Answer:
[tex]\frac{7}{3} + \frac{e^2 - e}{2}[/tex]
Step-by-step explanation:
By definition:
Work done along the path is the line integral along that path denoted as:
Work Done = [tex]\int\limits^C {F} \, dr[/tex]
Note: dr = dx i + dy j
Given that: [tex]F (x,y) = x^2 i + ye^x j[/tex]
F (x, y) dot product with dr = [tex] x^2 dx + ye^x dy[/tex]
Work done = [tex]\int\limits^C {(x^2 dx + ye^x dy)}[/tex] ... Eq 1
Given that C: [tex]y = \sqrt{x-1}[/tex]
[tex]dy = \frac{dx}{2\sqrt{x-1} }[/tex]
Replace the value of y and dy in Eq 1
[tex]Work done = \int\limits^C ({x^2 + \frac{e^x}{2} }) \, dx[/tex]
Limits of x are 1 to 2 respectively
[tex]Work done = \int\limits^2_1 ({x^2 + \frac{e^x}{2} }) \, dx[/tex]
= [tex](\frac{x^3}{3} + \frac{e^x}{2})\limits^2_1[/tex]
Evaluate limits to obtain
Work Done = [tex]\frac{7}{3} + \frac{e^2 - e}{2}[/tex]
The population of a small town is modeled by an exponential function of the form p t( ) = abt , where t represents the number of years since 2010. The population of the town was recorded as 425 in 2010 and 612 in 2012. Based on the data for the years 2010 and 2012, what is the value of b in the model?
To find the value of b in the exponential function, we can use the given data points for the years 2010 and 2012. By substituting the values into the equations, we can solve for b.
Explanation:To find the value of b in the exponential function, we can use the given data points for the years 2010 and 2012. Let's start by setting up two equations:
p(0) = ab0 = a = 425
p(2) = ab2 = 612
From the first equation, we know that a = 425. Substituting this value into the second equation:
425b2 = 612
Divide both sides of the equation by 425:
b2 = 612/425
Take the square root of both sides:
b = √(612/425)
Simplifying the expression gives us the value of b.
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A community college student interviews everyone in his own statistics class to determine who owns a car. Identify which sampling technique is used.
The student uses Census sampling, a technique where every individual in a chosen population is surveyed. This method is reasonable for small populations, but can be impractical for larger groups.
Explanation:The sampling technique used by the community college student in his statistics class is called Census sampling. This is because the student is collecting data from every individual in the total population of his statistics class. In other words, the student is not selecting a random or specific subset of the class; he is including everyone in his study. This can be useful for small populations, like a single class, as it provides data from all members, but it can be time-consuming and impractical for larger groups or populations.
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Thomas had 12 juice boxes he gave some to his sisters he now has more rhan 5 left.Which inequality can be used to find j the number of juice boxes thomas gave to his sisters?
Answer:
J < T - 5
Step-by-step explanation:
T = The number of juice boxes Thomas had
J = The number of juice boxes Thomas gave to his sisters
Thomas had 12 juice boxes
T = 12
He gave some to his sisters he now has more than 5 left.
T - J > 5
-J > 5 - T
J < -5 + T
J < T - 5
To determine the number of juice boxes Thomas gave to his sisters, the inequality 12 - j > 5 is used, which simplifies to j < 7, indicating that he gave away fewer than 7 juice boxes.
To find j, the number of juice boxes Thomas gave to his sisters, we start with the total number he had initially, which is 12. We know that he gave away some juice boxes and still has more than 5 left. If we let j represent the number of juice boxes given to his sisters, then 12 - j > 5 would be the inequality that can be used to determine j.
Since Thomas has more than 5 left, but we don't know the exact number, we use the inequality to represent the situation. Therefore, if we solve the inequality, subtracting 5 from both sides, we get j < 7. This means that Thomas gave away fewer than 7 juice boxes to his sisters because he had more than 5 remaining.
The following warm-up exercises involve skills that were covered in earlier sections.you will use these skills in the exercise set for this section.
1. The sum is S and the product is a maximum.
2. The product is 192 and the sum is a minimum.
3. The product is 192 and the sum of the first plus three times the second is a minimum.
4. The second number is the reciprocal of the first and the sum is a minimum.
5. The sum of the first and twice the second is 100 and the product is a maximum.
Answer:
1 3 5
Step-by-step explanation:
Miguel has a credit card bill of $7,250 with an interest rate of 16%. To pay his bill off in one year, he must make monthly payments of $657.80. To pay his bill off in 18 months, he must make monthly payments of $455.71. How much extra will he pay if he wants to make the lower monthly payments?
Answer:
$309.18
Step-by-step explanation:
To pay off in 12 months = 12 * 657.80 = $7,893.6
To pay off in 18 months = 18 * 455.71 = $8202.78
If he takes the lower monthly payments, he will end up paying 8202.78 - 7893.6 = $309.18
A certain club has 10 members, including Harry. One of the 10 members is to be chosen at random to be the president, one of the remaining 9 members is to be chosen at random to be the secretary, and one of the remaining 8 members is to be chosen at random to be the treasurer. What is the probability that Harry will be either the member chosen to be the secretary or the member chosen to be the treasurer?
A) 1/720B) 1/80C) 1/10D) 1/9E) 1/5
Answer: E) 1/5
Step-by-step explanation:
The probability of any member being selected for each of the 3 posts is 1/10 that is they have equal probabilities of being selected for any of the posts.
The probability that harry would be selected for;
Secretary Ps= 1/10
Treasurer Pt = 1/10
So the probability of being selected for either secretary or treasurer is
P = Ps + Pt
P = 1/10 + 1/10
P = 2/10
P = 1/5
Note: ignore the sequence of selection
What is 1000222222222222222+2233444444444444445555566666644444444444444546444547664533464646 2234 a.900000000000000000000000000000000000000000000000000000000 b.230000000000000000000000000000000000000000000000000000000 c. 1002020020202002020020200002929202999019920209209092992
Answer:
2.233444444e62 is the answer
Kristin spent $131 on shirts. Fancy shirts cost $28 and plain shirts cost $15. She bought seven total shirts. How many fancy and plain shirts did Kristin buy? Write two equations.
Answer:
2 fancy shirts and 5 plain shirts
Step-by-step explanation:
28x + 15x = 131
28(2) + 15(5) = 131
56 + 72 = 131
(there are no other equation i could find)
What is the solution? Round your answer to the nearest tenth
Help please step by step if so ?
Answer:
9.6.
Step-by-step explanation:
Because DE || AC:
x/12 = 8/10
10x = 96
x = 9.6.
please help!
A population of lizards decreases exponentially at a rate of 12.5% per year.
What is the equivalent monthly rate to the nearest hundredth of a percent?
0.20%
1.04%
1.11%
1.23%
90 students represent x percent of the boys at Jones Elementary School. If the boys at Jones Elementary make up 40% of the total school population of x students, what is x?
A. 125
B. 150
C. 225
D. 250
E. 500
Answer: C. 225
Step-by-step explanation:
To get the total population (x), we will take the 40% of the total population and equate to 90
40%× x = 90
40/100 × x = 90
40x/100= 90
Cross multiplying,
40x = 100 × 90.
x = 9000/40
x =225 C
Hallie rode her biycle 7 miles less than 3 times the number of miles Samantha rode. If Samantha rode her bicycle 23 miles, how many miles did Hallie ride?
Answer:
Hallie ride 62 miles on bicycle.
Step-by-step explanation:
Given:
Let the number of miles Samantha rode be 'x'.
Hallie rode her bicycle 7 miles less than 3 times the number of miles Samantha rode.
It means that number of miles Hallie ride is equal to 3 multiplied by number of miles Samantha rode and then subtracting by 7.
framing in equation form we get;
number of miles Hallie ride = [tex]3x-7[/tex]
But Given:
number of miles Samantha rode =23 miles.
Now by substituting the value of [tex]x=23[/tex] in above equation we get;
number of miles Hallie ride = [tex]3x-7 = 3\times23-7 = 69-7 = 62 \ miles[/tex]
Hence Hallie ride 62 miles on bicycle.
Which of the following would indicate that a dataset is skewed to the right?
a. The interquartile range is larger than the range.
b. The range is larger than the interquartile range.
c. The mean is much larger than the median.
d. The mean is much smaller than the median.
Answer: c. The mean is much larger than the median
Step-by-step explanation:
A dataset is skewed to the right when the peak of the dataset is located in the left( left of the mean), and it has a long right tail. It is also call positive skewed distribution. One of the characteristics of right skewed dataset is that the mean of the dataset is always greater/larger than the median and mode.
Therefore, for the case above if the mean is much larger than the median, it indicates that the dataset is skewed to the right.
A dataset is skewed to the right when the mean is much larger than the median. Therefore, the correct answer is option c.
When a dataset is skewed to the right, it means that the distribution of data is not symmetric, and it is stretched out more towards the higher values (right side) than the lower values (left side). This can be due to the presence of outliers or a natural characteristic of the data.
Now, let's look at why option "c" indicates right skewness:
c. The mean is much larger than the median.
The mean is the arithmetic average of all the values in the dataset, while the median is the middle value when the data is arranged in order. When a dataset is positively skewed (skewed to the right), it means that there are some significantly larger values in the right tail of the distribution that pull the mean to the right (towards higher values).
In this situation:
The mean gets pulled toward the larger values because the larger values have a greater impact on the mean due to their magnitude.
The median remains closer to the bulk of the data because it is not affected by extreme values as much as the mean.
So, when the mean is much larger than the median, it is an indication that there are significant outliers or a longer right tail in the dataset, which is a characteristic of a right-skewed distribution.
Therefore, the correct answer is option c.
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The number of square units in the area of circle O is equal to 16 times the number of units in its circumference Which of the following are diameters of circles that could fit completely inside circle 0? Indicate all such diametersa) 25b) 36c) 42d) 48e) 54f) 66g) 70
Answer:
The diameters of circles that could fit completely inside circle O are 25, 36, 42, 48 and 54.
Step-by-step explanation:
The actual diameter of the circle:
[tex]\pi r^{2} = 16 x \\2\pi r = x\\\\16(2\pi r)=16x\\\\32\pi r= \pi r^{2} \\\\\frac{32\pi r}{\pi r} = \frac{\pi r^{2} \\}{\pi r} \\\\r = 32[/tex]
Since the radius is equal to 32 units, the diameter is equal to 64 units.
Therefore, the diameters of circles that could fit completely inside circle O must be smaller than or equal to 64.
Each student that buys school lunch pays $2.75 the cafeteria typically brings between $1168.75 and $1438.25 how many students does the cafeteria typically serve
Answer:
The Inequality modelling the equation is [tex]425\leq x\leq 523[/tex].
The cafeteria typically serve lunch for students between 425 to 523.
Step-by-step explanation:
Given:
Each students pays for lunch = $2.75
Cafeteria brings between $1168.75 and $1438.25.
We need to find the number of students cafeteria typically serve.
Solution:
Let the number of student served be 'x'.
Now we can say that;
Total money make is equal to Each students pays for lunch multiplied by number of students served.
But total money made is in the form of range so we can say that;
[tex]1168.75\leq 2.75x\leq 1438.25[/tex]
Now Dividing all sides by 2.75 we get;
[tex]\frac{1168.75}{2.75}\leq \frac{2.75x}{2.75}\leq \frac{1438.25}{2.75}\\\\425\leq x\leq 523[/tex]
Hence the Inequality modelling the equation is [tex]425\leq x\leq 523[/tex].
Hence we can say that, The cafeteria typically serve students between 425 to 523.
If there are three different samples of the same size from a set population, is it possible to get three different values for the same statistic?
Yes, it is possible to get three different values for the same statistic when sampling from a set population due to sampling variation.
Explanation:Yes, it is possible to get three different values for the same statistic when sampling from a set population.
For example, let's consider a population of students' test scores. If three different samples are taken from this population, each sample may have different scores, resulting in different values for the same statistic such as the mean.
This variability in sample statistics is due to sampling variation, which is a natural occurrence when selecting different samples from the same population.
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Suppose a railroad rail is 3km and it expands on a hot day by 13 cm in length. Approximately how many meters would the center of the rail rise above the ground
Answer:
the rise of the center of the rail will be given by =[tex]\sqrt{hypotenuse^{2}\hspace{0.15cm} -\hspace{0.15cm} base^{2} }[/tex]
= [tex]\sqrt{1500.065^{2} \hspace{0.15cm} -\hspace{0.15cm}1500^{2} }[/tex] m = 13.964 m
Step-by-step explanation:
i) the normal length of the railroad is 3 km = 3000 m.
ii) on a hot day day the railroad rail expands by 13cm = 0.13m
iii) the center of the railroad is at 1500 m which is half of the total length.
iv) the expansion of the railroad in either half of the road is 0.065m which is half of the total expansion.
v) each half of the railroad can be represented by a right angled triangle whose base will be = 1500 m and hypotenuse will be = 1500.065 m .
vi) the rise of the center of the rail will be given by =[tex]\sqrt{hypotenuse^{2}\hspace{0.15cm} -\hspace{0.15cm} base^{2} }[/tex]
= [tex]\sqrt{1500.065^{2} \hspace{0.15cm} -\hspace{0.15cm}1500^{2} }[/tex] m = 13.964 m
The center of the rail would rise about 16.06 meters above the ground.
To find out how much the center of the rail rises above the ground due to expansion:
we can consider that the rail expands uniformly along its length.
If it expands by 13 cm over a length of 3 km, we can calculate the rise at the center using trigonometry, considering that the expansion causes the rail to form a very shallow arc.
The expansion forms a segment of a circle, where the rail length is the arc length, and the rise at the center is the height of the segment. We can use the formula for the height of a segment of a circle:
[tex]\[ h = r - \sqrt{r^2 - \left(\frac{l}{2}\right)^2} \][/tex]
Where:
h is the height of the segment (the rise at the center),
r is the radius of the circle (which we can approximate as the radius of the Earth, as the rail is very long compared to its curvature),
l is the arc length of the segment (the expansion of the rail).
Given that the Earth's radius is approximately 6371 km, we need to convert all lengths to meters:
[tex]\[ r = 6371 \times 1000 \text{ meters} \][/tex]
[tex]\[ l = 3 \times 1000 \times 100 \text{ meters} \][/tex]
[tex]\[ h = 6371 \times 1000 - \sqrt{(6371 \times 1000)^2 - \left(\frac{3 \times 1000 \times 100}{2}\right)^2} \][/tex]
[tex]\[ h \approx 6371000 - \sqrt{(6371000)^2 - (150000)^2} \][/tex]
[tex]\[ h \approx 6371000 - \sqrt{40641464900000 - 22500000000} \][/tex]
[tex]\[ h \approx 6371000 - \sqrt{40641442400000} \][/tex]
[tex]\[ h \approx 6371000 - 6370983.94 \][/tex]
[tex]\[ h \approx 16.06 \text{ meters} \][/tex]
PLZ HELP, GIVING BRAINLIEST!!
If the endpoints of the diameter of a circle are (3, 10) and (-1, 6), what are the coordinates of its center?
A. (-2,-2)
B. (2, 2)
C. (1, 8)
D. (2, 16)
At a lumber company, shelves are sold in 4 types of wood, 3 different widths and 3 different lengths. How many different types of shelves could be ordered?
Answer:
36
Step-by-step explanation:
Pretty simple
Multiply the numbers of different type of wood by the different type of length by the different type of width which is 4x3x3 = 36
4 wood type A B C D
3 length type L1 L2 L3
3 width type 1 2 3
So for wood A we have, (L1, 1) (L1,2)(L1,3)(L2,1)(L2,2)(L2,3)(L3,1)(L3,2)(L3,3)
for wood B we have, (L1, 1) (L1,2)(L1,3)(L2,1)(L2,2)(L2,3)(L3,1)(L3,2)(L3,3)
for wood C we have, (L1, 1) (L1,2)(L1,3)(L2,1)(L2,2)(L2,3)(L3,1)(L3,2)(L3,3)
for wood D we have, (L1, 1) (L1,2)(L1,3)(L2,1)(L2,2)(L2,3)(L3,1)(L3,2)(L3,3) if we count the combinations together we will arrive at 36
Esmerelda simplified a complex fraction. Her work is shown below. Negative 5 and one-fourth divided by three-halves = negative StartFraction 21 over 4 EndFraction divided by three-halves = (Negative StartFraction 21 over 4 EndFraction) (Three-halves) = Negative StartFraction 24 over 6 EndFraction = negative 4 What errors did Esmerelda make? Select three options.
Answer:
A. Esmeralda converted the mixed number to the wrong improper fraction.
D. Esmeralda did not divide –24 by 6 correctly.
E. Esmeralda did not use the reciprocal of the divisor.
Step-by-step explanation:
Evaluating Esmerald's simplified expression, the errors in her evaluation are :
Esmerelda did not use the reciprocal of the Divisor.Esmerelda added the numeratorEsmerelda added the denominatorThe appropriate evaluation procedure should be :
[tex]\frac{-5\frac{1}{4}}{\frac{3}{2}}[/tex]
Convert the Numerator to an improper fraction
[tex]\frac{\frac{21}{4}}{\frac{3}{2}}[/tex]
Take the reciprocal of the denominator
[tex]\frac{3}{2} = \frac{2}{3} [/tex]
Multiply the Numerator by the reciprocal of the denominator
[tex](-\frac{21}{4} )(\frac{2}{3}) = - \frac{42}{12} = -3 \frac{1}{2}[/tex]
Therefore, Esmeralda made three errors in her simplification procedure.
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if three pipes are all opened, they can fill an empty swimming pool in 3 hours. THe largest pipe alone takes one third the time that the smallest pipe takes and half the time the other pipe takes. how long would it takes each pipe to fill the pool by itself?
Answer: It will take the largest pipe 5.5 hours to fill the swimming pool alone.
It will take the smallest pipe 16.5 hrs to fill the swimming pool alone.
It will take the other pipe 11 hours to fill the pool alone.
Step-by-step explanation: let time needed to fill the swimming pool by the largest pipe be x ... eq (1)
Let time needed to fill the swimming pool by the smallest pipe be 3x ... eq(2)
Let time needed to fill the swimming pool by the other pipe be 2x ...eq(3)
The job to be done (to fill a swimming pool) be 3/x +3/3x+3/2x=1 ... eq(4)
Multiply 6x on both sides you will get:
6(3)+2(3)+3(3)=6x
18+6+9=6x
33=6x
33/6=x
X=5.5hours
Substitute x=5.5 into EQ 2 and 3
3x=3×5.5=16.5hours
2x=2×5.5=11hours
Check: substitute the value of x into eq3/5.5+3/16.5+3/11
0.545+0.182+0.273=0.9997=1
Grandma's Bakery sells single-crust apple pies for $6.99 and double-crust pies for $10.99. The total number of pies sold on Friday was 331.64. How many each type were sold?
Answer: the number of single-crust cherry pies that was sold is 16
the number of double-crust apple pies that was sold is 20
Step-by-step explanation:
Let x represent the number of single-crust cherry pies that was sold.
Let y represent the number of double-crust apple pies that was sold.
The total number of pies sold on a busy Friday was 36. This means that
x + y = 36
Grandma's Bakery sells single-crust apple pie for $6.99 and double-crust cherry pie for $10.99. If the amount collected for all the pies that day was $331.64, it means that
6.99x + 10.99y = 331.64 - - - - - - - - -1
Substituting x = 36 - y into equation 1, it becomes
6.99(36 - y) + 10.99y = 331.64
251.64 - 6.99y + 10.99y = 331.64
- 6.99y + 10.99y = 331.64 - 251.64
4y = 80
y = 80/4 = 20
x = 36 - y = x = 36 - 20
x = 16
Solve for x. Show all work please!
3(x + 5) = x - 7
Answer:
[tex]\displaystyle -11 = x[/tex]
Step-by-step explanation:
3x + 15 = x - 7
- 3x + 7 - 3x + 7
____________
[tex]\displaystyle \frac{22}{-2} = \frac{-2x}{-2} \\ \\ -11 = x[/tex]
I am joyous to assist you anytime.
If the graphs of two linear functions are perpendicular, describe the relationship between the slopes and the y-intercepts.
slopes:
a.The slopes are equal.
b. The slopes are negative reciprocals of one another.
c.The slopes are reciprocals of one another.
d.The slopes are inverses of one another.
e.There is no relationship.
y-intercepts:
a.The y-intercepts are equal.
b.The y-intercepts are not equal.
c.There is no relationship.
Answer:
Part 1) The slopes are negative reciprocals of one another.
Part 2) There is no relationship.
Step-by-step explanation:
Part 1)
we know that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)
[tex]m_1*m_2=-1[/tex]
Part 2)
The y-intercept is the value of y when the value of x is equal to zero
Two linear functions that are perpendicular, could have the same y-intercept (the y-intercept would be the point of intersection between both lines)
so
There is no relationship
A lone distance call costs 40 cents for the first three minutes and 10 cents for each additional minute. At most how many minutes can a person talk and not exceed $2?
Final answer:
A person can talk for at most 19 minutes on a long-distance call without exceeding a $2 limit, accounting for the initial charge and the cost of additional minutes.
Explanation:
To find out at most how many minutes a person can talk on a phone without exceeding $2, considering the initial charge is 40 cents for the first three minutes, and 10 cents for each additional minute, we need to calculate the total cost based on the number of minutes.
The problem can be broken down as follows:
The cost for the first 3 minutes is 40 cents.
After the initial 3 minutes, each additional minute costs 10 cents.
We have a budget of $2 (or 200 cents) to not exceed.
First, subtract the initial 40 cents from the total budget:
200 cents - 40 cents = 160 cents
With 160 cents left and each additional minute costing 10 cents:
160 cents[tex]\(\div\)[/tex] 10 cents = 16 additional minutes
Therefore, adding the initial 3 minutes:
3 + 16 = 19 minutes
A person can talk for at most 19 minutes without exceeding a $2 limit.
A system of linear equations with fewer equations than unknowns is sometimes called an underdetermined system. Can such a system have a unique solution? Explain.
Answer:
So such system with fewer equations than unknowns can never have a unique solution.
Step-by-step explanation:
Linear equations are equations which contain variable with degree 1.
The variables can be 1 or 2 or any other number
say there are n varaibles
Then to solve this we must have n independent equations.
If number of equations are less than number of variables we can have parametric solutions only with infinite points lying on it.
There is no chance for this to have a unique solution.
For unique solutions, there must be equal number of equations with the variables and the determinant formed by the coefficients should not be 0.
So such system with fewer equations than unknowns can never have a unique solution.
Curry youngest releativr is 5 years old. This is 79 years less than the age of his oldest relative.Write a subtraction equation that could be used to find the age of his oldest reletive
Answer:
The Subtraction equation use to find the age of his oldest relative is [tex]x-79=5[/tex].
Step-by-step explanation:
Given:
Age of youngest relative = 5 years
We need to write a subtraction equation that could be used to find the age of his oldest relative.
Solution:
Let the age of the oldest relative be 'x'.
Now given:
Age of youngest relative is 79 years less than the age of his oldest relative.
So we can say that;
Age of oldest relative minus 79 is equal to Age of the youngest relative.
framing in equation form we get;
[tex]x-79=5[/tex]
Hence the Subtraction equation use to find the age of his oldest relative is [tex]x-79=5[/tex].
Final answer:
The subtraction equation to find the age of Curry's oldest relative, based on the given information, is x - 5 = 79. Solving this equation reveals that the oldest relative is 84 years old.
Explanation:
The question involves setting up a subtraction equation to find the age of Curry's oldest relative, given that the youngest relative is 5 years old and this is 79 years less than the age of the oldest relative. We can represent the age of the oldest relative as x. The equation is based on the information that the difference in age between the oldest and youngest relatives is 79 years. Therefore, the equation can be set up as x - 5 = 79.
To solve for x, which represents the age of the oldest relative, you would add 5 to both sides of the equation to isolate x on one side. This results in x = 84. So, the oldest relative is 84 years old.
helpppppppp i need this fast
Option A:
Hence, x ÷ 4 > x – 12 is true for x = 20.
Solution:
To find which is the suitable inequality is true for the value x = 20.
Option A: x ÷ 4 > x – 12
⇒ [tex]\frac{x}{4}>x-12[/tex]
Multiply 4 on both sides of the inequality,
⇒ x > 4x – 48
Subtract 4x on both sides of the inequality,
⇒ –3x > – 48
⇒ 3x > 48
Divide 3 on both sides,
⇒ x > 16
If x = 20, then 20 > 16 is true.
Option B: 2x < x +22
Subtract x on both sides of the inequality,
⇒ x < 22
If x = 20, then 20 < 22 is false.
Option C: x + 30 > 3x
Subtract x on both sides of the inequality,
⇒ 30 > 2x
Divide by 2 on both sides of the inequality,
⇒ 15 > x
If x = 20, then 15 > 20 is false.
Option D: x – 5 < 2x – 35
Subtract x on both sides of the inequality,
⇒ – 5 < x – 35
Add 35 on both sides of the inequality,
⇒ 30 < x
If x = 20, then 30 < 20 is false.
Hence, x ÷ 4 > x – 12 is true for x = 20.
A piece of construction paper has a thickness of 4.3 x 10-3 inches. A piece of cardstock has thickness of 5.2 x 10-3 inches. How tall is a stack of 15 sheets of construction paper and 20 sheets of cardstock? Write your answer in scientific notation.
Answer:
1.685·10^-1 inches
Step-by-step explanation:
To find the total thickness, multiply the thickness of each sheet by the number of sheets and add the values for the different kinds of sheets:
(15)(4.3·10^-3) +(20)(5.2·10^-3) = (64.5 +104.0)·10^-3 = 168.5·10^-3
= 1.685·10^-1 . . . inches
Rich’s weekly salary is based on the number of pairs of shoes he sells. He is paid a base salary of $25, plus $5 for every pair of shoes he sells. The relationship between his pay (p) and pairs of shoes (s) sold can be represented by the linear equation p = 25 +5s. Determine Rich’s pay for a week in which he sold 7 pairs of shoes.
a.
$60
b.
$35
c.
$55
d.
$210
Answer:
A
Step-by-step explanation:
p = 25 + 5s
s = amount of shoes sold
Rich sold 7 shoes. Plug in 7 for s
p = 25 + 5(7)
p = 25 + 35
p = 60
Answer: the correct answer is a. $60
Step-by-step explanation:
Using the formula that states Rich's weekly salary
P= 25 + 5s , where p is the salary and s the number of pairs sold, then
P= $25 + $5*7
P=$25 + $ 35
P= $ 60