7. Determine if each sequence represents a function. Explain why
or why not. If it is a function, identify its domain and range.
Create a mapping to verify your answer.
a. 2, 4, 6, 8, 10, ...
b. 1, 0, 1, 0, 1, ...
c. 0, 5, 10, 15, 20, ...

The solution to log base 7 of 1 is x=0, which is the value of the power to which 7 must be raised to get the value 1.

The logarithm function is an inverse function of the exponential function, and it is defined as log_b(x) = y means b^y = x. In other words, it represents the power to which the base b must be raised to get the value x.

In this case, we are solving log_7(1), which means we are looking for the power to which 7 must be raised to get the value 1.

Since any number raised to the power of 0 is 1, we can say that 7^0 = 1, which means that log_7(1) = 0.

To solve log base 7 1, you need to find the value of x that satisfies the equation log_7(x) = 1.

Using the definition of logarithm, log_b(x) = y means b^y = x.

So to solve log7(1), we can set 1 = 7^x and get x = log7(1) = 0

So the solution to log base 7 of 1 is x=0.

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The images are formed when two plane mirrors are placed at 36 is 9

The term plane in math defined as a two-dimensional doubly ruled surface spanned by two linearly independent vectors.

Here we need to find the number of images are formed when two plane mirrors are placed at 36.

Here we have given that the generalization of the plane to higher dimensions is called a hyperplane.

And here we also know that the angle between two intersecting planes is known as the dihedral angle.

The by using the formula we have calculated as,

=> n = (360 / 36) - 1

=> n = 10 - 1

=> n = 9

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Possible way in which two consecutive odd numbers are added to sum of 2023 is by evaluation using the formula (2n - 1) + (2n + 1) = 2023, so that we have 1010.5 + 1012.5 = 2023

Consecutive odd numbers are a sequence of numbers that are separated by a difference of 2 and are all odd numbers. For example the first four odd numbers are: 1, 3, 5, and 7. Odd numbers can be generated using the formula 2n -1.

We shall represent the first odd number with (2n - 1) so that the two consecutive odd numbers will be expressed as:

(2n - 1) + (2n + 1) = 2023

2n + 2n = 2023

4n = 2023

n = 2023/4 {divide through by 4}

n = 505.75

Therefore the two consecutive odd numbers added to sum of 2023 are derived as:

2(505.75) - 1 = 1010.5 and 2(505.75) + 1 = 1012.5

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Answer: Well, let’s consider a number, [math]n[/math], it could be even or odd, it doesn’t ...

Step-by-step explanation:

CI will yield more amount, because simple interest generates earnings from principal only.

Interest rate is the amount charged over and above the principal amount by the lender from the borrower.

Given that, A recent college graduate is looking to begin saving for retirement. Option A is a savings account with 3.5% annual simple interest. Option B is a savings account with 3.5% annual interest compounded monthly.

Let the principal amount be, $20000

Solving for simple interest, we get,

SI = PRT / 100

= 20000×3.5×10 / 100

= 7000

Therefore, amount = $27000

Now, CI =

A = P(1+r)ⁿ

A = 20000(1+0.035/12)¹²⁰

A = 1241286.32

Therefore, we see that CI will yield more amount.

Hence, CI will yield more amount, because simple interest generates earnings from principal only.

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Answer:

b.

Step-by-step explanation:

5x ≥ 15 or x + 4 > 13

5x ≥ 15

x ≥ 15/5

x ≥ 3

x + 4 > 13

x > 13-4

x > 9.

So, the answer is x ≥ 3

So, the given system will have a unique solution when k=,1

A system of linear equations in two variables will have a unique solution when the equations are consistent and independent.

In this case, the system of equations is kx + 3y = k and 3x + ky = k.

One way to check for consistency and independence is by using the determinant of the coefficient matrix and comparing it to the determinant of the system. The determinant of the coefficient matrix is (kk) - (3ky) = k^2 - 3ky and the determinant of the system is k^2 - k.

For the system to have a unique solution, the determinant of the coefficient matrix must be non-zero and equal to the determinant of the system.

Therefore, the system will have a unique solution when k^2 - 3ky = k^2 - k.

Which means that k=1.

This system will have a unique solution when k=1, and the pair of linear equations will be 1x + 3y = 1 and 3x + ky = 1.

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The value of x is 3.67 in the given right angled triangle.

What is triangle ?

Triangle can be defined in which it consists of three sides , three angles and sum of three angles is always 180 degrees.

In the given triangle ,

Triangle STU ,

T = 90

S = 69

So, U = 180 - 90-69

U = 180 - 159

U = 21

And US  = 10

sin69 = TU/US

sin69 = TU / 10

0.93 = TU/ 10

93 / 100 = TU / 10

93/10 = TU

TU = 9.3

So, in the triangle

as per pythagores theorem ,

SU^2  = ST^2 + TU^2

10*10 = x*x + 9.3*9.3

x*x = 100-86.49

x*x = 13.51

x = 3.67  (Approx)

Hence, The value of x is 3.67 in the given right angles triangle.

