Evaluate each geometric series described. 2 - 6 + 18 – 54.... n=17

Answer:

-3/2

Step-by-step explanation:

:)

Answer:

The answer is -3/2

Step-by-step explanation:

I took the test.

Have a great day!!

Answer:

I don't know what the question is but if you are asking for the intersection of the 2 lines it is no solutions, these 2 lines are parallel due to having the same slope, which means they will never intersect.

No, the rank of the product of two n by n square matrices A and B, denoted as AB, cannot be less than n-1 if both A and B have ranks of n-1.

According to the Rank-Nullity theorem, for any matrix M, the sum of its rank and nullity is equal to the number of columns in M. In this case, the number of columns in AB is n, so the sum of the rank and nullity of AB must be n.

If rank(A) = rank(B) = n-1, it means that both A and B have nullity 1. The nullity of a matrix is the dimension of its null space, which consists of all vectors that get mapped to the zero vector when multiplied by the matrix. Since both A and B have rank n-1, their null spaces consist only of the zero vector.

Now, considering AB, if the rank of AB were less than n-1, it would mean that the nullity of AB is greater than 1.

However, this would violate the Rank-Nullity theorem since the sum of the rank and nullity of AB must be n, which is the number of columns.

Therefore,  if rank(A) = rank(B) = n-1, the rank of AB cannot be less than n-1.

For more such questions on rank

https://brainly.com/question/28839672

#SPJ8

Answer:

\(\huge\boxed{\sf 18^{-3}}\)

Step-by-step explanation:

\(\displaystyle \frac{18^4}{18^7}\)

So, the expression becomes:

= \(18 ^{4-7}\)

= \(18^{-3}\)

\(\rule[225]{225}{2}\)

The third graph is the only one that is an an odd-degree polynomial with a positive lead coefficient.

An even number of total minimums/maximums of the Polynomial is classified as an odd-degree polynomial. Now, we see that only the 3rd and 4th graphs are odd-degree polynomials because they have four total minimums/maximums.

For the polynomial to have a positive leading coefficient, the line must go up in the positive direction. This means that only the 1st and 3rd graphs have a positive leading coefficient due to the fact that their right-most line is going upwards.

Thus, we can say that the third graph is the only one that is an an odd-degree polynomial with a positive lead coefficient.

Read more about Polynomial Graph at; https://brainly.com/question/4685884

#SPJ5

Answer:

Trend wants to buy a new bicycle which costs 320$.

He has 35$ saved and earns 15$ each week.

After a number of weeks (a), the amount money he has: A = 35 + 15 x a

If Trend has enough money to buy that bicycle, we have the equation:

35 + 15 x a = 320

=> 15 x a = 320 - 35

=> 15 x a = 285

\(a = \frac{285}{15} = 19\)

=> After 19 weeks, Trent will have had enough money to buy that bicycle

Hope this helps!

:)

Answer:

x=6.4

Step-by-step explanation:

4^2+5^2=x^2

x=6.40

Answer:

\(t=\frac{2.8-3}{\frac{1.2}{\sqrt{64}}}=-1.33\)      

The degrees of freedom are given by:

\(df=n-1=64-1=63\)  

The p value for this case would be given by:

\(p_v =P(t_{63}<-1.33)=0.0942\)  

If we use a significance level lower than 9% we have enough evidence to FAIL to reject the null hypothesis that the true mean is greater or equal than 3 but if we use a significance level higher than 9% the conclusion is oppossite we reject the null hypothesis

Step-by-step explanation:

Information given  

\(\bar X=2.8\) represent the sample mean

\(s=1.2\) represent the standard deviation

\(n=64\) sample size      

\(\mu_o =3\) represent the value to verify

\(\alpha\) represent the significance level

t would represent the statistic (variable of interest)      

\(p_v\) represent the p value

Hypothesis to verify

We want to check if the true mean for this case is less than 3 minutes, the system of hypothesis would be:      

