Answer:
x=2 , y= (-1/2)
Step-by-step explanation:
3x + 2y = 5
2x + 4y = 2
Consider Equation 1:- (3x+2y=5)
Multiply both sides by 2
2(3x + 2y) = 5*2
6x + 4y = 10
Subtract both equations-
6x + 4y =10
-2x + 4y =2
=> 4x =8
x = 2
Substitute the value of x in equation 1
3*2 + 2y = 5
6 + 2y = 5
2y = 5-6
2y = (-1)
y = (-1/2)
Hope is helps ;)
Can someone please help me with this
[tex]x^{\frac{8}{15} }[/tex] is the value of yz when x=y⁵=z³ and x is positive.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Since x=y⁵=z³
Solve for yz as follows:
we can take the fifth root of x to get y, and the cube root of x to get z:
We can solve for yz as follows:
[tex]y=x^{\frac{1}{5} }[/tex]
[tex]z=x^{\frac{1}{3} }[/tex]
Now yz=[tex]x^{\frac{1}{5} }.x^{\frac{1}{3} }[/tex]
=[tex]x^{\frac{8}{15} }[/tex]
Hence, option A is correct, if x=y⁵=z³ then yz is [tex]x^{\frac{8}{15} }[/tex]
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ1
a coin is flipped and die is rolled once. what is the probability of flipping a heads on the coin and rolling a 5 on the die? give your answer as a reduced fraction.
The probability of flipping a heads on the coin and rolling a 5 on the die is 1/12 if a coin is flipped and die is rolled once.
The sample space for the coin toss is {H,T}, so there are two possible outcomes. The favorable one is H.
The probability of flipping a heads on the coin is equal to 1/2.
Die has six faces, meaning six possible outcomes, but we’re only interested in one of those outcomes: that roll of a 5. That means that only 1 in 6 outcomes is desirable and we can write it as 1/6
The probability of rolling a 5 on the die is equal to 1/6.
Since a coin is flipped and die is rolled independently, the joint probability is a product of above probabilities.
Therefore, the probability of flipping a heads on the coin and rolling a 5 on the die equals
[tex]\frac{1}{2} \times \frac{1}{6}\\= \frac{1}{12}[/tex]
To know more about probability
https://brainly.com/question/7681391
#SPJ4
Remember what we know about vertical angles and solve for x.
Then tell me the measure of Angle R.
The value of x by using vertical angles is 4, and the measure of angle R is 34°
Vertical Angles.Vertical angles are angles that are formed and are opposite of each other when two lines intersect. Vertical angles are congruent angles, it implies that they exhibit the same angle measure. Vertical here refers to the fact that they have the same Vertex (corner point).
From the information given:
6x + 10 = 8x + 2
6x - 8x = 2 - 10
-2x = -8
x = -8/-2
x = 4
The measure of angle R = 6x + 10
= 6(4) + 10
= 24 + 10
= 34°
Therefore, we can conclude that the measure of angle R is 34°
Learn more about vertical angles here:
https://brainly.com/question/1673457
#SPJ1
A sample of 100 students was randomly selected from a middle school in a large city. These participants were asked to select their favorite type of pizza: pepperoni, cheese, veggie, or Hawaiian. Pizza preference and gender were recorded for each participant. The results of the survey are summarized in the table. Pepperoni Cheese Veggie Hawaiian Total
Male 37 18 2 7 64
Female 13 17 3 3 36
Total 50 35 5 10 100
Part A
What proportion of participants prefer cheese pizza? Enter your answer as a decimal value
Proportion of participants prefer cheese pizza is 0.35 from the sample of 100 students was randomly selected.
A sample of 100 students was randomly selected from a middle school in a large city. These participants were asked to select their favorite type of pizza: pepperoni, cheese, veggie or Hawaiian pizza
The number of males who prefers chess pizza is 18.
The number of females who prefers chess pizza is 17.
The total number of students who prefer chess pizza is 18 + 17 = 35.
The total number of students is 100.
The proportion of students who prefers chess pizza is 35/100 = 0.35
To know more about probability
https://brainly.com/question/3504000
#SPJ4
Please help!!!
Match the new coordinates that define the figure after dilation with a center at the origin by the given scale factor.
