A CONVERSATION BETWEEN
SIN(X) AND TAN(X)?

Answer:

\(a_{n}\) = 8\(a_{n-1}\) ; a₁ = - 2

Step-by-step explanation:

a recursive formula in a geometric sequence allows a term to be found by multiplying the preceding term by the common ratio r

here r = \(\frac{a_{2} }{a_{1} }\) = \(\frac{-16}{-2}\) = 8 , then

\(a_{n}\) = 8\(a_{n-1}\) ; a₁ = - 2

Answer:

Step-by-step explanation:

To calculate the probability of winning any amount of money, we need to sum up the probabilities of winning each individual prize.

Given the probabilities stated on the game card:

Probability of winning $10 prize = 0.2

Probability of winning $5 prize = 0.1

Probability of winning $0 prize = 0.7

To find the probability of winning any amount of money, we add these probabilities together:

0.2 + 0.1 + 0.7 = 1

The sum of the probabilities is 1, which indicates that the total probability of winning any amount of money is 1 or 100%.

Therefore, the probability of winning any amount of money in this game is 100%.

Hope this answer your question

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The amount of force used to pull the cart from 60 N to 90 N, the new acceleration of the cart is, 1.5 m/s²

The definition of force is the pushing or pulling of anything. Push and pull are the result of two things interacting with one another. Stretch and crush are two more phrases that can be used to describe force.

Formula of force,

F = ma

Given that,

A man pulled a cart filled with stones that had a total mass of 60 kg

He increased the amount of force used to pull the cart from 60 N to 90 N

New acceleration of cart = ?

F  = ma

Old acceleration,

60  = 60a

a   =  1 m/s²

New acceleration,

90 = 60a

a   = 90/60

a   =  3/2

a   =  1.5 m/s²

Hence, the new acceleration is 1.5 m/s²

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Answer:

45% are female -> 72

100% are total -> x

x= 72• 100/45

x= 7200/45

x= 160

total= male+female

160= male + 72

male= 88

The product of the two linear functions is:

(fg)(x) =  8x^2 + 10x  - 3

A general linear funuction can be written as:

f(x)= a*x  +b

Let's say that our functions are:

f(x) = ax + b

g(x) = cx + d

The sum is:

(f + g)(x) = ax + b + cx + d = (a + c)x + (b + d)

(f - g)(x) = ax + b - cx - d  =(a - c)x + (b - d)

And we know that:

(f+g)(x)=-6x-2 and (f-g)(x)=-2x+4.

Then we can write:

(a + c)x + (b + d) = -6x - 2

(a - c)x + (b - d) = -2x + 4

Then we have 4 equations:

a + c = -6

b + d = -2

a  - c= -2

b - d = 4

Solving these we can get:

a = -4

c = -2

b = 1

d = -3

(you can check these values)

The two linear functions are:

f(x) = -4x + 1

g(x) = -2x - 3

The product is:

(fg)(x) = (-4x + 1)*(-2x - 3) = 8x^2 + 12x - 2x - 3

                                       = 8x^2 + 10x  - 3

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Answer: no she dosen't

Step-by-step explanation:

If you were to add up all three numbers

49.95+19.95+21.95=91.85

Which means she is $1.85 short to buy all of the items

Answer:

The answer is 60cm^2.

hope it helps..

The maximum area of a Norman window with a perimeter of 9 feet is 81π/4 square feet.

To find the maximum area of a Norman window with a given perimeter, we can use calculus. Let's denote the radius of the semicircle as r and the height of the rectangular window as h.The perimeter of the Norman window consists of the circumference of the semicircle and the sum of all four sides of the rectangular window. Therefore, we have the equation:

πr + 2h = 9We also know that the area of the Norman window is the sum of the area of the semicircle and the area of the rectangle, given by:

A = (πr^2)/2 + rh

To find the maximum area, we need to express the area function A in terms of a single variable. We can do this by substituting r from the perimeter equation:

r = (9 - 2h)/(π)

Now we can rewrite the area function in terms of h only:

A = (π/2) * ((9 - 2h)/(π))^2 + h * (9 - 2h)/(π)

Simplifying this equation, we get:

A = (1/2)(9h - h^2/π)

To find the maximum area, we differentiate the area function with respect to h, set it equal to zero, and solve for h:

dA/dh = 9/2 - h/π = 0

Solving this equation, we find:h = 9π/2

Substituting this value of h back into the area function, we get:

A = (1/2)(9 * 9π/2 - (9π/2)^2/π) = (81π/2 - 81π/4) = 81π/4

Therefore, the maximum area of a Norman window with a perimeter of 9 feet is 81π/4 square feet.

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The solution to the equation is x = 10 or x = -2.

An equation refers to a mathematical expression showing that two expressions are equal.

It must have variables (e.g. a, c, x, y), constants (like 1, 13, 50, etc), and mathematical operations (like +, -, *, /).

To solve for x, we shall start with the given equation:

x + 6 = √(2x + 29) + 9

Subtract 9 from both sides:

x - 3 = √(2x + 29)

Square both sides:

\((x - 3)^2\) = 2x + 29

Expand the left side:

\(x^2\) - 6x + 9 = 2x + 29

We then subtract 2x and 9 from both sides:

\(x^2\) - 8x - 20 = 0

Next, actor the quadratic equation:

(x - 10)(x + 2) = 0

Therefore, the equation x = 10 or x = -2

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Each expression with its equivalent expression are as followed:

(-3⁻²)⁰                  ⇒            1

3³. 3¹ . 3² .3⁻¹²     ⇒        1/729

-3⁵ ÷ -3⁸              ⇒        - 1/27

-3³ · 3³                ⇒         -729

A base number raised tο an expοnent is referred tο as a pοwer in mathematics, where base number is the factοr that is multiplied by itself and expοnent is the number οf times the same base number is multiplied.

When a base number is multiplied by an expοnent, it is said tο have been raised tο that expοnent. The base number is the factοr that is being multiplied by itself, and the expοnent represents hοw many times the base number has been multiplied.

a)  (-3⁻²)⁰

   since power of any number is 0 = 1

        (-3⁻²)⁰   =  1

b)  3³. 3¹ . 3² .3⁻¹²

    3³⁺¹⁺²⁻¹²

    =  3⁶⁻¹²

    = 3⁻⁶

    = 1/3⁶

    = 1/729

c)  -3⁵ ÷ -3⁸

    = -3⁵⁻⁸

    = -3⁻³

    = - 1/3³

    = - 1/27

d) -3³ · 3³

   = (-3 · 3)³

   = (-9)³

    = -729

Thus, we have the table as,

(-3⁻²)⁰                  ⇒            1

3³. 3¹ . 3² .3⁻¹²     ⇒        1/729

-3⁵ ÷ -3⁸              ⇒        - 1/27

-3³ · 3³                ⇒         -729

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Answer:

Linear positive association

The correct answer is option D: A line passes through the point (0, 0) and continues through the point (12, 3)

For the first question:

The table shows a proportional relationship between x and y. To describe what the graph of this proportional relationship would look like, we can examine the given data points.

The data points are (12, 3), (8, 26), and (24, ?). We can observe that as x increases, y also increases. This indicates a positive correlation between the variables. Additionally, we can see that the ratio of y to x remains constant for each data point.

Now, let's analyze the answer options:

A. A line passes through the point (0, 0) and continues through the point (3, 12).

This answer option does not align with the given data because there is no data point with an x-value of 3 and a corresponding y-value of 12.

B. A line passes through the point (0, 0) and continues through the point (2, 8).

This answer option aligns with the given data because (2, 8) is a valid data point from the table, and the line passes through the origin (0, 0).

C. A line passes through the point (0, 0) and continues through the point (6, 24).

This answer option does not align with the given data because there is no data point with an x-value of 6 and a corresponding y-value of 24.

D. A line passes through the point (0, 0) and continues through the point (12, 3).

This answer option aligns with the given data because (12, 3) is a valid data point from the table, and the line passes through the origin (0, 0).

Based on the analysis, the correct answer is option D: A line passes through the point (0, 0) and continues through the point (12, 3). This accurately represents the graph of the proportional relationship given in the table.

For the second question, I'm sorry, but you didn't provide the multiple-choice options or the complete question. Could you please provide the question and options so that I can assist you further?

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Answer:

(10, 5π/3)

Step-by-step explanation:

To convert rectangular coordinates (5, -5√3) to polar form, we can use the following formulas:

r = √(x^2 + y^2)

θ = arctan(y/x)

Substituting the given values, we get:

r = √(5^2 + (-5√3)^2) = √(25 + 75) = √100 = 10

θ = arctan((-5√3)/5) = arctan(-√3) = -π/3

Note that the value of θ is in the fourth quadrant, which corresponds to a negative angle. However, we need to express the angle θ in the range 0 ≤ θ < 2π. To do this, we can add 2π to the angle if it is negative:

θ = -π/3 + 2π = (5π/3)

Therefore, the rectangular coordinates (5, -5√3) in polar form are (10, 5π/3).

Step-by-step explanation:

remember, the sum of all angles in a triangle is always 180°.

1. you mean find the angle at A, yes ?

180 = angle A + angle B + angle C =

= angle A + 38 + 90

angle A = 180 - 38 - 90 = 90 - 38 = 52°

2. Pythagoras

AB² = 11² + 8.5² = 121 + 72.25 = 193.25

AB = 13.90143877... in

3. sine/cosine ratio is tangent.

sin(38) × AB = 8.5 in

cos(38) × AB = 11 in

sin(38)/cos(38) = tan(38) = 8.5/11 = 0.772727272...

sin(52) × AB = 11 in

cos(52) × AB = 8.5 in

sin(52)/cos(52) = tan(52) = 11/8.5 = 1.294117647...

4. they are equal. as sin(x) = cos(90-x).

5. they are equal. as cos(x) = sin(90-x).

6. 90°. again, the sum of all angles must be 180°. so, when one angle is all by itself already 90°, then there are only 90° left for the other 2 angles.

7. not sure what you mean by "kissing angles" but

a. sin(40°) = cos(90-40) = cos(50°) = 0.64278761...

b. cos(27°) = sin(90-27) = sin(63°) = 0.891006524...

c. sin(90°) = cos(90-90) = cos(0°) = 1

d. cos(65°) = sin(90 - 65) = sin(25°) = 0.422618262...

If the null hypothesis is correct, the probability that the test will result in a type 1 mistake is what is known as the alpha level for a hypothesis test. In other words, even in the absence of a treatment effect, the alpha level impacts the likelihood of collecting sample data in the critical zone.

The alpha level establishes the boundaries for identifying the key area that results in "extremely unlikely" or significant results that deviate from the null hypothesis. The likelihood of making a Type I error is one in twenty, according to researchers who use an alpha value or level of significance of.05.

The chance of rejecting the null hypothesis when it is true is known as the significance level, which is alternatively written as alpha or. For instance, a significance level of 0.05 represents a 5% probability of assuming the existence of a difference when none actually exists.

Hence we get the required answer.

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Answer:

$17,440

Step-by-step explanation:

the interest every year

=$16,000×3%

=$16,000×3/100

=$480

the balance after 3 years

=$16,000+3($480)

=$16,000+$1,440

=$17,440

You need to find the area of the hexagon, and the area of the triangle.

The formula for the area of a triangle is

\(a = \frac{bh}{2} \)

I hope this helps you a little.

Answer:

93.5 units^2

Step-by-step explanation:

a^2+b^2=c^2

a=3

b=?

c=6

b=√6^2-3^2

b=3√3=5.196

5.196×3=15.5884

15.5884×6

Answer:

x = 11.8

Step-by-step explanation:

Side a = 11.78983

Side b = 3

Side c = 10

Angle ∠A = 120° = 2.0944 rad = 2/3π

Angle ∠B = 12.731° = 12°43'50" = 0.22219 rad

Angle ∠C = 47.269° = 47°16'10" = 0.82501 rad

The answer for x is 11.8

If it is ....

\(3 {x}^{2} - 2x + 1 = \)

The coefficient of x² is (( 3 ))

& the coefficient of x is (( -2 ))

_________________________________

If it is .....

\(3x - 2x + 1\)

\(x + 1\)

The coefficient of x² is (( zero 0 ))

& the coefficient of x is (( 1 ))

The probability that a member of the drama club is a sophomore is3/17.

Probability is a measure of how probably an event is to do. Numerous events are insolvable to read with absolute delicacy. We can only anticipate the possibility of an event being, i.e. how probable they're to do, using it.

Probability can range from 0 to 1, with 0 indicating an insolvable event and 1 indicating a certain event. Probability for Class 10 is an important content for scholars because it discusses all of the abecedarian ideas of this discipline. The probability of all events in a sample space equals one.

In this, we've to find the probability of a drama club member who's also a sophomore.

Member of drama club who's sophomore = 3

Total number of members of drama club = 17

Probability = member of drama club who's sophomore/ total number of members of drama club

= 3/ 17.

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Answer: h = 22.5

Step-by-step explanation:

Total angle area of a 12 sided polygon is 1800

1. One angle would be 1800/12= 150

2. Add 30 one each side to cancel out and only leave 8h.

3. To get rid of the 8 we divide the the other side by 8.

The answer is 22.5

Answer: D 22.5 i got it right on the exam

Step-by-step explanation:

Answer:

x + 5 + 5x + 10 + 2y = 6x + 2y + 15

Step-by-step explanation:

Group like terms

= x + 5x + 2y + 5 + 10  

Add the number 5 + 10 = 15  

= x + 5x + 2y + 15

Add similar elements x + 5x = 6x  

= 6x + 2y + 15

Have a good day :)

The top left graph represents the weight of the radioactive isotope over time.

An exponential function has the definition presented according to the equation as follows:

\(y = ab^x\)

In which the parameters are given as follows:

The parameter values for the function in this problem are given as follows:

a = 96, b = 0.5.

Hence the function is given as follows:

\(y = 96(0.5)^x\)

Two points on the graph of the function are given as follows:

(1,48) and (2, 24).

Hence the top left graph represents the weight of the radioactive isotope over time.

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Answer:

Graph W

Step-by-step explanation:

The given information describes a radioactive decay process, where the weight of the isotope decreases by half at regular intervals. This type of decay is characteristic of exponential decay.

Based on the description, the graph that represents the weight of the radioactive isotope over time would be a decreasing exponential curve, where the y-axis represents the weight of the isotope (in grams), and the x-axis represents time (in hours).

The initial weight of the isotope is 96 grams, and after each subsequent hour, the weight becomes half of what it was in the previous hour. Therefore, the correct graph would start at 96 grams (the initial weight when x = 0) and then decrease by half every hour. It would be a curve that gets closer and closer to zero but never quite reaches it.

Initial weight: 96 grams

After 1 hour: 96 / 2 = 48 grams

After 2 hours: 48 / 2 = 24 grams

After 3 hours: 24 / 2 = 12 grams

After 4 hours: 12 / 2 = 6 grams

After 5 hours: 6 / 2 = 3 grams

So, the points on the graph would be:

Therefore, the graph that represents the weight of the radioactive isotope over time is Graph W.

Answer:

2m³ + 9m² - 19m - 11

Step-by-step explanation:

3f(m) - 2g(m)

= 3(3m² - 5m + 1) - 2(- m³ + 2m + 7) ← distribute parenthesis

= 9m² - 15m + 3 + 2m³ - 4m - 14 ← collect like terms

= 2m³ + 9m² - 19m - 11

C. e

Step-by-step explanation:

\( ln( {e}^{e} ) = e ln(e ) = e(1) = e\)

Answer:

option d.opposite / adjacent

Step-by-step explanation:

opposite /adjacent ratio represents the tangent of an angle .

hope it is helpful to you ☺️

Answer:

D.

Step-by-step explanation:

From the trigonometry shortcuts we can use the acronyms:

SOH  CAH  TOA

for an arbitrary angle Ф, plug in the length of the sides:

sin(Ф) = opposite/hypotenuse

cos(Ф) = adjacent/hypotenuse

tan(Ф) = opposite/adjacent

Answer: How to solve your question

Your question is

4

(

+

5

)

−

4

=

4

4(x+5)-4=4

4(x+5)−4=4

Solve

1

Distribute

4

(

+

5

)

−

4

=

4

{\color{#c92786}{4(x+5)}}-4=4

4(x+5)−4=4

4

+

2

0

−

4

=

4

{\color{#c92786}{4x+20}}-4=4

4x+20−4=4

2

Subtract the numbers

3

Subtract  

1

6

16

16

from both sides of the equation

4. Simplify

5. Divide both sides of the equation by the same term  

6. Simplify

Solution  

=

−

3

Step-by-step explanation: I got this from a website but i hope this helps!!!!

The way the numbers will be placed in the square box will be:

First row = 4 12 14

Second row = 2 10 18

Third row = 6 8 16

It should be noted that the question is simply about adding the numbers and getting 39 in each place.

This will be:

First row = 4 12 14 = 4 + 12 + 14 = 30

Second row = 2 10 18 = 2 + 10 + 18 = 30

Third row = 6 8 16 = 6 + 8 + 16 = 30

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Answer:  B. 78

Step-by-step explanation:

Given:

BC=CD

all the other sides of each triangle are radii, so they are all equal the 2 triangles are congruent.

>Both angles A =78

An angle from the radius is the same as the arc angle it creates.

The arc angle is double only if the angle touches the end of the circle not the radius.  that's why it's not 156

So, <BAC =78   so arc angle BC=78