Linear or exponential interest

The solution is, Option 4 is correct., the graph represents the following system of inequalities.

Explanation:

We are given two inequality y<-x-4 and y>2x-3.

We need to choose correct graph from given choices.

First we draw the graph of each equation

Equation 1: y<-x-4

We draw the graph using slope intercept form.

Slope=-1 and y-intercept (0,-4)

Test point (0,0). Put (0,0) into equation 1 y<-x-4

We get . This is false statement. Graph will shade away from point (0,0).

Equation 2: y<2x-3

We draw the graph using slope intercept form.

Slope=2 and y-intercept (0,-3)

Take test point (0,0). Put (0,0) into equation 2, y>2x-3

We get . This is true statement. Graph will shade towards the point (0,0).

Please take a look attachment for the graph.

Option 4 is correct.

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complete question:

Which graph represents the following system of inequalities?

y < -x - 4

y > 2x - 3

Rounding to the nearest hundredth, the diameter of the sphere is approximately 4.26 cm.

A sphere is simply a three-dimensional geometric object that is perfectly symmetrical in all directions.

The surface area of a sphere is expressed as:

S =  4πr²

Where S is the surface area and r is the radius of the sphere.

Given that surface area of 18.2π cm²

We can solve for the radius as follows:

S =  4πr²

r = √( S / 4π )

r = √( 18.2π / 4π )

r = 2.13 cm

The diameter of the sphere is twice the radius, so:

d = 2r

d = 2( 2.13cm )

d = 4.26 cm

Therefore, the diameter of the sphere is 4.26 cm.

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The category that had the highest relative frequency is given as follows:

Have chores.

To obtain the relative frequencies for each item, we must add the rows/columns that represent the items in this problem.

Hence the relative frequencies for each item are given as follows:

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Answer:

1/2

Step-by-step explanation:

1/12 +5/12=1/2

hope this helps

The Vector form is v = 11i + 0j.

We have,

P₁ =(-6,5), P2 = (5,5)

If we have the point p1 and p2 then the vector form p1 -> p2 is

v = p2 - p1

v = [ p(2x) - p(1x)) i + [ p (2y) - p(1y)] j

v = (5 - (-6)) i + (5 - 5)j

v = 11i + 0j

v = 11 i

Thus, the vector form is v = 11i + 0j.

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Answer:

tanx

Step-by-step explanation:

Answer:

577

Step-by-Step Explanation:

577 is right between 327 and 827.

327+827=1,154

1,154/2=577

A line on the graph which could represent this scenario is shown in the image attached below.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

Based on the information provided about this line, it can be modeled by this equation:

y = mx + c

y = 2x/3 + (-6)

y = 2x/3 - 6

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Katrina will need 24 bricks to build the wall around her backyard.

We have,

To determine the number of bricks needed for the wall, we need to divide the total length of the wall (432 inches) by the length of each brick (18 inches):

So,

Number of bricks = Total length of the wall / Length of each brick

Number of bricks = 432 inches / 18 inches

Number of bricks = 24 bricks

Therefore,

Katrina will need 24 bricks to build the wall around her backyard.

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The complete question:

Katrina is building a wall around her backyard using bricks that are 18 inches long. The wall needs to be 36 feet, or 432 inches, long.

Find the number of bricks needed to build around he backyard.

The percentage of Dinesh’s time spent on Project X is 36.90%.

We have,

From the table,

The total time spent on the X-project each week is given as:

= 23(1/3) + 16(1/3) + 9.33 + 4.20

= 23.33 + 16.33 + 9.33 + 4.20

= 53.19

This is the time spent on X-project for the month.

Now,

The total time spent on all the events in the table.

= 144.13

The percent of Dinesh’s time spent on Project X.

= 53.19/144.13 x 100

= 36.90%

Thus,

The percentage of Dinesh’s time spent on Project X is 36.90%.

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The area of the given rectangle is 34 squared units.

Determining the area of a rectangle with the coordinates

can be achieved through using the distance formula to calculate the magnitude of its sides and then applying the formula for the area pf rectangle we find the area.

Length of Side AB:

= square root of [(3 - (-5))^2 + (5 - 3)^2]

= square root of 68

Length of Side BC:

= square root of [ (4-3)^2 + (1 - 5)^2]

= square root of 17

Area of this rectangle  

= side AB × Side BC

= square root[68] x square root[17]

= square root of [68 times 17]

= square root of 1156

= 34 Square Units

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The binomial whose greatest common factor is 7a³ is 14a⁴ + 35a³.

Given, the a³ is not common in A and C.

Now, in 14a⁴ + 35a³

14a⁴ = 2 x 7 x a³ x a

35a³ = 7 x 5 x a³

So, the common factors of 14 and 35 is 7.

Then, 14a⁴ + 35a³

= ( 2 x 7 x a³ x a) + (  5 x 7 x a³)

= 7a³ (2a + 5)

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Answer:

Step-by-step explanation:

To distribute the expression 18+(d+3)(d-3)(4), you can use the distributive property of multiplication, which states that a(b+c) = ab + ac.

