$26 and all cell phone cases cost $14. Derrick is buying these products as gifts for his friends plans to spend at least $150
To find out how many of each product Derrick can buy, we can use algebra. Let's call the number of headphones x and the number of cell phone cases y. We can set up an equation to represent the situation:
26x + 14y = 150
Now we can solve for one of the variables in terms of the other. Let's solve for y:
14y = 150 - 26x
y = (150 - 26x)/14
Now we can plug in different values for x and see what values of y will result in a total cost of at least $150. For example, if x = 1, then y = (150 - 26)/14 = 8.86. This means that Derrick could buy 1 pair of headphones and 8 cell phone cases for a total cost of $150.
Similarly, if x = 2, then y = (150 - 52)/14 = 7. This means that Derrick could buy 2 pairs of headphones and 7 cell phone cases for a total cost of $150.
We can continue plugging in different values for x until we find a combination of products that will cost at least $150. Alternatively, we could use a graphing calculator or an online graphing tool to graph the equation and find the intersection points with the line y = 150. These intersection points will represent the combinations of products that will cost at least $150.
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A certain map shows two roads. Road A is 1 1/5 miles long but is 1 1/2 inches long on the map. What is the unit rate for inches per mile on this map? If road B is 12 miles long, how long is road B on the map?
The unit rate for inches per mile is 0.8 inches.
The length of road B is 9.6 inches on map.
What is Unit rate?Unit rate is the ratio of two different units, with denominator as 1. For example, kilometer/hour, meter/sec, miles/hour, salary/month, etc.
Road in inches = 1 1/5 = 6/5 inches
Road in miles = 1 1/2 miles =
Inches per mile = 6/5 / (3/2)
= 6/5 x 2/3
= 4/5
= 0.8 inches
If the road B is 12 miles long, on the map it would be;
= 0.8 x 12
= 9.6 inches
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3. Solve by factoring the equation 3x2 – 12x – 15 = 0 and explain what your solutions mean for the equation. Show your work.
The equation 3x² - 12x - 15 = 0 when solved by factoring has the solutions x = 5 and x = -1
How to get to the equation's solutionThe equation 3x² - 12x - 15 = 0, is a representation of the equation in the question.
The aforementioned problem is a quadratic equation, and factoring is one way to solve this kind of issue.
Divide 3 from the equation.
As a result, we have the following
x² - 4x - 5 = 0.
Expanding the equation, we get
x² + x - 5x - 5 = 0.
Factoring the equation, we get
x(x + 1) - 5(x + 1) = 0
The result is
(x - 5)(x + 1) = 0.
We can solve for x by getting
x = 5 and x = -1.
Thus, the equation's answers are 5 and -1.
And it means that there are actually two solutions to the equation.
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rocket travels 180 ft in 15 sec. What is the ratio of feet to seconds to the lowest term
Answer:
12ft: 1sec
Step-by-step explanation:
180ft : 15sec
180÷15=12
15÷15=1
soooo it's
12ft : 1sec in the lowest term
(Answer quick) Please show work.
Answer:
Step-by-step explanation:
The solution of inequality is n < - 9
What inequality whose solution set is represented by this graph???
The inequality that represents the set of solutions above the straight line is: x-3y<5
What is a linear inequality?
A linear inequality is an inequality in which one side is a linear expression in one or more variables, and the other side is a constant, or another linear expression. The solution set of a linear inequality is a region in the coordinate plane that satisfies the inequality.
Calculate the inequality to represent the set of solution by shaded region:
A linear inequality can be represented by a shaded region on the coordinate plane. The boundary of the region is a straight line, and the shaded region represents all the points in the plane that satisfy the inequality. In this case, the line that intersects the x-axis at (5,0) and the y-axis at (0, -5/3) represents the boundary of the region.
To find the inequality that represents the set of solutions above the line, we first need to find the equation of the line. We can use the point-slope form of the equation of a line, which relates the slope of the line and a point on the line to the equation of the line.
We know that the line passes through the points (5,0) and (0, -5/3), so we can calculate the slope of the line by using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the two points through which the line passes.
m = (-5/3 - 0) / (0 - 5) = 1/3
Now we can use the point-slope form of the equation of the line to write the equation of the line:
y - y1 = m(x - x1)
where (x1, y1) is one of the two points through which the line passes.
Using the point (5,0) as (x1, y1), we get:
y - 0 = (1/3)(x - 5)
y = (1/3)x - 5/3
3y = x - 5
To represent the set of solutions above the line, we need to use the greater than symbol. So the inequality that represents the set of solutions above the straight line is:
x-3y<5
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Please help me on 6,7and8
When 508,000,000 is written in scientific notation, what will be the value of the exponent?
Step-by-step explanation:
When 508,000,000 is written in scientific notation, it will be represented as:
5.08 x 10^8
Therefore, the value of the exponent is 8.
Natalie has three pairs of pants 10 black and blue and five shirts white black green blue and red each morning she randomly select a pair of pants and one shirt the following tree diagram represents the sample space for this count compound event outcomes may be listed using an ordered pair for example tan pants and red shirt can be listed as tan and red hey how many total outcomes are in a sample space be a list of favourable outcomes for a Natalie selecting a pair of pants and shirt that are the same colour see select the favourite outcomes for Natalie selecting a black shirt the list of favourable outcomes that Natalie selecting a list of blue article of clothing
Based on the given information, the sample space for the event can be represented using a tree diagram, where the first level consists of the three pants (black, blue, and tan) and the second level consists of the five shirts (white, black, green, blue, and red). Each branch represents a possible combination of a pair of pants and a shirt.
To find the total number of outcomes in the sample space, we can simply multiply the number of options for pants (3) by the number of options for shirts (5), giving us a total of 15 possible outcomes.
For Natalie selecting a pair of pants and shirt that are the same color, the favourable outcomes would be the combinations where the pants and shirt are either both black or both blue. These can be listed as:
Black pants and black shirt
Blue pants and blue shirt
For Natalie selecting a black shirt, the favourable outcomes would be the combinations where the shirt is black. These can be listed as:
Black pants and black shirt
Blue pants and black shirt
Tan pants and black shirt
For Natalie selecting a blue article of clothing, the favourable outcomes would be the combinations where either the pants or the shirt (or both) are blue. These can be listed as:
Black pants and blue shirt
Blue pants and white shirt
Blue pants and black shirt
Blue pants and green shirt
Blue pants and blue shirt
Tan pants and blue shirt
According To The Texas Parks And Wildlife Department, There Are About 40 White-Tailed Deer Per Square Mile In Each Of 35 Texas Counties. A Rectangular Area On A Ranch In One Of These Counties Measures \( 2.25 \) Miles By \( 6.7 \) Miles. How Many White-Tailed Deer Are Expected To Live In This Rectangular Area?
603 white-tailed deer are expected to live in the rectangular area. To find the total number of white-tailed deer in the rectangular area, we need to find the area of the rectangle first. The area of a rectangle is given by the formula:
Area = length × width
In this case, the length is 2.25 miles and the width is 6.7 miles. So, the area of the rectangle is:
Area = 2.25 × 6.7
Area = 15.075 square miles
According to the given information, there are about 40 white-tailed deer per square mile in each of 35 Texas counties. We need to find how many white-tailed deer are expected to live in a rectangular area that measures 2.25 miles by 6.7 miles.
Now, we can find the total number of white-tailed deer in the rectangular area by multiplying the area by the number of deer per square mile:
Total number of deer = 15.075 × 40
Total number of deer = 603
Therefore, there are expected to be 603 white-tailed deer in the rectangular area.
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18. To find the perimeter of a regular octagon, use the
expression 8s, where s represents side length. If the
side length of a regular octagon is 1. 5 feet, what is
its perimeter in feet?
The perimeter of a regular octagon, we use the expression 8s, where s represents side length. The perimeter of a regular octagon with side length 1.5 feet is equals to the 12 feet.
Regular octagon is a polygon with eight sides. The perimeter of a polygon is equals to the sum of all its sides. All eight sides of regular octagon are same measure. So, in other words the perimeter of Regular octagon is equal to eight times the length its side. Here,
Side length of a regular octagon
= 1.5 feet
=> Perimeter = 8 × 1.5 feet [An octagon has 8 sides]
=> Perimeter = 12 feet
Hence, required perimeter is 12 feet.
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Clay has a bag that contains 4 white marbles and 10 black marbles. Clay chooses a marble from the bag without looking, records the color, replaces it, then
chooses another marble. What is the theoretical probability that Clay chooses a white marble both times?
• 2.04%
O 8.16%
0 28.57%
O 51.02%
!!
Explanation:
There are 4 white marbles out of 4+10 = 14 total
4/14 = 2/7 is the probability of randomly picking a white marble.
(2/7)*(2/7) = 4/49 is the probability of picking two whites in a row, when the first marble is replaced.
