Given two sets X and Y, a relation between X and Y freely associates elements of X with elements of Y, with no restrictions.
A function is a relation with some restrictions: there must be exactly one element of Y connected with each element of X.
The set X is called the domain of the function, and it represents all the possible inputs that we can feed the function with. As we just said, every element of the domain must have a correlated element in Y.
The set Y is called the range of the function, and it represents all the possible outputs that the function can return.
The difference between function and relation and the relationship between the domain and the range of a function is discussed below
What is domain and range?The domain of a function is the set of values that we are allowed to plug into our function.
The range of a function is the set of values that the function assumes.
Let there be an X set and a Y set. An ordered pair (x,y) is called a relation in x and y. The first element in an ordered pair is called the domain, and the set of second elements is called the range of the relation.
A function is a particular kind of relation between sets. A function takes every element x in a starting set, called the domain, and tells us how to assign it to exactly one element y in an ending set, called the range.
For example, each person is in the following table is paired with a number representing his or her height:
Alex → 180 Claudia → 165 Gilbert → 204 Judith → 165
The given relation {(Alex, 180), (Claudia, 165), (Gilbert, 204), (Judith, 165)} is a function as every person is pairs with exactly one number, their height. The domain is (Alex, Claudia, Gilbert, Judith). The range is (165, 180, 204).
The domain is the input, the independent value—it's what goes into a function. The range is the output, the dependent value—it's what comes out. Domain and range may be limited to a few discrete values, or they may include all numbers everywhere, to infinity and beyond.
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Using the graph below, select all statements that are true.
A. f(0.6)=0
B. f(-3.2)=-3
C. f(5.1)=5
D. This is the graph of the greatest integer function.
E. This graph is one-to-one.
Answer:
A. f(0.6)=0
C. f(5.1)=5
D. This is the graph of the greatest integer function.
Step-by-step explanation:
The graph maps each x-value to the largest integer less than or equal to that value. That is the definition of the "greatest integer" function.
The "greatest integer" of -3.2 is -4, so B is not a correct choice. The graph does not pass the horizontal line test, so the function is not one-to-one, and E is not a correct choice.
Answer:
C, D, E
Step-by-step explanation:
A random sample of 64 freshmen spent an average of 14 hours per week watching television. the sample standard deviation was 32 hours per week. what is the critical value for a 95% confidence interval for the population mean?
Answer:
+/- 1.9983
Step-by-step explanation:
The critical values for a confidence interval for the population mean, with population standard deviation not known, are obtained from the student's t distribution.
The sample size is given as 64. The degrees of freedom will thus be;
sample size - 1 = 64 - 1 = 63
The confidence level is given as 95%. The level of significance will thus be;
100 - 95 = 5%.
The area in the right-tail will thus be 2.5%. Therefore, we looking for a t-value such that the area to its right is 2.5% and the degrees of freedom being 63. From the t-tables we have;
+/- 1.9983
Using the table below, write a function rule for the balance in the CD account after any number of years. Let y represent the value of the investment at the end of any year x.
CD/Year
Beginning Balance
Interest Earned
Ending Balance
Savings Account/Year
Beginning Balance
Interest Earned
Ending Balance
1
$700
$22
$722
1
$700
$25.90
$725.90
2
$722
$22
$744
2
$725.90
$26.86
$752.76
3
$744
$22
$766
3
$752.76
$27.85
$780.61
4
$766
$22
$788
4
$780.61
$28.88
$809.49
5
$788
$22
$810
5
$809.49
$29.95
$839.44
Answer:
y = 700 +22x
Step-by-step explanation:
The CD account balance is 722 after the first year and increases by $22 each year. The function rule is a linear function with a y-intercept of 700 and a slope of $22 per year.
y = 700 +22x . . . . . . ending balance after x years
The student council at Sparrowtown High School is making T-shirts to sell for a fundraiser, at a price of $12 apiece. The costs, meanwhile, are $10 per shirt, plus a setup fee of $72. Selling a certain number of shirts will allow the student council to cover their costs. How many shirts must be sold? What will the costs be?
(Algebra 2)
In which direction does the parabola open?
Answer:
up
Step-by-step explanation:
A graphing calculator, spreadsheet, or web site can help you with this one, or you can simply plot some points on a graph.