Here's how you can apply the distributive property to the expression:

First, simplify the expression inside the parentheses by using the difference of squares formula: (d+3)(d-3) = d^2 - 3d + 3d -9

(d+3)(d-3) = d^2 - 9

So now the expression becomes:

18 + (d^2 - 9)(4)

Next, use the distributive property to multiply 4 by each term inside the parentheses:

18 + 4d^2 - 36

Simplify by combining like terms:

4d^2 - 18

So the final result is 4d^2 - 18

Using the given data, a logarithmic regression equation of the form Bacteria = 447.91 * ln(12) - 1733.1 was found to model the relationship between time and bacteria population. So, the population of bacteria is about 44.1 at 12 hours.

Based on the provided data, we can use a logarithmic regression to model the relationship between time and bacteria population. Here's how to do it using Microsoft Excel

Enter the data into two columns one for time and one for bacteria population. Create a scatter plot of the data. Right-click on one of the data points in the plot and select "Add Trendline."

In the Trendline options, choose "Logarithmic" as the type of trendline. Check the box for "Display Equation on Chart" to show the equation for the trendline.

The resulting equation is

Bacteria = 447.91 * ln(Time) - 1733.1

This equation represents a logarithmic regression of the bacteria population over time.

To use this equation to predict the bacteria population at a specific time, substitute the time value into the equation and solve for the bacteria population. For example, if we want to predict the bacteria population at 12 hours, we can substitute 12 into the equation

Bacteria = 447.91 * ln(12) - 1733.1

Bacteria ≈ 44.1

So we would predict a bacteria population of about 44.1 at 12 hours.

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Answer:

Step-by-step explanation:

Answer:

The equation is y=-3

Step-by-step explanation:

The line is horizontal, cutting across the y-axis, which means it will be a y= line. The point it hits the y-axis is -3, so it is y=-3.

Answer: 9

Step-by-step explanation:-1 plus 9 equals 8

Answer: y = 9

Step-by-step explanation:

First of all, you right out your equation

x + y = 8

Secondly, you sub in the values you have

-1 + y = 8

Then you can swap your answer and y

-1 + 8 = y

Work out the answer

-1 + 8 = 9

Answer is y = 9

Answer:60, 6.75

Step-by-step explanation:

To solve the first prompt, we must create an equality statement.

[tex]\frac{10}{45}=\frac{x}{270}[/tex] X being the distance he can go in 4.5 hours.

In order to have came up with 270, we needed to take 4.5 hours and turn it into a measure of minutes to correspond to the minute value of 45.

This is found by multiplying 4.5 by 60.

Now that we have this done, we can cross multiply the equality statement.

[tex]10\cdot270=45x[/tex]

Simplify the first side

[tex]2700=45x[/tex]

Divide both sides by 45

[tex]\frac{2700}{45}=\frac{45x}{45}[/tex]

[tex]60=x[/tex]

This means that Jacob can bike 60 miles in 4.5 hours.

For the second prompt, we need to find how long it would take for him to bike 90 miles given the amount of time it took for him to bike 10 miles.

We can use an equality statement like this:

[tex]\frac{45}{10}=\frac{x}{90}[/tex]

Now we cross multiply:

[tex]45\cdot90=10\cdot x[/tex]

Simplify:

[tex]4050=10x[/tex]

Now we can divide both sides by 10.

[tex]\frac{4050}{10}=\frac{10x}{10}[/tex]

[tex]405=x[/tex]

This means that it would take Jacob 405 MINUTES to bike 90 miles.

To turn this into a measure of hours, we need to divide 405 by 60, which comes out to 6.75.

It would take Jacob 6.75 hours to bike 90 miles.

The total number of cups of grapes and raisins include the following: 5/6 cups of grapes and raisins.

In Mathematics and Geometry, a fraction is a numerical quantity (number or numeral) that is typically expressed as a quotient (ratio) or not expressed as a whole number. This ultimately implies that, a fraction simply refers to a part of a whole number.

Based on the information provided above, the total number of cups of grapes and raisins can be calculated as follows;

Fraction = 1/2 + 2/3

Fraction = (3 + 2)/6

Fraction = 5/6 cups of grapes and raisins.

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I am not able to create visual content such as an ERD diagram, but I can guide you through the process of creating an ERD for Happy Motor's purchasing department based on the functional description provided.

First, let's identify the entities in the description:

Department (with attributes: department code, name, email)

Vehicle Type (which is produced by each department)

Component (with attributes: component code, name, price)

Vendor (with attributes: vendor code, name, email)

Order (with attributes: order number, date, total amount)

Next, let's identify the relationships between the entities:

Each department produces one or more types of vehicles

Each vehicle type requires at least one or more different specific components

Each department makes orders to buy components from vendors

Each vendor provides one or more types of components

Each order contains several different components, but all components should be from the same vendor

Each component is provided by a specified vendor

An inventory is maintained to keep track of the quantity on hand (QOH) for each component

Based on these relationships, we can create an ERD with the following entities and relationships:

Department (department code, name, email) with a one-to-many relationship with Vehicle Type

Vehicle Type (vehicle type code, name) with a many-to-many relationship with Component

Component (component code, name, price) with a many-to-one relationship with Vendor

Vendor (vendor code, name, email) with a one-to-many relationship with Component and Order

Order (order number, date, total amount) with a many-to-many relationship with Component

To show the inventory relationship, we can add an attribute to the Component entity for QOH.

