The functions g(x) = -√x - 3 and h(x) = x + 4 meet the requirements, and f(x) = g(h(x)) is true for f(x) = -√(x+4) - 3.
We are given f(x) and we need to find functions g(x) and h(x) such that f(x) = g(h(x)). The given function is f(x) = -√(x+4) - 3.
To find g(x) and h(x), we can split the given function into two simpler functions. Let's first look at the inner function, which deals with the input of the square root. We can define h(x) as the function inside the square root, which is:
h(x) = x + 4
Now we need to find g(x) such that when h(x) is plugged into it, we get the original function f(x). Since we have the square root and a subtraction, we can define g(x) as:
g(x) = -√x - 3
Now let's verify if f(x) = g(h(x)):
g(h(x)) = g(x + 4) = -√(x + 4) - 3
As you can see, g(h(x)) = f(x), which confirms that the functions g(x) and h(x) we found satisfy the condition.
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You put $200 per month in an investment plan that pays an APR of 4.5%. How much money will you have after 23 years?
Compare this amount to the total deposits made over the time period.
After 23 years the investment plan will contain
The amount after 23 years on the investment plan is A = $358.20
Given data ,
$200 per month under a 4.5% annual percentage rate investing plan.
Now , A = P(1 + r/n)^(nt)
Where:
A is the total sum.
P stands for the initial deposit's principal.
The yearly interest rate is represented by the decimal r.
The yearly compounding rate of interest is determined by the number n.
The number of years is t.
A = 200(1 + 0.045/1)¹ˣ²³
A = 200(1.045)²³
A ≈ 200(1.791)
A ≈ $358.20
After 23 years, the investment plan will contain approximately $358.20
Total deposits = Monthly deposit amount x Number of months
Total deposits = $200 x (12 months/year) x 23 years
Total deposits = $200 x 12 x 23
Total deposits = $55,200
Consequently, $55,200 would be the total amount of deposits made during the 23-year period.
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You just purchased a house for $100,000 at a local county auction. You spent $50,000 to
renovate the house and netted $160,000 after sale expenses. What is your ROI?
The ROI (Return on Investment) for the above investment is 106.67%.
What is the Return on Investment?
ROI (Return on Investment) is one that is seen as a financial metric used to know the profitability of an investment relative to its cost.
The formula for ROI is:
ROI = (Net Profit / Cost of Investment) x 100%
Hence, the cost of investment is the sum of the price as well as the renovation cost, will be:
Cost of Investment = $100,000 + $50,000
= $150,000
Note that the The net profit from the sale of the house is $160,000.
So, the ROI can be calculated as:
ROI = (Net Profit / Cost of Investment) x 100%
= ($160,000 / $150,000) x 100%
= 106.67%
So, the ROI for the above investment is 106.67%.
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tuesday follows monday in a week express the probability as percent
The probability that Tuesday follows Monday in a week is 100%, or 1/1, since it is always true that Tuesday comes after Monday in a week. Expressed as a percentage, the probability is 100%.
Answer:
100%
Step-by-step explanation:
because according to our calendars, Tuesday is always after monday so the probability as percent is 100%.
Mary wants to hang a mirror in her room. The mirror and frame must have an area of 7 square feet. The mirror is 2 feet wide and 3 feet long. Which quadratic equation can be used to determine the thickness of the frame, x?
Square with an inner frame with height of 2 ft on the left frame and width of 3 ft on the top. Arrow on the bottom frame with an x and an arrow on the right frame with an x.
x2 + 14x − 2 = 0
2x2 + 10x − 7 = 0
3x2 + 12x − 7 = 0
4x2 + 10x − 1 = 0
Answer:
[tex](3 + 2x)(2 + 2x) = 7[/tex]
[tex]6 + 10x + 4{x}^{2} = 7[/tex]
[tex]4 {x}^{2} + 10x - 1 = 0[/tex]
Answer:
4x2 + 10x − 1 = 0
Step-by-step explanation:
The area of a desert in Africa is times the area of a desert in Asia. If the area of a desert in Asia is square miles, express the area of a desert in Africa as an algebraic expression in .
The algebraic expression for the area of a desert in Africa in terms of the area of a desert in Asia is y = 12x.
