Two mechanics worked on a car. The first mechanic charged $55 per hour, and the second mechanic charged $65 per hour. The mechanics worked for a combined total of 20 hours, and together they charged a total of $1250 . How long did each mechanic work?

The number which correctly represents the decimal 0.6 as a whole number is; 1.

It follows from the task content that the number which correctly represents the number 0.6 as a whole number is to be determined.

Since the given number is 0.6. It follows that the closest whole number can be determined by rounding off to th nearest whole number.

Hence, by rounding off; we have; 1.

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True, that {~v1, ~v2, ~v3, ~v4}is also a linearly dependent set.

What is a linearly independent set?

A collection of vectors is said to be linearly independent in vector space theory if no nontrivial linear combination of the vectors equals the zero vector. The vectors are considered to be linearly dependent if such a linear combination occurs.

(i.e., all coefficients = 0). A single element set {v} is linearly independent if and only if v ≠ 0.

Now,

As given that

x1v1 + x2v2 + x3v3 = 0 with x1, x2, x3 not all zero, then x1v1 + x2v2 + x3v3 + 0 v4 = 0 and still the coefficients are not ALL zero.

Hence,

        It is True that {~v1, ~v2, ~v3, ~v4}is also a linearly dependent set.

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The pair of transformations that could map ABC to A’B’C’, such that the triangles are similar but not congruent are dilation and rotation

Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent

Given data ,

Let the triangle be represented as ΔABC

Let the dilated triangle be represented as ΔA'B'C'

Let the dilation scale factor be represented as k

Now , when a triangle is dilated by a scale factor of k , there is a change in the shape of the triangle

After a dilation , the triangle will enlarge or compress by a factor k , but it will be similar to the parent triangle

Now , when the triangle is rotated , it only changes the initial coordinates of A , B and C

Hence , the transformations are dilation and rotation

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The amount of Carbon that will be presented in 2,000 years is given as follows:

7.85 grams.

An exponential function is defined as follows:

y = a(b)^(x/n).

In which:

Considering the initial amount of 10 grams and the half life of 5730 years, the parameters for this problem are given as follows:

a = 10, b = 0.5, n = 5730.

Hence the function is defined as follows:

y = 10(0.5)^(x/5730)

Then the amount after 2,000 years is given as follows:

y = 10(0.5)^(2000/5730)

y = 7.85 grams.

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So, using a heater with a heating output of 5900 kJ/min, it will take roughly 9.05 hours to heat the water in the hot tub from 65°F to 104°F.

When the temperature rises, atoms and molecules move faster and collide, creating thermal energy (also known as heat energy). Thermal energy is the energy that results from the heated substance's temperature.

Calculate the square footage or square metres of your room. The room's dimensions are then multiplied by its width, height, and length. Then double this amount by 6. For BTUs or 0.0606 for kW, respectively. 

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Answer:

177°

Step-by-step explanation:

A sector is the area between two radi.

We are given the perimeter of the sector as 21.4cm and the radius 4.2cm. Subtracting two radi from the perimeter will give us the arc of the sector as 13.

As we know, the formula for the length of an arc is: length of arc = ∅/360 × πd. Diameter is double the radius so in this case it's 8.4; so filling in the blanks our new formula is: 13 = ∅/360 × 8.4π.

We are trying to find ∅ which is the degree of the sector. So from this formula we can rearrange it by dividing 8.4π on both sides of the equation giving ¹³/8.4π = ∅/360; from here we multiply 360 on both sides and therefore getting ∅ on its own therefore allowing us to equate it.

Plug that all into a calculator and you get 177.3440794 so you can round it down to 177°

I saw this question a few minutes ago but spent a bit of time calculating it...sorry :)

Answer: The derivative of f(x) = 4x^3 - 5x^2 + 7x - 10 is given by f'(x) = 12x^2 - 10x + 7.

Step-by-step explanation:

The answer to the "different" question is: 32

The answer to the "same" question is: 2

Answer:

-a^2+7a

Step-by-step explanation:

The difference in the average weight of the four heaviest boxes and the four lightest boxes is 75 Kg.

Given:

The weight of boxes is :

1st box = 200 kg

2nd box = 300 kg

3rd box = 250 kg

4th box = 350 kg

5th box = 500 kg

Since , heavier weight = 500 Kg

lighter weight = 200 Kg

Average weight of four heaviest boxes =1400/4=350kg

Average weight of four lightest boxes =1100/4=275kg

∴ Difference =(350−200)/2=150/2=75kg

Hence , the difference in the average weight of the four heaviest boxes and the four lightest boxes is 75 Kg.

