The brother is 35 years old.
How to use the variable "b" to represent the brother's age?Let's use the variable "b" to represent your brother's age.
According to the problem, your brother's age minus nineteen (b - 19) is equal to your sister's age, which is 16. So we can write an equation:
b - 19 = 16
To solve for b, we can add 19 to both sides of the equation:
b - 19 + 19 = 16 + 19
Simplifying, we get:
b = 35
Therefore, your brother is 35 years old.
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Suppose an amusement park is being built in a city with a population of 100. Voluntary contributions are being solicited to cover the cost. Each citizen is being ask to give $100. The more people contribute, the larger the park will be and the greater the benefit to each citizen. But it is not possible to keep out the noncontributors; they get their share of this benefits anyway. Suppose that when there are n contributors in the population, where n can be any whole number between 0 and 100. The benefit to each citizen in monetary unit equivalents in n 2 dollars.
Required:
a. Suppose that initially no one is contributing. You are the mayor of the city. You would like everyone to contribute and can use persuasion on some people. What is the minimum number whom you need to persuade before everyone else will join voluntarily?
b. Find the Nash equilibria of the game where each citizen is deciding whether to contribute
The minimum number of people that need to be persuaded is two. When there are 0 contributor, 1 contributor, 2 or more contributor this is a the Nash equilibria.
a. Let's first calculate the benefit to each citizen when there are n contributors. According to the problem, the benefit is n^2 dollars. So when there are 0 contributors, the benefit to each citizen is 0 dollars. When there is 1 contributor, the benefit to each citizen is 1 dollar. When there are 2 contributors, the benefit to each citizen is 4 dollars. And so on, up to 10,000 dollars per citizen when all 100 citizens contribute.
Now let's think about the incentives of each citizen to contribute. If no one contributes, everyone gets 0 dollars of benefit. If one person contributes, that person gets 1 dollar of benefit, and everyone else gets 0 dollars. So each person has an incentive to free-ride, hoping that someone else will contribute.
But if two people contribute, each person gets 4 dollars of benefit, which is more than the 1 dollar cost of contributing. So once there are at least two contributors, it becomes rational for everyone else to contribute as well.
Therefore, the minimum number of people that need to be persuaded is two. Once two people contribute, it becomes rational for everyone else to contribute as well.
b. Let's consider the Nash equilibria of the game where each citizen is deciding whether to contribute. A Nash equilibrium is a situation where no one has an incentive to change their strategy, given the strategies of all the other players.
In this case, each citizen has two strategies: contribute or free-ride. Let's consider the case where n citizens are contributing. If everyone else is contributing, then it is rational to contribute as well, since the benefit of contributing is greater than the cost.
If everyone else is free-riding, then it is rational to free-ride as well, since the cost of contributing is greater than the benefit. However, if some people are contributing and some people are free-riding, then it may be rational to contribute, since the benefit of contributing may outweigh the cost, depending on the number of contributors.
Therefore, there are multiple Nash equilibria in this game, depending on the number of contributors. When there are 0 contributors, everyone is free-riding and this is a Nash equilibrium. When there is 1 contributor, that person is contributing and everyone else is free-riding, and this is a Nash equilibrium. When there are 2 or more contributors, everyone is contributing, and this is a Nash equilibrium.
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Solve the right triangle. Round decimal answers to the nearest tenth.
G
14
H
?
J
16
HJ~
m angle G ~
m angle J~
The required values are HJ = 2√15 units, ∠G = 67.5 Degrees, ∠J = 61.04 degree.
What is Right angled triangle?A triangle with two sides that are perpendicular to one another is known as a right triangle, right-angled triangle, or orthogonal triangle. It was previously known as a rectangled triangle. Trigonometry is based on the relationship between the right triangle's sides and other angles.
According to question:Given data
GH = 14 units and GJ = 16 units
Using Pythagorean theorem;
[tex]16^2 = 14^2 + HJ^2[/tex]
[tex]HJ = \sqrt{16^2-14^2}[/tex]
HJ = √60
HJ = 2√15 units
And
Cos(G) = 14/16 = 7/8
∠G = cos⁻¹(7/8)
∠G = 67.5 Degrees
And
Sin(J) = 14/16 = 7/8
∠J = Sin⁻¹(7/8)
∠J = 61.04 degree
Thus, required values are HJ = 2√15 units, ∠G = 67.5 Degrees, ∠J = 61.04 degree.
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HELP ME UNDERSTAND THIS
The estimated areas of each curve are listed below:
Case 1: A = 12.75
Case 2: A = 12.5
How to estimate the area of the function by use of rectangles and triangles
In this problem we must estimate the area above the x-axis and under a curve by using sums of rectangles and triangles according to the following expression:
A = {∑ [MIN (f(xₙ₋₁), f(xₙ))] + 0.5 · ∑ [MAX (f(xₙ₋₁), f(xₙ)) - MIN (f(xₙ₋₁), f(xₙ))]} · Δx, for n = {1, 2, 3, ..., N}
Where:
A - AreaN - Number of blocks.Case 1
A = (3.5 + 3.5 + 1.5) · 1 + 0.5 · (3.5 + 0.75 + 0.75 + 2 + 1.5) · 1
A = 8.5 + 0.5 · 8.5
A = 12.75
Case 2
A = (1 + 3 + 4) · 1 + 0.5 · (1 + 2 + 1.5 + 0.5 + 4) · 1
A = 8 + 4.5
A = 12.5
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PLEASE HELP! The graph of a rational function is shown below. Write the equation that represents this function.
THANK YOU.
Based on the following observations, we can write the equation of the rational function as: f(x) = (x + 1)/(x - 1)
What is rational function?A rational function is a type of mathematical function that is defined as the ratio of two polynomial functions.
In other words, it is a function that can be expressed as f(x) = p(x)/q(x), where p(x) and q(x) are polynomials and q(x) is not the zero polynomial.
To find the equation of the rational function represented by the given graph, we need to analyze the behavior of the graph and identify its key features. given below are the steps:
Look at the behavior of graph as x approaches infinity and negative infinity. The graph appears to have horizontal asymptotes at y = -1 and y = 1. This suggests that the function has a degree of 1 in both the numerator and denominator.
Identify any vertical asymptotes. The graph have vertical asymptote at x = 1. This suggests that the denominator of the function has a factor of (x - 1).
Look for any x-intercepts or y-intercepts.The graph's x-intercept and y-intercept are both at x = -1 and 1, respectively. This suggests that the numerator of the function has a factor of (x + 1) and that the function has a constant term of 1 in the numerator.
This function has a degree of 1 in both the numerator and denominator, a vertical asymptote at x = 1, and horizontal asymptotes at y = -1 and y = 1. It also has an x-intercept at x = -1 and a y-intercept at y = 1, which match the features of the graph given.
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A professional athlete wants to tile his bedroom in solid gold. Each square tile will be 16
inches long and 1/4 inches thick. If the density of gold is 11. 17 ounces per cubic inch and
the price of gold is $1,303. 80 per ounce, how much will each tile cost? Round your
answer is the nearest dollar.
To calculate the cost of each tile, we need to first determine the volume of each tile. The length and width of the tile are given as 16 inches, and the thickness is given as 1/4 inches, which can be converted to 0.25 inches. Therefore, the volume of each tile is 16 x 16 x 0.25 = 64 cubic inches.
Next, we need to determine the weight of gold in each tile. Since the density of gold is 11.17 ounces per cubic inch, the weight of gold in each tile is 64 x 11.17 = 715.68 ounces.
Finally, we can calculate the cost of each tile by multiplying the weight of gold by the price of gold per ounce. The price of gold is given as $1,303.80 per ounce, so the cost of each tile is 715.68 x $1,303.80 = $933,526.78. Rounded to the nearest dollar, each tile will cost $933,527.
In summary, each square tile made of solid gold and measuring 16 inches long and 1/4 inches thick will cost approximately $933,527. This cost is based on the density of gold, which is 11.17 ounces per cubic inch, and the price of gold, which is $1,303.80 per ounce.
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11. April shoots an arrow upward at a speed
of 80 feet per second from a platform 25
feet high. The pathway of the arrow can
be represented by the equation h =-
16t2 + 80t + 25, where h is the height
and t is the time in seconds. What is the
maximum height of the arrow? [3]
The maximum height of the arrow is 105 feet. To find the maximum height of the arrow, we need to determine the vertex of the quadratic function h = -16[tex]t^{2}[/tex] + 80t + 25.
