A projector enlarges an image in the ratio 20:1. What will be the size of an enlargement of a picture that is 8cm by 6cm?

The number of cases per batch that the manufacturer should produce to minimize cost is 462 cases per batch.

To minimize inventory costs, especially setup and holding costs, the economic order quantity (EOQ) technique is deployed.

The EOQ model refers to the ideal order or batch quantity a company should purchase per order or produce per batch to minimize its inventory costs.

Some of a company's inventory costs include holding costs, shortage costs, setup, and ordering costs.

Using the EOQ model shows the ideal minimum units that the manufacturer should produce per batch to minimize costs.

The EOQ formula is square root of: [2(setup costs)(demand rate)] / holding costs.

Annual demand = 22,638 cases

Storage cost per case = $7

Setup cost per batch = $33

Product unit cost = $15 per case

EOQ = square root of: [2(setup costs)(demand rate)] / holding costs.

= square root of 2 x $33 x 22,638/$7

= square root of 213,444

= 462

Number of batches = 49 (22,638/462)

Thus, the number of cases per batch that the manufacturer should produce to minimize cost is 462 cases per batch.

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Answer: [tex]-\frac{3}{16}[/tex]

Step-by-step explanation:

[tex]\frac{3}{4}(-\frac{1}{4} )[/tex]

multiply the numberator and denominator:

3*-1 = -3

and

4*4 = 16 so,

[tex]-\frac{3}{16}[/tex]  is the answer

Answer: [tex]\Large\boxed{-\frac{3}{16} }[/tex]

Step-by-step explanation:

Given information

x = - 1/4

Given expression

[tex]\dfrac{3}{4} ~x[/tex]

Substitute values into the expression

[tex]=\dfrac{3}{4} \times(-\dfrac{1}{4} )[/tex]

[tex]=\dfrac{3\times1}{4\times4}[/tex]

[tex]\Large\boxed{=-\frac{3}{16} }[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

The answer is 4'

Step-by-step explanation:

The answer is 4, 123456789, 6 12, 18, 24, 30, 36, 42, 48.

Answer:

3/4

Step-by-step explanation:

plug values in for x till you get it right

Answer:

x=70

Step-by-step explanation:

when added together, verticle angles equal 180 degrees.

2x-10+x+20=180

3x-10+20=180

3x-30=180

3x=210

x=70

Answer: 6x[tex]6x{2}+93x-126andx{2}+84[/tex]

Step-by-step explanation: The only thing you do is just to keep multiplying until you get your answer.

The rate of the slower cyclist is 16 mph while the rate of the faster cyclist is 21 mph.

let us assume the following;

x = rate of slower cyclist

x + 5 = rate of faster cyclist

We know that formula for distance is;

distance = travel time*rate

Thus;

2x + 2(x + 5) = 74

Since the two cyclists are a distance of 74 miles apart after a time 2 hours. Thus;

2x + 2x + 10 = 74

4x + 10 = 74

4x = 74 - 10

4x = 64

x = 64/4

x = 16

Rate of faster cyclist = 16 + 5 = 21 mph

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Answer:

16

Step-by-step explanation:

By the trapezoid midsegment theorem,

[tex]\frac{ST+6}{2}=11 \\ \\ ST+6=22 \\ \\ ST=16[/tex]

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

We can use Trapezoid midsegment property:

[tex] \qquad❖ \: \sf \: \dfrac{ST + QR}{2} = LM[/tex]

[tex] \qquad❖ \: \sf \: \dfrac{ST + 6}{2} = 11[/tex]

[tex] \qquad❖ \: \sf \: {ST + 6} =2 \times 11[/tex]

[tex] \qquad❖ \: \sf \: {ST + 6} =22[/tex]

[tex] \qquad❖ \: \sf \: {ST } =22 - 6[/tex]

[tex] \qquad❖ \: \sf \: {ST } =16[/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

Answer:

500 rocks

Step-by-step explanation:

25*20 = 500

1) Given - It is given in the problem

2) Corresponding Angles Postulate - If a transversal (line l) intersects two parallel lines (line h and line g), then the corresponding angles must be equal.

3) Transitive Property of Congruence - Since it's given that [tex]\angle1\cong\angle5[/tex] and we showed in line 2 that [tex]\angle1\cong\angle2[/tex], it should be true that [tex]\angle2\cong\angle5[/tex]

4) Converse of Corresponding Angles Postulate - If a transversal (line g) intersects two lines (lines l and m), and the corresponding angles that form have equal measure, then the lines are parallel.

1) Given - It is given in the problem

2) Definition of Angle Bisector - It's given that [tex]\overline{DC}[/tex] bisects [tex]\angle BDE[/tex], which means that [tex]\overline{DC}[/tex] is the angle bisector, and the angle is divided into two angles of the same measure.

3) Transitive Property of Congruence - Since we showed in line 2 that [tex]\angle1\cong\angle2[/tex] and its given that [tex]\angle2\cong\angle3[/tex], it should be true that [tex]\angle1\cong\angle3[/tex]

4) Converse of the Alternate Interior Angles Theorem - If a transversal ([tex]\overline{BD}[/tex]) intersects two lines ([tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex]) and the alternate interior angles formed have the same measure, then the lines are parallel.

Answer:20.00

Step-by-step explanation: next time include the table but i managed to find it anyway

Answer:

BA

CB

CA

Step-by-step explanation:

this simply means that such a letter combination stands for a line that goes through the points with these letters.

and a "ray" means a straight line (not one that goes around a corner). "from this figure" means lines (or connections between points) that are drawn in this graphic.

BA yes

B is just a point, no line. therefore, no.

DBA guys around a corner (from D to B, and then from there to A). therefore, no.

AD would be a straight line, but it is not drawn in the graphic. therefore, no.

ADB is partly not drawn, and it goes around a corner. therefore, no.

CB, CA are both straight lines in the graphic. yes.

The graph showing the temperature over the 5-day period will look exactly like the attached. On the y-axis, we have the Temperature and the x-axis the number of days.

Graphs and charts are useful visual aids because they make information accessible and easy to understand.

Therefore, it is not unexpected that print and electronic media frequently employ graphs.

When data is displayed as a graph rather than a table, it can often be easier to understand since the graph might show a pattern or comparison.

The graph shows the forecasted data against the actual data. It is to be noted that the data for the actual 5-day temperatures are made-up to help the analyst understand the differences between the forecasted and the actual data.

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The amount he can spend on marketing is $8,333.33.

The amount he can spend on supplies is $16,666.67

The amount he can spend on trainings is $12,500

The amount he can spend on travel is $2,500

The amount he can spend on equipment is $10,000

The amount he can spend on each category can be determined by multiplying the fraction of that category by the total department's budget.

The amount he can spend on marketing : 1/6 x $50,000 = $8,333.33.

The amount he can spend on supplies: 1/3 x $50,000 =  $16,666.67

The amount he can spend on trainings: 1/4 x 50,000 =  $12,500

The amount he can spend on travel $2: 1/20 x 50,000 = 2,500

The amount he can spend on equipment $: 1/5 x 50,000 = 10,000

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Answer:

12.63 weeks ~~ 13 weeks

Step-by-step explanation:

This is much like a banking question with compounded interest

FV = PV ( 1 + i)^n       FV = Future value = 1 m   PV = present value = .3

                                     i = periodic interest = .10     n = periods

1 = .3(1 + .1)^n      solve for n = the number of weeks

1/.3   = 1.1^n

log (1/.3) / log 1.1  = n = 12.63 weeks

Answer:

  x = 0

Step-by-step explanation:

Substituting the given "point" into the equation gives the possibilities for x.

Using (x, y) = (x, 8), the inequality becomes ...

  3x -4 < 8

Solving for x gives ...

  3x < 12 . . . . . . . add 4

  x < 4 . . . . . . . divide by 3

Any value of x less than 4 will make (x, 8) a solution to the inequality. For example, ...

  x = 0 . . . . . . (0, 8) is a solution to the inequality

Answer:

f^-1(x)=x-14

Step-by-step explanation:

change f(x) to y :y=x×14

interchange variables :x=y+14

move constant(14) to the left :x-14=f^-1(x)

Using relations in a right triangle, it is found that the length of AC is of 14 cm.

The relations in a right triangle are given as follows:

Researching this problem on the internet, we have that:

Hence the hypotenuse is found as follows:

sin(A) = 48/h

0.96 = 48/h

h = 48/0.96

h = 50 cm.

The length of side AC is the other leg of the triangle, found using the Pythagorean Theorem, hence:

[tex]x^2 + 48^2 = 50^2[/tex]

[tex]x^2 = \sqrt{50^2 - 48^2}[/tex]

x = 14 cm.

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(a) g(- 4) ≈ - 20.566, g(0) = - 8, g(4) = 4, g(6) = 0, g(8) = - 4

(b) g(x) is increasing in the interval [- 4, 2] and decreasing in the interval [4, 8].

(c) There is an up concavity and a decreasing behavior in the interval [2, 6].

(d) The points x = 2 and x = 6 are points of inflection of g(x).

(e) The equation of the line tangent to g(x) at x = 6 is y = - 4 · x + 24.

(f) The range of g(x) is [- 20.566, 4].

(g) The graph of g(x) is shown in the picture attached below.

In this problem we have a piecewise defined function formed by four functions, a circle-like function and three lines, whose integral has to be analyzed in all its characteristics. (a) The integral is described graphically by the area below the curve, where g(2) = 0 and the following properties of the integral are used:

g(- 4) = g(2) - [F(2) - F(- 4)]

g(- 4) = 0 - 0.25π · 4² - 4 · 2

g(- 4) ≈ - 20.566

g(0) = g(2) - [F(2) - F(0)]

g(0) = 0 - 4 · 2

g(0) = - 8

g(4) = g(2) + [F(4) - F(2)]

g(4) = 0 + 0.5 · (2) · (4)

g(4) = 4

g(6) = g(2) + [F(6) - F(2)]

g(6) = 0 + 0.5 · (2) · (4)  - 0.5 · (2) · (4)

g(6) = 0

g(8) = g(2) + [F(8) - F(2)]

g(8) = 0 + 0.5 · (2) · (4) - (2) · (4)

g(8) = - 4

(b) An interval of g(x) is increasing when f(x) > 0 and decreasing when f(x) < 0. Thus, g(x) is increasing in the interval [- 4, 2] and decreasing in the interval [4, 8].

(c) There is an up concavity and a decreasing behavior in the interval [2, 6].

(d) There are points of inflection for values of x such that f'(x) do not exists. The points x = 2 and x = 6 are points of inflection of g(x).

(e) We need to determine the slope and the intercept of the tangent line to determine the equation of the line:

Slope

m = f(6)

m = - 4

Intercept (x = 6, g(x) = 0)

b = g(x) - m · x

b = 0 - (- 4) · 6

b = 24

The equation of the line tangent to g(x) at x = 6 is y = - 4 · x + 24.

(f) The range of g(x) corresponds to the set of values of y that exists in the function. In accordance with the information given in (a), the range of g(x) is [- 20.566, 4].

(g) The graph of g(x) is shown in the picture attached below.

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Answer:[tex]DB \cong VT[/tex]

Step-by-step explanation:

All 3 sides need to be congruent.

Answer :LF is the abbreviation for linear feet Sq ft is the abbreviation for square feet L – lenght (e.g. room length) W – width (e.g. room width)

Liters to Cubic Feet formula. ft³ =. L * 0.035315. Show working Show result in exponential format More information: Cubic Feet.

Step-by-step explanation:

Answer:

First, transform the given equation into the slope intercept form.

-5x + 3y >= 9

3y >= 5x + 9

y >= 5/3x + 3

Then graph the line y = 5/3x + 3. Draw a solid line with y intercept 3 and slope of 5/3.

Finally, shade everything that is above the line.

The total number of eggs needed for b batches is n = 3b

The total number of eggs needed for 6 batches is 18.

Multiplication is one of the basic mathematical operation that is used to determine the product of two or more numbers. The sign used to denote multiplication is x. Other mathematical operations include addition, subtraction and division.

In order to determine the total number of eggs needed, multiply the number of eggs needed for one batch by the total number of batches.

Total eggs needed = eggs needed for one batch x total number of batches

n = 3 x b

n = 3b

6 x 3 = 18

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When a set of given numbers or items is to be arranged in a definite way or pattern, permutation can be used to determine the number of ways in which this can be done. Thus the required answer to the question is 990.

When a set of given numbers or items is to be arranged in a definite way or pattern, permutation can be used to determine the number of ways in which this can be done. The applicable formula is:

[tex]_{n} P_{r}[/tex] = [tex]\frac{n!}{(n - r)!}[/tex]

where: n is the total number of items given, and r is the number of items selected.

Thus the given question can be solved as :

[tex]_{11} P_{3}[/tex] = [tex]\frac{11!}{(11-3)!}[/tex]

       = [tex]\frac{11!}{8!}[/tex]

       = [tex]\frac{11 * 10 * 9 * 8!}{8!}[/tex]

       = 11 x 10 x 9

       = 990

[tex]_{11} P_{3}[/tex] = 990

Therefore, the required answer is 990.

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Answer:last option -5± √17

2

Step-by-step explanation:

Quadratic equations represent any equation that can be rearranged in standard forma (ax² + bx + c( =0(a, b & c) are known.

Quadratic equations can always be solved using the quadratic formula, but sometimes factoring or isolating the variable is also posible.

In the square equation ax² + bx + c = 0

[tex]\boldsymbol{\sf{x=\dfrac{-b\pm\sqrt{\Delta} }{2a} \ ,\Delta=b^{2}-4ac } }[/tex]

Let's calculate the discriminant of the quadratic equation:

Since the discriminant is greater than zero, then the quadratic equation has two real roots.

[tex]\boldsymbol{\sf{x_{1}=\dfrac{-b-\sqrt{\Delta} }{ 2\cdot a}=\dfrac{-5-\sqrt{17} }{2\cdot1} }}[/tex]

[tex]\boldsymbol{\sf{x_{2}=\dfrac{-b+\sqrt{\Delta} }{ 2\cdot a}=\dfrac{-5+\sqrt{17} }{2\cdot1} }}[/tex]

Solution:

[tex]\boldsymbol{\sf{x=\dfrac{-5\pm\sqrt{17} }{2} }}[/tex]

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Answer:

See below.

If the correct sum is 1155, then Ken had 495 stamps, and Henry had 660 stamps.

Step-by-step explanation:

Henry had h stamps.

Ken had k stamps.

After giving away 2/3 of his stamps, Henry ended up with 1/3 of his stamps, or h/3.

After giving away 3/4 of his stamps, ken ended up with 1/4 of his stamps, or k/4.

h/3 = k/4

h + k = 1156

4h = 3k

h = 1156 - k

4(1156 - k) = 3k

4624 - 4k = 3k

4624 = 7k

k = 4624/7

Stamps left: 0.25 × 4624/7 = 1156/7

h = 1156 - k

h = 1156 - 4624/7

h = 8092/7 - 4624/7

h = 3468/7 =495.43

Stamps left: 1/3 × 3468/7 = 1156/7

Total number of stamps left: 1156/7 + 1156/7 = 2312/7 = 330.29

The problem is solved correctly, but the numbers given must be incorrect since you cannot have a fraction of a stamp.

The absolute value inequality is given as |(p - 0.43)I ≤ 0.019

The proportion p = 43% = 0.43

Margin of error = 1.9% = 0.019

The value of the proportion can then be said to lie between

(0.43 - 0.019) ≤ p ≤ (0.43 + 0.019)

In order to convert to the absolute inequality we would be having

-0.019 ≤ (p - 0.43) ≤ 0.019

I (p - 0.43)I ≤ 0.019

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Answer: 9

Step-by-step explanation: it is what it is

15-6=9 omg i never knew

The solution of the given equation represented in the task content can be determined by first evaluating the LCM and hence is; y= 27.

The given equation is; (y-5)/2=(y+6)/3.

Hence, by multiplying the equation by 6, we have;

3(y-5) = 2(y+6)

3y -15 = 2y +12

y = 27.

Hence, it follows that the value of y which is a solution to the equation is; y = 27.

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The current value of his Roth IRA is $215,658.00

What is Roth IRA retirement account?

Roth IRA retirement account is a retirement account where the contributions to the account are invested after taxes after have been deducted.

In other words, when the individual make contributions, taxes are first of all, deducted so as to invest the after-tax contribution into the Roth IRA account

The account lost 1/3 of its original value of $215,658

balance after the loss=$215,658-(1/3*$215,658)

balance after the loss=$ 143,772.00

Now the account regained 1/2 of its new balance of $ 143,772.00

balance now=$143,772.00+(1/2*$143,772.00)

balance now=$215,658.00

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Complete with the missing fractions:

michael wittry has been investing in his roth IRA retirement account for 20 years. Two years ago his account was worth $215,658. after losing 1/3 of its origiInal value, it then gained 1/2 of its new value back, what is the current value of his roth IRA?