The positive value of the parameter t corresponding to a point on the parametric curve x = t^2 + 7, y = t^2 + t for which the tangent line passes through the origin is t = 7 + √56.
Given the parametric curve {x = t^2 + 7, y = t^2 + t}, we want to find the positive value of t corresponding to a point on the curve for which the tangent line passes through the origin (0, 0).
First, we find the derivative of the x and y equations to obtain the slope of the tangent line at the point (t^2 + 7, t^2 + t). The derivative of x = t^2 + 7 is
dx/ dt = 2t
and the derivative of y = t^2 + t is
dy/dt = 2t + 1
So, the slope of the tangent line at the point (t^2 + 7, t^2 + t) is
dy/dx = (dy/dt) / (dx/dt)
dy/dx = (2t + 1)/ 2t
dy/dx = 1 + 1/(2t)
Next, we use the fact that the slope of the tangent line is equal to the ratio of the change in y to the change in x between the point and the origin (0, 0). Since the origin is located at x = 0 and y = 0, we have:
(t^2 + t - 0) / (t^2 + 7 - 0) = 2t + 1)/ (2t)
2t(t^2 + t) = (2t + 1) (t^2 + 7)
2t^3 + 2t^2 = 2t^3 + t^2 + 14t + 7
t^2 - 14t = 7
t^2 - 14t + 49 = 7 + 49
(t - 7)^2 = 56
t - 7 = ±√56
t = 7 ± √56
As we require only positive value t = 7 + √56
--The question is incomplete, answering to the question below--
"find the positive value of the parameter t corresponding to a point on the parametric curve { x = t^2 + 7, y = t^2 + t for which the tangent line passes through the origin. answer exactly."
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a town is designing a rectangular park that will be 600 feet wide by 1000 feet long. on a scale drawing, the dimensions of the park are 12 inches wide by 20 inches long. a rectangular area of the park for swing sets is 0.5 inch wide by 2 inches long on the scale drawing. what is the actual length of the swing set area of the park?
The actual length of the swing set area is 0.5 * 20 feet = 10 feet.
Since the scale drawing represents the actual dimensions of the park,
We can use the ratio of the scale drawing dimensions to the actual dimensions to find the actual length of the swing set area.
Let's call the actual length of the swing set area L.
Then, on the scale drawing, the length of the swing set area is 0.5 inches.
The ratio of the actual length to the scale drawing length is 20 inches : L feet.
We can set up an equation to find L:
L * (20 inches / L feet) = 0.5 inches
Solving for L, we find:
L = (0.5 inches * L feet) / (20 inches / L feet)
= (0.5 * L feet) / (20 / L feet)
= (0.5 * L feet) / (20 / L feet)
= 0.5 * (L feet / 12 inches/foot)
= 0.5 * 20 feet
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Answer:
The answer is 100 feet. I took the quiz and it was 100 feet.
Step-by-step explanation:
what 26789 divide 43
an experiment requires a measurement before and after the presentation of a stimulus to 20 subjects. in the analysis of the data collected from this experiment, how many degrees of freedom are there in the test?
In a repeated measures design with 20 subjects, each subjected to 2 measurements (before and after stimulus presentation), the degrees of freedom in the test would be 19.
DF in Repeated Measures ExperimentThe problem is about an experiment in which a measurement is taken before and after a stimulus is presented to 20 subjects. The aim is to determine the number of degrees of freedom in the data analysis of the experiment.
Degrees of freedom (df) are a measure of the amount of variability in a set of data that is free to vary in the calculation of a statistical test. In a repeated measures design, the degrees of freedom are calculated as the number of subjects minus 1. In this case, with 20 subjects, the degrees of freedom would be 19.
The concept of degrees of freedom is used in both mathematics and physics, but the specific context of a t-test for dependent samples is commonly used in statistical analysis, particularly in the social sciences, psychology, and education research. So, it is more related to mathematics.
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Jim is going to order rose bushes from a local nursery. The delivery charge is $15.00. Each rose bush costs $18.75. What is the greatest number of rose bushes lim can he buy with 80.
Answer: 3 rose bushes
Step-by-step explanation:
1. First we must identify the unknown. We do not know how many rose bushes he can get, we will use "x" to represent this number.
2. We must set up an equation with the given information. We know the delivery fee will remain constant.
3. 15+18.75(x)=80
4. Subtract 15 from both sides and it leaves you with 18.75x=65
5. Then you must divide both sides by 18.75, which leaves you with x=3.46
6. We cannot buy .46 of a plant so we must round down to 3
7. Jim can buy 3 rose bushes
Adrian is going to an amusement park. The price of admission into the park is $35, and once he is inside the park, he will have to pay $3 for every ride he rides on. How much money would Adrian have to pay in total if he goes on 12 rides? How much would he have to pay if he goes on r rides?
The amount of money that Adrian will pay if he goes on the given amount of ride would be =$71
How to calculate the cost per ride?An amusement park is defined as the park where different recreational activities are being carried out.
The price of admission in the park = $35
The amount he pays for each ride at the amusement park= $3.
The amount for 12 rides= 3×12 = $36
Therefore the total amount of money that Adrian will pay if he goes to the amusement park for 12 rides would be = $36 + $35 =$71
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a box containis some chocolate. thw weight of the box and chocolate 360g. Alex eats 2/5 of the chocolate. the weight of the box and chocolate is now 248g. how much does the box weigh?
Answer: 80g
Step-by-step explanation:
we can write an equation for the weight of chocolate; 360-(2/5)x=248
when we solve that equation, we get x=280
since the total weight is 360, we can minus 280 from it to get the weight of the box
360-280=80
DeAndre has 190 square inches of plastic to make a cylindrical bird feeder. Which design should he choose? Explain.
DeAndre should select the shape that satisfy the equation -
r(2h + r) = (190/π).
What is cylinder?A cylinder has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes. In elementary geometry, it is considered a prism with a circle as its base. A cylinder may also be defined as an infinite curvilinear surface in various modern branches of geometry and topology.Given is that DeAndre has 190 square inches of plastic to make a cylindrical bird feeder.
He should choose the design whose total surface area is equivalent to 190 square inches. We can write the total surface area as -
2πrh + πr² = 190
πr(2h + r) = 190
r(2h + r) = (190/π)
Therefore, DeAndre should select the shape that satisfy the equation -
r(2h + r) = (190/π).
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can someone pls help
The required area of the parallelogram and pentagon is 91 unit² and 75 unit².
What is surface area?The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.
A parallelogram in is shown in figure 1 with the dimensions height = 7 and base = 13,
Area of the parallelogram = 13 × 7 = 91 unit²
Now,
A pentagon is shown in figure 2,
Area of the pentagon = 5 [1/2 × height × side]
= 5 [1/2 × 5 × 6]
= 75 suqare units.
Thus, the required area of the parallelogram and pentagon is 91 unit² and 75 unit².
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Compare the investment below to an investment of the same principal at the same rate compounded annually. principal: $7,000, annual interest: 9%, interest periods:4 , number of years:12 Question content area bottom Part 1 After 12 years, the investment compounded periodically will be worth $ enter your response here more than the investment compounded annually.
[tex]~~~~~~ \stackrel{\textit{\LARGE Quarterly}}{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$7000\\ r=rate\to 9\%\to \frac{9}{100}\dotfill &0.09\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &12 \end{cases}[/tex]
[tex]A = 7000\left(1+\frac{0.09}{4}\right)^{4\cdot 12} \implies A=7000(1.0225)^{48}\implies \boxed{A \approx 20367.48} \\\\[-0.35em] ~\dotfill[/tex]
[tex]~~~~~~ \stackrel{\textit{\LARGE Annually}}{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$7000\\ r=rate\to 9\%\to \frac{9}{100}\dotfill &0.09\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &12 \end{cases}[/tex]
[tex]A = 7000\left(1+\frac{0.09}{1}\right)^{1\cdot 12}\implies A=7000(1.09)^{12} \implies \boxed{A \approx 19688.65} \\\\[-0.35em] ~\dotfill\\\\ 20367.48~~ - ~~19688.65 ~~ \approx ~~ \text{\LARGE 678.83}[/tex]
At the end of any year a car is worth 5% less than what is was worth at the beginning of the year. if a car was brought for 10 000 in January 2009, its value in December 2009 was
Answer:If at the end of any year a car is worth 5% less than what it was worth at the beginning of the year, we can say that the car's value decreases by a factor of 0.95 (1 - 0.05) every year.
