The solution to the given inequality would be n ≤ 1/35 which is the correct answer would be an option (C).
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
We have to determine the solution of the inequality n minus three-fifths is less than or equal to negative four sevenths for n.
As per the given condition, translate the phrase into an algebraic inequality as :
⇒ n - 3/5 ≤ - (4/7)
⇒ n ≤ 3/5 - (4/7)
⇒ n ≤ (21 - 20)/35
⇒ n ≤ 1/35
Therefore, the solution to the given inequality would be n ≤ 1/35.
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Please help asap brainlyest to the best answer
Answer:
All of them work.
Step-by-step explanation:
An invertible function can be tested for by the horizontal line test. An function is not invertible is a horizontal line drawn anywhere crosses two or more points. A straight line is an invertible function as long as the slope is not equal to 0. With that, let's check A. From x = -6 to -4, the horizontal line test does not cross two points anywhere. A works. Let's check B. B also works because it passes the horizontal line test. C also works.
Aaquib can buy 25 liters of regular gasoline for $58.98 or 25 liters of permimum gasoline for 69.73. How much greater is the cost for 1 liter of premimum gasolinz? Round your quotient to nearest hundredth. show your work :)
The cost for 1 liter of premimum gasolinz is 1. 182 times greater
What is ratio?
A ratio can be described as the ordered pair of numbers, like x and y, written in the form of a rational numbers, x/y with the denominator greater than zero.
It is also described as the number of times a number or element would contain another one.
It is also known to compare two quantities, elements or numbers.
From the information given, we have that;
25 liters of regular gasoline is $58.9825 liters of permimum gasoline for $69.73To determine the value, we have;
Cost of 1 liter of 25 liters in permimum gasoline/Cost of 1 liter of 25 liters in regular gasoline
substitute the values
$69.73/ $58.98
Find the quotient
1. 182
Hence, the value is 1. 182
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The height of an item falling can be modeling by h^t=-16t^2+h^o. Where h^o is the initial height in feet, and h^t is the height in feet at time t in seconds. If I drop at a height of 18.9 feet,how long will it take the item to hit the ground.A. 2.09B.1.09C.1.19D.0.09
h(t) = -16t^2+h^0
object falls untill height becomes 0, so h(t) =0, h^0 = 18.9feet
0 = -16t^2 + 18.9
-18.9= -16t^2
-18.9/-16 = -16t^2/-16
t^2=1.18125
[tex]\begin{gathered} t\text{ =}\sqrt[]{1.18125} \\ t\text{ = 1.09sec} \end{gathered}[/tex]ANSWER= OPTION B
Jordan wants to solve the following system using the elimination method:2x + 3y = 10x + y = 7what numbers should the equation x + y = 7 be multiplied by to eliminate ya. -2b. 2c. -3d. 3
In elimination method one equation is multiplied by the negative coefficient of the other
so then in this case y have coefficient 3, the other equation have coefficient y is 1 . Then divide 3/1 = 3 and change sign ,gives -3.
Then the final answer is -3, option c)
According to a study of the power quality (sags and swells) of a transformer, for transformers built for heavy industry, the distribution of the number of sags per work has a mean of 346 with a standard deviation of72. Of interest is x, the sample mean number of sags per week for a random sample of 216 transformers. Completo parts a through d below.a. Find E(%) and interpret its valueE() -(Type an integer or a decimal. Do not round.)Interpret the value of E(). Select the correct choice below and fill in the answer box to complete your choice(Type an integer or a decimal. Do not round.)O A. For any random sample of 216 transformers, the mean number of sags por wook is always. B. 1 many random samples of 216 transformers are taken, then the mean of the sample variances is sags por wookOC. If many random samples of 218 transformers are taken, then the mean of the sample mean numbers of sags per week isOD. I many random samples of 216 transformers are taken, then the mean of the sample standard deviations is sags por wookb. Find Var()Var) -(Type an integer or a decimal Round to three decimal places as needed.)c. Describe the shape of the sampling distribution of Xwith mean - and standard deviation -(Type intogors or decimal Round to three decimal places as needed)The sampling distribution of xd. Howey is it to observe a sample mean number of sags por wook that exceeds 3007C
Given data:
Population Mean = 346
Standard Deviation = 72
Expected Value of e(x) = population mean = 346
Sample Size = 216
In this case, if many random samples of 216 are taken, then the mean of the sample mean numbers per week is 346. (Option C)
To solve for the variance of x or var(x), we follow the formula below:
[tex]var(x)=\frac{\sigma^2}{n}=\frac{(s\tan darddeviation)^2}{\text{sample size}}[/tex]In this case, the given standard deviation is 72 and the sample size is 216. Therefore, we have:
[tex]var(x)=\frac{72^2}{216}=\frac{5184}{216}=24[/tex]One of the properties of the Sampling Distribution of the Mean is that the sampling distribution of the mean is approximately normally distributed so long as the sample size is 30 or higher. Our sample mean here is 346 with a sample standard deviation of √24 or 4.899.
