You are investigating having business cards printed for your new game store. A local printing company charges $250 for the cardboard used and an hourly rate for labour of $40.

a. If h is the number of hours of labour required to print the cards, construct an equation for the cost
of the cards, C.

b. You have budgeted $1000 for the printing job. How many hours of labour can you afford? Give
your answer to the nearest minute.

c. The company estimates that it can print 1000 cards per hour of labour. How many cards will you
get printed with your current budget?

d. An alternative to printing is photocopying. The company charges 15 cents per side for the first 10 000 cards and then 10 cents per side for the remaining cards. Which is the cheaper option for 18 750 single-sided cards and by how much?

For the function g(x) we have:

The function g(x) is given by applying transformations to f(x), the transformations are:

The function is:

[tex]g(x) = -(x + 2)^2 + 5[/tex]

The graph is the one you can see below:

There you can see that the vertex is at (-2, 5), then the line of symmetry is:

x = -2.

And we have a maximum at the vertex, which is y = 5.

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The average speed can be shown as (A + B)/50 miles per minute, where the distance between town A and his home is A miles, and that from his home to town b is B miles, and the total time is 50 minutes.

The average speed of any object is given as the ratio of the total distance traveled by the body, to the total time taken.

Average Speed = Total Distance/Total Time.

In the question, we are informed that the person drove from town a to his home and then to town b, with the total journey time as 50 minutes.

We are asked to find the average speed of the person.

We assume the distance from town a to his home to be A miles.

We assume the distance from his home to town b to be B miles.

Thus, the total distance traveled = A + B miles.

The total time taken by the person is given to be 50 minutes.

We know that the average speed of any object is given as the ratio of the total distance traveled by the body, to the total time taken.

Thus, the average speed of the person can be shown as:

Average Speed = (A + B)/50 miles per minute.

Thus, the average speed can be shown as (A + B)/50 miles per minute, where the distance between town A and his home is A miles, and that from his home to town b is B miles, and the total time is 50 minutes.

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1) [tex]\overline{AB} \cong \overline{CD}[/tex], [tex]\overline{AD} \cong \overline{CB}[/tex], [tex]\overline{AX} \perp \overline{BD}[/tex], [tex]\overline{CY} \perp\overline{BD}[/tex] (given)

2) [tex]\overline{BD} \cong \overline{BD}[/tex] (reflexive property)

3) [tex]\triangle ABD \cong \triangle ACDB[/tex] (SSS)

4) [tex]\angle ADB \cong \angle CBY[/tex] (CPCTC)

5) [tex]\angle CYB[/tex] and [tex]\angle AXD[/tex] are right angles (perpendicular lines form right angles)

6) [tex]\triangle CYB[/tex] and [tex]\triangle AXD[/tex] are right triangles (a triangle with a right angle is a right triangle)

7) [tex]\triangle AXD \cong \triangle CYB[/tex] (HA)

8) [tex]\overline{AX} \cong \overline{CY}[/tex] (CPCTC)

The analysis which would be most appropriate for randomly assign people to one of three experimental conditions (Treatment A, Treatment B, Control) are-

A statistical test called an analysis of variance, or ANOVA, is used to compare the means of more than two groups.

A helpful framework for analysing how various variables affect various continuous variables is the general linear model (GLM).

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The complete question is -

Suppose you are performing an experiment where you randomly assign people to one of three experimental conditions (Treatment A, Treatment B, Control). Which analysis would be most appropriate?

Step 1

Using the points (2,0) and (-2, -3), we get the slope is

[tex]\frac{-3-0}{-2-2}=\frac{3}{4}[/tex]

Step 2

Using the point (2,0), the equation is

[tex]y=\frac{3}{4}(x-2)[/tex]

Step 3

Using the distributive property, we get [tex]y=\frac{3}{4}x-\frac{3}{2}[/tex].

Answer:

$ 51.36

Step-by-step explanation:

To find the sales tax multiply the tax rate by the cost of the product and then add to the cost.

Sales tax = tax rate * cost price

              = 7% * 48

              = 0.07 * 48

              = $ 3.36

Cost price = cost of product + sales tax

                 = 48 + 3.36

                 = $ 51.36

The point F as described in the task content is at point; 0.6 on the number line.

Since it follows from.tge task content that; point D is at -3, and point E Is at 6, it follows that the length of segment, DE is; |-3-6| = 9.

Consequently, since the ratio of Df to FE ls 2:3

It follows that point F is at -3 + (2/5) × 9.

Point F is therefore at 0.6 on the number line.

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The measurement of angle C in the given figure is 118°.

Given that are two lines intersecting at a point making 4 angles, 118°, C, D and B.

B and D are opposite to each other and C and 118° are opposite to each other.

We need to find the measurement of angle C.

To find the measurement of angle C, we can use the concept of vertical angles.

Vertical angles are a pair of non-adjacent angles formed when two lines intersect.

They are always congruent, meaning they have the same measure.

In this case, angle 118° and angle C are vertical angles. So, their measures are equal:

Angle C = 118°

Therefore, the measurement of angle C is 118°.

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Answer:

Incorrect

Step-by-step explanation:

Formula:

the Diagonal of a square with side square of lengths a

is equal to a√2.

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

Then

Diagonal of LMNO : 7√2

Then

OM = 7√2

…………………………………………

Using the Pythagorean theorem:

The diagonal of the rectangle PQRS is equal to :

√(14²+7²) = √245 = 7√5

Then

SQ = 7√5

………………

Conclusion:

7√5 ≠ 2×(7√2)

Therefore

Anna is not correct.

Answer:

Step-by-step explanation:

40 por ciento

Given that the distance and angle of elevation of the tree from P are 50 m. and 32°, and Q is 100 m. from P, we have;

a. The height of the tree is approximately 31.2 m.

b. i. The distance of Q from the base of the tree is 50•√5 m.

ii. The angle of elevation of the top of the tree from Q is approximately 15.6°

iii. The bearing of the tree from Q is 296.565°

a. tan(32°) = Height/50

Height = 50 × tan(32°) = 31.243 m.

b. i. The distance, d, of Q from the base of the tree is given by Pythagorean theorem as follows;

d = √(100² + 50²) = 50•√5

ii. The angle of elevation is given by trigonometric ratios as follows;

[tex]tan (\theta) = \frac{31.243}{50 \cdot \sqrt{5} } [/tex]

Which gives;

[tex]\theta= arctan \left( \frac{31.243}{50 \cdot \sqrt{5} } \right) \approx 15.6 ^{ \circ} [/tex]

iii. The angle formed at Q by the lines from Q to the point P and Q to the tree is found as follows;

Angle = arctan(50/100) ≈ 26.565°

The angle between the direction north of Q and a line from Q to the tree is therefore;

90° - 26.565° = 63.435°

The bearing, which is the angle described clockwise from the direction north of Q and the direction from Q to the tree, is therefore;

Bearing = 360° - 63.435° = 296.565°

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Answer: $18.51

Step-by-step explanation:
1015cm^3/7.95cm^3/g = 127.67g

127.67g/1000g = .128

.128*$.29 = $.037

$.037*500 = $18.51

Answer:

$1170

Step-by-step explanation:

1. We know that each steel part has a volume of 1015 cubic centimeters, and the machinist wants to make 500 of these. Then the total volume of the steel part the machinist will make will be 1015 x 500.

--> 1015 x 500

--> 507500 cubic centimeters.

2. The density of the steel part is 7.95 grams per one cubic centimeter. Then the total density of the 500 steel parts will be 507500 x 7.95.

--> 507500 x 7.95

--> 4,034,625 grams.

3. For every kilo of steel part, the cost is $0.29. We should first change the 4,034,625 gram to kilo. Since 1000 grams is a kilo, we divide 4,034,625 by 1000.

--> 4,034,625 grams / 1000 = 4034.625 kilograms.

Now we multiply 4034.625 by 0.29 to find the total cost.

--> 4034.625 x 0.29

--> 1170.04125.

Since the question specifically asked to round it to the nearest dollar, our final answer becomes $1170.

Answer: y = -2x + 1.

Step-by-step explanation:

From (-1, 3) follow the line to go 1 to the right and 2 down (because the slope is -2). That takes you to (0, 1). So the y-intercept is 1 and the equation is y = -2x + 1.

Answer:

Step-by-step explanation:

here is a solution and verify

If the function is

[tex]y = 4 e^x \cos(3x)[/tex]

then we have derivatives

[tex]Dy = 4 e^x \cos(3x) - 12 e^x \sin(3x)[/tex]

[tex]D^2y = -32 e^x \cos(3x) - 24 e^x \sin(3x)[/tex]

Now consider the linear ODE

[tex]aD^2y + bDy + cy = 0[/tex]

Substituting [tex]y[/tex] and its derivatives reduces the equation to

[tex](-32a + 4b + 4c) \cos(3x) + (-24a - 12b) \sin(3x) = 0[/tex]

Now,

[tex]-24a - 12b = 0 \implies b = -2a[/tex]

[tex]-32a + 4b + 4c = 0 \implies c = 10a[/tex]

Then the minimal ODE with the given solution is

[tex]aD^2y -2a Dy + 10ay = 0[/tex]

or

[tex]\boxed{D^2y  -2 Dy + 10y = 0}[/tex]

[tex]ac {}^{2} = cb {}^{2} + ba {}^{2} - 2(cb)( ba)(cos \alpha ) \\ ac {}^{2} = 21 {}^{2} + 26 {}^{2} - 2(21)(26)(cos112) \\ ac {}^{2} = 441 + 676 - 1092(cos112) \\ ac {}^{2} = 1526.07 \\ ac = 39.065[/tex]

Answer:

Step-by-step explanation:

The profit Mrs karki made from the Sari she sold at RS 11300 was 28.25%

An equation is an expression that shows the relationship between two numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

VAT = 13% = 0.13 * 8000 = 1040

Selling price - VAT = 11300 - 1040 = 10260

Profit = [(10260 - 8000)/8000] * 100% = 28.25%

The profit Mrs karki made from the Sari she sold at RS 11300 was 28.25%

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The figure with the new side length if Yasmin changed the scale factor to 1 inch : 3 and two-thirds feet is a square with side lengths of 7 and one third feet.

From the information given, the actual length of each side was 4 feet and the scale factor was 1 inch : 2 feet.

The new length will be:

= 2 × 3 2/3

= 7 1/3

Therefore, the new length is 7 1/3 feet.

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Answer:

Associative Property

For multiplication, the rule is "a(bc) = (ab)c"; in numbers, this means 2(3×4) = (2×3)4.

Answer:
3rd Option!

Step-by-step explanation:

EDGE 2022; good luck

Step-by-step explanation:

400 is the whole = 100%

20% (= 20 out of 100 equal parts of 100%) are red.

how many are that ?

well, again, 400 = 100%

1% = 100%/100 = 400/100 = 4

20% = 20×1% = 20×4 = 80

when you combine these 2 steps, you see you get 20% by multiplying the 100% by 20/100 or 0.20.

400 × 0.2 = 80

now,

35% are yellow.

35% = 35×1% = 35×4 = 140

or

400×0.35 = 140

red + yellow = 80 + 140 = 220

the rest are green

400 - 220 = 180

we would get this also by seeing that

red + yellow = 20% + 35% = 55%.

so, green has then the remaining 100-55 = 45%

and again

45% = 45×1% = 45×4 = 180

or

400×0.45 = 180

The formula is illustrated below:

It should be noted that a cylinder simply means a three dimensional solid which holds two parallel bases that are joined by a curved surface.

In this case, it can be seen that the formula that can be used to calculate the volume and the surface area of the cylinder is illustrated above.

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Answer:

[tex]\huge\boxed{\sf x = 65 \textdegree}[/tex]

Step-by-step explanation:

Using trigonometric ratio cos.

Here,

[tex]\displaystyle cos \theta =\frac{adjacent}{hypotenuse} \\\\cos \ x =\frac{12}{28} \\\\cos \ x = 0.43\\\\x = cos^{-1} 0.43\\\\x = 65 \textdegree\\\\\rule[225]{225}{2}[/tex]

Answer:

4x^2

Step-by-step explanation:

2x(2x) It is a square so we multiply the side by the side to get the area.

=2*x*2*x

=4*x2

=4x^2

Answer:

[tex]y-1=5(x-8)[/tex]

The type of polygon is a triangle

The coordinates are given as:

A (3, 4), B (3, 1), and C (5, 1).

The above shows that the number of vertices in the polygon is 3

A polygon that has 3 vertices is a triangle

Hence, the type of polygon is a triangle

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The measure of the length BP and BC are 6 and 10 respectively

The given figure is a circle containing two chords AD and BC. From the given diagram, the following are true

AP = PC

BP = PD

BC = BP + PC

Circle theorem includes the concept of tangents, sectors, angles, the chord of a circle and proofs. A circle is the locus of all points in a plane which are equidistant from a fixed point.

Given the following parameters

AP = 3.5,

PD = 6,

PC = 4

According to the expression above;

BP = PD = 6

BC =  BP + PC

BC = 6 + 4

BC = 10
Hence the measure of the length BP and BC are 6 and 10 respectively

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The height of the cylinder is (a) 8.75 meters

The given parameters are:

Volume = 315[tex]\pi[/tex]

Radius, r = 6

The volume of a cylinder is:

[tex]V = \pi r^2 h[/tex]

So, we have:

[tex]315\pi = \pi * 6^2 * h[/tex]

Divide both sides by 36[tex]\pi[/tex]

h = 8.75

Hence, the height of the cylinder is (a) 8.75 meters

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Answer:

AC=DC. (Given in figure)

AB=BD. (Given in figure

BC=BC. (Common)

that means triangle BAC is congruent to triangle BDC by SSS criterion

Answer:

if I am sick, then I will not come to school.

Step-by-step explanation: