The coordinates of APQR are P(0, 0), Q(0, 5), and R(4,4). APQR is rotated 180° counterclockwise about point P to form AP'Q'R'. What are the coordinates of the new triangle?

The coordinates of the vertex of the parabola are (3, -7). The focus of the parabola is located at (3, -3). The equation of the directrix is y = -11.

The given equation of the parabola is in the form (x - h)^2 = 4p(y - k), where (h, k) represents the vertex and p represents the distance between the vertex and the focus/directrix.

Comparing the given equation with the standard form, we can see that the vertex is at (3, -7).

The coefficient 4p in this case is 16, so p = 4. Since the parabola opens upward, the focus will be p units above the vertex. Therefore, the focus is located at (3, -7 + 4) = (3, -3).

To find the directrix, we need to consider the distance p below the vertex. Since the parabola opens upward, the directrix will be p units below the vertex. Hence, the equation of the directrix is y = -7 - 4 = -11.

In summary, the coordinates of the vertex are (3, -7), the focus is located at (3, -3), and the equation of the directrix is y = -11.

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The measures of the angles to the nearest degree are:

a) A ≈ 36 degrees

b) B ≈ 23 degrees

c) C ≈ 2 degrees

To find the measure of the angle to the nearest degree given trigonometric ratios, we can use inverse trigonometric functions.

Here are the steps to determine the angles:

a) sin A = 0.6018

Taking the inverse sine (arcsin) of both sides:

A = arcsin(0.6018)

Using a calculator, we find A ≈ 36 degrees (rounded to the nearest degree).

b) cos B = 0.9205

Taking the inverse cosine (arccos) of both sides:

B = arccos(0.9205)

Using a calculator, we find B ≈ 23 degrees (rounded to the nearest degree).

c) tan C = 0.0349

Taking the inverse tangent (arctan) of both sides:

C = arctan(0.0349)

Using a calculator, we find C ≈ 2 degrees (rounded to the nearest degree).

Therefore, the measures of the angles to the nearest degree are:

a) A ≈ 36 degrees

b) B ≈ 23 degrees

c) C ≈ 2 degrees.

Note: Trigonometric functions have periodicity, meaning there may be multiple angles with the same trigonometric ratio.

To determine the principal angle within a specific range, we use the inverse trigonometric functions.

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According to this inequality, the number of persons attending a theatrical inequality  play, denoted by p, must be less than or equal to 275 in order for everyone to have a seat.

In mathematics, an inequality is a non-equal connection between two expressions or values. As a result, imbalance leads to inequity. In mathematics, an inequality connects two values that are not equal. Inequality is not the same as equality. When two values are not equal, the not equal symbol is typically used (). Various disparities, no matter how little or huge, are utilised to contrast values. We resuming our current status quo. Yet a variety of things lead to inequality: Negative values on both sides are split or added.

a. The disparity in representing the voting age in the United States is as follows:

a ≥ 18

In order to be eligible to vote, a voter's age, denoted by a, must be more than or equal to 18 years old.

b. The inequality used to depict a theater's seating capacity is:

p ≤ 275

According to this inequality, the number of persons attending a theatrical play, denoted by p, must be less than or equal to 275 in order for everyone to have a seat.

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Answer:

Step-by-step explanation:

Ordered pair (0, 0) & (0.5, 2.5)  will fall on the line of graph

Step-by-step explanation:

Megan expects to save an average of 5 dollars per week from her babysitting earnings.

=> Saving Per  week  = 5 $

Saving in 0.5 Week = 0.5 * 5 = 2.5 $

hence ordered pair (0.5, 2.5)  will fall on the line of graph

Saving in 3 Week = 3 * 5 = 15 $

Hence (3, 18) will not fall on  line

Saving in 0 Week = 0.5 * 0 = 0 $

hence ordered pair (0, 0)  will fall on the line of graph

Saving in 4.5 Week = 4.5 * 5 = 22.5 $

Hence (4.5, 30) will not fall on  line

Ordered pair (0, 0) & (0.5, 2.5)  will fall on the line of graph

In mathematics, the graph of a function f is the set of ordered pairs, where {\displaystyle f(x)=y.} In the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.

here, we have,

Megan expects to save an average of 5 dollars per week from her babysitting earnings.

=> Saving Per  week  = 5 $

Saving in 0.5 Week = 0.5 * 5 = 2.5 $

hence ordered pair (0.5, 2.5)  will fall on the line of graph

Saving in 3 Week = 3 * 5 = 15 $

Hence (3, 18) will not fall on  line

Saving in 0 Week = 0.5 * 0 = 0 $

hence ordered pair (0, 0)  will fall on the line of graph

Saving in 4.5 Week = 4.5 * 5 = 22.5 $

Hence (4.5, 30) will not fall on line

Hence, Ordered pair (0, 0) & (0.5, 2.5)  will fall on the line of graph.

