Find the length of the​ arc, s, on a circle of radius r intercepted by a central angle θ. Express the arc length in terms of π. Then round your answer to two decimal places.
​Radius, r ​= 16 inches; Central​ angle θ = 75°

(Simplify your answer. Type an exact answer in terms of π. Use integers or fractions for any numbers in the​ expression.)

Answer in form of Pi and Inches

The inequalities that could show the weight of each horse are:

h ≤ 1248

t ≤ 352

To determine the inequalities that could show the weight of each horse, we can use the fact that the total weight of the horses and tack must be less than or equal to the capacity of the horse trailer. We can set up the following inequalities:

5h + 5t ≤ 8000

where h represents the average weight of each horse.

However, we don't know the value of t, so we need to express it in terms of h. We are given that the combined weight of the horses is 6,240 pounds, so we can write:

5h ≤ 6240

Solving for h, we get:

h ≤ 1248

This means that the weight of each horse must be less than or equal to 1,248 pounds.

Now we can substitute this upper bound for h into the first inequality to get:

5(1248) + 5t ≤ 8000

6240 + 5t ≤ 8000

5t ≤ 1760

t ≤ 352

This means that the average weight of tack per horse must be less than or equal to 352 pounds.

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The probability that an 18-year-old man picked at random is taller than 74 inches is approximately 0.0228 or 2.28%.

We have,

We can use the standard normal distribution to solve this problem by standardizing the height value using the formula:

z = (x - μ) / σ

where:

x = the height value (in inches)

μ = the mean height (in inches)

σ = the standard deviation (in inches)

Substituting the given values, we get:

z = (74 - 68) / 3

z = 2.0

Using a standard normal table or calculator, we can find the probability that a random standard normal variable is greater than 2.0 to be approximately 0.0228.

Therefore,

The probability that an 18-year-old man picked at random is taller than 74 inches is approximately 0.0228 or 2.28%.

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From the information provided, according to the table, if the purchase price of a car was less than $20,000, what is the probability that its Trepair costs were less than about 46%.

If a car had total repair costs of less than $10,000, what is the probability that its purchase price was more than $40.000 Express your about 20%.

Probability is a measure of the likelihood of an event happening. It is a numerical value between 0 and 1, where 0 indicates an event is impossible, and 1 indicates an event is certain.

So, calculating the probability of the events above happening in percentage is as follows:

A. 86/ (86+67+35) =

18/188 ≈ 46%.

Therefore, Blank 1 is about 46%

B. 40/(88+71+40) =

40/197 ≈ 20%.

Therefore, Blank 2 is about 20%.

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The Surface area of figure is 396.896 unit².

We have,

x = 4 unit, y = 13 unit and z = 7 unit.

First Surface Area of Cylinder

= 2πrh

= 2(3.14)(4)(7)

=  175.84 unit²

and, Surface Area of Cone

= πrl

= (3.14)(4)(13.6)

= 170.816 unit²

Thus, the Surface area of figure is

= 175.84 + 170.816 + 50.24

= 396.896 unit²

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The value of angle t is 126⁰.

The value of angle x is 70⁰.

The value of angle 5 is 85⁰.

The value of each of the missing angles is calculated as follows;

angle b = 27⁰ (vertical opposite angles are equal)

The value of angle t is calculated as follows;

b + t + 27 = 180 ( sum of angles on a straight line)

27 + t + 27 = 180

54 + t = 180

t = 180 - 54

t = 126⁰

The value of angle x is calculated as follows;

x + 30 + 80 = 180 (sum of angle in a triangle and vertical opposite angles)

x + 110 = 180

x = 180 - 110

x = 70⁰

The value of angle 5 is calculated as follows;

65 + 70 + (180 - 40) + ∠5 = 360 (sum of angles in a quadrilateral)

65 + 70 + 140 + ∠5 = 360

275 + ∠5 = 360

∠5 = 360 - 275

∠5 = 85⁰

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answer attached

see below

please give brainliest it will be much appreciated

Hope it helps :)

[tex]x + 4y = 9 \\

-x - 2y = 3 \\ eliminate \: one \: variable \: by \\ adding \: the \: equations \\ 2y = 12 \\ divide \: both \: sides \\ y = 6 \\ substitute \: the \: value \: of \: y \\ \: into \: equation \: ...2 \\ - x - 2(6) = 3 \\ solve \: the \: equation \\ - x - 12 = 3 \\ - x = 3 + 12 \\ - x = 15 \\ x = - 15 \\ SOLUTION \\ x = - 15 \\ y = 6 \\ Hope \: it \: helps :)[/tex]

The surface area of the composite solid is calculated to the nearest hundredth as: 113.09 square feet.

To find the surface area of the composite solid which is composed of a cone and a cylinder, do the following:

Find the surface area of the cone:

Surface area of cone = πrl

radius (r) = 4 ft

l = √(3² + 4²) = 5 ft

Plug in the values:

Surface area of cone = π * 4 * 5 ≈ 62.83 square feet.

Find the surface area of the cylinder:

Surface area of cylinder = 2πr(h + r)

radius (r) = 4 ft

h = 2 ft

Plug in the values:

Surface area of cylinder = 2 * π * 4 * (2 + 4) ≈ 150.80 square feet.

Find area of the surface both meet:

Area = πr² = π * 4² ≈ 50.27 square feet.

Surface area of the composite solid = 62.83 + 150.80 - 2(50.27)

= 113.09 square feet.

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The height of the building is given by h = 93.5 m

Given data ,

Let the proportion be represented as A

Now , the value of A is

The height of the pole is 3.3 meters and its shadow is 1.71 meters long. We can set up a proportion to find the height of the building:

Height of pole / Length of pole's shadow = Height of building / Length of building's shadow

3.3 m / 1.71 m = x / 48.25 m

Now we can cross-multiply and solve for "x":

3.3 m * 48.25 m = 1.71 m * x

159.825 m² = 1.71 m * x

x = 159.825 m² / 1.71 m

x ≈ 93.5 m

Hence , the height of the building is approximately 93.5 meters

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The answer of given question is 9/16.

An equation is a mathematical statement that shows the equality between two expressions. It typically consists of mathematical symbols, such as numbers, variables, operators, and equal signs. Equations are used to represent relationships between quantities and are commonly used in various fields of mathematics, science, and engineering to solve problems, make predictions, and describe phenomena.

A fraction is a mathematical representation of a part or parts of a whole. It consists of two numbers, separated by a horizontal or diagonal line, called the numerator and the denominator. The numerator represents the number of parts being considered, while the denominator represents the total number of equal parts that make up the whole.

3/8+4/5-5/16-3/10

(30+64-25-24)/80

45/80

=9/16

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Standard form of the equation for the circle with the following properties is (x + 7)² + (y + 6)²= 104.

A line segment through the center of a circle with its ends on the circle's circumference. Its value is twice of the radius.

An equation is a mathematical statement that asserts the equality between two expressions, typically containing one or more variables. It consists of two sides separated by an equals sign (=), indicating that the expressions on both sides have the same value. Equations are used to describe relationships, solve problems, and make predictions in various branches of mathematics, science, engineering, and other fields. They can be linear or nonlinear, and may involve arithmetic, algebraic, trigonometric, exponential, or other mathematical operations. Solving an equation involves finding the values of the variables that make the equation true.

To find the standard form of the equation for a circle, we can start by finding the center and radius of the circle using the given endpoints of a diameter.

The center of the circle is the midpoint of the diameter, which can be found by averaging the coordinates of the two endpoints. Let's denote the coordinates of the endpoints of the diameter as (x1, y1) and (x2, y2) respectively.

In this case, the coordinates of the endpoints are (x1, y1) = (-6, -1) and (x2, y2) = (-8, -11). Using the midpoint formula, we can find the center of the circle:

Center = ((x1 + x2)/2, (y1 + y2)/2)

Plugging in the values, we get:

Center = ((-6 + (-8))/2, (-1 + (-11))/2)

Center = ((-14)/2, (-12)/2)

Center = (-7, -6)

So, the center of the circle is (-7, -6).

The radius of the circle is half the length of the diameter, which can be found using the distance formula between the two endpoints of the diameter. Let's denote the distance between the endpoints as d.

The distance formula is given by:

d = sqrt((x2 - x1)² + (y2 - y1)²)

Plugging in the values, we get:

d = sqrt((-8 - (-6))² + (-11 - (-1))²)

d = sqrt((-2)² + (-10)²)

d = sqrt(4 + 100)

d = sqrt(104)

So, the radius of the circle is sqrt(104).

Now that we have the center and radius of the circle, we can write the standard form of the equation of the circle as:

(x - h)² + (y - k)²= r²

where (h, k) is the center of the circle and r is the radius of the circle.

Plugging in the values, we get:

(x - (-7))² + (y - (-6))² = (sqrt(104))²

(x + 7)² + (y + 6)²= 104

So, the standard form of the equation for the circle with endpoints of a diameter at (-6, -1) and (-8, -11) is (x + 7)² + (y + 6)² = 104

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It is not appropriate to generalize the findings of the survey to the entire school population.

What is survey?

The conclusion that about 8.6% of the students in the school have a January birthday is not necessarily valid based on the information provided.

The sample size of the survey is too small (only 3 students with January birthdays) and limited to one math class, so it may not be representative of the whole school population. Additionally, the sample is not randomly selected, which introduces the possibility of selection bias.

Therefore, it is not appropriate to generalize the findings of the survey to the entire school population. A more reliable way to determine the percentage of students with a January birthday would be to collect data from a larger, randomly selected sample of students across the entire school population.

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The number of years that it will take to grow 8 inches is 32 years.

We know that the diameter grows at a constant rate of 1/4 inches per year.

Then the amount that the diameter grows after x years is given by the linear equation:

D(x) = x*(1/4) in

We want to find the number of years that it takes to grow 8 inches, then we need to solve the linear equation:

8in =  x*(1/4) in

Now we can solve that equation for x, we will get:

8in/((1/4) in) = x

8*4 = x

32 = x

It will take 32 years.

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Caden needs to use 126 cubes to fill the box without empty space.

The volume of the box is:

42 in. x 1 in. x 3 in. = 126 cubic inches

The volume of each small cube is:

1 in. x 1 in. x 1 in. = 1 cubic inch

To fill the box, the number of cubes needed is the volume of the box divided by the volume of each cube:

126 cubic inches ÷ 1 cubic inch per cube = 126 cubes

Therefore, Caden needs to use 126 cubes to fill the box without empty space.

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Without seeing the graph of the linear function, it is impossible to determine if Tom's answer of 12 is correct or incorrect. However, it is important to understand the concept of slope and how it is calculated for a linear function.

The slope of a linear function represents the rate at which the y-coordinate changes for each unit increase in the x-coordinate. In other words, it measures the steepness of the line. Mathematically, the slope of a line is defined as the ratio of the change in the y-coordinate to the change in the x-coordinate between any two points on the line.

To calculate the slope of a line given its graph, one can choose any two points on the line and find the difference in their y-coordinates and x-coordinates. The slope is then the ratio of the change in y-coordinates to the change in x-coordinates. This can be expressed as:

slope = (change in y-coordinate) / (change in x-coordinate)

Now, if Tom has correctly identified two points on the line and calculated the difference in their y-coordinates and x-coordinates, and if he has obtained a ratio of 12 for the change in y-coordinate to the change in x-coordinate, then his answer of 12 for the slope would be correct.

However, it is also possible that Tom made an error in his calculation, or that he misread the graph, and obtained an incorrect answer. Therefore, it would be necessary to verify his calculations by checking the points he used and the formula he applied.

In conclusion, without further information about the graph of the linear function and the points chosen by Tom to calculate the slope, it is impossible to determine if his answer of 12 is correct or incorrect.

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The canoe traveled approximately a distance of 21.9ft.

let the distance the canoe travels be "d".

Initial position = 65 ft

After  7s,

The Final position is 40ft away

From the given information the canoe moves =(65-40)=25ft closer

Let x=25ft

Using the tangent function

we know that, tan(50degree)=x/d

therefore, d=25/tan(50 degree)

d=21.9ft

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The end behavior is if  x becomes very large the value of f(x) also becomes very large, The function will approach zero more slowly as x approaches negative infinity, because 7 is greater than 1.

To describe the end behavior of f(x), we need to consider the limit of f(x) as x approaches positive infinity and negative infinity. We can write this as:

lim f(x) as x → ±∞ = ±∞

This means that as x becomes very large (either positive or negative), the value of f(x) also becomes very large (either positive or negative).

b. If we change the base of the exponential function from 5/7 to 7, the graph of f(x) will change in the following ways:

The function will grow faster, because 7 is greater than 5/7.

The function will start at a higher value, because f(0) = 4(7)^0 = 4.

The function will approach zero more slowly as x approaches negative infinity, because 7 is greater than 1.

c. If we add a constant to the exponential function, the graph of f(x) will be shifted vertically by the amount of the constant. In this case, the graph of f(x) will be shifted downwards by 2 units, because we are subtracting 2 from the function.

The equation of the new function is:

f(x) = 4(5/7)ˣ - 2

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Answer:

Step-by-step explanation:

Given:

Proportion of students who are late for class in the population: p = 0.12

Sample size: n = 538

Margin of error: E = 0.03

The standard error of the proportion can be calculated using the formula:

SE = sqrt(p*(1-p)/n)

SE = sqrt(0.12*0.88/538)

SE = 0.019

The margin of error corresponds to a z-score at the 97.5th percentile (since we want the probability of the sample proportion being within 3% of the population proportion in either direction, which gives us a two-tailed test with an alpha level of 0.025 on each side). This z-score can be found using a standard normal distribution table or calculator and is approximately 1.96.

The margin of error can also be calculated using the formula:

E = z*(SE)

0.03 = 1.96*(0.019)

To find the probability that the sample proportion differs from the population proportion by less than 3%, we need to find the area under the standard normal distribution curve between the z-scores of -1.96 and 1.96. This area is equivalent to the probability of the sample proportion being within 3% of the population proportion. This probability can be found using a standard normal distribution table or calculator and is approximately 0.8534.

Therefore, the probability that the proportion of late students in a sample of 538 students would differ from the population proportion by less than 3% is 0.8534 or 85.34% (rounded to four decimal places)

Answer:

First, we need to find out how many people are male and female in the town:

Step-by-step explanation:

Male population = 48% of 42800 = 20544

Female population = 100% - 48% = 52% of 42800 = 22256

To find out how many more females there are than males, we need to subtract the male population from the female population:

Female population - Male population = 22256 - 20544 = 1712

Therefore, there are 1712 more females than males in the town.

Answer:

y = 2x

Step-by-step explanation:

If x > 5, then x - 5 is positive and x + 5 is also positive. So we can rewrite the equation as follows:

y = (x - 5) + (x + 5)

Simplifying the equation, we get:

y = 2x + 0

Therefore, the equation without using absolute value for the given conditions is y = 2x.

Hope this helps!

The additional information is required to prove the triangles are congruent with ASA Postulate is [tex]\bar{RS} \cong \bar{CS}[/tex] (option d)

In order to prove that two triangles are congruent using the ASA postulate, we need to know that they have two pairs of congruent angles and a congruent side that is in between those angles. The image below shows two triangles, but we do not have enough information to prove that they are congruent with the ASA postulate.

To use the ASA postulate, we need to have a congruent side in between the two congruent angles. In this case, we do not know if side RS is congruent to side CS. Therefore, we cannot use the ASA postulate to prove that these triangles are congruent.

In summary, to prove that two triangles are congruent using the ASA postulate, we need to have two pairs of congruent angles and a congruent side in between those angles. Without this information, we cannot use the ASA postulate to prove congruency.

Hence the correct option is (d)

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Answer:

Step-by-step explanation:

The volume of the triangular prism shown below is 48 cm²

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 area of triangular base = (1/2) * 12 cm * 8 cm = 48 cm²

The volume of triangular prism = area of base * height

Volume = 48 cm² * 34 cm = 1632 cm³

The volume of the triangular prism is 48 cm²

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Answer:

Step-by-step explanation:

temperature is heated half an hour

19°c+71°c=90°c

{since its increased by 71°c}

90°c-[2°c*30]=30°c

The solution to the Quadratic equation x², when x satisfies the equation 6x - 24 = 0, is x²= 16.

A quadratic equation is a polynomial equation of the second degree, meaning it contains one or more terms that involve a variable raised to the power of two. The standard form of a quadratic equation is:

ax^2 + bx + c = 0,where a, b, and c are constants, and x is the variable.

The given equation is 6x - 24 = 0.

To solve for x, we can isolate x on one side by adding 24 to both sides of the equation:

6x - 24 + 24 = 0 + 24

6x = 24

Then, we can solve for x by dividing both sides by 6:

6x/6 = 24/6

x = 4

Therefore, the solution to the equation 6x - 24 = 0 is x = 4.

Now, to solve for x², we can simply substitute x = 4 into the equation x²:

x² = 4²

x^2 = 16

Therefore, the solution to the equation x², when x satisfies the equation 6x - 24 = 0, is x² = 16.

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Answer:

The answer choice that contains only equations is:

A. 2 + H = 14 and K - 25 = 2

Explanation:

A. Both expressions are equations because they have an equal sign and a variable.

B. C-14C-14 is not an equation because it doesn't have an equal sign.

C. Both expressions are equations, but 22-y is not a complete equation (missing an equal sign).

D. Both expressions are equations, but 55= r-1 is not a complete equation (missing an equal sign).

Step-by-step explanation:

The error which Mason made was subtracting 5 from both sides.

The correct solution is x < 16 and it is shown on the number line below.

The best way to describe the temperature in the greenhouse before the heater stopped working is that it was at least 71 degrees.

An inequality that represent this situation is x + 21 ≥ 47 and the solution is x ≥ 26.

The inequalities that can be used to represent the situation are;

D. x - 7.35 ≥ 2.87

E. x ≥ 10.22

Based on the information provided about the math test, the following inequality must be solved by students;

x - 5 < 11

By adding 5 to both sides of the inequality, we have the following:

x - 5 + 5 < 11 + 5

x < 16

Therefore, the error which Mason made was subtracting 5 from both sides.

Since the temperature dropped 6 degrees before it was fixed and it was still at least 67 degrees when the heater started working again, we can model it as follows;

x - 4 ≥ 67

x ≥ 71

Since Ramiro has $21 and wants buy a skateboard that cost $47, the amount of money that he needs can be modeled by this inequality;

x + 21 ≥ 47

x ≥ 47 - 21

x ≥ 26

In conclusion, the inequalities that can be used to represent the total amount, x, Kendra needs for the bead are;

x - 7.35 ≥ 2.87

x ≥ 2.87 + 7.35

x ≥ 10.22

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The values of x, y and  z of the given parallelogram are: x = 12, y = -20 and z = -32

A quadrilateral has two pairs of sides are parallel to each and the four angles at the vertices are not equal to the right angle, and then the quadrilateral is called a parallelogram. Also, the opposite sides are equal in length.

The key properties of angles of a parallelogram are:

- If one angle of a parallelogram is a right angle, then all the angles are right angles

- Opposite angles of a parallelogram are equal (or congruent)

- Consecutive angles are supplementary angles to each other (that means they add up to 180 degrees)

Consecutive angles are supplementary and as such:

85 + 8x - 1 = 180

8x = 181 - 85

8x = 96

x = 96/8

x = 12

Opposite angles are equal and as such:

85 = -4y + 5

-4y = 80

y = -20

Similarly:

85 - 3z - 4 = 180

3z = -96

z = -96/3

z = -32

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The given expression is

[tex]2x+x^2[/tex]

So we can write the general rule for the sequence as

[tex]T_x=2x+x^2[/tex]

Recall that the domain of a sequence is the set of natural numbers.

Let us plug in some first few natural numbers to generate the sequence.

When [tex]x=1[/tex], we obtain,

[tex]T_1=2(1)+(1)^2[/tex]

[tex]\rightarrow T_1=2+1[/tex]

[tex]\rightarrow T_1=3[/tex]

When [tex]x=2[/tex], we obtain,

[tex]T_2=2(2)+(2)^2[/tex]

[tex]\rightarrow T_2=4+4[/tex]

[tex]\rightarrow T_2=8[/tex]

When [tex]x=3[/tex], we obtain,

[tex]T_3=2(3)+(3)^2[/tex]

[tex]T_3=6+9[/tex]

[tex]T_3=15[/tex]

When [tex]x=4[/tex], we obtain,

[tex]T_4=2(4)+(4)^2[/tex]

[tex]T_4=8+16[/tex]

[tex]T_4=24[/tex]

Therefore the number sequence produced by the given expression is,

[tex]\boxed{\bold{3, 8, 15, 24.}}[/tex]

The length of the missing leg for the triangles are: x = 7.01, f = 5.4, and d = 15.1 using the Pythagoras rule.

The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. 

By Pythagoras rule we can evaluate for b as follows:

x = √(7.5² - 2.5²)

x = √50

x = x = 7.0711

f = √[(√78)² - 7²]

f = √(78 - 49)

f = √29

f = 5.3852

d = 2 × √(11² × 8²)

d = 2 × √53

d = 15.0996

Therefore, the length of the missing leg for the triangles are: x = 7.01, f = 5.4, and d = 15.1 using the Pythagoras rule.

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