15. Write an equation that goes through point (-6, 8) and has a y-intercept of -4.

a)P(all seniors) =(25C3)/(30C3) =0.5665

b)P(All Juniors)=(5C3)/(30C3) =0.0025

c)P(2 senior and 1 Junior) =(25C2)(5C1)/(30C3) =0.3695

d)P(1 senior and 2 Junior) =(25C1)(5C2)/(30C3) =0.0616

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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!

C is the correct option

Here, we want to selct which of the plotted points in the graphs correctly represent the given points

The given points are (2,21/2) and (-1 1/2,-4)

As we can see on the graphs, there are four different marked points

We just need to select the graph that contains the points

What the point (2, 2 1/2) means is that we have point 2 on the x-axis and trace point 2 1/2 on the y-axis

This point is missing in the first two options

However, on the third option C, we can see this option

We can check if the second option is there too

(-1 1/2 , -4)

We have -1 1/2 on the x-axis and -4 on the y-axis

We can see this on the third option too

So option C is our correct answer

Step-by-step explanation:

Another music store rents trombones for $30 per month plus a yearly fee of $48. Which deal is better? Should Maria change her rental plan?

Part A: Maria needs a trombone for only 12 months. Renting the trombone costs $34 per month. She can buy the trombone for $495. Should she buy or rent the trombone? Explain.

Option 1, SHOP 1: [at $30 a month] When Maria rents for a year, or x = 12 months

This can be described by the equation:

30x + 48

where x = number of months rented

30(12) + 48

= $408

___________

Option 2, SHOP 2:  [at $34 a month] When Maria rents for a year, or x = 12 months

This can be described by the equation:

34x + 48

where x = number of months rented

34(12) + 48

= $456

___________

Option 2, buy: for $495

ANALYSIS:

Because Maria only needs the instrument for a year (12 months), Maria would do best to rent her instrument from option 1, shop 1 (renting at $30 a month + $48 yearly fee). Purchasing the instrument is the most costly.

Should Maria need the instrument longer than a year, then the option preference would change.

Answer: 2200

Step-by-step explanation:

33 1/3 of 66

ANSWER

EXPLANATION

We want to write the number given in scientific notation. The number is 80,023

Putting a number in scientific notation involves writing that number as a product of a number between 1 and 10 and a power of 10.

We do this by moving the decimal point from behind the last digit of the number (3) to just after the first digit (8).

We move the decimal point 4 times to the left, that is why the power of 10 is +4.

So, we have that 80,023 becomes:

The values of x are x = 13 and x = 1 when we have [tex](x-7)^{2} = 36[/tex].

According to the question,

We have the following information:

[tex](x-7)^{2} = 36[/tex]

Now, we will solve the expression on the left hand side using an identity.

The identity that will be used here is [tex](a-b)^{2}= a^{2}+ b^{2} -2ab[/tex].

In this case, we have a = x and b = 7.

[tex]x^{2}+ 7^{2} -2x*7[/tex] = 36

[tex]x^{2} +49-14x = 36[/tex]

Moving 36 from the right hand side to the left hand side:

[tex]x^{2} +49-14x-36 = 0\\x^{2} -14x+13 = 0[/tex]

Now, to find the values of x, we will factorize this expression by splitting the middle term such that the sum of two terms is -14x and their multiplication is 13[tex]x^{2}[/tex].

The two terms will be -13x and -x.

[tex]x^{2} -13x-x+13 = 0\\[/tex]

Taking x common from the first two terms and -1 common from the last two terms:

x (x-13) -1(x-13) = 0

Taking (x-13) as common:

(x-13) (x-1) = 0

x-13 = 0 and x-1 = 0

x = 13 and x = 1

Hence, the values of x are 13 and 1.

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Step-by-step explanation:

x^3 =64

x^2+x=64( you can write x^3 like this .there is not problem with it )

x+x= root 64

2x= 8 ( 8×8=64)

x=8÷2

x = 4

Answer: 18 mins

Step-by-step explanation

there is 3600 secs in an hour so do the same for this.

6 mins is 360 secs and times 360 by 3 is 1080 and then double it they figure out how many mins is 2160 im sorry if thats confusing.

Answer:

d

Step-by-step explanation: d

The behaviors of the function in the intervals is given as follows:

a) Increasing: (-∞, -4) and (-3, -2).

b) Decreasing: (-4, -3) and (-2, ∞).

c) Constant: No interval.

