Nat wants to buy a new bike for $240. She has already saved $67. Over the summer, she will earn $100 per month walking dogs. How many months will it take her to earn the rest of the money she needs to buy the bike?

Answer:

\(\huge\boxed{\sf |AB| = 4.0 \ units}\)

Step-by-step explanation:

Given that,

Point A = (x₁, y₁) = (1.5, 4.5)

Point B = (x₂, y₂) = (3.5, 1)

So,

x₁ = 1.5

y₁ = 4.5

x₂ = 3.5

y₂ = 1

Using distance formula to find the distance.

\(Distance = \sqrt{(x_2-x_2)^2+(y_2-y_1)^2} \\\\|AB| = \sqrt{(3.5-1.5)^2+(1-4.5)^2} \\\\|AB|=\sqrt{(2)^2+(-3.5)^2} \\\\|AB|=\sqrt{4+12.25} \\\\|AB|=\sqrt{16.25} \\\\|AB| = 4.0 \ units\\\\\rule[225]{225}{2}\)

Answer:

  Exponential

Step-by-step explanation:

If the depreciation is 6% of the current value each year, the function is exponential. (We believe this is the intent of the problem statement.)

__

If the depreciation is 6% of the original value each year, the function is linear.

_____

Comment on percent

Whenever you're working with percentages, you need to be clear about what it is a percentage of.

The horizontal distance of a raindrop that falls from the end of the roof to the center of the base of the house, obtained from the linear equation for the height of the roof is; x = 18 feet

A linear equation is an equation that has one as the highest index, and which when graphed, forms a straight line.

The linear function for the height of the roof is, h(x) = -|x| + 34

Where;

h(x) = The height of the roof

x = The horizontal distance from the center of the roof

The minimum height of the roof, obtained from the diagram = 16 feet

Therefore, we get, when h(x) 16, substituting the value h(x) = 16, in the function for the height of the roof, we get;

h(x) = -|x| + 34

h(x) = 16

Therefore, 16 = -|x| + 34 (substitution property)

|x| = 34 - 16 = 18

The distance from the center of the house, which corresponds to the least height of the roof, which is the end of the roof and the location at which the raindrop falls is; x = 18 feet

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Answer:

14x+11

Step-by-step explanation:

4(2x-1)+3(2x+5)

8x-4+6x+15

14x+11

The ordered pair are (-5/3, 0) and (0, 5)

Given the equation y = 3x + 5

To get the ordered pair of the equation, we will find the x and y-intercept

The x-intercept of the equation occur at y = 0

0 = 3x + 5

-3x = 5

x = -5/3

Hence the ordered pair of the solution is (-5/3, 0)

The y-intercept of the equation occur at x = 0

y = 3(0) + 5

y = 0 + 5

y = 5

Hence the ordered pair of the solution is (0, 5)

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The amount that Benjamin must save every month to pay off the discounted premium is $ 40. 80

The total premium for the year would be $ 637. 20

The amount that Benjamin's discounted premium would come to for the year is:

= 1, 080 x ( 1 - 66 %)

= $ 367. 20

The amount he would need to save every month on deployment is :

= 367. 20 / 9

= $ 40. 80

His total premium would be :

= 367. 20 + ( 1, 080 / 12 x 3 months when he comes back )

= $ 637. 20

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The ATI Capstone Comprehensive Assessment evaluation normally comprises of multiple-choice questions, with 90 to 130 possible answers. Certain versions may also include extra alternative questions kinds, such as fill-in-the-blank or select-all-that-apply

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The tires and the traction control system work in tandem to ensure maximum traction and stability, minimizing the risk of traction loss and improving overall vehicle control and safety.

The two most important parts of a vehicle in preventing traction loss are the tires and the traction control system.

Tires: Tires are the primary point of contact between the vehicle and the road surface. The quality and condition of the tires greatly influence traction. Tires with good tread depth and appropriate tread pattern are essential for maintaining grip on the road. Tread depth helps to channel water, snow, or debris away from the tire, preventing hydroplaning or loss of traction. Additionally, tire pressure should be properly maintained to ensure even contact with the road. Choosing tires suitable for the specific driving conditions, such as all-season, winter, or performance tires, is crucial for optimal traction and handling.

