You can replace any letter in function notation with any number.

A.
True

B.
False

by trigonometry the magnitude of the force P so that the resultant force exerted on the stake is vertical. The magnitude of the force is 196.6 N.

When a force system acts on an item, the difference between the forces is referred to as the Resultant force. When an item is under the influence of two or more forces, the combined force may be calculated by adding up the separate forces. The forces in all directions will be the same for all the forces if they are all acting in the same direction. The SI unit for resultant force is the Newton.

Given that,

α = 30°

Using the triangle rule, and the law of sines:

120 N / Sin 30° = P / Sin 25°

or, P =  (Sin 25° /  Sin 30°) × 120

or, P = 101.428 N

or, P = 101.4 N

and also, θ = 180 - 25 - 30

θ = 125°

the value of resultant is:

120 N / Sin 30° = R / Sin 25°

or, R = 196.6 N

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Answer:

I. Radius, r = 5.82 in

II. S.A of a sphere = 19.61 meters

Step-by-step explanation:

Given the following data;

I. Volume of cylinder = 542π in³

Height = 16 in

To find the radius of the cylinder;

Volume of cylinder = πr²h

542π = πr²*16

Dividing both sides by π, we have;

542 = 16r²

r² = 542/16

r² = 33.875

Radius, r = 5.82 in

II. Volume of sphere = 5.055π m³

To find the surface area of the sphere;

First of all, we would find the radius of the sphere.

\( Volume \; of \; a \; sphere = \frac {4}{3} \pi r^{3} \)

Substituting into the formula, we have;

\( 5.055 \pi = \frac {4}{3} \pi r^{3} \)

Cross-multiplying, we have;

\( 5.055 \pi * 3 = 4 \pi r^{3} \)

\( 15.165 \pi = 4 \pi r^{3} \)

Dividing both sides by 4π, we have;

\( 3.79 = r^{3} \)

Taking the cube root of both sides, we have;

r = 1.56 m

Next, we find the surface area (S.A) of the sphere;

S.A of a sphere = 4πr

S.A of a sphere = 4*3.142*1.56

S.A of a sphere = 19.61 meters

The correct responses found using trigonometric ratios are as follows;

1. The depth of the water = 15 × tan(4°) = 1.049 m

The height of Brooke's boot = 1 m

Therefore;

2. The angle of elevation of the plan = arccos(99/100) ≈ 8.110°

Given that the angle of elevation the plan, 8.110°, is more than 8° limit, we find;

3. Height reached by the plane = 9 × tan(21°) = 3.455

Therefore;

4. Height of the chimney at the factory = 50 × tan(51°) = 61.745

The minimum chimney height = 65 m.

Therefore;

6. Length of the bridge = 72 × tan(55°) ≈ 102.83

Therefore;

7. Height reached by the ladder = 26 × sin(43°) ≈ 17.7

Therefore;

8. Height reached by the ski lift = 1000 × sin(29°) ≈ 484.8

Therefore;

9. Height reached by plane = 26 × tan(9°) ≈ 4.12

The plane flies under the cloud therefore;

10. Length required for the metal brace = 21/(cos(73°)) ≈ 71.83

Therefore;

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its x of course :)))

Answer:

5 (1 + 5)

Step-by-step explanation:

It would be this because the 5 would distribute itself multiplying into the 1 and other 5 equaling 5 + 25 and it is in the distributive property.

The weight of clothing is the ratio of weight to dye is different from the other ratios is B. 42 pounds.

Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).

It should be noted that from the information given, others have a ratio of 1:7. This is different for 42 pounds since the ratio is:

= 42/9

= 14:3

In conclusion, the correct option is B.

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Answer:

The tip was $14

Answer:

the answer is 29.1. hope this helped

Step-by-step explanation:

use a fkn calculator

Answer:

(a) all men = 3.6351 * 10^ -7

(b) all women = 2.3483* 10^ -4

(c) 8 men and 4 women = 0.0308

(d) 6 men and 6 women= 0.2170

Step-by-step explanation:

A jury pool has 15 men and 21 women, from which 12 jurors will be selected.

Total = 36 people

Probability of

(a) all men

= 15C12/36C12

= 455/1251677700

= 3.6351 * 10^ -7

(b) all women

= 21C12/36C12

= 293930/1251677700

= 2.3483* 10^ -4

(c) 8 men and 4 women

=( 15C8 * 21C4)/36C12

= (6435*5985)/1251677700

= 38513475/1251677700

= 0.0308

(d) 6 men and 6 women

= (15C6 * 21C6)/(36C12)

= (5005*54264)/1251677700

= 271591320/1251677700

= 0.2170

Answer:

0

Step-by-step explanation:

Slope = Δy/Δx

Slope = 10-10/4-1

Slope = 0/3

Slope = 0

It is a Horizontal Line

-Chetan K

if f is a bijection, then f-cube is also a bijection, and the inverse of f-cube is f^-1(y1/3). These results are important for understanding the properties of functions and their inverses.

Finding the inverse of the cube of a bijective function is an important step in understanding the properties of functions. To prove that f-cube is a bijection if f is a bijection, we can use the fact that for any two real numbers x and y, if x = y, then x1/3 = y1/3. This means that if f(x) = f(y), then (f(x))3 = (f(y))3, or f-cube(x) = f-cube(y). Since f is a bijection, this means that x = y, so f-cube is also a bijection.

To find the inverse of f-cube, we can use the fact that for any real number x, x1/3 is a well-defined real number. This means that if we have f-cube(x) = y, we can take the cube root of both sides to get f(x) = y1/3. Since f is a bijection, it has an inverse function f^-1, so we can apply this inverse to both sides to get x = f^-1(y1/3). This means that the inverse of f-cube is f^-1(y1/3).

In conclusion, if f is a bijection, then f-cube is also a bijection, and the inverse of f-cube is f^-1(y1/3). These results are important for understanding the properties of functions and their inverses.

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The grams of cocoa does it contains is 36.57 grams

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

Weight of the chocolate bar = 69

Proportion = 53%

This implies that

Grams of cocoa = weight of the chocolate bar * Proportion

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

Grams of cocoa = 53% * 69

Evaluate the products

Grams of cocoa = 36.57

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Answer:

Therefore, the angle ∠CDA is 58°.

Step-by-step explanation:

∠CDA = 58°

In the given figure, let's consider the angle ∠CDA as x.

Since AB is the diameter of the circle, we know that the angle subtended by any diameter at any point on the circumference is always 90°. Therefore, ∠CAB = 90°.

In triangle CAD, the sum of angles is 180°. So, we have:

∠CAD + ∠CDA + ∠CAB = 180°

Substituting the known values:

32° + x + 90° = 180°

Combining like terms:

x + 122° = 180°

Subtracting 122° from both sides:

x = 180° - 122°

x = 58°

Answer:

This is the answer!!!

Step-by-step explanation:

(-2, 10].

First of all, let's refresh the concepts of domain and range when talking about mathematical functions.

In simple terms, the domain of a function are the values that the function can work with, the allowed inputs, which happen to be the same as values of the common used variable "x", the dependent variable. We can easily tell the domain of a by looking at its horizontal extension, what values of "x" it passes by.

Now, the domain is the total opposite, those are the outputs, or the "y" values that the function returns after evualiating an "x" value. These can be seen by analyzing the vertical extension of the graph, what values of "y" the function can reach.

In the given graph, we may see that the lowest "y" value the graph outputs (vertically) is -2, and we also see that the circle in that number doesn't have a fill color, it's transparent, that means that tne function doesn't contain the value of -2. Therefore, y > -2. Now, on the upper end of the function, we can see that highest "y" value the function can reach is 10, marked with a filled circle, which means that the function contains said value, hence, y ≤ 10.

Now, writting in interval notation, remember that the square brackets "[]" are meant to be used next to a value that the function contains. Also, the parentheses "()" are meant to a value that the function doesn't contain.

Previously, we mentioned that the function doesn't contain value "-2", therefore, we may write:

(-2...

Now, to finish writting the interval, we mentiones that value 10 is contained in the function, hence, we finish writting the interval notation as follows:

(-2, 10].

Final answer: (-2, 10].

When writting in interval notaion, the symbol of infinity "∞" must always be written next to a parenthesis symbol.

Answer:

\(\boxed {x < 4}\)

Step-by-step explanation:

Solve the given inequality:

\(5x - 1 < 2x + 11\)

-Take \(2x\) and subtract it from \(5x\):

\(5x - 1 - 2x < 2x - 2x + 11\)

\(3x - 1 < 11\)

-Add both sides by \(1\):

\(3x - 1 + 1 < 11 + 1\)

\(3x < 12\)

-Since \(3\) is positive, then the inequality sign remains the same. So, divide both sides by \(3\):

\(\frac{3x}{3} < \frac{12}{3}\)

\(\boxed {x < 4}\) (final answer)

29 years from now, the father will be 49 years old.

Let's start by setting up the given information:

Currently, the father is 20 years old, and the son is 5 years old.

In 10 years, the father will be twice as old as the son.

The father is currently four times as old as the son.

Determine the age of the father and son in 10 years:

In 10 years, the father's age will be 20 + 10 = 30 years.

In 10 years, the son's age will be 5 + 10 = 15 years.

Write equations based on the given information:

The father's age in 10 years will be twice the son's age in 10 years: 30 = 2 × 15.

The father's current age is four times the son's current age: 20 = 4 × 5.

Solve the equations:

From the second equation, we find that the son's current age is 5 years.

Plugging this value into the first equation, we get: 30 = 2 × (5 + 10).

Simplifying further, we have: 30 = 2 × 15, which is true.

Determine the current age of the son in 29 years:

The son's current age is 5 years.

Adding 29 years to the son's current age, we find that the son will be 5 + 29 = 34 years old.

Determine the current age of the father in 29 years:

The father's current age is 20 years.

Adding 29 years to the father's current age, we find that the father will be 20 + 29 = 49 years old.

Therefore, 29 years from now, the father will be 49 years old.

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If he wants an average of 84, he needs to get at least 93 points.

Remember that the average value between 3 values A, B, and C is:

(A + B + C)/3

Here we know that the first two scores are 76 and 83 points, let's say that the third score is x, if we want to have an average of 84 or more, then we need to solve:

(76 + 83 + x)/3 = 84

159 + x = 252

x = 252 - 159

x = 93

So he needs to get at least 93 points in the next exam.

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Answer:

qs,wdnfm.ew fw v

Step-by-step explanation:

wdmc vw.mv / n,v

Answer:

15/49

Step-by-step explanation:

3*10=30

14*7=98

30/98

15/49

Relative interest refers to the comparison of interest rates between different financial instruments or investment opportunities. It allows individuals or investors to assess and evaluate the attractiveness of various options based on their potential returns.

1. Understand the basic concept: Interest is the cost of borrowing money or the return earned on invested funds. Relative interest involves comparing the interest rates of different financial instruments or investments to determine which one offers a more favorable return.

2. Identify the investment options: Start by identifying the different investment opportunities or financial instruments available. These can include savings accounts, certificates of deposit (CDs), bonds, stocks, or other investment vehicles.

3. Research interest rates: Research and gather information about the current interest rates offered by each investment option. This information can usually be found on financial websites, through financial institutions, or by consulting with a financial advisor.

4. Compare interest rates: Once you have the interest rates for each investment option, compare them side by side. Look for the differences in rates and identify which options offer higher or lower returns.

5. Assess risk and return: Consider the level of risk associated with each investment option. Higher returns often come with higher risk, so it's essential to evaluate the risk-reward tradeoff.

6. Make an informed decision: Based on the comparison of interest rates and the risk-reward assessment, make an informed decision on which investment option aligns with your financial goals and risk tolerance.

Always remember to consider your financial goals, risk tolerance, and consult with a financial advisor if needed.

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Answer: p/7 + 8

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

4. Between 11:30 and 12:00, they did nothing. The graph didn't go up or down, it just stayed the same meaning they did nothing.

5. 5 miles an hour

Step-by-step explanation:

Answer:

a. will also not be rejected at the 1% level.

Step-by-step explanation:

A hypothesis is rejected if:

The p-value is larger than the significance level.

Hypothesis is not rejected at a 5% level of significance

This means that the p-value is > 0.05.

At the 1% level:

p-value > 0.01, so it will never be rejected, and thus, the correct answer is given by option a.

Using the percentage concept, it is found that 60% of the students voted to donate a telescope.

The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:

\(P = \frac{a}{b} \times 100\%\)

In this problem:

The percentage is given by:

\(P = \frac{300}{500} \times 100\% = 60\%\)

60% of the students voted to donate a telescope.

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Answer:

#1 ((2, 0), (3, 2), (5, 1)) = right isoceles triangle ✔️

#2 ((4, 2), (6, 2), (5, 3.73)) = acute isosceles triangle ❌

so it is not part of graph

#3 ((-5, 2), (-4, 4), (-2, 2)) = Acute scalene triangle ✔️

#4 ((-3, 1), (-3, 4), (-1, 1)) = Right scalene triangle (or right triangle)✔️

#5 ((-4, 2), (-2, 4), (-1, 4)) = Obtuse scalene triangle ✔️

Step-by-step explanation:

the triangles are correct

Answer:

(2,0), B(3,2),C(5,1) is isosceles right angel

(-5,2), B(-4,4), C(-2,2) acute scalene triangle

(-3,1), B(-3,4), C(-1,1) right angel

(-4,2), B9-2,4), C(-1,4) obtuse scalene triangle

Step-by-step explanation:

Answer:

Length of side AB = 5

Step-by-step explanation:

A regular polygon is one in which all angles are equal and all the sides have the same length.

Now, it means that;

AB = BC = CD = DE = AE

We are told that BC is represented by 3x - 4 while DE is represented by the expression 4x - 9.

Thus, from equal length of sides of a regular polygon, we have;

3x - 4 = 4x - 9

4x - 3x = 9 - 4

x = 5

Thus, length of BC = 3(5) - 4 = 15 - 4 = 11

Therefore, Length of AB = 5

Answer:

26, -0.85, 17

Step-by-step explanation:

hi! so for 14, you can plug in -11 for every x in the equation.

f(-11)= 15-(-11)

=15+11

=26

your answer is 26.

for 15, we can plug in 0.3 for x.

g(0.3)=-2.5(0.3)-0.1

= -0.75-0.1

= -0.85

your answer is -0.85.

for 16, you can plug in -17 for x.

f(-17)= -(-17)

=17

your answer is 17.

Answer:

14:   26

15: -8.5

16:  17

Step-by-step explanation:

The f(x) basically gives you what x is, as the inside of parenthesis means the value of x. You then can plug in x into the equation for each of the equations. Whenever you get something like 24- (-42) The negatives cancel out and you add the two values together instead.

Hope this helps!

Answer:

Value of equation = 144

Step-by-step explanation:

Given:

5g + 7g + g(5 + 7)

when g = 6

Find:

Value of equation

Computation:

5g + 7g + g(5 + 7)

5g + 7g + g(12)

5(6) + 7(6) + (6)(12)

30 + 42 + 72

Value of equation = 144