Find the average rate of change of the function: f(x)=x²-3 between the values [3,5]​

Answer: (-4.5,-3)

Step-by-step explanation:

                  (-9,-2)    (9,-6)    1:3

      [tex]\displaystyle\\\boxed {x=\frac{x_1+\lambda x_2}{1+ \lambda} \ \ \ \ \ \ y=\frac{y_1+\lambda y_2}{1+\lambda} }[/tex]  

[tex]\displaystyle\\x_1=-9\ \ \ \ x_2=9\ \ \ \ \ y_1=-2\ \ \ \ \ \ y_2=-6\ \ \ \ \ \lambda=1:3=\frac{1}{3} \\\\x=\frac{-9+(\frac{1}{3})(9) }{1+\frac{1}{3} } \\\\x=\frac{-9+3}{\frac{(1)(3)+1}{3} } \\\\x=\frac{-6}{\frac{3+1}{3} } \\\\x=\frac{(-6)(3)}{4} \\\\x=\frac{-18}{4}\\\\x=-4.5 \\\\y=\frac{-2+(\frac{1}{3} )(-6)}{1+\frac{1}{3} } \\\\y=\frac{-2+(-2)}{\frac{4}{3} } \\\\y=\frac{(-4)(3)}{4} \\\\y=-3\\Thus,(-4.5,-3)[/tex]

The average number of hours the family had the television set on is 3 hours.

The average of a set of numbers is calculated by adding the numbers together and dividing it by the total number. Average is also known as mean. Average is a measure of central tendency. Other measures of central tendency are mode and median.

Average = sum of the numbers / total number

Average = (5 + 2 + 1 + 2 + 1 + 2 + 6) / 7 =

19 / 7 = 2.714 hours

To round off a number to the nearest whole number, if the tenth digit is equal to 5 or greater than five, add one to the units digit. If this is not the case, the unit digit remain unchanged. In both cases, the tenth digit is replaced with o.

Because the tenth digit in 2.714 is greater than 5, the number becomes 3 hours.

To learn more about average, please check: https://brainly.com/question/25842202

#SPJ1

The answer of the given inequality is 5/2<x<5

To solve this given inequality we need to 1st understand what is inequality then we will be easily able to solve this sum.

It is a relationship between inequal values. the word inequality means not equal. to compare the values whether it is less or greater than then different inequalities are used. We can easily identify when an equation is called an inequality equation when we will see the sign ≤ , ≥ ,< ,>. This sign means that the expression is an inequality.

Here in the sum we will be solving the equation in two parts in the 1st part we will be taking the  part 2x<4x-5 and in the 2nd part we wil take the equation 4x-5<15

On solving the 1st part :

∴ 2x<4x-5

=> 2x-4x<-5

=> -2x<-5

=> 2x>5     [Multiplying boyh sides by minus sign]

=> x>5/2

On solving the 2nd part :

∴ 4x-5<15

=> 4x<15+5

=> 4x<20

=> x<5

So on solving the inequality we got that  5/2<x<5

learn more about inequalities here :

https://brainly.com/question/25275758

#SPJ9

54.5 % students got failed

• Percentage in mathematics is defined as the number or ratio which can be expresses as a fraction of 100. If we want to calculate the percent of the number, we need to divide the number by the whole and multiply by 100.

• Percentage are dimensionless quantity. Percentage means pert per hundred. Percentage can also be represented in fraction form such as 0.5% or 0.25%.

• For example Prince got 98% marks in Maths which means that he has scored 98 marks out of 100.

According to the Question

Number of boys = 1100

Number of girls = 900

%age of boys passed = 50%

%age of girls passed = 40%

No of boys failed = ((100-50)*1100)/100

= 550

No of girl failed = ((100-40)*900)/100

= 540

Total number of students =1100+900 = 2000

Total number of students failed = 1090

Percentage  of students failed = 1090/2000 *100 = 54.5

54.5 % students got failed

Learn more about percentage here

https://brainly.com/question/843074

#SPJ9

The graph of Linear Equation is always a straight line .

Answer:

3.75 miles per hour

Step-by-step explanation:

Diane is walking 2.5 miles in 40 minutes.

2.5/40 = 0.0625 miles per minute

There are 60 minutes in an hour.

0.0625 * 60 = 3.75

Diane is walking at a speed of 3.75 miles per hour.

