The price of a ticket is increased from $32 to $96.
a What percentage of $32 is $96?
b What is the percentage increase?

Answer:

Step-by-step explanation:

Using the compound interest formula \(A = P(1+\frac{r}{n} )^{nt}\)

A = amount compounded (in $)

P = Principal (in $)

r = rate (in %)

t = time it takes to accumulate fund (in years)

n = time of compounding (in years)

Given P = $10,000, r = 4%, t = 3.5 years n = 1/12 years (since it is compounded monthly)

\(A = 10000(1+\frac{0.04}{(1/12)} )^{(3.5)(1/12)}\\A = 10000(1+0.48)^{0.2916}\\A = 10000(1.48)^{0.2916}\\A = 10000*1.12111\\A = 11,211.1\)

Amount he will compound after 3.5years will be $11,211.1.

Amount he should invest daily = Amount compounded/time taken (in days)

Since 3.5years ≈ 1278 days

Amount he should invest daily = $11,211.1/1278

Amount he should invest daily  = $8.77

Answer:

-24

Step-by-step explanation:

b²-2ac

⇒Plug in the values given in places and simplify.

\(=(-4)^{2} -2(-4)(-5)\\=16-2(20)\\=16-40\\=-24\)

-24 is the answer after substitution of the known values.

The answer is 80, because if you work backwards, you add 30 by 10, which equals 40, 40*2 equals 80.

A two-dimensional array declared as int a[3][5] has a total of 15 elements. This is because it consists of 3 rows and 5 columns, and the total number of elements can be calculated by multiplying the number of rows by the number of columns (3 * 5 = 15).

A two-dimensional array declared as int a[ 3 ][ 5 ] has a total of 15 elements. This is because a two-dimensional array is essentially an array of arrays, where each "row" is itself an array of elements. In this case, we have 3 rows and 5 columns, so there are a total of 3 x 5 = 15 elements in the array. To understand this conceptually, we can think of the array as a table with 3 rows and 5 columns. Each element in the array corresponds to a cell in this table. So, we have a total of 15 cells in the table, and therefore a total of 15 elements in the array. It's important to note that when we declare an array in C++, we specify the number of rows and columns that we want the array to have. This means that the size of the array is fixed at compile time and cannot be changed during runtime. If we want to add or remove elements from the array, we would need to declare a new array with a different size. In conclusion, a two-dimensional array declared as int a[ 3 ][ 5 ] has 15 elements, corresponding to the 15 cells in a table with 3 rows and 5 columns.

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Answer:

D is the right graph

Answer:

The first one would be the third one and the second one would be the second one.

Step-by-step explanation:

The first quadrant is a (Positive, Positive), the second one is a (Negative, Positive), the third one is a (Negative, Negative) and the fourth one is a (Positive, Negative)

The line y = -x, passing through the origin in the xy-plane, forms a 45-degree angle with the positive x-axis.

The slope-intercept form of a linear equation is y = mx + b, where m represents the slope of the line. In this case, the equation y = -x has a slope of -1. The slope indicates the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

To determine the angle between the line and the positive x-axis, we need to find the angle that the line's slope makes with the x-axis. Since the slope is -1, the line rises 1 unit for every 1 unit it runs. This means the line forms a 45-degree angle with the x-axis.

The angle can also be determined using trigonometry. The slope of the line (-1) is equal to the tangent of the angle formed with the x-axis. Therefore, we can take the inverse tangent (arctan) of -1 to find the angle. The arctan(-1) is -45 degrees or -π/4 radians. However, since the line is in the positive x-axis direction, the angle is conventionally expressed as 45 degrees or π/4 radians.

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ANSWER

C. 12

EXPLANATION

1/3 of the pizzas is:

Therefore, 6 pizzas were cheese and the rest were pepperoni:

There were 12 pepperoni pizzas.

Number of boys = a - b

Number of children in the class = a

Number of girls in the class = b

Number of boys = Total - Girls

                              a - b

Answer:

Try y=x²+4

Step-by-step explanation:

y=-x+4

when its perpendicular you change the -x to x. When you have a perpendicular equation flip the sign and if fraction flip the fraction as well but there isn't a fraction here so you just change the -x to a +x and then work out the problem like this

y-3=x(x- -1)

y-3=x²+1

 +3     +3

__________

y=x²+4

(C) x=-5, y=6 is the solution of the equation 2x+3y=8

To find out which among the following options are solutions of the equation 2x+3y=8, we can substitute the values of x and y in the equation and see if it holds true or not.

a) x=0, y=5 : 2(0) + 3(5) = 0 + 15 = 15 != 8

b) x=3, y=2 : 2(3) + 3(2) = 6 + 6 = 12 != 8

c) x=-5, y=6 : 2(-5) + 3(6) = -10 + 18 = 8 = 8

d) x=-1, y=-2 : 2(-1) + 3(-2) = -2 + -6 = -8 != 8

so the value of left hand side and right hand side of a), b) ,d) is not equals to each other and hence they won't be the equation solution .

So the correct answer is (c) x=-5, y=6

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The given statement "The this pointer is not automatically passed to static member functions of a class." is false as static member functions can be called without creating an object of the class, and the "this" pointer is used to refer to the current instance of the class. Since no instance is required for static member functions, the "this" pointer is not applicable in this case.

In object-oriented programming, a class is a blueprint for creating objects, and member functions are functions defined within a class that can be called on objects of that class.

Static member functions, also known as class methods, are special member functions that are associated with the class itself rather than any specific object or instance of the class. They are declared using the "static" keyword.

Since static member functions do not operate on specific instances of the class, they do not have access to the "this" pointer. The "this" pointer is a hidden pointer that points to the current object instance, allowing non-static member functions to access the data members and other member functions of the object. However, static member functions do not have this pointer because they are not tied to any specific object.

Static member functions can only access static members of the class, which include static variables and other static member functions. They can be called using the class name itself, without creating an instance of the class. This is because they are not associated with any particular object but rather with the class as a whole.

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21 is the total number of possible outcomes by fundamental counting principle.

A number system is defined as a system of writing to express numbers.

Fundamental Counting Principle states that if an event can occur in m different ways, and another event can occur in n different ways, then the total number of occurrences of the events is m × n.

As we observe there are 3 different sizes.

There are seven different flavours.

By fundamental counting principle multiply 7 and 3

7×3

We get 21

Hence, 21 is the total number of possible outcomes by fundamental counting principle.

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Answer: I believe the answer is 3.07 but I may be wrong so if you want you can wait for another answer :D

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

  C.  142°

Step-by-step explanation:

You want the angle between vectors u=3i+√3j and v=-2i-5j.

There are a number of ways the angle between the vectors can be found. For example, the dot-product relation can give you the cosine of the angle:

  u•v = |u|·|v|·cos(θ) . . . . . . where θ is the angle of interest

You can find the angles of the vectors individually, and subtract those:

  u = |u|∠α

  v = |v|∠β

  θ = α - β

When the vectors are expressed as complex numbers, the angle between them is the angle of their quotient:

  \(\dfrac{\vec{u}}{\vec{v}}=\dfrac{|\vec{u}|\angle\alpha}{|\vec{v}|\angle\beta}=\dfrac{|\vec{u}|}{|\vec{v}|}\angle(\alpha-\beta)=\dfrac{|\vec{u}|}{|\vec{v}|}\angle\theta\)

This method is used in the calculation shown in the first attachment. The angle between u and v is about 142°.

A graphing program can draw the vectors and measure the angle between them. This is shown in the second attachment.

__

Additional comment

The approach using the quotient of the vectors written as complex numbers is simply computed using a calculator with appropriate complex number functions. There doesn't seem to be any 3D equivalent.

The dot-product relation will work with 3D vectors as well as 2D vectors.

<95141404393>

Answer:

4444444444445566tfcgyjbde467jndw34u

The set of side length similar to the given one is 1.6 meters, 2 meters, 3.2 meters.

Option A.

Given is a side length of a triangle has side lengths of 8 meters, 10 meters, and 16 meters.

We know that the similar triangles has proportional side lengths,

8/1.6 = 5

10/2 = 5

16/3.2 = 5

Hence the set of side length similar to the given one is 1.6 meters, 2 meters, 3.2 meters.

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Step-by-step explanation:

In mathematics, factorization or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind. For example, 3 × 5 is a factorization of the integer 15, and is a factorization of the polynomial x² – 4. 

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This is the general solution to the given differential equation using separation of variables.

To solve the given differential equation using separation of variables, we'll rearrange the equation and separate the variables:

dy / dx = (xy + 8y - x - 8) / (xy - 7y + x - 7)

First, we'll rewrite the numerator and denominator separately:

dy / dx = [(x - 1)(y + 8)] / [(x - 1)(y - 7)]

Next, we can cancel out the common factor (x - 1) in both the numerator and denominator:

dy / dx = (y + 8) / (y - 7)

Now, we'll separate the variables by multiplying both sides by (y - 7):

(y - 7) dy = (y + 8) dx

To solve the equation, we'll integrate both sides:

∫ (y - 7) dy = ∫ (y + 8) dx

Integrating the left side with respect to y:

(1/2) y^2 - 7y = ∫ (y + 8) dx

Simplifying the right side:

(1/2) y^2 - 7y = xy + 8x + C

where C is the constant of integration.

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Answer:

0.0000000000783

Step-by-step explanation:

Since the exponent is negative you will move the decimal point 11 places to the left, including the number 7.

Answer:

the correct answer is y = 2x+1

We are 95% confident that the true proportion of auto accidents with teenaged drivers falls between 16.1% and 23.9%.

To get the 95% confidence interval for the proportion of auto accidents with teenaged drivers, we need to use a sample of auto accidents and calculate the proportion of those accidents that involved a teenaged driver. Then, we can use a formula to calculate the interval that we are 95% confident contains the true proportion in the population.
Assuming we have a random sample of auto accidents, we can use the following formula:
95% confidence interval = sample proportion +/- (z-score)*(standard error)
The z-score corresponds to the level of confidence we want to use, which is 1.96 for a 95% confidence interval. The standard error is calculated as the square root of (sample proportion*(1 - sample proportion))/sample size.
Let's say we have a sample of 500 auto accidents and 100 of them involved a teenaged driver. The sample proportion is 0.2 (100/500). Using the formula above, we get: 95% confidence interval = 0.2 +/- (1.96)*(sqrt(0.2*(1-0.2)/500)) = 0.2 +/- 0.039
= (0.161, 0.239)
Therefore, we are 95% confident that the true proportion of auto accidents with teenaged drivers falls between 16.1% and 23.9%.

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The number of men living in the village is 260.

A collection of many linear equations that include the same variables is referred to as a system of linear equations. A linear equation system is often composed of two or more linear equations with two or more variables.A linear equation with two variables, x and y, has the following general form:

                                           \(ax + by = c\)

Given:

Total inhabitants in the village: 817

Number of children: 241

There are 56 more women than men in the village

Total adults = Total inhabitants - Number of children

Total adults = 817 - 241

Total adults = 576

Let number of men in the village be 'x' and number of women in the village be 'y',

∴ y=x+56 (given) ..................(1)

Also, x+y=576 .................(2)

From equation (1) and (2),

x + (x + 56) = 576

2x + 56 = 576

2x = 576 - 56

2x = 520

x = 520 / 2

x = 260

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The metric system is an international system of measurement that uses the base unit of the meter to measure length or distance. The meter is defined as the length of the path traveled by light in a vacuum during a specific fraction of a second.

It is an essential unit of the International System of Units (SI) and is used to measure distance, length, height, and width in most countries worldwide.

The meter is equivalent to approximately 39.37 inches, making it a longer unit of measurement than the inch, which is used in the imperial system of measurement. The metric system is based on a decimal system, which makes it easier to convert between units of length. For instance, one kilometer (km) is equal to 1,000 meters, and one centimeter (cm) is equal to 0.01 meters.

The metric system is widely used in science, industry, and daily life. It is the standard system of measurement used in most countries worldwide, except for the United States, which primarily uses the imperial system of measurement. However, it is essential to understand the metric system, as it is becoming increasingly popular in many fields and is a fundamental part of global communication.

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Answer: 27%

Step-by-step explanation:

The cash price of the bond is $10,898.92.The accrued interest is $315.32.

The cash price of the bond, we need to determine the present value of the bond's future cash flows. The bond has a face value (redeemable at par) of $22,000 and a coupon rate of 5.3%. Since the interest is payable semi-annually, each coupon payment would be half of 5.3%, or 2.65% of the face value. The bond matures on May 12, 2008, and the purchase date is June 07, 2001, which gives a total of 28 semi-annual periods.

Using the formula for present value of an annuity, we can calculate the present value of the coupon payments. The yield is 9.8% compounded semi-annually, so the semi-annual discount rate is half of 9.8%, or 4.9%. Plugging in the values into the formula, we get:

Coupon payment = $22,000 * 2.65% = $583

Present value of coupon payments = $583 * [(1 - (1 + 4.9%)^(-28)) / 4.9%] = $10,315.32

To calculate the present value of the face value, we need to discount it to the present using the same discount rate. Plugging in the values, we get:

Present value of face value = $22,000 / (1 + 4.9%)^28 = $5883.60

Finally, we add the present value of the coupon payments and the present value of the face value to obtain the cash price of the bond:

Cash price = Present value of coupon payments + Present value of face value = $10,315.32 + $5,883.60 = $10,898.92.

Accrued interest refers to the interest that has accumulated on the bond since the last interest payment date. In this case, the last interest payment date was on June 7, 2001, and the purchase date is also June 7, 2001, so no interest has accrued yet.

The accrued interest can be calculated by multiplying the coupon payment by the fraction of the semi-annual period that has elapsed since the last interest payment. Since no time has passed between the last interest payment and the purchase date, the fraction is 0. Thus, the accrued interest is $583 * 0 = $0.

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We can be 95% confidence interval that the true mean reading achievement score for the population of third graders falls within the interval (74.02, 75.98).

The margin of error for a 95% confidence interval for the mean reading achievement score for a population of third graders depends on the sample size, standard deviation, and the level of confidence desired.

Assuming the sample is randomly selected and follows a normal distribution, the margin of error (E) for a 95% confidence interval can be calculated using the following formula:

E = 1.96 * (s / √(n))

where s is the sample standard deviation, n is the sample size, and 1.96 is the z-score associated with a 95% confidence level.

For example, if we have a sample of 100 third graders with a sample standard deviation of 5, the margin of error for a 95% confidence interval would be:

E = 1.96 * (5 / √(100))

= 0.98

Therefore, the 95% confidence interval for the mean reading achievement score for the population of third graders would be the sample mean plus or minus the margin of error:

sample mean ± margin of error

For instance, if the sample mean is 75, the 95% confidence interval for the mean reading achievement score would be:

=75 ± 0.98 or (74.02, 75.98)

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Answer:

don't worry about this question