Quesion is in picture

The equation of the possible way to begin solving for x is 2/5x - 7/20x = 3/4 - 1/2

From the question, we have the following parameters that can be used in our computation:

-3/4 + 2/5x = 7/20x -1/2

The first step is to collect the like terms

So, we have

2/5x - 7/20x = 3/4 - 1/2

This represents an equation of the possible way to begin solving for x

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well, the interest is going to be the increase factor on both cases, so we can simply check how much each will accumulate to in those 4 years

\(~~~~~~ \stackrel{\textit{\LARGE University Bank}}{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$4000\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &4 \end{cases}\)

\(A = 4000\left(1+\frac{0.05}{4}\right)^{4\cdot 4} \implies A=4000(1.0125)^{16}\implies \boxed{A \approx 4879.56} \\\\[-0.35em] ~\dotfill\)

\(~~~~~~ \stackrel{\textit{\LARGE Rosemont Savings Bank}}{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$4000\\ r=rate\to 5.5\%\to \frac{5.5}{100}\dotfill &0.055\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus two} \end{array}\dotfill &2\\ t=years\dotfill &4 \end{cases}\)

\(A = 4000\left(1+\frac{0.055}{2}\right)^{2\cdot 4} \implies A=4000(1.0275)^8\implies \boxed{A \approx 4969.52} ~~ \textit{\LARGE \checkmark}\)

Answer:

To find the missing value for the exponential function, we need to identify the common ratio (r) of the exponential function, as the function can be represented as y = a(r^x), where a is the initial value.

Starting with the first two points, we can set up an equation:

24 = a(r^-2)

16.8 = a(r^-1)

Dividing the second equation by the first equation, we get:

16.8/24 = (r^-1)/(r^-2)

0.7 = r

Now we can use the third point to solve for a:

11.76 = a(0.7^0)

11.76 = a

Finally, we can use the last point to solve for y:

y = 11.76(0.7^x)

Plugging in x = 1, we get:

y = 11.76(0.7)

y = 8.232

Therefore, the missing value is 8.232, and the graph that best fits the equation is Graph A.

The missing value for the exponential function is 8.232.

The graph that best fits the equation is Graph A.

An exponential function is a Mathematical function in the form f (x) = \(a^x\), where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

We know the standard form of exponential function is

y = a\((r^x)\), where a is the initial value.

Now, taking the first two points we get

24 = a(\(r^{-2\))

and, 16.8 = a(\(r^{-1\))

Dividing the above equation we get

16.8/24 = (\(r^{-1\))/ (\(r^{-2\))

r = 0.7

Now, find the value of a

11.76 = a(\(0.7^0\))

11.76 = a

So, y = 11.76(\(0.7^x\))

For x=1 the above equation gives

y = 11.76(0.7)

y = 8.232

and the graph that best fits the equation is Graph A.

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Answer:b

Step-by-step explanation:

By graphing or visualizing the parabolic shape, we can observe where the graph intersects the x-axis, which represents the solutions to the equation. In this case, the solutions are x = -3 and x = 1.

To solve the quadratic equation x^2 + 2x - 3 = 0 by graphing, we can plot the graph of the equation and find the x-values where the graph intersects the x-axis.

First, let's rearrange the equation to the standard form: x^2 + 2x - 3 = 0.

We can create a graph by plotting points for different values of x and then connecting them. However, I can describe the process and the key points on the graph.

1. Find the x-intercepts: These are the points where the graph intersects the x-axis. To find them, set y (the equation) equal to zero and solve for x:

  0 = x^2 + 2x - 3.

  This quadratic equation can be factored as (x + 3)(x - 1) = 0.

  Therefore, x = -3 or x = 1.

2. Plot the points: Plot the points (-3, 0) and (1, 0) on the graph. These are the x-intercepts.

3. Draw the graph: The graph of the equation x^2 + 2x - 3 = 0 is a parabola that opens upward. It will pass through the x-intercepts (-3, 0) and (1, 0).

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Answer:

w(25) = 96

There are 96 wolves in the year 2020

Step-by-step explanation:

Given:

\(w(x)=14\cdot 1.08^{x}\)

w(25) =

\(w(25)=14\cdot 1.08^{25}\\\\= 14 * (6.848)\\\\=95.872\\\\\approx 96\)

Number of years : 1995 + 25 = 2020

In 2020, there are 96 wolves

The applied overhead cost for job 201 is $36,000 and total cost for job 201 under direct materials cost as allocation base is $86,000.

Allocation base is a technique utilized in accounting to designate the cost of something to its use or product to recognize the price of the finished product.

Example provides the total overhead cost at $120,000 for the period, the base data of $100,000 direct material cost and 500 direct labor hours. The base data are used to calculate the predetermined factory overhead rate, which is used to apply overhead costs to work in progress.

The predetermined factory overhead rate is calculated by dividing the total overhead cost for the period by the base data. The predetermined factory overhead rate is multiplied by the actual activity in the allocation base to obtain the applied overhead cost.

Direct materials cost as allocation base $30,000 is the actual direct material cost used in job 201. The predetermined factory overhead rate is calculated by dividing the total overhead cost for the period by the direct material cost, which is $120,000/$100,000=120%.

The applied overhead cost for job 201 is $30,000*120% = $36,000.

Total cost for job 201 under direct materials cost as allocation base is $30,000+$20,000+$36,000 = $86,000.

-Direct labor cost as allocation base:

The actual direct labor cost used in job 201 is $20,000. The predetermined factory overhead rate is calculated by dividing the total overhead cost for the period by the direct labor cost, which is $120,000/$100,000=120%.

The applied overhead cost for job 201 is $20,000*120% = $24,000.

Total cost for job 201 under direct labor cost as allocation base is $30,000+$20,000+$24,000 = $74,000.

-Direct labor hours as allocation base:

The actual direct labor hours used in job 201 is 400 hours.

The predetermined factory overhead rate is calculated by dividing the total overhead cost for the period by the direct labor hours, which is $120,000/500 hours = $240 per hour.The applied overhead cost for job 201 is $240*400 hours = $96,000.

Total cost for job 201 under direct labor hours as allocation base is $30,000+$20,000+$96,000 = $146,000.

-Physical output as allocation base: The actual output in units completed for job 201 is 2,000 shirts.

The predetermined factory overhead rate is calculated by dividing the total overhead cost for the period by the output in units, which is $120,000/10,000 units = $12 per unit.

The applied overhead cost for job 201 is $12*2,000 units = $24,000.Total cost for job 201 under physical output as allocation base is $30,000+$20,000+$24,000 = $74,000.

-Machine hours as allocation base: The actual machine hours used in job 201 is 240 hours.

The predetermined factory overhead rate is calculated by dividing the total overhead cost for the period by the machine hours, which is $120,000/5,000 hours = $24 per hour.

The applied overhead cost for job 201 is $24*240 hours = $5,760.

Total cost for job 201 under machine hours as allocation base is $30,000+$20,000+$5,760 = $55,760.

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Answer:

angle ced is a right ange

so the m angels debate =135 m angle aeb =35

so the answer is 135+35 =170

180 is a all side sim

=180-170=10 answer

Answer:

∠CED is a right angle.

∠CEA is a right angle.

m∠CEB = m∠BEA

m∠DEB = 135°

For the given function f(x) = 2x³ + 6x² - 5x - 3 , g(x) = 3x - 4 , the value of

(f -g)(x) =  2x³ + 6x² -8x + 1 .

As given in the question,

Function is given by :

f(x) = 2x³ + 6x² - 5x - 3 , g(x) = 3x - 4

Substitute the value in the given function and simplified it ,

( f - g )(x)

=  { 2x³ + 6x² - 5x - 3 } - { 3x - 4 }

= 2x³ + 6x² - 5x - 3 -3x + 4

= 2x³ + 6x² -5x -3x -3 + 4

= 2x³ + 6x² - 8x + 1

Therefore,  for the given function f(x) = 2x³ + 6x² - 5x - 3 , g(x) = 3x - 4 , the value of (f -g)(x) =  2x³ + 6x² -8x + 1 .

The complete question is:

If for the given function ,

f(x) = 2x³ + 6x² - 5x - 3 , g(x) = 3x - 4

Find the value of (f - g)(x).

a. 2x³ + 6x² -8x + 1

b. 2x³ + 6x² + 2x+1

c. 2x³ + 6x² + 2x -7

d. 2x³ + 6x² + 8x⁷

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Answer:

113

Step-by-step explanation:

First we need to find theother 2 angles of the triangle.

We are given that the top angle is 60°

We know that the angles of a triangle add up to 180°

To find the bottom left angle of the triangle...

We can see that it is alternate exterior angles so they will equal.

To find the third angle of the triangle...

180 - 60 (given angle) -53 (alternate exterior angle) = 67°

Now we know that the bottom right angle inside the triangle is 67°.

To find x...

subtract 67 from 180 because the like is a combination of x and the 67° angle we just found. (a straight line angle = 180°)

180 - 67 = 113

Hello!

The distance, d, is less than 200 miles.

B. d > 200

Answer:

I REALLY DON'T KNOW IM DOIN IT FOR THE POINTS

Step-by-step explanation:

Answer:

Step-by-step explanation:

The associative property lets you move parentheses in a sum or product. That is, it doesn't matter which sum or product you compute first.

The commutative property lets you swap the order of operands in a sum or product.

The identity property says the operation using the identity element gives the original value, unchanged.

Answer:

Step-by-step explanation:

Robert's dimes are anywhere between 17 and 19.

Nickels

are worth 5 cents, and

dimes

are worth 10 cents. Since Robert has 10 nickels, he already has 50 cents. To reach a minimum of $2.20, or 220 cents, Robert needs at least 170 more cents. Because each dime is worth 10 cents, he needs a minimum of 17 dimes. If he has a maximum of 29 coins in total, subtracting the 10 nickels means that he can have up to 19 dimes. So, Robert could have anywhere between 17 and 19 dimes.

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Answer:

the 1st one!

Step-by-step explanation:

Answer:

Step-by-step explanation:

1. Title of the graph → Comparison of the Plant Growth

2. y-axis represents the height of the plants in centimeters.

3. On day 2:

   Height of plant A (plant outside) = 5.1 cm

   Height of plant B (plant near the window) = 2.25 cm

4. Plant outside shows great increase in the height.

    On day 5,

    Height of the plant outside = 6.75 cm

    Growth in height from day 2 to day 5 = 6.75 - 5.1

                                                                   = 1.65 cm

    Height of the plant near the window = 2.5 cm

    Growth in height of the plant from day 2 to day 5 = 2.5 - 2.25

                                                                                        = 0.25 cm

    Therefore, plant outside shows the great increase in height.

5. Plant near the window grew 0.25 cm in height.

(a) √2 · √8. The simplified surd expression is 4.

(b) √80. The simplified surd expression is  4√5.

(c) √5/√20. The simplified surd expression is  1/2.

(d) √20. The simplified surd expression is  2√5.

The given surd expression is simplified as follows;

(a) √2 · √8

we can simplify it as;

√2 · √8 = √(2 x 8) = √16 = 4

(b) √80

we can simplify it as;

√80 = √ (16 x 5) = √16  x √5 = 4√5

(c) √5/√20

we can simplify it as;

√5/√20  x  √20 / √20

= (√5  x √20 ) /(20)

= √100 / 20

= 10/20

= 1/2

(d) √20

we can simplify it as;

√20 = √4  x √5 = 2√5

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To verify if the relation is a function, it must be verified if from each value of x only one arrow departs.

A relation represents a function when each input value is mapped to a single output value.

In mapping notation, with the arrows, it must be verified if there is no input from which more than one arrow departs.

The problem is incomplete, hence the general procedure to verify if the relation is a function was presented.

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Answer:

The answer would be 59

Step-by-step explanation:

first 9 times 6 which is 54 then you add 4 and 54 plus 4 is 59 and also PEMDAS first is Multiplication and then addition hope this helps :D And keep learning !

Answer:

B) 6

Step-by-step explanation:

Let the number be x

Product of 6 and square of number plue 15 : (6x²) + 15

Coefficient of x² = 6

Answer: It is similar to triangle ABC and has coordinates A′(8, −12), B′(4, −16), and C′(−20, 8)

Step-by-step explanation: Dilated triangles are never congruent, only similar (unless the dilation factor is exactly 1).

The coordinates of an image dilated about the origin are those of the pre-image multiplied by the dilation factor. For example,

 A' = 2A

 A'(8, -12) = 2×A(4, -6)

These facts are all you need to know to choose the correct answer (shown above).

Answer: 1/2

Step-by-step explanation:

I took the quiz!

3888

Step-by-step explanation:

take

36×18×6=3888

Answer:

1191 cm²

Step-by-step explanation:

Area of parallelogram = base X vertical height.

Call the vertical line h.

h/ sin 80  =  7/ sin 10

h = (7 sin 80) / sin 10

= 39.7.

Area of parallelogram = 30 X 39.7

= 1191 cm²

The Area of Parallelogram whose side length is 30 cm is 1,190.952 square cm.

Given:

Side length = 30 cm

Using Trigonometry

tan 80 = P / Base

5.6712 = P / 7

P = 39.6984 cm

Using the formula for Area of parallelogram

= Base x height

= 30 x 39.6984

= 1,190.952 square cm.

Therefore, the area is 1,190.952 square cm.

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The the coefficient of variation for set a is 15.7% and the coefficient of variation for set b is 22.3%.

The formula for calculating the coefficient of variation is:

CV = (standard deviation / mean) x 100%

where standard deviation is a measure of the spread of the data around the mean. The CV expresses the standard deviation as a percentage of the mean.

To calculate the CV for set a, we first need to find the mean and standard deviation of the data set. The mean can be calculated by adding all the values and dividing by the number of values.

Mean = (3.97 + 3.47 + 3.99 + 4.30 + 3.16 + 3.07 + 4.24 + 2.94 + 3.56 + 3.43 + 3.06 + 3.34 + 4.35 + 3.57) / 14 = 3.65

The standard deviation can be calculated using a calculator or a spreadsheet software such as Microsoft Excel. For this set, the standard deviation is 0.574.

CV = (0.574 / 3.65) x 100% = 15.7%

To calculate the CV for set b, we need to first remove the dollar sign from each value and then find the mean and standard deviation.

Mean = ($24,800 + $30,000 + $22,300 + $20,400 + $19,000 + $32,200 + $23,000 + $23,000 + $24,000 + $27,200 + $34,900) / 11 = $25,727.27

The standard deviation can be calculated using a calculator or spreadsheet software. For this set, the standard deviation is $5,746.38.

CV = ($5,746.38 / $25,727.27) x 100% = 22.3%

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Answer:

It's dependent, the y intercept is 3/7 and slope is -2/3 for both of them

Step-by-step explanation:

Answer:

Step-by-step explanation:

Comment

The formula for density is D = m/V

Therefore the units of density is

Density = grams/cm^3

All golden rectangles are similar and the ratio length/width = golden ratio = \(\frac{1 + \sqrt{5} }{2}\).

What is golden Rectangle ?

A golden rectangle is a rectangle that can be cut up into a square and a rectangle similar to the original one. More precisely,

Let ABCD be a rectangle, with width AB < length BC. Then there is a point E on segment AD and a point F on segment BC so that BFEA is a square. i.e., AE = BF = AB (and consequently EF = AB also). Then FCDE is a rectangle. We say that ABCD is a golden rectangle if FCDE is similar to ABCD.

Theorem:  All golden rectangles are similar and the ratio length/width = golden ratio = \(\frac{1 + \sqrt{5} }{2}\).

Corollary.  If ABCD is a golden rectangle, so is the sub - rectangle FCDE (as defined below).

Proof:  Let a = AB = width and b = BC = length of a golden rectangle.  Then for ABCD the ratio length/width = b/a and for FCDE the ratio length/width = a/(b-a).  The rectangles are similar if and only if these ratios are equal, so, if we set k = b/a, then b = ka and k = b/a = a/(b-a) = a/(ka – a) = 1/(k-1).

Therefore k is a root of k^2 – k – 1 = 0; also, k is a positive number.  By the quadratic formula the only positive root of this polynomial is the golden ratio \(\frac{1 + \sqrt{5} }{2}\\\).

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Answer:

18 cheetos bags, 12 takis bags

Step-by-step explanation:

Assigning:

Let x = number of cheetos bag(s)

Let y = number of takis bag(s)

System of Equations:

x + y = 30

15x + 40y = 750

Solving:

Isolate y in first equation : y = 30 - x

Substitute into second equation:

15x + 40(30 - x) = 750,

15x + 1200 - 40x = 750,

-25x = - 450,

x = 18 cheetos bags

y = 30 - 18 = 12 takis bags

Answer:

the solution for the system is;

\(c = 18 \\ t = 12\)

Step-by-step explanation:

Let C be the number of cheetos bags that you will buy and T the corresponding number of Takis bags.

Since you're going to buy a total of 30 bags, then;

\(c + t = 30\)

Since the Cheetos bag cost $15, then the total cost for C bags is 15C. The same way, since the Takis bag cost $40, the total cost for T bags is 40T. Since you will spend $750, then;

\(15c + 40t = 750\)

Use the substitution method to solve the system. To do so, isolate one variable from the first equation and substitute the resulting expression into the second equation;

\(c + t = 30 \\ c = 30 - t\)

Substitute that expression for C into the second equation and solve for T:

\(15c + 40t = 750 \\ 15(30 - t) + 40t = 750 \\ 450 - 15t + 40t = 750 \\ 450 + 25t = 750 \\ 25t = 750 - 450 \\ 25t = 300 \\ t = \frac{300}{25} \\ t = 12\)

Substitute back T=12 into the expression for C;

\(c = 30 - t \\ c = 30 - 12 \\ c = 18\)

Therefore, the solution for the system is;

\(c = 18 \\ t = 12\)

Which mean that you buy 12 bags of Takis and 18 bags of Cheetos.