Use the triangle below to determine which of the following statements are true a. (Sin A)^2 + ( Cos A)^2=1.

The answers of the given question based on the probability to tick pair of events is independent or not independent the answer is (1)  ✔ Independent (2)  ✔ Not independent (3) ✔ Independent.

An event is  subset of possible outcomes in  random experiment or situation. In probability theory,  event is defined  any set of outcomes that can be assigned  probability. Events can be simple, consisting of  single outcome, or compound, consisting of two or more outcomes.

Events are  essential concept in probability theory, as they allow us to reason about  likelihood of different outcomes in uncertain situations.

The pairs of events  can be analyzed as follows:

(1) Pick a disk from a box at random and replace it.

   Pick another disk from the same box at random.

These events are independent because the outcome of the first event does not affect the outcome of the second event. Each pick is like starting with a fresh box, and the probability of picking any particular disk is the same for each pick.

Tick: ✔ Independent

(2) Pick a disk from a box at random and do not replace it.

    Pick another disk from the same box at random.

These events are not independent event because the outcome of the first event affects the outcome of the second event. After the first pick, there is one less disk in the box, and the probability of picking any particular disk changes for the second pick.

Tick: ✔ Not independent

(3) Pick a disk from a box at random and do not replace it.

    Roll a dice.

These events are independent because the outcome of one event does not affect the outcome of the other event. Picking a disk and rolling a dice are unrelated actions and one doesn't affect the outcome of the other.

Tick: ✔ Independent

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The value of 3/12 of 100 is 25 .

In the question ,

a fraction 3/12 is given ,

we have to find the value of 3/12 of 100 .

to find the value , we first convert both the numbers into fraction

So 100 in fraction form can be written as 100/1

So the value 3/12 of 100 means

= \(\frac{3}{12} *\frac{100}{1}\)

multiplying the numerator with numerator

and multiplying denominator with denominator .

we get = 300/12

on further  simplification ,

we have ,

= 75/3

= 25

So , 3/12 of 100 = 25

Therefore , The value of 3/12 of 100 is 25 .

The given question is incomplete , the complete question is

What is the value of 3/12 of 100 ?

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Answer:

the 3rd answer

Step-by-step explanation:

:)

The correct answer is C.

All you have to do is count each letter. The amount you get is the number to the right of the letter.

For example: There are 6 Carbons, 12 Hydrogens, and 2 Oxygens. Your answer shows the correct form is should be in, C6H12O2

The size of this year's offspring pumpkins in your pumpkin patch is correlated with the sizes of their midparent pumpkins, with a regression line slope of 0.75.

To interpret the given information, we can break it down into the following steps:

1. Regression Line Slope: The slope of the regression line indicates the strength and direction of the relationship between the sizes of the offspring pumpkins and their midparent pumpkins. In this case, the slope is given as 0.75.

2. Correlation: The positive slope of 0.75 suggests a positive correlation between the sizes of the offspring pumpkins and their midparent pumpkins. This means that as the size of the midparent pumpkin increases, the size of the offspring pumpkin tends to increase as well.

3. Magnitude of the Slope: The magnitude of the slope (0.75) indicates the degree of correlation. A slope close to 1 suggests a strong positive correlation, meaning that the sizes of the offspring pumpkins closely follow the sizes of their midparent pumpkins.

4. Progeny's Size Prediction: With a known slope of 0.75, you can use the regression line equation to predict the size of the offspring pumpkins based on the sizes of their midparent pumpkins.

In summary, the given slope of 0.75 indicates a positive correlation between the sizes of the offspring pumpkins and their midparent pumpkins. This information can be used to predict the size of the offspring pumpkins based on the sizes of their midparent pumpkins in your pumpkin patch.

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Answer:

38.3 =x or x=141.8

Step-by-step explanation:

Using the law of sines

sin 27         sin x

----------- = ------------

11                   15

Using cross products

15 sin 27 = 11 sin x

15/11 sin 27 = sin x

Taking the inverse sin of each side

sin^-1 (15/11 sin 27 )= sin ^-1(sin x)

38.24883302 =  x

To the nearest tenth

38.2 =x

or

x=141.8

Answer:

38.2 degrees

Step-by-step explanation:

Use the law of sines

(sin 27)/11=(sinx)15

15sin(27)=11sin(x)

[15sin(27)]/11=sin(x)

x=arcsin[15sin(27)]/11

rounded to nearest tenth, x=38.2

Answer:

49

Step-by-step explanation:

Multiply out (a+b)^2

(a+b)^2 = (a+b)(a+b) = a^2 + ab + ba + b^2 ; not ab = ba so,

= a^2 + 2ab + b^2 = a^2 + b^2 + 2ab ; now subtitue in given values

=25 + 2(12) = 25 + 24 = 49

So (a+b)^2 = 49

Answer:

i need the answer ;(

Step-by-step explanation:

An alpha particle with a charge of +2e and a mass of 6.64 × 10^-27 kg enters an electric field of 1.2 × 10^3 N/C. The alpha particle is accelerated from rest through a distance of 3.7 cm.

Find the speed of the alpha particle when it emerges from the electric field and the time taken to travel the distance.   More than 100 words.Electric fields accelerate charged particles. Alpha particles have a charge of +2e and a mass of 6.64 × 10^-27 kg, where e is the fundamental unit of charge.

The electric field that is responsible for the acceleration of the alpha particle can be calculated as follows:F = EqWhere F is the electric force, E is the electric field, and q is the charge of the particle.

The electric field can, therefore, be calculated as:E = F/qE = (2 × 1.6 × 10^-19) / (6.64 × 10^-27)E = 1.2 × 10^3 N/CThe alpha particle is accelerated from rest, meaning that its initial velocity is zero.  

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ANSWER:

$366.89

Given:

Cost of a gallon of paint = $29.95

x gallons of paint will cost: $29.95 * x gallons

Since Nikki needs 12.25 gallon of paints, the price she would spend on paint will be:

Nikki will spend $366.89 to complete the painting project

According to the given standard deviation, the engineer would need a sample size of at least 75 wires to estimate the mean length to within 0.025 feet with 99% confidence.

To estimate the mean length of the wires being cut, the engineer needs to determine the sample size needed to achieve a certain level of confidence and level of precision. In this case, the engineer wants to estimate the mean length to within 0.025 feet with 99% confidence. This means that there is a 99% chance that the true population mean falls within the estimated range.

To determine the sample size needed, the engineer can use a formula that takes into account the desired level of confidence, level of precision, and the standard deviation of the population. The formula is:

n = (z² x s²) / E²

Where:

n = sample size needed

z = z-score for desired level of confidence (99% = 2.58)

s = standard deviation of the population (0.15 feet)

E = level of precision (0.025 feet)

Plugging in the values, we get:

n = (2.58² x 0.15²) / 0.025²

n = 74.83 ≈ 75

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Answer:

Simplify  14 x 2 to 28

x=28

Answer:

The equation after applying the Distributive property:

6 = 9x + 27

The equation solved:

x = -2.33333333

Step-by-step explanation:

The distributive property means that you will multiply the items inside of the parenthesis by the number right out side, in this case (x + 3) by 9.

9 * x = 9x

9 * 3 = 27

our new equation will look like:

6 = 9x + 27

now we will be able to solve!

let’s start by subtracting 27 from both sides.

27 - 27 = 0

6 - 27 = -21

9x = -21

divide both sides by 9.

9x/9 = x

-21/9 = -2.33333333

x = -2.33333333

The value of x from the given equation is x=-7/3.

The given equation is 6=9(x+3).

The distributive property states that an expression which is given in form of A (B + C) can be solved as A × (B + C) = AB + AC.

Using distributive property

6=9(x+3)

⇒ 6=9x+27

⇒ 9x=-21

⇒ x=-21/9

⇒ x=-7/3

Therefore, the value of x from the given equation is x=-7/3.

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Main Answer: The total area is 26.5 square units.

Supporting Question and Answer:

How can the integral of the absolute value of a function be split into multiple intervals?

When dealing with the integral of the absolute value of a function over an interval, if the function changes its behavior or slope within that interval (such as crossing the x-axis or changing sign), the integral needs to be split into multiple intervals based on those points of change. Each interval is then integrated separately, considering the appropriate sign of the function within each sub-interval, to obtain the total area.

Body of the Solution:To find the total area between the graph of the function f(x)=−x−1 and the x-axis over the interval [−3,6],we need to integrate the absolute value of the function over that interval.

Since the function is negative in the given interval, we can rewrite it as f(x)=∣x+1∣ to simplify the calculations.

To find the total area, we need to evaluate the integral of ∣f(x)∣ over the interval [−3,6]:

Total Area=    \(\int\limits^6_{-3} {|f(x)|} \,dx\)

Since the function f(x)=∣x+1∣ changes its slope at x=−1, we need to split the integral into two parts:

Total Area=   \(\int\limits^{-1}_{-3} {-(x+1)} \, dx +\int\limits^6_{-1} {(x+1)} \, dx\)

Simplifying and evaluating each integral:

Total Area=\([-\frac{1}{2}(-1)^{2} -(-1)]-[-\frac{1}{2}(-3)^{2} -(-3)]+[\frac{1}{2} (6^{2})+6]-[\frac{1}{2} (-1)^{2}+(-1)]\)

Total Area=\([\frac{1}{2}]-[-\frac{3}{2}]+[\frac{1}{2} (48)]-[-\frac{1}{2}]\)

Total Area=24+\(\frac{5}{2}\)

Total Area=26.5

Therefore, the total area between the graph of the function f(x)=−x−1 and the x-axis over the interval [−3,6] is 26.5 square units.

Final Answer:Thus, the total area between the graph of the function f(x)=−x−1 and the x-axis over the interval [−3,6] is 26.5 square units.

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The total area between the graph of the function f(x) = -x - 1 and the x-axis over the interval [-3, 6] is 10 square units.

To find the total area between the graph of the function f(x) = -x - 1 and the x-axis over the interval [-3, 6], we need to calculate the definite integral of the absolute value of the function within that interval.

The graph of f(x) = -x - 1 is a linear function with a negative slope. It intersects the x-axis at x = -1.

Since the function is negative for all x-values within the interval [-3, -1) and positive for all x-values within the interval (-1, 6], we can split the integral into two parts and take the absolute value of the function within each interval.

First, we calculate the integral from -3 to -1:

∫[-3,-1] |-x - 1| dx

Integrating the absolute value of -x - 1 within the interval [-3, -1], we get:

∫[-3,-1] |-x - 1| dx = ∫[-3,-1] (x + 1) dx

\(= [(1/2)x^2 + x] |-3,-1\)

= [(-1/2) - (-7/2)]

= 6/2

= 3

Next, we calculate the integral from -1 to 6:

∫[-1,6] | -x - 1| dx

Integrating the absolute value of -x - 1 within the interval [-1, 6], we get:

∫[-1,6] |-x - 1| dx = ∫[-1,6] -(x + 1) dx

\(= [-(1/2)x^2 - x] |-1,6\)

= [(-17/2) - (-3/2)]

= -7

To find the total area, we sum the absolute values of the two integrals:

Total Area = |3| + |-7| = 3 + 7 = 10

Therefore, the total area between the graph of the function f(x) = -x - 1 and the x-axis over the interval [-3, 6] is 10 square units.

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Answer:

trapezoid

Step-by-step explanation:

parallelograms require two sets of parallel lines while trapezoids do not, only requiring one set. it is possible to get a trapezoid with 2 90 degree angles.

Answer:

The answer is option D.

Equation of a line is y = mx + c

m = slope

c = intercept on y axis

y-4= -2/3 (x-6)

y = -2/3x + 4 + 4

y = -2/3x + 8

From the above equation

m= -2/3

Since the lines are perpendicular the slope of the line is the negative inverse of the original line.

so m = 3/2

Equation of the line using point (-2 , -2) is

y + 2 = 3/2(x+2)

y = 3/2x + 3 - 2

y = 3/2x + 1

That's the last option

Hope this helps

The linear equation with the given characteristics is given by:

\(y = \frac{3}{2}x + 1\)

It is given by:

y = mx + b.

In which:

When two lines are perpendicular, the multiplication of their slopes is -1, hence:

\(-\frac{2}{3}m = -1\)

\(2m = 3\)

\(m = \frac{3}{2}\)

Then:

\(y = \frac{3}{2}x + b\)

It passes through the point (-2, -2), hence:

\(-2 = \frac{3}{2}(-2) + b\)

\(-3 + b = -2\)

\(b = 1\)

Hence, the equation is:

\(y = \frac{3}{2}x + 1\)

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Answer:

x=21°. :Angles subtended by the same arc

y=42°. :180-(117+21),angles subtended by the same arc

Answer:

Slope: -1/4; Y-Intercept: 1.5

Step-by-step explanation:

Step 1: Find the slope. The best way to do this is to transform the two given points to y=mx+b form. When given two points, the best way to find the slope will be to do y2-y1/x2-x1. In this equation it would be -2-0/2+6, which is -2/8, simplified is -0.25 or -1/4. So we have the slope, which can determine the length of the line.

Step 2: Find the Y-Intercept. Finding the Y-intercept is so much simpler when given a graph, since all you have to do is find where the line goes through the y-axis, which in this case is (0,1.5), meaning that the y-intercept is 1.5 (note: the y-intercept can also be found when x=0, for example (0,9).

Hope this helped, good luck!

The equation of the line into slope-intercept form is y = x/3 - 6

Linear equations are equations that have constant average rates of change.

Note that the constant average rates of change can also be regarded as the slope or the gradient

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

9y−3x= −54

Rewrite properly

This gives

9y - 3x = -54

Divide through the equation by 3

So, we have the following representation

9y/3 - 3x/3 = -54/3

Evaluate

3y - x = -18

To rewrite as slope-intercept form is to make y the subject

So, we have

3y = x - 18

Divide through the equation by 3

So, we have the following representation

y = x/3 - 6

Hence, the equation is y = x/3 - 6

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Answer:

Set1 = 1/12

Set2 = 1/12

Set3 = -12

Step-by-step explanation:

Substitute, use Keep-Change-Flip to handle division when there's fractions involved. See image.

Also to multiply fractions, multiply

top×top and bottom×bottom straight across. Also negative times a negative is a positive and negative is like opposite so -(-6) is 6 and -(-1/2) is 1/2.

see image.

When a population which grows exponentially at the rate of 1.55%, will take 44.7 years become double.

Exponential growth function is defined as a function that shows an increase within a population that occurs at the same rate over time. When populations experience doubling or tripling in numbers, can assume the data increases exponentially. We have, a population grows exponentially.

The growth rate of population = 1.55%

Let us assume initial population be "P₀". We have to determine the time ( in years ) will it take the population to double, i.e., excepted value = 2P₀.

As we know, exponential population growth function is, P = P₀ eʳᵗ

where, P ---> total expected population

P₀ --> initial population

r --> population growth rate

t --> time period (in years)

P = 2P₀ , r = 1.55% = 0.0155 , substituting all known values in above formula,

2P₀ = P₀e⁰.⁰¹⁵⁵ᵗ

=> 2 = e⁰.⁰¹⁵⁵ᵗ

Taking natrual logarithm both sides

=> ln 2 = ln (e⁰.⁰¹⁵⁵ᵗ )

=> ln 2 = 0.0155 ×t ln e

=> 0.6931 = 0.0155 ×t ( since ln e = 1)

=> t = 0.6931/0.0155

=> t = 44.719 ~ 44.7

So, required value of t is 44.7 years.

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Answer:

\(\huge \fbox \pink {A}\huge \fbox \green {n}\huge \fbox \blue {s}\huge \fbox \red {w}\huge \fbox \purple {e}\huge \fbox \orange {r}\)

\(3x - 2x + 4 = 2 + x + 2 \\ x + 4 = 4 + x \\ x - x = 4 - 4 \\ 0 = 0\)

•°• LHS = RHS

✏ Hence, proved.

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Answer:

X + 4 = 4 + x

X - x = 4 - 4

0 = 0

LHS = RHS

Answer:

The last one(D)

Step-by-step explanation:

-1×-1=1

1*3=3

____

9*1=9

12-9=3

Answer:

85 people

Step-by-step explanation:

in a country , if 17 out of every 20 people are literate, then;

17 literate = 20 people

To get the number of literate people in 100

x literate = 100 people

Divide both expressions

17/x = 20/100

Cross multiply

20x = 17 * 100

x = 1700/20

x = 85

Hence 85 people are literate out of 100 people

Answer:

that don't even make sense

Answer:

The LCM of 10 and 12 is 60

Step-by-step explanation:

Hope this helped! :)

Answer:

i think its 60

Step-by-step explanation:

Steps to solve:

m - 2/6 < -1

~Add 2/6 to both sides

m < -4/6

Best of Luck!

The equations that represent proportional relationships are y = x/3, y = (1/4)x and y = 2x

A relationship can either be a direct, inverse, or even joint relationship

For instance, if y is directly proportional to x, hence;

y = kx

k is the constant of variation

Similarly, if y is inversely proportional to x, hence;

y = k/x

k is the constant of variation

From the given options, we need to find the expressions that are similar to the equations above.

The equations that represent proportional relationships are y = x/3, y = (1/4)x and y = 2x

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Answer:

The slope is 6

Step-by-step explanation:

Y2-Y1 / X2-X1

-3-(-9) / -1-(-2)

6

Answer:

m = 6

Step-by-step explanation:

slope (m) = rise / run

rise = y2 - y1 = -3 - (-9) = 6

run = x2 - x1 = -1 - (-2) = 1

slope = 6/1 = 6