Pls answer and show all work

The number of miles you need to drive to pay less by taking rate 2 is less than 500 miles

Let

Number of miles = x

Rate 1:

30 + 0.12x

Rate 2:

60 + 0.06x

Rate 2 < Rate1

60 + 0.06x < 30 + 0.12x

60 - 30 < 0.12x - 0.06x

30 < 0.06x

divide both sides by 0.06

x < 30/0.06

x < 500 miles

Therefore, you need to drive less than 500 miles to pay less by taking rate 2.

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One possible recursive function for this sequence is a n = a n-1 - 3, where a n is the nth term in the sequence and a n-1 is the previous term.

A function is a rule or mapping that relates a set of inputs to a set of outputs. It is a mathematical expression that takes one or more inputs and produces a corresponding output. Functions are essential for solving problems in mathematics, science, engineering, and computing. They can be used to describe relationships, simplify calculations, and to create models that enable us to understand the behavior of complex systems.

This recursive function states that each successive term in the sequence is three less than the previous term. Therefore, the sequence will continue to decrease by three each time. For example, the sixth term would be -11 (a 5 -3) and the tenth term would be -21 (a 9 -3).

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The equation that will be used to represent the number of purple and pink flowers would be =

For the pink flowers = r = 180 - 4(0)

For the purple flowers = r = 180 - 4(45)

A garden is defined as an area that is being prepared for the purpose of cultivation of various flower, shrubs and grass.

The total number of flowers in the garden = 180

The number of pink flower beds = 4

The number of purple flower beds = 4

The number of pink flowers in each bed = 45

Therefore, the number of total pink flowers = 4 × 45 = 180

Since the pink flowers is the total of 180 which is also the quantity of flowers in the garden, the quantity of flowers in the purple bed would be = 0

Thus, 180 = 4(45) + 4(0)

For the pink flowers = r = 180 - 4(0)

For the purple flowers = r = 180 - 4(45)

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Answer:

$161.38

Step-by-step explanation:

12*0.99=11.88$

50*2.99=149.50$

11.88+149.50=161.38

The equations that could be used to find the price of one tire patch is given as follows:

The price for each tire patch is constant, meaning that a linear function is used to model the situation.

He initially had $22.20, and then for each tire purchased, his amount decays by the slope, hence the function that models the situation is given as follows:

f(t) = 22.2 - tx.

In which t is the number of tires purchased.

He purchased 4 tires, hence:

f(4) = 22.2 - 4x.

After the purchase, he had $1.90 remaining, hence:

1.9 = 22.2 - 4x.

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The solution the system of equations y = x – 15 and y = –2x + 3 is (6, -9)

An equation shows the relationship between numbers and variables in an expression.

Given the system of equations:

y = x – 15    (1) and

y = –2x + 3   (2)

From equation 1, substitute y = x - 15 into equation 2 using substitution method:

x - 15 = -2x + 3

x + 2x = 3 + 15

3x = 18

x = 6

substitute x = 6 in equation 1:

y = 6 - 15 = -9

y = -9

The solution is (6, -9)

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Answer:

D. (6, -9)

Step-by-step explanation:

Edge 2023

The expanded from of the expression y(3.05x−3.75)−2.25y as required to be determined I. the task content is; 3.05xy - 6y.

It follows from the task content that the expanded form of the given expression is to be determined.

Since the given expression is;

y ( 3.05x − 3.75 ) − 2.25y

Hence, by the distributive property; we have that;

3.05xy - 3.75y - 2.25y

= 3.05xy - 6y

Ultimately, the expanded form of the expression is; 3.05xy - 6y.

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The second inequality in the system tells us about the budget of the cost of each package of notepad.

A mathematical comparison of two integers or algebraic expressions that uses the terms greater than, larger than or equal to, less than, or less than or equal represents inequalities.

Given that the budget for the notepads is $160.

Assume the cost of package of 24 is $16 for each package and the cost of package of 6 is $5.40 for each package.

The second inequality in the system of equations represents the equation of the budget that would be spent to buy the notepads.

Hence, 16x +5.40y ≤ 160 represents the budget.

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The cylinder's volume is 2769.5 in³ with a base radius of 7 in and a height of 18 in.

One of the most fundamental curvilinear geometric shapes, a cylinder has historically been a three-dimensional solid. It is regarded as a prism with a circle as its base in basic geometry.

The formula for calculating the volume of a cylinder is:

V = πr²h

where;

r is the radius = 7in

h is the height = 18in

Substitute the given parameters to have:

V = π(7)² * 18

V = 2769.5 in³

Hence the volume of the cylinder has a base radius of 7in and a height of 18in is 2769.5 in³

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The number of votes the Candidate B receive is (c) 60

From the question, we have the following parameters that can be used in our computation:

Candidate A Candidate B

12 20

18 30

27 45

36 ?

