How do you find the term in a Aromatic sequence

The type of sytudy that we have here is the observational study.

In an observational study, the researcher observes and analyzes data from individuals without actively intervening or manipulating any variables.

In this case, the researcher is observing and comparing the health outcomes of two groups of individuals: those who have eaten a vegan diet for the past five years and those who have not.

The participants are not randomly assigned to the groups, and the researcher does not actively control or manipulate the diet of the individuals.

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Answer:

Step-by-step explanation: [-2.19] = -3

[3.67] = 3

[-0.83] = -1

The domain of this function is a group of real numbers that are divided into intervals such as [-5, 3), [-4, 2), [-3, 1), [-2, 0) and so on. This explains the domain and range relations of a step function.

This can be generalized as given below:

[x] = -2, -2 ≤ x < -1

[x] = -1, -1 ≤ x < 0

[x] = 0, 0 ≤ x < 1

[x] = 1, 1 ≤ x < 2

Answer:

y = - \(\frac{3}{2}\) x

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 2, 3) and (x₂, y₂ ) = (0, 0) ← 2 points on the line

m = \(\frac{0-3}{0-(-2)}\) = \(\frac{-3}{0+2}\) = - \(\frac{3}{2}\) , then

y = - \(\frac{3}{2}\) x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (0, 0 )

0 = - \(\frac{3}{2}\) (0) + c = 0 + c , so

c = 0

y = - \(\frac{3}{2}\) x + 0 , that is

y = - \(\frac{3}{2}\) x

Answer:

48

Step-by-step explanation:

4*2*3 for the 4 flaps

2*4*3 for the 2 tops

(4*2*3) + (2*4*3) = 48

Answer:

52 square inches

Step-by-step explanation:

to find the surface area of a rectangular prism the formula is

S.A.=2(l*w+l*h+w*h)

2(4*3+4*2+3*2)

=52 square inches

here l is length w is width and h is height

Answer:

y=3x-3

Step-by-step explanation:

Answer:

The correct answer is B.

Approximately 200 students received a test score between 70.5 and 80.

The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).

First, let's find the slope of the line using the formula:

slope (m) = (change in y) / (change in x)

m = (0 - 4) / (5 - 3)

m = -4 / 2

m = -2

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Using the point (3, 4) as our reference point, we have:

y - 4 = -2(x - 3)

Expanding the equation:

y - 4 = -2x + 6

Simplifying:

y = -2x + 10

Now, let's check the given options to find the linear function with the same y-intercept:

Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)

The y-intercept is the same as the given line (10). So, this option is correct.

Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)

The y-intercept is not the same as the given line. So, this option is not correct.

Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

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Looking at the orientation of each figure, first we need a reflection over the y-axis, this way the orientation of ABCD will match the orientation of EHGF.

After this reflection, the position of each point will be:

(To find the position after a reflection over the y-axis, we need to switch the signal of the x-coordinates)

Now, let's write the coordinates of EHGF:

Comparing each corresponding pair of points, we can see that in order to map A'B'C'D' into EHGF, we need to decrease the x-coordinates by 4 units and decrease the y-coordinates by 4 units:

Therefore the answers are y, -4 and -4.

For the equation 75x+30y=1500,  x is (100 - 2y) / 5 and y is (100 - 5x) / 2.

An equation is a mathematical statement that uses symbols and numbers to express a relationship between two or more variables. It states that two expressions are equal to each other.

We can solve for x and y in the equation 75x + 30y = 1500 by using algebraic manipulation.

First, we can simplify the equation by dividing both sides by the greatest common factor of 75 and 30, which is 15:

(75x + 30y) / 15 = 1500 / 15

Simplifying the left side gives:

5x + 2y = 100

Next, we can isolate one of the variables. Let's isolate y by subtracting 5x from both sides:

5x + 2y - 5x = 100 - 5x

Simplifying the left side gives:

2y = 100 - 5x

by dividing both sides by 2:

y = (100 - 5x) / 2

This is the equation for y in terms of x. We can use this equation to solve for y given a value of x, or we can substitute it back into the original equation to solve for x in terms of y.

Let's solve for x in terms of y by isolating x in the equation 5x + 2y = 100:

5x = 100 - 2y

Dividing both sides by 5 gives:

x = (100 - 2y) / 5

This is the equation for x in terms of y. We can use this equation to solve for x given a value of y, or we can substitute it back into the original equation to solve for y in terms of x.

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The intersection consists of the elements that are contained in all of the intervals.

(5,6) is the answer

Please let me know if im wrong!

Answer:

Step-by-step explanation:

We can use the given formula to model the temperature of the turkey as it warms up:

T = Ta + (To - Ta) * e^(-kt)

where Ta is the initial temperature of the turkey (38°F), To is the temperature of the room (72°F), T is the temperature of the turkey at time t, and k is the decay constant that we need to find.

We are given that the temperature of the turkey reaches 47°F after 15 minutes. So we can substitute these values into the equation and solve for k:

47 = 38 + (72 - 38) * e^(-k*15)

Simplifying this equation, we get:

9 = 34 * e^(-15k)

Taking the natural logarithm of both sides, we get:

ln(9/34) = -15k

Solving for k, we get:

k = -ln(9/34) / 15

Using a calculator, we can evaluate this expression to be approximately 0.0494, rounded to four decimal places.

Now that we have found the value of k, we can use the same formula to determine the temperature of the turkey after 120 minutes:

T = 38 + (72 - 38) * e^(-0.0494*120)

Simplifying this equation, we get:

T = 72 - 34 * e^(-5.928)

Using a calculator, we can evaluate this expression to be approximately 68°F, rounded to the nearest degree.

Therefore, the temperature of the turkey after 120 minutes is approximately 68°F.

The temperature of the turkey after 120 minutes is approximately 67°F

A refrigerator, also known as a fridge, is an appliance that is used for storing food and other perishable items at low temperatures to prevent them from spoiling.

We are given the equation:

T = Ta + (To - Ta)e^(-kt)

We know that the turkey's temperature at time t=0 is 38°F, and after 15 minutes it is 47°F. Substituting these values in the equation, we get:

47 = 38 + (72 - 38)e^(-k*15)

9 = 34e^(-15k)

e^(-15k) = 9/34

Taking natural logarithm on both sides, we get:

-15k = ln(9/34)

k = -ln(9/34)/15

k ≈ 0.0704 (rounded to four decimal places)

Using this value of k, we can find the temperature of the turkey after 120 minutes:

T = Ta + (To - Ta)e^(-kt)

T = 38 + (72 - 38)e^(-0.0704*120)

T ≈ 67°F

Therefore, the temperature of the turkey after 120 minutes is approximately 67°F

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Answer:

The pvalue of the test is 0.0083 < 0.1, which means that there is enough evidence to conclude that residents of Legacy Ranch use less water on average

Step-by-step explanation:

The American Water Works Association reports that the per capita water use in a single-family home is 69 gallons per day. Test that the residents use less water.

At the null hypothesis, we test that the mean is 69, that is:

\(H_0: \mu = 69\)

At the alternate hypothesis, we test that the mean is less than 69, that is:

\(H_a: \mu < 69\)

The test statistic is:

As we have the standard deviation for the sample, we use the t-statistic.

\(t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}\)

In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.

69 is tested at the null hypothesis:

This means that \(\mu = 69\)

Thirty-six owners responded, and the sample mean water use per day was 64 gallons with a standard deviation of 8.8 gallons per day.

This means that \(n = 36, X = 64, s = 8.8\)

Value of the test statistic:

\(t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}\)

\(t = \frac{64 - 69}{\frac{8.8}{\sqrt{36}}}\)

\(t = -3.41\)

Pvalue of the test and decision:

The pvalue of the test is the probability of finding a mean less than 64, which is the pvalue of t = -3.41, found on the t-table with 36 - 1 = 35 degrees of freedom on a one-tailed test.

With calculator help, the pvalue is 0.0083.

The pvalue of the test is 0.0083 < 0.1, which means that there is enough evidence to conclude that residents of Legacy Ranch use less water on average

Answer:

A= $18 B=3

Step-by-step explanation:

He gets $9 off each game. 51 multiplied by 3 is $153. I hope this helps!! Please mark me brainliest!

Answer:

1/5x^4

Step-by-step explanation:

To change a negative exponent to a positive one, flip it into a reciprocal. This is what I have done here.

The complement of A∪B is A′∩B ′.

A set of components in the universal set that are not a part of the initial set is known as the complement of a set in mathematics. Discover what a subset and its complement are, how to calculate a subset's complement, and the proper notation to use when writing a subset and its complement.

Given, universal set, U={1,2,3,4,5,6,7}

A={1,2,5,7}

B={3,4,5,6}

(A∪B) ′=U−(A∪B)

={1,2,3,4,5,6,7}−{1,2,3,4,5,6,7}=ϕ

A′∩B′=(U−A)n(U−B)

={3,4,6}n{1,2,7}=ϕ

Hence ( A∪B)′=A′∩B ′.

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Your analysis is correct. Here's a summary:

If it is sunny, then it is 80° Fahrenheit. (Original statement)

Converse: If it is 80° Fahrenheit, then it is sunny. (Valid)

If it is 80° Fahrenheit, then it is sunny. (Original statement)

Converse: If it is sunny, then it is 80° Fahrenheit. (Valid)

If it is not sunny, then it is not 80° Fahrenheit. (Original statement)

Converse: If it is not 80° Fahrenheit, then it is not sunny. (Invalid)

Counterexample: A day that is not 80° Fahrenheit and not sunny (e.g., 70° and cloudy).

If it is 80° Fahrenheit, then it is sunny. (Original statement)

Converse: If it is sunny, then it is 80° Fahrenheit. (Invalid)

Counterexample: A day that is 80° Fahrenheit and cloudy.

In cases 1 and 2, the original statements and their converses are valid because the relationship between "sunny" and "80° Fahrenheit" holds in both directions. However, in cases 3 and 4, the converses are invalid because there are counterexamples where the second part of the statement (either "not 80° Fahrenheit" or "cloudy") does not necessarily imply the first part ("not sunny" or "80° Fahrenheit").

No, the expression (x^3 - 1) / (x^2 - 1) does not simplify to x.

To simplify the expression, let's first factorize both the numerator and denominator.

The numerator can be factorized using the difference of cubes formula: a^3 - b^3 = (a - b)(a^2 + ab + b^2). So, we have (x^3 - 1) = (x - 1)(x^2 + x + 1).

The denominator is a difference of squares: a^2 - b^2 = (a - b)(a + b). Therefore, (x^2 - 1) = (x - 1)(x + 1).

Now, we can simplify the expression by canceling out the common factors in the numerator and denominator:

[(x - 1)(x^2 + x + 1)] / [(x - 1)(x + 1)]

The (x - 1) terms cancel out, leaving us with:

x^2 + x + 1 / (x + 1)

So, the simplified form of the expression is (x^2 + x + 1) / (x + 1), which is not equal to x.

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The function f(x) = -4(x+2)² - 12 can be rewritten in the form

f(x) = -4x² - 16x - 28.

The concept used in this problem is expanding and simplifying an algebraic expression. We are given a quadratic function in a different form, and we need to rewrite it in standard form, which is in the form of f(x) = ax² + bx + c.

This involves expanding and simplifying the squared term and combining like terms. The process of expanding and simplifying an algebraic expression is a fundamental concept in algebra.

Here we have

f(x)= -4(x+2)²- 12      

To rewrite the function f(x) = -4(x+2)² - 12 in form f(x) = ax² + bx + c

Expand the squared term and simplify the expression.

The steps are as follows:

f(x) = -4(x+2)² - 12 (original function)

f(x) = -4(x² + 4x + 4) - 12 (expand the squared term)

f(x) = -4x² - 16x - 16 - 12 (distribute the -4)

f(x) = -4x² - 16x - 28 (combine like terms)

Therefore,

The function f(x) = -4(x+2)² - 12 can be rewritten in the form

f(x) = -4x² - 16x - 28.

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Answer:

Step-by-step explanation:

let the jobs be x and y, so that

x+y=32--------1

9x+7y=248----2

x=32-y

substitute x=32-y for x in equation 2 we have

9(32-y)+7y=248

open bracket we have

288-9y+7y=248

-2y=248-288

-2y=-40

2y=40

divide both sides by 2 we have

y=40/2

y= 10 hours

subtitute y=10 for y in equation 1 to find x

x+10=32--------1

x=32-10

x=22

x=22 hours

The prove of the given trigonometric function is given below.

The given trigonometric function is,

(sin⁴(x) - cos⁴(x))/(sin²(x) - cos²(x))

Now proceed left hand side of the given expression:

We can write the expression  as,

⇒[(sin²(x))² - (cos²(x))²]/(sin²(x) - cos²(x))

Since we know that ,

Algebraic identity:

a² - b²  = (a-b)(a+b)

Therefore the above expression be

⇒(sin²(x) - cos²(x))(sin²(x) + cos²(x))/(sin²(x) - cos²(x))

⇒(sin²(x) + cos²(x))

Since we know that,

Trigonometric Identities come in handy when trigonometric functions are used in an expression or equation. Trigonometric identities hold for all values of variables on both sides of an equation. Geometrically, these identities include one or more trigonometric functions (such as sine, cosine, and tangent).

Then,

sin²(x) + cos²(x)² = 1 is an trigonometric identity

Hence,

(sin⁴(x) - cos⁴(x))/(sin²(x) - cos²(x)) = 1

Hence proved.

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The value of m + n is given as follows:

A. 18.

The exponential expression for this problem is defined as follows:

\((x^5y^6)^{\frac{1}{5}}(x^3y^4}^{\frac{1}{4}}\)

Applying the power of power rule, we have that the exponents are given as follows:

Then the values of m and n are given as follows:

m = 7, n = 11.

Thus the sum is given as follows:

m + n = 7 + 11 = 18.

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Answer:

The usual representation of a proportional relationship is ...

y = kx

You want the constant of proportionality (k) to be 7/10, so this is ...

y = (7/10)x

Dividing by x gives the equivalent relationship ...

y/x = 7/10

Answer:4

Step-by-step explanation:2+2=4

The term "100 points" usually indicates a high level of achievement or success in a particular area.

The term "100 points" can refer to a number of different things depending on the context. For example, in sports, it could refer to a team scoring 100 points in a game.

In wine tasting, it could refer to a perfect score given to a wine by a critic or judge. In school, it could refer to receiving a perfect score on an exam or assignment worth 100 points.

It's important to note that while a perfect score of 100 points is often seen as the ultimate goal, it's not always necessary or even possible in some situations. In many cases, simply doing your best and striving for improvement is enough to be considered successful.

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Answer:

slope = 7/2 or 3.5 as a decimal.

y-intercept = 1 or (0, 1) in coordinate form.

Answer:

\(709*68=48212\)

ans = 48212

Answer:

\(\huge\boxed{\sf 38}\)

Step-by-step explanation:

= a³ + b (6 + c)

Put a = 2, b = 3 and c = 4

= (2)³ + 3 (6 + 4)

= 8 + 3(10)

= 8 + 30

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

Answer:

Step-by-step explanation:

the requied answer is 38.

according to the question the value of a=2,b=3,c=4.

here,

to find the value of   a³ + b (6 + c)we have to do it in steps:

step 1: solve the bracket (6+4) =10.

step 2:  solve the value of a³ =8.

now put these values ,

=8+3(10)

=38.

The Length is 5 inches and the Breadth is 15 inches

What is Perimeter?

A perimeter is a closed route that covers, surrounds, or outlines a two-dimensional form or length. The circumference of a circle or an ellipse is its perimeter. There are various practical applications for calculating the perimeter.

Solution:

Perimeter of Rectangle = 2*(Length + Breadth)

According to the question

Breadth = 3*Length

Perimeter = 40

40 = 2*(Length + 3*Length)

20 = 4*Length

Length = 5 inch

Breadth = 15 inch

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Therefore, the freight train traveled for 16.67 + 10 = 26.67 hours before the passenger train caught up with it.

let's call the time it took for the passenger train to catch up with the freight train "t" (in hours).

During this time, the freight train traveled at its average speed of 45 km/h for t + 10 hours, while the passenger train traveled at its average speed of 72 km/h for t hours.

We know that the distance both trains traveled is the same, since the passenger train caught up with the freight train. So, we can set up the following equation:

distance traveled by freight train = distance traveled by passenger train

\((45 km/h) x (t + 10 h) = (72 km/h) x t\)

Simplifying this equation, we get:

\(45t + 450 = 72t\)

\(27t = 450\)

t = 16.67 hours

Therefore, the freight train traveled for 16.67 + 10 = 26.67 hours before the passenger train caught up with it.

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number one take the second