“The sum of 3 consecutive odd numbers is 69.” What is the third number in this sequence?

Answer:

did u ever find the asnwer? cuz I need it rn

Step-by-step explanation:

An arithmetic sequence is a sequence with a constant

 increase or decrease also known as the constant difference

In the sequence 10, 40, 70, 100, ….

The constant difference between the terms is 30

A recursive formula for a sequence would be:

a1= first term in the sequence

an = term you are trying to find

an-1 = previous term in the sequence

d = constant difference

Explicit Formulas: 

A formula that allows you to find the nth term of the sequence by substituting known values in the expression.

Formula : an = a1 + d( n - 1)

a1= first term in the sequence

an = current term in the sequence

d = constant difference

n = term number

Solution: 

Write the explicit formula of the sequence 4, 7, 10, 13, 16 ….

Formula for explicit term:

an = ___ + ___( n - 1)

Simplify: an = ___ + ___n

In the sequence 4, 7, 10, 13, ….

To find the 11th term explicitly, I plug in the into the formula I just made: 

an = 1 + 3n

a11 = 1 + 3(11)   

a11 = 34 

Find the 15th term of the sequence using the formula: an = 1 + 3n

Write the recursive formula of the sequence 4, 7, 10, 13, ….

Recursive formula:

a1 =

an = a  n  - 1

In the sequence 4, 7, 10, 13, 16 ….

To find the 5th term recursively, I plug it into the formula I just made: 

  an = an-1 + 3

a5 = a5-1 + 3   in words: 5th  term equals the 4th term plus 3

a5 = 13 + 3 

a5 = 16  

Recursive and Explicit Formulas for Arithmetic (Linear) Sequences

Answer: 43839.13

Step-by-step explanation:

Final answer:

To calculate the amount in the account after 29 years, use the formula for compound interest. The amount in the account will be approximately $40,882.53.

Explanation:

To calculate the amount in the account after 29 years, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal (initial amount), r is the annual interest rate (as a decimal), n is the number of times interest is compounded per year, and t is the number of years. In this case, the principal is $4400, the annual interest rate is 8.25%, and since it is not specified, we'll assume interest is compounded annually. So, the formula becomes:

A = 4400(1 + 0.0825/1)^(1*29)

To calculate this, we can enter the expression into a calculator or spreadsheet:

A = 4400(1 + 0.0825)^(29)

After evaluating this expression, we find that the amount in the account after 29 years will be approximately $40,882.53.

Sampling is the choosing of a group of individuals from within a statistical population to estimate attributes of the entire population. Options C & D are right.

Sampling is the choosing of a group of individuals from within a statistical population to estimate attributes of the entire population in statistics, quality assurance, and survey methods.

The following options are right;

C. The manager selects 20 boards at random each day for 5 days and examines them.

Reason;

This method, which involves sampling 30 boards in a row an hour after manufacturing begins, does not yield a significant sample size.

Furthermore, if a component of the equipment fails later in the day, the statistics will be deceptive. Similarly, statistics will be deceptive if the gear is only defective until it "warms up."

D. The manager sends an email to 20 customers who buy lumber from the mill, asking each how many of the boards they bought the past week was defective. Results from the first 5 customers to respond are tallied.

Reason;

These  technique, a voluntary survey, is likely to elicit replies solely from those who have strong feelings about their product.

Hence Options C & D are right.

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Methods B and D are biased for determining defective boards, while methods A and C minimize bias. Random sampling across different times and responses reduces bias in data.

The goal is to determine which sampling methods are likely to be biased when finding the percentage of defective boards produced by a sawmill.

In summary, method B and method D are likely to introduce bias in sampling. Methods A and C are designed to minimize bias and provide a more accurate representation of defective boards.

(n-2) triangles can be formed by drawing all the diagonals from a single vertex.

a polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain.

Given a convex polygon with n vertices, the number of triangles that can be formed by drawing all the diagonals from a single vertex can be calculated.

a diagonal is a line segment joining two vertices of a polygon or polyhedron, when those vertices are not on the same edge

Let's consider a convex polygon with 4 vertices.

