Simplify
5^3
5^7
leaving your answer in index form.

The value of the indicated probability P(A or B) is 0.85

The probabilities are given as

P(A) = 0.55

P(B) = 0.5

P(A and B) = 0.2

The indicated probability is given as

P(A or B)

This is calculated using the following equation

So, we have

P(A or B) = P(A) + P(B) - P(A and B)

So, we have

P(A or B) = 0.55 + 0.5 - 0.2

Evaluate the like terms

P(A or B) = 0.85

Hence, the value of the indicated probability P(A or B) is 0.85

Read more about probability at

https://brainly.com/question/24756209

#SPJ1

Answer:

  12 square units

Step-by-step explanation:

You want the area of polygon FGHJ from its vertices, using some unspecified formula.

We don't know what formula you were given, but one that we like is ...

  [tex]\displaystyle A=\dfrac{1}{2}\left|\sum_{k=1}^n{x_k(y_{k+1}-y_{k-1})}\right|[/tex]

This formula is implemented in the attached spreadsheet. The line marked Area gives half the absolute value of the sum of the numbers above.

For the given points, the formula is computed by the attached spreadsheet. We recommend this approach whenever repetitive math is involved. You will note that repeating the first two point coordinates makes the formula more straightforward.

The area of this 4×3 rectangle is 12 square units.

after you open your keyboard click on the "?123" button then click on the "=\<" button then there u will look for the upside down V

Step-by-step explanation:

thank you !!

Consecutive integers are those numbers that follow each other. They follow in a sequence or in order. For example, a set of natural numbers are consecutive integers.

As discussed , the numbers that follow each other in an order are called consecutive numbers or consecutive integers. These integers go from smallest to the highest, i.e. in ascending order. Some of the examples are:

From the above examples, we can see, the integers follow each other in a sequence. The difference between preceding and succeeding integers is always equal to 1.

So, given question, we can write:

For a consecutive integers, the number either increases by 1 or decreases.

First we take option 1:

12,22,32

Find out difference,

22-12=10       ,        32-22=10

The difference is '10'

Hence it is not consecutive integer.

We take option 2:

100,99,98

Find out difference,

100-99=1        ,          99-98=1

The difference is '1'

Hence it is consecutive integer.

We take option 3:

-11,-10,-9

Find out difference,

=-10-(-11)      ,       =-9-(-10)

=11-10=1       ,       =-9+10=1        

The difference is '1'

Hence it is consecutive integer.

We take option 4:

10,11,12

Find out difference,

11-10=1        ,          12-11=1

The difference is '1'

Hence it is consecutive integer.

So, 12,22,32 is not contain consecutive integer, because the difference is '10'. For a consecutive integers, the number either increases by 1 or decreases.

Learn more about event correlation here: brainly.com/question/1767889

#SPJ9

The 3 common multiples of 31, 18, and 20 are 5580, 11160 and 16740.

Here, we have three numbers- 31, 18, and 20

To find 3 common multiples of these numbers, we first find the least common multiple or LCM of these 3 numbers.

31 is a prime number, hence it can be written as- 31 × 1

18 can be written as- 3 × 3 × 2

20 can be written as- 5 × 2 × 2

Thus, the LCM of 31, 18 and 20 will be-

3 × 3 × 5 × 2 × 2× 31 × 1

= 5580

Thus, we found the least common multiple of 31, 18 and 20.

Now, the other 2 multiples will be multiples of the LCM itself.

The other two numbers can be-

5580 × 2 = 11,160

5580 × 3 = 16,740

Thus, the 3 common multiples of 31, 18, and 20 are 5580, 11160 and 16740.

Learn more about the LCM here-

https://brainly.com/question/20739723

#SPJ9

The two numbers which satisfy the condition that the difference between them be; 16 as required in the task content are; 17 and 1.

It follows from the task content that the two numbers whose difference amount to 16 are to be determined as required in the task content.

Given the numbers in discuss as; x and y such that;

x - y = 16

To find:

The numbers x and y.

Therefore, the possible numbers are such that; x = 17 and y = 1.

Ultimately, the two possible combination of number such that their difference is 16 are; 17 and 1.

Read more on difference of numbers;

https://brainly.com/question/148825

#SPJ1

Answer:

Hello,

P=(1,2)

Step-by-step explanation:

[tex]\overrightarrow{OP}=\overrightarrow{OA}+\dfrac{2}{3} *\overrightarrow{AB}\\\\=(-3,-4)+\dfrac{2}{3} *(3-(-3),5-(-4))\\\\=(-3,-4)+\dfrac{2}{3}*(6,9)\\\\=(-3,-4)+2*(2,3)\\\\=(-3,-4)+(4,6)\\\\\boxed{=(1,2)}\\[/tex]

The x-value that is a solution of the system is x = 3.

Here we have the system of equations:

3x+y+2z= -10

x+5y+2z= -12

-2x+3y = -1

And we want to find the value of x.

Using the third equation we can write y in terms of x:

y = (-1 + 2x)/3

Now we can replace that in the other two equations:

3x + (-1 + 2x)/3 + 2z= -10

x + 5*(-1 + 2x)/3 + 2z= -12

We can simplify thes two to get:

(3 + 2/3)*x + 2z = -10 + 1/3 = -29/3

(1 + 2/3)*x + 2z = -12 +5/3 = -31/3

Now if we subtract these two equations we will get:

(3 + 2/3)*x - (1 + 2/3)*x = -29/3 + 31/3  = 2/3

2x = 2/3

x = (2/3)/2 = 1/3

x = 1/3

The x-value that is a solution of the system is x = 3.

If you want to learn more about systems of equations:

https://brainly.com/question/13729904

#SPJ1

Answer:

3

Step-by-step explanation:

You are asked to find the slope of the function.
You can find the slope using the formula [tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex].

For simplicity, I'll take the points (0, 0) and (1, 3) and substitute their coordinates into the formula.

[tex]m = \frac{3 - 0}{1 - 0} \to \frac31 \to 3[/tex]

Therefore, [tex]y = 3x[/tex]

The answer of given expression [tex]343c^3+d^3[/tex] will be [tex](7c + d)(49c^2-7cd+d^2)[/tex]

We have given an expression [tex]343c^3+d^3[/tex] which can be written as [tex](7c)^3+(d)^3[/tex]

Using identity [tex]a^3 + b^3 = (a + b) (a^2 - ab + b^2)[/tex].   ...(1)

Put a = 7c and b = d in equation (1) , we get

  [tex](7c)^3 + (d)^3 = (7c + d) ((7c)^2 - 7cd + (d)^2)\\\\(7c)^3 + (d)^3 =(7c + d)(49c^2-7cd+d^2)[/tex]

Learn more about algebraic expression here :

https://brainly.com/question/4344214

#SPJ9

The equation of the obtained inverse function is y=x/4 - 1/2.

The given function is f(x)=4x+2.

The inverse function is represented [tex]f^{-1}[/tex] with regard to the original function [tex]f[/tex] and the domain of the original function becomes the range of the inverse function and the range of the given function becomes the domain of the inverse function. The graph of the inverse function is obtained by swapping (x, y) with (y, x) with reference to the line y = x.

The inverse function f(x)=4x+2 can be solved as follows:

Now, f(x)=4x+2

⇒y=4x+2

⇒x=4y+2

⇒x-2=4y

⇒y=(x-2)/4

The graph of the function and inverse function is plotted as given below.

From the graph, the coordinates are (0, -0.5) and (2, 0).

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

=(0+0.5)/(2-0)

=0.5/2

=1/4

Put, m=1/4 and (2, 0) in y=mx+b

We get, 0=1/4 (2)+b

b=-1/2

Then, the equation is y=x/4 - 1/2

Therefore, the equation of the obtained inverse function is y=x/4 - 1/2.

To learn more about the inverse function visit:

https://brainly.com/question/2541698.

#SPJ1

The width and length of the rectangle are 11 and 13 cm respectively

The perimeter of a shape is the sum of the side lengths of the shape

For all regular quadrilaterals, you add up the side lengths to determine the perimeter

The given parameters about the rectangle are

Perimeter = 37 + Width

Length = Width + 2 i.e. consecutive odd integers, and width is smaller

Rewrite the above equations as

p = 37 + w

l = w + 2

The perimeter of a rectangle is

p = 2 x (l + w)

Substitute p = 37 + w in the above equation

So, we have

2 x (l + w)= 37 + w

Substitute l = w+ 2 in the above equation

So, we have

2 x (w + 2 + w)= 37 + w

Evaluate the like terms in the above equation

So, we have

2 x (2w + 2)= 37 + w

Open the bracket in the above equation

So, we have

4w + 4= 37 + w

Evaluate the like terms in the above equation

So, we have

3w = 33

Divide both sides of the above equation by 3

So, we have

w = 11

Recall that

l = w + 2

So, we have

l = 11 + 2

Evaluate

l = 13

Hence, the width and length of the rectangle are 11 and 13 cm respectively

Read more about perimeter at

https://brainly.com/question/18019422

#SPJ1

Answer:

323

Step-by-step explanation:

Integer = whole number

.6 always rounds upwards

The decimal that represents the portion of people who own dog will be 0.32.

It should be noted that decimal numbers are the numbers that are used for denoting numbers that have while numbers and fractions.

In this case, it was stated that Isaac read that 32% of people owned dogs.

Therefore, the decimal that represents the portion of people who own dog will be:

= 32 / 100

= 0.32.

The decimal that represents the portion of people who own dog will be 0.32.

Learn more about decimals on

brainly.com/question/1827193

#SPJ1

Isaac read that 32% of people owned dogs. What decimal represents the portion of people who own dog?

Answer:

(4a3-5a-3)(2a2-7a+3)

Step-by-step explanation:

use 4a3 to multiply everything in the both brackets=

8a⁵-28a⁴+12a³. then use -5a to multiply everthing in the both brackets =

8a⁵-28a⁴+12a³-10a³+35a²-15a. then use -3a to multiply everthing in the both brackets =

8a⁵-28a⁴+12a³-10a²+35a²-15a-6a²-21a-9.then you furthermore solve=

8a⁵-28a⁴+2a³+29a²-36a-9

[tex]f^{-1}[/tex](f(6.022)) is 6.022 and [tex]f^{-1}[/tex](-10) + f(6) is -4

The general evaluation of function is

[tex]f^{-1}[/tex](f(x)) = x

Here we have to find [tex]f^{-1}[/tex](f(6.022))

Therefore [tex]f^{-1}[/tex](f(6.022)) = 6.022

Now we have to find the value of [tex]f^{-1}[/tex](-10) + f(6)

Form the table of values, we have

[tex]f^{-1}[/tex](-10) = -6 and f(6) = -10

So we have

[tex]f^{-1}[/tex](-10) + f(6) = 6 + (-10)

                     = 6 -10

                     = -4

Therefore [tex]f^{-10}[/tex] (-10)+ f(6) = -4

To know more about the inverse function refer to the link given below:

https://brainly.com/question/11735394

#SPJ1

Answer:

Step-by-step explanation:

Bro u just subtract...:)

547.25(day 1) - 327.875(day2) = 219.375 miles as the difference(just use a calculator)

The equation of the line will be x = -6, that is, option B.

Here, we are given that a line passes through point (-6,-9) and perpendicular to y = 1/4

If two line are perpendicular to each other, the product of their slopes is equal to -1.

Here, the slope of y = 1/4 will be 0 as y is a constant value and not changing.

Let the slope of the given equation be m

them m × 0 = -1

m = -1/0

Thus, the slope is not defined, this means that the line will be parallel to x axis of the form x = k.

Now, we know that the line passes through point (-6,-9). This means that if y = -9, x will be -6. But we know that x will take only one value for all values of y.

Thus, the equation of the line will be x = -6, that is, option B.

Learn more about equation of a line here-

https://brainly.com/question/13763238

#SPJ9

Your question was incomplete. Check for the full content below-

Select the correct answer.

Which equation represents the line that is perpendicular to y = 1/4 and passes through (-6-9)?

OA. x= -9

OB. x=-6

Oc. y=9

OD. y= -4

The answers are :

1. a) 10^-5 relates to the hundred-thousandths place. The number 3 will be in the hundred thousandths place followed by 0 which is in ten thousands place. The places before 3 will each hold digit 0.

b) The standard form will be 0.000032.

2. The standard form will be 0.000007

3. The standard form will be 0.0000875

What is the standard form ?

Any number that we can write as a decimal number, between 1.0 and 10.0, multiplied by a power of 10, is said to be in standard form.

It is given that the number is 3.2 × 10^-5.

Let's simplify it. So , we get ;

= [tex]\frac{3.2}{10^5}[/tex]

= [tex]\frac{3.2}{100000}[/tex]

= 0.000032

1.

a)

10^-5 in standard form will be :

= 0.00001

So , we can conclude that 10^-5 relates to the hundred-thousandths place.

When we write 3.2 × 10^-5 in the standard form it will be equal to 0.000032.

The number 3 will be in the hundred thousandths place followed by 0 which is in ten thousandths place.

The places before 3 will each hold digit 0.

b)

The standard form of 3.2 × 10^-5 will be 0.000032.

2.

Diameter of an atom in gold is about 7 × 10 ^-6.

Let's express this to standard form.

So ,

7 × 10 ^-6

= [tex]\frac{7}{10^6}[/tex]

= [tex]\frac{7}{1000000}[/tex]

= 0.000007

3.

Average mass of one flea which is 8.75 × 10^-5. Let's represent this in standard form :

8.75 × 10^-5

= [tex]\frac{8.75}{100000}[/tex]

= 0.0000875

Therefore , the answers are :

1.

a) 10^-5 relates to the hundred-thousands place. The number 3 will be in the hundred thousands place followed by 0 which is in ten thousands place. The places before 3 will each hold digit 0.

b) The standard form will be 0.000032.

2. The standard form will be 0.000007

3. The standard form will be 0.0000875

Learn more about standard form here ;

https://brainly.com/question/5757613

#SPJ1

Answer:

[tex] \sqrt[16]{5 |2| } sdh[/tex]

usmsks

Answer:

[tex]K^{2}[/tex]

Step-by-step explanation:

[tex]\frac{K^{-4} }{K^{-6} } \\= \frac{K^{6} }{K^{4} } \\= K^{6-4} \\= K^{2}[/tex]

Answer:

7/8 or 0.875

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

[tex]3\frac{1}{2} = \frac{3*2+1}{2} = \frac{7}{2} \\\\\frac{7}{2} \div 4=\frac{7}{2}*4=7*2=14[/tex]

The amount of medicine required by a patient weighing 130 pounds is 186 milligrams of medicine.

A ratio is a comparison of two or more numbers that indicates their sizes and amount in relation to each other.

We have,

Patients weighing 195 pounds require 279 milligrams of medicine.

We can write this in ratio as:

= 279 / 195

Now,

We need to have both patients in proportion.

Proportion means their ratios must be equal.

Let the amount of medicine required for the second patient be M.

We have,

279 / 195 = M / 130

We will find M.

(279 x 130) / 195 = M

M = 186

Thus the amount of medicine required by a patient weighing 130 pounds is 186 milligrams of medicine.

Learn more about ratios here:

https://brainly.com/question/1504221

#SPJ1

The correct safe-breaker code is given by 6437346.

It is given that the number is palindrome. Palindrome is a combination of letters or symbols which when written in reverse order gives the same combination of letters or symbols when written in normal order. Let the seven-digit code be given by abcdefg. As it is palindrome therefore, a=g, b=f, c=e, and d=d. Also, first digit is double than third digit that is a=2c.

According to question d=7, c=f-1 and,

b=7-3 = 4.

Since the number is palindrome so b=f. Therefore f=4.

Now, c=f-1 => c = 4-1 = 3, and c = e = 3.

Also, a=2c => a=6.

Thus, the numbers are a=6, b=4, c=3, d=7, e=3, f=4, g=6 and the combination is 6437346.

Learn more about Palindrome at:

brainly.com/question/21901688

#SPJ1

The correct combination of the safe is 241742

We can solve the problem following a few steps. Let's assume the third number is x

So, the first digit is 2x according to the question.

Thus the fourth number is 7,

Now we can conclude that , 4 = x + 3  ( second number = sixth number , as mentioned earlier )

4 = x + 3

or , x = 4 - 3

or , x = 1  

After solving this equation we can use the value of x  as 1

∵  Hence the numbers are,

To know more about equations visit ,

https://brainly.com/question/10413253?referrer=searchResults

#SPJ1

Answer:

Will Give Brainliest!!!! Match each step with the correct justification.

Given: QM MR

a. Given

2+2=4-1=3 quick maths

The numbers in this problem are classified as follows:

A. Rational.

B. Rational.

C. Irrational.

Hence:

More can be learned about rational and irrational numbers at brainly.com/question/5186493

#SPJ1

In the shadow of the tree, Height = 4 feet

Given :

A  32-foot tree is directly between you and the sun

you are standing 105 feet away from the tree

the tree casts a 120-foot shadow

Trigonometry is one of the most important branches in mathematics that finds huge application in diverse fields. The branch called “Trigonometry” basically deals with the study of the relationship between the sides and angles of the right-angle triangle. Hence, it helps to find the missing or unknown angles or sides of a right triangle using trigonometric formulas, functions, or trigonometric identities. In trigonometry, the angles can be either measured in degrees or radians.

In this article, let us discuss the six important trigonometric functions, ratios, trigonometry tables, formulas, and identities that help to find the missing angles or sides of a right triangle.

Trigonometry is one of the important branches in the history of mathematics that deals with the study of the relationship between the sides and angles of a right-angled triangle.

Solution :

Trigonometry

Length of shadow= 120-105

Length if shadow= 15 feet

height= x

X/15= 32/120

X= 15*32/120

x= 15* 16/60

x= 15*8/30

x= 15*4/15

x= 4

X = 4 feet

Height = 4 feet

In the shadow of the tree, Height = 4 feet

More details :

#SPJ9