The consecutive integers that are odd numbers are 17, 19 and 21.
How to determine the value of three consecutive integers
In this problem we need to find the values of three consecutive integers that odd integers such that the following equation is satisfied:
x₁ + x₂ = 3 · x₃ - 27
Please notice that two odd numbers are consecutive when their difference is 2.
x₁ + (x₁ + 2) = 3 · (x₁ + 4) - 27
2 · x₁ + 2 = 3 · x₁ + 12 - 27
2 · x₁ + 2 = 3 · x₁ - 15
17 = x₁
x₁ = 17
Thus, the three odd integers that are consecutive are 17, 19 and 21, respectively.
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f(x) = a(x - h)² + k.
f(x) = 3x² + 6x + 2.
Answer:
f(x) = 3(x + 1)² - 1a = 3, h = - 1, k = - 1
Step-by-step explanation:
It is assumed you need to convert the given function into vertex form.
Converting in below steps:
f(x) = 3x² + 6x + 2 = 3(x² + 2x) + 2 = 3(x² + 2x + 1) - 3 + 2 = 3(x + 1)² - 1We got:
a = 3, h = - 1, k = - 1An aircraft factory manufactures airplane engines. The unit cost C (the cost in dollars to make each airplane engine) depends on the number of engines made. Ifx engines are made, then the unit cost is given by the function C(x) = 0.5x ^ 2 - 150x + 26, 777 . How many engines must be made to minimize the unit cost?Do not round your answer.number of airplane engines________
EXPLANATION:
We are given the unit cost to produce x number of airplanes as follows;
[tex]C(x)=0.5x^2-150x+26777[/tex]However, to minimize the unit cost, we need to first take the derivative of the cost function and then find its value at zero.
Thuis is shown below;
[tex]C(x)=0.5x^2-150x+26777[/tex][tex]\frac{d}{dx}=2(0.5)x^{2-1}-1(150)x^{1-1}+0[/tex]Note that for a derivative, the constant term is always equal to zero. We can now simplify what we have above;
[tex]\frac{d}{dx}=1x^1-150[/tex][tex]\frac{d}{dx}=x-150[/tex]We now set this equal to zero and simplify;
[tex]x-150=0[/tex]Add 150 to both sides;
[tex]x=150[/tex]ANSWER:
Therefore, to minimize the unit cost, 150 engines must be made.
A house has increased in value by 38% since it was purchased. If the current value is $345,000, what was the value when it was purchased?
The formula for calculating the percent change over time is:
[tex]\begin{gathered} p=\frac{N-O}{O}\cdot100 \\ \text{ Where} \\ p\text{ is the percent change } \\ N\text{ is the new value } \\ O\text{ is the old value} \end{gathered}[/tex]In this case, we have:
[tex]\begin{gathered} p=38 \\ N=345000 \\ O=x \end{gathered}[/tex][tex]\begin{gathered} p=\frac{N-O}{O}\cdot100 \\ 38=\frac{345000-x}{x}\cdot100 \\ \text{ Multiply by x from both sides} \\ 38x=x\cdot\frac{345000-x}{x}\cdot100 \\ 38x=(345000-x)100 \\ \text{ Divide by 100 from both sides} \\ \frac{38x}{100}=\frac{(345000-x)100}{100} \\ 0.38x=345000-x \\ \text{ Add x from both sides} \\ 0.38x+x=345000-x+x \\ 1.38x=345000 \\ \text{ Divide by 1.38 from both sides} \\ \frac{1.38x}{1.38}=\frac{345000}{1.38} \\ x=250000 \end{gathered}[/tex]AnswerThe value of the house when purchased is 250,000.
36. The histogram shows the ages of the first 45 U.S. presidents on their firstInauguration Day.13TFrequency12111098765432104075Age (years)The ages of 20 of the 45 presidents are shown below.42, 43, 45, 46, 49, 52, 53, 54, 54, 57, 57, 58, 59, 61, 62, 62, 66, 66, 69, 72A certain president's age is in the interval labeled T.What could be the acceptable range for the interval?42 to 4443 to 4945 to 4947 to 54
Note that the graph shows us that the minimum and maximum value of the ages are 40 and 75, respectively.
