Question 6 of 10
Which equation matches the graph of the greatest integer function given
below?

Answer:

a simple interest rate of 4.5%

Answer:

[tex]Height = x \frac{x^3+3x^2+4}{x^3+3x^2+8}[/tex]

Step-by-step explanation:

[tex]Volume = Base \ Area\ * Height[/tex]

[tex]Height = \frac{Volume}{Base \ Area}[/tex]

Where [tex]Volume = x^4+4x^3+8x+4[/tex] and [tex]Area = x^3+3x^2+8[/tex]

Putting in the formula

[tex]Height = \frac{x^4 + 4x^3 + 3x^2 + 8x + 4}{x^3 + 3x^2 + 8}[/tex]

Doing long division, we get

[tex]Height = x + \frac{x^3+3x^2+4}{x^3+3x^2+8}[/tex]

[tex]Height = x \frac{x^3+3x^2+4}{x^3+3x^2+8}[/tex]

This is the simplifies form and it can't be further simplified.

Answer:

[tex]x +1 - \frac{4}{x^3 + 3x^2 + 8}[/tex]

Step-by-step explanation:

[tex]volume=base \: area \times height[/tex]

[tex]height=\frac{volume}{base \: area}[/tex]

[tex]\mathrm{Solve \: by \: long \: division.}[/tex]

[tex]h=\frac{(x^4 + 4x^3 + 3x^2 + 8x + 4)}{(x^3 + 3x^2 + 8)}[/tex]

[tex]h=x + \frac{x^3 + 3x^2 + 4}{x^3 + 3x^2 + 8}[/tex]

[tex]h=x +1 - \frac{4}{x^3 + 3x^2 + 8}[/tex]

Answer:

angle C = 38 degrees

Step-by-step explanation:

Refer to attached figure (sorry, forgot to attach earlier)

Given

AIB = 109

Let

CAX = XAB = x

CBY = YBA = y

XIB = YIA = x+y    ........exterior angles

XIB = YIA = 180-109 = 71   ............ sum of angles on a line

=>

x+y = 71

ACB = 180 - 2x -2y  ................. sum of angles of a triangle

= 180 - 2(x+y)

= 180 - 2(71)

= 180 - 142

= 38

Answer:

its 9

Step-by-step explanation:

Answer:

c. 9i.

Step-by-step explanation:

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

= [tex]\sqrt{-1 * 9 * 9}[/tex]

= [tex]\sqrt{-1 * 9^2}[/tex]

= [tex]9\sqrt{-1}[/tex]

The square root of -1 is the same thing as i.

= [tex]9i[/tex]

So, your answer is C.

Hope this helps!

Answer:

108, 324, 972

Step-by-step explanation:

This sequence is multiplying by ✖️3.

4✖️3=12✖️3=36✖️3=108✖️3=324✖️3=972

Hope this helps!

Answer:

It takes 4 seconds for the projectile to hit the ground

Step-by-step explanation:

The height of the projectile after t seconds is given by the following equation:

[tex]h(t) = -16t^{2} + 32t + 128[/tex]

How long will it take the projectile to hit the ground?

It happens when [tex]h(t) = 0[/tex]

So

[tex]h(t) = -16t^{2} + 32t + 128[/tex]

[tex]-16t^{2} + 32t + 128 = 0[/tex]

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]\bigtriangleup = b^{2} - 4ac[/tex]

In this question:

[tex]-16t^{2} + 32t + 128 = 0[/tex]

So [tex]a = -16, b = 32, c = 128[/tex]

[tex]\bigtriangleup = 32^{2} - 4*(-16)*(128) = 9216[/tex]

[tex]t_{1} = \frac{-32 + \sqrt{9216}}{2*(-16)} = -2[/tex]

[tex]t_{2} = \frac{-32 - \sqrt{9216}}{2*(-16)} = 4[/tex]

Time is a positive measure, so:

It takes 4 seconds for the projectile to hit the ground

Answer:

y = -3.5x² + 2.7x -8.2

Step-by-step explanation:

the quadratic equation is set up as a² + bx + c, so just plug in the values

Answer:

[tex]-3.5x^2 + 2.7x -8.2[/tex]

Step-by-step explanation:

Quadratic functions are always formatted in the form [tex]ax^2+bx+c[/tex].

So, we can use your values of a, b, and c, and plug them into the equation.

A is -3.5, so the first term becomes [tex]-3.5x^2[/tex].

B is 2.7, so the second term is [tex]2.7x[/tex]

And -8.2 is the C, so the third term is [tex]-8.2[/tex]

So we have [tex]-3.5x^2+2.7x-8.2[/tex]

Hope this helped!

Answer: 36

Step-by-step explanation:

Simply do 24/(2/3) to get 36 2/3 ounce slices.

Hope it helps <3

Answer:

3906250

Step-by-step explanation:

We can notice that the ratio is 5. 10/2 = 5

Each term gets multiplied by 5 to get the next term.

250 × 5 = 1250 (5th term)

1250 × 5 = 6250 (6th term)

6250 × 5 = 31250 (7th term)

31250 × 5 = 156250 (8th term)

156250 × 5 = 781250 (9th term)

781250 × 5 = 3906250 (10th term)

The 10th term of the geometric sequence is 3906250.

Answer:

d ≈ 8.3

Step-by-step explanation:

This is kind of like the pythagorean theorem, but with one extra value.  Thus, [tex]d^2=l^2+w^2+h^2[/tex].

Plug in the values to get:

[tex]d^2=2^2+7^2+4^2\\d^2=4+49+16\\d^2=69\\d=\sqrt{69} \\[/tex]

Thus d ≈ 8.3

Answer:

Step-by-step explanation:

Perimeter of a rectangle = 2l + 2w

where l is the length

w is the width

The length of the rectangle is 2 feet longer than the width is written as

l = 2 + w

Perimeter = 20feet

So we have

20 = 2( 2 + w ) + 2w

20 = 4 + 2w + 2w

4w = 16

Divide both sides by 4

w = 4

Substitute w = 4 into l = 2 + w

That's

l = 2 + 4

l = 6

Hope this helps you

Answer:

w = 4 and L = 10

Step-by-step explanation:

perimeter of a rectangle = 2(l+w)

p = 20

L = 2 + w

w = ?

20 = 2(2 + w + w)

20 = 2(2 + 2w)

20/2 = 2 + 2w

10 = 2 + 2w

10 - 2 = 2w

8 = 2w

w = 8/2 = 4

L = w + 2

L = 4 +2 = 6

w = 4 and L = 10

Answer:

If you compute the slope between any two points that must be the same, that's how you can tell if a table represents a linear function.

Remember that the slope between any two points (x1,y1), (x2,y2) is

slope   =  ( y2 - y1 ) / (x2 - x1)

Step-by-step explanation:

If you compute the slope between any two points that must be the same, that's how you can tell if a table represents a linear function.

Remember that the slope between any two points (x1,y1), (x2,y2) is

slope   =  ( y2 - y1 ) / (x2 - x1)

Answer: The machine depreciates during the fifth year by $4000.

Step-by-step explanation:

Given: The resale value of a certain industrial machine decreases over a 8-year period at a rate that changes with time.

When the machine is x years old, the rate at which its value is changing is 200(x - 8) dollars per year.

Then, the machine depreciates A(x) during the fifth year as

[tex]A(x) =\int^{5}_1200(x - 8)\ dx\\\\=200|\frac{x^2}{2}-8x|^{5}_1\\\\=200[\frac{5^2}{2}-\frac{1^2}{2}-8(5)+8(1)]\\\\=200 [12-32]\\\\=200(-20)=-4000[/tex]

Hence, the machine depreciates during the fifth year by $4000.

Answer:

[tex]\boxed{\mathrm{Option \ 4}}[/tex]

Step-by-step explanation:

Given that

[tex]y-4 = x[/tex]

Adding 4 to both sides

[tex]y-4+4 = x+4\\[/tex]

[tex]y = x+4[/tex]

Answer:

the real deal is that you mistook if

cos(x)=y/z gives y=zcos(x)

Answer:

The position of the particle is described by [tex]s(t) = \frac{1}{3}\cdot t^{3} + \frac{5}{2}\cdot t^{2} - 5\cdot t + 6,\forall t \geq 0[/tex]

Step-by-step explanation:

The position function is obtained after integrating twice on acceleration function, which is:

[tex]a(t) = 2\cdot t + 5[/tex], [tex]\forall t \geq 0[/tex]

Velocity

[tex]v(t) = \int\limits^{t}_{0} {a(t)} \, dt[/tex]

[tex]v(t) = \int\limits^{t}_{0} {(2\cdot t + 5)} \, dt[/tex]

[tex]v(t) = 2\int\limits^{t}_{0} {t} \, dt + 5\int\limits^{t}_{0}\, dt[/tex]

[tex]v(t) = t^{2}+5\cdot t + v(0)[/tex]

Where [tex]v(0)[/tex] is the initial velocity.

If [tex]v(0) = -5[/tex], the particular solution of the velocity function is:

[tex]v(t) = t^{2} + 5\cdot t -5, \forall t \geq 0[/tex]

Position

[tex]s(t) = \int\limits^{t}_{0} {v(t)} \, dt[/tex]

[tex]s(t) = \int\limits^{t}_{0} {(t^{2}+5\cdot t -5)} \, dt[/tex]

[tex]s(t) = \int\limits^{t}_0 {t^{2}} \, dt + 5\int\limits^{t}_0 {t} \, dt - 5\int\limits^{t}_0\, dt[/tex]

[tex]s(t) = \frac{1}{3}\cdot t^{3} + \frac{5}{2}\cdot t^{2} - 5\cdot t + s(0)[/tex]

Where [tex]s(0)[/tex] is the initial position.

If [tex]s(0) = 6[/tex], the particular solution of the position function is:

[tex]s(t) = \frac{1}{3}\cdot t^{3} + \frac{5}{2}\cdot t^{2} - 5\cdot t + 6,\forall t \geq 0[/tex]

Answer:

Position of the particle is :

[tex]S(t)=\frac{1}{3}.t^3+\frac{5}{2}.t^2-5.t+6[/tex]

Step-by-step explanation:

Given information:

The particle is moving with an acceleration that is function of:

[tex]a(t)=2t+5[/tex]

To find the expression for the position of the particle first integrate for the velocity expression:

AS:

[tex]V(t)=\int\limits^0_t {a(t)} \, dt\\v(t)= \int\limits^0_t {(2.t+5)} \, dt\\\\v(t)=t^2+5.t+v(0)\\[/tex]

Where, [tex]v(0)[/tex] is the initial velocity.

Noe, if we tale the [tex]v(0) =-5[/tex] ,

So, the velocity equation can be written as:

[tex]v(t)=t^2+5.t-5[/tex]

Now , For the position of the particle we need to integrate the velocity equation :

As,

Position:

[tex]S(t)=\int\limits^0_t {v(t)} \, dt \\S(t)=\int\limits^0_t {(t^2+5.t-5)} \, dt\\S(t)=\frac{1}{3}.t^3+\frac{5}{2}.t^2-5.t+s(0)[/tex]

Where, [tex]S(0)[/tex] is the initial position of the particle.

So, we put the value [tex]s(0)=6[/tex] and get the position of the particle.

Hence, Position of the particle is :

[tex]S(t)=\frac{1}{3}.t^3+\frac{5}{2}.t^2-5.t+6[/tex].

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Answer:

The answer is A (Two squares)

Step-by-step explanation:

Any give square will have proportionate side lengths,as they are the same, meaning that if you dilute  one square it will always be proportinate

Answer:

it is a

Step-by-step explanation:

the other person is correct. and I did the test

Answer:

Disks = $4 each and Notebooks = $7 each

Step-by-step explanation:

-4(2D + 3N = 29)

3(5D + 4N = 48)

-8D - 12N = -116

15D + 12N = 144

7D = 28

D = $4

2(4) + 3N = 29

8 + 3N = 29

3N = 21

N = $7

Answer:

Here is the refactored function:

def rectangle_area(base, height):

   area = base * height

   return area    

print("The area is ", rectangle_area(5,6))

Step-by-step explanation:

The above program has a function rectangle_area that takes two variables base and height as parameters. The function then computes the area of rectangle by multiplying the values of base and height. The result of the multiplication is assigned to the variable area. Then the function returns the resultant area.

print("The area is ", rectangle_area(5,6)) statement calls rectangle_area() method by passing values of base and height i.e. 5 and 6 to compute the area. The output of this program is:

The area is 30

Note that the use of rectangle_area function name describes what the function does i.e. it computes the area of rectangle. By naming the parameters as base and height that clearly depicts that in order to compute rectangle are we need the base and height of rectangle. So this makes the code readable.

Answer:

3s-4bbb=17

Step-by-step explanation:

brother=4bbb

sister=3s

3s-4bbb=17

Answer:

[tex]a => b \equiv ( \neg a \ \lor \ b )[/tex]

Step-by-step explanation:

You can understand the statement from many perspectives, but in terms of proposition logic it is best to understand it as   "negation of a" or "  b" in mathematical terms is written like this

[tex]a => b \equiv ( \neg a \ \lor \ b )[/tex]

You can show that they are logically equivalent because they have the same truth table.

Answer: x= 7

Step-by-step explanation:

-2x= -14    Divide both sides by -2

x= 7  

check

-2(7) = -14

-14 = -14

Answer:

x = 7

Step-by-step explanation:

-2x = -14

Divide each side by -2

-2x/-2 = -14/-2

x = 7

Answer:

345

Step-by-step explanation:

1 + 4 = 5

4 + 5 = 9

16 + 9 = 25

64 + 25 = 89

1, 4, 16, and 64 are powers of 4.  The next power of 4 is 256.

256 + 89 = 345

The answer is 345 (don’t ask why)

Answer:The answer is c

Step-by-step explanation:

Answer:

Ok, we have a total of 26 letters, and we want to select 5 of them.

Of the 26 letters, 21 are consonants and 5 are vowels.

Suppose that we want to have the consonant in the first selection, so the probability of picking a consonant is equal to the quotient between the number of consonants and the total number of letters.

p = 21/26

now a letter has been selected, so in the set, we have 25 letters left.

In the next 4 selections, we must select vowels.

In the second selection the probability is:

p = 5/25

in the third, the prob is:

p = 4/24 (we already selected one vowel before, so now we only have 4 vowels)

The fourth selection:

p = 3/23

and the last selection:

p = 2/22

The total probability is equal to the product of all the individual proabilities, so we have:

P = (2/22)*(3/23)*(4/24)*(5/25)*(21/26)

Now, remember that we said that the consonant must be in the first place, but it can be in any of the five places, so if we add the permutations of the consonant letter we have:

P = 5*(2/22)*(3/23)*(4/24)*(5/25)*(21/26) =  0.0018

obviously 4 is bigger coz 12/7 will yeild you 1.71

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▹ Answer

Slope = -3

Y-intercept = 8

▹ Step-by-Step Explanation

y = mx + b

mx represents the slope.

b represents the y intercept.

therefore,

y = -3x + 8

Hope this helps!

CloutAnswers ❁

Brainliest is greatly appreciated!

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Answer:

[tex]\boxed{\mathrm{Slope:}-3 \: \: \: \:\: \mathrm{Y \: intercept:}8}[/tex]

Step-by-step explanation:

The general form of slope-intercept:

[tex]y=mx+b[/tex]

[tex]m:slope\\b:y \: intercept[/tex]

[tex]y=-3x+8[/tex]

[tex]m=-3\\b=8[/tex]

The slope is -3.

The y-intercept is (0, 8) or 8.

Answer:

Step-by-step explanation:

From the information given:

mean life span of a brand of automobile = 35,000

standard deviation of a brand of automobile = 2250 miles.

the z-score that corresponds to each life span are as follows.

the standard z- score formula is:

[tex]z = \dfrac{x - \mu}{\sigma}[/tex]

For x = 34000

[tex]z = \dfrac{34000 - 35000}{2250}[/tex]

[tex]z = \dfrac{-1000}{2250}[/tex]

z = −0.4444

For x = 37000

[tex]z = \dfrac{37000 - 35000}{2250}[/tex]

[tex]z = \dfrac{2000}{2250}[/tex]

z = 0.8889

For x = 3000

[tex]z = \dfrac{30000 - 35000}{2250}[/tex]

[tex]z = \dfrac{-5000}{2250}[/tex]

z = -2.222

From the above z- score that corresponds to their life span; it is glaring  that the tire with the life span 30,000 miles has an unusually short life span.

For x = 30,500

[tex]z = \dfrac{30500 - 35000}{2250}[/tex]

[tex]z = \dfrac{-4500}{2250}[/tex]

z = -2

P(z) = P(-2)

Using excel function (=NORMDIST -2)

P(z) = 0.022750132

P(z) = 2.28th percentile

For x =  37250

[tex]z = \dfrac{37250 - 35000}{2250}[/tex]

[tex]z = \dfrac{2250}{2250}[/tex]

z = 1

Using excel function (=NORMDIST 1)

P(z) = 0.841344746

P(z) = 84.14th percentile

For x = 35000

[tex]z = \dfrac{35000- 35000}{2250}[/tex]

[tex]z = \dfrac{0}{2250}[/tex]

z = 0

Using excel function (=NORMDIST 0)

P(z) = 0.5

P(z) = 50th percentile

a.  The z score of each life span should be -0.4444, 0.889, and 2.2222.

b.  The percentile of each life span should be 0.0228, 0.8413 and  0.5000.

Given that,

(a)

The z score should be

[tex]Z1 = \frac{34000-35000}{2250} = -0.4444\\\\Z2 = \frac{37000-35000}{2250} = 0.8889\\\\Z3 = \frac{30000-35000}{2250} = -2.2222\\\\[/tex]

The tire with life span of 30000 miles would be considered unusual

(b)

The percentile should be

[tex]Z1 = \frac{30500-35000}{2250} = -2[/tex]

p(Z1 < -2) = NORMSDIST(-2) = 0.0228

[tex]Z2 = \frac{37250-35000}{2250} = 1[/tex]

p(Z2 < 1) = NORMSDIST(1) = 0.8413

[tex]Z3 = \frac{35000-35000}{2250} = 0[/tex]

p(Z3 < 0) = NORMSDIST(0) = 0.5000

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Answer: Chi-square test

Step-by-step explanation:

A Chi-square test is a test used or applied to check or see if a relationship between two categorical variables. Example

The marketing firm trying to show their client that there is a linear relationship between sales and the amount of money the client has invested in radio advertisements uses chi-square method by comparing the two variables which are Sales made and Amount spent on advert or promotion on radio.

Answer:

Step-by-step explanation:

Firstly let us calculate the amount of hours you will have to work in a week.

Since you will have to work Mondays through Fridays, hence you will be working 5 days in a week.

Hence in a week you will work 8.5*5= 42.5 hours in a week

Since in 1 hours you are mandated to pick 45 units

Hence in 42.5 hours you will pick 42.5*45= 1912.5 units