Given:
Triangle ABC with vertices A (-1, 4), B( -4, 1), and C(-1, 1) is reflected across the y-axis and then translated 4 units to the left to form triangle A’B’C’.
To find:
The coordinates of the vertices of triangle A’B’C’.
Solution:
If triangle ABC reflected across y-axis, then
[tex](x,y)\to (-x,y)[/tex]
[tex]A(-1,4)\to A_1(1,4)[/tex]
[tex]B(-4,1)\to B_1(4,1)[/tex]
[tex]C(-1,1)\to C_1(1,1)[/tex]
Coordinates of image after reflection across y-axis are [tex]A_1(1,4),B_1(4,1),C_1(1,1).[/tex]
Then triangle translated 4 units to the left to form triangle A’B’C’.
[tex](x,y)\to (x-4,y)[/tex]
[tex]A_1(1,4)\to A'(-3,4)[/tex]
[tex]B_1(4,1)\to B'(0,1)[/tex]
[tex]C_1(1,1)\to C'(-3,1)[/tex]
Therefore, the vertices of triangle A’B’C’ are A’ (-3, 4), B’ (0, 1), C’ (-3, 1).
Hence, the correct option is B.
How much candy will each person get if 5 people share 6 1/2 pounds of Swedish fish.
Answer:
1 3/10 pounds of candy. Or around 1 pound
Step-by-step explanation:
6 1/2= 6.5
6.5/5=1.3
1.3 as a fraction is 1 3/10
A regional automobile dealership sent out fliers to prospective customers indicating that they had already won one of three different prizes: an automobile valued at $, a $ gas card, or a $ shopping card. To claim his or her prize, a prospective customer needed to present the flier at the dealership's showroom. The fine print on the back of the flier listed the probabilities of winning. The chance of winning the car was 1 out of , the chance of winning the gas card was 1 out of and the chance of winning the shopping card was out of 31,866, the chance of winning the gas card was 1 out of 31,866, and the chance of winning the shopping card was 31,864 out of 31,866.
Required:
a. How many fliers do you think the automobile dealership sent out?
b. Using your answer to (a) and the probabilities listed on the flier, what is the expected value of the prize won by a prospective customer receiving a flier?
c. Using your answer to (a) and the probabilities listed on the flier, what is the standard deviation of the value of the prize won by a prospective customer receiving a flier?
Answer:
(a) 31101
(b) $5.65
(c) $113.38
Step-by-step explanation:
The complete question is:
A regional automobile dealership sent out fliers to prospective customers indicating that they had already won one of three different prizes: an automobile valued at $20,000, a $125 gas card, or a $5 shopping card. To claim his or her prize, a prospective print on the back of the flier listed the probabilities of winning. The chance of winning the car was 1 out of 31,101, the chance of winning the gas card was 1 out of 31,101, and the chance of winning the shopping card was 31, 099 out of 31,101.
Solution:
The information provided is as follows:
[tex]P(\text{Car})=\frac{1}{31101}\\\\P(\text{Gas Card})=\frac{1}{31101}\\\\P(\text{Shopping Card})=\frac{31099}{31101}[/tex]
(a)
The number of fliers the automobile dealership sent out is, n = 31,101.
This is because the probability of winning any of the three prize is out of 31,101.
(b)
Compute the expected value of the prize won by a prospective customer receiving a flier as follows:
[tex]E(X)=\sum x\times P(X=x)[/tex]
[tex]=[20000\times \frac{1}{31101}]+[125\times \frac{1}{31101}]+[5\times \frac{31099}{31101}]\\\\=0.6431+0.0040+4.9997\\\\=5.6468\\\\\approx 5.65[/tex]
Thus, the expected value of the prize won by a prospective customer receiving a flier is $5.65.
(c)
Compute the standard deviation of the prize won by a prospective customer receiving a flier as follows:
[tex]SD(X)=\sqrt{V(X)}=\sqrt{E(X^{2}-(E(X))^{2}}[/tex]
[tex]=\sqrt{[(20000)^{2}\times \frac{1}{31101}+(125)^{2}\times \frac{1}{31101}+(5)^{2}\times \frac{31099}{31101}]-(5.65)^{2}}\\\\=\sqrt{12854.9011}\\\\=113.37947\\\\\approx 113.38[/tex]
Thus, the standard deviation of the prize won by a prospective customer receiving a flier is $113.38.
Find the value of x:
To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result. There you go!
The graph of the function, f, is shown. What is the domain of f?
