Solve the system of linear equations

Answer: 1560

Step-by-step explanation: The average rate of change of a function over an interval is the total change in the value of the function divided by the length of the interval. In this case, the function is f(x) = 10(2)^x and the interval is [3, 5].

To find the average rate of change of the function over the interval, we can first evaluate the function at the two endpoints of the interval, which are x = 3 and x = 5. At x = 3, the function has a value of f(3) = 10(2)^3 = 80. At x = 5, the function has a value of f(5) = 10(2)^5 = 3200.

The total change in the value of the function over the interval is then the difference between the values at the two endpoints, which is f(5) - f(3) = 3200 - 80 = 3120.

The length of the interval is 5 - 3 = 2, since it goes from x = 3 to x = 5. Therefore, the average rate of change of the function over the interval is the total change in the value of the function divided by the length of the interval, which is (3120) / 2 = 1560.

Therefore, the average rate of change of the function f(x) = 10(2)^x on the interval [3, 5] is 1560.

And we see that the solution is at (0,6) that is x=0, and y=6

The slope between two points is given by:

Then:

Therefore, the slope between the points is -1.

Answer:

AOB = 65°

DOE = 35°

AOC = 90°

EOB = 115°

DOB = 85°

Hope this helps!

Given statement solution is :-  Box-and-whisker plot, the box represents the interquartile range (IQR), which is the range between Q1 and Q3 (13 to 18). The line inside the box represents the median (15). The whiskers (lines extending from the box) represent the minimum and maximum values (12 and 20).

To construct a box-and-whisker plot using the given data, you first need to find the minimum, maximum, median, and quartiles. Here are the steps to create the box-and-whisker plot for the given data set:

Sort the data in ascending order:

12, 12, 13, 14, 14, 15, 15, 15, 16, 16, 17, 18, 20

Find the median (middle value) of the data set. Since the data set has an odd number of values, the median will be the middle value:

Median = 15

Find the lower quartile (Q1), which is the median of the lower half of the data set.

Counting from the start, the lower half of the data set is:

12, 12, 13, 14, 14

Q1 = 13

Find the upper quartile (Q3), which is the median of the upper half of the data set.

Counting from the end, the upper half of the data set is:

17, 18, 20

Q3 = 18

Find the minimum and maximum values in the data set:

Minimum = 12

Maximum = 20

Now that we have the necessary values, we can construct the box-and-whisker plot:

lua

Copy code

       |                 |

 12  |      -------------|    

 13  |                 |

 14  |              ----  

 15  |           -------

 16  |      -------------|    

 17  |                 |

 18  |              ----  

 20  |                 |

       |_________________|

In this box-and-whisker plot, the box represents the interquartile range (IQR), which is the range between Q1 and Q3 (13 to 18). The line inside the box represents the median (15). The whiskers (lines extending from the box) represent the minimum and maximum values (12 and 20).

For such more questions on Box-Whisker Plot Requested

https://brainly.com/question/12343132

#SPJ8

The equation that represents the cost constraint in this situation is 11x + 6y = 200

Let x represent the number of adult tickets and y represent the number of children tickets.

An after-school  program has a budget of $200, hence:

11x + 6y = 200

Plotting the graph using online geogebra graphing tool.

Find out more on equation at: https://brainly.com/question/2972832

Answer:

√ 96

log  ∨13  ( 28 )

log  ∨2  ( 16 )

click brainliest and thanks

Answer:

length-x

width-x-4

area-- length* width

192=X*(X-4)

x^2-4x-192=0

x^2-16x+12x-192=0

X(x-16)+12(x-16)=0

(x-16),(X+12)

X= 16 because X cannot be negative like (-12)

the dimensions of the classroom will be

length = 16

width = 12

I hope this will help everyone

First, let's create two variables to express the girls' ages.

x=age of girl 1

y = age of girl 2

Now, let's create our expressions

x+y = 24

x-y=6

Let's solve by elimination

2x = 30

Divide both sides by 2

x=15

We can plug 15 in for x into one of our expressions

15 + y = 24

Subtract both sides by 15

y = 9

The older girl is 15 years old and the younger girl is 9 years old.

Answer:

68% of the data points lie between 10 and 18.

Step-by-step explanation:

one standard deviation to left of mean = 14 - 4 =10

one standard deviation to right of mean = 14 + 4 = 18

68% of data is in this region.

so the answer is 68% of the data points lie between 10 and 18.

Answer:

First graph

Step-by-step explanation:

Here we have x ≥ 0, and y ≥ - 2, not x ≥ 0 and y ≥ 0. Thus, it doesn't restricts us fully to quadrant 1, but somewhat off considering y ≥ - 2. Now all we have to do is plot the following system of inequalities -

\(\begin{bmatrix}8x+12y\le \:92\\ 11x+7y\le \:79\\ x+y\ge \:5\end{bmatrix}\)

Convert each into slope intercept form -

\(\begin{bmatrix}y\le \frac{23-2x}{3}\\ y\le \frac{79-11x}{7}\\ y\ge \:5-x\end{bmatrix}\)

Which should be bounded by a small region similar to graph 1! The shaded region represents each intersection with respect to their restriction to quadrant 1.

Hope that helps!

Answer:

C

Step-by-step explanation:

So we have the expression:

\(((-3)^2)^3\)

Use the power of a power property, where:

\((a^b)^c=a^{b\cdot c}\)

So:

\(((-3)^2)^3=(-3)^{2\cdot 3}\)

Simplify:

\(=(-3)^6\)

Our answer is C

Answer:

(-3)⁶

Step-by-step explanation:

( (-3)² )³

= (-3)⁽²⁾⁽³⁾

= (-3)⁶

Answer:

So the diameter of the pipe with the insulation around it is approximately 18.84 inches / 2 = 9.42 inches.

Step-by-step explanation:

To find the diameter of the pipe with the insulation around it, we can use the formula for the circumference of a circle:

C = 2 * π * r

Where:

· C = circumference of the pipe

· π = the mathematical constant approximately equal to 3.14

· r = the radius of the pipe

Using the given information, we know that the pipe’s diameter is 2.5 inches and that the insulation around the pipe is 0.5 inch thick. Therefore, the radius of the pipe with the insulation around it is:

r = 2.5 inches + 0.5 inch = 3 inches

Plugging in the values:

C = 2 * π * 3

C = 6.28 * 3

C = 18.84 inches

Note that this is only an approximation, as the thickness of the insulation is slightly larger than the diameter of the pipe. To obtain a more accurate result, we would need to use a geometric area formula or a numerical integration technique.

your answer would be 96

Answer:

sorry

Step-by-step explanation:

I really don't know answer

Answer:

the expected number of pairs of people who have the same birthday is 14

Step-by-step explanation:

The computation of the expected number of pairs of people who have the same birthday is as follows:

= 100 (100 - 1) ÷ 2 × 365

= 100 × 99 ÷ 730

= 9900 ÷ 730

= 13.5616

= 14

Therefore, the expected number of pairs of people who have the same birthday is 14

Answer: Your answer will be $240

Step-by-step explanation:

the area of the trapezoid is 10√3 km² (approximately 17.3 km²).To find the area of a trapezoid, we use the formula A = (1/2) * (b₁ + b₂) * h

what is trapezoid ?

A trapezoid is a quadrilateral with at least one pair of parallel sides. The parallel sides are called the bases of the trapezoid, and the other two sides are called the legs. The height (or altitude) of a trapezoid is the perpendicular distance between the two bases. The formula for the area of a trapezoid

In the given question,

To find the area of a trapezoid, we use the formula:

A = (1/2) * (b₁ + b₂) * h

where A is the area, b₁ and b₂ are the lengths of the parallel sides of the trapezoid, and h is the height (or perpendicular distance between the parallel sides).

In this case, we are not given the height, but we can still find the area if we make some assumptions. Let's assume that the trapezoid is isosceles, which means that the two non-parallel sides are equal in length. Then we can draw an altitude from one of the vertices to the opposite base, which will bisect the base and create two right triangles.

Using the Pythagorean theorem, we can find the length of the altitude:

a² + (b₁ - b₂)² = (2a)²

Simplifying and solving for a, we get:

a² + (b₁- b₂)² = 4a²

3a² = (b₁ - b₂)²

a = (1/√3) * |b₁ - b₂|

Since we know that the sum of the non-parallel sides is 10 km, we can write:

b₁ + b₂ = 10

Let's assume that b1 is the longer base, so we can write:

b₁ = 8 km

b₂ = 10 - b₁ = 2 km

Substituting these values into the formula for the altitude, we get:

a = (1/√3) * |8 - 2| = (1/√3) * 6 = 2√3 km

Now we can use the formula for the area of a trapezoid to find the area:

A = (1/2) * (b1 + b2) * h

A = (1/2) * (8 + 2) * 2√3

A = 10√3 km²

Therefore, the area of the trapezoid is 10√3 km² (approximately 17.3 km²).

To know more about trapezoid , visit:

https://brainly.com/question/8643562

#SPJ1

Answer:

3x√7y

Step-by-step explanation:

Answer:

1,982

Step-by-step explanation:

i got It right on edge 2020

The library raised $320,100 when 400 books were sold per day.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

Number of days book sale = 4

The library paid for advertisement each day = $25

Cost of each book (b) =  $2.00.

The expression represents the amount of money the library raised at the book sale.

= 4(25) + 2b(400)

Now,

Substitute b = 400 into the expression.

= 4(25) + 2(400)(400)

= 4(25) + 320000

= 320100

Therefore,

The library raised $320,100 when 400 books were sold per day.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ2

Answer:

Explanations:

The formula for calculating the slope of a line passing through the coordinates (x1, y1) and (x2, y2) is expressed using the formula:

For the line "m"

Using the coordinate points

Using the

Answer:

0.75 can be written as :-

\( \frac{75}{100} \)

and in simplest form it is:-

\( \frac{3}{4} \)

so the answer is 3/4

Answer:

X=r+h

Step-by-step explanation:

add h to both sides to get the x variable by itself

so X-h+h=r+h

simplify:

X=r+h

Answer:

x = h + r

Step-by-step explanation:

x - h = r               (Add h to both sides to get x alone)

   +h  = +h

x = h + r

Answer:it might be A

Answer:

1, 2 * 3^3 * 17

2, 8

Step-by-step explanation:

64 is perfect sqr root 8*8 = 64

Answer:

about 27 are ripe

Step-by-step explanation:

100 mangos

5*20=100

2*20=40

40 are rotten

3*33=99 which is about 100

1*33=33

33 are green

40+33=73

100-73=27

Answer:

0.67

Step-by-step explanation:

all you need to do is divide 10 by 15

There are 400 students in the hall.

Given,

There are 20 students kept in each row and each column of a square hall.

We need to know how many students are in total in the square hall.

In a square all four sides are equal.

If we have a square hall then the number of rows and columns must be equal.

So we have 20 rows and 20 columns in the square hall.

Total number of students in the square hall  

= Number of rows x number of columns    

= 20 x 20    

= 400 students

We can also find the total number of students by calculating the number of students in all the rows or in all the columns.

If one row = 20 students

then,

20 rows = 20 x 20 students = 400 students.

If one column = 20 students,

then,

20 columns = 20 x 20 students = 400 students.

Thus, the total number of students in the square hall is 400 students

Learn more about calculating the number of rows and columns problems here:

https://brainly.com/question/18830558

#SPJ2