Find the average rate of change of the function on the interval specified.
g(x) = 7x3 − 4
on
[−3, 3]

The value of minimum usual value is, [tex]\mu-2\sigma=-119.2[/tex]

The value of maximum usual value is, [tex]\mu+2\sigma=1311.2[/tex]

Given the values of the parameters of Binomial Distribution are,

Total number of trials (n) = 1490

probability of success in one trial is (p) = 2/5

The probability of failure in on trial is given by,

[tex]q=1-p=1-\frac{2}{5}=\frac{5-2}{5}=\frac{3}{5}[/tex]

For Binomial distribution we know that,

Mean [tex](\mu)=np=1490\times\frac{2}{5}=596[/tex]

and Standard Deviation [tex](\sigma)=\sqrt{npq}=\sqrt{1490\times\frac{2}{5}\times\frac{3}{5}}=357.6[/tex]

Now, calculating the required measurement we get,

The minimum usual value is given by,

Mean -2 Standard Deviation [tex]=\mu-2\sigma=596-2\times357.6=-119.2[/tex]

The maximum usual value is given by,

Mean + 2 Standard Deviation [tex]=\mu+2\sigma=596+2\times357.6=1311.2[/tex]

Hence the minimum and maximum usual values are -119.2 and 1311.2 respectively.

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Answer:

-5

Step-by-step explanation:

Since g(x) is f(x) shifted 5 units down, g(x) = f(x) -5. Therefore k = -5

Answer:

No

Step-by-step explanation:

If these two individual statements are true, it means they share the same elements of set C. In addition to this, sets A and B could have additional elements, hence this cannot be true.

Answer:

They are not parallel

Step-by-step explanation:

original equation

10x + 3y = -3

subtract 10x

3y = -10x - 3

divide by 3

y = -10/3x - 1

original equation

5x - 4y = -3

subtract 5x

-4y = -5x-3

divide by -4

y = 5/4x + 3/4

the slopes are not equal to each other (5/4x and -10/3x) so they are not parallel

Answer:

k = 1

Step-by-step explanation:

Discriminant

[tex]b^2-4ac\quad\textsf{when }\:ax^2+bx+c=0[/tex]

[tex]\textsf{when }\:b^2-4ac > 0 \implies \textsf{two real roots}[/tex]

[tex]\textsf{when }\:b^2-4ac=0 \implies \textsf{one real root}[/tex]

[tex]\textsf{when }\:b^2-4ac < 0 \implies \textsf{no real roots}[/tex]

As we need to determine the value of k that will give one solution, set the discriminant to zero.

Given equation:

[tex]y=kx^2-4x+4[/tex]

Therefore:

Substitute these values into the discriminant and solve for k:

[tex]\begin{aligned}b^2-4ac & = 0\\\implies (-4)^2-4(k)(4) & = 0\\16-16k & = 0\\16k & = 16\\\implies k & = 1\end{aligned}[/tex]

Answer:

f(x)=x-2x+3; f(x)=-bx

x-2x=3=-bx

x+4x+3=0

(x+3) (x+1) = 0

x=-3 or x=-1

when x+-3. f(x)=b x(-3)=18

x=-1. f(x) = - b x (-1) = b

so system of equations : ( -3, -18)

; (-),b

Step-by-step explanation:

hope it helps

Total amount she paid to repay her loan was $17,687

Amount is the total sum  of money paid to the bank.It is basically the sum of interest and principal amount.

Principal is the sum of money taken from the bank

Interest is the sum of money charge by the bank during the period of loan repayment.

Rate of interest is the rate at which interest is charge in the principal sum

Time is the total period of the loan repayment.

Simple interest = (P x Rx T)/100

where, P=principal

           R=rate of interest

           T= time

Amount= Principal +Interest

As per question,

P=$17000

R=6.8%

I=$687

Amount=P+I

              =$17000+687

              =$17687

Therefore,Total amount she paid to repay her loan was $17,687

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The answers are as follow:

a) y'= -2x/y

b) y' = -4/y

The technique of implicit differentiation allows you to find the derivative of y with respect to x without having to solve the given equation for y.

Given:

x²y+4y=8

On differentiation

applying product rule

2xy+ x²y'  = 0

2xy = - x²y'  

2y = -xy'

y'= -2x/y

b) equation of the tangent line to the graph when x = 2.

y' = -4/y

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Answer:

N. The number of people purchasing coffee each day in a coffee shop

Step-by-step explanation:

A fraction of a person could not buy coffee because every person is a whole person. If something is not a person, it's not a person. Therefore, the only numbers you could add to this value are 0 and 1.

The graph of [tex]\mathbf{y=\sin{3x}}[/tex] is given by,

Here given the function is [tex]y=\sin{3x}[/tex]

when [tex]x=0\Rightarrow y=\sin{3\times 0}=\sin0=0[/tex], then it passes through the origin (0,0).

When [tex]x=\frac{\pi}{6}\Rightarrow y=\sin{3\times\frac{\pi}{6}}=\sin\frac{\pi}{2}=1[/tex]

Since we know that, [tex]-1\leq\sin{x}\leq1,\forall x[/tex], then the function has maximum height at [tex]x=\frac{\pi}{6}[/tex].

Again when [tex]x=\frac{\pi}{3}\Rightarrow y=\sin{(3\times\frac{\pi}{3})}=\sin\pi=0[/tex], again the function is 0.

So clearly the function is the Oscillating function with a maximum value of the function as 1 and a minimum value of the function as -1.

Range of the oscilaltion of the function = 1-(-1) = 1+1 = 2

Using graphing calculator we get the graph of function [tex]y=\sin3x[/tex],

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Opposite values are those values which on the number line has the same distance between them and zero. The temperature in each city is PoT=-PhT and PhT =+PoT.

Opposite values are those values which on the number line has the same distance between them and zero. Although the sign on the values may be difference. For example if the first value is 4, then its opposite value is -4.

In general, the temperature equation for Portland, Maine is stated mathematically as

PoT=-PhT

As it is given in the question that the Portland, Maine and Phoenix, Arizona had opposite values. Also, the temperature in Portland is lower than in Phoenix. Therefore, the temperature in each city can be written as,

PoT=-PhT

PhT =+PoT

Hence, the temperature in each city is PoT=-PhT and PhT =+PoT.

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Answer: 2xy

Step-by-step explanation: 2xy is the answer bra

Answer:

105.6397

ROUNDED ANSWER:

105

Answer:

Gabrielle is 27

Mikhail is 9

Step-by-step explanation:

g = 3m

g + m = 36

since g = 3m we can substitute it in the equation

g + m = 36 as

3m + m = 36

4m = 36

m = 9

3m = 27 which is g

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Answer:

x² + 6x + 9

Explanation:

[tex]\sf = \left(x+3\right)^2[/tex]

Use perfect square formula: (a + b)² = a² + 2ab + b²

[tex]= \sf x^2 + 2(x) (3) + 3^2[/tex]

simplify the following

[tex]= \sf x^2 + 6x +9[/tex]

Hence Maria is not correct. The correct answer is x² + 6x + 9.

Answer:

2y - 9x

Step-by-step explanation:

2y + 3 ( x - 4x )

First, solve the brackets.

2y + 3x - 12x

Combine like terms.

2y - 9x

Answer:

[tex]\sf 2y-9x[/tex]

Step-by-step explanation:

Hi There Student! Let me help you out on this question.

________________________________________________________

In this problem, we are given an expression [tex]\longmapsto\pmb{2y+3(x-4x)}[/tex], and asked to simplify it.

                                    ↪

First, we can perform the operation inside the parentheses, x-4x:

[tex]\longmapsto\sf 2y+3(-3x)}[/tex].

Now we can multiply 3 times -3x:

[tex]\longmapsto\sf 2y-9x[/tex]

And that is our final answer, because 2y and -9x are not like terms.

Hope that this helped! Have a good day ahead.

Best Wishes!

[tex]\star\bigstar\overline{\overline{\underline{\underline{\textsf {Reach far. Aim high. Dream big.}}}}}\bigstar\star[/tex]

 ◆◈-Greetings!-◈◆

-______________________________

u=-54

you have -54 because

-54(-2)=108/9=12

Answer:

u =-54

Step-by-step explanation:

-2/9u=12

To solve for u multiply each side by -9/2 to isolate u

-9/2 * -2/9 u= 12 * -9/2

u =-54

Answer:

area of the circle

area=7.54

Answer: (1, -4) or y = -4

Step-by-step explanation:

    Given:

y = 3x - 7

    Plug in the value of 1 for x - given to us by "(1, ?)

y = 3x - 7

y = 3(1) - 7

    Multiply:

y = 3 - 7

    Subtract:

y = -4

               y = -4

The slope of the line that passes through (1, -3) and (0, 2) is: B. m = -5.

Slope (m) = rise / run = change in y / change in x.

Given the points, (1, -3) and (0, 2):

Slope (m) = (-3 - 2)/(1 - 0)

Slope (m) = -5/1

Slope (m) = -5

Therefore, the slope of the line is: B. m = -5.

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Answer:

[tex]2x^{2}[/tex] - 16x + 14

Step-by-step explanation:

(2x - 4)(x - 6)

= (2x + −4)(x + −6)

= (2x)(x) + (2x)(−6) + (−4)(x) + (−4)(−6)

= [tex]2x^{2}[/tex] − 12x − 4x + 24

= [tex]2x^{2}[/tex] - 16x + 14

Answer:

[tex]\textsf {0.08 miles per minute}[/tex]

Step-by-step explanation:

[tex]\textsf {Speed = Distance (Miles) / Time (Minute) }[/tex]

[tex]\textsf {Speed = 18 miles / 213 minutes }[/tex]

[tex]\textsf {Speed = 0.08 miles per minute }[/tex]

Answer:

The speed in miles per minute is 0.0845 mpm.

Step-by-step explanation:

The explanation above clearly states that a car travel a distance of 18 miles in a time of 213 minutes . And it is asking for speed in miles per minute. Keep this in mind that the symbol for miles per minute is mpm. Speed formula is distance ÷ time.

Speed = Distance ÷ Time

Speed = 18 m / 213 min

18 divided by 213 = 0.0845

speed = 0.0845 mpm

Therefore the speed in miles per minute is 0.0845 mpm.

The equation gives the measure of the central angle 7/5 times 3 60/2 π.

An angle with its vertex at the center of a circle and with sides that are radii of the circle.

radius= 5 feet.

Circumference of circle,

= 2πr

=2*3.14*5

= 31.4 feet.

Arc length = 7.

Then, the part of circle 7 feet arc have

=7/31.4

=0.2229

Also, 0.2229 * 360 = 80.244°

In radian,

80.244° = 1.4 radians

Hence, 7/5 times 360/2 π.

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Substitute [tex]y = \sqrt x[/tex], so that [tex]y^2 = x[/tex] and [tex]2y\,dy = dx[/tex]. Then the integral becomes

[tex]\displaystyle \int \frac{dx}{\sqrt{1 + \sqrt x}} = 2 \int \frac y{\sqrt{1+y}} \, dy[/tex]

Now substitute [tex]z=1+y[/tex], so [tex]dz=dy[/tex]. The integral transforms to

[tex]\displaystyle 2 \int \frac y{\sqrt{1+y}} \, dy = 2 \int \frac{z-1}{\sqrt z} \, dz = 2 \int \left(\sqrt z - \frac1{\sqrt z}\right) \, dz[/tex]

The rest is trivial. By the power rule,

[tex]\displaystyle \int \left(\sqrt z - \frac1{\sqrt z}\right) \, dz = \frac23 z^{3/2} - 2z^{1/2} + C = \frac23 \sqrt z (z - 3) + C[/tex]

Put everything back in terms of [tex]y[/tex], then [tex]x[/tex] :

[tex]\displaystyle 2 \int \frac y{\sqrt{1+y}} \, dy = \frac43 \sqrt{1+y} (y - 2) + C[/tex]

[tex]\displaystyle \int \frac{dx}{\sqrt{1+\sqrt x}} = \boxed{\frac43 \sqrt{1+\sqrt x} (\sqrt x - 2) + C}[/tex]

Answer:

516 students eat out 3 times a week

Step-by-step explanation:

22% of 2346 is 516.12 and a person can't be a decimal so it's 516

22 x 2346 = 51612
and 51612÷100 = 516.12

We would expect about 516 WHS students to eat out 3 time

percentage, a relative value indicating hundredth parts of any quantity.

Given that 22% of high school students say they eat out 3 times a week

We need to find the number of students  of the 2346 students who attend WHS would you expect eat out 3 times a week

We can start by using the proportion:

(22/100) = (x/2346)

where x is the number of students we would expect to eat out 3 times a week.

To solve for x, we can cross-multiply:

100x = 22 × 2346

100x = 51612

Divide both sides by 100

x = 516.12

Hence, we would expect about 516 WHS students to eat out 3 time

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========================================================

Explanation:

The range of x values is [tex]-1 \le x \le 1[/tex] which means x = -1 is the smallest and x = 1 is the largest possible.

Similarly the smallest y value is y = -1 and the largest is y = 1.

----------

Plug in the smallest x and y value to get

f(x,y) = x+5y

f(-1,-1) = -1+5(-1)

f(-1,-1) = -6

Therefore, the absolute min is -6

----------

Now plug in the largest x and y values

f(x,y) = x+5y

f(1,1) = 1+5(1)

f(1,1) = 6

The absolute max is 6

Answer:

The Answer is 50 or 50x

Answer: 15x^2+35x ✅

Step-by-step explanation:

Hii, do you need to distribute [tex]\boldsymbol{5x(3x+7)}[/tex]? No problem! (:

We can solve problems like this one by using what is known as the "distributive property". What it says is: If you have a term that comes before the parentheses, you multiply it times every single term in the parentheses. Let me show you what I mean...

[tex]\twoheadrightarrow\sf 5x(3x+7)[/tex]

[tex]\bullet[/tex] Multiply 5x tmes 3x and 7 - you will obtain

[tex]\twoheadrightarrow\sf 15x^2+35x[/tex] (if we multiply x times x we obtain x²)

Voila! There's our solution, cheers! (:

--

Hope that this helped! Best wishes.

[tex]\it Reach\quad far.\:Aim\quad high. \,Dream\quad big.[/tex]

[tex]\bigstar\underbrace[/tex]

--

a) Intercepts are the points on the x and y axis

In the graph:

x-int: (-2,0), (2,0)

y-int: (0,1)

b) Domain is the list of x-values and Range is the list of y-values that make this graph true

Interval notations of domain and range

(Square brackets because the circles are closed)

Domain: [3,3]

Range: [0,3]

c) Intervals of increase and decrease: where the graph is increasing and decreasing

Increasing: -2 to 0 & 2 to 3

Decreasing: -3 to -2 & 0 to 2

d)Even, odd or neither

It is an even degree as both of its hands are facing upwards

Hope it helps!

Step-by-step explanation:

You need to attach the table in order to get an answer.

By critically observing the given graphs, we can logically deduce that "graph C" returns greatest integer that is less than or equal (≤) to x.

A greatest integer function can be defined as a type of function which returns the greatest integer that is less than or equal (≤) to the number.

Mathematically, the greatest integer that is less than or equal (≤) to a number (x) is represented as follows:

y = [x].

By critically observing the given graphs, we can logically deduce that y in "graph C" returns greatest integer that is less than or equal (≤) to x.

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