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For the given data

(a) sample mean is 17 and sample standard deviation = 8.91 .

(b) the 95% confidence interval is (9.551 , 24.449)  .

(c) the 90% confidence interval is (11.032 , 22.968) .  .

In the question ,

the data is given as 25, 11, 12, 27,26, 22, 8,5.

So , the number of terms (n) = 8

Part(a)

the sample mean(μ)  is = (25+11+12+27+26+22+8+5)/8 = 17

the standard deviation is calculated as :

= √[(25 - 17)² + (11 - 17)² + (12 - 17)² + (27 - 17)² + (26  - 17)² + (22 - 17)² + (8 - 17)² + (5 - 17)²)]/7

Simplifying the above data further ,

we get

= 8.91

Part(b)

we know that at 95% confidence interval , the critical value is t₀.₀₂₅,₇ = 2.3646

So , the 95% confidence interval is :

= μ ± t₀.₀₂₅,₇*s/√n

= 17 ± 2.3646*8.91/√8

= 17 ± 7.449

So , the interval is ⇒ (9.551 , 24.449) .

Part(c)

we know that at 90% confidence interval , the critical value is t₀.₀₅,₇=1.8946

So , the 90% confidence interval is :

= μ ± t₀.₂₅,₇*s/√n

= 17 ± 1.8946*8.91/√8

= 17 ± 5.968

So , the interval is ⇒ (11.032 , 22.968) .

Therefore ,(a)  the sample mean and standard deviation are 17 and 8.91

(b) the 95% interval is (9.551 , 24.449) .

(c) the 90% interval is (11.032 , 22.968) .

The given question is incomplete , the complete question is

Let the following sample of 8 observations be drawn from a normal population with unknown mean and standard deviation: 25, 11, 12, 27,26, 22, 8,5.

(a) Calculate the sample mean and the sample standard deviation.

(b) Construct the 95% confidence interval for the population mean.

(c) Construct the 90% confidence interval for the population mean.

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Answer:

x = 13

Step-by-step explanation:

We know that 5x, x+12, and 90 makes a straight line, which is 180 degrees

5x + x+12 + 90 = 180

Combine like terms.

6x+102=180

Subtract 102 from each side.

6x+102-102=180-102

6x = 78

Divide each side by 6

6x/6 = 78/6

x = 13

Answer:

x = 13

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

We know that,

→ The angle of right angle is 90°.

Forming the equation,

→ (x + 12)° + (5x)° = 90°

Then the value of x will be,

→ (x + 12)° + (5x)° = 90°

→ x + 12 + 5x = 90

→ (x + 5x) + 12 = 90

→ 6x + 12 = 90

→ 6x = 90 - 12

→ 6x = 78

→ x = 78 ÷ 6

→ [ x = 13 ]

Hence, the value of x is 13.

Answer:

tourist: 28%

non-tourist: 72%

Step-by-step explanation:

total: 50

tourists: 14

non-tourists:50 - 14 = 36

tourist percentage: 14/50 × 100% = 28%

non-tourist percentage: 36/50 × 100 = 72%

The domain for the function is the interval [0, 14], which represents the feasible values for the length of one side of the rectangular garden.

To determine the appropriate values of the domain for the graph of the function \(A(t) = -t^2 + 14t\), we need to consider the situation and the constraints given.

The function A(t) represents the area of the rectangular garden as a function of the length of one of its sides, which is denoted by t.

We are also told that Marama plans to fence the garden with 28 feet of wired fencing.

Now, let's break down the problem and find the appropriate values for the domain.

We know that the perimeter of a rectangle is the sum of all its sides. In this case, since we have a rectangular garden, the perimeter can be represented as:

\(Perimeter = 2t + 2w\),

where t is the length of one side (the width) and w is the length of the other side (the width).

The problem states that Marama plans to use 28 feet of wired fencing. Therefore, the perimeter of the garden must equal 28 feet:

\(2t + 2w = 28\).

Simplifying this equation, we have:

\(t + w = 14\).

We can express w in terms of t as \(w = 14 - t\).

The area of a rectangle is given by the product of its length and width:

\(Area = t \times w\).

Substituting the expression for w from step 2, we have:

\(A(t) = t \times (14 - t)\).

Simplifying further:

\(A(t) = 14t - t^2\).

To determine the appropriate values of the domain, we need to consider the context of the problem. Since we are dealing with a physical garden, both the length and width must be positive numbers. Additionally, the values of t must be feasible given the constraints of the perimeter.

We know that \(t + w = 14\), so \(t + (14 - t) = 14\), which simplifies to \(14 = 14\).

This shows that the value of t can range from 0 to 14, inclusive.

Therefore, the appropriate values of the domain for the graph of the function \(A(t) = -t^2 + 14t\) are \(t \epsilon [0, 14]\).

To illustrate this graphically, we can plot the function \(A(t) = -t^2 + 14t\) and mark the appropriate values of the domain on the x-axis (representing t):

   ^

   |

A(t)|

   |

   |_______________________________

   0              t             14

The domain for the function is the interval [0, 14], which represents the feasible values for the length of one side of the rectangular garden.

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Answer:

a) 6ab

b) c⁶

c) 10y⁷

d) 12g⁴h⁵

Calculation of circumference of a circle of radius 1 is 6.28 units.

How to calculate circumference of the circle?

The respective formula for calculating-the-circumference of a circle is:

C = 2πr

where C denotes the circumference and r denotes the radius of the circle.

Substituting the given value of radius r = 1 and π = 3.14, we get:

C = 2 x 3.14 x 1

= 6.28

Therefore, the circumference of the circle with radius r = 1 is 6.28 units.

A circle's circumference is the distance around its circumference. It can be determined using the formula C = 2r, where C is the circumference of the circle and r is its radius. The value of π is a constant that represents the ratio of the circumference of a circle to its diameter, and is approximately equal to 3.14. To find the circumference of a circle, we simply need to multiply 2π by the radius of the circle.

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Answer:

7/9

Step-by-step explanation:

7 divided by 9 is .7777777777....

Answer:

42/11

Step-by-step explanation:

5 1/4 * 8/11

21/4 * 8/11

42/11

The slope which shows  the cost per guest is $35 per guest

The given cost for 50 guests is $2150.

The cost for 75 guests is $3025.

It can also be represented as:

(Guest, Cost) =(50, $2150) & (75, $3025)

The slope can now be calculated as

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (50, $2150) & (75, $3025)

Substituting the given values in the equation as follows:

Slope = (3025 - 2150)/(75 - 50)

Slope = 35

Hence, the slope is $35 per guest.

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\(\\ \rm\Rrightarrow sin\theta=\dfrac{Perpendicular}{Hypotenuse}\)

\(\\ \rm\Rrightarrow sin52=\dfrac{AC}{BC}\)

\(\\ \rm\Rrightarrow sin52=\dfrac{9.2}{B C}\)

\(\\ \rm\Rrightarrow B C=\dfrac{9.2}{sin52}\)

\(\\ \rm\Rrightarrow B C=9.3\)

Answer:

11.7  (3 s.f.)

Step-by-step explanation:

Given information:

As one of the given angles is 90°, the triangle is a right triangle.

Draw the triangle using the given information (see attached) to help visualize the problem.

To calculate the length of BC, use the sine trigonometric ratio:

\(\sf \sin(\theta)=\dfrac{O}{H}\)

where:

From inspection of the attached triangle:

Substitute the values into the formula and solve for BC:

\(\implies \sf \sin(52^{\circ})=\dfrac{9.2}{BC}\)

\(\implies \sf BC=\dfrac{9.2}{\sin(52^{\circ})}\)

\(\implies \sf BC=11.67496758...\)

\(\implies \sf BC=11.7\:\:(3 \:s.f.)\)

Therefore, the length of BC is 11.7 (3 s.f.).

Given:

Age of a man = 48 years.

His son is exactly three times younger than him.

Required:

Age of man’s son when the man is 60 years old.

Answer:

We have given that the age of a man is 48 years and his son is exactly three times younger than him.

Therefore, the age of his son (in years) is,

Then after 12 years the age of a man will be 60 years

Answer:

186cm im pretty sure

Step-by-step explanation:

Answer:

The perimeter is 186 centimeters.

Step-by-step explanation:

The perimeter is the combination of all the side lengths of a figure. So, to figure this one out, it would be:

31 + 31 + 31 + 31 + 31 + 31

Or in simpler terms:

31 times 6.

All you need to do is multiply, and the answer comes out to 186cm

Area of the composite figure is 189.25 in². Therefore, the given area A of the figure is Ture.

First, let us find the area of the rectangle.

Area = Length × Width

       = 15 in × 10 in

       = 150 in²

Then let us find the area of the semicircle.

Area = \(\frac{1}{2}\) × π r²

        =  \(\frac{1}{2}\) × 3.14 × 5 × 5

        = 0.5 × 3.14 × 25

        = 1.57 × 25

        = 39.25 in²

Now let us find the total area of the composite figure.

Total area = Area of the rectangle + Area of the semi-circle.

                = 150 in² + 39.25 in²

                = 189.25 in²

Area of the composite figure is 189.25 in². Therefore, the given area A of the figure is Ture.

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Answer:

A. 32.44

Step-by-step explanation:

Automobile owner has 40% chance for one accident in a year and 60% of zero accident in a year.

Let x is the loss of accident and y is the payment by insurer.

Y = 0 if X < 40,

x - 40 if 40 < x < 130

130 if x \(\geq\) 170

Then, Var [y] = E y^2

Var [y] = 1052.16

E = 32.437.

Answer:

b=2a/h

Step-by-step explanation:

The graph of this function will behave as (b) A graph of this function would slope downward, starting from a price of $100 dollars because the rate of change is less than 0 and the initial value is -10.

The demand function is given by d = 100 - 10p. This means that the quantity demanded (d) decreases as the price (p) increases.

The slope of the demand function is the rate of change of the quantity demanded with respect to the price. In this case, the slope is -10, which is negative. This indicates that as the price increases, the quantity demanded decreases.

The initial value of the demand function is 100, which represents the quantity demanded when the price is zero. This means that the demand function intersects the y-axis at (0, 100).

Therefore, the correct answer is (b) A graph of this function would slope downward, starting from a price of $100 dollars because the rate of change is less than 0 and the initial value is -10.

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Part A: The total area of the brick paver border is \(960\) square feet.

Part B: The total cost of the brick pavers needed for this project is $\(7,680\).

Part A: To find the total area of the brick paver border, we need to subtract the area of the pool from the area of the larger rectangle. The area of the pool is \(32\) feet multiplied by 12 feet, which is equal to \(384\)square feet.

The area of the larger rectangle is \(48\) feet multiplied by \(28\) feet, which is equal to \(1,344\) square feet. Therefore, the area of the brick paver border is \(1,344\) square feet minus \(384\) square feet, which equals \(960\) square feet.

Part B: If brick pavers cost $\(8\)per square foot, we can calculate the total cost by multiplying the cost per square foot by the total area of the brick paver border. The total area of the brick paver border is \(960\) square feet, and the cost per square foot is $\(8\).

Therefore, the total cost of the brick pavers needed for this project is $\(8\)multiplied by \(960\) square feet, which equals $\(7,680\).

Note: The calculations provided assume that the border consists of a single layer of brick pavers.

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The y-intercept of the line, written as a coordinate is expressed as: (0, -10).

The equation of a line where m is the slope and b is the y-intercept, is written in slope-intercept form as y = mx + b.

If we are given the equation of a line as: y = -4x - 10, it means that:

the slope (m) of the line is -4

the y-intercept of the line is -10.

This also implies that, when the line intercepts the y-axis at point -10. At this point, the corresponding x-value when y is -10 must be equal to 0.

Therefore, when x = 0, y = -10. This can be stated in the form of (0, b) as (0, -10).

In conclusion, it means that the y-intercept of the line, written as a coordinate is: (0, -10).

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The (g.f)(x)  of the two functions is:

(g.f) (x) = 6x + 37

A function is an expression that shows the relationship between the independent variable and the dependent variable.  A function is usually denoted by letters such as f, g, etc.

To find (g.f) (x), follow the steps below:

1. Substitute the value of f(x) into the function g(x).

2. Then simplify the expression.

That is:

f(x) = 3x+18

g(x) = 2x+1

Thus, we have:

(g.f) (x) = g(f(x))

(g.f) (x) = g(3x+18)

(g.f) (x) = 2(3x+18) + 1

(g.f) (x) = 6x+36 + 1

(g.f) (x) = 6x + 37

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Answer:

-1/2

Step-by-step explanation:

The volume of the sphere is approximately 3431.82 cubic miles.

To find the volume of a sphere, we need the radius of the sphere. The length of a great circle is the circumference of the sphere, which is related to the radius by the formula C = 2πr, where C is the circumference and r is the radius.

In this case, we are given that the length of the great circle is 60 miles. We can use this information to find the radius of the sphere.

C = 2πr

60 = 2πr

Divide both sides of the equation by 2π:

r = 60 / (2π)

r = 30 / π

Now that we have the radius, we can use the formula for the volume of a sphere:

V = (4/3)πr³

V = (4/3)π(30/π)³

V = (4/3)π(27000/π³)

V = (4/3)π(27000/π³)

V = (4/3)π(27000/π³)

V = (4/3)(27000/π²)

V = (4/3)(27000/9.87) (approximating π to 3.14)

V ≈ 3431.82 cubic miles

Therefore, the volume of the sphere is approximately 3431.82 cubic miles.

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Question

You are given the great circle of a sphere is a length of 60 miles. What is the volume of the sphere?

Answer:

Step-by-step explanation:

C(16, 4)   = 1820 ways

16

   C

     4                    = (16x15x14x13)  /  (4x3x2x1)

Answer: 100% more than 3026.9 is  6053.8

Step-by-step explanation:

If you have a calculator, you put 3026.9 plus 100%

Answer:

6053.8

Step-by-step explanation:

100% = 1.00

3026.9 + 3026.9(1.00) = 6053.8

Increasing a number by 100% is the same thing as doubling it