MODELING WITH MATHEMATICS
You design a frame to surround a rectangular photo. The width of the frame is the same on every side, as shown.

a. Write a polynomial that represents the combined area of the photo and the frame.

b. Find the combined area of the photo and the frame when the width of the frame is 4 inches.

The correct option is option D) it has range of 22

What is the range of a dataset?

It the difference between the minimum and maximum value of the dataset.

We are given a dataset with a histogram and we are asked to find out which of the given options does not describe the data

We find the answer by eliminating the correct option

Our given dataset contains 10 points

Hence the median will be the average of 5th and 6th element

Here the 5th and 6th elements are 17

Hence the median of the dataset is 17

Similarly 17 is repeated 4 times in the dataset. i.e highest number of times

Hence 17 is the mode of the dataset

If you look clearly at the histogram from median it is symmetrical that is left side equal to the right side

But if you look at the range the minimum value is 13 and maximum value is 21

Hence the range of the function is 21-13=8

And not 22

Hence the correct option is option D)

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By using implicit differentiation, the expression for dy/dx is: dy/dx = (e^y - 1) / (x - e^y)

To find the derivative of y with respect to x, dy/dx, using implicit differentiation on the equation xy + e^x = e^y, we follow these steps:

Differentiate both sides of the equation with respect to x. Treat y as a function of x and apply the chain rule where necessary.

d(xy)/dx + d(e^x)/dx = d(e^y)/dx

Simplify the derivatives using the chain rule and derivative rules.

y * (dx/dx) + x * (dy/dx) + e^x = e^y * (dy/dx)

Simplifying further:

1 + x * (dy/dx) + e^x = e^y * (dy/dx)

Rearrange the equation to isolate dy/dx terms on one side.

x * (dy/dx) - e^y * (dy/dx) = e^y - 1

Factor out (dy/dx) from the left side.

(dy/dx) * (x - e^y) = e^y - 1

Solve for (dy/dx) by dividing both sides by (x - e^y).

(dy/dx) = (e^y - 1) / (x - e^y)

Therefore, the expression for dy/dx is: dy/dx = (e^y - 1) / (x - e^y)

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Answer:

sss-

Step-by-step explanation:

i think

s orbital mentioned

Note that for all n shells electrons per shell is fixed like for p it's 6 and for d it's 10

Rule for electron in nth shell=2n²

The correct formula that defines an arithmetic sequence is option d) tn = 5n + 14.

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms remains constant. In other words, each term can be obtained by adding a fixed value (the common difference) to the previous term.

In option a) tn = 5 + 14, the term does not depend on the value of n and does not exhibit a constant difference between terms. Therefore, it does not represent an arithmetic sequence.

Option b) tn = 5n² + 14 represents a quadratic sequence, where the difference between consecutive terms increases with each term. It does not represent an arithmetic sequence.

Option c) tn = 5n(n+14) represents a sequence with a varying difference, as it depends on the value of n. It does not represent an arithmetic sequence.

Option d) tn = 5n + 14 represents an arithmetic sequence, where each term is obtained by adding a constant value of 5 to the previous term. The common difference between consecutive terms is 5, making it the correct formula for an arithmetic sequence.

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Answer:

19, 18, 15.5

Step-by-step explanation:

To solve this problem, you need to substitute the given values into the function.

b(x = -2) = 18 - 0.5(-2) = 18 + 1 = 19

b(x = 0) = 18 - 0.5(0) = 18 - 0 = 18

b(x = 5 ) = 18 - 0.5(5) = 18 - 2.5 = 15.5

Answer:

1/10

Step-by-step explanation:

20 21 22 23 24 25 26 27 28 29 30

X.   X.   X.  X.  X.  X.  X.  X.  X.  X.  V

1/10

20-29 all have a 2 in it meaning 30 is the only digit that doesnt have a 2 so 1/10 numbers

If one card taken from the bag then the probability that will not have the digit 2 on it is 1/11.

Probability shows possibility to happen an event, it defines that an event will occur or not. The probability varies from 0 to 1.

Given that,

Numbers from 20 to 30 are written on individual cards.

The total numbers of cards = 11

And numbers on cards = 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30

To find the probability of cards that have not the digit 2 on it.

