Answer: CHINA
Step-by-step explanation:
IAS CHINADU
Answer:
Bhutan is the answer.
Raj encoded a secret phrase using matrix multiplication. Using A = 1, B = 2, C = 3, and so on, he multiplied the clear
25
c-1² ₂]
text code for each letter by the matrix C=
85
38 46
location of spaces after you decode the text.
representing the encoded text is
to get a matrix that represents the encoded text. The matrix
111 135 111 95
101 153
55 45 41 44 64
4
What is the secret phrase? Determine the
The solution is, the answer is: The color is blue (D).
What is matrix?In mathematics, a matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.
here, we have,
Our matrix C is the encoder. Let X be our secret message and let B be our encoded message. Therefore the relationship between the 3 can be represented as:
CX = B
So we want to solve for X (our secret message). So using matrix algebra:
X = C^-1*B
where C^-1 is the inverse of C.
C^-1 = | 3 -2 |
|4 -3 |
So we take C^-1 and multiply it by matrix B to get X. Matrix B is already given to us. So just multiply those two. I used a calculator to get:
X = | 20 8 5 3 15 12 15 |
| 18 9 19 2 12 21 5 |
And since A = 1, B = 2, C = 3, etc....
We decode our message and it says:
X = | T H E C O L O |
| R I S B L U E |
So the answer is: The color is blue (D)
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Answer: D
Step-by-step explanation:
The following sample observations were randomly selected. (Round intermediate calculations and final answers to 2 decimal places.) x: 4 5 6 6 9 y: 3 6 5 7 7 pictureClick here for the Excel Data File 1. The regression equation is y : ______ + _____ x 2. When x is 8 this gives y: _____
The regression equation is y = 1.56 + 0.69⋅x².
What is an Equations?Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.
x: 4 5 6 6 9
y: 3 6 5 7 7
Σx=28, ΣΥ=27, Σxy = 163, Σx' = 174
a = ΣΥ ΣΑΣΑ Σ ΑΥ = 27-174-28-163 = 1.558
b= 5.163 28 27 /5-174-(28)2 = 0.686
y = 1.558 + 0.686x²
Hence, The regression equation is y = 1.56 + 0.69⋅x².
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Need help solving problem
The equations that determine the cost of each hamburger and each fries is 4x + 5y = 20 and 10x + 7y = 41.20
What is an equation?
An equation is an expression that shows the relationship between two numbers and variables using mathematical operations like addition, subtraction, multiplication, exponents
Let x represent the cost of each hamburger and y represent the cost of each fries.
She purchased 4 hamburgers and 5 fries for $20.00, hence:
4x + 5y = 20 (1)
She purchased 10 hamburgers and 7 fries for $41.20, hence:
10x + 7y = 41.20 (2)
From both equations, solving simultaneously:
x = 3; y = 1.6
The cost of each hamburger is $3 while the cost of each fries is $1.6
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Describe the type and degree of association in the scatter plot and what it means in terms of the time the player spent practicing and the number of points he scored in the game.
As the time a basketball player practices increases, the number of points scored in a game decreases with a weak linear association.
As the time a basketball player practices increases, the number of points scored in a game decreases with a weak nonlinear association.
As the time a basketball player practices increases, the number of points scored in a game increases with a strong linear association.
As the time a basketball player practices increases, the number of points scored in a game increases with a strong nonlinear association.
The correct statement regarding the association of the time the player spent practicing and the number of points he scored in the game is given as follows:
As the time a basketball player practices increases, the number of points scored in a game increases with a strong nonlinear association.
How to describe the association?The more the player practices, the better he/she performs, that is, the more points are scored, hence the number of points increases as the number of hours practiced increase.
However, there reaches a certain threshold where the player is as good as possible, hence the points tend to stabilize, meaning that there is a nonlinear association between the variables.
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Simply expression
Please show steps
The simplified expression for this problem is given as follows:
-3(x + y) = -3x - 3y.
What is the distributive property?With the application of the distributive property, the outer term multiplies each of the inner terms of the expression. If possible, these inner terms than can be added or subtracted combining the like terms.
