Use the measurement below in PQR to solve the triangle. m

Answer: 0.07

Step-by-step explanation:

Use the given functions to set up and simplify 5years. 7% = 0.075 years = 0.07

Maci and 2 appointments and Logan had 3 appointments.

The linear equation that represents the total amount earned by Maci is:

Total amount earned = (amount per appointment x number of appointments)  + tips

$170 = ($60 x a) + $50

$170 = $60a + $50

$170 - $50 = $60a

$120 = $60a

a = $120 / $60

a = 2

The linear equation that represents the total amount earned by Logan is:

Profit = total revenue - total cost

Profit = (fee per appointment  x number of appointments) + amount received in tips - (rental fee x number of appointments)

$235 = ($75 x a) + $40 - ($10 x a)

$235 = $75a + $40 - $10a

$235 = $65a + $40

$235 - $40 = $65a

$195 = $65a

a = $195 / 65

a = 3

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The correct option of system of equations that can be used to find the temperature at which the degrees Celsius and the degrees Fahrenheit would be equivalent is the option;

5·F - 9·C = 160

F - C = 0

A system of equation, is a set of equation that have common variables.

The equation for conversion of the temperature in degrees Celsius to the temperature in degrees Fahrenheit is; 9·C = 5·F - 160

When the temperature in degrees Celsius is equivalent to the temperature in degrees Fahrenheit, we get;

F = C

Therefore;

F - C = 0

Similarly, from the specified equation, we get;

9·C = 5·F - 160

5·F - 9·C = 160

The system of equation that would give the temperature where the degrees Celsius and degrees Fahrenheit are equivalent is therefore;

5·F - 9·C = 160

F - C = 0

(Which yields a temperature of 40°)

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The system of equations to find the original number is;a = 3b +1 and (10a + b) - (10b +a) = 45

From the task content;

Hence, the required system of equations is;

On this note, the required numbers can be evaluated from the equations above;

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Given:

The number of atoms =

The weight of each atom =

To find the total mass, multiply the total number of atoms by the weight of each atom

So, the total mass =

So, the answer is option 2. 0.67 grams

Answer:

120

Step-by-step explanation:

15*8=120

Answer:

the product of the decimal equivalents of all discount in the series

The horizontal distance which the car must have travelled is equal to 450 meters.

Mathematically, the gradient (slope) of a geometric figure or line can be calculated by using this formula:

Pitch (slope) = V/H

Where:

Based on the given image, we have the following distances and gradient (slope):

Rising vertical distance = 60

Horizontal distance (Run) = x

Gradient (slope) = 2/15

Substituting the given parameters into the formula, we have;

2/15 = 60/x

2x = 900

x = 450

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Based on the information given, there are a total of 118 solutions.

This is a problem of solving a Diophantine equation subject to some conditions. Let's introduce a new variable y4 = 20 - (x1 + x2 + x3 + x4). Then the problem can be restated as finding the number of solutions to:

x1 + x2 + x3 + y4 = 20

Subject to the following conditions:

0 ≤ x1 < 3

0 ≤ x2 < 4

0 ≤ x3 < 5

0 ≤ y4 < 6

We can solve this problem using the technique of generating functions. The generating function for each variable is:

(1 + x + x^2) for x1

(1 + x + x^2 + x^3) for x2

(1 + x + x^2 + x^3 + x^4) for x3

(1 + x + x^2 + x^3 + x^4 + x^5) for y4

The generating function for the equation is the product of the generating functions for each variable:

(1 + x + x^2)^3 (1 + x + x^2 + x^3 + x^4 + x^5)

We need to find the coefficient of x^20 in this generating function. We can use a computer algebra system or a spreadsheet program to expand the product and extract the coefficient. The result is: 1118

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Answer: This problem involves finding the number of non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20 subject to the given constraints. We can use the stars and bars method to solve this problem.

Suppose we have 20 stars representing the sum x₁ + x₂ + x3 + x₁. To separate these stars into four groups corresponding to x₁, x₂, x₃, and x₄, we need to place three bars. For example, if we have 20 stars and 3 bars arranged as follows:

**|**||

then the corresponding values of x₁, x₂, x₃, and x₄ are 2, 4, 6, and 8, respectively. Notice that the position of the bars determines the values of x₁, x₂, x₃, and x₄.

In general, the number of ways to place k identical objects (stars) into n distinct groups (corresponding to x₁, x₂, ..., xₙ-₁) using n-1 separators (bars) is given by the binomial coefficient (k+n-1) choose (n-1), which is denoted by C(k+n-1, n-1).

Thus, the number of non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20 subject to the given constraints is:

C(20+4-1, 4-1) = C(23, 3) = 1771

However, this count includes solutions that violate the upper bounds on x₁, x₂, x₃, and x₄. To eliminate these solutions, we need to use the principle of inclusion-exclusion.

Let Aᵢ be the set of non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20 subject to the given constraints, where xᵢ ≥ mᵢ for some integer mᵢ. Then, we want to find the cardinality of the set:

A = A₀ ∩ A₁ ∩ A₂ ∩ A₃

where A₀ is the set of all non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20, and Aᵢ is the set of solutions that violate the upper bound on xᵢ.

To find the cardinality of A₀, we use the formula above and obtain:

C(20+4-1, 4-1) = 1771

To find the cardinality of Aᵢ, we subtract the number of solutions that violate the upper bound on xᵢ from the total count. For example, to find the cardinality of A₁, we subtract the number of solutions where x₂ ≥ 4 from the total count. To count the number of solutions where x₂ ≥ 4, we fix x₂ = 4 and then count the number of solutions to the equation x₁ + 4 + x₃ + x₄ = 20 subject to the constraints 0 ≤ x₁ < 3, 0 ≤ x₃ < 5, and 0 ≤ x₄ < 6. This count is given by:

C(20-4+3-1, 3-1) = C(18, 2) = 153

Similarly, we can find the cardinalities of A₂ and A₃ by fixing x₃ = 5 and x₄ = 6, respectively. Using the principle of inclusion-exclusion, we obtain:

|A| = |A₀| - |A

Step-by-step explanation:

the slope is -4

hope this helps!!

Answer:

the slope is -4

Step-by-step explanation:

Answer:

A. -2, 9

B. -2, 4

C. -8, 4

D. -8, 9

ANSWER:

125/2 =125/2

PROVED

STEP BY STEP EXPLANATION

PUTTING THE VALUE OF X, WE HAVE

1/2×5×5×5=125/2

1/2×125=125/2

125/2=125/2

HENCE ,L.H.S =R.H.S

PROVED.

HOPE THIS WILL HELP YOU

Answer: 29

Step-by-step explanation:

all triangles equal to 180

180-97-54=29

Answer:

≈ 404.6666667

Step-by-step explanation:

70 - 8 ÷ 6 + 8 x 42

70 - 1.33333333 + 8 x 42

70 - 1.33333333 + 336

68.6666667 + 336

404.6666667

Answer:

10f + 5

Step-by-step explanation:

7f+5+3f (Given)

10f + 5 (combine like terms)

Answer:

15f is the correct answer

Answer:

They are both 42 cm

Step-by-step explanation:

Answer:

your just putting the numbers at the bottom into the line plot . so let's say  there is 333 u would up the three 3 on the plot .

Step-by-step explanation:

hope this helps let me know if u need a better explanation

The question is somewhat poorly posed because the equation doesn't involve θ at all. I assume the author meant to use x.

sec(x) = csc(x)

By definition of secant and cosecant,

1/cos(x) = 1/sin(x)

Multiply both sides by sin(x) :

sin(x)/cos(x) = sin(x)/sin(x)

As long as sin(x) ≠ 0, this reduces to

sin(x)/cos(x) = 1

By definition of tangent,

tan(x) = 1

Solve for x :

x = arctan(1) + nπ

x = π/4 + nπ

(where n is any integer)

In the interval 0 ≤ x ≤ 2π, you get 2 solutions when n = 0 and n = 1 of

x = π/4   or   x = 5π/4

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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The solution to the expression (2.8 × 10⁻⁹) − (6.9 × 10⁻⁸) gives -6.62 * 10⁻⁸

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the equation:

(2.8 × 10⁻⁹) − (6.9 × 10⁻⁸)

Making the exponents to be similar gives:

(2.8 × 10⁻⁹) − (69 × 10⁻⁹)

Simplifying gives:

-6.62 * 10⁻⁸

The solution to the expression (2.8 × 10⁻⁹) − (6.9 × 10⁻⁸) gives -6.62 * 10⁻⁸

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Answer:perpendicular bisector theorem

Step-by-step explanation:

Answer: A

Step-by-step explanation:

Answer:

The 8th term of the following sequence is 9375.

Step-by-step explanation:

Given the sequence

3/25, 3/5, 3, 15

As we know that a geometric sequence has a constant ratio and is defined by:

\(\:a_n=a_0\cdot r^{n-1}\)

so

\(\frac{3}{25},\:\frac{3}{5},\:3,\:15\)

\(\frac{\frac{3}{5}}{\frac{3}{25}}=5,\:\quad \frac{3}{\frac{3}{5}}=5,\:\quad \frac{15}{3}=5\)

As the ratio 'r' is the same.

so

\(r=5\)

As the first element of the sequence is

\(a_1=\frac{3}{25}\)

Therefore, the nth term is computed by

\(\:a_n=a_0\cdot r^{n-1}\)

\(a_n=\frac{3}{25}\cdot \:5^{n-1}\)

Putting n = 8 to determine the 8th term.

\(a_8=5^7\cdot \frac{3}{25}\)

\(a_8=\frac{3\cdot \:5^7}{25}\)

    \(=\frac{5^7\cdot \:3}{5^2}\)

     \(=5^5\cdot \:3\)

     \(=9375\)

Therefore, the 8th term of the following sequence is 9375.

The graph is missing, so i have attached it.

Answer:

From 0 hours to 2 hours.

Step-by-step explanation:

From the attached graph, we can see that on the y-axis, denotes the level of ibuprofen in the patient’s bloodstream while the x-axis denotes the amount of hours after the ibuprofen was taken.

Now, looking at the graph, we can see that the curve goes up from a time of 0 hours which corresponds to 0 mg of ibuprofen to a time of 2 hours which corresponds to 400 mg of ibuprofen.

After that point, the curve begins to to go down. Since we are concerned with increase, we will make do with the first statement.

Thus, we can say the period at which the level of ibuprofen increased was from 0 hours to 2 hours.

Answer: try using one of these websites

Step-by-step explanation:

https://quickmath.com/#c=solve&v1=6B%2BR%25287y%2BB%2529%253D4x%255E2y-15%255Cnl%2520&v3=B

https://www.cymath.com/

Answer:

5200300

Step-by-step explanation:

Use Combination

The different combinations without repetition of 12 people will be equal to 5,200,300.

When a whole number is multiplied by each natural number underneath it, the result is known as its factorial. The symbol "!" can represent the idea of a factorial. As a result, "n factorial" is just n and is defined as the sum of the first n natural integers.

As per the given information in the question,

Total number of people chosen by the board = 12

Total number of applicants = 25

Then the number of combinations without repetition will be = ²⁵C₁₂

= \(\frac{25 !}{12!(25-12)!}\)

= 25!/(12! × 13!)

= 5,200,300

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a) The distance from point P to the pole  is: 6.2 m

b) The height of the Pole is: 6.2 m

The triangle attached shows us the triangle formed as a result of the given word problem about angle of elevation and distance and height.

Now, we are given that:

The angle of elevation of the top of the pole =  45°

Angle of elevation of the top of the pole = 58°.

|PQ|= 10m

a) PR is distance from point P to the pole and using trigonometric ratios, gives us:

PR/sin 58 = 10/sin(180 - 58 - 45)

PR/sin 58 = 10/sin 77

PR = (10 * sin 58)/sin 77

PR = 8.7 m

b) P O can be calculated with trigonometric ratios as:

P O = PR * cos 45

P O = 8.7 * 0.7071

P O = 6.2 m

Now, the two sides of the isosceles triangle formed are equal and as such:

R O = P O

Thus, height of pole R O = 6.2 m

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Answer:

Hello,

answer: m∠arc ET=25°

Y is out the circle .

y is a exterior angle of the circle.

Step-by-step explanation:

m∠y=58.5°

m∠arc GM=142°

m∠arc ET=x°

m∠arc ET=25°

Answer:

20 sets

Step-by-step explanation:

320/16=20

He needs 320 ping pong balls, and he has 16, so divide the amount needed by the amount that comes in each containter.

Answer:

There are 210 ways

Step-by-step explanation:

The number of ways or combinations in which we can select x elements from a group of n elements where the order doesn't matter can be calculated as:

\(nCx=\frac{n!}{x!(n-x)!}\)

So, we have 10 teaching assistants and we need to choose 4 (one assistant per question) to grade each question. It means that n is equal to 10 and x is equal to 4.

Therefore, the number of ways that the assistants can be chosen to grade the exam are calculated as:

\(10C4=\frac{10!}{4!(10-4)!}=210\)