A taxi makes 56 trips between two cities which are 492 km apart. How much distance does the taxi cover in all?

Answer:

Listed below

Step-by-step explanation:

  1. To solve number 1 we need to find a common denominator.

A common denominator consists of two or more fractions that have the same denominator.

[tex]\frac{3}{4} =\frac{6}{8}[/tex]

How can we convert this? Well, to go from 4 to 8, we multiply by 2. Doing the same to the top number (Numerator) will get us a fraction of [tex]\frac{6}{8}[/tex].

Adding the two fractions together:

[tex]\frac{7}{8} +\frac{6}{8}= \frac{13}{8} or1 \frac{5}{8}[/tex]

Therefore, the answer to question 1 is [tex]1\frac{5}{8}[/tex].

   2.  If there are 60 students in a class, and [tex]\frac{3}{4}[/tex] of them are girls, we can use this equation to solve for the number of girls in the class:

We multiply by 0.75 because 0.75 is equivalent to [tex]\frac{3}{4}[/tex].

So, there are 45 girls in the class.

To solve for the rest of the class that are boys, we can use this equation:

The answer to question 2 is 15 boys.

  3. If the temperature was -2°C, and it is now 8°C, we can use this equation to solve for the temperature difference:

So, the temperature difference is 10°C.

  4. If Mt. Everest's elevation is at 29,028 feet, and the dead sea is -458, we can use this equation to solve for the difference in elevation:

Therefore, the difference in elevation is 29,486 feet.

The amount of lumber in a tract of timber, an owner randomly selected seventy 50-by-50-foot squares, and counted the number of trees with diameters exceeding 12 inches in each square is 16.67

In order to estimate the amount of lumber in a tract of timber, an owner will use a technique called sample size estimation.

By using this data, the owner can then calculate an estimate of the total amount of lumber present in the tract of timber.

In this case, the sample size is 70, the square size is 2500 square feet, and the diameter of the trees is 12 inches. Therefore, the formula becomes:

=> Total Trees = (Number of Trees in Sample / 70) x (2500 / 12).

If we plug in the number of trees counted in each square, we can find the total estimated number of trees in the tract of timber.

If the owner counted 7 trees in the first square, the formula would be

=> (7 / 70) x (2500 / 12) = 16.67.

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Complete Question:

To estimate the amount of lumber in a tract of timber, an owner randomly selected seventy 50-by-50-foot squares and counted the number of trees with diameters exceeding 12 inches in each square. The data are listed here.

7 9 8 10 3 7 7 9 9 11 7 9 5 5 10 10 9 8 2 8 5

Answer:

20 tons

Step-by-step explanation:

To convert pounds to tons, we need to divide the number of pounds by the number of pounds in a ton.

There are 2,000 pounds in one ton.

To convert 40,000 pounds to tons, we divide 40,000 by 2,000:

40,000 pounds / 2,000 pounds/ton = 20 tons

Therefore, 40,000 pounds is equivalent to 20 tons.

The solution for these discrete mathematics questions will be: a) No. The element d is in two of the sets. B) Yes C) No. The element 4 is in two of the sets. D) No. None of the sets contains 6. E) a) no b) yes

The study of mathematical structures that are discrete rather than continuous (it's similar to discrete variables and having a bijection with the set of natural numbers) is known as discrete mathematics. Graphs, integers, and logical statements are among the objects studied in discrete mathematics.

Both finite and infinite sets of objects can be studied in discrete mathematics. Some areas of discrete mathematics that deal with finite sets, especially those that have a bearing on business, are referred to as "finite mathematics" at times.

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Note that the full question is:

a) Is {{a, d, e}, {b, c}, {d, f}} a partition of {a, b, c, d, e, f }?

Yes or No

(b) Is {{w, x, v}, {u, y, q}, {p, z}} a partition of {p, q, u, v, w, x, y, z}?

Yes or No

(c) Is {{5, 4}, {7, 2}, {1, 3, 4}, {6, 8}} a partition of (1, 2, 3, 4, 5, 6, 7, 8}?

Yes or No

(d) Is {{3, 7, 8}, {2, 9}, {1, 4, 5}} a partition of {1, 2, 3, 4, 5, 6, 7, 8, 9}?

Yes or No

(e) Is {{1, 5}, {4, 7}, {2, 8, 6, 3}} a partition of {1, 2, 3, 4, 5, 6, 7, 8}?

Yes or No

The solutions are x=3.69 and x=-4.2

A quadratic equation is a second-order polynomial equation in a single variable x , ax2+bx+c=0. with a ≠ 0 .

2x²+x-31=0

Solve this with the quadratic formula

x=-b±√b²-4ac/2a

a=2,b=1,c=-31

x=-1±√1+248/4

x=-1±√249/4

x=-1+√249/4

x=-1 + 15.77/4 =14.77/4

x=3.6925

and x=-1-√249/4

x=-1 -15.77/4 =-4.1925

Hence, the solutions are x=3.69 and x=-4.2

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Karen received a 15% discount of $15, which brought the price down to $85.

Let's assume the original cost of the clothes was x dollars.

If Karen got a 15% discount, then she paid 85% of the original price.

This can be expressed in an equation as:

0.85x = 85

To find x, we need to isolate it on one side of the equation.

We can do this by dividing both sides by 0.85:

x = 85 / 0.85

x = 100

Hence, the original cost of the clothes was $100.

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The vertex form equation is illustrated below.

Directrix (d): The directrix is the horizontal line y = -2.

Focus (F): The focus is the point (0, 2).

Vertex (V): The vertex is the point (0, 0).

Equation: The equation of the parabola is y = 1/4x^2.

The vertex form of a parabola is given by y = a(x-h)^2 + k, where (h, k) is the vertex. We already know the vertex of this parabola, which is (0, 0). To find the value of a, we can use the fact that the distance between the focus and the vertex is equal to the distance between the directrix and the vertex.

The distance between the focus (0, 2) and the vertex (0, 0) is 2 units. The distance between the directrix y = -2 and the vertex (0, 0) is also 2 units. Therefore, we can say that 1/(4a) = 2, or a = 1/8.

So, the vertex form equation of the parabola is y = 1/8(x-0)^2 + 0, which simplifies to y = 1/8x^2.

Vertex: The vertex is (0, 0).

Axis of Symmetry (AOS): The axis of symmetry is the vertical line x = 0.

Domain: The domain of the parabola is all real numbers, because the parabola continues indefinitely in both directions along the x-axis.

Range: The range of the parabola is y >= 0, because the lowest point on the parabola is the vertex (0, 0).

Transformations: The only transformation applied to the basic parabola y = x^2 is a vertical compression by a factor of 1/8.

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Answer: x = 0, Y = 2    

              x = 1, Y = 5

Step-by-step explanation:

Y = −3x^2 + 6x + 2

Y = 3x + 2

We can set the two equations equal to each other, since they both equal Y:

−3x^2 + 6x + 2 = 3x + 2

−3x^2 + 3x = 0

 3x(-x + 1) = 0

This gives us two possible solutions:

x = 0

x = 1

When x = 0, Y = 3(0) + 2 = 2

When x = 1, Y = 3(1) + 2 = 5

Therefore, the solutions to the system of equations are:

x = 0, Y = 2

x = 1, Y = 5

The speed of the train is 28.5 miles per hour.

According to given condition :

One possible equation to solve for the speed of the train is:

speed = distance / time

In this case, the distance is 285 miles, and the time is 10 hours. Plugging in those values, we get:

speed = 285 / 10

Simplifying this expression, we get:

speed = 28.5

Therefore, the speed of the train is 28.5 miles per hour.

What is equation ?

An equation is a mathematical statement that shows that two expressions are equal. Equations typically use variables, numbers, and mathematical operations such as addition, subtraction, multiplication, and division. The purpose of an equation is to find the value(s) of the variable(s) that make the equation true.

For example, an equation might be:

2x + 3 = 7

This equation means that if we multiply x by 2 and then add 3, we get 7. The solution to this equation is x = 2, since if we substitute x = 2 into the equation, we get:

2(2) + 3 = 7

4 + 3 = 7

7 = 7

which is true.

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Answer:310.45

Step-by-step explanation:

Assuming that the iron plate is lifted to a height against the gravitational force, we can use the formula for potential energy:

Potential Energy = mass x gravity x height

where mass is in kg, gravity is 9.81 m/s^2, and height is in meters.

Rearranging the formula to solve for height, we have:

height = Potential Energy / (mass x gravity)

Plugging in the given values, we have:

height = 2000 J / (10 kg x 9.81 m/s^2)

height = 20.34 meters (rounded to two decimal places)

Therefore, the height of the iron plate is approximately 20.34 meters.

Answer:

2(8x−5+x^2 )

Step-by-step explanation:

2(3x−1+x^2+5x−4)

2((3x+5x)+(−1−4)+x^ )

2(8x−5+x^2 )

Answer: look at the image for the answer and explanation

Step-by-step explanation:

Answer:

the pressure at a temperature of 600 K is 9.6 pounds per square inch.

Step-by-step explanation:

If the pressure of a gas in a container varies directly as the temperature, then we can use the formula P1/T1 = P2/T2, where P1 is the initial pressure, T1 is the initial temperature, P2 is the final pressure, and T2 is the final temperature.

Using the values given in the problem, we can write:

8/500 = P2/600

Solving for P2, we get:

P2 = (8/500) * 600 = 9.6 pounds per square inch

Therefore, the pressure at a temperature of 600 K is 9.6 pounds per square inch.

Answer:

Using 3.14 for π, we have:

[tex]32(26) + \frac{1}{2} (3.14)( {13}^{2} ) = 1097.33[/tex]

about 1,097.33 square feet

The benefit of doing so is: If the teenager has earned less than $12,000 then they don't get the federal taxes withheld. It would be beneficial to the teen because they would get more money.

A teen might want to claim exemption from federal income taxes being withheld from their paycheck if they expect to earn less than the standard deduction amount for the tax year and they will not owe any federal income tax.

For the tax year 2022, the standard deduction amount for a single taxpayer who is not claimed as a dependent on another taxpayer's return is $12,950.

By claiming exemption from federal income taxes, the teen would have more money in their paycheck and would not have to wait to receive a tax refund when they file their tax return at the end of the year.

However, if the teen ends up earning more than the standard deduction amount or if they have other sources of taxable income, they may owe federal income tax and may have to pay a penalty for not having enough taxes withheld during the year.

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Answer: 0.58

Step-by-step explanation: ..

Answer:

k < 24

Step-by-step explanation:

The phrase "k less than 24" can be written as an algebraic expression using the symbol "<" which means "less than."

So, "k less than 24" can be written as:

k < 24

This means that the value of "k" is smaller than 24. For example, if k = 20, then 20 is less than 24, so the statement "k < 24" is true.

If k = 30, then 30 is not less than 24, so the statement "k < 24" is false.

I hope this helps!

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The factor that represents the area of the yard that can be mowed is (225 - x²).

What is area?

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

The total area of the lawn is given by the formula -

Area of square lawn = (side length of square lawn)²

= (15 yards)²

= 225 square yards

The shed is also a square, with side length x yards.

So, the area of the shed is -

Area of square shed = (side length of square shed)²

= x²

To find the area of the yard that can be mowed, we need to subtract the area of the shed from the total area of the lawn -

Area of yard that can be mowed = Area of square lawn - Area of square shed

= 225 - x²

Therefore, the value is obtained as (225 - x²).

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The sum of all the odd integers numbering from 1 to 99 is given by th e term 2500.

S = n(a + l)/2, where S is the sum of the successive numbers, n is the number of integers, an is the first term, and l is the last term, is the formula for computing the sum of integers.

Finding the sum of odd numbers from 1 to 99

so the series become

1 + 3 + 5 + 7 + ......+ 99

So this is arithmetic series with common difference of d = 2 and first term be a = 1 and last term be 99

l = a + (n-1)d

99 = 1 + (n-1) 2

n-1 = 98/2

n-1 = 49

n = 50

We know that sum of nth term of AP

s = n/2(a + l)

s = 50/2 (1 + 99)

s = 25(100)

s = 2500

Therefore, the sum of all odd number from 1 to 99 is 2500.

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Answer:

b = 50°

c = 130°

Step-by-step explanation:

B

Vertical angles are congruent (have the same measurement)

C

Adjacent angles ae supplemental (add to 180°)

Answer:

b = 50°

c = 130°

Step-by-step explanation:

Answer:ob

Step-by-step explanation:

The median age of the runners is 23.5.

By adding up all the numbers in a data collection and dividing by the total number of values in the set, the mean (average) of the data set can be determined. The median is the middle when a data set is sorted from least to greatest.

We must first arrange the ages from youngest to oldest in order to determine the median:

14, 15, 16, 19, 19, 23, 24, 27, 30, 31, 31, 33

The median will be the average of the sixth and seventh values in this sorted list because there are 12 runners:

(23 + 24) / 2 = 23.5 is the median.

Hence, 23.5 is the runners' median age.

The median, in terms of meaning, is the data set's middle value. In this instance, the age is the exact midpoint between the ages of the 12 racers. It is a central tendency index that shows how typical or representative the data are.

In this situation, the median age of 23.5 can be interpreted as the typical age of the marathon runners. Half of the runners were over 23.5 years old, and half were under that age. Although the middle figure is closer to the lower end of the age spectrum than the higher end, it can also help us estimate the runners' age range. The disparity between the runners' lowest and highest ages is not, however, directly shown.

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Answer:

hypotenuse squared

Step-by-step explanation:

for example

if we have a triangle with sides 6,8, and 10

then

36+64=100

the complete equation is

[tex]\sqrt{a^{2} +b^2[/tex]=c

The value of x when y = 8 is 13.5

If y is inversely proportional to x, it means that their product is a constant value.

We can represent this relationship using the formula:

y * x = k

where k is the constant of proportionality.

We are given that y = 27 when x = 4, so we can solve for k:

27 * 4 = k

This gives

k = 108

Now that we know the value of k, we can use it to find x when y = 8:

y * x = k

This guves

8 * x = 108

So, we have

x = 13.5

Hence, when y = 8, the value of x is 13.5.

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A rhombus with opposite sides are parallel and equal, and opposite angles are equal looks like Diamond.

A closed two-dimensional plane figure is a rhombus. It is regarded as a peculiar parallelogram, and due to its distinctive characteristics, it acquires a distinct identity as a quadrilateral. Due to its equal length sides, a rhombus is also known as an equilateral quadrilateral. The name "rhombus" is derived from the Greek word "rhombos," which really refers to a spinning object.

Due to the fact that it is a quadrilateral with two pairs of parallel sides, a rhombus can be considered a particular parallelogram. A rhombus also has equal sides on all four sides, exactly like a square. Because of this, it is often referred to as a tilted square. To comprehend the relationship between the rhombus shape, parallelogram, and square, look at the graphic below.

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The amount of money you have in your account after years 1, 2, 3, and 4 are $102.25, $204.5, $306.75 and $409 respectively.

Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan.

Given that, you have 100 dollars in your bank account, and you earn 2.25% interest per year.

We need to find the amount of money you have in your account after years 1, 2, 3, and 4 years

Find for Simple interset :-

Simple interset = PRT / 100

P = Principal amount, r = rate and  t = year

For 1 year, put t = 1

A = 100×1×2.25 / 100 + 100

= $102.25

To find the amount for 2nd, 3rd and 4th year, just multiply these numbers to the interset earned in 1st year,

For 2 year,

A = $102.25×2

A = $204.5

For 3 year,

A = $102.25×3

A = $306.75

For 4 year,

A = $102.25×4

A = $409

Hence, the amount of money you have in your account after years 1, 2, 3, and 4 are $102.25, $204.5, $306.75 and $409 respectively.

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If the long-term demand for oranges is the same as the short-term demand, a binding price ceiling will result in a shortage that is larger in long-run demand than the short-run demand. So the answers are shortage and larger.

A shortage occurs when there is a difference between the quantity that is supplied and the quantity that is required of a product, service, or resource. Surplus is a term used to describe situations where there is more supply than demand for a product, service, or resource.

So when the long-run demand is the same as the short-run demand, binding price ceilings typically result in a shortage when there is a lack of supply of products. And, the result will be larger in the case of the long run compared to the short run. Therefore, the first blank can be filled with shortage and the second blank with larger.

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The Volume of Alcohol when Mass is 1000 Kg and Density is 790kg/m³

is 1.265 m³

The relationship between a substance's mass and the amount of space it occupies is known as its density (volume). The density of a substance is determined by the mass, size, and arrangement of its atoms. Density (D) is defined as the product of a substance's mass and volume.

Given:

Mass of Alcohol = 1000 Kg

Density of alcohol = 790kg/m³

Using The formula

Density= Mass / Volume

790 = 1000/ Volume

Volume = 1000/ 790

Volume = 1.265 m³

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The Translation of given Question:

What volume in cubic meters does 1000kg of alcohol occupy with a density of 790kg/m3