Can you work out at what height the ladders cross?
Are you surprised that we don't need to know the distance between the
two walls?
Suppose now the first ladder is 10m above the
base of the second wall, with the second ladder
remaining as before.
Can you work out at what height the ladders
cross now?
5m
Suppose the first ladder meets the wall at a
height of a metres, as in the diagram.
At what height do the ladders cross now?
Suppose the second ladder meets the wall at a
height of b metres, as in the diagram.
At what height do the ladders cross now?
5m
nrich.maths.org/510
© University of Cambridge
10m
a
Answers
Three degrees of freedom remain after applying five equations to eight variables. The other five variables may theoretically be solved for by specifying any three of them.
What is the height of ladder ?Five equations link these eight variables together. There are two equations given by the Pythagorean Theorem.
[tex]a^ 2=x^ 2+w^2 \ b^2=y^2+w^{\} 2[/tex]\
Two more are provided by the side ratios of similar triangles.
[tex]x/w=c/v[/tex]
[tex]y/w=c/u[/tex]
The two triangles are connected by the fifth equation, which is a straightforward linear relationship.
[tex]w=u+v[/tex]
Three degrees of freedom remain after applying five equations to eight variables. The other five variables may theoretically be solved for by specifying any three of them. But it might or might not be simple. What comes next will involve two distinct circumstances.
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Related Questions
a telegraph pole is supported by a wire, the wire is attached to the pole 6m above the ground and to a point on the ground 2.5m from the foot of the pole calculate the total length of the wire needed, if an extra 0.8m is needed for the attachment.
Answers
A wire that supports telegraph poles is joined to them at intervals of 6 metres above the ground and 2.5 metres from the pole's foot for a total length of 7.3 metres.
What is the length between two telephone poles?Assume that x is the wire's length. [tex]$x^2=2.5^2+6^2$[/tex] Pythagorean theory [tex]$x^2=6.25+36$[/tex]
[tex]$x^2=6.25+36$\\ $x^2=42.25$[/tex]
As [tex]$x > 0, x=\sqrt{42,2 \sqrt{2}}=6, \sqrt{m}$[/tex]
Total length [tex]$=6.5+2.8=7.3 \mathrm{~m}$[/tex]
There are 50 metres between each telephone pole. Utility poles are made more stable by guy wires. The pole is covered by a ground wire the entire way around. Any power on the pole is safely directed underground by this device. This is a representation of the essential hardware that can differ depending on where you are found on a distribution pole. Typically, lineside telegraph poles are placed 60 to 70 yards apart, a little closer, and ideally within curves.
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the coefficient of determine (r2) gives information on both the direction of the linear relationship between 2 quantitative variables and the tightness of the linear relationship
Answers
The lowest possible value of R² is 0 and the highest possible value is 1. Put simply, the better a model is at making predictions, the closer its R² will be to 1.
The coefficient of determination (R²) measures how well a statistical model predicts an outcome. The outcome is represented by the model’s dependent variable.
The lowest possible value of R² is 0 and the highest possible value is 1. Put simply, the better a model is at making predictions, the closer its R² will be to 1.
Suppose that you perform a simple linear regression that predicts students’ exam scores (dependent variable) from their time spent studying (independent variable).
If the R2 is 0, the linear regression model doesn’t allow you to predict exam scores any better than simply estimating that everyone has an average exam score.
If the R2 is between 0 and 1, the model allows you to partially predict exam scores. The model’s estimates are not perfect, but they’re better than simply using the average exam score.
If the R2 is 1, the model allows you to perfectly predict anyone’s exam score.
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2. Evan runs a t-shirt business. He sells shirts for $10. After selling 10 shirts, Evan has $70. Assume x represents the number of shirts sold, and y represents the profit, use this information to fill in the blanks in the statement: How much money did Evan have before he sold any shirts?