Since, there is only one digit 30, which does not have digit 2,

Therefore, probability = favorable outcome / total outcome

= 1 / 11

The required probability of choosing a card that will not have the digit 2 on it is 1/11.

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The probability that at most 1 student is a sports fan is 0.9143.

Let us consider a binomial distribution,

where p = 5/100 = 0.05, q = 1 - 0.05 = 0.95, n = 10

We are required to find the probability of at most 1 student being a sports fan

P (x ≤ 1) = P (x = 0) + P (x = 1)P (x = 0)

= \(nCx * p^x * q^(n-x)P (x = 0) = 10C0 * 0.05^0 * 0.95^10P (x = 0) = 0.5987369392P (x = 1) = nCx * p^x * q^(n-x)P (x = 1) = 10C1 * 0.05^1 * 0.95^9P (x = 1)\)

= 0.3155915129P (x ≤ 1) = P (x = 0) + P (x = 1)P (x ≤ 1)

= 0.5987369392 + 0.3155915129P (x ≤ 1)

= 0.9143284521

Therefore, the probability that at most 1 student is a sports fan is 0.9143.

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The probability that the number drawn is a multiple of 2 or 3 is 8/15 or 0.53.

This can be easily found by finding the number of multiples of 2 and 3 between 1 and 15 and adding them together. The multiples of three go from 3 to 15 and therefore there are 5 such numbers. The multiples of two go from 2 to 14 and hence there are 7 such numbers. Therefore, when we add these two numbers together, we get 12.

This is the total number of multiples of 2 or 3 between 1 and 15. We divide this by the total number of elements in the box, which is 15, to get the probability that the number drawn is a multiple of 2 or 3. This comes out to be 8/15 or 0.53.

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The transformed function is:

g(x) = 2*|x - 4| - 6

And the graph can be seen below.

The original function is the parent absolute value function:

f(x) = |x|.

First, we stretch it vertically by a factor of 2, so we just multiply it by 2:

g(x) = 2*f(x).

Then, we move it 6 units down and 4 units to the right, this is written as:

g(x) = 2*f(x - 4) - 6.

Replacing f(x) by the actual function:

g(x) = 2*|x - 4| - 6

Now we just need to graph that, the graph of the transformed function can be seen below.

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Answer:

Answer: His estimate was low

Step-by-step explanation:

It's true that √16 is 4 and that √9 is 3

for √15 :

\( \sqrt{15} = 3.9\)

It's true that √15 lies between 3 and 4

\( \sqrt{15} : 3 < x < 4\)

Estimated answer :

\( = 3.5\)

Exact answer :

\( = 3.9\)

Therefore, the error:

\( \delta x = 3.9 - 3.5 \\ \\ = 0.4\)

Since error is less than 0.5, his estimation was moderate, [ low ]

Answer:

2,700 years

Explanation:

We were given the following details:

Half-life of carbon-14, T = 5600 years

78% of carbon-14 is left. This indicates that the amount of carbon-14 left is 78% of the initial amount:

We will calculate the time since when the tree died as shown below:

Therefore, the tree died 2,700 years ago

Answer:

\(f(x) = 3x - 4 \\ g(x) = - 2x + 7 \\ g(f(x)) = - 2(3x - 4) + 7 \\ g(f(x)) = - 6x + 8 + 7 \\ g(f(x)) = -6 x + 15 \\ g(f( - 2)) = - 6( - 2) + 15 \\ g(f( - 2)) = 12 + 15 \\ \boxed{g(f( - 2)) = 27}\)

Answer and explanation

as z= 7

3z -3

3(7) -3 =21-3 =18

Answer:

She paid $675.00, How is because she was paying $45 dollars per hours so $45 x 15 is $675.00 dollars.

Answer:

Step-by-step explanation:

Yes, he is correct because writing a negative symbol with a denominator and numerator makes the sense same. Because the negative is as a whole not only the numerator and not only the denominator. As it is a fraction which is a whole single identity.

3/4= 0.75, Therefore in each above three always the

-0.75= -0.75= -0.75 will give same value in each.

The length of the orthogonal projection of x onto a is equal to the magnitude of the projection vector.

