which quadratic function in standard form has the value a= -3.5, b=2.7, and c= -8.2?

Answer:

It will take Stephon about A: 163 seconds to run two laps when he is 192 months old.

Step-by-step explanation:

To find 163 seconds all I did was eyeball where 192 months is going to be on the x-axis and lined it up with the provided line of fit, then I ran it across the x-axis to the y-axis and I got around 163 seconds.

Given line of best fit is y = -2.1x + 565.6, where x is age in months and y is time in seconds, it take Stephon 162.4 seconds to run two laps on the track when he is 192 months old

A line of best fit is a straight line that minimizes the distance between it and some data. The line of best fit is used to express a relationship in a scatter plot of different data points.

Given in the question,

x =  age in months

y = time in seconds

Here, age of child is independent and time taken to run two laps is dependent variable.

given line of best fit :  y = -2.1x + 565.6

given y = 192 months

finding the value of y :

y = -2.1x + 565.6 = -2.1 * 192 + 565.6 = 162.4

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Answer: 1.7

Step-by-step explanation:

5 divided by 3=1.666666667

1.6 and next 6 in line is over 5 so the 6 turns to a 7

3*1.7= 5.1 but when rounded 1 tells 5 to stay down so it = 5

The area of the surface above the region R is 4096π square units.

Given that:

The function: [tex]f(x, y) = 64 + x^2 - y^2[/tex]

The region R is the disk with a radius of 8 units [tex]x^2 + y^2 \le 64[/tex].

To find the area of the surface given by z = f(x, y) that lies above the region R, to calculate the double integral over the region R of the function f(x, y) with respect to dA.

The integral for the area is given by:

[tex]Area = \int\int_R f(x, y) dA[/tex]

To evaluate this integral, we need to set up the limits of integration for x and y over the region R, which is the disk cantered at the origin with a radius of 8 units.

Using polar coordinates, we can parameterize the region R as follows:

x = rcos(θ)

y = rsin(θ)

where r goes from 0 to 8, and θ goes from 0 to 2π.

Now, rewrite the integral in polar coordinates:

[tex]Area =\int\int_R f(x, y) dA\\Area = \int_0 ^{2\pi} \int_0^8(64 + r^2cos^2(\theta) - r^2sin^2(\theta)) \times r dr d \theta[/tex]

Now, we can integrate with respect to r first and then with respect to θ:

[tex]Area = \int_0^{2\pi} \int_0^8] (64r + r^3cos^2(\theta) - r^3sin^2(\theta)) dr d \theta[/tex]

Integrate with respect to r:

[tex]Area = \int_0^{2\pi}[(32r^2 + (1/4)r^4cos^2(\theta) - (1/4)r^4sin^2(\theta))]_0^8 d \theta\\Area = \int_0^{2\pi} (2048 + 256cos^2(\theta) - 256sin^2(\theta)) d \theta[/tex]

Now, we can integrate with respect to θ:

[tex]Area = [2048\theta + 128(sin(2\theta) + \theta)]_0 ^{2\pi}[/tex]

Area = 2048(2π) + 128(sin(4π) + 2π) - (2048(0) + 128(sin(0) + 0))

Area = 4096π + 128(0) - 0

Area = 4096π square units

So, the area of the surface above the region R is 4096π square units.

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Answer:

probability of getting both are unripe

= 0.15

probability of getting both are ripe

= 0.375

Probability of one ripe and one unripe

=0.234375

Probability of at least one unripe

=0.625

Step-by-step explanation:

50 mangoes 20 of which are unriped in the first basket .

Riped = 50-20= 30

Probability of unripe = 20/50

Probability of unripe= 0.4

Probability of ripe = 30/50

Probability of ripe = 0.6

40 mangoes of which 15 are unripe In the second basket

Number of riped= 40-15= 25

Probability of unriped= 15/40

Probability of unriped= 0.375

Probability of riped= 25/40

Probability of riped= 0.625

probability of getting both are unripe

= 0.4*0.375

probability of getting both are unripe

= 0.15

probability of getting both are ripe

= 0.6*0.625

= 0.375

Probability of one ripe and one unripe

= 0.625*0375

= 0.234375

Probability of at least one unripe

= 1- probability of no unripe

= 1 - probability of both ripe

= 1-0.375

= 0.625

Answer:

x=-9

Step-by-step explanation:

6-15=-9

Answer:

-9

Step-by-step explanation:

When you add some thing to a negative that means you are actually subtract that number

The depth of hole is 0.609 inches.