We can count the number of bars on the histogram. We see that the are 7 bars in total.
Each bar consider the same age span, so that means that each bar represent an age span of the same amount of years.
To calculate this range, we first find the difference between the maximum and the minimum, that is
[tex]75-40=35[/tex]Now, we divide this number by the total number of bars. That is
[tex]\frac{35}{7}=5[/tex]So, each bar represents a range of 5 years .
Since the minimu is 40, this means that the first bar should represent ages from 40-44. Note that despite the difference between 44 and 40 is only 4, since we are including age 40 in the first bar, we have numbers 40,41,42,43,44 (5 numbers ) associated to the first bar.
This means that for the next one, which is the range T we are looking for, the correspondent age range should be 45-49
A scientist adds drops of liquid to a test tube. The test tube has marks every 1/5 ml.
Each drop contains 0.14 mL. Between which, two marks on the test tube will the liquid be after the sixth drop is added?
a. 1/5 and 2/5, between 0.2 and 0.4 mL's
b.2/5 and 3/5, between 0.4 and 0.6 ml's
c.3/5 and 4/5, between 0.6 and 0.8 mL's
d. 4/5 and 5/5, between 0.8 and 1 ml
The marks on the test tube where the liquid will be after the sixth drop is added is d. 4/5 and 5/5, between 0.8 and 1 ml.
How to calculate the value?From the information, the scientist adds drops of liquid to a test tube. The test tube has marks every 1/5 ml while each drop contains 0.14 mL.
In this case, it was stated that each drop is about 0.14mL. Therefore, it's important to note that the value of the 6th drop will be:
= Number of drops × Amount on each drop
= 6 × 0.14
= 0.84
In this case, 0.84 is between 0.8 and 1ml.
Therefore, the correct option is D.
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A bird flies downward 2 feet per second for 6 seconds. Then the bird flies up 7 feet. Which equation represents the total distance the bird travels
The equation that represents the total distance the bird travels would be; d = 1/3.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be one degree.
Given that bird flies downward 2 feet per second for 6 seconds. Therefore, the bird flies up 7 feet.
Since, a bird flies 2 feet = 1 second
Thus, for 6 seconds = 6 x 2 = 12 feet.
for 6 seconds = 12 feet.
Similarly, the bird flies up 7 feet = 6/12 x 7
= 42/12 = 3.5
Hence, the equation that represents the total distance the bird travels would be; d = 2/6 = 1/3.
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The perimeter of the figure is given. Find the length of the indicated side.?4x - 4Perimeter = 16x + 6The length of the indicated side is
Width = 4x + 7
Explanation:The perimeter of the rectangle shown = 16x + 6
The width of the rectangle = 4x - 4
Perimeter of a rectangle = 2(Length + Width )
16x + 6 = 2[ (4x - 4) x Width]
(16x + 6)/2 = (4x - 4) x width
8x + 3 = (4x - 4) x width
Width = 8x + 3 - (4x - 4)
Width = 8x - 4x + 3 + 4
Width = 4x + 7
How many different permutations can be formed using all the letters in the word COLORADO?
Ok, the number of different permutations are:
8!/3! (Considering the three O's)
round to nearest tenth 3.5÷2.29
Given
[tex]3.5\div2.29=1.528[/tex]Round to the nearest tenth, this is:
[tex]1.5[/tex]Answer: 1.5
hi please h3lp I have only 10 min to do this because it's due in 10 minutes and I've been trying to figure this out for a while
To graph the system
y ≤ 2x + 1
y < -x - 1
first, you have to graph the lines
y = 2x + 1
y = -x - 1
From the y-intercept and the slope, we know that the first line passes through the points:
(0, 1)
(0+1, 1+2) = (1, 3)
From the y-intercept and the slope, we know that the second line passes through the points:
(0, -1)
(0+1, -1-1) = (1, -2)
Next, we have to find if a point satisfies each equation or not, in order to know which region we have to shade. Taking for example the point (0, 0) and replacing it into the first inequality,
0 ≤ 2(0) + 1
0 ≤ 1
which is true, then we have to shade the region below the line y = 2x + 1
Replacing (0, 0) into the second inequality,
0 < -0 - 1
0 < -1
which is false, then we have to shade the region below the dotted line y = -x - 1
The final result is shown in the next picture.
This corresponds to graph X
6.
A mug is 3/7
full. The mug contains 1/2
of a cup of water. Find
the capacity of the mug. Write the
answer as a fraction or mixed
number in simplest form.
contains
The capacity of the mug is 7/6 cups.
What is the capacity of the mug?
Given,
A mug is 3/7 full.
The mug contains 1/2 of a cup of water.
Solution:
Let x be the water.
Water the mug has = 3/7 of x
= 3/7x
Since the water in the mug is 1/2 cup,
3/7x = 1/2
x = 1/2 ÷ 3/7
= 1/2 × 7/3
= 7/6
Therefore,
The capacity of the mug is 7/6 cups.
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Solution:17.Graph each system and determine the number of solutions that it has. If it has one solution,name it.A. X +2y=4y= -1/2x+2B. 2x-y=1y=-3
Systems of Equations
Given the system:
[tex]\begin{gathered} x+2y=4 \\ y=-\frac{1}{2}x+2 \end{gathered}[/tex]It's required to graph and find the solutions of the system.
Solving the first equation for y:
[tex]\begin{gathered} 2y=-x+4 \\ y=-\frac{1}{2}x+2 \end{gathered}[/tex]We can see both equations are exactly the same, so there is only one equation and one line.
Let's give x some values and graph the line.
x = 0:
[tex]\begin{gathered} y=-\frac{1}{2}\cdot0+2 \\ y=2 \end{gathered}[/tex]x = 2
[tex]\begin{gathered} y=-\frac{1}{2}\cdot2+2 \\ y=1 \end{gathered}[/tex]With the points (0, 2) and (2, 1) we graph the line as follows.
Since the number of equations is greater than the number of unknowns, the system has infinitely many solutions. For example, (0, 2) and (2, 1) are solutions for the system.
How do I graph this?
Select three x values and list them in a table to graph the equation. (Tip: pick values that are simple to calculate, such as 1, 0 and 1). To determine the associated y-coordinate, simplify the equation by substituting each value. Place the sorted pairings on a graph, and then draw a line between each point.
What is an equation graph?
Select three x values and list them in a table to graph the equation. (Tip: pick values that are simple to calculate, such as 1, 0 and 1). To determine the associated y-coordinate, simplify the equation by substituting each value. Place the sorted pairings on a graph, and then draw a line between each point.
example y = 1-1/3x,
x = -3,0,3,6
solution:
given x = -3,0,3,6 to above equation of a graph to get the points
y = 2,0,0,-1
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The slope of this line and the unit rate are the same.Price of Cookies at Bakery141210Find the unit ratefor the number ofcookies per dollar008Number of Cookies464[?] cookies$[ ]22 4 6 8 10 12 146 8Price ($)
SOLUTION
We want to find the unit rate for number of cookies per dollar. This can be done using the diagram below
So the unit rate is calculated thus
[tex]\begin{gathered} \text{Unit rate = }\frac{rise\text{ }}{\text{run}} \\ =\frac{14\text{ cookies }}{7\text{ dollars }} \\ =\frac{14}{7} \\ 2\text{ cookies per dollar} \end{gathered}[/tex]Hence the answer is 2
expand the square of a binomial (9y+2)^2
We will solve the following:
[tex](9y+2)^2=81y^2+36y+4[/tex]***Explanation***
We will have that in order to expand a polynomial of the form:
[tex](a+b)^2[/tex]We will proceed by using the following rule:
[tex](a+b)^2=a^2+2ab+b^2[/tex]In our case the solution for the given polynomial is [Step by step]:
[tex](9y+2)^2=(9y)^2+2(9y)(2)+(2)^2[/tex][tex]\Rightarrow(9y+2)^2=81y^2+36y+4[/tex]Referring to the figure, segment AB and segment NM are diameters of circle E. Find the angle of arc ACN
Since the segment MN is the diameter of the circle, the arc MACN has an angle with a measure of 180°, Then by adding the measures of the angles of the arcs MA, AC and CN we should get 180°, like this:
mMA + mAC + mCN = 180
By replacing 55° for mMA and 65° for mCN, we can solve for mAC to get:
55 + mAC + 65 = 180
120 + mAC = 180
120 - 120 + mAC = 180 - 120
mAC = 60
The measure of the arc ACN is calculated by adding the measures of the angles AC and CN, then we get:
mACN = mAC + mCN
mAC = 60 + 65
mAC = 125
Then, the angle of ACN has a measure of 125°
MATH please solve it now and let it be correct please
The value of X is ([tex](A-CB)^{-1}[/tex] CD.
Given,
AX[tex](D+BX)^{-1}[/tex] = C
Multiply both sides on the right by (D+BX):
AX[tex](D+BX)^{-1}[/tex] × (D+BX) = C × (D+BX)
AX ([tex](D+BX)^{-1}[/tex] (D+BX)) = C(D+BX)
AX × I = CD + CBX
AX = CD + CBX
Subtract CBX on both sides and factor:
AX – CBX = (CD + CBX) – CBX
AX – CBX = CD + (CBX – CBX)
AX – CBX = CD + 0
(A – CB)X = CD.
Multiply both sides on the left by [tex](A-CB)^{-1}[/tex] :
([tex](A-CB)^{-1}[/tex] × (A – CB)X = ([tex](A-CB)^{-1}[/tex] × CD
([tex](A-CB)^{-1}[/tex] × (A – CB)) X = ([tex](A-CB)^{-1}[/tex] CD
IX = ([tex](A-CB)^{-1}[/tex] CD
X = ([tex](A-CB)^{-1}[/tex] CD.
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1. Luna and Miles want to start selling baked goods to raise money for their gymnastics team to get new gear. Luna is baking double chocolate brownies with white chocolate chips and is selling them for $4 for each brownie. Miles is making oatmeal raisin cookies because that is his favorite and is selling them for $2 per cookie. Between the two of them they would like to raise $100. Write an equation in standard form and y intercept form to express the scenario. Identify one possible solution and explain what it means.
2.We can model real world situations given an equation, a table, or a graph. Identify a time when it would be better to use a table than a graph and explain why.
Using a system of equations, it is found that:
1.
Equation in standard form: 4x + 2y = 100.Equation in y-intercept form: y = -2x + 50.One possible solution is x = 10 and y = 30, meaning that she can sell 10 chocolate chips and 30 brownies.2. Tables are good for summarized data, that is, containing a few pairs of input - outputs solutions.
What is a system of equations?A system of equations is when multiple variables are related, and equations are built to find the numeric values of each variable, according to the relations built in the problem.
In the context of this problem, the variables are given as follows:
Variable x: number of chocolate chips sold.Variable y: number of cookies sold.Considering that they want to raise $100, and the prices of $4 for each chocolate chip and of $2 for each brownie, the equation is:
4x + 2y = 100.
In intercept form, the equation is given by:
2y = 100 - 4x
y = -2x + 50.
When x = 10, the solution of the system for y is given as follows:
y = -2(10) + 50 = -20 + 50 = 30.
Hence one possible solution is (x,y) = (10,30), meaning that she can sell 10 chocolate chips and 30 brownies.
In this question, we are given pairs of input-output that satisfy the given condition, hence tables are more appropriate than graphs.
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Answer:
1. 100=4x+2y and y = -2x+50
X=19, and Y=12
2. Graphs are better for showing trends. tables are better for showing precise data.
Step-by-step explanation:
Luna makes $4 per cookie, so her equation for her income is 4x. Miles makes $2 per cookie, so his equation is 2y. Since they want to make $100, that means that 100 = 4x+2y. Then put this in y-inercept form. Or, y=-2x+50
So now I need to find a solution for y = -2x+50, or 100=4x+2y. One way to do this is through substitution. We can use 12 as the y input.
This would mean that miles sold 12 brownies. Then, ---> = 19.
Therefore, a solution is x=19 and y=12. Meaning Luna sold 19 cookies and Miles sold 12 cookies. (19,12)
what will the temperature of the juice be 9 minutes after she puts it in the freezer?round off the answer to nearest degree Fahrenheit.
Let the formula be for time in seconds
Thus, we have:
[tex]T(t)=T_a+(T_0-T_a)e^{-kt}[/tex]T_a would be the freezer temperature, 4
T_0 would be the initial temp, which is 73
t is the time [9 minutes afterwards, t = 9]
k is 0.05
Substituting, we get:
[tex]\begin{gathered} T(t)=T_a+(T_0-T_a)e^{-kt} \\ T(9)=4_{}+(73-4_{})e^{-(0.05)(9)} \\ T(9)=4+69e^{-0.45} \\ T(9)\approx48 \end{gathered}[/tex]To nearest degree Fahrenheight, T = 48 degrees F
Answer: 47 degrees celcius
Step-by-step explanation:
David buys milk and lemons at the store.
.
. He pays a total of $40.01.
• He pays $2.89 for the milk.
• He buys 8 bags of lemons that each cost the same amount.
.
Which equation could be used to determine b, how much each bag of lemons costs?
Can someone tell
Me the equation could be used yo determine b, how much each bag of lemon cost
I'm not sure the right equation that we need to used for this problem.
The solution is, :
8x = 40.01 -2.89, is the equation could be used to determine b, how much each bag of lemons costs.
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.
here, we have,
given that,
David buys milk and lemons at the store.
. He pays a total of $40.01.
• He pays $2.89 for the milk.
• He buys 8 bags of lemons that each cost the same amount.
Cost of 1 bag of lemons = $ x
Cost of 8 bags of lemons = 8 *x = 8x
Cost of 8 bags of lemons = Total cost - cost of the eggs
8x = $40.01 - $2.89
so, 8x = 40.01 -2.89, is the equation.
Hence, The solution is, :
8x = 40.01 -2.89, is the equation could be used to determine b, how much each bag of lemons costs.
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compare the ratio of 3:5 and 4:7
Answer:
Step-by-step explanation:
The least common multiple of the denominators 5 and 7 is 35. Make the denominators of the fractions as 35 using multiplication. Compare the numerators. So, 3 : 5 is greater than 4 : 7.
Hope this helps!
67 km 230 m + 11 km 879 m
Answer:
79.10900 kilometers
Step-by-step explanation:
Answer:
79 kilometers 109 meters
help me pleasee!!
thank you <3
the interval notation is [-7,8] but i have no idea what roster notation is
Find the mean for the amounts: $17,482: $14,987; $13,521: $14,550; $18,570; $14,981
We have the following data set
17482
14987
13521
14550
18570
14981
there are 6 values, so we can find the mean by adding them all and dividing by 6
[tex]\operatorname{mean}=\frac{17482+14987+13521+14550+18570+14981}{6}=15681.83[/tex]Then, the mean is $15,681.83
Stephanie weighed a gallon of water that measured 8.75 pounds. A gallon of water should weigh 8.33 pounds. What is Stephanie’s percent of error?
Considering the definition of percent of error, the Stephanie’s percent of error in this case is 5.042%.
Definition of percent of errorPercent of error is a measure of how inaccurate a measurement is, standardized based on the size of the measurement.
In other words, the percent of error allows knowing the differences between the estimated value and the real value. The error may be due to the measurement method (tool or human error) or due to approximations used in the calculation (for example, rounding errors).
To calculate the percent of error you must:
Subtract the real value from the estimated value.Divide the result by the real number.Determines the absolute value of the result. The absolute value of a number is its distance from zero on a number line. Thus, the absolute value of a positive number is the number itself, and the absolute value of a negative number is its opposite.Multiply the result by 100 to get the value in percentage.Therefore, the expression for calculating the percent of error is
percent of error= [|real value - estimated value|÷ real value]×100
Stephanie’s percent of errorIn this case, you know:
Real value= 8.33 poundsEstimated value= 8.75 poundsReplacing in the definition of percent of error:
percent of error= [|8.33 pounds - 8.75 pounds|÷ 8.33 pounds]×100
Solving;
percent of error= [|-0.42 pounds|÷ 8.33 pounds]×100
percent of error= [0.42 pounds÷ 8.33 pounds]×100
percent of error= 0.05042×100
percent of error= 5.042%
Finally, the percent of error in this case is 5.042%.
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Solve each equation by using the method of your choice. Find exact solutions.
Given the quadratic equation:
[tex]16x^2-24x-27=0[/tex]To find the solutions for the given equation you have to apply the quadratic formula:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Where
a is the coefficient of the quadratic term
b is the coefficient of the x-term
c is the constant of the equation
For this equation, a= 16, b= -24, and c= -27, replace the values into the formula:
[tex]\begin{gathered} x=\frac{-(-24)\pm\sqrt[]{(-24)^2-4\cdot16\cdot(-27)}}{2\cdot16} \\ x=\frac{24\pm\sqrt[]{576+1728}}{32} \\ x=\frac{24\pm\sqrt[]{2304}}{32} \\ x=\frac{24\pm48}{32} \end{gathered}[/tex]Solve the addition and subtraction separately to determine both possible values of x:
-Addition:
[tex]\begin{gathered} x=\frac{24+48}{32} \\ x=\frac{72}{32} \\ x=\frac{9}{4} \end{gathered}[/tex]-Subtraction
[tex]\begin{gathered} x=\frac{24-48}{32} \\ x=-\frac{24}{32} \\ x=-\frac{3}{4} \end{gathered}[/tex]The solutions of the quadratic equation are x=9/4 and x=-3/4
Order the sides of the triangle from shortest to longest. (HINT: You need to find the missing angle first!) 85 40° X V
To find the missing angle we use that the sum of the inner angles of a triangle must add up 180º:
[tex]\angle W+\angle V+\angle X=180º[/tex]We know W and V, so we clear X:
[tex]\angle X=180º-\angle W-\angle V=180º-80º-40º=60º[/tex]To order the sides, you don't need the size of them. Let's take a look at the angles:
So, since the angle with vertex on W is the widest, the opposite side to it (the segment XV) will be the longest. Then, the second angle is the one in X, so the second largest side will be it's opposite side (segment WV).
And finally but not last, the shortest side will be the oposite one to the narrowest angle, the one in V.
In summary, the sides ordered from shortest to longest are: c-a-b
A die is toss three times let X be the sum of three numbers obtainedDetermine whether the random X has a binomial distribution if so take the number of trails N . If it doesn’t explain why
The given experiment is a die that is tossed three times.
X is the sum of the three numbers obtained.
You need to determine if the random X variable has a binomial distribution.
First, we need to understand what makes a random variable has a binomial distribution. There are 4 conditions to be met:
1. There are a fixed number of trials N
2. Each trial has only two possible outcomes: success or failure
3. The probability of success is equal in each trial
4. The trials are independent.
In this case, condition 1 is met, but condition 2 is not met, since in each trial we can obtain 6 different numbers, then there are not only two possible outcomes, but 6, then the sum of the three numbers has more than two possible outcomes. So, the random X variable doesn't have a binomial distribution.
I need help in math can you help me please
Given that the triangles are corresponding triangles, then ∠B ≅ ∠E, therefore:
m∠B = m∠E
Replacing with data:
3v + 4 = 8v - 6
3v is adding on the left, then it will subtract on the right
6 is subtracting on the right, then it will add on the left
4 + 6 = 8v - 3v
10 = 5v
5 is multiplying on the right, then it will divide on the left
10/5 = v
2 = v
Then, the measure of B is:
m∠B = 3v + 4 = 3(2) + 4 = 10°
The measure of angle B is 10°
For his phone service Bob pays the monthly fee of $30 and he pays an additional five cents per minute of use. At least he has been charged in a month is $94.70. What are the possible numbers of minutes he has used his phone in a month? Use m for the number of minutes and solve you’re in equality for m.
We can write an expression for the cost of Bob's phone service as follows:
First, remember that five cents are 0.05 dollars.
[tex]C=30+0.05m[/tex]Where C is the cost and m are the minutes.
We know that at least he has been charged in a month is $94.70.
We can express this as an inequality:
[tex]30+0.05m\ge94.70[/tex]To find the possible number of minutes, we have to solve the previous equation for m. This is:
[tex]\begin{gathered} 0.05m\ge94.70-30 \\ 0.05m\ge64.70 \\ m\ge\frac{64.70}{0.05} \\ m\ge1294 \end{gathered}[/tex]Therefore, the possible numbers of minutes he has used in his phone in a month are:
[tex]m\ge1294[/tex]