Can someone please help me with this problem involving Proofs involving similarity in right triangles.

Can Someone Please Help Me With This Problem Involving Proofs Involving Similarity In Right Triangles.

Answers

Answer 1

The statement and reason to complete the proof that TU² = TV · TW include the following:

Statement                                  Reason_____

TU² = TV · TW                        cross product.

What is the Tangent Secant Theorem?

In Mathematics and Geometry, the Tangent Secant Theorem states that if a secant segment and a tangent segment are drawn to an external point outside a circle, then, the product of the length of the external segment and the secant segment's length would be equal to the square of the tangent segment's length.

By applying the Tangent Secant Theorem to the given triangles after the definition of similarity step, we would cross-multiply as follows:

TU/TW = TV/TU                  definition of similarity

TU(TU) = TV(TW)                    cross product.

TU² = TV · TW                        cross product.

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Related Questions

0. A good is worth K2 500 cash. It can also be purchased by K200 deposit and monthly instalments of K103.50 for 2 years in hire purchase. What is the interest charged on hire purchase? (1 mark)​

Answers

If good is worth K2 500 cash and it can also be purchased by K200 deposit and monthly instalments of K103.50 for 2 years in hire purchase, the interest charged on hire purchase is K184.

To find the interest charged on the hire purchase, we need to compare the total amount paid through hire purchase to the cash price of the good.

The monthly instalments are K103.50 and the hire purchase term is 2 years, so the total amount paid through hire purchase is:

K103.50/month × 24 months = K2,484

In addition, there is a deposit of K200, so the total amount paid through hire purchase and deposit is:

K2,484 + K200 = K2,684

Since the cash price of the good is K2,500, the interest charged on hire purchase is:

K2,684 - K2,500 = K184

In summary, if someone wants to purchase the good through hire purchase, they need to pay a deposit of K200 and monthly instalments of K103.50 for 2 years. The total amount paid through hire purchase and deposit is K2,684, and the interest charged on hire purchase is K184.

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Given E is the midpoint of AC. complete the flowchart proof below. Note that the
last statement and reason have both been filled in for you.

Answers

1. The reason is that E bisects line AC and is perpendicular to line AC.

2. The reason is that the angles are alternate interior angles.

What are alternate interior angles?

Alternate interior angles are made when a transversal joins two co-planar lines. These can be found on the inner side of the parallel lines, but on their transverse sides. The transversal goes through the two co-planar lines at two separate points.

1. We are given a statement that E is the midpoint of AC.

The reason is that E bisects line AC and is perpendicular to line AC, therefore it is the mid point of AC.

2. We are given that ∠D ≅ ∠B.

The reason is that DC ║ AB. We know that when two lines are parallel, alternate interior angles are equal.

The angle ∠D and ∠B are alternate interior angles and therefore they are equal.

Hence, the required solutions have been obtained.

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The complete question has been attached below.

Consider the following function.

g(x, y) = e^(− 4x^2 + 7y^2 + 14√8y

(a) Find the critical point of g.
If the critical point is (a, b) then enter 'a,b' (without the quotes) into the answer box.
(b) Using your critical point in (a), find the value of D(a, b) from the Second Partials test that is used to classify the critical point.
(c) Use the Second Partials test to classify the critical point from (a).

Answers

The critical point of the function g is (0,0), the value of D(0,0) is -6272, and the critical point is a saddle point.

(a) To find the critical point of g, we need to find the partial derivatives of g with respect to x and y, and set them equal to zero:

[tex]∂g/∂x = -8xe^(-4x^2+7y^2+14√8y) = 0[/tex]

[tex]∂g/∂y = 14ye^(-4x^2+7y^2+14√8y) + 14√8e^(-4x^2+7y^2+14√8y) = 0[/tex]

From the first equation, we get x = 0. Substituting this value into the second equation, we get:

[tex]14ye^(7y^2+14√8y) + 14√8e^(7y^2+14√8y) = 0[/tex]

Dividing both sides by [tex]14e^(7y^2+14√8y)[/tex], we get:

y + √8 = 0

Thus, the critical point of g is (0, -√8).

(b) To find the value of D(a,b) from the Second Partials test, we need to compute the second-order partial derivatives of g with respect to x and y:

[tex]∂^2g/∂x^2 = 32x^2e^(-4x^2+7y^2+14√8y) - 8e^(-4x^2+7y^2+14√8y)[/tex]

[tex]∂^2g/∂y^2 = 98y^2e^(-4x^2+7y^2+14√8y) + 196√8ye^(-4x^2+7y^2+14√8y) + 686e^(-4x^2+7y^2+14√8y)[/tex]

[tex]∂^2g/∂x∂y = -112xye^(-4x^2+7y^2+14√8y) - 196√8xe^(-4x^2+7y^2+14√8y)[/tex]

At the critical point (0, -√8), we have:

[tex]∂^2g/∂x^2 = -8[/tex]

[tex]∂^2g/∂y^2 = 686[/tex]

[tex]∂^2g/∂x∂y = 0[/tex]

Therefore, D(0, -√8) =[tex](∂^2g/∂x^2)(∂^2g/∂y^2) - (∂^2g/∂x∂y)^2[/tex] = (-8)(686) - [tex](0)^2[/tex] = -5488.

(c) Since D(0, -√8) is negative, and [tex]∂^2g/∂x^2[/tex] is negative at the critical point, the Second Partials test tells us that (0, -√8) is a saddle point.

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Your friend incorrectly says that the reflection of EFG to its image E'F'G' is a reflection across the x-axis

a. What is your friend’s mistake

b. What is the correct description of the reflection

Answers

a. Your friend's mistake is that the reflection of EFG to its image E'F'G' is not a reflection across the x-axis.

b. The correct description of the reflection is a reflection across the line y = x.

What is The correct description of the reflection

The correct description of the reflection are:

a. Your friend's mistake is that the reflection of EFG to its image E'F'G' is not a reflection across the x-axis.

b. The correct description of the reflection is a reflection across the line y = x.

This is because the line of reflection is the perpendicular bisector of the segment connecting each point to its image. In this case, the segment connecting E to E' has a slope of 1 (since it is a diagonal line), so the perpendicular bisector of this segment must have a slope of -1.

The line with slope -1 passing through the midpoint of this segment (which is the point on the line y = x) is the line of reflection. Therefore, the reflection of EFG to its image E'F' is a reflection across the line y = x, not the x-axis.

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An electronic book has a file size of 2.4 megabytes what is the file size in megabytes of 16 of these electronic books?

Answers

Answer:

38.4 megabytes for 16 electronic books

Step-by-step explanation:

2.4 megabytes per electronic book

2.4 megabytes x 16 electronic books = 38.4 megabytes

What's the area of the park in square units

Answers

There is nothing to work off of in this question, please repost with a picture of the problem or describe the image with the values so we can help you:)

A garden is being built in the shape below. How many square yards of space will the garden occupy?

Answers

the answer would be 16 yards

SOME PLEASE HELP IVE BEEN STRUGGLING!!!!!!! MIDDLE SCHOOL MATH BTW !!!!

In the figure below, what is m∠ABE, in degrees?

PLEASE LOOK AT THE PICTURE BELOW!!!!! I REALLY NEED HELP!!! SHOW WORK!!!!!!!!!!!!

Answers

This is a matter of supplementary angles, where two angles add up to 180° or form a straight line.

Angle EBC and ABE are supplementary angles.

So:

Take the angle of EBC ( 63° ) and subtract this value from 180°:

180° - 63° = 117°

Hope this helps!

1-5 above involves dividing a whole number by a fraction less than 1
What happens to the quotients compared to the dividends? Explain your answer

Answers

Answer:

The quotient will have a larger value than the dividend.

Step-by-step explanation:

Example:

15 ÷ [tex]\frac{1}{2}[/tex]

[tex]\frac{5}{\frac{1}{2} }[/tex]

[tex]\frac{\frac{15}{1} }{\frac{1}{2} }[/tex]  x [tex]\frac{\frac{2}{1} }{\frac{2}{1} }[/tex] = [tex]\frac{\frac{30}{1} }{1}[/tex] = 30

Our quotient of 30 has a larger value than the dividend of 15.

Helping in the name of Jesus.

HELP ASAP PLS HELP ASAP ASAP ASAP
A net of a rectangular pyramid is shown.

A net of a rectangular pyramid with a base with dimensions of 14 inches by 17 inches. The two larger triangular faces have a height of 12 inches. The smaller triangular face has a height of 12.9 inches.

What is the surface area of the pyramid?

311.3 in2
384.6 in2
441.3 in2
622.6 in2

Answers

The rectangular pyramid's surface area therefore approximates 622.6 in2, which is closest to option 4.

what is rectangle ?

A rectangular is a four-sided polygon in geometry with opposite sides that are parallel and of equal length. It contains four diagonals that cross one another at 90 degree angles. A rectangle is also a rhombus, a rectangle with all sides of equal length, and a parallelogram, a trapezoid with the opposite sides parallel. In the formula A = l w, where l stands for length and w for width, the area of such a rectangle is determined. P = 2l + 2w is a formula that yields the perimeter. In the fields of engineering, design, and architecture, rectangles are used frequently.

given

The Pythagorean theorem can be used to determine the base of the smaller triangle, which equals the pyramid's slant height.

Slant height is equal to (12.5 + 12.9) in (rounded to one decimal place)

Hence, the smaller triangle's area is:

A(small triangular) = 1/2 x 17.8 in, 17.8 in, and 12.9 in, or 115.1 in2.

By summing the areas of all the pyramid's faces, we can determine the overall surface area of the structure:

A (base) + 2 x A (big triangle) + A Equals total surface area (small triangle)

Surface area total = 238 in2 + 2 x 84 in2 + 115.1 in2

Surface area total = 622.1 in2 (rounded to one decimal place)

The rectangular pyramid's surface area therefore approximates 622.6 in2, which is closest to option 4.

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6 cm 10 m 3 m 4 m The front of Mr. Smith's house is shown in the picture above. (a) What is the area of the shaded triangle?​

Answers

The base and height could also be converted to meters to maintain consistency in units, resulting in an area of 0.3 square meters

What is triangle?

A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.

To calculate the area of the shaded triangle, we can use the formula for the area of a triangle:

Area = 1/2 * base * height

Given that the base of the triangle is the width of the rectangle, which is 6 cm, and the height is the diagonal line connecting the top corners of the rectangle, which is 10 m, we can now substitute these values into the formula and calculate the area of the shaded triangle.

Converting the height to centimeters for consistency:

Height = 10 m * 100 cm/m = 1000 cm

Plugging in the values:

Area = 1/2 * 6 cm * 1000 cm = 3000 cm²

So, the area of the shaded triangle is 3000 square centimeters. Please note that it's important to use consistent units when performing calculations, so make sure to convert measurements to the same unit if necessary. In this case, we converted the height to centimeters to match the units of the base, which was given in centimeters.

Therefore, the base and height could also be converted to meters to maintain consistency in units, resulting in an area of 0.3 square meters.

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Find area and perimeter

Answers

Answer:

Area = π+4

Perimeter = 4π+4

Step-by-step explanation:

1) The two semi-circles make one whole circle

2) one square.

Area

1) formula for the area of a circle = [tex]r^{2}\pi[/tex]

The diameter is 2 which means the radius is 1

so the area of the circle is equal to π

2) to find the area of a square you multiply the sides

2x2=4

So to find the total area you add [tex]\pi +4[/tex]

which leaves us with [tex]\pi +4[/tex]

Perimeter

1) the formula for the perimeter of a circle = [tex]2\pi r[/tex]

Since the radius is 1

the perimeter of both circles is 4π

2) to find the perimeter of only part of the square (two sides), you have to add them together

2+2=4

So the total perimeter is 4π+4

Adama rolls a die with faces labeled 1 through 10. If he rolls the die 40 times how many times would he expect it to land on a number less than 10?

Answers

Adama can expect the die to land on a number less than 10 about 36 times in 40 rolls.

What is probability?

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is essentially what probability means.

The die has 10 faces, with numbers 1 through 10, but we are interested in the number of times it will land on a number less than 10. That means, there are 9 possible outcomes for each roll to be less than 10.

The expected number of times the die will land on a number less than 10 can be calculated by multiplying the probability of getting a number less than 10 on each roll by the total number of rolls.

The probability of getting a number less than 10 on each roll is 9/10, since there are 9 faces with numbers less than 10 out of the total of 10 faces.

Therefore, the expected number of times the die will land on a number less than 10 is:

E = (9/10) x 40 = 36

Therefore, Adama can expect the die to land on a number less than 10 about 36 times in 40 rolls.

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☆ 36 times.

— your in college ? im in seventh grade and got this question !

A rectangular placemat is 18 inches long and 12 inches wide. What is the area of ​​this tablecloth in square inches?

a. 216
b. 60
c. 54
d. 900

Answers

In a rectangle, there are 2 pairs of congruent sides. Therefore, the area of a rectangle can be found using:

[tex]\text{A}=\text{l} \times \text{w}[/tex]

We know that the length is 18 and the width is 12, so we can multiply 18 in for l, and 12 in for w.

[tex]\text{A}=\text{18} \times \text{12}[/tex]

Multiply the numbers together

[tex]\text{A}=216[/tex]

So, the area is 216 inches.

To find the area of a rectangular placemat, you multiply the length by the width. In this case, the length is 18 inches and the width is 12 inches. Therefore, the area of the tablecloth is:

Area = Length × Width

Area = 18 inches × 12 inches

Area = 216 square inches

So, the correct answer is option a. 216.

Claim: The mean pulse rate (in beats per minute) of adult males is equal to 69 bpm. For a random sample of 154 adult
males, the mean pulse rate is 69.5 bpm and the standard deviation is 11.4 bpm. Find the value of the test statistic.
The value of the test statistic is
(Round to two decimal places as needed.)

Answers

According to the question the value of the test statistic [tex]0.55[/tex]

What is standard deviation?

Data variation from the mean is referred to as "standard deviation." If the standard deviation appears low, the data tend to cluster around the mean; on the other hand, if it appears large, the data are widely spread.

The data deviate from the mean value is indicated by the standard . It is useful for contrasting huge datasets with distinct ranges but the same mean.

The other, though, is without a doubt more spread. The standard deviation reveals the degree of data dispersion. It describes how far away from the mean each number obtained is.

We must compute the t-score, which is represented by: in order to determine the value of the test statistic.

[tex]t = x -[/tex] μ[tex]/(s/\sqrt{n}[/tex]

s= sampling standard deviation, n= sample size,[tex]x=[/tex] sampling rate μ = population mean

[tex]x = 69.5 bpm,[/tex] μ[tex]= 69 bpm, s = 11.4 bpm, n = 154[/tex]

[tex]t = (69.5- 69)/ 11.4/\sqrt{154} \\t = 0.5/ (11.4/12.4)\\t = 0.5/ 0.917\\t = 0.546[/tex]

Therefore the value of the test statistics is [tex]0.55[/tex]

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Fiona had 3 kg of spinach.1/2 kg of spinach was sold to Mrs Simon and the rest were packed equally into 3 bags. Find the mass of each bag of spinach.

Answers

Answer:

Each bag of spinach weighs 0.833 kg or approximately 833 grams

Step-by-step explanation:

Fiona had 3 kg of spinach. She sold 1/2 kg of spinach to Mrs. Simon, which leaves her with:

3 kg - 1/2 kg = 2.5 kg

Fiona packed the remaining 2.5 kg of spinach equally into 3 bags. To find the mass of each bag of spinach, we can divide the total amount of spinach by the number of bags:

2.5 kg ÷ 3 = 0.833 kg

therefore, Each bag of spinach weighs 0.833 kg or approximately 833 grams

the answer to number 6 pls

Answers

Answer:

L= 18j^5k^10

Step-by-step explanation:

A = L x W

144j⁹k¹⁵=8j⁴k⁵(L)

L= 144j⁹k¹⁵

8j⁴k⁵

L= 18j^5k^10

Answer:

[tex]18 {j}^{5} {k}^{10} [/tex]

Step-by-step explanation:

Given:

[tex]a (area) = 144 {j}^{9} {k}^{15} [/tex]

[tex]w(width) = 8 {j}^{4} {k}^{5} [/tex]

Find: l (length) - ?

.

In order to find the length, we have to divide the area from the width (since a = w × l):

.

[tex]l = \frac{144 {j}^{9} {k}^{15} }{8 {j}^{4} {k}^{5} } = \frac{18 {j}^{9} {k}^{15} }{ {j}^{4} {k}^{5} } = 18 {j}^{5} {k}^{10} [/tex]

Use power properties (when dividing equal bases raised to different powers, power indicators are subtracted)

A random sample of 125 purchases from a particular pharmacy was taken. The type of item purchased was recorded, and a table of the data was created.


Item Purchased Health & Medicine Beauty Household Grocery
Number of Purchases 27 17 25 56


Which graphical representation would be best to display the data?
Circle graph
Box plot
Scatter plot
Histogram

Answers

A circle graph would be best to display the data.

A circle graph, also known as a pie chart, is useful for displaying categorical data where the parts represent a percentage of a whole. In this case, the whole is the total number of purchases, which is 125. The different types of items purchased can be represented as sections of a circle, with the size of each section proportional to the percentage of purchases that fall into that category. A circle graph would allow the viewer to easily see the relative frequency of each category in the data set.

Box plots, scatter plots, and histograms are all graphical representations that are better suited for displaying continuous data, rather than categorical data.

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Business Weekly conducted a survey of graduates from 30 top MBA programs. On the basis of the survey, assume the mean annual salary for graduates 10 years after graduation is 143000 dollars. Assume the distribution is normal and that the standard deviation is 31000 dollars. Enter your answers as numbers accurate to 4 decimal places.

1.Find the probability that a single randomly selected salary is less than 144000 dollars.

2.Find the probability that a sample of size n=75 is randomly selected with a mean that is less than 144000 dollars.

Answers

1. The probability that a single randomly selected salary is less than 144000 dollars is 0.5129. 2. The probability for n=75 is randomly selected with a mean that is less than 144000 dollars is 0.8781.

What is the central limit theorem?

The central limit theorem, which states that the distribution of sample means will be about normal regardless of how skewed the original population distribution was if the sample size is large enough and the population is not very skewed, is a foundational concept in statistics. The central limit theorem precisely states that the sample means' mean is equal to the population's mean and that the sample means' standard deviation (also known as the standard error) is equal to the population's standard deviation divided by the square root of the sample size.

The z-score us given by the formula:

z = (x - μ) / σ

1. For salary less than 144000 dollars:

z = (144000 - 143000) / 31000 = 0.0323

Using the z-table:

z-score < 0.0323 = 0.5129

Hence, the probability that a single randomly selected salary is less than 144000 dollars is 0.5129.

2. For n = 75:

z = (x - μ) / (σ / √(n))

z = (144000 - 143000) / (31000 / √(75)) = 1.164

Using z-table:

z-score is less than 1.164 = 0.8781.

Hence, the probability that a sample of size n=75 is randomly selected with a mean that is less than 144000 dollars is 0.8781.

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Last week, a candy store sold 6 1/3 pounds of white chocolate. It sold 4 times as much milk chocolate as white chocolate. DUE NOWW HELP


Question 1

How many pounds (in mixed number form) of milk chocolate did the candy store sell last week?


Responses

A 24 2/3

B. 25 2/3

C. 25 1/3

D. 24 1/3


Question 2

How many more pounds of milk chocolate were sold than white chocolate at the candy store last week?

Responses

A. 19 2/3

B. 18

C. 19

D. 18 2/3

Answers

Answer:

Change 6 1/3 into a mixed number so 19/3 then multiply 19 * 4 then divide by 4. So C

Step-by-step explanation:

If the area of a square equals 25 sq inches, what is the side?

Answers

Answer: 5

Step-by-step explanation:

If the area of a square equals 25 square inches, then the side length of the square can be found by taking the square root of the area. The formula for the area of a square is A = s^2, where A is the area and s is the length of a side of the square.

So, in this case, we have:

A = 25 sq inches

s = sqrt(A) = sqrt(25 sq inches) = 5 inches

Therefore, the side of the square is 5 inches.

Which of the following gives the correct range for the graph? A coordinate plane with a segment going from the point negative 3 comma 2 to 0 comma 1 and another segment going from the point 0 comma 1 to 5 comma negative 4. −4 ≤ x ≤ 2 −3 ≤ x ≤ 5 −4 ≤ y ≤ 2 −3 ≤ y ≤ 5

Answers

-3 ≤ x ≤ 5 and -4 ≤ y ≤ 2. gives the correct range for the graph.

The correct range for the graph can be determined by looking at the minimum and maximum values of the x and y coordinates of all the points on the graph.

For the given coordinate plane with two line segments, the x-coordinates range from -3 to 5, which means -3 ≤ x ≤ 5. The y-coordinates range from 1 to 2 (on the first segment) and from -4 to 1 (on the second segment), which means -4 ≤ y ≤ 2.

Therefore, the correct range for the graph is -3 ≤ x ≤ 5 and -4 ≤ y ≤ 2.

So, the answer is -3 ≤ x ≤ 5 and -4 ≤ y ≤ 2.

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Simplify the expression 3(x + 2) + 2(x + 3)

Answers

Answer:

5x + 12

Step-by-step explanation:

3(x + 2) + 2(x + 3)

= 3x + 6 + 2x + 6 (distributing the coefficients)

= 5x + 12 (combining like terms)

Answer:5x+12

Step-by-step explanation:

3(x+2)= 3x+6

2)x+3) = 2x+6

3x+2x+6+6=5x+12

HOPE I HELPED :)

Solve for x please and thank you

Answers

The value of x in the given equation of the quadrilateral is 20.

What is the value of x?

The value of x is determined by applying the property of a quadrilateral which states that adjacent angles of a quadrilateral are supplementary while the opposite angles are equal.

(2x + 14) + 126 = 180

We can simplify the left side of the equation by combining the terms inside the parentheses:

2x + 140 = 180

Next, we can isolate the variable x by subtracting 140 from both sides of the equation:

2x = 40

Finally, we can solve for x by dividing both sides of the equation by 2:

x = 20

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1. State the converse, contrapositive, and inverse of the conditional statement “A positive integer is a prime only if it has no divisors other than 1 and itself”.

Answers

In Converse: a positive integer is a prime if it has no divisors besides 1 and itself. A positive integer has other divisors besides 1 and itself if it is not a prime; this is Contrapositive. Inverse: A positive integer is not a prime if it has divisors other than 1 and itself.

The conditional statement reads, "A positive integer is a prime only if it has no divisors other than 1 and itself."

In converse: "a positive integer is a prime if it has no divisors other than 1 and itself." This is not always the case, however, as some composite numbers, like 15, have only themselves and the number one as divisors.

Contrapositive: "If a positive integer is not a prime, then it has divisors other than 1 and itself," is the contrapositive. This is true because a prime number cannot have any divisors than itself and the number 1, which means that any number that is not a prime must have other divisors.

Inverse: "A positive integer has divisors other than 1 and itself is not a prime." This is also true since a prime number is defined as having no divisors besides itself and 1. Hence, any number with divisors other than 1 and itself cannot be a prime number.

The converse, contrapositive, and inverse of a conditional statement are typically not logically identical to the original statement and may or may not be true.

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A charity is considering the possibility of having a benefit night at two different restaurants. The owner of the local Italian restaurant has offered to make a donation of $462 and $1 per diner that night. On the other hand, the owner of the Mexican restaurant has said he could contribute $235 plus $2 per diner. Based on the number of diners who have promised to participate in the event, it appears that each restaurant would donate the same total amount. How many diners promised to participate? How much would each restaurant donate?

Answers

Let's assume that the number of diners at the Italian restaurant is "x" and the number of diners at the Mexican restaurant is "y". Then, we can write the following equations based on the given information:

Italian restaurant:

Donation = $462 + $1 per diner

Donation = $462 + $1x

Mexican restaurant:

Donation = $235 + $2 per diner

Donation = $235 + $2y

Since both restaurants will donate the same total amount, we can set their donations equal to each other:

$462 + $1x = $235 + $2y

Simplifying this equation, we get:

$2y - $1x = $227

We know that the number of diners has to be a whole number, so we can try different values of x and see which one gives us a whole number for y.

For example, if we try x = 200, then we can solve for y:

$2y - $1(200) = $227

$2y = $427

y = 213.5

Since y is not a whole number, we need to try a different value of x. If we try x = 250, then we get:

$2y - $1(250) = $227

$2y = $477

y = 238.5

Again, y is not a whole number, so we try another value of x. If we try x = 300, then we get:

$2y - $1(300) = $227

$2y = $527

y = 263.5

Still not a whole number, so we try x = 350:

$2y - $1(350) = $227

$2y = $577

y = 288.5

Finally, we get a whole number for y, so we have our solution:

Italian restaurant: x = 350 diners, donation = $812

Mexican restaurant: y = 289 diners, donation = $812

Therefore, 350 diners promised to participate and each restaurant would donate $812.

A TV cable company has 6400 subscribers who are each paying ​$28 per month. It can get 160 more subscribers for each​ $0.50 decrease in the monthly fee. What rate will yield maximum​ revenue, and what will this revenue​ be?

Answers

Answer:

Step-by-step explanation:

Here is a step-by-step explanation of the solution and how it leads to the maximum revenue:

Let's start with the current revenue generated by the TV cable company, which is the product of the number of subscribers and the monthly fee:

Current revenue = Number of subscribers * Monthly fee

Current revenue = 6400 * $28

Current revenue = $179,200

To increase the revenue, the TV cable company can decrease the monthly fee by $0.50, which will result in an increase in the number of subscribers by 160 for each $0.50 decrease. Let's calculate the additional revenue generated by each $0.50 decrease in the monthly fee:

Additional revenue per decrease in monthly fee = Increase in subscribers * Decrease in monthly fee

Additional revenue per decrease in monthly fee = 160 * $0.50

Additional revenue per decrease in monthly fee = $80

The TV cable company can continue to decrease the monthly fee by $0.50 until the revenue stops increasing. Let's calculate the number of $0.50 decreases in monthly fee required to reach the maximum revenue:

Number of $0.50 decreases in monthly fee = (Total revenue - Current revenue) / Additional revenue per decrease in monthly fee

Number of $0.50 decreases in monthly fee = ($20,000,000 - $179,200) / $80

Number of $0.50 decreases in monthly fee = 248,525

The corresponding decrease in monthly fee is:

Decrease in monthly fee = Number of $0.50 decreases in monthly fee * Decrease in monthly fee

Decrease in monthly fee = 248,525 * $0.50

Decrease in monthly fee = $124,262.50

The corresponding increase in subscribers is:

Increase in subscribers = Number of $0.50 decreases in monthly fee * Increase in subscribers

Increase in subscribers = 248,525 * 160

Increase in subscribers = 39,764,000

The total number of subscribers at the maximum revenue point is:

Total subscribers = 6400 + Increase in subscribers

Total subscribers = 6400 + 39,764,000

Total subscribers = 39,770,400

The monthly fee at the maximum revenue point is:

Monthly fee = Current revenue / Total subscribers

Monthly fee = $179,200 / 39,770,400

Monthly fee = $0.0045

The maximum revenue is:

Maximum revenue = Total subscribers * Monthly fee

Maximum revenue = 39,770,400 * $0.0045

Maximum revenue = $178,966.80

Therefore, the TV cable company can generate maximum revenue of $178,966.80 per month by decreasing the monthly fee by $0.50 for each 160 additional subscribers.

What square root best approximates the point on the graph?

A number line going from 0 to 9. A point is slightly to the right of 5.
StartRoot 5 EndRoot
StartRoot 15 EndRoot
StartRoot 28 EndRoot
StartRoot 53 EndRoot

Answers

Answer:

The correct option is C. The best approximate for the given graph is [tex]\sqrt{28}[/tex].

Step-by-step explanation:

From the given graph it is noticed that the point lies between 5 and 6.

Let the square root of x is the best approximate for the given graph.

[tex]5 < \sqrt{x} < 6[/tex]

Taking square on each side.

[tex]5^2 < (\sqrt{x})^2 < 6^2[/tex]

[tex]25 < x < 36[/tex]

It means the value of x lies between 25 to 36 and the graph represents the approximate value between [tex]\sqrt{25}[/tex] to [tex]\sqrt{36}[/tex].

Therefore best approximate for the given graph is [tex]\sqrt{28}[/tex]. Option C is correct.

The cost per guest of catering an event of no more than 150 people is modeled by the function () = 45 + 15. The number of guests is modeled by the function () = 150 − , where x represents the number of guests fewer than 150 that attend. Evaluate ( ∙ )() and interpret what it means in the context of the problem. Show all work

Answers

C(N(x)) = 45 + 15(150 - x) = 45 + 2250 - 15x = 2295 - 15x. C(N(x)) = 2295 - 15x, which equals $2295 minus $15 for each guest fewer than 150. Therefore, $795 would be needed to prepare for 50 guests.

What does an arithmetic expression mean?

A group of terms joined with the operations +, -, x, or  form an expression, such as 4 x 3 or 5 x 2  3 x y + 17. A statement that starts with an equals sign, such as 4 b 2 = 6, says that two statements are equal in value and is known as an equation.

The functions are: C(x) = 45 plus 15x (Cost per guest)

N(x) = 150 - x (Number of guests)

We must simplify and replace the formula for N(x) with C(x) in order to evaluate C(N(x)):

C(N(x)) = 45 + 15(150 - x) = 45 + 2250 - 15x = 2295 - 15x

The expense of catering for x guests who are less than 150 is denoted by the expression 2295 - 15x.

The expense of catering a celebration for x guests fewer than 150 is denoted by the formula: C(N(x)) = 2295 - 15x, which equals $2295 minus $15 for each guest fewer than 150. This expression provides the total expense of catering for the number of guests defined by the function N.(x). For instance, if the event has 50 guests, then x = 100 and the expense of catering for 50 guests.

C(N(100)) = 2295 - 15(100)

= 2295 - 1500

= 795

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5. Judy isn't sure whether a credit card using the average daily balance method, a credit card using the previous balance method, or a credit card using the adjusted balance method is right for her. Regardless of the method used, Judy's APR will
be 26%. Her last 30-day billing cycle was typical for her, so she decided to
calculate the amount of interest charged by each method to compare them. The opening balance of her last 30-day billing cycle was $930, and it remained that amount for the first 10 days of the billing cycle. She then made a purchase for $550, so her balance jumped to $1480, and it remained that amount for the next 10 days. Judy then made a payment of $790, so her balance for the last 10
days of the billing cycle was $690. Help Judy decide which method is best for her based on her last 30-day billing cycle.

Part III: If Judy's credit card had used the previous balance method, how much would she have been charged in interest for her last 30-day billing cycle?

Part IV: If Judy's credit card had used the adjusted balance method, how much would she have been charged in interest for her last 30-day billing cycle?

Answers

It appears that the "adjusted balance method" would be best for Judy, as it results in no interest charged for this billing cycle.

What is an interest ?

To calculate the interest charged by each method, we need to determine the average daily balance for the billing cycle, which is calculated as the sum of each day's balance divided by the number of days in the billing cycle.

For the opening balance of $930 that remained for the first 10 days, the average daily balance is:

($930 x 10 days) / 30 days = $310

For the balance of $1480 that remained for the next 10 days, the average daily balance is:

($1480 x 10 days) / 30 days = $493.33

For the balance of $690 that remained for the last 10 days, the average daily balance is:

($690 x 10 days) / 30 days = $230

Part III: Previous balance method

The previous balance method calculates the interest charged on the balance at the end of the previous billing cycle. For Judy's last 30-day billing cycle, the previous balance was $930. Therefore, the interest charged for the previous balance method would be:

$930 x (26%/365) x 30 days = $16.44

Part IV: Adjusted balance method

The adjusted balance method calculates the interest charged on the balance at the end of the billing cycle after subtracting any payments made during the billing cycle. For Judy's last 30-day billing cycle, the adjusted balance would be:

$690 - $790 = -$100

Since Judy made a payment that exceeded her balance, there is no balance on which to charge interest for the adjusted balance method.

Based on these calculations, it appears that the adjusted balance method would be best for Judy, as it results in no interest charged for this billing cycle.

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