Pls answer quickly, make sure to answer all parts
Find the area of the region bounded by the line y =3x -6 and line y=-2x+8 and
a) the x-axis. b) the y-axis. c) the line y=6. d) the line x=5.

The average rate of change over the interval [3,4] is given as follows:

3.

The average rate of change of a function is given by the change in the output divided by the change in the input.

The numeric values for the ends of the interval are given as follows:

Then the change in the output is of:

32 - 29 = 3.

The change in the input is of:

4 - 3 = 1.

Hence the rate is of:

r = 3/1

r = 3.

More can be learned about the average rate of change of a function at brainly.com/question/11627203

#SPJ1

The transformation that fully transforms Shape A to Shape C is reflected in the x =6.5

There are two ways of reflection.

Along x-axis:

(x, y) – (x, -y)

Along y-axis:

(x, y) - (-x, y)

We have,

The line x = 2, x = 6, and x = 6.5 is given on the graph below.

Shape A is reflected in the line with equation x = 2 to get Shape B.

Shape B is reflected in the x = 6 to get Shape C.

Now,

Shape A is reflected in the x =6.5 to get Shape C.

Thus,

The transformation that fully transforms Shape A to Shape C is reflected in the x =6.5

Learn more about reflections here:

https://brainly.com/question/12463306

#SPJ9

Option B : The market for DVDs is described by a downward sloping demand curve and an upward sloping supply curve. The price ceiling of $12 per DVD will result in a shortage of DVDs.

In a competitive market, the market price of a good will be set at the intersection of the demand curve and the supply curve. This is the point where the quantity of the good that consumers are willing to buy at a given price is equal to the quantity that producers are willing to sell. At this market price, producer surplus is equal to the area above the supply curve and below the market price, up to the quantity supplied.

In this scenario, the producer surplus will be equal to the area between the supply curve and the price ceiling, up to the quantity that is supplied. Based on the diagram, the producer surplus will be equal to $900,000.

So, the answer to the question is $900,000.

To learn more about price ceiling please click on below link        

https://brainly.com/question/28018539

#SPJ4

The above figure shows the market for DVDs. The government decides that all citizens deserve to watch affordable DVDs so a price ceiling of $12 per DVD is placed on DVDs. After this price ceiling is in effect, producer surplus equals ________.

A. $1,800,000

B. $900,000

C. $400,000

D. $200,000

E. $100,000

Answer:

The sum of all numbers between 1 and 100 that are divisible by 4 or 7 can be found by using the concept of multiples. First, let's find all the multiples of 4 between 1 and 100. These are 4, 8, 12, 16, ..., 96. To find the number of multiples of 4 between 1 and 100, we can divide 100 by 4 and round down to the nearest whole number. That gives us 25. So, we have 25 multiples of 4 between 1 and 100.

Next, let's find all the multiples of 7 between 1 and 100. These are 7, 14, 21, 28, ..., 98. To find the number of multiples of 7 between 1 and 100, we can divide 100 by 7 and round down to the nearest whole number. That gives us 14. So, we have 14 multiples of 7 between 1 and 100.

Now we need to add up all the multiples of 4 and 7, but we have to make sure not to count any number twice, since some numbers may be divisible by both 4 and 7. For example, 28 is divisible by both 4 and 7. To avoid double counting, we need to find the multiples of 4 * 7 = 28. These are 28, 56, 84. There are 3 multiples of 28 between 1 and 100. So, we subtract these 3 numbers from the sum of all multiples of 4 and 7.

Finally, the sum of all numbers between 1 and 100 that are divisible by 4 or 7 is:

(4 + 8 + 12 + ... + 96) + (7 + 14 + 21 + ... + 98) - (28 + 56 + 84)

= (4 * 25) + (7 * 14) - (28 * 3)

= 100 + 98 - 84

= 114

So, the sum of all numbers between 1 and 100 that are divisible by 4 or 7 is 114.

The percentage of the atmosphere made up of element 2 is 17%.

According to its definition, a percentage is any number relative to 100. It is shown with the sign %. "Out of 100" is what the percentage means. Consider dividing any quantity or item into 100 identical bits.

Given that in the pie chart, the atmosphere is distributed in different parts by which it is made.

The data is,

Element 1 = 76%

Element 2 = 17%

Other = 76%

The amount of element 2 in the atmosphere is 17%.

To know more about percentages follow

https://brainly.com/question/24304697

#SPJ9

Answer: A 90° rotation around the origin maps point (x, y) to (-y, x). So, the image of point J after a 90° rotation is J' = (-2, 2) -> (-2, -2).

A reflection across the line x = 3 maps point (x, y) to (2x - 3, y). So, the image of point J' after a reflection across x = 3 is J'' = (-2, -2) -> (4, -2).

Similarly, we can find the images of K and L:

K' = (-2, 6) -> (-6, -2)

K'' = (-6, -2) -> (-2, -2)

L' = (-8, 2) -> (2, -8)

L'' = (2, -8) -> (8, -2)

Therefore, the image of triangle JKL after the 90° rotation and reflection is triangle PQR, with vertices P = J'', Q = K'', and R = L''.

The area of triangle PQR can be found using the Shoelace Formula:

P = [(4 -2) + (-2 -2) + (8 -2) * (-2 - (-8))]/2 = [6 + 4 * 6]/2 = 30/2 = 15 square units.

So, the area of triangle PQR is 15 square units.

Step-by-step explanation:

Step-by-step explanation:

The missing sides of the two right triangles are B ≈ 75.5, b ≈ 10.7 and a ≈ 6.9.

In this problem we find two similar right triangles. Two triangles are similar when they have congruent angles and sides that are not congruent but proportional. Sides in right triangles are related each other by means of Pythagorean theorem:

r² = x² + y²

Where:

According to the statement, we need to use the following relationships:

B = √(C² - A²)

a / A = b / B = c / C

If we know that A = 49, C = 90 and c = 12.7, then the lengths of missing sides are:

B = √(90² - 49²)

B = √5699  (approx. 75.5)

b = B × (c / C)

b = √5699 × (12.7 / 90)

b = 127√5699 / 900 (approx. 10.7)

a = A × (c / C)

a = 49 × (12.7 / 90)

a = 6233 / 900 (approx. 6.9)

To learn more on similar triangles: https://brainly.com/question/29073104

#SPJ1

Answer:

1

Step-by-step explanation:

everything to power of 0 is 1, except for 0^0 is undefined

The total surface area of this cone is equal to 735.1 square meters.

Mathematically, the total surface area (TSA) of a cone can be calculated by using this mathematical expression:

Total surface area (TSA) of a cone = πr(l + r)

Where:

Substituting the given parameters into the total surface area (TSA) (SA) of a cone formula, we have the following;

Total surface area (TSA) of a cone = πr(l + r)

Total surface area (TSA) of a cone = 3.142 × 6 × (33 + 6)

Total surface area (TSA) of a cone = 3.142 × 6 × (39)

Total surface area (TSA) of a cone = 735.1 square meters.

Read more on total surface area here: https://brainly.com/question/30253224

#SPJ1

Answer: The number of ways to form a group of 5 students from a class of 20 students is calculated using the combination formula:

C(20,5) = 20! / (5! * (20-5)!) = 15504

So, there are 15,504 different ways in which 5 students can form a group.

Step-by-step explanation:

The area of the shape for the quilt block is 166.5 in²

The area is the region bounded by the shape of an object. The space covered by the figure or any two-dimensional geometric shape, in a plane, is the area of the shape

Given that, a quilt has blocks of design on it, we need to find the area of the block,

To find the area of the block = sum of the areas of the right triangle and the rectangle,

Area of the block = 16 × 9 + 6 × 7.5 × 1/2 = 166.5 in²

Hence, the area of the shape for the quilt block is 166.5 in²

Learn more about areas, click;

https://brainly.com/question/27444262

#SPJ9

The figure is unavailable is the question is solved for the figure attached

The product of 486 as a product of it's prime factor is 2¹×3⁵

A prime factor is a natural number, other than 1, whose only factors are 1 and itself. The first few prime numbers are actually 2, 3, 5, 7, 11, and so on.

Expressing a number as a product of it's prime factors simply means that we are going to use only prime numbers as factors.

for example expressing 12 as a product of it's factor means 2²× 3 i.e 4 × 3 will give 12

Similar expressing 486 as a product of it's prime factors;

486/2 = 243

243/3 = 81

81/3 = 27

27/3 = 9

9/3 = 3

3/3 = 1

therefore 486 = 2¹× 3⁵

learn more about prime factors from

https://brainly.com/question/18187355

#SPJ1

Answer: 46ft

Step-by-step explanation:

Alright so for this you must reference the pythagorean theorem which is:

a^2+b^2=c^2. c^2 is always the diagonal side and a^2 and b^2 the other two sides.

You can therefore set this up like this:

a^2+20^2=50^2 (where a is the side you are looking for- listed as x)

Solve:

a^2=50^2-20^2

a^2=2500-400

a^2=2100

sqrt(a^2)=sqrt(2100)

a= 45.8257569496

Round: a (or x)=46

The expression that represents the value of the stock after two years in terms of x is 1.6144x

After the first year, the value of the stock increased by 39%, which means that the stock's new value will be -

x + 0.39x = 1.39x

After the second year, the value of the stock decreased by 16%, which means that the stock's new value will be -

1.39x - 0.16(1.39x) = 1.16(1.39x)

Simplifying this expression, we get,

1.16(1.39x) = 1.6144x

Therefore, the expression that represents the value of the stock after two years in terms of x is 1.6144x.

Read more about expressions:

brainly.com/question/28036476

#SPJ4

The complete question is -

Aubrey bought stock in a company two years ago that was worth x dollars. During the first year that he owned the stock, it increased by 39%. During the second year the value of the stock decreased by 16%. Write an expression in terms of x that represents the value of the stock after the two years have passed.

The values of x, y and z are;

x. x = 60° y = 55°

xi. x = 68° y = 56° z = 56°

xiii. x = 40° y = 50°

xiv. x = 40° y = 50°

A triangle is a 3-sided polygon that has three edges and three vertices. The most important property of a triangle is that the sum of the internal angles of a triangle that always equals 180 degrees. This property is called angle sum property of triangle.

x. x = 60° (corresponding angles are equal)

y + 65° + 60° = 180° (Sum of angles in a triangle equals 180°)

y + 125° = 180°

y = 180° - 125°

y = 55°

xi. y = 56° (corresponding angles are equal)

y = z = 56° (angles in equal sides of a triangle are equal)

x + 56° + 56° = 180° (Sum of angles in a triangle equals 180°)

x + 112° = 180°

x = 180° - 112°

x = 68°

xiii. x + 140° = 180° (sum of angles on a straight line equals 180°)

x = 180° - 140°

x = 40°

y + 90° + 40° = 180° (sum of angles in a triangle equals 180°)

y + 130° = 180°

y = 180° - 130°

y = 50°

xiv. y + 130° = 180° (sum of angles on a straight line equals 180°)

y = 180° - 130°

y = 50°

x + 90° + 50° = 180° (sum of angles in a triangle equals 180°)

x + 140° = 180°

x = 180° - 140°

x = 40°

Learn more about triangles here: https://brainly.com/question/1058720

#SPJ1

The average rate of change of the function is 1.6

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

The graph

The interval is given as

−4≤x≤1.

From the graph, we have

f(-4) = -4

f(1) = 4

The average rate of change at this interval is calculated as

Rate = Change in function values/Change in x values

So, we have

Rate = (-4 - 4)/(-4 - 1)

Evaluate

Rate = 1.6

Hence, the rate is 1.6

Read more about average rate of change at

https://brainly.com/question/30689149

#SPJ1

X = 2 (two) students study all three subjects (physics, geography, and economics). This can be found by adding the number of students who study only two subjects (6 + 4 + 5 = 15) and subtracting that from the total number of students who study at least one subject (55 - 20 = 35), since each of these 15 students who study two subjects is counted twice in the totals for each subject.

The number of students who study physics only is 10. This can be found by subtracting the number of students who study physics and at least one other subject (21 - 6 - 5 - 2 = 8) from the total number of students who study physics (21).

The number of students who study exactly one of the two subjects is 25. This can be found by adding the number of students who study each subject only (10 + 11 + 9) and subtracting that from the total number of students (55 - 20 = 35).

learn more about union sets: https://brainly.com/question/28278437

#SPJ1

Answer:

If the height of the triangle is 11 cm greater than its corresponding base, we can represent the base as b and the height as h = b + 11.

Using the formula for the area of a triangle, A = (1/2) bh, we can substitute the values of b and h:

A = (1/2) (b)(b + 11)

A = (1/2) b^2 + (1/2) 11b

If the base of the triangle is 10 cm, then we can substitute b = 10 into the equation:

A = (1/2) (10^2) + (1/2) 11 * 10

A = 50 + 55

A = 105 cm^2

So, the area of the triangle is 105 cm^2.

Step-by-step explanation:

The simple interest on Rs 7560 will be Rs 1102.50 at a rate of 25/4% per annum after approximately 1 month (0.09 years).

Simple interest is a type of interest that is calculated only on the principal amount of a loan or investment, and not on any accumulated interest. It is usually calculated as a percentage of the principal amount, multiplied by the time period for which the interest is being calculated.

We can use the formula for simple interest to solve this problem:

Simple Interest (SI) = Principal (P) x Rate (R) x Time (T)

We know that the principal is Rs 7560, the rate is 25/4% per annum, and the interest is Rs 1102.50. Substituting these values into the formula, we get:

1102.50 = 7560 x (25/4) x T

Simplifying:

1102.50 = 47250T/4

Multiplying both sides by 4 to eliminate the fraction:

1102.50 x 4 = 47250T

4410 = 47250T

Dividing both sides by 47250:

T = 4410/47250

T = 0.093 or approximately 0.09 years.

To convert this to months or days, we can multiply by 12 or 365, respectively.

To learn more about simple interest click on,

https://brainly.com/question/27976154

#SPJ4

The discriminant of a quadratic equation in standard form, [tex]ax^2 + bx + c = 0[/tex] , is given by the expression: [tex]b^2 - 4ac[/tex]

The expression gives the discriminant: [tex]b^2 - 4ac[/tex]

This expression is used to determine the nature of the roots of the quadratic equation. Specifically, if the discriminant is positive, then the equation has two real and distinct roots. If the discriminant is zero, then the equation has one real root with a multiplicity of 2. If the discriminant is negative, then the equation has two complex conjugate roots.

A quadratic equation is a second-degree polynomial equation in one variable, typically written in the form:

[tex]ax^2 + bx + c = 0[/tex]

where x is a variable and a, b, and c are constants. The coefficient "a" cannot be zero, since otherwise, the equation would become a linear equation.

For more such questions on Equation: brainly.com/question/29657983

#SPJ4

By understanding what composite numbers are and how they relate to rolling a die, we can determine the expected number of times Ms. Rod will roll a composite number in 57 rolls.

A composite number is a positive integer that has at least one positive divisor other than one or itself. In other words, a composite number is a number that can be factored into smaller positive integers.

To find the number of times Ms. Rod should expect to roll a composite number, we need to know how many numbers from 1 to 6 are composite. Only two numbers are prime in this range, namely 2 and 3. This means that the other four numbers (4, 5, and 6) are composite. Therefore, out of the 6 possible outcomes of rolling the die, 4 of them are composite numbers.

We can use this information to calculate the expected number of times Ms. Rod will roll a composite number. We know that she is rolling the die 57 times, and each roll has a probability of 4/6 (or 2/3) of resulting in a composite number. Therefore, we can use the formula for the expected value of a discrete random variable, which is:

Expected value = (number of trials) x (probability of success)

Plugging in the values, we get:

Expected value = 57 x 2/3

Expected value = 38

Therefore, we can expect Ms. Rod to roll a composite number about 38 times out of 57 rolls. However, it's important to note that this is just an expected value, and the actual number of times she rolls a composite number may vary.

To know more about composite number here.

https://brainly.com/question/28199758

#SPJ4

The expression to measure {x} can be written as -

{x - 10} + {2x +40} + 90 = 180

We can write the Pythagoras theorem as - The sum of the squares of the base and perpendicular is equal to the square of the hypotenuse.

Mathematically -

(hypotenuse)² = (base)² + (perpendicular)²

Given is a right triangle ABC

We an write the expression to measure {x} as -

{x - 10} + {2x +40} + 90 = 180

Therefore, the expression to measure {x} can be written as -

{x - 10} + {2x +40} + 90 = 180

To solve more questions on functions & expressions, visit the link below

brainly.com/question/17613163

#SPJ9

The average of the middle two figures, which are 18 and 19, is the median of the lower half. Q1 = (18+19)/2, which equals 18.5. The average of the middle two values—32 and 32—represents the median of the upper half. Q3 = (32+32)/2 = 32 as a result.

Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

First, we calculate the median for the lower and higher halves of the data. The values up to the median are found in the lower half and are as follows:

9, 12, 18, 18, 19, 20, 26, 28

The upper half consists of the values from the median onwards, which are:

29, 31, 31, 32, 32, 34, 35, 37

The median of the lower half is the average of the middle two values, which are 18 and 19. Therefore,

Q1 = (18+19)/2

= 18.5.

The median of the upper half is the average of the middle two values, which are 32 and 32. Therefore,

Q3 = (32+32)/2

= 32.

To know more about median visit:-

https://brainly.com/question/28060453

#SPJ1

Answer:

lower quartile = 75

Step-by-step explanation:

the lower quartile Q₁ is situated at the left side of the box.

lower quartile Q₁ = 75

The trustworthiness of the prediction depends on the specific data and relationship between the predictor and response variable, and must be evaluated on a case-by-case basis.

To determine the trustworthiness of a prediction using a simple linear regression equation, we need to assess the degree of linearity and the strength of the relationship between the predictor and the response variable.

If the relationship between the predictor and response is linear, the simple linear regression model is appropriate, and if the relationship is strong, the predictions will be more trustworthy.

So, if we have four values for the predictor, we would need to evaluate the scatterplot of the predictor and response variable to determine the linearity and strength of the relationship.

If the scatterplot shows a clear and strong linear relationship between the predictor and the response variable, with a relatively small amount of scatter around the line of best fit, then we can be more confident that our predictions using the simple linear regression equation will be trustworthy.

On the other hand, if the scatterplot shows a weak or non-linear relationship, or a high amount of scatter around the line of best fit, then the predictions using the simple linear regression equation may not be as trustworthy.

Therefore, the trustworthiness of the prediction depends on the specific data and relationship between the predictor and response variable, and must be evaluated on a case-by-case basis.

Learn more about simple linear regression here https://brainly.com/question/29665935

#SPJ4

The distribution of the number of people with diabetes in a sample of 100 can be modeled using the binomial distribution, with a probability of success of 10.5%.

The binomial distribution has certain properties, such as the mean and variance, that can be used to make inferences about the population. For example, the mean of the distribution is given by:

μ = np

where n is the sample size and p is the probability of success.

The distribution of the number of people with diabetes in a sample of 100 can be modeled using the binomial distribution. The binomial distribution describes the number of successes in a fixed number of independent trials, where each trial has the same probability of success.

In our case, a success is a person with diabetes, and the probability of success is the prevalence of diabetes in the population, which is 10.5%. The number of trials is 100, which is the sample size. Therefore, the distribution of the number of people with diabetes in our sample can be written as:

X ~ B(100, 0.105)

Where X is the random variable representing the number of people with diabetes in our sample, and B(100, 0.105) denotes the binomial distribution with 100 trials and a probability of success of 0.105.

In our case, the mean number of people with diabetes in our sample is:

μ = 100 x 0.105 = 10.5

This means that we expect, on average, to find 10.5 people with diabetes in our sample of 100.

To know more about distribution here.

https://brainly.com/question/29062095

#SPJ4

Step-by-step explanation:

h represents the number of hours

15 represents the initial price for bike rentals

0.75h represents that for every hour, the price of bike rentals increases by 0.75

The measure of side AB of the triangle is given by equation AB = 3.5 cm

If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.

Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides

Given data ,

Let the first triangle be represented as ΔACE

Let the second triangle be represented as ΔBCD

The measure of side AC = 14 cm

The measure of side EC = 84 cm

The measure of side ED = 21 cm

Now , ΔACE is similar to ΔBCD

So , corresponding sides of similar triangles are in the same ratio

Substituting the values in the equation , we get

AB / AC = ED / EC

AB / 14 = 21 / 84

Multiply by 14 on both sides of the equation , we get

AB = ( 1/4 ) 14

AB = 3.5 cm

Therefore , the value of AB is 3.5 cm

Hence , the measure of side AB of triangle is 3.5 cm

To learn more about similar triangles click :

https://brainly.com/question/29378183

#SPJ1