Find the exact value of sine, cosine and tangent of each angle. Rationalize the denominator if needed.


7 π/ 6

Answer:

if you was asking for *solve for X* it is -2/15

Step-by-step explanation:

sorry if this dose not help

Answer:

261.5 ft^2

Step-by-step explanation:

Surface Area of a rectangular prism = Length x Width x Height

= 8.5ft x 6ft x 5.5ft

= 261.5 ft

This is a pond in the shape of a prism. It is completely full of water. Colin has to wait for the pond to completely empty is 2hrs and 30minutes.

We have a pond which is completely filled with the water.

Area of the side face ( trapezium shaped)

= 1/2 x (1.4 + 0.6) x 2

= 2 m²

Volume = area x height (here width)

V = 2x1 = 2 m³

The level goes down by 20cm in the first 30 mins

Volume of water that will be taken down =

=0.2 x 1 x 2

=0.4 m³ ( upper water will form cuboid face)

Now,

⇒0.4 m³ water is taken out in 30 minutes

⇒1 m³ water is taken out in 30/0.4 minutes

⇒2 m³ water is taken out in 30/0.4 x 2 minutes

⇒30x2/0.4

⇒150 minutes.

So the pond will be completely empty in 150 min that is 2hrs30mins.

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If K is the midpoint of JL, and (JL = 48), then (JK = KL = 24) and (a = 88).

As per the question statement, K is the midpoint of JL, and (JL = 48).

We are required to calculate the values of JK and KL and, also the value of "a" if [KL = (a - 24)].

Since, K is the midpoint of JL, then K divides JL into two equal line segments, JK and KL.

Therefore, lengths of JK and KL will be \(\frac{JL}{2}=\frac{48}{2}=24\), i.e., (JK = KL = 24).

Also, since [KL = (a - 24)],

\(24 = (a -24)\\or, a = [24-(-24)]\\or,a = (24+24)\\or,a = 88\)

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Given: AQ ≅ RQ, it should be noted that AQY ≅ RQF based on SAS Congruence. Therefore, AQY ≅ RQF.

Given: AQ ≅ RQ

∠YAF and ∠FRY are right angles.

Prove: AQY ≅ RQF

1. AQ ≅ RQ (Given)

2. ∠YAF and ∠FRY are right angles (Given)

3. ∠AQY = ∠RQF (Vertical angles are congruent)

4. AQ = RQ (Given)

5. AY = RY (Side-Angle-Side Congruence)

6. ∠QYA = ∠RFQ (Angle-Side-Angle Congruence)

7. AQY ≅ RQF (SAS Congruence)

Therefore, AQY ≅ RQF.

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Given: AQ ≅ RQ

∠YAF and ∠FRY are right angles.

Prove: AQY ≅ RQF

Answer:

Option 2

Step-by-step explanation:

Using point-slope form, the line passes through (3, 1).

Option 2 is the only choice that satisfes this.

\(\quad \huge \quad \quad \boxed{ \tt \:Answer }\)

\(\qquad \tt \rightarrow \: Graph \:\: 2\)

____________________________________

\( \large \tt Solution \: : \)

The equation is given in its point slope form :

\(\qquad \tt \rightarrow \:y - 1 = \dfrac{2}{3} (x - 3)\)

And the general equation in point slope form is :

\(\qquad \tt \rightarrow \:y - y_1 = m(x - x_1)\)

by comparing these two, we can get

And \({ (x_1 , y_1) } \) satisfies the equation, so the line (graph) of this equation should have point (3 , 1) lying on it.

And the only graph satisfying this condition is graph 2, therefore The graph 2 is the required graph.

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

Step-by-step explanation:

step one:

Given the sample space, which is the value of individual number of colored balls in the bin

Red balls=5

Yellow balls=3 and

Green balls= 4

And the sample size is the sum of all the colored balls in the bin

The sample size S= {5+3+4}= 12

step two:

The probability of choosing a red ball in an event can be expressed as, the total number of the red balls over the total number of balls in the bin

P(r)= 5/12

Hence the probability of selecting a red ball in one event 5/12

The expression that represents the total cost of buying and shipping the baseball cards,

= 6(1.75) + 5(9.5) + 2(20.5) + 4

Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.

