What is the difference of the rational expressions below?

The statement which is true regarding the values of x and y is option C; x=y+360n , for any positive integer n.

The algebraic sum of Coterminal angles at a point is 360°.

From the given information;

Angle x is coterminal with angle y.

If the measure of angle x is greater than the measure of angle y.

Then, the statement which is correct is will be as;

x = y + 360n , for any positive integer n.

Read more on coterminal angles;

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Answer:

$41.685        

Step-by-step explanation:

Given:-

- The material cost per square foot, C = $1.25

- The two boxes have the dimensions:

         Box 1 : ( 9 x 9 x 10 ) in

         Box 2: ( 11 x 7 x 10 ) in

Find:-

so how much does a company save by choosing to make 50 of Box 2 instead of Box 1?

Solution:-

- We will first determine the surface areas of the two boxes Box 1 ( A1 ) & Box 2 (A2).

               A1 : 2*( 9*9) + 4*( 9*10) = 522 in^2 = 43.5 ft^2

               A2 : 2*(11*7) + 2*(11*10) + 2*(7*10) = 514 in^2 = 42.833 ft^2

- Determine the cost for each box:

               Cost of box 1 = A1*C = 43.5*$1.25 = $54.375

               Cost of box 2 = A2*C = 42.833*$1.25 = $53.5413

- The amount saved by the company by choosing to make 50 Box 2 as compared to 50 Box 1:

               Amount saved = 50*(Cost of box 1 - Cost of box 2)

                                         = 50*( 54.375 - 53.5413 )

                                         = $41.685        

Answer:

324

Step-by-step explanation

the answer is c. i do online work, yw!

Answer:

(9, -7)

Step-by-step explanation:

[tex]x^2+y^2+18x+14y+105=0\\[/tex]

Rearrange like x and y terms next to each other, then complete the square on both.

[tex](x-9)^2-361 + (y+7)^2 - 49 + 105 = 0[/tex]

The negative of the # numbers instead the brackets give you the centre of the circle.

The given equation does not represent a circle because the radius is an imaginary number.

The given equation represents a circle in the Cartesian coordinate plane. The general form of a circle equation is (x - h)² + (y - k)² = r², where (h, k) is the centre of the circle and r is the radius. By rearranging the equation, we can find the centre by completing the square for both x and y.

For the given equation, x² + y² + 18x + 14y + 105 = 0, we complete the square for x by adding (18/2)² = 81 to both sides of the equation and for y by adding (14/2)² = 49 to both sides of the equation. This gives us:

(x² + 18x + 81) + (y² + 14y + 49) + 105 - 81 - 49 = 0

(x + 9)² + (y + 7)² = -175

The equation (x + 9)² + (y + 7)² = -175 does not represent a circle because the radius, which is the square root of -175, is an imaginary number. Therefore, the given equation does not have a real centre or radius.

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Answer:

? = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Take two points in this case, (-2,4) and (0,5)

Use rise over run for slope to find ?

5-4/0+2 = 1/2

To find the other blank, enter one of the two points into the existing equation.

y = 1/2x + b

5 = 0 + b

b = 5

The equation is y = 1/2x + 5

Answer: B and A

Step-by-step explanation:

(X+3)2 = 2×x + 2×3

= 2x + 6

Likewise

2(x+3) = 2×x +. 2×3

= 2x + 6

Hence they are both same

2.(X +3) still equivalent to 2x +6

Answer:

A and B

Step-by-step explanation:

In this question, we are asked to pick the options which have the same value as the expression in the question.

Firstly, let’s expand the main expression in the question.

Mathematically, expanding this, we have 2x + 6

now let’s consider the options one after the other.

Options A and B are correct as they mean the same thing and would refer to the expression in the question.

Option c is wrong. Expanding option c would yield 2x + 4

option d is wrong as the multiplication is only between 2 and x and does not cover 3. This makes the expression as 2x + 3

option E is is also wrong as it is same as D but expressed in another fashion

option F is is wrong also as expanding would give 6 + 3x which is different from 2x + 6

If the sample mean is close to 32 ounces or the sample standard deviation is large, it is less likely that we will reject the null hypothesis.

To determine if there is sufficient evidence to conclude that the mean amount of milk in cartons is less than 32 ounces, we would conduct a hypothesis test. The null hypothesis (H0) would state that the mean amount of milk in cartons is at least 32 ounces, while the alternative hypothesis (Ha) would state that the mean amount is less than 32 ounces.

