33. let a d 2 4 1 0 4 0 3 2 2 6 3 3 5 and b d 2 4 4 1 4 3 5 . denote the columns of a by a 1, a 2, a 3, and let w d span fa 1; a 2; a 3g. a. is b in fa 1; a 2; a 3g? how many vectors are in fa 1; a 2; a 3g? b. is b in w ? how many vectors are in w ? c. show that a 1 is in w . [hint: row operations are unneces-sary.]

Answers

Answer 1

a1 is a linear combination of w1, w2, and w3, and is thus a vector in w.

a. No, b is not in fa 1; a 2; a 3g. There are 3 vectors in fa 1; a 2; a 3g.

b. Yes, b is in w. There are 4 vectors in w.

c. To show that a1 is in w, we need to show that a1 is a combination of the vectors in w. We can do this by constructing a linear combination of the vectors in w that results in a1. In this case, we can take w1 = (2, 4, 1, 0), w2 = (4, 0, 3, 2), and w3 = (2, 6, 3, 3). Now we can set up a linear combination of these vectors, with coefficients c1, c2, and c3, to equal a1. Thus, we have: c1(2, 4, 1, 0) + c2(4, 0, 3, 2) + c3(2, 6, 3, 3) = (2, 0, 0, 0). Solving for c1, c2, and c3, we get c1 = 2, c2 = -2, and c3 = 0. Therefore, a1 is a linear combination of w1, w2, and w3, and is thus a vector in w.

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Related Questions

How many solutions does this system have? x + 4 y = 6. y = 2 x minus 3a. one b. two c. an infinite number d. no solution

Answers

According to the graph, the system of equations x + 4y = 6 and y = 2 x -3 has one solution that is (2,1)

In math the term called graph is defined as a diagram showing the relation between variable quantities, typically of two variables, each measured along one of a pair of axes at right angles.

Here we know that the following equation are known:

=> x + 4y = 6

=> y = 2x - 3

And here we need to find the number of solution for the equations.

Here we have to plot the equation on the graph then we get the graph like the following.

While we looking into the graph, we have identified that the intersection point in the graph is (2,1) and there is no other intersecting point.

Therefore, option (a) is correct.

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Please help with this problem!

Answers

The maximized value of the objective function is 3

How to maximize the objective function

From the question, we have the following parameters that can be used in our computation:

C = x + y

Subject to

y >= 0

x >= 0

4x + 2y <= 8

2x - y <= 0

When the graphs of these inequalities are plotted (see attachment), we have the following feasible regions

(x, y) = (0, 0) and (1, 2)

This means that

C = 0 + 0 = 0

C = 1 + 2 = 3

3 is greater than 0

Hence, the maximized value is 3

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What is the value of f(150)?

Answers

Answer:

Step-by-step explanation:So make sure you learn this in fifth grade so basically whatever your line go to let's say if it lands on 79 I mean 70 and that's like I mean 150 it depends on what you're using

enter the value of n for the eqation 5 n = 5 11 times 5 3

Answers

For the equation 5^n = 5^11 × 5³ the value of n using the exponents rule is obtained as n = 14.

What is an exponent?

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.

The given equation is 5^n = 5^11 × 5³

Since, the base of the exponents is same, so apply the operations on the powers of the base.

The value of n can be found by following the exponent rule.

The exponent rule is - a^(b) × a^(c) = a^(b + c)

Write the equation according to the rule -

5^n = 5^(11 + 3)

Use the arithmetic operation of addition -

5^n = 5^(14)

n = 14

Therefore, the value of n is obtained as 14.

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2x^2-5x-2=0 quadratic formula

Answers

Step-by-step explanation:

First add you two numbers in parethese and then subtract thhat and dit =0

I need help with this question please and thank you

Answers

The type of transformation and scale factor as required are;

16) Rotation

17) Reflection

18) Dilation

19) n = 5

20)P = r = 4

What is the type of transformation?

There are different types of transformation as follows;

1) Translation: This type of translation is defined as moving the object in space by keeping its size, shape or orientation constant. In a translation, each point of the shape must be moved in the same direction and for the same distance

2) Dilation: This type of translation expands or contracts the object by keeping its orientation or shape the same. This is also known as resizing.