Null hypothesis:\(\mu \geq 3\)      

Alternative hypothesis:\(\mu < 3\)      

The statistic for this case is given by:

\(t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}\) (1)      

Replacing we got:

\(t=\frac{2.8-3}{\frac{1.2}{\sqrt{64}}}=-1.33\)      

The degrees of freedom are given by:

\(df=n-1=64-1=63\)  

The p value for this case would be given by:

\(p_v =P(t_{63}<-1.33)=0.0942\)  

If we use a significance level lower than 9% we have enough evidence to FAIL to reject the null hypothesis that the true mean is greater or equal than 3 but if we use a significance level higher than 9% the conclusion is oppossite we reject the null hypothesis

An order-preserving function is one where x < y implies f(x) < f(y). An isomorphism is a one-to-one order-preserving function between two partially ordered sets, while an automorphism is an isomorphism of a set to itself.

In the given excerpt, it explains the concepts of order-preserving functions, isomorphisms, and automorphisms in the context of partially ordered sets.

Order-Preserving Function:

A function f: P -> Q, where P and Q are partially ordered sets, is said to be order-preserving if for any elements x and y in P, if x < y, then f(x) < f(y). In other words, the function preserves the order relation between elements in P when mapped to elements in Q.

Increasing Function:

If P and Q are linearly ordered sets, then an order-preserving function is also referred to as an increasing function. It means that for any elements x and y in P, if x < y, then f(x) < f(y).

Isomorphism:

A one-to-one function f: P -> Q is called an isomorphism of P and Q if it satisfies two conditions:

a. f is order-preserving: For any elements x and y in P, if x < y, then f(x) < f(y).

b. f is onto (surjective): Every element in Q has a pre-image in P.

When an isomorphism exists between (P, <) and (Q, <), it means that the two partially ordered sets have a structure that is preserved under the isomorphism. In other words, they have the same ordering relationships.

Automorphism:

An automorphism of a partially ordered set (P, <) is an isomorphism from P to itself. It means that the function f: P -> P is both order-preserving and bijective (one-to-one and onto). Essentially, an automorphism preserves the structure and order relationships within the same partially ordered set.

These concepts are fundamental in understanding the relationships and mappings between partially ordered sets, particularly in terms of preserving order, finding correspondences, and exploring the symmetry within a set.

Learn more about function here:

https://brainly.com/question/11624077

#SPJ8

Answer:

Step-by-step explanation:

The area of the square is given as 1134 m². Let's assume that the side length of the square is "s". Then, we can write the area of the square as s² = 1134. Solving for "s", we get s = √1134. The perimeter of the square is given by P = 4s. Substituting the value of "s", we get P = 4√1134. To simplify this expression, we can factor out the perfect square factor of 36 from 1134, which gives us 1134 = 36 x 31. Therefore, P = 4√(36 x 31) = 4 x 6√31 = 24√31. Hence, the perimeter of the square is 24√31 m.

The equation be y = -250x + 5000 then the value of x be 18.

A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression in mathematics.

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Two expressions joined by an equal sign form a mathematical statement known as an equation.

A condition on a variable (or variables) is a pair of expressions in the variable (or variables) that have the same value. The solution or root of the equation is the quantity at which the variable's value satisfies the equation. If you swap the LHS and RHS, an equation still makes sense.

Let the given equation be y = -250x + 5000

simplifying the above equation

−250x + 5000 = 500

Subtract 5000 from both sides, we get

−250x + 5000 − 5000 = 500 − 5000

−250x = −4500

Divide both sides by -250, we get

−250x/-250 = −4500/-250

Therefore, the value of x be 18.

To learn more about equation refer to:

https://brainly.com/question/2228446

#SPJ1

Answer:

B. m = 5/4

Step-by-step explanation:

Slope m = (y2 - y1)/(x2 - x1)

m = (-10 - -5)/(1 - 5) = -5/-4 = 5/4

On graph B, the group of birds seems to have twice as much as the group of mammals.

The change in scale on the y-axis from 50 to 85 in increments of 5 in Graph A to 0 to 80 in increments of 10 in Graph B makes the differences between the groups appear larger in Graph B.

As a result, the height of the bar for birds is approximately twice as much as the height of the bar for mammals in Graph B, which may not be apparent in Graph A.

Therefore, the correct option is (a) On graph B, the group of birds seems to have twice as much as the group of mammals.

Learn more about Graph here:

https://brainly.com/question/17267403

#SPJ1

Answer:

A. the angular speed is 3771.4 rad/min

b. 5921 rpms

Step-by-step explanation: I just got this same question right on a test.

The Option C is correct.

Given equations are,

             \(y = 2x - 6\\\\y= -4x + 3\)

When we draw the graph of both equation of line.

Then these lines intersect at a point \((1.5,-3)\).

So that option C is correct.

The correct graph is attached below.

Learn more about the system of equations here:

https://brainly.com/question/13729904

Answer:

Tbh this question has me confused, but I would go with C? If the question is looking for the distributive property, then C may be the way to go.

The value of c for which the solution satisfies the initial condition y(2)= 9 is c = 9 - e^{-2}.

Let us solve this problem step by step.

For the given equation: y' + 2y = e^{-x}

We have the solution as: y = ce^{-2x} + e^{-x}

We have to find the value of c for which the solution satisfies the initial condition y(2)= 9.

Substituting x = 2 in the above equation, we get:

9 = c + e^{-2}.

Therefore, we can solve for c as:

c = 9 - e^{-2}

Hence, the value of c for which the solution satisfies the initial condition y(2)= 9 is c = 9 - e^{-2}.

Learn more about initial condition here:

https://brainly.com/question/13243199

#SPJ4

Answer:

67.98,68.11, 68.6

After answering the presented questiοn, we can cοnclude that The fοrmula tο find the area and perimeter οf a twο-dimensiοnal shape depends οn the type οf shape

An equatiοn in mathematics is a statement that states the equality οf twο expressiοns. An equatiοn is made up οf twο sides that are separated by an algebraic equatiοn (=). Fοr example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the value "9." The purpοse οf equatiοn sοlving is tο determine the value οr values οf the variable(s) that will allοw the equatiοn tο be true.

The fοrmula tο find the area and perimeter οf a twο-dimensiοnal shape depends οn the type οf shape. Here are sοme cοmmοn fοrmulas:

1. Rectangle:

• Area: A = length x width

• Perimeter: P = 2(length + width)

2. Square:

• Area: A = side x side (οr A = side²)

• Perimeter: P = 4 x side

3. Circle:

• Area: A = π x radius²

• Circumference (perimeter): C = 2π x radius (οr C = π x diameter)

4. Triangle:

• Area: A = (base x height) / 2

• Perimeter: P = side1 + side2 + side3

5. Trapezοid:

• Area: A = ((base1 + base2) x height) / 2

• Perimeter: P = side1 + side2 + side3 + side4

To know more about Area and Perimeter visit:

https://brainly.com/question/11957642

#SPJ1

Answer:

\(y = -14 \frac{4}{11} \)

Step-by-step explanation:

\(100 - 17y = 258 - 6y \\ \\Bring \: like \: terms \: together. \\ 6y - 17y = 258 - 100 \\ -11y = 158 \\ y = 158/(-11) \\y = -14 \frac{4}{11} \)

Answer:

Step-by-step explanation:

The lowest common denominator is defined as the set of fraction denominators with the lowest common multiple. The lowest positive integer with more than one denominator in the set is LCD.

Given that the Peanuts are sold in 8-ounce and 12-ounce packages

We have to determine the number of ounces you can buy from each package to have equal amounts of each package size

8 = 2 × 2 × 2

12 = 2 × 2 × 3

The LCDs 8 and 12 are 24

Thus, three 8 oz packets and two 12 oz packets.

Therefore, you can buy from each package to have equal amounts of each package size the number o ounces as 3 packets of 8 ounces and 2 packets of 12 ounces.

Step-by-step explanation:

The general formula of a quadratic equation is

\(a {x}^{2} + bx + c\)

while the general formula for finding the vertex is

\(a({x - h})^{2} + k\)

first of all, you have to set the value of

\(x = \frac{ - b}{2a} \)

From the given equation, a = 2; b = -12 and c = 13. therefore, x = -(-12)/2(2) = 12/4 = 3

The 3 gotten is the answer for the value of h. To get k, substitute the value of h into the quadratic equation.

k = 2(3)^2 - 12(3) + 13 = -5

Therefore, the Vertex is V(h,k) = V(3,-5)

The required by the principle of mathematical induction, the statement is true for all integers n ≥ 0.

Mathematical induction is a method of proof commonly used in mathematics to prove that a statement is true for all positive integers.

The process involves two steps:

Here,
First, we need to prove the statement is true for the base case n=0,

When n=0, we have,

\(\sum_{i=1}^{1} i * 2^i = 1*2^1 = 2\)

and

\(n * 2^{n+2} + 2 = 0*2^{0+2} + 2 = 2\)

Therefore, the statement is true for n=0.

Next, we assume the statement is true for some arbitrary integer k, meaning:

\(\sum_{i=1}^{k+1} i * 2^i = k * 2^{k+2} + 2\)

We want to show that the statement is also true for n=k+1,

\(\sum_{i=1}^{k+2} i * 2^i = (k+1) * 2^{k+3} + 2\)

We can rewrite the left-hand side of the equation as,

\(=\sum_{i=1}^{k+2} i * 2^i \\= \sum_{i=1}^{k+1} i * 2^i + (k+2) * 2^{k+2} \\= k * 2^{k+2} + 2 + (k+2) * 2^{k+2} \\= (k+1) * 2^{k+3} + 2\)

This last step used the assumption that the statement is true for n=k.

Therefore, by the principle of mathematical induction, the statement is true for all integers n ≥ 0.

Learn more about mathematical induction here:

https://brainly.com/question/29503103
#SPJ1

Answer:

Step-by-step explanation:

add 12 for every hour  and to find the answer 12 times 7

it will be 4:00p.m when they have 84.

hope this helps

Step-By-Step Explanation:

Let x be the amount of sales of Tonia in a year.

8% of her sales is:

Her salary is this plus $35,000. If 'y' is the total yearly salary of Tonia, the equaltion is:

We want y > 50,000. Replacing this value and solving for x:

Answer:

The equality is 50,000 < 0.08x + 35,000

Tonia needs to sell over 187,500 sales to earn $50,000

We can simplify cosec(t)tant(t) to sec(t). A trigonometric function is a mathematical function that relates the angles of a triangle to the ratios of its sides.

The most common trigonometric functions are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).

To simplify the expression cosec(t)tant(t), we need to use the trigonometric identity:

cosec(t) = 1/sin(t)

tant(t) = sin(t)/cos(t)

Substituting these expressions into the original expression, we get:

cosec(t)tant(t) = (1/sin(t))(sin(t)/cos(t))

The sin(t) term in the numerator and denominator cancel out, leaving:

cosec(t)tant(t) = 1/cos(t)

Recalling the definition of secant, sec(t) = 1/cos(t), we can express the simplified expression as:

cosec(t)tant(t) = 1/sec(t)

Therefore, we can simplify cosec(t)tant(t) to sec(t).

Learn more about trigonometric identity :

https://brainly.com/question/3785172

#SPJ1

Answer:

4.82 Estimated 4 people

Step-by-step explanation:

Total number of medals= 12+ 36+18= 66

66/45x65/44x64/43x63/42= 4.819955

Answer:

The number is 10

Step-by-step explanation:

let the number be x

6x=2x-40

4x=-40

x=-10