TRIGONOMETRY PERIMETER

The given relation (-2,6)(-4,3)(3,-2)(8,6) is a function as every input has a single output.

A relation is set to be a function when every input has a single output.

In the given relation, -2,-4,3,8 has single output. Therefore, it is a function.

So, -2,-4,3 and 8 are the elements of the domain of the given

relation.

Here domain ={-2,-4,3,8} and range ={6,3,-3}

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The given statement about the intermediate value theorem is false

The given statement is

"Intermediate value theorem states that if a function, f, with an interval, [a, b], as its domain, takes values f(a) and f(b) at each end of the interval, then it also takes any value between f(a) and f(b) at some point within the interval"

But according to Intermediate value theorem "if a continuous function f with an interval, [a, b], as its domain, takes values f(a) and f(b) at each end of the interval, then it also takes any value between f(a) and f(b) at some point within the interval"

So if we takes discontinuous function the given statement will be wrong

Therefore, the statement is false

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The total length, in inches, of the four cut boards is 130 inches.

Addition is one of the basic mathematical operations where two or more numbers is added to get a bigger number.

The process of doing addition is also called as finding the sum.

Given that, the length of each of the cut pieces of the board are 7½ inches, 10½ inches, 9 inches, and 5½ inches.

We have to find the total length of the board.

Total length of the board is found by adding each length.

Total length = 7½ + 10½ + 9 + 5½

Mixed fraction can be converted to improper fraction by cross multiplication.

7½ = (7 * 2 + 1) / 2, 10½ = (10 * 2 + 1) / 2 and 5½ = (5 * 2 + 1) / 2

Total length = 15/2 + 21/2 + 9 + 11/2

                    = (15/2 + 21/2 + 11/2) + 9

                     = 47/2 + 9

                     = 65/2

Again improper fraction can be converted to mixed fraction.

Total length of a board = 32 1/2 inches

But there are 4 boards.

Total length of the 4 boards = 4 × 65/2 = 130 inches

Hence the total length is 130 inches.

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Answer: D. the division property of equality

Step-by-step explanation:

In step three you will be dividing -2.5 divided by -0.3 to get a.

Answer:

SSS

Step-by-step explanation:

Since [tex]\overline{AD} \cong \overline{AD}[/tex] by the reflexive property, there are three pairs of congruent sides.

At the same average speed, it would take Mr Jacobs 3 hours and 12 minutes to cover a distance of 352 km.

To calculate the time it would take Mr Jacobs to cover a distance of 352 km at the same average speed, use the following formula:

Time = (Distance / Average Speed) * 60

Time = (352 km / 220 km/h) * 60

Time = (1.6) * 60

Time = 96 minutes

Time = 1 hour and 36 minutes

Therefore, it would take Mr Jacobs 3 hours and 12 minutes to cover a distance of 352 km at the same average speed.

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Answer:

a the answer for angle 1 is also 52

b the answer for angle 3 is 180- 112= 68

The area of Norway's is 24% more than the area of Colorado.So, the area of Colorado is approximately 260,449 square kilometers.

What is Area?

Area is a measurement of the amount of two-dimensional space occupied by a surface or an object. In mathematics, area is a scalar quantity that describes the size of a region in a plane. The units of area are typically square units, such as square meters, square centimeters, square inches, etc.

The formula for the area of a shape depends on the shape itself. For example, the area of a rectangle is equal to its length multiplied by its width, while the area of a circle is equal to π times the square of its radius. Other common shapes and their area formulas include triangles, parallelograms, and trapezoids.

Let's call the area of Colorado "x". If Norway's area is 24% more than Colorado, then Norway's area can be represented as x + 0.24x = 1.24x.

To find the area of Colorado, we can set up an equation:

1.24x = area of Norway

x = area of Norway / 1.24

The area of Norway is 323,802 square kilometers. Therefore, the area of Colorado can be calculated as:

x = 323,802 / 1.24

x = 260,449 square kilometers

So, the area of Colorado is approximately 260,449 square kilometers.

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The surface area of a cuboid is 600 cm².

The surface area of a cuboid is the total space occupied by it. A cuboid is a six-faced three-dimensional shape in which each face is in the shape of a rectangle.

Given that, a cuboid whose 6 faces have 10 cm.

We know that, surface area of a cuboid = 2(lb+bh+hl)

= 2(10×10+10×10+10×10)

= 2(100+100+100)

= 2(300)

= 600 cm²

Therefore, the surface area of a cuboid is 600 cm².

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The equation of line shown on the coordinate plane is,

⇒ y = - 1/4x

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (0, 0) and (4, -1).

Now,

Since, The equation of line passes through the points (0, 0) and (4, -1).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (- 1 - 0) / (4 - 0)

m = - 1 / 4

Thus, The equation of line with slope - 1/4 is,

⇒ y - 0 = - 1/4 (x - 0)

⇒ y = - 1/4x

Therefore, The equation of line passes through the points (0, 0) and

(4, -1) will be;

⇒ y = - 1/4x

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We can use the Pythagorean theorem to solve this problem. Let's call the distance from the ball to the center of the green "d". We know that the marker is 150 yards from the center of the green, and the golfer has paced off 35 yards in a direction 110 degrees from the marker.

Let's use x to represent the horizontal distance from the marker to the ball, and y to represent the vertical distance from the marker to the ball. Then, we have:

x = 35 * cos(110)

y = 35 * sin(110)

Using the Pythagorean theorem, we can find the distance "d" from the ball to the center of the green:

d^2 = x^2 + (y + 150)^2

Plugging in the values for x and y, we get:

d^2 = 35^2 * cos(110)^2 + (35 * sin(110) + 150)^2

d^2 = 1225 + (150 + 35 * sin(110))^2

Using a calculator, we can find that sin(110) = 0.939, so:

d^2 = 1225 + (150 + 31.65)^2

d^2 = 1225 + (181.65)^2

d^2 = 1225 + 32762.7225

Taking the square root of both sides:

d = sqrt(1225 + 32762.7225)

d = sqrt(33987.7225)

d = 183.83

Rounding to the nearest yard:

d = 184 yards

So, the ball is 184 yards from the center of the green.

Answer:

y = 2; x = 1/4

Step-by-step explanation:

We can solve for y then x using elimination.  We can multiply the first equation by -4 to cancel out the xs:

[tex]-1(3y=4x+5)\\\\4y=4x+7\\-3y=-4x-5\\\\y=2\\\\[/tex]

Now, we can plug in this 2 for y in any of two equations to find x:

[tex]3(2)=4x+5\\6=4x+5\\1=4x\\1/4=x[/tex]

At 100 machines the unit cost will be minimum and the minimum cost is 11985.

The lowest point on the graph, that is referred to as the minimum, or min, is the vertex of a parabola. The highest point on the graph, that referred to as the maximum, or max, is the vertex of a parabola.

The formula for the minimum value is given by -b/2a

Here we have

The medical equipment industry manufactures X-ray machines. If x machines are made, the unit cost is given by the function
C(x) = 0.9x²-180x+20,985.  

Compare given C(x) with the standard equation ax² + bx + c  

=> a = 0.9, b = -180 and c = 20,985  

We can find the x - coordinate where the minimum value occurs using the formula -b/2a    

The x-coordinate where the minimum value occurs = - (- 180)/2(0.9)

= (180)/1.8 = 100

Hence at x = 100, the unit cost will be minimum

The unit cost can be calculated as follows

C(100) = 0.9(100)²-180(100)+20,985

= 0.9(10000) -18000 + 20,985    

= 9000 - 18000 + 20985

= 11985

Therefore,

At 100 machines the unit cost will be minimum and the minimum cost is 11985.

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The distance between the given pair of points (3,-4) and (9,-9) is 7.8 unit.

The distance formula used in finding the distance between two points is expressed as;

D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

Given the data in the question;

Point 1 ( 3,-4 )

Point 2 ( 9,-9 )

Plug the given values into the distance formula and simplify.

D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

D = √( ( 9 - 3 )² + ( -9 - (-4) )² )

D = √( ( 9 - 3 )² + ( -9 + 4 )² )

D = √( ( 6 )² + ( -5 )² )

D = √( 36 + 25 )

D = √( 61 )

D = 7.8 units

Therefore, the distance between the of points is 7.8 units.

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Option b. This would tell you the proportion of students who attend college in their home state. A large proportion means that students prefer to attend college in their home state and a small proportion means that students prefer to attend college in a different state.

The variable computed as the number of students in each state who attend college in the state divided by the total number of students from the state who attend college can provide insights into students' preferences for attending college in their home state. A large proportion of students who attend college in their home state indicates that students prefer to stay close to home for higher education, while a small proportion suggests that they are more likely to attend college in a different state. This information can be useful for policymakers and educators to better understand the higher education preferences of their state's students and to develop policies and programs to encourage more students to attend college within their home state.

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Complete question:

The U.S. Census Bureau collects a large amount of information concerning higher education. For example, the bureau provides a table that includes the following variables: state, number of students from the state who attend college, number of students who attend college in their home state.

Consider a variable computed as the number of students in each state who attend college in the state divided by the total number of students from the state who attend college. Explain how you would use this variable to describe something about the states.

a. This would tell you the proportion of the state’s population that attend college in their home state. A large proportion means that less of the state’s population attend college while a small proportion means that more of the state’s population attend college.

b. This would tell you the proportion of students who attend college in their home state. A large proportion means that students prefer to attend college in their home state and a small proportion means that students prefer to attend college in a different state.

c. This would tell you the proportion of students who attend college in their home state. A large proportion means that students prefer to attend college outside their home state and a small proportion means that students prefer to attend college in their home state.

d. This would tell you the proportion of the state’s population that attend college in their home state. A large proportion means that more of the state’s population attend college while a small proportion means that less of the state’s population attend college.

Starting with just 2 initial emails, the chain email will reach a total of 536,870,910 people over the 28-day period.

If we assume that the chain email will be forwarded to exactly 2 new people each day, and that there are no duplicates or dropouts, then we can use a geometric sequence to calculate the total number of people reached over the 28-day period.

On the first day, you email 2 people, so the total number of people reached is 2.

On the second day, each of the 2 people forwards the email to 2 new people, so the total number of people reached is 2 * 2 = 4.

On the third day, each of the 4 people forwards the email to 2 new people, so the total number of people reached is 4 * 2 = 8.

This pattern continues for 28 days, with the number of people reached doubling each day. Therefore, the total number of people reached over the 28-day period is:

2 + 4 + 8 + 16 + ... + 2^28

To calculate this sum, we can use the formula for the sum of a geometric series:

S = a(1 - r^n) / (1 - r)

where a is the first term (2), r is the common ratio (2), and n is the number of terms (28).

Plugging in these values, we get:

S = 2(1 - 2^28) / (1 - 2)

= 2(1 - 268,435,456) / (-1)

= 536,870,910

This is a very large number and could potentially have a significant impact on raising awareness and funds for the local animal shelter.

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Answer: 5 Months

Step-by-step explanation:

Alright, we know he will make $120 a month (since 50 + 70 = 120)

(Let's have months=m)

So now we need to figure out for how many months (m) will he need to get to $600.

We know 120 a month so we can get the equation: 120m=600

Now all we have to do is solve for m

Divide both sides by two to get m=5

Checking Answers

70(5)=350

50(5)=250

250+350=600

So this solution works.

Answer: 5 months

Step-by-step explanation: so, what you have to do is add up 120 5 times so in total you will have 600 so the answer is 5 months.

The value of x and y in the system of equations, are 10 and 44, therefore, the number of booster pack and premade deck are 10 and 44 respectively.

A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Given that, a deck contains 266 cards which have 9 booster packs and 4 premade decks, and 10 booster packs and 5 premade decks, which included a total of 320 cards.

Let the number of booster pack and premade deck be x and y,

Establishing the system of equations,

9x + 4y = 266....(i)

10x + 5y = 320

2x + y = 64...(ii)

Multiplying eq(ii) by 4 and subtract eq(ii) from eq(i)

(9x + 4y = 266) - (8x + 4y = 256)

x = 10

Put x = 10 in eq(ii)

20 + y = 64

y = 44

Hence, the value of x and y in the system of equations, are 10 and 44, therefore, the number of booster pack and premade deck are 10 and 44 respectively.

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Jayden needs to purchase 3900 square feet of sod to cover his front and back yards.

The unitary method is a mathematical technique used to solve problems by finding the value of one unit and then multiplying or dividing to find the value of the whole. In this case, the unit we will use is square feet.

To calculate the area of the front yard, we need to multiply its length by its width. So, we have:

Area of front yard = Length x Width = 50 ft x 70 ft = 3500 sq ft

To find the area of the back yard, we use the same formula:

Area of back yard = Length x Width = 10 ft x 40 ft = 400 sq ft

Now, we need to add the two areas to find the total area that requires sod. So, we have:

Total area = Area of front yard + Area of back yard

=> 3500 sq ft + 400 sq ft = 3900 sq ft

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Based on the information in the graph, we can infer that the area of the three triangles is the same. In this case the area would be 45 cm².

To calculate the area of the triangles we must calculate the area of one of them taking into account that all three have the same dimensions. According to the above, we must apply the following formula:

Then we must replace the values of the base and the height:

So the area of the triangles would be 45cm.

Note: This question is incomplete. Here is the complete information:

question

What is the area of the triangles?

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In a primary care setting with a baseline cervical cancer prevalence of 15%, the screening test would have a sensitivity of 94.3% and a specificity of 85.7%. The PPV would be 53.1% and the NPV would be 98.8%.

To calculate the test performance of the screening test in a primary care setting with a 15% baseline cervical cancer prevalence,

we can use the same sensitivity and specificity values obtained in the study, but apply them to a different population.

Given that the prevalence of cervical cancer is 15%, the number of true positives (TP) and false negatives (FN) in the screened population would be:

TP = Prevalence x Sensitivity x Number screened

TP = 0.15 x 0.91 x 3300

TP = 449.19, rounded to 449.

FN = Number with disease - TP

FN = 0.15 x 3300 - 449

FN = 26.5, rounded to 27.

Similarly, the number of true negatives (TN) and false positives (FP) in the screened population would be:

TN = (1 - Prevalence) x Specificity x Number screened

TN = 0.85 x 0.85 x 3300

TN = 2382.75, rounded to 2383.

FP = Number without disease - TN

FP = 0.85 x 3300 - 2383

FP = 396.5, rounded to 397.

Using these values, we can construct the following 2x2 contingency table for the primary care setting:

Actual condition:-

Test outcome       Positive (P)                          Negative (N)

Disease (D)       True positive (TP = 449)         False negative (FN = 27)

No disease (ND) False positive (FP = 397)  True negative (TN = 2383)

Using this contingency table, we can calculate the following test performance measures:

Sensitivity = TP / (TP + FN) = 449 / (449 + 27) = 0.943, or 94.3%.

Specificity = TN / (FP + TN) = 2383 / (397 + 2383) = 0.857, or 85.7%.

Positive predictive value (PPV) = TP / (TP + FP) = 449 / (449 + 397) = 0.531, or 53.1%.

Negative predictive value (NPV) = TN / (FN + TN) = 2383 / (27 + 2383) = 0.988, or 98.8%.

Therefore, in a primary care setting with a baseline cervical cancer prevalence of 15%, the screening test would have a sensitivity of 94.3% and a specificity of 85.7%. The PPV would be 53.1% and the NPV would be 98.8%.

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Answer:

m<20

Step-by-step explanation:

The function shown in this graph is y = x + 4

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

The graph

On the graph, we can see a straight line

This means that the graph is a linear function

This can be represented as

y = mx + c

From the graph, we have

c = 4 (because the graph intersects the y-axis at y = 4)

m = 1 (because a unit change in x gives a unit change in y)

So, we have

y = x + 4

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Answer:

13 buses are required.

Step-by-step explanation:

To find the number of minibuses required, take the total number of fans and divide by the number of fans each bus holds.

220 /18

12 2/9

We need to round up to make sure all the fans get on a bus.

13 buses are required.

Answer:

64

Step-by-step explanation:

Answer:

X        Y

2        1

4        7

5        10

Step-by-step explanation:

The values of a, b and c based on the information will be 2, 3, 4.

The square root of c which is 4 will be 2.

From the information, it was stated that the sum of the three consecutive integers, a, b and c, is 9.

This can be Illustrated as:

a + a + 1 + a + 2 = 9

3a + 3 = 9

3a = 9 - 3

a = 6 / 3

a = 2

b will be 2 + 1 = 3

c will be 2 + 2 = 4

The square root of c which is 4 will be:

= ✓4

= 2

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The sum of three consecutive integers, a, b and c, is 9.

(a) What is the greatest possible value of b?

(b) Find the square root of the largest possible value of c.

Answer: $212,019 to raise a child from birth to 17 years in a household with an annual income of $64,000.

Explanation:

To find out the total cost of raising a child in a household with an annual income of $64,000, we can plug in x = 64,000 into the equation y = 1.55x + 110,419:

y = 1.55x + 110,419

y = 1.55 * 64,000 + 110,419

y = 101,600 + 110,419

y = $212,019

So, it would approximately cost $212,019 to raise a child from birth to 17 years in a household with an annual income of $64,000.