A) -$30
B) $30
C) $100
D) $0
Answers
Answer:
D
Step-by-step explanation:
The statement says that Evan sells shirts for $10 and after selling 10 shirts, he has $70. We know that the profit is the revenue (the amount of money earned) minus the costs. In this case, the revenue is the amount of money Evan earns from selling shirts and the costs are the amount of money Evan has spent on producing and buying the shirts. We can use this information to set up the equation y = 10x - c where y is the profit, x is the number of shirts sold, and c is the costs.
Given that Evan has $70 after selling 10 shirts, we can substitute 10 for x and 70 for y into the equation to get:
70 = 10(10) - c
Solving for c we get:
c = -30
This means that the costs were $30. To find out how much money Evan had before he sold any shirts we need to subtract the costs from the initial amount. Evan had $0 before he sold any shirts, so the answer is D) $0.
find $a$ if $a$ and $b$ are integers such that $x^2 - x - 1$ is a factor of $ax^{17} bx^{16} 1$.
Answers
a must be equal to zero for the given equation to be true.
The given polynomial can be written in the form [tex]$(x-1)(x+1) = 0$[/tex]. This expression can be equated to zero to solve for $x$. By equating it to zero and solving, we can find that [tex]$x = 1$[/tex] and [tex]$x = -1$[/tex]. We can substitute each of these values into the given equation and solve for $a$.
Forx = 1:
[tex]$a(1)^{17}b(1)^{16}1 = 0$ \\ $a\cdot 1 \cdot b \cdot 1 \cdot 1 = 0$\\$a \cdot b = 0$[/tex]
Therefore, $a$ must be equal to zero for the given equation to be true.
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A poll of 1,000 randomly selected registered voters was taken and 680 responded that they favor candidate X for mayor (p 1 = 0.6800). Just before the election, another poll of 900 registered voters was taken and 598 individuals responded that they favor candidate X (p 2 = 0.6644). A 90% two-proportion z confidence interval for the true difference between p 1 and p 2was found to be (-0.0199, 0.0510). What is the meaning of the interval in the context of the problem?
a)There has been no change in support for the candidate.
b)There has been a substantial drop in support for the candidate.
c)There has been a substantial gain in support for the candidate.
d)It is probable for the candidate to get most of the votes because the confidence interval includes zero.
e)It is not probable for the candidate to get most of the votes because support has dropped below 50%.
Answers
The meaning of the interval is "there has been no change in support for the candidate". Thus, option (a) is correct.
The 90% two-proportion z-confidence interval (-0.0199, 0.0510) represents the likely range of the genuine difference between the two polls in support of candidate X.
Because the interval comprises 0, the difference in support between the two polls is unlikely to be statistically significant. In other words, there is no compelling evidence that there has been a significant shift in support for the candidate.
Options b), c), d), and e) imply a substantial change in support for the candidate, either positive or negative.
Thus, option (a) is correct.
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Can some help? I will give brainliest!
Answers
Answer: the answer I don’t know
Step-by-step explanation:
i got it nevermind!!!! dont need help
Answers
The Vales of x in the equations are : 1) 3 (2) 1 (3) 5 (4) 14 (5) 10 respectively
How to solve an equation?A linear equation in one variable is that in which the highest power of its variable is 1
The given equations and their solutions are
2x +1 = 7
By collecting like terms we have
2x = 3
x = 3
2) The given equation is 4x +7 = 11
By collecting like terms we have
4x = 4
Making x the subject we have
x = 1
3) 2x -3 = 7
By collecting like terms we have
2x = 10
Making x the subject we have
x = 5
4) 1/2 x - 3 = 7
By collecting like terms we have
1/2x = 7
x= 14
5) The given equation is 3x - 11 = 19
By collecting like terms we have
3x= 30
Therefore x= 10
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Find the surface area of the soild.
Answers
Answer:
288
Solution
(8x5)x4=160
(8x8)x2=64
160+64=288
At a restaurant, hot chocolate can be purchased in two different cup sizes. A 12-ounce cup costs $3.60 and a 16-ounce cup costs $4.80.
Is the linear relationship between cup size and cost also proportional? Why or why not?
Yes, the constant of proportionality is 0.3.
Yes, there is no constant of proportionality.
No, the constant of proportionality is 0.3.
No, there is no constant of proportionality.
Answers
The relationship between the cup size and the cost is proportional and the constant of proportionality is 0.3.
How to solve proportional relationship?At a restaurant, hot chocolate can be purchased in two different cup sizes. A 12-ounce cup costs $3.60 and a 16-ounce cup costs $4.80.
Let's find if the relationships of the variables are proportional.
proportional relationship are relationships between two variables where their ratios are equivalent.
Therefore, proportional relationship is rep[resented as follows:
y = kx
where
k = constant of proportionalityHence,
3.6 = 12k
k = 3.6 / 12
k = 0.3
4.80 = 16k
k = 4.8 / 16
k = 0.3
Therefore, the constant of proportionality is 0.3
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Answer:
The relationship between the cup size and the cost is proportional and the constant of proportionality is 0.3.
Step-by-step explanation:
During 2022, Frank Stewart purchased 220 shares of common stock issued by Red Hot Food Processing for $3100 including commission. Later in the same year, Frank sold the shares for $3200 after commission. Calculate the following. (Round all answers to two decimal places.)
1: profit of his stock transaction
2: Percentage return on investment:
Answers
The computation of the profit and percentage return on Frank Stewart's stock transaction is as follows:
1) Profit = $1002) Percentage return = $3.23%.What are profits and percentage returns?Profits represent the gain generated from an investment or business activity.
The percentage returns are the profits expressed as a percentage of the investment.
The percentage returns are also known as the return on investment (ROI).
Total investment in the common stock of Red Hot Food Processing = $3,100
The sales proceeds after commission = $3,200
Profit = $100 ($3,200 - $3,100)
Percentage return = 3.23% ($100/$3,100 x 100)
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identify whether each of the following variables is a nominal, ordinal, discrete, or continuous variable.
Answers
variables is a nominal, ordinal, discrete, or continuous variable.Nominal: Labels/categories. Ordinal: Order/ranking. Discrete: Whole numbers. Continuous: Any value in range
Nominal variable: A nominal variable is a type of variable that is used to name, label, or categorize particular attributes that are being measured. It is often used in survey research to represent different categories or groups.
Ordinal variable: An ordinal variable is a type of variable that is used to represent a specific order or ranking of values. It is frequently used when measuring psychological or social characteristics, such as job satisfaction or political opinions.
Discrete variable: A discrete variable is a type of variable that can only take on certain values, such as whole numbers. It is often used to count the number of specific events or occurrences within a given time period.
Continuous variable: A continuous variable is a type of variable that can take on any value within a given range. It is typically used to measure quantity or amount, such as the height or weight of an individual.
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PLS help ASAP anything will help me
Answers
Answer:
1. x/0=7
2.x+1=2
3. x=7
Step-by-step explanation:
1. you can't divide by zero so it's undefined
2. x=1
3. when you graph this on a graph, the line goes on forever, as long as it satisfies the equation x+1.
The Palestinian ministry of sports has four basketball games on a particular night. The ministry wants to assign four teams of officials to the four games in a way that will minimize the total distance traveled by the officials. The supply is always one team of officials and the demand is for only one team of officials at each game. The distances in km for each team of officials to each game location are shown in the following table: officials 1 2 3 a 90 10 100 b 50 40 40 c 60 170 90 A) Formulate this problem as Assignment Model (the objective function and constraint equations for the demand and supply). b) Use QM to solve the Model.
Answers
The optimal solution is to assign team 1 to game A, team 2 to game C, and team 3 to game B. The total distance traveled by the officials is 200km.
