A law firm is going to designate associates and partners to a big new case. The daily rate charged to the client for each associate is $800 and the daily rate for each partner is $1800. The law firm designated twice as many partners as associates to the case and was able to charge the client $17600 per day for these lawyers' services. Write a system of equations that could be used to determine the number of associates assigned to the case and the number of partners assigned to the case. Define the variables that you use to write the system.

The value of the trignometric expression sin(a+b) is 0.3.

Given the trignometric equations sin a + cos b = -0.2 and sin b + cos a = 1.6

So, squaring both equations and adding them

we have

[tex](sin a + cos b)^2 = -0.2^2\\(sin a + cos b)^2 = 0.04\\sin^2a+cos^2b + 2 sina cos b= 0.04\\(sin b + cos a)^2 = 1.6^2\\sin^2b+cos^2a + 2 sinb cos a= 2.56\\\\[/tex]

adding both equations

[tex]sin^2a+cos^2b + 2 sina cos b + sin^2b+cos^2a + 2 sinb cos a= 0.04+2.56\\[/tex]

1+1+2( sina cos b + cos a sin b)= 2.6

2( sina cos b + cos a sin b) = 0.6

( sina cos b + cos a sin b) = 0.3

We know that sin(a+b)= ( sina cos b + cos a sin b)

So,

sin(a+b)=0.3

Therefore, the value of sin(a+b)  = 0.3

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In a case whereby there are 10 boys and 15 girls and the teacher chooses a student by random, then the probability that a boy will be chosen is 2/5 which means Jenny is right.

Since there are  there are 10 boys and 15 girls, then the total number of the population will be (10+15)=25

Then the probability of that a boy will be chosen if one of them is been chosen at random will then be =10/25 = 2/5

Therefore, Jenny is very correct because the  probability of that a boy will be chosen if one of them is been chosen at random will then be 2/5.

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The unit price per ounce of the jar of jam is $0.50

From the question, the given parameters are

Volume = 5 oz

Cost of jam = $2.50

The unit rate of the jam is calculated as

Unit rate = Cost of jam/Volume

Substitute the known values in the above equation

So, we have the following equation

Unit rate = 2.50/5

Evaluate the quotient

So, we have the following equation

Unit rate = 0.5

Hence, the unit price per ounce is $0.50

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Answer:

x=16

Step-by-step explanation:

I apologize I have not done geo in a while so I am not sure what the theorem is, but there is a theorem that states that when a transversal intersects with two parallel lines, two angles that are facing the same direction are the same angle. (the two white angles that i have marked are equal)

next, two lines that intersect each other will have the same angle measurements on opposite sides (the green marked angles are equal)

so that means 3x - 8 = x + 24

and when you simplify that, you get 2x = 32 ---> x = 16

The vertex and the axis of symmetry are (-2, -6) and x = -2, respectively

The equation of the function is given as

f(x) = x^2 + 4x - 2

The above equation is a quadratic equation

Next, we plot the equation on a graph (see attachment)

The vertex of the graph is the minimum or the maximum of the graph

In this case, we have

Minimum= (-2, -6)

This means that

Vertex = (-2, -6)

The axis of symmetry is the x-coordinates of the vertex

So, we have

x = -2

Hence, the vertex is (-2, -6) and the axis of symmetry is x = -2

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Step-by-step explanation:

-2x + 3y = -6

-3x - 2y = 11

-5x + y = 5

y = 5 + 5

y = 10

-2x + 3(10) = -6

-2x + 30 = -6

-2x = -6 - 30

-2x = -36

x = -18

i have no idea

The mathematical expression is as follows.

1) 4(v +3)

2) 15v -7

An algebraic expression is one that has been constructed using integer constants, variables, and algebraic operations. A good example of an algebraic expression is 3x 2 2xy + c.

Given Data

Suppose the number is v

1) To obtain: four times the product of v and 3.

Accordingly, we must first add v and 3, and then multiply the result by 4.

The mathematical expression is as follows.

= 4(v+3)

2) Assume that v is the given integer.

What we're aiming for is: 7 less than 15 times v.

This calls for multiplying the v by 15 and then taking 7 out of the result.

The expression in algebra would be as follows:

= 15v - 7

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Answer: 8x-3

Step-by-step explanation

2x + 6 + 6x - 9

8x - 3

Answer:

8x - 3

Step-by-step explanation:

2(x+3) + 3(2x-3)

2x+6 + 6x-9

2x+6x + 6-9

= 8x - 3

Answer: m = 5.5

Step-by-step explanation:

9680 / 1760 = m

m = 5.5

The simplified expression of (2^3×2^4) is 2^7

The expression is given as

(2^3×2^4)

The base of the above expression are the same

i.e. Base = 2

This means that we can apply the law of indices

When the law of indices is applied, we have the following equation:

(2^3×2^4) = 2^(3 + 4)

Evaluate the sum in the above equation

So, we have

(2^3×2^4) = 2^7

Hence, the simplified expression of the expression given as (2^3×2^4) is 2^7

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Answer:

Step-by-step explanation:

Simply 24/8 to 3.

-12/x = 3
Since x is the number being divided, we take the divisor and divide it by the quotient.

x = -12/3 = -4.

Answer:

Step-by-step explanation:

1630089 is the answer

By using internal angles of the triangles and the definition of supplementary angles, the measure of the angle MNP is equal to 54°.

Herein we find a geometric system formed by two common semirrays with a common vertex at point N and a line segment MP such that triangle MPN is a right triangle. By Euclidean geometry we know that the sum of the measures in the internal angles equals 180°:

m ∠ NMP + m ∠ MNP + m ∠ MPN = 180°      (1)

And the two angles at point P are supplementary angles:

24 · x + m ∠ MPN = 180°      (2)

Then, by (1):

90° + 9 · x + m ∠ MPN = 180°

m ∠ MPN = 90° - 9 · x

By (1) in (2):

24 · x + 90° - 9 · x = 180°

15 · x = 90°

x = 6

Then, the measure of the angle MPN is equal to:

m ∠ MNP = 9 · x

m ∠ MNP = 9 · 6

m ∠ MNP = 54°

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Answer:

Step-by-step explanation:

By dividing and multiplyinh the decimal by 10, we will see that:

-0.6 = -6/10

Here we have the following decimal: -0.6

And we want to write it as a fraction.

To do so, we just need to multiply it and divide it by 10 as many times as digits we have after the decimal point. In this case we have only one digit after the decimal point, so we multiply and divide by 10 only once.

-0.6 = -0.6*(10/10) = (-0.6*10)/10 = -6/10

That is the fraction form of the given decimal.

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If a costumer decides to pay in cash then saved £3.6.

What is mean by Percentage?

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

To Calculate the percent of a number , divide the number by whole number and multiply by 100.

Given that;

A cash discount of 8% is allowed on an item which costs £45.

Now, The amount of Saved money calculated as;

Since, A cash discount of 8% is allowed on an item which costs £45.

Hence,

Saved money = 8% of £45

                      = 8 x 45 / 100

                      = 3.6

Thus, Saved money = 3.6

Therefore, If a costumer decides to pay in cash then saved £3.6.

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For this study, the mean of 16.7 minutes is an example of a (B) Statistic.

So, the appropriate choice is an option (B).

Therefore, for this study, the mean of 16.7 minutes is an example of a (B) Statistic.

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The correct question is given below:
A researcher is interested in the travel time of Utrecht University students to college. A group of 50 students is interviewed. Their mean travel time in 16.7 minutes. For this study, the mean of 16.7 minutes is an example of a(n)

A. Parameter

B. Statistic

C. Population

D. Sample.

Answer:

17052 1/2

You're Welcome

All the expressions like (a), (b) and (c) are true sentences in the form of inequality.

What is inequality expression?

The inequality expression in a sentence consist of two algebraic expression with the inequality symbols. And the solution of an inequality is a number which when substituted for the variable to makes the inequality as a true statement.

According to the question, the given inequality expressions in the form of the sentence is as follows:

(a) 2(3/4) > 2.68;

(b) 7.895 x 10² > 5.43 x 10³;

(c) √63 > 8.11;

(d) |-1.5| > |3.2|

In this, all the expressions like (a), (b) and (c) are true sentences in the form of inequality.

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The area when Alex has a circular rug the radius of the rug is 5 1/4 feet is 86.625 feet².

It should be noted that the area of a circle is given the formula:

Area of a circle = πr²

where π = 22/7

r = radius = 5 1/4

Therefore, the area will be:

Area = πr²

Area = 22/7 × (5 1/4)²

Area = 22/7 × 25 1/16

Area = 86.625 feet²

The area is 86.625 feet².

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Answer:

b = 13.5

Step-by-step explanation:

There are different ways you can solve this equation. Let me know if you'd like to know a different way.

Have a Good Rest of Your Day.