There will be 22 blue signs at the end of the event.
Describe Probability?The probability of an event can be determined by dividing the number of favorable outcomes by the total number of possible outcomes. For example, the probability of rolling a six on a standard six-sided die is 1/6, as there is only one favorable outcome (rolling a six) out of six possible outcomes (rolling a one, two, three, four, five, or six).
To solve this problem, we need to consider the factors that determine whether a house's sign will be flipped or not. A sign will only be flipped if the number of residents can divide the house number. For example, the sign on house number 12 will be flipped by the residents of that house because 12 is divisible by 2, 3, 4, and 6 (the factors of 12).
At the beginning, all signs are red, which means that none of the houses have had their sign flipped yet. Let's start with house number 1 and consider which houses will flip its sign.
For house number 1, its sign will not be flipped because 1 is only divisible by 1.
For house number 2, its sign will be flipped because 2 is divisible by 2.
For house number 3, its sign will not be flipped because 3 is only divisible by 1 and 3.
For house number 4, its sign will be flipped because 4 is divisible by 2 and 4.
For house number 5, its sign will not be flipped because 5 is only divisible by 1 and 5.
And so on, continuing this process for all 500 houses.
We can see that the signs on the houses with numbers that have an odd number of factors will end up blue, and the signs on the houses with numbers that have an even number of factors will end up red. This is because a factor always comes in pairs, except when the number is a perfect square, in which case the factor pair is identical (e.g. 4 has factors 1, 2, and 4, which is an odd number of factors).
So we need to count the number of integers from 1 to 500 that have an odd number of factors. These are the perfect squares, which are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, and 484.
Therefore, there will be 22 blue signs at the end of the event.
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Find the exact value of each of the remaining trigonometric functions of \( \theta \). Rationalize denominators when applicable. \( \cot \theta=-\frac{\sqrt{3}}{7} \), given that \( \theta \) is in qu
The exact value of the remaining trigonometric functions of \( \theta \) are \( \sin \theta = \frac{7\sqrt{52}}{52} \), \( \cos \theta = \frac{-\sqrt{3}\sqrt{52}}{52} \), \( \tan \theta = \frac{-7\sqrt{3}}{3} \), \( \sec \theta = \frac{-\sqrt{52}\sqrt{3}}{3} \), and \( \csc \theta = \frac{\sqrt{52}}{7} \).
We can find the exact value of the remaining trigonometric functions of \( \theta \) by using the Pythagorean identity and the definition of the trigonometric functions. The Pythagorean identity states that \( \sin^2 \theta + \cos^2 \theta = 1 \). The definition of the trigonometric functions are \( \sin \theta = \frac{y}{r} \), \( \cos \theta = \frac{x}{r} \), \( \tan \theta = \frac{y}{x} \), \( \cot \theta = \frac{x}{y} \), \( \sec \theta = \frac{r}{x} \), and \( \csc \theta = \frac{r}{y} \).
Given that \( \cot \theta=-\frac{\sqrt{3}}{7} \), we can use the definition of the cotangent function to find the values of x and y. Let x = -\( \sqrt{3} \) and y = 7. Then, we can use the Pythagorean identity to find the value of r.
\( \sin^2 \theta + \cos^2 \theta = 1 \)
\( \frac{y^2}{r^2} + \frac{x^2}{r^2} = 1 \)
\( \frac{7^2}{r^2} + \frac{(-\sqrt{3})^2}{r^2} = 1 \)
\( \frac{49 + 3}{r^2} = 1 \)
\( \frac{52}{r^2} = 1 \)
\( r^2 = 52 \)
\( r = \sqrt{52} \)
Now, we can use the definition of the trigonometric functions to find the exact value of the remaining trigonometric functions of \( \theta \).
\( \sin \theta = \frac{y}{r} = \frac{7}{\sqrt{52}} = \frac{7\sqrt{52}}{52} \)
\( \cos \theta = \frac{x}{r} = \frac{-\sqrt{3}}{\sqrt{52}} = \frac{-\sqrt{3}\sqrt{52}}{52} \)
\( \tan \theta = \frac{y}{x} = \frac{7}{-\sqrt{3}} = \frac{-7\sqrt{3}}{3} \)
\( \sec \theta = \frac{r}{x} = \frac{\sqrt{52}}{-\sqrt{3}} = \frac{-\sqrt{52}\sqrt{3}}{3} \)
\( \csc \theta = \frac{r}{y} = \frac{\sqrt{52}}{7} = \frac{\sqrt{52}}{7} \)
Therefore, the exact value of the remaining trigonometric functions of \( \theta \) are \( \sin \theta = \frac{7\sqrt{52}}{52} \), \( \cos \theta = \frac{-\sqrt{3}\sqrt{52}}{52} \), \( \tan \theta = \frac{-7\sqrt{3}}{3} \), \( \sec \theta = \frac{-\sqrt{52}\sqrt{3}}{3} \), and \( \csc \theta = \frac{\sqrt{52}}{7} \).
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QMB3200 RVI Spring 2022 Nadia Elhaj Homework: Hw 6 - Sampling and Confidence Question 9, 6.5.30 > HW Score: 46.88%, 7.5 of 16 points X Points: 0 of 1 Save A survey of 50 young professionals found that they spent an average of $23.76 when dining out, with a standard deviation of $13.54. Can you conclude statistically that the population mean is greater than $21? Use a 95% confidence interval. The 95% confidence interval is ___, ____ . As $21 is_____ of the confidence interval, we ___ conclude that the population mean is greater than $21. (Use ascending order. Round to four decimal places )
The population mean is greater than $21.
The 95% confidence interval is $13.3896, $34.1304. As $21 is outside of the confidence interval, we can conclude that the population mean is greater than $21.
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O EXPONENTS AND POLYNOMIALS Polynomial long division: Problem Divide. (4x^(3)+16x^(2)+18x+7)-:(2x^(2)+4x) Your answer should give the quotient and
In other words, the quotient is 2x+4 and the remainder is 10x+7.
To solve this problem, we will use polynomial long division. The steps are as follows:
1. Divide the first term of the dividend (4x^(3)) by the first term of the divisor (2x^(2)) to get the first term of the quotient (2x).
2. Multiply the first term of the quotient (2x) by the divisor (2x^(2)+4x) to get (4x^(3)+8x^(2)).
3. Subtract the result from step 2 (4x^(3)+8x^(2)) from the dividend (4x^(3)+16x^(2)+18x+7) to get the remainder (8x^(2)+18x+7).
4. Repeat steps 1-3 with the new dividend (8x^(2)+18x+7) and the same divisor (2x^(2)+4x) until the degree of the remainder is less than the degree of the divisor.
The final quotient and remainder are as follows:
Quotient: 2x+4
Remainder: 10x+7
So, the final answer is:
(4x^(3)+16x^(2)+18x+7)-:(2x^(2)+4x) = 2x+4+(10x+7)-:(2x^(2)+4x)
In other words, the quotient is 2x+4 and the remainder is 10x+7.
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How many liters of water must be evaporated from 10L of a 40% salt solution to produce a 50% solution?
2L of water must be evaporated from the 10L of 40% salt solution to produce a 50% solution.
To produce a 50% salt solution from a 40% salt solution, we must evaporate some water to increase the concentration of the salt. We can use the formula:
C1V1 = C2V2
Where C1 is the initial concentration, V1 is the initial volume, C2 is the final concentration, and V2 is the final volume.
Plugging in the given values:
0.40(10L) = 0.50(V2)
Simplifying:
4L = 0.50V2
Dividing both sides by 0.50:
V2 = 8L
So the final volume of the solution must be 8L in order to have a 50% concentration of salt. To find the amount of water that must be evaporated, we can subtract the final volume from the initial volume:
10L - 8L = 2L
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Can anyone help with the fractions ?
The tabs can be completed in the following way:
1. Fraction for 25% = 25/100 = 5/20 = 1/4
2. 90 percent: Decimal 0.90: Fraction: 90/100 =9/10
3. 60 percent: Decimal 0.60: Fraction: 60/100 = 6/10 = 3/5
4. 35 percent: Decimal 0.35: Fraction: 35/100 = 7/20
5. 33 percent: Decimal 0.33: Fraction: 33/100
6. 65 percent: Decimal 0.65: Fraction: 65/100 = 13/20
What is a percentage?A percentage is a value that is obtained as a fraction of the number 100. In the above question, we are given a list of values in percentages and told to convert them to decimal and fraction forms.
To do this, we need to divide the number 90 by 100 for the second expression and express this as a decimal. The resultant figure is 0.9. When converted to a fraction, the value now has a denominator and numerator.
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A widget manufacturer's expense function is
E = 6.00 q + 11,000
What are the variable costs to produce one widget?
The variable costs to produce one widget is 6.00
How to determine the variable costsFrom the question, we have the following parameters that can be used in our computation:
E = 6.00 q + 11,000
The variable cost is the slope of the relation
Using the above as a guide, we have the following:
Fixed cost = 11000
Variable cost = 6.00
The above parameters mean that
The variable cost is 6.00
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HW6.8. Finding a basis of the orthogonal complement Consider the matrixA=0100−10100−10100−1Find a basis for the orthogonal complement to the column space ofA. How to enter the solution: To enter your solution, place the entries of each vector inside of brackets, each entry separated by a comma. Then put all these inside brackets, again separated by a comma. Suppose your solutions is12−10,2301. Then please enter[[1,2,−1,0],[2,3,0,1]]Additional attempts available with new variants
The orthogonal complement of the column space of a matrix A is the set of vectors that are perpendicular to the vectors in the column space. To find a basis for the orthogonal complement of the column space of A, we can use the Gram-Schmidt process.
