Hello, a little confused on this section. Thanks for your help!

The measure of the central angle is 0.75 radians

An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.

The area of a figure is the amount of space it occupies in its two dimensional state.

The length of an arc with an angle of Ф is given by:

Length of arc = (Ф/360) * (π * diameter)

The diameter is 16 cm and intercepted arc length is 6 cm, hence:

Length of arc = (Ф/360) * (π * diameter)

6 = (Ф/360) * (π * 16)

Ф = 42.97°

Ф = 42.97° * π/180 = 0.75 radian

The measure of the central angle is 0.75 radians

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Answer:

error in Step 2

Step-by-step explanation:

2(x - 3) + 3x = 19

Step 1 : 2x - 6 + 3x = 19 ← simplify left side by collecting like terms

Step 2 : 5x - 6 = 19 ← add 6 to both sides

Step 3 : 5x - 6 + 6 = 19 + 6

Step 4 : 5x = 25 ← divide both sides by 5

Step 5 : x = 5

Error was made by student in Step 2 who should have added 2x and 3x, not multiplied 2 × 3

The stem and leaf plot of the daily low temperatures in degrees Fahrenheit in a city for February is :

Stem        |       Leaves

1                |  7   7   8   9

2               |  1     1    2    2    6    6   6   8

3               |  1   8

Key : 2  | 3 means 23

A stem and leaf diagram is a method of visually displaying data that enables efficient and speedy organization and summarization of considerable amounts of information. In the storyline, a table structure is employed where the primary column, referred to as the "stem", includes the initial digit(s) of the data, while the secondary column, known as the "leaf", includes the remaining digit(s).

The data we are given is:

17, 17, 18, 19, 21, 21, 22, 22, 26, 26, 26, 28, 31, and 38

One the stem side, we will include the first number of the temperature and on the leaf side, we increase the second.

The stem will appear just once so 17, 17, 18, and 19 will have a stem of 1. The leaves will appear the number of times we see the numbers so those same numbers would be 7, 7, 8, and 19.

Stem        |       Leaves

1                |  7   7   8   9

Doing this for the other temperatures gives:

Stem        |       Leaves

1                |  7   7   8   9

2               |  1     1    2    2    6    6   6   8

3               |  1   8

Key : 2  | 3 means 23

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Answer:

.125 should be your answer. Have a Great Day!

Step-by-step explanation:

Step-by-step explanation:

The total price of sneakers including tax will be equal to $20.75.

The Latin phrase "per centum," which means "by the hundred," is where the English word "percentage" comes from. Percentage segments are those with a numerator of 100. In other words, it is a connection where the whole is always deemed to be valued 100.

As per the given information in the question,

Price of sneakers = $20

Tax on sneakers = 3.75%

Then, the amount of tax will be,

(20 × 3.75)/100

= 75/100

= $0.75

Then, the total price of the sneakers will be,

$20 + $0.75

= $20.75

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The consumer surplus is approximately $145.83.

To find the consumer surplus, we first need to find the demand function's inverse, which gives us the willingness to pay for each unit of the product. The demand function is:

D(x) = √(739 - 3x)

Setting D(x) equal to the equilibrium price of $25, we get:

25 = √(739 - 3x)

Squaring both sides, we get:

625 = 739 - 3x

Solving for x, we get:

So at a price of $25 per unit, the consumer is willing to buy 38 units per month.

Now we can calculate the consumer's surplus.

The consumer\(x = (739 - 625) / 3 = 38\) surplus is the difference between the total amount that consumers are willing to pay for a certain quantity of a good and the total amount they actually pay. In this case, the consumer's surplus can be calculated as:

\(CS = \int_0^{38} [D(x) - 25] dx\)

where D(x) is the demand function, and the integral is taken over the range of 0 to 38, which represents the quantity demanded at a price of $25 per unit.

Evaluating this integral, we get:

\(CS = \int_0^{38} [\sqrt{(739 - 3x)} - 25] dx\\\\= [1/6 (739 - 3x)^{(3/2)} - 25x]_0^{38}\\\\= \$ 145.83\)

Therefore, the consumer surplus is approximately $145.83.

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When x is equal to 1, the Function f(x) = -4x - 5 yields a value of -9.

The find ƒ(1) for the function f(x) = -4x - 5, we need to substitute x = 1 into the function and evaluate the expression.

Replacing x with 1, we have:

ƒ(1) = -4(1) - 5

Simplifying further:

ƒ(1) = -4 - 5

ƒ(1) = -9

Therefore, when x is equal to 1, the value of the function f(x) = -4x - 5 is ƒ(1) = -9.

Let's break down the steps taken to arrive at the solution:

1. Start with the function f(x) = -4x - 5.

2. Replace x with 1 in the function.

3. Evaluate the expression by performing the necessary operations.

4. Simplify the expression to obtain the final result.

In this case, substituting x = 1 into the function f(x) = -4x - 5 gives us ƒ(1) = -9 as the output.

It is essential to note that the notation ƒ(1) represents the value of the function ƒ(x) when x is equal to 1. It signifies evaluating the function at a specific input value, which, in this case, is 1.

Thus, when x is equal to 1, the function f(x) = -4x - 5 yields a value of -9.

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Answer:

dowry taking and giving are social crimes

Answer: 2/3 of a gallon per minute

Step-by-step explanation:

You can find the rate by subtracting the amount of gallons she observed and dividing it by the time.

7 - 5 = 2 and 2 gallons/3 mins = 2/3 of a gallon each minute.

The y-coordinate of -3f(x-1) when x = 0 is -63

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

The table of values

So, we have

-3f(x - 1)

When x = 0, we have

y = -3f(0 - 1)

This gives

y = -3f(-1)

From the table, we have

y = -3 * 21

Evaluate

y = -63

Hence, the y-coordinate is -63

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The median of the data collected from a track meet  is 2 meters.

The median is the middle number in a sorted, ascending or descending list of numbers.

To calculate the median of the given date, we folloe the steps below.

Collected date: 1, 4, 6, 2, 4, 3, 2/3, 1/3, 1/2

Step 1: Rearreange the date in accending order.

Step 2: Pick the middle of the number in the arranged data

Hence, the median of the data collected is 2 meters.

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Answer:

2.5

Step-by-step explanation:

Answer:

x = -13

Step-by-step explanation:

-2 (x + 4) = 18

distributive property  -2x + (-8) = 18

simplify   -2x - 8 = 18

cancel out 8 by addition  -2x = 26

cancel out -2 by division  x = -13

Answer:

Fractions are equal when one fraction can be obtained from the other.

Step-by-step explanation:

equality means a relationship between two quantities or, more generally two mathematical expressions, asserting that the quantities have the same value, or that the expressions represent the same mathematical object.

Answer:

the product of the decimal equivalents of all discount in the series

Answer:

Unlabeled side length = 15.00 units

Step-by-step explanation:

Because this is a right triangle, we can find the unlabeled side length using the Pythagorean theorem, which is

a^2 + b^2 = c^2, where

In the triangle, we're given that the legs are 12 and 9 units and the unlabeled side is the hypotenuse, which we must find:

Step 1:  Plug in 12 for a and 9 for b and simplify:

12^2 + 9^2 = c^2

144 + 81 = c^2

225 = c^2

Step 2:  Take the square root of both sides to solve for c, the hypotenuse (aka the unlabeled side):

± √225 = √(c)^2

± 15 = c

15.00 units = c

Although taking the square root of a number produced both a positive and negative answer since squaring both a positive and negative answer gives us a positive answer (e..g, 15 * 15 = 225 and -15 * -15 = 225), you can't have a negative measure.  Therefore, c, the unlabeled side length = 15.00 units.

Answer:

depends on the ammount

Step-by-step explanation:

Hello !

you made a typo with the c^-2 because otherwise it does not make a round result

\(a^{2} *b^{2} *c^{2} \\\\= 1^{2} *2^{2}* (-3)^{2} \\\\= 1*4*9\\\\\boxed{= 36}\)

The range of the function is the set of all real numbers greater than or equal to -2, because the lowest possible value of the function is -2, which occurs at x = 2.

What is a piecewise function ?

A piecewise function is a function that is defined by different equations on different parts of its domain. The graph of a piecewise function consists of several distinct parts, each corresponding to a different equation.

The graph shown is an example of a piecewise function. The function is defined using different equations on different intervals of the domain.

On the interval from negative infinity to negative 2, the function is defined by the equation y = 2. This means that the value of the function is always 2 on this interval, regardless of the value of x.

On the interval from negative 2 to 2, the function is defined by the equation y = -x. This means that the value of the function is equal to the negative of x on this interval.

On the interval from 2 to positive infinity, the function is defined by the equation y = 2. This means that the value of the function is always 2 on this interval, regardless of the value of x.

At the point x = -2, the function experiences a discontinuity, because the two equations that define it have different values at this point. The function is not differentiable at this point, because it does not have a well-defined tangent line.

The domain of the function is the set of all real numbers, because there are no restrictions on the values of x that are allowed.

Therefore, The range of the function is the set of all real numbers greater than or equal to -2, because the lowest possible value of the function is -2, which occurs at x = 2.

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The area of the enclosed shape is about 14.47 km^2.

We are given that;

056° for 9.8km and  3.5 km on a bearing of 112°

Now,

We can see that the enclosed shape is a triangle with sides 9.8 km, 3.5 km, and z km, and angles 56°, 112°, and y°. We can use the fact that the sum of angles in a triangle is 180° to find y:

y = 180° - 56° - 112°

y = 12°

Now we can use the cosine rule to find z:

z^2 = 9.8^2 + 3.5^2 - 2(9.8)(3.5)cos(12°)

z^2 ≈ 101.87

z ≈ 10.09

Therefore, Fred is about 10.09 km away from his start point.

To find the area of the enclosed triangle, we can use the sine rule to find x, the height of the triangle:

sin(56°) = x/9.8

x = 9.8 sin(56°)

x ≈ 8.27

The area of a triangle is given by half the base times the height, so:

A = (1/2)(3.5)(8.27)

A ≈ 14.47

Therefore, by trigonometric ratios the answer will be 14.47 km^2.

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Answer:

\(\displaystyle A=\frac{20}{3}\)

Step-by-step explanation:

\(\displaystyle A=\int^2_{-2}(|x|-(x^2-2))\,dx\\\\A=2\int^2_0(x-(x^2-2))\,dx\\\\A=2\int^2_0(-x^2+x+2)\,dx\\\\A=2\biggr(-\frac{x^3}{3}+\frac{x^2}{2}+2x\biggr)\biggr|^2_0\\\\A=2\biggr(-\frac{2^3}{3}+\frac{2^2}{2}+2(2)\biggr)\\\\A=2\biggr(-\frac{8}{3}+2+4\biggr)\\\\A=2\biggr(-\frac{8}{3}+6\biggr)\\\\A=2\biggr(\frac{10}{3}\biggr)\\\\A=\frac{20}{3}\)

Bounds depend on whether you use -x or +x instead of |x|, but you double regardless. See the attached graph for a visual.

We rule up the team members, say by Social Security number. We now ask each in turn her/his job explanation and political affiliation and data the information.

For any person, the information can be recorded as an instruct pair (x ,y) where x is one of B or W, and y is one of R, D, or I. So, there are for any person 6 possible records. The team conclusion is a sequence of such records, of length 15. Thus, for our team there are 6^15 possible results.

How many of these results have at least one blue-collar worker? How many have no blue-collar worker? Then x=W, and y can still take on any of 3 values, for a total of 3^15 possibilities. Thus, the number of possible summaries with at least one B is 6^15−3^15.

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Answer: 10 ounces for $2.40

Step-by-step explanation: The trick behind these problems, always divide. 2.40/10ounces is $0.24. 2.08/8ounces is $0.26. Better deal, therefore smaller answer of the 2, because it's cheaper.

The set of ordered pairs above: is a function.

The mapping diagram above: is a function.

y = x²: is a function.

The table above: is not a function.

In Mathematics and Geometry, a function is a mathematical equation which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.

Based on the set of ordered pairs, mapping diagram, and the equation above, we can reasonably infer and logically deduce that it represent a function because the input values (domain, x-value, or independent values) are uniquely mapped to the output values (range, y-value or dependent values).

In this context, we can reasonably infer and logically deduce that the table does not represent a function because the input value (-1) has more than output values (2 and 4 respectively).

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A line can be divided in proportions using ratios. The point at which a line is divided in ratios is calculated using: \([\frac{mx_2+ nx_1}{m+n},\frac{my_2+ ny_1}{m+n}]\)

Given that:

\(RS : ST = 5 : 1\)

The coordinates of RT are not given. So, I will solve using a general explanation.

When a line is divided into ratios, the point (S) at which the line is divided is calculated using the following line ratio formula:

\(S = [\frac{mx_2+ nx_1}{m+n},\frac{my_2+ ny_1}{m+n}]\)

Assume the coordinate of R and T is:

\(R = (1,6)\\T = (7,2)\)

\(RS : ST = 5 : 1\) means:

\(m:n = 5:1\)

So, point S is:

\(S = [\frac{5\times 7+ 1 \times 1}{5+1},\frac{5 \times 2+ 1 \times 6}{5+1}]\)

\(S = [\frac{36}{6},\frac{16}{6}]\)

\(S = [6,\frac{8}{3}]\)

Hence, if the coordinates of R and T are:

\(R = (1,6)\\T = (7,2)\)

And the line ratio is:

\(m:n = 5:1\)

The coordinate of S is:

\(S = [6,\frac{8}{3}]\)

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Answer:

Step-by-step explanation:

Answer:

D) 4.9 units, 14.2 units

Step-by-step explanation:

I assume that we will be using trigonmetry as this is a right triangle

The two ratios that will be used are CAH (Cosine = adjacent/hypotneuse)

and SOH (Sine = opposite/hypotneuse)

While it does not matter which acute angle the problem is to, I decided to set up the triangle like so in the picture attached

This means x = adjacent and y = opposite here

Now we just need to plug in the numbers to find the missing variables

x) cos(19) = x/15

(15)cos(19) = x/15(15)

~14.2 = x

y) sin(19) = y/15

(15)sin(19) = y/15(15)

~4.9 = y

Hope that helps a bit

I took waaay too long to explain this lol

The value of x for the triangle is 14.2 and the value of y is 4.9. The correct option is D.

Trigonometry is the branch of mathematics that establishes a relationship between the sides and angles of a right-angle triangle.

The mathematical trigonometric functions, sometimes referred to as circle, angle, or goniometric functions, relate the angle of a right-angled triangle to the ratios of its two side lengths.

Calculate the value of x as below,

xcos(19) = x/15

(15)cos(19) = x/15(15)

14.2 = x

The value of y is calculated as,

ysin(19) = y/15

(15)sin(19) = y/15(15)

4.9 = y

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Answer:

yes

Step-by-step explanation:

y + es = yes so do you understand i think i made it pretty clear. if not let me know.