Solve the following problem.
1. If a is indirectly proportional to b, then a=k/b, where k is a constant or fixed number. If a=8 when b=6, find the value of k.

Using the value of k in number 1, find:
2. a if b=3
3. a if b=4
4. a if b=12
5. a if b=1.5
6. a if b=3.6
7. a if b=4.8
8. b if a=3
9. b if a=4
10. b if a=4.5
11. b if a= 4.8
12. b if a=3.6
13. b if a=6

Jacks meeting lasted for 160 min or 2 hrs 40 min.

Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future.

Given is that jacks meeting stared at 2:45 pm and ended at 5:25 pm.

The time for which the meeting lasted can be written as -

{i} = 2:45 pm

{i + 60 minutes} = 3:45 pm

{i + (2 x 60) minutes} = 4:45 pm

{i + (2 x 60 + 40) minutes} = 5:25 pm

{f} = 5 : 25 pm

The meeting lasted for -

2 x 60 + 40

160 minutes

or

2 hours 40 minutes

Therefore, Jacks meeting lasted for 160 min or 2 hrs 40 min.

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Distance and time here is directly proportional to each other and the term '3' shows that the distance is increasing, is 3 times of the time, increased.

Given,

A snail is moving away from a rock.

The equation d=3t represents the relationship between the distance, d , in inches that the snail is from the rock and time, t, in minutes.

The number '3' is constant term, which basically represents the the distance covered by the snail, in terms of time or, the rate of increment of distance is terms of time.

Distance and time here is directly proportional to each other and the term '3' shows that the distance is increasing, is 1/3 of the time, increased.

For example if the snail is moving for 1 unit time, the t will be considered as 1. so, the d will be 3*1 = 3, i.e. 3 unit distance will be covered by the snail in 1 unit time.

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Answer:80

Step-by-step explanation:by5 will be this and 20 by 10 mulltiply 60 by 9

Answer:

Step-by-step explanation:

In addition and subtraction, the identity is 0. In multiplication and division, the identity is 1. That means that if 0 is added to or subtracted from n, then n remains the same. Also, if n is multiplied or divided by 1, then n remains the same  

ORRRRRRRRR

Five Properties of Addition

Closure property of Addition.

Commutative property of Addition.

Associative property of Addition.

Additive identity property of Addition.

Additive inverse property of Addition.

Answer:

11. ∠5 and ∠7 are corresponding angles

12. ∠1 and ∠8 are alternate exterior angles

13. ∠3 and ∠6 are alternate interior angles

14. ∠6 and ∠7 are consecutive interior angles.

15. ∠1 = 58

    ∠2 = 122

    ∠3 = 58

    ∠5 = 122

    ∠6 = 58

    ∠7 = 122

    ∠8 = 58

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Assuming the bags are filled at a constant rate, the average time it takes to fill one bag of leaves is 5 minutes.

To calculate the average time it takes to fill one bag of leaves, we need to know the total amount of time spent filling bags and divide that by the number of bags filled.

First, we know that the staff works an average of six hours per day. Since mowing and raking typically take four hours, we can assume that the remaining two hours are spent filling bags.

To find out how long it takes to fill one bag, we divide the total time spent filling bags by the number of bags filled. In this case, it would be:

(2 hours) / (24 bags) = 0.083 hours (or 5 minutes)

So the average time it takes to fill one bag of leaves is 5 minutes.

It's important to note that this is an average time and may not reflect the exact time it takes for each bag to be filled. Factors such as the size of the bag, the type of leaves being filled, and the skill level of the staff could all affect the time it takes to fill a bag.

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The Two steps equation in mathematics can be solved within exactly two steps by performing operation on both sides of the equation .

What is a Two Step Equation ?

The Two Step Equation can be defined as the equations that can be solved exactly within two steps.

When solving the  two step equation, we have to perform the operation on both sides of equals to sign.

To solve the equation we need to perform same operation on both sides of equation.

For Example ⇒ Solve [tex]3x+3=12[/tex] ;

Step1 : we Subtract 3 from both sides to isolate the variable x.

⇒ [tex]3x + 3 - 3 = 12 - 3[/tex]

⇒ [tex]3x = 9[/tex]

Step2 : We Divide both the sides of equation by 3 and solve for x.

⇒ [tex]\frac{3x}{3} =\frac{9}{3}[/tex]

⇒ [tex]x = 3[/tex] ;

Therefore , the given equation is solved in two steps .

The given question is incomplete , the complete question is

How do you solve a 2 step equation ?

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Answer:

-5

Step-by-step explanation:

Let n = an integer

Let (n+2) = the next consecutive odd integer

n + 7( n + 2) = -26  Distribute the 7

n + 7n + 7(2) = -26

n + 7n + 14 = -26  Combine like terms

8n +14 = -26  Subtract 14 from both sides

8n + 14 - 14 = -26 -14

8n = -40  Divide both sides by 8

n = -5

The next consecutive odd integer would be -3

Consecutive just means the next number.

Answer:

Step-by-step explanation:

(f.g)(x)=[tex]-3*(-3x)^{2}+3=-27x^{2}+3[/tex]

Answer:

2x + 1 = 29

Step-by-step explanation:

There are a lot of answers.

2x + 1 = 29

2x + 1 = 29  Subtract 1 from both sides

2x = 28  Divide both sides by s

x = 14

Start off knowing that x will be 14, then multiply 14 by some number and then add or subtract some number from that and put that on the other side of the equal sign.

x = 14

14 x 2 = 28 and then add 1 to that to get 29

2x + 1 = 29

Answer: Do you want x=14 or for it to equal 14, because I have it both ways. For x=14, an acceptable two step equation would be 2x-5=23. If you want it to equal 14, then you can write 5x-1=14

Step-by-step explanation:

For x=14:

2x-5=23

Add 5 on both sides

2x=28

x=14

For the equation to equal 14:

5x-1=14

Add one on both sides

5x=15

x=3

For given right triangle, the length of hypotenuse x = 4/√3

Here we have been given a 30° - 60°- 90° right triangle.

A side opposie to angle 60 degrees measures 2 units.

And x is the hypotenuse of right tirnagle.

To find the value of x, consider sine of angle 60 degrees.

sin(60°) = (opposite side of angle 60°) / hypotenuse

From tirgonometric table, sin(60°) = √3 / 2

So, above equation becomes,

√3/ 2 = 2/x

x = 2 × (2/√3)

x = 4/√3

We can see that the value of x is in in simplest radical form with a rational denominator.

Therefore, x = 4/√3

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The angle between the 5cm and 7cm sides to the nearest degree should measure approximately 71 degrees.

To construct a triangle with sides 7cm, 5cm and 6cm, start by drawing a straight line of 7cm length using the ruler. Next, use the compasses to draw an arc from one end of the line, with a radius of 5cm. Then, draw another arc from the same point of the line, with a radius of 6cm. Where the arcs intersect, draw a straight line connecting them to complete the triangle.

To measure the size of the angle between the 5cm and 7cm sides, use the compasses to draw a small arc from the vertex of the angle, and measure the angle using the ruler. To ensure accuracy, divide the angle into smaller, easier-to-measure angles. Repeat the process until the angle is measured to the nearest degree. In this case, the angle between the sides of 5cm and 7cm is approximately 71 degrees.

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The first left turn, the value of d will be -1i, indicating that the robot is now facing north.

Value is the worth of something, which can be measured in terms of money, time or importance. It is something that is sought after and desired. Value can also be seen in terms of a person's character, morals, beliefs, and principles. It is an intangible concept that is difficult to quantify, but it is often sought after and is an important aspect of life. Value is what makes something worthwhile and irreplaceable.

The robot will need to be able to detect walls. As it moves through the maze, it will need to be able to detect when it is about to hit a wall. This can be done using sensors. The sensors should be able to detect the wall and the distance from the wall. This will allow the robot to turn in the correct direction and avoid hitting the wall.

The robot will also need to be able to detect when it has reached the end of the maze. This can be done by programming the robot to recognize when it has come to a dead end, or when it has reached a certain point in the maze. Once the robot has reached the end, it can then turn around and exit the maze.

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In the given case, Matthew would have a negative z score and John would have a positive z score.

A z-score is a measurement of how far an observation or data point is from the distribution's mean. An observation is said to be above the mean if the z-score is positive, while it is said to be below the mean if the z-score is negative. Therefore, it is possible that John's z-score would be positive, showing that he is taller than the average for his age group if he is one of the tallest children in his class at the age of 7.

In contrast, if 12-year-old Matthew is among the smallest students in his class, it is likely that his z-score will be negative, suggesting that he is shorter than the norm for his age group. Therefore, John would have a positive z-score but Matthew would have a negative one if he is shorter than average for his age group.

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If Cherri brought $2100 computer on an installment plan and made $400 down payment and monthly payment for $79. 50 for the next two years, then the interest amount is $208 .

the cost of the computer is = $2100 ;

the amount paid as down payment is = $400 ;

the amount that will be paid in monthly installment is = $79.50 ;

the time for the loan is = 24 months ;

So , the amount paid as installment is 24 months is = [tex]24 \times79.50[/tex]

= $1908 .

So , the total amount paid by Cherri with installment plan is = [tex]\$1908+\$400[/tex]

= $2308 .

So , the interest amount paid is = [tex]\$2308-\$2100[/tex]

= $208 .

Therefore , Cherri will pay $208 as interest .

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Option c: y = -x + 5 represents scatter plot 1, Option g: The relationship is not linear represents scatter plot 2, Option a: y = 3x represents scatter plot 3, and Option f: y = x + 3 represents scatter plot 4.

What is a scatter plot?

The graphs that show the association between two variables in a data set are called scatter plots. It displays data points either on a Cartesian system or a two-dimensional plane.

The given equations are -

a. y = 3x

b. y = 4x - 2

c. y = -x + 5

d. y = -5x

e. y = -2x - 4

f. y = x + 3

g. The relationship is not linear.

The first scatter plot is going from positive y-axis to positive x-axis in a linear form. The graph for the equation that goes from positive y-axis to positive x-axis is y = -x + 5.

The second scatter plot is a curved parabola going and not a linear plot. So, the scatter plot is said to be a non-linear scatter plot.

The third scatter plot is going from positive x-axis to infinity in a linear form. The graph for the equation that goes from x-axis to infinity is y = 3x.

The fourth scatter plot is going from positive y-axis to infinity in a linear form. The graph for the equation that goes from positive y-axis to infinity is y = x + 3.

Therefore, scatter plot 1 is represented by equation y = -x + 5, scatter plot 2 is not linear, scatter plot 3 is represented by equation y = 3x and scatter plot 4 is represented by equation y = x + 3.

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The midpoint of the x-intercepts of f(x) = (x - 2)(x - 4) is (3, 0).

The midpoint of a line segment is known as the midpoint in geometry. It is the centroid of the segment and of the ends, and it is equally distant from both of them. It cuts the section in half.

A compass and straightedge setup can be used to locate the midpoint of the line segment they determine given two points of interest. By initially building a lens out of circular arcs with equal radii centered at the two endpoints and joining the cusps of the lens, one can determine the midpoint of a line segment immersed in a plane. The midpoint of the segment is then the place where the line joining the cusps intersects the segment.

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A customer purchased 1/4 pound of ham, 1 1/2 pounds of turkey, 1 pound of roast beef, and 3/4 pound of bologna. Therefore, the customer pay for the purchase before sales tax is $22.

Sales tax:

A sales tax is a tax paid to a governing body on the sale of certain goods and services. Laws generally allow sellers to collect taxes from consumers at the time of purchase. When a tax on goods or services is paid by consumers directly to the governing body, it is usually called a use tax. Laws often provide excise and use tax exemptions for certain goods or services, such as: food, education, medicine, etc. Value Added Tax (VAT) charged on goods and services is related to sales tax.

For Example:

I am shopping at The Clothing Boutique and would like to estimate the total after tax before checking out. After counting the total price of the items in the cart, the total is $100. Sales tax in this county is 9.5%, so you charge 9.5% (100 x 0.095) of $100.

According to the question:

The purchase before sales tax:

                   = 1/4 × $5.99 + 1 1/2 × $4.99 + 1 × $6.99 + 3/4 ×2.99

                   = $1.5 + $7.5 + $6.99 + $5.24

                   = $21.23 ≈ $22

Therefore,  the customer pay for the purchase before sales tax is $22.

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If the value of y = 0, then it make the straight line on the graph.

The term graph in math is defined as the way that is used to represent a set of data to make it easier to understand and interpret statistical information.

Here we have the expression y = 0.

And here we know that the y coordinate is constant which is 0 for given equation and only x coordinate is variable.

Therefore it represent the x-axis.

Therefore, basically y=0 is the linear equation to denote the x - axis, here as all the points on the x- axis, then we have their y co-ordinate = 0.

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The inequality to represent each situation is Harry > 60 inches, Sherry ≠ 4 years, and Hank ≥ $7.50.

a) Harry: This inequality states that Harry is taller than 60 inches. This is likely referring to Harry's height, as most people measure height in inches. This inequality can also be written as Harry ≥ 60 inches, emphasizing that Harry is at least 60 inches tall.

b) Sherry: This inequality states that Sherry is not equal to 4 years. This could be referring to Sherry's age, as it is common to measure age in years. This inequality can also be written as Sherry ≠ 4 years, emphasizing that Sherry is not exactly 4 years old.

c) Hank: This inequality states that Hank is greater than or equal to $7.50. This is likely referring to Hank's amount of money, as it is common to measure money in dollars. This inequality can also be written as Hank ≥ $7.50, emphasizing that Hank has at least $7.50.

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The diameter of the circle is 30 feet

To compute the diameter of the circle, we can use the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the hypotenuse is the diameter of the circle, and the other two sides are the radius and the distance between the chord and the center of the circle.

