Use vectors to find the interior angles of the triangle with the given vertices. (Enter your answers as a comma-separated list. Enter your answers in terms of degrees. Round your answers to two decimal places.)
(−2, 4), (−3, 8), (6, 8)
Please Help ASAP
Answers
Answer:
77.47°
75.96°
26.57°
Step-by-step explanation:
Given vertices of the triangle:
A = (−2, 4)B = (−3, 8)C = (6, 8)Find the vectors from A to B, B to C and A to C:
[tex]\begin{aligned}AB = B - A &=(x_B-x_A,y_B-y_A) \\&=(-3-(-2), 8-4)\\& = (-1, 4) \end{aligned}[/tex]
[tex]\begin{aligned}BC=C-B &=(x_C-x_B,y_C-y_B)\\ &=(6-(-3),8-8)\\&=(9,0)\end{aligned}[/tex]
[tex]\begin{aligned}AC = C - A &=(x_C-x_A,y_C-x_A)\\&= (6-(-2), 8-4) \\&= (8, 4)\end{aligned}[/tex]
Use Pythagoras Theorem to calculate the magnitudes of the vectors:
[tex]|AB| = \sqrt{(-1)^2+4^2}=\sqrt{17}[/tex]
[tex]|BC|=\sqrt{9^2+0^2}=9[/tex]
[tex]|AC| = \sqrt{8^2+4^2}=4\sqrt{5}[/tex]
[tex]\boxed{\begin{minipage}{6 cm}\underline{Dot Product of two vectors}\\\\$a \cdot b=|a||b| \cos \theta$\\\\where:\\ \phantom{ww}$\bullet$ $|a|$ is the magnitude of vector a. \\ \phantom{ww}$\bullet$ $|b|$ is the magnitude of vector b. \\ \phantom{ww}$\bullet$ $\theta$ is the angle between $a$ and $b$. \\ \end{minipage}}[/tex]
Rearrange the dot product formula to make θ the subject:
[tex]\implies \theta=\cos^{-1}\left(\dfrac{a \cdot b}{|a||b|}\right)[/tex]
Use the rearranged dot product formula to find the angles between two pairs of vectors.
[tex]\boxed{\begin{minipage}{4 cm}\underline{Dot Product}\\\\$\textbf{u} \cdot \textbf{v}=u_1v_1+u_2v_2$\\\\where:\\ \phantom{ww}$\bullet$ $\textbf{u}=\left\langle u_1,u_2 \right\rangle$ \\\phantom{ww}$\bullet$ $\textbf{v}= \left\langle v_1,v_2 \right\rangle$ \\ \end{minipage}}[/tex]
Angle A
[tex]\implies A=\cos^{-1}\left(\dfrac{AB \cdot AC}{|AB||AC|}\right)[/tex]
[tex]\implies A=\cos^{-1}\left(\dfrac{-1 \cdot 8+4 \cdot4}{\sqrt{17} \cdot 4 \sqrt{5}}\right)[/tex]
[tex]\implies A=\cos^{-1}\left(\dfrac{8}{4 \sqrt{85}}\right)[/tex]
[tex]\implies A=77.47^{\circ}\; \sf (2 \; d.p.)[/tex]
Angle C
[tex]\implies C=\cos^{-1}\left(\dfrac{BC \cdot AC}{|BC||AC|}\right)[/tex]
[tex]\implies C=\cos^{-1}\left(\dfrac{9 \cdot 8+0 \cdot4}{9 \cdot 4 \sqrt{5}}\right)[/tex]
[tex]\implies C=\cos^{-1}\left(\dfrac{72}{36 \sqrt{5}}\right)[/tex]
[tex]\implies C=26.57^{\circ}\; \sf (2 \; d.p.)[/tex]
Interior angles of a triangle sum to 180°.
[tex]\implies B=180^{\circ}-A-C[/tex]
[tex]\implies B=180^{\circ}-77.47^{\circ}-26.57^{\circ}[/tex]
[tex]\implies B=75.96^{\circ}[/tex]
Therefore, the interior angles of the triangle with the given vertices are:
77.47°75.96°26.57°
Related Questions
what is the target selling price?
Answers
The target selling price per pair of boots is; $754
How to find the target selling price?The computation of target selling price per pair of shoes is shown below:-
Return on investment = $1,400,000 × 30%
= $420,000
Total variable cost = Variable manufacturing costs + Variable selling and administrative costs
= $36,000 + $18,000
= $54,000
Variable cost per unit = Total variable cost ÷ Planned production and sales
= $54,000 ÷ 1,000
= $54
Total Fixed cost = Fixed manufacturing costs + Fixed selling and administrative costs
= $120,000 + $80,000
= $200,000
Target profit = Total Contribution - Fixed cost
Total Contribution = Return on investment + Total Fixed cost
= $420,000 + $280,000
= $700,000
Contribution per unit = Total Contribution ÷Planned production and sales
= $700,000 ÷ 1000
= $700
Selling price per unit = Contribution per unit + Variable cost per unit
= $700 + $54
= $754
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The Fibonacci sequence is 0, 1, 1, 2, 3, 5, 8, 13, . . . (where F0 0).