Use a calculator to find that 4/49 = 0.0816 approximately.
That converts to 8.16% after moving the decimal point two spots to the right. This is equivalent to multiplying by 100.
The federal excise tax on cigarettes is $3.80 per carton. In Wisconsin the state excise tax on cigarettes is $17.70 per carton. If a carton of cigarettes contains 10 packs, what is the total excise tax per pack in Wisconsin?
The total excise tax per pack is $2.15.
What is the total excise tax?The total excise tax is the sum of the federal excise tax and the state excise tax.
Excise tax is the tax that is levied at the moment of manufacture of a good or service. Excise tax is usually levied on alcoholic or tobacco products.
Total excise tax = federal excise tax + state excise tax
$3,80 + $17.70 = $21.50
The total excise tax per pack can be known by dividing the total excise tax by the total number of packs.
Total excise tax per pack = $21.50 / 10 = $2.15
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Consistent and Dependent Consistent and Independent Inconsistent y=-x+1 y=-x y=x+2 y=x y=x y=2x 00*30:03
The first system is inconsistent, the second system is consistent and dependent, and the third system is consistent and independent.
A system of equations can be classified as consistent, dependent, or inconsistent. A consistent system has at least one solution. A dependent system has infinitely many solutions, and an inconsistent system has no solution.
The first system of equations, y=-x+1 and y=-x, is inconsistent. This is because there is no value of x that can make both equations true at the same time. The graphs of these equations would be parallel lines that never intersect, meaning there is no solution.
The second system of equations, y=x+2 and y=x, is consistent and dependent. This is because there are infinitely many solutions that make both equations true. The graphs of these equations would be the same line, meaning every point on the line is a solution.
The third system of equations, y=x and y=2x, is consistent and independent. This is because there is only one solution that makes both equations true. The graphs of these equations would be two lines that intersect at one point, meaning there is only one solution.
In summary, the first system is inconsistent, the second system is consistent and dependent, and the third system is consistent and independent.
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Lee wants to make at least $400 profit from selling t-shirts. The initial start up costs for making t-shirts is $125. Write an inequality that represents the amount of sales, s, that Lee must have to reach the goal.
The inequality that represents the amount of sales, [tex]s$,[/tex] that Lee must have to reach the goal is:
[tex]$$s \geq \frac{525}{p}$$[/tex]
What is profit ?In business and finance, profit refers to the monetary gain earned by a business or individual after subtracting the expenses from the total revenue. In other words, profit is the difference between the amount of money earned from selling goods or services and the total cost of producing or delivering those goods or services. Profit is often used as a key performance indicator (KPI) to measure the financial success of a business or individual.
According to given information ?Let's assume that the cost of making one t-shirt is c and Lee sells each t-shirt for p.
To make at least $400 profit, Lee's revenue from sales p must be greater than or equal to the sum of the startup costs $125 and the desired profit $400:
[tex]$$p\times s \geq 125+400$$[/tex]
We can simplify this inequality to:
[tex]$$p\times s \geq 525$$[/tex]
Therefore, the inequality that represents the amount of sales, [tex]s$,[/tex] that Lee must have to reach the goal is:
[tex]$$s \geq \frac{525}{p}$$[/tex]
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Each fall, thousands of mushroom hunters search the forest for truffles. A set of plots of equal size in an old-growth forest in Northern California was surveyed to count the number of truffles. The resulting distribution is presented in the following table. Are truffles randomly located around the forest? If not, are they clumped or dispersed? How can you tell? (the mean number of truffles per plot is 0.60)
Include the hypotheses you are testing, the chi-square value, the critical value, p-value, and conclusion Number of truffles per plot frequency
0 203
1 39
2 18
3 13
>3 15
As the variance/mean ratio is significantly greater than 1, the population is found to be a clumped distribution.
What is a Clumped Distribution?A clumped distribution, also known as an aggregated distribution, is a pattern of dispersion or arrangement of individuals within a population where they are found in groups or clusters. This means that individuals within a population are more likely to be found in certain areas, while other areas may have few or no individuals.
From the table in the attached image, it can be seen that
the variance= sum of (x - 0.6)^2/ sum of frequency
= 362.88/288
= 1.26
Variance/mean = 1.26/0.6 = 2.1 which is greater than 1
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If you travel 200 miles in four hours, then your average speed for the trip is average speed =200/(no response) =( (No Response) mi/h
If you travel 200 miles in four hours, then your average speed for the trip is 50 miles per hour. This is calculated by dividing the total distance traveled (200 miles) by the total time taken (4 hours).
Start with the formula for average speed: average speed = total distance / total timePlug in the given values for total distance and total time: average speed = 200 miles / 4 hoursSimplify the equation by dividing 200 by 4: average speed = 50 mi/hThe final answer is 50 miles per hour.So, if you travel 200 miles in four hours, your average speed is 50 mi/h.
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find the volume pls help asap
Answer: I think the answer is B. 241.13
Step-by-step explanation:
Formula for the volume of a cube is length of an edge cubed.
[tex]6^3=216[/tex]
Formula for the volume of a cone is [tex]\pi r^2\frac{h}{3}[/tex]
Half of 4 is 2, so the equation will be [tex]\pi 2^2\frac{6}{3}=25.13[/tex]
Add them together to get the answer
[tex]216+25.13=241.13[/tex]
I might be wrong, because I haven't done this in a long time, but I tried to do as much as possible, so forgive me if this is wrong.
HELP PLEASE I WILL GIVE POINTS PLEASE HELP PLS PLS
Answer:
Air
Step-by-step explanation:
it's asking you to look at the chart and find which substance is densest by comparing it to how fast sound can move through it (the speed of sound in the substance). In my opinion copper is not the densest material because sound moves through it the fastest; which means the particles in copper are not as densely held together. Air however, shows that sound can only travel 330 meters per second which is incredibly slow compared to the other listed materials, so by that logic it must be the densest.
DESCRIPTIVE ANALYTICS
A producer of computer aided design software for the aerospace
industry receives numerous calls for technical support. Tracking
software is used to monitor response and resolution
In the case of the producer of computer-aided design software for the aerospace industry, descriptive analytics can be used to analyze the data collected from the tracking software to monitor the response and resolution of technical support calls.
Descriptive analytics is a method used to collect, analyze and summarize data. In the case of the aerospace industry, descriptive analytics can be used to track the response and resolution of technical support calls. This helps to provide insights into the quality of service and make decisions about future changes to optimize the process.
In the case of the producer of computer-aided design software for the aerospace industry, descriptive analytics can be used to analyze the data collected from the tracking software to monitor the response and resolution of technical support calls.
By analyzing this data, the producer can gain insights into the most common types of technical support issues, the average response and resolution times, and any trends or patterns in the data. This information can then be used to improve the technical support process, identify areas for improvement, and develop strategies to prevent future technical support issues.
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Find the equation of a line with the properties given. Write the equation in the form indicated. Through (3,5) and parallel to the line whose equation is ( y=-6x+4 ). Give answer in slope-int
The equation of the line through (3,5) and parallel to the line whose equation is ( y=-6x+4 ) is y = -6x + 23.
To find the equation of a line with the given properties, we need to use the concept of parallel lines and the point-slope form of a linear equation.
Parallel lines have the same slope, so the slope of the new line will be the same as the slope of the given line ( y=-6x+4 ), which is -6.
Next, we can use the point-slope form of a linear equation, which is (y - y1) = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Plugging in the given point (3, 5) and the slope -6, we get:
y - 5 = -6(x - 3)
Simplifying the equation, we get:
y - 5 = -6x + 18
y = -6x + 23
Finally, we can write the equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. The equation of the new line is y = -6x + 23.
Therefore, the equation of the line through (3,5) and parallel to the line whose equation is ( y=-6x+4 ) is y = -6x + 23.
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Camden multiplied two binomials and got the product of 49x^(2)-100. Find the two binomials that Camden must have multiplied.
The two binomials that Camden must have multiplied and got the product of 49x^(2)-100 are (7x+10) and (7x-10).
To find the two binomials that Camden must have multiplied to get the product of 49x^(2)-100, we can use the process of factoring. Factoring is the process of breaking down a larger expression into two or more smaller expressions that can be multiplied together to get the original expression.
One way to factor the expression 49x^(2)-100 is to look for two binomials that have a difference of squares. A difference of squares is an expression of the form a^(2)-b^(2), which can be factored into (a+b)(a-b).
In this case, we can see that 49x^(2) is a perfect square, as it is equal to (7x)^(2), and 100 is also a perfect square, as it is equal to 10^(2). Therefore, we can factor the expression 49x^(2)-100 into (7x+10)(7x-10).
So, the two binomials that Camden must have multiplied are (7x+10) and (7x-10).
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Help! Please, thank you
Answer:
Step-by-step explanation:
OK so im not that smart im only in 8th grade but i think the answers either A or B. hope i kind of helped you and good luck and have a nice day.
\[ \begin{array}{l} n=4 \\ -1,4, \text { and } 3+2 i \text { are zeros; } \\ f(1)=-144 \end{array} \] \[ f(x)= \] (Type an expression using \( x \) as the variable. Simplify your answer.)
Plugging in \( x = 1 \) gives us \[ -144 = (1+1)(1-4)(1^2 - 6(1) + 13) = (2)(-3)(8) = -48a \] Solving for \( a \) gives us \[ a = \frac{-144}{-48} = 3 \] So, the expression for \( f(x) \) is \[ f(x) = 3(x+1)(x-4)(x^2 - 6x + 13) \]
To find the expression for \( f(x) \), we need to use the fact that the zeros of a polynomial are the values of \( x \) that make the polynomial equal to zero. This means that if \( -1, 4, \) and \( 3+2i \) are zeros of \( f(x) \), then the factors of \( f(x) \) are \[ (x+1)(x-4)(x-(3+2i))(x-(3-2i)) \] Now, we can simplify the last two factors by multiplying them together: \[ (x-3-2i)(x-3+2i) = (x-3)^2 - (2i)^2 = x^2 - 6x + 9 - 4i^2 = x^2 - 6x + 9 + 4 = x^2 - 6x + 13 \] So, the expression for \( f(x) \) is \[ f(x) = (x+1)(x-4)(x^2 - 6x + 13) \] Now, we can use the fact that \( f(1) = -144 \) to find the value of the leading coefficient of \( f(x) \). Plugging in \( x = 1 \) gives us \[ -144 = (1+1)(1-4)(1^2 - 6(1) + 13) = (2)(-3)(8) = -48a \] Solving for \( a \) gives us \[ a = \frac{-144}{-48} = 3 \] So, the expression for \( f(x) \) is \[ f(x) = 3(x+1)(x-4)(x^2 - 6x + 13) \] This is the final answer.
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15. On a 45 questions exam, a student gets 40%. How many questions did this student get correct? 16. A vitamin tablet, which weighs 250 milligrams, contains 35 milligrams of vitamin C. What percent of the weight of this tablet is vitamin C? 17. Five years ago, a secretary made $11,200 annually. The secretary now makes $17,920 annually. By what percent has this secretary's salary been increased? 18. A typist was able to increase his speed by 120% to 42 words per minute. What was her original typing speed? 19. A salesperson makes a commission of 12% on the total amount of each sale. If, in one month, she makes a total of $8,520 in sales, how much has she made in commission? 20. A salesperson receives a salary of $850 per month plus a commission of 82% of her sales. If, in a particular month, she sells $22,800 worth of merchandise, what will be her monthly earnings?
15. The student got 18 questions correct.
16. The weight of vitamin C in that tablet is 14%.
17. The secretary's salary has been increased by 60%.
18. The typist's original typing speed was 21 words per minute.
19. The salesperson made $1,022.40 in commission.
20. The salesperson's monthly earnings will be $19,546.
How to calculate the percentage?15. On a 45 questions exam, a student gets 40%.
The number of correct questions that the student got is
= 40% × 45 questions
= 18 questions
16. A vitamin tablet, which weighs 250 milligrams, contains 35 milligrams of vitamin C.
The percent of the weight of this tablet is vitamin C is
= 35mg/250mg × 100%
= 14%
17. Five years ago, a secretary made $11,200 annually. The secretary now makes $17,920 annually.
The percentage the secretary's salary has been increased by
= ($17,920/$11,200 × 100%) - 100%
= 160% - 100%
= 60%
18. A typist was able to increase his speed by 120% to 42 words per minute.
Her original typing speed was
= 42/120% × 100%
= 42/1.2
= 21 words per minute
19. A salesperson makes a commission of 12% on the total amount of each sale. In one month, she makes a total of $8,520 in sales.
In that month, she made a commission of
= $8,520 × 12%
= $1,022.40
20. A salesperson receives a salary of $850 per month plus a commission of 82% of her sales. In a particular month, she sells $22,800 worth of merchandise.
Her monthly earnings will be
= $850 salary + 82% × $22,800
= $19,546
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Eyeglassomatic manufactures eyeglasses for different retailers. The number of days it takes to fix defects in a pair of eyeglasses and the probability that it will take that number of days are in the table.
a) State the random variable.
Select an answer
rv X = the number of eyeglasses made
rv X = the probability that it will take that number of days to fix
rv
b) If you were to make the corresponding histogram for this frequency table, what shape would the histogram be?
✓ Select an answer
Right-skewed
Uniform
Left-skewed
Bell-shaped
c) Find the mean number of days to fix defects.
Put the numeric answer rounded to 3 decimal places in the first box and the correct units in the second box.
The mean number of days to fix defects is 3.2 days.
The random variable in this case is the number of days it takes to fix defects in a pair of eyeglasses. Therefore, the correct answer is:
rv X = the number of days to fix defects
The corresponding histogram for this frequency table would be right-skewed. This is because there is a higher probability of it taking fewer days to fix the defects, with the probability decreasing as the number of days increases.
To find the mean number of days to fix defects, we need to multiply each number of days by its corresponding probability and then sum the results. The formula for this is:
mean = ∑(x * P(x))
Where x is the number of days and P(x) is the probability of it taking that number of days.
Using the data from the table, we can calculate the mean as follows:
mean = (1 * 0.1) + (2 * 0.2) + (3 * 0.3) + (4 * 0.25) + (5 * 0.1) + (6 * 0.05)
mean = 0.1 + 0.4 + 0.9 + 1 + 0.5 + 0.3
mean = 3.2
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Find the gradients of lines A and B.
B
-2
6
O
-21
Fet
A
4
72%
X
The gradient of line A is 4/72% or 0.0555.The gradient of line B is -2/6 or -0.3333.
What is value?Value is the worth of something, or the amount of importance, good qualities, or benefits that something has. It is determined by the amount of effort, time, and resources that have been put into it. Value can also refer to a person's moral or ethical principles and standards. It is the measure of worth that someone places on something or someone. Ultimately, value is subjective, as it is based on individual opinion.
The gradients of lines A and B indicate the rate of change of the line in relation to the x-axis. The gradient of line A is positive, which indicates that the line is increasing as it moves along the x-axis. This means that the y-value of the line is increasing as the x-value increases. On the other hand, line B has a negative gradient, which means that the y-value of the line is decreasing as the x-value increases. This means that the line is decreasing as it moves along the x-axis. This is why the gradients of lines A and B are different.
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whats the answer to this?
Answer:
Answer is C
Step-by-step explanation:
using long divison:
Twenty-seven times the weight in kilogram of a baby elephant increased by 400 pounds is less than the weight in kilogram of an adult elephant
The weight of the baby elephant is less than 212.59 kilograms which can be calculated using inequality.
To solve this problem, we need to use the inequality and the given information to find the weight of the baby elephant and the adult elephant. We can write the inequality as follows:
27w + 400 < a
Where w is the weight of the baby elephant in kilograms, and a is the weight of the adult elephant in kilograms. We can rearrange this inequality to get:
w < (a - 400)/27
Now, we can plug in the given information to find the weight of the baby elephant and the adult elephant. For example, if the weight of the adult elephant is 6000 kilograms, we can plug this into the inequality and get:
w < (6000 - 400)/27
w < 212.59
Similarly, we can plug in different values for the weight of the adult elephant to find the weight of the baby elephant.
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21. A path 1 m wide is built along the border and inside a square garden of side 30 m. Find:
(i) the area of the path
(ii) the cost of planting grass in the remaining portion of the garden at the rate of Rs 40 per m2
(i) The area of the path is 120x - 4x² square meters.
(ii) The cost of planting grass in the remaining portion of the garden at the rate of Rs 40 per m² is (900 - 120x + 4x²) × 40
To find the area of the path and the remaining portion of the garden, we need to first find the dimensions of the inner square after the path has been constructed.
Let the width of the path be "x" meters. Then the dimensions of the inner square garden will be (30-2x) meters on each side.
(i) The area of the path can be found by subtracting the area of the inner square from the area of the outer square.
Area of outer square = 30 × 30 = 900 sq.m.
Area of inner square = (30-2x) × (30-2x) = 900 - 120x + 4x² sq.m.
Area of path = Area of outer square - Area of inner square
= 120x - 4x² sq.m.
(ii) The remaining portion of the garden is the area of the inner square.
Area of remaining portion = (30-2x) × (30-2x) sq.m.
= 900 - 120x + 4x² sq.m.
The cost of planting grass in the remaining portion of the garden at the rate of Rs 40 per m² can be found by multiplying the area of the remaining portion by the rate.
Cost of planting grass = Area of remaining portion × Rate
= (900 - 120x + 4x²) × 40
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