Which of the following are considered measures of variability?

I. mean
II. interquartile range
III. mean absolute deviation

Answer:

[tex]\boxed{108\sqrt{3}\text{ in}^{2}}[/tex]

Step-by-step explanation:

An apothem is a perpendicular drawn from the centre of the triangle to one of its sides.

The three apothems OD, OE, and OF divide  ∆ABC into six smaller congruent triangles.

1. Area of ∆OCD

CotOCD = OD/OC

cot30 = CD/6

√3 = CD/6

CD = 6√3

A= ½bh

A = ½ × 6√3 × 6 = 18√3  in²

2. Area of ∆ABC

A = 6 × area of ∆OCD = 6 × 18√3 = 108√3 in²

[tex]\text{The area of the triangle is }\boxed{108 \sqrt{3} \text{ in}^{2}}[/tex]

Answer:

just had this question :/ 108√3

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

use pythagoras theorem:

sqrt of: a^2+b^2  = c

where

a=24

b=7

c=x

so substitute these values in the theorem:

sqrt: 24^2+7^2=25

hope this helps!

Answer:

25

Step-by-step explanation:

a²+b²+c²

24²+7²=c²

576+49=625

√625=25

Answer:

The solution of inequality is c>7

Step-by-step explanation:

We need to solve the inequality c-8>-1.

c-8 > -1

Adding +8 on both sides

c-8+8 > -1+8

c>7

So, the solution of inequality is c>7

Answer: 225x

Step-by-step explanation:

Use distribution to get rid of the parenthesis.

5x * 36 + 5x*9

180x + 45x

Now combine like terms

225x

Answer:

Simplifying

4u = 10.24

Solving

4u = 10.24

Solving for variable 'u'.

Move all terms containing u to the left, all other terms to the right.

Divide each side by '4'.

u = 2.56

Simplifying

u = 2.56

Step-by-step explanation:

Answer:

[tex]u=2.56[/tex]

Step-by-step explanation:

The given equation is

[tex]4u=10.24[/tex]

We want to solve for the variable u, in the linear equation above.

We divide both sides by 4 to obtain;

[tex]\frac{4u}{4} =\frac{10.24}{4}[/tex]

We simplify to get;

[tex]u=2.56[/tex]

The angle that is congruent to angle 1 is angle 4 (m∠ 4).

What is congruent angle?

Congruent angles are angles that have the same measure in degrees or radians. So, if two angles are congruent, it means that they are equal in size.

From the diagram of the parallel lines, the angle that is all congruent to angle 1 include;

m∠ 1 = m∠ 4 (vertically opposite angles are equal)

m∠ 2 = m∠ 5 (vertically opposite angles)

m∠ 3  = m∠ 6 (vertically opposite angles)

So m∠ 1 = m∠ 4

Thus, the angle that is congruent to angle 1 is angle 4.

Answer:

slope

Step-by-step explanation:

Answer:

The slope / gradient measures the steepness of a line.

Hope this helps :)

Have a great day !

5INGH

Step-by-step explanation:

2x + 7 = -9

2x = -9 - 7

2x = -16

x = -16/2

x = -8

15 - 4x

15 - 4.(-8)

15 + 32

47

Answer:

x²+y²-4y-46=0

Step-by-step explanation:

the equation of a circle is in the form (x - a)² + (y - b)² = r², where (a,b) is the center of the circle

the equation is (x - 0)² + (y - 2)² = r², where r is the radius. But r is the distance from (0,2) to (7,3)

the distance from two points is given by r² = (x₁ -x₂)² + (y₁ - y₂)²

r²= (0 - 7)² + (2 - 3)²

r² = 49 + 1 = 50

hence the equation is  

                  (x)² + (y - 2)² = 50

                  x²+y²-4y+4 = 50

                 x²+y²-4y-46= 0

Answer:

x

3

+

2

x

2

+

9

x

+

18

x3+2x2+9x+18

Factor out the greatest common factor from each group.

Tap for more steps...

x

2

(

x

+

2

)

+

9

(

x

+

2

)

x2(x+2)+9(x+2)

Factor the polynomial by factoring out the greatest common factor,  

x

+

2

x+2

.

