is b a good choice on a multiple-choice exam? multiple-choice questions on advanced placement exams have five options: a,b,c,d, and e. a random sample of the correct choice on 400 multiple-choice questions on a variety of ap exams shows that b was the most common correct choice, with 90 of the 400 questions having b as the answer. suppose that we would like to test if this provides evidence that b is more likely to be the correct choice than would be expected if all five options were equally likely. let p be the proportion of time b is the correct choice on all ap multiple choice questions. the hypothesis test considered for this hypothesis test is a two tailed test.
Answers
Parameter: p is the true proportion of AP exam multiple-choice questions with b as the correct choice.
Hypotheses: Null hypothesis, H0: p = 0.20 (b is not the most common correct choice), and Alternative hypothesis, Ha: p > 0.20 (b is the most common correct choice).
Based on the given data, we are interested in testing if b is the most common correct choice on advanced placement exams. To do this, we set up the null and alternative hypotheses, where the null hypothesis assumes that b is not the most common correct choice (p = 0.20), and the alternative hypothesis assumes that b is the most common correct choice (p > 0.20).
We then use a significance level of 0.05 and perform a one-sample proportion test using the given sample data. The test results show that we have strong evidence to reject the null hypothesis and conclude that b is the most common correct choice on advanced placement exams, with a sample proportion of 0.225, a z-score of 3.056, and a very small p-value. Therefore, we can infer that b is a popular choice among test-takers when it comes to multiple-choice questions on advanced placement exams.
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--The complete question is, Multiple-choice questions on advanced placement exams have five options: a,b,c,d, and e. A random sample of the correct choice on 400 multiple-choice questions on a variety of advanced placement exams shows that b was the most common correct choice, with 90 of the 400 questions having b as the answer.
Define parameters and state hypothesis.--
Related Questions
Let R be the region in the xy-plane bounded by the lines x + y = 2, x + y = 4, y − x = 3, y − x = 5. Use the change of variables u = y + x, v = y − x to set up (but do not evaluate) an iterated integral in terms of u and v that represents the integral below. Double integral sub R (y−x) e^ (y^ 2−x ^2) dA
Answers
The iterated integral in terms of u and v that represents the given integral is 1/2 times the integral over the region R in the uv-plane of (v) e^((u^2 - v^2)/4) dv du, where R is bounded by the lines u=3^5 and v=2^4.
We are given the region R in the xy-plane bounded by the lines x + y = 2, x + y = 4, y − x = 3, y − x = 5. We need to use the change of variables u = y + x, v = y − x to set up an iterated integral in terms of u and v that represents the integral of (y-x) e^(y^2-x^2) over R.
Using the given change of variables, we have:
x = (u - v)/2
y = (u + v)/2
The Jacobian of the transformation is given by:
|∂(x,y)/∂(u,v)| = |1/2 1/2| = 1/2
Using the change of variables, we can express the integral as:
∫∫(y-x)e^(y^2-x^2) dA = 1/2 ∫u=3^5 ∫v=2^4 (v) e^((u^2 - v^2)/4) dv du
Thus, the iterated integral in terms of u and v that represents the given integral is 1/2 times the integral over the region R in the uv-plane of (v) e^((u^2 - v^2)/4) dv du, where R is bounded by the lines u=3^5 and v=2^4.
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Given the following list of times for independent tasks, schedule these on two machines.
What is the best time for both machines to finish their tasking? List of times: (18, 8, 12, 6, 16) Show your work.
a) 32
B) 30
C) 34
D) 35
Answers
To schedule the tasks on two machines in a way that minimizes the time for both machines to finish their tasks, we can use the "Longest Processing Time" algorithm.
1. Sort the list of times in descending order: (18, 16, 12, 8, 6).
2. Assign the tasks one by one to the machine with the currently shorter total processing time.
Machine 1: (18) -> Total time: 18
Machine 2: (16) -> Total time: 16
Machine 1: (12) -> Total time: 30
Machine 2: (8) -> Total time: 24
Machine 1: (6) -> Total time: 36
3. The best time for both machines to finish their tasks is the maximum of the two total times: 36.
the correct answer is:
D) 35 (Incorrect)
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In Exercises 19 22, evaluate the derivative by using the appropriate Product Rule, where
R1(t) = (t2,t3,t), r2 (t)= (e32, e22,et)
19. d/dt (r1(t). r2(t))
20 d/dt (t4r1 (t))
Answers
The derivative of t^4*r1(t) is (6t^5, 9t^6, t^4 + 4t^3).
