find the value of sin(θ) for an angle θ in standard position with a terminal ray that passes through the point (-5, -12)
​

Given:

Given that each vertex of the polygon forms a right angle.

The measurements of the sides of the polygon were given.

We need to determine the area of the polygon.

Let us divide the polygon into 3 rectangles.

Area of the rectangle can be determined using the formula, [tex]A=length \times width[/tex]

Area of rectangle 1:

The length of rectangle 1 is 17 inches.

The width of rectangle 1 is 8.5 inches.

The area of rectangle 1 is given by

[tex]17 \times 8.5 =144.5 \ in^2[/tex]

Area of rectangle 2:

The length of rectangle 2 is 16.5 inches.

The width of rectangle 2 is (17 - 9) = 8 inches.

The area of rectangle 2 is given by

[tex]16.5 \times 8 =132 \ in^2[/tex]

Area of rectangle 3:

The length of rectangle 3 is 13 inches.

The width of rectangle 3 is 11 inches.

The area of rectangle 3 is given by

[tex]13 \times 11=143 \ in^2[/tex]

Area of the polygon:

The area of the polygon can be determined by adding the areas of the three rectangles.

Thus, we have;

[tex]Area=144.5+132+143[/tex]

[tex]Area=419.5 \ in^2[/tex]

Thus, the area of the figure is 419.5 square inches.

Hence, Option B is the correct answer.

Answer:

56.6 square yards.

Step-by-step explanation:

Given:

A fountain in the park has two circular pools that are the same size.

Question asked:

What is the total area of the pools if the radius is 3 yards ?

Solution:

First of all we will calculate the area of a circular pool.

As we know:

[tex]Area\ of\ circle=\pi r^{2}[/tex]

                       [tex]=\frac{22}{7} \times(3)^{2} \\ \\ =\frac{22}{7}\times9\\ \\ =\frac{198}{7} \\ \\ =28.28\ square\ yards[/tex]

Area of circular pool nearest tenth = 28.3 square yards

Now, as given that both pools are of same size.

Total area of the pools = 28.3 square yards + 28.3 square yards

                                      = 56.6 square yards.

Thus, the total area of the pools are 56.6 square yards.

Answer:

ur answer is 56.5 and 18

Step-by-step explanation:

The mean is 59

Add all the scores together, then divide by the number of test scores

The mean of the scores to the nearest 10th Score Number of Students is 59.

We have given a data,

80,85,6,90,95,100,6,8

Mean is the adding all the scores together, then divide by the number of test scores.

So we have given a data,

80,85,6,90,95,100,6,8

80+85+6+90+95+100+6+8=470

The number of of test scores=8

[tex]mean=\frac{470}{8}=58.75[/tex]

Mean≈59

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Answer:

D is correct E is correct F is correct

Step-by-step explanation:

72/12=6 ft per year

2 yards= 6 ft per year

18/3=6 ft per year

The equivalent rates to 6 feet per year are 18 inches per year, 12 feet in 4 years, 72 inches per year, 2 yards per year, and 18 feet in 3 years.

The student is asking about equivalent rates. To determine which rates are equivalent to 6 feet per year, we need to compare each option against the given rate. The conversion factors needed for this problem are:

Option A: 2 inches per year is not equivalent to 6 feet per year.

Option B: 18 inches per year is equivalent to 6 feet per year because 18 inches is 1.5 feet, and thus, 1.5 feet multiplied by 4 would give us 6 feet in 4 years.

Option C: 12 feet in 4 years is equivalent to 6 feet per year because dividing 12 feet by 4 years gives us 3 feet per year, which is half of the given rate.

Option D: 72 inches per year is equivalent to 6 feet per year because 72 divided by 12 is 6.

Option E: 2 yards per year is equivalent to 6 feet per year because 2 multiplied by 3 is 6.

Option F: 18 feet in 3 years is equivalent to 6 feet per year because dividing 18 feet by 3 years gives us 6 feet per year.

Thus, the equivalent rates to 6 feet per year from the options given are 18 inches per year, 12 feet in 4 years, 72 inches per year, 2 yards per year, and 18 feet in 3 years.

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Answer:

2

Step-by-step explanation:

4 -2f

Let f =1

4 - 2(1)

Multiply and divide first

4 -2

2

Answer:

The first option....x^2-x-12

Step-by-step explanation:

Answer: x^2-x-12

Step-by-step explanation: correct answer

Answer:

400 ping pong balls

Step-by-step explanation:

Let the total number of ping pong balls =x

Out of x ping pong balls, 80 are marked with a blue dot

Out of 80 ping pong balls, 16 are marked with a blue dot.

Expressing it as a ratio:

x:80=80:16

[tex]\frac{x}{80}=\frac{80}{16}\\ 16x=80X80\\x=6400 \div 16\\x=400[/tex]

There are an estimate of 400 ping pong balls in the container.

Answer:

7/4

Step-by-step explanation:

We know that US = RU, so we can just set those expressions equal to each other.

US = 3m + 2

RU = -m + 9

US = RU  ⇒  3m + 2 = -m + 9  ⇒  4m = 7  ⇒  m = 7/4

Hope this helps!

Answer:

7/4 or 1¾

Step-by-step explanation:

Since US = UR

3m + 2 = -m + 9

4m = 7

m = 7/4

m = 1¾

Answer:

The correct answer is 2.912 cm.

Step-by-step explanation:

A company is designing a new cylindrical water bottle.

Volume of a cylinder is given by π × [tex]r^{2}[/tex] × h, where h is the height of the cylinder and r is the radius of the cylinder.

The volume of each bottle will be 211 [tex]cm^{3}[/tex].

The height (h) of the water bottle be 7.9 cm.

Let the radius of the bottle be r cm.

∴ π × [tex]r^{2}[/tex] × h = 211 ; (π = 3.15)

⇒ [tex]r^{2}[/tex] × 24.885 = 211

⇒ r = 2.912

The radius of the water bottle is 2.912 cm.

Answer:

9

Step-by-step explanation:

To find the common ratio, take the second term and divide by the first

36/72 = 1/2

To find the next term, take the last term and multiply by the common ratio

18*1/2 = 9

Answer:

9.

Step-by-step explanation:

The common ratio = 36/72 = 18/36 = 1/2.

So the next term is 18 * 1/2 = 9.

Answer:

Assets: $231,775

Liabilities: $180,275

Net worth: $51,500

Step-by-step explanation:

- Assest is something of value. ex. house, barns, tractors. To find this take...

215,000+12,500+1,875+2,400=$231,775

(All these numbers are good things he has, not debt.)

- Liability is debt you will need to repay. ex. loans or accounts payable. To find this take...

175,000+4,000+1,275=$180,275

- Net worth is the difference between your total assests and total liabilities. Knowing difference is subtraction, we should subtract assests minus liablities. To find this take...

$231,775-$180,275=$51,500

- Hope this helps! If you have any further questions or other problems you need help on please let me know as I would be glad to help.

Answer:16

Step-by-step explanation:AC is half of ED

Answer:

Step-by-step explanation:

opposite= 8 : the length opposite angle c

adjacent=15 : the length next to angle c, not the hypotenuse

hypotenuse= 17 : the hypotenuse will always be opposite the right angle

[tex]sinC=\frac{opposite}{hypotenuse}\\ \\sinC=\frac{8}{17}[/tex]

[tex]cosC=\frac{adjacent}{hypotenuse}\\\\cosC=\frac{15}{17}[/tex]

[tex]tanC=\frac{opposite}{adjacent} \\\\tanC=\frac{8}{15}[/tex]

Answer:

Δπ Min = -0.0709

Δπ Max = -0.0535

Step-by-step explanation:

Here we have

[tex]z=\frac{(\hat{p_{1}}-\hat{p_{2}})-(\mu_{1}-\mu _{2} )}{\sqrt{\frac{\hat{p_{1}}(1-\hat{p_{1}}) }{n_{1}}-\frac{\hat{p_{2}}(1-\hat{p_{2}})}{n_{2}}}}[/tex]

Where:

[tex]{\hat{p_{1}}[/tex] = 13% = 0.13

[tex]\hat p_{2}[/tex] = 14% = 0.14

n₁ = 163

n₂ = 160

Therefore, we have;

[tex]z=\frac{(\hat{p_{1}}-\hat{p_{2}})}{\sqrt{\frac{\hat{p_{1}}(1-\hat{p_{1}}) }{n_{1}}-\frac{\hat{p_{2}}(1-\hat{p_{2}})}{n_{2}}}}[/tex]

Plugging the values gives

z = -0.263

CI 90% =  critical z = [tex]\pm[/tex]1.644

The minimum difference in true proportion = -0.0709

The maximum difference in true proportion = 0.0535.

Answer:

A university wants to estimate the average distance that commuter students travel to get to class with an error of ±3 miles and 90 percent confidence. What sample size would be needed, assuming that travel distances are normally distributed with a range of X = 0 to X = 50 miles, using the Empirical Rule μ ± 3σ to estimate σ.

The required sample size, n=(zσ/E)² = 21.0

Step-by-step explanation:

The estimated σ here  = (range)/6 = (50/6) = 8.33

In the case of  90 % , CI value of z = 1.64

standard deviation, σ=  8.33

margin of error E = 3

The required sample size, n=(zσ/E)² = 21.0

Answer:

n = 21

Step-by-step explanation:

Solution:-

- Let denote a random variable "X" : average distance that commuter students travel to get to class.

- The population is given to be normally distributed, such that:

                    Range X: [ 0 , 50 ] miles

- We will use the given range coupled with the empirical rule for normal distribution to determine the mean (u) and standard deviation of population (σ):

                   P ( μ - 3σ < X < μ + 3σ) = 0.997  ..... (Empirical Rule)

- According to the standardized results for Z-table:

                   P ( -3 < Z < 3 ) = 0.997

So,               P ( Z ≤ 3 ) = 1 - (1 - 0.997) / 2 = 0.9985

                   P ( Z ≥ -3 ) = 1 - (1 - 0.997) / 2 = 0.9985

- The standardized values for the given data can now be determined:

                   P ( X ≥ μ - 3σ ) = P ( Z ≥ -3 ) = 0.9985

                   X ≥ μ - 3σ  = Upper limit - 0.9985*( Range )

                   X ≥ μ - 3σ  = 50 - 0.9985*( 50 )

                  μ - 3σ = 0.075   ..... Eq1

                   P ( X ≤ μ + 3σ ) = P ( Z ≤ 3 ) = 0.9985

                   X ≤ μ + 3σ  = Lower limit + 0.9985*( Range )

                   X ≤ μ + 3σ  = 0 + 0.9985*( 50 )

                  μ + 3σ = 49.925   ..... Eq2

- Solve the Eq1 and Eq2 simultaneously:

                   2μ = 50 , μ = 25 miles                  

                    3σ = 24.925

                    σ = 8.30833

- Hence, the normal distribution parameters are:

                    X ~ N ( μ , σ^2 )

                    X ~ N ( 25 , 8.308^2 )

- The standard error in estimation of average distance that commuter students travel to get to class is E = ±3 miles for the confidence level of 90%.

- The Z-critical value for confidence level of 90%, Z-critical = 1.645  

- The standard error estimation statistics is given by the following relation with "n" sample size.

                     E = Z-critical*σ /√n    

                     n = [ Z-critical*σ /E ]^2

- Plug in the values:

                     n = [ 1.645*8.308/3]^2    

                     n = 20.75306 ≈ 21  

Answer: The sample size needed to estimate average distance that commuter students travel to get to class with error of ±3 miles and 90 percent confidence, is n = 21.      

Answer:

840cm cubed

Step-by-step explanation:

720+120

Answer:

[tex]x \approx 21.080\,ft[/tex], [tex]y = 29.080\,ft[/tex]

Step-by-step explanation:

The total area of the pool and the walkway is:

[tex](x + 6\,ft)\cdot (y + 6\,ft) = 950\,ft^{2}[/tex]

[tex](x + 6\,ft)\cdot (x + 14\,ft) = 950\,ft^{2}[/tex]

[tex]x^{2} + 20\cdot x + 84\,ft^{2} = 950\,ft^{2}[/tex]

[tex]x^{2} + 20\cdot x - 866\,ft^{2} = 0[/tex]

The roots of the second-order polynomial is:

[tex]x_{1} \approx 21.080\,ft[/tex] and [tex]x_{2} \approx -41.081\,ft[/tex]

The only possible root is:

[tex]x \approx 21.080\,ft[/tex]

The other dimension of the pool is:

[tex]y = x + 8\,ft[/tex]

[tex]y = 21.080\,ft + 8\,ft[/tex]

[tex]y = 29.080\,ft[/tex]

Answer:

452.16 inches squared

Step-by-step explanation:

Answer:

452.39 in.^2

Step-by-step explanation:

since the width of the box is 24, the diameter of the circles is also 24.

using 12 as the radius, we plug it into the equation pi(12)^2 and we get 452.39 in^2

Answer:

x > 5

Step-by-step explanation:

Step 1 :

Equation at the end of step 1 :

(4x + 2) - (2x - 4 • (x - 8)) > 0

Step 2 :

Step 3 :

Pulling out like terms :

3.1 Pull out like factors :

6x - 30 = 6 • (x - 5)

Equation at the end of step 3 :

6 • (x - 5) > 0

Step 4 :

4.1 Divide both sides by 6

Solve Basic Inequality :

4.2 Add 5 to both sides

x > 5

Answer:

Hence the required dimension is 4cm.

Step-by-step explanation:

Given:

An Isosceles triangle with uneven side=l+1 cm

Area= 6 sq cm

To Find:

Height of Triangle.

Solution:

We know that area of triangle given by,

Area=1/2*base*height.

Here height =1+base

6=1/2((b+1)*b

12=(b+1)*b.

b^2+b-12=0

(b-3)(b+4)=0

b=3 or b=-4

So length never be negative

so b=3 cm

And height=b+1=3+1=4 cm.

x²+9x+8

Rewrite

(x+1)(x+8)

Distribute

x²+8x+1x+8

Simplify

x²+9x+8

Answer:

[tex]x^{2}[/tex] + 9x + 8    i hope this helps!   :)

Step-by-step explanation:

distribute the x to the x and 8   [tex]x^{2}[/tex] + 8x

distribute the 1 to the x and 8   x + 8

put the two together   [tex]x^{2}[/tex] + x + 8x + 8

combine like terms   [tex]x^{2}[/tex] + 9x + 8

Given:

The given equation of the line is [tex]y=0.216x+32.575[/tex]

We need to determine the slope of the equation.

Slope:

Let us determine the slope of the equation.

The general form of the equation of the line is given by

[tex]y=mx+b[/tex]

where m is the slope of the equation and b is the y - intercept.

Now, we shall compare the general form of the equation of the line with the given equation, we have;

[tex]m= 0.216[/tex]  and  [tex]b=32.575[/tex]

Thus, the slope of the equation of the line is [tex]m= 0.216[/tex]

the slope is 0.216

And just in case you need it the y-intercept is 32.575

I hope this was helpful :)

Answer:

46 feet

Step-by-step explanation:

Perimeter of rectangle needed =

[tex]14+14+7= 35\\[/tex]

Half of the circumference of a circle needed =

[tex]\frac{1}{2} \pi d = \frac{1}{2} * \frac{22}{7} * 7= 11[/tex]

Total perimeter needed =

[tex]35 + 11=46[/tex]

Answer:

46 ft

Step-by-step explanation:

John will need to put a fence along 3 sides of the rectangle: 14 ft, 7 ft, 14 ft

He also needs to put a fence along the half circle:

C (circumference) = 2×π×r = π×d

⇒C÷2 = π×d÷2 = 22/7×7÷2 = 22÷2 = 11 ft

Together: 14 + 7 + 14 + 11 = 46 ft

Answer:

The distance as product of 38 and a power of 10 is [tex]38*10^{6}[/tex]

Step-by-step explanation:

In math when we're dealing with big numbers like this we express them in power of 10, since it'll be easyer to read that way. We take the parts of the number to the left that are not equal to "0", in this case 38, and multiply it by a power of 10. The expoent to this power of 10 will be the number of "0" after the 38 and before the ",". In this case the closest distance from Earth to Venus is 38,000,000 (there's a typo in the question). So we take the 38 and multiply it by [tex]10^{6}[/tex], since there are 6 zeros.

The distance as product of 38 and a power of 10 is [tex]38*10^{6}[/tex]

Answer:

distance travelled first day is 542 miles while that travelled on second day = 271 miles.

Step-by-step explanation:

please kindly see the attached files for details

Richard and Linda travel 542 miles on the first day and 271 miles on the second day to reach Hilton Head Island, with the total distance being 813 miles.

The student's question pertains to splitting a total distance into two parts, with a given ratio between the two parts. Since Richard and Linda travel twice as far on the first day as the second day, we can let the distance traveled on the second day be x miles. Therefore, the distance they travel on the first day would be 2x miles.

The total distance traveled to Hilton Head is 813 miles, so we can write an equation based on the sum of the distances traveled on both days: 2x (first day) + x (second day) = 813 miles. Simplifying this equation, we have 3x = 813 miles. Dividing both sides of the equation by 3 yields x = 271 miles.

This means that Richard and Linda travel 271 miles on the second day and 2 * 271 miles, which is 542 miles, on the first day. So, the distances Richard and Linda travel to Hilton Head Island on the first and second days are 542 miles and 271 miles, respectively.

Answer:

There will be one person on 1 square yard of land after 1,892,147.588 years.

Step-by-step explanation:

Continuous exponential growth formula:

[tex]P(t)=Pe^{rt}[/tex]

P(t)= Population after t years.

P= Initial population

r=rate of growth.

t= time in year

Given that,

Growth rate of country A (r)= 4.9% per year=0.049 per year.

Initial population (P)= 151,000.

Land area of country area= 14,000,000,000 square yards.

There will be one person on one  square yard of land.

So, there will be 14,000,000,000  person for 14,000,000,000 square yard of land in country A.

P(t)=14,000,000,000 person

[tex]\therefore 14,000,000,000= 151,000 e^{0.049t}[/tex]

[tex]\Rightarrow e^{0.049t}=\frac{ 14,000,000,000}{ 151,000}[/tex]

Taking ln both sides

[tex]\Rightarrow ln|e^{0.049t}|=ln|\frac{ 14,000,000,000}{ 151,000}|[/tex]

[tex]\Rightarrow {0.049t}=ln|\frac{ 14,000,000,000}{ 151,000}|[/tex]

[tex]\Rightarrow t}=\frac{ln|\frac{ 14,000,000,000}{ 151,000}|}{0.049}[/tex]

[tex]\Rightarrow t}=1,892,147.588[/tex] years

There will be one person for every square yard of land after 1,892,147.588 years.

Answer:

y=−259x+8

Step-by-step explanation:

i think this might be the answer but not sure

Answer:D

Step-by-step explanation:

Answer:

487.5 miles

Step-by-step explanation:

The actual distance between the cities is 487.5 miles.

Two or more ratios made to be equivalent to each other is termed as the method of proportion.

That is, if 'a' related to 'b' is proportional to 'p' related to 'q', then,

a : b : : p : q

⇒ a/b = p/q

⇒ aq = bp

Here we have the scale on a map reads 1/2 inch as 75 miles.

We have to find the actual distance of two cities if the distance between the cities in the map is 3 and 1/4 inches.

3 and 1/4 inches = (3 × 4 + 1) / 4 = 13/4 inches.

Let x be the actual distance between the cities.

Using proportion,

1/2 : 75 : : 13/4 : x

[tex]\frac{1/2}{75}[/tex] = [tex]\frac{13/4}{x}[/tex]

1/2 × x = 13/4 × 75

1/2 × x = 243.75

x = 487.5

Hence the actual distance between the cities is 487.5 miles.

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Answer:

C 5/7

Step-by-step explanation:

We can find the slope of a line using

m = (y2-y1)/(x2-x1)

   = (-5 - -10) /(-2 - -9)

   = (-5 +10)/(-2+9)

   5/7