What is the slope and y-intercept of the equation on the graph?

A. M=3/2,y-int=-3
B.m=3/2,y-int=3
C.m=2/3,y-int=-3
D.m=2/3,y-int=4

Step-by-step explanation:

Let y1 and y2 be (e^x)/2, and (xe^x)/2 respectively.

The Wronskian of them functions be

W = (y1y2' - y1'y2)

y1 = (e^x)/2 = y1'

y2 = (xe^x)/2

y2' = (1/2)(x + 1)e^x

W = (1/4)(x + 1)e^(2x) - (1/4)xe^(2x)

= (1/4)(x + 1 - x)e^(2x)

W = (1/4)e^(2x)

Since the Wronskian ≠ 0, we conclude that functions are linearly independent, and hence, form a set of fundamental solutions.

Answer:

W = (1/4)(x + 1)e^(2x) - (1/4)xe^(2x)

= (1/4)(x + 1 - x)e^(2x)

W = (1/4)e^(2x)

Step-by-step explanation:

Answer:

72°

Step-by-step explanation:

Angle 8 and angle 14 are corresponding angles.

∠8=∠14

72=∠14

Answer:

a) 1.93

b) 97.32% of men are SHORTER than 6 feet 3 inches

c) 2.71

d) 0.34% of women are TALLER than 5 feet 11 inches

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

a. If a man is 6 feet 3 inches tall, what is his z-score (to two decimal places)?

For man, [tex]\mu = 69.8, \sigma = 2.69[/tex]

A feet has 12 inches, so this is Z when X = 6*12 + 3 = 75. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{75 - 69.8}{2.69}[/tex]

[tex]Z = 1.93[/tex]

b. What percentage of men are SHORTER than 6 feet 3 inches?

Z = 1.93 has a pvalue of 0.9732

97.32% of men are SHORTER than 6 feet 3 inches

c. If a woman is 5 feet 11 inches tall, what is her z-score (to two decimal places)?

For woman, [tex]\mu = 64.1, \sigma = 2.55[/tex]

Here we have X = 5*12 + 11 = 71.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{71 - 64.1}{2.55}[/tex]

[tex]Z = 2.71[/tex]

d. What percentage of women are TALLER than 5 feet 11 inches?

Z = 2.71 has a pvalue of 0.9966

1 - 0.9966 = 0.0034

0.34% of women are TALLER than 5 feet 11 inches

Answer:

All real numbers

Step-by-step explanation:

The domain is where the graph touches all of the x-coordinates. This parabola touches all x-coordinates from -infinity to +infinity (all real numbers) because it continues outward forever.

Answer: all real numbers

Step-by-step explanation:

The domain is how many x values are possible, but there is no limit to that, it is infinite. So the domain is all real numbers.

Answer:

The height (corresponding to the [tex] \\ 92^{nd}[/tex] percentile) is (to the nearest inch) 73 inches (and, approximately, only 8% of adult males are taller than this height.)

Step-by-step explanation:

Roughly speaking, the [tex] \\ 92^{nd}[/tex] percentile is the x value (in the distribution) for which 92% of the observations in the [normal] distribution are below this x value, and 8% of the observations are above this x value.

To answer this question, we already know that:

Strategy for solving the question

For solving this, we have to use here the following key concepts: z-scores, the cumulative standard normal distribution, and the cumulative standard normal table.

Z-scores

To find the [tex] \\ 92^{nd}[/tex] percentile, we can use z-scores or standardized values. A z-score is a value that tells us the distance in standard deviations units from the mean. When the z-score is positive, it means that the value is above the mean. A negative indicates that the z-score is below the mean. The formula to obtain a z-score is as follows:

[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]

Where

Cumulative standard normal distribution and corresponding table

We still need to know the corresponding z-score, z, for the cumulative probability of 92%. For this, we have to consult the standard normal table, available on the Internet or in any Statistics books.

In this case, we look in the different columns of the standard normal table a probability value (exact or approximate) to 0.92 and then find the value for z that corresponds to this probability. The value for z is between 1.40 (0.91924) and 1.41 (0.92073).

Using z = 1.40 in [1], we have:

[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]

[tex] \\ 1.40 = \frac{x - 69}{3}[/tex]

Then, solving for x:

Multiplying by 3 at each side of the equation:

[tex] \\ 1.40 * 3 = x - 69[/tex]

Adding 69 at both sides of the equation:

[tex] \\ (1.40 * 3) + 69 = x[/tex]

[tex] \\ x = (1.40 * 3) + 69[/tex]

[tex] \\ x = 4.20 + 69[/tex]

[tex] \\ x = 73.20[/tex]

That is, the [tex] \\ 92^{nd}[/tex] percentile is 73.20 inches, and to the nearest inch, this percentile is 73 inches.

This result indicates that, approximately, 92% of the heights are below 73 inches, and only 8% of heights are taller than this height.  

The shaded area in the graph below shows an area of 0.08076 (8.076%) for 73.20 inches.  

Answer:

Step-by-step explanation:

When the time is 3:40pm

(a)The angle between the two hands in standard position is drawn and attached below.

(b)Now, each hour = 30 degrees

Therefore, the angle between 3 and 8 in an anticlockwise movement

= 7 X 30 =210 degrees

Stating the angle as a negative angle, we have:

[tex]210^\circ-360^\circ=-150^\circ\\$The angle as a negative angle is -150^\circ[/tex]

Option D is the correct answer.

Answer:

D. ∠B and ∠C are congruent.

Step-by-step explanation:

Since, ∠A and ∠B are supplementary.

Therefore,

∠A + ∠B = 180°.....(1)

Since, ∠A and ∠C are supplementary.

Therefore,

∠A + ∠C = 180°.....(2)

From equations (1) & (2)

∠A + ∠B = ∠A + ∠C

=> ∠B = ∠C

Hence, ∠B and ∠C are congruent.

Answer:

False

Step-by-step explanation:

from *millermoldwarp*

"Events are called dependent when the probability of an event depends on the occurrence of another. When event A depends on event B, the probability that A occurs, given that B has occurred, is different from the probability that A occurs only ."

hopes this helps

Answer:false

Step-by-step explanation:

Answer:

μ = 9.504

Step-by-step explanation:

I get complete question that is x is a normally distributed random variable with a standard deviation of 4.00. find the mean of x when 64.8% of the area lies to the left of 11.02

given data

standard deviation = 4

solution

we know that that

X ∞ Normal ( μ , 4²)     ...............1

so Probability P will be express as

P ( X < 11.02 ) = 64.8%

so here

P ( Z < [tex]\frac{11.02- \mu }{4}[/tex] ) = 0.648

Z for 0.648  = [tex]\frac{11.02- \mu }{4}[/tex]  

0.379 = [tex]\frac{11.02- \mu }{4}[/tex]  

solve it we get

μ = 9.504

Answer:

It is explained below

Step-by-step explanation:

Taking into account the required points we can say the following:

In this case measuring the duration of hair is reliable. The purpose for my opinion is that regardless of how often Joni will degree a persons hair the effects will always be more or less the same. There fore, we are able to rely on the fact that the outcomes may be similar this method is reliable. On the other hand, this technique isn't valid, due to the fact the length of a persons' hair has nothing to do with political opinion. The prediction theory that occurs to me with respect to the model is that the longer the person's hair is, the more they tend to be liberal, due to the rebellious thinking of the left-wing.

Complete question is;

A utility company offers a lifeline rate to any household whose electricity usage falls below 240 kWh during a particular month. Let A denote the event that a randomly selected household in a certain community does not exceed the lifeline usage during January, and let B be the analogous event for the month of July (A and B refer to the same household). Suppose P(A) = 0.7, P(B) = 0.5, and P(A ∪ B) = 0.8. Compute the following.

a. P(A ∩ B).

b. The probability that the lifeline usage amount is exceeded in exactly one of the two months.

Answer:

A) 0.4

B) 0.4

Step-by-step explanation:

We are given;

P(A) = 0.7, P(B) = 0.5, and P(A ∪ B) = 0.8

A) To solve this question, we will use the the general probability addition rule for the union of two events which is;

P(A∪B) = P(A) + P(B) − P(A∩B)

Making P(A∩B) the subject of the equation, we have;

P(A∩B) = P(A) + P(B) − P(A∪B)

Thus, plugging in the relevant values, we have;

P(A∩B) = 0.7 + 0.5 - 0.8

P(A∩B) = 0.4

B)The probability that the lifeline usage amount is exceeded in exactly one of the two months can be described in terms of A and B as:

P(A but not B) + P(B but not A) = P(A∩B') + P(B∩A')

where;

A' is compliment of set A

B' is compliment of set B

Now,

P(A∩B') = 0.7 − 0.4 = 0.3

P(B∩A') = 0.5 − 0.4 = 0.1

Thus;

P(A but not B) + P(B but not A) = 0.1 + 0.3 = 0.4

Answer:

Jomo Kenyatta

Step-by-step explanation:

Jomo Kenyatta was a Kenyan politician, who was one of the first African anti-colonial figures. He became the prime minister of Kenya from 1963 to 1964, and after Kenyan independence in 1964, he became president of Kenya. Jomo Kenyatta was born into a family of Kikuyu farmers in Kiambu, present day Kenya which was then, British East Africa. He had his basic schooling in a missionary school before proceeding to study at Moscow's Communist University of the Toilers of the East, University College London, and the London School of Economics.

Answer:

Jomo Kenyatta

Step-by-step explanation:

took the test

Answer:

Type of error: Run-on(comma splice).

Best revision to fix it: Adding a semicolon after beginners .

Explanation:

A run-on sentence is described as a sentence in which two independent clauses are joined inappropriately. It could be either comma splice where the two independent clauses are incorrectly linked using a comma or fused sentence when the two clauses run-on without employing appropriate coordinating conjunction or punctuation marks to separate the two ideas.

In the given sentence, it exemplifies a comma splice type of run-on sentence error. To fix this error, a semicolon after 'beginners' can be employed instead of a comma. This will help in connecting the two ideas appropriately where the first idea leads the second. Thus, the final sentence reads as:

'The guitar is another excellent instrument for beginners; however, it takes more practice than a recorder.'

Answer:

Many people play a musical instrument music can be soothing. A lot of schools teach the recorder; it is inexpensive and easy to play. The guitar is another excellent instrument for beginners, it takes more practice than a recorder.

What type of error is present in the underlined sentence?

✔ run-on

Which is the best revision to fix the error?

✔ adding a semicolon after instrument

Step-by-step explanation:

Answer: 35%

Step-by-step explanation:

If no is 10, 10 x 0.65 = 6.5. OR

10 - 35% of 10 = 6.5

  Multiplying by 0.65 is the same as decreasing by 35%

Let the number is 'a' and percentage decrease is 'b',

Expression for the given statement will be,

a × 0.65 = a - (b% of a)

[tex]0.65a=a(1-\frac{b}{100})[/tex]

[tex]0.65=1-\frac{b}{100}[/tex]

[tex]\frac{b}{100}=1-0.65[/tex]

[tex]b=100(0.35)[/tex]

[tex]b=35[/tex]

    Therefore, Multiplying by 0.65 is the same as decreasing by 35%.

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Answer:

AT least 14 classrooms to hold the total number of students

Step-by-step explanation:

Since  we don't know the numer of girls in the school, let's call it "x".

What we know is that the number of girls plus the number of boys gives the total number of students. This is:

x + 129 = Total number of students

Now, since 5/8 of the total number of students are girls, and understanding that 5/8 = 0.625 in decimal form, then we write the equation that states:

"5/8 of the school's population are girls" as:

0.625 (x + 129) = x

then we solve for "x":

0.625 x + 0.625 * 129 = x

0.625 * 129 = x - 0.625 x

80.625 = x (1 - 0.625)

80.625 = 0.375 x

x = 80.625/0.375

x = 215

So now we know that the total number of students is: 215 + 129 = 344

and if each classroom can hold 25 students, the number of classroom needed for 344 students is:

344/25 = 13.76

so at least 14 classrooms to hold all those students

Answer:8 i ithink

Step-by-step explanation:

Answer:

12, go for 24.

Step-by-step explanation:

There are 6 sides of a cube.

There are 2 pairs of parallel line segments for each side.

6 x 2 = 12

Although that answer is not there, you should go for 24. Since there are 2 variables for each line segment, 12 x 2 = 24. Not sure, hope this helps.

:/

p-value < 0.05, reject null hypothesis and we can conclude that data is not consistent with distributor's claim.

Given, data of toiletry distributors.

Total number of observations

= 170 + 105 + 80 + 45

= 400

Expected count = [tex]p_i \times 400[/tex]

Calculation table is attached below.

Test statistic:

Chi square score

= 6.429 + 0.438 + 0.000 + 7.779

= 14.645

Degree of freedom:

df = 4-1

=3

p-value = CHIDIST(14.645,3)

= 0.00215

Therefore , p-value < 0.05

Reject null hypothesis and we can conclude that data is not consistent with distributor's claim.

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Answer:

Step-by-step explanation:

Given the rate at which the volume V (in dollars) of sales is changing is approximated by the equation

V ' ( t ) = − 26400 e^− 0.49 t .

t = time (in days)

.v'(6) can be derived by simply substituting t = 6 into the modelled equation as shown:

V'(6) = − 26400 e− 0.49 (6)

V'(6) = -26400e-2.94

V'(6) = -26400×-0.2217

V'(6) = $5852.88

V'(6) = $5,853 to nearest dollars

V'(6) = 585300cents to nearest cent

To get v(6), we need to get v(t) first by integrating the given function as shown:

V(t) = ∫−26400 e− 0.49 t dt

V(t) = -26,400e-0.49t/-0.49

V(t) = 53,877.55e-0.49t + C.

When t = 0, V(t) = $170,000

170,000 = 53,877.55e-0 +C

170000 = 53,877.55(2.7183)+C

170,000 = 146,454.37+C

C = 170,000-146,454.37

C = 23545.64

V(6) = 53,877.55e-0.49(6)+ 23545.64

V(6) = -11,945.63+23545.64

V(6) = $11,600 (to the nearest dollars)

Since $1 = 100cents

$11,600 = 1,160,000cents

Answer:

22.11 miles per gallon

Step-by-step explanation:

1 km = 0.621371 miles

1 litre = 0. 264172 gallon

Given

Mileage of car =  9.4 Milometers per liter of gasoline

Mileage of car = 9.4 Km/ litres

now we will use 0.621371 miles for Km and 0. 264172 gallon for litres

Mileage of car = 9.4 * 0.621371 miles/ 0. 264172 gallon

Mileage of car = 9.4 * 2.3521 miles/ gallon

Mileage of car = 22.11  miles/ gallon

Thus, 9.4 Km/litres is same as 22.11 miles per gallon.

Answer: 7.2 inches

Step-by-step explanation:

3/4th of 8 feet = 6 ft.

Balance = 2 feet

1/3 of 2 feet = 2/3 = 0.67 ft = 8 inches

◇Given :-

The denominator of a fraction is increased by a number and numerator will be doubled

To find

We have to find the required number or fraction

[tex]\underline{\bigstar{\sf\ \ Solution:-}}[/tex]

Now let us consided as the number be a

Then

The given fraction is 5/9

[tex]:\implies\sf \dfrac{5\times 2}{9+a}= 1\\ \\ \\ :\implies\sf \dfrac{10}{9+a}=1\\ \\ \\ :\implies\sf 10= 1(9+a)\\ \\ \\ :\implies\sf 10-9=a\\ \\ \\ :\implies\sf 1=a [/tex]

Answer:

N(L) = 20

The expected number of left handed people is 20.

Step-by-step explanation:

Given;

Percentage of left handed people P(L) = 10%

Total number of selected people N(T) = 200

The Expected number of left handed people N(L) is;

N(L) = Total number of selected people × Percentage of left handed people/100%

N(L) = N(T) × P(L)/100%

Substituting the given values;

N(L) = 200 × 10%/100%

N(L) = 200 × 0.1

N(L) = 20

The expected number of left handed people is 20.

=========================================================

Work Shown:

The green triangle in the back has height 2.6 and an unknown base x. Half of this is x/2, which I'll call y. So y = x/2.

The green triangle in the back is split along the vertical dotted line to get two right triangles. The base of each right triangle is y = x/2.

Use the Pythagorean theorem to find y. Use that to find x

a^2+b^2 = c^2

y^2+(2.6)^2 = (3.2)^2

y^2 + 6.76 = 10.24

y^2 = 10.24 - 6.76

y^2 = 3.48

y = sqrt(3.48) .... apply square root

y = 1.8654758 approximately

x/2 = 1.8654758

x = 2*1.8654758

x = 3.7309516 also approximate

The base of the triangle is roughly 3.7309516 meters

We can now find the area of one green triangle

area of triangle = base*height/2 = 3.7309516*2.6/2 = 4.85023708

two triangles have approximate area 2*(4.85023708) = 9.70047416

----------------------------------

So far we've only considered the triangular faces. There are 3 more faces which are the rectangular sides. These are known as the lateral sides.

One way to get the lateral surface area is to multiply the perimeter of the triangle by the depth of the prism

perimeter of triangle = (side1)+(side2)+(side3)

perimeter = 3.7309516 + 3.2 + 3.2

perimeter = 10.1309516

lateral surface area = (depth)*(perimeter)

lateral surface area = (8.26)*(10.1309516)

lateral surface area = 83.681660216

----------------------------------

The last step is to add this lateral surface area onto the area of the two triangles to get the full surface area

surface area = (triangular area) + (lateral surface area)

surface area = (9.70047416) + (83.681660216)

surface area = 93.382134376

surface area = 93.382 square cm

Answer:

Degree: 4; Type: quartic; Leading coefficient: 1

Step-by-step explanation:

Answer:

equation: y = 3x + 14

number of coins after 30 months: 104 coins

Hope this helps :)

An equation is formed of two equal expressions. The number of coins that will be with Deandre after a period of 30 months is 104 coins.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

As it is given that in the initial phase Deandre saves 14 coins. While he adds 3 coins each month. Therefore, the equation that will represent the number of coins that Deandre will have after a period of x months can be written as,

y = 14 + 3x

where y is the number of coins and x is the number of months.

After a period of x=30 months, the number of coins that will be with Deandre can be written as,

[tex]y = 14 + 3x\\\\y = 14 + 3(30)\\\\y = 104[/tex]

Thus, the number of coins that will be with Deandre after a period of 30 months is 104 coins.

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Answer:

The recurrence relation for aₙ is  aₙ = 2aₙ - 1 + 2aₙ -2 ; is n≥ 3 with the initial conditions as a₁ =3; a₂ = 8

Step-by-step explanation:

Solution

Recurrence relation for n - digit ternary sequence with no occurrence of consecutive 0's in them.

Ternary sequence is sequence with each of digits either 0, 1 or 2.

Now

Let aₙ = denote the number of n - digit ternary sequence with no occurrence of consecutive 0's in them.

Let us first find few initial values of aₙ

For n = 1

a₁ represent the number of 1- digit ternary sequence with no occurrence of consecutive 0's in them.  

This 1-digit sequence can be either 0 or 1 or 2.

Thus,

a₁ = 3

For n =2

a₂ represent the number of 2- digit ternary sequence with no occurrence of consecutive 0's in them.

This 2-digit sequence can have either 0 or 1 or 2 as each of its two digit, but making sure that there are no two consecutive 0 in the sequence.

here are " 9 " 2-digit ternary sequence ........... (three choices for 1st digit and three choices for 2nd digit)  

But one of these 9 sequence there are consecutive 0's .... (00)  

So we eliminate this one sequence.

So, a₂ = 8

Now

let us find the recurrence relation

Fir n ≥ 3

aₙ s the number of n - digit ternary sequence with no occurrence of the consecutive 0's in them.

For the first case: if 1st digit of this n - digit ternary sequence is 1 or 2

Let assume the 1st digit of this n - digit ternary sequence is 1.  

Then for remaining n - 1 digits of this n - digit ternary sequence we have to make sure that there is no consecutive 0's in them.

For example, we have to form a n-1-digit ternary sequence with no occurrence of consecutive 0's in them which is by definition aₙ -1

So,

The number of n - digit ternary sequence with no occurrence of consecutive 0's in them if 1st digit of this sequence is 1 is aₙ -1.

Likewise, the number of n - digit ternary sequence with no occurrence of consecutive 0's in them if 1st digit of this sequence is 2 is aₙ -1.

So  

If 1st digit of this n - digit ternary sequence is 1 or 2, then the number of n - digit ternary sequence with no occurrence of consecutive 0's in them is shown as:

aₙ-1 + aₙ -1 = 2aₙ -1

For the second case: if 1st digit of this n - digit ternary sequence is 0

If 1st digit of this n - digit ternary sequence is 0, then the next digit cannot be 0 as well because that would make two consecutive 0's in the sequence Thus,

If 1st digit of this n - digit ternary sequence is 0, the next term can be either 1 or 2.

So there are 2 choices for 2nd digit.  

After this there are more n-2 digits.  

Then

For remaining n - 2 digits of this n - digit ternary sequence we have to make sure that there is no consecutive 0's in them  

For example, we have to form a n-2-digit ternary sequence with no occurrence of consecutive 0's in them. which is by definition aₙ - 2.

Now,

The total number of sequence in this case is given as:

2aₙ -2........... (2 choices for 2nd digit and aₙ - 2 choices for remaining n-2 digit)

Hence  

The number of n - digit ternary sequence with no occurrence of consecutive 0's in them if 1st digit of this sequence is 0 is aₙ = 2aₙ - 1 + 2aₙ -2 which is n≥ 3

Now,

The recurrence relation for aₙ is shown below:

aₙ = 2aₙ - 1 + 2aₙ -2; is n≥ 3

With the initial conditions as a₁ =3; a₂ = 8

Answer:

A shape with two pairs of parallel lines, perpendicular lines, and two pairs of equal sides can be best described as a rectangle.

Answer:

19467649.76 lb-ft^2/s^2

Step-by-step explanation:

diameter of the pool d = 20 ft

radius = d/2 = 20/2 = 10 ft

height of pool side h = 6 ft

depth of water d = 5 ft

the force on the bottom of the pool due to the water in the pool is

F = pgdA

where p = density of water = 62.4 lb/ft^3

g = acceleration due to gravity = 32.17 ft/s^2

Area A = [tex]\pi r^{2}[/tex] = [tex]3.142 * 10^{2}[/tex] = 314.2 ft^2

Force on pool bottom = 64.2 x 32.17 x 5 x 314.2 = 3244608.29 lb-ft/s^2

work done = force times the height the water will be pumped

work = F x h = 3244608.29 x 6 = 19467649.76 lb-ft^2/s^2

The work (in ft-lb) is required to pump all of the water out over the side is :

Formula:

F = pgdA

p = density of water = 62.4 lb/ft^3

g = acceleration due to gravity = 32.17 ft/s^2

Area A = [tex]\pi r2\\[/tex] = 314.2 ft^2

The work (in ft-lb) is required to pump all of the water out over the side is 19467649.76 lb-ft^2/s^2.

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Answer:

Range: (negative infinity, 5]

Step-by-step explanation:

The range is the output/y values. The highest output when you plug in x will be 5. Therefore, your range's max will be at 5.

Answer:

C. The 4 columns of UQ list the total costs for materials, labor, and overhead used to manufacture products B and C during the 4 quarters of the year.

Step-by-step explanation:

[tex]U=\left\begin{array}{ccc}\\$Cost of Materials\\ $Cost of Labour\\ $Cost of Overhead\end{array}\right\left(\begin{array}{cc}$Product B&$Product C\\0.45&0.42\\ 0.25&0.35\\ 0.15&0.15\end{array}\right)[/tex]

[tex]q_1[/tex] is a vector in the set of real numbers [tex]R^2[/tex] that lists the output​ (measured in​ dollars) of products B and C manufactured during the first quarter of the​ year.

Therefore:

[tex]UQ=\left\begin{array}{ccc}\\$Cost of Materials\\ $Cost of Labour\\ $Cost of Overhead\end{array}\right\left(\begin{array}{cc}$Product B&$Product C\\0.45&0.42\\ 0.25&0.35\\ 0.15&0.15\end{array}\right)\left(\begin{array}{ccc}q_{1B}\\q_{1C}\end{array}\right)\left(\begin{array}{ccc}q_{2B}\\q_{2C}\end{array}\right)\left(\begin{array}{ccc}q_{3B}\\q_{3C}\end{array}\right)\left(\begin{array}{ccc}q_{4B}\\q_{4C}\end{array}\right)[/tex]

[tex]=\left(\begin{array}{c|c|c|c}q_1&q_2&q_3&q_4\\0.45q_{1B}+0.42q_{1C}&0.45q_{2B}+0.42q_{2C}&0.45q_{3B}+0.42q_{3C}&0.45q_{4B}+0.42q_{4C}\\0.25q_{1B}+0.35q_{1C}&0.25q_{2B}+0.35q_{2C}&0.25q_{3B}+0.35q_{3C}&0.25q_{4B}+0.35q_{4C}\\0.15q_{1B}+0.15q_{1C}&0.15q_{2B}+0.15q_{2C}&0.15q_{3B}+0.15q_{3C}&0.15q_{4B}+0.15q_{4C}\end{array}\right)[/tex]Therefore, UQ has 4 columns and 3 rows.

The 4 columns of UQ list the total costs for materials(Row 1), labor(Row 2), and overhead(Row 3) used to manufacture products B and C during the 4 quarters of the year.