The rate of change of the temperature on the time interval is -2°C. This means that, in average, for each hour that passes the temperature decreases by 2 degrees Celcius.
What is the rate of change on the temperature?A rate of change is defined as the quotient between the difference in some measure (in this case it will be the difference between the final temperature and the initial temperature) and the time interval in which it happens.
Here we know that:
final temperature = -5°C
Initial temperature = 13°C
And this change goes from 3 P.M. to midnight, so the change happens on an interval of 9 hours.
Then the rate of change of the temperature is:
r = (-5°C - 13°C)/9h = -2°C/h
So for each hour, the temperature decreases by 2°C.
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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]
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 )
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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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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a football team travels to an away game in cars that seat five players and vans that can hold nine players. If there are 47 players on the team find the equation for this situation
The equation to illustrate the information when the football team travels to an away game is 5c + 9v = 47.
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.
Let cars = c
Let van = v
The equation will be 5c + 9v = 47.
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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
how are the zeros of a polynomial function related to the equation and graph of a function
The way that zeros of a polynomial function is related to the equation and graph of a function because they act as solutions to the equation and also x-intercepts of a graph.
What graphing relationship does a zero have?When the quadratic equation's graph crosses the x-axis, those points are known as the zeros of the equation.
The graph's x-intercepts and a function's zeros are the same thing. If the zero of f has an odd multiplicity, the graph of f will cross the x-axis at that x value. The x-axis will be touched by the graph of f if it has an even multiplicity zero.
Hence, A polynomial's zeros are the answers to any equation such as p(x) = 0, where p(x) stands for the polynomial. Since the values of x where y = 0 if we graph this polynomial as y = p(x). In other words, these are the graph's x-intercepts.
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Two rockets are to be launched at the same time from NASA headquarters in Florida, and are to meet at a space station many miles from Earth. The first rocket is to travel at 19,200 miles per hour and the second rocket will travel at 18,000 miles per hour. If the first rocket is scheduled to reach the space station 0.5 of an hour before the second rocket, how far is the space station from NASA headquarters?
By solving a linear equation, it can be calculated that
The space station is at a distance of 144000 miles from NASA headquarters
What is linear equation?
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Here, a linear equation needs to be solved
Let the space station be d miles from NASA headquarters
Speed of the first rocket = 19200 miles/hour
Speed of the second rocket = 18000 miles /hour
Time taken by the first rocket to reach the space station = [tex]\frac{d}{19200}[/tex]
Time taken by the second rocket to reach the space station = [tex]\frac{d}{18000}[/tex]
By the problem,
[tex]\frac{d}{18000} - \frac{d}{19200} = 0.5\\\\\frac{16d - 15d}{288000} = 0.5\\\\\frac{d}{288000} = 0.5\\\\d = 288000 \times 0.5\\\\d = 144000 \ miles[/tex]
The space station is at a distance of 144000 miles from NASA headquarters
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If f(x) is an exponential function where f(-3) = 11 and ƒ(4) = 55, then find the
value of f(-1), to the nearest hundredth.
The value of the exponential function (-1) will be equal to f(-1) = -0.02.
What is an exponential function?The mathematical expression f(x)=exp or e^x denotes the exponential function. The word, unless specifically stated differently, normally refers to the positive-valued function of a real variable, though it can be extended to complex numbers or adapted to other mathematical objects.
Given that f(x) is an exponential function where f(-3) = 11 and ƒ(4) = 55. The value of the exponential function will be calculated as,
[tex]y=ax^b[/tex]
[tex]11=a(-3)^b\\55=a(4)^b[/tex]
Calculate the value of constants,
log5 = blog(4 / 3)
b = 0.7 / 0.125
b = 5.6
The value of 'a' will be,
11 = a(-3)⁵°⁶
a = -0.02
The exponential function f(-1) will be calculated as,
f(-1) = -0.02(-1)⁵°⁶
f(-1) = -0.02
Therefore, the value of the exponential function (-1) will be equal to f(-1) = -0.02.
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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
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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What is the product of the complex numbers below? 7-i / 3+i
Answer: 2-i
Step-by-step explanation:
multiply the fraction by 3-i/3-i
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].
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 solution to -4(8-3x) ≥ 6x - 8?
O
4
x²--1/32
O x≤
xs--1/72
Ox≥4
Ox≤4
Answer:
x ≥ 4
Step-by-step explanation:
-4 ( 8 - 3x ) ≥ 6x - 8
First, solve the brackets.
- 32 + 12x ≥ 6x - 8
Subtract 6x from both sides.
- 32 + 12x - 6x ≥ - 8
- 32 + 6x ≥ - 8
Add 32 to both sides.
6x ≥ - 8 + 32
6x ≥ 24
Divide 6 by both sides.
x ≥ 4
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.
Please help, i dont understand
The equation of lines are (a) x - 2y + 6 = 0
(b) 2x - y - 4 = 0
(c) x - y + 1 = 0
(d) 4x + 3y + 4 = 0
Slope-intercept form of the equation -> y = mx + c
Slope = m = [tex]\frac{y2-y1}{x2-x1}[/tex]
(a) A(0,3) and B(6,6)
m = [tex]\frac{6-3}{6-0}[/tex]
= 3/6
= 1/2
Putting the value in equation,
3 = (1/2)*0 + c
c = 3
Equation -> y = (1/2)x + 3
2y = x + 6
x - 2y + 6 = 0
(b) A(0,-4) and B(5,6)
m = [tex]\frac{6+4}{5-0}[/tex]
= 10/5
= 2
Putting the value in equation,
-4 = (2)*0 + c
c = -4
Equation -> y = (2)x - 4
2x - y - 4 = 0
(c) A(-4,-3) and B(2,3)
m = [tex]\frac{3+3}{2+4}[/tex]
= 6/6
= 1
Putting the value in equation,
3 = (1)*2 + c
3 = 2 + c
c = 3 - 2
c = 1
Equation -> y = (1)x + 1
y = x + 1
x - y + 1 = 0
(d) A(-6,4) and B(3,-8)
m = [tex]\frac{-8-4}{3+6}[/tex]
= -12/9
= -4/3
Putting the value in equation,
-8 = (-4/3)*3 + c
-8 = -4 + c
c = -8 + 4
c = -4
Equation -> y = (-4/3)x - 4
3y = -4x - 4
4x + 3y + 4 = 0
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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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The ratio of boys to girls in a class is 2:3 if there are 48 pupils in the class.How many boy and girls are there?
tysm po
) Nike deposits N5,000.00 in a savings bank account. If she is paid an interest rate of 5% per annum for 2 years, how much is the simple interest? NOO. O
The simple interest that Nike will receive after 2 years is $500.
The principal amount =$5000
Rate = 5% = 0.05
Time = 2 years
Now simple interest = PRT = 5000 × 0.05 × 2 = 500
Hence the simple interest earned by Nike is $500
Calculating the amount of interest that will be owed on a sum of money at a certain rate and for a specific period of time is possible using simple interest.
Simple interest does not change the principal amount in the same way as compound interest, which adds the interest of one year's principal to the next year's principal to calculate interest.
A loan is a sum of money that a person obtains from a bank or another type of financial institution in order to pay bills. A few types of loans are personal, student, auto, and mortgage loans.
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What is the expression 9-z when z=8
If Ø (theta) is an angle in standard position and its terminal side passes through the point (-9,5), find the exact value of sec Ø (theta) in simplest radical form.
For the given data, ∅ is the given angle in standard position, terminal side passes through (-9,5) then the exact value of sec∅= ( - √106/ 9 ) in simplest radical form.
As given in the question,
For the given angle ∅ (theta) in standard position:
Terminal side of ∅ is passes through the point ( -9, 5 )
( -9 , 5 ) represents ∅ is in the second quadrant.
In second quadrant sine in positive and cosine is negative.
Base is negative and altitude is positive.
Base = -9
Altitude = 5
Using Pythagoras theorem,
Hypotenuse² = (-9)² + (5)²
⇒ Hypotenuse = √106
cos ∅ = -9 / √106
sec ∅ = 1/ cos ∅
= - √106/9 ( simplest radical form )
Therefore, for the given data, ∅ is the given angle in standard position, terminal side passes through (-9,5) then the exact value of
sec∅= ( - √106/ 9 ) in simplest radical form.
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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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A caterer charges a $40 fee plus an additional $6.25 per person. She determines the total cost, C, for x people by using the equation shown above. How much will a party cost for 80 people?
1.You need to earn at least $90. You earn $7 for each hour you work.
Which inequality represents the number of hours h that you need to
work?
(Look at the picture for options for the answer)
2. Write a graph that represents the solution
Answer:
Inequality:
Graph choice:
Step-by-step explanation:
Inequality
It says at least 90, which means we have to use the greater than or equal to sign
Our inequality so far: 90≥______
Now it says you earn 7 dollars per hour, which means 7 times the number of hours you work or 7h. Our inequality now looks like this:
90≥7h
The answer choice that matches is A (90≥7h = 7h≤90)
For the second question on the bottom, I added an image.
(Answer is B)
Here is the histogram of a data distribution. All class widths are 1
Which of the following numbers is closest to the mean of this distribution?
The number that is closest to the mean of the distribution is 4 (option C)/
What is the mean?A histogram is used to represent data graphically. The histogram is made up of rectangles whose area is the product of the frequency of the rectangle and the width of the rectangle.
Mean is the average of a set of numbers. It is determined by multiplying each bar in the histogram by its height, add the multiplication value for all the bars together and dividing it by the total frequency of the bars.
Mean = [(1 x 1) + (2 x 2) + (3 x 3) + (4 x 4) + (5 x 3) + (6 x 2) + (7 x 1)] / (1 + 2 + 3 + 4 + 3 + 2 + 1)
Mean = (1 + 4 + 9 + 16 + 15 + 12 + 7) / 16
Mean = 64 / 16
Mean = 4
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1/3[6y+3]-24=3[1/3y-6]
y-3=y-7
x+2x=1/3x-8
y-9=y-2
x-5=6x-5
step by step explanation please
Answer:
Step 1: Simplify both sides of the equation.
1/3(6y+3)−24 = 3(1/3y−6)
1/3(6y) + 1/3(3) -24 = 3(1/3y) + 3(-6)
2y +1 −24 = y−18
2y −23 = y −18
Subtract y from both sides.
2y−23−y=y−18−y
y−23=−18
Step 3: Add 23 to both sides.
y−23+23 = −18+23
y = 5
Step-by-step explanation:
Zack and his friends went to a movie on Thursday afternoon. It took 25 minutes to drive to the theater. They arrived at the theater 1 hour and 15 minutes before the movie started. Once it started, the movie lasted for 1 hour and 20 minutes and ended at 4:20 P.M. What time did Zack and his friends leave for the movies
Answer:
2:20
Step-by-step explanation:
The movie started at 3:00 PM they got there at 2:45. and it took them 25 mins to get there meaning they left at 2:20.
What is the measure of each angle of a regular 22-gon? If necessary, round to the nearest tenth.
The measure of each angle of a regular 22-gon is 163.6 degrees.
How to find the sum of angles of a polygon?In geometry, a polygon can be defined as a flat or plane, two-dimensional closed shape bounded with straight sides.
Polygon can be named base on the number of sides they possess. For example pentagon has 5 sides, hexagon has 6 sides, heptagon has 7 sides, octagon has 8 sides, nonagon has 9 sides and decagon has 10 sides.
Therefore, a regular polygon is one which sides and angles are congruent.
A regular 22-gon has 22 sides.
The measure of each angle of 22-gon can be found as follows;
angle= 180(n - 2) / n
where
n = number of sides
angle = 180 (22 - 2) / 22
each angle = 180(20) / 22
each angle = 3600 / 22
Therefore,
each angle = 163.636363636
each angle = 163.6 degrees.
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How do I solve this question
The partial fraction is proved.
What is a fraction?
If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.
Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.
=3x²+8x+4/(x²-4)(3x-2)
=3x2+8x+4/(x2-4)(3x-2)
= 3x2+6x+2x+4/(x2-4)(3x-2)
=3x(x+2)+2(x+2)/(x2-4)(3x-2)
Hence proved, l.h.s = r.h.s
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