1. (3.0) dilated by scale factor of 1/3 a (0, 6)
2. (3,4) dilated by scale factor of 1/3 scale factor b (1,0)
3. (0,4) after dilation with a scale factor of 1/3 c (0, 4/3)
4. (3,0) after dilation with a scale factor of 3/2 d (1, 4/40
5. (3,4) after dilation with scale factor of 3/2 e (9/2, 0)
6. (0,4) after dilation with a scale factor of 3/2 f (9/2, 6)
The required (0,4) after dilation with a scale factor of 1/3 is (0, 4/3). Option C is correct.
What is the scale factor?The scale factor is defined as the ratio of the modified change in length to the original length.
here,
Since let the coordinate before dilation be (x, y),
Now when applying the scale factor to the coordinate, the transformation equation is given as,
(X, Y) = (sx , sy) where s is the scale factor,
Since matching the above equation with the option,
(3.0) dilated by a scale factor of 1/3 a (0, 6) (False)
(3,4) dilated by a scale factor of 1/3 scale factor b (1,0) (False)
(0,4) after dilation with a scale factor of 1/3 is (0, 4/3) (True)
Thus, the required (0,4) after dilation with a scale factor of 1/3 is (0, 4/3). Option C is correct.
Learn more about Scale factors here:
https://brainly.com/question/22312172
#SPJ1
in a sample of 20 men, the mean height was 178 cm. in a sample of 30 women, the mean height was 164 cm. what was the mean height for b oth groups put together?
In a sample of 20 men, the mean height was 178 cm and a sample of 30 women, the mean height was 164 cm, then the mean height for both groups combined is approximately 172.4 cm.
To find the mean height for both groups combined, we need to calculate the weighted average of the means of each group, where the weight of each group is proportional to its sample size.
We can begin by finding the total height of all the individuals in both groups combined. The total height for the men's group would be 20 multiplied by the mean height of 178 cm, which is 3560 cm.
Similarly, the total height for the women's group would be 30 multiplied by the mean height of 164 cm, which is 4920 cm. Adding these two values gives a total height of 8480 cm for both groups combined.
Next, we need to find the total sample size, which is the sum of the sample sizes of the two groups. The total sample size is 20 + 30 = 50.
Finally, we can calculate the weighted average of the means of each group using the formula:
Weighted average = (weight of group 1 * mean of group 1 + weight of group 2 * mean of group 2) / (weight of group 1 + weight of group 2)
In this case, the weights of each group are proportional to their sample sizes. Therefore, the weighted average can be calculated as:
Weighted average = (20/50 * 178 cm) + (30/50 * 164 cm) = 172.4 cm
In summary, to find the mean height for both groups combined, we need to calculate the weighted average of the means of each group, where the weight of each group is proportional to its sample size. This is done by multiplying the sample size of each group by its mean height, adding the values, and then dividing by the total sample size.
To learn more about mean click on,
https://brainly.com/question/3699952
#SPJ4
Order the values from least to greatest. |2.7|, 0, 1.3, |-1|, 2
0 |-1| , 1.3 , 2, |2.7|
Step-by-step explanation:
it's right because |-1| is an absolute value and the absolute value is 1
Answer:
0, |- 1| , 1.3, 2, |2.7|
Step-by-step explanation:
The absolute value of any number, x, denoted by |x| is the positive of that number
So | 2.7 | = 2.7
| - 1 | = 1
Therefore the order of the absolute values is
0, 1, 1.3, 2, 2.7 which is the same as 0, |- 1| , 1.3, 2, |2.7|
what is the perimeter of this rectangle
18 yd
19 yd
please help
Answer:
= 74cm²
Step-by-step explanation:
Perimeter of a rectangle
[tex] = 2(l) + 2(w)[/tex]
therefore
= 2(18) + 2(19)
= 36 + 38
= 74cm².
HELP PLEASE!!!
Solve for the y-intercept given a slope of -2 and a point of (3,-2)
After solving for the line with slope as -2 and point (3,-2) , the y intercept is (0,4) .
We use the Point Slope form of a linear equation to write the equation of a line given its slope and a point on the line.
So , the point slope form is ⇒ y - y₁ = m(x - x₁) ;
Where m = slope , and (x₁, y₁) = point on line .
So , by using the slope (m = -2) and point (x₁, y₁) = (3, -2),
Substituting these values and simplifying further ,
We get ; ⇒ y -(-2) = (-2)×(x - 3) ;
⇒ y + 2 = (-2)×(x) + (-2)×(-3) ;
Subtracting 2 from both sides,
we have ;
⇒ y = -2x + 4
The y intercept of line is value of "y" when x = 0.
So , we substitute x = 0 in the equation of line y = -2x + 4 ;
that means ⇒ y = -2(0) + 4 ;
⇒ y = 4 .
Therefore, the y intercept of the line with slope "-2" and passing through the point (3, -2) is (0, 4).
Learn more about Y-Intercept here
https://brainly.com/question/16609931
#SPJ4
If m∠HZJ = 38°, what is m∠HZG?
Answer:
142 degrees
Step-by-step explanation:
since line GJ is a straight line, its angle measure is 180 degrees. The measure of angle HZJ is 38. Angle HZJ and angle HZG are supplementary, which means their angle measures add up to 180 degrees. So,
180-38=142.
Hope this answer helps!! :D
Carson is a songwriter who collects royalties on his songs whenever they are played in
a commercial or a movie. Carson will earn $20 every time one of his songs is played
in a commercial and he will earn $120 every time one of his songs is played in a
movie. Carson's songs were played on 5 more commercials than movies, and his total
earnings on the royalties from all commercials and movies was $38o. Determine the
number of commercials and the number of movies on which Carson's songs were
played.
Carson's songs were played on commercials and
movies.
Answer:
20×5=100
380-100=280
280÷120=2 and 40 remain
40÷20=2
5+2=7commercials 2 moviesSegment AC is the angle bisector of
The figure is not to scale.
Which of the following additional statements would allow us to prove that
suppose that a particular nba player makes of his free throws. assume that late in a basketball game, this player is fouled and is awarded two free throws.
a. What is the probability that he will make both free throws? (to decimals) b. What is the probability that he will make at least one free throw? (to decimals) c. What is the probability that he will miss both free throws? (to decimals) d. Late in basketball game; team often intentionally fouls an opposing player in order to stop the game clock: The usual strategy is t0 intentionally foul the other team's worst free-throw shooter: Assume the team' worst free throw shooter makes 58% of his free throws Calculate the probabilities for this player as shown in parts (2), (b), and (c) and show that intentionally fouling this player who makes 58% of his free throws is better strategy than intentionally fouling the player who makes 89% of his free throws. Assume as in parts (a), (b), and (c) that two free throws will be awarded.
1. What is the probability that this player will make both throws? (to 4 decimals) 2. What is the probability that will make at least one tlrow? (to decimals) 3. What is the probability that thils player wIll mlss bolhi Urows? (to decimals)
Step-by-step explanation:
suppose you brought 45 shares of telecommunications company 4 years ago at a price of $63.00 per share. you just sold it for $71.50 per share. how much did you make
6
Find b.
5 m
4 m
M
b
10 m
The value of b is given as follows:
b = 12.5 m.
How to obtain the value of b?The value of b is obtained applying the proportions in the context of the problem.
The rule of three is given as follows:
5 m - b m.
4 m - 10 m.
Applying cross multiplication, the value of b is obtained as follows:
4b = 50
b = 50/4
b = 12.5 m.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
Anita puts $300.00 into an account to use for school expenses. The account earns 2%
interest, compounded continuously. How much will be in the account after 8 years?
Use the formula A = Pet, where A is the balance (final amount), P is the principal (starting
amount), e is the base of natural logarithms (2.71828), r is the interest rate expressed as a
decimal, and it is the time in years.
Round your answer to the nearest cent.
The amount in the account after 8 years will be $352.05.
What is Compound Interest?Compound interest is when you receive interest on both your interest income and your savings.
Given:
P = $300
R= 2%
T = 8 years
We have to use the function
A = P[tex]e^{rt[/tex]
A = 300.00[tex](2.71828)^{(0.02)(8)[/tex]
A = $352.05
Learn more about Compound Interest here:
https://brainly.com/question/28642748
#SPJ1
R, S, Q and P are the midpoints of OC, CB, BA and OA respectively.