Answer:
D : [-2,0) U (0, infinity) ; -2<=x<0 U x>0
Solve the problem.
Two forces of 575 newtons and 271 newtons act at a point. The resultant force is 657 newtons. Find the angle between the forces.
The resultant force is
→F=321.9N at−165.4°
The equilibrant is
→Feq=321.9N at14.6°
Explanation:
This problem requires that we resolve the force vectors into x- and y-components.
Once this is done, we can add the components easily, as the one 2-dimensional problem will be two 1-dimensional problems.
Finally, we will convert the resultant force into standard form and find the equilibrant.
Resolve into components:
F1x=F1cos180°=215(−1)=−215N
F1y=F1sin180°=0N
F2x=F2cos(−140°)=126(−0.766)=−96.5N
F1y=F1sin(−140°)=126(−0.643)=−81.0N
Note the change of the angle used to give the direction of F2. Standard angles (rotation from the x-axis; counterclockwise is +) should be used to avoid sign errors in the results.
Now, we add the components:
Fx=F1x+F2x=−311.5N
Fy=F1y+F2y=−81.0N
Technically, this is the resultant force. However, it should be changed back into standard form. Here's how:
F=√(
Explain how you can determine that the following
system has one unique solution – without actually
solving the system.
2x+y = 4
2y = 6- 2x
A 7,000-seat theater is interested in determining whether there is a difference in attendance between shows on Tuesday evening and those on Wednesday evening. Two independent samples of 25 weeks are collected for Tuesday and Wednesday. The mean attendance on Tuesday evening is calculated as 5,500, while the mean attendance on Wednesday evening is calculated as 5,850. The known population standard deviation for attendance on Tuesday evening is 550 and the known population standard deviation for attendance on Wednesday evening is 445. Which of the following is the value of the appropriate test statistic?A. z = -2.4736B. z = 2.4736C. tdf=−2.4736D. td f=2.4736
Answer:
A. z = -2.4736
Step-by-step explanation:
n1 = 25
n2 = 25
x1 = 5500
x2 = 5850
Sd1= 550
Sd2 = 445
Null hypothesis
μ1 - μ2 = 0
Alternate
μ1 - μ2 != 0
Pooled variance = ((25-1)*550²)+((25-1)*445²)/25+25-2
= 7260000+4752600/48
= 250262.5
Pooled sd = √250262.5
= 500.26243
Test statistic
Z =
5500-5850+10/500.26243*√1/25+1/25
= -2.47357 approximately
-2.4736
equation of the horizontal line that passes through the point (-5,1)
Answer:
y = -1.
Step-by-step explanation:
The value of y is -1 as it passes through the y axis. The values of x on the line are infinite.
This line's equation is y = -1.
-2x(x+12)+3(x+12) please please
"ect the best answer for the question.
- A polygon that has all sides the same measure and all angles the same measure is called what?
Answer:
Regular Polygon
Step-by-step explanation:
A polygon is a plane (two-dimensional) shape with straight sides.
Examples include triangles, quadrilaterals, pentagons, hexagons, etc.
A polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length) is called a Regular Polygon.
Please help me this brought my grade down and I need to get it up by next week please please help im giving all my points away for it
Answer:
Step-by-step explanation:
The size of the left upper chamber of the heart is one measure of cardiovascular health. When the upper left chamber is enlarged, the risk of heart problems is increased. The paper "Left Atrial Size Increases with Body Mass Index in Children" (International Journal of Cardiology [2009]:1-7) described a study in which the left atrial size was measured for a large number of children age 5 to 15 years. Based on this data, the authors concluded that for healthy children, left atrial diameter was approximately normally distributed with a mean of 26.4 mm and a standard deviation of 4.2 mm.Approximately what proportion of healthy children has left atrial diameters less than 24 mm?Approximately what proportion of healthy children has left atrial diameters greater than 32 mm?Approximately what proportion of healthy children has left atrial diameters between 25 and 30 mm?For healthy children, what is the value for which only about 20% have a larger left atrial diameter?
Answer:
so you need the value for the 20% right ?
Step-by-step explanation:
Given that <2=<6.
Which theorem proves that line d is parallel to line e.
A. Alternate interior angle theorem
B.Converse of the alternate exterior angle
theorem
C.Converse of the alternate interior angle
theorem
D.Alternate Exterior angle theorem
Answer: B . Converse of the alternate exterior angle theorem.
The converse of the alternate exterior angle proves that line d is parallel to line e which is the correct answer would be an option (C).
