A local radio station is running a contest were 35 people have qualified. From these qualifiers, 3 will be randomly selected to win a trip to the Bahamas. How many different possibilities are there for the outcome of this contest?

For the given right-angled triangle the measure of the angle is 11.30°.

Given adjacent base of the triangle =  10

given opposite side of the triangle = 2

To find out the angle we can use a little bit of trigonometry. By trigonometry, we know that tan ∠ = opposite side / adjacent side.

So, we can use the above tan ∠ relation to find the angle.

Tan ∠ = opposite side / adjacent side

Tan ∠ = 2/10

Tan ∠ = 1/5

∠ = Tan⁻¹(1/5)

∠ = 11.30°.

From the above explanation, we can conclude that the measure of the angle for the given right triangle is 11.30°.

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The interquartile range of the data will be 0.215.

The lower half is:

7.86, 7.87, 7.99, 8.03

The median of the lower half is:

(Q1) = (7.87 + 7.99) / 2 = 7.93

The upper half is:

8.06, 8.08, 8.09, 8.20, 8.43

The median of the upper half is:

(Q3) = (8.09 + 8.20) / 2 = 8.145

The IQR is the difference between the third and first quartiles:

IQR = Q3 - Q1 = 8.145 - 7.93 = 0.215

Lower outlier threshold: Q1 - 1.5 x IQR = 7.93 - 1.5 x 0.215 = 7.5955

Upper outlier threshold: Q3 + 1.5 x IQR = 8.145 + 1.5 x 0.215 = 8.4795

None of the data points fall outside these thresholds, so there are no outliers in this data set.

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Without knowing the exact number of turtles in 2005, we cannot determine the exact number of turtles in 2010. However, we can use the information given to set up an equation.

Let x be the number of sea turtles in 2005.

According to the problem, the number of sea turtles in 2010 was twice the amount in 2005, or 2x.

We can set up an equation:

2x = number of sea turtles in 2010

We don't know the exact value of x, so we cannot solve for the number of turtles in 2010.

The equation of the line parallel to the graph of 2x - 3y = 7 and containing the point (-3,-3) is y = (2/3)x - 1.

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given the equation of the graph: 2x - 3y = 7.

First, we need to rearrange the given equation into slope-intercept form (y = mx + b) by solving for y:

2x - 3y = 7

-3y = -2x + 7

y = (2/3)x - 7/3

The slope of the given line is 2/3.

Hence, any line parallel to it will also have a slope of 2/3.

Using the point-slope form, we determine the equation of the line that passes through (-3,-3) and has a slope of 2/3:

y - y1 = m(x - x1)

y - (-3) = (2/3)(x - (-3))

y + 3 = (2/3)x + 2

y = (2/3)x - 1

Therefore, the equation of the line is y = (2/3)x - 1.

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Answer:

The yellow region is 13.73 cm squared

Step-by-step explanation:

---

Area of square:

[tex]8 * 8 = 64 cm^2[/tex]

Area of the 4 quarter-circles:

[tex]4(\pi r^2)/4[/tex]

The fours cancel each other, we are left with:

[tex]\pi r^2[/tex]

r = 4, so substitute that, we get:

[tex]\pi 4^2 = 16 \pi cm^2[/tex]

Which can be approximated to 50.27 cm squared

Subtract the area of the circle from the square:

[tex]64 - 50.27 = 13.73 cm^2[/tex]

So the area of the yellow region is 13.73 cm squared

The price of the bed after mark up is $475.00

Discount results in the reduction of the selling price of the product, which makes it more attractive for the customer.

The first discount given is 25% , therefore the price of the bed before mark up is

25/100 × 800

= 25×8

= 200

the price before mark up = 800-200 = $600

Another 25% is given after the first sale, there the price of the bed after mark up is

25/100 × 600

=$ 125

price after markup = 600-125

= $475.00

therefore the price of the bed after markup is $475.00

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Based on an exponential decay factor, Michael's stereo equipment will be worth $2,116 after 8 years, given the decreasing rate of 9% per year.

The decay factor is represented by (1 - r), where r is the constant periodic decreasing rate.

The decay factor is used in exponential decay functions to determine the depreciated value of an asset.

Current price of stereo equipment = $2,500

Annual decreasing rate = 9%

Decrease factor = 0.91 (100% - 9%)

The number of years = 8 years

Value of the equipment after 8 years = ($2,500 x 0.91^8)

= $2,116.125 ($2,500 x 0.47025)

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Answer: 100.48 cubic feet

Step-by-step explanation:

Answer:

x = 7.9 (nearest tenth)

y = 24.6° (nearest tenth)

Step-by-step explanation:

Pythagoras Theorem explains the relationship between the three sides of a right triangle. The square of the hypotenuse (longest side) is equal to the sum of the squares of the legs of a right triangle.

[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]

As we have been given the lengths of both legs of the right triangle, we can use Pythagoras Theorem to find the length of the hypotenuse, x:

[tex]\begin{aligned}3.2^2+7^2&=x^2\\10.24+49&=x^2\\59.24&=x^2\\x^2&=59.24\\x&=\sqrt{59.24}\\x&=7.6967525...\\x&=7.9\; \sf (nearest\;tenth)\end{aligned}[/tex]

Therefore, x = 7.9.

[tex]\hrulefill[/tex]

The tangent ratio is a trigonometric ratio that relates the angle of a right triangle to the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

[tex]\boxed{\begin{minipage}{7 cm}\underline{Tangent trigonometric ratio} \\\\$\sf \tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\end{minipage}}[/tex]

As we have been given the lengths of the sides that are opposite and adjacent angle y, we can use the tangent trigonometric ratio to find the measure of angle y:

[tex]\begin{aligned}\tan(y)&=\dfrac{3.2}{7}\\y&=\tan^{-1}\left(\dfrac{3.2}{7}\right)\\y&=\vphantom{\dfrac12}24.5671713...^{\circ}\\y&=24.6^{\circ}\;\sf (nearest\;tenth)\end{aligned}[/tex]

Therefore, y = 24.6°.

The value of the expression "(x²y - 2z)/4", when x = 12 , y = 8 and z = 6, is (c) 285.

An "Expression" is defined as a combination of numbers, variables, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation, which are written using mathematical symbols and follow certain rules.

We have to evaluate the expression : (x²y - 2z)/4, if x = 12 , y = 8 and z = 6,

To evaluate , we substitute x = 12 , y = 8 and z = 6, in the expression,

So, We have,

⇒ (12² × 8 - 2×6)/4,

⇒ (144 × 8 - 12)/4,

⇒ (144 × 8 - 12)/4,

⇒ (1152 - 12)/4,

⇒ 1140/4,

⇒ 285,

Therefore, the value of the given expression, when x=12, y=8, and z=6, is 285, the correct option is (c).

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The dimensions of the rectangular block indicates;

(a) The largest number of bricks that can be cut from the block is 48 bricks

(b) The volume of the wood left is 216 cm³

The volume of the rectangular block is the product of the length, L, width, W, and height, H.

1. The dimensions of the rectangular block indicates that the block volume is; V = 24 cm × 9 cm × 7 cm = 1,512 cm³

The largest number of bricks that have side lengths of 3 cm that can be cut from the block is therefore;

Number of cubes; (24)/3 × (9)/3 × (7)/3 ⇒ 8 × 3 × 2 = 48

(b) The volume of wood left = 1512 - 48 × 3 × 3 × 3 = 216

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The piecewise function is

f(x) = { x -3 , x≤3

             8, -3 < x ≤ 5

           x+10, x>6

For values less than or equal to -3, we have a line with a positive slope. We have two lines, y = x - 2, and y = x - 3.

1. For y = x - 2

-5 = -3 - 2= -5

2. For y = x - 3

-5 = -3-3 = -6

The fact that the domain is specified for x less than -3  further demonstrates that the first choice is not an option.

Additionally, we know that the function's value is equal to 8 for the range from x greater than -3 to less than or equal to 5.

Additionally, the equation is given as y = -x + 10 and the line has a negative slope for values greater than 6.

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The car will be worth half its original value after 4 years

A graph for straight-line depreciation for a car is given.

a

The number of years the car totally depreciates is 8 years as seen in the graph which is x -intercept.

Step 3/7

The model makes straight-line depreciation. In a straight line depreciation equation, the intercepts are

(0, maximum car value) and (maximum lifespan,0)

Let y represent the value of the car at any time during its lifetime. The minimum y -value is zero dollars and the maximum y -value is the purchase price of $25,600

The intercepts are (0, 25, 600) and (8,0)

Determine the slope of the equation.

Two points determine a line, so only two points are needed to determine the slope of a line.

Let the coordinates of the -intercept be the first point. That is, (xi,yi) = (0, 25, 600)

Let the coordinates of the -intercept be the second point. That is (x2, y2)= (8,0)

Use the slope ratio as shown below;

The slope of the depreciation equation is.

-3200

The general form for the equation of a straight line is:

y = mx + b

Where m represents the slope of the line and b represents the y-intercept.

The slope is -3,200 and the -intercept is 25,600 as obtained.

Therefore, the straight line depreciation equation is:

y = -3,200x + 25,600

Therefore, the value of the car after 4 years is $12,800

b.

Use the depreciation equation and substitute x=5 years to find the car worth after 5 years.

Therefore, the value of the car after 5 years is $9,600

c.

The half value of the car is half of $25,600 which is $12,800

The car will be worth half its original value after 4 years

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Answer: x=4, sides = 12, 8, 6, 8

Step-by-step explain

Perimeter means the sum of all sides of a shape, in this example there are four sides add the sides and set it equal to 34.

X+8+x+4+2x-2+x²-2x=34

x²+2x+10=34

x²+2x-24

(x-4)(x+6)

x=4, x=-6

x can not be -6 because then the x+4 side would be -2, therefore it is extraneous and x=4 is the correct answer.

Now to find side lengths just plug in 4 for x

4+8=12

4+4=8

2*4-2=6

4*4-2*4=8

The equation expressing d as a function of t can be found by using the formula for distance traveled with constant speed:

d = vt

where d is the distance, v is the constant speed, and t is the time elapsed.

In this case, the speed is 150 cm/s, so the equation is:

d = 150t

To find the total distance traveled in meters at t = 2 seconds, we need to first find the total distance traveled in centimeters at t = 2 seconds:

d = 150t

d = 150(2)

d = 300 cm

To convert to meters, we divide by 100:

d = 300/100

d = 3 meters

Therefore, at t = 2 seconds, the object has traveled a total distance of 3 meters.

Answer:

[tex](x-2)(x+16)[/tex]

Step-by-step explanation:

Use graphing calculator and find the x-intercepts.

The ratio of 8 : 1/3 is equivalent to the simplified ratio of 24 : 1.

To analyze and describe the ratio 8 : 1/3, we need to convert the fraction to a ratio with a whole number. One way to do this is to express the fraction as a ratio with a denominator of 3:

1/3 = 1:3

Now we can rewrite the ratio 8 : 1/3 as:

8 : 1:3

We can simplify this ratio by multiplying both terms by 3 to get rid of the fractional term:

8 × 3 : 1:3 × 3

24 : 1

Therefore, the ratio 8 : 1/3 is equivalent to the simplified ratio 24 : 1. This means that for every unit in the second part of the ratio, there are 24 units in the first part of the ratio. In other words, the first part of the ratio is 24 times larger than the second part.

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Answer: ≅ $0.02

Step-by-step explanation:

First, lets find the area of the large triangle

0.5 x 14 x 11 = 77 mm^2

Next lets find the area of the middle rectangle:

4 x 14 = 56 mm^2

Last lets find the area of the small triange:

0.5 x 14 x 3 = 21 mm^2

So the total area is: 77 + 56 + 21 = 154 mm^2

the total cost is given to be: 1.52 + 0.42 + 0.92 = $2.86

dividing the cost by the area to find the cost/mm:

2.86/154 ≅ $0.02

Answer:

14 mins

Step-by-step explanation:

2/6 = x/42

6x=84

x=14

A negative correlation may be seen on the graph. The birth rate declines over time. This indicates that the number of births per 1000 persons in the US has been declining over time.

Answer:

26

Step-by-step explanation:

Answer:

The expression $11.75x + $20 represents the total price for the order, including delivery to the school.

In this expression, 'x' represents the number of boxes of paints being purchased, and $11.75 represents the cost of each box. The term $11.75x represents the total cost of the boxes of paints based on the number of boxes being purchased.

The term $20 represents the delivery cost to the school, which is added to the total cost of the boxes of paints.

By multiplying the cost per box ($11.75) by the number of boxes (x) and adding the delivery cost ($20), you can calculate the total price for the order, including delivery.

The trigonometry functions when evaluated are shown below

In trigonometry, sine (sin), cosine (cos), and tangent (tan) are three basic functions that relate angles to the sides of a right triangle.

They are defined as follows:

sin A = opposite side/hypotenuse.

cos A = adjacent side/hypotenuse.

tan A = opposite side/adjacent side.

So, we have

Figure 1

Figure 2

Figure 3

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Answer:

see below

Step-by-step explanation:

The Reason for #1 is literally GIVEN to you.

Statement #2: Since the Base Angles of an isosceles triangle are congruent, this statement should be ∠CAB≅∠CBA.

Reason #3: Notice that the statement repeats itself (AB=AB). This demonstrates the REFLEXIVE property.

Reason #4: (Clue) Note which items have been Given or Proven congruent and use it as the triangle congruence property. It helps to actually mark them. Your choices are SSS, SAS, ASA, and AAS.

Reason #5: (Clue) Since the triangles of which AM and BN are of part are now proven congruent, these Corresponding Parts are Congruent as well.

Answer:

25$ if the tickets were involved it would be 70$

Santiago would have to pay $87 in total if he bought 6 snacks for everyone to share. The cost increases to $60 + 4.5*x when a variable number of snacks, represented by x, are bought.

The topic of this question is

Mathematics

, specifically about using multiplication and addition in problem-solving.

Firstly, Santiago is going to see a movie with his 3 kids. Therefore, he needs to buy 4 tickets. If each ticket costs $15, then the total cost for movie tickets will be 4 * 15 = $60.

Secondly, if Santiago buys 6 snacks for everybody to share with each snack costing $4.50, the total cost for snacks will be 6 * 4.5 = $27. The total money Santiago would have to pay for his family would then be the sum of the costs of the tickets and snacks, which is 60 + 27 = $87.

Regarding the case when Santiago bought x snacks for everybody to share, the total cost would become 60 + 4.5*x. This formula gives the total cost based on the given number of snacks.

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Answer:

[tex]f(0) = 6.2 \sqrt{4.5} + 18 = 31.2[/tex]