A) Objective Function:
Minimize Z = 90x1A + 10x1B + 100x1C + 50x2A + 40x2B + 40x2C + 60x3A + 170x3B + 90x3C
Constraints:
x1A + x1B + x1C = 1
x2A + x2B + x2C = 1
x3A + x3B + x3C = 1
x1A, x1B, x1C, x2A, x2B, x2C, x3A, x3B, x3C ≥ 0
B) The optimal solution is as follows:
x1A = 1
x1B = 0
x1C = 0
x2A = 0
x2B = 0
x2C = 1
x3A = 0
x3B = 1
x3C = 0
Z = 200 km
1. Create the objective function
Z = 90x1A + 10x1B + 100x1C + 50x2A + 40x2B + 40x2C + 60x3A + 170x3B + 90x3C
2. Set the constraints
x1A + x1B + x1C = 1
x2A + x2B + x2C = 1
x3A + x3B + x3C = 1
x1A, x1B, x1C, x2A, x2B, x2C, x3A, x3B, x3C ≥ 0
3. Solve the linear programming problem
Using QM, the optimal solution is:
x1A = 1
x1B = 0
x1C = 0
x2A = 0
x2B = 0
x2C = 1
x3A = 0
x3B = 1
x3C = 0
4. Calculate the total distance
Z = 90x1A + 10x1B
The optimal solution is to assign team 1 to game A, team 2 to game C, and team 3 to game B. The total distance traveled by the officials is 200km.
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Over the last 50 years the average cost of a car has increased by a total of 1,126%. If the average cost of a car today is 30.031, how much was the average cost 50 years ago.
Answers
The amount of average cost 50 years ago will be $2,667.05.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
Over the last 50 years, the average cost of a car has increased by a total of 1,126%. If the average cost of a car today is 30,031. Then the amount of average cost 50 years ago will be given as,
⇒ $30,031 / 1,126%
⇒ $30,031 / 11.26
⇒ $2,667.05
The amount of average cost 50 years ago will be $2,667.05.
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Guess the value of the limit (if it exists) by evaluating the function at the given numbers. (It is suggested that you report answers accurate to at least six decimal places.) Let f(x) : (cos(12x) - cos(3x))/x^2 We want to find the limit lim x=0 from (cos(12x) - cos(3x))/x^2 Start by calculating the values of the function for the inputs listed in this table. x fx 0.2 24.987664 0.1 -98.998848 0.05 -19.923683 0.01 -99.853172 0.001 -998.62855 0.0001 -9989.29525 0.00001 -99862.9534' Based on the values in this table, it appears : lim x=0 from (cos(12x) - cos(3x))/x^2=
Answers
The limit of the function (cos(12x) - cos(3x))/x^2 as x approaches 0 is approximately -99862.9534, as determined by evaluating the function at various values near x=0.
Let f(x) : (cos(12x) - cos(3x))/x^2
We want to find the limit lim x=0 from (cos(12x) - cos(3x))/x^2
Step 1: Calculate the value of the function for x=0.2
fx = (cos(12(0.2)) - cos(3(0.2)))/(0.2)^2
fx = (cos(2.4) - cos(0.6))/0.04
fx = (0.92358 - 0.95105)/0.04
fx = -24.987664
Step 2: Calculate the value of the function for x=0.1
fx = (cos(12(0.1)) - cos(3(0.1)))/(0.1)^2
fx = (cos(1.2) - cos(0.3))/0.01
fx = (0.9589 - 0.9511)/0.01
fx = -98.998848
Step 3: Calculate the value of the function for x=0.05
fx = (cos(12(0.05)) - cos(3(0.05)))/(0.05)^2
fx = (cos(0.6) - cos(0.15))/0.0025
fx = (0.9802 - 0.9657)/0.0025
fx = -19.923683
Step 4: Calculate the value of the function for x=0.01
fx = (cos(12(0.01)) - cos(3(0.01)))/(0.01)^2
fx = (cos(0.12) - cos(0.03))/0.0001
fx = (0.9999 - 0.9998)/0.0001
fx = -99.853172
Step 5: Calculate the value of the function for x=0.001
fx = (cos(12(0.001)) - cos(3(0.001)))/(0.001)^2
fx = (cos(0.012) - cos(0.003))/0.000001
fx = (0.999983 - 0.999971)/0.000001
fx = -998.62855
Step 6: Calculate the value of the function for x=0.0001
fx = (cos(12(0.0001)) - cos(3(0.0001)))/(0.0001)^2
fx = (cos(0.0012) - cos(0.0003))/0.00000001
fx = (0.99999983 - 0.99999971)/0.00000001
fx = -9989.29525
Step 7: Calculate the value of the function for x=0.00001
fx = (cos(12(0.00001)) - cos(3(0.00001)))/(0.00001)^2
fx = (cos(0.00012) - cos(0.00003))/0.0000000001
fx = (0.9999999983 - 0.9999999971)/0.0000000001
fx = -99862.9534
Therefore, the limit of the function
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Evaluate ∭ (x + y + z) dV , where E is the solid in the first octant that lies under the paraboloid z = 9 − x^2 − y^2.
Answers
By evaluating ∭ (x + y + z) dV, the final answer is 342.
What is the change of variables method?
In mathematics, a change of variables is a basic technique used to simplify problems in which the original variables are replaced with functions of other variables. The intent is that when expressed in new variables, the problem may become simpler, or equivalent to a better-understood problem.
We can evaluate the triple integral by using the change of variables method. We can set u = x, v = y, and w = z, and find the corresponding bounds for each variable in terms of the original bounds.
Then, we have
∭ (x + y + z) dV = ∭ (u + v + w) det(J) du dv dw,
where J is the Jacobian matrix of the transformation and det(J) is its determinant.
We know that 0 <= x <= 3, 0 <= y <= 3, and 0 <= z <= 9 - x^2 - y^2. Therefore, we have:
u = x, 0 <= u <= 3
v = y, 0 <= v <= 3
w = z, 0 <= w <= 9 - u^2 - v^2
The determinant of the Jacobian matrix is 1, so we can simplify the integral to:
∭ (u + v + w) du dv dw = ∫(0,3) ∫(0,3) ∫(0,9-u^2-v^2) (u+v+w) dw dv du
= ∫(0,3) ∫(0,3) (u+v)(w) + (1/3)(w^3) dv du
Hence, By solving this iteratively we get the final answer as 342.
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if TU=10 and UV=10, , what is TV
Answers
Answer:
TV = 20
Step-by-step explanation:
TV is given by the formula
TV =TU + UV
From the question
TU = 10
AND
UV = 10
Therefore
TV= 10 + 10
TV = 20.
A random survey of autos parked in the student lot and the staff lot at a large university classified the brands by county of origin, as seen in the accompanying table. Are there differences in the national origins of cars driven by students and staff?
Answers
Yes there is difference in the national origins of cars driven by students and staff, and that is 31 cars.
Following is the table showing the data of the survey of auto parked in the student lot and the staff lot, classified the brands by the country of origin. we can see that total number of car of all the given countries, driven by the students is 195. And the total number of car of all the given countries, driven by the staff is 164.
So the difference is 195 - 164 = 31 cars.
--The given question is incomplete, the complete question is
"A random survey of autos parked in the student lot and the staff lot at a large university classified the brands by country of origin, as seen in the accompanying table. Are there any difference in the national origins of cars driven by students and staff?
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approximately where does the particle achieve its greatest possible acceleration on the interval 0 to b?
Answers
The greatest positive acceleration occurs at the midpoint of the interval, when the particle is changing velocity most rapidly.
What is velocity?
Velocity is a measure of the rate of change of an object's position over a period of time. It is a vector quantity, which means it has both magnitude (or size) and direction. Velocity is usually expressed in terms of distance traveled per unit of time, such as meters per second (m/s). Velocity can be determined by dividing the distance traveled by the time taken. For example, if an object travels 20 meters in 5 seconds, its velocity would be 4 m/s. Velocity can also be calculated by taking the derivative of the object's position with respect to time.
The particle will achieve its greatest positive acceleration at the midpoint of the interval, at t = b/2.
This is because the acceleration is greatest when the velocity is changing most rapidly.
At the beginning of the interval, the particle has zero velocity, so it has no acceleration.
At the end of the interval, the particle has reached its maximum velocity, and the rate of change of velocity is zero, so it has no acceleration. Therefore, the greatest positive acceleration occurs at the midpoint of the interval, when the particle is changing velocity most rapidly.
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what is the slope through the line of (6, 3) and (5, -1)
Answers
Answer:
slope is 4
Step-by-step explanation:
question a factory manager selected a random sample of parts produced on an old assembly line and a random sample of parts produced on a new assembly line. the difference between the sample proportion of defective parts made on the old assembly line and the sample proportion of defective parts made on the new assembly line (old minus new) was 0.006. under the assumption that all conditions for inference were met, a hypothesis test was conducted with the alternative hypothesis being the proportion of defective parts made on the old assembly line is greater than that of the new assembly line. the pp-value of the test was 0.018.
Answers
Two methods can be used to administer the test.
A different theoryAbsent HypothesisThe justification for each of them is given below.What is hypothesis?Writing down the hypothesis throughout the proposal phase is required. Instead of a hypothesis that develops as a result of looking at the data, this will help to keep the research effort concentrated on the main goal and establish a firmer foundation for evaluating the study's outcomes. For these questions, answer option C is the best choice.Another possibility is that there are more faulty parts produced on the old assembly line than on the new assembly line.The value of the p is equal to 0.018, which is equivalent to 0.06 under the null hypothesis that the proportion of defective components produced on the old assembly line is equal to that produced on the new assembly line.Therefore, We infer that the solution to these questions is option C. The likelihood of noticing a difference of 0.006 is 0.018 if there is no difference in the proportions of all defective parts produced on the two assembly lines.
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From the observation deck of a skyscraper, Morgan measures a 67∘ angle of depression to a ship in the harbor below. If the observation deck is 955 feet high, what is the horizontal distance from the base of the skyscraper out to the ship? Round your answer to the nearest hundredth of a foot if necessary.
Answers
Answer:
405.37
Step-by-step explanation:
tan(67) = 955/ X
(tan(67) )(X), (955) (X)
X tan(67) = 955
X tan(67)/ tan(67) = 955/ tan(67)
X= 405.37
Please hurry
The distance between two cities is listed
as 2,462 miles. Which number represents
the best approximation of this distance
in miles?
alsvej
2.4 × 10²
K
2.4 x 10³
L
2.5 × 10²
M 2.5 × 10³
N 2.6 × 10³
Answers
Answer:
M
Step-by-step explanation:
2,462 rounded is 2,500
2.5 × 10^3= 2,500
The answer is 2.5 × 10³ Because its = 2500
Andys total bill for lunch is 20 dollars the cot of the drink is 15 % of the total bill and the rest is the cost of the food .what percent of the total bill did Andys food cost ?what was the cost of the food?
Answers
Answer:
The answer would be [tex]x[/tex]=17 because the food cost 85% of Andy's bill, that is, $17.
Step-by-step explanation:
Since 15% of the $20 bill Andy paid was for drink, it means that (100−15)% of the same amount will be for food. Hence, the food came to 85% of the bill.The amount (x) Andy paid for food therefore is:
[tex]x[/tex]= 20 x 85/100
[tex]x[/tex]= 1 x 85/5
[tex]x[/tex] = 85/5
[tex]x[/tex] = 17
So, the answer would be 17$.
mr. starnes and his wife have 6 grandchildren: connor, declan, lucas, piper, sedona, and zayne. they have 2 extra tickets to a holiday show, and will randomly select which 2 grandkids get to see the show with them.
Answers
The probability of each combination occurring is 1/15.
Let G be the set of grandchildren, G={Connor, Declan, Lucas, Piper, Sedona, Zayne}.
We can use the formula of nP2 to calculate the possible outcomes of the two grandkids being selected, where n is the number of elements in the set G or 6:
6P2 = 6!/(4!2!) = (6 x 5)/2 = 15
Therefore, there are 15 possible combinations in which the two tickets to the holiday show could go to. These 15 combinations are:
Combination 1: Connor and Declan
Combination 2: Connor and Lucas
Combination 3: Connor and Piper
Combination 4: Connor and Sedona
Combination 5: Connor and Zayne
Combination 6: Declan and Lucas
Combination 7: Declan and Piper
Combination 8: Declan and Sedona
Combination 9: Declan and Zayne
Combination 10: Lucas and Piper
Combination 11: Lucas and Sedona
Combination 12: Lucas and Zayne
Combination 13: Piper and Sedona
Combination 14: Piper and Zayne
Combination 15: Sedona and Zayne
The probability of each combination occurring is 1/15.
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The variables x and y are proportional.Use the vaules to find the constant aof proportonality.Then write the equation that relates x and y. When y = 20, x=12.
PLEASE HELP
Answers
The equation that relates x and y is: x = 3y/ 5
What is direct proportion?A direct proportion is a variation in which two given variables are related to one another in such a way that as the value of one increases, the values of the other also increases.
Thus, given that x and y are proportional, we have;
x [tex]\alpha[/tex] y
x = ky
But x = 12, and y = 20. Then;
12 = k*20
k = 12/ 20
= 3/5
So that,
substituting the value of k, to have
x = 3/5 * y
= 3y/ 5
x = 3y/ 5
Therefore, the equation that relates x and y is: x = 3y/ 5
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Dean measured a picnic area near the river and made a scale drawing. The picnic area is 9 inches wide in the drawing. The actual picnic area is 81 yards wide. What is the scale of the drawing?
Answers
Answer:
1 inch = 9 yards
Step-by-step explanation:
Compute the expression shown below.
3
(3.0 × 10-3) ³
Submit your answer in scientific notation.
Answers
The result of the given expression in the scientific notation is 2.7 × 10⁻⁸.
What is the scientific notation answer?
Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10. For example, 650,000,000 can be written in scientific notation as 6.5 ✕ 10⁸.
To compute the expression (3.0 × 10⁻³)³, we can use the following steps.
Multiply 3.0 × 10⁻³ by itself three times.
The expression (3.0 × 10⁻³)³ can be calculated as follows:
(3.0 × 10⁻³)³ = (3.0)³ × (10⁻³)³ = 27 × 10⁻⁹
So the answer in scientific notation is 2.7 × 10⁻⁸.
Therefore, the answer in scientific notation is 2.7 × 10⁻⁸.
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what is the slope through the line of (-8, 11) and (-1, -5)
Answers
Answer:
-2.29
Step-by-step explanation:
Slope is Y - Y/X - X
- 5 - 11/ - 1 - (- 8)
-16/-1+8
-16/7
-2.29
If f(x) is an exponential function where f(3.5)=10 and f(9.5)=30, then find the value of f(12), to the nearest hundredth
Answers
The equation for an exponential function is f(x) = [tex](ab)^{x}[/tex], where a and b are constants, and the value of f(12) is 1144.14.
What is an exponential function?An exponential function is one that raises the independent variable to a power. It is typically stated as f(x) = [tex]b^{x}[/tex], where b is the base and x is the exponent. Several real-world phenomena, such as population expansion, radioactive decay, and compound interest, are modelled using exponential functions.
The equation for an exponential function is f(x) = [tex](ab)^{x}[/tex], where a and b are constants.
Since we know that f(3.5) = 10 and f(9.5) = 30, we can solve for a and b.
We first need to solve for b. We can use the equation: b = f(x) / f(x-1)
So, b = 30 / 10 = 3
Now, we can solve for a. We can use the equation: a = f(x) / [tex]b^{x}[/tex]
So, a = 10 / [tex](3)^{3.5}[/tex] = 0.093
Now, we can plug in the values for a and b and x = 12 into our equation to find f(12).
f(12) = 0.093 * [tex]3^{12}[/tex] = 1144.14
Therefore, the value of f(12), to the nearest hundredth, is 1144.14.
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