Suppose f(x) is continuous on [3,6] and −3≤f′(x)≤5 for all x in (3,6). Use the Mean Value Theorem to estimate f(6)−f(3).

Answer:

c) 81.5

Step-by-step explanation:

Listing the 25 ages in crescent order:

60 61 62 63 64 65 66 68 68 69 70 73 73 74 75 76 76 81 81 82 86 87 89 90 92

The upper or third quartile's position is given by:

[tex]Q_3=N_{\frac{3}{4}(n+1)}\\Q_3}=N_{\frac{3}{4}(25+1)}=N_{19.5}[/tex]

This means that the third quartile is the average between the 19th and 20th numbers:

[tex]Q_3=\frac{81+82}{2} \\Q_3 = 81.5[/tex]

The upper quartile is 81.5.

Answer:

Step-by-step explanation:    AS YOU KHOW THW ABSOLUTE VALUE OF A QUESTION IS NUMBER ITSELF IF THERE IS MINUS SIGH THEN THE  SIGH OF A NUMBER WILL BECOME PLUS OR IF THERE IS A PLUS SIGH THEN THERE IT WILL REMAIN AS IT IS. IF THERE IS NO NUMBER WITH THE MINUS SIGH THEN THE MINUS SIGH WILL REAMIN AS IT IS.

+2 +9  -   +2

The answer has same sigh, then Plus answer will you get is

+11 - 2 then you will minus the answer will be

+9

HOPE IT HELP YOU

Answer:

x = 5

Step-by-step explanation:

52 = y since they are the base angles of an isosceles triangle and the base angles are equal

The sum of the angles of a triangle are 180

52+y+14x+6 =180

Substitute for y

52+52+14x+6 = 180

Combine like terms

110 + 14x = 180

Subtract 110 from each side

110+14x-110 = 180-110

14x =70

Divide by 14

14x/14 = 70/14

x =5

√(16 - x^2) is defined only for -4 ≤ x ≤ 4, and is continuous over this domain, so

[tex]\displaystyle\lim_{x\to-4^+}\sqrt{16-x^2}=\sqrt{16-(-4)^2}=0[/tex]

From the other side, the limit does not exist, because all x < -4 do not belong to the domain.

Taken together, the two-sided limit also does not exist.

Answer:

Amount that Brian has after 2 years = £6932.53

Step-by-step explanation:

To find, the amount that Brian will have after 2 years:

Formula for amount where compound interest is applicable:

[tex]A = P \times (1+\dfrac{R}{100})^t[/tex]

Where A is the amount after t years time

P is the principal.

R is the rate of interest.

In the question, we are given the following details:

Principal amount,P = £6300

Rate of interest,R = 4.9%

Time,t = 2 years

Putting the values in formula:

[tex]A = 6300 \times (1+\dfrac{4.9}{100})^2\\\Rightarrow 6300 \times (\dfrac{104.9}{100})^2\\\Rightarrow 6932.53[/tex]

Hence, Amount that Brian has after 2 years = £6932.53

Answer:

THE ANSWER IS ABOVE

Step-by-step explanation:

hahahaha

Answer:

The Transformations are R(O , -90°) & R(O , 270)

Step-by-step explanation:

* Lets revise the rotation of a point

- If point (x , y) rotated about the origin by angle 90° anti-clock wise

∴ Its image is (-y , x)

- If point (x , y) rotated about the origin by angle 90° clock wise

 (270° anti-clockwise or -90°)

∴ Its image is (y , -x)

- If point (x , y) rotated about the origin by angle 180°

∴ Its image is (-x , -y)

* There is no difference between rotating 180° clockwise (-180°) or  

anti-clockwise (180°) around the origin

* Lets solve the problem

∵ One vertex of a triangle is located at (0, 5) on a coordinate grid

∵ The image of the point after the transformation is (5 , 0)

- The coordinates are switched with each other

∴ There is no rotation with 180° or -180° because in the rotation with

 180° and -180° around the origin we change only the signs of the

 coordinates without switch them

∴ There is a rotation with 90° are 270° or -90°

- The zero has no sign

- When we rotate the point (0 , 5) by -90° or 270° around the origin

 we will change the sign of x-coordinate and switch the two

 coordinates

∴ The image of the point is (y , -x)

∵ x = 0 and y = 5

- There is no sign for zero, so we switch the coordinates only

∴ The vertex is located at (5, 0)

∴ The Transformations are R(O , -90°) & R(O , 270)

Answer:

R(O , -90°) & R(O , 270)

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

Given

y = x² - 2x - 8

To find the x- intercepts let y = 0 , that is

x² - 2x - 8 = 0 ← in standard form

(x - 4)(x + 2) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 4 = 0 ⇒ x = 4

x + 2 = 0 ⇒ x = - 2

x- intercepts : x = - 2, x = 4

The x- coordinate of the vertex is mid way between the x- intercepts, that is

[tex]x_{vertex}[/tex] = [tex]\frac{-2+4}{2}[/tex] = [tex]\frac{2}{2}[/tex] = 1

Substitute x = 1 into the equation for corresponding y- coordinate

y = 1² - 2(1) - 8 = 1 - 2 - 8 = - 9

vertex = (1, - 9 )

Answer:

1/5

Step-by-step explanation:

switch sides, delete both common factors and your stuck with 5k=1. then you put both in a fraction and it gets you 1/5

Answer:

[tex] AC = \sqrt(26) \approx 5.1 [/tex]

Step-by-step explanation:

The diagonals are AC and BD.

Now we find the lengths of the diagonals using the distance formula.

[tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]

AC:

[tex] AC = \sqrt{(6 - 5)^2 + (7 - 2)^2} [/tex]

[tex] AC = \sqrt{(1)^2 + (5)^2} [/tex]

[tex] AC = \sqrt{1 + 25} [/tex]

[tex] AC = \sqrt{26} [/tex]

BD:

[tex] BD = \sqrt{(9 - 2)^2 + (5 - 4)^2} [/tex]

[tex] BD = \sqrt{(7)^2 + (1)^2} [/tex]

[tex] BD = \sqrt{49 + 1} [/tex]

[tex] BD = \sqrt{50} [/tex]

Since sqrt(26) < sqrt(50), then the shorter diagonal is AC.

Answer: AC = sqrt(26) or approximately 5.1

Answer:

A = (5.2)

Step-by-step explanation:

c2= (6-5)^2 + (7-2)^2

To find AC we calculate within parenthesis (6-5) : 1

c2= 1 + (7-2)^2

calculate within parenthesis (7-2) : 5

c2 = 1^2 + 5^2

then calculate exponents 1^2:1

c^2 = 1+5^2

add and subtract left to right

c^2 = 1+25

c^2 =26

Sr of 26 = 5.09901951359

Which means the closest answer is A = 5.2

To find BD we calculate within parenthesis (9-2):7

c2= (9-2)^2 + (5 - 4)^2

calculate within parenthesis (5-4) : 1

c2 = (7)^2 + (1)^2

calculate exponents 1 ^2 : 1

c2 = 49 +1

add and subtract left to right

c2 = 50

Sr of 50 = 7.07106781187

Answer:

object have been reduced by a factor of 4 on paper or the drawing have been increased by a factor of 4 on land .

Step-by-step explanation:

What a scale factor of 1:4 means.

Simply it means that the reals size of the object on land have been reduced in the drawing in the paper.

Now for scale factor of 1:4 in particular it means that the object have been reduced by a factor of 4 on paper or the drawing have been increased by a factor of 4 on land .

Example if the drawing has measurements of 4 inches on paper, then on land it will be 16 inches

Answer:

Vector is equal to vector b. For two vectors to be equal, they must have both the magnitude and the directions equal.

Step-by-step explanation:

Answer:

Option 2 is correct

Step-by-step explanation:

One number is 2 times another number plus 3. Their sum is 21.

"One number is 2 times another number plus 3" translated to

x = smaller number = another number

It is also given that: Their sum is 21.