Given:

Jake is buying baseball cards for his brother in college.

The price of a card is based on its condition.

The table shows the total cost of x number of cards for each condition.

He buys 6 that are in fair condition, 5 that are in good condition, and 2 that are in excellent condition.

The shipping cost for the baseball cards is $4.00.

The expression that represents the total cost of buying and shipping the baseball cards,

= 6(1.75) + 5(9.5) + 2(20.5) + 4

= 10.5 + 47.5 + 41 + 4

= 103

Therefore, the total cost is $103.

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Answer:

Step-by-step explanation:

Q1

Q2

Q3

Q4

Answer: D. height when first thrown

Step-by-step explanation:

         The constant term, 5, in this equation represents the height of the ball when it was first thrown. This means that our answer is option D.

         This constant term (5) is also the y-intercept. When we graph this equation, the line starts at (0, 5) if you ignore the negative values since we cannot have a negative time for this scenario. This is a visual representation of the ball being thrown.

Answer:

LM = √34

Step-by-step explanation:

L is at (-7, 4), and M is at (-2, 1).

LM

\( \sqrt{ {( - 7 - ( - 2))}^{2} - {(4 - 1)}^{2} } \)

\( \sqrt{ {( - 5)}^{2} + {3}^{2} } = \sqrt{25 + 9} = \sqrt{34} \)

The amount Shirley paid for the Fax machine is $488.

Shirley buys a fax machine and sells it to Devi at a gain of 25% on the cost price.

let the cost Shirley bought the machine = x

Therefore,

selling price = 25% of x + x = 0.25x + x = 1.25x

Devi then sells the fax machine to Amirah at a loss of 250 on the price at which she buys it from Shirley.

Amirah pays $360 for the fax machine.

Therefore,

loss = cost price - selling price

250 = 1.25x - 360

Therefore,

250 + 360 = 1.25x

610 = 1.25x

x = 610 / 1.25

x = $488

Therefore, the amount Shirley paid for the Fax machine is $488.

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Let's calculate the products and check if they indeed have the same value:

Product of 32 and 46:

32 * 46 = 1,472

Reverse the digits of 23 and 64:

23 * 64 = 1,472

As you mentioned, the products are the same. This phenomenon is not unique to this particular pair of numbers. In fact, it occurs with any pair of two-digit numbers whose digits, when reversed, are the same as the product of the original numbers.

To find two other pairs of two-digit numbers that have this property, we can explore a few examples:

Product of 13 and 62:

13 * 62 = 806

Reversed digits: 31 * 26 = 806

Product of 17 and 83:

17 * 83 = 1,411

Reversed digits: 71 * 38 = 1,411

As for determining if a given pair of two-digit numbers will have this property without actually performing the multiplication, there is a simple rule. For any pair of two-digit numbers (AB and CD), if the sum of A and D equals the sum of B and C, then the products of the original and reversed digits will be the same.

For example, let's consider the pair 25 and 79:

A = 2, B = 5, C = 7, D = 9

The sum of A and D is 2 + 9 = 11, and the sum of B and C is 5 + 7 = 12. Since the sums are not equal (11 ≠ 12), we can determine that the products of the original and reversed digits will not be the same for this pair.

Therefore, by checking the sums of the digits in the two-digit numbers, we can determine whether they will have the property of the products being the same when digits are reversed.

The number of different ways that three speakers can be​ selected is 10 ways

Given the names of choice to be Ben, Will, Stewart, Hilary, and Kate. This means that we have a total of 5 name choices.

If the members of students activities are to select three speakers among these people, the number of ways this can be done is by using the combination rule as shown;

\(nCr=\frac{n!}{(n-r)!r!}\)

From the question, n = 5 and r = 3. On substituting

\(5C3=\frac{5!}{(5-3)!3!}\\5C3=\frac{5!}{2!3!}\\5C3=\frac{5 \times 4 \times 3!}{2 \times 3!} \\5C3=\frac{20}{2}\\5C3 = 10 ways\)

Hence the number of different ways that three speakers can be​ selected is 10 ways.

