a) The highway affected the growth of many plant species, which serve as food for the deer. Option D
b) There will be fewer population of the birds. Option C
What is the carrying capacity?The carrying capacity of an ecosystem is the maximum number of individuals of a particular species that can be supported by the available resources in that ecosystem.
It is the point at which the population growth rate becomes zero, as the resources needed to sustain the population (such as food, water, and space) become limited. Carrying capacity can change over time due to factors such as climate change, pollution, and human activity.
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Find the distance of the line segment joining the two points: (2,0) (0,-2)
The distance of the line segment joining the two points is [tex]2\sqrt{2}[/tex].
What is the distance between two points ( p,q) and (x,y)?The shortest distance (length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:
[tex]D = √[(x-p)² + (y-q)²] D = \sqrt{(x-p)^2 + (y-q)^2} \: \rm units.[/tex]
Given;
The two points;
(2,0) (0,-2)
Now,
D=[tex]\sqrt{(0-2)^2+(-2-0)^2}[/tex]
=2[tex]\sqrt{2}[/tex]
Therefore, the distance between two points will be 2[tex]\sqrt{2}[/tex]
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How to find the area of the major sector
The area of the major sector in the given diagram is 115.5 sq.unit.
What is a Major sector?The region having a greater area is known as Major Sector while the one which has a smaller area is the minor sector.
A sector with a central angle greater than 180° is called a major sector and the formula is given below:
/360° ₓ r²
The radius is 7m and is 270°
Therefore 270/360 × 3.142 × 7² = 115.5sq.unit.
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a real estate office handles an apartment complex with 80 units. when the rent is $360 per month, all 80 units are occupied. when the rent is $405, however, the average number of occupied units drops to 77. assume that the relationship between the monthly rent p and the demand x is linear. (the term demand refers to the number of occupied units.) (a) write a linear equation expressing x in terms of p. x
the relationship between the monthly rent (p) and the demand (x) is p(x) = -15x + 1560.
A real estate office handles an apartment complex with 80 units. When the rent per unit is $360 per month, all 80 units are occupied. However, when the rent is $405per month, the average number of occupied units drops to 77. Assume that the relationship between the monthly rent (p) and the demand (x) is linear.
Since the equation will be linear, we only need two coordinates to write the equation.
They are given, we can assign the values x = no.of units and y = rent:
x1 = 80, y1 = 360
and
x2 = 77, y2 = 405
Find the slope: m = (y2-y1)/(x2-x1)
m = (405-360)÷(77-80) = 45÷(-3)= -15
The slope m= -15
A) Write the equation of the line giving the demand (x) in terms of the rent (p)
Use the point/slope equation.
Using the point/slope formula: y - y1 = m(x - x1)
y - 360= -15(x - 80)
y - 360 = -15x + 1200
y = -15x + 1200 + 360
y = -15x + 1560
or
p(x) = -15x + 1560
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What is the sequence of transformations that maps △ABC to △A′B′C′? Select from the drop-down menus to correctly identify each step. Step 1: Choose... Step 2: Choose... Two triangles on the coordinate plane. Triangle A B C has vertex A at negative 1 comma 2, vertex B at negative 2 comma 5, and vertex C at negative 5 comma 1. Triangle A prime B prime C prime has vertex A prime at 3 comma negative 2, vertex B prime at 4 comma negative 5, and vertex C prime at 7 comma negative 1.
The sequence of transformation which includes a reflection and a translation that maps triangle ΔABC to ΔA'B'C' are;
A reflection across the y-axisA translation of 2 units to the rightA reflection across the x-axisWhat is a reflection transformation?A reflection transformation is one in which the mirror image of the figure is produced, on the other side of a line known as the line of reflection.