The above parameters mean that

The rate increase proportionally

Using the above as a guide, we have the following ratio

Ratio = Candidate A : Candidate B

Using one of the values, we have

Candidate A : Candidate B = 12 : 20

substitute the known values in the above equation, so, we have the following representation

36 : Candidate B = 12 : 20

Express as fraction

Candidate B/36 = 20/12

So, we have

Candidate B = 36 * 20/12

Evaluate

Candidate B = 60

Hence, the number of votes is 60

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The way that the exponent illustrated as x ^7/3 can be written is 3✓x^7

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

Expressing large numbers in terms of powers is known as an exponent. Therefore, the exponent describes the number of times a number has been multiplied by itself.

Exponentiation is a mathematical operation that involves the base number (b) and the exponent (or power) number (n), and is written as bn. Its pronunciation is "b (raised) to the (power of) n." Exponentiation corresponds to base multiplication when n is a positive integer; therefore, bn is the result of multiplying n bases:

In this case, it should be noted that x ^7/3 will simply be the cube root of x raised to power 7. This is illustrated as x ^7/3.

Therefore, the correct option is C.

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Answer:

it's very simple D

if you throw -ve sign to g(x) sign will change

and do simple calculation

Answer:

To find the difference between the two functions, we can subtract g(x) from f(x):

f(x) - g(x) = (5x² - 2x + 7) - (2x² + 6x + 3)

= 5x² - 2x + 7 - 2x² - 6x - 3

= 3x² - 8x + 4

Therefore, the difference between the two functions is f(x) - g(x) = 3x² - 8x + 4, which is answer D.

Step-by-step explanation:

Answer:

y = -5x + 60

Step-by-step explanation:

You have two ordered pairs (3, 45) and (5,35)

y = mx + b

We need to find the slope and the y-intercept

Slope:

change in y over the change in x

(3,45) (5, 35)

The y's are 35 and 45.  You find the change by subtracting.

35 - 45 = -10

The x's are 5 and 3.  You find the change by subtracting,

5-3 = 2

[tex]\frac{-10}{2}[/tex] = -5

The slope (m) is -5

y-intercept:

Use of the on the points.  I will use (3, 45)

x = 3

y = 45

slope = -5

y = mx + b  Substitute in what you know and solve for b

45 = -5(3) + b

45 = -15 +b  Add 15 to both sides

60 = b

The y-intercept (b) is 60.

y = -5x + 60

The situations are classified as survey, observational study or experiment as follows:

3. Experiment.

4. Observational study.

5. Survey.

6. Survey.

7. Survey.

The definitions for each of these three cases are given as follows:

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The 4 basic types of lines are  Curved Lines, Straight Lines, Horizontal Lines, and  Vertical Lines.

How do lines work?

A straight group of points that stretch in opposing directions is what is known as a line.

the 4 basic types of lines are:

a) Curved Lines: A curved line is any line that is not straight. A curve results from a point that is not moving in a straight line.

b) Straight Lines: A straight line is the shortest path between any two points. We obtain a straight line if a point moves only in that direction.

c) Horizontal Lines: A horizontal line is any straight line that extends from left to right. Vertical lines are perpendicular to the y-axis and parallel to the x-axis.

d) Vertical Lines: From top to bottom or bottom to up, vertical lines are straight up and down. A vertical line is perpendicular to the x-axis and parallel to the y-axis.

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The solution set of this system of equations is a no solution or zero solution.

In Mathematics, the solution set of any system of equations simply refers to all of the set of values that correctly satisfy all the equations.

In this scenario, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;

y = x² + 2x + 2         ........equation 1.

y = x + 1                    ........equation 2.

Based on the graph (see attachment), we can reasonably infer and logically deduce that the given system of equations has no solution (zero solution) because it does not have a point of intersection for the lines on the graph representing each of the system of equations.

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Answer:

B

Step-by-step explanation:

Distance = rate x  time

The rate is 3/15

distance = (3/15) (50)

distance = 10 miles

In order to make Natasha's survey data more reliable, she could increase the sample size, conduct the survey on different day or time, or extend the days of the survey.

Conducting a survey with a sample size of only 30 workers, the survey results may not be representative of the entire population of 215 workers. Increasing the sample size would help to ensure that the survey results are more representative of the population. Moreover, she could also increase the data reliability by conducting the survey on different day or time can also gives different results since the transportation way can vary day by day. Another way Natasha could make the survey data more reliable would be to extend the survey over the course of several days rather than just one day.

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In order to make Natasha's survey data more reliable, she could increase the sample size, conduct the survey on different day or time, or extend the days of the survey.

Conducting a survey with a sample size of only 30 workers, the survey results may not be representative of the entire population of 215 workers. Increasing the sample size would help to ensure that the survey results are more representative of the population. Moreover, she could also increase the data reliability by conducting the survey on different day or time can also gives different results since the transportation way can vary day by day. Another way Natasha could make the survey data more reliable would be to extend the survey over the course of several days rather than just one day.

