The difference between two numbers is 4. If twice the larger number x is equal to three more than three times the smaller number y, what is the value of 2x + 3y?

With regard to promoting standards of excellence, Lafasto and Larson (2001) identified three Rs that help improve performance:

The LaFasto and Larson Model investigated team effectiveness. It is founded on the premise that, while individuals might be highly competent and talented, teams solve the most challenging issues.

It doesn't matter how skilled an individual is if they can't operate as part of a team.

They studied the traits of 75 highly successful teams. They discovered that high standards of excellence were a critical component in team performance.

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Answer:

C

Step-by-step explanation:

what is the greatest common factor of 72 and 54 ?

in other words, what is the biggest number that divides both numbers without remainder ?

I use a prime factor analysis (identify all the prime factors).

72 :

72 ÷ 2 = 36

36 ÷ 2 = 18

18 ÷ 2 = 9

9 ÷ 2 no

9 ÷ 3 = 3

3 ÷ 3 = 1 finished

72 = 2⁴×3²

54 :

54 ÷ 2 = 27

27 ÷ 2 no

27 ÷ 3 = 9

9 ÷ 3 = 3

3 ÷ 3 = 1 finished

54 = 2×3³

the largest number that can divide them both without remainder is the combination of the prime factors they have in common :

2 × 3² = 18

Answer:

It will take them approximately 51.43 minutes to complete the project together

Step-by-step explanation:

This is what is called a "shared job" problem.

The best way to work on them is to start by finding the "portion" of the job done by each of the people in the unit of time.

So, for example, Sarah completes the project in 90 minutes, so in the unit of time (that is 1 minute) she completed 1/90 of the total project

Betty completes the project in 120 minutes, so in the unit of time (1 minute) she completes 1/120 of the total project.

We don't know how long it would take for them to complete the project when working together, so we call that time "x" (our unknown).

Now, when they work together completing the entire job in x minutes, in the unit of time they would have done 1/x of the total project.

In the unite of time, the fraction of the job done together (1/x) should equal the fraction of the job done by Sarah (1/90) plus the fraction of the job done by Betty. This in mathematical form becomes:

\(\frac{1}{x} =\frac{1}{90} +\frac{1}{120}\\\frac{1}{x} =\frac{4}{360} +\frac{3}{360}\\\frac{1}{x} =\frac{7}{360} \\x=\frac{360}{7} \\x=51.43\,\,min\)

So it will take them approximately 51.43 minutes to complete the project together.

Answer:

Step-by-step explanation:

The distance is:

Return trip will take:

Answer:

21

Step-by-step explanation:

Volume of a cuboid is given by

V = l*w*h

924 = 4 (x+1) (x+11)

FOIL

924 = 4(x^2 +11x+x+11)

924 = 4(x^2+12x+11)

Divide each side by 4

231 = (x^2+12x+11)

Subtract 231 from each side

0 = x^2 +12x +11-231

0 = x^2 +12x - 220

Factor

0 = (x+22) (x-10)

Using the zero product property

x+22 =0  x-10 =0

x=-22  x=10

We cannot have a negative length

x=10

The side lengths are 4, 10+1, 10+11

4,11,21

The longest is 21

The two points (0,-4) and (-4/3,0) are solutions to the inequality 6x +2y<-8.

Given the inequality 6x +2y<-8,

The equation 6x - 2y = 8 divides the coordinate plane into two parts. The shaded region contains all points with coordinates (x,y).

Such that 6x + 2y > 8. Because the sign of the inequality is not equal (is strongly <), the boundary line should be dashed.

Choose two points:

When x = 0, 2y< -8, and y can be -4. You get point (0, -4);

if y=0, then 6x <-8, and x can be -4/3. You get the idea (-4/3,0).

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Answer: 4.375% I think

Step-by-step explanation:

Answer:

C. 4.375%

Step-by-step explanation:

Answer and Step-by-step explanation:

The real line is the line whose points are real numbers. The symbol used for the entire line is R.                

A point is chosen on line as the origin. Points are right or positive, and points to the left are negative.

The main properties of real numbers are commutative, Associative, and Distributive. Real numbers are closed, have an identity element, additive inverse, multiplicative inverse, and zero product. When we choose a uniform random number, it should satisfy all these conditions of real numbers.

Choose a random number on the real line; for example, when we choose zero (0), it does not satisfy the multiplicative inverse.

Multiplicative inverse is a x 1/a = 1, but for 0, 1/0 it is undefined.

Hence it is not possible for a  random number from the whole real line.

The value of c from c−7.6=−4 is 3.6.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

These values are frequently represented in algebra by symbols such as x, y, z, p, or q, and these symbols are known as variables.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

c−7.6=−4

Now, solve for c

Add 7.6 both side

c- 7.6 + 7.6 = -4 + 7.6

c = 3.6

Hence, the value of c is 3.6.

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Answer:

2193 ft

Step-by-step explanation:

You're basically solving for the hypotenuse (h) of a right triangle with a base angle of 20° and an opposite leg of 750 ft.

sin20 = 750/h

h = 750/sin20 ≈ 2193 ft

Answer:

Step-by-step explanation:

5 ≤ - 3x- 3 ≤ 10

x

few notes about inequality

the direction of the inequality doesn't change if you

the direction of the inequality does change

if you

\(step - 1 : difine\)

\(5 \leqslant - 3x - 3 \leqslant 10\)

\(step - 2 : \\ add \: 3 \: in \: each \: sides\)

\(5 + 3 \leqslant - 3x - 3 + 3 \leqslant 10 + 3\)

\(8 \leqslant - 3x \leqslant 13\)

\(step - 3 : \\ divide \: - 3\: from \: each \: sides \: \\ and \: swap \: the \: inequalily\)

\( \therefore - \frac{8}{3} \geqslant x \geqslant - \frac{13}{3} \)

Answer:

length is 20 and width is 9

Step-by-step explanation

Answer:

A. ∠A = 68°, ∠B = 22°, AB = 2.9cm

Step-by-step explanation:

I calculated it logically

The area of the rhombus, obtained from the dimensions, of the diagonals, found from the trigonometric of sines of the angle can be presented as follows;

Area = 8·√3

The area of a plane figure is the two dimensional space occupied by the figure on a plane.

The measure of the angle ABC, m∠ABC = 60°

The length of the segment AE = 2 units

The diagonals of a rhombus bisect each other at right angles, and the right angles through which they pass, therefore;

BE = ED, m∠AEB = 90°

m∠ABE = 30°

sin(30°) = AE/AB

sin(30°) = 2/AB

AB = 2/(sin(30°)) = 4

AB = 4

BE = √(4² - 2²) = √(12) = 2·√3

Therefore; AC = 2 + 2 = 4

BD = 2·√3 + 2·√3 = 4·√3

The area of a rhombus = (1/2) × The product of the length of the diagonals

Therefore;

Area of the rhombus = (1/2) × (4·√3) × 4 = 8·√3

The area of the rhombus = 8·√3

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Projectile B begins its descent 1 seconds before Projectile A does.

In Mathematics and Geometry, the y-intercept of any graph or table such as a quadratic equation or function, generally occurs at the point where the value of "x" is equal to zero (x = 0).

By critically observing the table shown in the image attached above, we can reasonably infer and logically deduce the following y-intercept of Projectile A:

y-intercept = (0, 44).

Maximum height = (4, 300).

When t = 0, the y-intercept of Projectile B can be calculated as follows;

h(t) = -16t² + 96t

h(0) = -16(0)² + 96(0)

h(0) = 0.

For the maximum height, we have:

h(t) = -16t² + 96t

h'(t) = -32t + 96

32t = 96

t = 96/32

t = 3

Difference in time = 4 - 3

Difference in time = 1 seconds.

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The number of lights L that are on after t minutes of the stage shows is,

A. L = (1/2)t + 10.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, When the show starts, 10 lights are on which is a constant in out function.

Every 30 seconds or (1/2) a minute 1 more light comes on.

∴  The function best models the number of lights that are on after t minutes of the stage shows is,

L = (1/2)t + 10.

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The Price after Mark up will be $141.3945.

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

Given:

The product is to be marked up 17%.

Its current price is $120.85.

Now, the Price after marked up is

= 120.85 + 17% of 120.85

= 120.85 + 20.5445

= $141.3945

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Luis traveled approximately 31,736.8 inches on his bicycle.

We have,

To find the distance that Luis traveled on his bicycle, we need to calculate the circumference of the tires and then multiply it by the number of complete turns.

Given:

Radius of the tires (r) = 20p (2.54) inches

Number of complete turns (n) = 50

The circumference of a circle can be calculated using the formula:

Circumference = 2πr

Substituting the given radius into the formula, we have:

Circumference = 2π * (20p) inches

Now we can calculate the distance traveled (d):

Distance = Circumference x Number of complete turns

Distance = 2π x (20p) x 50 inches

To simplify the calculation, we can approximate π as 3.14:

Distance ≈ 2 x 3.14 x (20 x 2.54) x 50 inches

Calculating this expression, we find:

Distance ≈ 31736.8 inches

Therefore,

Luis traveled approximately 31,736.8 inches on his bicycle.

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The complete question.

What is the distance that Luis traveled on his bicycle rolled 20p (2.54) after the tires gave 50 complete turns

The value of x in the angles is 12 degrees

The figure that completes the question and the required parameters is added as an attachment

From the figure, we have the following parameters and angles

A = 5x - 15

B = 2x + 21

Also from the figure, we can see that the angles A and B are vertical angles

As a general rule, vertical angles have the same measure

This in other words mean that they are congruent angles

So, we have

A = B

Substitute the known values in the above equation

So, we have the following equation

5x - 15 = 2x + 21

Collect the like terms

5x - 2x = 15 + 21

Evaluate the like terms

3x = 36

Divide both sides by 3

x = 12

Hence, the solution of x in the lines is 12 degrees

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The probabilities of the events and their values are shown below

The total number of marbles in the bag is 13, with 6 blue, 2 green, and 5 red.

P(Blue or Green) represents the probability of selecting a blue or green marble on the first pick.

This is calculated as follows:

P(Blue or Green) = P(Blue) + P(Green)

= 6/13 + 2/13

= 61.5%

P(Blue and Green) represents the probability of selecting a blue marble and a green marble on two consecutive picks, with replacement.

Therefore:

P(Blue and Green) = P(Blue) * P(Green)

= (6/13) * (2/13)

= 7.1%

P(Blue and Green) represents the probability of selecting a blue marble and a green marble on two consecutive picks, without replacement.

Therefore:

P(Blue and Green) = P(Blue) * P(Green)

= (6/13) * (2/12)

= 7.7%

P(Blue) represents the probability of selecting a blue marble on the first pick.

This is simply the proportion of blue marbles in the bag:

P(Blue) = 46.2%

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Given:

Height of the cone, h = 7 ft

Diameter of the cone = 6 ft

Let's find the lateral surface area of the cone.

To find the lateral area of the cone, apply the formula:

Where r is the radius of the cone.

To find the radius, we have:

Therefore, we have:

Therefore, the lateral area of the cone is approximately 72 ft²

ANSWER:

The most effective way to describe multivariate relationships is by means of graphs and multiple variables.

The term "multivariate analysis" refers to a broad variety of statistical methods, not simply one particular approach. These methods enable you to comprehend your data more thoroughly in light of particular commercial or real-world settings.

Multivariate analysis is therefore a key idea to understand if you're wanting to be a data analyst or data scientist.

The breadth of knowledge that multivariate analysis offers is its one key benefit. The insights you find are far more applicable to the actual world because you're drawing a lot more thorough picture of what's happening when you explore numerous factors.

There are two different kinds of multivariate analytic techniques: interdependence techniques, which examine the structure of a dataset, and dependency techniques, which examine the cause-and-effect interactions between variables.

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As a result, multivariate analysis is a crucial concept to comprehend if you wish to work as a data analyst or data scientist.

The main advantage of multivariate analysis is the breadth of knowledge it provides. Since you're looking at many different elements, you're getting a much more complete picture of what's going on, which makes the insights you discover much more applicable to the real world.

There are two major categories of multivariate analytic approaches: dependency techniques, which look at the cause-and-effect relationships between variables, and interdependence techniques, which look at the dataset's structure.

The algebraic expression: 3y + 3 = -11

To solve for y, first subtract 3 from both sides.

3y = -14

Divide both sides by 3

y = -14/3

the height decreases

..

Answer:

\(x = \frac{y - 4}{7}\)

Step-by-step explanation:

\(y = 7x + 4 \\\\y - 4 = 7x\\\\\frac{y - 4}{7} = \frac{7x}{7}\\ \\ \frac{y - 4}{7} = x\)

Answer:

???

Notes:

Hi, sorry, but I can't really do this if I don't know what 15 shirts cost, or if there isn't an equation of some sort. (Sorry again...)

Answer:

7 schools have fewer than 50 classrooms.

Answer:

3/4

Step-by-step explanation:

There are 3 numbers greater than 1. 2, 3, and 4. Since there are 4 numbers total, we get a 3/4 chance.

Answer:

3/4

Step-by-step explanation:

There are four options and 3 of them =3 or greater than 1

P(3 or greater than 1) = 3/4