a cell phone company charges an initial price of $400 for a new phone and then $50 each month after the purchase. if c (t) is a rational function that represents the average monthly cost of owning the cell phone, what is the range of the function? r: ℝ r: (–[infinity], [infinity]) r: (0, 400) r: (50, 450)
The range of the average cost function of a cell phone that has an initial and monthly costs $400 and $50 is r:(50, 400)
Which method can be used to find the range of the average cost function?Initial price for the cell phone = $400
Charges per month after purchase = $50
The rational function representing the average monthly cost = c(t)
Required; The range of the average monthly cost function, c(t)
Solution:
The total cost of owning the cell phone, C, is therefore;
C = 400 + 50•∆tWhere;
∆t = The number of months after purchase
The average monthly cost is therefore;
[tex]c(t) = \frac{C}{ \Delta t} [/tex]
At ∆t ≈ 0, we have;
C ≈ 400
The cost for the month at ∆t ≈ 0, is therefore, c(t) = $400
At ∆t ≈ ∞, we have;
[tex] \lim\limits_{∆t→∞} \frac{400}{ ∆t} = 0[/tex]Therefore;
[tex] \lim\limits_{∆t→∞} c(t) = \frac{400+ 50× ∆t}{ ∆t} ≈ 50[/tex]
Which gives;
The range of c(t) is (50, 400)
The correct option is therefore;
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Aliza needs to run at a rate faster than 8.2 feet per second in order to exceed her fastest time in a race. After running for 15 minutes, her coach determines that she is running at an average rate of 5.8 miles per hour. He converts the average rate to feet per second as shown below:
He concludes that she is not running fast enough to exceed her fastest time.
Coach's errors are;
Wrong conversion when converting hour to seconds
There is wrong conclusion since Eliza was running fast enough at a speed of 34ft/s compared to 8.8ft/s
The speed required by eliza is 8.8 ft/s
Converting 5.8miles to feet per second
Taking the coach conversion
This shows that 5.8mi/hr is equivalent to 34.0ft/s in accordance with coach conversion rate.
The coach made the first error by taking 60s as 1hr instead of 3600s as 1hr
The mistake that Eliza is not running fast enough to exceed her fastest time. Eliza is running at pace as her speed at 34ft/s exceed 8.8ft/s.
Hence the second error was the wrong conclusion made by the coach.
The average rate is a measure of how much the function changed per unit, on average, over that interval. It is founded from the slope of the line connecting the interval's endpoints on the function's graph.Learn more about average rate here:
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consider the line y=-7x-1 what is the slope of a line perpendicular to this one
Answer:
1/7
Step-by-step explanation:
y = -7x - 1 so slope is -7
The slopes of two perpendicular lines are negative reciprocals of each other
so negative reciprocal of -7 is 1/7
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]y = \stackrel{\stackrel{m}{\downarrow }}{-7}x-1\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
thus a line perpendicular to that slope will have a slope of
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{-7}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{-7}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{-7}\implies {\LARGE \begin{array}{llll} \cfrac{1}{7} \end{array}}}}[/tex]
An investigator wants to test for the presence of simple sugars in a sample. She adds reagent to her sample and also to a sample of distilled water. What reagent should she have added?.
The investigator can test the presence of simple sugars in the sample by using Benedict's solution.
What is Benedict's test ?Simple carbs are tested for using Benedict's Test. With free ketone or aldehyde functional groups, reducing sugars (monosaccharides and some disaccharides) are recognized by the Benedict's test.
What is Benedict's solution?Benedict's solution turns orange or brick red when heated in the presence of simple carbohydrates. The reducing characteristic of simple carbs is what triggers this response. The Benedict's solution changes color as a result of the reduction of copper (II) ions to copper (I) ions.
The produced red copper(I) oxide precipitates out of solution because it cannot be dissolved in water. This explains how the precipitate was created. The closer the final hue is approaching brick-red and the more precipitate is generated as the reducing sugar concentration rises. Copper oxide, a brick-red solid, can occasionally precipitate out of a solution and gather at the test tube's bottom.