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So the slope of the line between these two points is 0.177, which can be rounded to 0.18

To calculate the slope of a line between two points, you need to use the following formula:

slope = (y2 - y1) / (x2 - x1)

Where (x1, y1) and (x2, y2) are the coordinates of the two points. In this case, we are using weight as the explanatory variable, so x1 = 3.5 (the weight of the rat), y1 = 4.5 (the cost of feeding the rat), x2 = 30 (the weight of the beagle), and y2 = 9.2 (the cost of feeding the beagle). Plugging these values into the formula, we get:

slope = (9.2 - 4.5) / (30 - 3.5)

slope = 4.7 / 26.5

slope = 0.177

So the slope of the line between these two points is 0.177, which can be rounded to 0.18. The slope represents the average change in the dependent variable (feed cost) per unit change in the independent variable (weight). So, in this case it means that the feed cost increase of 0.18 dollar per pound.

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Using weight as the explanatory variable, the slope of the line between two points (3,5, 4.50) and (30, 9.20) is 0.17

In this question we have been given a Rat weighs 3. 5 pounds and costs $4. 50 per week to feed, while a Beagle weighs 30 pounds and costs $9. 20 per week to feed.

Using weight as the explanatory variable, we need to find the slope of the line between these two points.

Here weight is  the explanatory variable i.e., an independent Variable

This means, we place the values of weight on the x-axis and the feed cost on the y-axis.

So, the two data points from the weight and feed cost data set would be:

(3,5, 4.50) and (30, 9.20)

Let m be the slope of line between these two points

Using the formula of slope,

m = (9.20 - 4.50) / (30 - 3)

m = 0.1741

m = 0.17

Therefore, the required slope is 0.17

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The z-score corresponding to an observation of 284 is -1.02

To calculate the z-score, you need to know the mean (μ) and standard deviation (σ) of the normal distribution. Given that X~n(335, 50), the mean is 335 and the standard deviation is 50.

        (x - μ) / σ

       (284 - 335) / 50 = -1.02

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Answer:

12

Step-by-step explanation:

The pattern of association refers to the relationship that exists between two variables such as positive, negative, or no correlation.

In mathematics, a pattern of association refers to the relationship between two or more variables. This relationship can take several forms, such as a positive correlation, a negative correlation, or no correlation.

A positive correlation exists when the variables increase or decrease together. This means that as one variable increases, the other variable also increases and vice versa.

A negative correlation exists when the variables move in opposite directions. As one variable increases, the other variable decreases and vice versa.

A no correlation exists when there is no relationship between the variables. This means that the variables do not change together and there is no pattern in the data.

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Answer:AC>BC>AB

Step-by-step explanation:We can compare the lengths of the sides with the angles given the side opposite to the largest angle is the largest and vice versa.

Angle ABC=75 greatest angle therefore the side opposite to it is the largest.

We will find the parallel line:

y = (2/3)*x - 11/3

And the perpendicular line:

y = (-3/2)*x + 5

Here we start with the linear equation, we will get:

2x - 3y = 9

We can rewrite it to get:

-3y = 9 - 2x

y = 9/-3  - 2x/-3

y = -3 + (2/3)x

Remember that two lines are parallel if the lines have the same slope, so the equation of the parallel line will be something like:

y = (2/3)*x + b

And this line must pass through (4, -1), replacing these values we will get:

-1 = (2/3)*4 + b

-1 = 8/3 + b

-1 - 8/3 = b

-3/3 - 8/3 = b

-11/3 = b

So the linear equation parallel is:

y = (2/3)*x - 11/3

Now let's find the perpendicular line. Remember that two lines are perpendicular if the product between the slopes is equal to -1, then if the slope of the perpendicular line is m, we need to solve:

m*(2/3) = -1

m = -3/2

Then the perpendicular line is something like:

y = (-3/2)*x + b

To find te value of b, we need to replace the values of the point (4, -1) there, we will get:

-1 = (-3/2)*4 + b

-1 = -6 + b

-1 + 6 = b

5 = b

So the perpendicular line is:

y = (-3/2)*x + 5

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Answer:

See below

Step-by-step explanation:

Answer:

Square

Step-by-step explanation:

each side of a square is equal and there are 4 line segments

Answer:

angle 1: 51

angle 2: 39

angle 3: 101

angle 4: 40

angle 5: 6

angle 6: 140

Step-by-step explanation:

I haven't done this in a while so hopefully this is right:) hope this helps

Answer: sin(f) are correct trigonometric ratios for triangle DEF.

Step-by-step explanation: Sin(d) = cos(e) = tan(d) = sin(e) = tan(d) = sin(f)

Solving the quadratic equation, we will see that the frisbee will hit the ground after 8.5 seconds.

We know that the height of the frisbee is modeled by the quadratic equation:

h(t) = -0.07*t^2 + 0.007*t + 5

The frisbee will hit the ground when h(t) = 0, so we just need to solve the quadratic equation:

0 = -0.07*t^2 + 0.007*t + 5

We can just use the quadratic formula to get the solutions:

[tex]t = \frac{-0.007 \pm \sqrt{0.007^2 - 4*(-0.07)*5} }{2*-0.07} \\\\t = \frac{-0.007 \pm 1.18 }{-0.14}[/tex]

We only care for the positive solution, which is:

t = (-0.007 - 1.18)/-0.14 = 8.5

So the frisbee will hit the ground after 8.5 seconds.

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