If the area of a desert in Asia is x square miles, then the area of a desert in Africa is 12 times that, or 12x square miles. We can express this algebraically by using a variable to represent the area of the desert in Africa, such as y:
y = 12x
Here, y represents the area of the desert in Africa, and we know that it is 12 times the area of the desert in Asia, represented by x. We can substitute any value for x to find the corresponding value of y. For example, if the area of the desert in Asia is 1000 square miles, then the area of the desert in Africa is:
y = 12x = 12(1000) = 12,000 square miles
Correct Question:
The area of a desert in Africa is 12 times the area of a desert in Asia. If the area of a desert in Asia is x square miles , express the area of a desert in Africa as an algebraic expression x.
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Which of the points below correctly plots the point (−1,π/4)?
A polar graph
Select the correct answer below:
A
B
C
D
Answer: Correct answer is B
Step-by-step explanation:
Remember that the coordinates (−1,π4) tell us the radius r=−1 and the angle θ=π4. So the point should be on the circle labeled 1 and form an angle of π4 with the negative x-axis. Point B is the correct point.
slope of A=(9,8) B=(-2,0)
Answer: 8/11
Step-by-step explanation:
Slope is given by rise/run or (y_2-y_1)/(x_2-x_1).
(x_1,y_1)=(9,8) and (x_2,y_2)=(-2,0)
So (y_2-y_1)/(x_2-x_1)= (0-8)/(-2-9)=-8/-11=8/11
The directional derivative of f= x^2 y z^3 along x = e^-t , y = 1 + 2 sint , z = t -cost at t =0
The directional derivative of f = x²yz³ along vector i + 2j + 2k at x = [tex]e^{-t}[/tex] , y = 1 + 2 sin t , z = t -cost at t =0 is 2/3.
Given that the functions are,
x = [tex]e^{-t}[/tex]
y = 1 + 2 sin t
z = t - cos t
At t = 0 the point will be,
x = e⁰ = 1
y = 1 + 2 sin 0 = 1
z = 0 - cos 0 = -1
So the point is (1, 1, -1).
The vector is,
a = i + 2j + 2k
unit vector of a = (i + 2j + 2k)/√(1² + 2² + 2²) = (i + 2j + 2k)/3
Given the function is, f = x²yz³
Grad. f = 2xyz³.i + x²z³.j + 3x²yz².k
directional derivative is given by
= (Grad. f)*(unit vector of a) at (1, 1, -1)
= (2xyz³.i + x²z³.j + 3x²yz².k)*(i + 2j + 2k)/3 at (1, 1, -1)
= (2xyz³ + 2x²z³ + 6x²yz²)/3 at (1, 1, -1)
= (-2 - 2 +6)/3
= 2/3
Hence required directional derivative is 2/3.
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The question is incomplete. The complete question will be -
"The directional derivative of f= x^2 y z^3 along vector i + 2j + 2k at x = e^-t , y = 1 + 2 sin t , z = t -cost at t =0"
Tim has 6 more books than Moby. The variable m represents the number of books Moby has. Which expression represents the number of books Tim has?
Answer m+6=b
Step-by-step explanation:
m means Moby since Moby is being added by six compared to Tim, we put a 6 after m to show how many more books Tim has, then we use b for book.
Answer: The number of books belonging to Tim is m+6
Step-by-step explanation: Here variable "m " represents the number of books Moby owns.
Let "b" be the variable representing the number of books owned by Tim.
The question directs that Tim has 6 more books than Moby.
To find the number of books belonging to Tim, one has to add six more books than that of Moby
Therefore by the simple addition of these variables, we will get to know the solution
So, the number of books belonging to Tim (b) will be m+6,
that is m+6=b
Hence proved.
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A construction company will be penalized each day of delay in construction for bridge. The penalty will be $4000 for the first day and will increase by $10000 for each following day. Based on its budget, the company can afford to pay a maximum of $ 165000 toward penalty. Find the maximum number of days by which the completion of work can be delayed.
Answer:
The answer toy our problem is, The maximum number of days by which the completion of work can be delayed is 15.
Step-by-step explanation:
We are given that the penalty amount paid by the construction company from the first day as sequence, 4000, 5000, 6000, ‘ and so on ‘. The company can pay 165000 as penalty for this delay at maximum that is
[tex]S_{n}[/tex] = 165000.
Let us find the amount as arithmetic series as follows:
4000 + 5000 + 6000
The arithmetic series being, first term is [tex]a_{1}[/tex] = 4000, second term is [tex]a_{2}[/tex] = 5000.