The vertex is the highest point on the graph of the function, which represents the maximum height of the arrow.
To find the t-value at the vertex, we use the formula t = -b/2a, where a = -16 and b = 80. Plugging these values into the formula gives us t = -80/(2(-16)) = 2.5 seconds.
To find the maximum height, we plug t = 2.5 into the equation to get h = -16[tex](2.5)^{2}[/tex] + 80(2.5) + 25 = 105 feet. Therefore, the maximum height of the arrow is 105 feet.
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Q4 (6 points) Use Mean value theorem to prove va + 3 1. Using methods other than the Mean Value Theorem will yield no marks. (Show all reasoning). Hint: Choose a > 1 and apply MVT to f(x) = V6x +3 - x - 2 on the interval [1.a) +
Using the Mean Value Theorem, we have proven that √(6a+3) < a + 2 for all a > 1.
To prove √(6a+3) <a + 2 for all a > 1 using the Mean Value Theorem, we will begin by defining a function f(x) as:
f(x) = √(6x+3)
We can see that f(x) is a continuous and differentiable function for all x > -1/2.
Now, let's choose two values of a, such that a > 1 and b = a + h, where h is a positive number. By the Mean Value Theorem, there exists a value c between a and b such that
f(b) - f(a) = f'(c)(b-a)
where f'(c) is the derivative of f(x) evaluated at c.
Now, let's evaluate the derivative of f(x) as:
f'(x) = 3/(√(6x+3))
Thus, we can write
f(b) - f(a) = f'(c)(b-a)
√(6(a+h)+3) - √(6a+3) = f'(c)h
Dividing both sides by h and taking the limit as h → 0, we get
lim h→0 (√(6(a+h)+3) - √(6a+3))/h = f'(a)
Now, we can evaluate the limit on the left-hand side using L'Hopital's rule
lim h→0 (√(6(a+h)+3) - √(6a+3))/h = lim h→0 [3/(√(6(a+h)+3)) - 3/(√(6a+3))] = 3/(2√(6a+3))
Therefore, we have
f'(a) = 3/(2√(6a+3))
Now, we can use this value to rewrite the inequality as
√(6a+3) - (a + 2) < 0
Multiplying both sides by 2√(6a+3) and simplifying, we get
3 < 4a + 2√(6a+3)
Subtracting 4a from both sides and squaring, we get
9 < 16a^2 + 16a + 24a + 12
Simplifying, we get
0 < 16a^2 + 40a + 3
This inequality holds for all a > 1, so we have proved that
√(6a+3) < a + 2 for all a > 1.
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The given question is incomplete, the complete question is:
Use Mean value theorem to prove √(6a+3) <a + 2 for all a > 1. Using methods other than the Mean Value Theorem will yield
12 Let f(x)= x²/4(x+1) Find all critical numbers of f. As your answer please input the sum of all critical numbers.
The critical numbers of f(x) are x = -1, 0, and 1 and The sum of all critical numbers is 0.
How to find the critical numbers?To find the critical numbers of f(x) = x²/4(x+1), we need to find the values of x where the derivative of f(x) is equal to zero or does not exist.
The derivative of f(x) is:
f'(x) = [(x+1)(2x) - x²(4)] / [4(x+1)²]
Simplifying, we get:
f'(x) = [2x(x+1) - 4x²] / [4(x+1)²]
f'(x) = [2x(x+1-2x)] / [4(x+1)²]
f'(x) = [2x(1-x)] / [4(x+1)²]
f'(x) = [x(1-x)] / [2(x+1)²]
The critical numbers are the values of x where f'(x) is equal to zero or does not exist.
Setting f'(x) = 0, we get:
x(1-x) = 0
This equation is true when x = 0 or x = 1.
Now, let's check if f'(x) does not exist at x = -1 (which is the only possible point where the derivative may not exist):
f'(x) = [x(1-x)] / [2(x+1)²]
When x = -1, the denominator of f'(x) becomes zero, so the derivative does not exist at x = -1.