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The total number of throws will be equal to 16.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The total number of throws will be calculated by adding all the throws,
Total throws = ( 3 / 5 ) + 15 + ( 2 / 5)

Total throws = ( 3 + 75 + 2) / 5

Total throws = 80 / 5

Total throws = 16

Therefore, the total number of throws will be equal to 16.

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Answer:

The answer is 24.

Step-by-step explanation:

I graphed it out, and calculated it and this is what I got. I am terribly sorry if this is wrong. Please forgive, but I think it is right.

Answer:

D

Step-by-step explanation:

Answer: between hours 2 and hours 3

Step-by-step explanation:

Answer:

m = 2

Step-by-step explanation:

6m = 12

6 × m = 12

m = 12 ÷ 6

m = 2

If it helps, then pls like and mark as brainliest!

Answer:

m = 2

Step-by-step explanation:

6m = 12

6m = 6^2

• get rid of common element which is 6. Devide both side by six.

6m ÷ 6 = 6^2 ÷ 6

m = 2

Answer:

25

Step-by-step explanation:

Because when you add all the cost and divide by the amount of tickets you get 25

To formulate a linear programming model, let N represent the amount spent on newspaper advertising and R represent the amount spent on radio advertising.

The objective is to maximize the value of total audience exposure, which can be measured using the exposure index. Let's denote this as Z.
The constraints are as follows:
1. The budget constraint: N + R ≤ $5,000.
2. At least 25% of the budget must be spent on each type of media: N ≥ $1,250 and R ≥ $1,250.
3. The amount spent on local newspaper advertising must be at least twice the amount spent on radio advertising: N ≥ 2R.
Therefore, the linear programming model can be written as follows:
Maximize Z = 40N + 70R
Subject to:
N + R ≤ 5000
N ≥ 1250
R ≥ 1250
N ≥ 2R
(b) To solve this problem using Excel Solver, you can set up a spreadsheet model with the following columns: Newspaper Dollars Allocated, Radio Dollars Allocated, Total Exposure Index.
In the Newspaper Dollars Allocated column, input the formula "=N" to represent the amount spent on newspaper advertising. In the Radio Dollars Allocated column, input the formula "=R" to represent the amount spent on radio advertising.
In the Total Exposure Index column, input the formula "=40*N+70*R" to calculate the total exposure index based on the allocated budget.
Use Excel Solver to set up the optimization problem. Set the objective cell as the Total Exposure Index column and set the constraints for the budget, minimum spending, and newspaper-radio ratio.
After running the Solver, it will provide the optimal values for N and R (the amount spent on newspaper and radio advertising, respectively), as well as the maximum value of total audience exposure (rounded to the nearest integer).

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Explanation:

The graph of the linear equation y = -1/3x, aka y = -x/3, goes through the points (0,0) and (3,-1). To generate any point, plug in a value for x to get its paired value of y.

Another way to graph this line is to start at (0,0). Then move down 1 and over to the right 3 units to arrive at (3,-1). Draw a straight line through those points.

The graph is shown in the diagram below. Points B, C, F, H, J are all below that red line.

By using the factorization, the least square solution for Ax=b is x = [247; -135; 85]/126

we can find the least-squares solution of Ax = b using the QR factorization of A by first;

Find the QR factorization of A:

A = QR

where

Q is an orthogonal matrix and

R is an upper-triangular matrix.

Using back substitution, Solve the system Rx = Qᵀb for x

The QR factorization of A can be found using the Gram-Schmidt process as shown below;

q1 = (2/√(6), 1/√(6), 1/√(6))

v2 = [4, 1, 0] - projq1([4, 1, 0]) = [8/3, 1/3, -2/3]

q2 = v2 / ||v2|| = (8/9, 1/9, -2/9)

v3 = [1, 0, 1] - projq1([1, 0, 1]) - projq2([1, 0, 1]) = [-1/3, -1/3, 2/3]

q3 = v3 / ||v3|| = (-1/3√(2), -1/3√(2), 1/3√(2))

Therefore, we have;

Q = [q1, q2, q3] = [2/√(6), 8/9, -1/3√(2); 1/√(6), 1/9, -1/3√(2); 1/√(6), -2/9, 1/3√(2)]

R = QᵀA = [√(6), 7√(2)/3, 5√(2)/3; 0, 2√(2)/3, -1/3√(2); 0, 0, 2/3√(2)]

To solve the system Rx = Qᵀb, we have:

Qᵀ×b = [3√(6)/2, -H√(6)/6, 17√(2)/18]ᵀ

R×x = [√(6)×x1 + 7√(2)×x2/3 + 5√(2)x3/3 = 3√(6)/2;

2√(2)×x2/3 - 1/3√(2)×x3 = -H√(6)/6;

2/3√(2)×x3 = 17√(2)/18]

Solving for x3 in the third equation, we have;

x3 = (17/18)√(2)

Substituting this into the second equation,

2√(2)x2/3 - 1/3√(2)(17/18)√(2) = -H√(6)/6

computing for x2, we get:

x2 = -9/14

Substituting for the value of x2 and x3 into the first equation,

√(6)x1 + 7√(2)(-9/14)/3 + 5√(2)×(17/18)/3 = 3√(6)/2

computing for x1, we get:

x1 = 13/21

Hence, the least-squares solution of Ax = b is;

x = [x1; x2; x3] = [13/21; -9/14; 17/18]  or

x = [247; -135; 85]/126 (By simplifying the answer)

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The value of x that makes the rational expression undefined is x = -3.

The given rational expression is (-6x + 42) / (3x + 9).

To find the values of x that make this expression undefined, we need to determine when the denominator becomes zero.

In this case, the expression becomes undefined when the denominator (3x + 9) equals zero.

So, we set the denominator equal to zero and solve for x:

3x + 9 = 0

Subtracting 9 from both sides:

3x = -9

Dividing both sides by 3:

x = -3

Therefore, the value of x that makes the rational expression undefined is x = -3.

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Which represents all the values of x that make the rational expression -6x + 42/3x + 9 undefined?

The distance between the Woozy Wheel and the Roller Rail is 13 units.

To determine the distance between the Woozy Wheel and the Roller Rail, we can use the distance formula in the coordinate plane.

The coordinates of the Woozy Wheel are (-14, 1), and the coordinates of the Roller Rail are (-2, -4).

Using the distance formula, the distance (d) between two points (x₁, y₁) and (x₂, y₂) is given by:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Substituting the coordinates of the Woozy Wheel and the Roller Rail into the formula:

d = √((-2 - (-14))² + (-4 - 1)²)

= √(12² + (-5)²)

= √(144 + 25)

= √169

= 13

Therefore, the distance between the Woozy Wheel and the Roller Rail is 13 units.

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Answer:

4

Step-by-step explanation:

Answer:2+2 = 4.............

Answer:

[C]  \(\displaystyle \frac{-3}{250}\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Calculus

Step-by-step explanation:

Step 1: Define

Identify

\(\displaystyle g(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h}\)

\(\displaystyle f(x) = \frac{3}{\sqrt{x - 4}}\)

\(\displaystyle g(29)\)

Step 2: Differentiate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Derivatives

Book: College Calculus 10e

The percentage of staff under 40 is 47.4%

The fraction of staff who drink water is 16/57

The probability of a random staff member being under 40 and drinking tea is 4/57.

a) The percentage of staff under 40 will be:

Total staff under 40 = 4 + 13 + 10 = 27

Total staff = 4 + 13 + 10 + 12 + 12 + 6 = 57

Percentage of staff under 40 = (27/57) x 100%

Percentage of staff under 40 = 47.4%

b) The fraction of staff who drink water will be:

Total staff who drink water = 10 + 6 = 16

Total staff = 57

Fraction of staff who drink water = 16/57

c) The probability that a randomly chosen staff member was under 40 and drank tea will be:

Staff under 40 who drink tea = 4

Total staff = 57

Probability = 4/57

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Answer:

option B should be correct