Here, we have to calculate the walking speed of Diane in miles per hour, we need to convert the time from minutes to hours since the walking distance is given in miles.

Diane walks 2.5 miles in 40 minutes.

To convert 40 minutes to hours, we divide by 60 (since there are 60 minutes in an hour):

40 minutes ÷ 60 = 2/3 hours

Now, we can calculate Diane's walking speed (or rate) in miles per hour:

Diane's walking speed = Distance / Time

Diane's walking speed = 2.5 miles / (2/3) hours

To divide by a fraction, we can multiply by its reciprocal:

Diane's walking speed = 2.5 miles * (3/2) hours

Now, simplify:

Diane's walking speed = 7.5 miles / 2 hours

Finally, divide:

Diane's walking speed = 3.75 miles per hour

So, Diane is walking at a speed of 3.75 miles per hour.

To learn more on speed click:

brainly.com/question/28224010

#SPJ7

Considering the concepts of the mean and the standard deviation, we have that:

When the measure of 84 is added, we have that:

More can be learned about the mean and the standard deviation of a data-set at https://brainly.com/question/26941429

#SPJ1

Answer:

i hope this is the answer

Step-by-step explanation:

The given function is not the odd function.

According to the statement

We have to find about the odd function.

So, For this purpose, we know that the

The odd function is that the function f is odd if the subsequent equation holds for all x and −x within the domain of f : −f(x)=f(−x) − f ( x ) = f ( − x ) Geometrically, the graph of an odd function has rotational symmetry with relevance the origin, meaning that its graph remains unchanged after a rotation of 180∘ about the origin.

From the given information:

dimetri says that a function that's fabricated from terms where the variable is raised only to an odd power are going to be an odd function

Then

Algebraically, an odd function is one where f(-x) = -f(x). this suggests that if we substitute -x for each x within the function, it should be the identical as switching every sign up the function. This doesn't always work.

For example, if f(x)=x³+7:

f(-x)=(-x)³+7=-x³+7.

However, since the 7 did not become -7, it is not the same as -f(x), so it is not an odd function.

So, The given function is not the odd function.

Learn more about odd function here

https://brainly.com/question/4031409

#SPJ4

Answer:

The correct is the 9100πx

Explanatory variable: The type of pill the men took each day.

Response variable: Whether a subject had a heart attack.

We have been given that :

Participated candidates are 400

Men are divided randomly so we find out explanatory and response  variable.

The explanatory variable is the variable that is manipulated by the researcher. Explanatory Variable also known as the independent or predictor variable, it explains variations in the response variable; in an experimental study, it is manipulated by the researcher.

Response variable: Response Variable is the result of the experiment where the explanatory variable is manipulated. It is a factor whose variation is explained by the other factors. Response Variable is often referred to as the Dependent Variable or the Outcome Variable.

To know more about explanatory variable and response variable

visit: brainly.com/question/17647745

SPJ4

Translating the given word problem into a set of linear equations, Mariana's age is 15 years old.

Translate the given word problem into algebraic equations.

Let x be Mariana's age

Let y be Yaritza's age

Mariana is younger than Yaritza, their ages are consecutive odd integers.

Since the difference of  consecutive odd integers is 2, then:

y = x + 2  ....... (1)

Sum of Mariana's age and 5 times Yaritza's age is 100.

x + 5y = 100   ..... (2)

Substitute equation (1) to equation (2)

x + 5y = 100

x + 5(x+2) = 100

6x + 10 = 100

6x = 90

x = 15

Thus, Mariana's age is 15 years old.

Learn more about solving linear equations here:

https://brainly.com/question/25645169

#SPJ4

Answer:

15

Step-by-step explanation:

i just got it right on delta

The equation will be (2w ,+ 3) + (w + 2) + (3w + 4) = 600

The ratio in lowest term will be 2:1:3

When they donate $50, the ratio will be 1:4.

a. The equation based on the information will be:

(2w + 3) + (w + 2) + (3w + 4) = 600

6w + 9 = 600

6w = 600 - 9

6w = 591

Divide

w = 591/6

w = 98.5

b. Therefore, (2w + 3) = 2×98.5 + 3 = 200

(w + 2) = 98.5 + 2 = 100.5

(3w + 4) = 3(98.5) + 4 = 299.5

The ratio in lowest term will be 2:1:3.

c. When they donate $50, the ratio will be:

= (50 × 3)/600

= 150/600

= 1:4

Learn more about expressions on

brainly.com/question/22048677

#SPJ1

The area of the triangle is  5√11 cm²

The area of a triangle can be found as follows:

area of a triangle = 1 / 2 bh

where

Therefore,

b = base of the triangle = 2(√6² - 5²) = 2(√36 - 25) = 2√11 cm

h = height of the triangle = 5 cm

area of the triangle = 1 / 2 × 2√11 × 5

area of the triangle = 5√11

area of the triangle =  5√11 cm²

learn more on triangle here: https://brainly.com/question/27701864

#SPJ1

Answer:

(3,1)

Step-by-step explanation:

Y axis = Arrow that goes up and Down

X axis = Arrow that goes from left to right

To find point J, you have to go up 3 on the Y axis.

Then, go to the right once.

now that your on point J, you have to write the coordinates.

(Y axis, X axis) = (3,1)

Answer:

Step-by-step explanation:

Es de dividir 8/5 entre los 4 niños, tipo:

8/5 ÷ 1/4 =8/20 esto sale de multiplicar 8x1 y 4x5 debido a que cuando divides fracciones, se multiplican los factores.

Luego 8/20 se simplifica dividiendo todo por 4 y queda 2/5 que es el resultado.

Respuesta: Cada niño comió 2/5

Espero te sirva!

The amount of butter that Tony needs to put in each cake will be 2.25 cups.

From the information, Tony is making a tiered cake for a party and he use 9 cups of butter from the refrigerator to make 4 cakes.

The amount of butter that he needs to put in each cake will be:.

= Number if cups / Number of cakes

= 9 / 4.

= 2.25 cups

Therefore, the amount of butter that Tony needs to put in each cake will be 2.25 cups.

Learn more about expressions on:

brainly.com/question/723406

#SPJ1

The quotient of the expression is 4x+1.

An expression is a set of terms combined using the operations +, – , x or ÷. An expression is a number, a variable, or a combination of numbers and variables and operation symbols. An expression is in simplest form when no terms can be combined

Given:

The expression is

[tex](4x^{2} - 7x - 2) / (x-2)[/tex]

By long division method the following steps are :

Divide the tens column dividend by the divisor. Then Multiply the divisor by the quotient in the tens place column ,Subtract the product from the divisor then at last Bring down the dividend in the ones column and repeat.

We have to find the quotient of the expression.

According to given question we have

[tex](4x^{2} - 7x - 2) / (x-2)\\\\=(x-2)(4x+1)/(x-2)\\\\=4x+1[/tex]

Therefore, the quotient of the expression is 4x+1.

Learn more details about expression  here:

https://brainly.com/question/14083225

#SPJ1

The acutal width of the picnic area by using proportion if the scale used is 3 inches : 2 yards will be 60 yards.

Let the actual width of the picnic area be x yards.

According to the given question.

Laura measured a picnic area near the river and made a scale drawing.

The scale she used was 3 inches : 2 yards.

⇒ The scale is 3 inches : 2 yards

The width of the picnic area in the drawing is 90 inches.

As we know that, a proportion is a fraction of a total amount, and the measures are related using a rule of three.

Thereofore, the acutal width of the picnic area by using proportion if the scale used is 3 inches : 2 yards is given by

3inches : 2 yards = 90inches : x

⇒ 3x = 180

⇒ x = 60yards

The acutal width of the picnic area by using proportion if the scale used is 3 inches : 2 yards will be 60 yards.

Find out more information about scale here:

https://brainly.com/question/28060140

#SPJ4

 The random sample proportion.

Probability distribution is a statistical function that describes all the possible values and likelihoods that a random variable can take within a given range.

at 90% confidence interval: The Central 90% of any normal   distribution is: Z_(α/2) = 1.960

 Error = E = ±5% = ±0.05

Applying the normal  Probability distribution

= 0.70 ≤ P≤  0.77(this means that we are 90% confident that the true proportion of jet with wiring problem fall with 0.70 and 0.77, hence there is no need for the airline to conduct further sampling, rather, they should just inspect all the planes)

learn more about  Probability distribution : brainly.com/question/14210034

#SPJ4

4/3 cups of margarine will he need to make 4 batches of dog biscuits.

A fraction is a piece of the entire. The number is shown as a quotient in mathematics, in which the numerator and denominator are split. Both are integers in a straightforward fraction. The numerator, as well as the denominator of a complex fraction, as well as the denominator of a complex portion, is a fraction.

Zero, a positive natural number, or an unsigned negative integer are all examples of integers. The inverses of corresponding positive numbers, which are additive, are the negative numbers. The blackboard bold math b Z or boldface Z is a common way to represent the set of integers in mathematical terminology.

There are four batches of dog biscuits.

Making a batch requires 1/3 cup of margarine.

As we can see that for 1 batch of dog biscuits required 1/3 cup of margarine.

So to make 4 batches of dog biscuits:

= (1/3)*4

= 4/3

4/3 cups of margarine will he need to make 4 batches of dog biscuits.

To know more about fraction visit:

https://brainly.com/question/10354322

#SPJ4

answer:

1/5^2

=

1/25

step-by-step

1) 5^5/5^7=

5*5*5*5*5

-------------------

5*5*5*5*5*5*5

2) aka

1/5^2= 1/25 (.04)

The value of input are {1, 2, 3, 4, 5}.

The value of output are {4, 5}.

What is Coordinates?

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

The points are given as;

{(1, 5) , (2, 4) , (3, 5) , (3, 4) , (4, 4) , (5, 5)}

Now, All points are shown in graph.

Clearly, The input of points are,

x = {1, 2, 3, 4, 5}.

And, The output of points are,

y = {4, 5}

So, The value of input are {1, 2, 3, 4, 5}.

The value of output are {4, 5}.

Learn more about the coordinates visit:

https://brainly.com/question/1047474

#SPJ1

Answer:

S(-3,7)

Step-by-step explanation:

Rise/Run

M(1,4) R(5,1)

1+run=5        4+rise=1

run=4              rise= -3

1-4= -3       4+3=7

Answer:

A. y≤2x²-8x+3

Step-by-step explanation:

If you graph the function y≤2x²-8x+3, you would see that these both match.

The inequality y ≤ 2x² - 8x + 3 represents the given graph.

An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.

Here, The y-intercept is 3, not -3, so answer C is eliminated

Choose a point that is clearly in the shaded area or one that is clearly in the unshaded region

Here, I choose the point (0, 0) and substituted these values in the equation and since 0 < 3,

Option A is the correct answer

Thus, the inequality y ≤ 2x² - 8x + 3 represents the given graph.

Learn more about Inequality from:

brainly.com/question/20383699

#SPJ5

Answer:

X=10

Step-by-step explanation:

-20=4x-6x

4x-6x=-20

[tex]\frac{-2x}{-2} =\frac{-20}{-2}[/tex]

X=10

Answer:

x = 10

Step-by-step explanation:

STEPS FOR SOLVING LINEAR EQUATION

−20=4x−6x

Combine 4x and −6x to get −2x.

−20=−2x

Swap sides so that all variable terms are on the left hand side.

−2x=−20

Divide both sides by −2.

x=

−2

−20

​

Divide −20 by −2 to get 10.

x=10

The Hugo's error is that , he did the translation incorrectly. He should have translated triangle by 3 unit right and then 1 unit up.

In geometry, a triangle is defined as the shape which has three sides and also has three angles. We can say that a triangle is a type of polygon with three sides and three vertex. Triangle follows angle sum theorem.

According to triangle Angle Sum theorem, the measurement of the sum of all interior angles of a triangle is always equals to 180°. That means, For a given triangle say ΔABC if ∠A, ∠B and ∠C are the interior angles then their sum i.e. ∠A + ∠B + ∠C = 180°.

Some important formula of triangles:

In the question given,

the equation of line is y=2

The Hugo's error is that , he did the translation incorrectly. He should have translated triangle by 3 unit right and then 1 unit up.

To know more about triangles, visit :

brainly.com/question/22737630

#SPJ9

The complete question is :

Hugo grapes triangle PQR and (Rt*T<3,1>)(Δ PQR), where the equation of the line t is y=2, made exactly one error. Explain Hugo’s error.

Answer:

Step-by-step explanation:

You multiply the weight per gallon by the number of gallons, which is 3205.

So, 8.34 x 3205

Banks are known to carry out different functions. The common financial service called savings.

Financial services is known to be a very wide term that comprises of all of the activities such as banking, investing, and insurance.

Financial services by banks includes savings, investment, etc. Savings is thee process whereby bank helps to keep the money of its customers. It is known to be the most common services offered by banks.

Learn more about  Financial services at:

https://brainly.com/question/9928158

#SPJ1