Traction Control System: The traction control system is a vehicle safety feature that helps prevent the wheels from slipping or spinning on low-traction surfaces. It uses various sensors to monitor the speed and rotation of the wheels. If the system detects a loss of traction, it will automatically reduce engine power and apply braking force to the wheels that are slipping. By modulating power delivery and braking, the traction control system helps maintain traction and prevent wheel spin, especially in challenging conditions like slippery roads or during quick acceleration.

The tires and the traction control system work in tandem to ensure maximum traction and stability, minimizing the risk of traction loss and improving overall vehicle control and safety.

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Answer:

1/81

Step-by-step explanation:

You just tap the calculator

Answer:

8

Step-by-step explanation:

x=25-17

x=8

don't forget to collect like terms

The given sequence defined by a1 = 1 and an+1 = 5 - 1/an is increasing, meaning each term is greater than the previous term. Additionally, all terms in the sequence are less than 5.

To prove that the sequence is increasing, we need to show that each term is greater than the previous term. We can do this by induction.

For the base case, a1 = 1.

Now, assuming an > an-1, let's consider an+1:

an+1 = 5 - 1/an

Since an > an-1, 1/an > 1/(an-1), and 5 - 1/an < 5 - 1/(an-1).

From the induction assumption, 5 - 1/(an-1) < 5 - 1/an-1.

Therefore, 5 - 1/an < 5 - 1/(an-1), which means an+1 > an. Hence, the sequence is increasing.

To prove that an < 5 for all n, we can also use induction.

For the base case, a1 = 1 < 5.

Assuming an < 5, let's consider an+1:

an+1 = 5 - 1/an

Since an < 5, 1/an > 1/5.

Therefore, 5 - 1/an < 5 - 1/5 = 4.8.

Hence, an+1 = 5 - 1/an < 4.8, which means an+1 < 5. Thus, an < 5 for all n.

Therefore, we have shown that the sequence defined by a1 = 1 and an+1 = 5 - 1/an is increasing, and all terms in the sequence are less than 5.

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Given:

Required:

We need to find the rate of change of the given equation.

Explanation:

Consider the given equation.

Differentiate with respect to x.

We know that dy/dx is the rate of the given function.

Differentiate dy/dx with respect to x.

The function is increasing, and the rate is decreasing.

Final answer:

Increasing at a decreasing rate.

The value of p-hat (the sample proportion) is 0.24, or 24% if total number of skittles in a sample is 300 out of which 72 skittles are purple.

The sample proportion, denoted by p-hat, is the proportion of purple skittles in the sample. We can calculate p-hat by dividing the number of purple skittles by the total number of skittles in the sample

p-hat = number of purple skittles / total number of skittles in sample

In this case, we have

Number of purple skittles = 72

Total number of skittles in sample = 300

Therefore,

p-hat = 72/300 = 0.24

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Therefore, the factored form of the right side of the formula is 2πr(r + h).

A cylinder is a three-dimensional geometric shape that consists of a circular base and a curved surface that connects the base's circumference to a parallel circle at the other end of the shape. It is a type of prism with circular bases. The two circular bases of the cylinder are parallel and congruent, meaning that they have the same size and shape. The curved surface of the cylinder is composed of all the points that are equidistant from both bases. The cylinder is a common shape in real-life objects, such as cans, pipes, and drinking glasses. Its volume and surface area formulas are frequently used in geometry and applied mathematics.

Here,

Starting with the given formula:

A = 2πr² + 2πrh

We can factor out a common factor of 2πr:

A = 2πr(r + h)

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Answer:

Let a be the first term and d be the common difference.