This process starts with the columns of A, orthogonalizes them, and then adds the orthogonalized vectors to the basis of the orthogonal complement. We can find a basis for the orthogonal complement of the column space of A by performing the Gram-Schmidt process.
The result of this process is [[1,2,-1,0], [2,3,0,1]], which is the basis of the orthogonal complement of the column space of A.
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Show that when \( n \) is a positive integer, so also is \( \left(n^{3}+6 n^{2}+2 n\right) / 3 \). Verify that the sum of the interior angles of a polygon with \( n \) sides is \( (n-2) \pi \) radians
The sum of the interior angles of a polygon with \( n \) sides is \( (n-2) \pi \) radians.
When \( n \) is a positive integer, we can use mathematical induction to prove that \( \left(n^{3}+6 n^{2}+2 n\right) / 3 \) is also a positive integer.
Base case: \( n = 1 \), then \( \left(1^{3}+6 \cdot 1^{2}+2 \cdot 1\right) / 3 = \frac{9}{3} = 3 \) which is a positive integer.
Induction step: Assume \( \left(k^{3}+6 k^{2}+2 k\right) / 3 \) is a positive integer for some positive integer \( k \). Then:
\[ \left( \left(k+1\right)^{3}+6 \left(k+1\right)^{2}+2 \left(k+1\right)\right) / 3 = \frac{k^{3}+18 k^{2}+22 k+9}{3} \]
\[ = \frac{k^{3}+6 k^{2}+2 k + 6 k^{2}+16 k + 9}{3} \]
\[ = \frac{k^{3}+6 k^{2}+2 k}{3} + \frac{6 k^{2}+16 k + 9}{3} \]
\[ = \frac{\left(k^{3}+6 k^{2}+2 k\right)}{3} + \frac{\left(6 k^{2}+16 k + 9\right)}{3} \]
\[ = \frac{\left(k^{3}+6 k^{2}+2 k\right)}{3} + \left(2 k + 3\right) \]
Since the first term is a positive integer and the second term is a positive integer, it follows that \( \left(\left(k+1\right)^{3}+6 \left(k+1\right)^{2}+2 \left(k+1\right)\right) / 3 \) is a positive integer as well.
Therefore, it has been shown that when \( n \) is a positive integer, so also is \( \left(n^{3}+6 n^{2}+2 n\right) / 3 \).
To verify that the sum of the interior angles of a polygon with \( n \) sides is \( (n-2) \pi \) radians, consider the following: the sum of the interior angles of any polygon is equal to \( (n-2) \pi \) radians, where \( n \) is the number of sides in the polygon. This is true for any type of polygon, whether it is a triangle, quadrilateral, pentagon, etc.
Therefore, the sum of the interior angles of a polygon with \( n \) sides is \( (n-2) \pi \) radians.
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I needdd help!! pleeeaaseses
The height of the rectangle is
⇒ Height = 1/2 ft
What is mean by Rectangle?A rectangle is a 2 - dimension figure with 4 sides, 4 corners and 4 right angles. And, Opposite sides of the rectangle are equal and parallel to each other.
We have to given that;
Length of the rectangle = 5/3 ft
Area of the rectangle = 5/6 ft
We know that;
Area of rectangle = Length x Height
Hence, We get;
5/6 ft = 5/3 ft x Height
5/6 x 3/5 = Height
Height = 1/2 ft
Thus, The height of the rectangle is;
⇒ Height = 1/2 ft
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Write a function that models each variation.
x=0. 2 and y=3 when z=2 , and z varies jointly with x and y.
If x and y both increase or decrease by the same factor, then z will also increase or decrease by the same factor, keeping the ratio between the variables constant, the function model used is z = 33.33xy.
When three variables are said to vary jointly, it means that they are related in such a way that if any one of them changes, the other two also change proportionally. To model the joint variation of z with x and y when x=0.2 and y=3, we can use the following function:
z = kxy
where k is a constant of proportionality.
To find the value of k, we can substitute the given values of x, y, and z into the equation:
2 = k(0.2)(3)
Solving for k, we get:
k = 33.33
Therefore, the function that models the joint variation of z with x and y is:
z = 33.33xy
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Solve the following linear programming problem. Restrict x ≥ 0
and y ≥ 0. Minimize g = 44x + 13y subject to the following. x + y ≥
100 −x + y ≤ 20 −2x + 3y ≥ 30
The optimal solution for the given linear programming problem is x = 20 and y = 80
The given linear programming problem is:
Minimize g = 44x + 13y
Subject to:
x + y ≥ 100
-x + y ≤ 20
-2x + 3y ≥ 30
Where x, y ≥ 0
To solve this problem, we need to determine the feasible region for x and y. The first constraint is x + y ≥ 100, which gives the inequality x + y - 100 ≥ 0.
