A group of computer engineers secured a loan to fund a new startup in Silicon Valley. The bank gives them a loan in the amount of 1.8​one point eight million dollars. The engineers estimate that their business will be able to make a profit of approximately $0.6​zero point six million per year. They keep track of their debts, profits, and overall financial status on a balance sheet. They enter the debt as a negative value and all profits as positive values.
Define a unit for the amount of time since the company began. Enter a variable for the amount of time since the company began and use this variable to write an expression for the expected financial status.
What was the financial status of the company when it began?
If the estimates were correct, how many years was it before the financial status of the company was 11.4​eleven point four million dollars?
After completing the worksheet, graph your model.

Answer: 1.095

Step-by-step explanation:

The function is increasing, so the rate of change must be greater than 1.

In order to move a the constant terms to the right hand side, we need to subtract 0.4 from both sides of the equation.

In an equation, the constant terms are those terms that do not have any alphabet attached to them. In this case, 4 and 0.4 are constant terms.

In order to move a the constant terms to the right hand side, we need to subtract 0.4 from both sides of the equation thus;

-9x + 0.4 - 0.4 = 4 - 0.4

-9x = 3.6

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Answer:

(8,-3)

Step-by-step explanation:

Midpoint Formula: [tex](\frac{x^{1}+x^{2} }{2}, \frac{y^{1} +y^{2} }{{2} } )[/tex]

Plug in your numbers from the coordinates:

(10+6/2, -7+1/2)

(16/2, -6/2)

(8,-3)

Number of males in the meet were 8.

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant.

Let the number of males be x.

∴ Number of females = x + 7

Total number of people attending meet = Number of male +

                                                                    Number of  females

23 = x + x + 7

23 = 2x + 7

16 = 2x

x = 8.

Thus number of males in the meet were 8.

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The lower bound is 147.5 and the upper bound is 152.5.

Given the weight of an apple 150 g rounded to the nearest 5g.

We have to find lower bound and upper bound.

Lower bound is an element less than or equal to all the elements in a given set.

Upper bound is an element greater than all the elements in a given set.

Lower bound= Number 1- (Number nearest to  which number 1 is rounded)/2

Upper bound=Number 1+(number nearest to which number 1 is rounded)/2

Weight of an apple =150 g

Lower bound=150-5/2

=150-2.5

=147.5

Upper bound=150+5/2

=150+2.5

=152.5

Hence the lower bound is 147.5 and upper bound is 152.5.

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The company's profit in fifth month will be $506.25

Profit : The gain in an expenditure, that is when the return is higher than the original amount, then the gained extra amount is called profit.

Example : If someone sell a toy of $10 in $15, then he gained profit & his profit is $(15-10) = $5.

A company earns a profit of $100 the first month it is in business.

Every month after that, the company earns a profit that is 1.5 times the previous month's profit.

In 1st Month,

Profit = $100

In 2nd Month,

Profit = 1.5 times of profit of 1st month

         = 1.5 × $100

         = $150

In 3rd Month,

Profit = 1.5 times of the profit of 2nd month

         = 1.5 × $150

         = $225

In 4th Month,

Profit = 1.5 times of the profit of 3rd month

         = 1.5 × $225

         = $337.5

In 5th Month,

Profit = 1.5 times of the profit of 4th month

         = 1.5 × $337.5

         = $506.25

So, the profit of 5th month = $506.25

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Answer:

(x - 7) , (x + 4)

Step-by-step explanation:

given the zeros of a quadratic equation x = a and x = b , then

the corresponding factors are (x - a) and (x - b)

here the zeros are x = 7 and x = - 4 then factors are

(x - 7) and (x - (- 4) ) , that is

(x - 7) and (x + 4)

Considering the definition of an inequality and system of inequalities, the correct option is: "No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100."

An inequality is the existing inequality between two algebraic expressions, connected through the signs:

An inequality contains one or more unknown values ​​called unknowns, in addition to certain known data.

Solving an inequality consists of finding all the values ​​of the unknown for which the inequality relation holds.

A system of inequalities is made up of two or more inequalities.

The solution will be formed by the intersection of the half-planes of each of the inequalities, that is, it will be the enclosure that all the inequalities have in common. That is, the solution of the system is given by the region of the common plane of the half-planes that define each one of the inequalities.

In this case:

Then, the system of inequality is:

[tex]\left \{ {{4c+6a\leq 120} \atop {4c+4a\leq 100}} \right.[/tex]

On the other hand, the company can build 20 child bikes and 6 adult bikes in the week. So, checking the equations, for given c=20 and a=6:

4×20 + 6×6= 116 < 120

4×20 + 4×6= 104 >100

Finally, the correct option is: "No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100."

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Answer:

10

Step-by-step explanation:

2 legs because you walked into the room and 4 legs of the bed and 4 legs of the chair.

The answer will be either 8 or 4 or 0.

What is a riddle?

A riddle is an intentionally framed ambiguous question or statement that requires ingenuity and critical thinking to solve or understand.

In the given riddle, all the two dogs, four horses, one giraffe and a duck are lying on the bed. Three chickens are flying over a chair.

Assumptions:

1) Bed is placed on the ground.

2) Bed and chair considered are of standard type.

case1:

If we consider the legs of only living organisms, the number of legs on the ground at the given instant will be 0.

case2:

If that's not the case, then a typical chair will have four legs, and a standard bed will also have four legs. So a total of 8 legs will be on the ground or floor of the room.

case3:

And if we consider the possibility of the chair being placed on the bed, then the legs of the chair will not touch the ground. So a total of 4 legs will be on the ground or floor of the room.

∴ From different perspectives, the number of legs on the ground will be either 8 or 4 or 0.

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Option B is correct

Why

3x=21

3(7) =21

21=21

Step-by-step explanation:

Answer:

[tex]-3x=21 , -7[/tex]

Step-by-step explanation:

[tex]-3x=21\\x=\frac{21}{-3} =-7[/tex]

The length of the hypotenuse of right triangle ΔDEF is 50.44 units

The hypotenuse side can be found using Pythagoras theorem,

Therefore,

c² = a² + b²

where

Therefore,

x² = 39² + 32²

x² = 1521 + 1024

x = √2545

x = 50.4479930225

x = 50.44

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The P(teacher and video games) = 4%; the two events are not independent.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

P(teacher and video games) = number of teachers who play video game / total number of respondents

6/150 = 0.04 = 4%

Independents events are events whose occurrence do not depend on each other. They are random events.

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Answer:

The P(junior and video games) = 32%; the two events are not independent.

Step-by-step explanation:

i got it right aswell

The missing dimension is x + 4

The given parameters are:

Area = 4x^2 + 13x - 12

Length = 4x - 3

The width is calculated using:

Width = Area/Length

This gives

Width = (4x^2 + 13x - 12)/(4x - 3)

Expand

Width = (4x^2 + 16x - 3x - 12)/(4x - 3)

Factorize

Width = (4x(x + 4) - 3(x + 4)/(4x - 3)

Factor out x + 4

Width = (4x - 3)(x + 4)/(4x - 3)

Cancel out the common factor

Width = x + 4

Hence, the missing dimension is x + 4

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Answer: 3491.91 radians

Step-by-step explanation:

The total distance in inches traveled by car = 63,360 inches (1 mile)

Total Revolution made by tire through traveling =

[tex]=\frac{63360}{\pi *36.30}[/tex]

We know 1 revolution angle made by tire = 2π radian (360 degrees/1 revolution of unit circle)

In   [tex]\frac{63360}{\pi *36.30}[/tex] ,

the revolution angle made by the tire =

[tex]=2\pi * \frac{63360}{\pi 36.60}[/tex]

[tex]=2 * \frac{63360}{ 36.60}[/tex]

[tex]= 3491.91[/tex] radian

Answer:

706.858347

Step-by-step explanation:

Answer:

1080.

Step-by-step explanation:

0.00025 tonnes = 0.00025 * 1000 = 0.25 kg.

Total number of packets

(3 *90) / 0.25

= 12*90

= 1080.

Answer:

43

Step-by-step explanation:

52-9=43

Both the given statements are true. The figure is given below.

We need to determine whether the stated conclusion is valid based on the given information.

In geometry, the midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment.

Given: If a point is the midpoint of a segment, then it divides the segment into two congruent segments. R is the midpoint of QS.

Conclusion: QR=RS.

Given: If a point is the midpoint of a segment, then it divides the segment into two congruent segments. AB=BC

Conclusion: B divides AC into two congruent segments

Both the given statements are true. The figure is given below.

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Answer:

x=5

Step-by-step explanation:

solution,

3x+7=22

or,3x=22-7

or,3x=15

or,x=15/3

:×=5

The value of x in the equation 3x + 7 = 22 is x = 5.

To find the value of x in the equation 3x + 7 = 22, we can solve for x as follows:

Subtract 7 from both sides of the equation:

3x + 7 - 7 = 22 - 7

3x = 15

Divide both sides of the equation by 3 to isolate x:

(3x)/3 = 15/3

x = 5

Therefore, the value of x in the equation 3x + 7 = 22 is x = 5.

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All multiple of 6 under 14 are: -12, -6, 0, 6, 12

How do we get 14 here:

√200= 14.142 (Round to thousandth place)

This is how many x we have found.

A multiple in math is the number you get when you multiply a certain number by using an integer. for example, multiples of 5 are: 10, 15, 20, 25, 30…, and so forth. Multiples of 7 are 14, 21, 28, 35, 42, 49…and many others.

In math, the meaning of a multiple is the product result of one number multiplied by another number. Here, 56 is a multiple of the integer 7. Here is an example of multiples: Fun facts. 0 is a multiple of every number as the product of 0 multiplied by any number is 0.

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Answer:

They are congruent because GH ≅ GF, JF ≅ JH, and FH ≅ FH.

Step-by-step explanation:

Answer:

B = (-1, 0)

C = (1, 0)

Step-by-step explanation:

Properties of an Equilateral Triangle

Given:

Drawing an altitude from vertex A divides the triangle into two 30-60-90 triangles.

A 30-60-90 triangle is special right-angled triangle where:

Therefore, the formula for the sides is: b : b√3 : 2b, where:

As Vertex A has the co-ordinates (0, √3), the side opposite the 60° angle is √3 units.

Using the ratios to find b (shortest side length):

b√3 = √3  ⇒  b = 1

As the altitude divides BC into two equal line segments, and the length of the shortest side of the right triangles is 1 unit, the coordinates of B are C are:

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Using the p-value method, the decision rule is:

Depends on if the p-value is less or more than the significance level:

In this problem, we have a two-tailed test, as we are testing if the mean is different of a value. For a significance level of 0.1, the critical value of z(when a p-value of 0.1 is obtained) is of |z| = 1.645, hence the decision rule is:

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Answer:

The volume of the prism increased by a factor of 64.

Step-by-step explanation:

Given that the original prism and the increased prism are similar, we have that the scale factor is:

Area ∝  (length of side) x (length of side)

If the area increases by a factor of 16, each side increases by a scale factor of √16 = 4. Regarding the volume:

Volume ∝ (length of side) x (length of side) x (length of side)

Thus the increase factor for the volume, in this case, is 4 x 4 x 4 = 64.

The Simplified algebraic expression for the statement "n divided by 2 plus five minus n" is given by 5-(n/2).

Algebraic Expression is a mathematical expression involving variables, Numbers, other mathematical quantities, and mathematical operations and combinations of them.

Here given statement is "n divided by 2 plus five minus n"

Now we have to write the above given statement as simplified algebraic expression.

"n divided by 2" is given by = n/2

then "n divided by 2 plus five" is given by = (n/2)+5

there after "n divided by 2 plus five minus n" is given by = (n/2)+5-n

Simplifying the total algebraic expression we get,

(n/2)+5-n = 5-{n-(n/2)} = 5-((2n-n)/2) = 5-(n/2)

Hence the suitable Simplified algebraic expression for the given statement is given by = 5-(n/2)

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Using it's concept, it is found that the approximate perimeter of the front of the garage is:

A. about 36 ft.

The perimeter of a figure is given by the total length of it's boundary.

In this problem, we have that:

[tex]t = \sqrt{3^2 + 5^2} = 5.83[/tex]

Hence the perimeter of the figure is:

P = 10 + 2 x 7 + 2 x 5.83 = 35.66.

Rounding, it is of about 36 ft, hence option A is correct.

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Answer: 9 : 4

Step-by-step explanation:

45 : 20

simplify

9 : 4

Answer:

Yes

Step-by-step explanation:

Let's assume that x=1/y.

For y=1, x=1

For y=2, x=0.5

For y=4, x=0.25

And so on

The point 0 represents the surface of the water. The height of the slide is 7 feet above the surface of the water. The bottom of the pole can be represented by -2 on the number line.

An equation is an expression that shows the relationship between two or more numbers and variables.

Given that −8 represents the depth of water in the swimming pool. Hence:

The point 0 represents the surface of the water. The height of the slide is 7 feet above the surface of the water. The bottom of the pole can be represented by -2 on the number line.

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