Given, the total depth of the block of  wood is  [tex]\frac{13}{16}[/tex] inches.

Since the hole is [tex]\frac{3}{4}[/tex] of the total depth, so the depth of the hole will be,

[tex]D=\frac{3}{4} \times\frac{13}{16}[/tex]

Or, [tex]D=\frac{39}{64}[/tex]

[tex]D=0.609375 \ in[/tex]

Hence the depth of hole is 0.609 inches.

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Answer:

B

Step-by-step explanation:

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.

Hey there! I'm happy to help!

We see that the father is 60 years old, and the son is half of that age, so this means that the son is 30 years old.

We want to see the age the son was at when the father was four times his age. We know that the father is thirty years older than him, so we can write this equation with s representing the age of the son.

s+30=4s   (30 years older than the son is equal to to four times the son's age at the time)

We subtract 30 from both sides.

s=4s-30

We subtract 4s from both sides.

-3s=-30

We divide both sides by -3.

s=10

Therefore, the boy was 10 when his father was four times his age. This is because his father would have been 40 because that is 30 more years than 10, and it is four times ten!

Have a wonderful day! :D

Answer:

[tex] f(x) = 6x^2 +2 , -6 <x<9[/tex]

[tex] f(x) = 12 , 9 \leq x <13[/tex]

And we want to evaluate f(x=9)

And for this case the answer would be:

[tex] f(9)= 12[/tex]

Best answer:

O 12

Step-by-step explanation:

For this problem we have the following function given:

[tex] f(x) = 6x^2 +2 , -6 <x<9[/tex]

[tex] f(x) = 12 , 9 \leq x <13[/tex]

And we want to evaluate f(x=9)

And for this case the answer would be:

[tex] f(9)= 12[/tex]

Best answer:

O 12

Answer:

the answer is c...............

Answer:

I am pretty sure that it is  C

Step-by-step explanation:

A 1,3 so 3 < 3 no not true

   x,y

B -12,50   50< -36 Also not true

    x  ,  y

C  9  ,  4   4<27 Yes    4< 5 YEPPP

D 4,10   10<12 Yes          10<5 NOOPPPPPEEEE

Answer:

3

Step-by-step explanation:

[tex]a^{2} +b^{2} =c^{2}[/tex]

[tex]x^{2} +b^{2} =(3\sqrt{2} )^{2}[/tex]

[tex]3*3=9[/tex][tex]\sqrt{2} *\sqrt{2} =2[/tex]

[tex]2*9=18[/tex]

9*2=18

x^2=9

b^2=9

x=3

Answer:

Computation of Grade Point Average (GPA):

GPA = Total Weighted Points divided by total credit hours

= 45/19

= 2.37 on 4.00 Grade Average

Step-by-step explanation:

a) Data and Computations:

Courses  Grade Letters  Credit Hours  Quality Points  Weighted Points

1                        B                     4                        3                      12

2                       B                     5                        3                      15

3                       A                     1                         4                       4

4                       C                     5                        2                     10

5                       D                     4                        1                       4

Total                                       19 credit hours                         45 Points

b) GPA = Total Weighted Points divided by total credit hours

= 45/19

= 2.37

c) The GPA for this student is the total weighted points (which is a product of the credit hours (loads) and the quality point) expressed as a ratio of the total credit hours for the courses she took.  The grade point average ensures that the each point used in calculating the GPA is weighed by the credit hours allocated to the course.  The resultant figure of 2.37 implies that out of 4.00 grade points, the student scored 2.37, translating to about 59%.

Answer:

K = 40

Step-by-step explanation:

As they said that 28 is 12 less than K , it means that you've to add them to get the answer. So , 28 + 12 = 40 which is represented by the variable "K"

Hope it helps and pls mark as brainliest : )

Answer:

Step-by-step explanation:

28 is 12 less than k

Let's create an equation:

[tex]28 = k - 12[/tex]

Now, let's solve:

[tex]28 = k - 12[/tex]

Move variable to L.H.S and change its sign

Similarly, Move constant to R.H.S and change its sign

[tex] - k = - 12 - 28[/tex]

Calculate the difference

[tex] - k = - 40[/tex]

Change the signs on both sides of the equation

[tex]k = 40[/tex]

Hope this helps...

Best regards!!

Answer:

∠1 is 150°

∠2 is 30°

∠3 is 150°

∠4 is 30°

Step-by-step explanation:

∠1 is vertically opposite to ∠3 so they are equal

360° - (150° + 150°) = 360° - 300° = 60°

∠2 and ∠4 must sum to 60°

Step-by-step explanation:

From the question

∠1 is opposite to ∠ 3 and vertically opposite angles are equal

So

∠1 = ∠ 3

That's

∠ 3 and ∠ 4 are on a straight line and angles on a straight line add up to 180°

So to find ∠4, subtract ∠3 from 180°

That's

∠ 4 = 180 - ∠ 3

∠ 4 = 180 - 150

Since ∠ 4 and ∠ 2 are opposite they are also equal

That's

∠ 4 = ∠ 2

Therefore

Hope this helps you

Answer:

8*4*3=96 boxes in total

Step-by-step explanation:

I think. I just multiplies the 3 numbers. Hope this helps (:

Answer:

8*4*3=96 boxes in total

Step-by-step explanation:

I just multiplies the 3 numbers.

Answer:

g(-2)= -2 + 5 =3  ( here we chose the function g(x)= x+5 as x< 3)

Step-by-step explanation:

g(3)= is not defined ( function is defined for x<3 and x>3 but not x=3)

g(4) = 6-4=2 ( here we chose the function g(x)= 6-x as x> 3)

Answer:

first is 18

second is 36

third is -10

fourth is -10

Answer:

The range is found by subtracting the minimum data entry from the maximum data entry.

Step-by-step explanation:

The range is found by subtracting the minimum data entry from the maximum data entry.

It is easy to compute.

It uses only two entries from the data set.

Answer:

80

Step-by-step explanation:

Answer:

Step by step explanation

Total length of pole = 21.3 m

Length of pole inside the ground = 0.2 m

Let length of pole outside the ground be X,

So, according to the Question,

[tex]x + 0.2 = 21.3[/tex]

Move constant to R.H.S and change its sign

[tex]x = 21.3 - 0.2[/tex]

Calculate the difference

[tex]x = 21.1 \: m[/tex]

Hope this helps...

Good luck on your assignment...

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 option A.

Step-by-step explanation:

Using the properties of logarithms

that's

[tex] log(x) - log(y) = log( \frac{x}{y} ) [/tex]

log 2 - log 14 is

[tex] log(2) - log(14) = log( \frac{2}{14} ) [/tex]

Simplify

We have the final answer as

[tex] log( \frac{1}{7} ) [/tex]

Hope this helps you

Answer:

log ( 1/7)

Step-by-step explanation:

log2-log14

We know that log ( a/b) = log a - log b

log (2 /14)

log ( 1/7)

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:

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:

3:1

Step-by-step explanation:

75%=[tex]\frac{75}{100}[/tex]=[tex]\frac{3}{4}[/tex]

25%=[tex]\frac{25}{100}[/tex]=[tex]\frac{1}{4}[/tex]

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: k = 7

Step-by-step explanation:

12k=84

Divide(12)

k=7

Hope it helps <3

Answer:

Step-by-step explanation:

The product of 12 and k is 84

let's create an equation:

[tex]12k = 84[/tex]

Divide both sides of the equation by 12

[tex] \frac{12 \: k}{12} = \frac{84}{12} [/tex]

Calculate

[tex]k = 7[/tex]

Hope this helps...

Best regards!!