The product of the length of 2 unequal poles before cutting 2 cm from each was 285 cm. Their present sum after cutting 2cm from each is 30cm. What is the length of the shorter pole? The product of the length of 2 unequal poles before cutting 2 cm from each was 285 cm . Their present sum after cutting 2cm from each is 30cm . What is the length of the shorter pole ?​

The amount invested at each rate

Investment at 7% = $25000

Investment at 2%  = $11,000

Investment definition is an asset acquired or invested in to build wealth and save money from the hard earned income or appreciation.

Given:

Larry Mitchell invested = $36,000 at 7% annual simple interest

the rest at 2% annual simple interest.

Total investment = 36000

let the investment at 7% is x

then, invested at 2% = 36000 - x

Total interest earned = $1,970

Simple interest = principal * rate * time

Investment at 4%:

(x * 0.07) + [(36000 - x) * 0.02] = 1970

0.07x + 720 - 0.02x= 1970

0.05x = 1970-720

0.05x = 1250

x= 25000

Hence,

Investment at 7% = $25000

Investment at 2% = $36,000 - $25000 = $11,000

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Last option: (50, 30); 50 adult tickets and 30 child tickets

A linear equation is an equation in which the highest power of the variable is always 1.

We have the system of equations:

x + y = 80

6x + 4y = 420

We will use elimination method to solve it:  

Multiply the first equation by -6 and then add the equations:

- 6x - 6y = -480

6x + 4y = 420  

We get:

-2y = -60

After dividing both sides by -2 we get:

y = 30

then plugging 30 in place of y into the original first equation we get:

x+30=80

Then subtracting 30 from both sides we get:

x = 50

The solution to the system is (50, 30)

Then notice the second equation 6x+4y=420 clear indicates that x represents the tickets for adults since the price for adults $6 is the coefficient of the x-term, while the price for children which is $4 is attached as coefficient in front of the y.

Thus, x=50 means there were sold 50 adult tickets. And y=30 that there were sold 30 child tickets.

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Answer:

( 50, 30)

Step-by-step explanation:

Answer:

x = - 5/2

Step-by-step explanation:

Using the law of indices

. a^-n = 1/a^n

. (a^4)^5 = a^5×4 = a^20

Note : When two base are equal , we equate the Exponents.

3^4x-5 = (1/27)^2x+10

= 3^4x-5 = (27^-1)^2x+10

= 3^4x-5 = (3^-3)^2x+10

= 3^4x-5 = 3^ -3(2x+10)

= 3^4x-5 = 3^ -6x-30

The two base are 3 so we equate the exponents.

= 4x - 5 = -6x - 30

= 4x + 6x = -30+5

= 10x = -25

= 10x/10 = -25/10

x = -25/10

x = - 5/2

X is -5/2

Answer:

No solution

Step-by-step explanation:

Step-by-step explanation:

1. True

2. False

3. True

5. Falsw

6.True

7.True

8.False

10.True

15. always

17. always

The value of DG is 4x + 45

From the question, we are to determine the value of DG

From the given information,

DE = 2x + 17

EF = 8

FG = 2x + 20

Then,

DG = DE + EF + FG

DG = 2x + 17 + 8 + 2x + 20

DG = 4x + 45

Hence, the value of DG is 4x + 45

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Answer:

A = 5, B = 9, C = 6

Step-by-step explanation:

let me know if you want an explanation :))

The expression of base area of box will be 4x + x²

The area of a a rectangle occupies is the space it takes up inside the limitations of its four sides. The dimensions of a rectangle determine its area. Basically, the area formula is the product of the rectangle's length and width.

Given,

Length = 4+x

width = x

height = x²+1

We have to find the expression of base area of box

Given the length, width, and height

The formula for area of rectangle is as follow:

Area of rectangle = length x width

Area of rectangle = (4+x) x (x)

Area of rectangle = 4x + x²

Hence the expression of base area of box will be 4x + x²

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Answer:

which p? there isn't any p in above equation

Answer:

  y ≈ 15272.9(1.06306^x) . . . . from regression tool

  y = 15300(1.0624^x) . . . . calculated "by hand"

Step-by-step explanation:

An exponential model is one that uses the exponential function ...

  f(x) = a·b^x

to model the data. The value of 'a' is the function value when x=0, the initial value. The value of 'b' is the growth factor, the multiplier between function values for successive values of x.

__

An exponential regression tool makes short work of this. Such tools are available on some calculators, apps, and spreadsheets. All that is required is entering the data into a table and invoking the tool. The one shown in the attachment tells you the model is approximately ...

  y ≈ 15272.9(1.06306^x)

__

We can average the growth rate factors a couple of different ways. When we think of "averaging," we usually think of the arithmetic mean, the sum of values divided by their number. If we average the growth rates in this way, we get ...

  average rate of growth =

  ((161/153) +(173/161) +(184/173) +(196/184) +(207/196) +(220/207))/6 ≈ 1.0624

Using the first table value as the initial value, the model formed this way is ...

  y = 15300(1.0624^x)

__

For exponential growth it may make more sense to compute the geometric mean. This is the n-th root of the product of n numbers. In this case, it reduces to the 6-th root of the ratio of the last to the first:

  average rate of growth = (220/153)^(1/6) ≈ 1.0624

This gives the same growth factor as above, hence the same model.

The second attachment shows the application of this model to the domain used in the table. We see there are some minor differences when rounding the function value to the nearest hundred.

The differences in our two models seem to arise from rounding the data values in the table to the nearest hundred.

__

The values given in the table can be used in different ways to arrive at two similar, but different exponential models of the table data:

Interestingly, the function calculated "by hand" has a very slightly better correlation with the table data. The difference in correlation coefficients is in the 6th decimal place.

Part 1

[tex](f\circ g)(x)=f(g(x))=\frac{\frac{1}{x}}{\frac{1}{x}-3}[/tex]

Multiplying the numerator and denominator by x,

[tex](f\circ g)(x)=\boxed{\frac{1}{1-3x}}[/tex]

Part 2

The domain for this function is all values of x except for when the denominator equals 0 (because then, it would be undefined).

The denominator is equal to 0 when x=1/3, so the domain is [tex]\boxed{x \neq \frac{1}{3}}[/tex]

Based on the amount being taxed, the period of taxation, and the tax, the annual percentage of tax is 19.96%.

Assuming this rate was x, the following formula would apply:

Annual rate/ 365 days a year x number of days x amount to be taxed = Tax amount

Solving gives:

x/365 x 32 x 8,000 = 140

701.369863x = 140

x = 140 / 701.369863

= 19.96%

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Answer:

I think its x = 7

I belive it is

Answer:

[tex]\displaystyle{f(x+1)=|x-6|-4}[/tex]

Step-by-step explanation:

To evaluate [tex]\displaystyle{f(x+1)}[/tex], substitute [tex]\displaystyle{x}[/tex] to [tex]\displaystyle{x+1}[/tex] so we should have:

[tex]\displaystyle{f(x+1) = |x+1-7|-4}[/tex]

Evaluate the expression and finally, we have:

[tex]\displaystyle{f(x+1)=|x-6|-4}[/tex]

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Answer:

49 + 28 = 7(7 + 4)

Step-by-step explanation:

49 bags of soil one week

28 bags of soil the next week

49 + 28 bags of soil purchased in total

Find the GCF (Greatest Common Factor) of 49 and 28.

49/7 = 7

28/7 = 4 (GCF is 7 since it is the largest number that can divide both 49 and 28 equally)

Factor out the GCF + rewrite division above (optional for visualization)

49/7 = 7 -> 49 = 7 * 7

28/7 = 4 -> 28 = 7 * 4

49 + 28 = 7(7 + 4)

Let me know if you have any questions!

Numerical Expression

The expression consists of numbers and arithmetic operators. It does not contain equality or inequality symbols.

find the common denominator and thin combine the numerators over the common denominator trhin simplify each term thin simplify by adding subtracing  thin the result can be shown in multiple forms

exact form 19/2

decimal form 9.5

mixed number form 9 1/2

the end behavior is:

If we have a polynomial of even degree, then the end behavior in both ends is the same one.

Particularly, in these cases (even degree) we only need to look at the leading coefficient. If it is positive, then as x tends to infinity and negative infinity, the function tends to infinity.

In this case, the polynomial is:

y = 9x⁴ + 8x - 2

Notice that the degree is 4, even, and the leading coefficient is 9 (positive).

Then the end behavior is:

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The Maximax decision is that Susan should build a very large gas station due to the largest value of row maximums.

A decision table can be defined as a type of table that is used for the graphical representation of the actions to perform, especially based on given conditions and business level rules.

The decision table for Susan’s problem is shown below:

Size            Good market   Fair market   Poor market    Row maximum

Small              50,000           20,000            -10,000           50,000

Medium          80,000           30,000            -20,000          80,000

Large              100,000          30,000            -40,000          100,000

Very large      300,000         25,000            -160,000         300,000

Thus, the Maximax decision is for Susan to build a very large gas station due to the largest value of row maximums.

For the Maximin decision, we have:

Size            Good market   Fair market   Poor market    Row minimum

Small              50,000           20,000            -10,000           -10,000

Medium          80,000           30,000            -20,000          -20,000

Large              100,000          30,000            -40,000          -40,000

Very large      300,000         25,000            -160,000         -160,000

Therefore, the Maximin decision is that Susan should build a small gas station due to the largest value of row minimums.

For the equally likely decision, we would find the row average:

Row 1 = (50,000 + 20,000 - 10,000)/3 = 20,000.

Row 2 = (80,000 + 30,000 - 20,000)/3 = 30,000.

Row 3 = (100,000 + 30,000 - 40,000)/3 = 30,000.

Row 4 = (300,000 + 25,000 - 160,000)/3 = 55,000.

Hence, the equally likely decision is that Susan should build a very large gas station due to the largest value of row average.

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Complete Question:

Even though independent gasoline stations have been having a difficult time, Susan has been thinking about starting her own independent gasoline station. Susan’s problem is to decide how large her station should be. The annual returns will depend on both the size of her station and a number of marketing factors related to the oil industry and demand for gasoline.  After a careful analysis, Susan developed the following table:

a. Develop a decision table for this problem

b. What is the maximax decision?

c. What is the maximin decision?

d. What is the equally likely decision?

Answer:

1.  x = 55°

2.  x = 11°

3.  x = 30°

4.  x = 19°

Step-by-step explanation:

Trigonometric Identities

[tex]\sin(x)=\cos(90^{\circ}-x)[/tex]

[tex]\cos(x)=\sin(90^{\circ}-x)[/tex]

Question 1

[tex]\begin{aligned}\implies \sin(35) & =\cos(90-35)\\ & = \cos(55)\end{aligned}[/tex]

[tex]\implies x=55^{\circ}[/tex]

Question 2

[tex]\begin{aligned}\implies \cos(79) & =\sin(90-79)\\ & = \sin(11)\end{aligned}[/tex]

[tex]\implies x=11^{\circ}[/tex]

Question 3

[tex]\begin{aligned}\cos(x)& =\sin(2x)\\\implies \cos(x)& =\sin(90^{\circ}-x)\\\\\implies 2x & = 90-x\\3x & = 90\\x & = 30^{\circ}\end{aligned}[/tex]

Question 4

[tex]\begin{aligned}\sin(x+4)& =\cos(4x-9)\\\implies \sin(\theta)& =\cos(90^{\circ}-\theta)\\\\\implies x+4 & = 90-(4x-9)\\x+4 & = 90-4x+9\\5x & = 95\\x & = 19^{\circ}\end{aligned}[/tex]

should i create the world problem with 12 3 and 9?

The balance in Yolanda's saving plan after 14 years is; $9,455.36

We want to find the balance in Yolanda's saving plan after 14 years.

For Yolanda;

PV = 0

PMT = 250

i% = 4%/12 = 0.33%

N = 14 yrs * 12 = 168

FV = ?

For Zach:

PV = 0

PMT = $3300

i% = 4%

N = 14 yrs

FV = ?

From online future value calculator, we have;

Yolanda FV = $9,455.36

Zach FV = $47,204.19

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Opposite values are those values which on the number line has the same distance between them and zero. The temperature in each city is PoT=-PhT and PhT =+PoT.

Opposite values are those values which on the number line has the same distance between them and zero. Although the sign on the values may be difference. For example if the first value is 4, then its opposite value is -4.

In general, the temperature equation for Portland, Maine is stated mathematically as

PoT=-PhT

As it is given in the question that the Portland, Maine and Phoenix, Arizona had opposite values. Also, the temperature in Portland is lower than in Phoenix. Therefore, the temperature in each city can be written as,

PoT=-PhT

PhT =+PoT

Hence, the temperature in each city is PoT=-PhT and PhT =+PoT.

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Answer:

No. (-1/2) is not an integer

Integers involve all the no. +ve and -ve. which can be written without fraction. ie whole no. are counted as integers.

(-1/2) is a fraction

Answer:

whats the question? please explain

Answer:

16П or approximately 50.3)

Step-by-step explanation:

The area of a circle is equal to П*r²

Since the circle is inside a rectangle with side that is equal to 8, we know that d = 8

2r = d

r = 8/2

r = 4

A = П*r²

A = П*16

А = 16П ( or 16*3.141592653589793238... = 50.26548... ≈ 50.3)

Answer:

area = 50.27 [tex]cm^2[/tex]

Step-by-step explanation:

In the diagram, we see that the diameter of the circle is 8cm. Therefore the radius of the circle is 8/2 = 4cm.

[tex]area \hspace{0.15cm}of \hspace{0.15cm}circle = $\pi$r^2[/tex]

                        = π [tex](4)^2[/tex]

                        = 50.27 [tex]cm^2[/tex]

Answer:

ANSWER IS B

Step-by-step explanation:

NEXT TIME USE any graph website online