A copy machine makes 32 copies per minute. How long does it take to make 136 copies?

15 kilograms of the first type should be mixed with 25 kilograms of the other kind

If the blend costs  $5.50/kg, then:

on each kg at $5.00/kg, gain = $0.50  ($5.50 - $5.00)

on each kg at $5.80/kg, loss = $0.30  ($5.50 - $5.80)

Hence 3kg of the first kind must be mixed with 5kg of the second so that the gain on the first (3 x $0.50) is exactly the same as the loss on the second (5 x $0.30)

The required proportion is 3:5

In order to find how many kilograms of each type are needed to make 40kg, we will use the proportion obtained:

We have 3:5, total share = 3+5 = 8

First kind share = 3/8 x 40 kg = 15 kg

Second kind share = 5/8 x 40 kg = 25kg

Therefore, 15  kilograms of the first type is needed and 25 kilograms of the other kind is needed

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Answer:

D stays for 1 and as B is -6

the length of BD should be 7

good luck <3!

From the given figure

a) The value of y = 6

b) The length of the line RS = 39 units

The length of the line ST = 38 units

The length of the line RS = 6y + 3

The length of the line ST = 5y + 8

The length of the line RT = 77

From the line we can say that

RT = RS + ST

77 = 6y + 3 + 5y + 8

Add the like terms

11y + 11 = 77

11y = 77 - 11

11y = 66

y = 66/11

y = 6

The value of y = 6

The length of RS = 6y + 3

= 6×6 + 3

= 36 + 3

= 39 units

The length of the line ST = 5y + 8

= 5×6 + 8

= 30 + 8

= 38 units

Hence, from the given figure

a) The value of y = 6

b) The length of the line RS = 39 units

The length of the line ST = 38 units

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Answer: 6 dollars

Step-by-step explanation:

Freida would have earned at the end of the year an interest of $6 for the $200  investment at 3% interest for 1 year.

The principle amount is $200

The saving account earns a interest of 3%

We need to calculate that Frieda have earned at the end of the year.

Interest = PRT/100

where p is principle

r is rate of interest

and t is the time period

= 200 x 3 x 1 / 100

= 6

Therefore, Freida would have earned an interest of $6 for the $200  investment at 3% interest for 1 year.

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On the coordinate (0,7) the value of P is maximum 280.

What is a Linear Inequality?

In mathematics, inequality denotes a mathematical expression in which neither side is equal. In Math, an inequality occurs when a connection produces a non-equal comparison between two expressions or two integers.

Solution:

First of all to solve the Linear Inequality we need to plot the graph of the given equations.

Kindly find the attached graph

To maximise the equation P = 30x + 40y

we need to find the corner values of x and y.

According to the graph, the corner values of (x,y) are

(5,0), (3,4) and (0,7)

putting the values in the equation P = 30x + 40y

at x = 5 and y = 0

P = 150

at x = 3 and y = 4

P = 250

at x = 0 and y = 7

P = 280

So, on the cordinate (0,7) the value of P is maximum i.e. 280.

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Answer:

nik

Step-by-step explanation:

Answer:

[tex]m=6[/tex]

Step-by-step explanation:

Start by subtracting 3 from both sides

[tex]15=2m+3\\15-3=2m+3-3\\12=2m[/tex]

Now, divide both sides by 2!

[tex]\frac{12}{2}=\frac{2}{2}m\\ 6=m\\ m=6[/tex]

Answer:

m=6

i think this help you

The y-coordinate of the y-intercept of the polynomial function is -36.

Given:

polynomial function defined below.

f(x) = (x + 6) (5x² + 2)(x − 3)

To find y intercept put x = 0 in the function.

y = (0+6)(5*0^2+2)(0-3)

= 6*(5*0+2)*(-3)

= 6*(0+2)(-3)

= 6*2*(-3)

= 12(-3)

= -36

Therefore The y-coordinate of the y-intercept of the polynomial function is -36.

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Answer:

Boss's statement is not misleading.

Explanation:

To find the median, we need to find the middle number.

8.00, 8.50, 9.00, 9.50, 10.00, 23.50

9.00 and 9.50 are in the middle.

And in the middle of those two is 9.25.

Step-by-step explanation:

Let us identify which quadratic function is positive. Yeah, let's start.

Y = [tex]{ \red{ \sf{2 {x}^{2} - 17x + 30}}}[/tex]

By using factorisation method,

[tex]{ \red{ \sf{2 {x}^{2} - 12x - 5x + 30}}}[/tex]

Take common factors

[tex]{ \red{ \sf{2x(x - 6) - 5(x - 6)}}}[/tex]

[tex]{ \red{ \sf{(2x - 5)}}} \: \: \: \: \: \: \: || \: \: \: \: \: { \red{ \sf{(x - 6)}}}[/tex]

[tex]{ \red{ \sf{2x - 5 = 0}}} \: \: || \: \: { \red{ \sf{x - 6 = 0}}}[/tex]

[tex]{ \red{ \sf{2x = 5}}} \: \: \: \: \: \: \: \: \: || \: \: \: \: { \red{ \boxed{ \green{ \sf{x = 6}}}}}[/tex]

[tex]{ \red{ \sf{{ \frac{ \cancel2}{ \cancel2}x}}}} = { \red{ \sf{ \frac{5}{2}}}}[/tex]

[tex]{ \red{ \boxed{ \green{ \sf{x = \frac{5}{2}}}}}} [/tex]

____________________________________

Y = [tex]{ \blue{ \sf {{ - x}^{2} - 6x - 8}}}[/tex]

By using factorisation method,

[tex]{ \blue{ \sf{ - {x}^{2} - 2x - 4x - 8}}}[/tex]

Take common factors

[tex]{ \blue{ \sf{ - x(x + 2) - 4(x + 2)}}}[/tex]

[tex]{ \blue{ \sf{( - x - 4)}}} \: \: \: \: \: || \: \: \: \: \: { \blue{ \sf{(x + 2)}}}[/tex]

[tex]{ \blue{ \sf{- x - 4 = 0}}} \: \: \: \: \: || \: \: \: \: \: { \blue{ \sf{x + 2 = 0}}}[/tex]

[tex]{ \blue{ \boxed{ \green{ \sf{x = -4}}}}} \: \: \: \: \: || \: \: \: \: \: { \blue{ \boxed{ \green{ \sf{x = -2}}}}}[/tex]

Hence, the first quadratic function is positive and second quadratic function is negative.

Answer:

[tex]\textsf{$y = 2x^2 - 17x + 30$: \quad $\left(-\infty, \dfrac{5}{2}\right) \cup (6, \infty)$}[/tex]

[tex]\textsf{$y = - x^2 - 6x - 8$: \quad $\left(-\infty, -4\right) \cup (-2, \infty)$}[/tex]

Step-by-step explanation:

A function is positive when it is above the x-axis, and negative when it is below the x-axis.

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

Given quadratic equation:

[tex]y = 2x^2 - 17x + 30[/tex]

Factor the equation:

[tex]\implies y = 2x^2 - 17x + 30[/tex]

[tex]\implies y = 2x^2 - 5x-12x + 30[/tex]

[tex]\implies y=x(2x-5)-6(2x-5)[/tex]

[tex]\implies y=(x-6)(2x-5)[/tex]

The x-intercepts of the parabola are when y = 0.

To find the x-intercepts, set each factor equal to zero and solve for x:

[tex]\implies x-6=0 \implies x=6[/tex]

[tex]\implies 2x-5=0 \implies x=\dfrac{5}{2}[/tex]

Therefore, the x-intercepts are x = ⁵/₂ and x = 6.

The leading coefficient of the given function is positive, so the parabola opens upwards.  

The function is positive when it is above the x-axis.

Therefore, the function is positive for the values of x less than the smallest x-intercept and more than the largest x-intercept:

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

Given quadratic equation:

[tex]y = - x^2 - 6x - 8[/tex]

Factor the equation:

[tex]\implies y = - x^2 - 6x - 8[/tex]

[tex]\implies y = -(x^2 +6x +8)[/tex]

[tex]\implies y = -(x^2 +4x +2x+8)[/tex]

[tex]\implies y = -((x(x+4)+2(x+4))[/tex]

[tex]\implies y = -(x+4)(x+2)[/tex]

The x-intercepts of the parabola are when y = 0.

To find the x-intercepts, set each factor equal to zero and solve for x:

[tex]\implies x+4=0 \implies x=-4[/tex]

[tex]\implies x+2=0 \implies x=-2[/tex]

Therefore, the x-intercepts are x = -4 and x = -2.

The leading coefficient of the given function is negative, so the parabola opens downwards.  

The function is negative when it is below the x-axis.

Therefore, the function is negative for the values of x less than the smallest x-intercept and more than the largest x-intercept:

Answer:

  (-2, -5), (2, 11)

Step-by-step explanation:

You want the coordinates of the points on the curve y = x³ +3 where the tangent lines are parallel to y = 12x -1.

The slope of the tangent line is the x-coefficient in its equation: 12.

The slope of the curve is given by its derivative:

  y' = 3x²

We want the x-values where the slope is 12. These are the solutions to ...

  12 = 3x²

  4 = x² . . . . . . . . . . divide by 3

  x = ±√4 = ±2 . . . . . take the square root

The coordinates of the points with x = ±2 are ...

  y = (±2)³ +3 = ±8 +3 = {-5, 11}

The tangent points are (-2, -5) and (5, 11).

__

Additional comment

The attached graphs and table show the solutions to y'=0 and the corresponding point locations. It also shows the tangent line equations (in point-slope form).

Considering the sine function in this problem, we have that:

The general sine function has the definition presented as follows:

f(x) = asin(b(x+c))+d.

The coefficients are given as follows:

For this problem, the function is:

h(θ ) = 8.5 sin (θ + 180°) + 40

The amplitude is of:

a = 8.5.

The function should oscillate between:

-8.5 and 8.5.

However, with the vertical shift of 40, the minimum and maximum values are given as follows:

The measure of each cycle of the cosine function is of:

2π = 360º.

The function has a phase shift to the right of 180º, hence the graph is given by the image at the end of the answer, for two cycles, that is, between 0 and 4π.

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Answer: y=-2x²-6x

Step-by-step explanation:

Its x-intercepts are 0 and -3, and the graph goes through the point (-1,4)

Hence we have three coordinates of the equation y=ax²+bx+c    (1):

                                    (0,0)   (-3,0)   (-1,4)

Let's substitute these coordinates into formula (1):

[tex]0=a(0)^2+b(0)+c\\0=a(-3)^2+b(-3)+c\\4=a(-1)^2+b(-1)+c\\\\0=0+0+c\\0=9a-3b+c\\4=a-b+c\\\\0=c\\0=9a-3b+0\\0=a-b+0\\\\c=0\\9a-3b=0\ \ (1)\\a-b=4\ \ \ \ \ (2)\\\\c=0\\\\[/tex]

Divide both parts of the equation (1) by 3 and multiply both parts of the equation (2) by -1: :

[tex]3a-b=0\\-a+b=-4\\\\[/tex]

Sum these equations:

[tex]2a=-4[/tex]

Divide both parts of the equation by 2:

[tex]a=-2[/tex]

We substitute the value of a=-2 into equation (2):

[tex]-2-b=4\\[/tex]

Divide both parts of the equation by -1:

[tex]2+b=-4\\\\2+b-2=-4-2\\\\b=-6[/tex]

[tex]Thus, \\\\y=-2x^2-6x+0\\\\y=-2x^2-6x[/tex]

Vertical angles are opposite of each othe. Attached is a picture of how it looks:

I hope this helps!

Answer:

6

Step-by-step explanation:

The cardinal number of a finite set is the number of elements of the set.

cardinal number = 6

The number 49 is a composite number because it has more than two factors.

A prime number is a natural number greater than one that cannot be calculated as the product of two smaller natural numbers. A composite number is a natural number greater than one that is not prime. 5 is prime, for example, because the only ways to write it as a product, 1 5 or 5 1, involve 5 itself.

Numbers with more than two factors are known as composite numbers. Non-prime numbers are composite numbers because they can be divided by more than two numbers.

A positive integer is a composite number. which is not the case (i.e., which has factors other than 1 and itself). The first few composite numbers (sometimes abbreviated as "composites") are 4, 6, 8, 9, 10, 12, 14, 15, and 16.

A composite number is one that can be formed by multiplying two smaller positive integers. It is a positive integer with at least one divisor other than 1 and itself. Every positive integer is either composite, prime, or the unit 1, so composite numbers are those that are neither prime nor a unit.

In this case, the factor of 49 are 1, 7 and 49. Therefore, it's a composite number.

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Answer:

0.6

Step-by-step explanation:

The model’s distances isn't proportional to the actual dimensions of the solar system as B. No, because the ratios of model length to actual distance are different for the two planets.

Ratio demonstrates how many times one number can fit into another number. It is used to show the comparison between two or more things

In this case, in model, the distance from the sun to Earth is 7 inches and the distance from the sun to Neptune is 19 inches. This can be illustrated as:

= 7/19

= 0.368

If the actual distance from the sun to Earth is 91.549 million miles and the actual distance from the sun to Neptune is 2,780.5 million miles, the ratio is:

= 91.549 / 2780.5

= 0.0329

Therefore, since they're different numbers, the information doesn't illustrate a proportional ratio.

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The expression that represents the quotient of the given model is x + 5. The correct option is C. x + 5

From the question, we are to determine the expression that represent the quotient of the given model

From the given model, we can write that

x | x² + x + x + x + x + x

Dividing by using the long division

  x + 1 + 1 + 1 + 1 + 1      

x | x² + x + x + x + x + x

Thus, the quotient of the expression is

x + 1 + 1 + 1 + 1 + 1

Further simplification,

NOTE: 1 + 1 + 1 + 1 + 1 = 5

Then,

The expression x + 1 + 1 + 1 + 1 + 1  becomes

x + 5

Hence, the expression is x + 5

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The diagram that matches the given situation is as shown below.

The correct answer is an Option C

We know that, in the mapping of functions, we map certain parameters to a set of other parameter functions.

In this question, we have been given the function h relates Kami's age in years to her height in inches on her birthday that year.

It means that her ages would be one-one the left to map her height. that means there were 2 times were despite her age difference, her height remained the same.

From the given options, the correct one that represents the required mapping is:

h(14) = 64

h(15) = 64

Therefore, the diagram that matches the given situation is as shown below.

The correct answer is an Option C

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A statement of given information can be used in a two column proof

The two-column proof is summarized in the statement and reason columns, and each statement must have a verified reason. Two-column proof reasons are usually given information, vocabulary definitions, hypotheses, and previously proven theorems.

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3. The amount of retained earnings transferred to the paid-in capital accounts (capitalized) for the stock dividend is $72,000.

4. The per-share cost of the treasury stock purchased is $10.

5. The net income earned by the Atticus Group this year was $217,500.

Stock dividends do not affect the cash account, unlike cash dividends.

Instead, the deduction is made from the retained earnings.

When the stock dividends are distributed, they are capitalized to the paid-in capital accounts (common stock and additional paid-in capital).

January 5 Dividend $17,500 Dividends Payable $17,500 (35,000 x $0.50)

Retained Earnings $17,500 Dividend $17,500

March 20 Treasury Stock $20,000 Paid-in Capital in Excess $30,000 Cash $50,000 ($50,000/5,000)

April 5 Dividend $15,000 Dividends Payable $15,000 (30,000 x $0.50)

Retained Earnings $15,000 Dividend $15,000

July 5 Dividend $15,000 Dividends Payable $15,000 (30,000 x $0.50)

Retained Earnings $15,000 Dividend $15,000

July 31 Stock Dividend $72,000 Dividends Issuable $72,000 (30,000 x 20% x $12)

Retained Earnings $72,000 Stock Dividend $72,000

August 14 Dividends Issuable $72,000 Common Stock $24,000 Paid-in Capital in excess of par value $48,000

October 5 Dividend $18,000 Dividends Payable $18,000 (36,000 x $0.50)

Retained Earnings $18,000 Dividend $18,000

Ending balance  $440,000

Add:

Dividend $17,500

Dividends $15,000

Dividends $15,000

Dividends $72,000

Dividends $18,000 $137,500

Less Beginning balance $360,000

Net income = $217,500

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Refer to the attachment for the required table:

What is the unit rate?

A unit rate is a cost for only one of anything. This is expressed as a ratio with a denominator of 1. For instance, if you covered 70 yards in 10 seconds, you did so at an average speed of 7 yards per second. Although both of the ratios—70 yards in 10 seconds and 7 yards in one second—are rates, only the latter is a unit rate.

From the table,

For 0 hours, distance = 15 miles

For 1 hour, distance = 80 miles

Difference between distances= 80-15=65 miles

Since it is given that, it is at a constant rate,  for every hour there is an increase of 65 miles in distance.

The completed table is shown in the attachment.

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By taking a quotient between the lengths, we will see that 98 pieces of 1/4 foot can be made.

We know that the total length of the rope is (24 + 1/2) ft, to see how many pieces of 1/4 feet we can take from that rope, we need to take the quotient between the total length and the length of the pieces.

It gives:

Q = (24 + 1/2)ft/(1/4)ft = 4*(24 + 1/2)

Q = 4*24 + 4*(1/2)

Q = 96 + 4/2

Q = 96 + 2 = 98

So 98 pieces of 1/4 foot can be made.

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The sum of angles at a point is equal 360 degrees and using that, the value of x is 261 degrees.

Angles around a point describes the sum of angles that can be arranged together so that they form a full turn. Angles around a point add to 360°.

In this question, when we sum all angles up, it will give us the sum of 360 degrees.

20 + 40 + 39 + x = 360

x + 99 = 360

x = 360 - 99

x = 261

x has a value of 261 degrees.

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Answer:

Below

Step-by-step explanation:

All of the angles labeled sum up to a right angle = 90 °

x+4     +      x+4        +  x+4      = 90

3x + 12 = 90

3x = 78

x = 26°

Answer:

x = 26

Step-by-step explanation:

from the diagram

∠ BFC + ∠ CFD + ∠ DFE = ∠ BFE , that is

x + 4 + x + 4 + x + 4 = 90

3x + 12 = 90 ( subtract 12 from both sides )

3x = 78 ( divide both sides by 3 )

x = 26

Answer: 210 liters

Step-by-step explanation: