Leo has three times as many colored marbles as he has clear-glass marbles. In total, he has 60 marbles. How many clear-glass marbles does he have?

If;

then these variables must meet the following conditions below;

In rational expressions (fractional numbers), if the denominators are equal, arithmetic operations are performed with the numerators. Therefore;

If we add both equations at the same time, we get the following result;

Now that we have found the unknown x, we can find the unknown y.

Now let's write our fraction pairs.

Answer:

[tex]\frac{5}{11}[/tex] and [tex]\frac{2}{11}[/tex]

Step-by-step explanation:

let the 2 fractions be x and y , x > y , then

x + y = [tex]\frac{7}{11}[/tex] → (1)

x - y = [tex]\frac{3}{11}[/tex] → (2)

add the 2 equations term by term to eliminate y

2x + 0 = [tex]\frac{10}{11}[/tex]

2x = [tex]\frac{10}{11}[/tex] ( divide both sides by 2 )

x = [tex]\frac{5}{11}[/tex]

substitute x = [tex]\frac{5}{11}[/tex] into (1) and solve for y

[tex]\frac{5}{11}[/tex] + y = [tex]\frac{7}{11}[/tex] ( subtract [tex]\frac{5}{11}[/tex] from both sides )

y = [tex]\frac{2}{11}[/tex]

the pair of fractions are [tex]\frac{5}{11}[/tex] and [tex]\frac{2}{11}[/tex]

Nathan's salary is $48 and Will's salary which three times of Nathan's salary is $144.

What is salary?

An employment contract may include a salary clause as a type of recurring payment from an employer to an employee. In contrast, piece wages are paid separately for each job, hour, or other unit rather than on a regular schedule. Salary can also be seen from the perspective of operating a corporation as the expense of obtaining and keeping employees to carry out operations; this is known as a personnel expense or salary expense. Payroll accounts are used in accounting to record salaries.

It is given in the question that Will's salary is three times Nathan's salary.

So, lets assume that Nathan's salary is X it implies that Will's salary will be 3 times X = 3X

Together they earn $ 192.

So,

X + 3X = 192

4X = 192

X = 192/4

X = 48

Therefore, Nathan's Salary is $48

Since, Will's salary is 3 times of Nathan's salary,

So,

Will's salary = 3 (48) = 144

Therefore, Will's Salary is $144

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There is a mistake in the first step. The correct way to add the linear expression is (−3.78b + 12) − (4.82b − 16) = -8.6b + 18

An expression is used to show the relationship between the variables.

The linear expression to add is as follows: (−3.78b + 12) − (4.82b − 16)

Firstly we open the bracket on the right side by multiplying the negative sign by the numbers in the brackets.

(−3.78b + 12) − (4.82b − 16)

−3.78b + 12 - 4.82b + 16

Combine like terms

−3.78b + 12 - 4.82b + 16

-3.78b - 4.82b + 12 + 16

Add the like terms

-3.78b - 4.82b + 12 + 16

-8.6b + 18

Therefore, she made the mistake in the first step.

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Answer: 2200

Step-by-step explanation:

33 1/3 of 66

Approximate value of d = 4.29 cm.

The Cosine Rule states in trigonometry that the square of the length of any side of a given triangle is equal to the sum of the squares of the other sides minus twice the product of the other two sides multiplied by the cosine of angle contained between them. Cosine rule is also known as the law of cosines or the Cosine Formula.

In Δ ADR , AR = d, DR = 8 cm. AD = 5 cm. ∠D = 28°

By using cosine rule,

AR² = AD² + DR² - 2 AD ×DR CosD

AR² = 5² + 8² - 2×(5)×(8) × Cos 28°

AR² = 25 + 64 - 80 Cos 28°

AR² = 89 - 80 Cos 28°

AR² = 89 - 80 × (0.8829)

AR² = 89 - 70.6358

AR² = 18.3641

AR = 4.29 cm. = d

Thus, approximate value of d = 4.29 cm.

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Answer:

Martha exercises 310 minutes more than Greg in a 31-day month!

Step-by-step explanation:

30x

40x

Where x equals the number of days.

Let's plug it in:

30(31) = 930

40(31) = 1240

Let's subtract:

1240 - 930 = 310

MEANING Marta exercises 310 minutes more than Greg in a 31-day month!

Answer:

24

Step-by-step explanation:

If the ratio of racers to divers is 6:2 then compare that to 18:x

6 times 3 is 18

2 times 3 is 6

x is 6

Now add 6 and 18

You get 24

Answer: Look at photo. Your y intercept is -1 and the line goes up 4 and right 1.

Step-by-step explanation: Look at your last number, the -1. That should be on the y axis. Put that number there and then take 4x which can also be read as 4/1x and from the point of -1, go up 4 and right 1.

The slope of the line is 3/7.

The slope of line will be calculated using the formula :

Slope = [tex] \frac{y_{2} - y_{1}}{x_{2} - x_{1}} [/tex]

The first point is (-2, 7) and second point is (-9, 4). So, [tex] y_{2}[/tex] = 4, [tex] y_{1}[/tex] = 7, [tex] x_{2}[/tex] = -9 and [tex] x_{1}[/tex] = -2. Keep the values in formula to find the values of slope of the line.

Slope = (4 - 7)/(-9 - -2)

Performing subtraction in numerator and denominator

Slope = -3/-7

Cancelling the negative signs we get -

Slope = 3/7

Thus, the slope of the line is 3/7.

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Answer:

d

Step-by-step explanation: d

Answer:

The last one

Step-by-step explanation:

this is really hard to read but you have to see which y values increase by a constant amount. Only the last case is linear in which each value increases by 3

The slope of the line = change in y / change in x = 4/3.

The slope of a line is the rise over the run, which is the change in y/change in x = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]

To calculate the slope of the line that is given, chose any two points on the line as plotted in the given graph, say:

(30, 20) = [tex](x_1, y_1)[/tex]

(60, 60) = [tex](x_2, y_2)[/tex]

Substitute each of these values into the slope formula, [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]:

Slope for the given line (m) = (60 - 20)/(60 - 30)

Slope for the given line (m) = 40/30

Slope for the given line (m) = 4/3.

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We need to use simple division to solve the problem. The number of cards each friend received is 11.

It is said that Landon has 56 cards, he kept 12 cards for himself, so we can subtract 12 cards from the whole lot to get the total number of cards he distributes among his friends.

56-12=44

There are 44 cards that he will distribute among his friends equally, we can get that by simply dividing the total number of cards by the number of friends which is 4.

number of cards for each friend=44/4=11

Therefore the number of cards each friend received is 11.

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To determine the price per ounce walter paid to ship the package you can use cross multiplication.

If 5.5 ounces ______$2.53

Then 1 ounce______$x

He will pay $0.46 per ounce

Answer:

w = 135

Step-by-step explanation:

-27 = -w/5

multiply both sides by 5:

5(-27) = 5(-w/5)

- 135 = -w

divide both sides by -1:

- 135/-1 = -w/-1

w = 135

[tex]\sqrt{\cfrac{4x^2}{3y}}\implies \cfrac{\sqrt{4x^2}}{\sqrt{3y}}\implies \cfrac{\sqrt{2^2x^2}}{\sqrt{3y}}\implies \cfrac{2x}{\sqrt{3y}}[/tex]

Answer:

[tex]\frac{2x}{\sqrt{3y} }[/tex]

Step-by-step explanation:

Hope that's helps.

Answer:

  27. 48°, 132°

  28. The expressions resolve to both angles being 0°, a contradiction to the lines being distinct.

Step-by-step explanation:

Given a figure showing parallel lines crossed by a transversal with marked angles, you want to know (27) the measures of consecutive interior angles that have a ratio of 4:11, and (28) the contradiction in corresponding angles being marked (60-2x)° and (2x-60)°.

The two marked angles are consecutive interior angles, so are supplementary. Using x for the smaller angle value, we can write the equation ...

  x/(180-x) = 4/11 . . . . . the given ratio of the two angles

Multiplying by 11(180-x) gives ...

  11x = 4(180-x)

  15x = 4(180) . . . . add 4x and simplify

  x = 48 . . . . . . . . divide by 15

Then the obtuse angle is ...

  180 -48 = 132

The measures of the angles are ∠1 = 48°, ∠2 = 132°.

The two marked corresponding angles are congruent, so ...

  (60 -2x)° = (2x -60)°

  4x = 120 . . . . . . . . . . . divide by °, add 2x+60

  x = 30 . . . . . . . . . . divide by 4

  60 -2x = 60 -2(30) = 0

  2x -60 = 2(30) -60 = 0

The marked values require the angles to be 0°, which means the transversal is coincident with each of the "parallel" lines.

The given angle values require the lines not to be distinct, as the diagram shows they are.

Dennis's curtain company needs 252 feet long fabric to make 63 curtains.

Given,

The length of a curtain = 43 inches

Number of curtains they want to make = 63

We have to find the length of fabric in foot needed to make 63 curtains.

1 foot = 1/12 inches

Now,

The total length of fabric needed in inches = Number of curtains × Length of 1 curtain = 63 × 48 = 3024 inches

Convert this into feet.

That is,

3024 × 1/12 = 252 feet.

Therefore,

Dennis's curtain company needs 252 feet long fabric to make 63 curtains.

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Answer: 174

Step-by-step explanation: ok so we divide 220 by 11 to get 20 and times that by two to get 20 children on this journey then see that all children paid and 70 percent of adults so 70 percent of 220 is 154 and then 154 + 20 is 174 so thats the number of fares paid

Answer:

He can buy 8 pounds

Step-by-step explanation:

13.75/5=2.75

22/2.75=8 or 8 pounds the to check your answer 2.75x8=22

The train should travel at a speed of 30√5 miles/hour on a 300​-mile trip to minimize the total cost for the​ trip?

Given the cost per hour for fuel to run is v^2/15 dollars:

Labor cost=$300 per hour

Calculate the velocity to travel on a 300-miles trip:

Total time t=Distance/speed

                  =300/v

                 t=300/v

Total cost=(fixed cost*time)+(variable cost*time), where fixed cost is $300 per hour and variable cost is v^2/15 dollars , and time t=300/v

Total cost=(300*300/v)+((v^2/15)*(300/v))

               =(90000/v)+(300v/15)

Now, to minimize the total cost on a 300-mile trip, we differentiate the total cost with respect to the velocity:

Let the d/dv of total cost be C(v):

C(v) =(-90000/v^2+300/15=0

(-90000/v^2+300/15)=0

90000/v^2=300/15

90000/v^2=20

v^2=90000/20

v^2=4500

v=√4500

v=30√5 miles/hour

Hence, the speed is 30√5 miles/hour

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the dimensions of the box that minimize the amount of material used is 4.641cm by 4.641cm by 2.32cm

Let the side of the square base be x

h be the height of the box

Volume V = x²h

50 = x²h

h = 50/x² ..... 1

Surface area =  x² + 2xh + 2xh

Surface area S =  x² + 4xh  ...... 2

Substitute 1 into 2;

From 2; S =  x² + 4xh

S = x² + 4x(50/x²)

S = x² + 200/x

To minimize the amount of material used; dS/dx = 0

dS/dx = 2x - 200/x²

0 = 2x - 200/x²

0 = 2x³ - 200

2x³ = 200

x³ = 100

x = ∛100

x = 4.6416cm

Since V = x²h

50 = 4.642²h

h = 50/21.548

h = 2.32cm

Hence the dimensions of the box that minimize the amount of material used is 4.641cm by 4.641cm by 2.32cm

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Yes, I do agree with Jamie.

1 is NEITHER a prime number NOR a composite number.

Reason for agreeing:-

We know that a PRIME NUMBER is any given number that has only one as a factor. I.e it is only divisible by 1 AND ITSELF.

And, a COMPOSITE NUMBER is any number that is divisible by a number other than one and itself.

Here in the case of 1, we see that it is divisible by 1 and itself, and since it cannot have any other factor we can't put in either of the two categories

The domain of a function are the values for which the function is defined or in the other words, it is the set of all possile values that the function accepts.

Therefore:

Answer:

3/10 hope this helps you answer your question!

Let g = cost of granola bars

b = cost of a bottle of water

10g+12b = 23

5g + 4b = 10

Multiply the second equation by -2

-10g -8b = -20

Add this to the first equation

10g+12b = 23

-10g -8b = -20

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

4b = 3

Divide by 4

4b/4 = 3/4

b = 3/4 or .75

Now find g

5g + 4(3/4) = 10

5g + 3 = 10

5g = 7

g = 7/5

g = 1.4

We want to find 1g+ 1b

1.4+ .75 =2.15

Part B

We want our income to be at least 150

The cost of granola bars is 1.4 and we are selling x of them

The cost of water is .75 and we are selling y of them

It must be at least >=

1.4x + .75y >= 150

The four functions with a local minima are:

y = x², y = |x|, y = sin x, y = cos x

A function f(x) has a local minima if its second derivative, f''(x) > 0 at the point where f'(x) = 0.

We use this to find which among the functions y = x, y = x², y = x³, y = |x|, y = 1/x, y = eˣ, y = √x, y = ln x, y = sin x, y = cos x, y = int(x), y = 1/(1+e⁻ˣ) has a local minima.

y' = 1. There is no point x such that y' = 0. So it has no local minima.

y' = 2x

y' = 0

⇒ 2x = 0

⇒ x = 0

y'' = 2 > 0

So y = x² has a local minima at x = 0

y' = 3x²

y' = 0

⇒ 3x² = 0

⇒ x = 0

y'' = 6x = 0 at x = 0

So y = x³ has no local minima.

i.e., y = x, when x ≥ 0 and y = -x , when x < 0

So y ' = 1, when x ≥ 0 and y' = -1, when x < 0

But at x = 0, y = 0 and y' = 0.

Now y'' = 0 everywhere. But the graph of y = |x| clearly shows that y = |x| has a local minimum at x = 0.

y' = -1/x²

Here, y' is nowhere zero and hence doesn't has a local minima.

y' = eˣ

 eˣ is nowhere zero and hence it does not has a local minima.

y' = 1/2√x

Here also  y' is nowhere zero and hence it does not has a local minima.

y' = 1/x

Here also y' is  nowhere zero and hence it does not has a local minima.

y' = cos x

y' = 0

⇒ cos x = 0

⇒ x = (2n+1)π/2, n = 0,1,2,....

y'' = -sin x

-sin ((2n+1)π/2)  = -1, when n = 0,2,4,... and -sin ((2n+1)π/2)  = 1, when n = 1,3,5,....

So y = sin x has local minima at x = (2n+1)π/2, where n = 1,3,5,....

y' = -sin x

y' = 0

⇒ -sin x = 0

⇒ x = nπ

y'' = -cos x

-cos(nπ) = (-1)ⁿ⁺¹

So, -cos(nπ) = 1, when n = 1,3,5,.... and -cos(nπ) = -1, when n = 0,2,4,...

Hence y = cos x has local minima at x = nπ with n = 1,3,5,....

y' = x

y' = 0

⇒ x = 0

y'' = 1 >0

So y = int (x) has local minima at x = 0

y' = e⁻ˣ/(1+e⁻ˣ)²

y' = 0

⇒ e⁻ˣ/(1+e⁻ˣ)² = 0

⇒ e⁻ˣ = 0

⇒ 1/eˣ = 0 which is not possible anywhere.

Hence y = 1/1+e⁻ˣ has no local minima.

Finally the four functions with local minima are:

y = x², y = |x|, y = sin x, y = cos x

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Answer:

you gave no context....so ill just guess 3.

The set  S:{42} will make the inequality false.

By definition, one can apply any monotonically rising function to both sides of an inequality without affecting how they relate to one another (provided that both expressions are in the domain of that function).

Given inequality is :

3/8 m - 9 < 1/4 m + 2

Solving the inequality we get:

or, m < 40

Therefore of all the elements of the set 42 makes the inequality false.

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