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Total number of outcomes (n) = 2

Let E be the event of getting a yellow colored side of the coin.

Therefore, n(E) = 1

Therefore, P(E) = n(E)/n = 1/2

Answer:

1/2

Hope it helps.

If you have any query, feel free to ask.

The graph that depicts a function is graph when the vertical line test is used (b).

By visually counting the number of times the curve crosses vertical lines, the vertical line test is a graphical approach for verifying whether a curve in the plane accurately depicts the graph of a function. the graph of a function can only be intersected by any vertical line in the plane once as a result.

A graph must satisfy the vertical line test in order to be considered a function representation. The vertical line test requires that the line from the x-axis only once crosses an associated y-value.

Graphs (a), (c), and (e) fail the vertical line test, indicating that they do not reflect a function.

So, graph is the name of the graph that represents a function (b)

The complete question is:

Use the vertical- line Test to determine which graph represents a function? I'm thinking it's the first one...

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Answer:

Step-by-step explanation:

Answer: 63 gingerbread cookies

Step-by-step explanation: Okay, to find the answer to this problem, we shall use this formula:

Final amount = Whole # * Part % / 100

So, now let's plug in the numbers to find the answer:

Final amount = 90 * 70 / 100

= 6300/ 100

= 63

Therefore, Kenny ordered a total of 63 gingerbread cookies. I hope this helped!

The var() function in R is used to calculate sample variance. In those uncommon situations where you want a populace change, utilize the populace mean to work out the example difference and duplicate.

The outcome by (n-1)/n; Take note of the fact that sample variance converges on population variance as sample size increases.

R's sample variance and standard deviation are specified by var(y), which tells R to calculate the sample variance of Y by employing n-1 "degrees of freedom," where n is the number of observations in Y. On the other hand, sd(y) tells R to return the sample standard deviation of y by employing n-1 degrees of freedom. sqrt(var(y)) equals sd(y).

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Answer:

= - 23.

Step-by-step explanation:

7x - 2y + 5 xy + x 2

From the question

x = -1

and

y = 2

7(-1) - 2(2) + 5 (-1)(2) + (-1) 2

= -7 - 4 + 5 (-2) - 2

= -7 - 4 -10 - 2

= - 11 - 12

= - 23.

Answer: liner

Step-by-step explanation:

Answer:

Step-by-step explanation:

linear, because the slope intercept fomat is y=mx+b it's just that the y intercept is zero so they just excluded it. So the equation would be y=8.75x+0 but they just removed the zero to simplify. So yes, it is linear

Yes, a probability distribution is given.

The mean of this probability distribution is 1.62 and the standard deviation is 0.84.

Mean = ΣxP(x) = 0*0.108 + 1*0.354 + 2*0.390 + 3*0.148 = 1.62

Standard Deviation = √Σ(x-mean)2P(x) = √(0-1.62)2*0.108 + (1-1.62)2*0.354 + (2-1.62)2*0.390 + (3-1.62)2*0.148 = 0.84

This is a probability distribution for a situation in which college students are randomly elected and arranged in groups of three. The number of people in the group who claim to take one or more online courses is the random variable, or x. The probability distribution is given by the values of x and the probabilities associated with them (P(x)). From the given values, we can calculate the mean and standard deviation of the distribution. The mean of the distribution is 1.62, and the standard deviation is 0.84. This means that, on average, 1.62 students in the groups of three will say that they take one or more online courses. The standard deviation of 0.84 implies that the actual number of students in the groups who say that they take online courses will vary from the mean value by about 0.84 students

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The equation of the graphed function is given as follows:

f(x) = x³ + 2x² - 5x - 6.

The equation of the function is obtained considering the Factor Theorem, as a product of the linear factors of the function.

From the graph, the zeros of the function are:

Hence the function is:

f(x) = a(x + 3)(x + 1)(x - 2).

In which a is the leading coefficient.

Expanding the product, we have that:

f(x) = a(x² + 4x + 3)(x - 2)

f(x) = a(x³ + 2x² - 5x - 6).

When x = 0, y = -6, hence the leading coefficient a is obtained as follows:

-6a = -6

a = 1.

Hence the function is:

f(x) = x³ + 2x² - 5x - 6.

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The commutative property applies only to addition and multiplication of real numbers.

What is commutative property in math?

This law simply states that with addition and multiplication of numbers, you can change the order of the numbers in the problem and it will not affect the answer. Subtraction and division are NOT commutative.

The commutative property of real numbers states that for any real numbers a and b, a + b = b + a and a * b = b * a. In other words, the order in which two real numbers are added or multiplied does not change the result. This property applies to both addition and multiplication of real numbers.

Therefore, the commutative property applies only to addition and multiplication of real numbers.

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Answer:

0.52

Step-by-step explanation:

25-12=13

boys are equal to 13

the probability of picking a boy at random will be;

13/25=0.52

The experimental probability that the next customer to come into Chandler's boutique wears a size small is; 1/19

Theoretical probability is defined as the term used to describe what we expect to happen based on math theory, while experimental probability refers to what actually happens when the actual situation is tried out as an experiment.

In this question, we are given;

Number of small wears = 3

Number of medium wears = 32

Number of large wears = 22

Thus;

Total number of wears = 3 + 32 + 22

= 57

Probability that next customer wears small size = 3/57 = 1/19

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Keiha sells computer software she sells 1800 if no books are sold.

Let y signify her overall salary (in dollars).

Let x be the volume of History is Fun that she sells.

Keep in mind that a change can be an improvement or a problem. Use a positive number to indicate an increase. Use a negative integer to indicate a reduction.

Consider the case when the equation =y+180070x connects x and y.

The number of books sold will affect the variable 70x in equation y=1800 + 70x.

Y=70x+1800=70(0)+1800=1800 if no books are sold.

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Full question

Keiko is a software saleswoman. Let y represent her total pay (in dollars). Let x represent the number of copies of History is Fun she sells. Suppose that x and y are related by the equation 2200 + 90x = y. Note that a change can be an increase or a decrease. For an increase, use a positive number. For a decrease, use a negative number.

What is the change in Keiko's total pay for each copy of History is Fun she sells?

Her displacement is 9.43 miles, and her office is 5 miles west and 8 miles north from her house

Let's use the notation (x, y) to denote Beth's position, we assume she starts at the point (0, 0).

First she travels 9 miles west and 9 miles north, so the new position is:

(0 - 9, 0 + 9) = (-9, 9)

Then travels 6 miles west and 6 miles nort

(-9 - 6, 9 + 6) = (-15, 15)

then travel 10 miles east and 7 miles south to their office

(-15 + 10, 15 - 7) = (-5, 8)

So the office is 5 miles west and 8 miles north from her house, and the displacement is equal as the absolute value of that point.

dispacement = √( (-5)² + 8²) = 9.43

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The inverse operations can be graphed by determining the inverse of the function by swapping the x and y variables,

Not all functions have inverses, and in order for a function to have an inverse, it must be a one-to-one function that is, there must not be repeated output for many inputs which indicates that not all functions have inverses. The various steps to graph inverse functions can be noted as -

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On solving the exponential function A(t) = 80 (0.965)^t, the number of animals will drop to 15 after 47 years.

What is an exponential function?

The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

The number of animals studied for the research = 80

The decrease rate of certain species = 3.5%

The rate of decay in exponential term = (1 - 0.035) = 0.965

The exponential function for the situation is -

A(t) = 80 (0.965)^t

Where, t is the number of time periods in years and A(t) = change in the population of animals.

The number of animals drop to 15.

So, substitute the value of A(t) = 15 in the equation -

A(t) = 80 (0.965)^t

15 =  80 (0.965)^t

15/80 = 0.965^t

0.1875 = 0.965^t

ln(0.1875) = t ln(0.965)

t = ln(0.1875)/ln(0.965)

t = -1.6739/-0.0356

t = 47.01

Therefore, the time period value is obtained as t=41 years.

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The height of the building is given as follows:

36 ft.

In this problem, we have two similar triangles, meaning that their side lengths are proportional.

As the triangles are similar, the equation involving proportions for the equivalent side lengths is given as follows:

x/6 = 45/7.5.

Applying the division on the right side of the equality, we have that:

45/7.5 = 6.

Hence:

x/6 = 6.

Applying cross multiplication, the height is given as follows:

x = 6(6) = 36 ft.

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Using factoring, we do the following actions to make rational expressions simpler:

As much as you can, factor the numerator and denominator. Any factors that appear in both the numerator and the denominator should be eliminated. Your expression gets simplified as a result. How is an expression factorized:

Step 1 is to identify the expression's prime factors.

Step 2: Find the GCF by enclosing the common factors.

Write each term in the expression as a combination of the GCF and the final factor in step 3.

Step 4: Simplify the equation by applying the distributive property.

Y=12(x-6)(x+2) is an illustration of a quadratic function in factored form. This shape can be examined to determine the vertex as well as the graph's x-intercepts.

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The inequality that represents the amount of money Shenelle can spend on snacks is given as follows:

x + 10.25 ≤ 25.

The solution to the inequality is of:

x ≤ 14.75.

Meaning that she can spend at most $14.75 on the snacks.

The total amount that Shenelle has is given as follows:

$25.

Her spendings are given as follows:

Hence the inequality is given as follows:

x + 10.25 ≤ 25.

The solution is obtained as follows:

x ≤ 25 - 10.25.

x ≤ 14.75.

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Answer:

1 [tex]\frac{5}{9}[/tex]

Step-by-step explanation:

Both blocks contain 9 stars

left block has all 9 shaded = [tex]\frac{9}{9}[/tex] = 1

right block has 5 shaded = [tex]\frac{5}{9}[/tex]

mixed number = 1 + [tex]\frac{5}{9}[/tex] = 1 [tex]\frac{5}{9}[/tex]