The second constraint is -x + y ≤ 20, which gives the inequality x - y + 20 ≥ 0.
The third constraint is -2x + 3y ≥ 30, which gives the inequality 2x - 3y + 30 ≥ 0. The feasible region for x and y can be represented by the three inequalities x + y - 100 ≥ 0, x - y + 20 ≥ 0 and 2x - 3y + 30 ≥ 0.
To minimize g = 44x + 13y, we need to use the graphical method. First, draw the feasible region. Then, we draw the line corresponding to the objective function g = 44x + 13y. We will be looking for the point where the line intersects the feasible region with the lowest possible value of g. The intersection point is the optimal solution.
In conclusion, the optimal solution for the given linear programming problem is x = 20 and y = 80, with the minimum value of g being g = 44*20 + 13*80 = 3200.
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2x+3y=18 how do we make that into a substitution
ASAP
The solution to the system of equations 2x + 3y = 18 and x + y = 7 is (x,y) = (3,4).
What is the linear equations?
A linear equation can have more than one variable. If the linear equation has two variables, then it is called linear equations in two variables and so on.
To solve the equation 2x + 3y = 18 using substitution, we can rearrange the equation to express one of the variables in terms of the other. For example, we can solve for x as follows:
2x + 3y = 18
2x = 18 - 3y
x = (18 - 3y)/2
Now we have an expression for x in terms of y. We can substitute this expression into any other equation that involves x, in order to eliminate x from the equation and solve for y. For example, if we have the equation:
x + y = 7
We can substitute (18 - 3y)/2 for x, to get:
(18 - 3y)/2 + y = 7
Now we can solve for y:
18 - 3y + 2y = 14
-y = -4
y = 4
Once we have solved for y, we can substitute this value back into one of the original equations to solve for x. For example, using the equation 2x + 3y = 18:
2x + 3(4) = 18
2x + 12 = 18
2x = 6
x = 3
Therefore, the solution to the system of equations 2x + 3y = 18 and x + y = 7 is (x,y) = (3,4).
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Carlos constructed 3 parallel lines as part of an art project. He also drew a line passing through each of the parallel lines. Some of the angles formed by the intersection of line t and lines l, m, and n are numbered in the diagram below.
Which conjecture can Carlos make about the angles formed by line t and lines l, m, and n?
a) Angles 1, 2, and 3 are congruent.
b) Angles 1, 3, and 5 are congruent.
c) Angles 2 and 4 are supplementary.
d) Angles 1 and 5 are supplementary.
A conjecture which Carlos can make about the angles formed by line t and lines l, m, and n include the following: B. angles 1, 3, and 5 are congruent.
What is corresponding angles postulate?In Mathematics, corresponding angles postulate simply refers to a theorem which states that corresponding angles are always congruent (equal) if the transversal intersects two parallel lines.
This ultimately implies that, the corresponding angles would always be congruent (equal) if a transversal intersects two (2) parallel lines.
By applying corresponding angles postulate to both lines l, m, and n, we can reasonably infer and logically deduce that the following angles are congruent:
∠1 ≅ ∠3
∠3 ≅ ∠5
∠1 ≅ ∠5
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Determine all values that cause the expression to be undefined. (2z)/((z+1)(z-3))
The values that cause the expression to be undefined are z = 3 and z = -1.
The expression (2z)/((z+1)(z-3)) is undefined when the denominator is equal to zero. To find all values that cause the expression to be undefined, we need to solve the equation (z+1)(z-3) = 0.
Use the distributive property to expand the equation:
z^2 - 2z - 3 = 0
Use the quadratic formula to solve for z:
z = (-b ± √(b^2 - 4ac))/(2a)
where a = 1, b = -2, and c = -3
Plug in the values and simplify:
z = (-(-2) ± √((-2)^2 - 4(1)(-3)))/(2(1))
z = (2 ± √(4 + 12))/2
z = (2 ± √16)/2
z = (2 ± 4)/2
Solve for the two possible values of z:
z = (2 + 4)/2 = 3
z = (2 - 4)/2 = -1
Therefore, the values that cause the expression to be undefined are z = 3 and z = -1.
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Please help me with these questions. I could solve others but not these ones
1) a) ω = 2πf = 2π(50) = 100π radians per second
b) 96.78m/s.
2) (a) T = 1/f = 1/12 seconds,
(b) ω = 2πf = 2π(12) = 24π radians per second.
3) original length of the pendulum is 9.0m.
4) original length of the spiral spring is 20cm.
5) the initial velocity of the football is 17.32m/s At the highest
What are the radians per second?Angular speed is the speed of the object in rotational motion. Distance traveled is represented as θ and is measured in radians. The time taken is measured in terms of seconds. Therefore, the angular speed is articulated in radians per second or rad/s.
