I need to find tan (theta) for angle theta , the angle between the x-axis and the line that connects the origin to point (3,2)

The volumes of the 20% solution, 35% solution, and 80% solution used by the chemist are 18 liters, 12 liters, and 24 liters, respectively.

The chemist has three different acidic solutions. The first solution contains 20% acid, the second contains 35% acid, and the third contains 80% acid. She created 54 liters of a 50% acid mixture, using all 3 solutions. The number of liters of 80% solution used is 2 times the number of liters of 35% solution used.

Let the amounts of 20% solution, 35% solution, and 80% solution used be x, y, and z. We already know that z = 2y. We can write equations as given below.

The sum of the volumes must be equal to the final volume.

x + y + z = 54

x + y + 2y = 54

x = 54 - 3y

Now we will write the equation using the concentrations of the acid.

50%*54 = 20%*x + 35%*y + 80%*z

27 = 0.2(54 - 3y) + 0.35y + 0.8(2y)

2700 = 20(54 - 3y) + 35y + 80(2y)

2700 = 1080 - 60y + 35y + 160y

1620 = 135y

y = 1620/135 = 12

z = 2y = 2*12 = 24

x = 54 - 3y = 54 - 36 = 18

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Answer: 1 is 77 3 is 231 5 is 308 and 7 is 385

Step-by-step explanation:

Answer:

6 video games

Step-by-step explanation:

We can solve this question with an algebraic equation.

29.95x + 5.95 = 185.65

29.95x + 5.95 - 5.95 = 185.65 - 5.95

29.95x ÷ 29.95 = 179.7 ÷ 29.95

x = 6

The probability of each outcome in the sample space = 1/16

The probability of getting a sum of 5 = 1/4

Step-by-step explanation:

We have been given a four-sided die is a pyramid whose four faces are labeled with the numbers 1, 2, 3 and 4

sample space = {(1,1), (1,2), (1,3), (1,4), (2,1),(2,2), (2,3), (2,4),(3,1), (3,2), (3,3), (3,4), (4,1), (4,2), (4,3), (4,4)}

Two fair 4-sided dices are rolled and all sixteen possible outcomes are equally likely.

The possible outcomes can be deduced by making combinations of different faces with a particular face.

given that each of the outcomes in the sample space is equally likely. So the probability of each outcome in the sample space is the same.

now we find the probability of each of the outcomes in the sample space

(a) when two dices are rolled, we have n(s) = 4*4=16

the chances of getting the outcome as (1,1) n(a) = 1

the probability of getting the outcome as (1,1) p(a)= n(a)/n(b)

p(a) = 1/16

so the probability of each outcome in the sample space = 1/16

(b) P(A) is the probability of getting 5 as a sum

   P(A) = Total outcomes with 5 as a sum/Total outcomes

  Total outcomes with 5 as sum= 4

  Total outcomes= 16

  P(A)=4/16=1/4

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Answer:

y = - x + 4

Step-by-step explanation:

Use point-slope form: y-k = m(x-h) for point (h,k) with slope m

now just plug and chug:

y-4 = -1(x-0)

y-4 = -x

y= -x+4

not sure about what you meant by "solution." Just gonna assume that you were looking for the equation.

Richard earned a cumulative GPA of 2.5 in all four semesters.

Here, we know that the cumulative GPA for the first 3 semesters is 2.0

He had earned 42 credits in total in all three semesters.

Cumulative GPA = Total points earned/credits rewarded

Hence,

Total points earned in 3 semestes= 2 X 42

= 84 points

In the fourth semester,

he had earned 14 credits with a GPA of 4.0

Hence total points earned = 4 X 14

= 56 points

Therefore, total points earned in all four semesters = 84 + 56 points

140 points

Total credits = 14 + 42

= 56

Hence, the cumulative GPA of all 4 semesters

= 140/56

= 2.5 points.

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Answer:

is there a graph for this

Step-by-step explanation:

i need a grapg or to know what they wanted to know

Answer:

though the answers are scattered but I worked them all , just patiently study it.

Solving an equation we will see that x = 13, then the measure of interior angle G is 63°.

Here we have the 3 interior angles of a triangle defined with a variable x.

m∠E = (5x + 6)°

m∠F = (4x - 6)°

m∠G = (5x - 2)°

Now, remember that the sum of the interior angles of a triangle is always equal to 180°.

Then we can write:

(5x + 6)° + (4x - 6)° +  (5x - 2)° = 180°

We can solve this for x.

14x - 2 = 180

14x = 180 + 2

x = 182/14 = 13

Now that we know the value of x, we can find the value of angle G.

m∠G = (5x - 2)° = (5*13 - 2)° = (15 - 2)° = 63°

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The value of x for the given triangle is 4.5

A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.

The sum of all three angles of a triangle is always 180°

In the given triangle ABC,

∠A=(9x+16)°, ∠B=(6x+15)°

And the extrior angle ∠C=(19x+3)°

Use the external angle property,

The sum of two interior angles is equal to an exterior angle.

Therefor,

∠C=∠A+∠B

(19x+3)°=(9x+16)°+(6x+5)°

19x+3=15x+21

4x=18

x=4.5

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The length of each side of the playground is 150 feet.

From the question, we are to determine the length of each side of the playground.

From the given information,

The perimeter of a square is given by the formula,

P = 4l

Where P is the perimeter of the square

and l is the length of a side of the square

"The playground at DeVille Elementary School is square-shaped, and has a perimeter of 600 feet."

That is,

P = 600 feet

Now, we will determine the value of l

Substitute the value of P into the equation

P = 4l

600 = 4l

Divide both sides by 4

600/4 = 4l/4

150 = l

Therefore,

l = 150 feet

Hence, the length is 150 feet

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Mia's error in her thinking was that she interchanged the coordinate of both the x- and y-axis. Also, the point would actually be located at (5, 8).

In Mathematics, a reflection across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate would change from positive to negative. Therefore, a reflection across the x-axis is given by this transformation rule:

(x, y)                   →               (x, -y)

In Geometry, a reflection across the y-axis of a graph is given by this transformation rule (x, y) → (-x, y).

(x, y)                   →               (-x, y)

(-5, -8)                   →            (5, -8)

Next, we would apply another reflection across the x-axis of a graph as follows:

(x, y)                   →               (x, -y)

(5, -8)                   →            (5, 8)

In conclusion, we can logically deduce that Mia was wrong in her calculations.

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If R and S are parallel lines and ∠1= 4x-3 and ∠7= 3x+4, The measure of ∠2 will be 179.

When two lines or rays converge at the same point, the measurement between them is called an "Angle."

It is given that, R and S are parallel lines and <1= 4x-3 and <7= 3x+4,

From the given figure it is obtained that R and S are parallel lines,

∠1=∠7

4x-3=3x+4

4x-3x=4+3

7x=7

x=1

If the ∠1 and ∠2 are supplementary,

∠1+∠2=180

4x-3+∠2=180

∠2=180-4x+3

Substitute the value of x,

∠2=180-4(1)+3

∠2=179

Thus, if R and S are parallel lines and ∠1= 4x-3 and ∠7= 3x+4, The measure of ∠2 will be 179.

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3x(2x+1)-8(2x+1)

6x²+3x-16x+16

6x²+13+16

Evaluated expression of the given mathematical expression is (9+2gh+5g)/g.

Given the mathematical expression is 9/g + 2h + 5.

So, now the LCM (g,1,1) = g

So evaluating the given expression we get,

9/g + 2h + 5 = (9+2gh+5g)/g

Hence the evaluated expression is (9+2gh+5g)/g .

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The account balance after 10 years is $7200.

It should be noted that simple interest is calculated as:

= (Principal × Rate × Time) / 100

= ($3000 × 1.4 × 10) / 100

= $4200

The total amount that will be in the account will be:

= Principal + Interest

= $3000 + $4200

= $7200

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The equation of the line in point slope form is as follows:

Linear equation can be represented in different form such as point slope form, slope intercept form, standard form and general form.

Therefore, equation in point slope form can be represented as follows:

y - y₁ = m(x - x₁)

where

Therefore, let's find the point slope form of the lines.

1) through: (5, 4) and (-2, 5)

m = 5 - 4 / -2 - 5

m = 1 /- 7 = - 1 / 7

Therefore,

y - 4 = - 1 / 7(x - 5)

2) through: (4, -5) and (0, 2)

m = 2 + 5 / 0 - 4

m = 7 / -4 = - 7 / 4

Therefore,

y + 5 = - 7 / 4(x - 4)

3) through: (0, 4) and (2, 1)

m = 1 - 4 / 2 - 0

m = - 3/ 2

Therefore,

y - 4 = - 3 / 2(x - 0)

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The Natural Unemployment Rate based on the information is 5%.

The natural rate of unemployment is the lowest unemployment rate when inflation is stable, or the unemployment rate when inflation is not accelerating. The natural rate of unemployment (NAIRU) is the rate of unemployment caused by all factors other than changes in aggregate demand. Potential GDP estimates are based on the long-term natural rate.

The unemployment rate is the proportion of the total labor force that is unemployed but actively looking for work and willing to work. Cyclical unemployment is associated with an industry's business cycle. It is a direct result of a drop in consumer demand, which has resulted in a drop in labor demand. If cyclical unemployment rises, it indicates that the economy is slowing, which is not good.

Cyclical unemployment occurs when labor forces are reduced as a result of business cycles or economic fluctuations. If you are cyclically unemployed, it means that your employer has laid you off to save money during a period of slow business.

In this case, the unemployment will be:

= Actual unemployment rate - Cyclical unemployment rate

= 12% - 7%

= 5%

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Answer:B

Step-by-step explanation:no points on be colide with each other on either axis

The expression equivalent to the expression -90 - 60w is -30(3 + 2w),  (-9 - 6w)10 and  -20(4.5 + 3w)

We need to find the expressions that are equivalent to given expression

We solve the expression and check,

A) -30(3 + 2w)

-90 - 60w

Yes it is equivalent.

B) (-9 - 6w)10

-90 - 60w

Yes it is equivalent.

C) -3(30 - 20w)

-90 + 60w

No it is not equivalent.

D)(6 + 4w)15

90 + 60w

No it is not equivalent.

E) -20(4.5 + 3w)

-90 - 60w

Yes it is equivalent.

Therefore, The expression equivalent to the expression -90 - 60w is -30(3 + 2w),  (-9 - 6w)10 and  -20(4.5 + 3w)

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The amount of money that would be in the account after 9 years, giving the interest rate and the amount invested is $23, 777.52

The amount in the account after 9 years is called the future value of the amount that Serenity invested.

To find this future value, you use the future value formula which is:

= Amount invested x ( 1 + interest rate) ^ number of years

The amount in the account after 9 years would therefore be:

= 16, 000 x ( 1 + 4.5%) ⁹

= $23777.52224662808994653125

= $23, 777.52

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The area of the square is (x²/2) square units.

We are given a square. The length of the diagonal of the square is x units. We have to find the area of the square in terms of "x".

Let the side of the square be denoted by the variable "s". We will use the Pythagorean theorem to find the length of the side of the square.

s² + s² = x²

2s² = x²

s² = x²/2

s = √(x²/2)

s = (x/√2)

The area of the square is given by the square of the side length. Let the area of the square be denoted by the variable "A".

A = s²

A = (x/√2)²

A = x²/2

Hence, the area of the square is (x²/2) square units.

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At the 97% confidence interval estimate of the population mean is

(80.55, 77.45).

Following are the calculation to the confidence interval :

Given that,

σ = 15

n = 430

X = 79

Here C = 97% = 0.97

⇒ α = 1 -C = 1 - 0.97 = 0.03

∴ Zₙ =  Zₙ/2 = Z₀.₀₁₅ = 2.17

Now,

97% confidence interval,

C.I = X ± σ/√n

     = 79 ± 2.17 × (15/√430)

     = 79 + 2.17 × (15/ 21)                [taking round figure of √430=2.0736441]

     = 80.55

Now taking the negative sign,

        = 79 - 2.17 × (15/√430)

        = 79 - 2.17 × (15/ 21)

        = 77.45

The final answer is (80.55, 77.45).

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The required graph of the given line y = -(2/3)x + 1 is shown in the attached figure.

The equation of the line is given in the question as:

y = -(2/3)x + 1

First, we have to find the intercepts of the equation y = -(2/3)x + 1

The y-intercept is the value of y when the value of x is appropriately zero.

For x = 0

y = -2/3(0)+1

y = 1

The y-intercept is the point where (0.1)

Determine the x-intercept.

The x-intercept is the value of x when the value of y equals zero.

For y = 0

0 = (-2/3)x + 1

-1 = (-2/3)x

x = 3/2 or 1.5

The y-intercept is the point (1.5,0).

To graph, the line, draw the intercepts and connect the dots as indicated in the image.

As a result, the graph for the line y = -(2/3)x + 1 is provided below.

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Given system has no solution.

The correct answer is an option (D)

In this question, we have been given the graph of system of equations.

The solution of given system is the point of intersection of all lines.

We can observe that the graph of any two lines intersected at points (2, -1), (-2, 3) and (0, 3)

But there is no common point of intersection for given system.

This means, the system has no solution.

Therefore, the given system has no solution.

The correct answer is an option (D)

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The dividend growth rate of Kiefer service company is 0.16% . Dividend growth rate can be determined by using the return rate formula.

Dividend growth rate is the annual rate of growth that a particular stock's dividends experience over a specified period of time.

We have given that ,

Common stocks sells or current price = $36.84

Market rate of return (R) = 25.8 %

Annual dividend (D) = $1.61

Rate of return is defined as net gain or loss of। an investments over a specified time period . It is expressed as a percentage of investment initial cost .

Using the formula,

Rate of return = (D1/ current price )+growth rate where,

D1 --> divided of previous year

putting all the values in above formula we get,

15.8 = ( 1.61/36.84) + growth rate

=> growth rate= 15.8 - (1.61/36.84) = 15.756

Hense, the dividend growth rate for Kiefer service company is 0.16%.

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Answer:

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the question is already answerd by Yna9141

here is his text:

The average of the certain set of data can be calculated by dividing the sum of the given numbers/data by their count.

(a) In this item, we are given with: -0.05, 0.09, -0.04, -0.08

Their sum is as follows:  

                S = (-0.0.5) + (0.09) + (-0.04) + (-0.08)

                  S = -0.08

Then, divide the sum by 4.

                  M = -0.08 / 4 = -0.02

b. The answer to this question can be calculated through the equation below,

                    M₂ = (S + F) / 5

Substituting the known values,

                 -0.01 = (-0.08 + F) / 5

the value of F is equal to 0.03.

Answer:

15a: -0.02 15b: 0.03

Step-by-step explanation:

15a.

To find the mean, you need to add the values together and divide by the number of values.

(-0.05+0.09+-0.04+-0.08)/4

Simplify:

(-0.05+0.09-0.04-0.08)/4

(-0.05+0.09-0.12)/4

(0.09-0.05-0.12)/4

(0.04-0.12)/4

-0.08/4

-0.02

15b.

let's say the change for Friday is "x"

insert the numbers and add in -0.08 from earlier:

(-0.08+x)/5=-0.01

rearrange (-0.08+x):

(x-0.08)/5=-0.01

multiply both sides by 5:

x-0.08=-0.05

add 0.08 to both sides:

x=0.03