What is the sale price of a pillow originally priced at 12 dollars

The expressions are simplified to;

a. 4pq

b. t³

Algebraic expressions are defined as expressions that are made up of terms, variables, coefficients, factors and constants.

These algebraic expressions are also made up of mathematical or arithmetic operations, such as;

From the information given, we have that;

The expressions are;

1.  p x q x 4

Multiply the terms, we have that;

4qp

2.t x t x t

Multiply the terms, we get;

t³

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Answer:

B. 33

Step-by-step explanation:

Step 1:  Find total measure of ∠R:

Step 2:  Find total measure, m, of ∠Q:

m∠P + m∠Q + m∠R = 180

m∠Q = 180 - (m∠P + m∠R)

m∠Q = 180 - (60 + 76)

m∠Q = 180 - 136

m∠Q = 44°

Since QA bisects ∠Q into two congruent angles, we divide 44 by 2 to find the measures of each angle made by the bisector:  44/2 = 22.

Step 3:  Find x by setting the sum of the 38° angle, the 22° angle, and angle C equal to 180:

38 + (3x + 21) + 22 = 180

60 + 3x + 21 = 180

81 + 3x = 180

3x = 99

x = 33

Thus, x equals 33.

The units that each student used, given the measurement that they got and all of them being right was:

The height of a bookshelf is typically measured in inches, feet, or yards .

Student A measured 72 units, which is equal to 6 feet. Student B measured 2 units, which is equal to 24 inches .

Student C measured 6 units, which is equal to 18 yards. All three students are correct, as they all used different units to measure the same height .

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Full question is:

Three students measure the height of a bookshelf. Student A measures 72 units, Student B measures 2 units, and Student C measures 6 units. The teacher says all three students are correct. What units did each student use?

The value of the missing segment n using the product of intersecting chord theorem is 14cm

The product of the segments of two intersecting chords are equal.

The segments of the chords ;

Chord 1 = 4 and n

Chord 2 = 7 and 8

The principle can be related Mathematically thus ;

4 × n = 7 × 8

4n = 56

Divide both sides by 4

4n/4 = 56/4

n = 14

Therefore, the value of n in the question is 14cm

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By using this absolute value equation, the chef can determine the range of cake diameters that meet the desired margin of error of 3 inches and make an informed decision when purchasing the cake.

The absolute value of the difference between the actual diameter of the cake and the ideal diameter of 24 inches should be less than or equal to 3 inches.

To describe the statement using an absolute value equation, let's define the variable "d" as the actual diameter of the cake.

The ideal diameter of the cake is given as 24 inches.

The margin of error is specified as 3 inches, which means the chef is willing to accept a cake with a diameter within 3 inches of the ideal size.

Considering the margin of error, we can express the acceptable range of diameters for the cake as follows:

d - 24 ≤

This inequality states that the difference between the actual diameter "d" and the ideal diameter of 24 inches should be less than or equal to 3 inches, indicating that the actual diameter should be no more than 3 inches larger or smaller than 24 inches.

However, to represent this condition using an absolute value equation, we need to remove the inequality signs.

We can rewrite the inequality above using absolute value:

|d - 24| ≤ 3

This absolute value equation states that the absolute value of the difference between the actual diameter "d" and the ideal diameter of 24 inches should be less than or equal to 3 inches.

It encompasses both possibilities of the actual diameter being within 3 inches greater or smaller than 24 inches.

By using this absolute value equation, the chef can determine the range of cake diameters that meet the desired margin of error of 3 inches and make an informed decision when purchasing the cake.

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Answer: (x+6)(x-3)

Step-by-step explanation:

y=x^2+3x-18

(x+6)(x-3 )

Answer: rental is $415, and the standard deviation is $5.

Step-by-step explanation:

If about 99.7 percent of the monthly rentals fall between 400 and 430, it implies that this range encompasses three standard deviations from the mean.

To calculate the mean, we can find the midpoint of the given range:

Mean = (400 + 430) / 2 = 415

Since the range of three standard deviations covers about 99.7 percent of the data in a normal distribution, we can use this information to estimate the standard deviation (σ).

Standard deviation (σ) = (430 - 415) / 3 = 15 / 3 = 5

Therefore, based on the given information, the mean monthly rental is $415, and the standard deviation is $5.

Answer:

15.36

Step-by-step explanation:

192*0.02*4= 15.36

Answer:

The distance from each chord to the center of the circle is approximately 12.09 inches.

Step-by-step explanation:

To find the distance from each chord to the center of the circle, we can use the following formula:

[tex]d = \sqrt{r^2-(l/2)^2}[/tex]

Where:

- "d" is the distance from the chord to the center of the circle,

- "r" is the radius of the circle, and

- "l" is the length of the chord.

Given that the diameter of the circle is 29 inches, we can find the radius by dividing the diameter by 2:

[tex]r = 29/2 = 14.5[/tex] Inches

Now, let's calculate the distance from each chord to the center of the circle:

For the first chord with a length of 16 inches:

[tex]d_{1} =\sqrt{14.5^2-(16/2)^2} = \sqrt{210.25-64} = \sqrt{146.25} = 12.09[/tex] Inches

For the second chord with a length of 16 inches:

[tex]d_{2} = \sqrt{14.5^2-(16/2)^2} = \sqrt{210.25-64} = \sqrt{146.25} = 12.09[/tex] Inches

Therefore, the distance from each chord to the center of the circle is approximately 12.09 inches.

Check the picture below.

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{14.5}\\ a=\stackrel{adjacent}{8}\\ o=\stackrel{opposite}{x} \end{cases} \\\\\\ x=\sqrt{ 14.5^2 - 8^2}\implies x=\sqrt{ 210.25 - 64 } \implies x=\sqrt{ 146.25 }\implies x\approx 12.09[/tex]

Answer: 70 + 3 + [tex]\frac{9}{100}[/tex]

Step-by-step explanation:

     Firstly, what is expanded form? Expanded form is a sum of a number's digit place values.

     For example, the expanded form of 814 is 800 + 10 + 4.

To find the expanded form of 73.09, we will do the same as the example provided above. However, we have a decimal. This means we will use a fraction. This 9 is in the hundredth place, so we will use the fraction  [tex]\frac{9}{100}[/tex].

73.09 = 70 + 3 + [tex]\frac{9}{100}[/tex]

Answer:

1. 176,500 centimeters

2. 940,000 centimeters

3.42,000,000 grams

Step-by-step explanation:

Convertion:

1.1.1

1765m to cm

1 meter = 100 centimeters

Therefore, 1765 meters =1765*100 centimeters = 176,500 centimeters

1.1.2

9.4 km to cm

1 kilometer = 1000 meters

First convert it into m.

9.4 kilometers = 9.4*1000 meters = 9400 meters

then in cm

1 meter = 100 centimeters

Therefore, 9400 meters = 9400*100 centimeters = 940,000 centimeters

1.1.3

4.2 tons to grams

1 ton = 1000 kilograms

First convert it into kilogram

1 kilogram = 1000 grams

Therefore, 4.2 tons = 4.2*1000 kilograms = 4200 kilograms

then in grams

4200 kilograms = 4200*1000 grams = 42,000,000 grams

I hope this helps! Let me know if you have any other questions.

Answer:

----------------------

In ΔNOP, we are given:

Use the law of cosines to find side o:

Now, use the law of sines to find ∠N:

So,  ∠N is approximately 10°.

Answer:

5.25 feet tall

Step-by-step explanation:

Doug's height / Doug's shadow = Statue's height / Statue's shadow

x / 3.5 = 12 / 8

Cross-multiplying:

8x = 3.5 * 12

8x = 42

Dividing both sides by 8:

x = 42 / 8

x ≈ 5.25

1)

The trigonometric functions :

sinA = 5/13 , cosA = 13/12 , tanA = 5/13

Given,

Right angled triangle with:

P = 5

B = 12

H = 13

Then trigonometric ratios,

sinA = P/H

cosA = B/H

tanA = P/B

Hence the ratios can be defined as,

sinA = 5/13

cosA = 12/13

tanA = 5/12

2)

The value x in the radical form 10.77

Given,

Right angled triangle,

Perpendicular = 4

Base = 10

Hypotenuse = x

Apply pythagora's theorem,

P² + B² = H²

4² + 10² = H²

16 + 100 = H²

H = 10.77

Hence the value of x is 10.77 .

3)

The value of x in radical form

Given,

P = 56

B = x

H = 106

Apply pythagora's theorem,

P² + B² = H²

56² + x² = 106²

x = 90

Hence the value of x is 90 .

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Answer:

664 Square yards

Step-by-step explanation:

Surface area= 2lw+2lh+2hw

=2(17×6)+2(17×10)+2(10×6)

=2(102)+2(340)+2(120)

=204+340+120

=664 Square yards

The Euclid math contest is the annual contest held by the University of Waterloo. The students from grade-11 to grade-12 can participate in the Euclid math contest.

Euclid contest is a Mathematics contest for senior-level high school students. This contest was participated by nearly 22000 students worldwide every year. This contest allows the students to demonstrate their knowledge of secondary school mathematics. This competition was held by the University of Waterloo.

The senior-grade students will participate in this contest and it takes 2 and a half hours to complete the contest. It has 10 questions and the total mark for the contest is 100. The University of Waterloo values the results from the Euclid math contest when it comes to admission and scholarship offers.

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The value of y is 2 * √3.

In the second right triangle, we have a 60-degree angle and a leg opposite to that angle labeled y. The hypotenuse of the first right triangle is equal to the leg of the second right triangle.

Let's denote the hypotenuse of the first right triangle as h. From the first right triangle, we know that the vertical leg is equal to the square root of 2.

Using trigonometric ratios, we can relate the sides of a right triangle as follows:

sin(angle) = opposite/hypotenuse

In the first right triangle, the angle is 45 degrees, and the opposite side is the square root of 2. Therefore, we have:

sin(45 degrees) = √2 / h

By rearranging the equation, we can solve for h:

h = √2 / sin(45 degrees)

Using the value of sin(45 degrees) = 1/√2, we can simplify the equation:

h = √2 / (1/√2) = √2 * √2 = 2

Now, we can find the value of y in the second right triangle. Since the hypotenuse of the first right triangle is equal to the leg of the second right triangle, we have:

y = 2 * √3

Therefore, the value of y is 2 * √3.

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You have the derivative of a product:

first limit (7x+3)

second limit (4-3x)

The Rule for the derivative of a product is:

(first limit × derivative of second limit) + (second limit × derivative of first limit)

f(x) = (7x+3)(4-3x)

f'(x)=(7x+3)×-3 + (4-3x)×7 = -21x- 9 + 28-21x

f'(x) = -42x + 19

Answer:

--------------

Given function:

In order to find its inverse, first swap x and y:

Then solve for y:

The inverse function is y= √x.

Answer:

Step-by-step explanation:

This number line says that  we can take all values of x that are less than or equal to 2. That is, the solution is

                                  [tex]x\leq 2[/tex]

NOTE: if the circle at 2 were not filled in then that would mean x<2 (2 would not be an accepted value of x)

Answer:

64π

Step-by-step explanation:

To calculate the surface area (S.A) of the circle with a radius (r) of 4 inches and a height (h) of 6 inches, we need to consider both the curved surface area (lateral surface area) and the area of the circular base.

The curved surface area, also known as the lateral surface area, is calculated using the formula:

L.A = 2πrh

Substituting the given values, we have:

L.A = 2π(4)(6)

L.A = 48π square inches

The area of the circular base is calculated using the formula:

A = πr^2

Substituting the given radius, we have:

A = π(4^2)

A = 16π square inches

To find the total surface area (S.A), we need to sum the lateral surface area (L.A) and the area of the circular base (A):

S.A = L.A + A

S.A = 48π + 16π

S.A = 64π square inches

Therefore, the surface area (S.A) of the given circle is 64π square inches.

The total number of data values (games played) represented in the table is 14.

To determine the total number of data values (games played) represented in the frequency table, we need to sum up the frequencies for each category (number of goals scored).

The frequency represents the number of games in which a particular number of goals was scored.

Let's calculate the total number of games played by summing up the frequencies:

Total number of games played =

Frequency of 0 goals + Frequency of 1 goal + Frequency of 2 goals + Frequency of 3 goals + Frequency of 4 goals + Frequency of 7 goals + Frequency of 9 goals

Total number of games played = 1 + 3 + 2 + 4 + 2 + 1 + 1

Total number of games played = 14

We must add the frequencies for each category (number of goals scored) to get the total number of data values (games played) reflected in the frequency table.

The number of games with a specific amount of goals scored is the frequency.

Let's add up the frequencies to determine the total number of games played:

Total games played = Frequency of 0 goals, Frequency of 1, Frequency of 2, Frequency of 3, Frequency of 4, Frequency of 7, and Frequency of 9 goals.

Total games played: 1 plus 3 plus 2 plus 4 plus 2 plus 1 plus 1

14 games were played in total.

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Answer:

–6x – 3

Step-by-step explanation:

To find the expression that is equivalent to 3(–2x – 1), we need to distribute the 3 to each term inside the parentheses.

When we distribute 3 to –2x, we get:

3 * –2x = –6x

When we distribute 3 to –1, we get:

3 * –1 = –3

Therefore, the expression equivalent to 3(–2x – 1) is:

–6x – 3.

Answer:

-6x - 3

Step-by-step explanation:

Distribute 3 through the parenthesis:

[tex]\sf{3(-2x-1)}[/tex]

[tex]\sf{3*(-2x)+3*(-1)}[/tex]

[tex]\sf{-6x-3}[/tex]

Hence, the expression that is equivalent  to 3(-2x - 1) is -6x - 3.

While these examples demonstrate some practical applications, divisibility rules are primarily mathematical tools that assist in simplifying calculations, verifying results, and understanding number properties.

Divisibility rules can be applied in various real-life scenarios, particularly in mathematics, finance, and everyday calculations. Here are a few examples:

Checking for even or odd numbers: The divisibility rule for 2 states that a number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8). This rule can be helpful when determining if a given quantity or count is even or odd. For example, in inventory management, you can quickly estimate the number of items in a collection by checking the parity of the count.

Divisibility by 3: The divisibility rule for 3 states that a number is divisible by 3 if the sum of its digits is divisible by 3. This rule can be useful when dealing with numbers or quantities that need to be evenly distributed or divided.

Divisibility by 9: The divisibility rule for 9 states that a number is divisible by 9 if the sum of its digits is divisible by 9. This rule can be applied in various financial calculations, such as checking if a large number is divisible by 9 to verify the accuracy of calculations involving money, invoices, or balances.

Divisibility by 10: The divisibility rule for 10 states that a number is divisible by 10 if its last digit is 0. This rule is often used in practical situations like determining if a given quantity can be divided evenly into groups of 10 or used in financial transactions involving rounding to the nearest multiple of 10.

Checking prime numbers: Divisibility rules can also help in determining whether a number is prime. For example, the rule that states a number is not divisible by any number greater than its square root can be used to quickly eliminate potential factors when checking for primality.

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The nth roots of perfect nth powers evaluates to:

[tex]\sqrt[5]{-32}[/tex] = -2

[tex]-\sqrt[4]{256}[/tex] = -4

Perfect nth Power is an integer which is obtained from multiplying a single integer by itself n times.

The nth root of a Perfect nth Power is an integer which when multiplied by itself n times it will produce the original value under the radical.

To find the nth roots of perfect nth powers with signs, you can use the following steps:

1. Write the perfect nth power as a product of nth roots.

2. Find the nth root of each factor.

3. Combine the nth roots to get the final answer.

[tex]\sqrt[5]{-32}[/tex] = [tex]\sqrt[5]{-2^{5} }[/tex]

         = -2

-[tex]\sqrt[4]{256}[/tex] = -[tex]\sqrt[4]{4^{4} }[/tex]

           = -4

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The probability of either events A or B occurring is determined as 0.89.

The probability of either events occurring is calculated by applying the following formula as shown below;

P (A or B ) = P ( A ) + P ( B )

The probability of A is calculated as follows;

P ( A ) = A / total outcome

P ( A ) = ( 20 ) / ( 20 + 12 + 4 )

P ( A ) = ( 20 ) / ( 36 )

P ( A ) = 5/9

The probability of B is calculated as follows;

P ( B ) = B / total outcome

P ( B ) = 12 / 36

P ( B ) = 1/3

The probability of either A or B is calculated as follows;

P (A or B) = 5/9  +  1/3

P (A or B) = 8/9 = 0.89

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