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Answer: Gross pay = $733.04

Step-by-step explanation:

The equation x = √-x + 6 cannot have any real solutions, because taking the square root of a negative number is not a real number. So the answer is none of the options listed.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical phrase with two equal sides separated by an equal sign is called an equation. Linear equations are classified into three types: point-slope, standard, and slope-intercept. Identity equations and conditional equations are the two types of equations. An identity holds true for all possible values of the variables. A conditional equation is valid only for certain values of the variables. An equation consists of two expressions joined by an equals sign ("=").

Here,

The equation x = √-x + 6 cannot have any real solutions, because taking the square root of a negative number is not a real number.

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Answer:

Step-by-step explanation:

If Martha needs 28 strawberries for every 4 smoothies she makes, then she needs 7 strawberries per smoothie.

Answer:

(3, - 4 )

Step-by-step explanation:

under a reflection in the x- axis

a point (x, y ) → (x, - y ) , then

(- 3, 4 ) → (- 3, - 4 )

under a reflection in the y- axis

a point (x, y ) → (- x, y ) , then

(- 3, - 4 ) → (3, - 4 )

Answer:

y=-5x+15.

Step-by-step explanation:

1. if the given slope is (-5), then it is possible to make up the required equation in slope-interception form: y=-5x+interception, where 'interception' is unknown number;

2. in order to calculate the 'interception' it is enought to substitute the given coordinates of the point into the last equation (y=5; x=2):

5=-5*2+interception; ⇒ interception=15. Then

3. finally, the required equqaiton is y=-5x+15.

Answer: 4 hours

Step-by-step explanation: y int = 120, slope = 30

Answer:

15

Step-by-step explanation:

The distance can't be negative.

20-5=15

(a) To be eligible for Mensa, an individual's IQ must be in the top 2% of the population. This means that the IQ score must be greater than or equal to the 97th percentile of the normal distribution. We can use the standard normal distribution table to find the 97th percentile.

Since the mean IQ score is 100 and the standard deviation is 15, we can standardize the IQ score to find the z-score:

z = (IQ - mean) / standard deviation

z = (IQ - 100) / 15

The 97th percentile corresponds to a z-score of 2.33. To find the IQ score, we can reverse the standardization formula:

IQ = z x standard deviation + mean

IQ = 2.33 x 15 + 100

IQ = 146.95

So, the lowest Stanford-Binet IQ you could have and still be eligible to join Mensa is 147.

(b) To be eligible for Mensa on the basis of the quantitative reasoning part of the GRE exam, an individual's score must be in the top 2% of the population. This means that the score must be greater than or equal to the 97th percentile of the normal distribution. We can use the standard normal distribution table to find the 97th percentile.

Since the mean score on the quantitative reasoning part of the GRE is 151.3 and the standard deviation is 8.7, we can standardize the score to find the z-score:

z = (score - mean) / standard deviation

z = (score - 151.3) / 8.7

The 97th percentile corresponds to a z-score of 2.33. To find the score, we can reverse the standardization formula:

score = z x standard deviation + mean

score = 2.33 x 8.7 + 151.3

score = 162.291

So, the score required to be eligible for Mensa on the basis of the quantitative reasoning part of the GRE exam is approximately 162. Round to the nearest whole number, the score would be 162.

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The time it would take for the rock to reach the ground is given as follows:

3.19 seconds.

The quadratic equation that models a projectile's height is given as follows:

y = -9.81t² + v(0)t + h(0).

In which:

The parameters for this problem are given as follows:

v(0) = 0, h(0) = 100.

The rock reaches the ground when y = 0, hence:

9.81t² = 100

t = sqrt(100/9.81)

t = 3.19 seconds.

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Answer:

two plus two equals five

Step-by-step explanation:

Let S₁ and S₂ be subsets of a vector space V. So, proves are shown as well.

A vector space, also known as a linear space, is a collection of vectors that have been put together and multiplied ("scaled") by integers known as scalars. Real numbers are frequently seen as being scalars. Scalar multiplication by rational numbers, complex numbers, etc., on the other hand, seldom occurs. The term "subspace" refers to a vector space that is enclosed within another vector space. Each subspace is a vector space in and of itself, but it also has a definition in relation to another (bigger) vector space. We'll soon find out that there are a lot of different subspaces from earlier parts that we already know about.

Let, S₁ and S₂ be subsets of vector space V

Now, S₁ ⊆  V, S₂ ⊆  V

(S₁ ∩ S₂) ⊆ V

Let, x ⊆ span (S₁ ∩ S₂)

x ∈ span (S₁) and x ∈ span (S₂)

x ∈ span (S₁ ∩ S₂)

∴ span (S₁ ∩ S₂) ⊆ span (S₁) ∩ span (S₂)

span (S₁ ∩ S₂) =  span (S₁) ∩ span (S₂)

where either S₁ ⊆ S₂ or, S₂ ⊆ S₁

span (S₁ ∩ S₂) ≠  span (S₁) ∩ span (S₂)

where, (S₁ ⊆ S₂) = ∅ but span (S₁) ∩ span (S₂)

(S₁ ∩ S₂) = ∅ i.e. span (S₁ ∩ S₂)

but span (S₁) = R₁²

span (S₂) = R₁²

Thus, span (S₁) ∩ span (S₂) = R₁²

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The absolute value of the sum of two integers does not exceed the sum of the absolute values ​​of these integers. ∀x, ∀y, |x + y|≤|x| + |y| .

What is inequality?

An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.

The absolute value of the sum of two integers does not exceed the sum of the absolute values ​​of these integers. ∀x, ∀y, |x + y|≤|x| + |y| .

This inequality, sometimes called as the triangle inequality.

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The absolute value of the sum of two integers does not exceed the sum of the absolute values ​​of these integers. ∀x, ∀y, |x + y|≤|x| + |y| .

What is inequality?

An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.

The absolute value of the sum of two integers does not exceed the sum of the absolute values ​​of these integers. ∀x, ∀y, |x + y|≤|x| + |y| .

This inequality, sometimes called as the triangle inequality.

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Answer:

30

Step-by-step explanation:

before

p:r

=8:5

after

p:r

=5:5

3 units=18

1 unit=6

no. of marbles Ravi has=5 units=6×5=30

The rational numbers in this problem are given by these following letters:

A, B, C, D, E, G, I, K, L, O.

Rational numbers are the whole numbers plus decimals that can be represented by fractions, involving both positive and negative numbers.

The set of irrational numbers is composed by numbers that cannot be represented by fractions, such as non-exact roots, which are non-terminating and non-repeating decimal numbers.

The irrational numbers are justified as follows:

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The cotangent of an angle is obtained dividing the cosine of the angle by the sine of the angle, that is:

cot(x) = cos(x)/sin(x).

The three trigonometric ratios are defined as follows:

The cotangent function is the inverse of the tangent function, that is:

cot(x) = 1/tan(x)

cot(x) = 1/(sin(x)/cos(x))

cot(x) = cos(x)/sin(x).

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The angles are alternate interior angles

<4 and <6

<3 and <5.

The fundamental characteristics listed below make it simple to recognise parallel lines.

Given:

As, from the property of parallel line we have the following properties

So, from the figure the pair angles shows alternate interior angle

<4 and <6

<3 and <5.

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a) For two distinct real roots: x > 0 or x > m

b) For two distinct real roots: x > 0 or x > 2m

c) For two distinct real roots: x > 0 or x > 4

This is based on the quadratic equation.

Only non-negative integer powers of x are present in the quadratic equation, making it a polynomial equation. In actuality, the Latin word quadratus, which means square, is the root of the term quadratic. The quadratic equation has the generic form ax² + bx + c = 0. where x is an unknowable variable and a, b, and c are mathematical coefficients.

a) Quadratic equation: x² - 4x + m = 0

The discriminant: Δ = b² - 4ac

Δ = (2x)² - 4.x.(m)

Δ = 4x² - 4mx

Δ = 4x (x - m)

For two distinct real roots: Δ > 0

4x (x - m) > 0

x > 0 or x > m

For two real roots: Δ ≥ 0

4x (x - m) ≥ 0

x ≥ 0 or x ≥ m

For a repeated root: Δ = 0

4x (x - m) = 0

x = 0 or x = m

(b) Quadratic equation: mx² + 3x + 2 = 0

The discriminant: Δ = b² - 4ac

Δ = (3x)² - 4.mx.(2)

Δ = 4x² - 8mx

Δ = 4x (x - 2m)

For two distinct real roots: Δ > 0

4x (x - 2m) > 0

x > 0 or x > 2m

For two real roots: Δ ≥ 0

4x (x - 2m) ≥ 0

x ≥ 0 or x ≥ 2m

For a repeated root: Δ = 0

4x (x - 2m) = 0

x = 0 or x = 2m

(c) Quadratic equation: x² - mx + 1 = 0

The discriminant: Δ = b² - 4ac

Δ = (x)² - 4.x.(1)

Δ = x² - 4x

Δ = x (x - 4)

For two distinct real roots: Δ > 0

x (x - 4) > 0

x > 0 or x > 4

For two real roots: Δ ≥ 0

x (x - 4) ≥ 0

x ≥ 0 or x ≥ 4

For a repeated root: Δ = 0

x (x - 4) = 0

x = 0 or x = 4

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