Answer:
a. (2, 5)
b. 0
Step-by-step explanation:
The function is y = f(x)
If we plug in a value for x, we should get a value for y and that (x, y) will be a point
a. We have x = 2 and y = f(2) = 5
So x = 2, y = 5 is a point otherwise written as (2, 5)
b. If y = 0, when x = 5 then f(5) = 0
Suppose a basketball player has made 273 out of 385 free throws. If the player makes the next 3 free throws, I will pay you $27. Otherwise you pay me $16. Step 2 of 2 : If you played this game 891 times how much would you expect to win or lose?
By probability, If you played 891 times, you expect to lose $16.
Total Possible Throws = 385
Number of throws = 273
Let P(T) be the Probability that the player makes the next throw
P(T) = 273 / 385
The probability that the player makes the next three throws is then given by:
= P(T) × P(T) × P(T)
= 273 / 385 × 273 / 385 × 273 / 385
= (273 / 385)²
= 0.35653794139
= 0.357
Let P(T') be the probability the player doesn't make the next two throws
P(T') = 1 - P(T)
P(T') = 1 - 0.357
P(T') = 0.643
The expected gain for the player turns is given by:
(Probability of making both throws) * $27 + (Probability of NOT making both throws) x ( - $16 )
= 0.357 × $27 - 0.643 × $16
= $9.639 - $10.288
= - $0.649
b.
The probability that he makes the next 891 throws.
= P(T)⁸⁹¹
= (273/385)⁸⁹¹
Let P(T') be the probability the player doesn't make the next three throws
P( T' ) = 1 - P( T )
P( T' ) = 1 - 19.449493e-134
P( T' ) = 1
The expected gain or loss for the player turns is given by:
(Probability of making all 626 throws) * $5 + (Probability of NOT making all 626 throws) x (-$10)
= (273/385)⁸⁹¹ × 27 + 1 × - 16
= - $16
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Newton's law of cooling is T = AeW! + C, where is the temperature of the object at time t, and is the constant temperature of the surrounding medium. Supposethat the room temperature is 73, and the temperature of a cup of coffee is 174' when it is placed on the table. How long will it take for the coffee to cool to 131" fork = 0.06889192 Round your answer to two decimal places.
Solution
We are given the equation
[tex]T=Ae^{-kt}+C[/tex]Room temperature, C = 73 degrees
Temperature at time t = 0, is T = 174 degrees
[tex]\begin{gathered} T=Ae^{-kt}+C \\ 174=Ae^0+73 \\ 174=A+73 \\ A=174-73 \\ A=101 \end{gathered}[/tex]Therefore, the equation becomes
[tex]T=101e^{-kt}+73[/tex]We want to find t = ?, when T = 131 degrees and k = 0.0688919
[tex]\begin{gathered} T=101e^{-0.0688919t}+73 \\ 131=101e^{-0.0688919t}+73 \\ 131-73=101e^{-0.0688919t} \\ 58=101e^{-0.0688919t} \\ e^{-0.0688919t}=\frac{58}{101} \\ e^{-0.0688919t}=\frac{58}{101} \\ -0.0688919t=ln(\frac{58}{101}) \\ t=-\frac{1}{0.0688919}ln(\frac{58}{101}) \\ t=8.051418328 \\ t=8.05minutes\text{ \lparen to two decimal places\rparen} \end{gathered}[/tex]Therefore, the answer is
[tex]8.05minutes[/tex]Which is the graph of the given function? ft=5sin3t
The graph is based on amplitude.
Given the function:
f(t) = 5sin3t
To draw the graph of above function.
The function g(t) = sin t is a periodic function with amplitude [tex]a_{0}[/tex] = 1 and period [tex]t_{0}[/tex] = 2[tex]\pi[/tex]
For our case, the 5 that multiplies g (t) increases the amplitude so that,
a = 5 x 1 = 5 and the 3 that multiplies the variable increases the period being t = 2[tex]\pi[/tex] x 1/3 = 2[tex]\pi[/tex]/3
What is Graph?
Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter. Each object in a graph is called a node.
See the graph in the bottom of explanation.
Hence, The graph is based on amplitude.
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A plane flies 452 miles north andthen 767 miles west.What is the angle of theplane's resultant vector?Hint: Draw a vector diagram.[?]
see the figure below to better understand the problem
we have that
tan(x)=452/767
The flight of a fireworks rocket is given by the function: h(t)= -16t^2 + 84t+5 Where h(t) is the height in feet and t, the time in seconds. How long will the rocket take to reach its maximum height?Round your answer to 2 decimal places.
Given:
The flight of a fireworks rocket is given by the function:
[tex]h(t)=-16t^2+84t+5[/tex]Required:
How long will the rocket take to reach its maximum height?
Explanation:
We will first find critical points
[tex]\begin{gathered} h^{\prime}(t)=-32t+84 \\ \text{ Now, put }h^{\prime}(t)=0 \\ t=\frac{21}{8} \\ \text{ At }t=\frac{21}{8}\text{ we get stationary points.} \end{gathered}[/tex]To check maximum and minimum value
[tex]\begin{gathered} h^{\prime}^{\prime}(t)=-32(<0) \\ \text{ At }t=\frac{21}{8}\text{ the function is maximum.} \end{gathered}[/tex]Asnwer
in how many ways can 9 people stand in a line
Write a number sentence that results in the sum or difference of zero.
Answer:
5x + 3 = 0
OR
35*35 /35 -35
hope this helps
What is the volume of the cone?5 cm21 cmA 70π cm³B 105 cm³C 175 cm³D 525 cm³
The formula to find the volume of a cone is:
[tex]\begin{gathered} V=\frac{1}{3}\pi r^2h \\ \text{ Where} \\ r\text{ is the radius of the base} \\ h\text{ is the height} \end{gathered}[/tex]So, we have:
[tex]\begin{gathered} r=5cm \\ h=21cm \end{gathered}[/tex][tex]\begin{gathered} V=\frac{1}{3}\pi r^{2}h \\ V=\frac{1}{3}\pi(5cm)^{2}(21cm) \\ V=\frac{1}{3}\pi(525cm^3) \\ V=\frac{525\pi}{3}cm^3 \\ V=175\pi cm^3 \end{gathered}[/tex]Answer
C 175π
11 Evaluate d-fif d = 7 and f = -15.
If f(x) = 3x² + 5x-4, then
f(x+h)-f(x)
h
(3x+3h)²+(5x+5h)-4-(3x²+5x-4)
h
3(x+h)2 +5x-4-3x²-5x+4
h
is equal to which of the following?
3(x+h)² +5(x+h)-4-3x²+5x-4
h
3(x2+2xh+h²)+5(x+h)-4-(3x2 +5x-4)
h
function f(x) =[tex]3x^{2} +5x -4[/tex] then ,
= [tex]\frac{F(x + h)- F(x)}{h}[/tex]
= [tex]\frac{3(x+h)^{2}+5(x+h)-4 -3x^{2} - 5x +4}{h}[/tex]
What are functions ?The core concept of mathematics' calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given that : f(x) =[tex]3x^{2} +5x -4[/tex]then ,= [tex]\frac{F(x + h)- F(x)}{h}[/tex]
= [tex]\frac{F(x + h)- F(x)}{h}[/tex]
= [tex]\frac{F(x + h)- F(x)}{h}[/tex]
= [tex]\frac{3(x^{2} +2xh +h^{2} )+5(x+h)-4 -(3x^{2} +5x -4)}{h}[/tex]
= [tex]\frac{3(x+h)^{2}+5(x+h)-4 -3x^{2} - 5x +4}{h}[/tex]
hence option d is correct
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Ebony is building a shelf to hold two boxes shown. What is the least width she should make the shelf?
Answer:
There exists the same question from other source that shows the two boxes.
Box 1 has a length of 4/5 feet
Box 2 has a length of 3/4 feet
Because Ebony is trying to find the total amount of space needed to hold the boxes, use addition.
Here, is the solution:
= 4 / 5 + 3 / 4
= (16 + 15) / 20
= 31 / 20
So, Ebony can make a shelf at least 31/20 feet wide or 1 11/20 feet.
Which of the following best defines the term ""algorithm""?
A combination of zeroes and ones that represents an instruction to the computer
The rules for writing instructions in a specific programming language
A set of step-by-step instructions to solve a problem or perform a task
A way to write programming code in short English phrases to describe the program components
The basic definition of algorithm is A set of step-by-step instructions to solve a problem or perform a task.
Option c is the right answer.
Find the vertex of the graph f(x)=-x^2+6x+1
Giving the function
[tex]f(x)=x^2+6x+1[/tex]the vertex is giving by
[tex]h=\frac{-b}{2a}[/tex]where
a=1
b=6
c=1
then
[tex]h=\frac{-6}{2*1}[/tex][tex]h=\frac{-6}{2}=-3[/tex]then
[tex]f(-3)=-3^2+6(-3)+1[/tex][tex]f(-3)=9-18+1[/tex][tex]f(-3)=-8[/tex]then the vertex is in the point
(-3,-8)
simplify completely: 3b2 – 75 / 3b2 – 27b + 60
Answer:
[tex]\frac{(b+5)}{(b-4)}[/tex]
Step-by-step explanation:
[tex]\frac{3b^{2}-75}{3b^{2}-27b + 60}[/tex]
[tex]\frac{3(b^{2}-25)}{3(b^{2}-9b + 20)}[/tex]
Simplify numerator:
where [tex](b^{2} -25) = (b-5)(b+5)[/tex]
[tex]\frac{3(b-5)(b+5)}{3(b^{2}-9b + 20)}[/tex]
Simplify denominator:
looking at [tex]b^{2} - 9b + 20[/tex]
where a = 1
b = -9
and c = 20
We are looking for two numbers that sum to -9 and multiply to 20:
-5 + (-4) = -9
-5 * (-4) = 20
so [tex]b^{2} -9b+20 = (b-5)(b-4)[/tex]
insert into denominator:
[tex]\frac{3(b-5)(b+5)}{3(b-4)(b-5)}[/tex]
remove: 3(b-5) from numerator and denominator:
[tex]\frac{(b+5)}{(b-4)}[/tex]
-m/3=-4 what is m????
Between 6pm and 7pm, 5 mystery novels, 3 non-fiction books, 7 picture books, and 2 science fiction novels were returned to the library. What is the experimental probability that the next book returned to the library is a picture book?
Find the distance between these two points(-5,3) (-2,-3)
Explanations:
Let the first pont be P (-5, 3)
[tex]x_1=-5,y_1=\text{ 3}[/tex]Let the second point be Q (-2, -3)
[tex]x_2=-2,y_2=\text{ -3}[/tex]The distance between two points is given by the equation:
[tex]\begin{gathered} PQ\text{ = }\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{Substituting the values of x}_1,y_1,x_2,y_2\text{ into the given equation } \\ PQ\text{ = }\sqrt{(-2-(-5))^2+(-3-3)^2} \\ PQ\text{ = }\sqrt{(-2+5)^2+(-6)^2} \\ PQ\text{ = }\sqrt{(3)^2+(-6)^2} \\ PQ\text{ = }\sqrt{9+36} \\ PQ\text{ = }\sqrt{45} \end{gathered}[/tex]The distance between the two points is √45 units
Find the solution(s) to x2 - 16x + 64 = 0.O A. x= -2 and x = 32O B. x = 8 and x= -8O C. x = 8 only7O D. x = 4 and x = 16
Given:
Given the quadratic equationt
[tex]x^2-16x+64=0[/tex]Required: Solution to the quadratic equation
Explanation:
Write the quadratic equation as
[tex]\begin{gathered} (x-8)^2=0 \\ \implies x-8=0 \\ \implies x=8 \end{gathered}[/tex]Option C is correct.
Final Answer: The solution t the squadratic equation is x = 8 only.
In the similaritytransformation of AABCto ADFE, AABC was dilated bya scale factor of [? ], reflectedacross the [ ], and movedthrough the translation [ ].
Given
To find:
The scale factor for the dilation of ΔABC to ΔDEF.
Explanation:
It is given that
Beth has 2 jobs and at her first job she earns $12.25 and worked 36 hours. At her second job, she earns $9.00 per hour and worked 12 hours. How much did she earn for both jobs?
Beth earns $21.25 for both the jobs by working 36 hours at one job and 12 hours at another job
What is Addition?Addition: Addition is a way of combining things and counting them together as one large group. Addition in math is a process of combining two or more numbers. Addends are the numbers added, and the result or the final answer we get after the process is called the sum
Given that, Beth has 2 jobs and at her first job she earns $12.25 and worked 36 hours. At her second job, she earns $9.00 per hour and worked 12 hours
Her earnings for both the jobs is addition of her salary gives the answer
on adding $12.25+$9.00 = $21.25
She earns $21.25 for both the jobs by working 36 hours at one job and 12 hours at another job
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please help asap!a. if the input is -8, what is the output?b. if the output was 21, what was the input?
a) The output is 45
b) The input was -4
Here, we want to use the relationship between the input and the output to answer the questions
While x is our input, f(x) is given as our output
The relationship between the two is given as;
[tex]f(x)\text{ = -6x-3}[/tex]a) Here, we have an input, and we want to get the output
To solve this, we just need to substitute the value of -8 for x in the relation
We have this as follows;
[tex]\begin{gathered} f(-8)\text{ = -6(-8)-3} \\ f(-8)\text{ = 48-3 = 45} \end{gathered}[/tex]b) Here, we have the output, but we want to get the input
What this simply mean is that we are to find the value of x
We simply substitute 21 for f(x)
Thus, we have;
[tex]\begin{gathered} 21\text{ = -6x-3} \\ 21\text{ + 3 = -6x} \\ \\ -6x\text{ = 24} \\ \\ x\text{ = }\frac{24}{-6} \\ \\ x\text{ = -4} \end{gathered}[/tex]You transform the point (1, -2) by reflecting it over the y-axis. What are the coordinates of the new point?
The coordinates of the image after it is reflected is -1, -2)
How to determine the coordinates of the reflected point?The coordinate of the point is given as
Point = (1, -2)
The transformation rule is given as
Reflection over the y-axis
The mathematical representation of this transformation rule is
(x, y) = (-x, y)
So, we have
Point = (1, -2)
This gives
Image = (-1, -2)
Hence, the coordinates of the reflected point is -1, -2)
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A rented office space has a monthly income of $3,800. A suitable gross income multiplier derived from market data is 11.1. What would the estimated value be? Round to the nearest $1,000.
The estimated value after round will be $506,000.
What is Rounding number?
To making a number simpler but keeping its value close to what it was, is called Rounding.
Given that;
Monthly income of a rented office = $3,800
A suitable gross income multiplier derived from market data = 11.1.
Now,
We know that;
Gross income multiplier = Sale price ÷ Gross income
Here, Gross income multiplier = 11.1
And, The annual gross income will be,
= Monthly gross income x Number of month in a year
= $3,800 x 12
= $45,600
Thus, Estimated sale price is calculated as;
11.1 = Estimated Sale price ÷ $45,600
Estimated Sale price = 45,600 x 11.1
= $506,160
After round off we get;
Estimated Sale price = $506,000
Thus, The estimated value after round will be $506,000.
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A professor has students keep track of the social interactions for a week the number of social interactions over the week and selling in the following group frequency distribution how many students had at least 60 social interactions for the week?
For at lest 60 social interaction:
So social interaction is:
60 - 64 4
65 - 69 3
70 - 74 0
75 - 79 4
So student of these social interaction is:
[tex]\begin{gathered} =4+3+0+4 \\ =11 \end{gathered}[/tex]So total 11 students had at lest 60 social interaction.
What is the axis of symmetry, vertex, and y-intercept for f(x)=0.5x^2-2x-2
U
For the axis of symmetry, formula is,
[tex]x=\frac{-b}{2a}[/tex][tex]\begin{gathered} \text{where a=0.5 and b=-2} \\ x=\frac{-(-2)}{2(0.5)}=\frac{2}{1}=2 \end{gathered}[/tex]Hence, the axis of symmetry is 2.
To find the vertex, f(x)=0,
[tex]\begin{gathered} 0=0.5x^2-2x-2 \\ \text{Multiply both sides by 2} \\ 0=x^2-4x-4 \\ 0=(x^2-4x)-4 \\ 0=(x-2)^2-(4-2_{} \\ 0=(x-2)^2-2 \\ \text{Vertex are (2, -2)} \end{gathered}[/tex]Hence, the vertex are (2, -2).
[tex]y-intercept\text{ is -2}[/tex]
Hence, y-intercept is -2.
Eric picks 5/8 basket of strawberries. Kiki picks 1/5 basket of strawberries. Which answer is the most accurate estimate for how many more baskets of strawberries Eric picks than Kiki? 0 baskets 1/2 basket 3/4 basket 1 basket
The number exists described mathematically as a quotient, where the numerator and denominator exist split. Both are integers in a simple fraction. The baskets of strawberries Eric picks than Kiki exists 17 / 40.
What is meant by fractions?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. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
Based on the given conditions, formulate: 5/8 - 1/5
Find common denominator and write the numerators above common denominator: (5 × 5) / (8 × 5) - 8 / (8 × 5)
Calculate the product or quotient: 25 / 40) - (8 / 40)
Write the numerators over the common denominator: (25 - 8) / 40
Calculate the sum or difference: 17 / 40
get the result: 42.5% or 0.425
Therefore, the correct answer is 42.5% or 0.425.
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Simplify the following fraction: \frac{16}{18}
18
16
The simplest form of the fraction 18/16 is 9/4.
Fraction:
A fraction is a number that represents part of a whole.
A fraction is written in the form p/q, where q ≠ 0.
Given,
There has been given a fraction 18/16, that has to be simplified.
The steps to simplifying fractions,
First, we have to find the GCD (or HCF) of numerator and denominator
GCD of 16 and 18 is 2
Now we have to divide both the numerator and denominator by the GCD
16 ÷ 2
18 ÷ 2
Now we get the reduced fraction as, 8/9.
Therefore, 16/18 simplified to lowest terms is 8/9.
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what is the mathematical expression of “the sum of a number x and three”
Answer: X + 3
Step-by-step explanation:
Sum hints as to an addition statement and it specifies a variable X and the number 3 so the expression would be X + 3.
SUM MEANS ADDITION
HERE IT MEANS THE ADDITION OF x and 3
written as
[tex]x + 3[/tex]
HOPE THIS HELPS
Pentagon ZEBRA is similar to pentagon
LIONS. What is the length of RA in feet?
E
22 ft
13 ft
Z
18 ft
R
20 ft
A
10.4 ft
I
14.4 ft
17.6 ft
N 12 ft S
L
16 ft
A plane shape measuring 0.4 feet has five straight sides and five angles.
What is pentagon?The geometric shape known as a pentagon has five sides and five angles. Penta here means five, and pentagon means angle. One of the different kinds of polygons is the pentagon. A regular pentagon's internal angles add up to 540 degrees.
Pentagonal form
The pentagon is a polygon with five sides and five angles, just like other polygons including triangles, quadrilaterals, squares, and rectangle
There are various pentagon shapes depending on the sides, angles, and vertices, such as both a regular and irregular pentagon
Concave and convex pentagon.
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find the value or measure. Assume all lines that appear to the tangent are tangent. mJH=
From the arc-angle relationship
By comparing both pictures, we have that
[tex]55=\frac{76+mJH}{2}[/tex]now, we must isolate MJH, hence we have
[tex]\begin{gathered} 76+\text{mJH}=2\cdot55 \\ 76+\text{mJH}=110 \end{gathered}[/tex]and we must move 76 to the right hand side as -76, this gives
[tex]\begin{gathered} \text{mJH}=110-76 \\ \end{gathered}[/tex]Finally, mJH is 34.
