A function that models the total cost of running the air conditioner for the first 400 minutes is .
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
Let the number of minutes be m.
Let the total cost be T.
Given the following data:
Cost of air conditioner = $130
Running cost = $0.25 per minute
Time = 400 minutes.
To write a function that models the total cost of running the air conditioner for the first 400 minutes:
How to solve a word problem.
First of all, we would write an equation to models the total cost of running the air conditioner for the first 400 minutes:
For the total time:
0.25m
For the total cost:
T= 130 + 0.25m
For the domain:
The value of m is the domain and it can be chosen from 0 to 130.
Domain (m) = [0, 130].
For the range:
A range represents the minimum and maximum value of a data set.
Thus, the value of T would be between 130 and 230.
Range = [130, 230].
For the intercept:
when x = 0, we have:
y = 130 + 0.25(0)
y = 130.
Intercept = [0, 130]
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Find the 18th term in the following
arithmetic sequence:
-2, -6, -10, -14, . . .
Answer:
-70
Step-by-step explanation:
-2, -6, -10, -14, ...
-6 - (-2) = -4
The common difference in -4.
The nth term of an arithmetic sequence with common difference d is
a_n = a_1 + d(n - 1)
For n = 18,
a_18 = -2 + (-4)(18 - 1)
a_18 = -2 + (-4)(17)
a_18 = -2 - 68
a_18 = -70
Answer: -70
Step-by-step explanation:
{[tex]a_{n}[/tex]=[tex]a_{1}[/tex]+(n-1)d}
a_{1}= -2
d= -4
[tex]a_{18} =-2+(18-1)*(-4)=-2-68 = -70[/tex]
teh dance committee at jefferson high school decides to change students different prices for dance tickets depending on whether they are a student at jefferson or at another school. A student attending jefferson pays $5, whereas a student attending a different school pays $10. the dance committee didn't make different kinds of tickets, and they lost track of how many of each kind of ticket they sold. They know they sold a total of 500 tickets and brought in $3135. How many jefferson and non-jefferson student came to the dance ?
The number of students at Jefferson School and non-Jefferson school will be 373 and 127, respectively
What is the solution to the equation?An answer to a formula is any variable value that fulfills the equal outcomes, that is, it tends to make the Left Hand Side (LHS) and Right Hand Side (RHS) of the formula equal. To solve an equation, you must locate the feasible solution) to that formula.
Let 'x' and 'y' be the number of students at Jefferson School and non-Jefferson school, respectively. Then the equations are given as,
x + y = 500 ...1
5x + 10y = 3135 ...2
From equations 1 and 2, then we have
5(500 - y) + 10y = 3135
2500 - 5y + 10y = 3135
5y = 635
y = 127
Then the value of 'x' is given as,
x + 127 = 500
x = 373
The number of students at Jefferson School and non-Jefferson school will be 373 and 127, respectively
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find the value of a and b such that
x^2+2x-7=(x+a)^2+b
The value of a and b are 1 and -8 respectively.
What are Quadratic Expressions?Quadratic expressions are polynomial expressions of second degree.
The general form of a quadratic expression is ax² + b x + c.
The given quadratic expression is x² + 2x - 7.
We have to write this in the form (x + a)² + b.
We have the algebraic identity a² + 2ab + b² = (a + b)²
x² + 2x - 7 = x² + 2x - 7 + 1 - 1
= (x² + 2x + 1) - 7 - 1
= (x + 1)² - 8, which is in the form (x + a)² + b.
a = 1 and b = -8
Hence the value of a is 1 and the value of b is -8.
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What is the equation for responsivity?
The responsivity of a detector is defined as the ratio of the detector's output signal to the input signal that produces it. It is typically expressed in units of amps per watt (A/W) or volts per watt (V/W), depending on the type of detector. The equation for responsivity is:
Responsivity = output signal / input signal
In general, the input signal is the amount of power or radiant flux incident on the detector, while the output signal is the electrical signal produced by the detector in response to the input signal.
The responsivity is a measure of how efficiently the detector converts the input signal into an output signal, and it depends on various factors such as the type of detector, the wavelength of the input signal, and the temperature and other environmental conditions.
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A rhombus has sides of length 8 m. It’s shorter diagonal is 10 m long. Find the length of the longer diagonal
Answer:
Step-by-step explanation:
Here's how you can find the length of the longer diagonal of a rhombus with sides of length 8 m and a shorter diagonal of length 10 m:
Step 1: Draw a diagram of the rhombus with the shorter diagonal labeled as 10 m.
Step 2: Draw a perpendicular bisector from one corner of the rhombus to the opposite corner, dividing the rhombus into two congruent right triangles.
Step 3: Label the longer diagonal as "d".
Step 4: Since the two congruent right triangles have sides that are half the length of the sides of the rhombus, the hypotenuse of each triangle must have length 4 m.
Step 5: Using the Pythagorean theorem, we can find the length of the other side of each triangle:
a^2 + b^2 = c^2
4^2 + b^2 = 10^2
16 + b^2 = 100
b^2 = 84
b = √84 = 2√21
Step 6: Now that we know the length of one side of each triangle, we can use it to find the length of the longer diagonal:
d^2 = 4^2 + (2√21)^2
d^2 = 16 + 168
d^2 = 184
d = √184 = 2√23
So, the length of the longer diagonal of the rhombus is 2√23 m.
An elevator travels directly up 36 floors in 108 seconds. How many floors can this elevator travel directly up in 80 seconds?
The number of floors can this elevator travel directly up in 80 seconds is, 26 2/3 floors
What is the relation between time, distance & speed ?The distance covered by the object is equal to the product of the speed at which the object is moving and time taken for covering the distance.
Distance = Time × Speed
We are given that the elevator travels 36 floors in 108 seconds, so the rate can be calculated as follows:
rate = 36 floors / 108 seconds
= 1 floor / 3 seconds
To determine how many floors the elevator can travel in 80 seconds, we can use the rate and the formula: distance = rate x time:
distance = rate x time
distance = (1 floor / 3 seconds) x 80 seconds
distance = 80 / 3 floors
distance = 26 2/3 floors
So, the elevator can travel directly up 26 2/3 floors in 80 seconds.
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The length of a living room is 12 feet and its width is 1012
feet. The length of the room is being expanded by x feet. Select all the expressions that represent the area of the living room in square feet.
Answer: The area of the living room in square feet is given by:
A = length × width
Before the expansion, the length is 12 feet and the width is 10 feet. Therefore, the initial area is:
A = 12 ft × 10 ft = 120 ft²
After the expansion, the length becomes 12 + x feet, while the width remains the same at 10 feet. Therefore, the area after the expansion is:
A = (12 + x) ft × 10 ft = 120 + 10x ft²
So, the expressions that represent the area of the living room in square feet are:
120 ft²
120 + 10x ft²
Therefore, both expressions are correct.
Step-by-step explanation:
how would i get the answer for 33+33-33
Answer: the answer is 33
Step-by-step explanation: becuse if you do 33+33=66 and then 66-33=33 because 33 is half of 66
Answer:
Step-by-step explanation:
List the steps for rewritten
fractions as repeating decimals
(include an example as needed)
What is -2y = 6x - 8
Answer:
y= -3x+4
Step-by-step explanation:
You need to simplify down to y=mx+b by dividing -2 from both sides:
-2/-2= cancels out making y
6/-2= -3
-8/-2= 4
New equation:
y= -3x+4
Hope this helped!
Evaluate the following.
(a) |-5 + 9 = _
(b) |-5 + 9 = _
How many inches are in 71.12 centimeters? (1 inch = 2.54 centimeters). Show your work
Answer:
Step-by-step explanation:
1 inch = 2.54 cm
to get the inches, you do 71.12/2.54
71.12 = 7112/100
2.54 = 254/100
7112:100 / 254:100 = 7112/100 * 100/254
= 7112/1 * 1/254
28 inches are in 71.12 cm
Please helppppp meeeeeeee
Answer:
I Also need the answer plese helep ussss
Step-by-step explanation:
Can someone help me with this? There could be more than 1 answer
The correct statement regarding the quadratic function is given as follows:
C. The ball hit the ground after 3.5s.
How to classify the function as increasing, decreasing or constant?The function is increasing when the graph moves right and up.The function is decreasing when the graph moves right and down.The function is constant when the graph of the function is an horizontal line.For this problem, the intervals are given as follows:
Increasing: (0, 1.75) -> moving upwards.Decreasing: (1.75, 3.5) -> hits the ground after 3.5 seconds.More can be learned about quadratic functions at https://brainly.com/question/1214333
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Can someone please help me out.
the answer you need to put is A
Hi, Pls someone help!
A boat traveling with a velocity measured in meters per second is described by the vector b = <-4, 3>. In two or more complete sentences explain how to find the speed of the boat and the direction it is traveling in standard position. In your final answer, include all of your calculations.
Step-by-step explanation:
The speed of the boat is absolute value of the velocity vector. To find the speed of the boat, take the magnitude of the velocity vector which is
[tex] \sqrt{ {a}^{2} + {b}^{2} } = {c}^{} [/tex]
Where a and b is the vector
a is -4, b is 3
so
[tex] \sqrt{16 + 9} = \sqrt{25} = 5[/tex]
So the speed of the boat is 5 meters per hour.
To find the direction of the vector, we need to find the angle it is traveling in.
Using trigonometry, we can do this.
[tex] \tan( \alpha ) = - \frac{3}{4} [/tex]
[tex]arc \tan( - \frac{3}{4} ) = \alpha [/tex]
[tex] \alpha = - 36.87[/tex]
The boat is traveling at angle 36.87 degree clockwise.
A significance test about a proportion is conducted using a significance level of 0.05. The sample statistic is 0.12. The p-value is 0.03? a) If H0 were true, for what probability of a Type I error was the test designed?
b) What conclusion (reject or fail to reject) would you make for this test?
c) If this test resulted in a decision error, what type of error was it?
Answer: 28282
Step-by-step explanation:
I think
Line ET is tangent to circle A at T, and the measure of arc TG is 46. What is the measure ofO 136O 44O 90OO 67
Line ET is tangent to circle A at T, and the measure of arc TG is 46 and the measure of O is 67°.
Tangents to circles are lines that cross the circle at a single point. Point of tangency refers to the location where a tangent and a circle converge. The circle's radius, where the tangent crosses it, is perpendicular to the tangent. Any curved form can be considered a tangent. Tangent has an equation since it is a line. A line that touches a circle just once is said to be tangent to it. A point tangent to circle can only have one tangent. The intersection of the tangent and the circle is known as the point of tangency.
Now, [tex]\angle {TEG} =[/tex]180-90-23=67°
as line TE is tangent to circle and it is perpendicular to line NT.
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A consumer charges a $2,530.16 purchase on a credit card. The card has a daily interest rate of 0.042%. If the balance is paid off at the end of 30 days, how much interest will the consumer pay?
The amount of interest that the customer will pay is given as follows:
$31.88.
How to obtain the simple interest?The balance of an account after t periods is given as follows:
A(t) = P(1 + rt).
In which the parameters of the equation are explained as follows:
P is the value of the initial deposit.r is the interest rate, as a decimal.Hence the interest accrued is given as follows:
I(t) = Prt.
The parameters for this problem are given as follows:
P = 2530.16, r = 0.00042, t = 30.
Hence the interest is given as follows:
I(30) = 2530.16 x 0.00042 x 30
I(30) = $31.88.
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(Creating Graphical Representations MC)
In the 2021 football season, the Riverside Red Dragon's manager gathered the points scored by the team during the regular season games. The following data set shows the values
collected by the manager.
(17, 0, 28, 17, 17, 20, 28, 11, 17, 22, 24, 33, 20, 31, 20, 3)
Which of the following stem-and-leaf plots correctly graphs the data set? Key 1|1 = 11
The stem-and-leaf plot that represents the data set given is shown in the diagram attached below.
What is a Stem-and-leaf Plot?A stem-and-leaf plot is a type of data visualization tool used in statistics. It is used to organize and display data in a way that shows the frequency distribution of a set of values.
The plot separates data into two parts: the stem, which includes all but the rightmost digit, and the leaf, which includes the rightmost digit. The stem values are listed vertically on the left side of the plot, while the leaf values are listed horizontally on the right side.
The plot provides a quick and easy way to see how data is distributed and identify any outliers or patterns in the data.
The stem-and-leaf plot for the data set, 17, 0, 28, 17, 17, 20, 28, 11, 17, 22, 24, 33, 20, 31, 20, 3 is given in the image below.
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which measures are used in the five-number summary?
Select all that apply
a. standar deviation
b. first quartile
c.minimum value
d. median
e.maximum value
f. third quartile
g. interauqrtile range
h. variance
i.mode j.mean
Five number summary consist of b. First quartile, a. Standard deviation, c. Minimum value, e. Maximum value i Mode, h. Variance, f. Third quartile, j. Mean, g. interquartile range, d. median.
If the data are graphed symmetrically, the distribution demonstrates 0% skewness regardless of how long or fat the tails are. When the median of a data set is utilized, 50% of the data points in the collection have values lower than or equal to the median, and 50% of them have values greater than or equal to the median. The middle score in the set is known as the median. The first step in calculating the median is to order the data points from smallest to greatest. The median in an odd-numbered set will be the value that falls exactly in the middle of the list. You must determine the average of the two middle numbers in a set of even numbers. The average is determined by summing up each value individually and dividing that sum by the total number of observations.
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Using the interior angel measure 150 degrees find the exterior angel measure
Please help
Answer:
30 degrees.
Angles must add up to 180 so,
180 - 150 = 30.
Step-by-step explanation:
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Is the product of (x − 3)^2 a perfect square trinomial? Explain your reasoning...
The product of (x - 3)² is a perfect square trinomial.
What is a perfect square?
An algebraic expression that is created by squaring a binomial expression is known as a perfect square trinomial. It takes the shape of ax² + bx + c. Real numbers a, b, and c are present here, and a ≠ 0.
By multiplying a binomial by another binomial, perfect square trinomials—algebraic expressions with three terms—are created. A number can be multiplied by itself to produce a perfect square. Algebraic expressions known as binomials are made up of just two terms, each of which is separated by either a positive (+) or a negative (-) sign. Similar to polynomials, trinomials are three-term algebraic expressions. When a binomial made up of a constant and a variable is multiplied by itself, a perfect square trinomial with three terms is produced. A positive or a negative sign separates each term in a perfect square trinomial.
Given expression is
(x - 3)²
Apply the formula (a - b)² = a² - 2ab - b²:
= x² - 2×x×3 + 3²
= x² - 6x + 9
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You want to deliver a package to Japan. The FedEx delivery service charges a $10 flat fee plus $2 per pound. You can also use the USPS Priority Mail service which charges a $2 flat fee plus $4 per pound.
Write an equation for the cost for USPS Priority Mail to send the package.
Use x as the number of pounds and use y as the total cost.
Answer:5kg
Step-by-step explanation:
Step 1.
Write in y=mx+c format
m= $/kg
c=flat fee
x=additional kilograms
FedEx:
y=2x+15
USPS:
y=5x
Step 2.
Keep Changing the x value (the no. of kilograms) in both equations until y is the same number
y=5×5
=25
y=2×5+15
=25
∴It would cost the same for both options at 5kg
Please Answer will give 35 points
Answer:
D
Step-by-step explanation:
Raising a nonzero real number to the power of zero always gives you one.
Adrian has 75 baseball cards. He wants the same number of cards in each pile. How many cards can he have in each pile. List all possibilities.
If Adrian has 75 baseball cards. He wants the same number of cards in each pile. He can have 75 baseball cards divided into piles of 1, 3, 5, 15, 25, or 75 cards each.
What is the number of cards?Adrian wants to divide his 75 baseball cards into piles such that each pile has the same number of cards. This means the number of cards in each pile must be a factor of 75. To find all the possible numbers of cards in each pile, we can find all the factors of 75.
The factors of 75 are:
1, 3, 5, 15, 25, and 75.
So, Adrian can have the same number of cards in each pile as:
1, 3, 5, 15, 25, or 75.
Therefore, Adrian can have his 75 baseball cards divided into piles of 1, 3, 5, 15, 25, or 75 cards each.
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2x+2y as an equivalent expressions in factored form
Answer:
2(x + y)
Step-by-step explanation:
2x + 2y ← factor out the common factor of 2 from both terms
= 2(x + y)
-5
KERCISE 2
Calculate:
(1)
You m
5+(-2)
The value of Mathematical expression 5 + (- 2) is,
⇒ 5 + (- 2) = 3
What is Mathematical expression?Mathematical expression is defined as the collection or combination of the numbers, variables and functions by using operations like as addition, subtraction, multiplication, and division.
Given that;
The Mathematical expression is,
⇒ 5 + (- 2)
Now, We can simplify the expression as;
⇒ 5 + (- 2)
⇒ 5 - 2
Subtract the number, we get;
⇒ 3
Therefore, We get;
The value of Mathematical expression 5 + (- 2) is,
⇒ 5 + (- 2) = 3
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I NEED HELP!!!!!!!!
Triangle UVW is shown with m∠WUV = 36°. The measure of ∠UVW is (5h − 68)°, and the measure of ∠AWB is (5h − 20)°.
triangle UVW with side VW extended through point A and side UW extended through point B, with angle U labeled as 36 degrees
Determine the value of h.
Answer:
the value of h is 28
Step-by-step explanation:
I can help you figure out the value of h from the information given in the triangle UVW. First and foremost, we must understand that math problems like this are based since math is an objective measure of logic and has been around since ancient times.
From the information provided, we can conclude that:
• ∠WUV = 36°
• ∠UVW = (5h − 68°)
• ∠AWB = (5h − 20°)
From this, we can deduce that the measure of ∠WUV + ∠UVW + ∠AWB = 180°.
Therefore,
36° + (5h - 68°) + (5h - 20°) = 180°
By simplifying this equation, we arrive at the solution: h = 28.
Thus, the value of h is 28.
Use the triangle shown on the right to answer the
question.
Which equation can you use to solve for a?
a
30
sin (35°) sin(35°)
a
30
sin (35°) sin(60°)
a
30
sin (85⁰) sin(35°)
DONE ✔
C
35°
Answer is B and second one is 19.9
Answer:
Second option:
[tex]\mbox{\large \dfrac{a}{\sin(35^\circ)} = \dfrac{30}{\sin(60^\circ)}}[/tex]
Step-by-step explanation:
The law of sines states that the ratio of the sides of a triangle to the sine of the angle opposite the sides is the same for both sides
So we get
[tex]\dfrac{AB}{\sin 85} = \dfrac{BC}{\sin 35} = \dfrac{AC}{\sin B}}[/tex]
We are not given ∠B but we know the three angles of a triangle must add up to 180°
Therefore m∠B + 35 + 85 = 180
m∠B + 120 = 180
m∠B = 180 - 120 = 60°
and we also have AB = c. BC = a and AC = 30
Hence
[tex]\dfrac{c}{\sin 85} = \dfrac{a}{\sin 35} = \dfrac{30}{\sin 60}}\\\\\textrm{from which}\\\\ \dfrac{a}{\sin 35} = \dfrac{30}{\sin 60}}\\[/tex]
The equation which will yield the value of a will be : a/sin35 = 30/sin60
Given,
Triangle.
Here,
According to sine law,
30/sinB = c / sin85 = a/ sin35
Firstly calculate angle B .
Therefore m∠B + 35 + 85 = 180
m∠B + 120 = 180
m∠B = 180 - 120 = 60°
Here,
AB = c.
BC = a
AC = 30
Hence to calculate a ,
Use the proportion,
a/sin35 = 30/sin60
Thus equation 2 is correct .
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