Law of cosines: a2=b2+c2-2bccos(A)
What is the measure of angle N to the nearest whole degree

The area of the shaded region is 84.82 cm².

The area of the shaded region is calculated by subtracting the area of the sector from the area of the entire circle.

Since the angle of the sector is 90 degrees, we can conclude that the entire circle is divided into four.

Area of the shaded region = πr² - 1/4(πr²) = 3/4πr²

where;

The area of the shaded region is calculated as;

A = 3/4πr²

A = 3/4 x π ( 6 cm )²

A = 84.82 cm²

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The standard form of the equation for the given p value and theta is equal to -x + y = 26√2.

Standard form of the equation is :

x cosθ + y sinθ = p

Here p = 26 and theta 'θ' = 3π /4

Substitute the value in the standard form we get,

x cos (3π/4 ) + y sin( 3π /4 ) = 26

⇒ x cos ( π - π/4 ) + y sin ( π - π/4 ) = 26

⇒ - x cosπ/4 + y sinπ/4 = 26

Substitute the value of cosπ/4 and sinπ/4 is equal to 1/√2 we get,

⇒ -x /√2 + y / √2 = 26

⇒ -x + y = 26√2

Therefore, the standard form of the equation is equal to -x + y = 26√2.

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Answer:

Step-by-step explanation:

You want to know which functions have 5 in their domain, and what the function value is at x=5.

It is more convenient to do the second part first, as that tells you the answer to the first part:

f(5) = 5² -3·5 = 25 -15 = 10 . . . . 5 is in the domain

g(5) = (5 -5)/5 = 0/5 = 0 . . . . 5 is in the domain

h(5) = √(5 -10) = √(-5) . . . . UNDEFINED; 5 is not in the domain

A rocket is launched with height function h(t)= -16t²+88t for time 't' in seconds the rocket is in the air for the time t = 5.5 seconds.

A rocket launched with height function :

h(t)= -16t²+88t

't' represents the time in seconds

'h' is the height of rocket.

Time for which rocket is in the air given by :

When h(t) = 0

Substitute the value we get,

⇒  -16t²+88t = 0

⇒ -16t ( t - 5.5 ) = 0

⇒ -16 ≠ 0 or t ≠ 0 or ( t - 5.5 ) = 0

Time can never be zero.

hence,

( t - 5.5 ) = 0

⇒ t = 5.5 seconds

Therefore, the time of the rocket when it is in the air  is equal to 5.5 seconds.

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Los dos números dados en el conjunto de preguntas anterior son 32 y 160. Para resolver este problema, se puede establecer una ecuación con variables.

Sea x el número más pequeño, entonces el número más grande sería 5x. La suma de ambos es 192, por lo que

Al resolver esta ecuación simple, se obtiene que x = 32, y por lo tanto, 5x = 160. Estos son los dos números que cumplen con los requisitos dados en la pregunta.

En matemáticas, la sumatoria es la suma de una secuencia de cualquier tipo de números, llamados sumandos o sumandos; el resultado es su suma o total.

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The volume of the cedar canoe with a mass of 40 kilograms and a density of 400 kilograms per cubic meter is 0.1 cubic meters.

Density is expressed mathematically as;

p = m / v

Where m is mass and v is volume.

Given that;

To determine the volume, plug the given values into the above formula and solve for v.

p = m / v

v = m / p

v = 40kg / 400 kg/m³

v = 40kgm³ / 400 kg

v = 40m³ / 400

v = 0.1 m³

Therefore, the volume is 0.1 cubic meters.

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Answer:

90

Step-by-step explanation:

45+45=90

Answer:

20 liters of white paint, 12 liters of red paint

Step-by-step explanation:

Let w = liters of red paint and r = liters of red paint

[tex] \frac{w}{r} = \frac{5}{3} [/tex]

[tex]w = \frac{5}{3} r[/tex]

[tex]w + r = 32[/tex]

[tex] \frac{5}{3} r + r = 32[/tex]

[tex] \frac{8}{3} r = 32[/tex]

[tex]r = 12[/tex]

[tex]w = 20[/tex]

A regular solid shape is defined as a three-dimensional object that has all its faces congruent and all its vertices congruent. In other words, all faces have the same shape and size and all vertices have the same angle measures.

Among the options provided, only the cube is a regular solid shape. A cube is a three-dimensional object that has six equal square faces. Each face is a square and each vertex has the same angle measure. The edges of a cube are congruent and the shape is highly symmetrical.

The cylinder is not a regular solid shape because it has two congruent circular faces and one curved surface, which is not congruent to the other two faces. The vertices of a cylinder also have different angle measures.

The cuboid is not a regular solid shape because it has six rectangular faces, and the shape is not highly symmetrical. The vertices of a cuboid also have different angle measures.

In conclusion, a regular solid shape must have congruent faces and congruent vertices, and only a cube satisfies these conditions. It is important to note that not all regular shapes are regular solid shapes, for example, a sphere is a regular shape, but it is not a regular solid shape because it has no faces, vertices or edges.

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Answer: B,C,D

Step-by-step explanation:

Since the only requirement is that the width needs to be at least 50 yds. B, C,D all work.

Answer:

0.43

Step-by-step explanation:

Rounding to 2 decimal places means keeping only 2 digits after the decimal point and adjusting the third digit, based on the rules of rounding. In this case, the number 0.4277 would be rounded to 0.43. This is because the third digit after the decimal point (7) is 5 or greater, so we round up the second digit (2) to 3. This gives us the rounded number 0.43, which has only 2 decimal places.

Answer:18

Step-by-step explanation:

Answer:18

Step-by-step explanation:

The equation representing the hanger is 3x - 2y = 0 and when x = 6, y = 9

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, the weight of the square is y

And, the weight of the triangle is x

Now, the equation according to the diagram is;

x + 3y = 4x + y

4x - x + 3y - y = 0

3x - 2y = 0

Now, when, x  = 6

So, y =

3x - 2y = 0

3x = 2y

3(6) = 2y

18 = 2y

y = 9

Hence, the equation representing the hanger is 3x - 2y = 0 and when x = 6, y = 9

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A wheel of cheese has a radius of 7 inches and a height of 3 inches

The approximate surface area of this wheel of cheese is 458.4 square inches.

To get the surface area of a cylinder,  we have to calculate the area of the lateral surface and add the areas of the two circular end faces.

The lateral surface area of a cylinder is calculated as 2 * pi * r * h, where r is the radius and h is the height.

So the lateral surface area in this scenario would be: 2 * 3.14 * 7 * 3 = 150.52 square inches.

The area of the two end faces must then be calculated. we know, Pi * r^2, where r is the radius, gives the area of a circle.

So the area of each end face in this situation would be 3.14 * 7^2 = 153.94 square inches.

Total surface area= lateral surface area + end face area

=150.52 + 153.94 + 153.94 = 458.4 square inches (approximately)

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Answer:2+n/7

Step-by-step explanation:

Simplify the expression

Answer:

Step-by-step explanation:

[tex]2123.72 = 4 \times 3.14 \times {r}^{2} [/tex]

[tex]2123.72 = 12.57 {r}^{2} [/tex]

[tex] \frac{12.57 {r}^{2} }{12.57} = \frac{2123.72}{12.57} [/tex]

[tex] {r}^{2} = 168.95[/tex]

[tex]r = 13.0[/tex]

[tex] \frac{4}{3}\pi {r}^{3} [/tex]

[tex] \frac{4}{3} \times 3.14 \times {13}^{3} = 9202.77 {m}^{3} [/tex]

Answer: Let's assume that there are "m" jokes written by male authors and "f" jokes written by female authors, such that m + f = total number of jokes in the magazine.

If a joke by a man is told first, there are (m - 1)! ways to arrange the remaining m - 1 jokes written by male authors and f! ways to arrange the jokes written by the female author. The total number of ways the jokes can be delivered is (m - 1)! * f!.

So, the answer is (m - 1)! * f! ways to deliver the jokes if a joke by a man is told first.

Step-by-step explanation:

Answer:

I belive the answer is "5x+35"?

Answer:

x=29

Step-by-step explanation:

3x+15+2x+20=180; 3x+2x=145; 5x=145; x=29

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A linear equation giving the value v of the equipment during the 5 years it will be in use is v = 955 - 191t

A linear equation models a linear relationship between two variables, where the rate of change between the two variables is constant. In this case, we can model the value of the equipment as it depreciates over time using a linear equation.

Since the value of the equipment decreases linearly over time, we can write an equation in the form:

v = a - bt

where v is the value of the equipment in year t, a is the initial value of the equipment, and b is the constant rate of depreciation.

Since the initial value of the equipment is $955, we can set a equal to 955. To find the constant rate of depreciation, we need to find the change in value over the 5 years it will be in use and divide by the number of years. Assuming after 5 years the value is 0,

constant rate of depreciation = 955/ 5

= 191

So, with a = 955 and b = $191 per year, the linear equation that models the value of the equipment over time is:

v = 955 - 191t

This equation gives the value of the equipment in year t based on the initial value and the constant rate of depreciation.

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The monthly payment is  $86.55. The result is obtained by using the formula for simple interest.

The simple interest of an amount of money can be counted by the following formula.

I = P × r × t

Where

A motocross company offers a loan to buy an ATV for $4,000. Loan Offer 9.3% Simple Interest.

If it is for 6 years, find the monthly payment!

We have

It is not mentioned that the simple interest apply per year or per month. We assume the simple interest is per year. It will be

I = P × r × t

I = $4,000 × 9.3% × 6

I = $2,232

The total money to be paid will be

A = P + I

A = $4,000 + $2,232

A = $6,232

The monthly payment is

MP = A/t

MP = $6,232/(6 × 12)

MP = $6,232/72

MP = $86.55

Hence, the person who borrows for $4,000 to buy an ATV should pay $86.55 each month for 6 years.

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The probability of having no defectives in a sample of size 3 from a lot of 24 items with 5 known defectives is 0.0403 or approximately 4%.

The probability of having no defectives in a sample of size 3 from a lot of 24 items with 5 known defectives can be calculated using the binomial probability formula. The formula is given by:

P(X=k) = (n choose k) * p^k * (1-p) ^(n-k)

where:

n = sample size (3)

k = number of successful trials (0)

p = probability of success (probability of an item being non-defective)

Since there are 24 items in the lot and 5 of them are known to be defective, the probability of success (p) is equal to 19/24.

Plugging in the values, we get:

P(X=0) = (3 choose 0) * (19/24) ^0 * (5/24) ^3

= 1 * 1 * (5/24) ^3

= (5/24) ^3

= 0.0403

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The ordered pair that lies on the inverse of the function is (25, 0)

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

g(x)=−(x−3)^3−2.

Set x = 0

So, we have the following representation

g(0) =−(0−3)^3−2.

Evaluate the expression

This gives

g(0) = 25.

So, the ordered pair of teh inverse is (25, 0)

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Answer: -3,4

Step-by-step explanation:

Answer:

x= 19

Step-by-step explanation:

6x+4+4x-14= 180

10x-10= 180

10x= 190

x= 19

1601000 students were awarded a bachelor’s degree in 2009.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

First, notice that the table is in thousands, remember that.

Now, we need to go to the part of the row of the table where we have "Bachelor".

There we can see that in 2009, a marginal total of 1,601 thousands got that degree.

Then we can conclude that in 2009, a total of:

1,601×100 = 1,601,000 students got a bachelor's degree.

Hence, 1601000 students were awarded a bachelor’s degree in 2009.

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Answer:

C. 1,601,000

Step-by-step explanation:

This is the correct answer.

Answer:

a = 68°

Step-by-step explanation:

a and 112° are a linear pair and sum to 180° , that is

a + 112° = 180° ( subtract 112° from both sides )

a = 68°

Answer:

$14087.49

Step-by-step explanation:

APR=8%,

monthly interest rate (r)=8%/12=0.08/12

Monthly payment, A=$250

After 4 years, n=4*12 = 48 months,

the balance P is therefore

P= A((1+r)^n-1)/i

=250((1+0.08/12)^48-1)/(0.08/12)

=14087.49