A small business was founded by three friends whose capital shares are: Aries-$120, Gemini-$240, and Leo-$360.
Their profit for the week reached $540. The profit will be divided in proportion to their investment.

What percent of the capital shares was invested by Leo?​

The sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

To translate the inequality expression "2/3y - 9 < y + 1" into a sentence, we can break it down into smaller parts:

"2/3y" represents two-thirds of a number.

"9" represents the number nine.

"y + 1" represents the number increased by one.

Now let's construct the sentence:

"Nine less than two-thirds of a number" - This refers to the expression "2/3y - 9," indicating that we have subtracted nine from two-thirds of a number.

"is less than" - This is the comparison symbol in the inequality.

"the number" - This refers to the expression "y + 1," representing the number increased by one.

Combining these parts, we form the sentence: "Nine less than two-thirds of a number is less than the number."

Hence, the correct sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

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Answer:

Step-by-step explanation:

f(t)=t²-5t , t≤-10

f(-10)=(-10)²-5(-10)=100+50=150

Step-by-step explanation:

19can be factorised as ,

1× 19

19 × 1

All factors= 1 and 19

since it has only two factors 1 and the number itself so it is a prime number .

Numbers which have more than 2 factors ( 1 and the number itself) are called composite numbers .

And we are done!

- Rishabh

Answer: The factors of 19 are 1 and 19. 19 is a prime number.

Step-by-step explanation:

To find the factors of 19, we need to find all the whole numbers that can be multiplied to equal 19. The factors of 19 are 1 and 19. Since 19 only has two factors, 1 and 19, it is a prime number. To confirm this, we can also check if 19 is divisible by any numbers other than 1 and itself. Since it is not, we can conclude that 19 is a prime number.

Answer:

A.) No

B.) test statistic = - 3.108

Check explanation

Step-by-step explanation:

H0: m = 105 versus H1: m ≠ 105

Sample size, n = 35, since we have a large sample size, greater than 30.

B.)

xbar = 101.9 ; s = 5.9

Test statistic :

T = (xbar - μ) ÷ (s/√n)

T = (101.9 - 105) / (5.9/√35)

T = - 3.1 / 0.9972820

Test statistic = - 3.11

Pvalue from Tstatistic, df = 34

Pvalue = 0.003772( Pvalue calculator)

Pvalue is the probability of obtaining a value more extreme or exactly that of the test statistic.

At α = 0.01

Pvalue < α ; We fail to reject the Null

Answer:

five thousand seven hundred and eighty-nine

Step-by-step explanation:

The expression represents the distributive property from the list of options is (b) a(b + c) = ab + ac

The distributive property is a mathematical property that applies to multiplication and addition or subtraction.

It states that when you multiply a number (or variable) by a  sum or difference inside parentheses, you can distribute the multiplication across the terms inside the parentheses.

This is represented by the following formula:

a(b + c) = ab + ac

This is represented by Option (B)

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A.  The payback period is 7.2 years. The net present value of the proposed investment is 3720.55.

B. No, the project does not meet the company's cash payback criteria.

C.  Yes, the project does meet the net present value criteria for acceptance.

A. The truck costs $55,440 and generates annual cost savings of $7,700. So the payback period is the cost of the truck divided the expected amount the truck will generate.

                $55,440 / $7,700 = 7.2 years

To solve for the net present value, we say

Net Present Value = ∑ [(Cash inflow in period t) / (1 + \(r^{t}\)] - Initial Investment.

NPV = (($7,700 / (1 + 0.08)¹) = 7 129.63

+ ($7,700 / (1 + 0.08)²) = 6601.51

+ .($7,700 / (1 + 0.08)³ = 6112.51

+ ($7,700 / (1 + 0.08)⁴) = 5659.73

+ ($7,700 / (1 + 0.08)⁵) = 5240.49

+ ($7,700 / (1 + 0.08)⁶) = 4 852.31

+ ($7,700 / (1 + 0.08)⁷) = 4492.88

+($7,700 / (1 + 0.08)⁸)  = 4160.07

+ ($27,600 / (1 + 0.08)⁸)) = 14911.42

- $55,440

We add all these values together and subtract by  $55,440

7 129.63 + 6601.51 + 6112.51 + 5659.73 + 5240.49 +4 852.31 + 4492.88 + 4160.07 + 14911.42 - $55,440

59160.55 - 55,440

NPV = 3720.55

B. The cash payback period of the project is 7.2 years. The company's cash payback criteria state that a project should not be accepted unless it has a payback period that is less than 50% of the asset's estimated useful life, which would be 4 years which is 50% of 8 years. Since 7.2 years is greater than 4 years, the project does not meet the company's cash payback criteria.

C. The positive NPV of $3,720.55 shows that embarking on the prooject will be valuable to the company. This means the project meets the NPV criteria for acceptance.

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Answer:

Step-by-step explanation:

∡5 = 42°

find: ∡ 14

solution:

since ∡5 = ∡13 = 42°

∡14 = 180 - ∡13

      = 180 - 42

      = 138°

Answer:

x^3 + 4x^2 + 5x + 2.

Step-by-step explanation:

(x+1)(x+1)(x+2) = (x^2 + x + x + 1)(x + 2) = (x^2 + 2x + 1)(x + 2) = x^3 + 2x^2 + 2x^2 + 4x + x + 2 = x^3 + 4x^2 + 5x + 2.

Hope this helps!

The best representation of the number of tiles that will be needed to cover the Floor is 80 tiles.

The number of tiles needed to cover the floor, we can calculate the total area of the floor and divide it by the area of each tile.

The area of the floor is given by the product of its length and width: 15 feet * 12 feet = 180 square feet.

The area of each tile is given by the product of its length and width: 1.5 feet * 1.5 feet = 2.25 square feet.

To find the number of tiles needed, we divide the total area of the floor by the area of each tile:

Number of tiles = (Total area of the floor) / (Area of each tile) = 180 square feet / 2.25 square feet = 80 tiles.

therefore, the best representation of the number of tiles that will be needed to cover the floor is 80 tiles.

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Answer:

Step-by-step explanation: [-2.19] = -3

[3.67] = 3

[-0.83] = -1

The domain of this function is a group of real numbers that are divided into intervals such as [-5, 3), [-4, 2), [-3, 1), [-2, 0) and so on. This explains the domain and range relations of a step function.

This can be generalized as given below:

[x] = -2, -2 ≤ x < -1

[x] = -1, -1 ≤ x < 0

[x] = 0, 0 ≤ x < 1

[x] = 1, 1 ≤ x < 2

Answer:

y = - \(\frac{3}{2}\) x

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 2, 3) and (x₂, y₂ ) = (0, 0) ← 2 points on the line

m = \(\frac{0-3}{0-(-2)}\) = \(\frac{-3}{0+2}\) = - \(\frac{3}{2}\) , then

y = - \(\frac{3}{2}\) x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (0, 0 )

0 = - \(\frac{3}{2}\) (0) + c = 0 + c , so

c = 0

y = - \(\frac{3}{2}\) x + 0 , that is

y = - \(\frac{3}{2}\) x

Therefore, the quotient when x³ - x² - 3x + 2 is divided by x - 2 is x² - 2x - 5 with a remainder of -3.

To find the quotient when x³ - x² - 3x + 2 is divided by x - 2, we will use the long division method. Here is the solution:  

Step 1: The first term of the quotient is x². Multiply x² by x - 2 to get x³ - 2x². Subtract this product from x³ - x² to get: x² - 3x² = -2x²

Step 2: Bring down the next term of the dividend, which is -3x. The new dividend is -2x² - 3x.

Step 3: The second term of the quotient is -2x. Multiply -2x by x - 2 to get -2x² + 4x. Subtract this product from -2x² - 3x to get -5x.

Step 4: Bring down the last term of the dividend, which is +2. The new dividend is -5x + 2. Step 5: The third term of the quotient is -5. Multiply -5 by x - 2 to get -5x + 10. Subtract this product from -5x + 2 to get -3.

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Answer:

1

Step-by-step explanation:

\(F =\cos 0^{\circ} = 1\)

You need to multiply by 5 instead of 6 because each pair of opposite faces on a cuboid has the same area, so by considering one face from each pair, you ensure that you don't count any face twice.

When calculating the total surface area of a cuboid, you need to understand the concept of face pairs.

A cuboid has six faces, but each face has a pair that is identical in size and shape.

Let's break down the reasoning behind multiplying by 5 instead of 6 in the given scenario.

To find the surface area of a cuboid, you can add up the areas of all its faces.

However, each pair of opposite faces has the same area, so you avoid double-counting by only considering one face from each pair. In this case, you have five pairs of faces:

(1) top and bottom, (2) front and back, (3) left and right, (4) left and back, and (5) right and front.

By multiplying the average area of a pair of faces by 5, you account for all the distinct face pairs.

Essentially, you are considering one face from each pair and then summing their areas.

Since all the pairs have the same area, multiplying the average area by 5 gives you the total surface area.

When dividing 150 by 4 (to find the average area of a pair of faces), you are essentially finding the area of a single face.

Then, by multiplying this average area by 5, you ensure that you account for all five pairs of faces, providing the total surface area of the cuboid.

Thus, multiplying by 5 is necessary to correctly calculate the total surface area of the cuboid by accounting for the face pairs while avoiding double-counting.

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Answer:

8

Step-by-step explanation:

3/4 cup leaves 1/4 cup from each cup

1/4+1/4+1/4=3/4

so it would be 3/4+3/4+3/4+3/4+3/4+3/4+3/4+3/4=8 cups

The approximation of the area of f(x) = x² + 2x, from x = 2 to x = 10, is given as follows:

320 units squared.

The area under a curve is approximated using the definite integral of the function that defines the curve within it's bounds.

As it is specified that the area should be approximated using rectangles, a Left Riemann Sum will be used to approximate the area.

First we must obtain the Delta value, which is the difference between the bounds of the integral, divided by the number of intervals, thus, considering four intervals, we have that:

\(\Delta_x = \frac{10 - 2}{4} = 2\)

Then the values of x at which the numeric values are calculated are obtained as follows:

\(x_i = a + \Delta_x(i - 1)\)

Thus the values of x are of:

The numeric values are given as follows:

Then the definite integral is obtained as follows:

\(\sum_{i = 1}^n \Delta_x f(x_i)\)

Meaning that the result of the integral is of:

2(8 + 24 + 48 + 80) = 320 units squared.

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Answer:

hope it is correct

Step-by-step explanation:

Since QUOR is a parallelogram, it means that opposite angles are congruent. Therefore, we have:

∠Q = ∠O and ∠UQA + ∠O = 180°

Since CD || RO, we have:

∠ORA = ∠O and ∠BUQ + ∠Q = 180°

Combining these equations, we get:

∠UQA + ∠BUQ + ∠ORA = 360°

Since ∠BUQ + ∠Q = 180°, we have:

∠BUQ = 180° - ∠Q

Substituting this into the previous equation, we get:

∠UQA + (180° - ∠Q) + ∠O = 360°

Simplifying, we get:

∠UQA = ∠Q - ∠O

Since ∠Q = ∠O (because QUOR is a parallelogram), we have:

∠UQA = 0°

Therefore, none of the given angles (A) ∠BAR, (B) ∠BUQ, or (C) ∠ORA is congruent to ∠UQA.

Answer:

\(2000 {(1 + \frac{.07}{12}) }^{5 \times 12} = 2835.25\)

Answer: There is no way 200 is the answer. it should be 103.055

Step-by-step explanation: See, 36 miles can stop in 53 feet. We want to know how many feet are there when 70 miles fast. We can write  that as 36/53 = 70/x. 36 corresponds to 70 and 53 corresponds to x. Do it and you get 103.055

The dimensions of the room are approximately 7 meters by 10.5 meters.

In Mathematics, dimensions are referred to as measures of size such as length, width, and height of an object or a shape. A rectangle has length and width as its dimensions that define the area of a rectangle.

Let's start by using algebra to represent the information given in the problem. Let x be the width of the rectangular room, then the length is 1.5 times the width or 1.5x.

The perimeter of a rectangle is the sum of the lengths of all its sides, which can be expressed as:

\(\text{Perimeter} = 2(\text{length} + \text{width})\)

Substituting the values we have for length and width, we get:

\(\rightarrow35 = 2(1.5\text{x} + \text{x})\)

Simplifying the equation, we get:

\(\rightarrow35 = 2(2.5\text{x})\)

\(\rightarrow35 = 5\text{x}\)

\(\rightarrow\text{x}=\dfrac{35}{5}\)

\(\rightarrow\bold{x\thickapprox7}\)

So the width of the room is 7 meters.

To find the length, we can substitute x into the expression we have for the length:

\(\rightarrow\text{Length} = 1.5\text{x}\)

\(\rightarrow\text{Length} = 1.5(7)\)

\(\rightarrow\bold{Length=10.5}\)

So the length of the room is 10.5 meters.

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Joey's actual speed is 143.59 mph, and his actual direction is slightly west of northwest.

Given that Joey's aircraft speed: 188 mph

Wind speed: 60 mph

Wind direction: 150 degrees (measured clockwise from due north)

We can consider the wind as a vector, which has both magnitude (speed) and direction.

The wind vector can be represented as follows:

Wind vector = 60 mph at 150 degrees

We convert the wind direction from degrees to a compass bearing.

Since 150 degrees is measured clockwise from due north, the compass bearing is 360 degrees - 150 degrees = 210 degrees.

Joey's aircraft speed vector = 188 mph at 0 degrees (due northwest)

Wind vector = 60 mph at 210 degrees

To find the resulting velocity vector, we add these two vectors together. This can be done using vector addition.

Converting the wind vector into its x and y components:

Wind vector (x component) = 60 mph × cos(210 degrees)

= -48.98 mph (negative because it opposes the aircraft's motion)

Wind vector (y component) = 60 mph×sin(210 degrees)

= -31.18 mph (negative because it opposes the aircraft's motion)

Now, we can add the x and y components of the two vectors to find the resulting velocity vector:

Resulting velocity (x component) = 188 mph + (-48.98 mph) = 139.02 mph

Resulting velocity (y component) = 0 mph + (-31.18 mph) = -31.18 mph

Magnitude (speed) = √((139.02 mph)² + (-31.18 mph)²)

= 143.59 mph

Direction = arctan((-31.18 mph) / 139.02 mph)

= -12.80 degrees

The magnitude of the resulting velocity vector represents Joey's actual speed, which is approximately 143.59 mph.

The direction is given as -12.80 degrees, which indicates the deviation from the original northwest direction.

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Answer:

The probability is 0.33

Step-by-step explanation:

Please find the attachment for detail

Answer:

C is the correct answer

jane is 1,116 years old.

Step-by-step explanation:

first you have to subtract 1345 minus 116. Which will give you 1229. Then you subtract that by 113.

Answer:

The value of cos(theta) is;

Explanation:

Given that;

Recall that from trigonometry;

So;

To get the hypotenuse;

Also;

Therefore, the value of cos(theta) is;

Answer:

A, E, C

Step-by-step explanation:

The statements are correct when comparing the experimental and theoretical probability that will be A, C, and E.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

In a spinner, there are 3 stars and 1 heart.

Then the theoretical probability of the star is given as,

⇒ 3 / 4

⇒ 0.75

Then the theoretical probability of the heart is given as,

⇒ 1/4

⇒ 0.25

Mary Jane spins the spinner 15 times. The arrow lands 6 times on a star and 9 times on the heart.

The experimental probability of the heart is given as,

⇒ 9 / 15

⇒ 0.60

The experimental probability of the star is given as,

⇒ 6 / 15

⇒ 0.40

The statements are correct when comparing the experimental and theoretical probability that will be A, C, and E.

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The better deal between the offer at Mystic Bank and Four Rivers Bank is the deal at Mystic Bank.

In order to determine which bank has the better offer, the future value of the investment options have to be determined.

The future value of an investment is a function of the amount investment, the number of compounding, the years of the investment and the interest rate.

When an investment is compounded semi-annually, it means that it grows exponentially twice in a year. When an investment is compounded quarterly, it means that is grows exponentially four times in a year.

The formula for calculating future value:

FV = P (1 + r)^nm

Where:

Interest rate at Mystic bank = 10% /2 = 5%

Interest rate at Four Rivers Bank = 8% / 4 = 2%

Future value of the investment at Mystic bank :

$10,000 x (1.05)^(2 x 4) = $14,774.55

Future value of the investment at Four Rivers Bank :

$10,000 x (1.02)^(4 x 4) = $13,727.86

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Answer:

165

Step-by-step explanation:

The quotient of the expressions −48.132 and −0.84 will be 57.30. Then the correct option is C.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Division means the separation of something into different parts, sharing of something among different people, places, etc.

Given −48.132 ÷ −0.84.

Then the value of the expression will be

⇒ −48.132 / −0.84

If in the numerator and the denomination, the negative sign is present, then both will cancel out each other.

⇒ 48.132 / 0.84

⇒ 57.30

The quotient of the expressions −48.132 and −0.84 will be 57.30.

Then the correct option is C.

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