a survey was conducted on 218 undergraduates from duke university who took an introductory statistics course in spring 2012. among many other questions, this survey asked them about their gpa and the number of hours they spent and studying per week. based on this study, can we conclude that studying longer hours leads to higher gpas?

A function that gives the total cost, C in dollars, to be a member of the gym given the number of months, m is C = 7.99m + 30

The table that shows the total cost to be a member of the gym for different numbers of months is:

Number of Months     Total Cost

           3                        $53. 97

          6                         $77. 94

          12                        $125. 88

The rate of change of total cost per month would be,

m = [tex]\frac{77. 94-53. 97}{6-3}\\\\[/tex]

m = 7.99

so, the function for the total cost would be,

C = 7.99m + d          .......(1)

where d is the fixed cost of the gym

For m = 3, C = 53.97

53. 97 = 7.99m + d

53. 97 = 7.99(3) + d

d = 30

So, function (1) would be,

C = 7.99m + 30

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A. On the sixth day, the plant grows to 64 times its original height.

B. On the nth day, the plant would  [tex]2^n[/tex] time its original height.

A. From the given condition we can that the growth of the plant shows a geometric progression with a first term of 2 and a common ratio of 2.

On the first day, the plant grows to [tex]2^1[/tex] = 2 times its original height.

On the second day, the plant grows to [tex]2^2[/tex] = 4 times its original height.

Similarly, on the sixth day, the plant grows to [tex]2^6[/tex] = 64 times its original height.

B. The nth term of the progression can be calculated by multiplying the first term by the common ratio raised to the power of n-1.

In this case, the first term is 2 and the common ratio is 2. So the nth term is [tex]2 * 2^{n-1} = 2^n[/tex]

Hence, on the nth day, the plant grows to [tex]2^n[/tex] times its original height.

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Step-by-step explanation:

this creates a right-angled triangle 2.5 ft above the ground.

the string is the Hypotenuse (the side opposite to the 90° angle). the air distance to the height of the kite is one leg, and the height of the kite minus the 2.5 ft is leg 2.

in the trigonometric triangle the up/down side is sine (multiplied by the Hypotenuse or radius of the circle) of the angle at the center of the circle. and the left/right side is cosine (again multiplied by the Hypotenuse or radius) of the angle.

so, the height of the kite above ground is

105×sin(28°) + 2.5 = 51.79451409... ≈ 51.79 ft.

Answer:

1750 BOOKS

Step-by-step explanation:

Answer:

There were a total of 14 books on Friday and 2396 on Saturday to find the total amount sold on both days you will add the two together.

1,461 + 2,396 = 3,857

A. There were a total of 3, 857 books sold on both days.

To find how many more books were sold on Saturday than Friday, youn will subtract.

2,396 - 1,461 = 935

B. 835 more books were sold on Saturday than Friday.

Step-by-step explanation:

Hope it helps! =D

A conversion of this equation in standard form to slope-intercept is y = 4x/5 - 3.

In Mathematics, the slope-intercept form of a line can be calculated by using this linear equation:

y = mx + c

Where:

Based on the information provided about the line, it is represented by this equation;

8x + 10y = -30

Making y the subject of formula in the above equation, we have the following:

10y = 8x - 30

y = 8x/10 - 30/10

y = 4x/5 - 3

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Answer:

C

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

It could only represent large colleges, not all colleges.  Sampling requires similar characteristics to represent the entire population of testing.

The solution of the given equation is 1.6. It has been represented and solved as a real-world problem below.

The given equation is = - 20 + 2x5 = 4

We can rewrite this equation as = - 4 + 2x5 = 20

Let us suppose that person A has x number of bananas that they have taken out from a stock full of bananas. They continue taking x number of bananas two more times. They then stop and see that person B has already taken 4 bananas from the stock. We can write this equation as -

= 4 + 2x

Person A saw knew that there were 20 bananas in total. So, we can write it as -

= 4 + 2x = 20

Person A then resumed and took x number of bananas again 5 more times. We can rewrite this as -

= 4 + 2x5 = 20

Solving this equation, we get -

= 4 + 10x = 20

= 10x = 20-4 = 16

= x = 16/10

= x = 1.6

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Answer:

b

Step-by-step explanation:

One of the most important things to do to protect endangered animals is to reduce the amount of habitat destruction caused by human activities.

This can be done by creating protected areas and limiting or banning activities like logging, mining, or development in sensitive areas. Additionally, it is important to reduce over-hunting and poaching of these animals. This can be accomplished by establishing quotas and strict regulations on allowable hunting and fishing, as well as increasing enforcement efforts to catch violators. It is also important to understand the life cycles and behaviors of the threatened species so that we can better protect them. This can be done through field research, monitoring, and analyzing population trends. Finally, it is important to develop conservation plans and strategies to protect the species. These could include habitat restoration, reintroduction programs, captive breeding, and other measures to ensure their survival.

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The negative values, zero and the positive numbers lesser than 12 and equal to twelve are solutions of inequality.

A relationship between two expressions or values that are not equal to each other is called 'inequality.

We need to find the solutions for the inequality k≤12

k lesser than or equal to twelve.

Which means the solution of the inequality are the values which are lesser than or equal to 12.

The solution of the inequality k≤12 is (-∞, 12]

All the negative values, zero and the positive numbers lesser than 12 and equal to twelve are solutions of inequality.

Hence,  the negative values, zero and the positive numbers lesser than 12 and equal to twelve are solutions of inequality.

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Answer:

Multiply all of the terms of each polynomial and then combine like terms. Example: Multiply: ( 2 x 2 + x − 3 ) ( x 2 − 2 x + 5 ) . Solution: Multiply each term of the first trinomial by each term of the second trinomial and then combine like terms.

Step-by-step explanation:

Σ^n=1 -144 (1/2)n-1

This is a finite geometric series with n

=4, a₁-144, and r = 2.

S = a₁ (1-r") / (1 − r)

S-144 (1 - (1/2)) / (1 - 1/2)

S=-270

If you wanted to find the infinite sum (n

= ∞0)

:S = a₁ / (1 − r)

S-144/(1-1/2)

S=-288

Answer:

To graph the inequality y ≤ x - 2 on the axes, you would:

Plot the line y = x - 2 on the graph. The line will be a straight line passing through the point (-2,0) and has a slope of 1.

Determine the direction of the inequality symbol. Since it is a less-than-or-equal-to symbol, we will shade the region that is less than or equal to the line.

Shade the region that is less than or equal to the line in the graph. In this case, the region above the line y = x - 2.

The line is solid, it's not dotted.

Note: The graph will be a straight line that is tilted towards the top right of the coordinate axes, the region above the line will be shaded.

Step-by-step explanation:

Answer:

give me brainlist please

Step-by-step explanation:

We can use the formula for conditional probability and the formula for the probability of the union of events to find P(C).

Using the formula for conditional probability, we can find P(A|B) = P(A n B) / P(B) = 0.05 / 0.26 = 0.192

Using the formula for conditional probability again, we can find P(A|C) = P(A n C) / P(C) = 0.05 / P(C)

Since A and C are independent events, we know that P(A|C) = P(A), so we can write:

0.05 / P(C) = 0.24

Solving for P(C) we get P(C) = 0.05/0.24 = 0.208

Alternatively, we can use the formula for the probability of the union of events:

P(A u B u C) = P(A) + P(B) + P(C) - P(A n B) - P(A n C) - P(B n C) + P(A n B n C)

We know that P(A u B u C) = 1 - P((A u B u C)^/) = 1 - 0.33 = 0.67

and we know the values of P(A), P(B), P(A n B), P(A n C), P(B n C), P(A n B n C)

We can substitute these values into the above equation to find P(C)

P(C) = 0.67 - 0.24 - 0.26 + 0.05 + 0.05 + 0.05 - 0.02 = 0.208

So P(C) = 0.208

Answer:

Slope is 3.5

There is a proportional relationship between the variables x and y

The other statements are false.

The slope is 3.5, not 7

A linear relationship is the same a proportional relationship so statement 4 is always false

The graph does pass through (0, 0)

Step-by-step explanation:

Consider the first 2 pairs of coordinates, (2, 7) and (6, 21);

The increase in x is from 2 to 6, i.e. an addition of 4, the increase in y is from 7 to 21, i.e. an addition of 14;

Now consider the the 2nd and 3rd pairs of coordinates, (6, 21) and (8, 28);

The increase in x is from 6 to 8, i.e. an addition of 2, the increase in y is from 21 to 28, i.e. an addition of 7;

So, with the first 2 pairs of coordinates, an increase of 4 in x resulted in an increase of 14 in y and with the second 2 pairs of coordinates, an increase of 2 in x resulted in an increase of 7 in y, i.e. (+4, +14) and (+2, + 7);

2 × (+2, +7) = (+4, 14)

Or:

(+4, +14) ÷ 2 = (+2, +7)

This means a line from the 1st point to the 2nd point and a line from the 2nd point to the 3rd point will have the same gradient:

To find the slope simple, find the increase in y resulting from an increase of 1 in x, so:

(+2, +7) ÷ 2 = (+1, +3.5)

The gradient (or slope) is 3.5;

If there is a line with a fixed gradient that passes through all the points, then the relationship is proportional, also linear;

This is the case for this question;

If we follow the pattern backwards as well, so the point:

(2, 7) - (+2, +7) = (0,0)

This means (0,0) lies on the line.

(0,0), (2, 7), (4, 14), (6, 21), (8, 28), (10, 35), (12, 42), (14, 49), etc.

All these points would lie on the line, just add 2 to x, add 7 to y;

You would find the same points plus others by the rule, add 1 to x, add 3.5 to y.

The procedure that cannot be used are:

A. Knowing that 3² + 4² = 5², draw any two sides with a right angle between them. The third side will fit to form a right triangle.

B.

Knowing that 3 + 4 > 5, draw the 3 cm side and the 4 cm side with a right angle between them. The 5 cm side will fit to form a right triangle.

C.

Knowing that 3 + 5 > 6, draw the 3 cm side and the 5 cm side with a right angle between them. The 6 cm side will fit to form a right triangle.

The Pythagorean theorem states that the result obtained by squaring the value of the hypotenuse of a right angled triangle is equal to the sum of the squares of the values other two sides of the triangle.

The hypotenuse of a a given triangle is usually longer that the other two sides.

Therefore, the correct procedure when lengths such as 3 cm, 4 cm, 5 cm, and 6 cm should be knowing that 3² + 4² = 5², draw the 3 cm side and the 4 cm side with a right angle between them. The 5 cm side will fit to form a right triangle.

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The given graph is represented by the following inequalities (C) y ≤ 2x − 2, y > −x + 3.

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way.

The majority of the time, size comparisons between two numbers on the number line are made.

If an inequality matching y > -ax + b is solved, area A will be shaded above a dashed line with a negative slope.

Such inequality exists between Options A and C.

The solution of an inequality that fits y ax + b will be below a solid line with a positive slope where region B is shaded (for some positive a).

The only option with the correct inequality symbol is Choice C.

We discover that choice C matches the graph when we closely examine it.

Region A matches y > -x+3 because the line with a negative slope has a slope of -1 and a y-intercept of 3.

Region B corresponds to y 2x -2 because the line with a positive slope has a slope of +2 and a y-intercept of -2.

Therefore, the given graph is represented by the following inequalities (C) y ≤ 2x − 2, y > −x + 3.

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Correct question:

In the graph, the area above f(x) is shaded and labeled A, the area below g(x) is shaded and labeled B, and the area where f(x) and g(x) have shading in common is labeled AB.

Graph of two intersecting lines. The line g of x is solid, and goes through the points 0, negative 2 and 1, 0 and is shaded in below the line. The other line f of x is dashed, and goes through the points 0, 3, 3, 0 and is shaded in above the line.

The graph represents which system of inequalities?

Group of answer choices

a. y > 2x − 3

y > −x − 3

b. y < 2x − 2

y < −x + 3

c. y ≤ 2x − 2

y > −x + 3

d. None of the above

The factorization of the given expression is p(4p-12q+qp).

The factorization method uses basic factorization formula to reduce any algebraic or quadratic equation into its simpler form, where the equations are represented as the product of factors instead of expanding the brackets. The factors of any equation can be an integer, a variable, or an algebraic expression itself.

The given expression is 4p²-12pq+qp².

Group and factor out the greatest common factor (GCF), then combine.

Here, the greatest common factor of the terms is p

Now, p(4p-12q+qp)

Therefor, the factorization of the given expression is p(4p-12q+qp).

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8) The Length of major arc MQN is; ⁵/₄πr

Length of minor arc MPN is; ³/₄πr

9) Length of major arc HJK is; ¹³/₁₅πr

Length of minor arc MPN is; ⁴/₁₅πr

The formula that is used to find the length of an arc is;

L = (θ/360) * 2πr

where;

L is length of arc

θ is central angle

r is radius

8) We are not given the radius and as such;

Length of major arc MQN = (225/360) * 2πr

= ⁵/₄πr

Length of minor arc MPN = ((360 - 225)/360) * 2πr

= ³/₄πr

9) Length of major arc HJK = (312/360) * 2πr

= ¹³/₁₅πr

Length of minor arc MPN = ((360 - 312)/360) * 2πr

= ⁴/₁₅πr

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After reflection over the x-axis the ordered pair is at (-4, 7).

When two different media come together at an interface, a wavefront might change direction so that it returns to the first medium, which is known as reflection.

When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the x-axis is (x, -y).

Here,

The reflection of point (-4, 7) across the x-axis is (-4, -7).

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The sum between the functions:

f(x) = 3x² - 2x + 6

g(x) = 7x - 4

is (f + g)(x) = 3x² + 5x + 2

Here we have two functions which are:

f(x) = 3x² - 2x + 6

g(x) = 7x - 4

And we want to add these to get f + g,  so we only need to add the two functions, we will get:

f(x) + g(x) = (3x² - 2x + 6) + (7x - 4)

Grouping like terms we will get:

(3x² - 2x + 6) + (7x - 4) = (3x²) + (-2x + 7x) + (6 - 4)

And now we can simplify that to get:

(3x²) + (-2x + 7x) + (6 - 4) = 3x² + 5x + 2

The sum is:

(f + g)(x) = 3x² + 5x + 2

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The unit cost of an apple and a pear are $1.27 and $1. 98 respectively.

Algebraic expressions are defined as expressions that comprises of variables, factors, constants, terms and coefficients.

They are also made up of arithmetic operations like;

From the information given, we have that;

Let the apples be x

Let the pears by y

2x + 3y = 2.40

5x - 3y = 6.5

Let's solve the simultaneous equation

-1(2x + 3y = 2.40)

-2x - 3y = -2. 40

5x - 3y = 6.5

-2x - 5x = -2. 40 - 6.5

-7x = -8.9

x = $1.27

substitute the value for y

-2y -5(1.27) = -2.40

y = $1. 98

Hence, the values are $1.27 and $1. 98

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The total distance from the starting point is 7.21 miles

Now, According to the question:

The movements are represented as:

[tex]N_1= 1miles\\E_1= 2miles\\\\N_2 =3 miles\\\\E_2 = 4miles[/tex]

To find the distance from the starting point.

First, calculate the total distance towards North.

[tex]N = N_1+N_2[/tex]

N = 1 + 3

N = 4 miles

Next, calculate the total distance towards East

[tex]E = E_1+E_2[/tex]

E = 2 + 4

E = 6 miles

The total distance from the starting point is calculated using Pythagoras theorem.

[tex]D^2=N^2+E^2[/tex]

[tex]D^2[/tex] = [tex]4^2+6^2[/tex]

[tex]D^2[/tex] = 16 + 36

[tex]D^2 =[/tex] 52

[tex]D = \sqrt{52}[/tex]

D = 7.21

Hence, The total distance from the starting point is 7.21 miles

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The inverse of the function will be x=(4y-2)/(y+2) where x is the inverse of the function given in i.

What is a function?

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).

There are several types of functions in math. Some important types are:

Injective function or One to one function: When there is mapping for a range for each domain between two sets.

Surjective functions or Onto function: When there is more than one element mapped from domain to range.

Polynomial function: The function which consists of polynomials.

Inverse Functions: The function which can invert another function.In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x.

Now,

As given

f(x)=2(x+1)/4-x

from here x will be inverse of the function

Therefore

y(4-x)=2x+2

4y-yx=2x+2

4y-2=x(y+2)

x=(4y-2)/(y+2)

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The evaluation of the equation to find the value of n in the rational function [tex]\frac{1}{n^2} + \frac{1}{n} = \frac{1}{2\cdot n^2}[/tex] is; n = -1/2

A rational function is a function that contains rational fractions, such that the dividend and the divisor are polynomial expressions.

2) The specified rational equation or function can be presented as follows;

The above equation consists of rational expressions. The expressions can be resolved by collecting like terms as follows;

The like terms are terms that can be resolved by simple addition or subtraction.

1/n = 1/(2·n²) - 1/(n²) = (1 - 2)/(2·n²) = -1/(2·n²)

1/n = -1/(2·n²)

Multiplying both sides by n, we get;

(1/n) × n = (-1/(2·n²)) × n

(1/n) × n = 1 = (-1/(2·n))

1 = (-1/(2·n))

Multiplying both sides by n, we get;

1 × n = (-1/(2·n)) × n

n = -1/2

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A linear equation - y = 5x -7 is a slant line with intercepts for linear equations. A vertical line is x = 2. A line that runs through the origin is y = 3/4x.

A slant line with intercepts is y = 1/2x + 3. A horizontal line is y = 9. The line x = -1 runs vertically.

A direct condition is one that has a level of 1 as its most extreme worth. As a result, there is no variable in a linear equation with an exponent greater than 1. The graph of a linear equation will always be straight.

This line is not horizontal or vertical when the equation is graphed; rather, it is slant.

Additionally, this line does not traverse the origin. As a result, this equation has intercepts and slant lines.

Since there is no y-intercept in this equation, it will be a vertical line that runs parallel to the y-axis.

Additionally, this line does not traverse the origin. As a result, this equation has a line that runs vertically.

This line is not horizontal or vertical when the equation is graphed; rather, it is slant.

Additionally, this line actually traverses the origin. As a result, the origin of this equation is traversed by slant lines.

This line is not horizontal or vertical when the equation is graphed; rather, it is slant.

Additionally, this line does not traverse the origin. This equation is therefore a slant line with intercepts.

Since there is no x-intercept in this equation, it will be a horizontal line that runs parallel to the x-axis.

Additionally, this line does not traverse the origin. As a result, there is a horizontal line in this equation.

Since there is no y-intercept in this equation, it will be a vertical line that runs parallel to the y-axis.

Additionally, this line does not traverse the origin. As a result, this equation has a line that runs vertically.

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The largest exterior angle of hexagone is 108°.

Given that exterior angle of a hexagon are x, 3x, 4x, 5x, 8x and 9x.

Exterior angles are those that run parallel to a polygon’s inner angles but are located outside of polygon.

We know that sum of exterior angle of any polygon is 360°.

So, sum of exterior angle of hexagon will be 360°.

x + 3x + 4x + 5x + 8x + 9x = 360°

30x = 360°

x = 360° / 30

x = 12°

Now the largest angle = 9 * 12 = 108°

Therefore, the largest angle of hexagon is 108°.

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The answer to each question are:

a). probability of an insect of this type surviving its first day is 0.8

b). probability of an insect of this type surviving it's first three days is 0.512.

c). probability of an insect of this type dying on its fourth day is 0.2.

d). If 200 insects of this type are being studied in a laboratory, 102 to be alive after the third day.

What is the probability?

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are.

a). The probability that an insect of this type survives its first day is 1 - 0.2 = 0.8.

b). The probability that an insect of this type survives it's first three days is 0.8 * 0.8 * 0.8 = 0.512.

c). The probability that an insect of this type dies on its fourth day is 0.2.

d). The expected number of days that an insect of this type would survive is not determinable with the information given.

e). If 200 insects of this type are being studied in a laboratory, you would expect approximately 200 * 0.512 = 102.24 to be alive after the third day. Round down to 102 insects.

Hence, The answer to each question is:

a). probability of an insect of this type surviving its first day is 0.8

b). probability of an insect of this type surviving it's first three days is 0.512.

c). probability of an insect of this type dying on its fourth day is 0.2.

d). If 200 insects of this type are being studied in a laboratory, 102 to be alive after the third day.

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