Calculate how much you would have in 20 years if you saved $3,000 a year at an annual rate of 8 percent with the company contributing $750 a year. Use Exhibit 1-B. (Round time value factor to 3 decimal places and answer to the nearest whole dollar.)

Answer:

$1,136

Step-by-step explanation:

The required matches for the given equation of line are explain below.

The general equation of a straight line is y = mx + c, where m is the inclination, and y = c is the worth where the line cuts the y-hub. This number c is known as the block on the y-pivot. The condition of a straight line with slope m and block c on the y-hub is y = mx + c.

We will find the graph, by using general form of equation

y =  -3x + 5

Its y-intercept is 5,and angle is negative,So graph(3) is matches

similarly,

y = - 1/5x + 3

Its y-intercept is 3,So graph(1) is matches

y=1/3x + 5

Its y-intercept is 5,and angle is Positive,So graph(4) is matches

y= 3x + 1/5

Its y-intercept is 1/5,and angle is more than one,So graph(2) is matches

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Therefore in this question the solution of particular equation is  108 children and 175 adults in the amusement park on that particular day.

When two expressions' values are set to be equal by a mathematical statement, that statement is known as an equation. To put it another way, it is a mathematical expression that means "this is equivalent to that." An equal sign, a mathematical expression, and a mathematical expression can all be seen on the left side of the symbol. The right ride of the equation frequently contains zero.

Let's first configure our system by giving x and y meaningful definitions. Let x be the total number of kids and y be the total number of adults.

Children cost $1.50, while adults cost $4.00. The number of kids, x, is multiplied by 1.5 to determine how much money a group of kids will cost. The 1.5x symbol stands for this. We will use 4y for adults, who must pay $4 to enter. On the specified day, $862 in total revenue was earned. We must add 1.5x and 4y to get at this sum.

1.5x + 4y = 862 equation required

Second equation: The total number of individuals present on the day is 283. X and Y, or the number of children and adults, must be added together to arrive at this figure.

x + y = 283

System of equations:

1.5x + 4y = 862

x +   y = 283

Thus,

x + y = 283  

y = 283 - x

Substitute y = 283 - x

862=1.5x + 4 (283 - x)  

1.5x + 1132 - 4x = 862

1132 - 2.5x = 862          

-2.5x = -270                  

x = 108

Substitute x =108 back into y = 283 - x

y = 283 - 108 = 175

Therefore there were 108 children and 175 adults in the amusement park on that particular day.

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For 45th set up 140 toothpicks  are required.

A progression of numbers in which the difference between any two succeeding numbers is always a fixed amount is known as arithmetic progression (AP). It also goes by the name Arithmetic Sequence.

given:

For First Figure, 8 toothpicks are used

For Second Figure, 11 toothpicks are used

For Third Figure, 14 toothpicks are used

So, we get the series 8, 11, 14, ...

Now, for n= 45

Using Arithmetic Progression

[tex]a_{45} = a+ (45- 1) d[/tex]

     = 8 + 44(3)

     = 140

Hence, for 45th set up 140 toothpicks  are required.

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The option that is a strict inequality is A. y>4

It should be noted that inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal.

Inequalities involving < or ">" are considered "strict inequalities," whereas those involving "" or "" are not. If you "switch" the two sides of an inequality, you must then reverse the inequality symbol's direction. For example, because 4 5 is true, it follows that 5 > 4.

In conclusion, the correct option is A.

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Answer:

slope 6

y intercept 4

y = 6x + 4

Step-by-step explanation:

The slope is the change in y over the change in x.  

Look at he two points (0,4) and (1,10)

The y started at 4 and went up to 10.  That is a distance of 6.

AT the same time, the x changes from 0 tp 1 (0,4) (1,10).  That is a distance of 1.

6/1 = 6

The y intercept is where the line crosses the y axis.  It crosses at (0,4).  4 is the y intercept

y = mx + b  Put the slope is for m and the y intercept for b

y = 6x + 4

Answer:

18 Skittles and 7 Kit Kats

Linear system of equations in two variables

Step-by-step explanation:

We a linear system of two equations which can be solved simultaneously

Total pieces of candy equation
s + k = 25    [1]

Total cost equation
0.8s + 0.9k = 20.70   [2]

Multiply [1] by 0.80
0.80s + 0.80k =  20 [3]

Subtract [3] from [2]

0.80s + 0.90k = 20.70
             [tex]-[/tex]
0.80s + 0.80k =  20
[tex]\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots[/tex]
0.1k   = 0.70

k = 0.70/0.10 = 7

In [1]
[tex]s + 7 = 25\\\\s = 25-7\\\\s = 18\\\\[/tex]

Answer: 18 Skittles and 7 Kit Kats

The x - intercept is (25, 0) and the y - intercept is (0, 10).

What is intercepts?

The x-intercept and y-intercept are the points at which a line crosses the x- and y-axes, respectively.

Put y = 0 and work out x to find the x-intercept.

Set x = 0 and work out y to find the y-intercept.

Given: You are ordering shirts for the math club at your school.

Short-sleeved shirts cost $ 8 each.

Long-sleeved shirts cost $ 20 each. You have a budget of $ 200 for the shirts.

The equation 8 x+20 y=200 models the total cost,

where x is the number of short-sleeved shirts and y is the number of long-sleeved shirts.

To find the x - intercept plug y = 0 in the above equation.

⇒ 8x + 20(0) = 200

                8x = 200

                  x = 25

So, the point becomes, (25, 0).

To find y - intercept plug x = 0 in the above equation.

⇒ 8(0) + 20y = 200

              20y = 200

                  y = 10

So the point becomes, (0, 10).

Hence, the x - intercept is (25, 0) and the y - intercept is (0, 10).

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Answer:

f(11) = 228

Step-by-step explanation:

Answer given in the screenshot below. ↓

The volume is 2679.46ft^3.

What is  volume?

Volume is a measurement of three-dimensional space that is occupied. It is frequently expressed numerically using SI-derived units, as well as different imperial or US-standard units. Volume and the definition of length are related.

We know that

The volume of the cone is equal to

[tex]V=\frac{1}{3} \pi r^2 h[/tex]

where

r is the radius of the circular base of the cone [tex]$\mathrm{h}$[/tex] is the height of the cone

we have

[tex]$$\begin{aligned}& r=16 f t \\& h=10 f \mathrm{t}\end{aligned}$$[/tex]

assume

[tex]\pi=3.14[/tex]

substitute the values

[tex]$$\begin{aligned}& V=\frac{1}{3}(3.14)(16)^2(10) \\& V=2679.46 f t^3\end{aligned}$$[/tex]

The drawing in the attached figure

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Answer: 7

Step-by-step explanation: 7+2

The pressure of 28 inches of mercury occurs about 6 miles from the eye of hurricane.

In essence, atmospheric pressure is the force that the weight of the air above a particular point on the Earth's surface exerts at that location.

In other words, the weight of the air molecules as a whole determines the atmospheric pressure, which is produced by the air that surrounds the Earth.

Lower pressure is felt by air molecules at higher altitudes because there are fewer molecules pressing down on them from above, while higher pressure is felt by air molecules at lower altitudes because they are closer together and are under more pressure from molecules piled on top of them.

F(x) is the pressure in inches of mercury

It is given pressure 28 inches of mercury

Put F(x) equal to 28

F(x) = 0.48㏑(x+2) +27

28 = 0.48㏑(x+2) + 27

28-27= 0.48㏑(x+2)

1= 0.48㏑(x+2)

1/0.48= ㏑(x+2)

25/12= ㏑(x+2)

x+2= [tex]e^{\frac{25}{12} }[/tex]

x+2=8.03119

x=8.03119-2

x= 6.03119

x = 6(round off)

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Answer:

Below

Step-by-step explanation:

Angle 2     or  angle  HFE

Vertex is F

GF and  FE   are the sides of angle 1

It will take 54 days for Teri's account to earn an amount of $5000.

Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.

It occurs when interest is reinvested, or added to the loaned capital rather than paid out, or when the borrower is required to pay it, so that interest is generated the next period on the principal amount plus any accumulated interest. In finance and economics, compound interest is common.

It is given by formula

A = [tex]p*e^{r*t}[/tex]

where:

A is final amount

p is principal amount

r is rate of interest and

t, is time period

Given: A= $5000, p=$1500, r=2.25% = 0.0225

To find: time period to get compounded amount

5000=1500×[tex]e^{0.0225*t}[/tex]

[tex]e^{0.0225t}[/tex] = [tex]\frac{10}{3}[/tex]

0.0225t = ㏑ ([tex]\frac{10}{3}[/tex])

t = 53.5099 ≈ 54 days  

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Answer:

The tree lights and the porch lights will blink together every 12 seconds.

Step-by-step explanation:

In order to determine when the two sets of lights will blink together, you must find the least common multiple (LCM) of the time periods for each set of lights. The LCM of 4 and 6 is 12, which means that the tree lights and the porch lights will both blink again after 12 seconds have passed. Therefore, they will blink together every 12 seconds.

Answer: [tex]y=-\frac{4}{3}x+2[/tex]

Step-by-step explanation:

The slope of [tex]AB[/tex] is [tex]-4/3[/tex]. Thus, the slope of [tex]CD[/tex] is also [tex]-4/3[/tex].

Thus, the equation of [tex]CD[/tex] can be found as follows:

[tex]y-10=-\frac{4}{3}(x+6)\\\\y-10=-\frac{4}{3}x-8\\\\y=-\frac{4}{3}x+2[/tex]

The total of all multiples of either the first or second integer from the previous issue that are below 1000 will be 233168.

Manifold is the fundamental definition of multiplicity. A multiple in mathematics refers to the outcome of multiplying two numbers together. In mathematics, multiples are the results of multiplying an integer by a given number. A number that is produced by multiplying a given integer by a natural number is referred to as a multiple of that number. The factors of 20, for instance, are 1, 2, 4, 5, 10, and 20. The multiples of 20 include, for instance, 20, 40, 60, 80, 100, etc.

Here,

The statement of the problem is to sum the multiples of 3 and 5 below 1000, not up to and equal 1000.

The equation is attached in image,

166833+99500−33165=233168

The sum of all the multiples of the first integer from the last problem or the second integer from the last problem - below 1000 will be 233168.

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The global maximum value of a differentiable function f(x) on a closed interval [a, b] must occur at a critical value or an endpoint is correct. Statement C.

The critical value is the value of x for which the double derivative of the function f(x) becomes zero.

When double derivative becomes zero, the graph of the function is neither increasing nor decreasing and hence, the the function attains either

a maxima or a minima.

Hence, he global maximum value of a differentiable function f(x) on a closed interval [a, b] must occur at a critical value or an endpoint.

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The required simplification of given function is [tex]\frac{(x-1)^{2}}{x-2}[/tex] and restriction on domain are x  ≠ 1, 2.

The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0. We can also define special functions whose domains are more limited.

We have,

[tex]\frac{(x+3)(x-1)}{x-2}[/tex] ÷ [tex]\frac{x+3}{x-1}[/tex]

[tex]\frac{(x+3)(x-1)}{x-2}[/tex] × [tex]\frac{x-1}{x+3}[/tex]

[tex]\frac{(x-1)^{2}}{x-2}[/tex]

For domain, Function should have solution should not be not defined.

For this, denominator must not equal to zero

Then, x -2 ≠ 0, x - 1  ≠ 0

x  ≠ 2, x  ≠ 1

Thus, option(3) [tex]\frac{(x-1)^{2}}{x-2}[/tex] x  ≠ 1,2 is correct.

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Answer:

  (b)  (x -1)²/(x -2), x ≠ -3, 1, 2

Step-by-step explanation:

You want to know the domain restrictions and the simplified form of ...

  [tex]\dfrac{(x+3)(x-1)}{(x-2)}\div\dfrac{x+3}{x-1}[/tex]

We can "invert and multiply", then cancel the common factor from numerator and denominator.

  [tex]\dfrac{(x+3)(x-1)}{x-2}\div\dfrac{x+3}{x-1}=\dfrac{(x+3)(x-1)}{x-2}\times\dfrac{x-1}{x+3}=\dfrac{(x+3)(x-1)^2}{(x+3)(x-2)}\\\\=\dfrac{(x-1)^2}{x-2}\qquad x\ne -3[/tex]

The values of x that must be excluded from the domain are those values for which any part of this expression is undefined. The expression is undefined when any denominator is zero: at x = 2 (left "factor"), at x = 1 (right "factor"), and at x = -3.

The factor (x +3) doesn't show up in the simplified form, but it is a "hole" in the graph of the original expression—a value of x where the function is not defined.

Here is a summary of what you get at the restricted values:

The simplified form with restrictions is ...

  [tex]\boxed{\dfrac{(x-1)^2}{x-2},\ x \ne -3,1,2}[/tex]

Answer:

$40.63

Step-by-step explanation:

If the phone company charges $17.75 already, and each minute costs $0.13, then we can do an equation that looks something like this:

17.75 + (0.13 × 176) = total price

We need to figure out how much 0.13 multiplied by 176 is.

0.13 × 176 = 22.88

Now that we figured out that 0.13 multiplied by 176 is equal to 22.88, we need to add the monthly access fee.

22.88 + 17.75 = 40.63

The monthly cost will be $40.63.

To solve for x, we need to isolate x on one side of the equation. To do this, we can first move all the terms that do not contain x to the right side of the equation by adding 3x and 2 to both sides:

2x - 2 + 3x + 2 = -3x + 13 + 3x + 2

5x = -3x + 15

8x = 15

Dividing both sides by 8, we get:

x = 15/8

= 1.875

Therefore, the value of x is approximately 1.875.

The value of x in equation 2x-2= -3x+13 is 3

To solve this equation we need to find the value of x so that all x terms should be one side and all constants should be at ones side:

2x+3x=13+2

5x=15

Now divide both side with 5 then, we get:

5x/5=15/5

x=3

Therefore, the value of x is 3

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The lowest cost per ounce is  12 ounces of soda which cost $0.72.

An 8-ounce of soda can costs $0.96, a 12-ounce soda can costs $0.72 and 32 ounces of a cup of soda costs $2.24.

The lowest cost per ounce can be calculated as follows:

For  8 ounces of soda can costs $0.96.

cost per ounces = 0.96 / 8

cost per ounce = 0.12 dollars per ounce

For  12 ounces soda can costs $0.72.

cost per ounces = 0.72 / 12

cost per ounce = 0.06 dollars per ounce

For  32 ounces soda can cost $2.24.

cost per ounces = 2.24 / 32

cost per ounce = 0.07 dollars per ounce

Therefore, the lowest is 12 ounces of a soda can.

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The probability of getting a Hybrid car = 3/14

The probability formula states that the ratio of favorable outcomes to all outcomes determines the likelihood that an event will occur.

The formula for the probability of an event is given by

P(E) = No of favorable outcomes/ total number of outcomes  

Here we have

The ratio of hybrid cars to gasoline-powered cars is 3:11

Let 3x and 11x be the number of hybrid cars and gasoline-powered cars
[ Since they are in 3: 11 ratio]  

Then total number of cars = 3x + 11x = 14x

From the given data,

Total number of cars = 280

=> 14x = 280

=>  x = 20

Number of Hybrid cars, 3x = 3(20) = 60

Here we select a car from a random experiment

Number of outcome = 280

Number of outcomes that we get Hybrid car = 60  

Thus the probability of getting a Hybrid car = [tex]\frac{60}{280}[/tex]

= [tex]\frac{6}{28}[/tex] =  [tex]\frac{3}{14}[/tex]  

Therefore,

The probability of getting a Hybrid car = 3/14

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Complete question:

The ratio of hybrid cars to gasoline-powered cars in the parking lot of a local office building is 3:11. if there are 280 cars in the lot and one is to be selected at random to get the reserved parking space nearest the building, find the probability the car selected is a hybrid. express your answer as a fraction.

The equation represents the volume of the box as V = - 4s³ + 250s².

The correct option is option A

The volume of any object is the capacity. How much it can hold.

The formula of volume is a product of length, breadth and height.

Volume = L × B × H

Given:

The perimeter of the square base of side s plus height h = 250cm

as per the given question,

The perimeter of the square base of side s plus height h = 250cm

2( s + s ) + h = 250

2 (2s) + h = 250

4s + h = 250

We can express h in the terms of s as,

h= 250 - 4s

Volume = length X breadth X height

Volume = s × s × h

V = s² × h

V = s² × (250 - 4s)

V = 250s² - 4s³

The equation represents the volume of the box as V = - 4s³ + 250s².

The correct option is option A

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After solving the given expression, the value obtained is [tex](m^1^8^n)[/tex]. Hence, option C is correct.

To streamline a phrase, one must use many techniques to make it shorter and simpler. The actions needed to reduce things are carried out in a predetermined sequence known as BODMAS.

Minimize a fraction to its simplest form to make it simpler. A fraction is said to be in its simplest form if both its numerator and denominator only include the integer.

As  per the given information in the question,

The expression is,

[tex](m^6^n)^3[/tex]

=  [tex](m^1^8^n)[/tex]

Therefore, option C is correct.

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The probability that the randomly selected time interval is longer than 95 minutes while solving for the mean time of the eruptions is 0.3192.

mean of x = 85 minutes

σ = 21.25 minutes

x ~ N(σ², μ)

p(x < 95)

1-p(x≤95)

1 - p(z≤0.47)

Using the z table here

1-0.6808 = 0.3192

Probability of x > 95 = 0.3192

b. n = 20

from central limit theorem

1 - p (z < 2.1045)

1-0.99826 = 0.0174

1 - p (z < 2.58)

1-0.9951

= 0.0049

. What we can observe from these results is that as the sample increase is increasing from 1, 20 to 30, the probability keeps decreasing.e. The probability is very small so one has to be doubtful if they are a really the population mean or if it has to be more than that.

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The total number of different room designs is 1296.

According to the fundamental counting principle, if there are n ways to do one thing and m ways to do another, then there are n×m methods to accomplish both things.

Given that, there are 6 paint colors, 4 types of flooring, 6 different curtains, 3 furniture sets, and 3 light fixtures.

As per the basic principle of counting, the total number of different room designs is:
6 × 4 × 6 × 3 × 3

= 1296

Hence, the total number of different room designs is 1296.

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