3rd term = 1407

a+2d = 1407  ------- 1

10th term = 1183

a+9d = 1183  ------- 2

By solving 1 and 2, a = 1471 and d = -32

so the general term T(n) = 1471 + (n-1)(-32)

                                          = 1471 - 32n +32

                                          = -32n + 1503

-32n + 1503 \(\geq\) 0

            -32n \(\geq\) -1503

                  n \(\leq\) 46.96875

The number of positive terms = 46

Removing values from a binary search tree requires finding the node to be removed, finding its successor if it has two children, and then removing the node. These operations maintain the values in the tree and ensure that it remains a valid binary search tree.

What will be the following tree (M 3, L = 3)?

A) To insert 4 into the tree, we first compare it to the root node 50. Since 4 is less than 50, we move to the left subtree and compare it to the node 10. Since 4 is less than 10, we continue down the left subtree and reach a null position where we can insert the new node with a value of 4.

The updated tree would be:

     50
    /  \
  10   53
 / \     \
4  11    98
        /  \
      39   100

B) To remove values 10 and 11 from the tree, we first search for them starting at the root node 50. We compare them to each node we encounter and move to the left or right subtree depending on their values.

We first find the value 10 at the left child of the root. We then check its children and see that it has two children, so we cannot simply remove it. We need to find its successor, which is the minimum value in its right subtree.

The minimum value in the right subtree of 10 is 11, so we replace the value of 10 with 11 and remove the node with value 11.

The updated tree would be:

     50
    /  \
  11   53
   \     \
    4    98
        /  \
      39   100

We then repeat this process for the value 11 and remove it from the tree.

The final updated tree would be:

     50
      \
      53
       \
        4
        \
        98
       /  \
     39   100

In summary, removing values from a binary search tree requires finding the node to be removed, finding its successor if it has two children, and then removing the node. These operations maintain the values in the tree and ensure that it remains a valid binary search tree.

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Step-by-step explanation:

gave you in Photo..... please do mark as brainlist

Answer:

They’re both 0.28??

Step-by-step explanation:

0.28 = 0.28

The probability that the battery lasts between 12,000 and 14,000 miles is approximately 0.084.

The number of miles that a car can run before its battery wears out follows an exponential distribution with an average value of 11,000 miles. The probability that the battery lasts between 12,000 and 14,000 miles can be calculated as follows:

P(12,000 < x < 14,000) = P(x < 14,000) - P(x < 12,000)

To calculate the probabilities on the right-hand side of the equation, we can use the formula for the cumulative distribution function (CDF) of an exponential distribution:

F(x) = 1 - e^(-x/λ)

where λ is the mean value of the distribution. In this case, λ = 11,000 miles.

Plugging in the values and solving, we get:

P(12,000 < x < 14,000) = F(14,000) - F(12,000)

= (1 - e^(-14,000/11,000)) - (1 - e^(-12,000/11,000))

= e^(-12,000/11,000) - e^(-14,000/11,000)

≈ 0.242 - 0.158

≈ 0.084

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The units on both sides of equation x = vt + 1/2at^2 are units of distance or length.

On the left side of the equation, x represents the position or distance traveled by an object. On the right side of the equation, vt represents the distance traveled by the object due to its initial velocity (v) in a specific time interval (t). The second term, 1/2at^2, represents the additional distance traveled due to acceleration (a) of the object in that same time interval.

The units of v, a, and t will affect the units of the entire equation. For example, if v is measured in meters per second, a in meters per second squared, and t in seconds, then x will be measured in meters. It is important to ensure consistent units throughout any calculation to obtain accurate results.

Therefore, The units on both sides of equation x = vt + 1/2at^2 are units of distance or length.

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Answer:

m=70°

Step-by-step explanation:

m=180-110

reason - angle on a straight line equals 180

m=70°

there you go

Answer:

It is 4x + 4y.

Step-by-step explanation:

All you have to do is add all of the y's toghther and then add all of the x's toghther.

Answer:

4x+4y

Step-by-step explanation:

Combine the four "x" so x+x+x+x likewise the four "y" y+y+y+y.

