the first three terms of a sequence are given. round to the nearest thousandth (if necessary) 462, 453, 444. find the 30th term

Answer:

4.

Step-by-step explanation:

Change of base formula is

logb x = loga x / loga b

So logx 25 = log5 25 /log5 x

Now log5 25 = log5 5^2 = 2, so:

logx 25 = 2 / log5 x

So log5 x^2 * logx 25

= log5 x^2 * 2 /log5 x

= 2 log5 x * 2 / log5 x

= 4.

The end-points of the line segment will be negative 1.25 and 0.25.

A number line refers to a straight line in mathematics that has numbers arranged at regular intervals or portions along its width. A number line is often shown horizontally and can be postponed in any direction.

The length of the line segment is 1.50 units and the midpoint of the line segment is negative 0.50. Then the end-points of the line segment are given as,

⇒ - 0.50 ± (1.50) / 2

Simplify the expression, then we have

⇒ - 0.50 ± (1.50) / 2

⇒ - 0.50 - (1.50) / 2, - 0.50 + (1.50) / 2

⇒ - 0.50 - 0.75, - 0.50 + 0.75

⇒ - 1.25, 0.25

The end-points of the line fragment will be negative 1.25 and 0.25.

More about the number line link is given below.

https://brainly.com/question/13189025

#SPJ1

Greetings from Brasil...

The point (-2; -4) is in the blue area, so it is the solution to the equation;

The point (-1; -5) is in the blue area, so it is the solution to the equation;

The point (0; -3) is in the blue area, so it is the solution to the equation;

The point (2; -1) is exactly on the function line. As this line is dashed, it does not include its values, so this point is not a solution (no point on the dashed line is a solution)

The value of x in the parallelogram is 112°.

In a parallelogram, adjacent angles are always supplementary. This means that the sum of two adjacent angles in a parallelogram is always 180 degrees.

To understand this concept, let's consider a parallelogram ABCD. The opposite sides of a parallelogram are parallel and equal in length, and the opposite angles are congruent. Adjacent angles are those that share a side. Let's say angle A and angle B are adjacent angles in the parallelogram.

Since opposite angles of a parallelogram are congruent, we have angle A is congruent to angle C, and angle B is congruent to angle D.

Now, let's consider angle A and angle B. The sum of angle A and angle B is equal to the sum of angle C and angle D because opposite angles are congruent.

Therefore, we can conclude that angle A + angle B = angle C + angle D = 180 degrees.

This property holds true for all parallelograms. So, in any parallelogram, the adjacent angles are always supplementary, meaning their sum is 180 degrees.

For the given question, we know x° + 68° = 180°.

Then x° = 180° - 68°

x° = 112°

For more such questions on parallelogram

https://brainly.com/question/20526916

#SPJ8

The total time taken for the entire journey is 2.8 hours.

To calculate the total time taken for the entire journey, we can use the formula:

Time = Distance / Speed

For the first part of the journey, the car travels a distance of 112 km at an average speed of 70 km/h. Using the formula, the time taken for this part is:

Time1 = 112 km / 70 km/h = 1.6 hours

For the second part of the journey, the car travels a further distance of 60 km at an average speed of 50 km/h. Again, using the formula, the time taken for this part is:

Time2 = 60 km / 50 km/h = 1.2 hours

To find the total time for the entire journey, we sum up the times for both parts:

Total Time = Time1 + Time2 = 1.6 hours + 1.2 hours = 2.8 hours

For more such questions on time

https://brainly.com/question/26862717

#SPJ8

The coordinates of the image of the point Q is Q'(3, 6).

Transformation of geometrical figures or points is the manipulation of a given figure to some other way.

Different types of transformations are Rotation, Reflection, Glide reflection, Translation and Dilation.

From the given graph, we have point Q(-4, 4).

Here the point is translated.

After translation, the original figure is shifted from a place to another place without affecting it's size.

The rule of translation is given as the point (x, y) is translated as (x + 1, y + 2).

So the given point is (-4, 4).

(-4, 4) after translation becomes by the definition (-4 + 1, 4 + 2).

So the required point is (-3, 6).

Hence the image of point Q is (-3, 6).

To learn more about Translation, click on the link given below :

https://brainly.com/question/12463306

#SPJ1

Your question is incomplete, Probably, the correct graph for the question is given below.