(

x

+

2

)

(

x

2

+

9

)

(x+2)(x2+9)

Step-by-step explanation:

Answer:

(x + 2)(x + 3)(x - 3)

Step-by-step explanation:

Given that x = - 2 is a zero then (x + 2) is a factor

Dividing x³ + 2x² - 9x - 18 by (x + 2) gives

x³ + 2x² - 9x - 18 = (x + 2)(x² - 9) = (x + 2)(x + 3)(x - 3)

Answer:

72,67,75,60,77 (mean 70.2)

68,74,69,64,77  (mean 70.4)

64,74,73,69,73  (mean 70.6)

69,68,72,69,76  (mean 70.8)

Step-by-step explanation:

Answer:

Option B. Linear

[tex]y=4x+18[/tex]

Step-by-step explanation:

Let

x----> the time in hours

y----> the total inches of snow on the ground

we know that

The function that best model this situation is the linear function

so

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

In this problem

[tex]m=4\frac{in}{h}[/tex]

[tex]b=18\ in[/tex] ----> the y-intercept

substitute

[tex]y=4x+18[/tex]

Question:

A ski resort has 18 inches of snow on the ground. The snow is falling at a rate of 4 inches per hour. Which type of functions best models this situation?

A) exponential

B) linear

C) quadratic

D) radical

Answer & Step-by-step explanation:

It is given that a ski resort has 18 inches of snow on the ground. The snow is falling at a rate of 4 inches per hour.

If a function has constant rate of change, then the it is a linear function.

It the given case the rate of change is constant so linear function best model this situation.

The slope intercept form of linear function is

f(x)=mx+b           ... (1)

where, m is slope and b is y-intercept or initial value.

Ski resort has 18 inches of snow on the ground it means initial value is 18.

The snow is falling at a rate of 4 inches per hour. So, m=4.

Substitute m=4 and b=18 in equation (1).

f(x)=4x+18

Therefore Linear decreasing function best model this situation and the required function is f(x)=4x+18.

Hope this helps.

Answer:

c=3

Step-by-step explanation:

We have 2 points, we can find the slope using

m = (y2-y1)/(x2-x1)

Substituting into this equation

-1/4 = (4-5)/(7-c)

-1/4 = -1/(7-c)

Multiply both sides by -1

1/4 = 1/(7-c)

The denominators have to be the same

4 = 7-c

Subtract 7 from each side

4-7 = 7-7-c

-3 = -c

Multiply by -1

3 =c

Answer:

t = –3.382

Step-by-step explanation:

Claim: FICO credit scores are greater than 675

Thus, x = 675

We are given:

Sample size = n = 50

Sample Mean = u = 719

Sample Standard deviation = s = 92

The formula to find the t-statistic is:

[tex]t=\frac{x-u}{\frac{s}{\sqrt{n} } }[/tex]

Using the above values, we get:

[tex]t=\frac{675-719}{\frac{92}{\sqrt{50} } }\\\\ t=-3.382[/tex]

Thus, the value of test statistic is -3.382. So 3rd option gives the correct answer.

Answer:

t = 3.382

Step-by-step explanation:

gradpoint

15x+320

X=21.3

Mulitply 3 and 5 to get 15x

Multiply 20 and 16 to get 320

Divide each side by 15

The value of x (3x+20) (5x-16) is  x=0 or x= 16/5 or x= -20/3

Writing a number or other mathematical object as the sum of numerous factors—typically smaller or simpler objects of the same kind—is known as factorization or factoring in mathematics. For instance, the polynomial x² - 4 and the integer 15 can both be factored by the number 3 × 5.

Given

Let's solve your equation step-by-step.

x(3x+20)(5x−16)=0

15x³+52x²−320x=0

Step 1: Factor left side of equation.

x(5x−16)(3x+20)=0

Step 2: Set factors equal to 0.

x=0 or 5x−16=0 or 3x+20=0

x=0 or x= 16/5 or x= -20/3

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Check the picture below.

Answer:

B. [tex]m\angle CAD=\frac{m\widehat {CD}-m\widehat {GE}}{2}[/tex].

Step-by-step explanation:

We have been given an image of a circle. We are asked to find the measure of angle CAD.