Note that this is just a general outline of the ERD, and there may be additional details that need to be considered based on the specific requirements of Happy Motor's purchasing department.

To represent the inventory maintained for each component, the Component entity would have an attribute for quantity on hand (QOH).The ERD for Happy Motor® purchasing department would have the following entities and relationships:

Entities:
1. Department - with attributes: department code (PK), name, email
2. Vehicle Type - with attributes: type code (PK), name
3. Component - with attributes: component code (PK), name, price
4. Vendor - with attributes: vendor code (PK), name, email
5. Order - with attributes: order number (PK), date, total amount
Relationships:
1. Department orders Component - one-to-many (1:N) relationship between Department and Component
2. Component belongs to Vehicle Type - many-to-one (N:1) relationship between Component and Vehicle Type
3. Component is provided by Vendor - many-to-one (N:1) relationship between Component and Vendor
4. Order contains Component - many-to-many (M:N) relationship between Order and Component
5. Order is placed by Department - many-to-one (N:1) relationship between Order and Department
6. Order is placed with Vendor - many-to-one (N:1) relationship between Order and Vendor
Additionally, to represent the inventory maintained for each component, the Component entity would have an attribute for quantity on hand (QOH).

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The choices that are equivalent to the expression 4√3 will be ✓48 and ✓24.✓2.

It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.

In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.

4✓3 will be:

= ✓4² × ✓3

= ✓48

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No, It is not possible for 75% of the people surveyed at the park to purchase any two combination of the treats unless 14 people from the 'No preference group" decide to pick a treat. The two best frozen treat to pick will be Ice-cream sandwich and frozen fruit bar. With these two, 174 people are guaranteed to purchase the product.

To find the 75% chance of people surveyed buying any two combination we say

58 + 95 + 79 + 17 = 250

75% of 250 = 187.5 which is 188

We need to see if 188 of people will pick up a treat based on the survey

58 + 95 = 153 < 188

95 + 79 = 174 < 188  however, if  14 people from no preference group purchase, then, this is the best combination.

58 + 79 =  137 < 188

The answer provided is based on the question below as seen in the picture;

Is it possible to select a combination of two frozen treats so that 75% of the people surveyed would be able to purchase their favorite? If so, which two types of frozen treats should you select? Use words and numbers to justify your answer

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Answer: The jar that would experience the greatest pressure is Jar D.

This is because the pressure of a gas is directly proportional to its temperature (according to the ideal gas law). Since all four jars have the same number of gas molecules, the jar with the highest temperature (Jar D) would have the greatest pressure.

Step-by-step explanation:

Answer:

The normalization property of the distribution law states that the sum of probabilities of all possible outcomes must equal 1. In this case, we have:

P(X=k) = c/2^k, for k = 0, 1, 2, ...

To find the value of the constant c, we need to use the normalization property:

∑ P(X=k) = ∑ c/2^k = c/2^0 + c/2^1 + c/2^2 + ... = 1

To simplify this expression, we can use the formula for the sum of an infinite geometric series:

∑ a*r^n = a/(1-r), where a is the first term, r is the common ratio, and n goes from 0 to infinity.

In this case, a = c, r = 1/2, and n goes from 0 to infinity. So we have:

∑ P(X=k) = ∑ c/2^k = c/2^0 + c/2^1 + c/2^2 + ... = c/(1-1/2) = 2c

Setting this expression equal to 1, we get:

2c = 1

c = 1/2

Therefore, the value of the constant c is 1/2.

Step-by-step explanation:

The plot of the given point must be at.

the third circle and at the 9th ray clockwise from the positive x-axis.

Here we want to plot the point (3, -135°).

Remember that a point whose polar coordiantes are (R, θ) must be ploted along the circumference of a circle of radius R, at the angle θ measured counterclockwise from the positive x-axis.

Then here we need to have a circle of radius of 3 units, and plot the point at -135° from the positive x-axis.

Now, each of the rays has 15° on it, then the point should be graphed on the third circle (radius of 3 units) and at the 9th ray clockwise from the positive x-axis (clockwise because the angle is negative, and 9th ray because 9*15 = 135)

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The required statements that are true for the given function are mentioned below.

There are many possible statements that could be true for the function h, given the information provided. Here are a few examples:

is a linear function that passes through the points (-2, 2) and (8, 19).

h is a quadratic function that has a maximum value of 25 at x = 11.

h is a piecewise function that equals 1 for -3 ≤ x ≤ 0, 2x + 3 for 0 < x ≤ 4, and 19 - x for 4 < x ≤ 11.

h is a logarithmic function that equals 1 at x = -3 and approaches 25 as x approaches 11.

Each of these statements is consistent with the given domain, range, and function values at x = -2 and x = 8. There are many other possible statements that could be true for h as well.

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