Mrs. Hooper teaches piano lessons 5 days a week. She teaches for a total of 3 hours per day. How many minutes does she teach each week?

Answer:

Senior citizen ticket: $9

Child ticket: $13

Step-by-step explanation:

This can be solved by creating a system of equations:

[tex]f(x)=7x+5y=128[/tex]

and

[tex]g(x)=8x+10y=202[/tex]

where x is the cost of a senior citizen ticket and y is the cost of a child ticket.

Solve equation 2 for 5y:

[tex]8x+10y=202\\10y=202-8x\\\frac{10y}{x}=\frac{202-8x}{2}\\5y=101-4x[/tex]

Substitute (101-4x) for 5y in equation 1:

[tex]7x+(101-4x)=128\\3x+101=128\\(3x+101)-101=(128)-101\\3x=27\\\frac{3x}{3}=\frac{27}{3}\\x=9[/tex]

Substitute 9 for x in equation 2:

[tex]8(9)+10y=202\\72+10y=202\\(72+10y)-72=(202)-72\\10y=130\\\frac{10y}{10}=\frac{130}{10}\\y=13[/tex]

A senior citizen ticket costs $9 and a child's ticket costs $13.

To check these values, insert them into the equations:

[tex]128=7(9)+5(13)\\128=63+65\\128=128[/tex]

and

[tex]202=8(9)+10(13)\\202=72+130\\202=202[/tex]

The exact surface area of the cylinder in terms of π is = 10 π

What is the answer for surface area?

As a refresher, the surface area of an object is the sum of the areas of all of its faces, or the exterior surfaces of its three dimensions. It is calculated in square units.

Where can I find the surface area?

A three-dimensional shape's surface area is the total area on its surface. Add the areas of each of the six rectangular sides of a cuboid to determine its surface area. The cuboid's length, width, and height can also be labeled, and the surface area (SA) can be calculated using the formula SA=2lw+2lh+2hw.

Given that :

Radius = 1 1/4 cm

Height = 2 3/4 cm

Surface area is 2π r h + 2π r² = 2π ( 1 1/4 cm*2 3/4 cm) + 2π (1 1/4)²

= 2π (55/16) + 2π (25/16)

= 160/16 π

= 10 π

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The two triangles are similar under SSS conditions if all three sides of one triangle are in proportion to the three sides of another triangle.

If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent.

Slide, twist, flip, and turn these triangles to create an identical appearance.

They are in alignment with one another when moved.

According to the SSS test for triangle similarity, two triangles are considered similar if their third sides are proportionate to one another.

Therefore, the two triangles are similar under SSS conditions if all three sides of one triangle are in proportion to the three sides of another triangle.

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Answer:

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

Given:

Perimeter is:

or

The perimeter is at most 96 cm (not greater than):

The matching choice is A.

The mean of grade-point averages of 20 college seniors selected at random from a graduating class is 2.50.

Mean is the average of all numbers in the data set. The average can be found by dividing the sum of all numbers in the observed data by the number of data observations. This helps researchers, statisticians, etc. to find mean values in datasets. The formula for calculating the

average is:

mean = sum of values / number of values

It is denoted by X-bar.

We have the grade-point averages of 20 college seniors. The the random sample of graduating class as :

2.2, 1.6 ,2.7, 2.2, 2.4, 2.6, 3.8, 3.0, 2.5, 3.3, 1.8, 2.3, 3.3, 2.8, 2.0, 3.2, 2.1, 2.0, 2.9, 1.3

The Sum of grade point averages of 20 college seniors is calculated as follows,

∑ x = 2.2 + 1.6 + 2.7 + 2.2 + 2.4 + 2.6+ 3.8 + 3.0 + 2.5 + 3.3 + 1.8 + 2.3 + 3.3 + 2.8 + 2.0 + 3.2 + 2.1 + 2.0 + 2.9 + 1.3

∑x = 50

Total number of colleges , n = 20

Mean of distribution is calculated as follows,

X- bar = ∑x / n

where n is number of observations

X- bar = 50/20

=> X-bar = 2.5

Hence, required mean is 2.5 ..

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Complete question:

The grade-point averages of 20 college seniors selected at random from a graduating class are as follows:

2.2, 1.6 ,2.7, 2.2, 2.4, 2.6, 3.8, 3.0, 2.5, 3.3, 1.8, 2.3, 3.3, 2.8, 2.0, 3.2, 2.1, 2.0, 2.9, 1.3 Calculate the mean?

9/8 is the result when we divide 3/4 by 2/3

Step 1. Take reciprocal of  the second fraction (the one you want to divide by)

Step 2. Multiply the first fraction by the second faction's reciprocal.

Step 3. Convert the result in the lowest form.

When the numerator and the denominator of the fraction do not have any common factors, the fraction is said to be in its simplest form. For instance, 12 is the most basic version of 6/12.

so the result = (3/4) / (2/3)

=> (3/4) * (3/2)

=> (3*3)/(4*2)

=>9/8

so the result obtanied after the above division is 9/8.

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Answer:

no

Step-by-step explanation:

The number of gallons of water the city's residents waste last year are 7388.181 by percentage concept.

A quantity or ratio that is expressed as a fraction of 100 is known as a "a%" in mathematics (from the Latin per centum, "by a hundred"). A% is a dimensionless (pure) number without any measuring units. The Latin word "percentum," which means "hundred" or "by the hundred," is the source of the English term "percent." Over time, the Italian term per cento, which originally meant "for a hundred," shrank to become the symbol for "percent." Per was frequently abbreviated to "p" and finally disappeared altogether.

No. of gallons of water wasted by Hillsdale are 8127 gallons.

110%  -----> 8127

100%  ----->?

x=(100×8127)/110

x= 7388.181

Therefore, the number of gallons of water the city's residents waste last year are 7388.181.

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Answer:

The Eastern Continental Trail is 5,376 miles and the Erie Canalway Trail is 384 miles

Step-by-step explanation:

I took 5,760 divided it by 15 and got 384, I then subtracted 5,760 by 384 and got 5,376

An equation of the form z= a+ib, where a and b are real numbers, is defined to be a complex number. The real part is denoted by Re z = a and the imaginary part is denoted by Im z = ib.

Now, According to the question:

Let's know:

What are Complex Numbers?

A complex number is the sum of a real number and an imaginary number. A complex number is of the form a + ib and is usually represented by z. Here both a and b are real numbers. The value 'a' is called the real part which is denoted by Re(z), and 'b' is called the imaginary part Im(z).  Also, ib is called an imaginary number.

Representation of the Complex Numbers:

z = a + ib

'a' represent the Real part

'ib' represent imaginary number and imaginary part.

Some of the examples of complex numbers are :

2 + 3i , -3 - 4i , 1/2 + 1/3i etc.

Power of i

The alphabet i is referred to as the iota and is helpful to represent the imaginary part of the complex number. Further the iota(i) is very helpful to find the square root of negative numbers. We have the value of [tex]i^2[/tex] = -1, and this is used to find the value of √-4 = √[tex]i^2[/tex]4 = ±2i  The value of [tex]i^2[/tex] = -1 is the fundamental aspect of a complex number. Let us try and understand more about the increasing powers of i.

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The number of pounds of peanuts the company uses is 6 pounds peanuts/1 pound raisins * 33 pounds raisins = 198 pounds peanuts.

To solve this problem, you can set up a system of equations to represent the given information. The first equation represents the fact that the company uses 138 pounds of peanuts for every 2/3 pound of raisins:

138 pounds peanuts / 2/3 pound raisins = x pounds peanuts

The second equation represents the fact that the company makes 245 pounds of trail mix using only peanuts and raisins:

x pounds peanuts + y pounds raisins = 245 pounds trail mix

To solve for the number of pounds of peanuts used, you can substitute the first equation into the second equation:

(138 pounds peanuts / 2/3 pound raisins) + y pounds raisins = 245 pounds trail mix

Multiplying both sides of the equation by 2/3 to eliminate the fraction, we get:

138 pounds peanuts + (2/3)y pounds raisins = (2/3)(245 pounds trail mix)

Combining like terms, we get:

138 pounds peanuts + (2/3)y pounds raisins = (2/3)(245 pounds)

Simplifying the right side of the equation, we get:

138 pounds peanuts + (2/3)y pounds raisins = 160 pounds

Subtracting 138 pounds from both sides of the equation, we get:

(2/3)y pounds raisins = 160 pounds - 138 pounds

Simplifying the right side of the equation, we get:

(2/3)y pounds raisins = 22 pounds

Dividing both sides of the equation by 2/3, we get:

y pounds raisins = (3/2)(22 pounds)

Simplifying the right side of the equation, we get:

y pounds raisins = 33 pounds

Substituting this value into the first equation, we get:

138 pounds peanuts / 2/3 pound raisins = 33 pounds raisins

Multiplying both sides of the equation by 2/3, we get:

138 pounds peanuts / (2/3)(33 pounds raisins) = 33 pounds raisins

Simplifying the right side of the equation, we get:

138 pounds peanuts / 22 pounds raisins = 33 pounds raisins

Dividing both sides of the equation by 22 pounds raisins, we get:

138 pounds peanuts / 22 pounds raisins / 33 pounds raisins = 33 pounds raisins / 22 pounds raisins

Simplifying the equation, we get:

6 pounds peanuts / 1 pound raisins = 33 pounds raisins / 22 pounds raisins

This equation shows that for every 1 pound of raisins the company uses, they use 6 pounds of peanuts.

Therefore, the number of pounds of peanuts the company uses is 6 pounds peanuts/1 pound raisins * 33 pounds raisins = 198 pounds peanuts.

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138 pounds peanuts / 2/3 pound raisins = x pounds peanuts

The second equation represents the fact that the company makes 245 pounds of trail mix using only peanuts and raisins:

x pounds peanuts + y pounds raisins = 245 pounds trail mix

(138 pounds peanuts / 2/3 pound raisins) + y pounds raisins = 245 pounds trail mix

138 pounds peanuts + (2/3)y pounds raisins = (2/3)(245 pounds trail mix)

138 pounds peanuts + (2/3)y pounds raisins = (2/3)(245 pounds)

138 pounds peanuts + (2/3)y pounds raisins = 160 pounds

(2/3)y pounds raisins = 160 pounds - 138 pounds

(2/3)y pounds raisins = 22 pounds

y pounds raisins = (3/2)(22 pounds)

y pounds raisins = 33 pounds

138 pounds peanuts / 2/3 pound raisins = 33 pounds raisins

138 pounds peanuts / (2/3)(33 pounds raisins) = 33 pounds raisins

138 pounds peanuts / 22 pounds raisins = 33 pounds raisins

138 pounds peanuts / 22 pounds raisins / 33 pounds raisins = 33 pounds raisins / 22 pounds raisins

6 pounds peanuts / 1 pound raisins = 33 pounds raisins / 22 pounds raisins

This equation shows that for every 1 pound of raisins the company uses, they use 6 pounds of peanuts.

Therefore, the number of pounds of peanuts the company uses is 6 pounds peanuts/1 pound raisins * 33 pounds raisins = 198 pounds peanuts.

We say cubic polynomial if the degree of polynomial is odd number, and the graph is said cubic polynomial graph.

The equation which has only positive integer exponent are called   polynomial function. Such as 6x³+4x²+2x+1=0 where the power 3,2, 1 are the degree of polynomial.

The polynomial function whose first degree is odd number is called cubic polynomial.

hence, the graph is cubic polynomial.

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The probability it rains on both days is 0.175

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

P(Rain) = 0.5

P(Rain next day) = P(Rain) - 0.15

The probability it rains on both days is then calculated as

P(Rain both days) = P(Rain next day) * P(Rain)

Substitute the known values in the above equation, so, we have the following representation

P(Rain both days) = 0.5 * (0.5 - 0.15)

Evaluate

P(Rain both days) = 0.175

Hence, the probability is 0.175

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Answer:

A ∪ B = [3, 9)

Step-by-step explanation:

Set X is 3, and all number greater than 3 up, but not including, 5.

Set Y is all numbers from 4 to 9, but not including 4 or 9.

The union of the sets is all numbers from 3 up to 9, including 3 but not including 9.
A ∪ B = [3, 9)

The coefficient of x in the expression 5x³ 7x² is 5. This means that for every x in the expression, 5 will be multiplied by it. This means that in the expression 5x³ 7x², 5 will be multiplied by x three times and seven will be multiplied by x twice.

The coefficient of x in the expression 5x³ 7x² is 5. This means that for every x in the expression, 5 will be multiplied by it. To calculate the coefficient of x, we need to first expand the expression. The expanded form of the expression 5x³ 7x² is 5x³ + 7x². Here, we can see that 5 is multiplied by x three times and seven is multiplied by x twice. This indicates that the coefficient of x is 5. This can be understood by considering the following example:

Let's say we have the expression 5x³ 7x² = 5x³ + 7x².

Here, 5 is multiplied by x three times and seven is multiplied by x twice. This means that the coefficient of x is 5. This can be written as 5x³ + 7x² = 5x³ + 7x x 1 = 5x(x² + x). Hence, the coefficient of x in the expression 5x³ 7x² is 5.The coefficient of x in the expression 5x³ 7x² can be calculated using the following steps:

Expand the expression 5x³ 7x².

The expanded form of the expression is 5x³ + 7x².

Here, we can see that 5 is multiplied by x three times and seven is multiplied by x twice. This indicates that the coefficient of x is 5.

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The cumulative frequency distribution is a type of statistical representation that shows the total number of data points in a sample that are less than or equal to a given value. It is often used to understand the distribution of data within a sample and to identify patterns or trends.

To construct a cumulative frequency distribution for given data, follow these steps:

For example, given the following data:

The cumulative frequency distribution would be:

Data Point | Frequency | Cumulative Frequency

      10         |        1           |                1  

      15         |        1           |                2

     20         |        1           |                3

     25         |        1           |                4

     30         |        1           |                5

     35         |        1           |                6

     40         |        1           |                7

     45         |        1           |                8

This distribution could be represented in a graph by plotting the data points on the x-axis and the cumulative frequencies on the y-axis and connecting the points with a line.

The answer is general since the data is not provided.

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Answer: 4

Step-by-step explanation: 10, 6, 4, 4, 6, 4, 1.

In total, there are seven numbers.

The fourth number, number four (4), is the middle because it's in the middle.

The activities you desire to do with your money during the next several months or years are considered short-term financial objectives.

When you earn interest on your interest earnings as well as the money you have saved, this is known as compound interest. The interest you get is referred to as compound interest. Using simple math, you can see how this works: if you have $100 and it generates 5% interest annually, you will have $105 at the end of the first year. You'll have $110.25 at the conclusion of the second year.

The activities you desire to do with your money during the next several months or years are considered short-term financial objectives as compound interest. Setting a budget, creating an emergency fund, and paying off debt are some important short-term objectives.

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Answer:

B

Step-by-step explanation:

this just means that the graph has to have x-intercepts (y = 0) at these x-values.

so, which graph intersects the x-axis at x = -7/3 and x = 1/2 ?

only B does that.

the others have other x-intercept points.

Answer:

Square! #N#The sides and angles of a square: The sides of a square are all congruent (the same length.) The angles of a square are all congruent (the same size and measure.) Remember that a 90 degree angle is called a "right angle.". So, a square has four right angles. Opposite angles of a square are congruent.

hope this helps

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Step-by-step explanation:

A translation occurs whenever an object is transported from one place to another without altering its dimension, form, or orientation.

A translation occurs whenever an object is transported from one place to another without altering its dimension, form, or orientation. We can draw the translation in the coordinate plane if we know which way and how far to move the figure.

The triangle can be translated in the following ways:

Step 1: In the first step, determine the coordinates of each vertex of the triangle.

Step 2: To translate each point, add the horizontal translation value to the x-coordinate of each vertex and the vertical translation value to the y-coordinate of each point. Add a negative number if either the vertical or horizontal translation for these translations is downhill or to the left.

Step 3: Plot the three translated points and draw the triangle by drawing a straight line between each pair of points.

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Section 3 have 205 spots, according to the given question.

What do you mean by section?

A section is a part or component that, when combined with the other components, forms the total. like the rhythm section of the band that is reviewed in the arts section of a newspaper.

According to the given question,

We have the given information:

A 900 car parking lot is divided into 3 sections. There are 330 spots in Section 1. Section 2 holds 160 more than the amount of cars in Section 3.

Firstly,

900 - 330 = 570 (spots in section 2 and 3)

Secondly,

There are x spots in section 3 and (x + 160) spots in section 2.

So we have :

x + x + 160 = 570

2x = 410

x = 205

Therefore, the section 3 have 205 spots.

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Equation 3x2 + 2x + 1 = 0's discriminant is -8.

D = b2 - 4ac is the quadratic equation's discriminant.

where a, b, and c are the coefficients of the equation in the form ax² + bx + c = 0.

Therefore,

D = b² - 4ac

= 2² - 4(3)(1)

= -8

The discriminant of a quadratic equation is found by using the formula D = b² - 4ac, where a, b, and c are the coefficients of the equation in the form ax² + bx + c = 0. In this case, a = 3, b = 2, and c = 1, so the discriminant would be D = b² - 4ac = 2² - 4(3)(1) = -8.

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Answer: $115,000

Step-by-step explanation:

The common stock is 9000 times 5 = $45000

To Paid-in Capital in Excess of Par = 160,000 - 45,000 = $115,000

We apply the rational root theorem to identify potential rational roots.

Given,

How do you identify a possible logical root?

We can utilize the following parameters in our calculation based on the question:

We have to calculate the potential rational root of a function;

Here,

The following procedures are used to apply the rational root theorem to the possible rational root.

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A unit rate is a rate with a denominator of one.

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The titular conjecture was most likely put forth in the 1930s by Lothar Collatz.

Odd numbers are those that cannot be evenly divided by two. It cannot be evenly split into two different integers. An odd number will leave a leftover when divided by two. 1, 3, 5, 7, and other odd numbers are instances. The idea of odd numbers is identical to that of even numbers. Odd numbers satisfy the congruence when divided by two, leaving a residue of 1. A number's parity indicates how odd it is; an odd number has parity 1, whereas an even number has parity 0.

Given

The titular conjecture was most likely put forth in the 1930s by Lothar Collatz.

The issue seems like a practical joke.

Pick any number you like. Add 1 and multiply it by 3 if it's an odd number.

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The coordinates of point B is (1, -1)

Define Reflection on a Point

A reflection point occurs when a figure is constructed around a single point known as the point of reflection or centre of the figure. For every point in the figure, another point is found directly opposite to it on the other side.

Given,

Point A (7, 1) is reflected over the point (4, 0)

We know that,

The reflected point will be equidistant from the point over which it is reflected as the original point and in the same line as the original point and the reflected point.

Find the difference between the x and y values of the given points

For x value = 4 - 7 = -3

For y value = 0 - 1  = -1

Now, add the value to the reflection point.

x - axis : 4 +(-3) = 1

y - axis : 0 + (-1) = -1

Hence, the coordinates of point B is (1, -1)

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Answer:

y = x + 2

Step-by-step explanation:

Each y value is 2 greater than the x value

Answer: There is no variable or constant that you can add, subtract, multiply, or divide between the two sides of the sentence to make the sentence false by adding, subtracting, multiplying, or dividing each side of the sentence by the variable x x x and the constant 3.

Answer: No. Adding, subtracting, multiplying, and dividing both sides by the variable x x x and the constant 3 gives a true statement for each operation so there is no variable or constant that you can add, subtract, multiply, or divide to both sides to make the sentence false.

Step-by-step explanation: