Which of the following are consistent with the observed relationship between growth in real GDP and changes in the unemployment rate as shown in Figure 8-5? Which are not?a. A rise in the unemployment rate accompanies a fall in real GDP.b. An exceptionally strong business recovery is associated with a greater percentage of the labor force being employed.c. Negative real GDP growth is associated with a fall in the unemployment rate.
a. A rise in the unemployment rate accompanies a fall in real GDP. - Consistent
b. An exceptionally strong business recovery is associated with a greater percentage of the labor force being employed. - Not consistent
c. Negative real GDP growth is associated with a fall in the unemployment rate. - Not consistent
This is consistent with the observed relationship between real GDP growth and changes in the unemployment rate. An increase in real GDP is associated with a decrease in the unemployment rate, and vice versa.
This is because when GDP increases, businesses are able to hire more workers, leading to a decrease in the unemployment rate. Conversely, when GDP decreases, businesses may have to lay off employees or reduce their hours, leading to an increase in the unemployment rate.
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The complete question is:
Which of the following are consistent with the observed relationship between growth in real GDP and changes in the unemployment rate as shown in Figure 8-5? Which are not?
a. A rise in the unemployment rate accompanies a fall in real GDP.
b. An exceptionally strong business recovery is associated with a greater percentage of the labor force being employed.
c. Negative real GDP growth is associated with a fall in the unemployment rate.
Find the 96th term of the arithmetic sequence 1, -12, -25
Answer:a
Step-by-step explanation:
The first term of an ap is 29 and the seventh term is -13 what is the value of the tenth term
Step-by-step explanation:
an arithmetic progression or arithmetic sequence is a sequence of terms, where the difference bergen neighboring terms is a constant d for the whole sequence.
a1 = 29
a2 = 29 + d
a3 = a2 + d = a1 + d + d = 29 + 2d
...
an = 29 + (n-1)d
a7 = -13 = 29 + 6d
-42 = 6d
d = -42/6 = -7
therefore,
a10 = 29 + 9×-7 = 29 - 63 = -34
the average rent of one bedroom apartment in brooklyn is 2700 in 2021,if rent will increase 2.5% in 2022 and 2.5% in 2023.what would be the average rent in 2023?
The average rent of a one-bedroom apartment in Brooklyn is estimated to be $2,836.69 in 2023 after the 2.5% increase in both 2022 and 2023
What is the percentage increase?
Percentage increase is a measure of how much a value or quantity has increased relative to its original value, expressed as a percentage.
To calculate the percentage increase, you can use the following formula:
Percentage increase = (New value - Old value) / Old value x 100%
If the average rent of a one-bedroom apartment in Brooklyn is $2,700 in 2021, and it increases by 2.5% in both 2022 and 2023, we can calculate the average rent in 2023 as follows:
Calculate the increase in rent due to the 2.5% increase in 2022:
2.5% of $2,700 = 0.025 x $2,700 = $67.50
The new rent in 2022 will be $2,700 + $67.50 = $2,767.50
Calculate the increase in rent due to the 2.5% increase in 2023:
2.5% of $2,767.50 = 0.025 x $2,767.50 = $69.19
The new rent in 2023 will be $2,767.50 + $69.19 = $2,836.69
Therefore, the average rent of a one-bedroom apartment in Brooklyn is estimated to be $2,836.69 in 2023 after the 2.5% increase in both 2022 and 2023.
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A system is made up of two subsystems, A and B, connected in-series (i.e., the system fails if either subsystem fails). Subsystem A is made up of components 1 and 2, connected in series. Component 1 fails according to a Poisson process with rate 0.2 per month, whereas component 2 fails as a Poisson process with rate 0.08 per month. Subsystem B is made up of a single component 3, which is subject to repeated disruptions. The disruptions arrive as a Poisson. process with rate 1.2 per month but only 20% of them cause the failure of component 3.
a) Find the probability that the system will fail during a 3-month period.
b) Find the probability that there will be no more than two failures of the system during a 6-month period.
c) Find the probability that the next system failure will occur within a year.
