4) Which is the best deal?OA) $56 for 25 gallonsB) $32.05 for 15 gallonsO C) $51.29 for 23 gallonsOD) $22.50 for 10 gallons

Given:

Lucy needs to memorize words on a vocabulary list for Korean class.

Let the number of words on the list = x

She has memorized 20 of the words, which is four-fifths of the list.

So, we can write the following equation:

Solve the equation for (x), multiply both sides by 5/4

So, the answer will be:

The number of words on the list = 25

Given that:

Cost of the new plumbing fixtures = $160

Labor charge per hour = $50

Let x denotes the number of hours of labor. Then,

It represents the required relation.

By using properties of angles, it is obtained that

x = 18.5°, y = 37°

Angle

When two straight lines intersect, an angle is formed. The point of intersection is called the vertex of the angle and the lines are called the arms of the angle.

Here,

[tex]\angle COF = 90^{\circ}\\[/tex]

By the problem,

4x + 90  + 16 = 180 [Angle on a straight line]

4x + 106 = 180

4x = 180 - 106

4x = 74

[tex]\\x = \frac{74}{4}\\x = 18.5^{\circ}[/tex]

AB and CD are straight lines

[tex]\angle DOB = 16^{\circ}[/tex]  [Vertically opposite angle]

By the problem,

90 + 2y + 16 = 180 [ Angle on a straight line]

2y  + 106 = 180

2y = 180 - 106

2y = 74

[tex]y = \frac{74}{2}\\y = 37^{\circ}[/tex]

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The map, every 1-inch drawing represents 2.917 miles in reality, using conversation.

What is conversation ?

A unit's use depends on the context; for example, a room's area is expressed in metres, yet a pencil's length and thickness are expressed in centimetres and millimetres, respectively.

Therefore, converting one unit to another is necessary. We must first understand the link between units in order to comprehend the concept of unit conversion.

When addressing many problems in mathematics, unit conversion is necessary. Mathematical conversions are necessary to perform the necessary calculations.

In the map, every 1 inch drawing represents 2.917 miles in reality.  

the meaning of the unit rate. 3/ 10 in. = 7 /8 mi

1 in = (7/8) mi ÷ (3/10)

= 7/8 * (10/3) = 70/24

1 in = (70/24) mi

Hence the map, every 1-inch drawing represents 2.917 miles in reality.

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Solution

The hexagon given is a regular hexagon. With apothem of 15 in

Area of a hexagon =

Let us calculate the perimeter of the hexagon

From the triangle above,

First, divide the annual interest rate by 2 to find the semiannual interest rate:

Next, identify the number of periods when the 2.75% increase will be appliad. In a period of 10 years, there are 20 semiannual periods.

Each period, the initial investment gets multiplied by a factor of:

Over 20 semiannual periods, the initial investment will get multiplied by a factor of:

Therefore, after 10 years, the amount of money in the account is:

To the nearest cent, the amount of money in the account will be:

Answer:ez 90 degrees

Step-by-step explanation:

The given function is

This equation represents a parabola which is expressed in its vertex form

Where (h,k) is the vertex. Using this rule, the vertex of the given parabola would be (6,8).

Answer:

The polar form is

r = √11a

Explanation:

The given equation is

x^2 + y^2 = 11a

Recall,

x = rcosθ

y = rsinθ

By substituting these values into the equation, we have

(rcosθ )^2 + ( rsinθ)^2 = 11a

r^2cos^2θ + r^2sin^2θ = 11a

r^2cos^2θ + r^2sin^2θ - 11a = 0

By factorizing r^2, we have

r^2(cos^2θ + sin^2θ) = 11a

Recall, cos^2θ + sin^2θ = 1

Thus, we have

r^2 = 11a

Taking the square root of both sides,

r = √11a

The polar form is

r = √11a

start by writing the equation in standard form

then give values to x

for x=2

for x=4

Milo needs to cover 12 miles in 48.6 minutes, as the percentage.

What is percentage?

A percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one-hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified. A portion per hundred is what the percentage denotes. The percentage refers to one in a hundred. The % sign is used to denote it.