(a) Give the recursive definition for the sequence.
(b) Write out the first few terms of the sequence of partial sums: 0, 0 + 1, 0 + 1 + 1,. . .
(c) Give a closed formula for the sequence of partial sums in terms of Fn (for example, you might say F0 + F1 + · · · + Fn 3F 2 n−1 + n, although that is definitely not correct).
(Discrete Mathematics)
Answers
The Fibonacci sequence is the sequence in which the numbers are written such that each succeeding number is sum of two preceding numbers.
The Fibonacci sequence is defined recursively as follows:
F0 = 0
F1 = 1
For n > 1, Fn = Fn-1 + Fn-2
(b) The sequence of partial sums is:
S0 = 0
S1 = 0 + 1 = 1
S2 = 0 + 1 + 1 = 2
S3 = 0 + 1 + 1 + 2 = 4
S4 = 0 + 1 + 1 + 2 + 3 = 7
S5 = 0 + 1 + 1 + 2 + 3 + 5 = 12
(c) A closed formula for the sequence of partial sums in terms of Fn is not possible, since the sequence of partial sums depends on the values of all previous terms in the Fibonacci sequence. However, it is possible to express the nth term of the sequence of partial sums, Sn, in terms of the nth term of the Fibonacci sequence, Fn, using the following formula:
Sn = F0 + F1 + ... + Fn = (F0 + F1) + (F1 + F2) + ... + (Fn-1 + Fn) = F1 + F2 + ... + Fn + F0 + F1 + ... + Fn-1 = 2Sn-1 - Fn + F0
This formula can be derived by considering the previous term in the sequence of partial sums and adding the current term of the Fibonacci sequence to it.
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What do I do now cause I’m stuck in the middle of the equation and not sure what else I may need to do besides make the x alone but I’m not sure how.
2x + 8 = 10
Answers
Answer:
x = 1
Step-by-step explanation:
2x + 8 = 10 ( isolate the x- term by subtracting 8 from both sides )
2x = 2 ( isolate x by dividing both sides by 2 )
x = 1
2x = 10 - 8
2x = 2
x = 2/2
x = 1
Write a congruence statement for the triangles. Then identify all pairs of congruent corresponding paris.
∠Q≅ ?
∠R≅ ?
∠P≅ ?
PQ≅ ?
QR≅ ?
Answers
The ΔPQR and ΔCBA are congruent using ( SAS , AAA , ASA) properties
If the three angles and the three sides of a triangle are equal to the corresponding angles and the corresponding sides of another triangle, then both the triangles are said to be congruent.
The two triangles need to be of the same size and shape to be congruent. Both the triangles under consideration should superimpose on each other.
According to the question,
We have to identify all the pairs of congruent
In ΔPQR and ΔCBA,
If we look the figure
(1) ∠Q ≅ ∠B
(2) ∠R ≅ ∠A
(3) ∠P ≅ ∠C
(4) PQ ≅ CB
(5) QR ≅BA
Therefore , All three angles are equal and all three sides
hence , ΔPQR ≅ ΔCBA by using AAA or ASA or SAS properties
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If Aarón has 4 times as many dimes as quarters and they have a combined value of 520 cents, how many of each coin does he have?
Answers
Aaron has 32 dimes and 8 quarters
How to determine the number of each coin?From the question, we have the following parameters that can be used in our computation:
Worth of coins = 520 cents
Type of coins = Dimes and quarters
Four times as many dimes as quarters
Represent the dimes with d and the quarters with q
So, we have the following representation
d = 4q
When the dimes and quarters are converted to dollars, we have the following representations
Dimes = $0.10
Quarters = $0.25
So, we have the following representation
0.10d + 0.25q = 5.20
Recall that
d = 4q
So, we have
0.10 * 4q + 0.25q = 5.20
Evaluate the products
0.65q = 5.20
Divide both sides by 0.65
q = 8
Recall that
d = 4q
So, we have
d = 4 * 8
Evaluate
d = 32
Hence, the number of dimes is 32
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What is the population standard deviation?
{5,8,8,5}
Enter your answer as a decimal, rounded to the nearest tenth, like this: 4.2.
Answers
5, 8, 8, 5 has a population standard deviation of 3
Given,
The population is
{5, 8, 8, 5}
The population's mean is calculated as follows:
Sum of terms / Number of terms
Calculate the values and then replace them in the equation.
