x1 = 5 and x2 = 0
The following LP problem in a spreadsheet MAX: 4x1 + 4x2 Subject to: 2x1 + 4x2 <= 20, 3x1 + 5x2 <= 15, and x1, x2 >= 0.A spreadsheet is a type of software that allows users to store and analyze data in a grid-like format of rows and columns. Spreadsheets are commonly used for data entry, financial modeling, and other calculations.In the given problem, we are supposed to find the maximum value of the function 4x1 + 4x2 subject to the constraints 2x1 + 4x2 <= 20, 3x1 + 5x2 <= 15, and x1, x2 >= 0.The first two constraints are represented by inequalities. That means, the values of x1 and x2 can be any non-negative values that satisfy the constraints. Mathematically, the constraints can be represented as:2x1 + 4x2 <= 20⇒ x2 <= 5 - 0.5x1--------(1)3x1 + 5x2 <= 15⇒ x2 <= 3 - 0.6x1--------(2)Note that, we have represented the constraints in such a way that x2 is the subject of the inequality. This is done to make it easier to graph and find the feasible region.To find the feasible region, we need to graph both inequalities (1) and (2) on a coordinate plane. The feasible region is the shaded area that is common to both regions. It is given below:The feasible region is the triangular-shaped region. Since x1 and x2 are both non-negative, we need to consider only the values of x1 and x2 that are within the feasible region.Now, to maximize the function 4x1 + 4x2, we need to find the optimal solution. We do this by finding the intersection points of the lines that represent the equation 4x1 + 4x2 = k, where k is a constant.The equation 4x1 + 4x2 = k can be rearranged as x2 = (-x1 + k/4)This equation represents a line with a slope of -1 and a y-intercept of k/4. We can graph this line for different values of k to find the optimal solution. The line for k = 0 is shown below:We can see that the line passes through the feasible region at point (0, 0) and (5, 0). This means that the maximum value of the function is 4x1 + 4x2 = 4(5) + 4(0) = 20 at point (5, 0).Thus, the maximum value of the function 4x1 + 4x2 subject to the constraints 2x1 + 4x2 <= 20, 3x1 + 5x2 <= 15, and x1, x2 >= 0 is 20 at x1 = 5 and x2 = 0.
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Find the output, b, when the input, a, is 6
b= -1 - 7a
When a=6, the value of b is equals to -43.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
An algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division, which can be simplified and evaluated.
In other words, an algebraic expression is a collection of terms and coefficients that are connected by mathematical operators.
Substitute the value of a=6 into the expression for b:
b = -1 - 7a
b = -1 - 7(6)
b = -1 - 42
b = -43
Therefore, when a=6, the value of b is -43.
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Angle N = 40 degrees, side NP = 8, angle Q = 40 degrees, and side QS = 8. What additional information would you need to prove that ΔNOP ≅ ΔQRS by ASA?
a
Angle O is congruent to angle R.
b
Angle P is congruent to angle S.
c
Side NO is congruent to side QR.
d
Side OP is congruent to side RS.
Answer:
Option d: Side OP is congruent to side RS.
To prove that ΔNOP ≅ ΔQRS by ASA, we need to show that:
1. ∠N ≅ ∠Q (given)
2. Side NP ≅ Side QS (given)
3. Side OP ≅ Side RS (additional information needed)
Hence, option d is the correct answer.
GEOMETRY PLEASE HELPPP
The solution to the given proportion is 7 / 8. The solution has been obtained by using the cross multiplication method.
What is the cross multiplication method?The cross multiplication approach involves multiplying the denominator of the first phrase by the numerator of the second fraction, and vice versa.
We are given a proportion as
2 / (3b - 3) = 4 / (1 - 2b)
Now, by using cross multiplication method, we get
⇒2 (1 - 2b) = 4 (3b - 3)
⇒2 - 4b = 12b - 12
⇒-16b = -14
⇒16b = 14
⇒b = 14 / 16
⇒b = 7 / 8
Hence, the solution to the given proportion is 7 / 8.
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Which equations have the same value of x as Three-fifths (30 x minus 15) = 72? Select three options. 18 x minus 15 = 72 50 x minus 25 = 72 18 x minus 9 = 72 3 (6 x minus 3) = 72 x = 4.5
The three equations that have the same value of x as the original equation are:
18x - 15 = 72
3(6x - 3) = 72
x = 4.5
What is an equation?
An equation is a statement that two expressions are equal. It typically contains one or more variables (represented by letters) and mathematical operations such as addition, subtraction, multiplication, and division. Equations can be used to represent relationships between quantities or to solve for unknown values.
The correct options are:
18x - 15 = 72
18x - 9 = 72
x = 4.5
To see why, we can start by simplifying the original equation:
Three-fifths (30x - 15) = 72
(3/5)(30x - 15) = 72
18x - 9 = 72
18x - 15 = 72 + 15
18x = 87
x = 87/18
So we see that x = 87/18 is the solution to the original equation.
Now let's check each of the answer choices:
18x - 15 = 72
Solving for x, we get x = 87/18, which is the same as the solution to the original equation. This equation is equivalent to the original equation.
50x - 25 = 72
Solving for x, we get x = 97/50, which is not the same as the solution to the original equation. This equation is not equivalent to the original equation.
18x - 9 = 72
Solving for x, we get x = 81/18 = 9/2, which is not the same as the solution to the original equation. This equation is not equivalent to the original equation.
3(6x - 3) = 72
Simplifying, we get 18x - 9 = 72, which is equivalent to the second equation listed above. So this equation is also equivalent to the original equation.
x = 4.5
This is the same solution as the original equation, so this equation is also equivalent to the original equation.
Therefore, the three equations that have the same value of x as the original equation are:
18x - 15 = 72
3(6x - 3) = 72
x = 4.5
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Write an algebraic expression for each word expression then evaluate the expression for these values of the variable 1, 6, 13.5. five the quotient of 100 and the sum of B and 24
Answer:
the quotient of 100 and the sum of B and 24
Step-by-step explanation:
The word expression is: "the quotient of 100 and the sum of B and 24"
The algebraic expression is: 100 / (B + 24)
To evaluate this expression for the values 1, 6, and 13.5, we substitute each value in turn for B and simplify:
When B = 1:
100 / (1 + 24) = 100 / 25 = 4
When B = 6:
100 / (6 + 24) = 100 / 30 = 3.33...
When B = 13.5:
100 / (13.5 + 24) = 100 / 37.5 = 2.666...
Therefore, the values of the expression for B = 1, 6, and 13.5 are approximately 4, 3.33, and 2.67, respectively.
CAN I GET SOME HELP PLS
*problem in image*
(the drawn part was some help the teacher gave us bc the image is pretty dark)
Answer:
he walks 300 meters
Step-by-step explanation:
nbsjdjsj d f f f f f f f. f f f f f f f f f f
Determine whether the ordered pair is a solution of (5,6) {(x+y=11),(x-y=-1):} No Yes
Yes, the ordered pair (5,6) is a solution of the system of equations {(x+y=11),(x-y=-1):}.
To check if an ordered pair is a solution of a system of equations, we can plug the values of the ordered pair into the equations and see if they are true.
For the first equation, x + y = 11, we can plug in 5 for x and 6 for y:
5 + 6 = 11
This is true, so the ordered pair satisfies the first equation.
For the second equation, x - y = -1, we can again plug in 5 for x and 6 for y:
5 - 6 = -1
This is also true, so the ordered pair satisfies the second equation.
Since the ordered pair satisfies both equations, it is a solution of the system of equations.
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You are 14ft away from a flagpole and are looking up at if from an angle of 74.4 How is the flagpole ?
Answer:
23.4 ft tall
Step-by-step explanation:
Answer:
Step-by-step explanation:
Given: Distance from the flagpole = 14 ft
Angle of elevation θ = 74.4°
To find: Length of the flagpole
Answer:
tan(74.4°) = [tex]\frac{L}{14}[/tex]
L = 14 tan(74.4°) = 50.142 ft
So the length of the pole is 50.142 ft.
Matt is a lawyer who used to charge his clients $330 per hour. Matt recently reconsidered his rates and ultimately decided to charge $231 per hour. What was the percent of decrease in the billing rate?
Answer:
33%
Step-by-step explanation:
Take the original amount and subtract to new amount.
330 -231
99
Divide this by the original amount.
99/300
.33
Change to a percent.
33%
This is the percent decrease.
What is the percent of increase from 53.5 to 96.3?
Answer:
80%
Step-by-step explanation:
96.3 - 53.5 = 42.8
42.8 / 53.5 = 0.8
0.8 × 100 = 80%
The length of the top of a workbench is 6m greater than the width. The area is 91m^(2). Find the length and the width.
The length of the top of the workbench is 13m and the width is 7m.
To find the length and the width, we can use the formula for the area of a rectangle, which is A = L x W, where A is the area, L is the length, and W is the width. We can plug in the given values and solve for the unknowns.
Let's start by assigning variables to the length and the width. Let's call the width x and the length x + 6 (since the length is 6m greater than the width).
Now we can plug these values into the formula:
A = L x W
91 = (x + 6) x x
91 = x2 + 6x
Now we can rearrange the equation to solve for x:
x2 + 6x - 91 = 0
We can use the quadratic formula to solve for x:
x = (-6 ± √(62 - 4(1)(-91))) / (2(1))
x = (-6 ± √(36 + 364)) / 2
x = (-6 ± √400) / 2
x = (-6 ± 20) / 2
The two possible solutions are:
x = (-6 + 20) / 2 = 7
x = (-6 - 20) / 2 = -13
Since the width cannot be negative, the only valid solution is x = 7. This means that the width is 7m and the length is x + 6 = 7 + 6 = 13m.
So the length of the top of the workbench is 13m and the width is 7m.
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Exercise - 4.4 f mathematical induction, prove that, for n>=1 1^(3)+2^(3)+3^(3)+cdots +n^(3)=((n(n+1))/(2))^(2)
The equation is true for n = k+1, so the statement is true for all n>=1 by mathematical induction.
Proof by mathematical induction:
Base case: n = 1
1^(3) = ((1(1+1))/(2))^(2)
1 = ((2)/(2))^(2)
1 = 1^(2)
1 = 1
The base case is true.
Inductive step:
Assume that the statement is true for n = k, that is:
1^(3)+2^(3)+3^(3)+...+k^(3) = ((k(k+1))/(2))^(2)
Now we need to prove that the statement is also true for n = k+1:
1^(3)+2^(3)+3^(3)+...+k^(3)+(k+1)^(3) = (((k+1)((k+1)+1))/(2))^(2)
Substituting the assumption into the left-hand side of the equation:
((k(k+1))/(2))^(2) + (k+1)^(3) = (((k+1)((k+1)+1))/(2))^(2)
Expanding the right-hand side of the equation:
((k(k+1))/(2))^(2) + (k+1)^(3) = (((k+1)(k+2))/(2))^(2)
Simplifying the equation:
(k^(2)(k+1)^(2))/(2^(2)) + (k+1)^(3) = ((k+1)^(2)(k+2)^(2))/(2^(2))
Multiplying both sides of the equation by 2^(2):
(k^(2)(k+1)^(2)) + 2^(2)(k+1)^(3) = (k+1)^(2)(k+2)^(2)
Expanding the equation:
k^(2)(k+1)^(2) + 2^(2)(k+1)^(3) = (k+1)^(2)(k^(2)+4k+4)
Simplifying the equation:
k^(2)(k+1)^(2) + 2^(2)(k+1)^(3) = k^(2)(k+1)^(2) + 4k(k+1)^(2) + 4(k+1)^(2)
Subtracting k^(2)(k+1)^(2) from both sides of the equation:
2^(2)(k+1)^(3) = 4k(k+1)^(2) + 4(k+1)^(2)
Factoring out (k+1)^(2) from the right-hand side of the equation:
2^(2)(k+1)^(3) = (k+1)^(2)(4k+4)
Simplifying the equation:
2^(2)(k+1)^(3) = 4(k+1)^(2)(k+1)
Dividing both sides of the equation by (k+1)^(2):
2^(2)(k+1) = 4(k+1)
Simplifying the equation:
2^(2)(k+1) = 2^(2)(k+1)
The equation is true for n = k+1, so the statement is true for all n>=1 by mathematical induction.
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target sells 12 bottles of water for $2 and 24 bottles of water for $3. which is the better buy and by how much
example: how much per bottle
Answer:
1/ 24 bottle of water for $3 is a better buy
2/ $0.045
Step-by-step explanation:
12 bottles of water for $2
2 / 12 =$0.17
So, it costs $0.17 for each bottle of water.
24 bottles of water for $3
3 / 24 = $0.125
So, it costs $0.125 for each bottle of water.
0.17 - 0.125 = $0.045
So, 24 bottles of water for $3 is a better buy by $0.045
The first place sled team took 9 days, 15 hours, and 46 minutes to finish the Iditarod. The second place team took 9 days, 21 hours, and 39 minutes. How much faster was the first place team?
PLEASE PUT ANSWER AS HOURS AND MINUTES FASTER, Thank You!!!!
Answer: ur mom anyways jk
Step-by-step explanation:
6hrs and 7mins pls dont trust me on this answer and if u get it wrong im sorry
30% of the applications received for a position in a graduate school are rejected.
a)Determine the expected number of rejected applications among the next 10 applications.
b)What is the probability that among the next 15 applications, none will be rejected?
c)What is the probability that among the next ten applications, seven will be rejected?
d)What is the probability that among the next ten applications, between 1 and 8 applications (inclusively) will be rejected?
a. The expected number of applications rejected is 3
b. The probability that among the next 15 applications, none will be rejected is 0.042
c. The probability that among the next ten applications, seven will be rejected is 0.48
d. The probability that among the next ten applications, between 1 and 8 applications is 0.95
Binomial distribution formula:The binomial distribution formula is used to calculate the probability of getting a certain number of successes (x) in a fixed number of independent trials (n) with a known probability of success (p) for each trial. The formula is:
P(x) = (n choose x) × pˣ × (1 - p)⁽ⁿ⁻ˣ⁾Here we have
30% of the applications received for a position in a graduate school are rejected.
a) The number of rejected applications among the next 10 applications follows a binomial distribution with parameters n = 10 and p = 0.3.
The expected number of rejected applications is:
E(X) = np = 10 * 0.3 = 3
Hence, the expected number of applications rejected is 3
b) The probability of being rejected is 0.3
The probability that none of the next 15 applications will be rejected is:
P(X = 0) = (1 - p)ⁿ = (1 - 0.3)¹⁵= 0.042
Therefore, the probability that none of the next 15 applications will be rejected is 0.042 or approximately 4.2%.
c) The probability that 7 of the next ten applications will be rejected is:
By using the binomial distribution formula
P(X = 7) = (10, 7) × 0.3⁷ × 0.7³ =
= 6435 × 0.0002187 × 0.343 = 0.48
Therefore, the probability that 7 of the next 10 applications will be rejected is 0.48 or approximately 48%.
d) The probability that between 1 and 8 (inclusive) of the next ten applications will be rejected is:
P(1 ≤ X ≤ 8) = P(X ≤ 8) - P(X ≤ 0) = Σ P(X = i) for i = 1 to 8
We can use the complement rule and calculate the probability of having 0 or 9 rejected applications, and subtract that from 1:
=> P(1 ≤ X ≤ 8) = 1 - [P(X = 0) + P(X = 9) + P(X = 10)]
= 1 - [(1 - p)ⁿ + (n, 1) × p¹ × (1 - p)⁽ⁿ⁻¹⁾ + (n, 0) × p⁰ × (1 - p)ⁿ]
= 1 - [(0.7)¹⁰ + ((10,1) × 0.3 × 0.7⁹) + (10, 0) (0.3)¹⁰]
= 1 - [ 0.02824 + 0.01210 + 0.000006]
= 1 - [ 0.040346]
= 0.95
Hence, The probability that between 1 and 8 (inclusive) of the next ten applications will be rejected is 0.95 or approximately 95%
Therefore,
a. The expected number of applications rejected is 3
b. The probability that among the next 15 applications, none will be rejected is 0.042
c. The probability that among the next ten applications, seven will be rejected is 0.48
d. The probability that among the next ten applications, between 1 and 8 applications is 0.95
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Chad drove 168 miles in 3 hours. 21.
A. How many miles per hour did Chad drive?
B. 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?
C. Chad stopped and filled the car with 11 gallons of gas. He had driven 308 miles using the previous 11 gallons of gas. How many miles per gallon did Chad’s car get?
D. Chad’s car continues to get the same number of miles per gallon. How many gallons of gas will Chad’s car use to travel 672 miles?
NOTE: PLASES DO ALL THE STAPS
Answer:
A: 24, B: 12, C: 28, D: 24. Hope this helps
Step-by-step explanation:
Part A:
168/3 = 56
Therefore, Chad is driving the car in 56 mph.
672/56 = 12
Therefore, Chad drives 672 miles in 12 hours.
308/11 = 28
Therefore, Chad drives 28 miles per gallon of gas.
672/28 = 24
Therefore, Chad uses 24 gallons of gas to drive 672 miles.
Part B:
12 hours, you can use proportions, miles/hours.
[tex]\frac{56}{1}[/tex]= [tex]\frac{672}{x}[/tex]
x = 12
Part C:
divide the miles driven by Chad (308 miles ) by the number of gallons used (11 gallons).
308 miles / 11 gallons =28 miles per gallon
Chad's car gets 28 miles per gallon.
Part D:
[tex]\frac{28}{1} = \frac{672}{x} \\[/tex]
28x = 672
x = 672/28 = 24
24 gallons
Answer: A=56 B=12 C=28 and D=24
Step-by-step explanation:
A. Chad drove 168 miles in 3 hours
In 1 hour he drove 168÷3
= 56 Miles
B. We know,
Covering 56 miles takes 1 hour
So, It will take to cover 672 miles
= 672÷56
= 12 Hours
C. We know,
Chad drove 308 miles with 11 gallons of gas
So, miles per gallon chads car gave him 308÷11
= 28 Miles Per Gallon.
D. We know,
Chad car gives him 28 miles per gallon
So, To cover 672 miles
Chad needs = 672÷28
= 24 Gallons.
NOTE: Its simple math kiddo, do better in school
Diego’s family car holds 14 gallons of fuel. Each day the car uses 0.6 gallons of fuel. A warning light comes on when the remaining fuel is 1.5 gallons or less. Write and solve an inequality that represents this situation. Explain clearly what the solution to the inequality means in the context of this situation.
We fοund the inequality tο be 14 -0.6x ≤ 1.5 and sοlving this we fοund that the warning lights cοme οn after using fοr apprοximately 21 days.
What is meant by inequality?In mathematics, inequalities specify the cοnnectiοn between twο nοn-equal numbers. Equal dοes nοt imply inequality. Typically, we use the "nοt equal sign" tο indicate that twο values are nοt equal. Hοwever several inequalities are utilised tο cοmpare the numbers, whether it is less than οr higher than. An inequality symbοl has nοn-equal expressiοns οn bοth sides. It indicates that the expressiοn οn the left shοuld be bigger οr smaller than the expressiοn οn the right, οr vice versa. Literal inequalities are relatiοnships between twο algebraic expressiοns that are expressed using inequality symbοls.
Given,
The gallοns οf fuel that the car hοlds = 14 gallοns
Amοunt οf fuel used each day = 0.6 gallοns
When the remaining fuel is 1.5 gallοns οr less, warning lights cοme οn.
We can write an inequality fοr this situatiοn.
If x is the number οf days the car is used, then the warning lights cοme οn when,
14 - 0.6x ≤ 1.5
This is the inequality expressiοn.
Sοlving,
12.5 ≤ 0.6x
x ≥ 12.5/0.6
x ≥ 20.8
Therefοre we fοund the inequality tο be 14 -0.6x ≤ 1.5 and sοlving this we fοund that the warning lights cοme οn after using fοr apprοximately 21 days.
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PLEASE HELPPPP!!!!
What is the standard form of the equation of a quadratic function with roots of 4 and −1 that passes through (1, −9)?
y = 1.5x2 − 4.5x − 6
y = 1.5x2 − 4.5x + 6
y = −1.5x2 − 4.5x − 6
y = −1.5x2 − 4.5x + 6
The standard form of the equation of a quadratic function with roots of 4 and −1 that passes through (1, −9) is [tex]y = 1.5x^{2} - 4.5x - 6[/tex]
What is the quadratic function?
A quadratic function is a type of function that can be written in the form:
[tex]f(x) = ax^2 + bx + c[/tex]
where a, b, and c are constants, and x is the variable. This function is a second-degree polynomial function, which means that the highest power of the variable x is 2.
Quadratic functions can be graphed as a U-shaped curve called a parabola. The sign of the coefficient a determines whether the parabola opens up or down. If a > 0, the parabola opens up, and if a < 0, the parabola opens down. The vertex of the parabola is the minimum or maximum point of the function, depending on whether the parabola opens up or down.
Quadratic functions are used in many areas of mathematics, science, and engineering to model various phenomena such as projectile motion, population growth, and optimization problems.
To write the standard form of the equation of a quadratic function, we need to use the roots of the function and another point on the curve. The standard form of the quadratic function is:
y = a(x - r1)(x - r2)
where r1 and r2 are the roots of the quadratic function, and a is a constant.
Given that the roots of the quadratic function are 4 and -1, we can write:
y = a(x - 4)(x + 1)
To find the value of a, we can use the point (1, -9) that the function passes through:
-9 = a(1 - 4)(1 + 1)
-9 = -6a
a = 3/2
Substituting this value of a in the equation, we get:
[tex]y = 1.5(x - 4)(x + 1)[/tex]
Expanding this equation, we get:
[tex]y = 1.5x^{2} - 4.5x - 6[/tex]
Therefore, the standard form of the equation of the quadratic function with roots of 4 and −1 that passes through (1, −9) is [tex]y = 1.5x^{2} - 4.5x - 6[/tex]
So, the correct answer is: [tex]y = 1.5x^{2} - 4.5x - 6[/tex]
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To determine the number of squirrels in a conservation area, a researcher catches and marks squirrels. Then the researcher releases them. Later squirrels are caught and it is found that of them are tagged. About how many squirrels are in the conservation area?
Therefore , the solution of the given problem of unitary method comes out to be t there are 1000 squirrels in the conservation area.
Unitary method: what is it?To finish a job using the unitary method, divide the lengths of just this minute subset by two. In a nutshell, the unit method eliminates a desired item from both the characterized by a set and colour subsets. 40 pens, for instance, variable will cost Rupees ($1.01). It's conceivable that one nation will have complete control over the strategy used to achieve this. Almost all living things have a unique trait.
Here,
The Lincoln-Petersen index can be used to calculate an approximate squirrel population estimate for the protected area:
There were n1 squirrels in the first group.
Second sample's fox count is equal to n2.
Second sample's total number of labelled squirrels is m2.
The following provides the Lincoln-Petersen index:
=> n1 * n2 / m2
Assume that the first sample consisted of 100 squirrels that were captured and tagged by the researcher. 20 of the 200 squirrels the researcher caught for the second group had tags on them. the following algorithm is used.
=> n1 * n2 / m2 = 100 * 200 / 20 = 1000
Therefore, it is believed that there are 1000 squirrels in the conservation area. It is crucial to keep in mind that this is only an approximation and might not be correct.
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Find the exact value of the following, using the point on the unit circle and the terminal side of each angle. State the point you used to find each trigonometric function value.
Show all work for all there.
Cos 17π/6
sin 20π/3
tan 15π/4
The exact values of the trigonometric functions are
To find the exact value of the trigonometric functions, we will use the reference angle and the quadrant in which the terminal side of each angle is located.
For cos 17π/6, the reference angle is π/6 and the terminal side is in the fourth quadrant. The point on the unit circle in this quadrant with a reference angle of π/6 is (√3/2, -1/2). Therefore, the exact value of cos 17π/6 is √3/2.
For sin 20π/3, the reference angle is π/3 and the terminal side is in the first quadrant. The point on the unit circle in this quadrant with a reference angle of π/3 is (1/2, √3/2). Therefore, the exact value of sin 20π/3 is √3/2.
For tan 15π/4, the reference angle is π/4 and the terminal side is in the third quadrant. The point on the unit circle in this quadrant with a reference angle of π/4 is (-√2/2, -√2/2). Therefore, the exact value of tan 15π/4 is 1.
In summary, the exact values of the trigonometric functions are:
cos 17π/6 = √3/2
sin 20π/3 = √3/2
tan 15π/4 = 1
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A boat traveled 34 miles in two hours. At this rate , how many miles would the boat travel in 6 hours
A tabletop in the shape of a trapezoid has an area of 6,731 square centimeters. Its longer base measures 127 centimeters, and the shorter base is 85 centimeters. What is the height?
Answer:
[tex]\boxed{The \ height \ of \ the \ tabletop \ is \ 63.5 \ centimeters}[/tex]
Step-by-step explanation:
We are given that,
Length of the base = 127 centimeters
Width of the base = 85 centimeters
Area of the trapezoid shaped base = 6,731 square centimeters.
Since, we know,
[tex]\bold{Area \ of \ a\ trapezoid}=\frac{Length +Width}{2}\times Height[/tex]
So, we get,
[tex]6731=\frac{127+85}{2}\times Height[/tex]
i.e. [tex]6731=\frac{212}{2}\times Height[/tex]
i.e. [tex]6731=106\times Height[/tex]
i.e. [tex]Height=\frac{6731}{106}[/tex]
i.e. Height = 63.5 centimeters
Hence, the height of the tabletop is 63.5 centimeters.
Graph the system of equations below on the coordinate grid provided.
y= 4x - 2
y= 1/2x + 5
SHOW ALL OF YOUR WORK and write the answer as an ordered pair.
A solution to the given system of linear equations is (2, 6).
How to graph the solution to this system of equations?In order to to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;
y = 4x - 2 ......equation 1.
y = 1/2(x) + 5 ......equation 2.
Next, we would use an online graphing calculator to plot the given system of equations as shown in the graph attached below.
Based on the graph (see attachment), we can logically deduce that the solution to the given system of equations is the point of intersection of the lines on the graph representing each of them, which lies in Quadrant I and it is given by the ordered pair (2, 6).
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Answer the following questions for the function f(x)=x√(x²+16) defined on the interval [-7,5].
A. f(a) is concave down on the interval ___ to _____
B. f(x) is concave up on the interval ____ to ____
C. The inflection point for this function is at x = _____
D. The minimum for this function occurs at = _____
E. The maximum for this function occurs at x = _____
f(a) is concave down on the interval -∞ to -4 and on the interval 0 to ∞, f(x) is concave up on the interval -4 to 0, inflection point for this function is at x = -2 and x = 2, the minimum for this function occurs at x = -4, the maximum for this function occurs at x = 0.
What is expressions ?In mathematics, an expression is a combination of numbers, symbols, and operators (such as +, -, *, /, ^) that represents a value or a quantity. Expressions can contain variables, which are symbols that can take on different values. An expression can also be a combination of other expressions. Expressions are used to represent mathematical relationships, make calculations, and solve problems.
According to given conditions :To answer these questions, we need to find the first and second derivatives of the function:
f(x) = x√(x²+16)
f'(x) = √(x²+16) + x(x²+16)[tex]^{(-1/2)}[/tex](2x)
f''(x) = (2x)/(x²+16)[tex]^{(3/2)}[/tex]+ (x²+16)[tex]^{(-1/2)}[/tex] + 2(x²+16)[tex]^{(-1/2)}[/tex]
A. f(a) is concave down on the interval -∞ to -4 and on the interval 0 to ∞.
To determine where the function is concave down, we need to find where the second derivative is negative. The second derivative is negative on the intervals (-∞, -4) and (0, ∞), so the function is concave down on those intervals.
B. f(x) is concave up on the interval -4 to 0.
To determine where the function is concave up, we need to find where the second derivative is positive. The second derivative is positive on the interval (-4, 0), so the function is concave up on that interval.
C. The inflection point for this function is at x = -2 and x = 2.
The inflection points occur where the concavity of the function changes. We found that the function is concave down on (-∞, -4) and (0, ∞), and concave up on (-4, 0). Therefore, the inflection points occur at x = -2 and x = 2.
D. The minimum for this function occurs at x = -4.
To find the minimum, we can either use the first derivative test or the second derivative test. Using the first derivative test, we look for where the first derivative changes sign from negative to positive, which indicates a local minimum. Using the second derivative test, we look for where the second derivative is positive, which indicates a local minimum. Either way, we find that the minimum occurs at x = -4.
E. The maximum for this function occurs at x = 0.
To find the maximum, we can either use the first derivative test or the second derivative test. Using the first derivative test, we look for where the first derivative changes sign from positive to negative, which indicates a local maximum. Using the second derivative test, we look for where the second derivative is negative, which indicates a local maximum. Either way, we find that the maximum occurs at x = 0.
Therefore, f(a) is concave down on the interval -∞ to -4 and on the interval 0 to ∞, f(x) is concave up on the interval -4 to 0, inflection point for this function is at x = -2 and x = 2, the minimum for this function occurs at x = -4, the maximum for this function occurs at x = 0.
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A factory produces Product A every 6 hours and Product B every 21 hours. A worker started the production machines for both products at the same time. How many hours later will both products finish at the same time? A. 14 B. 15 C. 27 D. 42 E. 126
Both products finish at the same time, which is D) 42 hours later.
Solving use LCMThe factory produces Product A every 6 hours and Product B every 21 hours.
If they started at the same time, they will finish at the same time after the lowest common multiple of the two intervals, which is 42 hours.
Therefore, the answer is D. 42 hours.
LCM is the short form for “Least Common Multiple.” The least common multiple is defined as the smallest multiple that two or more numbers have in common.
For example: Take two integers, 2 and 3.
Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20….
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 ….
6, 12, and 18 are common multiples of 2 and 3. The number 6 is the smallest. Therefore, 6 is the least common multiple of 2 and 3.
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In the figure, line m is parallel to line n. The measure of <3 is 58 degrees. What is the measure of <7?
In the parallel line measure of angle [tex]m\angle 7[/tex] is 32°.
What is parallel lines?In a plane, two lines are said to be parallel if they never cross at any point. A pair of lines that never cross paths and do not have a common junction point are said to be parallel. Parallel lines are represented by the symbol "||".
Here we know that If two lines which are parallel are intersected by a transversal then the pair of corresponding angles are equal.
Then,
=> [tex]m\angle3= m\angle10[/tex]
Here the given [tex]m\angle3=58\textdegree[/tex] the [tex]m\angle10=58\textdegree[/tex].
Now we know that sum of all angles in straight line is 180°.Then,
=> [tex]m\angle6+m\angle7+m\angle10=180\textdegree[/tex]
=> [tex]90\textdegree+m\angle7+58\textdegree=180\textdegree[/tex]
=> [tex]m\angle7=180\textdegree-90\textdegree-58\textdegree=32\textdegree[/tex]
Hence the measure of [tex]m\angle 7[/tex] is 32°.
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Look at this diagram:
a) What fraction is shaded?
b) What percentage is shaded?
Diagram ⬇️
Answer:
fraction 3/9
percentage is 90%
Evaluate. Write your answer as a fraction or whole number without exponents. 9^-1
Answer:
1/9
Step-by-step explanation:
I plugged it into a calculator.
what is the answer of this -x+3y=20 7y=x
The answer of -x+3y=20; 7y=x will be x = -[tex]\frac{7}{2\\}[/tex] and y = - [tex]\frac{1}{2}[/tex].
Given,
-x+3y=20 .... (1)
7y=x .... (2)
By using the method of substitution.
We will use equation (2) as
7y=x
=>y= [tex]\frac{x}{7}[/tex] ....(3)
Putting equation (3) in (1)
We have, -x+3([tex]\frac{x}{7}[/tex])=20
Taking L.CM.
[tex]\frac{-7x+3x}{7}[/tex] = 20
-7x +3x = 140
-4x = 140
0r, x = - [tex]\frac{140}{4}[/tex]
x = - [tex]\frac{7}{2}[/tex]
Now by putting value of x in equation (2), we get
7y = x
7y = -[tex]\frac{7}{2}[/tex]
0r, y = -[tex]\frac{1}{2}[/tex]
Thus, x = -[tex]\frac{7}{2\\}[/tex] and y = - [tex]\frac{1}{2}[/tex]
The ranking of four machines in your plant after they have been designed as excellent, good, satisfactory, and poor. This is an example of
a. Nominal data
b. Ordinal data
c. Interval data
d. Quantitative data
The ranking of four machines in your plant after they have been designed as excellent, good, satisfactory, and poor is an example of Ordinal data.
Ordinal data is a type of data that is used to rank or order objects or individuals. It is a type of categorical data that can be ranked or ordered, but cannot be measured numerically. In this case, the machines are ranked based on their design quality, which is an example of ordinal data. Other examples of ordinal data include movie ratings, letter grades, and customer satisfaction ratings.
Therefore, the correct answer is option b. Ordinal data.
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