Milo can run 12 miles in 60 minutes.

She needs to reduce the time by 19%

So we have to calculate the 19%of 60

= 19/100* 60

=57/5 minutes

= 11.4

So the time he needs to achieve will be 60-11.4 = 48.6 minutes.

Hence, he needs to cover 12 miles in 48.6 minutes.

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B. graph B

Represents the quadratic equation y=x²-4x-12 with D > 0 . So the equation represents 2 zeros which comes to be 6 and -2.

What is Quadratic equation ??

A second-degree polynomial equation, which must contain at least one squared component, is what is known as a quadratic. Quadratic equations is another name for them. The quadratic equation's general form is as follows:

ax + by +c = 0

To draw the graph of quadratic equation:

Given quadratic equation,

x²-4x-12 = y

Put y = 0

So we get zeros as 6 and -2

Hence the graph will  cut the X axis at 6 and -2

We get the desired graph as graph B.

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y+1=6/11(x+4) is the equation in point-slope form of the line that passes through the points (7, 5) and (−4, −1).

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The given two points are  (7, 5) and (−4, −1)

m=-1-5/-4-7

=-6/-11

=6/11

The point slope intercept form is y- y₁=m(x-x₁) through (-4,-1)

y-(-1)=6/11(x-(-4))

y+1=6/11(x+4)

Hence, y+1=6/11(x+4) is the equation in point-slope form of the line that passes through the points (7, 5) and (−4, −1).

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Answer:

(1,0) (0,-2)

Step-by-step explanation:

For PART A: the height of the pole in the right angle triangle is 30 ft and the correct option is C

For PART B: the lenght of wire 1 in the right angle triangle is 45 ft and the right option is D

A right-angled triangle is a polygon of three sides having one angle as 90 degrees(right angle).

Part A

To calculate the height of the pole in the right angle triangle, we use the formula below.

Formula:

From the diagram,

Given:

Substitute these values into equation 1 and solve for P

Part B

Similarly, fine the length of wire 1, we use the formula below.

Formula:

From the diagram,

Given:

Substitute these values into equation 2 and solve for x

Hence, the height of the pole is 30 ft and the lenght of wire 1 is 45 ft.

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Number of women's are 9,078.83.

What is Proportional?

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

In​ 2005, 10.9 out of every 50 employees at a company were women.

Now,

Since, In​ 2005, 10.9 out of every 50 employees at a company were women.

Let number of women's in 41,646 total company​ employees = x

So, We can formulate by the definition of proportion as;

⇒ 10.9 / 50 = x / 41,646

Solve for x as;

⇒ 10.9 × 41,646 / 50 = x

⇒ x = 9,078.83

Thus, Number of women's are 9,078.83.

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The greatest number of plates Annie can arrange if she plans to use 8 apples and 20 apricots is 4 plates.

To find the greatest number of plates Annie can arrange, find the greatest common factor of and 20;

8 = 1, 2, 4, and 8

20 = 1, 2, 4, 5, 10, and 20

The greatest common factor of 8 and 20 is 4

Number of apples on each plate = 8/4

= 2

Number of apricots on each plate = 20/4

= 5

In conclusion, the greatest number of plates is 4 consisting of 2 apples and 5 apricots each.

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Answer:

Step-by-step explanation:

i am also confused with this one so...

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The probability of the company's order from first-time customers with the sample proportion less than 0.28 will be 0.6103.

Total percent of company’s orders from first-time customers are 35%

Probability of the company's orders from first-time customers are 35/100 = 0.35.

Total number of customers in the random sample is 62.

Minimum given probability of company’s order from first time customers is 0.28

And the minimum probability of company’s order not from first time customers will be 1 - 0.28 = 0.72

Therefore,

As per the given question, Let P(z<0.28) is the required probability, where

Z = (0.28 - 0.35)/sqrt(0.28x0.72/62)

  = (0.28 - 0.35)/sqrt(0.28x0.0112)

  =(0.28 - 0.35)sqrt(0.003250)

  = (-0.07)/sqrt(0.003250)

  = -0.07/0.057

  = -1.228

From the z-score, we can get P( z<0.28 ) = 0.6103 ( From standard normal table )

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The equation can be used for "the total cost of buying x chocolate bars, such that each one costs $3.50"

Here we have the linear equation:

y = 3.5*x

And we want to make a word problem that can be represented by this.

