In a graph, x represents the number of months since a business opened, and y represents the total amount of money the business has earned. The following three points are from the graph: (2, 1990) (5, 4225) (9, 7205) Find the slope and y-intercept. Explain what each represents.

Answer:

A

Step-by-step explanation:

100% slope is -3 because you need to move down 3 times which is -3 and move to the right once which is 1

Slope= rise/run

Slope=-3/1 which equals -3

y-intercept= 2 because you just look at the y-axis and see any points that connects to it while the x is zero

To ensure that the remainder of the series Σk=0 [infinity] 5(-1)^k/k! is less than 10^-1 in magnitude, we need to sum at least 4 terms.

The series Σk=0 [infinity] 5(-1)^k/k! is a convergent series, which means that the sum of the series approaches a finite value as the number of terms in the series approaches infinity. However, when we sum a finite number of terms, the sum of the series is an approximation to the true value of the sum. The difference between the true value of the sum and the sum of the finite number of terms is called the remainder.

To find the remainder of the series Σk=0 [infinity] 5(-1)^k/k!, we need to determine how many terms we need to sum to ensure that the remainder is less than 10^-1 in magnitude. One way to do this is to use the formula for the remainder of a convergent series:

|Rn| ≤ an+1/(1-r)

where Rn is the remainder after summing the first n terms of the series, an+1 is the (n+1)th term of the series, and r is the common ratio of the series.

In this case, the common ratio of the series is -1/5, and the (n+1)th term of the series is 5*(-1)^(n+1)/(n+1)! . We want to find the smallest value of n such that |Rn| ≤ 10^-1. Substituting these values into the formula for the remainder, we get:

|5*(-1)^(n+1)/(n+1)!| ≤ 10^-1/(1-(-1/5))

Simplifying this inequality, we get:

|(n+1)!| ≥ 120*(5/4)^(n+1)

Taking the logarithm of both sides of this inequality, we get:

log|(n+1)!| ≥ log[120*(5/4)^(n+1)]

Using Stirling's approximation for n!, we can simplify the left-hand side of this inequality:

(n+1)*log(n+1) - (n+1) ≥ log[120*(5/4)^(n+1)]

Simplifying the right-hand side, we get:

(n+1)*log(n+1) - (n+1) ≥ log(120) + (n+1)*log(5/4)

Dividing both sides by log(n+1), we get:

n+1 - 1/log(n+1) ≥ (log(120) + (n+1)*log(5/4))/log(n+1)

This inequality can be solved numerically to find that the smallest value of n that satisfies the inequality is n = 3.87 (rounded to two decimal places). Since n must be an integer, we need to round up to n = 4. Therefore, we need to sum at least 4 terms of the series Σk=0 [infinity] 5(-1)^k/k! to ensure that the remainder is less than 10^-1 in magnitude.

To learn more about magnitude click here: brainly.com/question/31022175

#SPJ11

Answer: I think it’s a

Step-by-step explanation:

Answer: Choice C)  \(-6 \le x \le 2\)

The domain is the set of possible x values or allowed inputs. The left-most point has x = -6 as the smallest allowed x value, while the right-most point has x = 2 as the largest allowed x value.

The domain is the set of numbers between -6 and 2, including both endpoints. So we write \(-6 \le x \le 2\)

If you want the domain written in interval notation, then you would have [-6, 2]. The square brackets tell the reader "include the endpoint".

Answer:

5

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Solution for What is 12.5 percent of 40:

12.5 percent *40 =

(12.5:100)*40 =

(12.5*40):100 =

500:100 = 5

Now we have: 12.5 percent of 40 = 5

Question: What is 12.5 percent of 40?

Percentage solution with steps:

Step 1: Our output value is 40.

Step 2: We represent the unknown value with $x$.

Step 3: From step 1 above,$40=100\%$.

Step 4: Similarly, $x=12.5\%$.

Step 5: This results in a pair of simple equations:

$40=100\%(1)$.

$x=12.5\%(2)$.

Step 6: By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of both

equations have the same unit (%); we have

$\frac{40}{x}=\frac{100\%}{12.5\%}$

Step 7: Again, the reciprocal of both sides gives

$\frac{x}{40}=\frac{12.5}{100}$

$\Rightarrow x=5$

Therefore, $12.5\%$ of $40$ is $5$

Answer:

26.25 or 26 1/4

Step-by-step explanation:

Formula for rectangular prism:

\(V=lwh\)

Substitute in our known values:

V=3.5(5)(1.5)

solve

V=26.25

The volume is 26.25 (decimal form) or 26 1/4.

Hope this helps! :)

Answer: 26.25 in³

Step-by-step explanation:

Given volume formula for a rectangular prism:

     V = LWH

First, I am going to turn the \(\frac{1}{2}\)s into 0.5 to make it easier to multiply using a calculator. 3 and one-half becomes 3.5 and 1 and a half becomes 1.5.

Substitute known values and solve by multiplying.

     V = LWH

     V = (3.5 in)(5 in)(1.5 in)

     V = 26.25 in³

Answer:

12.11

Step-by-step explanation:

Answer:

3.01

+9.10

=12.11

Step-by-step explanation:

good luck

Answer: m (slope) = 0

Step-by-step explanation:

The slope can be found through the equation (y2-y1)/(x2-x1)

(-4, -9) and (4, -9) can be: (x1, y1) and (x2, y2)

We can plug the variables into the formula above:

(-9-(-9))/(4-(-4) = 0/8

The slope is 0.

Answer: slope=0

Step-by-step explanation:

usually slopes are found by taking

change in y

-----------------

change in x

but in all horizontal lines (matching y values, -9 in this case) the line has no slope as it doesn't go up or down.

Using Pythagoras theorem, the length of the pole is 57 feet

Pythagoras theorem states that “In a right-angled triangle,  the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°.

In this problem, assuming the pole runs down to the ground.

We can apply Pythagoras's theorem to find the height of the the conical roof.

Taking half the length of the the wall, i.e it's diameter = 72 /2 = 36ft

Using Pythagoras theorem;

45² = 36² + x²

x² = 45² - 36²

x² = 729

x = √729

x = 27 feet

The height of the conical roof is 27

The length of the pole = height of the conical roof + height of cylindrical wall

Length of pole = 27 + 30 = 57 ft

The length of the pole is 57ft

Learn more on Pythagoras theorem here;

https://brainly.com/question/343682

#SPJ1

Answer:

Step-by-step explanation:

compare with y=mx+b

m=-1

b=4

(b)

area of triangle=1/2×4×4=8 square units.

Answer:

To determine the speed, we can use the formula:

speed = distance / time

where distance is measured in feet and time is measured in minutes.

In this case, the distance is 264 feet and the time is 3 minutes. Plugging these values into the formula, we get:

speed = 264 feet / 3 minutes

simplifying, we get:

speed = 88 feet/minute

Therefore, the equipment is traveling at a speed of 88 feet per minute.

Answer:

8.62

Step-by-step explanation:

Use the Pythagorean theorem.

b= \(\sqrt{c^{2}-a^{2} }\)

b=\(\sqrt{10.5^{2}-6^{2} }\)

b= \(\sqrt{110.25-36\)

b=\(\sqrt{74.25}\)

b= 8.62

Answer:

W(2) = 5

Step-by-step explanation:

Because when you look at the graph, the y value is 5 when the x value is 2.

Answer:

w(2) = 5

Step-by-step explanation:

by using rise over run to find the slope easily, you get a slope of 4 and an equation of w(x) = 4x - 3, -3 being the y-intercept

to calculate w(2):

w(2) = 4(2) - 3

w(2) = 8 - 3

w(2) = 5

or you could just look at when y is 2 and see that the corresponding x value is 5 but i wanted to provide a longer explanation in case :)

Answer: $18,552.9

Step-by-step explanation:

given data:

currency on hand = $100,000 Brazilian dollar.

curreach desired = us dollars.

if $1 USD = $5.39 Brazilian dollar.

therefore;

$100,000 Brazilia USD

= $100,000/5.39

= $18552.9 USD.

The desired amount in US dollars is $18,552.9

Answer:

5,210.00 Is my best bet.

Gerard concluded that triangle with given sides cannot be used as  building-frame support because it is not right triangle, he come to this conclusion because the Pythagoras-theorem is not satisfied.

In order to check if a triangle is "right-triangle", Gerard used the Pythagorean theorem. According to this theorem, in right triangle, the square of length of hypotenuse (the side opposite the right angle) is equal to sum of squares of other two sides,

So, the squares of the given sides are :

Square of √95 feet = (√95)² = 95 feet

Square of 8 feet = 8² = 64 feet

Square of √150 feet = (√150)² = 150 feet

We see that, 95 feet + 64 feet = 159 feet ≠ 150 feet,

Since the square of the longest side (√150) is not equal to the sum of the squares of the other two sides (√95 and 8), the Pythagorean-theorem is not satisfied.

Therefore, Gerard concluded that the triangle with sides √95 feet, 8 feet, and √150 feet is not a right triangle.