Combine like terms:

3x+3 = 21

Answer:

I do questions like these everyday so I have too much experience. Let me explain step by step for you.

Brainliest?

First lets set 2 variables x and y

Lets make 2 equations.

x=3+2*y

Thats because it says 'x' is 3 more (+) than 2 times(*) 'y'

Now lets set second, we know both of them add up to 27.

x+y = 27

Since we know what x is equal to (look above equation)

We can replace it.

x is replaced with 3+2*y

3+2y+y = 27

3+4y = 27

Simplify 27-3 = 24

24/4 = 6

Now lets plug in for x

3+2*6 = 15

15 - x

6 - y

:))

Answer:

P(3) = 0.0244

P(3) = 2.44%

the probability that all three selected have driven while under the influence of alcohol is 2.44% or 0.0244

Step-by-step explanation:

Given;

The probability that they have driven while under the influence of alcohol is;

P = 29% = 0.29

the probability that all three selected have driven while under the influence of alcohol is;

P(3) = P × P × P

P(3) = 0.29 × 0.29 × 0.29

P(3) = 0.024389

P(3) = 0.0244

P(3) = 2.44%

the probability that all three selected have driven while under the influence of alcohol is 2.44% or 0.0244

Answer:

Step-by-step explanation:

The formula to calculate the forecast could be determine by using the exponential smoothing method :

[tex]Ft = F(t-1) + \alpha [A(t-1) - F(t-1)][/tex]

Where ,Ft is the Forecast for period t

F(t-1) is the Forecast for the period previous to t

A(t-1) is the Actual demand for the period previous to t

[tex]\alpha[/tex] = Smoothing constant

To get the forecast for may and june   the above formula with [tex]\alpha =0.5[/tex] and april forecast of 500 will be used

For march

[tex]=500+0.5(520-500)\\\\=500+0.5\times20\\\\=500+10\\\\=510[/tex]

For April

[tex]=510+0.5(535-510)\\\\=510+0.5\times25\\\\=510+12.5\\\\=522.5[/tex]

For May

[tex]=522.5+0.5(550-5225)\\\\=522.5+0.5\times27.5\\\\=522.5+13.75\\\\=536.25[/tex]

So forecast for May = 536.25

Answer:

x = 17 or x = ±7i

Step-by-step explanation:

x³ − 17x² + 49x − 833 = 0

x² (x − 17) + 49 (x − 17) = 0

(x² + 49) (x − 17) = 0

x = 17 or ±7i

Answer:

Probability that one of the giftcards will go to a student athlete and one will go to a freshman = 26.4%

Step-by-step explanation:

At Central High School, 55% of students play a school sport. Also, 24% of the student population is in ninth grade. No ninth graders are allowed to play school sports. If two students are selected at random to receive a gift card, what is the probability that one will go to a student athlete and one will go to a freshman? Write the answer as a percent rounded to the nearest tenth of a percent.

Solution

Probability that a student plays a school sport, that is, probability that a student is a student athlete = P(S) = 55% = 0.55

Probability that a student is in the ninth grade, that is, probability that a student is a freshman = P(F) = 24% = 0.24

It was given that no freshman is allowed to play sports, hence, it translates that the event that a student is a student athlete and the event that a student is a freshman are mutually exclusive.

P(S n F) = 0

If two students are then picked at random to receive a gift card, we require the probability that one will go to a student athlete and one will go to a freshman.

Probability that the first one goes to a student athlete = P(S) = 0.55

Probability that the second one goes to a freshman ≈ 0.24

Probability that the first one goes to a freshman = P(F) = 0.24

Probability that the second one goes to a student athlete ≈ 0.55

Probability that one will go to a student athlete and one will go to a freshman

= (0.55 × 24) + (0.24 × 0.55)

= 0.132 + 0.132

= 0.264

= 26.4% in percent to the nearest tenth.

Hope this Helps!!

Answer:

42

Step-by-step explanation:

Mean = Sum of numbers/ Total numbers

Sum of 6 numbers = 32 x 6

= 192

If one number is excluded the mean reduce by 2 . so it becomes 30

Sum of 5 Numbers = 5 x 30

=150

Therefore the excluded number is

= 192 - 150

= 42.

Answer:

  27 : 1

Step-by-step explanation:

The faces of a regular tetrahedron are equilateral triangles. The incenter, circumcenter, and centroid are all the same point, located 1/3 of the distance from the edge to the opposite vertex of the face. The vertical height of the point that is 1/3 the slant height from the base is 1/3 of the height of the tetrahedron.

Then the "inscribed" tetrahedron has 1/3 the height of the original. The ratio of volumes is the cube of the ratio of linear dimensions, so the ratio of the larger volume to the smaller is ...

  3³ : 1³ = 27 : 1

Answer:

-14 / 3

Step-by-step explanation:

- Divergence theorem, expresses an explicit way to determine the flux of a force field ( F ) through a surface ( S ) with the help of "del" operator ( D ) which is the sum of spatial partial derivatives of the force field ( F ).

- The given force field as such:

                      [tex]F = (x^2y) i + (xy^2) j + (3xyz) k[/tex]

Where,

         i, j, k are unit vectors along the x, y and z coordinate axes, respectively.

- The surface ( S ) is described as a tetrahedron bounded by the planes:

                      [tex]x = 0 \\y = 0\\x + 2y + z = 2[/tex]

                      [tex]z = 0\\[/tex]

- The divergence theorem gives us the following formulation:

                      [tex]_S\int\int {F} \,. dS = _V\int\int\int {D [F]} \,. dV[/tex]

- We will first apply the del operator on the force field as follows:

                      [tex]D [ F ] = 2xy + 2xy + 3xy = 7xy[/tex]

- Now, we will define the boundaries of the solid surface ( Tetrahedron ).

- The surface ( S ) is bounded in the z - direction by plane z = 0 and the plane [ z = 2 - x - 2y ]. The limits of integration for " dz " are as follows:

                      dz: [ z = 0 - > 2 - x - 2y ]

- Now we will project the surface ( S ) onto the ( x-y ) plane. The projection is a triangle bounded by the axes x = y = 0 and the line: x = 2 - 2y. We will set up our limits in the x- direction bounded by x = 0 and x = 2 - 2y. The limits of integration for " dx " are as follows:

                     dx: [ x = 0 - > 2 - 2y ]

- The limits of "dy" are constants defined by the axis y = 0 and y = -2 / -2 = 1. Hence,

                    dy: [ y = 0 - > 1 ]

- Next we will evaluate the triple integral as follows:

                   [tex]\int\int\int ({D [ F ] }) \, dz.dx.dy = \int\int\int (7xy) \, dz.dx.dy\\\\\int\int (7xyz) \, | \limits_0^2^-^x^-^2^ydx.dy\\\\\int\int (7xy[ 2 - x - 2y ] ) dx.dy = \int\int (14xy -7x^2y -14 xy^2 ) dx.dy\\\\\int (7x^2y -\frac{7}{3} x^3y -7 x^2y^2 )| \limits_0^2^-^2^y.dy \\\\\int (7(2-2y)^2y -\frac{7}{3} (2-2y)^3y -7 (2-2y)^2y^2 ).dy \\\\[/tex]

                 [tex]7 (-\frac{(2-2y)^3}{6} + (2-2y)^2 ) -\frac{7}{3} ( -\frac{(2-2y)^4}{8} + (2-2y)^3) -7 ( -\frac{(2-2y)^3}{6}y^2 + 2y.(2-2y)^2 )| \limits^1_0\\\\ 0 - [ 7 (-\frac{8}{6} + 4 ) -\frac{7}{3} ( -\frac{16}{8} + 8 ) -7 ( 0 ) ] \\\\- [ \frac{56}{3} - 14 ] \\\\\int\int {F} \, dS = -\frac{14}{3}[/tex]

Answer:53/6

Step-by-step explanation:

Let X be the other rational number

-5/6+X=8

Add 5/6 to both sides

-5/6+5/6+X=8+5/6

0+X= 53/6 (inverse property)

X=53/6. (Identity property)

Answer:

a=5

b=15

Step-by-step explanation:

By following the pattern on the table we can see that the x is increasing by 1 and the y is increasing by 3 each time. Therefore, the next set of numbers would be (5,15).

