The parent function is [tex]y = ab^x[/tex]
A function for the translation indicated is [tex]y = ab^{x+6} - 7[/tex].
What is a translation?In Mathematics and Geometry, the vertical translation a geometric figure or graph downward simply means adding a digit to the value on the y-coordinate of the pre-image or function.
In Mathematics and Geometry, a horizontal translation to the right is modeled by this mathematical equation g(x) = f(x - N) while a vertical translation to the negative y-direction (downward) is modeled by this mathematical equation g(x) = f(x) - N.
Where:
N represents an integer.g(x) and f(x) represent functions.In this scenario, we can logically deduce that the graph of the parent function was translated or shifted to the left (horizontally) by 6 units and downward (vertically) by 7 units;
[tex]y = ab^x[/tex]
[tex]y = ab^{x+6} - 7[/tex]
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Use the relationship given in the right triangle and the inverse sine, cosine, and tangent functions to write 0 as a function of x in three different ways. It is not
necessary to rationalize the denominator.
a
-√√81-x²³.c-9
The measure of inverse of sinθ is c/√ (c² - a²)..
What is the measure of inverse of sinθ?The measure of inverse of sinθ is calculated by applying trigonometry identities for right triangles.
Mathematically, the trig identities are represented using the following method;
SOH CAN TOA
SOH is for sine θ
CAH is fof cos θ
TOA is for tan θ
From the diagram we need find the value of the opposite side;
b = √ (c² - a²)
Sin θ = b/c
The inverse of b/c = c/b
1/sinθ = c/b = c/√ (c² - a²).
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URGENT! Can someone please help?
a. The missing values of the logarithm expression is log₃(40).
b. The missing values of the logarithm expression is log₅(8).
c. The missing values of the logarithm expression is log₂(1/25).
What is the missing of the logarithm expression?The missing values of the logarithm expression is calculated as follows;
(a). log₃5 + log₃8, the expression is simplified as follows;
log₃5 + log₃8 = log₃(5 x 8) = log₃(40)
(b). The log expression is simplified as;
log₅3 - log₅X = log₅3/8
log₅X = log₅8
X = 8
(c). The log expression is simplified as;
-2log₂5 = log₂Y
log₂5⁻² = log₂Y
5⁻² = Y
1/25 = Y
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m/1 = x and m/2 = 2x. Find
the value of 'x'.
Answer:
-m = x is the answer hope it helps
[8 points] Find the y-intercept and graph the equation by
making a table of values with three points,
2) y=-3x+2
SEENE
Answer:
The answer is (0,2) (1,-1) (2,-4)
Step-by-step explanation:
The slope is -3.
Because of this, you go down 3 and to the side 1 (it's also called rise/run).
I REALLY HOPE THIS HELPS!!!!
how much cardboard is needed to make the single slice pizza box shown
that would be 5 pieces of cardboard needed
Find the missing angle
Answer:
I Think 62°
Step-by-step explanation:
A basket contains 3 green, 4 yellow, 5 blue and 6 red tickets, one of which is randomly selected.
Giving your answer in its simplest form, what's the theoretical probability of not drawing a yellow ticket?
Probability of not drawing a yellow ticket =
Again using theoretical probability, determine the chance of getting a green or red ticket. Give your answer as a fraction in its simplest form.
Probability of drawing a green or red ticket =
The theoretical probability of drawing a green or red ticket is 1/2 or 0.5.
We have,
There are a total of 3 + 4 + 5 + 6 = 18 tickets in the basket.
The probability of drawing a yellow ticket.
= 4/18
Since there are 4 yellow tickets out of 18 total tickets.
The probability of not drawing a yellow ticket is equal to the probability of drawing a green, blue, or red ticket.
There are 3 + 5 + 6 = 14 tickets that are not yellow.
The probability of not drawing a yellow ticket.
= 14/18
= 7/9
To find the probability of drawing a green or red ticket, we need to add the probabilities of drawing a green ticket and a red ticket.
The probability of drawing a green ticket.
= 3/18
The probability of drawing a red ticket.
= 6/18
Now,
The probability of drawing a green or red ticket is
= 3/18 + 6/18
= 9/18
= 1/2
Thus,
The theoretical probability of drawing a green or red ticket is 1/2 or 0.5.
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How many times can u write your name in 12 minutes using variables Based on your recorded values, write an equation that represents the relationship between the time you spent doing the activity and the amount of the activity you completed. Make sure to define your variables
:D
The following equation denotes the correlation between the duration and output of an activity: A = kT
How to explain the equationIt should be noted that A represents the amount of production, T is the period of working on the task, and k consists of a constant ratio.
Therefore, it can be conclusively stated that the culminating yield is in direct correlation to the amount of effort contributed, as denoted by the factor of proportionality k, thus producing a linear relationship when displayed upon a graph.
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John is w years old. His sister is 16 years old and his brother is twice
John's age. All three siblings have a total age of 31.
a) Write an equation to represent this.
b) Solve your equation to find out John's age.
Answer: 16* 2
Step-by-step explanation:
SVM & Kernel Methods Problem 1 (10 points) In this problem we would like to compare the solutions of hard and soft SVMs on a linearly seperable dataset. Let n > 1 be a fixed number. Is it true that there exists C > 0 such that for every sample S of n training examples with binary label, which are linearly separable, the hard-SVM and the soft-SVM (with parameter C) solutions will return exactly the same weight vector. Justify your answer. (Hint: consider n = 2, d = 1 and S = {(x1, yı), (x2, y2)}. Let a > 0 and consider x1 = a, yı = 1, X2 = –a, y2 = -1. Derive the optimal solution for hard and soft SVM and compare the results.)
It is not true that there exists a C > 0 such that for every sample S of n training examples with binary label, which are linearly separable, the hard-SVM and the soft-SVM (with parameter C) solutions will return exactly the same weight vector.
This can be shown by considering the case where n = 2, d = 1 and S = {(x1, yı), (x2, y2)}. Let a > 0 and consider x1 = a, yı = 1, X2 = –a, y2 = -1.
For the hard-SVM, the optimal solution is to find the weight vector w that maximizes the margin between the two classes while ensuring that all training examples are classified correctly. In this case, the margin is 2a and the weight vector is w = (0, 1) or w = (0, -1), depending on the choice of the positive and negative class labels.
For the soft-SVM with parameter C, the optimal solution is to find the weight vector w and the slack variables ξi that minimize the objective function:
min ||w||^2 + CΣξi
s.t. yi(wT xi) ≥ 1 - ξi, ξi ≥ 0
In this case, since the data is linearly separable, the slack variables will be zero for all training examples and the optimal solution will be the same as for the hard-SVM. However, if C is chosen to be a large value, the soft-SVM may allow some misclassifications by penalizing them with the slack variables. In this case, the optimal solution will be different from the hard-SVM.
Therefore, it is not always true that the hard-SVM and soft-SVM solutions will return exactly the same weight vector for linearly separable data, but they may be the same if the parameter C is chosen appropriately.
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[tex]\frac{v-2}{2v^2+10v} + \frac{1}{2v+10}=\frac{1}{2}[/tex]
Show all steps
The value of variable 'v' in the expression ( v - 2 ) / (2v² + 10v ) + 1 / ( 2v + 10 ) = 1 / 2 is equal to -4.
The expression is equal to,
( v - 2 ) / (2v² + 10v ) + 1 / ( 2v + 10 ) = 1 / 2
Simplify the expression we have,
⇒ ( v - 2 ) / 2v ( v + 5 ) + 1 / 2( v+ 5 ) = 1 / 2
Take the least common multiple of the denominator we have,
⇒ [( v - 2 ) + 2 ] / 2v( v+ 5 ) = 1 / 2
⇒ v / 2v( v+ 5 ) = 1 / 2
Multiply both the sides of the expression by 2 we get,
⇒ 1 / 2( v+ 5 ) = 1 / 2
⇒ 1 /( v + 5 ) = 1
Cross multiply the expression we get,
⇒ v + 5 = 1
Subtract 5 from the both the sides of the equation we get,
⇒ v = -4
Therefore , the value of v in the given expression is equal to -4.
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Area of a regular polygon work
Answer:
Step-by-step explanation:
[tex]\frac{x}{18} =cot~30\\x=18cot~30=18 \times \sqrt{3} =18\sqrt{3} \\base=36\sqrt{3} \\area~of~triangle=3\times \frac{1}{2} \times36\sqrt{3} \times 18=972\sqrt{3} \approx 1683.55~mm^2[/tex]
Look at the picture
According to the information, we can infer that the area of the triangle is: 19 1/4ft²
How to calculate the area of the triangle?To calculate the area of the triangle, we need to use the formula for the area of a triangle:
Area = (1/2) x base x heightwhere,
Base = 5 1/2 ftHeight = 7 ft.How to find the height of the triangle?To find the height of the triangle, we need to use the Pythagorean theorem, which relates the slant height, height, and half the base:
(slant height)^2 = (height)^2 + (1/2 base)^2Substituting the given values, we get:
(1/3)^2 = (7)^2 + (1/2 x 5 1/2)^2(1/9) = 49 + (15/4)(1/9) = (196/4 + 15/4)(1/9) = (211/4)Multiplying both sides by 36, we get:
4 = 844.44...So the height of the triangle is approximately 2.04 ft.
