Write down the expression that results when the change of base formula is applied to log4(x+2).

Given expression are:

a) -5 - 8 - 11 -... - 269 = -11823.

b) 1 - 3 + 9 - ... + 243 = 364.

a) To find the sum of the given expressions, we first have to identify the type of the sequence.

The first expression is an arithmetic sequence with common difference -3.

Using the formula of the sum of arithmetic sequence, we can find the sum of the sequence.

Formula to find sum of n terms in an arithmetic sequence:

Sn = (n/2) [2a + (n-1)d]

where n is the number of terms in the sequence, a is the first term and d is the common difference)

To find the sum of the first expression, we need to calculate the number of terms in the sequence.

Given, First term, a = -5 Common difference, d = -3 Last term, l = -269

Using the formula for finding nth term in an arithmetic sequence:

l = a + (n-1)d-269

= -5 + (n-1) (-3)-269

= -5 -3n + 3-3n

= -267n = 89

Therefore, there are 89 terms in the sequence.

Now, using the formula of the sum of the arithmetic sequence:

Sn = (n/2) [2a + (n-1)d]S89

= (89/2) [2(-5) + (89-1) (-3)]S89

=  (89/2) [-10 - 264]S89

= -11823

The sum of the

is -11823.

b)The second expression is a geometric sequence with common ratio 3.

Using the formula of the sum of geometric sequence, we can find the sum of the sequence.

Formula to find sum of n terms in a geometric sequence:

S = [a(1-r^n)] / [1-r]where n is the number of terms in the sequence, a is the first term and r is the common ratio

To find the sum of the second expression, we need to calculate the number of terms in the sequence.

Given, First term, a = 1 Common ratio, r = 3 Last term, l = 243

Using the formula for finding nth term in a geometric sequence:

l = ar^(n-1)243

= 1 x 3^(n-1)3^(n-1)

= 243n-1 = 5n = 6

Therefore, there are 6 terms in the sequence.

Now, using the formula of the sum of the geometric sequence:

S = [a(1-r^n)] / [1-r]S

= [1(1-3^6)] / [1-3]S

= [1-729] / (-2)S

= 364

The sum of the geometric sequence is 364.

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Answer:

a no b yes c no d no e yes

Step-by-step explanation:

Answer:

k = - 10

Step-by-step explanation:

6=9+3(k+9)

3(k+9)=-3

k+9= -1

k= -10

The value of k is -10.

Division is one of the operation in mathematics where number is divided  into equal parts as that of a definite number.

Given a function 3x² + kx + 9.

Divide the function with x - 3.

Do the long division process.

After doing the long division,

(3x² + kx + 9) / (x - 3), we get the quotient as 3x + (k + 9) and the remainder as 9 + 3(k + 9).

9 + 3(k + 9) = 6

3(k + 9) = -3

k + 9 = -1

k = -1 - 9

k = -10

Hence the number k has the value -10.

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Answer:

so so so sorry I usually don't do this but you know

Step-by-step explanation:

should have never be a

Answer:

Step-by-step explanation:

3x6= 18 then 14000 x 18 = 252,000

Answer:

Bad little boy

That's what you're acting like

I really don't buy

That you're that kind of guy

And if you are

Why do you want to hang out with me?

Step-by-step explanation:

i had to look in the internet hehe click the ❤️

please

Answer:

80%

Step-by-step explanation:

100% is full so you do 100%-20%=80% so thats the answer

Answer:

9 units

Step-by-step explanation:

got it right on edg

Answer: uhhhhhhhhhhhhhhhhhhh whats the question?

Step-by-step explanation:

Answer:

Step-by-step explanation:

easy

Answer:

it is 2

Step-by-step explanation:

rise over run

it goes up 2 points and

moves right 1 point

2/1 =2

No, such a simple directed graph with at least three vertices and the property that deg+(v) + deg¯(v) = 1 cannot exist.

The property deg+(v) + deg¯(v) = 1 implies that for every vertex v in the graph, the sum of its in-degree (deg¯(v)) and out-degree (deg+(v)) is equal to 1. In a directed graph, the in-degree of a vertex represents the number of incoming edges, while the out-degree represents the number of outgoing edges.

If we consider a graph with at least three vertices, let's say v1, v2, and v3, and apply the given property, we would have:

deg+(v1) + deg¯(v1) = 1

deg+(v2) + deg¯(v2) = 1

deg+(v3) + deg¯(v3) = 1

However, this leads to a contradiction. In a directed graph, the sum of in-degrees and out-degrees of all vertices is always equal. Therefore, if we sum up the equations above, we would get:

deg+(v1) + deg+(v2) + deg+(v3) + deg¯(v1) + deg¯(v2) + deg¯(v3) = 3

Since each term on the left-hand side of the equation is at least 1 (due to the property), the sum would be at least 6. This contradicts the fact that the sum should be equal to 3.

Hence, a simple directed graph with at least three vertices and the property deg+(v) + deg¯(v) = 1 cannot exist.

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Answer:

Hi! The other answer is not correct to your question

The answer to your question is n= [tex]\frac{dc}{(c+d)(c-d)}[/tex]

Step-by-step explanation:

Solve the rational equation by combining expressions and isolating the variable n

※※※※※※※※※※※※※※※

⁅Brainliest is greatly appreciated!⁆

- Brooklynn Deka

Hope this helps!!

Answer:

y=4x+5

Step-by-step explanation:

y=mx+c

gradient =m

y intercept=c

m=4

c=5

so

y=4x+5

Answer:

y=4x+9

Step-by-step explanation:

y=mx+b

y=4x+b

5=4(-1)+b

5=-4+b

b=9

y=4x+9

1. The population of interest are all named storms that have made landfall in the United States since 2000.

2. The parameter of interest is the mean µ of sustained wind speed of the storms. Therefore, the correct answer is option B.  

The other options are not correct as follows:

Option A. The average π sustained wind speed of the storms at the time they made landfall - The term "average" is equivalent to "mean." However, π is not applicable since it denotes the constant 3.14159....

Option C. The proportion µ of the wind speed of storm - Proportion refers to a fraction or percentage of a whole, so this answer is illogical because µ denotes the mean.

Option D. The mean µ of sustained wind speed of the storms - This answer is wrong because it is not the correct order.

Option E. The proportion π of the number of storms with high wind speed - This answer is incorrect since π denotes the constant 3.14159..., and it is not applicable in this context.

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The population of interest is all named storms that have made landfall in the United States since 2000. The parameter of interest would be the mean sustained wind speed of the storms at the time they made landfall, as you're seeking the average wind speed at the moment of landfall.

The population of interest refers to the complete group of individuals or cases that a researcher is interested in studying. In this case, it would be all named storms that have made landfall in the United States since 2000.

The parameter of interest is a numerical measure that describes a characteristic of a population. Based on the information in question 1, the parameter of interest would be D. The mean µ sustained wind speed of the storms at the time they made landfall. This is because you're interested in knowing the average wind speed of the storms at the moment they hit the land, not the proportion of storms with high wind speed or any other aspect of the storms.

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It is impossible for a graph to have exactly one vertex of odd degree.

Vertex is  described as a point on a polygon where the sides or edges of the object meet or where two rays or line segments meet.

The total of all vertices' degrees in any graph is always even. This is so because each edge adds two degrees—one for each endpoint—to the overall number of degrees.

The total number of degrees at all vertices must therefore be an even number.

If a graph had exactly one vertex of odd degree, the sum of the degrees of all other vertices would be even.

if we  add an odd degree to an even sum, the result would be in an odd total degree count, which contradicts the fact that the sum of all degrees in a graph is always even.

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Answer:

A whole number is any positive integer greater than zero and is not a fraction or a decimal. Any whole number can be divided by itself and one so therefor all pairs of whole numbers have a GCF of one. However the bigger the number the more factors it can have so the GCF of a pair of whole numbers may have a greater GCF than 1.

Step-by-step explanation:

The relation ‘equal to’ is an equivalence relation on A.

a) To give an example of an onto function f: A → B, we need to ensure that every element in set B is mapped to from set A. Since set B has three elements (5, 6, 7) and set A has four elements (1, 2, 3, 4), it is impossible to have an onto function from A to B.

This is because there are more elements in A than in B, so at least one element in B will not have a corresponding element in A.

b) A function g: A → B is a one-to-one function if each element of set A is paired with a distinct element in set B. Let us create a table to get the one-to-one function g.

Table of one-to-one function gA1234B5677The function g: A → B can be defined by g(1) = 5, g(2) = 6, g(3) = 7 and g(4) = 7.

Hence, this is a one-to-one function.

c) An equivalence relation is a relation that is reflexive, symmetric, and transitive.

We can define an equivalence relation on set A using the relation ‘equal to’. Every element of set A is equal to itself, i.e., ∀ a ∈ A, a = a.

Hence, this is a reflexive relation on A. Also, if a and b are two elements of A such that a = b, then b = a.

Hence, this is a symmetric relation on A. Also, if a, b, and c are three elements of A such that a = b and b = c, then a = c. Hence, this is a transitive relation on A.

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Answer:

The two numbers that multiply to -5 and add to 4 are:

5 and -1

Step-by-step explanation:

5 • -1= -5

5 - 1= 4

Answer: D. There are at least two oatmeal cookies next to each other.

Step-by-step explanation:

Alright so basically we can use process of elimination to determine what is true or false so

A. States the farthest to the left is chocolate but we can't prove that because all we know is the cookie farthest to the right is chocolate so this is false

B. Same reason as A we cannot prove what cookie is farthest to the left because we are not given a pattern so B is false

C. Since there are definitely twice as many girls as boys in the class and that also means there are twice as many oatmeal cookies then we cannot prove that 2 chocolate cookies have to be next to each other so also false

D. This has to be true because if there are twice as many girls as boys and more oatmeal than chocolate then is whatever cookie line combinataion we will have at least 2 oatmeal cookies next to each other So this is true

E. This is most definitely not true because the question tells us that twice as many girls gave him oatmeal so if anything there are more oatmeal cookies

Answer:

B (3, -4)

Step-by-step explanation:

A( -7, 2)

midpt ( -2, -1)

Equation:

(x + 5, y - 3)

Solve for B:

( -2, -1)

(x + 5, y - 3)

(3, -4)

Answer:

volume = 720 in³

Step-by-step explanation:

volume = 1/3Bh = 1/3 x 72 x 30 = 720 in³

To interpolate the function f(x) = x ln(2+1) by a second-order polynomial on equidistant nodes on the interval (0,1), we can use the Lagrange interpolation formula.

To interpolate f(T) by a second-order polynomial on equidistant nodes on (0,1), we need three equidistant nodes. Let's denote these nodes as x₀, x₁, and x₂, with x₀ = 0, x₁ = h, and x₂ = 2h, where h = (1-0)/2 = 1/2.

We can construct the Lagrange polynomial P₂(x) of degree 2 that interpolates f(x) at these nodes. The Lagrange interpolation formula for P₂(x) is:

P₂(x) = f(x₀) × L₀(x) + f(x₁) × L₁(x) + f(x₂) × L₂(x)

where L₀(x), L₁(x), and L₂(x) are the Lagrange basis polynomials.

Using the given function f(x) = x ln(2+1), we can evaluate f(x₀), f(x₁), and f(x₂). Plugging these values into the Lagrange interpolation formula, we obtain the second-order polynomial interpolation for f(T).

To estimate the error, we can use the error formula for polynomial interpolation. The error term E(x) is given by:

E(x) = f(x) - P₂(x)

To calculate the error, we would need to evaluate the derivative of f(x) and find its maximum value on the interval (0,1). However, without knowing the interval (T), we cannot estimate the error.

In summary, we can interpolate f(T) by a second-order polynomial on equidistant nodes on (0,1) using the Lagrange interpolation formula. However, without specifying the interval (T), it is not possible to estimate the error.

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Answer:

24

Explanation: base times height divided by 2

Answer:

D) 24

Step-by-step explanation:

Area of a triangle:

A = 1/2bh

Given:

b = 12

h = 4

Work:

A = 1/2bh

A = 1/2(12)(4)

A = 6(4)

A = 24

The p-value can be calculated to test the null hypothesis that the average running time of HP laptops is 120 minutes against the alternative hypothesis that it is not equal to 120 minutes.

The p-value for testing the hypothesis that the average time for the HP laptops is not equal to 120 minutes can be calculated using a t-test. Given a sample mean of 122 minutes, a sample size of 60, a null hypothesis mean of 120 minutes, and a standard deviation of 25 minutes, we can calculate the t-value and find the corresponding p-value.

To calculate the t-value, we use the formula: t = (sample mean - null hypothesis mean) / (sample standard deviation / sqrt(sample size))

Plugging in the values, we get: t = (122 - 120) / (25 / sqrt(60))

Calculating the t-value, we find t ≈ 0.894

To find the p-value associated with this t-value, we can refer to a t-distribution table or use statistical software. The p-value represents the probability of observing a t-value as extreme as the one obtained, assuming the null hypothesis is true.

Since the p-value (0.757) is greater than the commonly used significance level of 0.05, we fail to reject the null hypothesis. This suggests that there is not enough evidence to conclude that the average running time of HP laptops is significantly different from 120 minutes.

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9514 1404 393

Answer:

  15/28

Step-by-step explanation:

We can rearrange the problem a bit and make it a little simpler.

  1 2/7 - 3/4 = (1 -3/4) + 2/7 = 1/4 + 2/7

  = (7+4·2)/(4·7) = 15/28

_____

The sum of fractions can always be found by ...

  [tex]\dfrac{a}{b}+\dfrac{c}{d}=\dfrac{ad+bc}{bd}\\\\\dfrac{1}{4}+\dfrac{2}{7}=\dfrac{1\cdot7+4\cdot2}{4\cdot7}=\dfrac{7+8}{28}=\dfrac{15}{28}[/tex]

Answer:

Answer is in the image below

Answer:

P is simply the mark or letter that the point will be called. In this case we have -3,-5. You will move left 3 spaces from the origin and down 5 places from the spot you marked -3. After that will be point P

Answer:

i think ik it the aswer is c