The little cubes can be possible to remove in number of 18 cubes maximum.
What is cube ?
A cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. Viewed from a corner it is a hexagon and its net is usually depicted as a cross. The cube is the only regular hexahedron and is one of the five Platonic solids.
The original surface area is (3x3) x 6 = 54 units.
A unit cube has 6 units of area, so we need 9 cubes.
Remove all the cubes except the original eight corners and the center cube.
The 3×3×3 cube has a surface area of 6×3×3 square units. Taking the 27 smaller units and connecting them to form a single entity, the maximum exposed surface area per cube is 6 square units. If nine of these are connected vertex to vertex in any shape then the objective is achieved. So a maximum of 18 of the small cubes can be removed.
Hence , The little cubes can be possible to remove in number of 18 cubes maximum.
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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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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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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:
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.
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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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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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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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.
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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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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To test if a regression coefficient is less than a critical value, C
, we conduct a one-sided test on the _________ tail of a ___________ distribution.
we conduct a one-sided test on the statistic one tail of a critical area of distribution.
The critical value for a two-tailed test of h0: β1 = 0 at α = .05 in a simple regression with 22 observations is 4.35.
What is a critical value?
A critical value can be calculated for different types of hypothesis tests. The critical value of a particular test can be interpreted from the distribution of the test statistic and the significance level.
Test of significance of linear regression between x and y.
Null hypothesis: There is no significant linear relationship between x and y.
Alternative hypothesis: There is a significant linear relationship between x and y.
Test statistic:
F0 = Mean square due to regression/ mean squared error ~ F(1, n-2)
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which pair of numbers does not have a least common multiple less than 100
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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I. Express each ratio 25 2 II. Express each num 1.
Each one of the given ratios should be expressed in its simplest form as follows:
50:150 = 1:3.25:40 = 5:8.33:99 = 1:3.What is a ratio?In Mathematics, a ratio can be defined as a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.
In this exercise, you are required to express each of the given ratios in its simplest form. Therefore, we would divide both sides of the ratio by highest common factor (HCF) as follows;
50:150 = 50/150 = 1/5 = 1:5. (divide both sides by 50).
25:40 = 25/40 = 5:8. (divide both sides by 5).
33:99 = 1:3. (divide both sides by 33).
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Complete Question:
Express each one of the following ratios in its simplest form.
(i) 50: 150
(ii) 25:40
(iii) 33 : 99
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:
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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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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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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select the correct answer. Which hyperbola has both vertices in the same quadrant?
Option (d) is the correct answer i.e. that hyperbola has both vertices in the same quadrant.
How does hyperbola work?A hyperbola is a conic section in analytical geometry that is formed when a plane intersects a double right circular cone at an angle that spans both cone halves.
Let's see each option one by one:
(a) We've a = 11 and b = 10
This hyperbola is centered at (-10,3) and has vertices as (1,3) and (-21,3).
So, both vertices are not in the same quadrant.
(b) We've a = 9 and b = 12
This hyperbola is centered at (-6,8) and has vertices as (-6,17) and (-6,-1).
So, both vertices are not in the same quadrant.
(c) We've a = 12 and b = 8
This hyperbola is centered at (1,11) and has vertices as (13,11) and (-11,11).
So, both vertices are not in the same quadrant.
(d) We've a = 9 and b = 11
This hyperbola is centered at (-1,10) and has vertices as (-1,19) and (-1,1).
So, both vertices in the same quadrant.
Hence, option (d) is the correct answer.
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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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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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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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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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The mortgage is $158,750. Interest is 6.25% monthly payment is $1,168. How much will the principal be after the third payment?
How do I know what formula to use to figure the correct answer?
These are the choices:
A. $344.74
B. $342.95
C. $341.18
D. $826.82
Answer:
Step-by-step explanation:
B. $342.95 is your answer
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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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?"--
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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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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:
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