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question 9(multiple choice worth 5 points) (04.02 mc) orio and ted buy an equal number of comic books every month. the following equation shows the number of comic books, y, that orio has after x months: y
Orio and Ted buy an equal number of comic books every month. Orio has 9 more comic books than Ted.
What are a definition and an example of a linear equation?
A linear equation is an algebraic equation with each term having an exponent of 1, and a straight line is produced when the equation is graphed. Y=mx+b is an illustration of a linear equation.The following equation shows the number of comic books, y, that Orio has after x months:
y = 2x + 15
Using the equation y=mx+b to find Orio's number of comic books, we can plug 2 months to substitute for the variable x.
y = 2(2) + 15
y = 4+15,
y = 19.
We know Ted has 10 comics after 2 months from the graph.
19-10= 9
Therefore, Orio has 9 more comic books than Ted.
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The complete question is -
Orio and Ted buy an equal number of comic books every month. The following equation shows the number of comic books, y, that Orio has after x months: y = 2x + 15 The following graph shows the number of comic books, y, that Ted has after x months: Graph shows Months on x axis and Number of Comic Books on y axis. The scale on x axis is shown from 0 to 5 at increments of 1. The scale on y axis is shown from 0 to 14 at increments of 2. The title of the graph is Teds Comic Books. A straight line is shown which joins the ordered pair 0, 6 and 4, 14 After 2 months, how many more comic books does Orio have than Ted?
If $5 deposited is represented by +$5, how can $3 withdrawn from the bank
be represented
Answer:
-3
Step-by-step explanation:
Taking out 3 would give you a negative number
1.2.PS-12
Determine whether the given number belongs to each set.
Integers
72
72
Whole
Numbers
?
Vyriole
Numbers
Yes
?
integers
Yes
Rational
Numbers
?
Katorial
Numbers
No
Click to select your answer(s) and then click Check Answer.
All parts showing
Clear All
Answer: Yes it is rational number because it has a terminating decimal expansion
Step-by-step explanation:
Define Rational number:
rational number, in arithmetic, a number that can be represented as the quotient p/q of two integers such that q ≠ 0. In addition to all the fractions, the set of rational numbers includes all the integers, each of which can be written as a quotient with the integer as the numerator and 1 as the denominator.
Yes it is rational number because it has a terminating decimal expansion.
7/2=3.5
Define Integer:
An integer is a whole number (not a fractional number) that can be positive, negative, or zero. Examples of integers are: -5, 1, 5, 8, 97, and 3,043. Examples of numbers that are not integers are: -1.43, 1 3/4, 3.14.
all integers between -7 and 2 in increasing order are:
-6,-5,-4,-3,-2,-1,0 and 1.
since, it has to be in increasing order -6 will come first and 1 at the last.
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The label on a car's antifreeze container claims to protect the car between -40°C and 125°C. To covert Celsius temperature to Fahrenheit temperature, the formula is C = 5/9 (F - 32). Write a compound inequality to determine the Fahrenheit temperature range at which the antifreeze protects the car.
The compound inequality to determine the Fahrenheit temperature range is given by [tex]-40 < \frac{5}{9}(F-32) < 125[/tex] .
An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The most frequent application is to size-compare two numbers on a number line.
Inequality is represented by:
The notation x < y means that x is less than y.The notation x > y means that x is greater than y.The notation x ≤ y or x ⩽ y means that x is less than or equal to y The notation x ≥ y or x ⩾ y means that x is greater than or equal to yA compound inequality is of the form : a < x < b implies that the value of x lies between the values of a and b.
According to the question if temperature is denoted in Celsius the inequality can be written as : -40° < °C < 125°
Now we know that the relation between C and F can be written as
[tex]C=\frac{5}{9}(F-32)[/tex]
Therefore the required inequality will be of the form:
[tex]-40 < \frac{5}{9}(F-32) < 125[/tex]
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the biggest advantage of correlational research includes: multiple choice question. the use of important manipulated variables. the use of important variables in a real-world setting. the ability to draw causal conclusions. the use of random assignment.