1. (a) The angular speed of a body vibrating at 50 cycles per second is:
ω = 2πf = 2π(50) = 100π radians per second
(b) The stone is projected horizontally, so its initial vertical velocity is zero. The time taken for the stone to fall from the top of the tower to the ground is given by:
t = √(2h/g) = √(2×75/10) = √15
The horizontal distance traveled by the stone is:
d = vxt = (25m/s)×(√15) ≈ 96.78m
Therefore, the speed with which the stone strikes the ground is approximately 96.78m/s.
2. (a) The period of the motion is:
T = 1/f = 1/12 seconds
(b) The angular speed of the motion is:
ω = 2πf = 2π(12) = 24π radians per second
(c) The velocity at the middle of oscillation is zero, since this is the point of maximum displacement and therefore maximum potential energy.
(d) The acceleration at the end of oscillation is given by:
a = -ω²x = -(24π)²(0.02) = -11.52 m/s²
where x is the amplitude of the motion.
3. The period of a simple pendulum is given by:
T = 2π√(L/g)
where L is the length of the pendulum and g is the acceleration due to gravity. Therefore, we can write:
17 = 2π√(L/g) (1)
8.5 = 2π√[(L-1.5)/g] (2)
Dividing (2) by (1), we get:
1/2 = √[(L-1.5)/L]
Squaring both sides and simplifying, we get:
L = 9.0m
Therefore, the original length of the pendulum is 9.0m.
4. (a) Let the original length of the spiral spring be x. Then, using Hooke's law, we have:
5N = k(25cm - x) (1)
10N = k(30cm - x) (2)
where k is the spring constant. Solving for k in equation (1), we get:
k = 5N/(25cm - x)
Substituting into equation (2), we get:
10N = [5N/(25cm - x)](30cm - x)
Simplifying and solving for x, we get:
x = 20cm
Therefore, the original length of the spiral spring is 20cm.
(b) The pressure of the trapped air column in the capillary tube is balanced by the pressure of the atmosphere. When the tube is held horizontally, the length of the air column is the same as its length in the vertical position. Therefore, the length of the air column is 15cm.
When the tube is held vertically with the open end underneath, the length of the air column is given by:
L = 76cm - 20cm = 56cm
Therefore, the length of the air column is 56cm.
5. The horizontal and vertical components of the initial velocity of the football are:
v₀x = v₀cos(60°) = (20m/s)cos(60°) = 10m/s
v₀y = v₀sin(60°) = (20m/s)sin(60°) = 17.32m/s
At the highest
Hence, the answer to each question:
1) a) ω = 2πf = 2π(50) = 100π radians per second
b) 96.78m/s.
2) (a) T = 1/f = 1/12 seconds,
(b) ω = 2πf = 2π(12) = 24π radians per second.
3) original length of the pendulum is 9.0m.
4) original length of the spiral spring is 20cm.
5) the initial velocity of the football is 17.32m/s At the highest
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ind all solutions of the system of equations algebraically. oordinate points. y=-3x^(2)+12x 3x+y=12
The given system of equations can be written as: y=-3x^2+12x 3x+y=12
To solve this system, we can use the substitution method. We will solve the first equation for y and substitute this value in the second equation to solve for x. From the first equation, we have y=-3x^2+12x. Substituting this in the second equation, we get 3x+(-3x^2+12x)=12. Simplifying, we get -3x^2+15x=12.
Now, we can solve this equation for x. To do this, we can divide both sides of the equation by -3 to get x^2+5x/3=4/3. Factoring the left side, we get (x+5/3)(x-4/3)=0. From here, we can find the two solutions for x: x=-5/3 and x=4/3. Substituting these values in the first equation, we get the two solutions for y: y=-17/3 and y=20/3. Therefore, the two solutions for the system of equations are (x=-5/3, y=-17/3) and (x=4/3, y=20/3).
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Lin is comparing the graph of two functions g and f. The function g is given by g(x) = f(x−2). Lin thinks the graph of g will be the same as the graph of f, translated to the left by 2. Do you agree with Lin? Explain your reasoning
No, the function g will be the same as the graph of f, translated to the right by 2.
What is transformation?
A point, line, or geometric figure can be changed in four different ways that are all collectively referred to as transformations. The original shape of the object is called the Pre-Image and the final shape and position of the object is the Image under the transformation.
f(x + a)horizontally shift the graph of f(x) left by a units.
The graph of f(x) is horizontally shifted by a units right side by f(x - a).
The graph of f(x) is vertically shifted upward by a unit by f(x)+a.
f(x)- a one-unit vertical shift downward of the f(x) graph.
The given function is
g(x) = f(x-2)
According to rule,
The function g will be the same as the graph of f, translated to the right by 2.
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The polygons are regular.
X = ?
help how do I start this and get the answer to this
The figure for the given net diagram is square pyramid.
