The surface area of a triangular prism is 60 square centimeters. What is the surface area of a similar prism that is smaller by a scale factor of 1 5th

To determine the ticket prices at Family Flicks, we create a system of equations using variables A for adult tickets and C for child tickets, then solve for A and C using the given information.

To find the adult and child ticket prices for movies at Family Flicks, we can establish a system of equations based on the information provided. Let's denote the price of an adult ticket as A and the price of a child ticket as C. From the first family's purchase, we have the equation 2A + 3C = $27.75. The second family's purchase gives us the second equation 3A + 2C = $32.25. Solving this system of equations will provide us with the prices for the adult and child tickets.

Answer: it would be a good deal because if you do you 1/3x (3.14) or pie x (5) cause it’s the diameter and 10 divided by 2 is 5

Step-by-step explanation:

Answer:

The salary a salesperson expects to earn in 3 years, according to the graph is $40,000

Step-by-step explanation:

The estimated salary for a salesperson with 3 years of employment is $45,000.

Without the scatter plot, it's impossible to give an exact answer, but we can make an estimate based on the trend line. Assuming the trend line is a straight line, we can use the equation of the line to estimate the salary for a salesperson with 3 years of employment.

The equation of a straight line can be written in a slope-intercept form as y = mx + b, where y is the dependent variable (salary in this case), x is the independent variable (years of employment in this case), m is the slope of the line, and b is the y-intercept (the value of y when x = 0).

To find the equation of the trend line, Tony would have used statistical software or a calculator to calculate the slope and y-intercept of the line of best fit. He could also have done this by hand using the least squares regression method.

Once we have the equation of the trend line, we can substitute x = 3 to estimate the salary for a salesperson with 3 years of employment.

For example, if the equation of the trend line is y = 5000x + 30000 (where y is the salary in dollars and x is the years of employment), then we can estimate that a salesperson with 3 years of employment can expect to earn:

y = 5000(3) + 30000

y = 15000 + 30000

y = 45000

So the estimated salary for a salesperson with 3 years of employment is $45,000.

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To serve 73 people at a party, 4 cakes are needed since each cake serves 24 people and it is not possible to have a fraction of a cake.

To determine how many cakes are needed for a party with 70 guests and 3 staff members, we need to calculate the total number of servings required and then divide this by the number of servings each cake provides.

First, we add the number of guests and staff to find the total number of people at the party:

Each cake serving is designed to serve 24 people. We divide the total number of people by the number of servings per cake to find out how many cakes are needed:

(Total number of people) ÷ (Servings per cake) = Number of cakes

73 ÷ 24 = 3.04166667

Since you cannot have a fraction of a cake, you need to round up to the next whole number. Therefore, you need 4 cakes to have enough servings for everyone at the party.

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4 cakes are needed for the party to ensure that each of the 70 guests and 3 staff members receives a serving of cake.

To determine the number of cakes needed, we must first calculate the divide that number by the number of servings each cake provides.

 First, we add the number of guests to the number of staff:

70 guests + 3 staff = 73 people in total.

 Next, we need to ensure that each person gets one serving of cake. Since each cake serves 24 servings, we divide the total number of people by the number of servings per cake:

73 people · 24 servings per cake = 3 cakes with some servings left over.

 Since we cannot serve a fraction of a cake, we must round up to the nearest whole number to ensure that there are enough servings for everyone. Therefore, we need 4 cakes in total to serve all 73 people at the party.

 In conclusion, 4 cakes are needed for the party to ensure that each of the 70 guests and 3 staff members receives a serving of cake.

Answer:

only A. and E.

Step-by-step explanation:

The answer would be option(A) and (E) are show a geometric series.

A. 2 + 3 + 4.5 + 6.75 + …

E. 8 + 4 + 2 + 1 + …

Geometric sequence or series is defined as a sequence of numbers such that the next term is either increasing or decreasing by a specific ratio referred to as a geometric sequence.

The standard equation for geometric series as:

Tₙ = a₁ rⁿ⁻¹

where a₁ is the first term and r is the common ratio.

A. 2 + 3 + 4.5 + 6.75 + …

Here, first term a₁ = 2 ,

The common ratio r = 3/2 = 4.5/3 = 6.75/4.5 = 1.5

So, this is a geometric series.

E. 8 + 4 + 2 + 1 + …

Here, first term a₁ = 8 ,

The common ratio r = 4/8 = 2/4 = 1/2 = 0.5

So, this is a geometric series.

Hence, the option(A) and (E) are show a geometric series.

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If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.

The Triangle Proportionality Theorem asserts that a line drawn parallel to one side of a triangle divides the other two sides proportionally. This is related to the properties of similar triangles, where the corresponding sides of similar triangles are proportional due to the AAA similarity criterion.

The Triangle Proportionality Theorem states that if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally. This means that the segments created on one side of the triangle are in the same ratio as the corresponding segments on the other side of the triangle. For example, in [tex](\Delta ABC)[/tex] with a line parallel to [tex](\overline{BC})[/tex], the theorem asserts that [tex](\frac{AD}{DB} = \frac{AE}{EC})[/tex].

This concept is deeply rooted in the properties of similar triangles which are based on the Angle-Angle-Angle (AAA) similarity criterion. According to the AAA theorem, if two triangles have corresponding angles that are equal, then their corresponding sides are proportional. Thus, if two triangles are similar, the lengths of their corresponding sides form a proportion such as [tex](\frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF})[/tex], where each fraction is the ratio of a pair of corresponding sides.

The principles of the Triangle Proportionality Theorem can be applied in various geometric problems, often to compare the lengths of sides within the same triangle or in two similar triangles. It is also useful in determining distances or heights by applying the theorem to real-life scenarios, such as calculating the height of a wall using the shadow it casts, provided the sun's rays are considered parallel.

Answer:

(7,a) Where a ∈ R - {7}

OR

(-2,a) where a ∈ R - {-2}

Step-by-step explanation:

The coordinates of the given line from the right to the left are:

(7,1) and (-2,1)

So, to make a right triangle, we need to make a right angle or by another words, we need to a make a perpendicular line to the given line (i.e: a vertical line parallel to the y-axis at one of the given points)

So, the third vertex must be on the line x=7 or x=-2

So, the coordinates of the third vertex is:

(7,a) Where a ∈ R - {7}

OR

(-2,a) where a ∈ R - {-2}

Answer:

(5, −4)

Step-by-step explanation:

A right triangle is a triangle in which one angle is a right angle (a 90-degree angle). (thank usatestprep)

Answer:

The amount of Mark's Total payment is $9478.15.

Step-by-step explanation:

Given : Mark borrowed $5,500 at 11.5 percent for five years.

To find : What is the amount of Mark's total payment?          

Solution :

Using compound interest formula,

[tex]A=P(1+r)^t[/tex]

Where A is the amount, 

P is the principle P=5,500  

r is the rate r=11.5%=0.115

t is the time t= 5 years

Substitute the value,

[tex]A=P(1+r)^t[/tex]

[tex]A=5500(1+0.115)^5[/tex]

[tex]A=5500(1.115)^5[/tex]

[tex]A=5500(1.7233)[/tex]

[tex]A=9478.15[/tex]

Therefore, The amount of Mark's Total payment is $9478.15.

Answer:

[tex]y > -x+4[/tex]

Step-by-step explanation:

we know that

The solution of the inequality is the shaded area above the dotted line

The slope of the dotted line is negative

The y-intercept of the dotted line is (0,4)

The x-intercept of the dotted line is (4,0)

Find the slope of the dotted line

[tex]m=(0-4)/(4-0)\\ m=-1[/tex]

The equation of the dotted line in slope intercept form is equal to

[tex]y=mx+b[/tex]

we have

[tex]m=-1[/tex]

[tex]b=4[/tex] -----> y-intercept

substitute

[tex]y=-x+4[/tex]

Find the equation of the inequality

Remember that the solution is the shaded area above the dotted line therefore

The inequality is

[tex]y > -x+4[/tex]

The set of all numbers on a number line is called the "Real Numbers".

Any number that can be represented as the ratio of two integers and where the denominator is not zero is referred to as rational.

The set of all numbers on a number line is called the "Real Numbers".

A number that has an equivalent terminating or repeating decimal is called a "Rational Number".

A number that has an equivalent decimal that is non-repeating is called an "Irrational Number".

Any number that can be written as a fraction of integers is a "Rational Number".

Hence, the set of all numbers on a number line is called the "Real Numbers".

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Answer: the answer is C. 45.

The slope value of the line drawn is 2

Choosing the points to be used to calculate the slope from the graph;

Slope = Rise / Run

This means:

Slope = -6/-3

slope = 2

Therefore, the value of the slope is 2

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The probability you will pick two black marbles out of the bag without replacing the first one chosen is, 1 / 7.

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

Given that;

There are 3 black marbles and 4 red marbles in a bag.

Hence, Total number of marbles = 3 + 4 = 7

Thus, The probability you will pick one black marbles out of the bag is,

⇒ 3 / 7

And, The probability you will pick another black marbles out of the bag is,

⇒ 2 / 6

⇒ 1 / 3

Thus, The probability you will pick two black marbles out of the bag without replacing the first one chosen is,

⇒ 3/7 × 1/3

⇒ 1/7

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Answer:

the answer is D

Step-by-step explanati

The question involves simplifying arithmetic expressions with square roots and division, emphasized on correctly applying order of operations and rules for dealing with exponents.

The student's question involves simplifying expressions containing the square root and the division operation. To simplify expressions like 12 + √35 divided by 2 and 12 - 2√35 divided by 2, we need to perform operations step by step, applying the correct order of operations.

When parenthesis is used, it indicates that we should evaluate that part of the expression first, followed by multiplication or division, and finally addition or subtraction. It is important to pay careful attention to the operation signs and ensure that each step is followed correctly. Working with square roots and division can be tricky, but by breaking down the expression into smaller parts and solving them one by one, we can arrive at the correct answer.

For instance, to solve expressions like 3².35, we need to apply the exponential rules, such as xPx9 = x(p+q). This indicates that you should add the exponents when multiplying numbers with the same base. While this particular rule may not directly apply to the expression in question, knowing rules for operations with exponents can help simplify complex arithmetic expressions.