(n-2) triangles can be formed by drawing all the diagonals from a single vertex.

Hence, (n-2) triangles can be formed by drawing all the diagonals from a single vertex.

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Answer:

what they r trying to say is n is 3 so 3+11=14

Answer:

$0.40

Step-by-step explanation:

Did the test, K12

A ray in geometric optics represents the path of light as a straight line originating from a point, while a line segment is a part of a line with two endpoints and a measurable length. The properties mentioned can be used to determine if they define a ray or a line segment.

A ray in geometric optics is a straight line that originates at some point. In the context of light, a ray represents the path of light as it travels. When light encounters objects or changes media, it may change direction but it continues to travel in a straight line or as a ray. We can think of a ray of light as a straight line or a laser ray.

A line segment, on the other hand, is a part of a line with two endpoints. It has a definite length and can be measured. In the context of light, a line segment would indicate a finite path of light.

Given the properties mentioned, we can determine if they define a ray or a line segment. If the properties describe a straight line with no defined endpoints, it is a ray. If the properties suggest a line with two endpoints and a measurable length, it is a line segment.

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The ordered pairs will be the points on the parallel line are

(-8, 8) and (2, 2)

(-2, 1) and (3, -2)

A slope of a line is the change in y coordinate with respect to the change in x coordinate.

If [tex](x_{1} ,y_{1} )[/tex] and [tex](x_{2} , y_{2} )[/tex] be the two points then the slope of the line is given by

[tex]slope = \frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]

According to the given question.

We have slope of a line is [tex]\frac{-3}{5}[/tex].

As, we know that the two parallel lines have the same slope.

Now according to the given ordered pairs

A). (-8, 8) and (2, 2)

[tex]slope = \frac{2-8}{2+8} = \frac{-6}{10} =\frac{-3}{5}[/tex]

Therefore, (-8, 8) and (2, 2) are the ordered pairs could be the points on the parallel line.

B) (-5, -1) and (0, 2)

[tex]slope = \frac{2+1}{0+5} =\frac{3}{5} \neq \frac{-3}{5}[/tex]

Hence, the ordered pair (-5, -1) and (0, 2) will never be the points on the parallel line.

C) (-3, 6) and (6, -9)

[tex]slope = \frac{-9-6}{6+3} =\frac{-15}{9} =\frac{-5}{3}\neq \frac{-3}{5}[/tex]

The ordered pair (-3, 6) and (6, -9) will never be the points on the parallel line.

D). (-2, 1) and (3, -2)

[tex]slope = \frac{-2-1}{3+2} =\frac{-3}{5}[/tex]

Therefore, (-2, 1) and (3, -2) are the ordered pairs could be the points on the parallel line.

E). (0, 2) and (5, 5)

[tex]slope = \frac{5-2}{5-0} =\frac{3}{5} \neq \frac{-3}{5}[/tex]

Therefore, (0, 2) and (5, 5) are the ordered pairs could not be the points on the parallel line.

Hence, the ordered pairs will be the points on the parallel line are

(-8, 8) and (2, 2)

(-2, 1) and (3, -2)

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To determine if the given ordered pairs could be points on a parallel line with a slope of -3/5, we can calculate the slope of each line and compare it to the original slope. The pairs (D) (-2, 1) and (3, -2) have a slope of -3/5, making them parallel.

A line with a slope of -3/5 is a line that slopes downwards from left to right. In order for a line to be parallel to this line, it must have the same slope. To determine if the given ordered pairs could be points on a parallel line, we can calculate the slope of each line and compare it to the slope of the original line.

B) (-5, -1) and (0, 2): The slope of this line is (2 - (-1))/(0 - (-5)) = 3/5, which is different from the original slope of -3/5. Therefore, this line is not parallel.

D) (-2, 1) and (3, -2): The slope of this line is (-2-(-2))/(3-(-2)) = -3/5, which is equal to the original slope of -3/5. Therefore, this line is parallel.

E) (0, 2) and (5, 5): The slope of this line is (5 - 2)/(5 - 0) = 3/5, which is different from the original slope of -3/5. Therefore, this line is not parallel.

