Calculate the rate of change for the quadratic function over the given interval: f(x)=x^2 + 4x +5 ; -4 =< x =< -2

Add all the times together:

27.81 + 26.89 + 26.55 + 25.48 = 106.73 seconds.

1 minute = 60 seconds.

106 - 60 = 46

Total time: 1 minute and 46.73 seconds.

Answer:

106.73

Step-by-step explanation:

27.81 + 26.89 + 26.55 + 25.48 = 106.78

So in conclusion, the answer is 106.78

Answer:

f(a) is the remainder of f(x)/x_a

so hence the remainder of 4×3- 5x2+3x-1/x-2 is (4.(2)^2) - (5.(2)^2) + (3.2) - 1 = 17

Answer:  D) 17

Step-by-step explanation:

You can use long division or synthetic division.  I will use synthetic division because it is the simplest and quickest method:

x - 2 = 0  -->  x = 2

2  |  4     -5     3     -1

   |  ↓      8     6     18

      4      3     9     17    ← REMAINDER

Answer:

Final answer is [tex]-112\cdot\sqrt{2}a^5[/tex].

Step-by-step explanation:

Given expression is [tex](a-\sqrt{2})^8[/tex].

Now we need to find the fourth term of the given expression  [tex](a-\sqrt{2})^8[/tex]. So apply the nth term formula using binomial expansion.

exponent n=8

4th term means we use r=4-1=3

x=2, [tex]y=-\sqrt{2}[/tex]

rth term in expansion of [tex](x+y)^n[/tex] is given by formula:

[tex]\frac{n!}{\left(n-r\right)!\cdot r!}x^{\left(n-r\right)}\cdot y^r[/tex]

[tex]=\frac{8!}{\left(8-3\right)!\cdot3!}\cdot a^{\left(8-3\right)}\cdot\left(-\sqrt{2}\right)^3[/tex]

[tex]=\frac{8!}{5!\cdot3!}\cdot a^5\cdot\left(-2\sqrt{2}\right)[/tex]

[tex]=\frac{40320}{120\cdot6}\cdot a^5\cdot\left(-2\sqrt{2}\right)[/tex]

[tex]=56\cdot a^5\cdot\left(-2\sqrt{2}\right)[/tex]

[tex]=-112a^5\cdot\sqrt{2}[/tex]

[tex]=-112\cdot\sqrt{2}a^5[/tex]

Hence final answer is [tex]-112\cdot\sqrt{2}a^5[/tex].

felix got 51 questions correct

1,0,-1,7,7.

The range always be the Y values

Answer:

Expanded Notation Form:

300 + 70 + 2 + 0.3= 372.3

Expanded Factors Form:

3 x 100 + 7 x 10 + 2 x 1 + 3 x 0.1 = 372.3

Hope this helps!!

Answer:

The answer is D my friends. Good luck.

Step-by-step explanation:

The equation of the line parallel to 2x + 4y = 6 and passing through the point (6, 4) is y = -0.5x + 7.

To find an equation of a line parallel to a given line, we need to find a line with the same slope.

First, we need to rewrite the original equation 2x + 4y = 6 in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

By rearranging the equation, we get y = -0.5x + 1.5.

Since the new line is parallel to the original line, it will have the same slope.

Therefore, the equation of the line parallel to 2x + 4y = 6 and passing through the point (6, 4) is y = -0.5x + 7.

Answer:

B. f(-1)=6

C.  The domain of f(x) is the set {-2.-1,0,1,2,3,4,5,6}

Step-by-step explanation:

To find f(5) from the table means, the y-value that corresponds to x=5.

This value is 12.

This implies that:

f(5)=12

Also the y-value that corresponds to -1 is 6.

Hence f(-1)=6

The domain of f(x) are the set of all the x-values.

The domain is : {-2.-1,0,1,2,3,4,5,6}

The range for f(x) is the set of all the corresponding y-values.

From the table, the range is: {5,6,7,8,9,10,11,12,13}

Answer:

the width is 9 23/30 feet ≈ 9.767 ft

Step-by-step explanation:

Let w represent the width of the train car. Then 6 times the width is 6w, and 8 ft less than that is (6w-8). We are told this amount is 50.6 feet, so we have ...

6w -8 = 50.6

6w = 58.6 . . . . . . . add 8; next divide by 6

58.6/6 = w = 586/60 = 293/30 = 9 23/30 . . . . feet

This is a repeating decimal: 9.766666...

The width of the train car is 9 23/30 ft, about 9.77 ft.

Answer: the answer is C

The histogram and dot plot that represent the order of varying shirt sizes are illustrations of charts

The dataset on the dot plot can be represented using the following frequency table

Shirt size     Frequency

    8                     0  

   10                     1

   12                     3

   14                     3

   16                     5

   18                     4

   20                    2

   22                    1

   24                    1

   26                   0

Since the options are not given, the next step is to plot and upload the histogram using a graphing tool

See attachment for the histogram that represents the dot plot

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The volume of the conical perfume bottle is 77.38 cubic centimeters of perfume, answer D.

To calculate the volume of a conical perfume bottle, we use the formula for the volume of a cone, which is V = (1/3)
3.14r²h, where r is the radius and h is the height of the cone. Given the radius of 3.7 centimeters and a height of 5.4 centimeters, we calculate:

V = (1/3)
3.14 * (3.7 cm)² * 5.4 cm
= (1/3) * 3.14 * 13.69 cm2 * 5.4 cm
= (1/3) * 3.14 * 73.926 cm3
= 3.14 * 24.642 cm3
= 77.38 cubic centimeters

Therefore, the perfume bottle can hold approximately 77.38 cubic centimeters of perfume, which corresponds to answer choice D.

Answer:

- 0.0625

Step-by-step explanation:

Again, I don't know of another way besides Calculus other than letting x = something very tiny.

When you use calculus, the answer approaches - 1/16 = - 0.0625 (I think). So we'll let x = 0.01 and see how that goes.

numerator: 1/(0.01 + 4) - 1/4

(0.24938 - 0.25) / 0.01

- 0.000623 / 0.01 = - 0.0623 which is  pretty close considering what I used for x. You could try it with 0.0001 which will get much closer.

Answer:

60 cm^2

Step-by-step explanation:

The formula for the area of a triangle is ...

A = (1/2)bh

where b is the length of the base, and h is the height. Your triangle shows a base length of 12 cm + 3 cm = 15 cm, and a height of 8 cm. Using these values in the formula, we have ...

A = (1/2)(15 cm)(8 cm) = 60 cm^2

Answer:

1 is my answer but I could be wrong

Answer:

the answer is 0.00221184

Step-by-step explanation:

as we can see 3rd term is product of first two terms

4th term is product of third and second term

5th term is the product of fourth and third term

 the next term in the sequence which is the sixth term will be the product of fifth and fourth term

Answer:

The next term of geometric sequence is 0.025 which is the probability of dropped call.      

Step-by-step explanation:

We are given the following information in the question:

The probability of a customer experiencing a dropped call decreases formed the geometric sequence.

The geometric sequence is:

0.8, 0.4, 0.2, 0.1, 0.05

First term = a = 0.8

Common difference = r =[tex]\frac{a_{n}}{a_{n-1}} = \frac{0.4}{0.8} = \frac{1}{2}[/tex]

We have to find the next term of the geometric series to find the next probability.

Next term of sequence =

[tex]a_n = a_{n-1}\times r\\= 0.05\times \displaystyle\frac{1}{2}\\\\= 0.025[/tex]

Hence, the next term of geometric sequence is 0.025 which is the probability of dropped call.

let's recall that on the IV Quadrant the x/cosine is positive and the y/sine is negative, and of course the hypotenuse is just a radius unit and therefore never negative.

[tex]\bf sin(\theta )=\cfrac{\stackrel{opposite}{-7}}{\stackrel{hypotenuse}{15}}\impliedby \textit{let's find the \underline{adjacent side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}[/tex]

[tex]\bf \pm\sqrt{15^2-(-7)^2}=a\implies \pm\sqrt{176}=a\implies \stackrel{\textit{IV Quadrant}}{+\sqrt{176}=a} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill cos(\theta )=\cfrac{\stackrel{adjacent}{\sqrt{176}}}{\stackrel{hypotenuse}{15}}~\hfill[/tex]

Answer:

The difference in investment between the smallest investor an largest investor is $40,000

Step-by-step explanation:

Let

x ---> the contribution of the smallest investor

y ---> the contribution of the middle investor

z ---> the contribution of the largest investor

we know that

x+y+z=140,000 -----> equation A

x/y=3/4 -----> y=(4/3)x ----> equation B

x/z=3/7 ----> z=(7/3)x ----> equation C

substitute equation B and equation C in equation A and solve for x

x+(4/3)x+(7/3)x=140,000

(14/3)x=140,000

x=140,000*3/14

x=$30,000

Find the value of y

y=(4/3)x ----> y=(4/3)(30,000)=$40,000

Find the value of z

z=(7/3)x ----> z=(7/3)(30,000)=$70,000

Find the difference in investment between the smallest investor an largest investor

z-x=$70,000-$30,000=$40,000

Answer: Less than

Step-by-step explanation:

2 3/4 yards equals 99 inches

the answer is Less than.

Answer:

If it is 40 total then:

about 3 more hours

Exact answer:

2.545454... hours

If it is 40 more:

about 4 hours

Exact answer:

3.63636363... hours

Answer:

• 3 hours

• 11 hours

• 12 hours

Step-by-step explanation:

Check with substitution in the inequality: 12 + 11h > 40

X^(3•2) =X^ 6

Think of an example such as :

(2^3)^2=8^2=64 is the same with

2^(3•2) = 2^6 = 64

Answer= x^6

When two exponents are multiplied together the two exponents multiply.

Answer:

The ratio is [tex]\frac{1}{492}[/tex]

Step-by-step explanation:

Remember that

1 ft=12 in

The Eiffel Tower is 984 feet

Convert to inches

984 ft=984*12=11,808 in

Find the ratio of the height of the model to the height of the actual Eiffel Tower

The height of the model is 24 in

The height of the actual Eiffel Tower is 11,808 in

the ratio is equal to

[tex]\frac{24}{11,808}=\frac{1}{492}[/tex]

That means----> The height of the actual Eiffel Tower is 492 times greater than the height of the model

To find the ratio of the height of the model to the actual Eiffel Tower, convert the model's height to feet (24 inches = 2 feet) and then divide by the tower's height (2 feet / 984 feet) to get the simplified ratio of 1:492.

To calculate the ratio of the height of the model Eiffel Tower to the actual Eiffel Tower, we need to ensure both measurements are in the same unit. Since the actual Eiffel Tower's height is given in feet and the model's height is in inches, we will convert one of these measurements so they can be directly compared.

First, we convert the model's height from inches to feet. We know that 1 foot equals 12 inches, so:

24 inches × (1 foot / 12 inches) = 2 feet.

Now we have the model's height in feet, and we can form the ratio:

Height of model / Height of actual Eiffel Tower = 2 feet / 984 feet.

By simplifying this fraction, we get:

1 / 492.

So, the ratio of the height of the model to the height of the actual Eiffel Tower is 1:492.

No, she should not use her standard deduction because it is less than the deduction she will get from itemizing OPTION B is correct answer.

What is Standard deduction ?

Standard deduction is that amount of someone's income, for which tax is not to be paid, thus reducing the tax bill amount. The amount of the standard deduction is based on one's filing status, age, disability, dependency etc.

Zeituni's standard deduction on her federal income tax return is $5700.

she paid $4670 in state taxes and $1180 in mortgage interest last year, totaling to = $4670+ $1180

                 = $5850

So, no, she should not use her standard deduction because it is less than the deduction she will get from itemizing.

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Zeituni should itemize her deductions, as the total of her state taxes and mortgage interest ($5850) is more than her standard deduction ($5700). So the correct answer is B.

To decide whether Zeituni should use her standard deduction or itemize her deductions, we should add up her state taxes and mortgage interest. The total of her state taxes ($4670) and mortgage interest ($1180) comes to $5850. Comparing this with her standard deduction of $5700, we can see that $5850 is more than $5700. Thus, the better option would be for Zeituni to itemize her deductions.

So the answer is B. No, because it's less than the deduction she would get from itemizing.

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The standard form of the equation of the parabola with a focus at (0, 8) and a directrix at y = -8 is y = 1/32 x², as it is the only option that correctly represents a parabola opening upward with the vertex at the origin and a focus 8 units away.

To find the standard form of the equation of the parabola with a focus at (0, 8) and a directrix at y = -8, we begin by noting that the vertex of the parabola will be midway between the focus and directrix. Since the focus is 8 units above the x-axis and the directrix is 8 units below the x-axis, the vertex is at the origin (0, 0).

The distance between the vertex and the focus (which is also the distance between the vertex and the directrix) is 8 units; this distance is the value 'p' in the parabola's standard equation.

The parabola opens upward because the focus is above the directrix. The standard form for an upward-opening parabola centered at the origin is y =  {1}/{4p}x². In our case, p = 8, so the equation becomes y =  {1}/{4(8)}x² which simplifies to y =  {1}/{32}x².

Based on the options available, the correct standard form of the equation of the parabola is A. y =  {1}/{32}x².

Answer: 65 seats in row 20

Step-by-step explanation: 3 = 31, 6 = 37 the difference is 3 rows but 6 seats so its going up 2 every row therefor you need 14 rows after row 6 so 14 * 2 + 37 = 65 seats

By finding a linear equation, we will see that on the row 20 there are 65 seats.

Here we have a linear relationship, that can be written as:

y = a*x + b

Where a is the slope and b the y-intecept.

We know that if a line passes through two points (x₁, y₁) and (x₂, y₂), the slope is:

[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

In this case, we have points of the form (row, seats), and the two points that we have are:

(3, 31) and (6, 37)

So the slope is:

[tex]a = \frac{37 - 31}{6 - 3} = 2[/tex]

So the equation is:

y = 2*x + b

To find the value of b, we replace one of the points in the equation. If we use the first one, we have x = 3 and y = 31, so:

31 = 2*3 + b

31 = 6 + b

31 - 6 = 25 = b

The equation is:

y = 2x + 25

The number of seats in row 20 is what we get if we replace x by 20, then:

y = 2*20 + 25 = 65

If you want to learn more about linear equations, you can read:

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Step-by-step Answer:

If trapezium DBCE is one-fourth of the area of the triangle ABC, that means that the area of triange ADE is (1 - 1/4) = three-fourth of ABC.

Since DE is parallel to BC, we can prove that triangles ADE and ABC are similar.

Similar triangles have corresponding sides proportional, and area is proportional to the square of the linear proportions.

From this we can conclude that

(DE/BC)^2 = 3/4

DE/BC = sqrt(3/4) = sqrt(3)/2

DE = sqrt(3)/2 * 20 = 10 sqrt(3) = 17.320508 cm (to 6 decimal places).

On the subject of similar figures/volumes, if we know the ratio of linear dimensions (such as the side of a cube) as k, then the ratio of AREA of similar squares would be k^2.

Example: A square would have a side of 8 (area=8^2=64), and a (similar) square has a side of 10 (area = 10^2= 100).  The

ratio of areas = 64/100 = (8^2/10^2) = (8/10)^2

Here 8/10 is the ratio of linear dimensions = k, and the ratio of areas is k^2 = (8/10)^2 = 64/100.

The same works for cubes (or similar volumes) where the volumes would be proportional to k^3.

Answer:

The Phase Shift is how far the function is shifted horizontally from the usual position.

Step-by-step explanation:

Answer:

  y = (1/2)|x -8| -3

Step-by-step explanation:

The first five points fall on a straight line with a slope of ...

  ∆y/∆x = -0.5/1 = -0.5

The last point is not on that line.

So, several options are available:

Answer:

1040.70 is the answer

Step-by-step explanation:

that is the total

Answer:

$80.00

Step-by-step explanation:

The deposit slip shows the value Vera received. If you look closely at the right side of the ticket has a one table, next to the table, has the denomination of each field of the table. The penultimate denomination is called "Less cash received" that represents the amount Vera wants to receive directly from that check. That is, vera received 80.00 dollars.

Answer:

Option B) $122,140

Step-by-step explanation:

we know that

The formula to calculate continuously compounded interest is equal to

[tex]A=P(e)^{rt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest in decimal  

t is Number of Time Periods  

e is the mathematical constant number

we have  

[tex]t=5\ years\\ P=\$100,000\\ r=0.04[/tex]  

substitute in the formula above  

[tex]A=\$100,000(e)^{0.04*5}=\$122,140.28[/tex]  

Round to the nearest dollar

[tex]\$122,140.28=\$122,140[/tex]  

Answer:

$277.91

Step-by-step explanation:

"The ​26-week average of the two highest salaried quarters of the year leading to her application" would be the average of $13,500 and $12,775, or

$13,500 + $12,775

---------------------------- = $13137.50

            2

Dividing this by 26 weeks (equivalent to 6 months), we get $505.29.

Nancy's weekly employment benefit would be 55% of that, or $277.91.

Answer: $555.82

Step-by-step explanation: