What are the first three terms of the sequence represented by the recursive formula

Answer:

Two trail maps:

Trail on the first map is 8 cm

Trail on the second map is 6 cm

Scale on first map is 1 cm : 2 km

A. What is the scale factor from the map to the actual trail? 

For the first map, the scale factor is 1 cm: 2km. Therefore the actual trail is 8 centimeters * 2 kilometers = 16 km. 

The scale factor of the second map is 16 km / 6 cm = 2.67 km : 1 cm 

B. The length of the actual trail is 16 kilometers. 

Answer:

Given:  

Two trail maps:

Trail on the first map = 8 cm

Trail on the second map = 6 cm

Scale on first map = 1 cm : 2 km

A) What is the scale factor from the map to the actual trail?  

For the first map, the scale factor is 1 cm: 2km. Therefore the actual trail is 8 centimeters * 2 kilometers = 16 km.  

The scale factor of the second map is 16 km / 6 cm = 2.67 km : 1 cm  

B) The length of the actual trail is 16 kilometers.  

Step-by-step explanation:

Answer:

A. (-6, 5, 5)

Step-by-step explanation:

A suitable calculator can reduce the augmented matrix for the system.

[tex]\boxed{x=1, \y=-1, \ z=2}[/tex]

We will use the Gaussian elimination method to solve this problem. To do so, let's follow the following steps:

Step 1: Let's multiply first equation by −2. Next, add the result to the second equation. So:

[tex]\begin{array}{ cccc }~~ x&+~~2~ y&-~~~~~ z&~=~-3\\&-~~~5~ y&+~~3~ z&~=~11\\~~ x&-~~~~~ y&+~~~~ z&~=~4\end{array}[/tex]

Step 2: Let's multiply first equation by −1. Next, add the result to the third equation. Thus:

[tex]\begin{array}{ cccc }~~ x&+~~2~ y&-~~~~~ z&~=~-3\\&-~~~5~ y&+~~3~ z&~=~11\\&-~~~3~ y&+~~2~ z&~=~7\end{array}[/tex]

Step 3: Let's multiply second equation by −35, Next, add the result to the third equation. Therefore:

[tex]\begin{array}{ cccc }~~ x&+~~2~ y&-~~~~~ z&~=~-3\\&-~~~5~ y&+~~3~ z&~=~11\\&&+~~\frac{ 1 }{ 5 }~ z&~=~\frac{ 2 }{ 5 }\end{array}[/tex]

Step 4: solve for z, then for y, then for x:

[tex] \frac{ 1 }{ 5 } ~ z & = \frac{ 2 }{ 5 } \\ \\ \boxed{z & = 2}[/tex]

[tex]-5y+3z &= 11\\-5y+3\cdot 2 &= 11\\ \\ \boxed{y &= -1}[/tex]

By substituting [tex]y=-1 \ and \ z=2[/tex] into the first equation, we get the [tex]x[/tex]. So:

[tex]x+2(-1)-2=-3 \\ \\ x-2-2=-3 \\ \\ \boxed{x=1}[/tex]

Answer:

X= 1, y= -1, z= 2

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

c. positive 3 or 1; negative 1

Answer:

D

Step-by-step explanation:

(x + 5)x = 104

Distribute:

x² + 5x = 104

Subtract 104 from both sides:

x² + 5x − 104 = 0

Answer:

250 tickets

Step-by-step explanation:

300/1.2 or 120%

= 250 tickets

Answer:

250 tickets

Step-by-step explanation:

Answer:

a) Let b represent the number of blue marbles placed in the second jar. Then 34-b is the number of yellow marbles in the second jar, and 25 - (34-b) is the number of yellow marbles remaining in the first jar. That value simplifies to b-9. The positive difference between b and (b-9) is 9.  

b) Let n, d, p represent the numbers of nickels, dimes, and pennies, respectively.  

.. (5n + 10d + p)/(n + d + p) = 7 ... the average value of the collection is 7 cents per coin  

.. (5(n-1) + 10d + (p+5))/((n-1) + d + (p+5)) = 6 ... replacing one nickel with pennies changes the average to 6 cents per coin  

Multiplying by the denominator and subtracting the right side of each resulting equation gives  

.. 10d + 5n + p = 7d + 7n + 7p  

.. 10d + 5n + p = 6d + 6n + 6p + 24  

Subtracting the second equation from the first gives  

.. 0 = d + n + p - 24 ... tells us the total number of coins is 24. This tells us the total value is $1.68 = 24*$0.07.  

This sum will consist of at least 3 pennies. If that is all the pennies, then the remaining 21 nickels and dimes must add to $1.65. If all were nickels, the value of the 21 coins would be $1.05. We have $0.60 more than that. For each nickel traded for a dime, we gain $.05, so 12 of the 21 nickels must be traded for dimes to raise the total coin value to $1.65.  

Alternatively, you can write two equations in the two unknowns:  

.. d + n = 21  

.. 10d + 5n = 165  

Subtracting 5 times the first equation from the second gives  

.. 5d = 60 ... which gives the same answer as reasoned above.  

There are 3 pennies, 9 nickels, 12 dimes. (If there are 8 pennies to start, then the number of nickels is zero, so it is impossible to trade one for 5 pennies. The solution shown is the only one.)

Answer:

The function in choice

A) [tex]h(t) = -16(t - 3)^{2} + 34[/tex]

could possibly represent this relationship.

Step-by-step explanation:

Consider the vertex form of parabolas with a local extrema at [tex](x_{0}, y_{0})[/tex].

[tex]y = a(x - x_{0})^{2} + y_0[/tex].

Note the minus sign in front of [tex]x_0[/tex] in this expression.

The coefficient [tex]a[/tex] cannot be zero. The value of [tex]a[/tex] depends on the direction and width of the parabola's opening:

For this parabola,

Among the four functions, only the function in A) meets the requirements.

Answer:

The final angle is 124°

Step-by-step explanation:

1. Getting the total sum of all angles:

The general rule to get the sum of all interior angles is as follows:

sum of interior angles = (n-2)*180

where n is the number of sides

We know that a heptagon has 7 sides, therefore:

sum of interior angles of a heptagon = (7-2)*180 = 5 * 180 = 900°

2. Getting the missing angle:

We know that the total sum of all 7 angles is 900°

We also know that the sum of 6 of those angles = 776°

This means that:

measure of the last angle = 900 - 776

measure of last angle = 124°

The final angle is 124°

Hope this helps :)

Answer:

124 degrees

Step-by-step explanation:

Answer:

it is 0 because cosine is the x and sine is the y. Sin is 1 and cos is 0

Final answer:

The graph of an equation reveals all possible solutions, and a system of equations can be solved graphically by finding the intersection points of their lines. Changing the slope or intercept allows manipulation of these lines, and growth rates show the rate of increase as perce

Explanation:

The graph of an equation illustrates the relationship between two variables and reveals the set of all possible solutions that satisfy the equation. When graphing a line, the slope dictates the direction and steepness of the line, while the intercept indicates where the line crosses the y-axis. To manipulate a line on a graph, you can change the slope or the intercept, altering its position and angle.

To solve a system of equations using graphs, plot each equation on the same set of axes. The point where the lines intersect represents the solution to the system, which is the set of values that satisfies all equations simultaneously. If using tables, input different values for one variable and solve for the other to find ordered pairs. When the pairs from different equations match, you've found an approximate solution. A growth rate can be determined by calculating the percentage change and can be interpreted as the rate at which a quantity increases over time.

Learning how to read and manipulate a graph is critical to interpret and express equations visually. Graphs not only convey solutions but also the behavior of equations, such as trends and growth rates, which are essential in understanding and communicating mathematical concepts effectively.

let's take a peek at the graph.

the graph of the equation touches the x-axis at 1, 2 and 3, at 1 it crosses it, at 2 it crosses it, at 3 is doesn't cross it, it simply bounces off of it.

on the roots/solutions the graph crosses the x-axis, they have ODD multiplicity, on the solutions it bounces off of it, they have EVEN multiplicity, so then.

x = 1 => x - 1 = 0  <------ one  factor

x = 2 => x - 2 = 0 <------ another factor

x = 3 => x - 3 = 0  <------ another factor, BUT with even multiplicity

(x-1)¹(x-2)¹(x-3)² = f(x)

(x-1)(x-2)(x-3)² = f(x).

Answer: 13

Step-by-step explanation:

Divide 325 by 25

I can't give you the correct answer but you can guess for it, cause I can give you the the scop of the length of KL.

So, as we know this;

The sum of the two sides of a triangle is greater than the third and the difference between the two sides is less than the third.

10+5 >= KL >= 10-5

15 >= KL >= 5

based on your option, the answer should be:

9 in  

Answer:

1/5; 20%

Step-by-step explanation:

If she is only choosing 2 shirts, and they both have to be white, the probability of choosing those 2 white shirts out of 10 white shirts is 2/10 or, equivalently, 1/5.  In percent form, this is 20%

The probability of a woman randomly choosing two white shirts from a collection of 14 shirts (10 white and 4 red) is approximately 49%, derived through the process of combinations calculation in the field of probability.

The question relates to the field of probability in mathematics. To calculate her probability of selecting two white shirts, we first need to understand the number of total possible outcomes when she is selecting 2 out of the 14 shirts. This is represented by the combination formula C(n, r) = n! / r!(n-r)!, where n is the total number of items to choose from and r is the number of items to choose. Using this combination formula, we find that there are C(14, 2) = 91 total possible combinations of shirts she could end up with.

Next, we need to find the number of combinations that involve her picking 2 white shirts. As there are 10 white shirts, this is represented by C(10, 2) = 45. So, the probability of her taking two white shirts is then the number of desired outcomes divided by the total number of outcomes, or 45 / 91 which simplifies to approximately 0.4945 or 49% when rounded to the nearest whole percent.

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Answer:

A

Step-by-step explanation:

The equation will be in the form

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 5) and (x₂, y₂ ) = (2.5, 0) ← 2 points on the line

m = [tex]\frac{0-5}{2.5-0}[/tex] = - 2

The line crosses the y- axis at (0, 5) ⇒ c = 5

y = - 2x + 5 or

y = 5 - 2x → A

Answer:

C. withdrawl of $1000 from a checking account

Step-by-step explanation:

When you withdraw money from a checking account, you lose the amount of money which you withdraw.  In this situation, you are withdrawing $1000, which means you have -1000 dollars in your checking account

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Answer:

Step-by-step explanation:

area=6×11.4×13÷2=444.6 yd²

Final answer:

The area of a regular hexagon with an apothem of 11.4 yards and a side of 13 yards is approximately 444.6 square yards when rounded to the nearest tenth.

Explanation:

To find the area of a regular hexagon with a given apothem and side length, you can use the formula for the area of a regular polygon:

Area = (1/2) × Perimeter × Apothem

In this case, the perimeter of the hexagon can be calculated by multiplying the length of one side by 6 (since a hexagon has 6 sides). Therefore, the Perimeter = 13 yards × 6 = 78 yards.

Now, plug the values into the area formula:

Area = (1/2) × 78 yards × 11.4 yards

Area = (1/2) × 889.2 square yards

Area = 444.6 square yards

So, the area of the regular hexagon is approximately 444.6 square yards, when rounded to the nearest tenth.

Answer:

3 terms. All of the numbers are considered terms.

Step-by-step explanation:

If it asked for variables, it would be 2.

FICA taxes on a W-2 form include Social Security and Medicare taxes, summed up at a standard rate of 7.65% of gross wages. To know the total FICA taxes paid, one must multiply the gross wages by 7.65% based on the provided rates.

The question is asking for the total FICA taxes paid, which includes both Social Security and Medicare taxes. The information provided indicates that the employee pays 6.2% for Social Security and 1.45% for Medicare, which are standard rates for FICA tax deductions. To calculate the total amount of FICA taxes, add these percentages together to get a combined rate of 7.65%. If you know the gross wages, you multiply this amount by 7.65% to find the total FICA tax contribution on your W-2 form. If the actual gross wages earned are unknown, the calculation cannot be completed without this figure.

It is important to note that your employer also matches the FICA tax contributions, and some economists argue that this employer contribution effectively reduces employees' wages, meaning that employees might bear the total cost of these taxes indirectly.

Answer:

A) 2k+4

Step-by-step explanation:

To solve for terms of x, we need to. she sure that x is on its own side while every other term is on the other side.

To start, we will cross multiply. If we have a/b=c/d, then ad=bc

We can perform the same calculation here,

6/x=3/(k+2)

6(k+2)=3x

Divide both sides by 3

2(k+2)=x

x=2k+4

Answer:

  1329

Step-by-step explanation:

A suitable calculator can tell you the minimum score is 1329.

Using the concept of z-scores and normal distributions, the lowest possible SAT score a student needs to qualify for acceptance into a top university, that requires top 5% of SAT scores, is approximately 1328.

The subject of your question falls under Mathematics, particularly statistics. The problem involves understanding SAT scores and how they apply to scholarships. The problem also asks for the understanding of z-scores and how they apply to normal distributions.

In this case, the SAT score requirement is stated to be within the top 5% of all test-takers. In terms of z-scores, this requirement matches with a z-score of approximately 1.64, since z-scores of this value represent the cut-off for the top 5% in a normal distribution.

To calculate the corresponding SAT score, we use the formula for z-score which is Z = (X - μ) / σ, where X is the SAT score, μ is the mean and σ is the standard deviation. We rearrange the formula to find X, where X = Z * σ + μ. Since we know the mean (μ = 1000), standard deviation (σ = 200), and Z (Z = 1.64), we can substitute these values to get X = 1.64 * 200 + 1000 = 1328.

Therefore, the lowest possible score a student needs to qualify for acceptance into the university is approximately 1328.

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Answer:

See below.

Step-by-step explanation:

The model may have the scale written somewhere. Try looking for it.

If you can't find it, then you can calculate this way.

Search online for the real motorcycle's length.

Then divide the scale model's length, 18 inches, by the real length. Express that as a ratio. That is the scale.

Let's say the length of a real motorcycle of this type is 90 inches.

Divide 18 inches by 90 inches.

18/90 = 1/5

The scale, then, is 1:5.

Answer:

  A. This is a linear function because there is a common difference of 2

Step-by-step explanation:

Differences are ...

The differences of 2 are common, so this is an arithmetic function.

Option: A is the correct answer.

A.   This is a linear function because there is a common difference of 2.

Linear function--

A function is said to be linear if the rate of change is constant.

i.e. the function is increasing by a fixed constant.

Here the table is given by:

Hour (x) Number of Customers f(x)

    1               3

    2                  5

    3                  7

From the table of values we observe that as the value of increasing by 1 the value of y is increasing by 2.

i.e. the rate of change is constant i.e. 2.

Also, the common difference is 2.

since,

5-3=2

and 7-5=2

Hence, the table represents a linear function.

Answer:

The equation is 5x + 10y = 800

Step-by-step explanation:

* Lets explain what is the equation and how can we make one

- The equation is a mathematical statement that two things are equal.

- It consists of two expressions, one on each side of an equal sign (=).

* Lets solve the problem

- There are two types of vehicles, large one and small one

- The cost of washing the small vehicle is $5

- The cost of washing the larger vehicle is $10

- They collected from washing both is $800

- To make an equation for the amount collected let the number of the

 small vehicles is x and the number of the large vehicles is y

∵ x is the number of the small vehicles were washed

∵ y is the number of the large vehicles were washed

∵ The cost of washing the small vehicle is $5

∵ The cost of washing the larger vehicle is $10

∴ The money collected from the small vehicles = 5 × x = 5x

∴ The money collected from the large vehicles = 10 × y = 10y

- find the total money collected from both

∴ The amount of money collected from both = 5x + 10y

∵ The amount of money collected is $800

- Equate the two expressions above

∴ 5x + 10y = 800

* The equation is 5x + 10y = 800

Answer:

$.80 and 1.25

Step-by-step explanation:

hope this helps

Answer:

Option D.(60, 135)

Step-by-step explanation:

Let

x -----> the number of acres of peas

y ----> the number of acres of carrots

we know that

The inequality that represent the problem is equal to

[tex]x+y\leq 200[/tex]

so

Verify each case

case A) (-50,160)

substitute the value of x and the value of y in the inequality and then compare the result

[tex]-50+160\leq 200[/tex]

[tex]110\leq 200[/tex] ----> is true

The point is a solution for the inequality, but is not a viable solution because the number of acres can not be a negative number

case B) (80,160)

substitute the value of x and the value of y in the inequality and then compare the result

[tex]80+160\leq 200[/tex]

[tex]240\leq 200[/tex] ----> is not true

therefore

The point is not a solution

case C) (75,-200)

substitute the value of x and the value of y in the inequality and then compare the result

[tex]75-200\leq 200[/tex]

[tex]-125\leq 200[/tex] ----> is true

The point is a solution for the inequality, but is not a viable solution because the number of acres can not be a negative number

case D) (60,135)

substitute the value of x and the value of y in the inequality and then compare the result

[tex]60+135\leq 200[/tex]

[tex]195\leq 200[/tex] ----> is true

therefore

The point is a viable solution

[tex]\displaystyle\sum_{n=2}^{91}(3n+8)=\sum_{n=1}^{91}(3n+8)-a_1=(*)\\\\S_n=\dfrac{a_1+a_n}{2}\cdot n\\a_1=3\cdot1+8=11\\n=91\\a_n=3n+8\\d=a_n-a_{n-1}\\a_2=3\cdot2+8=14\\d=14-11=3\\a_{91}=11+(91-1)\cdot 3=11+90\cdot3=281\\\\S_{91}=\dfrac{11+281}{2}\cdot91=146\cdot91=13286\\\\(*)=13286-11=\boxed{13275}[/tex]

Answer:

Distributive Law : x= [tex]\frac{11}{10}[/tex]

Step-by-step explanation:

5(2x - 1) = 6

Using Distributive law on right hand side we get

5*2x - 5 * 1 = 6

10x - 5 = 6

Now we add 5 on both hand sides

10x-5+5=6+5

10x= 11

Now we divide both sides by 10

[tex]\frac{10x}{10} = \frac{11}{10}[/tex]

Hence we get

x= [tex]\frac{11}{10}[/tex]

Answer:

  1.5

Step-by-step explanation:

The coordinate values of point J are 1.5 times those of point A, so if dilation is about the origin, the scale factor is 1.5.

If the dilation is about some other point, this problem statement does not contain enough information to tell what the scale factor might be.