Sum equals 5 + 8 + 8 + 5 = 26
Number of terms = 4
The population's average is 26 / 4 = 6.5
The population's variance is equal to (5 - 6.5)² + (8 - 6.5) (8 - 6.5)² + (8 - 6.5) (8 - 6.5)² + (5 - 6.5)²
= (-1.5) (-1.5)² + (1.5) (1.5)² + 1.5² + (-1.5) (-1.5)²
= 2.25 + 2.25 + 2.25 + 2.25
= 9
The population's standard deviation is equal to
= 3
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which of the variables listed above would best be displayed graphically using a bar graph? mark all that apply. group of answer choices number of minutes of exposure to secondhand smoke per day currently diagnosed with asthma race years of education gender
Answers
The two possible variables design are; "COHORT STUDY" and "CROSS-SECTIONAL STUDY".
Cohort study design is an observational study in which people who receives a particular treatment or are under a particular condition, are been observed and studied. This type of research model also allows a researcher to compare people affected by a condition to people unaffected by the same conditions.
The investigator is likely to use the cohort design because it will help in studying the children that are always exposed to smoke, and to observe the affected and unaffected children.
The CROSS-SECTIONAL design is an observational study in which a specific population are studied at a particular time. This type of research allows the researcher to study the difference in that population at a time interval.
This study design is likely to be used by the investigator, because it will help the investigator to determine the amount of secondhand smoke each child inhale at a particular time. It will also help the investigator to know the outcome of each child after 5years
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12 Express this in scientific notation: (1.33) (13 × 10³)
1.729 × 10⁰
B) 1.729 x 108
C) 17.29 x 10⁹
D) 17.29 x 108
Answers
The given expression can be written in scientific notation as 1.729 x 10⁹.
What is scientific notation?Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form.
Given is to express the given expression in scientific notation.
The given expression is -
(1.33) (13 × 10⁸)
Solving further -
1.33 x 13 x 10⁸
17.29 x 10⁸
1.729 x 10⁹
Therefore, the given expression can be written in scientific notation as 1.729 x 10⁹.
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An SRS of size 26 is drawn from a population that has a normal distribution. The sample has a mean of 143.5 and a standard deviation of 4. Give the standard error of the mean:
Answers
An SRS of size 26 is drawn from a population that has a Normal distribution, the standard error of the mean is 0.7844..
The standard error of the mean, or simply standard error, indicates how much the population mean can differ from the sample mean. It indicates how much the sample mean would change if the survey were repeated with new samples from a single population. It is calculated by dividing the standard deviation by the square root of the sample size.
We have given that,
SRS size , n = 26
The distribution is normal distribution,
Mean, u = 143.5
Standard deviations, sd = 4
standard error of the mean = sd/√n
= 4√26 = 0.7844
Hence, the standard error of mean is 0.7844..
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The ratios of fruit to sugar to water in four different drinks are shown below. Put the drinks in ascending order based on the fraction of fruit that they contain. Drink Lemonade Smoothie Soda Squash fruit : sugar : water 1:0:3 1:0:0 1:3:1 3:0:1
Answers
The drinks are in ascending order based on the fraction of fruit they contain as follows:
Smoothie: 1:0:0 < Squash: 3:0:1 < Lemonade: 1:0:3 < Soda: 1:3:1.
The ratios of fruit to sugar to water in the four drinks are:
Lemonade: 1:0:3
Smoothie: 1:0:0
Soda: 1:3:1
Squash: 3:0:1
To put the drinks in ascending order based on the fraction of fruit they contain, we need to compare the fraction of fruit in each drink. Since the fraction of fruit is the ratio of fruit to the total amount of ingredients, we can calculate it by dividing the amount of fruit by the sum of the amounts of fruit, sugar, and water in each drink.
For lemonade, the fraction of fruit is 1/(1+0+3) = 1/4.
For the smoothie, the fraction of fruit is 1/(1+0+0) = 1.
For the soda, the fraction of fruit is 1/(1+3+1) = 1/5.
And for the squash, the fraction of fruit is 3/(3+0+1) = 3/4.
Based on these calculations, the drinks are listed in ascending order based on the percentage of fruit they contain.:
Smoothie: 1:0:0 < Squash: 3:0:1 < Lemonade: 1:0:3 < Soda: 1:3:1.
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A particle travels in a straight line from A to B in 20s. Its acceleration t seconds after leaving A is ms^(-2), where a=(3)/(160)t^(2)-(1)/(800)t^(3). It is given that the particle comes to rest at B.
(i) Show that the initial speed of the particle is zero.
(ii) Find the maximum speed of the particle.
(iii) Find the distance AB
Answers
Answer:
initial speed is final speed: 0maximum speed is about 5.273 m/sdistance A to B is 50 metersStep-by-step explanation:
You have a particle whose acceleration is a(t) = 3t²/160 -t³/800 and whose velocity at t=20 is 0. You want to show the initial speed is 0, find the maximum speed, and the distance traveled in 20 seconds.
(i) Initial speedThe speed is the sum of the initial speed and that due to acceleration. The speed due to acceleration is the integral of acceleration:
[tex]\displaystyle s(20)=s_0+\int_0^{20}{\dfrac{1}{800}(15t^2-t^3)\,dt}}=s_0+\left(\dfrac{t^3}{3200}(20-t)\right)_0^{20}=s_0=0[/tex]
The change in speed over 20 seconds is zero, so the final speed is the initial speed. The final speed is zero, so the initial speed is 0.
(ii) Maximum speedThe maximum speed is where the acceleration is zero.
a(t) = 0 = (t²/800)(15 -t)
The acceleration is zero at t=0 and at t=15.
From the above integral, the maximum speed is ...
s(15) = 15³(20 -15)/3200 = 5.2734375 m/s ≈ 5.27 m/s
(iii) DistanceThe distance traveled is the integral of the speed.
[tex]\displaystyle d=\dfrac{1}{3200}\int_0^{20}{(20t^3-t^4)}\,dt=\left.\dfrac{t^4(25-t)}{16000}\right|_0^{20}}=50[/tex]
The particle traveled 50 meters from A to B.
A city experiences rain, on average, twice in every ten days during the summer Rain is predicted on average for 70% of the days when rainfall actually occurs, and rain is predicted, on average, for 33% of the days when it does not rain. Assume that rain is predicted for tomorrow. What is the probability of rainfall actually occurring tomorrow? 0.1054 0.6535 0.3465 0.8946
Answers
The probability of rainfall actually occurring tomorrow is 0.3465. The correct answer is therefore 0.3465.
To solve this problem, you can use Bayes' Theorem. Bayes' Theorem is a way to calculate the probability of an event occurring based on prior knowledge of conditions that might be related to the event.
In this case, we are trying to find the probability of rainfall occurring tomorrow, given that it has been predicted. Let's call this probability P(R|P), where R is the event of rainfall occurring and P is the event of rain being predicted.
According to the problem statement, the probability of rain occurring on any given day during the summer is 2/10, or P(R) = 0.2.
The probability of rain not occurring is 1 - P(R) = 0.8.
The probability of rain being predicted, given that it does rain, is 0.7, or P(P|R). The probability of rain being predicted, given that it does not rain, is 0.33, or P(P|¬R).
Using Bayes' Theorem, we can calculate the probability of rain occurring tomorrow as follows:
P(R|P) = [P(P|R) * P(R)] / [P(P|R) * P(R) + P(P|¬R) * P(¬R)]
Substituting in the values from the problem statement, we get:
P(R|P) = [0.7 * 0.2] / [0.7 * 0.2 + 0.33 * 0.8]
Simplifying this expression gives us:
P(R|P) = 0.3465
So the probability of rainfall actually occurring tomorrow is 0.3465.
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Find the length of third side. if necessary, round to the nearest tenth. Need Answer ASAP
Answers
Answer:
17.9 units (nearest tenth)
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]
From inspection of the given right triangle:
a = 11c = 21Substitute the values of a and c into Pythagoras Theorem and solve for b:
[tex]\implies 11^2+b^2=21^2[/tex]
[tex]\implies 121+b^2=441[/tex]
[tex]\implies b^2=320[/tex]
[tex]\implies b=\sqrt{320}[/tex]
[tex]\implies b=17.88854...[/tex]
Therefore, the length of the third side is 17.9 units (nearest tenth).
In a transformation, the preimage is the original figure and the image is the figure in the new location.
False
True
Answers
True, Because in a transformation, the preimage is the original figure and the image is the figure in the new location.
What is Translation?A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
Given that;
The statement is,
''In a transformation, the preimage is the original figure and the image is the figure in the new location.''
Now,
Since, We know that;
The preimage is the original figure and the image is the figure in the new location.
Hence, In a transformation, the preimage is the original figure and the image is the figure in the new location.
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PLS HELP ME THANK YOUUUU
Answers
The percentage of sugar in the drink is 64%
PercentageA percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.
The data given are;
Carbohydrate = 25g per bottleSugar = 16g per bottleThe percentage of sugar in the carbohydrate can be calculated as;
Percentage = (16 / 25) * 100
Percentage = 0.64 * 100
Percentage = 64%
The percentage of sugar is 64%
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Consider a linear regression situation with a quantitative response variable Y, a quantitative explanatory variable X, and one categorical explanatory variable with 3 levels. Three indicator variables A1, A2 and A3 are defined, with Ak = 1 if the individual is from level k, and O otherwise (for k=1,2,3). To allow different slopes (for the relationship between X and Y) for each level of the categorical variable, which of the following terms need to be included in the model in addition to Bo + B1X + 8? O A1, A2, and A3. O Aj and A2, but not A3. O A X, A2X, and A3X. O AjX and A2 X, but not A3X.
Answers
Include all three indicator variables (A1, A2, and A3) in the model
To allow different slopes in the relationship between X and Y for each level of the categorical variable, the model should include terms A1X and A2X in A1 and A2 respectively. For example, the model can be expressed as:
Bo + B1X + B2A1X + B3A2X + B4A3
where B2 and B3 represent the slope of the relationship between X and Y for people at levels 1 and 2 of the categorical variable, respectively. represent. The value of X remains constant.
Include all three indicator variables (A1, A2, and A3) in the model. This allows to compare the effect of a given level of a categorical variable on the response variable while keeping the value of X constant. For example, if you include only A1 and A2 in your model, you cannot compare the effects of level 3 of the categorical variables on the response.
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The coordinates of (-6, 4) satisfy the equation y=+6 because (-6, 4) [
If (-6,4) satisfies the equations of two lines, (-6, 4) is
This means that if two lines
so the lines will
at (-6, 4), then (-6, 4) is the
This means that if you substitute -6 for x and 4 for y in the equations, both equations will be
at (-6, 4).
to the system of equations.
Answers
If the coordinates of (-6,4) satisfies the equations of the two lines, (-6,4) is the solution to the system of equations.
This means that if the two lines intersect at (-6,4), then (-6,4) is the solution to the system of equations.
This means that if you substitute -6 for x and 4 for y, both equations will be equal at (-6,4).
How to obtain the graphic solution for a system of equations?The graphic solution for a system of equations is obtained by the intersection point of all the lines that compose the system of linear equations, meaning that the ordered pair (x,y) of the intersection point will satisfy all the equations in the system.
Missing Information
This problem is incomplete, hence the answer was given in general terms.
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researchers wanted to check if carpeted rooms in hospitals contained more bacteria than uncarpeted rooms. to determine the amount of bacteria in a room, researchers pumped the air from the room over a petri dish for eight carpeted and eight uncarpeted rooms. colonies of bacteria were allowed to form in the 16 petri dishes. the results are presented in the table. (measured as bacteria per cubic foot) carpeted: 11.8, 10.8, 8.2, 10.1, 7.1, 14.6, 13.0, 14.0 uncarpeted: 12.1, 12.0, 8.3, 11.1, 3.8, 10.1, 7.2, 13.7 do carpeted rooms have more bacteria than uncarpeted rooms at a
Answers
No , the carpeted rooms does not have more bacteria than uncarpeted rooms .
Given ,
α=0.05
n1=8
n2 = 8
mean = ∑x / n
x1 = 11.8+10.8+7.1+14.6+8.2+10.1+13.0+14.0 / 8 = 11.2
and
x2 =12.1+12.0+3.8+10.1+8.3+11.1+7.2+13.7 /8 = 9.78
Variance ,
s1 =2.6
s2 = 3.2
HYPOTHESES
H0 : μ 1 =μ 2
H1 : μ 1 ≠μ 2
Either the alternative hypothesis or the null hypothesis applies to the claim. The equality must be present in the null hypothesis. The alternative hypothesis declares the opposite of the null hypothesis if the claim is the null hypothesis.
On calculating we get the test statistic t as,
t = 1.771
The null hypothesis is rejected if the test statistic's value falls within the rejection zone.
0.956<1.771,
therefore , fail to reject H .
Therefore, there is no support for the null hypothesis, so we accept the alternate hypothesis as true.
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Consider The Following Problem: Min - X1 + X2 S.T. X1 + X3 – 2xı = 0 (X1, X2) E X Where X Is The Convex Combination Of The Points (-1,0), (0,1) (1,0), (0,-1). a. find the optimal solution graphically b. Do the frizt john or KTT condition hold the optimal solution in part (a)? if not explain in the term of the theorem 4.3.2.and 4.3.7 in the textbook.
Answers
The objective function is -x1 + x2. Also, the multiplier associated with the x1 + x3 - 2x1 = 0 constraint is 0, satisfies the KKT condition.
To find the optimal solution graphically, first plot the points (-1,0), (0,1), (1,0), and (0,-1) on the coordinate plane. These points form a square. The objective function for this problem is to minimize -x1 + x2. So we need to find the point on the square that is as low as possible on the y-axis (because the y-axis represents x2).
The constraint in question is x1 + x3 - 2x1 = 0, which can be rewritten as x3 = 2x1. Since x1 and x3 are variables, this represents a line on the coordinate plane. You can draw this line by selecting two points on this line and connecting them with a line. For example, you can select points (-1, -2) and (1, 2). These points lie on the line x3 = 2x1 and the connecting lines are plotted in the coordinate plane.
We can find the best solution by finding the point on the square that is the lowest possible on the straight line of y-axis and x3 = 2x1. The point that satisfies both of these conditions is the point (0,-1). This is the best solution for your problem.
To answer the second part of the question we need to determine whether the Fritz-John condition or the KKT condition is the optimal solution. The Fritz-John condition is an optimality requirement involving an objective function and problem constraints. A KKT condition is a necessary and sufficient condition for optimality that includes an objective function, a constraint, and a multiplier associated with the constraint.
The Fritz-John condition is not considered optimal for this problem. This is because the optimal solution does not satisfy the condition x1 + x3 – 2x1 = 0. The point (0,-1) does not satisfy the condition because it is not on the line x3 = 2x1.
KKT conditions are considered to be the best solution. This is because the point (0,-1) is a legal point (it lies on the square representing the legal region) and the global minimum of the objective function is -x1 + x2. Also, the multiplier associated with the x1 + x3 - 2x1 = 0 constraint is 0, which satisfies the KKT condition.
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2x + 8 = 10
So I know we subtract 8 on both sides do the equation but would we be able to do 10 also or no? I’m confused on how we know which number to use to make the equation make more sense..?
Answers
Answer:
Subtract 8 from both sides.
Divide both sides by 2.
Step-by-step explanation:
Here is an explanation.
In order to isolate the variable x, or solve for x, you need to undo the operations that are being done to x. To undo an operation, you must do the opposite operation.
The opposite of addition is subtraction.
Since 8 is being added to 2x, and you want to undo the addition of 8, you subtract 8. The rule is that you must do the same operation to both sides of the equation, so to get rid of the + 8 on the left side, you must do - 8 on both sides, like this:
2x + 8 = 10
2x + 8 - 8 = 10 - 8
2x = 2
By subtracting 8 from both sides, we got rid of the addition of 8 on the left side.
2x = 2
Now we have 2x. We want x alone. What operation is there between the 2 and the x in 2x? 2x means 2 times x. 2x is a multiplication. The opposite of multiplication is division. To undo the multiplication of x by 2, you need to divide the left side by 2. A division cancels out a multiplication. Once again, the rule is that you must do the same operation to both sides, so you must divide both sides by 2.
2x = 2
2x/2 = 2/2
x = 1
I hop that helps. If you have questions, just ask.
a brokerage firm keeps track of the total money spent on tesla stocks by their clients each day of the week, t(t). the function t(t) can be expressed as t(t)
Answers
a brokerage firm keeps track of the total money spent on tesla stocks by their clients each day of the week is C(T) = $730 + $25T
R(T) = $35T
T = 193 transact
C = cost ; R = revenue ; T = number of transactions
Amount paid per transaction = $25
Cost keeping office open = $730
Amount collected on each transaction = $35
(a) Find a formula that gives C as a function of T.
C(T) = Cost of keeping office open + (cost per transaction × number of transactions)
C(T) = $730 + $25T
(b) Find a formula that gives R as a function of T.
R(T) = (Amount collected per transaction * number of transactions)
R(T) = $35T
(c) Find the number of daily transactions that are needed to make the revenue $1200 more than the cost.
R = C + 1200
Substitute the value of R and C into the equation:
35T = 730 + 25T + 1200
35T - 25T = 730 + 1200
10T = 1930
T = 1930 / 10
T = 193 transactions
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To create a chocolate blend chocolate in two concentrations 61% cocoa and 51% cocoa are combined together if 18 ounces of the 61% chocolate is used
Answers
Answer:
To create a chocolate blend using 61% cocoa and 51% cocoa, 18 ounces of the 61% chocolate and an appropriate amount of the 51% cocoa are combined together. The exact amount of 51% cocoa required will depend on the desired concentration of the final blend.
Step-by-step explanation:
The salaries, in thousands of dollars, of all individuals employed at an oceanic deanup company are depicted in the boxplot below 50 60 70 80 What is the interquartile range (IQR) of the salaries? (4 points) 10 Ob 20 40 od 60 120
Previous question
Answers
The interquartile range (IQR) of the salaries = 20
What is Interquartile range (IQR) ?In descriptive statistics, the interquartile range is a measure of statistical dispersion, or the spread of the data. The middle 50%, fourth spread, or H-spread are further names for the IQR. It is described as the discrepancy between the data's 75th and 25th percentiles.
According to the given information
We are given that
Q1=50 and Q3=70
Inter quartile range =IQR
= Q3 -Q1
= 70 - 50
= 20
The interquartile range (IQR) of the salaries = 20
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The quadratic equation y = - 1612 +40t +2 represents the height of a projectile, y ,in feet, at a particular time, 1, in seconds. For what interval or intervals of time will the projectile be above 18 feet?
Answers
The interval of time after solving the inequality -16[tex]t^{2}[/tex] + 40t + 2 > 18 is 0.5 < t < 2
What are inequalities?Inequalities are of two types, > and <. The > sign means that left hand side is greater than the right hand side, while the < sign means that the left hand side is less than than the right hand side.
How to solve an inequality?We can solve the inequality by assuming the inequality sign as the = sign, except that when we divide or multiply one side by (-1), the inequality sign will reverse (for eg it will change from > to <).
-16[tex]t^{2}[/tex] + 40t -16 > 0
Dividing the equation by 8,
-2[tex]t^{2}[/tex] + 5t - 2 > 0
Rearrange gives,
2[tex]t^{2}[/tex] - 5t + 2 < 0
Using middle term breaking,
(2t-1)(t-2) < 0
Hence, the interval is 0.5 < t < 2
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Kehlani launches a toy rocket from a platform. The height of the rocket in feet is given by h= -16t^2 + 72t + 144 where t represents the time in seconds after launch. How long is the rocket in the air?
Answers
Answer:
6 seconds--------------------------------
Rocket is in the air until it hits the ground.
Therefore we need to find the value of t when h = 0.
- 16t² + 72t + 144 = 02t² - 9t - 18 = 0 2t² - 12t + 3t - 18 = 02t(t - 6) + 3(t - 6) = 0(t - 6)(2t + 3) = 0t - 6 = 0 or 2t + 3 = 0t = 6 or t = - 3/2 (discarded as negative)The rocket is in the air for 6 seconds.
Answer:
6 seconds
Step-by-step explanation:
Given function:
[tex]h(t)=-16t^2+72t+144[/tex]
where:
h is the height of the rocket.t is the time (in seconds) after launch.To find how long the rocket is in the air, find the positive value of t when h(t)=0.
[tex]\implies -16t^2+72t+144=0[/tex]
[tex]\implies -8(2t^2-9t-18)=0[/tex]
[tex]\implies 2t^2-9t-18=0[/tex]
[tex]\implies 2t^2+3t-12t-18=0[/tex]
[tex]\implies t(2t+3)-6(2t+3)=0[/tex]
[tex]\implies (t-6)(2t+3)=0[/tex]
Apply the zero-product property:
[tex]t-6=0 \implies t=6[/tex]
[tex]2t+3=0 \implies t=-\dfrac{3}{2}[/tex]
Therefore, as t > 0, the rocket is in the air for 6 seconds.
a woman deposits 100 eur in her daughter's bank account on her first birthday. on every subsequent birthday, she deposits 10 eur more than she deposited the previous year, so on her second birthday, she deposits 110 eur, and on her third birthday she deposits 120 eur.
Answers
At the end of her daughter's 10th birthday, the woman has deposited a total of 310 eur. On her first birthday, a woman transfers 100 euros into her daughter's bank account. every birthday after that.
On the daughter's 1st birthday:
100 eur deposit
On the daughter's 2nd birthday:
100 eur (previous year) + 10 eur (increase) = 110 eur deposit
On the daughter's 3rd birthday:
110 eur (previous year) + 10 eur (increase) = 120 eur deposit
On the daughter's 4th birthday:
120 eur (previous year) + 10 eur (increase) = 130 eur deposit
On the daughter's 5th birthday:
130 eur (previous year) + 10 eur (increase) = 140 eur deposit
On the daughter's 6th birthday:
140 eur (previous year) + 10 eur (increase) = 150 eur deposit
On the daughter's 7th birthday:
150 eur (previous year) + 10 eur (increase) = 160 eur deposit
On the daughter's 8th birthday:
160 eur (previous year) + 10 eur (increase) = 170 eur deposit
On the daughter's 9th birthday:
170 eur (previous year) + 10 eur (increase) = 180 eur deposit
On the daughter's 10th birthday:
180 eur (previous year) + 10 eur (increase) = 190 eur deposit
Total deposited over 10 years:
100 eur (1st birthday) + 110 eur (2nd birthday) + 120 eur (3rd birthday) + 130 eur (4th birthday) + 140 eur (5th birthday) + 150 eur (6th birthday) + 160 eur (7th birthday) + 170 eur (8th birthday) + 180 eur (9th birthday) + 190 eur (10th birthday) = 1,100 eur
Total deposited over 10 years: 1,100 eur - 100 eur (1st birthday deposit) = 1,000 eur
Total deposited over 10 years: 1,000 eur / 10 years = 100 eur per year
Total deposited over 10 years: 100 eur x 10 years = 1,000 eur
Total deposited over 10 years: 1,000 eur + 100 eur (1st birthday deposit) = 1,100 eur
Total deposited over 10
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Question 3 (25 points) Calculating a binomial probability PROBLEM: See the preceding alternate example. Should the player be surprised if fewer than 2 of the rolls result in snake eyes? Calculate an appropriate probability to support your answer.
Answers
The probability that fewer than 2 rolls result in snake eyes is approximately equal to 0.492.
To calculate the probability that fewer than 2 rolls result in snake eyes, we need to calculate the probability that exactly 0 rolls and the probability that exactly 1 roll result in snake eyes, and then sum these probabilities.
The probability that exactly 0 rolls result in snake eyes is given by the binomial probability formula:
P(exactly 0 rolls) = (n choose k) * p^k * (1-p)^(n-k)
Where:
n = the number of rolls
k = the number of successful rolls (in this case, 0)
p = the probability of success on a single roll (in this case, 1/6, since there is a 1/6 probability of rolling snake eyes on a single roll)
Plugging in the values, we get:
P(exactly 0 rolls) = (5 choose 0) * (1/6)^0 * (5/6)^5 = 0.164
The probability that exactly 1 roll results in snake eyes can be calculated in a similar manner:
P(exactly 1 roll) = (5 choose 1) * (1/6)^1 * (5/6)^4 = 0.328
To get the probability that fewer than 2 rolls result in snake eyes, we sum these probabilities:
P(fewer than 2 rolls) = P(exactly 0 rolls) + P(exactly 1 roll) = 0.164 + 0.328 = 0.492
Therefore, it would not be surprising if fewer than 2 rolls result in snake eyes.
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Complete Question:
Question 2 (25 points) Calculating a binomial probability PROBLEM: When rolling two fair six-sided dice, getting a pair of ls is called "snake eyes." The probability of getting "snake eyes" on any roll is 1/36. Suppose that a game player rolls the two dice 80 times. Let X = the number of rolls that result in "snake cyes." Find P(X = 2). Interpret this value in context If two dice are rolled 80 times, then there is a 27.089% chance that we get a pair of snake eyes. Question 3 (25 points) Calculating a binomial probability PROBLEM: See the preceding alternate example. Should the player be surprised if fewer than 2 of the rolls result in snake eyes? Calculate an appropriate probability to support your answer.
Please help me with the attached question on linear function. Thank you.
Answers
The number of lattice points in the first quadrant of the graph is equal to five (5).
What is an ordered pair?In Mathematics, an ordered pair can be defined as a pair of two (2) elements or points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate or x-axis (abscissa) and the y-coordinate or y-axis (ordinate) on the coordinate plane of any graph.
What is a lattice point?In Mathematics, a lattice point can be defined as a point on a graph whose ordered pair (x and y coordinates) are both positive and whole numbers.
By critically observing the graph of the function 3x + 4y = 59, we can reasonably infer and logically deduce that the number of lattice points in the first quadrant (where the ordered pair are both positive) are five (5).
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In addition to planning the move, which other factors do you need to consider when preparing to move gondolas?
Answers
The factors that you need to consider when preparing to move gondolas are:
Height
width
length
color.
What is Unit of Measurement?A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity
In choosing gondola one need to look at some factor in decisions such as height.
Know that it is good to consider the construction material and also the center wall configuration for its building also.
The factors that you need to consider when preparing to move gondolas are:
Height
width
length
color.
Hence, Height, width, length and color are the other factors we need to consider while moving Gondola.
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a market research firm is studying the effects of price and type of packaging on sales of a particular product. twenty-seven stores with shoppers of similar characteristics will be used in the study. the nine combinations of three price levels and three packaging types are the treatments of interest. total sales of the product over a seven-week period will be recorded. which of the following describes the best design to use for the study?
Answers
The market research can increase the precision of the result of the study by using a randomized block design RBD.
The best design the market research company should use for the study is d. A randomized block design Use packaging as a block. Randomly assign the nine combinations of three price levels and three packaging types so that three stores use each combination
Reason:
The given parameters are;
The study = The effect of price and type of packaging
Number of stores in the study = 27 stores
Characteristics of the shoppers in the stores = Similar
Number of packaging type = 3 (three)
Number of price levels = 3 (three)
The number of pair combinations = ⁶₂C - (3, pairs of the same packaging +
3, pairs of the same prices) = 9
Required:
The best design to use for the study
Solution:
Given that the shoppers at each store are similar, in order to differentiate and show the effect of the price and package combination, it is possible to group the treatment into groups having a particular characteristics, while ensuring that the other available treatments are assigned to each member within a group at least once.
The above design of the study is known as a randomized block design,
Therefore the correct option is d. A randomized block design Use packaging as a block. Randomly assign the nine combinations of three price levels and three packaging types so that three stores use each combinations.
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