Now we can plug in the values for the base and height into the formula for the area:
Area = (1/2) x 5 1/2 x 7Area = 19.25 square feetArea = 19 1/4ft²Therefore, the area of the triangle is approximately 19.25 square feet.
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Anna took a job that paid $116 the first week. She was guaranteed a raise of 7% each week. How much money will she make in all over 10 weeks? Round the answer to the nearest cent, and number answer only.
Anna will make $1602.71 in all over 10 weeks.
Here, the first week salary of Anna = $116
i.e., the initial salary a = $116
She was guaranteed a raise of 7% each week.
so, her salary in the next week would be,
116 + 7% of 116
7 percent of 116 is:
116 × 7/100 = 8.12
so, her salary will be $124.12
So, the equation for the salary after 'm' weeks would be,
[tex]n = 116\times (1 + 0.07)^{m - 1}\\\\n = 116\times (1 .07)^{m - 1}[/tex]
Using this equation , the salary in the second week m = 2 would be,
n = 124.12
Salary in the third week m = 3 would be,
n = 116 × [tex](1.07)^{3-1}[/tex]
n = 132.81
Salary in the fourth week m = 4 would be,
n = 116 × [tex](1.07)^{4-1}[/tex]
n = 142.11
Salary in the fifth week m = 5 would be,
n = 116 × [tex](1.07)^{5-1}[/tex]
n = 152.05
Salary in the sixth week m = 6 would be,
n = 116 × (1.07)⁶⁻¹
n = 162.7
Salary in the seventh week m = 7 would be,
n = 116 × (1.07)⁷⁻¹
n = 174.08
Salary in the eighth week m = 8 would be,
n = 116 × (1.07)⁸⁻¹
n = 186.27
Salary in the nineth week m = 9 would be,
n = 116 × (1.07)⁹⁻¹
n = 199.31
And the salary after the tenth week m = 10 would be,
n = 116 × (1.07)¹⁰⁻¹
n = 213.26
The total money after 10 weeks would be,
T = 116 + 124.12 + 132.81+ 142.11 + 152.05 + 162.7 + 174.08 + 186.27 + 199.31 + 213.26
T = $1602.71
This is the required amount.
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(Time limit) Tell if the graph is a function or not.
Give me the domain and range.
The graph is a function: yes.
The domain of this function is: x ≥ -3.
The range of this function: all real numbers.
What is a range?In Mathematics and Geometry, a range can be defined as the set of all real numbers that connects with the elements of a domain.
Furthermore, the horizontal extent of any graph of a function represents all domain values and they are always read and written from smaller to larger numerical values, and from the left-hand side of the graph to the right-hand side.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = {-3, ∞}, x ≥ -3, or -3 ≤ x ≤ ∞.
Range = {-∞, ∞} or all real numbers.
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I need explanation for example 8.
Thankyou
There is a probability of 94/315 that the problem will be solved.
We are given that P has a chance of solving the problem of 2/7, Q has a chance of solving the problem of 4/7, and R has a chance of solving the problem of 4/9. To find the probability that the problem is solved, we need to consider all possible scenarios in which the problem can be solved.
The probability of this scenario is 2/7. If P solves the problem, then it does not matter whether Q or R solve it, the problem is already solved. Therefore, the probability of the problem being solved in this scenario is 2/7.
The probability of this scenario is 4/7. If Q solves the problem, then it does not matter whether P or R solve it, the problem is already solved. Therefore, the probability of the problem being solved in this scenario is 4/7.
The probability of this scenario is 4/9. If R solves the problem, then it does not matter whether P or Q solve it, the problem is already solved. Therefore, the probability of the problem being solved in this scenario is 4/9.
The probability of this scenario is (1-2/7) * (1-4/7) * (1-4/9) = 3/35. This is because the probability of P not solving the problem is 1-2/7, the probability of Q not solving the problem is 1-4/7, and the probability of R not solving the problem is 1-4/9. To find the probability of none of them solving the problem, we multiply these probabilities together.
To find the probability of the problem being solved, we need to add the probabilities of all the scenarios in which the problem is solved. Therefore, the probability of the problem being solved is:
2/7 + 4/7 + 4/9 = 94/315
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PLEASE HELP ME !!! I NEED THIS TO GRADUATE
Which of the following expressions are equivalent to the expression below? 8 x + 32 y 4 ( 4 x + 8 y ) − 2 ( 4 x ) 8 ( x + 4 y ) ( 2 x + 12 y ) + ( 6 x + 18 y )
The expressions that are equivalent to the expression 8x + 32y are:
4(4 x + 8y) − 2(4x)
8(x + 4y)
How to write equivalent expressions?Equivalent expressions are expressions that work the same even though they look different.
If two algebraic expressions are equivalent, then the two expressions have the same value when we substitute the same value(s) for the variable(s).
Let's simply the options to see if they are equivalent to the expression 8x + 32y:
4(4 x + 8y) − 2(4x) = 16x + 32y - 8x
= 8x + 32y
8(x + 4y) = 8x + 32y
(2x + 12y) + (6x + 18y) = 2x + 6x + 12y + 18y
= 8x + 30y
Therefore, only 4(4 x + 8y) − 2(4x) and 8(x + 4y) are equivalent to the expression below.
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Complete Question
Which of the following expressions are equivalent to the expression below?
8x + 32y
4(4 x + 8y) − 2(4x)
8(x + 4y)
(2x + 12y) + (6x + 18y)
Question attached. You dont need to send working out just and answer to 2dp
The value of length of AG is,
AG = 157.02
We have to given that;
AD = 31 cm
DC = 22 cm
Hence, We get;
AC = √31² + 22²
AC = √961 + 484
AC = √1445
AC = 38
Thus, We get;
cos 76° = AC / AG
0.242 = 38 / AG
AG = 38/0.242
AG = 157.02
Therefore, The value of length of AG is,
AG = 157.02
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Find the median of the data. $93,81,94,71,89,92,94,99$
Answer:
92.5
Step-by-step explanation:
First, we need to put the data in order from smallest to largest:
$71, 81, 89, 92, 93, 94, 94, 99$
There are 8 numbers in the data set, which is an even number. To find the median, we need to average the two middle numbers.
The middle two numbers are 92 and 93, so the median is:
$(92+93)/2 = 92.5$
Therefore, the median of the data is 92.5.
Please help! I will mark brainiest! I do not understand the parenthesis being added.
Answer:
<4√97,-9√97>
Step-by-step explanation:
First, we need to find the values of A-C and B-D:
A-C = < 3, 6 > - < 7, -3 > = < -4, 9 >
B-D = < 4, -7 > - < 0, 2 > = < 4, -9 >
Next, we need to find the magnitude of A-C, which is denoted by |A-C| and is equal to the square root of the sum of the squares of its components:
|A-C| = √((-4)^2 + 9^2) =√(97)
Now we can substitute all the values into the expression |A-C|(B-D) and evaluate:
|A-C|(B-D) = √(97) * < 4, -9 >
= < 4√(97), -9√(97) >
So the final answer is < 4√(97), -9√(97) >.
A plane takes off at a 10 degree angle. How far away is the plane (ground distance) once it reaches an altitude (height) of 30,000 feet?
We are missing a side or and angle? Regular or Inverse Trig?
The ground distance of the plane is 170,138.5 ft.
What is the ground distance of the plane?
The ground distance of the plane is calculated by applying trigonometry ratio as shown below;
SOH CAH TOA
SOH = sin θ = opposite /hypothenuse side
TOA = tan θ = opposite side / adjacent side
CAH = cos θ = adjacent side / hypothenuse side
The height attained by the plane is the opposite side, while the ground distance is the adjacent side
tan (10) = 30,000 ft/d
d = 30,000 ft/tan(10)
d = 170,138.5 ft
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Después de analizar un conjunto de datos se encontró que la desviación estandar es igual a 9, se requiere conocer
ahora, el valor de la varianza
The variance of the data-set in this problem is given as follows:
81 units squared.
How to obtain the variance of the data-set?The standard deviation for the data-set in this problem is given as follows:
9 units.
The relation between the standard deviation and the variance is that the standard deviation is the square root of the variance, hence the variance is the square of the standard deviation.
Hence the variance of the data-set in this problem is given as follows:
(9 units)² = 81 units².
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(1 point) (a) Find a vector parametric equation for the part of the saddle = z = x y inside the cylinder 2+2=9 x 2 + y 2 = 9 .
New homeowners hire a painter to paint rooms in their house. The painter pays $100 for supplies and charges the homeowners $25 for each room they want painted.
Which of the following graphs shows the relationship between the amount of money the painter earns, in dollars, and the number of rooms he paints?
a coordinate grid with the x axis labeled rooms painted and the y axis labeled amount of money earned and a line going from the point 0 comma 100 through the point 4 comma 0
a coordinate grid with the x axis labeled rooms painted and the y axis labeled amount of money earned and a line going from the point 0 comma negative 100 through the point 4 comma 0
a coordinate grid with the x axis labeled rooms painted and the y axis labeled amount of money earned and a line going from the point 0 comma 100 through the point 4 comma 200
a coordinate grid with the x axis labeled rooms painted and the y axis labeled amount of money earned and a line going from the point 0 comma negative 100 through the point 4 comma negative 200
The correct graph is: a coordinate grid with the x-axis labeled rooms painted and the y-axis labeled amount of money earned and a line going from the point (0,100) through the point (4,200).
What is a Graph?In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.
The points on the graph often represent the relationship between two or more things.
The painter pays $100 for supplies, which is a fixed cost, and charges $25 for each room painted, which is a variable cost.
Therefore, the relationship between the amount of money the painter earns and the number of rooms he paints can be represented by a linear equation in slope-intercept form:
Amount earned = (price per room) x (number of rooms painted) + (fixed cost)
In this case, the price per room is $25, the number of rooms painted is the x-value, and the fixed cost is $100. Thus, the equation is:
Amount earned = 25x + 100
To graph this equation, we can plot two points and draw a line through them. One point is when no rooms are painted, which gives the painter $100 for the fixed cost:
(0,100)
The other point is when four rooms are painted, which gives the painter:
Amount earned = 25(4) + 100 = 200
So the other point is:
(4, 200)
The correct option :
a coordinate grid with the x axis labeled rooms painted and the y axis labeled amount of money earned and a line going from the point 0 comma 100 through the point 4 comma 200.
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One notebook and 2 packs of pencils cost $7.20 two notebooks and 2 packs of paper cost $10.90.How much does 1 pack of paper cost
Answer:
5.45
Step-by-step explanation:
literally do 10.9/2
Thanks to an initiative to recruit top students, an administrator at a college claims that this year's entering
class must have a greater mean IQ score than that of entering classes from previous years. The
administrator tests a random sample of 17 of this year's entering students and finds that their mean IQ score
is 114, with a standard deviation of 15. The college records indicate that the mean IQ score for entering
students from previous years is 113.
Is there enough evidence to conclude, at the 0.05 level of significance, that the population mean IQ score, μ,
of this year's class is greater than that of previous years? To answer, assume that the IQ scores of this year's
entering class are approximately normally distributed.
Perform a one-tailed test. Then complete the parts below.
(If Rococcan consult a list of
Answer: The answer is B and im 100% correct
Step-by-step explanation:
Find the surface area
The surface area of the prism is 70.44 yd²
What is surface area of prism?A prism is a solid shape that is bound on all its sides by plane faces. There are different types of prism, triangular prism, rectangular prism e.t.c
The surface area of a prism is expressed as;
SA = 2B +pH
where B is the base area and p is the perimeter of the base and h is the height of the prism
Base area = 1/2 bh
= 1/2 × 3 × 3 = 4.5 yd²
The hypotenuse of the triangle = √3²+3²
= √9+9 = √18 = 4.24
perimeter of the base = 4.24+3+3 = 10.24yds
Therefore,
SA = 2×4.5 + 10.24 × 6
SA = 9 + 61.44
SA = 70.44 yd²
therefore the surface area of the prism is 70.44yd²
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Luciana bought a total of 7 textbooks at the bookstore. She bought four more textbooks than journals. How many journals did she buy
SIMPLIFY the expression: 12x - 7y - 8x + 3y
Answer:
the simplified expression is 4x - 4y
Step-by-step explanation:
1. Rewrite!
12x - 7y - 8x + 3y
2. Combine like terms:
12x - 8x - 7y + 3y
3. Solve both sides to simplify
12 x - 8x = 4x
and
-7y + 3y = -4y
So, 4x - 4y is your answer.