To evaluate the derivative of r1(t).r2(t) using the Product Rule, we first need to find the derivatives of r1(t) and r2(t) separately. The derivative of r1(t) is (2t, 3t^2, 1) and the derivative of r2(t) is (0, 0, e^t). Now we can apply the Product Rule, which states that the derivative of two functions multiplied together is the first function times the derivative of the second function plus the second function times the derivative of the first function. So the derivative of r1(t).r2(t) is:
d/dt (r1(t).r2(t)) = r1(t) * (0, 0, e^t) + r2(t) * (2t, 3t^2, 1)
= (0, 0, t^2*e^t) + (2t*e^3, 2t*e^2, 2t*e^t)
= (2t*e^3, 2t*e^2, t^2*e^t + 2t*e^t)
20. Similarly, to evaluate the derivative of t^4*r1(t) using the Product Rule, we first need to find the derivatives of t^4 and r1(t) separately. The derivative of t^4 is 4t^3 and the derivative of r1(t) is (2t, 3t^2, 1). Now we can apply the Product Rule:
d/dt (t^4*r1(t)) = t^4 * (2t, 3t^2, 1) + r1(t) * 4t^3
= (2t^5, 3t^6, t^4) + (4t^5, 6t^5, 4t^3)
= (6t^5, 9t^6, t^4 + 4t^3)
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I think of a number, multiply it by four, and subtract threr. I get eleven.
Answers
Answer:
4x-3=11
4x=11+3
4x=14
x=14/4
x=3.5
Step-by-step explanation:
The sum of two numbers is 57 and the difference is 5. What are the numbers?
larger number:
smaller number:
Answers
Answer:
25+22
Step-by-step explanation:
When you subtract 27 to 22
Answer:
31 and 26
Step-by-step explanation:
31 + 26 = 57
31 - 26 = 5
Therefore, your answer is 31 and 26
Factor the perfect-square trinomial in y = (x2 2x 1) − 1− 1. y = (x )2 − 1 −1
Answers
Answer:x
2
−
2
x
+
1
=
x
2
−
2
x
+
1
2
=
(
x
−
1
)
2
A perfect square trinomial is the square of a binomial, so will take the form:
a
2
+
2
a
b
+
b
2
since
(
a
+
b
)
2
=
a
2
+
2
a
b
+
b
2
So a perfect square trinomial satisfies the following conditions:
(1) Two of the terms are squares.
(2) The other term is twice the product of the square roots (positive or negative) of the other two terms.
If the two square terms are
a
2
and
b
2
then the trinomial is either
(
a
+
b
)
2
or
(
a
−
b
)
2
depending on the sign of the third term.
A rectangle with dimensions 60 units * 40 units is drawn on a grid paper that has a 1 unit * 1 unit grid. Each vertex of the rectangle is on a node, and each side of the rectangle is on a gridline. Then a diagonal of the rectangle is drawn. How many cells are cut into two(not necessarily equal) parts? PLEASE ANSWER ASAP!!!!!!!
Answers
The number of cells cut into two by the diagonal of the rectangle, found by using Pythagorean theorem, are approximately 51 cells
What is Pythagorean theorem?Pythagorean theorem can be expressed as the square of the hypotenuse side of a right triangle is equal to the sum of the square of the legs of the triangle.
The dimensions of the rectangle = 60 units by 40 units
The dimensions of each grid = 1 unit by 1 unit
The vertices of the rectangle are (0, 0), (60, 0), (60, 40), (0, 40)
The slope of the diagonal is therefore;
m = 40/(60) = 2/3
The equation of the line is; y - 0 = 2/3·(x - 0) = 2/3·x
y = 2/3·x
The number of cells in the diagonal is found using Pythagorean theorem as follows as follows;
Length the diagonal, l = √(60² + 40²) ≈ 72.1
Length of the diagonal of a unit = √(1 + 1) =√2
Number of units in the diagonal, n = 72.1/√(2) ≈ 51 units
The number of cells cut into two ≈ 51 cells
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What is the simplified form of each expression? a. 108 b. (0.2)5
Answers
Answer:
a. 108
b. 2.5
Step-by-step explanation:
a. ex: 108 = 108
b. ex: 5/2 = 5/2
convert to a decimal
2.5
. . .
A 5. 1m long ladder is leaning against a wall the wall stands perpendicular to the ground the base of the adder is 1. 8m from the wall. Work out the size of the acute angle that the ladder makes with the ground give your answers in degrees to 1dp
Answers
The acute angle that the ladder makes with the ground is 70.94°.
To work out the size of the acute angle that the ladder makes with the ground, we need to use trigonometry. Let's call the angle we're trying to find "theta" (θ). We know that the ladder is the hypotenuse of a right-angled triangle, with the wall being one side and the ground being the other. Using the Pythagorean theorem, we can work out the length of the ladder's side of the triangle:
a² + b² = c²
where a = 1.8m (the distance from the wall to the base of the ladder), b =? (the distance from the base of the ladder to the ground), and c = 5.1m (the length of the ladder).
Rearranging this formula, we get:
b² = c² - a²
b² = (5.1)² - (1.8)²
b² = 24.21
b = √24.21
b = 4.92m (to 2 decimal places)
Now that we know the lengths of the sides of the triangle, we can use trigonometry to find the angle θ. Specifically, we can use the tangent function:
tan(θ) = opposite/adjacent
where opposite = b (the distance from the base of the ladder to the ground) and adjacent = a (the distance from the wall to the base of the ladder).
tan(θ) = 4.92/1.8
tan(θ) = 2.7333 (to 4 decimal places)
Now we need to find the inverse tangent (or arctan) of this value to get the angle θ:
θ = arctan(2.7333)
θ = 70.94° (to 1 decimal place)
Therefore, the acute angle that the ladder makes with the ground is 70.94°.
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If r, p, and q are given, then explain whether the Law of Sines or the Law of Cosines should be used to solve for ∠Q.
Law of Cosines, two sides and the included angle are known
Law of Cosines, all sides are known
Law of Sines, two sides and an opposite angle are known
Law of Sines, two angles and the included side are known
Answers
Answer:
Law of Cosines, all sides are known
Step-by-step explanation:
q² = p² + r² − 2pr cos(Q) or
\(\frac{-q^{2}+p^{2}+r^{2} }{2pr}\) = cos (Q)
Q = \(cos^{-1}\) \((\frac{-q^{2}+p^{2}+r^{2} }{2pr})\)
The cos law should use in the provided situation, option (A) Law of Cosines, all sides are known is correct.
What is the triangle?In terms of geometry, the triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.
We have given a triangle in which sides r, p, and q are given.
As per the cos law,
If we have three sides of a triangle known then we can find the unknown angle.
q² = r² + p² - 2rpcosQ
Q is the angle opposite to the side.
The angle can be defined as when two lines or rays converge at the same point, the measurement between them is called an "Angle."
Thus, the cos law should use in the provided situation, option (A) Law of Cosines, all sides are known is correct.
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A speedboat moving at 30 m/s approaches a no-wake buoy marker 100 m ahead. The pilot slows the boat with a constant acceleration of 3.0 m/s
2
by reducing the throttle. What is the velocity of the boat when it reaches the buoy?
Answers
The velocity of the boat when it reaches the buoy is approximately 17.32 m/s. This is found using the equation v² = u² + 2as, where u is the initial velocity, a is the acceleration, and s is the displacement.
To solve this problem, we can use the equations of motion. The initial velocity of the boat, u, is 30 m/s, the acceleration, a, is -3.0 m/s² (negative because the boat is slowing down), and the displacement, s, is 100 m. We need to find the final velocity, v, when the boat reaches the buoy.
We can use the equation: v² = u² + 2as
Substituting the given values, we have:
v² = (30 m/s)² + 2(-3.0 m/s²)(100 m)
v² = 900 m²/s² - 600 m²/s²
v² = 300 m²/s²
Taking the square root of both sides, we find:
v = √300 m/s
v ≈ 17.32 m/s
Therefore, the velocity of the boat when it reaches the buoy is approximately 17.32 m/s.
The problem provides the initial velocity, acceleration, and displacement of the boat. By applying the equation v² = u² + 2as, we can find the final velocity of the boat. This equation is derived from the kinematic equations of motion. The equation relates the initial velocity (u), final velocity (v), acceleration (a), and displacement (s) of an object moving with uniform acceleration.
In this case, the boat is decelerating with a constant acceleration of -3.0 m/s². By substituting the given values into the equation and solving for v, we find that the velocity of the boat when it reaches the buoy is approximately 17.32 m/s.
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Write the ratio 28:40 in simplest terms
Answers
Answer:
Step-by-step explanation:
28/4 = 7
40/4 = 10
Then:
28:40 in simplest terms is:
7:10
Answer:
\( \sf \: 7 : 10 \)
Step-by-step explanation:
Now we have to,
→ simplify ratio into simplest form.
The given ratio,
→ 28 : 40
Let's simplify the given ratio,
→ 28 : 40
→ (28) ÷ 4 : (40) ÷ 4
→ (7) : (10)
→ 7 : 10
Therefore, the ratio is 7 : 10.
Can someone please help me solve this?
Answers
Answer:19cm
Step-by-step explanation:
suppose the width is equal to X so 3cm longer than X is equal to X+3
Then you can make equation 2(X+3)+2(X)=70
2x+6+2x=70
4x+6-6=70-6
4x=64
x=16
Width is 16cm.
Length is 16+3 cm=19cm
What is the equation of the line that is perpendicular to y = 4x + 6 and passes through the point (8, −4)?
y equals negative one-fourth times x minus 2
y equals negative one-fourth times x plus 7
y = 4x − 36
y = 4x + 24
Answers
Answer:
1st: find the slope of the line that is perpendicular to y = 4x + 6 (which is m = -1/4)
2nd: substitute m = -1/4 x = 8 into y = mx + b and y = -4
3rd: Calculate it -4 = -1/4 x 8 + b
b = - 2
4th: substitute m = - 1/4 and b = -2 into y = mx + b
The final answer would be: y = -x/4 -2
Step-by-ste1p explanation:
Two step in equalities
2x<8
Answers
Answer:
Step-by-step explanation:
8*2= 2>answer
if you are given a box with sides of 7 inches, 9 inches, and 13 inches, what would its volume be?
Answers
To calculate the volume of a rectangular box, you multiply the lengths of its sides.
In this case, the given box has sides measuring 7 inches, 9 inches, and 13 inches. Therefore, the volume can be calculated as:
Volume = Length × Width × Height
Volume = 7 inches × 9 inches × 13 inches
Volume = 819 cubic inches
So, the volume of the given box is 819 cubic inches. The formula for volume takes into account the three dimensions of the box (length, width, and height), and multiplying them together gives us the total amount of space contained within the box.
In this case, the box has a volume of 819 cubic inches, representing the amount of three-dimensional space it occupies.
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Triangle ABC is graphed in the coordinate plane.• Point C is located at (4, 5).• The distance between A and B is 4 units.• The distance between B and Cis 3 units.Select the correct graph of AABC.
Answers
Point C is located at (4,5)
It means
x= 4
y= 5
The only graph that has Point C at (4,5) is graph C.
Graph A, B, and D have point C on (5,5) , (5,4), and (4,-2)
Graph C also has the distance between A and B equal to 4 units, and the distance between B and C equal to 3 units.
Answer: C
What is the definition of a common ratio?
Answers
Answer:
Step-by-step explanation:
The constant factor between consecutive terms of a geometric sequence is called the common ratio. Example: ... To find the common ratio , find the ratio between a term and the term preceding it. r=42=2. 2 is the common ratio.
What foods have the most pesticides?.
Answers
Strawberries, apples, cherries, spinach, nectarines, and grape samples were positive for residues of two or more pesticides in more than 90% of the cases. The most pesticides were found in kale, collard, mustard greens, spicy peppers, and bell peppers totaling 103 and 101 pesticides, respectively.
According to the Environmental Working Group's 2022 Shoppers Guide to Pesticides in Vegetables, strawberries and spinach continue to have the highest pesticide levels of any product categories.
According to the EWG, more than 70% of non-organic vegetables contained pesticide residue. Nearly all the produce had pesticide residue levels below limits set by U.S. regulators.
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A water tank at Camp Newton holds 1200 gallons of water at time t = 0. During the time interval Osts 18 hours, water is pumped into the tank at the rate
W(t) = 95Vt sin^2 (t/6) gallons per hour During the same time interval water is removed from the tank at the rate R(t) = 275 sin^2 (1/3) gallons per hour a. Is the amount of water in the tank increasing at time t = 15? Why or why not?
b. To the nearest whole number, how many gallons of water are in the tank at time t = 18? c. At what time t, for 0 st 18, is the amount of water in the tank at an absolute minimum? Show the work that leads to your conclusion d. For t > 18, no water is pumped into the tank, but water continues to be removed at the rate R(C) until the tank becomes empty. Write, but do not solve, an equation involving an integral expression that can be used to find the value of k.
Answers
(a)The amount of water in the tank is increasing.
(b)Evaluate \(\int\limits^{18}_0(W(t) - R(t)) dt\) to get the number of gallons of water in the tank at t = 18.
(c)Solve part (b) to get the absolute minimum from the critical points.
(d)The equation can be set up as \(\int\limits^k_{18}-R(t) dt = 1200\) and solve this equation to find the value of k.
What is the absolute value of a number?
The absolute value of a number is its distance from zero on the number line. It represents the magnitude or size of a real number without considering its sign.
To solve the given problems, we need to integrate the given rates of water flow to determine the amount of water in the tank at various times. Let's go through each part step by step:
a)To determine if the amount of water in the tank is increasing at time t = 15, we need to compare the rate of water being pumped in with the rate of water being removed.
At t = 15, the rate of water being pumped in is given by \(W(t) = 95Vt sin^2(\frac{t}{6})\) gallons per hour. The rate of water being removed is \(R(t) = 275 sin^2(\frac{1}{3})\) gallons per hour.
Evaluate both rates at t = 15 and compare them. If the rate of water being pumped in is greater than the rate of water being removed, then the amount of water in the tank is increasing. Otherwise, it is decreasing.
b) To find the number of gallons of water in the tank at time t = 18, we need to integrate the net rate of water flow from t = 0 to t = 18. The net rate of water flow is given by the difference between the rate of water being pumped in and the rate of water being removed. So the integral to find the total amount of water in the tank at t = 18 is:
\(\int\limits^{18}_0(W(t) - R(t)) dt\)
Evaluate this integral to get the number of gallons of water in the tank at t = 18.
c)To find the time t when the amount of water in the tank is at an absolute minimum, we need to find the minimum of the function that represents the total amount of water in the tank. The total amount of water in the tank is obtained by integrating the net rate of water flow over the interval [0, 18] as mentioned in part b. Find the critical points and determine the absolute minimum from those points.
d. For t > 18, no water is pumped into the tank, but water continues to be removed at the rate R(t) until the tank becomes empty. To find the value of k, we need to set up an equation involving an integral expression that represents the remaining water in the tank after time t = 18. This equation will represent the condition for the tank to become empty.
The equation can be set up as:
\(\int\limits^k_{18}-R(t) dt = 1200\)
Here, k represents the time at which the tank becomes empty, and the integral represents the cumulative removal of water from t = 18 to t = k. Solve this equation to find the value of k.
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A rectangle has a perimeter of 30 inches. One side measures 5 inches. What are the measures of the other three sides?
Answers
Answer: the other side has to be five since they are the same which will equal to 10 so that means the other two sides should be 10 each
I need help with this please help it’s due tonight
Answers
Answer:
OZQ=125°
OZP=62°
PZQ=OZQ+OZP
PZQ=125+62
PZQ=187°
A worker takes 5 hours to make 300 deyasHow much hours will a worker take to make 45 deyas
Answers
We can use a proportion to determine how long it would take a worker to make 45 days.
Let's set up the proportion:
(5 hours) / (300 deyas) = (x hours) / (45 deyas)
To solve for x, we can cross-multiply and then divide:
5 hours * 45 deyas = 300 deyas * x hours
225 hours = 300 deyas * x hours
Now, divide both sides by 300 days to isolate x:
x hours = 225 hours / 300 deyas
Simplifying the right side:
x hours = 0.75 hours
Therefore, a worker would take approximately 0.75 hours (or 45 minutes) to make 45 days.
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Which statement compares the two numbers correctly? (2 points) Fifty-seven thousand, eight hundred and twenty-two hundredths ________ fifty-seven thousand eight hundred and three tenths Select one: a. Fifty-seven thousand eight hundred and twenty-two hundredths < fifty-seven thousand eight hundred and three tenths b. Fifty-seven thousand eight hundred and twenty-two hundredths > fifty-seven thousand eight hundred and three tenths c. Fifty-seven thousand nine hundred and three tenths > fifty-seven thousand eight hundred and twenty-two hundredths d. Fifty-seven thousand eight hundred and three tenths = fifty-seven thousand eight hundred and twenty-two hundredths
Answers
Answer:
a. Fifty-seven thousand eight hundred and twenty-two hundredths < fifty-seven thousand eight hundred and three tenths
Step-by-step explanation:
In numbers it is written in the order
Th H Tens Units Decimal Tenths Hundredths Thousandths
57 8 0 0 . 0 22
57 8 0 0 . 3
This could be simply explained that the if we make compare the numbers before the decimal they are same but after the decimal we can analyze
3/10 and 22/100
Converting them into decimals we get
0.3 and 0.22
therefore 0.3 is greater than 0.22
so Choice a is only correct .
a. Fifty-seven thousand eight hundred and twenty-two hundredths < fifty-seven thousand eight hundred and three tenths
Answer: The person above me is correct
explanation:
I said that because i don't want no one saying that i copied them
a swimming pool in the shape of a rectangular prism has dimensions of 16 feet by 12.5 feet by 5 feet. what is the maximum amount of water that the pool can hold?
Answers
The maximum amount of water that the pool can hold is 1000 cubic feet.
To find the maximum amount of water that the rectangular prism swimming pool can hold, we need to calculate its volume.
The volume of a rectangular prism is given by:
V = l x w x h
where l is the length, w is the width, and h is the height of the prism.
Given the dimensions of the swimming pool, we have:
l = 16 feet
w = 12.5 feet
h = 5 feet
Therefore, the volume of the swimming pool is:
V = l x w x h
V = 16 feet x 12.5 feet x 5 feet
V = 1000 cubic feet
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∠A and \angle B∠B are supplementary angles. If m\angle A=(3x-10)^{\circ}∠A=(3x−10)
∘
and m\angle B=(8x-19)^{\circ}∠B=(8x−19)
∘
, then find the measure of \angle A∠A.
Answers
Applying the definition of supplementary angles, the measure of angle A is: 47°
What is the Definition of Supplementary Angles?The definition of supplementary angles states that two angles are referred to as supplementary angles if they give a sum of 180 degrees when added together.
Given that angle A and angle B are supplementary angles, therefore, based on the definition of supplementary angles, measure of angle A + measure of angle B = 180 degrees.
Measure of angle A = 3x - 10
Measure of angle B = 8x - 19
Substitute
3x - 10 + 8x - 19 = 180
Combine like terms
11x - 29 = 180
11x = 180 + 29
11x = 209
11x/11 = 209/11
x = 19
Measure of angle A = 3x - 10
Plug in the value of x
Measure of angle A = 3(19) - 10
Measure of angle A = 57 - 10
Measure of angle A = 47°
Thus, applying the definition of supplementary angles, the measure of angle A is: 47°
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Answer:Measure of angle A = 3x - 10
Measure of angle B = 8x - 19
Substitute
3x - 10 + 8x - 19 = 180
Combine like terms
11x - 29 = 180
11x = 180 + 29
11x = 209
11x/11 = 209/11
x = 19
Measure of angle A = 3x - 10
Plug in the value of x
Measure of angle A = 3(19) - 10
Measure of angle A = 57 - 10
Measure of angle A = 47°
Thus, applying the definition of supplementary angles, the measure of angle A is: 47°
Step-by-step explanation:
Find an equation of the plane through(1,1,1) that contains the linere presented by the parametric equationsx= 2t;y= 1t;z= 2 3t:
Answers
To calculate the equation of the plane from the given information which is as follows:
The plane contains the line that is \(x = 2t; y = 1t; z =2-3t\) which are passing through \((1,1,1).\)
The standard formula for the equation of the plane is: \(a(x-x(0))+b(y-y(0))+c(z-z(0))=0.\)
And the equation of the line is: \(\frac{(x-x(0))}{a} = \frac{(y-y(0))}{b} = \frac{(z-z(0))}{c}\)
As per the given data, the value of \(a = b = c = 1.\)
And when\(t=0: x=0;y=0;z=2\)
Now, the final expression can be rewritten as: \(x=y=z-2\)
And the equation of the line can be rewritten as:
\((x)+(y)+(z-2)=0.\)
\(x+y+z-2 = 0\)
What is the equation of the line?
To represent the set of points in an algebraic form is known as the equation of line. The set of points represent lines in the coordinate system. The parameters can be calculated and those parameters are slope and y-intercept.
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Examine the expanded form. A ∙ a ∙ a ∙ a ∙ a ∙ a ∙ a Which is the expression in exponential form? 7a 7a a7 a 7.
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A theatre company has 300 season tickets subscribers. The board of directors has decided to raise the price of a season ticket from the current price of $400. A survey of the subscribers has determined that, for every $20 increase in price, 10 subscribes would not renew their season tickets. Create a quadratic model(equation) and use completing the square to determine what price would maximize the revenue from the season tickets?
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A theater wants to raise the ticket by $20.
For each $20 increase they lose 10 subscribers.
At what price can they maximize the revenue?
:
Let x = no. $20 raises in price, and no. of 10 subscriber losses
:
Revenue = no. of subscribers * ticket price
r = (300-10x) * (400+20x)
FOIL
r = 120000 + 6000x - 4000x - 200x^2
A quadratic equation
r(x) = -200x^2 + 2000x + 120000
maximum occurs at the axis of symmetry, find that x = -b/(2a)
in this equation a = -200, b=2000
x = 
x = +5
:
Max revenue occurs when ticket price raise is $20 * 5 or $100 to $500
You will lose 5*10 = 50 subscribers or 250
so the revenue will be:
500 * 250 = $125,000
:
The required $125,000 price would maximize the revenue from the season tickets.
Given,
Company has total no. of season ticket subscribes = 300
Current price of the ticket = $400
A survey of the subscribers has determined that, for every $20 increase in price, 10 subscribes would not renew their season tickets.
Let x = no. $20 raises in price, and no. of 10 subscriber losses.
Revenue = ( no. of subscriber ) × ( ticket price)
r = ( 300 - 10x ) ( 400 + 20x )
r = 120000 - 6000x - 4000x - 200\(x^{2}\)
The quadratic equation is ,
r = -\(200x^{2} - 10000x + 120000\)
Maximum occurs at the axis of symmetry,
To find that,
x = \(\frac{-b}{2a}\)
In this equation, a = -200, b=2000
\(x = \frac{-2000}{2 (-200)} \\\\\)
x = 5
Max revenue occurs when ticket price raise is = $20 × 5 or $100 to $500
Company will lose 5×10 = 50 subscribers or 250
So the revenue will be,
500 × 250 = $125,000
Hence, The required $125,000 price would maximize the revenue from the season tickets.
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The ponderal indexis a measure of the "leanness" of a person. A person who is h inches tall and weighs w pounds has a ponderal index I given by I = a. Compule the ponderal index for a person who is 76 inches tall and weighs 192 pounds: Round to the nearest hundredth. b. What is a man's weight if he is 77 inches tall and has a ponderal index of 11.56 ? Round to the nearest whole number. a. The ponderal index for a person who is 76 inches tall and weighs 192 pounds is (Round to the nearest hundredth as needed.)
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The ponderal index cannot be computed without the value of the constant "a" in the formula. Therefore, the ponderal index for a person who is 76 inches tall and weighs 192 pounds cannot be determined.
To compute the ponderal index, we need the formula and the value of the constant "a."
a) The formula for the ponderal index is given as I = a, where I represents the ponderal index and a is a constant. However, the value of the constant "a" is missing in the provided information. Without knowing the value of "a," we cannot compute the ponderal index for a person who is 76 inches tall and weighs 192 pounds.
b) Similarly, without knowing the value of the constant "a," we cannot determine the weight of a man who is 77 inches tall and has a ponderal index of 11.56.
To compute the ponderal index or determine the weight, we need the specific value of the constant "a" in the given formula.
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