Find the range of the given data set.
-4, -3, -1, -1, 0, 1
-5
-3
3
5

Answer:

(B) {6,6,7}

Step-by-step explanation:

A criterion to determine if each triplet represents a triangle is the Law of Cosine, which states that:

[tex]a^{2} = b^{2}+c^{2}-2\cdot b \cdot c \cdot \cos \theta[/tex]

Where [tex]a[/tex], [tex]b[/tex] and [tex]c[/tex] are sides of the triangle and [tex]\theta[/tex] is the angle opposite to side [tex]a[/tex]. Now, let is clear the cosine function:

[tex]2\cdot a \cdot b\cdot \cos \theta = b^{2}+c^{2}-a^{2}[/tex]

[tex]\cos \theta = \frac{b^{2}+c^{2}-a^{2}}{2\cdot b \cdot c}[/tex]

Cosine is a bounded function between -1 and 1, a triplet corresponds to a triangle if and only if result is located between upper and lower bounds. Now let is evaluate each triplet:

a) [tex]a = 2[/tex], [tex]b = 5[/tex], [tex]c = 9[/tex]

[tex]\cos \theta =\frac{5^{2}+9^{2}-2^{2}}{2\cdot (5)\cdot (9)}[/tex]

[tex]\cos \theta = 1.133[/tex] (Absurd)

The triplet does not represent a triangle.

b) [tex]a = 6[/tex], [tex]b = 6[/tex], [tex]c = 7[/tex]

[tex]\cos \theta =\frac{6^{2}+7^{2}-6^{2}}{2\cdot (6)\cdot (7)}[/tex]

[tex]\cos \theta = 0.583[/tex] (Reasonable)

The triplet represents a triangle.

c) [tex]a = 6[/tex], [tex]b = 4[/tex], [tex]c = 2[/tex]

[tex]\cos \theta = \frac{4^{2}+2^{2}-6^{2}}{2\cdot (4)\cdot (2)}[/tex]

[tex]\cos \theta = -1[/tex] (Absurd)

The triplet does not represent a triangle, but a straight line.

d) [tex]a = 7[/tex], [tex]b = 8[/tex], [tex]c = 1[/tex]

[tex]\cos \theta = \frac{8^{2}+1^{2}-7^{2}}{2\cdot (8)\cdot (1)}[/tex]

[tex]\cos \theta = 1[/tex] (Absurd)

The triplet does not represent a triangle, but a straight line.

Hence, the correct answer is B.

Answer:

15

Step-by-step explanation:

25-10=15

You take out 10 cents and u have 15 left

Answer:

P₄(x) = ln3 + 1/3 (x-3) - 1/9*2! (x-3)² + 2/27*3! (x-3)³ - 2/27*4! (x - 3)⁴

Step-by-step explanation:

Given:

f(x) = ln(x)

n = 4

c = 3

To find:

nth Taylor polynomial for the function, centered at c

Solution:

The Taylor series for f(x) = ln x centered at 3 is:

[tex]P_{n}(x) = f(c) + \frac{f'(c)}{1!}(x-c)+\frac{f''(c)}{2!}(x-c)^{2} +\frac{f'''(c)}{3!}(x-c)^{3}+...+\frac{f^{n} (c)}{n!}(x-c)^{n}[/tex]

Since c = 3 So,

[tex]P_{4}(x) = f(3) + \frac{f'(3)}{1!}(x-3)+\frac{f''(3)}{2!}(x-3)^{2} +\frac{f'''(3)}{3!}(x-3)^{3}+...+\frac{f^{n} (3)}{n!}(x-3)^{n}[/tex]

Now

f(3) = ln 3

f'(x) = 1/x ⇒ f'(3) = 1/3

f''(x) = -1/x² ⇒ f''(3) = -1/3² = -1/9

f'''(x) = 2/x³  ⇒ f'''(3) = 2/3³ = 2/27

f[tex]^{(4)}[/tex] (x) = -6/x⁴ ⇒ f[tex]^{(4)}[/tex] (3) = -6/3⁴ = -6/81 = - 2/27

So Taylor polynomial for n=4 is:

P₄(x) = ln3 + 1/3 (x-3) - 1/9*2! (x-3)² + 2/27*3! (x-3)³ - 2/27*4! (x - 3)⁴

Answer:

Step-by-step explanation:

Given the equation [tex]2\sin^2(x) = 1 \\[/tex], we are to find all the values of x in the interval  [0, 2π] that satisfies the equation.

Simplifying the equation:

[tex]2\sin^2(x) = 1 \\\\sin^2x = \frac{1}{2} \\\\[/tex]

Square both sides of the equation;

[tex]\sqrt{sin^2x } = \sqrt{\frac{1}{2} } \\\\sin(x) = \sqrt{0.5}\\ \\sin(x) = 0.7071\\\\x = sin^{-1}0.7071\\\\x \approx 45^0[/tex]

The general formula for sin(x)  is x = nπ + (-1)ⁿ∝ where n = 0, 1, 2, 3...

Since ∝ = 45° = π/4.

x = nπ + (-1)ⁿπ/4

when n = 1

x = π + (-1)¹π/4

x =  π - π/4

x = 3π/4

Hence the values of x within the given interval are π/4 and 3π/4

Answer:

9/14

Step-by-step explanation:

33 animals at the shelter are dogs.

Answer:

7g-100%

x-38,25

38,25*7:100=2,6775g

7g-2,6775g=4,4325g

Step-by-step explanation:

Answer

Kelvin 223  669 < 356  

Lori 55                165 < 356  

Vanessa 265  795 < 356  

Devon 172          516 < 356  

Celia 112           336 < 356

Step-by-step explanation:

Answer:

Step-by-step explanation:

343

Answer:

7^3

Step-by-step explanation:

7 to the power of 3. Because there are 3, 7's so you are multiplying 7 3 times

Answer:

The number 18 is a counterexample for Option D - If a number is divisible by 2, then it is also divisible by 4.

Step-by-step explanation:

To find : The number 18 is a counterexample for which of the following conditional statements?

Solution :

For a conditional statement to be true then it is true for all cases that satisfy the condition.

A counterexample is given to prove a conditional statement false.

Now, Examine all the conditions

A. If a number is divisible by 2, it is even.

18 is even and divisible by 2 - True

B.  If a number is odd, then it is not divisible by 2.

18 is not odd so it is divisible by 2 - True

C. If a number is even, then it ends with 0, 2, 4, 6, or 8.

18 ends with 8 so it is even - True

D. If a number is divisible by 2, then it is also divisible by 4.

18 is divisible by 2 but 18 is not divisible by 4 - False

Therefore, The number 18 is a counterexample for Option D - If a number is divisible by 2, then it is also divisible by 4.

Answer:

I THINK IT WILL BE HELPFUL

Answer:

x+5y+2z sry if itss wrong lol

Step-by-step explanation:

Answer:

that is the outsider part.of something

the sum of the areas of all the faces of a three dimension figure or in 3-D shapes

Answer:

Step-by-step explanation:

The mean value μ = 205  , standard deviation of population σ = 25

no of people n = 40

standard deviation of sample of 40 people = σ / √n

σ₁ = 25 / √ 40 = 3.95

probability between 200 and 205

P ( 200 < X < 205 ) = P ( Z= (210 - 205)  / 3.95  -  P ( Z= (200 - 205)  / 3.95

= P ( Z = + 1.26 ) - P ( - 1.26 )

= .8962 - .1038

= .7924

Probability is 79.24 % .

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{64}}}}}[/tex]

Step-by-step explanation:

If ' n ' is the cardinal number of a set, the number of subsets of a given set can be obtained by using the formula 2ⁿ

Given,

N = { 1 , 42 , 65 , 12 , 31 , 27 }

where n ( total number of elements ) = 6

So, the number of possible subsets of set N :

= 2ⁿ

= 2⁶

= 2 × 2 × 2 × 2 × 2 × 2

= 64

Hope I helped!

Best regards!!

Answer:

the answer is the letter A

Answer:

A

Step-by-step explanation:

It's A because -6 * 2 equals -12 which is less than zero

Answer:

attached below is the missing part of the question and the solution

A) 60%, 40%

B) 25%

C) 60%

Step-by-step explanation:

a) The accuracy of always-taken for this sequence of branch outcomes = 60%

The accuracy of always -not-taken for this sequence of branch outcomes = 40%

b) The accuracy of the 2-bit predictor for the first four branches assuming that the predictor starts off in the bottom left state = 25%

C)the accuracy of the 2-bit predictor if this pattern is repeated forever = 60% ( was stopped after the fourth iteration because the fourth and third iterations are the same)  =

Step-by-step explanation:

A = 280² ft²

A = (200 + 80)² ft²

A = [200² + 2(200)(80) + 80²] ft²

A = (40000 + 32000 + 6400) ft²

A = 78400 ft²

The required area of the dog park using polynomial is 6771204 feet².

Polynomial is an algebraic expression that has more than two terms. In other words, it is a combination of different variables with mathematical operations.

Given that,

The area of the park = square of the side length a = 2802 feet².

To find the area of the park, using polynomial use

Formula of area of square = (a)²

= (2802)²

= (2800 + 2)²

Use formula (a + b)² = a² + b² + 2ab

= (2800)² + (2)² + 2 x 2800 x 2

= 6,760,000 + 4 + 11200

= 6771204 feet²

The required area of the dog park is 6771204 feet².

To know more about Polynomial on:

https://brainly.com/question/11536910

#SPJ3

Answer:

(3,-5)

Step-by-step explanation:

To find the x coordinate of the  midpoint, add the  x coordinates together and divide by 2

The x coordinate is

(x1+x2)/2

We know one point and the midpoint

( -1+x)/2 = 1

Multiply by 2

-1 +x = 2

Add 1

x =2+1

x=3

To find the y coordinate of the midpoint, add the  y coordinates together and divide by 2

The y coordinate is

(y1+y2)/2

We know one point and the midpoint

(3+y)/2 = -1

Multiply by 2

3+y = -2

Subtract 3

y = -2-3

y =-5

The other endpoint is (3,-5)

Answer:

B(3, -5)

Step-by-step explantion

We know that these formulas can be used to find the mid point between 2 points on a graph

[tex]\frac{a_{1} +b_{1}}{2}= c_{1}\\ \frac{a_{2} +b_{2}}{2} =c_{2}[/tex]

Now we plot these points in

A(-1, 3), C(1, -1)

[tex]\frac{-1+b_{1}}{2} =1 \\\frac{3+b_{2}}{2} =1[/tex]

And we can find that

[tex]b_{1}= 3\\b_{2}=-5[/tex]

Therefore we get the answer of (3, -5)

Hope that helped you with your problem!! :)

Answer:

Larger number = 37

Smaller Number = 11

Step-by-step explanation:

Lets take x as the bigger number and y as the smaller number

x + y = 48

What do we know?

The larger number is 7 less than four times the smaller number

so 4y - 7 = x

Lets replace the equation obove with x

4y - 7 + y = 48

5y - 7 = 48

5y = 48 + 7

y = 55/5

y = 11

Then multiply 11 by 4 11 times 4 = 44 and subtract by 7 44 - 7 = 37

To recheck add 37  to 11 and u should get 48

Answer:

7

Step-by-step explanation:

:)

it's so easy :))))))))

Answer:

Half of 14 is 7

Step-by-step explanation:

Answer:

Step-by-step explanation:

=-3-i-5-3i

=-8-4i

Answer:

7 movies

Step-by-step explanation:

Given

membership cost for 1 month = $10

rent for 1 movie = $2

Maximum money to be spent by a member = $24

Let the no. of movie rented by x

Thus, total rent for x movies = x* rent for 1 movie = x*$2 = $2x

Total spending for 1 month = membership cost for 1 month +  total rent for x        movies

Total spending for 1 month = 10 +2x

Given that he can spend at most $24

Total spending for 1 month <= 24

10 + 2x <= 24

2x <= 24-10

2x <= 14

x <= 14/2

x <= 7

Thus, movies rented can be less than or equal to 7.

since we have to find the maximum movies rented in 23, it will be 7

Thus, at most 7 movies can be rented.

Answer:

  4 years

Step-by-step explanation:

The formula for simple interest is useful here.

  I = Prt

where P is the principal invested at rate r for t years.

Fill in the given values and solve for t:

  81 = 450×0.045×t

  81/20.25 = t = 4

It will take 4 years for 450 to yield 81.

Answer:

106

Step-by-step explanation:

The area of one of the triangles is 1/2*5*3

The area is 7.5, but there are 2 triangles so the combined area is 15

The area for whole rectangle is 7*(5+3+5)=7*13=91

So the total area is 91+15= 106

Answer:

0.001km

1km is 1000m

So, 1m is 1m divided by 1000km

Which gives 0.001km

There are 0.001 kilometres in 1 metre.

1000 metre =1 kilometre

1 metre=1/1000 kilometre

Answer:

38°

Step-by-step explanation:

∠4=∠2

∠2=∠6

∠6=38°

So ∠4=38°

Answer:

The answer is 38°

Step-by-step explanation:

When both lines are parallel, their vertical opposite angles will be the same. So ∠4 = 38°.

Answer:

10:25

Step-by-step explanation:

mow the lawn 1:10

trim bushes: 0:30

put down mulch: 0:35

shower: 0:20

Total time = 1:10 + 0:30 + 0:35 + 0:20 = 1:95 = 2:35

She needs 2 hours and 35 minutes to do everything.

1:00 p.m. = 13:00

13:00 - 2:35 = 12:60 - 2:35 = 10:25

She should start work at 10:35 a.m.

Answer:

(6, -17)

Step-by-step explanation:

Given the coordinate of a midpoint, (5, -12), and one endpoint, (4, -7), the other endpoint can be determined as follows:

The midpoint formula is given as [tex] M(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}) [/tex].

Since we are given ordered pairs of the midpoint and one endpoint, we would find the other ordered pair of the endpoint as shown below.

Let the other endpoint be [tex] (x_1, y_1) [/tex]

Midpoint = M(5, -12)

Let the given endpoint = [tex] (4, -7) = (x_2, y_2) [/tex]

Thus:

[tex] M(5, -12) = (\frac{x_1 + 4}{2}, \frac{y_1 +(-7)}{2}) [/tex]

Rewrite the equation to find the coordinates of the other endpoints

[tex] 5 = \frac{x_1 + 4}{2} [/tex] and [tex] -12 = \frac{y_1 - 7}{2} [/tex]

Solve for each:

[tex] 5 = \frac{x_1 + 4}{2} [/tex]

[tex] 5*2 = \frac{x_1 + 4}{2}*2 [/tex]

[tex] 10 = x_1 + 4 [/tex]

[tex] 10 - 4 = x_1 + 4 - 4 [/tex]

[tex] 6 = x_1 [/tex]

[tex] x_1 = 6 [/tex]

[tex] -12 = \frac{y_1 - 7}{2} [/tex]

[tex] -12*2 = \frac{y_1 - 7}{2}*2 [/tex]

[tex] -24 = y_1 - 7 [/tex]

[tex] -24 + 7 = y_1 - 7 + 7 [/tex]

[tex] -17 = y_1 [/tex]

[tex] y_1 = -17 [/tex]

Ordered pair of the other endpoint is (6, -17)