To find the car's value in December 2009, we can use the formula:
Car value at end of year = Car value at beginning of year * (1 - 0.05)^(number of years)
Plugging in the given values, we get:
Car value in December 2009 = 10,000 * (1 - 0.05)^1 = 9,500
So the car's value in December 2009 is 9,500 dollars.
Step-by-step explanation:
Answer:
9500
Step-by-step explanation:
If you didn't understand that one (which I personally found a little complicated) the answer can be found like this.
1. You firstly find the decrease which is 5/100 × 10000 (5/100 can also be written as 5%) and the answer will be 500
2. Then you take the original value and you minus the loss in worth of the car —> 10000-500 = 9500
What is 32(4x+6) in simplified form
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{ASSUMING:}[/tex]
[tex]\mathsf{\dfrac{3}{2}(4x + 6)}[/tex]
[tex]\huge\textbf{If so, distribute \boxed{\rm{\bf \dfrac{3}{2}}} within the}\\\\\huge\textbf{parentheses}[/tex]
[tex]\mathsf{\dfrac{3}{2}(4x + 6)}[/tex]
[tex]\mathsf{= \dfrac{3}{2}(4x) + \dfrac{3}{2}(6)}[/tex]
[tex]\mathsf{= \dfrac{3}{2}\times \dfrac{4}{1}x + \dfrac{3}{2} \times \dfrac{6}{1}}[/tex]
[tex]\mathsf{= \dfrac{3\times4}{2\times1}x +\dfrac{3\times6}{2\times1}}[/tex]
[tex]\mathsf{= \dfrac{12}{2}x +\dfrac{18}{2}}[/tex]
[tex]\mathsf{= 6x + 9}[/tex]
[tex]\huge\textbf{Therefore your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{6x + 9}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
solve the simultaneous equation. y=5-x ,x^2-2y^2-1=0
In the given simultaneous linear equation, the value for x is 3 and the value for y is 2.
Explain simultaneous linear equation.A system of simultaneous linear equations is any set of two or more linear equations that share the same variables involved. Obtaining values for the unknown variables that simultaneously satisfy all of the equations is required to solve such a system.
In the given question,
x + y = 5.......(i)
x2 - 2y2 = 1.......(ii)
x = 5 - y.........(iii)
Substituting x in equation(ii) = (5 - y)2 - 2y2 = 1
25- 10y + y2 - 2y2 = 1
25 - 1 = y2 + 10y
y2 + 10y2 - 24 = 0
(y + 12)(y - 2) = 0
Then Either y + 12 = 0 or y - 2 = 0
= (-12, 2)
Thus, y = 2
Now, substituting the value of y in equation (i),
x + y = 5
x + 2 = 5
x = 5 - 2
x = 3
Therefore x = 3 and y = 2.
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A 75 kg box is being pulled across the floor with a force of 465 N. If the kinetic coefficient of friction is 0.57, what is the acceleration of the box?
The acceleration of an object is interpreted as the rate of change at which its speed varies with time. When the motion is vertical, the object has an acceleration when its speed varies, while when the speed is constant, the acceleration is equal to zero. The acceleration of the box is 0.614 m/s.
What is acceleration?In mechanics, acceleration is defined as the rate of change of an object's velocity with respect to time. Vector quantities are accelerations. The orientation of an object's acceleration is determined by the orientation of its net force.Deceleration occurs when acceleration is directed in the opposite direction as the velocity of an object.Deceleration is always defined in physics as the slowing down of an object, which means that the magnitude of the velocity decreases.The rate of change of displacement is defined as velocity. The rate of change of velocity is defined as acceleration. Because it includes both magnitude and direction, velocity is a vector quantity. Because it is simply the rate of change of velocity, acceleration is also a vector quantity.To learn more about acceleration refer to:
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Exponential growth: what it is, why it matters, and how to spot it
An expansion within a population that happens at the same pace across time is represented by the function of exponential growth.
What is exponential growth?It is reasonable to suppose that data grows exponentially as populations double or triple in size. Exponentially decaying data is the reverse of exponentially growing data. When your data are visualized on a graph, the pattern an exponential function displays appears as an ascending curve. f(x) = a(1 + r)x is another formula you may use to compute exponential growth.F(x) stands for the function and is a term.The starting value of your data is indicated by the a variable.Growth rate is indicated by the variable r.Period of time is represented by the x variable.Examples :
The analyst can determine the possible returns after three, five, and ten years if the customer deposits an initial starting capital of $5,000 into their compound savings account. The analyst decides: Using a 5% interest rate
Upon completion of three years: ($5,000)(1 + 0.05)(3) = $5,788
Upon completion of five years: ($5,000)(1 + 0.05)(5) = $6,381
A decade later, ($5,000)(1 + 0.05)(10) = $8,144
The Complete Question is exponential growth.
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alice is holding up the top vertex of a triangular banner attached to the ground by two anchors on the bottom vertices. what is the area of the banner of alice reaches her arm up above the ground and the anchors on the bottom are apart?
Let's call the length of the bottom side of the triangular banner "b". When Alice reaches her arm up above the ground, the height of the banner changes from its original height of "h" to a new height of "h'". The area of the banner can be calculated using the formula:
A = (b * h') / 2
The new height "h'", can be calculated using the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side (the hypotenuse).
In this case, the two shorter sides are the original height "h" and the difference between the length of Alice's arm and the original height, which we will call "d". The longest side is the distance between the two anchors, which we will call "a".
So:
h^2 + d^2 = a^2
We can solve for "d" using this equation:
d = sqrt(a^2 - h^2)
And then we can find "h'" using:
h' = h + d
So the area of the banner can be calculated as:
A = (b * (h + sqrt(a^2 - h^2))) / 2
The solution assumes that the banner is a right triangle, with one vertex at the top, one vertex at the bottom, and a straight side along the ground connecting the two bottom vertices.
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A hospital operating room needs to schedule three knee surgeries and two hip surgeries in a day. Suppose that an operating room needs to schedule three knee, four hip, and five shoulder surgeries. Assume that all schedules are equally likely. Determine the probability for each of the following: (a) All hip surgeries are completed before another type of surgery (b) The schedule begins with a hip surgery (c) The first and last surgeries are hip surgeries. (d) The first two surgeries are hip surgeries.
To calculate the probability a) P = (4C4 x 3C3)/(12C12) = 1/12. (b) P = (4C1 x 3C3 x 5C5)/(12C12) = 1/12. (c) P= (4C1 x 3C3 x 4C3 x 5C4)/(12C12) = 1/9. (d) P= (4C2 x 3C3 x 5C5)/(12C12) = 1/36.
(a) To calculate the probability that all hip surgeries are completed before another type of surgery, we first determine the total number of possible combinations of surgeries (12C12). We then calculate the number of combinations with four hip surgeries and three knee surgeries (4C4 x 3C3). We divide the number of combinations with the desired schedule by the total number of combinations to get the probability (1/12). (b) To calculate the probability that the schedule begins with a hip surgery, we first determine the total number of possible combinations of surgeries (12C12). We then calculate the number of combinations with one hip surgery, three knee surgeries, and five shoulder surgeries (4C1 x 3C3 x 5C5). We divide the number of combinations with the desired schedule by the total number of combinations to get the probability (1/12). (c) To calculate the probability that the first and last surgeries are hip surgeries, we first determine the total number of possible combinations of surgeries (12C12). We then calculate the number of combinations with one hip surgery at the start, three knee surgeries, three hip surgeries, and four shoulder surgeries (4C1 x 3C3 x 4C3 x 5C4). We divide the number of combinations with the desired schedule by the total number of combinations to get the probability (1/9). (d) To calculate the probability that the first two surgeries are hip surgeries, we first determine the total number of possible combinations of surgeries (12C12). We then calculate the number of combinations with two hip surgeries, three knee surgeries, and five shoulder surgeries (4C2 x 3C3 x 5C5). We divide the number of combinations with the desired schedule by the total number of combinations to get the probability (1/36).
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A car moving at a constant speed passed a timing device at t=0. After 6 seconds, the car has traveled 684 ft. Write a linear function rule to model the distance in feet d the car has traveled any number of seconds t after passing the timing device.
The linear function rule is d = ?
Answer:
Step-by-step explanation:
219y+608=−121156 219y+608=−121156 219y+608=−121156 v 219y+608=−121156v219y+608=−121156vvv219y+608=−121156= 365
Answer:
d = 114t
Step-by-step explanation:
distance = rate * time
therefore, rate = distance/time
684 ft in 6 sec = 114 ft per sec (this is the 'rate')
so the distance can be calculated by multiplying time in seconds to get distance in feet
d = 114t
find an equation of the sphere with center (−4, 2, 6) and radius 7. correct: your answer is correct. what is the intersection of this sphere with the yz-plane? incorrect: your answer is incorrect.
The equation of sphere is (x + 4)² + (y - 2)² + (z - 6)² = 49 and the intersection is a circle of radius √33 on yz - plane.
A sphere, like a ball, is defined as a perfectly spherical geometrical entity in three dimensions.
the general equation of a sphere is (x – a)² + (y – b)² + (z – c)² = r² where (a, b, c) is the centre of the sphere and r is the radius of the sphere.
Given, the centre of the sphere C(−4, 2, 6) and radius of sphere 7 units
Equation of sphere: (x - (-4))² + (y - 2)² + (z - 6)² = 7²
(x + 4)² + (y - 2)² + (z - 6)² = 49
It is given that the sphere is intersecting with yz - plane which means x = 0
so, (0 + 4)² + (y - 2)² + (z - 6)² = 49
(y - 2)² + (z - 6)² = 33
The intersection is a circle of radius √33 on yz - plane.
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Three boys shared D 10,500.00 in the ratio 6:7: 8. Find the largest share.
Answer:
Step-by-step explanation:
let the common ratio be x.
boy 1 share= 6x
boy 2 share= 7x
boy 3 share= 8x
-------------------------------
21x= 10500.00
=> x= 10500/21
x= 500
6 x 500= $3000
7x 500= $3500
8 x 500= $28000
therefore, boy 3 has the largest share of $28000.
There i only one carton of pear. Jo want to buy 3/4 of it, and Max to buy 1/3 of it. Will there be enough?
The only one carton of pear is not enough because the sum of both Jo and Max requirement is max than the one.
There is only one carton of pear.
Jo want to buy 3/4 of it, and Max to buy 1/3 of it.
To check whether one carton of pear is enough for both Jo and Max we firstly add the part of Jo and Max to find the total pear they want. Then we check the one pear is enough y subtracting.
Now finding the total pear that Jo and Max want:
Total Pear they want = Jo want + Max want
Total Pear they want = 3/4 + 1/3
To add we equal the denominator.
Multiply and divide by 12 on both number
Total Pear they want = 3/4 × 12/12 + 1/3 × 12/12
Total Pear they want = 9/12 + 4/12
Total Pear they want = (9 + 4)/12
Total Pear they want = 13/12
Total Pear they want = 1 1/12
As we can see that the sum of both Jo and Max requirement is max than the one pear. So the only one carton of pear is not enough.
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Use the Box plot below
By using the box plots, each statistical value should be completed as follows;
Mean: cannot be determined.
Median: equal for data sets X and Y.
Range: greater for data set X.
Interquartile range: greater for data set Y.
How to calculate the range?Mathematically, the range of a data set can be calculated by using this formula;
Range of X = Highest number - Lowest number
Range of X = 65 - 20
Range of X = 45.
Range of Y = Highest number - Lowest number
Range of Y = 55 - 20
Range of Y = 35.
How to calculate the interquartile range (IQR)?Mathematically, interquartile range (IQR) of a data set and it is typically calculated as the difference between the first quartile (Q₁) and third quartile (Q₃):
Interquartile range (IQR) of X = Q₃ - Q₁
Interquartile range (IQR) of X = 55 - 35
Interquartile range (IQR) of X = 20.
Interquartile range (IQR) of Y = Q₃ - Q₁
Interquartile range (IQR) of Y = 50 - 25
Interquartile range (IQR) of Y = 25.
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In this figure, a || b || c and m/5 = 155°
What is m/3 ?
25°
65°
155°
I don't know.
25 Degres it is a obtuse angle using the dewy decimal system
Answer:
The person above me is correct
25
Step-by-step explanation:
PLEASE HELP MEEE!!! WILL GIVE BRAINLIEST!!!
Identify the coordinates of a point (-7,-6) under the rotation of 90° clockwise around the origin.
The new coordinates of the point (-7, -6) are (-6, 7).
How to determine the transformationFrom the question, we have the following parameters that can be used in our computation:
(x, y) = (-7, -6)
The rule is given as
A rotation of 90° clockwise around the origin.
Mathematically, this can be represented as
(x, y) = (y, -x)
So, we have
Image = (-6, 7)
Hence, the image is (-6, 7)
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The table represents an exponential function.
x y
1 6
2 4
3 8/3
4 16/9
What is the multiplicative rate of change of the function?
