The geometric sequence an = 2an – 1 with an initial value of a1 = LaTeX: \frac{1}{8}1 8 represents the amount of money a person has saved after n years of investing. What is the sum of the first 11 terms?

The number of adult tickets purchased is 12.

What is the arithmetic operation?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.

Let no. of adult = x

No. of children = 28 -x

So, 7. 25 * x + (28 - x) *4. 50  = 159

⇒2.75x +126=159

⇒2.75x =33

⇒x=33/2.75

x=12

Hence, the number of adult tickets purchased is 12.

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Answer:

-24

Step-by-step explanation:

2(6)(-2)

Answer: To find the area of the pre-image and the image, you can use the coordinates of the vertices of the shapes to calculate the lengths of the sides and use the formula for the area of a triangle:

Area = (base * height)/2

For the pre-image, the coordinates are X(3,18) Y(18,18) and Z(18,9). The base of the triangle is the distance between X and Z, which is 18 - 3 = 15. The height of the triangle is the distance between Y and Z, which is 18 - 9 = 9. The area of the pre-image is therefore:

Area = (15 * 9)/2 = 67.5

For the image, the coordinates are X’(1,6) Y’(6,6) Z’ (6,3). The base of the triangle is the distance between X’ and Z’, which is 6 - 1 = 5. The height of the triangle is the distance between Y’ and Z’, which is 6 - 3 = 3. The area of the image is therefore:

Area = (5 * 3)/2 = 7.5

The relationship between the two areas is that the area of the image is smaller than the area of the pre-image. This is because the image has been scaled down in size relative to the pre-image. The amount by which the image has been scaled down can be calculated by dividing the area of the image by the area of the pre-image:

Scale factor = area of image / area of pre-image = 7.5 / 67.5 = 0.11

This means that the image has been scaled down by a factor of 0.11 relative to the pre-image.

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want to know the areas and their relationship of the preimage with coordinates X(3,18), Y(18,18), and Z(18,9), and the image with coordinates X’(1,6), Y’(6,6), Z’ (6,3).

When you plot the points on a graph, you see they define right triangles. Each has sides aligned with the x- and y-axes, so it is easy to find their dimensions by counting grid squares or subtracting coordinates.

The preimage triangle is 18-3 = 15 units in the x-direction, and 18-9 = 9 units in the y-direction.

The image triangle is 6-1 = 5 units in the x-direction, and 6-3 = 3 units in the y-direction.

We notice that both the coordinates and the dimensions of the image triangle are 1/3 those of the preimage triangle.

The area of each triangle is given by the formula ...

  A = 1/2bh

Using the dimensions we found above, the areas are ...

  preimage area: 1/2(15)(9) = 135/2 = 67.5 . . . . square units

  image area: 1/2(5)(3) = 15/2 = 7.5 . . . . square units

We have observed that the image dimensions are 1/3 those of the preimage. The image area is 7.5/67.5 = 1/9 of that of the preimage. This value is the square of the scale factor of the dimensions,

Answer:

1:11

Step-by-step explanation:

We know

There are 25 tables that seat 4 people

First, we find the total number of tables by taking

25 + 30 = 55 tables

Then we find the ratio of tables that seat 4 people to the total number of tables by

5 / 55 = 1/11 = 1:11

So, the ratio is 1:11

Darnell's constant speed, as determined by the solution, is 20 miles per hour.

It covers linear transformations more broadly as well as vectors, matrices, and vector spaces. One area of mathematics is linear algebra. In comparison to other areas of mathematics that are frequently driven by innovative ideas and unresolved problems, linear algebra is a discipline that is very well understood.

Distance=8 miles

Time taken is=32 minutes

speed=distance/time

speed=15 miles/hour

Darnel has travelled a distance of 1.5x5/60=0.125 miles in under five minutes.

Hector bicycle speed = distance/time

hector speed of bike=  20 miles/hour

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Therefore , the solution of the given problem of equation comes out to be  each diagonal measures 8.4 units in length..

An equation is a mathematical representation of two equal variables, one on each side of a "equals" sign. Everyday issues can be resolved with equations. We commonly look for pre algebra help to deal with problems in real life. Pre-algebra contains the fundamental concepts of mathematics.

Here,

Given: 16x + 2 = 36x - 6

8 = 20x

x = 8/20,

simplifying to 2/5, or 0.4

You would set the two equations equal to one another and find x because a rectangle's diagonals are congruent.

Re-enter the value of x into a single of the equations.

=>16(0.4) + 2

=>6.4 + 2

=>8.4

To make sure, confirm with the other diagonal.

=>36(0.4) - 6

=>14.4 - 6

=>8.4

Each diagonal measures 8.4 units in length..

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The complete question is "To find the diagonal  x value by the given equation  16x + 2 = 36x - 6 "

Answer:

Price after discount is $54

You save $36

Step-by-step explanation:

The Trigonometric inequality Sec (x)< cot(x) will hold true in π/2 < x < π.

How can a trigonometric inequality be expressed?

The intervals where the trigonometric inequality sec (x) cot (x) always holds true are what we are looking for.

This can also be expressed as: 1/cos (x) < 1/tan (x)

Now, this is only possible in the fourth quadrant, where cos x is positive and tan (x) is negative, where: π/2 < x < π.

The values for sin, cos, and tan are all positive in the first quadrant.

Only positive values for sin are present in the second quadrant.

The tan values in the third quadrant are all positive.

Only positive values for cos are present in the fourth quadrant.

Therefore the inequality Sec(x) < cot(x) will hold true in π/2 < x < π.

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Answer:

[tex] \sf \: x = 7[/tex]

Step-by-step explanation:

Now we have to,

→ find the required value of x.

Forming the equation,

→ 2x + 5 = 3x - 2

Then the value of x will be,

→ 2x + 5 = 3x - 2

→ 2x - 3x = -2 - 5

→ -x = -7

→ [ x = 7 ]

Hence, the value of x is 7.

Answer:

40%

Step-by-step explanation:

1 and 3/5 as a fraction is 8/5 which as a percent is 160%.

25% of 16 is 4

160%/4 = 40%

Yes it is possible to make the prediction about Ramiro's School but not completely.

It is possible to use the information from Ramiro's sample to make predictions about the school-wide results, but it is important to note that the sample may not be fully representative of the entire population of students at the school. There may be sampling biases or other factors that affect the results.

With that said, based on the information provided, we can calculate the proportion of students in Ramiro's sample who use the library in a certain way, and then use that proportion to estimate the number of students at the school who use the library in that way.

For example, if Ramiro's sample shows that 40 out of the 60 people he surveyed use the library to study, we can estimate that approximately 40/60 = 67% of the school's students use the library to study. We can then use this proportion to estimate that approximately 540 x 67% = 361 students at the school use the library to study.

It's important to note that these predictions are based on sample data and they may not be accurate. To make more accurate predictions, a larger, more representative sample would be needed.

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A logarithmic curve is a mathematical function.

A logarithmic curve, also known as a logarithmic function, is a type of mathematical function that describes a relationship between a variable x and a variable y in which the logarithm of y is a linear function of x.

The general form of a logarithmic function is y = logb(x), where b is the base of the logarithm, and x and y are real numbers. The base of the logarithm can be any positive number, but the most common bases used are 10 (common logarithm) and e (natural logarithm).

The graph of a logarithmic function is a curve that starts at negative infinity and increases gradually as x increases. The slope of the curve becomes closer to zero as x increases, and it is undefined for x=0 or x<0.

Logarithmic functions are often used in many areas of science, engineering, and mathematics to model real-world phenomena that exhibit exponential growth or decay, such as population growth, radioactive decay, sound levels and more.

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Answer: u = -3

Step-by-step explanation:

   To solve the equation, we will isolate the u variable by simplifying and using inverse operations.

Given:

   4(3u + 5) = 2(2u - 2)

Distribute the 4 and the 2:

   12y + 20 = 4u - 4

Subtract 20 from both sides of the equation:

   12y = 4u - 24

Subtract 4u from both sides of the equation:

   8u = -24

Divide both sides of the equation by 8:

   u = -3

Answer:

Step-by-step explanation:

The mean of 4 5 6 7 8

there are 5 numbers in sequence, you can solve at a glance by looking at the number in the middle, or add the numbers and divide them by their number, in any case the answer will be 6

4 5 6 7 8    (6 is central)

or

(4 + 5 + 6 + 7 + 8) : 5 =

30 : 5 =

6

a) Using the slope-intercept equation, after 4 years of working at the new company, Nachelle's salary will be $73,000 per annum.

b) After t years of working at the new company, Nachelle's salary will be $57,000 + $4,000(t).

The slope-intercept equation is in the form of y = mx + b.

The slope intercept describes the equation of a straight line, where m is the slope of the line, y and x are the y and x coordinates, and b is its y-intercept.

Initial starting salary per year = $57,000

Annual raise in salary = $4,000

Period = 4 years

Salary after 4 years = $73,000 [$57,000 + $4,000(4)]

Salary after t years = $57,000 + $4,000(t)

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In order to find the hypotenuse of the triangle

We need to find the other sides of a right triangle

Length of the 1st side of a right triangle is connected with a square with area 144[tex]cm^{2}[/tex]

Hence in order to find the side we

[tex]\sqrt{144} = side[/tex]

[tex]12 = side[/tex]

Length of the second side is connected to a small square with area 25[tex]cm^{2}[/tex]

[tex]\sqrt{25} = side[/tex]

[tex]5 = side[/tex]

Now we can find the hypotenuse of a right triangle with the phytogorean theorem

[tex]a^{2}+ b^{2} = c^{2}[/tex]

[tex]12^{2}+ 5^{2} = c^{2} \\169 = c^{2}[/tex]

[tex]\sqrt{169}= c[/tex]

[tex]13 = c[/tex]

Hence , the hypotenuse of a right triangle is 13cm

Answer:

  more than 110

Step-by-step explanation:

You want to know the number of $6 tickets that must be sold to pay for the $660 cost of a school play and make a profit.

The profit is the difference between revenue and cost. The revenue from the sale of n tickets will be 6n. We want the profit to be positive, so we want ...

  6n -660 > 0 . . . . . . positive profit

  n -110 > 0 . . . . . . divide by 6

  n > 110 . . . . . . add 110

More than 110 tickets must be sold to make a profit.

__

Additional comment

Sale of exactly 110 tickets will cover the cost, but there will be no profit.

The domain of a function is the set of all input values (x-values) for which the function produces a valid output (y-value). In this case, the function f(x) = (x+2)(x+6) is defined for all real numbers, so the domain is all real numbers.

What do a function example's range and domain mean?

A straightforward function, such as f(x) = x2, can have a domain (what goes in) of just the counting numbers 1, 2, 3, etc., and a range (what comes out) of the set 1, 4, 9, etc. Another function, g(x) = x2, may have an integer domain of..., -3, -2, -1, 0... 1, 2, 3, and its range is..., 1, 4, 9,...

The range of a function is the set of all possible output values (y-values) produced by the function. The function f(x) = (x+2)(x+6) is a polynomial, and all polynomials of the form (ax^2 + bx + c) with real coefficients (a,b,c) have range is all real numbers. The range of the function f(x) = (x+2)(x+6) is also all real numbers.

So the answer is

The domain is all real numbers, and the range is all

real numbers.

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Answer: 37

Step-by-step explanation:

divide the total that she spent over how much each game is (166.50/4.50). this will give you the number of games that she played.

A line which is confined between two endpoints is known as a line segment. In other words, we can say that a line segment is a portion of a line that is connected by two points.

The length of the line segment does not vary and the distance between them does not change. The units in which a line can be calculated in centimetres, millimetres, meters, inches, or feet.

The difference between a line segment and a line is that the line segment had two endpoints while the line extends indefinitely. When only one side of the line has an endpoint, it is called a ray or a half-open line segment.

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If the hypotenuse is given to the 45 45  90 triangles, the leg of the triangle is calculated after dividing the hypotenuse by [tex]\sqrt{2}[/tex].

The 45, 45, and 90 triangle is a type of isosceles triangle where the two legs are the same as each other and other non-right angles are both 45 degrees. Most of the time, Pythagoras' theorem is used for finding out the missing legs and hypotenuses of 45, 45, and 90 triangles.

If the leg of the triangle is equal to a, then:

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The graph of the inequality system is attached. The coordinate of a point in the solution set is (-1, 2).

In order to graph the system of inequalities graphically, consider the equation of each inequality.

y = x – 1

y = x - 4

Choosing a few values of x, plot the graph for each equation. Shade the area bounded by the line based on the inequality. If the inequality is less than, shade the area right to the line and if the inequality is greater than, shade the area left to the line. Hence, y < x – 1 is represented by red area and y > x – 4 is represented by blue area. The overlapping shaded area contains the coordinates that represent the solution of the inequality system. The coordinate of a point in the solution set is (-1, 2).

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Answer:

see image

Step-by-step explanation:

Right at the point (1,2) there's a nice point. Going up and right along the line there's another nice point at (5,5)

To get from one point to the next, you can draw a stair-step line that goes up3 and over4. The slope is up3/over4.

m = 3/4

The slope is 3/4. See image.

A given set of expressions are known as equivalent expression if and only if the result after evaluating those expression is the same number.

Example,

3 + 2 = 5

4 + 1 =  5

5 + 0 = 5

These three are equivalent as because the sum of all of them is same , i.e., 5.

An equivalent expression is an expression which consists of variables, coefficients, constants, and mathematical functions such as addition, subtraction, multiplication, and division.

In general, if two objects are identical, they are then called as identical.

These expressions are also known as duplicates of each other though they look different but they are same.

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required equation is, y=3x-37.

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.

Here, given that,

we have to find,

the equation of a line that passes through the point (7,-16) with slope 3.

we know,

y = mx+c

i.e. -16 = 3*7+c

so, c= -37

hence, required equation is, y=3x-37.

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Answer:2/5

Step-by-step explanation:

2/5+1/5 equals 3/5, so if the rest of the mixture is chili powder, it would be 2/5

Answer:

(0, -54)

Step-by-step explanation:

We find the y-intercept by plugging in 0 for x:

[tex]y=-2(x-3)(x-9)\\y=-2(0-3)(0-9)\\y=-2*-3*-9\\y=6*-9\\y=-54[/tex]

The domain of √ (square root) is all non-negative real numbers.

The domain of a function represents the set of all input values that can be used in the function without resulting in an undefined or meaningless output.

The square root function, represented by √, is only defined for non-negative real numbers. This is because the square root of any negative number is not a real number, it becomes an imaginary number.

This is because in order for the square root to be defined, the radicand (the value inside the square root symbol) must be greater than or equal to zero. Therefore, any real number greater than or equal to zero can be used as the input for the square root function, making its domain all non-negative real numbers.

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The graph of the function f(x) = 2x² + 2x - 2 is plotted and attached

The graphs of the function is plotted by making a table of value for a number of the x values and the corresponding y values as done below

Using the function the table is created as f(x) = 2x² + 2x - 2

For x = -4, y =  2 * (-4)² + 2 * (-4) - 2 =  22

For x = -2, y =  2 * (--2)² + 2 * (-2) - 2 =  4

For x = 0, y =  2 * (0)² + 2 * (0) - 2 =  -2

For x = 2, y =  2 * (2)² + 2 * (2) - 2 =  10

For x = 4, y =  2 * (4)² + 2 * (4) - 2 =  38

The table of values

x     y

-4   22

-2   4

0    -2

2     10

4    38

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a) The data on the y-axis: the numbers of people in each salary category.

b) The data on the x-axis: salaries

c) The distribution of salaries is skewed to the right.

We know that a histogram is a graph in which the x-axis is a quantitative variable split into bins, and the y-axis is the frequency.

For given distribution of salaries for individuals, the Y-axis would have the frequency i.e., the numbers of people in each salary category.

And x-axis would have income, because this is out quantitative variable of interest.

consider the following histogram.

We can observe that the graph of distribution of salaries is skewed to the right, because most income data are positively skewed. There would be a substantial number of individuals at or near the lowest salary level, but some people make a tremendously high salary.

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