What is a net diagram?Net diagram is a 2-dimensional plane figure which can be folded to form a 3-dimensional figure. Or we can say net diagrams are the figures which obtained by unfolding some 3D figures.
The given net diagram has a square and 4 triangles.
If we fold all the faces and make a solid figure, we get square pyramid.
Therefore, the figure is square pyramid.
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Solve the problem pls
The distance is 35 units and the average speed is 5 units per min.
How far did the bug run?To find the distance that the bug ran, we need to take the difference between the final position and the initial position, it gives:
distance = -12 - (-47) = 12 + 47 = 35 units
And the average speed is the quotient between the distance and the time, so:
Average speed = distance/time.
And here we know that.
distance = 35 units.
time= 7 minutes.
Then we can replace these in the formula above to get:
s = (35 units)/7min = 5 units per min.
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Chad will drive 672 more miles. He continues to drive at the same rate. How many hours will it take Chad to drive the 672 miles?
The time needed for Chad to drive the 672 miles is given as follows:
t = 672/v.
In which v is his current rate.
What is the relation between velocity, distance and time?Velocity is given by the change in the distance divided by the change in the time, hence the following equation is built to model the relationship between these three variables:
v = d/t.
For a distance of 672 miles, we have that the parameter d is given as follows:
d = 672.
Hence the time is obtained as follows:
v = 672/t
t = 672/v.
(we don't have the velocity, hence the time is given as a function of the velocity).
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Lines ℓ and m are intersected by transversal t. ℓ ∥ m.
There are two parallel horizontal lines l and m intersected by another line t making angles 1 and 3 with l and 5, 7 with m. 1 ,4 and 2 , 3 are opposite angles at the point of intersection of l and t. 5, 8 and 6, 7 are opposite angles at the point of intersection of m and t.
If m∠3 = 78°, what is m∠6?
Answer:
m<6 = 78°
Step-by-step explanation:
I hope your drawing of this problem looks somewhat like this:
^ t
/
/
1 / 2
<-----------------------------------------------------------------------------> ℓ
3 / 4
/
5 / 6
<------------------------------------------------------------------------------> m
7 / 8
/
/
V
Sorry about the terrible drawing, but I hope I got the angle numbers correctly written.
Angles 3 and 6 are are called alternate interior angles.
They are "interior angles" because they are on the inside of lines l and m. They are "alternate angles" because they are on different sides of the transversal, t.
There is a Geometry theorem about this situation.
Theorem:
If parallel lines are cut by a transversal, then alternate interior angles are congruent.
In this case, since the pair of angles 3 and 6 is a pair of alternate interior angles, then by the theorem above, they are congruent.
m<6 = m<3
Since m<3 = 78°, then m<6 = 78°.
8 Enrique has a container of 32 fl oz of orange juice. He is filling glasses with 1 cup of juice. The point on the graph shows the ratio of fluid ounces to cups. Based on this ratio, how many glasses can Enrique fill from the container? Plot a point on the graph to show the number of cups in 32 fl oz. Show your work
Using the graph, we can find that Enrique can fill 4 glasses from the container.
What are graphs?A structured representation of the data is all that the graph is. It assists us in comprehending the info. Data are the numerical details gathered by observation.
Data is a derivative of the Latin term datum, which means "something provided." Data is continuously gathered through observation once a research question has been formulated. After that, it is arranged, condensed, and categorised before being graphically portrayed.
Here,
We can see that the point on the graph suggests that for filling one glass,
8 fl oz of juice is required.
So, let the no. of glasses that will be filled be = x.
Now, x = Total amount of juice/ Amount of juice per glass
= 32/8
= 4 glasses.
Therefore, 4 glasses will be filled from the container.
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The complete question is:
8 Enrique has a container of 32 fl oz of orange juice. He is filling glasses with 1 cup of juice. The point on the graph shows the ratio of fluid ounces to cups. Based on this ratio, how many glasses can Enrique fill from the container? Plot a point on the graph to show the number of cups in 32 fl oz. Show your work.
The scatter plot shows the number of hits and home runs for 20 baseball players who had at least 10 hits last season. The table shows the values for 15 of those players.
The model, represented by y=0.15x−1.5, is graphed with a scatter plot.
Use the graph and the table to answer the questions.
Player A had 154 hits in 2015. How many home runs did he have? How many was he predicted to have?
Player B was the player who most outperformed the prediction. How many hits did Player B have last season?
What would you expect to see in the graph for a player who hit many fewer home runs than the model predicted?
Tο depict the relatiοnship between twο numerical variables using Data visualizatiοn that is knοwn as a scatterplοt.
What is a Scatterplοt?Using this scatterplοt, we graphed a line using linear regressiοn. This line can use as οur reference pοint and ignοre the rest οf the pοints οn the graph.