The vertices of the triangle ΔABC are A(-1, 2), B(-2, 5), C(-5, 1), the vertices of triangle ΔA'B'C' are A'(3, -2), B'(4, -5), C'(7, -1)
A reflection of the triangle ΔABC across the y-axis, we get;
A''(1, 2), B''(2, 5), C''(5, 1)
A reflection of the triangle ΔA'B'C', across the x-axis produces;
A'''(3, 2), B'''(4, 5), C'''(7, 1)
The rule that maps the coordinates of the vertices of ΔA''B''C'' to the coordinates of the vertices of ΔA'''B'''C''' is a translation of triangle 2 units to the right,
Therefore, the sequence of transformation that maps ΔABC to ΔA'B'C' are;
A reflection across the y-axis, followed by ⇒A translation of two units to the right, then ⇒ A reflection across the x-axis.
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Assume f(x) has a continuous second derivative. Show that f(b) = f(a) + f'(a)(b-a) + ∫ₐᵇf"(x)(b-x)dx
Assume f(x) has a continuous second derivative. The expression "f(b) = f(a) + f'(a)(b-a) + ∫ₐᵇf"(x)(b-x)dx" is TRUE.
How can we show that the expression true?To show that f(b) = f(a) + f'(a)(b-a) + ∫ₐᵇf"(x)(b-x)dx, we will use Taylor's theorem with a remainder in the integral form.
Taylor's theorem states that for any function f(x) that has a continuous kth derivative, we can express the function at any point x = b as:
f(b) = f(a) + f'(a)(b-a) + (1/2!)f''(a)(b-a)^2 + ... + (1/k!)f^(k)(c)(b-a)^k
where c is some value between a and b.
If we take the limit as k approaches infinity, we get:
f(b) = f(a) + f'(a)(b-a) + ∫ₐᵇf"(x)(b-x)dx
This is known as the Taylor's theorem with a remainder in the integral form.
This equation shows that f(b) is equal to f(a) plus the linear approximation of f'(a)(b-a) plus the remaining error term ∫ₐᵇf"(x)(b-x)dx which is the integral of the second derivative of f(x) times (b-x) from a to b.
This is true because f"(x) is continuous on the interval [a, b], so the integral of f"(x) over that interval exists. And because the second derivative of f(x) is continuous, the integral can be evaluated.
Therefore, assuming that f(x) has a continuous second derivative, we can conclude that f(b) = f(a) + f'(a)(b-a) + ∫ₐᵇf"(x)(b-x)dx
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If f(-8) = 1, then the point ( ____ , ____ ) is on the graph of f.
If f(-8) = 1, then the point (-8, 1) is on the graph of f.
How to obtain the point on the graph of the function?The numeric value of the function at x = -8 is given as follows:
f(-8) = 1.
The format of each point on the coordinate plane is given as follows:
(x,y).
In which y is the numeric value of the function at x, meaning that the point can also be written as follows:
(x, f(x)).
Considering that when x = -8, f(x) = 1, the point is given as follows:
(-8,1).
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Alexandria walks 171 meters due west, then 480 meters due south and finally 427 meters due east.
How far is Alexandria from her starting point?
meters
Answer: To find the distance Alexandria is from her starting point, you can use the Pythagorean theorem.
The theorem states that in a right triangle, the square of the hypotenuse (the distance between the starting point and the final point) is equal to the sum of the squares of the other two sides (the distance traveled north or south and the distance traveled east or west).
In this case, the distance traveled north or south is 480 meters (the distance traveled due south) and the distance traveled east or west is 427 meters (the distance traveled due east) - 171 meters (the distance traveled due west) = 256 meters.
So, using the Pythagorean theorem:
Distance = √(480^2 + 256^2)
Distance = √(230400 + 65536)
Distance = √(295936)
Distance = 544.98 meters
So Alexandria is 544.98 meters away from her starting point.
Step-by-step explanation:
First person to answer the questions on the picture get brainiest!!!!
1. Yes. A dilation is performed on the figure. The ratio of the two figures is same. 2. No. The ratios of the sides of the figures are not equal and no transformation is applied.
What are transformations?The transformation, or f: X X, is the name given to the function, f, that maps to itself. After the transformation, the pre-image X becomes the picture X. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation. A function can be moved in one way or another using translation, rotation, reflection, and dilation. A function can also be scaled using rotation around a point. Two-dimensional mathematical figures move about a coordinate plane according to transformations.