Therefore, the critical numbers of f(x) are x = -1, 0, and 1.
The sum of all critical numbers is:
-1 + 0 + 1 = 0
Hence, the answer is 0.
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In a major urban area, the percentage of male drivers between the ages of 19 and 29 who did not regularly use their seatbealts was 28%
(a) Identifying the population, parameter, sample, and statistic for a study on the percentage of male drivers between the ages of 19 and 29 who did not regularly use seatbelts before and after a campaign.
(b) Stating the null and alternative hypotheses for a significance test on whether the percentage of male drivers not using seatbelts has decreased after the campaign.
(a) Population: All male drivers between the ages of 19 and 29 in the major urban area.
Parameter: The percentage of male drivers between the ages of 19 and 29 in the major urban area who do not regularly use seatbelts after the radio and television campaign and stricter enforcement by the local police.
Sample: 100 male drivers between the ages of 19 and 29 who were polled.
Statistic: The percentage of male drivers between the ages of 19 and 29 in the sample who did not wear their seatbelts, which is 24%.
(b) The null hypothesis is that the percentage of male drivers between the ages of 19 and 29 who do not regularly use seatbelts in the major urban area has not decreased after the radio and television campaign and stricter enforcement by the local police.
The alternative hypothesis is that the percentage of male drivers between the ages of 19 and 29 who do not regularly use seatbelts in the major urban area has decreased after the radio and television campaign and stricter enforcement by the local police.
Mathematically, the hypotheses can be stated as follows:
H0: p >= 0.28
Ha: p < 0.28
where p is the proportion of male drivers between the ages of 19 and 29 who do not regularly use seatbelts in the major urban area after the radio and television campaign and stricter enforcement by the local police.
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The question is -
In a major urban area, the percentage of male drivers between the ages of 19 and 29 who did not regularly use seatbelts was 28%. After a major radio and television campaign and stricter enforcement by the local police, researchers want to know if the percentage of male drivers between the ages of 19 and 29 who did not regularly use seatbelts has decreased. They polled a random sample of 100 males between the ages of 19 and 29 and find the percentage who didn’t wear their seatbelts was 24%.
(a) Identify the population, parameter, sample, and statistic.
(b) State appropriate hypotheses for performing a significance test.
The target to the right is in your backyard. What is the probability of hitting the bulls eye (center circle) when you shoot an arrow? The radius of the bulls eye is 2ft and the radius of the target is 6ft. (Use 3. 14 for pi)
The probability of hitting the bulls eye (center circle) when we shoot an arrow with radius of the bulls eye is 2ft and the radius of the target is 6ft is 11.1%.
Assuming that we are shooting randomly at the target and the arrow can land anywhere within the target area, the probability of hitting the bull's eye (center circle) can be calculated as the ratio of the area of the bull's eye to the area of the entire target.
The area of the bull's eye can be calculated as follows:
Area of bull's eye = π x (radius of bull's eye)²
Area of bull's eye = 3.14 x 2²
Area of bull's eye = 12.56 square feet
The area of the entire target can be calculated as follows:
Area of target = π x (radius of target)²
Area of target = 3.14 x 6²
Area of target = 113.04 square feet
Therefore, the probability of hitting the bull's eye can be calculated as:
Probability of hitting bull's eye = Area of bull's eye / Area of target
Probability of hitting bulls eye = 12.56 / 113.04
Probability of hitting bulls eye = 0.111 or approximately 11.1%
So, the probability of hitting the bull's eye (center circle) when we shoot an arrow randomly at the target is approximately 11.1%.
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In the figure, AABC and ADEF are similar. what’s the scale factor from AABC to ADEF?
Answer:
3
Step-by-step explanation:
We can see that in figure ABC, line segment AB is 5 ft.
We can also see that in figure DEF, line segment DE is 15 ft.
How did we get from 5 to 15?
We multiplied by 3, so the scale factor is 3.
Hope this helps! :)
Given that quadrilateral PQRS is a parallelogram, how can you prove that it is also a rectangle?
A. Use the distance formula to find the length of both diagonals to see if they are congruent.
B. Find the slopes of all sides to determine if the angles are right angles.
C. Both A and B are valid.
D. None of these
Given that quadrilateral PQRS is a parallelogram, you can prove that it is also a rectangle by A: Use the distance formula to find the length of both diagonals to see if they are congruent and B: Find the slopes of all sides to determine if the angles are right angles. Therefore, the correct option is C: C. Both A and B are valid.
