Rachel bought 15 packs of colored pencils with four pencils in each pack. She also
bought 32 packs of glitter pencils with two pencils in each pack. Write and evaluate an
expression to find the total number of pencils she bought.

Answer:

Answer:

x = 22

Step-by-step explanation:

2x+10+79 = 6x+1

89-1 = 6x-2x

88 = 4x

22 = x

The measure of the unknown value {x} in the given figure is 22.

An angle is formed when two rays have the same end point. The common end point is called vertex.

Given is to find the measure of the unknown value {x}.

The external angle will be equal to the sum of two internal opposite angles. Mathematically, we can write -

6x + 1 = 2x + 10 + 79

6x - 2x = 88

4x = 88

x = 22

Therefore, the measure of the unknown value {x} in the given figure is 22.

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Answer:

The number must be between 80 and 83.666002653408

Step-by-step explanation:

The square root of 6400 is 80 and the square root of 7000 is 83.666002653408 so it would be between those numbers.

The company should strive to minimize the number of faulty headsets.

Explanation:The company tests the headsets to identify the faulty ones, but 3.5% are still faulty. A company that manufactures headsets has a 3.5% faulty rate, even after testing. This means that 96.5% of the headsets manufactured are not faulty. The company conducts testing to identify and eliminate the faulty headsets. This quality assurance procedure ensures that the faulty headsets do not reach the customers, ensuring their satisfaction and trust in the company. Even though the company tests the headsets, 3.5% of the headsets are still faulty, and they need to ensure that the number reduces further. Therefore, the company should focus on improving its manufacturing process to reduce the number of faulty headsets further.

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Answer:

10 units

Step-by-step explanation:

Distance from P(6, -9) to O ( 0, 0 ) PO

Let

X1 = 6          X2 = 0

Y1 = -9         Y2 = 0

Formula of Distance

\(\sqrt{(x2 - x 1) + (y2 - y1)}\)

\(\sqrt{6^{2} +(-9^{2}) }\)

\(\sqrt{100}\)

10 units

2x +12=-4

2x= -4-12

2x=-16

x=-16/2

x= -8

Step-by-step explanation:

2x+12=-4

2x=-4-12

x=-16/2

x=-8

hope this helps you

have a good day.

The argument "p v q q   (Therefore) p" is invalid based on the truth tables that lists all possible combinations.

A truth table is a table that lists all possible combinations of truth values for the propositional variables involved in an argument and shows the resulting truth values for the entire argument. To test the validity of the argument "p v q q   (Therefore) p," we can construct a truth table.

Let's consider two propositional variables, p and q, which can take the truth values True (T) or False (F). In the argument, p v q q represents the logical disjunction (OR) of p and q twice. The conclusion, p, states that p must be true.

Constructing a truth table for this argument, we can observe that if both p and q are False (F), then p v q q will also be False (F). In this case, the conclusion p cannot be true since p is False (F). Therefore, there exist combinations of truth values where the premises are true, but the conclusion is false, indicating that the argument is invalid.

In summary, the argument "p v q q   (Therefore) p" is invalid based on the truth table, which shows that there are cases where the premises are true but the conclusion is false.

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The minimum number of students that must be in the professor's class in order to guarantee that at least 2 answer sheets are identical is 1025.

In order to answer this question, we need to use the Pigeonhole Principle, which states that if there are n pigeonholes and more than n objects, then at least one pigeonhole must contain more than one object.
In this case, the "pigeonholes" are the different possible combinations of answers for the 5 questions, and the "objects" are the students in the class.

Since there are 4 possible responses for each question, there are 4^5 = 1024 possible combinations of answers.
Now, suppose there are only 1023 students in the class.

Each student can choose one of the 1024 possible combinations of answers, and since there are more students than combinations, at least one combination must be chosen by two or more students.

Here are 5 questions, the total number of different answer sheets is 4^5 = 1024.

This represents the "pigeonholes." 3.

To guarantee that at least two answer sheets are identical, we need 1024 + 1 = 1025 students. This represents the "pigeons.

" According to the Pigeonhole Principle, if there are n pigeonholes and n+1 pigeons, at least one pigeonhole must contain at least two pigeons.

In this case, having 1025 students (pigeons) ensures that at least two students have identical answer sheets (pigeonholes).
But we want to guarantee that at least 2 answer sheets are identical.

This means we need to have one more student than the number of possible combinations, so that there is no way for each combination to be chosen by a different student.

Therefore, the minimum number of students required in the professor's class is 1024 + 1 = 1025.
So if there are 1025 or more students in the class, we can be sure that at least two answer sheets must be identical.

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The required work done in lifting the laptop to a height of 2 feet will be 263.79 foot-poundal.

Total weight of the laptop is 4.1 pounds

Acceleration due to gravity = 32.17 ft/\(s^{2}\)

Now the height to which the laptop has been lifted = 2 feet

Since, there is no mentioned velocity of the laptop, therefore the kinetic energy will be zero

Therefore, the total work in lifting the laptop will be equal to the change in potential energy.

Potential energy is the energy that comes by virtue of its position with reference to other

Therefore, potential energy = mgh

Where, m = mass of the laptop = 4.1 pounds

g = acceleration due to gravity = 32.17 ft/\(s^{2}\)

h = height to which the laptop is lifted =  2 feet

Therefore potential energy = (4.1)(32.17)(2) = 263.79 foot-poundal

263.79 foot-poundal is the required work done.

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Answer:

Its a right triangle

Step-by-step explanation:

Answer:

It is a right angle.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The area (A) of the sector is calculated as

A = area of circle × fraction of circle

   = πr² × \(\frac{80}{360}\)

   = π × 0.9² × \(\frac{8}{36}\)

   = 0.81π × \(\frac{2}{9}\)

   = 0.09π × 2

   = 0.18π in² → D

Answer:

Step-by-step explanation:
<ABC is 72 degrees.

1) This triangle is isosceles because two sides are equivalent. Thus, <C and <B are the same.
2) We know that <A + <B + <C = 180 in total
3. x + 2x + 2x = 5x
5x = 180
x = 36
4. <ABC = 2x = 2(36) = 72

Here the data is slightly right skewed which means there is no symmetry in the distribution of waiter tips. We, cannot determine the probability for this case.

Now, we will look into the details of distribution,

Mean of distribution = $9.60

The standard deviation of the skewed data = $5.40

Tip to the waiter = $20

Now, understand a few terms,

Normal distribution, also known as  Gaussian distribution, is very commonly used for randomly generated variables.

The graph of normal distribution has some parameters: the average or mean which is the maximum point of the graph and it is the point about which the graph is symmetrical, and the standard deviation which tells how much each data point is away from the mean.

As the data is skewed so we can,t use the normal distribution, and no other details about the model and distribution are given in the problem. So, we cannot determine the Probability for this case.

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The dimensions of the rectangle are 10 feet (length) and 8 feet (width).

To find the dimensions of the rectangle with an area of 80 square feet and a width that is 2 feet less than the length,

follow these steps:

1. Let the length of the rectangle be L feet and the width be W feet.

2. According to the given information, W = L - 2.

3. The area of a rectangle is calculated by multiplying its length and width: Area = L × W.

4. Substitute the given area and the relationship between L and W into the equation: 80 = L × (L - 2).

5. Solve the quadratic equation: 80 = L² - 2L.

6. Rearrange the equation: L² - 2L - 80 = 0.

7. Factor the equation: (L - 10)(L + 8) = 0.

8. Solve for L: L = 10 or L = -8 (since the length cannot be negative, L = 10).

9. Substitute L back into the equation for W: W = 10 - 2 = 8.

So, the dimensions of the rectangle are 10 feet (length) and 8 feet (width).