Answer:

{2x}/{5} -6+{-x}/{5}

Step-by-step explanation:

Hii!

=(x+y)+(3x-2y)

=(x+3x) + (y-2y)

= 4x- y

Hope it helps:)

The polynomial 11x⁵  + x⁴ - 4x³ - 5x² + 8 denotes the expression P - Q. The correct option is option A.

What is an expression?

A mathematical expression is a phrase that contains a minimum of two numbers or variables and at least one mathematical operation. It is possible to multiply, divide, add, or subtract in math. An expression has the following structure: Expression is (Math Operator, Number/Variable, Number/Variable)

Given polynomials are:

P = 11x⁵  + 9x⁴ - 4x³ - 7x² + 5

Q = (2x² + 1) (4x² - 3)

Simplify the polynomial Q = (2x² + 1) (4x² - 3):

Q = (2x² + 1) (4x² - 3)

Q = 2x²(4x² - 3) + 1(4x² - 3)

Q = 8x⁴ - 6x² + 4x² - 3

Add like terms:

Q = 8x⁴ - 2x² - 3

Now calculate P + Q

P + Q = 11x⁵  + 9x⁴ - 4x³ - 7x² + 5 + 8x⁴ - 2x² - 3

Combine like terms:

P + Q = 11x⁵ + (9x⁴ + 8x⁴) - 4x³  + (- 7x² - 2x²) + 5 - 3

P + Q = 11x⁵ + 17x⁴ - 4x³ - 9x² + 2

Now calculate P - Q

P - Q = 11x⁵  + 9x⁴ - 4x³ - 7x² + 5 - (8x⁴ - 2x² - 3)

P - Q = 11x⁵  + 9x⁴ - 4x³ - 7x² + 5 - 8x⁴ + 2x² + 3

P - Q = 11x⁵  + (9x⁴ - 8x⁴) - 4x³ + (-7x² + 2x² )+ (5 + 3)

P - Q = 11x⁵  + x⁴ - 4x³ - 5x² + 8

Now calculate Q - P

Q - P =  8x⁴ - 2x² - 3 - (11x⁵  + 9x⁴ - 4x³ - 7x² + 5)

Q - P =  8x⁴ - 2x² - 3 - 11x⁵  - 9x⁴ + 4x³ + 7x² - 5

Combine like terms:

Q - P = - 11x⁵ + (8x⁴ - 9x⁴) + 4x³ + (- 2x² + 7x²) - 3 - 5

Q - P = - 11x⁵- x⁴ + 4x³ + 5x² - 8

To learn more about operation, click on the below link:

https://brainly.com/question/22735845

#SPJ1

Answer:

80°, 40° and 60°

Step-by-step explanation:

Name the second angle X and the first angle to 2X (because it is twice the measure of angle number two) and the third angle to 20°+X (because it was 20° more than the second angle)

so we will have an equation of

180°=2x + x + (20°+x)

160°=4x

40°=x

so the second angle is 40° as it is represented by just one X

therefore the first angle which is twice the measure is 80° and the third angle which is 20° more is 60°. hope that helps!

Answer:

m = 2, c = 1

Explanation: In the y = mx + b (or y = mx + c) format, the m is the slope of the line and the c/b is the y-intercept, or where the line crosses the y-axis. If we substitute the information from the given equation, y = 2x + 1, into the general formula, we know that the m is 2 and c is 1.

Mean (X + Y) = Mean (X) + Mean (Y).

The above statement is false.

Discrete Random Variable:

A discrete random variable can be defined as a type of variable whose value depends on the numerical outcome of some random phenomenon. Also called a random variable. Discrete random variables are always easily countable integers. A probability mass function is used to describe the probability distribution of a discrete random variable.

Probability Distributions of Discrete Random Variables:

Probability distributions of discrete random variables list the probabilities associated with each possible outcome. Also called probability function or probability mass function.

The probability of a discrete random variable is between 0 and 1. Also, the sum of the probabilities of a discrete random variable is equal to 1. The probability distribution of discrete random variables resembles the normal distribution.

Example:

Suppose two dice are rolled and a random variable X is used to represent the sum of the numbers. The minimum value of X goes from result 1 + 1 = 2 to 2 and the maximum value goes from result 6 + 6 = 12 to 12. Therefore, X can have any value between 2 and 12 (inclusive). If probabilities are assigned to each outcome, we can determine the probability distribution of X.

Discrete random variables should not be confused with algebraic variables. Algebraic variables represent the values ​​of unknown quantities in computable algebraic equations. However, a discrete random variable can have a range of possible values ​​that result from experimentation.

Learn more about Discrete Random Variable:

https://brainly.com/question/12970235

#SPJ4

Answer:

  geometric, 1/4

Step-by-step explanation:

An arithmetic sequence will have a common difference. A geometric sequence will have a common ratio. If neither of those describes the sequence, it is "neither."

Obviously the difference between numbers in this sequence is decreasing, so this is not an arithmetic sequence.

__

The ratios of adjacent terms are ...

  -320/-1280 = -80/-320 = -20/-80 = -5/-20 = 1/4

The sequence is a geometric sequence with a common ratio of 1/4.

The total amount of sugar that was consumed by Kylie in the past nine (9) days is equal to 3 units of sugar.

In Mathematics and Statistics, a line plot refers a type of graph that is used to graphically represent a data set above a number line, while using crosses, dots, or any other mathematical symbol.

Based on the data and information provided in the line plot shown in the image attached above, we can calculate the total amount of sugar that was consumed by Kylie in the past nine (9) days as follows:

Total sugar consumed = (1/8 + 1/8 + 1/8) + 1/4 + (3/8 + 3/8 + 3/8) + (5/8 + 5/8)

Total sugar consumed = 3(1/8) + 1/4 + 3(3/8) + 2(5/8)

Total sugar consumed = 3/8 + 1/4 + 9/8 + 10/8

Total sugar consumed = 22/8 + 1/4

Total sugar consumed = (22 + 2)/8

Total sugar consumed = 24/8

Total sugar consumed = 3 units of sugar.

Read more on line plot here: https://brainly.com/question/28741427

#SPJ1

Answer:

$7.94

Step-by-step explanation:

All you have to do is add the prices of both of the bought items.

$3.15 + $4.79 = $7.94

(PLEASE MARK ME AS BRAINLIEST!!!)

Answer:

$7.94

Step-by-step explanation:

3.15+4.79=7.94

If you want to include tax. 7.94*1.06=8.42

I'm assuming though that you do not want the tax answer.

Answer:

There is everything in the image

The Side-Angle-Side postulate is satisfied. Then the triangle ΔMHA and ΔTHA are congruent with each other.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

In an isosceles triangle, the two legs of the triangle are congruent and their opposite angles too.

A triangle MAT is an isosceles triangle and point H is the midpoint of MT.

In triangle ΔMHA and ΔTHA, we have

AH = AH (Common sides)

MH = HT (H is the midpoint of MT)

∠AMH = ∠ATH (Isosceles angles)

The Side-Angle-Side postulate is satisfied. Then the triangle ΔMHA and ΔTHA are congruent with each other.

More about the triangle link is given below.

https://brainly.com/question/25813512

#SPJ2

Answer:

i think its

x^2 + (y + 2)^2 = 21.

Step-by-step explanation:

Answer:

14 hostas and 12 geraniums

Answer:

1.20731707e-7

Step-by-step explanation:

The angle of elevation of the top of the tower from the point on the ground is approximately 30.96 degrees.

To find the angle of elevation of the top of the tower, we can use trigonometry.

Let's denote the angle of elevation as θ.

In a right triangle, the tangent of an angle is equal to the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

In this case, the side opposite the angle is the height of the tower (10√3 m), and the side adjacent to the angle is the distance from the point on the ground to the foot of the tower (30 m).

Using the tangent function, we can write:

tan(θ) = opposite/adjacent

= (10√3 m) / (30 m)

= (√3/3)

To find the angle θ, we can take the inverse tangent (arctan) of (√3/3):

θ = arctan(√3/3)

Calculating this angle using a calculator, we get:

θ ≈ 30.96 degrees

Therefore, the angle of elevation of the top of the tower from the point on the ground is approximately 30.96 degrees.

for such more question on elevation

https://brainly.com/question/26424076

#SPJ11

Answer: 13

Step-by-step explanation:

cost for 3 hours: 7+2(3)=13

cost for t hours: 7+2t

Answer:

13

Step-by-step explanation:

Answer:

1.

Collinear points mean they are on the same line. That leaves us with answer d. F, E, G

2.

In this case, the intersection of the 2 planes is a line. 2 points both planes contain are B and C, so the intersection can be named as answer b: Line BC

3.

2 points define a line, so therefore the answer to the question is answer b. 1

Hoped this helped. If it did, could you please consider giving me a brainliest? :)

Answer:

175% increase

Step-by-step explanation:

answer:

6.4

Step-by-step explanation:

4^2+5^2=c^2

16+25

square root of 41

c^2=6.4

a) The degree of the interpolant is 3.

b) Required system of equations are

\(a_0 + 3a_1 + 9a_2 = 4 \\ a_0 + 5a_1 + 25a_2 = 80 \\ a_0 + 7a_1 + 49a_2 = 188 \\ a_0 + 10a_1 = 245 \\ a_0 + 13a_1 = 305 \\ a_0 + a_1 + a_2 + a_3 = 9 \\ a_0 + 2a_1 + 4a_2 + 6a_3 = 15 \\ a_0 + 4a_1 + 16a_2 + 36a_3 = 87 \\ a_0 + 6a_1 + 36a_2 + 216a_3 = 279\)

c) Required Vandermonde matrix corresponding to the system of equations are [ 1 3 9; 1 5 25; 1 7 49], [1 10; 1 13], [1 1 1 1; 1 2 4 6; 1 4 16 36; 1 6 36 216].

a) How to determine the degree of the interpolant?

To determine the degree of the interpolant, we count the number of data points in each set, subtract one, and take the minimum of the resulting values. This is because a polynomial of degree n can exactly interpolate n+1 distinct data points.

For the first set, we have 3 data points, so the interpolant can have degree at most 2.

For the second set, we have 2 data points, so the interpolant can have degree at most 1.

For the third set, we have 4 data points, so the interpolant can have degree at most 3.

b) How to find the interpolant for each set?

To find the interpolant for each set, we need to solve a system of equations. Let f(x) be the interpolant for each set, and let \(x_i\) be the x-coordinate of the ith data point, and yi be the corresponding y-coordinate. Then we need to find the coefficients \(a_0, a_1, ..., a_n\) such that \(f(x_i) = a_i(x_i)^n + a_{i-1}(x_i)^{(n-1)} + ... + a_1 \times x_i + a_0 = y_i\) for i = 1, 2, ..., m, where m is the number of data points in the set. This gives us m equations in n+1 unknowns.

For the first set,

\(a_0 + 3a_1 + 9a_2 = 4 \\ a_0 + 5a_1 + 25a_2 = 80 \\ a_0 + 7a_1 + 49a_2 = 188\)

For the second set,

\(a_0 + 10a_1 = 245 \\ a_0 + 13a_1 = 305\)

For the third set,

\(a_0 + a_1 + a_2 + a_3 = 9 \\ a_0 + 2a_1 + 4a_2 + 6a_3 = 15 \\ a_0 + 4a_1 + 16a_2 + 36a_3 = 87 \\ a_0 + 6a_1 + 36a_2 + 216a_3 = 279\)

c) The Vandermonde matrix corresponding to the system of equations is an m x (n+1) matrix V, where the ith row is \( [x_i^n, x_i^{(n-1)}, ..., x_1, 1] \) for i = 1, 2, ..., m. The columns of the matrix correspond to the coefficients of the interpolant.

For the first set,

V = [ 1 3 9; 1 5 25; 1 7 49]

For the second set,

V = [1 10; 1 13]

For the third set,

V = [1 1 1 1; 1 2 4 6; 1 4 16 36; 1 6 36 216]

Learn more about Matrix here,

https://brainly.com/question/1279486

#SPJ1

Answer:  -2

Step-by-step explanation:

4y/4 = -8/4

     y = -2

Answer:

Step-by-step explanation:

Answer is -2

Answer:

\(5 { \times 54}^{2} \)

Answer:

Step-by-step explanation:

i am working on the assumption that nobody does all three of them

i got 4 because including the people that do swimming and park, the total number of people that do swimming is 22.

the same logic goes for cycling: including the people that do swimming and visit the national park, the total is 23.

so that means that find how many people do swimming and cycling, we have to add the people doing only swimming, with the people doing both swimming and park and then subtract that answer from 22 which gives you 4