Answer:
To solve the problem, we need to add 23 7/8 and 3 1/2 to find the final price.
First, we need to convert 3 1/2 to an improper fraction:
3 1/2 = (2 x 3) + 1/2 = 7/2
Next, we need to find a common denominator between 8 and 2:
8 = 8/1
2 = 2/1 x 4/4 = 8/4
Now we can add the two fractions:
23 7/8 + 3 1/2
= 23 14/16 + 3 8/16 (using 16 as the common denominator)
= 27 6/16
= 27 3/8
Therefore, the stock was priced at $27 3/8 at the end of trading.
with k being all the numbers from one to 100, whats x3+y3+z3=k?
X = -80538738812075974, Y = 80435758145817515,
and Z = 12602123297335631 are the values of x,y,z of whole numbers.
What in mathematics is a whole number?
Complete numbers the sum of all natural numbers plus zero. not a decimal or fraction. {0, 2, 3, 4, 5 6, 7, 8, 9, 10, 11 …} Integer. a negative number, zero, or a counting number.
Natural numbers with a starting value of 1 and higher are considered whole numbers. Let's examine a few instances of entire numbers. The alphabet "W" stands for the collection of whole numbers. W = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,.…}
x3+y3+z3=k, with k being all the numbers from one to 100
X = -80538738812075974,
Y = 80435758145817515,
and Z = 12602123297335631
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Please help it’s for tmr
Leo has a number of toy soldiers between 27 and 54. If you want to group them four by four, there are none left, seven by seven, 6 remain, five by five, 3 remain. How many toy soldiers are there?
The answer is 48 but I need step by step explanation
The number of toy soldiers that Leo has is 48.
How many toy soldiers does Leo have?The first step is to determine the multiples of 4 that lie between 27 and 54. A multiple of a number is the product of an integer and that number.
Multiplies of 4 that lie between 27 and 54 = 28, 32, 36, 40, 44, 48, 52
Now divide each of the multiples by 7 :
28 / 7 = 4
32 / 7 = 4 remainder 4
36 / 7 = 5 remainder 1
40 / 7 = 5 remainder 5
44 / 7 = 6 remainder 2
48 / 7 = 6 remainder 6
52 / 7 = 7 remainder 3
It only 48 that meets this criteria. This means that the number is 48.
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I NEED HELP ON THIS ASAP!!
We can plot the lines x = 260, y = 320, and x + y = 380 to graph these limitations, and we can highlight the area that satisfies each requirement.
A constraint formula is what is it?We refer to x and y as being limited by g(x,y)=c, which is also referred to as the constraint equation. Constrained maximum or constrained minimum points, respectively, are positions (x,y) that meet the constraint equation g(x,y)=c and are maxima or minima of f(x,y).
Let's indicate the quantity of black walnut and mahogany boards sold, respectively, using the variables x and y.
x ≤ 260 (constraint on the number of mahogany boards)
x + y ≤ 380 (constraint on the total number of boards sold)
y ≤ 320 (constraint on the number of black walnut boards)
We also understand that the quantity of sold boards cannot be zero, hence we have:
x ≥ 0
y ≥ 0
Last but not least, our goal is to maximise profit, as indicated by the expression:
P = 20x + 6y
When all the restrictions are combined, the following inequality system results:
x ≤ 260
y ≤ 320
x + y ≤ 380
x ≥ 0
y ≥ 0
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Jessie is considering a purchase of a $135,000 home at 5. 5%. Under this rate,
her mortgage payment would be $766. 51. If she purchases a point, her new
mortgage payment is $755. 96. How many months would it take her to break-
even on the points purchase?
As per unitary method, the number of months would take her to break - even on the points purchase is 128
To break even on the points purchase, Jessie needs to recoup the cost of the point through the savings in her monthly mortgage payments. In this case, the cost of the point is 1% of the loan amount, which is $1,350.
To calculate the break-even point, we can use the following formula:
Break-even point = Cost of point / Monthly savings
In this case, the monthly savings is the difference between the original mortgage payment ($766.51) and the new mortgage payment with the point ($755.96), which is $10.55 per month.
Substituting the values, we get:
Break-even point = $1,350 / $10.55
Break-even point = 128 months
Therefore, it would take Jessie 128 months, or just over 10 years, to break even on the points purchase.
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Helllllppppp due tomorrow
Answer: Area = 47.5m(2)
Step-by-step explanation:
Area = Pie X r(2) / 2
Area = 3.14 X 5.5(2)/2
Area = 47.4925
Select all of the following that are linear functions.
x = 5
y
-2
4
0
1
2
-2.
4
5
x + 7 = 4y
A) x = 5 is not a linear function since it is a vertical line and does not have a slope. B) The table description does not provide enough information to determine if it is a linear function. C) x + 7 = 4y is a linear function in slope-intercept form (y = (1/4)x + 7/4).
A linear function is a mathematical function that can be represented by a straight line with a constant slope. The equation of a linear function can be written in the form y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis). Option A (x = 5) is not a linear function, as it is a vertical line with an undefined slope. Option B is a linear function, as the table describes points that can be plotted to form a straight line. Option C is also a linear function, but it is in a different form (x + 7 = 4y). This equation can be rearranged to y = (1/4)x + 7/4, which is in the standard form of a linear function.
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Answer: C.) x + 7 = 4y and D
Step-by-step explanation: i hope this helps
in part i, you will evaluate an aircraft altimeter data sample from different companies to determine if there are any differences in error. you have the following three options for running the appropriate t-test. option 1 - compare one brand against a hypothesized mean to determine if the brand is statistically different than the assumed norm. in this case, you would have to cite where the hypothesized population mean came from. option 2 - compare one brand against another to see if there are significant differences between them. option 3 - compare either altimeter error of acme or brand x before adjustment and calibration and after adjustment and calibration to see if there are any differences in the means (performance). based on the type of dependent variable data (ratio) and the type of question in the scenario, you will use a t-test. as you know, there are three different types of t-tests you can use: one sample t-test (test for one population mean using excel) two sample t-test (hypothesis test for two population means using excel) paired t-test (compare before and after values for one type using excel)
From the following three options for running the appropriate t-test, Both Options (2) and (3) could be applicable depending on the specific research question being investigated.
The appropriate t-test to use in this scenario is paired t-test. This test compares before and after values for one type using excel. In this scenario, you would be comparing either the altimeter error of ACME or brand x before adjustment and calibration and after adjustment and calibration to see if there are any differences in the means (performance).
Based on the scenario described, Option 1 is not appropriate because there is no hypothesized population mean to compare against. Therefore, we can exclude this option.
Option 2, comparing one brand against another, could be appropriate if we want to investigate if there are any significant differences in altimeter error between brands. This would be a two-sample t-test.
Option 3, comparing the altimeter error of one brand before and after calibration, could also be appropriate to see if the adjustment and calibration had a significant impact on the altimeter's performance. This would be a paired t-test.
This test is the appropriate test to use because the dependent variable data in this scenario is the ratio and the type of question requires a paired t-test. In this scenario, you are comparing the performance of the two brands before and after adjustment and calibration, which requires paired t-test to answer the research question.
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What is the linear equation of a line that goes through (-4, 3) and (0,6)?
Answer:
y=(3/4)x+6
Step-by-step explanation:
Point 1 (-4,3)
Point 2 (0,6)
To obtain the slope, we apply the formula:
m= (6-3) / (0- (-4))
m= 3 / 4
We replace in the equation y=mx+b.
We take any point.
=> (0,6)
y=mx+b
6=(3/4)(0)+b
b=6
Joining all the terms:
y=(3/4)x+6
I need help, what does this mean
Answer:
2125 ft/min
33,000 ft
y = -2125x + 33,000
Step-by-step explanation:
A. -2125 feet per minute. You get this number when you divide 17,000 by 8 (rise over run). You could also use the formula y2-y/x2-x1 with the points (0, 33,000) and (8, 17,000).
B. 33,000 feet is the height of the plane before it starts descending, so it must be the starting value.
C. Plug in the values you got for A and B into the slope formula y = mx + b
y = -2125x + 33,000
An online retailer receives 5% off of all the sales made into here website
After answering the prοvided questiοn, we can cοnclude that the 5% expressiοn discοunt is mοst likely intended tο encοurage custοmers tο purchase.
What is expressiοn ?A cοllectiοn οf symbοls, digits, and cοnglοmerates in mathematics that resemble a pattern οr statistical cοrrelatiοn is knοwn as an expressiοn. Real numbers, mutables, and cοmbinatiοns οf the twο are all acceptable types οf expressiοns. A few examples οf mathematical οperatοrs are additiοn, subtractiοn, rapid spread, divisiοn, and expοnentiatiοn. Expressiοns are frequently used in mathematics, geοmetry, and shape. They are used fοr equatiοn sοlving, representing mathematical fοrmulas, and simplifying mathematical relatiοnships.
All purchases made thrοugh the οnline stοre's website appear tο be eligible fοr a 5% discοunt. The custοmer will thus save 5% οff the tοtal cοst οf the purchase with each sale. Fοr instance, if a custοmer spends $100 οn gοοds, they will get a $5 discοunt, lοwering the final cοst tο $95.
It's wοrth nοting that the retailer may chοοse tο sacrifice prοfits in οrder tο οffer this discοunt. Alternatively, they may have negοtiated lοwer prices with their suppliers οr implemented οther cοst-cutting measures tο cοmpensate fοr the cοst οf the discοunt. In any case, the 5% discοunt is mοst likely intended tο encοurage custοmers tο purchase.
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Complete question:
Angela compro un terreno rectangular que tiene un perimetro de
10x - 28a
Si el ancho del terreno es 2x - 4a
¿Cual es la expresión que muestra la medida del largo del terreno?
The expression that shows the measurement of the length of the land is L = 3x - 10a.
Let L be the length of the rectangular plot.
We know that the perimeter of a rectangle is given by the sum of the lengths of all its sides. In this case, the perimeter is 10x - 28a, so we can write:
Perimeter = 2L + 2W
10x - 28a = 2L + 2(2x - 4a)
10x - 28a = 2L + 4x - 8a
2L = 6x - 20a
L = 3x - 10a
In other words, the length of the land is equal to three times the width minus ten times the value of 'a'.
To explain this equation in a little more detail, we can say that the length of the rectangular plot is dependent on both the width of the land and the value of 'a'.
The expression tells us that as the value of 'a' increases, the length of the land decreases, and as the width of the land increases, the length of the land also increases. This equation is useful because it allows us to calculate the length of the land without having to measure it directly, as long as we know the value of 'a' and the width of the land.
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If the p-value of the coefficient of an X variable in a regression is 0.001, then it is reasonable to say that the coefficient of the X variable is 0 in the population regression line. true or false?
The given statement is false becasue If the p-value of the coefficient of an X variable in a regression is 0.001, then it suggests that there is significant evidence that the coefficient is different from 0 in the population regression line.
A p-value is a value that represents the probability of obtaining the observed results of a statistical hypothesis test. The p-value is used as an alternative to rejection point to give the smallest level of significance at which the null hypothesis would be rejected. It can be used to test hypotheses in statistics.
If the p-value is less than the significance level (α), then the null hypothesis is rejected. However, if the p-value is greater than the significance level (α), then the null hypothesis is not rejected. Therefore, we reject the null hypothesis if the p-value is less than or equal to the level of significance.
So, if the p-value of the coefficient of an X variable in a regression is 0.001, it suggests that the coefficient is statistically significant and different from 0 in the population regression line. Hence, the statement "it is reasonable to say that the coefficient of the X variable is 0 in the population regression line" is false.
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Drag the appropriate answer from the
choices given into the box provided.
A function is graphed on the
coordinate grid. The output for the function when the input is -1 is?
Answer:
This graph shows a quadratic curve with roots 0 and -4
The polynomial is therefore
x² -x(α+β) + αβ
x² -x(0-4) + 0(-4)
x² +4x +0
x² + 4x
But it's an n-shaped curve, meaning a is negative
Multiply through by -1
-x² - 4x
y = -x² - 4x
So when the input value x = -1
y = -(-1)² + 4(-1)
y = -(1) - 4
y = -1 - 4
y = -3
Check the graph to confirm
suppose point p divides the directed line segment xy so that the ratio of xp to py is 3 to 5 . describe point r that divides the directed line segment yx so that the ratio of yr to rx is 5 to 3 .a. R and P are the same pointb. Point R is halfway between point P and point Xc. The distance from point X is the same as the distance prom point P to point Yd. Point R is three fifths of the way from point P to point Y along PY
For point, p divides the directed line segment xy so that the ratio of xp to py is 3 to 5 correct option is d. Point R is three-fifths of the way from point P to point Y along PY.
The directed line segments divide a line into ratios, and each ratio has different properties. The properties of ratios of points on a line are dependent on the way the line is divided. For instance, suppose point p divides the directed line segment xy so that the ratio of xp to py is 3 to 5. We can describe point r that divides the directed line segment yx so that the ratio of yr to rx is 5 to 3 as follows:
We can solve this problem using the concept of directed line segments and the properties of ratios of points on a line.
Since P divides the directed line segment XY in the ratio 3:5, we can write:
XP = (3/8)XY and PY = (5/8)XY
Now, let's consider the directed line segment YX. We want to find a point R on this segment such that YR:RX = 5:3.
We can express YR and RX in terms of XY using the fact that YX = -XY:
YR = (5/8)YX and RX = (3/8)YX
Substituting -XY for YX, we get:
YR = (-5/8)XY and RX = (-3/8)XY
To find the location of point R, we need to find the distance from Y to R along the directed line segment YX. We can do this by adding the distances from Y to P and from P to R:
YR = YP + PR
Using the ratios we derived earlier, we can express YP and PR in terms of XY:
YP = PY = (5/8)XY
PR = R - P = (3/8)XY - (3/8)XY = 0
Therefore, YR = (5/8)XY + 0 = (5/8)XY
This means that point R is located at a distance of 5/8 of the length of YX from Y. So, the correct answer is (d) Point R is three-fifths of the way from point P to point Y along PY.
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prove that the cardinality of the cross product of two sets is the cardinality of each individual set multiplied by each other
We need to use mathematical logic to prove that the cardinality of the cross product of two sets is the cardinality of each individual set multiplied by each other.
Let's take an example of two sets A and B.
Let's say, A={a, b} and B={1, 2, 3}
To find the cardinality of the cross-product of A and B, we need to make all possible ordered pairs with A and B.
{(a, 1), (a, 2), (a, 3), (b, 1), (b, 2), (b, 3)}
Counting the number of ordered pairs, we get six.
So, the cardinality of the cross-product of two sets A and B equals the cardinality of each set multiplied by the other. Here,
|A| = 2 and |B| = 3,
so |A x B| = 2 x 3
= 6.
Therefore, it is proved that the cardinality of the cross product of two sets is the cardinality of each individual set multiplied by each other.
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One family spent $45 on movie tickets for 2 adults and 3 childr
Another family spent $40 for 2 adults and 2 children. What are
prices of the adult movie tickets and the child movie tickets?
Answer:The prices of the adult movie tickets and the child movie tickets are $15 and $5 respectively.
Given that, the Jones family spent $45 on movie tickets for 2 adults and 3 children.
Step-by-step explanation:What is a linear system of equations?
A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
Let cost of adult tickets be x and the cost of children tickets be c.
The Jones family spent $45 on movie tickets for 2 adults and 3 children.
2a+3c=45 ------(I)
The Smith family spent $40 for 2 adults and 2 children.
2a+2c=40
a+c=20 ------(II)
From equation (II), we have a=20-c
Substitute a=20-c in equation (I), we get
2(20-c)+3c=45
⇒ 40-2c+3c=45
⇒ c=$5
Put c=5 in equation (II), we get
a+5=20
⇒ a=$15
Explain how to solve the given equation for "x".
X = 2 is the solution of the given equation for "x".
What does a math equation mean?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. For instance, 3x + 5 = 14 is an equation where 3x + 5 and 14 are two expressions separated by the 'equal' sign.
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. By solving for x, we discover that x equals 7, which is the value for the variable.
8ˣ = (25)
8ˣ = (5)²
X = 2
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Ty worked 5 nights this week at an ice cream shop. He earned $23, $29, $25, and $16 in tips. The average amount he earned in tips for the 5 nights was $22. Is the amount he earned in tips on night 5 more or less than the average amount? Select the correct answer and explanation.
Ty made more money in tips on night 5 than usual because $49 is more than the standard $22 tip level.
what is equation ?A mathematical statement that demonstrates the equality of two expressions is known as an equation. Mathematical operations like addition, subtraction, multiplication, and division may be used, and it frequently involves one or more variables that are represented by letters. Equations are employed in a variety of mathematical and scientific contexts, from the solution of straightforward algebraic problems to the modeling of intricate physical systems. Finding the values of the variables that equalize both sides of the equation is necessary to solve an equation.
given
On night 5, he received the following in tips:
Total tips: ($23 + $29 + $25 + $16) multiplied by the sum of the tips from the first four nights equals $22 * 5.
Ty made more money in tips on night 5 than usual because $49 is more than the standard $22 tip level.
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Answer:
Step-by-step explanation:
a class has a ratio of boys to girls of 3:4 for each statement below
The correct statement explain for the given ratio of boys to girls of 3:4 is - this fraction of girls in the class is found to be 4/7.
Explain about the ratio of the number?Irrespective whatever how a ratio is expressed, it is crucial to reduce it to the fewest whole numbers, just like with any fraction. To accomplish this, divide the integers by their largest common factor after discovering it.
Ratios can also be expressed as a fraction because they are straightforward division problems. Some folks prefer to use merely words to express ratios.
Class contains a ratio of boys to girls of 3: 4.
So, Boys / Girl = 3 / 4
Total students = boys + girls.
Total students = 3 + 4 = 7
So,
Girl / Total = 4/7
Thus, the correct statement explain for the given ratio of boys to girls of 3:4 is - this fraction of girls in the class is found to be 4/7.
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The complete question is-
A class has a ratio of boys to girls 3:4.
Select correct option:
a) The fraction of boys in the class is 3/4
b) The fraction of girls in the class is 4/7
c) The number of boys in the class is 6
d) The number of pupils in the class is 12
Construct triangle ABC, in which AB = 5 cm, angle BAC = 95° and
angle ABC = 34°.
Measure the length of BC.
Give your answer to 1 d.p.
The length of BC is approximately 3.5 cm
What is a triangle?A triangle is described as a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.
We construct triangle ABC, through the following steps:
Draw a line segment AB of length 5 cm.At point A, draw a ray that makes an angle of 95 degrees with AB.At point B, draw a ray that makes an angle of 34 degrees with AB.The intersection point of the two rays is point C, which is the third vertex of the triangle.The law of sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.
Mathematically shown as:
a/sin(A) = b/sin(B) = c/sin(C)
5/sin(95) = BC/sin(34)
BC = (5*sin(34))/sin(95)
BC ≈ 3.5cm
In conclusion, the length of BC is approximately 3.5 cm.
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Complete the table of values for y=1/2x^3-2x+1
Table of values:
x y
-2 5
-1 3/2
0 1
1 1/2
2 1
We may solve for y by substituting the supplied values of x into the equation [tex]y=1/2x3-2x+1[/tex] and completing Table of values .
For instance,[tex]y=1/2(-2)3-2(-2)+1[/tex] Equals 5 when[tex]x=-2.[/tex] The equivalent values of y for x=-1, 0, 1, and 2 are similarly found.
The ordered pairs (x,y) that fulfil the equation are displayed in the resultant table. These points allow us to graph the equation and see how the curve looks. In this instance, the equation describes a cubic function with two turning points at (-1,3/2) and (1,1/2), as well as a horizontal intercept at (0,1).
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Is [tex]a^2(a-0.4)^3[/tex] completely factored?
The original question was to completely factor this:
[tex]a^5-0.064a^2[/tex]
Answer:
[tex]\bf a^2* (a - 0.4)(a^2 + 0.4a + 0.16)[/tex]
Step-by-step explanation:
Factorize:
First take out the common term a².
[tex]a^5 - 0.064a^2= a^2*(a^3 - 0.064)\\\\[/tex]
Now, factorize using the identity a³ - b³
a³ - b³ = (a - b) (a² + ab + b²)
[tex]a^2 * (a^2 - 0.064) = a^2 * (a^3 - 0.4^3)[/tex]
[tex]= a^2 * (a - 0.4) * (a^2 + a*0.4 + 0.4^2)\\\\=a^2 * (a - 0.4)(a^2 + 0.4a + 0.16)[/tex]
list and describe the four scales of measurement. please provide an example of each one. which measures of central tendency apply to each scale of measurement?
Measurement scales refer to the various methods of assigning scores to measurements according to their precision and accuracy. There are four primary scales of measurement; nominal, ordinal, interval, and ratio.
The four measurement scales and their definitions are listed below:
Nominal scale: This is the lowest level of measurement. It is used to name, classify, or identify objects, events, or groups. It has no logical order, and its units cannot be compared or arranged in a sequence.
Examples of the nominal scale include; gender (male or female), marital status (single or married), color (black or white), and so on.
Ordinal scale: This scale includes a more elaborate classification than nominal measurement. It distinguishes between levels of preference or priority, but it does not have a constant distance between the levels.
Examples of the ordinal scale include; rankings (first, second, third, and so on), level of satisfaction (very happy, happy, neutral, unhappy, very unhappy), and so on.
Interval scale: This scale has a constant distance between its units, and its elements can be compared or arranged in a sequence. It does not have a true zero.
Examples of the interval scale include; temperature (measured in Fahrenheit or Celsius), time (measured in seconds, minutes, or hours), and so on.
Ratio scale: This is the highest level of measurement, where it has a constant distance between its units, its elements can be compared or arranged in a sequence, and it has a true zero.
Examples of the ratio scale include; weight, length, height, and so on. Measures of central tendency include; mean, median, and mode. The mean is the average of all the data points in a set, the median is the middle value in a set of data, and the mode is the value that occurs most often. The table below provides an example of each measurement scale and the appropriate measures of central tendency for each. Scales of Measurement Examples Measures of Central Tendency Nominal Scale Gender Mean Ordinal Scale Ranking Median Interval Scale Temperature Mean Ratio Scale Height Mode.
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an offshore oil well is 5 kilometers off the coast. the refinery is 6 kilometers down the coast. laying pipe in the ocean is twice as expensive as on land. how many kilometers down the coast should the pipe be laid in order to minimize the cost?
An offshore oil well is 5 kilometers off the coast. The refinery is 6 kilometers down the coast. Laying pipe in the ocean is twice as expensive as on land. Kilometers down the coast should the pipe be laid in order to minimize the cost, the pipe should be laid approximately 8.62 km down the coast to minimize the cost.
How do we minimize the cost?Let the distance down the coast where the pipe is laid be x. Therefore, the distance from the refinery to the point where the pipe meets the shore will be (x + 5) km. The total distance of the pipe can be found using the Pythagorean Theorem.[tex]D = \sqrt{((x + 5)^2 + 6^2) } = \sqrt{(x^2+ 10x + 61)}[/tex] km
Let C(x) be the cost of laying the pipe down the coast at a distance x. Then
[tex]C(x) = 2[(x + 5) + 6] + 1.5[/tex][tex]D= 2(x + 11) + 1.5\sqrt{(x^2 + 10x + 61)}[/tex]Now, to minimize the cost, we have to find the value of x that minimizes C(x). The first derivative of C(x) is:[tex]C'(x) = 2 + 1.5 [x^2 + 10x + 61]^{-1/2} [2x + 10][/tex] After simplifying,[tex]C'(x) = [2(x^2 + 10x + 61) + 1.5(2x + 10)] [x^2 + 10x + 61]^{-1/2}= (3x^2 + 23x + 82) [x^2 + 10x + 61]^{-1/2}= 0[/tex] (at a minimum point)
Now we can solve for x using the above equation.[tex](3x^2 + 23x + 82) = 0[/tex] ⇒ [tex]3(x^2 + 7.67x + 27.33) = 0[/tex] Using the quadratic formula; x = {-b ± √(b² - 4ac)}/2 a We get, x = {-23 ± √(23² - 4(3)(82))}/2(3)x = {-23 ± √(529 - 984)}/6x = {-23 ± √(-455)}/6x = -3.03 or -8.62 Since x must be positive, x = -3.03 is not possible. Hence, the distance down the coast where the pipe should be laid in order to minimize the cost is :x = -8.62Therefore, the pipe should be laid approximately 8.62 km down the coast to minimize the cost.
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Un robot salta sobre una recta numérica iniciando en el cero. Las reglas del juego son
las siguientes si mira hacia tu mano derecha, la longitud de cada salto se expresa
con un número positivo y, si mira hacia tu mano izquierda, con un número negativo.
También: si salta de frente (o sea, en la dirección que está mirando), el número
de saltos se expresa con un número positivo, y si salta de espaldas (es decir, en
la dirección contraria a la que está mirando), el número de saltos se considera con
un número negativo.
Observa los siguientes saltos del robot, su posición final en cada caso y contesta en tu
cuaderno las preguntas
Each subsequent jump will be exactly one unit longer in length than the one before it after the initial jump, which can be one unit in length. Each jump has the option of going either left or right.
The translation of the question is
A robot jumps on a number line starting at zero. The rules of the game are the following if you look at your right hand, the length of each jump is expressed with a positive number and, if facing your left hand, with a negative number.
Also: if you jump straight ahead (that is, in the direction you are facing), the number number of jumps is expressed as a positive number, and if you jump backwards (i.e., on the opposite direction to the one you are looking at), the number of hops is considered with a negative number. Observe the following jumps of the robot, its final position in each case and answer in your notebook the questions
When closely examined, it is simple to conclude that:
If you have consistently jumped in the appropriate direction, you will arrive at point p = 1 + 2 + 3 + 4 +... + n after n jumps.
You would be at point p - 2k in any of these n leaps if you leapt left in the kth hop (k=n) rather than right.
Moreover, after n leaps, you can be anywhere between n * (n + 1) / 2 and -(n * (n + 1) / 2) with the same parity as n * (n + 1) / 2 by carefully selecting which jumps to go left and which to go right.
The trick is to imitate jumping while keeping the aforementioned facts in mind. Always jump to the right, and if at some time you arrive at a location that has the same parity as X and is at or beyond X, you'll know the answer.
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PLEASE HURRY!!!!!!!!!!!!
Graph the solution to this inequality on the number line.
−5+x≥−3
Answer: 2
Step-by-step explanation:
To graph the solution to the inequality -5 + x ≥ -3 on the number line, we first need to isolate x.
Adding 5 to both sides of the inequality, we get:
x ≥ 2
This means that any value of x greater than or equal to 2 will satisfy the inequality. To graph this solution on a number line, we draw a closed circle at the point 2 and shade all the points to the right of 2, including the point 2 itself.
The resulting graph looks like this:
------•-------------------------------->
2
The shaded region on the right of 2 represents all the values of x that make the inequality true.
The data in the table below shows the average temperature in Northern Latitudes:
The line of best fit for the data is approximately y=-1.07x+92.87.
a) True
b) False
The line of best fit for the data is approximately y = -1.07x + 92.87: A) True.
How to find an equation of the line of best fit for the data?In order to determine a linear equation for the line of best fit that models the data points contained in the table, we would have to use a graphing calculator (scatter plot).
In this scenario, the latitude would be plotted on the x-axis of the scatter plot while the average temperature would be plotted on the y-axis of the scatter plot.
On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit on the scatter plot.
From the scatter plot (see attachment) which models the relationship between the latitude and average temperature, a linear equation for the line of best fit is given by:
y = -1.07x + 92.87
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A dart is thrown horizontally at a speed of 10 m/ s at the bull’s-eye of a dartboard 2.4 m away, as in the following figure. (a) How far below the intended target does the dart hit? (b) What does your answer tell you about how proficient dart players throw their darts?
(a) The horizontal velocity of the dart remains constant throughout its motion, so it will take 0.24 seconds to reach the target (since distance = speed × time) and the dart will fall a distance of 0.28 m
During this time, the dart will also be accelerating downwards due to gravity at a rate of 9.81 m/s². The vertical distance fallen can be calculated using the formula: distance = ½ × acceleration × time². Thus, the dart will fall a distance of:
distance = ½ × 9.81 m/s² × (0.24 s)² ≈ 0.28 m
Therefore, the dart will hit the board 0.28 meters below the intended target.
(b) This calculation suggests that even highly skilled dart players may not hit the bull's-eye every time, due to the influence of gravity on the dart's trajectory.
However, skilled players can adjust their aim and release the dart with the correct velocity and angle to hit their target consistently. They may also use techniques such as "aiming high" to compensate for the effect of gravity. Overall, this calculation highlights the importance of understanding the physics of projectile motion in the sport of darts.
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A pentagon has four of its angles equal. If the
size of the fifth angle is 60°, find the size of each
of the four equal angles.
Answer:
120 degrees
Step-by-step explanation:
The sum of the interior angles of a pentagon is given by the formula, where S is the sum of the interior angles, and n is the number of sides of the polygon:
S = (n - 2) × 180 degrees
For a pentagon, n = 5, so we have:
S = (5 - 2) × 180 = 540 degrees
If four of the angles are equal, we can let x be the measure of each of those angles. Then, we can write an equation for the sum of the angles:
4x + 60 = 540
Solving for x, we get:
4x = 540 - 60 = 480
x = 480/4 = 120
Therefore, each of the four equal angles in the pentagon has a measure of 120 degrees.
y is inversely proportional to the square of x. It is given that y = 8 for a particular value of x. k= When x increases by 300%, find the new value of y,
Answer:
1/2 or .5
Step-by-step explanation:
If y is inversely proportional to the square of x, we can express this relationship using the formula:
y = k/x^2
where k is a constant of proportionality. We are told that y = 8 for a particular value of x, so we can substitute these values into the equation:
8 = k/x^2
To find the value of k, we can solve for it:
k = 8x^2
Now we are asked to find the new value of y when x increases by 300%. This means that the new value of x will be 4 times the original value (since an increase of 300% means an increase by a factor of 3, and we need to add the original value to get the new value). So we can substitute 4x for x in our equation:
y = k/(4x)^2 = k/16x^2
We already know the value of k, so we can substitute it in and simplify:
y = (8x^2)/(16x^2) = 1/2
Therefore, the new value of y is 1/2 when x increases by 300%.