To prove that PQRS is a rectangle, we need to show that all angles are right angles.
Option A: Using the distance formula, we can find the lengths of both diagonals, PR and QS. If PR and QS are congruent, then we know that opposite sides of the parallelogram are congruent and parallel (since PQRS is a parallelogram). If we can also show that PR and QS intersect at a 90-degree angle, then we have proven that PQRS is a rectangle.
Option B: Finding the slopes of all sides can help us determine if the angles are right angles. If the product of the slopes of adjacent sides is -1, then we know that the sides are perpendicular (since the slope of a line perpendicular to another line is the negative reciprocal of its slope). If we can show that all adjacent sides have slopes that multiply to -1, then we have proven that PQRS is a rectangle.
Both options A and B can be used to prove that PQRS is a rectangle, so the correct answer is C.
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At a large university, 15% of students are left-handed. A psychology professor selects a random sample of 10 students and records L = the number of left-handed students in the sample. Starting on line 1 of the random-number table, how many left-handed students occur in the first trial of the simulation if we let 00-14 represent left-handed students?
The number of left-handed students in the first trial of the simulation can be found by following the above steps and counting the occurrences of two-digit numbers within the 00-14 range on line 1 of the random-number table.
To find out how many left-handed students occur in the first trial of the simulation, you'll need to follow these steps,
1. Identify the probability range for left-handed students, which is 00-14 as you've mentioned.
2. Start on line 1 of the random-number table.
3. Read each two-digit number on the line and check if it falls within the range 00-14.
4. Count the number of times a number within the 00-14 range appears in the first 10 two-digit numbers (since you're selecting a random sample of 10 students).
5. The count of numbers within the 00-14 range represents the number of left-handed students in the first trial of the simulation.
By doing the aforementioned processes and counting the occurrences of two-digit numbers between the ranges of 00 and 14 on line 1 of the random-number table, it is possible to determine the number of left-handed pupils in the simulation's first trial.
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3. Represent and Connect A jar has 20 marbles: 6 black, 4 brown, 8 white, and 2 blue. Julie draw
a marble from the jar.
a. What is the sample space?
b. What is the probability Julie will draw a white marble?
c. Which is more likely to happen, drawing a black marble or drawing either a brown
or blue marble?
d. Using this jar of marbles, what event has a probability of 0?
The event that has a probability of 0 is selecting a yellow marble
Other probabilities are listed below
Identifying the sample space and the probabilitiesThe items in the jar are given as
6 black, 4 brown, 8 white, and 2 blue.
These items are the sample space of this event
Hence, the sample space is 6 black, 4 brown, 8 white, and 2 blue.
For the probability Julie will draw a white marble, we have
P(White) = White/Total
So, we have
P(White) = 8/20
Simplify
P(White) = 2/5
For the event that is more likely to happen, we have
P(black marble) = 6/20
P(brown or blue marble) = (4 + 2)/20
P(brown or blue marble) = 6/20
The probabilities are equal
So, both events have equal likelihood
The event that has a probability of 0 could be the probability of selecting a yellow marble
This is because the jar has no yellow marble
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I NEED HELP ON THIS ASAP!! PLEASE, IT'S DUE TODAY!!!! I WILL GIVE BRAINLIEST!
Step-by-step explanation:
A, 7^(x+3) = 823, 543
7^(x+3) = 823, 543
7^(x+3) = 7^7 ....... write in the power form which it's base must be 7 in order to equalify the power
x+3 = 7
x = 4
B, 4^ -4x = 4^-8
4 ^ -4x = 1/65, 536
4^ -4x = 1/4^8 ........ write in the power form
4^ -4x = 4^-8
-4x = -8 ..... write equality among the power cause it's base is same
x=2
C, 1/(6^(x-5) ) = 1296
1/(6^(x-5) ) = 1296
6^-(x-5) = 1296
6^-(x-5) = 6^4........ write in the power form
-(x-5) = 4
-x + 5 = 4
-x = -11
x = 1
D, 1/3^x+7 = 1/243
1/3^x+7 = 1/243
3 ^ -(x+7) = 3^-5 .... write in the power form
-(x+7) = -5
-x-7 = -5
-x = 2
x= -2
A right rectangular prism has a length of f 2 feet, a width of 3 feet, and a height of
1
1/2/14 feet. Unit cubes with side lengths of foot are added to completely fill the prism
with no space remaining. What is the volume, in cubic feet, of the right rectangular
prism?
Show your work.
The volume, in cubic feet, of the right rectangular prism is 9 cubic feet
What is the volume, in cubic feet, of the right rectangular prism?From the question, we have the following parameters that can be used in our computation:
A right rectangular prism has a length of 2 feet, a width of 3 feet, and a height of 1 2/4 feet
Using the above as a guide, we have the following:
Volume = Length * Width * height
Substitute the known values in the above equation, so, we have the following representation
Volume = 2 * 3 * (1 2/4)
Evaluate
Volume = 9
Hence, the volume is 9 cubic feet
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A rectangular prism has a volume of 27 in³ If a rectangular pyramid has a base and height congruent to the prism, what is the volume of the pyramid?
___in³
fill in the blank
ty
find the number of triangles that can be formed using 14 points in a plane such that 4 points are collinear?
The number of triangles that can be formed using 14 points in a plane such that 4 points are collinear is 360.
If 4 points are collinear, then we can choose any 3 of those points to form a line segment, which cannot be extended to form a triangle.
we need to choose 3 points from the 14 points such that no 3 of them are collinear.
The number of triangles that can be formed from n non-collinear points in a plane is given by the formula:
C(n,3) = n(n-1)(n-2)/6
where C(n,3) is the binomial coefficient for choosing 3 items out of n.
So, to find the number of triangles that can be formed using 14 points in a plane such that 4 points are collinear,
we first need to find the number of ways to choose 3 points from 14 points, and then subtract the number of ways to choose 3 points from the 4 collinear points.
That is:
Total number of triangles = C(14,3) - C(4,3)
Total number of triangles = 364 - 4
Total number of triangles = 360
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Find the slope of the line through points 6,3 and 12,7
The slope of the line through points (6,3) and (12,7) is 2/3.
To find the slope of a line, we use the formula:
Slope = (y2 - y1) / (x2 - x1)
In this case, we have two points: (6, 3) and (12, 7). We can label them as follows:
x1 = 6
y1 = 3
x2 = 12
y2 = 7
Now we can plug these values into the formula:
Slope = (y2 - y1) / (x2 - x1)
Slope = (7 - 3) / (12 - 6)
Slope = 4 / 6
Slope = 2/3
Therefore, the slope of the line through the points (6, 3) and (12, 7) is 2/3.
The slope of a line tells us how steep it is. A positive slope means the line goes up as you move from left to right, while a negative slope means the line goes down. In this case, since the slope is positive (2/3), we know that the line goes up as we move from left to right.
The slope also tells us how much the y-value changes for every one unit of x-value. In this case, for every one unit we move to the right, the y-value goes up by 2/3.
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d. What are some other numbers of magazine subscriptions Andre could
have sold and still reached his goal?
The inequality to describe the number of subscriptions Andre must sell to reach his goal is 3s + 25 ≥ C.
What are inequalities ?
Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
here , we have,
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Assuming the cost of soccer cleats to be 'C' and the number of subscriptions to be 's'.
∴ The inequality that represents this situation is 3s + 25 ≥ C to real his goal.
Hence, The inequality to describe the number of subscriptions Andre must sell to reach his goal is 3s + 25 ≥ C.
Quadrilateral klmn is similar to quadrilateral opqr. find the measure of side op.
round your answer to the nearest tenth if necessary.
n
13
m
r
57
q
27
k
p
0
answer:
submit answer
The measure of side OP in quadrilateral OPQR is 0.
To find the measure of side OP in quadrilateral OPQR, which is similar to quadrilateral KLMN, follow these steps:
1. Identify the corresponding sides in both quadrilaterals. In this case, side OP corresponds to side KL, side OQ corresponds to side KM, side PQ corresponds to side LN, and side QR corresponds to side MN.
2. Determine the scale factor between the quadrilaterals by comparing the lengths of corresponding sides. Since we have the lengths of sides KM (13), LN (27), and MN (57), we can use the ratio of KM/LN (13/27) or MN/LN (57/27) as the scale factor.
3. Apply the scale factor to the length of side KL (0) to find the length of side OP. Since the length of side KL is 0, multiplying by the scale factor (either 13/27 or 57/27) will still result in a length of 0 for side OP.
4. Round your answer to the nearest tenth if necessary. In this case, the length of side OP is 0, so rounding is not necessary.
So, the measure of side OP in quadrilateral OPQR is 0.
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The sum of the numerator and denominator of the fraction is 12. If the denominator is increased by 3, the fraction becomes 12. Find the fraction.
Let the fraction be x/y.
We know that x + y = 12, and that (x) / (y + 3) = 12.
Multiplying both sides of the second equation by (y + 3), we get:
x = 12(y + 3)
Substituting this into the first equation, we get:
12(y + 3) + y = 12
Expanding and simplifying, we get:
13y + 36 = 12
Subtracting 36 from both sides, we get:
13y = -24
Dividing both sides by 13, we get:
y = -24/13
Substituting this value of y into the equation x + y = 12, we get:
x - 24/13 = 12
Multiplying both sides by 13, we get:
13x - 24 = 156
Adding 24 to both sides, we get:
13x = 180
Dividing both sides by 13, we get:
x = 180/13
Therefore, the fraction is 180/13 divided by -24/13, which simplifies to -15/2.
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Answer:
Step-by-step explanation:
AngleSideSide because it's bad
but also, if you had an angle, a side and a side
For your example: let's say CD≅AS
You could change the angle of S or D and the parameters of the triangle would still be true. Because you can change something and still have AngleSideSide be true, would make them not congruent any more.
If Sarah uses 3/4 yard of ribbon to make a hair bow. How many yards of ribbon will Sarah use to make 9 hair bows?
If Sarah uses 3/4 yard of ribbon to make a hair bow, she will need 6 and 3/4 yards of ribbon to make 9 hair bows.
To find out how many yards of ribbon Sarah will use to make 9 hair bows, we need to multiply the amount of ribbon used for one hair bow (3/4 yard) by the number of hair bows she wants to make (9).
So, the equation we need to use is:
3/4 yard of ribbon per hair bow x 9 hair bows = ? yards of ribbon
To solve for the answer, we can simplify the equation:
3/4 x 9 = 27/4
So Sarah will need 27/4 yards of ribbon to make 9 hair bows.
To convert this fraction to a mixed number, we can divide the numerator (27) by the denominator (4) and write the remainder as a fraction:
27 ÷ 4 = 6 with a remainder of 3
In summary, Sarah will need 6 and 3/4 yards of ribbon to make 9 hair bows, if she uses 3/4 yard of ribbon to make one hair bow.
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Your doing practice 3
Based on the information, the three numbers are 14, 34, and 70.
What are the numbers?Based on the information, the second number = 3x - 8
The third number is five times the first number, which can be written as:
third number = 5x
The sum of the three numbers is 118, so we can write an equation:
x + (3x - 8) + 5x = 118
9x - 8 = 118
Adding 8 to both sides:
9x = 126
x = 236 / 914
Now we can use this value of x to find the other two numbers:
second number = 3x - 8 = 3(14) - 8 = 34
third number = 5x = 5(14) = 70
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This graph represents a quadratic function. The graph shows a downward parabola vertex at (0, 9) and passes through (minus 4, minus 7), (minus 3, 0), (3, 0), and (4, minus 7). What is the value of a in this function’s equation? A. 2 B. 1 C. -1 D. -2
Answer:
Based on the given information, we can conclude that the graph represents a quadratic function. The vertex of the parabola is located at (0, 9) and the function passes through several points including (-4, -7), (-3, 0), (3, 0), and (4, -7).
To find the equation of the function, we need to determine the value of "a" in the equation f(x) = ax^2 + bx + c. Since the vertex is located at (0, 9), we know that the x-coordinate of the vertex is 0. Therefore, we can use the vertex form of the equation, which is f(x) = a(x - 0)^2 + 9, or simply f(x) = ax^2 + 9.
Next, we can use one of the given points to solve for "a". Let's use the point (-3, 0).
0 = a(-3)^2 + 9
0 = 9a - 9
9 = 9a
a = 1
Therefore, the value of "a" in the equation of the function is B. 1.
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I Need Help quick please look at the photo, and the table you have to figure out if the numbers in the table represent a linear, quadratic, or a exponential function and you have to write the function that models the data in the time. And if anyone helps me give me the correct answer please and thank you
Answer:
The data in the table represent an exponential function.
[tex]y = 2( {3}^{x} )[/tex]
A cable rigging must be run from the ground through the top of a guidepost 10 feet high, and continue in a straight line to the face of a building that stands 20 feet from the post along the ground.
(a) How high up the building should the cable be attached if the area of the right triangle formed by the cable, ground, and building is to be minimized?
(b) If the length of the cable is to be minimized, what angle θ should it make with the face of the building?
(a) To minimize the area of the right triangle formed by the cable, ground, and building, we need to minimize the length of the cable. To do this, we can use the Pythagorean theorem:
c^2 = a^2 + b^2
where c is the length of the cable, a is the distance from the guidepost to the point where the cable is attached to the building, and b is the distance from that point to the ground.
Since we want to minimize c, we can differentiate the equation with respect to a and set the derivative equal to zero:
dc/da = 2a/c = 0
Solving for a, we get a = c/2. This means that the point where the cable is attached to the building should be halfway up the building, or 10 feet high.
(b) To minimize the length of the cable, we can use the principle of least action, which states that the path taken by the cable is the one that minimizes the integral of the tension along the cable.
Assuming that the tension in the cable is constant, we can use the law of sines to find the angle θ:
sin θ / 20 = sin (90° - θ) / c
where c is the length of the cable.
We want to minimize c, so we can differentiate the equation with respect to θ and set the derivative equal to zero:
d(c)/d(θ) = -20cos(θ) / sin^2(θ) + cos(θ) / sin(θ) * dc/d(θ) = 0
Solving for dc/d(θ), we get:
dc/d(θ) = 20c * tan(θ)
Substituting this into the original equation, we get:
-20cos(θ) / sin^2(θ) + cos(θ) / sin(θ) * 20c * tan(θ) = 0
Simplifying, we get:
cos(θ) / sin(θ) = tan(θ)
Solving for θ, we get:
θ = 45°
Therefore, to minimize the length of the cable, it should make an angle of 45° with the face of the building.
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Which of the following is a counterexample for the following statement?
“If a line intersects a circle, then it intersects it in two points.”
According to the information, and example of a counterexample is: A line can cross the circle only at one point.
What would be a counterexample for this statement?To find a counterexample to this statement we must read it carefully and identify the main idea of it. In this case you are stating that a line always crosses a circle at two points.
Later we must analyze this statement and evaluate if it is true or false. In this case it is false because we can make a line that crosses a circle only once. So, the counter example sentence would be.
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An exponential function is given by the equation y=3x. Using the points x and x+1, show that the y-values increase by a factor of 3 between any two points separated by x2−x1=1. (4 points)
The given exponential function satisfies the property of increasing by a factor of 3 between any two points separated by x2−x1=1.
An exponential function is a mathematical function of the form f(x) = a^x, where a is a positive constant and x is any real number. The base a is typically a number greater than 1, and the function grows or decays rapidly depending on whether a is greater than or less than 1.
Exponential functions are commonly used to model processes that exhibit exponential growth or decay, such as population growth, radioactive decay, and compound interest. They also arise in various areas of mathematics and science, including calculus, probability theory, and physics.
We are given the exponential function [tex]y=3^x.[/tex]
Let x1 be any value of x, then the corresponding y-value is [tex]y1=3^{(x_1)[/tex]
Let x2=x1+1 be the next value of x, then the corresponding y-value is [tex]y2=3^x2=3^(x1+1)=3*3^x1.[/tex]
So, we can see that y2 is 3 times y1, which means the y-values increase by a factor of 3 between any two points separated by x2−x1=1.
Therefore, the given exponential function satisfies the property of increasing by a factor of 3 between any two points separated by x2−x1=1.
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