What are the angles of △ABC with side lengths a=12, b=21, and c=14?

Round each angle to the nearest tenth of a degree and use that rounded value to find the remaining angles.

The theoretical probability of drawing a green or red ticket is 1/2 or 0.5.

We have,

There are a total of 3 + 4 + 5 + 6 = 18 tickets in the basket.

The probability of drawing a yellow ticket.

= 4/18

Since there are 4 yellow tickets out of 18 total tickets.

The probability of not drawing a yellow ticket is equal to the probability of drawing a green, blue, or red ticket.

There are 3 + 5 + 6 = 14 tickets that are not yellow.

The probability of not drawing a yellow ticket.

= 14/18

= 7/9

To find the probability of drawing a green or red ticket, we need to add the probabilities of drawing a green ticket and a red ticket.

The probability of drawing a green ticket.

= 3/18

The probability of drawing a red ticket.

= 6/18

Now,

The probability of drawing a green or red ticket is

= 3/18 + 6/18

= 9/18

= 1/2

Thus,

The theoretical probability of drawing a green or red ticket is 1/2 or 0.5.

Learn more about probability here:

https://brainly.com/question/14099682

#SPJ1

Step-by-step explanation:

3.3% = .033 in decimal

Use the compounding formula

a)  P(t) = 18000 (1 + .033)^t        

b)   for t =2 this computes to 19207.6  bacteria

The area of the rhombus is derived to be 70 square units

In calculating for the area of a rhombus, we multiply the length of its two diagonals and divide the result by two

For the given rhombus, we have diagonals:

5 + 5 = 10 and 7 + 7 = 14

thus;

Area of the rhombus = (10 × 14)/2

Area of the rhombus = 140/2

Area of the rhombus = 70 square units.

Therefore, the area of the rhombus is derived to be 70 square units.

Read more about rhombus here:https://brainly.com/question/88523

#SPJ1

The annual premium for a Whole Life insurance policy, for the healthy male, would be A. $ 2, 881.61

From the given table, a 28 year old male would have to pay $ 17. 76 for each $ 1,000 of coverage of Whole Life Insurance.

For a policy that is worth $ 162, 253 therefore, the annual premium would therefore be:

= Amount per thousand / 1, 000 x  Policy coverage

= 17. 76 / 1, 000 x 162, 253

= 0.01776 x 162, 253

= $ 2, 881.61

In conclusion, the annual premium is $ 2, 881.61 .

Find out more on annual premium at https://brainly.com/question/25280754

#SPJ1

Answer:

Rs 2150.81.

Step-by-step explanation:

The interest rate for the first two years is 6% per annum, which is halved for each six-month period. Therefore, the interest for the first two years would be (6950*(1+(0.03))^8) - 6950 = Rs 1373.53.

For the third year, the interest rate is 9% per annum, which is also halved for each six-month period. Therefore, the interest for the third year would be (6950*(1+0.045))^2 - 6950 = Rs 777.28.

Hence, the total compound interest for three years would be Rs 2150.81.

Answer:7

Step-by-step explanation:

use the Pythagoras theorem to find su (40^2-32^2) take the square root =24 use this to solve for ru. (25^2-24^2=49) square root of 49 is

The radius of the circle is 35.98 in, the diameter is 71.96 in. and the area of the circle is 4066.98 sq. in.

Here, the circumference of circle is C=226.08 in

We know that the formula for the circumference of circle is C = 2πr

Using this formula we find the value of radius 'r',

C = 2πr

226.08 = 2πr

r = 226.08 / 2π

r = 35.98 in

And the diameter of the circle would be,

d = 2r

d = 2 × 35.98

d = 71.96 in.

And the area of the circle would be,

A = π × r²                                                                  

A = π × 35.98²

A = 4066.98 sq. in.

Therefore, the required area is  4066.98 sq. in.

Learn more about the area of the circle here:

https://brainly.com/question/28642423

#SPJ1

The complete question is:

Solve for radius and diameter then what is the area of the circle if the circumference of circle is C=226.08 in.

The area of the circular pateo is 50.24 square yards.

Remember that for a circle of radius R, the area is given by the formula:

A = pi*R²

Where pi = 3.14

Here we know that the patio is circular, and it has a diameter of 4 yards, then the radius is:

R = 4yd/2

R = 2 yd

Replacing that in the area formula we will get:

A = 3.14*(2yd)²

A = 50.24 yd²

Learn more about area at:

https://brainly.com/question/24487155

#SPJ1

Answer:

The sample mean birth weight for the 195 boys is 3.04 kilograms and the sample standard deviation is 0.71 kilograms.

Step-by-step explanation:

Answer: 6

Step-by-step explanation:

There are six possible ways that the three boys can initially choose shirts: ABC, ACB, BAC, BCA, CAB, CBA.

The sample of hospitals would we need to be 99 percent confident that the sample mean is within 0.5 days of the population mean is A. 48

We want to find the sample size (n) that would give us a confidence interval of 0.5 days, so we can rearrange the formula to solve for n:

n = (z*σ/CI)^2

Plugging in the given values:

z = 2.576 (for 99% confidence level)

σ = 1.2 days

CI = 0.5 days

n = (2.576 × 1.2/0.5)²

n ≈ 48

Therefore, the correct option is A.

Learn more about sample on

https://brainly.com/question/24466382

#SPJ1

The domain of the vector function is : ( -6, -2) ∪ ( -2, 6)

The given vector function can be correctly expressed as:

r(t) = (t-2)i / (t+2) + sintj + ln(36-t²)k²

The domain of the given function can be determined by finding the domain of each respective component.

(t-2)i / (t+2)

Not defined, t = -2

Thus, the domain of the first component of the vector = (-∞, 2) ∪ (2, ∞)

The 2nd component = sin t

No restriction on t,

The 3rd component of the function is ㏑(36 - t²)

we know,

Natural number is defined for +ve numbers,

i.e.

36 - t² > 0

(6 + t) (6 - t) > 0

thus, it satisfies the inequality -6 < t < 6

The third domain = (-6,6)

Hence, the domain of the vector function is : ( -6, -2) ∪ ( -2, 6)

Learn more about vector function click;

https://brainly.com/question/31473715

#SPJ1

The company sales in year 14, given the rate of increase and the amount made in sales would be C $3,656,872.

In the first year, the sales of the company were $ 475, 000 and this sales is scheduled or predicted to grow at 17 %.

This means that the company sales in year 14 would be :

= Initial sales x ( 1 + rate ) ^ number of years

Initial sales = $ 475, 000

Rate = 17 %

Number of years = 14 years

The company sales in year 14 is:

= 475, 000 x ( 1 + 17 %) ¹⁴

= $3, 656, 872

Find out more on company sales at https://brainly.com/question/29342346

#SPJ1

The correct statement regarding whether the graph represents a function is given as follows:

No, it is not a function.

A graph represents a function if it has no vertically aligned points, that is, each value of x is mapped to only one value of y. Vertically aligned points mean that a value of x is mapped to multiple values of y, that is, a single input is mapped to multiple outputs which disqualify the relation as a function.

In the graph, we have that at x = 0 = y-axis, the function has three numeric values, which is a case of vertically aligned points, hence the graph does not represent a function.

More can be learned about graphs and functions at https://brainly.com/question/12463448

#SPJ1

An expression that represent PS include the following: C. (NP + NQ + QR)/NR - NR.

In Mathematics and Geometry, the Tangent Secant Theorem states that if a secant segment and a tangent segment are drawn to an external point outside a circle, then, the product of the length of the external segment and the secant segment's length would be equal to the square of the tangent segment's length.

By applying the Tangent Secant Theorem to this circle, we have the following:

NP × PS = NQ × QR

PS = (NQ × QR)/NP

In terms of line segment NR, the expression can be rewritten as follows;

(NP + NQ + QR)/NR - NR

Read more on Tangent Secant Theorem here: https://brainly.com/question/26826991

#SPJ1

The solution to the inequality is:

0 < a  or a ≤ -5

An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g. 2x > 4.

We have: -1 -10a < -1 or 10 + 3a ≤ -5 and we want to solve for the variable "a".

-1 -10a < -1      or  10 + 3a ≤ -5

-10a < -1 + 1    or  3a ≤ -5 - 10

-10a < 0          or  3a ≤ -15  

a < 0/(-10)      or   a ≤ -15/3

a > 0              or   a ≤ -5

Since a a > 0  is the same as 0 < a. We can say:

0 < a  or a ≤ -5

Thus,  0 < a ≤ -5

Learn more about inequality on:

brainly.com/question/25275758

#SPJ1

a) An equation that represents the amount of money that Gilberto

receives during a school year:  y = 5 + (0.5) x

b) The number of correct answers Gilberto needs to buy a new shirt that costs $25 = 40

Let us assume that y represents the amount of money and x represents the number of correct answers.

We know that One dollar = 100 cents.

so, 50¢ = 0.5 dollars

From the described informtaion, we can write the equation that represents the amount of money that Gilberto receives during a school year as: y = 5 + (0.5) x

Now we need to find the number of correct answers Gilberto needs to buy a new shirt that costs $25

i.e., for y = 25, we need to find the value of x.

Substitute y = 25 in above equation.

25 = 5 + (0.5) x

We solve this equation for x

(0.5) x = 20

x = 20 / (0.5)

x = 40

This means that he needs to give 40 correct answers.

Learn more about an equation here:

https://brainly.com/question/28243079

#SPJ1

The complete question is:

Gilberto's  grandfather gives Gilberto $5 and then 50¢ for each math question he answers correctly on his math exams for the year.

a. Write an equation that represents the amount of money that Gilberto

receives during a school year. Explain what the variables and numbers mean.

b. Use the equation to find the number of correct answers Gilberto needs to buy a new shirt that costs $25. Show your work.

The volume of a cube is calculated by multiplying the length of one side by itself twice. In this case, the volume of the foam cube is 5 in. x 5 in. x 5 in. = 125 cubic inches.

Density is calculated by dividing the mass of an object by its volume. In this case, the density of the foam cube is 62 g / 125 cubic inches = 0.496 g/cubic inch.

So, the volume of the foam cube is 125 cubic inches and its density is 0.496 g/cubic inch.

Answer:

Step-by-step explanation:

You want the number of day passes sold for $61 and weekend passes sold for $110 if 257 more day passes were sold, and sales totaled $307745.

Let w represent the number of weekend passes sold. Then w+257 is the number of day passes sold. The total revenue is ...

  61(w+257) +110(w) = 307745

Simplifying the equation, we have ...

  171w +15677 = 307745

  171w = 292068 . . . . . . . . subtract 15677

  w = 1708 . . . . . . . . . . . divide by 171

  w+257 = 1965 . . . day passes sold

1965 day passes and 1708 weekend passes were sold.

<95141404393>

It should be noted that 81.85% of the scores are between 72 and 87.

The probability that a score is greater than 77 is approximately 0.8413.

a) The z-score for 72 is calculated as:

z = (72 - 82) / 5 = -2

The z-score for 87 is calculated as:

z = (87 - 82) / 5 = 1

0.8413 - 0.0228 = 0.8185

So, approximately 81.85% of the scores are between 72 and 87.

b) The z-score for 77 is calculated as:

z = (77 - 82) / 5 = -1

1 - 0.1587 = 0.8413

Therefore, the probability that a score is greater than 77 is approximately 0.8413 (or 84.13%).

Learn more about probability on

https://brainly.com/question/24756209

#SPJ1

Answer:

Answer:

= 6 R 25

= 6 25/27

187 divided by 27 equals

6 with a remainder of 25

Step-by-step explanation:

m² × m² is equal to m⁴.

w³ × w² is equal to w⁵.

5k³ × 4k⁴ × k is equal to 20k⁸.

The length of each side of the square is 9x.

A simplification of the expression 28x³ ÷ 4x is 7x².

In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:

A = LB

Where:

By substituting the given parameters into the formula for the area of a rectangle, we have the following;

Area of rectangle = (27x) × (3x)

Area of rectangle = 81x²

Note: Area of square = Area of rectangle

Area of square = (side length)²

81x² = (side length)²

Side length = √(81x²)

Side length = 9x

Read more on area of a rectangle here: https://brainly.com/question/18159221

#SPJ1

The angle BFC is the angle that is complementary to AFB

Whenever the sum of two angles adds up to 90 degrees, they are defined as complementary angles. Take 30 and 60 degrees, for instance; they are complementary angles.

From the definition we have to find the angle when if added to AFB would give us the sum of 90 degrees

AFC is a 90 degree angles

We have AFC = AFB + BFC

90 = 78 + BFC

BFC  = 90 - 78

= 12

Hence the angle BFC is the complementary angle

Read more on angles here:https://brainly.com/question/25716982

#SPJ1

Answer:

[tex]\huge\boxed{\sf x = 10\°}[/tex]

Step-by-step explanation:

According to the statement,

92° + x + 78° = 180°

170° + x = 180°

x = 180° - 170°

[tex]\rule[225]{225}{2}[/tex]

Each person would get approximately 0.67 small pizzas when 12 friends share 8 small pizzas equally.

If 12 friends shared 8 small pizzas equally, we can divide the total number of pizzas by the number of friends to determine how much pizza each person gets.

Total number of pizzas = 8 small pizzas

Number of friends = 12

To find how much pizza each person gets, we divide the total number of pizzas by the number of friends;

Pizza per person = Total number of pizzas/Number of friends

Pizza per person = 8 small pizzas / 12 friends

Pizza per person = 0.67 small pizzas

Therefore, each person would get 0.67 small pizzas.

To know more about pizzas here

https://brainly.com/question/23055668

#SPJ1

Answer:

Step-by-step explanation:

(a)  

16

36

​

=

4

9

​

36:16=9:4

(b)  

144

324

​

=

4

9

​

324:144=9:4

(c)  

1125

125

​

=

1125

125

​

=

45

5

​

=

9

1

​

∴125:1125=1:9

Answer: -4rootx+3root3x

Step-by-step explanation:

think of the expression under the radicals as like terms, you can only add those that are the exact same 1-5=-4(rootx) can't do anything with the middle

The quadratic function to represent the total area of the park and the path will be 6(x² + 7x + 6).

Given that:

Width, W = x

Length, L = 6x

Path width, d = 3

The rectangle's area will be given as,

Area of the rectangle = L × W square units

The quadratic function to represent the total area of the park and the path will be given as,

A = (x + 2 · 3) (6x + 2 · 3)

A = (x + 6)(6x + 6)

A = 6(x + 6)(x + 1)

A = 6(x² + 7x + 6)

The quadratic function to represent the total area of the park and the path will be 6(x² + 7x + 6).

More about the area of the rectangle link is given below.

https://brainly.com/question/20693059

#SPJ1