What is the average rate of change of the function over the interval x = 0 to x = 5? f(x)=4^2x+1

Enter your answer, as a simplified fraction,

Answer:

1-x represents the percent of the original price being paid.

Step-by-step explanation:

The expression 24(1−x) gives the discounted price of a pair of shorts, where x is the percent of the discount written in decimal form.

For example , 10% is the discount percentage

1 - 10% = 90% will be the percentage of original price to be paid

Here x represents the percent of the discount

so 1-x represents the percent of the original price being paid.

Answer:

percent of original price being paid

Step-by-step explanation:

You solve the substitution method to solve a system of equality by expressing one variable in terms of the other using one equation, and then plugging this expression in the other(s).

In this case, the first equation gives us a way to express n in terms of m. So, we can replace every occurrence of n in the second equation with the given formula.

The result is

[tex] 14m+2n=-8 \iff 14m+2(-7m-4)=-8 \iff 14m-14m-8=-8 \iff -8=-8 [/tex]

So, the second equation turned to be an equality, i.e. an equation where both sides are the same.

This implies that the system has infinitely many solutions, because every couple [tex] (n,m) [/tex] such that [tex] n=-7m-4 [/tex] is a solution to the system, because it satisfies both equations: the first is trivially satisfied, whereas the second is an identity, and as such is satisfied by any value of the variable.

Answer:

We are given:

[tex]R^{2}=12.7\%[/tex]

The interpretation of [tex]R^{2}[/tex] is the amount of variation in response variable that is explained by the explanatory variable in the model

Therefore, the interpretation of [tex]R^{2}=12.7\%[/tex] is 12.7% of variation in gpa response variable is explained by the jobs explanatory variable in the given linear regression model.

the R-squared statistic of 12.7% suggests that there is a weak linear relationship between the number of hours worked and GPA among the sampled students, and the majority of the variation in GPA is due to factors beyond the number of hours worked.

The R-squared statistic, often denoted as R², measures the goodness of fit of a linear regression model. In this context, where the R-squared statistic is 12.7%, it means that approximately 12.7% of the variability in GPA can be explained by the linear relationship with the number of hours per week students work.

More specifically:

- 12.7% of the variation in GPAs among the students in the sample can be accounted for by the linear regression model with the number of hours worked as the predictor variable.

- The remaining 87.3% of the variability in GPAs is not explained by this model and is attributed to other factors or sources of variation that are not included in the model.

In summary, the R-squared statistic of 12.7% suggests that there is a weak linear relationship between the number of hours worked and GPA among the sampled students, and the majority of the variation in GPA is due to factors beyond the number of hours worked.

Learn more about R-squared statistic here

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Answer:a number cube

Step-by-step explanation:

Answer: A number cube is correct to chosen five out of six residents of Mayville have library cards.

Step-by-step explanation:

A number cube is the best to simulate this scenario and predict whether a randomly chosen resident has a library card.

As Coin has only 2 outcomes "Head" and "Tail".

A 5-sector sector spinner has only 5 outcomes we need six outcomes.

A bag of 11 marbles has no differentiated with respect to colors etc.

Hence, A number cube is correct to chosen five out of six residents of Mayville have library cards.

Answer:

We have to find the equation of least squares regression line in order to find the number of ice cream cones that the shopkeeper to sell if the temperature is 106 degrees. We can use excel regression data analysis tool to find the equation of the regression line. The excel output is attached here.

The equation of the least squares regression line is:

[tex]\hat{y}=46.587+5.080x[/tex]

Now, if the temperature is 106 degrees, then the number of cones expected to be sold is given below:

[tex]\hat{y}=46.587+5.080 \times 106[/tex]

         [tex]=585.1 \approx 585[/tex]

Therefore, the number of ice cream cones that the shopkeeper would expect to sell if the temperature is 106 degrees is 585.

Answer:

351 adults and 275 students

Step-by-step explanation:

We can set-up a system of equations to find the number of adults. We know students and adults attended. We will let s be the number of students and a be the number of adults. Since 626 tickets were purchased, then s+a=626.

We also know that 74 fewer student tickets then adult tickets. So s+76=a, the number of student tickets plus 76 will be the number of adult tickets.

We will solve by substituting one equation into the other. We substitute a=76+s into s+a=626. Simplify and isolate the variable a.

s+a=626

s+76+s=626

2s+76=626

2s+76-76=626-76

2s=550

s=275

This means that 275 students attended and 351 adults attended since 275+351=626.

By setting up a system of equations and solving for the number of adult tickets, we are able to determine that 350 adult tickets were sold for the school play.

To find out how many adult tickets were sold, we can set up an equation to model the situation. Let A be the number of adult tickets and S be the number of student tickets. We are given that a total of 626 tickets were sold, which can be described by the equation A + S = 626. We are also told that there were 74 fewer student tickets sold than adult tickets, described by the equation S = A - 74.

To solve for A, we can substitute (A - 74) for S in the first equation, giving us A + (A - 74) = 626. Simplifying this, we get 2A - 74 = 626. Adding 74 to both sides, we get 2A = 700. Finally, dividing both sides by 2, we find A = 350.

Therefore, 350 adult tickets were sold.

Answer:

ds/dt =8  when t =1.5

Step-by-step explanation:

s = t^2 + 5t - 8

We want to find ds/dt

ds/dt = 2t +5

evaluated when t=1.5

ds/dt = 2(1.5) +5

ds/dt = 3+5

ds/dt =8  when t =1.5

Replace t with 1.5 seconds and solve for s:

s = 1.5^2 + 5(1.5) -8

s = 2.25+7.5-8

s= 9.75 -8

s = 1.75

Rate of change is S/t

Rate of change = 1.75 / 1.5

Rate of change of s = 1.17

For a general quadratic equation with rational coefficients

[tex]ax^2+bx+c=0,\,\,\,\,a,b,c \in Q[/tex]

the two solutions are:

[tex]x_{1,2} = \frac{-b\pm\sqrt{b^2-4ac}}{2a}=\frac{-b\pm\sqrt{D}}{2a}[/tex]

where D is the determinant.

Clearly, a solution will a rational number as long as [tex]\sqrt{D}[/tex] is rational. However, it can be shown that a square root of an integer is only rational if its value is an integer. In other words, [tex]\sqrt{D}[/tex] is rational if and only if the determinant is a perfect square, [tex]D=n^2, \,\,\,n\in N[/tex], otherwise the square root is irrational. Therefore the coefficients of quadratic equations that are to have rational solutions must satisfy the following condition:

[tex]b^2-4ac=n^2\,\,\,n\in N[/tex]

Answer:

i think the answer would be C

Step-by-step explanation:

since it seemed you had to divide the numbers a hundred would turn into ten and ninety would turn into nine and because you have one negative and one positive that means it would have to be a negative so it would be

10 - 9i

Answer: B

Step-by-step explanation:

[tex]\sqrt{100} + \sqrt{-81}[/tex]

  [tex]\sqrt{100} + \sqrt{-81}[/tex]

=    10    +    9i

Answer:

y = 2x - 1

Step-by-step explanation:

The line passes through points A(1, 1) and B(2, 3).

The slope-intercept form of the equation of a line is

y = mx + b,

where m = slope, and b = y-intercept.

We see from the graph that the y-intercept is -1, so b = -1, and we have

y = mx - 1

Going from point A to point B, we go up two units and right 1 unit. Slope = m = difference in y over difference in x, so

m = 2/1 = 2

The equation is

y = 2x - 1

Answer: 2x + -1

Step-by-step explanation: In this problem, we're asked to write the equation of the given line in slope-intercept form.

Slope-intercept form is the same thing as y = mx + b form where m represents the slope of the line and b represents the y-intercept. So our first step is to find the slope and the y-intercept of the given line.

To find the slope, we use the ratio rise over run between any two points on the line. To get from point A to point B along this line, we rise 2 units and run 1 unit. So our slope or rise over run is 2/1 or just 2.

Next, to find the y-intercept, it's important  to understand that the y-intercept is the point where the line crosses the y-axis. Notice that this line crosses the y-axis at the point (0,-1) which means that the y-intercept is -1.

Therefore, m = 1/2 and b = -1 and we substitute these values into our formula for m and b to get y = 2x + -1.

So the equation of the given line in slope-intercept form is y = 2x + -1.

Answer: f(x) = x + 2; f(12) = 14

Step-by-step explanation:

The parent function of f(x) = x has been shifted up 2 units

⇒ f(x) = x + 2

  f(12) = 12 + 2

         = 14

Answer:

y = 2x+4

Step-by-step explanation:

We need to find the slope

m = (y2-y1)/(x2-x1)

 = (8--6)/(2--5)

  = (8+6)/(2+5)

  = 14/7

  =2

Now we can use the point slope form of a line

y-y1 = m(x-x1)

y--6 = 2 (x--5)

y+6 = 2(x+5)

If we want it in slope intercept form

Distribute the 2

y+6 = 2x+10

Now subtract the 6 from both side

y+6-6=2x+10-6

y = 2x+4

Answer:

Given  the statement: Jason spends 1/3 of each day sleeping

Since, a day has 24 hours and

Jason spends each day [tex]\frac{1}{3}\times 24 = 8 hours [/tex] in sleeping .

Remaining Jason spend awake each day,  24 - 8 = 16 hours.

In 1 day  =  Jason spend 16 hours in awake

then;

in 1 week(i.e, 7 days) =   [tex]16 \times 7 = 112 hours[/tex] spend in awake.

To find the total number of days Jason spend awake in 1 week.

Divide 112 hours by 24 we get;

[tex]\frac{112}{24} = \frac{14}{3} =4\frac{2}{3}[/tex] days

therefore, [tex]4\frac{2}{3}[/tex] is the total number of day that Jason spend awake  in 1 week.

First multiply C by F by multiplying each row in C by each column in F:

12 * -2 + 0*0 + 1.5*2   12*0 + 0*8 + 1.5*1

1*-2 -6*0 +7.2       1*0-6*8 +7*1

to get a matrix of:

-21   1.5

12   -41

Now subtract that matrix from B:

2- -21 = 2+21 = 23

8 - 1.5 = 6.5

0.6 - 12 = -11.4

3 - -41 = 3+41 = 44

So you have:

23   6.5

-11.4   44

Which makes C the correct answer.

Answer:

D.525 M

Step-by-step explanation:

We know the equation

d = st

where d is the distance, s is the speed and t is the time

The problem gives us the speed of 35 m/s and the time of 15 seconds

s = 35 m/s and t =15 s, we can substitute them in

d =st

d = 35 * 15

d = 525 m

Answer:

525 m

Step-by-step explanation:

Answer:25

Step-by-step explanation:cause it is

To calculate the number of trucks Team Three expects to load based on the information provided.

To calculate the number of trucks Team Three expects to load:

Calculate 3.5 times the number of trucks loaded by team one: 5.5 trucks x 3.5 = 17.5 trucks.

Therefore, team three expects to load 17.5 trucks.

Answer:

Step-by-step explanation:

The edge length (s) of an equilateral triangle is (2/3)√3 times the height. This means the edge length of your triangle is ...

... s = (2/3)√3 × 12√2 = 8√6

The perimeter is 3 times the side length:

... p = 3s = 3×8√6 = 24√6 . . . cm

The area is half the product of edge length and height:

... a = (1/2)sh = (1/2)(8√6)(12√2) = 48√12 = 96√3 . . . cm²

The perimeter of the equilateral triangle is 24√6 cm, and its area is 96√3 cm².

To find the perimeter and area of an equilateral triangle with a given height, we can follow these steps:

First, let's denote the side length of the equilateral triangle as a. In an equilateral triangle, the height (h) can be found using the formula:

h = (a√3)/2

We know the height is 12√2 cm. Therefore,12√2 = (a√3)/2

To find the side length a, we can rearrange the equation: a = 2 * 12√2 / √3

Simplify the expression: a = 24√2 / √3

Multiplying numerator and denominator by √3 to rationalize the denominator: a = 24√6 / 3

a = 8√6

Now, the perimeter (P) of the equilateral triangle is given by: P = 3a

Substitute the value of a: P = 3 * 8√6

P = 24√6 cm

Next, we calculate the area (A) using the formula: A = (base * height) / 2

In an equilateral triangle, the base is equal to the side length a, and the height is given as 12√2 cm:

A = (8√6 * 12√2) / 2

Multiplying the bases and simplifying: A = (96√12) / 2

Since √12 can be simplified to 2√3: A = (96 * 2√3) / 2

A = 96√3 cm²

The perimeter of the equilateral triangle is 24√6 cm, and its area is 96√3 cm².

Answer:

D) n=25

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

I didi the quiz

Answer:

The answer is C. AAA is not a congruency postulate because the side lengths may be different sizes although the angles are the same.

triangles ABC and DEF are congruent by the Side-Side-Side (SSS) postulate.

In other words, if two triangles have all three corresponding sides equal, then the triangles are congruent.

So the answer to the question is B. Congruent - SSS.

If triangles ABC and DEF are congruent, and if so, to name the postulate that applies.

The triangles are congruent because they have the same side lengths and angles. This can be seen from the following:

AD = BE (given)

∠ADB=∠BED (vertical angles)

AB = EF (given)

∠ABD=∠EBD (corresponding angles when  AD ∥ EF  )

BC = DF  (given)

Therefore, triangles ABC and DEF are congruent by the Side-Side-Side (SSS) postulate

Answer:

Answer is B) 120

Answer:

$3.6

Step-by-step explanation:

We are told that the pie store is having a 20% off sale on all of its pies. The pie you want regularly costs $18.

To find the amount saved with the discount let us find 20% of 18.

[tex]\text{The amount saved with discount}=\frac{20}{100}\times 18[/tex]

[tex]\text{The amount saved with discount}=0.20\times 18[/tex]

[tex]\text{The amount saved with discount}=3.6[/tex]

Therefore, the amount saved with the discount is $3.6.

Answer: 1.1 seconds

Step-by-step explanation:

leap = 4t²  ; leap = 4 ft 11 inches, find t

[tex]4\frac{11}{12} = 4t^2[/tex]

[tex]\frac{59}{12} = 4t^2[/tex]

[tex]\frac{59}{48} = t^2[/tex]

[tex]\sqrt{\frac{59}{12}} = \sqrt{t^2}[/tex]

[tex]\sqrt{1.23} = t[/tex]

1.1 = t

Given Equations :

✿  5x + 3y = -6 -------------- [1]

✿  3x - 2y = 4 -------------- [2]

Multiplying Equation [1] with 2, We get :

⇒ 10x + 6y = -12 ----------- [3]

Multiplying Equation [2] with 3, We get :

⇒ 9x - 6y = 12 ---------- [4]

Adding Both Equations [3] and [4], We get :

⇒ (10x + 6y) + (9x - 6y) = -12 + 12

⇒ 19x = 0

⇒ x = 0

Substituting x = 0 in Equation [1], We get :

⇒ 5(0) + 3y = -6

⇒ 3y = -6

⇒ y = -2

⇒ (x , y) = (0 , -2)

Option (a) is the Answer

Answer: A (0, -2)

Step-by-step explanation:

5x + 3y = -6   →   2(5x + 3y = -6)   →   10x + 6y = -12

3x  - 2y =  4   →   3(3x  - 2y =  4)   →   9x  - 6y = 12

                                                          19x           =  0

                                                              x          =  0

Now, input "x = 0" into one of the equations and solve for y:

5x + 3y = -6

5(0) + 3y = -6

         3y = -6

           y = -2

Answer:

6x^2 +81x - 17

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

7x-15

Step-by-step explanation:

We cannot solve for x since this is  an expression

((6x+9) (x+12) -sqrt(49+76) ^2

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

(49+7x) -64

Lets simplify the numerator

((6x+9) (x+12) -sqrt(49+76) ^2

Simplify what is inside the last parentheses

((6x+9) (x+12) -sqrt(125) ^2

Squaring a square root leaves the original number

((6x+9) (x+12) -(125)

FOIL the first two terms

First 6x*x = 6x^2

Outer:  6x*12 = 72x

Inner: 9x

Last : 9*12 = 108

Add them together

6x^2 +72x+9x+108 = 6x^2 +81x+108

Subtract the 125

6x^2 +81x+108-125

6x^2 +81x - 17

Now lets simplify the denominator

(49+7x) -64

49+7x-64

7x-15

6x^2 +81x - 17

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

7x-15

Answer: (1,3)

All you're doing is looking for where the two lines cross, or the point of intersection. What you can do is draw a vertical line through this intersection point to see that the vertical line lands on x = 1 on the x axis. At the same time, draw a horizontal line to the y axis and it will get to y = 3.

So together x = 1 and y = 3 pair up to get (x,y) = (1,3)

The degree of this polynomial is 9

Answer:

Answer in image

Step-by-step explanation:

Answer in image

Final answer:

To find out how much longer we have before we finish the movie, subtract the time already watched from the total duration of the movie.

Explanation:

To find out how much longer we have before we finish the movie, we need to subtract the time we have already watched from the total duration of the movie.

Given that the movie is 28 minutes and 58 seconds long, and we have already watched 13 minutes and 44 seconds, we subtract the time already watched from the total duration:

28 minutes 58 seconds - 13 minutes 44 seconds = 15 minutes 14 seconds.

Therefore, we have 15 minutes and 14 seconds left before we finish the movie.