We can actually deduce here that the biggest advantage of correlational research is: The use of important variables in a real-world setting.
What is correlational research?A correlational research is actually known to be the research that investigates relationships between two variables or more. It does this without the researcher trying to manipulate or control any of the variables.
Correlational research is known to be a non-experimental type of quantitative research. In this research, the researcher assesses the statistical relationship that exists between the variables.
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name the sides of the angle.
Which of these is a non-real complex number?
(i) Simplify
n²-(n+ a)(n-a).
(ii) Hence evaluate
326541 8292-326541833 x 326541 825.
Answer: 16
Step-by-step explanation:
[tex]n^2-(n+a)(n-a)=\\n^2-(n^2-a^2)=\\n^2-n^2+a^2=\\a^2[/tex]
[tex]326541829^2-326541833*326541825=\\32654129^2-(32654129+4)(326541129-4)=\\4^2=\\4*4=\\16[/tex]
Find the measure of LBOD
m LBOD=
Classify LBOD
The measure of angle BOD is 65°
Calculating measure of anglesFrom the question, we are to determine the measure of angle BOD (m ∠ BOD)
The measure of angle BOD can be determine from the given protractor.
To determine the measure of angle BOD, we will read from line BO, in the counterclockwise direction, to line DO.
Reading in the counterclockwise direction, line BO is on 0°, and line DO is on midpoint of 60° and 70°.
The midpoint of 60° and 70° is 65°
Hence, the measure of angle BOD is 65°.
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URGENT!! ILL GIVE BRAINLIEST! 100 POINTS
Please answer the 2 question in photo [ Brainliest + points ]
Answer:
3.) Obtuse &. 4.) Acute. ????
Step-by-step explanation:
Answer:
3. obtuse
4. acute
Step-by-step explanation:
Hope this helps
Four representations of the same data are shown below.
Verbal Description
Shay pays a $4 monthly fee in addition to the data and minutes charges on her cell phone bill, x.
Equation
y = x + 4
Table
A 2-column table with 3 rows. Column 1 is labeled x with entries 30 dollars, 40 dollars, 50 dollars. Column 2 is labeled y with entries 34 dollars, 44 dollars, 54 dollars.
Graph
Cell Phone Bill
A graph with data/minutes charges on the x-axis and total bill on the y-axis. A line goes through points (0, 4) and (3, 7).
Which two representations are considered to be only partial representations?
the equation and the verbal description
the verbal description and the graph
the table and the equation
the graph and the table
Mark this and return
The two representations which are considered to be only partial representations include the following: D. the graph and the table.
What is a function?A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for mapping an input variable to an output variable.
What is a graph?A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.
In this scenario, the following are complete representations of the same data because they are valid for all possible x values:
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which expression shows the prime factorization of 40? 2 × 2 × 5 2 × 2 × 5 2 × 2 × 2 × 5 2 × 2 × 2 × 5 2 × 5 × 5 2 × 5 × 5 2 × 5 × 5 × 5
The expression 2×2×2×5 shows the prime factorization of 40.
Prime factorization:
The number 40 is equal to
2 x 2 x 2 x 5, or = 40
23 x 5. = 40
What does prime factorization serve as?In mental arithmetic, fractions, finding square roots, and computing the HCF and LCM of two smaller numbers, prime factorization is a highly helpful tool when working with whole numbers. A whole number higher than 1 whose only elements are 1 and itself is referred to as a prime number. A whole number that may be split evenly into another number is referred to as a factor.
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Answer:
2 × 2 × 2 × 5
Step-by-step explanation:
2 × 2 × 2 × 5 = 4 × 2 × 5 = 8 × 5 = 40
Please help
Isolate a variable in each system. You may need to use the distributive property to simplify the equation. Show your work.
Answer:
it's true, not false.
Step-by-step explanation:
it's true, not false.
Describe two ways in which you can solve: [tex]-\frac{1}{2} (5x-9)=17[/tex]
Answer:
Method 1 is distribution of the -1/2 to 5x and -9. Method 2 is simplification by multiplying -1/2 to both sides of the equation.
Step-by-step explanation:
Method 1: Method 2:
[tex]-\frac{1}{2} (5x-9)=17[/tex] [tex]-\frac{1}{2} (5x-9)=17[/tex]
[tex]-\frac{1}{2}[/tex](5x-9)=17 [tex]-\frac{1}{2}[/tex](5x-9)=17
[tex]-\frac{1}{2}[/tex]*5x-([tex]-\frac{1}{2}[/tex]*9)=17 [tex]-\frac{1}{2}[/tex]*(-2)(5x-9)=17*(-2)
[tex]-\frac{5}{2}[/tex]x+([tex]\frac{1}{2}[/tex]*9)=17 5x-9=-34
[tex]-\frac{5}{2}[/tex]x+9/2=17 5x-9+9=-34+9
([tex]-\frac{5}{2}[/tex]x+9/2=17)*2 5x=-25
-5x+9=34 5x/5=-25/5
-5x+9-9=34-9 x=-5
-5x=25
-5x/(-5)=25/(-5)
x=-5
Broo someone help pllss
========================================================
Explanation:
15 - 2.5x is the same as 15 + (-2.5)x
Then we can swap the terms to get -2.5x+15
Therefore, the original equation is the same as -2.5x+15 = 40
To solve this equation, we follow PEMDAS in reverse. So instead of starting with the "P", we start with the "S". There's no subtraction operations to undo, so we move onto the "A". There is an additional operation to undo, which is the +15
To undo the +15, we subtract 15 from both sides
-2.5x+15 = 40
-2.5x+15-15 = 40-15
-2.5x = 25
The next step after this would be to divide both sides by -2.5 to undo the multiplication. The -2.5x means "-2.5 times x".
(14) Given L lI M || N, find the value of x.
Based on the corresponding angles theorem, the value of x is: 64°.
What is the Corresponding Angles Theorem?When two angles that are formed by a transversal and two parallel lines lie in relative position to each other on each of the parallel lines, they are called corresponding angles. According to the corresponding angles theorem, both angles are congruent to each other.
Angle x and 64 degrees are corresponding angles. They are therefore congruent to each other.
Thus, x = 64° [corresponding angles theorem]
In summary, based on the corresponding angles theorem, the value of x is: 64°.
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A square field has an area of 22,500 square feet. To the nearest foot, what is the diagonal across the field?
The length of the diagonal across the field is 212.132 feet.
What is a square?A rectangle whose all sides are equal is called a square.
A square is always a rectangle, parallelogram, and a quadrilateral but its reverse statement may or may not be true.(ie it is not always necessary that a rectangle is a square or a parallelogram is a square).
Given that a square field has an area of 22,500 square feet. Now, the length of the side of the square field can be written as,
Area of the square field = (Length of square field)²
22,500 square feet = (Length of square field)²
Length of square field = √(22,500 sq. feet)
Length of square field = 150 feet
Now, the length of the diagonal of the field can be written as,
(Length of the diagonal)² = 2(Length of the side of square field)²
(Length of the diagonal)² = 2(150²)
(Length of the diagonal)² = 45,000 sq. feet
(Length of the diagonal) = 212.132 feet
Hence, the length of the diagonal across the field is 212.132 feet.
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b) Find the values of y.
y² = 169
I wrote that it equals to 13 but it’s not right. Please help!!
Arnie decides to make 3 cups of dark orange paint and 3 cups of light orange paint. How many ounces of yellow paint does he need?