We can see that angle CAD is formed by two intersecting secants outside the circle.

Intersecting secants theorem states that when two secants intersects outside a circle, then the measure of angle formed by secants is half the difference of intercepted arcs.

[tex]m\angle CAD=\frac{\text{Larger arc-Smaller arc}}{2}[/tex]

[tex]m\angle CAD=\frac{m\widehat {CD}-m\widehat {GE}}{2}[/tex]

Therefore, option B is the correct choice.

Answer:

x = 1.33333333

y = -0.66666667

Step-by-step explanation:

The answers have to be those numbers EXACTLY.

8x + 13y = 2

8(1.33333333) + 13(-0.66666667) = 2

10.66666667 - 8.66666667 = 2

2 = 2

y  = x - 2

-0.66666667 = 1.33333333 - 2

-0.66666667 = -0.66666667

Answer:

x = 1.34

y = -0.67

Step-by-step explanation:

Simplify brackets

10x - 4 = 8x + 14

Add 4 to both sides

10x = 8x + 14 + 4

Simplify 8x + 14 + 4 to 8x + 18

10x = 8x + 18

Subtract 8x from both sides

10x - 8x = 18

Simplify 10x - 8x to 2x

2x = 18

Divide both sides by 2

x = 18/2

Simplify 18/2 to 9

x = 9

10x - 4 = 8x + 14

Step 1: Combine like terms

x's go with x's (10x and 8x). To do this subtract 8x to both sides

(10x - 8x) - 4 = (8x-8x) + 14

2x - 4 = 14

Normal numbers go with normal numbers (-4 and 14). To do this add 4 to both sides

2x + (-4 + 4) = 14 + 4

2x = 18

Step 2: Isolate x by dividing 2 to both sides

2x/2 = 18/2

x = 9

Hope this helped!

Answer:

Options 1,2,6,7 are correct statements.

Step-by-step explanation:

In the given figure lines m and n are cut by a transversal t.

Among all the statements the options that are correct are :

1)<1 and <5 are corresponding angles.(The angles in matching corners are called corresponding angles)

2)<3 and <6 are alternate interior angles .(The angles that are formed on opposite sides of the transversal and inside the two lines are alternate interior angles)

6)<4 and <6 are same side consecutive angles.(consecutive angles lie on the same side of the transversal)

7)<1 and <8 are alternate exterior angles.( These angles lie on the exterior side of the lines and on opposite side of the transversal)

Answer:

Step-by-step explanation:

Answer:

x=29

Step-by-step explanation:

x+61=90

61-61

90-61

x=29

Answer: 29

Step-by-step explanation:

Add the right angle which would equal 90 degrees with the 61 degrees. Now you get 151. Subtract 151 from 180, which is half of the circle. Now you have 29 degrees.

Answer:

A. Transformation

Step-by-step explanation:

Transformation is the responsible for the changing the size of the object without changing the shape. Then the correct option is A.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

The transformation is the process of making the shape of an object to be increased or decreased without changing the shape of the object that depends on the scale factor.

If the size of the object is increased then the scale factor is greater than one.

If the size of the object is decreased then the scale factor is less than one.

More about the geometry link is given below.

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Answer:

C) 23 yd^2

Step-by-step explanation:

We can break  this figure into two rectangles.

One rectangle is a vertical triangle that is 3 yd across by 7 yds down

The area of this figure is

A = lw

   = 3 * 7 = 21

The other rectangle is 1 yd across and by 2 yds down  

The area of this figure is

A = lw

   = 1 * 2 = 2

The total area is the sum of the two figures

A = 21 +2 = 23

Its c hope this helped

Answer:

[tex]y=ln(2x)[/tex]

Step-by-step explanation:

we have

[tex]e^{y}=2x[/tex]

Applying ln both sides

[tex]ln(e^{y})=ln(2x)[/tex]

[tex]y*ln(e)=ln(2x)[/tex]

Remember that

[tex]ln(e)=1[/tex]

substitute

[tex]y=ln(2x)[/tex]

Answer:

Y=ln 2x

Step-by-step explanation:I just did it on edg 2020

Answer:

Final answer is [tex]x^2-x-12[/tex].