Answer: a) The probability that the system will fail during a 3-month period can be calculated as the sum of the probabilities of subsystem A and subsystem B failing, since the system fails if either one fails. The probability of subsystem A failing in 3 months is given by P(A) = 1 - e^(-0.2 * 3) * (1 + 0.2 * 3 + (0.2 * 3)^2 / 2!) = 0.0664. The probability of subsystem B failing in 3 months is given by P(B) = 1 - e^(-1.2 * 3) * (1 + 0.2 * 3 + (0.2 * 3)^2 / 2!) = 0.36. Therefore, the probability that the system will fail in 3 months is P(system) = P(A) + P(B) = 0.0664 + 0.36 = 0.4264.
b) To find the probability that there will be no more than two failures of the system during a 6-month period, we need to use the cumulative distribution function (CDF) of the Poisson distribution. Let X be the number of failures of the system in 6 months. The CDF is given by F(x) = P(X <= x) = 1 - P(X > x), where P(X > x) is the probability that there will be more than x failures. Therefore, the probability that there will be no more than two failures of the system during a 6-month period is given by F(2) = 1 - P(X > 2). We can use the formula for the Poisson distribution to find P(X > 2), which is P(X > 2) = e^(-6 * (P(A) + P(B))) * ((6 * (P(A) + P(B)))^3 / 3! + (6 * (P(A) + P(B)))^2 / 2! + 6 * (P(A) + P(B)) / 1! + 1). Plugging in the values for P(A) and P(B) from part (a), we get F(2) = 1 - e^(-6 * 0.4264) * ((6 * 0.4264)^3 / 3! + (6 * 0.4264)^2 / 2! + 6 * 0.4264 / 1! + 1) = 1 - 0.2079 = 0.7921.
c) To find the probability that the next system failure will occur within a year, we need to find the cumulative distribution function (CDF) of the time between failures, which is the sum of the time between failures of subsystem A and subsystem B. Let X be the time between failures of subsystem A, which follows an exponential distribution with rate 0.2 per month. Let Y be the time between failures of subsystem B, which also follows an exponential distribution with rate 1.2 * 0.2 = 0.24 per month. Then the CDF of the time between failures is given by F(t) = P(X + Y <= t) = 1 - P(X + Y > t0.2 * 12) * e^(-0.24 * 12) = 1 - 0.17 = 0.83. Therefore, the probability that the next system failure will occur within a year is 0.83.
Step-by-step explanation:
Find an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing utility, use it to graph the function and verify the real zeros and the given function value.
n=3
4 and 2i are zeros
f(1)=-30
The function for the given zeros is f(x)=2x³-8x²+8x-32.
What are the zeros of the polynomial function?The zeros of polynomial refer to the values of the variables present in the polynomial equation for which the polynomial equals 0.
Given that, n=3.
x=4 and x=2i
We then know that the third root must be x=-2i
Now, f(x)=a(x-4)(x-2i)(x+2i)
= a(x-4)(x²-(-2i)²)
= a(x-4)(x²-(-4))
= a(x-4)(x²+4)
= ax²(x-4)+4(x-4)
f(x)= a(x³-4x²+4x-16)
f(1)=a(1³-4×1²+4×1-16)
-30=a(1-4+4-16)
a=2
Now, f(x)=2(x³-4x²+4x-16)
f(x)=2x³-8x²+8x-32
Therefore, the function is f(x)=2x³-8x²+8x-32.
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where is the local (relative) maximum for the graph below?
The local maximum for the graph below is given at point b.
How to classify the function as increasing, decreasing or constant, and how it relates to the local maximum?The function is increasing when the graph moves right and up.The function is decreasing when the graph moves right and down.The function is constant when the graph of the function is an horizontal line.A function has a local maximum when it changes from increasing to decreasing.
For the graphed function, we have that the function is increasing until point b, and then it starts to decrease, hence the local maximum is given at point b.
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(1.3+0.2) divided by 5+2.7 using BODMAS/PEDMAS
Answer:
3
Step-by-step explanation:
Parenthesis
Exponent
Division
Multiplication
Addition
Subtraction
(1.3+0.2) ÷ 5+2.7
paranthesis first
1.5 ÷ 5 + 2.7
Division next
0.3 +2.7= 3
Annie made 4 glasses of juice,her 5 friends drank 1/2 glass each.what fraction of juice was left? how to solve it
[tex]\frac{5}{2}[/tex] juice was left when Annie made 4 glasses of juice, her 5 friends drank [tex]\frac{1}{2}[/tex] glass each.
Meaning of fraction = An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction.
Annie made 4 glasses of juice
To find = fraction of juice that was left
Total glasses of juice = 4
Her 5 friends drank 1/2 glass each
= 5 × [tex]\frac{1}{2}[/tex]
= [tex]\frac{5}{2}[/tex]
Fraction of juice that left,
5 - [tex]\frac{5}{2}[/tex]
Subtracting by taking LCM,
= [tex]\frac{10 - 5}{2}[/tex]
= [tex]\frac{5}{2}[/tex]
[tex]\frac{5}{2}[/tex] juice was left when Annie made 4 glasses of juice, her 5 friends drank 1/2 glass each.
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The cost for shipping a package that weighs x pounds from Boise
to Los Angeles is shown at the right. How much more does
Shipping Central charge than Globe Delivery?
Shipping Central charges $0.51 more than Globe Delivery for any given weight of the package.
How to calculate this?The cost for shipping a package that weighs x pounds from Boise to Los Angeles is shown below.
Company Cost ($)
Shipping Central 3x+3.50
Globe Delivery 2x + 2.99
To determine the amount more Shipping Central charges than Globe Delivery, you can subtract the cost function for Globe Delivery from the cost function for Shipping Central.
The difference between the two cost functions is:
3x + 3.50 - (2x + 2.99) = x + 0.51 = $0.51 + x
This means that, for any given weight of the package, Shipping Central charges $0.51 more than Globe Delivery.
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22.1.3 Quiz: Selecting a House: Fairly Priced?
Question 5 of 10
A house is listed for sale at $235,000, but the listing does not include square
footage of the house. Based on the comps, the line of best fit is
y=0.06x + 60.5. If the price is fair, what size (in square feet) should the house
be?
OA. 2850 ft2
OB. 2900 ft2
OC. 20,000 ft²
OD. 2350 ft²
Size of the house should be 2900 ft².
Correct option is B.
What is linear equation?A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.
Given,
Equation for the line that expresses price of house
y = 0.06x + 60.5
where y is the price in thousand dollars, x is area in square feet.
Price of the house = $235000
⇒ y = 235
Then,
235 = 0.06x + 60.5
0.06x = $235 - 60.5
0.06x = 174.5
x = 174.5/0.06
x = 2908.33 ≈ 2900
Hence, 2900 ft² should be the size of the house.
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for each inequality write all the one digit integers that satisfy it a>2
Possible answers are:
3
4
5
6
7
8
9
For every point on the graph of f(x), there is a point on the graph of F^-1(x) with reversed coordinates. TRUE or FALSE
you will get 40 points for answering it!
The statement, For every point on the graph of f(x), there is a point on the graph of F⁻¹(x) with reversed coordinates is false.
What is inverse function?In relation to the original function f, the inverse function is denoted by the symbol f⁻¹, and both the original function's domain and its range are transformed into the inverse function's domain and range, respectively. Swapping (x, y) with (y, x) with reference to the line y = x yields the graph of the inverse function.
We know that inverse of function is NOT the reciprocal of f. The composition of the function f and the reciprocal function f inverse gives the domain value of x.
Hence, the statement, For every point on the graph of f(x), there is a point on the graph of F⁻¹(x) with reversed coordinates is false.
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A copy machine makes 187 copies in 4 minutes and 15 seconds. How many copies does it make per minute?
copies per minute
The copy machine make 44 copies per minute.
What is the unitary method?The unitary method is the method of solving a problem by the first value of a single unit and than finding the value of single unit by multiplying. Unitary method is a technique by which we can find the value of a single unit from the value of multiple data and also the value of more than one unit from the value of single unit. This is a method that we use for most of the calculations in mathematics;
We are given that Time copy machine take= 4min 15sec
Number of copies=187
Now, 1min=60sec
4min=240sec
Total time=240+15 =255sec
Therefore, 255sec=187copies
60sec= 187 x 60/255
=44
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Shaun White, the Flying Tomato, is rolling down a 30° ramp on his skateboard (because he's not just a snowboarding gold medalist, the bro can skate too). The total mass of Shaun and his skateboard is 75 kg. The rolling friction between the skateboard wheels and the concrete is 9N acting backward against the skateboard. The drag force due to air resistance is 11 N acting backwards against Shaun. What is Shaun's acceleration? 30° 4.64 m/s2 down the slope
Previous question
If the drag force due to air resistance is 11 N acting backwards against Shaun. Shaun's acceleration is 4.64 m/s^2 down the slope.
To find Shaun's acceleration, we need to calculate the net force acting on him and his skateboard. The net force is the vector sum of all the forces acting on the object. We can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and its acceleration:
Net force = mass × acceleration
Let's break down the forces acting on Shaun and his skateboard:
The force of gravity, which acts vertically downwards with a magnitude of mg, where m is the total mass of Shaun and his skateboard and g is the acceleration due to gravity (9.8 m/s^2).
F₁ = m * g * sin(30°) = 75 kg * 9.8 m/s^2 * sin(30°) = 367.5 N
The force due to rolling friction between the skateboard wheels and the concrete, which acts backward against the skateboard.
F₂ = 9 N (given)
The drag force due to air resistance, which acts backward against Shaun.
F₃ = 11 N (given)
Now, let's add up the forces to get the net force:
Net force = F₁ - F₂ - F₃
= 367.5 N - 9 N - 11 N
= 347.5 N
Using Newton's second law of motion, we can now calculate Shaun's acceleration:
acceleration = Net force / mass
= 347.5 N / 75 kg
= 4.64 m/s^2 (down the slope)
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How can i put this in slope intercept form?
X int= 5; Y int= -2
When sales representatives for a pharmaceutical company drive to out-of-town meetings that require an overnight stay, they receive $140 for lodging plus $0.60 per mile driven. How many miles did Joe drive if his company reimbursed him $290 for an overnight trip?
Question content area bottom
Part 1
The equation is enter your response here. Joe drove enter your response here miles.
(Type an equation using x as the variable.)
solve for equation and miles Joe drove
Joe was given $329 for an overnight trip because he drove a distance of 220 miles
How to solve Word Problems ?
Five Easy Steps to Solving Word Problems (WASSP)
Write (or draw) what you know.Ask the question.Set up a math problem that could answer the question.Solve the math problem to get an answer.Put the answer in a sentence to see if the answer makes sense!Given Data
Amount rep receive = $175
Added amount per mile driven = $0.70
Reimbursed/Total = $329
The Mathematical relation for this scenario is
Total amount = Amount Receive+ 0.7*Distance driven
let the distance driven be x
Substituting our given data into the relation we have
329= 175+ 0.7*x
329-175 = 0.7x
154 = 0.7x
divide both sides by 0.7
x = 154/0.7
x = 220miles
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Para todo x en A:123,x+2 al cuadrado es igual a x al cuadrado+2, verdadero o falso?
The given conclusion "(x + 2)² = (x² + 2)" is false.
What are the various set representation methods?The two set representation methods are -
Roster formSet - builder formGiven is the set A{1, 2, 3}.
(x + 2)² should be equal to (x² + 2) for all x ∈ A.
We can write -
(1 + 2)² = 1² + 2
9 ≠ 3
Therefore, the given conclusion "(x + 2)² = (x² + 2)" is false.
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{Question in english -
For all x in A: {1, 2, 3}, (x + 2)² is equal to (x² + 2). True or false?}
Look at the inequality below.
−6 ≥ 13 + 5×
Which of these values of x makes the inequality true?
A -3.9
B -1.2
C -7/15
D 3/13
Answer:
a -3.9
Step-by-step explanation:
Subtract 13 from both sides which makes it -19 > 5x. then divide by 5 on both sides
Brainliest, please help me! Thanks :)
Answer:
A and D
Step-by-step explanation:
They both dont touch and go in the sam direction
Answer:
Below
Step-by-step explanation:
It APPEARS that First and last choices are true.....the lines do not cross in the picture...BUT you cannot say for SURE they are parallel without more information about the angles at D E H and I ....or markings
Binomial distribution calculation
If n=5 and p=0.7, find P(x=4)
Give at least 4 decimal places.
The binomial distribution P( x = 4 ) if n = 5 and p = 0.7 is 0.3602.
What is the binomial distribution?Binomial probability distribution determines the probability of a discrete random variable.
Given that;
n = 5p = 0.7p( x = 4 )Using the formula, probability mass function;
P( X = x ) = ⁿCₓPˣ( 1 - P )ⁿ⁻ˣ
P( X = x ) = ⁵Cₓ × 0.7ˣ × ( 1 - 0.7 )⁵⁻ˣ
Now for P( x = 4 )
P( X = 4 ) = ⁵C₄ × 0.7⁴ × ( 1 - 0.7 )⁵⁻⁴
P( X = 4 ) = ⁵C₄ × 0.7⁴ × ( 1 - 0.7 )
P( X = 4 ) = 5 × 0.2401 × 0.3
P( X = 4 ) = 0.3602
Therefore, the value of P( x = 4 ) is 0.3602.
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A right square pyramid has an altitude of 10 and each side of the base is 6. To the nearest tenth of a centimeter, what is the distance from the apex, or top of the pyramid, to each vertex of base?
The distance from the apex, or top of the pyramid, to each vertex of base is 10.9.
What is a right rectangular pyramid?A right rectangular pyramid is a pyramid, with four slant sides, and a rectangular base, such that all the sides are congruent and the vertex is atop of the midpoint of the base rectangle.
Suppose the base of the pyramid has length = l units, and width = w units.
Suppose that the height of the pyramid is of h units, then:
[tex]v = \dfrac{l \times w \times h}{3} \: \rm unit^3[/tex]
is the volume of that pyramid.
The base is a rectangle with length = L units, and width = W units, so its area is:
[tex]b = l \times w\: \rm unit^2[/tex]
Given that;
Altitude of pyramid= 10
Each side base of pyramid= 6
Now,
So using pythagorean theorem,
x2=y2+(10)2....1
with y half of the length of the diagonal of the base.
2y=length of the diagnol
and (2y)2 = 72
4y2=72
y = 3√2.
So substitute y in eq1 and get x
( 3√2)2+(10)2=(x)2
(x)2=118
x=10.86.
x≈10.9
Therefore, the side of right square pyramid will be 10.9.
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Consider the line 8x-5y=1
what is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line
Answer:
[tex]\frac{8}{5}[/tex] and - [tex]\frac{5}{8}[/tex]
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
8x - 5y = 1 ( subtract 8x from both sides )
- 5y = - 8x + 1 ( divide through by - 5 )
y = [tex]\frac{8}{5}[/tex] x - [tex]\frac{1}{5}[/tex] ← in slope- intercept form
with slope m = [tex]\frac{8}{5}[/tex]
• Parallel lines have equal slopes
then the slope of a parallel line is m = [tex]\frac{8}{5}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{8}{5} }[/tex] = - [tex]\frac{5}{8}[/tex]
Interpret the scatter plot based on the shape of the distribution.
Answer: Looks like a positive correlation with an outlier in the lower left.
Step-by-step explanation:
convert the following measurement
Answer:
3.4 x 10⁻² kg · m²/s²
Step-by-step explanation:
[tex]3.4\times \:10^5=340000[/tex]
The numerator is in g.cm² and the denominator is the same s²
So we only need to convert the numerator from g.cm² to kg.m²
1 kg = 1000 grams = 10³ grams
1 gm = 1/10³ kg
1 gm = 10⁻³ kg
1 m = 100 cm = 10² cm
1 m² = 100² cm² = (10²)² = 10⁴ cm²
Or 1 cm² = 1/10⁴ cm² = 10⁻⁴ cm²
Therefore to convert g · cm² to kg · m² we multiply by
(10⁻³) · (10⁻⁴) = 10⁻⁷
Therefore 3.4 x 10⁵ g · cm² = 3.4 x 10⁵ x 10⁻⁷ kg · m²
= 3.4 x 10⁻² kg · m²/s²
Use the data in the table below, which shows the employment status of individuals in a particular town by age group.
Age
0-17
18-25
26-34
35-49
50 +
Full-time
21
267
492
535
520
Part-time
187
200
67
195
166
Unemployed
356
135
28
133
231
If a person is randomly chosen from the town's population, what is the probability that the person is under 18 or employed part-time?
X
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The probability that the person is under 18 or employed part-time is 179/864.
What is experimental probability?Experimental probability calculates the probability of some event from the results of experiments.
For an event E, we get the experimental probability of that event
[tex]P_e(E) = \dfrac{\text{Number of times E occurred}}{\text{Number of times experiments was done}}[/tex]
where,[tex]P_e(E)[/tex] is denoting experimental probability of occurrence of E.
Given that;
The table of age, full time, part time, unemployed
Now,
Total number of people who are between the age group 35-49
= 581+179+104
= 864
Number of people who are employed part time= 179
Number of people employed part time in age group 35-49/ Total people in age group 35-49
= 179/864
Therefore, the probability will be 179/864.
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Miguel Rodriguez borrowed $200 from his brother Julio to pay for books and tuition. He agreed to pay Julio in 6 months with simple annual interest at 6.3%
Answer:
simple interest is $6.8
Miguel pay the amount to Julio at the end of 6 months was $206.8
Step-by-step explanation:
Given : Miguel Rodriguez borrowed $200 from his brother Julio to pay for books and tuition. He agreed to pay Julio in 6 months with simple annual interest at 6.8%.
To Find : a) How much will the interest amount to?
b) What amount must Miguel pay Julio at the end of 6 months?
Solution :
Formula for simple interest :
Where rate is in decimal
Time is in years
So, rate of interest = 6.8 % = 0.068
Time = 6 months = 6/12=0.5
Principal = $200
Thus= 200x0.068x0.5=6.8
When solving an inequality, if you the coefficient is negative, as in-3x > 9, the inequality
True
False
"When solving an inequality, if you the coefficient is negative, as in-3x > 9, the inequality" statement becomes: true
What is an inequality?A relationship that compares two numbers or other mathematical expressions in an unequal way is known as an inequality in mathematics. On the number line, it is most frequently used to compare the sizes of two numbers. The equals sign in the equation-like phrase 7x 4 > 2x + 5 has been replaced by an arrowhead. This is a prime instance of inequality. This indicates that the left half, 7x 4, is larger than the right part, 2x + 5, in the equation. Finding the values of x for which the inequality holds true will be of importance to us.
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Que es el crecimiento exponencial?
The concept of exponential growth function is discussed below.
What is exponential function?An exponential function is of the form -
y = A(B)ˣ
Given is to explain exponential growth.
Exponential growth of a quantity happens if the rate of instantaneous change is directly proportional to the quantity itself. The general exponential function is -
y = A(B)ˣ
More specifically -
[tex]$f(x)=a(1+r)^{x}[/tex]
where -
f(x) = exponential growth function
{a} = initial amount
{r} = growth rate
{x} = number of time intervals
Therefore, the concept of exponential growth function is discussed above.
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{Question in english -
What is exponential growth?}
Drag figures and equations to the table to show the net and surface area of the rectangular prism.
The numbers are
W = 3cm.
I = 6cm.
H =3cm.
Pleaseee helppp
According to the posed question, the rectangular prism's surface area would be 90 cm2.
What is a Rectangular Prism's Surface Area?
The total surface area of a rectangular prism's rectangular faces is alluded to as the prism's surface area. There are two distinct types of it: lateral surface area and total surface area. In contradiction to the lateral surface area, which only includes the lateral faces and omit the base areas, the total surface area of a rectangular prism refers to the area among all six faces.
Given, W = 3 cm, L = 6 cm, and H = 3 cm
surface area = 2 (WL + LH + HW)
= 2 (18 + 18 + 9)
= 2× 45 = 90 cm².
Consequently, the rectangular prism's surface area is 90 cm².
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