OR = a, CS = b and OP = c
А
Show that RS is parallel to PQ
We know that RS is parallel to PQ by comparing RS and PQ and both vector have the same value and hence prove to be parallel.
We know that R, S, Q and P are midpoints of OC, CB, BA and OA, and we are given that OR = a, CS = b and OP = c
we have to prove that RS is parallel to PQ,
therefore we need to find, PQ = PA + AQ,
= c - c + a + b = a + b,
since we get that PA = OP = c
therefore when we compare RS and PQ ,we get,
RS = PQ = a + b
now that it is clear that both the vectors are same and have the same value we can conclude that they are parallel.
To learn more about quadrilaterals, click here:
brainly.com/question/13805601
#SPJ4
Please help me I’m stuck:)
Answer:
(a) (0,0)
Step-by-step explanation:
Solving with Elimination method-
Take the first equation- 3x - 2y = 6
Multiply both sides by 2
2(3x - 2y) = 2*6
6x - 4y = 12
Subtract Both the equations-
6x - 4y = 12
- 6x - 4y = 12
= 0 = 0
The answer is (0,0)
Hey circle has a diameter of 30 cm what is the circumference?
Use 3.14 for pie and do not round your answer be sure to include the correct unit in your answer 
Answer:
94.2cm
Step-by-step explanation:
Diameter 30cm
π = 3.14
Circumference of a circle is given by the formula:
C = 2πr
r = radius
Radius is equal to half of the diameter
30/2 = 15cm
Sub into equation:
C = 2(3.14)(15)
C = 94.2cm
a group of roommates equally shared the 6000$ in rent for an apartment. when four of the roomates moved out, those roomates remaining still shared the 6000$ rent equally, but each roomate's share of the rent increased by 250$. how many roomates were there orginally
The original number of roommates was 6, determined by comparing the original and new shares of rent per roommate and solving for the minimum number of roommates that satisfies the inequality.
Let's assume that there were 'x' original roommates in the apartment.
When the rent was shared equally among 'x' roommates, each roommate's share was:
[tex]6000/x[/tex]
After four roommates moved out, the remaining roommates continued to share the same rent of $6000 but each person's share increased by $250. So the new share per roommate is:
[tex](6000/x) + 250[/tex]
Since the number of roommates decreased by 4, the new number of roommates is:
[tex]x - 4[/tex]
We know that the new share per roommate is greater than the original share per roommate, so we can set up the following inequality:
[tex](6000/x) + 250 > 6000/x[/tex]
Simplifying the inequality, we get:
[tex]250 > 6000/x - 6000/x[/tex]
[tex]250 > 6000/x^2[/tex]
[tex]x^2 > 24[/tex]
[tex]x > 4.9[/tex]
Since the number of roommates must be a whole number, the minimum value for x is 6.
Therefore, there were originally 6 roommates in the apartment.
The solution involves setting up an inequality to compare the original share of the rent per roommate with the new share of the rent per roommate, and then solving for the minimum number of original roommates that satisfies the inequality.
Learn more about whole number here:
https://brainly.com/question/29885808
#SPJ4
Explain how a formula can help solve problems.
Answer:
A formula can help solve problems as it gives the person a step-by-step mini key or guide when needing to actually answer a mathematical or scientific equation or question.
A computer and printer cost a total of $954. The cost of the computer is two times the cost of the printer. Find the cost of each item.
A math test has 12 multiplication problems and 24 division problems.
What is the ratio value of multiplication problems to division problems?
Answer as a fraction in simplest form.
A 1/2
its just like you have 1 cookie and 2 apples whats the ratio to cookies from apples
Determine the occupant load of a one room daycare that is 20' by 30' !
The occupant load of a one room daycare that is 20' by 30' is 17 people.
The occupant load of the daycare room can be determined by using the formula:
Occupant load = Area of room / Occupant load factor
From the case, we know that the area of the room is 20' x 30', then:
Room area = 600 square feet.
The occupant load factor for a daycare is typically 35 square feet per person. This means that each person in the daycare should have at least 35 square feet of space.
Using the formula, the occupant load of the one room daycare is:
Occupant load = 600 square feet / 35 square feet per person = 17.14 people
Therefore, the occupant load of the one room daycare is 17 people. This means that the daycare can safely accommodate 17 people at one time.