Step-by-step explanation:

Given expression is [tex]\left(x-4\right)\left(x+3\right)[/tex].

Now we need to find the product of the given expression [tex]\left(x-4\right)\left(x+3\right)[/tex].

[tex]\left(x-4\right)\left(x+3\right)[/tex]

[tex]=x\left(x-4\right)+3\left(x-4\right)[/tex]

[tex]=x^2-4x+3x-12[/tex]

combine like terms

[tex]=x^2-1x-12[/tex]

[tex]=x^2-x-12[/tex]

Hence final answer is [tex]x^2-x-12[/tex].

ANSWER

[tex](x-4)(x+3) = {x}^{2} - x - 12[/tex]

EXPLANATION

The given product is (x-4)(x+3)

We expand using the distributive property to obtain:

[tex](x-4)(x+3) = x(x + 3) - 4(x + 3)[/tex]

Expand the parenthesis to obtain:

[tex](x-4)(x+3) = {x}^{2} + 3x- 4x - 12[/tex]

Combine the similar terms to get:

[tex](x-4)(x+3) = {x}^{2} - x - 12[/tex]

Answer:

this answer is 25893

Step-by-step explanation:

13+6+24+18+33+5+13+48+9+11+36+28+15+6+13(all divided by 15)

278÷15

=18.5333

The mean, or average, of the numbers 13, 6, 24, 18, 33, 5, 13, 48, 9, 11, 36, 28, 15, 6, 13 is calculated by adding up all the values and dividing the total by the number of values. The mean of these numbers is approximately 18.13.

The subject of your question is Mathematics and it appears that you are asking about how to calculate the mean, or average, of a set of values which are 13, 6, 24, 18, 33, 5, 13, 48, 9, 11, 36, 28, 15, 6, 13. To do this, you should add up all the values and divide the total by the number of values.

So the mean of these numbers is approximately 18.13.

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For this case we have two functions of the form y = f (x). We must find the quotient of the following functions:

[tex]f (x) = x + 2\\g (x) = 3x + 5[/tex]

So, we have by definition:

[tex]\frac {f (x)} {g (x)} = \frac {x + 2} {3x + 5}[/tex]

Answer:

[tex]\frac {f (x)} {g (x)} = \frac {x + 2} {3x + 5}[/tex]

with 3x + 5 different from zero, so that the function is defined

Answer:

[tex]\frac{f(x)}{g(x)}=\frac{x+2}{3x+5}[/tex]

where [tex]x\ne -\frac{5}{3}[/tex]

Step-by-step explanation:

The given functions are:

f(x) = x + 2 and g(x) = 3x + 5

[tex]\frac{f(x)}{g(x)}=\frac{x+2}{3x+5}[/tex]

Since this is a rational function, the function will not be defined where denominator equals zero.

We need to restrict the function or define the domain.

This is a rational function defined for [tex]x\ne -\frac{5}{3}[/tex]

Answer:

d is the closest to the real answer assuming the question is asking for an estimate

The first step would be to A. Subtract 7.4 - 3.6.

You use the PEMDAS rule

Steps:

1. Parenthesis

2. Exponents

3. Multiplication

4. Division

5. Addition

6. Subtraction

Subtract 7.4−3.6 is the first step in evaluating the expression

In mathematics, an expression or mathematical expression exists as a finite combination of signs that stands well-formed according to laws that depend on the context.

The Bodmas rule is arranged according to the letters in the acronym BODMAS, which stand for brackets, order of powers or roots, division, and multiplication. A stands for addition and S for subtraction. According to the BODMAS rule, multi-operator mathematical equations must be resolved in the BODMAS order from left to right.

Given

According to BODMAS rule

Subtract 7.4 - 3.6 will be performed since it is within brackets.

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The term which refers to a pictorial representation of given set of data involving two variables is:

           A-  graph

We know that

In mathematics, a graph is a diagram that is used to represent a relationship between the two variables one is a independent variable and the other is a dependent variable.

It is just the set of all the ordered pairs of the type: (x,y) where x is the domain of the function and y is the range of the function.

Hence, the answer is:

                 Option: A

         ( A-- Graph)