TOPIC 1 ANGLES AND TRIANGLES
SKILLS PRACTICE continued
PROBLEM SET 2: Classifying Angles
> Identify each pair of angles as complementary, supplementary, or vertical angles.

Answer:

10

Step-by-step explanation:

The expected value for the game is 2/3.

The average value we would anticipate to find if we repeated an experiment several times is the anticipated value of a random variable. It is calculated by averaging the outcomes of multiplying each potential result of the random variable by the associated probability. In other words, it's the weighted average of all potential possibilities, with the weights being the likelihoods that each outcome would actually happen. In several disciplines, including finance, economics, and engineering, predictions and judgements are made using the expected value, a fundamental idea in probability theory.

Let us suppose the profit = X.

Thus,

Probability of winning twice our wager = 1/6 thus, the expected value is:

(2)(1/6) = 1/3

No, for profit equal to wager we have:

(1)(1/3) = 1/3

The total expected value is:

E(X) = (1/3) + (1/3) + 0 = 2/3

Hence, the expected value for the game is 2/3.

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Answer:

X2 = 1.697916 X3 = 1.431

Step-by-step explanation:

use Newton's formula of the method of approximating of zeros of a function : x_n+1. = x_n - f(x_n)/f'(x_n)

Answer:

im pretty sure its the first one that you chose :)

Step-by-step explanation:

We can solve the equation to find it's number of solutions, but we already know it only has 1 solution because it is a linear equation (y is raised to the first power).

[tex]3y + 5 - 2y = 11[/tex]

[tex]y + 5 = 11[/tex]

[tex]y = 6[/tex]

This confirms that there is only 1 solution.

Strategic decisions occur infrequently and involve long-term decisions.

Decision making is the process of taking decisions from two or more alternatives.

Strategic decision making is one of the important decision making process in an organization. This is one of the best ways to achieve the goals and objectives of an organization.

This is a long term process of decision making since it focus on long term goals.

So this does not occur frequently.

Hence the correct option is (A) infrequently and involve long-term decisions.

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Answer:

The graph will be translated down 2 units.

The new horizontal asymptote is y=2 because the graph now crosses over the y axis at 2. This is at the point (0,2).

The final image points are: L'(-2,-1), K'(0,-2), J'(2,-3)

It should be noted that to innitiate the first transformation, we must translate three units in a positive y-direction and two units to the left along the x-axis. This is accomplished via adding three to the respective points' measurements on the y-axis and immediately subtracting two from the x-coordinates. Consequently, the consecutive coordinates of J, K, and L become:

J(3,3), K(5,2), L(3,1)

Subsequently, the second alteration requires that we reflect across the x-axis; this can simply be achieved by inverting the y-values of each given point. In conclusion, the modified coordinates of J', K', and L' are now:

J'(3,-3), K'(5,-2), L'(3,-1)

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Answer:

At a 0.01 significance level, we reject the null hypothesis and conclude that the predicted weight of 65.89 kg is significantly different from the actual weight, which could be anywhere between 53.45 kg and 78.32 kg.

Step-by-step explanation:

Given the linear regression equation:

y = -107 + 1.13x

where x is the height in cm and y is the weight in kg.

To find the predicted value of y for a person with a height of 153 cm, we substitute x = 153 into the regression equation:

y = -107 + 1.13(153)

y = -107 + 172.89

y = 65.89

Therefore, the best predicted weight for an adult male who is 153 cm tall is 65.89 kg.

To check if this predicted value is statistically significant at a 0.01 significance level, we can perform a hypothesis test.

Null Hypothesis: The predicted weight for a person with a height of 153 cm is not significantly different from the actual weight.

Alternative Hypothesis: The predicted weight for a person with a height of 153 cm is significantly different from the actual weight.

We can use a t-test to test this hypothesis, with the test statistic:

t = (y_predicted - y_actual) / (s / sqrt(n))

where y_predicted is the predicted weight, y_actual is the actual weight, s is the standard error of the estimate, and n is the sample size.

The standard error of the estimate can be calculated using:

s = sqrt((1 - r^2) * Sy^2)

where Sy is the sample standard deviation of the y variable.

From the given information, we have:

Sy = 22.77 kg

r = 0.303

Therefore,

s = sqrt((1 - 0.303^2) * 22.77^2) = 20.19 kg

The sample size is n = 100.

Substituting these values into the t-test formula, we get:

t = (65.89 - y_actual) / (20.19 / sqrt(100))

t = (65.89 - y_actual) / 2.019

We want to test at a 0.01 significance level, which corresponds to a two-tailed test with a critical value of t = ±2.576 (from a t-distribution with 98 degrees of freedom, since n-2=98).

If the absolute value of t is greater than 2.576, we reject the null hypothesis and conclude that the predicted weight is significantly different from the actual weight.

Substituting t = 2.576 and t = -2.576 into the t-test formula, we get:

2.576 = (65.89 - y_actual) / 2.019

y_actual = 53.45 kg

-2.576 = (65.89 - y_actual) / 2.019

y_actual = 78.32 kg

Therefore, at a 0.01 significance level, we reject the null hypothesis and conclude that the predicted weight of 65.89 kg is significantly different from the actual weight, which could be anywhere between 53.45 kg and 78.32 kg.

Answer: All of the slopes are the same.

Using the Pythagoras theorem, we can find the value of x to be = 10ft.

Option B is correct.

The right-angled triangle's three sides are related in line with the Pythagoras theorem, also referred to as the Pythagorean theorem. The hypotenuse of a triangle's other two sides add up to a square, according to the Pythagorean theorem, which states that.

Here in the question,

We have 2 right-angled triangles.

So, base of the large triangle, x

= √ (13² - 12²) + √ (13² - 12²)

= √ 5² + √ 5²

= 5 + 5

= 10ft.

Therefore, the length of the side, x = 10ft.

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Using the fundamental identities, the equivalent expressions are hereby matched as follows:

a. 2 csc (θ) cot (θ) = 2 sin²(θ) / (sin(θ) + cos(θ))

b. 2 sec (θ) tan (θ) = (2 sec²(θ)) - 2 sec(θ)

c. 2 cot (θ) = 2 / sin(θ) - csc(θ)

d. 2 csc² (θ) = 2 / (csc(θ) - 1)(csc(θ) + 1)

Using the fundamental identities, rewrite each expression as follows:

a. 2 csc (θ) cot (θ) = 2 / sin(θ) * cos(θ) = 2 cos(θ) / sin(θ) = 2 / sin(θ) - 2 / sin(θ) + 2 cos(θ) / sin(θ) = 2 / sin(θ) - 2 / (1 + cot(θ)) = (2 - 2 sin(θ)) / (sin(θ) + cos(θ)) = (2 sin²(θ)) / (sin(θ) + cos(θ))

b. 2 sec (θ) tan (θ) = 2 / cos(θ) * sin(θ) / cos(θ) = 2 sin(θ) / cos²(θ) = 2 / cos²(θ) - 2 / cos(θ) = (2 sec²(θ)) - 2 sec(θ)

c. 2 cot (θ) = 2 cos(θ) / sin(θ) = 2 / sin(θ) - 2 / sin²(θ) = 2 / sin(θ) - csc(θ)

d. 2 csc² (θ) = 2 / sin²(θ) = 2 / (1 - cos²(θ)) = 2 / (1 - cos(θ))(1 + cos(θ)) = 2 / (csc(θ) - cot(θ))(csc(θ) + cot(θ)) = 2 / (csc(θ) - 1)(csc(θ) + 1)

Therefore, the matches are:

a. 2 csc (θ) cot (θ) = 2 sin²(θ) / (sin(θ) + cos(θ))

b. 2 sec (θ) tan (θ) = (2 sec²(θ)) - 2 sec(θ)

c. 2 cot (θ) = 2 / sin(θ) - csc(θ)

d. 2 csc² (θ) = 2 / (csc(θ) - 1)(csc(θ) + 1)

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Therefore, the expression (7-3i) + (x - 2i)² - (4i + 2x²) in the simplest a + bi form is: -2x² - 1 - (4x + 7i)

Linear Equation                   General Form                    Example

Slope intercept form             y = mx + b                            y + 2x = 3

Point–slope form                   y – y1 = m(x – x1 )              y – 3 = 6(x – 2)

General Form                            Ax + By + C = 0               2x + 3y – 6 = 0

Intercept form                        x/a + y/b = 1                 x/2 + y/3 = 1

As a Function f(x) instead of y      f(x) = x + C                         f(x) = x + 3

The Identity Function                      f(x) = x                     f(x) = 3x

Constant Functions                      f(x) = C                       f(x) = 6

Let's start by expanding the square term (x - 2i)² using the formula for (a + b)²:

(x - 2i)² = x² - 4xi + 4i²

Note that i² = -1, so we can simplify this expression to:

(x - 2i)² = x² - 4xi - 4

Substituting this expression and the given values into the original expression, we get:

(7 - 3i) + (x² - 4xi - 4) - (4i + 2x²)

Grouping the real and imaginary terms, we get:

(7 - 4 - 2x²) + (-3i - 4i - 4x) + (x²)

Simplifying the real part, we get:

-2x² - 1

Simplifying the imaginary part, we get:

-7i - 4x

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A fair die is rolled twice, then the probability that the sum is greater than 10 is 1/12.

Finding the total number of possible outcomes when the dice is rolled twice:

A total of 6*6 = 36 outcomes are possible as there are 6 outcomes for the first roll and 6 outcomes for the second.

Making a list of all results that add up to greater than 10:

5 + 6 = 11

6 + 5 = 11

6 + 6 = 12

There are only three favorable outcomes.

So, the probability of getting a number greater than 10 =

[tex]\frac{no\ of\ favorable\ outcomes}{total\ number\ of\ possible\ outcomes}[/tex]

P(sum > 10) = 3/36 = 1/12

Therefore, there is a 1/12 probability that the sum of the two dice is greater than 10.

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The volume of the figure is equal 30 cubic feet.

The new volume of the figure is equal 60 cubic feet.

If Molly sells all of the dog beds, she would earn $6.25.

In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:

Volume of a rectangular prism = L × W × H

Where:

By substituting the given dimensions (parameters) into the formula for the volume of a rectangular prism, we have;

Volume of figure = 5 × 3 × 2

Volume of figure = 30 cubic feet.

When the height is doubled, we have;

Volume of figure = 5 × 3 × 2(2)

Volume of figure = 60 cubic feet.

For the cost of fabric used, we have:

Cost of fabric used = 2.5 × $4.50

Cost of fabric used = $11.25

Profit = selling price - cost

Profit = $17.50 - $11.25

Profit = $6.25.

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In the given diagram, the measure of angle BAC, m ∠BAC, is 66°

From the question, we are to calculate the measure of the unknown angle

In the given diagram, we have a circle

We are to calculate the measure of angle BAC, m ∠BAC

From one circle theorems, we have that

The angle subtended by an arc at the center of a circle is twice the angle subtended at the circumference

Thus,

From the give circle, we can write that

132° = 2 × m ∠BAC

Divide both sides by 2

132° / 2 = m ∠BAC

66° = m ∠BAC

Therefore,

m ∠BAC = 66°

Hence,

Measure of the angle is 66°

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Step-by-step explanation:

Q1. By linear pair, I know that 72* + unknown angle = 180*

therefore unknown angle = 180-72 = 108*

Now because this is a pentagon, the total of all interior angles of a polygon equals 540*

so 108* + 100* + 110* + 45* (Half of 90 , written as a semi-square) + Y* = 540

Y* = 540 - 363 = 177*

Q2. 360 - (80+70+110) = q

q = 360 - 220 =  140*


Q3. 160+160+ S* = 360*

360* - 320* = S*

S* = 40*

Hope it helps

the principal or invested amount is $41.38

The computation of the invest amount is given below:

As we know that

Principal = Amount ÷ (1 + rate × time)

= $48 ÷ (1 + 0.04 × 4)

= $48 ÷ 1.16

= $41.38

Hence, the principal or invested amount is $41.38

Basically we have applied the above formula so that the same would be calculated

The balance on the account of the Telkom account holder, every month was :

We know that May was one and half times June :

M = 1. 5 x J

July was R 50 more than June :

L = J + 50

Total spent was R 575 :

M + J + L = R 575

Then we can solve by substitution:
( 1. 5 J ) + J + ( J + 50 ) = 575

3. 5 J + 50 = 575

3. 5 J = 525

J = 525 / 3. 5 = R 150

L would be:

= 150 + 50

= R 200

M would be:

= 1. 5 x 150

= R 225

The balances for the Telkom account holder is therefore May - R 225, June - R 150, and July R 200.

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Answer:0.70

Step-by-step explanation:

The temperature is rising at a rate of 7.5 degrees Celsius per second along the bug's path after 2 seconds.

A derivative of a function with regard to an independent variable is defined as differentiation. In calculus, differentiation can be used to calculate the function per unit change in the independent variable.

We can use the chain rule of differentiation to find how fast the temperature is changing on the bug's path. Let T denote the temperature function, and let x and y be functions of time t given by x = sqrt(2) + t and y = 1 + t/2. Then the temperature function on the bug's path is given by T(x(t), y(t)), and we want to find dT/dt at t = 2.

Using the chain rule, we have:

dT/dt = dT/dx * dx/dt + dT/dy * dy/dt

We are given Tx(2, 9) = 7 and Ty(2, 9) = 1, so we can evaluate the partial derivatives at (x, y) = (2, 9):

dT/dx(2, 9) = 7

dT/dy(2, 9) = 1

To find dx/dt and dy/dt, we can take the derivatives of x and y with respect to t:

dx/dt = 1

dy/dt = 1/2

Now we can plug in the values:

dT/dt = 7 * 1 + 1 * 1/2

dT/dt = 7.5

Therefore, the temperature is rising at a rate of 7.5 degrees Celsius per second along the bug's path after 2 seconds.

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We refer to a function as periodic if it repeats across time with a fixed interval.

It is written as f(x) = f(x + p), where p denotes the function's period and is a real number.

Period is defined as the elapsed time between the two instances of the wave.

Here, we have,

A function's period is the amount of time between repetitions of the function. A trigonometric function's period is defined as the length of one complete cycle.

A periodic function is one whose values repeat at regular intervals. For instance, periodic functions include the trigonometric functions, which repeat every 2 pi radians.

Waves, oscillations, and other periodic events are all described by periodic functions in science. A period is the amount of time that separates two waves, whereas a periodic function is a function that repeats its values at regular intervals.

Each set of numbers that are separated by a comma in a number when expressed in standard form is known as a period. It has four periods, making it 5,913,603,800. The place value chart displays each period using a distinct color.

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Okay, to find the maximum number of shovels that can be produced with $10,000, we need to do the following:

1) Set the cost function C(N(h)) = 10,000. So: 990h + 430 = 10,000

2) Subtract 430 from both sides: 990h = 9,570

3) Divide both sides by 990: h = 9.75 (round to 10 hours)

4) Substitute 10 hours into the function for number of shovels:

N(10) = 30(10) = 300 shovels

Therefore, the maximum number of shovels that can be produced with $10,000 is 300 shovels.

Let me know if you have any other questions!

This distance in miles is 181.3 miles.

It's worth noting that the conversion factor of 1 kilometer equals 0.621371 miles is an exact value defined by international agreement, so there is no rounding involved in the conversion itself. The rounding occurs only when expressing the result in a specific number of decimal places. It's also worth noting that conversions between units of measurement are important in many fields, including science, engineering, and international trade.

To convert kilometers to miles, we can use the conversion factor of 1 kilometer equals 0.621371 miles. Therefore, to find the distance between Eilat and Jerusalem in miles, we can multiply the given distance of 292 kilometers by 0.621371:

292 km × 0.621371 = 181.344052 miles

Rounding this result to the nearest tenth gives:

181.3 miles

Therefore, the distance between Eilat and Jerusalem is approximately 181.3 miles.

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The calculated value of the surface area of the cuboid is 188cm²

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

This means that

Height = 168/24 = 7

Length = 24/4 = 6

The surface area of the cuboid is then calculated as

Area = 2 * (lw + wh + lh)

Substitute the known values in the above equation, so, we have the following representation

Area = 2 * (4 * 6 + 4 * 7 + 7 * 6)

Evaluate

Area = 188

Hence, the area is 188cm²

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