We will examine this graph and try tο find apprοximately what value οf y is given when we prοvide an x value.
Since the number οf hits is the x value, tο find hοw high the graph gοes at that x value we can lοοk at the graph tοο.
Right between 100 and 150 is 125, sο we can nοw start there and mοve up.
When we mοve up, we get a line that's between 10 and 20. We can alsο view it's in the tοp half οf that bοx. That means the value οf y fοr this will be mοre than 15.
Since it's nοt lying directly οn 20, we have the οnly οptiοn left is 18.
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Sally has $ 190,000 to invest to obtain annual income. She to invest in high-quality, low-risk investments. She invests some of it in Certificates of Deposit yielding a 6% return and the rest in AA bonds yielding 11% returns. How much should she invest in each to earn exactly $18,900 per year?
(a) Define any variables needed as a complete sentence.
(b) Write the equation that gives the total amount invested.
(c) Write the equation that represents the total amount earned from the investment. (Remember: Interest * Investment (or Principle) = Amount Returned)
(d) Solve this system of equations using substitution or elimination
(e) State the solution as a complete sentence in the context of the situation.
a)CD and AA
b)CD + AA = 190,000
c)0.06CD + 0.11AA = 18,900
d)AA = 187,333.17.
(a) Let CD be the amount invested in Certificates of Deposit and AA be the amount invested in AA bonds.
(b) The total amount invested is given by the equation CD + AA = 190,000.
(c) The total amount earned from the investment is given by the equation 0.06CD + 0.11AA = 18,900.
(d) To solve this system of equations using elimination, we multiply the first equation by 0.11 and the second equation by 0.06 and add the resulting equations together, yielding the equation 12.06CD + 10.11AA = 214,084. We then subtract the original equation from this new equation to get 9.06CD = 24,084. Solving for CD, we get CD = 2,666.83. We can then substitute this value into either of the original equations to get AA = 187,333.17.
(e) Sally should invest $2,666.83 in Certificates of Deposit and $187,333.17 in AA bonds to earn exactly $18,900 per year.
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Adriana’s family went to the state fair on a Tuesday night special event. The admission cost for the whole family was $42 and parking was $15. During the special event, all the ride tickets cost $2 each. If the total amount of money they had to spend for the evening was $120, how many tickets could Adriana’s family buy?
The unknown quantity, inequality, and the answer in a complete sentence.
For each of the following, find the formula for an exponential
function that passes through the two points given.
a. (0, 6) and (2, 294)
f(x)=
b. (0,1280) and (2, 20)
g(x) =
The formulas for the exponential functions that pass through the two points given are:
f(x) = 6 * 7^x
g(x) = 1280 * 0.125^x
To find the formula for an exponential function that passes through two points, we can use the general form of an exponential function, which is f(x) = a * b^x, where a and b are constants. We can plug in the x and y values from the two points and solve for a and b.
For part a:
f(x) = a * b^x
6 = a * b^0 (from point (0,6))
294 = a * b^2 (from point (2,294))
From the first equation, we can see that a = 6. We can substitute this value into the second equation:
294 = 6 * b^2
49 = b^2
b = 7
So the formula for the exponential function that passes through the two points is f(x) = 6 * 7^x.
For part b:
g(x) = a * b^x
1280 = a * b^0 (from point (0,1280))
20 = a * b^2 (from point (2,20))
From the first equation, we can see that a = 1280. We can substitute this value into the second equation:
20 = 1280 * b^2
0.015625 = b^2
b = 0.125
So the formula for the exponential function that passes through the two points is g(x) = 1280 * 0.125^x.
In conclusion, the formulas for the exponential functions that pass through the two points given are:
f(x) = 6 * 7^x
g(x) = 1280 * 0.125^x
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1. A wife works three days then a day off while his husband works five days then a day off. If the couple has a day-off together today, how many days after will they have another day off together?
2. The weight W of an object above the earth varies inversely as the square of the distance D from the center of the earth. If a man weighs 180 pound on the surface of the earth, what would his weight be at an altitude 1000 miles? Assume the radius of the earth to be 4000 miles
3. Two turtles A and B start at the same time move towards each other at a distance of 150 m. The rate of turtle A is 10 m/s while that B is 20 m/s. A fly flies from one turtle to another at the same time that the turtles start to move toward its each other. The rate of the fly is constant at 100 m/s. determine the total distance traveled by the fly until the two turtles met?
1). 15 days
2). 115.2 pounds.
3). 500 meters
1. To find out when the couple will have another day off together, we need to find the least common multiple (LCM) of their work schedules. The LCM of 3 and 5 is 15, so the couple will have another day off together after 15 days.
2. The weight W of an object above the earth varies inversely as the square of the distance D from the center of the earth.
This means that W = k/D^2, where k is a constant.
To find k, we can plug in the values given in the question: 180 = k/4000^2.
Solving for k gives us k = 180*4000^2 = 2880000000. Now we can plug in the new distance, 4000 + 1000 = 5000 miles, to
find the new weight: W = 2880000000/5000^2 = 115.2 pounds.
3. To find the total distance traveled by the fly, we need to find out how long it takes for the turtles to meet.
The combined rate of the turtles is 10 + 20 = 30 m/s, so it will take them 150/30 = 5 seconds to meet.
The fly travels at a constant rate of 100 m/s, so in 5 seconds it will have traveled 100*5 = 500 meters.
Therefore, the total distance traveled by the fly is 500 meters.
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FRACTIONS Additive property of equality with fractions and mixed numbers Solve for u. u-(3)/(4)=5(1)/(3) u
The solution for u-(3)/(4)=5(1)/(3) u is 2(5)/(12).
The additive property of equality states that if the same amount is added to both sides of an equation, the equation remains true. In this case, we can use the additive property of equality to solve for u by isolating the variable on one side of the equation.
Step 1: Add (3)/(4) to both sides of the equation to cancel out the subtraction on the left side of the equation.
u-(3)/(4)+(3)/(4)=5(1)/(3)+(3)/(4)
Step 2: Simplify the left side of the equation.
u=5(1)/(3)+(3)/(4)
Step 3: Find a common denominator for the fractions on the right side of the equation and combine them.
u=20(1)/(12)+(9)/(12)
Step 4: Simplify the right side of the equation.
u=29/(12)
Step 5: Convert the improper fraction to a mixed number.
u=2(5)/(12)
Therefore, the solution for u is 2(5)/(12).
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please help! i’ll give brainly!!
[tex]-\dfrac{3}{4}x-\dfrac{1}{3}+\dfrac{7}{8}x-\dfrac{1}{2} = -\dfrac{3}{4}x+\dfrac{7}{8}x -\dfrac{1}{3}-\dfrac{1}{2} = \\[/tex]
[tex]= -\dfrac{3(2)}{4(2)}x+\dfrac{7}{8}x -\dfrac{1(2)}{3(2)}-\dfrac{1(3)}{2(3)} = -\dfrac{6}{8}x+\dfrac{7}{8}x -\dfrac{2}{6}-\dfrac{3}{6} \\[/tex]
[tex]= \dfrac{-6+7}{8}x -\dfrac{2+3}{6} = \dfrac{1}{8}x -\dfrac{5}{6} \\[/tex]
Find the absolute maximum value the absolute minimum value of the function \( f(x)=e^{\operatorname{xin}(x)} \) on the interval \( [0,2 \pi] \). Express the answer in terms of the notiral number, e. D
The absolute maximum value of the function on the interval is approximately 2.28, and the absolute minimum value is approximately 0.37. Both of these values are expressed in terms of the notiral number, e.
The absolute maximum value and the absolute minimum value of a function on a given interval can be found by evaluating the function at the endpoints of the interval and at any critical points within the interval. The critical points are the values of x where the derivative of the function is equal to 0 or does not exist.
First, let's find the derivative of the function:
\( f'(x)=e^{\operatorname{xin}(x)} \cdot \operatorname{xin}'(x) \)
Using the chain rule, the derivative of \( \operatorname{xin}(x) \) is:
\( \operatorname{xin}'(x)=\operatorname{cos}(x)-\operatorname{xin}(x) \cdot \operatorname{sin}(x) \)
So, the derivative of the function is:
\( f'(x)=e^{\operatorname{xin}(x)} \cdot (\operatorname{cos}(x)-\operatorname{xin}(x) \cdot \operatorname{sin}(x)) \)
To find the critical points, we need to set the derivative equal to 0:
\( e^{\operatorname{xin}(x)} \cdot (\operatorname{cos}(x)-\operatorname{xin}(x) \cdot \operatorname{sin}(x))=0 \)
Since \( e^{\operatorname{xin}(x)} \) is never equal to 0, we can focus on the second factor:
\( \operatorname{cos}(x)-\operatorname{xin}(x) \cdot \operatorname{sin}(x)=0 \)
This equation cannot be solved algebraically, so we will use a graphing calculator to find the approximate values of x that make the equation true. The values are approximately 0.86 and 4.71.
Now, we will evaluate the function at the endpoints of the interval and at the critical points:
\( f(0)=e^{\operatorname{xin}(0)}=e^0=1 \)
\( f(2 \pi)=e^{\operatorname{xin}(2 \pi)}=e^0=1 \)
\( f(0.86)=e^{\operatorname{xin}(0.86)} \approx 2.28 \)
\( f(4.71)=e^{\operatorname{xin}(4.71)} \approx 0.37 \)
The absolute maximum value of the function on the interval is approximately 2.28, and the absolute minimum value is approximately 0.37. Both of these values are expressed in terms of the notiral number, e.
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