We would have to find our common difference ‘ d ‘ by subtracting the first term from the second term as shown below:
[tex]d = a_{2} - a_{1} = 5000 - 4000 = 1000[/tex]
The sum of the arithmetic series with our first term ‘ a ‘ which the common difference being, [tex]S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ][/tex] ( ‘ d ‘ being the difference. )
Next we can substitute a = 4000, d = 1000 and [tex]S_{n}[/tex] = 165000 in “ [tex]S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ][/tex] “ which can be represented as:
Determining, [tex]S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ][/tex]
⇒ 165000 = [tex]\frac{n}{2}[/tex] [( 2 x 4000 ) + ( n - 1 ) 1000 ]
⇒ 2 x 165000 = n(8000 + 1000n - 1000 )
⇒ 330000 = n(7000 + 1000n)
⇒ 330000 = 7000n + [tex]1000n^2[/tex]
⇒ [tex]1000n^2[/tex] + 7000n - 330000 = 0
⇒ [tex]1000n^2[/tex] ( [tex]n^2[/tex] + 7n - 330 ) = 0
⇒ [tex]n^2[/tex] + 7n - 330 = 0
⇒ [tex]n^2[/tex] + 22n - 15n - 330 = 0
⇒ n( n + 22 ) - 15 ( n + 22 ) = 0
⇒ ( n + 22 )( n - 15 ) = 0
⇒ n = -22, n = 15
We need to ‘ forget ‘ the negative value of ‘ n ‘ which will represent number of days delayed, therefore, we get n=15.
Thus the answer to your problem is, The maximum number of days by which the completion of work can be delayed is 15.
Brooke believes she's getting a great deal on a car - zero down and
payments of only $260 per month for 6 years (72 months). She estimates
the additional costs of owning a car: insurance - $960 per year, registration
- $240 per year, and gas and maintenance of $175 per month.
How much will this car cost her over the life of the loan?
Answer:
First, you need to calculate the total cost of the loan. The monthly payment is $260, and there are 72 payments over 6 years. The total cost of the loan is 72 months * $260/month = $18,720
Next, you calculate the total cost of owning the car for 6 years. The insurance will cost $960 per year, so over 6 years it will cost $960/year * 6 years = $5,760
The registration will cost $240 per year, so over 6 years it will cost $240/year * 6 years = $1,440
The gas and maintenance will cost $175 per month, so over 6 years it will cost $175/month * 72 months = $12,600
Now you can add up all the costs to find the total cost of owning the car over the life of the loan:
Loan cost + insurance cost + registration cost + gas/maintenance cost
= $18,720 + $5,760 + $1,440 + $12,600
= $38,520
Therefore, the car will cost Brooke $38,520 over the life of the loan, including all additional costs of owning the car.
Answer:
$38,520
Step-by-step explanation:
To calculate the total cost of the car, we need to consider the following expenses:
Monthly payments:
$260/month x 72 months = $18,720
Insurance:
$960/year x 6 years = $5,760
Registration:
$240/year x 6 years = $1,440
Gas and maintenance:
$175/month x 12 months/year x 6 years = $12,600
Therefore, the total cost of the car over the life of the loan is:
$18,720 (monthly payments) + $5,760 (insurance) + $1,440 (registration) + $12,600 (gas and maintenance) = $38,520
So, while Brooke may think she's getting a good deal with zero down and low monthly payments, the total cost of the car over the life of the loan is quite high. It's important to consider all the additional costs associated with owning a car before making a decision to purchase one.
1. The possible missing terms to make x²_____+100 a perfect square trinomial are
a. 4x and 25x.
b. -10x and 10x.
c. -20x and 20x.
d. -4x and -25x.
Answer:
c. -20x and 20x
Step-by-step explanation:
x² is the square of x.
100 is the square of 10 and of -10.
The middle term of (a + b)² is 2ab.
For b = 10:
2ab = 20x
for b = -10:
2ab = -20x
Answer: c. -20x and 20x
(ECONOMICS- sorry there’s no button for it )
What motivates producers and consumers in the black market
The motivations for producers and consumers in the black market are largely driven by financial incentives and a desire to avoid legal consequences.
The black market refers to the illegal trade of goods and services that are not permitted by law, such as drugs, counterfeit items, and stolen goods. Producers and consumers in the black market are motivated by a variety of factors, including:
High profits, Producers in the black market can earn higher profits than they would in legal markets due to the lack of regulation and taxes.
Escaping legal consequences: Producers and consumers may participate in the black market to avoid legal consequences, such as fines or imprisonment, for engaging in illegal activities.
Limited availability, Some goods and services are only available on the black market due to legal restrictions or limited supply.
Low prices, Consumers in the black market can often purchase goods and services at lower prices than in legal markets due to the lack of taxes and regulations.
Desire for anonymity, The black market can provide anonymity for both producers and consumers, allowing them to engage in illegal activities without fear of detection or retribution.
However, participating in the black market also comes with significant risks, including the possibility of arrest, fines, and even violence.
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Two step for T+4=-7 ?
Answer:
Step-by-step explanation:
T+4 = -7
T = -7 -4
T = -11
Find a function of the form
or (picture) whose graph matches the function shown below:
The sinusoidal function of the form y = A·sin(k·x) + C that matches the function in the graph is; y = 4·sin((π/5)·x) - 1
What is a sinusoidal function?A sinusoidal function is a periodic function based on the sine or cosine functions.
The form of the function is y = A·sin(k·x)
The peak and trough of the graph are; (-7.5, 3), (-2.5, -5)
The amplitude of the function is therefore; A = (3 - (-5))/2 = 4
The vertical shift of the function is; C = (3 + (-5))/2 = -1
The period of the graph (Number of input x-values required to complete a cycle) = 2.5 - (-7.5) = 10 = 2·π/k
Therefore; k = 2·π/10 = π/5
The horizontal shift can be found as follows;
When x = 0, y = -1, therefore;
-1 = 4 × sin(π/5 × (0 - θ)) - 1
arcsin(0/4) = π/5 × (- θ)
θ = 0
The sinusoidal function is therefore;
y = 4·sin((π/5)·x) - 1
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Find two numbers such that their sum is 12 and their product is 23.
Let's call the two numbers we're trying to find x and y. We know that x + y = 12 and xy = 23. From the first equation, we can solve for one of the variables in terms of the other. So if we subtract x from both sides, we get y = 12 - x. Now we can substitute this expression for y into the second equation to get x(12 - x) = 23. Expanding this out, we get 12x - x^2 = 23. Rearranging, we get x^2 - 12x + 23 = 0. This quadratic equation can be factored as (x - 2)(x - 10) = 0. So either x = 2 and y = 10, or x = 10 and y = 2.
Answer:
The two numbers are 2 and 10.
The weight of oranges growing in an orchard is normally distributed with a mean weight of 6.5 oz. and a standard deviation of 1 oz. Using the empirical rule, determine what interval would represent weights of the middle 99.7% of all oranges from this orchard.
i Got u Bro! Answer:(3.5, 9.5)
:D
A circular racetrack has a circumference of one mile. What is the diameter of the racetrack in feet?
The diameter of the racetrack in feet is 1,681.53 feet.
How to calculate the circumference of a circle?In Mathematics and Geometry, the circumference of a circle can be determined by using the following mathematical equations:
C = πD or C = 2πr
Where:
C represents the circumference of a circle.D represents the diameter of a circle.r represents the radius of a circle.Conversion factor;
1 mile = 5280 feet
By substituting the given parameters into the formula for the circumference of a circle, we have the following;
5280 = 3.14 × D
Diameter, D = 5280/3.14
Diameter, D = 1,681.53 feet.
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Find a quadratic equation which has solutions x=4/9 and x=9/2. Write the quadratic form in the simplest standard form x^2+bx+c
Answer:
[tex](x - \frac{4}{9} )(x - \frac{9}{2} ) = 0[/tex]
[tex] {x}^{2} - \frac{89}{18} x + 2 = 0[/tex]
Write a few sentences that contain practical information about memory, thinking, and learning and describe how it helps a student become a better learner
Memory, thinking, and learning are interconnected cognitive processes that are essential for academic success.
We have,
Memory, thinking, and learning are interconnected cognitive processes that are essential for academic success.
Research has shown that memory can be improved through techniques such as repetition, active recall, and mnemonic devices.
Critical thinking skills, such as analysis and evaluation, are important for understanding and retaining information.
Effective learning strategies include breaking down complex material into smaller, manageable parts and using visual aids to enhance understanding and retention.
Thus,
Developing these cognitive skills can help a student become a more efficient learner, retain information more effectively, and perform better academically.
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solve for x.
[tex]\frac{2}{3}x=\frac{4}{9}[/tex]
[tex]x=\frac{8}{27} \\\\x=\frac{2}{3} \\\\x=2\\\\x=3[/tex]
Step-by-step explanation:
[tex] \frac{2x}{3} = \frac{4}{9} \\ 2x \times 9 = 4 \times 3 \\ 18x = 12 \\ x = \frac{12}{18} \\ x = \frac{2}{3} [/tex]
x=2/3
I hope it helped you
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write a quadratic function that passes through points (5,0) (9,0) (7,-20)
The quadratic function that passes through points is P(x) = 5(x - 5)(x - 9)
Writing the quadratic function that passes through pointsFrom the question, we have the following requirements that can be used in our computation:
Zeros at (5,0) (9,0) Point (7,-20)The quadratic function, P(x), in factored form is represented as
P(x) = a * product of (x - zeros)
So, we have
P(x) = a(x - 5)(x - 9)
Using the point (7, -20), we have
a(7 - 5)(7 - 9) = -20
So, we have
a = 5
Recall that
P(x) = a(x - 5)(x - 9)
So, we have
P(x) = 5(x - 5)(x - 9)
Hence, the function is P(x) = 5(x - 5)(x - 9)
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can someone help me with this
The sine equation for the object's height is given as follows:
d = -5sin(0.24t).
How to define the sine function?The standard definition of the sine function is given as follows:
y = Asin(Bx) + C.
The parameters are given as follows:
A: amplitude.B: the period is 2π/B.C: vertical shift.The amplitude for this problem is of 5 inches, hence:
A = 5.
The period is of 1.5 seconds, hence the coefficient B is given as follows:
2π/B = 1.5
B = 1.5/2π
B = 0.24.
The function starts moving down, hence it is negative, so:
d = -5sin(0.24t).
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Find the volume of the shape below. Round to the nearest tenth. Use
the pi button on the calculator.
Volume =
12 cm
cm³
The volume of the sphere as shown in the diagram is 904.3 cm³.
What is a sphere?A sphere is a three-dimensional round-shaped object.
To calculate the volume of the sphere, we use the formula below
Formula:
V = 4πr³/3...................... Equation 1Where:
V = Volume of the spherer = Radius of the sphereπ = PieFrom the question,
Given:
r = 12/2 = 6 cmπ = 3.14Substitute these values into equation 1
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what is the missing step in this proof GIVEN: ABC with AD/DB= CB/BB PROVE: DE||AC
The missing step in this proof is option A. ∠ABC ≅ ∠DBE
How did we arrive at this assertion?In order to bring about the SAS similarity criterion, the angle between the proportional sides should be congruent in the two triangles. Thus, the said angle is the same angle (angle B) in both triangles, which is reason for citing the reflexive property. It showcases ∠B ≅ ∠B.
Therefore, the answer choice showcasing angle B is option A. ∠ABC ≅ ∠DBE
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The complete question goes thus:
what is the missing step in this proof GIVEN: ABC with AD/DB= CB/BB PROVE: DE||AC
1. AD:DB = CE:EB Given
2. AD:DB+1 = CE:EB+1 Addition Property of Equality
3. (AD+DB)/DB = (CE+EB)/EB Using common denominators
4. AB = AD+ DB and CB = CE +EB segment addition
5. AB:DB = CB:EB Substitution property of equality
6. [Fill in missing statement from choices below] Reflexive property of congruence
7. ΔABC ~ ΔDBE SAS similarity criterion
8. ∠BAC ≅ ∠BDE Corresponding angles of similar triangles are congruent.
9. DE||AC If the corresponding angles formed by two lines cut by a transversal are congruent, then the lines are parallel.
What is the missing step in this proof?
A. ∠ABC ≅ ∠DBE
B. ∠BCA ≅ ∠BDE
C. ∠ACB ≅ ∠DEB
D. ∠BDE ≅ ∠ADE
E. ∠CAB ≅ ∠DAC
Let X and Y be the following sets: X = { 3 , 8 , 9 , 12 } Y = { 8 , 9 } Which of the following is the set X ∖ Y
The set X/Y is the same as saying the set of all elements that are in X but not in Y and the answer is {3, 12}.
Understanding SetA set is a collection of distinct objects, called elements and are usually enclosed within braces { }.
An example of a set is the set of even numbers between 1 and 10 which can be written as {2, 4, 6, 8, 10}.
Types of set
Finite and Infinite Sets: A finite set is a set that has a specific number of elements, whereas an infinite set has an unlimited number of elements.
Empty Set: The empty set, denoted by ∅ or {} is a set that has no elements.
Singleton Set: A singleton set is a set that contains only one element. For example, {5} is a singleton set.
Subset: A subset is a set whose elements are all members of another set. For example, {1, 2} is a subset of {1, 2, 3, 4}.
Universal Set: The universal set is the set of all elements under consideration. It is usually denoted by U.
Disjoint Set: Two sets are disjoint if they have no common elements. For example, {1, 2} and {3, 4} are disjoint sets.
Equal Set: Two sets are equal if they have exactly the same elements.
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Polygon ABCD is drawn with vertices at A(1, 5), B(1, 0), C(−1, −1), D(−4, 2). Determine the image vertices of A′ if the preimage is rotated 270° counterclockwise.
A′(−1, −5)
A′(−1, 5)
A′(−5, 1)
A′(5, −1
Answer:
(d) A'(5, -1)
Step-by-step explanation:
You want the coordinates of A(1, 5) after it has been rotated 270° CCW about the origin.
RotationThe transformation for rotation 270° CCW is the same as that for rotation 90° CW:
(x, y) ⇒ (y, -x)
For the given point, this is ...
A(1, 5) ⇒ A'(5, -1)
The image of A is A'(5, -1), choice D.
CAN SOMEONE HELP WITH THIS QUESTION?
The velocity at pART a = 584
The velocity in answer B = 576
How to solve for velocityThe change in time = 4
distance traveled using the 20 second interbval is
4[ 31 + 31 + 33 + 28 + 23 ]
= 4 * 146
= 584
At the end of the time periods the velocities would be:
4[31 + 33 + 28 + 23 + 29]
= 4 x 144
= 576
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Consider the equation that gives the volume of a square pyramid, where
• V represents the volume in cubic feet,
• b represents the length of each side of the pyramid's base in feet, and
• h represents the height of the pyramid in feet.
V= 1²
3
Enter an equation for which the solution is the height of a pyramid, in feet, when its volume is 48 cubic feet and the
length of each side of its base is 4 feet.
An equation for which the solution is the height of a pyramid, in feet, when its volume is 48 cubic feet and the length of each side of its base is 4 feet is h = 3(48)/4².
How to calculate the volume of a square pyramid?In Mathematics and Geometry, the volume of a square pyramid can be calculated by using the following formula:
Volume of a square pyramid, V = 1/3 × a² × h
Where:
h represent the height of a square pyramid.a represent the side length of the base of a square pyramid.By making "h" the subject of formula, the side length of the base of a square pyramid can be determined as follows;
V = 1/3 × a² × h
3V = a²h
Height, h = 3V/a²
Height, h = 3(48)/4²
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If a fair coin is tossed twice the possible outcomes are HH, HT, TH or TT, where HH means both tosses are heads and HT means that the first toss is a head and the second toss is a tail, etc. Since the coin is fair, a 50-50 chance of getting a head or a tail, we assign a probability of 1/4 to each of the four outcomes. Assuming that a fair coin was tossed twice, find the probability that exactly one of the tosses is a head and the other toss is a tail.
Assuming that a fair coin was tossed twice, the probability that exactly one of the tosses is a head and the other toss is a tail is 1/2.
The probability of a certain event happening is the number of ways that event can occur, divided by the total number of possible outcomes. In this case, we are interested in finding the probability that exactly one of the two coin tosses results in a head and the other results in a tail.
There are two possible outcomes that satisfy this condition: HT and TH. Since the coin is fair, each of these outcomes has a probability of 1/4. Therefore, the total probability of getting exactly one head and one tail is:
P(HT or TH) = P(HT) + P(TH) = 1/4 + 1/4 = 1/2
In other words, there is a 50-50 chance of getting exactly one head and one tail when a fair coin is tossed twice.
To see why this is the case, we can think of each toss as an independent event with two possible outcomes (head or tail). There are four possible outcomes when we toss a coin twice, and two of these outcomes satisfy the condition of exactly one head and one tail. Therefore, the probability of getting exactly one head and one tail is 2/4, which simplifies to 1/2.
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