Learn more about Triangle here

https://brainly.com/question/29119900

#SPJ4

The given question is incomplete, the complete question is

Gerard concluded that the triangle with sides √95 feet, 8 feet, and √150 cannot be used as a building frame support on the house because it is not a right triangle. How did Gerard come to that conclusion? explain.

Answer:

167

Step-by-step explanation:

By BODMAS rule,

13 + 14 x 11

= 13 + ( 14 x 11 )

= 13 + 154

= 167

Note : -

B - Brackets

O - Of

D - Division

M - Multiplication

A - Addition

S - Subtraction

Answer:

Step-by-step explanation:

No it doesn't. When you get stuck on a question like this one, you should go to Desmos and graph the equation. I've done that for you.

Correctly stated the equation should read f(x) = (x + 2)^2 + 4

As you can see from the graph the vertex is at -2,4. To find the x value of the vertex, create a small equation

x + 2 = 0

x = - 2

That will turn what is inside the brackets into 0. The value for x is always what will turn (x + a) to zero.

Answer:

\(i^{12}\) = 1

Step-by-step explanation:

Using the rule of exponents

\(a^{m}\) × \(a^{n}\) = \(a^{(m+n)}\)

Then

\(i^{12}\) = \(i^{4}\) × \(i^{8}\) = 1 × 1 = 1 ← ( view table for values )

The given statement "An algorithm is a calculation that determines how long it will take to solve a problem." is False.

An algorithm is not just a calculation that determines how long it will take to solve a problem. An algorithm is a step-by-step set of instructions or a process used to solve a problem or perform a specific task. It is a systematic approach that allows a computer or human to break down a problem into smaller, manageable parts and reach a solution effectively.

Algorithms are the foundation of computer programming and can be applied in various fields such as mathematics, data processing, and problem-solving. They can be simple, like finding the largest number in a list, or complex, like solving a Rubik's Cube.

Efficiency is a key factor in evaluating algorithms. The time and resources required for an algorithm to solve a problem can vary greatly depending on the method used. However, the primary purpose of an algorithm is to provide a clear and concise procedure to reach a solution, rather than just estimating the time needed to solve a problem.

In summary, an algorithm is a well-defined process designed to perform a specific task or solve a problem, rather than just calculating the time required to do so. Its effectiveness depends on its efficiency, accuracy, and the simplicity of the steps involved.

To know more about Algorithm, refer to the link below:

https://brainly.com/question/21172316#

#SPJ11

The percentage decrease when original is 180 and the new is 150 is 16.7%

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred. Per 100 is what the word percent means. It is represented by %.

In this case, the original is 180 and the new is 150. The percentage decrease will be:

= (180 - 150) / 180 × 100

= 30/180 × 100

= 1/6 × 100

= 16.7%

The percentage is 16.7%

Learn more about percentages on:

brainly.com/question/24304697

#SPJ1

A dot plot that represent this data set is shown in the image attached below.

In Mathematics and Statistics, a dot plot can be defined as a type of line plot that is typically used for the graphical representation of a data set above a number line, especially through the use of crosses or dots.

Based on the information provided about this high school survey, we can reasonably infer and logically deduce that the average daily text for the month with the highest frequency is 300.

In this scenario, we would use an online graphing calculator to construct a dot plot with respect to a number line that accurately fit the data set.

Read more on dot plots here: brainly.com/question/30486649

#SPJ1

The required white effective interest rate is 0.71% more than his nominal interest rate.

Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.

Here,

White Effective interest R,
\(R=(1+i/m)^m)-1\\R=(1+0.1362/4)^4)-1\\R =0.1433*100=\)
R = 14.33 percent

So

Difference in interest = 14.33%-13.62%
                                    =0.71%

Thus, the required white effective interest rate is 0.71% more than his nominal interest rate.

Learn more about compound interest here:

https://brainly.com/question/14295570

#SPJ1

Answer:

b,c,f

Step-by-step explanation:

Answer: B

Hope this helps :)

Two decimals are 0.34, 0.83, and 0.83 and Holland could have used it to make a sum of 2.

A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9. Based on the basic value of its digits, different types of number systems exist.

We get x + x = 2x by using x to signify our missing values and the assumption that there are two missing values. We obtain the equation 2x + 0.34 since it is the product of these integers and 0.34; after setting it equal to 2, 2x + 0.34 equals 2.

First, take 0.34 off both sides to get 2x = 1.66. To get x = 0.83, divide both sides by 2 now.

Therefore, the decimals are 0.34, 0.83, and 0.83.

Learn more about the number system here:

https://brainly.com/question/21751836

#SPJ1

Here's the solution,

figure 1.

by using trigonometry,

=》

\( \sin(60) = \dfrac{5 \sqrt{3} }{y} \)

=》

\( \dfrac{ \sqrt{3} }{2} = \dfrac{5 \sqrt{3} }{y} \)

=》

\( \dfrac{1}{y} = \dfrac{ \sqrt{3} }{2 \times 5 \sqrt{3} } \)

=》

\( \dfrac{1}{y} = \dfrac{1}{10} \)

=》

\(y = 10\)

And,

=》

\( \cos(60) = \dfrac{w}{y} \)

=》

\( \dfrac{1}{2} = \dfrac{w}{10} \)

=》

\(w = 5\)

So, values are :

figure 2.

Since, it's an isosceles triangle, w = y,

So, by pythagoras theorem :

=》

\( {w}^{2} + {y}^{2} = (7 \sqrt{2} ) {}^{2} \)

=》

\( {w}^{2} + {w}^{2} = 98\)

=》

\(2 {w}^{2} = 98\)

=》

\( {w}^{2} = 49\)

=》

\(w = \sqrt{49} \)

=》

\(w = 7\)

and we know, w = y, so their values will be equal to 7 units.

Both ratios represent the proportion of 1 part to 2 parts, and therefore they are equivalent.

If the corresponding components of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional.

1/2 and 5/10 are equivalent ratios, and therefore they represent the same proportion. To see this, we can simplify 5/10 by dividing both the numerator and denominator by their greatest common factor, which is 5:

\($\frac{5}{10} = \frac{5 \div 5}{10 \div 5} = \frac{1}{2}$$\)

So both ratios represent the proportion of 1 part to 2 parts, and therefore they are equivalent.

To know more about ratio visit:

brainly.com/question/29467965

#SPJ1

if the terminal point indicated by t is in the provided quadrant, the first equation in terms of the second quadrant iv; cos(t), sin(t). \(\sin t=\sqrt{1-\frac{1}{\sec ^2 t}}\)

Trig identities come in handy when we need to express one trig function in terms of another. The most famous trig identity is derived straight from the Pythagorean Theorem:

sin² t +  cos² t = 1

For an angle t in Quadrant IV, we know sin t is positive.

From the trig identity sin² t +  cos² t = 1

we can also write as:

sin t + cos t:

Now,

sin² t + cos² t = 1

sin² t   = 1 -  cos² t

sin t = ±√( 1 -  cos² t)

As noted above,

sin t is positive for t in the Quadrant IV, and so we have

sin t = √( 1 -  cos² t)

We know that

\(\cos t=\frac{1}{\sec t}\)

So, the equation will be

\(\sin t=\sqrt{1-\frac{1}{\sec ^2 t}}\)

To know more about Trig Identities visit:

https://brainly.com/question/10376944

#SPJ4

Answer:

all 3 options are true : A, B, C

Step-by-step explanation:

warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.

they say that A and C are correct.

but I am going to show you that if A and C are correct, then also B must be correct.

therefore, my given answer above is the actual correct answer (no matter what the test systems say).

originally the information about the alignment of the point F in relation to point E was missing.

therefore, I considered both options :

1. F is on the same vertical line as E.

2. F is not on the same vertical line as E.

because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :

the vertical line of EF is like a mirror between the left and the right half of the picture.

A is mirrored across the vertical line resulting in B. and vice versa.

the same for C and D.

this leads to the effect that all 3 given congruence relationships are true.

if we consider assumption 2, none of the 3 answer options could be true.

but if the assumptions are true, then all 3 options have to be true.

now, for the "why" :

remember what congruence means :

both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.

for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.

so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.

therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.

but do you notice something ?

both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.

now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.

therefore, AC must be equal to BD.

and that means that AC is congruent to BD.

because lines have no other congruent criteria - only the lengths must be identical.

The correct option is (C):the market has not provided a socially optimal amount of goods and services. Market-failure means the market has not provided a socially optimal amount of goods and services.

Market failure is a term used to describe a situation where the market has not provided an optimal allocation of goods and services from a social perspective. This means that the market has failed to allocate resources efficiently, resulting in a suboptimal outcome. Market failure can occur due to a variety of reasons, such as externalities, information asymmetry, public goods, and monopoly power. In such situations, government intervention may be required to correct the market failure and ensure the provision of socially optimal goods and services.

To know more about  market-failure, visit:

brainly.com/question/14769153

#SPJ11