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The values of b for which the given inequality will be satisfied are: b = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9 , 10, 11, 12}

The given inequality which shows the status of the purchase by Amy and her friends is,

0.89 b + 1.82 ≤ 12.50

where b is the number of burgers they can purchase.

Solving the given inequality we get,

0.89 b + 1.82 - 1.82 ≤ 12.50 - 1.82 [Subtracting 1.82 from both sides]

0.89 b ≤ 10.68

(0.89 b)/0.89 ≤ 10.68/0.89 [Dividing 0.89 with both sides]

b ≤ 12

since b represents the number of burgers so it cannot be negative or fraction.

So the values for which the inequality will be satisfied are: b = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9 , 10, 11, 12}.

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The question is incomplete. Complete question will be -

Marcella would not be able to win the competition because the length of her string is 159.75 feet which is less than 162 feet need to win.

An equation is an expression that shows the relationship between two or more numbers and variables.

Trigonometric ratio is used to show the relationship between the sides and angles of a right triangle.

Let l represent the length of the string, hence:

sin(28) = l / 75

l = 159.75 feet < 162 feet

Marcella would not be able to win the competition because the length of her string is 159.75 feet which is less than 162 feet need to win.

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Answer:

invitations = 4

napkins = 2

Step-by-step explanation:

Answer is -5/8 as the slope

Shock advertisement are a type of advertising strategy that aims to provoke strong emotional responses from viewers by presenting controversial, shocking, or disturbing content.

An example of a shock add is Poking fun at events

By displaying content that is debatable, surprising, or upsetting, shock advertisement try to elicit strong emotional reactions from their target audience.

The goals of shock advertisements are to draw attention, leave a lasting impression, and elicit conversation about the good or message they are promoting.

These commercials frequently defy accepted norms, step outside of the box, and employ vivid imagery or provocative storytelling approaches.

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A rational equation is defined as the quotient of two polynomials, with the denominator not being zero. It is a type of algebraic expression that involves variables and rational functions with rational exponents.

The error in the given rational equation is that it's not allowed to cancel out the x-2 and X+2 terms, as they are in the denominators. It is because of the fact that it may make the denominator zero, which would result in undefined expressions. Therefore, we need to find the least common multiple (LCM) of the denominators and then convert the equation into equivalent forms with the same denominator.B):

Correction of the error1-2/x-2 = x+1/X+2Given rational equation can be re-written as:((1 - 2)/(x - 2)) = ((x + 1)/(X + 2))The LCM of x - 2 and X + 2 is (x - 2) (X + 2).Multiplying the numerator and denominator of the left side by (X + 2) and the numerator and denominator of the right side by (x - 2) we get,(1 - 2)(X + 2) = (x + 1) (x - 2)Now simplify the equation:2X - 3x = -3The given rational equation becomes 2X - 3x = -3 after correction.Note: You should always double-check if the obtained solution satisfies the initial equation.

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The shape parameter of the Gamma distribution is 10 and the rate parameter is 15/4.

To determine the shape and rate parameters of the Gamma distribution, we need to relate it to the Poisson distribution.

In the Poisson distribution, the average rate (λ) is equal to the shape parameter (k) multiplied by the rate parameter (θ). In this case, the average rate is 4 calls per 15 minutes, so λ = 4/15.

For the Gamma distribution, the shape parameter (k) is equal to the number of phone calls (n),  and the rate parameter (θ) is equal to the reciprocal of the average rate (λ). Therefore, k = 10 and θ = 1/λ.

Substituting the value of λ, we have k = 10 and θ = 15/4.

So, the shape parameter of the Gamma distribution is 10 and the rate parameter is 15/4.

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Answer:

1. To make a bell curve (a normal distribution) with a mean of 41 and a standard deviation of 5, we can use the following values on the x-axis:

x = 21, 26, 31, 36, 41, 46, 51, 56, 61

These values are symmetric around the mean of 41, and each value is one standard deviation away from the mean.

On the y-axis, we can mark the percentage of people in each interval, which is calculated using the area under the curve. The total area under the curve is 100%.

2. To find the percentage of people who were below 31 years old, we need to calculate the area under the curve to the left of x = 31. Using a standard normal distribution table or calculator, we can find this area to be approximately 0.0228, or 2.28%.

So, about 2.28% of people were below 31 years old.

3. To find the percentage of people who were above 31 years old, we can subtract the percentage of people below 31 years old from 100%.

100% - 2.28% = 97.72%

So, about 97.72% of people were above 31 years old.

4. To find the percentage of people between 41 and 46 years old, we need to calculate the area under the curve between x = 41 and x = 46. Using a standard normal distribution table or calculator, we can find this area to be approximately 0.3413, or 34.13%.

So, about 34.13% of people were between 41 and 46 years old.

5. To find the percentage of people older than Kip (who is 38 years old), we need to calculate the area under the curve to the right of x = 38. Using a standard normal distribution table or calculator, we can find this area to be approximately 0.6306, or 63.06%.

So, about 63.06% of people were older than Kip.

Step-by-step explanation:

Answer:2.92cm

Step-by-step explanation:

Answer:

2.92

Step-by-step explanation:

The equation for finding the Diameter for a circle is \(C/\pi =D\) where C is the circumference and d is the diameter.

First, substitute in the values for the equation:

\(9.18/\pi =D\)

Then divide it out:

\(2.92356687898=D\)

Then, round to the second decimal point or the hundredths place:

D=2.92

Answer:

9 m , 23 m , 23 m

Step-by-step explanation:

let the third side be represented by x , then the 2 equal sides are

3x - 4 and 3x - 4

the perimeter (P) is the sum of the 3 sides

P = x + 3x - 4 + 3x - 4 = 7x - 8

given P = 55 m , then equating

7x - 8 = 55 ( add 8 to both sides )

7x = 63 ( divide both sides by 7 )

x = 9

3x - 4 = 3(9) - 4 = 27 - 4 = 23

sides of triangle are 9 m , 23 m and 23 m

Answer:

\(D = 170\º\)

Step-by-step explanation:

Given

Shape: Pentagon

\(A = 87\º\)

\(B = 125\º\)

\(C = 63\º\)

\(E = 95\º\)

Required

Find D

From the sum of angles in a Pentagon; we have that

\(A + B + C + D + E = 540\)

Substitute values for A, B, C and E

\(87\º + 125\º + 63\º + D + 95\º = 540\º\)

Collect Like Terms

\(87\º + 125\º + 63\º + 95\º + D = 540\º\)

\(370\º + D = 540\º\)

Collect Like Terms

\(D = 540\º - 370\º\)

\(D = 170\º\)

Hence, from the list of given options, the correct answer is 170

Answer:

The equation of the line in fully simplified slope-intercept form is \(y=-0.4x-4\)

Step-by-step explanation:

The equation of the line in fully simplified slope-intercept form can be calculated as follows ?

The first step is to calculate the slope \(m\) of the given line using the slope formula as follows

\(m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)

Take two coordinates on the given line

\((-5,-2)~ \text{and} ~(5,-6)\)

Substitute \(-6\) for \(y_{2}\), \(-2\) for \(y_{1}\), \(5\) for \(x_{2}\), \(-5\) for \(x_{1}\)  in the slope formula

\(m=\frac{-6-(-2)}{5-(-5)}\)

Take out the brackets in the numerator and the denominator at the right side of the equation

\(m=\frac{-6+2}{5+5}\)

Simplify the numerator and the denominator at the right side of the equation

\(m=\frac{-4}{10}\)

Convert the value of \(m\) into decimal

\(m=-0.4\)

The second step is to find the slope-intercept form of the given line by the point-slope form formula as follows

\(y-y_{1}=m\cdot (x-x_{1})\)

Take any coordinates on the given line,  take \((-5,-2)\)

Substitute \(-2\) for \(y_{1}\),  \(-5\) for \(x_{1}\), \(-0.4\) for \(m\)  

\(y-(-2)=-0.4\cdot (x-(-5))\)

Take out the inner bracket on the right side of the equation

\(y-(-2)=-0.4\cdot (x+5)\)

Take out the bracket on the left side of the equation

\(y+2=-0.4\cdot (x+5)\)

Expand the right side of the equation

\(y+2=-0.4x -2\)

Substract \(2\) from both sides of the equation

\(y+2-2=-0.4x -2-2\)

Simplify the equation

\(y=-0.4x -4\)

Hence the equation of the line in fully simplified slope-intercept form is \(y=-0.4x-4\)

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Answer:

(8/4)100 = 200

Step-by-step explanation:

Simplify the following:

8/4×100

Hint: | Express 8/4×100 as a single fraction.

8/4×100 = (8×100)/4:

(8×100)/4

Hint: | In (8×100)/4, divide 100 in the numerator by 4 in the denominator.

4 | | 2 | 5

| 1 | 0 | 0

- | | 8 |  

| | 2 | 0

| - | 2 | 0

| | | 0:

8×25

Hint: | Multiply 8 and 25 together.

8×25 = 200:

Answer: 200

I believe that the answer is 200

13.2 credits are earned per semester.

The outcome you receive when you add together two or more numbers and divide the sum by the variety of amounts: Since the sum of the three numbers is 39 and 39 divided by three is 13, the average of the three numbers 7, 12, and 20 is 13.

The sample size \((x bar)\) provides the most accurate point estimate of the genuine population mean (μ) ( if the true population mean is unknown).

Given: A study at the nearby institution using a sample of 80 students discovered that each student obtained 13.2 credit hours on average per semester.

\(x bar\) = 13.2 credits per semester, for example.

The sample mean, or μ = \(x bar\)= 13.2 credit hours per semester, should thus be considered the best point estimate for the average number of credit hours per semester for all students at the local college.

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Question 1a

To calculate the book value at the end of the first year using straight-line depreciation, we need to determine the annual depreciation expense first. The straight-line method assumes that the asset depreciates by an equal amount each year over its useful life. Therefore, we can use the following formula to calculate the annual depreciation:

Annual Depreciation = (Cost - Salvage Value) / Useful Life

Substituting the given values, we get:

Annual Depreciation = ($200,000 - $20,000) / 10 years = $18,000 per year

This means that the tractor will depreciate by $18,000 each year for the next 10 years.

To determine the book value at the end of the first year, we need to subtract the depreciation expense for the year from the original cost of the tractor. Since one year has passed, the depreciation expense for the first year will be:

Depreciation Expense for Year 1 = $18,000

Therefore, the book value of the tractor at the end of the first year will be:

Book Value = Cost - Depreciation Expense for Year 1

= $200,000 - $18,000

= $182,000

So the book value of the tractor at the end of the first year, December 31, 2022, using straight-line depreciation is $182,000. so the answer is D

Question 1(b)

To determine the farmer's noncurrent liabilities, we need to use the information provided to calculate the total liabilities and then subtract the current liabilities from it. Here's the step-by-step solution:

Calculate the total current liabilities using the current ratio:

Current Ratio = Current Assets / Current Liabilities

2 = $80,000 / Current Liabilities

Current Liabilities = $80,000 / 2

Current Liabilities = $40,000

Calculate the total liabilities using the debt/equity ratio:

Debt/Equity Ratio = Total Liabilities / Owner Equity

1.0 = Total Liabilities / $100,000

Total Liabilities = $100,000 * 1.0

Total Liabilities = $100,000

Subtract the current liabilities from the total liabilities to get the noncurrent liabilities:

Noncurrent Liabilities = Total Liabilities - Current Liabilities

Noncurrent Liabilities = $100,000 - $40,000

Noncurrent Liabilities = $60,000

Therefore, the farmer's noncurrent liabilities are $60,000. so the answer is B.