What is the side length of the smaller square in the diagram?

The slope of the line that passes through the given pair of points is, -3/7.

What is slope of the line?

A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively. where "m" represents a line's slope. So, the slope of a line is tanθ.

Given: (8, -2), (1, 1)

Since, if two points [tex](x_1, y_1), (x_2, y_2)[/tex] are given then slope (m) is defined as,

[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex].

Here,

[tex](x_1, y_1) = (8, -2)\\(x_2, y_2)=(1, 1)[/tex]

So, the slope can be defined as,

[tex]m = \frac{1-(-2)}{1-8} \\m=\frac{3}{-7} \\m=-\frac{3}{7}[/tex]

Hence, the slope of the line that passes through the given pair of points is, -3/7.

To know more about the slope of the line, click on the link

https://brainly.com/question/27212023

#SPJ9

The no. of ways to select the 2 blue balls and 2 orange balls from the urn is 0.4545

No. of Blue balls in the urn = 6

No. of Orange balls in the urn = 6

Total no. of balls in the urn = No. of blue balls + No. of orange balls

                                            = 6 + 6

                                           = 12 balls

No. of blue balls to be selected = 2

No. of orange balls to be selected = 2

No. of balls to be selected = 4

The total. no of ways 4 balls can be selected =[tex]^{12}C_{4}[/tex]

The No. of ways 2 blue balls can be selected = [tex]^{6}C_{2}[/tex]

The No. of ways 2 orange balls can be selected =    [tex]^{6}C_{2}[/tex]

Therefore, No. of ways to select 2 blue balls and 2 orange balls from the urn

                      =  [tex]^{6}C_{2} \times ^{6}C_{2} /^{12}C_{4}[/tex]

Probability = No. of ways to select blue balls x No. of ways to select orange balls / Total no. of ways to select balls

                         P = (15×15)/495

                             = 225 / 495

                          P = 0.4545

Therefore,  the no. of ways to select blue and orange balls is 0.4545

Learn more about the probability at

brainly.com/question/11234923

#SPJ4

There are 100 4-digit positive integers are possible between 1000 and 9999.

Our first step is to divide the four digit number into four places: tens, hundreds, and thousands.

To solve this problem, we must start from the right-hand side and find how many even numbers should be placed where the desired answer can be obtained.

There are a total of [0, 2, 4, 6, and 8] objects

There should only be one digit on one place, since it is the only digit that makes the number divisible by five

There are 1 ways to fill the one's place, so the total number is 1.

It is possible to take any number from the given sets of even numbers in the tens place,

There are five ways to fill one place, so there are five ways to fill it.

Taking a look at the hundreds place,

All numbers can be placed in the hundreds place from the given sets, so all numbers can be taken from the hundreds place.

Therefore, there are five ways to fill the hundreds place.

Taking a look at the thousands,

It is possible to fill thousands of places with 4 numbers from a given set of even numbers.

Therefore, there are four ways to fill the thousands place

The next step is to use the concept of factorial to find the number of ways to make a 4-digit number from even numbers that are divisible by 5.

To fill the respective places, we will multiply all the ways we calculated

= 4 × 5 × 5 × 1

= 100

Hence, there 100 4-digit positive integers possible.

Question

how many 4-digit positive integers (that is, integers between 1000 and 9999, inclusive) having only even digits are divisible by 5?

To Learn more about Similar 4-digit positive integers Questions:

https://brainly.com/question/14136627

#SPJ4

Answer:

Step-by-step explanation:

do I

Answer:

C

Step-by-step explanation:

In the graph, you can see an asymptote is happening for x=-5, so look for an equation that divides by 0 for x=-5. That is clearly C, for x=-5 the denominator is 0.

Answer:

i have the similar question just radius is changed frm 12 to 20 cm..

hopefully this will help u ...^⁠_⁠^

Step-by-step explanation:

750 people go on a coach trip each coach can hold 55 people How many coaches are needed?

750/55 = 13.636 coaches are needed.

Because you cannot have a partial coach, you round up to needing 14 coaches.

It is equivalent to 8^x/3

acc to our question-

to write a square root into fraction. To do that, you just have to apply the formula :

x^power/root

Then, here it gives . 8^x/3

learn more about equivalent equations click here:

https://brainly.com/question/2972832

#SPJ13

For Maia's birthday celebration, the bare minimum amount of packets of plates, napkins, and cups she needs to purchase is 15, 12, and 10, respectively.

acc to our question-

Learn more about Fraction:

brainly.com/question/1301963

#SPJ13

After using the probability distribution table, the given table does not show a probability distribution. The statement 1 is correct.

In the given question, we have to check which statement is correct regarding to the given option.

The given statements are:

(1) This table does not show a probability distribution.

(2) This table shows a probability distribution.

Before checking the statement we learn about a probability distribution table.

In a probability distribution table every result of a statistical experiment is connected to the likelihood that the result will actually occur. An experiment's result is recorded as a random variable, which is typically written with a capital letter.

As we can see that there is given the probability of having the blue, green, yellow and red color.

So the given table does not show a probability distribution.

So the statement 1 is correct.

To learn more about probability distribution link is here

brainly.com/question/14210034

#SPJ1

Answer: 11.1%

Step-by-step explanation:

The formula for percent error is:

|Actual-predicted/predicted| * 100%

In the context of the problem:

Actual = 16 ft

Predicted = 18 ft

Plug these values into the equation:

|16-18/18| * 100% = percent error

11.11% = percent error
If you have any other problems about percent error, you should be able to just plug these values into the formula

Answer:

Step-by-step explanation:

volume of a sphere = ⁴/3 π r³. r = D/2. V = 4/3 × π × (D/2)³. V = 4/3 × π × D³/8. V = ⅓ × π × D³/2. V = ⅓× π × (24mm)³/2.

The number of pages read by her will be 36.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Marion read 616 pages in 14 days, The number of pages each day will be calculated as,

N = 616 / 17

Divide the number 616 by 17,

N = 36.23

N = 36

Therefore, the number of pages read by her will be 36.

To know more about an expression follow

https://brainly.com/question/14039858

#SPJ1

The range of scores that Marjorie's can receive in the final exam to earn a C in the course is 67 to 82  .

in the question ,

it is given that

the Marjorie's score in the tests are 67 , 78 , 75 , 78 .

let the score in the final exam be "x"

it is given that the final exam score is worth 6 test scores , which means

the score in final exam is = 6x

and the total number of tests = 6+4 = 10

given that to get the grade C minimum average is = 70

that is  (67 + 78 + 75 + 78 + 6x)/10 = 70

67 + 78 + 75 + 78 + 6x = 700

298 + 6x = 700

6x = 700 - 298

6x = 402

x = 402/6

x = 67

given that to get the grade C maximum average is = 79

that is  (67 + 78 + 75 + 78 + 6x)/10 = 79

67 + 78 + 75 + 78 + 6x = 790

298 + 6x = 790

6x = 790 - 298

6x = 492

x = 492/6

x = 82

the range of scores is 67 to 82 .

Therefore , The range of scores that Marjorie's receive in the final exam to earn a C in the course is 67 to 82  .

Learn more about Average  here

https://brainly.com/question/12191218

#SPJ1

There are 20 ways to paint the fence consisting of six panels each with one color out of green, red, and magenta.

There is a total of 6 panels and 3 paint colors and each panel has to be painted with only 1 color.

∴ Total number of panels = 6

Total number of colors = 3 (green, red, and magenta)

To calculate the number of ways to paint 6 panels with one of the 3 colors, the formula of combination is used. Combinations are ways of selecting objects from a group or collections, in a way that the order of the objects does not matter.

The number of ways or the combinations of 6 panels taken with each color out of 3 at a time is given by [tex]^6C_3[/tex]

[tex]^6C_3[/tex] = 6! / [3! (6-3)!]

[tex]^6C_3[/tex] = (6*5*4*3*2*1) / [3*2*1 (3)!]

[tex]^6C_3[/tex] = 720 / (6*6)

[tex]^6C_3[/tex] = 720 / 36

[tex]^6C_3[/tex] = 20

Therefore, 20 combinations are possible to paint 6 panels each with only one color out of green, red, and magenta.

To know more about combinations,

brainly.com/question/20211959

#SPJ4

The the coordinates of the vertex is at (-2, 1) and the axis of symmetry at x = -3

The quadratic function is given by

f(x) = [tex]-3(x+2)^2[/tex] + 1

The vertex form of the quadratic function is

f(x) = [tex]a(x-h)^2[/tex] + k

Where (h, k)  is the coordinates of the vertex

x =  h is the axis of symmetry

Compare the given function and the vertex form of the quadratic function and find the value of the each term

The value of h = -2

The value of k = 1

The coordinates of the vertex = (-2, 1)

The axis of symmetry is at x = h

h = -2

Draw the graph using the details

Hence, the the coordinates of the vertex is at (-2, 1) and the axis of symmetry at x = -3

Learn more about vertex form here

brainly.com/question/21500885

#SPJ1

Answer:

Step-by-step explanation:

COP = Constant of Proportionality. • y varies directly to x. > If 10 miles varies directly to 5 minutes,. – then 10 = y and 5 = x. • Unit Rate (1, r). > (x, y).

After ≈16.61 years the population will increased by  times it's original amount.

What do you mean by population?

A population is the entire set of people in a group, whether that group is a country or a collection of people who share a certain trait. A population is the group of people from which a statistical sample is taken in statistics.

Given: If a population doubles every 5  years.

Assume,  'A' is the starting population, and 't' is the passing time in years.

Given the fact that a population doubles every five years, our population is growing exponentially, as per the question.

Here, the equation can be written as follows: [tex]A(t) = A(2)^{\frac{t}{5} }[/tex]                    (1)

We now need to determine when the population will have multiplied by 10 by that time.

Let's substitute [tex]A(t) = 10A[/tex]  in the above equation.

[tex]10A = A(2)^{\frac{t}{5} }[/tex]

[tex]10 = (2)^{\frac{t}{5} }[/tex]

Taking the natural log of both sides we get:

[tex]ln10 = \frac{t}{5} \times ln2[/tex]                        {[tex]ln(a)^n= nln(a)[/tex]}

2.3025 x 5 = t x 0.6931

[tex]t = \frac{2.3025}{0.6931}\\t = 16.6096[/tex]

Therefore, After ≈16.61 years the population will increased by  times it's original amount.

Learn more about Exponential function here:

https://brainly.com/question/2456547

#SPJ13

Answer: No Solution

Explanation: 10 + r = 3 + r - 7

Combine like terms: 10 + r = -4 + r

Subtract R to both sides: 10 = 4

There is NO SOLUTION

A. Applying the trigonometric ratio, the length of pole = 29.6 ft.

B. 23.1 ft.

C. Length of wire 1 = 45.1 feet.

The trigonometric ratios are:

Part A: Apply the trigonometric ratio, tan ∅ = opp/adj, to find the length of the pole

∅ = 41°

Opp. = length of pole

Adj. = 34 ft

Substitute

tan 41 = length of pole/34

Length of pole = (tan 41)(34) = 29.6 ft.

Part B:

Let the distance between the base of the pole and wire 2 be represented as x. Therefore, apply tan ∅ = opp/adj.

∅ = 38

Opp. = x

Adj. = 29.6 ft

Therefore:

tan 38 = x/29.6

x = (tan 38)(29.6)

x = 23.1 ft.

Part C: Use the Pythagorean theorem to find the length of wire 1.

Length of wire 1 = √34² + 29.6²)

= 45.1 feet.

Learn more about the trigonometric ratios on:

https://brainly.com/question/10417664

#SPJ1

The equation of the graph given in the diagram which represents an absolute value function is: y = |x - 3| + 5.

The equation, in vertex form, of a absolute value function is expressed as y = a|x – h| + k, where:

From the graph, we know that:

Vertex (h, k) = (3, 5)

Substitute h = 3 and k = 5 into the equation, y = a|x – h| + k:

y = a|x - 3| + 5

A point on the graph is (5, 7). To find the value of a, substitute x = 5 and y = 7 into the equation y = a|x - 3| + 5:

7 = a|5 - 3| + 5

7 = 2a + 5

7 - 5 = 2a + 5 - 5 [subtraction property of equality]

2 = 2a

Divide both sides by 2

2/2 = 2a/2 [division property of equality]

Substitute a = 1 into y = a|x - 3| + 5:

y = |x - 3| + 5 [equation of the absolute value function]

Learn more about equation of absolute value function on:

https://brainly.com/question/25290500

#SPJ1

Answer:

2 swimming pool lengths

Step-by-step explanation:

to answer this we divide 1/2 by 1/4

1/2/1/4

1/2x4/1=4/2

2 swimming pool lengths

hopes this helps please mark brainliest

The factors of the quadratic equation are x≥-4, x≥2 and lies in the interval (-∞, -4]∪[2, ∞)

A quadratic equation is any equation that can be rearranged in standard form as ax²+bx+c=0 where x represents an unknown value and a, b, and c represent known numbers. In general, a = 0; equations with a = 0 are considered degenerate because the equation becomes linear or even simpler. The numbers a, b, and c are the equation's coefficients, and they can be distinguished by referring to them as the quadratic coefficient, linear coefficient, and constant or free term, respectively.

To find x-intercept y=0

y≥x²+2x-8

x²+2x-8≥0

x²+4x-2x-8≥0

x(x+4)-2(x+4)≥0

(x-2)(x+4)≥0

∴x≥-4, x≥2

∴(-∞, -4]∪[2, ∞)

Therefore, the factors of the quadratic equation are x≥-4, x≥2 and lies in the interval (-∞, -4]∪[2, ∞)

To know more about quadratic equation, visit:

https://brainly.com/question/17177510

#SPJ1

Step-by-step explanation:

remember, the sum of all angles in a triangle is always 180°.

now let's consider the white, "cut-out" triangle on the left side.

the purple one angles at the top and bottom corner are 45°.

the withe outer angles at the same corners (they are the inner angles for the white triangle) are complementary angles (together they have 90°) to the purple ones, because due to the equal angles at the top and bottom we know the connection between the 2 45° angles (the white baseline) is at a 90° angle to the 45° to 135° sides.

so the 2 baseline angles of the left white triangle are also 45° (45+45 = 90).

and that means that the third white angle is

180 - 45 - 45 = 90°.

and because a full circle around the 3x° point must have 360° (as any full circle), we know that both angles (90° and 3x°) together are 360°.

360 = 90 + 3x

270 = 3x

x = 90°

3x = 270°

Answer:

30 feet^3

Step-by-step explanation:

length x width x height

3 x 2 x 5

=30

The last four digits of the number nn are 4944

Given that,

Let nn stand for the lowest positive integer that can be represented in base-1010 using only the numbers 44 and 99, with at least one of each. This number must be divisible by both 44 and 9,9.

The last two digits of n must be divisible by 4 for n to be divisible by 4.

So last digits of n will be 44.

And for divisiblity by 9, sum of all digits of n has to be divisible by 9.

As two digits are fixed and their total is 8, next feasible total will be 45 so 9 can be atleast one time in n.

And as statement says n has to be smallest number n will be 4444444944

So last 4 digits of n are 4944.

Therefore, nn's last four numbers are 4944.

Learn more about positive integer :

brainly.com/question/28165413

#SPJ4

Answer:

13

Step-by-step explanation:

416/96 = 4.33333

416 is 4.333 times 96, so he needs 4.333 times 3 bundles.

4.3333 × 3 = 13

Answer: 13

Answer:

13

Step-by-step explanation:

you see how much it covers initially. (96/3=32) then 416/32=13

The theoretical probability of choosing a tile with the letter p is 1/8

The letter of the word MISSISSIPPI are written on separate tiles lying down on the table and tile is chosen at random and the the letter is noted and then the tile is lied again on the table.

Probability of the event is,

P(E) = Total favorable outcomes/Total possible outcomes.

Total possible outcomes in this case are 11 because there are a total of 11 letters.

The total favorable outcomes that the chosen letter is P is,

Total favorable outcomes = ¹¹C₁/(2!)(2!)(2!)

Total favorable outcomes = 11/8

Probability P that chosen number is P is,

P = (11/8)/11

P = 1/8

So, the probability that the chosen tile is with letter P is 1/8.

To know more about probability, visit,

https://brainly.com/question/24756209

#SPJ4