what is the solution for

an= -3an-1-3an-2-an-3, a0=1, a1=0, a2=5

a) (-1-4n+3n^2)(-1)^n
b) (1-4n-3n^2)(-1)^n
c) (1+4n+3n^2)(-1)^n

Answer:

\(\frac{t^2-16}{t^2-8t+16}\)

We can factorise the numerator which the difference of squares formula:

\(x^2-y^2=(x+y)(x-y)\)

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

\(\frac{t^2-4^2}{t^2-8t+16} =\frac{(t+4)(t-4)}{t^2-8t+16}\)

Next, factorise the denominator:

\(\frac{t^2-4^2}{t^2-8t+16} =\frac{(t+4)(t-4)}{(t-4)^2}\)

\(\frac{(t+4)(t-4)}{(t-4)(t-4)}\)

Cancel out the common factor of (t-4):

\(\frac{t+4}{t-4}\)

In the given scenario slope is increasing and the value of increasing slope is 2.

Slope may be defined as the extent of steepness of a curve in a graph in the given question x is given by miles driven in the cab and y represents the cost. y is the dependent variable and x in independent because the cost depends on the amount of miles driven. Here, in the question as the miles driven by the car increases the cost also increases. This proves that if the data is plotted on graph, it will give an increasing slope.

The value of slope can be determined by

Slope = (10.0 - 7.50)/(2.50 - 1.25)

Slope = 2.5/1.25

Slope = 2

This also gives a positive value. Thus, the slope is increasing.

Learn more about Slope at:

brainly.com/question/27781455

#SPJ9

Thw sequence computed shows that the value will be:

a. 201

b. 4020

a. 1, 3, 5, 7

100th term will be:

= a + (n - 1)d

= 3 + (100 - 1)2

= 3 + 198

= 201

b. 60, 100, 140

100th term will be:

= a + (n - 1)d

= 60 + (100 - 1)40

= 60 + 3960

= 4020

Learn more about sequence on:

brainly.com/question/6561461

#SPJ1

The equation (x + 3)²+ (y - 5)² = 16 represents a circle with center Z(-3,5) and a radius of 4 units.

The correct option is D.

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle.

Given:

A circle with center Z(-3,5) and a radius of 4 units.

And the general formula of the circle,

(x – h)²+ (y - k)² = r²,

where (h, k) is the center and r is the radius of the circle.

So, the equation is,

(x + 3)²+ (y - 5)² = 4²

(x + 3)²+ (y - 5)² = 16

Therefore, the equation is (x + 3)²+ (y - 5)² = 16.

To learn more about the circle;

https://brainly.com/question/29142813

#SPJ1

Answer:

Q1 -  The length of the side AC is:  12

Q2 - Hence, the distance in kilometers from the courthouse to the library is 12

Q3 - The distance in kilometers, from the courthouse to the bus station is: 15

Q4 - The length of side AB is 3

Q5 - The length of side AD is: 9

Step-by-step explanation:

Question1:

7 - (-5) = 7 + 5

12

2  -  2

0

AC = √ (12)^2 + (0)^2

AC  =  √ 144

AC   = 12

Question 2:

In this question, we need to use the distance formula to calculate the distance between the courthouse and the library.

The distance formula is:  √ (x2 - x1)^2  +  (y2 - y1)^2

The coordinates of the library are ( -5, 2) and the coordinates of the courthouse are (7, 2)

We can substitute these values into the distance formula to get:

√ (7 - (-5))^2 + (2 - 2)^2 = √ 12^2 = 12

Hence, the distance in kilometers from the courthouse to the library is 12

Question 3:

In this question we need to use the distance formula to calculate the distance between the courthouse and the bus station:

The distance formula: √ (x2  - x1)^2  + (y2 - y1)^2

The coordinates of the courthouse are (7, 3) and the coordinates of the bus station are ( -8, 3)

√ ( -8, - 7)^2  +  (3 - 3)^2  =  √ 225  =  15

The distance in kilometers, from the courthouse to the bus station is: 15

Question 4:

√(x2 - x1)^2 + (y2 - y1)^2

(-4, 3) and (-4, 6) into √(x2 - x1)^2  + (y2 - y1)^2

√(-4 + 4)^2  + (6  - 3)^2

√(-4 + 4)^2 + (6 - 3)^2

√0^2 + (6 - 3)^2

√3^2

The length of side AB is: 3

Question 5:

( - 2) - (7)  =  - 9

(2)  -  (2)  = 0

AD = √ ( -9)^2  +  (0)^2

AD = √ 81

AD = 9

The length of side AD is: 9

Hope this helps!

Answer:

Z(1.16)

Step-by-step explanation:

Let's start by expressing "Z increased by 16%" using algebra.

Let Z be the original value of some quantity.

To increase Z by 16%, we need to add 16% of Z to Z:

Z + 0.16Z

Simplifying this expression by factoring out Z, we get:

Z(1 + 0.16)

Combining like terms, we have:

Z(1.16)

Therefore, "Z increased by 16%" can be expressed algebraically as:

Z increased by 16% = Z(1.16)

Using it's concept, it is found that the sample space of T and S is:

{{8, [850-1500]}, {9, [850-1500]}, {10, [850-1500]}, {11, [850-1500]}, {12, [850-1500]}, {13, [850-1500]}, {14, [850-1500]}}

The sample space is the set that contains all possible outcomes for an experiment.

In this problem:

Considering that for each time, the cost will be between $850 and $1500, the sample space for T and S is:

{{8, [850-1500]}, {9, [850-1500]}, {10, [850-1500]}, {11, [850-1500]}, {12, [850-1500]}, {13, [850-1500]}, {14, [850-1500]}}

You can learn more about sample space at https://brainly.com/question/25861936

Answer:

C)  30 and 38

Step-by-step explanation:

In a normal distribution, 95% of the data points fall within two standard deviations of the mean.

Given:

To find the two values between which 95% of the data lies, subtract and add two standard deviations to the mean:

⇒ μ - 2σ = 34 - 2(2) = 34 - 4 = 30

⇒ μ + 2σ = 34 + 2(2) = 34 + 4 = 38

Therefore, 95% of the data lies between the values:

The answer to the equation −0.22x + x − 0.33x is 0.11x.

The answer is 0.11x. To solve this, we can start by rearranging the terms of the equation. The equation can be written as:

−0.22x + x − 0.33x = −0.22 + 0.33x

We then subtract x from both sides of the equation, resulting in:

−0.22x − x = −0.22 + 0.33x − x

We then combine like terms on the left side of the equation, resulting in:

−1.22x = −0.55

Finally, we divide both sides of the equation by -1.22 to solve for x, resulting in:

x = 0.11

Therefore, the answer is 0.11x.

Learn more about equation here:

https://brainly.com/question/10413253

#SPJ1

Complete question

What is the value of -0.22+−0.33−0.22x+x−0.33x?

the total distance covered by the bus is 41.67 km in 50 minutes.

For first 25 minutes:

Speed of the bus = 40 km / hr.

Time = 25 minutes

Distance = Speed × Time

Distance = 40 km / hr. × 25 / 60 hr.

Distance = 16.67 km

For the next 25 minutes:

Speed of the bus = 60 km / hr.

Time = 25 minutes

Distance = Speed × Time

Distance = 60 km / hr. × 25 / 60 hr.

Distance = 25 km

Total distance covered = 16.67 km + 25 km

Total distance covered = 41.67 km.

Therefore, we get that, the total distance covered by the bus is 41.67 km in 50 minutes.

Learn more about distance here:

https://brainly.com/question/7243416

#SPJ9

Answer:

it eqals 2

Step-by-step explanation:

Answer:

x+4

Step-by-step explanation:

Answer:

75 nickels.

Step-by-step explanation:

Here is the system of equations you can use:

0.05n+0.1d=6.25 (which can be converted to 5n+10d=625)

3d=n

5(3d)+10d=625

15d+10d=625

25d=625

d=25

3(25)=n

n=75

Answer:

\(54\pi \: {cm}^{2} \)

Step-by-step explanation:

Given:

A cone

l = 15 cm

r (radius) = 3 cm

Find: A (surface area) - ?

\(a(surface) = \pi {r}^{2} + \pi \times r \times l\)

\(a(surface) = \pi \times {3}^{2} + \pi \times 3 \times 15 = 9\pi + 45\pi = 54\pi \: {cm}^{2} \)

Answer:

I think your good but just in case check part C on first page also check 3c and 2.

Step-by-step explanation:

Answer: Sorry, I’m lazy today so I’ll just answer the first question, letter a. The answer is 30 cups of red paint.

Step-by-step explanation: Since you need 2 cups of blue paint and 4 cups of red paint, the ratio of the amount of cups you need for each paint is 1 cup of blue for every 2 cups of red. You need 15 cups of blue so you multiply it by 2 and you get 30. I hope this wasn’t confusing and I hope this helps. Please listen to you teacher because it would really help you on your work.

The lengths of the other two sides of the right triangle are 24m and 25m, respectively.

Let's assume the consecutive integers representing the lengths of the other two sides of the right triangle are x and x + 1, where x is the smaller integer. We are given that the shortest side measures 7m. Now, we can use the Pythagorean theorem to solve for the lengths of the other two sides.

According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

Using this theorem, we have the equation:

\(7^2 + x^2 = (x + 1)^2\)

Expanding and simplifying this equation, we get:

\(49 + x^2 = x^2 + 2x + 1\)

Now, we can cancel out \(x^2\) from both sides of the equation:

49 = 2x + 1

Next, we can isolate 2x:

2x = 49 - 1

2x = 48

Dividing both sides by 2, we find:

x = 24

Therefore, the smaller integer representing the length of one side is 24, and the consecutive integer representing the length of the other side is 24 + 1 = 25.

Hence, the lengths of the other two sides of the right triangle are 24m and 25m, respectively.

For more question on lengths visit:

https://brainly.com/question/28322552

#SPJ8

Answer:

t = 7

Step-by-step explanation:

5(2t - 3) – 7.5t = 0.5(12 – t)

5*2t - 3*5 - 7.5t = 12*0.5 - t *0.5

10t - 15 - 7.5t = 6 - 0.5t           {Now, combine like terms}

10t - 7.5t - 15 = 6 - 0.5t

         2.5t -15 = 6 - 0.5t      {Add 15 to both sides}    

         2.5t      = 6 - 0.5t + 15

              2.5t = 21 - 0.5t       { Add 0.5t to both sides}

    2.5t + 0.5t = 21  

                 3t = 21     {Divide both sides by 3}

                   t = 21/3

t = 7

Answer:

149 sq. ft

Step-by-step explanation:

For the triangle:

Base = 16-9 = 7 ft

Area of Triangle = 1/2 of  b.h

= 1/2 of 7 * 6

= 21 sq. ft

Area of Rectangle = l.b

= 5 * 16

= 128 sq. ft

Total Area = 149 sq. ft

Answer:

2/5 x 7" is 70.

Step-by-step explanation:

To solve this problem, you need to perform the operation of multiplication. In this case, the problem can be solved by multiplying 2 by 5, and then multiplying the result by 7.

The order of operations, also known as the hierarchy of operations, tells us the order in which we should perform calculations in a math problem. The order of operations is important because it ensures that calculations are done in the correct sequence and that the final result is accurate.

In this problem, the multiplication operation should be done before the division operation, because multiplication and division have the same precedence and should be done from left to right.

So, to solve the problem, you would first multiply 2 by 5 to get 10, and then multiply 10 by 7 to get the final result of 70.

Therefore, the answer to the problem "2/5 x 7" is 70.

Answer: =2.8

Step-by-step explanation:

2/5 x 7

=0.4 * 7

=2.8

Answer:

x=2

CE=58

Step-by-step explanation:

10x+9=18x-7

16=8x

x=2

10(2)+9+18(2)-7=

20+9+36-7=58

Answer: b = 11.62

Step-by-step explanation:

We can use this formula to solve for b:

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

\(b^{2} =\) \(\sqrt{12^{2}-3^2 }\)

\(b^2= \sqrt{144-9}\)

= 11.61895004

We can round that to 11.62.

Hope this helped!

Answer:

Step-by-step explanation:

In statistics, about 68 percent of values come in one standard deviation of the mean by using a standard normal model.   Approximately 95% of the data were all within two standard deviations from the mean. Almost all of the data are in the range of three standard deviations of the mean (roughly 99.7%).

The 68-95-99.7 law, also known as the Empirical Rule, is based on this evidence. 68 percent of the data values of a naturally distributed data collection of small children with a mean of 8.2 and a standard deviation of 10.8 would be between -2.2 and 19.0.

Within a mean of 14.1 as well as a standard deviation of 8.2, 68 percent of the data values in a usually distributed data collection of older children would be between 5.9 and 22.3.

However, we cannot conclude that the data is naturally distributed since the real actual data vary from the usual normal curve computed above.

Hence, various measures like either goodness of fit or theory testing, would be used for this.

ΔABC ≅ ΔEDC by the SAS postulate.

Postulate of Side-Angle-Side (SAS) ,The two triangles are said to be congruent if two sides and the included angle of one triangle match those of another triangle by two sides and the included angle.

According to the SAS Postulate, two triangles are congruent if their two sides and included angles are identical to those of another triangle's two sides and included angle

The midpoint of DB and AE Given is at C.

BC ≅ CD Two equal portions are produced by the midway C.

AC ≅ CE Two equal portions are produced by the midway C.

ACB and DCE Congruent vertical angles exist.

By the SAS postulat, ABC becomes EDC.

To learn more about  SAS postulate refer to:

https://brainly.com/question/1311007

#SPJ4

The factored expression of 4x³ - 2x² + 8x - 4 is (2x² + 4)(2x - 1) by grouping

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

4x³ - 2x² + 8x - 4

Group the expression in 2's

So, we have

(4x³ - 2x²) + (8x - 4)

Factorize each group

2x²(2x - 1) + 4(2x - 1)

So, we have

(2x² + 4)(2x - 1)

Hence, the factored expression is (2x² + 4)(2x - 1)

Read more about expression at

https://brainly.com/question/31819389

#SPJ1

Answer:

8.72 in fraction is 872/100 so this one is in the hundereds

0.827 in fraction is 872/1000 and this one is in the thousands

Rounding to the nearest liter, the volume of the liquid in the pipe is approximately 0.01 liters. Therefore, none of the options A, B, C, or D provided is the correct answer.

To calculate the volume of the liquid in the cylindrical steel pipe, we need to find the difference in volume between the solid cylinder (hollow part) and the hollow cylinder.

Given:

Length of the cylindrical steel pipe (hollow part) = 21 cm

Radius of the solid cylinder = 0.4 cm

Radius of the hollow cylinder = 0.1 cm

First, let's calculate the volume of the solid cylinder (hollow part):

V1 = π × \(r1^2\) × h

V1 = π × \((0.4 cm)^2\) × 21 cm

Next, let's calculate the volume of the hollow cylinder:

V2 = π × \(r2^2\) × h

V2 = π × \((0.1 cm)^2\) × 21 cm

Now, we can find the volume of the liquid in the pipe by subtracting V2 from V1:

Volume of liquid = V1 - V2

Let's calculate these values:

V1 = π ×\((0.4 cm)^2\) × 21 cm ≈ 10.572 cm³

V2 = π × \((0.1 cm)^2\) × 21 cm ≈ 0.693 cm³

Volume of liquid = V1 - V2 ≈ 10.572 cm³ - 0.693 cm³ ≈ 9.879 cm³

To convert the volume from cubic centimeters (cm³) to liters (L), we divide by 1000:

Volume of liquid in liters ≈ 9.879 cm³ / 1000 ≈ 0.009879 L

Rounding to the nearest liter, the volume of the liquid in the pipe is approximately 0.01 liters.

Therefore, none of the options A, B, C, or D provided is the correct answer.

for such more question on volume

https://brainly.com/question/6204273

#SPJ8

Answer:

28

Step-by-step explanation:

Hope this helps

The total savings that the couple Puan Yani and her husband have now is A) RM126,000.

The total savings of the couple can be determined by addition.

Addition is one of the four basic mathematical operations, including subtraction, divsion, and multiplication.

Let the amount that Puan Yani has in her savings account, a = RM24,700

Let the amount that her husband has than Puan Yani = RM75,300

The total amount that her husband has = a + 75,300

= RM100,000 (R24,700 + RM75,300)

The additional amount that Puan Yani deposited at the end of May = RM1,300

The total amount that Puan Yani has in her savings account at the end of May = RM26,000 (RM24,700 + RM1,300)

The total savings in the couple's accounts = RM126,000 (RM100,000 + RM26,000)

Learn more about the total savings at https://brainly.com/question/30537019.

#SPJ1

Answer:

2040 miles and gas mileage is 51/gallon

Step-by-step explanation:

1) Number of participants whose headache remained is: 62

2) The probability of randomly selecting an individual whose headache remained is: 0.4133

3) The probability of randomly selecting an individual whose headache remained and took a placebo is: 0.2933

From the table, we have the parameters as:

Number of participants that took medicine and headache went away = 120

Number of participants that took placebo and headache went away = 68

Number of participants that took and headache remained = 18

Number of participants that took placebo and headache remained = 44

1) Number of participants whose headache remained = 18 + 44 = 62

2) The probability of randomly selecting an individual whose headache remained is:

62/(62 + 120 + 68)

= 62/150

= 0.4133

3) The probability of randomly selecting an individual whose headache remained and took a placebo is:

44/150 = 0.2933

Read more about  probability of random selection at: https://brainly.com/question/251701

#SPJ1