Answer: f(x)=2-x^2

Step-by-step explanation:

The quadratic equation is

y=ax^2+bx+c

and c is equal to the y-intercept.

in the twi graphs shown both have the same shape but different y-intervepts.

c(the y-intercept) in the first graph is 5 and in the second graph(F) is 2.

On the graphing calculator it says that f(x)=2-x^2 is the correct answer therefore it is correct.

Answer:

C.

Step-by-step explanation:

Base area = 9 × 13

= 117 square feet

Now

Volume of pyramid = (1/3)(A)(H)

= (1/3)(117)(30)

= 117 × 10

= 1170 cubic feet

Answer:

a. All measures exist

b. The Mean and the mode

c. Positively skewed

d. The mean and the median

Step-by-step explanation:

a. The frequencies of the data are;

1       2

2      4

3       1

5       2

6       3

9        1

11        1

14        1

15       1

18       1

The formula for mode is given as follows;

The mean = 108/17 = 6.35

The median of 1 1 2 2 2 2 3 5 5 6 6 6 9 11 14 15 18 = (n + 1)/2th term = 9th term  

∴ The median = 5

The mode = 3×Median - 2 × Mean = 15 - 2 × 6.35 = 2.29

Hence all exist

The answer is none theses measures

b. Whereby 18 is replaced by 39 the mean will be then be

(108 + 39 - 18)/17 = 7.59

The median, which is the 9th term remain the same;

Hence only the mean and mode will be affected

c. Since more values are concentrated on the left side of the data distribution, the distribution is positively skewed

d. The largest measurement = 18 the 17th term

Removal will give

Mean = (108 - 18)/16 = 5.625 Mean changes

Median = (16 + 1)/2 th term = 8.5th term = 5 The median remains the same

The mode = 3(Mean - Median) changes

Therefore, the mean and the median will be changed.

Answer:

339 bricks.

Step-by-step explanation:

We have the weight of each brick and what the truck can support. Therefore what we must do is pass all to the same unit of measurement to calculate the quantity of bricks.

In this case we will pass everything to pounds.

We have that a 1 pound is 16 ounces, therefore 14 would be:

14 ounces * 1 pound / 16 ounces = 0.875 pounds

In addition we have that 1 ton is 2204.62 pounds, therefore 3/4 would be:

3/4 ton * 2204.62 pounds / 1 ton = 1653.467 pounds

Therefore, in total the brick weighs 4,875 pounds (4 + 0.875) and the truck can support 1653,467 pounds, the number of bricks would be:

1653.467 / 4.875 = 339.17

In other words, it can support about 339 bricks.

Answer:

Draw a Venn diagram with the left circle labeled brother, and the right labeled sister. Label the middle both and fhe outisde neither. Put 5 in brother, 3 in sister, 6 in both and 6 in neithrr.

Step-by-step explanation:

11+9 = 20

20-6 = 14

20-14=6

There are 6 that have both

Answer:

It is c he revived 10.21

Step-by-step explanation:

Answer:

Step-by-step explanation:

An option to buy a stock is priced at $150. If the stock closes above 30 next Thursday, the option will be worth $1000. If it closes below 20, the option will be worth nothing, and if it closes between 20 and 30, the option will be worth $200. A trader thinks there is a 50% chance that the stock will close in the 20-30 range, a 20% chance that it will close above 30, and a 30% chance that it will fall below 20.

a) Let X represent the price of the option

$1000         20/100 = 0.2

$200          50/100 = 0.5

$0              30/100 = 0.3

b) Expected option price

[tex]= \sum x.P(X=x)\\\\ = 1000 * 0.2 + 200 * 0.5 + 0 = \$ 300[/tex]

Therefore expected gain = $300 - $150 = $150

c) The trader should buy the stock. Since there is an positive expected gain($150) in trading that stock option.