The domain of the function is [ - 6 , ∞ ]
A radical function is the one provided.
It should be noted that a radical function can only be specified for values that will result in the radicand being larger than or equal to zero.
As a result, either the radicand of the provided function must be larger than or equal to zero, or:
Thus we can write it as
x + 6 ≥ 0
subtract 6 from both LHS and RHS
x + 6 - 6 ≥ 0 - 6
x ≥ - 6
Therefore the domain of the function is [ - 6 , ∞ ]
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Suppose a basketball player has made 215 out of 322 free throws. If the player makes the next 2 free throws, I will pay you $32. Otherwise you pay me $24. Step 1 of 2 : Find the expected value of the proposition. Round your answer to two decimal places. Losses must be expressed as negative values.
The expected value of the proposition is -$1007.41
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
P(X = x) = [tex]C_{n},x.p^x.(1-p)^n^-^x[/tex]
In which [tex]C_{x},x[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{x},x= \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Suppose a basketball player has made 215 out of 322 free throws.
This means that p = 215/322 = 0.6677
2 free throws:
This means that
Probability of making two free throws.
This is P(X = 2).
P(X = x) = [tex]C_{n},x.p^x.(1-p)^n^-^x[/tex]
P(X = 2) = [tex]C_{2},2.(0.6677)^2.(0.3323)^0[/tex] = 0.29629
Expected value:
If he makes both free throws, you earn $24. So 0.29629 probability of you earning $24.
Otherwise, you have to pay $32. 1 - 0.29629 = 31.70371 probability of you losing $32.
E = 0.29629*24 - 31.70371*32 = -1007.41
Hence, The expected value of the proposition is -$1007.41
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List 1 4/5, -7/4, 41%, and -1.3 from greatest to least.
The descending order to the list is 1, 4/5, 41%, -1.3, -7/4.
What us descending order?
When numbers are arranged from greatest to smallest or highest to lowest it is said to be in descending order.
Main Body:
To solve this question we need to convert all numbers into decimal system.
calculate:
1 can be written as 1.00
4/5 can be written as 0.8
-7/4 = -1.75
41% = 41/100 = 0.41
-1.3 can remain as it is because it itself is in decimal form.
Hence the order from greatest to smallest is as
1 > 0.8 > 0.41 > -1.3 > -1.75
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HEEELPPPPPPPP Rearrange the formula v = 2gh for h. A) h = v 2g B) h = 2v g C) h = v2 g D) h = v2 2g
Rearranging the equation, making h the subject of the formula, h = v² / 2g
How to rearrange formula?we rearrange equations and formulas by using inverse operations to make one variable the subject of the formula.
In order to change the subject of, or rearrange, a formula items in the formula need to be arranged so a different variable is the subject.
In our case the the formula needs to be rearrange to make h the subject of the formula.
Therefore,
v = √2gh
square both sides of the equation
v² = (√2gh)²
v² = 2gh
divide both sides by 2g
v² / 2g = 2gh / 2g
h = v² / 2g
Therefore,
h = v² / 2g
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Differentiate the function with respect to x.
Differentiation of the function [tex]f(x) = (-x^{2} - 4)x^{5}[/tex] with respect to [tex]x[/tex] is [tex]f'(x) = -7x^{6} - 20x^{4}[/tex].
What is the differentiation of the function?
A function differentiation is a method of displaying the rate of change of a function at a given moment. It is the slope of the tangent line at a point on a graph for real-valued functions.
We have,
[tex]f(x) = (-x^{2} - 4)x^{5}[/tex]
By simplifying the given function, we get
[tex]f(x) = -x^{7} - 4x^{5}[/tex]
Now, we will differentiate the given function with respect to [tex]x[/tex].
[tex]\frac{d}{dx} f(x) = \frac{d}{dx} (-x^{7} - 4x^{5})[/tex]
[tex]f'(x) = \frac{d}{dx} (-x^{7}) - \frac{d}{dx} (4x^{5}))[/tex]
[tex]f'(x) = -7x^{6} - 20x^{4}[/tex]
Hence, differentiation of the given function with respect to [tex]x[/tex] is [tex]f'(x) = -7x^{6} - 20x^{4}[/tex].
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Sketch the graph of the quadratic function and the axis of symmetry. State the vertex, and give the equation for the axis of symmetry.
f(x)=-3(x+2)²+1
Use the graphing tool to graph the function as a solid curve and the axis of symmetry as a dashed line.
The function f(x) = -3(x + 2)² + 1 has it's vertex as (-2, 1) and an axis of symmetry x = -2
Graph of Quadratic FunctionThe graph of a quadratic function is called a parabola and has a curved shape. One of the main points of a parabola is its vertex. It is the highest or the lowest point on its graph. You can think of like an endpoint of a parabola.
In the given function;
f(x) = -3(x + 2)² + 1
Axis of symmetry is x = -2vertex = (-2, 1)Kindly find the attached graph of the function below
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What is the value of (−13)4
Answer: -52
Step-by-step explanation: multiply by breaking apart a factor (-13) x 4
Answer:
28561
Step-by-step explanation:
Find the Exact Value:
Raise -13 to the power of 4.
28561 is the answer.
help please i am stuck on this problem ??
Answer:
Evaluating the function [tex]f(x)=2x^2[/tex] for the first five positive integers of [tex]x[/tex]:
[tex]f(1)=2(1)^2=2(1)=2[/tex]
[tex]f(2)=2(2)^2=2(4)=8[/tex]
[tex]f(3)=2(3)^2=2(9)=18[/tex]
[tex]f(4)=2(4)^2=2(16)=32[/tex]
[tex]f(5)=2(5)^2=2(25)=50[/tex]
Describe the features of the function that can be easily seen when a quadratic function is given
in the form: y= A(x− ℎ)^2+kand how they can be identified from the equation.
From the given equation y = A(x-h)² +k it is identified that this quadratic function represents the parabola with vertex (h, k).
As given in the question,
Given equation is :
y = A(x-h)² +k
Standard basic parabola equation is y = x² where parabola pass through (0, 0) .
In the given quadratic function y = A(x-h)² +k , it represent equation of parabola which is U shaped .
Value of A > 0 then it open in upward direction .
Value of A <0 then it is open in downward direction.
Vertex of the given parabola y = A(x-h)² +k is (h, k).
Line of symmetry is given by vertical line x =h.
Therefore, from the given equation y = A(x-h)² +k it is identified that this quadratic function represents the parabola with vertex (h, k).
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select shapes which have one line of symmetry
Answer:
A semicircle has 1 line of symmetry.
Step-by-step explanation:
Select the correct answer A developer buys an empty lot to build a small house. What is the area of the lot?
A. 323 yd²
B. 183 yd²
C. 193 yd²
D. 171 yd²
The area of the plot is 193 sq.yd.
What is Area?Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.
Given that, A developer buys an empty lot to build a small house.
To find the area, we need to be divided the figure into triangles and rectangles
Area of the first triangle = (1/2) * base * height
base = 17 unit and height = 10 unit
= (1/2) * 17 * 10
= 17*5=85 sq. unit
Area of the second triangle = (1/2)* 9* 8
=36 sq. unit
Area of the rectangle = base * height
base = 9 unit and height = 7 unit
Area = 9*7= 63 sq. unit
Area of the last triangle = (1/2) * 2*9
= 9 unit
Adding all the areas to get the area of the plot = 85+36+63+9
Hence, Area of the plot = 193 sq.yd.
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Harry is paid semimonthly. His
Semimonthly salary is $2,052. What is his
annual salary?
Answer:
$12,312
Step-by-step explanation:
$2,052 * 6 = $12,312
Question as shown in the image:
Answer:
arc ABC ≈ 18.2 cm
Step-by-step explanation:
the length of the arc ABC is calculated as
arc = circumference of circle × fraction of circle
the angle around the centre O is 360° , then
angle subtended by arc = 360° - 100° = 260°
then
arc = 2πr × [tex]\frac{260}{360}[/tex] ( t is the radius = 4 )
= 2π × 4 × [tex]\frac{26}{36}[/tex]
= 8π × [tex]\frac{13}{18}[/tex]
= [tex]\frac{8\pi (13)}{18}[/tex]
≈ 18.2 cm (to 3 significant figures )
A gallon of water contains 128 fluid ounces. A rain barrel can hold 6,400 ounces of rainwater.
Estimate how many gallons of water can the barrel hold?
Answer:
50 gallons
Step-by-step explanation:
6400 ÷ 128
= 50
A surveyor is determining the area of a triangle piece of land bordered by three stretts. In the coordinate plane,the vertices of the triangle are at 0,0 -100,-300,and 200 -200. One unit in the coordinate plane represents 1m.what is the area of piece of land
The area of the piece of land with coordinates (0, 0), (-100, 300) and (200, -200) is as measured by the surveyor is 4000 square meter
How to calculate the area of the piece of the landThe given coordinates being plotted as
A (0, 0)
B (-100, 300)
C (200, -200)
Area of triangle is solved by 0.5 * base * height
dimensions from attached plot, BC = 316.2, Aa = 253
= 0.5 * BC * Aa
= 0.5 * 253 * 316.2
= 39 999.3 approximately 40 000
The plot gave an area of 40 000 square units on paper converting using the given scale which is: One unit in the coordinate plane represents 1m
1 unit = 1 m
1 square unit = 1 square meter
4000 square units = ?
cross multiplying
? = 4000 square units
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if Julie average arts test score at 85 and what would you predict her average math test score would be
1. Her Average would be 80
2. Yes, there are more dots around points 80.
Richard and two have a combined age of 26. Richard is 5 years old than twice Teos age. How old are Richard and Teo?
Answer:
R = 19 yr old; T = 7 yr old
Step-by-step explanation:
From the information given, we can create a system of equations to find both Richard and Teo's ages, letting R represent Richard's age and T represent Teo's age.
Thus we have:
[tex]R +T=26\\2T+5=R\\\\2T+5+T=26\\3T+5=26\\3T=21\\T=7\\\\R+7=26\\R=19[/tex]
When you plug in the numbers, you find that twice Teo's age is 14 as 7*2 = 14. 5 more than 14 is 19 as 14 + 5 = 19.
When five times a number is decreased by 9 , the result is 26 . What is the number?
Answer:
5x-9=26
Step-by-step explanation:
5x=35
5 5
x = 7
mark me on brainliest please follow me to
Answer:
x = 7
Step-by-step explanation:
When five times a number is decreased by 9 , the result is 26 . What is the number?
5x - 9 = 26
add 9 to both sides:
5x - 9 + 9 = 26 + 9
5x =35
divide both sides by 5:
5x/5 =35/5
x = 7
Given the position function:
s(t) = sin t
where t is measured in seconds and
s is measured in feet, find the
average velocity on the interval [0, π].
The Roxbury CC Tigers basketball team scored 12 points in the first 6 minutes of a game. If they continue at the same pace, how much will they score during the entire 40 minute game?
84 i think?
im not sure if i did my math properly
Answer:
80
Step-by-step explanation:
40 ÷ 6 = 6.66666667 x 12 = 80
Suppose that f(x)= −4x^2+5.
(A) Find the slope of the line tangent to f(x) at x= 1.
(B) Find the instantaneous rate of change of f(x) at x= 1.
(C) Find the equation of the line tangent to f(x) at x= 1. y=
The slope of the line tangent to f(x) at x = 1 is -8
The instantaneous rate of change of f(x) at x = 1 is -8
The equation of line tangent to f(x) at x = 1 is y = -8x + 9
What is a tangent to a curve?The tangent line to a curve at a given point is the line which intersects the curve at the point and has the same instantaneous slope as the curve at the point.
so the slope of a line at that point is the slope of the curve at that point.
f(x) = -4[tex]x^{2}[/tex] + 5
To find the slope, we differentiate f(x) with respect to x
dy/dx = d/dx( -4[tex]x^{2}[/tex]) + d/dx(5)
= -8x + 0
dy/dx = -8x
The slope = -8x
at x = 1,
the slope becomes, -8(1) = -8
The instantaneous rate of change of f(x) at x = 1 is the same as the slope of the line tangent to f(x) = -8
The slope of the line is -8
to find the equation of the tangent line, we need to find the coordinates of the point the line touches the curve.
one of the coordinates x = 1, to find y, we substitute x into f(x)
f(x) = -4[tex](1)^{2}[/tex] + 5
f(x) = 1
so the point is (1, 1)
so equation of straight line
[tex]\frac{y - y_{1} }{x - x_{1} }[/tex] = m
y - 1/x - 1 = -8
by cross multiplying
y - 1 = -8(x - 1)
y - 1 = -8x +8
y = -8x + 9
In conclusion,
The slope o the line tangent to f(x) at x = 1 is -8
The instantaneous rate off change of f(x) at x = 1 is -8
The equation of line tangent to f(x) at x = 1 is y = -8x + 9
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1/3 divide by 4 3/4 simplest form
Step-by-step explanation:
first put 4 3/4 into a improper fraction ---> 19/4
you get 19/4 because 4 is equal to 16/3 plus the 3/4
then you will do keep, flip change so it becomes multiplication
so instead of 1/3 divided by 19/4 it will be 1/3 x 4/19 then
multiply it out to get 19/12
Let a=2 b=5 c= -3
8b-4b=4b Please help quick!!!!!
Answer:
40-20= 20
Step-by-step explanation:
8(5)- 4(5)= 4(5)
40-20=20
HELP PLEASE HELP I NEED HELP PLEASEEEEEEEEEEE
The first and the second differences are shown in the table, the values of the second differences are constant, therefore, the relation is linear.
What is a linear relation?A straight-line link between two variables is referred to statistically as a linear relationship (or linear association).
The first and the second differences are:
x y first differences second differences
4 18 ----
5 28 10 ------
6 35 7 -3
7 39 4 -3
8 40 1 -3
9 38 -2 -3
The values of second differences are constant, therefore, the relation is linear.
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The next model of a sports car will cost 13.6% less than the current model. The current model costs $42,000. How much will the price decrease in dollars? What
will be the price of the next model?
Decrease in price:
Price of next model:
The decrease in price in dollars of the next model of the car is $5712 and the price of next model is $36288.
According to the question,
We have the following information:
The next model of a sports car will cost 13.6% less than the current model. The current model costs $42,000.
We will find the 13.6% of 42,000 to find the decrease in the price of the next model:
(13.6*42000)/100
$5712
Now, the price of next model will be:
42000-5712
$36288
Hence, the decrease in price in dollars of the next model of the car is $5712 and the price of next model is $36288.
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Traveling with the current certain boat went 9 mph against the same boat it only went 1 mph what is the speed of the current how fast would the Bogo if there were no current
If traveling with the current certain boat went 9 mph against the same boat it only went 1 mph the speed of the current is 4km/h and no current is 5km/h.
How to determine the speed?Let b represent the speed of the boat
Let c represent the speed of the current
Downstream:
b + c = 9
Upstream:
b - c = 1
Subtraction
2c = 9-1
2c = 8
Divide both side by 2c
c = 8/2
c = 4 km/h (current)
No current
b = 9 - 4
b = 5 km/h
Therefore the speed is 4km/h and no current is 5km/h.
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In tic-tac-toe, a 3 by 3 grid is filled with X's and O's. How many ways is there to fill the grid so that there is at least 4 of each symbol in the grid?
The number of ways to fill the tic-tac-toe grid, with at least 4 of each symbol in the grid, using the arrangements formula, is of:
252.
What is the arrangements formula?The number of possible arrangements that can be chosen from a set of n elements is given by the factorial of n, as follows:
[tex]A_n = n![/tex]
When the elements arranged can be repeated, the number of arrangements is presented as follows:
[tex]A_{n}^{n_1, n_2, \cdots, n_n} = \frac{n!}{n_1! \times n_2! \cdots n_3!}[/tex]
In which [tex]n_1, n_2, \cdots, n_n[/tex] represent the number of repetitions of each element.
For the tic-tac-toe grid, we have that the possible ways to organize the nine positions with at least four instances of each symbol is given as follows:
5 X's and 4 O's.4 X's and 5 O's.Hence the number of ways to fill up the grid is given as follows:
[tex]\frac{9!}{5!4!} + \frac{9!}{4!5!} = 2 \times 156 = 252[/tex]
Thus 252 ways to fill up the grid.
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Last year when the 6th graders attended camp the ratio of boys to girls was 4:6. If there were 50 more girls how many boys attended camp?
By using concept of ratio, it can be calculated that
100 boys attended the camp
What is ratio?
Ratio between two numbers determines how much one number is greater than the other.
The first part of the ratio is called antecedent and the second part of the ratio is called consequent.
Here, concept of ratio will be used
Let the number of boys be 4x and the number of girls be 6x
There were 50 more girls than boys
By the problem,
6x - 4x = 50
2x = 50
[tex]x = \frac{50}{2}[/tex]
x = 25
Number of boys who attended the camp = 4 [tex]\times[/tex] 25 = 100
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PLEASE HELP!!!! "CLEVERLY CONICS Portfolio"
Choose one of your conic examples to study in greater detail. Complete the table to create the graph and equation for your chosen example.
1. If possible, use a photo of the structure or item. Otherwise, draw a detailed sketch.
2. Measure and label the key dimensions of the shape in order to duplicate them in a to-scale graph. Be sure to label your units of measure to reflect the actual measurements.
3. Draw the underlying conic section on a coordinate grid.
4. Identify the coordinates of the appropriate key parts of the conic section.
5. Determine the closest approximation of the equation in standard form for the conic section.
Answer:
Hello there! While I didn't have this assignment, I found the assignment on Coursehero and took the liberty of downloading the pdf.
BE SURE TO USE QUILLBOT FOR PARAPHRASING AND PREPOSTSEO FOR PLAGIARISM CHECKING
Step-by-step explanation:
ERROR ANALYSIS Describe and correct the error in finding m/1. X 115° +39° + m/1 = 360° 154° +m1 = 360° m1= 206
Ms. Morgan is a science teacher. She found that 30% of her 120 students are athletes. Mr. Gregory is a math teacher. He found that 27, or 15%, of his student are athletes. Complete parts a and b below.
Of the part, the whole, and the percent, an information which is still unknown to Ms. Morgan is the number of non-athletes and it is equal to 84 students.
Of the part, the whole, and the percent, an information which is still unknown to Mr. Gregory is the total number of students and it is equal to 180 students.
How to determine the unknown information?Since the Ms. Morgan found that 30% of her 120 students are athletes, the known and unknown values include the following:
Known value (whole) = 120 students.
Known value (percent) = 30%
Unknown value (part) = ?
Next, we would determine the unknown value as follows:
Number of athletes = 30/100 × 120
Number of athletes = 30 × 1.2
Number of athletes = 36 students.
Unknown value (non-athletes) = 120 students - 36 students
Unknown value (non-athletes) = 84 students.
Since Mr. Gregory found that 27, or 15%, of his student are athletes, the known and unknown values include the following:
Known value (part) = 27 students.
Known value (percent) = 15%
Unknown value (whole) = ?
For the unknown value, we have:
Let the variable T represent the total number of students.
15/100 × T = 27
0.15T = 27
Total number of students, T = 27/0.15
Total number of students, T = 180 students.
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Complete Question:
Ms. Morgan is a science teacher. She found that 30% of her 120 students are athletes. Mr. Gregory is a math teacher. He found that 27, or 15%, of his student are athletes. Complete parts a and b below.
a. Of the part, the whole, and the percent, which information is still unknown to Ms. Morgan? Find this unknown value.
b. Of the part, the whole, and the percent, which information is still unknown to Mr. Gregory? Find this unknown value.