The simplest example would be something like "the total cost of buying x items of a cost equal to the constant of proportionality"

So let's suppose that there is a chocolate bar in a given store that costs $3.50 per unit.

So, if you buy x of these, the total cost will be modeled (in dollars) by the equation:

y = 3.50*x

Which is the same equation that we have above:

y = 3.5*x

Where the second 0 on the constant factor is trivial and can not be written.

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ANSWER

Yes, it can.

EXPLANATION

First of all, let us sort the data according to increasing value:

Time (minutes) 18 20 20 22 22 23 25 30

Duration (minutes) 38 40 42 41 42 44 47 52

As we can already see, the duration of the ride seems to increase as the amount of time after 8 am that she got on the bus.

This means that the Duration of the ride and the time Layne got on the bus have a linear relationship and so, YES, the duration of the ride can be represented as a function of the time Layne got on the bus.

Let's take a look at our triangle:

Using the law of cosines, we'll get that:

Solving for angle G, we'll get:

This way,

Answer:

x=25

vertical angles are congruent so

4x-25=75

+25

4x=100

÷4

x=25

Answer:

x = 25°

Step-by-step explanation:

We know that,

→ opposite angles are equal.

Forming the equation,

→ (4x - 25)° = 75°

Now the value of x will be,

→ (4x - 25)° = 75°

→ 4x = 75° + 25°

→ x = 100°/4

→ [ x = 25° ]

Hence, the value of x is 25°.

Solution

Area of the rectangle = length x breadth

A. Write an equation to showing relationship between x and y:

The equation for the relationship between x and y is

3x + 2y = 30

To calculate the periodic payment (PMT) we use the following formula:

Where "FV" is the Future Value, "i" is the interest rate, and "n" is the number of periods. Replacing the known values we get:

Solving the operations:

Step-by-step explanation:

Order from least to greatest. -0.36, 0.65 , - 8/15, 1/5

-0.36 = -0.36

0.65 = 0.65

- 8/15 = - 0.533333

1/5 = 0.2

least to greatest:

- 8/15 , -0.36 , 1/5 , 0.65

The momentum of the person is zero and the momentum of the bike is 1332.

A person is riding a 14 kg bike at velocity of 18m/s

The momentum of bike = mass x velocity

p = (14 + 60) 18

= 1332

The velocity of the person with respect to the bike is 0

p = mv

p = 60 x 0

p = 0

Therefore, the momentum of the person is zero and the momentum of the bike is 1332.

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Answer:

[tex]1\frac{5}{7}\text{ lb}[/tex]

Step-by-step explanation:

First, convert [tex]2\frac{1}{7}\text{ lb}[/tex] to an improper fraction (to make the math easier):

[tex]2\frac{1}{7}=\frac{15}{7}\text{ lb}[/tex]

Next, since the question asks about how much salmon is left over, find that fraction. After cooking one-fifth of the salmon, four-fifths remain:

[tex]\frac{5}{5}-\frac{1}{5}=\frac{4}{5}[/tex]

Then, multiply the two:

[tex]\frac{15}{7}\times\frac{4}{5}=\frac{60}{35}\text{ lb}[/tex]

Finally, convert back to a mixed fraction:

[tex]\frac{60}{35}\text{ lb}=1\frac{25}{35}\text{ lb}=1\frac{5}{7}\text{ lb}[/tex]

This is a way we can organize a linear equation:

[tex]y=mx+b[/tex]

We're given:

[tex]12x + 4y = 8[/tex]

To organize this equation in slope-intercept form, we have to focus on isolating y:

[tex]12x + 4y = 8\\4y = - 12x +8\\y = - 3x +2[/tex]

[tex]y = - 3x +2[/tex]

The answer is y= negative 3 plus 2

Answer: 9.7 seconds

Step-by-step explanation:

[tex]16t^2 =1503\\\\t^2 =1503/16\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7[/tex]