Learn more about Occupant Load here: brainly.com/question/29673678
#SPJ11
Wendy walked 2 miles in 30 minutes. At this rate, how many miles could Wendy walk in 90 minutes?
Suppose a magazine ranks the best paying college degrees in a country. The following data show the median starting salary, the mid-career salary, and the percentage increase from starting salary to mid-career salary for the 20 college degrees with the highest mid-career salary. Degree starting salary mid-career salary : Degree Starting Salary Mid-Career Salary % Increase
College Degree A 59,400 105,000 77
College Degree B 56,400 101,000 79
College Degree C 54,800 101,000 84
College Degree D 64,800 105,000 62
College Degree E 53,500 93,400 75
College Degree F 61,200 87,700 43
College Degree G 56,200 97,700 74
College Degree H 50,400 87,000 73
College Degree I 48,800 97,800 100
College Degree J 60,800 105,000 73
College Degree K 47,500 91,500 93
College Degree L 41,500 88,300 113
College Degree M 49,300 87,100 77
College Degree N 50,900 90,300 77
College Degree O 46,400 88,300 90
College Degree P 63,900 105,000 64
College Degree Q 93,000 159,000 71
College Degree R 50,700 99,600 96
College Degree S 56,700 91,300 61
College Degree T 50,000 93,400 87
(a) using a class width of 10, construct a histogram for the percentage increase in the starting salary. A histogram with 8 class labels along the horizontal axis is given. The horizontal axis is labeled: % increase. The vertical axis is labeled: frequency. Centered over the leftmost label, 40-49. 9, a bar is drawn 1 unit tall. Moving to the right, information about the remaining bars (beginning with class label) is listed. 50-59. 9: 1 unit tall 60-69. 9: 3 units tall 70-79. 9: 3 units tall 80-89. 9: 7 units tall 90-99. 9: 4 units tall 100-109. 9: no bar 110-119. 9: 1 unit tall a histogram with 8 class labels along the horizontal axis is given. The horizontal axis is labeled: % increase. The vertical axis is labeled: frequency. Centered over the leftmost label, 40-49. 9, a bar is drawn 7 units tall. Moving to the right, information about the remaining bars (beginning with class label) is listed. 50-59. 9: 4 units tall 60-69. 9: no bar 70-79. 9: 1 unit tall 80-89. 9: 1 unit tall 90-99. 9: 1 unit tall 100-109. 9: 3 units tall 110-119. 9: 3 units tall a histogram with 8 class labels along the horizontal axis is given. The horizontal axis is labeled: % increase. The vertical axis is labeled: frequency. There is no bar centered over the leftmost label, 40-49. 9. Moving to the right, information about the remaining bars (beginning with class label) is listed. 50-59. 9: 1 unit tall 60-69. 9: 4 units tall 70-79. 9: 3 units tall 80-89. 9: 7 units tall 90-99. 9: 3 units tall 100-109. 9: 1 unit tall 110-119. 9: 1 unit tall a histogram with 8 class labels along the horizontal axis is given. The horizontal axis is labeled: % increase. The vertical axis is labeled: frequency. Centered over the leftmost label, 40-49. 9, a bar is drawn 1 unit tall. Moving to the right, information about the remaining bars (beginning with class label) is listed. 50-59. 9: no bar 60-69. 9: 4 units tall 70-79. 9: 7 units tall 80-89. 9: 3 units tall 90-99. 9: 3 units tall 100-109. 9: 1 unit tall 110-119. 9: 1 unit tall (b) comment on the shape of the distribution. The histogram is ---select---. (c) develop a stem-and-leaf display for the percentage increase in the starting salary. (enter numbers from smallest to largest separated by spaces. Enter none for stems with no values. ) Leaf Unit = 1
4 5 6 7 8 9 10 11
The histogram of the magazine ranks the best paying college degrees in a country is illustrated below.
A histogram is a graphical representation of data that displays the frequency distribution of a set of continuous or discrete data
To construct a histogram, we would first need to determine the range of the data. In this case, the range would be the difference between the highest and lowest starting salaries or mid-career salaries. We would then divide the range into several intervals or "bins" of equal width.
For example, if we use a bin width of $10,000, the first bin would be $40,000-$49,999, the second bin would be $50,000-$59,999, and so on.
We would then count the number of degrees that fall into each bin and plot the counts as bars on a graph, with the bin ranges on the x-axis and the frequency counts on the y-axis. The resulting graph would be a histogram, showing the distribution of the data.
It is important to label the axes of the histogram and include a title that accurately reflects the data being presented.
To know more about histogram here.
https://brainly.com/question/30354484
#SPJ4
Complete Question:
Suppose a magazine ranks the best paying college degrees in a country. The following data show the median starting salary, the mid- career salary, and the percentage increase from starting salary to mid-career salary for the 20 college degrees with the highest mid- career salary.
Degree Starting Salary | Mid-Career Salary | % Increase
College Degree A 59,400 104,000 75 College Degree B 56,400 101,000 79 College Degree C 54,800 101,000 84 College Degree D 64,800 104,000 60 College Degree E 53,500 93,400 75 College Degree F 61,200 87,700 43 College Degree G 56,200 97,700 74 College Degree H 50,400 87,000 73 College Degree I 48,800 97,800 100 College Degree J 60,800 107,000 76 College Degree K 47,500 91,500
Frequency 40-49.9
Using a class width of 10, construct a histogram for the percentage increase in the starting salary.
a school cafeteria wants to find out what combinations of food and beverage students are ordering. the results are represented in the two-way table below: food pizza hamburger salad water 11 7 23 beverage slurpee 18 19 5 soda 28 12 14 of the students who ordered salad, what is the probability that a student also ordered water? a.) 42 over 137 b.) 23 over 42 c.) 19 over 42 d.) 23 over 137
The probability that a student ordered a hamburger and a Slurpee is Option D) 23 over 137.
What is probability?Generally, To find the probability that a student ordered a hamburger and a Slurpee, we need to divide the number of students who ordered a hamburger and a Slurpee by the total number of students.
From the table, we can see that 23 students ordered a salad and a water.
There were a total of 38 + 12 + 14 + 18 + 28 + 7 + 23 = 137 students in the cafeteria.
Therefore, the probability that a student ordered a salad and a water is 23/137, or about 0.17.
Therefore, the correct answer is d) 23 over 137.
To know more about probability
https://brainly.com/question/30621488
#SPJ4
Select the correct answer. A parabola has a minimum value of 0, a y-intercept of 4, and an axis of symmetry at x = -2. Which graph matches the description?
A. A parabola declines through (negative 0 point 2, 5), (0, 4), (0 point 5, 2), (1, 1) and (2, 0) and rises through (3, 1), (4, 4) and (4 point 5, 6) on the x y coordinate plane.
B. A parabola declines through (negative 4, 4), (negative 3, 1), (negative 2, 0) and rises through (negative 1, 1), (0, 4) and (0 point 2, negative 5) on the x y coordinate plane. C. A curve declines through (negative 6,1) and (negative 4, 0) and rises through (negative 2, 1), (negative 1, 2), (0, 4) and (0 point 5, 5) on the x y coordinate plane. D. A curve declines through (negative 1, 6), (0, 4), (1, 2), (2, 1), (4, 0) and (6, 1) on the x y coordinate plane.
The correct option for a parabola with given details is D i.e. A curve declines through (negative 1, 6), (0, 4), (1, 2), (2, 1), (4, 0) and (6, 1) on the x y coordinate plane.
What exactly is a parabola?
A parabola is a U-shaped plane curve in which any point is an equal distance from both a fixed point (known as the focus) and a fixed straight line (known as the directrix).
In general, if the directrix is parallel to the y-axis, the typical parabola equation is: y² = 4ax.
If the parabola is sideways, i.e., the directrix is parallel to the x-axis, the conventional parabola equation is x² = 4ay.
Aside from these two, if the parabola is in the negative quadrants, the equation can also be y²= -4ax and x² = -4ay.
Now,
The Graph is drawn for option D in the image and it matches the
details provided in the question.
Hence,
The correct option for a parabola with given details is A curve declines through (negative 1, 6), (0, 4), (1, 2), (2, 1), (4, 0) and (6, 1) on the x y coordinate plane.
To know more about Parabola visit the link
https://brainly.com/question/21685473?referrer=searchResults
#SPJ1
For the given matrix A find a 3x2 matrix B such that AB=I, where I is the 2x2 identity matrix. [Hint: If B1 and B2 are the columns of B, then ABj = Ij.]A =1 2 11 1 1
AB = [1 0] is the 2x2 identity matrix so, AB=I.
[0 1]
To find a 3x2 matrix B such that AB=I, we need to solve the equation:
A × B = I
where I is the 2x2 identity matrix. We can use the hint given to us to find the columns of B.
Let B1 and B2 be the columns of B. Then we have:
A × B1 = I1
A × B2 = I2
where I1 and I2 are the columns of the 2x2 identity matrix I.
We can solve for B1 and B2 by setting up and solving the following systems of linear equations:
For B1:
1 × B1[1] + 1 × B1[2] = 1
2 × B1[1] + 1 × B1[2] = 0
1 × B1[1] + 1 × B1[2] = 0
For B2:
1 × B2[1] + 1 × B2[2] = 0
2 × B2[1] + 1 × B2[2] = 1
1 × B2[1] + 1 × B2[2] = 0
Solving these systems of equations, we get:
B1 = [-1, 1]
B2 = [1, -1]
Therefore, the 3x2 matrix B that satisfies AB=I is:
B = [-1 1]
[ 1 -1]
[ 0 0]
We can verify that AB is indeed equal to the 2x2 identity matrix I:
A × B = [1 2 1] × [-1 1 0] = [(-1)+2 (1)+(-1) 0+0] = [1 0]
[1 1 1] [ 1 -1 0] [ 1+1 (1)+(-1) 1+0] [0 1]
Therefore, AB = I:
AB = [1 0]
[0 1]
Learn more about matrix at
https://brainly.com/question/28180105
#SPJ4
The question is -
For the given matrix A find a 3x2 matrix B such that AB=I, where I is the 2x2 identity matrix. [Hint: If B1 and B2 are the columns of B, then ABj = Ij.]
A = 1 2 1
1 1 1
What is the answer of Thomas made 8,700 mL8,700 mL8, comma, 700, start text, space, m, L, end text of tomato soup. He packed 1.6 L1.6 L1, point, 6, start text, space, L, and end text of the soup in his kids' lunches. He then froze half of the remaining soup.
How many milliliters of soup did Thomas freeze?..... ml
Thomas packed 1.6 L1.6 L1, point, 6, start text, space, L, and end text of the soup in his kids' lunches and had firmed 7100 ml of haze.
What's meant by equation?
A fine statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x- 5 = 16, for case. When this equation is answered, we discover that the value of the variable x is 7. The description of an equation in algebra is a fine statement that demonstrates the equivalency of two fine expressions. For case, the two equations 3x 5 and 14, which are separated by the' equal' sign, make up the equation 3x 5 = 14. An equation is a fine expression with two equal sides and an equal sign. 4 6 = 10 is an illustration of an equation.Given that;
He made 8700 ml haze and he packed1.6 liter haze.
1 liter = 1000 milliliters
liter = 1.6 × 1000
litre = 1600 ml
Chancing the firmed haze-
8700 ml- 1600 ml
7100 ml.
Hence
Frozen haze = 7100 milliliters.
To learn more about equation, refer to:
brainly.com/question/1859113
#SPJ1
a random sample of 75 units is drawn from a production process every half hour. the fraction of nonconforming product manufactured is 0.01. what is the probability that if the fraction nonconforming really is 0.01?
The probability of obtaining a random sample of 75 units from a production process where the true fraction of nonconforming product is 0.01 is extremely high. This is because 0.01 is an extremely low fraction, meaning that out of the 75 units in the sample, only 0.75 would be expected to be nonconforming.
The probability that the fraction of nonconforming product is exactly 0.01 (with 0.75 nonconforming units out of 75) can be calculated using the binomial distribution. This distribution assumes that each unit has an independent probability of being nonconforming, and that this probability is the same for each unit. The probability that the sample will have exactly 0.75 nonconforming units out of 75 is 0.907.
Thus, the probability that the true fraction of nonconforming product is exactly 0.01 is very high, and it is likely that a random sample of 75 units drawn from the production process will have a fraction nonconforming that is close to 0.01.
To learn more about random sample:
https://brainly.com/question/24466382
#SPJ4