1. Yes. A dilation is performed on the figure. The ratio of the two figures is same.
2. No. The ratios of the sides of the figures are not equal and no transformation is applied.
3. Yes. A translation is performed on the figure to shift the transformation with 2 units.
4. No. The ratios of the sides of the figure are not same.
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Which inequality is represented by this graph?
Answer:
0 > x
Step-by-step explanation:
The open circle indicates that x cannot be equal to zero, which rules out the last two options. Since the line is going to the right (towards numbers greater than 0), x must be greater than zero, which means that the first option is correct.
Answer:
x > 0
Step-by-step explanation:
we see the blue line. it covers everything that is larger than 0.
the dot on 0 is empty, which indicates that the point (here 0) itself is not included.
therefore, the second answer option (x > 0) is correct.
Why is 5/100 not equal to 0.5
Answer: Because instead it equals 0.005
Step-by-step explanation:
The reason 5/100 is not equal to 0.5 is that they are written in different forms.
5/100 is written in the form of a fraction, where the numerator (5) represents the number of parts out of a whole, and the denominator (100) represents the total number of parts in the whole. So, 5/100 represents 5 parts out of 100 parts, which is equal to 0.05.
On the other hand, 0.5 is written in decimal form. It represents the number of parts out of 1, where the digits to the right of the decimal point represent the number of tenths, hundredths, thousandths and so on. So, 0.5 represents 5 tenths, or 5 parts out of 10 parts.
In conclusion, while they represent the same value, they are written in different forms and it's important to know how to read and convert them correctly.
three students, a, b, and c are accused of creating a contradiction. three facts are known: if a is not guilty, then b and c are both guilty. either a is not guilty, or b is guilty. either b is not guilty, or c is not guilty. which one of the following statements correctly identifies the guilty students? [hint: review the end of the lecture for section 2.2.] group of answer choices either a or b is guilty, but not both, and c is guilty. neither a nor c is guilty, but b is guilty. only one of the three is not guilty and it is not a and not b. exactly two of the students are guilty.
Exactly two of the students are guilty. This can be deduced by looking at the facts given and understanding that if A is not guilty, then both B and C are guilty, while either B is not guilty or C is not guilty. This implies that exactly two of the students are guilty.
Given the three facts, we can determine that either A or B is guilty, but not both, and C is guilty. This means that exactly two of the students are guilty.
Since the statement either A is not guilty, or B is guilty, and the statement either B is not guilty, or C is not guilty, both cannot be true. This means that exactly two of the students are guilty.
Given the three facts, we can determine that either A or B is guilty, but not both, and C is guilty. This means that exactly two of the students are guilty. Since the statement either A is not guilty, or B is guilty, and the statement either B is not guilty, or C is not guilty, both cannot be true. This means that only one of the three is not guilty and it is not A or B. Therefore, exactly two of the students are guilty. This can be deduced by looking at the facts given and understanding that if A is not guilty, then both B and C are guilty, while either B is not guilty or C is not guilty. This implies that exactly two of the students are guilty.
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from a group of 8 women and 6 men, a committee consisting of 3 men and 3 women is to be formed. how many different committees are possible if ross, sheldon. first course in probability, a (p. 16). pearson education. kindle edition.
There are 16128 ways to form the committee when 2 of the men refuse to serve together, 23040 ways to form the committee when 2 of the women refuse to serve together, and 5040 ways to form the committee when 1 man and 1 woman refuse to serve together.
(a) When two of the men refuse to serve together, there are 6 men to choose from for the first 3 positions, 4 for the next, and 2 for the last. So there are 6 × 4 × 2 = 48 ways to choose the 3 men.
There are 8 women to choose from for the first 3 positions, so there are 8 × 7 × 6 = 336 ways to choose the 3 women. Thus there are 48 × 336 = 16128 ways to form the committee when 2 of the men refuse to serve together.
(b) When two of the women refuse to serve together, there are 8 women to choose from for the first position, 6 for the next, and 4 for the last. So there are 8 × 6 × 4 = 192 ways to choose the 3 women.
There are 6 men to choose from for the first 3 positions, so there are 6 × 5 × 4 = 120 ways to choose the 3 men. Thus there are 192 × 120 = 23040 ways to form the committee when 2 of the women refuse to serve together.
(c) When 1 man and 1 woman refuse to serve together, there are 7 women to choose from for the first 3 positions and 6 men to choose from for the last 3 positions.
So there are 7 × 6 × 5 × 4 × 3 = 5040 ways to form the committee when 1 man and 1 woman refuse to serve together.
The answer to each of the questions is the number of different committees that can be formed under the given conditions.
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--The given question is incomplete; the complete question is
"From a group of 8 women and 6 men, a committee consisting of 3 men and 3 women is to be formed. How many different committees are possible if (a) 2 of the men refuse to serve together? (b) 2 of the women refuse to serve together? (c) 1 man and 1 woman refuse to serve together?"--
The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer.
Three polynomials are factored below, but some coefficients and constants are missing. All of the missing values of a, b, c, and
d are integers.
1. x² - 8x + 15 = (ax + b)(cx + d)
2. 2x³ - 8x² - 24x = 2x(ax + b)(cx + d)
3.6x² + 14x + 4 = (ax + b)(cx + d)
Fill in the table with the missing values of a, b, c, and d.
b
a
1. 1
2. 1
3.
Submit
Pass
-5
1
C
1
2
d
Question ID: 504360
-6
Save an
150
d = 4
b = -3. c = 1
a = 3 and d = 1
What are three polynomials factorized below?
To get the missing values in the table, we will factorize the given expression and compare the factored expression with the expression containing the missing constants.
1) For the expression x²+2x-8, on factorizing we have;
x²+2x-8
= (x²+4x)-(2x-8)
Factoring out the common terms from both parenthesis;
= x(x+4)-2(x+4)
= (1x+4)(1x-2)
= (1x-2)(1x+4)
Comparing the resulting expression with (ax+b)(cx+d)
a = 1, b = -2, c = 1 and d = 4
2) For the expression 2x³+2x²-24x
Factoring out the common term we will have;
= 2x(x²+x-12)
= 2x(x²-3x+4x-12)
= 2x{x(x-3)+4(x-3)}
= 2x{(x+4)(x-3)}
= 2x(1x-3)(1x+4)
Comparing the resulting expression with 2x(ax+b)(cx+d)
a = 1, b = -3. c = 1 and d = 4
3) For the expression 6x²-15x-9 we will have;
On simplifying,
= 6x²+3x-18x-9
= 3x(2x+1)-9(2x+1)
= (3x-9)(2x+1)
Comparing the resulting expression with (ax+b)(cx+d)
a = 3, b = -9, c = 2 and d = 1
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Please help
Determine whether the following statement makes sense or does not make sense and explain your reasoning.
The word imaginary in imaginary numbers tells that these numbers are undefined
View image
The correct answer is OB. The statement does not make sense as a and b are real numbers in the imaginary number of the form a + bi. Hence, the imaginary numbers are defined and interpreted in the set of real numbers also.
What is imaginary number and determine it?Imaginary numbers are defined as the set of numbers of the form a + bi, where a and b are real numbers and i is the imaginary unit.
It is a mathematical concept that extends the real numbers system, by introducing a new number i which is defined as the square root of -1. It allows us to solve equations which are not solvable in real numbers.
The word "imaginary" is used to denote the presence of the imaginary unit i, which is not a real number but is used to extend the real numbers. It does not mean that these numbers are undefined.
Hence, the statement "The word imaginary in imaginary numbers tells that these numbers are undefined" is not true, as the imaginary numbers are defined and interpreted in the set of real numbers also.
In summary, the statement is not making sense as the imaginary numbers are defined in the set of complex numbers.
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select the correct prefix to complete the equality. drag the appropriate labels to their respective targets. note: not all labels will be used.
The answers for the given units are 1 g = 0.001 kg; 1 m = 1000 mm; 1 cm = 10 mm; 1 dL = 100 mL; 1 kg = 1000 g; 1 pg = 1 × 10⁻¹² g; 1 g = 1 × 10¹² pg; and 1 mL = 1 cc.
A unit is a name given to a known quantity that is used to measure something. A gram is one-thousandth of a kilogram used to measure weight. This is written as 1 g = 0.001 kg or 10⁻³ kg and kg to g is written as 1 kg = 1000 g. In terms of their relationship, 1 m and 0.001 mm are equivalent. This is written as 1 m = 1000 mm or 10³ mm. The relationship between millimeters and centimeters is written as 1 cm = 10 mm.
Over a milliliter, a deciliter is greater. This is written as 1 dL = 100 mL. The relationship between picogram and gram is written as 1 pg = 1 × 10⁻¹² g
and 1 g = 1 × 10¹² pg. The relationship between a milliliter and a cubic centimeter is written as 1 mL = 1 cc.
The required answers are
1 g = 0.001 kg
1 m = 1000 mm
1 cm = 10 mm
1 dL = 100 mL
1 kg = 1000 g
1 pg = 1 × 10⁻¹² g
1 g = 1 × 10¹² pg
1 mL = 1 cc
The complete question is -
Select the correct prefix to complete the equality. Drag the appropriate labels to their respective targets. Note: not all labels will be used.
1 g = -----kg
1 m = -----mm
1 cm = ----- mm
1 dL = ----- mL
1 kg = ----- g
1 pg = ----- g
1 g = ----- pg
1 mL = ----- cc
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Can some help me solve this geometry question?
The length of NQ for this problem is given as follows:
NQ = 5.
How to obtain the length NQ?In this problem, we have two similar triangles, meaning that their side lengths are proportional.
The lengths for this problem are given as follows:
NO = 8.NQ = x.QR = x - 1.QP = 5.The similar triangles are given as follows:
PQR and PNO.
The equivalent side lengths are given as follows:
5 and 5 + x.x - 1 and 8.Hence the proportional relationship is given as follows:
5/(5 + x) = (x - 1)/8
Applying cross multiplication, we have that:
(x + 5)(x - 1) = 40
x² + 4x - 5 = 40
x² + 4x - 45 = 0.
Hence:
(x + 9)(x - 5) = 0.
The positive solution is:
x - 5 = 0
x = 5.
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If 15 workers can build a wall in 48 hours, how many workers will be
required to do the same work in 30 hours?
Answer:
24 workers
Step-by-step explanation:
solution
A wall can be built in 48 hrs by = 15 workers
A wall can be built in 1 hr by = 15× 48 workers
A wall can be built in 30 hrs by= 15 × 48/ 30 workers
= 24 workers
A person in a car is driving at 60 km/h toward a ferry whose whistle is blowing at 400 Hz. (a) What frequency does she hear? (b) The ferry leaves the dock and heads directly away from the driver at 15 km/h, still blowing its whistle. What frequency does she hear now?
a. The frequency which she hears is 440Hz.
b. The person in the car would hear a frequency of 391.98 Hz when the ferry leaves the dock and heads directly away from the driver.
(a) The frequency that the person in the car hears is affected by the motion of the car and the sound source (the ferry). The effect is called the Doppler effect, which causes the perceived frequency of sound to change depending on the observer and the relative motion of the source.
If the car is moving toward the ferry, the frequency will be higher than the actual frequency of the sound. The perceived frequency is given by the formula:
f' = f (v + v_s) / (v + v_s)
where
f = the actual frequency of the sound (400 Hz)
v = the velocity of sound (approximately 340 m/s)
[tex]v_s[/tex] = the velocity of the car (60 km/h = 16.67 m/s)
So,
f' = 400(340 + 16.67) / (340 - 16.67) = 400(356.67) / 323.33 = 440 Hz
Hence, the frequency which she hears is 440Hz.
(b) The perceived frequency when the ferry leaves the dock and heads directly away from the driver is also affected by the Doppler effect.
f' = f (v - v_s) / (v - v_s)
where
f = the actual frequency of the sound (400 Hz)
v = the velocity of sound (approximately 340 m/s)
v_s = the velocity of the ferry (15 km/h = 4.17 m/s)
So,
f' = 400(340 - 4.17) / (340 + 4.17) = 400(335.83) / 344.17 = 391.98 Hz
The person in the car would hear a frequency of 391.98 Hz when the ferry leaves the dock and heads directly away from the driver.
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Please help
Fill in each answer box so that the resulting statement is true.
the following data represent glucose blood levels (mg/100 ml) after a 12-hour fast for a random sample of 70 women (reference: american journal of clinical nutrition, vol. 19, pp. 345-351). 45 66 83 71 76 64 59 59 76 82
80 81 85 77 82 90 87 72 79 69
83 71 87 69 81 76 96 83 67 94
101 94 89 94 73 99 93 85 83 80
78 80 85 83 84 74 81 70 65 89
70 80 84 77 65 46 80 70 75 45
101 71 109 73 73 80 72 81 63 74
For this problem, use six classes.
(a) Find the class width
(b) Make a frequency table showing class limits, class boundaries, midpoints, frequencies, relative frequencies, and cumulative frequencies. (Give relative frequencies to 4 decimal places.
(c) Draw a histogram.
(d) Draw a relative-frequency histogram.
(e) Categorize the basic distribution shape.
(f) Draw an ogive. (Graph each point and the closed line segments connecting the points to create your graph.)
The class width is 10.
What is Histogram ?A histogram is a representation of statistical data that makes use of rectangles to illustrate the frequency of data items in a series of equal-sized numerical intervals. The independent variable is represented along the horizontal axis and the dependent variable is plotted along the vertical axis in the most popular type of histogram.
Given:
Order the data increasingly
45,45,46,59,59,63,64,65,65,66,67,69,69,70,70,70,71,71,71,72,72, 73,73,73,74,74,75,76,76,76,77,77,78,79,80,80,80,80,80,80,81,81
81,81,82,82,83,83,83,83,83,84,84,85,85,85,87,87,89,89,90,93,94
94,94,96,99,101,101,109
Now, the range: maximum-minimum
= 109-45 = 64
Now, Divide the range by the number of classes you wish to distribute the data,
= 64/6
= 10.66 (round to 11)
Create intervals of type [a,b] starting with the first datum, and then add the class width to create the interval classes.
[45,56), [56,67), [67,78), [78,89), [89,100), [100,111)
Then, Create a frequency table that includes class boundaries (the smallest and largest data in the class), midpoints (adding the endpoints and dividing by 2), frequencies (the amount of data that fall into the class), relative frequencies (the frequency of the class divided by the total number of data, in this case 70), and cumulative frequencies (the sum of the frequencies of the class plus the previous ones)
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Bay City Balloons studied the demand in Bay City before opening a hot air balloon company. The owners expected to book 375 hot air balloon rides in their first ninety days of business. Instead, they booked 392 rides in that period. What is the percent error for the company's estimate?
+4.533 is the percent error for the company's estimate
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
Given, Bay City Balloons studied the demand in Bay City before opening a hot air balloon company. The owners expected to book 375 hot air balloon rides in their first ninety days of business. Instead, they booked 392 rides in that period.
Since percentage error:
Percent error is the difference between the estimated value and the actual value in comparison to the actual value and is expressed as a percentage. In other words, the percent error is the relative error multiplied by 100.
Thus in our case
Percentage error = ((392 - 375)/ 375) * 100
Percentage error = 4.533
therefore, the percent error for the company's estimate is +4.533.
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8 times the sum of 2 and a number
The word problem "8 times the sum of 2 and a number" is equal to 8(2 + n).
What is an algebraic expression?In Mathematics, an algebraic expression simply refers to a mathematical equation that can be used for showing the relationship which exist between two (2) or more variables, numerical quantities, as well as in conjunction with different mathematical operations.
Assuming the variable n represents the unknown numerical value (number), we would translate the word problem into an algebraic expression as follows;
Algebraic expression = 8 × (2 + n)
Algebraic expression = 8(2 + n).
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Answer the following
The type of slope for each function is given as follows:
Zero, Positive, Positive, Undefined.
How to classify the slope of a line?There are four types of lines, and their slopes are classified as follows:
Constant horizontal line: slope of zero.Constant vertical line: undefined slope.Increasing line: positive slope.Decreasing line: negative slope.There is a mistake in the options or in the graph, as both graphs b and c are increasing lines.
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Question content area top Part 1 Think About the Process Use the algebra tiles to help you solve the equation 2x - 4 = 10. What is the first step in solving the equation using algebra tiles? What is the solution to the equation?
The solution to the equation is x = 7.
What is the linear equation in one variable?
A linear equation in one variable is an equation of the form ax + b = 0, where a and b are constants and x is the variable. The general form of a linear equation in one variable is ax + b = 0, where a and b are constants and x is the variable. The graph of a linear equation in one variable is a straight line.
The first step in solving the equation 2x - 4 = 10 using algebra tiles would be to add 4 to both sides of the equation to get 2x = 14. The next step would be to divide both sides of the equation by 2 to get x = 7.
Hence, the solution to the equation is x = 7.
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TRUE OR FALSE if you have a logical statement in five variables how many rows do you need in the truth table that you would use to evaluate it? answer with an integer.
We need 32 rows in the truth table that would use to evaluate a logical statement in five variables.
To find out the number of rows in a truth table with 5 variables, we should know what is a truth table.
A truth table is a study of a logic function by listing all possible values the function can attain. The top row illustrates logical variables and combinations in increasing complexity leading up to the final function.
The number of rows that a truth table needs is decided by the number of basic statement letters involved in the set formulas that will be involved in the set of formulas.
The formula to calculate the number of rows is equal to 2ⁿ, where n is the number of basic statement letters involved.
Number of rows = 2ⁿ
If the number of variables in a truth table is 5, then the number of rows = 2⁵
2⁵ = 2×2× 2× 2× 2
= 32
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A scale drawn on the map shows that 1 inch represents 20 miles. If two cities
are 2.5 inches apart on the map, what is the distance between them in real
life?
OA. 40 miles
B. 30 miles
O C. 50 miles
OD. 20 miles
SUBMIT
Using the arithmetic operation of multiplication, two cities having a distance of 2.5 inches on map have an actual distance of 50 miles.
What is arithmetic operation?
A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.
The value of 1 inch on scale = 20 miles.
The distance between two cities on map = 2.5 inches
To find the distance between two cities in actual use the arithmetic operation of multiplication.
Let the original distance value in miles be x.
The equation for distance will be -
x = 2.5 × 20
Solve the equation -
x = 2.5 × 20
x = 50
Therefore, the actual distance in miles is 50 miles.
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Given sin � = 21 29 sinA= 29 21 and that angle � A is in Quadrant I, find the exact value of cot � cotA in simplest radical form using a rational denominator.
The exact value of cot A is .20/21
What is rational denominator?The denominator means moving the radical term square root or cube root to the numerator such that a denominator is a whole number.
We have been given that sin( A ) = 21/29 and angle A is in quadrant 1. We are asked to find the exact value of cot (A) in simplest radical form.
We know that sine relates opposite side of right triangle with hypotenuse.
Since = opposite
hypotenuse
This means that opposite side is 21 units and hypotenuse is 29 units.
We know that cotangent relates adjacent side of right triangle with adjacent side.
Cot = Adjacent
opposite
Now we will find adjacent side using Pythagoras theorem as:
Adjacet² = hypotenuse² - opposite²
Adjacent² = 29² - 21²
Adjacent² = 841 - 441
Adjacent² =400
Let us take positive square root on both sides:
√Adjacent² = √400
Adjacent = 20
Therefore, adjacent side of angle A is 20 units.
Cot (A) = 20/21
The exact value of cot A is .20/21
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Two similar rectangular prisms. The smaller prism has a base length of 12 meters. The larger prism has a base length of 15 meters. The equations over the larger prism are the following.
Surface Area = 1575 square meters
Volume = 4050 cubic meters
Find the surface area and volume of the smaller similar solid
Answer:
Step-by-step explanation:
which pair of numbers does not have a least common multiple less than 100
Laura rents out small and large trucks. She has a total of 22 trucks. The number of large trucks is two more than triple the number of small trucks. how many of each type of truck does she have?
Answer:
see below
Step-by-step explanation:
S+L = 22
L=2+3S
so S+2+3S =22
4S=22-2 = 20
S =5
L =17
Answer:
Step-by-step explanation: