John drives his car on two roads for a total of 6 hours. On one road, he can drive at 100 km/h and on the other, he drives at a speed of 80 km/h. If he drives a total distance of 530 km, how long does he drive on each road?


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Answer:

[tex]df = \sqrt{ {29}^{2} - {20}^{2} } = 21 \\ \sin(d) = \frac{20}{29} \\ \cos(d) = \frac{21}{29} \\ \tan(d) = \frac{20}{21} \\ \sin(e) = \frac{21}{29} \\ \cos(e) = \frac{20}{29} \\ \tan(e) = \frac{21}{20} [/tex]

Answer:

Step-by-step explanation:

First, use the pythagorean theorem to complete the vales of each sides of the triangle. Then, use the respective trigonometric formulas and inverse the answer to compute the degree of every corners.

The total time taken by the experienced bricklayer to complete the job as per given condition is equal to 13 hours.

As given in the question,

Let the time taken by experienced bricklayer be 't' hours

Then time taken by apprentice bricklayer be '2t' hours

Time to complete 1 complete work is

Experienced bricklayer worked for 4 hours

Apprentice bricklayer worked for ( 4 + 14 ) = 18 hours

Required equation to complete 1 work is :

( 4/x) + ( 18 /2x) = 1

⇒( 8 + 18 )/ 2x = 1

⇒26/2 = x

⇒ x = 13 hours

Therefore, time taken by the experienced bricklayer to complete the job is equal to 13 hours.

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T(60) > T(10) + T(30) means that the number of tenants living on 60th floor is greater than the sum of tenants that are living in 10th and 30th floor.

n = number of floor of the Princess Tower (Floor Number)

T(n) is a function of n (floor number) which tells how many tenants are beings living on the nth floor

Tenant means a person occupying a rented land or property (A resident for simple understanding)

Therefore:

The statement:  T(60) > T(10) + T(30)

Means that: The number of tenants living on 60th floor is greater than the sum of tenants living on 10th and 30th floor.

Just for an example If we have T(60) = 30, T(10) = 10, T(30) = 5

Then T(60) > T(10) + T(30) means that 30 > 10 + 5 which becomes 30 > 15

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Answer:280

Step-by-step explanation:

The probability that none of the five students chosen at random are mechanical engineering majors is 0.0111 or about 1.11%.

The probability that none of the five students chosen at random are mechanical engineering majors is

=(51/100) * (50/99) * (48/98) * (47/97) * (46/96)

= 0.0111

This means that the probability is about 1.11%

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

The probability means that the chances of an event to occur or do not occur and it lies between the range of 0 and 1.

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Answer:

9(w+4)7

Step-by-step explanation:

I got this answer too, just like the person before me

De acuerdo con la información del enunciado, el resultado de esta operación matemática (división) es 0,13

Esta división da como resultado un número decimal de varios valores por lo que podemos repetir este procedimiento tantas veces sea necesario dependiendo de la exactitud de nuestras necesidades.

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Answer:

36.3 units²

Step-by-step explanation:

Area of a trapezoid = A = ((a+b)/2)h = [tex]\frac{a+b}{2}[/tex]h

a = 4

b = 1.5+7=8.5

solve for h using pythagorean theorem:

1.5² + h² = 6²

h² = 36 - 2.25 = 33.75

h = [tex]\sqrt{33.75}[/tex] = 5.81

A = [tex]\frac{4+8.5}{2}[/tex](5.81) = 36.3125

Answer:0.5

Step-by-step explanation:

On solving the provided question, we can say that The probability of a person purchasing both a beverage and gasoline is 0.060, or 6%.

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

At a gas station, 84% of customers buy gasoline

[tex]P (A) = 0.84[/tex]

5% of customers buy gasoline and a beverage

[tex]P (B) = = 0.05[/tex]

conditional probability = P (A and B) = P(A) × P(B/A)

[tex]P(B/A) = P (A and B) / P(A)\\P ( B/A ) = 0.0595 = 0.060 or 6%\\[/tex]

The likelihood of a person purchasing both a beverage and gasoline is 0.060, or 6%.

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a) The unit prices to determine the best buy are as follows:

b) The best buy is the 14-ounce bottle of salad dressing with a unit cost of $0.24 since they are all Grade A products.

The unit price or cost is the cost for an item or a unit.

The unit price can be compared to the unit rate, which is the quotient of the total cost and the number of units.

                              6 ounces   14 ounces   20 ounces

Total costs               $1.56           $3.36          $5.60

Unit cost                  $0.26          $0.24          $0.28

                            ($1.56/6)      ($3.36/14)     ($5.60/20)

Thus, buying a 14-ounce bottle of salad dressing is more economical than others.

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The Hindu-Arabic numeral system is superior to other numeral systems because of its invention of the number 0. This allows for the representation of the concept of nothingness or absence, which allows for the development of more advanced mathematical operations such as negative numbers and decimal fractions.

The two purposes of numerals or digits are to show the cardinal value (how many) and to show the place value (10s, 100s, 1000s). The cardinal value is the actual quantity of a number, while the place value is the position of a digit in a number, which determines its value in relation to other digits.

The natural numbers are the numbers used in a counting process and do not include 0. They include the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and so on to infinity. The principle of closure is the idea that certain operations, such as addition and multiplication, will always result in a natural number when performed on natural numbers. However, subtraction and division do not result in natural numbers in all cases.

Integers are positive and negative numbers that start at 0 and expand infinitely in both directions. They are closed under addition, multiplication, and subtraction. However, division is not closed under integers.

Rational numbers are numbers that can be expressed as the quotient of two integers. Irrational numbers are non-terminating, non-repeating decimals.

The three axioms of equality are the reflexive property (A = A), the symmetric property (if A = B, then B = A), and the transitive property (if A = B and B = C, then A = C).

The commutative property states that the order of the numbers does not affect the result in operations such as addition and multiplication. The associative property states that the grouping of numbers does not affect the result in operations such as addition and multiplication. The distributive property states that multiplication can be distributed over addition.

The unity element for multiplication is the number 1, which serves as the identity element for multiplication. The zero element for addition is 0, which serves as the identity element for addition. Dividing by 0 is an error and not allowed.

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The area covered by the roller in one full revelation is 1674 square inches.

Step-by-step explanation:

Given that You are using a 9 inch paint roller to paint a wall of your bedroom. The roller has a dimension of 158 inches as diameter and a nap thickness of 14 inch, as shown,

The nap is the fuzzy materials on the surface roller. How much area does the roller cover in one full revelation

The parameters to be considered are:

Diameter = 158 inches

Thickness = 14 inches

After one revolution rolling, the dimensions of the length will be:

L = 14 + 158 + 14

L = 186 inches.

Let the width be equal to 9 inches

The area covered = L × W

Substitute L and W into the formula

Area = 186 × 9

Area = 1674 square inches.

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To graph an absolute value function, choose several values of x and find some ordered pairs. Plot the points on a coordinate plane and connect them.

Absolute value equations are the equations in which the absolute value operator is used.

To graph such an equation, we must first get rid of the absolute value equation by dividing the equation into different parts. Then graph the equations of these parts separately.

If the value of the expression or the number inside the operator is negative, then the result is the negative of the expression or the number.

Suppose we have an expression: |x+1|

If (x+1) is positive or equal to 0, then  |x+1| =x+1

However, if (x+1) is negative, then |x+1| =-(x+1)=-x-1.

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It can be concluded that -

Given are the questions as shown in the image.

[1] -

Greater is the value of amount of tablespoon of sugar per oz of tea, sweetest it will be.

For table {1}, we can write -

m₁ = (12/18) = 2/3

For table {2}, we can write -

m₂ = 6/16 = 3/8

m₁ = 2/3 = (2 x 8)/(3 x 8) = 16/24

m₂ = 3/8 = (3 x 3)/(8 x 3) = 9/24

m₁ > m₂

Version A of iced tea will be sweetest.

[2] -

Greater is the value of amount of strawberry puree per unit of the total amount of liquid, stronger will be the strawberry flavor.

For Nick -

m₁ = 8/12 = 80/120

For Sam -

m₂ = 12/20 = 72/120

m₁ > m₂

Hence, Nick's claim is true.

Therefore, it can be concluded that -

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A triangle with given lengths 4cm , 5cm , and 6cm is scalene and acute angled triangle.

As given in the question,

In the given triangle ,

Lengths of the sides of a triangle is given by :

4cm , 5cm , and 6cm.

All the sides are of different measure , it is a scalene triangle.

Apply cosine rule to find the measure of largest angle:

c = 6cm is the longest side opposite to largest angle.

c² = a² + b²- 2abcosα

⇒ 6² = 4² + 5² - 2(4)(5)cosα

⇒cosα = ( 16 + 25 - 36 ) / 40

⇒ cosα = 5/40

⇒ α = cos⁻¹( 1/8)

⇒ α = 82.8° < 90°

It is an acute angled triangle.

Therefore, for the given lengths of the triangle it is a scalene and acute angled triangle.

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Answer:

y = 136

x=15

Step-by-step explanation:

to work this question out you must know the angles on a straight line add up to 180 degrees. By doing that we can find the top angle inside of the triangle.

180 - 104 = 76

to find x we need to know that angles in a triangle add up to 180 degrees.

180 =  (3x-1) + 4x + 76

To solve for x, we can first simplify the equation.

180 = (3x-1) + 4x + 76

This can be re-arranged as:

(3x-1) + 4x = 104

and then combined as:

7x = 105

Finally, we can solve for x by dividing both sides by 7:

x = 105/7

x = 15

So the value of x that satisfies the equation is 15

to find y we need to know that angles on a line equal 180

180 = (3(15)-1) + y

180 = 44 + y

To find the value of y, we can subtract 44 from both sides

y = 180-44

y = 136

The number included in the set of integers that when added to -4 gives a sum less than zero are 0, -2 and 3

The question wants us to find the numbers included in the set of integers that when added to -4 gives a sum less than zero.

The options are 3, 7, 9, -2, 4 and 0.

Therefore,

let

the number added = x

Hence,

-4 + x < 0

Base on the options, the numbers that fits into the inequality are as follows:

The numbers are 0, -2 and 3.

Therefore,

-4 + 0 < 0

-4 + -2 < 0

-4 + 3 < 0

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Correct option is A, the cost of the meal plan is non-linear.

The simplest approach to tell if a function is linear is to look at its graph. A linear function produces a straight line on a graph. A nonlinear function is not straight and is curved in some way. A linear function results in a straight line on a graph. As a result, non-linear functions can be of any kind. Although determining a function's linearity from its input/output table or equation is the simplest method, it is also possible to do so.

Based on the given conditions, formulate:

The definition of linear function

8-10 meals = (135-123) = (10-8) =10/2=5

10-12 meals: (155-135) = (12-10)

=20/2

= 10

12-21 meals: (220-155) = (21-12)

= 65/9

=7 2/9

5 < 7 2/9 < 10

So the cost of the meal plan is non-linear.

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Complete question -

The dimensions of the rectangular field with a minimum cost are x = 50 m and y = 2 m.

Let x be the length of the north-south sides and y be the length of the east-west sides.

The area will be given by: A = xy

The cost will be given by: C = 20x + 5y

We have to find the dimensions (x and y) that minimize the cost C subject to the constraint that the area A is 100 m2.

Using the constraint, we have:

A = xy = 100

We can solve this equation for one of the variables in terms of the other, say x in terms of y.

We get: x = 100/y

Substituting this into the cost equation, we get:

C = 20(100/y) + 5y

Differentiating this equation with respect to y and equating it to 0, we get:

dC/dy = 20/y2 - 5 = 0

or, y2 = 4

or, y = ±2

We choose the positive value for y, so y = 2

Substituting this value of y in the equation for x, we get:

x = 100/2 = 50

Therefore, the dimensions of the rectangular field with a minimum cost are x = 50 m and y = 2 m.

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The scale factor of the dilation is the ratio of the lengths of the corresponding sides of the two triangles. Since triangle ABC and triangle A'B'C' both have side lengths of AB, BC, and CA, the scale factor is 1.

1. Calculate the length of the sides of triangle ABC:

AB = length of side AB of triangle ABC

BC = length of side BC of triangle ABC

CA = length of side CA of triangle ABC

2. Calculate the length of the sides of triangle A'B'C':

A'B' = length of side A'B' of triangle A'B'C'

B'C' = length of side B'C' of triangle A'B'C'

C'A' = length of side C'A' of triangle A'B'C'

3. Calculate the scale factor of the dilation:

Scale factor = (AB/A'B') x (BC/B'C') x (CA/C'A')

= (length of side AB of triangle ABC / length of side A'B' of triangle A'B'C')

x (length of side BC of triangle ABC / length of side B'C' of triangle A'B'C')

x (length of side CA of triangle ABC / length of side C'A' of triangle A'B'C')

= 1 x 1 x 1

= 1

Therefore, the scale factor of the dilation is 1.

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Answer:

To solve the simultaneous equations by substitution, we can first solve one equation for one of the variables, and then substitute that expression into the other equation. Here is one way to solve the given equation:

2x - 3y = 8

We can solve for x by adding 3y to both sides:

2x = 3y + 8

We can divide both sides by 2 to get x by itself:

x = (3y + 8)/2

Now we can substitute this expression for x into the other equation:

2((3y + 8)/2) - 3y = 8

Simplifying and solving for y:

3y + 8 - 3y = 8

8 = 8

So the solution for y is any value.

Now we can substitute the value of y into the equation x = (3y + 8)/2 and we'll get the value of x.

x = (3 * y + 8) / 2

For example if we substitute y = 2

x = (3 * 2 + 8) / 2 = 14/2 = 7

So the solution for the simultaneous equations is x = 7, y = 2

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Answer:

Step-by-step explanation:

The equation given:

[tex]15 + \left(3x\right) = 24[/tex]

Our goal is to find x. To find x, what I like to do is add the given values together, then subtract them by 24 to find x's value.

[tex]15 + 3 = 18\\24 - 18 = x\\x = 6[/tex]

Hope this helps!

7019 gallons of water will be in the pool.

Initial volume of water = 8000 gal

Daily reduction = 1.3%

Time = 10 days

Required equation:

=8000*(1- 0.013)^10

=8000*0.987^10

=7018.7781 ≈ 7019 rounded to the nearest gallon.

An expression that uses constant algebraic numbers, variables, and algebraic operations is known as an algebraic expression in mathematics (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)

In contrast, since they are not derived from integer constants and algebraic operations, transcendental numbers like and e are not algebraic. The definition of e necessitates an infinite number of algebraic operations, while the construction of is typically done as a geometric relationship.

Any expression that can be converted into a rational fraction using the properties of the arithmetic operations is said to be rational (commutative properties and associative properties of addition and multiplication, distributive property and rules for the operations on the fractions).

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Answer:

Ian is correct

Step-by-step explanation:

The range of a function is the set of all possible values that the function can take. In other words, it is the values of y lying between minimum and maximum

From the graph we can see that the minimum value of y = 0

Maximum value of y = 30

So the range is 0 ≤ y ≤ 30

So Ian is correct

(Note that y ≤ 30 can include negative values which is not possible in this case)

Therefore , the solution of the given problem of equation comes out to be 1 hour is required to generate 81$ .  

The equal symbol (=) is used to indicate equivalency in a statement for a mathematical model, which combines two statements. In algebra, an equation is a claim that establishes the similarity of two mathematics. The formula 78x + 5 = 14 connects the two numbers, for example. The statements on either face of a letter form a mathematical connection. Typically, the symbol is the lone element and the only variable. For example, 9x – 4 = 2.

Here,

Given :c = 18h + 63

Where c is cost in dollars

and h is hour spend.

Thus ,

To find the maximum amount of time to generate $81

So,

Using equation:

81 = 18h + 63

=> 18h = 81-63

=> 18h = 18

=> h =1

Therefore , the solution of the given problem of equation comes out to be 1 hour is required to generate 81$ .  

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We can see from the provided data that it is obviously divergent.

Convergent sequence occurs when, as n approaches infinity, you arrive at a final as well as constant term through a number of terms. Divergent sequences are those in which individual terms never stabilize; instead, they constantly grow or decrease as n approaches infinity, approaching either infinity or -infinity.

A series diverges when it moves up, down, to infinity or minus infinity without settling on a value.

The series' parts are becoming larger and larger while being interrupted by some constant "1" (however they are useless in this situation since the series is divergent because there are always two numbers that follow an intercepting "1" that are greater by 1 than the two that came before it).

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The value of y'' at the point where x = 0 is 8.

A derivative is a mathematical concept that measures how much a function changes as its input (or independent variable) changes. It is often represented by the symbol "dy/dx" or "f'(x)", and is used to calculate the slope of a function at a particular point.

To find the value of y'' at the point where x = 0, we first take the derivative of the equation with respect to x. This gives us y' + 8exy' = 0. Then, we take the derivative of this equation with respect to x again, which gives us y'' + 8exy'' + 8ey' = 0. Substituting x = 0 into this equation gives us y'' + 0 + 8e(0) = 0, which simplifies to y'' = 8.

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If a forest covers 51,000 acres. A survey finds that 0.4​% of the forest is​ old-growth trees. The number of  acres of​ old-growth trees that are​ there is: 204 acres.

Using this formula to find the number of acres that are there.

Number of acres = Number of forest covers acres × Forest old growth tree percentage

Where:

Number of forest covers acres = 51,000 acres

Forest old growth tree percentage = 0.4% or 0.004

Let plug in the formula

Number of acres = 51,000 acres × 0.004

Number of acres = 204 acres

Therefore we can conclude that the number of acres  is 204 acres.

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