4 Type the correct answer in the box. Use numerals instead of words. A car enters a traffic circle at point R. and moves counterclockwise 296 feet before exiting the traffic circle at point P. To the nearest degree, what is the measure of the central angle, ZPQR? 150 ft Q m. All rights reserved. The measure of ZPQR is approximately ?​

The values of x in the triangles are x = 17 and x = 52

Triangle 1

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

The triangle

Using the law of cosines to solve for x, we have

x^2 = 7^2 + (8√2)^2 - 2 * 7 * (8√2) * cos(135 degrees)

Evaluate the like terms and multiply

x^2 = 289

Take the square roots

x = 17

Triangle 2

Here, we have"

Using the law of cosines to solve for x, we have

x^2 = 28^2 + 32^2 - 2 * 28 * 32 * cos(120 degrees)

Evaluate the like terms and multiply

x^2 = 2704

Take the square roots

x = 52

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The length of the steering device will be 4.5 inches.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

The steering device extends to point T, and the diameter of the steering wheel is 15 inches long. Then the length of the steering device is given as,

7.5² = h² + 6²

56.25 = h² + 36

h² = 56.25 - 36

h² = 20.25

h = 4.5 inches

The length of the steering device will be 4.5 inches.

The diagram is given below.

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The cost of printing x business cards can be represented by the linear function C(x) = 0.05x + 20.  The cost of printing 950 business cards is $67.50.

The cost of printing business cards is a linear function, C(x) = mx + b, where C(x) is the cost of printing x business cards, m is the rate at which the cost increases as the number of cards increases, and b is the constant term or the cost of printing zero business cards. In this case, m = 0.05 and b = 20.

The equation C(x) = 0.05x + 20 represents the cost of printing x business cards, where x is the number of cards printed. The term 0.05x represents the cost of printing x cards at a rate of $0.05 per card, and the term 20 represents a fixed cost of $20, regardless of the number of cards printed.

To find the cost of printing 950 business cards, we simply substitute x = 950 into the equation:

C(950) = 0.05 * 950 + 20

C(950) = 47.5 + 20

C(950) = 67.5

Therefore, the cost of printing 950 business cards is $67.50.

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The infinite series ax/a+x can be written in the form of a summation notation as [tex]Σ ( (−1)^n * (x^(n+1))/(a^(n+1)))[/tex], which can be used to calculate the sum of the series for any value of x and a.

The infinite series representing ax/a+x can be written as:

[tex]∑n=0∞(−1)nx^n+1a^n+1[/tex]

The first 5 terms of this series can be calculated as follows:

[tex]Term 1 = (x/(a+x))Term 2 = -(x^2/a^2+2ax+x^2) 4Term 3 = (x^3/a^3+3a^2x+3ax^2+x^3) Term 4 = -(x^4/a^4+4a^3x+6a^2x^2+4ax^3+x^4)Term 5 = (x^5/a^5+5a^4x+10a^3x^2+10a^2x^3+5ax^4+x^5)[/tex]

The general formula for the infinite series can be written as:

[tex]∑n=0∞(−1)nx^n+1a^n+1 = (x/(a+x)) - (x^2/a^2+2ax+x^2) + (x^3/a^3+3a^2x+3ax^2+x^3) - (x^4/a^4+4a^3x+6a^2x^2+4ax^3+x^4) + (x^5/a^5+5a^4x+10a^3x^2+10a^2x^3+5ax^4+x^5) + ...[/tex]

The summation notation for this series can be written as:

[tex]∑n=0∞(−1)nx^n+1a^n+1 = Σ ( (−1)^n * (x^(n+1))/(a^(n+1)))[/tex]

This formula can be used to calculate the sum of the infinite series for any value of x and a.

The infinite series ax/a+x can be written in the form of a summation notation as [tex]Σ ( (−1)^n * (x^(n+1))/(a^(n+1)))[/tex], which can be used to calculate the sum of the series for any value of x and a.

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The coordinate for the image of point H( -1, -5) under a 90° clockwise rotation about the origin is, (- 5, 1)

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

Given that;

The coordinate of the point H( -1, -5)

Now, The rule for the 90° clockwise rotation about the origin is,

(x, y) = (y, - x)

Hence, The coordinate for the image of point H( -1, -5) under a 90° clockwise rotation about the origin is,

(- 1, - 5) = (- 5, 1)

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The values of the expressions when evaluated are 10000 and 1000

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

This means that

Species = 10^4 = 10000

Threatened = 10^3 = 1000

Hence, the values are 10000 and 1000

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Answer:

Step-by-step explanation:

this is a simultaneous  equation type. so there are only 2 solutions. one for X and one for Y

To find the product of all integer divisors of 105 that also divide 14, we need to first find all the divisors of 105 and then find which of those divisors also divide 14.

The divisors of 105 can be found by listing all the positive integers that divide 105 exactly. To do this, we can use a divisibility test for each number up to the square root of 105:

Does 1 divide 105 exactly? Yes, so 1 is a divisor of 105.

Does 3 divide 105 exactly? Yes, so 3 is a divisor of 105.

Does 5 divide 105 exactly? Yes, so 5 is a divisor of 105.

Does 7 divide 105 exactly? Yes, so 7 is a divisor of 105.

Does 11 divide 105 exactly? No.

Does 15 divide 105 exactly? Yes, so 15 is a divisor of 105.

Does 21 divide 105 exactly? Yes, so 21 is a divisor of 105.

Does 35 divide 105 exactly? Yes, so 35 is a divisor of 105.

Since 105 is a composite number, the divisors of 105 can also be found by multiplying pairs of the divisors found above. This gives us the following divisors of 105:

1, 3, 5, 7, 15, 21, 35, 105

Next, we need to find which of these divisors also divide 14. To do this, we can perform a similar divisibility test for each divisor:

Does 1 divide 14 exactly? Yes, so 1 is a divisor of 14.

Does 3 divide 14 exactly? No.

Does 5 divide 14 exactly? No.

Does 7 divide 14 exactly? Yes, so 7 is a divisor of 14.

Does 15 divide 14 exactly? No.

Does 21 divide 14 exactly? No.

Does 35 divide 14 exactly? No.

So, the divisors of 105 that also divide 14 are 1 and 7. To find the product of these divisors, we simply multiply them:

1 * 7 = 7

Thus, the product of all integer divisors of 105 that also divide 14 is 7.

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The value of the probability P(z < -2.6) is 0.0046612

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

To calculate the probability P(z < -2.6), we make use of a graphing calculator

Using the above as a guide, we have the following:

P(z < -2.6) = 0.0046612

Hence, the value is 0.0046612

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The system of equations is x + y = 16 & 6x + 4y = 76, then  the amount x is 6 yards of regular quilting fabric and the amount y is 10yards of sateen fabric she purchased.

She bought 6 Sateen fabrics and 10 quilting fabrics.

She uses quilt to make two types of fabrics.

Let the amount of each sateen fabric = x

Let the amount of each quilting fabric = y

The Sateen fabrics cost $6 per yard.

Therefore, for x amount it will be as follows:

6x

The quilting fabrics cost $4 per yard.

Therefore, for y amount it will be as follows:

4y

A system of equations is a collection of two or more equations with a same set of unknowns.

According to the condition the amount of quilting is 'x' and the amount of sateen is 'y', then the price of the quilting fabric is 6x and the price of then sateen fabric is 4y;

The 76$ she spends can be written as 4x+6y=76;

Total of 16 yards can be written as x+y=16;

So the required system of Equations is:

⇒4x+6y=76

⇒x + y=16

Therefore,

⇒x + y = 16

⇒6x + 4y = 76

⇒6x + 6y = 96

⇒6x + 4y = 76

⇒2y = 20

⇒y = 20 / 2

⇒y = 10

⇒x + y = 16

⇒x + 10 = 16

⇒x = 16 - 10

⇒x = 6

Therefore, the system of equations is x + y = 16 & 6x + 4y = 76, then  the amount x is 6 yards of regular quilting fabric and the amount y is 10yards of sateen fabric she purchased.

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Answer:

2×(a+b)

Step-by-step explanation:

to find the perimeter of a rectangle, we should use this formula

This is my answer so if I am wrong then correct me

Answer:

[tex]width = \dfrac{75*(5-\sqrt{2}}{23}[/tex]

Step-by-step explanation:

To find the width of the rectangle, divide the area by the length.

      [tex]Width = \dfrac{area}{length}[/tex]

                 [tex]=\dfrac{75}{\sqrt{2}+5}\\\\\\\text{To rationalize, multiply the denominator and the numerator by } \ \sqrt{2}-5[/tex]

              [tex]=\dfrac{75* (5 - \sqrt{2})}{(5+\sqrt{2})(5-\sqrt{2})}\\\\\\=\dfrac{75*(5-\sqrt{2})}{5^2 - (\sqrt{2})^2}\\\\\\=\dfrac{75(5-\sqrt{2})}{25-2}\\\\\\=\dfrac{75*(5-\sqrt{2})}{23}[/tex]

Answer:

Let the width of the rectangle be w. Then we have:

[tex]lw = 75[/tex]

[tex]w(\sqrt{2} + 5) = 75[/tex]

[tex]w = \frac{75}{\sqrt{2} + 5}[/tex]

Multiplying both the numerator and denominator by [tex]\sqrt{2} - 5[/tex], we get:

[tex]w = \frac{75(\sqrt{2} - 5)}{(\sqrt{2} + 5)(\sqrt{2} - 5)}[/tex]

Simplifying the denominator, we get:

[tex]w = \frac{75(\sqrt{2} - 5)}{-1}[/tex]

[tex]w = -75\sqrt{2} + 375[/tex]

Therefore, the width of the rectangle is approximately 264.1 cm.

Answer: 10

Step-by-step explanation:

because

The elevation gain from the base of the chairlift to the top is 835.2 m

Consider the following diagram.

The chairlift rises at a constant angle of 37°

i.e., the angle of elevation (∠ACB) = 37°

The length of the chairlift ride is 1,392 m

This means, for right triangle ABC, the length of hypotenuse AC = 1392 m

To find  the elevation gain from the base of the chairlift to the top i.e., the length of side AB.

Consider the sine of angle ∠ACB

sin(∠ACB) = AB/AC

sin(37°) = AB/1392

3/5 = AB/1392

AB = 835.2 m

Therefore, the elvation gain is 835.2 m

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The surface area and volume of the figure is 108 cm² and 96 cm³ respectively

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

The surface area of the figure = 2(1/2 * 4 cm * 3 cm) + (8 cm * 3 cm) + (8 cm * 4 cm) + (8 cm * 5 cm) = 108 cm²

The volume of figure = area of base * height = (1/2 * 4 cm * 3 cm) * 8 cm = 96 cm³

The surface area and volume of the figure is 108 cm² and 96 cm³ respectively

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The distance between the points (-7,1) and (-7,-5) on the coordinate plane is 6 units.

The distance formula is a useful tool in many areas of mathematics and science, such as geometry, physics, and engineering. It can be used to find the distance between two points in any number of dimensions, not just two dimensions as in the coordinate plane In addition, the distance formula can also be used to find the length of a line segment in the coordinate plane, which is just the distance between its endpoints. This can be useful in finding the shortest distance between two points, or in finding the length of a path that connects two points.

The distance formula is a mathematical equation used to find the distance between two points in the coordinate plane. It makes use of the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side (the hypotenuse).

In the coordinate plane, we can represent each point by its coordinates (x1, y1) and (x2, y2). The distance between the points is then given by the equation:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

For the points (-7,1) and (-7,-5), we can plug in the values into the equation:

distance = sqrt((-7-(-7))^2 + (-5-1)^2) = sqrt(0^2 + (-6)^2) = sqrt(36) = 6

So the distance between the points (-7,1) and (-7,-5) on the coordinate plane is 6 units.

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The median of the data set is 12.

The mean is 11.29.

Increasing every piece of data by the same value increases the mean and median by the same amount.

The median of the data set is the middle value when the data is arranged in numerical order. To find the median of the data set, we need to arrange the data in increasing order: 9, 10, 11, 12, 12, 13, 34. The median of this data set is 12.

The mean of the data set is the average of all the values. To find the mean, we need to add up all the values and divide by the number of values: (9 + 10 + 11 + 12 + 12 + 13 + 34) / 7 = 11.29.

If every piece of data in the set is increased by 20 after treatment, the new values are 29, 30, 31, 32, 32, 33, 54. The new median is 32 and the new mean is 35.29.

When every piece of data is increased by the same value, the mean and median will increase by the same amount.

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 Total volume of the salt shaker is 56.52+706.5=763.02 cm³

The volume of a Right Circular Cylinder. In general, the volume of a right cylinder is the area of the base times the height of the cylinder. The area of the circular base is given by the formula A = πr2. Substitute to get V = πr²h.

Given here: The volume of a salt shaker  

The radius of the salt shaker which is 5 cm

Thus the volume of the cylinderical salt shaker is = π×3²×5²

                                                                                  =706.5 cm³

and the volume of the hemisphere at the top is=  (2/3)πr³

                                                                               =56.52 cm³

Hence, Total volume of the salt shaker is 56.52+706.5=763.02 cm³

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The complete question is Which is a better estimate for the volume of a salt shaker? where radius =3 cm and height =5 cm

Erik’s average speed was 113.957 miles per hour.

Average speed refers to the overall speed of an object over a certain time period. To find average speed, we need to divide the total distance traveled by the time it took to travel that distance.

In this case, Erik rode his motorbike 2623 miles in 23 hours, so we need to divide 2623 by 23 to find his average speed in miles per hour.

Mathematically, average speed can be represented as follows:

Average speed = Total distance ÷ Total time

So in this case,

Average speed = 2623 miles ÷ 23 hours

Calculating the answer, we get

Average speed = 113.957 mph

Complete Question:

Erik rides his motorbike 2623 miles in 23 hours. What is Erik’s average speed in miles per hour? Enter the number in the box.

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Answer:

y = -3(x + 0.5)² - 45.25

Step-by-step explanation:

a = -3

b = -3

c = -47

h = -b/2a = -(-3)/2(-3) = -1/2

k = c - b²/(4(-3)) = -46 - (-3)²/(-12) = -45.25

f(x) = -3(x - (-1/2))² - 45.25

y = -3(x + 0.5)² - 45.25

The number of mice in the category is 38

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

The histogram

The total number of mice with birth weights below 12 g is the sum of the frequency of bars less than 12 g

Using the above as a guide, we have the following:

Total = 4 * 4 + 4 + 4 + 7 + 7

Evaluate

Total = 38

Hence, the number of mice is 38

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Answer:

8 / 47 = 0.17021276595 btw u can just use a calculator

Answer:

x = 3

Step-by-step explanation:

[tex]2x - 9 = -3[/tex]

[tex]2x = 6[/tex]

[tex]x = 3[/tex]

Answer:

x = 35°

Step-by-step explanation:

The triangle is an isosceles triangle since two sides are formed by the radii of the circle

Therefore m∠C = x°

The angle 70° is the exterior angle of the triangle

Exterior angle = sum of interior angles

70° = x + x = 2x

2x = 70

x = 35°

The minimum payment of the credit card will be $40.37.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that Daniel's credit card has a minimum monthly payment of 2.78% of the card's balance. If Darryl currently owes $1,452.28.

The minimum payment will be calculated as;-

Minimum payment = ( 1452.28 )  x ( 2.78 / 100 )

Minimum payment = $40.37

Therefore, the minimum amount for the credit card bill is $40.37.

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Answer:

Step-by-step explanation:

A = bh.

To solve, find factors of seven the fit the description such as 7 and 1.

The length is 7, the width is 6 units less.

So, the width is 1un and the length is 7un.

The equation that shows the rate at which she travels is given as r = 300/t

An equation is a mathematical statement that asserts the equality of two expressions. Equations are used to describe relationships between variables and to solve problems by finding the values of unknowns.

An equation is comprised of two expressions separated by an equal sign (=). The expressions can be as simple as a number or as complex as a combination of numbers, variables, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. The goal of solving an equation is to find the value of the variable that makes the equation true.

In this problem, we can represent the rate at which we travel by

r = 300 / t

where;

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Answer:

Step-by-step explanation:

Let's call the number of rows "x". The number of plants in each row would be 2x - 10. We know that the total number of plants is 600, so we can set up an equation:

x * (2x - 10) = 600

Expanding the left side:

x^2 + 10x - 600 = 0

We can solve for x using the quadratic formula:

x = (-10 ± √(10^2 - 4 * 1 * -600)) / 2 * 1

x = (-10 ± √(100 + 2400)) / 2

x = (-10 ± 50) / 2

x = 20 or -5 (but x cannot be negative, as the number of rows must be a positive integer)

So, there are 20 rows with 10 plants in each row. The number of plants in each row is 2x - 10 = 2 * 20 - 10 = 30.

M(8)<M(4) means that 8th drive was less expensive than 4th drive.

M(n) denotes Aiden's fee (in dollars) for his n^th drive on a certain day.

The reason for the m(8) is that the model fee for this is nth driver for a certain  day.  this implies M (8) < M (4)

M(8) is Aiden's fee for his 8th drive;

M(4) is Aiden's fee for his 4th drive

In conclusion, Aiden's fee for his 8th drive is greater than his drive for the 4th drive

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A triangle has three bisectors, each of which is a line that divides one of the angles of the triangle into two equal parts.The incenter is equidistant from the three sides of the triangle and is the center of the inscribed circle, which is the circle that is tangent to all three sides of the triangle.

A triangle is a two-dimensional geometric shape that has three straight sides and three angles. It is one of the simplest and most fundamental shapes in geometry, and it is widely studied in mathematics, science, and engineering. Triangles can have different types of angles and sides, which give rise to various classifications and properties. For example, a triangle can be classified as equilateral (all sides and angles are equal), isosceles (two sides and two angles are equal), or scalene (all sides and angles are different).

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