A manufacturer makes two type if products X and z at each if two different locations A and B. the materials used to make each if the products are steel, glass and plastic. suppose it takes three units of steel, one unit of glass and two units of plastic to make one unit of product X and four units of steel and one half units of glass and three units of plastic to make one unit of product Z. suppose further that steel, glass and plastic cost birr 10, 2, and 3 per unit respectively at location A. at location B steel, glass abd plastic cost 9,3 and 4 per unit respectively. using matrix algebra. find the material cost of making one of each product at each of the two locations.​

Answers

Answer 1

Using matrix algebra, the material cost of making one of each product at each location is as follows:​

                       Product X    Product Z

Location A        birr 38          birr 50

Location B        birr 38          birr 49.5

What is matrix algebra?

Matrix algebra involves the arrangement of numbers in a rectangular array.

Matrices are arranged in columns and rows to express some mathematical values.

Data and Calculations:Matrix O: Materials Requirement Per Unit

                      Steel    Glass    Plastic

Product X         3            1             2

Product Z         4          0.5           3

Matrix P: Materials Cost Per Unit

                      Steel    Glass    Plastic

Location A      10           2           3

Location B       9           3           4

Matrix R: (O x P) Material Cost of Product X

                      Steel    Glass    Plastic   Total

Location A     30           2           6          38

Location B     27           3           8          38

Matrix R: (O x P) Material Cost of Product Z

                      Steel    Glass    Plastic   Total

Location A     40          1             9          50

Location B     36          1.5         12         49.5

Thus, Product X costs birr 38 at locations A and B, respectively, while Product Z costs birr 50 and birr 49.5 at locations A and B, respectively.

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Related Questions

If a and b are two distinct primes, the ab2 has ___ positive divisors.

Answers

The number ab², where a and b are prime numbers, has 6 divisors.

How many divisors are for the given expression?

Remember that any number can be written as a product of primes, for example, 15 can be written as:

15 = 3*5

Where 3 and 5 are primes.

Such that the divisors of 15 are the factors made with the primes on the right side.

So for the number:

N = a*b^2 = a*b*b

The divisors are:

a, b, a*b, b*b

And trivially, itself and 1, so there are a total of 6 divisors.

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Help me with this I’m stuck!!!

Answers

The intersection between the complement of set A and the complement of set B is 7.

What is a Venn diagram?

A Venn diagram is a visual representation that shows mathematical sets as circular curves inside of a rectangle (known as the universal set).

From the Venn diagram, we are to find the intersection between the complement of set A and the complement of set B.

[tex]\mathbf{A^c = \{ 7,6,11 \}} \\ \\ \\ \mathbf{B^c = \{7,9,13 \}}[/tex]

Therefore, the intersection between the two sets is the set of elements that exists in both of them. Therefore, we have:

[tex]\mathbf{n(A^c \cap B^c) = \{7\}}[/tex]

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Fine the IRQ of the data set. 11,13,9,4,6,5,8,10



PLEASE HELP!!!!!!!!!!!!!!

Answers

Answer:

   5

Explanation:

Data Set : {11, 13, 9, 4, 6, 5, 8, 10}

Arrange ascendingly: {4, 5, 6, 8, 9, 10, 11, 13}

Quartiles:

Q1 --> 5.5Q2 --> 8.5Q3 --> 10.5

Interquartile Range: Q3 - Q1 = 10.5 - 5.5 = 5

Proper ascending ordered set

{4,5,6,8,9,10,11,13}

Q1

6+5/2=5.5

Q3

11+10/2=10.5

IRQ

Q3-Q1=10.5-5.5=5

A player shoots a basketball from a height of 6 feet. The equation, , gives the height, h, of the basketball after t seconds. Describe the height, rounded to the nearest tenth of a foot, of the basketball after 1.5 seconds, assuming no other player touches the ball.

feet above the ground

Answers

It will be 6 - 4.875 = 1.125 feet above the ground or 1.1 feet (rounded to the nearest tenth of a foot).

All you need to do is to replace t in the given equation with 1.5:

[tex]h=-16(1.5)^2+25(1.5)+6[/tex]

h=-4.875

The value is negative so we can assume that after 1.5 seconds the ball will be 4.875 feet lower than it was shot from.

What is the height?

The measurement of someone or something from head to foot or from base to top.

But we also know that it was shot from a height of 6 feet,

So it will be 6 - 4.875 = 1.125 feet above the ground or 1.1 feet (rounded to the nearest tenth of a foot).

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Select all radical expressions that are equivalent to...

Answers

Answer:

B AND E

Step-by-step explanation:

hope that helpsndbwbe

The area of a rectangle is 44m2 , and the length of the rectangle is 3m
less than double the width. Find the dimensions of the rectangle.

Answers

Answer:

width=11/2

length=8

Step-by-step explanation:

44=(2w-3) x w area for a rectangle (44) = the length (2w-3) times the width (w)

44=2w^2 - 3w  distribute

2w^2-3w-44 = 0 subtract 44 from both sides

(w+4)(2w-11) factor

width=11/2

(11/2 x 2) - 3

length = 8

If the cost, C, for manufacturing x units of a certain product is given by C= x² + 10x + 65, find the number of units manufactured at a cost of $7265

Answers

Answer:

80

Step-by-step explanation:

when you do the math you get two answers, -90 and 80

we dont use -90 because -90 units cannot be manufactured

square root of 0.98 simplified

Answers

Answer:

0.98994949366117

√0.98 = 0.98994949366117

Step 1:

Divide the number (0.98) by 2 to get the first guess for the square root.

First guess = 0.98/2 = 0.49.

Step 2:

Divide 0.98 by the previous result. d = 0.98/0.49 = 2.

Average this value (d) with that of step 1: (2 + 0.49)/2 = 1.245 (new guess).

Error = new guess - previous value = 0.49 - 1.245 = 0.755.

0.755 > 0.01. As error > accuracy, we repeat this step again.

Step 3:

Divide 0.98 by the previous result. d = 0.98/1.245 = 0.7871485944.

Average this value (d) with that of step 2: (0.7871485944 + 1.245)/2 = 1.0160742972 (new guess).

Error = new guess - previous value = 1.245 - 1.0160742972 = 0.2289257028.

0.2289257028 > 0.01. As error > accuracy, we repeat this step again.

Step 4:

Divide 0.98 by the previous result. d = 0.98/1.0160742972 = 0.9644963982.

Average this value (d) with that of step 3: (0.9644963982 + 1.0160742972)/2 = 0.9902853477 (new guess).

Error = new guess - previous value = 1.0160742972 - 0.9902853477 = 0.0257889495.

0.0257889495 > 0.01. As error > accuracy, we repeat this step again.

Step 5:

Divide 0.98 by the previous result. d = 0.98/0.9902853477 = 0.9896137535.

Average this value (d) with that of step 4: (0.9896137535 + 0.9902853477)/2 = 0.9899495506 (new guess).

Error = new guess - previous value = 0.9902853477 - 0.9899495506 = 0.0003357971.

0.0003357971 <= 0.01. As error <= accuracy, we stop the iterations and use 0.9899495506 as the square root.

So, we can say that the square root of 0.98 is 0.989 with an error smaller than 0.01 (in fact the error is 0.0003357971). this means that the first 3 decimal places are correct. Just to compare, the returned value by using the javascript function 'Math.sqrt(0.98)' is 0.9899494936611666.

Note: There are other ways to calculate square roots. This is only one of them.

To round it to the tenths, it's 1

To round to the hundredths, it's.99

Thousandth is.990

Investments increase exponentially by
about 26% every 3 years. If you made a
$2,000 investment, how much money
would you have after 45 years?
Future Amount = $[?]
Hint: Future Amount = (1 + r)
Į(1
←time
periods
initial growth

Answers

Answer:

29

Step-by-step explanation:

if you calculate the mathimatical equipment to the $2,000 it'll be better

Suppose that the speed at which cars go on the freeway is normally distributed with mean 65 mph and
standard deviation 6 miles per hour. Let X be the speed for a randomly selected car
b. If one car is randomly chosen, find the probability that it is traveling more than 63 mph.

Answers

Answer:

B) the probability that is traveling more than 63 mph is 0.6293 (or 62.93%)

Step-by-step explanation:

Given:

Normally DistributedMean (μ) = 65 mphStandard Deviation (σ) = 6 miles per hour

Finding the Probability:

If one car is randomly chosen, we want the probability that is traveling more than 63 mph is,

P(X > 63)

To find the value of z,

z = x - μ / σ

z is the standard scorex is the observed valueμ is the mean of the sampleσ is the standard deviation of the sample

z = 63 - 65 / 6

z = -2 / 6

z = -1 / 3 which is approximately -0.33

Using Z table (attached below):

z = -0.33

to find this on the table

on the vertical side under z go to -0.3on the horizontal next to z, go to .03

The area under the curve is 0.3707

P(z > 63) = 1 - P(z < 63)

               = 1 - 0.3707

               = 0.6293

Hence the probability that is traveling more than 63 mph is 0.6293

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Find the area.
O 121.12 ft²
O 53.1 ft²
O 152.3 ft²
O212 ft²
7 ft
8 ft

Answers

The area of the geometry will be 53.1 square feet. Then the correct option is B.

What is Geometry?

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

The figure is the combination of the triangle and semicircle.

Then the area will be

Area = area of triangle + area of semicircle

Area of triangle = 1/2 x 8 x 7

Area of triangle = 28 square ft

Area of semicircle = (π / 8)  x 8²

Area of semicircle = 25.13 square ft

Then the area of the geometry will be

Area = 28 + 25.13

Area = 53.1 square feet

Then the correct option is B.

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T(h) = - A - B * cos((pi*h)/12) Where T is the temperature in degrees Fahrenheit and h is the number of hours from midnight (0 <= h <= 24) . a. The initial temperature at midnight was - 15 degrees * F and at Noon of New Year's Day it was 5 degrees * F Find A and B. b. Find the average temperature for the first 10 hours. C. Find an expression for the rate that the temperature is changing with respect to h.

Answers

The value of A and B is 5 , 10 ;The average temperature for first ten hours is  -7.466 degree F ; an expression for the rate that the temperature is changing with respect to h ; dt/dh = +B sin ((pi*h)/12)

What is a Function ?

A function is a mathematical statement used to correlate two variables.

The function given is

T(h) = - A - B * cos((pi*h)/12)

T is the temperature in degrees Fahrenheit and

h is the number of hours from midnight (0 <= h <= 24)

a. The initial temperature at midnight was - 15 degrees * F and

at Noon of New Year's Day it was 5 degrees * F

At midnight h = 0

T(h) = -15 degrees F

-15 = -A-B* cos 0

-15 = -A-B

A+B = 15------------------- (1)

At noon , h = 12 , T(h)= 5

- A - B*  cos(pi) = 5

-A - B (-1) = 5

B -A = 5 ----------------------- (2)

Solving equation 1 and 2

2B = 20

B = 10

A = 5

The value of A and B is 5 , 10

The average temperature for first ten hours is  -7.466 degree F

Find an expression for the rate that the temperature is changing with respect to h

dt/dh = +B sin ((pi*h)/12)

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An angle measures 37*. What is the measure of its supplement?

Answers

Answer:

143°

Step-by-step explanation:

supplementary angles are angles that combine to form a straight line (and we know that a straight line = 180 degrees)

you can think of an angle as needing another angle to "supplement" it into being a full line.

So, we know that one angle = 37°

And that: one angle + supplementary angle = 180 degrees

                 37° + x  = 180°

                - 37           -37

                     x    = 143

So, the measure of this angle's supplement is 143°

hope this helps!!

Answer:

143 degrees

Step-by-step explanation:

180 - 37 = 143

A 3-gallon bucket of paint costs $108.60. What is the price per quart?

Answers

Answer:

9.05

Step-by-step explanation:

make gallons into quarts

quar prefix in many languages means 4

1 gallon is 4 quarts

3 gallons is 4 times 3 -> 12 quarts

just by seeing 108 and 12 the answer will be around 9

108.90 ÷ 12 = 9.05

9.05 because that’s the answer

You have loaned a friend $100 and will charge him 5% annua simple interest when he pays it back.

Answers

The annual interest would be $5 if you have loaned a friend $100 and will charge him 5% annually and the total amount would be $105.

What is simple interest?

It is defined as the interest based on the principal amount, it does not include the compounded amount. The interest calculates on the initial amount of borrowed amount.

We have:

You have loaned a friend $100 and will charge him 5% annually.

As we know:

A = P(1 + rt)

P = $100

r = 5% = 0.05

t = 1 years

A = 100(1 + 0.05×1)

A = $105

I = A - P = 105 - 100 = $5

Thus, the annual interest would be $5 if you have loaned a friend $100 and will charge him 5% annually and the total amount would be $105.

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Which of the numbers below are whole numbers?
A. 546
B. 7317
C. 1/3
D. 47
E. 93.3.
F. 907.68

Answers

A, B, D because they’re not fractions or decimals

Find the number of distinguishable ways the letters of the following word can be arranged. KNICKKNACK

Answers

The number of distinguishable ways the letters of the following word can be arranged 'KNICKKNACK' is 37800.

When the order of the arrangements counts, a permutation is a mathematical technique that establishes the total number of alternative arrangements in a collection. Choosing only a few items from a collection of options in a specific sequence is a common task in arithmetic problems.

The number of different permutations of n objects with m₁ repeated items, m₂ repeated items,...,mₙ repeated items can be computed as

m!/(m₁!)(m₂!)...(mₙ!)

Here, the letter 'KNICKKNACK' is a total of 10 letters with 4 K's, 2 N's, 1 I, 2 C's, and 1 A.

So, the number of possible arrangements is

(10!)/(4!*2!*1!*2!*1!) = (10*9*8*7*6*5*4!)/(4!*2*2) = 10*9*7*6*5*2 = 37800

Therefore the number of distinguishable ways the letters of the following word can be arranged 'KNICKKNACK' is 37800.

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factorize of 2a³-a²+a-2​

Answers

Answer:  (a - 1)(2a² + a + 2)

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

Explanation:

Use the rational root theorem to determine this list of possible rational roots: 1, -1, 1/2, -1/2

Plug each possible root one at a time into the original expression given. If the simplified result is 0, then that possible root is an actual root.

If we tried say a = -1, then,

2a³-a²+a-2​ = 2(-1)³-(-1)²+(-1)-2​ = -6

The result is not zero, so a = -1 is not an actual root.

But if we tried say a = 1, then,

2a³-a²+a-2​ = 2(1)³-1²+1-2​ = 0

We get 0 so a = 1 is an actual root. I'll let you try the other values, but you should find that a = 1 is the only rational root.

Since a = 1 is a root, this makes (a-1) to be a factor.

From here, use either synthetic or polynomial long division to determine the other factor. Refer to the diagram below for each method.

Regardless of which method you pick, the quotient is 2a² + a + 2 which is the other factor needed. The remainder of 0 tells us we have (a-1) as a factor. For more information, check out the remainder theorem.

How many gallons of a 60% antifreeze solution must be mixed with 70 gallons of 15% antifreeze to get a mixture that is 50% antifreeze?

Answers

There are 245 gallons of antifreeze solution required.

What is Percentage?

Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100.

Here, Let 60% antifreeze solution  volume = x

15% antifreeze solution volume = 15%

Final concentration 50%

Process

             0.6x + 0.15(70) = 0.5(70 + x)

Simplification

                 0.6x + 10.5 = 35 + 0.5x

                 0.6x - 0.5x = 35 - 10.5

                          0.1x = 24.5

                             x = 24.5/0.1

                            x = 245 gallons

Thus, There are 245 gallons of antifreeze solution required.

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Need some help. Urgently. Please explain and answer.

Answers

Find volume

πr²hπ(4)²(10)16π(10)160π

Density=12g/cm³

We know

mAss=Density ×Volume

12(160)π1920π6031g

Answer:

6032 g

Step-by-step explanation:

The battery can be modeled as a cylinder.

Volume of a cylinder

  [tex]\sf V=\pi r^2 h[/tex]

where:

r is the radiush is the height

Given:

r = 4 cmh = 10 cm

Substitute the given values into the formula and solve for v:

[tex]\begin{aligned}\textsf{Volume of a cylinder} & =\sf \pi r^2 h \\ \implies \textsf{Volume of the battery} & = \sf \pi (4)^2(10)\\ v& = \sf 160 \pi\:\:cm^3\end{aligned}[/tex]

Density equation

  [tex]\rho =\dfrac{m}{v}[/tex]

where:

[tex]\rho[/tex] is densitym is massv is volume

Given:

   [tex]\rho = 12 \dfrac{\text{g}}{\sf cm^3}[/tex]

   [tex]v=160 \pi \sf \:\:cm^3[/tex]

Substitute the given values into the Density equation and solve for m:

[tex]\begin{aligned}\rho & =\dfrac{m}{v}\\\implies 12 \dfrac{\text{g}}{\sf cm^3} & = \dfrac{m}{160 \pi \sf \:\:cm^3}\\m & = 12 \dfrac{\text{g}}{\sf cm^3} \cdot 160 \pi \sf \:\:cm^3\\m & = 12 \cdot 160 \pi \:\text{g}\\ m & = 1920\pi\:\text{g}\\ m & = 6031.857895...\:\text{g}\end{aligned}[/tex]

Therefore, the total mass of the battery to the nearest gram is 6032 g.

Including jose, there are 8 people in his family
If order matters, how many ways can he arrange his family members into a row of 5 seats if jose must sit in the first seat?

Answers

The number of ways Jose can arrange his family members into a row of 5 seats if Jose must sit in the first seat is 840.

What is multiplication?

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.

The number of ways Jose can make his family sit is,

Number of ways = number of ways people can sit on the first sit × number of ways people can sit on the second sit × number of ways people can sit on the third sit × number of ways people can sit on the fourth sit × number of ways people can sit on the fifth sit

Since Jose wants to sit on the first seat there are only options for the first seat, therefore,

Number of ways = 1 × 7 × 6 × 5 × 4 = 840

Hence, the number of ways Jose can arrange his family members into a row of 5 seats if Jose must sit in the first seat is 840.

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Instructions: Complete the following proof by dragging and dropping the
correct reason in the spaces below.
Statement
Complete the Proof
8x5= 2x + 1
6x5=1
6x = 6
x = 1
Reason
1

Someone help proofs aren’t my thing

Answers

The solution to the given linear equation is x=1

Solution to linear equation

Linear equations are equations that has a leading degree of 1.

Given the linear equation as shown below;

8x - 5= 2x + 1

Subtract 2x from both sides

8x - 2x - 5 = 2x + 1-2x

6x - 5  = 1

Add 5 to both sides

6x - 5 + 5 = 5 + 1

6x  = 6

Divide both sides by 6

6x/6 = 6/6

x = 1

Hence the solution to the given linear equation is x=1

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i needs help with it ​

Answers

Answer:

a)  initial height = 0 m

b)  8 s

c)  vertex = (4, 32)

    maximum height = 32 m

Step-by-step explanation:

Given equation:

[tex]h=-2t^2+16t[/tex]

where:

h is the height of the arrow about the ground (in metres)t is the time (in seconds)

Part (a)

The initial height of the arrow will be at the beginning of its journey, so when t = 0

Substitute t = 0 into the equation and solve for h:

[tex]\implies h=-2(0)^2+16(0)[/tex]

[tex]\implies h=0[/tex]

Therefore, the initial height of the arrow is 0 m.

Part (b)

The arrow will hit the ground when the height is 0 m.

Substitute h = 0 into the given equation:

[tex]\implies -2t^2+16t=0[/tex]

Factor out -2t:

[tex]\implies -2t(t-8)=0[/tex]

Therefore:

[tex]\implies -2t=0 \implies t=0[/tex]

And:

[tex]\implies t-8=0 \implies t=8[/tex]

Therefore, the arrow will hit the ground at 8 seconds.

Part (c)

The vertex is the turning point of a parabola - it's minimum or maximum point.

As the leading coefficient for the given equation is negative, the parabola opens downwards and so its vertex is its maximum point.

There are different ways to find the vertex of a parabola. The easiest way to find the x-coordinate is by calculating the midpoint of the x-intercepts.

We have determined that the arrow has a height of 0 m at 0 seconds and 8 seconds.  Therefore, t = 0 and t = 8 are the x-intercepts.  The midpoint is halfway between zero and 8, so the midpoint is t = 4

To find the y-coordinate, substitute t = 4 into the equation and solve for h:

[tex]\implies h=-2(4)^2+16(4)[/tex]

[tex]\implies h=-32+64[/tex]

[tex]\implies h=32[/tex]

Therefore, the coordinates of the vertex are (4, 32)

The maximum height is the y-coordinate of the vertex.

Therefore, the maximum height is 32 m

find 7x +y when x=7 and y=1

Answers

Answer:

7x+y

7(7)+1

49+1

50

Step-by-step explanation:

please mark me as brainlest

Answer:

7x + y

x=7 y=1

7(7) + 1

49 + 1

= 50

hi can you please help me with this question.

I need explanation too.

I'll like and rate your answer if your answer is right.


0 like and 1 rate for nonsense answer.
0 like and 2 rate if it's incorrect.
0 like and 3 rate if it is un-answer
1 like and 4 rate if it's correct a bit
1 like and 5 rate if it's very good answer.

Answers

Answer:

It appears to already be solved. What do you need help with?

Step-by-step explanation:

The triangular prism below has a base area of 28.7 units² and a height of 11 units.
Find its volume.

Answers

The volume of the triangular prism is 315.70 units³.

What is the volume?

A triangular prism is a three-dimensional shape that has a triangular base.

Volume =base area x height

28.7 x 11 = 315.70 units³

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Andres rolls a standard six-sided die, numbered from 1 to 6. Which word or phrase
describes the probability that he will roll a number greater than or equal to 1?

Answers

I don't know what the word or phrase is, but with the parameters you've given, 100%


How do you write 189% as a fraction, mixed number, or whole number?

Answers

To write .189 as a fraction you have to write .189 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.
.189 = .189/1 = 1.89/10 = 18.9/100 = 189/1000

And finally we have:
.189 as a fraction equals 189/1000

NEED ASAP

The scatter plot below shows the amount of profit earned per month by a bagel shop over a period of 11 months.



Write an equation for the line of best fit that models the relationship between profit in thousands, p, and time in months,m. Then, use your equation to predict the profit the bagel shop will earn in month 12. Round slope and -y intercept to the nearest tenth.

Answers

The bagel shop will earn $9625 in 12 months.

What is a Scatter Plot ?

Scatter plot are graphs that identifies relation between x and y variables.

The scatter points are given in the graph and we have to determine the equation that best fits the data .

the points in the scatter plot is

(3,4) and (8,6)

The slope of the equation

y = mx +c is given by

m =(y2 - y1)/(x2-x1)

m = (9-4)/(11-3)

m = 5/8 = 0.625

The equation is

y= 0.625x +2.125

for 12 months

y = 9.625 thousand = 9625 thousand in 12 months

Therefore the bagel shop will earn $9625 in 12 months.

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Answer:

$9,625 is the answer, and $9,300 is the rounded answer

Step-by-step explanation:

general formula: y=ax-b

required form: p=am-b

choose two dots: (11,9), (3,4)

find the slope: 9-4/11-3=5/8 -> p=5/8

put it into an equation: f(11)=6&7/8-b=9, f(3)=1&7/8-b=4

finding the y-intercept: -9+6&7/8=2&1/8, -4+1&7/8=2&1/8 -> b=2&1/8

forming a whole equation: p=5/8m+2&1/8

predict the profit in December: p=7&4/8+2&1/8=9&5/8

the bagel shop will earn $9,625 in December

round them to the nearest tenth:  p=0.6m+2.1

predict the profit in December: p=7.2+2.1=9.3 -> $9,300

If a line has a slope of 4 and goes through the point open parentheses short dash 1 comma 1 close parentheses, then the equation for the line in slope-intercept form is ______________.

a.)
y equals short dash 4 x minus 3

b.)
y equals 4 x plus 3

c.)
y equals 4 x plus 5

d.)
y equals short dash 4 x minus 5

Answers

You are given the slope = 4 and a point is (-1,1)

The equation of a line is written as y - mx + b where m is the slope and b is the y intercept

Using the slope you now have y = 4x + b

Solve for b by replacing x and y with the values of the point:

1 = 4(-1) + b

Simplify:

1 = -4 + b

Add 4 to both sides:

b = 5

The equation of the line is C.) y = 4x + 5

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