The null hypothesis: [tex]\( H_0: \mu \geq 32 \)[/tex]

The alternative hypothesis: [tex]\( H_a: \mu < 32 \)[/tex]

Here is the step-by-step process to conduct the hypothesis test:

1. **Identify the sample mean [tex](\( \bar{x} \))[/tex] and the sample standard deviation (s).** These values would be calculated from the sample of 22 cartons.

2. **Calculate the test statistic (t-score).** The formula for the t-score in a one-sample t-test is:

[tex]\[ t = \frac{\bar{x} - \mu_0}{\frac{s}{\sqrt{n}}} \][/tex]

where [tex]\( \mu_0 \)[/tex] is the hypothesized mean (32 ounces in this case), [tex]\( \bar{x} \)[/tex] is the sample mean, [tex]\( s \)[/tex] is the sample standard deviation, and [tex]\( n \)[/tex] is the sample size.

3. **Determine the degrees of freedom (df).** For a one-sample t-test, the degrees of freedom are [tex]\( n - 1 \)[/tex], where [tex]\( n \)[/tex] is the sample size. In this case, [tex]\( df = 22 - 1 = 21 \)[/tex].

4. **Find the critical t-value or p-value.** Using the degrees of freedom, we can find the critical t-value from a t-distribution table or calculate the p-value. The significance level (α) is typically set at 0.05 for such tests.

5. **Make a decision.** If the test statistic is less than the critical t-value or if the p-value is less than α, we reject the null hypothesis in favor of the alternative hypothesis. This would mean there is sufficient evidence to conclude that the mean amount of milk in cartons is less than 32 ounces.

6. **Calculate the p-value.** The p-value is the probability of observing a sample mean at least as extreme as the one observed, assuming the null hypothesis is true. It can be calculated using statistical software or a t-distribution table.

7. **Report the results.** If the p-value is less than α, we report that there is sufficient evidence to conclude that the mean amount of milk in cartons is less than 32 ounces. If the p-value is greater than α, we report that there is not enough evidence to conclude that the mean amount is less than 32 ounces.

Without the actual sample data (sample mean and sample standard deviation), we cannot perform the calculations or make a conclusion. However, if the sample mean is substantially less than 32 ounces and the sample standard deviation is small, it is more likely that we will reject the null hypothesis. Conversely, if the sample mean is close to 32 ounces or the sample standard deviation is large, it is less likely that we will reject the null hypothesis.

Answer:

35

Step-by-step explanation:

You would have to get rid of the 7. To do that you would divide each side by 7 to get s=35

The measure of angle CBD in a regular pentagon with perimeter 60 cm is 108°. This conclusion assumes that CBD refers to an internal angle of the pentagon and is based on the formula for internal angles of a regular polygon.

The subject of the question is related to a regular pentagon which is a polygon with 5 equal sides and equal angles. If the perimeter of the regular pentagon is 60 cm, it means each side measures 60/5 = 12 cm.

The question is asking for the measure of angle CBD. In a regular pentagon, angles are not directly named but it's likely referring to an internal angle of the pentagon. Based on this assumption, we can calculate the measure of an internal angle of a regular polygon using the formula: (n-2) x 180° / n where 'n' is the number of sides. Substituting '5' in place of 'n' because a pentagon has 5 sides, we get (5-2) x 180° / 5, which results in 108°. Therefore, if CBD is an internal angle then it measures 108 degrees.

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Answer:

A =32 units^2

Step-by-step explanation:

This figure is a trapezoid

We can find the area from

A = 1/2(b1+b2)h  where b1 and b2 are the base length and h is the height

A = 1/2(4+12) *4

A = 1/2 (16)*4

A =32 units^2

Final answer:

There are 6 strawberries in the bowl.

Explanation:

To find the number of strawberries in the bowl, we can set up an equation based on the given information. Let's assume the number of strawberries is S.

The problem states that there are 3 times as many blueberries as strawberries, so we can write this as:

18 = 3S.

To solve for S (the number of strawberries), we can divide both sides of the equation by 3:

S = 6.

Therefore, there are 6 strawberries in the bowl.

Answer: displacement is a measure that includes direction

Displacement is the difference between a starting point and a ending point

Displacement is measured as a straight line between a starting point and an ending point

Step-by-step explanation:

Answer:

13 cm

Step-by-step explanation:

Volumes should be equal

20 × 70 × 29 = 3.14 × 31² × h

h = 13.4546683723 cm

Answer:

120

Step-by-step explanation:

Each time you add 40 to gas(oz)

Answer: 120 ounces of gas

Step-by-step explanation: Given: 40 ounces of gas to 1 ounce of oil

We need to find: __ ounces of gas to 3 ounces of oil

What we know:

1 × 40 = 40 ounces of gas

2 × 40 = 80 ounces of gas

3 × 40 = 120 ounces of gas

So, all you needed to do was multiply 3 times 40 to get 120 ounces of gas.

Conclusion: The answer is 120 ounces of gas.

Answer: B

Step-by-step explanation:

Both the mean and the median will decrease, but the mean will decrease by more than the median.

Answer:

Both the mean and the median will decrease, but the mean will decrease by more than the median.

Step-by-step explanation:

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Answer:

b) It is the common difference.

Step-by-step explanation:

In arithmetic sequence the difference between one term and other term is constant. The slope of the line related to the arithmetic sequence is Common Difference.

In arithmetic sequence the difference between one term and other term is constant

We need to find how slope of the line related to the arithmetic sequence.

A common difference is a difference between any term and its preceding term in an arithmetic sequence. The slope of the line related to the arithmetic sequence is common difference.

Therefore common difference is related to arithmetic sequence.

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Answer:

A waterfall has a height of 1500 feet. A pebble is thrown upward from the top of the falls with an initial velocity of 24 feet per second. The​ height, h, of the pebble after t seconds is given by the equation h =−16t^2+24t+1500. How long after the pebble is thrown will it hit the​ ground?

Pebble will hit the ground after 10.46 seconds.

Step-by-step explanation:

Given:

The​ height, "h" of the pebble after t seconds, "h" = −16t^2+24t+1500

We have to find the time it will take to hit the ground.

For this we have to put h = 0 and solve the quadratic.

Quadratic formula:

⇒ Standard equation : [tex]ax^2+bx+c=0[/tex]

⇒ [tex]x =\frac{-b\pm \sqrt{(b)^2-4ac} }{2a}[/tex]

Now,

Solving the above equation with quadratic formula after comparing its values with the standard equation.

⇒ [tex]a=-16,\ b=24,\ c=1500[/tex]

⇒ [tex]t =\frac{-b\pm \sqrt{(b)^2-4ac} }{2a}[/tex]

⇒ [tex]t =\frac{-24\pm \sqrt{(24)^2-4(-16)(1500)} }{2(-16)}[/tex]

⇒ [tex]t =\frac{-24\pm \sqrt{576+96,000} }{-32}[/tex]

⇒ [tex]t =\frac{-24\pm(310.76)}{-32}[/tex]

⇒ [tex]t =\frac{-24+(310.76)}{-32}[/tex]                         ⇒ [tex]t =\frac{-24-(310.76)}{-32}[/tex]

⇒ [tex]t =-\frac{286.76}{32}[/tex]                                ⇒ [tex]t =\frac{334.76}{32}[/tex]

⇒ [tex]t=-8.96\ sec[/tex]                            ⇒ [tex]t=10.46\ sec[/tex]

Discarding the negative values.

The pebble will hit the ground after 10.46 seconds.

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

An aquarium tank can hold 6600 liters of water. There are two pipes that can be used to fill the tank. The first pipe alone can fill the tank in 55 minutes. The second pipe can fill the tank in 66 minutes by itself. When both pipes are working together, how long does it take them to fill the tank?

Given Information:

Time to fill tank by first pipe = 55 minutes

Time to fill tank by first pipe = 66 minutes

Total capacity  of tank = 6600 liters

Required Information:

Time required to fill tank when both pipes are working together = ?

Answer:

Time required to fill tank when both pipes are working together = 30 mins

Step-by-step explanation:

The rate of filling the tank of the first pipe is,

first pipe = [tex]\frac{6600}{55} = 120[/tex] [tex]L/m[/tex]

The rate of filling the tank of the second pipe is,

second pipe = [tex]\frac{6600}{66}= 100[/tex] [tex]L/m[/tex]

Let x is the time to fill the tank when both pipes are used so the equation becomes,

[tex]120 + 100 = \frac{6600}{x}[/tex]

[tex]120x + 100x = 6600[/tex]

[tex]220x = 6600[/tex]

[tex]x = \frac{6600}{220}[/tex]

[tex]x = 30[/tex] [tex]mins[/tex]

Therefore, it would take 30 minutes to fill the entire tank when both pipes are used to fill the tank.

Answer:

(5x−2) and (x+2)

Step-by-step explanation:

Answer:

(5x-2)(x+2)

If you want to check your answer mulitply (5x-2)(x+2) and you get the same

trinomial 5x2 + 8x - 4.

The surface area of the cereal box is 2600 square centimeters. Volume of the cereal box is 7500 cubic centimeters.

The surface area of the cereal box in the image is 2600 square centimeters. The volume of the cereal box is 7500 cubic centimeters.

To calculate the surface area, we need to find the area of each of the six faces of the box and add them all up. The two largest faces have dimensions 25 cm by 30 cm, so their area is 25 * 30 = 750 square centimeters each. The two next-largest faces have dimensions 10 cm by 30 cm, so their area is 10 * 30 = 300 square centimeters each. The two smallest faces have dimensions 25 cm by 10 cm, so their area is 25 * 10 = 250 square centimeters each. Therefore, the total surface area of the box is 750 + 750 + 300 + 300 + 250 + 250 = 2600 square centimeters.

To calculate the volume, we simply multiply the length, width, and height of the box together. The length is 25 cm, the width is 10 cm, and the height is 30 cm, so the volume is 25 * 10 * 30 = 7500 cubic centimeters.

Here is a table summarizing the surface area and volume of the cereal box:

|      Property   |                 Value                 |

|--------------------|--------------------------------------|

| Surface area | 2600 square centimeters|

|      Volume     |  7500 cubic centimeters |

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Answer:

6π in

Step-by-step explanation:

Length of arc

[tex] = 2\pi \: r \frac{120}{360} [/tex]

[tex] = 2\pi \times 9 \times \frac{1}{3} [/tex]

[tex] = 6\pi[/tex] in

Final answer:

The population of the United States grew from around 5 million in 1800 to approximately 281 million in 2000, with growth rates declining over time due to lower birth rates and increasing reliance on immigration.

Explanation:

The population growth of the United States from 1800 to 2000 showcases remarkable changes over two centuries. Starting with the beginning of the 19th century, the US population was around 5 million and by the year 2000, it had grown to approximately 281 million according to the decennial census data. This substantial increase can be attributed to various factors including immigration, natural growth, and economic prosperity.

During the early 1800s, the population saw a significant surge, increasing by 38% between 1800 and 1810. However, as time progressed, the growth rate began to slow down. Between 1900 and 1910, the growth rate was at 21%, and it further reduced to 10% between 2000 and 2010. The declining growth rates in the later years are linked to a decrease in the total fertility rate (TFR), which at 1.9, is below the replacement rate of 2.1. The nation's population started to rely more on immigration for its growth as the birth rates declined.

In terms of economic impact, the period between 1850 and 1860 is noted for its astounding economic growth despite political tensions, where the nation's wealth and various economic indicators such as farm value and product manufacturing saw increases surpassing 100%.

Answer:

I = Prt

I = 1500(.118)(2) = 354

Total amount to pay = $1854

Monthly payment = $77.25

Step-by-step explanation:

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Answer:

A =176 cm^2

Step-by-step explanation:

The area of a trapezoid is found by

A =1/2 (b1+b2) *h

where b1 and b2 are the lengths of the bases

A =1/2(12+10) *16

A = 1/2(22)*16

A =176 cm^2

Answer:

$1.1

Step-by-step explanation:

First take if 110% is equals to $1.21 what about 100%

1.21×100=121÷110= $1.1

Step-by-step explanation:

x + y = 6 ...................equation 1

x - y = 10 ..................equation 2

Solving equation 1 and 2

x + y = 6

x - y = 10

2x = 16

x = 16 /2

Therefore x = 8

Now

putting x = 8 in equation 1

8 + y = 6

y = 6 -8

y = -2

hope it was helpful :)

Answer:

x=8 and y= -2

Step-by-step explanation:

x+y=6

x-y=10      +              ( add them together)

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

2x=16                          ( substitute/ plug x back in )

x=8

8+y=6

8-y=10

y=-2

Answer:

It is A.

Look at the attachment down below:

Step-by-step explanation:

The equation is used to find the unknown length (a) will be 17² =15² + a². Then the correct option is A.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

A right triangle has a side with length 15 meters and a hypotenuse with length 17 meters.

The other side is labeled a.

17² =15² + a²

Then the correct option is A.

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