What are Alternate Interior Angles?Alternate Interior Angles are defined as the pair of angles created on the inner side of the parallel lines and on the opposite sides of the transversal when two parallel lines are intersected by a transversal are referred to as alternate internal angles.
According to the alternate exterior angles theorem, if two parallel lines are intersected by a transversal, the alternate exterior angles are congruent. In light of this, the converse of the alternate exterior angle theorem would state that if the two outside angles are congruent, the lines that the transversal cuts must be parallel.
The graph indicates that the outer angles are congruent (both equal x) shows that the lines are parallel.
Therefore, the converse of the alternate exterior angle proves that line d is parallel to line e.
Learn more about Alternate Interior Angles here:
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Help easy question......Branliest reward
Answer:
78
Step-by-step explanation:
Answer:
y=42.91
Step-by-step explanation:
cos 35=y/53
0.81=y/53
y=0.81*53
y=42.91
Hi-Tech, Inc., is a computer training company serving metropolitan Toronto, Canada. The firm contracts a group of part-time instructors to teach a variety of courses concurrently at its downtown location. While demand is so high that any class offered will be filled immediately, Hi-Tech is looking at only two courses at this time: Introduction to Computers (ITC) and Creation of Web Pages (CWP). Each ITC class requires 7.5 hours of preparation/instruction time and contributes a profit of $720, whereas each CWP class calls for only 3 hours and contributes $300. Available time for these two courses is limited to 56 hours a day. There is a restriction on the maximum number of trainees that can be efficiently handled. More specifically, at most 100 students can be accommodated on a daily basis without putting a strain on the facility and support staff. Additionally, each course has a class size limit - 6 for ITC and 12 for CWP. Hi-Tech would like to maximize the daily total profit from both courses so that it could offer certain other courses on a "goodwill" basis. Formulate an AILP for management to decide how many classes should be scheduled for each subject daily
What is the objective function?
Answer:
The AILP for management to decide how many classes should be scheduled for each subject daily is
The objective function is mathematically represented as
[tex]M = P_c * a + P_w * b[/tex]
=> [tex]M = 720 a + 300 b[/tex]
Now the first constraints to this functions is
[tex]t_c * x + t_w * y \le t_a[/tex]
=> [tex] 7.5 x + 3 y \le 56[/tex]
Another constraints to this function is
[tex]k x + u y \le N[/tex]
=> [tex]6 x + 2 y \le 100[/tex]
Here x and y are the number of classes
Step-by-step explanation:
From the question we are told that
The time required for each ITC class is [tex]t_c = 7.5 \ hours[/tex]
The profit of each ITC class is [tex]P_c = \$ 720[/tex]
The time require for CWP class is [tex]t_w = 3 \ hours[/tex]
The profit for CWP class is [tex]P_w = \$ 300[/tex]
The total time available is [tex]t_a = 56 \ hours / day[/tex]
the maximum number of trainee that can be accommodated in a daily basis is [tex]N = 100[/tex]
The class size limit for ITC is [tex]k =6[/tex]
The class size limit for CWP is [tex]u =12[/tex]
Generally the aim of Hi-Tech is to maximize profit
So the objective function will be a function that maximizes profit
Generally the objective function is mathematically represented as
[tex]M = P_c * a + P_w * b[/tex]
=> [tex]M = 720 a + 300 b[/tex]
Now the constraints to this functions are
[tex]t_c * x + t_w * y \le t_a[/tex]
=> [tex] 7.5 x + 3 y \le 56[/tex]
Another constraints to this function is
[tex]k x + u y \le N[/tex]
=> [tex]6 x + 2 y \le 100[/tex]
Here x and y are the number of classes
If -7 is added to a number, the result is 12. What
is the number?
A. -5
B. 5
C. 12
D. 19
Answer:
D. 19
Step-by-step explanation:
-7+19=12
Answer:
D. 19
Step-by-step explanation:
Help please will give brainlest!!!
Answer:
1.55 or 31/20 which is 1 11/20 gallons
Step-by-step explanation:
a store sells jump rope. Each jump rope cots the sa
You haven't finished the question.
You need to finish the question before it can be answered.
Consider the following figure where l1 and l2 are parallel and cut by transversals g1
and g2.
Part A: Determine the values of M, N, V and R.
Answer:
m: 88
n: 112
v: 88
r: 112
Step-by-step explanation:
four ponds of banana cost $2.60. what is the cost perpond?
Answer:
.65c
Step-by-step explanation:
2.60/4 equals .65
Answer:
.65
Step-by-step explanation:
2.06 divided by 4=.65
Hope this helped!
The angle represents the phase shift, determined by the initial conditions of the experiment or the position of the weight at t = 0. If the weight is at its maximum positive position (weight is above equilibrium) at t = 0, then = 0. If the weight is at its maximum negative position (spring is stretched and weight is below equilibrium) at t = 0, then . If the weight is traveling in the negative direction and passing through equilibrium at t = 0, then . In the response box, describe the initial condition of our experiment; specifically, describe the position of the weight and the direction in which it was traveling.
Answer:
the weight was approaching the equilibrium position from the positive direction. The weight was on its way down, with the spring stretching
Step-by-step explanation:
This is the word for word answer but be careful and don´t copy it exactly!! paraphrase the answer using your own words
3. Reason Can you write
3+ 4+ 7 = 14 as a multiplication
sentence? Explain.
Answer:
3 + 4 + 7 = 14
7 + 7 = 14
2(7) = 14
Step-by-step explanation:
I WILL PICK YOU BRAINLIEST PLS, help with this! no one has really answered any of my questions so if you could help me with this on that would be great
Answer:
A = 28 cm^2 (4+24)
B = 34 cm^2 (40-6)
C = 96 cm^2 (150-54)
D = 40 cm^2 (1/2(8*5) + 1/2(8+5))
Step-by-step explanation:
Answer:
Step-by-step explanation:
) Samantha has 6/7 of a apple pie. Drayden has 3/7 of a apple pie. How much pie do they have altogether? (Make sure to simply if possible) *
10 points
1 and 2/7
9/14
3/7
9/10
2) After her birthday party, Kelsey has 8/9 of pizza left over. Her best friend Savanna ate 1/9 of the leftover pizza. How much of Kelsey's pizza is left? *
10 points
10/9
7/9
None
1/3
3) Simplify the following fraction: 9/12 *
10 points
4/6
9/12 - You can't simplify
1/2
3/4
Answer: 1 2/7, 7/9,3/4
Step-by-step explanation: 9/7 you had to make a whole then make the fraction 2/7. 7/9 you literally just had to subtract 8-1 to gt 7 and because the denominator didn't need to change it so that makes it 7/9. And the last one 9/12 well 3 can go into 9 and 12 evenly. For 9 it goes in 3 times and for 12 it goes in 3 to any you get 3/4.
A DJ is preparing a playlist of 23 songs. How many different ways can the DJ arrange the first four songs on the playlist?
Answer:
Sample Response: The third DJ had (3r)/2 songs. Multiply r by 3 because the second DJ had 3 times as many as the first. Then divide that number by 2 because the third DJ has half as many.
DJ can arrange 88,55 times the first four songs on the playlist.
What is permutation and combination?Permutation and combination are ways to arrange values in a set. In permutation the order of arrangement matters, but in combination the order of arrangement does not matter,
Given that,
DJ prepares a playlist of 23 songs.
Since, DJ arranges the first four songs on the playlist,
The ways to arrange the song on the playlist,
= [tex]^{23}C_4[/tex]
= 23 ! / (4! x (23 - 4)! )
= 23 ! / (4! x 19!)
= (23 x 22 x 21 x 20 x 19!) / (4 x 3 x 2 x 1 x 19!)
= 23 x 11 x 7 x 5
= 8855
There are 8,855 ways to arrange first 4 songs.
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What are the solutions to the quadratic equation below?
3x2 +16x + 21 = 0
Answer:
-3 and -7/3
Step-by-step explanation:
You could solve by factoring.
To do that, you find 2 numbers that multiply to 21, but add up to 16 when you multiply one of them by 3.
In this case, 3 and 7 would work, because 3*3 + 7 = 16, and 3 * 7 = 21.
Therefore, we can factor the equation to (3x+7)(x+3).
The solutions of the equations are -3 and -7/3.
Find the product of 7 and 4.76.
Answer:
33.32
Explantion: 7x4.76
Find H, help me and get brainlist.
Answer:
it is 19
Step-by-step explanation:
-68 divided (-4)
Help ASAP
Answer:
Two negatives = positive (17)
Step-by-step explanation:
Answer:
Today: Wednesday, 14 October 2020
Hour: 12.58 WIB
______________________________
-68 divinded (-4) is 17
6y-2+x
I need Help Thursday 22 oct
Answer:
x+6y-2 is the simplfied answer
Step-by-step explanation: