Tell whether a triangle can have the given angle measures. 5 2/3∘, 64 1/3∘, 87∘

The expression for the perimeter is P = 12x - 16

The given parameters are

Length = 3x + 1

Width = 3x - 9

The perimeter is calculated as

P = 2 * (Width + Length)

So, we have

P = 2 * (3x + 1 + 3x - 9)

Evaluate

P = 2* (6x - 8)

Expand

P = 12x - 16

Hence, the expression for the perimeter is P = 12x - 16

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The Coalition for Airline Passengers Rights, Health, and Safety averages 400 calls a day to help stranded travelers deal with airlines. The hotline is staffed for 16 hours a day.

To calculate the average number of calls in different time intervals and the probability of different events related to these calls.

Part 1:

a. 60-minute interval average number of calls: 400/16 = 25 calls

30-minute interval average number of calls: 25/2 = 12.5 calls

15-minute interval average number of calls: 12.5/2 = 6.25 calls

Part 2:

b. To find the probability of exactly 6 calls in a 15-minute interval, we can use the Poisson distribution formula. Let's assume that the average number of calls in a 15-minute interval is 6.25. Then, the probability of exactly 6 calls in a 15-minute interval is:

P(6 calls) = (e^-6.25)*(6.25^6)/6! = 0.0686

c. To find the probability of no calls in a 15-minute interval, we can use the Poisson distribution formula. Let's assume that the average number of calls in a 15-minute interval is 6.25. Then, the probability of no calls in a 15-minute interval is:

P(0 calls) = e^-6.25 = 0.0047

d. To find the probability of at least two calls in a 15-minute interval, we can use the cumulative distribution function of the Poisson distribution. Let's assume that the average number of calls in a 15-minute interval is 6.25. Then, the probability of at least two calls in a 15-minute interval is:

P(X >= 2) = 1 - P(0 calls) - P(1 call) = 1 - 0.0047 - (e^-6.25)*(6.25^1)/1! = 0.9906

Thus, the average number of calls in a 60-minute interval is 25, in a 30-minute interval is 12.5, and in a 15-minute interval is 6.25. The probability of exactly 6 calls in a 15-minute interval is 0.0686, the probability of no calls in a 15-minute interval is 0.0047, and the probability of at least two calls in a 15-minute interval is 0.9906.

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The polynomial graph has only one relative maximum at point b.

A function's graph can be used to determine the relative peaks and minima of the function. A relative maximum or minimum is a point that is higher than the points directly adjacent to it on both sides. The opposite is true for a relative maximum or minimum. When drawing a curve, relative maxima and minima are crucial spots that can be discovered using either the first or second derivative test.

Given, a polynomial function by observing the graph itself we conclude that the graph has no absolute maxima as it is going towards negative and positive infinity but it has a relative maximum a point b.

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Answer:

3

Step-by-step explanation:

24 divided by 8 is 3

Answer:

m = - 1 , m = 0 , m = \(\frac{7}{2}\)

Step-by-step explanation:

2m³ - 5m² - 7m = 0 ← factor out common factor m from each term

m(2m² - 5m - 7) = 0

factorise the quadratic 2m² - 5m - 7

consider the factors of the product of the coefficient of the m² term and the constant term which sum to give the coefficient of the m- term

product = 2 × - 7 = - 14 and sum = - 5

the factors are + 2 and - 7

use these factors to split the m- term

2m² + 2m - 7m - 7 ( factor the first/second and third/fourth terms )

2m(m + 1) - 7(m + 1) ← factor out (m + 1) from each term

(m + 1)(2m - 7)

then

2m³ - 5m² - 7m = 0

m(m + 1)(2m - 7) = 0 ← in factored form

equate each factor to zero and solve for m

m = 0

m + 1 = 0 ( subtract 1 from both sides )

m = - 1

2m - 7 = 0 ( add 7 to both sides )

2m = 7 ( divide both sides by 2 )

m = \(\frac{7}{2}\)

solutions are m = - 1 , m = 0 , m = \(\frac{7}{2}\)

Alice is standing at the top of a carnival slide. One base is 15 m, one base is 20 m, and the height is 16. The  angle, , in which Alice must slide to the nearest degree is: 61.63°.

AC=√AD²+CD²

AC=√16²+15²

AC=√483

AB=√AD²+BD²

AB=√16²+20²

AB=√656

Using law of cosine

BC=√BD²+CD²-2(BD)(CD)(Cos BDC)

BC=√20²+15²-2(20) (15) Cos88°

BC=√604.06

CosФ=AB²+AC²-BC²÷2(AB)(AC)

CosФ=656+483-604.06÷2(√656) (√483)

CosФ=0.475

Ф=cos^-1 0.475=61.63°

Therefore  Alice is standing at the top of a carnival slide. One base is 15 m, one base is 20 m, and the height is 16. The  angle, , in which Alice must slide to the nearest degree is: 61.63°.

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Shapes in mathematics are simply geometry figures

The shape of the tent is a triangular prism.

From the complete question, the shape has the following faces

When a shape has the above highlights, then the shape is a triangular prism.

The dimensions of the faces are not given.

However, we have the following area formulas:

Hence, the shape is a triangular prism.

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Answer: j = 6

Step-by-step explanation:

the answer is six because the question says 15 is 9 more which is simple subtraction so u do 15-9=6.

Answer:

you have 15 cats but your neighbor had 9 more than you but your mom has J cats. How many cats do you all have together

Step-by-step explanation:

Answer:

Step-by-step explanation:

x² = 80² + 39²

x² = 6400 + 1521

x² = 7921

x = 89 inches

the answer is 6 because theres need to be a total of 9 and they put 3 cups so 9 minus 3 equals 6

For the  trigonometric identity

11. If cos 27° = x, then the value of tan 63° interims of "x" is  x/√1 - x²

12. If Θ be an acute angle and 7sin²Θ + 3 cos²Θ= 4, then tan Θ is  1/√3

13. The value of tan 80° × tan 10° + sin² 70° + sin² 20° is 2

14. The value of (sin 47°/cos 43°)² + (cos 43°/sin 47°) -  4 cos²45° is 0

15. If 2 (cos²Θ - sin²Θ) = 1, Θ is a positive acute angle them the value of Θ is  30°

16. If 5 tan Θ = 4, then (5 sin Θ - 3 cos Θ)/(5 sin Θ + 2 cos Θ) is equal to 1/6

17. If sin(x + 20)° = cos (x + 10)° then the value of "x" is  30°

18. The value of (sin 65°)/ (cos 25°) is 1

To solve the various   trigonometric identity;

11. Given: cos 27° = x

We know that cos (90 - θ) = sin θ

So, cos 63° = sin 27°

And sin 63° = √1 - cos²27°

Substituting cos 27° = x, we get

sin 63° = √1 - x²

Therefore, Therefore, tan 63° = sin 63° / cos 63° = cos 27° / cos 63° = x / cos 63°.

= x/√1 - x²

12. Given: Θ is an acute angle and 7sin²Θ + 3 cos²Θ= 4

Since Θ is an acute angle, sin²Θ + cos²Θ = 1

Substituting sin²Θ + cos²Θ = 1 into the equation 7sin²Θ + 3 cos²Θ= 4, we get

7 (sin²Θ/ cos²Θ) + 3 = 4/cos²Θ - 4 sec²Θ

⇒ 7tan²Θ + 3 = 4(1 + tan²Θ)

⇒ 7tan²Θ + 3 = 4 + 4 tan²Θ

⇒3 tan²Θ = 1

⇒ tan²Θ = 1/3

⇒ tanΘ = 1/√3

13. For tan 80° × tan 10° + sin² 70° + sin² 20°

⇒ tan 80° = cot (90 - 80)° = cot 10°

⇒  sin 70° = cos (90 - 70) = cos 20°

⇒ cot 10° × tan 10° +  cos 20° + sin² 20°

= 1 + 1 = 2

14. (sin 47°/cos 43°)² + (cos 43°/sin 47°) - 4 cos²45°

= (sin 47°/cos43°)² + (cos 43°/sin 47°)² - 4(1/√2)²

= (sin (90° - 43°)/cos43°)² +  (cos (90° - 47°)/sin)²  = 4(1/2)

= (cos 43°/cos 43°)² + (sin 47°/ sin   47°)² - 2

= 1 + 1 - 2 = 0

15. 2 (cos²Θ - sin²Θ) = 1

cos²Θ - sin²Θ = 1/2

Since Θ is an acute angle, sin²Θ + cos²Θ = 1

Substituting sin²Θ + cos²Θ = 1 into the equation cos²Θ - sin²Θ = 1/2, we get

cos²Θ - (1 - cos²Θ) = 1/2

2cos²Θ = 3/2

cos Θ = √3/2(cos 30° = (√3)/2

= 30°

16. Given: 5 tan Θ = 4

We know that tan Θ = sin Θ / cos Θ

So, 5 sin Θ / cos Θ = 4

5 sin Θ = 4 cos Θ

Dividing both sides of the equation by 5, we get

sin Θ / cos Θ = 4/5

∴ sin Θ = 4/5 cos Θ

given that the expression is (5 sin Θ - 3 cos Θ)/(5 sin Θ + 2 cos Θ)

we substitute sin Θ = 4/5 cos Θ  into the equation

⇒(5 × 4/5 cos Θ  - 3 cos Θ)/(5 × 4/5 cos Θ  + 2 cos Θ)

= (4-3)/(4 + 2) = 1/6

17. Given: sin(x + 20)° = cos (x + 10)°

We know that sin(90 - θ) = cos θ

So, sin(x - 20)° = sin(90 - (3x + 10))°

⇒ (x - 20)° = (90 - (3x + 10))°

⇒ x - 20° = 90° - 3x + 10

⇒ 4 x = 120°

⇒ x = 120°/4

⇒ x = 30°

18. To find the value of (sin 65°) / (cos 25°), we can use the trigonometric identity:

To solve this, we can use the following trigonometric identities:

sin(90 - θ) = cos θ

cos(90 - θ) = sin θ

We can also use the fact that sin²θ + cos²θ = 1.

Rewrite sin (65°) / cos (25°)

⇒ sin (65°) = cos (25°)

∴ cos (25°)/ cos (25°) = 1

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Answer:

If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.

6(3x) = 4(4x + 1)

18x = 16x + 4

2x = 4

x = 2

Answer:

The depreciation tax shield for this project in year 4 is $178.24.

Explanation:

To calculate the depreciation tax shield for this project in year 4, we need to first determine the depreciation expense for year 4 using the MACRS three-year class life category and the double-declining balance (DDB) method.

From Table 12.8 on page 415 of the textbook, we can see that the depreciation rate for year 1 is 33.33%, for year 2 it is 44.45%, for year 3 it is 14.81%, and for year 4 it is 7.41%.

Using the DDB method, we can calculate the depreciation expense for each year as follows:

Year 1: Depreciation expense = $14,000 x 33.33% = $4,667

Year 2: Depreciation expense = ($14,000 - $4,667) x 44.45% = $3,554

Year 3: Depreciation expense = ($14,000 - $4,667 - $3,554) x 14.81% = $830

Year 4: Depreciation expense = ($14,000 - $4,667 - $3,554 - $830) x 7.41% = $557

The total depreciation expense over the four years is the sum of the individual year's depreciation expenses, which is:

$4,667 + $3,554 + $830 + $557 = $9,608

Now, we can calculate the depreciation tax shield in year 4. The depreciation tax shield is the amount of the depreciation expense that reduces the firm's taxable income, multiplied by the tax rate. In year 4, the depreciation tax shield is:

Depreciation tax shield = Depreciation expense in year 4 x Tax rate

Depreciation tax shield = $557 x 32% = $178.24

Therefore, the depreciation tax shield for this project in year 4 is $178.24.

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But the answer is correct though...

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Bing Chilling

It's over...

No more to read

Happy birthday if it's ur birthday...

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A²+B²= C²

31²+ 21²= z²

961+441 = z²

1402= z²

z= 37.443290454

Answer:

\(y=x^3-12x^2+48x-58\)

Step-by-step explanation:

Transformation Rules

\(f(x+a)=f(x) \: \textsf{translated}\:a\:\textsf{units left}\)

\(f(x-a)=f(x) \: \textsf{translated}\:a\:\textsf{units right}\)

Given equation: \(y=x^3+6\)

If the graph of the equation is translated 4 units to the right, then we replace \(x\) with \((x-4)\):

\(\implies y=(x-4)^3+6\)

\(\implies y=(x-4)(x-4)(x-4)+6\)

\(\implies y=(x-4)(x^2-8x+16)+6\)

\(\implies y=x^3-8x^2+16x-4x^2+32x-64+6\)

\(\implies y=x^3-12x^2+48x-58\)

Answer:

Step-by-step explanation:

Given

Translating 4 units right

Answer:

a) 0.8088 = 80.88% probability that there are at most 2 typos on a page.

b) 0.0858 = 8.58% probability that there are exactly 10 typos in a 5-page paper.

c) 0.001 = 0.1% probability that there are exactly 2 typos on each page in a 5-page paper.

d) 0.717 = 71.7% probability that there is at least one page with no typos in a 5-page paper.

e) 0.2334 = 23.34% probability that there are exactly two pages with no typos in a 5-page paper.

Step-by-step explanation:

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

\(P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}\)

In which

x is the number of sucesses

e = 2.71828 is the Euler number

\(\mu\) is the mean in the given interval.

Binomial distribution:

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

The number of typos made by a student follows Poisson distribution with the rate of 1.5 typos per page.

This means that \(\mu = 1.5n\), in which n is the number of pages.

(a) Find the probability that there are at most 2 typos on a page.

One page, which means that \(\mu = 1.5\)

This is

\(P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)\)

In which

\(P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}\)

\(P(X = 0) = \frac{e^{-1.5}*(1.5)^{0}}{(0)!} = 0.2231\)

\(P(X = 1) = \frac{e^{-1.5}*(1.5)^{1}}{(1)!} = 0.3347\)

\(P(X = 2) = \frac{e^{-1.5}*(1.5)^{2}}{(2)!} = 0.2510\)

\(P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.2231 + 0.3347 + 0.2510 = 0.8088\)

0.8088 = 80.88% probability that there are at most 2 typos on a page.

(b) Find the probability that there are exactly 10 typos in a 5-page paper.

5 pages, which means that \(n = 5, \mu = 5(1.5) = 7.5\).

This is P(X = 10). So

\(P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}\)

\(P(X = 10) = \frac{e^{-7.5}*(7.5)^{10}}{(10)!} = 0.0858\)

0.0858 = 8.58% probability that there are exactly 10 typos in a 5-page paper.

(c) Find the probability that there are exactly 2 typos on each page in a 5-page paper.

Two typos on a page: 0.2510 probability.

Two typos on each of the 5 pages: (0.251)^5 = 0.001

0.001 = 0.1% probability that there are exactly 2 typos on each page in a 5-page paper.

(d) Find the probability that there is at least one page with no typos in a 5-page paper.

0.2231 probability that a page has no typo, so 1 - 0.2231 = 0.7769 probability that there is at least one typo in a page.

(0.7769)^5 = 0.283 probability that every page has at least one typo.

1 - 0.283 = 0.717 probability that there is at least one page with no typos in a 5-page paper.

(e) Find the probability that there are exactly two pages with no typos in a 5-page paper.

Here, we use the binomial distribution.

0.2231 probability that a page has no typo, so \(p = 0.02231\)

5 pages, so \(n = 5\)

We want P(X = 2). So

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 2) = C_{5,2}.(0.2231)^{2}.(0.7769)^{3} = 0.2334\)

0.2334 = 23.34% probability that there are exactly two pages with no typos in a 5-page paper.

Answer:

Is there diagram for this?

Answer:

A is the correct answer

We can label the point (75, 50) as the optimal solution for the banquet, as it represents the maximum number of guests that can be invited while staying within the constraints.

What is banquet?

A banquet is a large formal meal that usually involves multiple courses and is served to a group of people on special occasions such as weddings, awards ceremonies, or fundraising events. Banquets often include speeches, presentations, and entertainment, and are typically held in a large venue such as a hotel ballroom, banquet hall, or conference center. Banquets can be hosted for a variety of purposes, such as to honor a special guest, celebrate an achievement, or raise money for a charitable cause.

To create a graph showing the solution region of the system of inequalities representing the constraints of the situation, we can use custom relationships to define the variables and constraints.

Let's define the variables:

Let x be the number of adult guests.

Let y be the number of student guests.

Now, let's write the system of inequalities representing the constraints of the situation:

The total number of guests cannot exceed 125: x + y ≤ 125

The cost of hosting the banquet cannot exceed $3375: 45x + 15y ≤ 3375

To graph this system of inequalities, we can plot the boundary lines of each inequality and shade the region that satisfies all the constraints.

The boundary lines of each inequality are:

x + y = 125 (the line that connects the points (0, 125) and (125, 0))

45x + 15y = 3375 (the line that connects the points (0, 225) and (75, 0))

To find the viable combinations of guests that satisfy all the constraints, we need to shade the region that is below the line x + y = 125 and to the left of the line 45x + 15y = 3375.

The resulting graph should look like this:

The point where the two lines intersect, (75, 50), represents the maximum number of adult guests (75) and the maximum number of student guests (50) that can be invited to the banquet while staying within the budget and venue capacity. Any point within the shaded region represents a viable combination of guests.

We can label the point (75, 50) as the optimal solution for the banquet, as it represents the maximum number of guests that can be invited while staying within the constraints.

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Answer:

32115

Step-by-step explanation:

Step1

Converting 431 to base 10.

4*102=400

3*101=30

1*100=1

Adding all to get Ans=43110

Step2 converting 43110 to 5

The equation calculation formula for 43110 number to 5 is like this below.

5|431

5|86|1

5|17|1

5|3|2

5|3|3

Ans:32115

Answer:

Random

Step-by-step explanation:

The event that was picked from the bag is unbiased thus it will be a Random sample thus option (A) is correct.

Sampling is collecting some items in a lot randomly to predict opinions about the lot.

For example; the Selection of goods, selection of people

Sampling is a useful technique because if we do it for all samples then it will take time and cost as well.

As per the given,

The cards have different names and are put into a bag.

Since no group and same name are written on the cards thus it will be a purely unbiased situation.

Thus, it will be a random sample.

Hence "The event that was picked from the bag is unbiased thus it will be a Random sample".

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Answer:

Step-by-step explanation:

You need only take 45% of 200

Music = 45/100 * 200

Music = 9000/100

Music = 90

So of a grade of 200, there are 90 who take music.

Answer:

Srry This Is Late

I'll Say The Answer Is B

(Let Me Know If I'm Right)

Step-by-step explanation:

Answer:

J=130

Step-by-step explanation:

180-90-40=50

180-50=130

Answer:

Step-by-step explanation:

∠B₁DB = 60°

△B₁BD is a 30°-60°-90° triangle. The sides are in the ratio 1:√3:2

B₁D = 37 ⇒ BD = 37/2 = 18.5

BB₁ = 18.5√3

△ABD is isosceles

AB = AD = BD/√2 = 18.5/√2

volume = AB × AD × BB₁

= (18.5/√2) × (18.5/√2) × 18.5√3

= 18.5³√3/2

≅ 5483 cubic units

Hey there! :-)

-8+r>-8

r>-8+8

r>0

Hope it helps!

~Just a joyful teen

#HaveAnAmazingDay

\(GraceRosalia\)

Hey there!

-8 + r > -8

= r > -8 + 8

= r > 0.

Steps :-

Hope it helps ya!

Answer:

The answer are

B and C

Step-by-step explanation:

r=d/2=12/2=6

r=16/2=8

Circumference=2pir

C=2×6pi

C=12pi

C=2pir

C=2×8pi

C=16pi

each pound of shimp costs $13.99

Answer:

I will prefer the cone having volume 21.21 cubic inches.

Step-by-step explanation:

A cup of ice cream holds ice cream = 21.21 cubic inches

Since volume of a cone = Capacity of the cone to hold the ice cream

Volume of an another cone having radius (r) = 1.5 inches and height (h) = 3 inches will be,

         V = \(\frac{1}{3}(\pi)(r^{2} )(h)\)

           = \(\frac{1}{3}(\pi )(1.5)^{2}(3)\)

           = 7.069

           ≈ 7.07 cubic inches

Since the volume of the second cone is less than the first cone, I will prefer the first cone with volume = 21.21 inches³