Use the Pythagorean theorem to find the unknown side of the right triangle.
I need help please

Required purchase price is $120 and advertised price is $300.

How much did Danielle purchase the antique dresser for?

Let's assume that Danielle purchased the antique dresser for $x.

According to the problem, she advertised it for 250% of her purchase price, which means she advertised it for,

250% of x = 2.5x

She sold the dresser for 15% less than the advertised price of 2.5x, so she sold it for,

(1 - 0.15) × 2.5x = 2.125x

We know that the selling price was $255, so we can set up the equation,

2.125x = 255

Solving for x,

x = 120

Therefore, Danielle purchased the antique dresser for $120.

What was her initial advertised price?

To find the initial advertised price, we can plug x = 120 into the expression 2.5x,

2.5x = 2.5 × 120 = 300

So, the initial advertised price was $300.

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The number of parents you have to sample is calculated as: 5918

The formula for the margin of error here is:

E = z(σ/√n)

where:

E is margin of error

σ is standard deviation

n is sample size

We are given:

E = 2

σ = $78.5

At 95% Confidence Level, z = 1.96

Thus:

2 = 1.96(78.5/√n)

Square both sides to get:

4 = 23672.9/n

n = 23672.9/4

n = 5918

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The range of [tex]f(x) = \frac{1}{3x+4}[/tex] is all real numbers except for 0 i.e. {y ∈ R, y ≠ 0} and there is no x-intercept in f(x) = 1/(3x - 4)

The range of [tex]f(x) = \frac{1}{3x+4}[/tex] is all real numbers except for 0.

To see this, note that the denominator of [tex]f(x) = \frac{1}{3x+4}[/tex], can take any real value except -4/3, since division by zero is undefined.

Therefore, f(x) can take any value except 0, which means the range of f(x) is {y ∈ R, y ≠ 0}

The reciprocal of a is 1/a

From the list of options, we have

f(x) = 1/(x + 3)

The reciprocal is x + 3 and this is a linear function

So, the reciprocal of a function that is linear is f(x) = 1/(x + 3)

The reciprocal function of the form f(x) = 1/x has a vertical asymptote at x = 0.

Similarly, the reciprocal function of the form f(x) = 1/(ax + b) has a vertical asymptote at x = -b/a.

Comparing the given functions with the above form, we can see that:

f(x) = 1/(x + (5/2)) is of the required form with a = 1 and b = 5/2.

So, it has a vertical asymptote at x = -(5/2)/1 = -5/2.

Therefore, the function with a vertical asymptote at x = -5/2 is option (a), f(x) = 1/(x + (5/2)).

The correct answer is (d) All of the above, as all functions a, b and c have a horizontal asymptote at y = 0, when solved by graphs

As x approaches (5/3)^+ (from the right-hand side), the function f(x) approaches positive infinity.

So, the true statement is (b) f(x) -> oo

Given that

f(x) = 1/(3x - 4)

So, we have

1/(3x - 4) = 0

This gives

1 = 0

This means that there is no x-intercept.

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The end behavior of f(x) is described as follows:

The end behavior of a function is given by the limit of the function is the input x goes to either negative infinity or positive infinity.

The function for this problem is given as follows:

f(x) = 4(5/7)^x.

It is an exponential function with base with absolute value less than 1, hence the end behavior is given as follows:

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Answer: The regular price of the sofa is $705.71.

Step-by-step explanation:

Regular price = Sale price / (1 - Discount rate)

* 65% = 0.65

Regular price = $247 / (1 - 0.65) = $247 / 0.35 = $705.71

Every subgroup of Z is cyclic and is generated by a unique nonnegative integer. This property makes Z a particularly simple and well-behaved group for studying group theory.

Group theory is a branch of abstract algebra that studies mathematical structures called groups. Group theory provides a powerful framework for studying symmetry, structures, and transformations in various areas of mathematics, physics, chemistry, and other fields of science. It has applications in cryptography, coding theory, crystallography, quantum mechanics, and many other areas of science and engineering.

The set of integers subject to addition, or Z, is an example of an abelian group in group theory. A subset that also forms a group by addition is referred to as a subgroup of Z. It turns out that every Z subgroup is cyclic, i.e., created by a single element.

Let H be a subgroup of Z to be more precise. H is closed under addition since Z is an additive group, and it includes the identity element (0). We can demonstrate that H is produced by a, which means that every element in H can be written as a multiple of a, by looking at the lowest positive integer in H (if any), indicated as a. Thus, H becomes a cyclic subgroup with an as its generator.

Moreover, this generator a is exclusive to H. Assume that H contains a second positive integer b that likewise yields H. We can demonstrate that the set of multiples of a and b is indeed the same set, which suggests that a and b produce the same subgroup H. As a result, a = b, and H has a unique generator.

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The coefficient of the squared term in the parabola's equation is: -5

We are given the following information in the question:

Vertex of parabola: (2,-4)

Also, (x = 3, y = -1) lies on the parabola.

The general equation of parabola is of the form:

y = a(x - h)² + k

where:

(h, k) is the vertex of the parabola

Putting h = 2, k = -4 in the equation, we get:

y = a(x - 2)² - 4

Now, putting x = -3 and y = -3 in the above equation, we get:

-3 = a(-3 - 2)² - 4

a = 1/25

The second parabola is of the form:

x = a(y + 4)² + 2

At -3, -3:

-3 = a + 2

a =-5

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Answer:Let's use the formula for the area of a sector to find the radius of the sector:

Area of sector = (1/2) * radius^2 * angle in radians

We know the area of the sector is 75pi/16 and the angle in radians is 3pi/8, so we can plug those values in and solve for the radius:

75pi/16 = (1/2) * radius^2 * 3pi/8

Simplifying:

75pi/16 = (3/16) * radius^2 * pi

Multiplying both sides by 16/3pi:

25 = radius^2

Taking the square root of both sides:

radius = ±5

Since a radius can't be negative, we have:

radius = 5

Therefore, the radius of the sector is 5 units.

Answer:

y = - [tex]\frac{1}{5}[/tex] x + 6

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 5x + 1 ← is in slope- intercept form

with slope m = 5

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{5}[/tex]

the y- intercept c = 6 , then

y = - [tex]\frac{1}{5}[/tex] x + 6 ← equation of line A

The expansion will be:

a) (x-6) (x+7) = x² + x - 42

b) (2x-3)(5x-4) = 10x² - 23x + 12

c (x+3)(x+5) = x² + 8x + 15

The factorization will be:

a) 2(x+3)

b) 3x(3x-4)

c) 2(12x² + 8x-1)

An equation simply has to do with the statement that illustrates the variables given.

In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

Therefore, the expansion will be:

a) (x-6) (x+7) = x² + x - 42

b) (2x-3)(5x-4) = 10x² - 23x + 12

c (x+3)(x+5) = x² + 8x + 15

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Based on the data, the appropriate 95% confidence interval is (0.039, 0.361), which is closest to the answer option (0.038, 0.362).

A specific type of ordinary dispersion with a mean of 0 and a standard deviation of 1 is known as a standard typical conveyance.

We may use the following calculation to create a 95% confidence interval for the variation in the proportion of students taking an AP class in each region:

(East - West) ± z*√[(East proportion)(1 - East proportion)/East sample size + (West proportion)(1 - West proportion)/West sample size]

where z* denotes the critical value of the standard normal distribution for the desired level of confidence, East proportion denotes the percentage of East students who took at least one AP class, West proportion denotes the percentage of West students who took at least one

AP class, East sample size denotes the sample size of East students, and West sample size denotes the sample size of West students.

Using the given data, we have East proportion = 20/50 = 0.4, West proportion = 16/80 = 0.2, East sample size = 50, and West sample size = 80.

The crucial value z* for a 95% confidence level can be calculated using a conventional normal distribution table or calculator and is roughly 1.96.

after entering each value into the formula:

(0.4 - 0.2) ± 1.96√[(0.4)(0.6)/50 + (0.2)(0.8)/80]

= 0.2 ± 0.161

As a result, the answer choice (0.038, 0.362) comes the closest to the right 95% confidence interval based on the data, which is (0.039, 0.361).

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The restrictions on the expression are x = -9/5 and x = -4 and the simplified expression is (2x - 1)/(x + 4)

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

[tex]\frac{10x^2 + 13x - 9}{5x^2 + 29x + 36}[/tex]

When the above expressions are factorized, we have

[tex]\frac{10x^2 + 13x - 9}{5x^2 + 29x + 36} = \frac{(5x + 9)(2x - 1)}{(5x + 9)(x + 4)}[/tex]

To calculate the restrictions, we set the denominator to 0

So, we have

(5x + 9)(x + 4) = 0

Evaluate

x = -9/5 and x = -4

So, the restrictions are x = -9/5 and x = -4

Next, we simplify the expression

[tex]\frac{10x^2 + 13x - 9}{5x^2 + 29x + 36} = \frac{(5x + 9)(2x - 1)}{(5x + 9)(x + 4)}[/tex]

Cancel out the common factors

[tex]\frac{10x^2 + 13x - 9}{5x^2 + 29x + 36} = \frac{2x - 1}{x + 4}[/tex]

Hence, the simplified expression is (2x - 1)/(x + 4)

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Answer: 2x

Step-by-step explanation: Separate variables from numbers, 4x-2x=2x, and 1-1=0. Therefore, the answer is 2x.

Answer:

2(x+1)

Step-by-step explanation:

Add you 1s together, than take a 2x out and that vies you 2 on the outside 2x/2= x and 2/2= 1 which gives you your answer.

The graph of the functions (A) y=x+5 (B) y=-(x+5)  and  (C) y=|x+5| are added as an attachment

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

To mark all points on the same coordinate plane, we simply plot the graphs of the three functions on the same graph

Using the above as a guide, we have the following:

The graph of the functions (A) y=x+5 (B) y=-(x+5)  and  (C) y=|x+5| are added as an attachment

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Answer:

Katherine needs 1 unit of insulin for 15 g of carbohydrates.

Step-by-step explanation:

To find out how many units of insulin Katherine should inject for her lunch which has 60 g of carbohydrates, we can use the following proportion:

1 unit : 15 g = x units : 60 g

where x is the number of units of insulin Katherine should inject.

To solve for x, we can cross-multiply:

1 unit * 60 g = 15 g * x units

60 = 15x

x = 4

Therefore, Katherine should inject 4 units of insulin for her lunch.

By performing the division, the jogging track is 0.45 miles long.

Division is a mathematical operation that involves the splitting of a quantity into equal parts or groups.

The problem asks us to convert a length of 792 yards to miles. To do this, we need to use a conversion factor to relate yards to miles. We know that there are 1760 yards in a mile, so we can use this relationship to convert the length in yards to miles.

To convert yards to miles, we divide the length in yards by the number of yards in a mile. This is because we want to cancel out the units of yards and be left with the corresponding number of miles.

So, 792 yards / 1760 yards/mile gives us the length of the jogging track in miles. We can simplify this expression by performing the division to get the result of 0.45 miles. Therefore, the jogging track is 0.45 miles long.

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a) The 95% confidence interval for a sample size of 34 is given as follows: (17.26, 20.34).

b) The 95% confidence interval for a sample size of 61 is given as follows: (17.67, 19.63).

c) Increasing the sample size, the margin of error decreases.

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the following rule:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which the variables of the equation are presented as follows:

The margin of error is defined as follows:

[tex]M = t\frac{s}{\sqrt{n}}[/tex]

From this we get that it is inversely proportional to the square root of the sample size, hence if we increasing the sample size, the margin of error will decrease.

The mean and the standard error are given as follows:

[tex]\mu = 18.8, s = 4.4[/tex]

For a sample size of 34, we have 33 degrees of freedom, hence, using a t-table, the critical value is given as follows: 2.0345.

Hence the bounds of the interval are given as follows:

For a sample size of 61, we have 60 degrees of freedom, hence, using a t-table, the critical value is given as follows: t= 2.

Hence the bounds of the interval are given as follows:

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Answer:

B. chocolate-peanut butter cups and chocolate-caramel bites

Step-by-step explanation:

Chocolate-peanut butter cups cost $11.46 per pound, so one-half pound costs $5.73.

Chocolate-caramel bites cost $9.62 per pound, so one-half pound costs $4.81.

$5.73 + $4.81 = $10.54, so B is the correct answer.

The area of the irregular pentagon is determined using it's coordinates. Its area is: 30.5

First indicate the coordinates:

A (1,4)

B(4, 3)

C(4, -3)

D(-1-2)

E(-1.5, 2)

Using the shoe lace formula:

Area = (1/2) | (x1y2 + x2y3 + ... + xny1) - (y1x2 + y2x3 + ... + ynx1) |

where n is the number of vertices, and

(x1,y1), (x2,y2), ..., (xn,yn) are the coordinates of the vertices in clockwise or counterclockwise order.

Plugging in the values,

Area = Area = (1/2) | (1*3 + 4*(-3) + 4*2 + (-1.5)*(-2) + (-1)*4) - (4*3 + 4*(-1.5) + (-1)*(-3) + 3*2 + (-2)*1) |

Area = 30.5

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Using the combination formula, it is found that there are 3300 ways to choose the songs.

The order in which the musics are chosen is not important, hence the combination formula is used to solve this question.

What is the combination formula?

��,�Cn,x is the number of different combinations of x objects from a set of n elements, given by:

��,�=�!�!(�−�)!Cn,x=x!(n−x)!n!

For the rock songs, we have three from a set of eleven, hence:

�11,3=11!3!8!=165C11,3=3!8!11!=165

For the alternative songs, we have four from a set of five, hence:

�5,4=5!4!1!=5C5,4=4!1!5!=5

For the rap songs, we have three from a set of four, hence:

�4,3=4!3!1!=4C4,3=3!1!4!=4

Since the songs are independent, the total number of ways is given by:

�=165×5×4=3300T=165×5×4=3300

hope this helps you

Using the combination formula, it is found that there are 3300 ways to choose the songs.

The order in which the musics are chosen is not important, hence the combination formula is used to solve this question.

What is the combination formula?

��,�Cn,x is the number of different combinations of x objects from a set of n elements, given by:

��,�=�!�!(�−�)!Cn,x=x!(n−x)!n!

For the rock songs, we have three from a set of eleven, hence:

�11,3=11!3!8!=165C11,3=3!8!11!=165

For the alternative songs, we have four from a set of five, hence:

�5,4=5!4!1!=5C5,4=4!1!5!=5

For the rap songs, we have three from a set of four, hence:

�4,3=4!3!1!=4C4,3=3!1!4!=4

Since the songs are independent, the total number of ways is given by:

�=165×5×4=3300T=165×5×4=3300

hope this helps you

Answer:

D. 67 square inches

Step-by-step explanation:

The area of a 16-inch pizza is:

A = πr^2 = π(8)^2 = 64π

Since the pizza was cut into 12 equal slices, each slice has an area of:

64π / 12 = 16π/3

Each boy ate 4 slices, so the total area of pizza each boy ate is:

4(16π/3) = 64π/3

Rounding to the nearest whole square inch, we have:

64π/3 ≈ 67 square inches

Therefore, the answer is D. Each boy ate approximately 67 square inches of pizza.

Hope this helps!

Answer:

32

Step-by-step explanation:

m∠S = tan⁻¹(5/8) = 32⁰

To find MR, we take the derivative of the demand curve with respect to Q:

MR = dP/dQ = 900 - 0.06Q

To find MC, we need to take the derivative of the quadratic cost function with respect to Q:

C(Q) = 500 + 10Q + 0.005Q^2

MC = dC/dQ = 10 + 0.01Q

To find AC, we divide the total cost by the quantity:

AC = C(Q)/Q = (500 + 10Q + 0.005Q^2)/Q = 500/Q + 10 + 0.005Q

To find P, we use the demand curve and solve for Q:

P = 900 - 0.03Q

Q = (900 - P)/0.03

Explanation:

To find P, we use the demand curve and solve for Q:

P = 900 - 0.03Q

Q = (900 - P)/0.03

To find MR, we take the derivative of the demand curve with respect to Q:

MR = dP/dQ = 900 - 0.06Q

Now we can graph MC, AC, P, and MR:

|

P  |        /MR

  |       /

  |      /

  |     /

  |    /

  |   /

  |  / AC

  | /

MC |/

  |------------- Q

Note:

The graph is a rough sketch and not drawn to scale. The MC curve is upward-sloping, the AC curve is U-shaped, the P curve is downward-sloping, and the MR curve lies below the P curve and is also downward-sloping.

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A square prism has the following characteristics:

Number of faces: 6

Number of vertices: 8

Number of edges: 12

A cuboid has the following characteristics:

Number of faces: 6

Number of vertices: 8

Number of edges: 12

What is meant by square prism?

A square prism is a three-dimensional geometric shape with two parallel square bases and rectangular faces connecting the two bases. It has 8 vertices, 12 edges, and 6 rectangular faces.

What is meant by cuboid?

A cuboid is a three-dimensional geometric shape with six rectangular faces, where opposite faces are equal in size and shape. It has 8 vertices, 12 edges, and 6 rectangular faces. A cuboid is also known as a rectangular prism.

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The values of x and y in the given figure are 10.5 and 15 respectively in the quadrilateral

We have to find the values of x and y in quadrilateral

4y+14+7y+1=180

Combine like terms

11y+15=180

Subtract 15 from both sides

11y=180-15

11y=165

Divide both sides by 11

y=15

The value of y is 15

Now 7x+1+105=180

7x+106=180

Subtract 106 from both sides

7x=180-106

7x=74

Divide both sides by 7

x=10.5

Hence, the values of x and y in the given figure are 10.5 and 15 respectively

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The new angular speed, ω₂, is four times the initial angular speed, ω₁.

To solve this problem, we can use the conservation of angular momentum. The initial and final angular momenta should be equal:

I₁ω₁ = I₂ω₂

Where I₁ and I₂ are the initial and final moments of inertia, respectively.

Assuming the particles are connected in a circular arrangement, the moment of inertia can be calculated using:

I = n * m * r²

Where n is the number of particles and r is the distance from the center of rotation.

Now we have:

(n * m * L²)ω₁ = (n * m * (0.5L)²)ω₂

Simplifying the equation, we get:

ω₂ = 4ω₁

So the new angular speed, ω₂, is four times the initial angular speed, ω₁.

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A system of small particles, each with mass m, is connected by light strings of length L. The system is rotating at an initial angular speed ω₁. If the strings are shortened to 0.5L, what is the new angular speed, ω₂?

Yes, an answer can be incorrect even if it looks reasonable

Yes, an answer can be incorrect even if it looks reasonable. This is because an answer might seem reasonable on the surface but may not be correct due to various reasons such as calculation errors, incorrect assumptions, or misinterpretation of the problem.

For instance, in a math problem that involves converting units of measurement, a student may have calculated the answer and arrived at a number that seems reasonable.

However, if the student used the wrong conversion factor or made an error in calculations, the answer would be incorrect despite appearing reasonable.

Similarly, in a word problem, an answer may seem reasonable but might not take into account all the given information, resulting in an incorrect solution.

Therefore, it is important to double-check answers and verify that they make sense in the context of the problem and that all the given information has been taken into account to ensure accuracy.

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The solution is : The measure of angle ADC is 115°.

Here, we have,

Let A, B, C represent the vertex angle measures of ΔABC.

Then the sum of angles in ΔADC is ...

 A/2 +∠ADC + C/2 = 180°

Multiplying by 2 gives ...

 A + C + 2×∠ADC = 360°

From the given information, we know ...

 A + C + 50° = 180° . . . . . sum of angles in ΔABC

This lets us write an expression for (A +C):

 A + C = 130° . . . . . . . . subtract 50° from the previous equation

Substituting for A+C, we get ...

 130° + 2×∠ADC = 360°

 2×∠ADC = 230° . . . . . . . . . subtract 130°

 ∠ADC = 115° . . . . . . . . . . . divide by 2

The measure of angle ADC is 115°.

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complete question:

The measure of an angle ABC is 50°,AD bisects angle BAC, and DC bisects angle BCA. The measure of angle ADC is what?​