• 1/3
• 2/3
•2
•9
The required multiplicative rate in the given function is 3 / 4.
Option B is correct.
What is an exponential function?The function which is in format f(x) =a^x where a is constant and x is variable, the domain of this exponential function lies (-∞, ∞).
Here,
From the table of the exponential functions,
The multiplicative factor is given as,
K = y₂/y₁
K = [9 / 8] / [3/2]
K = 3 / 4
Thus, the required multiplicative rate in the given function is 3 / 4. Option B is correct.
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can two intersecting circles have two common tangents?
Answer:
Yes.
Step-by-step explanation:
They will be either side of the 2 circles.
Need answer soon thank you
The translation needed to obtain the graph of g(x) = [tex]9^{x}-4[/tex] from the graph of f(x) = [tex]9^{x}[/tex] is a shift down 4 units.
What is graph?Graph is a type of data structure that is used to store and organize data in a visual representation. It consists of nodes, which store the data, and edges that connect the nodes. Graphs can be used to represent networks, relationships between different entities, or even mathematical equations. Graphs are versatile and can be used in many different applications, from engineering to data science. Graphs are also used to represent complex data structures and are often used to simplify and organize data for easier analysis.
This is because subtracting 4 from [tex]9^{x}[/tex] is the same as shifting the graph of f(x) down 4 units on the y-axis, resulting in the graph of g(x).
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Kendra watches the moon change from a new moon to a full moon. Which of the following descriptions is accurate? (Select all that apply.)
Responses
The moon is waxing.
The moon is waxing.
The moon is waning.
The moon is waning., ,
The moon appears to get smaller.
The moon appears to get smaller.
The moon appears to get bigger.
The moon appears to get bigger.
The moon does not change.
The correct description is that moon is waxing.
Which of the following descriptions is accurate?The theory used in this question is the lunar cycle, which is the process by which the moon changes its shape and illumination over the course of a month.
The waxing phase of the lunar cycle is when the moon is gradually getting bigger and more illuminated.
The waning phase is when the moon is gradually getting smaller and less illuminated.
The moon is waxing:
This is an accurate description because when the moon changes from a new moon to a full moon, it is said to be waxing.
This means that the moon is gradually getting bigger, and its illuminated side is increasing.
This process is called the waxing phase of the moon's cycle.
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Find the value of h in the graph
Thanks
Answer:
See below
Step-by-step explanation:
The graph is of f(x) is shifted 1 unit to the LEFT to get g(x)
so 4^x is now 4^(x+1)
then 4^(x+1) = 4^(x-h)
would mean h = - 1
What is the rule for an exponential graph?
One significant mathematical function that has the form is the exponential function, f(x) = [tex]$$a^x[/tex].
What is meant by exponential graph?If f(x) = [tex]$$a^x[/tex], where x is the input variable and is expressed as an exponent, is the formula for an exponential function. In addition to being dependent on the exponential function, the exponential curve also depends on the value of x. One significant mathematical function that has the form is the exponential function. f(x) = [tex]$$a^x[/tex].
The four fundamental characteristics of exponential functions are their y-intercept, horizontal asymptote, domain (the range of x values at which the function occurs), and constant growth factor, b.
Calculating the exponential growth or decay of a set of given data is done using an exponential function. According to the power to the power rule, "If the base increased to a power is being raised to another power, then the two powers are multiplied and the base remains the same."
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3. What is the probability an individual student likes between 5.5 and 8.5 songs from Eminem?
This indicates that there is an about 0.1587 chance that a particular student will like Eminem tracks between 5.5 and 8.5.
Explain about the probability?The quantity of possible outcomes is known as probability. all events that could possibly occur. For instance, there is a 1 in 2 chance of receiving a head when flipping a coin, and there are 2 possible outcomes overall (a head or tail). P(heads) = 12 is the formula.
There are four primary categories of probability: axiomatic, axiomatic, classical, and empirical. Probability is the area of mathematics that deals with the possibility of a random event.
How likely something is to occur is known as its probability. We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out. Statistics describes the examination of events subject to probability.
To find:
P(X < 5.5)
Z = -1.0
However;
P(X< 5.5) = P(Z < -1.0)
P(X< 5.5) = 0.1587
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