Calculate the approximate degree measure of the angle, given the following expression: tan(y°) = 4.12 Round your answer to the nearest tenth.​

Answer:

in both questions the answer is option d.

The roots of a quadratic equation are the values of x that make the equation equal to 0.

The general form of a quadratic equation is [tex]ax^2[/tex] + bx + c = 0, where a, b, and c are constants.

To find the roots of the equation [tex]ax^2[/tex] - 16 = 0, we can use the quadratic formula:

x = (-b +/- sqrt(b^2 - 4ac))/(2a)

In this case, a = 1, b = 0, and c = -16. Plugging these values into the quadratic formula, we get:

x = (-0 +/- sqrt(0^2 - 41(-16)))/(2*1)

x = (-0 +/- sqrt(256))/(2)

x = (-0 +/- 16)/(2)

The roots of the equation are x = 8 and x = -8.

The complete question is:-

What are the roots of the quadratic equation x2 − 16 =0?

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In the equation c(n) = 50+4n, the value of c(7) is equal to 78.

Absolutely one element of Y is assigned to every element of X in a mathematical function from a set X to a set Y. Both the set X and the set Y are referred to as the function's domain and codomain, respectively.

Al-Biruni and Sharaf al-Din al-Tusi were two Persian mathematicians who developed the earliest known approach to function and its concept. The basic conception of functions was the relationship between fluctuating quantities and other variables. An illustration of this is how time affects a planet's position. In the past, the idea was developed with the infinitesimal calculus around the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable.

This is how the function is defined:

The equation c(n) = 50+4n defines function c, and n is the number of visits.

The function displays the cost in USD per month.

Thus, the following formula can be used to get the value of c(7):

c(7) = 50+4n

c(7) = 50+4(7)

= 50+28

=78

Therefore, c(7)=78

So, the value of c(7)=78.

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No it is not reasonable , because the number of medium T-shirts is not 3 times the number of large T-shirts .

Given :

Let say that the class need x medium and y large t - shirts .

so ,

x + y = 216

x = 3y

substitute

3y + y = 216

4y = 216

divide by 4 on both sides

4y / 4 = 216 / 4

y = 216/4

y = 54

x = 54 * 3

= 162

so here we need 162 medium t - shirts and 54 large t - shirts

given 72 large and 144 medium t - shirts so it not reasonable .

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Answer:

The next two terms in the Fibonacci sequence would be 23 and 37.

Step-by-step explanation:

The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones, usually starting with 0 and 1. So the next term in the sequence is found by adding the two previous terms, like this:

1 + 4 = 5

4 + 5 = 9

5 + 9 = 14

9 + 14 = 23

14 + 23 = 37

Answer:

[tex]c=2.50x[/tex]

Step-by-step explanation:

The cost per pound of chicken is [tex]50/20=\$2.50[/tex].

So, the equation is [tex]c=2.50x[/tex].

Answer:

30 shirts

Step-by-step explanation:

What we know:

30 seconds = 3 shirts

1 minute 30 seconds = 9 shirts

30 seconds per each 3 shirts

shirts:      3, 6, 9, 12, 15, 18, 21, 24, 27, 30

minutes: .5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5

Answer:

30 shirts

Step-by-step explanation:

First make the graph of the functions, then  if the two graphs are symmetric with respect to the line y = x (mirror images over y = x ), then they are inverse functions.

Symmetric

A figure or shape that can be divided into two equal parts by a line is called symmetric figures.

Inverse Functions

The inverse function of a function f  is a function that undoes the operation of f. The inverse of f exists if and only if f is bijective, and if it exists, is denoted by F^-1.

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Solving for two variables (normally denoted as "x" and "y") requires two sets of equations.

Assuming you have two equations, the best way for solving for both variables is to use the substitution method, which involves solving for one variable as far as possible, then plugging it back in to the other equation. Knowing how to solve a system of equations with two variables is important for several areas, including trying to find the coordinate for points on a graph.

Write out the two equations that have the two variables you want to solve. For this example, we will find the value for "x" and "y" in the two equations "3x + y = 2" and "x + 5y = 20"

Solve for one of the variables in on one of the equations. For this example, let's solve for "y" in the first equation. Subtract 3x from each side to get "y = 2 - 3x"

Plug in the y value found from the first equation in to the second equation in order to find the x value. In the previous example, this means the second equation becomes "x + 5(2- 3x) = 20"

Solve for x. The example equation becomes "x + 10 - 15x = 20," which is then "-14 x + 10 = 20." Subtract 10 from each side, divide by 14 and you have end up with x = -10/14, which simplifies to x = -5/7.

Plug in the x value in to the first equation to find out the y value. y = 2 - 3(-5/7) becomes 2 + 15/7, which is 29/7.

Check your work by plugging in the x and y values in to both of the equations.

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Yes, a 7th grader may be taken algebra. Depending on the school district, and capacity some 7th graders may be able to take algebra as an elective or as part of their regular curriculum.

Algebra is the branch of mathematics that helps in the rendering of problems or situations in the form of mathematical expressions.

It includes variables like x, y, z, and mathematical operations like addition, subtraction, multiplication, and division to form a meaningful mathematical expression.

Some of the branches of mathematics such as trigonometry, calculus, coordinate geometry, involve the use of algebra. One example is in algebra is 2x + 4 = 8.

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If the four-digit personal identification number (PIN) cannot start with a 0 and must be an odd number, then 0 four-digit pins are conceivable.

There are 10 possible digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) that can be used in a four-digit PIN. However, we are told that the PIN cannot begin with a 0, so there are only 9 possible digits that can be used for the first digit.

For the second, third, and fourth digits, any of the 10 digits can be used. Therefore, there are 9 x 10 x 10 x 10 = 9,000 four-digit PINs that can be created using any of the 10 digits.

We are also told that the PIN must be an odd number. This means that the last digit of the PIN must be odd. There are 5 odd digits (1, 3, 5, 7, and 9), so there are 5 possible digits that can be used for the last digit.

For the first three digits, any of the 9 digits that can be used for the first digit can be used. Therefore, there are 9 x 10 x 10 = 900 four-digit PINs that can be created using only odd digits.

However, we have double-counted the PINs that begin with 0. Since these PINs are not allowed, we need to subtract them from the total number of possible PINs. There are 9 x 10 x 10 = 900 four-digit PINs that begin with 0, so we need to subtract these from the total number of possible PINs.

The final number of possible four-digit PINs that cannot begin with 0 and must be odd is 900 - 900 = 0. Therefore, there are 0 four-digit PINs that meet these criteria.

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Answer:

$1772.10

Step-by-step explanation:

10% = 0.1

Take 1611 times 0.1 = $161.10

So, the 10% cheaper is $161.10

We add both numbers to find the price of last year's season ticket!

1611 + 161.10 = $1772.10

So, the price of last year season's ticket is $1772.10

Let's check to see if it is correct!

$1772.10 - $161.10 = $1611

So, my answer is correct!

Answer:

$1,790

Step-by-step explanation:

x -.1x = 1611  Combine like terms

.9x = 1611  Divide both sides by .9

x = 1790

Check:

1790 - .1(1790) = 1611

1790 - 179 = 1611

1611 = 1611

Yes, the number 16 is a square.

It is the square of the number 4, since 4 x 4 = 16.

A square root is a factor in mathematics that, when multiplied by itself, equals the initial number. For instance, 3 and -3 are both square roots of 9.

The square of a number's root is the value under the root. For instance, (3 + 2) = 3. Any even number's square unit will only include even numbers.

Each and every nonnegative real number x has a distinct nonnegative square root, known as the primary square root, which is represented by the symbol x, also known as the radical sign or radix. As an illustration, we write 9=3 to denote that 3 is the number 9's fundamental square root. The word (or integer) whose square root is being examined is known as the radicand. The word or number that appears beneath the radical symbol, in this case, 9, is referred to as the radicand. The principal square root can alternatively be expressed in exponent notation for nonnegative x as x1/2.

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To find the median of a set of numbers, you need to arrange the numbers in order from smallest to largest, and then find the middle number. In this case, the numbers are already in order: 2, 3, 4, 4, 6, 9.

There are 6 numbers in the set, so the median is the middle number, which is 4.

the median value, which is arrived at by sorting all the data points and selecting the central one (or if there are two middle numbers, taking the mean of those two numbers). Example: When the numbers are sorted, the number 4 is in the middle (1, 4, 7), making it the median of the numbers 4, 1 and 7.

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The value of p when x = 21 is p = 32/3 .

Given :

we know that ,

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form  p * x = k or p = k / x

we know that

For p = 14, x = 16

Find the value of k

k = p * x

substitute the values

k = 14 * 16

= 224

so

The equation is equal to

p = 224 / x

if x = 21

substitute the value of x in the equation

p = 224 / 21

Divide by 7 both numerator and denominator

p = 32 / 3

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Answer:

C, D

Step-by-step explanation:

Compare each choice with

x² + 5x - 8 = 0

A.

x² + 7x - 9 = 2x + 1

x² + 5x - 10 = 0

No

B.

x² + 4x - 5 = x - 3

x² + 3x - 2 = 0
No

C.

x² + 10x - 2 = 5x + 6

x² + 5x - 8 = 0

Yes

D.

12x + 4 = 7x + 12 - x²

x² + 5x - 8 = 0

Yes

Answer: C, D

We can determine the height of a triangle when we know the base and area of the triangle using the area formula of triangle in base and height, that is

A = 1/2 × b × h

A triangle is a three sided polygon. The height of the triangle is the perpendicular distance of the not-included vertex to the considered base.

The formula to determine area of a triangle of base b and height h is

A = 1/2 × b × h

Therefore to determine the height of a triangle when base and area is given, we substitute the given values in appropriate units in the formula.

h = 2×A/ b

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Answer:

144 seconds

Step-by-step explanation:

4.5 seconds = 5 pages

x second = 160 pages

cross multiply

you get: 5x= 160 ×4.5

which equals 720 divide it by 5 you get 144

Answer:

Base: 135 Pound

Torso: 135 Pound

Step-by-step explanation:

The snowman Weighed is 472 pounds

The head was 202 Pound

We have to find the total weight of the base and torso

472 - 202 = 270 pound

So, 270 pounds is the total weight of the base and torse

We know the base and torso weigh the same amount

So take 270 divided by 2 = 135 Pound

So, the Base weight is 135 Pound

      the Torso weight is 135 Pound

Answer:

101 pounds

Step-by-step explanation:

if the torso and base weighs the same as the head

then each by itself should weigh 101 pounds

I hope this helps

and i hope i understood the question

The inverse of function y = x² is ±√x .

Given equation,

y = x²

We have to find the inverse.

By interchanging x and y variables,

y² = x

Solve this equation for y now. This is the inverse of this function.

Take the square root of both sides.

y = ±√x

Then the inverse of the function given is :

f⁻¹(x) = ±√x

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To find the total balance in an account that earns a simple interest rate of 8% per year, we can use the formula A = P(1 + rt), where A is the total balance, P is the initial principal (or amount invested), r is the annual interest rate, and t is the number of years. In this case, the annual interest rate is 8%, so we can substitute 0.08 for r in the formula. Since Kadeem wants to find his total balance in one step, we can set t equal to 1 year. So, to find Kadeem's total balance in one year in one step, he needs to multiply his current balance by 1 + 0.08 = 1.08. Therefore, Kadeem should multiply his current balance by 1.08 to find his total balance in a year in one step.

In the given group of answer choices x-intercept, the only point that has a y-coordinate of 0 is (0, -1).

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We can identify an expression to see the numbers, variables and mathematical operator between them.

An expression consists of at least two terms along with a sign. Terms can be a constant and variables or constant and variables accompanied by a number. In each case, there is one symbols in between. As example, 2+3z is a expression where 2 is a number called constant which is separated from variables z by a addition sign +, 3 is called coefficient of z.

Mathematical expression is made up of combination of terms. We can find an expression with two or more numerical terms which are called numerical expression. Besides there are fractional expression with or without variables. We can identify an algebraic expression to observe that it has numbers, variables and operator. We can distinguish an equation from an expression by an equal sign. Whenever, an equal sign is present among the mathematical terms then the expression is called equation.

As example. the above expression is written as 2+3z=0

it is an equation, and we can determine the unknown value z.

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The missing number in the pair of equivalent expressions is 9.

To solve this problem, you can use the model provided to represent the expressions 15 + 9 and 5 + 3.

For the expression 15 + 9, you can place 15 in the first row of five squares and 9 in the second row of five squares, like this:

[15] [9]

For the expression 5 + 3, you can place 5 in the first row of three squares and 3 in the second row of three squares, like this:

[5] [3]

Then, you can use the model to find the missing number in the pair of equivalent expressions. Since the two expressions are equivalent, the missing number should be in the same position as the number 3 in the second row of the model.

If you look at the first expression, you can see that the missing number is in the same position as the number 9. Therefore, the missing number in the pair of equivalent expressions is 9.

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Answer: 17 gallons of gas to travel 748 miles

Step-by-step explanation:

First, we have to find how many miles he can travel with 1 gallon of gas

Take 308 divided by 7 = 44 miles of travel per gallon of gas

Then take 748 divided by 44 = 17 gallons

So, it takes 17 gallons of gas to travel 748 miles

Answer:

Isaac needs 17 gallons of gas to travel 748 miles.

Step-by-step explanation:

This problem is giving you the ratio of gallons to miles.

⭐A ratio is a fraction that compares two different units

⭐ In this problem, the units are gallons and miles

In order to find how many gallons Isaac needs to travel 748 miles, we need to create a proportion.

⭐ A proportion is when you make two ratios equal to each other to solve for one unit

First, let's identify the ratios in this situation. Let x = the number of gallons needed to travel 748 miles.

Ratio 1: 7 gallons/ 308 miles

Ratio 2: x gallons/748 miles

Now, set these two ratios equal to each other. Remember to keep the same units as either the numerator or denominator.

[tex]\frac{7}{308} = \frac{x}{748}[/tex]

Next, cross multiply to solve for x.

[tex]7(748) = 308x\\5,236 = 308x\\x = 17[/tex]

∴ Isaac needs 17 gallons of gas to travel 748 miles!

Here, 25 and 25 are both middle numbers we can average them to get the median, which is 25.

The median of the data is given by the middle number which is obtained after arranging all the data in a certain order.

For example, we have numbers 1,2,3,4 and 5 which is a data of five data points.

Now, here if we see that two numbers are to the left of 3 and two numbers are to the right of 3, therefore the median of this data is 3.

In higher standards, the formulae of median are given by -

Divide the number of observations by two.  

Now here arise two cases -

1. If there are an odd number of observations, round that number up, and the value in that position is the median.

2. If the number of observations is even, take the average of the values found above and below that position.

So, in a similar manner the median here is given by 25.

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The equation Y=-2x is a linear equation, which can be plotted on a graph as a straight line.

The equation can be written in slope-intercept form as y=mx+b, where m is the slope and b is the y-intercept. In this case, the slope is m=-2 and the y-intercept is b=0. Therefore, the equation can be written as y=-2x+0.

The slope of the line is negative, meaning that as x increases, y decreases. The y-intercept is zero, which means that the line passes through the origin (0,0).

For example, if x = 2, then y = -2(2) + 0 = -4. Therefore, the point (2, -4) is on the line. Similarly, if x = 4, then y = -2(4) + 0 = -8, so the point (4, -8) is also on the line.

The graph of the equation y=-2x would thus be a line starting at the origin (0,0) with a negative slope. As x increases, y decreases, and the line never crosses the y-axis.

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Answer:

X is a variable, the value depends on the equation

ME adds up the variances and divides the result by n. In this context, an error is defined as an uncertainty in a measurement or the difference between the measured value and the true/correct value.

In mathematics and statistics, the mean is the average of a set of variables. The simple arithmetic mean (add the numbers and divide the total by the number of observations), geometric mean, and harmonic mean are all ways for calculating the mean. The mean (average) of a data set is computed by adding all of the numbers in the set and dividing by the number of values in the set. When arranging data from smallest to greatest, the median is the value in the middle. The mode is the most commonly occurring number in a data set.

Here,

Subtract each measurement from another.

Find the absolute value of each difference from Step 1.

Add up all of the values from Step 2.

Divide Step 3 by the number of measurements.

Mean Error (ME) is calculated by adding the variances and dividing the result by n. An error in this sense is an uncertainty in a measurement, or the discrepancy between the measured value and the true/correct value.

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From the provided sample, The mean variance and standard deviation of the sample is given by [tex]\bar x = \frac{\sum x}{n} , variance = {standard deviation }^2[/tex] and

[tex]\sqrt \frac{\sum {(x-\bar x)^2}}{n-1}[/tex] .

Sampling is the process of choosing a portion of a statistical population to estimate attributes of the entire population in statistics, quality control, and survey methods. Statisticians try to get samples that are typical of the population under consideration.

The arithmetic mean, also known as the arithmetic average or simply the mean or average, is the sum of a set of numbers divided by the total number of numbers in the set. The collection frequently consists of a series of findings from a survey, experiment, or observational study.

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.

sample size =n .

[tex]\sum x[/tex] = sum of sample data.

[tex]\bar x = \frac {\sum x}{n}[/tex] (sample mean)

sample standard deviation(s) = [tex]\sqrt \frac{\sum {(x-\bar x)^2}}{n-1}[/tex]

[tex]variance = standard deviation ^2[/tex]

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