Considering the graph of the function, we get that a function f(x) is increasing when it is "moving northeast", that is, to the right and up on the graph, meaning that when x increases, y increases.

Hence, in the context of this problem, considering the given graph the function is increasing on these following intervals:

Considering the graph of the function, we get that a function f(x) is decreasing when it is "moving southeast", that is, to the right and down on the graph, meaning that when x increases, y decreases.

Hence, in the context of this problem, considering the given graph the function is decreasing on these following intervals:

A function is constant when the graph is an horizontal line, that is, when changing the value of x causes no effect to the value of y, it remains constant.

Hence, there are no intervals in which the graph of the function is constant.

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1) Since the equation is y= -3x+3, let's fill in that table by plugging into them the given values for x

x | y= -3x +3 | y

-1 | y=-3(-1)+3 | 6

0 | | 3

1 | | 0

2| | -3

2) Let's plot that equation for points (-1,6) (0,3), (1,0) and (2,-3)

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]

Answer

x=10.

Step-by-step explanation:

-2.3x-4.2x=-66.3

-2.3+-4.2=-6.5x

-6.5x÷-6.5

-66.3÷-6.5

x=10.

Answer:

180

Step-by-step explanation:

9x20

Marilyn's capital gain is 73%.

Marilyn purchased 2,000 shares

$25.43 per share

She sold them for $44.10 per share

Solution:

Capital gain per share = 44.10 - 25.43 = $18.67

Capital gain  for  2,000 shares = 2000*18.67

= $37,340

Her capital gain is $37,340.

The price of 2000 shares she bought initially = 2,000*25.43

= $50,860

Her capital gain in percentage =  37,340/50,860*100

= 73.41

That is,

73%

Her capital gain is 73%.

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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:

[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.

Answer:

3/10 hope this helps you answer your question!

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

Answer:

7.25

Step-by-step explanation:

Barangay Maligaya is 28.5km

Since Ricardo traveled 12.75km by Jeep and 8.5km by tricycle and rest by hiking

Jeep = 12.75

Tricycle = 8.5

Hiking = 12.75 + 8.5

=21.25

Total= 28.5

=28.5 -21.25

= 7.25

A graph of the image of triangle V'W'X' after a rotation of 90° counterclockwise about the origin is: graph A.

A rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

In Geometry, rotating a point 90° about the origin in a counterclockwise (anticlockwise) would produce a point that has the coordinates (-y, x).

Note: Each interval on this graph represents 1 unit.

By applying a rotation of 90° counterclockwise to triangle VWX, the coordinates of the vertices of the image triangle V'W'X' include the following:

(x, y)                    →            (-y, x)

Point V = (-2, -4)   →     Point V' = (-(-4), -2) = (4, -2)

Point W = (-2, -2)   →    Point W' = (-(-2), -2) = (2, -2)

Point X = (-5, -4)   →  Point X' = (-(-4), -5) = (4, -5)

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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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The quadratic function of h (x) in vertex form will be;

⇒ h(x) = (x + 2)² − 3

What is substitution method?

To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.

Given that;

The values of x and h (x) for the quadratic function is given as;

x = -3, -2, -1, 0, 1, 2, 3,

h (x) = -2, -3, -2, 1, 6, 13, 22

Now,

Let the quadratic function is,

h (x) = ax² + bx + c

Substitute x = -3 and h (x) = -2 in above quadratic function we get;

h (x) = ax² + bx + c

- 2 = a × (-3)² + b × -3 + c

- 2 = 9a - 3b + c

And, Substitute x = -2 and h (x) = -3 in above quadratic function we get;

h (x) = ax² + bx + c

- 3 = a × (-2)² + b × -2 + c

- 3 = 4a - 2b + c

And, Substitute x = -1 and h (x) = -2 in above quadratic function we get;

h (x) = ax² + bx + c

- 2 = a × (-1)² + b × -1 + c

- 2 = a - b + c

After solving we get;

a = 1 , b = 4 and c = 1

Substitute all the values in above quadratic equation, we get;

h (x) = ax² + bx + c

h (x) = 1 × x² + 4x + 1

h (x) = x² + 4x + 1

h (x) = x² + 4x + 4 - 4 + 1

h (x) = (x + 2)² - 3

Thus, The quadratic function of h (x) in vertex form will be;

⇒ h(x) = (x + 2)² − 3

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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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