For this problem, the outer term -3 multiplies both of the inner terms, x and y, hence:
-3x.-3y.Hence the simplified expression is defined as follows:
-3(x + y) = -3x - 3y.
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An ellipse has a vertex at (–5, 0), a co-vertex at (0, 4), and a center at the origin. Which is the equation of the ellipse in standard form?
The equation of the ellipse in standard form is 16x² + 25y² = 400.
What is the standard form of the equation of an ellipse?The standard form of the equation of an ellipse centered at the origin is:
x²/a² + y²/b² = 1
where a is the distance from the center to a vertex along the x-axis, and b is the distance from the center to a co-vertex along the y-axis.
In this case, we know that the center of the ellipse is at (0,0), a vertex is at (-5,0), and a co-vertex is at (0,4).
The distance from the center to a vertex along the x-axis is the absolute value of the x-coordinate of the vertex, which is 5. So, a = 5.
The distance from the center to a co-vertex along the y-axis is the absolute value of the y-coordinate of the co-vertex, which is also 4.
So, b = 4.
Substituting these values into the standard form equation, we get:
(x²/5²) + (y²/4²) = 1
Simplifying and multiplying by 5² and 4², we get the standard form equation of the ellipse:
16x² + 25y² = 400
Therefore, the equation of the ellipse in standard form is 16x² + 25y² = 400.
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What is a placebo? Describe the placebo effect and how it can make experiments difficult to interpret. How can making an experiment single-blind or double-blind help?
What is a placebo?
A. A placebo refers to a specific member of a sample from which data are collected.
B. A placebo refers to any problem in the design or conduct of a statistical study that tends to favor certain results.
C. A placebo refers to a situation in which a patient improves simply because they believe they are receiving a useful treatment.
D. A placebo lacks the active ingredients of a treatment being tested in a study, but is identical in appearance to the treatment.
The placebo effect refers to an experiment where neither the participants nor the experimenters know who belongs to the treatment group and who belongs to the control group. As a result, it is impossible for the experiments to link certain effects to certain patients, which make the results difficult to interpret.
What is the placebo effect is an experimental study refers to the?
The placebo effect is a phenomenon where people report real improvement after taking a fake or nonexistent treatment, called a placebo. Because the placebo can't actually cure any condition, any beneficial effects reported are due to a person's belief or expectation that their condition is being treated.
Hence , The placebo effect refers to an experiment where neither the participants nor the experimenters know who belongs to the treatment group and who belongs to the control group. As a result, it is impossible for the experiments to link certain effects to certain patients, which make the results difficult to interpret.
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C. A placebo refers to a situation in which a patient improves simply because they believe they are receiving a useful treatment.
Toby is buying milk. He needs 3 liters. A half-liter of costs $2.43. A 250 -milliliter container of costs $1.42. What should Toby buy so he gets 3 liters at the lowest price?
Answer:
6 half-liter
Step-by-step explanation:
To get 3 liters of milk, Toby has two options:
Option 1: Buy 6 half-liter containers
The cost of one half-liter container is $2.43, so the cost of six such containers is 6 x $2.43 = $14.58.
Option 2: Buy 12 250-milliliter containers
The cost of one 250-milliliter container is $1.42, which is equivalent to $5.68 per liter (since 1 liter is equal to 4 250-milliliter containers). Therefore, the cost of 3 liters (which is equivalent to 12 250-milliliter containers) is 12 x $1.42 = $17.04.
Therefore, Toby should buy 6 half-liter containers as it is the cheaper option.
A triangle has two sides of length 7 and 10. What is the largest possible whole-number length for the third side?
Answer:
The largest possible whole-number length for the third side of a triangle with two sides of length 7 and 10 is 13. This is due to the fact that the two given lengths must be added together, and then subtracted from the third side in order to create a valid triangle. Therefore, the third side must be at least 13 in order to create a triangle.
Sno-Cone at the carnival has the shape of a hemisphere on top of an inverted cone. What is the volume of the sno-cone if its radius is 5 cm and the height of the conical portion is 9.6 cm?
The volume of the sno-cone is approximately 774.9 cm³.
Describe Volume of hemisphere?The volume of a hemisphere is the amount of space that a hemisphere (a half-sphere) takes up. A hemisphere is a three-dimensional shape that is half of a sphere, and it is created by cutting a sphere in half along a plane that passes through the center of the sphere.
The formula for the volume of a hemisphere is given by:
V = (2/3)πr³
Where V is the volume of the hemisphere, π is the mathematical constant pi (approximately 3.14), and r is the radius of the hemisphere.
To use this formula, you simply need to know the radius of the hemisphere. To find the radius, measure the distance from the center of the sphere to the edge of the hemisphere. Then, plug this value into the formula and simplify to find the volume.
The volume of the sno-cone can be calculated by finding the volume of the hemisphere and the volume of the cone separately and then adding them together.
Volume of the hemisphere = (2/3)πr³
where r is the radius of the hemisphere
Given r = 5 cm, the volume of the hemisphere is
(2/3)π(5)³ = (500/3)π ≈ 523.6 cm³
Volume of the cone = (1/3)πr²h
Given r = 5 cm and h = 9.6 cm, the volume of the cone is
(1/3)π(5)²(9.6) ≈ 251.3 cm³
The volume of the sno-cone is the sum of the volume of the hemisphere and the volume of the cone, which is
523.6 + 251.3 ≈ 774.9 cm³
Therefore, the volume of the sno-cone is approximately 774.9 cm³.
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Guys help!!
Slope of one of the dotted lines:
Slope of the line of reflection:
I'LL MARK THE BRAINLIEST!
Carlos uses a food delivery service to order lunch. He paid $13.75 for lunch, which included the cost of the food and a delivery fee, which is 10% of cost of the food.
What was the cost of Carlos' lunch before the delivery fee?
Answer: 3
Step-by-step exp lanation:
divided
g five cards are dealt from a standard deck of playing cards.what is the probability that the you dealt 5 cards from same suit.
Answer:
the probability of being dealt 5 cards from the same suit is approximately 0.00198, or about 0.198%.
Step-by-step explanation:
The total number of ways to choose 5 cards from a deck of 52 cards is given by the combination formula:
C(52, 5) = 52! / (5! (52 - 5)!) = 2,598,960
Now, we need to count the number of ways of choosing 5 cards from the same suit. There are 4 suits in a deck of cards (hearts, diamonds, clubs, and spades), so we need to count the number of ways to choose 5 cards from each of these suits and add them up.
For each suit, the number of ways of choosing 5 cards from that suit is given by the combination formula:
C(13, 5) = 13! / (5! (13 - 5)!) = 1,287
So the total number of ways of choosing 5 cards from the same suit is:
4 * 1,287 = 5,148
Therefore, the probability of getting 5 cards from the same suit is:
5,148 / 2,598,960 ≈ 0.00198
So the probability of being dealt 5 cards from the same suit is approximately 0.00198, or about 0.198%.
A certain market has both an express checkout line and a superexpress checkout line. Let X1 denote the number of customers in line at the express checkout at a particular time of day, and let X2 denote the number of customers in line at the superexpress checkout at the same time. Suppose the joint pmf of X1 and X2 is as given in the accompanying table. (a) What is P(X1 = 1, X2 = 1), that is, the probability that there is exactly one customer in each line? P(X1 = 1, X2 = 1) = (b) What is P(X1 = X2), that is, the probability that the numbers of customers in the two lines are identical? P(X1 = X2) = (c) Let A denote the event that there are at least two more customers In one line than in the other line. Express A in terms of X1 and X2. Calculate the probability of this event. P(A) = (d) What is the probability that the total number of customers in the two lines is exactly four? At least four? P(exactly four) = P(at least four) =
Required probability P(A)= 0.46. The problem here is a Joint Probability Distribution exercise. See the answers and explanation below.
What is Joint Probability Distribution?Joint Probability Distribution can be simply described as the likelihood of two events (variables) occurring at the same time. These two events are commonly referred to as event A and event B, and their formal names are: p (A and B).
here, we have,
What is the solution to the questions?
A - The likelihood that each line has exactly one customer: The probability relates to the associated row and column.
X₁ = 1 and X₂ = 1
P (X₁ = 1, X₂ =1) = 0.15
B - The sum of the diagonal elements of the joint pmf indicates the likelihood that the amount of clients in both lines is the same:
P(X₁ = X₂) =) p(0,0) + p (1,1) + p(2, 2) + p(3,3
= 0.08 + 0.15 + 0.10 + 0.07
= 0.4
Hence,
C - Let A represent the situation in which there are at least two more clients than the other line: The following are examples of variable combinations:
X₂ =0 ; X₁ = 2,3, 4
X₂ =1 ; X₁ = 3, 4
X₂ =2 ; X₁ = 0, 4
X₂ =3 ; X₁ = 0, 1
The probability is thus computed as follows:
P (A) = p(1, 3) + p (2,2) + p(2, 3) + p(3,1) + p(3,2) + p(3,3) + p(4,0) + p(4,1) + p(4,2) + p(4,3)
= 0.04 + 0.10 +0.06 + 0.03 + 0.04+ 0.07 + 0.00 + 0.01 + 0.05 + 0.06
= 0.46
Hence , P(A)= 0.46
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7. Charles is designing a backsplash with a pattern of
diamond-shaped tiles as shown. If m /1 = 65°,
find m2. Explain your reasoning.
The measure of angle m2 is 65°, the reason is interior opposite angles.
What is the sum of all the exterior angles of a regular polygon?For a regular polygon of any number of sides, the sum of its exterior angle is 360° (full angle).
Exterior angle is an measure of rotation between one extended side(we extend it virtually) of the polygon with its adjacent side which is not extended. Also, due to polygon being regular, let it be having 'n' sides, all the exterior angles are of same measure, and therefore, their measure is (360/n)°.
We are given that;
The measure of angle 1= 65°
Now,
By interior opposite angle property
Angle 1 = Angle 2
Substituting the value of angle 1
65°= angle 2
Therefore, by interior angle property the answer will be 65°.
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What is the future value of $2,500 deposited for one year earning a 14 percent interest rate annually
Answer: $2,850
Step-by-step explanation:
Hope this helped you. Brainliest if possible! :D
I also answered first! (Please don't copy my answer for anyone that answer this question!) :D
Suppose you are designing short walls to go across the front of flower beds. The walls will be built with small concrete blocks in the design shown here. Each block is 1-foot long by 1-foot wide by 1-foot high. Only whole blocks can be used for the walls.
What is not a symbolic representation of the relationship between the number of blocks in each wall, b, and the length of each wall in feet, f?
Answer:
f/ 3 4 5 6
b/ 8 10 12 14
Step-by-step explanation:
the 4th wall has 6×3-4=14
so the relationship is
f/ 3 4 5 6
b/ 8 10 12 14
What is the value of n in the figure?
Answer:
n = 14
Step-by-step explanation:
Theorem:
In a triangle, the measure of an exterior angle equals the sum of the measures of the two remote interior angles.
12n - 8 = 8n - 4 + 52
4n = 56
n = 14
A study was conducted showing the relationship between the average maintenance cost and the age of a car in years.
Number of observations: 13
Least Squares | Standard | T
Parameter | Estimate | Error | Statistic| P-Value
Intercept | 54.7757 | 54.87 | 0.998282 | 0.3396
Slope | 120.689 | 11.8442 | 10.1898 | 0.0000
a) What is the formula for the regression function based on the output above (Write your equation in the context of question)?
b) Interpret the slope of the regression equation (In the context of question)?
c) Construct an 95% interval to predict the maintenance cost for a car that is 7 years old?
d) Based on this analysis, can we conclude that a relationship exists between the maintenance cost and the age of the car in years? What is the null and alternative hypothesis? Justify your answer using three steps process.
Step-by-step explanation:
classic Christian from x x + 4 + 8 is equal to 21 what is the answer
A 15-foot pole is leaning against a tree. The bottom of the pole is 8 feet away from the bottom of the tree. Approximately how high up the tree does the top of the pole reach? responses 1. 9 feet 1. 9 feet 7. 0 feet 7. 0 feet 12. 7 feet 12. 7 feet 17. 0 feet.
If A 15-foot pole is leaning against a tree and bottom of the pole is 8 feet away from the bottom of the tree. then the top of the pole reaches option (C) 12.7 feet
We can use the Pythagorean theorem to solve this problem. Let's call the height we're trying to find "x". Then, we have a right triangle where the pole is the hypotenuse, the distance from the bottom of the pole to the tree is one leg, and the height we're trying to find is the other leg. Using the Pythagorean theorem, we have:
15^2 = 8^2 + x^2
225 = 64 + x^2
Group the like terms
161 = x^2
x ≈ 12.7 feet
Therefore, the correct option is (c) 12.7 feet
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the figure shows the graph of a function.
f(x)=
The domain are the possible input while the range are the possible output of a function.
(a) The domain = [-√2, √2], the range = [0, 2]
(b) The domain = [-1, 1], the range = [0, 1]
(c) The domain = [-1, 1], the range = [0, -1]
(d) The domain = [0, 2], the range = [0, 1]
(e) The domain = [-(2 + √2), (√2 - 2)], the range = [0, 2]
Reasons:
The given functions can be expressed by the equation; (-x + 1)·(x + 1) = -x² + 1
Therefore, we have;
(a) y = f(x) + 1 = -x² + 1 + 1 = -x² + 2
The x-intercept of the above function are, x = √2, and x = -√2
Which gives;
The domain = [-√2, √2]
The range = [0, 2]
(b) y = 3·f(x) = 3 × (-x² + 1) = -3·x² + 3
At the x–intercepts, we have;
-3·x² + 3 = 0
x = ±1
The domain = [-1, 1]
The maximum value of y is given at x = 0, therefore;
= -3 × 0² + 3 = 3
The range = [0, 1]
(c) y = -f(x) = -(-x² + 1) = x² - 1
At the x–intercepts, x² - 1 = 0
x = ± 1
The domain = [-1, 1]
The minimum value of y is given at x = 0, which is y = -1
The range = [0, -1]
(d) y = f(x - 1) = -(x - 1)² + 1 = -x² + 2·x
At the x–intercepts, we have; -x² + 2·x = 0, which gives;
(-x + 2)·x = 0
Which gives, x = 0, or x = 2
The domain = [0, 2]
The maximum value of y is given when x = -b/(2·a) = -2/(2×(-1)) = 1
y = f(1) = -1² + 2×1 = 1
Therefore;
The range = [0, 1]
(e) y = f(x + 2) + 1 = (-(x + 2)² + 1) + 1 = -x² - 4·x - 2
At the x–intercepts, we have; -x² - 4·x - 2 = 0, which gives;
x = -(2 + √2) or x = x = √2 - 2
The domain = [-(2 + √2), (√2 - 2)]
The maximum value of y is given when x = -4/(2)) = -2
Which gives;
-(-2)² - 4·(-2) - 2 = 2
The range = [0, 2]
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An open cardboard box is 20 cm long, 12 cm
wide and 8 cm deep (Fig. 14.9). Calculate
the total area of cardboard in the box.
The Total Surface area of cardboard in the box is 992 cm².
What is Total Surface Area?The region that includes the base(s) and the curved portion is referred to as the total surface area. It is the overall area that the object's surface occupies. The total area of a shape with a curved base and surface is equal to the sum of the two areas.
Given:
length= 20 cm
width = 12 cm
height= 8 cm
So, the TSA of Cuboid
= 2(lw + wh + lh)
=2( 20 x 12 + 12 x 8 + 8 x 20)
=2( 240 + 96 + 160)
= 2(496)
= 992 cm²
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Write a polynomial f(x) that satisfies the given conditions. Polynomial of lowest degree with zeros of -1/4 (multiplicity 2) and 2/3 (multiplicity 1) and with f(0)=2.
f(x)=?
Answer:
Step-by-step explanation:
To obtain a polynomial of lowest degree with the given zeros and leading coefficient, we can use the fact that if a polynomial has a root of multiplicity m, then the factor (x - r)^m appears in the polynomial. Therefore, we can write:
f(x) = A(x + 1/4)^2(x - 2/3)
where A is a constant that we need to determine to satisfy the condition f(0) = 2.
To find A, we substitute x = 0 into f(x) and set the result equal to 2:
f(0) = A(0 + 1/4)^2(0 - 2/3) = -A/27 = 2
Solving for A, we find that A = -54.
Therefore, the polynomial f(x) is:
f(x) = -54(x + 1/4)^2(x - 2/3)
An electrician purchases some outdoor lighting for a customer at a wholesale price of $950.40. The customer would
have paid the retail price of $1320. What was the wholesale discount?
(Type a whole number or an exact decimal of the decimal does not terminate round to one decimal place)
Answer:
the wholesale discount is 28%.
Step-by-step explanation:
To find the wholesale discount, we need to calculate the difference between the retail price and the wholesale price as a percentage of the retail price. We can use the following formula:
Wholesale discount = ((Retail price - Wholesale price) / Retail price) x 100%
Substituting the given values into the formula, we get:
Wholesale discount = ((1320 - 950.40) / 1320) x 100%
Wholesale discount = (369.60 / 1320) x 100%
Wholesale discount = 0.28 x 100%
Therefore, the wholesale discount is 28%.
To write the answer as a whole number or an exact decimal, we can multiply 0.28 by 100 to get:
Wholesale discount = 28%
So the wholesale discount is 28%.
Can someone check my wrong answers for another excercise?
The answers to the probability problem have been stated below
How to solve the probabilityThe mean of the distribution would be 29
The standard deviation would be 8.7/√40 = 1.38
If the sample was larger, the mean would stay the same, the standard error would decrease.
3. The corresponding z score with
43.8 - 29 / 8.7
= 1.70
b. z = (43.8-29)/(8.7/√40) = 8.94
14.8 /1.38
= 10.7
c) the fisherman is more likely to catch one fish
d) z = (30.8-29)/(8.7/√40) = 1.26
= 1.8 / 1.38
= 1.304
e) He is more likely to catch 40 fishes.
4.a) Proportion in the middle = 0.95
Proportion on left and right side of normal curve = (1-0.95)/2
= 0.025
Z score at p = 0.025 using excel = NORM.S.INV(0.025) = 1.96
X1 = µ - z*σ = 29 - (1.96)*8.7
= 11.948
X2 = µ + z*σ = 29 + (1.96)*8.7
= 46.052
between 11.948 and 46.052
b)
Proportion in the middle = 0.95
Proportion on left and right side of normal curve = (1-0.95)/2 = 0.025
NORM.S.INV(0.025) = 1.96
x1 = 29 - (1.96)*8.7/√40
= 29 - 2.698
= 26.30
x2 = 29 + 2.698
= 31.698
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There are 2.5 times the amount of girls in a class than boys. If there are 35 students in the class, calculate the number of girls in the class.
Answer:
25
Step-by-step explanation:
Let's assume the number of boys in the class is "x". Then, according to the problem, the number of girls in the class is 2.5 times the number of boys, which can be expressed as:
number of girls = 2.5 * number of boys
We also know that the total number of students in the class is 35. Therefore, we can write an equation in terms of "x" as follows:
x + 2.5x = 35
Simplifying the above equation, we get:
3.5x = 35
Dividing both sides by 3.5, we get:
x = 10
This means that there are 10 boys in the class. To find the number of girls, we can use the equation we derived earlier:
number of girls = 2.5 * number of boys
number of girls = 2.5 * 10 = 25
Therefore, there are 25 girls in the class.
visitors to a park can take four different paths that lead to a lake. path w is 51 meters shorter than plath y. path y is 116 meters longer than path x. path z is 85 meters longer than path w. which path is the longest?
Path z is the longest path that leads to the lake.
Describe Algebraic Expression?An algebraic expression is a combination of numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. It is a mathematical phrase that can contain one or more terms separated by mathematical operators.
For example, 3x + 4y - 2z is an algebraic expression that contains three terms: 3x, 4y, and -2z. Each term is made up of a coefficient and a variable, where the coefficient is the numerical value that multiplies the variable.
In algebraic expressions, variables are used to represent unknown values, and the expression can be evaluated by substituting known values for the variables. For instance, if x = 2, y = 3, and z = 1, then the expression 3x + 4y - 2z can be evaluated as 3(2) + 4(3) - 2(1) = 12.
Algebraic expressions can also include exponentiation, roots, and other advanced mathematical operations. They are widely used in mathematics and other fields, such as physics and engineering, to represent relationships between variables and to model real-world situations.
Let's start by assigning variables to each path:
Let x be the length of path x (in meters).
Then path y is 116 meters longer than path x, so its length is x + 116.
Path w is 51 meters shorter than path y, so its length is x + 116 - 51 = x + 65.
Path z is 85 meters longer than path w, so its length is x + 65 + 85 = x + 150.
To find the longest path, we need to compare the lengths of all four paths. We can do this by looking at the expressions we just derived:
Path x has length x.
Path y has length x + 116.
Path w has length x + 65.
Path z has length x + 150.
Since all four paths have a common component of x, the lengths of the paths can be compared by comparing the values of the expressions that add to x. We can see that x + 150 is the largest expression, which means that path z is the longest.
Therefore, path z is the longest path that leads to the lake.
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This is about Linear equations, please help.
Answer:
Step-by-step explanation:
line a is 5ft
Please i need help due in 25 minutess
The evaluation of the two more bids Bruno received, and the equations, table and graph obtained from the bids are as follows;
The variables used for the bids are;x = The number of books
y = The total charge based on the pricing
The equations are;
Bid 7: y = 15·x + 3
Bid 8: y = 10·x + 40
Please find the completed table in the following explanation part
Part B;
Please find attached the graph of the two equations, created with MS Excel
What is an equation?An equation is a mathematical statement indicating that the quantity, magnitude or values of two expressions are the same.
The amount Bid 7 charges per book = $15
Amount paid upfront for Bid 7 = $5
Amount Bid 8 charges upfront = $40
Amount Bid 8 charges per book = $10
The variables are;
x = The amount charged per booky = The total amount paidThe equations are;
Bid 7: y = 15·x + 5Bid 8: y = 10·x + 40The table of values can be presented as follows;
Bid 7 [tex]{}[/tex] Bid 8
x [tex]{}[/tex] y = 15·x + 5 y = 10·x + 40
0 [tex]{}[/tex] 5 [tex]{}[/tex] 40
3 [tex]{}[/tex] 50 [tex]{}[/tex] 70
5 [tex]{}[/tex] 80 [tex]{}[/tex] 90
7 [tex]{}[/tex] 110 [tex]{}[/tex] 110
10 [tex]{}[/tex] 155 [tex]{}[/tex] 140
Part B;
Please find attached the required graph of the two equations, showing the legend and the scale for the x and y axis created with MS Excel.
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Find the standard form of the eclipse with end points of Major Axis (2,2) & (8,2) and minor axis (5,3) & (5,1)
Answer:
Step-by-step explanation:
Pour trouver la forme standard de l'équation d'une ellipse à partir des extrémités des grands axes et des petits axes, nous pouvons utiliser les formules suivantes:
Le centre de l'ellipse est le point (h, k), où h est la moyenne des coordonnées x des extrémités des grands axes et k est la moyenne des coordonnées y des extrémités des petits axes. Donc,
h = (2 + 8) / 2 = 5
k = (3 + 1) / 2 = 2
Donc, le centre de l'ellipse est (5, 2).
La distance a est la moitié de la longueur du grand axe, donc
a = (8 - 2) / 2 = 3
La distance b est la moitié de la longueur du petit axe, donc
b = (3 - 1) / 2 = 1
Maintenant, nous pouvons utiliser ces valeurs pour écrire l'équation de l'ellipse en forme standard:
(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1
En substituant les valeurs trouvées précédemment, nous avons:
(x - 5)^2 / 3^2 + (y - 2)^2 / 1^2 = 1
Ce qui est la forme standard de l'équation de l'ellipse.