\dfrac{\alpha\pi r^2}{360}=\dfrac{60\pi \cdot 1^2}{360}=\dfrac{\pi}{6}\\\\\\P(A)=\dfrac{\dfrac{\pi}{6}}{\dfrac{9\sqrt3}{4}}\\\\P(A)=\dfrac{\pi}{6}\cdot\dfrac{4}{9\sqrt3}\\\\P(A)=\dfrac{2\pi}{27\sqrt3}\\\\P(A)=\dfrac{2\pi\sqrt3}{27\cdot3}\\\\P(A)=\dfrac{2\pi\sqrt3}{81}\approx13.4\%[/tex]
Answer:
13.44%
Step-by-step explanation:
For DG to have length of 1 or less, point G must be contained in a sector of a circle with center at point D, radius of 1, and a central angle of 60°.
The area of that sector is
[tex]A_s = \dfrac{n}{360^\circ}\pi r^2[/tex]
[tex]A_s = \dfrac{60^\circ}{360^\circ} \times 3.14159 \times 1^2[/tex]
[tex] A_s = 0.5254 [/tex]
The area of the triangle is
[tex] A_t = \dfrac{1}{2}ef \sin D [/tex]
[tex]A_t = \dfrac{1}{2}\times 3 \times 3 \sin 60^\circ[/tex]
[tex] A_t = 3.8971 [/tex]
The probability is the area of the sector divided by the area of the triangle.
[tex]p = \dfrac{A_s}{A_t} = \dfrac{0.5254}{3.8971} = 0.1344[/tex]
piz help me!!!!
[tex]look \: at \: pic \: piz[/tex]
The phone company offers to long-distance plans the first charges a flat value of five dollars per month plus $.99 each minute used and the second charge is $10 a month plus $.79 for each minute used if X represents the number of minutes use each month which system each of equations represent the amount of money why are you spin
Answer:
The systems of equation for the amount spent are as follows
[tex]Y= 0.99x+5[/tex]
[tex]Y= 0.79x+10[/tex]
Step-by-step explanation:
In this problem we are expect to give a model or an equation that represents the amount of money spent per month given a fix subscription amount and a variable fee which is based on extra minutes spent.
let Y represent the amount of money spent in total for the month
The first case:
Subscription =$5
charges per minutes = $0.99
therefore the amount spent can be modeled as
[tex]Y= 0.99x+5[/tex]
The second case:
Subscription =$10
charges per minutes = $0.79
therefore the amount spent can be modeled as
[tex]Y= 0.79x+10[/tex]
Solve for x. 7^8 = 7^8 * 7^x
Answer:
x=0
Step-by-step explanation:
Lemma 1: 1a=a
Holds true for any real number a.
7^0=1
x=0
Which products result in a difference of squares? Select three options. A. (x minus y)(y minus x) B. (6 minus y)(6 minus y) C. (3 + x z)(negative 3 + x z) D. (y squared minus x y)(y squared + x y) E. (64 y squared + x squared)(negative x squared + 64 y squared)
Answer:
C D E
Step-by-step explanation:
Edg
Out of the given options, options C, D and E are a difference of squares.
What is the difference of squares?Difference of Squares, two terms that are squared and separated by a subtraction sign.
Given are, options,
D) (y squared minus x y)(y squared + x y) = (y²-xy)(y²+xy) = y⁴-(xy)²
E) (64 y squared + x squared)(negative x squared + 64 y squared) = (64y²+x²)(64y²-x²) = (64y)⁴-x⁴
C) (3 + x z)(negative 3 + x z) = (3+xz)(3-xz) = 3²-(xz)²
Hence, out of the given options, options C, D and E are a difference of squares.
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Tricks for solving trigonometry proof question easily ??
Answer: do do that you need a firm understanding of trig. once you do, you can see all the steps and solve a trig proof problem easily. So go back to solving regular trig questions, and keep asking yourself why this formula works. once you have understanding of that, you can solve trig proof problems with ease.
Step-by-step explanation:
Find the area of the following shape.
Answer:
57 units^2
Step-by-step explanation:
First find the area of the triangle on the left
ABC
It has a base AC which is 9 units and a height of 3 units
A = 1/2 bh = 1/2 ( 9) *3 = 27/2 = 13.5
Then find the area of the triangle on the right
DE
It has a base AC which is 6 units and a height of 1 units
A = 1/2 bh = 1/2 ( 6) *1 = 3
Then find the area of the triangle on the top
It has a base AC which is 3 units and a height of 3 units
A = 1/2 bh = 1/2 ( 3) *3 = 9/2 = 4.5
Then find the area of the rectangular region
A = lw = 6*6 = 36
Add them together
13.5+3+4.5+36 =57 units^2
Answer:
Total Area = 57 sq. units
Step-by-step explanation:
will make it simple and short
Total Area = A1 + A2 + A3
A1 = (7 + 6) * 6/2 = 39 sq. units (area of a trapezoid)
A2 = 1/2 (9 * 3) = 13.5 sq. units (area of a triangle)
A3 = 1/2 (3 * 3) = 4.5 sq. units (area of a triangle)
Total Area = 39 + 13.5 + 4.5 = 57 sq. units
please help :) 1) Scientists develop knowledge by making blank about the natural world that may lead to a scientific question. 2) A scientific question may lead to a(n) blank , which can be tested. The results of blank can lead to changes in scientific knowledge.
Answer:
You just answered my question so you can ask yours, what a sped. Now i'm doing the same thing.
Step-by-step explanation:
I need help pls will give you five stars and a big thank you comrade
Answer:
B, f(x) = ( x+2) ^2(x-1) (x+3)
Step-by-step explanation:
Looking at the x- intercepts, the line passes at 2, -1, and 3, so B is you answer (:
Fill in the blank with a constant, so that the resulting expression can be factored as the product of two linear expressions: 2ab-6a+5b+___
Answer:
-15
Step-by-step explanation:
We proceed as follows;
In this question, we want to fill in the blank so that we can have the resulting expression expressed as the product of two different linear expressions.
Now, what to do here is that, when we factor the first two expressions, we need the same kind of expression to be present in the second bracket.
Thus, we have;
2a(b-3) + 5b + _
Now, putting -15 will give us the same expression in the first bracket and this gives us the following;
2a(b-3) + 5b-15
2a(b-3) + 5(b-3)
So we can have ; (2a+5)(b-3)
Hence the constant used is -15
for the answer: The florist needs at least 1/3 gallons of nutrient rich water for each bushel of flowers he buys. If w is the gallons of water and f is the bushels of flowers, then:
w≥1/3f
I don't understand how you derive this equation.
Answer:
see below
Step-by-step explanation:
The phrase "at least" indicates that you use the symbol ≥, so that's where they got the ≥ from. The amount of water needed for each bushel is 1/3 * f or 1/3f because you need 1/3 gallons of water per one bushel. We know that the amount of water needed is at least 1/3 gallons per bushel. Since the amount of water is w, "at least" is ≥ and 1/3 gallons per bushel is 1/3f, the inequality is w ≥ 1/3f. I hope this makes sense.
After years of maintaining a steady population of 32,000, the population of a town begins to grow exponentially. After 1 year and an increase of 8% per year, the population is 34,560. Which equation can be used to predict, y, the number of people living in the town after x years? (Round population values to the nearest whole number.) y = 32,000(1.08)x y = 32,000(0.08)x y = 34,560(1.08)x y = 34,560(0.08)x
Answer:
y = 32,000(1.08)^x
Step-by-step explanation:
The exponential growth equation is y = a(1 + r)^x, where a is the initial amount, r is rate as a decimal, and x is the time.
In this situation, 32,000 is the initial amount (a) and 0.08 is the rate (r)
If we plug these into the equation, we get the equation y = 32,000(1.08)^x
So, y = 32,000(1.08)^x is the correct answer.
Answer:
A
Step-by-step explanation:
on edge 2020
Maria cut four equivalent lengths of ribbon. Each was 5 eighths of a yard long. How many yards of fabric did she cut?
Answer:
2.5 Yards
Step-by-step explanation:
Multiply 5/8 by 4
If 4th term of an AP is 0. Prove that 25th term is triple the 11th term
Answer:
The 4th term = a+3d = 0,
or a = -3d.
The 25th term = a+24d = -3d+24d = 21d. ...
the 25th term is 3 times the 11th term. Proved.
Answer:
a^25 = 3 x a^11 .
Step-by-step explanation:
Given a^4 = 0
That is (a + 3d) = 0
⇒ a = - 3d ........... (1)
nth term of AP is given by an = a + (n – 1)d
a^11 = a + 10d = – 3d + 10d = 7d [From (1)]
a^25 = a+ 24d = – 3d + 24d = 21d [From (1)]
Hence
The answer is a^25=3 x a^11
chose the equivelent expresion 5⁶ a.(5⁴)² b.(5⁻²)⁻³ c.(5¹)⁵
Answer:
[tex]\Large \boxed{(5^{-2})^{-3}}[/tex]
Step-by-step explanation:
Applying the law of exponents : [tex](a^b)^c=a^{bc}[/tex]
[tex](5^4)^2 = 5^{4 \times 2} = 5^{8}[/tex]
[tex](5^{-2})^{-3}=5^{-2 \times -3}=5^6[/tex]
[tex](5^1)^5 =5^{1 \times 5}=5^5[/tex]
Answer:
[tex]\huge\boxed{Option \ B}[/tex]
Step-by-step explanation:
[tex]5^6[/tex] is equivalent to
=> [tex](5^4)^2 = 5^{4*2} = 5^ 8[/tex]
=> [tex](5^{-2})^{-3} = 5^{-2*-3} = 5^6[/tex] ← Correct
=> [tex](5^1)^5 = 5^{1*5} = 5^5[/tex]
At a potluck, Agatha brings four dishes, Bertha brings three dishes, and five other friends bring no dishes but instead money to help pay for the food. If all the dishes are eaten up, and everyone eats the same amount, what fraction of the money should go to Bertha?
Answer:
3/7
Step-by-step explanation:
Agatha brings four dishes, Bertha brings three dishes. The total number of dishes brought = dishes brought by Agatha + dishes brought by Bertha.
Total dishes = 4 + 3 = 7 dishes
The remaining five friends brought money for the dishes. Therefore the fraction of money going to Bertha is the ratio of dishes brought to Bertha to the total number of dishes multiplied by the money. Therefore:
Fraction of the money should go to Bertha = dishes brought by Bertha/total dishes
Fraction of the money should go to Bertha = 3/7 × money
Select the correct answer.
Solve the system of equations.
y = x + 3
y = x^2 - 2x - 1
A. (1,4) and (-4,1)
B. (-1,4) and (4,1)
C. (-1,7 and (4,2)
D. (-1,2) and (4,7)
Answer:
( 4,7) ( -1,2)
Step-by-step explanation:
y = x + 3
y = x^2 - 2x - 1
Set the equations equal to each other
x + 3 = x^2 - 2x - 1
Subtract x from each side
3 = x^2 -3x -1
Subtract 3 from each side
0 = x^2 -3x -4
Factor
0 = ( x-4) ( x+1)
Using the zero product property
x-4 =0 x+1 =0
x = 4 x=-1
Find y for each x
x=4 y =x+3 y = 4+2 y=7
x = -1 y = x+3 y = -1+3 y = 2
( 4,7) ( -1,2)
Answer:
D. (-1, 2) and (4, 7).
Step-by-step explanation:
Eliminating y:
x^2 - 2x - 1 = x + 3
x^2 - 3x - 4 = 0
(x - 4)(x + 1) = 0
x = -1, 4.
When x = -1, y = -1 + 3 = 2.
When x = 4, y = 4 + 3 = 7.
So the answer is (-1, 2) and (4, 7).
Approximately what is the length of the rope for the kite sail, in order to pull the ship at an angle of 45° and be at a vertical height of 150 m, as shown in the diagram opposite?
Answer:
212m
Step-by-step explanation:
The set up will be equivalent to a right angled triangle where the height is the opposite side facing the 45° angle directly. The length of the rope will be the slant side which is the hypotenuse.
Using the SOH, CAH, TOA trigonometry identity to solve for the length of the rope;
Since we have the angle theta = 45° and opposite = 150m
According to SOH;
Sin theta = opposite/hypotenuse.
Sin45° = 150/hyp
hyp = 150/sin45°
hyp = 150/(1/√2)
hyp = 150×√2
hyp = 150√2 m
hyp = 212.13m
Hence the length of the rope for the kite sail, in order to pull the ship at an angle of 45° and be at a vertical height of 150 m is approximately 212m
By applying trigonometry ratio, the length of the rope for the kite to sail would be: 212 m.
Recall:
Trigonometry ratios used to solve a right triangle are: SOH CAH TOAThe diagram describing the situation is attached below (see attachment).
Thus:
The reference angle [tex](\theta) = 45^{\circ}[/tex]
Let the length of the rope be x = Hypotenuse
Opposite = 150 m
To find the length of the rope (x), apply SOH
Thus:
[tex]Sin(\theta) = \frac{Opp}{Hyp}[/tex]
Substitute[tex]Sin(45) = \frac{150}{x}[/tex]
Multiply both sides by x[tex]x \times Sin(45) = \frac{150}{x} \times x\\\\x \times Sin(45) = 150[/tex]
Divide both sides by sin(45)[tex]\frac{x \times Sin(45)}{Sin(45)} = \frac{150}{ Sin(45)} \\\\\mathbf{x = 212 $ m}[/tex]
Therefore, by applying trigonometry ratio, the length of the rope for the kite to sail would be: 212 m.
Learn more here:
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algebraic expression twice the difference of a number and 5. with x being "a number"
Answer:
2(x-5)
Step-by-step explanation:
Answer:
the answer to your question is 5xa^2
or you can use symbolab calculator online
The population distribution of SAT scores is normal with a mean of μ=500 and a standard deviation of SD=100. For example, what is the probability of randomly selecting an individual from this population who has an SAT score greater than 700?
Answer:
0.02275
Step-by-step explanation:
We use the z score formula to solve for this
z-score is given as: z = (x-μ)/σ
where x is the raw score,
μ is the population mean
σ is the population standard deviation
In the above question:
mean of μ=500
a standard deviation of SD=100
raw score x = 700
Hence, z score = (700 - 500)/ 100
= 200/100
= 2
z score = 2
Using the z score table of normal distribution to find the Probability of z = 2
P( x = z)
= P(x = 700)
= P( z = 2)
= 0.97725
P(x>700) = 1 - P(x = 700)
= 1 - 0.97725
= 0.02275
Therefore, the probability of randomly selecting an individual from this population who has an SAT score greater than 700 is 0.02275
There are five red balls, three yellow balls, and four green balls in a bin. In each event, you pick one ball from the bin and observe the color of the ball. The balls are only distinguishable by their colors. After observation, you put the ball back into the bin.
What is the probability of choosing a red ball in an event?
Answer:
5/12Step-by-step explanation:
step one:
Given the sample space, which is the value of individual number of colored balls in the bin
Red balls=5
Yellow balls=3 and
Green balls= 4
And the sample size is the sum of all the colored balls in the bin
The sample size S= {5+3+4}= 12
step two:
The probability of choosing a red ball in an event can be expressed as, the total number of the red balls over the total number of balls in the bin
P(r)= 5/12
Hence the probability of selecting a red ball in one event 5/12
2. A cylinder has a height of 4.5 cm and a diameter of 1.5 cm. What is the surface area of the cylinder in square centimeters? Use 3.14 for pi.
21.2
31.8
7.9
24.7
Answer:
[tex] SA = 24.73~cm^3 [/tex]
Step-by-step explanation:
[tex] SA = 2\pi r^2 + 2\pi r h [/tex]
r = d/2 = (1.5 cm)/2 = 0.75 cm
[tex] SA = 2(3.14)(0.75~cm)^2 + 2(3.14)(0.75~cm)(4.5~cm) [/tex]
[tex] SA = 24.73~cm^3 [/tex]
Answer:
24.7
Step-by-step explanation:
took this exam and got it right
Give another name plane L
Answer:
Any one of these three works:
plane MOU
plane MNU
plane NOU
Step-by-step explanation:
A plane can be named by a single letter, such as L in this problem, or by any three non-collinear points that lie on the plane. Non-collinear points are points that do not all lie in a single line.
Points M, N, O, and U lie on plane L, so you can choose any 3 of the 4 points to name the plane with, but make sure all 3 points are non-collinear.
To name plane L with points, you cannot use points MNO together since they are collinear, but you can name it using point U plus any two of the points M, N, and O.
plane L can be named
plane MOU
plane MNU
plane NOU
Do not name it plane MNO
What is the average time for the toy car to move 1.0 m on dirt? 20.2 s, 24.4 s, 28.1 s or 60.7 A student collected data about the distance a ball falls over time. Which type of graph should he use to represent the data? circle graph, scatterplot, histogram or bar graph
Answer:
1) Incomplete question
2) Scatterplot
Step-by-step explanation:
1) The question is incomplete. To calculate the average time required for the toy car to move, the formula to be used will be
velocity = distance ÷ time
Hence; time = distance ÷ velocity
2) There are two variables in the question; the distance (it takes the ball to fall) and the time. The type of graph (from the option) that can have two variables represented on it is a scatterplot.
Answer:
answer; A. 20.2 s.
Step-by-step explanation:
i had the same question but i had a graph to help me anyways
20.0 + 19.2 + 21.5 = 60.7 s, but you divide the total by 3, then here is your answer: 20.23333333333333 and you simplify it to 20.2 s,
in this figure ST || QR, PT = 4cm, TR = 8cm, area of PQR = 90cm^2. Find PT:TR please help me
Answer: The required ratio is PT:TR = 1:2.
Step-by-step explanation:
Given: In triangle PQR, ST || QR, PT = 4cm, TR = 8cm, area of PQR = 90 cm².
To find : PT:TR
.i.e. Ratio of PT to TR.
Here, PT:TR[tex]=\dfrac{PT}{TR}[/tex]
[tex]=\dfrac{4\ cm}{8\ cm}[/tex]
Divide numerator and denominator by 4 , we get
[tex]\dfrac{1}{2}[/tex]
Therefore, the required ratio is PT:TR = 1:2.
Bias can _____ be completely eliminated. a) always b)sometimes c) never
Answer:
the answer is c.
Step-by-step explanation:
c is the only reasonable option.
Which of the following represents the solution for -2 ≤ 7 - x < 11 ?
Answer:
A
Step-by-step explanation:
- 2 ≤ 7 - x < 11
-9 ≤ - x - x < 4
9 ≥ x x > -4
Answer:
Hey there!
-2 ≤ 7 - x < 11
-9 ≤ - x < 4
9 ≥ x > -4
-4 < x ≤ 9
A closed circle means greater than or equal to or less than or equal to, while an open circle means greater or less than. From this equation, we see that number line A is correct.
Let me know if this helps :)
Convert the following:
1 meter is equivalent to
ao feet (rounded to the nearest hundredth)
Answer:
1 meter = 3.28 feet
Step-by-step explanation:
The unit of conversion from meters to feet is given as follows;
By convention
1 yard = 09144 meters
1 yard = 3 feet
Therefore, we have;
1 foot = 0.9144/3 = 0.3048 m
Alternatively we can get;
1 inch = 0.0254 meters
1 foot = 12 inches
Therefore, we have;
1 foot = 12 × 0.0254 = 0.3048 meter
Which gives;
1 foot = 0.3048 meter
Given that 0.3048 meter = 1 foot, to find the measure of 1 meter, we proceed by dividing both sides of the equation by 0.3048 to get
0.3048/0.3048 meter = 1/0.3048 foot = 3.28084 feet
1 meter = 3.28084 feet. ≈ 3.28 feet to the nearest hundredth
If f(x)= Square root of X +12 and g(x)= 2 Square root of X what is the value of (f-g)(144)
Answer:
0
Step-by-step explanation:
