What is the nth term rule of the linear sequence below?
-5, -2, 1, 4, 7,....
T₁=

An offshore oil well is 5 kilometers off the coast. The refinery is 6 kilometers down the coast. Laying pipe in the ocean is twice as expensive as on land. Kilometers down the coast should the pipe be laid in order to minimize the cost, the pipe should be laid approximately 8.62 km down the coast to minimize the cost.

Let the distance down the coast where the pipe is laid be x. Therefore, the distance from the refinery to the point where the pipe meets the shore will be (x + 5) km. The total distance of the pipe can be found using the Pythagorean Theorem.[tex]D = \sqrt{((x + 5)^2 + 6^2) } = \sqrt{(x^2+ 10x + 61)}[/tex] km

Let C(x) be the cost of laying the pipe down the coast at a distance x. Then

Now, to minimize the cost, we have to find the value of x that minimizes C(x). The first derivative of C(x) is:[tex]C'(x) = 2 + 1.5 [x^2 + 10x + 61]^{-1/2} [2x + 10][/tex] After simplifying,[tex]C'(x) = [2(x^2 + 10x + 61) + 1.5(2x + 10)] [x^2 + 10x + 61]^{-1/2}= (3x^2 + 23x + 82) [x^2 + 10x + 61]^{-1/2}= 0[/tex] (at a minimum point)

Now we can solve for x using the above equation.[tex](3x^2 + 23x + 82) = 0[/tex] ⇒ [tex]3(x^2 + 7.67x + 27.33) = 0[/tex] Using the quadratic formula; x = {-b ± √(b² - 4ac)}/2 a We get, x = {-23 ± √(23² - 4(3)(82))}/2(3)x = {-23 ± √(529 - 984)}/6x = {-23 ± √(-455)}/6x = -3.03 or -8.62 Since x must be positive, x = -3.03 is not possible. Hence, the distance down the coast where the pipe should be laid in order to minimize the cost is :x = -8.62Therefore, the pipe should be laid approximately 8.62 km down the coast to minimize the cost.

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Answer:The prices of the adult movie tickets and the child movie tickets are $15 and $5 respectively.

Given that, the Jones family spent $45 on movie tickets for 2 adults and 3 children.

Step-by-step explanation:What is a linear system of equations?

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Let cost of adult tickets be x and the cost of children tickets be c.

The Jones family spent $45 on movie tickets for 2 adults and 3 children.

2a+3c=45 ------(I)

The Smith family spent $40 for 2 adults and 2 children.

2a+2c=40

a+c=20 ------(II)

From equation (II), we have a=20-c

Substitute a=20-c in equation (I), we get

2(20-c)+3c=45

⇒ 40-2c+3c=45

⇒ c=$5

Put c=5 in equation (II), we get

a+5=20

⇒ a=$15

The Simple random sampling method is equivalent to a lottery system in which all the available names are placed in a container, the container is shaken, and the names of the "winners" or participants are then drawn out in an unbiased manner.

What is Simple random sampling?

The Simple random sampling is a sampling technique in which every member of the population has an equal chance of being chosen as a sample. The samples are chosen randomly, without any specific criterion. In this method, the selection of individuals for the sample is done without any specific pattern. This means that each member of the population is equally likely to be selected as a sample.In Simple random sampling, each member of the population is assigned a number, and the samples are selected using a random number generator or drawing names out of a hat. The selected samples are then analyzed to make predictions about the entire population.For example, if a researcher wanted to know the average age of students in a school, they might use Simple random sampling to choose a sample of 50 students. The researcher would assign each student a number and then use a random number generator to select the samples.There are some advantages and disadvantages of Simple random sampling, which are listed below:Advantages of Simple random sampling It is easy to understand and conduct the process.Each member of the population has an equal chance of being selected as a sample.It ensures that the sample is representative of the entire population.Disadvantages of Simple random sampling It can be time-consuming to select the samples.There may be a chance of human error when selecting samples.The sample size may not be large enough to draw meaningful conclusions.

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Answer:

I got 162?

Step-by-step explanation:

I broke down each individual shape (7 rectangles and 2 triangles) and used each shapes surface area formula.

triangle surface area formula is 1/2*b*h, and there are 2 of the same triangles of the exact same size and 7 rectangles. 3 are same size rectangles, 2 are same size rectangles and the other 2 are different sized rectangles. Then add altogether.

Probability of the number being part of A∩B= 2/9

The Venn diagram, a style of diagram that illustrates the logical connection between sets, was created by John Venn in the 1880s. The examples are used to illustrate fundamental set connections and introduce basic set theory in the fields of probability, logic, statistics, linguistics, and computer science.

A Venn diagram is a type of visual representation that uses circles to show the relationships between various items or constrained groups of objects. Circles that coincide and those that intersect have certain properties in common. Venn diagrams are helpful for visually illustrating the relationship and differences between two ideas.

The probability of an occurrence is a figure used to indicate the likelihood that the event will occur. It is expressed as a figure between 0 and 1, or between 0% and 100%, when expressed as a percentage. The likelihood that the occurrence will occur increases with the probability.

In this question,

A∩B= 4,9

Probability of the number being part of A∩B= 2/9

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Ty made more money in tips on night 5 than usual because $49 is more than the standard $22 tip level.

A mathematical statement that demonstrates the equality of two expressions is known as an equation. Mathematical operations like addition, subtraction, multiplication, and division may be used, and it frequently involves one or more variables that are represented by letters. Equations are employed in a variety of mathematical and scientific contexts, from the solution of straightforward algebraic problems to the modeling of intricate physical systems. Finding the values of the variables that equalize both sides of the equation is necessary to solve an equation.

given

On night 5, he received the following in tips:

Total tips: ($23 + $29 + $25 + $16) multiplied by the sum of the tips from the first four nights equals $22 * 5.

Ty made more money in tips on night 5 than usual because $49 is more than the standard $22 tip level.

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Answer:

Step-by-step explanation:

Table of values:

x y

-2 5

-1 3/2

0 1

1 1/2

2 1

We may solve for y by substituting the supplied  values of x into the equation [tex]y=1/2x3-2x+1[/tex] and completing Table of values .

For instance,[tex]y=1/2(-2)3-2(-2)+1[/tex] Equals 5 when[tex]x=-2.[/tex] The equivalent values of y for x=-1, 0, 1, and 2 are similarly found.

The ordered pairs (x,y) that fulfil the equation are displayed in the resultant table. These points allow us to graph the equation and see how the curve looks. In this instance, the equation describes a cubic function with two turning points at (-1,3/2) and (1,1/2), as well as a horizontal intercept at (0,1).

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The volume of the solid whose base is the region inside the circle with radius 3 if the cross sections taken parallel to one of the diameters are equilateral triangles is 81/2*\sqrt3 by using the slicing method.

To find the volume of the solid whose base is the region inside the circle with radius 3, we need to integrate the area of the cross sections taken parallel to one of the diameters, which are equilateral triangles.

Let's consider a cross section of the solid taken at a distance x from the center of the circle.

Since the cross section is an equilateral triangle, all its sides have the same length.

Let  this length be y. Since the triangle is equilateral, its height can be found using the Pythagorean theorem as follows:

[tex]height = \sqrt{(y^2 - (y/2)^2)} = \sqrt{(3/4y^2)}= \sqrt{3/2y}[/tex]

Therefore, the area of the cross section at a distance x from the center of the circle is:

[tex]A(x) = (1/2)y\sqrt{3/2y} = \sqrt{3/4y^2}[/tex]

Now, we need to integrate this area over the range of x from -3 to 3 (since the circle has radius 3):

[tex]V = \int\ [-3,3]\sqrt{3/4*y^2} dx[/tex]

To find the limits of integration for y, we need to consider the equation of the circle:

[tex]x^2 + y^2= 3^2[/tex]

Solving for y, we get:

[tex]y =\pm\sqrt{(3^2 - x^2)}=\pm\sqrt{(9^2 - x^2)}[/tex]

Since we want the cross sections to be equilateral triangles, we know that y is equal to the height of an equilateral triangle with side length equal to the diameter of the circle, which is 2*3 = 6. Therefore, we can write:

[tex]y = 3*\sqrt{3}[/tex]

Substituting this into the integral, we get:

[tex]V = \int\ [-3,3] \sqrt{3/4*(3\sqrt3)^2} dx[/tex]

[tex]= \int\ [-3,3] 27/4*\sqrt{3} dx[/tex]

Integrating, we get:

[tex]V = [27/4\sqrt{3x}]*[-3,3][/tex]

[tex]= 81/2*\sqrt{3}[/tex]

Therefore, the volume of the solid is [tex]81/2*\sqrt3[/tex]cubic units

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The line of best fit for the data is approximately y = -1.07x + 92.87: A) True.

In order to determine a linear equation for the line of best fit that models the data points contained in the table, we would have to use a graphing calculator (scatter plot).

In this scenario, the latitude would be plotted on the x-axis of the scatter plot while the average temperature would be plotted on the y-axis of the scatter plot.

On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the latitude and average temperature, a linear equation for the line of best fit is given by:

y = -1.07x + 92.87

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The cookers at healthy Bakery could make 323 bagels in 17 hours, and their rate is 19 bagels according to hour.

To find out how many bagels the cookers could make in 17 hours, we will use the unitary method, which involves finding the rate at which the cookers can make bagels and additionally multiplying that price through the wide variety of hours labored.

Let the rate at which the cookers can make bagels be r bagels in line with hour. We also can set up the subsequent share

190 bagels/ 10 hours = r bagels 1 hour

Simplifying this proportion, we get

r = 190 bagels/ 10 hours

r = 19 bagels/ 1 hour

So the cookers can make 19 bagels in keeping with hour.

To find out how many bagels they could make in 17 hours, we can multiply the rate via the number of hours

19 bagels/ hour × 17 hours = 323 bagels

Therefore, the cookers at healthy Bakery could make 323 bagels in 17 hours, and their rate is 19 bagels according to hour.

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We can plot the lines x = 260, y = 320, and x + y = 380 to graph these limitations, and we can highlight the area that satisfies each requirement.

We refer to x and y as being limited by g(x,y)=c, which is also referred to as the constraint equation. Constrained maximum or constrained minimum points, respectively, are positions (x,y) that meet the constraint equation g(x,y)=c and are maxima or minima of f(x,y).

Let's indicate the quantity of black walnut and mahogany boards sold, respectively, using the variables x and y.

x ≤ 260 (constraint on the number of mahogany boards)

x + y ≤ 380 (constraint on the total number of boards sold)

y ≤ 320 (constraint on the number of black walnut boards)

We also understand that the quantity of sold boards cannot be zero, hence we have:

x ≥ 0

y ≥ 0

Last but not least, our goal is to maximise profit, as indicated by the expression:

P = 20x + 6y

When all the restrictions are combined, the following inequality system results:

x ≤ 260

y ≤ 320

x + y ≤ 380

x ≥ 0

y ≥ 0

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X = 2 is the solution of  the given equation for "x".

What does a math equation mean?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. For instance, 3x + 5 = 14 is an equation where 3x + 5 and 14 are two expressions separated by the 'equal' sign.

                           A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. By solving for x, we discover that x equals 7, which is the value for the variable.

8ˣ = (25)

 8ˣ =  (5)²

  X = 2

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Answer:

The answer is 4

Step-by-step explanation:

yeeeeeeeee

Answer:

4

Step-by-step explanation:

25% of 16

Change the percent to decimal form.

.25 * 16

4

The length of BC is approximately 3.5 cm

A triangle is described as a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.

We construct triangle ABC, through the following steps:

The law of sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.

Mathematically shown as:

a/sin(A) = b/sin(B) = c/sin(C)

5/sin(95) = BC/sin(34)

BC = (5*sin(34))/sin(95)

BC ≈ 3.5cm

In conclusion, the length of BC is approximately 3.5 cm.

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The following statements correctly describe how the graph of the geometric sequence: 640, 160, 40, 10, ... should appear:

The given sequence is 640, 160, 40, 10, ... which is a geometric sequence.

Here, the first term is 640 and the common ratio is ¼

The terms of a geometric sequence can be written as an = a₁(r)⁽ⁿ⁻¹⁾

Here, a₁ = 640, and r = ¼.

Hence, the nth term of the given sequence is given by the formula:

an = 640(1/4)⁽ⁿ⁻¹⁾

The graph of the given sequence will appear as shown below:

The given sequence is a decreasing sequence, which means the terms of the sequence keep decreasing as the value of n increases.

Therefore, the graph will show exponential decay.

The domain of the sequence will be the set of natural numbers, which is {1, 2, 3, ...}, since we cannot find any term before the first term.

Therefore, the first term is the initial term and we can count the other terms of the sequence in natural numbers.

Hence, the domain will be the set of natural numbers.

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Answer:

the graph will show exponential decay.

the domain will be the set of natural numbers.

Step-by-step explanation:

The answer above is correct.

Twice a number decreased by four is less than 8 is x< 6.

2x - 4 < 8

2x < 8 + 4

2x < 12

x < 12 / 2

x < 6

Inequality refers to the unequal distribution of resources, opportunities, and outcomes among individuals or groups in a society. It can manifest in various forms, including economic inequality, social inequality, gender inequality, and racial inequality. Economic inequality refers to the unequal distribution of wealth and income, where some individuals or groups have access to more resources and opportunities than others.

Social inequality refers to the unequal distribution of social status and power, which can lead to marginalized groups being excluded from certain societal benefits. Gender and racial inequality refer to the unequal treatment and opportunities that certain genders or races face in society. Inequality can have negative consequences on individuals and society, including lower levels of social trust, reduced economic growth, and increased social tensions.

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Complete Question: -

Twice a number decreased by four is less than 8 is equation or inequality

The expression that shows the measurement of the length of the land is L = 3x - 10a.

Let L be the length of the rectangular plot.

We know that the perimeter of a rectangle is given by the sum of the lengths of all its sides. In this case, the perimeter is 10x - 28a, so we can write:

Perimeter = 2L + 2W

10x - 28a = 2L + 2(2x - 4a)

10x - 28a = 2L + 4x - 8a

2L = 6x - 20a

L = 3x - 10a

In other words, the length of the land is equal to three times the width minus ten times the value of 'a'.

To explain this equation in a little more detail, we can say that the length of the rectangular plot is dependent on both the width of the land and the value of 'a'.

The expression tells us that as the value of 'a' increases, the length of the land decreases, and as the width of the land increases, the length of the land also increases. This equation is useful because it allows us to calculate the length of the land without having to measure it directly, as long as we know the value of 'a' and the width of the land.

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Answer:

  true

Step-by-step explanation:

You want to know if weight and self-esteem have a negative correlation if an increase in weight causes self-esteem to go down (the slope is negative).

The slope of the line of best fit has the same sign as the correlation coefficient. The magnitude of the correlation coefficient is the ratio of the covariance to the product of the standard deviations of the variables.

It is true that the weight and self-esteem have negative correlation.

Check the picture below.

Using percentages we know that the markup price of the pair of shoes will be $6.3.

In mathematics, a percentage is a number or ratio that is expressed as a fraction of 100.

Although "pct," "pct," and occasionally "pc" are also used as abbreviations, the percent symbol "%" is most usually used to denote it.

A% is a number that has neither dimensions nor a defined unit of measurement.

When expressing a proportionate share of a total, percentages are frequently utilized.

(Similarly, the term "per mille" or the sign "%" can be used to denote a number as a fraction of 1,000.)

So, the market price of the store would be:

= 4.50/100 * 40

= 0.045 * 40

= 1.8

Markup price: 1.8 + 4.5 = $6.3

Therefore, using percentages we know that the markup price of the pair of shoes will be $6.3.

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Each subsequent jump will be exactly one unit longer in length than the one before it after the initial jump, which can be one unit in length. Each jump has the option of going either left or right.

The translation of the question is

A robot jumps on a number line starting at zero. The rules of the game are the following if you look at your right hand, the length of each jump is expressed with a positive number and, if facing your left hand, with a negative number.

Also: if you jump straight ahead (that is, in the direction you are facing), the number number of jumps is expressed as a positive number, and if you jump backwards (i.e., on the opposite direction to the one you are looking at), the number of hops is considered with a negative number. Observe the following jumps of the robot, its final position in each case and answer in your notebook the questions

When closely examined, it is simple to conclude that:

If you have consistently jumped in the appropriate direction, you will arrive at point p = 1 + 2 + 3 + 4 +... + n after n jumps.

You would be at point p - 2k in any of these n leaps if you leapt left in the kth hop (k=n) rather than right.

Moreover, after n leaps, you can be anywhere between n * (n + 1) / 2 and -(n * (n + 1) / 2) with the same parity as n * (n + 1) / 2 by carefully selecting which jumps to go left and which to go right.

The trick is to imitate jumping while keeping the aforementioned facts in mind. Always jump to the right, and if at some time you arrive at a location that has the same parity as X and is at or beyond X, you'll know the answer.

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A) x = 5 is not a linear function since it is a vertical line and does not have a slope. B) The table description does not provide enough information to determine if it is a linear function. C) x + 7 = 4y is a linear function in slope-intercept form (y = (1/4)x + 7/4).

A linear function is a mathematical function that can be represented by a straight line with a constant slope. The equation of a linear function can be written in the form y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis). Option A (x = 5) is not a linear function, as it is a vertical line with an undefined slope. Option B is a linear function, as the table describes points that can be plotted to form a straight line. Option C is also a linear function, but it is in a different form (x + 7 = 4y). This equation can be rearranged to y = (1/4)x + 7/4, which is in the standard form of a linear function.

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Answer: C.) x + 7 = 4y and  D

Step-by-step explanation: i hope this helps

The given statement is false becasue If the p-value of the coefficient of an X variable in a regression is 0.001, then it suggests that there is significant evidence that the coefficient is different from 0 in the population regression line.

A p-value is a value that represents the probability of obtaining the observed results of a statistical hypothesis test. The p-value is used as an alternative to rejection point to give the smallest level of significance at which the null hypothesis would be rejected. It can be used to test hypotheses in statistics.

If the p-value is less than the significance level (α), then the null hypothesis is rejected. However, if the p-value is greater than the significance level (α), then the null hypothesis is not rejected. Therefore, we reject the null hypothesis if the p-value is less than or equal to the level of significance.

So, if the p-value of the coefficient of an X variable in a regression is 0.001, it suggests that the coefficient is statistically significant and different from 0 in the population regression line. Hence, the statement "it is reasonable to say that the coefficient of the X variable is 0 in the population regression line" is false.

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After collecting the data, Maria found that the number of points per game for a particular basketball player is normally

with a mean of 14 points and a standard deviation of 2 points. Based on the empirical rule, what is the probability that the player scored less than 8 points in a randomly selected game?

To solve this problem, we'll need to use the formula for a standard normal distribution:z = (x - μ) / σwhere z is the standard score, x is the raw score, μ is the population mean, and σ is the population standard deviation. We'll need to calculate the standard score for x = 8, which gives us:[tex]z = (8 - 14) / 2z = -3.0[/tex]

Now, using the standard normal distribution table or calculator, we can find the probability that a randomly selected game results in a score less than 8 points. The area to the left of z = -3.0 is approximately 0.0013, which means that the probability of a randomly selected game resulting in a score less than 8 points is 0.0013 or 0.13%.Therefore, the probability that in a randomly selected game, the player scored less than 8 points is 0.13%.

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In Δ ABC and Δ PQR, if AB = PR, BC = RQ and AC = PQ, then Δ ABC is congruent to Δ PRQ, which means option D is the right answer.

The congruency theorem is used to determine the relation between two similar looking figures in two dimensional space. The word congruent itself means being in harmony. There are different rules which are used to determine the congruency between the triangles.

These rules are given as follows:

In the given question, it is given that sides AB = PR, BC = RQ and AC = PQ, this implies that the congruency can be setup using SSS rule, which if followed will suggest that Δ ABC will be congruent to Δ PRQ.

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(a) The solution to the differential equation isx(t) = 10(1 - e^(-0.005t))

To solve the differential equation dx/dt = 0.005(10 - x), we can use separation of variables:

dx / (10 - x) = 0.005 dt

Integrating both sides:

-ln|10 - x| = 0.005t + C

where C is the constant of integration. Solving for x:

|10 - x| = e^(-0.005t - C)

Since x cannot be negative, we can drop the absolute value sign and solve for C using the initial condition that x(0) = 0:

C = -ln(10)

Therefore, the solution to the differential equation is:

x(t) = 10 - e^(-0.005t - ln(10))

Simplifying:

x(t) = 10(1 - e^(-0.005t))

(b) New bills will make up 90% of the currency in circulation after approximately 461 days.

We want to find the value of t such that x(t) = 0.9(10) = 9. Plugging this into our solution from part (a):

9 = 10(1 - e^(-0.005t))

Dividing both sides by 10 and taking the natural logarithm:

ln(0.1) = -0.005t

Solving for t:

t = 200 ln(10) = 460.51

Therefore, new bills will make up 90% of the currency in circulation after approximately 461 days.

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Answer:

This graph shows a quadratic curve with roots 0 and -4

The polynomial is therefore

x² -x(α+β) + αβ

x² -x(0-4) + 0(-4)

x² +4x +0

x² + 4x

But it's an n-shaped curve, meaning a is negative

Multiply through by -1

-x² - 4x

y = -x² - 4x

So when the input value x = -1

y = -(-1)² + 4(-1)

y = -(1) - 4

y = -1 - 4

y = -3

Check the graph to confirm

Answer:

1/2 or .5

Step-by-step explanation:

If y is inversely proportional to the square of x, we can express this relationship using the formula:

y = k/x^2

where k is a constant of proportionality. We are told that y = 8 for a particular value of x, so we can substitute these values into the equation:

8 = k/x^2

To find the value of k, we can solve for it:

k = 8x^2

Now we are asked to find the new value of y when x increases by 300%. This means that the new value of x will be 4 times the original value (since an increase of 300% means an increase by a factor of 3, and we need to add the original value to get the new value). So we can substitute 4x for x in our equation:

y = k/(4x)^2 = k/16x^2

We already know the value of k, so we can substitute it in and simplify:

y = (8x^2)/(16x^2) = 1/2

Therefore, the new value of y is 1/2 when x increases by 300%.

Answer:

120 degrees

Step-by-step explanation:

The sum of the interior angles of a pentagon is given by the formula, where S is the sum of the interior angles, and n is the number of sides of the polygon:

S = (n - 2) × 180 degrees

For a pentagon, n = 5, so we have:

S = (5 - 2) × 180 = 540 degrees

If four of the angles are equal, we can let x be the measure of each of those angles. Then, we can write an equation for the sum of the angles:

4x + 60 = 540

Solving for x, we get:

4x = 540 - 60 = 480

x = 480/4 = 120

Therefore, each of the four equal angles in the pentagon has a measure of 120 degrees.

7. Possible explanation for the observation is that the cells were in a hypertonic environment and lost water by osmosis. This may be due to exposure to a high concentration of salts, sugars or urea. Cells may also become crenated when exposed to low temperatures

.8. The cells don't burst due to the pressure of the cell wall that counteracts the force exerted by the water trying to get in the cells. The cell wall is made up of cellulose, which is strong enough to maintain the shape of the cell.

9. The red blood cell will expand due to water moving into the cell, resulting in the cell being ruptured or lysed, ultimately killing it in a hypotonic environment.

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