So, we can write the equation:

diameter^2 = radius^2 + (distance between chord and center)^2

We know the radius is half the diameter, so we can substitute that in:

diameter^2 = (diameter/2)^2 + (15)^2

And we can solve for the diameter:

diameter^2 = diameter^2/4 + 225

diameter^2 = diameter^2/4 + 225

4diameter^2 = diameter^2 + 900

3diameter^2 = 900

diameter^2 = 900/3

diameter = sqrt(900/3)

So the diameter of the circle is 30 feet.

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The triangle given is similar to using SAS. Sharon is wrong and the value of KL is 14.

there are three types of triangle similarity criteria known. those are

Given, two Triangle ΔGHI and ΔKLJ. Also, we can see in the figure That ratio of there two known sides is equal and they both have a similar angle.

the ratio of two sides of given triangles

4/8 and 5/10

hence, the ratio of both the side is equal that is 1/2

from the SAS theorem:

Two triangles are said to be comparable if their two sides are in the same ratio as the two sides of another triangle and their two sides' angles inscribed in both triangles are equal.

thus, given triangles are similar.

Since the Ratio of all three sides would be equal.

hence, HI / KL = 1/2

the third side of the triangle JKL, KL is 14.

Therefore, The given triangle is comparable to using SAS. Sharon is mistaken; The value of KL is 14.

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5 * root(x ^ 2, 3) is the equivalent expression.

Simply multiplying the radicands and placing the result behind the radical sign is all that is required to multiply two square roots. The square root of the product of the radicands, in other words, is equal to the product of two square roots.

Only if the numbers under the radical sign are equal can you add or subtract square roots themselves. The original number will still be in the radical sign after adding or subtracting the coefficients (numbers in front of the radical sign). Implement the suggested action.

5 * root(x ^ 2, 3) is the equivalent expression.

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Using the normal distribution, we have that diameters at the 0.34th percentile are 0.2 standard deviations, that is, 0.127 inches above the mean.

Probability is the likelihood that a particular experiment result will appear a certain number of times. It cannot be less than zero or greater than one. A 100% chance of an outcome occurring exists if the outcome is 1, for example. If the result is greater than 1, there is a greater chance that it will occur.

In a normal distribution with mean  and standard deviation , the z-score of a measure X is given by:

It measures how many standard deviations the measure X is from the mean.

After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

In this problem:

34th percentile is X when Z has a p-value of 0.34, so X when Z = 0.6331.

It means that the diameter is 0.44 standard deviations = 0.6331x0.2 = 0.127 inches above the mean.

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1, 15, 29, 43, 57 , the common difference is constant which is 14 and formula 1 + 14(n-1)

37, 34, 31, 29, 26 the common difference is constant which is -3 and formula is 37 - 3(n-1)

-4, 5, 14, 23, 32, the common difference is constant which is 9 and formula is -4 + 9(n-1).

The series where the common difference between any two next words stays constant is known as an arithmetic sequence. Let's review what a sequence is. A collection of numbers that follow a pattern is called a sequence. As an illustration, the numbers 1, 6, 11, 16,... are an arithmetic sequence because they follow a pattern in which the preceding term is multiplied by 5 to produce each subsequent number. There are two formulae for arithmetic sequences.

The equation to determine the nth term in an arithmetic series

The formula for calculating the sum of an arithmetic sequence's first n terms

There are two definitions for an arithmetic sequence. It is a "series where the differences between every two succeeding terms are the identical" or "each term in an arithmetic sequence is formed by adding a fixed number (positive, negative, or zero) to its preceding term."

Option 1, 4 and 6 are in Arithmatic Sequence as

In 1:

1, 15, 29, 43, 57 , the common difference is constant which is 14 and formula 1 + 14(n-1)

again in 4 :

37, 34, 31, 29, 26 the common difference is constant which is -3 and formula is 37 - 3(n-1)

and in 6

-4, 5, 14, 23, 32, the common difference is constant which is 9 and formula is -4 + 9(n-1).

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Answer:

1. 99/104

2. 4/3

3. 6/5

4. 52/25

5. 57/58

6. 33/100

7. 1/2

8. 8/5

9. 4

10. 4/3

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The fractions is simplified to 8ac²/ 5

A fraction can be described as the part of a whole element, number or variable.

There are different types of fractions, which includes;

Examples of improper fractions; 5/3, 7/5

Examples of proper fractions; 3/4, 5/6

Examples of mixed fractions; 3 1/2, 4 5/6

Examples of simple fractions; 1/2 , 1/ 4

From the information given, we have that;

[tex]\frac{32a^2bc^3}{20abc}[/tex]

This is simplified to;

32 × a × a × b × c × c × c/ 20 × a × b × c

Divide the common terms

8ac²/ 5

Hence, the fractions is 8ac²/ 5

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Answer: b

Step-by-step explanation:

4-3

——-

13.40- 10.05

= 1/3.35

=b