A train leaves city A at 0800 h and travels at a uniform speed of 60 kmh¹ towards city B. Another train leaves city B at the same instance and travels at a uniform speed of 40 kmh¹ towards city A. If the distance between the two cities A and B is 100 km, calculate the time at which the two trains pass each other.​

Answer:0.6

Step-by-step explanation:

20/3 is 6

Based on the number of bushels that the farmer has to sell, the equation that represents the total change in the number of bushels after seven days is 220 - 15⁵/₈(7).

The farmer has a total of 220 bushels of wheat to sell and then sells about 15⁵/₈ every day.

After 7 days, the total change in the number of bushels would be:

= Total bushels to be sold - Bushels of wheat already sold

= Total bushels to be sold - (Number of bushels sold per day x Number of days)
= 220 - 15⁵/₈(7)

= 110 bushels of wheat

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The time taken by Peter to arrange the chairs all by himself is 10/3 minutes.

Given that :-

Katrina can arrange the chairs in the classroom in 5 minutes.

One day peter helped her and took both of them 2 minutes to arrange the chairs.

We have to find the time taken by Peter to arrange the chairs all by himself.

LCM (5,2) = 10

Let the total work of arranging the chairs is of 10 units.

We know that,

Efficiency of a person = Total Work/Time taken by person

Hence,

Efficiency of Katrina = 10/5 = 2 units

Efficiency of Katrina + Efficiency of Peter = 10/2 = 5 units

Hence,

Efficiency of Peter = 5 - 2 = 3 units

Hence, time taken by Peter to arrange the chairs all by himself  = 10/3 minutes.

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The representation of the expression is 4 < x + 7

The mathematical statement is given as

"4 less than the sum of a number and 7"

Sum means Plus

So, we have the following representation

"4 less than the sum of a number and 7" ⇒  4 less than a number + 7"

Let the number be x

So, we have

"4 less than the sum of a number and 7" ⇒  4 less than x + 7"

Less than as used here means <

So, we have

"4 less than the sum of a number and 7" ⇒  4 < x + 7"

Hence, the expression represented by "4 less than the sum of a number and 7" is  4 < x + 7

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The simplified form of the expression 4(4y-[tex]7y^{2}[/tex])-9(5y+2) is -28[tex]y^{2}[/tex]-29y-18

The given the expression is 4(4y-[tex]7y^{2}[/tex])-9(5y+2)

To solve this problem first we have to use the distributive property

The distributive property states that multiplying the sum of two or more variables by a number gives the same result as when each variable is multiplied individually by the number and the products are added together

The distributive property of addition

A(B+C) = AB + AC

The distributive property of subtraction

A(B-C) = AB - AC

The given equation is 4(4y-[tex]7y^{2}[/tex])-9(5y+2)

Apply distributive property

4(4y-[tex]7y^{2}[/tex])-9(5y+2) = 16y -28[tex]y^{2}[/tex]-45y-18

Rearrange the terms

-28[tex]y^{2}[/tex]-45y+16y-18 = -28[tex]y^{2}[/tex]-29y-18

Hence, the simplified form of the expression 4(4y-[tex]7y^{2}[/tex])-9(5y+2) is -28[tex]y^{2}[/tex]-29y-18

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The number of volunteers needed for each case is given as follows:

a. 0.4 miles: 5.

b. 2/7 miles: 7.

c. 0.125 miles: 16.

d. 6/45 miles: 15.

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using the unit rates of the context of the problem along with basic arithmetic operations, especially multiplication and division.

In this problem, a two mile section will be cleaned, hence the number of volunteers needed is calculated as follows:

n = 2/s.

In which s is the section cleaned by each volunteer.

In item a, the section is of 0.4 miles, hence the number of volunteers is given as follows:

n = 2/0.4 = 5 volunteers.

In item b, the section is of 2/7 miles, hence the number of volunteers is given as follows:

n = 2/(2/7) = 2 x 7/2 = 7 volunteers.

In item c, the section is of 0.125 miles, hence the number of volunteers is given as follows:

n = 2/0.125 = 2/(1/8) = 2 x 8 = 16 volunteers.

In item d, the section is of 6/45 miles, hence the number of volunteers is given as follows:

n = 2/(6/45) = 2 x 45/6 = 90/6 = 15 volunteers.

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If the family’s monthly income is $3,286, Wren family budgets for entertainment each month is $328.60.

Income, which is typically stated in the monetary terms, is the spending and saving opportunity acquired by an entity within a given duration. Conceptually, income is hard to define, and different fields may have the distinct definitions. For instance, a person's income may differ from their income as defined by law and in an economic sense.

Haig-Simons income, which defines income as Consumption + Change in Net Worth and is commonly applied in economics, is a very significant definition of income.

Income is a total that includes any wages, salaries, profits, interest payments, rent, or other forms of earnings received in a calendar year for families and individuals in the United States, as defined by tax law. Gross income less taxes and other deductions (such as required pension payments) is a common definition of discretionary income and is frequently used as a benchmark to assess the wellbeing of taxpayers.

The idea may include the accumulation of both monetary and non-monetary consumption capacity, with the former (monetary) serving as a stand-in for total income in the field of public economics.

Gross income for a business is the total revenue less the cost of items sold. Costs are subtracted from revenue by cost of goods sold, expenses, depreciation, interest, and taxes to arrive at net income.

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Answer:

9h=p

9 times the number of hours worked equals the total pay.

The definition for the function is y = {-2x +1   x < 1 ; -x + 2   x ≥ 1. The correct option is b.

From the question, we are to determine the equation for the function

First, we will determine the equation for when x < 1

Picking the points (-1, 3) and (0, 1)

Using the formula,

(y - y₁) / (x - x₁) = (y₂ - y₁) / (x₂ - x₁)

(y - 3) / (x - -1) = (1 - 3) / (0 - -1)

(y - 3) / (x + 1) = -2 / (0 + 1)

(y - 3) / (x + 1) = -2 / 1

(y - 3) / (x + 1) = -2

y - 3 = -2(x + 1)

y - 3 = -2x - 2

y = -2x - 2 + 3

y = -2x + 1

Thus,

When x < 1, the function is y = -2x + 1

Now, determine the equation for when x ≥ 1

Picking the points (1, 1) and (2, 0)

(y - y₁) / (x - x₁) = (y₂ - y₁) / (x₂ - x₁)

(y - 1) / (x - 1) = (0 - 1) / (2 - 1)

(y - 1) / (x - 1) = -1 / 1

(y - 1) / (x - 1) = -1

y - 1 = -1(x - 1)

y - 1 = -x + 1

y = -x + 1 + 1

y = -x + 2

Thus,

When x ≥ 1, the function is y = -x + 2

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Surface area of a cylinder= 2πr(h+r)

=2×22/7×5×(13+5)

=31.43×(18)

=565.74meter squared

Answer:

8/9 cups is the correct answer

Step-by-step explanation:

when we put gasoline in a car that will depend on how much it will cost us, also for example if we are going to buy popcorn depending on how many we buy will be the price

Step-by-step explanation:

equate the two small distances to the total distance and solve for x

The inequality that describes the domain is 0 ≤ x ≤ 5

The given parameters are

Size of tank = 3 gallons

Rate = 0.6 gallons per hour

The highest number of time is calculated as

Time = Size of tank/Rate

Substitute the known values in the above equation

So, we have the following equation

Time = 3/0.6

Evaluate

Time = 5

The domain is then represented as

0  ≤ x ≤ Time

This gives

0 ≤ x ≤ 5

Hence, the domain of the situation is 0  ≤ x ≤ 5

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Based on the report that digital music had led to a global revenue of $6.85 billion, the option that describes the accuracy of this report is that B. The report is probably accurate because the number is not very specific.

Digital music revenue recognition might vary from country to country. This means that what constitutes revenue for one country, might not be revenue in another. For that reason, we cannot say that businesses measure revenue accurately.

The report can however be very accurate even if it isn't completely accurate. This shown by the number not being specific to the last cent.

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Answer:

Hope the picture will help you

The quadratic equation that has roots (-1 - √2)/3 and (-1 + √2)/3 is:

x² + (2/3)x - 1/9 = 0

We have been given the roots of quadratic equation.

(-1 - √2)/3 and (-1 + √2)/3

We need to find the quadratic equation.

Since (-1 - √2)/3 and (-1 + √2)/3 are roots, (x - (-1 - √2)/3) and (x - (-1 + √2)/3) must be the factors of the quadratic equation.

So, the required quadratic equation would be,

(x - (-1 - √2)/3) * (x - (-1 + √2)/3) = 0

x[x - (-1 + √2)/3) ] - ( (-1 - √2)/3) [x - (-1 + √2)/3] = 0

x² - x(-1 + √2)/3 - x(-1 - √2)/3 + [(-1 - √2)(-1 + √2)]/9 = 0

x² - x(-2/3) + (1 - 2)/9 = 0

x² + (2/3)x - 1/9 = 0

Therefore, the quadratic equation that has roots (-1 - √2)/3 and (-1 + √2)/3 is: x² + (2/3)x - 1/9 = 0

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Using the exterior angle of a polygon theorem, the value of the missing angle is 58°

From the question, we are to calculate the value of the missing angle.

From the given information, the missing angle is (3x -2)°.

To calculate the value of the missing angle,

First, we will determine the value of x

From the Exterior angle of a polygon theorem, we can write that

90° + (3x + 12)° + (4x - 10)° + (3x - 2)° + 70° = 360°

(3x + 12)° + (4x - 10)° + (3x - 2)° = 360° - 70° - 90°

3x° + 12° + 4x° - 10° + 3x° - 2° = 200°

10x° = 200° + 2° + 10° - 12°

10x° = 200°

x = 200/10

x = 20

The missing angle is (3x -2)°

Substitute the value of x

(3(20) -2)°

= (60 -2)°

= 58°

Thus,

The missing angle measure is 58°

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Answer:

0.635

Step-by-step explanation:

This is half way between 0.63 and 0.64.

Hope this helps!

Answer:

1

Step-by-step explanation:

The opposite of a number is the number on the other side of 0 number line, and the same distance from 0.

Answer:

y=x/4

Step-by-step explanation:

if the line is perpendicular (m2)=-1/(m1)

m2=1/4

y=x/4+c

sub in 8,2

2=8/4+c

c=0

equation is therefore y=x/4

If a space rover has a mass of 3900 kg, then its weight on Earth N will be 38220 N.

Weight can be described as the body's relative mass  which can be regarded as the quantity of matter that can be found in the particles of the object and the unit can be written as Newton.

To calculate the weight of a particular particles, we can use the formular (mg) which is that product of the mass of the object to that of the gravity.

from the question, the gravity is been given as  g-9.81m/s

Then the weight = (3900 kg* 9.8) = 38220 N

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The amount of money would be $1115.45 the zoo makes selling the waste that day.

A Z-score is defined as the fractional representation of data point to the mean using standard deviations.

They charge farmers $5 per pound for the daily feces from the elephants. If an elephant's daily waste production is at or below the 10th percentile for the distribution of waste which is given in the question.

To determine the amount of money would the zoo make selling the waste that day.

P(z ≤ z₀) = 0.1

z₀ = -1.28

⇒z₀ =(x₀ -μ ) / σ

Substitute the values and solve for x₀,

⇒ -1.28 =(x₀ -250 ) / 21

⇒x₀ = (-1.28)×21 - 250

⇒x₀ = 223.09

So the amount of money would be as :

⇒ 223.09 × 5

⇒ 1115.45

Therefore, the amount of money would be $1115.45 the zoo makes selling the waste that day.

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Answer:

A.) 30 degrees

Step-by-step explanation:

Brainly pls :)

Answer: 5.18 x 10^-3

Step-by-step explanation:

0.00518

**Move the decimal 3 spaces to the right**

5.18

**Since it goes like 0.00, you want to make sure the exponent is negative**

5.18 x 10^-3

Hope this helped <3

Step-by-step explanation:

I hope this will be helpful for you.

[tex]2x(x+3)-(12x-4)\\=2x^{2} +6x-12x+4\\=2x^{2} -6x+4[/tex]

I hope this helps.

Answer:

164 cm

Step-by-step explanation:

(4x6) / 2= 12

12x2=24  because there are 2 triangles

10x6=60  for the rectangle

(4x10) x 2=80 for the sides

80+60=140

140+24=164