Answer:
6.0 ounces
Step-by-step explanation:
If f(x-1)=x³+3x²-3x+7, find f(1)
Answer: f(1)=21
Step-by-step explanation:
f(x-1)=x³+3x²-3x+7
f(x-1)=(x-1+1)³+3(x-1+1)²-3(x-1+1)+7
f(1)=(1+1)³+3(1+1)²-3(1+1)+7
f(1)=(2)³+3(2)²-3(2)+7
f(1)=8+3(4)-6+7
f(1)=8+12+1
f(1)=21
A case of 24 pairs of the same kind of sports shoes costs a little more than $800. Explain whether $28 per pair with tax included is a good estmate of the price
Answer:
$ 33.33
Step-by-step explanation:
can you make me brainliest pls
1. Is x = 2, y = 6, z = 1 a solution to the system of equations? Explain.
1.5x + y-z = 8
x + 3y = 18
2y + z = 13
2. If y = 6, find the values of and z.
x
4x+y=z=15
x + 2y + z = 38
The solution to the system of equation is x = 6, y = 4, z = 5
The equation is
1.5x + y - z = 8
x + 3y = 18
2y + z = 13
From this we have,
y = 8 - 1.5x + z
x + 3y = 18
2y + z = 13
x + 3(8 - 1.5x + z) = 18
2(8 - 1.5x + z) + z = 13
Apply the Distributive Property
x + 24 - 4.5x + 3z = 18
16 - 3x + 2z + z = 13
Combine like terms
-3.5x + 24 +3z = 18
16 - 3x + 3z = 13
Rearrange variables to the left side of the equation
-3.5x + 3z = 18 - 24
-3x + 3z = 13 - 16
Subtract the two equation
-3.5x + 3z - (-3x + 3z ) = 18-24 - ( 13-16)
-3.5x + 3z + 3x -3z = 18 - 24 - 13 + 16
-3.5x + 3x = 18 - 24 - 13 + 16
x = 6
Substitute the value of x in one of the equation
-3×6 + 3z = 13 - 16
-18 + 3z = -3
3z = 15
z = 5
Now put the value of x and z
y = 8 - 1.5x + z
y = 8 - 1.5×6 + 5
= 8 -9 + 5
= 4
Therefore the solution to the system of equation is x= 6, y = 4 and z = 5
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if m<4=35 degrees, find m<2 and m<3
35, ∠2 and ∠4 are alternate interior angles, so m∠2 = m∠4.
What is alternate interior angles?
Two angles that are on the interior of and, but on different sides of the transversal, are said to be alternate interior angles. The alternate interior angles theorem states that the alternate interior angles must be congruent if two parallel lines are cut by a transversal.Given
m∠4=35
From the image given, angle 2 and angle 4 lie on opposite side of the line that intercepts the two parallel lines, AB and CD. Angle 2 and angle 4 both lie within the parallel lines.
Therefore, ∠2 and ∠4 are alternate interior angles.
Thus,
m ∠2 = m∠4 (alternate interior angles theorem)
since m∠4 = 35°
therefore m∠2 = 35°
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Use the expression 5x + 2y + 9 − 7 to identify: a. The terms, b. The coefficients, c. The constants.
The required answers are,
a. The terms - 5x, 27, 9, -7
b. The coefficients - 5 and 2
c. The constants - 9 and -7
What is an expression?An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.
Now the given expression is 5x + 2y + 9 − 7
Now the terms in the equation are 5x, 27, 9, -7
Therefore,
Terms = 5x, 27, 9, -7
Now coefficient is a number or any symbol representing a constant value that is multiplied by the variable.
So the variables in the given expressions are x and y.
And their multiples are 5 and 2, 5 is in multiplication of x and 2 is in multiplication of y.
Thus, coefficients are, 5 and 2
or, Coefficients = 5 and 2
Now th constants are the numbers that are not in multiplication with the variable. Thus, their value remains unchanged.
So in the given expression 9 and -7 are the constants that are not in multiplication with the variables.
Thus,
Constants = 9 and -7
Hence we get,
Terms = 5x, 27, 9, -7
Coefficients = 5 and 2
Constants = 9 and -7
Thus, the required answers are,
a. The terms -5x, 27, 9, -7
b. The coefficients - 5 and 2
c. The constants - 9 and -7
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help 32. (a) and (b)
Answer:
Below
Step-by-step explanation:
a) He answered 9 questions, lets say that he answered all 9 correctly
= 9x5 = 45 points (highest)
b) He answered 9 questions, lets say that he answered them all wrongly
0-(5x9)
0-45
-45