The length of the orthogonal projection of x onto a can be found using the formula:
|proj_a(x)| = |x| * cos(theta),
where |proj_a(x)| is the length of the projection, |x| is the magnitude of x, and theta is the angle between x and a.
To calculate the length, we need to find the magnitude of x and the cosine of the angle between x and a.

The magnitude of x is sqrt(4^2 + (-5)^2 + 1^2) = sqrt(42), which is approximately 6.48. The cosine of the angle theta can be found using the dot product: cos(theta) = (x . a) / (|x| * |a|) = (4*2 + (-5)2 + 14) / (6.48 * sqrt(24)) ≈ 0.47.

Therefore, the length of the orthogonal projection of x onto a is approximately 6.48 * 0.47 = 3.04.


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Answer:

Option c

My logic:

The commutative property of multiplication states that you can multiply a string of numbers in any order and receive the same answer.

Hope this helps!

The points on a graph are the points that lie on the graph

The ordered pair on the graph of \(\mathbf{x =\frac{1}{3}(y - \frac 18)}\) would be \(\mathbf{( \frac{5}8},2)\)

The points are not given; so, I will give a general explanation

The equation is given as:

\(\mathbf{x =\frac{1}{3}(y - \frac 18)}\)

Assume that the value of y, is 2

The equation becomes

\(\mathbf{x = \frac 13(2 - \frac 18)}\)

Take LCM

\(\mathbf{x = \frac 13(\frac{16-1}8)}\)

\(\mathbf{x = \frac 13(\frac{15}8)}\)

Divide

\(\mathbf{x = \frac{5}8}\)

So, the ordered pair would be \(\mathbf{( \frac{5}8},2)\)

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The expression to find out how many weeks it will take him to save up enough money to buy the new TV is, x = 3960 / 55.

Since we know that,

Mathematical expressions consist of at least two numbers or variables, at least one maths operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows:

Expression: (Math Operator, Number/Variable, Math Operator)

Peter gets a salary of $125 per week.

He wants to buy a new television that cost $3,960.

Now, If he saves $55 per week.

let he saves for x weeks.

So, 3960 = 55x

x = 3960 / 55

x = 72

Thus, the required expression is x = 3960/ 55.

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The complete question is:

Peter gets a salary of $125 per week. He wants to buy a new television that cost $3,960. If he saves $55 per week, which of the following expressions could he use to figure out how many weeks it will take him to save up enough money to buy the new TV ?

Note: I don’t really like giving people answers. but i like them to learn. So i will teach you how to find a average of something, and using that method try to solve this problem

To find a average of something all you need to do is to add the numbers up and divide it by the total  is. As for example, pretend we have two bags, one with 5 marbles and the other one with 3 marbles. now you have to add them all up 5+3=8. Know we know the total numbers of marblas. So we know we have to bags right?l we divide 8 by 2 which is 4. i really hope you learned how to find the average of something. Hope this helps a lot!

Answer:

y = x + 7

Step-by-step explanation:

The line rises at a slope of 1 and intercepts the y-axis at 7.

The values gotten for the  coordinate plane are;

The Reason for the obtained value is that since thee rule for the dilation of ΔRST is:

Then, the distance that exist between the x-coordinate of R and T will be:

3 - 0

= 3

Then the distance between the y-coordinate of R and T will be:

4 - (-2)

= 6

Note that the location of the point R' is said to be relative to point T and as such:

The location of point R'

= (-1 + 3, 2 - 2)

= R'(2, 0)

Hence R' is (-1, 2) from T, and the coordinates of R' is (2, 0)

Therefore, The values gotten for the  coordinate plane are;

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Answer:

C.) ✔ 3

D.) ✔ 6

B.) ✔ 1 unit left, 2 units up

D.) ✔ (2, 0)

Step-by-step explanation: i hope this helps :)

Answer:

m= ^6

Step-by-step explanation:

There does not exist a group homomorphism φ : D2n → G′ such that ker(φ) = {1, s}.

(a) To show that NG(H) = G, we need to show that every element of G normalizes H. Let g ∈ G, and let h ∈ H. Since H = ker(φ), we know that φ(h) = 1. Now, we need to show that ghg⁻¹ ∈ H. Using the properties of a homomorphism, we can write:

φ(ghg⁻¹) = φ(g)φ(h)φ(g⁻¹) = φ(g)1φ(g⁻¹) = φ(g)φ(g⁻¹) = φ(gg⁻¹) = φ(1) = 1

Therefore, ghg⁻¹ ∈ H, and so g normalizes H. Since this is true for any g ∈ G, we can conclude that NG(H) = G.

(b) Suppose there exists a group homomorphism φ : D2n → G′ such that ker(φ) = {1, s}. Since s ∈ ker(φ), we know that φ(s) = 1. However, we also know that rs = sr⁻¹, and so φ(rs) = φ(sr⁻¹). Using the properties of a homomorphism, we can write:

φ(r)φ(s) = φ(s)φ(r⁻¹) = φ(s)φ(r)⁻¹

Since φ(s) = 1, this simplifies to:

φ(r) = φ(r)⁻¹

But this means that φ(r) is its own inverse, and so φ(r)² = 1. However, we also know that rn = 1, and so φ(rn) = 1. Using the properties of a homomorphism, we can write:

φ(rn) = φ(r)ⁿ = (φ(r)²)ⁿ/2 = 1ⁿ/2 = 1

But this means that n/2 must be an integer, which contradicts the fact that n > 2. Therefore, there does not exist a group homomorphism φ : D2n → G′ such that ker(φ) = {1, s}.

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The first term of the infinite geometric series is 625.Let's dive deeper into the explanation.

We are given that the sum of the infinite geometric series is \(\( \frac{15625}{24} \)\)and the common ratio is\(\( \frac{1}{25} \).\)The formula for the sum of an infinite geometric series is \(\( S = \frac{a}{1 - r} \)\), where \( a \) is the first term and \( r \) is the common ratio.
Substituting the given values into the formula, we have \(\( \frac{15625}{24} = \frac{a}{1 - \frac{1}{25}} \).\)To find the value of \( a \), we need to isolate it on one side of the equation.
To do this, we can simplify the denominator on the right-hand side.\(\( 1 - \frac{1}{25} = \frac{25}{25} - \frac{1}{25} = \frac{24}{25} \).\)
Now, we have \(\( \frac{15625}{24} = \frac{a}{\frac{24}{25}} \).\) To divide by a fraction, we multiply by its reciprocal. So, we can rewrite the equation as \( \frac{15625}{24} \times\(\frac{25}{24} = a \).\)
Simplifying the right-hand side of the equation, we get \(\( \frac{625}{1} = a \).\)Therefore, the first term of the infinite geometric series is 625.
In conclusion, the first term of the given infinite geometric series is 625, which corresponds to option (a).



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The planet that has the larger mass is the planet B and the measurements in standard forms are

From the question, we have the following parameters that can be used in our computation:

Planet A = 5*10^26 kilograms

Planet B = 2*10^28 kilograms

Rewrite the masses properly

So, we have

Planet A = 5*10²⁶ kilograms

Planet B = 2*10²⁸ kilograms

The exponent 28 is greater than the exponent 26

This means that

2*10²⁸ is greater than 5*10²⁶

So, we have

Planet B has the larger mass

When the measurements are expressed in standard forms, we have

Planet A = 500000000000000000000000000 kilograms

Planet B = 20000000000000000000000000000 kilograms

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Answer:

Step-by-step explanation:

Step one:

given data

we are told that the initial bill is $74

thereafter they gave a tip worth 18% of the bill

let us compute what 18% of $74 will amount to

Step two:

=18/100*74

=0.18*74

=$13.32

The added expenses is $13.32

Hence the total cost is

the initial bill plus the tip

=74+13.32

=$87.32

The a-values of the business are classified as follows:

The a-value of a business depends on the behavior of the earning function for these business, as follows:

From the table given by the image at the end of the answer, for the lawn care business, a concave down parabola represents the situation, as the earnings start increasing but then during the 3rd month they start to decrease. Hence, the a-value of the business is negative.

For the dog walking and for the house-sitting business, the values are always increasing over the time interval of the table, hence the a-value of these two businesses is positive.

The table is given by the image at the end of the answer.

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Alice paid $25 for her pair of jeans, and Jeff paid $4 for the steaks.

Let's calculate the final amount paid by Alice and Jeff for their purchases.

Alice:

Jeff:

So, Alice paid $25 for her pair of jeans, and Jeff paid $4 for the steaks.

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