a, b real numbers and
1 is less than a is less b is less than 4
How many different integer values ​​is the sum of a + b?

Answer:

it would be 8 meters in 10 seconds,Because it travels 6 meters for 3 seconds stops for 5 seconds. So then it would be 6 meters in 8 seconds then it travels 2 meters in two seconds. Which would essentially be 8 meters in 10 seconds.

When the original claim is expressed in symbolic form, we have p < 0.045.

To symbolize the initial claim adequately, we must assign a value to parameter p.

Let us designate p as the ratio of households possessing solely landline telephones without wireless communication devices.

The original statement denotes that indisputably below 4.5% of households are equipped with exclusively traditional telephone dialers, and absent from contemporary wireless communication alternatives; this assertion can be formulated symbolically as:

p < 0.045

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The question is:

Express the original claim in symbolic form. Let the parameter represent a value with respect to homes that have only a landline telephone and no wireless phone.

Step-by-step explanation:

N(y)+N(1)=4|3y-8|-4 + 4|3-8|-4

=4|3y-8| +12

To graph the inequality, first, we notice that since

is a strict inequality, meaning it is not inclusive, then the line that will be the border or the shaded region will be dashed.

Now, to know if the shaded region lays above or below the line, we consider the point (0,0) and notice that:

Therefore, (0,0) is not a solution to the inequality and the shaded region is the one above the line.

Answer:

Hello!

The distance, d, is less than 200 miles.

B. d > 200

Answer:

Increasing

0°≤x≤180°

Decreasing

180°≤x≤360°

a)The value of acceleration will be 4.8 m/s²

b)The total distance travelled is 505 m.

a) As all the movement happens along a straight line, we need to define an axis only, which we call x-axis, being the positive direction the one followed by the car.

We can choose to place our origin at the location where the motorcycle was stopped at the side of the road (assuming that it is the same point  for the car when it passes him), so our initial position is 0.

We can also choose our time origin to be the same as the instant that the motorcycle starts from rest, so t₀ = 0.

With these assumptions, and assuming also that the acceleration is constant, we can write two equations, one for the car (at constant speed) and the another one for the motorcycle, as follows:

xc = vx*t

xm= 1/2*a*t²

When the motorcycle passes the car, both distances traveled from the origin will be equal each other, i.e., xc = xm :

⇒ vx*t = 1/2*a*t²

We have as givens vx=35 m/s and t = 14.5 sec when both equations are equal each other.

⇒ 35 m/s* 14.5 s = 1/2*a*(14.5)²(s)²

Solving for a:

a = (2* 35 m/s) / 14.5 s = 4.8 m/s²

b) Replacing the value of a in the equation for xm, we have:

xm = 1/2*4.8 m/s²* (14.5)²s² = 505 m.

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The area of the enclosed shape is about 14.47 km^2.

We are given that;

056° for 9.8km and  3.5 km on a bearing of 112°

Now,

We can see that the enclosed shape is a triangle with sides 9.8 km, 3.5 km, and z km, and angles 56°, 112°, and y°. We can use the fact that the sum of angles in a triangle is 180° to find y:

y = 180° - 56° - 112°

y = 12°

Now we can use the cosine rule to find z:

z^2 = 9.8^2 + 3.5^2 - 2(9.8)(3.5)cos(12°)

z^2 ≈ 101.87

z ≈ 10.09

Therefore, Fred is about 10.09 km away from his start point.

To find the area of the enclosed triangle, we can use the sine rule to find x, the height of the triangle:

sin(56°) = x/9.8

x = 9.8 sin(56°)

x ≈ 8.27

The area of a triangle is given by half the base times the height, so:

A = (1/2)(3.5)(8.27)

A ≈ 14.47

Therefore, by trigonometric ratios the answer will be 14.47 km^2.

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Answer:

32. A

33. B

Step-by-step explanation:

32. Mean: In order to find the mean, add all of the #up which is 194 then divide by how many # there is

33. Start by crossing out the beginning # and the end # all the way till you get the # without another pair in the end

The image of the point L(-4,0) after a dilation with a center of (0,0) and a scale factor of 7 is the point L'(-28,0).

A dilation with a center of (0,0) and a scale factor of 7 means that every point in the plane will be multiplied by a factor of 7 from the origin.

To find the image of the point L(-4,0) after a dilation with a center of (0,0) and a scale factor of 7, we can simply multiply the coordinates of L by the scale factor.

The coordinates of the image point L' will be:

L' = (-4 × 7, 0 × 7) = (-28, 0)

Therefore, the image of the point L(-4,0) after a dilation with a center of (0,0) and a scale factor of 7 is the point L'(-28,0).

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Answer:

Hi! Hope this helps!

Step-by-step explanation:

A verb is used to describe actions.

Example: I JUMPED over the rock. In this sentence the verb is JUMPED

a ver

Step-by-step explanation:

a verb is a word used to describe an action , state , occurrence and forming the main part of a predicate of a sentence

Answer:

Nora received 35 purple pins.

Step-by-step explanation:

If Nora received 50 pins, and 70% of the pins were purple, to calculate the number of purple pins Nora received, we must find 70% of 50.

To find 70% of 50, we can multiply 50 by the decimal form of 70%:

\(50 * .7=35\)

Therefore, we can conclude that since 70% of the 50 pins Nora received were purple, and 70% of 50 is 35, Nora received 35 purple pins.

Answer:

35 purple pins

Step-by-step explanation:

Given information,

→ Total pins = 50

→ Purple pins = 70%

Now the number of purple pins is,

→ 70% of 50

→ (50/100) × 70

→ 0.5 × 70

→ 35 purple pins

Hence, there are 35 purple pins.

Answer:

x=3

Step-by-step explanation:

Hey there!

In order to solve this equation, we must first distribute the 3

3x + 9 = -4x + 30

Now we combine like terms

7x = 21

Then we divide both sides by 7 to get x by itself

x = 21/7

x = 3

Answer: x=3

Step-by-step explanation:

To solve the given equation, it means to find the value of x. We want to use inverse properties to isolate x. The inverse properties are add/subtract and multiply/divide. Be sure to use the corresponding inverse operation.

3(x+3)=-4x+30                 [distribute]

3x+9=-4x+30                    [add both sides by 4x]

7x+9=30                            [subtract both sides by 9]

7x=21                                 [divide both sides by 7]

x=3

Therefore, we get x=3.

Step-by-step explanation:

Solve for X for one equation then input that value into the other equation.

x+2y=9

x=9-2y

x-y=3

(9-2y)-y=3

9-3y=3

6=3y

y=2

x=5

The value of the y-coordinate of the system of equations is y=2.

I hope it help

Answer:

D. Cant be determined

Step-by-step explanation: The triangle is flipped so you dont know what at nor b is one the other triangle

Answer:

Neal has to work 68 more minutes

Step-by-step explanation:

Hey there!

In order to find the answer to this question, we must first find the average amount of work he as done so far.

He has spent 26, 57, 33, and 41 minutes so far on homework

In total, he has worked 157 minutes in total

Now to find how much more minutes he has to do, we need to subtract the total amount of minutes he has to do all week and the amount of time he has already worked

In this case, Neal has to work at least 225 minutes in 5 days and he already did 157 minutes of work

Now we subtract:

225 - 157 = 68

This means, Neal has to work 68 more minutes to have an average of 45 minutes each day for 5 days

The area of the shaded region of the rectangle is approximately 573.92 square feet.

The figure in the image is that of a rectangle with a semi-circle inscribed in it.

The area of rectangle is expressed as:

Area = Length × Width

The area of semi-circle is expressed as:

Area = 1/2 × πr²

To determine the area of the shaded region, we simply subtract the area of the semi-circle from the area of the rectangle.

Area of shaded region = area of rectangle - area of semi-circle

Area of shaded region = ( Length × Width ) - ( 1/2 × πr² )

From the image:

Length = 40 ft

Width = 20 ft

Radius r = 12 ft

Plug the values into the above formula:

Area of shaded region = ( Length × Width ) - ( 1/2 × πr² )

Area of shaded region = ( 40 × 20 ) - ( 1/2 × 3.14 × 12² )

Area of shaded region = ( 800 ) - ( 226.08 )

Area of shaded region = 573.92 ft²

Therefore, the area is approximately 573.92 square feet.

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Given statement solution is :- Math Proficiency conceptual knowledge involves understanding the fundamental concept of division and its relationship to fractions, enabling flexibility in solving division problems with different fractions. Procedural knowledge, on the other hand, focuses on following a specific set of steps to achieve a correct solution without necessarily comprehending the underlying concept.

3.1 Activity: Procedural and Conceptual Understanding in Action

Content Area: Fractions

Problem: Comparing Fractions

Objective: Students will demonstrate both procedural and conceptual understanding of comparing fractions.

Activity Steps:

Begin by introducing the concept of fractions and reviewing the basic procedures for comparing fractions (e.g., finding a common denominator, cross-multiplying).

Provide students with a set of fraction comparison problems (e.g., 2/3 vs. 3/4, 5/8 vs. 7/12) and ask them to solve the problems using the traditional procedural approach.

After students have solved the problems procedurally, engage them in a group discussion to explore the underlying concepts and relationships between fractions. Ask questions such as:

What does it mean for one fraction to be greater than or less than another?

Can you explain why we need a common denominator when comparing fractions?

How can you visually represent and compare fractions to better understand their relative sizes?

Introduce visual aids, such as fraction bars or manipulatives, to help students visualize the fractions and compare them conceptually. Encourage students to reason and explain their thinking.

Have students revisit the fraction comparison problems and solve them again, this time using the conceptual understanding gained from the group discussion and visual aids.

Compare the students' procedural solutions with their conceptual solutions, and discuss the similarities and differences.

Conclude the activity by emphasizing the importance of both procedural and conceptual understanding in solving fraction comparison problems effectively.

By incorporating both procedural and conceptual approaches, this activity allows students to develop a deeper understanding of comparing fractions. The procedural approach provides them with the necessary steps to solve problems efficiently, while the conceptual approach helps them grasp the underlying principles and relationships involved in fraction comparison.

3.2 Example: Conceptual Knowledge vs. Procedural Knowledge

Conceptual knowledge refers to the understanding of underlying concepts, principles, and relationships within a domain, whereas procedural knowledge focuses on knowing the specific steps or procedures to perform a task without necessarily understanding the underlying concepts.

Example: Division of Fractions

Conceptual Knowledge: Understanding the concept of division as the inverse operation of multiplication, and recognizing that dividing fractions is equivalent to multiplying by the reciprocal of the divisor. This understanding allows for generalization and application of division concepts to various fractions.

Procedural Knowledge: Following the specific steps to divide fractions, such as "invert the divisor and multiply" or "keep-change-flip" method. This knowledge involves applying the procedure without necessarily grasping the underlying concept or reasoning behind it.

In this example, Math Proficiency conceptual knowledge involves understanding the fundamental concept of division and its relationship to fractions, enabling flexibility in solving division problems with different fractions. Procedural knowledge, on the other hand, focuses on following a specific set of steps to achieve a correct solution without necessarily comprehending the underlying concept.

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Answer:

(b) more than twice as much y as x

Step-by-step explanation:

At all incomes for which Harold consumes positive amounts of both goods, he will consume more than twice as much y as x.

To see this, we can consider the budget constraint that determines the amount of x and y that Harold can afford to consume. Let I be Harold's income and px and py be the prices of x and y, respectively. Then the budget constraint can be expressed as:

I = px * x + py * y

Substituting the given values for I, px, and py, we get:

I = 1 * x + 2 * y

This equation represents a line in the xy-plane, with slope -2 and y-intercept I/2. This line represents the set of all combinations of x and y that Harold can afford to consume, given his income and the prices of x and y.

Since the utility function U(x,y) = (x+3)(y+2) is a positive linear transformation of x and y, it follows that the slope of the budget constraint will be equal to the slope of the indifference curve at any point on the budget constraint. Therefore, the slope of the budget constraint (-2) represents the relative amounts of x and y that Harold will consume.

Since the slope of the budget constraint is negative, Harold will consume more y than x. Moreover, since the absolute value of the slope is greater than 1, Harold will consume more than twice as much y as x.

Therefore, the correct answer is (b) more than twice as much y as x.

I hope this helps! Let me know if you have any other questions or need further assistance.

Answer: 10,000

Step-by-step explanation: here's how I got my answer:

Since we are finding the decrease from 2005-2015, we need to multiply 1/20 by 10, since the timespan is 10 years worth of decreasing.

So, 1/2 * 10 =1/2

So, since we have 1/2 as the overall decrease in the population within the 10 years, we divide 20,000 by 1/2 or 20,000 by 2, and we get 10,000. I hope this helps.

Answer:

9 ft

Step-by-step explanation:

Answer:  $130 money did Brenda and Hazel have all together before buying decorations and snacks.

Here, we have,

You want to know Brenda and Hazel's combined money when the ratio of their remaining balances is 1 : 4 after Brenda spent $58 and Hazel spent $37. They had the same amount to start with.

Setup

Let x represent the total amount the two women started with. Then x/2 is the amount each began with, and their fnal balance ratio is ...

 (x/2 -58) : (x/2 -37) = 1 : 4

Solution

Cross-multiplying gives ...

 4(x/2 -58) = (x/2 -37)

 2x -232 = x/2 -37 . . . . . . eliminate parentheses

 3/2x = 195 . . . . . . . . . . . . add 232-x/2

 x = (2/3)(195) = 130 . . . . . multiply by 2/3

Brenda and Hazel had $130 altogether before their purchases.

Alternate solution

The difference in their spending is $58 -37 = $21.

This is the same as the difference in their final balances.

That difference is 4-1 = 3 "ratio units", so each of those ratio units is $21/3 = $7.

Their ending total is 1+4 = 5 ratio units, or $35.

The total they started with is $58 +37 +35 = $130.

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complete question:

Brenda and Hazel decide to throw a surprise party for their friend, Aerica. Brenda and Hazel each go to the store with the same amount of money. Brenda spends $58 on decorations, and Hazel spends $37 on snacks. When they leave the store, the ratio of Brenda’s money to Hazel’s money is 1 : 4. How much money did Brenda and Hazel have all together before buying decorations and snacks?

Given the function:

f(x) = 3x - 2

Let's find the inverse of the function f⁻¹(x).

To find the inverse of the function, apply the following steps:

• Step 1.

Rewrite y for f(x)

• Step 2.

Interchange the x and y variables:

• Step 3.

Solve for y.

Add 2 to both sides:

• Step 4.

Divide all terms by 3:

Answer:

Step-by-step explanation:

The growth rate of the investment is represented by the constant multiplier in the exponential term of the formula y = 20000(1.035)x. In this case, the constant multiplier is 1.035, which represents the annual growth rate of the investment account.

To calculate the growth rate as a percentage, we can subtract 1 from the constant multiplier, and then multiply the result by 100.

So, the growth rate of the investment is:

1.035 - 1 = 0.035

0.035 * 100 = 3.5%

Therefore, the growth rate of the investment is 3.5%.