So, the parallel lines are (D) (-2, 1) and (3, -2).

Final answer:

The circumference of the lid is approximately 132 millimeters, Thus, option D is correct.

Explanation:

To find the circumference [tex](\( C \))[/tex] of the lid, we use the formula for the circumference of a circle:

[tex]\[ C = \pi \times d \][/tex]

Where [tex]\( d \)[/tex] is the diameter of the circle.

Given that the diameter (\( d \)) of the lid is 42 millimeters and using the value of [tex]\( \pi \)[/tex] as [tex]\( \frac{22}{7} \)[/tex], we can calculate the circumference as follows:

[tex]\[ C = \frac{22}{7} \times 42 \][/tex]

[tex]\[ C = \frac{22 \times 42}{7} \][/tex]

[tex]\[ C = \frac{924}{7} \][/tex]

[tex]\[ C \approx 132 \, \text{mm} \][/tex]

Therefore, the circumference of the lid is approximately 132 millimeters, which corresponds to option D.

The equation in slope - intercept form is as - y[h] = 2000h + 4000 and for 4 hours of filming, the production cost would be $12000.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is a television production company charges a basic fee of $4000 and then $2000 per hour when filming a commercial.

Assume that the number of hours required for filming the commercial be [h]. Then, we can write, the equation as follows -

y[h] = 2000h + 4000

The graph of the equation is attached with the answer.

For 4 hours of filming, the production cost would be -

y[4] = 2000 x 4 + 4000 = 8000 + 4000 = 12000

Therefore, the equation in slope - intercept form is as - y[h] = 2000h + 4000 and for 4 hours of filming, the production cost would be $12000.

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Answer:

(g o f) (x) = 2x + 16

Step-by-step explanation:

" (g o f) (x) )" is called "the composition of f and g."

Evaluating this involves substituting the function f(x) = 2x + 1 for x in g(x) = x+14:

(g o f) (x) = 2(x+1) + 14, or

(g o f) (x) = 2x + 2 + 14, or

(g o f) (x) = 2x + 16

Answer:

2x+29

Step-by-step explanation:

a p e x

Answer:

The graph of the function is the last graph.

Step-by-step explanation:

To know which graph represents the function [tex]g(x)=3.5^{x-1}[/tex] you should give values to x and compare it with the values on the graphs, as follows:

When x=-3

[tex]g(-3)=3.5^{-3-1}[/tex]

[tex]g(-3)=3.5^{-4}[/tex]

[tex]g(-3)=0.007[/tex]

So, the first point is (-3, 0.007)

When x=-2

[tex]g(-2)=3.5^{-2-1}[/tex]

[tex]g(-2)=3.5^{-3}[/tex]

[tex]g(-2)=0.02[/tex]

So, the second point is (-2, 0.02)

When x=-1

[tex]g(-1)=3.5^{-1-1}[/tex]

[tex]g(-1)=3.5^{-2}[/tex]

[tex]g(-1)=0.08[/tex]

So, the third point is (-1, 0.08)

When x=0

[tex]g(0)=3.5^{0-1}[/tex]

[tex]g(0)=3.5^{-1}[/tex]

[tex]g(0)=0.29[/tex]

So, the fourth point is (0, 0.29)

When x=1

[tex]g(1)=3.5^{1-1}[/tex]

[tex]g(1)=3.5^{0}[/tex]

[tex]g(1)=1[/tex]

So, the fifth point is (1, 1)

When x=2

[tex]g(2)=3.5^{2-1}[/tex]

[tex]g(2)=3.5^{1}[/tex]

[tex]g(2)=3.5[/tex]

So, the fourth point is (2, 3.5)

If you compares all the points, the graph of the function is the last graph.

Answer:

[tex]3[/tex] (Square root of [tex]2[/tex]) units

Step-by-step explanation:

we know that

The larger triangle is an isosceles right triangle

so

Applying the Pythagoras Theorem

[tex]6^{2} =x^{2} +x^{2} \\ 36=2x^{2} \\18=x^{2}\\x=\sqrt{18}\ units \\x=3\sqrt{2}\ units[/tex]