How likely is it to observe a sample mean number of sags per week that exceeds 390?
For this one, we have this formula to use:
[tex]z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt[]{n}}}[/tex]Our bar "x" is 390. The "myu" symbol is our population mean which is 346. This σ symbol is the population standard deviation 72 and n is our sample size = 216.
[tex]z=\frac{390-346}{\frac{72}{\sqrt[]{216}}}=\frac{44}{2\sqrt[]{6}}=8.98[/tex]Under a normal curve, the areas defined are between z = -3.5 to z = +3.5. Since our z should exceed > 8.98 and thus far greater than +3.5, then we can say that the probability of having a sample mean that exceeds 390 is zero.
Which of the following is an x-intercept of the graph of the function shown below? f(x) = x2 + 6x + 9 O A. x = 6 O B. x=9 O C. X=-3 O D. x = 3 PREVIOUS Type here to search
Given:
The function is,
[tex]f(x)=x^2+6x+9[/tex]Explanation:
For x-intercept of the function f(x) = 0. So
[tex]0=x^2+6x+9[/tex]Solve the equation for x.
[tex]\begin{gathered} x^2+6x+9=0 \\ x^2+3x+3x+9=0 \\ x(x+3)+3(x+3)=0 \\ (x+3)(x+3)=0 \\ x=-3,-3 \end{gathered}[/tex]So x-intercept of the function is x = -3.
Answer: x = -3
Option C is correct
Select mode<11/11 -10. Write and solve the equation modeled below.Equation:X=Solution:
2=-8-x Equation
x=-10
Explanation
Step 1
the scale is in balance, that indicates that the weights to the right and left are equal
Let
left side=2 squares of 1 each
then
left side=2
Step 2
rigth side=8 times (1) plus -x
rigth side=(8*-1)-x
rigth side=-8-x
Step 3
finally
[tex]\begin{gathered} \text{left side= rigth side} \\ \text{replacing} \\ 2=-8-x\text{ Equation (1)} \end{gathered}[/tex]Step 4
finally solve equation (1) for x
[tex]\begin{gathered} 2=-8-x \\ \text{add 8 in both sides} \\ 2+8=-8-x+8 \\ 10=-x \\ \text{Multiply each side by -1} \\ 10\cdot-1=-x\cdot-1 \\ -10=x \end{gathered}[/tex]I hope this helps you
suppose the probability of a horse winning a race is 0.04. what are the odds of winning? express your answer in the form a:b
The probability of a horse winning a race is
[tex]Pr(\text{ win)=0.04}[/tex]The probability of the horse losing will be calculated as
[tex]Pr(\text{lose)}=\text{ 1- Pr(win)}[/tex]By substituting the value, we will have
[tex]\begin{gathered} Pr(\text{lose)}=\text{ 1- Pr(win)} \\ Pr(\text{lose)}=1-0.04 \\ Pr(\text{lose)}=0.96 \end{gathered}[/tex]The formula used to calculate the odds of winning is given below as
[tex]\text{Odds of winning=}\frac{pr(\text{ win)}}{Pr(loose)}[/tex]By substituting the values, we will have
[tex]\begin{gathered} \text{Odds of winning=}\frac{pr(\text{ win)}}{Pr(loose)} \\ \text{Odds of winning}=\frac{0.04}{0.96} \\ \text{Odds of winning}=\frac{4}{96} \\ \text{Odds of winning}=\frac{1}{24} \\ \text{Odds of winning}=1\colon24 \end{gathered}[/tex]Hence,
The odds of winning = 1 : 24
1,936 divided by 8 in long division
Answer:
242.
Step-by-step explanation:
Basically, you have to put the 2 numbers "1936" and "8" down. After you put the 2 numbers down, you have to figure out how many times 8 goes into 19 which is 2 times.
You put the 2 above the 1 in 1936. After you put the 2 up there, you have to figure out 2 x 8 which is 16. You have to put the 16 below the 19 and subtract 19 by 16 which is 3.
After you finish that equation, you must bring the 3 down next to the 3 you wrote down on 19 - 16. The number turns into 33 and you have to figure out how many times 8 goes into 33 which is 4 times. You put the 4 next to the 2 above and then do 4 x 8 which is 32. You do 33 - 32 which is 1.
You bring the 6 down in 1936. It turns into a 16. You now have to figure out how many times 8 goes into 16 which is 2 times. You put 2 next to the 2 and the 4 above and that turns the number into 242.
You then have to do 2 x 8 which is 16 and put 16 under the 16 from 33 - 32. That'll make an equation which is 16 - 16 which is 0. There is no remainder and all the numbers were added above so 242 is your answer.
Hopefully, this has helped, tried my best!
=================================
Long Division - Solution and Process
=================================
We are given the Divisor 8 and the Dividend 1,936.
242 ← Our Final Solution
8 | 1936
16
___
33
32
____
16
16
0
The quotient of the given problem would be 242 with a remainder of 0, or simply 242.
Hope this helps!
An archer releases an arrow with an initial velocity of 24 feet per second at a height of 16 feet. The path the arrow takes can be modeled using the function f(x)=−16x2+24x+16, where f(x) represents the height, in feet, of the arrow and x represents the time the arrow travels in seconds. How many seconds until the arrow hits the ground? Round your answer to the nearest hundredth if necessary. Do not include units in your answer.
Answer:
18.25
Step-by-step explanation:
From the quadratic equation given, the time it will take till the arrow hits the ground is 22.75 seconds
How many seconds until the arrow hits the ground?To determine when the arrow hits the ground, we need to find the value of x when the height, f(x), is equal to 0. In other words, we need to solve the equation:
To solve this quadratic equation, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a),
where a, b, and c are the coefficients of the quadratic equation
In this case, a = -16, b = 24, and c = 16. Substituting these values into the quadratic formula:
x = (-(24) ± √((24)² - 4(-16)(16))) / (2(-16)).
Simplifying further:
x = (-24 ± √(576 + 1024)) / (-32),
x = (-24 ± √(1600)) / (-32),
x = (-24 ± 40) / (-32).
x = -101/4 or x = 101/4
Since x≠ negative;
x = 101/4 = 22.75 seconds
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100 POINTS!!! And BRAINLIEST
Select the correct option for each
cos(-25°) = _____.
cos 115°
cos 25°
sin 25°
-cos 335°
sin(-136°) = _____.
sin (-316)°
-sin 44°
-sin 316°
-cos 44°
tan(-212°) = _____.
-cot 32°
tan 32°
cot 32°
-tan 32°
cot(-315°) = _____.
cot (-45)°
cot 135°
cot 45°
-cot 45°
Using equivalent angles, the correct options are given as follows:
cos(-25°) = cos(25º).sin(-136º) = -sin(44º).tan(-212º) = -tan(32º).cot(-315º) = cot(45º).Cos(-25º)Negative 25 degrees is on the fourth quadrant, with the positive angle measure being given by:
360 - 25 = 335º.
The equivalent angle on the first quadrant is of 360º - 335º = 25º, and the cosine on the first quadrant is positive, just like in the fourth, hence:
cos(-25°) = cos(25º).
Sin(-136º)The positive angle measure is given as follows:
360 - 136 = 224º.
Which is on the third quadrant, in which both the sine and the cosine are negative.
The equivalent angle on the first quadrant is given as follows:
224º - 180º = 44º.
Hence the expression is:
sin(-136º) = -sin(44º).
Tan(-212º)The positive angle measure is given as follows:
360 - 212 = 148º.
Which is on the second quadrant, in which the tangent is negative.
The equivalent angle on the first quadrant is given as follows:
180º - 148º = 32º.
Hence the expression is:
tan(-212º) = -tan(32º).
Cot (-315º)The positive angle is given as follows:
360 - 315 = 45º.
Which is already on the first quadrant, hence the expression is given as follows:
cot(-315º) = cot(45º).
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question included as a photo
a. The linear Equations :
3x + (x+42)= 90
⇒4x +42 =90
b. ∠ 1 = 36° and ∠2 =54°
How do you find the solution to a linear equation?In one of the equations, separate one of the two variables.In the other equation, substitute the expression that is equal to the isolated variable from Step 1.For the final variable, solve the linear equation.Systems of equations can be solved using one of three techniques: graphing, substitution, or elimination. Simply plot the provided equations on a graph and locate the point(s) where they all cross to solve a problem by graphing. You may find the values of the variables you are working for by finding the coordinate of this point.
here
4x+42 = 90 ⇒ x=12
∠1 =4 x 12=36 and ∠2 = 12+42=54
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resume the line between (4 -4) and (-4 -4)for was the form inside of the right time of (-4,4) is reflect over both axes to create the triangles third vertex how long will the resultant base be
For this case we have two points given:
(-4, -4) and (-4,4)
The third vertex for this case would be:
(4,-4)
And then the resulting base would be:
d= 4+4 = 8
correct answer:
8 units
what percentage of the eggs were not at room temperature? do not include (%) in the answer round the answer to the nearest whole number .
Given a table represents the number of eggs that hatched at 3 different temperature:
The total number of eggs = 14 + 11 = 25
There are just 25 eggs in each time to make the experiment
The number of eggs was not hatched at room temperature = 11
so, the percentage will be =
[tex]\frac{11}{25}\cdot100=44[/tex]So, the answer will be = 44
Which inequality is represented by the graph?
Answer:
[tex]y < \frac{5}{3} x - 3 \\ [/tex]
Step-by-step explanation:
- General linear equation of a line passing through point (x, y) with a gradient m and y-intercept (0, c) is ;
[tex]{ \rm{y = mx + c}}[/tex]
- As finding gradient, m; consider points (0, -3) and (3, 2) from the graph;
[tex]{ \rm{slope \: m = \frac{2 - ( - 3)}{3 - 0} }} \\ \\ { \rm{m = \frac{5}{3} }}[/tex]
- Then our equation becomes y = 5/3x + c
- Consider point (0, -3), relate it with (0, c) hence c is -3;
[tex]{ \rm{y = \frac{5}{3}x - 3 }}[/tex]
- If you see the format of the coordinates, x coordinates are greater than y coordinates, hence y < x
[tex]{ \rm{y < \frac{5}{3}x - 3 }} \\ [/tex]
Answer:
[tex]y < \dfrac{5}{3}x-3[/tex]
Step-by-step explanation:
All given answer options have the same linear equation:
[tex]y=\dfrac{5}{3}x-3[/tex]
Therefore, there is no need to work out the equation of the line for this question as it is already given.
When graphing inequalities:
< or > : dashed line.≤ or ≥ : solid line.< or ≤ : shade under the line.> or ≥ : shade above the line.From inspection of the graph there is:
A dashed line.Shading under the line.Therefore, the inequality that is represented by the graph is:
[tex]y < \dfrac{5}{3}x-3[/tex]
A microwave is placed on top of two boxes. One box is 3 feet 5 inches tall, the other box is 2 feet 8 inches tall, and the microwave is 3 feet 10 inches tall. How tall are they combined? Write your answer in feet and inches. Use a number less than 12 for inches.
The combined length is 9 feet 11 inches
What is length?
Distance is measured by length. Length is a quantity having the dimension distance in the International System of Quantities. Most measuring systems use a base unit for length from which all other units are derived. The metre is the basic unit of length in the International System of Units (SI). The greatest extended dimension of a stationary item is typically believed to be its length. This is not always the case, as it may depend on the location of the item. Height, sometimes known as vertical length or vertical extent, and width, breadth, or depth are all words used to describe the length of a stationary object. When length is the greatest dimension, width or breadth generally relate to a lesser dimension.
Given, length of a box = 3 feet 5 inches
length of another box = 2 feet 8 inches
length of microwave = 3 feet 10 inches
Total length = 3 feet 5 inches + 2 feet 8 inches + 3 feet 10 inches
= 9 feet 11 inches
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1) Ned started jogging at 2:50. If he jogged for 3 hours and 30 minutes, what time was it when he finished?
Data
Starting hour = 2:50
Time = 3 h 30 min
Addition
1
2:50
+ 3:30
6:20 Use the hexadecimal system to solve this problem.
i need help with subtracting,multiplying,dividing,and adding fractions.
Adding fractions
To add two fractions, you have to make sure that the numbers in the denominator are the same.
For the fractions
[tex]\frac{1}{2}+\frac{2}{5}[/tex]The denominators are different, you have to look for a common factor between 2 and 5, the quickest way is to multiply them, you know that 10 is both a multiple of 2 and of 5.
Multiply 1/2 by 5 to obtain the equivalent expressed in tenths and multiply 2/5 by 2 to obtain the equivalent fraction in tenths
[tex]\frac{1}{2}\cdot5=\frac{5}{10}[/tex][tex]\frac{2}{5}\cdot2=\frac{4}{10}[/tex]Now that both fractions have the same denominator you can add them
[tex]\frac{5}{10}+\frac{4}{10}=\frac{5+4}{10}=\frac{9}{10}[/tex]Subtracting Fractions
You must apply the same procedure when subtracting two different fractions. First find a common factor so that the denominator is the same for both fractions:
[tex]\frac{1}{2}-\frac{1}{5}[/tex]As before, the common factor is 10, so the equivalent fractions will be:
[tex]\frac{5}{10}-\frac{4}{10}=\frac{5-4}{10}=\frac{1}{10}[/tex]Dividing fractions
To divide two fractions you have to do the following steps.
1- Invert the fraction that corresponds to the denominator of the division, i.e. the one you want to divide for (the second one).
This is called a reciprocal fraction.
2-Multiply the first fraction, the one you want to divide by the reciprocal fraction.
3-If possible, simplify the result.
1-Invert the denominator of the division
[tex]\frac{2}{5}=\frac{5}{2}[/tex]2-Multiply the denominator by the reciprocal fraction
[tex]\frac{1}{2}\cdot\frac{5}{2}=\text{ }\frac{1\cdot5}{2\cdot2}=\frac{5}{4}[/tex]1/2 divided by 2/5 equals 5/4
11) What is the slope of the line below * X
to find the slope of a line select the two points given.
in this case the point to the left will be (-4,-1) and the one to the right will be (3,1)
use the formula of the slope to calculate
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]replace the points into the formula
[tex]\begin{gathered} m=\frac{1-(-1)}{3-(-4)} \\ m=\frac{2}{7} \end{gathered}[/tex]the slope of the line will be 2/7
The table below shows the students in an Algebra class.GirlsBoysTotalOwn a graphing Do not own a graphingcalculatorcalculator125176713Total181230What is the probability that a randomly chosen student will be a girl and own a graphingcalculator?
Explanation:
The total number of students in the algebra class is given below as
[tex]n(S)=30[/tex]The number of girsl who won a graphing calculator is given below as
[tex]\begin{gathered} n(G_h\cap G_n)=12 \\ where, \\ G_h=have\text{ }graphing\text{ }calculator \\ G_n=does\text{ }not\text{ }have\text{ }graphing \end{gathered}[/tex]Concept:
To figure out the probabaility that a randomly chosen student will be a girl and own a graphing calculator, we will use the formula below
[tex]Pr(G_h\cap G_n)=\frac{n(G_h\cap G_n)}{n(S)}[/tex]By substituting the values, we will have
[tex]\begin{gathered} Pr(G_{h}\operatorname{\cap}G_{n})=\frac{n(G_{h}\operatorname{\cap}G_{n})}{n(S)} \\ Pr(G_h\operatorname{\cap}G_n)=\frac{12}{30} \\ Pr(G_h\operatorname{\cap}G_n)=\frac{2}{5} \end{gathered}[/tex]Hence,
The final answer is
[tex]\frac{2}{5}[/tex]The FOUTH OPTION is the correct answer
Finding slope and y-interceptfor this equation.-5x - y = 14
Finding slope and y-intercept
for this equation.
-5x - y = 14
we know that
the equation of the line in slope intercept form is equal to
y=mx+b
where
m is the slope
b is the y-intercept
In this problem we have
-5x-y=14
Isolate the variable y
y=-5x-14
therefore
slope is -5y-intercept is -14jayel gas $30. every month she gets 15% interest. how much money does she have after 4 months
The money she will have after 4 months would be 31.50 dollars.
What is simple interest?Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of the principal amount, rate, and period.
Simple Interest = (Principal × Rate × Time) / 100
If the initial amount (also called as principal amount) is given as 30, and the interest rate is 15% annually, and it is left for 4 months for that simple interest, then the interest amount earned is given by:
4 month = 0.333 year
Therefore,
Simple Interest = (Principal × Rate × Time) / 100
Simple Interest = (30 × 15× 0.333) / 100
Simple Interest = 31.50
Hence, the money she will have after 4 months would be 31.50 dollars.
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Sheldon thought of a natural number, and then he added the next natural number to it.
He got the sum of 75. What was Sheldon's number?
Using a system of equations, it is found that Sheldon's number is of 37.
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 context of the problem.
For this problem, we have to consider that:
The natural number is of x.The next natural number is the successor of x, represented by x + 1.The sum of these numbers is given by:
x + x + 1 = 2x + 1 (combining the like terms).
The sum is equals to 75, hence we can solve for the natural number x as follows:
2x + 1 = 75
2x = 74
x =74/2
x = 37. (which is Sheldon's natural number).
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HELP ASAP WILL GIVE THE BRAINLIEST TO ANYONE WHO ANSWERS THIS CORRECTLY HELP ASAP
Answer: the answer is B or the second option /note b and the second option are the same thing
Step-by-step explanation:
n/a
Answer: The second one
Step-by-step explanation:
You have to go down 3 boxes, and go 6 boxes to the right in order to correlate with the same letter
Find the slope of the line shown in the graph below enter your answer as a simplified improper fraction if necessary
The slope is 1
Explanation:Choose the points (2, -3) and (4, -1)
The slope is:
[tex]\begin{gathered} y=\frac{-1-(-3)}{4-2}=\frac{-1+3}{4-2} \\ \\ =\frac{2}{2}=1 \end{gathered}[/tex]Add/Subtract. Express your answer as a polynomial in standard formMultiply/Dividea) (5^3)(6^4)b) (6^7)(1/2^8)c) (1/2 ^5)(1/3 ^9)d) 14^5 7^2
To multiply them, we will multiply the coefficient 5 and 6
5 * 6 = 30
for x we will add their power to multiply them
[tex](5x^3)(6x^4)=(5\times6)(x^{3+4})=30x^7[/tex][tex](6x^7)(\frac{1}{2}x^8)[/tex]We will multiply 6 by 1/2
6 * 1/2 = 3
Then add the power of x
[tex](6x^7)(\frac{1}{2}x^8)=(6\times\frac{1}{2})(x^{7+8})=3x^{15}[/tex]What’s -4(x-2)
show step by step !
Normally, by order of operations, we simplify what's in the parenthesis first. However, since we don't know the value of x, it is already simplified. So we use the distributive property to distribute -4 to the binomial.
-4(x - 2)
(-4 × x) + (-4 x -2)
-4x + 8
Answer:
-4x+8
Step-by-step explanation:
-4×(x)=-4x
-4×-2=8
a tiling of the plane occurs when we fill the entire infinite playing with a repeated pattern . the image to the right shows a portion of one such tiling. The pattern extends forever in all directions. A give all angles of rotational symmetry between 0 and 360 degrees about the two marked points. point A: Point B:
EXPLANATION
Let's see the facts:
The angles of symmetry in point A is 60 degrees because the plane in point A is divided in 6 parts, so dividing 360° by 6 give us 60°. The same reasoning applies for the point B dividing it by 3 parts.
The angles of symmetry in point B is 120 degrees.
what % less 60 is 51
To find the percent we are looking for we can use the rule of three:
[tex]\begin{gathered} 60\rightarrow100 \\ 51\rightarrow x \end{gathered}[/tex]then:
[tex]\begin{gathered} x=\frac{51\cdot100}{60} \\ x=85 \end{gathered}[/tex]This means that 51 is 85% of 60.
Therefore 51 is 15% less than 60.
A wireless company offers two cell phone plans. For the month of September Plan A charges $35 plus $0.25 per minute for calls. Plan B charges$20 plus $0.50 per minute for calls. ?
EXPLANATION
Let's see the facts:
Plan A --> $35 + $0.25/minute
Plan B --> $20 + $0.5/minute
Let's call "x" to the number of minutes that a person could talk.
Here we have two equations as follows:
(1) 35 + 0.25x
(2) 20 + 0.5x
Where x represents the number of minutes a person talks on the phone.
We need to equal both equations in order to obtain the same cost.
35 + 0.25x = 20 + 0.5x
Now, we need to solve this equality as shown as follows:
-Subtracting -35 to both sides:
35 + 0.25x -35 = 20 + 0.5x -35
-Adding similar terms:
0.25x = 0.5x - 15
-Subtracting -0.5x to both sides:
0.25x - 0.5x = -15
-Adding similar terms:
-0.25x = -15
-Dividing both sides by -0.25:
x = -15/-0.25
-Simplifying:
x= 60 minutes
So, when a person talks for 60 minutes the cost of both plans is the same.