A pack of cinnamon-scented pencils sells for $6.00. What is the sales tax rate if the total cost of the pencils is $6.42?

Please show how you did it

Answer:

Step-by-step explanation:

You want to find the number of puzzles solved by each boy if they solved 35 puzzles together, and 1/3 of the number Andy solved is twice the number Dale solved.

Let 'a' and 'd' represent the numbers of puzzles solved by Andy and Dale, respectively. Then ...

  a + d = 35

  1/3a = 2d

Multiplying the second equation by 3, we get an expression for 'a' that can be used in the first equation:

  a = 6d

  6d +d = 35

  d = 35/7 = 5

  a = 6(5) = 30

Andy solved 30 puzzles; Dale solved 5.

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there are 10 short answer questions on the test, we get this answer after solving.

Let's assume that the number of multiple choice questions on the test is "m", and the number of short answer questions is "s".

From the given information, we can set up a system of equations:

m + s = 30 (The total number of questions on the test is 30)

1m + 3s = 50 (The total number of points on the test is 50)

To solve for "s", we can use the first equation to find "m" in terms of "s":

m = 30 - s

Then we can substitute this expression for "m" into the second equation:

1(30 - s) + 3s = 50

Simplifying and solving for "s", we get:

30 - s + 3s = 50

2s = 20

s = 10

Therefore, there are 10 short answer questions on the test.

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Complete Question

Diego’s history teacher writes a test for the class with 30 question. The test is worth 50 points and has two types of questions: multiple choice worth 1 points each, and short answer problems worth 3 points each. How many short answer questions are in the test? Explain or show you reasoning.

The probability that an incoming call is for firefighting equipment (or any other reason besides medical assistance) is 0.33 or 33%.

The statement "the probability that an incoming call is for medical assistance is 0.67" can be expressed as:

P(Medical Assistance) = 0.67

This means that out of all incoming calls to the fire station, the probability that the call is for medical assistance is 0.67 or 67%. The complement of this event, which is the probability that an incoming call is NOT for medical assistance, is:

P(Not Medical Assistance) = 1 - P(Medical Assistance) = 1 - 0.67 = 0.33

In science, the probability of an event is a number that indicates how likely the event is to occur. It is expressed as a number in the range from 0 and 1, or, using percentage notation, in the range from 0% to 100%. The more likely it is that the event will occur, the higher its probability

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Answer: Yes. for each input there is exactly

ONE output

Step-by-step explanation:

I did the test and it was true.

The coordinates of the other endpoint are (17, 3).

In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and then divide by two (2):

Midpoint R = [(x₁ + x₂)/2, (y₁ + y₂)/2]

Next, we would determine the coordinate of MP with midpoint M at (7, 3) as follows;

12 = (7 + x₂)/2

24 = 7 + x₂

x₂ = 24 - 7

x₂ = 17.

For the other co-ordinate of P on line segment MP, we have:

3 = (3 + y₂)/2

6 = 3 + y₂

y₂ = 6 - 3

y₂= 3.

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The formula for given sequence is aₙ = 0.3(-0.2)ⁿ⁻¹ i.e. E.

What exactly is a sequence?

A sequence is a collection of numbers that follows pattern. Olivia, for example, has been offered a position with a beginning monthly pay of $1000 and a yearly raise of $500. Can you figure out her monthly pay for the first three years? The prices will be $1000, $1500, and $2000. Note that Olivia's income over a number of years creates a sequence as they follow a pattern where the numbers increase by $500 each time.

Now,

Given sequence is 0.3,-0.06, 0.012, -0.0024, 0.00048, ...

Of all given options only E satisfies the given sequence because

for E

a₁=0.3*-0.2¹⁻¹

=0.3*1

=0.3

a₂=0.3*-0.2²⁻¹

=-0.3*0.2

=-0.006

a₃=0.3*-0.2³⁻¹

=0.3*0.04

=0.012

hence,

          The formula for given sequence is aₙ = 0.3(-0.2)ⁿ⁻¹.

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The time and distance of both the boys Jake and Ethan when they meet with each other is equal to 40 minutes after covering 5 miles.

Constant rate by which Jake run is equal to  8 minutes per mile.

Rate of Ethan longboard for first two miles = 5 minutes per mile

Rate of Ethan longboard for rest of the miles = 10 minutes per mile

Time taken by each of them is :

Miles       Time taken by Jake (minutes)       Time taken by Ethan(minutes)

1                    8 min                                                 5 min

2                   16 min                                                10 min

3                    24 min                                               20 min

4                    32 min                                               30 min

5                    40 min                                               40 min

6                     48 min                                               50 min

Therefore , time and distance at which Jake and Ethan  meet is equal to 40 minutes that is at 5 miles.

The above question is incomplete , the complete question is:

Jake will run at a constant rate of 8 minutes per mile. Ethan will longboard at rate of 5 minutes per mile for the first two miles then will slow down and longboard at a rate of 10 minutes per mile. Make two tables finding the times for each boys results for 1,2,3,4,5 and 6 miles.

Find out the time and distance at which both meet.

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The number of students attended the play are 400 in number.

Two or more expressions with an Equal sign is called as Equation.

At a local play, student tickets cost $5 each and adult tickets cost $10 each. If ticket sales were $3,000

5x+10y=3000

The total number of tickets are 500

x+y=500

y=500-x

Now plug this in above equation

5x+10(500-x)=3000

5x+5000-10x=3000

5000-5x=3000

Add 5x on both sides

5000-3000=5x

2000=5x

Divide both sides by 5

400=x

Hence, the number of students attended the play are 400 in number.

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We can rewrite ln(27000) in terms of ln(5) and ln(6) as ln(27000) = 3ln(5) + 3ln(6) by using logarithmic property.

Due of their connection to exponential functions, logarithmic functions are crucial. Logarithms can be used to examine exponential equations and the properties of exponential functions.

We can use the logarithmic property that says:

log_a(xⁿ) = n×log_a(x)

to break down 27000 into factors that involve 5 and 6.

First, we can write:

27000 = 5³× 6³

When we take the natural logarithm of both sides, we obtain:

ln(27000) = ln(5³ × 6³)

Using the property above, we can simplify this expression as:

ln(27000) = ln(5³) + ln(6³)

Using another logarithmic property that says:

log_a(bⁿ) = c×log_a(b)

we can further simplify the expression:

ln(27000) = 3ln(5) + 3ln(6)

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The statement is True ' The height of a supply curve at a quantity of 100 represents the minimum price required to induce a producer to supply the hundredth unit"

A supply curve: what is it?

The relationship between the quantity of a good that a producer is willing to sell and the price of the good is graphically represented by the supply curve in economics.

The maximum price a producer will accept to sell a given quantity of the good is represented by the height of the supply curve at that quantity.

As a result, the minimum price necessary to persuade a producer to supply the 100th unit of the good is represented by the height of the supply curve at a quantity of 100.

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The solution that will satisfy the linear inequality y ≥ x + 4 include the following:

2. (-1, 4).

4. (0, 4).

In order to determine which ordered pairs are valid and true solutions based on the given linear inequality, we would have to test the given ordered pairs by substituting their values into the linear inequality as follows;

For ordered pair (0, 0), we have:

y ≥ x + 4

0 ≥ 0 + 4

0 ≥ 4 (False).

For ordered pair (-1, 4), we have:

y ≥ x + 4

4 ≥ -1 + 4

4 ≥ 3 (True).

For ordered pair (2, 3), we have:

y ≥ x + 4

3 ≥ 2 + 4

3 ≥ 6 (False).

For ordered pair (0, 4), we have:

y ≥ x + 4

4 ≥ 0 + 4

4 ≥ 4 (True).

For ordered pair (-1, 4), we have:

y ≥ x + 4

0 ≥ -1 + 4

0 ≥ 3 (False).

In this exercise, we would use an online graphing calculator to plot the given system of inequalities 2x + y < 1 and 4x - 3y ≥ 12 as shown on the number line attached below.

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Solving the equation: x - 1/x = 15/13

We will see that the value of x is 28/13

For a number x, we define the reciprocal number as 1/x.

We know that the difference between theses two is 15/13, then we can write:

x - 1/x = 15/13

(x² - x)/x = 15/13

(x² - x) = (15/13)*x

x² - x - (15/13)*x = 0

x² - (1 + 15/13)*x = 0

x² - (28/13)*x = 0

x*(x - 28/13) = 0

x = 0 is not a solution, because 1/x exists, then the solution is x = 28/13.

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the number of different possible teams that can be formed is equal to nCr, or n!/(r!(n-r)!).

Assuming that the state narcotics bureau has more than 5 agents from which to choose, the number of different possible teams that can be formed is equal to the number of combinations of 5 agents out of the total number of agents the bureau has. This can be calculated using the formula nCr (n choose r), where n is the total number of agents and r is the number of agents in each team, which in this case is 5.

Therefore, the number of different possible teams that can be formed is equal to nCr, or n!/(r!(n-r)!).

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Beth's rate of travel is 2.2 meters per second and Amy's line is steeper

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

The table of values

See attachment for the graph

From the graph, we have

Beth's rate of travel = 2.2 meters per second

This is so because from the graph:

As x increases by 1. y increases by 2/2

Here, we have

Amy's rate of travel = 75/30 meters per second

Evaluate

Amy's rate of travel = 2.5 meters per second

The higher the rate, the steeper the line

This means that Amy's line is steeper

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The two correct statements are a. The rate of change is 3 over the interval 1 ≤ x ≤ 2 & The rate of change is 3 over the interval 1 ≤ x ≤ 3. And as well as The rate of change is 5 over the interval 2 ≤ x ≤ 3 is also correct statement.

Divide the change in y-values by its change in x-values to determine the average rate of change. Identifying changes in measurable parameters as average speed or mean velocity calls for the knowledge of the average rate of change.

The average rate is the concentration change over a selected time period. It matters when you take the measurements. The solution is to find the slopes of the line to the concentrations time versus curve at that location.

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Answer:

10 packages

Step-by-step explanation:

When Mr. Rankin opens the box and looks straight down on it, he could see two packages. The 12x9 paper package can fit two, side by side in the 18X12 box.

Then there also can fit a stack 5 packages tall. Each bundle is 2 inches tall and the box is 10 inches tall.

Two stacks, 5 deep is 10 packages. see image.

Answer:

17 people surveyed own a cat.

Step-by-step explanation:

Let d stand for dog, c stand for cat, and b stand for both. In total, d + c + b = 100 people. The number of people who own a dog is four times the number of people who own a cat, so d = 4c. In the problem, it's given that 15 people own both a dog and a cat. So, b can be replaced with 15. Now, d + c + 15 = 100. This system of equations can be solved by substitution.

d = 4c

d + c + 15 = 100

4c + c + 15 = 100

5c + 15 = 100

5c = 85

c = 17

Check:

The number of dog owners is 4 * 17, or 68.

68 + 17 + 15 = 100

Shawn made 4 round trips to visit his grandma.

The travel time is the amount of time it takes to travel from one location to another. The specific method for calculating travel time depends on the mode of transportation being used. Here are some general guidelines for calculating travel time:

Let's start by converting the total travel time to minutes:

5 hours and 12 minutes = 5 × 60 + 12 = 312 minutes

Let's call the number of round trips that Shawn made "x".

For each round trip, Shawn has to travel to his grandma's apartment and then back home. The total time for each round trip is:

time per round trip = time to get there + time to get back + time to walk to/from parking

time per round trip = 35 + 35 + 4 + 4 = 78 minutes

So the total travel time for all of the round trips is:

total travel time = time per round trip x number of round trips

312 = 78x

Solving for "x", we get:

x = 312/78 = 4

Therefore, Shawn made 4 round trips to visit his grandma.

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Work Shown:

48w+23

48*3+23

144+23

167

It takes 167 minutes to cook 3 kg of meat.

Convert this to hours+minutes format.

167 min = 120 min + 47 min

167 min = 120/60 hr + 47 min

167 min = 2 hr + 47 min

To find the x-intercepts of a rational function of the form f(x) = p(x)/q(x), we set p(x) = 0 and solve for x. To find the vertical asymptotes, we set q(x) = 0 and solve for x.

Vertical asymptotes are vertical lines that a function approaches but never touches or crosses as the independent variable (usually denoted as x) approaches a certain value.

To find the x-intercepts of the function, we need to set the numerator of the rational function equal to zero and solve for x. This is because x-intercepts occur when the function value is equal to zero. Therefore, we can write:

p(x) = 0

Solving this equation will give us the values of x where the function intersects the x-axis. It is important to note that if p(x) has a degree greater than or equal to q(x), then the function will have a slant asymptote instead of a vertical asymptote.

To find the vertical asymptotes of the function, we need to look at the denominator of the rational function. Vertical asymptotes occur when the function approaches infinity or negative infinity as x approaches a certain value. In the case of a rational function, this happens when the denominator is equal to zero. Therefore, we can write:

q(x) = 0

Solving this equation will give us the values of x where the function has a vertical asymptote. It is important to note that if the degree of q(x) is greater than the degree of p(x), then the function will have a horizontal asymptote instead of a vertical asymptote.

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The expected number of rolls is 12.The probability of rolling an even number on a fair, 6-sided die is 3/6, or 1/2.

The probability of rolling an even number on a fair, 6-sided die is 3/6, or 1/2. Therefore, the expected number of rolls can be calculated by multiplying the probability of rolling an even number (1/2) by the number of sides on the die (6). In this case, 1/2 x 6 = 12.

The expected number of rolls to get a specific result on a fair die can be calculated by multiplying the probability of achieving that result by the number of sides on the die. For example, if you wanted to know the expected number of rolls to get an odd number on a fair, 6-sided die, you would multiply the probability of rolling an odd number (3/6, or 1/2) by the number of sides on the die (6). In this case, 1/2 x 6 = 3. The same calculation could be applied to determine the expected number of rolls to get a specific number (e.g. a 4) on a fair, 6-sided die. The probability of rolling a 4 would be 1/6, and the expected number of rolls to get a 4 would be 1/6 x 6 = 6.

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The letter grades (A, B, C, D, F) for business analysis students are categories that represent different levels of achievement, so the variable's classification is (b) Categorical Data.

The Categorical data are defined as the variables that represent characteristics or attributes, and they are often expressed as labels or categories.

The Quantitative data, on the other hand, are  the numerical values which  represent measurements or quantities.

Since the letter grades are not numerical values and do not represent a measurement or quantity, they cannot be classified as quantitative data.

Therefore , the letter grades represents a Categorical Variables .

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The given question is incomplete , the complete question is

The letter grades (A, B, C, D, F) of business analysis students are recorded by a professor. this variable's classification .

(a) is time series data

(b) is categorical data

(c) is quantitative data

(d) cannot be determined

Answer: 25 inches

Step-by-step explanation:

cos60 = adjacent over hypotenuse

cos60 = a/50

50cos60 = 25

Answer:

Step-by-step explanation:

the probability of drawing a face card=12/52

drawing the king of diamonds=1/52

Answer:

Probability of face is 12/52

The value of a₄ is 19.

What is arithmetic progression?

A progression or sequence of numbers known as an arithmetic sequence maintains a consistent difference between each succeeding term and its predecessor. The common difference in that mathematical progression is the constant difference.

Here, we have

Given: a₁ ​ =7 and aₙ ​ = aₙ₋₁ + 4

We have to find the value of a₄.

a₁ ​ =7

aₙ ​ = aₙ₋₁ + 4

aₙ ​- aₙ₋₁ = 4

The common difference is 4.

In order to solve, replace the value of the previous answer with the equation for the next answer.

a₁ = 7

a₂ = 7 + 4 = 11

a₃ = 11 + 4 = 15

a₄ = 15 + 4 = 19

Hence, the value of a₄ is 19.

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Brianna is correct, the distance around a rectangular pool with dimensions of 40 feet by 20 feet is 120 feet, which can be calculated by adding up the lengths of all four sides: (40 + 20 + 40 + 20) feet = 120 feet.

Brianna is correct, the distance around a rectangular pool with dimensions of 40 feet by 20 feet is indeed 120 feet. To calculate the distance around the pool, we need to add up the lengths of all four sides, which are equal in length. In this case, the length and width of the pool are both 40 feet and 20 feet, respectively. So, to find the distance around the pool, we add up these four lengths:

40 feet + 20 feet + 40 feet + 20 feet = 120 feet

Therefore, the total distance around the pool is 120 feet.

To determine the distance around the pool, Brianna needs to measure the length and width of the pool. If the pool is rectangular, she can measure the length and width and add up the lengths of all four sides to find the total distance around the pool. If the pool is a different shape, Brianna would need to measure the lengths of each side and add them up to find the total distance around the pool. This information can then be used to calculate the amount of stone needed for the edging around the pool. By knowing the total distance around the pool, Brianna's parents would have a good estimate of how much stone they need to buy for the edging, which is typically sold by the linear foot.

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The complete question is:

In the backyard, Brianna's parents constructed a swimming pool. The pool's circumference, according to Brianna, is 120 feet.

40 Ft

20 Ft

1. Is she correct? Explain why or why not. (You must mention the following in your explanation: If she is right, demonstrate the steps she took to determine the pool's circumference. Determine the right distance and demonstrate all effort if she is mistaken.)

2. So that her parents will know how many feet of stone to purchase for the pool's edging, describe (using words this time) how Brianna would calculate the distance around the pool.

Answer:

∠ B = 121°

Step-by-step explanation:

ABCD is a cyclic quadrilateral

• opposite angles sum to 180°

∠ B and ∠ D are opposite angles , then

∠ B + 59° = 180° ( subtract 59° from both sides )

∠ B = 121°

Option A is correct. Use HL to prove two triangles are congruent.

Given:

In triangle ABC and triangle DEF as shown in figure below.

AB≅DE   [leg]                 [Given]

AC≅DF    [Hypotenuse side]      [Given]

∠B = ∠D = 90°

HL(Hypotenuse -Leg) postulates states that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

Then, by HL postulates;

ΔABC ≅ ΔDEF.

Therefore, the method you use to prove the two triangle congruent is, HL.

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