3) Rotation: This type of transformation has an object about a fixed point without changing its size or shape.

4) Reflection: This type of translation is called reflection because it flips the object across a line by keeping its shape or size constant.

16) This transformation is rotation based on the definitions above.

17) This type of transformation is a reflection as it is like the image was flipped across a line more like a mirror image.

18) This called dilation as the scale factor was adjusted to produce the new image.

19) Scale Factor = 6/3 = 2

Thus;

n = 10/2 = 5

20) Scale factor = 12/9 = 4/3

Thus;

P = r = 3 * 4/3

= 4

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remember that we don't consider degenerate triangles unless specially instructed otherwise. two side lengths of a triangle are and . what is the longest possible integer length of the third side of the triangle?

Answers

The minimum value of the third side is 9 cm, and The maximum value of the third side is 6.7 cm.

The minimum value of the third side is when the triangle is a degenerate triangle, meaning that the third side is a line segment joining the two endpoints of the first two sides, which is equal to 3 cm + 6 cm = 9 cm.

The maximum value of the third side is when the triangle is a right triangle, and the two sides are the legs. According to the Pythagorean theorem, the third side (the hypotenuse) should be equal to the square root of 3² + 6² = 9 + 36 = 45, which is equal to 6.7 cm.

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--The given question is incorrect; the correct question is

"The length of two sides of a triangle are 3cm and 6cm. What could be the minimum and maximum value of its third side?"--

The polygons are similar, but not necessarily drawn to scale. Find the value of x.

Answers

The value of x is 5.5

What is a polygon?

The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.

Given;

The two polygons are similar

So,

x-1/6=16/21

x/6-1/6=16/21

x/6=16/21+1/6

x=5.5

y+1/32=21/24

y/32+1/32=7/8

y=3

Therefore, the value of x in polygon will be 5.5

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What percent of the area under the tandard normal ditribution lie within two tandard deviation of the mean?

Answers

Approximately 95.45% of the area under the standard normal distribution lies within two standard deviations of the mean.

Area Under Standard Normal Distribution Within Two Standard Deviations of the Mean

The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. This means that 68.27% of the area under the standard normal distribution lies within 1 standard deviation of the mean, and 95.45% of the area under the standard normal distribution lies within 2 standard deviations of the mean.

This is because the standard deviation is a measure of the spread of the data; the larger the standard deviation, the more spread out the data is.

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A group of students were asked which club they planned to join.

Club Percent of Students
Garden Club 0.1
Robotics Club 0.2
Technology Club 0.5
Zoology Club 0.2

Compare the probabilities of a randomly selected student joining a club and interpret the likelihood. Choose the statement that is true.
The student will be more unlikely to join the Robotics Club than the Garden Club because P(Robotics) < P(Garden).
The student will be equally likely to join the Zoology Club or Robotics Club because P(Robotics) = P(Zoology).
The student will be more likely to join the Zoology Club than the Robotics Club because P(Zoology) > P(Robotics).
The student will be more likely to join the Garden Club than the Robotics Club because P(Garden) > P(Robotics).

Answers

The statement that is most likely to be true in the question that we have here is that : The student will be equally likely to join the Zoology Club or Robotics Club because P(Robotics) = P(Zoology). Option 2

What is meant by probability?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, if we are unclear of how an event will turn out. Statistics is the study of occurrences subject to probability.

In the question the probability of robotics is 0.2 while the probability of zoology club is 0.2 as well.

They have equal probability

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Answer: Answer B

Step-by-step explanation:

A 6 ft. tall man flies a kite and lets out 100 feet of string. The angle of elevation of the string is 52° . How high off the ground is the kite?

Answers

The kite is 84.8 feet off the ground.

What is an angle of elevation?

The angle produced whenever an object if viewed above the horizontal plane is termed the angle of elevation.

To determine how high off the ground is the kite, we have;

let the altitude of the kite from the man's head be represented by s,

Sin θ = opposite/ hypotenuse

Sin 52 = s/ 100

s = Sin 52*100

= 0.7880*100

s = 78.8 feet

The height of the kite off the ground = 78.8 + 6

= 84.8

The height of the kite off the ground is 84.8 feet.

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Can someone please help me on this?

A linear function is plotted on the coordinate plane with the following points: (0, 3) and (2, 7). What is the rate of change (slope) and the initial value (y-intercept) for the linear function?

Answers

The rate of change for the linear function is 2.

The initial value for the linear function is 3.

What is an equation of a line?

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The points on the coordinate plane:

(0, 3) and (2, 7)

Now,

The equation of the line.

y = mx + c

Slope = m

m = (7 - 3) / (2 - 0)

m = 4/2

m = 2

Now,

(0, 3) = (x, y)

3 = 2 x 0 + c

3 = 0 + c

c = 3

The y-intercept is 3.

Thus,

The rate of change is 2.

The initial value is 3.

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Arabella wants to buy 42 dresses.
Each dress costs £8.70.
Estimate the cost of Arabella's 42 dresses

Answers

Answer:

378 Euros

Step-by-step explanation:

A good way to estimate is to round to the nearest whole number or 10th and then multiply:

8.70 --> 9.00 (since 7 > 5 you round up to the nearest whole number, in this case 9)

then you multiply. A good way to do this in your head is doing:

split 42 into 2 numbers:
40, 2

then multiply by nine:

9 * 4 = 36 (9 * 40 = 360) added a zero since we multiplied by 40, its just easier to multiply by smaller numbers

9 * 2 = 18

then add the two numbers together:

360 + 18 = 378 Euros

The actual answer with a calculator is 365.4 Euros, so for an estimation its fairly close.

Another way you could solve it is to just round 8.70 --> 10 (rounding to the nearest 10th)

then:

10 * 42 = 420 (nice)

I don't recommend it since its way too off from the original value, but could be good for quick estimations.

hope this helped you :)

what is the product for (2x+1) and (5-x)

Answers

The product for (2x+1) and (5-x) is -2x²+9x+5.

What is Fraction?

A fraction represents a part of a whole.

We have to find the product of (2x+1)(5-x)

We use distributive property to find the product.

2x(5-x)+1(5-x)

10x-2x²+5-x

-2x²+10x-x+5

Add the like terms

-2x²+9x+5

Hence, the product for (2x+1) and (5-x) is -2x²+9x+5.

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a numerical measure of linear association between two variables is the . a. standard deviation b. covariance c. coefficient of variation d. variance

Answers

option b is correct - covariance

The correlation coefficient (r ) is a numerical measure that measures the strength and direction of a linear relationship between two quantitative variables.

Covariance

A numerical measure of linear association between two variables.

Covariance is a measure of how changes in one variable are associated with changes in a second variable. Specifically, covariance measures the degree to which two variables are linearly associated. However, it is also often used informally as a general measure of how monotonically related two variables are. It is similar to variance, but where variance tells you how a single variable varies, covariance tells you how two variables vary together.

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help me pls , thanks :)
its about funtions and i rlly need help on this

Answers

The given relations are:

1) It is a function.

2) not a function.

3)it is a function.

4) not a function.

Are the relations functions or not?

A function is a relation that maps inputs into outputs, such that each output needs to be mapped into a single input.

1) For example, the first relation each input (left row) is mapped into a single output, thus, it is a function.

2) Here theinput 9 is mapped into two different outputs, then it is not a function.

3) The notation used here is (input, output), so we can see that no input is repeated,so it is a functon.

4) The input 9 is mapped into 3 different outputs, then it is not a function.

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a number increased by 7 given 20

Answers

Answer:

Step-by-step explanation:

Help me please thhhannkkk youuu

Answers

Answer:

25 . 3 %

Step-by-step explanation:

it has the circuits of the brain

15. Use the given degree of confidence and sample data to find a confidence interval for the

population standard deviation c. Assume that the population has a normal distribution.

Round the confidence interval limits to the same number of decimal places as the sample

standard deviation.

College students' annual earnings: 98% confidence; n = 9, x = $3959, s = $886

Answers

Confidence interval will be between $831.57 and $1040.67.

To find a confidence interval for the population standard deviation, we can use the formula:

(sample standard deviation / square root of sample size) x t-multiplier

where t-multiplier is based on the degree of confidence and the sample size.

For a 98% confidence interval and a sample size of 9, the t-multiplier is 2.821 (from a t-table or a calculator with a t-distribution function).

So the confidence interval for the population standard deviation is:

(886 / sqrt(9)) x 2.821 = (886 / 3) x 2.821 = 295.33 x 2.821

= 831.57 to 1040.67

Therefore, we can be 98% confident that the population standard deviation of the annual earnings of college students falls between $831.57 and $1040.67.

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the value of
3(2x+3) when x=5

Answers

Answer:

Step-by-step explanation:

3(2x + 3) = 6x + 9 = 6(5) + 9 = 39

[tex]3(2x+3)[/tex] when x is 5

Substitute for x with the given value:

[tex]3(2(5)+3)[/tex]

[tex]3(10+3)[/tex]

[tex]3(13)[/tex]

[tex]=\fbox{39}[/tex]

The prom committee is decorating the venue for prom and wants to hang lights above the diagonals of the rectangular room. If DH=44.5 feet, EF=39 feet, and m∠GHF=128° , find m∠HEF .

Answers

The measure of the angle m∠HEF = 64°, for the diagonals of rectangular room.

Define the term linear pair?A linear pair is just a pair of neighboring angles created by the intersection of two lines. 1 and 2 create a linear pair in the illustration. The same holds true for pairs 1, 2, 3, and 4. A linear pair's two angles are always supplementary, that means that the sum of their measurements is 180 degrees.

The given data:

DH=44.5 feet, EF=39 feet, and m∠GHF=128°

As, GE is the straight line.

Thus,

m∠EHF = 180 - 128 (sum of all angles of line is 180, linear pair)

= 52°

Now,

m∠HEF = 180 - 52 / 2 (isosceles triangle)

m∠HEF = 64°

Thus, the measure of the angle m∠HEF = 64°, for the diagonals of rectangular room.

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The diagram for the question is attached.

what is the greatest two-digit prime number with the property that the product of its digits is also a prime number?

Answers

The greatest two-digit prime number with the property that the product of its digits is also a prime number is 37, since 3 x 7 = 21.

The greatest two-digit prime number with the property that the product of its digits is also a prime number is 37, since 3 x 7 = 21. Prime numbers are those numbers greater than 1 that are divisible only by 1 and itself. Two-digit prime numbers are those number between 10 and 99. The prime numbers between 10 and 99 are 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97. The product of the digits of 37 is 3 x 7 = 21, which is also a prime number. Therefore, the greatest two-digit prime number with the property that the product of its digits is also a prime number is 37.

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Shane invested $3,500 in a savings account that pays 4% interest

semiannually (every 6 months). How much money will he have in his

account in 5 years?

Answers

The money in Shane's account after five years will be $4900.

The formula for simple interest is -

S.I. = PRT/100, where P is principal, R is rate of interest, T is time and SI is simple interest. Interest is calculated semi-annually then t will be 5×2 years.

Keep the values in formula -

S.I. = 3500 × 4 × 5 × 2/100

Performing multiplication in numerator on Right Hand Side of the equation

S.I. = 1,40,000/100

Cancelling common zero on Right Hand Side of the equation

S.I. = $1400

Total amount = Principal + Interest

Keep the values in formula -

Total amount = 3500 + 1400

Performing addition

Total amount = $4900

The total money in account will be $4900.

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Systems of Equations and Inequalities 2020-2021 / 5 of 18

Two students were shopping for school supplies. They need spirals which cost x dollars and pens which cost y dollars. One student bought

2 spirals and 3 pens for $8. 66. Another student bought 4 spirals and 5 pens for $15. 20. Find the unit cost of a spiral.

1

Answers

Each notebook is $5 and each thumb drive is $12.

To Locate:

The price per notebook and per flash drive

Explain x and y:

Let's say a notebook costs x dollars.

I'll pay whatever a thumb drive costs.

Form equations:

4x + y = 32 ------------------------ [ 1 ]

3x + 2y = 39 ---------------------- [ 2 ]

Equation [ 1 ] x 2:

8x + 2y = 64 ---------------------- [ 3 ]

[ 3 ] - [ 2 ] :

5x = 25

x = 5

Substitute x = 5 into [ 1 ]:

4(5) + y = 32

20 + y = 32

y = 32 - 20

y = 12

Find the cost of each notebook and each thumb drive:

notebook = x

notebook = $5

thumb-drive = y

thumb-drive = $12

Each notebook is $5 and each thumb drive is $12.

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of the 900 students at columbia middle school, there are 324 7th graders. If one student is chosen at random to lead the pledge at a school assembly, what is the probability the person chosen will be a 7th grader? Use prime factorization to reduce the answer.

Answers

Answer:

Step-by-step explanation:

im am sorry but i dont understand so i cant answer this question see you later!

Solve for x. Express your answer in simplest radical form if necessary.
81 = x²

Answers

Answer:

Step-by-step explanation:√81 = √x²

9 = square root cancel square = x

A company produces a range of 5 computers models which bring in high volume

Assuming that the factory works equally to produce models for 9 hours days 7 days per week, which monitor bring in the highest revenue

Answers

The model with the highest revenue is model D

How to determine the model with the highest revenue

From the question, we have the following parameters that can be used in our computation:

Model A Model B Model C Model D Model E

Time to manufacture (mins) (t) 15 18 13 20 17

% Of monitors sold (s) 75% 73% 84% 95% 81%

Cost per monitor (c) $175 $188 $145 $198 $170

The factor works 9 hours for 7 days

So, the total duration per unit time is

D = 9 hours * 7/t

D = 63/t

Convert t to hours

D = 63 * 60/t

D = 3780/t

The total revenue is then calculated as

R = c * D * s

So, we have

Model A = 175 * 3780/15 * 75% = 33075

Model B = 188 * 3780/18 * 73% = 28820

Model C = 145 * 3780/13 * 84% = 35444

Model D = 198 * 3780/20 * 95% = 35551

Model E = 170 * 3780/17 * 81% = 30569

The highest value above is 35551

Hence, the model is model D

Answers

Histogram II shows the distribution of the students’ balance-scale readings, so the correct answer is option (b).

It is stated that most students are very good at reading the scale. Thus, most of the students will read the scale accurately around the actual weight (i.e., around 1.6 ounces), and very few will read far below or far above the accurate weight of 1.6 ounces.

As a large portion of the understudy score tremendous and ought to have rough equivalent aptitude; in this manner, the histogram ought to be around symmetrical.

Therefore, histogram II (symmetrical distribution) shows the perfect distribution of the students' balance-scale readings.

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The complete question is:

(a) Histogram I

(b) Histogram II

(d) Histogram IV

can someone help me please?

Answers

Answer:

Step-by-step explanation:

a) A(11) > M(11)

45 > 40

Go to x axis where t=11 then go straight up to find the y values (temp.) on each line

b) Look for where the lines intersect. This is where t≈47, t≈60

c) M(t) < A(t) where t=2, t=11

Look for where the Minn. line (dashed orange) is BELOW the Aspen line (solid blue)

Given reflections R₁ and Rk where "h" is a line with equation
x = -3 and "k" is a line with equation x = 2, how can you determine
the distance of the translation resulting from the composition
Rk Rh

Answers

The distance of the translation resulting from the composition of the two reflections Rk and Rh is equal to |1 + 2x|

How to determine the distance of the translation

To determine the distance of the translation resulting from the composition of two reflections Rk and Rh, we can calculate the difference in x-coordinates of the pre-image and image points.

Reflection Rk reflects points over the line x = 2,

So the x-coordinate of a point and its reflection would have a difference of 2 - x, where x is the x-coordinate of the original point.

Reflection Rh reflects points over the line x = -3,

So the x-coordinate of a point and its reflection would have a difference of -3 - x

When we compose the two reflections

The x-coordinate of a point and its image will have a difference of (2 - x) - (-3 - x)

Evaluate

Distance = 5

Hence, the distance is 5 units