___
Only the highest-degree terms matter for answering this question. Leaving the others out, the form is ...
y = x^2
This tells you that y gets more positive for larger and larger values of x, regardless of their sign. Thus the graph of it is U-shaped, opening upward.
Given the conditional statement: p → ~q Choose the logically equivalent statement.
A. p → q
B. ~p → q
C. q → p
D. q → ~p
Answer: The correct option is
(D) q → ~p.
Step-by-step explanation: We are given to select the statement that is logically equivalent to the conditional statement p → ~q.
We know that
two conditional statements are said to be logically equivalent if the truth tables of both the statements are same.
That is, they have same truth values under similar conditions.
The truth table is given by
p q ~p ~q p → ~q p → q ~p → q q → p q → ~p
T T F F F T T T F
T F F T T F T T T
F T T F T T T F T
F F T T T T F T T
So, the truth values of p → ~q is same as the truth values of q → ~p. They must be logically equivalent.
Thus, option (D) is CORRECT.
Answer:
D). q → ~p
Step-by-step explanation:
I just did the assignment on Edge... It's 100% correct... Hope this helps!!
Also heart and rate if you found this answer helpful... Have a nice day!! :)
I don't understand this. Can someone please help me?
Answer:
a) 16 in²
b) 20 cm²
Step-by-step explanation:
In any prism, a cross section parallel to parallel faces will have the same shape and area as either of those faces. (That is why we say a prism has a uniform cross section.)
a) The face(s) parallel to the cut plane are squares 4 in on a side, so that is the shape of the cross section. Its area is (4 in)² = 16 in².
__
b) The face(s) parallel to the cut plane are rectangles 4 cm by 5 cm. That is the shape of the cross section. Its area is (4 cm)(5 cm) = 20 cm².
Please answer this multiple choice question correctly for 30 points and brainliest!!
Answer:
B. 12n + 2(25) ≤ 100
Step-by-step explanation:
The inequality you are asked for is intended to express ...
shirt cost + pant cost (is less than or equal to) Sandy's budget
The cost of n shirts at $12 each will be 12n. The cost of 2 pants at $25 each is 2(25). Then the inequality is ...
12n + 2(25) ≤ 100 . . . . . matches choice B
Please Help!! 35 Points!!!
Insert <, >, or = to make the sentence true.
12 __ 25
>
=
[tex]\frac{1}{2}[/tex] > [tex]\frac{2}{5}[/tex]
The wider/open part of the symbol (aka the mouth) faces the larger number, which in this case is [tex]\frac{1}{2}[/tex].
Hope this helped!
~Just a girl in love with Shawn Mendes
20 points One diagonal of a rhombus has endpoints (-10, 1) and (2, 9).
What are the endpoints of the other diagonal?
(-7, 7) and (-1, 3)
(-4, 7) and (2, 7)
(-2, 2) and (-6, 8)
(-6, 2) and (-2, 8)
Final answer:
To find the endpoints of the other diagonal of the rhombus, we can use the fact that diagonals of a rhombus bisect each other. The endpoints of the other diagonal are (-7, 7) and (-1, 3). Therefore, Option A is the correct answer.
Explanation:
To find the endpoints of the other diagonal of the rhombus, we can use the fact that diagonals of a rhombus bisect each other, meaning they intersect at their midpoints. We can find the midpoint by taking the average of the x-coordinates and the average of the y-coordinates of the given endpoints of the first diagonal.
For the given endpoints (-10, 1) and (2, 9), the midpoint would be ((-10 + 2)/2, (1 + 9)/2), which simplifies to (-4, 5).
Since the diagonals bisect each other, the other diagonal would have the same midpoint. Therefore, the endpoints of the other diagonal would be (-4, 5) and the reflection of (-4, 5) across the midpoint of the given diagonal, which is the midpoint of (-10, 1) and (2, 9). Thus, the correct answer is (-4, 5) and its reflection across (-4, 5), which is (-7, 7) and (-1, 3).
It costs 31.95d + 0.10m dollars to rent a car for d days and drive it m miles. How much does it cost to rent a car for 5 days if the car is driven a total of 600 miles ?
Answer:
$219.75
Step-by-step explanation:
Just plug in the values
x = final cost
31.95(5) + 0.10(600) = x
159.75 + 60 = x
219.75 = x
Evaluate the expression.
Answer:
C
Step-by-step explanation:
at least two have to be in the same place (i think), and that’s the only one that does that
Answer:
55/56 ≈ 0.982143
Step-by-step explanation:
nPk = n!/(n-k)!
Your expression is ...
1 - (6·5·4·3)/(8·7·6·5·4·3) = 1 - 1/(8·7) = 1 - 1/56 = 55/56 ≈ 0.982143
A rectangular garden measures 3 feet by 15 feet the gardener decides to extend the garden 1 foot in each of the four directions what is the perimeter of the new garden in feet
The perimeter of the new garden after extension is 44 feet.
Explanation:To find the perimeter of the new garden, we need to determine the dimensions after the extension. The original garden measures 3 feet by 15 feet, and the gardener decides to extend it by 1 foot in each direction. This means the new dimensions are 5 feet by 17 feet.
To find the perimeter, we add up all the sides of the rectangle. The formula for the perimeter of a rectangle is:
P = 2(l + w)
where P represents the perimeter, l represents the length of the rectangle, and w represents the width of the rectangle. Plugging in the values, we have:
P = 2(5 + 17) = 2(22) = 44 feet
Therefore, the perimeter of the new garden is 44 feet.
HELP!! I don't understand this question!!
Answer:
The answer would be c.
Step-by-step explanation:
What I'm understanding from this question is,
In the first attachment, Which has the questions selected on Shows there are two shapes.
Those two shapes have to go in to the identify the tessellation Created using the given regular polygons.
As you can see in answer C. Both shapes are represented in that tessellation.
For example, In the attachment below ] I will be showing you an example of what the question might look like for This certain tessellation.
You obviously know that square is tiltedMake a diamond shaped. That is why the diamond and hexagon is correct!
hope this helps! if it helps in any way plz mark as branliest !
He function h(t) = 210 – 15t models the altitude of a hot air balloon over time t, in minutes. Explain what h(10) means in the context of the real-world scenario, and how to find its value.
Answer:
Step-by-step explanation:
h(10) would be the height of the balloon at 10 seconds
.Tom is throwing darts at a target. In his last 30 throws, Tom has hit the target 20 times. You want to know the estimated probability that exactly one out of the next three throws does not hit the target.
Step-by-step explanation:
In his last 30 throws, Tom hit the target 20 times and missed 10 times.
p = probability he misses the target = ⅓
q = probability he hits the target = ⅔
Using binomial probability:
P = nCr (p)^r (q)^(n-r)
Given n = 3, r = 1, p = ⅓, and q = ⅔:
P = ₃C₁ (⅓)¹ (⅔)³⁻¹
P = (3) (⅓) (⅔)²
P = 4/9
There is a 4/9 probability that he misses exactly 1 of his next 3 throws.
By applying binomial probability, the estimated probability that exactly one (1) out of the next three (3) throws doesn't hit the target is 4/9.
How to determine the estimated probability?In order to determine the estimated probability that exactly one (1) out of the next three (3) throws doesn't hit the target, we would apply binomial probability equation:
[tex]P =\; ^nC_r (p)^r (q)^{(n-r)}[/tex]
Based on the information given, we can deduce the following points:
Probability that Tom misses the target (p) = 10/30 = ⅓Probability that Tom hits the target (q) = 20/30 = ⅔Number of next throws (n) = 3.Number of throws taken at a time (r) = 1.Substituting the given parameters into the equation, we have;
P = ³C₁ × (⅓)¹ × (⅔)³⁻¹
P = 3 × (⅓)¹ × (⅔)²
P = 3 × ⅓ × (⅔)²
P = 1 × 4/9
P = 4/9.
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The ages of sunitha and raseeda are in ratio of 7:8 ten years from now there ages will be 9:10 find there present age
Answer:
Sunitha: 35Raseeda: 40Step-by-step explanation:
Both numbers of the ratio units used to express the ratio in ten years are 2 higher than at present. Thus, each ratio unit must stand for 5 years. That would make their current ages ...
Sunitha: 7·5 = 35
Raseeda: 8·5 = 40
_____
If you can't figure the answer right away from the change in ratio units, then you may need to write a couple of equations:
s/r = 7/8(s+10)/(r+10) = 9/10These can be translated to standard form, which may make some methods of solution easier:
7r -8s = 09r -10s = 10These have solution (r, s) = (40, 35).
Which products result in a difference of squares? Check all that apply. (5z + 3)(–5z – 3) (w – 2.5)(w + 2.5) (8g + 1)(8g + 1) (–4v – 9)(–4v + 9) (6y + 7)(7y – 6) (p – 5)(p – 5)
Answer:
(w - 2.5)(w + 2.5)
(-4v - 9)(-4v + 9)
Step-by-step explanation:
* Lets explain what is the a difference of two squares
- If we multiply two binomial and the answer just two terms with
negative sign between them and the two terms are square numbers
we called this answer a difference of two squares
- Examples
# (a + b)(a - b)
- Lets multiply them
∵ (a × a) + (a × -b) + (b × a) + (b × -b)
∴ a² - ab + ba - b²
- Add the like term
∵ ab = ba
∴ -ab + ba = 0
∴ (a + b)(a - b) = a² - b² ⇒ difference of two squares
- From above the difference of two squares appears when we
multiply sum and difference of the same two terms
# (a + b) ⇒ is the sum of a and b
# (a - b) ⇒ is the difference of a and b
* Now lets solve the problem
- In (5z + 3)(-5z - 3)
∵ (5z + 3) ⇒ is the sum of 5z and 3
∵ (-5z - 3) ⇒ is the difference of -5z and 3
∵ 5z ≠ - 5z
∴ They are not the sum and difference of the same two terms
∴ The product result not in a difference of squares
- In (w - 2.5)(w + 2.5)
∵ (w - 2.5) is the difference between w and 2.5
∴ (w + 2.5) is the sum of w and 2.5
∴ They are the sum and difference of the same two terms
∴ The product result in a difference of squares
- In (8g + 1)(8g + 1)
∵ The two brackets are the sum of 8g and 1
∴ They are not the sum and difference of the same two terms
∴ The product result not in a difference of squares
- In (-4v - 9)(-4v + 9)
∵ (-4v - 9) is the difference between -4v and 9
∵ (-4v + 9) is the sum of -4v and 9
∴ They are the sum and difference of the same two terms
∴ The product result in a difference of squares
- In (6y + 7)(7y - 6)
∵ (6y + 7) is the sum of 6y and 7
∵ (7y - 6) is the difference between 7y and 6
∵ 6y ≠ 7y and 7 ≠ 6
∴ They are not the sum and difference of the same two terms
∴ The product result not in a difference of squares
- In (p - 5)(p - 5)
∵ The two brackets are the difference of p and 5
∴ They are not the sum and difference of the same two terms
∴ The product result not in a difference of squares
Answer:
option 2 and 4
Step-by-step explanation:
Really trying to pass this exam and graduate can someone smart please help me with these problems im running out of time ..
Answer:
1172.08 square inches
Step-by-step explanation:
Total surface area is area of all the surfaces.
Cylinder:
Top surface = πr^2 = π(4)^2 = 16(3.14) = 50.24
Lateral Surface = 2πrh = 2π(4)(9) = 72π = 72(3.14) = 226.08
Rectangular Prism:
2 sides = 2*(11*11) = 242
front and back = 2*(16*11) = 352
bottom = 16 * 11 = 176
Top part (it is top rectangle - bottom of cylinder) = (16*11) - (π(4)^2) = 125.76
Adding all up, we get:
50.24 + 226.08 + 242 + 352 + 176 + 125.76 = 1172.08 square inches
The longer leg of a 30°-60°-90° triangle measures [tex]9\sqrt{3}[/tex] inches. What is the length of the shorter leg?
A. 18 inches
B. [tex]18\sqrt{3}[/tex] inches
C. [tex]9\sqrt{3}[/tex] inches
D. 9 inches
Answer:
D. 9
Step-by-step explanation:
The Pythagorean triple for a 30-60-90 right triangle is (x, x√3, 2x). The side across from the 30° angle is x, the side across from the 60° angle is x√3, and the side across from the right angle is 2x (which is also the hypotenuse). If the side across from the 60° angle is given as 9√3, we can set that equal to the identity for that leg:
9√3 = x√3 and solve for x. Divide both sides by the √3 to get that x = 9
Answer:
The correct answer is option D. 9
Step-by-step explanation:
Points to remember
It a right triangle with angles 30°, 60 and 90° the n the sides are in the ratio,
Shorter leg : longer leg : hypotenuse = 1 : √3 : 2
To find the length of shorter leg
Here it is given that, longer length = 9√3
We have,
Shorter leg : longer leg : hypotenuse = 1 : √3 : 2 = Shorter leg : 9√3: hypotenuse
Therefore shorter leg = 9√3/√3 = 9
what is the quotient? 4x^2+3x+2 divided by x-3
For this case, we must build a quotient that, when multiplied by the divisor, eliminates the terms of the dividend until it reaches the remainder.
quotient: [tex]4x + 15[/tex]
Divisor: x-3
Dividend: [tex]4x ^ 2 + 3x + 2[/tex]
Remainder: 47
It must be fulfilled that:
Dividend = Quotient * Divisor + Remainder
Answer:
See attached image
((Please Answer with A B C or D))
If x = 3 inches, what is the perimeter of the figure above?
A. (36[tex]\sqrt{2}[/tex] + 36) inches
B. (6[tex]\sqrt{2}[/tex] + 12) inches
C. 72 inches
D. (6[tex]\sqrt{3}[/tex] + 12) inches
Answer:
B. (6√2 + 12) inches
Step-by-step explanation:
The length of the kite edge at upper left is ...
x/sin(45°) = x/(1/√2) = x√2
The length of the kite edge at upper right is ...
x/sin(30°) = x/(1/2) = 2x
The perimeter of the kite is double the sum of the lengths of these edges:
P = 2(x√2 +2x) = 2x(√2 +2)
For x=3 in, this is ...
P = 2·(3 in)(√2 +2)
P = (6√2 +12) in
_____
The sine of an angle is the ratio of the side opposite to the hypotenuse. Here, the side opposite is x, and the hypotenuse is the kite edge of interest.
x/hypotenuse = sin(angle)
hypotenuse = x/sin(angle) . . . . . solve for hypotenuse
Answer:
B
Step-by-step explanation:
I was told to put down A B C or D
And B was right
Factor 60x2 – 155x + 100 completely.
A. 5(4x + 5)(3x + 4)
B. (20x – 25)(3x – 4)
C. 5(4x – 5)(3x – 4)
D. (4x – 5)(15x – 20)
Hey there! Thanks for asking your question here on Brainly.
First, we can factor a 5 out of each term in the trinomial. This leaves us with: 5(12x^2 - 31x + 20)
Second, we need to multiply 12 * 20 and find a factor pair of the product, 240, which equals -31. This factor pair would be -15 and -16. This now leaves us with: 5((12x^2 - 16)(-15x + 20))
Third, we need to simplify each binomial in parenthesis. By doing so, what is left inside of each parenthesis should be the same if this step is done correctly. This leaves us with: 5(4x(3x - 4)-5(3x - 4))
Fourth and finally, we construct our new factored trinomial! The outside number stays, as well as one of the inner parenthesis binomials. Use the terms you factored out of the parenthesis in step three to construct another
binomial. This leaves us with: 5(4x - 5)(3x - 4) and the correct answer is C.
Hope this helps! If there's anything else I can help you with, please let me know! :)
Evaluate the line integral c (2x3 − y3) dx + (4x3 + y3) dy where c is the unit circle, and verify green's theorem for this case
Parameterize [tex]C[/tex]
[tex]x=\cos t[/tex]
[tex]y=\sin t[/tex]
with [tex]0\le t\le2\pi[/tex]. Then the line integral of [tex]\langle2x^3-y^3,4x^3+y^3\rangle[/tex] along [tex]C[/tex] is
[tex]\displaystyle\int_0^{2\pi}\langle2\cos^3t-\sin^3t,4\cos^3t+\sin^3t\rangle\cdot\langle-\sin t,\cos t\rangle\,\mathrm dt[/tex]
[tex]\displaystyle=\int_0^{2\pi}(4\cos^4t-2\cos^3t\sin t+\cos t\sin t^3+\sin^4t)\,\mathrm dt=\boxed{\frac{15\pi}4}[/tex]
By Green's theorem, the line integral is equivalent to
[tex]\displaystyle\iint_{x^2+y^2\le1}\left(\frac{\partial(4x^3+y^3)}{\partial x}-\frac{\partial(2x^3-y^3)}{\partial y}\right)\,\mathrm dx\,\mathrm dy[/tex]
[tex]=\displaystyle\iint_{x^2+y^2\le1}(12x^2+3y^2)\,\mathrm dx\,\mathrm dy[/tex]
[tex]=\displaystyle\int_0^{2\pi}\int_0^1(12r^2\cos^2\theta+3r^2\sin^2\theta)r\,\mathrm dr\,\mathrm d\theta[/tex]
[tex]=\displaystyle\int_0^{2\pi}\int_0^1(9r^3\cos^2\theta+3r^3)\,\mathrm dr\,\mathrm d\theta=\boxed{\frac{15\pi}4}[/tex]
To evaluate the line integral along the unit circle, we can parametrize the circle using x = cos(t) and y = sin(t). The resulting integral is 6 times the integral of cos squared(t) times cos(t).
Explanation:To evaluate the line integral, we need to parametrize the unit circle. Let's use x = cos(t) and y = sin(t) as the parameterization. The differential arc length is given by ds = √(dx² + dy²) = dt. Substituting these into the line integral, we get:
∫(2cos³(t) - sin³(t)) dt + ∫(4cos³(t) + sin³(t)) dt = ∫(6cos³(t)) dt
Since the unit circle can be parameterized from 0 to 2π, the integral becomes:
∫[6cos³(t)] dt = 6 ∫[(cos(t))³] dt = 6 ∫[cos³(t)] dt = 6[∫(cos²(t)cos(t)) dt]
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Need help with this one, no clue how to solve this. If someone could explain what's going on like I'm 5 it'd be much appreciated.
Find x.
Question 10
cos 45 = x/10
cos 45(10) = x
(1/sqrt{2})*10 = x
10/sqrt{2} = x
Rationalize the denominator.
[10/sqrt{2}] • [sqrt{2}/sqrt{2}] = x
10•sqrt{2} ÷ 2 = x
5• sqrt{2} = x
Felicity set the thermostat in her living room to 68°F. The room temperature t, in degrees Fahrenheit, m minutes after the thermostat is activated, satisfies t = 2cos(0.21m) + 68. Determine the period of the function and explain what it represents. Include the maximum and minimum temperatures in your answer.
Answer with explanation:
Temperature in the living room =68°F
The equation which satisfies ,the room temperature t, in degrees Fahrenheit, m minutes after the thermostat is activated, satisfies
t=2 Cos (0.21 m) +68----------(1)
⇒To determine the period of the function
Z= A cos (sx+q)+r
As period of cos x is 2 π.
So,the given function has period
[tex]=\frac{2\pi}{s}[/tex]
So, the period of function 1, is given by
[tex]=\frac{2\pi}{0.21}[/tex]
⇒The meaning of period of the function is that after every period of [tex]=\frac{2\pi}{0.21}[/tex] the temperature of the room increases or decreases by an integer equal to 2.
⇒Cosine function has maximum value of 1 , and Minimum value of -1.
-1 ≤ Cos x ≤ 1
So, the Maximum value of function = 2 ×1+68°=70°----Maximum Temperature
And, the minimum value of function = 2 ×(- 1)+68°=66°----Minimum Temperature
Final answer:
The period of the cosine function used to model the room temperature controlled by a thermostat is about 29.9155 minutes. This is the time it takes for the temperature to complete one full cycle of oscillation between the maximum of 70°F and the minimum of 66°F.
Explanation:
Felicity set the thermostat in her living room to 68°F. The room temperature t, in degrees Fahrenheit, m minutes after the thermostat is activated, satisfies t = 2cos(0.21m) + 68. This function describes a cosine wave, typical for oscillator systems like a thermostat regulating room temperature. To determine the period of the function, we examine the cosine part of the equation.
The general form of a cosine function is y = A cos(Bx + C) + D, where the period is 2π/B. Here, A is the amplitude, B affects the period, C is the phase shift, and D is the vertical shift. In Felicity's thermostat function, B = 0.21. The period of the function is therefore 2π/0.21, which is approximately 29.9155 minutes. This period represents the time it takes for the room temperature to go from a maximum value back to that value again after one complete cycle.
The max temperature is 2 + 68 = 70°F, and the min temperature is -2 + 68 = 66°F. These represent the highest and lowest temperatures the room will reach with the current thermostat settings.
What is 3/4 times 710?
Answer:
532.5 or 532[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
3/4 x 710
= 3 x 710 ÷ 4
= 532.5 or 532[tex]\frac{1}{2}[/tex]
Final answer:
To find 3/4 times 710, multiply 710 by 3 to get 2130, then divide that result by 4 to get 532.5. Therefore, 3/4 times 710 equals 532.5.
Explanation:
The question asks for the result of multiplying 3/4 with 710. To perform this calculation we simply take the number 710 and multiply it by the fraction 3/4. Multiplying a whole number by a fraction involves multiplying the numerator of the fraction by the whole number and then dividing the result by the denominator of the fraction.
Here's a step-by-step breakdown:
Multiply the whole number 710 by the numerator of the fraction, 3.Therefore, 3/4 times 710 is 532.5.
Suppose you have a bucket of sand containing 5.5 billion grains of sand ( 5.5×109 grains). Most of the grains of sand are white, but there are some brown grains mixed evenly throughout. If the concentration of brown sand is 2.0% , how many grains of brown sand are in the bucket?
Answer:
1.1×10^8
Step-by-step explanation:
2% of 5.5 billion is ...
2×10^-2 × 5.5×10^9 = 11×10^7 = 1.1×10^8
About 1.1×10^8 grains of brown sand are in the bucket.
Answer:
Grains of brown sand are in the bucket are [tex]1.1\times 10^8 grains[/tex].
Step-by-step explanation:
Total number sand grains in the bucket =[tex] 5.5\times 10^9 grain[/tex]
Concentration of brown sand grains = 2.0%
Number of brown brain in the bucket be x
[tex]\%=\frac{\text{Brown sand grains}}{\text{Total sand grains}}\times 100[/tex]
[tex]2.0\%=\frac{x}{5.5\times 10^9 grain}\times 100[/tex]
[tex]x=1.1\times 10^8 grains[/tex]
Grains of brown sand are in the bucket are [tex]1.1\times 10^8 grains[/tex].
For the function f(x)=[tex]\frac{\sqrt{x} }{5} +2[/tex]
A. ƒ –1(x) = 25(x – 2)2, x ≥ 2
B. ƒ –1(x) = 25x2 – 2, x ≥ 0
C. ƒ –1(x) = 5(x – 2)2, x ≥ 0
D. ƒ –1(x) = 25(x – 2)2, x ≥ 0
Answer:
[tex]f^{-1}(x)=25(x-2)^2[/tex]
Step-by-step explanation:
The inverse function can be found by solving ...
f(y) = x
(√y)/5 +2 = x
(√y)/5 = x -2 . . . . . subtract 2
√y = 5(x -2) . . . . . . multiply by 5
y = 25(x -2)² . . . . . square both sides
The inverse function is ...
[tex]f^{-1}(x)=25(x-2)^2[/tex]
_____
About the graph
The inverse of a function is its mirror image across the line y = x.
The revenue each season from tickets at the theme part is represented by t(x) = 5x. The cost to pay the employees each season is represented by r(x) = (1.5)x. Examine the graph of the combined function for total profit and estimate the profit after four seasons.
A. 1
B. 5
C. 10
D. 15
Answer: D. 15
Step-by-step explanation:
Given : The revenue each season from tickets at the theme part is represented by [tex]t(x) = 5x[/tex] .
The cost to pay the employees each season is represented by [tex]r(x) = (1.5)x[/tex].
From the given graph , we can see that at 4th season, the profit = 15
Hence, the estimated profit after four seasons. =15
The correct option is d. 15, is the estimated profit after four seasons, rounded to the nearest integer.
Given : The revenue each season from tickets at the theme part is represented by t(x) = 5x .
The cost to pay the employees each season is represented by r(x) = (1.5)x.
From the given graph , we can see that at 4th season, the profit = 15
Hence, the estimated profit after four seasons. =15