ETA 4



Answer the following:



Myla bought an item P2,500. She decided to sell it wil 2% markup. How much will Myla’s selling price be?



Joan sold her old iphone for P5000 at 8% markdown rate. Find the markdown and the original cost of the phone.



A student assistant bought an item for P520 but later decided to sell it at P550. What is the markup?



Mother organize a garage sale and earned P120 on one item at 60% markdown. How much did mother buy the item?



The cost of a t-sirt from the manufacturer is P400. If loan wants a 30% markup based on the selling price, how much will her selling price be?

discount amount= CP-Disount percentage

or,480=CP-25/100

or480×100+25 =CP

48025 is the original price of shirt

The new total bill including the tip of 15% is $59.01.

To find the amount of the tip, we can multiply the total bill by the percentage as a decimal:

tip = 0.15 * $51.31 = $7.70

To find the new total including the tip, we can add the tip to the original bill:

new total = $51.31 + $7.70 = $59.01

So the new total, including a 15% tip, will be $59.01.

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There is not sufficient evidence at the α=0.05 level to conclude that the proportion of people in Antonia's city that can speak more than one language is greater than 26%.

Here's a step-by-step explanation:

1. Identify the null hypothesis (H₀) and the alternative hypothesis (Hₐ): H₀: p = 0.26, Hₐ: p > 0.26.

2. Determine the significance level (α): α = 0.05.

3. Calculate the test statistic (z): In this case, z ≈ 2.25.

4. Determine the P-value: The P-value is given as approximately 0.1.

5. Compare the P-value to the significance level: If the P-value is less than or equal to the significance level (α), reject the null hypothesis. In this case, 0.1 > 0.05, so we do not reject the null hypothesis.

Based on the information provided, there is not sufficient evidence at the α=0.05 level to conclude that the proportion of people in Antonia's city that can speak more than one language is greater than 26%.

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9. Let's start by defining the variable.

Let's say the number we're trying to find is "x".

Now, let's translate the problem into an equation:

2(x - 4) = x + 6

We can simplify this equation by distributing the 2:

2x - 8 = x + 6

Next, let's isolate the variable on one side of the equation by subtracting x from both sides:

x - 8 = 6

Finally, we can solve for x by adding 8 to both sides:

x = 14

Therefore, the number we're looking for is 14.

10. Let's start by defining the variable.

Let's say the number we're trying to find is "x".

Now, let's translate the problem into an equation:

-(x) - 5 = 3(x + (-7))

We can simplify the right side of the equation by first simplifying the expression inside the parentheses:

-(x) - 5 = 3(x - 7)

Next, we can distribute the 3:

-(x) - 5 = 3x - 21

Let's isolate the variable on one side of the equation by adding x to both sides:

-(x) + x - 5 = 3x + x - 21

Simplifying the left side of the equation:

-5 = 4x - 21

Now, we can isolate the variable by adding 21 to both sides:

-5 + 21 = 4x

Simplifying the left side of the equation:

16 = 4x

Finally, we can solve for x by dividing both sides by 4:

x = 4

Therefore, the number we're looking for is 4.

Therefore, the molarity of the sugar solution is 0.3704 M at 25°C. Therefore, the molality of the NaCl solution is 1.8994 mol/kg.

In mathematics, an equation is a statement that asserts the equality of two expressions. An equation typically consists of two sides separated by an equal sign (=). The expressions on either side of the equal sign may contain variables, constants, coefficients, and mathematical operations.

Here,

1. To calculate the molarity of a sugar solution, we need to first determine the number of moles of solute (glucose, C6H12O6) present in the solution. We can then divide this number of moles by the volume of the solution in liters to obtain the molarity. The number of moles of glucose in the solution can be calculated as follows:

Number of moles = mass of solute / molar mass of solute

Number of moles = 100.0 g / 180 g/mol

Number of moles = 0.5556 mol

Next, we can calculate the molarity of the solution using the following formula:

Molarity = number of moles / volume of solution (in L)

Molarity = 0.5556 mol / 1.50 L

Molarity = 0.3704 M

2. To calculate the molality of a solution, we need to know the number of moles of solute (NaCl) per kilogram of solvent (water).

First, let's calculate the number of moles of NaCl:

Number of moles = mass of NaCl / molar mass of NaCl

Number of moles = 200.0 g / 58.5 g/mol

Number of moles = 3.4188 mol

Next, we need to calculate the mass of the solvent (water) in kilograms:

Mass of solvent = 2.00 kg - 0.200 kg

Mass of solvent = 1.80 kg

Note that we subtracted the mass of the NaCl from the total mass of the solution to obtain the mass of the solvent.

Finally, we can calculate the molality of the solution using the following formula:

Molality = number of moles of solute / mass of solvent (in kg)

Molality = 3.4188 mol / 1.80 kg

Molality = 1.8994 mol/kg

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The general solution to the given differential equation:

[tex]y = (9x + C)e^(-6x)[/tex]

To solve the given differential equation, dy + 6ydx = 9e^(-6x)dx, we can first rewrite it as a first-order linear differential equation:

[tex]dy/dx + 6y = 9e^(-6x)[/tex]

Now, we will find the integrating factor, which is e^(∫P(x)dx), where P(x) is the coefficient of y in the equation:

Integrating factor =[tex]e^(∫6dx) = e^(6x)[/tex]

Next, we multiply the entire differential equation by the integrating factor:

[tex]e^(6x)(dy/dx + 6y) = 9e^(-6x)e^(6x)[/tex]

This simplifies to:

[tex]e^(6x)(dy/dx) + 6e^(6x)y = 9[/tex]

Now, the left side of the equation is the derivative of the product of y and the integrating factor:
[tex]d/dx(y * e^(6x)) = 9[/tex]

To solve for y, integrate both sides with respect to x:

[tex]∫[d/dx(y * e^(6x))]dx = ∫9dx[/tex]

This results in:

[tex]y * e^(6x) = 9x + C[/tex]

Finally, we solve for y by dividing by e^(6x):

[tex]y = (9x + C)e^(-6x)[/tex]

And that is the general solution to the given differential equation.

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Hi! To solve for the unknown value in the equation "x + 61 + 42 = degrees", follow these steps:

1. Combine the known values (61 and 42) by adding them together: 61 + 42 = 103.
2. Rewrite the equation with the combined values: x + 103 = degrees.
3. To isolate the unknown value (x), subtract 103 from both sides of the equation: x = degrees - 103.

So, the unknown value x can be found by subtracting 103 from the given degrees value.

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The capacity of 1 thumb drive is 4 gigabytes and the capacity of 1 compact disk is 2 gigabytes.

The first step is to form the system of equations that represent the information in the question:

4x + y = 18 equation 1

4x + 3y = 22 equation 2

The elimination method would be used to determined the required values.

Subtract equation 1 from equation 2

2y = 4

y = 4/2

y = 2

Substitute for y in equation 1: 4x + 2 = 18

4x = 18 - 2

4x = 16

x = 16/4

x = 4

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Check the picture below.

[tex]\textit{area of a circular ring}\\\\ A=\pi (R^2 - r^2) ~~ \begin{cases} R=\stackrel{outer}{radius}\\ r=\stackrel{inner}{radius}\\[-0.5em] \hrulefill\\ R=5\\ r=3 \end{cases}\implies A=\pi (5^2-3^2)\implies A\approx 50.27~cm^2[/tex]

Dominic will need to save a minimum of $121 per month to pay for his portion of the first year's tuition.

Dominic's parents will pay 80% of the annual tuition cost, which is:

0.8 x $7,260 = $5,808

So, Dominic will need to pay the remaining 20% of the tuition cost, which is:

0.2 x $7,260 = $1,452

Since Dominic has one year to save his portion of the tuition, he will need to save:

$1,452 / 12 months = $121 per month

Therefore, Dominic will need to save a minimum of $121 per month to pay for his portion of the first year's tuition.

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The probability is approximately 45.4% (rounded to the nearest tenth of a percent).

To find the probability that a randomly selected point within the circle falls in the white area, we need to find the area of the white region and divide it by the total area of the circle.

The total area of the circle is:

A = πr² = π(4 cm)² = 16π cm²

The area of the white region can be found by subtracting the area of the two semicircles from the area of the circle:

White area = A - 2(1/2π(2.5 cm)²) = 16π - 2(4.375π) = 7.25π cm²

So, the probability that a randomly selected point within the circle falls in the white area is:

P(white area) = (white area)/(total area) = (7.25π)/(16π) ≈ 45.4%

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The equation expressing y, as the total number of volumes in the library, in terms of x, the number of mouths after march 2004 is y = 400x + 60,000.

The equation expressing y, as the total number of volumes in the library, in terms of x, the number of mouths after march 2004 is determined as follows;

Using general linear equation;

y = mx + b

where:

The initial volume as at March = 60,000

the rate = 400 volumes / month

The equation is determined as;

y = 400x + 60,000

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Answer:

Step-by-step explanation:

[tex]x^{2}[/tex]=a²+b²

x²=6²+2.5²

x²=36+6.25

x²=42.25

√x=√42.25

x=6.5

Answer:

6.5

Step-by-step explanation:

6^2 + 2.5^2 = c^2

•36 + 6.25 = c^2

•42.25 = c^2

• find square root of 42.25 = 6.5

• 6.5 = C

Answer:

It seems that the three students each calculated the volume of a sphere with a radius of 6 centimeters, but arrived at different results. Diego found the volume to be 288 cubic centimeters, Andre approximated it to be 904 cubic centimeters, and Noah calculated it to be 226 cubic centimeters. It's interesting to see the variation in their calculations.

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Ordered pairs must be placed in the following order: (6, 1), (8, 8), (12, 22). (20, 50). The right answer is D.

According to the assertions, it deals with a number of operations in mathematics.

For the first series, let the number be x, and for the second, let it be y.

The first rule is to multiply by 2, then, beginning with 6, remove 4.

The sequence can be written as 6 is the first number: = 2x - 4

next number = 2(6) - 4

                    = 12-4

                    =  8

The following phrase is thus 8. The following two terms can be written as 12 and 20.

Values of x = 6, 8, 12, 20

The second rule is to add three and then multiply by two, counting backward from one.

= (y + 3)2

First term = 1

Next term = (1 + 3)2

               =  8

The next two words can be acquired in a similar manner.

y = 1, 8, 22, 50

Therefore, ordered pairs must be placed in the following order: (6, 1), (8, 8), and (12, 22). (20, 50). The right answer is D.

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Correct question:

The first rule is to multiply by 2, then subtract 4 starting from 6. The second rule is to add 3, then multiply by 2 starting from 1. What are the first four ordered pairs using the two sequences?

A. (0, 0) (6, 1), (8, 2), (12, 22)

B. (6, 1), (10, 8), (14,22), (22, 50)

C. (6, 1), (8, 8), (12, 20), (20, 45)

D. (6, 1), (8, 8), (12, 22), (20, 50)

The most likely factor to push the price of a company's stock higher is an increase in demand for the company's stock. Option A.

A stock's price will often increase when there is greater demand than there is supply. Various things, such as good news about the company's financial performance, new product releases or innovations, positive analyst reports, or general market trends, can contribute to this increased demand.

The company's financial performance may benefit from a rise in product demand, but if investors do not view it as a key growth engine for the business, it may not necessarily transfer into a higher stock price.

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Answer:

k = - 0.36 or k = 30.36

Step-by-step explanation:

k² - 30k = 11

to complete the square

add ( half the coefficient of the k- term )² to both sides

k² + 2(- 15)k + 225 = 11 + 225

(k - 15)² = 236 ( take square root of both sides )

k - 15 = ± [tex]\sqrt{236}[/tex] ≈ ± 15.36 ( to the nearest hundredth )

add 15 to both sides

k = 15 ± 15.36

Then

k = 15 - 15.36 = - 0.36

or

k = 15 + 15.36 = 30.36

It will take approximately 60.9 days for 650 mg of chromium-51 to decay to 200 mg.

What is Equation ?

An equation is a mathematical statement that shows that two expressions are equal. It typically contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.

The decay of a radioactive substance can be modeled by the following equation:

N(t) = N₀ * [tex](1/2)^{(t/T) }[/tex]

where:

N(t) is the amount of the substance remaining after time t

N₀ is the initial amount of the substance

T is the half-life of the substance

We can use this equation to find how long it will take for 650 mg of chromium-51 to decay to 200 mg.

Let's first find the decay constant (λ) for chromium-51:

λ = ㏒(2) ÷ T = ㏒(2) ÷ 28 = 0.0248 (rounded to 4 decimal places)

Now we can use the equation:

N(t) = N₀ * [tex]e^{(-λ*t)}[/tex]

We know that N₀ = 650 mg and N(t) = 200 mg, so we can solve for t:

200 = 650 * [tex]e^{(-0.0248*t)}[/tex]

Dividing both sides by 650:

0.3077 =   [tex]e^{(-0.0248*t)}[/tex]

Taking the natural logarithm of both sides:

㏒(0.3077) = -0.0248*t

Solving for t:

t = ㏒(0.3077) : (-0.0248) ≈ 60.9 days

Therefore, it will take approximately 60.9 days for 650 mg of chromium-51 to decay to 200 mg.

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Andre's claim that the greatest product possible in the game is 987x65 is incorrect.

While 987x65 is a large product, it is not the greatest possible product in the game. In fact, a larger product can be obtained by multiplying the two largest numbers available in the game. Without knowing the specific rules of the game, it is impossible to determine the exact greatest product, but it is certain that 987x65 is not it.

To elaborate, the game likely has certain constraints or rules that limit the numbers that can be multiplied. It may be possible to combine multiple numbers to create a larger product, or to find a different pair of numbers that yield a larger product. Therefore, without knowing the specifics of the game's rules, it is impossible to determine the greatest possible product.

The actual greatest product possible in the game will depend on the specific rules and constraints that are in place. It may be possible to combine multiple numbers to create an even larger product, or to find a different pair of numbers that yield a larger product. Without knowing the specifics of the game's rules, it is impossible to determine the greatest possible product.

In mathematics, the concept of maximum or greatest products is important and is studied in various areas such as algebra, number theory, and calculus. In real-world applications, maximum products play a critical role in determining profits, yields, and returns on investments in economics and finance. In engineering, the concept of maximum product is used in optimization problems, where the goal is to maximize or minimize a certain function or output.

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The evaluated probability of randomly choosing a  participant dreams in black and white or color is 0.13, under the condition that the given Students are passing from psychology surveyed 200 of their fellow students regarding their dreams.

Probability means the possible chances of an event occurring in a particular time frame. It is a considered a branch of mathematics that deals with the occurrence of a random event.

The value is presented from zero to one. Probability has been induced in math to predict how prone are the events going to occur. The meaning of probability is basically the express  something that is likely to happen.

Black Probability = 4/200=0.02

White Probability = 12/200=0.06

Probability of all other color = 10/200=0.05

So, probability of randomly choosing a participant dreams in black and white or color =0.02+0.06+0.05=0.13

Therefore, the probability of randomly selecting participant dreams in black and white or color = 0.13

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The complete question is

Students majoring in psychology surveyed 200 of their fellow students about their dreams. The results of the survey are shown in the Venn diagram. Let B be the event that the participant dreams in black and white and let C be the event that the participant dreams in color.

What is the probability that a randomly selected participant dreams in black and white or color?

The expression that fits perfect for the given requirement is 5z + 7.50, under the condition that a food truck owner charges z dollars per burrito combo and $1.50 for a side of guacamole.

Here we have to apply the principles of solving algebraic equations, due to the expression provided.

From the  given information, here the food truck owner charges z dollars per burrito combo along with $1.50 for a side of guacamole.

According to the information it is given that the  expression is  5(z+1.50)  which helps to state the total cost of 5 burrito combos and 5 sides of guacamole.

Lets now formulate the expression for the given required equation

= 5(z + 1.50)

= 5z + 7.50.

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A food truck owner charges z dollars per burrito combo and $1.50 for a side of guacamole. The expression 5(z+1.50) represents the total cost of 5 burrito combos and 5 sides of guacamole. What expression also represent the cost of 5 burrito combos and 5 sides if guacamole that cost 1.50 each.

The proportion of this word problem is 6 : 1 where Neil Armstrong weighed approximately 27.5 pounds on the moon.

The proportion of a word problem represents the relationship between two or more quantities. In this case, the proportion can be set up as:

Weight on Earth : Weight on Moon = 6 : 1

Using the information provided in the problem, we know that Neil Armstrong weighed 165 pounds on Earth. We can use this information to find his weight on the moon by setting up a proportion:

165 : x = 6 : 1

where x represents his weight on the moon. To solve for x, we can cross-multiply and simplify:

165 * 1 = 6 * x

x = 165/6

x ≈ 27.5

Therefore, Neil Armstrong weighed approximately 27.5 pounds on the moon.

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Step-by-step explanation:

180° + 42° + x = 360°

222° + x = 360°

x = 138°

Answer:

138

Step-by-step explanation:

Since a circle is 360 degrees and it is split in half, each half would equal 180 degrees so you would subtract 42 from 180

The volume of the larger cone will be 48 cm³.

This is because when a shape is enlarged by a scale factor of 2, the volume is increased by a factor of 2³ (or 8). So, 6 x 8 = 48.


When we enlarge a shape by a scale factor, we are multiplying all of its dimensions by that factor. In the case of a cone, this means that we are increasing the radius and the height of the cone by a factor of 2.

We can use the formula for the volume of a cone to find out how the volume changes when we enlarge it. The formula for the volume of a cone is V = (1/3)πr²h, where r is the radius and h is the height.

If we multiply the radius and the height of the cone by 2, we get a new cone with a radius of 2r and a height of 2h. Plugging these new values into the formula for the volume of a cone, we get:

V' = (1/3)π(2r)²(2h) = (1/3)π(4r²)(2h) = (8/3)πr²h

We can simplify this expression by multiplying the original volume by 8/3:

V' = (8/3) x 6 = 48

So the volume of the larger cone is 48 cubic centimeters.

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The derivatives of the given functions are:

A) h'(x) = (1/2)√xen(x)[2+In(x)]

B) h'(x) = (1/x) - V2V

C) h'(x) = (2/x) + 2

D) h'(x) = 0

A) To find the derivative of h(x) = √xen(x), we use the product rule of differentiation. Let u = √x and v = en(x).

Then, h(x) = uv, and h'(x) = u'v + uv'.

We have u' = (1/2)x^(-1/2) and v' = en(x)(1/x).

Substituting the values, we get h'(x) = (1/2)√xen(x)[2+In(x)].

B) To find the derivative of h(x) = In(x) + V2V, we use the sum rule of differentiation.

Using the properties of logarithms, we rewrite the function as h(x) = In(x) + (1/2)ln(x).

Taking the derivative, we get h'(x) = (1/x) - V2V.

C) To find the derivative of h(x) = V2 In(x) + 2, we use the sum rule of differentiation.

Taking the derivative, we get h'(x) = (2/x) + 2.

D) To find the derivative of h(x) = In(30) + 2ln(x), we use the sum rule of differentiation.

Taking the derivative, we get h'(x) = 0, since the derivative of a constant is always zero.

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Therefore, the equation of the line that passes through the points (-3, 6) and (-5, 9) in slope-intercept form is:

y = -3/2 x + 3/2

Step-by-step explanation:

To find the equation of the line that passes through the points (-3, 6) and (-5, 9) in slope-intercept form (y = mx + b), we need to first find the slope of the line using the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) = (-3, 6) and (x2, y2) = (-5, 9).

m = (9 - 6) / (-5 - (-3))

m = 3 / (-2)

m = -3/2

Now that we have the slope, we can use either of the two given points and the slope to find the y-intercept (b) of the line:

y = mx + b

6 = (-3/2)(-3) + b

6 = 9/2 + b

b = 6 - 9/2

b = 3/2

The area of the playground include the following: 900 square yards.

In Mathematics and Geometry, the area of a regular polygon can be calculated by using this formula:

Area = (n × s × a)/2

Where:

In Mathematics and Geometry, the area of a parallelogram can be calculated by using the following formula:

Area of a parallelogram, A = base area × height

Area of playground, A = 45 × 20

Area of a playground, A = 900 square yards.

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D. Both the height and weight distribution are symmetric about the mean.

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With the surface area of the square pyramid 84 square inches and side length of the base is 6, the value of x is 4 inches, by assuming x as the slant height of the square pyramid.

Assuming that x refers to the slant height of the square pyramid, we can use the formula for the surface area of a square pyramid to solve for x:

Surface area of a square pyramid = base area + (0.5 x perimeter of base x slant height)

Since the base of the square pyramid is a square with side length 6,

the base area is 6² = 36 square inches.

The perimeter of the base is 4 times the side length, so it is 4 x 6 = 24 inches.

Substituting these values into the formula and simplifying, we get:

84 = 36 + (0.5 x 24 x x)

84 - 36 = 12x

48 = 12x

x = 4

Therefore, the value of x, the slant height of the square pyramid, is 4 inches.

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