The solution of the given equation are (1/2 , 17/2) and (-3 , 12)

The two equation that we have been given are :

    y = 9 – x            (1)

    y = 2x² + 4x + 6       (2)

We will solve this simultaneously, from equation (1) we will equate the value of y in equation (2) we get

       9 – x = 2x² + 4x + 6

        3 = 2x² + 5x

2x² + 5x – 3 = 0

Now to find the factors of the value x we will use quadratic formula.

   x = (-b±√b² – 4ac)/2a

   x = [ -5 ± √25 + 24 ]/4

   x = [ -5 ± 7 ]/4

x = (-5 + 7)/4              and                 x = (-5 – 7)/4

x = 1/2     and    x= -3

putting the required value of x in equation (1) we get

y = 9 – 1/2            and             y = 9 – (-3)

y = 17/2      and    y = 12

Hence the solution of the equation is (1/2 , 17/2) and (-3 , 12)

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Answer:

x=-6

k=51

Step-by-step explanation:

for the first one: we know that the angles of a triangle = 180

so, 30+90+66+x=180

x=-6

for the second one, the exterior angle is equal to the two opposite interior angles

so, 163=112+k

k=51

Here's an example of a for-loop in Python to create arrays \(x_2\) and \(y_2\)  with n unequally spaced points using the given formula.

import numpy as np

n = 200  # Number of points

\(x_2\) = np.zeros(n)

\(y_2\)  = np.zeros(n)

for k in range(1, n + 1):

   \(x_2\) [k - 1] = -np.cos(np.pi * (k - 1) / n) * 2 * np.pi

   \(y_2\) [k - 1] = 2.5 * \(x_2\) [k - 1]**2 + 0.1

# Printing the resulting arrays

print("\(x_2\) :", \(x_2\) )

print("\(y_2\) :", \(y_2\) )

In this code, we initialize empty arrays \(x_2\)  and \(y_2\)  with zeros. Then, the for-loop iterates over the values of k from 1 to n, and the formula \(x_2\)  = -cos(pi*(k-1)/n)*2*pi is applied to calculate each value of \(x_2\) . The corresponding value of \(y_2\)  is calculated using the given function 2.5\(x^{2}\) + 0.1. Finally, the resulting arrays \(x_2\)  and \(y_2\) are printed.

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Answer:

They have 70 piece of candy together

Step-by-step explanation:

Since Joe has 55 and Niya have 15, this means that you have to do addition to find the total.

55+15=70

AB is not perpendicular to CD

Perpendicular lines are two separate lines that cross one other at a right angle, or a 90° angle. Example: Because AB and XY overlap at a 90° angle, AB is perpendicular to XY in this instance.

Lines that cross one other at an angle are known as perpendicular lines. Their slopes are the reciprocal opposites of one another.

Given A (-2, 4, 0),B(1, 1, 1),C(2, 3, 4),D (3, 21, -8)

(-1,3,-1) for AB

(-1,-18,12) for CD

For the lines AB and CD to be perpendicular

a 1a2+b1b2+c1c2=0

-1(-1)+3(-18)+(-1)(12)

=1-54−12=-65not equal to 0

∴ AB not perpendicular to CD

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Complete question:

Kono divides The numerator and the denominator of 48 over 72 by the greatest common factor to simplify the fraction in one step by what number does he divide

Answer:

2/3

Step-by-step explanation:

Given the number : 48 / 72

Obtain the greatest common factor of 48 and 72

- - - - 48 - - - - 72

- 2-- 24 - - - - 36

- 2 - 12 - - - - - 18

- 2 - 6 - - - - - - 9

- 3 - 2 - - - - - - 3

The greatest common factor of 48 and 72 is hence (2 * 2 * 2 * 3) = 24

Hence, divide both the numerator and denominator by 24 ;

Numerator = 48/24 = 2

Denominator = 72 / 24 = 3

= 2/3

Answer:

234.8

Step-by-step explanation:

Multiply the amount of protein in one meal by the number of meals

58.7 * 4

234.8

Step-by-step explanation:

\({ \longmapsto{ \sf{58.7 \times 4 = 234.8}}}\)

The Dog Pet Gets 234.8 Grams Of Protien In 4eals